id	sid	tid	token	lemma	pos
ejpam-3704	1	1	european	european	PROPN
ejpam-3704	1	2	journal	journal	PROPN
ejpam-3704	1	3	of	of	ADP
ejpam-3704	1	4	pure	pure	ADJ
ejpam-3704	1	5	and	and	CCONJ
ejpam-3704	1	6	applied	apply	VERB
ejpam-3704	1	7	mathematics	mathematic	NOUN
ejpam-3704	1	8	vol	vol	NOUN
ejpam-3704	1	9	.	.	PROPN
ejpam-3704	2	1	13	13	NUM
ejpam-3704	2	2	,	,	PUNCT
ejpam-3704	2	3	no	no	INTJ
ejpam-3704	2	4	.	.	NOUN
ejpam-3704	2	5	3	3	NUM
ejpam-3704	2	6	,	,	PUNCT
ejpam-3704	2	7	2020	2020	NUM
ejpam-3704	2	8	,	,	PUNCT
ejpam-3704	2	9	483	483	NUM
ejpam-3704	2	10	-	-	SYM
ejpam-3704	2	11	497	497	NUM
ejpam-3704	2	12	issn	issn	PROPN
ejpam-3704	2	13	1307	1307	NUM
ejpam-3704	2	14	-	-	SYM
ejpam-3704	2	15	5543	5543	NUM
ejpam-3704	2	16	–	–	PUNCT
ejpam-3704	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3704	2	18	published	publish	VERB
ejpam-3704	2	19	by	by	ADP
ejpam-3704	2	20	new	new	PROPN
ejpam-3704	2	21	york	york	PROPN
ejpam-3704	2	22	business	business	PROPN
ejpam-3704	2	23	global	global	ADJ
ejpam-3704	2	24	hyper	hyper	ADJ
ejpam-3704	2	25	homomorphism	homomorphism	PROPN
ejpam-3704	2	26	and	and	CCONJ
ejpam-3704	2	27	hyper	hyper	ADJ
ejpam-3704	2	28	product	product	NOUN
ejpam-3704	2	29	of	of	ADP
ejpam-3704	2	30	hyper	hyper	ADJ
ejpam-3704	2	31	up	up	ADP
ejpam-3704	2	32	-	-	PUNCT
ejpam-3704	2	33	algebras	algebras	PROPN
ejpam-3704	2	34	rohaima	rohaima	PROPN
ejpam-3704	2	35	m.	m.	PROPN
ejpam-3704	2	36	amairanto1,∗	amairanto1,∗	PROPN
ejpam-3704	2	37	,	,	PUNCT
ejpam-3704	2	38	rowena	rowena	PROPN
ejpam-3704	2	39	t.	t.	PROPN
ejpam-3704	2	40	isla2	isla2	PROPN
ejpam-3704	2	41	1	1	NUM
ejpam-3704	2	42	department	department	NOUN
ejpam-3704	2	43	of	of	ADP
ejpam-3704	2	44	mathematics	mathematic	NOUN
ejpam-3704	2	45	,	,	PUNCT
ejpam-3704	2	46	mindanao	mindanao	PROPN
ejpam-3704	2	47	state	state	PROPN
ejpam-3704	2	48	university	university	PROPN
ejpam-3704	2	49	-	-	PUNCT
ejpam-3704	2	50	university	university	NOUN
ejpam-3704	2	51	training	training	NOUN
ejpam-3704	2	52	center	center	NOUN
ejpam-3704	2	53	,	,	PUNCT
ejpam-3704	2	54	9700	9700	NUM
ejpam-3704	2	55	marawi	marawi	PROPN
ejpam-3704	2	56	city	city	PROPN
ejpam-3704	2	57	,	,	PUNCT
ejpam-3704	2	58	philippines	philippines	PROPN
ejpam-3704	2	59	2	2	NUM
ejpam-3704	2	60	department	department	NOUN
ejpam-3704	2	61	of	of	ADP
ejpam-3704	2	62	mathematics	mathematic	NOUN
ejpam-3704	2	63	and	and	CCONJ
ejpam-3704	2	64	statistics	statistic	NOUN
ejpam-3704	2	65	,	,	PUNCT
ejpam-3704	2	66	college	college	NOUN
ejpam-3704	2	67	of	of	ADP
ejpam-3704	2	68	science	science	NOUN
ejpam-3704	2	69	and	and	CCONJ
ejpam-3704	2	70	mathematics	mathematic	NOUN
ejpam-3704	2	71	,	,	PUNCT
ejpam-3704	2	72	mindanao	mindanao	PROPN
ejpam-3704	2	73	state	state	PROPN
ejpam-3704	2	74	university	university	PROPN
ejpam-3704	2	75	-	-	PUNCT
ejpam-3704	2	76	iligan	iligan	PROPN
ejpam-3704	2	77	institute	institute	PROPN
ejpam-3704	2	78	of	of	ADP
ejpam-3704	2	79	technology	technology	PROPN
ejpam-3704	2	80	,	,	PUNCT
ejpam-3704	2	81	9200	9200	NUM
ejpam-3704	2	82	iligan	iligan	ADJ
ejpam-3704	2	83	city	city	NOUN
ejpam-3704	2	84	,	,	PUNCT
ejpam-3704	2	85	philippines	philippine	NOUN
ejpam-3704	2	86	abstract	abstract	ADJ
ejpam-3704	2	87	.	.	PUNCT
ejpam-3704	3	1	in	in	ADP
ejpam-3704	3	2	this	this	DET
ejpam-3704	3	3	paper	paper	NOUN
ejpam-3704	3	4	,	,	PUNCT
ejpam-3704	3	5	we	we	PRON
ejpam-3704	3	6	investigate	investigate	VERB
ejpam-3704	3	7	the	the	DET
ejpam-3704	3	8	concept	concept	NOUN
ejpam-3704	3	9	of	of	ADP
ejpam-3704	3	10	regular	regular	ADJ
ejpam-3704	3	11	congruence	congruence	NOUN
ejpam-3704	3	12	relation	relation	NOUN
ejpam-3704	3	13	on	on	ADP
ejpam-3704	3	14	hyper	hyper	ADJ
ejpam-3704	3	15	upalgebras	upalgebra	NOUN
ejpam-3704	3	16	and	and	CCONJ
ejpam-3704	3	17	establish	establish	VERB
ejpam-3704	3	18	some	some	DET
ejpam-3704	3	19	homomorphism	homomorphism	NOUN
ejpam-3704	3	20	theorems	theorem	NOUN
ejpam-3704	3	21	on	on	ADP
ejpam-3704	3	22	such	such	ADJ
ejpam-3704	3	23	algebras	algebra	NOUN
ejpam-3704	3	24	.	.	PUNCT
ejpam-3704	4	1	we	we	PRON
ejpam-3704	4	2	also	also	ADV
ejpam-3704	4	3	examine	examine	VERB
ejpam-3704	4	4	the	the	DET
ejpam-3704	4	5	notion	notion	NOUN
ejpam-3704	4	6	of	of	ADP
ejpam-3704	4	7	hyper	hyper	ADJ
ejpam-3704	4	8	product	product	NOUN
ejpam-3704	4	9	of	of	ADP
ejpam-3704	4	10	hyper	hyper	ADJ
ejpam-3704	4	11	up	up	ADP
ejpam-3704	4	12	-	-	PUNCT
ejpam-3704	4	13	algebras	algebras	X
ejpam-3704	4	14	.	.	PUNCT
ejpam-3704	5	1	2020	2020	NUM
ejpam-3704	5	2	mathematics	mathematics	PROPN
ejpam-3704	5	3	subject	subject	NOUN
ejpam-3704	5	4	classifications	classification	NOUN
ejpam-3704	5	5	:	:	PUNCT
ejpam-3704	5	6	08a30	08a30	NOUN
ejpam-3704	5	7	,	,	PUNCT
ejpam-3704	5	8	08a99	08a99	VERB
ejpam-3704	5	9	key	key	ADJ
ejpam-3704	5	10	words	word	NOUN
ejpam-3704	5	11	and	and	CCONJ
ejpam-3704	5	12	phrases	phrase	NOUN
ejpam-3704	5	13	:	:	PUNCT
ejpam-3704	5	14	hyper	hyper	ADJ
ejpam-3704	5	15	up	up	ADP
ejpam-3704	5	16	-	-	PUNCT
ejpam-3704	5	17	algebra	algebra	NOUN
ejpam-3704	5	18	,	,	PUNCT
ejpam-3704	5	19	regular	regular	ADJ
ejpam-3704	5	20	congruence	congruence	NOUN
ejpam-3704	5	21	relation	relation	NOUN
ejpam-3704	5	22	,	,	PUNCT
ejpam-3704	5	23	hyper	hyper	ADJ
ejpam-3704	5	24	homomorphisms	homomorphism	NOUN
ejpam-3704	5	25	of	of	ADP
ejpam-3704	5	26	hyper	hyper	ADJ
ejpam-3704	5	27	up	up	ADP
ejpam-3704	5	28	-	-	PUNCT
ejpam-3704	5	29	algebras	algebra	NOUN
ejpam-3704	5	30	,	,	PUNCT
ejpam-3704	5	31	hyper	hyper	ADJ
ejpam-3704	5	32	product	product	NOUN
ejpam-3704	5	33	of	of	ADP
ejpam-3704	5	34	hyper	hyper	ADJ
ejpam-3704	5	35	up	up	ADP
ejpam-3704	5	36	-	-	PUNCT
ejpam-3704	5	37	algebras	algebras	X
ejpam-3704	5	38	1	1	NUM
ejpam-3704	5	39	.	.	PUNCT
ejpam-3704	5	40	introduction	introduction	NOUN
ejpam-3704	5	41	in	in	ADP
ejpam-3704	5	42	1934	1934	NUM
ejpam-3704	5	43	,	,	PUNCT
ejpam-3704	5	44	f.	f.	PROPN
ejpam-3704	5	45	marty	marty	PROPN
ejpam-3704	6	1	[	[	X
ejpam-3704	6	2	7	7	X
ejpam-3704	6	3	]	]	PUNCT
ejpam-3704	6	4	first	first	ADV
ejpam-3704	6	5	introduced	introduce	VERB
ejpam-3704	6	6	the	the	DET
ejpam-3704	6	7	concept	concept	NOUN
ejpam-3704	6	8	of	of	ADP
ejpam-3704	6	9	hyperstructure	hyperstructure	PROPN
ejpam-3704	6	10	theory	theory	NOUN
ejpam-3704	6	11	at	at	ADP
ejpam-3704	6	12	the	the	DET
ejpam-3704	6	13	8th	8th	ADJ
ejpam-3704	6	14	congress	congress	PROPN
ejpam-3704	6	15	of	of	ADP
ejpam-3704	6	16	scandinavian	scandinavian	ADJ
ejpam-3704	6	17	mathematics	mathematic	NOUN
ejpam-3704	6	18	.	.	PUNCT
ejpam-3704	7	1	this	this	PRON
ejpam-3704	7	2	led	lead	VERB
ejpam-3704	7	3	to	to	ADP
ejpam-3704	7	4	the	the	DET
ejpam-3704	7	5	formulation	formulation	NOUN
ejpam-3704	7	6	of	of	ADP
ejpam-3704	7	7	hyper	hyper	ADJ
ejpam-3704	7	8	bckalgebra	bckalgebra	NOUN
ejpam-3704	7	9	by	by	ADP
ejpam-3704	7	10	y.	y.	PROPN
ejpam-3704	7	11	jun	jun	PROPN
ejpam-3704	7	12	et	et	PROPN
ejpam-3704	7	13	al	al	PROPN
ejpam-3704	7	14	.	.	PUNCT
ejpam-3704	8	1	[	[	X
ejpam-3704	8	2	11	11	NUM
ejpam-3704	8	3	]	]	PUNCT
ejpam-3704	8	4	,	,	PUNCT
ejpam-3704	8	5	hyper	hyper	ADJ
ejpam-3704	8	6	bci	bci	NOUN
ejpam-3704	8	7	-	-	NOUN
ejpam-3704	8	8	algebra	algebra	NOUN
ejpam-3704	8	9	by	by	ADP
ejpam-3704	8	10	x.	x.	PROPN
ejpam-3704	8	11	long	long	PROPN
ejpam-3704	9	1	[	[	X
ejpam-3704	9	2	6	6	NUM
ejpam-3704	9	3	]	]	PUNCT
ejpam-3704	9	4	,	,	PUNCT
ejpam-3704	9	5	and	and	CCONJ
ejpam-3704	9	6	many	many	ADJ
ejpam-3704	9	7	other	other	ADJ
ejpam-3704	9	8	classes	class	NOUN
ejpam-3704	9	9	of	of	ADP
ejpam-3704	9	10	algebras	algebras	PROPN
ejpam-3704	9	11	.	.	PUNCT
ejpam-3704	10	1	r.	r.	PROPN
ejpam-3704	10	2	borzooei	borzooei	PROPN
ejpam-3704	10	3	and	and	CCONJ
ejpam-3704	10	4	h.	h.	PROPN
ejpam-3704	10	5	harizavi	harizavi	PROPN
ejpam-3704	11	1	[	[	X
ejpam-3704	11	2	1	1	NUM
ejpam-3704	11	3	]	]	PUNCT
ejpam-3704	11	4	defined	define	VERB
ejpam-3704	11	5	the	the	DET
ejpam-3704	11	6	regular	regular	ADJ
ejpam-3704	11	7	congruence	congruence	NOUN
ejpam-3704	11	8	relation	relation	NOUN
ejpam-3704	11	9	on	on	ADP
ejpam-3704	11	10	a	a	DET
ejpam-3704	11	11	hyper	hyper	ADJ
ejpam-3704	11	12	bck	bck	NOUN
ejpam-3704	11	13	-	-	PUNCT
ejpam-3704	11	14	algebra	algebra	NOUN
ejpam-3704	11	15	,	,	PUNCT
ejpam-3704	11	16	constructed	construct	VERB
ejpam-3704	11	17	a	a	DET
ejpam-3704	11	18	quotient	quotient	NOUN
ejpam-3704	11	19	hyper	hyper	ADJ
ejpam-3704	11	20	bck	bck	NOUN
ejpam-3704	11	21	-	-	PUNCT
ejpam-3704	11	22	algebra	algebra	NOUN
ejpam-3704	11	23	,	,	PUNCT
ejpam-3704	11	24	established	establish	VERB
ejpam-3704	11	25	some	some	DET
ejpam-3704	11	26	homomorphism	homomorphism	NOUN
ejpam-3704	11	27	theorems	theorem	NOUN
ejpam-3704	11	28	,	,	PUNCT
ejpam-3704	11	29	and	and	CCONJ
ejpam-3704	11	30	got	get	VERB
ejpam-3704	11	31	some	some	DET
ejpam-3704	11	32	related	relate	VERB
ejpam-3704	11	33	results	result	NOUN
ejpam-3704	11	34	involving	involve	VERB
ejpam-3704	11	35	the	the	DET
ejpam-3704	11	36	hyper	hyper	ADJ
ejpam-3704	11	37	product	product	NOUN
ejpam-3704	11	38	of	of	ADP
ejpam-3704	11	39	hyper	hyper	ADJ
ejpam-3704	11	40	bck	bck	NOUN
ejpam-3704	11	41	-	-	PUNCT
ejpam-3704	11	42	algebras	algebras	PROPN
ejpam-3704	11	43	.	.	PUNCT
ejpam-3704	12	1	g.	g.	PROPN
ejpam-3704	12	2	flores	flores	PROPN
ejpam-3704	12	3	and	and	CCONJ
ejpam-3704	12	4	g.	g.	PROPN
ejpam-3704	12	5	petalcorin	petalcorin	PROPN
ejpam-3704	13	1	[	[	X
ejpam-3704	13	2	2	2	X
ejpam-3704	13	3	]	]	PUNCT
ejpam-3704	13	4	introduced	introduce	VERB
ejpam-3704	13	5	regular	regular	ADJ
ejpam-3704	13	6	congruence	congruence	NOUN
ejpam-3704	13	7	relation	relation	NOUN
ejpam-3704	13	8	on	on	ADP
ejpam-3704	13	9	a	a	DET
ejpam-3704	13	10	hyper	hyper	ADJ
ejpam-3704	13	11	bci	bci	NOUN
ejpam-3704	13	12	-	-	NOUN
ejpam-3704	13	13	algebra	algebra	NOUN
ejpam-3704	13	14	and	and	CCONJ
ejpam-3704	13	15	presented	present	VERB
ejpam-3704	13	16	some	some	DET
ejpam-3704	13	17	isomorphism	isomorphism	NOUN
ejpam-3704	13	18	theorems	theorem	NOUN
ejpam-3704	13	19	on	on	ADP
ejpam-3704	13	20	hyper	hyper	ADJ
ejpam-3704	13	21	bci	bci	NOUN
ejpam-3704	13	22	-	-	PUNCT
ejpam-3704	13	23	algebras	algebra	NOUN
ejpam-3704	13	24	.	.	PUNCT
ejpam-3704	14	1	in	in	ADP
ejpam-3704	14	2	2017	2017	NUM
ejpam-3704	14	3	,	,	PUNCT
ejpam-3704	14	4	a.	a.	NOUN
ejpam-3704	14	5	iampan	iampan	NOUN
ejpam-3704	14	6	[	[	X
ejpam-3704	14	7	4	4	X
ejpam-3704	14	8	]	]	PUNCT
ejpam-3704	14	9	defined	define	VERB
ejpam-3704	14	10	a	a	DET
ejpam-3704	14	11	new	new	ADJ
ejpam-3704	14	12	algebraic	algebraic	ADJ
ejpam-3704	14	13	structure	structure	NOUN
ejpam-3704	14	14	called	call	VERB
ejpam-3704	14	15	a	a	DET
ejpam-3704	14	16	up	up	NOUN
ejpam-3704	14	17	-	-	PUNCT
ejpam-3704	14	18	algebra	algebra	NOUN
ejpam-3704	14	19	and	and	CCONJ
ejpam-3704	14	20	showed	show	VERB
ejpam-3704	14	21	that	that	SCONJ
ejpam-3704	14	22	the	the	DET
ejpam-3704	14	23	notion	notion	NOUN
ejpam-3704	14	24	of	of	ADP
ejpam-3704	14	25	up	up	ADV
ejpam-3704	14	26	-	-	PUNCT
ejpam-3704	14	27	algebras	algebras	PROPN
ejpam-3704	14	28	is	be	AUX
ejpam-3704	14	29	a	a	DET
ejpam-3704	14	30	generalization	generalization	NOUN
ejpam-3704	14	31	of	of	ADP
ejpam-3704	14	32	ku	ku	PROPN
ejpam-3704	14	33	-	-	PUNCT
ejpam-3704	14	34	algebras	algebras	PROPN
ejpam-3704	14	35	that	that	PRON
ejpam-3704	14	36	was	be	AUX
ejpam-3704	14	37	introduced	introduce	VERB
ejpam-3704	14	38	by	by	ADP
ejpam-3704	14	39	c.	c.	PROPN
ejpam-3704	14	40	prabpayak	prabpayak	NOUN
ejpam-3704	14	41	and	and	CCONJ
ejpam-3704	14	42	u.	u.	NOUN
ejpam-3704	14	43	leerawat	leerawat	NOUN
ejpam-3704	15	1	[	[	X
ejpam-3704	15	2	8	8	NUM
ejpam-3704	15	3	]	]	PUNCT
ejpam-3704	15	4	.	.	PUNCT
ejpam-3704	16	1	recently	recently	ADV
ejpam-3704	16	2	,	,	PUNCT
ejpam-3704	16	3	d.	d.	PROPN
ejpam-3704	16	4	gomisong	gomisong	VERB
ejpam-3704	17	1	[	[	X
ejpam-3704	17	2	3	3	NUM
ejpam-3704	17	3	]	]	PUNCT
ejpam-3704	17	4	applied	apply	VERB
ejpam-3704	17	5	hyperstuctures	hyperstucture	NOUN
ejpam-3704	17	6	to	to	ADP
ejpam-3704	17	7	up	up	ADV
ejpam-3704	17	8	-	-	PUNCT
ejpam-3704	17	9	algebras	algebras	NOUN
ejpam-3704	17	10	in	in	ADP
ejpam-3704	17	11	her	her	PRON
ejpam-3704	17	12	graduate	graduate	ADJ
ejpam-3704	17	13	thesis	thesis	NOUN
ejpam-3704	17	14	following	follow	VERB
ejpam-3704	17	15	the	the	DET
ejpam-3704	17	16	structure	structure	NOUN
ejpam-3704	17	17	of	of	ADP
ejpam-3704	17	18	hyper	hyper	PROPN
ejpam-3704	17	19	ku	ku	PROPN
ejpam-3704	17	20	-	-	PUNCT
ejpam-3704	17	21	algebras	algebras	PROPN
ejpam-3704	17	22	by	by	ADP
ejpam-3704	17	23	s.	s.	PROPN
ejpam-3704	17	24	mostafa	mostafa	PROPN
ejpam-3704	17	25	et	et	PROPN
ejpam-3704	17	26	al	al	PROPN
ejpam-3704	17	27	.	.	PUNCT
ejpam-3704	18	1	[	[	X
ejpam-3704	18	2	5	5	NUM
ejpam-3704	18	3	]	]	PUNCT
ejpam-3704	18	4	.	.	PUNCT
ejpam-3704	19	1	d.	d.	PROPN
ejpam-3704	19	2	romano	romano	PROPN
ejpam-3704	19	3	gave	give	VERB
ejpam-3704	19	4	an	an	DET
ejpam-3704	19	5	equivalent	equivalent	ADJ
ejpam-3704	19	6	definition	definition	NOUN
ejpam-3704	19	7	of	of	ADP
ejpam-3704	19	8	hyper	hyper	ADJ
ejpam-3704	19	9	up	up	NOUN
ejpam-3704	19	10	-	-	PUNCT
ejpam-3704	19	11	algebra	algebra	NOUN
ejpam-3704	19	12	in	in	ADP
ejpam-3704	19	13	[	[	X
ejpam-3704	19	14	10	10	NUM
ejpam-3704	19	15	]	]	PUNCT
ejpam-3704	19	16	and	and	CCONJ
ejpam-3704	19	17	proved	prove	VERB
ejpam-3704	19	18	that	that	SCONJ
ejpam-3704	19	19	every	every	DET
ejpam-3704	19	20	hyper	hyper	ADJ
ejpam-3704	19	21	ku	ku	NOUN
ejpam-3704	19	22	-	-	PUNCT
ejpam-3704	19	23	algebra	algebra	PROPN
ejpam-3704	19	24	is	be	AUX
ejpam-3704	19	25	a	a	DET
ejpam-3704	19	26	hyper	hyper	ADJ
ejpam-3704	19	27	up	up	NOUN
ejpam-3704	19	28	-	-	PUNCT
ejpam-3704	19	29	algebra	algebra	NOUN
ejpam-3704	19	30	.	.	PUNCT
ejpam-3704	20	1	he	he	PRON
ejpam-3704	20	2	also	also	ADV
ejpam-3704	20	3	introduced	introduce	VERB
ejpam-3704	20	4	the	the	DET
ejpam-3704	20	5	quotient	quotient	NOUN
ejpam-3704	20	6	of	of	ADP
ejpam-3704	20	7	a	a	DET
ejpam-3704	20	8	hyper	hyper	ADJ
ejpam-3704	20	9	up	up	NOUN
ejpam-3704	20	10	-	-	PUNCT
ejpam-3704	20	11	algebra	algebra	NOUN
ejpam-3704	20	12	in	in	ADP
ejpam-3704	20	13	[	[	PUNCT
ejpam-3704	20	14	9	9	NUM
ejpam-3704	20	15	]	]	PUNCT
ejpam-3704	20	16	.	.	PUNCT
ejpam-3704	21	1	in	in	ADP
ejpam-3704	21	2	this	this	DET
ejpam-3704	21	3	paper	paper	NOUN
ejpam-3704	21	4	,	,	PUNCT
ejpam-3704	21	5	we	we	PRON
ejpam-3704	21	6	investigate	investigate	VERB
ejpam-3704	21	7	the	the	DET
ejpam-3704	21	8	concept	concept	NOUN
ejpam-3704	21	9	of	of	ADP
ejpam-3704	21	10	regular	regular	ADJ
ejpam-3704	21	11	∗corresponding	∗corresponde	VERB
ejpam-3704	21	12	author	author	NOUN
ejpam-3704	21	13	.	.	PUNCT
ejpam-3704	22	1	doi	doi	NOUN
ejpam-3704	22	2	:	:	PUNCT
ejpam-3704	22	3	https://doi.org/10.29020/nybg.ejpam.v13i3.3704	https://doi.org/10.29020/nybg.ejpam.v13i3.3704	PRON
ejpam-3704	22	4	email	email	NOUN
ejpam-3704	22	5	addresses	address	NOUN
ejpam-3704	22	6	:	:	PUNCT
ejpam-3704	22	7	rohaima87@yahoo.com	rohaima87@yahoo.com	PROPN
ejpam-3704	22	8	(	(	PUNCT
ejpam-3704	22	9	r.	r.	PROPN
ejpam-3704	22	10	amairanto	amairanto	PROPN
ejpam-3704	22	11	)	)	PUNCT
ejpam-3704	22	12	,	,	PUNCT
ejpam-3704	22	13	rowena.isla@g.msuiit.edu.ph	rowena.isla@g.msuiit.edu.ph	PROPN
ejpam-3704	22	14	(	(	PUNCT
ejpam-3704	22	15	r.	r.	PROPN
ejpam-3704	22	16	isla	isla	PROPN
ejpam-3704	22	17	)	)	PUNCT
ejpam-3704	22	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3704	23	1	483	483	NUM
ejpam-3704	23	2	c	c	NOUN
ejpam-3704	23	3	©	©	PROPN
ejpam-3704	23	4	2020	2020	NUM
ejpam-3704	23	5	ejpam	ejpam	VERB
ejpam-3704	23	6	all	all	DET
ejpam-3704	23	7	rights	right	NOUN
ejpam-3704	23	8	reserved	reserve	VERB
ejpam-3704	23	9	.	.	PUNCT
ejpam-3704	24	1	r.	r.	PROPN
ejpam-3704	24	2	amairanto	amairanto	PROPN
ejpam-3704	24	3	,	,	PUNCT
ejpam-3704	24	4	r.	r.	PROPN
ejpam-3704	24	5	isla	isla	PROPN
ejpam-3704	24	6	/	/	SYM
ejpam-3704	24	7	eur	eur	PROPN
ejpam-3704	24	8	.	.	PUNCT
ejpam-3704	25	1	j.	j.	PROPN
ejpam-3704	25	2	pure	pure	PROPN
ejpam-3704	25	3	appl	appl	PROPN
ejpam-3704	25	4	.	.	PROPN
ejpam-3704	25	5	math	math	PROPN
ejpam-3704	25	6	,	,	PUNCT
ejpam-3704	25	7	13	13	NUM
ejpam-3704	25	8	(	(	PUNCT
ejpam-3704	25	9	3	3	NUM
ejpam-3704	25	10	)	)	PUNCT
ejpam-3704	25	11	(	(	PUNCT
ejpam-3704	25	12	2020	2020	NUM
ejpam-3704	25	13	)	)	PUNCT
ejpam-3704	25	14	,	,	PUNCT
ejpam-3704	25	15	483	483	NUM
ejpam-3704	25	16	-	-	SYM
ejpam-3704	25	17	497	497	NUM
ejpam-3704	25	18	484	484	NUM
ejpam-3704	25	19	congruence	congruence	NOUN
ejpam-3704	25	20	relation	relation	NOUN
ejpam-3704	25	21	on	on	ADP
ejpam-3704	25	22	a	a	DET
ejpam-3704	25	23	hyper	hyper	ADJ
ejpam-3704	25	24	up	up	NOUN
ejpam-3704	25	25	-	-	PUNCT
ejpam-3704	25	26	algebra	algebra	NOUN
ejpam-3704	25	27	and	and	CCONJ
ejpam-3704	25	28	present	present	VERB
ejpam-3704	25	29	some	some	DET
ejpam-3704	25	30	homomorphism	homomorphism	NOUN
ejpam-3704	25	31	theorems	theorem	NOUN
ejpam-3704	25	32	on	on	ADP
ejpam-3704	25	33	hyper	hyper	ADJ
ejpam-3704	25	34	up	up	ADP
ejpam-3704	25	35	-	-	PUNCT
ejpam-3704	25	36	algebras	algebras	X
ejpam-3704	25	37	.	.	PUNCT
ejpam-3704	26	1	we	we	PRON
ejpam-3704	26	2	also	also	ADV
ejpam-3704	26	3	examine	examine	VERB
ejpam-3704	26	4	the	the	DET
ejpam-3704	26	5	concept	concept	NOUN
ejpam-3704	26	6	of	of	ADP
ejpam-3704	26	7	hyper	hyper	ADJ
ejpam-3704	26	8	product	product	NOUN
ejpam-3704	26	9	of	of	ADP
ejpam-3704	26	10	hyper	hyper	ADJ
ejpam-3704	26	11	up	up	ADV
ejpam-3704	26	12	-	-	PUNCT
ejpam-3704	26	13	algebras	algebra	NOUN
ejpam-3704	26	14	and	and	CCONJ
ejpam-3704	26	15	extend	extend	VERB
ejpam-3704	26	16	it	it	PRON
ejpam-3704	26	17	to	to	ADP
ejpam-3704	26	18	the	the	DET
ejpam-3704	26	19	hyper	hyper	ADJ
ejpam-3704	26	20	product	product	NOUN
ejpam-3704	26	21	of	of	ADP
ejpam-3704	26	22	an	an	DET
ejpam-3704	26	23	arbitrary	arbitrary	ADJ
ejpam-3704	26	24	family	family	NOUN
ejpam-3704	26	25	of	of	ADP
ejpam-3704	26	26	hyper	hyper	ADJ
ejpam-3704	26	27	up	up	ADP
ejpam-3704	26	28	-	-	PUNCT
ejpam-3704	26	29	algebras	algebras	X
ejpam-3704	26	30	.	.	PUNCT
ejpam-3704	27	1	2	2	X
ejpam-3704	27	2	.	.	X
ejpam-3704	27	3	preliminaries	preliminary	NOUN
ejpam-3704	27	4	let	let	VERB
ejpam-3704	27	5	h	h	NOUN
ejpam-3704	27	6	be	be	AUX
ejpam-3704	27	7	a	a	DET
ejpam-3704	27	8	nonempty	nonempty	ADV
ejpam-3704	27	9	set	set	VERB
ejpam-3704	27	10	and	and	CCONJ
ejpam-3704	27	11	p∗(h	p∗(h	PROPN
ejpam-3704	27	12	)	)	PUNCT
ejpam-3704	27	13	be	be	VERB
ejpam-3704	27	14	the	the	DET
ejpam-3704	27	15	set	set	NOUN
ejpam-3704	27	16	of	of	ADP
ejpam-3704	27	17	all	all	DET
ejpam-3704	27	18	nonempty	nonempty	ADJ
ejpam-3704	27	19	subsets	subset	NOUN
ejpam-3704	27	20	of	of	ADP
ejpam-3704	27	21	h.	h.	PROPN
ejpam-3704	27	22	a	a	DET
ejpam-3704	27	23	hyperoperation	hyperoperation	NOUN
ejpam-3704	27	24	on	on	ADP
ejpam-3704	27	25	h	h	NOUN
ejpam-3704	27	26	is	be	AUX
ejpam-3704	27	27	a	a	DET
ejpam-3704	27	28	mapping	mapping	NOUN
ejpam-3704	27	29	from	from	ADP
ejpam-3704	27	30	h	h	NOUN
ejpam-3704	27	31	×h	×h	PROPN
ejpam-3704	27	32	into	into	ADP
ejpam-3704	27	33	p∗(h	p∗(h	PROPN
ejpam-3704	27	34	)	)	PUNCT
ejpam-3704	27	35	.	.	PUNCT
ejpam-3704	28	1	definition	definition	NOUN
ejpam-3704	28	2	1	1	NUM
ejpam-3704	28	3	.	.	PUNCT
ejpam-3704	29	1	[	[	X
ejpam-3704	29	2	3	3	X
ejpam-3704	29	3	]	]	X
ejpam-3704	29	4	a	a	DET
ejpam-3704	29	5	hyper	hyper	ADJ
ejpam-3704	29	6	up	up	ADP
ejpam-3704	29	7	-	-	PUNCT
ejpam-3704	29	8	algebra	algebra	NOUN
ejpam-3704	29	9	is	be	AUX
ejpam-3704	29	10	a	a	DET
ejpam-3704	29	11	set	set	ADJ
ejpam-3704	29	12	h	h	NOUN
ejpam-3704	29	13	with	with	ADP
ejpam-3704	29	14	constant	constant	ADJ
ejpam-3704	29	15	0	0	NUM
ejpam-3704	29	16	and	and	CCONJ
ejpam-3704	29	17	hyperoperation	hyperoperation	NOUN
ejpam-3704	29	18	~	~	PUNCT
ejpam-3704	29	19	satisfying	satisfy	VERB
ejpam-3704	29	20	the	the	DET
ejpam-3704	29	21	following	follow	VERB
ejpam-3704	29	22	axioms	axiom	NOUN
ejpam-3704	29	23	:	:	PUNCT
ejpam-3704	29	24	for	for	ADP
ejpam-3704	29	25	all	all	DET
ejpam-3704	29	26	x	x	NOUN
ejpam-3704	29	27	,	,	PUNCT
ejpam-3704	29	28	y	y	PROPN
ejpam-3704	29	29	,	,	PUNCT
ejpam-3704	29	30	z	z	PROPN
ejpam-3704	29	31	∈	∈	PROPN
ejpam-3704	29	32	h	h	NOUN
ejpam-3704	29	33	,	,	PUNCT
ejpam-3704	29	34	(	(	PUNCT
ejpam-3704	29	35	hup1	hup1	PROPN
ejpam-3704	29	36	)	)	PUNCT
ejpam-3704	30	1	[	[	X
ejpam-3704	30	2	(	(	PUNCT
ejpam-3704	30	3	x~	x~	PROPN
ejpam-3704	30	4	y	y	NOUN
ejpam-3704	30	5	)	)	PUNCT
ejpam-3704	30	6	~	~	PUNCT
ejpam-3704	30	7	(	(	PUNCT
ejpam-3704	30	8	x~	x~	PROPN
ejpam-3704	30	9	z	z	X
ejpam-3704	30	10	)	)	PUNCT
ejpam-3704	30	11	]	]	X
ejpam-3704	30	12	�	�	PROPN
ejpam-3704	30	13	y	y	PROPN
ejpam-3704	30	14	~	~	PUNCT
ejpam-3704	30	15	z	z	X
ejpam-3704	30	16	,	,	PUNCT
ejpam-3704	30	17	(	(	PUNCT
ejpam-3704	30	18	hup2	hup2	PROPN
ejpam-3704	30	19	)	)	PUNCT
ejpam-3704	30	20	0	0	PUNCT
ejpam-3704	31	1	~	~	PUNCT
ejpam-3704	31	2	x	x	SYM
ejpam-3704	31	3	=	=	PRON
ejpam-3704	31	4	{	{	PUNCT
ejpam-3704	31	5	x	x	NOUN
ejpam-3704	31	6	}	}	PUNCT
ejpam-3704	31	7	,	,	PUNCT
ejpam-3704	31	8	(	(	PUNCT
ejpam-3704	31	9	hup3	hup3	PROPN
ejpam-3704	31	10	)	)	PUNCT
ejpam-3704	31	11	x~	x~	PROPN
ejpam-3704	31	12	0	0	PUNCT
ejpam-3704	31	13	=	=	SYM
ejpam-3704	31	14	{	{	PUNCT
ejpam-3704	31	15	0	0	NUM
ejpam-3704	31	16	}	}	PUNCT
ejpam-3704	31	17	,	,	PUNCT
ejpam-3704	31	18	(	(	PUNCT
ejpam-3704	31	19	hup4	hup4	X
ejpam-3704	31	20	)	)	PUNCT
ejpam-3704	31	21	x	x	PROPN
ejpam-3704	31	22	�	�	PROPN
ejpam-3704	31	23	y	y	PROPN
ejpam-3704	31	24	and	and	CCONJ
ejpam-3704	31	25	y	y	PROPN
ejpam-3704	31	26	�	�	PROPN
ejpam-3704	31	27	x	x	PUNCT
ejpam-3704	31	28	imply	imply	VERB
ejpam-3704	31	29	x	x	X
ejpam-3704	31	30	=	=	SYM
ejpam-3704	31	31	y	y	PROPN
ejpam-3704	31	32	,	,	PUNCT
ejpam-3704	31	33	where	where	SCONJ
ejpam-3704	31	34	x	x	X
ejpam-3704	31	35	�	�	PROPN
ejpam-3704	31	36	y	y	PROPN
ejpam-3704	31	37	is	be	AUX
ejpam-3704	31	38	defined	define	VERB
ejpam-3704	31	39	by	by	ADP
ejpam-3704	31	40	0	0	NUM
ejpam-3704	31	41	∈	∈	PROPN
ejpam-3704	31	42	y~	y~	PROPN
ejpam-3704	31	43	x	x	PUNCT
ejpam-3704	31	44	and	and	CCONJ
ejpam-3704	31	45	for	for	ADP
ejpam-3704	31	46	every	every	DET
ejpam-3704	31	47	a	a	PROPN
ejpam-3704	31	48	,	,	PUNCT
ejpam-3704	31	49	b	b	PROPN
ejpam-3704	31	50	⊆	⊆	NUM
ejpam-3704	31	51	h	h	NOUN
ejpam-3704	31	52	,	,	PUNCT
ejpam-3704	31	53	a	a	DET
ejpam-3704	31	54	�	�	PROPN
ejpam-3704	31	55	b	b	PROPN
ejpam-3704	31	56	is	be	AUX
ejpam-3704	31	57	defined	define	VERB
ejpam-3704	31	58	by	by	ADP
ejpam-3704	31	59	:	:	PUNCT
ejpam-3704	31	60	for	for	ADP
ejpam-3704	31	61	all	all	DET
ejpam-3704	31	62	a	a	DET
ejpam-3704	31	63	∈	∈	PROPN
ejpam-3704	31	64	a	a	PRON
ejpam-3704	31	65	,	,	PUNCT
ejpam-3704	31	66	there	there	PRON
ejpam-3704	31	67	exists	exist	VERB
ejpam-3704	31	68	b	b	PROPN
ejpam-3704	31	69	∈	∈	PROPN
ejpam-3704	31	70	b	b	NOUN
ejpam-3704	31	71	such	such	ADJ
ejpam-3704	31	72	that	that	SCONJ
ejpam-3704	31	73	a	a	DET
ejpam-3704	31	74	�	�	PROPN
ejpam-3704	31	75	b.	b.	PROPN
ejpam-3704	31	76	in	in	ADP
ejpam-3704	31	77	such	such	ADJ
ejpam-3704	31	78	case	case	NOUN
ejpam-3704	31	79	,	,	PUNCT
ejpam-3704	31	80	we	we	PRON
ejpam-3704	31	81	call	call	VERB
ejpam-3704	31	82	“	"	PUNCT
ejpam-3704	31	83	�	�	PROPN
ejpam-3704	31	84	”	"	PUNCT
ejpam-3704	31	85	the	the	DET
ejpam-3704	31	86	hyperorder	hyperorder	NOUN
ejpam-3704	31	87	in	in	ADP
ejpam-3704	31	88	h.	h.	PROPN
ejpam-3704	31	89	a	a	DET
ejpam-3704	31	90	hyper	hyper	ADJ
ejpam-3704	31	91	up	up	ADP
ejpam-3704	31	92	-	-	PUNCT
ejpam-3704	31	93	algebra	algebra	NOUN
ejpam-3704	31	94	h	h	NOUN
ejpam-3704	31	95	with	with	ADP
ejpam-3704	31	96	constant	constant	ADJ
ejpam-3704	31	97	0	0	NUM
ejpam-3704	31	98	and	and	CCONJ
ejpam-3704	31	99	hyperoperation	hyperoperation	NOUN
ejpam-3704	31	100	~	~	PUNCT
ejpam-3704	31	101	is	be	AUX
ejpam-3704	31	102	denoted	denote	VERB
ejpam-3704	31	103	by	by	ADP
ejpam-3704	31	104	(	(	PUNCT
ejpam-3704	31	105	h;~	h;~	NOUN
ejpam-3704	31	106	,	,	PUNCT
ejpam-3704	31	107	0	0	NUM
ejpam-3704	31	108	)	)	PUNCT
ejpam-3704	31	109	.	.	PUNCT
ejpam-3704	32	1	by	by	ADP
ejpam-3704	32	2	(	(	PUNCT
ejpam-3704	32	3	hup2	hup2	PROPN
ejpam-3704	32	4	)	)	PUNCT
ejpam-3704	32	5	or	or	CCONJ
ejpam-3704	32	6	(	(	PUNCT
ejpam-3704	32	7	hup3	hup3	PROPN
ejpam-3704	32	8	)	)	PUNCT
ejpam-3704	32	9	,	,	PUNCT
ejpam-3704	32	10	x~	x~	PROPN
ejpam-3704	32	11	y	y	PROPN
ejpam-3704	32	12	6=	6=	PROPN
ejpam-3704	32	13	∅	∅	NOUN
ejpam-3704	32	14	for	for	ADP
ejpam-3704	32	15	all	all	DET
ejpam-3704	32	16	x	x	NOUN
ejpam-3704	32	17	,	,	PUNCT
ejpam-3704	32	18	y	y	PROPN
ejpam-3704	32	19	∈	∈	PROPN
ejpam-3704	32	20	h.	h.	PROPN
ejpam-3704	32	21	note	note	VERB
ejpam-3704	32	22	that	that	SCONJ
ejpam-3704	32	23	in	in	ADP
ejpam-3704	32	24	[	[	X
ejpam-3704	32	25	10	10	NUM
ejpam-3704	32	26	]	]	PUNCT
ejpam-3704	32	27	,	,	PUNCT
ejpam-3704	32	28	x	x	PRON
ejpam-3704	32	29	�	�	PROPN
ejpam-3704	32	30	y	y	PROPN
ejpam-3704	32	31	is	be	AUX
ejpam-3704	32	32	defined	define	VERB
ejpam-3704	32	33	by	by	ADP
ejpam-3704	32	34	romano	romano	NOUN
ejpam-3704	32	35	as	as	ADP
ejpam-3704	32	36	0	0	NUM
ejpam-3704	32	37	∈	∈	PROPN
ejpam-3704	32	38	x~	x~	PROPN
ejpam-3704	32	39	y.	y.	PROPN
ejpam-3704	32	40	thus	thus	ADV
ejpam-3704	32	41	,	,	PUNCT
ejpam-3704	32	42	(	(	PUNCT
ejpam-3704	32	43	hup1	hup1	PROPN
ejpam-3704	32	44	)	)	PUNCT
ejpam-3704	32	45	in	in	ADP
ejpam-3704	32	46	[	[	X
ejpam-3704	32	47	3	3	NUM
ejpam-3704	32	48	]	]	PUNCT
ejpam-3704	32	49	and	and	CCONJ
ejpam-3704	32	50	[	[	X
ejpam-3704	32	51	10	10	NUM
ejpam-3704	32	52	]	]	PUNCT
ejpam-3704	32	53	are	be	AUX
ejpam-3704	32	54	equivalent	equivalent	ADJ
ejpam-3704	32	55	;	;	PUNCT
ejpam-3704	32	56	that	that	PRON
ejpam-3704	32	57	is	is	ADV
ejpam-3704	32	58	,	,	PUNCT
ejpam-3704	32	59	0	0	NUM
ejpam-3704	32	60	∈	∈	PROPN
ejpam-3704	32	61	(	(	PUNCT
ejpam-3704	32	62	y~	y~	PROPN
ejpam-3704	32	63	z)~	z)~	PROPN
ejpam-3704	32	64	[	[	X
ejpam-3704	32	65	(	(	PUNCT
ejpam-3704	32	66	x~	x~	PROPN
ejpam-3704	32	67	y)~	y)~	PROPN
ejpam-3704	32	68	(	(	PUNCT
ejpam-3704	32	69	x~	x~	PROPN
ejpam-3704	32	70	z	z	PROPN
ejpam-3704	32	71	)	)	PUNCT
ejpam-3704	32	72	]	]	PUNCT
ejpam-3704	32	73	.	.	PUNCT
ejpam-3704	33	1	moreover	moreover	ADV
ejpam-3704	33	2	,	,	PUNCT
ejpam-3704	33	3	(	(	PUNCT
ejpam-3704	33	4	hup2	hup2	PROPN
ejpam-3704	33	5	)	)	PUNCT
ejpam-3704	33	6	to	to	ADP
ejpam-3704	33	7	(	(	PUNCT
ejpam-3704	33	8	hup4	hup4	PROPN
ejpam-3704	33	9	)	)	PUNCT
ejpam-3704	33	10	are	be	AUX
ejpam-3704	33	11	identical	identical	ADJ
ejpam-3704	33	12	,	,	PUNCT
ejpam-3704	33	13	with	with	ADP
ejpam-3704	33	14	“	"	PUNCT
ejpam-3704	33	15	◦	◦	NOUN
ejpam-3704	33	16	”	"	PUNCT
ejpam-3704	33	17	denoted	denote	VERB
ejpam-3704	33	18	by	by	ADP
ejpam-3704	33	19	“	"	PUNCT
ejpam-3704	33	20	~	~	PUNCT
ejpam-3704	33	21	”	"	PUNCT
ejpam-3704	33	22	.	.	PUNCT
ejpam-3704	33	23	example	example	NOUN
ejpam-3704	34	1	1	1	NUM
ejpam-3704	34	2	.	.	PUNCT
ejpam-3704	35	1	[	[	X
ejpam-3704	35	2	3	3	X
ejpam-3704	35	3	]	]	X
ejpam-3704	35	4	let	let	NOUN
ejpam-3704	35	5	h	h	NOUN
ejpam-3704	35	6	=	=	PRON
ejpam-3704	35	7	{	{	PUNCT
ejpam-3704	35	8	0	0	NUM
ejpam-3704	35	9	,	,	PUNCT
ejpam-3704	35	10	a	a	DET
ejpam-3704	35	11	,	,	PUNCT
ejpam-3704	35	12	b	b	NOUN
ejpam-3704	35	13	,	,	PUNCT
ejpam-3704	35	14	c	c	AUX
ejpam-3704	35	15	}	}	PUNCT
ejpam-3704	35	16	be	be	AUX
ejpam-3704	35	17	a	a	DET
ejpam-3704	35	18	set	set	NOUN
ejpam-3704	35	19	.	.	PUNCT
ejpam-3704	36	1	define	define	VERB
ejpam-3704	36	2	the	the	DET
ejpam-3704	36	3	hyperoperation	hyperoperation	NOUN
ejpam-3704	36	4	~	~	PUNCT
ejpam-3704	36	5	by	by	ADP
ejpam-3704	36	6	the	the	DET
ejpam-3704	36	7	following	follow	VERB
ejpam-3704	36	8	cayley	cayley	ADJ
ejpam-3704	36	9	table	table	NOUN
ejpam-3704	36	10	:	:	PUNCT
ejpam-3704	36	11	~	~	PUNCT
ejpam-3704	36	12	0	0	PUNCT
ejpam-3704	36	13	a	a	DET
ejpam-3704	36	14	b	b	X
ejpam-3704	36	15	c	c	NOUN
ejpam-3704	36	16	0	0	PUNCT
ejpam-3704	36	17	{	{	PUNCT
ejpam-3704	36	18	0	0	NUM
ejpam-3704	36	19	}	}	PUNCT
ejpam-3704	36	20	{	{	PUNCT
ejpam-3704	36	21	a	a	NOUN
ejpam-3704	36	22	}	}	PUNCT
ejpam-3704	36	23	{	{	PUNCT
ejpam-3704	36	24	b	b	NOUN
ejpam-3704	36	25	}	}	PUNCT
ejpam-3704	36	26	{	{	PUNCT
ejpam-3704	36	27	c	c	NOUN
ejpam-3704	36	28	}	}	PUNCT
ejpam-3704	36	29	a	a	DET
ejpam-3704	36	30	{	{	PUNCT
ejpam-3704	36	31	0	0	NUM
ejpam-3704	36	32	}	}	PUNCT
ejpam-3704	36	33	{	{	PUNCT
ejpam-3704	36	34	0,a	0,a	NOUN
ejpam-3704	36	35	}	}	PUNCT
ejpam-3704	36	36	{	{	PUNCT
ejpam-3704	36	37	0,b	0,b	NOUN
ejpam-3704	36	38	}	}	PUNCT
ejpam-3704	36	39	{	{	PUNCT
ejpam-3704	36	40	c	c	NOUN
ejpam-3704	36	41	}	}	PUNCT
ejpam-3704	36	42	b	b	NOUN
ejpam-3704	36	43	{	{	PUNCT
ejpam-3704	36	44	0	0	NUM
ejpam-3704	36	45	}	}	PUNCT
ejpam-3704	36	46	{	{	PUNCT
ejpam-3704	36	47	a	a	NOUN
ejpam-3704	36	48	}	}	PUNCT
ejpam-3704	36	49	{	{	PUNCT
ejpam-3704	36	50	0,b	0,b	NOUN
ejpam-3704	36	51	}	}	PUNCT
ejpam-3704	36	52	{	{	PUNCT
ejpam-3704	36	53	c	c	NOUN
ejpam-3704	36	54	}	}	PUNCT
ejpam-3704	36	55	c	c	NOUN
ejpam-3704	36	56	{	{	PUNCT
ejpam-3704	36	57	0	0	NUM
ejpam-3704	36	58	}	}	PUNCT
ejpam-3704	36	59	{	{	PUNCT
ejpam-3704	36	60	0,a	0,a	NOUN
ejpam-3704	36	61	}	}	PUNCT
ejpam-3704	36	62	{	{	PUNCT
ejpam-3704	36	63	0,b	0,b	NOUN
ejpam-3704	36	64	}	}	PUNCT
ejpam-3704	36	65	{	{	PUNCT
ejpam-3704	36	66	0,a	0,a	PROPN
ejpam-3704	36	67	,	,	PUNCT
ejpam-3704	36	68	c	c	NOUN
ejpam-3704	36	69	}	}	PUNCT
ejpam-3704	36	70	then	then	ADV
ejpam-3704	36	71	,	,	PUNCT
ejpam-3704	36	72	(	(	PUNCT
ejpam-3704	36	73	h;~	h;~	NOUN
ejpam-3704	36	74	,	,	PUNCT
ejpam-3704	36	75	0	0	NUM
ejpam-3704	36	76	)	)	PUNCT
ejpam-3704	36	77	is	be	AUX
ejpam-3704	36	78	a	a	DET
ejpam-3704	36	79	hyper	hyper	ADJ
ejpam-3704	36	80	up	up	NOUN
ejpam-3704	36	81	-	-	PUNCT
ejpam-3704	36	82	algebra	algebra	NOUN
ejpam-3704	36	83	.	.	PUNCT
ejpam-3704	37	1	proposition	proposition	NOUN
ejpam-3704	37	2	1	1	NUM
ejpam-3704	37	3	.	.	PUNCT
ejpam-3704	38	1	[	[	X
ejpam-3704	38	2	3	3	NUM
ejpam-3704	38	3	,	,	PUNCT
ejpam-3704	38	4	10	10	NUM
ejpam-3704	38	5	]	]	PUNCT
ejpam-3704	38	6	let	let	VERB
ejpam-3704	38	7	h	h	PRON
ejpam-3704	38	8	be	be	AUX
ejpam-3704	38	9	a	a	DET
ejpam-3704	38	10	hyper	hyper	ADJ
ejpam-3704	38	11	up	up	NOUN
ejpam-3704	38	12	-	-	PUNCT
ejpam-3704	38	13	algebra	algebra	NOUN
ejpam-3704	38	14	.	.	PUNCT
ejpam-3704	39	1	then	then	ADV
ejpam-3704	39	2	the	the	DET
ejpam-3704	39	3	following	follow	VERB
ejpam-3704	39	4	hold	hold	NOUN
ejpam-3704	39	5	for	for	ADP
ejpam-3704	39	6	all	all	DET
ejpam-3704	39	7	x	x	NOUN
ejpam-3704	39	8	,	,	PUNCT
ejpam-3704	39	9	y	y	PROPN
ejpam-3704	39	10	,	,	PUNCT
ejpam-3704	39	11	z	z	PROPN
ejpam-3704	39	12	∈	∈	PROPN
ejpam-3704	39	13	h	h	NOUN
ejpam-3704	39	14	and	and	CCONJ
ejpam-3704	39	15	for	for	ADP
ejpam-3704	39	16	every	every	DET
ejpam-3704	39	17	nonempty	nonempty	NOUN
ejpam-3704	39	18	subsets	subset	NOUN
ejpam-3704	39	19	a	a	DET
ejpam-3704	39	20	,	,	PUNCT
ejpam-3704	39	21	b	b	NOUN
ejpam-3704	39	22	,	,	PUNCT
ejpam-3704	39	23	c	c	PROPN
ejpam-3704	39	24	⊆	⊆	NUM
ejpam-3704	39	25	h	h	NOUN
ejpam-3704	39	26	:	:	PUNCT
ejpam-3704	39	27	(	(	PUNCT
ejpam-3704	39	28	i	i	NOUN
ejpam-3704	39	29	)	)	PUNCT
ejpam-3704	39	30	0	0	PUNCT
ejpam-3704	40	1	~	~	PUNCT
ejpam-3704	40	2	0	0	X
ejpam-3704	40	3	=	=	SYM
ejpam-3704	40	4	{	{	PUNCT
ejpam-3704	40	5	0	0	NUM
ejpam-3704	40	6	}	}	PUNCT
ejpam-3704	40	7	(	(	PUNCT
ejpam-3704	40	8	ii	ii	NOUN
ejpam-3704	40	9	)	)	PUNCT
ejpam-3704	40	10	0	0	NUM
ejpam-3704	41	1	~a	~a	PUNCT
ejpam-3704	41	2	=	=	SYM
ejpam-3704	41	3	a	a	DET
ejpam-3704	41	4	(	(	PUNCT
ejpam-3704	41	5	iii	iii	NOUN
ejpam-3704	41	6	)	)	PUNCT
ejpam-3704	41	7	z	z	NOUN
ejpam-3704	41	8	�	�	PROPN
ejpam-3704	41	9	z	z	PROPN
ejpam-3704	41	10	(	(	PUNCT
ejpam-3704	41	11	iv	iv	X
ejpam-3704	41	12	)	)	PUNCT
ejpam-3704	41	13	a	a	DET
ejpam-3704	41	14	⊆	⊆	NUM
ejpam-3704	41	15	b	b	NOUN
ejpam-3704	41	16	implies	imply	VERB
ejpam-3704	41	17	a	a	DET
ejpam-3704	41	18	�	�	PROPN
ejpam-3704	41	19	b	b	PROPN
ejpam-3704	41	20	r.	r.	PROPN
ejpam-3704	41	21	amairanto	amairanto	PROPN
ejpam-3704	41	22	,	,	PUNCT
ejpam-3704	41	23	r.	r.	PROPN
ejpam-3704	41	24	isla	isla	PROPN
ejpam-3704	41	25	/	/	SYM
ejpam-3704	41	26	eur	eur	PROPN
ejpam-3704	41	27	.	.	PUNCT
ejpam-3704	42	1	j.	j.	PROPN
ejpam-3704	42	2	pure	pure	PROPN
ejpam-3704	42	3	appl	appl	PROPN
ejpam-3704	42	4	.	.	PROPN
ejpam-3704	42	5	math	math	PROPN
ejpam-3704	42	6	,	,	PUNCT
ejpam-3704	42	7	13	13	NUM
ejpam-3704	42	8	(	(	PUNCT
ejpam-3704	42	9	3	3	NUM
ejpam-3704	42	10	)	)	PUNCT
ejpam-3704	42	11	(	(	PUNCT
ejpam-3704	42	12	2020	2020	NUM
ejpam-3704	42	13	)	)	PUNCT
ejpam-3704	42	14	,	,	PUNCT
ejpam-3704	42	15	483	483	NUM
ejpam-3704	42	16	-	-	SYM
ejpam-3704	42	17	497	497	NUM
ejpam-3704	42	18	485	485	NUM
ejpam-3704	42	19	(	(	PUNCT
ejpam-3704	42	20	v	v	NOUN
ejpam-3704	42	21	)	)	PUNCT
ejpam-3704	42	22	x~	x~	PROPN
ejpam-3704	42	23	z	z	PROPN
ejpam-3704	42	24	�	�	PROPN
ejpam-3704	42	25	z	z	PROPN
ejpam-3704	42	26	(	(	PUNCT
ejpam-3704	42	27	vi	vi	NOUN
ejpam-3704	42	28	)	)	PUNCT
ejpam-3704	42	29	a~	a~	PROPN
ejpam-3704	42	30	0	0	NUM
ejpam-3704	43	1	=	=	SYM
ejpam-3704	43	2	{	{	PUNCT
ejpam-3704	43	3	0	0	NUM
ejpam-3704	43	4	}	}	PUNCT
ejpam-3704	43	5	(	(	PUNCT
ejpam-3704	43	6	vii	vii	PROPN
ejpam-3704	43	7	)	)	PUNCT
ejpam-3704	43	8	a	a	DET
ejpam-3704	43	9	�	�	PROPN
ejpam-3704	43	10	{	{	PUNCT
ejpam-3704	43	11	0	0	NUM
ejpam-3704	43	12	}	}	PUNCT
ejpam-3704	43	13	implies	imply	VERB
ejpam-3704	43	14	a	a	DET
ejpam-3704	43	15	=	=	SYM
ejpam-3704	43	16	{	{	PUNCT
ejpam-3704	43	17	0	0	NUM
ejpam-3704	43	18	}	}	PUNCT
ejpam-3704	43	19	(	(	PUNCT
ejpam-3704	43	20	viii	viii	NOUN
ejpam-3704	43	21	)	)	PUNCT
ejpam-3704	43	22	a~	a~	PROPN
ejpam-3704	43	23	(	(	PUNCT
ejpam-3704	43	24	b	b	X
ejpam-3704	43	25	~	~	SYM
ejpam-3704	43	26	c	c	X
ejpam-3704	43	27	)	)	PUNCT
ejpam-3704	44	1	=	=	SYM
ejpam-3704	44	2	b	b	X
ejpam-3704	44	3	~	~	PUNCT
ejpam-3704	44	4	(	(	PUNCT
ejpam-3704	44	5	a~	a~	PROPN
ejpam-3704	44	6	c	c	PROPN
ejpam-3704	44	7	)	)	PUNCT
ejpam-3704	44	8	(	(	PUNCT
ejpam-3704	44	9	ix	ix	PROPN
ejpam-3704	44	10	)	)	PUNCT
ejpam-3704	44	11	0	0	NUM
ejpam-3704	44	12	�	�	PROPN
ejpam-3704	44	13	x	x	SYM
ejpam-3704	44	14	(	(	PUNCT
ejpam-3704	44	15	x	x	X
ejpam-3704	44	16	)	)	PUNCT
ejpam-3704	44	17	x	x	SYM
ejpam-3704	44	18	∈	∈	PROPN
ejpam-3704	44	19	(	(	PUNCT
ejpam-3704	44	20	0	0	NUM
ejpam-3704	44	21	~	~	SYM
ejpam-3704	44	22	y	y	X
ejpam-3704	44	23	)	)	PUNCT
ejpam-3704	44	24	implies	imply	VERB
ejpam-3704	44	25	x	x	X
ejpam-3704	44	26	�	�	PROPN
ejpam-3704	44	27	y	y	PROPN
ejpam-3704	44	28	definition	definition	NOUN
ejpam-3704	44	29	2	2	NUM
ejpam-3704	44	30	.	.	PUNCT
ejpam-3704	45	1	[	[	X
ejpam-3704	45	2	3	3	X
ejpam-3704	45	3	]	]	X
ejpam-3704	45	4	let	let	VERB
ejpam-3704	45	5	(	(	PUNCT
ejpam-3704	45	6	h;~	h;~	NOUN
ejpam-3704	45	7	,	,	PUNCT
ejpam-3704	45	8	0	0	NUM
ejpam-3704	45	9	)	)	PUNCT
ejpam-3704	45	10	and	and	CCONJ
ejpam-3704	45	11	(	(	PUNCT
ejpam-3704	45	12	h	h	NOUN
ejpam-3704	45	13	′;~′	′;~′	PROPN
ejpam-3704	45	14	,	,	PUNCT
ejpam-3704	45	15	0′	0′	NUM
ejpam-3704	45	16	)	)	PUNCT
ejpam-3704	45	17	be	be	AUX
ejpam-3704	45	18	hyper	hyper	ADJ
ejpam-3704	45	19	up	up	ADP
ejpam-3704	45	20	-	-	PUNCT
ejpam-3704	45	21	algebras	algebras	X
ejpam-3704	45	22	.	.	PUNCT
ejpam-3704	46	1	a	a	DET
ejpam-3704	46	2	mapping	mapping	NOUN
ejpam-3704	46	3	f	f	NOUN
ejpam-3704	46	4	:	:	PUNCT
ejpam-3704	46	5	h	h	PROPN
ejpam-3704	46	6	→	→	PUNCT
ejpam-3704	46	7	k	k	PROPN
ejpam-3704	46	8	is	be	AUX
ejpam-3704	46	9	called	call	VERB
ejpam-3704	46	10	a	a	DET
ejpam-3704	46	11	hyper	hyper	ADJ
ejpam-3704	46	12	homomorphism	homomorphism	NOUN
ejpam-3704	46	13	if	if	SCONJ
ejpam-3704	46	14	(	(	PUNCT
ejpam-3704	46	15	hh1	hh1	NOUN
ejpam-3704	46	16	)	)	PUNCT
ejpam-3704	46	17	f(0	f(0	NOUN
ejpam-3704	46	18	)	)	PUNCT
ejpam-3704	46	19	=	=	SYM
ejpam-3704	46	20	0′	0′	PROPN
ejpam-3704	46	21	,	,	PUNCT
ejpam-3704	46	22	(	(	PUNCT
ejpam-3704	46	23	hh2	hh2	NOUN
ejpam-3704	46	24	)	)	PUNCT
ejpam-3704	46	25	f(x~	f(x~	PROPN
ejpam-3704	46	26	y	y	PROPN
ejpam-3704	46	27	)	)	PUNCT
ejpam-3704	46	28	=	=	SYM
ejpam-3704	46	29	f(x	f(x	PROPN
ejpam-3704	46	30	)	)	PUNCT
ejpam-3704	46	31	~′	~′	NOUN
ejpam-3704	46	32	f(y	f(y	NOUN
ejpam-3704	46	33	)	)	PUNCT
ejpam-3704	46	34	for	for	ADP
ejpam-3704	46	35	all	all	DET
ejpam-3704	46	36	x	x	NOUN
ejpam-3704	46	37	,	,	PUNCT
ejpam-3704	46	38	y	y	PROPN
ejpam-3704	46	39	∈	∈	PROPN
ejpam-3704	46	40	h.	h.	NOUN
ejpam-3704	47	1	the	the	DET
ejpam-3704	47	2	following	follow	VERB
ejpam-3704	47	3	definitions	definition	NOUN
ejpam-3704	47	4	are	be	AUX
ejpam-3704	47	5	analogous	analogous	ADJ
ejpam-3704	47	6	to	to	ADP
ejpam-3704	47	7	the	the	DET
ejpam-3704	47	8	ones	one	NOUN
ejpam-3704	47	9	given	give	VERB
ejpam-3704	47	10	by	by	ADP
ejpam-3704	47	11	borzooei	borzooei	PROPN
ejpam-3704	47	12	and	and	CCONJ
ejpam-3704	47	13	harizavi	harizavi	PROPN
ejpam-3704	47	14	[	[	X
ejpam-3704	47	15	1	1	NUM
ejpam-3704	47	16	]	]	PUNCT
ejpam-3704	47	17	for	for	ADP
ejpam-3704	47	18	regular	regular	ADJ
ejpam-3704	47	19	congruence	congruence	NOUN
ejpam-3704	47	20	realtions	realtion	NOUN
ejpam-3704	47	21	on	on	ADP
ejpam-3704	47	22	hyper	hyper	ADJ
ejpam-3704	47	23	bck	bck	NOUN
ejpam-3704	47	24	-	-	PUNCT
ejpam-3704	47	25	algebras	algebras	PROPN
ejpam-3704	47	26	.	.	PUNCT
ejpam-3704	48	1	definition	definition	NOUN
ejpam-3704	48	2	3	3	X
ejpam-3704	48	3	.	.	PUNCT
ejpam-3704	49	1	let	let	VERB
ejpam-3704	49	2	θ	θ	NOUN
ejpam-3704	49	3	be	be	AUX
ejpam-3704	49	4	an	an	DET
ejpam-3704	49	5	equivalence	equivalence	NOUN
ejpam-3704	49	6	relation	relation	NOUN
ejpam-3704	49	7	on	on	ADP
ejpam-3704	49	8	a	a	DET
ejpam-3704	49	9	hyper	hyper	ADJ
ejpam-3704	49	10	up	up	ADP
ejpam-3704	49	11	-	-	PUNCT
ejpam-3704	49	12	algebra	algebra	NOUN
ejpam-3704	49	13	h	h	NOUN
ejpam-3704	49	14	and	and	CCONJ
ejpam-3704	49	15	a	a	DET
ejpam-3704	49	16	,	,	PUNCT
ejpam-3704	49	17	b	b	PROPN
ejpam-3704	49	18	⊆	⊆	NUM
ejpam-3704	49	19	h.	h.	NOUN
ejpam-3704	50	1	then	then	ADV
ejpam-3704	50	2	(	(	PUNCT
ejpam-3704	50	3	i	i	NOUN
ejpam-3704	50	4	)	)	PUNCT
ejpam-3704	50	5	aθb	aθb	NOUN
ejpam-3704	50	6	if	if	SCONJ
ejpam-3704	50	7	there	there	PRON
ejpam-3704	50	8	exists	exist	VERB
ejpam-3704	50	9	a	a	DET
ejpam-3704	50	10	∈	∈	PROPN
ejpam-3704	50	11	a	a	DET
ejpam-3704	50	12	and	and	CCONJ
ejpam-3704	50	13	b	b	NOUN
ejpam-3704	50	14	∈	∈	PROPN
ejpam-3704	50	15	b	b	NOUN
ejpam-3704	50	16	such	such	ADJ
ejpam-3704	50	17	that	that	DET
ejpam-3704	50	18	aθb	aθb	NOUN
ejpam-3704	50	19	;	;	PUNCT
ejpam-3704	50	20	(	(	PUNCT
ejpam-3704	50	21	ii	ii	NOUN
ejpam-3704	50	22	)	)	PUNCT
ejpam-3704	50	23	aθ̄b	aθ̄b	NOUN
ejpam-3704	50	24	if	if	SCONJ
ejpam-3704	50	25	for	for	ADP
ejpam-3704	50	26	all	all	DET
ejpam-3704	50	27	a	a	DET
ejpam-3704	50	28	∈	∈	PROPN
ejpam-3704	50	29	a	a	PRON
ejpam-3704	50	30	,	,	PUNCT
ejpam-3704	50	31	there	there	PRON
ejpam-3704	50	32	exists	exist	VERB
ejpam-3704	50	33	b	b	PROPN
ejpam-3704	50	34	∈	∈	PROPN
ejpam-3704	50	35	b	b	NOUN
ejpam-3704	50	36	such	such	ADJ
ejpam-3704	50	37	that	that	DET
ejpam-3704	50	38	aθb	aθb	NOUN
ejpam-3704	50	39	and	and	CCONJ
ejpam-3704	50	40	for	for	ADP
ejpam-3704	50	41	all	all	DET
ejpam-3704	50	42	b	b	PROPN
ejpam-3704	50	43	∈	∈	ADJ
ejpam-3704	50	44	b	b	NOUN
ejpam-3704	50	45	,	,	PUNCT
ejpam-3704	50	46	there	there	PRON
ejpam-3704	50	47	exists	exist	VERB
ejpam-3704	50	48	a	a	DET
ejpam-3704	50	49	∈	∈	NOUN
ejpam-3704	50	50	a	a	DET
ejpam-3704	50	51	such	such	ADJ
ejpam-3704	50	52	that	that	DET
ejpam-3704	50	53	aθb	aθb	NOUN
ejpam-3704	50	54	;	;	PUNCT
ejpam-3704	50	55	(	(	PUNCT
ejpam-3704	50	56	iii	iii	X
ejpam-3704	50	57	)	)	PUNCT
ejpam-3704	50	58	θ	θ	PROPN
ejpam-3704	50	59	is	be	AUX
ejpam-3704	50	60	called	call	VERB
ejpam-3704	50	61	a	a	DET
ejpam-3704	50	62	congruence	congruence	NOUN
ejpam-3704	50	63	relation	relation	NOUN
ejpam-3704	50	64	on	on	ADP
ejpam-3704	50	65	h	h	NOUN
ejpam-3704	50	66	if	if	SCONJ
ejpam-3704	50	67	whenever	whenever	SCONJ
ejpam-3704	50	68	xθy	xθy	PROPN
ejpam-3704	50	69	and	and	CCONJ
ejpam-3704	50	70	x′θy′	x′θy′	NUM
ejpam-3704	50	71	,	,	PUNCT
ejpam-3704	50	72	then	then	ADV
ejpam-3704	50	73	(	(	PUNCT
ejpam-3704	50	74	x	x	X
ejpam-3704	50	75	~	~	NOUN
ejpam-3704	50	76	x′)θ̄(y	x′)θ̄(y	X
ejpam-3704	50	77	~	~	SYM
ejpam-3704	50	78	y′	y′	NUM
ejpam-3704	50	79	)	)	PUNCT
ejpam-3704	50	80	,	,	PUNCT
ejpam-3704	50	81	for	for	ADP
ejpam-3704	50	82	all	all	DET
ejpam-3704	50	83	x	x	NOUN
ejpam-3704	50	84	,	,	PUNCT
ejpam-3704	50	85	y	y	PROPN
ejpam-3704	50	86	,	,	PUNCT
ejpam-3704	50	87	x′	x′	NUM
ejpam-3704	50	88	,	,	PUNCT
ejpam-3704	50	89	y′	y′	NOUN
ejpam-3704	50	90	∈	∈	PROPN
ejpam-3704	50	91	h	h	NOUN
ejpam-3704	50	92	;	;	PUNCT
ejpam-3704	50	93	(	(	PUNCT
ejpam-3704	50	94	iv	iv	X
ejpam-3704	50	95	)	)	PUNCT
ejpam-3704	50	96	θ	θ	PROPN
ejpam-3704	50	97	is	be	AUX
ejpam-3704	50	98	called	call	VERB
ejpam-3704	50	99	a	a	DET
ejpam-3704	50	100	regular	regular	ADJ
ejpam-3704	50	101	congruence	congruence	NOUN
ejpam-3704	50	102	relation	relation	NOUN
ejpam-3704	50	103	on	on	ADP
ejpam-3704	50	104	h	h	NOUN
ejpam-3704	50	105	if	if	SCONJ
ejpam-3704	50	106	θ	θ	PROPN
ejpam-3704	50	107	is	be	AUX
ejpam-3704	50	108	a	a	DET
ejpam-3704	50	109	congruence	congruence	NOUN
ejpam-3704	50	110	relation	relation	NOUN
ejpam-3704	50	111	on	on	ADP
ejpam-3704	50	112	h	h	NOUN
ejpam-3704	50	113	and	and	CCONJ
ejpam-3704	50	114	whenever	whenever	SCONJ
ejpam-3704	50	115	(	(	PUNCT
ejpam-3704	50	116	x~	x~	PROPN
ejpam-3704	50	117	y)θ{0	y)θ{0	ADJ
ejpam-3704	50	118	}	}	PUNCT
ejpam-3704	50	119	and	and	CCONJ
ejpam-3704	50	120	(	(	PUNCT
ejpam-3704	50	121	y	y	NOUN
ejpam-3704	50	122	~	~	PUNCT
ejpam-3704	50	123	x)θ{0	x)θ{0	NUM
ejpam-3704	50	124	}	}	PUNCT
ejpam-3704	50	125	,	,	PUNCT
ejpam-3704	50	126	then	then	ADV
ejpam-3704	50	127	xθy	xθy	VERB
ejpam-3704	50	128	for	for	ADP
ejpam-3704	50	129	all	all	DET
ejpam-3704	50	130	x	x	NOUN
ejpam-3704	50	131	,	,	PUNCT
ejpam-3704	50	132	y	y	PROPN
ejpam-3704	50	133	∈	∈	PROPN
ejpam-3704	50	134	h.	h.	NOUN
ejpam-3704	50	135	the	the	DET
ejpam-3704	50	136	set	set	NOUN
ejpam-3704	51	1	[	[	X
ejpam-3704	51	2	x]θ	x]θ	NOUN
ejpam-3704	51	3	=	=	SYM
ejpam-3704	51	4	{	{	PUNCT
ejpam-3704	51	5	y	y	PROPN
ejpam-3704	51	6	∈	∈	PROPN
ejpam-3704	51	7	h	h	NOUN
ejpam-3704	51	8	:	:	PUNCT
ejpam-3704	51	9	yθx	yθx	NOUN
ejpam-3704	51	10	}	}	PUNCT
ejpam-3704	51	11	is	be	AUX
ejpam-3704	51	12	called	call	VERB
ejpam-3704	51	13	the	the	DET
ejpam-3704	51	14	congruence	congruence	NOUN
ejpam-3704	51	15	class	class	NOUN
ejpam-3704	51	16	determined	determine	VERB
ejpam-3704	51	17	by	by	ADP
ejpam-3704	51	18	x.	x.	PROPN
ejpam-3704	51	19	3	3	NUM
ejpam-3704	51	20	.	.	PUNCT
ejpam-3704	51	21	regular	regular	ADJ
ejpam-3704	51	22	congruence	congruence	NOUN
ejpam-3704	51	23	relations	relation	NOUN
ejpam-3704	51	24	and	and	CCONJ
ejpam-3704	51	25	hyper	hyper	ADJ
ejpam-3704	51	26	homomorphisms	homomorphism	NOUN
ejpam-3704	51	27	on	on	ADP
ejpam-3704	51	28	hyper	hyper	NOUN
ejpam-3704	51	29	up	up	ADP
ejpam-3704	51	30	-	-	PUNCT
ejpam-3704	51	31	algebras	algebras	NOUN
ejpam-3704	51	32	all	all	PRON
ejpam-3704	51	33	throughout	throughout	ADP
ejpam-3704	51	34	,	,	PUNCT
ejpam-3704	51	35	h	h	NOUN
ejpam-3704	51	36	,	,	PUNCT
ejpam-3704	51	37	h	h	NOUN
ejpam-3704	51	38	′	′	NOUN
ejpam-3704	51	39	,	,	PUNCT
ejpam-3704	52	1	h	h	NOUN
ejpam-3704	52	2	′′	′′	PROPN
ejpam-3704	52	3	are	be	AUX
ejpam-3704	52	4	hyper	hyper	ADJ
ejpam-3704	52	5	up	up	ADP
ejpam-3704	52	6	-	-	PUNCT
ejpam-3704	52	7	algebras	algebras	X
ejpam-3704	52	8	.	.	PUNCT
ejpam-3704	53	1	proposition	proposition	NOUN
ejpam-3704	53	2	2	2	NUM
ejpam-3704	53	3	.	.	PUNCT
ejpam-3704	54	1	if	if	SCONJ
ejpam-3704	54	2	f	f	PROPN
ejpam-3704	54	3	:	:	PUNCT
ejpam-3704	54	4	h	h	PROPN
ejpam-3704	54	5	−→	−→	ADJ
ejpam-3704	54	6	h	h	NOUN
ejpam-3704	54	7	′	′	NOUN
ejpam-3704	54	8	is	be	AUX
ejpam-3704	54	9	a	a	DET
ejpam-3704	54	10	hyper	hyper	ADJ
ejpam-3704	54	11	homomorphism	homomorphism	NOUN
ejpam-3704	54	12	,	,	PUNCT
ejpam-3704	54	13	then	then	ADV
ejpam-3704	54	14	for	for	ADP
ejpam-3704	54	15	all	all	DET
ejpam-3704	54	16	nonempty	nonempty	ADJ
ejpam-3704	54	17	subsets	subset	NOUN
ejpam-3704	54	18	a	a	DET
ejpam-3704	54	19	,	,	PUNCT
ejpam-3704	54	20	b	b	NOUN
ejpam-3704	54	21	⊆	⊆	NUM
ejpam-3704	54	22	h	h	NOUN
ejpam-3704	54	23	we	we	PRON
ejpam-3704	54	24	have	have	VERB
ejpam-3704	54	25	f(a	f(a	NOUN
ejpam-3704	54	26	~	~	SYM
ejpam-3704	54	27	b	b	X
ejpam-3704	54	28	)	)	PUNCT
ejpam-3704	54	29	=	=	SYM
ejpam-3704	54	30	f(a	f(a	NOUN
ejpam-3704	54	31	)	)	PUNCT
ejpam-3704	54	32	~′	~′	NOUN
ejpam-3704	54	33	f(b	f(b	PROPN
ejpam-3704	54	34	)	)	PUNCT
ejpam-3704	54	35	.	.	PUNCT
ejpam-3704	55	1	proof	proof	NOUN
ejpam-3704	55	2	.	.	PUNCT
ejpam-3704	56	1	let	let	VERB
ejpam-3704	56	2	f	f	NOUN
ejpam-3704	56	3	:	:	PUNCT
ejpam-3704	56	4	h	h	PROPN
ejpam-3704	56	5	−→	−→	ADJ
ejpam-3704	56	6	h	h	NOUN
ejpam-3704	56	7	′	′	NUM
ejpam-3704	56	8	be	be	AUX
ejpam-3704	56	9	a	a	DET
ejpam-3704	56	10	hyper	hyper	ADJ
ejpam-3704	56	11	homomorphism	homomorphism	NOUN
ejpam-3704	56	12	and	and	CCONJ
ejpam-3704	56	13	∅	∅	NOUN
ejpam-3704	56	14	6=	6=	NOUN
ejpam-3704	56	15	a	a	PRON
ejpam-3704	56	16	,	,	PUNCT
ejpam-3704	56	17	b	b	PROPN
ejpam-3704	56	18	⊆	⊆	NUM
ejpam-3704	56	19	h.	h.	NOUN
ejpam-3704	56	20	let	let	VERB
ejpam-3704	56	21	x	x	PUNCT
ejpam-3704	56	22	∈	∈	NOUN
ejpam-3704	56	23	f(a	f(a	X
ejpam-3704	56	24	~	~	SYM
ejpam-3704	56	25	b	b	X
ejpam-3704	56	26	)	)	PUNCT
ejpam-3704	56	27	=	=	PUNCT
ejpam-3704	57	1	f	f	X
ejpam-3704	58	1			PROPN
ejpam-3704	58	2	⋃	⋃	PROPN
ejpam-3704	58	3	a∈a	a∈a	ADJ
ejpam-3704	58	4	,	,	PUNCT
ejpam-3704	58	5	b∈b	b∈b	NOUN
ejpam-3704	58	6	a~	a~	PROPN
ejpam-3704	58	7	b	b	PROPN
ejpam-3704	58	8	.	.	PROPN
ejpam-3704	58	9	then	then	ADV
ejpam-3704	58	10	there	there	PRON
ejpam-3704	58	11	exist	exist	VERB
ejpam-3704	58	12	a	a	DET
ejpam-3704	58	13	∈	∈	PROPN
ejpam-3704	58	14	a	a	PRON
ejpam-3704	58	15	and	and	CCONJ
ejpam-3704	58	16	b	b	NOUN
ejpam-3704	58	17	∈	∈	PROPN
ejpam-3704	58	18	b	b	NOUN
ejpam-3704	58	19	such	such	ADJ
ejpam-3704	58	20	that	that	SCONJ
ejpam-3704	58	21	x	x	SYM
ejpam-3704	58	22	∈	∈	PROPN
ejpam-3704	58	23	f(a~	f(a~	PROPN
ejpam-3704	58	24	b	b	NOUN
ejpam-3704	58	25	)	)	PUNCT
ejpam-3704	58	26	.	.	PUNCT
ejpam-3704	59	1	since	since	SCONJ
ejpam-3704	59	2	f	f	PROPN
ejpam-3704	59	3	is	be	AUX
ejpam-3704	59	4	a	a	DET
ejpam-3704	59	5	hyper	hyper	ADJ
ejpam-3704	59	6	homomorphism	homomorphism	NOUN
ejpam-3704	59	7	,	,	PUNCT
ejpam-3704	59	8	x	x	PROPN
ejpam-3704	59	9	∈	∈	PROPN
ejpam-3704	59	10	f(a	f(a	NOUN
ejpam-3704	59	11	)	)	PUNCT
ejpam-3704	59	12	~′	~′	NOUN
ejpam-3704	59	13	f(b	f(b	PROPN
ejpam-3704	59	14	)	)	PUNCT
ejpam-3704	59	15	⊆	⊆	NUM
ejpam-3704	59	16	⋃	⋃	NOUN
ejpam-3704	59	17	f(a	f(a	NOUN
ejpam-3704	59	18	)	)	PUNCT
ejpam-3704	59	19	∈	∈	PROPN
ejpam-3704	59	20	f(a	f(a	NOUN
ejpam-3704	59	21	)	)	PUNCT
ejpam-3704	59	22	,	,	PUNCT
ejpam-3704	59	23	f(b	f(b	PROPN
ejpam-3704	59	24	)	)	PUNCT
ejpam-3704	59	25	∈	∈	PROPN
ejpam-3704	59	26	f(b	f(b	PROPN
ejpam-3704	59	27	)	)	PUNCT
ejpam-3704	59	28	f(a	f(a	NOUN
ejpam-3704	59	29	)	)	PUNCT
ejpam-3704	59	30	~′	~′	NOUN
ejpam-3704	59	31	f(b	f(b	PROPN
ejpam-3704	59	32	)	)	PUNCT
ejpam-3704	59	33	=	=	SYM
ejpam-3704	59	34	f(a	f(a	NOUN
ejpam-3704	59	35	)	)	PUNCT
ejpam-3704	59	36	~′	~′	NOUN
ejpam-3704	59	37	f(b	f(b	PROPN
ejpam-3704	59	38	)	)	PUNCT
ejpam-3704	59	39	.	.	PUNCT
ejpam-3704	60	1	r.	r.	PROPN
ejpam-3704	60	2	amairanto	amairanto	PROPN
ejpam-3704	60	3	,	,	PUNCT
ejpam-3704	60	4	r.	r.	PROPN
ejpam-3704	60	5	isla	isla	PROPN
ejpam-3704	60	6	/	/	SYM
ejpam-3704	60	7	eur	eur	PROPN
ejpam-3704	60	8	.	.	PUNCT
ejpam-3704	61	1	j.	j.	PROPN
ejpam-3704	61	2	pure	pure	PROPN
ejpam-3704	61	3	appl	appl	PROPN
ejpam-3704	61	4	.	.	PROPN
ejpam-3704	61	5	math	math	PROPN
ejpam-3704	61	6	,	,	PUNCT
ejpam-3704	61	7	13	13	NUM
ejpam-3704	61	8	(	(	PUNCT
ejpam-3704	61	9	3	3	NUM
ejpam-3704	61	10	)	)	PUNCT
ejpam-3704	61	11	(	(	PUNCT
ejpam-3704	61	12	2020	2020	NUM
ejpam-3704	61	13	)	)	PUNCT
ejpam-3704	61	14	,	,	PUNCT
ejpam-3704	61	15	483	483	NUM
ejpam-3704	61	16	-	-	SYM
ejpam-3704	61	17	497	497	NUM
ejpam-3704	61	18	486	486	NUM
ejpam-3704	61	19	thus	thus	ADV
ejpam-3704	61	20	,	,	PUNCT
ejpam-3704	61	21	f(a	f(a	X
ejpam-3704	61	22	~	~	SYM
ejpam-3704	61	23	b	b	X
ejpam-3704	61	24	)	)	PUNCT
ejpam-3704	61	25	⊆	⊆	NUM
ejpam-3704	61	26	f(a	f(a	NOUN
ejpam-3704	61	27	)	)	PUNCT
ejpam-3704	61	28	~′	~′	NOUN
ejpam-3704	61	29	f(b	f(b	PROPN
ejpam-3704	61	30	)	)	PUNCT
ejpam-3704	61	31	.	.	PUNCT
ejpam-3704	62	1	now	now	ADV
ejpam-3704	62	2	,	,	PUNCT
ejpam-3704	62	3	let	let	VERB
ejpam-3704	62	4	y	y	PROPN
ejpam-3704	62	5	∈	∈	PROPN
ejpam-3704	62	6	f(a	f(a	PROPN
ejpam-3704	62	7	)	)	PUNCT
ejpam-3704	62	8	~′	~′	NOUN
ejpam-3704	62	9	f(b	f(b	PROPN
ejpam-3704	62	10	)	)	PUNCT
ejpam-3704	63	1	=	=	SYM
ejpam-3704	63	2	⋃	⋃	NOUN
ejpam-3704	63	3	f(a	f(a	NOUN
ejpam-3704	63	4	)	)	PUNCT
ejpam-3704	63	5	∈	∈	PROPN
ejpam-3704	63	6	f(a	f(a	NOUN
ejpam-3704	63	7	)	)	PUNCT
ejpam-3704	63	8	,	,	PUNCT
ejpam-3704	63	9	f(b	f(b	PROPN
ejpam-3704	63	10	)	)	PUNCT
ejpam-3704	63	11	∈	∈	PROPN
ejpam-3704	63	12	f(b	f(b	PROPN
ejpam-3704	63	13	)	)	PUNCT
ejpam-3704	63	14	f(a	f(a	NOUN
ejpam-3704	63	15	)	)	PUNCT
ejpam-3704	63	16	~′	~′	NOUN
ejpam-3704	63	17	f(b	f(b	PROPN
ejpam-3704	63	18	)	)	PUNCT
ejpam-3704	63	19	.	.	PUNCT
ejpam-3704	64	1	then	then	ADV
ejpam-3704	64	2	there	there	PRON
ejpam-3704	64	3	exist	exist	VERB
ejpam-3704	64	4	f(a	f(a	NOUN
ejpam-3704	64	5	)	)	PUNCT
ejpam-3704	64	6	∈	∈	PROPN
ejpam-3704	64	7	f(a	f(a	PROPN
ejpam-3704	64	8	)	)	PUNCT
ejpam-3704	64	9	and	and	CCONJ
ejpam-3704	64	10	f(b	f(b	PROPN
ejpam-3704	64	11	)	)	PUNCT
ejpam-3704	64	12	∈	∈	PROPN
ejpam-3704	64	13	f(b	f(b	PROPN
ejpam-3704	64	14	)	)	PUNCT
ejpam-3704	64	15	such	such	ADJ
ejpam-3704	64	16	that	that	SCONJ
ejpam-3704	64	17	y	y	PROPN
ejpam-3704	64	18	∈	∈	PROPN
ejpam-3704	64	19	f(a	f(a	PROPN
ejpam-3704	64	20	)	)	PUNCT
ejpam-3704	64	21	~′	~′	NOUN
ejpam-3704	64	22	f(b	f(b	PROPN
ejpam-3704	64	23	)	)	PUNCT
ejpam-3704	64	24	.	.	PUNCT
ejpam-3704	65	1	since	since	SCONJ
ejpam-3704	65	2	f	f	PROPN
ejpam-3704	65	3	is	be	AUX
ejpam-3704	65	4	a	a	DET
ejpam-3704	65	5	hyper	hyper	ADJ
ejpam-3704	65	6	homomorphism	homomorphism	NOUN
ejpam-3704	65	7	,	,	PUNCT
ejpam-3704	65	8	y	y	PROPN
ejpam-3704	65	9	∈	∈	PROPN
ejpam-3704	65	10	f(a~	f(a~	PROPN
ejpam-3704	65	11	b	b	X
ejpam-3704	65	12	)	)	PUNCT
ejpam-3704	65	13	∈	∈	PROPN
ejpam-3704	65	14	f	f	PROPN
ejpam-3704	66	1			PROPN
ejpam-3704	66	2	⋃	⋃	PROPN
ejpam-3704	66	3	a∈a	a∈a	ADJ
ejpam-3704	66	4	,	,	PUNCT
ejpam-3704	66	5	b∈b	b∈b	NOUN
ejpam-3704	66	6	a~	a~	PROPN
ejpam-3704	66	7	b	b	PROPN
ejpam-3704	66	8			PROPN
ejpam-3704	66	9	=	=	SYM
ejpam-3704	66	10	f(a	f(a	PROPN
ejpam-3704	66	11	~	~	SYM
ejpam-3704	66	12	b	b	NOUN
ejpam-3704	66	13	)	)	PUNCT
ejpam-3704	66	14	.	.	PUNCT
ejpam-3704	67	1	thus	thus	ADV
ejpam-3704	67	2	,	,	PUNCT
ejpam-3704	67	3	f(a	f(a	NOUN
ejpam-3704	67	4	)	)	PUNCT
ejpam-3704	67	5	~′	~′	NOUN
ejpam-3704	67	6	f(b	f(b	PROPN
ejpam-3704	67	7	)	)	PUNCT
ejpam-3704	67	8	⊆	⊆	NUM
ejpam-3704	67	9	f(a	f(a	X
ejpam-3704	67	10	~	~	SYM
ejpam-3704	67	11	b	b	NOUN
ejpam-3704	67	12	)	)	PUNCT
ejpam-3704	67	13	.	.	PUNCT
ejpam-3704	68	1	therefore	therefore	ADV
ejpam-3704	68	2	,	,	PUNCT
ejpam-3704	68	3	f(a	f(a	X
ejpam-3704	68	4	~	~	SYM
ejpam-3704	68	5	b	b	X
ejpam-3704	68	6	)	)	PUNCT
ejpam-3704	68	7	=	=	SYM
ejpam-3704	68	8	f(a	f(a	NOUN
ejpam-3704	68	9	)	)	PUNCT
ejpam-3704	68	10	~′	~′	NOUN
ejpam-3704	68	11	f(b	f(b	PROPN
ejpam-3704	68	12	)	)	PUNCT
ejpam-3704	68	13	.	.	PUNCT
ejpam-3704	69	1	definition	definition	NOUN
ejpam-3704	69	2	4	4	NUM
ejpam-3704	69	3	.	.	PUNCT
ejpam-3704	70	1	let	let	VERB
ejpam-3704	70	2	f	f	NOUN
ejpam-3704	70	3	:	:	PUNCT
ejpam-3704	70	4	h	h	PROPN
ejpam-3704	70	5	−→	−→	ADJ
ejpam-3704	70	6	h	h	NOUN
ejpam-3704	70	7	′	′	NUM
ejpam-3704	70	8	be	be	AUX
ejpam-3704	70	9	a	a	DET
ejpam-3704	70	10	hyper	hyper	ADJ
ejpam-3704	70	11	homomorphism	homomorphism	NOUN
ejpam-3704	70	12	.	.	PUNCT
ejpam-3704	71	1	we	we	PRON
ejpam-3704	71	2	say	say	VERB
ejpam-3704	71	3	that	that	SCONJ
ejpam-3704	71	4	f	f	PROPN
ejpam-3704	71	5	is	be	AUX
ejpam-3704	71	6	a	a	DET
ejpam-3704	71	7	hyper	hyper	ADJ
ejpam-3704	71	8	monomorphism	monomorphism	NOUN
ejpam-3704	71	9	if	if	SCONJ
ejpam-3704	71	10	f	f	PROPN
ejpam-3704	71	11	is	be	AUX
ejpam-3704	71	12	one	one	NUM
ejpam-3704	71	13	-	-	PUNCT
ejpam-3704	71	14	to	to	ADP
ejpam-3704	71	15	-	-	PUNCT
ejpam-3704	71	16	one	one	NUM
ejpam-3704	71	17	,	,	PUNCT
ejpam-3704	71	18	and	and	CCONJ
ejpam-3704	71	19	f	f	PROPN
ejpam-3704	71	20	is	be	AUX
ejpam-3704	71	21	a	a	DET
ejpam-3704	71	22	hyper	hyper	ADJ
ejpam-3704	71	23	epimorphism	epimorphism	NOUN
ejpam-3704	71	24	if	if	SCONJ
ejpam-3704	71	25	f	f	PROPN
ejpam-3704	71	26	is	be	AUX
ejpam-3704	71	27	onto	onto	ADP
ejpam-3704	71	28	;	;	PUNCT
ejpam-3704	71	29	f	f	X
ejpam-3704	71	30	is	be	AUX
ejpam-3704	71	31	a	a	DET
ejpam-3704	71	32	hyper	hyper	ADJ
ejpam-3704	71	33	isomorphism	isomorphism	NOUN
ejpam-3704	71	34	,	,	PUNCT
ejpam-3704	71	35	denoted	denote	VERB
ejpam-3704	71	36	by	by	ADP
ejpam-3704	71	37	∼=h	∼=h	NOUN
ejpam-3704	71	38	,	,	PUNCT
ejpam-3704	71	39	if	if	SCONJ
ejpam-3704	71	40	f	f	PROPN
ejpam-3704	71	41	is	be	AUX
ejpam-3704	71	42	both	both	PRON
ejpam-3704	71	43	one	one	NUM
ejpam-3704	71	44	-	-	PUNCT
ejpam-3704	71	45	to	to	ADP
ejpam-3704	71	46	-	-	PUNCT
ejpam-3704	71	47	one	one	NUM
ejpam-3704	71	48	and	and	CCONJ
ejpam-3704	71	49	onto	onto	ADP
ejpam-3704	71	50	.	.	PUNCT
ejpam-3704	72	1	lemma	lemma	PROPN
ejpam-3704	72	2	1	1	X
ejpam-3704	72	3	.	.	PUNCT
ejpam-3704	72	4	suppose	suppose	VERB
ejpam-3704	73	1	f	f	X
ejpam-3704	73	2	:	:	PUNCT
ejpam-3704	73	3	h	h	PROPN
ejpam-3704	73	4	−→	−→	ADJ
ejpam-3704	73	5	h	h	NOUN
ejpam-3704	73	6	′	′	NOUN
ejpam-3704	74	1	and	and	CCONJ
ejpam-3704	74	2	g	g	NOUN
ejpam-3704	74	3	:	:	PUNCT
ejpam-3704	74	4	h	h	NOUN
ejpam-3704	75	1	′	′	NUM
ejpam-3704	75	2	−→	−→	ADJ
ejpam-3704	75	3	h	h	NOUN
ejpam-3704	75	4	′′	′′	PROPN
ejpam-3704	75	5	are	be	AUX
ejpam-3704	75	6	both	both	PRON
ejpam-3704	75	7	hyper	hyper	ADJ
ejpam-3704	75	8	homomorphisms	homomorphism	NOUN
ejpam-3704	75	9	(	(	PUNCT
ejpam-3704	75	10	epimorphisms	epimorphism	NOUN
ejpam-3704	75	11	)	)	PUNCT
ejpam-3704	75	12	of	of	ADP
ejpam-3704	75	13	hyper	hyper	ADJ
ejpam-3704	75	14	up	up	ADP
ejpam-3704	75	15	-	-	PUNCT
ejpam-3704	75	16	algebras	algebras	X
ejpam-3704	75	17	.	.	PUNCT
ejpam-3704	76	1	then	then	ADV
ejpam-3704	76	2	g	g	PROPN
ejpam-3704	76	3	◦	◦	NOUN
ejpam-3704	76	4	f	f	PROPN
ejpam-3704	76	5	is	be	AUX
ejpam-3704	76	6	a	a	DET
ejpam-3704	76	7	hyper	hyper	ADJ
ejpam-3704	76	8	homomorphism	homomorphism	NOUN
ejpam-3704	76	9	(	(	PUNCT
ejpam-3704	76	10	epimorphism	epimorphism	NOUN
ejpam-3704	76	11	)	)	PUNCT
ejpam-3704	76	12	of	of	ADP
ejpam-3704	76	13	hyper	hyper	ADJ
ejpam-3704	76	14	up	up	ADP
ejpam-3704	76	15	-	-	PUNCT
ejpam-3704	76	16	algebras	algebras	X
ejpam-3704	76	17	.	.	PUNCT
ejpam-3704	77	1	the	the	DET
ejpam-3704	77	2	following	following	ADJ
ejpam-3704	77	3	result	result	NOUN
ejpam-3704	77	4	establishes	establish	VERB
ejpam-3704	77	5	the	the	DET
ejpam-3704	77	6	transitivity	transitivity	NOUN
ejpam-3704	77	7	of	of	ADP
ejpam-3704	77	8	the	the	DET
ejpam-3704	77	9	relation	relation	NOUN
ejpam-3704	77	10	θ̄	θ̄	ADJ
ejpam-3704	77	11	on	on	ADP
ejpam-3704	77	12	h.	h.	PROPN
ejpam-3704	77	13	lemma	lemma	PROPN
ejpam-3704	78	1	2	2	X
ejpam-3704	78	2	.	.	PUNCT
ejpam-3704	78	3	let	let	VERB
ejpam-3704	78	4	θ	θ	NOUN
ejpam-3704	78	5	be	be	AUX
ejpam-3704	78	6	an	an	DET
ejpam-3704	78	7	equivalence	equivalence	NOUN
ejpam-3704	78	8	relation	relation	NOUN
ejpam-3704	78	9	on	on	ADP
ejpam-3704	78	10	h	h	NOUN
ejpam-3704	78	11	and	and	CCONJ
ejpam-3704	78	12	a	a	PRON
ejpam-3704	78	13	,	,	PUNCT
ejpam-3704	78	14	b	b	PROPN
ejpam-3704	78	15	⊆	⊆	NUM
ejpam-3704	78	16	h.	h.	NOUN
ejpam-3704	78	17	if	if	SCONJ
ejpam-3704	78	18	aθ̄b	aθ̄b	PRON
ejpam-3704	78	19	and	and	CCONJ
ejpam-3704	78	20	bθ̄c	bθ̄c	ADJ
ejpam-3704	78	21	,	,	PUNCT
ejpam-3704	78	22	then	then	ADV
ejpam-3704	78	23	aθ̄c	aθ̄c	ADJ
ejpam-3704	78	24	.	.	PUNCT
ejpam-3704	79	1	proof	proof	NOUN
ejpam-3704	79	2	.	.	PUNCT
ejpam-3704	80	1	suppose	suppose	VERB
ejpam-3704	80	2	that	that	SCONJ
ejpam-3704	80	3	aθ̄b	aθ̄b	PRON
ejpam-3704	80	4	and	and	CCONJ
ejpam-3704	80	5	bθ̄c	bθ̄c	PROPN
ejpam-3704	80	6	.	.	PUNCT
ejpam-3704	81	1	since	since	SCONJ
ejpam-3704	81	2	aθ̄b	aθ̄b	NUM
ejpam-3704	81	3	,	,	PUNCT
ejpam-3704	81	4	by	by	ADP
ejpam-3704	81	5	definition	definition	NOUN
ejpam-3704	81	6	3(ii	3(ii	NUM
ejpam-3704	81	7	)	)	PUNCT
ejpam-3704	81	8	,	,	PUNCT
ejpam-3704	81	9	for	for	ADP
ejpam-3704	81	10	each	each	DET
ejpam-3704	81	11	a	a	DET
ejpam-3704	81	12	∈	∈	PROPN
ejpam-3704	81	13	a	a	DET
ejpam-3704	81	14	(	(	PUNCT
ejpam-3704	81	15	respectively	respectively	ADV
ejpam-3704	81	16	b	b	PROPN
ejpam-3704	81	17	∈	∈	PROPN
ejpam-3704	81	18	b	b	X
ejpam-3704	81	19	)	)	PUNCT
ejpam-3704	81	20	,	,	PUNCT
ejpam-3704	81	21	there	there	PRON
ejpam-3704	81	22	exists	exist	VERB
ejpam-3704	81	23	b	b	PROPN
ejpam-3704	81	24	∈	∈	PROPN
ejpam-3704	81	25	b	b	PROPN
ejpam-3704	81	26	(	(	PUNCT
ejpam-3704	81	27	respectively	respectively	ADV
ejpam-3704	81	28	a	a	DET
ejpam-3704	81	29	∈	∈	PROPN
ejpam-3704	81	30	a	a	NOUN
ejpam-3704	81	31	)	)	PUNCT
ejpam-3704	81	32	such	such	ADJ
ejpam-3704	81	33	that	that	DET
ejpam-3704	81	34	aθb	aθb	NOUN
ejpam-3704	81	35	.	.	PUNCT
ejpam-3704	82	1	similarly	similarly	ADV
ejpam-3704	82	2	,	,	PUNCT
ejpam-3704	82	3	since	since	SCONJ
ejpam-3704	82	4	bθ̄c	bθ̄c	ADJ
ejpam-3704	82	5	,	,	PUNCT
ejpam-3704	82	6	for	for	ADP
ejpam-3704	82	7	all	all	DET
ejpam-3704	82	8	b	b	PROPN
ejpam-3704	82	9	∈	∈	ADP
ejpam-3704	82	10	b	b	PROPN
ejpam-3704	82	11	(	(	PUNCT
ejpam-3704	82	12	respectively	respectively	ADV
ejpam-3704	82	13	c	c	X
ejpam-3704	82	14	∈	∈	PROPN
ejpam-3704	82	15	c	c	X
ejpam-3704	82	16	)	)	PUNCT
ejpam-3704	82	17	,	,	PUNCT
ejpam-3704	82	18	there	there	PRON
ejpam-3704	82	19	exists	exist	VERB
ejpam-3704	82	20	c	c	NOUN
ejpam-3704	82	21	∈	∈	PROPN
ejpam-3704	82	22	c(respectively	c(respectively	ADV
ejpam-3704	82	23	b	b	PROPN
ejpam-3704	82	24	∈	∈	PROPN
ejpam-3704	82	25	b	b	NOUN
ejpam-3704	82	26	)	)	PUNCT
ejpam-3704	82	27	such	such	ADJ
ejpam-3704	82	28	that	that	DET
ejpam-3704	82	29	bθc	bθc	NOUN
ejpam-3704	82	30	.	.	PUNCT
ejpam-3704	83	1	since	since	SCONJ
ejpam-3704	83	2	by	by	ADP
ejpam-3704	83	3	assumption	assumption	NOUN
ejpam-3704	83	4	θ	θ	PROPN
ejpam-3704	83	5	is	be	AUX
ejpam-3704	83	6	an	an	DET
ejpam-3704	83	7	equivalence	equivalence	NOUN
ejpam-3704	83	8	relation	relation	NOUN
ejpam-3704	83	9	for	for	ADP
ejpam-3704	83	10	each	each	PRON
ejpam-3704	83	11	a	a	DET
ejpam-3704	83	12	∈	∈	PROPN
ejpam-3704	83	13	a	a	DET
ejpam-3704	83	14	(	(	PUNCT
ejpam-3704	83	15	respectively	respectively	ADV
ejpam-3704	83	16	c	c	X
ejpam-3704	83	17	∈	∈	PROPN
ejpam-3704	83	18	c	c	X
ejpam-3704	83	19	)	)	PUNCT
ejpam-3704	83	20	,	,	PUNCT
ejpam-3704	83	21	there	there	PRON
ejpam-3704	83	22	exists	exist	VERB
ejpam-3704	83	23	c	c	NOUN
ejpam-3704	83	24	∈	∈	PROPN
ejpam-3704	83	25	c(respectively	c(respectively	ADV
ejpam-3704	83	26	a	a	DET
ejpam-3704	83	27	∈	∈	PROPN
ejpam-3704	83	28	a	a	NOUN
ejpam-3704	83	29	)	)	PUNCT
ejpam-3704	83	30	such	such	ADJ
ejpam-3704	83	31	that	that	DET
ejpam-3704	83	32	aθc	aθc	NOUN
ejpam-3704	83	33	.	.	PUNCT
ejpam-3704	84	1	therefore	therefore	ADV
ejpam-3704	84	2	,	,	PUNCT
ejpam-3704	84	3	aθ̄c	aθ̄c	PROPN
ejpam-3704	84	4	.	.	PUNCT
ejpam-3704	85	1	lemma	lemma	PROPN
ejpam-3704	85	2	3	3	X
ejpam-3704	85	3	.	.	PUNCT
ejpam-3704	86	1	let	let	VERB
ejpam-3704	86	2	θ	θ	NOUN
ejpam-3704	86	3	be	be	AUX
ejpam-3704	86	4	an	an	DET
ejpam-3704	86	5	equivalence	equivalence	NOUN
ejpam-3704	86	6	relation	relation	NOUN
ejpam-3704	86	7	on	on	ADP
ejpam-3704	86	8	h.	h.	PROPN
ejpam-3704	86	9	then	then	ADV
ejpam-3704	86	10	the	the	DET
ejpam-3704	86	11	following	following	NOUN
ejpam-3704	86	12	are	be	AUX
ejpam-3704	86	13	equivalent	equivalent	ADJ
ejpam-3704	86	14	:	:	PUNCT
ejpam-3704	86	15	(	(	PUNCT
ejpam-3704	86	16	i	i	NOUN
ejpam-3704	86	17	)	)	PUNCT
ejpam-3704	86	18	θ	θ	PROPN
ejpam-3704	86	19	is	be	AUX
ejpam-3704	86	20	a	a	DET
ejpam-3704	86	21	congruence	congruence	NOUN
ejpam-3704	86	22	relation	relation	NOUN
ejpam-3704	86	23	on	on	ADP
ejpam-3704	86	24	h	h	NOUN
ejpam-3704	86	25	;	;	PUNCT
ejpam-3704	86	26	(	(	PUNCT
ejpam-3704	86	27	ii	ii	NOUN
ejpam-3704	86	28	)	)	PUNCT
ejpam-3704	86	29	if	if	SCONJ
ejpam-3704	86	30	xθy	xθy	PROPN
ejpam-3704	86	31	,	,	PUNCT
ejpam-3704	86	32	then	then	ADV
ejpam-3704	86	33	(	(	PUNCT
ejpam-3704	86	34	x~	x~	X
ejpam-3704	86	35	a)θ̄(y	a)θ̄(y	X
ejpam-3704	86	36	~	~	PUNCT
ejpam-3704	86	37	a	a	X
ejpam-3704	86	38	)	)	PUNCT
ejpam-3704	86	39	and	and	CCONJ
ejpam-3704	86	40	(	(	PUNCT
ejpam-3704	86	41	a~	a~	PROPN
ejpam-3704	86	42	x)θ̄(a~	x)θ̄(a~	PROPN
ejpam-3704	86	43	y	y	PROPN
ejpam-3704	86	44	)	)	PUNCT
ejpam-3704	86	45	for	for	ADP
ejpam-3704	86	46	all	all	DET
ejpam-3704	86	47	a	a	DET
ejpam-3704	86	48	,	,	PUNCT
ejpam-3704	86	49	x	x	NOUN
ejpam-3704	86	50	,	,	PUNCT
ejpam-3704	86	51	y	y	PROPN
ejpam-3704	86	52	∈	∈	PROPN
ejpam-3704	86	53	h.	h.	NOUN
ejpam-3704	86	54	proof	proof	NOUN
ejpam-3704	86	55	.	.	PUNCT
ejpam-3704	87	1	(	(	PUNCT
ejpam-3704	87	2	i	i	NOUN
ejpam-3704	87	3	)	)	PUNCT
ejpam-3704	88	1	=	=	NOUN
ejpam-3704	88	2	⇒	⇒	NOUN
ejpam-3704	88	3	(	(	PUNCT
ejpam-3704	88	4	ii	ii	NOUN
ejpam-3704	88	5	)	)	PUNCT
ejpam-3704	88	6	let	let	VERB
ejpam-3704	88	7	θ	θ	NOUN
ejpam-3704	88	8	be	be	AUX
ejpam-3704	88	9	a	a	DET
ejpam-3704	88	10	congruence	congruence	NOUN
ejpam-3704	88	11	relation	relation	NOUN
ejpam-3704	88	12	on	on	ADP
ejpam-3704	88	13	h	h	NOUN
ejpam-3704	88	14	and	and	CCONJ
ejpam-3704	88	15	a	a	PRON
ejpam-3704	88	16	,	,	PUNCT
ejpam-3704	88	17	x	x	NOUN
ejpam-3704	88	18	,	,	PUNCT
ejpam-3704	88	19	y	y	PROPN
ejpam-3704	88	20	∈	∈	PROPN
ejpam-3704	88	21	h.	h.	PROPN
ejpam-3704	88	22	suppose	suppose	VERB
ejpam-3704	88	23	xθy	xθy	PROPN
ejpam-3704	88	24	.	.	PUNCT
ejpam-3704	89	1	since	since	SCONJ
ejpam-3704	89	2	θ	θ	PROPN
ejpam-3704	89	3	is	be	AUX
ejpam-3704	89	4	a	a	DET
ejpam-3704	89	5	congruence	congruence	NOUN
ejpam-3704	89	6	relation	relation	NOUN
ejpam-3704	89	7	on	on	ADP
ejpam-3704	89	8	h	h	PROPN
ejpam-3704	89	9	and	and	CCONJ
ejpam-3704	89	10	aθa	aθa	PROPN
ejpam-3704	89	11	,	,	PUNCT
ejpam-3704	89	12	(	(	PUNCT
ejpam-3704	89	13	x	x	X
ejpam-3704	89	14	~	~	PUNCT
ejpam-3704	89	15	a)θ̄(y	a)θ̄(y	X
ejpam-3704	89	16	~	~	PUNCT
ejpam-3704	89	17	a	a	X
ejpam-3704	89	18	)	)	PUNCT
ejpam-3704	89	19	and	and	CCONJ
ejpam-3704	89	20	(	(	PUNCT
ejpam-3704	89	21	a	a	PRON
ejpam-3704	89	22	~	~	PUNCT
ejpam-3704	89	23	x)θ̄(a	x)θ̄(a	PUNCT
ejpam-3704	89	24	~	~	PUNCT
ejpam-3704	89	25	y	y	X
ejpam-3704	89	26	)	)	PUNCT
ejpam-3704	89	27	,	,	PUNCT
ejpam-3704	89	28	by	by	ADP
ejpam-3704	89	29	definition	definition	NOUN
ejpam-3704	89	30	3(iii	3(iii	NUM
ejpam-3704	89	31	)	)	PUNCT
ejpam-3704	89	32	.	.	PUNCT
ejpam-3704	90	1	(	(	PUNCT
ejpam-3704	90	2	ii	ii	NOUN
ejpam-3704	90	3	)	)	PUNCT
ejpam-3704	90	4	=	=	NOUN
ejpam-3704	90	5	⇒	⇒	NOUN
ejpam-3704	90	6	(	(	PUNCT
ejpam-3704	90	7	i	i	NOUN
ejpam-3704	90	8	)	)	PUNCT
ejpam-3704	90	9	assume	assume	VERB
ejpam-3704	90	10	xθy	xθy	PROPN
ejpam-3704	90	11	.	.	PUNCT
ejpam-3704	91	1	let	let	VERB
ejpam-3704	91	2	x	x	PRON
ejpam-3704	91	3	,	,	PUNCT
ejpam-3704	91	4	y	y	PROPN
ejpam-3704	91	5	,	,	PUNCT
ejpam-3704	91	6	x′	x′	NUM
ejpam-3704	91	7	,	,	PUNCT
ejpam-3704	91	8	y′	y′	NOUN
ejpam-3704	91	9	∈	∈	PROPN
ejpam-3704	91	10	h.	h.	PROPN
ejpam-3704	91	11	suppose	suppose	VERB
ejpam-3704	91	12	that	that	SCONJ
ejpam-3704	91	13	xθy	xθy	PROPN
ejpam-3704	91	14	and	and	CCONJ
ejpam-3704	91	15	x′θy′.	x′θy′.	NUM
ejpam-3704	91	16	by	by	ADP
ejpam-3704	91	17	(	(	PUNCT
ejpam-3704	91	18	ii	ii	NOUN
ejpam-3704	91	19	)	)	PUNCT
ejpam-3704	91	20	,	,	PUNCT
ejpam-3704	91	21	(	(	PUNCT
ejpam-3704	91	22	x	x	X
ejpam-3704	91	23	~	~	PUNCT
ejpam-3704	91	24	x′)θ̄(y	x′)θ̄(y	X
ejpam-3704	91	25	~	~	PUNCT
ejpam-3704	91	26	x′	x′	NUM
ejpam-3704	91	27	)	)	PUNCT
ejpam-3704	91	28	and	and	CCONJ
ejpam-3704	91	29	(	(	PUNCT
ejpam-3704	91	30	y	y	PROPN
ejpam-3704	91	31	~	~	PUNCT
ejpam-3704	91	32	x′)θ̄(y	x′)θ̄(y	X
ejpam-3704	92	1	~	~	PUNCT
ejpam-3704	92	2	y′	y′	NUM
ejpam-3704	92	3	)	)	PUNCT
ejpam-3704	92	4	,	,	PUNCT
ejpam-3704	92	5	so	so	SCONJ
ejpam-3704	92	6	that	that	SCONJ
ejpam-3704	92	7	by	by	ADP
ejpam-3704	92	8	lemma	lemma	PROPN
ejpam-3704	92	9	2	2	NUM
ejpam-3704	92	10	,	,	PUNCT
ejpam-3704	92	11	(	(	PUNCT
ejpam-3704	92	12	x	x	X
ejpam-3704	92	13	~	~	PUNCT
ejpam-3704	92	14	x′)θ̄(y	x′)θ̄(y	X
ejpam-3704	92	15	~	~	PUNCT
ejpam-3704	92	16	y′	y′	NUM
ejpam-3704	92	17	)	)	PUNCT
ejpam-3704	92	18	.	.	PUNCT
ejpam-3704	93	1	by	by	ADP
ejpam-3704	93	2	definition	definition	NOUN
ejpam-3704	93	3	3(iii	3(iii	NUM
ejpam-3704	93	4	)	)	PUNCT
ejpam-3704	93	5	,	,	PUNCT
ejpam-3704	93	6	θ	θ	PROPN
ejpam-3704	93	7	is	be	AUX
ejpam-3704	93	8	a	a	DET
ejpam-3704	93	9	congruence	congruence	NOUN
ejpam-3704	93	10	relation	relation	NOUN
ejpam-3704	93	11	on	on	ADP
ejpam-3704	93	12	h.	h.	PROPN
ejpam-3704	93	13	r.	r.	PROPN
ejpam-3704	93	14	amairanto	amairanto	PROPN
ejpam-3704	93	15	,	,	PUNCT
ejpam-3704	93	16	r.	r.	PROPN
ejpam-3704	93	17	isla	isla	PROPN
ejpam-3704	93	18	/	/	SYM
ejpam-3704	93	19	eur	eur	PROPN
ejpam-3704	93	20	.	.	PUNCT
ejpam-3704	94	1	j.	j.	PROPN
ejpam-3704	94	2	pure	pure	PROPN
ejpam-3704	94	3	appl	appl	PROPN
ejpam-3704	94	4	.	.	PROPN
ejpam-3704	94	5	math	math	PROPN
ejpam-3704	94	6	,	,	PUNCT
ejpam-3704	94	7	13	13	NUM
ejpam-3704	94	8	(	(	PUNCT
ejpam-3704	94	9	3	3	NUM
ejpam-3704	94	10	)	)	PUNCT
ejpam-3704	94	11	(	(	PUNCT
ejpam-3704	94	12	2020	2020	NUM
ejpam-3704	94	13	)	)	PUNCT
ejpam-3704	94	14	,	,	PUNCT
ejpam-3704	94	15	483	483	NUM
ejpam-3704	94	16	-	-	SYM
ejpam-3704	94	17	497	497	NUM
ejpam-3704	94	18	487	487	NUM
ejpam-3704	94	19	theorem	theorem	NOUN
ejpam-3704	94	20	1	1	NUM
ejpam-3704	94	21	.	.	PUNCT
ejpam-3704	94	22	suppose	suppose	VERB
ejpam-3704	94	23	that	that	SCONJ
ejpam-3704	94	24	θ	θ	PROPN
ejpam-3704	94	25	and	and	CCONJ
ejpam-3704	94	26	θ′	θ′	NOUN
ejpam-3704	94	27	are	be	AUX
ejpam-3704	94	28	regular	regular	ADJ
ejpam-3704	94	29	congruence	congruence	NOUN
ejpam-3704	94	30	relations	relation	NOUN
ejpam-3704	94	31	on	on	ADP
ejpam-3704	94	32	h	h	NOUN
ejpam-3704	94	33	with	with	ADP
ejpam-3704	94	34	[	[	X
ejpam-3704	94	35	0]θ	0]θ	X
ejpam-3704	94	36	=	=	PUNCT
ejpam-3704	95	1	[	[	X
ejpam-3704	95	2	0]θ′	0]θ′	NUM
ejpam-3704	95	3	.	.	PUNCT
ejpam-3704	96	1	then	then	ADV
ejpam-3704	96	2	θ	θ	X
ejpam-3704	96	3	=	=	PUNCT
ejpam-3704	97	1	θ′.	θ′.	ADP
ejpam-3704	97	2	proof	proof	NOUN
ejpam-3704	97	3	.	.	PUNCT
ejpam-3704	98	1	let	let	VERB
ejpam-3704	98	2	θ	θ	NOUN
ejpam-3704	98	3	and	and	CCONJ
ejpam-3704	98	4	θ′	θ′	NOUN
ejpam-3704	98	5	be	be	AUX
ejpam-3704	98	6	regular	regular	ADJ
ejpam-3704	98	7	conguence	conguence	ADJ
ejpam-3704	98	8	relations	relation	NOUN
ejpam-3704	98	9	on	on	ADP
ejpam-3704	98	10	h	h	NOUN
ejpam-3704	98	11	with	with	ADP
ejpam-3704	98	12	[	[	X
ejpam-3704	98	13	0]θ	0]θ	X
ejpam-3704	98	14	=	=	PUNCT
ejpam-3704	99	1	[	[	X
ejpam-3704	99	2	0]θ′	0]θ′	X
ejpam-3704	99	3	.	.	PUNCT
ejpam-3704	100	1	since	since	SCONJ
ejpam-3704	100	2	θ	θ	PROPN
ejpam-3704	100	3	and	and	CCONJ
ejpam-3704	100	4	θ′	θ′	NOUN
ejpam-3704	100	5	are	be	AUX
ejpam-3704	100	6	both	both	DET
ejpam-3704	100	7	equivalence	equivalence	NOUN
ejpam-3704	100	8	relations	relation	NOUN
ejpam-3704	100	9	on	on	ADP
ejpam-3704	100	10	h	h	NOUN
ejpam-3704	100	11	,	,	PUNCT
ejpam-3704	100	12	it	it	PRON
ejpam-3704	100	13	suffices	suffice	VERB
ejpam-3704	100	14	to	to	PART
ejpam-3704	100	15	show	show	VERB
ejpam-3704	100	16	that	that	DET
ejpam-3704	100	17	xθy	xθy	PROPN
ejpam-3704	101	1	if	if	SCONJ
ejpam-3704	101	2	and	and	CCONJ
ejpam-3704	101	3	only	only	ADV
ejpam-3704	101	4	if	if	SCONJ
ejpam-3704	101	5	xθ′y	xθ′y	PROPN
ejpam-3704	101	6	for	for	ADP
ejpam-3704	101	7	all	all	DET
ejpam-3704	101	8	x	x	NOUN
ejpam-3704	101	9	,	,	PUNCT
ejpam-3704	101	10	y	y	PROPN
ejpam-3704	101	11	∈	∈	PROPN
ejpam-3704	101	12	h.	h.	PROPN
ejpam-3704	101	13	let	let	VERB
ejpam-3704	101	14	xθy	xθy	NOUN
ejpam-3704	101	15	.	.	PUNCT
ejpam-3704	102	1	since	since	SCONJ
ejpam-3704	102	2	θ	θ	PROPN
ejpam-3704	102	3	is	be	AUX
ejpam-3704	102	4	a	a	DET
ejpam-3704	102	5	congruence	congruence	NOUN
ejpam-3704	102	6	relation	relation	NOUN
ejpam-3704	102	7	on	on	ADP
ejpam-3704	102	8	h	h	NOUN
ejpam-3704	102	9	,	,	PUNCT
ejpam-3704	102	10	by	by	ADP
ejpam-3704	102	11	lemma	lemma	PROPN
ejpam-3704	102	12	3	3	NUM
ejpam-3704	102	13	,	,	PUNCT
ejpam-3704	102	14	(	(	PUNCT
ejpam-3704	102	15	x	x	X
ejpam-3704	102	16	~	~	PROPN
ejpam-3704	102	17	x)θ̄(x	x)θ̄(x	X
ejpam-3704	102	18	~	~	SYM
ejpam-3704	102	19	y	y	PROPN
ejpam-3704	102	20	)	)	PUNCT
ejpam-3704	102	21	.	.	PUNCT
ejpam-3704	103	1	note	note	VERB
ejpam-3704	103	2	that	that	SCONJ
ejpam-3704	103	3	0	0	NUM
ejpam-3704	103	4	∈	∈	NOUN
ejpam-3704	103	5	x	x	NOUN
ejpam-3704	103	6	~	~	PUNCT
ejpam-3704	103	7	x	x	PUNCT
ejpam-3704	103	8	by	by	ADP
ejpam-3704	103	9	proposition	proposition	NOUN
ejpam-3704	103	10	1(iii	1(iii	NUM
ejpam-3704	103	11	)	)	PUNCT
ejpam-3704	103	12	.	.	PUNCT
ejpam-3704	104	1	thus	thus	ADV
ejpam-3704	104	2	by	by	ADP
ejpam-3704	104	3	definition	definition	NOUN
ejpam-3704	104	4	3(ii	3(ii	NUM
ejpam-3704	104	5	)	)	PUNCT
ejpam-3704	104	6	,	,	PUNCT
ejpam-3704	104	7	there	there	PRON
ejpam-3704	104	8	exists	exist	VERB
ejpam-3704	104	9	an	an	DET
ejpam-3704	104	10	element	element	NOUN
ejpam-3704	104	11	s	s	PART
ejpam-3704	104	12	∈	∈	PROPN
ejpam-3704	104	13	x~	x~	PUNCT
ejpam-3704	104	14	y	y	PROPN
ejpam-3704	104	15	such	such	ADJ
ejpam-3704	104	16	that	that	DET
ejpam-3704	104	17	0θs	0θs	NOUN
ejpam-3704	104	18	.	.	PUNCT
ejpam-3704	105	1	it	it	PRON
ejpam-3704	105	2	follows	follow	VERB
ejpam-3704	105	3	that	that	PRON
ejpam-3704	105	4	s	s	VERB
ejpam-3704	105	5	∈	∈	PROPN
ejpam-3704	106	1	[	[	X
ejpam-3704	106	2	0]θ	0]θ	X
ejpam-3704	106	3	=	=	PUNCT
ejpam-3704	107	1	[	[	X
ejpam-3704	107	2	0]θ′	0]θ′	NUM
ejpam-3704	107	3	.	.	PUNCT
ejpam-3704	108	1	hence	hence	ADV
ejpam-3704	108	2	,	,	PUNCT
ejpam-3704	108	3	(	(	PUNCT
ejpam-3704	108	4	x~	x~	PROPN
ejpam-3704	108	5	y)θ′{0	y)θ′{0	PROPN
ejpam-3704	108	6	}	}	PUNCT
ejpam-3704	108	7	.	.	PUNCT
ejpam-3704	109	1	in	in	ADP
ejpam-3704	109	2	a	a	DET
ejpam-3704	109	3	similar	similar	ADJ
ejpam-3704	109	4	manner	manner	NOUN
ejpam-3704	109	5	,	,	PUNCT
ejpam-3704	109	6	since	since	SCONJ
ejpam-3704	109	7	xθy	xθy	PROPN
ejpam-3704	109	8	,	,	PUNCT
ejpam-3704	109	9	(	(	PUNCT
ejpam-3704	109	10	y	y	X
ejpam-3704	109	11	~	~	PUNCT
ejpam-3704	109	12	x)θ̄(y	x)θ̄(y	X
ejpam-3704	109	13	~	~	PUNCT
ejpam-3704	109	14	y	y	X
ejpam-3704	109	15	)	)	PUNCT
ejpam-3704	109	16	.	.	PUNCT
ejpam-3704	110	1	also	also	ADV
ejpam-3704	110	2	,	,	PUNCT
ejpam-3704	110	3	0	0	NUM
ejpam-3704	110	4	∈	∈	PROPN
ejpam-3704	110	5	y	y	PROPN
ejpam-3704	110	6	~	~	PUNCT
ejpam-3704	110	7	y	y	PROPN
ejpam-3704	110	8	implies	imply	VERB
ejpam-3704	110	9	that	that	SCONJ
ejpam-3704	110	10	there	there	PRON
ejpam-3704	110	11	exists	exist	VERB
ejpam-3704	110	12	t	t	PROPN
ejpam-3704	110	13	∈	∈	PROPN
ejpam-3704	110	14	y	y	PROPN
ejpam-3704	110	15	~	~	PUNCT
ejpam-3704	110	16	x	x	PUNCT
ejpam-3704	110	17	such	such	ADJ
ejpam-3704	110	18	that	that	DET
ejpam-3704	110	19	0θt	0θt	NOUN
ejpam-3704	110	20	.	.	PUNCT
ejpam-3704	111	1	hence	hence	ADV
ejpam-3704	111	2	,	,	PUNCT
ejpam-3704	111	3	t	t	PROPN
ejpam-3704	111	4	∈	∈	PROPN
ejpam-3704	112	1	[	[	X
ejpam-3704	112	2	0]θ	0]θ	X
ejpam-3704	112	3	=	=	PUNCT
ejpam-3704	113	1	[	[	X
ejpam-3704	113	2	0]θ′	0]θ′	NUM
ejpam-3704	113	3	.	.	PUNCT
ejpam-3704	114	1	thus	thus	ADV
ejpam-3704	114	2	,	,	PUNCT
ejpam-3704	114	3	(	(	PUNCT
ejpam-3704	114	4	y	y	PROPN
ejpam-3704	114	5	~	~	PUNCT
ejpam-3704	114	6	x)θ′{0	x)θ′{0	PROPN
ejpam-3704	114	7	}	}	PUNCT
ejpam-3704	114	8	.	.	PUNCT
ejpam-3704	115	1	now	now	ADV
ejpam-3704	115	2	,	,	PUNCT
ejpam-3704	115	3	since	since	SCONJ
ejpam-3704	115	4	(	(	PUNCT
ejpam-3704	115	5	x	x	X
ejpam-3704	115	6	~	~	PUNCT
ejpam-3704	115	7	y)θ′{0	y)θ′{0	PROPN
ejpam-3704	115	8	}	}	PUNCT
ejpam-3704	115	9	,	,	PUNCT
ejpam-3704	115	10	(	(	PUNCT
ejpam-3704	115	11	y	y	PROPN
ejpam-3704	115	12	~	~	PUNCT
ejpam-3704	115	13	x)θ′{0	x)θ′{0	PROPN
ejpam-3704	115	14	}	}	PUNCT
ejpam-3704	115	15	,	,	PUNCT
ejpam-3704	115	16	and	and	CCONJ
ejpam-3704	115	17	θ′	θ′	NOUN
ejpam-3704	115	18	is	be	AUX
ejpam-3704	115	19	a	a	DET
ejpam-3704	115	20	regular	regular	ADJ
ejpam-3704	115	21	congruence	congruence	NOUN
ejpam-3704	115	22	relation	relation	NOUN
ejpam-3704	115	23	,	,	PUNCT
ejpam-3704	115	24	we	we	PRON
ejpam-3704	115	25	have	have	VERB
ejpam-3704	115	26	xθ′y	xθ′y	NOUN
ejpam-3704	115	27	by	by	ADP
ejpam-3704	115	28	definition	definition	NOUN
ejpam-3704	115	29	3(iv	3(iv	NUM
ejpam-3704	115	30	)	)	PUNCT
ejpam-3704	115	31	.	.	PUNCT
ejpam-3704	116	1	similarly	similarly	ADV
ejpam-3704	116	2	,	,	PUNCT
ejpam-3704	116	3	let	let	VERB
ejpam-3704	116	4	xθ′y	xθ′y	PROPN
ejpam-3704	116	5	.	.	PUNCT
ejpam-3704	117	1	then	then	ADV
ejpam-3704	117	2	(	(	PUNCT
ejpam-3704	117	3	x~	x~	PROPN
ejpam-3704	117	4	x)θ̄′(x~	x)θ̄′(x~	PROPN
ejpam-3704	117	5	y	y	PROPN
ejpam-3704	117	6	)	)	PUNCT
ejpam-3704	117	7	.	.	PUNCT
ejpam-3704	118	1	also	also	ADV
ejpam-3704	118	2	,	,	PUNCT
ejpam-3704	118	3	0	0	NUM
ejpam-3704	118	4	∈	∈	PROPN
ejpam-3704	118	5	x~	x~	NUM
ejpam-3704	118	6	x	x	PRON
ejpam-3704	118	7	implies	imply	VERB
ejpam-3704	118	8	that	that	SCONJ
ejpam-3704	118	9	there	there	PRON
ejpam-3704	118	10	exists	exist	VERB
ejpam-3704	118	11	an	an	DET
ejpam-3704	118	12	element	element	NOUN
ejpam-3704	118	13	s	s	PART
ejpam-3704	118	14	∈	∈	PROPN
ejpam-3704	118	15	x~	x~	PUNCT
ejpam-3704	118	16	y	y	PROPN
ejpam-3704	118	17	such	such	ADJ
ejpam-3704	118	18	that	that	SCONJ
ejpam-3704	118	19	0θ′s	0θ′s	X
ejpam-3704	118	20	.	.	PUNCT
ejpam-3704	119	1	furthermore	furthermore	ADV
ejpam-3704	119	2	,	,	PUNCT
ejpam-3704	119	3	s	s	VERB
ejpam-3704	119	4	∈	∈	PROPN
ejpam-3704	120	1	[	[	X
ejpam-3704	120	2	0]θ′	0]θ′	NOUN
ejpam-3704	120	3	=	=	PUNCT
ejpam-3704	121	1	[	[	X
ejpam-3704	121	2	0]θ	0]θ	NOUN
ejpam-3704	121	3	.	.	PUNCT
ejpam-3704	122	1	so	so	ADV
ejpam-3704	122	2	,	,	PUNCT
ejpam-3704	122	3	(	(	PUNCT
ejpam-3704	122	4	x~	x~	PROPN
ejpam-3704	122	5	y)θ{0	y)θ{0	ADJ
ejpam-3704	122	6	}	}	PUNCT
ejpam-3704	122	7	.	.	PUNCT
ejpam-3704	123	1	by	by	ADP
ejpam-3704	123	2	similar	similar	ADJ
ejpam-3704	123	3	argument	argument	NOUN
ejpam-3704	123	4	,	,	PUNCT
ejpam-3704	123	5	we	we	PRON
ejpam-3704	123	6	will	will	AUX
ejpam-3704	123	7	obtain	obtain	VERB
ejpam-3704	123	8	(	(	PUNCT
ejpam-3704	123	9	y	y	NOUN
ejpam-3704	123	10	~	~	PUNCT
ejpam-3704	123	11	x)θ̄′(y	x)θ̄′(y	PUNCT
ejpam-3704	123	12	~	~	PUNCT
ejpam-3704	123	13	y	y	X
ejpam-3704	123	14	)	)	PUNCT
ejpam-3704	123	15	.	.	PUNCT
ejpam-3704	124	1	since	since	SCONJ
ejpam-3704	124	2	0	0	NUM
ejpam-3704	124	3	∈	∈	PROPN
ejpam-3704	124	4	y	y	PROPN
ejpam-3704	124	5	~	~	PUNCT
ejpam-3704	124	6	y	y	X
ejpam-3704	124	7	,	,	PUNCT
ejpam-3704	124	8	there	there	PRON
ejpam-3704	124	9	exists	exist	VERB
ejpam-3704	124	10	v	v	ADP
ejpam-3704	124	11	∈	∈	PROPN
ejpam-3704	124	12	y	y	NOUN
ejpam-3704	124	13	~	~	PUNCT
ejpam-3704	124	14	x	x	PUNCT
ejpam-3704	124	15	such	such	ADJ
ejpam-3704	124	16	that	that	SCONJ
ejpam-3704	124	17	0θ′v	0θ′v	NUM
ejpam-3704	124	18	.	.	PUNCT
ejpam-3704	125	1	so	so	ADV
ejpam-3704	125	2	,	,	PUNCT
ejpam-3704	125	3	v	v	NOUN
ejpam-3704	125	4	∈	∈	PROPN
ejpam-3704	126	1	[	[	X
ejpam-3704	126	2	0]θ′	0]θ′	NOUN
ejpam-3704	126	3	=	=	PUNCT
ejpam-3704	127	1	[	[	X
ejpam-3704	127	2	0]θ	0]θ	NOUN
ejpam-3704	127	3	.	.	PUNCT
ejpam-3704	128	1	hence	hence	ADV
ejpam-3704	128	2	,	,	PUNCT
ejpam-3704	128	3	(	(	PUNCT
ejpam-3704	128	4	y	y	NOUN
ejpam-3704	128	5	~	~	PUNCT
ejpam-3704	128	6	x)θ{0	x)θ{0	NUM
ejpam-3704	128	7	}	}	PUNCT
ejpam-3704	128	8	.	.	PUNCT
ejpam-3704	129	1	since	since	SCONJ
ejpam-3704	129	2	θ	θ	PROPN
ejpam-3704	129	3	is	be	AUX
ejpam-3704	129	4	a	a	DET
ejpam-3704	129	5	regular	regular	ADJ
ejpam-3704	129	6	congruence	congruence	NOUN
ejpam-3704	129	7	relation	relation	NOUN
ejpam-3704	129	8	,	,	PUNCT
ejpam-3704	129	9	we	we	PRON
ejpam-3704	129	10	have	have	VERB
ejpam-3704	129	11	xθy	xθy	NOUN
ejpam-3704	129	12	.	.	PUNCT
ejpam-3704	130	1	we	we	PRON
ejpam-3704	130	2	now	now	ADV
ejpam-3704	130	3	reformulate	reformulate	VERB
ejpam-3704	130	4	the	the	DET
ejpam-3704	130	5	quotient	quotient	NOUN
ejpam-3704	130	6	structure	structure	NOUN
ejpam-3704	130	7	of	of	ADP
ejpam-3704	130	8	a	a	DET
ejpam-3704	130	9	hyper	hyper	ADJ
ejpam-3704	130	10	up	up	ADP
ejpam-3704	130	11	-	-	PUNCT
ejpam-3704	130	12	algebra	algebra	NOUN
ejpam-3704	130	13	presented	present	VERB
ejpam-3704	130	14	in	in	ADP
ejpam-3704	130	15	[	[	X
ejpam-3704	130	16	9	9	NUM
ejpam-3704	130	17	]	]	PUNCT
ejpam-3704	130	18	via	via	ADP
ejpam-3704	130	19	regular	regular	ADJ
ejpam-3704	130	20	congruence	congruence	NOUN
ejpam-3704	130	21	relation	relation	NOUN
ejpam-3704	130	22	on	on	ADP
ejpam-3704	130	23	a	a	DET
ejpam-3704	130	24	hyper	hyper	ADJ
ejpam-3704	130	25	up	up	ADP
ejpam-3704	130	26	-	-	PUNCT
ejpam-3704	130	27	algebra	algebra	NOUN
ejpam-3704	130	28	h.	h.	NOUN
ejpam-3704	130	29	theorem	theorem	NOUN
ejpam-3704	130	30	2	2	NUM
ejpam-3704	130	31	.	.	PUNCT
ejpam-3704	131	1	[	[	X
ejpam-3704	131	2	9	9	NUM
ejpam-3704	131	3	]	]	PUNCT
ejpam-3704	131	4	let	let	VERB
ejpam-3704	131	5	θ	θ	NOUN
ejpam-3704	131	6	be	be	AUX
ejpam-3704	131	7	a	a	DET
ejpam-3704	131	8	regular	regular	ADJ
ejpam-3704	131	9	congruence	congruence	NOUN
ejpam-3704	131	10	relation	relation	NOUN
ejpam-3704	131	11	on	on	ADP
ejpam-3704	131	12	h	h	NOUN
ejpam-3704	131	13	,	,	PUNCT
ejpam-3704	131	14	i	i	PRON
ejpam-3704	131	15	=	=	PUNCT
ejpam-3704	131	16	i0	i0	PROPN
ejpam-3704	131	17	=	=	PUNCT
ejpam-3704	132	1	[	[	X
ejpam-3704	132	2	0]θ	0]θ	X
ejpam-3704	132	3	and	and	CCONJ
ejpam-3704	132	4	h	h	NOUN
ejpam-3704	132	5	/	/	SYM
ejpam-3704	132	6	i	i	PRON
ejpam-3704	132	7	=	=	PUNCT
ejpam-3704	132	8	{	{	PUNCT
ejpam-3704	132	9	ix	ix	X
ejpam-3704	132	10	:	:	PUNCT
ejpam-3704	132	11	x	x	SYM
ejpam-3704	132	12	∈	∈	PROPN
ejpam-3704	132	13	h	h	NOUN
ejpam-3704	132	14	}	}	PUNCT
ejpam-3704	132	15	,	,	PUNCT
ejpam-3704	132	16	where	where	SCONJ
ejpam-3704	132	17	ix	ix	ADV
ejpam-3704	132	18	=	=	PUNCT
ejpam-3704	133	1	[	[	X
ejpam-3704	133	2	x]θ	x]θ	ADV
ejpam-3704	133	3	for	for	ADP
ejpam-3704	133	4	all	all	DET
ejpam-3704	133	5	x	x	SYM
ejpam-3704	133	6	∈	∈	PROPN
ejpam-3704	133	7	h.	h.	NOUN
ejpam-3704	133	8	then	then	ADV
ejpam-3704	133	9	h	h	X
ejpam-3704	133	10	/	/	SYM
ejpam-3704	133	11	i	i	PRON
ejpam-3704	133	12	with	with	ADP
ejpam-3704	133	13	the	the	DET
ejpam-3704	133	14	hyperoperation	hyperoperation	NOUN
ejpam-3704	133	15	~	~	PUNCT
ejpam-3704	133	16	and	and	CCONJ
ejpam-3704	133	17	hyperorder	hyperorder	PROPN
ejpam-3704	133	18	�	�	PROPN
ejpam-3704	133	19	which	which	PRON
ejpam-3704	133	20	are	be	AUX
ejpam-3704	133	21	defined	define	VERB
ejpam-3704	133	22	as	as	SCONJ
ejpam-3704	133	23	follows	follow	VERB
ejpam-3704	133	24	ix	ix	ADV
ejpam-3704	133	25	~	~	PUNCT
ejpam-3704	133	26	iy	iy	X
ejpam-3704	133	27	=	=	PUNCT
ejpam-3704	133	28	{	{	PUNCT
ejpam-3704	133	29	iz	iz	INTJ
ejpam-3704	133	30	:	:	PUNCT
ejpam-3704	133	31	z	z	PROPN
ejpam-3704	133	32	∈	∈	PROPN
ejpam-3704	133	33	x~	x~	NUM
ejpam-3704	133	34	y	y	SYM
ejpam-3704	133	35	}	}	PUNCT
ejpam-3704	133	36	and	and	CCONJ
ejpam-3704	133	37	ix	ix	PROPN
ejpam-3704	133	38	�	�	PROPN
ejpam-3704	133	39	iy	iy	PROPN
ejpam-3704	133	40	if	if	SCONJ
ejpam-3704	133	41	and	and	CCONJ
ejpam-3704	133	42	only	only	ADV
ejpam-3704	133	43	if	if	SCONJ
ejpam-3704	133	44	i	i	PRON
ejpam-3704	133	45	∈	∈	VERB
ejpam-3704	133	46	iy	iy	X
ejpam-3704	134	1	~	~	PUNCT
ejpam-3704	134	2	ix	ix	ADV
ejpam-3704	134	3	is	be	AUX
ejpam-3704	134	4	a	a	DET
ejpam-3704	134	5	hyper	hyper	ADJ
ejpam-3704	134	6	up	up	NOUN
ejpam-3704	134	7	-	-	PUNCT
ejpam-3704	134	8	algebra	algebra	NOUN
ejpam-3704	134	9	which	which	PRON
ejpam-3704	134	10	is	be	AUX
ejpam-3704	134	11	called	call	VERB
ejpam-3704	134	12	the	the	DET
ejpam-3704	134	13	quotient	quotient	NOUN
ejpam-3704	134	14	hyper	hyper	ADJ
ejpam-3704	134	15	up	up	ADP
ejpam-3704	134	16	-	-	PUNCT
ejpam-3704	134	17	algebra	algebra	NOUN
ejpam-3704	134	18	.	.	PUNCT
ejpam-3704	134	19	example	example	NOUN
ejpam-3704	135	1	2	2	NUM
ejpam-3704	135	2	.	.	PUNCT
ejpam-3704	135	3	let	let	VERB
ejpam-3704	135	4	h	h	NOUN
ejpam-3704	135	5	=	=	PRON
ejpam-3704	135	6	{	{	PUNCT
ejpam-3704	135	7	0	0	NUM
ejpam-3704	135	8	,	,	PUNCT
ejpam-3704	135	9	1	1	NUM
ejpam-3704	135	10	,	,	PUNCT
ejpam-3704	135	11	2	2	NUM
ejpam-3704	135	12	,	,	PUNCT
ejpam-3704	135	13	3	3	NUM
ejpam-3704	135	14	}	}	PUNCT
ejpam-3704	135	15	be	be	AUX
ejpam-3704	135	16	a	a	DET
ejpam-3704	135	17	set	set	NOUN
ejpam-3704	135	18	.	.	PUNCT
ejpam-3704	136	1	define	define	VERB
ejpam-3704	136	2	the	the	DET
ejpam-3704	136	3	hyperoperation	hyperoperation	NOUN
ejpam-3704	136	4	~	~	PUNCT
ejpam-3704	136	5	by	by	ADP
ejpam-3704	136	6	the	the	DET
ejpam-3704	136	7	following	following	ADJ
ejpam-3704	136	8	cayley	cayley	ADJ
ejpam-3704	136	9	table	table	NOUN
ejpam-3704	136	10	:	:	PUNCT
ejpam-3704	136	11	~	~	PUNCT
ejpam-3704	136	12	0	0	NUM
ejpam-3704	137	1	1	1	NUM
ejpam-3704	137	2	2	2	NUM
ejpam-3704	137	3	3	3	NUM
ejpam-3704	137	4	0	0	NUM
ejpam-3704	137	5	{	{	PUNCT
ejpam-3704	137	6	0	0	NUM
ejpam-3704	137	7	}	}	PUNCT
ejpam-3704	137	8	{	{	PUNCT
ejpam-3704	137	9	1	1	NUM
ejpam-3704	137	10	}	}	PUNCT
ejpam-3704	137	11	{	{	PUNCT
ejpam-3704	137	12	2	2	NUM
ejpam-3704	137	13	}	}	PUNCT
ejpam-3704	137	14	{	{	PUNCT
ejpam-3704	137	15	3	3	NUM
ejpam-3704	137	16	}	}	SYM
ejpam-3704	137	17	1	1	NUM
ejpam-3704	137	18	{	{	PUNCT
ejpam-3704	137	19	0	0	NUM
ejpam-3704	137	20	}	}	PUNCT
ejpam-3704	137	21	{	{	PUNCT
ejpam-3704	137	22	0,1	0,1	NOUN
ejpam-3704	137	23	}	}	PUNCT
ejpam-3704	137	24	{	{	PUNCT
ejpam-3704	137	25	0,2	0,2	NUM
ejpam-3704	137	26	}	}	PUNCT
ejpam-3704	137	27	{	{	PUNCT
ejpam-3704	137	28	1,3	1,3	NUM
ejpam-3704	137	29	}	}	SYM
ejpam-3704	137	30	2	2	NUM
ejpam-3704	137	31	{	{	PUNCT
ejpam-3704	137	32	0	0	NUM
ejpam-3704	137	33	}	}	PUNCT
ejpam-3704	137	34	{	{	PUNCT
ejpam-3704	137	35	1	1	NUM
ejpam-3704	137	36	}	}	PUNCT
ejpam-3704	137	37	{	{	PUNCT
ejpam-3704	137	38	0,2	0,2	NUM
ejpam-3704	137	39	}	}	PUNCT
ejpam-3704	137	40	{	{	PUNCT
ejpam-3704	137	41	3	3	NUM
ejpam-3704	137	42	}	}	SYM
ejpam-3704	137	43	3	3	NUM
ejpam-3704	137	44	{	{	PUNCT
ejpam-3704	137	45	0	0	NUM
ejpam-3704	137	46	}	}	PUNCT
ejpam-3704	137	47	{	{	PUNCT
ejpam-3704	137	48	0,1	0,1	NOUN
ejpam-3704	137	49	}	}	PUNCT
ejpam-3704	137	50	{	{	PUNCT
ejpam-3704	137	51	0,2	0,2	NUM
ejpam-3704	137	52	}	}	PUNCT
ejpam-3704	137	53	{	{	PUNCT
ejpam-3704	137	54	0,1,3	0,1,3	NOUN
ejpam-3704	137	55	}	}	PUNCT
ejpam-3704	137	56	by	by	ADP
ejpam-3704	137	57	routine	routine	ADJ
ejpam-3704	137	58	calculations	calculation	NOUN
ejpam-3704	137	59	,	,	PUNCT
ejpam-3704	137	60	(	(	PUNCT
ejpam-3704	137	61	h;~	h;~	NOUN
ejpam-3704	137	62	,	,	PUNCT
ejpam-3704	137	63	0	0	NUM
ejpam-3704	137	64	)	)	PUNCT
ejpam-3704	137	65	is	be	AUX
ejpam-3704	137	66	a	a	DET
ejpam-3704	137	67	hyper	hyper	ADJ
ejpam-3704	137	68	up	up	NOUN
ejpam-3704	137	69	-	-	PUNCT
ejpam-3704	137	70	algebra	algebra	NOUN
ejpam-3704	137	71	.	.	PUNCT
ejpam-3704	138	1	define	define	VERB
ejpam-3704	138	2	a	a	DET
ejpam-3704	138	3	relation	relation	NOUN
ejpam-3704	138	4	θ	θ	PROPN
ejpam-3704	138	5	on	on	ADP
ejpam-3704	138	6	h	h	NOUN
ejpam-3704	138	7	by	by	ADP
ejpam-3704	138	8	θ	θ	PROPN
ejpam-3704	138	9	=	=	SYM
ejpam-3704	138	10	{	{	PUNCT
ejpam-3704	138	11	(	(	PUNCT
ejpam-3704	138	12	0	0	NUM
ejpam-3704	138	13	,	,	PUNCT
ejpam-3704	138	14	0	0	NUM
ejpam-3704	138	15	)	)	PUNCT
ejpam-3704	138	16	,	,	PUNCT
ejpam-3704	138	17	(	(	PUNCT
ejpam-3704	138	18	1	1	NUM
ejpam-3704	138	19	,	,	PUNCT
ejpam-3704	138	20	1	1	NUM
ejpam-3704	138	21	)	)	PUNCT
ejpam-3704	138	22	,	,	PUNCT
ejpam-3704	138	23	(	(	PUNCT
ejpam-3704	138	24	0	0	NUM
ejpam-3704	138	25	,	,	PUNCT
ejpam-3704	138	26	2	2	NUM
ejpam-3704	138	27	)	)	PUNCT
ejpam-3704	138	28	,	,	PUNCT
ejpam-3704	138	29	(	(	PUNCT
ejpam-3704	138	30	2	2	NUM
ejpam-3704	138	31	,	,	PUNCT
ejpam-3704	138	32	0	0	NUM
ejpam-3704	138	33	)	)	PUNCT
ejpam-3704	138	34	,	,	PUNCT
ejpam-3704	138	35	(	(	PUNCT
ejpam-3704	138	36	2	2	NUM
ejpam-3704	138	37	,	,	PUNCT
ejpam-3704	138	38	2	2	NUM
ejpam-3704	138	39	)	)	PUNCT
ejpam-3704	138	40	,	,	PUNCT
ejpam-3704	138	41	(	(	PUNCT
ejpam-3704	138	42	3	3	NUM
ejpam-3704	138	43	,	,	PUNCT
ejpam-3704	138	44	3	3	NUM
ejpam-3704	138	45	)	)	PUNCT
ejpam-3704	138	46	}	}	PUNCT
ejpam-3704	138	47	.	.	PUNCT
ejpam-3704	139	1	by	by	ADP
ejpam-3704	139	2	lemma	lemma	PROPN
ejpam-3704	139	3	3	3	NUM
ejpam-3704	139	4	,	,	PUNCT
ejpam-3704	139	5	it	it	PRON
ejpam-3704	139	6	can	can	AUX
ejpam-3704	139	7	be	be	AUX
ejpam-3704	139	8	verified	verify	VERB
ejpam-3704	139	9	that	that	SCONJ
ejpam-3704	139	10	θ	θ	PROPN
ejpam-3704	139	11	is	be	AUX
ejpam-3704	139	12	a	a	DET
ejpam-3704	139	13	congruence	congruence	NOUN
ejpam-3704	139	14	relation	relation	NOUN
ejpam-3704	139	15	on	on	ADP
ejpam-3704	139	16	h.	h.	PROPN
ejpam-3704	139	17	moreover	moreover	ADV
ejpam-3704	139	18	,	,	PUNCT
ejpam-3704	139	19	by	by	ADP
ejpam-3704	139	20	routine	routine	ADJ
ejpam-3704	139	21	calculations	calculation	NOUN
ejpam-3704	139	22	,	,	PUNCT
ejpam-3704	139	23	θ	θ	PROPN
ejpam-3704	139	24	is	be	AUX
ejpam-3704	139	25	a	a	DET
ejpam-3704	139	26	regular	regular	ADJ
ejpam-3704	139	27	congruence	congruence	NOUN
ejpam-3704	139	28	relation	relation	NOUN
ejpam-3704	139	29	.	.	PUNCT
ejpam-3704	140	1	consider	consider	VERB
ejpam-3704	140	2	i0	i0	PROPN
ejpam-3704	141	1	=	=	PUNCT
ejpam-3704	141	2	i	i	NOUN
ejpam-3704	141	3	=	=	PUNCT
ejpam-3704	142	1	[	[	X
ejpam-3704	142	2	0]θ	0]θ	X
ejpam-3704	142	3	=	=	SYM
ejpam-3704	142	4	{	{	PUNCT
ejpam-3704	142	5	0	0	NUM
ejpam-3704	142	6	,	,	PUNCT
ejpam-3704	142	7	2	2	NUM
ejpam-3704	142	8	}	}	PUNCT
ejpam-3704	142	9	,	,	PUNCT
ejpam-3704	142	10	i1	i1	PROPN
ejpam-3704	142	11	=	=	PUNCT
ejpam-3704	142	12	{	{	PUNCT
ejpam-3704	142	13	1	1	NUM
ejpam-3704	142	14	}	}	PUNCT
ejpam-3704	142	15	,	,	PUNCT
ejpam-3704	142	16	and	and	CCONJ
ejpam-3704	142	17	i3	i3	NOUN
ejpam-3704	142	18	=	=	SYM
ejpam-3704	142	19	{	{	PUNCT
ejpam-3704	142	20	3	3	NUM
ejpam-3704	142	21	}	}	PUNCT
ejpam-3704	142	22	.	.	PUNCT
ejpam-3704	143	1	then	then	ADV
ejpam-3704	143	2	h	h	X
ejpam-3704	143	3	/	/	SYM
ejpam-3704	143	4	i	i	PRON
ejpam-3704	143	5	=	=	PUNCT
ejpam-3704	143	6	{	{	PUNCT
ejpam-3704	143	7	i	i	PROPN
ejpam-3704	143	8	,	,	PUNCT
ejpam-3704	143	9	i1	i1	PROPN
ejpam-3704	143	10	,	,	PUNCT
ejpam-3704	143	11	i3	i3	PROPN
ejpam-3704	143	12	}	}	PUNCT
ejpam-3704	143	13	.	.	PUNCT
ejpam-3704	144	1	thus	thus	ADV
ejpam-3704	144	2	,	,	PUNCT
ejpam-3704	144	3	our	our	PRON
ejpam-3704	144	4	cayley	cayley	ADJ
ejpam-3704	144	5	table	table	NOUN
ejpam-3704	144	6	is	be	AUX
ejpam-3704	144	7	as	as	SCONJ
ejpam-3704	144	8	follows	follow	VERB
ejpam-3704	144	9	:	:	PUNCT
ejpam-3704	144	10	~	~	PUNCT
ejpam-3704	144	11	i	i	PRON
ejpam-3704	144	12	i1	i1	PROPN
ejpam-3704	144	13	i3	i3	PROPN
ejpam-3704	144	14	i	i	PRON
ejpam-3704	144	15	{	{	PUNCT
ejpam-3704	144	16	i	i	NOUN
ejpam-3704	144	17	}	}	PUNCT
ejpam-3704	144	18	{	{	PUNCT
ejpam-3704	144	19	i1	i1	PROPN
ejpam-3704	144	20	}	}	PUNCT
ejpam-3704	144	21	{	{	PUNCT
ejpam-3704	144	22	i3	i3	PROPN
ejpam-3704	144	23	}	}	PUNCT
ejpam-3704	144	24	i1	i1	PROPN
ejpam-3704	144	25	{	{	PUNCT
ejpam-3704	144	26	i	i	PROPN
ejpam-3704	144	27	}	}	PUNCT
ejpam-3704	144	28	{	{	PUNCT
ejpam-3704	144	29	i	i	PROPN
ejpam-3704	144	30	,	,	PUNCT
ejpam-3704	144	31	i1	i1	PROPN
ejpam-3704	144	32	}	}	PUNCT
ejpam-3704	144	33	{	{	PUNCT
ejpam-3704	144	34	i1	i1	PROPN
ejpam-3704	144	35	,	,	PUNCT
ejpam-3704	144	36	i3	i3	PROPN
ejpam-3704	144	37	}	}	PUNCT
ejpam-3704	144	38	i3	i3	NOUN
ejpam-3704	144	39	{	{	PUNCT
ejpam-3704	144	40	i	i	NOUN
ejpam-3704	144	41	}	}	PUNCT
ejpam-3704	144	42	{	{	PUNCT
ejpam-3704	144	43	i	i	PROPN
ejpam-3704	144	44	,	,	PUNCT
ejpam-3704	144	45	i1	i1	PROPN
ejpam-3704	144	46	}	}	PUNCT
ejpam-3704	144	47	{	{	PUNCT
ejpam-3704	144	48	i	i	PROPN
ejpam-3704	144	49	,	,	PUNCT
ejpam-3704	144	50	i1	i1	PROPN
ejpam-3704	144	51	,	,	PUNCT
ejpam-3704	144	52	i3	i3	PROPN
ejpam-3704	144	53	}	}	PUNCT
ejpam-3704	144	54	r.	r.	PROPN
ejpam-3704	144	55	amairanto	amairanto	PROPN
ejpam-3704	144	56	,	,	PUNCT
ejpam-3704	144	57	r.	r.	PROPN
ejpam-3704	144	58	isla	isla	PROPN
ejpam-3704	144	59	/	/	SYM
ejpam-3704	144	60	eur	eur	PROPN
ejpam-3704	144	61	.	.	PUNCT
ejpam-3704	145	1	j.	j.	PROPN
ejpam-3704	145	2	pure	pure	PROPN
ejpam-3704	145	3	appl	appl	PROPN
ejpam-3704	145	4	.	.	PROPN
ejpam-3704	145	5	math	math	PROPN
ejpam-3704	145	6	,	,	PUNCT
ejpam-3704	145	7	13	13	NUM
ejpam-3704	145	8	(	(	PUNCT
ejpam-3704	145	9	3	3	NUM
ejpam-3704	145	10	)	)	PUNCT
ejpam-3704	145	11	(	(	PUNCT
ejpam-3704	145	12	2020	2020	NUM
ejpam-3704	145	13	)	)	PUNCT
ejpam-3704	145	14	,	,	PUNCT
ejpam-3704	145	15	483	483	NUM
ejpam-3704	145	16	-	-	SYM
ejpam-3704	145	17	497	497	NUM
ejpam-3704	145	18	488	488	NUM
ejpam-3704	145	19	by	by	ADP
ejpam-3704	145	20	routine	routine	ADJ
ejpam-3704	145	21	calculations	calculation	NOUN
ejpam-3704	145	22	,	,	PUNCT
ejpam-3704	145	23	h	h	NOUN
ejpam-3704	145	24	/	/	SYM
ejpam-3704	146	1	i	i	PRON
ejpam-3704	146	2	is	be	AUX
ejpam-3704	146	3	a	a	DET
ejpam-3704	146	4	hyper	hyper	ADJ
ejpam-3704	146	5	up	up	NOUN
ejpam-3704	146	6	-	-	PUNCT
ejpam-3704	146	7	algebra	algebra	NOUN
ejpam-3704	146	8	.	.	PUNCT
ejpam-3704	147	1	to	to	PART
ejpam-3704	147	2	establish	establish	VERB
ejpam-3704	147	3	the	the	DET
ejpam-3704	147	4	first	first	ADJ
ejpam-3704	147	5	hyper	hyper	ADJ
ejpam-3704	147	6	isomorphism	isomorphism	NOUN
ejpam-3704	147	7	theorem	theorem	VERB
ejpam-3704	147	8	on	on	ADP
ejpam-3704	147	9	hyper	hyper	ADJ
ejpam-3704	147	10	up	up	ADP
ejpam-3704	147	11	-	-	PUNCT
ejpam-3704	147	12	algebras	algebras	X
ejpam-3704	147	13	,	,	PUNCT
ejpam-3704	147	14	we	we	PRON
ejpam-3704	147	15	first	first	ADV
ejpam-3704	147	16	reformulate	reformulate	VERB
ejpam-3704	147	17	some	some	DET
ejpam-3704	147	18	results	result	NOUN
ejpam-3704	147	19	on	on	ADP
ejpam-3704	147	20	hyper	hyper	ADJ
ejpam-3704	147	21	homomorphisms	homomorphism	NOUN
ejpam-3704	147	22	of	of	ADP
ejpam-3704	147	23	hyper	hyper	NOUN
ejpam-3704	147	24	upalgebras	upalgebra	NOUN
ejpam-3704	147	25	.	.	PUNCT
ejpam-3704	148	1	lemma	lemma	PROPN
ejpam-3704	148	2	4	4	NUM
ejpam-3704	148	3	.	.	PUNCT
ejpam-3704	149	1	[	[	X
ejpam-3704	149	2	9	9	NUM
ejpam-3704	149	3	]	]	PUNCT
ejpam-3704	149	4	let	let	VERB
ejpam-3704	149	5	θ	θ	NOUN
ejpam-3704	149	6	be	be	AUX
ejpam-3704	149	7	a	a	DET
ejpam-3704	149	8	regular	regular	ADJ
ejpam-3704	149	9	congruence	congruence	NOUN
ejpam-3704	149	10	relation	relation	NOUN
ejpam-3704	149	11	on	on	ADP
ejpam-3704	149	12	h	h	NOUN
ejpam-3704	150	1	and	and	CCONJ
ejpam-3704	150	2	i	i	PRON
ejpam-3704	150	3	=	=	PUNCT
ejpam-3704	151	1	[	[	X
ejpam-3704	151	2	0]θ	0]θ	NOUN
ejpam-3704	151	3	.	.	PUNCT
ejpam-3704	152	1	then	then	ADV
ejpam-3704	152	2	the	the	DET
ejpam-3704	152	3	mapping	mapping	NOUN
ejpam-3704	152	4	π	π	X
ejpam-3704	152	5	:	:	PUNCT
ejpam-3704	152	6	h	h	PROPN
ejpam-3704	153	1	−→	−→	ADJ
ejpam-3704	153	2	h	h	NOUN
ejpam-3704	153	3	/	/	SYM
ejpam-3704	153	4	i	i	PRON
ejpam-3704	153	5	which	which	PRON
ejpam-3704	153	6	is	be	AUX
ejpam-3704	153	7	defined	define	VERB
ejpam-3704	153	8	by	by	ADP
ejpam-3704	153	9	π(x	π(x	NOUN
ejpam-3704	153	10	)	)	PUNCT
ejpam-3704	153	11	=	=	SYM
ejpam-3704	154	1	ix	ix	PROPN
ejpam-3704	154	2	,	,	PUNCT
ejpam-3704	154	3	for	for	ADP
ejpam-3704	154	4	all	all	DET
ejpam-3704	154	5	x	x	SYM
ejpam-3704	154	6	∈	∈	PROPN
ejpam-3704	154	7	h	h	NOUN
ejpam-3704	154	8	,	,	PUNCT
ejpam-3704	154	9	is	be	AUX
ejpam-3704	154	10	a	a	DET
ejpam-3704	154	11	hyper	hyper	ADJ
ejpam-3704	154	12	epimorphism	epimorphism	NOUN
ejpam-3704	154	13	which	which	PRON
ejpam-3704	154	14	is	be	AUX
ejpam-3704	154	15	called	call	VERB
ejpam-3704	154	16	the	the	DET
ejpam-3704	154	17	canonical	canonical	ADJ
ejpam-3704	154	18	epimorphism	epimorphism	NOUN
ejpam-3704	154	19	.	.	PUNCT
ejpam-3704	155	1	theorem	theorem	NOUN
ejpam-3704	155	2	3	3	NUM
ejpam-3704	155	3	.	.	PUNCT
ejpam-3704	156	1	[	[	X
ejpam-3704	156	2	9	9	NUM
ejpam-3704	156	3	]	]	X
ejpam-3704	156	4	(	(	PUNCT
ejpam-3704	156	5	hyper	hyper	ADJ
ejpam-3704	156	6	homomorphism	homomorphism	NOUN
ejpam-3704	156	7	theorem	theorem	VERB
ejpam-3704	156	8	)	)	PUNCT
ejpam-3704	156	9	let	let	VERB
ejpam-3704	156	10	θ	θ	NOUN
ejpam-3704	156	11	be	be	AUX
ejpam-3704	156	12	a	a	DET
ejpam-3704	156	13	regular	regular	ADJ
ejpam-3704	156	14	congruence	congruence	NOUN
ejpam-3704	156	15	on	on	ADP
ejpam-3704	156	16	h	h	NOUN
ejpam-3704	157	1	and	and	CCONJ
ejpam-3704	157	2	i	i	PRON
ejpam-3704	157	3	=	=	PUNCT
ejpam-3704	158	1	[	[	X
ejpam-3704	158	2	0]θ	0]θ	NOUN
ejpam-3704	158	3	.	.	PUNCT
ejpam-3704	159	1	if	if	SCONJ
ejpam-3704	159	2	f	f	PROPN
ejpam-3704	159	3	:	:	PUNCT
ejpam-3704	159	4	h	h	PROPN
ejpam-3704	159	5	−→	−→	ADJ
ejpam-3704	159	6	h	h	NOUN
ejpam-3704	159	7	′	′	NOUN
ejpam-3704	159	8	is	be	AUX
ejpam-3704	159	9	a	a	DET
ejpam-3704	159	10	hyper	hyper	ADJ
ejpam-3704	159	11	homomorphism	homomorphism	NOUN
ejpam-3704	159	12	of	of	ADP
ejpam-3704	159	13	hyper	hyper	ADJ
ejpam-3704	159	14	up	up	ADP
ejpam-3704	159	15	-	-	PUNCT
ejpam-3704	159	16	algebras	algebra	NOUN
ejpam-3704	159	17	such	such	ADJ
ejpam-3704	159	18	that	that	SCONJ
ejpam-3704	159	19	i	i	PRON
ejpam-3704	159	20	is	be	AUX
ejpam-3704	159	21	contained	contain	VERB
ejpam-3704	159	22	in	in	ADP
ejpam-3704	159	23	the	the	DET
ejpam-3704	159	24	kernel	kernel	NOUN
ejpam-3704	159	25	of	of	ADP
ejpam-3704	159	26	f	f	PROPN
ejpam-3704	159	27	,	,	PUNCT
ejpam-3704	159	28	then	then	ADV
ejpam-3704	159	29	f̄	f̄	NOUN
ejpam-3704	159	30	:	:	PUNCT
ejpam-3704	160	1	h	h	X
ejpam-3704	160	2	/	/	SYM
ejpam-3704	160	3	i	i	PRON
ejpam-3704	160	4	−→	−→	ADJ
ejpam-3704	160	5	h	h	NOUN
ejpam-3704	160	6	′	′	NOUN
ejpam-3704	160	7	,	,	PUNCT
ejpam-3704	160	8	which	which	PRON
ejpam-3704	160	9	is	be	AUX
ejpam-3704	160	10	defined	define	VERB
ejpam-3704	160	11	by	by	ADP
ejpam-3704	160	12	f̄(ix	f̄(ix	NOUN
ejpam-3704	160	13	)	)	PUNCT
ejpam-3704	160	14	=	=	SYM
ejpam-3704	160	15	f(x	f(x	PROPN
ejpam-3704	160	16	)	)	PUNCT
ejpam-3704	160	17	,	,	PUNCT
ejpam-3704	160	18	for	for	ADP
ejpam-3704	160	19	all	all	DET
ejpam-3704	160	20	x	x	SYM
ejpam-3704	160	21	∈	∈	PROPN
ejpam-3704	160	22	h	h	NOUN
ejpam-3704	160	23	,	,	PUNCT
ejpam-3704	160	24	is	be	AUX
ejpam-3704	160	25	a	a	DET
ejpam-3704	160	26	unique	unique	ADJ
ejpam-3704	160	27	hyper	hyper	ADJ
ejpam-3704	160	28	homomorphism	homomorphism	NOUN
ejpam-3704	161	1	such	such	ADJ
ejpam-3704	161	2	that	that	DET
ejpam-3704	161	3	f̄	f̄	PROPN
ejpam-3704	161	4	◦	◦	NOUN
ejpam-3704	161	5	π	π	PROPN
ejpam-3704	161	6	=	=	SYM
ejpam-3704	161	7	f	f	PROPN
ejpam-3704	161	8	,	,	PUNCT
ejpam-3704	161	9	where	where	SCONJ
ejpam-3704	161	10	π	π	PROPN
ejpam-3704	161	11	denotes	denote	VERB
ejpam-3704	161	12	the	the	DET
ejpam-3704	161	13	canonical	canonical	ADJ
ejpam-3704	161	14	epimorphism	epimorphism	NOUN
ejpam-3704	161	15	and	and	CCONJ
ejpam-3704	161	16	◦	◦	NOUN
ejpam-3704	161	17	is	be	AUX
ejpam-3704	161	18	the	the	DET
ejpam-3704	161	19	composition	composition	NOUN
ejpam-3704	161	20	map	map	NOUN
ejpam-3704	161	21	.	.	PUNCT
ejpam-3704	162	1	theorem	theorem	ADJ
ejpam-3704	162	2	4	4	NUM
ejpam-3704	162	3	.	.	PUNCT
ejpam-3704	163	1	(	(	PUNCT
ejpam-3704	163	2	first	first	ADJ
ejpam-3704	163	3	hyper	hyper	PROPN
ejpam-3704	163	4	isomorphism	isomorphism	NOUN
ejpam-3704	163	5	theorem	theorem	VERB
ejpam-3704	163	6	)	)	PUNCT
ejpam-3704	163	7	let	let	VERB
ejpam-3704	163	8	θ	θ	NOUN
ejpam-3704	163	9	be	be	AUX
ejpam-3704	163	10	a	a	DET
ejpam-3704	163	11	regular	regular	ADJ
ejpam-3704	163	12	congruence	congruence	NOUN
ejpam-3704	163	13	relation	relation	NOUN
ejpam-3704	163	14	on	on	ADP
ejpam-3704	163	15	h	h	NOUN
ejpam-3704	164	1	and	and	CCONJ
ejpam-3704	164	2	i	i	PRON
ejpam-3704	164	3	=	=	PUNCT
ejpam-3704	165	1	[	[	X
ejpam-3704	165	2	0]θ	0]θ	NOUN
ejpam-3704	165	3	.	.	PUNCT
ejpam-3704	166	1	if	if	SCONJ
ejpam-3704	166	2	f	f	PROPN
ejpam-3704	166	3	:	:	PUNCT
ejpam-3704	166	4	h	h	PROPN
ejpam-3704	166	5	−→	−→	ADJ
ejpam-3704	166	6	h	h	NOUN
ejpam-3704	166	7	′	′	NOUN
ejpam-3704	166	8	is	be	AUX
ejpam-3704	166	9	a	a	DET
ejpam-3704	166	10	hyper	hyper	ADJ
ejpam-3704	166	11	homomorphism	homomorphism	NOUN
ejpam-3704	166	12	of	of	ADP
ejpam-3704	166	13	hyper	hyper	ADJ
ejpam-3704	166	14	upalgebras	upalgebra	NOUN
ejpam-3704	166	15	such	such	ADJ
ejpam-3704	166	16	that	that	DET
ejpam-3704	166	17	ker	ker	NOUN
ejpam-3704	167	1	f	f	PROPN
ejpam-3704	167	2	=	=	SYM
ejpam-3704	167	3	i	i	PROPN
ejpam-3704	167	4	,	,	PUNCT
ejpam-3704	167	5	then	then	ADV
ejpam-3704	167	6	h	h	PROPN
ejpam-3704	167	7	/	/	SYM
ejpam-3704	167	8	ker	ker	PROPN
ejpam-3704	167	9	f	f	PROPN
ejpam-3704	167	10	∼=h	∼=h	PROPN
ejpam-3704	167	11	imf	imf	PROPN
ejpam-3704	167	12	.	.	PUNCT
ejpam-3704	168	1	proof	proof	NOUN
ejpam-3704	168	2	.	.	PUNCT
ejpam-3704	169	1	define	define	VERB
ejpam-3704	169	2	f̄	f̄	NOUN
ejpam-3704	169	3	:	:	PUNCT
ejpam-3704	169	4	h	h	X
ejpam-3704	169	5	/	/	SYM
ejpam-3704	169	6	i	i	PRON
ejpam-3704	169	7	−→	−→	NOUN
ejpam-3704	169	8	h	h	NOUN
ejpam-3704	169	9	′	′	NUM
ejpam-3704	169	10	by	by	ADP
ejpam-3704	169	11	f̄(ix	f̄(ix	NOUN
ejpam-3704	169	12	)	)	PUNCT
ejpam-3704	169	13	=	=	SYM
ejpam-3704	169	14	f(x	f(x	PROPN
ejpam-3704	169	15	)	)	PUNCT
ejpam-3704	169	16	for	for	ADP
ejpam-3704	169	17	all	all	PRON
ejpam-3704	169	18	x	x	SYM
ejpam-3704	169	19	∈	∈	PROPN
ejpam-3704	169	20	h.	h.	NOUN
ejpam-3704	169	21	let	let	VERB
ejpam-3704	169	22	x	x	PRON
ejpam-3704	169	23	,	,	PUNCT
ejpam-3704	169	24	y	y	PROPN
ejpam-3704	169	25	∈	∈	PROPN
ejpam-3704	169	26	h.	h.	NOUN
ejpam-3704	169	27	then	then	ADV
ejpam-3704	169	28	ix	ix	INTJ
ejpam-3704	169	29	,	,	PUNCT
ejpam-3704	169	30	iy	iy	PROPN
ejpam-3704	169	31	∈	∈	PROPN
ejpam-3704	169	32	h	h	PROPN
ejpam-3704	169	33	/	/	SYM
ejpam-3704	169	34	i.	i.	PROPN
ejpam-3704	169	35	from	from	ADP
ejpam-3704	169	36	theorem	theorem	ADJ
ejpam-3704	169	37	3	3	NUM
ejpam-3704	169	38	,	,	PUNCT
ejpam-3704	169	39	f̄	f̄	PROPN
ejpam-3704	169	40	is	be	AUX
ejpam-3704	169	41	a	a	DET
ejpam-3704	169	42	hyper	hyper	ADJ
ejpam-3704	169	43	homomorphism	homomorphism	NOUN
ejpam-3704	169	44	.	.	PUNCT
ejpam-3704	170	1	thus	thus	ADV
ejpam-3704	170	2	,	,	PUNCT
ejpam-3704	170	3	f̄(ix	f̄(ix	X
ejpam-3704	170	4	~	~	PUNCT
ejpam-3704	170	5	iy	iy	X
ejpam-3704	170	6	)	)	PUNCT
ejpam-3704	170	7	=	=	SYM
ejpam-3704	170	8	f̄(ix	f̄(ix	NOUN
ejpam-3704	170	9	)	)	PUNCT
ejpam-3704	170	10	~′	~′	NOUN
ejpam-3704	170	11	f̄(iy	f̄(iy	NOUN
ejpam-3704	170	12	)	)	PUNCT
ejpam-3704	170	13	and	and	CCONJ
ejpam-3704	170	14	f̄(i	f̄(i	NUM
ejpam-3704	170	15	)	)	PUNCT
ejpam-3704	170	16	=	=	NOUN
ejpam-3704	170	17	0′.	0′.	NOUN
ejpam-3704	170	18	suppose	suppose	VERB
ejpam-3704	170	19	that	that	SCONJ
ejpam-3704	170	20	f̄(ix	f̄(ix	NOUN
ejpam-3704	170	21	)	)	PUNCT
ejpam-3704	170	22	=	=	SYM
ejpam-3704	170	23	f̄(iy	f̄(iy	NOUN
ejpam-3704	170	24	)	)	PUNCT
ejpam-3704	170	25	with	with	ADP
ejpam-3704	170	26	x	x	PRON
ejpam-3704	170	27	,	,	PUNCT
ejpam-3704	170	28	y	y	PROPN
ejpam-3704	170	29	∈	∈	PROPN
ejpam-3704	170	30	h.	h.	PROPN
ejpam-3704	170	31	then	then	ADV
ejpam-3704	170	32	f(x	f(x	PROPN
ejpam-3704	170	33	)	)	PUNCT
ejpam-3704	170	34	=	=	SYM
ejpam-3704	170	35	f(y	f(y	NOUN
ejpam-3704	170	36	)	)	PUNCT
ejpam-3704	170	37	.	.	PUNCT
ejpam-3704	171	1	since	since	SCONJ
ejpam-3704	171	2	f	f	PROPN
ejpam-3704	171	3	is	be	AUX
ejpam-3704	171	4	a	a	DET
ejpam-3704	171	5	hyper	hyper	ADJ
ejpam-3704	171	6	homomorphism	homomorphism	NOUN
ejpam-3704	171	7	,	,	PUNCT
ejpam-3704	171	8	0′	0′	X
ejpam-3704	171	9	=	=	SYM
ejpam-3704	171	10	f(0	f(0	NOUN
ejpam-3704	171	11	)	)	PUNCT
ejpam-3704	171	12	∈	∈	NOUN
ejpam-3704	171	13	f(x~	f(x~	PROPN
ejpam-3704	171	14	x	x	X
ejpam-3704	171	15	)	)	PUNCT
ejpam-3704	171	16	=	=	SYM
ejpam-3704	171	17	f(x	f(x	PROPN
ejpam-3704	171	18	)	)	PUNCT
ejpam-3704	171	19	~′	~′	NOUN
ejpam-3704	171	20	f(x	f(x	PROPN
ejpam-3704	171	21	)	)	PUNCT
ejpam-3704	171	22	=	=	SYM
ejpam-3704	171	23	f(x	f(x	PROPN
ejpam-3704	171	24	)	)	PUNCT
ejpam-3704	171	25	~′	~′	NOUN
ejpam-3704	171	26	f(y	f(y	NOUN
ejpam-3704	171	27	)	)	PUNCT
ejpam-3704	171	28	=	=	SYM
ejpam-3704	171	29	f(x~	f(x~	PROPN
ejpam-3704	171	30	y	y	PROPN
ejpam-3704	171	31	)	)	PUNCT
ejpam-3704	171	32	.	.	PUNCT
ejpam-3704	172	1	so	so	ADV
ejpam-3704	172	2	,	,	PUNCT
ejpam-3704	172	3	there	there	PRON
ejpam-3704	172	4	exists	exist	VERB
ejpam-3704	172	5	an	an	DET
ejpam-3704	172	6	element	element	NOUN
ejpam-3704	172	7	u	u	NOUN
ejpam-3704	172	8	∈	∈	PROPN
ejpam-3704	172	9	x~	x~	PROPN
ejpam-3704	172	10	y	y	PROPN
ejpam-3704	172	11	such	such	ADJ
ejpam-3704	172	12	that	that	DET
ejpam-3704	172	13	f(u	f(u	PROPN
ejpam-3704	172	14	)	)	PUNCT
ejpam-3704	172	15	=	=	SYM
ejpam-3704	173	1	0′	0′	PROPN
ejpam-3704	173	2	,	,	PUNCT
ejpam-3704	173	3	that	that	ADV
ejpam-3704	173	4	is	is	ADV
ejpam-3704	173	5	,	,	PUNCT
ejpam-3704	173	6	u	u	NOUN
ejpam-3704	173	7	∈	∈	NOUN
ejpam-3704	173	8	kerf	kerf	NOUN
ejpam-3704	174	1	=	=	PUNCT
ejpam-3704	174	2	i	i	NOUN
ejpam-3704	174	3	=	=	PUNCT
ejpam-3704	175	1	[	[	X
ejpam-3704	175	2	0]θ	0]θ	NOUN
ejpam-3704	175	3	.	.	PUNCT
ejpam-3704	176	1	thus	thus	ADV
ejpam-3704	176	2	,	,	PUNCT
ejpam-3704	176	3	uθ0	uθ0	NOUN
ejpam-3704	176	4	and	and	CCONJ
ejpam-3704	176	5	(	(	PUNCT
ejpam-3704	176	6	x	x	PART
ejpam-3704	176	7	~	~	PUNCT
ejpam-3704	176	8	y)θ{0	y)θ{0	CCONJ
ejpam-3704	176	9	}	}	PUNCT
ejpam-3704	176	10	.	.	PUNCT
ejpam-3704	177	1	also	also	ADV
ejpam-3704	177	2	,	,	PUNCT
ejpam-3704	177	3	0′	0′	X
ejpam-3704	177	4	=	=	SYM
ejpam-3704	177	5	f(0	f(0	NOUN
ejpam-3704	177	6	)	)	PUNCT
ejpam-3704	177	7	∈	∈	PROPN
ejpam-3704	177	8	f(x	f(x	NOUN
ejpam-3704	177	9	~	~	PUNCT
ejpam-3704	177	10	x	x	X
ejpam-3704	177	11	)	)	PUNCT
ejpam-3704	177	12	=	=	SYM
ejpam-3704	177	13	f(x	f(x	PROPN
ejpam-3704	177	14	)	)	PUNCT
ejpam-3704	177	15	~′	~′	NOUN
ejpam-3704	177	16	f(x	f(x	PROPN
ejpam-3704	177	17	)	)	PUNCT
ejpam-3704	177	18	=	=	SYM
ejpam-3704	177	19	f(y	f(y	NOUN
ejpam-3704	177	20	)	)	PUNCT
ejpam-3704	177	21	~′	~′	NOUN
ejpam-3704	177	22	f(x	f(x	PROPN
ejpam-3704	177	23	)	)	PUNCT
ejpam-3704	177	24	=	=	SYM
ejpam-3704	178	1	f(y	f(y	NOUN
ejpam-3704	178	2	~	~	PUNCT
ejpam-3704	178	3	x	x	X
ejpam-3704	178	4	)	)	PUNCT
ejpam-3704	178	5	.	.	PUNCT
ejpam-3704	179	1	thus	thus	ADV
ejpam-3704	179	2	,	,	PUNCT
ejpam-3704	179	3	there	there	PRON
ejpam-3704	179	4	exists	exist	VERB
ejpam-3704	179	5	an	an	DET
ejpam-3704	179	6	element	element	NOUN
ejpam-3704	179	7	v	v	ADP
ejpam-3704	179	8	∈	∈	PROPN
ejpam-3704	179	9	y	y	PROPN
ejpam-3704	179	10	~	~	PROPN
ejpam-3704	179	11	x	x	SYM
ejpam-3704	179	12	such	such	ADJ
ejpam-3704	179	13	that	that	SCONJ
ejpam-3704	179	14	f(v	f(v	NOUN
ejpam-3704	179	15	)	)	PUNCT
ejpam-3704	179	16	=	=	VERB
ejpam-3704	179	17	0′.	0′.	NOUN
ejpam-3704	179	18	moreover	moreover	ADV
ejpam-3704	179	19	,	,	PUNCT
ejpam-3704	179	20	v	v	NOUN
ejpam-3704	179	21	∈	∈	NOUN
ejpam-3704	179	22	kerf	kerf	NOUN
ejpam-3704	180	1	=	=	PUNCT
ejpam-3704	180	2	i	i	NOUN
ejpam-3704	180	3	=	=	PUNCT
ejpam-3704	181	1	[	[	X
ejpam-3704	181	2	0]θ	0]θ	X
ejpam-3704	181	3	and	and	CCONJ
ejpam-3704	181	4	vθ0	vθ0	NOUN
ejpam-3704	181	5	.	.	PUNCT
ejpam-3704	182	1	thus	thus	ADV
ejpam-3704	182	2	,	,	PUNCT
ejpam-3704	182	3	(	(	PUNCT
ejpam-3704	182	4	y	y	NOUN
ejpam-3704	182	5	~	~	PUNCT
ejpam-3704	182	6	x)θ{0	x)θ{0	NUM
ejpam-3704	182	7	}	}	PUNCT
ejpam-3704	182	8	.	.	PUNCT
ejpam-3704	183	1	since	since	SCONJ
ejpam-3704	183	2	θ	θ	PROPN
ejpam-3704	183	3	is	be	AUX
ejpam-3704	183	4	a	a	DET
ejpam-3704	183	5	regular	regular	ADJ
ejpam-3704	183	6	congruence	congruence	NOUN
ejpam-3704	183	7	relation	relation	NOUN
ejpam-3704	183	8	,	,	PUNCT
ejpam-3704	183	9	it	it	PRON
ejpam-3704	183	10	follows	follow	VERB
ejpam-3704	183	11	that	that	SCONJ
ejpam-3704	183	12	xθy	xθy	PROPN
ejpam-3704	183	13	.	.	PUNCT
ejpam-3704	184	1	thus	thus	ADV
ejpam-3704	184	2	,	,	PUNCT
ejpam-3704	184	3	ix	ix	ADP
ejpam-3704	185	1	=	=	PROPN
ejpam-3704	185	2	iy	iy	PROPN
ejpam-3704	185	3	.	.	PUNCT
ejpam-3704	186	1	hence	hence	ADV
ejpam-3704	186	2	,	,	PUNCT
ejpam-3704	186	3	f̄	f̄	PROPN
ejpam-3704	186	4	is	be	AUX
ejpam-3704	186	5	one	one	NUM
ejpam-3704	186	6	-	-	PUNCT
ejpam-3704	186	7	to	to	ADP
ejpam-3704	186	8	-	-	PUNCT
ejpam-3704	186	9	one	one	NUM
ejpam-3704	186	10	,	,	PUNCT
ejpam-3704	186	11	thus	thus	ADV
ejpam-3704	186	12	ker	ker	VERB
ejpam-3704	186	13	f̄	f̄	PROPN
ejpam-3704	187	1	=	=	PROPN
ejpam-3704	187	2	(	(	PUNCT
ejpam-3704	187	3	ker	ker	NOUN
ejpam-3704	187	4	f)/i	f)/i	PROPN
ejpam-3704	187	5	⊆	⊆	NUM
ejpam-3704	187	6	h	h	NOUN
ejpam-3704	187	7	/	/	SYM
ejpam-3704	188	1	i	i	PRON
ejpam-3704	188	2	is	be	AUX
ejpam-3704	188	3	trivial	trivial	ADJ
ejpam-3704	188	4	,	,	PUNCT
ejpam-3704	188	5	which	which	PRON
ejpam-3704	188	6	occurs	occur	VERB
ejpam-3704	188	7	if	if	SCONJ
ejpam-3704	188	8	and	and	CCONJ
ejpam-3704	189	1	only	only	ADV
ejpam-3704	189	2	if	if	SCONJ
ejpam-3704	189	3	ker	ker	PROPN
ejpam-3704	189	4	f	f	PROPN
ejpam-3704	189	5	=	=	PROPN
ejpam-3704	189	6	i.	i.	PROPN
ejpam-3704	189	7	clearly	clearly	ADV
ejpam-3704	189	8	,	,	PUNCT
ejpam-3704	189	9	i	i	PRON
ejpam-3704	189	10	m	m	VERB
ejpam-3704	189	11	f̄	f̄	NOUN
ejpam-3704	189	12	=	=	PUNCT
ejpam-3704	190	1	i	i	PRON
ejpam-3704	190	2	m	m	VERB
ejpam-3704	190	3	f	f	PROPN
ejpam-3704	190	4	and	and	CCONJ
ejpam-3704	190	5	f̄	f̄	NOUN
ejpam-3704	190	6	:	:	PUNCT
ejpam-3704	191	1	h	h	X
ejpam-3704	191	2	/	/	SYM
ejpam-3704	192	1	i	i	PRON
ejpam-3704	192	2	−→	−→	VERB
ejpam-3704	193	1	i	i	PRON
ejpam-3704	193	2	m	m	VERB
ejpam-3704	193	3	f	f	VERB
ejpam-3704	193	4	is	be	AUX
ejpam-3704	193	5	onto	onto	ADP
ejpam-3704	193	6	.	.	PUNCT
ejpam-3704	194	1	therefore	therefore	ADV
ejpam-3704	194	2	,	,	PUNCT
ejpam-3704	194	3	h	h	PROPN
ejpam-3704	194	4	/	/	SYM
ejpam-3704	194	5	ker	ker	PROPN
ejpam-3704	194	6	f	f	PROPN
ejpam-3704	194	7	∼=h	∼=h	PROPN
ejpam-3704	194	8	imf	imf	PROPN
ejpam-3704	194	9	.	.	PUNCT
ejpam-3704	195	1	lemma	lemma	PROPN
ejpam-3704	195	2	5	5	X
ejpam-3704	195	3	.	.	PUNCT
ejpam-3704	196	1	let	let	VERB
ejpam-3704	196	2	f	f	NOUN
ejpam-3704	196	3	:	:	PUNCT
ejpam-3704	196	4	h	h	PROPN
ejpam-3704	196	5	−→	−→	ADJ
ejpam-3704	196	6	h	h	NOUN
ejpam-3704	196	7	′	′	NUM
ejpam-3704	196	8	be	be	AUX
ejpam-3704	196	9	a	a	DET
ejpam-3704	196	10	hyper	hyper	ADJ
ejpam-3704	196	11	homomorphism	homomorphism	NOUN
ejpam-3704	196	12	on	on	ADP
ejpam-3704	196	13	hyper	hyper	NOUN
ejpam-3704	196	14	up	up	ADP
ejpam-3704	196	15	-	-	PUNCT
ejpam-3704	196	16	algebras	algebra	VERB
ejpam-3704	197	1	with	with	ADP
ejpam-3704	197	2	i	i	PROPN
ejpam-3704	197	3	=	=	PUNCT
ejpam-3704	198	1	[	[	X
ejpam-3704	198	2	0]θ	0]θ	X
ejpam-3704	198	3	and	and	CCONJ
ejpam-3704	198	4	j	j	NOUN
ejpam-3704	198	5	=	=	PUNCT
ejpam-3704	199	1	[	[	X
ejpam-3704	199	2	0′]θ′	0′]θ′	NOUN
ejpam-3704	199	3	where	where	SCONJ
ejpam-3704	199	4	θ	θ	NOUN
ejpam-3704	199	5	and	and	CCONJ
ejpam-3704	199	6	θ′	θ′	NOUN
ejpam-3704	199	7	are	be	AUX
ejpam-3704	199	8	regular	regular	ADJ
ejpam-3704	199	9	congruence	congruence	NOUN
ejpam-3704	199	10	relations	relation	NOUN
ejpam-3704	199	11	on	on	ADP
ejpam-3704	199	12	h	h	NOUN
ejpam-3704	199	13	and	and	CCONJ
ejpam-3704	199	14	h	h	NOUN
ejpam-3704	199	15	′	′	NOUN
ejpam-3704	199	16	,	,	PUNCT
ejpam-3704	199	17	respectively	respectively	ADV
ejpam-3704	199	18	.	.	PUNCT
ejpam-3704	200	1	suppose	suppose	VERB
ejpam-3704	200	2	that	that	SCONJ
ejpam-3704	200	3	i	i	PRON
ejpam-3704	200	4	⊆	⊆	NUM
ejpam-3704	200	5	ker	ker	NOUN
ejpam-3704	200	6	f	f	X
ejpam-3704	200	7	.	.	PUNCT
ejpam-3704	201	1	then	then	ADV
ejpam-3704	201	2	for	for	ADP
ejpam-3704	201	3	all	all	DET
ejpam-3704	201	4	x	x	NOUN
ejpam-3704	201	5	,	,	PUNCT
ejpam-3704	201	6	y	y	PROPN
ejpam-3704	201	7	∈	∈	PROPN
ejpam-3704	201	8	h	h	NOUN
ejpam-3704	201	9	,	,	PUNCT
ejpam-3704	201	10	xθy	xθy	PROPN
ejpam-3704	201	11	implies	imply	VERB
ejpam-3704	201	12	that	that	SCONJ
ejpam-3704	201	13	f(x)θ′f(y	f(x)θ′f(y	ADJ
ejpam-3704	201	14	)	)	PUNCT
ejpam-3704	201	15	.	.	PUNCT
ejpam-3704	202	1	proof	proof	NOUN
ejpam-3704	202	2	.	.	PUNCT
ejpam-3704	203	1	let	let	VERB
ejpam-3704	203	2	f	f	NOUN
ejpam-3704	203	3	:	:	PUNCT
ejpam-3704	203	4	h	h	PROPN
ejpam-3704	203	5	−→	−→	ADJ
ejpam-3704	203	6	h	h	NOUN
ejpam-3704	203	7	′	′	NUM
ejpam-3704	203	8	be	be	AUX
ejpam-3704	203	9	a	a	DET
ejpam-3704	203	10	hyper	hyper	ADJ
ejpam-3704	203	11	homomorphism	homomorphism	NOUN
ejpam-3704	203	12	with	with	ADP
ejpam-3704	203	13	i	i	PRON
ejpam-3704	203	14	=	=	PUNCT
ejpam-3704	204	1	[	[	X
ejpam-3704	204	2	0]θ	0]θ	X
ejpam-3704	204	3	⊆	⊆	NUM
ejpam-3704	204	4	ker	ker	NOUN
ejpam-3704	204	5	f	f	PROPN
ejpam-3704	204	6	and	and	CCONJ
ejpam-3704	204	7	j	j	PROPN
ejpam-3704	204	8	=	=	PUNCT
ejpam-3704	205	1	[	[	X
ejpam-3704	205	2	0′]θ′	0′]θ′	NOUN
ejpam-3704	205	3	where	where	SCONJ
ejpam-3704	205	4	θ	θ	NOUN
ejpam-3704	205	5	and	and	CCONJ
ejpam-3704	205	6	θ′	θ′	NOUN
ejpam-3704	205	7	are	be	AUX
ejpam-3704	205	8	regular	regular	ADJ
ejpam-3704	205	9	congruence	congruence	NOUN
ejpam-3704	205	10	relations	relation	NOUN
ejpam-3704	205	11	on	on	ADP
ejpam-3704	205	12	h	h	NOUN
ejpam-3704	205	13	and	and	CCONJ
ejpam-3704	205	14	h	h	NOUN
ejpam-3704	205	15	′	′	NOUN
ejpam-3704	205	16	,	,	PUNCT
ejpam-3704	205	17	respectively	respectively	ADV
ejpam-3704	205	18	.	.	PUNCT
ejpam-3704	206	1	let	let	VERB
ejpam-3704	206	2	x	x	PRON
ejpam-3704	206	3	,	,	PUNCT
ejpam-3704	206	4	y	y	PROPN
ejpam-3704	206	5	∈	∈	PROPN
ejpam-3704	206	6	h	h	NOUN
ejpam-3704	206	7	such	such	ADJ
ejpam-3704	206	8	that	that	DET
ejpam-3704	206	9	xθy	xθy	PROPN
ejpam-3704	206	10	.	.	PUNCT
ejpam-3704	207	1	since	since	SCONJ
ejpam-3704	207	2	θ	θ	PROPN
ejpam-3704	207	3	is	be	AUX
ejpam-3704	207	4	a	a	DET
ejpam-3704	207	5	regular	regular	ADJ
ejpam-3704	207	6	congruence	congruence	NOUN
ejpam-3704	207	7	relation	relation	NOUN
ejpam-3704	207	8	,	,	PUNCT
ejpam-3704	207	9	we	we	PRON
ejpam-3704	207	10	have	have	AUX
ejpam-3704	207	11	xθx	xθx	VERB
ejpam-3704	207	12	and	and	CCONJ
ejpam-3704	207	13	(	(	PUNCT
ejpam-3704	207	14	x~	x~	PROPN
ejpam-3704	207	15	x)θ̄(x~	x)θ̄(x~	PROPN
ejpam-3704	208	1	y	y	X
ejpam-3704	208	2	)	)	PUNCT
ejpam-3704	208	3	by	by	ADP
ejpam-3704	208	4	definition	definition	NOUN
ejpam-3704	208	5	3(iii	3(iii	NUM
ejpam-3704	208	6	)	)	PUNCT
ejpam-3704	208	7	.	.	PUNCT
ejpam-3704	209	1	since	since	SCONJ
ejpam-3704	209	2	0	0	NUM
ejpam-3704	209	3	∈	∈	PROPN
ejpam-3704	209	4	x~	x~	PUNCT
ejpam-3704	209	5	x	x	PUNCT
ejpam-3704	209	6	by	by	ADP
ejpam-3704	209	7	proposition	proposition	NOUN
ejpam-3704	209	8	1(iii	1(iii	NUM
ejpam-3704	209	9	)	)	PUNCT
ejpam-3704	209	10	,	,	PUNCT
ejpam-3704	209	11	there	there	PRON
ejpam-3704	209	12	exists	exist	VERB
ejpam-3704	209	13	an	an	DET
ejpam-3704	209	14	element	element	NOUN
ejpam-3704	209	15	u	u	NOUN
ejpam-3704	209	16	∈	∈	PROPN
ejpam-3704	209	17	x~	x~	PROPN
ejpam-3704	209	18	y	y	PROPN
ejpam-3704	209	19	such	such	ADJ
ejpam-3704	209	20	that	that	DET
ejpam-3704	209	21	0θu	0θu	NOUN
ejpam-3704	209	22	.	.	PUNCT
ejpam-3704	210	1	thus	thus	ADV
ejpam-3704	210	2	,	,	PUNCT
ejpam-3704	210	3	u	u	PROPN
ejpam-3704	210	4	∈	∈	PROPN
ejpam-3704	210	5	i	i	NOUN
ejpam-3704	210	6	⊆	⊆	NUM
ejpam-3704	210	7	ker	ker	NOUN
ejpam-3704	210	8	f	f	X
ejpam-3704	210	9	,	,	PUNCT
ejpam-3704	210	10	that	that	ADV
ejpam-3704	210	11	is	is	ADV
ejpam-3704	210	12	,	,	PUNCT
ejpam-3704	210	13	f(u	f(u	PROPN
ejpam-3704	210	14	)	)	PUNCT
ejpam-3704	211	1	=	=	NOUN
ejpam-3704	211	2	0′.	0′.	NOUN
ejpam-3704	212	1	it	it	PRON
ejpam-3704	212	2	follows	follow	VERB
ejpam-3704	213	1	that	that	SCONJ
ejpam-3704	213	2	f(u	f(u	PROPN
ejpam-3704	213	3	)	)	PUNCT
ejpam-3704	213	4	∈	∈	PROPN
ejpam-3704	213	5	h	h	NOUN
ejpam-3704	213	6	′	′	NOUN
ejpam-3704	214	1	and	and	CCONJ
ejpam-3704	214	2	f(u)θ′0′.	f(u)θ′0′.	PROPN
ejpam-3704	214	3	since	since	SCONJ
ejpam-3704	214	4	f	f	PROPN
ejpam-3704	214	5	is	be	AUX
ejpam-3704	214	6	a	a	DET
ejpam-3704	214	7	hyper	hyper	ADJ
ejpam-3704	214	8	homomorphism	homomorphism	NOUN
ejpam-3704	214	9	,	,	PUNCT
ejpam-3704	214	10	f(u	f(u	PROPN
ejpam-3704	214	11	)	)	PUNCT
ejpam-3704	214	12	∈	∈	PROPN
ejpam-3704	214	13	f(x	f(x	PROPN
ejpam-3704	214	14	~	~	SYM
ejpam-3704	214	15	y	y	NOUN
ejpam-3704	214	16	)	)	PUNCT
ejpam-3704	214	17	=	=	SYM
ejpam-3704	214	18	f(x)~′f(y	f(x)~′f(y	PROPN
ejpam-3704	214	19	)	)	PUNCT
ejpam-3704	214	20	,	,	PUNCT
ejpam-3704	214	21	thus	thus	ADV
ejpam-3704	214	22	(	(	PUNCT
ejpam-3704	214	23	f(x	f(x	PROPN
ejpam-3704	214	24	)	)	PUNCT
ejpam-3704	214	25	~′	~′	NOUN
ejpam-3704	214	26	f(y))θ̄′{0′	f(y))θ̄′{0′	PROPN
ejpam-3704	214	27	}	}	PUNCT
ejpam-3704	214	28	.	.	PUNCT
ejpam-3704	215	1	using	use	VERB
ejpam-3704	215	2	similar	similar	ADJ
ejpam-3704	215	3	argument	argument	NOUN
ejpam-3704	215	4	,	,	PUNCT
ejpam-3704	215	5	with	with	ADP
ejpam-3704	215	6	yθy	yθy	NOUN
ejpam-3704	215	7	,	,	PUNCT
ejpam-3704	215	8	we	we	PRON
ejpam-3704	215	9	have	have	VERB
ejpam-3704	215	10	(	(	PUNCT
ejpam-3704	215	11	f(y	f(y	NOUN
ejpam-3704	215	12	)	)	PUNCT
ejpam-3704	215	13	~′	~′	NOUN
ejpam-3704	215	14	f(x))θ̄′{0′	f(x))θ̄′{0′	NOUN
ejpam-3704	215	15	}	}	PUNCT
ejpam-3704	215	16	.	.	PUNCT
ejpam-3704	216	1	since	since	SCONJ
ejpam-3704	216	2	θ′	θ′	NOUN
ejpam-3704	216	3	is	be	AUX
ejpam-3704	216	4	a	a	DET
ejpam-3704	216	5	regular	regular	ADJ
ejpam-3704	216	6	congruence	congruence	NOUN
ejpam-3704	216	7	relation	relation	NOUN
ejpam-3704	216	8	,	,	PUNCT
ejpam-3704	216	9	by	by	ADP
ejpam-3704	216	10	definition	definition	NOUN
ejpam-3704	216	11	3(iv	3(iv	NUM
ejpam-3704	216	12	)	)	PUNCT
ejpam-3704	216	13	we	we	PRON
ejpam-3704	216	14	have	have	VERB
ejpam-3704	216	15	f(x)θ′f(y	f(x)θ′f(y	ADJ
ejpam-3704	216	16	)	)	PUNCT
ejpam-3704	216	17	.	.	PUNCT
ejpam-3704	217	1	r.	r.	PROPN
ejpam-3704	217	2	amairanto	amairanto	PROPN
ejpam-3704	217	3	,	,	PUNCT
ejpam-3704	217	4	r.	r.	PROPN
ejpam-3704	217	5	isla	isla	PROPN
ejpam-3704	217	6	/	/	SYM
ejpam-3704	217	7	eur	eur	PROPN
ejpam-3704	217	8	.	.	PUNCT
ejpam-3704	218	1	j.	j.	PROPN
ejpam-3704	218	2	pure	pure	PROPN
ejpam-3704	218	3	appl	appl	PROPN
ejpam-3704	218	4	.	.	PROPN
ejpam-3704	218	5	math	math	PROPN
ejpam-3704	218	6	,	,	PUNCT
ejpam-3704	218	7	13	13	NUM
ejpam-3704	218	8	(	(	PUNCT
ejpam-3704	218	9	3	3	NUM
ejpam-3704	218	10	)	)	PUNCT
ejpam-3704	218	11	(	(	PUNCT
ejpam-3704	218	12	2020	2020	NUM
ejpam-3704	218	13	)	)	PUNCT
ejpam-3704	218	14	,	,	PUNCT
ejpam-3704	218	15	483	483	NUM
ejpam-3704	218	16	-	-	SYM
ejpam-3704	218	17	497	497	NUM
ejpam-3704	218	18	489	489	NUM
ejpam-3704	218	19	theorem	theorem	NOUN
ejpam-3704	218	20	5	5	NUM
ejpam-3704	218	21	.	.	PUNCT
ejpam-3704	219	1	let	let	VERB
ejpam-3704	219	2	θ	θ	NOUN
ejpam-3704	219	3	and	and	CCONJ
ejpam-3704	219	4	θ′	θ′	NOUN
ejpam-3704	219	5	be	be	AUX
ejpam-3704	219	6	regular	regular	ADJ
ejpam-3704	219	7	congruence	congruence	NOUN
ejpam-3704	219	8	relations	relation	NOUN
ejpam-3704	219	9	on	on	ADP
ejpam-3704	219	10	hyper	hyper	ADJ
ejpam-3704	219	11	up	up	ADP
ejpam-3704	219	12	-	-	PUNCT
ejpam-3704	219	13	algebras	algebras	NOUN
ejpam-3704	219	14	h	h	PROPN
ejpam-3704	219	15	and	and	CCONJ
ejpam-3704	219	16	h	h	NOUN
ejpam-3704	219	17	′	′	NOUN
ejpam-3704	219	18	,	,	PUNCT
ejpam-3704	219	19	respectively	respectively	ADV
ejpam-3704	219	20	,	,	PUNCT
ejpam-3704	220	1	such	such	ADJ
ejpam-3704	220	2	that	that	SCONJ
ejpam-3704	220	3	i	i	PRON
ejpam-3704	220	4	=	=	PUNCT
ejpam-3704	221	1	[	[	X
ejpam-3704	221	2	0]θ	0]θ	X
ejpam-3704	221	3	and	and	CCONJ
ejpam-3704	221	4	j	j	NOUN
ejpam-3704	221	5	=	=	PUNCT
ejpam-3704	222	1	[	[	X
ejpam-3704	222	2	0′]θ′	0′]θ′	NOUN
ejpam-3704	222	3	.	.	PUNCT
ejpam-3704	223	1	if	if	SCONJ
ejpam-3704	223	2	f	f	PRON
ejpam-3704	223	3	:	:	PUNCT
ejpam-3704	223	4	h	h	PROPN
ejpam-3704	223	5	−→	−→	ADJ
ejpam-3704	223	6	h	h	NOUN
ejpam-3704	223	7	′	′	NOUN
ejpam-3704	223	8	is	be	AUX
ejpam-3704	223	9	a	a	DET
ejpam-3704	223	10	hyper	hyper	ADJ
ejpam-3704	223	11	homomorphism	homomorphism	NOUN
ejpam-3704	223	12	of	of	ADP
ejpam-3704	223	13	hyper	hyper	ADJ
ejpam-3704	223	14	up	up	ADP
ejpam-3704	223	15	-	-	PUNCT
ejpam-3704	223	16	algebras	algebra	NOUN
ejpam-3704	223	17	such	such	ADJ
ejpam-3704	223	18	that	that	SCONJ
ejpam-3704	223	19	xθy	xθy	PROPN
ejpam-3704	224	1	if	if	SCONJ
ejpam-3704	224	2	and	and	CCONJ
ejpam-3704	224	3	only	only	ADV
ejpam-3704	224	4	if	if	SCONJ
ejpam-3704	224	5	f(x)θ′f(y	f(x)θ′f(y	ADJ
ejpam-3704	224	6	)	)	PUNCT
ejpam-3704	224	7	,	,	PUNCT
ejpam-3704	224	8	for	for	ADP
ejpam-3704	224	9	all	all	DET
ejpam-3704	224	10	x	x	NOUN
ejpam-3704	224	11	,	,	PUNCT
ejpam-3704	224	12	y	y	PROPN
ejpam-3704	224	13	∈	∈	PROPN
ejpam-3704	224	14	h	h	NOUN
ejpam-3704	224	15	,	,	PUNCT
ejpam-3704	224	16	then	then	ADV
ejpam-3704	224	17	there	there	PRON
ejpam-3704	224	18	exists	exist	VERB
ejpam-3704	224	19	a	a	DET
ejpam-3704	224	20	unique	unique	ADJ
ejpam-3704	224	21	hyper	hyper	ADJ
ejpam-3704	224	22	homomorphism	homomorphism	NOUN
ejpam-3704	224	23	f∗	f∗	NOUN
ejpam-3704	224	24	:	:	PUNCT
ejpam-3704	224	25	h	h	X
ejpam-3704	224	26	/	/	SYM
ejpam-3704	224	27	i	i	PRON
ejpam-3704	224	28	−→	−→	ADJ
ejpam-3704	224	29	h	h	NOUN
ejpam-3704	224	30	′/j	′/j	NOUN
ejpam-3704	225	1	such	such	ADJ
ejpam-3704	225	2	that	that	DET
ejpam-3704	225	3	π′	π′	VERB
ejpam-3704	225	4	◦	◦	NOUN
ejpam-3704	225	5	f	f	X
ejpam-3704	225	6	=	=	SYM
ejpam-3704	225	7	f∗	f∗	NOUN
ejpam-3704	225	8	◦	◦	NOUN
ejpam-3704	225	9	π	π	X
ejpam-3704	225	10	where	where	SCONJ
ejpam-3704	225	11	π	π	PROPN
ejpam-3704	225	12	and	and	CCONJ
ejpam-3704	225	13	π′	π′	NUM
ejpam-3704	225	14	are	be	AUX
ejpam-3704	225	15	the	the	DET
ejpam-3704	225	16	canonical	canonical	ADJ
ejpam-3704	225	17	epimorphisms	epimorphism	NOUN
ejpam-3704	225	18	and	and	CCONJ
ejpam-3704	225	19	◦	◦	NOUN
ejpam-3704	225	20	is	be	AUX
ejpam-3704	225	21	the	the	DET
ejpam-3704	225	22	composition	composition	NOUN
ejpam-3704	225	23	map	map	NOUN
ejpam-3704	225	24	.	.	PUNCT
ejpam-3704	226	1	h	h	PROPN
ejpam-3704	226	2	f−→	f−→	PROPN
ejpam-3704	226	3	h	h	PROPN
ejpam-3704	226	4	′yπ	′yπ	PROPN
ejpam-3704	226	5	yπ′	yπ′	PROPN
ejpam-3704	226	6	h	h	NOUN
ejpam-3704	226	7	/	/	SYM
ejpam-3704	226	8	i	i	PRON
ejpam-3704	226	9	f∗−→	f∗−→	VERB
ejpam-3704	226	10	h	h	NOUN
ejpam-3704	226	11	′/j	′/j	PROPN
ejpam-3704	226	12	proof	proof	NOUN
ejpam-3704	226	13	.	.	PUNCT
ejpam-3704	227	1	consider	consider	VERB
ejpam-3704	227	2	the	the	DET
ejpam-3704	227	3	mapping	mapping	NOUN
ejpam-3704	227	4	f∗	f∗	NOUN
ejpam-3704	227	5	:	:	PUNCT
ejpam-3704	227	6	h	h	X
ejpam-3704	227	7	/	/	SYM
ejpam-3704	227	8	i	i	PRON
ejpam-3704	227	9	−→	−→	ADJ
ejpam-3704	227	10	h	h	NOUN
ejpam-3704	227	11	′/j	′/j	PROPN
ejpam-3704	227	12	defined	define	VERB
ejpam-3704	227	13	by	by	ADP
ejpam-3704	227	14	f∗(ix	f∗(ix	NOUN
ejpam-3704	227	15	)	)	PUNCT
ejpam-3704	227	16	=	=	SYM
ejpam-3704	227	17	jf(x	jf(x	NOUN
ejpam-3704	227	18	)	)	PUNCT
ejpam-3704	227	19	,	,	PUNCT
ejpam-3704	227	20	for	for	ADP
ejpam-3704	227	21	all	all	PRON
ejpam-3704	227	22	x	x	SYM
ejpam-3704	227	23	∈	∈	PROPN
ejpam-3704	227	24	h.	h.	NOUN
ejpam-3704	227	25	let	let	VERB
ejpam-3704	227	26	x	x	PRON
ejpam-3704	227	27	,	,	PUNCT
ejpam-3704	227	28	y	y	PROPN
ejpam-3704	227	29	∈	∈	PROPN
ejpam-3704	227	30	h	h	NOUN
ejpam-3704	227	31	such	such	ADJ
ejpam-3704	227	32	that	that	SCONJ
ejpam-3704	227	33	ix	ix	ADP
ejpam-3704	228	1	=	=	PROPN
ejpam-3704	228	2	iy	iy	PROPN
ejpam-3704	228	3	.	.	PUNCT
ejpam-3704	229	1	then	then	ADV
ejpam-3704	229	2	xθy	xθy	PROPN
ejpam-3704	229	3	and	and	CCONJ
ejpam-3704	229	4	so	so	ADV
ejpam-3704	229	5	f(x)θ′f(y	f(x)θ′f(y	ADJ
ejpam-3704	229	6	)	)	PUNCT
ejpam-3704	229	7	by	by	ADP
ejpam-3704	229	8	assumption	assumption	NOUN
ejpam-3704	229	9	.	.	PUNCT
ejpam-3704	230	1	hence	hence	ADV
ejpam-3704	230	2	,	,	PUNCT
ejpam-3704	230	3	f∗(ix	f∗(ix	NOUN
ejpam-3704	230	4	)	)	PUNCT
ejpam-3704	230	5	=	=	SYM
ejpam-3704	230	6	jf(x	jf(x	X
ejpam-3704	230	7	)	)	PUNCT
ejpam-3704	230	8	=	=	PUNCT
ejpam-3704	230	9	jf(y	jf(y	PRON
ejpam-3704	230	10	)	)	PUNCT
ejpam-3704	231	1	=	=	SYM
ejpam-3704	231	2	f∗(iy	f∗(iy	NOUN
ejpam-3704	231	3	)	)	PUNCT
ejpam-3704	231	4	and	and	CCONJ
ejpam-3704	231	5	f∗	f∗	NOUN
ejpam-3704	231	6	is	be	AUX
ejpam-3704	231	7	well	well	ADV
ejpam-3704	231	8	-	-	PUNCT
ejpam-3704	231	9	defined	define	VERB
ejpam-3704	231	10	.	.	PUNCT
ejpam-3704	232	1	let	let	VERB
ejpam-3704	232	2	ix	ix	ADV
ejpam-3704	232	3	,	,	PUNCT
ejpam-3704	232	4	iy	iy	PROPN
ejpam-3704	232	5	∈	∈	PROPN
ejpam-3704	232	6	h	h	NOUN
ejpam-3704	232	7	/	/	SYM
ejpam-3704	232	8	i	i	PROPN
ejpam-3704	232	9	and	and	CCONJ
ejpam-3704	232	10	jt	jt	PROPN
ejpam-3704	232	11	∈	∈	PROPN
ejpam-3704	233	1	f∗(ix	f∗(ix	PROPN
ejpam-3704	233	2	~	~	PUNCT
ejpam-3704	233	3	iy	iy	PROPN
ejpam-3704	233	4	)	)	PUNCT
ejpam-3704	233	5	.	.	PUNCT
ejpam-3704	234	1	then	then	ADV
ejpam-3704	234	2	there	there	PRON
ejpam-3704	234	3	exists	exist	VERB
ejpam-3704	234	4	an	an	DET
ejpam-3704	234	5	element	element	NOUN
ejpam-3704	234	6	t′	t′	NOUN
ejpam-3704	234	7	∈	∈	NOUN
ejpam-3704	234	8	x	x	X
ejpam-3704	234	9	~	~	PUNCT
ejpam-3704	234	10	y	y	PRON
ejpam-3704	234	11	such	such	ADJ
ejpam-3704	234	12	that	that	SCONJ
ejpam-3704	234	13	jf(t′	jf(t′	PROPN
ejpam-3704	234	14	)	)	PUNCT
ejpam-3704	234	15	=	=	SYM
ejpam-3704	234	16	f∗(it′	f∗(it′	X
ejpam-3704	234	17	)	)	PUNCT
ejpam-3704	234	18	=	=	SYM
ejpam-3704	234	19	jt	jt	PROPN
ejpam-3704	234	20	.	.	PUNCT
ejpam-3704	235	1	now	now	ADV
ejpam-3704	235	2	,	,	PUNCT
ejpam-3704	235	3	t′	t′	NUM
ejpam-3704	235	4	∈	∈	NOUN
ejpam-3704	235	5	x	x	X
ejpam-3704	235	6	~	~	PUNCT
ejpam-3704	235	7	y	y	PROPN
ejpam-3704	235	8	implies	imply	VERB
ejpam-3704	235	9	f(t′	f(t′	PROPN
ejpam-3704	235	10	)	)	PUNCT
ejpam-3704	235	11	∈	∈	PROPN
ejpam-3704	235	12	f(x	f(x	PROPN
ejpam-3704	235	13	~	~	PUNCT
ejpam-3704	235	14	y	y	X
ejpam-3704	235	15	)	)	PUNCT
ejpam-3704	235	16	=	=	SYM
ejpam-3704	235	17	f(x	f(x	PROPN
ejpam-3704	235	18	)	)	PUNCT
ejpam-3704	235	19	~′	~′	NOUN
ejpam-3704	235	20	f(y	f(y	NOUN
ejpam-3704	235	21	)	)	PUNCT
ejpam-3704	235	22	.	.	PUNCT
ejpam-3704	236	1	so	so	ADV
ejpam-3704	236	2	,	,	PUNCT
ejpam-3704	236	3	jt	jt	PROPN
ejpam-3704	236	4	=	=	SYM
ejpam-3704	236	5	jf(t′	jf(t′	PROPN
ejpam-3704	236	6	)	)	PUNCT
ejpam-3704	236	7	∈	∈	PROPN
ejpam-3704	236	8	jf(x	jf(x	PROPN
ejpam-3704	236	9	)	)	PUNCT
ejpam-3704	236	10	~	~	PUNCT
ejpam-3704	237	1	′	′	NUM
ejpam-3704	237	2	jf(y	jf(y	PRON
ejpam-3704	237	3	)	)	PUNCT
ejpam-3704	238	1	=	=	SYM
ejpam-3704	238	2	f∗(ix	f∗(ix	NOUN
ejpam-3704	238	3	)	)	PUNCT
ejpam-3704	238	4	~′	~′	NOUN
ejpam-3704	238	5	f∗(iy	f∗(iy	NOUN
ejpam-3704	238	6	)	)	PUNCT
ejpam-3704	238	7	.	.	PUNCT
ejpam-3704	239	1	hence	hence	ADV
ejpam-3704	239	2	,	,	PUNCT
ejpam-3704	239	3	f∗(ix	f∗(ix	PROPN
ejpam-3704	239	4	~	~	PUNCT
ejpam-3704	239	5	iy	iy	INTJ
ejpam-3704	239	6	)	)	PUNCT
ejpam-3704	239	7	⊆	⊆	NUM
ejpam-3704	239	8	f∗(ix	f∗(ix	NOUN
ejpam-3704	239	9	)	)	PUNCT
ejpam-3704	239	10	~′	~′	NOUN
ejpam-3704	239	11	f∗(iy	f∗(iy	NOUN
ejpam-3704	239	12	)	)	PUNCT
ejpam-3704	239	13	.	.	PUNCT
ejpam-3704	240	1	next	next	ADV
ejpam-3704	240	2	,	,	PUNCT
ejpam-3704	240	3	let	let	VERB
ejpam-3704	240	4	js	js	PROPN
ejpam-3704	240	5	∈	∈	PROPN
ejpam-3704	240	6	f∗(ix	f∗(ix	NOUN
ejpam-3704	240	7	)	)	PUNCT
ejpam-3704	240	8	~′	~′	NOUN
ejpam-3704	240	9	f∗(iy	f∗(iy	NOUN
ejpam-3704	240	10	)	)	PUNCT
ejpam-3704	240	11	=	=	SYM
ejpam-3704	240	12	jf(x	jf(x	NOUN
ejpam-3704	240	13	)	)	PUNCT
ejpam-3704	240	14	~	~	PUNCT
ejpam-3704	240	15	′	′	NUM
ejpam-3704	240	16	jf(y	jf(y	PRON
ejpam-3704	240	17	)	)	PUNCT
ejpam-3704	240	18	.	.	PUNCT
ejpam-3704	241	1	then	then	ADV
ejpam-3704	241	2	s	s	VERB
ejpam-3704	241	3	∈	∈	PROPN
ejpam-3704	241	4	f(x	f(x	PROPN
ejpam-3704	241	5	)	)	PUNCT
ejpam-3704	241	6	~′	~′	NOUN
ejpam-3704	241	7	f(y	f(y	NOUN
ejpam-3704	241	8	)	)	PUNCT
ejpam-3704	242	1	=	=	SYM
ejpam-3704	242	2	f(x	f(x	X
ejpam-3704	242	3	~	~	PUNCT
ejpam-3704	242	4	y	y	X
ejpam-3704	242	5	)	)	PUNCT
ejpam-3704	242	6	.	.	PUNCT
ejpam-3704	243	1	now	now	ADV
ejpam-3704	243	2	,	,	PUNCT
ejpam-3704	243	3	s	s	PROPN
ejpam-3704	243	4	∈	∈	PROPN
ejpam-3704	243	5	f(x~	f(x~	PROPN
ejpam-3704	243	6	y	y	PROPN
ejpam-3704	243	7	)	)	PUNCT
ejpam-3704	243	8	implies	imply	VERB
ejpam-3704	243	9	there	there	PRON
ejpam-3704	243	10	exists	exist	VERB
ejpam-3704	243	11	w	w	PROPN
ejpam-3704	243	12	∈	∈	PROPN
ejpam-3704	243	13	x~	x~	PROPN
ejpam-3704	244	1	y	y	PROPN
ejpam-3704	244	2	such	such	ADJ
ejpam-3704	244	3	that	that	SCONJ
ejpam-3704	244	4	f(w	f(w	NOUN
ejpam-3704	244	5	)	)	PUNCT
ejpam-3704	245	1	=	=	SYM
ejpam-3704	245	2	s	s	X
ejpam-3704	245	3	,	,	PUNCT
ejpam-3704	245	4	that	that	ADV
ejpam-3704	245	5	is	is	ADV
ejpam-3704	245	6	,	,	PUNCT
ejpam-3704	245	7	iw	iw	PROPN
ejpam-3704	245	8	∈	∈	NOUN
ejpam-3704	245	9	ix	ix	ADP
ejpam-3704	245	10	~	~	PUNCT
ejpam-3704	245	11	iy	iy	PROPN
ejpam-3704	245	12	and	and	CCONJ
ejpam-3704	245	13	js	js	PROPN
ejpam-3704	245	14	=	=	SYM
ejpam-3704	245	15	jf(w	jf(w	X
ejpam-3704	245	16	)	)	PUNCT
ejpam-3704	245	17	=	=	SYM
ejpam-3704	246	1	f∗(iw	f∗(iw	PROPN
ejpam-3704	246	2	)	)	PUNCT
ejpam-3704	246	3	∈	∈	PROPN
ejpam-3704	246	4	f∗(ix	f∗(ix	NOUN
ejpam-3704	246	5	~	~	PUNCT
ejpam-3704	246	6	iy	iy	PROPN
ejpam-3704	246	7	)	)	PUNCT
ejpam-3704	246	8	.	.	PUNCT
ejpam-3704	247	1	therefore	therefore	ADV
ejpam-3704	247	2	,	,	PUNCT
ejpam-3704	247	3	f∗(ix	f∗(ix	NOUN
ejpam-3704	247	4	)	)	PUNCT
ejpam-3704	247	5	~′	~′	NOUN
ejpam-3704	247	6	f∗(iy	f∗(iy	NOUN
ejpam-3704	247	7	)	)	PUNCT
ejpam-3704	247	8	⊆	⊆	NUM
ejpam-3704	247	9	f∗(ix	f∗(ix	PROPN
ejpam-3704	247	10	~	~	PUNCT
ejpam-3704	247	11	iy	iy	INTJ
ejpam-3704	247	12	)	)	PUNCT
ejpam-3704	247	13	and	and	CCONJ
ejpam-3704	247	14	so	so	ADV
ejpam-3704	247	15	f∗(ix	f∗(ix	PROPN
ejpam-3704	247	16	~	~	PUNCT
ejpam-3704	247	17	iy	iy	INTJ
ejpam-3704	247	18	)	)	PUNCT
ejpam-3704	247	19	=	=	SYM
ejpam-3704	247	20	f∗(ix	f∗(ix	NOUN
ejpam-3704	247	21	)	)	PUNCT
ejpam-3704	247	22	~′	~′	NOUN
ejpam-3704	247	23	f∗(iy	f∗(iy	NOUN
ejpam-3704	247	24	)	)	PUNCT
ejpam-3704	247	25	.	.	PUNCT
ejpam-3704	248	1	moreover	moreover	ADV
ejpam-3704	248	2	,	,	PUNCT
ejpam-3704	248	3	f∗(i	f∗(i	PROPN
ejpam-3704	248	4	)	)	PUNCT
ejpam-3704	248	5	=	=	SYM
ejpam-3704	248	6	jf(0	jf(0	PROPN
ejpam-3704	248	7	)	)	PUNCT
ejpam-3704	249	1	=	=	NOUN
ejpam-3704	249	2	j0′	j0′	NOUN
ejpam-3704	249	3	=	=	SYM
ejpam-3704	249	4	j.	j.	PROPN
ejpam-3704	249	5	also	also	ADV
ejpam-3704	249	6	,	,	PUNCT
ejpam-3704	249	7	dom(π′	dom(π′	PUNCT
ejpam-3704	249	8	◦	◦	NOUN
ejpam-3704	249	9	f	f	X
ejpam-3704	249	10	)	)	PUNCT
ejpam-3704	250	1	=	=	SYM
ejpam-3704	250	2	h	h	NOUN
ejpam-3704	251	1	=	=	SYM
ejpam-3704	251	2	dom(f∗	dom(f∗	PROPN
ejpam-3704	251	3	◦	◦	NOUN
ejpam-3704	251	4	π	π	NOUN
ejpam-3704	251	5	)	)	PUNCT
ejpam-3704	251	6	.	.	PUNCT
ejpam-3704	252	1	let	let	VERB
ejpam-3704	252	2	x	x	SYM
ejpam-3704	252	3	∈	∈	PROPN
ejpam-3704	252	4	h.	h.	NOUN
ejpam-3704	252	5	then	then	ADV
ejpam-3704	252	6	(	(	PUNCT
ejpam-3704	252	7	π′	π′	NOUN
ejpam-3704	252	8	◦	◦	NOUN
ejpam-3704	252	9	f)(x	f)(x	NOUN
ejpam-3704	252	10	)	)	PUNCT
ejpam-3704	252	11	=	=	SYM
ejpam-3704	252	12	π′(f(x	π′(f(x	NOUN
ejpam-3704	252	13	)	)	PUNCT
ejpam-3704	252	14	)	)	PUNCT
ejpam-3704	252	15	=	=	SYM
ejpam-3704	253	1	jf(x	jf(x	X
ejpam-3704	253	2	)	)	PUNCT
ejpam-3704	253	3	=	=	SYM
ejpam-3704	253	4	f∗(ix	f∗(ix	NOUN
ejpam-3704	253	5	)	)	PUNCT
ejpam-3704	253	6	=	=	SYM
ejpam-3704	253	7	f∗(π(x	f∗(π(x	PROPN
ejpam-3704	253	8	)	)	PUNCT
ejpam-3704	253	9	)	)	PUNCT
ejpam-3704	254	1	=	=	PUNCT
ejpam-3704	254	2	(	(	PUNCT
ejpam-3704	254	3	f∗	f∗	NOUN
ejpam-3704	254	4	◦	◦	NOUN
ejpam-3704	254	5	π)(x	π)(x	PROPN
ejpam-3704	254	6	)	)	PUNCT
ejpam-3704	254	7	.	.	PUNCT
ejpam-3704	255	1	thus	thus	ADV
ejpam-3704	255	2	,	,	PUNCT
ejpam-3704	255	3	π′	π′	NOUN
ejpam-3704	255	4	◦	◦	NOUN
ejpam-3704	255	5	f	f	X
ejpam-3704	255	6	=	=	SYM
ejpam-3704	255	7	f∗	f∗	NOUN
ejpam-3704	255	8	◦	◦	NOUN
ejpam-3704	255	9	π	π	X
ejpam-3704	255	10	.	.	PUNCT
ejpam-3704	256	1	next	next	ADV
ejpam-3704	256	2	,	,	PUNCT
ejpam-3704	256	3	we	we	PRON
ejpam-3704	256	4	let	let	VERB
ejpam-3704	256	5	φ	φ	NOUN
ejpam-3704	256	6	:	:	PUNCT
ejpam-3704	256	7	h	h	X
ejpam-3704	256	8	/	/	SYM
ejpam-3704	256	9	i	i	PRON
ejpam-3704	256	10	−→	−→	ADJ
ejpam-3704	256	11	h	h	NOUN
ejpam-3704	256	12	′/j	′/j	PROPN
ejpam-3704	256	13	be	be	AUX
ejpam-3704	256	14	a	a	DET
ejpam-3704	256	15	homomorphism	homomorphism	NOUN
ejpam-3704	256	16	such	such	ADJ
ejpam-3704	256	17	that	that	SCONJ
ejpam-3704	256	18	π′	π′	NOUN
ejpam-3704	256	19	◦	◦	NOUN
ejpam-3704	256	20	f	f	X
ejpam-3704	256	21	=	=	SYM
ejpam-3704	256	22	φ	φ	PROPN
ejpam-3704	256	23	◦	◦	PROPN
ejpam-3704	256	24	π	π	PROPN
ejpam-3704	256	25	.	.	PUNCT
ejpam-3704	257	1	note	note	VERB
ejpam-3704	257	2	that	that	PRON
ejpam-3704	257	3	dom(π′	dom(π′	PUNCT
ejpam-3704	258	1	◦	◦	NOUN
ejpam-3704	258	2	f	f	X
ejpam-3704	258	3	)	)	PUNCT
ejpam-3704	259	1	=	=	SYM
ejpam-3704	259	2	h	h	NOUN
ejpam-3704	260	1	=	=	SYM
ejpam-3704	260	2	dom(φ	dom(φ	PROPN
ejpam-3704	260	3	◦	◦	NOUN
ejpam-3704	260	4	π	π	NOUN
ejpam-3704	260	5	)	)	PUNCT
ejpam-3704	260	6	.	.	PUNCT
ejpam-3704	261	1	then	then	ADV
ejpam-3704	261	2	φ	φ	PROPN
ejpam-3704	261	3	=	=	SYM
ejpam-3704	261	4	f∗	f∗	NOUN
ejpam-3704	261	5	since	since	SCONJ
ejpam-3704	261	6	for	for	ADP
ejpam-3704	261	7	all	all	DET
ejpam-3704	261	8	x	x	SYM
ejpam-3704	261	9	∈	∈	PROPN
ejpam-3704	261	10	h	h	NOUN
ejpam-3704	261	11	,	,	PUNCT
ejpam-3704	261	12	we	we	PRON
ejpam-3704	261	13	have	have	VERB
ejpam-3704	261	14	φ(ix	φ(ix	NUM
ejpam-3704	261	15	)	)	PUNCT
ejpam-3704	261	16	=	=	SYM
ejpam-3704	261	17	φ(π(x	φ(π(x	NOUN
ejpam-3704	261	18	)	)	PUNCT
ejpam-3704	261	19	)	)	PUNCT
ejpam-3704	262	1	=	=	SYM
ejpam-3704	262	2	jπ(x	jπ(x	X
ejpam-3704	262	3	)	)	PUNCT
ejpam-3704	262	4	=	=	SYM
ejpam-3704	262	5	π′(f(x	π′(f(x	NOUN
ejpam-3704	262	6	)	)	PUNCT
ejpam-3704	262	7	)	)	PUNCT
ejpam-3704	263	1	=	=	SYM
ejpam-3704	263	2	(	(	PUNCT
ejpam-3704	263	3	π′	π′	NOUN
ejpam-3704	263	4	◦	◦	NOUN
ejpam-3704	263	5	f)(x	f)(x	NOUN
ejpam-3704	263	6	)	)	PUNCT
ejpam-3704	263	7	=	=	SYM
ejpam-3704	263	8	(	(	PUNCT
ejpam-3704	263	9	f∗	f∗	NOUN
ejpam-3704	263	10	◦	◦	NOUN
ejpam-3704	263	11	π)(x	π)(x	NUM
ejpam-3704	263	12	)	)	PUNCT
ejpam-3704	263	13	=	=	SYM
ejpam-3704	263	14	f∗(ix	f∗(ix	NOUN
ejpam-3704	263	15	)	)	PUNCT
ejpam-3704	263	16	.	.	PUNCT
ejpam-3704	264	1	theorem	theorem	ADJ
ejpam-3704	264	2	6	6	NUM
ejpam-3704	264	3	.	.	PUNCT
ejpam-3704	265	1	suppose	suppose	VERB
ejpam-3704	266	1	f	f	X
ejpam-3704	266	2	:	:	PUNCT
ejpam-3704	266	3	h	h	PROPN
ejpam-3704	266	4	−→	−→	ADJ
ejpam-3704	266	5	h	h	NOUN
ejpam-3704	266	6	′	′	NOUN
ejpam-3704	266	7	is	be	AUX
ejpam-3704	266	8	a	a	DET
ejpam-3704	266	9	hyper	hyper	ADJ
ejpam-3704	266	10	epimorphism	epimorphism	NOUN
ejpam-3704	266	11	of	of	ADP
ejpam-3704	266	12	hyper	hyper	ADJ
ejpam-3704	266	13	up	up	ADP
ejpam-3704	266	14	-	-	PUNCT
ejpam-3704	266	15	algebras	algebras	ADV
ejpam-3704	266	16	,	,	PUNCT
ejpam-3704	266	17	θ′	θ′	NUM
ejpam-3704	266	18	is	be	AUX
ejpam-3704	266	19	a	a	DET
ejpam-3704	266	20	regular	regular	ADJ
ejpam-3704	266	21	conruence	conruence	NOUN
ejpam-3704	266	22	relation	relation	NOUN
ejpam-3704	266	23	on	on	ADP
ejpam-3704	266	24	h	h	PROPN
ejpam-3704	266	25	′	′	NOUN
ejpam-3704	266	26	and	and	CCONJ
ejpam-3704	266	27	j	j	PROPN
ejpam-3704	267	1	=	=	PUNCT
ejpam-3704	268	1	[	[	X
ejpam-3704	268	2	0′]θ′.	0′]θ′.	ADV
ejpam-3704	268	3	then	then	ADV
ejpam-3704	268	4	there	there	PRON
ejpam-3704	268	5	exists	exist	VERB
ejpam-3704	268	6	a	a	DET
ejpam-3704	268	7	regular	regular	ADJ
ejpam-3704	268	8	congruence	congruence	NOUN
ejpam-3704	268	9	relation	relation	NOUN
ejpam-3704	268	10	θ	θ	PROPN
ejpam-3704	268	11	on	on	ADP
ejpam-3704	268	12	h	h	PRON
ejpam-3704	268	13	such	such	ADJ
ejpam-3704	268	14	that	that	DET
ejpam-3704	268	15	h	h	NOUN
ejpam-3704	268	16	/	/	SYM
ejpam-3704	268	17	i	i	PROPN
ejpam-3704	268	18	∼=h	∼=h	VERB
ejpam-3704	268	19	h	h	PROPN
ejpam-3704	268	20	′/j	′/j	PROPN
ejpam-3704	268	21	,	,	PUNCT
ejpam-3704	269	1	where	where	SCONJ
ejpam-3704	269	2	i	i	PRON
ejpam-3704	269	3	=	=	PUNCT
ejpam-3704	270	1	[	[	X
ejpam-3704	270	2	0]θ	0]θ	NOUN
ejpam-3704	270	3	.	.	PUNCT
ejpam-3704	271	1	proof	proof	NOUN
ejpam-3704	271	2	.	.	PUNCT
ejpam-3704	272	1	define	define	VERB
ejpam-3704	272	2	θ	θ	PROPN
ejpam-3704	272	3	on	on	ADP
ejpam-3704	272	4	h	h	NOUN
ejpam-3704	272	5	by	by	ADP
ejpam-3704	272	6	xθy	xθy	PROPN
ejpam-3704	272	7	if	if	SCONJ
ejpam-3704	273	1	and	and	CCONJ
ejpam-3704	273	2	only	only	ADV
ejpam-3704	273	3	if	if	SCONJ
ejpam-3704	273	4	f(x)θ′f(y	f(x)θ′f(y	ADJ
ejpam-3704	273	5	)	)	PUNCT
ejpam-3704	273	6	,	,	PUNCT
ejpam-3704	273	7	for	for	ADP
ejpam-3704	273	8	all	all	DET
ejpam-3704	273	9	x	x	NOUN
ejpam-3704	273	10	,	,	PUNCT
ejpam-3704	273	11	y	y	PROPN
ejpam-3704	273	12	∈	∈	PROPN
ejpam-3704	273	13	h.	h.	PROPN
ejpam-3704	273	14	let	let	VERB
ejpam-3704	273	15	x	x	SYM
ejpam-3704	273	16	∈	∈	PROPN
ejpam-3704	273	17	h.	h.	PROPN
ejpam-3704	273	18	then	then	ADV
ejpam-3704	274	1	f(x	f(x	PROPN
ejpam-3704	274	2	)	)	PUNCT
ejpam-3704	274	3	∈	∈	PROPN
ejpam-3704	274	4	h	h	NOUN
ejpam-3704	274	5	′	′	NOUN
ejpam-3704	275	1	and	and	CCONJ
ejpam-3704	275	2	so	so	ADV
ejpam-3704	275	3	,	,	PUNCT
ejpam-3704	275	4	by	by	ADP
ejpam-3704	275	5	reflexivity	reflexivity	NOUN
ejpam-3704	275	6	of	of	ADP
ejpam-3704	275	7	θ′	θ′	NOUN
ejpam-3704	275	8	on	on	ADP
ejpam-3704	275	9	h	h	NOUN
ejpam-3704	275	10	′	′	NOUN
ejpam-3704	275	11	,	,	PUNCT
ejpam-3704	275	12	we	we	PRON
ejpam-3704	275	13	have	have	VERB
ejpam-3704	275	14	f(x)θ′f(x	f(x)θ′f(x	NOUN
ejpam-3704	275	15	)	)	PUNCT
ejpam-3704	275	16	.	.	PUNCT
ejpam-3704	276	1	it	it	PRON
ejpam-3704	276	2	follows	follow	VERB
ejpam-3704	276	3	that	that	PRON
ejpam-3704	276	4	xθx	xθx	PROPN
ejpam-3704	276	5	and	and	CCONJ
ejpam-3704	276	6	θ	θ	PROPN
ejpam-3704	276	7	is	be	AUX
ejpam-3704	276	8	a	a	DET
ejpam-3704	276	9	reflexive	reflexive	ADJ
ejpam-3704	276	10	relation	relation	NOUN
ejpam-3704	276	11	on	on	ADP
ejpam-3704	276	12	h.	h.	PROPN
ejpam-3704	276	13	assume	assume	VERB
ejpam-3704	276	14	that	that	SCONJ
ejpam-3704	276	15	xθy	xθy	PROPN
ejpam-3704	276	16	,	,	PUNCT
ejpam-3704	276	17	where	where	SCONJ
ejpam-3704	276	18	x	x	X
ejpam-3704	276	19	,	,	PUNCT
ejpam-3704	276	20	y	y	PROPN
ejpam-3704	276	21	∈	∈	PROPN
ejpam-3704	276	22	h.	h.	PROPN
ejpam-3704	277	1	so	so	ADV
ejpam-3704	277	2	,	,	PUNCT
ejpam-3704	277	3	f(x	f(x	PROPN
ejpam-3704	277	4	)	)	PUNCT
ejpam-3704	277	5	,	,	PUNCT
ejpam-3704	277	6	f(y	f(y	NOUN
ejpam-3704	277	7	)	)	PUNCT
ejpam-3704	277	8	∈	∈	PROPN
ejpam-3704	277	9	h	h	NOUN
ejpam-3704	277	10	′	′	NOUN
ejpam-3704	277	11	and	and	CCONJ
ejpam-3704	277	12	f(x)θ′f(y	f(x)θ′f(y	ADJ
ejpam-3704	277	13	)	)	PUNCT
ejpam-3704	277	14	.	.	PUNCT
ejpam-3704	278	1	hence	hence	ADV
ejpam-3704	278	2	,	,	PUNCT
ejpam-3704	278	3	f(y)θ′f(x	f(y)θ′f(x	PROPN
ejpam-3704	278	4	)	)	PUNCT
ejpam-3704	278	5	which	which	PRON
ejpam-3704	278	6	will	will	AUX
ejpam-3704	278	7	imply	imply	VERB
ejpam-3704	278	8	that	that	PRON
ejpam-3704	278	9	yθx	yθx	VERB
ejpam-3704	278	10	.	.	PUNCT
ejpam-3704	279	1	thus	thus	ADV
ejpam-3704	279	2	,	,	PUNCT
ejpam-3704	279	3	θ	θ	PROPN
ejpam-3704	279	4	is	be	AUX
ejpam-3704	279	5	a	a	DET
ejpam-3704	279	6	symmetric	symmetric	ADJ
ejpam-3704	279	7	relation	relation	NOUN
ejpam-3704	279	8	on	on	ADP
ejpam-3704	279	9	h.	h.	PROPN
ejpam-3704	279	10	suppose	suppose	VERB
ejpam-3704	279	11	xθy	xθy	PROPN
ejpam-3704	279	12	and	and	CCONJ
ejpam-3704	279	13	yθz	yθz	PROPN
ejpam-3704	279	14	,	,	PUNCT
ejpam-3704	279	15	where	where	SCONJ
ejpam-3704	279	16	x	x	X
ejpam-3704	279	17	,	,	PUNCT
ejpam-3704	279	18	y	y	PROPN
ejpam-3704	279	19	,	,	PUNCT
ejpam-3704	279	20	z	z	PROPN
ejpam-3704	279	21	∈	∈	PROPN
ejpam-3704	279	22	h.	h.	PROPN
ejpam-3704	279	23	then	then	ADV
ejpam-3704	279	24	f(x)θ′f(y	f(x)θ′f(y	PROPN
ejpam-3704	279	25	)	)	PUNCT
ejpam-3704	279	26	and	and	CCONJ
ejpam-3704	279	27	f(y)θ′f(z	f(y)θ′f(z	PROPN
ejpam-3704	279	28	)	)	PUNCT
ejpam-3704	279	29	,	,	PUNCT
ejpam-3704	279	30	for	for	ADP
ejpam-3704	279	31	all	all	DET
ejpam-3704	279	32	x	x	NOUN
ejpam-3704	279	33	,	,	PUNCT
ejpam-3704	279	34	y	y	PROPN
ejpam-3704	279	35	,	,	PUNCT
ejpam-3704	279	36	z	z	PROPN
ejpam-3704	279	37	∈	∈	PROPN
ejpam-3704	279	38	h.	h.	PROPN
ejpam-3704	279	39	note	note	VERB
ejpam-3704	279	40	that	that	SCONJ
ejpam-3704	279	41	f(x	f(x	PROPN
ejpam-3704	279	42	)	)	PUNCT
ejpam-3704	279	43	,	,	PUNCT
ejpam-3704	279	44	f(y	f(y	NOUN
ejpam-3704	279	45	)	)	PUNCT
ejpam-3704	279	46	,	,	PUNCT
ejpam-3704	279	47	f(z	f(z	PROPN
ejpam-3704	279	48	)	)	PUNCT
ejpam-3704	280	1	∈	∈	PROPN
ejpam-3704	280	2	h	h	NOUN
ejpam-3704	280	3	′	′	NOUN
ejpam-3704	280	4	and	and	CCONJ
ejpam-3704	280	5	by	by	ADP
ejpam-3704	280	6	transitivity	transitivity	NOUN
ejpam-3704	280	7	of	of	ADP
ejpam-3704	280	8	θ′	θ′	NOUN
ejpam-3704	280	9	on	on	ADP
ejpam-3704	280	10	h	h	NOUN
ejpam-3704	280	11	′	′	NOUN
ejpam-3704	280	12	,	,	PUNCT
ejpam-3704	280	13	we	we	PRON
ejpam-3704	280	14	have	have	VERB
ejpam-3704	280	15	f(x)θ′f(z	f(x)θ′f(z	NOUN
ejpam-3704	280	16	)	)	PUNCT
ejpam-3704	280	17	.	.	PUNCT
ejpam-3704	281	1	thus	thus	ADV
ejpam-3704	281	2	,	,	PUNCT
ejpam-3704	281	3	xθz	xθz	NOUN
ejpam-3704	281	4	on	on	ADP
ejpam-3704	281	5	h	h	NOUN
ejpam-3704	281	6	and	and	CCONJ
ejpam-3704	281	7	θ	θ	PROPN
ejpam-3704	281	8	is	be	AUX
ejpam-3704	281	9	a	a	DET
ejpam-3704	281	10	transitive	transitive	ADJ
ejpam-3704	281	11	relation	relation	NOUN
ejpam-3704	281	12	on	on	ADP
ejpam-3704	281	13	h.	h.	PROPN
ejpam-3704	281	14	therefore	therefore	ADV
ejpam-3704	281	15	,	,	PUNCT
ejpam-3704	281	16	θ	θ	PROPN
ejpam-3704	281	17	is	be	AUX
ejpam-3704	281	18	an	an	DET
ejpam-3704	281	19	equivalence	equivalence	NOUN
ejpam-3704	281	20	relation	relation	NOUN
ejpam-3704	281	21	on	on	ADP
ejpam-3704	281	22	h.	h.	PROPN
ejpam-3704	281	23	next	next	ADV
ejpam-3704	281	24	,	,	PUNCT
ejpam-3704	281	25	we	we	PRON
ejpam-3704	281	26	will	will	AUX
ejpam-3704	281	27	show	show	VERB
ejpam-3704	281	28	that	that	SCONJ
ejpam-3704	281	29	θ	θ	PROPN
ejpam-3704	281	30	is	be	AUX
ejpam-3704	281	31	a	a	DET
ejpam-3704	281	32	congruence	congruence	NOUN
ejpam-3704	281	33	relation	relation	NOUN
ejpam-3704	281	34	.	.	PUNCT
ejpam-3704	282	1	let	let	VERB
ejpam-3704	282	2	a	a	DET
ejpam-3704	282	3	,	,	PUNCT
ejpam-3704	282	4	x	x	NOUN
ejpam-3704	282	5	,	,	PUNCT
ejpam-3704	282	6	y	y	PROPN
ejpam-3704	282	7	∈	∈	PROPN
ejpam-3704	282	8	h	h	NOUN
ejpam-3704	282	9	such	such	ADJ
ejpam-3704	282	10	that	that	DET
ejpam-3704	282	11	xθy	xθy	PROPN
ejpam-3704	282	12	.	.	PUNCT
ejpam-3704	283	1	then	then	ADV
ejpam-3704	283	2	f(x)θ′f(y	f(x)θ′f(y	ADJ
ejpam-3704	283	3	)	)	PUNCT
ejpam-3704	283	4	.	.	PUNCT
ejpam-3704	284	1	since	since	SCONJ
ejpam-3704	284	2	f(a	f(a	PROPN
ejpam-3704	284	3	)	)	PUNCT
ejpam-3704	284	4	,	,	PUNCT
ejpam-3704	284	5	f(x	f(x	PROPN
ejpam-3704	284	6	)	)	PUNCT
ejpam-3704	284	7	,	,	PUNCT
ejpam-3704	284	8	f(y	f(y	NOUN
ejpam-3704	284	9	)	)	PUNCT
ejpam-3704	284	10	∈	∈	PROPN
ejpam-3704	284	11	h	h	NOUN
ejpam-3704	284	12	′	′	NOUN
ejpam-3704	284	13	and	and	CCONJ
ejpam-3704	284	14	θ′	θ′	NOUN
ejpam-3704	284	15	is	be	AUX
ejpam-3704	284	16	a	a	DET
ejpam-3704	284	17	congruence	congruence	NOUN
ejpam-3704	284	18	relation	relation	NOUN
ejpam-3704	284	19	on	on	ADP
ejpam-3704	284	20	h	h	PROPN
ejpam-3704	284	21	′	′	PROPN
ejpam-3704	284	22	,	,	PUNCT
ejpam-3704	284	23	from	from	ADP
ejpam-3704	284	24	r.	r.	PROPN
ejpam-3704	284	25	amairanto	amairanto	PROPN
ejpam-3704	284	26	,	,	PUNCT
ejpam-3704	284	27	r.	r.	PROPN
ejpam-3704	284	28	isla	isla	PROPN
ejpam-3704	284	29	/	/	SYM
ejpam-3704	284	30	eur	eur	PROPN
ejpam-3704	284	31	.	.	PUNCT
ejpam-3704	285	1	j.	j.	PROPN
ejpam-3704	285	2	pure	pure	PROPN
ejpam-3704	285	3	appl	appl	PROPN
ejpam-3704	285	4	.	.	PROPN
ejpam-3704	285	5	math	math	PROPN
ejpam-3704	285	6	,	,	PUNCT
ejpam-3704	285	7	13	13	NUM
ejpam-3704	285	8	(	(	PUNCT
ejpam-3704	285	9	3	3	NUM
ejpam-3704	285	10	)	)	PUNCT
ejpam-3704	285	11	(	(	PUNCT
ejpam-3704	285	12	2020	2020	NUM
ejpam-3704	285	13	)	)	PUNCT
ejpam-3704	285	14	,	,	PUNCT
ejpam-3704	285	15	483	483	NUM
ejpam-3704	285	16	-	-	SYM
ejpam-3704	285	17	497	497	NUM
ejpam-3704	285	18	490	490	NUM
ejpam-3704	285	19	lemma	lemma	PROPN
ejpam-3704	285	20	3	3	NUM
ejpam-3704	285	21	it	it	PRON
ejpam-3704	285	22	follows	follow	VERB
ejpam-3704	285	23	that	that	SCONJ
ejpam-3704	285	24	(	(	PUNCT
ejpam-3704	285	25	f(x	f(x	PROPN
ejpam-3704	285	26	)	)	PUNCT
ejpam-3704	285	27	~	~	PUNCT
ejpam-3704	286	1	f(a))θ̄′(f(y	f(a))θ̄′(f(y	X
ejpam-3704	286	2	)	)	PUNCT
ejpam-3704	286	3	~	~	PUNCT
ejpam-3704	286	4	f(a	f(a	NOUN
ejpam-3704	286	5	)	)	PUNCT
ejpam-3704	286	6	)	)	PUNCT
ejpam-3704	287	1	and	and	CCONJ
ejpam-3704	287	2	(	(	PUNCT
ejpam-3704	287	3	f(a	f(a	NOUN
ejpam-3704	287	4	)	)	PUNCT
ejpam-3704	287	5	~	~	PUNCT
ejpam-3704	287	6	f(x))θ̄′(f(a	f(x))θ̄′(f(a	X
ejpam-3704	287	7	)	)	PUNCT
ejpam-3704	287	8	~	~	SYM
ejpam-3704	287	9	f(y	f(y	NOUN
ejpam-3704	287	10	)	)	PUNCT
ejpam-3704	287	11	)	)	PUNCT
ejpam-3704	287	12	.	.	PUNCT
ejpam-3704	288	1	thus	thus	ADV
ejpam-3704	288	2	,	,	PUNCT
ejpam-3704	288	3	(	(	PUNCT
ejpam-3704	288	4	x	x	X
ejpam-3704	288	5	~	~	PUNCT
ejpam-3704	288	6	a)θ̄(y	a)θ̄(y	X
ejpam-3704	288	7	~	~	PUNCT
ejpam-3704	288	8	a	a	X
ejpam-3704	288	9	)	)	PUNCT
ejpam-3704	288	10	and	and	CCONJ
ejpam-3704	288	11	(	(	PUNCT
ejpam-3704	288	12	a	a	PRON
ejpam-3704	288	13	~	~	PUNCT
ejpam-3704	288	14	x)θ̄(a	x)θ̄(a	PUNCT
ejpam-3704	288	15	~	~	PUNCT
ejpam-3704	288	16	y	y	X
ejpam-3704	288	17	)	)	PUNCT
ejpam-3704	288	18	.	.	PUNCT
ejpam-3704	289	1	therefore	therefore	ADV
ejpam-3704	289	2	,	,	PUNCT
ejpam-3704	289	3	by	by	ADP
ejpam-3704	289	4	lemma	lemma	PROPN
ejpam-3704	289	5	3	3	NUM
ejpam-3704	289	6	,	,	PUNCT
ejpam-3704	289	7	θ	θ	PROPN
ejpam-3704	289	8	is	be	AUX
ejpam-3704	289	9	a	a	DET
ejpam-3704	289	10	congruence	congruence	NOUN
ejpam-3704	289	11	relation	relation	NOUN
ejpam-3704	289	12	on	on	ADP
ejpam-3704	289	13	h.	h.	PROPN
ejpam-3704	289	14	let	let	VERB
ejpam-3704	289	15	x	x	PRON
ejpam-3704	289	16	,	,	PUNCT
ejpam-3704	289	17	y	y	PROPN
ejpam-3704	289	18	∈	∈	PROPN
ejpam-3704	289	19	h	h	NOUN
ejpam-3704	289	20	such	such	ADJ
ejpam-3704	289	21	that	that	SCONJ
ejpam-3704	289	22	(	(	PUNCT
ejpam-3704	289	23	x~	x~	PROPN
ejpam-3704	289	24	y)θ{0	y)θ{0	ADJ
ejpam-3704	289	25	}	}	PUNCT
ejpam-3704	289	26	and	and	CCONJ
ejpam-3704	289	27	(	(	PUNCT
ejpam-3704	289	28	y	y	NOUN
ejpam-3704	289	29	~	~	PUNCT
ejpam-3704	289	30	x)θ{0	x)θ{0	NUM
ejpam-3704	289	31	}	}	PUNCT
ejpam-3704	289	32	.	.	PUNCT
ejpam-3704	290	1	then	then	ADV
ejpam-3704	290	2	f(x	f(x	PROPN
ejpam-3704	290	3	)	)	PUNCT
ejpam-3704	290	4	,	,	PUNCT
ejpam-3704	290	5	f(y	f(y	NOUN
ejpam-3704	290	6	)	)	PUNCT
ejpam-3704	290	7	∈	∈	PROPN
ejpam-3704	290	8	h	h	NOUN
ejpam-3704	290	9	′	′	NOUN
ejpam-3704	291	1	and	and	CCONJ
ejpam-3704	291	2	there	there	PRON
ejpam-3704	291	3	exist	exist	VERB
ejpam-3704	291	4	a	a	DET
ejpam-3704	291	5	∈	∈	NOUN
ejpam-3704	291	6	(	(	PUNCT
ejpam-3704	291	7	x	x	X
ejpam-3704	291	8	~	~	SYM
ejpam-3704	291	9	y	y	NUM
ejpam-3704	291	10	)	)	PUNCT
ejpam-3704	291	11	and	and	CCONJ
ejpam-3704	291	12	b	b	X
ejpam-3704	291	13	∈	∈	PROPN
ejpam-3704	291	14	(	(	PUNCT
ejpam-3704	291	15	y	y	NOUN
ejpam-3704	291	16	~	~	PUNCT
ejpam-3704	291	17	x	x	X
ejpam-3704	291	18	)	)	PUNCT
ejpam-3704	291	19	such	such	ADJ
ejpam-3704	291	20	that	that	SCONJ
ejpam-3704	291	21	aθ0	aθ0	PROPN
ejpam-3704	291	22	and	and	CCONJ
ejpam-3704	291	23	bθ0	bθ0	PROPN
ejpam-3704	291	24	.	.	PUNCT
ejpam-3704	292	1	since	since	SCONJ
ejpam-3704	292	2	f	f	PROPN
ejpam-3704	292	3	is	be	AUX
ejpam-3704	292	4	a	a	DET
ejpam-3704	292	5	hyper	hyper	ADJ
ejpam-3704	292	6	homomorphism	homomorphism	NOUN
ejpam-3704	292	7	and	and	CCONJ
ejpam-3704	292	8	f(0	f(0	NOUN
ejpam-3704	292	9	)	)	PUNCT
ejpam-3704	293	1	=	=	SYM
ejpam-3704	293	2	0′	0′	NUM
ejpam-3704	293	3	,	,	PUNCT
ejpam-3704	293	4	f(a	f(a	NOUN
ejpam-3704	293	5	)	)	PUNCT
ejpam-3704	293	6	∈	∈	PROPN
ejpam-3704	294	1	f(x	f(x	PROPN
ejpam-3704	294	2	~	~	PUNCT
ejpam-3704	294	3	y	y	X
ejpam-3704	294	4	)	)	PUNCT
ejpam-3704	294	5	=	=	SYM
ejpam-3704	294	6	f(x	f(x	PROPN
ejpam-3704	294	7	)	)	PUNCT
ejpam-3704	294	8	~′	~′	NOUN
ejpam-3704	294	9	f(y	f(y	NOUN
ejpam-3704	294	10	)	)	PUNCT
ejpam-3704	294	11	and	and	CCONJ
ejpam-3704	294	12	f(b	f(b	PROPN
ejpam-3704	294	13	)	)	PUNCT
ejpam-3704	294	14	∈	∈	PROPN
ejpam-3704	294	15	f(y	f(y	NOUN
ejpam-3704	294	16	~	~	PUNCT
ejpam-3704	294	17	x	x	X
ejpam-3704	294	18	)	)	PUNCT
ejpam-3704	294	19	=	=	SYM
ejpam-3704	294	20	f(y	f(y	NOUN
ejpam-3704	294	21	)	)	PUNCT
ejpam-3704	294	22	~′	~′	NOUN
ejpam-3704	294	23	f(x	f(x	PROPN
ejpam-3704	294	24	)	)	PUNCT
ejpam-3704	294	25	such	such	ADJ
ejpam-3704	294	26	that	that	DET
ejpam-3704	294	27	f(a)θ′0′	f(a)θ′0′	NOUN
ejpam-3704	294	28	and	and	CCONJ
ejpam-3704	294	29	f(b)θ′0′.	f(b)θ′0′.	PROPN
ejpam-3704	294	30	thus	thus	ADV
ejpam-3704	294	31	,	,	PUNCT
ejpam-3704	294	32	(	(	PUNCT
ejpam-3704	294	33	f(x	f(x	PROPN
ejpam-3704	294	34	)	)	PUNCT
ejpam-3704	294	35	~′	~′	NOUN
ejpam-3704	294	36	f(y))θ′{0′	f(y))θ′{0′	PROPN
ejpam-3704	294	37	}	}	PUNCT
ejpam-3704	294	38	and	and	CCONJ
ejpam-3704	294	39	(	(	PUNCT
ejpam-3704	294	40	f(y	f(y	NOUN
ejpam-3704	294	41	)	)	PUNCT
ejpam-3704	294	42	~′	~′	NOUN
ejpam-3704	294	43	f(x))θ′{0′	f(x))θ′{0′	NOUN
ejpam-3704	294	44	}	}	PUNCT
ejpam-3704	294	45	.	.	PUNCT
ejpam-3704	295	1	since	since	SCONJ
ejpam-3704	295	2	θ′	θ′	NOUN
ejpam-3704	295	3	is	be	AUX
ejpam-3704	295	4	a	a	DET
ejpam-3704	295	5	regular	regular	ADJ
ejpam-3704	295	6	congruence	congruence	NOUN
ejpam-3704	295	7	relation	relation	NOUN
ejpam-3704	295	8	on	on	ADP
ejpam-3704	295	9	h	h	PROPN
ejpam-3704	295	10	′	′	PROPN
ejpam-3704	295	11	,	,	PUNCT
ejpam-3704	295	12	f(x)θ′f(y	f(x)θ′f(y	PROPN
ejpam-3704	295	13	)	)	PUNCT
ejpam-3704	295	14	,	,	PUNCT
ejpam-3704	295	15	implying	imply	VERB
ejpam-3704	295	16	that	that	SCONJ
ejpam-3704	295	17	xθy	xθy	NOUN
ejpam-3704	295	18	.	.	PUNCT
ejpam-3704	296	1	therefore	therefore	ADV
ejpam-3704	296	2	,	,	PUNCT
ejpam-3704	296	3	θ	θ	PROPN
ejpam-3704	296	4	is	be	AUX
ejpam-3704	296	5	a	a	DET
ejpam-3704	296	6	regular	regular	ADJ
ejpam-3704	296	7	congruence	congruence	NOUN
ejpam-3704	296	8	relation	relation	NOUN
ejpam-3704	296	9	on	on	ADP
ejpam-3704	296	10	h.	h.	PROPN
ejpam-3704	296	11	next	next	ADV
ejpam-3704	296	12	,	,	PUNCT
ejpam-3704	296	13	let	let	VERB
ejpam-3704	296	14	x	x	PUNCT
ejpam-3704	296	15	∈	∈	PROPN
ejpam-3704	296	16	i	i	PRON
ejpam-3704	296	17	=	=	PUNCT
ejpam-3704	297	1	[	[	X
ejpam-3704	297	2	0]θ	0]θ	NOUN
ejpam-3704	297	3	.	.	PUNCT
ejpam-3704	298	1	since	since	SCONJ
ejpam-3704	298	2	xθ0	xθ0	NOUN
ejpam-3704	298	3	and	and	CCONJ
ejpam-3704	298	4	f(0	f(0	NOUN
ejpam-3704	298	5	)	)	PUNCT
ejpam-3704	298	6	=	=	SYM
ejpam-3704	298	7	0′	0′	NUM
ejpam-3704	298	8	,	,	PUNCT
ejpam-3704	298	9	f(x)θ′0′.	f(x)θ′0′.	PROPN
ejpam-3704	298	10	it	it	PRON
ejpam-3704	298	11	follows	follow	VERB
ejpam-3704	298	12	that	that	SCONJ
ejpam-3704	298	13	f(x	f(x	PROPN
ejpam-3704	298	14	)	)	PUNCT
ejpam-3704	298	15	∈	∈	PROPN
ejpam-3704	299	1	[	[	X
ejpam-3704	299	2	0′]θ′	0′]θ′	NOUN
ejpam-3704	299	3	=	=	SYM
ejpam-3704	299	4	j	j	PROPN
ejpam-3704	299	5	,	,	PUNCT
ejpam-3704	299	6	so	so	ADV
ejpam-3704	299	7	x	x	SYM
ejpam-3704	299	8	∈	∈	PROPN
ejpam-3704	299	9	f−1(j	f−1(j	PROPN
ejpam-3704	299	10	)	)	PUNCT
ejpam-3704	299	11	.	.	PUNCT
ejpam-3704	300	1	thus	thus	ADV
ejpam-3704	300	2	,	,	PUNCT
ejpam-3704	300	3	i	i	PROPN
ejpam-3704	300	4	⊆	⊆	NUM
ejpam-3704	300	5	f−1(j	f−1(j	NOUN
ejpam-3704	300	6	)	)	PUNCT
ejpam-3704	300	7	.	.	PUNCT
ejpam-3704	301	1	on	on	ADP
ejpam-3704	301	2	the	the	DET
ejpam-3704	301	3	other	other	ADJ
ejpam-3704	301	4	hand	hand	NOUN
ejpam-3704	301	5	,	,	PUNCT
ejpam-3704	301	6	let	let	VERB
ejpam-3704	301	7	y	y	PROPN
ejpam-3704	301	8	∈	∈	PROPN
ejpam-3704	301	9	f−1(j	f−1(j	PROPN
ejpam-3704	301	10	)	)	PUNCT
ejpam-3704	301	11	.	.	PUNCT
ejpam-3704	302	1	then	then	ADV
ejpam-3704	302	2	f(y	f(y	NOUN
ejpam-3704	302	3	)	)	PUNCT
ejpam-3704	302	4	∈	∈	PROPN
ejpam-3704	302	5	j	j	NOUN
ejpam-3704	302	6	=	=	PUNCT
ejpam-3704	303	1	[	[	X
ejpam-3704	303	2	0′]θ′	0′]θ′	NOUN
ejpam-3704	303	3	and	and	CCONJ
ejpam-3704	303	4	f(y)θ′0′.	f(y)θ′0′.	PROPN
ejpam-3704	303	5	hence	hence	ADV
ejpam-3704	303	6	,	,	PUNCT
ejpam-3704	303	7	yθ0	yθ0	PROPN
ejpam-3704	303	8	and	and	CCONJ
ejpam-3704	303	9	y	y	PROPN
ejpam-3704	303	10	∈	∈	PROPN
ejpam-3704	304	1	[	[	X
ejpam-3704	304	2	0]θ	0]θ	X
ejpam-3704	304	3	=	=	SYM
ejpam-3704	304	4	i	i	PROPN
ejpam-3704	304	5	,	,	PUNCT
ejpam-3704	304	6	implying	imply	VERB
ejpam-3704	304	7	that	that	DET
ejpam-3704	304	8	f−1(j	f−1(j	NOUN
ejpam-3704	304	9	)	)	PUNCT
ejpam-3704	304	10	⊆	⊆	NUM
ejpam-3704	304	11	i.	i.	NOUN
ejpam-3704	304	12	thus	thus	ADV
ejpam-3704	304	13	,	,	PUNCT
ejpam-3704	304	14	i	i	PROPN
ejpam-3704	304	15	=	=	SYM
ejpam-3704	304	16	f−1(j	f−1(j	PROPN
ejpam-3704	304	17	)	)	PUNCT
ejpam-3704	304	18	.	.	PUNCT
ejpam-3704	305	1	now	now	ADV
ejpam-3704	305	2	,	,	PUNCT
ejpam-3704	305	3	let	let	VERB
ejpam-3704	305	4	π	π	PRON
ejpam-3704	305	5	:	:	PUNCT
ejpam-3704	305	6	h	h	NOUN
ejpam-3704	306	1	′	′	NUM
ejpam-3704	307	1	−→	−→	ADJ
ejpam-3704	307	2	h	h	NOUN
ejpam-3704	307	3	′/j	′/j	PROPN
ejpam-3704	307	4	be	be	AUX
ejpam-3704	307	5	the	the	DET
ejpam-3704	307	6	canonical	canonical	ADJ
ejpam-3704	307	7	hyper	hyper	ADJ
ejpam-3704	307	8	epimorphism	epimorphism	NOUN
ejpam-3704	307	9	and	and	CCONJ
ejpam-3704	307	10	define	define	VERB
ejpam-3704	307	11	f̄	f̄	NOUN
ejpam-3704	307	12	:	:	PUNCT
ejpam-3704	307	13	h	h	PROPN
ejpam-3704	307	14	−→	−→	ADJ
ejpam-3704	307	15	h	h	NOUN
ejpam-3704	307	16	′/j	′/j	NOUN
ejpam-3704	307	17	by	by	ADP
ejpam-3704	307	18	f̄	f̄	PROPN
ejpam-3704	308	1	=	=	PUNCT
ejpam-3704	308	2	π	π	PROPN
ejpam-3704	308	3	◦	◦	NOUN
ejpam-3704	308	4	f	f	X
ejpam-3704	308	5	.	.	PUNCT
ejpam-3704	309	1	since	since	SCONJ
ejpam-3704	309	2	π	π	PROPN
ejpam-3704	309	3	and	and	CCONJ
ejpam-3704	309	4	f	f	PROPN
ejpam-3704	309	5	are	be	AUX
ejpam-3704	309	6	both	both	PRON
ejpam-3704	309	7	hyper	hyper	ADJ
ejpam-3704	309	8	epimorphisms	epimorphism	NOUN
ejpam-3704	309	9	of	of	ADP
ejpam-3704	309	10	hyper	hyper	ADJ
ejpam-3704	309	11	up	up	ADP
ejpam-3704	309	12	-	-	PUNCT
ejpam-3704	309	13	algebras	algebras	X
ejpam-3704	309	14	,	,	PUNCT
ejpam-3704	309	15	by	by	ADP
ejpam-3704	309	16	lemma	lemma	PROPN
ejpam-3704	309	17	1	1	NUM
ejpam-3704	309	18	,	,	PUNCT
ejpam-3704	309	19	f̄	f̄	PROPN
ejpam-3704	309	20	is	be	AUX
ejpam-3704	309	21	a	a	DET
ejpam-3704	309	22	hyper	hyper	ADJ
ejpam-3704	309	23	epimorphism	epimorphism	NOUN
ejpam-3704	309	24	.	.	PUNCT
ejpam-3704	310	1	observe	observe	VERB
ejpam-3704	310	2	that	that	DET
ejpam-3704	310	3	ker	ker	PROPN
ejpam-3704	310	4	f̄	f̄	PROPN
ejpam-3704	310	5	=	=	PUNCT
ejpam-3704	310	6	{	{	PUNCT
ejpam-3704	310	7	x	x	PUNCT
ejpam-3704	310	8	∈	∈	PROPN
ejpam-3704	310	9	h	h	NOUN
ejpam-3704	310	10	:	:	PUNCT
ejpam-3704	310	11	f̄(x	f̄(x	NUM
ejpam-3704	310	12	)	)	PUNCT
ejpam-3704	311	1	=	=	SYM
ejpam-3704	311	2	j	j	PROPN
ejpam-3704	311	3	}	}	PUNCT
ejpam-3704	311	4	=	=	SYM
ejpam-3704	311	5	{	{	PUNCT
ejpam-3704	311	6	x	x	PUNCT
ejpam-3704	311	7	∈	∈	PROPN
ejpam-3704	311	8	h	h	NOUN
ejpam-3704	311	9	:	:	PUNCT
ejpam-3704	311	10	π(f(x	π(f(x	PROPN
ejpam-3704	311	11	)	)	PUNCT
ejpam-3704	311	12	)	)	PUNCT
ejpam-3704	312	1	=	=	PUNCT
ejpam-3704	312	2	j	j	PROPN
ejpam-3704	312	3	}	}	PUNCT
ejpam-3704	312	4	=	=	SYM
ejpam-3704	312	5	{	{	PUNCT
ejpam-3704	312	6	x	x	PUNCT
ejpam-3704	312	7	∈	∈	PROPN
ejpam-3704	312	8	h	h	NOUN
ejpam-3704	312	9	:	:	PUNCT
ejpam-3704	312	10	jf(x	jf(x	X
ejpam-3704	312	11	)	)	PUNCT
ejpam-3704	313	1	=	=	SYM
ejpam-3704	313	2	j	j	PROPN
ejpam-3704	313	3	}	}	PUNCT
ejpam-3704	313	4	=	=	SYM
ejpam-3704	313	5	{	{	PUNCT
ejpam-3704	313	6	x	x	PUNCT
ejpam-3704	313	7	∈	∈	PROPN
ejpam-3704	313	8	h	h	NOUN
ejpam-3704	313	9	:	:	PUNCT
ejpam-3704	313	10	f(x	f(x	PROPN
ejpam-3704	313	11	)	)	PUNCT
ejpam-3704	313	12	∈	∈	PROPN
ejpam-3704	314	1	j	j	PROPN
ejpam-3704	314	2	}	}	PUNCT
ejpam-3704	314	3	=	=	SYM
ejpam-3704	314	4	{	{	PUNCT
ejpam-3704	314	5	x	x	PUNCT
ejpam-3704	314	6	∈	∈	PROPN
ejpam-3704	314	7	h	h	NOUN
ejpam-3704	314	8	:	:	PUNCT
ejpam-3704	314	9	x	x	SYM
ejpam-3704	314	10	∈	∈	PROPN
ejpam-3704	314	11	f−1(j	f−1(j	PROPN
ejpam-3704	314	12	)	)	PUNCT
ejpam-3704	314	13	}	}	PUNCT
ejpam-3704	314	14	=	=	SYM
ejpam-3704	314	15	{	{	PUNCT
ejpam-3704	314	16	x	x	PUNCT
ejpam-3704	314	17	∈	∈	PROPN
ejpam-3704	314	18	h	h	NOUN
ejpam-3704	314	19	:	:	PUNCT
ejpam-3704	314	20	x	x	X
ejpam-3704	314	21	∈	∈	PROPN
ejpam-3704	314	22	i	i	NOUN
ejpam-3704	314	23	}	}	PUNCT
ejpam-3704	314	24	=	=	SYM
ejpam-3704	314	25	i.	i.	NOUN
ejpam-3704	314	26	therefore	therefore	ADV
ejpam-3704	314	27	,	,	PUNCT
ejpam-3704	314	28	by	by	ADP
ejpam-3704	314	29	the	the	DET
ejpam-3704	314	30	first	first	ADJ
ejpam-3704	314	31	hyper	hyper	PROPN
ejpam-3704	314	32	isomorphism	isomorphism	NOUN
ejpam-3704	314	33	theorem	theorem	VERB
ejpam-3704	314	34	,	,	PUNCT
ejpam-3704	314	35	h	h	NOUN
ejpam-3704	314	36	/	/	SYM
ejpam-3704	314	37	i	i	PROPN
ejpam-3704	314	38	∼=h	∼=h	VERB
ejpam-3704	314	39	h	h	PROPN
ejpam-3704	314	40	′/j	′/j	PROPN
ejpam-3704	314	41	.	.	PUNCT
ejpam-3704	315	1	theorem	theorem	ADJ
ejpam-3704	315	2	7	7	NUM
ejpam-3704	315	3	.	.	PUNCT
ejpam-3704	316	1	let	let	VERB
ejpam-3704	316	2	f	f	NOUN
ejpam-3704	316	3	:	:	PUNCT
ejpam-3704	316	4	h	h	PROPN
ejpam-3704	316	5	−→	−→	ADJ
ejpam-3704	316	6	h	h	NOUN
ejpam-3704	316	7	′	′	NUM
ejpam-3704	316	8	be	be	AUX
ejpam-3704	316	9	a	a	DET
ejpam-3704	316	10	hyper	hyper	ADJ
ejpam-3704	316	11	epimorphism	epimorphism	NOUN
ejpam-3704	316	12	on	on	ADP
ejpam-3704	316	13	hyper	hyper	NOUN
ejpam-3704	316	14	up	up	ADP
ejpam-3704	316	15	-	-	PUNCT
ejpam-3704	316	16	algebras	algebras	X
ejpam-3704	316	17	and	and	CCONJ
ejpam-3704	316	18	let	let	VERB
ejpam-3704	316	19	θ	θ	PROPN
ejpam-3704	316	20	and	and	CCONJ
ejpam-3704	316	21	ω	ω	NUM
ejpam-3704	316	22	be	be	AUX
ejpam-3704	316	23	relations	relation	NOUN
ejpam-3704	316	24	on	on	ADP
ejpam-3704	316	25	h	h	NOUN
ejpam-3704	316	26	and	and	CCONJ
ejpam-3704	316	27	h	h	NOUN
ejpam-3704	316	28	′	′	NOUN
ejpam-3704	316	29	,	,	PUNCT
ejpam-3704	316	30	respectively	respectively	ADV
ejpam-3704	316	31	,	,	PUNCT
ejpam-3704	316	32	defined	define	VERB
ejpam-3704	316	33	by	by	ADP
ejpam-3704	316	34	xθy	xθy	PROPN
ejpam-3704	316	35	⇐	⇐	ADJ
ejpam-3704	316	36	⇒	⇒	PROPN
ejpam-3704	316	37	f(x)ωf(y	f(x)ωf(y	NOUN
ejpam-3704	316	38	)	)	PUNCT
ejpam-3704	316	39	for	for	ADP
ejpam-3704	316	40	all	all	DET
ejpam-3704	316	41	x	x	NOUN
ejpam-3704	316	42	,	,	PUNCT
ejpam-3704	316	43	y	y	PROPN
ejpam-3704	316	44	∈	∈	PROPN
ejpam-3704	316	45	h.	h.	NOUN
ejpam-3704	316	46	then	then	ADV
ejpam-3704	316	47	θ	θ	PROPN
ejpam-3704	316	48	is	be	AUX
ejpam-3704	316	49	a	a	DET
ejpam-3704	316	50	regular	regular	ADJ
ejpam-3704	316	51	congruence	congruence	NOUN
ejpam-3704	316	52	relation	relation	NOUN
ejpam-3704	316	53	on	on	ADP
ejpam-3704	316	54	h	h	NOUN
ejpam-3704	316	55	if	if	SCONJ
ejpam-3704	317	1	and	and	CCONJ
ejpam-3704	317	2	only	only	ADV
ejpam-3704	317	3	if	if	SCONJ
ejpam-3704	317	4	ω	ω	PROPN
ejpam-3704	317	5	is	be	AUX
ejpam-3704	317	6	a	a	DET
ejpam-3704	317	7	regular	regular	ADJ
ejpam-3704	317	8	congruence	congruence	NOUN
ejpam-3704	317	9	relation	relation	NOUN
ejpam-3704	317	10	on	on	ADP
ejpam-3704	317	11	h	h	NOUN
ejpam-3704	317	12	′.	′.	PROPN
ejpam-3704	317	13	proof	proof	NOUN
ejpam-3704	317	14	.	.	PUNCT
ejpam-3704	318	1	utilizing	utilize	VERB
ejpam-3704	318	2	the	the	DET
ejpam-3704	318	3	proof	proof	NOUN
ejpam-3704	318	4	of	of	ADP
ejpam-3704	318	5	theorem	theorem	NOUN
ejpam-3704	318	6	6	6	NUM
ejpam-3704	318	7	,	,	PUNCT
ejpam-3704	318	8	we	we	PRON
ejpam-3704	318	9	only	only	ADV
ejpam-3704	318	10	need	need	VERB
ejpam-3704	318	11	to	to	PART
ejpam-3704	318	12	show	show	VERB
ejpam-3704	318	13	that	that	SCONJ
ejpam-3704	318	14	θ	θ	PROPN
ejpam-3704	318	15	is	be	AUX
ejpam-3704	318	16	a	a	DET
ejpam-3704	318	17	regular	regular	ADJ
ejpam-3704	318	18	congruence	congruence	NOUN
ejpam-3704	318	19	relation	relation	NOUN
ejpam-3704	318	20	on	on	ADP
ejpam-3704	318	21	h	h	NOUN
ejpam-3704	318	22	implies	imply	VERB
ejpam-3704	318	23	that	that	SCONJ
ejpam-3704	318	24	ω	ω	PROPN
ejpam-3704	318	25	is	be	AUX
ejpam-3704	318	26	a	a	DET
ejpam-3704	318	27	regular	regular	ADJ
ejpam-3704	318	28	congruence	congruence	NOUN
ejpam-3704	318	29	relation	relation	NOUN
ejpam-3704	318	30	on	on	ADP
ejpam-3704	318	31	h	h	PROPN
ejpam-3704	318	32	′.	′.	PROPN
ejpam-3704	318	33	suppose	suppose	VERB
ejpam-3704	318	34	θ	θ	NOUN
ejpam-3704	318	35	is	be	AUX
ejpam-3704	318	36	a	a	DET
ejpam-3704	318	37	regular	regular	ADJ
ejpam-3704	318	38	congruence	congruence	NOUN
ejpam-3704	318	39	relation	relation	NOUN
ejpam-3704	318	40	on	on	ADP
ejpam-3704	318	41	h.	h.	PROPN
ejpam-3704	318	42	let	let	VERB
ejpam-3704	318	43	u	u	NOUN
ejpam-3704	318	44	,	,	PUNCT
ejpam-3704	318	45	v	v	NOUN
ejpam-3704	318	46	,	,	PUNCT
ejpam-3704	318	47	w	w	PROPN
ejpam-3704	318	48	∈	∈	PROPN
ejpam-3704	318	49	h	h	NOUN
ejpam-3704	318	50	′.	′.	NOUN
ejpam-3704	318	51	then	then	ADV
ejpam-3704	318	52	there	there	PRON
ejpam-3704	318	53	exist	exist	VERB
ejpam-3704	318	54	x	x	NOUN
ejpam-3704	318	55	,	,	PUNCT
ejpam-3704	318	56	y	y	PROPN
ejpam-3704	318	57	,	,	PUNCT
ejpam-3704	318	58	z	z	PROPN
ejpam-3704	318	59	∈	∈	PROPN
ejpam-3704	318	60	h	h	NOUN
ejpam-3704	318	61	such	such	ADJ
ejpam-3704	318	62	that	that	SCONJ
ejpam-3704	318	63	f(x	f(x	NOUN
ejpam-3704	318	64	)	)	PUNCT
ejpam-3704	319	1	=	=	SYM
ejpam-3704	319	2	u	u	NOUN
ejpam-3704	319	3	,	,	PUNCT
ejpam-3704	319	4	f(y	f(y	NOUN
ejpam-3704	319	5	)	)	PUNCT
ejpam-3704	319	6	=	=	SYM
ejpam-3704	319	7	v	v	NOUN
ejpam-3704	319	8	,	,	PUNCT
ejpam-3704	319	9	and	and	CCONJ
ejpam-3704	319	10	f(z	f(z	PROPN
ejpam-3704	319	11	)	)	PUNCT
ejpam-3704	320	1	=	=	SYM
ejpam-3704	320	2	w.	w.	NOUN
ejpam-3704	320	3	since	since	SCONJ
ejpam-3704	320	4	θ	θ	PROPN
ejpam-3704	320	5	is	be	AUX
ejpam-3704	320	6	an	an	DET
ejpam-3704	320	7	equivalence	equivalence	NOUN
ejpam-3704	320	8	relation	relation	NOUN
ejpam-3704	320	9	on	on	ADP
ejpam-3704	320	10	h	h	PROPN
ejpam-3704	320	11	,	,	PUNCT
ejpam-3704	320	12	xθx	xθx	PROPN
ejpam-3704	320	13	,	,	PUNCT
ejpam-3704	320	14	thus	thus	ADV
ejpam-3704	320	15	u	u	NOUN
ejpam-3704	320	16	=	=	NOUN
ejpam-3704	320	17	f(x)ωf(x	f(x)ωf(x	PROPN
ejpam-3704	320	18	)	)	PUNCT
ejpam-3704	320	19	=	=	SYM
ejpam-3704	320	20	u	u	NOUN
ejpam-3704	320	21	and	and	CCONJ
ejpam-3704	320	22	ω	ω	PROPN
ejpam-3704	320	23	is	be	AUX
ejpam-3704	320	24	a	a	DET
ejpam-3704	320	25	reflexive	reflexive	ADJ
ejpam-3704	320	26	relation	relation	NOUN
ejpam-3704	320	27	on	on	ADP
ejpam-3704	320	28	h	h	PROPN
ejpam-3704	320	29	′.	′.	PROPN
ejpam-3704	320	30	suppose	suppose	VERB
ejpam-3704	320	31	uωv	uωv	PROPN
ejpam-3704	320	32	.	.	PROPN
ejpam-3704	321	1	then	then	ADV
ejpam-3704	321	2	xθy	xθy	PROPN
ejpam-3704	321	3	and	and	CCONJ
ejpam-3704	321	4	since	since	SCONJ
ejpam-3704	321	5	θ	θ	PROPN
ejpam-3704	321	6	is	be	AUX
ejpam-3704	321	7	a	a	DET
ejpam-3704	321	8	symmetric	symmetric	ADJ
ejpam-3704	321	9	relation	relation	NOUN
ejpam-3704	321	10	on	on	ADP
ejpam-3704	321	11	h	h	PROPN
ejpam-3704	321	12	,	,	PUNCT
ejpam-3704	321	13	yθx	yθx	NOUN
ejpam-3704	321	14	,	,	PUNCT
ejpam-3704	321	15	so	so	SCONJ
ejpam-3704	321	16	vωu	vωu	NOUN
ejpam-3704	321	17	and	and	CCONJ
ejpam-3704	321	18	ω	ω	PROPN
ejpam-3704	321	19	is	be	AUX
ejpam-3704	321	20	a	a	DET
ejpam-3704	321	21	symmetric	symmetric	ADJ
ejpam-3704	321	22	relation	relation	NOUN
ejpam-3704	321	23	on	on	ADP
ejpam-3704	321	24	h	h	PROPN
ejpam-3704	321	25	′.	′.	PROPN
ejpam-3704	321	26	suppose	suppose	VERB
ejpam-3704	321	27	uωv	uωv	PROPN
ejpam-3704	321	28	and	and	CCONJ
ejpam-3704	321	29	vωw	vωw	NOUN
ejpam-3704	321	30	.	.	PUNCT
ejpam-3704	322	1	then	then	ADV
ejpam-3704	322	2	xθy	xθy	PROPN
ejpam-3704	322	3	and	and	CCONJ
ejpam-3704	322	4	yθz	yθz	PROPN
ejpam-3704	322	5	.	.	PUNCT
ejpam-3704	323	1	since	since	SCONJ
ejpam-3704	323	2	θ	θ	PROPN
ejpam-3704	323	3	is	be	AUX
ejpam-3704	323	4	a	a	DET
ejpam-3704	323	5	transitive	transitive	ADJ
ejpam-3704	323	6	relation	relation	NOUN
ejpam-3704	323	7	on	on	ADP
ejpam-3704	323	8	h	h	PROPN
ejpam-3704	323	9	,	,	PUNCT
ejpam-3704	323	10	xθz	xθz	PROPN
ejpam-3704	323	11	,	,	PUNCT
ejpam-3704	323	12	that	that	ADV
ejpam-3704	323	13	is	is	ADV
ejpam-3704	323	14	,	,	PUNCT
ejpam-3704	323	15	uωw	uωw	PROPN
ejpam-3704	323	16	.	.	PUNCT
ejpam-3704	324	1	thus	thus	ADV
ejpam-3704	324	2	,	,	PUNCT
ejpam-3704	324	3	ω	ω	PROPN
ejpam-3704	324	4	is	be	AUX
ejpam-3704	324	5	an	an	DET
ejpam-3704	324	6	equivalence	equivalence	NOUN
ejpam-3704	324	7	relation	relation	NOUN
ejpam-3704	324	8	on	on	ADP
ejpam-3704	324	9	h	h	PROPN
ejpam-3704	324	10	′.	′.	PROPN
ejpam-3704	324	11	let	let	VERB
ejpam-3704	324	12	b	b	NUM
ejpam-3704	324	13	,	,	PUNCT
ejpam-3704	324	14	u	u	NOUN
ejpam-3704	324	15	,	,	PUNCT
ejpam-3704	324	16	v	v	NOUN
ejpam-3704	324	17	∈	∈	NOUN
ejpam-3704	324	18	h	h	NOUN
ejpam-3704	324	19	′	′	NOUN
ejpam-3704	324	20	and	and	CCONJ
ejpam-3704	324	21	uωv	uωv	PROPN
ejpam-3704	324	22	.	.	PUNCT
ejpam-3704	325	1	then	then	ADV
ejpam-3704	325	2	there	there	PRON
ejpam-3704	325	3	exist	exist	VERB
ejpam-3704	325	4	a	a	DET
ejpam-3704	325	5	,	,	PUNCT
ejpam-3704	325	6	x	x	X
ejpam-3704	325	7	,	,	PUNCT
ejpam-3704	325	8	y	y	PROPN
ejpam-3704	325	9	∈	∈	PROPN
ejpam-3704	325	10	h	h	NOUN
ejpam-3704	325	11	such	such	ADJ
ejpam-3704	325	12	that	that	DET
ejpam-3704	325	13	b	b	X
ejpam-3704	325	14	=	=	SYM
ejpam-3704	325	15	f(a	f(a	PROPN
ejpam-3704	325	16	)	)	PUNCT
ejpam-3704	325	17	,	,	PUNCT
ejpam-3704	325	18	u	u	NOUN
ejpam-3704	325	19	=	=	PROPN
ejpam-3704	325	20	f(x	f(x	PROPN
ejpam-3704	325	21	)	)	PUNCT
ejpam-3704	325	22	,	,	PUNCT
ejpam-3704	325	23	v	v	X
ejpam-3704	325	24	=	=	SYM
ejpam-3704	325	25	f(y	f(y	NOUN
ejpam-3704	325	26	)	)	PUNCT
ejpam-3704	325	27	,	,	PUNCT
ejpam-3704	325	28	and	and	CCONJ
ejpam-3704	325	29	xθy	xθy	PROPN
ejpam-3704	325	30	.	.	PUNCT
ejpam-3704	326	1	since	since	SCONJ
ejpam-3704	326	2	θ	θ	PROPN
ejpam-3704	326	3	is	be	AUX
ejpam-3704	326	4	a	a	DET
ejpam-3704	326	5	congruence	congruence	NOUN
ejpam-3704	326	6	relation	relation	NOUN
ejpam-3704	326	7	on	on	ADP
ejpam-3704	326	8	h	h	NOUN
ejpam-3704	326	9	and	and	CCONJ
ejpam-3704	326	10	a	a	DET
ejpam-3704	326	11	∈	∈	PROPN
ejpam-3704	326	12	h	h	NOUN
ejpam-3704	326	13	,	,	PUNCT
ejpam-3704	326	14	(	(	PUNCT
ejpam-3704	326	15	a	a	DET
ejpam-3704	326	16	~	~	PUNCT
ejpam-3704	326	17	x)θ̄(a	x)θ̄(a	PUNCT
ejpam-3704	326	18	~	~	PUNCT
ejpam-3704	326	19	y	y	X
ejpam-3704	326	20	)	)	PUNCT
ejpam-3704	326	21	by	by	ADP
ejpam-3704	326	22	r.	r.	PROPN
ejpam-3704	326	23	amairanto	amairanto	PROPN
ejpam-3704	326	24	,	,	PUNCT
ejpam-3704	326	25	r.	r.	PROPN
ejpam-3704	326	26	isla	isla	PROPN
ejpam-3704	326	27	/	/	SYM
ejpam-3704	326	28	eur	eur	PROPN
ejpam-3704	326	29	.	.	PUNCT
ejpam-3704	327	1	j.	j.	PROPN
ejpam-3704	327	2	pure	pure	PROPN
ejpam-3704	327	3	appl	appl	PROPN
ejpam-3704	327	4	.	.	PROPN
ejpam-3704	327	5	math	math	PROPN
ejpam-3704	327	6	,	,	PUNCT
ejpam-3704	327	7	13	13	NUM
ejpam-3704	327	8	(	(	PUNCT
ejpam-3704	327	9	3	3	NUM
ejpam-3704	327	10	)	)	PUNCT
ejpam-3704	327	11	(	(	PUNCT
ejpam-3704	327	12	2020	2020	NUM
ejpam-3704	327	13	)	)	PUNCT
ejpam-3704	327	14	,	,	PUNCT
ejpam-3704	327	15	483	483	NUM
ejpam-3704	327	16	-	-	SYM
ejpam-3704	327	17	497	497	NUM
ejpam-3704	327	18	491	491	NUM
ejpam-3704	327	19	lemma	lemma	PROPN
ejpam-3704	327	20	3	3	NUM
ejpam-3704	327	21	.	.	PUNCT
ejpam-3704	328	1	hence	hence	ADV
ejpam-3704	328	2	,	,	PUNCT
ejpam-3704	328	3	f(a)~′	f(a)~′	NOUN
ejpam-3704	328	4	f(x	f(x	PROPN
ejpam-3704	328	5	)	)	PUNCT
ejpam-3704	329	1	=	=	PUNCT
ejpam-3704	330	1	f(a~	f(a~	PROPN
ejpam-3704	330	2	x)ω̄f(a~	x)ω̄f(a~	PROPN
ejpam-3704	330	3	y	y	NOUN
ejpam-3704	330	4	)	)	PUNCT
ejpam-3704	330	5	=	=	SYM
ejpam-3704	330	6	f(a)~′	f(a)~′	NOUN
ejpam-3704	330	7	f(y	f(y	NOUN
ejpam-3704	330	8	)	)	PUNCT
ejpam-3704	330	9	,	,	PUNCT
ejpam-3704	330	10	that	that	ADV
ejpam-3704	330	11	is	is	ADV
ejpam-3704	330	12	,	,	PUNCT
ejpam-3704	330	13	(	(	PUNCT
ejpam-3704	330	14	b~′	b~′	PROPN
ejpam-3704	330	15	u)ω̄(b~′	u)ω̄(b~′	PROPN
ejpam-3704	330	16	v	v	NOUN
ejpam-3704	330	17	)	)	PUNCT
ejpam-3704	330	18	.	.	PUNCT
ejpam-3704	331	1	similarly	similarly	ADV
ejpam-3704	331	2	,	,	PUNCT
ejpam-3704	331	3	since	since	SCONJ
ejpam-3704	331	4	θ	θ	PROPN
ejpam-3704	331	5	is	be	AUX
ejpam-3704	331	6	a	a	DET
ejpam-3704	331	7	congruence	congruence	NOUN
ejpam-3704	331	8	relation	relation	NOUN
ejpam-3704	331	9	on	on	ADP
ejpam-3704	331	10	h	h	NOUN
ejpam-3704	331	11	and	and	CCONJ
ejpam-3704	331	12	a	a	DET
ejpam-3704	331	13	∈	∈	PROPN
ejpam-3704	331	14	h	h	NOUN
ejpam-3704	331	15	,	,	PUNCT
ejpam-3704	331	16	(	(	PUNCT
ejpam-3704	331	17	x	x	X
ejpam-3704	331	18	~	~	PUNCT
ejpam-3704	331	19	a)θ̄(y	a)θ̄(y	X
ejpam-3704	331	20	~	~	PUNCT
ejpam-3704	331	21	a	a	X
ejpam-3704	331	22	)	)	PUNCT
ejpam-3704	331	23	.	.	PUNCT
ejpam-3704	332	1	so	so	ADV
ejpam-3704	332	2	,	,	PUNCT
ejpam-3704	332	3	f(x	f(x	PROPN
ejpam-3704	332	4	)	)	PUNCT
ejpam-3704	332	5	~′	~′	NOUN
ejpam-3704	332	6	f(a	f(a	NOUN
ejpam-3704	332	7	)	)	PUNCT
ejpam-3704	333	1	=	=	SYM
ejpam-3704	333	2	f(x~	f(x~	ADJ
ejpam-3704	333	3	a)ω̄f(y	a)ω̄f(y	NOUN
ejpam-3704	333	4	~	~	PUNCT
ejpam-3704	333	5	a	a	X
ejpam-3704	333	6	)	)	PUNCT
ejpam-3704	333	7	=	=	SYM
ejpam-3704	333	8	f(y	f(y	NOUN
ejpam-3704	333	9	)	)	PUNCT
ejpam-3704	333	10	~′	~′	NOUN
ejpam-3704	333	11	f(a	f(a	PROPN
ejpam-3704	333	12	)	)	PUNCT
ejpam-3704	333	13	,	,	PUNCT
ejpam-3704	333	14	that	that	ADV
ejpam-3704	333	15	is	is	ADV
ejpam-3704	333	16	,	,	PUNCT
ejpam-3704	333	17	(	(	PUNCT
ejpam-3704	333	18	u~′	u~′	ADJ
ejpam-3704	333	19	b)ω̄(v	b)ω̄(v	PROPN
ejpam-3704	333	20	~′	~′	NOUN
ejpam-3704	333	21	b	b	NOUN
ejpam-3704	333	22	)	)	PUNCT
ejpam-3704	333	23	.	.	PUNCT
ejpam-3704	334	1	hence	hence	ADV
ejpam-3704	334	2	,	,	PUNCT
ejpam-3704	334	3	ω	ω	PROPN
ejpam-3704	334	4	is	be	AUX
ejpam-3704	334	5	a	a	DET
ejpam-3704	334	6	congruence	congruence	NOUN
ejpam-3704	334	7	relation	relation	NOUN
ejpam-3704	334	8	on	on	ADP
ejpam-3704	334	9	h	h	PROPN
ejpam-3704	334	10	′.	′.	PROPN
ejpam-3704	334	11	now	now	ADV
ejpam-3704	334	12	,	,	PUNCT
ejpam-3704	334	13	let	let	VERB
ejpam-3704	334	14	u	u	NOUN
ejpam-3704	334	15	,	,	PUNCT
ejpam-3704	334	16	v	v	PROPN
ejpam-3704	334	17	∈	∈	NOUN
ejpam-3704	334	18	h	h	NOUN
ejpam-3704	334	19	′	′	NUM
ejpam-3704	334	20	such	such	ADJ
ejpam-3704	334	21	that	that	PRON
ejpam-3704	334	22	(	(	PUNCT
ejpam-3704	334	23	u	u	NOUN
ejpam-3704	334	24	~′	~′	NOUN
ejpam-3704	334	25	v)ω{0′	v)ω{0′	NOUN
ejpam-3704	334	26	}	}	PUNCT
ejpam-3704	334	27	and	and	CCONJ
ejpam-3704	334	28	(	(	PUNCT
ejpam-3704	334	29	v	v	NUM
ejpam-3704	334	30	~′	~′	NOUN
ejpam-3704	334	31	u)ω{0′	u)ω{0′	NOUN
ejpam-3704	334	32	}	}	PUNCT
ejpam-3704	334	33	.	.	PUNCT
ejpam-3704	335	1	since	since	SCONJ
ejpam-3704	335	2	(	(	PUNCT
ejpam-3704	335	3	u	u	NOUN
ejpam-3704	335	4	~′	~′	NOUN
ejpam-3704	335	5	v)ω{0′	v)ω{0′	NOUN
ejpam-3704	335	6	}	}	PUNCT
ejpam-3704	335	7	and	and	CCONJ
ejpam-3704	335	8	f	f	PROPN
ejpam-3704	335	9	is	be	AUX
ejpam-3704	335	10	a	a	DET
ejpam-3704	335	11	hyper	hyper	ADJ
ejpam-3704	335	12	epimorphism	epimorphism	NOUN
ejpam-3704	335	13	,	,	PUNCT
ejpam-3704	335	14	it	it	PRON
ejpam-3704	335	15	follows	follow	VERB
ejpam-3704	335	16	that	that	SCONJ
ejpam-3704	335	17	there	there	PRON
ejpam-3704	335	18	exist	exist	VERB
ejpam-3704	335	19	s	s	PROPN
ejpam-3704	335	20	,	,	PUNCT
ejpam-3704	335	21	t	t	PROPN
ejpam-3704	335	22	∈	∈	PROPN
ejpam-3704	335	23	h	h	NOUN
ejpam-3704	335	24	such	such	ADJ
ejpam-3704	335	25	that	that	PRON
ejpam-3704	335	26	f(s	f(s	ADV
ejpam-3704	335	27	)	)	PUNCT
ejpam-3704	335	28	=	=	SYM
ejpam-3704	335	29	u	u	NOUN
ejpam-3704	335	30	,	,	PUNCT
ejpam-3704	335	31	f(t	f(t	PROPN
ejpam-3704	335	32	)	)	PUNCT
ejpam-3704	335	33	=	=	SYM
ejpam-3704	335	34	v	v	NOUN
ejpam-3704	335	35	,	,	PUNCT
ejpam-3704	335	36	f(s	f(	NOUN
ejpam-3704	335	37	~	~	PUNCT
ejpam-3704	335	38	t	t	X
ejpam-3704	335	39	)	)	PUNCT
ejpam-3704	335	40	=	=	PUNCT
ejpam-3704	335	41	f(s	f(	NOUN
ejpam-3704	335	42	)	)	PUNCT
ejpam-3704	335	43	~′	~′	NOUN
ejpam-3704	335	44	f(t	f(t	NOUN
ejpam-3704	335	45	)	)	PUNCT
ejpam-3704	335	46	=	=	SYM
ejpam-3704	335	47	(	(	PUNCT
ejpam-3704	335	48	u	u	NOUN
ejpam-3704	335	49	~′	~′	NOUN
ejpam-3704	335	50	v)ω{0′	v)ω{0′	NOUN
ejpam-3704	335	51	}	}	PUNCT
ejpam-3704	335	52	.	.	PUNCT
ejpam-3704	336	1	similarly	similarly	ADV
ejpam-3704	336	2	,	,	PUNCT
ejpam-3704	336	3	(	(	PUNCT
ejpam-3704	336	4	v	v	X
ejpam-3704	336	5	~′	~′	NOUN
ejpam-3704	336	6	u)ω{0′	u)ω{0′	NOUN
ejpam-3704	336	7	}	}	PUNCT
ejpam-3704	336	8	implies	imply	VERB
ejpam-3704	336	9	f(t~	f(t~	NOUN
ejpam-3704	336	10	s	s	PART
ejpam-3704	336	11	)	)	PUNCT
ejpam-3704	336	12	=	=	SYM
ejpam-3704	336	13	f(t	f(t	NOUN
ejpam-3704	336	14	)	)	PUNCT
ejpam-3704	336	15	~′	~′	NOUN
ejpam-3704	336	16	f(s	f(	NOUN
ejpam-3704	336	17	)	)	PUNCT
ejpam-3704	337	1	=	=	SYM
ejpam-3704	337	2	(	(	PUNCT
ejpam-3704	337	3	v	v	NUM
ejpam-3704	337	4	~′	~′	NOUN
ejpam-3704	337	5	u)ω{0′	u)ω{0′	NOUN
ejpam-3704	337	6	}	}	PUNCT
ejpam-3704	337	7	.	.	PUNCT
ejpam-3704	338	1	hence	hence	ADV
ejpam-3704	338	2	,	,	PUNCT
ejpam-3704	338	3	(	(	PUNCT
ejpam-3704	338	4	s~	s~	PROPN
ejpam-3704	338	5	t)θ{0	t)θ{0	NOUN
ejpam-3704	338	6	}	}	PUNCT
ejpam-3704	338	7	and	and	CCONJ
ejpam-3704	338	8	(	(	PUNCT
ejpam-3704	338	9	t~	t~	NOUN
ejpam-3704	338	10	s)θ{0	s)θ{0	NOUN
ejpam-3704	338	11	}	}	PUNCT
ejpam-3704	338	12	.	.	PUNCT
ejpam-3704	339	1	since	since	SCONJ
ejpam-3704	339	2	θ	θ	PROPN
ejpam-3704	339	3	is	be	AUX
ejpam-3704	339	4	a	a	DET
ejpam-3704	339	5	regular	regular	ADJ
ejpam-3704	339	6	congruence	congruence	NOUN
ejpam-3704	339	7	relation	relation	NOUN
ejpam-3704	339	8	on	on	ADP
ejpam-3704	339	9	h	h	NOUN
ejpam-3704	339	10	,	,	PUNCT
ejpam-3704	339	11	it	it	PRON
ejpam-3704	339	12	follows	follow	VERB
ejpam-3704	339	13	that	that	SCONJ
ejpam-3704	339	14	sθt	sθt	NOUN
ejpam-3704	339	15	and	and	CCONJ
ejpam-3704	339	16	uωv	uωv	PROPN
ejpam-3704	339	17	.	.	PUNCT
ejpam-3704	340	1	therefore	therefore	ADV
ejpam-3704	340	2	,	,	PUNCT
ejpam-3704	340	3	ω	ω	PROPN
ejpam-3704	340	4	is	be	AUX
ejpam-3704	340	5	a	a	DET
ejpam-3704	340	6	regular	regular	ADJ
ejpam-3704	340	7	congruence	congruence	NOUN
ejpam-3704	340	8	relation	relation	NOUN
ejpam-3704	340	9	on	on	ADP
ejpam-3704	340	10	h	h	PROPN
ejpam-3704	340	11	′.	′.	PROPN
ejpam-3704	340	12	remark	remark	VERB
ejpam-3704	340	13	1	1	NUM
ejpam-3704	340	14	.	.	PUNCT
ejpam-3704	341	1	let	let	VERB
ejpam-3704	341	2	f	f	NOUN
ejpam-3704	341	3	:	:	PUNCT
ejpam-3704	341	4	h	h	PROPN
ejpam-3704	341	5	−→	−→	ADJ
ejpam-3704	341	6	h	h	NOUN
ejpam-3704	341	7	′	′	NUM
ejpam-3704	341	8	be	be	AUX
ejpam-3704	341	9	a	a	DET
ejpam-3704	341	10	hyper	hyper	ADJ
ejpam-3704	341	11	epimorphism	epimorphism	NOUN
ejpam-3704	341	12	on	on	ADP
ejpam-3704	341	13	hyper	hyper	NOUN
ejpam-3704	341	14	up	up	ADP
ejpam-3704	341	15	-	-	PUNCT
ejpam-3704	341	16	algebras	algebras	X
ejpam-3704	341	17	and	and	CCONJ
ejpam-3704	341	18	let	let	VERB
ejpam-3704	341	19	θ	θ	PROPN
ejpam-3704	341	20	and	and	CCONJ
ejpam-3704	341	21	ω	ω	NUM
ejpam-3704	341	22	be	be	AUX
ejpam-3704	341	23	the	the	DET
ejpam-3704	341	24	relations	relation	NOUN
ejpam-3704	341	25	on	on	ADP
ejpam-3704	341	26	h	h	NOUN
ejpam-3704	341	27	and	and	CCONJ
ejpam-3704	341	28	h	h	NOUN
ejpam-3704	341	29	′	′	NOUN
ejpam-3704	341	30	,	,	PUNCT
ejpam-3704	341	31	respectively	respectively	ADV
ejpam-3704	341	32	,	,	PUNCT
ejpam-3704	341	33	as	as	SCONJ
ejpam-3704	341	34	defined	define	VERB
ejpam-3704	341	35	in	in	ADP
ejpam-3704	341	36	theorem	theorem	NOUN
ejpam-3704	341	37	7	7	NUM
ejpam-3704	341	38	.	.	PUNCT
ejpam-3704	342	1	then	then	ADV
ejpam-3704	342	2	(	(	PUNCT
ejpam-3704	342	3	i	i	NOUN
ejpam-3704	342	4	)	)	PUNCT
ejpam-3704	342	5	ω	ω	PROPN
ejpam-3704	342	6	is	be	AUX
ejpam-3704	342	7	called	call	VERB
ejpam-3704	342	8	the	the	DET
ejpam-3704	342	9	regular	regular	ADJ
ejpam-3704	342	10	congruence	congruence	NOUN
ejpam-3704	342	11	relation	relation	NOUN
ejpam-3704	342	12	induced	induce	VERB
ejpam-3704	342	13	by	by	ADP
ejpam-3704	342	14	f	f	PROPN
ejpam-3704	342	15	and	and	CCONJ
ejpam-3704	342	16	θ	θ	PROPN
ejpam-3704	342	17	,	,	PUNCT
ejpam-3704	342	18	and	and	CCONJ
ejpam-3704	342	19	(	(	PUNCT
ejpam-3704	342	20	ii	ii	NOUN
ejpam-3704	342	21	)	)	PUNCT
ejpam-3704	342	22	θ	θ	PROPN
ejpam-3704	342	23	is	be	AUX
ejpam-3704	342	24	called	call	VERB
ejpam-3704	342	25	the	the	DET
ejpam-3704	342	26	regular	regular	ADJ
ejpam-3704	342	27	congruence	congruence	NOUN
ejpam-3704	342	28	relation	relation	NOUN
ejpam-3704	342	29	induced	induce	VERB
ejpam-3704	342	30	by	by	ADP
ejpam-3704	342	31	f	f	PROPN
ejpam-3704	342	32	and	and	CCONJ
ejpam-3704	342	33	ω	ω	PROPN
ejpam-3704	342	34	.	.	PUNCT
ejpam-3704	342	35	theorem	theorem	NOUN
ejpam-3704	342	36	8	8	NUM
ejpam-3704	342	37	.	.	PUNCT
ejpam-3704	343	1	let	let	VERB
ejpam-3704	343	2	f	f	NOUN
ejpam-3704	343	3	:	:	PUNCT
ejpam-3704	343	4	h	h	PROPN
ejpam-3704	343	5	−→	−→	ADJ
ejpam-3704	343	6	h	h	NOUN
ejpam-3704	343	7	′	′	NUM
ejpam-3704	343	8	be	be	AUX
ejpam-3704	343	9	a	a	DET
ejpam-3704	343	10	hyper	hyper	ADJ
ejpam-3704	343	11	epimorphism	epimorphism	NOUN
ejpam-3704	343	12	on	on	ADP
ejpam-3704	343	13	hyper	hyper	ADJ
ejpam-3704	343	14	up	up	ADP
ejpam-3704	343	15	-	-	PUNCT
ejpam-3704	343	16	algebras	algebras	X
ejpam-3704	343	17	.	.	PUNCT
ejpam-3704	344	1	then	then	ADV
ejpam-3704	344	2	there	there	PRON
ejpam-3704	344	3	is	be	VERB
ejpam-3704	344	4	a	a	DET
ejpam-3704	344	5	one	one	NUM
ejpam-3704	344	6	-	-	PUNCT
ejpam-3704	344	7	to	to	ADP
ejpam-3704	344	8	-	-	PUNCT
ejpam-3704	344	9	one	one	NUM
ejpam-3704	344	10	correspondence	correspondence	NOUN
ejpam-3704	344	11	between	between	ADP
ejpam-3704	344	12	the	the	DET
ejpam-3704	344	13	regular	regular	ADJ
ejpam-3704	344	14	congruence	congruence	NOUN
ejpam-3704	344	15	relations	relation	NOUN
ejpam-3704	344	16	on	on	ADP
ejpam-3704	344	17	h	h	NOUN
ejpam-3704	344	18	′	′	NOUN
ejpam-3704	344	19	and	and	CCONJ
ejpam-3704	344	20	the	the	DET
ejpam-3704	344	21	regular	regular	ADJ
ejpam-3704	344	22	congruence	congruence	NOUN
ejpam-3704	344	23	relations	relation	NOUN
ejpam-3704	344	24	on	on	ADP
ejpam-3704	344	25	h	h	NOUN
ejpam-3704	344	26	such	such	ADJ
ejpam-3704	344	27	that	that	DET
ejpam-3704	344	28	ker	ker	PROPN
ejpam-3704	345	1	f	f	PROPN
ejpam-3704	345	2	is	be	AUX
ejpam-3704	345	3	contained	contain	VERB
ejpam-3704	345	4	in	in	ADP
ejpam-3704	345	5	the	the	DET
ejpam-3704	345	6	regular	regular	ADJ
ejpam-3704	345	7	congruence	congruence	NOUN
ejpam-3704	345	8	class	class	NOUN
ejpam-3704	345	9	containing	contain	VERB
ejpam-3704	345	10	0	0	NUM
ejpam-3704	345	11	.	.	PUNCT
ejpam-3704	346	1	proof	proof	NOUN
ejpam-3704	346	2	.	.	PUNCT
ejpam-3704	347	1	let	let	VERB
ejpam-3704	347	2	f	f	NOUN
ejpam-3704	347	3	:	:	PUNCT
ejpam-3704	347	4	h	h	PROPN
ejpam-3704	347	5	−→	−→	ADJ
ejpam-3704	347	6	h	h	NOUN
ejpam-3704	347	7	′	′	NUM
ejpam-3704	347	8	be	be	AUX
ejpam-3704	347	9	a	a	DET
ejpam-3704	347	10	hyper	hyper	ADJ
ejpam-3704	347	11	epimorphism	epimorphism	NOUN
ejpam-3704	347	12	of	of	ADP
ejpam-3704	347	13	hyper	hyper	ADJ
ejpam-3704	347	14	up	up	ADP
ejpam-3704	347	15	-	-	PUNCT
ejpam-3704	347	16	algebras	algebra	NOUN
ejpam-3704	347	17	and	and	CCONJ
ejpam-3704	347	18	a	a	DET
ejpam-3704	347	19	=	=	X
ejpam-3704	347	20	{	{	PUNCT
ejpam-3704	347	21	θ	θ	NOUN
ejpam-3704	347	22	:	:	PUNCT
ejpam-3704	347	23	θ	θ	NOUN
ejpam-3704	347	24	is	be	AUX
ejpam-3704	347	25	a	a	DET
ejpam-3704	347	26	regular	regular	ADJ
ejpam-3704	347	27	congruence	congruence	NOUN
ejpam-3704	347	28	relation	relation	NOUN
ejpam-3704	347	29	on	on	ADP
ejpam-3704	347	30	h	h	PROPN
ejpam-3704	347	31	with	with	ADP
ejpam-3704	347	32	ker	ker	PROPN
ejpam-3704	347	33	f	f	PROPN
ejpam-3704	348	1	⊆	⊆	NUM
ejpam-3704	348	2	[	[	X
ejpam-3704	348	3	0]θ	0]θ	NUM
ejpam-3704	348	4	}	}	SYM
ejpam-3704	348	5	b	b	NOUN
ejpam-3704	348	6	=	=	SYM
ejpam-3704	348	7	{	{	PUNCT
ejpam-3704	348	8	ω	ω	NOUN
ejpam-3704	348	9	:	:	PUNCT
ejpam-3704	348	10	ω	ω	PROPN
ejpam-3704	348	11	is	be	AUX
ejpam-3704	348	12	a	a	DET
ejpam-3704	348	13	regular	regular	ADJ
ejpam-3704	348	14	congruence	congruence	NOUN
ejpam-3704	348	15	relation	relation	NOUN
ejpam-3704	348	16	on	on	ADP
ejpam-3704	348	17	h	h	NOUN
ejpam-3704	348	18	′	′	NUM
ejpam-3704	348	19	}	}	PUNCT
ejpam-3704	348	20	.	.	PUNCT
ejpam-3704	349	1	define	define	VERB
ejpam-3704	349	2	γ	γ	X
ejpam-3704	349	3	:	:	PUNCT
ejpam-3704	349	4	a	a	DET
ejpam-3704	349	5	−→	−→	NOUN
ejpam-3704	349	6	b	b	NOUN
ejpam-3704	349	7	by	by	ADP
ejpam-3704	349	8	γ(θ	γ(θ	PROPN
ejpam-3704	349	9	)	)	PUNCT
ejpam-3704	349	10	=	=	SYM
ejpam-3704	349	11	ω	ω	PROPN
ejpam-3704	349	12	,	,	PUNCT
ejpam-3704	349	13	where	where	SCONJ
ejpam-3704	349	14	ω	ω	PROPN
ejpam-3704	349	15	is	be	AUX
ejpam-3704	349	16	the	the	DET
ejpam-3704	349	17	regular	regular	ADJ
ejpam-3704	349	18	congruence	congruence	NOUN
ejpam-3704	349	19	relation	relation	NOUN
ejpam-3704	349	20	on	on	ADP
ejpam-3704	349	21	h	h	NOUN
ejpam-3704	349	22	′	′	NOUN
ejpam-3704	349	23	induced	induce	VERB
ejpam-3704	349	24	by	by	ADP
ejpam-3704	349	25	f	f	PROPN
ejpam-3704	349	26	and	and	CCONJ
ejpam-3704	349	27	θ	θ	PROPN
ejpam-3704	349	28	.	.	PUNCT
ejpam-3704	350	1	then	then	ADV
ejpam-3704	350	2	ω	ω	PROPN
ejpam-3704	350	3	∈	∈	PROPN
ejpam-3704	350	4	b.	b.	PROPN
ejpam-3704	350	5	let	let	VERB
ejpam-3704	350	6	θ1,θ2	θ1,θ2	PROPN
ejpam-3704	350	7	∈	∈	PROPN
ejpam-3704	350	8	a	a	DET
ejpam-3704	350	9	such	such	ADJ
ejpam-3704	350	10	that	that	DET
ejpam-3704	350	11	ω1	ω1	PROPN
ejpam-3704	350	12	=	=	SYM
ejpam-3704	350	13	γ(θ1	γ(θ1	NOUN
ejpam-3704	350	14	)	)	PUNCT
ejpam-3704	350	15	=	=	SYM
ejpam-3704	350	16	γ(θ2	γ(θ2	PROPN
ejpam-3704	350	17	)	)	PUNCT
ejpam-3704	351	1	=	=	PUNCT
ejpam-3704	352	1	ω2	ω2	ADJ
ejpam-3704	352	2	.	.	PUNCT
ejpam-3704	353	1	then	then	ADV
ejpam-3704	353	2	for	for	ADP
ejpam-3704	353	3	all	all	DET
ejpam-3704	353	4	x	x	NOUN
ejpam-3704	353	5	,	,	PUNCT
ejpam-3704	353	6	y	y	PROPN
ejpam-3704	353	7	∈	∈	PROPN
ejpam-3704	353	8	h	h	NOUN
ejpam-3704	353	9	,	,	PUNCT
ejpam-3704	353	10	xθ1y	xθ1y	PROPN
ejpam-3704	353	11	⇔	⇔	PROPN
ejpam-3704	353	12	f(x)ω1f(y	f(x)ω1f(y	PROPN
ejpam-3704	353	13	)	)	PUNCT
ejpam-3704	353	14	⇔	⇔	X
ejpam-3704	353	15	f(x)ω2f(y	f(x)ω2f(y	PROPN
ejpam-3704	353	16	)	)	PUNCT
ejpam-3704	353	17	⇔	⇔	PROPN
ejpam-3704	353	18	xθ2y	xθ2y	PROPN
ejpam-3704	353	19	.	.	PUNCT
ejpam-3704	354	1	hence	hence	ADV
ejpam-3704	354	2	,	,	PUNCT
ejpam-3704	354	3	θ1	θ1	PROPN
ejpam-3704	354	4	=	=	SYM
ejpam-3704	354	5	θ2	θ2	PROPN
ejpam-3704	354	6	and	and	CCONJ
ejpam-3704	354	7	γ	γ	PROPN
ejpam-3704	354	8	is	be	AUX
ejpam-3704	354	9	well	well	ADV
ejpam-3704	354	10	-	-	PUNCT
ejpam-3704	354	11	defined	define	VERB
ejpam-3704	354	12	and	and	CCONJ
ejpam-3704	354	13	one	one	NUM
ejpam-3704	354	14	-	-	PUNCT
ejpam-3704	354	15	to	to	ADP
ejpam-3704	354	16	-	-	PUNCT
ejpam-3704	354	17	one	one	NUM
ejpam-3704	354	18	.	.	PUNCT
ejpam-3704	355	1	now	now	ADV
ejpam-3704	355	2	,	,	PUNCT
ejpam-3704	355	3	let	let	VERB
ejpam-3704	355	4	ω	ω	NUM
ejpam-3704	355	5	∈	∈	PROPN
ejpam-3704	355	6	b	b	PROPN
ejpam-3704	355	7	and	and	CCONJ
ejpam-3704	355	8	consider	consider	VERB
ejpam-3704	355	9	the	the	DET
ejpam-3704	355	10	induced	induced	ADJ
ejpam-3704	355	11	regular	regular	ADJ
ejpam-3704	355	12	congruence	congruence	NOUN
ejpam-3704	355	13	relation	relation	NOUN
ejpam-3704	355	14	θ	θ	PROPN
ejpam-3704	355	15	on	on	ADP
ejpam-3704	355	16	h.	h.	PROPN
ejpam-3704	355	17	if	if	SCONJ
ejpam-3704	355	18	x	x	PROPN
ejpam-3704	355	19	∈	∈	PROPN
ejpam-3704	355	20	ker	ker	NOUN
ejpam-3704	356	1	f	f	X
ejpam-3704	356	2	,	,	PUNCT
ejpam-3704	356	3	then	then	ADV
ejpam-3704	356	4	f(x	f(x	PROPN
ejpam-3704	356	5	)	)	PUNCT
ejpam-3704	357	1	=	=	SYM
ejpam-3704	357	2	f(0	f(0	NOUN
ejpam-3704	357	3	.	.	PUNCT
ejpam-3704	357	4	)	)	PUNCT
ejpam-3704	358	1	so	so	ADV
ejpam-3704	358	2	,	,	PUNCT
ejpam-3704	358	3	f(x)ωf(0	f(x)ωf(0	PROPN
ejpam-3704	358	4	)	)	PUNCT
ejpam-3704	358	5	implies	imply	VERB
ejpam-3704	358	6	xθ0	xθ0	PROPN
ejpam-3704	358	7	.	.	PUNCT
ejpam-3704	359	1	thus	thus	ADV
ejpam-3704	359	2	,	,	PUNCT
ejpam-3704	359	3	ker	ker	PROPN
ejpam-3704	359	4	f	f	PROPN
ejpam-3704	360	1	⊆	⊆	NUM
ejpam-3704	360	2	[	[	X
ejpam-3704	360	3	0]θ	0]θ	NOUN
ejpam-3704	360	4	and	and	CCONJ
ejpam-3704	360	5	so	so	ADV
ejpam-3704	360	6	,	,	PUNCT
ejpam-3704	360	7	θ	θ	PROPN
ejpam-3704	360	8	∈	∈	PROPN
ejpam-3704	360	9	a.	a.	NOUN
ejpam-3704	360	10	lastly	lastly	ADV
ejpam-3704	360	11	,	,	PUNCT
ejpam-3704	360	12	we	we	PRON
ejpam-3704	360	13	show	show	VERB
ejpam-3704	360	14	that	that	SCONJ
ejpam-3704	360	15	γ	γ	PROPN
ejpam-3704	360	16	is	be	AUX
ejpam-3704	360	17	onto	onto	ADP
ejpam-3704	360	18	,	,	PUNCT
ejpam-3704	360	19	that	that	ADV
ejpam-3704	360	20	is	is	ADV
ejpam-3704	360	21	,	,	PUNCT
ejpam-3704	360	22	γ(θ	γ(θ	PROPN
ejpam-3704	360	23	)	)	PUNCT
ejpam-3704	360	24	=	=	SYM
ejpam-3704	360	25	ω	ω	PROPN
ejpam-3704	360	26	.	.	PUNCT
ejpam-3704	360	27	suppose	suppose	VERB
ejpam-3704	360	28	γ(θ	γ(θ	PROPN
ejpam-3704	360	29	)	)	PUNCT
ejpam-3704	360	30	=	=	SYM
ejpam-3704	360	31	ω′	ω′	PROPN
ejpam-3704	360	32	for	for	ADP
ejpam-3704	360	33	some	some	DET
ejpam-3704	360	34	ω′	ω′	PROPN
ejpam-3704	360	35	∈	∈	PROPN
ejpam-3704	360	36	b.	b.	PROPN
ejpam-3704	360	37	then	then	ADV
ejpam-3704	360	38	by	by	ADP
ejpam-3704	360	39	the	the	DET
ejpam-3704	360	40	definitions	definition	NOUN
ejpam-3704	360	41	of	of	ADP
ejpam-3704	360	42	ω	ω	NUM
ejpam-3704	360	43	and	and	CCONJ
ejpam-3704	360	44	θ	θ	PROPN
ejpam-3704	360	45	,	,	PUNCT
ejpam-3704	360	46	for	for	ADP
ejpam-3704	360	47	each	each	DET
ejpam-3704	360	48	t	t	NOUN
ejpam-3704	360	49	∈	∈	PROPN
ejpam-3704	360	50	h	h	NOUN
ejpam-3704	360	51	′	′	NOUN
ejpam-3704	360	52	,	,	PUNCT
ejpam-3704	360	53	tω′0′	tω′0′	PROPN
ejpam-3704	360	54	⇔	⇔	PROPN
ejpam-3704	360	55	t	t	PROPN
ejpam-3704	360	56	=	=	SYM
ejpam-3704	360	57	f(x	f(x	PROPN
ejpam-3704	360	58	)	)	PUNCT
ejpam-3704	360	59	and	and	CCONJ
ejpam-3704	360	60	xθ0	xθ0	NOUN
ejpam-3704	360	61	for	for	ADP
ejpam-3704	360	62	some	some	DET
ejpam-3704	360	63	x	x	SYM
ejpam-3704	360	64	∈	∈	PROPN
ejpam-3704	360	65	h	h	NOUN
ejpam-3704	360	66	⇔	⇔	PROPN
ejpam-3704	360	67	f(x)ωf(0)⇔	f(x)ωf(0)⇔	PROPN
ejpam-3704	360	68	tω0′.	tω0′.	PROPN
ejpam-3704	360	69	thus	thus	ADV
ejpam-3704	360	70	,	,	PUNCT
ejpam-3704	361	1	[	[	X
ejpam-3704	361	2	0′]ω	0′]ω	PUNCT
ejpam-3704	361	3	=	=	SYM
ejpam-3704	361	4	[	[	X
ejpam-3704	361	5	0′]ω′	0′]ω′	NOUN
ejpam-3704	361	6	and	and	CCONJ
ejpam-3704	361	7	by	by	ADP
ejpam-3704	361	8	theorem	theorem	NOUN
ejpam-3704	361	9	1	1	NUM
ejpam-3704	361	10	,	,	PUNCT
ejpam-3704	361	11	ω	ω	NUM
ejpam-3704	361	12	=	=	PUNCT
ejpam-3704	361	13	ω′.	ω′.	VERB
ejpam-3704	361	14	hence	hence	ADV
ejpam-3704	361	15	,	,	PUNCT
ejpam-3704	361	16	γ(θ	γ(θ	PROPN
ejpam-3704	361	17	)	)	PUNCT
ejpam-3704	362	1	=	=	SYM
ejpam-3704	362	2	ω	ω	PROPN
ejpam-3704	362	3	.	.	PUNCT
ejpam-3704	363	1	therefore	therefore	ADV
ejpam-3704	363	2	,	,	PUNCT
ejpam-3704	363	3	γ	γ	X
ejpam-3704	363	4	is	be	AUX
ejpam-3704	363	5	a	a	DET
ejpam-3704	363	6	bijection	bijection	NOUN
ejpam-3704	363	7	.	.	PUNCT
ejpam-3704	364	1	r.	r.	PROPN
ejpam-3704	364	2	amairanto	amairanto	PROPN
ejpam-3704	364	3	,	,	PUNCT
ejpam-3704	364	4	r.	r.	PROPN
ejpam-3704	364	5	isla	isla	PROPN
ejpam-3704	364	6	/	/	SYM
ejpam-3704	364	7	eur	eur	PROPN
ejpam-3704	364	8	.	.	PUNCT
ejpam-3704	365	1	j.	j.	PROPN
ejpam-3704	365	2	pure	pure	PROPN
ejpam-3704	365	3	appl	appl	PROPN
ejpam-3704	365	4	.	.	PROPN
ejpam-3704	365	5	math	math	PROPN
ejpam-3704	365	6	,	,	PUNCT
ejpam-3704	365	7	13	13	NUM
ejpam-3704	365	8	(	(	PUNCT
ejpam-3704	365	9	3	3	NUM
ejpam-3704	365	10	)	)	PUNCT
ejpam-3704	365	11	(	(	PUNCT
ejpam-3704	365	12	2020	2020	NUM
ejpam-3704	365	13	)	)	PUNCT
ejpam-3704	365	14	,	,	PUNCT
ejpam-3704	365	15	483	483	NUM
ejpam-3704	365	16	-	-	SYM
ejpam-3704	365	17	497	497	NUM
ejpam-3704	365	18	492	492	NUM
ejpam-3704	365	19	4	4	NUM
ejpam-3704	365	20	.	.	PUNCT
ejpam-3704	365	21	hyper	hyper	ADJ
ejpam-3704	365	22	product	product	NOUN
ejpam-3704	365	23	of	of	ADP
ejpam-3704	365	24	hyper	hyper	ADJ
ejpam-3704	365	25	up	up	ADV
ejpam-3704	365	26	-	-	PUNCT
ejpam-3704	365	27	algebras	algebras	NOUN
ejpam-3704	365	28	throughout	throughout	ADP
ejpam-3704	365	29	this	this	DET
ejpam-3704	365	30	section	section	NOUN
ejpam-3704	365	31	,	,	PUNCT
ejpam-3704	365	32	h	h	NOUN
ejpam-3704	365	33	and	and	CCONJ
ejpam-3704	365	34	k	k	PROPN
ejpam-3704	365	35	shall	shall	AUX
ejpam-3704	365	36	mean	mean	VERB
ejpam-3704	365	37	the	the	DET
ejpam-3704	365	38	hyper	hyper	ADJ
ejpam-3704	365	39	up	up	ADP
ejpam-3704	365	40	-	-	PUNCT
ejpam-3704	365	41	algebras	algebras	X
ejpam-3704	365	42	(	(	PUNCT
ejpam-3704	365	43	h,~h	h,~h	NOUN
ejpam-3704	365	44	,	,	PUNCT
ejpam-3704	365	45	0h	0h	PROPN
ejpam-3704	365	46	)	)	PUNCT
ejpam-3704	365	47	and	and	CCONJ
ejpam-3704	365	48	(	(	PUNCT
ejpam-3704	365	49	k,~k	k,~k	NOUN
ejpam-3704	365	50	,	,	PUNCT
ejpam-3704	365	51	0k	0k	NOUN
ejpam-3704	365	52	)	)	PUNCT
ejpam-3704	365	53	with	with	ADP
ejpam-3704	365	54	�	�	PROPN
ejpam-3704	365	55	h	h	PROPN
ejpam-3704	365	56	and	and	CCONJ
ejpam-3704	365	57	�	�	PROPN
ejpam-3704	365	58	k	k	PROPN
ejpam-3704	365	59	as	as	ADP
ejpam-3704	365	60	their	their	PRON
ejpam-3704	365	61	hyper	hyper	ADJ
ejpam-3704	365	62	orders	order	NOUN
ejpam-3704	365	63	,	,	PUNCT
ejpam-3704	365	64	respectively	respectively	ADV
ejpam-3704	365	65	.	.	PUNCT
ejpam-3704	366	1	the	the	DET
ejpam-3704	366	2	following	follow	VERB
ejpam-3704	366	3	introduction	introduction	NOUN
ejpam-3704	366	4	of	of	ADP
ejpam-3704	366	5	the	the	DET
ejpam-3704	366	6	hyper	hyper	ADJ
ejpam-3704	366	7	product	product	NOUN
ejpam-3704	366	8	of	of	ADP
ejpam-3704	366	9	two	two	NUM
ejpam-3704	366	10	hyper	hyper	ADJ
ejpam-3704	366	11	up	up	ADP
ejpam-3704	366	12	-	-	PUNCT
ejpam-3704	366	13	algebras	algebras	PROPN
ejpam-3704	366	14	is	be	AUX
ejpam-3704	366	15	influenced	influence	VERB
ejpam-3704	366	16	by	by	ADP
ejpam-3704	366	17	the	the	DET
ejpam-3704	366	18	construction	construction	NOUN
ejpam-3704	366	19	of	of	ADP
ejpam-3704	366	20	the	the	DET
ejpam-3704	366	21	hyper	hyper	ADJ
ejpam-3704	366	22	product	product	NOUN
ejpam-3704	366	23	of	of	ADP
ejpam-3704	366	24	two	two	NUM
ejpam-3704	366	25	hyper	hyper	ADJ
ejpam-3704	366	26	bck	bck	NOUN
ejpam-3704	366	27	-	-	PUNCT
ejpam-3704	366	28	algebras	algebras	PROPN
ejpam-3704	366	29	by	by	ADP
ejpam-3704	366	30	borzooei	borzooei	PROPN
ejpam-3704	366	31	et	et	PROPN
ejpam-3704	366	32	al	al	PROPN
ejpam-3704	366	33	.	.	PUNCT
ejpam-3704	367	1	[	[	X
ejpam-3704	367	2	12	12	NUM
ejpam-3704	367	3	]	]	PUNCT
ejpam-3704	367	4	,	,	PUNCT
ejpam-3704	367	5	as	as	SCONJ
ejpam-3704	367	6	cited	cite	VERB
ejpam-3704	367	7	in	in	ADP
ejpam-3704	367	8	[	[	X
ejpam-3704	367	9	1	1	NUM
ejpam-3704	367	10	]	]	PUNCT
ejpam-3704	367	11	.	.	PUNCT
ejpam-3704	368	1	suppose	suppose	VERB
ejpam-3704	368	2	h	h	NOUN
ejpam-3704	368	3	and	and	CCONJ
ejpam-3704	368	4	k	k	PROPN
ejpam-3704	368	5	are	be	AUX
ejpam-3704	368	6	hyper	hyper	ADJ
ejpam-3704	368	7	up	up	ADP
ejpam-3704	368	8	-	-	PUNCT
ejpam-3704	368	9	algebras	algebras	X
ejpam-3704	368	10	.	.	PUNCT
ejpam-3704	369	1	then	then	ADV
ejpam-3704	369	2	h	h	NOUN
ejpam-3704	369	3	×k	×k	PROPN
ejpam-3704	369	4	=	=	PUNCT
ejpam-3704	369	5	{	{	PUNCT
ejpam-3704	369	6	(	(	PUNCT
ejpam-3704	369	7	a	a	PRON
ejpam-3704	369	8	,	,	PUNCT
ejpam-3704	369	9	b)|a	b)|a	ADP
ejpam-3704	369	10	∈	∈	PROPN
ejpam-3704	369	11	h	h	NOUN
ejpam-3704	369	12	and	and	CCONJ
ejpam-3704	369	13	b	b	X
ejpam-3704	369	14	∈	∈	PROPN
ejpam-3704	369	15	k	k	NOUN
ejpam-3704	369	16	}	}	PUNCT
ejpam-3704	369	17	.	.	PUNCT
ejpam-3704	370	1	define	define	VERB
ejpam-3704	370	2	the	the	DET
ejpam-3704	370	3	hyperoperation	hyperoperation	NOUN
ejpam-3704	370	4	“	"	PUNCT
ejpam-3704	370	5	~	~	PUNCT
ejpam-3704	370	6	”	"	PUNCT
ejpam-3704	370	7	on	on	ADP
ejpam-3704	370	8	h	h	NOUN
ejpam-3704	370	9	×k	×k	VERB
ejpam-3704	370	10	by	by	ADP
ejpam-3704	370	11	(	(	PUNCT
ejpam-3704	370	12	a	a	DET
ejpam-3704	370	13	,	,	PUNCT
ejpam-3704	370	14	b	b	NOUN
ejpam-3704	370	15	)	)	PUNCT
ejpam-3704	370	16	~	~	PUNCT
ejpam-3704	370	17	(	(	PUNCT
ejpam-3704	370	18	c	c	X
ejpam-3704	370	19	,	,	PUNCT
ejpam-3704	370	20	d	d	NOUN
ejpam-3704	370	21	)	)	PUNCT
ejpam-3704	370	22	=	=	SYM
ejpam-3704	370	23	(	(	PUNCT
ejpam-3704	370	24	a	a	DET
ejpam-3704	370	25	~	~	NOUN
ejpam-3704	370	26	h	h	NOUN
ejpam-3704	370	27	c	c	NOUN
ejpam-3704	370	28	,	,	PUNCT
ejpam-3704	370	29	b	b	X
ejpam-3704	370	30	~	~	SYM
ejpam-3704	370	31	k	k	X
ejpam-3704	370	32	d	d	NOUN
ejpam-3704	370	33	)	)	PUNCT
ejpam-3704	370	34	and	and	CCONJ
ejpam-3704	370	35	hyperorder	hyperorder	NOUN
ejpam-3704	370	36	“	"	PUNCT
ejpam-3704	370	37	�	�	PROPN
ejpam-3704	370	38	”	"	PUNCT
ejpam-3704	370	39	by	by	ADP
ejpam-3704	370	40	(	(	PUNCT
ejpam-3704	370	41	a	a	PRON
ejpam-3704	370	42	,	,	PUNCT
ejpam-3704	370	43	b	b	NOUN
ejpam-3704	370	44	)	)	PUNCT
ejpam-3704	370	45	�	�	PROPN
ejpam-3704	370	46	(	(	PUNCT
ejpam-3704	370	47	c	c	NOUN
ejpam-3704	370	48	,	,	PUNCT
ejpam-3704	370	49	d)	d)	NOUN
ejpam-3704	370	50	⇐	⇐	ADJ
ejpam-3704	370	51	⇒	⇒	PROPN
ejpam-3704	370	52	a	a	DET
ejpam-3704	370	53	�	�	PROPN
ejpam-3704	370	54	h	h	NOUN
ejpam-3704	370	55	c	c	PROPN
ejpam-3704	370	56	and	and	CCONJ
ejpam-3704	370	57	b	b	PROPN
ejpam-3704	370	58	�	�	PROPN
ejpam-3704	370	59	k	k	PROPN
ejpam-3704	370	60	d	d	PROPN
ejpam-3704	370	61	for	for	ADP
ejpam-3704	370	62	all	all	PRON
ejpam-3704	370	63	(	(	PUNCT
ejpam-3704	370	64	a	a	DET
ejpam-3704	370	65	,	,	PUNCT
ejpam-3704	370	66	b	b	NOUN
ejpam-3704	370	67	)	)	PUNCT
ejpam-3704	370	68	,	,	PUNCT
ejpam-3704	370	69	(	(	PUNCT
ejpam-3704	370	70	c	c	X
ejpam-3704	370	71	,	,	PUNCT
ejpam-3704	370	72	d	d	NOUN
ejpam-3704	370	73	)	)	PUNCT
ejpam-3704	370	74	∈	∈	PROPN
ejpam-3704	371	1	h×	h×	PRON
ejpam-3704	371	2	k.	k.	NOUN
ejpam-3704	371	3	for	for	ADP
ejpam-3704	371	4	every	every	DET
ejpam-3704	371	5	(	(	PUNCT
ejpam-3704	371	6	a	a	DET
ejpam-3704	371	7	,	,	PUNCT
ejpam-3704	371	8	b	b	NOUN
ejpam-3704	371	9	)	)	PUNCT
ejpam-3704	371	10	,	,	PUNCT
ejpam-3704	371	11	(	(	PUNCT
ejpam-3704	371	12	c	c	X
ejpam-3704	371	13	,	,	PUNCT
ejpam-3704	371	14	d	d	NOUN
ejpam-3704	371	15	)	)	PUNCT
ejpam-3704	371	16	⊆	⊆	NUM
ejpam-3704	371	17	h×k	h×k	NOUN
ejpam-3704	371	18	,	,	PUNCT
ejpam-3704	371	19	(	(	PUNCT
ejpam-3704	371	20	a	a	PRON
ejpam-3704	371	21	,	,	PUNCT
ejpam-3704	371	22	b	b	NOUN
ejpam-3704	371	23	)	)	PUNCT
ejpam-3704	371	24	�	�	PROPN
ejpam-3704	371	25	(	(	PUNCT
ejpam-3704	371	26	c	c	NOUN
ejpam-3704	371	27	,	,	PUNCT
ejpam-3704	371	28	d	d	NOUN
ejpam-3704	371	29	)	)	PUNCT
ejpam-3704	372	1	if	if	SCONJ
ejpam-3704	372	2	and	and	CCONJ
ejpam-3704	372	3	only	only	ADV
ejpam-3704	372	4	if	if	SCONJ
ejpam-3704	372	5	for	for	ADP
ejpam-3704	372	6	all	all	PRON
ejpam-3704	372	7	(	(	PUNCT
ejpam-3704	372	8	a	a	PRON
ejpam-3704	372	9	,	,	PUNCT
ejpam-3704	372	10	b	b	NOUN
ejpam-3704	372	11	)	)	PUNCT
ejpam-3704	372	12	∈	∈	PROPN
ejpam-3704	372	13	(	(	PUNCT
ejpam-3704	372	14	a	a	DET
ejpam-3704	372	15	,	,	PUNCT
ejpam-3704	372	16	b	b	NOUN
ejpam-3704	372	17	)	)	PUNCT
ejpam-3704	372	18	,	,	PUNCT
ejpam-3704	372	19	there	there	PRON
ejpam-3704	372	20	exists	exist	VERB
ejpam-3704	372	21	(	(	PUNCT
ejpam-3704	372	22	c	c	X
ejpam-3704	372	23	,	,	PUNCT
ejpam-3704	372	24	d	d	NOUN
ejpam-3704	372	25	)	)	PUNCT
ejpam-3704	372	26	∈	∈	PROPN
ejpam-3704	372	27	(	(	PUNCT
ejpam-3704	372	28	c	c	X
ejpam-3704	372	29	,	,	PUNCT
ejpam-3704	372	30	d	d	NOUN
ejpam-3704	372	31	)	)	PUNCT
ejpam-3704	372	32	such	such	ADJ
ejpam-3704	372	33	that	that	SCONJ
ejpam-3704	372	34	(	(	PUNCT
ejpam-3704	372	35	a	a	PRON
ejpam-3704	372	36	,	,	PUNCT
ejpam-3704	372	37	b	b	NOUN
ejpam-3704	372	38	)	)	PUNCT
ejpam-3704	372	39	�	�	PROPN
ejpam-3704	372	40	(	(	PUNCT
ejpam-3704	372	41	c	c	NOUN
ejpam-3704	372	42	,	,	PUNCT
ejpam-3704	372	43	d	d	NOUN
ejpam-3704	372	44	)	)	PUNCT
ejpam-3704	372	45	.	.	PUNCT
ejpam-3704	373	1	then	then	ADV
ejpam-3704	373	2	(	(	PUNCT
ejpam-3704	373	3	h	h	PROPN
ejpam-3704	373	4	×k;~	×k;~	PROPN
ejpam-3704	373	5	,	,	PUNCT
ejpam-3704	373	6	(	(	PUNCT
ejpam-3704	373	7	0h	0h	X
ejpam-3704	373	8	,	,	PUNCT
ejpam-3704	373	9	0k	0k	NOUN
ejpam-3704	373	10	)	)	PUNCT
ejpam-3704	373	11	)	)	PUNCT
ejpam-3704	373	12	is	be	AUX
ejpam-3704	373	13	called	call	VERB
ejpam-3704	373	14	the	the	DET
ejpam-3704	373	15	hyper	hyper	ADJ
ejpam-3704	373	16	product	product	NOUN
ejpam-3704	373	17	of	of	ADP
ejpam-3704	373	18	h	h	PROPN
ejpam-3704	373	19	and	and	CCONJ
ejpam-3704	373	20	k.	k.	PROPN
ejpam-3704	373	21	theorem	theorem	VERB
ejpam-3704	373	22	9	9	NUM
ejpam-3704	373	23	.	.	PUNCT
ejpam-3704	374	1	[	[	X
ejpam-3704	374	2	9	9	NUM
ejpam-3704	374	3	]	]	PUNCT
ejpam-3704	374	4	let	let	VERB
ejpam-3704	374	5	h	h	NOUN
ejpam-3704	374	6	and	and	CCONJ
ejpam-3704	374	7	k	k	PROPN
ejpam-3704	374	8	be	be	AUX
ejpam-3704	374	9	hyper	hyper	ADJ
ejpam-3704	374	10	up	up	ADP
ejpam-3704	374	11	-	-	PUNCT
ejpam-3704	374	12	algebras	algebras	X
ejpam-3704	374	13	.	.	PUNCT
ejpam-3704	375	1	then	then	ADV
ejpam-3704	375	2	h	h	PROPN
ejpam-3704	375	3	×k	×k	NOUN
ejpam-3704	375	4	is	be	AUX
ejpam-3704	375	5	a	a	DET
ejpam-3704	375	6	hyper	hyper	ADJ
ejpam-3704	375	7	up	up	NOUN
ejpam-3704	375	8	-	-	PUNCT
ejpam-3704	375	9	algebra	algebra	NOUN
ejpam-3704	375	10	.	.	PUNCT
ejpam-3704	376	1	theorem	theorem	ADJ
ejpam-3704	376	2	10	10	NUM
ejpam-3704	376	3	.	.	PUNCT
ejpam-3704	377	1	let	let	VERB
ejpam-3704	377	2	α1	α1	PROPN
ejpam-3704	377	3	:	:	PUNCT
ejpam-3704	377	4	h1	h1	VERB
ejpam-3704	377	5	−→	−→	ADJ
ejpam-3704	377	6	k1	k1	NOUN
ejpam-3704	377	7	and	and	CCONJ
ejpam-3704	377	8	α2	α2	NOUN
ejpam-3704	377	9	:	:	PUNCT
ejpam-3704	377	10	h2	h2	PROPN
ejpam-3704	377	11	−→	−→	PROPN
ejpam-3704	377	12	k2	k2	PROPN
ejpam-3704	377	13	be	be	AUX
ejpam-3704	377	14	hyper	hyper	ADJ
ejpam-3704	377	15	homomorphisms	homomorphism	NOUN
ejpam-3704	377	16	of	of	ADP
ejpam-3704	377	17	hyper	hyper	ADJ
ejpam-3704	377	18	up	up	ADP
ejpam-3704	377	19	-	-	PUNCT
ejpam-3704	377	20	algebras	algebras	X
ejpam-3704	377	21	.	.	PUNCT
ejpam-3704	378	1	define	define	VERB
ejpam-3704	378	2	α	α	NOUN
ejpam-3704	378	3	:	:	PUNCT
ejpam-3704	378	4	h1	h1	VERB
ejpam-3704	378	5	×h2	×h2	PROPN
ejpam-3704	378	6	−→	−→	ADJ
ejpam-3704	378	7	k1	k1	NOUN
ejpam-3704	378	8	×k2	×k2	PROPN
ejpam-3704	378	9	by	by	ADP
ejpam-3704	378	10	α((a	α((a	PROPN
ejpam-3704	378	11	,	,	PUNCT
ejpam-3704	378	12	b	b	NOUN
ejpam-3704	378	13	)	)	PUNCT
ejpam-3704	378	14	)	)	PUNCT
ejpam-3704	379	1	=	=	SYM
ejpam-3704	379	2	(	(	PUNCT
ejpam-3704	379	3	α1(a	α1(a	NUM
ejpam-3704	379	4	)	)	PUNCT
ejpam-3704	379	5	,	,	PUNCT
ejpam-3704	379	6	α2(b	α2(b	NUM
ejpam-3704	379	7	)	)	PUNCT
ejpam-3704	379	8	)	)	PUNCT
ejpam-3704	379	9	for	for	ADP
ejpam-3704	379	10	all	all	PRON
ejpam-3704	379	11	(	(	PUNCT
ejpam-3704	379	12	a	a	PRON
ejpam-3704	379	13	,	,	PUNCT
ejpam-3704	379	14	b	b	NOUN
ejpam-3704	379	15	)	)	PUNCT
ejpam-3704	379	16	∈	∈	PROPN
ejpam-3704	379	17	h1	h1	PROPN
ejpam-3704	379	18	×h2	×h2	PROPN
ejpam-3704	379	19	.	.	PUNCT
ejpam-3704	380	1	then	then	ADV
ejpam-3704	380	2	(	(	PUNCT
ejpam-3704	380	3	i	i	NOUN
ejpam-3704	380	4	)	)	PUNCT
ejpam-3704	380	5	α	α	PROPN
ejpam-3704	380	6	is	be	AUX
ejpam-3704	380	7	a	a	DET
ejpam-3704	380	8	hyper	hyper	ADJ
ejpam-3704	380	9	homomorphism	homomorphism	NOUN
ejpam-3704	380	10	;	;	PUNCT
ejpam-3704	380	11	(	(	PUNCT
ejpam-3704	380	12	ii	ii	NOUN
ejpam-3704	380	13	)	)	PUNCT
ejpam-3704	380	14	ker	ker	NOUN
ejpam-3704	381	1	α	α	PROPN
ejpam-3704	381	2	=	=	NOUN
ejpam-3704	381	3	ker	ker	PROPN
ejpam-3704	381	4	α1	α1	PROPN
ejpam-3704	381	5	×	×	PROPN
ejpam-3704	381	6	ker	ker	PROPN
ejpam-3704	381	7	α2	α2	PROPN
ejpam-3704	381	8	;	;	PUNCT
ejpam-3704	381	9	(	(	PUNCT
ejpam-3704	381	10	iii	iii	X
ejpam-3704	381	11	)	)	PUNCT
ejpam-3704	382	1	i	i	PRON
ejpam-3704	382	2	m	m	VERB
ejpam-3704	382	3	α	α	NOUN
ejpam-3704	382	4	=	=	PUNCT
ejpam-3704	383	1	i	i	NOUN
ejpam-3704	383	2	m	m	VERB
ejpam-3704	383	3	α1	α1	PROPN
ejpam-3704	383	4	×	×	VERB
ejpam-3704	383	5	i	i	PRON
ejpam-3704	383	6	m	m	VERB
ejpam-3704	383	7	α2	α2	ADJ
ejpam-3704	383	8	;	;	PUNCT
ejpam-3704	383	9	and	and	CCONJ
ejpam-3704	383	10	(	(	PUNCT
ejpam-3704	383	11	iv	iv	X
ejpam-3704	383	12	)	)	PUNCT
ejpam-3704	383	13	α	α	PROPN
ejpam-3704	383	14	is	be	AUX
ejpam-3704	383	15	a	a	DET
ejpam-3704	383	16	hyper	hyper	ADJ
ejpam-3704	383	17	monomorphism	monomorphism	NOUN
ejpam-3704	383	18	(	(	PUNCT
ejpam-3704	383	19	respectively	respectively	ADV
ejpam-3704	383	20	,	,	PUNCT
ejpam-3704	383	21	hyper	hyper	ADJ
ejpam-3704	383	22	epimorphism	epimorphism	NOUN
ejpam-3704	383	23	)	)	PUNCT
ejpam-3704	383	24	if	if	SCONJ
ejpam-3704	383	25	and	and	CCONJ
ejpam-3704	383	26	only	only	ADV
ejpam-3704	383	27	if	if	SCONJ
ejpam-3704	383	28	αi	αi	PRON
ejpam-3704	383	29	is	be	AUX
ejpam-3704	383	30	a	a	DET
ejpam-3704	383	31	hyper	hyper	ADJ
ejpam-3704	383	32	monomorphism	monomorphism	NOUN
ejpam-3704	383	33	(	(	PUNCT
ejpam-3704	383	34	respectively	respectively	ADV
ejpam-3704	383	35	,	,	PUNCT
ejpam-3704	383	36	hyper	hyper	ADJ
ejpam-3704	383	37	epimorphism	epimorphism	NOUN
ejpam-3704	383	38	)	)	PUNCT
ejpam-3704	383	39	for	for	ADP
ejpam-3704	383	40	each	each	DET
ejpam-3704	383	41	i	i	NOUN
ejpam-3704	383	42	=	=	NOUN
ejpam-3704	383	43	1	1	NUM
ejpam-3704	383	44	,	,	PUNCT
ejpam-3704	383	45	2	2	NUM
ejpam-3704	383	46	.	.	PUNCT
ejpam-3704	383	47	proof	proof	NOUN
ejpam-3704	383	48	.	.	PUNCT
ejpam-3704	384	1	define	define	VERB
ejpam-3704	384	2	α	α	NOUN
ejpam-3704	384	3	:	:	PUNCT
ejpam-3704	384	4	h1	h1	VERB
ejpam-3704	384	5	×	×	PROPN
ejpam-3704	384	6	h2	h2	NOUN
ejpam-3704	384	7	−→	−→	NOUN
ejpam-3704	384	8	k1	k1	NOUN
ejpam-3704	384	9	×	×	PROPN
ejpam-3704	384	10	k2	k2	PROPN
ejpam-3704	384	11	by	by	ADP
ejpam-3704	384	12	α((a	α((a	PROPN
ejpam-3704	384	13	,	,	PUNCT
ejpam-3704	384	14	b	b	NOUN
ejpam-3704	384	15	)	)	PUNCT
ejpam-3704	384	16	)	)	PUNCT
ejpam-3704	385	1	=	=	SYM
ejpam-3704	385	2	(	(	PUNCT
ejpam-3704	385	3	α1(a	α1(a	NUM
ejpam-3704	385	4	)	)	PUNCT
ejpam-3704	385	5	,	,	PUNCT
ejpam-3704	385	6	α2(b	α2(b	NUM
ejpam-3704	385	7	)	)	PUNCT
ejpam-3704	385	8	)	)	PUNCT
ejpam-3704	385	9	for	for	ADP
ejpam-3704	385	10	all	all	PRON
ejpam-3704	385	11	(	(	PUNCT
ejpam-3704	385	12	a	a	PRON
ejpam-3704	385	13	,	,	PUNCT
ejpam-3704	385	14	b	b	NOUN
ejpam-3704	385	15	)	)	PUNCT
ejpam-3704	385	16	∈	∈	PROPN
ejpam-3704	385	17	h1	h1	PROPN
ejpam-3704	385	18	×h2	×h2	PROPN
ejpam-3704	385	19	.	.	PUNCT
ejpam-3704	386	1	(	(	PUNCT
ejpam-3704	386	2	i	i	NOUN
ejpam-3704	386	3	)	)	PUNCT
ejpam-3704	386	4	let	let	VERB
ejpam-3704	386	5	(	(	PUNCT
ejpam-3704	386	6	a	a	DET
ejpam-3704	386	7	,	,	PUNCT
ejpam-3704	386	8	b	b	NOUN
ejpam-3704	386	9	)	)	PUNCT
ejpam-3704	386	10	,	,	PUNCT
ejpam-3704	386	11	(	(	PUNCT
ejpam-3704	386	12	c	c	X
ejpam-3704	386	13	,	,	PUNCT
ejpam-3704	386	14	d	d	NOUN
ejpam-3704	386	15	)	)	PUNCT
ejpam-3704	386	16	∈	∈	PROPN
ejpam-3704	386	17	h1	h1	PROPN
ejpam-3704	386	18	×	×	PROPN
ejpam-3704	386	19	h2	h2	NOUN
ejpam-3704	386	20	such	such	ADJ
ejpam-3704	386	21	that	that	SCONJ
ejpam-3704	386	22	(	(	PUNCT
ejpam-3704	386	23	a	a	DET
ejpam-3704	386	24	,	,	PUNCT
ejpam-3704	386	25	b	b	NOUN
ejpam-3704	386	26	)	)	PUNCT
ejpam-3704	386	27	=	=	SYM
ejpam-3704	387	1	(	(	PUNCT
ejpam-3704	387	2	c	c	X
ejpam-3704	387	3	,	,	PUNCT
ejpam-3704	387	4	d	d	NOUN
ejpam-3704	387	5	)	)	PUNCT
ejpam-3704	387	6	.	.	PUNCT
ejpam-3704	388	1	then	then	ADV
ejpam-3704	388	2	a	a	DET
ejpam-3704	388	3	=	=	SYM
ejpam-3704	388	4	c	c	PROPN
ejpam-3704	388	5	and	and	CCONJ
ejpam-3704	388	6	b	b	X
ejpam-3704	388	7	=	=	SYM
ejpam-3704	388	8	d.	d.	PROPN
ejpam-3704	388	9	now	now	ADV
ejpam-3704	388	10	,	,	PUNCT
ejpam-3704	388	11	since	since	SCONJ
ejpam-3704	388	12	α1	α1	PROPN
ejpam-3704	388	13	and	and	CCONJ
ejpam-3704	388	14	α2	α2	NOUN
ejpam-3704	388	15	are	be	AUX
ejpam-3704	388	16	well	well	ADV
ejpam-3704	388	17	-	-	PUNCT
ejpam-3704	388	18	defined	define	VERB
ejpam-3704	388	19	maps	map	NOUN
ejpam-3704	388	20	,	,	PUNCT
ejpam-3704	388	21	it	it	PRON
ejpam-3704	388	22	follows	follow	VERB
ejpam-3704	388	23	that	that	SCONJ
ejpam-3704	388	24	α((a	α((a	PROPN
ejpam-3704	388	25	,	,	PUNCT
ejpam-3704	388	26	b	b	NOUN
ejpam-3704	388	27	)	)	PUNCT
ejpam-3704	388	28	)	)	PUNCT
ejpam-3704	389	1	=	=	SYM
ejpam-3704	389	2	(	(	PUNCT
ejpam-3704	389	3	α1(a	α1(a	NUM
ejpam-3704	389	4	)	)	PUNCT
ejpam-3704	389	5	,	,	PUNCT
ejpam-3704	389	6	α2(b	α2(b	NUM
ejpam-3704	389	7	)	)	PUNCT
ejpam-3704	389	8	)	)	PUNCT
ejpam-3704	390	1	=	=	SYM
ejpam-3704	390	2	(	(	PUNCT
ejpam-3704	390	3	α1(c	α1(c	NOUN
ejpam-3704	390	4	)	)	PUNCT
ejpam-3704	390	5	,	,	PUNCT
ejpam-3704	390	6	α2(d	α2(d	NOUN
ejpam-3704	390	7	)	)	PUNCT
ejpam-3704	390	8	)	)	PUNCT
ejpam-3704	391	1	=	=	PUNCT
ejpam-3704	391	2	α((c	α((c	NOUN
ejpam-3704	391	3	,	,	PUNCT
ejpam-3704	391	4	d	d	NOUN
ejpam-3704	391	5	)	)	PUNCT
ejpam-3704	391	6	)	)	PUNCT
ejpam-3704	391	7	.	.	PUNCT
ejpam-3704	392	1	so	so	ADV
ejpam-3704	392	2	,	,	PUNCT
ejpam-3704	392	3	α	α	PROPN
ejpam-3704	392	4	is	be	AUX
ejpam-3704	392	5	a	a	DET
ejpam-3704	392	6	well	well	ADV
ejpam-3704	392	7	-	-	PUNCT
ejpam-3704	392	8	defined	define	VERB
ejpam-3704	392	9	map	map	NOUN
ejpam-3704	392	10	.	.	PUNCT
ejpam-3704	393	1	observe	observe	VERB
ejpam-3704	393	2	that	that	SCONJ
ejpam-3704	393	3	(	(	PUNCT
ejpam-3704	393	4	0h1	0h1	NUM
ejpam-3704	393	5	,	,	PUNCT
ejpam-3704	393	6	0h2	0h2	NUM
ejpam-3704	393	7	)	)	PUNCT
ejpam-3704	394	1	∈	∈	PROPN
ejpam-3704	394	2	h1	h1	VERB
ejpam-3704	394	3	×	×	PROPN
ejpam-3704	394	4	h2	h2	NOUN
ejpam-3704	394	5	.	.	PUNCT
ejpam-3704	395	1	since	since	SCONJ
ejpam-3704	395	2	α1	α1	PROPN
ejpam-3704	395	3	and	and	CCONJ
ejpam-3704	395	4	α2	α2	NOUN
ejpam-3704	395	5	are	be	AUX
ejpam-3704	395	6	hyper	hyper	ADJ
ejpam-3704	395	7	homomorphisms	homomorphism	NOUN
ejpam-3704	395	8	,	,	PUNCT
ejpam-3704	395	9	by	by	ADP
ejpam-3704	395	10	(	(	PUNCT
ejpam-3704	395	11	hh1	hh1	INTJ
ejpam-3704	395	12	)	)	PUNCT
ejpam-3704	395	13	we	we	PRON
ejpam-3704	395	14	have	have	VERB
ejpam-3704	395	15	α((0h1	α((0h1	NOUN
ejpam-3704	395	16	,	,	PUNCT
ejpam-3704	395	17	0h2	0h2	NUM
ejpam-3704	395	18	)	)	PUNCT
ejpam-3704	395	19	)	)	PUNCT
ejpam-3704	396	1	=	=	SYM
ejpam-3704	396	2	(	(	PUNCT
ejpam-3704	396	3	α1(0h1	α1(0h1	NOUN
ejpam-3704	396	4	)	)	PUNCT
ejpam-3704	396	5	,	,	PUNCT
ejpam-3704	396	6	α2(0h2	α2(0h2	NUM
ejpam-3704	396	7	)	)	PUNCT
ejpam-3704	396	8	)	)	PUNCT
ejpam-3704	397	1	=	=	SYM
ejpam-3704	397	2	(	(	PUNCT
ejpam-3704	397	3	0k1	0k1	NUM
ejpam-3704	397	4	,	,	PUNCT
ejpam-3704	397	5	0k2	0k2	NUM
ejpam-3704	397	6	)	)	PUNCT
ejpam-3704	397	7	r.	r.	PROPN
ejpam-3704	397	8	amairanto	amairanto	PROPN
ejpam-3704	397	9	,	,	PUNCT
ejpam-3704	397	10	r.	r.	PROPN
ejpam-3704	397	11	isla	isla	PROPN
ejpam-3704	397	12	/	/	SYM
ejpam-3704	397	13	eur	eur	PROPN
ejpam-3704	397	14	.	.	PUNCT
ejpam-3704	398	1	j.	j.	PROPN
ejpam-3704	398	2	pure	pure	PROPN
ejpam-3704	398	3	appl	appl	PROPN
ejpam-3704	398	4	.	.	PROPN
ejpam-3704	398	5	math	math	PROPN
ejpam-3704	398	6	,	,	PUNCT
ejpam-3704	398	7	13	13	NUM
ejpam-3704	398	8	(	(	PUNCT
ejpam-3704	398	9	3	3	NUM
ejpam-3704	398	10	)	)	PUNCT
ejpam-3704	398	11	(	(	PUNCT
ejpam-3704	398	12	2020	2020	NUM
ejpam-3704	398	13	)	)	PUNCT
ejpam-3704	398	14	,	,	PUNCT
ejpam-3704	398	15	483	483	NUM
ejpam-3704	398	16	-	-	SYM
ejpam-3704	398	17	497	497	NUM
ejpam-3704	398	18	493	493	NUM
ejpam-3704	398	19	and	and	CCONJ
ejpam-3704	398	20	by	by	ADP
ejpam-3704	398	21	(	(	PUNCT
ejpam-3704	398	22	hh2	hh2	NOUN
ejpam-3704	398	23	)	)	PUNCT
ejpam-3704	398	24	,	,	PUNCT
ejpam-3704	398	25	α((a	α((a	PROPN
ejpam-3704	398	26	,	,	PUNCT
ejpam-3704	398	27	b	b	NOUN
ejpam-3704	398	28	)	)	PUNCT
ejpam-3704	398	29	~	~	PUNCT
ejpam-3704	398	30	(	(	PUNCT
ejpam-3704	398	31	c	c	X
ejpam-3704	398	32	,	,	PUNCT
ejpam-3704	398	33	d	d	NOUN
ejpam-3704	398	34	)	)	PUNCT
ejpam-3704	398	35	)	)	PUNCT
ejpam-3704	399	1	=	=	SYM
ejpam-3704	399	2	α((a~	α((a~	PROPN
ejpam-3704	399	3	c	c	NOUN
ejpam-3704	399	4	,	,	PUNCT
ejpam-3704	399	5	b~	b~	PROPN
ejpam-3704	399	6	d	d	NOUN
ejpam-3704	399	7	)	)	PUNCT
ejpam-3704	399	8	)	)	PUNCT
ejpam-3704	400	1	=	=	PRON
ejpam-3704	400	2	{	{	PUNCT
ejpam-3704	400	3	α((u	α((u	PROPN
ejpam-3704	400	4	,	,	PUNCT
ejpam-3704	400	5	v))|u	v))|u	PROPN
ejpam-3704	400	6	∈	∈	PROPN
ejpam-3704	400	7	a~	a~	PROPN
ejpam-3704	400	8	c	c	PROPN
ejpam-3704	400	9	,	,	PUNCT
ejpam-3704	400	10	v	v	NOUN
ejpam-3704	400	11	∈	∈	NOUN
ejpam-3704	400	12	b~	b~	PROPN
ejpam-3704	400	13	d	d	NOUN
ejpam-3704	400	14	}	}	PUNCT
ejpam-3704	400	15	=	=	SYM
ejpam-3704	400	16	{	{	PUNCT
ejpam-3704	400	17	(	(	PUNCT
ejpam-3704	400	18	α1(u	α1(u	NOUN
ejpam-3704	400	19	)	)	PUNCT
ejpam-3704	400	20	,	,	PUNCT
ejpam-3704	400	21	α2(v))|u	α2(v))|u	PUNCT
ejpam-3704	400	22	∈	∈	PROPN
ejpam-3704	400	23	a~	a~	PROPN
ejpam-3704	400	24	c	c	PROPN
ejpam-3704	400	25	,	,	PUNCT
ejpam-3704	400	26	v	v	NOUN
ejpam-3704	400	27	∈	∈	NOUN
ejpam-3704	400	28	b~	b~	PROPN
ejpam-3704	400	29	d	d	NOUN
ejpam-3704	400	30	}	}	PUNCT
ejpam-3704	400	31	=	=	SYM
ejpam-3704	400	32	(	(	PUNCT
ejpam-3704	400	33	α1(a~	α1(a~	PROPN
ejpam-3704	400	34	c	c	NOUN
ejpam-3704	400	35	)	)	PUNCT
ejpam-3704	400	36	,	,	PUNCT
ejpam-3704	400	37	α2(b~	α2(b~	PROPN
ejpam-3704	400	38	d	d	NOUN
ejpam-3704	400	39	)	)	PUNCT
ejpam-3704	400	40	)	)	PUNCT
ejpam-3704	400	41	=	=	SYM
ejpam-3704	400	42	(	(	PUNCT
ejpam-3704	400	43	α1(a	α1(a	NUM
ejpam-3704	400	44	)	)	PUNCT
ejpam-3704	400	45	~	~	PUNCT
ejpam-3704	400	46	α1(c	α1(c	X
ejpam-3704	400	47	)	)	PUNCT
ejpam-3704	400	48	,	,	PUNCT
ejpam-3704	400	49	α2(b	α2(b	NUM
ejpam-3704	400	50	)	)	PUNCT
ejpam-3704	400	51	~	~	PUNCT
ejpam-3704	400	52	α2(d	α2(d	X
ejpam-3704	400	53	)	)	PUNCT
ejpam-3704	400	54	)	)	PUNCT
ejpam-3704	401	1	=	=	SYM
ejpam-3704	401	2	α(a	α(a	NOUN
ejpam-3704	401	3	,	,	PUNCT
ejpam-3704	401	4	b	b	NOUN
ejpam-3704	401	5	)	)	PUNCT
ejpam-3704	401	6	~	~	PUNCT
ejpam-3704	401	7	α(c	α(c	NOUN
ejpam-3704	401	8	,	,	PUNCT
ejpam-3704	401	9	d	d	NOUN
ejpam-3704	401	10	)	)	PUNCT
ejpam-3704	401	11	.	.	PUNCT
ejpam-3704	402	1	hence	hence	ADV
ejpam-3704	402	2	,	,	PUNCT
ejpam-3704	402	3	α	α	PROPN
ejpam-3704	402	4	is	be	AUX
ejpam-3704	402	5	a	a	DET
ejpam-3704	402	6	hyper	hyper	ADJ
ejpam-3704	402	7	homomorphism	homomorphism	NOUN
ejpam-3704	402	8	.	.	PUNCT
ejpam-3704	403	1	(	(	PUNCT
ejpam-3704	403	2	ii	ii	NOUN
ejpam-3704	403	3	)	)	PUNCT
ejpam-3704	403	4	by	by	ADP
ejpam-3704	403	5	definition	definition	NOUN
ejpam-3704	403	6	,	,	PUNCT
ejpam-3704	403	7	ker	ker	NOUN
ejpam-3704	404	1	α	α	PROPN
ejpam-3704	404	2	=	=	SYM
ejpam-3704	404	3	{	{	PUNCT
ejpam-3704	404	4	(	(	PUNCT
ejpam-3704	404	5	a	a	PRON
ejpam-3704	404	6	,	,	PUNCT
ejpam-3704	404	7	b	b	NOUN
ejpam-3704	404	8	)	)	PUNCT
ejpam-3704	404	9	∈	∈	PROPN
ejpam-3704	404	10	h1	h1	PROPN
ejpam-3704	404	11	×h2|α((a	×h2|α((a	PROPN
ejpam-3704	404	12	,	,	PUNCT
ejpam-3704	404	13	b	b	NOUN
ejpam-3704	404	14	)	)	PUNCT
ejpam-3704	404	15	)	)	PUNCT
ejpam-3704	405	1	=	=	SYM
ejpam-3704	405	2	(	(	PUNCT
ejpam-3704	405	3	0k1	0k1	NUM
ejpam-3704	405	4	,	,	PUNCT
ejpam-3704	405	5	0k2	0k2	NUM
ejpam-3704	405	6	)	)	PUNCT
ejpam-3704	405	7	}	}	PUNCT
ejpam-3704	405	8	=	=	SYM
ejpam-3704	405	9	{	{	PUNCT
ejpam-3704	405	10	(	(	PUNCT
ejpam-3704	405	11	a	a	PRON
ejpam-3704	405	12	,	,	PUNCT
ejpam-3704	405	13	b	b	NOUN
ejpam-3704	405	14	)	)	PUNCT
ejpam-3704	405	15	∈	∈	PROPN
ejpam-3704	405	16	h1	h1	PROPN
ejpam-3704	405	17	×h2|(α1(a	×h2|(α1(a	PROPN
ejpam-3704	405	18	)	)	PUNCT
ejpam-3704	405	19	,	,	PUNCT
ejpam-3704	405	20	α2(b	α2(b	NUM
ejpam-3704	405	21	)	)	PUNCT
ejpam-3704	405	22	)	)	PUNCT
ejpam-3704	406	1	=	=	SYM
ejpam-3704	406	2	(	(	PUNCT
ejpam-3704	406	3	0k1	0k1	NUM
ejpam-3704	406	4	,	,	PUNCT
ejpam-3704	406	5	0k2	0k2	NUM
ejpam-3704	406	6	)	)	PUNCT
ejpam-3704	406	7	}	}	PUNCT
ejpam-3704	406	8	=	=	SYM
ejpam-3704	406	9	{	{	PUNCT
ejpam-3704	406	10	(	(	PUNCT
ejpam-3704	406	11	a	a	PRON
ejpam-3704	406	12	,	,	PUNCT
ejpam-3704	406	13	b	b	NOUN
ejpam-3704	406	14	)	)	PUNCT
ejpam-3704	406	15	∈	∈	PROPN
ejpam-3704	406	16	h1	h1	PROPN
ejpam-3704	406	17	×h2|α1(a	×h2|α1(a	PROPN
ejpam-3704	406	18	)	)	PUNCT
ejpam-3704	406	19	=	=	NOUN
ejpam-3704	406	20	0k1	0k1	NOUN
ejpam-3704	406	21	and	and	CCONJ
ejpam-3704	406	22	α2(b	α2(b	NUM
ejpam-3704	406	23	)	)	PUNCT
ejpam-3704	406	24	=	=	PUNCT
ejpam-3704	406	25	0k2	0k2	NUM
ejpam-3704	406	26	}	}	PUNCT
ejpam-3704	406	27	=	=	SYM
ejpam-3704	406	28	{	{	PUNCT
ejpam-3704	406	29	(	(	PUNCT
ejpam-3704	406	30	a	a	PRON
ejpam-3704	406	31	,	,	PUNCT
ejpam-3704	406	32	b	b	NOUN
ejpam-3704	406	33	)	)	PUNCT
ejpam-3704	406	34	∈	∈	PROPN
ejpam-3704	406	35	h1	h1	PROPN
ejpam-3704	406	36	×h2|a	×h2|a	VERB
ejpam-3704	406	37	∈	∈	PROPN
ejpam-3704	406	38	ker	ker	PROPN
ejpam-3704	406	39	α1	α1	PROPN
ejpam-3704	406	40	,	,	PUNCT
ejpam-3704	406	41	b	b	PROPN
ejpam-3704	406	42	∈	∈	PROPN
ejpam-3704	406	43	ker	ker	NOUN
ejpam-3704	406	44	α2	α2	PROPN
ejpam-3704	406	45	}	}	PUNCT
ejpam-3704	407	1	=	=	SYM
ejpam-3704	407	2	ker	ker	NOUN
ejpam-3704	407	3	α1	α1	PROPN
ejpam-3704	407	4	×	×	PROPN
ejpam-3704	407	5	ker	ker	PROPN
ejpam-3704	407	6	α2	α2	PROPN
ejpam-3704	407	7	.	.	PUNCT
ejpam-3704	408	1	(	(	PUNCT
ejpam-3704	408	2	iii	iii	X
ejpam-3704	408	3	)	)	PUNCT
ejpam-3704	408	4	by	by	ADP
ejpam-3704	408	5	definition	definition	NOUN
ejpam-3704	408	6	,	,	PUNCT
ejpam-3704	408	7	i	i	PRON
ejpam-3704	408	8	m	m	VERB
ejpam-3704	408	9	α	α	NOUN
ejpam-3704	408	10	=	=	X
ejpam-3704	408	11	{	{	PUNCT
ejpam-3704	408	12	α((a	α((a	NOUN
ejpam-3704	408	13	,	,	PUNCT
ejpam-3704	408	14	b))|(a	b))|(a	NOUN
ejpam-3704	408	15	,	,	PUNCT
ejpam-3704	408	16	b	b	X
ejpam-3704	408	17	)	)	PUNCT
ejpam-3704	408	18	∈	∈	PROPN
ejpam-3704	408	19	h1	h1	PROPN
ejpam-3704	408	20	×h2	×h2	PROPN
ejpam-3704	408	21	}	}	PUNCT
ejpam-3704	408	22	=	=	SYM
ejpam-3704	408	23	{	{	PUNCT
ejpam-3704	408	24	(	(	PUNCT
ejpam-3704	408	25	α1(a	α1(a	NUM
ejpam-3704	408	26	)	)	PUNCT
ejpam-3704	408	27	,	,	PUNCT
ejpam-3704	408	28	α2(b))|(a	α2(b))|(a	PROPN
ejpam-3704	408	29	,	,	PUNCT
ejpam-3704	408	30	b	b	NOUN
ejpam-3704	408	31	)	)	PUNCT
ejpam-3704	408	32	∈	∈	PROPN
ejpam-3704	408	33	h1	h1	PROPN
ejpam-3704	408	34	×h2	×h2	PROPN
ejpam-3704	408	35	}	}	PUNCT
ejpam-3704	408	36	=	=	SYM
ejpam-3704	408	37	{	{	PUNCT
ejpam-3704	408	38	(	(	PUNCT
ejpam-3704	408	39	α1(a	α1(a	NUM
ejpam-3704	408	40	)	)	PUNCT
ejpam-3704	408	41	,	,	PUNCT
ejpam-3704	408	42	α2(b))|α1(a	α2(b))|α1(a	PROPN
ejpam-3704	408	43	)	)	PUNCT
ejpam-3704	408	44	∈	∈	PROPN
ejpam-3704	409	1	i	i	PROPN
ejpam-3704	409	2	m	m	PROPN
ejpam-3704	409	3	α1	α1	PROPN
ejpam-3704	409	4	,	,	PUNCT
ejpam-3704	409	5	α2(b	α2(b	NUM
ejpam-3704	409	6	)	)	PUNCT
ejpam-3704	409	7	∈	∈	PROPN
ejpam-3704	410	1	i	i	PRON
ejpam-3704	410	2	m	m	VERB
ejpam-3704	410	3	α2	α2	ADJ
ejpam-3704	410	4	}	}	PUNCT
ejpam-3704	411	1	=	=	PUNCT
ejpam-3704	412	1	i	i	PRON
ejpam-3704	412	2	m	m	VERB
ejpam-3704	412	3	α1	α1	PROPN
ejpam-3704	412	4	×	×	VERB
ejpam-3704	412	5	i	i	NOUN
ejpam-3704	412	6	m	m	VERB
ejpam-3704	412	7	α2	α2	ADJ
ejpam-3704	412	8	.	.	PUNCT
ejpam-3704	413	1	(	(	PUNCT
ejpam-3704	413	2	iv	iv	X
ejpam-3704	413	3	)	)	PUNCT
ejpam-3704	413	4	suppose	suppose	VERB
ejpam-3704	413	5	that	that	SCONJ
ejpam-3704	413	6	α	α	PROPN
ejpam-3704	413	7	is	be	AUX
ejpam-3704	413	8	one	one	NUM
ejpam-3704	413	9	-	-	PUNCT
ejpam-3704	413	10	to	to	ADP
ejpam-3704	413	11	-	-	PUNCT
ejpam-3704	413	12	one	one	NUM
ejpam-3704	413	13	.	.	PUNCT
ejpam-3704	414	1	let	let	VERB
ejpam-3704	414	2	a	a	PRON
ejpam-3704	414	3	,	,	PUNCT
ejpam-3704	414	4	c	c	PROPN
ejpam-3704	414	5	∈	∈	PROPN
ejpam-3704	414	6	h1	h1	PROPN
ejpam-3704	414	7	and	and	CCONJ
ejpam-3704	414	8	b	b	NOUN
ejpam-3704	414	9	,	,	PUNCT
ejpam-3704	414	10	d	d	PROPN
ejpam-3704	414	11	∈	∈	PROPN
ejpam-3704	414	12	h2	h2	NOUN
ejpam-3704	415	1	such	such	ADJ
ejpam-3704	415	2	that	that	PRON
ejpam-3704	415	3	α1(a	α1(a	NUM
ejpam-3704	415	4	)	)	PUNCT
ejpam-3704	415	5	=	=	SYM
ejpam-3704	415	6	α1(c	α1(c	NOUN
ejpam-3704	415	7	)	)	PUNCT
ejpam-3704	415	8	and	and	CCONJ
ejpam-3704	415	9	α2(b	α2(b	NUM
ejpam-3704	415	10	)	)	PUNCT
ejpam-3704	415	11	=	=	SYM
ejpam-3704	415	12	α2(d	α2(d	PROPN
ejpam-3704	415	13	)	)	PUNCT
ejpam-3704	415	14	.	.	PUNCT
ejpam-3704	416	1	then	then	ADV
ejpam-3704	416	2	α((a	α((a	PROPN
ejpam-3704	416	3	,	,	PUNCT
ejpam-3704	416	4	b	b	NOUN
ejpam-3704	416	5	)	)	PUNCT
ejpam-3704	416	6	)	)	PUNCT
ejpam-3704	416	7	=	=	SYM
ejpam-3704	416	8	(	(	PUNCT
ejpam-3704	416	9	α1(a	α1(a	NUM
ejpam-3704	416	10	)	)	PUNCT
ejpam-3704	416	11	,	,	PUNCT
ejpam-3704	416	12	α2(b	α2(b	NUM
ejpam-3704	416	13	)	)	PUNCT
ejpam-3704	416	14	)	)	PUNCT
ejpam-3704	417	1	=	=	SYM
ejpam-3704	417	2	(	(	PUNCT
ejpam-3704	417	3	α1(c	α1(c	NOUN
ejpam-3704	417	4	)	)	PUNCT
ejpam-3704	417	5	,	,	PUNCT
ejpam-3704	417	6	α2(d	α2(d	NOUN
ejpam-3704	417	7	)	)	PUNCT
ejpam-3704	417	8	)	)	PUNCT
ejpam-3704	418	1	=	=	PUNCT
ejpam-3704	418	2	α((c	α((c	NOUN
ejpam-3704	418	3	,	,	PUNCT
ejpam-3704	418	4	d	d	NOUN
ejpam-3704	418	5	)	)	PUNCT
ejpam-3704	418	6	)	)	PUNCT
ejpam-3704	418	7	.	.	PUNCT
ejpam-3704	419	1	since	since	SCONJ
ejpam-3704	419	2	α	α	PROPN
ejpam-3704	419	3	is	be	AUX
ejpam-3704	419	4	one	one	NUM
ejpam-3704	419	5	-	-	PUNCT
ejpam-3704	419	6	to	to	ADP
ejpam-3704	419	7	-	-	PUNCT
ejpam-3704	419	8	one	one	NUM
ejpam-3704	419	9	,	,	PUNCT
ejpam-3704	419	10	(	(	PUNCT
ejpam-3704	419	11	a	a	DET
ejpam-3704	419	12	,	,	PUNCT
ejpam-3704	419	13	b	b	NOUN
ejpam-3704	419	14	)	)	PUNCT
ejpam-3704	419	15	=	=	SYM
ejpam-3704	419	16	(	(	PUNCT
ejpam-3704	419	17	c	c	X
ejpam-3704	419	18	,	,	PUNCT
ejpam-3704	419	19	d	d	NOUN
ejpam-3704	419	20	)	)	PUNCT
ejpam-3704	419	21	,	,	PUNCT
ejpam-3704	419	22	that	that	ADV
ejpam-3704	419	23	is	is	ADV
ejpam-3704	419	24	,	,	PUNCT
ejpam-3704	419	25	a	a	DET
ejpam-3704	419	26	=	=	SYM
ejpam-3704	419	27	c	c	NOUN
ejpam-3704	419	28	and	and	CCONJ
ejpam-3704	419	29	b	b	X
ejpam-3704	419	30	=	=	PROPN
ejpam-3704	419	31	d.	d.	PROPN
ejpam-3704	419	32	thus	thus	ADV
ejpam-3704	419	33	,	,	PUNCT
ejpam-3704	419	34	α1	α1	PROPN
ejpam-3704	419	35	and	and	CCONJ
ejpam-3704	419	36	α2	α2	NOUN
ejpam-3704	419	37	are	be	AUX
ejpam-3704	419	38	one	one	NUM
ejpam-3704	419	39	-	-	PUNCT
ejpam-3704	419	40	to	to	ADP
ejpam-3704	419	41	-	-	PUNCT
ejpam-3704	419	42	one	one	NUM
ejpam-3704	419	43	maps	map	NOUN
ejpam-3704	419	44	.	.	PUNCT
ejpam-3704	420	1	conversely	conversely	ADV
ejpam-3704	420	2	,	,	PUNCT
ejpam-3704	420	3	assume	assume	VERB
ejpam-3704	420	4	that	that	SCONJ
ejpam-3704	420	5	α1	α1	PROPN
ejpam-3704	420	6	and	and	CCONJ
ejpam-3704	420	7	α2	α2	NOUN
ejpam-3704	420	8	are	be	AUX
ejpam-3704	420	9	one	one	NUM
ejpam-3704	420	10	-	-	PUNCT
ejpam-3704	420	11	to	to	ADP
ejpam-3704	420	12	-	-	PUNCT
ejpam-3704	420	13	one	one	NUM
ejpam-3704	420	14	maps	map	NOUN
ejpam-3704	420	15	.	.	PUNCT
ejpam-3704	421	1	suppose	suppose	VERB
ejpam-3704	421	2	(	(	PUNCT
ejpam-3704	421	3	a	a	DET
ejpam-3704	421	4	,	,	PUNCT
ejpam-3704	421	5	b	b	NOUN
ejpam-3704	421	6	)	)	PUNCT
ejpam-3704	421	7	,	,	PUNCT
ejpam-3704	421	8	(	(	PUNCT
ejpam-3704	421	9	c	c	X
ejpam-3704	421	10	,	,	PUNCT
ejpam-3704	421	11	d	d	NOUN
ejpam-3704	421	12	)	)	PUNCT
ejpam-3704	421	13	∈	∈	PROPN
ejpam-3704	421	14	h1×h2	h1×h2	NOUN
ejpam-3704	421	15	such	such	ADJ
ejpam-3704	421	16	that	that	PRON
ejpam-3704	421	17	α((a	α((a	PROPN
ejpam-3704	421	18	,	,	PUNCT
ejpam-3704	421	19	b	b	NOUN
ejpam-3704	421	20	)	)	PUNCT
ejpam-3704	421	21	)	)	PUNCT
ejpam-3704	422	1	=	=	PUNCT
ejpam-3704	422	2	α((c	α((c	NOUN
ejpam-3704	422	3	,	,	PUNCT
ejpam-3704	422	4	d	d	NOUN
ejpam-3704	422	5	)	)	PUNCT
ejpam-3704	422	6	)	)	PUNCT
ejpam-3704	422	7	.	.	PUNCT
ejpam-3704	423	1	then	then	ADV
ejpam-3704	423	2	(	(	PUNCT
ejpam-3704	423	3	α1(a	α1(a	NUM
ejpam-3704	423	4	)	)	PUNCT
ejpam-3704	423	5	,	,	PUNCT
ejpam-3704	423	6	α2(b	α2(b	NUM
ejpam-3704	423	7	)	)	PUNCT
ejpam-3704	423	8	)	)	PUNCT
ejpam-3704	423	9	=	=	SYM
ejpam-3704	423	10	α((a	α((a	PROPN
ejpam-3704	423	11	,	,	PUNCT
ejpam-3704	423	12	b	b	NOUN
ejpam-3704	423	13	)	)	PUNCT
ejpam-3704	423	14	)	)	PUNCT
ejpam-3704	424	1	=	=	PUNCT
ejpam-3704	424	2	α((c	α((c	NOUN
ejpam-3704	424	3	,	,	PUNCT
ejpam-3704	424	4	d	d	NOUN
ejpam-3704	424	5	)	)	PUNCT
ejpam-3704	424	6	)	)	PUNCT
ejpam-3704	425	1	=	=	PRON
ejpam-3704	425	2	(	(	PUNCT
ejpam-3704	425	3	α1(c	α1(c	NOUN
ejpam-3704	425	4	)	)	PUNCT
ejpam-3704	425	5	,	,	PUNCT
ejpam-3704	425	6	α2(d	α2(d	NOUN
ejpam-3704	425	7	)	)	PUNCT
ejpam-3704	425	8	)	)	PUNCT
ejpam-3704	425	9	.	.	PUNCT
ejpam-3704	426	1	this	this	PRON
ejpam-3704	426	2	means	mean	VERB
ejpam-3704	426	3	that	that	PRON
ejpam-3704	426	4	α1(a	α1(a	NUM
ejpam-3704	426	5	)	)	PUNCT
ejpam-3704	426	6	=	=	SYM
ejpam-3704	426	7	α1(c	α1(c	NOUN
ejpam-3704	426	8	)	)	PUNCT
ejpam-3704	426	9	and	and	CCONJ
ejpam-3704	426	10	α2(b	α2(b	NUM
ejpam-3704	426	11	)	)	PUNCT
ejpam-3704	426	12	=	=	SYM
ejpam-3704	426	13	α2(d	α2(d	PROPN
ejpam-3704	426	14	)	)	PUNCT
ejpam-3704	426	15	and	and	CCONJ
ejpam-3704	426	16	since	since	SCONJ
ejpam-3704	426	17	α1	α1	PROPN
ejpam-3704	426	18	and	and	CCONJ
ejpam-3704	426	19	α2	α2	NOUN
ejpam-3704	426	20	are	be	AUX
ejpam-3704	426	21	both	both	PRON
ejpam-3704	426	22	one	one	NUM
ejpam-3704	426	23	-	-	PUNCT
ejpam-3704	426	24	to	to	ADP
ejpam-3704	426	25	-	-	PUNCT
ejpam-3704	426	26	one	one	NUM
ejpam-3704	426	27	,	,	PUNCT
ejpam-3704	426	28	it	it	PRON
ejpam-3704	426	29	follows	follow	VERB
ejpam-3704	426	30	that	that	SCONJ
ejpam-3704	426	31	a	a	DET
ejpam-3704	426	32	=	=	SYM
ejpam-3704	426	33	c	c	NOUN
ejpam-3704	426	34	and	and	CCONJ
ejpam-3704	426	35	b	b	X
ejpam-3704	426	36	=	=	SYM
ejpam-3704	426	37	d.	d.	PROPN
ejpam-3704	426	38	hence	hence	ADV
ejpam-3704	426	39	,	,	PUNCT
ejpam-3704	426	40	(	(	PUNCT
ejpam-3704	426	41	a	a	DET
ejpam-3704	426	42	,	,	PUNCT
ejpam-3704	426	43	b	b	NOUN
ejpam-3704	426	44	)	)	PUNCT
ejpam-3704	426	45	=	=	SYM
ejpam-3704	426	46	(	(	PUNCT
ejpam-3704	426	47	c	c	X
ejpam-3704	426	48	,	,	PUNCT
ejpam-3704	426	49	d	d	NOUN
ejpam-3704	426	50	)	)	PUNCT
ejpam-3704	426	51	.	.	PUNCT
ejpam-3704	427	1	therefore	therefore	ADV
ejpam-3704	427	2	,	,	PUNCT
ejpam-3704	427	3	α	α	PROPN
ejpam-3704	427	4	is	be	AUX
ejpam-3704	427	5	one	one	NUM
ejpam-3704	427	6	-	-	PUNCT
ejpam-3704	427	7	to	to	ADP
ejpam-3704	427	8	-	-	PUNCT
ejpam-3704	427	9	one	one	NUM
ejpam-3704	427	10	.	.	PUNCT
ejpam-3704	428	1	suppose	suppose	VERB
ejpam-3704	428	2	α	α	PRON
ejpam-3704	428	3	is	be	AUX
ejpam-3704	428	4	onto	onto	ADP
ejpam-3704	428	5	.	.	PUNCT
ejpam-3704	429	1	let	let	VERB
ejpam-3704	429	2	x	x	PUNCT
ejpam-3704	429	3	∈	∈	PROPN
ejpam-3704	429	4	k1	k1	NOUN
ejpam-3704	429	5	and	and	CCONJ
ejpam-3704	429	6	y	y	PROPN
ejpam-3704	429	7	∈	∈	PROPN
ejpam-3704	429	8	k2	k2	PROPN
ejpam-3704	429	9	.	.	PUNCT
ejpam-3704	430	1	it	it	PRON
ejpam-3704	430	2	follows	follow	VERB
ejpam-3704	430	3	that	that	SCONJ
ejpam-3704	430	4	(	(	PUNCT
ejpam-3704	430	5	x	x	X
ejpam-3704	430	6	,	,	PUNCT
ejpam-3704	430	7	y	y	NOUN
ejpam-3704	430	8	)	)	PUNCT
ejpam-3704	430	9	∈	∈	PROPN
ejpam-3704	430	10	k1×k2	k1×k2	PROPN
ejpam-3704	430	11	.	.	PUNCT
ejpam-3704	431	1	since	since	SCONJ
ejpam-3704	431	2	α	α	PROPN
ejpam-3704	431	3	is	be	AUX
ejpam-3704	431	4	onto	onto	ADP
ejpam-3704	431	5	,	,	PUNCT
ejpam-3704	431	6	there	there	PRON
ejpam-3704	431	7	exists	exist	VERB
ejpam-3704	431	8	(	(	PUNCT
ejpam-3704	431	9	a	a	PRON
ejpam-3704	431	10	,	,	PUNCT
ejpam-3704	431	11	b	b	NOUN
ejpam-3704	431	12	)	)	PUNCT
ejpam-3704	431	13	∈	∈	PROPN
ejpam-3704	431	14	h1	h1	PROPN
ejpam-3704	431	15	×h2	×h2	PROPN
ejpam-3704	431	16	such	such	ADJ
ejpam-3704	431	17	that	that	SCONJ
ejpam-3704	431	18	(	(	PUNCT
ejpam-3704	431	19	α1(a	α1(a	NUM
ejpam-3704	431	20	)	)	PUNCT
ejpam-3704	431	21	,	,	PUNCT
ejpam-3704	431	22	α2(b	α2(b	NUM
ejpam-3704	431	23	)	)	PUNCT
ejpam-3704	431	24	)	)	PUNCT
ejpam-3704	432	1	=	=	SYM
ejpam-3704	432	2	α((a	α((a	PROPN
ejpam-3704	432	3	,	,	PUNCT
ejpam-3704	432	4	b	b	NOUN
ejpam-3704	432	5	)	)	PUNCT
ejpam-3704	432	6	)	)	PUNCT
ejpam-3704	433	1	=	=	SYM
ejpam-3704	433	2	(	(	PUNCT
ejpam-3704	433	3	x	x	X
ejpam-3704	433	4	,	,	PUNCT
ejpam-3704	433	5	y	y	PROPN
ejpam-3704	433	6	)	)	PUNCT
ejpam-3704	433	7	,	,	PUNCT
ejpam-3704	433	8	that	that	ADV
ejpam-3704	433	9	is	is	ADV
ejpam-3704	433	10	,	,	PUNCT
ejpam-3704	433	11	α1(a	α1(a	NUM
ejpam-3704	433	12	)	)	PUNCT
ejpam-3704	433	13	=	=	SYM
ejpam-3704	434	1	x	x	X
ejpam-3704	434	2	and	and	CCONJ
ejpam-3704	434	3	α2(b	α2(b	NUM
ejpam-3704	434	4	)	)	PUNCT
ejpam-3704	434	5	=	=	SYM
ejpam-3704	434	6	y	y	PROPN
ejpam-3704	434	7	for	for	ADP
ejpam-3704	434	8	some	some	DET
ejpam-3704	434	9	a	a	DET
ejpam-3704	434	10	∈	∈	PROPN
ejpam-3704	434	11	h1	h1	NOUN
ejpam-3704	434	12	and	and	CCONJ
ejpam-3704	434	13	b	b	PROPN
ejpam-3704	434	14	∈	∈	PROPN
ejpam-3704	434	15	h2	h2	NOUN
ejpam-3704	434	16	.	.	PUNCT
ejpam-3704	435	1	so	so	ADV
ejpam-3704	435	2	,	,	PUNCT
ejpam-3704	435	3	α1	α1	PROPN
ejpam-3704	435	4	and	and	CCONJ
ejpam-3704	435	5	α2	α2	NOUN
ejpam-3704	435	6	are	be	AUX
ejpam-3704	435	7	onto	onto	ADP
ejpam-3704	435	8	r.	r.	PROPN
ejpam-3704	435	9	amairanto	amairanto	PROPN
ejpam-3704	435	10	,	,	PUNCT
ejpam-3704	435	11	r.	r.	PROPN
ejpam-3704	435	12	isla	isla	PROPN
ejpam-3704	435	13	/	/	SYM
ejpam-3704	435	14	eur	eur	PROPN
ejpam-3704	435	15	.	.	PUNCT
ejpam-3704	436	1	j.	j.	PROPN
ejpam-3704	436	2	pure	pure	PROPN
ejpam-3704	436	3	appl	appl	PROPN
ejpam-3704	436	4	.	.	PROPN
ejpam-3704	436	5	math	math	PROPN
ejpam-3704	436	6	,	,	PUNCT
ejpam-3704	436	7	13	13	NUM
ejpam-3704	436	8	(	(	PUNCT
ejpam-3704	436	9	3	3	NUM
ejpam-3704	436	10	)	)	PUNCT
ejpam-3704	436	11	(	(	PUNCT
ejpam-3704	436	12	2020	2020	NUM
ejpam-3704	436	13	)	)	PUNCT
ejpam-3704	436	14	,	,	PUNCT
ejpam-3704	436	15	483	483	NUM
ejpam-3704	436	16	-	-	SYM
ejpam-3704	436	17	497	497	NUM
ejpam-3704	436	18	494	494	NUM
ejpam-3704	436	19	maps	map	NOUN
ejpam-3704	436	20	.	.	PUNCT
ejpam-3704	437	1	next	next	ADV
ejpam-3704	437	2	,	,	PUNCT
ejpam-3704	437	3	suppose	suppose	VERB
ejpam-3704	437	4	α1	α1	PROPN
ejpam-3704	437	5	and	and	CCONJ
ejpam-3704	437	6	α2	α2	NOUN
ejpam-3704	437	7	are	be	AUX
ejpam-3704	437	8	onto	onto	ADP
ejpam-3704	437	9	maps	map	NOUN
ejpam-3704	437	10	.	.	PUNCT
ejpam-3704	438	1	let	let	VERB
ejpam-3704	438	2	(	(	PUNCT
ejpam-3704	438	3	x	x	NOUN
ejpam-3704	438	4	,	,	PUNCT
ejpam-3704	438	5	y	y	NOUN
ejpam-3704	438	6	)	)	PUNCT
ejpam-3704	438	7	∈	∈	PROPN
ejpam-3704	438	8	k1	k1	PROPN
ejpam-3704	438	9	×k2	×k2	PROPN
ejpam-3704	438	10	.	.	PUNCT
ejpam-3704	439	1	then	then	ADV
ejpam-3704	439	2	x	x	SYM
ejpam-3704	439	3	∈	∈	PROPN
ejpam-3704	439	4	k1	k1	NOUN
ejpam-3704	439	5	and	and	CCONJ
ejpam-3704	439	6	y	y	PROPN
ejpam-3704	439	7	∈	∈	PROPN
ejpam-3704	439	8	k2	k2	PROPN
ejpam-3704	439	9	.	.	PUNCT
ejpam-3704	440	1	since	since	SCONJ
ejpam-3704	440	2	α1	α1	PROPN
ejpam-3704	440	3	and	and	CCONJ
ejpam-3704	440	4	α2	α2	NOUN
ejpam-3704	440	5	are	be	AUX
ejpam-3704	440	6	onto	onto	ADP
ejpam-3704	440	7	maps	map	NOUN
ejpam-3704	440	8	,	,	PUNCT
ejpam-3704	440	9	we	we	PRON
ejpam-3704	440	10	can	can	AUX
ejpam-3704	440	11	pick	pick	VERB
ejpam-3704	440	12	some	some	DET
ejpam-3704	440	13	elements	element	NOUN
ejpam-3704	440	14	a	a	DET
ejpam-3704	440	15	∈	∈	PROPN
ejpam-3704	440	16	h1	h1	NOUN
ejpam-3704	440	17	and	and	CCONJ
ejpam-3704	440	18	b	b	PROPN
ejpam-3704	440	19	∈	∈	PROPN
ejpam-3704	440	20	h2	h2	NOUN
ejpam-3704	440	21	such	such	ADJ
ejpam-3704	440	22	that	that	PRON
ejpam-3704	440	23	α1(a	α1(a	NUM
ejpam-3704	440	24	)	)	PUNCT
ejpam-3704	440	25	=	=	SYM
ejpam-3704	441	1	x	x	X
ejpam-3704	441	2	and	and	CCONJ
ejpam-3704	441	3	α2(b	α2(b	NUM
ejpam-3704	441	4	)	)	PUNCT
ejpam-3704	441	5	=	=	SYM
ejpam-3704	441	6	y	y	PROPN
ejpam-3704	441	7	,	,	PUNCT
ejpam-3704	441	8	that	that	ADV
ejpam-3704	441	9	is	be	AUX
ejpam-3704	441	10	,	,	PUNCT
ejpam-3704	441	11	α((a	α((a	PROPN
ejpam-3704	441	12	,	,	PUNCT
ejpam-3704	441	13	b	b	NOUN
ejpam-3704	441	14	)	)	PUNCT
ejpam-3704	441	15	)	)	PUNCT
ejpam-3704	442	1	=	=	SYM
ejpam-3704	442	2	(	(	PUNCT
ejpam-3704	442	3	α1(a	α1(a	NUM
ejpam-3704	442	4	)	)	PUNCT
ejpam-3704	442	5	,	,	PUNCT
ejpam-3704	442	6	α2(b	α2(b	NUM
ejpam-3704	442	7	)	)	PUNCT
ejpam-3704	442	8	)	)	PUNCT
ejpam-3704	443	1	=	=	SYM
ejpam-3704	443	2	(	(	PUNCT
ejpam-3704	443	3	x	x	X
ejpam-3704	443	4	,	,	PUNCT
ejpam-3704	443	5	y	y	NOUN
ejpam-3704	443	6	)	)	PUNCT
ejpam-3704	443	7	for	for	ADP
ejpam-3704	443	8	some	some	PRON
ejpam-3704	443	9	(	(	PUNCT
ejpam-3704	443	10	a	a	PRON
ejpam-3704	443	11	,	,	PUNCT
ejpam-3704	443	12	b	b	NOUN
ejpam-3704	443	13	)	)	PUNCT
ejpam-3704	443	14	∈	∈	PROPN
ejpam-3704	443	15	h1	h1	PROPN
ejpam-3704	443	16	×h2	×h2	PROPN
ejpam-3704	443	17	.	.	PUNCT
ejpam-3704	444	1	therefore	therefore	ADV
ejpam-3704	444	2	,	,	PUNCT
ejpam-3704	444	3	α	α	PROPN
ejpam-3704	444	4	is	be	AUX
ejpam-3704	444	5	onto	onto	ADP
ejpam-3704	444	6	and	and	CCONJ
ejpam-3704	444	7	(	(	PUNCT
ejpam-3704	444	8	iv	iv	X
ejpam-3704	444	9	)	)	PUNCT
ejpam-3704	444	10	holds	hold	NOUN
ejpam-3704	444	11	.	.	PUNCT
ejpam-3704	445	1	recall	recall	VERB
ejpam-3704	445	2	that	that	SCONJ
ejpam-3704	445	3	if	if	SCONJ
ejpam-3704	445	4	{	{	PUNCT
ejpam-3704	445	5	ak	ak	NOUN
ejpam-3704	445	6	:	:	PUNCT
ejpam-3704	445	7	k	k	PROPN
ejpam-3704	445	8	∈	∈	PROPN
ejpam-3704	446	1	i	i	PRON
ejpam-3704	446	2	}	}	PUNCT
ejpam-3704	446	3	is	be	AUX
ejpam-3704	446	4	a	a	DET
ejpam-3704	446	5	family	family	NOUN
ejpam-3704	446	6	of	of	ADP
ejpam-3704	446	7	sets	set	NOUN
ejpam-3704	446	8	,	,	PUNCT
ejpam-3704	446	9	the	the	DET
ejpam-3704	446	10	cartesian	cartesian	ADJ
ejpam-3704	446	11	product	product	NOUN
ejpam-3704	446	12	∏	∏	PROPN
ejpam-3704	446	13	k∈i	k∈i	NOUN
ejpam-3704	446	14	ak	ak	PROPN
ejpam-3704	446	15	is	be	AUX
ejpam-3704	446	16	the	the	DET
ejpam-3704	446	17	set	set	NOUN
ejpam-3704	446	18	of	of	ADP
ejpam-3704	446	19	all	all	DET
ejpam-3704	446	20	functions	function	NOUN
ejpam-3704	446	21	p	p	X
ejpam-3704	446	22	:	:	PUNCT
ejpam-3704	446	23	i	i	PRON
ejpam-3704	446	24	−→	−→	VERB
ejpam-3704	446	25	⋃	⋃	NOUN
ejpam-3704	446	26	k∈i	k∈i	NOUN
ejpam-3704	446	27	ak	ak	ADP
ejpam-3704	446	28	such	such	ADJ
ejpam-3704	446	29	that	that	SCONJ
ejpam-3704	446	30	p(k	p(k	NOUN
ejpam-3704	446	31	)	)	PUNCT
ejpam-3704	446	32	∈	∈	PROPN
ejpam-3704	446	33	ak	ak	PROPN
ejpam-3704	446	34	,	,	PUNCT
ejpam-3704	446	35	for	for	ADP
ejpam-3704	446	36	all	all	DET
ejpam-3704	446	37	k	k	PROPN
ejpam-3704	446	38	∈	∈	PROPN
ejpam-3704	446	39	i.	i.	NOUN
ejpam-3704	446	40	if	if	SCONJ
ejpam-3704	446	41	p	p	PROPN
ejpam-3704	446	42	∈	∈	PROPN
ejpam-3704	446	43	∏	∏	PROPN
ejpam-3704	446	44	k∈i	k∈i	NOUN
ejpam-3704	446	45	ak	ak	PROPN
ejpam-3704	446	46	such	such	ADJ
ejpam-3704	446	47	that	that	SCONJ
ejpam-3704	446	48	p(i	p(i	PROPN
ejpam-3704	446	49	)	)	PUNCT
ejpam-3704	447	1	=	=	PUNCT
ejpam-3704	447	2	ai	ai	AUX
ejpam-3704	447	3	∈	∈	NOUN
ejpam-3704	447	4	ai	ai	VERB
ejpam-3704	447	5	for	for	ADP
ejpam-3704	447	6	all	all	PRON
ejpam-3704	447	7	i	i	PRON
ejpam-3704	447	8	∈	∈	PROPN
ejpam-3704	448	1	i	i	PRON
ejpam-3704	448	2	,	,	PUNCT
ejpam-3704	448	3	then	then	ADV
ejpam-3704	448	4	we	we	PRON
ejpam-3704	448	5	will	will	AUX
ejpam-3704	448	6	denote	denote	VERB
ejpam-3704	448	7	p	p	NOUN
ejpam-3704	448	8	as	as	ADP
ejpam-3704	448	9	{	{	PUNCT
ejpam-3704	448	10	ai	ai	VERB
ejpam-3704	448	11	}	}	PUNCT
ejpam-3704	448	12	.	.	PUNCT
ejpam-3704	449	1	we	we	PRON
ejpam-3704	449	2	now	now	ADV
ejpam-3704	449	3	extend	extend	VERB
ejpam-3704	449	4	the	the	DET
ejpam-3704	449	5	hyper	hyper	ADJ
ejpam-3704	449	6	product	product	NOUN
ejpam-3704	450	1	h	h	NOUN
ejpam-3704	450	2	×	×	NOUN
ejpam-3704	450	3	k	k	PROPN
ejpam-3704	450	4	of	of	ADP
ejpam-3704	450	5	h	h	PROPN
ejpam-3704	450	6	and	and	CCONJ
ejpam-3704	450	7	k	k	PROPN
ejpam-3704	450	8	to	to	ADP
ejpam-3704	450	9	the	the	DET
ejpam-3704	450	10	hyper	hyper	ADJ
ejpam-3704	450	11	product	product	NOUN
ejpam-3704	450	12	of	of	ADP
ejpam-3704	450	13	an	an	DET
ejpam-3704	450	14	arbitrary	arbitrary	ADJ
ejpam-3704	450	15	family	family	NOUN
ejpam-3704	450	16	of	of	ADP
ejpam-3704	450	17	hyper	hyper	ADJ
ejpam-3704	450	18	up	up	ADP
ejpam-3704	450	19	-	-	PUNCT
ejpam-3704	450	20	algebras	algebras	X
ejpam-3704	450	21	.	.	PUNCT
ejpam-3704	451	1	let	let	VERB
ejpam-3704	451	2	{	{	PUNCT
ejpam-3704	451	3	hk	hk	NOUN
ejpam-3704	451	4	:	:	PUNCT
ejpam-3704	451	5	k	k	PROPN
ejpam-3704	451	6	∈	∈	PROPN
ejpam-3704	452	1	i	i	PRON
ejpam-3704	452	2	}	}	PUNCT
ejpam-3704	452	3	be	be	VERB
ejpam-3704	452	4	a	a	DET
ejpam-3704	452	5	family	family	NOUN
ejpam-3704	452	6	of	of	ADP
ejpam-3704	452	7	hyper	hyper	ADJ
ejpam-3704	452	8	up	up	ADP
ejpam-3704	452	9	-	-	PUNCT
ejpam-3704	452	10	algebras	algebras	X
ejpam-3704	452	11	.	.	PUNCT
ejpam-3704	453	1	for	for	ADP
ejpam-3704	453	2	each	each	DET
ejpam-3704	453	3	k	k	PROPN
ejpam-3704	453	4	∈	∈	PROPN
ejpam-3704	453	5	i	i	PRON
ejpam-3704	453	6	,	,	PUNCT
ejpam-3704	453	7	let	let	VERB
ejpam-3704	453	8	~k	~k	NOUN
ejpam-3704	453	9	,	,	PUNCT
ejpam-3704	453	10	0k	0k	NOUN
ejpam-3704	453	11	,	,	PUNCT
ejpam-3704	453	12	and	and	CCONJ
ejpam-3704	453	13	�	�	PROPN
ejpam-3704	453	14	k	k	PROPN
ejpam-3704	453	15	be	be	VERB
ejpam-3704	453	16	the	the	DET
ejpam-3704	453	17	hyperoperation	hyperoperation	NOUN
ejpam-3704	453	18	,	,	PUNCT
ejpam-3704	453	19	the	the	DET
ejpam-3704	453	20	zero	zero	NUM
ejpam-3704	453	21	element	element	NOUN
ejpam-3704	453	22	,	,	PUNCT
ejpam-3704	453	23	and	and	CCONJ
ejpam-3704	453	24	the	the	DET
ejpam-3704	453	25	hyperorder	hyperorder	NOUN
ejpam-3704	453	26	of	of	ADP
ejpam-3704	453	27	hk	hk	PROPN
ejpam-3704	453	28	,	,	PUNCT
ejpam-3704	453	29	respectively	respectively	ADV
ejpam-3704	453	30	.	.	PUNCT
ejpam-3704	454	1	let	let	VERB
ejpam-3704	454	2	g	g	PROPN
ejpam-3704	454	3	=	=	SYM
ejpam-3704	454	4	∏	∏	PROPN
ejpam-3704	454	5	k∈i	k∈i	NOUN
ejpam-3704	454	6	hk	hk	PROPN
ejpam-3704	454	7	and	and	CCONJ
ejpam-3704	454	8	define	define	VERB
ejpam-3704	454	9	the	the	DET
ejpam-3704	454	10	hyperoperation	hyperoperation	NOUN
ejpam-3704	454	11	~	~	PUNCT
ejpam-3704	454	12	as	as	SCONJ
ejpam-3704	454	13	follows	follow	VERB
ejpam-3704	454	14	:	:	PUNCT
ejpam-3704	454	15	for	for	ADP
ejpam-3704	454	16	{	{	PUNCT
ejpam-3704	454	17	xk	xk	ADJ
ejpam-3704	454	18	}	}	PUNCT
ejpam-3704	454	19	,	,	PUNCT
ejpam-3704	454	20	{	{	PUNCT
ejpam-3704	454	21	yk	yk	PROPN
ejpam-3704	454	22	}	}	PUNCT
ejpam-3704	454	23	∈	∈	PROPN
ejpam-3704	454	24	g	g	NOUN
ejpam-3704	454	25	,	,	PUNCT
ejpam-3704	454	26	{	{	PUNCT
ejpam-3704	454	27	xk	xk	PROPN
ejpam-3704	454	28	}	}	PUNCT
ejpam-3704	454	29	~	~	PUNCT
ejpam-3704	454	30	{	{	PUNCT
ejpam-3704	454	31	yk	yk	NOUN
ejpam-3704	454	32	}	}	PUNCT
ejpam-3704	454	33	=	=	SYM
ejpam-3704	454	34	∏	∏	PROPN
ejpam-3704	454	35	k∈i	k∈i	NOUN
ejpam-3704	454	36	(	(	PUNCT
ejpam-3704	454	37	xk	xk	PROPN
ejpam-3704	454	38	~	~	PUNCT
ejpam-3704	454	39	yk	yk	PROPN
ejpam-3704	454	40	)	)	PUNCT
ejpam-3704	454	41	.	.	PUNCT
ejpam-3704	455	1	since	since	SCONJ
ejpam-3704	455	2	xk	xk	PROPN
ejpam-3704	455	3	~	~	PUNCT
ejpam-3704	455	4	yk	yk	PROPN
ejpam-3704	455	5	6=	6=	PROPN
ejpam-3704	455	6	∅	∅	NOUN
ejpam-3704	455	7	for	for	ADP
ejpam-3704	455	8	each	each	DET
ejpam-3704	455	9	k	k	PROPN
ejpam-3704	455	10	∈	∈	PROPN
ejpam-3704	456	1	i	i	PRON
ejpam-3704	456	2	,	,	PUNCT
ejpam-3704	456	3	the	the	DET
ejpam-3704	456	4	axiom	axiom	NOUN
ejpam-3704	456	5	of	of	ADP
ejpam-3704	456	6	choice	choice	NOUN
ejpam-3704	456	7	ensures	ensure	VERB
ejpam-3704	456	8	us	we	PRON
ejpam-3704	456	9	that	that	SCONJ
ejpam-3704	456	10	∏	∏	NUM
ejpam-3704	456	11	k∈i	k∈i	NOUN
ejpam-3704	456	12	(	(	PUNCT
ejpam-3704	456	13	xk	xk	PROPN
ejpam-3704	456	14	~	~	PUNCT
ejpam-3704	456	15	yk	yk	PROPN
ejpam-3704	456	16	)	)	PUNCT
ejpam-3704	456	17	6=	6=	ADP
ejpam-3704	456	18	∅	∅	NOUN
ejpam-3704	456	19	,	,	PUNCT
ejpam-3704	456	20	and	and	CCONJ
ejpam-3704	456	21	so	so	ADV
ejpam-3704	456	22	~	~	PUNCT
ejpam-3704	456	23	is	be	AUX
ejpam-3704	456	24	indeed	indeed	ADV
ejpam-3704	456	25	a	a	DET
ejpam-3704	456	26	hyperoperation	hyperoperation	NOUN
ejpam-3704	456	27	.	.	PUNCT
ejpam-3704	457	1	the	the	DET
ejpam-3704	457	2	zero	zero	NUM
ejpam-3704	457	3	element	element	NOUN
ejpam-3704	457	4	of	of	ADP
ejpam-3704	457	5	g	g	PROPN
ejpam-3704	457	6	is	be	AUX
ejpam-3704	457	7	{	{	PUNCT
ejpam-3704	457	8	0k	0k	NOUN
ejpam-3704	457	9	}	}	PUNCT
ejpam-3704	457	10	,	,	PUNCT
ejpam-3704	457	11	and	and	CCONJ
ejpam-3704	457	12	under	under	ADP
ejpam-3704	457	13	the	the	DET
ejpam-3704	457	14	hyperoperation	hyperoperation	NOUN
ejpam-3704	457	15	~	~	PROPN
ejpam-3704	457	16	,	,	PUNCT
ejpam-3704	457	17	the	the	DET
ejpam-3704	457	18	hyperorder	hyperorder	NOUN
ejpam-3704	457	19	�	�	PROPN
ejpam-3704	457	20	is	be	AUX
ejpam-3704	457	21	established	establish	VERB
ejpam-3704	457	22	as	as	SCONJ
ejpam-3704	457	23	follows	follow	VERB
ejpam-3704	457	24	:	:	PUNCT
ejpam-3704	457	25	for	for	ADP
ejpam-3704	457	26	{	{	PUNCT
ejpam-3704	457	27	xk	xk	ADJ
ejpam-3704	457	28	}	}	PUNCT
ejpam-3704	457	29	,	,	PUNCT
ejpam-3704	457	30	{	{	PUNCT
ejpam-3704	457	31	yk	yk	PROPN
ejpam-3704	457	32	}	}	PUNCT
ejpam-3704	457	33	∈	∈	PROPN
ejpam-3704	457	34	g	g	NOUN
ejpam-3704	457	35	,	,	PUNCT
ejpam-3704	457	36	{	{	PUNCT
ejpam-3704	457	37	xk	xk	ADJ
ejpam-3704	457	38	}	}	PUNCT
ejpam-3704	457	39	�	�	PROPN
ejpam-3704	457	40	{	{	PUNCT
ejpam-3704	457	41	yk	yk	PROPN
ejpam-3704	457	42	}	}	PUNCT
ejpam-3704	457	43	⇐	⇐	ADJ
ejpam-3704	457	44	⇒	⇒	NOUN
ejpam-3704	457	45	{	{	PUNCT
ejpam-3704	457	46	0k	0k	PROPN
ejpam-3704	457	47	}	}	PUNCT
ejpam-3704	457	48	∈	∈	PROPN
ejpam-3704	457	49	{	{	PUNCT
ejpam-3704	457	50	yk}~	yk}~	NOUN
ejpam-3704	457	51	{	{	PUNCT
ejpam-3704	457	52	xk	xk	PROPN
ejpam-3704	457	53	}	}	PUNCT
ejpam-3704	457	54	⇐	⇐	ADJ
ejpam-3704	457	55	⇒	⇒	NOUN
ejpam-3704	457	56	{	{	PUNCT
ejpam-3704	457	57	0k	0k	PROPN
ejpam-3704	457	58	}	}	PUNCT
ejpam-3704	457	59	∈	∈	PROPN
ejpam-3704	457	60	∏	∏	PROPN
ejpam-3704	457	61	k∈i	k∈i	NOUN
ejpam-3704	457	62	(	(	PUNCT
ejpam-3704	457	63	yk	yk	NOUN
ejpam-3704	457	64	~	~	PUNCT
ejpam-3704	457	65	xk	xk	X
ejpam-3704	457	66	)	)	PUNCT
ejpam-3704	457	67	⇐	⇐	ADJ
ejpam-3704	457	68	⇒	⇒	NOUN
ejpam-3704	457	69	for	for	ADP
ejpam-3704	457	70	all	all	DET
ejpam-3704	457	71	k	k	PROPN
ejpam-3704	457	72	∈	∈	PROPN
ejpam-3704	457	73	i	i	PRON
ejpam-3704	457	74	,	,	PUNCT
ejpam-3704	457	75	0k	0k	NOUN
ejpam-3704	457	76	∈	∈	PROPN
ejpam-3704	457	77	yk	yk	PROPN
ejpam-3704	457	78	~	~	PUNCT
ejpam-3704	457	79	xk	xk	PROPN
ejpam-3704	458	1	⇐	⇐	PROPN
ejpam-3704	458	2	⇒	⇒	PROPN
ejpam-3704	458	3	for	for	ADP
ejpam-3704	458	4	all	all	DET
ejpam-3704	458	5	k	k	PROPN
ejpam-3704	458	6	∈	∈	PROPN
ejpam-3704	459	1	i	i	PRON
ejpam-3704	459	2	,	,	PUNCT
ejpam-3704	459	3	xk	xk	PROPN
ejpam-3704	459	4	�	�	PROPN
ejpam-3704	459	5	k	k	PROPN
ejpam-3704	459	6	yk	yk	PROPN
ejpam-3704	459	7	,	,	PUNCT
ejpam-3704	459	8	and	and	CCONJ
ejpam-3704	459	9	for	for	ADP
ejpam-3704	459	10	all	all	DET
ejpam-3704	459	11	∏	∏	NUM
ejpam-3704	459	12	k∈i	k∈i	PROPN
ejpam-3704	459	13	ak	ak	PROPN
ejpam-3704	459	14	,	,	PUNCT
ejpam-3704	459	15	∏	∏	PROPN
ejpam-3704	459	16	k∈i	k∈i	NOUN
ejpam-3704	459	17	bk	bk	ADP
ejpam-3704	459	18	⊆	⊆	NUM
ejpam-3704	459	19	∏	∏	NUM
ejpam-3704	459	20	k∈i	k∈i	PROPN
ejpam-3704	459	21	hk	hk	PROPN
ejpam-3704	459	22	,	,	PUNCT
ejpam-3704	459	23	∏	∏	PROPN
ejpam-3704	459	24	k∈i	k∈i	PROPN
ejpam-3704	459	25	ak	ak	PROPN
ejpam-3704	459	26	�	�	PROPN
ejpam-3704	459	27	∏	∏	PROPN
ejpam-3704	459	28	k∈i	k∈i	NOUN
ejpam-3704	459	29	bk	bk	ADP
ejpam-3704	459	30	⇐	⇐	ADJ
ejpam-3704	459	31	⇒	⇒	NOUN
ejpam-3704	459	32	∀{ak	∀{ak	VERB
ejpam-3704	459	33	}	}	PUNCT
ejpam-3704	459	34	∈	∈	PROPN
ejpam-3704	459	35	∏	∏	PROPN
ejpam-3704	459	36	k∈i	k∈i	PROPN
ejpam-3704	459	37	ak	ak	PROPN
ejpam-3704	459	38	,	,	PUNCT
ejpam-3704	459	39	∃{bk	∃{bk	ADJ
ejpam-3704	459	40	}	}	PUNCT
ejpam-3704	459	41	∈	∈	PROPN
ejpam-3704	459	42	∏	∏	PROPN
ejpam-3704	459	43	k∈i	k∈i	NOUN
ejpam-3704	459	44	bk	bk	VERB
ejpam-3704	459	45	such	such	ADJ
ejpam-3704	459	46	that	that	SCONJ
ejpam-3704	459	47	{	{	PUNCT
ejpam-3704	459	48	ak	ak	PROPN
ejpam-3704	459	49	}	}	PUNCT
ejpam-3704	459	50	�	�	PROPN
ejpam-3704	459	51	{	{	PUNCT
ejpam-3704	459	52	bk	bk	PROPN
ejpam-3704	459	53	}	}	PUNCT
ejpam-3704	459	54	⇐	⇐	ADJ
ejpam-3704	459	55	⇒	⇒	NOUN
ejpam-3704	459	56	∀k	∀k	NOUN
ejpam-3704	459	57	∈	∈	PROPN
ejpam-3704	460	1	i	i	PRON
ejpam-3704	460	2	,	,	PUNCT
ejpam-3704	460	3	∀ak	∀ak	PROPN
ejpam-3704	460	4	∈	∈	PROPN
ejpam-3704	460	5	ak,∃bk	ak,∃bk	PROPN
ejpam-3704	460	6	∈	∈	PROPN
ejpam-3704	460	7	bk	bk	VERB
ejpam-3704	460	8	such	such	ADJ
ejpam-3704	460	9	that	that	SCONJ
ejpam-3704	460	10	ak	ak	PROPN
ejpam-3704	460	11	�	�	PROPN
ejpam-3704	460	12	k	k	PROPN
ejpam-3704	460	13	bk	bk	PROPN
ejpam-3704	460	14	⇐	⇐	PROPN
ejpam-3704	460	15	⇒	⇒	NOUN
ejpam-3704	460	16	∀k	∀k	NOUN
ejpam-3704	460	17	∈	∈	PROPN
ejpam-3704	460	18	i	i	PROPN
ejpam-3704	460	19	,	,	PUNCT
ejpam-3704	460	20	ak	ak	PROPN
ejpam-3704	460	21	�	�	PROPN
ejpam-3704	460	22	k	k	PROPN
ejpam-3704	460	23	bk	bk	PROPN
ejpam-3704	460	24	.	.	PUNCT
ejpam-3704	461	1	then	then	ADV
ejpam-3704	461	2	(	(	PUNCT
ejpam-3704	461	3	g,~	g,~	PROPN
ejpam-3704	461	4	,	,	PUNCT
ejpam-3704	461	5	{	{	PUNCT
ejpam-3704	461	6	0k	0k	NOUN
ejpam-3704	461	7	}	}	PUNCT
ejpam-3704	461	8	)	)	PUNCT
ejpam-3704	461	9	is	be	AUX
ejpam-3704	461	10	called	call	VERB
ejpam-3704	461	11	the	the	DET
ejpam-3704	461	12	hyper	hyper	ADJ
ejpam-3704	461	13	product	product	NOUN
ejpam-3704	461	14	of	of	ADP
ejpam-3704	461	15	{	{	PUNCT
ejpam-3704	461	16	hk	hk	NOUN
ejpam-3704	461	17	:	:	PUNCT
ejpam-3704	461	18	k	k	PROPN
ejpam-3704	461	19	∈	∈	PROPN
ejpam-3704	461	20	i	i	X
ejpam-3704	461	21	}	}	PUNCT
ejpam-3704	461	22	.	.	PUNCT
ejpam-3704	462	1	lemma	lemma	PROPN
ejpam-3704	462	2	6	6	NUM
ejpam-3704	462	3	.	.	PUNCT
ejpam-3704	463	1	let	let	VERB
ejpam-3704	463	2	{	{	PUNCT
ejpam-3704	463	3	hk	hk	NOUN
ejpam-3704	463	4	:	:	PUNCT
ejpam-3704	464	1	k	k	PROPN
ejpam-3704	464	2	∈	∈	PROPN
ejpam-3704	465	1	i	i	PRON
ejpam-3704	465	2	}	}	PUNCT
ejpam-3704	465	3	be	be	VERB
ejpam-3704	465	4	a	a	DET
ejpam-3704	465	5	nonempty	nonempty	ADJ
ejpam-3704	465	6	family	family	NOUN
ejpam-3704	465	7	of	of	ADP
ejpam-3704	465	8	hyper	hyper	ADJ
ejpam-3704	465	9	up	up	ADP
ejpam-3704	465	10	-	-	PUNCT
ejpam-3704	465	11	algebras	algebras	X
ejpam-3704	465	12	.	.	PUNCT
ejpam-3704	466	1	suppose	suppose	VERB
ejpam-3704	466	2	that	that	SCONJ
ejpam-3704	466	3	ak	ak	PROPN
ejpam-3704	466	4	,	,	PUNCT
ejpam-3704	466	5	bk	bk	VERB
ejpam-3704	466	6	⊆	⊆	NUM
ejpam-3704	466	7	hk	hk	PROPN
ejpam-3704	466	8	,	,	PUNCT
ejpam-3704	466	9	for	for	ADP
ejpam-3704	466	10	all	all	DET
ejpam-3704	466	11	k	k	PROPN
ejpam-3704	466	12	∈	∈	PROPN
ejpam-3704	466	13	i.	i.	NOUN
ejpam-3704	466	14	then	then	ADV
ejpam-3704	466	15	for	for	ADP
ejpam-3704	466	16	each	each	DET
ejpam-3704	466	17	k	k	PROPN
ejpam-3704	466	18	∈	∈	PROPN
ejpam-3704	467	1	i	i	PROPN
ejpam-3704	467	2	,	,	PUNCT
ejpam-3704	467	3	r.	r.	PROPN
ejpam-3704	467	4	amairanto	amairanto	PROPN
ejpam-3704	467	5	,	,	PUNCT
ejpam-3704	467	6	r.	r.	PROPN
ejpam-3704	467	7	isla	isla	PROPN
ejpam-3704	467	8	/	/	SYM
ejpam-3704	467	9	eur	eur	PROPN
ejpam-3704	467	10	.	.	PUNCT
ejpam-3704	468	1	j.	j.	PROPN
ejpam-3704	468	2	pure	pure	PROPN
ejpam-3704	468	3	appl	appl	PROPN
ejpam-3704	468	4	.	.	PROPN
ejpam-3704	468	5	math	math	PROPN
ejpam-3704	468	6	,	,	PUNCT
ejpam-3704	468	7	13	13	NUM
ejpam-3704	468	8	(	(	PUNCT
ejpam-3704	468	9	3	3	NUM
ejpam-3704	468	10	)	)	PUNCT
ejpam-3704	468	11	(	(	PUNCT
ejpam-3704	468	12	2020	2020	NUM
ejpam-3704	468	13	)	)	PUNCT
ejpam-3704	468	14	,	,	PUNCT
ejpam-3704	468	15	483	483	NUM
ejpam-3704	468	16	-	-	SYM
ejpam-3704	468	17	497	497	NUM
ejpam-3704	468	18	495∏	495∏	PROPN
ejpam-3704	468	19	k∈i	k∈i	PROPN
ejpam-3704	468	20	ak	ak	PROPN
ejpam-3704	468	21	~	~	PUNCT
ejpam-3704	468	22	∏	∏	PROPN
ejpam-3704	468	23	k∈i	k∈i	NOUN
ejpam-3704	468	24	bk	bk	ADP
ejpam-3704	468	25	=	=	SYM
ejpam-3704	468	26	∏	∏	PROPN
ejpam-3704	468	27	k∈i	k∈i	NOUN
ejpam-3704	468	28	(	(	PUNCT
ejpam-3704	468	29	ak	ak	PROPN
ejpam-3704	468	30	~bk	~bk	PROPN
ejpam-3704	468	31	)	)	PUNCT
ejpam-3704	468	32	.	.	PUNCT
ejpam-3704	469	1	theorem	theorem	NOUN
ejpam-3704	469	2	11	11	NUM
ejpam-3704	469	3	.	.	PUNCT
ejpam-3704	470	1	suppose	suppose	VERB
ejpam-3704	470	2	that	that	SCONJ
ejpam-3704	470	3	{	{	PUNCT
ejpam-3704	470	4	hk	hk	NOUN
ejpam-3704	470	5	:	:	PUNCT
ejpam-3704	470	6	k	k	PROPN
ejpam-3704	470	7	∈	∈	PROPN
ejpam-3704	470	8	i	i	PRON
ejpam-3704	470	9	}	}	PUNCT
ejpam-3704	470	10	is	be	AUX
ejpam-3704	470	11	a	a	DET
ejpam-3704	470	12	nonempty	nonempty	ADJ
ejpam-3704	470	13	family	family	NOUN
ejpam-3704	470	14	of	of	ADP
ejpam-3704	470	15	hyper	hyper	ADJ
ejpam-3704	470	16	up	up	ADP
ejpam-3704	470	17	-	-	PUNCT
ejpam-3704	470	18	algebras	algebras	X
ejpam-3704	470	19	.	.	PUNCT
ejpam-3704	471	1	then	then	ADV
ejpam-3704	471	2	(	(	PUNCT
ejpam-3704	471	3	∏	∏	PROPN
ejpam-3704	471	4	k∈i	k∈i	NOUN
ejpam-3704	471	5	hk,~	hk,~	NOUN
ejpam-3704	471	6	,	,	PUNCT
ejpam-3704	471	7	{	{	PUNCT
ejpam-3704	471	8	0k	0k	NOUN
ejpam-3704	471	9	}	}	PUNCT
ejpam-3704	471	10	)	)	PUNCT
ejpam-3704	471	11	is	be	AUX
ejpam-3704	471	12	a	a	DET
ejpam-3704	471	13	hyper	hyper	ADJ
ejpam-3704	471	14	up	up	NOUN
ejpam-3704	471	15	-	-	PUNCT
ejpam-3704	471	16	algebra	algebra	NOUN
ejpam-3704	471	17	.	.	PUNCT
ejpam-3704	472	1	proof	proof	NOUN
ejpam-3704	472	2	.	.	PUNCT
ejpam-3704	473	1	suppose	suppose	VERB
ejpam-3704	473	2	{	{	PUNCT
ejpam-3704	474	1	hk	hk	NOUN
ejpam-3704	474	2	:	:	PUNCT
ejpam-3704	474	3	k	k	PROPN
ejpam-3704	474	4	∈	∈	PROPN
ejpam-3704	475	1	i	i	PRON
ejpam-3704	475	2	}	}	PUNCT
ejpam-3704	475	3	is	be	AUX
ejpam-3704	475	4	a	a	DET
ejpam-3704	475	5	nonempty	nonempty	ADJ
ejpam-3704	475	6	family	family	NOUN
ejpam-3704	475	7	of	of	ADP
ejpam-3704	475	8	hyper	hyper	ADJ
ejpam-3704	475	9	up	up	ADP
ejpam-3704	475	10	-	-	PUNCT
ejpam-3704	475	11	algebras	algebras	X
ejpam-3704	475	12	.	.	PUNCT
ejpam-3704	476	1	let	let	VERB
ejpam-3704	476	2	{	{	PUNCT
ejpam-3704	476	3	ak	ak	PROPN
ejpam-3704	476	4	}	}	PUNCT
ejpam-3704	476	5	,	,	PUNCT
ejpam-3704	476	6	{	{	PUNCT
ejpam-3704	476	7	bk	bk	VERB
ejpam-3704	476	8	}	}	PUNCT
ejpam-3704	476	9	,	,	PUNCT
ejpam-3704	476	10	{	{	PUNCT
ejpam-3704	476	11	ck	ck	INTJ
ejpam-3704	476	12	}	}	PUNCT
ejpam-3704	476	13	,	,	PUNCT
ejpam-3704	476	14	{	{	PUNCT
ejpam-3704	476	15	dk	dk	NOUN
ejpam-3704	476	16	}	}	PUNCT
ejpam-3704	476	17	∈	∈	PROPN
ejpam-3704	476	18	∏	∏	PROPN
ejpam-3704	476	19	k∈i	k∈i	PROPN
ejpam-3704	476	20	hk	hk	PROPN
ejpam-3704	476	21	.	.	PUNCT
ejpam-3704	477	1	then	then	ADV
ejpam-3704	477	2	ak	ak	PROPN
ejpam-3704	477	3	,	,	PUNCT
ejpam-3704	477	4	bk	bk	PROPN
ejpam-3704	477	5	,	,	PUNCT
ejpam-3704	477	6	ck	ck	INTJ
ejpam-3704	477	7	,	,	PUNCT
ejpam-3704	477	8	dk	dk	PROPN
ejpam-3704	477	9	∈	∈	PROPN
ejpam-3704	477	10	hk	hk	PROPN
ejpam-3704	477	11	for	for	ADP
ejpam-3704	477	12	all	all	DET
ejpam-3704	477	13	k	k	PROPN
ejpam-3704	477	14	∈	∈	PROPN
ejpam-3704	477	15	i.	i.	NOUN
ejpam-3704	477	16	we	we	PRON
ejpam-3704	477	17	will	will	AUX
ejpam-3704	477	18	show	show	VERB
ejpam-3704	477	19	first	first	ADV
ejpam-3704	477	20	that	that	SCONJ
ejpam-3704	477	21	~	~	PUNCT
ejpam-3704	477	22	is	be	AUX
ejpam-3704	477	23	a	a	DET
ejpam-3704	477	24	well	well	ADV
ejpam-3704	477	25	-	-	PUNCT
ejpam-3704	477	26	defined	define	VERB
ejpam-3704	477	27	hyperoperation	hyperoperation	NOUN
ejpam-3704	477	28	on	on	ADP
ejpam-3704	477	29	∏	∏	PROPN
ejpam-3704	477	30	k∈i	k∈i	NOUN
ejpam-3704	477	31	hk	hk	PROPN
ejpam-3704	477	32	.	.	PROPN
ejpam-3704	477	33	assume	assume	VERB
ejpam-3704	477	34	that	that	SCONJ
ejpam-3704	477	35	{	{	PUNCT
ejpam-3704	477	36	ak	ak	PROPN
ejpam-3704	477	37	}	}	PUNCT
ejpam-3704	477	38	=	=	PUNCT
ejpam-3704	477	39	{	{	PUNCT
ejpam-3704	477	40	bk	bk	VERB
ejpam-3704	477	41	}	}	PUNCT
ejpam-3704	477	42	and	and	CCONJ
ejpam-3704	477	43	{	{	PUNCT
ejpam-3704	477	44	ck	ck	NOUN
ejpam-3704	477	45	}	}	PUNCT
ejpam-3704	477	46	=	=	SYM
ejpam-3704	477	47	{	{	PUNCT
ejpam-3704	477	48	dk	dk	NOUN
ejpam-3704	477	49	}	}	PUNCT
ejpam-3704	477	50	,	,	PUNCT
ejpam-3704	477	51	for	for	ADP
ejpam-3704	477	52	all	all	DET
ejpam-3704	477	53	k	k	PROPN
ejpam-3704	477	54	∈	∈	PROPN
ejpam-3704	477	55	i.	i.	NOUN
ejpam-3704	477	56	then	then	ADV
ejpam-3704	477	57	ak	ak	PROPN
ejpam-3704	477	58	=	=	PUNCT
ejpam-3704	477	59	bk	bk	PROPN
ejpam-3704	477	60	and	and	CCONJ
ejpam-3704	477	61	ck	ck	NOUN
ejpam-3704	477	62	=	=	SYM
ejpam-3704	477	63	dk	dk	PROPN
ejpam-3704	477	64	for	for	ADP
ejpam-3704	477	65	all	all	DET
ejpam-3704	477	66	k	k	PROPN
ejpam-3704	477	67	∈	∈	PROPN
ejpam-3704	477	68	i.	i.	NOUN
ejpam-3704	478	1	so	so	ADV
ejpam-3704	478	2	,	,	PUNCT
ejpam-3704	478	3	{	{	PUNCT
ejpam-3704	478	4	ak}~	ak}~	NOUN
ejpam-3704	478	5	{	{	PUNCT
ejpam-3704	478	6	ck	ck	NOUN
ejpam-3704	478	7	}	}	PUNCT
ejpam-3704	478	8	=	=	SYM
ejpam-3704	478	9	∏	∏	NUM
ejpam-3704	478	10	k∈i	k∈i	NOUN
ejpam-3704	478	11	(	(	PUNCT
ejpam-3704	478	12	ak	ak	PROPN
ejpam-3704	478	13	~k	~k	PROPN
ejpam-3704	478	14	ck	ck	X
ejpam-3704	478	15	)	)	PUNCT
ejpam-3704	478	16	=	=	SYM
ejpam-3704	478	17	∏	∏	NUM
ejpam-3704	478	18	k∈i	k∈i	NOUN
ejpam-3704	478	19	(	(	PUNCT
ejpam-3704	478	20	bk	bk	NOUN
ejpam-3704	478	21	~k	~k	PUNCT
ejpam-3704	478	22	dk	dk	X
ejpam-3704	478	23	)	)	PUNCT
ejpam-3704	478	24	=	=	SYM
ejpam-3704	478	25	{	{	PUNCT
ejpam-3704	478	26	bk}~	bk}~	NOUN
ejpam-3704	478	27	{	{	PUNCT
ejpam-3704	478	28	dk	dk	NOUN
ejpam-3704	478	29	}	}	PUNCT
ejpam-3704	478	30	for	for	ADP
ejpam-3704	478	31	all	all	DET
ejpam-3704	478	32	k	k	PROPN
ejpam-3704	478	33	∈	∈	PROPN
ejpam-3704	478	34	i.	i.	NOUN
ejpam-3704	478	35	thus	thus	ADV
ejpam-3704	478	36	,	,	PUNCT
ejpam-3704	478	37	~	~	PUNCT
ejpam-3704	478	38	is	be	AUX
ejpam-3704	478	39	a	a	DET
ejpam-3704	478	40	well	well	ADV
ejpam-3704	478	41	-	-	PUNCT
ejpam-3704	478	42	defined	define	VERB
ejpam-3704	478	43	hyperoperation	hyperoperation	NOUN
ejpam-3704	478	44	on	on	ADP
ejpam-3704	478	45	∏	∏	PROPN
ejpam-3704	478	46	k∈i	k∈i	NOUN
ejpam-3704	478	47	hk	hk	PROPN
ejpam-3704	478	48	.	.	PUNCT
ejpam-3704	479	1	let	let	VERB
ejpam-3704	479	2	{	{	PUNCT
ejpam-3704	479	3	xk	xk	ADJ
ejpam-3704	479	4	}	}	PUNCT
ejpam-3704	479	5	,	,	PUNCT
ejpam-3704	479	6	{	{	PUNCT
ejpam-3704	479	7	yk	yk	NOUN
ejpam-3704	479	8	}	}	PUNCT
ejpam-3704	479	9	,	,	PUNCT
ejpam-3704	479	10	{	{	PUNCT
ejpam-3704	479	11	zk	zk	NOUN
ejpam-3704	479	12	}	}	PUNCT
ejpam-3704	479	13	∈∏	∈∏	ADJ
ejpam-3704	479	14	k∈i	k∈i	PROPN
ejpam-3704	479	15	hk	hk	PROPN
ejpam-3704	479	16	.	.	PUNCT
ejpam-3704	480	1	then	then	ADV
ejpam-3704	480	2	xk	xk	PROPN
ejpam-3704	480	3	,	,	PUNCT
ejpam-3704	480	4	yk	yk	PROPN
ejpam-3704	480	5	,	,	PUNCT
ejpam-3704	480	6	zk	zk	PROPN
ejpam-3704	480	7	∈	∈	PROPN
ejpam-3704	480	8	hk	hk	PROPN
ejpam-3704	480	9	for	for	ADP
ejpam-3704	480	10	all	all	DET
ejpam-3704	480	11	k	k	PROPN
ejpam-3704	480	12	∈	∈	PROPN
ejpam-3704	480	13	i.	i.	NOUN
ejpam-3704	480	14	now	now	ADV
ejpam-3704	480	15	,	,	PUNCT
ejpam-3704	480	16	for	for	ADP
ejpam-3704	480	17	each	each	DET
ejpam-3704	480	18	k	k	PROPN
ejpam-3704	480	19	∈	∈	PROPN
ejpam-3704	481	1	i	i	PRON
ejpam-3704	481	2	,	,	PUNCT
ejpam-3704	481	3	we	we	PRON
ejpam-3704	481	4	have	have	VERB
ejpam-3704	481	5	(	(	PUNCT
ejpam-3704	481	6	{	{	PUNCT
ejpam-3704	481	7	xk}~	xk}~	X
ejpam-3704	481	8	{	{	PUNCT
ejpam-3704	481	9	yk	yk	PROPN
ejpam-3704	481	10	}	}	PUNCT
ejpam-3704	481	11	)	)	PUNCT
ejpam-3704	481	12	~	~	PUNCT
ejpam-3704	481	13	(	(	PUNCT
ejpam-3704	481	14	{	{	PUNCT
ejpam-3704	481	15	xk}~	xk}~	X
ejpam-3704	481	16	{	{	PUNCT
ejpam-3704	481	17	zk	zk	PROPN
ejpam-3704	481	18	}	}	PUNCT
ejpam-3704	481	19	)	)	PUNCT
ejpam-3704	481	20	=	=	SYM
ejpam-3704	482	1	(	(	PUNCT
ejpam-3704	482	2	∏	∏	PROPN
ejpam-3704	482	3	k∈i	k∈i	NOUN
ejpam-3704	482	4	(	(	PUNCT
ejpam-3704	482	5	xk	xk	PROPN
ejpam-3704	482	6	~k	~k	PROPN
ejpam-3704	482	7	yk	yk	PROPN
ejpam-3704	482	8	)	)	PUNCT
ejpam-3704	482	9	)	)	PUNCT
ejpam-3704	483	1	~	~	PUNCT
ejpam-3704	483	2	(	(	PUNCT
ejpam-3704	483	3	∏	∏	PROPN
ejpam-3704	483	4	k∈i	k∈i	NOUN
ejpam-3704	483	5	(	(	PUNCT
ejpam-3704	483	6	xk	xk	PROPN
ejpam-3704	483	7	~k	~k	PUNCT
ejpam-3704	483	8	zk	zk	PROPN
ejpam-3704	483	9	)	)	PUNCT
ejpam-3704	483	10	)	)	PUNCT
ejpam-3704	483	11	=	=	SYM
ejpam-3704	483	12	(	(	PUNCT
ejpam-3704	483	13	∏	∏	PROPN
ejpam-3704	483	14	k∈i	k∈i	NOUN
ejpam-3704	483	15	(	(	PUNCT
ejpam-3704	483	16	xk	xk	PROPN
ejpam-3704	483	17	~k	~k	PUNCT
ejpam-3704	483	18	yk	yk	PROPN
ejpam-3704	483	19	)	)	PUNCT
ejpam-3704	483	20	~	~	PUNCT
ejpam-3704	483	21	(	(	PUNCT
ejpam-3704	483	22	xk	xk	PROPN
ejpam-3704	483	23	~k	~k	PUNCT
ejpam-3704	483	24	zk	zk	PROPN
ejpam-3704	483	25	)	)	PUNCT
ejpam-3704	483	26	)	)	PUNCT
ejpam-3704	483	27	.	.	PUNCT
ejpam-3704	484	1	since	since	SCONJ
ejpam-3704	484	2	for	for	ADP
ejpam-3704	484	3	each	each	DET
ejpam-3704	484	4	k	k	PROPN
ejpam-3704	484	5	∈	∈	PROPN
ejpam-3704	484	6	i	i	PRON
ejpam-3704	484	7	,	,	PUNCT
ejpam-3704	484	8	(	(	PUNCT
ejpam-3704	484	9	xk	xk	PROPN
ejpam-3704	484	10	~k	~k	PUNCT
ejpam-3704	484	11	yk	yk	PROPN
ejpam-3704	484	12	)	)	PUNCT
ejpam-3704	484	13	~	~	PUNCT
ejpam-3704	484	14	(	(	PUNCT
ejpam-3704	484	15	xk	xk	X
ejpam-3704	484	16	~k	~k	PUNCT
ejpam-3704	484	17	zk)	zk)	NUM
ejpam-3704	484	18	�	�	PROPN
ejpam-3704	484	19	k	k	PROPN
ejpam-3704	484	20	yk	yk	PROPN
ejpam-3704	484	21	~k	~k	PUNCT
ejpam-3704	484	22	zk	zk	PROPN
ejpam-3704	484	23	,	,	PUNCT
ejpam-3704	484	24	it	it	PRON
ejpam-3704	484	25	follows	follow	VERB
ejpam-3704	484	26	that∏	that∏	PRON
ejpam-3704	485	1	k∈i	k∈i	NOUN
ejpam-3704	485	2	(	(	PUNCT
ejpam-3704	485	3	xk	xk	PROPN
ejpam-3704	485	4	~k	~k	PUNCT
ejpam-3704	485	5	yk	yk	PROPN
ejpam-3704	485	6	)	)	PUNCT
ejpam-3704	485	7	~	~	PUNCT
ejpam-3704	485	8	(	(	PUNCT
ejpam-3704	485	9	xk	xk	PROPN
ejpam-3704	485	10	~k	~k	PUNCT
ejpam-3704	485	11	zk	zk	PROPN
ejpam-3704	485	12	)	)	PUNCT
ejpam-3704	485	13	�	�	PROPN
ejpam-3704	485	14	∏	∏	PROPN
ejpam-3704	485	15	k∈i	k∈i	NOUN
ejpam-3704	485	16	(	(	PUNCT
ejpam-3704	485	17	yk	yk	PROPN
ejpam-3704	485	18	~k	~k	PUNCT
ejpam-3704	485	19	zk	zk	PROPN
ejpam-3704	485	20	)	)	PUNCT
ejpam-3704	485	21	,	,	PUNCT
ejpam-3704	485	22	that	that	ADV
ejpam-3704	485	23	is	is	ADV
ejpam-3704	485	24	,	,	PUNCT
ejpam-3704	485	25	(	(	PUNCT
ejpam-3704	485	26	{	{	PUNCT
ejpam-3704	485	27	xk	xk	X
ejpam-3704	485	28	~	~	PUNCT
ejpam-3704	485	29	yk	yk	PROPN
ejpam-3704	485	30	}	}	PUNCT
ejpam-3704	485	31	)	)	PUNCT
ejpam-3704	485	32	~	~	PUNCT
ejpam-3704	485	33	(	(	PUNCT
ejpam-3704	485	34	{	{	PUNCT
ejpam-3704	485	35	xk	xk	X
ejpam-3704	485	36	~	~	PUNCT
ejpam-3704	485	37	zk	zk	PROPN
ejpam-3704	485	38	}	}	PUNCT
ejpam-3704	485	39	)	)	PUNCT
ejpam-3704	485	40	�	�	PROPN
ejpam-3704	485	41	{	{	PUNCT
ejpam-3704	485	42	yk}~	yk}~	NOUN
ejpam-3704	485	43	{	{	PUNCT
ejpam-3704	485	44	zk	zk	PROPN
ejpam-3704	485	45	}	}	PUNCT
ejpam-3704	485	46	.	.	PUNCT
ejpam-3704	486	1	this	this	PRON
ejpam-3704	486	2	means	mean	VERB
ejpam-3704	486	3	that	that	SCONJ
ejpam-3704	486	4	(	(	PUNCT
ejpam-3704	486	5	hup1	hup1	PROPN
ejpam-3704	486	6	)	)	PUNCT
ejpam-3704	486	7	holds	hold	VERB
ejpam-3704	486	8	on	on	ADP
ejpam-3704	486	9	∏	∏	PROPN
ejpam-3704	486	10	k∈i	k∈i	NOUN
ejpam-3704	486	11	hk	hk	PROPN
ejpam-3704	486	12	.	.	PUNCT
ejpam-3704	487	1	since	since	SCONJ
ejpam-3704	487	2	for	for	ADP
ejpam-3704	487	3	each	each	DET
ejpam-3704	487	4	k	k	PROPN
ejpam-3704	487	5	∈	∈	PROPN
ejpam-3704	487	6	i	i	PRON
ejpam-3704	487	7	,	,	PUNCT
ejpam-3704	487	8	0k	0k	NOUN
ejpam-3704	487	9	~k	~k	PUNCT
ejpam-3704	487	10	xk	xk	X
ejpam-3704	487	11	=	=	PUNCT
ejpam-3704	487	12	{	{	PUNCT
ejpam-3704	487	13	xk	xk	NOUN
ejpam-3704	487	14	}	}	PUNCT
ejpam-3704	487	15	,	,	PUNCT
ejpam-3704	487	16	it	it	PRON
ejpam-3704	487	17	follows	follow	VERB
ejpam-3704	487	18	that	that	SCONJ
ejpam-3704	487	19	{	{	PUNCT
ejpam-3704	487	20	0k}~	0k}~	NUM
ejpam-3704	487	21	{	{	PUNCT
ejpam-3704	487	22	xk	xk	PROPN
ejpam-3704	487	23	}	}	PUNCT
ejpam-3704	487	24	=	=	SYM
ejpam-3704	487	25	∏	∏	NUM
ejpam-3704	487	26	k∈i	k∈i	NOUN
ejpam-3704	487	27	(	(	PUNCT
ejpam-3704	487	28	0k	0k	NOUN
ejpam-3704	487	29	~k	~k	PUNCT
ejpam-3704	487	30	xk	xk	X
ejpam-3704	487	31	)	)	PUNCT
ejpam-3704	487	32	=	=	SYM
ejpam-3704	487	33	∏	∏	PROPN
ejpam-3704	487	34	k∈i	k∈i	NOUN
ejpam-3704	487	35	{	{	PUNCT
ejpam-3704	487	36	xk	xk	NOUN
ejpam-3704	487	37	}	}	PUNCT
ejpam-3704	487	38	.	.	PUNCT
ejpam-3704	488	1	references	reference	NOUN
ejpam-3704	488	2	496	496	NUM
ejpam-3704	488	3	thus	thus	ADV
ejpam-3704	488	4	,	,	PUNCT
ejpam-3704	488	5	(	(	PUNCT
ejpam-3704	488	6	hup2	hup2	PROPN
ejpam-3704	488	7	)	)	PUNCT
ejpam-3704	488	8	holds	hold	VERB
ejpam-3704	488	9	on	on	ADP
ejpam-3704	488	10	∏	∏	PROPN
ejpam-3704	488	11	k∈i	k∈i	NOUN
ejpam-3704	488	12	hk	hk	PROPN
ejpam-3704	488	13	.	.	PUNCT
ejpam-3704	489	1	moreover	moreover	ADV
ejpam-3704	489	2	,	,	PUNCT
ejpam-3704	489	3	since	since	SCONJ
ejpam-3704	489	4	for	for	ADP
ejpam-3704	489	5	each	each	DET
ejpam-3704	489	6	k	k	PROPN
ejpam-3704	489	7	∈	∈	PROPN
ejpam-3704	490	1	i	i	PRON
ejpam-3704	490	2	,	,	PUNCT
ejpam-3704	490	3	xk	xk	PROPN
ejpam-3704	490	4	~k	~k	PUNCT
ejpam-3704	490	5	0k	0k	NOUN
ejpam-3704	490	6	=	=	SYM
ejpam-3704	490	7	{	{	PUNCT
ejpam-3704	490	8	0k	0k	NOUN
ejpam-3704	490	9	}	}	PUNCT
ejpam-3704	490	10	,	,	PUNCT
ejpam-3704	490	11	it	it	PRON
ejpam-3704	490	12	follows	follow	VERB
ejpam-3704	490	13	that	that	SCONJ
ejpam-3704	490	14	{	{	PUNCT
ejpam-3704	490	15	xk}~	xk}~	X
ejpam-3704	490	16	{	{	PUNCT
ejpam-3704	490	17	0k	0k	NOUN
ejpam-3704	490	18	}	}	PUNCT
ejpam-3704	490	19	=	=	SYM
ejpam-3704	490	20	∏	∏	NUM
ejpam-3704	490	21	k∈i	k∈i	NOUN
ejpam-3704	490	22	(	(	PUNCT
ejpam-3704	490	23	xk	xk	PROPN
ejpam-3704	490	24	~k	~k	PUNCT
ejpam-3704	490	25	0k	0k	NOUN
ejpam-3704	490	26	)	)	PUNCT
ejpam-3704	490	27	=	=	SYM
ejpam-3704	490	28	∏	∏	PROPN
ejpam-3704	490	29	k∈i	k∈i	NOUN
ejpam-3704	490	30	{	{	PUNCT
ejpam-3704	490	31	0k	0k	NOUN
ejpam-3704	490	32	}	}	PUNCT
ejpam-3704	490	33	.	.	PUNCT
ejpam-3704	491	1	hence	hence	ADV
ejpam-3704	491	2	,	,	PUNCT
ejpam-3704	491	3	(	(	PUNCT
ejpam-3704	491	4	hup3	hup3	NOUN
ejpam-3704	491	5	)	)	PUNCT
ejpam-3704	491	6	holds	hold	VERB
ejpam-3704	491	7	on	on	ADP
ejpam-3704	491	8	∏	∏	PROPN
ejpam-3704	491	9	k∈i	k∈i	NOUN
ejpam-3704	491	10	hk	hk	PROPN
ejpam-3704	491	11	.	.	PUNCT
ejpam-3704	492	1	furthermore	furthermore	ADV
ejpam-3704	492	2	,	,	PUNCT
ejpam-3704	492	3	suppose	suppose	VERB
ejpam-3704	492	4	{	{	PUNCT
ejpam-3704	492	5	xk	xk	ADJ
ejpam-3704	492	6	}	}	PUNCT
ejpam-3704	492	7	�	�	PROPN
ejpam-3704	492	8	{	{	PUNCT
ejpam-3704	492	9	yk	yk	PROPN
ejpam-3704	492	10	}	}	PUNCT
ejpam-3704	492	11	and	and	CCONJ
ejpam-3704	492	12	{	{	PUNCT
ejpam-3704	492	13	yk	yk	PROPN
ejpam-3704	492	14	}	}	PUNCT
ejpam-3704	492	15	�	�	PROPN
ejpam-3704	492	16	{	{	PUNCT
ejpam-3704	492	17	xk	xk	PROPN
ejpam-3704	492	18	}	}	PUNCT
ejpam-3704	492	19	for	for	ADP
ejpam-3704	492	20	all	all	DET
ejpam-3704	492	21	k	k	PROPN
ejpam-3704	492	22	∈	∈	PROPN
ejpam-3704	492	23	i.	i.	NOUN
ejpam-3704	492	24	then	then	ADV
ejpam-3704	492	25	xk	xk	PROPN
ejpam-3704	492	26	�	�	PROPN
ejpam-3704	492	27	k	k	PROPN
ejpam-3704	492	28	yk	yk	PROPN
ejpam-3704	492	29	and	and	CCONJ
ejpam-3704	492	30	yk	yk	PROPN
ejpam-3704	492	31	�	�	PROPN
ejpam-3704	492	32	k	k	PROPN
ejpam-3704	492	33	xk	xk	PROPN
ejpam-3704	492	34	for	for	ADP
ejpam-3704	492	35	all	all	DET
ejpam-3704	492	36	k	k	PROPN
ejpam-3704	492	37	∈	∈	PROPN
ejpam-3704	492	38	i.	i.	NOUN
ejpam-3704	492	39	hence	hence	ADV
ejpam-3704	492	40	,	,	PUNCT
ejpam-3704	492	41	xk	xk	PROPN
ejpam-3704	492	42	=	=	PROPN
ejpam-3704	492	43	yk	yk	PROPN
ejpam-3704	492	44	for	for	ADP
ejpam-3704	492	45	all	all	DET
ejpam-3704	492	46	k	k	PROPN
ejpam-3704	492	47	∈	∈	PROPN
ejpam-3704	493	1	i	i	PRON
ejpam-3704	493	2	and	and	CCONJ
ejpam-3704	493	3	so	so	ADV
ejpam-3704	493	4	{	{	PUNCT
ejpam-3704	493	5	xk	xk	ADJ
ejpam-3704	493	6	}	}	PUNCT
ejpam-3704	493	7	=	=	SYM
ejpam-3704	493	8	{	{	PUNCT
ejpam-3704	493	9	yk	yk	PROPN
ejpam-3704	493	10	}	}	PUNCT
ejpam-3704	493	11	.	.	PUNCT
ejpam-3704	494	1	this	this	PRON
ejpam-3704	494	2	means	mean	VERB
ejpam-3704	494	3	that	that	SCONJ
ejpam-3704	494	4	(	(	PUNCT
ejpam-3704	494	5	hup4	hup4	PROPN
ejpam-3704	494	6	)	)	PUNCT
ejpam-3704	494	7	holds	hold	VERB
ejpam-3704	494	8	on	on	ADP
ejpam-3704	494	9	∏	∏	PROPN
ejpam-3704	494	10	k∈i	k∈i	NOUN
ejpam-3704	494	11	hk	hk	PROPN
ejpam-3704	494	12	.	.	PUNCT
ejpam-3704	495	1	therefore	therefore	ADV
ejpam-3704	495	2	,	,	PUNCT
ejpam-3704	495	3	(	(	PUNCT
ejpam-3704	495	4	∏	∏	PROPN
ejpam-3704	495	5	k∈i	k∈i	NOUN
ejpam-3704	495	6	hk,~	hk,~	NOUN
ejpam-3704	495	7	,	,	PUNCT
ejpam-3704	495	8	{	{	PUNCT
ejpam-3704	495	9	0k	0k	NOUN
ejpam-3704	495	10	}	}	PUNCT
ejpam-3704	495	11	)	)	PUNCT
ejpam-3704	495	12	is	be	AUX
ejpam-3704	495	13	a	a	DET
ejpam-3704	495	14	hyper	hyper	ADJ
ejpam-3704	495	15	up	up	NOUN
ejpam-3704	495	16	-	-	PUNCT
ejpam-3704	495	17	algebra	algebra	NOUN
ejpam-3704	495	18	.	.	PUNCT
ejpam-3704	496	1	acknowledgements	acknowledgement	NOUN
ejpam-3704	496	2	this	this	DET
ejpam-3704	496	3	research	research	NOUN
ejpam-3704	496	4	is	be	AUX
ejpam-3704	496	5	funded	fund	VERB
ejpam-3704	496	6	by	by	ADP
ejpam-3704	496	7	the	the	DET
ejpam-3704	496	8	philippine	philippine	PROPN
ejpam-3704	496	9	department	department	PROPN
ejpam-3704	496	10	of	of	ADP
ejpam-3704	496	11	science	science	NOUN
ejpam-3704	496	12	and	and	CCONJ
ejpam-3704	496	13	technologyaccelerated	technologyaccelerated	ADJ
ejpam-3704	496	14	science	science	NOUN
ejpam-3704	496	15	and	and	CCONJ
ejpam-3704	496	16	technology	technology	NOUN
ejpam-3704	496	17	human	human	ADJ
ejpam-3704	496	18	resource	resource	NOUN
ejpam-3704	496	19	development	development	NOUN
ejpam-3704	496	20	program	program	NOUN
ejpam-3704	496	21	(	(	PUNCT
ejpam-3704	496	22	dostasthrdp	dostasthrdp	PROPN
ejpam-3704	496	23	)	)	PUNCT
ejpam-3704	496	24	and	and	CCONJ
ejpam-3704	496	25	the	the	DET
ejpam-3704	496	26	mindanao	mindanao	PROPN
ejpam-3704	496	27	state	state	PROPN
ejpam-3704	496	28	university	university	PROPN
ejpam-3704	496	29	-	-	PUNCT
ejpam-3704	496	30	iligan	iligan	PROPN
ejpam-3704	496	31	institute	institute	PROPN
ejpam-3704	496	32	of	of	ADP
ejpam-3704	496	33	technology	technology	PROPN
ejpam-3704	496	34	.	.	PUNCT
ejpam-3704	497	1	the	the	DET
ejpam-3704	497	2	authors	author	NOUN
ejpam-3704	497	3	wish	wish	VERB
ejpam-3704	497	4	to	to	PART
ejpam-3704	497	5	express	express	VERB
ejpam-3704	497	6	their	their	PRON
ejpam-3704	497	7	sincere	sincere	ADJ
ejpam-3704	497	8	thanks	thank	NOUN
ejpam-3704	497	9	to	to	ADP
ejpam-3704	497	10	the	the	DET
ejpam-3704	497	11	reviewers	reviewer	NOUN
ejpam-3704	497	12	for	for	ADP
ejpam-3704	497	13	their	their	PRON
ejpam-3704	497	14	valuable	valuable	ADJ
ejpam-3704	497	15	suggestions	suggestion	NOUN
ejpam-3704	497	16	for	for	ADP
ejpam-3704	497	17	the	the	DET
ejpam-3704	497	18	improvement	improvement	NOUN
ejpam-3704	497	19	of	of	ADP
ejpam-3704	497	20	this	this	DET
ejpam-3704	497	21	paper	paper	NOUN
ejpam-3704	497	22	.	.	PUNCT
ejpam-3704	498	1	references	reference	NOUN
ejpam-3704	498	2	[	[	X
ejpam-3704	498	3	1	1	NUM
ejpam-3704	498	4	]	]	X
ejpam-3704	498	5	r.	r.	PROPN
ejpam-3704	498	6	borzooei	borzooei	PROPN
ejpam-3704	498	7	and	and	CCONJ
ejpam-3704	498	8	h.	h.	PROPN
ejpam-3704	498	9	harizavi	harizavi	PROPN
ejpam-3704	498	10	.	.	PUNCT
ejpam-3704	499	1	regular	regular	ADJ
ejpam-3704	499	2	congruence	congruence	NOUN
ejpam-3704	499	3	relations	relation	NOUN
ejpam-3704	499	4	on	on	ADP
ejpam-3704	499	5	hyper	hyper	ADJ
ejpam-3704	499	6	bck	bck	NOUN
ejpam-3704	499	7	-	-	PUNCT
ejpam-3704	499	8	algebras	algebras	PROPN
ejpam-3704	499	9	.	.	PUNCT
ejpam-3704	500	1	scientiae	scientiae	PROPN
ejpam-3704	500	2	mathematicae	mathematicae	VERB
ejpam-3704	500	3	japonicae	japonicae	PROPN
ejpam-3704	500	4	online	online	NOUN
ejpam-3704	500	5	,	,	PUNCT
ejpam-3704	500	6	pages	page	NOUN
ejpam-3704	500	7	217–231	217–231	NUM
ejpam-3704	500	8	,	,	PUNCT
ejpam-3704	500	9	2004	2004	NUM
ejpam-3704	500	10	.	.	PUNCT
ejpam-3704	501	1	[	[	X
ejpam-3704	501	2	2	2	X
ejpam-3704	501	3	]	]	X
ejpam-3704	501	4	g.	g.	PROPN
ejpam-3704	501	5	flores	flores	PROPN
ejpam-3704	501	6	and	and	CCONJ
ejpam-3704	501	7	g.	g.	PROPN
ejpam-3704	501	8	petalcorin	petalcorin	PROPN
ejpam-3704	501	9	.	.	PUNCT
ejpam-3704	502	1	some	some	DET
ejpam-3704	502	2	hyper	hyper	ADJ
ejpam-3704	502	3	isomorphism	isomorphism	NOUN
ejpam-3704	502	4	theorems	theorem	NOUN
ejpam-3704	502	5	on	on	ADP
ejpam-3704	502	6	hyper	hyper	ADJ
ejpam-3704	502	7	bcialgebra	bcialgebra	NOUN
ejpam-3704	502	8	.	.	PUNCT
ejpam-3704	503	1	journal	journal	PROPN
ejpam-3704	503	2	of	of	ADP
ejpam-3704	503	3	algebra	algebra	PROPN
ejpam-3704	503	4	and	and	CCONJ
ejpam-3704	503	5	applied	apply	VERB
ejpam-3704	503	6	mathematics	mathematic	NOUN
ejpam-3704	503	7	,	,	PUNCT
ejpam-3704	503	8	13(1):15–31	13(1):15–31	NUM
ejpam-3704	503	9	,	,	PUNCT
ejpam-3704	503	10	2015	2015	NUM
ejpam-3704	503	11	.	.	PUNCT
ejpam-3704	504	1	[	[	X
ejpam-3704	504	2	3	3	X
ejpam-3704	504	3	]	]	X
ejpam-3704	504	4	d.	d.	PROPN
ejpam-3704	504	5	gomisong	gomisong	PROPN
ejpam-3704	504	6	.	.	PUNCT
ejpam-3704	505	1	on	on	ADP
ejpam-3704	505	2	fully	fully	ADV
ejpam-3704	505	3	up	up	ADP
ejpam-3704	505	4	-	-	PUNCT
ejpam-3704	505	5	semigroups	semigroup	NOUN
ejpam-3704	505	6	and	and	CCONJ
ejpam-3704	505	7	hyper	hyper	ADJ
ejpam-3704	505	8	up	up	ADP
ejpam-3704	505	9	-	-	PUNCT
ejpam-3704	505	10	algebras	algebras	X
ejpam-3704	505	11	.	.	PUNCT
ejpam-3704	506	1	mindanao	mindanao	PROPN
ejpam-3704	506	2	state	state	PROPN
ejpam-3704	506	3	university	university	PROPN
ejpam-3704	506	4	-	-	PUNCT
ejpam-3704	506	5	iligan	iligan	PROPN
ejpam-3704	506	6	institute	institute	PROPN
ejpam-3704	506	7	of	of	ADP
ejpam-3704	506	8	technology	technology	PROPN
ejpam-3704	506	9	,	,	PUNCT
ejpam-3704	506	10	philippines	philippine	NOUN
ejpam-3704	506	11	,	,	PUNCT
ejpam-3704	506	12	2019	2019	NUM
ejpam-3704	506	13	.	.	PUNCT
ejpam-3704	507	1	[	[	X
ejpam-3704	507	2	4	4	NUM
ejpam-3704	507	3	]	]	PUNCT
ejpam-3704	507	4	a.	a.	NOUN
ejpam-3704	507	5	iampan	iampan	PROPN
ejpam-3704	507	6	.	.	PUNCT
ejpam-3704	508	1	a	a	DET
ejpam-3704	508	2	new	new	ADJ
ejpam-3704	508	3	branch	branch	NOUN
ejpam-3704	508	4	of	of	ADP
ejpam-3704	508	5	the	the	DET
ejpam-3704	508	6	logical	logical	ADJ
ejpam-3704	508	7	algebra	algebra	NOUN
ejpam-3704	508	8	:	:	PUNCT
ejpam-3704	508	9	up	up	ADP
ejpam-3704	508	10	-	-	PUNCT
ejpam-3704	508	11	algebras	algebras	X
ejpam-3704	508	12	.	.	PUNCT
ejpam-3704	508	13	journal	journal	PROPN
ejpam-3704	508	14	of	of	ADP
ejpam-3704	508	15	algebra	algebra	PROPN
ejpam-3704	508	16	and	and	CCONJ
ejpam-3704	508	17	related	related	ADJ
ejpam-3704	508	18	topics	topic	NOUN
ejpam-3704	508	19	,	,	PUNCT
ejpam-3704	508	20	5(1):35–54	5(1):35–54	NUM
ejpam-3704	508	21	,	,	PUNCT
ejpam-3704	508	22	2017	2017	NUM
ejpam-3704	508	23	.	.	PUNCT
ejpam-3704	509	1	[	[	X
ejpam-3704	509	2	5	5	X
ejpam-3704	509	3	]	]	PUNCT
ejpam-3704	509	4	s.	s.	PROPN
ejpam-3704	509	5	mostafa	mostafa	PROPN
ejpam-3704	509	6	f.	f.	PROPN
ejpam-3704	509	7	kareem	kareem	PROPN
ejpam-3704	509	8	and	and	CCONJ
ejpam-3704	509	9	b.	b.	PROPN
ejpam-3704	509	10	davvaz	davvaz	PROPN
ejpam-3704	509	11	.	.	PUNCT
ejpam-3704	510	1	hyper	hyper	ADJ
ejpam-3704	510	2	structure	structure	NOUN
ejpam-3704	510	3	theory	theory	NOUN
ejpam-3704	510	4	applied	apply	VERB
ejpam-3704	510	5	to	to	ADP
ejpam-3704	510	6	ku	ku	NOUN
ejpam-3704	510	7	-	-	PUNCT
ejpam-3704	510	8	algebra	algebra	PROPN
ejpam-3704	510	9	.	.	PUNCT
ejpam-3704	511	1	journal	journal	PROPN
ejpam-3704	511	2	of	of	ADP
ejpam-3704	511	3	hyperstructures	hyperstructure	NOUN
ejpam-3704	511	4	,	,	PUNCT
ejpam-3704	511	5	6(2):82–95	6(2):82–95	NUM
ejpam-3704	511	6	,	,	PUNCT
ejpam-3704	511	7	2017	2017	NUM
ejpam-3704	511	8	.	.	PUNCT
ejpam-3704	512	1	[	[	X
ejpam-3704	512	2	6	6	NUM
ejpam-3704	512	3	]	]	PUNCT
ejpam-3704	512	4	x.	x.	NOUN
ejpam-3704	512	5	long	long	ADJ
ejpam-3704	512	6	.	.	PUNCT
ejpam-3704	513	1	hyper	hyper	ADJ
ejpam-3704	513	2	bci	bci	NOUN
ejpam-3704	513	3	-	-	NOUN
ejpam-3704	513	4	algebra	algebra	NOUN
ejpam-3704	513	5	.	.	PUNCT
ejpam-3704	514	1	discuss	discuss	PROPN
ejpam-3704	514	2	math	math	NOUN
ejpam-3704	514	3	.	.	PUNCT
ejpam-3704	515	1	soc	soc	PROPN
ejpam-3704	515	2	.	.	PUNCT
ejpam-3704	515	3	,	,	PUNCT
ejpam-3704	515	4	26:5–19	26:5–19	NUM
ejpam-3704	515	5	,	,	PUNCT
ejpam-3704	515	6	2006	2006	NUM
ejpam-3704	515	7	.	.	PUNCT
ejpam-3704	516	1	[	[	X
ejpam-3704	516	2	7	7	X
ejpam-3704	516	3	]	]	X
ejpam-3704	516	4	f.	f.	PROPN
ejpam-3704	516	5	marty	marty	PROPN
ejpam-3704	516	6	.	.	PUNCT
ejpam-3704	517	1	sur	sur	PROPN
ejpam-3704	517	2	une	une	PROPN
ejpam-3704	517	3	generalisation	generalisation	PROPN
ejpam-3704	517	4	de	de	X
ejpam-3704	517	5	la	la	PROPN
ejpam-3704	517	6	notion	notion	PROPN
ejpam-3704	517	7	de	de	X
ejpam-3704	517	8	groupe	groupe	PROPN
ejpam-3704	517	9	.	.	PUNCT
ejpam-3704	518	1	in	in	ADP
ejpam-3704	518	2	8th	8th	ADJ
ejpam-3704	518	3	congress	congress	PROPN
ejpam-3704	518	4	des	des	PROPN
ejpam-3704	518	5	mathematician	mathematician	PROPN
ejpam-3704	518	6	scandinaves	scandinaves	PROPN
ejpam-3704	518	7	,	,	PUNCT
ejpam-3704	518	8	pages	page	NOUN
ejpam-3704	518	9	45–49	45–49	PROPN
ejpam-3704	518	10	,	,	PUNCT
ejpam-3704	518	11	stockholm	stockholm	PROPN
ejpam-3704	518	12	,	,	PUNCT
ejpam-3704	518	13	1934	1934	NUM
ejpam-3704	518	14	.	.	PUNCT
ejpam-3704	519	1	[	[	X
ejpam-3704	519	2	8	8	NUM
ejpam-3704	519	3	]	]	X
ejpam-3704	519	4	c.	c.	NOUN
ejpam-3704	519	5	prabpayak	prabpayak	NOUN
ejpam-3704	519	6	and	and	CCONJ
ejpam-3704	519	7	u.	u.	NOUN
ejpam-3704	519	8	leerawat	leerawat	PROPN
ejpam-3704	519	9	.	.	PUNCT
ejpam-3704	520	1	on	on	ADP
ejpam-3704	520	2	ideals	ideal	NOUN
ejpam-3704	520	3	and	and	CCONJ
ejpam-3704	520	4	congruence	congruence	NOUN
ejpam-3704	520	5	in	in	ADP
ejpam-3704	520	6	ku	ku	PROPN
ejpam-3704	520	7	-	-	PUNCT
ejpam-3704	520	8	algebras	algebras	PROPN
ejpam-3704	520	9	.	.	PUNCT
ejpam-3704	521	1	scientia	scientia	PROPN
ejpam-3704	521	2	magna	magna	PROPN
ejpam-3704	521	3	journal	journal	PROPN
ejpam-3704	521	4	,	,	PUNCT
ejpam-3704	521	5	5(1):54–57	5(1):54–57	NUM
ejpam-3704	521	6	,	,	PUNCT
ejpam-3704	521	7	2009	2009	NUM
ejpam-3704	521	8	.	.	PUNCT
ejpam-3704	522	1	references	reference	NOUN
ejpam-3704	522	2	497	497	NUM
ejpam-3704	523	1	[	[	X
ejpam-3704	523	2	9	9	NUM
ejpam-3704	523	3	]	]	X
ejpam-3704	523	4	d.	d.	PROPN
ejpam-3704	523	5	romano	romano	PROPN
ejpam-3704	523	6	.	.	PUNCT
ejpam-3704	524	1	quotient	quotient	NOUN
ejpam-3704	524	2	of	of	ADP
ejpam-3704	524	3	hyper	hyper	ADJ
ejpam-3704	524	4	up	up	ADP
ejpam-3704	524	5	-	-	PUNCT
ejpam-3704	524	6	algebras	algebras	X
ejpam-3704	524	7	.	.	PUNCT
ejpam-3704	525	1	preprint	preprint	NOUN
ejpam-3704	525	2	.	.	PUNCT
ejpam-3704	526	1	[	[	X
ejpam-3704	526	2	10	10	NUM
ejpam-3704	526	3	]	]	X
ejpam-3704	526	4	d.	d.	PROPN
ejpam-3704	526	5	romano	romano	PROPN
ejpam-3704	526	6	.	.	PUNCT
ejpam-3704	527	1	hyper	hyper	PROPN
ejpam-3704	527	2	up	up	ADP
ejpam-3704	527	3	-	-	PUNCT
ejpam-3704	527	4	algebras	algebras	PROPN
ejpam-3704	527	5	.	.	PUNCT
ejpam-3704	528	1	journal	journal	PROPN
ejpam-3704	528	2	of	of	ADP
ejpam-3704	528	3	hyperstructures	hyperstructure	NOUN
ejpam-3704	528	4	online	online	ADV
ejpam-3704	528	5	,	,	PUNCT
ejpam-3704	528	6	8(2):1–11	8(2):1–11	PROPN
ejpam-3704	528	7	,	,	PUNCT
ejpam-3704	528	8	2019	2019	NUM
ejpam-3704	528	9	.	.	PUNCT
ejpam-3704	529	1	[	[	X
ejpam-3704	529	2	11	11	NUM
ejpam-3704	529	3	]	]	X
ejpam-3704	529	4	y.	y.	PROPN
ejpam-3704	529	5	jun	jun	PROPN
ejpam-3704	529	6	m.	m.	PROPN
ejpam-3704	529	7	zahedi	zahedi	PROPN
ejpam-3704	529	8	x.	x.	PROPN
ejpam-3704	529	9	xin	xin	PROPN
ejpam-3704	529	10	and	and	CCONJ
ejpam-3704	529	11	r.	r.	PROPN
ejpam-3704	529	12	borzooei	borzooei	PROPN
ejpam-3704	529	13	.	.	PUNCT
ejpam-3704	530	1	on	on	ADP
ejpam-3704	530	2	hyper	hyper	ADJ
ejpam-3704	530	3	bck	bck	NOUN
ejpam-3704	530	4	-	-	PUNCT
ejpam-3704	530	5	algebra	algebra	NOUN
ejpam-3704	530	6	.	.	PUNCT
ejpam-3704	531	1	italian	italian	ADJ
ejpam-3704	531	2	journal	journal	NOUN
ejpam-3704	531	3	of	of	ADP
ejpam-3704	531	4	pure	pure	ADJ
ejpam-3704	531	5	and	and	CCONJ
ejpam-3704	531	6	applied	applied	ADJ
ejpam-3704	531	7	mathematics	mathematic	NOUN
ejpam-3704	531	8	,	,	PUNCT
ejpam-3704	531	9	10:127–136	10:127–136	NUM
ejpam-3704	531	10	,	,	PUNCT
ejpam-3704	531	11	2000	2000	NUM
ejpam-3704	531	12	.	.	PUNCT
ejpam-3704	532	1	[	[	X
ejpam-3704	532	2	12	12	NUM
ejpam-3704	532	3	]	]	X
ejpam-3704	532	4	r.	r.	PROPN
ejpam-3704	532	5	borzooei	borzooei	PROPN
ejpam-3704	532	6	a.	a.	PROPN
ejpam-3704	532	7	hasankhani	hasankhani	PROPN
ejpam-3704	532	8	m.	m.	PROPN
ejpam-3704	532	9	zahedi	zahedi	PROPN
ejpam-3704	532	10	and	and	CCONJ
ejpam-3704	532	11	y.	y.	PROPN
ejpam-3704	532	12	jun	jun	PROPN
ejpam-3704	532	13	.	.	PROPN
ejpam-3704	533	1	on	on	ADP
ejpam-3704	533	2	hyper	hyper	ADJ
ejpam-3704	533	3	k	k	NOUN
ejpam-3704	533	4	-	-	PUNCT
ejpam-3704	533	5	algebras	algebras	PROPN
ejpam-3704	533	6	.	.	PUNCT
ejpam-3704	534	1	mathematicae	mathematicae	PROPN
ejpam-3704	534	2	japonicae	japonicae	PROPN
ejpam-3704	534	3	,	,	PUNCT
ejpam-3704	534	4	52(1):113–121	52(1):113–121	NUM
ejpam-3704	534	5	,	,	PUNCT
ejpam-3704	534	6	2000	2000	NUM
ejpam-3704	534	7	.	.	PUNCT