id	sid	tid	token	lemma	pos
ejpam-4554	1	1	european	european	PROPN
ejpam-4554	1	2	journal	journal	PROPN
ejpam-4554	1	3	of	of	ADP
ejpam-4554	1	4	pure	pure	ADJ
ejpam-4554	1	5	and	and	CCONJ
ejpam-4554	1	6	applied	apply	VERB
ejpam-4554	1	7	mathematics	mathematic	NOUN
ejpam-4554	1	8	vol	vol	NOUN
ejpam-4554	1	9	.	.	PROPN
ejpam-4554	2	1	15	15	NUM
ejpam-4554	2	2	,	,	PUNCT
ejpam-4554	2	3	no	no	INTJ
ejpam-4554	2	4	.	.	NOUN
ejpam-4554	2	5	4	4	NUM
ejpam-4554	2	6	,	,	PUNCT
ejpam-4554	2	7	2022	2022	NUM
ejpam-4554	2	8	,	,	PUNCT
ejpam-4554	2	9	1854	1854	NUM
ejpam-4554	2	10	-	-	SYM
ejpam-4554	2	11	1868	1868	NUM
ejpam-4554	2	12	issn	issn	PROPN
ejpam-4554	2	13	1307	1307	NUM
ejpam-4554	2	14	-	-	SYM
ejpam-4554	2	15	5543	5543	NUM
ejpam-4554	2	16	–	–	PUNCT
ejpam-4554	3	1	ejpam.com	ejpam.com	X
ejpam-4554	3	2	published	publish	VERB
ejpam-4554	3	3	by	by	ADP
ejpam-4554	3	4	new	new	PROPN
ejpam-4554	3	5	york	york	PROPN
ejpam-4554	3	6	business	business	PROPN
ejpam-4554	3	7	global	global	ADJ
ejpam-4554	3	8	quotient	quotient	NOUN
ejpam-4554	3	9	pseudo	pseudo	NOUN
ejpam-4554	3	10	hyper	hyper	ADJ
ejpam-4554	3	11	gr	gr	ADJ
ejpam-4554	3	12	-	-	PUNCT
ejpam-4554	3	13	algebras	algebras	PROPN
ejpam-4554	3	14	ramises	ramise	NOUN
ejpam-4554	3	15	g.	g.	PROPN
ejpam-4554	3	16	manzano	manzano	PROPN
ejpam-4554	3	17	,	,	PUNCT
ejpam-4554	3	18	jr.1	jr.1	PROPN
ejpam-4554	3	19	,	,	PUNCT
ejpam-4554	3	20	gaudencio	gaudencio	PROPN
ejpam-4554	3	21	c.	c.	PROPN
ejpam-4554	3	22	petalcorin	petalcorin	PROPN
ejpam-4554	3	23	,	,	PUNCT
ejpam-4554	3	24	jr.2,∗	jr.2,∗	PROPN
ejpam-4554	3	25	1	1	NUM
ejpam-4554	3	26	office	office	NOUN
ejpam-4554	3	27	of	of	ADP
ejpam-4554	3	28	the	the	DET
ejpam-4554	3	29	mathematics	mathematics	PROPN
ejpam-4554	3	30	and	and	CCONJ
ejpam-4554	3	31	statistics	statistic	NOUN
ejpam-4554	3	32	programs	program	NOUN
ejpam-4554	3	33	,	,	PUNCT
ejpam-4554	3	34	college	college	NOUN
ejpam-4554	3	35	of	of	ADP
ejpam-4554	3	36	science	science	NOUN
ejpam-4554	3	37	,	,	PUNCT
ejpam-4554	3	38	university	university	NOUN
ejpam-4554	3	39	of	of	ADP
ejpam-4554	3	40	the	the	DET
ejpam-4554	3	41	philippines	philippine	NOUN
ejpam-4554	3	42	cebu	cebu	NOUN
ejpam-4554	3	43	,	,	PUNCT
ejpam-4554	3	44	lahug	lahug	NOUN
ejpam-4554	3	45	,	,	PUNCT
ejpam-4554	3	46	cebu	cebu	NOUN
ejpam-4554	3	47	city	city	NOUN
ejpam-4554	3	48	,	,	PUNCT
ejpam-4554	3	49	philippines	philippines	PROPN
ejpam-4554	3	50	2	2	NUM
ejpam-4554	3	51	department	department	NOUN
ejpam-4554	3	52	of	of	ADP
ejpam-4554	3	53	mathematics	mathematic	NOUN
ejpam-4554	3	54	and	and	CCONJ
ejpam-4554	3	55	statistics	statistic	NOUN
ejpam-4554	3	56	,	,	PUNCT
ejpam-4554	3	57	college	college	NOUN
ejpam-4554	3	58	of	of	ADP
ejpam-4554	3	59	science	science	NOUN
ejpam-4554	3	60	,	,	PUNCT
ejpam-4554	3	61	msu	msu	PROPN
ejpam-4554	3	62	-	-	PUNCT
ejpam-4554	3	63	iligan	iligan	PROPN
ejpam-4554	3	64	institute	institute	PROPN
ejpam-4554	3	65	of	of	ADP
ejpam-4554	3	66	technology	technology	PROPN
ejpam-4554	3	67	,	,	PUNCT
ejpam-4554	3	68	tibanga	tibanga	PROPN
ejpam-4554	3	69	,	,	PUNCT
ejpam-4554	3	70	iligan	iligan	ADJ
ejpam-4554	3	71	city	city	PROPN
ejpam-4554	3	72	,	,	PUNCT
ejpam-4554	3	73	philippines	philippine	NOUN
ejpam-4554	3	74	abstract	abstract	ADJ
ejpam-4554	3	75	.	.	PUNCT
ejpam-4554	4	1	a	a	DET
ejpam-4554	4	2	pseudo	pseudo	NOUN
ejpam-4554	4	3	hyper	hyper	ADJ
ejpam-4554	4	4	gr	gr	NOUN
ejpam-4554	4	5	-	-	PUNCT
ejpam-4554	4	6	algebra	algebra	NOUN
ejpam-4554	4	7	is	be	AUX
ejpam-4554	4	8	an	an	DET
ejpam-4554	4	9	algebraic	algebraic	ADJ
ejpam-4554	4	10	structure	structure	NOUN
ejpam-4554	4	11	involving	involve	VERB
ejpam-4554	4	12	two	two	NUM
ejpam-4554	4	13	distinct	distinct	ADJ
ejpam-4554	4	14	hyperoperations	hyperoperation	NOUN
ejpam-4554	4	15	.	.	PUNCT
ejpam-4554	5	1	properties	property	NOUN
ejpam-4554	5	2	of	of	ADP
ejpam-4554	5	3	this	this	DET
ejpam-4554	5	4	hyper	hyper	ADJ
ejpam-4554	5	5	algebra	algebra	NOUN
ejpam-4554	5	6	have	have	AUX
ejpam-4554	5	7	been	be	AUX
ejpam-4554	5	8	studied	study	VERB
ejpam-4554	5	9	and	and	CCONJ
ejpam-4554	5	10	given	give	VERB
ejpam-4554	5	11	illustrations	illustration	NOUN
ejpam-4554	5	12	.	.	PUNCT
ejpam-4554	6	1	this	this	DET
ejpam-4554	6	2	paper	paper	NOUN
ejpam-4554	6	3	focuses	focus	VERB
ejpam-4554	6	4	on	on	ADP
ejpam-4554	6	5	the	the	DET
ejpam-4554	6	6	quotient	quotient	NOUN
ejpam-4554	6	7	structure	structure	NOUN
ejpam-4554	6	8	of	of	ADP
ejpam-4554	6	9	pseudo	pseudo	NOUN
ejpam-4554	6	10	hyper	hyper	ADJ
ejpam-4554	6	11	gr	gr	NOUN
ejpam-4554	6	12	-	-	PUNCT
ejpam-4554	6	13	algebras	algebras	NOUN
ejpam-4554	6	14	.	.	PUNCT
ejpam-4554	7	1	from	from	ADP
ejpam-4554	7	2	an	an	DET
ejpam-4554	7	3	equivalence	equivalence	NOUN
ejpam-4554	7	4	relation	relation	NOUN
ejpam-4554	7	5	on	on	ADP
ejpam-4554	7	6	a	a	DET
ejpam-4554	7	7	pseudo	pseudo	NOUN
ejpam-4554	7	8	hyper	hyper	ADJ
ejpam-4554	7	9	gr	gr	NOUN
ejpam-4554	7	10	-	-	PUNCT
ejpam-4554	7	11	algebra	algebra	NOUN
ejpam-4554	7	12	h	h	NOUN
ejpam-4554	7	13	,	,	PUNCT
ejpam-4554	7	14	we	we	PRON
ejpam-4554	7	15	can	can	AUX
ejpam-4554	7	16	define	define	VERB
ejpam-4554	7	17	a	a	DET
ejpam-4554	7	18	congruence	congruence	NOUN
ejpam-4554	7	19	relation	relation	NOUN
ejpam-4554	7	20	on	on	ADP
ejpam-4554	7	21	h	h	NOUN
ejpam-4554	7	22	that	that	PRON
ejpam-4554	7	23	is	be	AUX
ejpam-4554	7	24	used	use	VERB
ejpam-4554	7	25	in	in	ADP
ejpam-4554	7	26	the	the	DET
ejpam-4554	7	27	construction	construction	NOUN
ejpam-4554	7	28	of	of	ADP
ejpam-4554	7	29	the	the	DET
ejpam-4554	7	30	quotient	quotient	NOUN
ejpam-4554	7	31	structure	structure	NOUN
ejpam-4554	7	32	h	h	PROPN
ejpam-4554	7	33	/	/	SYM
ejpam-4554	7	34	i	i	PROPN
ejpam-4554	7	35	,	,	PUNCT
ejpam-4554	7	36	where	where	SCONJ
ejpam-4554	7	37	i	i	PRON
ejpam-4554	7	38	is	be	AUX
ejpam-4554	7	39	the	the	DET
ejpam-4554	7	40	congruence	congruence	ADJ
ejpam-4554	7	41	class	class	NOUN
ejpam-4554	7	42	of	of	ADP
ejpam-4554	7	43	0	0	NUM
ejpam-4554	7	44	under	under	ADP
ejpam-4554	7	45	the	the	DET
ejpam-4554	7	46	congruence	congruence	PROPN
ejpam-4554	7	47	relation	relation	NOUN
ejpam-4554	7	48	.	.	PUNCT
ejpam-4554	8	1	moreover	moreover	ADV
ejpam-4554	8	2	,	,	PUNCT
ejpam-4554	8	3	some	some	DET
ejpam-4554	8	4	isomorphism	isomorphism	NOUN
ejpam-4554	8	5	theorems	theorem	NOUN
ejpam-4554	8	6	of	of	ADP
ejpam-4554	8	7	pseudo	pseudo	NOUN
ejpam-4554	8	8	hyper	hyper	ADJ
ejpam-4554	8	9	gr	gr	NOUN
ejpam-4554	8	10	-	-	PUNCT
ejpam-4554	8	11	algebras	algebra	NOUN
ejpam-4554	8	12	are	be	AUX
ejpam-4554	8	13	included	include	VERB
ejpam-4554	8	14	in	in	ADP
ejpam-4554	8	15	this	this	DET
ejpam-4554	8	16	paper	paper	NOUN
ejpam-4554	8	17	.	.	PUNCT
ejpam-4554	9	1	2020	2020	NUM
ejpam-4554	9	2	mathematics	mathematic	NOUN
ejpam-4554	9	3	subject	subject	NOUN
ejpam-4554	9	4	classifications	classification	NOUN
ejpam-4554	9	5	:	:	PUNCT
ejpam-4554	9	6	14l17	14l17	NUM
ejpam-4554	9	7	,	,	PUNCT
ejpam-4554	9	8	20n20	20n20	NUM
ejpam-4554	9	9	,	,	PUNCT
ejpam-4554	9	10	03g25	03g25	NOUN
ejpam-4554	9	11	key	key	ADJ
ejpam-4554	9	12	words	word	NOUN
ejpam-4554	9	13	and	and	CCONJ
ejpam-4554	9	14	phrases	phrase	NOUN
ejpam-4554	9	15	:	:	PUNCT
ejpam-4554	9	16	hyper	hyper	ADJ
ejpam-4554	9	17	algebras	algebra	NOUN
ejpam-4554	9	18	,	,	PUNCT
ejpam-4554	9	19	quotient	quotient	VERB
ejpam-4554	9	20	hyper	hyper	ADJ
ejpam-4554	9	21	algebras	algebras	PROPN
ejpam-4554	9	22	1	1	X
ejpam-4554	9	23	.	.	X
ejpam-4554	9	24	introduction	introduction	NOUN
ejpam-4554	9	25	algebraic	algebraic	PROPN
ejpam-4554	9	26	hyperstructures	hyperstructure	NOUN
ejpam-4554	9	27	were	be	AUX
ejpam-4554	9	28	introduced	introduce	VERB
ejpam-4554	9	29	by	by	ADP
ejpam-4554	9	30	a	a	DET
ejpam-4554	9	31	french	french	ADJ
ejpam-4554	9	32	mathematician	mathematician	NOUN
ejpam-4554	9	33	,	,	PUNCT
ejpam-4554	9	34	marty	marty	PROPN
ejpam-4554	10	1	[	[	X
ejpam-4554	10	2	6	6	NUM
ejpam-4554	10	3	]	]	PUNCT
ejpam-4554	10	4	,	,	PUNCT
ejpam-4554	10	5	in	in	ADP
ejpam-4554	10	6	1934	1934	NUM
ejpam-4554	10	7	.	.	PUNCT
ejpam-4554	11	1	they	they	PRON
ejpam-4554	11	2	represent	represent	VERB
ejpam-4554	11	3	a	a	DET
ejpam-4554	11	4	natural	natural	ADJ
ejpam-4554	11	5	extension	extension	NOUN
ejpam-4554	11	6	of	of	ADP
ejpam-4554	11	7	classical	classical	ADJ
ejpam-4554	11	8	hyperstructures	hyperstructure	NOUN
ejpam-4554	11	9	in	in	ADP
ejpam-4554	11	10	which	which	PRON
ejpam-4554	11	11	the	the	DET
ejpam-4554	11	12	composition	composition	NOUN
ejpam-4554	11	13	of	of	ADP
ejpam-4554	11	14	two	two	NUM
ejpam-4554	11	15	elements	element	NOUN
ejpam-4554	11	16	of	of	ADP
ejpam-4554	11	17	a	a	DET
ejpam-4554	11	18	given	give	VERB
ejpam-4554	11	19	set	set	NOUN
ejpam-4554	11	20	is	be	AUX
ejpam-4554	11	21	a	a	DET
ejpam-4554	11	22	set	set	NOUN
ejpam-4554	11	23	,	,	PUNCT
ejpam-4554	11	24	instead	instead	ADV
ejpam-4554	11	25	of	of	ADP
ejpam-4554	11	26	an	an	DET
ejpam-4554	11	27	element	element	NOUN
ejpam-4554	11	28	.	.	PUNCT
ejpam-4554	12	1	afterwards	afterwards	ADV
ejpam-4554	12	2	,	,	PUNCT
ejpam-4554	12	3	this	this	DET
ejpam-4554	12	4	new	new	ADJ
ejpam-4554	12	5	idea	idea	NOUN
ejpam-4554	12	6	was	be	AUX
ejpam-4554	12	7	expanded	expand	VERB
ejpam-4554	12	8	rapidly	rapidly	ADV
ejpam-4554	12	9	and	and	CCONJ
ejpam-4554	12	10	showed	show	VERB
ejpam-4554	12	11	itself	itself	PRON
ejpam-4554	12	12	as	as	ADP
ejpam-4554	12	13	a	a	DET
ejpam-4554	12	14	new	new	ADJ
ejpam-4554	12	15	view	view	NOUN
ejpam-4554	12	16	of	of	ADP
ejpam-4554	12	17	sets	set	NOUN
ejpam-4554	12	18	.	.	PUNCT
ejpam-4554	13	1	the	the	DET
ejpam-4554	13	2	introduction	introduction	NOUN
ejpam-4554	13	3	of	of	ADP
ejpam-4554	13	4	hyperstructure	hyperstructure	PROPN
ejpam-4554	13	5	theory	theory	NOUN
ejpam-4554	13	6	led	lead	VERB
ejpam-4554	13	7	to	to	ADP
ejpam-4554	13	8	the	the	DET
ejpam-4554	13	9	study	study	NOUN
ejpam-4554	13	10	of	of	ADP
ejpam-4554	13	11	several	several	ADJ
ejpam-4554	13	12	problems	problem	NOUN
ejpam-4554	13	13	of	of	ADP
ejpam-4554	13	14	noncommutative	noncommutative	ADJ
ejpam-4554	13	15	algebra	algebra	NOUN
ejpam-4554	13	16	.	.	PUNCT
ejpam-4554	14	1	algebraic	algebraic	PROPN
ejpam-4554	14	2	hyperstructure	hyperstructure	PROPN
ejpam-4554	14	3	theory	theory	NOUN
ejpam-4554	14	4	has	have	VERB
ejpam-4554	14	5	multiple	multiple	ADJ
ejpam-4554	14	6	applications	application	NOUN
ejpam-4554	14	7	to	to	ADP
ejpam-4554	14	8	other	other	ADJ
ejpam-4554	14	9	fields	field	NOUN
ejpam-4554	14	10	such	such	ADJ
ejpam-4554	14	11	as	as	ADP
ejpam-4554	14	12	:	:	PUNCT
ejpam-4554	14	13	geometry	geometry	NOUN
ejpam-4554	14	14	,	,	PUNCT
ejpam-4554	14	15	graphs	graph	NOUN
ejpam-4554	14	16	and	and	CCONJ
ejpam-4554	14	17	hypergraphs	hypergraph	NOUN
ejpam-4554	14	18	,	,	PUNCT
ejpam-4554	14	19	binary	binary	ADJ
ejpam-4554	14	20	relations	relation	NOUN
ejpam-4554	14	21	,	,	PUNCT
ejpam-4554	14	22	lattices	lattice	NOUN
ejpam-4554	14	23	,	,	PUNCT
ejpam-4554	14	24	groups	group	NOUN
ejpam-4554	14	25	,	,	PUNCT
ejpam-4554	14	26	relation	relation	NOUN
ejpam-4554	14	27	algebras	algebra	NOUN
ejpam-4554	14	28	,	,	PUNCT
ejpam-4554	14	29	artificial	artificial	ADJ
ejpam-4554	14	30	intelligence	intelligence	NOUN
ejpam-4554	14	31	,	,	PUNCT
ejpam-4554	14	32	probabilities	probability	NOUN
ejpam-4554	14	33	,	,	PUNCT
ejpam-4554	14	34	and	and	CCONJ
ejpam-4554	14	35	so	so	ADV
ejpam-4554	14	36	on	on	ADV
ejpam-4554	14	37	.	.	PUNCT
ejpam-4554	15	1	in	in	ADP
ejpam-4554	15	2	1966	1966	NUM
ejpam-4554	15	3	,	,	PUNCT
ejpam-4554	15	4	y.	y.	PROPN
ejpam-4554	15	5	imai	imai	PROPN
ejpam-4554	15	6	and	and	CCONJ
ejpam-4554	15	7	k.	k.	PROPN
ejpam-4554	15	8	iséki	iséki	PROPN
ejpam-4554	16	1	[	[	X
ejpam-4554	16	2	1	1	X
ejpam-4554	16	3	]	]	PUNCT
ejpam-4554	16	4	initiated	initiate	VERB
ejpam-4554	16	5	the	the	DET
ejpam-4554	16	6	notion	notion	NOUN
ejpam-4554	16	7	ofbck	ofbck	NOUN
ejpam-4554	16	8	-	-	PUNCT
ejpam-4554	16	9	algebra	algebra	NOUN
ejpam-4554	16	10	as	as	ADP
ejpam-4554	16	11	a	a	DET
ejpam-4554	16	12	generalization	generalization	NOUN
ejpam-4554	16	13	of	of	ADP
ejpam-4554	16	14	the	the	DET
ejpam-4554	16	15	concept	concept	NOUN
ejpam-4554	16	16	of	of	ADP
ejpam-4554	16	17	set	set	NOUN
ejpam-4554	16	18	-	-	PUNCT
ejpam-4554	16	19	theoretic	theoretic	NOUN
ejpam-4554	16	20	difference	difference	NOUN
ejpam-4554	16	21	and	and	CCONJ
ejpam-4554	16	22	propositional	propositional	ADJ
ejpam-4554	16	23	calculi	calculi	NOUN
ejpam-4554	16	24	.	.	PUNCT
ejpam-4554	17	1	furthermore	furthermore	ADV
ejpam-4554	17	2	,	,	PUNCT
ejpam-4554	17	3	y.b	y.b	PROPN
ejpam-4554	17	4	.	.	PROPN
ejpam-4554	17	5	jun	jun	PROPN
ejpam-4554	17	6	et	et	PROPN
ejpam-4554	17	7	al	al	PROPN
ejpam-4554	17	8	.	.	PUNCT
ejpam-4554	18	1	[	[	X
ejpam-4554	18	2	5	5	NUM
ejpam-4554	18	3	]	]	PUNCT
ejpam-4554	18	4	applied	apply	VERB
ejpam-4554	18	5	hyperstructure	hyperstructure	NOUN
ejpam-4554	18	6	theory	theory	NOUN
ejpam-4554	18	7	to	to	PART
ejpam-4554	18	8	bck	bck	VERB
ejpam-4554	18	9	-	-	PUNCT
ejpam-4554	18	10	algebras	algebras	PROPN
ejpam-4554	18	11	and	and	CCONJ
ejpam-4554	18	12	introduced	introduce	VERB
ejpam-4554	18	13	the	the	DET
ejpam-4554	18	14	notion	notion	NOUN
ejpam-4554	18	15	of	of	ADP
ejpam-4554	18	16	hyper	hyper	ADJ
ejpam-4554	18	17	bck	bck	NOUN
ejpam-4554	18	18	-	-	PUNCT
ejpam-4554	18	19	algebras	algebras	PROPN
ejpam-4554	18	20	as	as	ADP
ejpam-4554	18	21	a	a	DET
ejpam-4554	18	22	generalization	generalization	NOUN
ejpam-4554	18	23	of	of	ADP
ejpam-4554	18	24	bck	bck	NOUN
ejpam-4554	18	25	-	-	PUNCT
ejpam-4554	18	26	algebra	algebra	NOUN
ejpam-4554	18	27	.	.	PUNCT
ejpam-4554	19	1	∗corresponding	∗corresponde	VERB
ejpam-4554	19	2	author	author	NOUN
ejpam-4554	19	3	.	.	PUNCT
ejpam-4554	20	1	doi	doi	NOUN
ejpam-4554	20	2	:	:	PUNCT
ejpam-4554	20	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4554	https://doi.org/10.29020/nybg.ejpam.v15i4.4554	PUNCT
ejpam-4554	20	4	email	email	NOUN
ejpam-4554	20	5	addresses	address	VERB
ejpam-4554	20	6	:	:	PUNCT
ejpam-4554	20	7	rgmanzano@up.edu.ph	rgmanzano@up.edu.ph	PROPN
ejpam-4554	20	8	(	(	PUNCT
ejpam-4554	20	9	r.	r.	PROPN
ejpam-4554	20	10	manzano	manzano	PROPN
ejpam-4554	20	11	,	,	PUNCT
ejpam-4554	20	12	jr	jr	PROPN
ejpam-4554	20	13	.	.	PROPN
ejpam-4554	20	14	)	)	PUNCT
ejpam-4554	20	15	,	,	PUNCT
ejpam-4554	20	16	gaudencio.petalcorin@g.msuiit.edu.ph	gaudencio.petalcorin@g.msuiit.edu.ph	PROPN
ejpam-4554	20	17	(	(	PUNCT
ejpam-4554	20	18	g.	g.	PROPN
ejpam-4554	20	19	petalcorin	petalcorin	PROPN
ejpam-4554	20	20	,	,	PUNCT
ejpam-4554	20	21	jr	jr	PROPN
ejpam-4554	20	22	.	.	PUNCT
ejpam-4554	20	23	)	)	PUNCT
ejpam-4554	20	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4554	20	25	1854	1854	NUM
ejpam-4554	21	1	©	©	ADP
ejpam-4554	21	2	2022	2022	NUM
ejpam-4554	21	3	ejpam	ejpam	VERB
ejpam-4554	21	4	all	all	DET
ejpam-4554	21	5	rights	right	NOUN
ejpam-4554	21	6	reserved	reserve	VERB
ejpam-4554	21	7	.	.	PUNCT
ejpam-4554	22	1	r.	r.	PROPN
ejpam-4554	22	2	manzano	manzano	PROPN
ejpam-4554	22	3	,	,	PUNCT
ejpam-4554	22	4	jr	jr	PROPN
ejpam-4554	22	5	.	.	PROPN
ejpam-4554	22	6	,	,	PUNCT
ejpam-4554	22	7	g.	g.	PROPN
ejpam-4554	22	8	petalcorin	petalcorin	PROPN
ejpam-4554	22	9	,	,	PUNCT
ejpam-4554	22	10	jr	jr	PROPN
ejpam-4554	22	11	.	.	PROPN
ejpam-4554	22	12	/	/	SYM
ejpam-4554	22	13	eur	eur	PROPN
ejpam-4554	22	14	.	.	PUNCT
ejpam-4554	23	1	j.	j.	PROPN
ejpam-4554	23	2	pure	pure	PROPN
ejpam-4554	23	3	appl	appl	PROPN
ejpam-4554	23	4	.	.	PROPN
ejpam-4554	23	5	math	math	PROPN
ejpam-4554	23	6	,	,	PUNCT
ejpam-4554	23	7	15	15	NUM
ejpam-4554	23	8	(	(	PUNCT
ejpam-4554	23	9	4	4	NUM
ejpam-4554	23	10	)	)	PUNCT
ejpam-4554	23	11	(	(	PUNCT
ejpam-4554	23	12	2022	2022	NUM
ejpam-4554	23	13	)	)	PUNCT
ejpam-4554	23	14	,	,	PUNCT
ejpam-4554	23	15	1854	1854	NUM
ejpam-4554	23	16	-	-	SYM
ejpam-4554	23	17	1868	1868	NUM
ejpam-4554	23	18	1855	1855	NUM
ejpam-4554	23	19	r.a	r.a	PROPN
ejpam-4554	23	20	.	.	PROPN
ejpam-4554	23	21	indangan	indangan	PROPN
ejpam-4554	23	22	and	and	CCONJ
ejpam-4554	23	23	g.c	g.c	PROPN
ejpam-4554	23	24	.	.	PROPN
ejpam-4554	23	25	petalcorin	petalcorin	PROPN
ejpam-4554	24	1	[	[	X
ejpam-4554	24	2	2	2	X
ejpam-4554	24	3	]	]	PUNCT
ejpam-4554	24	4	defined	define	VERB
ejpam-4554	24	5	a	a	DET
ejpam-4554	24	6	new	new	ADJ
ejpam-4554	24	7	class	class	NOUN
ejpam-4554	24	8	of	of	ADP
ejpam-4554	24	9	algebraic	algebraic	PROPN
ejpam-4554	24	10	hyperstructure	hyperstructure	NOUN
ejpam-4554	24	11	called	call	VERB
ejpam-4554	24	12	hyper	hyper	ADJ
ejpam-4554	24	13	gr	gr	NOUN
ejpam-4554	24	14	-	-	NOUN
ejpam-4554	24	15	algebra	algebra	NOUN
ejpam-4554	24	16	.	.	PUNCT
ejpam-4554	25	1	in	in	ADP
ejpam-4554	25	2	this	this	DET
ejpam-4554	25	3	algebra	algebra	NOUN
ejpam-4554	25	4	,	,	PUNCT
ejpam-4554	25	5	they	they	PRON
ejpam-4554	25	6	presented	present	VERB
ejpam-4554	25	7	a	a	DET
ejpam-4554	25	8	helpful	helpful	ADJ
ejpam-4554	25	9	understanding	understanding	NOUN
ejpam-4554	25	10	on	on	ADP
ejpam-4554	25	11	how	how	SCONJ
ejpam-4554	25	12	this	this	DET
ejpam-4554	25	13	hyper	hyper	ADJ
ejpam-4554	25	14	algebra	algebra	NOUN
ejpam-4554	25	15	differs	differ	VERB
ejpam-4554	25	16	from	from	ADP
ejpam-4554	25	17	the	the	DET
ejpam-4554	25	18	rest	rest	NOUN
ejpam-4554	25	19	.	.	PUNCT
ejpam-4554	26	1	r.g	r.g	PROPN
ejpam-4554	26	2	.	.	PROPN
ejpam-4554	26	3	manzano	manzano	PROPN
ejpam-4554	26	4	and	and	CCONJ
ejpam-4554	26	5	g.c	g.c	PROPN
ejpam-4554	26	6	.	.	PROPN
ejpam-4554	26	7	petalcorin	petalcorin	PROPN
ejpam-4554	27	1	[	[	X
ejpam-4554	27	2	4	4	X
ejpam-4554	27	3	]	]	PUNCT
ejpam-4554	27	4	extended	extend	VERB
ejpam-4554	27	5	the	the	DET
ejpam-4554	27	6	study	study	NOUN
ejpam-4554	27	7	hyper	hyper	ADJ
ejpam-4554	27	8	gr	gr	NOUN
ejpam-4554	27	9	-	-	PUNCT
ejpam-4554	27	10	algebras	algebras	NOUN
ejpam-4554	27	11	by	by	ADP
ejpam-4554	27	12	intorducing	intorduce	VERB
ejpam-4554	27	13	a	a	DET
ejpam-4554	27	14	new	new	ADJ
ejpam-4554	27	15	definition	definition	NOUN
ejpam-4554	27	16	involving	involve	VERB
ejpam-4554	27	17	two	two	NUM
ejpam-4554	27	18	hyperoperations	hyperoperation	NOUN
ejpam-4554	27	19	.	.	PUNCT
ejpam-4554	28	1	this	this	PRON
ejpam-4554	28	2	gives	give	VERB
ejpam-4554	28	3	birth	birth	NOUN
ejpam-4554	28	4	to	to	ADP
ejpam-4554	28	5	pseudo	pseudo	NOUN
ejpam-4554	28	6	hyper	hyper	ADJ
ejpam-4554	28	7	gr	gr	NOUN
ejpam-4554	28	8	-	-	PUNCT
ejpam-4554	28	9	algebras	algebras	NOUN
ejpam-4554	28	10	.	.	PUNCT
ejpam-4554	29	1	2	2	X
ejpam-4554	29	2	.	.	X
ejpam-4554	29	3	preliminaries	preliminary	NOUN
ejpam-4554	29	4	let	let	VERB
ejpam-4554	29	5	h	h	NOUN
ejpam-4554	29	6	be	be	AUX
ejpam-4554	29	7	a	a	DET
ejpam-4554	29	8	nonempty	nonempty	ADJ
ejpam-4554	29	9	set	set	VERB
ejpam-4554	29	10	endowed	endow	VERB
ejpam-4554	29	11	with	with	ADP
ejpam-4554	29	12	a	a	DET
ejpam-4554	29	13	hyperoperation	hyperoperation	NOUN
ejpam-4554	29	14	“	"	PUNCT
ejpam-4554	29	15	∗	∗	NOUN
ejpam-4554	29	16	”	"	PUNCT
ejpam-4554	29	17	,	,	PUNCT
ejpam-4554	29	18	that	that	ADV
ejpam-4554	29	19	is	is	ADV
ejpam-4554	29	20	,	,	PUNCT
ejpam-4554	29	21	“	"	PUNCT
ejpam-4554	29	22	∗	∗	NOUN
ejpam-4554	29	23	”	"	PUNCT
ejpam-4554	29	24	is	be	AUX
ejpam-4554	29	25	a	a	DET
ejpam-4554	29	26	function	function	NOUN
ejpam-4554	29	27	from	from	ADP
ejpam-4554	29	28	h	h	PROPN
ejpam-4554	29	29	×	×	PROPN
ejpam-4554	29	30	h	h	NOUN
ejpam-4554	29	31	to	to	ADP
ejpam-4554	29	32	p	p	PROPN
ejpam-4554	29	33	∗(h	∗(h	PROPN
ejpam-4554	29	34	)	)	PUNCT
ejpam-4554	30	1	=	=	SYM
ejpam-4554	30	2	p	p	X
ejpam-4554	30	3	(	(	PUNCT
ejpam-4554	30	4	h	h	NOUN
ejpam-4554	30	5	)	)	PUNCT
ejpam-4554	30	6	\	\	NOUN
ejpam-4554	30	7	{	{	PUNCT
ejpam-4554	30	8	∅	∅	NOUN
ejpam-4554	30	9	}	}	PUNCT
ejpam-4554	30	10	.	.	PUNCT
ejpam-4554	31	1	for	for	ADP
ejpam-4554	31	2	two	two	NUM
ejpam-4554	31	3	nonempty	nonempty	ADJ
ejpam-4554	31	4	subsets	subset	NOUN
ejpam-4554	31	5	a	a	PRON
ejpam-4554	31	6	and	and	CCONJ
ejpam-4554	31	7	b	b	NOUN
ejpam-4554	31	8	of	of	ADP
ejpam-4554	31	9	h	h	NOUN
ejpam-4554	31	10	,	,	PUNCT
ejpam-4554	31	11	a	a	DET
ejpam-4554	31	12	∗	∗	NOUN
ejpam-4554	31	13	b	b	NOUN
ejpam-4554	31	14	=	=	PUNCT
ejpam-4554	31	15	⋃	⋃	NOUN
ejpam-4554	31	16	a∈a	a∈a	ADJ
ejpam-4554	31	17	,	,	PUNCT
ejpam-4554	31	18	b∈b	b∈b	VERB
ejpam-4554	31	19	a	a	DET
ejpam-4554	31	20	∗	∗	NOUN
ejpam-4554	31	21	b.	b.	NOUN
ejpam-4554	32	1	we	we	PRON
ejpam-4554	32	2	shall	shall	AUX
ejpam-4554	32	3	use	use	VERB
ejpam-4554	32	4	x	x	PUNCT
ejpam-4554	32	5	∗	∗	NOUN
ejpam-4554	32	6	y	y	PROPN
ejpam-4554	32	7	instead	instead	ADV
ejpam-4554	32	8	of	of	ADP
ejpam-4554	32	9	x	x	VERB
ejpam-4554	32	10	∗	∗	X
ejpam-4554	32	11	{	{	PUNCT
ejpam-4554	32	12	y	y	NOUN
ejpam-4554	32	13	}	}	PUNCT
ejpam-4554	32	14	,	,	PUNCT
ejpam-4554	32	15	{	{	PUNCT
ejpam-4554	32	16	x	x	NOUN
ejpam-4554	32	17	}	}	PUNCT
ejpam-4554	32	18	∗	∗	NOUN
ejpam-4554	32	19	y	y	NOUN
ejpam-4554	32	20	or	or	CCONJ
ejpam-4554	32	21	{	{	PUNCT
ejpam-4554	32	22	x	x	NOUN
ejpam-4554	32	23	}	}	PUNCT
ejpam-4554	32	24	∗	∗	NOUN
ejpam-4554	32	25	{	{	PUNCT
ejpam-4554	32	26	y	y	NOUN
ejpam-4554	32	27	}	}	PUNCT
ejpam-4554	32	28	.	.	PUNCT
ejpam-4554	33	1	when	when	SCONJ
ejpam-4554	33	2	a	a	PRON
ejpam-4554	33	3	is	be	AUX
ejpam-4554	33	4	a	a	DET
ejpam-4554	33	5	nonempty	nonempty	ADJ
ejpam-4554	33	6	subset	subset	NOUN
ejpam-4554	33	7	of	of	ADP
ejpam-4554	33	8	h	h	NOUN
ejpam-4554	33	9	and	and	CCONJ
ejpam-4554	33	10	x	x	PUNCT
ejpam-4554	33	11	∈	∈	PROPN
ejpam-4554	33	12	h	h	NOUN
ejpam-4554	33	13	,	,	PUNCT
ejpam-4554	33	14	we	we	PRON
ejpam-4554	33	15	agree	agree	VERB
ejpam-4554	33	16	to	to	PART
ejpam-4554	33	17	write	write	VERB
ejpam-4554	33	18	a	a	DET
ejpam-4554	33	19	∗x	∗x	PROPN
ejpam-4554	33	20	instead	instead	ADV
ejpam-4554	33	21	of	of	ADP
ejpam-4554	33	22	a	a	DET
ejpam-4554	33	23	∗	∗	NOUN
ejpam-4554	33	24	{	{	PUNCT
ejpam-4554	33	25	x	x	NOUN
ejpam-4554	33	26	}	}	PUNCT
ejpam-4554	33	27	.	.	PUNCT
ejpam-4554	34	1	similarly	similarly	ADV
ejpam-4554	34	2	,	,	PUNCT
ejpam-4554	34	3	we	we	PRON
ejpam-4554	34	4	write	write	VERB
ejpam-4554	34	5	x	x	PUNCT
ejpam-4554	34	6	∗a	∗a	ADJ
ejpam-4554	34	7	for	for	ADP
ejpam-4554	34	8	{	{	PUNCT
ejpam-4554	34	9	x	x	NOUN
ejpam-4554	34	10	}	}	PUNCT
ejpam-4554	34	11	∗a	∗a	ADJ
ejpam-4554	34	12	.	.	PUNCT
ejpam-4554	35	1	in	in	ADP
ejpam-4554	35	2	effect	effect	NOUN
ejpam-4554	35	3	,	,	PUNCT
ejpam-4554	35	4	a	a	DET
ejpam-4554	35	5	∗x	∗x	PROPN
ejpam-4554	35	6	=	=	SYM
ejpam-4554	35	7	⋃	⋃	NOUN
ejpam-4554	35	8	a∈a	a∈a	ADJ
ejpam-4554	35	9	a	a	DET
ejpam-4554	35	10	∗	∗	NOUN
ejpam-4554	35	11	x	x	PUNCT
ejpam-4554	35	12	and	and	CCONJ
ejpam-4554	35	13	x	x	ADJ
ejpam-4554	35	14	∗a	∗a	PROPN
ejpam-4554	35	15	=	=	SYM
ejpam-4554	35	16	⋃	⋃	NOUN
ejpam-4554	35	17	a∈a	a∈a	ADJ
ejpam-4554	35	18	x	x	NOUN
ejpam-4554	35	19	∗	∗	NOUN
ejpam-4554	35	20	a.	a.	NOUN
ejpam-4554	35	21	a	a	DET
ejpam-4554	35	22	set	set	NOUN
ejpam-4554	35	23	h	h	NOUN
ejpam-4554	35	24	endowed	endow	VERB
ejpam-4554	35	25	with	with	ADP
ejpam-4554	35	26	a	a	DET
ejpam-4554	35	27	family	family	NOUN
ejpam-4554	35	28	γ	γ	NOUN
ejpam-4554	35	29	of	of	ADP
ejpam-4554	35	30	hyperoperations	hyperoperation	NOUN
ejpam-4554	35	31	is	be	AUX
ejpam-4554	35	32	called	call	VERB
ejpam-4554	35	33	a	a	DET
ejpam-4554	35	34	hyperstructure	hyperstructure	NOUN
ejpam-4554	35	35	.	.	PUNCT
ejpam-4554	36	1	if	if	SCONJ
ejpam-4554	36	2	γ	γ	PROPN
ejpam-4554	36	3	is	be	AUX
ejpam-4554	36	4	singleton	singleton	NOUN
ejpam-4554	36	5	,	,	PUNCT
ejpam-4554	36	6	that	that	ADV
ejpam-4554	36	7	is	is	ADV
ejpam-4554	36	8	,	,	PUNCT
ejpam-4554	36	9	γ	γ	X
ejpam-4554	36	10	=	=	X
ejpam-4554	36	11	{	{	PUNCT
ejpam-4554	36	12	f	f	NOUN
ejpam-4554	36	13	}	}	PUNCT
ejpam-4554	36	14	,	,	PUNCT
ejpam-4554	36	15	then	then	ADV
ejpam-4554	36	16	the	the	DET
ejpam-4554	36	17	hyperstructure	hyperstructure	NOUN
ejpam-4554	36	18	is	be	AUX
ejpam-4554	36	19	called	call	VERB
ejpam-4554	36	20	a	a	DET
ejpam-4554	36	21	hypergroupoid	hypergroupoid	NOUN
ejpam-4554	36	22	.	.	PUNCT
ejpam-4554	37	1	definition	definition	NOUN
ejpam-4554	37	2	2.1	2.1	NUM
ejpam-4554	37	3	.	.	PUNCT
ejpam-4554	38	1	[	[	X
ejpam-4554	38	2	2	2	X
ejpam-4554	38	3	]	]	PUNCT
ejpam-4554	38	4	let	let	VERB
ejpam-4554	38	5	h	h	PRON
ejpam-4554	38	6	be	be	AUX
ejpam-4554	38	7	a	a	DET
ejpam-4554	38	8	nonempty	nonempty	ADV
ejpam-4554	38	9	set	set	VERB
ejpam-4554	38	10	with	with	ADP
ejpam-4554	38	11	“	"	PUNCT
ejpam-4554	38	12	⊛	⊛	NUM
ejpam-4554	38	13	”	"	PUNCT
ejpam-4554	38	14	a	a	DET
ejpam-4554	38	15	hyperoperation	hyperoperation	NOUN
ejpam-4554	38	16	on	on	ADP
ejpam-4554	38	17	h.	h.	PROPN
ejpam-4554	38	18	then	then	ADV
ejpam-4554	38	19	(	(	PUNCT
ejpam-4554	38	20	h;⊛	h;⊛	NUM
ejpam-4554	38	21	,	,	PUNCT
ejpam-4554	38	22	0	0	NUM
ejpam-4554	38	23	)	)	PUNCT
ejpam-4554	38	24	is	be	AUX
ejpam-4554	38	25	called	call	VERB
ejpam-4554	38	26	a	a	DET
ejpam-4554	38	27	hyper	hyper	ADJ
ejpam-4554	38	28	gr	gr	NOUN
ejpam-4554	38	29	-	-	PUNCT
ejpam-4554	38	30	algebra	algebra	NOUN
ejpam-4554	38	31	if	if	SCONJ
ejpam-4554	38	32	it	it	PRON
ejpam-4554	38	33	contains	contain	VERB
ejpam-4554	38	34	a	a	DET
ejpam-4554	38	35	constant	constant	ADJ
ejpam-4554	38	36	0	0	NUM
ejpam-4554	38	37	∈	∈	PROPN
ejpam-4554	38	38	h	h	NOUN
ejpam-4554	38	39	and	and	CCONJ
ejpam-4554	38	40	for	for	ADP
ejpam-4554	38	41	all	all	DET
ejpam-4554	38	42	x	x	NOUN
ejpam-4554	38	43	,	,	PUNCT
ejpam-4554	38	44	y	y	PROPN
ejpam-4554	38	45	,	,	PUNCT
ejpam-4554	38	46	z	z	PROPN
ejpam-4554	38	47	∈	∈	PROPN
ejpam-4554	38	48	h	h	NOUN
ejpam-4554	38	49	,	,	PUNCT
ejpam-4554	38	50	the	the	DET
ejpam-4554	38	51	following	follow	VERB
ejpam-4554	38	52	conditions	condition	NOUN
ejpam-4554	38	53	are	be	AUX
ejpam-4554	38	54	satisfied	satisfied	ADJ
ejpam-4554	38	55	:	:	PUNCT
ejpam-4554	39	1	[	[	X
ejpam-4554	39	2	hgr1	hgr1	X
ejpam-4554	39	3	]	]	X
ejpam-4554	39	4	(	(	PUNCT
ejpam-4554	39	5	x⊛	x⊛	PROPN
ejpam-4554	39	6	z)⊛	z)⊛	PROPN
ejpam-4554	39	7	(	(	PUNCT
ejpam-4554	39	8	y	y	PROPN
ejpam-4554	39	9	⊛	⊛	PROPN
ejpam-4554	39	10	z	z	PROPN
ejpam-4554	39	11	)	)	PUNCT
ejpam-4554	39	12	≪	≪	PUNCT
ejpam-4554	39	13	x⊛	x⊛	PROPN
ejpam-4554	39	14	y	y	NOUN
ejpam-4554	39	15	;	;	PUNCT
ejpam-4554	39	16	[	[	X
ejpam-4554	39	17	hgr2	hgr2	NOUN
ejpam-4554	39	18	]	]	X
ejpam-4554	39	19	(	(	PUNCT
ejpam-4554	39	20	x⊛	x⊛	INTJ
ejpam-4554	40	1	y)⊛	y)⊛	NOUN
ejpam-4554	40	2	z	z	NOUN
ejpam-4554	40	3	=	=	SYM
ejpam-4554	40	4	(	(	PUNCT
ejpam-4554	40	5	x⊛	x⊛	PROPN
ejpam-4554	40	6	z)⊛	z)⊛	PROPN
ejpam-4554	40	7	y	y	NOUN
ejpam-4554	40	8	;	;	PUNCT
ejpam-4554	40	9	[	[	X
ejpam-4554	40	10	hgr3	hgr3	X
ejpam-4554	40	11	]	]	X
ejpam-4554	40	12	x	x	SYM
ejpam-4554	40	13	≪	≪	VERB
ejpam-4554	40	14	x	x	X
ejpam-4554	40	15	;	;	PUNCT
ejpam-4554	40	16	[	[	X
ejpam-4554	40	17	hgr4	hgr4	X
ejpam-4554	40	18	]	]	X
ejpam-4554	40	19	0⊛	0⊛	NUM
ejpam-4554	40	20	(	(	PUNCT
ejpam-4554	40	21	0⊛	0⊛	NUM
ejpam-4554	40	22	x	x	NOUN
ejpam-4554	40	23	)	)	PUNCT
ejpam-4554	40	24	≪	≪	PUNCT
ejpam-4554	40	25	x	x	X
ejpam-4554	40	26	,	,	PUNCT
ejpam-4554	40	27	for	for	ADP
ejpam-4554	40	28	all	all	DET
ejpam-4554	40	29	x	x	PUNCT
ejpam-4554	40	30	̸=	̸=	PROPN
ejpam-4554	40	31	0	0	NUM
ejpam-4554	40	32	;	;	PUNCT
ejpam-4554	40	33	and	and	CCONJ
ejpam-4554	40	34	[	[	X
ejpam-4554	40	35	hgr5	hgr5	X
ejpam-4554	40	36	]	]	X
ejpam-4554	40	37	(	(	PUNCT
ejpam-4554	40	38	x⊛	x⊛	PROPN
ejpam-4554	40	39	y)⊛	y)⊛	NOUN
ejpam-4554	40	40	z	z	NOUN
ejpam-4554	40	41	≪	≪	VERB
ejpam-4554	40	42	y	y	PROPN
ejpam-4554	40	43	⊛	⊛	NUM
ejpam-4554	40	44	z.	z.	PROPN
ejpam-4554	40	45	where	where	SCONJ
ejpam-4554	40	46	x	x	X
ejpam-4554	40	47	≪	≪	VERB
ejpam-4554	40	48	y	y	PROPN
ejpam-4554	40	49	if	if	SCONJ
ejpam-4554	40	50	and	and	CCONJ
ejpam-4554	40	51	only	only	ADV
ejpam-4554	40	52	if	if	SCONJ
ejpam-4554	40	53	0	0	NUM
ejpam-4554	40	54	∈	∈	PROPN
ejpam-4554	40	55	x	x	SYM
ejpam-4554	40	56	⊛	⊛	NUM
ejpam-4554	40	57	y	y	PROPN
ejpam-4554	40	58	,	,	PUNCT
ejpam-4554	40	59	and	and	CCONJ
ejpam-4554	40	60	for	for	ADP
ejpam-4554	40	61	every	every	DET
ejpam-4554	40	62	a	a	PROPN
ejpam-4554	40	63	,	,	PUNCT
ejpam-4554	40	64	b	b	PROPN
ejpam-4554	40	65	⊆	⊆	NUM
ejpam-4554	40	66	h	h	NOUN
ejpam-4554	40	67	,	,	PUNCT
ejpam-4554	40	68	a	a	DET
ejpam-4554	40	69	≪	≪	ADJ
ejpam-4554	40	70	b	b	NOUN
ejpam-4554	40	71	means	mean	VERB
ejpam-4554	40	72	that	that	SCONJ
ejpam-4554	40	73	for	for	ADP
ejpam-4554	40	74	every	every	DET
ejpam-4554	40	75	a	a	DET
ejpam-4554	40	76	∈	∈	PROPN
ejpam-4554	40	77	a	a	PRON
ejpam-4554	40	78	,	,	PUNCT
ejpam-4554	40	79	there	there	PRON
ejpam-4554	40	80	exists	exist	VERB
ejpam-4554	40	81	b	b	PROPN
ejpam-4554	40	82	∈	∈	PROPN
ejpam-4554	40	83	b	b	NOUN
ejpam-4554	40	84	such	such	ADJ
ejpam-4554	41	1	that	that	SCONJ
ejpam-4554	41	2	a	a	DET
ejpam-4554	41	3	≪	≪	ADJ
ejpam-4554	41	4	b.	b.	PROPN
ejpam-4554	41	5	example	example	NOUN
ejpam-4554	41	6	2.2	2.2	NUM
ejpam-4554	41	7	.	.	PUNCT
ejpam-4554	42	1	[	[	X
ejpam-4554	42	2	2	2	X
ejpam-4554	42	3	]	]	PUNCT
ejpam-4554	42	4	let	let	NOUN
ejpam-4554	42	5	h	h	NOUN
ejpam-4554	42	6	=	=	PRON
ejpam-4554	42	7	{	{	PUNCT
ejpam-4554	42	8	0	0	NUM
ejpam-4554	42	9	,	,	PUNCT
ejpam-4554	42	10	1	1	NUM
ejpam-4554	42	11	,	,	PUNCT
ejpam-4554	42	12	2	2	NUM
ejpam-4554	42	13	}	}	PUNCT
ejpam-4554	42	14	.	.	PUNCT
ejpam-4554	43	1	define	define	VERB
ejpam-4554	43	2	the	the	DET
ejpam-4554	43	3	operation	operation	NOUN
ejpam-4554	43	4	“	"	PUNCT
ejpam-4554	43	5	⊛	⊛	NUM
ejpam-4554	43	6	”	"	PUNCT
ejpam-4554	43	7	by	by	ADP
ejpam-4554	43	8	the	the	DET
ejpam-4554	43	9	cayley	cayley	ADJ
ejpam-4554	43	10	table	table	NOUN
ejpam-4554	43	11	shown	show	VERB
ejpam-4554	43	12	below	below	ADV
ejpam-4554	43	13	.	.	PUNCT
ejpam-4554	44	1	⊛	⊛	NUM
ejpam-4554	44	2	0	0	NUM
ejpam-4554	44	3	1	1	NUM
ejpam-4554	44	4	2	2	NUM
ejpam-4554	44	5	0	0	NUM
ejpam-4554	44	6	{	{	PUNCT
ejpam-4554	44	7	0	0	NUM
ejpam-4554	44	8	}	}	PUNCT
ejpam-4554	44	9	{	{	PUNCT
ejpam-4554	44	10	0	0	NUM
ejpam-4554	44	11	}	}	PUNCT
ejpam-4554	44	12	{	{	PUNCT
ejpam-4554	44	13	0	0	NUM
ejpam-4554	44	14	}	}	SYM
ejpam-4554	44	15	1	1	NUM
ejpam-4554	44	16	{	{	PUNCT
ejpam-4554	44	17	0	0	NUM
ejpam-4554	44	18	,	,	PUNCT
ejpam-4554	44	19	1	1	NUM
ejpam-4554	44	20	,	,	PUNCT
ejpam-4554	44	21	2	2	NUM
ejpam-4554	44	22	}	}	PUNCT
ejpam-4554	44	23	{	{	PUNCT
ejpam-4554	44	24	0	0	NUM
ejpam-4554	44	25	,	,	PUNCT
ejpam-4554	44	26	1	1	NUM
ejpam-4554	44	27	}	}	PUNCT
ejpam-4554	44	28	{	{	PUNCT
ejpam-4554	44	29	0	0	NUM
ejpam-4554	44	30	,	,	PUNCT
ejpam-4554	44	31	1	1	NUM
ejpam-4554	44	32	}	}	SYM
ejpam-4554	44	33	2	2	NUM
ejpam-4554	44	34	{	{	PUNCT
ejpam-4554	44	35	0	0	NUM
ejpam-4554	44	36	,	,	PUNCT
ejpam-4554	44	37	2	2	NUM
ejpam-4554	44	38	}	}	PUNCT
ejpam-4554	44	39	{	{	PUNCT
ejpam-4554	44	40	0	0	NUM
ejpam-4554	44	41	,	,	PUNCT
ejpam-4554	44	42	1	1	NUM
ejpam-4554	44	43	,	,	PUNCT
ejpam-4554	44	44	2	2	NUM
ejpam-4554	44	45	}	}	PUNCT
ejpam-4554	44	46	{	{	PUNCT
ejpam-4554	44	47	0	0	NUM
ejpam-4554	44	48	,	,	PUNCT
ejpam-4554	44	49	2	2	NUM
ejpam-4554	44	50	}	}	PUNCT
ejpam-4554	44	51	by	by	ADP
ejpam-4554	44	52	routine	routine	ADJ
ejpam-4554	44	53	calculations	calculation	NOUN
ejpam-4554	44	54	,	,	PUNCT
ejpam-4554	44	55	(	(	PUNCT
ejpam-4554	44	56	h;⊛	h;⊛	X
ejpam-4554	44	57	,	,	PUNCT
ejpam-4554	44	58	0	0	NUM
ejpam-4554	44	59	)	)	PUNCT
ejpam-4554	44	60	is	be	AUX
ejpam-4554	44	61	a	a	DET
ejpam-4554	44	62	hyper	hyper	ADJ
ejpam-4554	44	63	gr	gr	NOUN
ejpam-4554	44	64	-	-	NOUN
ejpam-4554	44	65	algebra	algebra	NOUN
ejpam-4554	44	66	.	.	PUNCT
ejpam-4554	45	1	definition	definition	NOUN
ejpam-4554	45	2	2.3	2.3	NUM
ejpam-4554	45	3	.	.	PUNCT
ejpam-4554	46	1	[	[	X
ejpam-4554	46	2	2	2	X
ejpam-4554	46	3	]	]	PUNCT
ejpam-4554	46	4	a	a	DET
ejpam-4554	46	5	hyper	hyper	ADJ
ejpam-4554	46	6	gr	gr	NOUN
ejpam-4554	46	7	-	-	PUNCT
ejpam-4554	46	8	algebra	algebra	NOUN
ejpam-4554	46	9	h	h	NOUN
ejpam-4554	46	10	is	be	AUX
ejpam-4554	46	11	faithful	faithful	ADJ
ejpam-4554	46	12	if	if	SCONJ
ejpam-4554	46	13	for	for	ADP
ejpam-4554	46	14	all	all	DET
ejpam-4554	46	15	a	a	DET
ejpam-4554	46	16	,	,	PUNCT
ejpam-4554	46	17	b	b	PROPN
ejpam-4554	46	18	⊆	⊆	NUM
ejpam-4554	46	19	h	h	NOUN
ejpam-4554	46	20	,	,	PUNCT
ejpam-4554	46	21	0	0	NUM
ejpam-4554	46	22	∈	∈	PROPN
ejpam-4554	46	23	a	a	DET
ejpam-4554	46	24	⊛	⊛	NUM
ejpam-4554	46	25	b	b	NOUN
ejpam-4554	46	26	implies	imply	VERB
ejpam-4554	46	27	a	a	DET
ejpam-4554	46	28	≪	≪	PROPN
ejpam-4554	46	29	b.	b.	PROPN
ejpam-4554	46	30	r.	r.	PROPN
ejpam-4554	46	31	manzano	manzano	PROPN
ejpam-4554	46	32	,	,	PUNCT
ejpam-4554	46	33	jr	jr	PROPN
ejpam-4554	46	34	.	.	PROPN
ejpam-4554	46	35	,	,	PUNCT
ejpam-4554	46	36	g.	g.	PROPN
ejpam-4554	46	37	petalcorin	petalcorin	PROPN
ejpam-4554	46	38	,	,	PUNCT
ejpam-4554	46	39	jr	jr	PROPN
ejpam-4554	46	40	.	.	PROPN
ejpam-4554	46	41	/	/	SYM
ejpam-4554	46	42	eur	eur	PROPN
ejpam-4554	46	43	.	.	PUNCT
ejpam-4554	47	1	j.	j.	PROPN
ejpam-4554	47	2	pure	pure	PROPN
ejpam-4554	47	3	appl	appl	PROPN
ejpam-4554	47	4	.	.	PROPN
ejpam-4554	47	5	math	math	PROPN
ejpam-4554	47	6	,	,	PUNCT
ejpam-4554	47	7	15	15	NUM
ejpam-4554	47	8	(	(	PUNCT
ejpam-4554	47	9	4	4	NUM
ejpam-4554	47	10	)	)	PUNCT
ejpam-4554	47	11	(	(	PUNCT
ejpam-4554	47	12	2022	2022	NUM
ejpam-4554	47	13	)	)	PUNCT
ejpam-4554	47	14	,	,	PUNCT
ejpam-4554	47	15	1854	1854	NUM
ejpam-4554	47	16	-	-	SYM
ejpam-4554	47	17	1868	1868	NUM
ejpam-4554	47	18	1856	1856	NUM
ejpam-4554	47	19	definition	definition	NOUN
ejpam-4554	47	20	2.4	2.4	NUM
ejpam-4554	47	21	.	.	PUNCT
ejpam-4554	48	1	[	[	X
ejpam-4554	48	2	2	2	X
ejpam-4554	48	3	]	]	PUNCT
ejpam-4554	48	4	let	let	VERB
ejpam-4554	48	5	h	h	PRON
ejpam-4554	48	6	be	be	AUX
ejpam-4554	48	7	a	a	DET
ejpam-4554	48	8	hyper	hyper	ADJ
ejpam-4554	48	9	gr	gr	NOUN
ejpam-4554	48	10	-	-	PUNCT
ejpam-4554	48	11	algebra	algebra	NOUN
ejpam-4554	48	12	and	and	CCONJ
ejpam-4554	48	13	s	s	AUX
ejpam-4554	48	14	be	be	AUX
ejpam-4554	48	15	a	a	DET
ejpam-4554	48	16	subset	subset	NOUN
ejpam-4554	48	17	of	of	ADP
ejpam-4554	48	18	h	h	NOUN
ejpam-4554	48	19	containing	contain	VERB
ejpam-4554	48	20	0	0	NUM
ejpam-4554	48	21	.	.	PUNCT
ejpam-4554	49	1	if	if	SCONJ
ejpam-4554	49	2	s	s	PROPN
ejpam-4554	49	3	is	be	AUX
ejpam-4554	49	4	a	a	DET
ejpam-4554	49	5	hyper	hyper	ADJ
ejpam-4554	49	6	gr	gr	NOUN
ejpam-4554	49	7	-	-	NOUN
ejpam-4554	49	8	algebra	algebra	NOUN
ejpam-4554	49	9	with	with	ADP
ejpam-4554	49	10	respect	respect	NOUN
ejpam-4554	49	11	to	to	ADP
ejpam-4554	49	12	the	the	DET
ejpam-4554	49	13	hyperoperation	hyperoperation	NOUN
ejpam-4554	49	14	⊛	⊛	ADJ
ejpam-4554	49	15	on	on	ADP
ejpam-4554	49	16	h	h	NOUN
ejpam-4554	49	17	,	,	PUNCT
ejpam-4554	49	18	then	then	ADV
ejpam-4554	49	19	we	we	PRON
ejpam-4554	49	20	say	say	VERB
ejpam-4554	49	21	that	that	PRON
ejpam-4554	49	22	s	s	VERB
ejpam-4554	49	23	is	be	AUX
ejpam-4554	49	24	a	a	DET
ejpam-4554	49	25	hyper	hyper	ADJ
ejpam-4554	49	26	subgr	subgr	NOUN
ejpam-4554	49	27	-	-	PUNCT
ejpam-4554	49	28	algebra	algebra	NOUN
ejpam-4554	49	29	of	of	ADP
ejpam-4554	49	30	h.	h.	PROPN
ejpam-4554	49	31	theorem	theorem	VERB
ejpam-4554	49	32	2.5	2.5	NUM
ejpam-4554	49	33	.	.	PUNCT
ejpam-4554	50	1	[	[	X
ejpam-4554	50	2	2	2	NUM
ejpam-4554	50	3	]	]	PUNCT
ejpam-4554	50	4	(	(	PUNCT
ejpam-4554	50	5	hyper	hyper	ADJ
ejpam-4554	50	6	subgr	subgr	NOUN
ejpam-4554	50	7	-	-	PUNCT
ejpam-4554	50	8	algebra	algebra	NOUN
ejpam-4554	50	9	criterion	criterion	NOUN
ejpam-4554	50	10	)	)	PUNCT
ejpam-4554	50	11	let	let	VERB
ejpam-4554	50	12	h	h	NOUN
ejpam-4554	50	13	be	be	AUX
ejpam-4554	50	14	a	a	DET
ejpam-4554	50	15	hyper	hyper	ADJ
ejpam-4554	50	16	gr	gr	NOUN
ejpam-4554	50	17	-	-	PUNCT
ejpam-4554	50	18	algebra	algebra	NOUN
ejpam-4554	50	19	and	and	CCONJ
ejpam-4554	50	20	s	s	AUX
ejpam-4554	50	21	be	be	AUX
ejpam-4554	50	22	a	a	DET
ejpam-4554	50	23	nonempty	nonempty	ADJ
ejpam-4554	50	24	subset	subset	NOUN
ejpam-4554	50	25	of	of	ADP
ejpam-4554	50	26	h.	h.	PROPN
ejpam-4554	51	1	then	then	ADV
ejpam-4554	51	2	s	s	VERB
ejpam-4554	51	3	is	be	AUX
ejpam-4554	51	4	a	a	DET
ejpam-4554	51	5	hyper	hyper	ADJ
ejpam-4554	51	6	subgr	subgr	NOUN
ejpam-4554	51	7	-	-	PUNCT
ejpam-4554	51	8	algebra	algebra	NOUN
ejpam-4554	51	9	of	of	ADP
ejpam-4554	51	10	h	h	NOUN
ejpam-4554	51	11	if	if	SCONJ
ejpam-4554	52	1	and	and	CCONJ
ejpam-4554	52	2	only	only	ADV
ejpam-4554	52	3	if	if	SCONJ
ejpam-4554	52	4	x⊛	x⊛	PROPN
ejpam-4554	52	5	y	y	PROPN
ejpam-4554	52	6	⊆	⊆	NUM
ejpam-4554	52	7	s	s	NOUN
ejpam-4554	52	8	,	,	PUNCT
ejpam-4554	52	9	for	for	ADP
ejpam-4554	52	10	all	all	DET
ejpam-4554	52	11	x	x	NOUN
ejpam-4554	52	12	,	,	PUNCT
ejpam-4554	52	13	y	y	PROPN
ejpam-4554	52	14	∈	∈	PROPN
ejpam-4554	52	15	s.	s.	PROPN
ejpam-4554	52	16	definition	definition	NOUN
ejpam-4554	52	17	2.6	2.6	NUM
ejpam-4554	52	18	.	.	PUNCT
ejpam-4554	53	1	[	[	X
ejpam-4554	53	2	4	4	X
ejpam-4554	53	3	]	]	PUNCT
ejpam-4554	53	4	let	let	AUX
ejpam-4554	53	5	h	h	NOUN
ejpam-4554	53	6	be	be	AUX
ejpam-4554	53	7	a	a	DET
ejpam-4554	53	8	nonempty	nonempty	ADV
ejpam-4554	53	9	set	set	VERB
ejpam-4554	53	10	with	with	ADP
ejpam-4554	53	11	“	"	PUNCT
ejpam-4554	53	12	⊛	⊛	NUM
ejpam-4554	53	13	”	"	PUNCT
ejpam-4554	53	14	and	and	CCONJ
ejpam-4554	53	15	“	"	PUNCT
ejpam-4554	53	16	◦	◦	NOUN
ejpam-4554	53	17	”	"	PUNCT
ejpam-4554	53	18	be	be	AUX
ejpam-4554	53	19	the	the	DET
ejpam-4554	53	20	two	two	NUM
ejpam-4554	53	21	hyperoperations	hyperoperation	NOUN
ejpam-4554	53	22	on	on	ADP
ejpam-4554	53	23	h.	h.	PROPN
ejpam-4554	53	24	then	then	ADV
ejpam-4554	53	25	(	(	PUNCT
ejpam-4554	53	26	h;⊛,⊙	h;⊛,⊙	PROPN
ejpam-4554	53	27	,	,	PUNCT
ejpam-4554	53	28	0	0	NUM
ejpam-4554	53	29	)	)	PUNCT
ejpam-4554	53	30	is	be	AUX
ejpam-4554	53	31	called	call	VERB
ejpam-4554	53	32	a	a	DET
ejpam-4554	53	33	pseudo	pseudo	NOUN
ejpam-4554	53	34	hyper	hyper	ADJ
ejpam-4554	53	35	gr	gr	NOUN
ejpam-4554	53	36	-	-	PUNCT
ejpam-4554	53	37	algebra	algebra	NOUN
ejpam-4554	53	38	,	,	PUNCT
ejpam-4554	53	39	if	if	SCONJ
ejpam-4554	53	40	it	it	PRON
ejpam-4554	53	41	contains	contain	VERB
ejpam-4554	53	42	a	a	DET
ejpam-4554	53	43	constant	constant	ADJ
ejpam-4554	53	44	0	0	NUM
ejpam-4554	53	45	∈	∈	PROPN
ejpam-4554	53	46	h	h	NOUN
ejpam-4554	53	47	and	and	CCONJ
ejpam-4554	53	48	for	for	ADP
ejpam-4554	53	49	all	all	DET
ejpam-4554	53	50	x	x	NOUN
ejpam-4554	53	51	,	,	PUNCT
ejpam-4554	53	52	y	y	PROPN
ejpam-4554	53	53	,	,	PUNCT
ejpam-4554	53	54	z	z	PROPN
ejpam-4554	53	55	∈	∈	PROPN
ejpam-4554	53	56	h	h	NOUN
ejpam-4554	53	57	,	,	PUNCT
ejpam-4554	53	58	the	the	DET
ejpam-4554	53	59	following	follow	VERB
ejpam-4554	53	60	conditions	condition	NOUN
ejpam-4554	53	61	are	be	AUX
ejpam-4554	53	62	satisfied	satisfied	ADJ
ejpam-4554	53	63	:	:	PUNCT
ejpam-4554	54	1	[	[	X
ejpam-4554	54	2	phgr1	phgr1	X
ejpam-4554	54	3	]	]	X
ejpam-4554	54	4	(	(	PUNCT
ejpam-4554	54	5	x⊙	x⊙	PROPN
ejpam-4554	54	6	z)⊙	z)⊙	NOUN
ejpam-4554	54	7	(	(	PUNCT
ejpam-4554	54	8	y	y	PROPN
ejpam-4554	54	9	⊙	⊙	PROPN
ejpam-4554	54	10	z	z	PROPN
ejpam-4554	54	11	)	)	PUNCT
ejpam-4554	54	12	≪	≪	PUNCT
ejpam-4554	54	13	x⊙	x⊙	PROPN
ejpam-4554	54	14	y	y	PROPN
ejpam-4554	54	15	and	and	CCONJ
ejpam-4554	54	16	(	(	PUNCT
ejpam-4554	54	17	x⊛	x⊛	PROPN
ejpam-4554	54	18	z)⊛	z)⊛	PROPN
ejpam-4554	54	19	(	(	PUNCT
ejpam-4554	54	20	y	y	PROPN
ejpam-4554	54	21	⊛	⊛	PROPN
ejpam-4554	54	22	z	z	PROPN
ejpam-4554	54	23	)	)	PUNCT
ejpam-4554	54	24	≪	≪	PUNCT
ejpam-4554	54	25	x⊛	x⊛	PROPN
ejpam-4554	54	26	y	y	NOUN
ejpam-4554	54	27	;	;	PUNCT
ejpam-4554	54	28	[	[	X
ejpam-4554	54	29	phgr2	phgr2	NOUN
ejpam-4554	54	30	]	]	X
ejpam-4554	54	31	(	(	PUNCT
ejpam-4554	54	32	x⊙	x⊙	NOUN
ejpam-4554	54	33	y)⊛	y)⊛	NOUN
ejpam-4554	54	34	z	z	NOUN
ejpam-4554	54	35	=	=	SYM
ejpam-4554	54	36	(	(	PUNCT
ejpam-4554	54	37	x⊛	x⊛	ADP
ejpam-4554	54	38	z)⊙	z)⊙	NOUN
ejpam-4554	54	39	y	y	PROPN
ejpam-4554	54	40	;	;	PUNCT
ejpam-4554	54	41	[	[	X
ejpam-4554	54	42	phgr3	phgr3	X
ejpam-4554	54	43	]	]	PUNCT
ejpam-4554	54	44	0	0	PUNCT
ejpam-4554	55	1	∈	∈	NOUN
ejpam-4554	55	2	x⊛	x⊛	PROPN
ejpam-4554	56	1	x	x	X
ejpam-4554	56	2	and	and	CCONJ
ejpam-4554	56	3	0	0	NUM
ejpam-4554	56	4	∈	∈	PROPN
ejpam-4554	56	5	x⊙	x⊙	PROPN
ejpam-4554	56	6	x	x	SYM
ejpam-4554	56	7	;	;	PUNCT
ejpam-4554	56	8	[	[	X
ejpam-4554	56	9	phgr4	phgr4	X
ejpam-4554	56	10	]	]	X
ejpam-4554	56	11	0⊙	0⊙	NOUN
ejpam-4554	56	12	(	(	PUNCT
ejpam-4554	56	13	0⊛	0⊛	NUM
ejpam-4554	56	14	x	x	NOUN
ejpam-4554	56	15	)	)	PUNCT
ejpam-4554	56	16	≪	≪	PUNCT
ejpam-4554	56	17	x	x	X
ejpam-4554	56	18	,	,	PUNCT
ejpam-4554	56	19	for	for	ADP
ejpam-4554	56	20	all	all	DET
ejpam-4554	56	21	x	x	PUNCT
ejpam-4554	56	22	̸=	̸=	PROPN
ejpam-4554	56	23	0	0	NUM
ejpam-4554	56	24	;	;	PUNCT
ejpam-4554	56	25	and	and	CCONJ
ejpam-4554	57	1	[	[	X
ejpam-4554	57	2	phgr5	phgr5	X
ejpam-4554	57	3	]	]	X
ejpam-4554	57	4	(	(	PUNCT
ejpam-4554	57	5	x⊛	x⊛	INTJ
ejpam-4554	57	6	y)⊛	y)⊛	NOUN
ejpam-4554	57	7	z	z	NOUN
ejpam-4554	57	8	≪	≪	PUNCT
ejpam-4554	57	9	y	y	PROPN
ejpam-4554	57	10	⊙	⊙	PROPN
ejpam-4554	57	11	z.	z.	PROPN
ejpam-4554	58	1	where	where	SCONJ
ejpam-4554	58	2	x	x	X
ejpam-4554	58	3	≪	≪	VERB
ejpam-4554	58	4	y	y	PROPN
ejpam-4554	58	5	if	if	SCONJ
ejpam-4554	58	6	and	and	CCONJ
ejpam-4554	58	7	only	only	ADV
ejpam-4554	58	8	if	if	SCONJ
ejpam-4554	58	9	0	0	NUM
ejpam-4554	58	10	∈	∈	PROPN
ejpam-4554	58	11	x	x	X
ejpam-4554	58	12	⊙	⊙	PROPN
ejpam-4554	58	13	y	y	PROPN
ejpam-4554	58	14	and	and	CCONJ
ejpam-4554	58	15	0	0	NUM
ejpam-4554	58	16	∈	∈	PROPN
ejpam-4554	58	17	x	x	SYM
ejpam-4554	58	18	⊛	⊛	NUM
ejpam-4554	58	19	y	y	PROPN
ejpam-4554	58	20	,	,	PUNCT
ejpam-4554	58	21	and	and	CCONJ
ejpam-4554	58	22	for	for	ADP
ejpam-4554	58	23	every	every	DET
ejpam-4554	58	24	a	a	PROPN
ejpam-4554	58	25	,	,	PUNCT
ejpam-4554	58	26	b	b	PROPN
ejpam-4554	58	27	⊆	⊆	NUM
ejpam-4554	58	28	h	h	NOUN
ejpam-4554	58	29	,	,	PUNCT
ejpam-4554	58	30	a	a	DET
ejpam-4554	58	31	≪	≪	ADJ
ejpam-4554	58	32	b	b	NOUN
ejpam-4554	58	33	means	mean	VERB
ejpam-4554	58	34	that	that	SCONJ
ejpam-4554	58	35	for	for	ADP
ejpam-4554	58	36	every	every	DET
ejpam-4554	58	37	a	a	DET
ejpam-4554	58	38	∈	∈	PROPN
ejpam-4554	58	39	a	a	PRON
ejpam-4554	58	40	,	,	PUNCT
ejpam-4554	58	41	there	there	PRON
ejpam-4554	58	42	exists	exist	VERB
ejpam-4554	58	43	b	b	PROPN
ejpam-4554	58	44	∈	∈	PROPN
ejpam-4554	58	45	b	b	NOUN
ejpam-4554	58	46	such	such	ADJ
ejpam-4554	59	1	that	that	SCONJ
ejpam-4554	59	2	a	a	DET
ejpam-4554	59	3	≪	≪	ADJ
ejpam-4554	59	4	b.	b.	NOUN
ejpam-4554	59	5	example	example	NOUN
ejpam-4554	59	6	2.7	2.7	NUM
ejpam-4554	60	1	.	.	PUNCT
ejpam-4554	61	1	[	[	X
ejpam-4554	61	2	4	4	X
ejpam-4554	61	3	]	]	PUNCT
ejpam-4554	61	4	let	let	NOUN
ejpam-4554	61	5	h	h	NOUN
ejpam-4554	61	6	=	=	PRON
ejpam-4554	61	7	{	{	PUNCT
ejpam-4554	61	8	0	0	NUM
ejpam-4554	61	9	,	,	PUNCT
ejpam-4554	61	10	1	1	NUM
ejpam-4554	61	11	,	,	PUNCT
ejpam-4554	61	12	2	2	NUM
ejpam-4554	61	13	,	,	PUNCT
ejpam-4554	61	14	3	3	NUM
ejpam-4554	61	15	}	}	PUNCT
ejpam-4554	61	16	and	and	CCONJ
ejpam-4554	61	17	consider	consider	VERB
ejpam-4554	61	18	the	the	DET
ejpam-4554	61	19	following	follow	VERB
ejpam-4554	61	20	cayley	cayley	ADJ
ejpam-4554	61	21	tables	table	NOUN
ejpam-4554	61	22	below	below	ADV
ejpam-4554	61	23	.	.	PUNCT
ejpam-4554	62	1	⊛	⊛	NUM
ejpam-4554	63	1	0	0	NUM
ejpam-4554	63	2	1	1	NUM
ejpam-4554	63	3	2	2	NUM
ejpam-4554	63	4	3	3	NUM
ejpam-4554	63	5	0	0	NUM
ejpam-4554	63	6	{	{	PUNCT
ejpam-4554	63	7	0	0	NUM
ejpam-4554	63	8	,	,	PUNCT
ejpam-4554	63	9	1	1	NUM
ejpam-4554	63	10	}	}	PUNCT
ejpam-4554	63	11	{	{	PUNCT
ejpam-4554	63	12	0	0	NUM
ejpam-4554	63	13	,	,	PUNCT
ejpam-4554	63	14	1	1	NUM
ejpam-4554	63	15	}	}	PUNCT
ejpam-4554	63	16	{	{	PUNCT
ejpam-4554	63	17	0	0	NUM
ejpam-4554	63	18	,	,	PUNCT
ejpam-4554	63	19	1	1	NUM
ejpam-4554	63	20	}	}	PUNCT
ejpam-4554	63	21	{	{	PUNCT
ejpam-4554	63	22	0	0	NUM
ejpam-4554	63	23	,	,	PUNCT
ejpam-4554	63	24	1	1	NUM
ejpam-4554	63	25	}	}	SYM
ejpam-4554	63	26	1	1	NUM
ejpam-4554	63	27	{	{	PUNCT
ejpam-4554	63	28	0	0	NUM
ejpam-4554	63	29	,	,	PUNCT
ejpam-4554	63	30	1	1	NUM
ejpam-4554	63	31	}	}	PUNCT
ejpam-4554	63	32	{	{	PUNCT
ejpam-4554	63	33	0	0	NUM
ejpam-4554	63	34	,	,	PUNCT
ejpam-4554	63	35	1	1	NUM
ejpam-4554	63	36	}	}	PUNCT
ejpam-4554	63	37	{	{	PUNCT
ejpam-4554	63	38	0	0	NUM
ejpam-4554	63	39	,	,	PUNCT
ejpam-4554	63	40	1	1	NUM
ejpam-4554	63	41	}	}	PUNCT
ejpam-4554	63	42	{	{	PUNCT
ejpam-4554	63	43	0	0	NUM
ejpam-4554	63	44	,	,	PUNCT
ejpam-4554	63	45	1	1	NUM
ejpam-4554	63	46	}	}	SYM
ejpam-4554	63	47	2	2	NUM
ejpam-4554	63	48	{	{	PUNCT
ejpam-4554	63	49	0	0	NUM
ejpam-4554	63	50	,	,	PUNCT
ejpam-4554	63	51	2	2	NUM
ejpam-4554	63	52	}	}	PUNCT
ejpam-4554	63	53	{	{	PUNCT
ejpam-4554	63	54	0	0	NUM
ejpam-4554	63	55	,	,	PUNCT
ejpam-4554	63	56	1	1	NUM
ejpam-4554	63	57	,	,	PUNCT
ejpam-4554	63	58	2	2	NUM
ejpam-4554	63	59	}	}	PUNCT
ejpam-4554	63	60	{	{	PUNCT
ejpam-4554	63	61	0	0	NUM
ejpam-4554	63	62	,	,	PUNCT
ejpam-4554	63	63	2	2	NUM
ejpam-4554	63	64	}	}	PUNCT
ejpam-4554	63	65	{	{	PUNCT
ejpam-4554	63	66	0	0	NUM
ejpam-4554	63	67	,	,	PUNCT
ejpam-4554	63	68	1	1	NUM
ejpam-4554	63	69	,	,	PUNCT
ejpam-4554	63	70	2	2	NUM
ejpam-4554	63	71	}	}	SYM
ejpam-4554	63	72	3	3	NUM
ejpam-4554	63	73	{	{	PUNCT
ejpam-4554	63	74	0	0	NUM
ejpam-4554	63	75	,	,	PUNCT
ejpam-4554	63	76	1	1	NUM
ejpam-4554	63	77	,	,	PUNCT
ejpam-4554	63	78	2	2	NUM
ejpam-4554	63	79	}	}	PUNCT
ejpam-4554	63	80	{	{	PUNCT
ejpam-4554	63	81	0	0	NUM
ejpam-4554	63	82	,	,	PUNCT
ejpam-4554	63	83	3	3	NUM
ejpam-4554	63	84	}	}	PUNCT
ejpam-4554	63	85	{	{	PUNCT
ejpam-4554	63	86	0	0	NUM
ejpam-4554	63	87	,	,	PUNCT
ejpam-4554	63	88	1	1	NUM
ejpam-4554	63	89	,	,	PUNCT
ejpam-4554	63	90	3	3	NUM
ejpam-4554	63	91	}	}	PUNCT
ejpam-4554	63	92	{	{	PUNCT
ejpam-4554	63	93	0	0	NUM
ejpam-4554	63	94	,	,	PUNCT
ejpam-4554	63	95	3	3	NUM
ejpam-4554	63	96	}	}	PUNCT
ejpam-4554	63	97	⊙	⊙	X
ejpam-4554	63	98	0	0	NUM
ejpam-4554	64	1	1	1	NUM
ejpam-4554	64	2	2	2	NUM
ejpam-4554	64	3	3	3	NUM
ejpam-4554	64	4	0	0	NUM
ejpam-4554	64	5	{	{	PUNCT
ejpam-4554	64	6	0	0	NUM
ejpam-4554	64	7	,	,	PUNCT
ejpam-4554	64	8	1	1	NUM
ejpam-4554	64	9	}	}	PUNCT
ejpam-4554	64	10	{	{	PUNCT
ejpam-4554	64	11	0	0	NUM
ejpam-4554	64	12	,	,	PUNCT
ejpam-4554	64	13	1	1	NUM
ejpam-4554	64	14	}	}	PUNCT
ejpam-4554	64	15	{	{	PUNCT
ejpam-4554	64	16	0	0	NUM
ejpam-4554	64	17	,	,	PUNCT
ejpam-4554	64	18	1	1	NUM
ejpam-4554	64	19	}	}	PUNCT
ejpam-4554	64	20	{	{	PUNCT
ejpam-4554	64	21	0	0	NUM
ejpam-4554	64	22	,	,	PUNCT
ejpam-4554	64	23	1	1	NUM
ejpam-4554	64	24	}	}	SYM
ejpam-4554	64	25	1	1	NUM
ejpam-4554	64	26	{	{	PUNCT
ejpam-4554	64	27	1	1	NUM
ejpam-4554	64	28	}	}	PUNCT
ejpam-4554	64	29	{	{	PUNCT
ejpam-4554	64	30	0	0	NUM
ejpam-4554	64	31	,	,	PUNCT
ejpam-4554	64	32	1	1	NUM
ejpam-4554	64	33	}	}	PUNCT
ejpam-4554	64	34	{	{	PUNCT
ejpam-4554	64	35	0	0	NUM
ejpam-4554	64	36	,	,	PUNCT
ejpam-4554	64	37	1	1	NUM
ejpam-4554	64	38	}	}	PUNCT
ejpam-4554	64	39	{	{	PUNCT
ejpam-4554	64	40	0	0	NUM
ejpam-4554	64	41	,	,	PUNCT
ejpam-4554	64	42	1	1	NUM
ejpam-4554	64	43	}	}	SYM
ejpam-4554	64	44	2	2	NUM
ejpam-4554	64	45	{	{	PUNCT
ejpam-4554	64	46	0	0	NUM
ejpam-4554	64	47	,	,	PUNCT
ejpam-4554	64	48	2	2	NUM
ejpam-4554	64	49	}	}	PUNCT
ejpam-4554	64	50	{	{	PUNCT
ejpam-4554	64	51	0	0	NUM
ejpam-4554	64	52	,	,	PUNCT
ejpam-4554	64	53	2	2	NUM
ejpam-4554	64	54	}	}	PUNCT
ejpam-4554	64	55	{	{	PUNCT
ejpam-4554	64	56	0	0	NUM
ejpam-4554	64	57	,	,	PUNCT
ejpam-4554	64	58	1	1	NUM
ejpam-4554	64	59	,	,	PUNCT
ejpam-4554	64	60	2	2	NUM
ejpam-4554	64	61	}	}	PUNCT
ejpam-4554	64	62	{	{	PUNCT
ejpam-4554	64	63	0	0	NUM
ejpam-4554	64	64	,	,	PUNCT
ejpam-4554	64	65	1	1	NUM
ejpam-4554	64	66	,	,	PUNCT
ejpam-4554	64	67	2	2	NUM
ejpam-4554	64	68	}	}	SYM
ejpam-4554	64	69	3	3	NUM
ejpam-4554	64	70	{	{	PUNCT
ejpam-4554	64	71	0	0	NUM
ejpam-4554	64	72	,	,	PUNCT
ejpam-4554	64	73	3	3	NUM
ejpam-4554	64	74	}	}	PUNCT
ejpam-4554	64	75	{	{	PUNCT
ejpam-4554	64	76	0	0	NUM
ejpam-4554	64	77	,	,	PUNCT
ejpam-4554	64	78	1	1	NUM
ejpam-4554	64	79	,	,	PUNCT
ejpam-4554	64	80	3	3	NUM
ejpam-4554	64	81	}	}	PUNCT
ejpam-4554	64	82	{	{	PUNCT
ejpam-4554	64	83	0	0	NUM
ejpam-4554	64	84	,	,	PUNCT
ejpam-4554	64	85	1	1	NUM
ejpam-4554	64	86	,	,	PUNCT
ejpam-4554	64	87	3	3	NUM
ejpam-4554	64	88	}	}	PUNCT
ejpam-4554	64	89	{	{	PUNCT
ejpam-4554	64	90	0	0	NUM
ejpam-4554	64	91	,	,	PUNCT
ejpam-4554	64	92	1	1	NUM
ejpam-4554	64	93	,	,	PUNCT
ejpam-4554	64	94	3	3	NUM
ejpam-4554	64	95	}	}	PUNCT
ejpam-4554	64	96	by	by	ADP
ejpam-4554	64	97	routine	routine	ADJ
ejpam-4554	64	98	calculations	calculation	NOUN
ejpam-4554	64	99	,	,	PUNCT
ejpam-4554	64	100	we	we	PRON
ejpam-4554	64	101	see	see	VERB
ejpam-4554	64	102	that	that	SCONJ
ejpam-4554	64	103	(	(	PUNCT
ejpam-4554	64	104	h;⊛,⊙	h;⊛,⊙	PROPN
ejpam-4554	64	105	,	,	PUNCT
ejpam-4554	64	106	0	0	NUM
ejpam-4554	64	107	)	)	PUNCT
ejpam-4554	64	108	is	be	AUX
ejpam-4554	64	109	a	a	DET
ejpam-4554	64	110	pseudo	pseudo	NOUN
ejpam-4554	64	111	hyper	hyper	ADJ
ejpam-4554	64	112	gr	gr	NOUN
ejpam-4554	64	113	-	-	PUNCT
ejpam-4554	64	114	algebra	algebra	NOUN
ejpam-4554	64	115	.	.	PUNCT
ejpam-4554	65	1	remark	remark	NOUN
ejpam-4554	65	2	2.8	2.8	NUM
ejpam-4554	65	3	.	.	PUNCT
ejpam-4554	66	1	[	[	X
ejpam-4554	66	2	4	4	X
ejpam-4554	66	3	]	]	PUNCT
ejpam-4554	66	4	in	in	ADP
ejpam-4554	66	5	a	a	DET
ejpam-4554	66	6	pseudo	pseudo	NOUN
ejpam-4554	66	7	hyper	hyper	ADJ
ejpam-4554	66	8	gr	gr	NOUN
ejpam-4554	66	9	-	-	PUNCT
ejpam-4554	66	10	algebra	algebra	NOUN
ejpam-4554	66	11	h	h	NOUN
ejpam-4554	66	12	,	,	PUNCT
ejpam-4554	66	13	the	the	DET
ejpam-4554	66	14	following	follow	VERB
ejpam-4554	66	15	are	be	AUX
ejpam-4554	66	16	evident	evident	ADJ
ejpam-4554	66	17	:	:	PUNCT
ejpam-4554	66	18	(	(	PUNCT
ejpam-4554	66	19	i	i	NOUN
ejpam-4554	66	20	)	)	PUNCT
ejpam-4554	66	21	x	x	PUNCT
ejpam-4554	66	22	≪	≪	PUNCT
ejpam-4554	66	23	x	x	X
ejpam-4554	66	24	(	(	PUNCT
ejpam-4554	66	25	ii	ii	NOUN
ejpam-4554	66	26	)	)	PUNCT
ejpam-4554	66	27	(	(	PUNCT
ejpam-4554	66	28	x⊙	x⊙	PROPN
ejpam-4554	66	29	y)⊛	y)⊛	PROPN
ejpam-4554	66	30	z	z	NOUN
ejpam-4554	66	31	≪	≪	NOUN
ejpam-4554	66	32	(	(	PUNCT
ejpam-4554	66	33	x⊛	x⊛	ADP
ejpam-4554	66	34	z)⊙	z)⊙	PROPN
ejpam-4554	66	35	y	y	PROPN
ejpam-4554	66	36	r.	r.	PROPN
ejpam-4554	66	37	manzano	manzano	PROPN
ejpam-4554	66	38	,	,	PUNCT
ejpam-4554	66	39	jr	jr	PROPN
ejpam-4554	66	40	.	.	PROPN
ejpam-4554	66	41	,	,	PUNCT
ejpam-4554	66	42	g.	g.	PROPN
ejpam-4554	66	43	petalcorin	petalcorin	PROPN
ejpam-4554	66	44	,	,	PUNCT
ejpam-4554	66	45	jr	jr	PROPN
ejpam-4554	66	46	.	.	PROPN
ejpam-4554	66	47	/	/	SYM
ejpam-4554	66	48	eur	eur	PROPN
ejpam-4554	66	49	.	.	PUNCT
ejpam-4554	67	1	j.	j.	PROPN
ejpam-4554	67	2	pure	pure	PROPN
ejpam-4554	67	3	appl	appl	PROPN
ejpam-4554	67	4	.	.	PROPN
ejpam-4554	67	5	math	math	PROPN
ejpam-4554	67	6	,	,	PUNCT
ejpam-4554	67	7	15	15	NUM
ejpam-4554	67	8	(	(	PUNCT
ejpam-4554	67	9	4	4	NUM
ejpam-4554	67	10	)	)	PUNCT
ejpam-4554	67	11	(	(	PUNCT
ejpam-4554	67	12	2022	2022	NUM
ejpam-4554	67	13	)	)	PUNCT
ejpam-4554	67	14	,	,	PUNCT
ejpam-4554	67	15	1854	1854	NUM
ejpam-4554	67	16	-	-	SYM
ejpam-4554	67	17	1868	1868	NUM
ejpam-4554	67	18	1857	1857	NUM
ejpam-4554	67	19	(	(	PUNCT
ejpam-4554	67	20	iii	iii	NOUN
ejpam-4554	67	21	)	)	PUNCT
ejpam-4554	67	22	(	(	PUNCT
ejpam-4554	67	23	a⊙b)⊛	a⊙b)⊛	NOUN
ejpam-4554	67	24	c	c	NOUN
ejpam-4554	67	25	=	=	PUNCT
ejpam-4554	67	26	(	(	PUNCT
ejpam-4554	67	27	a⊛	a⊛	NOUN
ejpam-4554	67	28	c)⊙b	c)⊙b	PROPN
ejpam-4554	67	29	(	(	PUNCT
ejpam-4554	67	30	iv	iv	X
ejpam-4554	67	31	)	)	PUNCT
ejpam-4554	67	32	a	a	DET
ejpam-4554	67	33	⊆	⊆	NUM
ejpam-4554	67	34	b	b	NOUN
ejpam-4554	67	35	implies	imply	VERB
ejpam-4554	67	36	a	a	DET
ejpam-4554	67	37	≪	≪	ADJ
ejpam-4554	67	38	b.	b.	PROPN
ejpam-4554	67	39	example	example	NOUN
ejpam-4554	67	40	2.9	2.9	NUM
ejpam-4554	67	41	.	.	PUNCT
ejpam-4554	68	1	[	[	X
ejpam-4554	68	2	4	4	X
ejpam-4554	68	3	]	]	PUNCT
ejpam-4554	68	4	let	let	NOUN
ejpam-4554	68	5	h	h	NOUN
ejpam-4554	68	6	=	=	NOUN
ejpam-4554	68	7	n	n	CCONJ
ejpam-4554	68	8	∪	∪	X
ejpam-4554	68	9	{	{	PUNCT
ejpam-4554	68	10	0	0	NUM
ejpam-4554	68	11	}	}	PUNCT
ejpam-4554	68	12	be	be	AUX
ejpam-4554	68	13	the	the	DET
ejpam-4554	68	14	set	set	NOUN
ejpam-4554	68	15	of	of	ADP
ejpam-4554	68	16	all	all	DET
ejpam-4554	68	17	nonnegative	nonnegative	ADJ
ejpam-4554	68	18	integers	integer	NOUN
ejpam-4554	68	19	and	and	CCONJ
ejpam-4554	68	20	let	let	VERB
ejpam-4554	68	21	the	the	DET
ejpam-4554	68	22	hyperoperations	hyperoperation	NOUN
ejpam-4554	68	23	“	"	PUNCT
ejpam-4554	68	24	⊛	⊛	NUM
ejpam-4554	68	25	”	"	PUNCT
ejpam-4554	68	26	and	and	CCONJ
ejpam-4554	68	27	“	"	PUNCT
ejpam-4554	68	28	⊙	⊙	PROPN
ejpam-4554	68	29	”	"	PUNCT
ejpam-4554	68	30	be	be	AUX
ejpam-4554	68	31	defined	define	VERB
ejpam-4554	68	32	on	on	ADP
ejpam-4554	68	33	h	h	NOUN
ejpam-4554	68	34	as	as	SCONJ
ejpam-4554	68	35	follows	follow	VERB
ejpam-4554	68	36	:	:	PUNCT
ejpam-4554	68	37	x⊛	x⊛	PROPN
ejpam-4554	68	38	y	y	NOUN
ejpam-4554	68	39	=	=	PUNCT
ejpam-4554	68	40	{	{	PUNCT
ejpam-4554	68	41	0	0	NUM
ejpam-4554	68	42	,	,	PUNCT
ejpam-4554	68	43	x	x	NOUN
ejpam-4554	68	44	}	}	PUNCT
ejpam-4554	68	45	and	and	CCONJ
ejpam-4554	68	46	x⊙	x⊙	PROPN
ejpam-4554	68	47	y	y	PROPN
ejpam-4554	68	48	=	=	PUNCT
ejpam-4554	68	49	{	{	PUNCT
ejpam-4554	68	50	0	0	NUM
ejpam-4554	68	51	,	,	PUNCT
ejpam-4554	68	52	x	x	NOUN
ejpam-4554	68	53	,	,	PUNCT
ejpam-4554	68	54	y	y	PROPN
ejpam-4554	68	55	}	}	PUNCT
ejpam-4554	68	56	.	.	PUNCT
ejpam-4554	69	1	then	then	ADV
ejpam-4554	69	2	h	h	PROPN
ejpam-4554	69	3	is	be	AUX
ejpam-4554	69	4	a	a	DET
ejpam-4554	69	5	pseudo	pseudo	NOUN
ejpam-4554	69	6	hyper	hyper	ADJ
ejpam-4554	69	7	gr	gr	NOUN
ejpam-4554	69	8	-	-	PUNCT
ejpam-4554	69	9	algebra	algebra	NOUN
ejpam-4554	69	10	.	.	PUNCT
ejpam-4554	70	1	remark	remark	NOUN
ejpam-4554	70	2	2.10	2.10	NUM
ejpam-4554	70	3	.	.	PUNCT
ejpam-4554	71	1	[	[	X
ejpam-4554	71	2	4	4	X
ejpam-4554	71	3	]	]	PUNCT
ejpam-4554	71	4	note	note	NOUN
ejpam-4554	71	5	that	that	SCONJ
ejpam-4554	71	6	if	if	SCONJ
ejpam-4554	71	7	the	the	DET
ejpam-4554	71	8	two	two	NUM
ejpam-4554	71	9	hyperoperations	hyperoperation	NOUN
ejpam-4554	71	10	are	be	AUX
ejpam-4554	71	11	equal	equal	ADJ
ejpam-4554	71	12	,	,	PUNCT
ejpam-4554	71	13	that	that	ADV
ejpam-4554	71	14	is	is	ADV
ejpam-4554	71	15	,	,	PUNCT
ejpam-4554	71	16	⊛	⊛	ADJ
ejpam-4554	71	17	=	=	SYM
ejpam-4554	71	18	⊙	⊙	NOUN
ejpam-4554	71	19	,	,	PUNCT
ejpam-4554	71	20	then	then	ADV
ejpam-4554	71	21	a	a	DET
ejpam-4554	71	22	pseudo	pseudo	NOUN
ejpam-4554	71	23	hyper	hyper	ADJ
ejpam-4554	71	24	-	-	ADJ
ejpam-4554	71	25	gr	gr	ADJ
ejpam-4554	71	26	algebra	algebra	NOUN
ejpam-4554	71	27	h	h	NOUN
ejpam-4554	71	28	becomes	become	VERB
ejpam-4554	71	29	a	a	DET
ejpam-4554	71	30	hyper	hyper	ADJ
ejpam-4554	71	31	gr	gr	NOUN
ejpam-4554	71	32	-	-	NOUN
ejpam-4554	71	33	algebra	algebra	NOUN
ejpam-4554	71	34	.	.	PUNCT
ejpam-4554	72	1	definition	definition	NOUN
ejpam-4554	72	2	2.11	2.11	NUM
ejpam-4554	72	3	.	.	PUNCT
ejpam-4554	73	1	[	[	X
ejpam-4554	73	2	4	4	X
ejpam-4554	73	3	]	]	PUNCT
ejpam-4554	73	4	let	let	VERB
ejpam-4554	73	5	h	h	PRON
ejpam-4554	73	6	be	be	AUX
ejpam-4554	73	7	a	a	DET
ejpam-4554	73	8	pseudo	pseudo	NOUN
ejpam-4554	73	9	hyper	hyper	ADJ
ejpam-4554	73	10	gr	gr	NOUN
ejpam-4554	73	11	-	-	PUNCT
ejpam-4554	73	12	algebra	algebra	NOUN
ejpam-4554	73	13	and	and	CCONJ
ejpam-4554	73	14	s	s	AUX
ejpam-4554	73	15	be	be	AUX
ejpam-4554	73	16	a	a	DET
ejpam-4554	73	17	subset	subset	NOUN
ejpam-4554	73	18	of	of	ADP
ejpam-4554	73	19	h	h	NOUN
ejpam-4554	73	20	containing	contain	VERB
ejpam-4554	73	21	0	0	NUM
ejpam-4554	73	22	.	.	PUNCT
ejpam-4554	74	1	if	if	SCONJ
ejpam-4554	74	2	s	s	PRON
ejpam-4554	74	3	itself	itself	PRON
ejpam-4554	74	4	is	be	AUX
ejpam-4554	74	5	a	a	DET
ejpam-4554	74	6	pseudo	pseudo	NOUN
ejpam-4554	74	7	hyper	hyper	ADJ
ejpam-4554	74	8	gr	gr	NOUN
ejpam-4554	74	9	-	-	NOUN
ejpam-4554	74	10	algebra	algebra	NOUN
ejpam-4554	74	11	with	with	ADP
ejpam-4554	74	12	respect	respect	NOUN
ejpam-4554	74	13	to	to	ADP
ejpam-4554	74	14	the	the	DET
ejpam-4554	74	15	hyperoperations	hyperoperation	NOUN
ejpam-4554	74	16	⊛	⊛	NUM
ejpam-4554	74	17	and	and	CCONJ
ejpam-4554	74	18	⊙	⊙	NOUN
ejpam-4554	74	19	on	on	ADP
ejpam-4554	74	20	h	h	NOUN
ejpam-4554	74	21	,	,	PUNCT
ejpam-4554	74	22	then	then	ADV
ejpam-4554	74	23	s	s	VERB
ejpam-4554	74	24	is	be	AUX
ejpam-4554	74	25	called	call	VERB
ejpam-4554	74	26	a	a	DET
ejpam-4554	74	27	pseudo	pseudo	NOUN
ejpam-4554	74	28	hyper	hyper	ADJ
ejpam-4554	74	29	subgr	subgr	NOUN
ejpam-4554	74	30	-	-	PUNCT
ejpam-4554	74	31	algebra	algebra	NOUN
ejpam-4554	74	32	of	of	ADP
ejpam-4554	74	33	h.	h.	PROPN
ejpam-4554	74	34	theorem	theorem	VERB
ejpam-4554	74	35	2.12	2.12	NUM
ejpam-4554	74	36	.	.	PUNCT
ejpam-4554	75	1	[	[	X
ejpam-4554	75	2	4	4	NUM
ejpam-4554	75	3	]	]	PUNCT
ejpam-4554	75	4	(	(	PUNCT
ejpam-4554	75	5	pseudo	pseudo	NOUN
ejpam-4554	75	6	hyper	hyper	ADJ
ejpam-4554	75	7	subgr	subgr	NOUN
ejpam-4554	75	8	-	-	PUNCT
ejpam-4554	75	9	algebra	algebra	NOUN
ejpam-4554	75	10	criterion	criterion	NOUN
ejpam-4554	75	11	)	)	PUNCT
ejpam-4554	75	12	let	let	VERB
ejpam-4554	75	13	s	s	PRON
ejpam-4554	75	14	be	be	AUX
ejpam-4554	75	15	a	a	DET
ejpam-4554	75	16	nonempty	nonempty	ADJ
ejpam-4554	75	17	subset	subset	NOUN
ejpam-4554	75	18	of	of	ADP
ejpam-4554	75	19	a	a	DET
ejpam-4554	75	20	pseudo	pseudo	NOUN
ejpam-4554	75	21	hyper	hyper	ADJ
ejpam-4554	75	22	gr	gr	NOUN
ejpam-4554	75	23	-	-	PUNCT
ejpam-4554	75	24	algebra	algebra	NOUN
ejpam-4554	75	25	h.	h.	NOUN
ejpam-4554	76	1	then	then	ADV
ejpam-4554	76	2	s	s	VERB
ejpam-4554	76	3	is	be	AUX
ejpam-4554	76	4	a	a	DET
ejpam-4554	76	5	pseudo	pseudo	NOUN
ejpam-4554	76	6	hyper	hyper	ADJ
ejpam-4554	76	7	subgr	subgr	NOUN
ejpam-4554	76	8	-	-	PUNCT
ejpam-4554	76	9	algebra	algebra	NOUN
ejpam-4554	76	10	if	if	SCONJ
ejpam-4554	76	11	and	and	CCONJ
ejpam-4554	76	12	only	only	ADV
ejpam-4554	76	13	if	if	SCONJ
ejpam-4554	76	14	both	both	PRON
ejpam-4554	76	15	x⊛	x⊛	PROPN
ejpam-4554	76	16	y	y	PROPN
ejpam-4554	76	17	⊆	⊆	NUM
ejpam-4554	76	18	s	s	NOUN
ejpam-4554	76	19	and	and	CCONJ
ejpam-4554	76	20	x⊙	x⊙	PROPN
ejpam-4554	76	21	y	y	PROPN
ejpam-4554	76	22	⊆	⊆	NUM
ejpam-4554	76	23	s	s	NOUN
ejpam-4554	76	24	for	for	ADP
ejpam-4554	76	25	all	all	DET
ejpam-4554	76	26	x	x	NOUN
ejpam-4554	76	27	,	,	PUNCT
ejpam-4554	76	28	y	y	PROPN
ejpam-4554	76	29	∈	∈	PROPN
ejpam-4554	76	30	s.	s.	PROPN
ejpam-4554	76	31	example	example	NOUN
ejpam-4554	76	32	2.13	2.13	NUM
ejpam-4554	76	33	.	.	PUNCT
ejpam-4554	77	1	[	[	X
ejpam-4554	77	2	4	4	X
ejpam-4554	77	3	]	]	PUNCT
ejpam-4554	77	4	for	for	ADP
ejpam-4554	77	5	any	any	DET
ejpam-4554	77	6	pseudo	pseudo	NOUN
ejpam-4554	77	7	hyper	hyper	ADJ
ejpam-4554	77	8	gr	gr	NOUN
ejpam-4554	77	9	-	-	PUNCT
ejpam-4554	77	10	algebra	algebra	NOUN
ejpam-4554	77	11	h	h	NOUN
ejpam-4554	77	12	,	,	PUNCT
ejpam-4554	77	13	the	the	DET
ejpam-4554	77	14	set	set	NOUN
ejpam-4554	77	15	s	s	PART
ejpam-4554	77	16	=	=	X
ejpam-4554	77	17	{	{	PUNCT
ejpam-4554	77	18	0	0	NUM
ejpam-4554	77	19	}	}	PUNCT
ejpam-4554	77	20	is	be	AUX
ejpam-4554	77	21	a	a	DET
ejpam-4554	77	22	pseudo	pseudo	NOUN
ejpam-4554	77	23	hyper	hyper	ADJ
ejpam-4554	77	24	subgr	subgr	NOUN
ejpam-4554	77	25	-	-	PUNCT
ejpam-4554	77	26	algebra	algebra	NOUN
ejpam-4554	77	27	of	of	ADP
ejpam-4554	77	28	h.	h.	PROPN
ejpam-4554	77	29	3	3	NUM
ejpam-4554	77	30	.	.	PUNCT
ejpam-4554	78	1	quotient	quotient	NOUN
ejpam-4554	78	2	pseudo	pseudo	NOUN
ejpam-4554	78	3	hyper	hyper	ADJ
ejpam-4554	78	4	gr	gr	NOUN
ejpam-4554	78	5	-	-	PUNCT
ejpam-4554	78	6	algebras	algebras	NOUN
ejpam-4554	78	7	in	in	ADP
ejpam-4554	78	8	this	this	DET
ejpam-4554	78	9	section	section	NOUN
ejpam-4554	78	10	,	,	PUNCT
ejpam-4554	78	11	we	we	PRON
ejpam-4554	78	12	construct	construct	VERB
ejpam-4554	78	13	the	the	DET
ejpam-4554	78	14	structure	structure	NOUN
ejpam-4554	78	15	of	of	ADP
ejpam-4554	78	16	the	the	DET
ejpam-4554	78	17	quotient	quotient	NOUN
ejpam-4554	78	18	pseudo	pseudo	NOUN
ejpam-4554	78	19	hyper	hyper	ADJ
ejpam-4554	78	20	gr	gr	NOUN
ejpam-4554	78	21	-	-	PUNCT
ejpam-4554	78	22	algebra	algebra	NOUN
ejpam-4554	78	23	h	h	NOUN
ejpam-4554	78	24	/	/	SYM
ejpam-4554	78	25	i	i	PRON
ejpam-4554	78	26	from	from	ADP
ejpam-4554	78	27	a	a	DET
ejpam-4554	78	28	pseudo	pseudo	NOUN
ejpam-4554	78	29	hyper	hyper	ADJ
ejpam-4554	78	30	gr	gr	NOUN
ejpam-4554	78	31	-	-	PUNCT
ejpam-4554	78	32	algebra	algebra	NOUN
ejpam-4554	78	33	h	h	NOUN
ejpam-4554	78	34	via	via	ADP
ejpam-4554	78	35	congruence	congruence	PROPN
ejpam-4554	78	36	relation	relation	NOUN
ejpam-4554	78	37	.	.	PUNCT
ejpam-4554	79	1	all	all	PRON
ejpam-4554	79	2	throughout	throughout	ADV
ejpam-4554	79	3	,	,	PUNCT
ejpam-4554	79	4	we	we	PRON
ejpam-4554	79	5	denote	denote	VERB
ejpam-4554	79	6	a	a	DET
ejpam-4554	79	7	pseudo	pseudo	NOUN
ejpam-4554	79	8	hyper	hyper	ADJ
ejpam-4554	79	9	gr	gr	NOUN
ejpam-4554	79	10	-	-	PUNCT
ejpam-4554	79	11	algebra	algebra	NOUN
ejpam-4554	79	12	(	(	PUNCT
ejpam-4554	79	13	h,⊛,⊙	h,⊛,⊙	PROPN
ejpam-4554	79	14	,	,	PUNCT
ejpam-4554	79	15	0	0	NUM
ejpam-4554	79	16	)	)	PUNCT
ejpam-4554	79	17	simply	simply	ADV
ejpam-4554	79	18	by	by	ADP
ejpam-4554	79	19	h	h	NOUN
ejpam-4554	79	20	,	,	PUNCT
ejpam-4554	79	21	unless	unless	SCONJ
ejpam-4554	79	22	otherwise	otherwise	ADV
ejpam-4554	79	23	stated	state	VERB
ejpam-4554	79	24	.	.	PUNCT
ejpam-4554	80	1	definition	definition	NOUN
ejpam-4554	80	2	3.1	3.1	NUM
ejpam-4554	80	3	.	.	PUNCT
ejpam-4554	81	1	let	let	VERB
ejpam-4554	81	2	θ	θ	NOUN
ejpam-4554	81	3	be	be	AUX
ejpam-4554	81	4	an	an	DET
ejpam-4554	81	5	equivalence	equivalence	NOUN
ejpam-4554	81	6	relation	relation	NOUN
ejpam-4554	81	7	on	on	ADP
ejpam-4554	81	8	a	a	DET
ejpam-4554	81	9	pseudo	pseudo	NOUN
ejpam-4554	81	10	hyper	hyper	ADJ
ejpam-4554	81	11	gr	gr	NOUN
ejpam-4554	81	12	-	-	PUNCT
ejpam-4554	81	13	algebra	algebra	NOUN
ejpam-4554	81	14	h	h	NOUN
ejpam-4554	81	15	and	and	CCONJ
ejpam-4554	81	16	a	a	PRON
ejpam-4554	81	17	and	and	CCONJ
ejpam-4554	81	18	b	b	NOUN
ejpam-4554	81	19	be	be	AUX
ejpam-4554	81	20	nonempty	nonempty	X
ejpam-4554	81	21	subsets	subset	NOUN
ejpam-4554	81	22	of	of	ADP
ejpam-4554	81	23	h.	h.	PROPN
ejpam-4554	81	24	(	(	PUNCT
ejpam-4554	81	25	i	i	NOUN
ejpam-4554	81	26	)	)	PUNCT
ejpam-4554	81	27	aθb	aθb	NOUN
ejpam-4554	81	28	if	if	SCONJ
ejpam-4554	81	29	there	there	PRON
ejpam-4554	81	30	exist	exist	VERB
ejpam-4554	81	31	a	a	DET
ejpam-4554	81	32	∈	∈	PROPN
ejpam-4554	81	33	a	a	DET
ejpam-4554	81	34	and	and	CCONJ
ejpam-4554	81	35	b	b	NOUN
ejpam-4554	81	36	∈	∈	PROPN
ejpam-4554	81	37	b	b	NOUN
ejpam-4554	81	38	such	such	ADJ
ejpam-4554	81	39	that	that	DET
ejpam-4554	81	40	aθb	aθb	NOUN
ejpam-4554	81	41	;	;	PUNCT
ejpam-4554	81	42	(	(	PUNCT
ejpam-4554	81	43	ii	ii	NOUN
ejpam-4554	81	44	)	)	PUNCT
ejpam-4554	81	45	aθ̄b	aθ̄b	NOUN
ejpam-4554	81	46	if	if	SCONJ
ejpam-4554	81	47	for	for	ADP
ejpam-4554	81	48	every	every	DET
ejpam-4554	81	49	a	a	DET
ejpam-4554	81	50	∈	∈	PROPN
ejpam-4554	81	51	a	a	PRON
ejpam-4554	81	52	,	,	PUNCT
ejpam-4554	81	53	there	there	PRON
ejpam-4554	81	54	exists	exist	VERB
ejpam-4554	81	55	b	b	PROPN
ejpam-4554	81	56	∈	∈	PROPN
ejpam-4554	81	57	b	b	NOUN
ejpam-4554	81	58	such	such	ADJ
ejpam-4554	81	59	that	that	DET
ejpam-4554	81	60	aθb	aθb	NOUN
ejpam-4554	81	61	and	and	CCONJ
ejpam-4554	81	62	for	for	ADP
ejpam-4554	81	63	every	every	DET
ejpam-4554	81	64	b	b	PROPN
ejpam-4554	81	65	∈	∈	PROPN
ejpam-4554	81	66	b	b	NOUN
ejpam-4554	81	67	,	,	PUNCT
ejpam-4554	81	68	there	there	PRON
ejpam-4554	81	69	exists	exist	VERB
ejpam-4554	81	70	a	a	DET
ejpam-4554	81	71	∈	∈	NOUN
ejpam-4554	81	72	a	a	DET
ejpam-4554	81	73	such	such	ADJ
ejpam-4554	81	74	that	that	DET
ejpam-4554	81	75	aθb	aθb	NOUN
ejpam-4554	81	76	;	;	PUNCT
ejpam-4554	81	77	(	(	PUNCT
ejpam-4554	81	78	iii	iii	X
ejpam-4554	81	79	)	)	PUNCT
ejpam-4554	81	80	θ	θ	PROPN
ejpam-4554	81	81	is	be	AUX
ejpam-4554	81	82	called	call	VERB
ejpam-4554	81	83	a	a	DET
ejpam-4554	81	84	right	right	ADJ
ejpam-4554	81	85	⊛-congruence	⊛-congruence	NOUN
ejpam-4554	81	86	(	(	PUNCT
ejpam-4554	81	87	resp	resp	NOUN
ejpam-4554	81	88	.	.	PUNCT
ejpam-4554	82	1	right	right	ADJ
ejpam-4554	82	2	⊙-congruence	⊙-congruence	NOUN
ejpam-4554	82	3	)	)	PUNCT
ejpam-4554	82	4	on	on	ADP
ejpam-4554	82	5	h	h	NOUN
ejpam-4554	82	6	if	if	SCONJ
ejpam-4554	82	7	aθb	aθb	PRON
ejpam-4554	82	8	implies	imply	VERB
ejpam-4554	82	9	(	(	PUNCT
ejpam-4554	82	10	a⊛	a⊛	PROPN
ejpam-4554	82	11	u)θ̄(b⊛	u)θ̄(b⊛	NOUN
ejpam-4554	82	12	u	u	NOUN
ejpam-4554	82	13	)	)	PUNCT
ejpam-4554	82	14	(	(	PUNCT
ejpam-4554	82	15	resp	resp	NOUN
ejpam-4554	82	16	.	.	PUNCT
ejpam-4554	83	1	(	(	PUNCT
ejpam-4554	83	2	a⊙	a⊙	PROPN
ejpam-4554	83	3	u)θ̄(b⊙	u)θ̄(b⊙	PROPN
ejpam-4554	83	4	u	u	NOUN
ejpam-4554	83	5	)	)	PUNCT
ejpam-4554	83	6	)	)	PUNCT
ejpam-4554	83	7	for	for	ADP
ejpam-4554	83	8	all	all	DET
ejpam-4554	83	9	u	u	NOUN
ejpam-4554	83	10	in	in	ADP
ejpam-4554	83	11	h	h	NOUN
ejpam-4554	83	12	;	;	PUNCT
ejpam-4554	83	13	(	(	PUNCT
ejpam-4554	83	14	iv	iv	X
ejpam-4554	83	15	)	)	PUNCT
ejpam-4554	83	16	θ	θ	PROPN
ejpam-4554	83	17	is	be	AUX
ejpam-4554	83	18	called	call	VERB
ejpam-4554	83	19	a	a	DET
ejpam-4554	83	20	left	left	ADJ
ejpam-4554	83	21	⊛-congruence	⊛-congruence	NOUN
ejpam-4554	83	22	(	(	PUNCT
ejpam-4554	83	23	resp	resp	NOUN
ejpam-4554	83	24	.	.	PUNCT
ejpam-4554	84	1	left	leave	VERB
ejpam-4554	84	2	⊙-congruence	⊙-congruence	NOUN
ejpam-4554	84	3	)	)	PUNCT
ejpam-4554	84	4	on	on	ADP
ejpam-4554	84	5	h	h	NOUN
ejpam-4554	84	6	if	if	SCONJ
ejpam-4554	84	7	aθb	aθb	PRON
ejpam-4554	84	8	implies	imply	VERB
ejpam-4554	84	9	(	(	PUNCT
ejpam-4554	84	10	u	u	SYM
ejpam-4554	84	11	⊛	⊛	NUM
ejpam-4554	84	12	a)θ̄(u⊛	a)θ̄(u⊛	PROPN
ejpam-4554	84	13	b	b	X
ejpam-4554	84	14	)	)	PUNCT
ejpam-4554	84	15	(	(	PUNCT
ejpam-4554	84	16	resp	resp	NOUN
ejpam-4554	84	17	.	.	PUNCT
ejpam-4554	85	1	(	(	PUNCT
ejpam-4554	85	2	u⊙	u⊙	VERB
ejpam-4554	85	3	a)θ̄(u⊙	a)θ̄(u⊙	NOUN
ejpam-4554	85	4	b	b	NOUN
ejpam-4554	85	5	)	)	PUNCT
ejpam-4554	85	6	)	)	PUNCT
ejpam-4554	85	7	for	for	ADP
ejpam-4554	85	8	all	all	DET
ejpam-4554	85	9	u	u	NOUN
ejpam-4554	85	10	in	in	ADP
ejpam-4554	85	11	h	h	PROPN
ejpam-4554	85	12	;	;	PUNCT
ejpam-4554	85	13	r.	r.	PROPN
ejpam-4554	85	14	manzano	manzano	PROPN
ejpam-4554	85	15	,	,	PUNCT
ejpam-4554	85	16	jr	jr	PROPN
ejpam-4554	85	17	.	.	PROPN
ejpam-4554	85	18	,	,	PUNCT
ejpam-4554	85	19	g.	g.	PROPN
ejpam-4554	85	20	petalcorin	petalcorin	PROPN
ejpam-4554	85	21	,	,	PUNCT
ejpam-4554	85	22	jr	jr	PROPN
ejpam-4554	85	23	.	.	PROPN
ejpam-4554	85	24	/	/	SYM
ejpam-4554	85	25	eur	eur	PROPN
ejpam-4554	85	26	.	.	PUNCT
ejpam-4554	86	1	j.	j.	PROPN
ejpam-4554	86	2	pure	pure	PROPN
ejpam-4554	86	3	appl	appl	PROPN
ejpam-4554	86	4	.	.	PROPN
ejpam-4554	86	5	math	math	PROPN
ejpam-4554	86	6	,	,	PUNCT
ejpam-4554	86	7	15	15	NUM
ejpam-4554	86	8	(	(	PUNCT
ejpam-4554	86	9	4	4	NUM
ejpam-4554	86	10	)	)	PUNCT
ejpam-4554	86	11	(	(	PUNCT
ejpam-4554	86	12	2022	2022	NUM
ejpam-4554	86	13	)	)	PUNCT
ejpam-4554	86	14	,	,	PUNCT
ejpam-4554	86	15	1854	1854	NUM
ejpam-4554	86	16	-	-	SYM
ejpam-4554	86	17	1868	1868	NUM
ejpam-4554	86	18	1858	1858	NUM
ejpam-4554	86	19	(	(	PUNCT
ejpam-4554	86	20	v	v	NOUN
ejpam-4554	86	21	)	)	PUNCT
ejpam-4554	86	22	θ	θ	PROPN
ejpam-4554	86	23	is	be	AUX
ejpam-4554	86	24	called	call	VERB
ejpam-4554	86	25	a	a	DET
ejpam-4554	86	26	⊛-congruence	⊛-congruence	NOUN
ejpam-4554	86	27	(	(	PUNCT
ejpam-4554	86	28	resp	resp	NOUN
ejpam-4554	86	29	.	.	PUNCT
ejpam-4554	87	1	⊙-congruence	⊙-congruence	NOUN
ejpam-4554	87	2	)	)	PUNCT
ejpam-4554	87	3	on	on	ADP
ejpam-4554	87	4	h	h	NOUN
ejpam-4554	87	5	if	if	SCONJ
ejpam-4554	87	6	it	it	PRON
ejpam-4554	87	7	is	be	AUX
ejpam-4554	87	8	a	a	DET
ejpam-4554	87	9	right	right	NOUN
ejpam-4554	87	10	and	and	CCONJ
ejpam-4554	87	11	a	a	DET
ejpam-4554	87	12	left	left	ADJ
ejpam-4554	87	13	⊛-congruence	⊛-congruence	NOUN
ejpam-4554	87	14	(	(	PUNCT
ejpam-4554	87	15	resp	resp	NOUN
ejpam-4554	87	16	.	.	PUNCT
ejpam-4554	88	1	a	a	DET
ejpam-4554	88	2	right	right	NOUN
ejpam-4554	88	3	and	and	CCONJ
ejpam-4554	88	4	left	leave	VERB
ejpam-4554	88	5	⊙-congruence	⊙-congruence	NOUN
ejpam-4554	88	6	)	)	PUNCT
ejpam-4554	88	7	;	;	PUNCT
ejpam-4554	88	8	(	(	PUNCT
ejpam-4554	88	9	vi	vi	X
ejpam-4554	88	10	)	)	PUNCT
ejpam-4554	88	11	θ	θ	PROPN
ejpam-4554	88	12	is	be	AUX
ejpam-4554	88	13	called	call	VERB
ejpam-4554	88	14	a	a	DET
ejpam-4554	88	15	left	left	ADJ
ejpam-4554	88	16	congruence	congruence	NOUN
ejpam-4554	88	17	on	on	ADP
ejpam-4554	88	18	h	h	NOUN
ejpam-4554	88	19	if	if	SCONJ
ejpam-4554	88	20	it	it	PRON
ejpam-4554	88	21	is	be	AUX
ejpam-4554	88	22	a	a	DET
ejpam-4554	88	23	left	left	ADJ
ejpam-4554	88	24	⊛-congruence	⊛-congruence	NOUN
ejpam-4554	88	25	and	and	CCONJ
ejpam-4554	88	26	a	a	DET
ejpam-4554	88	27	left	left	ADJ
ejpam-4554	88	28	⊙-congruence	⊙-congruence	NOUN
ejpam-4554	88	29	on	on	ADP
ejpam-4554	88	30	h	h	NOUN
ejpam-4554	88	31	;	;	PUNCT
ejpam-4554	88	32	(	(	PUNCT
ejpam-4554	88	33	vii	vii	PROPN
ejpam-4554	88	34	)	)	PUNCT
ejpam-4554	88	35	θ	θ	PROPN
ejpam-4554	88	36	is	be	AUX
ejpam-4554	88	37	called	call	VERB
ejpam-4554	88	38	a	a	DET
ejpam-4554	88	39	right	right	ADJ
ejpam-4554	88	40	congruence	congruence	NOUN
ejpam-4554	88	41	on	on	ADP
ejpam-4554	88	42	h	h	NOUN
ejpam-4554	88	43	if	if	SCONJ
ejpam-4554	88	44	it	it	PRON
ejpam-4554	88	45	is	be	AUX
ejpam-4554	88	46	a	a	DET
ejpam-4554	88	47	right	right	ADJ
ejpam-4554	88	48	⊛-congruence	⊛-congruence	NOUN
ejpam-4554	88	49	and	and	CCONJ
ejpam-4554	88	50	a	a	DET
ejpam-4554	88	51	right	right	ADJ
ejpam-4554	88	52	⊙congruence	⊙congruence	NOUN
ejpam-4554	88	53	on	on	ADP
ejpam-4554	88	54	h	h	NOUN
ejpam-4554	88	55	;	;	PUNCT
ejpam-4554	88	56	(	(	PUNCT
ejpam-4554	88	57	viii	viii	NOUN
ejpam-4554	88	58	)	)	PUNCT
ejpam-4554	88	59	θ	θ	PROPN
ejpam-4554	88	60	is	be	AUX
ejpam-4554	88	61	called	call	VERB
ejpam-4554	88	62	a	a	DET
ejpam-4554	88	63	congruence	congruence	NOUN
ejpam-4554	88	64	relation	relation	NOUN
ejpam-4554	88	65	on	on	ADP
ejpam-4554	88	66	h	h	NOUN
ejpam-4554	88	67	if	if	SCONJ
ejpam-4554	88	68	it	it	PRON
ejpam-4554	88	69	is	be	AUX
ejpam-4554	88	70	a	a	DET
ejpam-4554	88	71	⊛-congruence	⊛-congruence	NOUN
ejpam-4554	88	72	and	and	CCONJ
ejpam-4554	88	73	⊙-congruence	⊙-congruence	NOUN
ejpam-4554	88	74	on	on	ADP
ejpam-4554	88	75	h	h	NOUN
ejpam-4554	88	76	;	;	PUNCT
ejpam-4554	88	77	and	and	CCONJ
ejpam-4554	88	78	(	(	PUNCT
ejpam-4554	88	79	ix	ix	ADJ
ejpam-4554	88	80	)	)	PUNCT
ejpam-4554	88	81	θ	θ	PROPN
ejpam-4554	88	82	is	be	AUX
ejpam-4554	88	83	called	call	VERB
ejpam-4554	88	84	a	a	DET
ejpam-4554	88	85	regular	regular	ADJ
ejpam-4554	88	86	congruence	congruence	NOUN
ejpam-4554	88	87	relation	relation	NOUN
ejpam-4554	88	88	on	on	ADP
ejpam-4554	88	89	h	h	NOUN
ejpam-4554	88	90	,	,	PUNCT
ejpam-4554	88	91	if	if	SCONJ
ejpam-4554	88	92	θ	θ	PROPN
ejpam-4554	88	93	is	be	AUX
ejpam-4554	88	94	a	a	DET
ejpam-4554	88	95	congruence	congruence	NOUN
ejpam-4554	88	96	relation	relation	NOUN
ejpam-4554	88	97	on	on	ADP
ejpam-4554	88	98	h	h	NOUN
ejpam-4554	88	99	and	and	CCONJ
ejpam-4554	88	100	for	for	ADP
ejpam-4554	88	101	any	any	DET
ejpam-4554	88	102	x	x	NOUN
ejpam-4554	88	103	,	,	PUNCT
ejpam-4554	88	104	y	y	PROPN
ejpam-4554	88	105	∈	∈	PROPN
ejpam-4554	88	106	h	h	NOUN
ejpam-4554	88	107	,	,	PUNCT
ejpam-4554	88	108	whenever	whenever	SCONJ
ejpam-4554	88	109	(	(	PUNCT
ejpam-4554	88	110	x⊛	x⊛	INTJ
ejpam-4554	88	111	y)θ{0	y)θ{0	ADP
ejpam-4554	88	112	}	}	PUNCT
ejpam-4554	88	113	,	,	PUNCT
ejpam-4554	88	114	(	(	PUNCT
ejpam-4554	88	115	y	y	PROPN
ejpam-4554	88	116	⊛	⊛	NUM
ejpam-4554	88	117	x)θ{0	x)θ{0	NUM
ejpam-4554	88	118	}	}	PUNCT
ejpam-4554	88	119	,	,	PUNCT
ejpam-4554	88	120	(	(	PUNCT
ejpam-4554	88	121	x⊙	x⊙	PROPN
ejpam-4554	88	122	y)θ{0	y)θ{0	NOUN
ejpam-4554	88	123	}	}	PUNCT
ejpam-4554	88	124	,	,	PUNCT
ejpam-4554	88	125	and	and	CCONJ
ejpam-4554	88	126	(	(	PUNCT
ejpam-4554	88	127	y	y	PROPN
ejpam-4554	88	128	⊙	⊙	PROPN
ejpam-4554	88	129	x)θ{0	x)θ{0	PROPN
ejpam-4554	89	1	}	}	PUNCT
ejpam-4554	89	2	,	,	PUNCT
ejpam-4554	89	3	we	we	PRON
ejpam-4554	89	4	have	have	VERB
ejpam-4554	89	5	xθy	xθy	PROPN
ejpam-4554	89	6	.	.	PUNCT
ejpam-4554	89	7	example	example	NOUN
ejpam-4554	90	1	3.2	3.2	NUM
ejpam-4554	90	2	.	.	PUNCT
ejpam-4554	91	1	let	let	VERB
ejpam-4554	91	2	h	h	NOUN
ejpam-4554	91	3	=	=	PRON
ejpam-4554	91	4	{	{	PUNCT
ejpam-4554	91	5	0	0	NUM
ejpam-4554	91	6	,	,	PUNCT
ejpam-4554	91	7	1	1	NUM
ejpam-4554	91	8	,	,	PUNCT
ejpam-4554	91	9	2	2	NUM
ejpam-4554	91	10	}	}	PUNCT
ejpam-4554	91	11	and	and	CCONJ
ejpam-4554	91	12	consider	consider	VERB
ejpam-4554	91	13	the	the	DET
ejpam-4554	91	14	following	follow	VERB
ejpam-4554	91	15	cayley	cayley	ADJ
ejpam-4554	91	16	tables	table	NOUN
ejpam-4554	91	17	below	below	ADV
ejpam-4554	91	18	.	.	PUNCT
ejpam-4554	92	1	⊛	⊛	NUM
ejpam-4554	92	2	0	0	NUM
ejpam-4554	92	3	1	1	NUM
ejpam-4554	92	4	2	2	NUM
ejpam-4554	92	5	0	0	NUM
ejpam-4554	92	6	{	{	PUNCT
ejpam-4554	92	7	0	0	NUM
ejpam-4554	92	8	}	}	PUNCT
ejpam-4554	92	9	{	{	PUNCT
ejpam-4554	92	10	0	0	NUM
ejpam-4554	92	11	}	}	PUNCT
ejpam-4554	92	12	{	{	PUNCT
ejpam-4554	92	13	0	0	NUM
ejpam-4554	92	14	}	}	SYM
ejpam-4554	92	15	1	1	NUM
ejpam-4554	92	16	{	{	PUNCT
ejpam-4554	92	17	0	0	NUM
ejpam-4554	92	18	,	,	PUNCT
ejpam-4554	92	19	1	1	NUM
ejpam-4554	92	20	}	}	PUNCT
ejpam-4554	92	21	{	{	PUNCT
ejpam-4554	92	22	0	0	NUM
ejpam-4554	92	23	,	,	PUNCT
ejpam-4554	92	24	1	1	NUM
ejpam-4554	92	25	}	}	PUNCT
ejpam-4554	92	26	{	{	PUNCT
ejpam-4554	92	27	0	0	NUM
ejpam-4554	92	28	,	,	PUNCT
ejpam-4554	92	29	1	1	NUM
ejpam-4554	92	30	}	}	SYM
ejpam-4554	92	31	2	2	NUM
ejpam-4554	92	32	{	{	PUNCT
ejpam-4554	92	33	0	0	NUM
ejpam-4554	92	34	,	,	PUNCT
ejpam-4554	92	35	2	2	NUM
ejpam-4554	92	36	}	}	PUNCT
ejpam-4554	92	37	{	{	PUNCT
ejpam-4554	92	38	0	0	NUM
ejpam-4554	92	39	,	,	PUNCT
ejpam-4554	92	40	2	2	NUM
ejpam-4554	92	41	}	}	PUNCT
ejpam-4554	92	42	{	{	PUNCT
ejpam-4554	92	43	0	0	NUM
ejpam-4554	92	44	,	,	PUNCT
ejpam-4554	92	45	2	2	NUM
ejpam-4554	92	46	}	}	PUNCT
ejpam-4554	92	47	⊙	⊙	X
ejpam-4554	92	48	0	0	NUM
ejpam-4554	93	1	1	1	NUM
ejpam-4554	93	2	2	2	NUM
ejpam-4554	93	3	0	0	NUM
ejpam-4554	93	4	{	{	PUNCT
ejpam-4554	93	5	0	0	NUM
ejpam-4554	93	6	}	}	PUNCT
ejpam-4554	93	7	{	{	PUNCT
ejpam-4554	93	8	0	0	NUM
ejpam-4554	93	9	,	,	PUNCT
ejpam-4554	93	10	1	1	NUM
ejpam-4554	93	11	}	}	PUNCT
ejpam-4554	93	12	{	{	PUNCT
ejpam-4554	93	13	0	0	NUM
ejpam-4554	93	14	,	,	PUNCT
ejpam-4554	93	15	2	2	NUM
ejpam-4554	93	16	}	}	SYM
ejpam-4554	93	17	1	1	NUM
ejpam-4554	93	18	{	{	PUNCT
ejpam-4554	93	19	0	0	NUM
ejpam-4554	93	20	,	,	PUNCT
ejpam-4554	93	21	1	1	NUM
ejpam-4554	93	22	}	}	PUNCT
ejpam-4554	93	23	{	{	PUNCT
ejpam-4554	93	24	0	0	NUM
ejpam-4554	93	25	,	,	PUNCT
ejpam-4554	93	26	1	1	NUM
ejpam-4554	93	27	}	}	PUNCT
ejpam-4554	93	28	{	{	PUNCT
ejpam-4554	93	29	0	0	NUM
ejpam-4554	93	30	,	,	PUNCT
ejpam-4554	93	31	1	1	NUM
ejpam-4554	93	32	,	,	PUNCT
ejpam-4554	93	33	2	2	NUM
ejpam-4554	93	34	}	}	SYM
ejpam-4554	93	35	2	2	NUM
ejpam-4554	93	36	{	{	PUNCT
ejpam-4554	93	37	0	0	NUM
ejpam-4554	93	38	,	,	PUNCT
ejpam-4554	93	39	2	2	NUM
ejpam-4554	93	40	}	}	PUNCT
ejpam-4554	93	41	{	{	PUNCT
ejpam-4554	93	42	0	0	NUM
ejpam-4554	93	43	,	,	PUNCT
ejpam-4554	93	44	1	1	NUM
ejpam-4554	93	45	,	,	PUNCT
ejpam-4554	93	46	2	2	NUM
ejpam-4554	93	47	}	}	PUNCT
ejpam-4554	93	48	{	{	PUNCT
ejpam-4554	93	49	0	0	NUM
ejpam-4554	93	50	,	,	PUNCT
ejpam-4554	93	51	2	2	NUM
ejpam-4554	93	52	}	}	PUNCT
ejpam-4554	93	53	then	then	ADV
ejpam-4554	93	54	(	(	PUNCT
ejpam-4554	93	55	h;⊛,⊙	h;⊛,⊙	PROPN
ejpam-4554	93	56	,	,	PUNCT
ejpam-4554	93	57	0	0	NUM
ejpam-4554	93	58	)	)	PUNCT
ejpam-4554	93	59	is	be	AUX
ejpam-4554	93	60	a	a	DET
ejpam-4554	93	61	pseudo	pseudo	NOUN
ejpam-4554	93	62	hyper	hyper	ADJ
ejpam-4554	93	63	gr	gr	NOUN
ejpam-4554	93	64	-	-	PUNCT
ejpam-4554	93	65	algebra	algebra	NOUN
ejpam-4554	93	66	.	.	PUNCT
ejpam-4554	94	1	define	define	VERB
ejpam-4554	94	2	θ	θ	PROPN
ejpam-4554	94	3	on	on	ADP
ejpam-4554	94	4	h	h	NOUN
ejpam-4554	94	5	by	by	ADP
ejpam-4554	94	6	θ	θ	PROPN
ejpam-4554	94	7	=	=	SYM
ejpam-4554	94	8	{	{	PUNCT
ejpam-4554	94	9	(	(	PUNCT
ejpam-4554	94	10	0	0	NUM
ejpam-4554	94	11	,	,	PUNCT
ejpam-4554	94	12	0	0	NUM
ejpam-4554	94	13	)	)	PUNCT
ejpam-4554	94	14	,	,	PUNCT
ejpam-4554	94	15	(	(	PUNCT
ejpam-4554	94	16	0	0	NUM
ejpam-4554	94	17	,	,	PUNCT
ejpam-4554	94	18	1	1	NUM
ejpam-4554	94	19	)	)	PUNCT
ejpam-4554	94	20	,	,	PUNCT
ejpam-4554	94	21	(	(	PUNCT
ejpam-4554	94	22	1	1	NUM
ejpam-4554	94	23	,	,	PUNCT
ejpam-4554	94	24	0	0	NUM
ejpam-4554	94	25	)	)	PUNCT
ejpam-4554	94	26	,	,	PUNCT
ejpam-4554	94	27	(	(	PUNCT
ejpam-4554	94	28	1	1	NUM
ejpam-4554	94	29	,	,	PUNCT
ejpam-4554	94	30	1	1	NUM
ejpam-4554	94	31	)	)	PUNCT
ejpam-4554	94	32	,	,	PUNCT
ejpam-4554	94	33	(	(	PUNCT
ejpam-4554	94	34	2	2	NUM
ejpam-4554	94	35	,	,	PUNCT
ejpam-4554	94	36	2	2	NUM
ejpam-4554	94	37	)	)	PUNCT
ejpam-4554	94	38	}	}	PUNCT
ejpam-4554	94	39	.	.	PUNCT
ejpam-4554	95	1	it	it	PRON
ejpam-4554	95	2	can	can	AUX
ejpam-4554	95	3	be	be	AUX
ejpam-4554	95	4	easily	easily	ADV
ejpam-4554	95	5	verified	verify	VERB
ejpam-4554	95	6	that	that	SCONJ
ejpam-4554	95	7	θ	θ	PROPN
ejpam-4554	95	8	is	be	AUX
ejpam-4554	95	9	an	an	DET
ejpam-4554	95	10	equivalence	equivalence	NOUN
ejpam-4554	95	11	relation	relation	NOUN
ejpam-4554	95	12	.	.	PUNCT
ejpam-4554	96	1	we	we	PRON
ejpam-4554	96	2	will	will	AUX
ejpam-4554	96	3	show	show	VERB
ejpam-4554	96	4	that	that	SCONJ
ejpam-4554	96	5	θ	θ	PROPN
ejpam-4554	96	6	is	be	AUX
ejpam-4554	96	7	a	a	DET
ejpam-4554	96	8	congruence	congruence	NOUN
ejpam-4554	96	9	relation	relation	NOUN
ejpam-4554	96	10	using	use	VERB
ejpam-4554	96	11	definition	definition	NOUN
ejpam-4554	96	12	3.1	3.1	NUM
ejpam-4554	96	13	.	.	PUNCT
ejpam-4554	97	1	since	since	SCONJ
ejpam-4554	97	2	xθx	xθx	PROPN
ejpam-4554	97	3	for	for	ADP
ejpam-4554	97	4	all	all	DET
ejpam-4554	97	5	x	x	SYM
ejpam-4554	97	6	∈	∈	PROPN
ejpam-4554	97	7	h1	h1	PROPN
ejpam-4554	97	8	,	,	PUNCT
ejpam-4554	97	9	we	we	PRON
ejpam-4554	97	10	have	have	VERB
ejpam-4554	97	11	(	(	PUNCT
ejpam-4554	97	12	a⊛x)θ̄(a⊛x	a⊛x)θ̄(a⊛x	NOUN
ejpam-4554	97	13	)	)	PUNCT
ejpam-4554	97	14	,	,	PUNCT
ejpam-4554	97	15	(	(	PUNCT
ejpam-4554	97	16	x⊛a)θ̄(x⊛a	x⊛a)θ̄(x⊛a	ADJ
ejpam-4554	97	17	)	)	PUNCT
ejpam-4554	97	18	,	,	PUNCT
ejpam-4554	97	19	(	(	PUNCT
ejpam-4554	97	20	a⊙x)θ̄(a⊙x	a⊙x)θ̄(a⊙x	NOUN
ejpam-4554	97	21	)	)	PUNCT
ejpam-4554	97	22	and	and	CCONJ
ejpam-4554	97	23	(	(	PUNCT
ejpam-4554	97	24	x⊙a)θ̄(x⊙a	x⊙a)θ̄(x⊙a	NOUN
ejpam-4554	97	25	)	)	PUNCT
ejpam-4554	97	26	.	.	PUNCT
ejpam-4554	98	1	therefore	therefore	ADV
ejpam-4554	98	2	,	,	PUNCT
ejpam-4554	98	3	the	the	DET
ejpam-4554	98	4	remaining	remain	VERB
ejpam-4554	98	5	elements	element	NOUN
ejpam-4554	98	6	of	of	ADP
ejpam-4554	98	7	θ	θ	PROPN
ejpam-4554	98	8	that	that	PRON
ejpam-4554	98	9	is	be	AUX
ejpam-4554	98	10	left	leave	VERB
ejpam-4554	98	11	for	for	ADP
ejpam-4554	98	12	verification	verification	NOUN
ejpam-4554	98	13	are	be	AUX
ejpam-4554	98	14	(	(	PUNCT
ejpam-4554	98	15	1	1	NUM
ejpam-4554	98	16	,	,	PUNCT
ejpam-4554	98	17	0	0	NUM
ejpam-4554	98	18	)	)	PUNCT
ejpam-4554	98	19	and	and	CCONJ
ejpam-4554	98	20	(	(	PUNCT
ejpam-4554	98	21	0	0	NUM
ejpam-4554	98	22	,	,	PUNCT
ejpam-4554	98	23	1	1	NUM
ejpam-4554	98	24	)	)	PUNCT
ejpam-4554	98	25	which	which	PRON
ejpam-4554	98	26	can	can	AUX
ejpam-4554	98	27	be	be	AUX
ejpam-4554	98	28	done	do	VERB
ejpam-4554	98	29	simultaneously	simultaneously	ADV
ejpam-4554	98	30	.	.	PUNCT
ejpam-4554	99	1	since	since	SCONJ
ejpam-4554	99	2	1θ0	1θ0	NUM
ejpam-4554	99	3	,	,	PUNCT
ejpam-4554	99	4	we	we	PRON
ejpam-4554	99	5	will	will	AUX
ejpam-4554	99	6	show	show	VERB
ejpam-4554	99	7	that	that	SCONJ
ejpam-4554	99	8	(	(	PUNCT
ejpam-4554	99	9	1⊛	1⊛	NUM
ejpam-4554	99	10	a)θ̄(0⊛	a)θ̄(0⊛	NOUN
ejpam-4554	99	11	a	a	X
ejpam-4554	99	12	)	)	PUNCT
ejpam-4554	99	13	,	,	PUNCT
ejpam-4554	99	14	(	(	PUNCT
ejpam-4554	99	15	a⊛	a⊛	NOUN
ejpam-4554	99	16	1)θ̄(a⊛	1)θ̄(a⊛	NUM
ejpam-4554	99	17	0	0	NUM
ejpam-4554	99	18	)	)	PUNCT
ejpam-4554	99	19	,	,	PUNCT
ejpam-4554	99	20	(	(	PUNCT
ejpam-4554	99	21	1⊙	1⊙	NUM
ejpam-4554	99	22	a)θ̄(0⊙	a)θ̄(0⊙	PROPN
ejpam-4554	99	23	a	a	PRON
ejpam-4554	99	24	)	)	PUNCT
ejpam-4554	99	25	and	and	CCONJ
ejpam-4554	99	26	(	(	PUNCT
ejpam-4554	99	27	a⊙	a⊙	PROPN
ejpam-4554	99	28	1)θ̄(a⊙	1)θ̄(a⊙	PROPN
ejpam-4554	99	29	0	0	NUM
ejpam-4554	99	30	)	)	PUNCT
ejpam-4554	99	31	for	for	ADP
ejpam-4554	99	32	all	all	DET
ejpam-4554	99	33	a	a	DET
ejpam-4554	99	34	∈	∈	PROPN
ejpam-4554	99	35	h.	h.	NOUN
ejpam-4554	99	36	for	for	ADP
ejpam-4554	99	37	a	a	DET
ejpam-4554	99	38	=	=	SYM
ejpam-4554	99	39	0	0	NUM
ejpam-4554	99	40	,	,	PUNCT
ejpam-4554	99	41	1⊛	1⊛	NUM
ejpam-4554	99	42	0	0	SYM
ejpam-4554	99	43	=	=	SYM
ejpam-4554	99	44	{	{	PUNCT
ejpam-4554	99	45	0	0	NUM
ejpam-4554	99	46	,	,	PUNCT
ejpam-4554	99	47	1}θ̄{0	1}θ̄{0	NUM
ejpam-4554	99	48	}	}	PUNCT
ejpam-4554	99	49	=	=	SYM
ejpam-4554	99	50	0⊛	0⊛	NUM
ejpam-4554	99	51	0	0	NUM
ejpam-4554	99	52	and	and	CCONJ
ejpam-4554	99	53	0⊛	0⊛	NUM
ejpam-4554	99	54	1	1	NUM
ejpam-4554	99	55	=	=	SYM
ejpam-4554	99	56	{	{	PUNCT
ejpam-4554	99	57	0}θ̄{0	0}θ̄{0	NUM
ejpam-4554	99	58	}	}	PUNCT
ejpam-4554	99	59	=	=	PUNCT
ejpam-4554	99	60	0⊛	0⊛	NUM
ejpam-4554	99	61	0	0	NUM
ejpam-4554	99	62	1⊙	1⊙	NUM
ejpam-4554	99	63	0	0	NUM
ejpam-4554	99	64	=	=	SYM
ejpam-4554	99	65	{	{	PUNCT
ejpam-4554	99	66	0	0	NUM
ejpam-4554	99	67	,	,	PUNCT
ejpam-4554	99	68	1}θ̄{0	1}θ̄{0	NUM
ejpam-4554	99	69	}	}	PUNCT
ejpam-4554	99	70	=	=	SYM
ejpam-4554	99	71	0⊙	0⊙	NOUN
ejpam-4554	99	72	0	0	NUM
ejpam-4554	99	73	and	and	CCONJ
ejpam-4554	99	74	0⊙	0⊙	NOUN
ejpam-4554	99	75	1	1	NUM
ejpam-4554	99	76	=	=	SYM
ejpam-4554	99	77	{	{	PUNCT
ejpam-4554	99	78	0}θ̄{0	0}θ̄{0	PROPN
ejpam-4554	99	79	}	}	PUNCT
ejpam-4554	99	80	=	=	SYM
ejpam-4554	99	81	0⊙	0⊙	NOUN
ejpam-4554	99	82	0	0	NUM
ejpam-4554	99	83	.	.	PUNCT
ejpam-4554	100	1	for	for	ADP
ejpam-4554	100	2	a	a	PRON
ejpam-4554	100	3	=	=	SYM
ejpam-4554	100	4	1	1	NUM
ejpam-4554	100	5	,	,	PUNCT
ejpam-4554	100	6	1⊛	1⊛	NUM
ejpam-4554	100	7	1	1	NUM
ejpam-4554	100	8	=	=	SYM
ejpam-4554	100	9	{	{	PUNCT
ejpam-4554	100	10	0	0	NUM
ejpam-4554	100	11	,	,	PUNCT
ejpam-4554	100	12	1}θ̄{0	1}θ̄{0	NUM
ejpam-4554	100	13	}	}	PUNCT
ejpam-4554	100	14	=	=	SYM
ejpam-4554	100	15	0⊛	0⊛	NUM
ejpam-4554	100	16	1	1	NUM
ejpam-4554	100	17	and	and	CCONJ
ejpam-4554	100	18	1⊛	1⊛	NUM
ejpam-4554	100	19	1	1	NUM
ejpam-4554	100	20	=	=	SYM
ejpam-4554	100	21	{	{	PUNCT
ejpam-4554	100	22	0	0	NUM
ejpam-4554	100	23	,	,	PUNCT
ejpam-4554	100	24	1}θ̄{0	1}θ̄{0	NUM
ejpam-4554	100	25	,	,	PUNCT
ejpam-4554	100	26	1	1	NUM
ejpam-4554	100	27	}	}	PUNCT
ejpam-4554	100	28	=	=	SYM
ejpam-4554	100	29	1⊛	1⊛	NUM
ejpam-4554	100	30	0	0	NUM
ejpam-4554	100	31	1⊙	1⊙	NUM
ejpam-4554	100	32	1	1	NUM
ejpam-4554	100	33	=	=	SYM
ejpam-4554	100	34	{	{	PUNCT
ejpam-4554	100	35	0	0	NUM
ejpam-4554	100	36	,	,	PUNCT
ejpam-4554	100	37	1}θ̄{0	1}θ̄{0	NUM
ejpam-4554	100	38	,	,	PUNCT
ejpam-4554	100	39	1	1	NUM
ejpam-4554	100	40	}	}	PUNCT
ejpam-4554	100	41	=	=	NOUN
ejpam-4554	100	42	0⊙	0⊙	NOUN
ejpam-4554	100	43	1	1	NUM
ejpam-4554	100	44	and	and	CCONJ
ejpam-4554	100	45	1⊙	1⊙	NUM
ejpam-4554	100	46	1	1	NUM
ejpam-4554	100	47	=	=	SYM
ejpam-4554	100	48	{	{	PUNCT
ejpam-4554	100	49	0	0	NUM
ejpam-4554	100	50	,	,	PUNCT
ejpam-4554	100	51	1}θ̄{0	1}θ̄{0	NUM
ejpam-4554	100	52	,	,	PUNCT
ejpam-4554	100	53	1	1	NUM
ejpam-4554	100	54	}	}	PUNCT
ejpam-4554	100	55	=	=	PUNCT
ejpam-4554	100	56	1⊙	1⊙	NUM
ejpam-4554	100	57	0	0	NUM
ejpam-4554	100	58	.	.	PUNCT
ejpam-4554	101	1	for	for	ADP
ejpam-4554	101	2	a	a	DET
ejpam-4554	101	3	=	=	SYM
ejpam-4554	101	4	2	2	NUM
ejpam-4554	101	5	,	,	PUNCT
ejpam-4554	101	6	1⊛	1⊛	NUM
ejpam-4554	101	7	2	2	NUM
ejpam-4554	101	8	=	=	SYM
ejpam-4554	101	9	{	{	PUNCT
ejpam-4554	101	10	0	0	NUM
ejpam-4554	101	11	,	,	PUNCT
ejpam-4554	101	12	1}θ̄{0	1}θ̄{0	NUM
ejpam-4554	101	13	}	}	PUNCT
ejpam-4554	101	14	=	=	SYM
ejpam-4554	101	15	0⊛	0⊛	NUM
ejpam-4554	101	16	2	2	NUM
ejpam-4554	101	17	and	and	CCONJ
ejpam-4554	101	18	2⊛	2⊛	NUM
ejpam-4554	101	19	1	1	NUM
ejpam-4554	101	20	=	=	SYM
ejpam-4554	101	21	{	{	PUNCT
ejpam-4554	101	22	0	0	NUM
ejpam-4554	101	23	,	,	PUNCT
ejpam-4554	101	24	2}θ̄{0	2}θ̄{0	NUM
ejpam-4554	101	25	,	,	PUNCT
ejpam-4554	101	26	2	2	NUM
ejpam-4554	101	27	}	}	PUNCT
ejpam-4554	101	28	=	=	NUM
ejpam-4554	101	29	2⊛	2⊛	NUM
ejpam-4554	101	30	0	0	NUM
ejpam-4554	101	31	1⊙	1⊙	NUM
ejpam-4554	101	32	2	2	NUM
ejpam-4554	101	33	=	=	SYM
ejpam-4554	101	34	{	{	PUNCT
ejpam-4554	101	35	0	0	NUM
ejpam-4554	101	36	,	,	PUNCT
ejpam-4554	101	37	1	1	NUM
ejpam-4554	101	38	,	,	PUNCT
ejpam-4554	101	39	2}θ̄{0	2}θ̄{0	NUM
ejpam-4554	101	40	,	,	PUNCT
ejpam-4554	101	41	2	2	NUM
ejpam-4554	101	42	}	}	PUNCT
ejpam-4554	101	43	=	=	SYM
ejpam-4554	101	44	0⊙	0⊙	NUM
ejpam-4554	101	45	2	2	NUM
ejpam-4554	101	46	and	and	CCONJ
ejpam-4554	101	47	2⊙	2⊙	NUM
ejpam-4554	101	48	1	1	NUM
ejpam-4554	101	49	=	=	SYM
ejpam-4554	101	50	{	{	PUNCT
ejpam-4554	101	51	0	0	NUM
ejpam-4554	101	52	,	,	PUNCT
ejpam-4554	101	53	1	1	NUM
ejpam-4554	101	54	,	,	PUNCT
ejpam-4554	101	55	2}θ̄{0	2}θ̄{0	NUM
ejpam-4554	101	56	,	,	PUNCT
ejpam-4554	101	57	2	2	NUM
ejpam-4554	101	58	}	}	PUNCT
ejpam-4554	101	59	=	=	SYM
ejpam-4554	101	60	2⊙	2⊙	NUM
ejpam-4554	101	61	0	0	X
ejpam-4554	101	62	.	.	PUNCT
ejpam-4554	101	63	therefore	therefore	ADV
ejpam-4554	101	64	,	,	PUNCT
ejpam-4554	101	65	θ	θ	PROPN
ejpam-4554	101	66	is	be	AUX
ejpam-4554	101	67	a	a	DET
ejpam-4554	101	68	congruence	congruence	NOUN
ejpam-4554	101	69	relation	relation	NOUN
ejpam-4554	101	70	.	.	PUNCT
ejpam-4554	102	1	r.	r.	PROPN
ejpam-4554	102	2	manzano	manzano	PROPN
ejpam-4554	102	3	,	,	PUNCT
ejpam-4554	102	4	jr	jr	PROPN
ejpam-4554	102	5	.	.	PROPN
ejpam-4554	102	6	,	,	PUNCT
ejpam-4554	102	7	g.	g.	PROPN
ejpam-4554	102	8	petalcorin	petalcorin	PROPN
ejpam-4554	102	9	,	,	PUNCT
ejpam-4554	102	10	jr	jr	PROPN
ejpam-4554	102	11	.	.	PROPN
ejpam-4554	102	12	/	/	SYM
ejpam-4554	102	13	eur	eur	PROPN
ejpam-4554	102	14	.	.	PUNCT
ejpam-4554	103	1	j.	j.	PROPN
ejpam-4554	103	2	pure	pure	PROPN
ejpam-4554	103	3	appl	appl	PROPN
ejpam-4554	103	4	.	.	PROPN
ejpam-4554	103	5	math	math	PROPN
ejpam-4554	103	6	,	,	PUNCT
ejpam-4554	103	7	15	15	NUM
ejpam-4554	103	8	(	(	PUNCT
ejpam-4554	103	9	4	4	NUM
ejpam-4554	103	10	)	)	PUNCT
ejpam-4554	103	11	(	(	PUNCT
ejpam-4554	103	12	2022	2022	NUM
ejpam-4554	103	13	)	)	PUNCT
ejpam-4554	103	14	,	,	PUNCT
ejpam-4554	103	15	1854	1854	NUM
ejpam-4554	103	16	-	-	SYM
ejpam-4554	103	17	1868	1868	NUM
ejpam-4554	103	18	1859	1859	NUM
ejpam-4554	103	19	definition	definition	NOUN
ejpam-4554	103	20	3.3	3.3	NUM
ejpam-4554	103	21	.	.	PUNCT
ejpam-4554	104	1	let	let	VERB
ejpam-4554	104	2	θ	θ	NOUN
ejpam-4554	104	3	be	be	AUX
ejpam-4554	104	4	a	a	DET
ejpam-4554	104	5	congruence	congruence	NOUN
ejpam-4554	104	6	relation	relation	NOUN
ejpam-4554	104	7	on	on	ADP
ejpam-4554	104	8	a	a	DET
ejpam-4554	104	9	pseudo	pseudo	NOUN
ejpam-4554	104	10	hypergr	hypergr	NOUN
ejpam-4554	104	11	-	-	PUNCT
ejpam-4554	104	12	algebrah	algebrah	NOUN
ejpam-4554	104	13	.	.	PUNCT
ejpam-4554	105	1	the	the	DET
ejpam-4554	105	2	congruence	congruence	ADJ
ejpam-4554	105	3	class	class	NOUN
ejpam-4554	105	4	of	of	ADP
ejpam-4554	105	5	x	x	PRON
ejpam-4554	105	6	,	,	PUNCT
ejpam-4554	105	7	denoted	denote	VERB
ejpam-4554	105	8	by	by	ADP
ejpam-4554	105	9	[	[	X
ejpam-4554	105	10	x]θ	x]θ	ADP
ejpam-4554	105	11	or	or	CCONJ
ejpam-4554	105	12	ix	ix	ADV
ejpam-4554	105	13	is	be	AUX
ejpam-4554	105	14	given	give	VERB
ejpam-4554	105	15	by	by	ADP
ejpam-4554	105	16	[	[	X
ejpam-4554	105	17	x]θ	x]θ	X
ejpam-4554	105	18	=	=	PUNCT
ejpam-4554	105	19	ix	ix	PROPN
ejpam-4554	106	1	=	=	PUNCT
ejpam-4554	107	1	{	{	PUNCT
ejpam-4554	107	2	y	y	PROPN
ejpam-4554	107	3	∈	∈	PROPN
ejpam-4554	107	4	h	h	NOUN
ejpam-4554	107	5	|xθy	|xθy	ADV
ejpam-4554	107	6	}	}	PUNCT
ejpam-4554	107	7	.	.	PUNCT
ejpam-4554	108	1	lemma	lemma	PROPN
ejpam-4554	108	2	3.4	3.4	NUM
ejpam-4554	108	3	.	.	PUNCT
ejpam-4554	109	1	let	let	VERB
ejpam-4554	109	2	θ	θ	NOUN
ejpam-4554	109	3	be	be	AUX
ejpam-4554	109	4	an	an	DET
ejpam-4554	109	5	equivalence	equivalence	NOUN
ejpam-4554	109	6	relation	relation	NOUN
ejpam-4554	109	7	on	on	ADP
ejpam-4554	109	8	h	h	NOUN
ejpam-4554	109	9	and	and	CCONJ
ejpam-4554	109	10	a	a	PRON
ejpam-4554	109	11	,	,	PUNCT
ejpam-4554	109	12	b	b	PROPN
ejpam-4554	109	13	⊆	⊆	NUM
ejpam-4554	109	14	h.	h.	NOUN
ejpam-4554	109	15	if	if	SCONJ
ejpam-4554	109	16	aθ̄b	aθ̄b	PRON
ejpam-4554	109	17	and	and	CCONJ
ejpam-4554	109	18	bθ̄c	bθ̄c	ADJ
ejpam-4554	109	19	,	,	PUNCT
ejpam-4554	109	20	then	then	ADV
ejpam-4554	109	21	aθ̄c	aθ̄c	ADJ
ejpam-4554	109	22	.	.	PUNCT
ejpam-4554	110	1	proof	proof	NOUN
ejpam-4554	110	2	.	.	PUNCT
ejpam-4554	111	1	let	let	VERB
ejpam-4554	111	2	a	a	DET
ejpam-4554	111	3	∈	∈	NOUN
ejpam-4554	111	4	a.	a.	NOUN
ejpam-4554	111	5	by	by	ADP
ejpam-4554	111	6	definition	definition	NOUN
ejpam-4554	111	7	3.1(ii	3.1(ii	NUM
ejpam-4554	111	8	)	)	PUNCT
ejpam-4554	111	9	,	,	PUNCT
ejpam-4554	111	10	there	there	PRON
ejpam-4554	111	11	exists	exist	VERB
ejpam-4554	111	12	b	b	PROPN
ejpam-4554	111	13	∈	∈	PROPN
ejpam-4554	111	14	b	b	NOUN
ejpam-4554	111	15	such	such	ADJ
ejpam-4554	111	16	that	that	DET
ejpam-4554	111	17	aθb	aθb	NOUN
ejpam-4554	111	18	.	.	PUNCT
ejpam-4554	112	1	also	also	ADV
ejpam-4554	112	2	,	,	PUNCT
ejpam-4554	112	3	there	there	PRON
ejpam-4554	112	4	exists	exist	VERB
ejpam-4554	112	5	c	c	PROPN
ejpam-4554	112	6	∈	∈	PROPN
ejpam-4554	112	7	c	c	NOUN
ejpam-4554	112	8	such	such	ADJ
ejpam-4554	112	9	that	that	DET
ejpam-4554	112	10	bθc	bθc	NOUN
ejpam-4554	112	11	.	.	PUNCT
ejpam-4554	113	1	by	by	ADP
ejpam-4554	113	2	transitivity	transitivity	NOUN
ejpam-4554	113	3	,	,	PUNCT
ejpam-4554	113	4	aθc	aθc	PROPN
ejpam-4554	113	5	.	.	PUNCT
ejpam-4554	114	1	let	let	VERB
ejpam-4554	114	2	c	c	PROPN
ejpam-4554	114	3	∈	∈	PROPN
ejpam-4554	114	4	c.	c.	NOUN
ejpam-4554	114	5	then	then	ADV
ejpam-4554	114	6	there	there	PRON
ejpam-4554	114	7	exists	exist	VERB
ejpam-4554	114	8	b	b	PROPN
ejpam-4554	114	9	∈	∈	PROPN
ejpam-4554	114	10	b	b	PROPN
ejpam-4554	114	11	such	such	ADJ
ejpam-4554	114	12	that	that	DET
ejpam-4554	114	13	bθc	bθc	NOUN
ejpam-4554	114	14	.	.	PUNCT
ejpam-4554	115	1	but	but	CCONJ
ejpam-4554	115	2	there	there	PRON
ejpam-4554	115	3	exists	exist	VERB
ejpam-4554	115	4	a	a	DET
ejpam-4554	115	5	∈	∈	NOUN
ejpam-4554	115	6	a	a	DET
ejpam-4554	115	7	such	such	ADJ
ejpam-4554	115	8	that	that	DET
ejpam-4554	115	9	aθb	aθb	NOUN
ejpam-4554	115	10	.	.	PUNCT
ejpam-4554	116	1	so	so	ADV
ejpam-4554	116	2	,	,	PUNCT
ejpam-4554	116	3	by	by	ADP
ejpam-4554	116	4	transitivity	transitivity	NOUN
ejpam-4554	116	5	,	,	PUNCT
ejpam-4554	116	6	aθc	aθc	PROPN
ejpam-4554	116	7	.	.	PUNCT
ejpam-4554	117	1	therefore	therefore	ADV
ejpam-4554	117	2	,	,	PUNCT
ejpam-4554	117	3	aθ̄c	aθ̄c	ADJ
ejpam-4554	117	4	.	.	PUNCT
ejpam-4554	118	1	□	□	PUNCT
ejpam-4554	118	2	lemma	lemma	PROPN
ejpam-4554	118	3	3.5	3.5	NUM
ejpam-4554	118	4	.	.	PUNCT
ejpam-4554	119	1	let	let	VERB
ejpam-4554	119	2	θ	θ	NOUN
ejpam-4554	119	3	be	be	AUX
ejpam-4554	119	4	an	an	DET
ejpam-4554	119	5	equivalence	equivalence	NOUN
ejpam-4554	119	6	relation	relation	NOUN
ejpam-4554	119	7	on	on	ADP
ejpam-4554	119	8	h	h	NOUN
ejpam-4554	119	9	such	such	ADJ
ejpam-4554	119	10	that	that	SCONJ
ejpam-4554	119	11	x⊛	x⊛	PROPN
ejpam-4554	119	12	0	0	PUNCT
ejpam-4554	120	1	=	=	SYM
ejpam-4554	120	2	x	x	X
ejpam-4554	120	3	and	and	CCONJ
ejpam-4554	120	4	x⊙	x⊙	PROPN
ejpam-4554	120	5	0	0	SYM
ejpam-4554	120	6	=	=	SYM
ejpam-4554	120	7	x	x	NOUN
ejpam-4554	120	8	,	,	PUNCT
ejpam-4554	120	9	for	for	ADP
ejpam-4554	120	10	all	all	DET
ejpam-4554	120	11	x	x	SYM
ejpam-4554	120	12	∈	∈	PROPN
ejpam-4554	120	13	h.	h.	NOUN
ejpam-4554	120	14	then	then	ADV
ejpam-4554	120	15	the	the	DET
ejpam-4554	120	16	following	follow	VERB
ejpam-4554	120	17	hold	hold	NOUN
ejpam-4554	120	18	:	:	PUNCT
ejpam-4554	120	19	(	(	PUNCT
ejpam-4554	120	20	i	i	NOUN
ejpam-4554	120	21	)	)	PUNCT
ejpam-4554	120	22	if	if	SCONJ
ejpam-4554	120	23	θ	θ	PROPN
ejpam-4554	120	24	is	be	AUX
ejpam-4554	120	25	a	a	DET
ejpam-4554	120	26	left	left	ADJ
ejpam-4554	120	27	⊛-congruence	⊛-congruence	NOUN
ejpam-4554	120	28	(	(	PUNCT
ejpam-4554	120	29	left	leave	VERB
ejpam-4554	120	30	⊙-congruence	⊙-congruence	NOUN
ejpam-4554	120	31	)	)	PUNCT
ejpam-4554	120	32	on	on	ADP
ejpam-4554	120	33	h	h	NOUN
ejpam-4554	120	34	,	,	PUNCT
ejpam-4554	120	35	then	then	ADV
ejpam-4554	120	36	[	[	X
ejpam-4554	120	37	0]θ	0]θ	PRON
ejpam-4554	120	38	is	be	AUX
ejpam-4554	120	39	a	a	DET
ejpam-4554	120	40	pseudo	pseudo	NOUN
ejpam-4554	120	41	hyper	hyper	ADJ
ejpam-4554	120	42	gr	gr	NOUN
ejpam-4554	120	43	-	-	PUNCT
ejpam-4554	120	44	ideal	ideal	NOUN
ejpam-4554	120	45	of	of	ADP
ejpam-4554	120	46	type	type	NOUN
ejpam-4554	120	47	8	8	NUM
ejpam-4554	120	48	.	.	PUNCT
ejpam-4554	120	49	(	(	PUNCT
ejpam-4554	120	50	ii	ii	NOUN
ejpam-4554	120	51	)	)	PUNCT
ejpam-4554	120	52	if	if	SCONJ
ejpam-4554	120	53	θ	θ	PROPN
ejpam-4554	120	54	is	be	AUX
ejpam-4554	120	55	a	a	DET
ejpam-4554	120	56	left	left	ADJ
ejpam-4554	120	57	congruence	congruence	NOUN
ejpam-4554	120	58	on	on	ADP
ejpam-4554	120	59	h	h	NOUN
ejpam-4554	120	60	,	,	PUNCT
ejpam-4554	120	61	then	then	ADV
ejpam-4554	120	62	[	[	X
ejpam-4554	120	63	0]θ	0]θ	PRON
ejpam-4554	120	64	is	be	AUX
ejpam-4554	120	65	a	a	DET
ejpam-4554	120	66	pseudo	pseudo	NOUN
ejpam-4554	120	67	hyper	hyper	ADJ
ejpam-4554	120	68	gr	gr	NOUN
ejpam-4554	120	69	-	-	PUNCT
ejpam-4554	120	70	ideal	ideal	NOUN
ejpam-4554	120	71	of	of	ADP
ejpam-4554	120	72	type	type	NOUN
ejpam-4554	120	73	4	4	NUM
ejpam-4554	120	74	.	.	PUNCT
ejpam-4554	120	75	proof	proof	NOUN
ejpam-4554	120	76	.	.	PUNCT
ejpam-4554	121	1	(	(	PUNCT
ejpam-4554	121	2	i	i	NOUN
ejpam-4554	121	3	)	)	PUNCT
ejpam-4554	121	4	suppose	suppose	VERB
ejpam-4554	121	5	that	that	SCONJ
ejpam-4554	121	6	θ	θ	PROPN
ejpam-4554	121	7	is	be	AUX
ejpam-4554	121	8	a	a	DET
ejpam-4554	121	9	left	left	ADJ
ejpam-4554	121	10	⊛-congruence	⊛-congruence	NOUN
ejpam-4554	121	11	.	.	PUNCT
ejpam-4554	122	1	let	let	VERB
ejpam-4554	122	2	y	y	PRON
ejpam-4554	122	3	∈	∈	PROPN
ejpam-4554	123	1	[	[	X
ejpam-4554	124	1	0]θ	0]θ	X
ejpam-4554	124	2	and	and	CCONJ
ejpam-4554	124	3	x	x	PUNCT
ejpam-4554	124	4	∈	∈	PROPN
ejpam-4554	125	1	[	[	X
ejpam-4554	125	2	0]≪θ⊛,y	0]≪θ⊛,y	NOUN
ejpam-4554	125	3	.	.	PUNCT
ejpam-4554	126	1	then	then	ADV
ejpam-4554	126	2	x⊛	x⊛	PROPN
ejpam-4554	126	3	y	y	PROPN
ejpam-4554	126	4	≪	≪	VERB
ejpam-4554	126	5	[	[	X
ejpam-4554	126	6	0]θ	0]θ	NOUN
ejpam-4554	126	7	.	.	PUNCT
ejpam-4554	127	1	then	then	ADV
ejpam-4554	127	2	for	for	ADP
ejpam-4554	127	3	all	all	DET
ejpam-4554	127	4	a	a	DET
ejpam-4554	127	5	∈	∈	NOUN
ejpam-4554	127	6	x⊛	x⊛	PUNCT
ejpam-4554	127	7	y	y	NOUN
ejpam-4554	127	8	,	,	PUNCT
ejpam-4554	127	9	there	there	PRON
ejpam-4554	127	10	exists	exist	VERB
ejpam-4554	127	11	b	b	PROPN
ejpam-4554	127	12	∈	∈	PROPN
ejpam-4554	128	1	[	[	X
ejpam-4554	128	2	0]θ	0]θ	NUM
ejpam-4554	128	3	such	such	ADJ
ejpam-4554	128	4	that	that	DET
ejpam-4554	128	5	0	0	NUM
ejpam-4554	128	6	∈	∈	PROPN
ejpam-4554	128	7	a⊛	a⊛	PROPN
ejpam-4554	128	8	b.	b.	PROPN
ejpam-4554	128	9	since	since	SCONJ
ejpam-4554	128	10	θ	θ	PROPN
ejpam-4554	128	11	is	be	AUX
ejpam-4554	128	12	a	a	DET
ejpam-4554	128	13	left	left	ADJ
ejpam-4554	128	14	⊛-congruence	⊛-congruence	NOUN
ejpam-4554	128	15	,	,	PUNCT
ejpam-4554	128	16	bθ0	bθ0	VERB
ejpam-4554	128	17	implies	imply	VERB
ejpam-4554	128	18	that	that	SCONJ
ejpam-4554	128	19	(	(	PUNCT
ejpam-4554	128	20	a⊛	a⊛	NOUN
ejpam-4554	128	21	b)θ̄(a⊛	b)θ̄(a⊛	ADJ
ejpam-4554	128	22	0	0	NUM
ejpam-4554	128	23	)	)	PUNCT
ejpam-4554	128	24	and	and	CCONJ
ejpam-4554	128	25	so	so	ADV
ejpam-4554	128	26	(	(	PUNCT
ejpam-4554	128	27	a⊛	a⊛	PROPN
ejpam-4554	128	28	b)θ̄a	b)θ̄a	NOUN
ejpam-4554	128	29	.	.	PUNCT
ejpam-4554	129	1	now	now	ADV
ejpam-4554	129	2	,	,	PUNCT
ejpam-4554	129	3	0	0	NUM
ejpam-4554	129	4	∈	∈	PROPN
ejpam-4554	129	5	a⊛	a⊛	PROPN
ejpam-4554	129	6	b	b	PROPN
ejpam-4554	129	7	and	and	CCONJ
ejpam-4554	129	8	(	(	PUNCT
ejpam-4554	129	9	a⊛b)θ̄a	a⊛b)θ̄a	PROPN
ejpam-4554	129	10	would	would	AUX
ejpam-4554	129	11	imply	imply	VERB
ejpam-4554	129	12	that	that	DET
ejpam-4554	129	13	0θa	0θa	NOUN
ejpam-4554	130	1	and	and	CCONJ
ejpam-4554	131	1	so	so	ADV
ejpam-4554	131	2	x⊛y	x⊛y	PROPN
ejpam-4554	132	1	⊆	⊆	NUM
ejpam-4554	133	1	[	[	X
ejpam-4554	133	2	0]θ	0]θ	NOUN
ejpam-4554	133	3	.	.	PUNCT
ejpam-4554	134	1	since	since	SCONJ
ejpam-4554	134	2	yθ0	yθ0	PROPN
ejpam-4554	134	3	and	and	CCONJ
ejpam-4554	134	4	θ	θ	PROPN
ejpam-4554	134	5	is	be	AUX
ejpam-4554	134	6	a	a	DET
ejpam-4554	134	7	left	left	ADJ
ejpam-4554	134	8	⊛-congruence	⊛-congruence	NOUN
ejpam-4554	134	9	,	,	PUNCT
ejpam-4554	134	10	(	(	PUNCT
ejpam-4554	134	11	x	x	PROPN
ejpam-4554	134	12	⊛	⊛	NUM
ejpam-4554	134	13	y)θ̄(x	y)θ̄(x	PROPN
ejpam-4554	134	14	⊛	⊛	NUM
ejpam-4554	134	15	0	0	NUM
ejpam-4554	134	16	)	)	PUNCT
ejpam-4554	134	17	.	.	PUNCT
ejpam-4554	135	1	thus	thus	ADV
ejpam-4554	135	2	,	,	PUNCT
ejpam-4554	135	3	for	for	ADP
ejpam-4554	135	4	all	all	DET
ejpam-4554	135	5	z	z	NOUN
ejpam-4554	135	6	∈	∈	NOUN
ejpam-4554	135	7	x	x	SYM
ejpam-4554	135	8	⊛	⊛	NUM
ejpam-4554	135	9	y	y	PROPN
ejpam-4554	135	10	,	,	PUNCT
ejpam-4554	135	11	we	we	PRON
ejpam-4554	135	12	have	have	VERB
ejpam-4554	135	13	zθx	zθx	NOUN
ejpam-4554	135	14	.	.	PUNCT
ejpam-4554	136	1	since	since	SCONJ
ejpam-4554	136	2	x	x	PROPN
ejpam-4554	136	3	⊛	⊛	ADV
ejpam-4554	136	4	y	y	PROPN
ejpam-4554	136	5	⊆	⊆	NUM
ejpam-4554	136	6	[	[	X
ejpam-4554	136	7	0]θ	0]θ	NUM
ejpam-4554	136	8	,	,	PUNCT
ejpam-4554	136	9	zθ0	zθ0	PROPN
ejpam-4554	136	10	.	.	PUNCT
ejpam-4554	136	11	by	by	ADP
ejpam-4554	136	12	commutativity	commutativity	NOUN
ejpam-4554	136	13	and	and	CCONJ
ejpam-4554	136	14	transitivity	transitivity	NOUN
ejpam-4554	136	15	,	,	PUNCT
ejpam-4554	136	16	zθ0	zθ0	PROPN
ejpam-4554	136	17	and	and	CCONJ
ejpam-4554	136	18	zθx	zθx	NOUN
ejpam-4554	136	19	means	mean	VERB
ejpam-4554	136	20	that	that	SCONJ
ejpam-4554	136	21	xθ0	xθ0	PROPN
ejpam-4554	136	22	.	.	PUNCT
ejpam-4554	137	1	hence	hence	ADV
ejpam-4554	137	2	,	,	PUNCT
ejpam-4554	137	3	x	x	PUNCT
ejpam-4554	137	4	∈	∈	PROPN
ejpam-4554	138	1	[	[	X
ejpam-4554	138	2	0]θ	0]θ	NOUN
ejpam-4554	138	3	.	.	PUNCT
ejpam-4554	139	1	therefore	therefore	ADV
ejpam-4554	139	2	,	,	PUNCT
ejpam-4554	139	3	[	[	X
ejpam-4554	139	4	0]θ	0]θ	X
ejpam-4554	139	5	is	be	AUX
ejpam-4554	139	6	a	a	DET
ejpam-4554	139	7	pseudo	pseudo	NOUN
ejpam-4554	139	8	hyper	hyper	ADJ
ejpam-4554	139	9	gr	gr	NOUN
ejpam-4554	139	10	-	-	PUNCT
ejpam-4554	139	11	ideal	ideal	NOUN
ejpam-4554	139	12	of	of	ADP
ejpam-4554	139	13	type	type	NOUN
ejpam-4554	139	14	8	8	NUM
ejpam-4554	139	15	.	.	PUNCT
ejpam-4554	140	1	similarly	similarly	ADV
ejpam-4554	140	2	,	,	PUNCT
ejpam-4554	140	3	it	it	PRON
ejpam-4554	140	4	is	be	AUX
ejpam-4554	140	5	easy	easy	ADJ
ejpam-4554	140	6	to	to	PART
ejpam-4554	140	7	show	show	VERB
ejpam-4554	140	8	that	that	SCONJ
ejpam-4554	140	9	[	[	X
ejpam-4554	140	10	0]θ	0]θ	X
ejpam-4554	140	11	is	be	AUX
ejpam-4554	140	12	a	a	DET
ejpam-4554	140	13	pseudo	pseudo	NOUN
ejpam-4554	140	14	hyper	hyper	ADJ
ejpam-4554	140	15	gr	gr	NOUN
ejpam-4554	140	16	-	-	PUNCT
ejpam-4554	140	17	algebra	algebra	NOUN
ejpam-4554	140	18	of	of	ADP
ejpam-4554	140	19	type	type	NOUN
ejpam-4554	140	20	8	8	NUM
ejpam-4554	140	21	for	for	ADP
ejpam-4554	140	22	the	the	DET
ejpam-4554	140	23	case	case	NOUN
ejpam-4554	140	24	of	of	ADP
ejpam-4554	140	25	left	left	ADJ
ejpam-4554	140	26	⊙-congruence	⊙-congruence	NOUN
ejpam-4554	140	27	.	.	PUNCT
ejpam-4554	141	1	(	(	PUNCT
ejpam-4554	141	2	ii	ii	NOUN
ejpam-4554	141	3	)	)	PUNCT
ejpam-4554	141	4	suppose	suppose	VERB
ejpam-4554	141	5	that	that	SCONJ
ejpam-4554	141	6	θ	θ	PROPN
ejpam-4554	141	7	is	be	AUX
ejpam-4554	141	8	a	a	DET
ejpam-4554	141	9	left	left	ADJ
ejpam-4554	141	10	congruence	congruence	NOUN
ejpam-4554	141	11	on	on	ADP
ejpam-4554	141	12	h.	h.	PROPN
ejpam-4554	141	13	let	let	VERB
ejpam-4554	141	14	y	y	PROPN
ejpam-4554	141	15	∈	∈	PROPN
ejpam-4554	142	1	[	[	X
ejpam-4554	143	1	0]θ	0]θ	X
ejpam-4554	143	2	and	and	CCONJ
ejpam-4554	143	3	x	x	PUNCT
ejpam-4554	143	4	∈	∈	PROPN
ejpam-4554	144	1	[	[	X
ejpam-4554	144	2	0]≪θ⊛,y	0]≪θ⊛,y	NOUN
ejpam-4554	144	3	.	.	PUNCT
ejpam-4554	145	1	then	then	ADV
ejpam-4554	145	2	x	x	X
ejpam-4554	145	3	⊛	⊛	NUM
ejpam-4554	145	4	y	y	PROPN
ejpam-4554	145	5	⊆	⊆	NUM
ejpam-4554	145	6	[	[	X
ejpam-4554	145	7	0]θ	0]θ	NOUN
ejpam-4554	145	8	.	.	PUNCT
ejpam-4554	146	1	this	this	PRON
ejpam-4554	146	2	means	mean	VERB
ejpam-4554	146	3	that	that	SCONJ
ejpam-4554	146	4	x	x	PROPN
ejpam-4554	146	5	⊛	⊛	ADV
ejpam-4554	146	6	y	y	PROPN
ejpam-4554	146	7	≪	≪	ADJ
ejpam-4554	146	8	[	[	X
ejpam-4554	146	9	0]θ	0]θ	NUM
ejpam-4554	146	10	.	.	PUNCT
ejpam-4554	147	1	then	then	ADV
ejpam-4554	147	2	for	for	ADP
ejpam-4554	147	3	all	all	DET
ejpam-4554	147	4	a	a	DET
ejpam-4554	147	5	∈	∈	NOUN
ejpam-4554	147	6	x	x	PUNCT
ejpam-4554	147	7	⊛	⊛	NUM
ejpam-4554	147	8	y	y	PROPN
ejpam-4554	147	9	,	,	PUNCT
ejpam-4554	147	10	there	there	PRON
ejpam-4554	147	11	exists	exist	VERB
ejpam-4554	147	12	b	b	PROPN
ejpam-4554	147	13	∈	∈	PROPN
ejpam-4554	148	1	[	[	X
ejpam-4554	148	2	0]θ	0]θ	NUM
ejpam-4554	148	3	such	such	ADJ
ejpam-4554	148	4	that	that	DET
ejpam-4554	148	5	0	0	NUM
ejpam-4554	148	6	∈	∈	PROPN
ejpam-4554	148	7	a	a	DET
ejpam-4554	148	8	⊛	⊛	NUM
ejpam-4554	148	9	b.	b.	NOUN
ejpam-4554	148	10	since	since	SCONJ
ejpam-4554	148	11	θ	θ	PROPN
ejpam-4554	148	12	is	be	AUX
ejpam-4554	148	13	a	a	DET
ejpam-4554	148	14	left	left	ADJ
ejpam-4554	148	15	⊛-congruence	⊛-congruence	NOUN
ejpam-4554	148	16	,	,	PUNCT
ejpam-4554	148	17	bθ0	bθ0	VERB
ejpam-4554	148	18	implies	imply	VERB
ejpam-4554	148	19	that	that	SCONJ
ejpam-4554	148	20	(	(	PUNCT
ejpam-4554	148	21	a⊛	a⊛	NOUN
ejpam-4554	148	22	b)θ̄(a⊛	b)θ̄(a⊛	ADJ
ejpam-4554	148	23	0	0	NUM
ejpam-4554	148	24	)	)	PUNCT
ejpam-4554	148	25	and	and	CCONJ
ejpam-4554	148	26	so	so	ADV
ejpam-4554	148	27	(	(	PUNCT
ejpam-4554	148	28	a⊛	a⊛	PROPN
ejpam-4554	148	29	b)θ̄a	b)θ̄a	NOUN
ejpam-4554	148	30	.	.	PUNCT
ejpam-4554	149	1	now	now	ADV
ejpam-4554	149	2	,	,	PUNCT
ejpam-4554	149	3	0	0	NUM
ejpam-4554	149	4	∈	∈	PROPN
ejpam-4554	149	5	a⊛	a⊛	PROPN
ejpam-4554	149	6	b	b	PROPN
ejpam-4554	149	7	and	and	CCONJ
ejpam-4554	149	8	(	(	PUNCT
ejpam-4554	149	9	a⊛	a⊛	PROPN
ejpam-4554	149	10	b)θ̄a	b)θ̄a	NOUN
ejpam-4554	149	11	would	would	AUX
ejpam-4554	149	12	imply	imply	VERB
ejpam-4554	149	13	that	that	DET
ejpam-4554	149	14	0θa	0θa	NOUN
ejpam-4554	150	1	and	and	CCONJ
ejpam-4554	151	1	so	so	ADV
ejpam-4554	151	2	x	x	PUNCT
ejpam-4554	151	3	⊛	⊛	ADJ
ejpam-4554	151	4	y	y	PROPN
ejpam-4554	151	5	⊆	⊆	NUM
ejpam-4554	151	6	[	[	X
ejpam-4554	151	7	0]θ	0]θ	NOUN
ejpam-4554	151	8	.	.	PUNCT
ejpam-4554	152	1	since	since	SCONJ
ejpam-4554	152	2	yθ0	yθ0	PROPN
ejpam-4554	152	3	and	and	CCONJ
ejpam-4554	152	4	θ	θ	PROPN
ejpam-4554	152	5	is	be	AUX
ejpam-4554	152	6	a	a	DET
ejpam-4554	152	7	left	left	ADJ
ejpam-4554	152	8	⊛-congruence	⊛-congruence	NOUN
ejpam-4554	152	9	,	,	PUNCT
ejpam-4554	152	10	(	(	PUNCT
ejpam-4554	152	11	x	x	PROPN
ejpam-4554	152	12	⊛	⊛	NUM
ejpam-4554	152	13	y)θ̄(x	y)θ̄(x	PROPN
ejpam-4554	152	14	⊛	⊛	NUM
ejpam-4554	152	15	0	0	NUM
ejpam-4554	152	16	)	)	PUNCT
ejpam-4554	152	17	or	or	CCONJ
ejpam-4554	152	18	equivalently	equivalently	ADV
ejpam-4554	152	19	(	(	PUNCT
ejpam-4554	152	20	x⊛	x⊛	PROPN
ejpam-4554	152	21	y)θ̄{x	y)θ̄{x	PROPN
ejpam-4554	152	22	}	}	PUNCT
ejpam-4554	152	23	.	.	PUNCT
ejpam-4554	153	1	thus	thus	ADV
ejpam-4554	153	2	,	,	PUNCT
ejpam-4554	153	3	for	for	ADP
ejpam-4554	153	4	all	all	DET
ejpam-4554	153	5	z	z	NOUN
ejpam-4554	153	6	∈	∈	PROPN
ejpam-4554	153	7	x⊛	x⊛	PROPN
ejpam-4554	153	8	y	y	PROPN
ejpam-4554	153	9	,	,	PUNCT
ejpam-4554	153	10	we	we	PRON
ejpam-4554	153	11	have	have	VERB
ejpam-4554	153	12	zθx	zθx	NOUN
ejpam-4554	153	13	.	.	PUNCT
ejpam-4554	154	1	since	since	SCONJ
ejpam-4554	154	2	x⊛	x⊛	PROPN
ejpam-4554	154	3	y	y	PROPN
ejpam-4554	154	4	⊆	⊆	NUM
ejpam-4554	154	5	[	[	X
ejpam-4554	154	6	0]θ	0]θ	NUM
ejpam-4554	154	7	,	,	PUNCT
ejpam-4554	154	8	zθ0	zθ0	PROPN
ejpam-4554	154	9	.	.	PUNCT
ejpam-4554	154	10	now	now	ADV
ejpam-4554	154	11	,	,	PUNCT
ejpam-4554	154	12	zθ0	zθ0	PROPN
ejpam-4554	154	13	and	and	CCONJ
ejpam-4554	154	14	zθx	zθx	NOUN
ejpam-4554	154	15	mean	mean	VERB
ejpam-4554	154	16	that	that	SCONJ
ejpam-4554	155	1	xθ0	xθ0	PROPN
ejpam-4554	155	2	.	.	PUNCT
ejpam-4554	156	1	hence	hence	ADV
ejpam-4554	156	2	,	,	PUNCT
ejpam-4554	156	3	x	x	PUNCT
ejpam-4554	156	4	∈	∈	PROPN
ejpam-4554	157	1	[	[	X
ejpam-4554	157	2	0]θ	0]θ	NOUN
ejpam-4554	157	3	.	.	PUNCT
ejpam-4554	158	1	similarly	similarly	ADV
ejpam-4554	158	2	,	,	PUNCT
ejpam-4554	158	3	if	if	SCONJ
ejpam-4554	158	4	y	y	PROPN
ejpam-4554	158	5	∈	∈	PROPN
ejpam-4554	159	1	[	[	X
ejpam-4554	159	2	0]θ	0]θ	X
ejpam-4554	159	3	and	and	CCONJ
ejpam-4554	159	4	x	x	PUNCT
ejpam-4554	159	5	∈	∈	PROPN
ejpam-4554	160	1	[	[	X
ejpam-4554	160	2	0]≪θ⊙,y	0]≪θ⊙,y	NOUN
ejpam-4554	160	3	,	,	PUNCT
ejpam-4554	160	4	then	then	ADV
ejpam-4554	160	5	x	x	X
ejpam-4554	160	6	∈	∈	PROPN
ejpam-4554	161	1	[	[	X
ejpam-4554	161	2	0]θ	0]θ	NOUN
ejpam-4554	161	3	.	.	PUNCT
ejpam-4554	162	1	therefore	therefore	ADV
ejpam-4554	162	2	,	,	PUNCT
ejpam-4554	162	3	[	[	X
ejpam-4554	162	4	0]θ	0]θ	X
ejpam-4554	162	5	is	be	AUX
ejpam-4554	162	6	a	a	DET
ejpam-4554	162	7	pseudo	pseudo	NOUN
ejpam-4554	162	8	hyper	hyper	ADJ
ejpam-4554	162	9	gr	gr	NOUN
ejpam-4554	162	10	-	-	PUNCT
ejpam-4554	162	11	ideal	ideal	NOUN
ejpam-4554	162	12	of	of	ADP
ejpam-4554	162	13	type	type	NOUN
ejpam-4554	162	14	4	4	NUM
ejpam-4554	162	15	.	.	PUNCT
ejpam-4554	163	1	□	□	PUNCT
ejpam-4554	163	2	the	the	DET
ejpam-4554	163	3	next	next	ADJ
ejpam-4554	163	4	example	example	NOUN
ejpam-4554	163	5	will	will	AUX
ejpam-4554	163	6	give	give	VERB
ejpam-4554	163	7	us	we	PRON
ejpam-4554	163	8	the	the	DET
ejpam-4554	163	9	idea	idea	NOUN
ejpam-4554	163	10	on	on	ADP
ejpam-4554	163	11	how	how	SCONJ
ejpam-4554	163	12	the	the	DET
ejpam-4554	163	13	quotient	quotient	NOUN
ejpam-4554	163	14	structure	structure	NOUN
ejpam-4554	163	15	on	on	ADP
ejpam-4554	163	16	a	a	DET
ejpam-4554	163	17	pseudo	pseudo	NOUN
ejpam-4554	163	18	hyper	hyper	ADJ
ejpam-4554	163	19	gr	gr	NOUN
ejpam-4554	163	20	-	-	PUNCT
ejpam-4554	163	21	algebra	algebra	NOUN
ejpam-4554	163	22	is	be	AUX
ejpam-4554	163	23	constructed	construct	VERB
ejpam-4554	163	24	.	.	PUNCT
ejpam-4554	163	25	example	example	NOUN
ejpam-4554	163	26	3.6	3.6	NUM
ejpam-4554	163	27	.	.	PUNCT
ejpam-4554	164	1	consider	consider	VERB
ejpam-4554	164	2	the	the	DET
ejpam-4554	164	3	pseudo	pseudo	NOUN
ejpam-4554	164	4	hyper	hyper	ADJ
ejpam-4554	164	5	gr	gr	NOUN
ejpam-4554	164	6	-	-	PUNCT
ejpam-4554	164	7	algebra	algebra	NOUN
ejpam-4554	164	8	h	h	NOUN
ejpam-4554	164	9	=	=	SYM
ejpam-4554	164	10	{	{	PUNCT
ejpam-4554	164	11	0	0	NUM
ejpam-4554	164	12	,	,	PUNCT
ejpam-4554	164	13	1	1	NUM
ejpam-4554	164	14	,	,	PUNCT
ejpam-4554	164	15	2	2	NUM
ejpam-4554	164	16	}	}	PUNCT
ejpam-4554	164	17	in	in	ADP
ejpam-4554	164	18	example	example	NOUN
ejpam-4554	164	19	3.2	3.2	NUM
ejpam-4554	164	20	.	.	PUNCT
ejpam-4554	165	1	the	the	DET
ejpam-4554	165	2	relation	relation	NOUN
ejpam-4554	165	3	θ	θ	PROPN
ejpam-4554	165	4	defined	define	VERB
ejpam-4554	165	5	on	on	ADP
ejpam-4554	165	6	h	h	NOUN
ejpam-4554	165	7	is	be	AUX
ejpam-4554	165	8	a	a	DET
ejpam-4554	165	9	congruence	congruence	NOUN
ejpam-4554	165	10	relation	relation	NOUN
ejpam-4554	165	11	as	as	SCONJ
ejpam-4554	165	12	shown	show	VERB
ejpam-4554	165	13	.	.	PUNCT
ejpam-4554	166	1	moreover	moreover	ADV
ejpam-4554	166	2	,	,	PUNCT
ejpam-4554	166	3	i	i	PRON
ejpam-4554	166	4	=	=	PUNCT
ejpam-4554	167	1	[	[	X
ejpam-4554	167	2	0]θ	0]θ	X
ejpam-4554	167	3	=	=	SYM
ejpam-4554	167	4	{	{	PUNCT
ejpam-4554	167	5	0	0	NUM
ejpam-4554	167	6	,	,	PUNCT
ejpam-4554	167	7	1	1	NUM
ejpam-4554	167	8	}	}	PUNCT
ejpam-4554	167	9	and	and	CCONJ
ejpam-4554	167	10	i2	i2	PROPN
ejpam-4554	167	11	=	=	PUNCT
ejpam-4554	167	12	{	{	PUNCT
ejpam-4554	167	13	2	2	NUM
ejpam-4554	167	14	}	}	PUNCT
ejpam-4554	167	15	.	.	PUNCT
ejpam-4554	168	1	let	let	VERB
ejpam-4554	168	2	h	h	NOUN
ejpam-4554	168	3	/	/	SYM
ejpam-4554	168	4	i	i	PRON
ejpam-4554	168	5	denote	denote	VERB
ejpam-4554	168	6	the	the	DET
ejpam-4554	168	7	set	set	NOUN
ejpam-4554	168	8	of	of	ADP
ejpam-4554	168	9	all	all	DET
ejpam-4554	168	10	congruence	congruence	NOUN
ejpam-4554	168	11	classes	class	NOUN
ejpam-4554	168	12	on	on	ADP
ejpam-4554	168	13	h	h	NOUN
ejpam-4554	168	14	,	,	PUNCT
ejpam-4554	168	15	that	that	ADV
ejpam-4554	168	16	is	is	ADV
ejpam-4554	168	17	,	,	PUNCT
ejpam-4554	168	18	h	h	NOUN
ejpam-4554	168	19	/	/	SYM
ejpam-4554	168	20	i	i	PRON
ejpam-4554	168	21	=	=	PUNCT
ejpam-4554	168	22	{	{	PUNCT
ejpam-4554	168	23	ix	ix	ADP
ejpam-4554	168	24	|x	|x	PROPN
ejpam-4554	168	25	∈	∈	PROPN
ejpam-4554	168	26	h	h	NOUN
ejpam-4554	168	27	}	}	PUNCT
ejpam-4554	168	28	.	.	PUNCT
ejpam-4554	169	1	in	in	ADP
ejpam-4554	169	2	our	our	PRON
ejpam-4554	169	3	case	case	NOUN
ejpam-4554	169	4	,	,	PUNCT
ejpam-4554	169	5	h	h	NOUN
ejpam-4554	169	6	/	/	SYM
ejpam-4554	169	7	i	i	NOUN
ejpam-4554	169	8	=	=	PUNCT
ejpam-4554	169	9	{	{	PUNCT
ejpam-4554	169	10	i	i	PROPN
ejpam-4554	169	11	,	,	PUNCT
ejpam-4554	169	12	i2	i2	PROPN
ejpam-4554	169	13	}	}	PUNCT
ejpam-4554	169	14	.	.	PUNCT
ejpam-4554	170	1	define	define	VERB
ejpam-4554	170	2	hyperoperations	hyperoperation	NOUN
ejpam-4554	170	3	r.	r.	PROPN
ejpam-4554	170	4	manzano	manzano	PROPN
ejpam-4554	170	5	,	,	PUNCT
ejpam-4554	170	6	jr	jr	PROPN
ejpam-4554	170	7	.	.	PROPN
ejpam-4554	170	8	,	,	PUNCT
ejpam-4554	170	9	g.	g.	PROPN
ejpam-4554	170	10	petalcorin	petalcorin	PROPN
ejpam-4554	170	11	,	,	PUNCT
ejpam-4554	170	12	jr	jr	PROPN
ejpam-4554	170	13	.	.	PROPN
ejpam-4554	170	14	/	/	SYM
ejpam-4554	170	15	eur	eur	PROPN
ejpam-4554	170	16	.	.	PUNCT
ejpam-4554	171	1	j.	j.	PROPN
ejpam-4554	171	2	pure	pure	PROPN
ejpam-4554	171	3	appl	appl	PROPN
ejpam-4554	171	4	.	.	PROPN
ejpam-4554	171	5	math	math	PROPN
ejpam-4554	171	6	,	,	PUNCT
ejpam-4554	171	7	15	15	NUM
ejpam-4554	171	8	(	(	PUNCT
ejpam-4554	171	9	4	4	NUM
ejpam-4554	171	10	)	)	PUNCT
ejpam-4554	171	11	(	(	PUNCT
ejpam-4554	171	12	2022	2022	NUM
ejpam-4554	171	13	)	)	PUNCT
ejpam-4554	171	14	,	,	PUNCT
ejpam-4554	171	15	1854	1854	NUM
ejpam-4554	171	16	-	-	SYM
ejpam-4554	171	17	1868	1868	NUM
ejpam-4554	171	18	1860	1860	NUM
ejpam-4554	171	19	⊗	⊗	NUM
ejpam-4554	171	20	and	and	CCONJ
ejpam-4554	171	21	⊚	⊚	VERB
ejpam-4554	171	22	on	on	ADP
ejpam-4554	171	23	h	h	NOUN
ejpam-4554	171	24	/	/	SYM
ejpam-4554	171	25	i	i	PRON
ejpam-4554	171	26	by	by	ADP
ejpam-4554	171	27	ix	ix	PROPN
ejpam-4554	171	28	⊗	⊗	PROPN
ejpam-4554	171	29	iy	iy	PROPN
ejpam-4554	172	1	=	=	PUNCT
ejpam-4554	172	2	{	{	PUNCT
ejpam-4554	172	3	iz	iz	INTJ
ejpam-4554	172	4	|	|	NOUN
ejpam-4554	172	5	z	z	NOUN
ejpam-4554	172	6	∈	∈	PROPN
ejpam-4554	172	7	x	x	SYM
ejpam-4554	172	8	⊛	⊛	NUM
ejpam-4554	172	9	y	y	NOUN
ejpam-4554	172	10	}	}	PUNCT
ejpam-4554	172	11	and	and	CCONJ
ejpam-4554	172	12	ix	ix	ADP
ejpam-4554	172	13	⊚	⊚	PROPN
ejpam-4554	172	14	iy	iy	PROPN
ejpam-4554	172	15	=	=	PUNCT
ejpam-4554	172	16	{	{	PUNCT
ejpam-4554	172	17	iz	iz	INTJ
ejpam-4554	172	18	|	|	NOUN
ejpam-4554	172	19	z	z	NOUN
ejpam-4554	172	20	∈	∈	PROPN
ejpam-4554	173	1	x	x	X
ejpam-4554	173	2	⊙	⊙	PROPN
ejpam-4554	173	3	y	y	PROPN
ejpam-4554	173	4	}	}	PUNCT
ejpam-4554	173	5	and	and	CCONJ
ejpam-4554	173	6	ix	ix	ADP
ejpam-4554	173	7	≪	≪	PROPN
ejpam-4554	173	8	iy	iy	PROPN
ejpam-4554	173	9	⇐	⇐	ADJ
ejpam-4554	173	10	⇒	⇒	PROPN
ejpam-4554	173	11	i0	i0	PROPN
ejpam-4554	173	12	∈	∈	PROPN
ejpam-4554	173	13	ix	ix	ADP
ejpam-4554	173	14	⊛	⊛	PROPN
ejpam-4554	173	15	iy	iy	PROPN
ejpam-4554	173	16	and	and	CCONJ
ejpam-4554	173	17	i0	i0	PROPN
ejpam-4554	173	18	∈	∈	PROPN
ejpam-4554	173	19	ix	ix	PROPN
ejpam-4554	173	20	⊙	⊙	PROPN
ejpam-4554	173	21	iy	iy	PROPN
ejpam-4554	173	22	.	.	PUNCT
ejpam-4554	174	1	thus	thus	ADV
ejpam-4554	174	2	,	,	PUNCT
ejpam-4554	174	3	for	for	ADP
ejpam-4554	174	4	our	our	PRON
ejpam-4554	174	5	case	case	NOUN
ejpam-4554	174	6	,	,	PUNCT
ejpam-4554	174	7	we	we	PRON
ejpam-4554	174	8	have	have	VERB
ejpam-4554	174	9	the	the	DET
ejpam-4554	174	10	following	follow	VERB
ejpam-4554	174	11	cayley	cayley	ADJ
ejpam-4554	174	12	tables	table	NOUN
ejpam-4554	174	13	:	:	PUNCT
ejpam-4554	175	1	⊗	⊗	PROPN
ejpam-4554	175	2	i	i	PROPN
ejpam-4554	175	3	i2	i2	PROPN
ejpam-4554	175	4	i	i	PRON
ejpam-4554	175	5	{	{	PUNCT
ejpam-4554	175	6	i	i	NOUN
ejpam-4554	175	7	}	}	PUNCT
ejpam-4554	175	8	{	{	PUNCT
ejpam-4554	175	9	i	i	PROPN
ejpam-4554	175	10	}	}	PUNCT
ejpam-4554	175	11	i2	i2	PROPN
ejpam-4554	175	12	{	{	PUNCT
ejpam-4554	175	13	i	i	PROPN
ejpam-4554	175	14	,	,	PUNCT
ejpam-4554	175	15	i2	i2	PROPN
ejpam-4554	175	16	}	}	PUNCT
ejpam-4554	175	17	{	{	PUNCT
ejpam-4554	175	18	i	i	PROPN
ejpam-4554	175	19	,	,	PUNCT
ejpam-4554	175	20	i2	i2	PROPN
ejpam-4554	175	21	}	}	PUNCT
ejpam-4554	175	22	⊚	⊚	NOUN
ejpam-4554	175	23	i	i	NOUN
ejpam-4554	175	24	i2	i2	PROPN
ejpam-4554	175	25	i	i	PRON
ejpam-4554	175	26	{	{	PUNCT
ejpam-4554	175	27	i	i	NOUN
ejpam-4554	175	28	}	}	PUNCT
ejpam-4554	175	29	{	{	PUNCT
ejpam-4554	175	30	i	i	PROPN
ejpam-4554	175	31	,	,	PUNCT
ejpam-4554	175	32	i2	i2	PROPN
ejpam-4554	175	33	}	}	PUNCT
ejpam-4554	175	34	i2	i2	PROPN
ejpam-4554	175	35	{	{	PUNCT
ejpam-4554	175	36	i	i	PROPN
ejpam-4554	175	37	,	,	PUNCT
ejpam-4554	175	38	i2	i2	PROPN
ejpam-4554	175	39	}	}	PUNCT
ejpam-4554	175	40	{	{	PUNCT
ejpam-4554	175	41	i	i	PROPN
ejpam-4554	175	42	,	,	PUNCT
ejpam-4554	175	43	i2	i2	PROPN
ejpam-4554	175	44	}	}	PUNCT
ejpam-4554	175	45	by	by	ADP
ejpam-4554	175	46	routine	routine	ADJ
ejpam-4554	175	47	calculations	calculation	NOUN
ejpam-4554	175	48	,	,	PUNCT
ejpam-4554	175	49	(	(	PUNCT
ejpam-4554	175	50	h	h	NOUN
ejpam-4554	175	51	/	/	SYM
ejpam-4554	175	52	i;⊗,⊚	i;⊗,⊚	PROPN
ejpam-4554	175	53	,	,	PUNCT
ejpam-4554	175	54	i	i	PROPN
ejpam-4554	175	55	)	)	PUNCT
ejpam-4554	175	56	is	be	AUX
ejpam-4554	175	57	a	a	DET
ejpam-4554	175	58	pseudo	pseudo	NOUN
ejpam-4554	175	59	hyper	hyper	ADJ
ejpam-4554	175	60	gr	gr	NOUN
ejpam-4554	175	61	-	-	NOUN
ejpam-4554	175	62	algebra	algebra	NOUN
ejpam-4554	175	63	.	.	PUNCT
ejpam-4554	176	1	lemma	lemma	PROPN
ejpam-4554	176	2	3.7	3.7	NUM
ejpam-4554	176	3	.	.	PUNCT
ejpam-4554	177	1	let	let	VERB
ejpam-4554	177	2	θ	θ	NOUN
ejpam-4554	177	3	be	be	AUX
ejpam-4554	177	4	a	a	DET
ejpam-4554	177	5	congruence	congruence	NOUN
ejpam-4554	177	6	relation	relation	NOUN
ejpam-4554	177	7	on	on	ADP
ejpam-4554	177	8	a	a	DET
ejpam-4554	177	9	pseudo	pseudo	NOUN
ejpam-4554	177	10	hyper	hyper	ADJ
ejpam-4554	177	11	gr	gr	NOUN
ejpam-4554	177	12	-	-	PUNCT
ejpam-4554	177	13	algebra	algebra	NOUN
ejpam-4554	177	14	h	h	NOUN
ejpam-4554	177	15	such	such	ADJ
ejpam-4554	177	16	that	that	PRON
ejpam-4554	177	17	xθx′	xθx′	PROPN
ejpam-4554	177	18	and	and	CCONJ
ejpam-4554	177	19	yθy′.	yθy′.	PROPN
ejpam-4554	177	20	then	then	ADV
ejpam-4554	177	21	(	(	PUNCT
ejpam-4554	177	22	x⊛	x⊛	PROPN
ejpam-4554	177	23	y)θ(x′	y)θ(x′	X
ejpam-4554	177	24	⊛	⊛	NUM
ejpam-4554	177	25	y′	y′	NUM
ejpam-4554	177	26	)	)	PUNCT
ejpam-4554	177	27	and	and	CCONJ
ejpam-4554	177	28	(	(	PUNCT
ejpam-4554	177	29	x⊙	x⊙	PROPN
ejpam-4554	177	30	y)θ(x′	y)θ(x′	PROPN
ejpam-4554	177	31	⊙	⊙	PROPN
ejpam-4554	177	32	y′	y′	NUM
ejpam-4554	177	33	)	)	PUNCT
ejpam-4554	177	34	.	.	PUNCT
ejpam-4554	178	1	proof	proof	NOUN
ejpam-4554	178	2	.	.	PUNCT
ejpam-4554	179	1	suppose	suppose	VERB
ejpam-4554	179	2	that	that	SCONJ
ejpam-4554	179	3	θ	θ	PROPN
ejpam-4554	179	4	is	be	AUX
ejpam-4554	179	5	a	a	DET
ejpam-4554	179	6	congruence	congruence	NOUN
ejpam-4554	179	7	relation	relation	NOUN
ejpam-4554	179	8	such	such	ADJ
ejpam-4554	179	9	that	that	PRON
ejpam-4554	179	10	xθx′	xθx′	PROPN
ejpam-4554	179	11	and	and	CCONJ
ejpam-4554	179	12	yθy′.	yθy′.	PROPN
ejpam-4554	179	13	then	then	ADV
ejpam-4554	179	14	ix	ix	ADV
ejpam-4554	179	15	=	=	PUNCT
ejpam-4554	179	16	ix′	ix′	PROPN
ejpam-4554	179	17	and	and	CCONJ
ejpam-4554	179	18	iy	iy	NOUN
ejpam-4554	179	19	=	=	PUNCT
ejpam-4554	179	20	iy′	iy′	NOUN
ejpam-4554	179	21	.	.	PUNCT
ejpam-4554	180	1	let	let	VERB
ejpam-4554	180	2	z	z	NOUN
ejpam-4554	180	3	∈	∈	PROPN
ejpam-4554	180	4	x	x	PUNCT
ejpam-4554	180	5	⊛	⊛	NUM
ejpam-4554	180	6	y.	y.	NOUN
ejpam-4554	181	1	then	then	ADV
ejpam-4554	181	2	iz	iz	INTJ
ejpam-4554	181	3	∈	∈	PROPN
ejpam-4554	181	4	ix	ix	ADP
ejpam-4554	181	5	⊗	⊗	PROPN
ejpam-4554	181	6	iy	iy	PROPN
ejpam-4554	182	1	=	=	PUNCT
ejpam-4554	182	2	ix′	ix′	PROPN
ejpam-4554	182	3	⊗	⊗	ADJ
ejpam-4554	182	4	iy′	iy′	NOUN
ejpam-4554	182	5	.	.	PUNCT
ejpam-4554	183	1	thus	thus	ADV
ejpam-4554	183	2	,	,	PUNCT
ejpam-4554	183	3	iz	iz	ADP
ejpam-4554	183	4	∈	∈	PROPN
ejpam-4554	183	5	ix′	ix′	X
ejpam-4554	183	6	⊗	⊗	ADJ
ejpam-4554	183	7	iy′	iy′	NOUN
ejpam-4554	183	8	.	.	PUNCT
ejpam-4554	184	1	this	this	PRON
ejpam-4554	184	2	means	mean	VERB
ejpam-4554	184	3	that	that	SCONJ
ejpam-4554	184	4	z	z	PROPN
ejpam-4554	184	5	∈	∈	PROPN
ejpam-4554	184	6	x′	x′	PROPN
ejpam-4554	184	7	⊛	⊛	NUM
ejpam-4554	184	8	y′.	y′.	NOUN
ejpam-4554	184	9	hence	hence	ADV
ejpam-4554	184	10	,	,	PUNCT
ejpam-4554	184	11	(	(	PUNCT
ejpam-4554	184	12	x⊛	x⊛	PROPN
ejpam-4554	184	13	y)θ(x′	y)θ(x′	X
ejpam-4554	184	14	⊛	⊛	ADJ
ejpam-4554	184	15	y′	y′	NUM
ejpam-4554	184	16	)	)	PUNCT
ejpam-4554	184	17	.	.	PUNCT
ejpam-4554	185	1	similarly	similarly	ADV
ejpam-4554	185	2	,	,	PUNCT
ejpam-4554	185	3	we	we	PRON
ejpam-4554	185	4	can	can	AUX
ejpam-4554	185	5	show	show	VERB
ejpam-4554	185	6	that	that	SCONJ
ejpam-4554	185	7	(	(	PUNCT
ejpam-4554	185	8	x⊙	x⊙	PROPN
ejpam-4554	185	9	y)θ(x′	y)θ(x′	PROPN
ejpam-4554	185	10	⊙	⊙	PROPN
ejpam-4554	185	11	y′	y′	NUM
ejpam-4554	185	12	)	)	PUNCT
ejpam-4554	185	13	.	.	PUNCT
ejpam-4554	186	1	□	□	PUNCT
ejpam-4554	186	2	we	we	PRON
ejpam-4554	186	3	will	will	AUX
ejpam-4554	186	4	now	now	ADV
ejpam-4554	186	5	show	show	VERB
ejpam-4554	186	6	in	in	ADP
ejpam-4554	186	7	general	general	ADJ
ejpam-4554	186	8	that	that	SCONJ
ejpam-4554	186	9	using	use	VERB
ejpam-4554	186	10	congruence	congruence	PROPN
ejpam-4554	186	11	relation	relation	NOUN
ejpam-4554	186	12	,	,	PUNCT
ejpam-4554	186	13	the	the	DET
ejpam-4554	186	14	quotient	quotient	NOUN
ejpam-4554	186	15	structure	structure	NOUN
ejpam-4554	186	16	obtained	obtain	VERB
ejpam-4554	186	17	is	be	AUX
ejpam-4554	186	18	a	a	DET
ejpam-4554	186	19	pseudo	pseudo	NOUN
ejpam-4554	186	20	hyper	hyper	ADJ
ejpam-4554	186	21	gr	gr	NOUN
ejpam-4554	186	22	-	-	PUNCT
ejpam-4554	186	23	algebra	algebra	NOUN
ejpam-4554	186	24	.	.	PUNCT
ejpam-4554	187	1	theorem	theorem	VERB
ejpam-4554	187	2	3.8	3.8	NUM
ejpam-4554	187	3	.	.	PUNCT
ejpam-4554	188	1	let	let	VERB
ejpam-4554	188	2	θ	θ	NOUN
ejpam-4554	188	3	be	be	AUX
ejpam-4554	188	4	a	a	DET
ejpam-4554	188	5	congruence	congruence	NOUN
ejpam-4554	188	6	relation	relation	NOUN
ejpam-4554	188	7	on	on	ADP
ejpam-4554	188	8	a	a	DET
ejpam-4554	188	9	pseudo	pseudo	NOUN
ejpam-4554	188	10	hyper	hyper	ADJ
ejpam-4554	188	11	gr	gr	NOUN
ejpam-4554	188	12	-	-	PUNCT
ejpam-4554	188	13	algebra	algebra	NOUN
ejpam-4554	188	14	h	h	NOUN
ejpam-4554	189	1	such	such	ADJ
ejpam-4554	189	2	that	that	SCONJ
ejpam-4554	189	3	i	i	PRON
ejpam-4554	189	4	=	=	PUNCT
ejpam-4554	190	1	[	[	X
ejpam-4554	190	2	0]θ	0]θ	X
ejpam-4554	190	3	and	and	CCONJ
ejpam-4554	190	4	h	h	NOUN
ejpam-4554	190	5	/	/	SYM
ejpam-4554	190	6	i	i	PRON
ejpam-4554	190	7	=	=	PUNCT
ejpam-4554	190	8	{	{	PUNCT
ejpam-4554	190	9	ix	ix	ADP
ejpam-4554	190	10	|x	|x	PROPN
ejpam-4554	190	11	∈	∈	PROPN
ejpam-4554	190	12	h	h	NOUN
ejpam-4554	190	13	}	}	PUNCT
ejpam-4554	190	14	,	,	PUNCT
ejpam-4554	190	15	where	where	SCONJ
ejpam-4554	190	16	ix	ix	ADV
ejpam-4554	190	17	=	=	PUNCT
ejpam-4554	191	1	[	[	X
ejpam-4554	191	2	x]θ	x]θ	ADV
ejpam-4554	191	3	for	for	ADP
ejpam-4554	191	4	all	all	DET
ejpam-4554	191	5	x	x	SYM
ejpam-4554	191	6	∈	∈	PROPN
ejpam-4554	191	7	h.	h.	NOUN
ejpam-4554	191	8	then	then	ADV
ejpam-4554	191	9	h	h	X
ejpam-4554	191	10	/	/	SYM
ejpam-4554	191	11	i	i	PRON
ejpam-4554	191	12	with	with	ADP
ejpam-4554	191	13	hyperoperations	hyperoperation	NOUN
ejpam-4554	191	14	⊗	⊗	ADJ
ejpam-4554	191	15	and	and	CCONJ
ejpam-4554	191	16	⊚	⊚	NUM
ejpam-4554	191	17	,	,	PUNCT
ejpam-4554	191	18	and	and	CCONJ
ejpam-4554	191	19	hyperorder	hyperorder	NOUN
ejpam-4554	191	20	≪	≪	PUNCT
ejpam-4554	191	21	which	which	PRON
ejpam-4554	191	22	are	be	AUX
ejpam-4554	191	23	defined	define	VERB
ejpam-4554	191	24	as	as	SCONJ
ejpam-4554	191	25	follows	follow	VERB
ejpam-4554	191	26	:	:	PUNCT
ejpam-4554	191	27	ix	ix	PROPN
ejpam-4554	192	1	⊗	⊗	PROPN
ejpam-4554	192	2	iy	iy	PROPN
ejpam-4554	193	1	=	=	PUNCT
ejpam-4554	194	1	{	{	PUNCT
ejpam-4554	195	1	iz	iz	INTJ
ejpam-4554	195	2	|	|	NOUN
ejpam-4554	195	3	z	z	NOUN
ejpam-4554	195	4	∈	∈	PROPN
ejpam-4554	195	5	x⊛	x⊛	PROPN
ejpam-4554	196	1	y	y	NOUN
ejpam-4554	196	2	}	}	PUNCT
ejpam-4554	196	3	and	and	CCONJ
ejpam-4554	196	4	ix	ix	ADP
ejpam-4554	196	5	⊚	⊚	PROPN
ejpam-4554	196	6	iy	iy	PROPN
ejpam-4554	197	1	=	=	PUNCT
ejpam-4554	197	2	{	{	PUNCT
ejpam-4554	197	3	iz	iz	INTJ
ejpam-4554	197	4	|	|	NOUN
ejpam-4554	197	5	z	z	PROPN
ejpam-4554	197	6	∈	∈	PROPN
ejpam-4554	197	7	x⊙	x⊙	PROPN
ejpam-4554	197	8	y	y	PROPN
ejpam-4554	197	9	}	}	PUNCT
ejpam-4554	197	10	,	,	PUNCT
ejpam-4554	197	11	and	and	CCONJ
ejpam-4554	197	12	ix	ix	ADP
ejpam-4554	197	13	≪	≪	PROPN
ejpam-4554	197	14	iy	iy	PROPN
ejpam-4554	197	15	⇐	⇐	ADJ
ejpam-4554	197	16	⇒	⇒	PROPN
ejpam-4554	197	17	i0	i0	PROPN
ejpam-4554	197	18	∈	∈	PROPN
ejpam-4554	197	19	ix	ix	ADP
ejpam-4554	197	20	⊗	⊗	PROPN
ejpam-4554	197	21	iy	iy	PROPN
ejpam-4554	197	22	and	and	CCONJ
ejpam-4554	197	23	i0	i0	PROPN
ejpam-4554	197	24	∈	∈	PROPN
ejpam-4554	197	25	ix	ix	ADP
ejpam-4554	197	26	⊚	⊚	PROPN
ejpam-4554	197	27	iy	iy	PROPN
ejpam-4554	197	28	.	.	PUNCT
ejpam-4554	197	29	is	be	AUX
ejpam-4554	197	30	a	a	DET
ejpam-4554	197	31	pseudo	pseudo	NOUN
ejpam-4554	197	32	hyper	hyper	ADJ
ejpam-4554	197	33	gr	gr	NOUN
ejpam-4554	197	34	-	-	PUNCT
ejpam-4554	197	35	algebra	algebra	NOUN
ejpam-4554	197	36	which	which	PRON
ejpam-4554	197	37	we	we	PRON
ejpam-4554	197	38	call	call	VERB
ejpam-4554	197	39	the	the	DET
ejpam-4554	197	40	quotient	quotient	NOUN
ejpam-4554	197	41	pseudo	pseudo	NOUN
ejpam-4554	197	42	hyper	hyper	ADJ
ejpam-4554	197	43	gr	gr	NOUN
ejpam-4554	197	44	-	-	PUNCT
ejpam-4554	197	45	algebra	algebra	NOUN
ejpam-4554	197	46	.	.	PUNCT
ejpam-4554	198	1	proof	proof	NOUN
ejpam-4554	198	2	.	.	PUNCT
ejpam-4554	199	1	let	let	VERB
ejpam-4554	199	2	us	we	PRON
ejpam-4554	199	3	show	show	VERB
ejpam-4554	199	4	first	first	ADV
ejpam-4554	199	5	that	that	SCONJ
ejpam-4554	199	6	the	the	DET
ejpam-4554	199	7	hyperoperations	hyperoperation	NOUN
ejpam-4554	199	8	⊗	⊗	ADJ
ejpam-4554	199	9	and	and	CCONJ
ejpam-4554	199	10	⊚	⊚	VERB
ejpam-4554	199	11	on	on	ADP
ejpam-4554	199	12	h	h	PROPN
ejpam-4554	199	13	/	/	SYM
ejpam-4554	199	14	i	i	PRON
ejpam-4554	199	15	are	be	AUX
ejpam-4554	199	16	well	well	ADV
ejpam-4554	199	17	-	-	PUNCT
ejpam-4554	199	18	defined	define	VERB
ejpam-4554	199	19	.	.	PUNCT
ejpam-4554	200	1	suppose	suppose	VERB
ejpam-4554	200	2	that	that	SCONJ
ejpam-4554	200	3	x	x	PROPN
ejpam-4554	200	4	,	,	PUNCT
ejpam-4554	200	5	y	y	PROPN
ejpam-4554	200	6	,	,	PUNCT
ejpam-4554	200	7	x′	x′	NUM
ejpam-4554	200	8	,	,	PUNCT
ejpam-4554	200	9	y′	y′	NOUN
ejpam-4554	200	10	∈	∈	PROPN
ejpam-4554	200	11	h	h	NOUN
ejpam-4554	200	12	such	such	ADJ
ejpam-4554	200	13	that	that	SCONJ
ejpam-4554	200	14	ix	ix	ADV
ejpam-4554	200	15	=	=	PUNCT
ejpam-4554	200	16	ix′	ix′	PROPN
ejpam-4554	200	17	and	and	CCONJ
ejpam-4554	200	18	iy	iy	NOUN
ejpam-4554	200	19	=	=	PUNCT
ejpam-4554	200	20	iy′	iy′	NOUN
ejpam-4554	200	21	.	.	PUNCT
ejpam-4554	201	1	let	let	VERB
ejpam-4554	201	2	iz	iz	INTJ
ejpam-4554	201	3	∈	∈	PROPN
ejpam-4554	201	4	ix	ix	ADP
ejpam-4554	201	5	⊗	⊗	PROPN
ejpam-4554	201	6	iy	iy	PROPN
ejpam-4554	201	7	.	.	PUNCT
ejpam-4554	202	1	then	then	ADV
ejpam-4554	202	2	there	there	PRON
ejpam-4554	202	3	exists	exist	VERB
ejpam-4554	202	4	u	u	NOUN
ejpam-4554	202	5	∈	∈	PROPN
ejpam-4554	202	6	x	x	X
ejpam-4554	202	7	⊛	⊛	ADP
ejpam-4554	202	8	y	y	NUM
ejpam-4554	202	9	such	such	ADJ
ejpam-4554	202	10	that	that	SCONJ
ejpam-4554	202	11	iu	iu	ADP
ejpam-4554	202	12	=	=	SYM
ejpam-4554	202	13	iz	iz	INTJ
ejpam-4554	202	14	.	.	PUNCT
ejpam-4554	203	1	since	since	SCONJ
ejpam-4554	203	2	xθx′	xθx′	PROPN
ejpam-4554	203	3	and	and	CCONJ
ejpam-4554	203	4	yθy′	yθy′	NUM
ejpam-4554	203	5	,	,	PUNCT
ejpam-4554	203	6	and	and	CCONJ
ejpam-4554	203	7	θ	θ	PROPN
ejpam-4554	203	8	is	be	AUX
ejpam-4554	203	9	a	a	DET
ejpam-4554	203	10	congruence	congruence	NOUN
ejpam-4554	203	11	on	on	ADP
ejpam-4554	203	12	h	h	NOUN
ejpam-4554	203	13	,	,	PUNCT
ejpam-4554	203	14	by	by	ADP
ejpam-4554	203	15	lemma	lemma	PROPN
ejpam-4554	203	16	3.7	3.7	NUM
ejpam-4554	203	17	,	,	PUNCT
ejpam-4554	203	18	(	(	PUNCT
ejpam-4554	203	19	x	x	PROPN
ejpam-4554	203	20	⊛	⊛	NUM
ejpam-4554	203	21	y)θ(x′θy′	y)θ(x′θy′	NUM
ejpam-4554	203	22	)	)	PUNCT
ejpam-4554	203	23	.	.	PUNCT
ejpam-4554	204	1	hence	hence	ADV
ejpam-4554	204	2	,	,	PUNCT
ejpam-4554	204	3	there	there	PRON
ejpam-4554	204	4	exists	exist	VERB
ejpam-4554	204	5	z′	z′	NUM
ejpam-4554	204	6	∈	∈	PROPN
ejpam-4554	204	7	x′	x′	PROPN
ejpam-4554	204	8	⊛	⊛	NUM
ejpam-4554	204	9	y′	y′	NOUN
ejpam-4554	204	10	such	such	ADJ
ejpam-4554	204	11	that	that	SCONJ
ejpam-4554	204	12	uθz′	uθz′	PROPN
ejpam-4554	204	13	and	and	CCONJ
ejpam-4554	204	14	thus	thus	ADV
ejpam-4554	204	15	,	,	PUNCT
ejpam-4554	204	16	iz′	iz′	PROPN
ejpam-4554	204	17	=	=	PRON
ejpam-4554	204	18	iu	iu	PROPN
ejpam-4554	204	19	.	.	PUNCT
ejpam-4554	204	20	since	since	SCONJ
ejpam-4554	204	21	iz′	iz′	PROPN
ejpam-4554	204	22	∈	∈	PROPN
ejpam-4554	204	23	ix′	ix′	X
ejpam-4554	204	24	⊗	⊗	ADJ
ejpam-4554	204	25	iy′	iy′	NOUN
ejpam-4554	205	1	and	and	CCONJ
ejpam-4554	205	2	iz	iz	INTJ
ejpam-4554	205	3	=	=	VERB
ejpam-4554	205	4	iu	iu	ADP
ejpam-4554	205	5	=	=	PUNCT
ejpam-4554	205	6	iz′	iz′	ADV
ejpam-4554	205	7	,	,	PUNCT
ejpam-4554	205	8	we	we	PRON
ejpam-4554	205	9	have	have	VERB
ejpam-4554	205	10	iz	iz	ADP
ejpam-4554	205	11	∈	∈	PROPN
ejpam-4554	205	12	ix′	ix′	X
ejpam-4554	205	13	⊗	⊗	ADJ
ejpam-4554	205	14	iy′	iy′	NOUN
ejpam-4554	205	15	.	.	PUNCT
ejpam-4554	206	1	thus	thus	ADV
ejpam-4554	206	2	,	,	PUNCT
ejpam-4554	206	3	ix⊗iy	ix⊗iy	NOUN
ejpam-4554	206	4	⊆	⊆	NUM
ejpam-4554	206	5	ix′⊗iy′	ix′⊗iy′	NOUN
ejpam-4554	206	6	.	.	PUNCT
ejpam-4554	207	1	similarly	similarly	ADV
ejpam-4554	207	2	,	,	PUNCT
ejpam-4554	207	3	we	we	PRON
ejpam-4554	207	4	can	can	AUX
ejpam-4554	207	5	show	show	VERB
ejpam-4554	207	6	that	that	SCONJ
ejpam-4554	207	7	ix′⊗iy′	ix′⊗iy′	PROPN
ejpam-4554	207	8	⊆	⊆	NUM
ejpam-4554	207	9	ix⊗iy	ix⊗iy	NOUN
ejpam-4554	207	10	.	.	PUNCT
ejpam-4554	208	1	hence	hence	ADV
ejpam-4554	208	2	,	,	PUNCT
ejpam-4554	208	3	ix⊗iy	ix⊗iy	NOUN
ejpam-4554	208	4	=	=	PUNCT
ejpam-4554	208	5	ix′⊗iy′	ix′⊗iy′	PROPN
ejpam-4554	208	6	.	.	PUNCT
ejpam-4554	209	1	therefore	therefore	ADV
ejpam-4554	209	2	,	,	PUNCT
ejpam-4554	209	3	the	the	DET
ejpam-4554	209	4	hyperoperation	hyperoperation	NOUN
ejpam-4554	209	5	“	"	PUNCT
ejpam-4554	209	6	⊗	⊗	PROPN
ejpam-4554	209	7	”	"	PUNCT
ejpam-4554	209	8	is	be	AUX
ejpam-4554	209	9	well	well	ADV
ejpam-4554	209	10	-	-	PUNCT
ejpam-4554	209	11	defined	define	VERB
ejpam-4554	209	12	.	.	PUNCT
ejpam-4554	210	1	similarly	similarly	ADV
ejpam-4554	210	2	,	,	PUNCT
ejpam-4554	210	3	we	we	PRON
ejpam-4554	210	4	can	can	AUX
ejpam-4554	210	5	show	show	VERB
ejpam-4554	210	6	that	that	SCONJ
ejpam-4554	210	7	ix	ix	PROPN
ejpam-4554	210	8	⊚	⊚	PROPN
ejpam-4554	210	9	iy	iy	X
ejpam-4554	210	10	=	=	PUNCT
ejpam-4554	211	1	ix′	ix′	X
ejpam-4554	211	2	⊚	⊚	NOUN
ejpam-4554	211	3	iy′	iy′	NOUN
ejpam-4554	211	4	so	so	SCONJ
ejpam-4554	211	5	that	that	SCONJ
ejpam-4554	211	6	“	"	PUNCT
ejpam-4554	211	7	⊚	⊚	PROPN
ejpam-4554	211	8	”	"	PUNCT
ejpam-4554	211	9	is	be	AUX
ejpam-4554	211	10	also	also	ADV
ejpam-4554	211	11	well	well	ADV
ejpam-4554	211	12	-	-	PUNCT
ejpam-4554	211	13	defined	define	VERB
ejpam-4554	211	14	.	.	PUNCT
ejpam-4554	212	1	now	now	ADV
ejpam-4554	212	2	,	,	PUNCT
ejpam-4554	212	3	since	since	SCONJ
ejpam-4554	212	4	h	h	NOUN
ejpam-4554	212	5	is	be	AUX
ejpam-4554	212	6	a	a	DET
ejpam-4554	212	7	pseudo	pseudo	NOUN
ejpam-4554	212	8	hyper	hyper	ADJ
ejpam-4554	212	9	gr	gr	NOUN
ejpam-4554	212	10	-	-	PUNCT
ejpam-4554	212	11	algebra	algebra	NOUN
ejpam-4554	212	12	,	,	PUNCT
ejpam-4554	212	13	0	0	NUM
ejpam-4554	212	14	∈	∈	PROPN
ejpam-4554	212	15	h	h	NOUN
ejpam-4554	212	16	and	and	CCONJ
ejpam-4554	212	17	so	so	ADV
ejpam-4554	212	18	,	,	PUNCT
ejpam-4554	212	19	i0	i0	PROPN
ejpam-4554	212	20	=	=	PUNCT
ejpam-4554	213	1	[	[	X
ejpam-4554	213	2	0]θ	0]θ	X
ejpam-4554	213	3	=	=	PUNCT
ejpam-4554	213	4	i	i	PRON
ejpam-4554	213	5	∈	∈	PROPN
ejpam-4554	213	6	h	h	NOUN
ejpam-4554	213	7	/	/	SYM
ejpam-4554	213	8	i.	i.	PROPN
ejpam-4554	213	9	hence	hence	ADV
ejpam-4554	213	10	,	,	PUNCT
ejpam-4554	213	11	h	h	PROPN
ejpam-4554	213	12	/	/	SYM
ejpam-4554	214	1	i	i	PRON
ejpam-4554	214	2	is	be	AUX
ejpam-4554	214	3	nonempty	nonempty	ADJ
ejpam-4554	215	1	and	and	CCONJ
ejpam-4554	215	2	i	i	NOUN
ejpam-4554	215	3	∈	∈	PROPN
ejpam-4554	215	4	h	h	PROPN
ejpam-4554	215	5	/	/	SYM
ejpam-4554	215	6	i.	i.	NOUN
ejpam-4554	215	7	it	it	PRON
ejpam-4554	215	8	remains	remain	VERB
ejpam-4554	215	9	to	to	PART
ejpam-4554	215	10	show	show	VERB
ejpam-4554	215	11	that	that	SCONJ
ejpam-4554	215	12	h	h	NOUN
ejpam-4554	215	13	/	/	SYM
ejpam-4554	215	14	i	i	PRON
ejpam-4554	215	15	satisfies	satisfy	VERB
ejpam-4554	215	16	all	all	DET
ejpam-4554	215	17	the	the	DET
ejpam-4554	215	18	axioms	axiom	NOUN
ejpam-4554	215	19	of	of	ADP
ejpam-4554	215	20	a	a	DET
ejpam-4554	215	21	pseudo	pseudo	NOUN
ejpam-4554	215	22	hyper	hyper	ADJ
ejpam-4554	215	23	gr	gr	NOUN
ejpam-4554	215	24	-	-	NOUN
ejpam-4554	215	25	algebra	algebra	NOUN
ejpam-4554	215	26	.	.	PUNCT
ejpam-4554	216	1	[	[	X
ejpam-4554	216	2	phgr1	phgr1	X
ejpam-4554	216	3	]	]	AUX
ejpam-4554	216	4	let	let	VERB
ejpam-4554	216	5	iw	iw	PRON
ejpam-4554	216	6	∈	∈	PROPN
ejpam-4554	216	7	(	(	PUNCT
ejpam-4554	216	8	ix	ix	INTJ
ejpam-4554	216	9	⊚	⊚	PROPN
ejpam-4554	216	10	iz	iz	NOUN
ejpam-4554	216	11	)	)	PUNCT
ejpam-4554	216	12	⊚	⊚	PROPN
ejpam-4554	216	13	(	(	PUNCT
ejpam-4554	216	14	iy	iy	INTJ
ejpam-4554	216	15	⊚	⊚	PROPN
ejpam-4554	216	16	iz	iz	PROPN
ejpam-4554	216	17	)	)	PUNCT
ejpam-4554	216	18	,	,	PUNCT
ejpam-4554	216	19	for	for	ADP
ejpam-4554	216	20	some	some	DET
ejpam-4554	216	21	ix	ix	PROPN
ejpam-4554	216	22	,	,	PUNCT
ejpam-4554	216	23	iy	iy	INTJ
ejpam-4554	216	24	,	,	PUNCT
ejpam-4554	216	25	iz	iz	INTJ
ejpam-4554	216	26	∈	∈	PROPN
ejpam-4554	216	27	h	h	PROPN
ejpam-4554	216	28	/	/	SYM
ejpam-4554	216	29	i.	i.	NOUN
ejpam-4554	216	30	then	then	ADV
ejpam-4554	216	31	there	there	PRON
ejpam-4554	216	32	are	be	VERB
ejpam-4554	216	33	iu	iu	ADP
ejpam-4554	216	34	∈	∈	NOUN
ejpam-4554	216	35	ix⊚	ix⊚	NOUN
ejpam-4554	216	36	iz	iz	INTJ
ejpam-4554	217	1	and	and	CCONJ
ejpam-4554	217	2	iv	iv	NUM
ejpam-4554	217	3	∈	∈	PROPN
ejpam-4554	217	4	iy	iy	INTJ
ejpam-4554	217	5	⊚	⊚	PROPN
ejpam-4554	217	6	iz	iz	INTJ
ejpam-4554	217	7	such	such	ADJ
ejpam-4554	217	8	that	that	SCONJ
ejpam-4554	217	9	iw	iw	PROPN
ejpam-4554	217	10	∈	∈	PROPN
ejpam-4554	217	11	iu⊚	iu⊚	NOUN
ejpam-4554	217	12	iv	iv	NUM
ejpam-4554	217	13	.	.	PUNCT
ejpam-4554	218	1	hence	hence	ADV
ejpam-4554	218	2	,	,	PUNCT
ejpam-4554	218	3	there	there	PRON
ejpam-4554	218	4	are	be	VERB
ejpam-4554	218	5	u	u	NOUN
ejpam-4554	218	6	′	′	NUM
ejpam-4554	218	7	∈	∈	PROPN
ejpam-4554	218	8	x⊙	x⊙	PROPN
ejpam-4554	219	1	z	z	PROPN
ejpam-4554	219	2	,	,	PUNCT
ejpam-4554	219	3	v′	v′	NOUN
ejpam-4554	219	4	∈	∈	PROPN
ejpam-4554	219	5	y⊙	y⊙	PROPN
ejpam-4554	219	6	z	z	NOUN
ejpam-4554	219	7	and	and	CCONJ
ejpam-4554	219	8	w′	w′	PROPN
ejpam-4554	219	9	∈	∈	PROPN
ejpam-4554	219	10	u	u	PROPN
ejpam-4554	219	11	⊙	⊙	VERB
ejpam-4554	219	12	v	v	ADP
ejpam-4554	219	13	such	such	ADJ
ejpam-4554	219	14	that	that	SCONJ
ejpam-4554	219	15	iu	iu	ADP
ejpam-4554	219	16	=	=	SYM
ejpam-4554	219	17	iu′	iu′	PROPN
ejpam-4554	219	18	,	,	PUNCT
ejpam-4554	219	19	iv	iv	X
ejpam-4554	219	20	=	=	SYM
ejpam-4554	219	21	iv′	iv′	NOUN
ejpam-4554	219	22	,	,	PUNCT
ejpam-4554	219	23	and	and	CCONJ
ejpam-4554	219	24	iw	iw	NOUN
ejpam-4554	219	25	=	=	SYM
ejpam-4554	219	26	iw′	iw′	NOUN
ejpam-4554	219	27	.	.	PUNCT
ejpam-4554	220	1	hence	hence	ADV
ejpam-4554	220	2	,	,	PUNCT
ejpam-4554	220	3	uθu′	uθu′	PROPN
ejpam-4554	220	4	,	,	PUNCT
ejpam-4554	220	5	vθv′	vθv′	ADV
ejpam-4554	220	6	and	and	CCONJ
ejpam-4554	220	7	wθw′.	wθw′.	PROPN
ejpam-4554	220	8	r.	r.	PROPN
ejpam-4554	220	9	manzano	manzano	PROPN
ejpam-4554	220	10	,	,	PUNCT
ejpam-4554	220	11	jr	jr	PROPN
ejpam-4554	220	12	.	.	PROPN
ejpam-4554	220	13	,	,	PUNCT
ejpam-4554	220	14	g.	g.	PROPN
ejpam-4554	220	15	petalcorin	petalcorin	PROPN
ejpam-4554	220	16	,	,	PUNCT
ejpam-4554	220	17	jr	jr	PROPN
ejpam-4554	220	18	.	.	PROPN
ejpam-4554	220	19	/	/	SYM
ejpam-4554	220	20	eur	eur	PROPN
ejpam-4554	220	21	.	.	PUNCT
ejpam-4554	221	1	j.	j.	PROPN
ejpam-4554	221	2	pure	pure	PROPN
ejpam-4554	221	3	appl	appl	PROPN
ejpam-4554	221	4	.	.	PROPN
ejpam-4554	221	5	math	math	PROPN
ejpam-4554	221	6	,	,	PUNCT
ejpam-4554	221	7	15	15	NUM
ejpam-4554	221	8	(	(	PUNCT
ejpam-4554	221	9	4	4	NUM
ejpam-4554	221	10	)	)	PUNCT
ejpam-4554	221	11	(	(	PUNCT
ejpam-4554	221	12	2022	2022	NUM
ejpam-4554	221	13	)	)	PUNCT
ejpam-4554	221	14	,	,	PUNCT
ejpam-4554	221	15	1854	1854	NUM
ejpam-4554	221	16	-	-	SYM
ejpam-4554	221	17	1868	1868	NUM
ejpam-4554	221	18	1861	1861	NUM
ejpam-4554	221	19	since	since	SCONJ
ejpam-4554	221	20	θ	θ	PROPN
ejpam-4554	221	21	is	be	AUX
ejpam-4554	221	22	a	a	DET
ejpam-4554	221	23	congruence	congruence	NOUN
ejpam-4554	221	24	relation	relation	NOUN
ejpam-4554	221	25	on	on	ADP
ejpam-4554	221	26	h	h	NOUN
ejpam-4554	221	27	,	,	PUNCT
ejpam-4554	221	28	by	by	ADP
ejpam-4554	221	29	lemma	lemma	PROPN
ejpam-4554	221	30	3.7	3.7	NUM
ejpam-4554	221	31	,	,	PUNCT
ejpam-4554	221	32	(	(	PUNCT
ejpam-4554	221	33	u⊙	u⊙	ADJ
ejpam-4554	221	34	v)θ(u′	v)θ(u′	NOUN
ejpam-4554	221	35	⊙	⊙	PROPN
ejpam-4554	221	36	v′	v′	PROPN
ejpam-4554	221	37	)	)	PUNCT
ejpam-4554	221	38	.	.	PUNCT
ejpam-4554	222	1	from	from	ADP
ejpam-4554	222	2	w′	w′	ADP
ejpam-4554	222	3	∈	∈	PROPN
ejpam-4554	222	4	u⊙	u⊙	ADJ
ejpam-4554	222	5	v	v	NOUN
ejpam-4554	222	6	,	,	PUNCT
ejpam-4554	222	7	there	there	PRON
ejpam-4554	222	8	exists	exist	VERB
ejpam-4554	222	9	a	a	DET
ejpam-4554	222	10	∈	∈	PROPN
ejpam-4554	222	11	u′	u′	PROPN
ejpam-4554	222	12	⊙	⊙	PROPN
ejpam-4554	222	13	v′	v′	PROPN
ejpam-4554	223	1	such	such	ADJ
ejpam-4554	223	2	that	that	SCONJ
ejpam-4554	223	3	w′θa	w′θa	NOUN
ejpam-4554	223	4	and	and	CCONJ
ejpam-4554	223	5	so	so	ADV
ejpam-4554	223	6	,	,	PUNCT
ejpam-4554	223	7	iw′	iw′	X
ejpam-4554	223	8	=	=	SYM
ejpam-4554	223	9	ia	ia	PROPN
ejpam-4554	223	10	.	.	PUNCT
ejpam-4554	223	11	thus	thus	ADV
ejpam-4554	223	12	,	,	PUNCT
ejpam-4554	223	13	iw	iw	PROPN
ejpam-4554	223	14	=	=	SYM
ejpam-4554	223	15	iw′	iw′	X
ejpam-4554	223	16	=	=	SYM
ejpam-4554	223	17	ia	ia	PROPN
ejpam-4554	223	18	.	.	PROPN
ejpam-4554	223	19	by	by	ADP
ejpam-4554	223	20	phgr1	phgr1	PROPN
ejpam-4554	223	21	on	on	ADP
ejpam-4554	223	22	h	h	NOUN
ejpam-4554	223	23	,	,	PUNCT
ejpam-4554	223	24	a	a	DET
ejpam-4554	223	25	∈	∈	NOUN
ejpam-4554	223	26	u′⊙v′	u′⊙v′	X
ejpam-4554	223	27	⊆	⊆	NUM
ejpam-4554	223	28	(	(	PUNCT
ejpam-4554	223	29	x⊙z)⊙	x⊙z)⊙	PROPN
ejpam-4554	223	30	(	(	PUNCT
ejpam-4554	223	31	y⊙z	y⊙z	NOUN
ejpam-4554	223	32	)	)	PUNCT
ejpam-4554	223	33	≪	≪	ADJ
ejpam-4554	223	34	x⊙y	x⊙y	NOUN
ejpam-4554	223	35	.	.	PUNCT
ejpam-4554	224	1	hence	hence	ADV
ejpam-4554	224	2	,	,	PUNCT
ejpam-4554	224	3	there	there	PRON
ejpam-4554	224	4	exists	exist	VERB
ejpam-4554	224	5	b	b	PROPN
ejpam-4554	224	6	∈	∈	PROPN
ejpam-4554	224	7	x⊙y	x⊙y	PUNCT
ejpam-4554	224	8	such	such	ADJ
ejpam-4554	224	9	that	that	SCONJ
ejpam-4554	224	10	a	a	DET
ejpam-4554	224	11	≪	≪	ADJ
ejpam-4554	224	12	b	b	NOUN
ejpam-4554	224	13	,	,	PUNCT
ejpam-4554	224	14	which	which	PRON
ejpam-4554	224	15	means	mean	VERB
ejpam-4554	224	16	that	that	SCONJ
ejpam-4554	224	17	0	0	NUM
ejpam-4554	224	18	∈	∈	PROPN
ejpam-4554	224	19	a	a	DET
ejpam-4554	224	20	⊙	⊙	PROPN
ejpam-4554	224	21	b	b	PROPN
ejpam-4554	225	1	and	and	CCONJ
ejpam-4554	225	2	0	0	NUM
ejpam-4554	225	3	∈	∈	PROPN
ejpam-4554	225	4	a	a	DET
ejpam-4554	225	5	⊛	⊛	NUM
ejpam-4554	225	6	b.	b.	PROPN
ejpam-4554	225	7	furthermore	furthermore	ADV
ejpam-4554	225	8	,	,	PUNCT
ejpam-4554	225	9	ib	ib	PROPN
ejpam-4554	225	10	∈	∈	PROPN
ejpam-4554	225	11	ix	ix	ADP
ejpam-4554	225	12	⊚	⊚	PROPN
ejpam-4554	225	13	iy	iy	PROPN
ejpam-4554	225	14	,	,	PUNCT
ejpam-4554	225	15	i0	i0	PROPN
ejpam-4554	225	16	∈	∈	PROPN
ejpam-4554	225	17	ia	ia	PROPN
ejpam-4554	225	18	⊚	⊚	PROPN
ejpam-4554	225	19	ib	ib	PROPN
ejpam-4554	225	20	,	,	PUNCT
ejpam-4554	225	21	andi0	andi0	PROPN
ejpam-4554	226	1	∈	∈	PROPN
ejpam-4554	226	2	ia	ia	PROPN
ejpam-4554	226	3	⊗	⊗	PROPN
ejpam-4554	226	4	ib	ib	PROPN
ejpam-4554	226	5	.	.	PUNCT
ejpam-4554	227	1	since	since	SCONJ
ejpam-4554	227	2	iw	iw	NOUN
ejpam-4554	227	3	=	=	SYM
ejpam-4554	227	4	iw′	iw′	NOUN
ejpam-4554	227	5	=	=	SYM
ejpam-4554	227	6	ia	ia	PROPN
ejpam-4554	227	7	,	,	PUNCT
ejpam-4554	227	8	we	we	PRON
ejpam-4554	227	9	have	have	VERB
ejpam-4554	227	10	i0	i0	PROPN
ejpam-4554	227	11	∈	∈	PROPN
ejpam-4554	227	12	iw	iw	INTJ
ejpam-4554	227	13	⊚	⊚	NOUN
ejpam-4554	227	14	ib	ib	NOUN
ejpam-4554	227	15	and	and	CCONJ
ejpam-4554	227	16	i0	i0	PROPN
ejpam-4554	227	17	∈	∈	PROPN
ejpam-4554	228	1	iw	iw	INTJ
ejpam-4554	228	2	⊗	⊗	PROPN
ejpam-4554	228	3	ib	ib	NOUN
ejpam-4554	228	4	which	which	PRON
ejpam-4554	228	5	means	mean	VERB
ejpam-4554	228	6	that	that	SCONJ
ejpam-4554	228	7	iw	iw	INTJ
ejpam-4554	228	8	≪	≪	ADJ
ejpam-4554	228	9	ib	ib	NOUN
ejpam-4554	228	10	.	.	PUNCT
ejpam-4554	229	1	this	this	PRON
ejpam-4554	229	2	implies	imply	VERB
ejpam-4554	229	3	that	that	SCONJ
ejpam-4554	229	4	(	(	PUNCT
ejpam-4554	229	5	ix	ix	ADP
ejpam-4554	229	6	⊚	⊚	PROPN
ejpam-4554	229	7	iz)⊚	iz)⊚	PROPN
ejpam-4554	229	8	(	(	PUNCT
ejpam-4554	229	9	iy	iy	INTJ
ejpam-4554	229	10	⊚	⊚	X
ejpam-4554	229	11	iz	iz	NOUN
ejpam-4554	229	12	)	)	PUNCT
ejpam-4554	229	13	≪	≪	VERB
ejpam-4554	229	14	ix	ix	PROPN
ejpam-4554	229	15	⊚	⊚	PROPN
ejpam-4554	229	16	iy	iy	PROPN
ejpam-4554	229	17	.	.	PUNCT
ejpam-4554	230	1	similarly	similarly	ADV
ejpam-4554	230	2	,	,	PUNCT
ejpam-4554	230	3	we	we	PRON
ejpam-4554	230	4	can	can	AUX
ejpam-4554	230	5	show	show	VERB
ejpam-4554	230	6	also	also	ADV
ejpam-4554	230	7	that	that	SCONJ
ejpam-4554	230	8	(	(	PUNCT
ejpam-4554	230	9	ix	ix	ADP
ejpam-4554	230	10	⊗	⊗	PROPN
ejpam-4554	230	11	iz)⊗	iz)⊗	PROPN
ejpam-4554	230	12	(	(	PUNCT
ejpam-4554	230	13	iy	iy	PROPN
ejpam-4554	230	14	⊗	⊗	PROPN
ejpam-4554	230	15	iz	iz	NOUN
ejpam-4554	230	16	)	)	PUNCT
ejpam-4554	230	17	≪	≪	PUNCT
ejpam-4554	230	18	ix	ix	PROPN
ejpam-4554	230	19	⊗	⊗	PROPN
ejpam-4554	230	20	iy	iy	PROPN
ejpam-4554	230	21	.	.	PUNCT
ejpam-4554	231	1	therefore	therefore	ADV
ejpam-4554	231	2	,	,	PUNCT
ejpam-4554	231	3	[	[	X
ejpam-4554	231	4	phgr1	phgr1	X
ejpam-4554	231	5	]	]	X
ejpam-4554	231	6	holds	hold	VERB
ejpam-4554	231	7	.	.	PUNCT
ejpam-4554	232	1	[	[	X
ejpam-4554	232	2	phgr2	phgr2	NOUN
ejpam-4554	232	3	]	]	X
ejpam-4554	232	4	let	let	VERB
ejpam-4554	232	5	iw	iw	PRON
ejpam-4554	232	6	∈	∈	PROPN
ejpam-4554	232	7	(	(	PUNCT
ejpam-4554	232	8	ix	ix	INTJ
ejpam-4554	232	9	⊚	⊚	PROPN
ejpam-4554	232	10	iy)⊗	iy)⊗	INTJ
ejpam-4554	232	11	iz	iz	INTJ
ejpam-4554	232	12	.	.	PUNCT
ejpam-4554	233	1	then	then	ADV
ejpam-4554	233	2	there	there	PRON
ejpam-4554	233	3	exists	exist	VERB
ejpam-4554	233	4	iu	iu	ADP
ejpam-4554	233	5	∈	∈	PROPN
ejpam-4554	233	6	ix	ix	ADP
ejpam-4554	233	7	⊚	⊚	PROPN
ejpam-4554	233	8	iy	iy	INTJ
ejpam-4554	233	9	such	such	ADJ
ejpam-4554	233	10	that	that	SCONJ
ejpam-4554	233	11	iw	iw	PROPN
ejpam-4554	233	12	∈	∈	PROPN
ejpam-4554	233	13	iu	iu	ADP
ejpam-4554	233	14	⊗	⊗	PROPN
ejpam-4554	233	15	iz	iz	INTJ
ejpam-4554	233	16	.	.	PUNCT
ejpam-4554	234	1	since	since	SCONJ
ejpam-4554	234	2	iu	iu	ADP
ejpam-4554	234	3	∈	∈	PROPN
ejpam-4554	234	4	ix	ix	ADP
ejpam-4554	234	5	⊚	⊚	PROPN
ejpam-4554	234	6	iy	iy	PROPN
ejpam-4554	234	7	,	,	PUNCT
ejpam-4554	234	8	there	there	PRON
ejpam-4554	234	9	exists	exist	VERB
ejpam-4554	234	10	u′	u′	PROPN
ejpam-4554	234	11	∈	∈	PROPN
ejpam-4554	234	12	x	x	SYM
ejpam-4554	234	13	⊙	⊙	PROPN
ejpam-4554	234	14	y	y	PROPN
ejpam-4554	234	15	such	such	ADJ
ejpam-4554	234	16	that	that	DET
ejpam-4554	234	17	uθu′	uθu′	PROPN
ejpam-4554	234	18	,	,	PUNCT
ejpam-4554	234	19	that	that	ADV
ejpam-4554	234	20	is	is	ADV
ejpam-4554	234	21	,	,	PUNCT
ejpam-4554	234	22	iu	iu	ADP
ejpam-4554	234	23	=	=	SYM
ejpam-4554	234	24	iu′	iu′	PROPN
ejpam-4554	234	25	.	.	PUNCT
ejpam-4554	235	1	hence	hence	ADV
ejpam-4554	235	2	,	,	PUNCT
ejpam-4554	235	3	iu′	iu′	PROPN
ejpam-4554	235	4	∈	∈	PROPN
ejpam-4554	235	5	ix	ix	ADP
ejpam-4554	235	6	⊚	⊚	PROPN
ejpam-4554	235	7	iy	iy	PROPN
ejpam-4554	235	8	.	.	PUNCT
ejpam-4554	236	1	since	since	SCONJ
ejpam-4554	236	2	iw	iw	PROPN
ejpam-4554	236	3	∈	∈	PROPN
ejpam-4554	236	4	iu	iu	ADP
ejpam-4554	236	5	⊗	⊗	PROPN
ejpam-4554	236	6	iz	iz	PUNCT
ejpam-4554	237	1	=	=	PUNCT
ejpam-4554	237	2	iu′	iu′	PROPN
ejpam-4554	237	3	⊗	⊗	PROPN
ejpam-4554	237	4	iz	iz	INTJ
ejpam-4554	237	5	,	,	PUNCT
ejpam-4554	237	6	there	there	PRON
ejpam-4554	237	7	exists	exist	VERB
ejpam-4554	237	8	w′	w′	PROPN
ejpam-4554	237	9	∈	∈	PROPN
ejpam-4554	237	10	u′	u′	PROPN
ejpam-4554	237	11	⊛	⊛	NUM
ejpam-4554	237	12	z	z	NOUN
ejpam-4554	237	13	such	such	ADJ
ejpam-4554	237	14	that	that	DET
ejpam-4554	237	15	w′θw	w′θw	NOUN
ejpam-4554	237	16	.	.	PUNCT
ejpam-4554	238	1	now	now	ADV
ejpam-4554	238	2	,	,	PUNCT
ejpam-4554	238	3	w′	w′	PROPN
ejpam-4554	238	4	∈	∈	PROPN
ejpam-4554	238	5	u′	u′	PROPN
ejpam-4554	238	6	⊛	⊛	NUM
ejpam-4554	238	7	z	z	NOUN
ejpam-4554	238	8	⊆	⊆	NUM
ejpam-4554	238	9	(	(	PUNCT
ejpam-4554	238	10	x	x	PROPN
ejpam-4554	238	11	⊙	⊙	PROPN
ejpam-4554	238	12	y	y	PROPN
ejpam-4554	238	13	)	)	PUNCT
ejpam-4554	238	14	⊛	⊛	NUM
ejpam-4554	238	15	z	z	NOUN
ejpam-4554	238	16	=	=	SYM
ejpam-4554	238	17	(	(	PUNCT
ejpam-4554	238	18	x	x	PROPN
ejpam-4554	238	19	⊛	⊛	NUM
ejpam-4554	238	20	z	z	NOUN
ejpam-4554	238	21	)	)	PUNCT
ejpam-4554	238	22	⊙	⊙	PROPN
ejpam-4554	238	23	y	y	PROPN
ejpam-4554	238	24	,	,	PUNCT
ejpam-4554	238	25	by	by	ADP
ejpam-4554	238	26	phgr2	phgr2	NOUN
ejpam-4554	238	27	on	on	ADP
ejpam-4554	238	28	h.	h.	PROPN
ejpam-4554	238	29	hence	hence	ADV
ejpam-4554	238	30	,	,	PUNCT
ejpam-4554	238	31	w′	w′	PROPN
ejpam-4554	238	32	∈	∈	PROPN
ejpam-4554	238	33	(	(	PUNCT
ejpam-4554	238	34	x	x	PROPN
ejpam-4554	238	35	⊛	⊛	NUM
ejpam-4554	238	36	z	z	NOUN
ejpam-4554	238	37	)	)	PUNCT
ejpam-4554	238	38	⊙	⊙	PROPN
ejpam-4554	238	39	y	y	PROPN
ejpam-4554	238	40	and	and	CCONJ
ejpam-4554	238	41	u′	u′	PROPN
ejpam-4554	238	42	⊛	⊛	NUM
ejpam-4554	238	43	z	z	NOUN
ejpam-4554	238	44	⊆	⊆	NUM
ejpam-4554	238	45	(	(	PUNCT
ejpam-4554	238	46	x	x	PROPN
ejpam-4554	238	47	⊙	⊙	PROPN
ejpam-4554	238	48	y	y	PROPN
ejpam-4554	238	49	)	)	PUNCT
ejpam-4554	238	50	⊛	⊛	NUM
ejpam-4554	238	51	z.	z.	PROPN
ejpam-4554	238	52	this	this	PRON
ejpam-4554	238	53	means	mean	VERB
ejpam-4554	238	54	that	that	SCONJ
ejpam-4554	238	55	there	there	PRON
ejpam-4554	238	56	exists	exist	VERB
ejpam-4554	238	57	b	b	PROPN
ejpam-4554	238	58	∈	∈	PROPN
ejpam-4554	238	59	x	x	SYM
ejpam-4554	238	60	⊛	⊛	NUM
ejpam-4554	238	61	z	z	NOUN
ejpam-4554	238	62	such	such	ADJ
ejpam-4554	238	63	that	that	SCONJ
ejpam-4554	238	64	w′	w′	PROPN
ejpam-4554	238	65	∈	∈	PROPN
ejpam-4554	238	66	b	b	PROPN
ejpam-4554	238	67	⊙	⊙	PROPN
ejpam-4554	238	68	y.	y.	PROPN
ejpam-4554	238	69	since	since	SCONJ
ejpam-4554	238	70	b	b	PROPN
ejpam-4554	238	71	∈	∈	PROPN
ejpam-4554	238	72	x	x	SYM
ejpam-4554	238	73	⊛	⊛	PROPN
ejpam-4554	238	74	z	z	NUM
ejpam-4554	238	75	,	,	PUNCT
ejpam-4554	238	76	ib	ib	PROPN
ejpam-4554	238	77	∈	∈	PROPN
ejpam-4554	238	78	ix	ix	ADP
ejpam-4554	238	79	⊗	⊗	PROPN
ejpam-4554	238	80	iz	iz	INTJ
ejpam-4554	238	81	.	.	PUNCT
ejpam-4554	239	1	also	also	ADV
ejpam-4554	239	2	,	,	PUNCT
ejpam-4554	239	3	iw′	iw′	X
ejpam-4554	239	4	∈	∈	PROPN
ejpam-4554	239	5	ib	ib	NOUN
ejpam-4554	239	6	⊚	⊚	PROPN
ejpam-4554	239	7	iy	iy	PROPN
ejpam-4554	239	8	.	.	PUNCT
ejpam-4554	240	1	thus	thus	ADV
ejpam-4554	240	2	,	,	PUNCT
ejpam-4554	240	3	iw	iw	PROPN
ejpam-4554	240	4	=	=	SYM
ejpam-4554	240	5	iw′	iw′	X
ejpam-4554	240	6	∈	∈	PROPN
ejpam-4554	240	7	ib	ib	NOUN
ejpam-4554	240	8	⊚	⊚	PROPN
ejpam-4554	240	9	iy	iy	PROPN
ejpam-4554	240	10	⊆	⊆	NUM
ejpam-4554	240	11	(	(	PUNCT
ejpam-4554	240	12	ix	ix	PROPN
ejpam-4554	240	13	⊗	⊗	PROPN
ejpam-4554	240	14	iz	iz	NOUN
ejpam-4554	240	15	)	)	PUNCT
ejpam-4554	240	16	⊚	⊚	PROPN
ejpam-4554	240	17	iy	iy	PROPN
ejpam-4554	240	18	.	.	PUNCT
ejpam-4554	241	1	hence	hence	ADV
ejpam-4554	241	2	,	,	PUNCT
ejpam-4554	241	3	(	(	PUNCT
ejpam-4554	241	4	ix	ix	ADP
ejpam-4554	241	5	⊚	⊚	PROPN
ejpam-4554	241	6	iy)⊗	iy)⊗	PROPN
ejpam-4554	241	7	iz	iz	CCONJ
ejpam-4554	241	8	⊆	⊆	NUM
ejpam-4554	241	9	(	(	PUNCT
ejpam-4554	241	10	ix	ix	PROPN
ejpam-4554	241	11	⊗	⊗	PROPN
ejpam-4554	241	12	iz)⊚	iz)⊚	PROPN
ejpam-4554	241	13	iy	iy	PROPN
ejpam-4554	241	14	.	.	PUNCT
ejpam-4554	242	1	for	for	ADP
ejpam-4554	242	2	the	the	DET
ejpam-4554	242	3	other	other	ADJ
ejpam-4554	242	4	set	set	NOUN
ejpam-4554	242	5	inclusion	inclusion	NOUN
ejpam-4554	242	6	,	,	PUNCT
ejpam-4554	242	7	let	let	VERB
ejpam-4554	242	8	iw	iw	PRON
ejpam-4554	242	9	∈	∈	PROPN
ejpam-4554	242	10	(	(	PUNCT
ejpam-4554	242	11	ix	ix	PROPN
ejpam-4554	242	12	⊗	⊗	PROPN
ejpam-4554	242	13	iz)⊚	iz)⊚	PROPN
ejpam-4554	242	14	iy	iy	PROPN
ejpam-4554	242	15	.	.	PUNCT
ejpam-4554	243	1	then	then	ADV
ejpam-4554	243	2	there	there	PRON
ejpam-4554	243	3	exists	exist	VERB
ejpam-4554	243	4	iu	iu	ADP
ejpam-4554	243	5	∈	∈	PROPN
ejpam-4554	243	6	ix	ix	ADP
ejpam-4554	244	1	⊗	⊗	PROPN
ejpam-4554	245	1	iz	iz	INTJ
ejpam-4554	246	1	such	such	ADJ
ejpam-4554	246	2	that	that	SCONJ
ejpam-4554	246	3	iw	iw	PROPN
ejpam-4554	246	4	∈	∈	PROPN
ejpam-4554	246	5	iu⊚iy	iu⊚iy	PROPN
ejpam-4554	246	6	.	.	PUNCT
ejpam-4554	247	1	since	since	SCONJ
ejpam-4554	247	2	iu	iu	ADP
ejpam-4554	247	3	∈	∈	PROPN
ejpam-4554	247	4	ix⊗iz	ix⊗iz	ADV
ejpam-4554	247	5	,	,	PUNCT
ejpam-4554	247	6	there	there	PRON
ejpam-4554	247	7	exists	exist	VERB
ejpam-4554	247	8	u	u	NOUN
ejpam-4554	247	9	′	′	NOUN
ejpam-4554	247	10	∈	∈	PROPN
ejpam-4554	247	11	x⊛z	x⊛z	PUNCT
ejpam-4554	248	1	such	such	ADJ
ejpam-4554	248	2	that	that	DET
ejpam-4554	248	3	uθu′	uθu′	PROPN
ejpam-4554	248	4	,	,	PUNCT
ejpam-4554	248	5	that	that	ADV
ejpam-4554	248	6	is	is	ADV
ejpam-4554	248	7	,	,	PUNCT
ejpam-4554	248	8	iu	iu	ADP
ejpam-4554	248	9	=	=	SYM
ejpam-4554	248	10	iu′	iu′	PROPN
ejpam-4554	248	11	.	.	PUNCT
ejpam-4554	249	1	hence	hence	ADV
ejpam-4554	249	2	,	,	PUNCT
ejpam-4554	249	3	iu′	iu′	PROPN
ejpam-4554	249	4	∈	∈	PROPN
ejpam-4554	249	5	ix⊗	ix⊗	PROPN
ejpam-4554	249	6	iz	iz	PROPN
ejpam-4554	249	7	.	.	PUNCT
ejpam-4554	250	1	since	since	SCONJ
ejpam-4554	250	2	iw	iw	PROPN
ejpam-4554	250	3	∈	∈	PROPN
ejpam-4554	250	4	iu⊚	iu⊚	NOUN
ejpam-4554	250	5	iy	iy	NOUN
ejpam-4554	250	6	=	=	PUNCT
ejpam-4554	250	7	iu′	iu′	PROPN
ejpam-4554	250	8	⊚	⊚	PROPN
ejpam-4554	250	9	iy	iy	PROPN
ejpam-4554	250	10	,	,	PUNCT
ejpam-4554	250	11	there	there	PRON
ejpam-4554	250	12	exists	exist	VERB
ejpam-4554	250	13	w	w	NOUN
ejpam-4554	250	14	′	′	NUM
ejpam-4554	250	15	∈	∈	PROPN
ejpam-4554	250	16	u′⊙y	u′⊙y	VERB
ejpam-4554	250	17	such	such	ADJ
ejpam-4554	250	18	that	that	DET
ejpam-4554	250	19	w′θw	w′θw	NOUN
ejpam-4554	250	20	.	.	PUNCT
ejpam-4554	251	1	now	now	ADV
ejpam-4554	251	2	,	,	PUNCT
ejpam-4554	251	3	w′	w′	PROPN
ejpam-4554	251	4	∈	∈	PROPN
ejpam-4554	251	5	u′	u′	PROPN
ejpam-4554	251	6	⊙	⊙	PROPN
ejpam-4554	251	7	y	y	PROPN
ejpam-4554	252	1	⊆	⊆	PROPN
ejpam-4554	252	2	(	(	PUNCT
ejpam-4554	252	3	x⊛	x⊛	ADP
ejpam-4554	252	4	z)⊙	z)⊙	NOUN
ejpam-4554	252	5	y	y	PROPN
ejpam-4554	252	6	=	=	PUNCT
ejpam-4554	252	7	(	(	PUNCT
ejpam-4554	252	8	x⊙	x⊙	PROPN
ejpam-4554	252	9	y)⊛	y)⊛	PROPN
ejpam-4554	252	10	z	z	NOUN
ejpam-4554	252	11	,	,	PUNCT
ejpam-4554	252	12	by	by	ADP
ejpam-4554	252	13	phgr2	phgr2	NOUN
ejpam-4554	252	14	on	on	ADP
ejpam-4554	252	15	h.	h.	PROPN
ejpam-4554	252	16	hence	hence	ADV
ejpam-4554	252	17	,	,	PUNCT
ejpam-4554	252	18	w′	w′	PROPN
ejpam-4554	252	19	∈	∈	PROPN
ejpam-4554	252	20	(	(	PUNCT
ejpam-4554	252	21	x⊙	x⊙	PROPN
ejpam-4554	252	22	y)⊛	y)⊛	PROPN
ejpam-4554	252	23	z	z	PROPN
ejpam-4554	252	24	and	and	CCONJ
ejpam-4554	252	25	u′⊙y	u′⊙y	VERB
ejpam-4554	252	26	⊆	⊆	NUM
ejpam-4554	252	27	(	(	PUNCT
ejpam-4554	252	28	x⊛z)⊙y	x⊛z)⊙y	PROPN
ejpam-4554	252	29	.	.	PUNCT
ejpam-4554	253	1	this	this	PRON
ejpam-4554	253	2	means	mean	VERB
ejpam-4554	253	3	that	that	SCONJ
ejpam-4554	253	4	there	there	PRON
ejpam-4554	253	5	exists	exist	VERB
ejpam-4554	253	6	b	b	PROPN
ejpam-4554	253	7	∈	∈	PROPN
ejpam-4554	253	8	x⊙y	x⊙y	PUNCT
ejpam-4554	253	9	such	such	ADJ
ejpam-4554	253	10	that	that	SCONJ
ejpam-4554	253	11	w′	w′	PROPN
ejpam-4554	253	12	∈	∈	PROPN
ejpam-4554	253	13	b⊛z	b⊛z	PROPN
ejpam-4554	253	14	.	.	PUNCT
ejpam-4554	254	1	now	now	ADV
ejpam-4554	254	2	,	,	PUNCT
ejpam-4554	254	3	b	b	PROPN
ejpam-4554	254	4	∈	∈	PROPN
ejpam-4554	254	5	x⊙y	x⊙y	X
ejpam-4554	254	6	implies	imply	VERB
ejpam-4554	254	7	ib	ib	PROPN
ejpam-4554	254	8	∈	∈	PROPN
ejpam-4554	254	9	ix⊚iy	ix⊚iy	PROPN
ejpam-4554	254	10	.	.	PUNCT
ejpam-4554	255	1	also	also	ADV
ejpam-4554	255	2	,	,	PUNCT
ejpam-4554	255	3	iw′	iw′	X
ejpam-4554	255	4	∈	∈	PROPN
ejpam-4554	255	5	ib⊗iz	ib⊗iz	NOUN
ejpam-4554	255	6	.	.	PUNCT
ejpam-4554	256	1	thus	thus	ADV
ejpam-4554	256	2	,	,	PUNCT
ejpam-4554	256	3	iw	iw	PROPN
ejpam-4554	256	4	=	=	SYM
ejpam-4554	256	5	iw′	iw′	X
ejpam-4554	256	6	∈	∈	NOUN
ejpam-4554	256	7	ib⊗iz	ib⊗iz	VERB
ejpam-4554	256	8	⊆	⊆	NUM
ejpam-4554	256	9	(	(	PUNCT
ejpam-4554	256	10	ix⊚iy)⊗iz	ix⊚iy)⊗iz	NOUN
ejpam-4554	256	11	.	.	PUNCT
ejpam-4554	257	1	hence	hence	ADV
ejpam-4554	257	2	,	,	PUNCT
ejpam-4554	257	3	(	(	PUNCT
ejpam-4554	257	4	ix	ix	PROPN
ejpam-4554	257	5	⊗	⊗	PROPN
ejpam-4554	257	6	iz)⊚	iz)⊚	PROPN
ejpam-4554	257	7	iy	iy	PROPN
ejpam-4554	257	8	⊆	⊆	NUM
ejpam-4554	257	9	(	(	PUNCT
ejpam-4554	257	10	ix	ix	INTJ
ejpam-4554	257	11	⊚	⊚	PROPN
ejpam-4554	257	12	iy)⊗	iy)⊗	INTJ
ejpam-4554	257	13	iz	iz	INTJ
ejpam-4554	257	14	.	.	PUNCT
ejpam-4554	257	15	therefore	therefore	ADV
ejpam-4554	257	16	,	,	PUNCT
ejpam-4554	257	17	(	(	PUNCT
ejpam-4554	257	18	ix	ix	PROPN
ejpam-4554	257	19	⊗	⊗	PROPN
ejpam-4554	257	20	iz)⊚	iz)⊚	PROPN
ejpam-4554	257	21	iy	iy	PROPN
ejpam-4554	258	1	=	=	PUNCT
ejpam-4554	258	2	(	(	PUNCT
ejpam-4554	258	3	ix	ix	INTJ
ejpam-4554	258	4	⊚	⊚	PROPN
ejpam-4554	258	5	iy)⊗	iy)⊗	INTJ
ejpam-4554	259	1	iz	iz	X
ejpam-4554	259	2	and	and	CCONJ
ejpam-4554	259	3	[	[	X
ejpam-4554	259	4	phgr2	phgr2	NOUN
ejpam-4554	259	5	]	]	PUNCT
ejpam-4554	259	6	holds	hold	VERB
ejpam-4554	259	7	.	.	PUNCT
ejpam-4554	260	1	[	[	X
ejpam-4554	260	2	phgr3	phgr3	X
ejpam-4554	260	3	]	]	PUNCT
ejpam-4554	260	4	by	by	ADP
ejpam-4554	260	5	phgr3	phgr3	NOUN
ejpam-4554	260	6	of	of	ADP
ejpam-4554	260	7	h	h	NOUN
ejpam-4554	260	8	,	,	PUNCT
ejpam-4554	260	9	0	0	NUM
ejpam-4554	260	10	∈	∈	PROPN
ejpam-4554	260	11	x⊛	x⊛	PROPN
ejpam-4554	261	1	x	x	X
ejpam-4554	261	2	and	and	CCONJ
ejpam-4554	261	3	0	0	NUM
ejpam-4554	261	4	∈	∈	PROPN
ejpam-4554	261	5	x⊙	x⊙	PROPN
ejpam-4554	261	6	x	x	PUNCT
ejpam-4554	261	7	which	which	PRON
ejpam-4554	261	8	means	mean	VERB
ejpam-4554	261	9	that	that	SCONJ
ejpam-4554	261	10	i0	i0	PROPN
ejpam-4554	261	11	∈	∈	PROPN
ejpam-4554	262	1	ix	ix	ADP
ejpam-4554	262	2	⊗	⊗	PROPN
ejpam-4554	262	3	ix	ix	X
ejpam-4554	263	1	and	and	CCONJ
ejpam-4554	263	2	i0	i0	PROPN
ejpam-4554	263	3	∈	∈	PROPN
ejpam-4554	263	4	ix	ix	ADP
ejpam-4554	263	5	⊚	⊚	PROPN
ejpam-4554	263	6	ix	ix	ADJ
ejpam-4554	263	7	.	.	PUNCT
ejpam-4554	264	1	this	this	PRON
ejpam-4554	264	2	means	mean	VERB
ejpam-4554	264	3	that	that	SCONJ
ejpam-4554	264	4	ix	ix	ADP
ejpam-4554	264	5	≪	≪	ADJ
ejpam-4554	264	6	ix	ix	PROPN
ejpam-4554	264	7	.	.	PUNCT
ejpam-4554	265	1	therefore	therefore	ADV
ejpam-4554	265	2	,	,	PUNCT
ejpam-4554	265	3	[	[	X
ejpam-4554	265	4	phgr3	phgr3	X
ejpam-4554	265	5	]	]	PUNCT
ejpam-4554	265	6	holds	hold	VERB
ejpam-4554	265	7	.	.	PUNCT
ejpam-4554	266	1	[	[	X
ejpam-4554	266	2	pghr4	pghr4	X
ejpam-4554	266	3	]	]	X
ejpam-4554	266	4	let	let	VERB
ejpam-4554	266	5	iw	iw	PRON
ejpam-4554	266	6	∈	∈	PROPN
ejpam-4554	266	7	i0	i0	PROPN
ejpam-4554	266	8	⊚	⊚	PROPN
ejpam-4554	266	9	(	(	PUNCT
ejpam-4554	266	10	i0	i0	PROPN
ejpam-4554	266	11	⊗	⊗	PROPN
ejpam-4554	266	12	ix	ix	PROPN
ejpam-4554	266	13	)	)	PUNCT
ejpam-4554	266	14	.	.	PUNCT
ejpam-4554	267	1	then	then	ADV
ejpam-4554	267	2	there	there	PRON
ejpam-4554	267	3	exists	exist	VERB
ejpam-4554	267	4	iu	iu	ADP
ejpam-4554	267	5	∈	∈	PROPN
ejpam-4554	267	6	i0	i0	PROPN
ejpam-4554	267	7	⊗	⊗	PROPN
ejpam-4554	267	8	ix	ix	PROPN
ejpam-4554	267	9	for	for	ADP
ejpam-4554	267	10	which	which	PRON
ejpam-4554	267	11	iw	iw	PRON
ejpam-4554	267	12	∈	∈	NOUN
ejpam-4554	267	13	i0	i0	PROPN
ejpam-4554	267	14	⊚	⊚	VERB
ejpam-4554	267	15	iu	iu	ADP
ejpam-4554	267	16	.	.	PUNCT
ejpam-4554	268	1	since	since	SCONJ
ejpam-4554	268	2	iu	iu	ADP
ejpam-4554	268	3	∈	∈	PROPN
ejpam-4554	268	4	i0⊗ix	i0⊗ix	NOUN
ejpam-4554	268	5	,	,	PUNCT
ejpam-4554	268	6	there	there	PRON
ejpam-4554	268	7	exists	exist	VERB
ejpam-4554	268	8	u	u	NOUN
ejpam-4554	268	9	′	′	NOUN
ejpam-4554	268	10	∈	∈	PROPN
ejpam-4554	268	11	0⊛x	0⊛x	NOUN
ejpam-4554	268	12	such	such	ADJ
ejpam-4554	268	13	that	that	SCONJ
ejpam-4554	268	14	uθu′	uθu′	PROPN
ejpam-4554	268	15	and	and	CCONJ
ejpam-4554	268	16	iu	iu	ADP
ejpam-4554	268	17	=	=	SYM
ejpam-4554	268	18	iu′	iu′	PROPN
ejpam-4554	268	19	.	.	PUNCT
ejpam-4554	269	1	hence	hence	ADV
ejpam-4554	269	2	,	,	PUNCT
ejpam-4554	269	3	iu′	iu′	PROPN
ejpam-4554	269	4	∈	∈	PROPN
ejpam-4554	269	5	i0⊗ix	i0⊗ix	PROPN
ejpam-4554	269	6	.	.	PUNCT
ejpam-4554	270	1	since	since	SCONJ
ejpam-4554	270	2	iw	iw	PROPN
ejpam-4554	270	3	∈	∈	PROPN
ejpam-4554	270	4	i0	i0	PROPN
ejpam-4554	270	5	⊚	⊚	NOUN
ejpam-4554	270	6	iu	iu	ADP
ejpam-4554	270	7	=	=	SYM
ejpam-4554	270	8	i0	i0	PROPN
ejpam-4554	270	9	⊚	⊚	NUM
ejpam-4554	270	10	iu′	iu′	PROPN
ejpam-4554	270	11	,	,	PUNCT
ejpam-4554	270	12	there	there	PRON
ejpam-4554	270	13	exists	exist	VERB
ejpam-4554	270	14	w′	w′	PROPN
ejpam-4554	270	15	∈	∈	PROPN
ejpam-4554	270	16	0⊙	0⊙	NOUN
ejpam-4554	270	17	u′	u′	PRON
ejpam-4554	270	18	such	such	ADJ
ejpam-4554	270	19	that	that	SCONJ
ejpam-4554	270	20	wθw′	wθw′	PROPN
ejpam-4554	270	21	and	and	CCONJ
ejpam-4554	270	22	iw	iw	NOUN
ejpam-4554	270	23	=	=	PUNCT
ejpam-4554	270	24	iw′	iw′	NOUN
ejpam-4554	270	25	.	.	PUNCT
ejpam-4554	271	1	now	now	ADV
ejpam-4554	271	2	,	,	PUNCT
ejpam-4554	271	3	w′	w′	PROPN
ejpam-4554	271	4	∈	∈	PROPN
ejpam-4554	271	5	0⊙u′	0⊙u′	NUM
ejpam-4554	271	6	⊆	⊆	NUM
ejpam-4554	271	7	0⊙	0⊙	NOUN
ejpam-4554	271	8	(	(	PUNCT
ejpam-4554	271	9	0⊛x	0⊛x	PROPN
ejpam-4554	271	10	)	)	PUNCT
ejpam-4554	271	11	≪	≪	PUNCT
ejpam-4554	271	12	x	x	X
ejpam-4554	271	13	,	,	PUNCT
ejpam-4554	271	14	by	by	ADP
ejpam-4554	271	15	phgr4	phgr4	NOUN
ejpam-4554	271	16	of	of	ADP
ejpam-4554	271	17	h.	h.	PROPN
ejpam-4554	271	18	this	this	PRON
ejpam-4554	271	19	means	mean	VERB
ejpam-4554	271	20	that	that	SCONJ
ejpam-4554	271	21	w′	w′	NOUN
ejpam-4554	271	22	≪	≪	VERB
ejpam-4554	271	23	x.	x.	NOUN
ejpam-4554	271	24	thus	thus	ADV
ejpam-4554	271	25	,	,	PUNCT
ejpam-4554	271	26	iw′	iw′	NUM
ejpam-4554	271	27	≪	≪	VERB
ejpam-4554	272	1	ix	ix	PROPN
ejpam-4554	272	2	.	.	PUNCT
ejpam-4554	273	1	now	now	ADV
ejpam-4554	273	2	,	,	PUNCT
ejpam-4554	273	3	iw	iw	PROPN
ejpam-4554	273	4	=	=	SYM
ejpam-4554	273	5	iw′	iw′	NOUN
ejpam-4554	273	6	and	and	CCONJ
ejpam-4554	273	7	so	so	ADV
ejpam-4554	273	8	,	,	PUNCT
ejpam-4554	273	9	iw	iw	INTJ
ejpam-4554	273	10	≪	≪	ADJ
ejpam-4554	273	11	ix	ix	ADJ
ejpam-4554	273	12	.	.	PUNCT
ejpam-4554	274	1	since	since	SCONJ
ejpam-4554	274	2	iw	iw	PROPN
ejpam-4554	274	3	∈	∈	PROPN
ejpam-4554	274	4	i0	i0	PROPN
ejpam-4554	274	5	⊚	⊚	PROPN
ejpam-4554	274	6	(	(	PUNCT
ejpam-4554	274	7	i0	i0	PROPN
ejpam-4554	274	8	⊗	⊗	PROPN
ejpam-4554	274	9	ix	ix	PROPN
ejpam-4554	274	10	)	)	PUNCT
ejpam-4554	274	11	,	,	PUNCT
ejpam-4554	274	12	we	we	PRON
ejpam-4554	274	13	have	have	VERB
ejpam-4554	274	14	i0	i0	PROPN
ejpam-4554	274	15	⊚	⊚	PROPN
ejpam-4554	274	16	(	(	PUNCT
ejpam-4554	274	17	i0	i0	PROPN
ejpam-4554	274	18	⊗	⊗	PROPN
ejpam-4554	274	19	ix	ix	PROPN
ejpam-4554	274	20	)	)	PUNCT
ejpam-4554	274	21	≪	≪	NOUN
ejpam-4554	274	22	ix	ix	PROPN
ejpam-4554	274	23	.	.	PUNCT
ejpam-4554	275	1	therefore	therefore	ADV
ejpam-4554	275	2	,	,	PUNCT
ejpam-4554	275	3	[	[	X
ejpam-4554	275	4	phgr4	phgr4	X
ejpam-4554	275	5	]	]	PUNCT
ejpam-4554	275	6	holds	hold	VERB
ejpam-4554	275	7	.	.	PUNCT
ejpam-4554	276	1	[	[	X
ejpam-4554	276	2	phrg5	phrg5	X
ejpam-4554	276	3	]	]	X
ejpam-4554	276	4	let	let	VERB
ejpam-4554	276	5	iw	iw	PRON
ejpam-4554	276	6	∈	∈	PROPN
ejpam-4554	276	7	(	(	PUNCT
ejpam-4554	276	8	ix	ix	PROPN
ejpam-4554	276	9	⊗	⊗	PROPN
ejpam-4554	276	10	iy	iy	PROPN
ejpam-4554	276	11	)	)	PUNCT
ejpam-4554	277	1	⊗	⊗	PROPN
ejpam-4554	277	2	iz	iz	INTJ
ejpam-4554	277	3	.	.	PUNCT
ejpam-4554	278	1	then	then	ADV
ejpam-4554	278	2	there	there	PRON
ejpam-4554	278	3	is	be	VERB
ejpam-4554	278	4	iu	iu	ADP
ejpam-4554	278	5	∈	∈	PROPN
ejpam-4554	278	6	ix	ix	ADP
ejpam-4554	279	1	⊗	⊗	PROPN
ejpam-4554	279	2	iy	iy	PROPN
ejpam-4554	279	3	such	such	ADJ
ejpam-4554	279	4	that	that	SCONJ
ejpam-4554	279	5	iw	iw	PROPN
ejpam-4554	279	6	∈	∈	PROPN
ejpam-4554	279	7	iu	iu	ADP
ejpam-4554	279	8	⊗	⊗	PROPN
ejpam-4554	279	9	iz	iz	INTJ
ejpam-4554	279	10	.	.	PUNCT
ejpam-4554	280	1	since	since	SCONJ
ejpam-4554	280	2	iu	iu	ADP
ejpam-4554	280	3	∈	∈	PROPN
ejpam-4554	280	4	ix	ix	ADP
ejpam-4554	280	5	⊗	⊗	PROPN
ejpam-4554	280	6	iy	iy	PROPN
ejpam-4554	280	7	,	,	PUNCT
ejpam-4554	280	8	there	there	PRON
ejpam-4554	280	9	exists	exist	VERB
ejpam-4554	280	10	u′	u′	PROPN
ejpam-4554	280	11	∈	∈	PROPN
ejpam-4554	280	12	x	x	X
ejpam-4554	280	13	⊛	⊛	NUM
ejpam-4554	280	14	y	y	NUM
ejpam-4554	280	15	such	such	ADJ
ejpam-4554	280	16	that	that	SCONJ
ejpam-4554	280	17	uθu′	uθu′	PROPN
ejpam-4554	280	18	and	and	CCONJ
ejpam-4554	280	19	iu	iu	ADP
ejpam-4554	280	20	=	=	SYM
ejpam-4554	280	21	iu′	iu′	PROPN
ejpam-4554	280	22	.	.	PUNCT
ejpam-4554	281	1	also	also	ADV
ejpam-4554	281	2	,	,	PUNCT
ejpam-4554	281	3	since	since	SCONJ
ejpam-4554	281	4	iw	iw	PROPN
ejpam-4554	281	5	∈	∈	PROPN
ejpam-4554	281	6	iu	iu	ADP
ejpam-4554	281	7	⊛	⊛	NUM
ejpam-4554	281	8	iz	iz	INTJ
ejpam-4554	281	9	,	,	PUNCT
ejpam-4554	281	10	there	there	PRON
ejpam-4554	281	11	exists	exist	VERB
ejpam-4554	281	12	w′	w′	PROPN
ejpam-4554	281	13	∈	∈	PROPN
ejpam-4554	281	14	u	u	PROPN
ejpam-4554	281	15	⊛	⊛	ADP
ejpam-4554	281	16	z	z	NOUN
ejpam-4554	281	17	such	such	ADJ
ejpam-4554	281	18	that	that	PRON
ejpam-4554	281	19	iw	iw	PROPN
ejpam-4554	281	20	=	=	SYM
ejpam-4554	281	21	iw′	iw′	NOUN
ejpam-4554	281	22	.	.	PUNCT
ejpam-4554	282	1	since	since	SCONJ
ejpam-4554	282	2	θ	θ	PROPN
ejpam-4554	282	3	is	be	AUX
ejpam-4554	282	4	a	a	DET
ejpam-4554	282	5	congruence	congruence	NOUN
ejpam-4554	282	6	on	on	ADP
ejpam-4554	282	7	h	h	NOUN
ejpam-4554	282	8	and	and	CCONJ
ejpam-4554	282	9	uθu′	uθu′	PROPN
ejpam-4554	282	10	,	,	PUNCT
ejpam-4554	282	11	by	by	ADP
ejpam-4554	282	12	lemma	lemma	PROPN
ejpam-4554	282	13	3.7	3.7	NUM
ejpam-4554	282	14	,	,	PUNCT
ejpam-4554	282	15	(	(	PUNCT
ejpam-4554	282	16	u	u	PROPN
ejpam-4554	282	17	⊛	⊛	ADJ
ejpam-4554	282	18	z)θ(u′	z)θ(u′	PROPN
ejpam-4554	282	19	⊛	⊛	NUM
ejpam-4554	282	20	z	z	PROPN
ejpam-4554	282	21	)	)	PUNCT
ejpam-4554	282	22	.	.	PUNCT
ejpam-4554	283	1	then	then	ADV
ejpam-4554	283	2	there	there	PRON
ejpam-4554	283	3	exists	exist	VERB
ejpam-4554	283	4	a	a	DET
ejpam-4554	283	5	∈	∈	PROPN
ejpam-4554	283	6	u′	u′	PROPN
ejpam-4554	283	7	⊛	⊛	NUM
ejpam-4554	283	8	z	z	NOUN
ejpam-4554	283	9	such	such	ADJ
ejpam-4554	283	10	that	that	DET
ejpam-4554	283	11	w′θa	w′θa	NOUN
ejpam-4554	283	12	.	.	PUNCT
ejpam-4554	284	1	thus	thus	ADV
ejpam-4554	284	2	,	,	PUNCT
ejpam-4554	284	3	iw	iw	PROPN
ejpam-4554	284	4	=	=	SYM
ejpam-4554	284	5	iw′	iw′	X
ejpam-4554	284	6	=	=	SYM
ejpam-4554	284	7	ia	ia	PROPN
ejpam-4554	284	8	.	.	PUNCT
ejpam-4554	285	1	now	now	ADV
ejpam-4554	285	2	,	,	PUNCT
ejpam-4554	285	3	a	a	DET
ejpam-4554	285	4	∈	∈	PROPN
ejpam-4554	285	5	u′	u′	PROPN
ejpam-4554	285	6	⊛	⊛	NUM
ejpam-4554	285	7	z	z	NOUN
ejpam-4554	285	8	⊆	⊆	NUM
ejpam-4554	285	9	(	(	PUNCT
ejpam-4554	285	10	x⊛	x⊛	PROPN
ejpam-4554	285	11	y)⊛	y)⊛	NOUN
ejpam-4554	285	12	z	z	NOUN
ejpam-4554	285	13	≪	≪	PUNCT
ejpam-4554	285	14	y⊙	y⊙	PROPN
ejpam-4554	285	15	z	z	NOUN
ejpam-4554	285	16	,	,	PUNCT
ejpam-4554	285	17	phgr5	phgr5	PROPN
ejpam-4554	285	18	on	on	ADP
ejpam-4554	285	19	h.	h.	PROPN
ejpam-4554	285	20	hence	hence	ADV
ejpam-4554	285	21	,	,	PUNCT
ejpam-4554	285	22	there	there	PRON
ejpam-4554	285	23	exists	exist	VERB
ejpam-4554	285	24	b	b	PROPN
ejpam-4554	285	25	∈	∈	PROPN
ejpam-4554	285	26	y	y	PROPN
ejpam-4554	285	27	⊙	⊙	PROPN
ejpam-4554	285	28	z	z	PROPN
ejpam-4554	285	29	such	such	ADJ
ejpam-4554	285	30	that	that	SCONJ
ejpam-4554	285	31	a	a	DET
ejpam-4554	285	32	≪	≪	ADJ
ejpam-4554	285	33	b.	b.	NOUN
ejpam-4554	285	34	this	this	PRON
ejpam-4554	285	35	means	mean	VERB
ejpam-4554	285	36	that	that	SCONJ
ejpam-4554	285	37	0	0	NUM
ejpam-4554	285	38	∈	∈	PROPN
ejpam-4554	285	39	a⊛	a⊛	PROPN
ejpam-4554	285	40	b	b	PROPN
ejpam-4554	285	41	and	and	CCONJ
ejpam-4554	285	42	0	0	NUM
ejpam-4554	285	43	∈	∈	PROPN
ejpam-4554	285	44	a⊙	a⊙	PROPN
ejpam-4554	285	45	b.	b.	PROPN
ejpam-4554	285	46	furthermore	furthermore	ADV
ejpam-4554	285	47	,	,	PUNCT
ejpam-4554	285	48	ib	ib	PROPN
ejpam-4554	285	49	∈	∈	PROPN
ejpam-4554	285	50	iy	iy	PROPN
ejpam-4554	285	51	⊚	⊚	INTJ
ejpam-4554	285	52	iz	iz	INTJ
ejpam-4554	285	53	,	,	PUNCT
ejpam-4554	285	54	i0	i0	PROPN
ejpam-4554	285	55	∈	∈	PROPN
ejpam-4554	285	56	ia	ia	PROPN
ejpam-4554	285	57	⊚	⊚	NUM
ejpam-4554	285	58	ib	ib	NOUN
ejpam-4554	285	59	,	,	PUNCT
ejpam-4554	285	60	and	and	CCONJ
ejpam-4554	285	61	i0	i0	PROPN
ejpam-4554	285	62	∈	∈	PROPN
ejpam-4554	285	63	ia	ia	PROPN
ejpam-4554	286	1	⊗	⊗	PROPN
ejpam-4554	286	2	ib	ib	PROPN
ejpam-4554	286	3	.	.	PUNCT
ejpam-4554	287	1	since	since	SCONJ
ejpam-4554	287	2	iw	iw	NOUN
ejpam-4554	287	3	=	=	SYM
ejpam-4554	287	4	iw′	iw′	NOUN
ejpam-4554	287	5	=	=	SYM
ejpam-4554	287	6	ia	ia	PROPN
ejpam-4554	287	7	,	,	PUNCT
ejpam-4554	287	8	we	we	PRON
ejpam-4554	287	9	have	have	VERB
ejpam-4554	287	10	i0	i0	PROPN
ejpam-4554	287	11	∈	∈	PROPN
ejpam-4554	287	12	iw	iw	INTJ
ejpam-4554	287	13	⊚	⊚	NOUN
ejpam-4554	287	14	ib	ib	NOUN
ejpam-4554	287	15	and	and	CCONJ
ejpam-4554	287	16	i0	i0	PROPN
ejpam-4554	287	17	∈	∈	PROPN
ejpam-4554	288	1	iw	iw	INTJ
ejpam-4554	288	2	⊗	⊗	PROPN
ejpam-4554	288	3	ib	ib	NOUN
ejpam-4554	288	4	and	and	CCONJ
ejpam-4554	288	5	hence	hence	ADV
ejpam-4554	288	6	,	,	PUNCT
ejpam-4554	288	7	iw	iw	INTJ
ejpam-4554	288	8	≪	≪	ADJ
ejpam-4554	288	9	ib	ib	NOUN
ejpam-4554	288	10	.	.	PUNCT
ejpam-4554	288	11	note	note	VERB
ejpam-4554	288	12	that	that	SCONJ
ejpam-4554	288	13	ib	ib	PROPN
ejpam-4554	288	14	∈	∈	PROPN
ejpam-4554	288	15	iy	iy	PROPN
ejpam-4554	288	16	⊚	⊚	INTJ
ejpam-4554	288	17	iz	iz	PROPN
ejpam-4554	288	18	.	.	PUNCT
ejpam-4554	289	1	thus	thus	ADV
ejpam-4554	289	2	,	,	PUNCT
ejpam-4554	289	3	(	(	PUNCT
ejpam-4554	289	4	ix	ix	PROPN
ejpam-4554	289	5	⊗	⊗	PROPN
ejpam-4554	289	6	iy)⊛	iy)⊛	PROPN
ejpam-4554	290	1	iz	iz	CCONJ
ejpam-4554	290	2	≪	≪	PROPN
ejpam-4554	290	3	iy	iy	PROPN
ejpam-4554	290	4	⊚	⊚	INTJ
ejpam-4554	290	5	iz	iz	PROPN
ejpam-4554	290	6	.	.	PUNCT
ejpam-4554	291	1	hence	hence	ADV
ejpam-4554	291	2	,	,	PUNCT
ejpam-4554	291	3	[	[	X
ejpam-4554	291	4	phgr5	phgr5	X
ejpam-4554	291	5	]	]	PUNCT
ejpam-4554	291	6	holds	hold	VERB
ejpam-4554	291	7	.	.	PUNCT
ejpam-4554	292	1	therefore	therefore	ADV
ejpam-4554	292	2	,	,	PUNCT
ejpam-4554	292	3	(	(	PUNCT
ejpam-4554	292	4	h	h	NOUN
ejpam-4554	292	5	/	/	SYM
ejpam-4554	292	6	i;⊗,⊚	i;⊗,⊚	PROPN
ejpam-4554	292	7	,	,	PUNCT
ejpam-4554	292	8	i	i	PROPN
ejpam-4554	292	9	)	)	PUNCT
ejpam-4554	292	10	is	be	AUX
ejpam-4554	292	11	a	a	DET
ejpam-4554	292	12	pseudo	pseudo	NOUN
ejpam-4554	292	13	hyper	hyper	ADJ
ejpam-4554	292	14	gr	gr	NOUN
ejpam-4554	292	15	-	-	NOUN
ejpam-4554	292	16	algebra	algebra	NOUN
ejpam-4554	292	17	.	.	PUNCT
ejpam-4554	293	1	□	□	PUNCT
ejpam-4554	293	2	lemma	lemma	PROPN
ejpam-4554	293	3	3.9	3.9	NUM
ejpam-4554	293	4	.	.	PUNCT
ejpam-4554	294	1	let	let	VERB
ejpam-4554	294	2	θ	θ	NOUN
ejpam-4554	294	3	and	and	CCONJ
ejpam-4554	294	4	θ′	θ′	NOUN
ejpam-4554	294	5	be	be	VERB
ejpam-4554	294	6	two	two	NUM
ejpam-4554	294	7	regular	regular	ADJ
ejpam-4554	294	8	congruences	congruence	NOUN
ejpam-4554	294	9	on	on	ADP
ejpam-4554	294	10	h	h	NOUN
ejpam-4554	294	11	such	such	ADJ
ejpam-4554	294	12	that	that	SCONJ
ejpam-4554	294	13	r.	r.	PROPN
ejpam-4554	294	14	manzano	manzano	PROPN
ejpam-4554	294	15	,	,	PUNCT
ejpam-4554	294	16	jr	jr	PROPN
ejpam-4554	294	17	.	.	PROPN
ejpam-4554	294	18	,	,	PUNCT
ejpam-4554	294	19	g.	g.	PROPN
ejpam-4554	294	20	petalcorin	petalcorin	PROPN
ejpam-4554	294	21	,	,	PUNCT
ejpam-4554	294	22	jr	jr	PROPN
ejpam-4554	294	23	.	.	PROPN
ejpam-4554	294	24	/	/	SYM
ejpam-4554	294	25	eur	eur	PROPN
ejpam-4554	294	26	.	.	PUNCT
ejpam-4554	295	1	j.	j.	PROPN
ejpam-4554	295	2	pure	pure	PROPN
ejpam-4554	295	3	appl	appl	PROPN
ejpam-4554	295	4	.	.	PROPN
ejpam-4554	295	5	math	math	PROPN
ejpam-4554	295	6	,	,	PUNCT
ejpam-4554	295	7	15	15	NUM
ejpam-4554	295	8	(	(	PUNCT
ejpam-4554	295	9	4	4	NUM
ejpam-4554	295	10	)	)	PUNCT
ejpam-4554	295	11	(	(	PUNCT
ejpam-4554	295	12	2022	2022	NUM
ejpam-4554	295	13	)	)	PUNCT
ejpam-4554	295	14	,	,	PUNCT
ejpam-4554	295	15	1854	1854	NUM
ejpam-4554	295	16	-	-	SYM
ejpam-4554	295	17	1868	1868	NUM
ejpam-4554	295	18	1862	1862	NUM
ejpam-4554	296	1	[	[	X
ejpam-4554	296	2	0]θ	0]θ	X
ejpam-4554	296	3	=	=	PUNCT
ejpam-4554	297	1	[	[	X
ejpam-4554	297	2	0]θ′	0]θ′	NUM
ejpam-4554	297	3	.	.	PUNCT
ejpam-4554	298	1	then	then	ADV
ejpam-4554	298	2	θ	θ	X
ejpam-4554	298	3	=	=	PUNCT
ejpam-4554	299	1	θ′.	θ′.	ADP
ejpam-4554	299	2	proof	proof	NOUN
ejpam-4554	299	3	.	.	PUNCT
ejpam-4554	300	1	it	it	PRON
ejpam-4554	300	2	is	be	AUX
ejpam-4554	300	3	enough	enough	ADJ
ejpam-4554	300	4	to	to	PART
ejpam-4554	300	5	show	show	VERB
ejpam-4554	300	6	that	that	SCONJ
ejpam-4554	300	7	xθy	xθy	NOUN
ejpam-4554	300	8	⇐	⇐	ADJ
ejpam-4554	300	9	⇒	⇒	PROPN
ejpam-4554	300	10	xθ′y	xθ′y	PROPN
ejpam-4554	300	11	.	.	PUNCT
ejpam-4554	301	1	if	if	SCONJ
ejpam-4554	301	2	xθy	xθy	PROPN
ejpam-4554	301	3	,	,	PUNCT
ejpam-4554	301	4	then	then	ADV
ejpam-4554	301	5	(	(	PUNCT
ejpam-4554	301	6	x	x	PROPN
ejpam-4554	301	7	⊛	⊛	NUM
ejpam-4554	301	8	x)θ̄(x	x)θ̄(x	X
ejpam-4554	301	9	⊛	⊛	NUM
ejpam-4554	301	10	y	y	NOUN
ejpam-4554	301	11	)	)	PUNCT
ejpam-4554	301	12	.	.	PUNCT
ejpam-4554	302	1	since	since	SCONJ
ejpam-4554	302	2	0	0	NUM
ejpam-4554	302	3	∈	∈	PROPN
ejpam-4554	302	4	x	x	SYM
ejpam-4554	302	5	⊛	⊛	NUM
ejpam-4554	302	6	x	x	PUNCT
ejpam-4554	302	7	and	and	CCONJ
ejpam-4554	302	8	θ	θ	PROPN
ejpam-4554	302	9	is	be	AUX
ejpam-4554	302	10	a	a	DET
ejpam-4554	302	11	congruence	congruence	NOUN
ejpam-4554	302	12	on	on	ADP
ejpam-4554	302	13	h	h	NOUN
ejpam-4554	302	14	,	,	PUNCT
ejpam-4554	302	15	there	there	PRON
ejpam-4554	302	16	exists	exist	VERB
ejpam-4554	302	17	z	z	NOUN
ejpam-4554	302	18	∈	∈	PROPN
ejpam-4554	302	19	x	x	X
ejpam-4554	302	20	⊛	⊛	NUM
ejpam-4554	302	21	y	y	PRON
ejpam-4554	302	22	such	such	ADJ
ejpam-4554	302	23	that	that	DET
ejpam-4554	302	24	0θz	0θz	NOUN
ejpam-4554	302	25	.	.	PUNCT
ejpam-4554	303	1	then	then	ADV
ejpam-4554	303	2	,	,	PUNCT
ejpam-4554	303	3	z	z	PROPN
ejpam-4554	303	4	∈	∈	PROPN
ejpam-4554	304	1	[	[	X
ejpam-4554	304	2	0]θ	0]θ	X
ejpam-4554	304	3	=	=	PUNCT
ejpam-4554	305	1	[	[	X
ejpam-4554	305	2	0]θ′	0]θ′	NOUN
ejpam-4554	305	3	and	and	CCONJ
ejpam-4554	305	4	z	z	NOUN
ejpam-4554	305	5	∈	∈	PROPN
ejpam-4554	306	1	[	[	X
ejpam-4554	306	2	0]′θ	0]′θ	NOUN
ejpam-4554	306	3	,	,	PUNCT
ejpam-4554	306	4	that	that	ADV
ejpam-4554	306	5	is	is	ADV
ejpam-4554	306	6	,	,	PUNCT
ejpam-4554	306	7	0θ′z	0θ′z	NUM
ejpam-4554	306	8	.	.	PUNCT
ejpam-4554	307	1	hence	hence	ADV
ejpam-4554	307	2	,	,	PUNCT
ejpam-4554	307	3	{	{	PUNCT
ejpam-4554	307	4	0}θ′(x⊛	0}θ′(x⊛	NOUN
ejpam-4554	307	5	y	y	NOUN
ejpam-4554	307	6	)	)	PUNCT
ejpam-4554	307	7	.	.	PUNCT
ejpam-4554	308	1	similarly	similarly	ADV
ejpam-4554	308	2	,	,	PUNCT
ejpam-4554	308	3	we	we	PRON
ejpam-4554	308	4	can	can	AUX
ejpam-4554	308	5	also	also	ADV
ejpam-4554	308	6	show	show	VERB
ejpam-4554	308	7	that	that	SCONJ
ejpam-4554	308	8	{	{	PUNCT
ejpam-4554	308	9	0}θ′(y⊛	0}θ′(y⊛	NUM
ejpam-4554	308	10	x	x	NOUN
ejpam-4554	308	11	)	)	PUNCT
ejpam-4554	308	12	.	.	PUNCT
ejpam-4554	309	1	thus	thus	ADV
ejpam-4554	309	2	,	,	PUNCT
ejpam-4554	309	3	xθ′y	xθ′y	PROPN
ejpam-4554	309	4	since	since	SCONJ
ejpam-4554	309	5	θ′	θ′	NOUN
ejpam-4554	309	6	is	be	AUX
ejpam-4554	309	7	regular	regular	ADJ
ejpam-4554	309	8	.	.	PUNCT
ejpam-4554	310	1	following	follow	VERB
ejpam-4554	310	2	the	the	DET
ejpam-4554	310	3	same	same	ADJ
ejpam-4554	310	4	argument	argument	NOUN
ejpam-4554	310	5	,	,	PUNCT
ejpam-4554	310	6	xθ′y	xθ′y	PROPN
ejpam-4554	310	7	implies	imply	VERB
ejpam-4554	310	8	xθy	xθy	PROPN
ejpam-4554	310	9	.	.	PUNCT
ejpam-4554	311	1	therefore	therefore	ADV
ejpam-4554	311	2	,	,	PUNCT
ejpam-4554	311	3	θ	θ	PROPN
ejpam-4554	311	4	=	=	SYM
ejpam-4554	311	5	θ′.	θ′.	ADP
ejpam-4554	311	6	□	□	SYM
ejpam-4554	311	7	4	4	X
ejpam-4554	311	8	.	.	PUNCT
ejpam-4554	312	1	isomorphism	isomorphism	NOUN
ejpam-4554	312	2	theorems	theorem	NOUN
ejpam-4554	312	3	of	of	ADP
ejpam-4554	312	4	pseudo	pseudo	NOUN
ejpam-4554	312	5	hyper	hyper	ADJ
ejpam-4554	312	6	gr	gr	NOUN
ejpam-4554	312	7	-	-	PUNCT
ejpam-4554	312	8	algebras	algebras	NOUN
ejpam-4554	312	9	this	this	DET
ejpam-4554	312	10	section	section	NOUN
ejpam-4554	312	11	discusses	discuss	VERB
ejpam-4554	312	12	some	some	DET
ejpam-4554	312	13	hyper	hyper	ADJ
ejpam-4554	312	14	isomorphism	isomorphism	NOUN
ejpam-4554	312	15	theorems	theorem	NOUN
ejpam-4554	312	16	of	of	ADP
ejpam-4554	312	17	pseudo	pseudo	NOUN
ejpam-4554	312	18	hyper	hyper	ADJ
ejpam-4554	312	19	gr	gr	NOUN
ejpam-4554	312	20	-	-	PUNCT
ejpam-4554	312	21	algebras	algebra	NOUN
ejpam-4554	312	22	,	,	PUNCT
ejpam-4554	312	23	namely	namely	ADV
ejpam-4554	312	24	,	,	PUNCT
ejpam-4554	312	25	the	the	DET
ejpam-4554	312	26	first	first	ADJ
ejpam-4554	312	27	and	and	CCONJ
ejpam-4554	312	28	the	the	DET
ejpam-4554	312	29	third	third	ADJ
ejpam-4554	312	30	hyper	hyper	ADJ
ejpam-4554	312	31	isomorphism	isomorphism	NOUN
ejpam-4554	312	32	theorems	theorem	VERB
ejpam-4554	312	33	.	.	PUNCT
ejpam-4554	313	1	all	all	ADV
ejpam-4554	313	2	throughout	throughout	ADP
ejpam-4554	313	3	,	,	PUNCT
ejpam-4554	313	4	h	h	NOUN
ejpam-4554	313	5	and	and	CCONJ
ejpam-4554	313	6	h	h	NOUN
ejpam-4554	313	7	′	′	NOUN
ejpam-4554	313	8	are	be	AUX
ejpam-4554	313	9	pseudo	pseudo	NOUN
ejpam-4554	313	10	hyper	hyper	ADJ
ejpam-4554	313	11	gr	gr	NOUN
ejpam-4554	313	12	-	-	PUNCT
ejpam-4554	313	13	algebras	algebra	NOUN
ejpam-4554	313	14	,	,	PUNCT
ejpam-4554	313	15	unless	unless	SCONJ
ejpam-4554	313	16	otherwise	otherwise	ADV
ejpam-4554	313	17	stated	state	VERB
ejpam-4554	313	18	.	.	PUNCT
ejpam-4554	314	1	lemma	lemma	PROPN
ejpam-4554	314	2	4.1	4.1	NUM
ejpam-4554	314	3	.	.	PUNCT
ejpam-4554	315	1	let	let	VERB
ejpam-4554	315	2	θ	θ	NOUN
ejpam-4554	315	3	be	be	AUX
ejpam-4554	315	4	a	a	DET
ejpam-4554	315	5	regular	regular	ADJ
ejpam-4554	315	6	congruence	congruence	NOUN
ejpam-4554	315	7	on	on	ADP
ejpam-4554	315	8	a	a	DET
ejpam-4554	315	9	pseudo	pseudo	NOUN
ejpam-4554	315	10	hyper	hyper	ADJ
ejpam-4554	315	11	gr	gr	NOUN
ejpam-4554	315	12	-	-	PUNCT
ejpam-4554	315	13	algebrah	algebrah	NOUN
ejpam-4554	316	1	and	and	CCONJ
ejpam-4554	316	2	i	i	PRON
ejpam-4554	316	3	=	=	PUNCT
ejpam-4554	317	1	[	[	X
ejpam-4554	317	2	0]θ	0]θ	NOUN
ejpam-4554	317	3	.	.	PUNCT
ejpam-4554	318	1	then	then	ADV
ejpam-4554	318	2	the	the	DET
ejpam-4554	318	3	map	map	NOUN
ejpam-4554	318	4	π	π	X
ejpam-4554	318	5	:	:	PUNCT
ejpam-4554	318	6	h	h	PROPN
ejpam-4554	319	1	−→	−→	ADJ
ejpam-4554	319	2	h	h	NOUN
ejpam-4554	319	3	/	/	SYM
ejpam-4554	320	1	i	i	PRON
ejpam-4554	320	2	defined	define	VERB
ejpam-4554	320	3	by	by	ADP
ejpam-4554	320	4	π(x	π(x	NOUN
ejpam-4554	320	5	)	)	PUNCT
ejpam-4554	321	1	=	=	SYM
ejpam-4554	321	2	ix	ix	PROPN
ejpam-4554	321	3	,	,	PUNCT
ejpam-4554	321	4	for	for	ADP
ejpam-4554	321	5	all	all	DET
ejpam-4554	321	6	x	x	SYM
ejpam-4554	321	7	∈	∈	PROPN
ejpam-4554	321	8	h	h	NOUN
ejpam-4554	321	9	,	,	PUNCT
ejpam-4554	321	10	is	be	AUX
ejpam-4554	321	11	an	an	DET
ejpam-4554	321	12	epimorphism	epimorphism	NOUN
ejpam-4554	321	13	,	,	PUNCT
ejpam-4554	321	14	called	call	VERB
ejpam-4554	321	15	the	the	DET
ejpam-4554	321	16	canonical	canonical	ADJ
ejpam-4554	321	17	epimorphism	epimorphism	NOUN
ejpam-4554	321	18	.	.	PUNCT
ejpam-4554	322	1	proof	proof	NOUN
ejpam-4554	322	2	.	.	PUNCT
ejpam-4554	323	1	let	let	VERB
ejpam-4554	323	2	x	x	PRON
ejpam-4554	323	3	,	,	PUNCT
ejpam-4554	323	4	y	y	PROPN
ejpam-4554	323	5	∈	∈	PROPN
ejpam-4554	323	6	h	h	NOUN
ejpam-4554	323	7	such	such	ADJ
ejpam-4554	323	8	that	that	SCONJ
ejpam-4554	323	9	x	x	X
ejpam-4554	323	10	=	=	PUNCT
ejpam-4554	323	11	y.	y.	NOUN
ejpam-4554	323	12	then	then	ADV
ejpam-4554	323	13	π(x	π(x	ADP
ejpam-4554	323	14	)	)	PUNCT
ejpam-4554	324	1	=	=	PRON
ejpam-4554	324	2	ix	ix	VERB
ejpam-4554	325	1	=	=	PUNCT
ejpam-4554	326	1	[	[	X
ejpam-4554	326	2	x]θ	x]θ	NOUN
ejpam-4554	326	3	=	=	PUNCT
ejpam-4554	327	1	[	[	X
ejpam-4554	327	2	y]θ	y]θ	NOUN
ejpam-4554	327	3	=	=	SYM
ejpam-4554	327	4	iy	iy	PROPN
ejpam-4554	327	5	=	=	PUNCT
ejpam-4554	327	6	π(y	π(y	PROPN
ejpam-4554	327	7	)	)	PUNCT
ejpam-4554	327	8	.	.	PUNCT
ejpam-4554	328	1	hence	hence	ADV
ejpam-4554	328	2	,	,	PUNCT
ejpam-4554	328	3	π	π	PROPN
ejpam-4554	328	4	is	be	AUX
ejpam-4554	328	5	a	a	DET
ejpam-4554	328	6	well	well	ADV
ejpam-4554	328	7	-	-	PUNCT
ejpam-4554	328	8	defined	define	VERB
ejpam-4554	328	9	map	map	NOUN
ejpam-4554	328	10	.	.	PUNCT
ejpam-4554	329	1	now	now	ADV
ejpam-4554	329	2	,	,	PUNCT
ejpam-4554	329	3	observe	observe	VERB
ejpam-4554	329	4	that	that	SCONJ
ejpam-4554	329	5	π(0	π(0	NOUN
ejpam-4554	329	6	)	)	PUNCT
ejpam-4554	329	7	=	=	SYM
ejpam-4554	329	8	i0	i0	PROPN
ejpam-4554	329	9	=	=	PUNCT
ejpam-4554	329	10	i.	i.	PROPN
ejpam-4554	329	11	next	next	ADV
ejpam-4554	329	12	,	,	PUNCT
ejpam-4554	329	13	we	we	PRON
ejpam-4554	329	14	will	will	AUX
ejpam-4554	329	15	show	show	VERB
ejpam-4554	329	16	that	that	SCONJ
ejpam-4554	329	17	π	π	PROPN
ejpam-4554	329	18	is	be	AUX
ejpam-4554	329	19	a	a	DET
ejpam-4554	329	20	homomorphism	homomorphism	NOUN
ejpam-4554	329	21	.	.	PUNCT
ejpam-4554	330	1	pick	pick	VERB
ejpam-4554	330	2	x	x	SYM
ejpam-4554	330	3	,	,	PUNCT
ejpam-4554	330	4	y	y	PROPN
ejpam-4554	330	5	∈	∈	PROPN
ejpam-4554	330	6	h.	h.	PROPN
ejpam-4554	330	7	let	let	VERB
ejpam-4554	330	8	j	j	PROPN
ejpam-4554	330	9	∈	∈	PROPN
ejpam-4554	330	10	π(x	π(x	PROPN
ejpam-4554	330	11	)	)	PUNCT
ejpam-4554	330	12	⊛	⊛	NUM
ejpam-4554	330	13	π(y	π(y	PROPN
ejpam-4554	330	14	)	)	PUNCT
ejpam-4554	330	15	.	.	PUNCT
ejpam-4554	331	1	then	then	ADV
ejpam-4554	331	2	j	j	PROPN
ejpam-4554	331	3	∈	∈	PROPN
ejpam-4554	331	4	ix	ix	ADP
ejpam-4554	331	5	⊛	⊛	PROPN
ejpam-4554	331	6	iy	iy	PROPN
ejpam-4554	331	7	and	and	CCONJ
ejpam-4554	331	8	so	so	ADV
ejpam-4554	331	9	there	there	PRON
ejpam-4554	331	10	exists	exist	VERB
ejpam-4554	331	11	element	element	NOUN
ejpam-4554	331	12	u	u	NOUN
ejpam-4554	331	13	∈	∈	PROPN
ejpam-4554	331	14	x	x	X
ejpam-4554	331	15	⊛	⊛	NUM
ejpam-4554	331	16	y	y	NUM
ejpam-4554	331	17	such	such	ADJ
ejpam-4554	331	18	that	that	PRON
ejpam-4554	331	19	j	j	PROPN
ejpam-4554	331	20	=	=	PRON
ejpam-4554	331	21	iu	iu	PROPN
ejpam-4554	331	22	=	=	SYM
ejpam-4554	331	23	π(u	π(u	PROPN
ejpam-4554	331	24	)	)	PUNCT
ejpam-4554	331	25	∈	∈	PROPN
ejpam-4554	331	26	π(x⊛y	π(x⊛y	PROPN
ejpam-4554	331	27	)	)	PUNCT
ejpam-4554	331	28	.	.	PUNCT
ejpam-4554	332	1	thus	thus	ADV
ejpam-4554	332	2	,	,	PUNCT
ejpam-4554	332	3	π(x)⊛π(y	π(x)⊛π(y	PROPN
ejpam-4554	332	4	)	)	PUNCT
ejpam-4554	332	5	⊆	⊆	NUM
ejpam-4554	332	6	π(x⊛y	π(x⊛y	PROPN
ejpam-4554	332	7	)	)	PUNCT
ejpam-4554	332	8	.	.	PUNCT
ejpam-4554	333	1	now	now	ADV
ejpam-4554	333	2	,	,	PUNCT
ejpam-4554	333	3	let	let	VERB
ejpam-4554	333	4	l	l	NOUN
ejpam-4554	333	5	∈	∈	PROPN
ejpam-4554	333	6	π(x⊛y	π(x⊛y	PROPN
ejpam-4554	333	7	)	)	PUNCT
ejpam-4554	333	8	.	.	PUNCT
ejpam-4554	334	1	then	then	ADV
ejpam-4554	334	2	there	there	PRON
ejpam-4554	334	3	exists	exist	VERB
ejpam-4554	334	4	an	an	DET
ejpam-4554	334	5	element	element	NOUN
ejpam-4554	334	6	v	v	ADP
ejpam-4554	334	7	∈	∈	NOUN
ejpam-4554	334	8	x	x	PUNCT
ejpam-4554	334	9	⊛	⊛	NUM
ejpam-4554	334	10	y	y	PRON
ejpam-4554	334	11	such	such	ADJ
ejpam-4554	334	12	that	that	SCONJ
ejpam-4554	334	13	l	l	NOUN
ejpam-4554	334	14	=	=	SYM
ejpam-4554	334	15	π(v	π(v	NOUN
ejpam-4554	334	16	)	)	PUNCT
ejpam-4554	334	17	=	=	SYM
ejpam-4554	334	18	iv	iv	X
ejpam-4554	334	19	.	.	PUNCT
ejpam-4554	334	20	note	note	VERB
ejpam-4554	334	21	that	that	SCONJ
ejpam-4554	334	22	iv	iv	X
ejpam-4554	334	23	∈	∈	NOUN
ejpam-4554	334	24	ix⊛	ix⊛	ADP
ejpam-4554	334	25	iy	iy	NOUN
ejpam-4554	334	26	=	=	PUNCT
ejpam-4554	334	27	π(x)⊛π(y	π(x)⊛π(y	PROPN
ejpam-4554	334	28	)	)	PUNCT
ejpam-4554	334	29	.	.	PUNCT
ejpam-4554	335	1	hence	hence	ADV
ejpam-4554	335	2	,	,	PUNCT
ejpam-4554	335	3	we	we	PRON
ejpam-4554	335	4	have	have	VERB
ejpam-4554	335	5	l	l	NOUN
ejpam-4554	335	6	∈	∈	PROPN
ejpam-4554	335	7	π(x)⊛π(y	π(x)⊛π(y	PROPN
ejpam-4554	335	8	)	)	PUNCT
ejpam-4554	335	9	and	and	CCONJ
ejpam-4554	335	10	π(x⊛	π(x⊛	VERB
ejpam-4554	335	11	y	y	NOUN
ejpam-4554	335	12	)	)	PUNCT
ejpam-4554	335	13	⊆	⊆	NUM
ejpam-4554	335	14	π(x)⊛π(y	π(x)⊛π(y	NUM
ejpam-4554	335	15	)	)	PUNCT
ejpam-4554	335	16	.	.	PUNCT
ejpam-4554	336	1	thus	thus	ADV
ejpam-4554	336	2	,	,	PUNCT
ejpam-4554	336	3	π(x⊛	π(x⊛	NOUN
ejpam-4554	336	4	y	y	NOUN
ejpam-4554	336	5	)	)	PUNCT
ejpam-4554	336	6	=	=	SYM
ejpam-4554	337	1	π(x)⊛π(y	π(x)⊛π(y	NUM
ejpam-4554	337	2	)	)	PUNCT
ejpam-4554	337	3	.	.	PUNCT
ejpam-4554	338	1	similarly	similarly	ADV
ejpam-4554	338	2	,	,	PUNCT
ejpam-4554	338	3	for	for	ADP
ejpam-4554	338	4	the	the	DET
ejpam-4554	338	5	hyperoperation	hyperoperation	NOUN
ejpam-4554	338	6	⊙	⊙	PROPN
ejpam-4554	338	7	,	,	PUNCT
ejpam-4554	338	8	we	we	PRON
ejpam-4554	338	9	can	can	AUX
ejpam-4554	338	10	show	show	VERB
ejpam-4554	338	11	that	that	SCONJ
ejpam-4554	338	12	π(x⊙	π(x⊙	PROPN
ejpam-4554	338	13	y	y	NOUN
ejpam-4554	338	14	)	)	PUNCT
ejpam-4554	338	15	=	=	PUNCT
ejpam-4554	339	1	π(x)⊙	π(x)⊙	PROPN
ejpam-4554	339	2	π(y	π(y	PROPN
ejpam-4554	339	3	)	)	PUNCT
ejpam-4554	339	4	.	.	PUNCT
ejpam-4554	340	1	thus	thus	ADV
ejpam-4554	340	2	,	,	PUNCT
ejpam-4554	340	3	π	π	PROPN
ejpam-4554	340	4	is	be	AUX
ejpam-4554	340	5	a	a	DET
ejpam-4554	340	6	hyper	hyper	ADJ
ejpam-4554	340	7	homomorphism	homomorphism	NOUN
ejpam-4554	340	8	.	.	PUNCT
ejpam-4554	341	1	let	let	VERB
ejpam-4554	341	2	ix	ix	PRON
ejpam-4554	341	3	∈	∈	PROPN
ejpam-4554	342	1	h	h	NOUN
ejpam-4554	342	2	/	/	SYM
ejpam-4554	342	3	i	i	PRON
ejpam-4554	342	4	with	with	ADP
ejpam-4554	342	5	x	x	PROPN
ejpam-4554	342	6	∈	∈	PROPN
ejpam-4554	342	7	h.	h.	NOUN
ejpam-4554	342	8	then	then	ADV
ejpam-4554	342	9	π(x	π(x	PUNCT
ejpam-4554	342	10	)	)	PUNCT
ejpam-4554	343	1	=	=	PRON
ejpam-4554	343	2	ix	ix	ADP
ejpam-4554	343	3	∈	∈	PROPN
ejpam-4554	343	4	h	h	PROPN
ejpam-4554	343	5	/	/	SYM
ejpam-4554	343	6	i.	i.	PROPN
ejpam-4554	343	7	therefore	therefore	ADV
ejpam-4554	343	8	,	,	PUNCT
ejpam-4554	343	9	π	π	PROPN
ejpam-4554	343	10	is	be	AUX
ejpam-4554	343	11	a	a	DET
ejpam-4554	343	12	surjective	surjective	ADJ
ejpam-4554	343	13	map	map	NOUN
ejpam-4554	343	14	and	and	CCONJ
ejpam-4554	343	15	so	so	ADV
ejpam-4554	343	16	,	,	PUNCT
ejpam-4554	343	17	an	an	DET
ejpam-4554	343	18	epimorphism	epimorphism	NOUN
ejpam-4554	343	19	.	.	PUNCT
ejpam-4554	344	1	□	□	PUNCT
ejpam-4554	344	2	theorem	theorem	ADJ
ejpam-4554	344	3	4.2	4.2	NUM
ejpam-4554	344	4	.	.	PUNCT
ejpam-4554	345	1	(	(	PUNCT
ejpam-4554	345	2	homomorphism	homomorphism	PROPN
ejpam-4554	345	3	theorem	theorem	VERB
ejpam-4554	345	4	)	)	PUNCT
ejpam-4554	345	5	let	let	VERB
ejpam-4554	345	6	θ	θ	NOUN
ejpam-4554	345	7	be	be	AUX
ejpam-4554	345	8	a	a	DET
ejpam-4554	345	9	regular	regular	ADJ
ejpam-4554	345	10	congruence	congruence	NOUN
ejpam-4554	345	11	relation	relation	NOUN
ejpam-4554	345	12	on	on	ADP
ejpam-4554	345	13	h	h	NOUN
ejpam-4554	346	1	and	and	CCONJ
ejpam-4554	346	2	i	i	PRON
ejpam-4554	346	3	=	=	PUNCT
ejpam-4554	347	1	[	[	X
ejpam-4554	347	2	0]θ	0]θ	NOUN
ejpam-4554	347	3	.	.	PUNCT
ejpam-4554	348	1	if	if	SCONJ
ejpam-4554	348	2	f	f	PROPN
ejpam-4554	348	3	:	:	PUNCT
ejpam-4554	348	4	h	h	PROPN
ejpam-4554	348	5	−→	−→	ADJ
ejpam-4554	348	6	h	h	NOUN
ejpam-4554	348	7	′	′	NOUN
ejpam-4554	348	8	is	be	AUX
ejpam-4554	348	9	a	a	DET
ejpam-4554	348	10	homomorphism	homomorphism	NOUN
ejpam-4554	348	11	of	of	ADP
ejpam-4554	348	12	pseudo	pseudo	NOUN
ejpam-4554	348	13	hyper	hyper	ADJ
ejpam-4554	348	14	gr	gr	NOUN
ejpam-4554	348	15	-	-	PUNCT
ejpam-4554	348	16	algebras	algebra	NOUN
ejpam-4554	348	17	such	such	ADJ
ejpam-4554	348	18	that	that	SCONJ
ejpam-4554	348	19	f(x	f(x	PROPN
ejpam-4554	348	20	)	)	PUNCT
ejpam-4554	348	21	≪	≪	PUNCT
ejpam-4554	348	22	f(y	f(y	NOUN
ejpam-4554	348	23	)	)	PUNCT
ejpam-4554	348	24	and	and	CCONJ
ejpam-4554	348	25	f(y	f(y	NOUN
ejpam-4554	348	26	)	)	PUNCT
ejpam-4554	348	27	≪	≪	PUNCT
ejpam-4554	348	28	f(x	f(x	PROPN
ejpam-4554	348	29	)	)	PUNCT
ejpam-4554	348	30	imply	imply	VERB
ejpam-4554	348	31	that	that	SCONJ
ejpam-4554	348	32	f(x	f(x	NOUN
ejpam-4554	348	33	)	)	PUNCT
ejpam-4554	348	34	=	=	SYM
ejpam-4554	348	35	f(y	f(y	NOUN
ejpam-4554	348	36	)	)	PUNCT
ejpam-4554	348	37	for	for	ADP
ejpam-4554	348	38	all	all	DET
ejpam-4554	348	39	x	x	NOUN
ejpam-4554	348	40	,	,	PUNCT
ejpam-4554	348	41	y	y	PROPN
ejpam-4554	348	42	∈	∈	PROPN
ejpam-4554	348	43	h	h	NOUN
ejpam-4554	348	44	,	,	PUNCT
ejpam-4554	348	45	then	then	ADV
ejpam-4554	348	46	f̄	f̄	NOUN
ejpam-4554	348	47	:	:	PUNCT
ejpam-4554	348	48	h	h	X
ejpam-4554	348	49	/	/	SYM
ejpam-4554	349	1	i	i	PRON
ejpam-4554	349	2	−→	−→	ADJ
ejpam-4554	349	3	h	h	NOUN
ejpam-4554	349	4	′	′	NOUN
ejpam-4554	349	5	,	,	PUNCT
ejpam-4554	349	6	which	which	PRON
ejpam-4554	349	7	is	be	AUX
ejpam-4554	349	8	defined	define	VERB
ejpam-4554	349	9	by	by	ADP
ejpam-4554	349	10	f̄(ix	f̄(ix	NOUN
ejpam-4554	349	11	)	)	PUNCT
ejpam-4554	349	12	=	=	SYM
ejpam-4554	349	13	f(x	f(x	PROPN
ejpam-4554	349	14	)	)	PUNCT
ejpam-4554	349	15	,	,	PUNCT
ejpam-4554	349	16	for	for	ADP
ejpam-4554	349	17	all	all	DET
ejpam-4554	349	18	x	x	SYM
ejpam-4554	349	19	∈	∈	PROPN
ejpam-4554	349	20	h	h	NOUN
ejpam-4554	349	21	,	,	PUNCT
ejpam-4554	349	22	is	be	AUX
ejpam-4554	349	23	a	a	DET
ejpam-4554	349	24	unique	unique	ADJ
ejpam-4554	349	25	homomorphism	homomorphism	NOUN
ejpam-4554	349	26	such	such	ADJ
ejpam-4554	349	27	that	that	DET
ejpam-4554	349	28	f̄	f̄	PROPN
ejpam-4554	349	29	◦	◦	NOUN
ejpam-4554	349	30	π	π	PROPN
ejpam-4554	349	31	=	=	SYM
ejpam-4554	349	32	f	f	PROPN
ejpam-4554	349	33	,	,	PUNCT
ejpam-4554	349	34	where	where	SCONJ
ejpam-4554	349	35	π	π	PROPN
ejpam-4554	349	36	denotes	denote	VERB
ejpam-4554	349	37	the	the	DET
ejpam-4554	349	38	canonical	canonical	ADJ
ejpam-4554	349	39	epimorphism	epimorphism	NOUN
ejpam-4554	349	40	and	and	CCONJ
ejpam-4554	349	41	◦	◦	NOUN
ejpam-4554	349	42	is	be	AUX
ejpam-4554	349	43	the	the	DET
ejpam-4554	349	44	composition	composition	NOUN
ejpam-4554	349	45	map	map	NOUN
ejpam-4554	349	46	.	.	PUNCT
ejpam-4554	350	1	moreover	moreover	ADV
ejpam-4554	350	2	,	,	PUNCT
ejpam-4554	350	3	if	if	SCONJ
ejpam-4554	350	4	i	i	PRON
ejpam-4554	350	5	=	=	PUNCT
ejpam-4554	350	6	ker	ker	PROPN
ejpam-4554	350	7	f	f	PROPN
ejpam-4554	350	8	,	,	PUNCT
ejpam-4554	350	9	then	then	ADV
ejpam-4554	350	10	f̄	f̄	PROPN
ejpam-4554	350	11	is	be	AUX
ejpam-4554	350	12	a	a	DET
ejpam-4554	350	13	monomorphism	monomorphism	NOUN
ejpam-4554	350	14	.	.	PUNCT
ejpam-4554	351	1	proof	proof	NOUN
ejpam-4554	351	2	.	.	PUNCT
ejpam-4554	352	1	let	let	VERB
ejpam-4554	352	2	θ	θ	NOUN
ejpam-4554	352	3	be	be	AUX
ejpam-4554	352	4	a	a	DET
ejpam-4554	352	5	regular	regular	ADJ
ejpam-4554	352	6	congruence	congruence	NOUN
ejpam-4554	352	7	relation	relation	NOUN
ejpam-4554	352	8	on	on	ADP
ejpam-4554	352	9	h	h	NOUN
ejpam-4554	352	10	and	and	CCONJ
ejpam-4554	352	11	i	i	PRON
ejpam-4554	352	12	=	=	PUNCT
ejpam-4554	353	1	[	[	X
ejpam-4554	353	2	0]θ	0]θ	NOUN
ejpam-4554	353	3	.	.	PUNCT
ejpam-4554	354	1	define	define	VERB
ejpam-4554	354	2	f̄	f̄	PROPN
ejpam-4554	354	3	:	:	PUNCT
ejpam-4554	354	4	h	h	X
ejpam-4554	354	5	/	/	SYM
ejpam-4554	354	6	i	i	PRON
ejpam-4554	354	7	−→	−→	NOUN
ejpam-4554	354	8	h	h	NOUN
ejpam-4554	354	9	′	′	NUM
ejpam-4554	354	10	by	by	ADP
ejpam-4554	354	11	f̄(ix	f̄(ix	NOUN
ejpam-4554	354	12	)	)	PUNCT
ejpam-4554	354	13	=	=	SYM
ejpam-4554	354	14	f(x	f(x	PROPN
ejpam-4554	354	15	)	)	PUNCT
ejpam-4554	354	16	for	for	ADP
ejpam-4554	354	17	all	all	PRON
ejpam-4554	354	18	x	x	SYM
ejpam-4554	354	19	∈	∈	PROPN
ejpam-4554	354	20	h.	h.	NOUN
ejpam-4554	354	21	let	let	VERB
ejpam-4554	354	22	x	x	PRON
ejpam-4554	354	23	,	,	PUNCT
ejpam-4554	354	24	y	y	PROPN
ejpam-4554	354	25	∈	∈	PROPN
ejpam-4554	354	26	h	h	NOUN
ejpam-4554	354	27	such	such	ADJ
ejpam-4554	354	28	that	that	SCONJ
ejpam-4554	354	29	ix	ix	ADP
ejpam-4554	354	30	=	=	PUNCT
ejpam-4554	354	31	iy	iy	PROPN
ejpam-4554	354	32	and	and	CCONJ
ejpam-4554	354	33	let	let	VERB
ejpam-4554	354	34	t	t	PROPN
ejpam-4554	354	35	∈	∈	PRON
ejpam-4554	354	36	ix	ix	ADP
ejpam-4554	355	1	=	=	PROPN
ejpam-4554	355	2	iy	iy	PROPN
ejpam-4554	355	3	.	.	PUNCT
ejpam-4554	356	1	since	since	SCONJ
ejpam-4554	356	2	h	h	PROPN
ejpam-4554	356	3	/	/	SYM
ejpam-4554	356	4	i	i	PRON
ejpam-4554	356	5	is	be	AUX
ejpam-4554	356	6	a	a	DET
ejpam-4554	356	7	pseudo	pseudo	NOUN
ejpam-4554	356	8	hyper	hyper	ADJ
ejpam-4554	356	9	gr	gr	NOUN
ejpam-4554	356	10	-	-	PUNCT
ejpam-4554	356	11	algebra	algebra	NOUN
ejpam-4554	356	12	,	,	PUNCT
ejpam-4554	356	13	by	by	ADP
ejpam-4554	356	14	[	[	X
ejpam-4554	356	15	phgr3	phgr3	X
ejpam-4554	356	16	]	]	PUNCT
ejpam-4554	356	17	,	,	PUNCT
ejpam-4554	356	18	t	t	PROPN
ejpam-4554	356	19	≪	≪	VERB
ejpam-4554	356	20	t	t	PROPN
ejpam-4554	356	21	and	and	CCONJ
ejpam-4554	356	22	so	so	ADV
ejpam-4554	356	23	,	,	PUNCT
ejpam-4554	356	24	ix	ix	ADP
ejpam-4554	356	25	≪	≪	PUNCT
ejpam-4554	356	26	iy	iy	PROPN
ejpam-4554	356	27	.	.	PUNCT
ejpam-4554	357	1	hence	hence	ADV
ejpam-4554	357	2	i	i	PRON
ejpam-4554	357	3	∈	∈	PROPN
ejpam-4554	357	4	ix	ix	ADP
ejpam-4554	357	5	⊛	⊛	PROPN
ejpam-4554	357	6	iy	iy	PROPN
ejpam-4554	358	1	and	and	CCONJ
ejpam-4554	358	2	i	i	PRON
ejpam-4554	358	3	∈	∈	PROPN
ejpam-4554	358	4	ix	ix	PROPN
ejpam-4554	358	5	⊙	⊙	PROPN
ejpam-4554	359	1	iy	iy	PROPN
ejpam-4554	359	2	.	.	PUNCT
ejpam-4554	360	1	it	it	PRON
ejpam-4554	360	2	follows	follow	VERB
ejpam-4554	360	3	that	that	SCONJ
ejpam-4554	360	4	there	there	PRON
ejpam-4554	360	5	exist	exist	VERB
ejpam-4554	360	6	z	z	NOUN
ejpam-4554	360	7	∈	∈	PROPN
ejpam-4554	360	8	x⊛	x⊛	PROPN
ejpam-4554	361	1	y	y	PROPN
ejpam-4554	361	2	and	and	CCONJ
ejpam-4554	361	3	z	z	PROPN
ejpam-4554	361	4	∈	∈	PROPN
ejpam-4554	361	5	x⊙	x⊙	PROPN
ejpam-4554	361	6	y	y	PROPN
ejpam-4554	361	7	such	such	ADJ
ejpam-4554	362	1	that	that	SCONJ
ejpam-4554	362	2	i	i	PRON
ejpam-4554	362	3	=	=	X
ejpam-4554	362	4	iz	iz	X
ejpam-4554	362	5	.	.	PUNCT
ejpam-4554	363	1	thus	thus	ADV
ejpam-4554	363	2	,	,	PUNCT
ejpam-4554	363	3	z	z	PROPN
ejpam-4554	363	4	∈	∈	PROPN
ejpam-4554	363	5	i	i	PRON
ejpam-4554	363	6	⊆	⊆	NUM
ejpam-4554	363	7	ker	ker	NOUN
ejpam-4554	363	8	f	f	PROPN
ejpam-4554	363	9	and	and	CCONJ
ejpam-4554	363	10	so	so	ADV
ejpam-4554	363	11	f(z	f(z	PROPN
ejpam-4554	363	12	)	)	PUNCT
ejpam-4554	364	1	=	=	NUM
ejpam-4554	364	2	0′.	0′.	NOUN
ejpam-4554	364	3	since	since	SCONJ
ejpam-4554	364	4	f	f	PROPN
ejpam-4554	364	5	is	be	AUX
ejpam-4554	364	6	a	a	DET
ejpam-4554	364	7	hyper	hyper	ADJ
ejpam-4554	364	8	homomorphism	homomorphism	NOUN
ejpam-4554	364	9	,	,	PUNCT
ejpam-4554	364	10	we	we	PRON
ejpam-4554	364	11	have	have	VERB
ejpam-4554	364	12	r.	r.	PROPN
ejpam-4554	364	13	manzano	manzano	PROPN
ejpam-4554	364	14	,	,	PUNCT
ejpam-4554	364	15	jr	jr	PROPN
ejpam-4554	364	16	.	.	PROPN
ejpam-4554	364	17	,	,	PUNCT
ejpam-4554	364	18	g.	g.	PROPN
ejpam-4554	364	19	petalcorin	petalcorin	PROPN
ejpam-4554	364	20	,	,	PUNCT
ejpam-4554	364	21	jr	jr	PROPN
ejpam-4554	364	22	.	.	PROPN
ejpam-4554	364	23	/	/	SYM
ejpam-4554	364	24	eur	eur	PROPN
ejpam-4554	364	25	.	.	PUNCT
ejpam-4554	365	1	j.	j.	PROPN
ejpam-4554	365	2	pure	pure	PROPN
ejpam-4554	365	3	appl	appl	PROPN
ejpam-4554	365	4	.	.	PROPN
ejpam-4554	365	5	math	math	PROPN
ejpam-4554	365	6	,	,	PUNCT
ejpam-4554	365	7	15	15	NUM
ejpam-4554	365	8	(	(	PUNCT
ejpam-4554	365	9	4	4	NUM
ejpam-4554	365	10	)	)	PUNCT
ejpam-4554	365	11	(	(	PUNCT
ejpam-4554	365	12	2022	2022	NUM
ejpam-4554	365	13	)	)	PUNCT
ejpam-4554	365	14	,	,	PUNCT
ejpam-4554	365	15	1854	1854	NUM
ejpam-4554	365	16	-	-	SYM
ejpam-4554	365	17	1868	1868	NUM
ejpam-4554	365	18	1863	1863	NUM
ejpam-4554	365	19	0′	0′	NUM
ejpam-4554	366	1	=	=	SYM
ejpam-4554	366	2	f(z	f(z	PROPN
ejpam-4554	366	3	)	)	PUNCT
ejpam-4554	366	4	=	=	SYM
ejpam-4554	366	5	f(x⊛y	f(x⊛y	NOUN
ejpam-4554	366	6	)	)	PUNCT
ejpam-4554	366	7	=	=	SYM
ejpam-4554	366	8	f(x)⊛f(y	f(x)⊛f(y	X
ejpam-4554	366	9	)	)	PUNCT
ejpam-4554	366	10	and	and	CCONJ
ejpam-4554	366	11	0′	0′	X
ejpam-4554	367	1	=	=	SYM
ejpam-4554	367	2	f(z	f(z	PROPN
ejpam-4554	367	3	)	)	PUNCT
ejpam-4554	367	4	=	=	SYM
ejpam-4554	367	5	f(x⊙y	f(x⊙y	NOUN
ejpam-4554	367	6	)	)	PUNCT
ejpam-4554	367	7	=	=	SYM
ejpam-4554	367	8	f(x)⊙f(y	f(x)⊙f(y	PROPN
ejpam-4554	367	9	)	)	PUNCT
ejpam-4554	367	10	.	.	PUNCT
ejpam-4554	368	1	it	it	PRON
ejpam-4554	368	2	follows	follow	VERB
ejpam-4554	368	3	that	that	SCONJ
ejpam-4554	368	4	f(x	f(x	PROPN
ejpam-4554	368	5	)	)	PUNCT
ejpam-4554	368	6	≪	≪	PUNCT
ejpam-4554	368	7	f(y	f(y	NOUN
ejpam-4554	368	8	)	)	PUNCT
ejpam-4554	368	9	.	.	PUNCT
ejpam-4554	369	1	using	use	VERB
ejpam-4554	369	2	the	the	DET
ejpam-4554	369	3	same	same	ADJ
ejpam-4554	369	4	argument	argument	NOUN
ejpam-4554	369	5	,	,	PUNCT
ejpam-4554	369	6	picking	pick	VERB
ejpam-4554	369	7	t′	t′	NUM
ejpam-4554	369	8	∈	∈	PROPN
ejpam-4554	369	9	iy	iy	PROPN
ejpam-4554	369	10	=	=	PUNCT
ejpam-4554	369	11	ix	ix	ADV
ejpam-4554	369	12	will	will	AUX
ejpam-4554	369	13	imply	imply	VERB
ejpam-4554	369	14	that	that	DET
ejpam-4554	369	15	f(y	f(y	NOUN
ejpam-4554	369	16	)	)	PUNCT
ejpam-4554	369	17	≪	≪	PUNCT
ejpam-4554	369	18	f(x	f(x	PROPN
ejpam-4554	369	19	)	)	PUNCT
ejpam-4554	369	20	.	.	PUNCT
ejpam-4554	370	1	thus	thus	ADV
ejpam-4554	370	2	,	,	PUNCT
ejpam-4554	370	3	by	by	ADP
ejpam-4554	370	4	the	the	DET
ejpam-4554	370	5	hypothesis	hypothesis	NOUN
ejpam-4554	370	6	f(x	f(x	PROPN
ejpam-4554	370	7	)	)	PUNCT
ejpam-4554	370	8	≪	≪	PUNCT
ejpam-4554	370	9	f(y	f(y	NOUN
ejpam-4554	370	10	)	)	PUNCT
ejpam-4554	370	11	and	and	CCONJ
ejpam-4554	370	12	f(y	f(y	NOUN
ejpam-4554	370	13	)	)	PUNCT
ejpam-4554	370	14	≪	≪	PUNCT
ejpam-4554	370	15	f(x	f(x	PROPN
ejpam-4554	370	16	)	)	PUNCT
ejpam-4554	370	17	imply	imply	VERB
ejpam-4554	370	18	that	that	SCONJ
ejpam-4554	370	19	f(x	f(x	NOUN
ejpam-4554	370	20	)	)	PUNCT
ejpam-4554	370	21	=	=	SYM
ejpam-4554	370	22	f(y	f(y	NOUN
ejpam-4554	370	23	)	)	PUNCT
ejpam-4554	370	24	.	.	PUNCT
ejpam-4554	371	1	hence	hence	ADV
ejpam-4554	371	2	,	,	PUNCT
ejpam-4554	371	3	f̄(ix	f̄(ix	NOUN
ejpam-4554	371	4	)	)	PUNCT
ejpam-4554	371	5	=	=	SYM
ejpam-4554	371	6	f̄(iy	f̄(iy	NOUN
ejpam-4554	371	7	)	)	PUNCT
ejpam-4554	371	8	and	and	CCONJ
ejpam-4554	371	9	f̄	f̄	PROPN
ejpam-4554	371	10	is	be	AUX
ejpam-4554	371	11	a	a	DET
ejpam-4554	371	12	well	well	ADV
ejpam-4554	371	13	-	-	PUNCT
ejpam-4554	371	14	defined	define	VERB
ejpam-4554	371	15	map	map	NOUN
ejpam-4554	371	16	.	.	PUNCT
ejpam-4554	372	1	let	let	VERB
ejpam-4554	372	2	ix	ix	ADV
ejpam-4554	372	3	,	,	PUNCT
ejpam-4554	372	4	iy	iy	PROPN
ejpam-4554	372	5	∈	∈	PROPN
ejpam-4554	372	6	h	h	PROPN
ejpam-4554	372	7	/	/	SYM
ejpam-4554	372	8	i.	i.	NOUN
ejpam-4554	372	9	we	we	PRON
ejpam-4554	372	10	will	will	AUX
ejpam-4554	372	11	show	show	VERB
ejpam-4554	372	12	that	that	SCONJ
ejpam-4554	372	13	f̄(ix	f̄(ix	PROPN
ejpam-4554	372	14	⊙	⊙	PROPN
ejpam-4554	372	15	iy	iy	PROPN
ejpam-4554	372	16	)	)	PUNCT
ejpam-4554	372	17	=	=	SYM
ejpam-4554	372	18	f̄(ix	f̄(ix	NOUN
ejpam-4554	372	19	)	)	PUNCT
ejpam-4554	372	20	⊙	⊙	NOUN
ejpam-4554	372	21	f̄(iy	f̄(iy	NOUN
ejpam-4554	372	22	)	)	PUNCT
ejpam-4554	372	23	.	.	PUNCT
ejpam-4554	373	1	let	let	VERB
ejpam-4554	373	2	w	w	PROPN
ejpam-4554	373	3	∈	∈	PROPN
ejpam-4554	373	4	f̄(ix	f̄(ix	PROPN
ejpam-4554	373	5	⊙	⊙	PROPN
ejpam-4554	373	6	iy	iy	PROPN
ejpam-4554	373	7	)	)	PUNCT
ejpam-4554	373	8	.	.	PUNCT
ejpam-4554	374	1	then	then	ADV
ejpam-4554	374	2	there	there	PRON
ejpam-4554	374	3	exists	exist	VERB
ejpam-4554	374	4	it	it	PRON
ejpam-4554	374	5	∈	∈	PROPN
ejpam-4554	375	1	ix	ix	PROPN
ejpam-4554	375	2	⊙	⊙	PROPN
ejpam-4554	375	3	iy	iy	PROPN
ejpam-4554	376	1	such	such	ADJ
ejpam-4554	376	2	that	that	PRON
ejpam-4554	376	3	w	w	PROPN
ejpam-4554	376	4	=	=	PUNCT
ejpam-4554	376	5	f̄(it	f̄(it	ADJ
ejpam-4554	376	6	)	)	PUNCT
ejpam-4554	376	7	=	=	SYM
ejpam-4554	376	8	f(t	f(t	NOUN
ejpam-4554	376	9	)	)	PUNCT
ejpam-4554	376	10	.	.	PUNCT
ejpam-4554	377	1	now	now	ADV
ejpam-4554	377	2	,	,	PUNCT
ejpam-4554	377	3	it	it	PRON
ejpam-4554	377	4	∈	∈	VERB
ejpam-4554	377	5	ix	ix	PROPN
ejpam-4554	377	6	⊙	⊙	PROPN
ejpam-4554	377	7	iy	iy	PROPN
ejpam-4554	377	8	implies	imply	VERB
ejpam-4554	377	9	that	that	SCONJ
ejpam-4554	377	10	t	t	PROPN
ejpam-4554	377	11	∈	∈	PROPN
ejpam-4554	377	12	x⊙	x⊙	PROPN
ejpam-4554	377	13	y	y	PROPN
ejpam-4554	377	14	and	and	CCONJ
ejpam-4554	377	15	w	w	NOUN
ejpam-4554	377	16	=	=	SYM
ejpam-4554	377	17	f(t	f(t	NOUN
ejpam-4554	377	18	)	)	PUNCT
ejpam-4554	377	19	∈	∈	PROPN
ejpam-4554	377	20	f(x⊙	f(x⊙	PROPN
ejpam-4554	377	21	y	y	NOUN
ejpam-4554	377	22	)	)	PUNCT
ejpam-4554	377	23	=	=	PUNCT
ejpam-4554	378	1	f(x)⊙	f(x)⊙	NUM
ejpam-4554	378	2	f(y	f(y	NOUN
ejpam-4554	378	3	)	)	PUNCT
ejpam-4554	378	4	=	=	PUNCT
ejpam-4554	378	5	f̄(ix)⊙	f̄(ix)⊙	VERB
ejpam-4554	378	6	f̄(iy	f̄(iy	NOUN
ejpam-4554	378	7	)	)	PUNCT
ejpam-4554	378	8	,	,	PUNCT
ejpam-4554	378	9	thus	thus	ADV
ejpam-4554	378	10	,	,	PUNCT
ejpam-4554	378	11	f̄(ix	f̄(ix	PROPN
ejpam-4554	378	12	⊙	⊙	PROPN
ejpam-4554	378	13	iy	iy	PROPN
ejpam-4554	378	14	)	)	PUNCT
ejpam-4554	379	1	⊆	⊆	NUM
ejpam-4554	379	2	f̄(ix)⊙	f̄(ix)⊙	ADJ
ejpam-4554	379	3	f̄(iy	f̄(iy	NOUN
ejpam-4554	379	4	)	)	PUNCT
ejpam-4554	379	5	.	.	PUNCT
ejpam-4554	380	1	now	now	ADV
ejpam-4554	380	2	,	,	PUNCT
ejpam-4554	380	3	let	let	VERB
ejpam-4554	380	4	u	u	PRON
ejpam-4554	380	5	∈	∈	PROPN
ejpam-4554	380	6	f̄(ix)⊙	f̄(ix)⊙	PROPN
ejpam-4554	380	7	f̄(iy	f̄(iy	NOUN
ejpam-4554	380	8	)	)	PUNCT
ejpam-4554	380	9	=	=	SYM
ejpam-4554	380	10	f(x)⊙f(y	f(x)⊙f(y	PROPN
ejpam-4554	380	11	)	)	PUNCT
ejpam-4554	380	12	=	=	SYM
ejpam-4554	380	13	f(x⊙y	f(x⊙y	NOUN
ejpam-4554	380	14	)	)	PUNCT
ejpam-4554	380	15	.	.	PUNCT
ejpam-4554	381	1	then	then	ADV
ejpam-4554	381	2	there	there	PRON
ejpam-4554	381	3	exists	exist	VERB
ejpam-4554	381	4	an	an	DET
ejpam-4554	381	5	element	element	NOUN
ejpam-4554	381	6	v	v	ADP
ejpam-4554	381	7	∈	∈	PROPN
ejpam-4554	381	8	x⊙	x⊙	PROPN
ejpam-4554	381	9	y	y	PROPN
ejpam-4554	381	10	such	such	ADJ
ejpam-4554	381	11	that	that	SCONJ
ejpam-4554	381	12	u	u	NOUN
ejpam-4554	381	13	=	=	NOUN
ejpam-4554	381	14	f(v	f(v	PROPN
ejpam-4554	381	15	)	)	PUNCT
ejpam-4554	381	16	.	.	PUNCT
ejpam-4554	382	1	hence	hence	ADV
ejpam-4554	382	2	,	,	PUNCT
ejpam-4554	382	3	iv	iv	NUM
ejpam-4554	382	4	∈	∈	PROPN
ejpam-4554	382	5	ix⊙	ix⊙	CCONJ
ejpam-4554	382	6	iy	iy	PROPN
ejpam-4554	382	7	,	,	PUNCT
ejpam-4554	382	8	and	and	CCONJ
ejpam-4554	382	9	we	we	PRON
ejpam-4554	382	10	have	have	VERB
ejpam-4554	382	11	u	u	NOUN
ejpam-4554	382	12	=	=	NOUN
ejpam-4554	382	13	f(v	f(v	PROPN
ejpam-4554	382	14	)	)	PUNCT
ejpam-4554	382	15	=	=	SYM
ejpam-4554	382	16	f̄(iv	f̄(iv	X
ejpam-4554	382	17	)	)	PUNCT
ejpam-4554	382	18	∈	∈	PROPN
ejpam-4554	382	19	f̄(ix⊙	f̄(ix⊙	PROPN
ejpam-4554	382	20	iy	iy	PROPN
ejpam-4554	382	21	)	)	PUNCT
ejpam-4554	382	22	.	.	PUNCT
ejpam-4554	383	1	thus	thus	ADV
ejpam-4554	383	2	,	,	PUNCT
ejpam-4554	383	3	f̄(ix)⊙	f̄(ix)⊙	ADJ
ejpam-4554	383	4	f̄(iy	f̄(iy	NOUN
ejpam-4554	383	5	)	)	PUNCT
ejpam-4554	383	6	⊆	⊆	NUM
ejpam-4554	383	7	f̄(ix	f̄(ix	PROPN
ejpam-4554	383	8	⊙	⊙	PROPN
ejpam-4554	383	9	iy	iy	PROPN
ejpam-4554	383	10	)	)	PUNCT
ejpam-4554	383	11	.	.	PUNCT
ejpam-4554	384	1	hence	hence	ADV
ejpam-4554	384	2	,	,	PUNCT
ejpam-4554	384	3	f̄(ix	f̄(ix	PROPN
ejpam-4554	384	4	⊙	⊙	PROPN
ejpam-4554	384	5	iy	iy	PROPN
ejpam-4554	384	6	)	)	PUNCT
ejpam-4554	385	1	=	=	SYM
ejpam-4554	385	2	f̄(ix)⊙	f̄(ix)⊙	VERB
ejpam-4554	385	3	f̄(iy	f̄(iy	NOUN
ejpam-4554	385	4	)	)	PUNCT
ejpam-4554	385	5	.	.	PUNCT
ejpam-4554	386	1	in	in	ADP
ejpam-4554	386	2	a	a	DET
ejpam-4554	386	3	similar	similar	ADJ
ejpam-4554	386	4	manner	manner	NOUN
ejpam-4554	386	5	,	,	PUNCT
ejpam-4554	386	6	we	we	PRON
ejpam-4554	386	7	can	can	AUX
ejpam-4554	386	8	show	show	VERB
ejpam-4554	386	9	that	that	SCONJ
ejpam-4554	386	10	f̄(ix	f̄(ix	PROPN
ejpam-4554	386	11	⊛	⊛	NUM
ejpam-4554	386	12	iy	iy	PROPN
ejpam-4554	386	13	)	)	PUNCT
ejpam-4554	387	1	=	=	PUNCT
ejpam-4554	387	2	f̄(ix)⊛	f̄(ix)⊛	ADJ
ejpam-4554	387	3	f̄(iy	f̄(iy	NOUN
ejpam-4554	387	4	)	)	PUNCT
ejpam-4554	387	5	.	.	PUNCT
ejpam-4554	388	1	hence	hence	ADV
ejpam-4554	388	2	,	,	PUNCT
ejpam-4554	388	3	f̄	f̄	PROPN
ejpam-4554	388	4	is	be	AUX
ejpam-4554	388	5	a	a	DET
ejpam-4554	388	6	homomorphism	homomorphism	NOUN
ejpam-4554	388	7	.	.	PUNCT
ejpam-4554	389	1	now	now	ADV
ejpam-4554	389	2	,	,	PUNCT
ejpam-4554	389	3	dom(f̄	dom(f̄	VERB
ejpam-4554	389	4	◦	◦	NOUN
ejpam-4554	389	5	π	π	NOUN
ejpam-4554	389	6	)	)	PUNCT
ejpam-4554	390	1	=	=	SYM
ejpam-4554	390	2	h	h	NOUN
ejpam-4554	390	3	=	=	NOUN
ejpam-4554	390	4	domf	domf	NOUN
ejpam-4554	390	5	and	and	CCONJ
ejpam-4554	390	6	for	for	ADP
ejpam-4554	390	7	all	all	DET
ejpam-4554	390	8	x	x	SYM
ejpam-4554	390	9	∈	∈	PROPN
ejpam-4554	390	10	h	h	NOUN
ejpam-4554	390	11	,	,	PUNCT
ejpam-4554	390	12	(	(	PUNCT
ejpam-4554	390	13	f̄	f̄	PROPN
ejpam-4554	390	14	◦	◦	NOUN
ejpam-4554	390	15	π)(x	π)(x	PROPN
ejpam-4554	390	16	)	)	PUNCT
ejpam-4554	390	17	=	=	SYM
ejpam-4554	390	18	f̄(π(x	f̄(π(x	NOUN
ejpam-4554	390	19	)	)	PUNCT
ejpam-4554	390	20	)	)	PUNCT
ejpam-4554	391	1	=	=	PUNCT
ejpam-4554	391	2	f̄(ix	f̄(ix	NOUN
ejpam-4554	391	3	)	)	PUNCT
ejpam-4554	391	4	=	=	SYM
ejpam-4554	391	5	f(x	f(x	PROPN
ejpam-4554	391	6	)	)	PUNCT
ejpam-4554	391	7	.	.	PUNCT
ejpam-4554	392	1	hence	hence	ADV
ejpam-4554	392	2	,	,	PUNCT
ejpam-4554	392	3	f̄	f̄	PROPN
ejpam-4554	392	4	◦	◦	NOUN
ejpam-4554	392	5	π	π	PROPN
ejpam-4554	392	6	=	=	SYM
ejpam-4554	392	7	f	f	PROPN
ejpam-4554	392	8	.	.	PUNCT
ejpam-4554	393	1	to	to	PART
ejpam-4554	393	2	show	show	VERB
ejpam-4554	393	3	the	the	DET
ejpam-4554	393	4	uniqueness	uniqueness	NOUN
ejpam-4554	393	5	of	of	ADP
ejpam-4554	393	6	f̄	f̄	PROPN
ejpam-4554	393	7	,	,	PUNCT
ejpam-4554	393	8	we	we	PRON
ejpam-4554	393	9	suppose	suppose	VERB
ejpam-4554	393	10	that	that	SCONJ
ejpam-4554	393	11	there	there	PRON
ejpam-4554	393	12	is	be	VERB
ejpam-4554	393	13	another	another	DET
ejpam-4554	393	14	homomorphism	homomorphism	NOUN
ejpam-4554	393	15	g	g	ADP
ejpam-4554	393	16	such	such	ADJ
ejpam-4554	393	17	that	that	SCONJ
ejpam-4554	393	18	g	g	PROPN
ejpam-4554	393	19	◦	◦	NOUN
ejpam-4554	393	20	π	π	PROPN
ejpam-4554	393	21	=	=	SYM
ejpam-4554	393	22	f	f	PROPN
ejpam-4554	393	23	.	.	PUNCT
ejpam-4554	394	1	let	let	VERB
ejpam-4554	394	2	x	x	SYM
ejpam-4554	394	3	∈	∈	PROPN
ejpam-4554	394	4	h.	h.	PROPN
ejpam-4554	394	5	then	then	ADV
ejpam-4554	394	6	g(ix	g(ix	PROPN
ejpam-4554	394	7	)	)	PUNCT
ejpam-4554	394	8	=	=	SYM
ejpam-4554	394	9	g(π(x	g(π(x	PROPN
ejpam-4554	394	10	)	)	PUNCT
ejpam-4554	394	11	)	)	PUNCT
ejpam-4554	395	1	=	=	SYM
ejpam-4554	395	2	f(x	f(x	PROPN
ejpam-4554	395	3	)	)	PUNCT
ejpam-4554	395	4	=	=	SYM
ejpam-4554	395	5	f̄(π(x	f̄(π(x	NOUN
ejpam-4554	395	6	)	)	PUNCT
ejpam-4554	395	7	)	)	PUNCT
ejpam-4554	395	8	=	=	SYM
ejpam-4554	395	9	f̄(ix	f̄(ix	NOUN
ejpam-4554	395	10	)	)	PUNCT
ejpam-4554	395	11	.	.	PUNCT
ejpam-4554	396	1	now	now	ADV
ejpam-4554	396	2	,	,	PUNCT
ejpam-4554	396	3	we	we	PRON
ejpam-4554	396	4	will	will	AUX
ejpam-4554	396	5	show	show	VERB
ejpam-4554	396	6	that	that	SCONJ
ejpam-4554	396	7	if	if	SCONJ
ejpam-4554	396	8	i	i	PRON
ejpam-4554	396	9	=	=	VERB
ejpam-4554	396	10	ker	ker	PROPN
ejpam-4554	396	11	f	f	PROPN
ejpam-4554	396	12	,	,	PUNCT
ejpam-4554	396	13	then	then	ADV
ejpam-4554	396	14	f̄	f̄	PROPN
ejpam-4554	396	15	is	be	AUX
ejpam-4554	396	16	a	a	DET
ejpam-4554	396	17	monomorphism	monomorphism	NOUN
ejpam-4554	396	18	.	.	PUNCT
ejpam-4554	396	19	suppose	suppose	VERB
ejpam-4554	396	20	that	that	SCONJ
ejpam-4554	396	21	f̄(ix	f̄(ix	NOUN
ejpam-4554	396	22	)	)	PUNCT
ejpam-4554	396	23	=	=	SYM
ejpam-4554	396	24	f̄(iy	f̄(iy	NOUN
ejpam-4554	396	25	)	)	PUNCT
ejpam-4554	396	26	with	with	ADP
ejpam-4554	396	27	x	x	PRON
ejpam-4554	396	28	,	,	PUNCT
ejpam-4554	396	29	y	y	PROPN
ejpam-4554	396	30	∈	∈	PROPN
ejpam-4554	396	31	h.	h.	PROPN
ejpam-4554	396	32	then	then	ADV
ejpam-4554	396	33	f(x	f(x	PROPN
ejpam-4554	396	34	)	)	PUNCT
ejpam-4554	396	35	=	=	SYM
ejpam-4554	396	36	f(y	f(y	NOUN
ejpam-4554	396	37	)	)	PUNCT
ejpam-4554	396	38	.	.	PUNCT
ejpam-4554	397	1	since	since	SCONJ
ejpam-4554	397	2	f	f	PROPN
ejpam-4554	397	3	is	be	AUX
ejpam-4554	397	4	a	a	DET
ejpam-4554	397	5	homomorphism	homomorphism	NOUN
ejpam-4554	397	6	and	and	CCONJ
ejpam-4554	397	7	by	by	ADP
ejpam-4554	397	8	[	[	X
ejpam-4554	397	9	phgr3	phgr3	X
ejpam-4554	397	10	]	]	PUNCT
ejpam-4554	397	11	,	,	PUNCT
ejpam-4554	397	12	0h′	0h′	NUM
ejpam-4554	397	13	=	=	SYM
ejpam-4554	397	14	f(0h	f(0h	NOUN
ejpam-4554	397	15	)	)	PUNCT
ejpam-4554	397	16	∈	∈	PROPN
ejpam-4554	397	17	f(x⊛	f(x⊛	NOUN
ejpam-4554	397	18	x	x	X
ejpam-4554	397	19	)	)	PUNCT
ejpam-4554	397	20	=	=	PUNCT
ejpam-4554	397	21	f(x)⊛	f(x)⊛	ADJ
ejpam-4554	397	22	f(x	f(x	PROPN
ejpam-4554	397	23	)	)	PUNCT
ejpam-4554	398	1	=	=	PUNCT
ejpam-4554	398	2	f(x)⊛	f(x)⊛	ADJ
ejpam-4554	398	3	f(y	f(y	NOUN
ejpam-4554	398	4	)	)	PUNCT
ejpam-4554	398	5	=	=	PUNCT
ejpam-4554	398	6	f(x⊛	f(x⊛	PROPN
ejpam-4554	398	7	y	y	PROPN
ejpam-4554	398	8	)	)	PUNCT
ejpam-4554	398	9	.	.	PUNCT
ejpam-4554	399	1	so	so	ADV
ejpam-4554	399	2	,	,	PUNCT
ejpam-4554	399	3	there	there	PRON
ejpam-4554	399	4	exists	exist	VERB
ejpam-4554	399	5	u	u	PROPN
ejpam-4554	399	6	∈	∈	PROPN
ejpam-4554	399	7	x⊛	x⊛	PROPN
ejpam-4554	400	1	y	y	PROPN
ejpam-4554	400	2	such	such	ADJ
ejpam-4554	400	3	that	that	DET
ejpam-4554	400	4	f(u	f(u	PROPN
ejpam-4554	400	5	)	)	PUNCT
ejpam-4554	400	6	=	=	SYM
ejpam-4554	400	7	0h′	0h′	NUM
ejpam-4554	400	8	.	.	PUNCT
ejpam-4554	401	1	hence	hence	ADV
ejpam-4554	401	2	,	,	PUNCT
ejpam-4554	401	3	u	u	PROPN
ejpam-4554	401	4	∈	∈	PROPN
ejpam-4554	401	5	ker	ker	NOUN
ejpam-4554	402	1	f	f	PROPN
ejpam-4554	402	2	=	=	SYM
ejpam-4554	402	3	i	i	PROPN
ejpam-4554	402	4	and	and	CCONJ
ejpam-4554	402	5	so	so	ADV
ejpam-4554	402	6	,	,	PUNCT
ejpam-4554	402	7	uθ0	uθ0	ADJ
ejpam-4554	402	8	.	.	PUNCT
ejpam-4554	403	1	it	it	PRON
ejpam-4554	403	2	follows	follow	VERB
ejpam-4554	403	3	that	that	SCONJ
ejpam-4554	403	4	(	(	PUNCT
ejpam-4554	403	5	x⊛	x⊛	INTJ
ejpam-4554	403	6	y)θ{0	y)θ{0	ADJ
ejpam-4554	403	7	}	}	PUNCT
ejpam-4554	403	8	.	.	PUNCT
ejpam-4554	404	1	also	also	ADV
ejpam-4554	404	2	,	,	PUNCT
ejpam-4554	404	3	0h′	0h′	NUM
ejpam-4554	404	4	=	=	SYM
ejpam-4554	404	5	f(0h	f(0h	NOUN
ejpam-4554	404	6	)	)	PUNCT
ejpam-4554	404	7	∈	∈	PROPN
ejpam-4554	404	8	f(x⊛	f(x⊛	NOUN
ejpam-4554	404	9	x	x	X
ejpam-4554	404	10	)	)	PUNCT
ejpam-4554	404	11	=	=	PUNCT
ejpam-4554	404	12	f(x)⊛	f(x)⊛	ADJ
ejpam-4554	404	13	f(x	f(x	PROPN
ejpam-4554	404	14	)	)	PUNCT
ejpam-4554	404	15	=	=	SYM
ejpam-4554	404	16	f(y)⊛	f(y)⊛	PROPN
ejpam-4554	404	17	f(x	f(x	PROPN
ejpam-4554	404	18	)	)	PUNCT
ejpam-4554	404	19	=	=	SYM
ejpam-4554	404	20	f(y	f(y	NOUN
ejpam-4554	404	21	⊛	⊛	NUM
ejpam-4554	404	22	x	x	NOUN
ejpam-4554	404	23	)	)	PUNCT
ejpam-4554	404	24	.	.	PUNCT
ejpam-4554	405	1	so	so	ADV
ejpam-4554	405	2	,	,	PUNCT
ejpam-4554	405	3	there	there	PRON
ejpam-4554	405	4	exists	exist	VERB
ejpam-4554	405	5	v	v	ADP
ejpam-4554	405	6	∈	∈	PROPN
ejpam-4554	405	7	y	y	PROPN
ejpam-4554	405	8	⊛	⊛	NUM
ejpam-4554	405	9	x	x	PUNCT
ejpam-4554	405	10	such	such	ADJ
ejpam-4554	405	11	that	that	SCONJ
ejpam-4554	405	12	f(v	f(v	NOUN
ejpam-4554	405	13	)	)	PUNCT
ejpam-4554	406	1	=	=	SYM
ejpam-4554	406	2	0h′	0h′	NUM
ejpam-4554	406	3	.	.	PUNCT
ejpam-4554	407	1	then	then	ADV
ejpam-4554	407	2	v	v	X
ejpam-4554	407	3	∈	∈	PROPN
ejpam-4554	407	4	ker	ker	NOUN
ejpam-4554	408	1	f	f	PROPN
ejpam-4554	408	2	=	=	SYM
ejpam-4554	408	3	i	i	PROPN
ejpam-4554	408	4	and	and	CCONJ
ejpam-4554	408	5	so	so	ADV
ejpam-4554	408	6	,	,	PUNCT
ejpam-4554	408	7	vθ0	vθ0	NOUN
ejpam-4554	408	8	.	.	PUNCT
ejpam-4554	409	1	hence	hence	ADV
ejpam-4554	409	2	,	,	PUNCT
ejpam-4554	409	3	(	(	PUNCT
ejpam-4554	409	4	y	y	PROPN
ejpam-4554	409	5	⊛	⊛	NUM
ejpam-4554	409	6	x)θ{0	x)θ{0	NUM
ejpam-4554	409	7	}	}	PUNCT
ejpam-4554	409	8	.	.	PUNCT
ejpam-4554	410	1	similarly	similarly	ADV
ejpam-4554	410	2	,	,	PUNCT
ejpam-4554	410	3	0h′	0h′	NUM
ejpam-4554	410	4	=	=	SYM
ejpam-4554	410	5	f(0h	f(0h	NOUN
ejpam-4554	410	6	)	)	PUNCT
ejpam-4554	410	7	∈	∈	PROPN
ejpam-4554	410	8	f(x⊙	f(x⊙	PROPN
ejpam-4554	410	9	x	x	NOUN
ejpam-4554	410	10	)	)	PUNCT
ejpam-4554	410	11	=	=	PUNCT
ejpam-4554	411	1	f(x)⊙	f(x)⊙	NUM
ejpam-4554	411	2	f(x	f(x	PROPN
ejpam-4554	411	3	)	)	PUNCT
ejpam-4554	411	4	=	=	PUNCT
ejpam-4554	412	1	f(x)⊙	f(x)⊙	NUM
ejpam-4554	412	2	f(y	f(y	NOUN
ejpam-4554	412	3	)	)	PUNCT
ejpam-4554	412	4	=	=	SYM
ejpam-4554	413	1	f(x⊙	f(x⊙	PROPN
ejpam-4554	413	2	y	y	NOUN
ejpam-4554	413	3	)	)	PUNCT
ejpam-4554	413	4	.	.	PUNCT
ejpam-4554	414	1	so	so	ADV
ejpam-4554	414	2	,	,	PUNCT
ejpam-4554	414	3	there	there	PRON
ejpam-4554	414	4	exists	exist	VERB
ejpam-4554	414	5	u	u	PROPN
ejpam-4554	414	6	∈	∈	PROPN
ejpam-4554	414	7	x	x	SYM
ejpam-4554	414	8	⊙	⊙	PROPN
ejpam-4554	414	9	y	y	PROPN
ejpam-4554	414	10	such	such	ADJ
ejpam-4554	414	11	that	that	DET
ejpam-4554	414	12	f(u	f(u	PROPN
ejpam-4554	414	13	)	)	PUNCT
ejpam-4554	415	1	=	=	SYM
ejpam-4554	416	1	0h′	0h′	NUM
ejpam-4554	416	2	.	.	PUNCT
ejpam-4554	417	1	this	this	PRON
ejpam-4554	417	2	means	mean	VERB
ejpam-4554	417	3	that	that	SCONJ
ejpam-4554	417	4	u	u	PROPN
ejpam-4554	417	5	∈	∈	PROPN
ejpam-4554	417	6	ker	ker	NOUN
ejpam-4554	418	1	f	f	PROPN
ejpam-4554	418	2	=	=	SYM
ejpam-4554	418	3	i	i	PROPN
ejpam-4554	418	4	and	and	CCONJ
ejpam-4554	418	5	so	so	ADV
ejpam-4554	418	6	,	,	PUNCT
ejpam-4554	418	7	uθ0	uθ0	NOUN
ejpam-4554	418	8	which	which	PRON
ejpam-4554	418	9	implies	imply	VERB
ejpam-4554	418	10	that	that	SCONJ
ejpam-4554	418	11	(	(	PUNCT
ejpam-4554	418	12	x⊙	x⊙	PROPN
ejpam-4554	418	13	y)θ{0	y)θ{0	NOUN
ejpam-4554	418	14	}	}	PUNCT
ejpam-4554	418	15	.	.	PUNCT
ejpam-4554	419	1	lastly	lastly	ADV
ejpam-4554	419	2	,	,	PUNCT
ejpam-4554	419	3	0h′	0h′	NUM
ejpam-4554	419	4	=	=	SYM
ejpam-4554	419	5	f(0h	f(0h	NOUN
ejpam-4554	419	6	)	)	PUNCT
ejpam-4554	419	7	∈	∈	PROPN
ejpam-4554	419	8	f(x⊙	f(x⊙	PROPN
ejpam-4554	419	9	x	x	NOUN
ejpam-4554	419	10	)	)	PUNCT
ejpam-4554	419	11	=	=	PUNCT
ejpam-4554	420	1	f(x)⊙	f(x)⊙	NUM
ejpam-4554	420	2	f(x	f(x	PROPN
ejpam-4554	420	3	)	)	PUNCT
ejpam-4554	420	4	=	=	PUNCT
ejpam-4554	421	1	f(y)⊙	f(y)⊙	PROPN
ejpam-4554	421	2	f(x	f(x	PROPN
ejpam-4554	421	3	)	)	PUNCT
ejpam-4554	421	4	=	=	SYM
ejpam-4554	421	5	f(y	f(y	PROPN
ejpam-4554	421	6	⊙	⊙	X
ejpam-4554	421	7	x	x	NOUN
ejpam-4554	421	8	)	)	PUNCT
ejpam-4554	421	9	.	.	PUNCT
ejpam-4554	422	1	r.	r.	PROPN
ejpam-4554	422	2	manzano	manzano	PROPN
ejpam-4554	422	3	,	,	PUNCT
ejpam-4554	422	4	jr	jr	PROPN
ejpam-4554	422	5	.	.	PROPN
ejpam-4554	422	6	,	,	PUNCT
ejpam-4554	422	7	g.	g.	PROPN
ejpam-4554	422	8	petalcorin	petalcorin	PROPN
ejpam-4554	422	9	,	,	PUNCT
ejpam-4554	422	10	jr	jr	PROPN
ejpam-4554	422	11	.	.	PROPN
ejpam-4554	422	12	/	/	SYM
ejpam-4554	422	13	eur	eur	PROPN
ejpam-4554	422	14	.	.	PUNCT
ejpam-4554	423	1	j.	j.	PROPN
ejpam-4554	423	2	pure	pure	PROPN
ejpam-4554	423	3	appl	appl	PROPN
ejpam-4554	423	4	.	.	PROPN
ejpam-4554	423	5	math	math	PROPN
ejpam-4554	423	6	,	,	PUNCT
ejpam-4554	423	7	15	15	NUM
ejpam-4554	423	8	(	(	PUNCT
ejpam-4554	423	9	4	4	NUM
ejpam-4554	423	10	)	)	PUNCT
ejpam-4554	423	11	(	(	PUNCT
ejpam-4554	423	12	2022	2022	NUM
ejpam-4554	423	13	)	)	PUNCT
ejpam-4554	423	14	,	,	PUNCT
ejpam-4554	423	15	1854	1854	NUM
ejpam-4554	423	16	-	-	SYM
ejpam-4554	423	17	1868	1868	NUM
ejpam-4554	423	18	1864	1864	NUM
ejpam-4554	423	19	thus	thus	ADV
ejpam-4554	423	20	,	,	PUNCT
ejpam-4554	423	21	there	there	PRON
ejpam-4554	423	22	exists	exist	VERB
ejpam-4554	423	23	v	v	ADP
ejpam-4554	423	24	∈	∈	PROPN
ejpam-4554	423	25	y	y	PROPN
ejpam-4554	423	26	⊙	⊙	PROPN
ejpam-4554	423	27	x	x	PUNCT
ejpam-4554	423	28	such	such	ADJ
ejpam-4554	423	29	that	that	SCONJ
ejpam-4554	423	30	f(v	f(v	NOUN
ejpam-4554	423	31	)	)	PUNCT
ejpam-4554	423	32	=	=	SYM
ejpam-4554	424	1	0h′	0h′	NUM
ejpam-4554	424	2	.	.	PUNCT
ejpam-4554	425	1	moreover	moreover	ADV
ejpam-4554	425	2	,	,	PUNCT
ejpam-4554	425	3	v	v	PROPN
ejpam-4554	425	4	∈	∈	PROPN
ejpam-4554	425	5	ker	ker	NOUN
ejpam-4554	426	1	f	f	PROPN
ejpam-4554	426	2	=	=	SYM
ejpam-4554	426	3	i	i	PROPN
ejpam-4554	426	4	and	and	CCONJ
ejpam-4554	426	5	vθ0	vθ0	ADJ
ejpam-4554	426	6	.	.	PUNCT
ejpam-4554	427	1	thus	thus	ADV
ejpam-4554	427	2	,	,	PUNCT
ejpam-4554	427	3	(	(	PUNCT
ejpam-4554	427	4	y	y	PROPN
ejpam-4554	427	5	⊙	⊙	PROPN
ejpam-4554	427	6	x)θ{0	x)θ{0	PROPN
ejpam-4554	427	7	}	}	PUNCT
ejpam-4554	427	8	.	.	PUNCT
ejpam-4554	428	1	since	since	SCONJ
ejpam-4554	428	2	θ	θ	PROPN
ejpam-4554	428	3	is	be	AUX
ejpam-4554	428	4	a	a	DET
ejpam-4554	428	5	regular	regular	ADJ
ejpam-4554	428	6	congruence	congruence	NOUN
ejpam-4554	428	7	relation	relation	NOUN
ejpam-4554	428	8	,	,	PUNCT
ejpam-4554	428	9	it	it	PRON
ejpam-4554	428	10	follows	follow	VERB
ejpam-4554	428	11	that	that	SCONJ
ejpam-4554	428	12	xθy	xθy	PROPN
ejpam-4554	428	13	.	.	PUNCT
ejpam-4554	429	1	thus	thus	ADV
ejpam-4554	429	2	,	,	PUNCT
ejpam-4554	429	3	ix	ix	ADP
ejpam-4554	429	4	=	=	PROPN
ejpam-4554	429	5	iy	iy	PROPN
ejpam-4554	429	6	.	.	PUNCT
ejpam-4554	430	1	therefore	therefore	ADV
ejpam-4554	430	2	,	,	PUNCT
ejpam-4554	430	3	f̄	f̄	PROPN
ejpam-4554	430	4	is	be	AUX
ejpam-4554	430	5	a	a	DET
ejpam-4554	430	6	one	one	NUM
ejpam-4554	430	7	-	-	PUNCT
ejpam-4554	430	8	to	to	ADP
ejpam-4554	430	9	-	-	PUNCT
ejpam-4554	430	10	one	one	NUM
ejpam-4554	430	11	map	map	NOUN
ejpam-4554	430	12	.	.	PUNCT
ejpam-4554	431	1	this	this	PRON
ejpam-4554	431	2	proves	prove	VERB
ejpam-4554	431	3	the	the	DET
ejpam-4554	431	4	theorem	theorem	NOUN
ejpam-4554	431	5	.	.	PUNCT
ejpam-4554	432	1	□	□	PUNCT
ejpam-4554	432	2	before	before	SCONJ
ejpam-4554	432	3	we	we	PRON
ejpam-4554	432	4	prove	prove	VERB
ejpam-4554	432	5	the	the	DET
ejpam-4554	432	6	first	first	ADJ
ejpam-4554	432	7	isomorphism	isomorphism	NOUN
ejpam-4554	432	8	theorem	theorem	NOUN
ejpam-4554	432	9	,	,	PUNCT
ejpam-4554	432	10	let	let	VERB
ejpam-4554	432	11	us	we	PRON
ejpam-4554	432	12	consider	consider	VERB
ejpam-4554	432	13	the	the	DET
ejpam-4554	432	14	following	follow	VERB
ejpam-4554	432	15	example	example	NOUN
ejpam-4554	432	16	which	which	PRON
ejpam-4554	432	17	is	be	AUX
ejpam-4554	432	18	a	a	DET
ejpam-4554	432	19	specific	specific	ADJ
ejpam-4554	432	20	case	case	NOUN
ejpam-4554	432	21	of	of	ADP
ejpam-4554	432	22	the	the	DET
ejpam-4554	432	23	next	next	ADJ
ejpam-4554	432	24	theorem	theorem	PROPN
ejpam-4554	432	25	.	.	PROPN
ejpam-4554	432	26	example	example	NOUN
ejpam-4554	432	27	4.3	4.3	NUM
ejpam-4554	432	28	.	.	PUNCT
ejpam-4554	432	29	consider	consider	VERB
ejpam-4554	432	30	the	the	DET
ejpam-4554	432	31	pseudo	pseudo	NOUN
ejpam-4554	432	32	hyper	hyper	ADJ
ejpam-4554	432	33	gr	gr	NOUN
ejpam-4554	432	34	-	-	PUNCT
ejpam-4554	432	35	algebra	algebra	NOUN
ejpam-4554	432	36	h	h	NOUN
ejpam-4554	432	37	=	=	SYM
ejpam-4554	432	38	{	{	PUNCT
ejpam-4554	432	39	0	0	NUM
ejpam-4554	432	40	,	,	PUNCT
ejpam-4554	432	41	1	1	NUM
ejpam-4554	432	42	,	,	PUNCT
ejpam-4554	432	43	2	2	NUM
ejpam-4554	432	44	}	}	PUNCT
ejpam-4554	432	45	in	in	ADP
ejpam-4554	432	46	example	example	NOUN
ejpam-4554	432	47	3.6	3.6	NUM
ejpam-4554	432	48	.	.	PUNCT
ejpam-4554	433	1	we	we	PRON
ejpam-4554	433	2	can	can	AUX
ejpam-4554	433	3	verify	verify	VERB
ejpam-4554	433	4	that	that	SCONJ
ejpam-4554	433	5	the	the	DET
ejpam-4554	433	6	given	give	VERB
ejpam-4554	433	7	congruence	congruence	NOUN
ejpam-4554	433	8	relation	relation	NOUN
ejpam-4554	433	9	θ	θ	PROPN
ejpam-4554	433	10	on	on	ADP
ejpam-4554	433	11	h	h	NOUN
ejpam-4554	433	12	is	be	AUX
ejpam-4554	433	13	regular	regular	ADJ
ejpam-4554	433	14	.	.	PUNCT
ejpam-4554	434	1	in	in	ADP
ejpam-4554	434	2	our	our	PRON
ejpam-4554	434	3	case	case	NOUN
ejpam-4554	434	4	,	,	PUNCT
ejpam-4554	434	5	i	i	PRON
ejpam-4554	434	6	=	=	PUNCT
ejpam-4554	435	1	[	[	X
ejpam-4554	435	2	0]θ	0]θ	X
ejpam-4554	435	3	=	=	SYM
ejpam-4554	435	4	{	{	PUNCT
ejpam-4554	435	5	0	0	NUM
ejpam-4554	435	6	,	,	PUNCT
ejpam-4554	435	7	1	1	NUM
ejpam-4554	435	8	}	}	PUNCT
ejpam-4554	435	9	and	and	CCONJ
ejpam-4554	435	10	i2	i2	PROPN
ejpam-4554	435	11	=	=	PUNCT
ejpam-4554	435	12	{	{	PUNCT
ejpam-4554	435	13	2	2	NUM
ejpam-4554	435	14	}	}	PUNCT
ejpam-4554	435	15	.	.	PUNCT
ejpam-4554	436	1	then	then	ADV
ejpam-4554	436	2	h	h	X
ejpam-4554	436	3	/	/	SYM
ejpam-4554	436	4	i	i	PRON
ejpam-4554	436	5	=	=	PUNCT
ejpam-4554	436	6	{	{	PUNCT
ejpam-4554	436	7	i	i	PROPN
ejpam-4554	436	8	,	,	PUNCT
ejpam-4554	436	9	i2	i2	PROPN
ejpam-4554	436	10	}	}	PUNCT
ejpam-4554	436	11	whose	whose	DET
ejpam-4554	436	12	cayley	cayley	NOUN
ejpam-4554	436	13	table	table	NOUN
ejpam-4554	436	14	is	be	AUX
ejpam-4554	436	15	shown	show	VERB
ejpam-4554	436	16	below	below	ADP
ejpam-4554	436	17	⊛	⊛	NUM
ejpam-4554	436	18	i	i	PROPN
ejpam-4554	436	19	i2	i2	PROPN
ejpam-4554	436	20	i	i	PRON
ejpam-4554	436	21	{	{	PUNCT
ejpam-4554	436	22	i	i	NOUN
ejpam-4554	436	23	}	}	PUNCT
ejpam-4554	436	24	{	{	PUNCT
ejpam-4554	436	25	i	i	PROPN
ejpam-4554	436	26	}	}	PUNCT
ejpam-4554	436	27	i2	i2	PROPN
ejpam-4554	436	28	{	{	PUNCT
ejpam-4554	436	29	i	i	PROPN
ejpam-4554	436	30	,	,	PUNCT
ejpam-4554	436	31	i2	i2	PROPN
ejpam-4554	436	32	}	}	PUNCT
ejpam-4554	436	33	{	{	PUNCT
ejpam-4554	436	34	i	i	PROPN
ejpam-4554	436	35	,	,	PUNCT
ejpam-4554	436	36	i2	i2	PROPN
ejpam-4554	436	37	}	}	PUNCT
ejpam-4554	436	38	⊙	⊙	NOUN
ejpam-4554	437	1	i	i	PRON
ejpam-4554	437	2	i2	i2	PROPN
ejpam-4554	437	3	i	i	PRON
ejpam-4554	437	4	{	{	PUNCT
ejpam-4554	437	5	i	i	NOUN
ejpam-4554	437	6	}	}	PUNCT
ejpam-4554	437	7	{	{	PUNCT
ejpam-4554	437	8	i	i	PROPN
ejpam-4554	437	9	,	,	PUNCT
ejpam-4554	437	10	i2	i2	PROPN
ejpam-4554	437	11	}	}	PUNCT
ejpam-4554	437	12	i2	i2	PROPN
ejpam-4554	437	13	{	{	PUNCT
ejpam-4554	437	14	i	i	PROPN
ejpam-4554	437	15	,	,	PUNCT
ejpam-4554	437	16	i2	i2	PROPN
ejpam-4554	437	17	}	}	PUNCT
ejpam-4554	437	18	{	{	PUNCT
ejpam-4554	437	19	i	i	PROPN
ejpam-4554	437	20	,	,	PUNCT
ejpam-4554	437	21	i2	i2	PROPN
ejpam-4554	437	22	}	}	PUNCT
ejpam-4554	437	23	by	by	ADP
ejpam-4554	437	24	routine	routine	ADJ
ejpam-4554	437	25	calculations	calculation	NOUN
ejpam-4554	437	26	,	,	PUNCT
ejpam-4554	437	27	h	h	NOUN
ejpam-4554	437	28	/	/	SYM
ejpam-4554	438	1	i	i	PRON
ejpam-4554	438	2	is	be	AUX
ejpam-4554	438	3	a	a	DET
ejpam-4554	438	4	pseudo	pseudo	NOUN
ejpam-4554	438	5	hyper	hyper	ADJ
ejpam-4554	438	6	gr	gr	NOUN
ejpam-4554	438	7	-	-	NOUN
ejpam-4554	438	8	algebra	algebra	NOUN
ejpam-4554	438	9	.	.	PUNCT
ejpam-4554	439	1	now	now	ADV
ejpam-4554	439	2	,	,	PUNCT
ejpam-4554	439	3	consider	consider	VERB
ejpam-4554	439	4	the	the	DET
ejpam-4554	439	5	set	set	NOUN
ejpam-4554	439	6	h	h	NOUN
ejpam-4554	439	7	′	′	NUM
ejpam-4554	439	8	=	=	PUNCT
ejpam-4554	440	1	{	{	PUNCT
ejpam-4554	440	2	0	0	NUM
ejpam-4554	440	3	,	,	PUNCT
ejpam-4554	440	4	1	1	NUM
ejpam-4554	440	5	}	}	PUNCT
ejpam-4554	440	6	together	together	ADV
ejpam-4554	440	7	with	with	ADP
ejpam-4554	440	8	the	the	DET
ejpam-4554	440	9	cayley	cayley	ADJ
ejpam-4554	440	10	tables	table	NOUN
ejpam-4554	440	11	below	below	ADP
ejpam-4554	440	12	⊛	⊛	NUM
ejpam-4554	440	13	0	0	NUM
ejpam-4554	440	14	1	1	NUM
ejpam-4554	440	15	0	0	NUM
ejpam-4554	440	16	{	{	PUNCT
ejpam-4554	440	17	0	0	NUM
ejpam-4554	440	18	}	}	PUNCT
ejpam-4554	440	19	{	{	PUNCT
ejpam-4554	440	20	0	0	NUM
ejpam-4554	440	21	}	}	SYM
ejpam-4554	440	22	1	1	NUM
ejpam-4554	440	23	{	{	PUNCT
ejpam-4554	440	24	0	0	NUM
ejpam-4554	440	25	,	,	PUNCT
ejpam-4554	440	26	1	1	NUM
ejpam-4554	440	27	}	}	PUNCT
ejpam-4554	440	28	{	{	PUNCT
ejpam-4554	440	29	0	0	NUM
ejpam-4554	440	30	,	,	PUNCT
ejpam-4554	440	31	1	1	NUM
ejpam-4554	440	32	}	}	PUNCT
ejpam-4554	440	33	⊙	⊙	X
ejpam-4554	440	34	0	0	NUM
ejpam-4554	440	35	1	1	NUM
ejpam-4554	440	36	0	0	NUM
ejpam-4554	440	37	{	{	PUNCT
ejpam-4554	440	38	0	0	NUM
ejpam-4554	440	39	}	}	PUNCT
ejpam-4554	440	40	{	{	PUNCT
ejpam-4554	440	41	0	0	NUM
ejpam-4554	440	42	,	,	PUNCT
ejpam-4554	440	43	1	1	NUM
ejpam-4554	440	44	}	}	SYM
ejpam-4554	440	45	1	1	NUM
ejpam-4554	440	46	{	{	PUNCT
ejpam-4554	440	47	0	0	NUM
ejpam-4554	440	48	,	,	PUNCT
ejpam-4554	440	49	1	1	NUM
ejpam-4554	440	50	}	}	PUNCT
ejpam-4554	440	51	{	{	PUNCT
ejpam-4554	440	52	0	0	NUM
ejpam-4554	440	53	,	,	PUNCT
ejpam-4554	440	54	1	1	NUM
ejpam-4554	440	55	}	}	PUNCT
ejpam-4554	440	56	by	by	ADP
ejpam-4554	440	57	routine	routine	ADJ
ejpam-4554	440	58	calculations	calculation	NOUN
ejpam-4554	440	59	,	,	PUNCT
ejpam-4554	440	60	h	h	NOUN
ejpam-4554	440	61	′	′	NOUN
ejpam-4554	440	62	is	be	AUX
ejpam-4554	440	63	a	a	DET
ejpam-4554	440	64	pseudo	pseudo	NOUN
ejpam-4554	440	65	hyper	hyper	ADJ
ejpam-4554	440	66	gr	gr	NOUN
ejpam-4554	440	67	-	-	PUNCT
ejpam-4554	440	68	algebra	algebra	NOUN
ejpam-4554	440	69	.	.	PUNCT
ejpam-4554	441	1	define	define	VERB
ejpam-4554	441	2	the	the	DET
ejpam-4554	441	3	map	map	NOUN
ejpam-4554	442	1	f	f	NOUN
ejpam-4554	442	2	:	:	PUNCT
ejpam-4554	442	3	h	h	PROPN
ejpam-4554	442	4	−→	−→	ADJ
ejpam-4554	442	5	h	h	NOUN
ejpam-4554	442	6	′	′	VERB
ejpam-4554	442	7	by	by	ADP
ejpam-4554	442	8	f(0	f(0	NOUN
ejpam-4554	442	9	)	)	PUNCT
ejpam-4554	442	10	=	=	SYM
ejpam-4554	442	11	0	0	PUNCT
ejpam-4554	442	12	=	=	SYM
ejpam-4554	442	13	f(1	f(1	PROPN
ejpam-4554	442	14	)	)	PUNCT
ejpam-4554	442	15	and	and	CCONJ
ejpam-4554	442	16	f(2	f(2	PROPN
ejpam-4554	442	17	)	)	PUNCT
ejpam-4554	442	18	=	=	SYM
ejpam-4554	443	1	1	1	X
ejpam-4554	443	2	.	.	PUNCT
ejpam-4554	444	1	then	then	ADV
ejpam-4554	444	2	f	f	PROPN
ejpam-4554	444	3	is	be	AUX
ejpam-4554	444	4	a	a	DET
ejpam-4554	444	5	homomorphism	homomorphism	NOUN
ejpam-4554	444	6	as	as	SCONJ
ejpam-4554	444	7	shown	show	VERB
ejpam-4554	444	8	in	in	ADP
ejpam-4554	444	9	table	table	NOUN
ejpam-4554	444	10	below	below	ADP
ejpam-4554	444	11	x	x	PROPN
ejpam-4554	444	12	y	y	PROPN
ejpam-4554	444	13	x⊛	x⊛	PROPN
ejpam-4554	444	14	y	y	PROPN
ejpam-4554	444	15	f(x⊛	f(x⊛	PROPN
ejpam-4554	444	16	y	y	PROPN
ejpam-4554	444	17	)	)	PUNCT
ejpam-4554	444	18	f(x	f(x	PROPN
ejpam-4554	444	19	)	)	PUNCT
ejpam-4554	444	20	f(y	f(y	NOUN
ejpam-4554	444	21	)	)	PUNCT
ejpam-4554	444	22	f(x)⊛	f(x)⊛	NOUN
ejpam-4554	444	23	f(y	f(y	NOUN
ejpam-4554	444	24	)	)	PUNCT
ejpam-4554	444	25	0	0	NUM
ejpam-4554	444	26	0	0	NUM
ejpam-4554	444	27	{	{	PUNCT
ejpam-4554	444	28	0	0	NUM
ejpam-4554	444	29	}	}	PUNCT
ejpam-4554	444	30	{	{	PUNCT
ejpam-4554	444	31	0	0	NUM
ejpam-4554	444	32	}	}	SYM
ejpam-4554	444	33	0	0	NUM
ejpam-4554	444	34	0	0	NUM
ejpam-4554	444	35	{	{	PUNCT
ejpam-4554	444	36	0	0	NUM
ejpam-4554	444	37	}	}	SYM
ejpam-4554	444	38	0	0	NUM
ejpam-4554	444	39	1	1	NUM
ejpam-4554	444	40	{	{	PUNCT
ejpam-4554	444	41	0	0	NUM
ejpam-4554	444	42	}	}	PUNCT
ejpam-4554	444	43	{	{	PUNCT
ejpam-4554	444	44	0	0	NUM
ejpam-4554	444	45	}	}	SYM
ejpam-4554	444	46	0	0	NUM
ejpam-4554	444	47	0	0	NUM
ejpam-4554	444	48	{	{	PUNCT
ejpam-4554	444	49	0	0	NUM
ejpam-4554	444	50	}	}	SYM
ejpam-4554	444	51	0	0	NUM
ejpam-4554	444	52	2	2	NUM
ejpam-4554	444	53	{	{	PUNCT
ejpam-4554	444	54	0	0	NUM
ejpam-4554	444	55	}	}	PUNCT
ejpam-4554	444	56	{	{	PUNCT
ejpam-4554	444	57	0	0	NUM
ejpam-4554	444	58	}	}	SYM
ejpam-4554	444	59	0	0	NUM
ejpam-4554	444	60	1	1	NUM
ejpam-4554	444	61	{	{	PUNCT
ejpam-4554	444	62	0	0	NUM
ejpam-4554	444	63	}	}	SYM
ejpam-4554	444	64	1	1	NUM
ejpam-4554	444	65	0	0	NUM
ejpam-4554	444	66	{	{	PUNCT
ejpam-4554	444	67	0	0	NUM
ejpam-4554	444	68	,	,	PUNCT
ejpam-4554	444	69	1	1	NUM
ejpam-4554	444	70	}	}	PUNCT
ejpam-4554	444	71	{	{	PUNCT
ejpam-4554	444	72	0	0	NUM
ejpam-4554	444	73	}	}	SYM
ejpam-4554	444	74	0	0	NUM
ejpam-4554	444	75	0	0	NUM
ejpam-4554	444	76	{	{	PUNCT
ejpam-4554	444	77	0	0	NUM
ejpam-4554	444	78	}	}	SYM
ejpam-4554	444	79	1	1	NUM
ejpam-4554	444	80	1	1	NUM
ejpam-4554	444	81	{	{	PUNCT
ejpam-4554	444	82	0	0	NUM
ejpam-4554	444	83	,	,	PUNCT
ejpam-4554	444	84	1	1	NUM
ejpam-4554	444	85	}	}	PUNCT
ejpam-4554	444	86	{	{	PUNCT
ejpam-4554	444	87	0	0	NUM
ejpam-4554	444	88	}	}	SYM
ejpam-4554	444	89	0	0	NUM
ejpam-4554	444	90	0	0	NUM
ejpam-4554	444	91	{	{	PUNCT
ejpam-4554	444	92	0	0	NUM
ejpam-4554	444	93	}	}	SYM
ejpam-4554	444	94	1	1	NUM
ejpam-4554	444	95	2	2	NUM
ejpam-4554	444	96	{	{	PUNCT
ejpam-4554	444	97	0	0	NUM
ejpam-4554	444	98	,	,	PUNCT
ejpam-4554	444	99	2	2	NUM
ejpam-4554	444	100	}	}	PUNCT
ejpam-4554	444	101	{	{	PUNCT
ejpam-4554	444	102	0	0	NUM
ejpam-4554	444	103	}	}	SYM
ejpam-4554	444	104	0	0	NUM
ejpam-4554	444	105	1	1	NUM
ejpam-4554	444	106	{	{	PUNCT
ejpam-4554	444	107	0	0	NUM
ejpam-4554	444	108	}	}	SYM
ejpam-4554	444	109	2	2	NUM
ejpam-4554	444	110	0	0	NUM
ejpam-4554	444	111	{	{	PUNCT
ejpam-4554	444	112	0	0	NUM
ejpam-4554	444	113	,	,	PUNCT
ejpam-4554	444	114	2	2	NUM
ejpam-4554	444	115	}	}	PUNCT
ejpam-4554	444	116	{	{	PUNCT
ejpam-4554	444	117	0	0	NUM
ejpam-4554	444	118	,	,	PUNCT
ejpam-4554	444	119	1	1	NUM
ejpam-4554	444	120	}	}	SYM
ejpam-4554	444	121	1	1	NUM
ejpam-4554	444	122	0	0	NUM
ejpam-4554	444	123	{	{	PUNCT
ejpam-4554	444	124	0	0	NUM
ejpam-4554	444	125	,	,	PUNCT
ejpam-4554	444	126	1	1	NUM
ejpam-4554	444	127	}	}	SYM
ejpam-4554	444	128	2	2	NUM
ejpam-4554	444	129	1	1	NUM
ejpam-4554	444	130	{	{	PUNCT
ejpam-4554	444	131	0	0	NUM
ejpam-4554	444	132	,	,	PUNCT
ejpam-4554	444	133	2	2	NUM
ejpam-4554	444	134	}	}	PUNCT
ejpam-4554	444	135	{	{	PUNCT
ejpam-4554	444	136	0	0	NUM
ejpam-4554	444	137	,	,	PUNCT
ejpam-4554	444	138	1	1	NUM
ejpam-4554	444	139	}	}	SYM
ejpam-4554	444	140	1	1	NUM
ejpam-4554	444	141	0	0	NUM
ejpam-4554	444	142	{	{	PUNCT
ejpam-4554	444	143	0	0	NUM
ejpam-4554	444	144	,	,	PUNCT
ejpam-4554	444	145	1	1	NUM
ejpam-4554	444	146	}	}	SYM
ejpam-4554	444	147	2	2	NUM
ejpam-4554	444	148	2	2	NUM
ejpam-4554	444	149	{	{	PUNCT
ejpam-4554	444	150	0	0	NUM
ejpam-4554	444	151	,	,	PUNCT
ejpam-4554	444	152	2	2	NUM
ejpam-4554	444	153	}	}	PUNCT
ejpam-4554	444	154	{	{	PUNCT
ejpam-4554	444	155	0	0	NUM
ejpam-4554	444	156	,	,	PUNCT
ejpam-4554	444	157	1	1	NUM
ejpam-4554	444	158	}	}	SYM
ejpam-4554	444	159	1	1	NUM
ejpam-4554	444	160	1	1	NUM
ejpam-4554	444	161	{	{	PUNCT
ejpam-4554	444	162	0	0	NUM
ejpam-4554	444	163	,	,	PUNCT
ejpam-4554	444	164	1	1	NUM
ejpam-4554	444	165	}	}	PUNCT
ejpam-4554	444	166	r.	r.	PROPN
ejpam-4554	444	167	manzano	manzano	PROPN
ejpam-4554	444	168	,	,	PUNCT
ejpam-4554	444	169	jr	jr	PROPN
ejpam-4554	444	170	.	.	PROPN
ejpam-4554	444	171	,	,	PUNCT
ejpam-4554	444	172	g.	g.	PROPN
ejpam-4554	444	173	petalcorin	petalcorin	PROPN
ejpam-4554	444	174	,	,	PUNCT
ejpam-4554	444	175	jr	jr	PROPN
ejpam-4554	444	176	.	.	PROPN
ejpam-4554	444	177	/	/	SYM
ejpam-4554	444	178	eur	eur	PROPN
ejpam-4554	444	179	.	.	PUNCT
ejpam-4554	445	1	j.	j.	PROPN
ejpam-4554	445	2	pure	pure	PROPN
ejpam-4554	445	3	appl	appl	PROPN
ejpam-4554	445	4	.	.	PROPN
ejpam-4554	445	5	math	math	PROPN
ejpam-4554	445	6	,	,	PUNCT
ejpam-4554	445	7	15	15	NUM
ejpam-4554	445	8	(	(	PUNCT
ejpam-4554	445	9	4	4	NUM
ejpam-4554	445	10	)	)	PUNCT
ejpam-4554	445	11	(	(	PUNCT
ejpam-4554	445	12	2022	2022	NUM
ejpam-4554	445	13	)	)	PUNCT
ejpam-4554	445	14	,	,	PUNCT
ejpam-4554	445	15	1854	1854	NUM
ejpam-4554	445	16	-	-	SYM
ejpam-4554	445	17	1868	1868	NUM
ejpam-4554	445	18	1865	1865	NUM
ejpam-4554	445	19	x	x	SYM
ejpam-4554	445	20	y	y	PROPN
ejpam-4554	445	21	x⊙	x⊙	PROPN
ejpam-4554	445	22	y	y	PROPN
ejpam-4554	445	23	f(x⊙	f(x⊙	PROPN
ejpam-4554	445	24	y	y	PROPN
ejpam-4554	445	25	)	)	PUNCT
ejpam-4554	445	26	f(x	f(x	PROPN
ejpam-4554	445	27	)	)	PUNCT
ejpam-4554	445	28	f(y	f(y	NOUN
ejpam-4554	445	29	)	)	PUNCT
ejpam-4554	445	30	f(x)⊙	f(x)⊙	PROPN
ejpam-4554	445	31	f(y	f(y	NOUN
ejpam-4554	445	32	)	)	PUNCT
ejpam-4554	445	33	0	0	NUM
ejpam-4554	445	34	0	0	NUM
ejpam-4554	445	35	{	{	PUNCT
ejpam-4554	445	36	0	0	NUM
ejpam-4554	445	37	}	}	PUNCT
ejpam-4554	445	38	{	{	PUNCT
ejpam-4554	445	39	0	0	NUM
ejpam-4554	445	40	}	}	SYM
ejpam-4554	445	41	0	0	NUM
ejpam-4554	445	42	0	0	NUM
ejpam-4554	445	43	{	{	PUNCT
ejpam-4554	445	44	0	0	NUM
ejpam-4554	445	45	}	}	SYM
ejpam-4554	445	46	0	0	NUM
ejpam-4554	445	47	1	1	NUM
ejpam-4554	445	48	{	{	PUNCT
ejpam-4554	445	49	0	0	NUM
ejpam-4554	445	50	,	,	PUNCT
ejpam-4554	445	51	1	1	NUM
ejpam-4554	445	52	}	}	PUNCT
ejpam-4554	445	53	{	{	PUNCT
ejpam-4554	445	54	0	0	NUM
ejpam-4554	445	55	}	}	SYM
ejpam-4554	445	56	0	0	NUM
ejpam-4554	445	57	0	0	NUM
ejpam-4554	445	58	{	{	PUNCT
ejpam-4554	445	59	0	0	NUM
ejpam-4554	445	60	}	}	SYM
ejpam-4554	445	61	0	0	NUM
ejpam-4554	445	62	2	2	NUM
ejpam-4554	445	63	{	{	PUNCT
ejpam-4554	445	64	0	0	NUM
ejpam-4554	445	65	,	,	PUNCT
ejpam-4554	445	66	2	2	NUM
ejpam-4554	445	67	}	}	PUNCT
ejpam-4554	445	68	{	{	PUNCT
ejpam-4554	445	69	0	0	NUM
ejpam-4554	445	70	,	,	PUNCT
ejpam-4554	445	71	1	1	NUM
ejpam-4554	445	72	}	}	SYM
ejpam-4554	445	73	0	0	NUM
ejpam-4554	445	74	1	1	NUM
ejpam-4554	445	75	{	{	PUNCT
ejpam-4554	445	76	0	0	NUM
ejpam-4554	445	77	,	,	PUNCT
ejpam-4554	445	78	1	1	NUM
ejpam-4554	445	79	}	}	SYM
ejpam-4554	445	80	1	1	NUM
ejpam-4554	445	81	0	0	NUM
ejpam-4554	445	82	{	{	PUNCT
ejpam-4554	445	83	0	0	NUM
ejpam-4554	445	84	,	,	PUNCT
ejpam-4554	445	85	1	1	NUM
ejpam-4554	445	86	}	}	PUNCT
ejpam-4554	445	87	{	{	PUNCT
ejpam-4554	445	88	0	0	NUM
ejpam-4554	445	89	}	}	SYM
ejpam-4554	445	90	0	0	NUM
ejpam-4554	445	91	0	0	NUM
ejpam-4554	445	92	{	{	PUNCT
ejpam-4554	445	93	0	0	NUM
ejpam-4554	445	94	}	}	SYM
ejpam-4554	445	95	1	1	NUM
ejpam-4554	445	96	1	1	NUM
ejpam-4554	445	97	{	{	PUNCT
ejpam-4554	445	98	0	0	NUM
ejpam-4554	445	99	,	,	PUNCT
ejpam-4554	445	100	1	1	NUM
ejpam-4554	445	101	}	}	PUNCT
ejpam-4554	445	102	{	{	PUNCT
ejpam-4554	445	103	0	0	NUM
ejpam-4554	445	104	}	}	SYM
ejpam-4554	445	105	0	0	NUM
ejpam-4554	445	106	0	0	NUM
ejpam-4554	445	107	{	{	PUNCT
ejpam-4554	445	108	0	0	NUM
ejpam-4554	445	109	}	}	SYM
ejpam-4554	445	110	1	1	NUM
ejpam-4554	445	111	2	2	NUM
ejpam-4554	445	112	{	{	PUNCT
ejpam-4554	445	113	0	0	NUM
ejpam-4554	445	114	,	,	PUNCT
ejpam-4554	445	115	1	1	NUM
ejpam-4554	445	116	,	,	PUNCT
ejpam-4554	445	117	2	2	NUM
ejpam-4554	445	118	}	}	PUNCT
ejpam-4554	445	119	{	{	PUNCT
ejpam-4554	445	120	0	0	NUM
ejpam-4554	445	121	,	,	PUNCT
ejpam-4554	445	122	1	1	NUM
ejpam-4554	445	123	}	}	SYM
ejpam-4554	445	124	0	0	NUM
ejpam-4554	445	125	1	1	NUM
ejpam-4554	445	126	{	{	PUNCT
ejpam-4554	445	127	0	0	NUM
ejpam-4554	445	128	,	,	PUNCT
ejpam-4554	445	129	1	1	NUM
ejpam-4554	445	130	}	}	SYM
ejpam-4554	445	131	2	2	NUM
ejpam-4554	445	132	0	0	NUM
ejpam-4554	445	133	{	{	PUNCT
ejpam-4554	445	134	0	0	NUM
ejpam-4554	445	135	,	,	PUNCT
ejpam-4554	445	136	2	2	NUM
ejpam-4554	445	137	}	}	PUNCT
ejpam-4554	445	138	{	{	PUNCT
ejpam-4554	445	139	0	0	NUM
ejpam-4554	445	140	,	,	PUNCT
ejpam-4554	445	141	1	1	NUM
ejpam-4554	445	142	}	}	SYM
ejpam-4554	445	143	1	1	NUM
ejpam-4554	445	144	0	0	NUM
ejpam-4554	445	145	{	{	PUNCT
ejpam-4554	445	146	0	0	NUM
ejpam-4554	445	147	,	,	PUNCT
ejpam-4554	445	148	1	1	NUM
ejpam-4554	445	149	}	}	SYM
ejpam-4554	445	150	2	2	NUM
ejpam-4554	445	151	1	1	NUM
ejpam-4554	445	152	{	{	PUNCT
ejpam-4554	445	153	0	0	NUM
ejpam-4554	445	154	,	,	PUNCT
ejpam-4554	445	155	1	1	NUM
ejpam-4554	445	156	,	,	PUNCT
ejpam-4554	445	157	2	2	NUM
ejpam-4554	445	158	}	}	PUNCT
ejpam-4554	445	159	{	{	PUNCT
ejpam-4554	445	160	0	0	NUM
ejpam-4554	445	161	,	,	PUNCT
ejpam-4554	445	162	1	1	NUM
ejpam-4554	445	163	}	}	SYM
ejpam-4554	445	164	1	1	NUM
ejpam-4554	445	165	0	0	NUM
ejpam-4554	445	166	{	{	PUNCT
ejpam-4554	445	167	0	0	NUM
ejpam-4554	445	168	,	,	PUNCT
ejpam-4554	445	169	1	1	NUM
ejpam-4554	445	170	}	}	SYM
ejpam-4554	445	171	2	2	NUM
ejpam-4554	445	172	2	2	NUM
ejpam-4554	445	173	{	{	PUNCT
ejpam-4554	445	174	0	0	NUM
ejpam-4554	445	175	,	,	PUNCT
ejpam-4554	445	176	2	2	NUM
ejpam-4554	445	177	}	}	PUNCT
ejpam-4554	445	178	{	{	PUNCT
ejpam-4554	445	179	0	0	NUM
ejpam-4554	445	180	,	,	PUNCT
ejpam-4554	445	181	1	1	NUM
ejpam-4554	445	182	}	}	SYM
ejpam-4554	445	183	1	1	NUM
ejpam-4554	445	184	1	1	NUM
ejpam-4554	445	185	{	{	PUNCT
ejpam-4554	445	186	0	0	NUM
ejpam-4554	445	187	,	,	PUNCT
ejpam-4554	445	188	1	1	NUM
ejpam-4554	445	189	}	}	PUNCT
ejpam-4554	445	190	according	accord	VERB
ejpam-4554	445	191	how	how	SCONJ
ejpam-4554	445	192	f	f	PROPN
ejpam-4554	445	193	is	be	AUX
ejpam-4554	445	194	being	be	AUX
ejpam-4554	445	195	defined	define	VERB
ejpam-4554	445	196	,	,	PUNCT
ejpam-4554	445	197	we	we	PRON
ejpam-4554	445	198	have	have	VERB
ejpam-4554	445	199	ker	ker	PROPN
ejpam-4554	445	200	f	f	PROPN
ejpam-4554	446	1	=	=	PUNCT
ejpam-4554	446	2	{	{	PUNCT
ejpam-4554	446	3	0	0	NUM
ejpam-4554	446	4	,	,	PUNCT
ejpam-4554	446	5	1	1	NUM
ejpam-4554	446	6	}	}	PUNCT
ejpam-4554	446	7	=	=	NOUN
ejpam-4554	447	1	[	[	X
ejpam-4554	447	2	0]θ	0]θ	X
ejpam-4554	447	3	=	=	PUNCT
ejpam-4554	447	4	i	i	PRON
ejpam-4554	447	5	and	and	CCONJ
ejpam-4554	447	6	imf	imf	PROPN
ejpam-4554	447	7	=	=	PUNCT
ejpam-4554	447	8	{	{	PUNCT
ejpam-4554	447	9	0	0	NUM
ejpam-4554	447	10	,	,	PUNCT
ejpam-4554	447	11	1	1	NUM
ejpam-4554	447	12	}	}	PUNCT
ejpam-4554	447	13	=	=	SYM
ejpam-4554	447	14	h	h	NOUN
ejpam-4554	447	15	′.	′.	NOUN
ejpam-4554	447	16	let	let	VERB
ejpam-4554	447	17	us	we	PRON
ejpam-4554	447	18	define	define	VERB
ejpam-4554	447	19	the	the	DET
ejpam-4554	447	20	map	map	NOUN
ejpam-4554	447	21	φ	φ	X
ejpam-4554	447	22	:	:	PUNCT
ejpam-4554	447	23	h	h	X
ejpam-4554	447	24	/	/	SYM
ejpam-4554	447	25	i	i	PRON
ejpam-4554	447	26	−→	−→	NOUN
ejpam-4554	447	27	h	h	NOUN
ejpam-4554	447	28	′	′	VERB
ejpam-4554	447	29	by	by	ADP
ejpam-4554	447	30	φ(ix	φ(ix	NUM
ejpam-4554	447	31	)	)	PUNCT
ejpam-4554	447	32	=	=	PRON
ejpam-4554	447	33	{	{	PUNCT
ejpam-4554	447	34	0	0	NUM
ejpam-4554	448	1	if	if	SCONJ
ejpam-4554	448	2	ix	ix	ADV
ejpam-4554	448	3	=	=	PUNCT
ejpam-4554	448	4	i	i	PRON
ejpam-4554	448	5	1	1	NUM
ejpam-4554	448	6	otherwise	otherwise	ADV
ejpam-4554	448	7	.	.	PUNCT
ejpam-4554	449	1	we	we	PRON
ejpam-4554	449	2	can	can	AUX
ejpam-4554	449	3	verify	verify	VERB
ejpam-4554	449	4	that	that	SCONJ
ejpam-4554	449	5	φ	φ	PROPN
ejpam-4554	449	6	is	be	AUX
ejpam-4554	449	7	an	an	DET
ejpam-4554	449	8	isomorphism	isomorphism	NOUN
ejpam-4554	449	9	.	.	PUNCT
ejpam-4554	450	1	moreover	moreover	ADV
ejpam-4554	450	2	,	,	PUNCT
ejpam-4554	450	3	h	h	NOUN
ejpam-4554	450	4	/	/	SYM
ejpam-4554	450	5	ker	ker	NOUN
ejpam-4554	450	6	f	f	PROPN
ejpam-4554	450	7	∼=	∼=	PROPN
ejpam-4554	450	8	imf	imf	PROPN
ejpam-4554	450	9	.	.	PUNCT
ejpam-4554	451	1	corollary	corollary	ADJ
ejpam-4554	451	2	4.4	4.4	NUM
ejpam-4554	451	3	.	.	PUNCT
ejpam-4554	452	1	(	(	PUNCT
ejpam-4554	452	2	first	first	ADJ
ejpam-4554	452	3	isomorphism	isomorphism	NOUN
ejpam-4554	452	4	theorem	theorem	VERB
ejpam-4554	452	5	)	)	PUNCT
ejpam-4554	452	6	let	let	VERB
ejpam-4554	452	7	θ	θ	NOUN
ejpam-4554	452	8	be	be	AUX
ejpam-4554	452	9	a	a	DET
ejpam-4554	452	10	regular	regular	ADJ
ejpam-4554	452	11	congruence	congruence	NOUN
ejpam-4554	452	12	relation	relation	NOUN
ejpam-4554	452	13	on	on	ADP
ejpam-4554	452	14	h	h	NOUN
ejpam-4554	453	1	and	and	CCONJ
ejpam-4554	453	2	i	i	PRON
ejpam-4554	453	3	=	=	PUNCT
ejpam-4554	454	1	[	[	X
ejpam-4554	454	2	0]θ	0]θ	NOUN
ejpam-4554	454	3	.	.	PUNCT
ejpam-4554	455	1	if	if	SCONJ
ejpam-4554	455	2	f	f	PROPN
ejpam-4554	455	3	:	:	PUNCT
ejpam-4554	455	4	h	h	PROPN
ejpam-4554	455	5	−→	−→	ADJ
ejpam-4554	455	6	h	h	NOUN
ejpam-4554	455	7	′	′	NOUN
ejpam-4554	455	8	is	be	AUX
ejpam-4554	455	9	a	a	DET
ejpam-4554	455	10	hyper	hyper	ADJ
ejpam-4554	455	11	homomorphism	homomorphism	NOUN
ejpam-4554	455	12	of	of	ADP
ejpam-4554	455	13	pseudo	pseudo	NOUN
ejpam-4554	455	14	hyper	hyper	ADJ
ejpam-4554	455	15	gralgebras	gralgebra	NOUN
ejpam-4554	455	16	such	such	ADJ
ejpam-4554	455	17	that	that	SCONJ
ejpam-4554	455	18	f(x	f(x	PROPN
ejpam-4554	455	19	)	)	PUNCT
ejpam-4554	455	20	≪	≪	PUNCT
ejpam-4554	455	21	f(y	f(y	NOUN
ejpam-4554	455	22	)	)	PUNCT
ejpam-4554	455	23	and	and	CCONJ
ejpam-4554	455	24	f(y	f(y	NOUN
ejpam-4554	455	25	)	)	PUNCT
ejpam-4554	455	26	≪	≪	PUNCT
ejpam-4554	455	27	f(x	f(x	PROPN
ejpam-4554	455	28	)	)	PUNCT
ejpam-4554	455	29	imply	imply	VERB
ejpam-4554	455	30	that	that	SCONJ
ejpam-4554	455	31	f(x	f(x	NOUN
ejpam-4554	455	32	)	)	PUNCT
ejpam-4554	455	33	=	=	SYM
ejpam-4554	455	34	f(y	f(y	NOUN
ejpam-4554	455	35	)	)	PUNCT
ejpam-4554	455	36	and	and	CCONJ
ejpam-4554	456	1	ker	ker	NOUN
ejpam-4554	456	2	f	f	PROPN
ejpam-4554	457	1	=	=	SYM
ejpam-4554	457	2	i	i	PROPN
ejpam-4554	457	3	,	,	PUNCT
ejpam-4554	457	4	then	then	ADV
ejpam-4554	457	5	h	h	PROPN
ejpam-4554	457	6	/	/	SYM
ejpam-4554	457	7	ker	ker	NOUN
ejpam-4554	457	8	f	f	PROPN
ejpam-4554	457	9	∼=	∼=	PROPN
ejpam-4554	457	10	imf	imf	PROPN
ejpam-4554	457	11	.	.	PUNCT
ejpam-4554	458	1	proof	proof	NOUN
ejpam-4554	458	2	.	.	PUNCT
ejpam-4554	459	1	by	by	ADP
ejpam-4554	459	2	theorem	theorem	NOUN
ejpam-4554	459	3	4.2	4.2	NUM
ejpam-4554	459	4	,	,	PUNCT
ejpam-4554	459	5	the	the	DET
ejpam-4554	459	6	map	map	NOUN
ejpam-4554	459	7	f̄	f̄	NOUN
ejpam-4554	459	8	:	:	PUNCT
ejpam-4554	459	9	h	h	X
ejpam-4554	459	10	/	/	SYM
ejpam-4554	459	11	ker	ker	NOUN
ejpam-4554	460	1	f	f	PROPN
ejpam-4554	460	2	−→	−→	NOUN
ejpam-4554	460	3	h	h	NOUN
ejpam-4554	460	4	′	′	NUM
ejpam-4554	460	5	is	be	AUX
ejpam-4554	460	6	a	a	DET
ejpam-4554	460	7	monomorphism	monomorphism	NOUN
ejpam-4554	460	8	and	and	CCONJ
ejpam-4554	460	9	by	by	ADP
ejpam-4554	460	10	remark	remark	NOUN
ejpam-4554	460	11	?	?	PUNCT
ejpam-4554	460	12	?	?	PUNCT
ejpam-4554	461	1	(	(	PUNCT
ejpam-4554	461	2	ii	ii	NOUN
ejpam-4554	461	3	)	)	PUNCT
ejpam-4554	461	4	,	,	PUNCT
ejpam-4554	461	5	f̄	f̄	NOUN
ejpam-4554	461	6	:	:	PUNCT
ejpam-4554	461	7	h	h	X
ejpam-4554	461	8	/	/	SYM
ejpam-4554	461	9	ker	ker	NOUN
ejpam-4554	461	10	f	f	PROPN
ejpam-4554	461	11	∼=	∼=	PROPN
ejpam-4554	461	12	i	i	PRON
ejpam-4554	461	13	m	m	PROPN
ejpam-4554	461	14	f̄	f̄	PROPN
ejpam-4554	461	15	is	be	AUX
ejpam-4554	461	16	an	an	DET
ejpam-4554	461	17	isomorphism	isomorphism	NOUN
ejpam-4554	461	18	.	.	PUNCT
ejpam-4554	462	1	thus	thus	ADV
ejpam-4554	462	2	,	,	PUNCT
ejpam-4554	462	3	h	h	PROPN
ejpam-4554	462	4	/	/	SYM
ejpam-4554	462	5	ker	ker	NOUN
ejpam-4554	462	6	f	f	PROPN
ejpam-4554	462	7	∼=	∼=	PROPN
ejpam-4554	463	1	i	i	PRON
ejpam-4554	463	2	m	m	VERB
ejpam-4554	463	3	f̄	f̄	PROPN
ejpam-4554	463	4	.	.	PUNCT
ejpam-4554	464	1	since	since	SCONJ
ejpam-4554	464	2	f̄(ix	f̄(ix	NOUN
ejpam-4554	464	3	)	)	PUNCT
ejpam-4554	464	4	=	=	SYM
ejpam-4554	464	5	f(x	f(x	PROPN
ejpam-4554	464	6	)	)	PUNCT
ejpam-4554	464	7	for	for	ADP
ejpam-4554	464	8	all	all	DET
ejpam-4554	464	9	x	x	SYM
ejpam-4554	464	10	∈	∈	PROPN
ejpam-4554	464	11	h	h	NOUN
ejpam-4554	464	12	,	,	PUNCT
ejpam-4554	464	13	i	i	PRON
ejpam-4554	464	14	m	m	VERB
ejpam-4554	464	15	f̄	f̄	NOUN
ejpam-4554	464	16	=	=	SYM
ejpam-4554	464	17	imf	imf	PROPN
ejpam-4554	464	18	.	.	PUNCT
ejpam-4554	465	1	hence	hence	ADV
ejpam-4554	465	2	,	,	PUNCT
ejpam-4554	465	3	the	the	DET
ejpam-4554	465	4	result	result	NOUN
ejpam-4554	465	5	follows	follow	VERB
ejpam-4554	465	6	.	.	PUNCT
ejpam-4554	466	1	□	□	PUNCT
ejpam-4554	466	2	proposition	proposition	NOUN
ejpam-4554	466	3	4.5	4.5	NUM
ejpam-4554	466	4	.	.	PUNCT
ejpam-4554	467	1	let	let	VERB
ejpam-4554	467	2	k	k	PRON
ejpam-4554	467	3	be	be	AUX
ejpam-4554	467	4	a	a	DET
ejpam-4554	467	5	pseudo	pseudo	NOUN
ejpam-4554	467	6	hyper	hyper	ADJ
ejpam-4554	467	7	subgr	subgr	NOUN
ejpam-4554	467	8	-	-	PUNCT
ejpam-4554	467	9	algebra	algebra	NOUN
ejpam-4554	467	10	of	of	ADP
ejpam-4554	467	11	h	h	NOUN
ejpam-4554	467	12	and	and	CCONJ
ejpam-4554	467	13	θ	θ	PROPN
ejpam-4554	467	14	a	a	DET
ejpam-4554	467	15	regular	regular	ADJ
ejpam-4554	467	16	congruence	congruence	NOUN
ejpam-4554	467	17	on	on	ADP
ejpam-4554	467	18	h	h	NOUN
ejpam-4554	468	1	and	and	CCONJ
ejpam-4554	468	2	i	i	PRON
ejpam-4554	468	3	=	=	PUNCT
ejpam-4554	469	1	[	[	X
ejpam-4554	469	2	0]θ	0]θ	X
ejpam-4554	469	3	.	.	PUNCT
ejpam-4554	470	1	define	define	VERB
ejpam-4554	470	2	k	k	NOUN
ejpam-4554	470	3	/	/	SYM
ejpam-4554	470	4	i	i	NOUN
ejpam-4554	470	5	=	=	PUNCT
ejpam-4554	470	6	{	{	PUNCT
ejpam-4554	470	7	ix	ix	ADP
ejpam-4554	470	8	∈	∈	PROPN
ejpam-4554	470	9	h	h	NOUN
ejpam-4554	470	10	/	/	SYM
ejpam-4554	471	1	i	i	PRON
ejpam-4554	471	2	|x	|x	NOUN
ejpam-4554	471	3	∈	∈	PROPN
ejpam-4554	471	4	k	k	NOUN
ejpam-4554	471	5	}	}	PUNCT
ejpam-4554	471	6	.	.	PUNCT
ejpam-4554	472	1	then	then	ADV
ejpam-4554	472	2	k	k	X
ejpam-4554	472	3	/	/	SYM
ejpam-4554	472	4	i	i	PRON
ejpam-4554	472	5	is	be	AUX
ejpam-4554	472	6	a	a	DET
ejpam-4554	472	7	pseudo	pseudo	NOUN
ejpam-4554	472	8	hyper	hyper	ADJ
ejpam-4554	472	9	subgr	subgr	NOUN
ejpam-4554	472	10	-	-	PUNCT
ejpam-4554	472	11	algebra	algebra	NOUN
ejpam-4554	472	12	of	of	ADP
ejpam-4554	472	13	h	h	NOUN
ejpam-4554	472	14	/	/	SYM
ejpam-4554	472	15	i.	i.	NOUN
ejpam-4554	472	16	proof	proof	NOUN
ejpam-4554	472	17	.	.	PUNCT
ejpam-4554	473	1	since	since	SCONJ
ejpam-4554	473	2	k	k	PROPN
ejpam-4554	473	3	is	be	AUX
ejpam-4554	473	4	a	a	DET
ejpam-4554	473	5	pseudo	pseudo	NOUN
ejpam-4554	473	6	hyper	hyper	ADJ
ejpam-4554	473	7	subgr	subgr	NOUN
ejpam-4554	473	8	-	-	PUNCT
ejpam-4554	473	9	algebra	algebra	NOUN
ejpam-4554	473	10	of	of	ADP
ejpam-4554	473	11	h	h	NOUN
ejpam-4554	473	12	,	,	PUNCT
ejpam-4554	473	13	0	0	NUM
ejpam-4554	473	14	∈	∈	PROPN
ejpam-4554	473	15	k	k	NOUN
ejpam-4554	473	16	and	and	CCONJ
ejpam-4554	473	17	so	so	ADV
ejpam-4554	473	18	,	,	PUNCT
ejpam-4554	474	1	[	[	X
ejpam-4554	474	2	0]θ	0]θ	X
ejpam-4554	474	3	=	=	PUNCT
ejpam-4554	475	1	i	i	PRON
ejpam-4554	475	2	∈	∈	PROPN
ejpam-4554	476	1	k	k	X
ejpam-4554	476	2	/	/	SYM
ejpam-4554	476	3	i	i	PRON
ejpam-4554	476	4	which	which	PRON
ejpam-4554	476	5	means	mean	VERB
ejpam-4554	476	6	that	that	SCONJ
ejpam-4554	476	7	k	k	PROPN
ejpam-4554	476	8	/	/	SYM
ejpam-4554	476	9	i	i	PRON
ejpam-4554	476	10	is	be	AUX
ejpam-4554	476	11	nonempty	nonempty	ADJ
ejpam-4554	476	12	.	.	PUNCT
ejpam-4554	477	1	let	let	VERB
ejpam-4554	477	2	ix	ix	ADV
ejpam-4554	477	3	,	,	PUNCT
ejpam-4554	477	4	iy	iy	PROPN
ejpam-4554	477	5	∈	∈	PROPN
ejpam-4554	477	6	k	k	PROPN
ejpam-4554	477	7	/	/	SYM
ejpam-4554	477	8	i.	i.	PROPN
ejpam-4554	477	9	then	then	ADV
ejpam-4554	477	10	x	x	PRON
ejpam-4554	477	11	,	,	PUNCT
ejpam-4554	477	12	y	y	PROPN
ejpam-4554	477	13	∈	∈	PROPN
ejpam-4554	477	14	k.	k.	PROPN
ejpam-4554	478	1	since	since	SCONJ
ejpam-4554	478	2	k	k	PROPN
ejpam-4554	478	3	is	be	AUX
ejpam-4554	478	4	a	a	DET
ejpam-4554	478	5	pseudo	pseudo	NOUN
ejpam-4554	478	6	hyper	hyper	ADJ
ejpam-4554	478	7	subgr	subgr	NOUN
ejpam-4554	478	8	algebra	algebra	NOUN
ejpam-4554	478	9	of	of	ADP
ejpam-4554	478	10	h	h	NOUN
ejpam-4554	478	11	,	,	PUNCT
ejpam-4554	478	12	x	x	PROPN
ejpam-4554	478	13	⊛	⊛	NUM
ejpam-4554	478	14	y	y	PROPN
ejpam-4554	478	15	⊆	⊆	NUM
ejpam-4554	478	16	k.	k.	PROPN
ejpam-4554	478	17	suppose	suppose	VERB
ejpam-4554	478	18	that	that	SCONJ
ejpam-4554	478	19	iz	iz	INTJ
ejpam-4554	478	20	∈	∈	PROPN
ejpam-4554	478	21	ix	ix	PROPN
ejpam-4554	478	22	⊛	⊛	PROPN
ejpam-4554	478	23	iy	iy	PROPN
ejpam-4554	478	24	.	.	PUNCT
ejpam-4554	479	1	then	then	ADV
ejpam-4554	479	2	z	z	PROPN
ejpam-4554	479	3	∈	∈	PROPN
ejpam-4554	479	4	x	x	SYM
ejpam-4554	479	5	⊛	⊛	NUM
ejpam-4554	479	6	y	y	PROPN
ejpam-4554	479	7	⊆	⊆	NUM
ejpam-4554	479	8	k.	k.	PROPN
ejpam-4554	479	9	thus	thus	ADV
ejpam-4554	479	10	,	,	PUNCT
ejpam-4554	479	11	iz	iz	INTJ
ejpam-4554	479	12	∈	∈	PROPN
ejpam-4554	480	1	k	k	NOUN
ejpam-4554	480	2	/	/	SYM
ejpam-4554	480	3	i	i	PRON
ejpam-4554	480	4	and	and	CCONJ
ejpam-4554	480	5	ix	ix	ADP
ejpam-4554	480	6	⊛	⊛	NUM
ejpam-4554	480	7	iy	iy	PROPN
ejpam-4554	480	8	⊆	⊆	NUM
ejpam-4554	480	9	k	k	PROPN
ejpam-4554	480	10	/	/	SYM
ejpam-4554	480	11	i.	i.	NOUN
ejpam-4554	480	12	similarly	similarly	ADV
ejpam-4554	480	13	,	,	PUNCT
ejpam-4554	480	14	suppose	suppose	VERB
ejpam-4554	481	1	that	that	SCONJ
ejpam-4554	481	2	iz	iz	INTJ
ejpam-4554	481	3	∈	∈	PROPN
ejpam-4554	481	4	ix	ix	PROPN
ejpam-4554	481	5	⊙	⊙	PROPN
ejpam-4554	481	6	iy	iy	PROPN
ejpam-4554	481	7	.	.	PUNCT
ejpam-4554	482	1	then	then	ADV
ejpam-4554	482	2	,	,	PUNCT
ejpam-4554	482	3	z	z	PROPN
ejpam-4554	482	4	∈	∈	PROPN
ejpam-4554	482	5	x	x	PUNCT
ejpam-4554	482	6	⊙	⊙	PROPN
ejpam-4554	482	7	y	y	PROPN
ejpam-4554	482	8	⊆	⊆	NUM
ejpam-4554	482	9	k	k	X
ejpam-4554	482	10	,	,	PUNCT
ejpam-4554	482	11	and	and	CCONJ
ejpam-4554	482	12	so	so	ADV
ejpam-4554	482	13	,	,	PUNCT
ejpam-4554	482	14	iz	iz	INTJ
ejpam-4554	482	15	∈	∈	PROPN
ejpam-4554	482	16	k	k	X
ejpam-4554	482	17	/	/	SYM
ejpam-4554	482	18	i.	i.	PROPN
ejpam-4554	482	19	thus	thus	ADV
ejpam-4554	482	20	,	,	PUNCT
ejpam-4554	482	21	ix	ix	PROPN
ejpam-4554	482	22	⊙	⊙	PROPN
ejpam-4554	482	23	iy	iy	PROPN
ejpam-4554	483	1	⊆	⊆	NUM
ejpam-4554	483	2	k	k	PROPN
ejpam-4554	483	3	/	/	SYM
ejpam-4554	483	4	i.	i.	PROPN
ejpam-4554	483	5	therefore	therefore	ADV
ejpam-4554	483	6	,	,	PUNCT
ejpam-4554	483	7	k	k	PROPN
ejpam-4554	483	8	/	/	SYM
ejpam-4554	483	9	i	i	PRON
ejpam-4554	483	10	is	be	AUX
ejpam-4554	483	11	a	a	DET
ejpam-4554	483	12	pseudo	pseudo	NOUN
ejpam-4554	483	13	hyper	hyper	ADJ
ejpam-4554	483	14	subgr	subgr	NOUN
ejpam-4554	483	15	-	-	PUNCT
ejpam-4554	483	16	algebra	algebra	NOUN
ejpam-4554	483	17	of	of	ADP
ejpam-4554	483	18	h	h	NOUN
ejpam-4554	483	19	/	/	SYM
ejpam-4554	483	20	i.	i.	NOUN
ejpam-4554	483	21	□	□	PUNCT
ejpam-4554	483	22	corollary	corollary	ADJ
ejpam-4554	483	23	4.6	4.6	NUM
ejpam-4554	483	24	.	.	PUNCT
ejpam-4554	484	1	let	let	VERB
ejpam-4554	484	2	θ1	θ1	PROPN
ejpam-4554	484	3	and	and	CCONJ
ejpam-4554	484	4	θ2	θ2	PROPN
ejpam-4554	484	5	be	be	AUX
ejpam-4554	484	6	regular	regular	ADJ
ejpam-4554	484	7	congruence	congruence	NOUN
ejpam-4554	484	8	relations	relation	NOUN
ejpam-4554	484	9	on	on	ADP
ejpam-4554	484	10	h	h	NOUN
ejpam-4554	484	11	,	,	PUNCT
ejpam-4554	484	12	with	with	ADP
ejpam-4554	484	13	j	j	PROPN
ejpam-4554	485	1	=	=	PUNCT
ejpam-4554	486	1	[	[	X
ejpam-4554	486	2	0]θ1	0]θ1	X
ejpam-4554	486	3	and	and	CCONJ
ejpam-4554	486	4	i	i	PRON
ejpam-4554	486	5	=	=	PUNCT
ejpam-4554	487	1	[	[	X
ejpam-4554	487	2	0]θ2	0]θ2	X
ejpam-4554	487	3	.	.	PUNCT
ejpam-4554	488	1	define	define	VERB
ejpam-4554	488	2	j	j	PROPN
ejpam-4554	488	3	/	/	SYM
ejpam-4554	488	4	i	i	PRON
ejpam-4554	488	5	=	=	PUNCT
ejpam-4554	488	6	{	{	PUNCT
ejpam-4554	488	7	ix	ix	ADP
ejpam-4554	488	8	∈	∈	PROPN
ejpam-4554	488	9	h	h	NOUN
ejpam-4554	488	10	/	/	SYM
ejpam-4554	489	1	i	i	PRON
ejpam-4554	489	2	|x	|x	NOUN
ejpam-4554	489	3	∈	∈	PROPN
ejpam-4554	489	4	j	j	PROPN
ejpam-4554	489	5	}	}	PUNCT
ejpam-4554	489	6	.	.	PUNCT
ejpam-4554	490	1	if	if	SCONJ
ejpam-4554	490	2	j	j	PROPN
ejpam-4554	490	3	is	be	AUX
ejpam-4554	490	4	a	a	DET
ejpam-4554	490	5	pseudo	pseudo	NOUN
ejpam-4554	490	6	hyper	hyper	ADJ
ejpam-4554	490	7	subgr	subgr	NOUN
ejpam-4554	490	8	-	-	PUNCT
ejpam-4554	490	9	algebra	algebra	NOUN
ejpam-4554	490	10	of	of	ADP
ejpam-4554	490	11	h	h	NOUN
ejpam-4554	490	12	,	,	PUNCT
ejpam-4554	490	13	then	then	ADV
ejpam-4554	490	14	j	j	PROPN
ejpam-4554	490	15	/	/	SYM
ejpam-4554	490	16	i	i	PROPN
ejpam-4554	490	17	is	be	AUX
ejpam-4554	490	18	a	a	DET
ejpam-4554	490	19	pseudo	pseudo	NOUN
ejpam-4554	490	20	hyper	hyper	ADJ
ejpam-4554	490	21	subgr	subgr	NOUN
ejpam-4554	490	22	-	-	PUNCT
ejpam-4554	490	23	algebra	algebra	NOUN
ejpam-4554	490	24	of	of	ADP
ejpam-4554	490	25	h	h	NOUN
ejpam-4554	490	26	/	/	SYM
ejpam-4554	490	27	i.	i.	NOUN
ejpam-4554	490	28	proof	proof	NOUN
ejpam-4554	490	29	.	.	PUNCT
ejpam-4554	491	1	by	by	ADP
ejpam-4554	491	2	definition	definition	NOUN
ejpam-4554	491	3	of	of	ADP
ejpam-4554	491	4	j	j	PROPN
ejpam-4554	491	5	/	/	SYM
ejpam-4554	491	6	i	i	PROPN
ejpam-4554	491	7	,	,	PUNCT
ejpam-4554	491	8	it	it	PRON
ejpam-4554	491	9	is	be	AUX
ejpam-4554	491	10	easy	easy	ADJ
ejpam-4554	491	11	to	to	PART
ejpam-4554	491	12	see	see	VERB
ejpam-4554	491	13	that	that	PRON
ejpam-4554	491	14	j	j	PROPN
ejpam-4554	491	15	/	/	SYM
ejpam-4554	491	16	i	i	PROPN
ejpam-4554	491	17	⊆	⊆	NUM
ejpam-4554	491	18	h	h	NOUN
ejpam-4554	491	19	/	/	SYM
ejpam-4554	491	20	i.	i.	NOUN
ejpam-4554	491	21	since	since	SCONJ
ejpam-4554	491	22	j	j	PROPN
ejpam-4554	491	23	is	be	AUX
ejpam-4554	491	24	a	a	DET
ejpam-4554	491	25	pseudo	pseudo	NOUN
ejpam-4554	491	26	hyper	hyper	ADJ
ejpam-4554	491	27	subgr	subgr	NOUN
ejpam-4554	491	28	-	-	PUNCT
ejpam-4554	491	29	algebra	algebra	NOUN
ejpam-4554	491	30	of	of	ADP
ejpam-4554	491	31	h	h	NOUN
ejpam-4554	491	32	,	,	PUNCT
ejpam-4554	491	33	by	by	ADP
ejpam-4554	491	34	proposition	proposition	NOUN
ejpam-4554	491	35	4.5	4.5	NUM
ejpam-4554	491	36	,	,	PUNCT
ejpam-4554	491	37	j	j	PROPN
ejpam-4554	491	38	/	/	SYM
ejpam-4554	491	39	i	i	PROPN
ejpam-4554	491	40	is	be	AUX
ejpam-4554	491	41	pseudo	pseudo	NOUN
ejpam-4554	491	42	hyper	hyper	ADJ
ejpam-4554	491	43	subgr	subgr	NOUN
ejpam-4554	491	44	-	-	PUNCT
ejpam-4554	491	45	algebra	algebra	NOUN
ejpam-4554	491	46	of	of	ADP
ejpam-4554	491	47	h.	h.	PROPN
ejpam-4554	491	48	□	□	PROPN
ejpam-4554	491	49	r.	r.	PROPN
ejpam-4554	491	50	manzano	manzano	PROPN
ejpam-4554	491	51	,	,	PUNCT
ejpam-4554	491	52	jr	jr	PROPN
ejpam-4554	491	53	.	.	PROPN
ejpam-4554	491	54	,	,	PUNCT
ejpam-4554	491	55	g.	g.	PROPN
ejpam-4554	491	56	petalcorin	petalcorin	PROPN
ejpam-4554	491	57	,	,	PUNCT
ejpam-4554	491	58	jr	jr	PROPN
ejpam-4554	491	59	.	.	PROPN
ejpam-4554	491	60	/	/	SYM
ejpam-4554	491	61	eur	eur	PROPN
ejpam-4554	491	62	.	.	PUNCT
ejpam-4554	492	1	j.	j.	PROPN
ejpam-4554	492	2	pure	pure	PROPN
ejpam-4554	492	3	appl	appl	PROPN
ejpam-4554	492	4	.	.	PROPN
ejpam-4554	492	5	math	math	PROPN
ejpam-4554	492	6	,	,	PUNCT
ejpam-4554	492	7	15	15	NUM
ejpam-4554	492	8	(	(	PUNCT
ejpam-4554	492	9	4	4	NUM
ejpam-4554	492	10	)	)	PUNCT
ejpam-4554	492	11	(	(	PUNCT
ejpam-4554	492	12	2022	2022	NUM
ejpam-4554	492	13	)	)	PUNCT
ejpam-4554	492	14	,	,	PUNCT
ejpam-4554	492	15	1854	1854	NUM
ejpam-4554	492	16	-	-	SYM
ejpam-4554	492	17	1868	1868	NUM
ejpam-4554	492	18	1866	1866	NUM
ejpam-4554	492	19	lemma	lemma	PROPN
ejpam-4554	492	20	4.7	4.7	NUM
ejpam-4554	492	21	.	.	PUNCT
ejpam-4554	493	1	let	let	VERB
ejpam-4554	493	2	θ1	θ1	PROPN
ejpam-4554	493	3	and	and	CCONJ
ejpam-4554	493	4	θ2	θ2	PROPN
ejpam-4554	493	5	be	be	AUX
ejpam-4554	493	6	regular	regular	ADJ
ejpam-4554	493	7	congruence	congruence	NOUN
ejpam-4554	493	8	relations	relation	NOUN
ejpam-4554	493	9	on	on	ADP
ejpam-4554	493	10	h	h	NOUN
ejpam-4554	493	11	,	,	PUNCT
ejpam-4554	493	12	with	with	ADP
ejpam-4554	493	13	j	j	PROPN
ejpam-4554	494	1	=	=	PUNCT
ejpam-4554	495	1	[	[	X
ejpam-4554	495	2	0]θ1	0]θ1	X
ejpam-4554	495	3	and	and	CCONJ
ejpam-4554	495	4	i	i	PRON
ejpam-4554	495	5	=	=	PUNCT
ejpam-4554	496	1	[	[	X
ejpam-4554	496	2	0]θ2	0]θ2	X
ejpam-4554	496	3	.	.	PUNCT
ejpam-4554	497	1	define	define	VERB
ejpam-4554	497	2	j	j	PROPN
ejpam-4554	497	3	/	/	SYM
ejpam-4554	497	4	i	i	PRON
ejpam-4554	497	5	=	=	PUNCT
ejpam-4554	497	6	{	{	PUNCT
ejpam-4554	497	7	ix	ix	ADP
ejpam-4554	497	8	∈	∈	PROPN
ejpam-4554	497	9	h	h	NOUN
ejpam-4554	497	10	/	/	SYM
ejpam-4554	498	1	i	i	PRON
ejpam-4554	498	2	|x	|x	NOUN
ejpam-4554	498	3	∈	∈	PROPN
ejpam-4554	498	4	j	j	PROPN
ejpam-4554	498	5	}	}	PUNCT
ejpam-4554	498	6	and	and	CCONJ
ejpam-4554	498	7	a	a	DET
ejpam-4554	498	8	relation	relation	NOUN
ejpam-4554	498	9	θ	θ	PROPN
ejpam-4554	498	10	on	on	ADP
ejpam-4554	498	11	h	h	PROPN
ejpam-4554	498	12	/	/	SYM
ejpam-4554	498	13	i	i	PRON
ejpam-4554	498	14	by	by	ADP
ejpam-4554	498	15	ixθiy	ixθiy	PROPN
ejpam-4554	498	16	if	if	SCONJ
ejpam-4554	498	17	and	and	CCONJ
ejpam-4554	498	18	only	only	ADV
ejpam-4554	498	19	if	if	SCONJ
ejpam-4554	498	20	xθ1y	xθ1y	PROPN
ejpam-4554	498	21	,	,	PUNCT
ejpam-4554	498	22	for	for	ADP
ejpam-4554	498	23	all	all	DET
ejpam-4554	498	24	ix	ix	PROPN
ejpam-4554	498	25	,	,	PUNCT
ejpam-4554	498	26	iy	iy	PROPN
ejpam-4554	498	27	∈	∈	PROPN
ejpam-4554	498	28	h	h	PROPN
ejpam-4554	498	29	/	/	SYM
ejpam-4554	498	30	i.	i.	NOUN
ejpam-4554	498	31	then	then	ADV
ejpam-4554	498	32	θ	θ	PROPN
ejpam-4554	498	33	is	be	AUX
ejpam-4554	498	34	a	a	DET
ejpam-4554	498	35	regular	regular	ADJ
ejpam-4554	498	36	congruence	congruence	NOUN
ejpam-4554	498	37	relation	relation	NOUN
ejpam-4554	498	38	and	and	CCONJ
ejpam-4554	498	39	[	[	PUNCT
ejpam-4554	498	40	i]θ	i]θ	NOUN
ejpam-4554	498	41	=	=	SYM
ejpam-4554	498	42	j	j	PROPN
ejpam-4554	498	43	/	/	SYM
ejpam-4554	498	44	i.	i.	PROPN
ejpam-4554	498	45	proof	proof	NOUN
ejpam-4554	498	46	.	.	PUNCT
ejpam-4554	499	1	define	define	VERB
ejpam-4554	499	2	a	a	DET
ejpam-4554	499	3	relation	relation	NOUN
ejpam-4554	499	4	θ	θ	PROPN
ejpam-4554	499	5	on	on	ADP
ejpam-4554	499	6	h	h	PROPN
ejpam-4554	499	7	/	/	SYM
ejpam-4554	499	8	i	i	PRON
ejpam-4554	499	9	by	by	ADP
ejpam-4554	499	10	ixθiy	ixθiy	PROPN
ejpam-4554	499	11	if	if	SCONJ
ejpam-4554	499	12	and	and	CCONJ
ejpam-4554	499	13	only	only	ADV
ejpam-4554	499	14	if	if	SCONJ
ejpam-4554	499	15	xθ1y	xθ1y	PROPN
ejpam-4554	499	16	,	,	PUNCT
ejpam-4554	499	17	for	for	ADP
ejpam-4554	499	18	all	all	DET
ejpam-4554	499	19	ix	ix	PROPN
ejpam-4554	499	20	,	,	PUNCT
ejpam-4554	499	21	iy	iy	PROPN
ejpam-4554	499	22	∈	∈	PROPN
ejpam-4554	499	23	h	h	PROPN
ejpam-4554	499	24	/	/	SYM
ejpam-4554	499	25	i.	i.	NOUN
ejpam-4554	499	26	we	we	PRON
ejpam-4554	499	27	will	will	AUX
ejpam-4554	499	28	show	show	VERB
ejpam-4554	499	29	that	that	SCONJ
ejpam-4554	499	30	θ	θ	PROPN
ejpam-4554	499	31	is	be	AUX
ejpam-4554	499	32	a	a	DET
ejpam-4554	499	33	regular	regular	ADJ
ejpam-4554	499	34	congruence	congruence	NOUN
ejpam-4554	499	35	relation	relation	NOUN
ejpam-4554	499	36	on	on	ADP
ejpam-4554	499	37	h	h	PROPN
ejpam-4554	499	38	/	/	SYM
ejpam-4554	499	39	i.	i.	NOUN
ejpam-4554	499	40	we	we	PRON
ejpam-4554	499	41	will	will	AUX
ejpam-4554	499	42	show	show	VERB
ejpam-4554	499	43	first	first	ADV
ejpam-4554	499	44	that	that	SCONJ
ejpam-4554	499	45	θ	θ	PROPN
ejpam-4554	499	46	is	be	AUX
ejpam-4554	499	47	an	an	DET
ejpam-4554	499	48	equivalence	equivalence	NOUN
ejpam-4554	499	49	relation	relation	NOUN
ejpam-4554	499	50	on	on	ADP
ejpam-4554	499	51	h	h	PROPN
ejpam-4554	499	52	/	/	SYM
ejpam-4554	499	53	i.	i.	PROPN
ejpam-4554	499	54	note	note	NOUN
ejpam-4554	499	55	that	that	SCONJ
ejpam-4554	499	56	θ1	θ1	NOUN
ejpam-4554	499	57	is	be	AUX
ejpam-4554	499	58	an	an	DET
ejpam-4554	499	59	equivalence	equivalence	NOUN
ejpam-4554	499	60	relation	relation	NOUN
ejpam-4554	499	61	on	on	ADP
ejpam-4554	499	62	h.	h.	PROPN
ejpam-4554	499	63	let	let	VERB
ejpam-4554	499	64	ix	ix	PRON
ejpam-4554	499	65	∈	∈	PROPN
ejpam-4554	499	66	h	h	PROPN
ejpam-4554	499	67	/	/	SYM
ejpam-4554	499	68	i.	i.	NOUN
ejpam-4554	499	69	then	then	ADV
ejpam-4554	499	70	x	x	SYM
ejpam-4554	499	71	∈	∈	PROPN
ejpam-4554	499	72	h	h	NOUN
ejpam-4554	499	73	and	and	CCONJ
ejpam-4554	499	74	xθ1x	xθ1x	PROPN
ejpam-4554	499	75	on	on	ADP
ejpam-4554	499	76	h	h	NOUN
ejpam-4554	499	77	,	,	PUNCT
ejpam-4554	499	78	that	that	ADV
ejpam-4554	499	79	is	is	ADV
ejpam-4554	499	80	,	,	PUNCT
ejpam-4554	499	81	ixθix	ixθix	PROPN
ejpam-4554	499	82	,	,	PUNCT
ejpam-4554	499	83	which	which	PRON
ejpam-4554	499	84	means	mean	VERB
ejpam-4554	499	85	that	that	SCONJ
ejpam-4554	499	86	reflexivity	reflexivity	NOUN
ejpam-4554	499	87	of	of	ADP
ejpam-4554	499	88	θ	θ	PROPN
ejpam-4554	499	89	on	on	ADP
ejpam-4554	499	90	h	h	PROPN
ejpam-4554	499	91	/	/	SYM
ejpam-4554	499	92	i	i	PRON
ejpam-4554	499	93	holds	hold	VERB
ejpam-4554	499	94	.	.	PUNCT
ejpam-4554	500	1	now	now	ADV
ejpam-4554	500	2	,	,	PUNCT
ejpam-4554	500	3	let	let	VERB
ejpam-4554	500	4	ix	ix	ADV
ejpam-4554	500	5	,	,	PUNCT
ejpam-4554	500	6	iy	iy	PROPN
ejpam-4554	500	7	∈	∈	PROPN
ejpam-4554	500	8	h	h	NOUN
ejpam-4554	500	9	/	/	SYM
ejpam-4554	500	10	i	i	PRON
ejpam-4554	500	11	such	such	ADJ
ejpam-4554	500	12	that	that	DET
ejpam-4554	500	13	ixθiy	ixθiy	PROPN
ejpam-4554	500	14	.	.	PUNCT
ejpam-4554	501	1	then	then	ADV
ejpam-4554	501	2	x	x	X
ejpam-4554	501	3	,	,	PUNCT
ejpam-4554	501	4	y	y	PROPN
ejpam-4554	501	5	∈	∈	PROPN
ejpam-4554	501	6	h	h	NOUN
ejpam-4554	501	7	and	and	CCONJ
ejpam-4554	501	8	xθ1y	xθ1y	PROPN
ejpam-4554	501	9	on	on	ADP
ejpam-4554	501	10	h.	h.	PROPN
ejpam-4554	501	11	since	since	SCONJ
ejpam-4554	501	12	θ1	θ1	PROPN
ejpam-4554	501	13	is	be	AUX
ejpam-4554	501	14	a	a	DET
ejpam-4554	501	15	symmetric	symmetric	ADJ
ejpam-4554	501	16	relation	relation	NOUN
ejpam-4554	501	17	on	on	ADP
ejpam-4554	501	18	h	h	NOUN
ejpam-4554	501	19	,	,	PUNCT
ejpam-4554	501	20	yθ1x	yθ1x	NOUN
ejpam-4554	501	21	on	on	ADP
ejpam-4554	501	22	h	h	NOUN
ejpam-4554	502	1	and	and	CCONJ
ejpam-4554	502	2	so	so	ADV
ejpam-4554	502	3	iyθix	iyθix	ADV
ejpam-4554	502	4	on	on	ADP
ejpam-4554	502	5	h	h	PROPN
ejpam-4554	502	6	/	/	SYM
ejpam-4554	502	7	i	i	PROPN
ejpam-4554	502	8	,	,	PUNCT
ejpam-4554	502	9	that	that	ADV
ejpam-4554	502	10	is	is	ADV
ejpam-4554	502	11	,	,	PUNCT
ejpam-4554	502	12	θ	θ	PROPN
ejpam-4554	502	13	is	be	AUX
ejpam-4554	502	14	a	a	DET
ejpam-4554	502	15	symmetric	symmetric	ADJ
ejpam-4554	502	16	relation	relation	NOUN
ejpam-4554	502	17	on	on	ADP
ejpam-4554	502	18	h	h	PROPN
ejpam-4554	502	19	/	/	SYM
ejpam-4554	502	20	i.	i.	NOUN
ejpam-4554	502	21	assume	assume	VERB
ejpam-4554	502	22	that	that	SCONJ
ejpam-4554	502	23	ixθiy	ixθiy	PROPN
ejpam-4554	502	24	and	and	CCONJ
ejpam-4554	502	25	iyθiz	iyθiz	NOUN
ejpam-4554	502	26	,	,	PUNCT
ejpam-4554	502	27	where	where	SCONJ
ejpam-4554	502	28	ix	ix	ADP
ejpam-4554	502	29	,	,	PUNCT
ejpam-4554	502	30	iy	iy	INTJ
ejpam-4554	502	31	,	,	PUNCT
ejpam-4554	502	32	iz	iz	INTJ
ejpam-4554	502	33	∈	∈	PROPN
ejpam-4554	502	34	h	h	NOUN
ejpam-4554	502	35	/	/	SYM
ejpam-4554	502	36	i.	i.	NOUN
ejpam-4554	502	37	then	then	ADV
ejpam-4554	502	38	x	x	PRON
ejpam-4554	502	39	,	,	PUNCT
ejpam-4554	502	40	y	y	PROPN
ejpam-4554	502	41	,	,	PUNCT
ejpam-4554	502	42	z	z	PROPN
ejpam-4554	502	43	∈	∈	PROPN
ejpam-4554	502	44	h	h	NOUN
ejpam-4554	502	45	and	and	CCONJ
ejpam-4554	502	46	xθ1y	xθ1y	PROPN
ejpam-4554	502	47	and	and	CCONJ
ejpam-4554	502	48	yθ1z	yθ1z	PROPN
ejpam-4554	502	49	on	on	ADP
ejpam-4554	502	50	h.	h.	PROPN
ejpam-4554	502	51	since	since	SCONJ
ejpam-4554	502	52	θ1	θ1	NOUN
ejpam-4554	502	53	is	be	AUX
ejpam-4554	502	54	transitive	transitive	ADJ
ejpam-4554	502	55	relation	relation	NOUN
ejpam-4554	502	56	on	on	ADP
ejpam-4554	502	57	h	h	NOUN
ejpam-4554	502	58	,	,	PUNCT
ejpam-4554	502	59	we	we	PRON
ejpam-4554	502	60	have	have	VERB
ejpam-4554	502	61	xθ1z	xθ1z	PROPN
ejpam-4554	502	62	which	which	PRON
ejpam-4554	502	63	tells	tell	VERB
ejpam-4554	502	64	us	we	PRON
ejpam-4554	502	65	that	that	DET
ejpam-4554	502	66	ixθiz	ixθiz	NOUN
ejpam-4554	502	67	.	.	PUNCT
ejpam-4554	503	1	hence	hence	ADV
ejpam-4554	503	2	,	,	PUNCT
ejpam-4554	503	3	θ	θ	PROPN
ejpam-4554	503	4	is	be	AUX
ejpam-4554	503	5	a	a	DET
ejpam-4554	503	6	transitive	transitive	ADJ
ejpam-4554	503	7	relation	relation	NOUN
ejpam-4554	503	8	on	on	ADP
ejpam-4554	503	9	h	h	PROPN
ejpam-4554	503	10	/	/	SYM
ejpam-4554	503	11	i.	i.	NOUN
ejpam-4554	503	12	therefore	therefore	ADV
ejpam-4554	503	13	,	,	PUNCT
ejpam-4554	503	14	θ	θ	PROPN
ejpam-4554	503	15	is	be	AUX
ejpam-4554	503	16	an	an	DET
ejpam-4554	503	17	equivalence	equivalence	NOUN
ejpam-4554	503	18	relation	relation	NOUN
ejpam-4554	503	19	.	.	PUNCT
ejpam-4554	504	1	now	now	ADV
ejpam-4554	504	2	,	,	PUNCT
ejpam-4554	504	3	we	we	PRON
ejpam-4554	504	4	will	will	AUX
ejpam-4554	504	5	show	show	VERB
ejpam-4554	504	6	that	that	SCONJ
ejpam-4554	504	7	θ	θ	PROPN
ejpam-4554	504	8	is	be	AUX
ejpam-4554	504	9	a	a	DET
ejpam-4554	504	10	congruence	congruence	NOUN
ejpam-4554	504	11	relation	relation	NOUN
ejpam-4554	504	12	on	on	ADP
ejpam-4554	504	13	h	h	PROPN
ejpam-4554	504	14	/	/	SYM
ejpam-4554	504	15	i.	i.	PROPN
ejpam-4554	504	16	note	note	NOUN
ejpam-4554	504	17	that	that	SCONJ
ejpam-4554	504	18	θ1	θ1	NOUN
ejpam-4554	504	19	is	be	AUX
ejpam-4554	504	20	a	a	DET
ejpam-4554	504	21	congruence	congruence	NOUN
ejpam-4554	504	22	relation	relation	NOUN
ejpam-4554	504	23	on	on	ADP
ejpam-4554	504	24	h.	h.	PROPN
ejpam-4554	504	25	let	let	VERB
ejpam-4554	504	26	ia	ia	PROPN
ejpam-4554	504	27	,	,	PUNCT
ejpam-4554	504	28	ix	ix	PROPN
ejpam-4554	504	29	,	,	PUNCT
ejpam-4554	504	30	iy	iy	PROPN
ejpam-4554	504	31	∈	∈	PROPN
ejpam-4554	504	32	h	h	NOUN
ejpam-4554	504	33	/	/	SYM
ejpam-4554	504	34	i	i	PRON
ejpam-4554	504	35	for	for	ADP
ejpam-4554	504	36	some	some	DET
ejpam-4554	504	37	a	a	PRON
ejpam-4554	504	38	,	,	PUNCT
ejpam-4554	504	39	x	x	X
ejpam-4554	504	40	,	,	PUNCT
ejpam-4554	504	41	y	y	PROPN
ejpam-4554	504	42	∈	∈	PROPN
ejpam-4554	504	43	h	h	NOUN
ejpam-4554	504	44	such	such	ADJ
ejpam-4554	504	45	that	that	SCONJ
ejpam-4554	504	46	ixθiy	ixθiy	PROPN
ejpam-4554	504	47	on	on	ADP
ejpam-4554	504	48	h	h	PROPN
ejpam-4554	504	49	/	/	SYM
ejpam-4554	504	50	i.	i.	PROPN
ejpam-4554	504	51	note	note	NOUN
ejpam-4554	504	52	that	that	SCONJ
ejpam-4554	504	53	θ1	θ1	NOUN
ejpam-4554	504	54	is	be	AUX
ejpam-4554	504	55	a	a	DET
ejpam-4554	504	56	regular	regular	ADJ
ejpam-4554	504	57	congruence	congruence	NOUN
ejpam-4554	504	58	.	.	PUNCT
ejpam-4554	505	1	by	by	ADP
ejpam-4554	505	2	definition	definition	NOUN
ejpam-4554	505	3	of	of	ADP
ejpam-4554	505	4	θ	θ	PROPN
ejpam-4554	505	5	on	on	ADP
ejpam-4554	505	6	h	h	PROPN
ejpam-4554	505	7	/	/	SYM
ejpam-4554	505	8	i	i	PROPN
ejpam-4554	505	9	,	,	PUNCT
ejpam-4554	505	10	xθ1y	xθ1y	VERB
ejpam-4554	505	11	on	on	ADP
ejpam-4554	505	12	h	h	NOUN
ejpam-4554	505	13	and	and	CCONJ
ejpam-4554	505	14	definition	definition	NOUN
ejpam-4554	505	15	3.1(viii	3.1(viii	NUM
ejpam-4554	505	16	)	)	PUNCT
ejpam-4554	505	17	,	,	PUNCT
ejpam-4554	505	18	(	(	PUNCT
ejpam-4554	505	19	a⊛x)θ̄1(a⊛y	a⊛x)θ̄1(a⊛y	NOUN
ejpam-4554	505	20	)	)	PUNCT
ejpam-4554	505	21	,	,	PUNCT
ejpam-4554	505	22	(	(	PUNCT
ejpam-4554	505	23	x⊛a)θ̄1(y⊛a	x⊛a)θ̄1(y⊛a	PROPN
ejpam-4554	505	24	)	)	PUNCT
ejpam-4554	505	25	,	,	PUNCT
ejpam-4554	505	26	(	(	PUNCT
ejpam-4554	505	27	a⊙x)θ̄1(a⊙y	a⊙x)θ̄1(a⊙y	NOUN
ejpam-4554	505	28	)	)	PUNCT
ejpam-4554	505	29	,	,	PUNCT
ejpam-4554	505	30	and	and	CCONJ
ejpam-4554	505	31	(	(	PUNCT
ejpam-4554	505	32	x⊙a)θ̄1(y⊙a	x⊙a)θ̄1(y⊙a	NOUN
ejpam-4554	505	33	)	)	PUNCT
ejpam-4554	505	34	.	.	PUNCT
ejpam-4554	506	1	thus	thus	ADV
ejpam-4554	506	2	,	,	PUNCT
ejpam-4554	506	3	for	for	ADP
ejpam-4554	506	4	each	each	DET
ejpam-4554	506	5	u	u	NOUN
ejpam-4554	506	6	∈	∈	PROPN
ejpam-4554	506	7	a⊛	a⊛	PROPN
ejpam-4554	506	8	x	x	NOUN
ejpam-4554	506	9	,	,	PUNCT
ejpam-4554	506	10	there	there	PRON
ejpam-4554	506	11	exists	exist	VERB
ejpam-4554	506	12	v	v	ADP
ejpam-4554	506	13	∈	∈	PROPN
ejpam-4554	506	14	a⊛	a⊛	NOUN
ejpam-4554	506	15	y	y	PROPN
ejpam-4554	506	16	such	such	ADJ
ejpam-4554	506	17	that	that	SCONJ
ejpam-4554	506	18	uθ1v	uθ1v	NOUN
ejpam-4554	506	19	and	and	CCONJ
ejpam-4554	506	20	for	for	ADP
ejpam-4554	506	21	each	each	DET
ejpam-4554	506	22	v	v	ADP
ejpam-4554	506	23	∈	∈	PROPN
ejpam-4554	506	24	a⊛	a⊛	PROPN
ejpam-4554	506	25	y	y	PROPN
ejpam-4554	506	26	,	,	PUNCT
ejpam-4554	506	27	there	there	PRON
ejpam-4554	506	28	exists	exist	VERB
ejpam-4554	506	29	u	u	NOUN
ejpam-4554	506	30	∈	∈	PROPN
ejpam-4554	506	31	a⊛	a⊛	NOUN
ejpam-4554	506	32	x	x	PUNCT
ejpam-4554	506	33	such	such	ADJ
ejpam-4554	506	34	that	that	SCONJ
ejpam-4554	506	35	uθ1v	uθ1v	NOUN
ejpam-4554	506	36	.	.	PUNCT
ejpam-4554	507	1	this	this	PRON
ejpam-4554	507	2	means	mean	VERB
ejpam-4554	507	3	that	that	SCONJ
ejpam-4554	507	4	for	for	ADP
ejpam-4554	507	5	each	each	DET
ejpam-4554	507	6	iu	iu	PROPN
ejpam-4554	507	7	∈	∈	PROPN
ejpam-4554	507	8	ia	ia	PROPN
ejpam-4554	507	9	⊛	⊛	NUM
ejpam-4554	507	10	ix	ix	PROPN
ejpam-4554	507	11	,	,	PUNCT
ejpam-4554	507	12	there	there	PRON
ejpam-4554	507	13	exists	exist	VERB
ejpam-4554	507	14	iv	iv	NUM
ejpam-4554	507	15	∈	∈	PROPN
ejpam-4554	507	16	ia	ia	PROPN
ejpam-4554	507	17	⊛	⊛	NUM
ejpam-4554	507	18	iy	iy	PROPN
ejpam-4554	507	19	such	such	ADJ
ejpam-4554	507	20	that	that	SCONJ
ejpam-4554	507	21	iuθiv	iuθiv	NOUN
ejpam-4554	507	22	and	and	CCONJ
ejpam-4554	507	23	for	for	ADP
ejpam-4554	507	24	every	every	DET
ejpam-4554	507	25	iv	iv	NUM
ejpam-4554	507	26	∈	∈	PROPN
ejpam-4554	507	27	ia	ia	PROPN
ejpam-4554	507	28	⊛	⊛	PROPN
ejpam-4554	507	29	iy	iy	PROPN
ejpam-4554	507	30	,	,	PUNCT
ejpam-4554	507	31	there	there	PRON
ejpam-4554	507	32	exists	exist	VERB
ejpam-4554	507	33	iu	iu	ADP
ejpam-4554	507	34	∈	∈	PROPN
ejpam-4554	507	35	ia	ia	PROPN
ejpam-4554	507	36	⊛	⊛	NUM
ejpam-4554	507	37	ix	ix	ADP
ejpam-4554	507	38	such	such	ADJ
ejpam-4554	507	39	that	that	SCONJ
ejpam-4554	507	40	iuθiv	iuθiv	NOUN
ejpam-4554	507	41	.	.	PUNCT
ejpam-4554	508	1	hence	hence	ADV
ejpam-4554	508	2	,	,	PUNCT
ejpam-4554	508	3	(	(	PUNCT
ejpam-4554	508	4	ia⊛	ia⊛	PROPN
ejpam-4554	508	5	ix)θ̄(ia⊛	ix)θ̄(ia⊛	NOUN
ejpam-4554	508	6	iy	iy	PROPN
ejpam-4554	508	7	)	)	PUNCT
ejpam-4554	508	8	.	.	PUNCT
ejpam-4554	509	1	in	in	ADP
ejpam-4554	509	2	a	a	DET
ejpam-4554	509	3	similar	similar	ADJ
ejpam-4554	509	4	manner	manner	NOUN
ejpam-4554	509	5	,	,	PUNCT
ejpam-4554	509	6	we	we	PRON
ejpam-4554	509	7	can	can	AUX
ejpam-4554	509	8	also	also	ADV
ejpam-4554	509	9	show	show	VERB
ejpam-4554	509	10	that	that	SCONJ
ejpam-4554	509	11	(	(	PUNCT
ejpam-4554	509	12	ix⊛	ix⊛	ADP
ejpam-4554	509	13	ia)θ̄(iy	ia)θ̄(iy	PROPN
ejpam-4554	509	14	⊛	⊛	NUM
ejpam-4554	509	15	ia	ia	PROPN
ejpam-4554	509	16	)	)	PUNCT
ejpam-4554	509	17	.	.	PUNCT
ejpam-4554	510	1	on	on	ADP
ejpam-4554	510	2	the	the	DET
ejpam-4554	510	3	other	other	ADJ
ejpam-4554	510	4	hand	hand	NOUN
ejpam-4554	510	5	,	,	PUNCT
ejpam-4554	510	6	for	for	ADP
ejpam-4554	510	7	each	each	DET
ejpam-4554	510	8	r	r	NOUN
ejpam-4554	510	9	∈	∈	PROPN
ejpam-4554	510	10	a	a	DET
ejpam-4554	510	11	⊙	⊙	NOUN
ejpam-4554	510	12	x	x	NOUN
ejpam-4554	510	13	,	,	PUNCT
ejpam-4554	510	14	there	there	PRON
ejpam-4554	510	15	exists	exist	VERB
ejpam-4554	510	16	s	s	PROPN
ejpam-4554	510	17	∈	∈	PROPN
ejpam-4554	510	18	a	a	DET
ejpam-4554	510	19	⊙	⊙	PROPN
ejpam-4554	510	20	y	y	PROPN
ejpam-4554	510	21	such	such	ADJ
ejpam-4554	510	22	that	that	SCONJ
ejpam-4554	510	23	rθ1s	rθ1s	PROPN
ejpam-4554	510	24	and	and	CCONJ
ejpam-4554	510	25	for	for	ADP
ejpam-4554	510	26	all	all	PRON
ejpam-4554	510	27	s	s	VERB
ejpam-4554	510	28	∈	∈	PROPN
ejpam-4554	510	29	a	a	DET
ejpam-4554	510	30	⊙	⊙	PROPN
ejpam-4554	510	31	y	y	PROPN
ejpam-4554	510	32	,	,	PUNCT
ejpam-4554	510	33	there	there	PRON
ejpam-4554	510	34	exists	exist	VERB
ejpam-4554	510	35	r	r	NOUN
ejpam-4554	510	36	∈	∈	PROPN
ejpam-4554	510	37	a	a	DET
ejpam-4554	510	38	⊙	⊙	NOUN
ejpam-4554	510	39	x	x	PUNCT
ejpam-4554	510	40	such	such	ADJ
ejpam-4554	510	41	that	that	SCONJ
ejpam-4554	510	42	rθ1s	rθ1s	PROPN
ejpam-4554	510	43	.	.	PUNCT
ejpam-4554	511	1	this	this	PRON
ejpam-4554	511	2	means	mean	VERB
ejpam-4554	511	3	that	that	SCONJ
ejpam-4554	511	4	for	for	ADP
ejpam-4554	511	5	each	each	DET
ejpam-4554	511	6	ir	ir	PROPN
ejpam-4554	511	7	∈	∈	PROPN
ejpam-4554	511	8	ia	ia	PROPN
ejpam-4554	511	9	⊙	⊙	PROPN
ejpam-4554	511	10	ix	ix	PROPN
ejpam-4554	511	11	,	,	PUNCT
ejpam-4554	511	12	there	there	PRON
ejpam-4554	511	13	exists	exist	VERB
ejpam-4554	511	14	is	be	AUX
ejpam-4554	511	15	∈	∈	PROPN
ejpam-4554	511	16	ia⊙	ia⊙	NUM
ejpam-4554	511	17	iy	iy	PRON
ejpam-4554	511	18	such	such	ADJ
ejpam-4554	511	19	that	that	DET
ejpam-4554	511	20	irθis	irθis	PROPN
ejpam-4554	511	21	and	and	CCONJ
ejpam-4554	511	22	for	for	ADP
ejpam-4554	511	23	every	every	PRON
ejpam-4554	511	24	is	be	AUX
ejpam-4554	511	25	∈	∈	PROPN
ejpam-4554	511	26	ia⊛	ia⊛	PROPN
ejpam-4554	511	27	iy	iy	PROPN
ejpam-4554	511	28	,	,	PUNCT
ejpam-4554	511	29	there	there	PRON
ejpam-4554	511	30	exists	exist	VERB
ejpam-4554	511	31	ir	ir	PROPN
ejpam-4554	511	32	∈	∈	PROPN
ejpam-4554	512	1	ia⊛	ia⊛	ADP
ejpam-4554	512	2	ix	ix	ADP
ejpam-4554	512	3	such	such	ADJ
ejpam-4554	512	4	that	that	DET
ejpam-4554	512	5	irθis	irθis	PROPN
ejpam-4554	512	6	.	.	PUNCT
ejpam-4554	513	1	hence	hence	ADV
ejpam-4554	513	2	,	,	PUNCT
ejpam-4554	513	3	(	(	PUNCT
ejpam-4554	513	4	ia	ia	PROPN
ejpam-4554	513	5	⊙	⊙	PROPN
ejpam-4554	513	6	ix)θ̄(ia	ix)θ̄(ia	PROPN
ejpam-4554	513	7	⊙	⊙	PROPN
ejpam-4554	513	8	iy	iy	PROPN
ejpam-4554	513	9	)	)	PUNCT
ejpam-4554	513	10	.	.	PUNCT
ejpam-4554	514	1	in	in	ADP
ejpam-4554	514	2	a	a	DET
ejpam-4554	514	3	similar	similar	ADJ
ejpam-4554	514	4	manner	manner	NOUN
ejpam-4554	514	5	,	,	PUNCT
ejpam-4554	514	6	we	we	PRON
ejpam-4554	514	7	can	can	AUX
ejpam-4554	514	8	also	also	ADV
ejpam-4554	514	9	show	show	VERB
ejpam-4554	514	10	that	that	SCONJ
ejpam-4554	514	11	(	(	PUNCT
ejpam-4554	514	12	ix	ix	PROPN
ejpam-4554	514	13	⊙	⊙	PROPN
ejpam-4554	514	14	ia)θ̄(iy	ia)θ̄(iy	PROPN
ejpam-4554	514	15	⊛	⊛	NUM
ejpam-4554	514	16	ia	ia	PROPN
ejpam-4554	514	17	)	)	PUNCT
ejpam-4554	514	18	.	.	PUNCT
ejpam-4554	515	1	therefore	therefore	ADV
ejpam-4554	515	2	,	,	PUNCT
ejpam-4554	515	3	θ	θ	PROPN
ejpam-4554	515	4	is	be	AUX
ejpam-4554	515	5	a	a	DET
ejpam-4554	515	6	congruence	congruence	NOUN
ejpam-4554	515	7	relation	relation	NOUN
ejpam-4554	515	8	on	on	ADP
ejpam-4554	515	9	h	h	PROPN
ejpam-4554	515	10	/	/	SYM
ejpam-4554	515	11	i.	i.	PROPN
ejpam-4554	515	12	finally	finally	ADV
ejpam-4554	515	13	,	,	PUNCT
ejpam-4554	515	14	we	we	PRON
ejpam-4554	515	15	will	will	AUX
ejpam-4554	515	16	show	show	VERB
ejpam-4554	515	17	that	that	SCONJ
ejpam-4554	515	18	θ	θ	PROPN
ejpam-4554	515	19	is	be	AUX
ejpam-4554	515	20	a	a	DET
ejpam-4554	515	21	regular	regular	ADJ
ejpam-4554	515	22	congruence	congruence	NOUN
ejpam-4554	515	23	relation	relation	NOUN
ejpam-4554	515	24	on	on	ADP
ejpam-4554	515	25	h	h	PROPN
ejpam-4554	515	26	/	/	SYM
ejpam-4554	515	27	i.	i.	PROPN
ejpam-4554	515	28	suppose	suppose	VERB
ejpam-4554	515	29	that	that	SCONJ
ejpam-4554	515	30	(	(	PUNCT
ejpam-4554	515	31	ix⊛	ix⊛	ADP
ejpam-4554	515	32	iy)θ{i	iy)θ{i	ADJ
ejpam-4554	515	33	}	}	PUNCT
ejpam-4554	515	34	,	,	PUNCT
ejpam-4554	515	35	(	(	PUNCT
ejpam-4554	515	36	iy	iy	PROPN
ejpam-4554	515	37	⊛	⊛	NUM
ejpam-4554	515	38	ix)θ{i	ix)θ{i	PROPN
ejpam-4554	515	39	}	}	PUNCT
ejpam-4554	515	40	,	,	PUNCT
ejpam-4554	515	41	(	(	PUNCT
ejpam-4554	515	42	ix⊙	ix⊙	X
ejpam-4554	515	43	iy)θ{i	iy)θ{i	NOUN
ejpam-4554	515	44	}	}	PUNCT
ejpam-4554	515	45	,	,	PUNCT
ejpam-4554	515	46	and	and	CCONJ
ejpam-4554	515	47	(	(	PUNCT
ejpam-4554	515	48	iy	iy	PROPN
ejpam-4554	515	49	⊙	⊙	PROPN
ejpam-4554	515	50	ix)θ{i	ix)θ{i	PROPN
ejpam-4554	515	51	}	}	PUNCT
ejpam-4554	515	52	.	.	PUNCT
ejpam-4554	516	1	then	then	ADV
ejpam-4554	516	2	there	there	PRON
ejpam-4554	516	3	exist	exist	VERB
ejpam-4554	516	4	u	u	PROPN
ejpam-4554	516	5	∈	∈	PROPN
ejpam-4554	516	6	x⊛	x⊛	PROPN
ejpam-4554	516	7	y	y	PROPN
ejpam-4554	516	8	,	,	PUNCT
ejpam-4554	516	9	v	v	PROPN
ejpam-4554	516	10	∈	∈	PROPN
ejpam-4554	516	11	y	y	PROPN
ejpam-4554	516	12	⊛	⊛	NUM
ejpam-4554	516	13	x	x	X
ejpam-4554	516	14	,	,	PUNCT
ejpam-4554	516	15	r	r	NOUN
ejpam-4554	516	16	∈	∈	PROPN
ejpam-4554	516	17	x	x	X
ejpam-4554	516	18	⊙	⊙	PROPN
ejpam-4554	516	19	y	y	PROPN
ejpam-4554	516	20	,	,	PUNCT
ejpam-4554	516	21	and	and	CCONJ
ejpam-4554	516	22	s	s	VERB
ejpam-4554	516	23	∈	∈	PROPN
ejpam-4554	516	24	y	y	PROPN
ejpam-4554	516	25	⊙	⊙	PROPN
ejpam-4554	516	26	x	x	PUNCT
ejpam-4554	516	27	such	such	ADJ
ejpam-4554	516	28	that	that	SCONJ
ejpam-4554	516	29	iuθ{i	iuθ{i	PROPN
ejpam-4554	516	30	}	}	PUNCT
ejpam-4554	516	31	,	,	PUNCT
ejpam-4554	516	32	ivθ{i	ivθ{i	PROPN
ejpam-4554	516	33	}	}	PUNCT
ejpam-4554	516	34	,	,	PUNCT
ejpam-4554	516	35	irθ{i	irθ{i	NOUN
ejpam-4554	516	36	}	}	PUNCT
ejpam-4554	516	37	,	,	PUNCT
ejpam-4554	516	38	and	and	CCONJ
ejpam-4554	516	39	isθ{i	isθ{i	NUM
ejpam-4554	516	40	}	}	PUNCT
ejpam-4554	516	41	,	,	PUNCT
ejpam-4554	516	42	that	that	ADV
ejpam-4554	516	43	is	is	ADV
ejpam-4554	516	44	,	,	PUNCT
ejpam-4554	516	45	uθ10	uθ10	PROPN
ejpam-4554	516	46	,	,	PUNCT
ejpam-4554	516	47	vθ10	vθ10	PROPN
ejpam-4554	516	48	,	,	PUNCT
ejpam-4554	516	49	rθ10	rθ10	PROPN
ejpam-4554	516	50	,	,	PUNCT
ejpam-4554	516	51	and	and	CCONJ
ejpam-4554	516	52	sθ10	sθ10	PROPN
ejpam-4554	516	53	.	.	PUNCT
ejpam-4554	517	1	so	so	ADV
ejpam-4554	517	2	we	we	PRON
ejpam-4554	517	3	have	have	VERB
ejpam-4554	517	4	,	,	PUNCT
ejpam-4554	517	5	(	(	PUNCT
ejpam-4554	517	6	x⊛	x⊛	PROPN
ejpam-4554	517	7	y)θ1{0	y)θ1{0	PROPN
ejpam-4554	517	8	}	}	PUNCT
ejpam-4554	517	9	,	,	PUNCT
ejpam-4554	517	10	(	(	PUNCT
ejpam-4554	517	11	y	y	PROPN
ejpam-4554	517	12	⊛	⊛	NUM
ejpam-4554	517	13	x)θ1{0},(x⊙	x)θ1{0},(x⊙	PROPN
ejpam-4554	517	14	y)θ1{0	y)θ1{0	PROPN
ejpam-4554	517	15	}	}	PUNCT
ejpam-4554	517	16	,	,	PUNCT
ejpam-4554	517	17	and	and	CCONJ
ejpam-4554	517	18	(	(	PUNCT
ejpam-4554	517	19	y	y	PROPN
ejpam-4554	517	20	⊙	⊙	PROPN
ejpam-4554	517	21	x)θ1{0	x)θ1{0	PROPN
ejpam-4554	517	22	}	}	PUNCT
ejpam-4554	517	23	.	.	PUNCT
ejpam-4554	518	1	since	since	SCONJ
ejpam-4554	518	2	θ1	θ1	NOUN
ejpam-4554	518	3	is	be	AUX
ejpam-4554	518	4	a	a	DET
ejpam-4554	518	5	regular	regular	ADJ
ejpam-4554	518	6	congruence	congruence	NOUN
ejpam-4554	518	7	relation	relation	NOUN
ejpam-4554	518	8	on	on	ADP
ejpam-4554	518	9	h	h	NOUN
ejpam-4554	518	10	,	,	PUNCT
ejpam-4554	518	11	xθ1y	xθ1y	PROPN
ejpam-4554	518	12	,	,	PUNCT
ejpam-4554	518	13	that	that	ADV
ejpam-4554	518	14	is	is	ADV
ejpam-4554	518	15	,	,	PUNCT
ejpam-4554	518	16	ixθiy	ixθiy	PROPN
ejpam-4554	518	17	.	.	PUNCT
ejpam-4554	519	1	therefore	therefore	ADV
ejpam-4554	519	2	,	,	PUNCT
ejpam-4554	519	3	θ	θ	PROPN
ejpam-4554	519	4	is	be	AUX
ejpam-4554	519	5	a	a	DET
ejpam-4554	519	6	regular	regular	ADJ
ejpam-4554	519	7	congruence	congruence	NOUN
ejpam-4554	519	8	relation	relation	NOUN
ejpam-4554	519	9	on	on	ADP
ejpam-4554	519	10	h	h	PROPN
ejpam-4554	519	11	/	/	SYM
ejpam-4554	519	12	i.	i.	NOUN
ejpam-4554	519	13	now	now	ADV
ejpam-4554	519	14	,	,	PUNCT
ejpam-4554	519	15	[	[	X
ejpam-4554	519	16	i]θ	i]θ	NOUN
ejpam-4554	519	17	=	=	SYM
ejpam-4554	519	18	{	{	PUNCT
ejpam-4554	519	19	ix	ix	PROPN
ejpam-4554	519	20	∈	∈	PROPN
ejpam-4554	519	21	h	h	NOUN
ejpam-4554	519	22	/	/	SYM
ejpam-4554	519	23	i	i	PRON
ejpam-4554	519	24	|	|	ADV
ejpam-4554	519	25	ixθi	ixθi	VERB
ejpam-4554	519	26	}	}	PUNCT
ejpam-4554	519	27	=	=	SYM
ejpam-4554	519	28	{	{	PUNCT
ejpam-4554	519	29	ix	ix	ADP
ejpam-4554	519	30	∈	∈	PROPN
ejpam-4554	519	31	h	h	NOUN
ejpam-4554	519	32	/	/	SYM
ejpam-4554	519	33	i	i	PROPN
ejpam-4554	519	34	|xθ10	|xθ10	NOUN
ejpam-4554	519	35	}	}	PUNCT
ejpam-4554	519	36	=	=	SYM
ejpam-4554	519	37	{	{	PUNCT
ejpam-4554	519	38	ix	ix	PROPN
ejpam-4554	519	39	∈	∈	PROPN
ejpam-4554	520	1	h	h	NOUN
ejpam-4554	520	2	/	/	SYM
ejpam-4554	521	1	i	i	PRON
ejpam-4554	521	2	|x	|x	X
ejpam-4554	521	3	∈	∈	PROPN
ejpam-4554	522	1	[	[	X
ejpam-4554	522	2	0]θ1	0]θ1	X
ejpam-4554	522	3	=	=	SYM
ejpam-4554	522	4	j	j	NOUN
ejpam-4554	522	5	}	}	PUNCT
ejpam-4554	522	6	=	=	SYM
ejpam-4554	522	7	{	{	PUNCT
ejpam-4554	522	8	ix	ix	PROPN
ejpam-4554	522	9	∈	∈	PROPN
ejpam-4554	522	10	h	h	NOUN
ejpam-4554	522	11	/	/	SYM
ejpam-4554	522	12	i	i	PRON
ejpam-4554	522	13	|x	|x	NOUN
ejpam-4554	522	14	∈	∈	PROPN
ejpam-4554	522	15	j	j	PROPN
ejpam-4554	522	16	}	}	PUNCT
ejpam-4554	522	17	=	=	SYM
ejpam-4554	522	18	j	j	PROPN
ejpam-4554	522	19	/	/	SYM
ejpam-4554	522	20	i	i	PRON
ejpam-4554	522	21	theorem	theorem	VERB
ejpam-4554	522	22	4.8	4.8	NUM
ejpam-4554	522	23	.	.	PUNCT
ejpam-4554	523	1	(	(	PUNCT
ejpam-4554	523	2	third	third	ADJ
ejpam-4554	523	3	isomorphism	isomorphism	NOUN
ejpam-4554	523	4	theorem	theorem	VERB
ejpam-4554	523	5	)	)	PUNCT
ejpam-4554	523	6	let	let	VERB
ejpam-4554	523	7	f	f	NOUN
ejpam-4554	523	8	:	:	PUNCT
ejpam-4554	523	9	h	h	PROPN
ejpam-4554	524	1	−→	−→	ADJ
ejpam-4554	524	2	h	h	NOUN
ejpam-4554	524	3	′	′	NUM
ejpam-4554	524	4	be	be	AUX
ejpam-4554	524	5	a	a	DET
ejpam-4554	524	6	homomorphism	homomorphism	NOUN
ejpam-4554	524	7	of	of	ADP
ejpam-4554	524	8	pseudo	pseudo	NOUN
ejpam-4554	524	9	hyper	hyper	ADJ
ejpam-4554	524	10	gr	gr	NOUN
ejpam-4554	524	11	-	-	PUNCT
ejpam-4554	524	12	algebras	algebras	ADJ
ejpam-4554	524	13	h	h	PROPN
ejpam-4554	524	14	and	and	CCONJ
ejpam-4554	524	15	h	h	NOUN
ejpam-4554	525	1	′	′	NUM
ejpam-4554	525	2	such	such	ADJ
ejpam-4554	525	3	that	that	SCONJ
ejpam-4554	525	4	f(x	f(x	PROPN
ejpam-4554	525	5	)	)	PUNCT
ejpam-4554	525	6	≪	≪	PUNCT
ejpam-4554	525	7	f(y	f(y	NOUN
ejpam-4554	525	8	)	)	PUNCT
ejpam-4554	525	9	and	and	CCONJ
ejpam-4554	525	10	f(y	f(y	NOUN
ejpam-4554	525	11	)	)	PUNCT
ejpam-4554	525	12	≪	≪	PUNCT
ejpam-4554	525	13	f(x	f(x	PROPN
ejpam-4554	525	14	)	)	PUNCT
ejpam-4554	525	15	imply	imply	VERB
ejpam-4554	525	16	that	that	SCONJ
ejpam-4554	525	17	f(x	f(x	NOUN
ejpam-4554	525	18	)	)	PUNCT
ejpam-4554	525	19	=	=	SYM
ejpam-4554	525	20	f(y	f(y	NOUN
ejpam-4554	525	21	)	)	PUNCT
ejpam-4554	525	22	.	.	PUNCT
ejpam-4554	526	1	suppose	suppose	VERB
ejpam-4554	526	2	further	far	ADV
ejpam-4554	526	3	that	that	SCONJ
ejpam-4554	526	4	θ1	θ1	PROPN
ejpam-4554	526	5	and	and	CCONJ
ejpam-4554	526	6	θ2	θ2	PROPN
ejpam-4554	526	7	are	be	AUX
ejpam-4554	526	8	regular	regular	ADJ
ejpam-4554	526	9	congruence	congruence	NOUN
ejpam-4554	526	10	relations	relation	NOUN
ejpam-4554	526	11	on	on	ADP
ejpam-4554	526	12	h	h	PROPN
ejpam-4554	526	13	r.	r.	PROPN
ejpam-4554	526	14	manzano	manzano	PROPN
ejpam-4554	526	15	,	,	PUNCT
ejpam-4554	526	16	jr	jr	PROPN
ejpam-4554	526	17	.	.	PROPN
ejpam-4554	526	18	,	,	PUNCT
ejpam-4554	526	19	g.	g.	PROPN
ejpam-4554	526	20	petalcorin	petalcorin	PROPN
ejpam-4554	526	21	,	,	PUNCT
ejpam-4554	526	22	jr	jr	PROPN
ejpam-4554	526	23	.	.	PROPN
ejpam-4554	526	24	/	/	SYM
ejpam-4554	526	25	eur	eur	PROPN
ejpam-4554	526	26	.	.	PUNCT
ejpam-4554	527	1	j.	j.	PROPN
ejpam-4554	527	2	pure	pure	PROPN
ejpam-4554	527	3	appl	appl	PROPN
ejpam-4554	527	4	.	.	PROPN
ejpam-4554	527	5	math	math	PROPN
ejpam-4554	527	6	,	,	PUNCT
ejpam-4554	527	7	15	15	NUM
ejpam-4554	527	8	(	(	PUNCT
ejpam-4554	527	9	4	4	NUM
ejpam-4554	527	10	)	)	PUNCT
ejpam-4554	527	11	(	(	PUNCT
ejpam-4554	527	12	2022	2022	NUM
ejpam-4554	527	13	)	)	PUNCT
ejpam-4554	527	14	,	,	PUNCT
ejpam-4554	527	15	1854	1854	NUM
ejpam-4554	527	16	-	-	SYM
ejpam-4554	527	17	1868	1868	NUM
ejpam-4554	527	18	1867	1867	NUM
ejpam-4554	527	19	with	with	ADP
ejpam-4554	527	20	j	j	PROPN
ejpam-4554	527	21	=	=	PUNCT
ejpam-4554	528	1	[	[	X
ejpam-4554	528	2	0]θ1	0]θ1	X
ejpam-4554	528	3	and	and	CCONJ
ejpam-4554	528	4	i	i	PRON
ejpam-4554	528	5	=	=	PUNCT
ejpam-4554	529	1	[	[	X
ejpam-4554	529	2	0]θ2	0]θ2	X
ejpam-4554	529	3	.	.	PUNCT
ejpam-4554	530	1	then	then	ADV
ejpam-4554	530	2	(	(	PUNCT
ejpam-4554	530	3	h	h	X
ejpam-4554	530	4	/	/	SYM
ejpam-4554	530	5	i)/(j	i)/(j	ADJ
ejpam-4554	530	6	/	/	SYM
ejpam-4554	530	7	i	i	NOUN
ejpam-4554	530	8	)	)	PUNCT
ejpam-4554	530	9	∼=	∼=	PROPN
ejpam-4554	530	10	h	h	NOUN
ejpam-4554	530	11	/	/	SYM
ejpam-4554	530	12	j	j	PROPN
ejpam-4554	530	13	,	,	PUNCT
ejpam-4554	530	14	where	where	SCONJ
ejpam-4554	530	15	j	j	PROPN
ejpam-4554	530	16	/	/	SYM
ejpam-4554	530	17	i	i	PRON
ejpam-4554	530	18	=	=	PRON
ejpam-4554	530	19	{	{	PUNCT
ejpam-4554	530	20	ix	ix	ADP
ejpam-4554	530	21	∈	∈	PROPN
ejpam-4554	530	22	h	h	NOUN
ejpam-4554	530	23	/	/	SYM
ejpam-4554	530	24	i	i	PRON
ejpam-4554	530	25	|x	|x	NOUN
ejpam-4554	530	26	∈	∈	PROPN
ejpam-4554	530	27	j	j	PROPN
ejpam-4554	530	28	}	}	PUNCT
ejpam-4554	530	29	.	.	PUNCT
ejpam-4554	531	1	proof	proof	NOUN
ejpam-4554	531	2	.	.	PUNCT
ejpam-4554	532	1	let	let	VERB
ejpam-4554	532	2	f	f	NOUN
ejpam-4554	532	3	:	:	PUNCT
ejpam-4554	532	4	h	h	PROPN
ejpam-4554	532	5	−→	−→	ADJ
ejpam-4554	532	6	h	h	NOUN
ejpam-4554	532	7	′	′	NUM
ejpam-4554	532	8	be	be	AUX
ejpam-4554	532	9	a	a	DET
ejpam-4554	532	10	homomorphism	homomorphism	NOUN
ejpam-4554	532	11	of	of	ADP
ejpam-4554	532	12	pseudo	pseudo	NOUN
ejpam-4554	532	13	hyper	hyper	ADJ
ejpam-4554	532	14	gr	gr	NOUN
ejpam-4554	532	15	-	-	PUNCT
ejpam-4554	532	16	algebras	algebras	ADJ
ejpam-4554	532	17	h	h	PROPN
ejpam-4554	532	18	and	and	CCONJ
ejpam-4554	532	19	h	h	NOUN
ejpam-4554	533	1	′	′	NUM
ejpam-4554	533	2	such	such	ADJ
ejpam-4554	533	3	that	that	SCONJ
ejpam-4554	533	4	f(x	f(x	PROPN
ejpam-4554	533	5	)	)	PUNCT
ejpam-4554	533	6	≪	≪	PUNCT
ejpam-4554	533	7	f(y	f(y	NOUN
ejpam-4554	533	8	)	)	PUNCT
ejpam-4554	533	9	and	and	CCONJ
ejpam-4554	533	10	f(y	f(y	NOUN
ejpam-4554	533	11	)	)	PUNCT
ejpam-4554	533	12	≪	≪	PUNCT
ejpam-4554	533	13	f(x	f(x	PROPN
ejpam-4554	533	14	)	)	PUNCT
ejpam-4554	533	15	imply	imply	VERB
ejpam-4554	533	16	that	that	SCONJ
ejpam-4554	533	17	f(x	f(x	NOUN
ejpam-4554	533	18	)	)	PUNCT
ejpam-4554	533	19	=	=	SYM
ejpam-4554	533	20	f(y	f(y	NOUN
ejpam-4554	533	21	)	)	PUNCT
ejpam-4554	533	22	.	.	PUNCT
ejpam-4554	534	1	suppose	suppose	VERB
ejpam-4554	534	2	further	far	ADV
ejpam-4554	534	3	that	that	SCONJ
ejpam-4554	534	4	θ1	θ1	PROPN
ejpam-4554	534	5	and	and	CCONJ
ejpam-4554	534	6	θ2	θ2	PROPN
ejpam-4554	534	7	are	be	AUX
ejpam-4554	534	8	regular	regular	ADJ
ejpam-4554	534	9	congruence	congruence	NOUN
ejpam-4554	534	10	relations	relation	NOUN
ejpam-4554	534	11	on	on	ADP
ejpam-4554	534	12	h	h	NOUN
ejpam-4554	534	13	with	with	ADP
ejpam-4554	534	14	j	j	PROPN
ejpam-4554	534	15	=	=	PUNCT
ejpam-4554	535	1	[	[	X
ejpam-4554	535	2	0]θ1	0]θ1	X
ejpam-4554	535	3	and	and	CCONJ
ejpam-4554	535	4	i	i	PRON
ejpam-4554	535	5	=	=	PUNCT
ejpam-4554	536	1	[	[	X
ejpam-4554	536	2	0]θ2	0]θ2	X
ejpam-4554	536	3	.	.	PUNCT
ejpam-4554	537	1	let	let	VERB
ejpam-4554	537	2	θ	θ	NOUN
ejpam-4554	537	3	be	be	AUX
ejpam-4554	537	4	a	a	DET
ejpam-4554	537	5	regular	regular	ADJ
ejpam-4554	537	6	congruence	congruence	NOUN
ejpam-4554	537	7	relation	relation	NOUN
ejpam-4554	537	8	on	on	ADP
ejpam-4554	537	9	h	h	PROPN
ejpam-4554	537	10	/	/	SYM
ejpam-4554	537	11	i	i	PRON
ejpam-4554	537	12	defined	define	VERB
ejpam-4554	537	13	in	in	ADP
ejpam-4554	537	14	lemma	lemma	PROPN
ejpam-4554	537	15	4.7	4.7	NUM
ejpam-4554	537	16	.	.	PUNCT
ejpam-4554	538	1	we	we	PRON
ejpam-4554	538	2	define	define	VERB
ejpam-4554	538	3	the	the	DET
ejpam-4554	538	4	map	map	NOUN
ejpam-4554	538	5	φ	φ	X
ejpam-4554	538	6	:	:	PUNCT
ejpam-4554	539	1	h	h	X
ejpam-4554	539	2	/	/	SYM
ejpam-4554	539	3	i	i	PROPN
ejpam-4554	539	4	→	→	SYM
ejpam-4554	539	5	h	h	X
ejpam-4554	539	6	/	/	SYM
ejpam-4554	539	7	j	j	NOUN
ejpam-4554	539	8	by	by	ADP
ejpam-4554	539	9	φ(ix	φ(ix	PROPN
ejpam-4554	539	10	)	)	PUNCT
ejpam-4554	539	11	=	=	SYM
ejpam-4554	540	1	jx	jx	PROPN
ejpam-4554	540	2	.	.	PROPN
ejpam-4554	540	3	suppose	suppose	VERB
ejpam-4554	540	4	that	that	SCONJ
ejpam-4554	540	5	ix	ix	PROPN
ejpam-4554	540	6	=	=	PROPN
ejpam-4554	540	7	iy	iy	PROPN
ejpam-4554	540	8	.	.	PUNCT
ejpam-4554	541	1	since	since	SCONJ
ejpam-4554	541	2	θ	θ	PROPN
ejpam-4554	541	3	is	be	AUX
ejpam-4554	541	4	a	a	DET
ejpam-4554	541	5	reflexive	reflexive	ADJ
ejpam-4554	541	6	relation	relation	NOUN
ejpam-4554	541	7	on	on	ADP
ejpam-4554	541	8	h	h	PROPN
ejpam-4554	541	9	/	/	SYM
ejpam-4554	541	10	i	i	PROPN
ejpam-4554	541	11	,	,	PUNCT
ejpam-4554	541	12	ixθiy	ixθiy	PROPN
ejpam-4554	541	13	on	on	ADP
ejpam-4554	541	14	h	h	PROPN
ejpam-4554	541	15	/	/	SYM
ejpam-4554	541	16	i	i	PRON
ejpam-4554	541	17	which	which	PRON
ejpam-4554	541	18	means	mean	VERB
ejpam-4554	541	19	that	that	SCONJ
ejpam-4554	541	20	xθ1y	xθ1y	PROPN
ejpam-4554	541	21	.	.	PUNCT
ejpam-4554	542	1	note	note	VERB
ejpam-4554	542	2	that	that	SCONJ
ejpam-4554	542	3	j	j	PROPN
ejpam-4554	543	1	=	=	PUNCT
ejpam-4554	544	1	[	[	X
ejpam-4554	544	2	0]θ1	0]θ1	NUM
ejpam-4554	544	3	.	.	PUNCT
ejpam-4554	545	1	now	now	ADV
ejpam-4554	545	2	,	,	PUNCT
ejpam-4554	545	3	if	if	SCONJ
ejpam-4554	545	4	x	x	PROPN
ejpam-4554	545	5	∈	∈	PROPN
ejpam-4554	545	6	j	j	NOUN
ejpam-4554	546	1	=	=	PUNCT
ejpam-4554	547	1	[	[	X
ejpam-4554	547	2	0]θ2	0]θ2	X
ejpam-4554	547	3	,	,	PUNCT
ejpam-4554	547	4	then	then	ADV
ejpam-4554	547	5	xθ10	xθ10	PROPN
ejpam-4554	547	6	and	and	CCONJ
ejpam-4554	547	7	0θ1x	0θ1x	NOUN
ejpam-4554	547	8	.	.	PUNCT
ejpam-4554	548	1	since	since	SCONJ
ejpam-4554	548	2	,	,	PUNCT
ejpam-4554	548	3	xθ1y	xθ1y	PROPN
ejpam-4554	548	4	,	,	PUNCT
ejpam-4554	548	5	by	by	ADP
ejpam-4554	548	6	transitivity	transitivity	NOUN
ejpam-4554	548	7	of	of	ADP
ejpam-4554	548	8	θ1	θ1	NOUN
ejpam-4554	548	9	on	on	ADP
ejpam-4554	548	10	h	h	NOUN
ejpam-4554	548	11	,	,	PUNCT
ejpam-4554	548	12	0θ1y	0θ1y	NOUN
ejpam-4554	548	13	and	and	CCONJ
ejpam-4554	548	14	so	so	ADV
ejpam-4554	548	15	yθ10	yθ10	PROPN
ejpam-4554	548	16	which	which	PRON
ejpam-4554	548	17	will	will	AUX
ejpam-4554	548	18	imply	imply	VERB
ejpam-4554	548	19	that	that	SCONJ
ejpam-4554	548	20	y	y	PROPN
ejpam-4554	548	21	∈	∈	PROPN
ejpam-4554	549	1	[	[	X
ejpam-4554	549	2	0]θ1	0]θ1	X
ejpam-4554	549	3	=	=	SYM
ejpam-4554	549	4	j	j	PROPN
ejpam-4554	549	5	.	.	PUNCT
ejpam-4554	550	1	thus	thus	ADV
ejpam-4554	550	2	,	,	PUNCT
ejpam-4554	550	3	φ(ix	φ(ix	NUM
ejpam-4554	550	4	)	)	PUNCT
ejpam-4554	550	5	=	=	SYM
ejpam-4554	550	6	jx	jx	PROPN
ejpam-4554	550	7	=	=	SYM
ejpam-4554	550	8	j	j	PROPN
ejpam-4554	550	9	=	=	SYM
ejpam-4554	550	10	jy	jy	PROPN
ejpam-4554	550	11	=	=	PUNCT
ejpam-4554	550	12	φ(iy	φ(iy	PROPN
ejpam-4554	550	13	)	)	PUNCT
ejpam-4554	550	14	and	and	CCONJ
ejpam-4554	550	15	φ	φ	PROPN
ejpam-4554	550	16	is	be	AUX
ejpam-4554	550	17	a	a	DET
ejpam-4554	550	18	well	well	ADV
ejpam-4554	550	19	-	-	PUNCT
ejpam-4554	550	20	defined	define	VERB
ejpam-4554	550	21	map	map	NOUN
ejpam-4554	550	22	.	.	PUNCT
ejpam-4554	551	1	we	we	PRON
ejpam-4554	551	2	will	will	AUX
ejpam-4554	551	3	now	now	ADV
ejpam-4554	551	4	show	show	VERB
ejpam-4554	551	5	that	that	SCONJ
ejpam-4554	551	6	φ	φ	PROPN
ejpam-4554	551	7	is	be	AUX
ejpam-4554	551	8	a	a	DET
ejpam-4554	551	9	homomorphism	homomorphism	NOUN
ejpam-4554	551	10	.	.	PUNCT
ejpam-4554	552	1	note	note	VERB
ejpam-4554	552	2	that	that	SCONJ
ejpam-4554	552	3	φ)(i	φ)(i	VERB
ejpam-4554	552	4	)	)	PUNCT
ejpam-4554	553	1	=	=	SYM
ejpam-4554	553	2	j	j	PROPN
ejpam-4554	553	3	.	.	PUNCT
ejpam-4554	554	1	let	let	VERB
ejpam-4554	554	2	ix	ix	ADV
ejpam-4554	554	3	,	,	PUNCT
ejpam-4554	554	4	iy	iy	PROPN
ejpam-4554	554	5	∈	∈	PROPN
ejpam-4554	554	6	h	h	PROPN
ejpam-4554	554	7	/	/	SYM
ejpam-4554	554	8	i.	i.	NOUN
ejpam-4554	554	9	let	let	VERB
ejpam-4554	554	10	jz	jz	PROPN
ejpam-4554	554	11	∈	∈	PROPN
ejpam-4554	554	12	φ(ix	φ(ix	PROPN
ejpam-4554	554	13	⊛	⊛	NUM
ejpam-4554	554	14	iy	iy	PROPN
ejpam-4554	554	15	)	)	PUNCT
ejpam-4554	554	16	.	.	PUNCT
ejpam-4554	555	1	then	then	ADV
ejpam-4554	555	2	,	,	PUNCT
ejpam-4554	555	3	there	there	PRON
ejpam-4554	555	4	exists	exist	VERB
ejpam-4554	555	5	iu	iu	ADP
ejpam-4554	555	6	∈	∈	PROPN
ejpam-4554	555	7	ix	ix	ADP
ejpam-4554	555	8	⊛	⊛	NUM
ejpam-4554	555	9	iy	iy	INTJ
ejpam-4554	555	10	such	such	ADJ
ejpam-4554	555	11	that	that	SCONJ
ejpam-4554	555	12	φ(iu	φ(iu	NOUN
ejpam-4554	555	13	)	)	PUNCT
ejpam-4554	555	14	=	=	SYM
ejpam-4554	555	15	jz	jz	PROPN
ejpam-4554	555	16	,	,	PUNCT
ejpam-4554	555	17	that	that	ADV
ejpam-4554	555	18	is	is	ADV
ejpam-4554	555	19	,	,	PUNCT
ejpam-4554	555	20	ju	ju	PROPN
ejpam-4554	555	21	=	=	SYM
ejpam-4554	555	22	φ(iu	φ(iu	NUM
ejpam-4554	555	23	)	)	PUNCT
ejpam-4554	555	24	=	=	SYM
ejpam-4554	555	25	jz	jz	PROPN
ejpam-4554	555	26	.	.	PROPN
ejpam-4554	555	27	since	since	SCONJ
ejpam-4554	555	28	iu	iu	ADP
ejpam-4554	555	29	∈	∈	PROPN
ejpam-4554	555	30	ix	ix	PROPN
ejpam-4554	555	31	⊛	⊛	PROPN
ejpam-4554	555	32	iy	iy	PROPN
ejpam-4554	555	33	,	,	PUNCT
ejpam-4554	555	34	u	u	PROPN
ejpam-4554	555	35	∈	∈	PROPN
ejpam-4554	555	36	x	x	PUNCT
ejpam-4554	555	37	⊛	⊛	ADP
ejpam-4554	555	38	y.	y.	PROPN
ejpam-4554	555	39	hence	hence	ADV
ejpam-4554	555	40	,	,	PUNCT
ejpam-4554	555	41	ju	ju	PROPN
ejpam-4554	555	42	∈	∈	PROPN
ejpam-4554	555	43	jx	jx	PROPN
ejpam-4554	555	44	⊛	⊛	PROPN
ejpam-4554	555	45	jy	jy	PROPN
ejpam-4554	555	46	.	.	PUNCT
ejpam-4554	556	1	thus	thus	ADV
ejpam-4554	556	2	,	,	PUNCT
ejpam-4554	556	3	jz	jz	PROPN
ejpam-4554	556	4	=	=	PROPN
ejpam-4554	556	5	ju	ju	PROPN
ejpam-4554	556	6	∈	∈	PROPN
ejpam-4554	556	7	jx	jx	PROPN
ejpam-4554	556	8	⊛	⊛	PROPN
ejpam-4554	556	9	jy	jy	PROPN
ejpam-4554	556	10	=	=	SYM
ejpam-4554	556	11	φ(ix	φ(ix	PROPN
ejpam-4554	556	12	)	)	PUNCT
ejpam-4554	556	13	⊛	⊛	NUM
ejpam-4554	556	14	φ(iy	φ(iy	NOUN
ejpam-4554	556	15	)	)	PUNCT
ejpam-4554	556	16	and	and	CCONJ
ejpam-4554	556	17	so	so	ADV
ejpam-4554	556	18	,	,	PUNCT
ejpam-4554	556	19	φ(ix	φ(ix	PROPN
ejpam-4554	556	20	⊛	⊛	NUM
ejpam-4554	556	21	iy	iy	NOUN
ejpam-4554	556	22	)	)	PUNCT
ejpam-4554	556	23	⊆	⊆	NUM
ejpam-4554	556	24	φ(ix	φ(ix	NUM
ejpam-4554	556	25	)	)	PUNCT
ejpam-4554	556	26	⊛	⊛	NUM
ejpam-4554	556	27	φ(iy	φ(iy	NOUN
ejpam-4554	556	28	)	)	PUNCT
ejpam-4554	556	29	.	.	PUNCT
ejpam-4554	557	1	next	next	ADV
ejpam-4554	557	2	,	,	PUNCT
ejpam-4554	557	3	let	let	VERB
ejpam-4554	557	4	jz′	jz′	NOUN
ejpam-4554	557	5	∈	∈	PROPN
ejpam-4554	557	6	φ(ix	φ(ix	PROPN
ejpam-4554	557	7	)	)	PUNCT
ejpam-4554	557	8	⊛	⊛	NUM
ejpam-4554	557	9	φ(iy	φ(iy	NOUN
ejpam-4554	557	10	)	)	PUNCT
ejpam-4554	558	1	=	=	SYM
ejpam-4554	558	2	jx	jx	PROPN
ejpam-4554	558	3	⊛	⊛	PROPN
ejpam-4554	558	4	jy	jy	PROPN
ejpam-4554	558	5	.	.	PUNCT
ejpam-4554	559	1	then	then	ADV
ejpam-4554	559	2	,	,	PUNCT
ejpam-4554	559	3	there	there	PRON
ejpam-4554	559	4	exists	exist	VERB
ejpam-4554	559	5	an	an	DET
ejpam-4554	559	6	element	element	NOUN
ejpam-4554	559	7	u′	u′	PROPN
ejpam-4554	559	8	∈	∈	PROPN
ejpam-4554	559	9	x	x	X
ejpam-4554	559	10	⊛	⊛	NUM
ejpam-4554	559	11	y	y	PRON
ejpam-4554	559	12	such	such	ADJ
ejpam-4554	559	13	that	that	DET
ejpam-4554	559	14	jz′	jz′	NOUN
ejpam-4554	560	1	=	=	PUNCT
ejpam-4554	560	2	ju′	ju′	X
ejpam-4554	560	3	=	=	PUNCT
ejpam-4554	560	4	φ(iu′	φ(iu′	NOUN
ejpam-4554	560	5	)	)	PUNCT
ejpam-4554	560	6	.	.	PUNCT
ejpam-4554	561	1	since	since	SCONJ
ejpam-4554	561	2	u′	u′	PROPN
ejpam-4554	561	3	∈	∈	PROPN
ejpam-4554	561	4	x	x	SYM
ejpam-4554	561	5	⊛	⊛	NUM
ejpam-4554	561	6	y	y	PROPN
ejpam-4554	561	7	,	,	PUNCT
ejpam-4554	561	8	iu′	iu′	PROPN
ejpam-4554	561	9	∈	∈	PROPN
ejpam-4554	561	10	ix	ix	ADP
ejpam-4554	561	11	⊛	⊛	PROPN
ejpam-4554	561	12	iy	iy	PROPN
ejpam-4554	561	13	and	and	CCONJ
ejpam-4554	561	14	jz′	jz′	NOUN
ejpam-4554	561	15	=	=	SYM
ejpam-4554	561	16	φ(iu′	φ(iu′	NOUN
ejpam-4554	561	17	)	)	PUNCT
ejpam-4554	561	18	∈	∈	PROPN
ejpam-4554	561	19	φ(ix	φ(ix	PROPN
ejpam-4554	561	20	⊛	⊛	NUM
ejpam-4554	561	21	iy	iy	PROPN
ejpam-4554	561	22	)	)	PUNCT
ejpam-4554	561	23	.	.	PUNCT
ejpam-4554	562	1	so	so	ADV
ejpam-4554	562	2	,	,	PUNCT
ejpam-4554	562	3	φ(ix)⊛	φ(ix)⊛	NOUN
ejpam-4554	562	4	φ(iy	φ(iy	NOUN
ejpam-4554	562	5	)	)	PUNCT
ejpam-4554	562	6	⊆	⊆	NUM
ejpam-4554	562	7	φ(ix	φ(ix	PROPN
ejpam-4554	562	8	⊛	⊛	NUM
ejpam-4554	562	9	iy	iy	PROPN
ejpam-4554	562	10	)	)	PUNCT
ejpam-4554	562	11	.	.	PUNCT
ejpam-4554	563	1	therefore	therefore	ADV
ejpam-4554	563	2	,	,	PUNCT
ejpam-4554	563	3	φ(ix	φ(ix	PROPN
ejpam-4554	563	4	⊛	⊛	NUM
ejpam-4554	563	5	iy	iy	PROPN
ejpam-4554	563	6	)	)	PUNCT
ejpam-4554	563	7	=	=	SYM
ejpam-4554	563	8	φ(ix)⊛	φ(ix)⊛	NOUN
ejpam-4554	563	9	φ(iy	φ(iy	NOUN
ejpam-4554	563	10	)	)	PUNCT
ejpam-4554	563	11	.	.	PUNCT
ejpam-4554	564	1	now	now	ADV
ejpam-4554	564	2	,	,	PUNCT
ejpam-4554	564	3	let	let	VERB
ejpam-4554	564	4	jz	jz	PROPN
ejpam-4554	564	5	∈	∈	PROPN
ejpam-4554	564	6	φ(ix	φ(ix	PROPN
ejpam-4554	564	7	⊙	⊙	NOUN
ejpam-4554	564	8	iy	iy	PROPN
ejpam-4554	564	9	)	)	PUNCT
ejpam-4554	564	10	.	.	PUNCT
ejpam-4554	565	1	then	then	ADV
ejpam-4554	565	2	,	,	PUNCT
ejpam-4554	565	3	there	there	PRON
ejpam-4554	565	4	exists	exist	VERB
ejpam-4554	565	5	an	an	DET
ejpam-4554	565	6	element	element	NOUN
ejpam-4554	565	7	iu	iu	ADP
ejpam-4554	565	8	∈	∈	PROPN
ejpam-4554	565	9	ix	ix	PROPN
ejpam-4554	565	10	⊙	⊙	PROPN
ejpam-4554	565	11	iy	iy	PROPN
ejpam-4554	566	1	such	such	ADJ
ejpam-4554	566	2	that	that	SCONJ
ejpam-4554	566	3	φ(iu	φ(iu	NOUN
ejpam-4554	566	4	)	)	PUNCT
ejpam-4554	566	5	=	=	SYM
ejpam-4554	566	6	jz	jz	PROPN
ejpam-4554	566	7	,	,	PUNCT
ejpam-4554	566	8	that	that	ADV
ejpam-4554	566	9	is	is	ADV
ejpam-4554	566	10	,	,	PUNCT
ejpam-4554	566	11	ju	ju	PROPN
ejpam-4554	566	12	=	=	SYM
ejpam-4554	566	13	φ(iu	φ(iu	NUM
ejpam-4554	566	14	)	)	PUNCT
ejpam-4554	566	15	=	=	SYM
ejpam-4554	567	1	jz	jz	PROPN
ejpam-4554	567	2	.	.	PROPN
ejpam-4554	567	3	since	since	SCONJ
ejpam-4554	567	4	iu	iu	ADP
ejpam-4554	567	5	∈	∈	PROPN
ejpam-4554	567	6	ix	ix	PROPN
ejpam-4554	567	7	⊙	⊙	PROPN
ejpam-4554	567	8	iy	iy	PROPN
ejpam-4554	567	9	,	,	PUNCT
ejpam-4554	567	10	u	u	PROPN
ejpam-4554	567	11	∈	∈	PROPN
ejpam-4554	567	12	x⊙	x⊙	PROPN
ejpam-4554	567	13	y.	y.	PROPN
ejpam-4554	567	14	hence	hence	ADV
ejpam-4554	567	15	,	,	PUNCT
ejpam-4554	567	16	ju	ju	PROPN
ejpam-4554	567	17	∈	∈	PROPN
ejpam-4554	567	18	jx	jx	PROPN
ejpam-4554	567	19	⊙	⊙	PROPN
ejpam-4554	567	20	jy	jy	PROPN
ejpam-4554	567	21	.	.	PUNCT
ejpam-4554	568	1	thus	thus	ADV
ejpam-4554	568	2	,	,	PUNCT
ejpam-4554	568	3	jz	jz	PROPN
ejpam-4554	568	4	=	=	PROPN
ejpam-4554	568	5	ju	ju	PROPN
ejpam-4554	568	6	∈	∈	PROPN
ejpam-4554	568	7	jx	jx	PROPN
ejpam-4554	568	8	⊙	⊙	PROPN
ejpam-4554	568	9	jy	jy	PROPN
ejpam-4554	568	10	=	=	SYM
ejpam-4554	568	11	φ(ix	φ(ix	PROPN
ejpam-4554	568	12	)	)	PUNCT
ejpam-4554	568	13	⊙	⊙	NOUN
ejpam-4554	568	14	φ(iy	φ(iy	PROPN
ejpam-4554	568	15	)	)	PUNCT
ejpam-4554	568	16	and	and	CCONJ
ejpam-4554	568	17	so	so	ADV
ejpam-4554	568	18	,	,	PUNCT
ejpam-4554	568	19	φ(ix	φ(ix	PROPN
ejpam-4554	568	20	⊙	⊙	NOUN
ejpam-4554	568	21	iy	iy	PROPN
ejpam-4554	568	22	)	)	PUNCT
ejpam-4554	568	23	⊆	⊆	NUM
ejpam-4554	568	24	φ(ix	φ(ix	NUM
ejpam-4554	568	25	)	)	PUNCT
ejpam-4554	568	26	⊙	⊙	NOUN
ejpam-4554	568	27	φ(iy	φ(iy	NUM
ejpam-4554	568	28	)	)	PUNCT
ejpam-4554	568	29	.	.	PUNCT
ejpam-4554	569	1	next	next	ADV
ejpam-4554	569	2	,	,	PUNCT
ejpam-4554	569	3	let	let	VERB
ejpam-4554	569	4	jz′	jz′	NOUN
ejpam-4554	569	5	∈	∈	PROPN
ejpam-4554	569	6	φ(ix	φ(ix	PROPN
ejpam-4554	569	7	)	)	PUNCT
ejpam-4554	569	8	⊙	⊙	NOUN
ejpam-4554	569	9	φ(iy	φ(iy	PROPN
ejpam-4554	569	10	)	)	PUNCT
ejpam-4554	570	1	=	=	SYM
ejpam-4554	570	2	jx	jx	PROPN
ejpam-4554	570	3	⊙	⊙	PROPN
ejpam-4554	570	4	jy	jy	PROPN
ejpam-4554	570	5	.	.	PUNCT
ejpam-4554	571	1	then	then	ADV
ejpam-4554	571	2	,	,	PUNCT
ejpam-4554	571	3	there	there	PRON
ejpam-4554	571	4	exists	exist	VERB
ejpam-4554	571	5	an	an	DET
ejpam-4554	571	6	element	element	NOUN
ejpam-4554	571	7	u′	u′	PROPN
ejpam-4554	571	8	∈	∈	PROPN
ejpam-4554	571	9	x	x	X
ejpam-4554	571	10	⊙	⊙	PROPN
ejpam-4554	571	11	y	y	PROPN
ejpam-4554	571	12	such	such	ADJ
ejpam-4554	571	13	that	that	DET
ejpam-4554	571	14	jz′	jz′	NOUN
ejpam-4554	572	1	=	=	PUNCT
ejpam-4554	572	2	ju′	ju′	X
ejpam-4554	572	3	=	=	PUNCT
ejpam-4554	572	4	φ(iu′	φ(iu′	NOUN
ejpam-4554	572	5	)	)	PUNCT
ejpam-4554	572	6	.	.	PUNCT
ejpam-4554	573	1	since	since	SCONJ
ejpam-4554	573	2	u′	u′	PROPN
ejpam-4554	573	3	∈	∈	PROPN
ejpam-4554	573	4	x	x	PROPN
ejpam-4554	573	5	⊙	⊙	PROPN
ejpam-4554	573	6	y	y	PROPN
ejpam-4554	573	7	,	,	PUNCT
ejpam-4554	573	8	iu′	iu′	PROPN
ejpam-4554	573	9	∈	∈	PROPN
ejpam-4554	573	10	ix	ix	PROPN
ejpam-4554	573	11	⊙	⊙	PROPN
ejpam-4554	573	12	iy	iy	PROPN
ejpam-4554	573	13	and	and	CCONJ
ejpam-4554	573	14	so	so	ADV
ejpam-4554	573	15	,	,	PUNCT
ejpam-4554	573	16	jz′	jz′	NOUN
ejpam-4554	573	17	=	=	SYM
ejpam-4554	573	18	φ(iu′	φ(iu′	NOUN
ejpam-4554	573	19	)	)	PUNCT
ejpam-4554	573	20	∈	∈	PROPN
ejpam-4554	573	21	φ(ix	φ(ix	PROPN
ejpam-4554	573	22	⊙	⊙	NOUN
ejpam-4554	573	23	iy	iy	PROPN
ejpam-4554	573	24	)	)	PUNCT
ejpam-4554	573	25	.	.	PUNCT
ejpam-4554	574	1	so	so	ADV
ejpam-4554	574	2	,	,	PUNCT
ejpam-4554	574	3	φ(ix)⊙	φ(ix)⊙	ADV
ejpam-4554	574	4	φ(iy	φ(iy	NOUN
ejpam-4554	574	5	)	)	PUNCT
ejpam-4554	574	6	⊆	⊆	NUM
ejpam-4554	574	7	(	(	PUNCT
ejpam-4554	574	8	ix	ix	PROPN
ejpam-4554	574	9	⊙	⊙	PROPN
ejpam-4554	574	10	iy	iy	PROPN
ejpam-4554	574	11	)	)	PUNCT
ejpam-4554	574	12	.	.	PUNCT
ejpam-4554	575	1	hence	hence	ADV
ejpam-4554	575	2	,	,	PUNCT
ejpam-4554	575	3	φ(ix	φ(ix	PROPN
ejpam-4554	575	4	⊙	⊙	NOUN
ejpam-4554	575	5	iy	iy	PROPN
ejpam-4554	575	6	)	)	PUNCT
ejpam-4554	576	1	=	=	PUNCT
ejpam-4554	576	2	φ(ix)⊙	φ(ix)⊙	ADP
ejpam-4554	577	1	φ(iy	φ(iy	NOUN
ejpam-4554	577	2	)	)	PUNCT
ejpam-4554	577	3	and	and	CCONJ
ejpam-4554	577	4	φ	φ	PROPN
ejpam-4554	577	5	is	be	AUX
ejpam-4554	577	6	a	a	DET
ejpam-4554	577	7	homomorphism	homomorphism	NOUN
ejpam-4554	577	8	.	.	PUNCT
ejpam-4554	578	1	now	now	ADV
ejpam-4554	578	2	,	,	PUNCT
ejpam-4554	578	3	ker	ker	PROPN
ejpam-4554	578	4	φ	φ	PROPN
ejpam-4554	578	5	=	=	SYM
ejpam-4554	578	6	{	{	PUNCT
ejpam-4554	578	7	ix	ix	PROPN
ejpam-4554	578	8	∈	∈	PROPN
ejpam-4554	578	9	h	h	NOUN
ejpam-4554	578	10	/	/	SYM
ejpam-4554	578	11	i	i	PRON
ejpam-4554	578	12	|φ(ix	|φ(ix	PROPN
ejpam-4554	578	13	)	)	PUNCT
ejpam-4554	578	14	=	=	PUNCT
ejpam-4554	579	1	[	[	X
ejpam-4554	579	2	0]θ1	0]θ1	NOUN
ejpam-4554	579	3	}	}	PUNCT
ejpam-4554	579	4	=	=	SYM
ejpam-4554	579	5	{	{	PUNCT
ejpam-4554	579	6	ix	ix	PROPN
ejpam-4554	579	7	∈	∈	PROPN
ejpam-4554	579	8	h	h	NOUN
ejpam-4554	579	9	/	/	SYM
ejpam-4554	579	10	i	i	PRON
ejpam-4554	579	11	|	|	ADV
ejpam-4554	579	12	jx	jx	PROPN
ejpam-4554	579	13	=	=	PUNCT
ejpam-4554	580	1	[	[	X
ejpam-4554	580	2	0]θ1	0]θ1	X
ejpam-4554	580	3	=	=	SYM
ejpam-4554	580	4	j	j	NOUN
ejpam-4554	580	5	}	}	PUNCT
ejpam-4554	580	6	=	=	SYM
ejpam-4554	580	7	{	{	PUNCT
ejpam-4554	580	8	ix	ix	PROPN
ejpam-4554	580	9	∈	∈	PROPN
ejpam-4554	580	10	h	h	NOUN
ejpam-4554	580	11	/	/	SYM
ejpam-4554	580	12	i	i	PRON
ejpam-4554	580	13	|x	|x	NOUN
ejpam-4554	580	14	∈	∈	PROPN
ejpam-4554	580	15	j	j	PROPN
ejpam-4554	580	16	}	}	PUNCT
ejpam-4554	580	17	=	=	SYM
ejpam-4554	580	18	j	j	PROPN
ejpam-4554	580	19	/	/	SYM
ejpam-4554	580	20	i.	i.	PROPN
ejpam-4554	580	21	by	by	ADP
ejpam-4554	580	22	lemma	lemma	PROPN
ejpam-4554	580	23	4.7	4.7	NUM
ejpam-4554	580	24	,	,	PUNCT
ejpam-4554	580	25	ker	ker	PROPN
ejpam-4554	580	26	φ	φ	PROPN
ejpam-4554	580	27	=	=	SYM
ejpam-4554	580	28	j	j	PROPN
ejpam-4554	580	29	/	/	SYM
ejpam-4554	580	30	i	i	NOUN
ejpam-4554	580	31	=	=	PUNCT
ejpam-4554	581	1	[	[	X
ejpam-4554	581	2	i]θ	i]θ	NOUN
ejpam-4554	581	3	.	.	PUNCT
ejpam-4554	582	1	lastly	lastly	ADV
ejpam-4554	582	2	,	,	PUNCT
ejpam-4554	582	3	we	we	PRON
ejpam-4554	582	4	will	will	AUX
ejpam-4554	582	5	show	show	VERB
ejpam-4554	582	6	that	that	SCONJ
ejpam-4554	582	7	φ	φ	PROPN
ejpam-4554	582	8	is	be	AUX
ejpam-4554	582	9	onto	onto	ADP
ejpam-4554	582	10	.	.	PUNCT
ejpam-4554	583	1	let	let	VERB
ejpam-4554	583	2	z	z	NOUN
ejpam-4554	583	3	∈	∈	PROPN
ejpam-4554	583	4	h	h	NOUN
ejpam-4554	583	5	and	and	CCONJ
ejpam-4554	583	6	iz	iz	INTJ
ejpam-4554	583	7	∈	∈	PROPN
ejpam-4554	583	8	h	h	PROPN
ejpam-4554	583	9	/	/	SYM
ejpam-4554	583	10	i.	i.	PROPN
ejpam-4554	583	11	thus	thus	ADV
ejpam-4554	583	12	,	,	PUNCT
ejpam-4554	583	13	there	there	PRON
ejpam-4554	583	14	exists	exist	VERB
ejpam-4554	583	15	an	an	DET
ejpam-4554	583	16	element	element	NOUN
ejpam-4554	583	17	iz	iz	INTJ
ejpam-4554	583	18	∈	∈	PROPN
ejpam-4554	583	19	h	h	NOUN
ejpam-4554	583	20	/	/	SYM
ejpam-4554	583	21	i	i	PRON
ejpam-4554	583	22	such	such	ADJ
ejpam-4554	583	23	that	that	SCONJ
ejpam-4554	583	24	φ(iz	φ(iz	NOUN
ejpam-4554	583	25	)	)	PUNCT
ejpam-4554	583	26	=	=	SYM
ejpam-4554	583	27	jz	jz	PROPN
ejpam-4554	583	28	and	and	CCONJ
ejpam-4554	583	29	so	so	ADV
ejpam-4554	583	30	φ	φ	PROPN
ejpam-4554	583	31	is	be	AUX
ejpam-4554	583	32	onto	onto	ADP
ejpam-4554	583	33	.	.	PUNCT
ejpam-4554	584	1	therefore	therefore	ADV
ejpam-4554	584	2	,	,	PUNCT
ejpam-4554	584	3	by	by	ADP
ejpam-4554	584	4	the	the	DET
ejpam-4554	584	5	first	first	ADJ
ejpam-4554	584	6	isomorphism	isomorphism	NOUN
ejpam-4554	584	7	theorem	theorem	VERB
ejpam-4554	584	8	,	,	PUNCT
ejpam-4554	584	9	(	(	PUNCT
ejpam-4554	584	10	h	h	NOUN
ejpam-4554	584	11	/	/	SYM
ejpam-4554	584	12	i)/(j	i)/(j	ADJ
ejpam-4554	584	13	/	/	SYM
ejpam-4554	584	14	i	i	NOUN
ejpam-4554	584	15	)	)	PUNCT
ejpam-4554	584	16	∼=	∼=	PROPN
ejpam-4554	584	17	imφ	imφ	NOUN
ejpam-4554	584	18	=	=	NOUN
ejpam-4554	584	19	h	h	PROPN
ejpam-4554	584	20	/	/	SYM
ejpam-4554	584	21	j	j	PROPN
ejpam-4554	584	22	.	.	PUNCT
ejpam-4554	585	1	□	□	PUNCT
ejpam-4554	585	2	acknowledgements	acknowledgement	NOUN
ejpam-4554	585	3	the	the	DET
ejpam-4554	585	4	authors	author	NOUN
ejpam-4554	585	5	would	would	AUX
ejpam-4554	585	6	like	like	VERB
ejpam-4554	585	7	to	to	PART
ejpam-4554	585	8	thank	thank	VERB
ejpam-4554	585	9	the	the	DET
ejpam-4554	585	10	referees	referee	NOUN
ejpam-4554	585	11	who	who	PRON
ejpam-4554	585	12	gave	give	VERB
ejpam-4554	585	13	their	their	PRON
ejpam-4554	585	14	brilliant	brilliant	ADJ
ejpam-4554	585	15	suggestions	suggestion	NOUN
ejpam-4554	585	16	in	in	ADP
ejpam-4554	585	17	refining	refine	VERB
ejpam-4554	585	18	this	this	DET
ejpam-4554	585	19	paper	paper	NOUN
ejpam-4554	585	20	before	before	ADP
ejpam-4554	585	21	publication	publication	NOUN
ejpam-4554	585	22	to	to	ADP
ejpam-4554	585	23	the	the	DET
ejpam-4554	585	24	european	european	PROPN
ejpam-4554	585	25	journal	journal	PROPN
ejpam-4554	585	26	of	of	ADP
ejpam-4554	585	27	pure	pure	ADJ
ejpam-4554	585	28	and	and	CCONJ
ejpam-4554	585	29	applied	applied	ADJ
ejpam-4554	585	30	mathematics	mathematic	NOUN
ejpam-4554	585	31	.	.	PUNCT
ejpam-4554	586	1	references	reference	NOUN
ejpam-4554	586	2	1868	1868	NUM
ejpam-4554	586	3	references	reference	NOUN
ejpam-4554	586	4	[	[	X
ejpam-4554	586	5	1	1	NUM
ejpam-4554	586	6	]	]	X
ejpam-4554	586	7	imai	imai	PROPN
ejpam-4554	586	8	,	,	PUNCT
ejpam-4554	586	9	y.	y.	PROPN
ejpam-4554	586	10	and	and	CCONJ
ejpam-4554	586	11	iseki	iseki	PROPN
ejpam-4554	586	12	,	,	PUNCT
ejpam-4554	586	13	k.	k.	PROPN
ejpam-4554	586	14	,	,	PUNCT
ejpam-4554	586	15	on	on	ADP
ejpam-4554	586	16	axiom	axiom	NOUN
ejpam-4554	586	17	systems	system	NOUN
ejpam-4554	586	18	of	of	ADP
ejpam-4554	586	19	propositional	propositional	ADJ
ejpam-4554	586	20	calculi	calculi	PROPN
ejpam-4554	586	21	xiv	xiv	PROPN
ejpam-4554	586	22	,	,	PUNCT
ejpam-4554	586	23	proc	proc	PROPN
ejpam-4554	586	24	.	.	PUNCT
ejpam-4554	587	1	japan	japan	PROPN
ejpam-4554	587	2	academy	academy	PROPN
ejpam-4554	587	3	,	,	PUNCT
ejpam-4554	587	4	42	42	NUM
ejpam-4554	587	5	(	(	PUNCT
ejpam-4554	587	6	1966	1966	NUM
ejpam-4554	587	7	)	)	PUNCT
ejpam-4554	587	8	,	,	PUNCT
ejpam-4554	587	9	19	19	NUM
ejpam-4554	587	10	-	-	SYM
ejpam-4554	587	11	22	22	NUM
ejpam-4554	587	12	.	.	PUNCT
ejpam-4554	588	1	[	[	X
ejpam-4554	588	2	2	2	NUM
ejpam-4554	588	3	]	]	PUNCT
ejpam-4554	588	4	indangan	indangan	PROPN
ejpam-4554	588	5	r.a	r.a	PROPN
ejpam-4554	588	6	.	.	PROPN
ejpam-4554	588	7	and	and	CCONJ
ejpam-4554	588	8	petalcorin	petalcorin	PROPN
ejpam-4554	588	9	g.c	g.c	PROPN
ejpam-4554	588	10	.	.	PROPN
ejpam-4554	588	11	,	,	PUNCT
ejpam-4554	588	12	some	some	DET
ejpam-4554	588	13	results	result	VERB
ejpam-4554	588	14	on	on	ADP
ejpam-4554	588	15	hyper	hyper	ADJ
ejpam-4554	588	16	gr	gr	NOUN
ejpam-4554	588	17	-	-	PUNCT
ejpam-4554	588	18	ideals	ideal	NOUN
ejpam-4554	588	19	of	of	ADP
ejpam-4554	588	20	a	a	DET
ejpam-4554	588	21	hyper	hyper	ADJ
ejpam-4554	588	22	gr	gr	NOUN
ejpam-4554	588	23	-	-	PUNCT
ejpam-4554	588	24	algebra	algebra	NOUN
ejpam-4554	588	25	,	,	PUNCT
ejpam-4554	588	26	journal	journal	NOUN
ejpam-4554	588	27	of	of	ADP
ejpam-4554	588	28	algebra	algebra	PROPN
ejpam-4554	588	29	and	and	CCONJ
ejpam-4554	588	30	applied	apply	VERB
ejpam-4554	588	31	mathematics	mathematic	NOUN
ejpam-4554	588	32	,	,	PUNCT
ejpam-4554	588	33	14	14	NUM
ejpam-4554	588	34	,	,	PUNCT
ejpam-4554	588	35	(	(	PUNCT
ejpam-4554	588	36	2016	2016	NUM
ejpam-4554	588	37	)	)	PUNCT
ejpam-4554	588	38	,	,	PUNCT
ejpam-4554	588	39	101	101	NUM
ejpam-4554	588	40	-	-	SYM
ejpam-4554	588	41	119	119	NUM
ejpam-4554	588	42	.	.	PUNCT
ejpam-4554	589	1	[	[	X
ejpam-4554	589	2	3	3	X
ejpam-4554	589	3	]	]	X
ejpam-4554	589	4	indangan	indangan	PROPN
ejpam-4554	589	5	r.a	r.a	PROPN
ejpam-4554	589	6	.	.	PROPN
ejpam-4554	589	7	,	,	PUNCT
ejpam-4554	589	8	petalcorin	petalcorin	PROPN
ejpam-4554	589	9	g.c	g.c	PROPN
ejpam-4554	589	10	.	.	PROPN
ejpam-4554	589	11	and	and	CCONJ
ejpam-4554	589	12	villa	villa	PROPN
ejpam-4554	589	13	,	,	PUNCT
ejpam-4554	589	14	a.a	a.a	PROPN
ejpam-4554	589	15	.	.	PROPN
ejpam-4554	589	16	,	,	PUNCT
ejpam-4554	589	17	some	some	DET
ejpam-4554	589	18	hyper	hyper	ADJ
ejpam-4554	589	19	homomorphic	homomorphic	ADJ
ejpam-4554	589	20	properties	property	NOUN
ejpam-4554	589	21	on	on	ADP
ejpam-4554	589	22	hyper	hyper	ADJ
ejpam-4554	589	23	gr	gr	NOUN
ejpam-4554	589	24	-	-	PUNCT
ejpam-4554	589	25	algebras	algebra	NOUN
ejpam-4554	589	26	,	,	PUNCT
ejpam-4554	589	27	journal	journal	NOUN
ejpam-4554	589	28	of	of	ADP
ejpam-4554	589	29	algebra	algebra	PROPN
ejpam-4554	589	30	and	and	CCONJ
ejpam-4554	589	31	applied	apply	VERB
ejpam-4554	589	32	mathematics	mathematic	NOUN
ejpam-4554	589	33	,	,	PUNCT
ejpam-4554	589	34	15	15	NUM
ejpam-4554	589	35	,	,	PUNCT
ejpam-4554	589	36	(	(	PUNCT
ejpam-4554	589	37	2017	2017	NUM
ejpam-4554	589	38	)	)	PUNCT
ejpam-4554	589	39	,	,	PUNCT
ejpam-4554	589	40	100121	100121	NUM
ejpam-4554	589	41	.	.	PUNCT
ejpam-4554	590	1	[	[	X
ejpam-4554	590	2	4	4	NUM
ejpam-4554	590	3	]	]	X
ejpam-4554	590	4	manzano	manzano	PROPN
ejpam-4554	590	5	,	,	PUNCT
ejpam-4554	590	6	jr	jr	PROPN
ejpam-4554	590	7	.	.	PROPN
ejpam-4554	590	8	,	,	PUNCT
ejpam-4554	590	9	r.g	r.g	PROPN
ejpam-4554	590	10	.	.	PROPN
ejpam-4554	590	11	and	and	CCONJ
ejpam-4554	590	12	petalcorin	petalcorin	PROPN
ejpam-4554	590	13	,	,	PUNCT
ejpam-4554	590	14	jr	jr	PROPN
ejpam-4554	590	15	.	.	PROPN
ejpam-4554	590	16	,	,	PUNCT
ejpam-4554	590	17	g.c	g.c	PROPN
ejpam-4554	590	18	.	.	PROPN
ejpam-4554	590	19	on	on	ADP
ejpam-4554	590	20	varieties	variety	NOUN
ejpam-4554	590	21	of	of	ADP
ejpam-4554	590	22	pseudo	pseudo	NOUN
ejpam-4554	590	23	hyper	hyper	ADJ
ejpam-4554	590	24	gr	gr	NOUN
ejpam-4554	590	25	-	-	PUNCT
ejpam-4554	590	26	ideals	ideal	NOUN
ejpam-4554	590	27	of	of	ADP
ejpam-4554	590	28	pseudo	pseudo	NOUN
ejpam-4554	590	29	hyper	hyper	ADJ
ejpam-4554	590	30	gr	gr	NOUN
ejpam-4554	590	31	-	-	PUNCT
ejpam-4554	590	32	algebras	algebra	NOUN
ejpam-4554	590	33	,	,	PUNCT
ejpam-4554	590	34	european	european	ADJ
ejpam-4554	590	35	journal	journal	PROPN
ejpam-4554	590	36	of	of	ADP
ejpam-4554	590	37	pure	pure	ADJ
ejpam-4554	590	38	and	and	CCONJ
ejpam-4554	590	39	applied	applied	ADJ
ejpam-4554	590	40	mathematics	mathematic	NOUN
ejpam-4554	590	41	,	,	PUNCT
ejpam-4554	590	42	12(3	12(3	NUM
ejpam-4554	590	43	)	)	PUNCT
ejpam-4554	590	44	,	,	PUNCT
ejpam-4554	590	45	(	(	PUNCT
ejpam-4554	590	46	2019	2019	NUM
ejpam-4554	590	47	)	)	PUNCT
ejpam-4554	590	48	,	,	PUNCT
ejpam-4554	590	49	821	821	NUM
ejpam-4554	590	50	-	-	SYM
ejpam-4554	590	51	833	833	NUM
ejpam-4554	590	52	.	.	PUNCT
ejpam-4554	591	1	[	[	X
ejpam-4554	591	2	5	5	NUM
ejpam-4554	591	3	]	]	X
ejpam-4554	591	4	jun	jun	PROPN
ejpam-4554	591	5	,	,	PUNCT
ejpam-4554	591	6	y.b	y.b	PROPN
ejpam-4554	591	7	.	.	PROPN
ejpam-4554	591	8	,	,	PUNCT
ejpam-4554	591	9	zahedi	zahedi	PROPN
ejpam-4554	591	10	,	,	PUNCT
ejpam-4554	591	11	m.m	m.m	PROPN
ejpam-4554	591	12	.	.	PROPN
ejpam-4554	591	13	,	,	PUNCT
ejpam-4554	591	14	xin	xin	PROPN
ejpam-4554	591	15	,	,	PUNCT
ejpam-4554	591	16	x.	x.	PROPN
ejpam-4554	591	17	l.	l.	PROPN
ejpam-4554	591	18	and	and	CCONJ
ejpam-4554	591	19	borzooei	borzooei	PROPN
ejpam-4554	591	20	,	,	PUNCT
ejpam-4554	591	21	r.	r.	PROPN
ejpam-4554	591	22	a.	a.	PROPN
ejpam-4554	591	23	on	on	ADP
ejpam-4554	591	24	hyper	hyper	ADJ
ejpam-4554	591	25	bck	bck	PROPN
ejpam-4554	591	26	-	-	PUNCT
ejpam-4554	591	27	algebras	algebra	NOUN
ejpam-4554	591	28	,	,	PUNCT
ejpam-4554	591	29	italian	italian	ADJ
ejpam-4554	591	30	journal	journal	NOUN
ejpam-4554	591	31	of	of	ADP
ejpam-4554	591	32	pure	pure	ADJ
ejpam-4554	591	33	and	and	CCONJ
ejpam-4554	591	34	applied	applied	ADJ
ejpam-4554	591	35	mathematics	mathematic	NOUN
ejpam-4554	591	36	,	,	PUNCT
ejpam-4554	591	37	8	8	NUM
ejpam-4554	591	38	(	(	PUNCT
ejpam-4554	591	39	2000	2000	NUM
ejpam-4554	591	40	)	)	PUNCT
ejpam-4554	591	41	,	,	PUNCT
ejpam-4554	591	42	127	127	NUM
ejpam-4554	591	43	-	-	SYM
ejpam-4554	591	44	136	136	NUM
ejpam-4554	591	45	.	.	PUNCT
ejpam-4554	592	1	[	[	X
ejpam-4554	592	2	6	6	NUM
ejpam-4554	592	3	]	]	X
ejpam-4554	592	4	marty	marty	PROPN
ejpam-4554	592	5	,	,	PUNCT
ejpam-4554	592	6	f.	f.	PROPN
ejpam-4554	592	7	,	,	PUNCT
ejpam-4554	592	8	sur	sur	PROPN
ejpam-4554	592	9	une	une	PROPN
ejpam-4554	592	10	generalization	generalization	NOUN
ejpam-4554	592	11	de	de	X
ejpam-4554	592	12	la	la	PROPN
ejpam-4554	592	13	notion	notion	PROPN
ejpam-4554	592	14	de	de	X
ejpam-4554	592	15	groupe	groupe	PROPN
ejpam-4554	592	16	,	,	PUNCT
ejpam-4554	592	17	in	in	ADP
ejpam-4554	592	18	proceedings	proceeding	NOUN
ejpam-4554	592	19	of	of	ADP
ejpam-4554	592	20	the	the	DET
ejpam-4554	592	21	8th	8th	ADJ
ejpam-4554	592	22	congress	congress	PROPN
ejpam-4554	592	23	math	math	NOUN
ejpam-4554	592	24	.	.	PUNCT
ejpam-4554	593	1	scandinaves	scandinave	NOUN
ejpam-4554	593	2	,	,	PUNCT
ejpam-4554	593	3	stockholm	stockholm	PROPN
ejpam-4554	593	4	:	:	PUNCT
ejpam-4554	593	5	1934	1934	NUM
ejpam-4554	593	6	,	,	PUNCT
ejpam-4554	593	7	45	45	NUM
ejpam-4554	593	8	-	-	SYM
ejpam-4554	593	9	49	49	NUM
ejpam-4554	593	10	.	.	PUNCT