id	sid	tid	token	lemma	pos
ejpam-4675	1	1	european	european	PROPN
ejpam-4675	1	2	journal	journal	PROPN
ejpam-4675	1	3	of	of	ADP
ejpam-4675	1	4	pure	pure	ADJ
ejpam-4675	1	5	and	and	CCONJ
ejpam-4675	1	6	applied	apply	VERB
ejpam-4675	1	7	mathematics	mathematic	NOUN
ejpam-4675	1	8	vol	vol	NOUN
ejpam-4675	1	9	.	.	PUNCT
ejpam-4675	2	1	16	16	NUM
ejpam-4675	2	2	,	,	PUNCT
ejpam-4675	2	3	no	no	INTJ
ejpam-4675	2	4	.	.	NOUN
ejpam-4675	2	5	1	1	NUM
ejpam-4675	2	6	,	,	PUNCT
ejpam-4675	2	7	2023	2023	NUM
ejpam-4675	2	8	,	,	PUNCT
ejpam-4675	2	9	577	577	NUM
ejpam-4675	2	10	-	-	SYM
ejpam-4675	2	11	586	586	NUM
ejpam-4675	2	12	issn	issn	PROPN
ejpam-4675	2	13	1307	1307	NUM
ejpam-4675	2	14	-	-	SYM
ejpam-4675	2	15	5543	5543	NUM
ejpam-4675	2	16	–	–	PUNCT
ejpam-4675	2	17	ejpam.com	ejpam.com	X
ejpam-4675	2	18	published	publish	VERB
ejpam-4675	2	19	by	by	ADP
ejpam-4675	2	20	new	new	PROPN
ejpam-4675	2	21	york	york	PROPN
ejpam-4675	2	22	business	business	PROPN
ejpam-4675	3	1	global	global	ADJ
ejpam-4675	3	2	first	first	ADJ
ejpam-4675	3	3	and	and	CCONJ
ejpam-4675	3	4	third	third	ADJ
ejpam-4675	3	5	isomorphism	isomorphism	NOUN
ejpam-4675	3	6	theorems	theorem	NOUN
ejpam-4675	3	7	for	for	ADP
ejpam-4675	3	8	the	the	DET
ejpam-4675	3	9	dual	dual	ADJ
ejpam-4675	3	10	b	b	NOUN
ejpam-4675	3	11	-	-	PUNCT
ejpam-4675	3	12	algebra	algebra	ADJ
ejpam-4675	3	13	jethro	jethro	PROPN
ejpam-4675	3	14	elijah	elijah	PROPN
ejpam-4675	3	15	bolima1,∗	bolima1,∗	PROPN
ejpam-4675	3	16	,	,	PUNCT
ejpam-4675	3	17	katrina	katrina	PROPN
ejpam-4675	3	18	belleza	belleza	PROPN
ejpam-4675	3	19	fuentes1	fuentes1	PROPN
ejpam-4675	3	20	1	1	NUM
ejpam-4675	3	21	department	department	NOUN
ejpam-4675	3	22	of	of	ADP
ejpam-4675	3	23	computer	computer	NOUN
ejpam-4675	3	24	,	,	PUNCT
ejpam-4675	3	25	information	information	NOUN
ejpam-4675	3	26	sciences	science	NOUN
ejpam-4675	3	27	,	,	PUNCT
ejpam-4675	3	28	and	and	CCONJ
ejpam-4675	3	29	mathematics	mathematic	NOUN
ejpam-4675	3	30	,	,	PUNCT
ejpam-4675	3	31	school	school	NOUN
ejpam-4675	3	32	of	of	ADP
ejpam-4675	3	33	arts	art	NOUN
ejpam-4675	3	34	and	and	CCONJ
ejpam-4675	3	35	sciences	science	NOUN
ejpam-4675	3	36	,	,	PUNCT
ejpam-4675	3	37	university	university	NOUN
ejpam-4675	3	38	of	of	ADP
ejpam-4675	3	39	san	san	PROPN
ejpam-4675	3	40	carlos	carlos	PROPN
ejpam-4675	3	41	,	,	PUNCT
ejpam-4675	3	42	6000	6000	NUM
ejpam-4675	3	43	cebu	cebu	NOUN
ejpam-4675	3	44	city	city	NOUN
ejpam-4675	3	45	,	,	PUNCT
ejpam-4675	3	46	philippines	philippine	NOUN
ejpam-4675	3	47	abstract	abstract	ADJ
ejpam-4675	3	48	.	.	PUNCT
ejpam-4675	4	1	in	in	ADP
ejpam-4675	4	2	this	this	DET
ejpam-4675	4	3	paper	paper	NOUN
ejpam-4675	4	4	,	,	PUNCT
ejpam-4675	4	5	some	some	DET
ejpam-4675	4	6	properties	property	NOUN
ejpam-4675	4	7	of	of	ADP
ejpam-4675	4	8	the	the	DET
ejpam-4675	4	9	dual	dual	ADJ
ejpam-4675	4	10	b	b	X
ejpam-4675	4	11	-	-	PUNCT
ejpam-4675	4	12	homomorphism	homomorphism	NOUN
ejpam-4675	4	13	are	be	AUX
ejpam-4675	4	14	provided	provide	VERB
ejpam-4675	4	15	,	,	PUNCT
ejpam-4675	4	16	along	along	ADP
ejpam-4675	4	17	with	with	ADP
ejpam-4675	4	18	the	the	DET
ejpam-4675	4	19	natural	natural	ADJ
ejpam-4675	4	20	dual	dual	ADJ
ejpam-4675	4	21	b	b	NOUN
ejpam-4675	4	22	-	-	PUNCT
ejpam-4675	4	23	homomorphism	homomorphism	NOUN
ejpam-4675	4	24	and	and	CCONJ
ejpam-4675	4	25	the	the	DET
ejpam-4675	4	26	fundamental	fundamental	ADJ
ejpam-4675	4	27	theorem	theorem	NOUN
ejpam-4675	4	28	of	of	ADP
ejpam-4675	4	29	dual	dual	ADJ
ejpam-4675	4	30	b	b	NOUN
ejpam-4675	4	31	-	-	PUNCT
ejpam-4675	4	32	homomorphisms	homomorphism	NOUN
ejpam-4675	4	33	for	for	ADP
ejpam-4675	4	34	dual	dual	ADJ
ejpam-4675	4	35	b	b	NOUN
ejpam-4675	4	36	-	-	PUNCT
ejpam-4675	4	37	algebras	algebras	X
ejpam-4675	4	38	.	.	PUNCT
ejpam-4675	5	1	the	the	DET
ejpam-4675	5	2	first	first	ADJ
ejpam-4675	5	3	and	and	CCONJ
ejpam-4675	5	4	third	third	ADJ
ejpam-4675	5	5	isomorphism	isomorphism	NOUN
ejpam-4675	5	6	theorems	theorem	NOUN
ejpam-4675	5	7	for	for	ADP
ejpam-4675	5	8	the	the	DET
ejpam-4675	5	9	dual	dual	ADJ
ejpam-4675	5	10	b	b	NOUN
ejpam-4675	5	11	-	-	PUNCT
ejpam-4675	5	12	algebra	algebra	NOUN
ejpam-4675	5	13	are	be	AUX
ejpam-4675	5	14	also	also	ADV
ejpam-4675	5	15	presented	present	VERB
ejpam-4675	5	16	in	in	ADP
ejpam-4675	5	17	the	the	DET
ejpam-4675	5	18	paper	paper	NOUN
ejpam-4675	5	19	.	.	PUNCT
ejpam-4675	6	1	2020	2020	NUM
ejpam-4675	6	2	mathematics	mathematic	NOUN
ejpam-4675	6	3	subject	subject	NOUN
ejpam-4675	6	4	classifications	classification	NOUN
ejpam-4675	6	5	:	:	PUNCT
ejpam-4675	6	6	47l45	47l45	NUM
ejpam-4675	6	7	,	,	PUNCT
ejpam-4675	6	8	08a35	08a35	VERB
ejpam-4675	6	9	key	key	ADJ
ejpam-4675	6	10	words	word	NOUN
ejpam-4675	6	11	and	and	CCONJ
ejpam-4675	6	12	phrases	phrase	NOUN
ejpam-4675	6	13	:	:	PUNCT
ejpam-4675	6	14	dual	dual	ADJ
ejpam-4675	6	15	b	b	X
ejpam-4675	6	16	-	-	PUNCT
ejpam-4675	6	17	algebra	algebra	NOUN
ejpam-4675	6	18	,	,	PUNCT
ejpam-4675	6	19	quotient	quotient	VERB
ejpam-4675	6	20	dual	dual	ADJ
ejpam-4675	6	21	b	b	NOUN
ejpam-4675	6	22	-	-	PUNCT
ejpam-4675	6	23	algebra	algebra	ADJ
ejpam-4675	6	24	,	,	PUNCT
ejpam-4675	6	25	fundamental	fundamental	ADJ
ejpam-4675	6	26	theorem	theorem	NOUN
ejpam-4675	6	27	of	of	ADP
ejpam-4675	6	28	dual	dual	ADJ
ejpam-4675	6	29	b	b	NOUN
ejpam-4675	6	30	-	-	PUNCT
ejpam-4675	6	31	homomorphism	homomorphism	NOUN
ejpam-4675	6	32	,	,	PUNCT
ejpam-4675	6	33	dual	dual	ADJ
ejpam-4675	6	34	b	b	NOUN
ejpam-4675	6	35	-	-	PUNCT
ejpam-4675	6	36	isomorphism	isomorphism	ADJ
ejpam-4675	6	37	1	1	NUM
ejpam-4675	6	38	.	.	PUNCT
ejpam-4675	7	1	introduction	introduction	NOUN
ejpam-4675	7	2	k.	k.	PROPN
ejpam-4675	7	3	belleza	belleza	PROPN
ejpam-4675	7	4	and	and	CCONJ
ejpam-4675	7	5	j.p	j.p	PROPN
ejpam-4675	7	6	.	.	PROPN
ejpam-4675	7	7	vilela	vilela	PROPN
ejpam-4675	7	8	in	in	ADP
ejpam-4675	7	9	their	their	PRON
ejpam-4675	7	10	paper	paper	NOUN
ejpam-4675	7	11	in	in	ADP
ejpam-4675	7	12	2019	2019	NUM
ejpam-4675	7	13	[	[	X
ejpam-4675	7	14	2	2	NUM
ejpam-4675	7	15	]	]	PUNCT
ejpam-4675	7	16	introduced	introduce	VERB
ejpam-4675	7	17	the	the	DET
ejpam-4675	7	18	dual	dual	ADJ
ejpam-4675	7	19	b	b	NOUN
ejpam-4675	7	20	-	-	PUNCT
ejpam-4675	7	21	algebra	algebra	NOUN
ejpam-4675	7	22	,	,	PUNCT
ejpam-4675	7	23	its	its	PRON
ejpam-4675	7	24	relationship	relationship	NOUN
ejpam-4675	7	25	with	with	ADP
ejpam-4675	7	26	other	other	ADJ
ejpam-4675	7	27	algebras	algebra	NOUN
ejpam-4675	7	28	,	,	PUNCT
ejpam-4675	7	29	and	and	CCONJ
ejpam-4675	7	30	its	its	PRON
ejpam-4675	7	31	characteristics	characteristic	NOUN
ejpam-4675	7	32	.	.	PUNCT
ejpam-4675	8	1	more	more	ADJ
ejpam-4675	8	2	studies	study	NOUN
ejpam-4675	8	3	were	be	AUX
ejpam-4675	8	4	then	then	ADV
ejpam-4675	8	5	conducted	conduct	VERB
ejpam-4675	8	6	on	on	ADP
ejpam-4675	8	7	the	the	DET
ejpam-4675	8	8	said	say	VERB
ejpam-4675	8	9	topic	topic	NOUN
ejpam-4675	8	10	.	.	PUNCT
ejpam-4675	9	1	one	one	NUM
ejpam-4675	9	2	of	of	ADP
ejpam-4675	9	3	the	the	DET
ejpam-4675	9	4	recent	recent	ADJ
ejpam-4675	9	5	papers	paper	NOUN
ejpam-4675	9	6	published	publish	VERB
ejpam-4675	9	7	by	by	ADP
ejpam-4675	9	8	k.	k.	PROPN
ejpam-4675	9	9	belleza	belleza	PROPN
ejpam-4675	9	10	and	and	CCONJ
ejpam-4675	9	11	j.r	j.r	PROPN
ejpam-4675	9	12	.	.	PROPN
ejpam-4675	9	13	albaracin	albaracin	PROPN
ejpam-4675	9	14	in	in	ADP
ejpam-4675	9	15	2022	2022	NUM
ejpam-4675	9	16	[	[	X
ejpam-4675	9	17	1	1	X
ejpam-4675	9	18	]	]	PUNCT
ejpam-4675	9	19	discussed	discuss	VERB
ejpam-4675	9	20	about	about	ADP
ejpam-4675	9	21	dual	dual	ADJ
ejpam-4675	9	22	b	b	NOUN
ejpam-4675	9	23	-	-	PUNCT
ejpam-4675	9	24	filters	filter	NOUN
ejpam-4675	9	25	and	and	CCONJ
ejpam-4675	9	26	dual	dual	ADJ
ejpam-4675	9	27	b	b	NOUN
ejpam-4675	9	28	-	-	PUNCT
ejpam-4675	9	29	subalgebras	subalgebras	PROPN
ejpam-4675	9	30	in	in	ADP
ejpam-4675	9	31	a	a	DET
ejpam-4675	9	32	topological	topological	ADJ
ejpam-4675	9	33	dual	dual	ADJ
ejpam-4675	9	34	b	b	NOUN
ejpam-4675	9	35	-	-	PUNCT
ejpam-4675	9	36	algebra	algebra	NOUN
ejpam-4675	9	37	,	,	PUNCT
ejpam-4675	9	38	wherein	wherein	SCONJ
ejpam-4675	9	39	the	the	DET
ejpam-4675	9	40	researchers	researcher	NOUN
ejpam-4675	9	41	first	first	ADV
ejpam-4675	9	42	constructed	construct	VERB
ejpam-4675	9	43	a	a	DET
ejpam-4675	9	44	congruence	congruence	NOUN
ejpam-4675	9	45	relation	relation	NOUN
ejpam-4675	9	46	on	on	ADP
ejpam-4675	9	47	a	a	DET
ejpam-4675	9	48	dual	dual	ADJ
ejpam-4675	9	49	balgebra	balgebra	NOUN
ejpam-4675	9	50	which	which	PRON
ejpam-4675	9	51	is	be	AUX
ejpam-4675	9	52	necessary	necessary	ADJ
ejpam-4675	9	53	in	in	ADP
ejpam-4675	9	54	creating	create	VERB
ejpam-4675	9	55	a	a	DET
ejpam-4675	9	56	natural	natural	ADJ
ejpam-4675	9	57	homomorphism	homomorphism	NOUN
ejpam-4675	9	58	from	from	ADP
ejpam-4675	9	59	one	one	NUM
ejpam-4675	9	60	dual	dual	ADJ
ejpam-4675	9	61	b	b	NOUN
ejpam-4675	9	62	-	-	PUNCT
ejpam-4675	9	63	algebra	algebra	NOUN
ejpam-4675	9	64	onto	onto	ADP
ejpam-4675	9	65	another	another	PRON
ejpam-4675	9	66	;	;	PUNCT
ejpam-4675	9	67	an	an	DET
ejpam-4675	9	68	important	important	ADJ
ejpam-4675	9	69	first	first	ADJ
ejpam-4675	9	70	step	step	NOUN
ejpam-4675	9	71	in	in	ADP
ejpam-4675	9	72	this	this	DET
ejpam-4675	9	73	study	study	NOUN
ejpam-4675	9	74	.	.	PUNCT
ejpam-4675	10	1	while	while	SCONJ
ejpam-4675	10	2	many	many	ADJ
ejpam-4675	10	3	other	other	ADJ
ejpam-4675	10	4	algebraic	algebraic	ADJ
ejpam-4675	10	5	structures	structure	NOUN
ejpam-4675	10	6	prepared	prepare	VERB
ejpam-4675	10	7	different	different	ADJ
ejpam-4675	10	8	approaches	approach	NOUN
ejpam-4675	10	9	in	in	ADP
ejpam-4675	10	10	constructing	construct	VERB
ejpam-4675	10	11	isomorphism	isomorphism	NOUN
ejpam-4675	10	12	to	to	ADP
ejpam-4675	10	13	their	their	PRON
ejpam-4675	10	14	respective	respective	ADJ
ejpam-4675	10	15	algebras	algebra	NOUN
ejpam-4675	10	16	(	(	PUNCT
ejpam-4675	10	17	see	see	VERB
ejpam-4675	10	18	[	[	X
ejpam-4675	10	19	6	6	NUM
ejpam-4675	10	20	]	]	PUNCT
ejpam-4675	10	21	,	,	PUNCT
ejpam-4675	10	22	[	[	X
ejpam-4675	10	23	3	3	NUM
ejpam-4675	10	24	]	]	PUNCT
ejpam-4675	10	25	,	,	PUNCT
ejpam-4675	10	26	[	[	X
ejpam-4675	10	27	5	5	NUM
ejpam-4675	10	28	]	]	NUM
ejpam-4675	10	29	)	)	PUNCT
ejpam-4675	10	30	,	,	PUNCT
ejpam-4675	10	31	j.	j.	PROPN
ejpam-4675	10	32	neggers	neggers	PROPN
ejpam-4675	10	33	and	and	CCONJ
ejpam-4675	10	34	h.s	h.s	PROPN
ejpam-4675	10	35	.	.	PROPN
ejpam-4675	10	36	kim	kim	PROPN
ejpam-4675	10	37	in	in	ADP
ejpam-4675	10	38	particular	particular	ADJ
ejpam-4675	10	39	,	,	PUNCT
ejpam-4675	10	40	presented	present	VERB
ejpam-4675	10	41	a	a	DET
ejpam-4675	10	42	fundamental	fundamental	ADJ
ejpam-4675	10	43	theorem	theorem	NOUN
ejpam-4675	10	44	of	of	ADP
ejpam-4675	10	45	b	b	NOUN
ejpam-4675	10	46	-	-	PUNCT
ejpam-4675	10	47	homomorphism	homomorphism	NOUN
ejpam-4675	10	48	for	for	ADP
ejpam-4675	10	49	b	b	NOUN
ejpam-4675	10	50	-	-	PUNCT
ejpam-4675	10	51	algebras	algebras	PROPN
ejpam-4675	10	52	and	and	CCONJ
ejpam-4675	10	53	using	use	VERB
ejpam-4675	10	54	the	the	DET
ejpam-4675	10	55	said	say	VERB
ejpam-4675	10	56	theorem	theorem	NOUN
ejpam-4675	10	57	created	create	VERB
ejpam-4675	10	58	the	the	DET
ejpam-4675	10	59	1st	1st	ADJ
ejpam-4675	10	60	and	and	CCONJ
ejpam-4675	10	61	3rd	3rd	ADJ
ejpam-4675	10	62	isomorphism	isomorphism	NOUN
ejpam-4675	10	63	theorems	theorem	VERB
ejpam-4675	10	64	for	for	ADP
ejpam-4675	10	65	the	the	DET
ejpam-4675	10	66	b	b	NOUN
ejpam-4675	10	67	-	-	PUNCT
ejpam-4675	10	68	algebra	algebra	NOUN
ejpam-4675	10	69	in	in	ADP
ejpam-4675	10	70	2002	2002	NUM
ejpam-4675	10	71	[	[	X
ejpam-4675	10	72	7	7	NUM
ejpam-4675	10	73	]	]	PUNCT
ejpam-4675	10	74	.	.	PUNCT
ejpam-4675	11	1	later	later	ADV
ejpam-4675	11	2	in	in	ADP
ejpam-4675	11	3	2015	2015	NUM
ejpam-4675	11	4	,	,	PUNCT
ejpam-4675	11	5	j.c	j.c	PROPN
ejpam-4675	11	6	.	.	PROPN
ejpam-4675	11	7	endam	endam	PROPN
ejpam-4675	11	8	and	and	CCONJ
ejpam-4675	11	9	j.p	j.p	PROPN
ejpam-4675	11	10	.	.	PROPN
ejpam-4675	11	11	vilela	vilela	PROPN
ejpam-4675	11	12	also	also	ADV
ejpam-4675	11	13	provided	provide	VERB
ejpam-4675	11	14	more	more	ADJ
ejpam-4675	11	15	insights	insight	NOUN
ejpam-4675	11	16	on	on	ADP
ejpam-4675	11	17	the	the	DET
ejpam-4675	11	18	properties	property	NOUN
ejpam-4675	11	19	of	of	ADP
ejpam-4675	11	20	normal	normal	ADJ
ejpam-4675	11	21	subsets	subset	NOUN
ejpam-4675	11	22	of	of	ADP
ejpam-4675	11	23	b	b	NOUN
ejpam-4675	11	24	-	-	PUNCT
ejpam-4675	11	25	algebra	algebra	NOUN
ejpam-4675	11	26	and	and	CCONJ
ejpam-4675	11	27	b	b	NOUN
ejpam-4675	11	28	-	-	PUNCT
ejpam-4675	11	29	homomorphism	homomorphism	NOUN
ejpam-4675	11	30	,	,	PUNCT
ejpam-4675	11	31	and	and	CCONJ
ejpam-4675	11	32	presented	present	VERB
ejpam-4675	11	33	proof	proof	NOUN
ejpam-4675	11	34	for	for	ADP
ejpam-4675	11	35	the	the	DET
ejpam-4675	11	36	2nd	2nd	ADJ
ejpam-4675	11	37	isomorphism	isomorphism	NOUN
ejpam-4675	11	38	theorem	theorem	NOUN
ejpam-4675	11	39	for	for	ADP
ejpam-4675	11	40	the	the	DET
ejpam-4675	11	41	b	b	NOUN
ejpam-4675	11	42	-	-	PUNCT
ejpam-4675	11	43	algebras	algebras	X
ejpam-4675	12	1	[	[	X
ejpam-4675	12	2	4	4	NUM
ejpam-4675	12	3	]	]	PUNCT
ejpam-4675	12	4	.	.	PUNCT
ejpam-4675	13	1	this	this	PRON
ejpam-4675	13	2	,	,	PUNCT
ejpam-4675	13	3	in	in	ADP
ejpam-4675	13	4	turn	turn	NOUN
ejpam-4675	13	5	warrants	warrant	NOUN
ejpam-4675	13	6	a	a	DET
ejpam-4675	13	7	need	need	NOUN
ejpam-4675	13	8	for	for	ADP
ejpam-4675	13	9	investigation	investigation	NOUN
ejpam-4675	13	10	of	of	ADP
ejpam-4675	13	11	the	the	DET
ejpam-4675	13	12	dual	dual	ADJ
ejpam-4675	13	13	b	b	NOUN
ejpam-4675	13	14	-	-	PUNCT
ejpam-4675	13	15	algebra	algebra	NOUN
ejpam-4675	13	16	as	as	ADP
ejpam-4675	13	17	to	to	ADP
ejpam-4675	13	18	whether	whether	SCONJ
ejpam-4675	13	19	the	the	DET
ejpam-4675	13	20	isomorphism	isomorphism	NOUN
ejpam-4675	13	21	theorems	theorem	NOUN
ejpam-4675	13	22	can	can	AUX
ejpam-4675	13	23	be	be	AUX
ejpam-4675	13	24	constructed	construct	VERB
ejpam-4675	13	25	within	within	ADP
ejpam-4675	13	26	the	the	DET
ejpam-4675	13	27	dual	dual	ADJ
ejpam-4675	13	28	b	b	NOUN
ejpam-4675	13	29	-	-	PUNCT
ejpam-4675	13	30	algebra	algebra	NOUN
ejpam-4675	13	31	since	since	SCONJ
ejpam-4675	13	32	there	there	PRON
ejpam-4675	13	33	exists	exist	VERB
ejpam-4675	13	34	a	a	DET
ejpam-4675	13	35	close	close	ADJ
ejpam-4675	13	36	relationship	relationship	NOUN
ejpam-4675	13	37	between	between	ADP
ejpam-4675	13	38	the	the	DET
ejpam-4675	13	39	b	b	NOUN
ejpam-4675	13	40	-	-	PUNCT
ejpam-4675	13	41	algebra	algebra	NOUN
ejpam-4675	13	42	and	and	CCONJ
ejpam-4675	13	43	the	the	DET
ejpam-4675	13	44	dual	dual	ADJ
ejpam-4675	13	45	b	b	NOUN
ejpam-4675	13	46	-	-	PUNCT
ejpam-4675	13	47	algebra	algebra	NOUN
ejpam-4675	13	48	[	[	X
ejpam-4675	13	49	2	2	NUM
ejpam-4675	13	50	]	]	PUNCT
ejpam-4675	13	51	.	.	PUNCT
ejpam-4675	14	1	∗corresponding	∗corresponde	VERB
ejpam-4675	14	2	author	author	NOUN
ejpam-4675	14	3	.	.	PUNCT
ejpam-4675	15	1	doi	doi	NOUN
ejpam-4675	15	2	:	:	PUNCT
ejpam-4675	15	3	https://doi.org/10.29020/nybg.ejpam.v16i1.4675	https://doi.org/10.29020/nybg.ejpam.v16i1.4675	ADP
ejpam-4675	15	4	email	email	NOUN
ejpam-4675	15	5	addresses	address	NOUN
ejpam-4675	15	6	:	:	PUNCT
ejpam-4675	15	7	15101364@usc.edu.ph	15101364@usc.edu.ph	NUM
ejpam-4675	15	8	(	(	PUNCT
ejpam-4675	15	9	j.e	j.e	PROPN
ejpam-4675	15	10	.	.	PROPN
ejpam-4675	15	11	bolima	bolima	PROPN
ejpam-4675	15	12	)	)	PUNCT
ejpam-4675	15	13	,	,	PUNCT
ejpam-4675	15	14	kebelleza@usc.edu.ph	kebelleza@usc.edu.ph	PROPN
ejpam-4675	15	15	(	(	PUNCT
ejpam-4675	15	16	k.b	k.b	PROPN
ejpam-4675	15	17	.	.	PROPN
ejpam-4675	15	18	fuentes	fuentes	PROPN
ejpam-4675	15	19	)	)	PUNCT
ejpam-4675	15	20	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4675	16	1	577	577	NUM
ejpam-4675	16	2	©	©	PROPN
ejpam-4675	16	3	2023	2023	NUM
ejpam-4675	16	4	ejpam	ejpam	NOUN
ejpam-4675	16	5	all	all	DET
ejpam-4675	16	6	rights	right	NOUN
ejpam-4675	16	7	reserved	reserve	VERB
ejpam-4675	16	8	.	.	PUNCT
ejpam-4675	17	1	j.e	j.e	PROPN
ejpam-4675	17	2	.	.	PROPN
ejpam-4675	17	3	bolima	bolima	PROPN
ejpam-4675	17	4	,	,	PUNCT
ejpam-4675	17	5	k.b	k.b	PROPN
ejpam-4675	17	6	.	.	PUNCT
ejpam-4675	17	7	fuentes	fuentes	PROPN
ejpam-4675	17	8	/	/	SYM
ejpam-4675	17	9	eur	eur	PROPN
ejpam-4675	17	10	.	.	PUNCT
ejpam-4675	18	1	j.	j.	PROPN
ejpam-4675	18	2	pure	pure	PROPN
ejpam-4675	18	3	appl	appl	PROPN
ejpam-4675	18	4	.	.	PROPN
ejpam-4675	18	5	math	math	PROPN
ejpam-4675	18	6	,	,	PUNCT
ejpam-4675	18	7	16	16	NUM
ejpam-4675	18	8	(	(	PUNCT
ejpam-4675	18	9	1	1	NUM
ejpam-4675	18	10	)	)	PUNCT
ejpam-4675	18	11	(	(	PUNCT
ejpam-4675	18	12	2023	2023	NUM
ejpam-4675	18	13	)	)	PUNCT
ejpam-4675	18	14	,	,	PUNCT
ejpam-4675	18	15	577	577	NUM
ejpam-4675	18	16	-	-	SYM
ejpam-4675	18	17	586	586	NUM
ejpam-4675	18	18	578	578	NUM
ejpam-4675	18	19	2	2	NUM
ejpam-4675	18	20	.	.	PUNCT
ejpam-4675	18	21	preliminaries	preliminary	NOUN
ejpam-4675	18	22	definition	definition	NOUN
ejpam-4675	18	23	1	1	NUM
ejpam-4675	18	24	.	.	PUNCT
ejpam-4675	19	1	[	[	X
ejpam-4675	19	2	2	2	X
ejpam-4675	19	3	]	]	PUNCT
ejpam-4675	19	4	a	a	DET
ejpam-4675	19	5	dual	dual	ADJ
ejpam-4675	19	6	b	b	NOUN
ejpam-4675	19	7	-	-	PUNCT
ejpam-4675	19	8	algebra	algebra	NOUN
ejpam-4675	19	9	,	,	PUNCT
ejpam-4675	19	10	(	(	PUNCT
ejpam-4675	19	11	or	or	CCONJ
ejpam-4675	19	12	db	db	NOUN
ejpam-4675	19	13	-	-	PUNCT
ejpam-4675	19	14	algebra	algebra	NOUN
ejpam-4675	19	15	)	)	PUNCT
ejpam-4675	19	16	,	,	PUNCT
ejpam-4675	19	17	x	x	X
ejpam-4675	19	18	is	be	AUX
ejpam-4675	19	19	a	a	DET
ejpam-4675	19	20	triple	triple	ADJ
ejpam-4675	19	21	(	(	PUNCT
ejpam-4675	19	22	x	x	NOUN
ejpam-4675	19	23	,	,	PUNCT
ejpam-4675	19	24	·	·	PUNCT
ejpam-4675	19	25	,	,	PUNCT
ejpam-4675	19	26	1	1	NUM
ejpam-4675	19	27	)	)	PUNCT
ejpam-4675	19	28	where	where	SCONJ
ejpam-4675	19	29	x	x	PRON
ejpam-4675	19	30	is	be	AUX
ejpam-4675	19	31	a	a	DET
ejpam-4675	19	32	non	non	ADJ
ejpam-4675	19	33	-	-	ADJ
ejpam-4675	19	34	empty	empty	ADJ
ejpam-4675	19	35	set	set	NOUN
ejpam-4675	19	36	with	with	ADP
ejpam-4675	19	37	a	a	DET
ejpam-4675	19	38	binary	binary	ADJ
ejpam-4675	19	39	operation	operation	NOUN
ejpam-4675	19	40	“	"	PUNCT
ejpam-4675	19	41	·	·	PUNCT
ejpam-4675	19	42	”	"	PUNCT
ejpam-4675	19	43	and	and	CCONJ
ejpam-4675	19	44	a	a	DET
ejpam-4675	19	45	constant	constant	ADJ
ejpam-4675	19	46	1	1	NUM
ejpam-4675	19	47	satisfying	satisfy	VERB
ejpam-4675	19	48	the	the	DET
ejpam-4675	19	49	following	follow	VERB
ejpam-4675	19	50	axioms	axiom	NOUN
ejpam-4675	19	51	for	for	ADP
ejpam-4675	19	52	all	all	DET
ejpam-4675	19	53	x	x	NOUN
ejpam-4675	19	54	,	,	PUNCT
ejpam-4675	19	55	y	y	PROPN
ejpam-4675	19	56	,	,	PUNCT
ejpam-4675	19	57	z	z	VERB
ejpam-4675	19	58	in	in	ADP
ejpam-4675	19	59	x	x	NOUN
ejpam-4675	19	60	:	:	PUNCT
ejpam-4675	19	61	(	(	PUNCT
ejpam-4675	19	62	db1	db1	NOUN
ejpam-4675	19	63	)	)	PUNCT
ejpam-4675	19	64	x	x	X
ejpam-4675	19	65	·	·	PUNCT
ejpam-4675	19	66	x	x	PUNCT
ejpam-4675	19	67	=	=	SYM
ejpam-4675	19	68	1	1	NUM
ejpam-4675	19	69	;	;	PUNCT
ejpam-4675	19	70	(	(	PUNCT
ejpam-4675	19	71	db2	db2	NOUN
ejpam-4675	19	72	)	)	PUNCT
ejpam-4675	19	73	1	1	NUM
ejpam-4675	19	74	·	·	PUNCT
ejpam-4675	19	75	x	x	SYM
ejpam-4675	20	1	=	=	PUNCT
ejpam-4675	20	2	x	x	X
ejpam-4675	20	3	;	;	PUNCT
ejpam-4675	20	4	(	(	PUNCT
ejpam-4675	20	5	db3	db3	PROPN
ejpam-4675	20	6	)	)	PUNCT
ejpam-4675	20	7	x	x	X
ejpam-4675	20	8	·	·	PUNCT
ejpam-4675	20	9	(	(	PUNCT
ejpam-4675	20	10	y	y	PROPN
ejpam-4675	20	11	·	·	PUNCT
ejpam-4675	20	12	z	z	X
ejpam-4675	20	13	)	)	PUNCT
ejpam-4675	20	14	=	=	SYM
ejpam-4675	20	15	(	(	PUNCT
ejpam-4675	20	16	(	(	PUNCT
ejpam-4675	20	17	y	y	PROPN
ejpam-4675	20	18	·	·	PUNCT
ejpam-4675	20	19	1	1	NUM
ejpam-4675	20	20	)	)	PUNCT
ejpam-4675	20	21	·	·	PUNCT
ejpam-4675	21	1	x	x	X
ejpam-4675	21	2	)	)	PUNCT
ejpam-4675	21	3	·	·	PUNCT
ejpam-4675	21	4	z.	z.	PROPN
ejpam-4675	21	5	example	example	NOUN
ejpam-4675	22	1	1	1	NUM
ejpam-4675	22	2	.	.	PUNCT
ejpam-4675	23	1	[	[	X
ejpam-4675	23	2	1	1	X
ejpam-4675	23	3	]	]	PUNCT
ejpam-4675	23	4	let	let	VERB
ejpam-4675	23	5	x	x	PUNCT
ejpam-4675	23	6	=	=	PRON
ejpam-4675	23	7	{	{	PUNCT
ejpam-4675	23	8	1	1	NUM
ejpam-4675	23	9	,	,	PUNCT
ejpam-4675	23	10	a	a	DET
ejpam-4675	23	11	,	,	PUNCT
ejpam-4675	23	12	b	b	NOUN
ejpam-4675	23	13	,	,	PUNCT
ejpam-4675	23	14	c	c	NOUN
ejpam-4675	23	15	}	}	PUNCT
ejpam-4675	23	16	with	with	ADP
ejpam-4675	23	17	the	the	DET
ejpam-4675	23	18	binary	binary	PROPN
ejpam-4675	23	19	operation	operation	NOUN
ejpam-4675	23	20	·	·	PUNCT
ejpam-4675	23	21	as	as	SCONJ
ejpam-4675	23	22	defined	define	VERB
ejpam-4675	23	23	in	in	ADP
ejpam-4675	23	24	the	the	DET
ejpam-4675	23	25	table	table	NOUN
ejpam-4675	23	26	:	:	PUNCT
ejpam-4675	23	27	·	·	PUNCT
ejpam-4675	23	28	1	1	X
ejpam-4675	23	29	a	a	DET
ejpam-4675	23	30	b	b	NOUN
ejpam-4675	23	31	c	c	NOUN
ejpam-4675	23	32	1	1	NUM
ejpam-4675	23	33	1	1	NUM
ejpam-4675	23	34	a	a	DET
ejpam-4675	23	35	b	b	NOUN
ejpam-4675	23	36	c	c	ADP
ejpam-4675	23	37	a	a	DET
ejpam-4675	23	38	a	a	DET
ejpam-4675	23	39	1	1	NUM
ejpam-4675	23	40	c	c	NOUN
ejpam-4675	23	41	b	b	PROPN
ejpam-4675	23	42	b	b	PROPN
ejpam-4675	23	43	b	b	PROPN
ejpam-4675	23	44	c	c	PROPN
ejpam-4675	23	45	1	1	NUM
ejpam-4675	23	46	a	a	DET
ejpam-4675	23	47	c	c	NOUN
ejpam-4675	23	48	c	c	NOUN
ejpam-4675	23	49	b	b	PROPN
ejpam-4675	23	50	a	a	DET
ejpam-4675	23	51	1	1	NUM
ejpam-4675	23	52	then	then	ADV
ejpam-4675	23	53	(	(	PUNCT
ejpam-4675	23	54	x	x	X
ejpam-4675	23	55	,	,	PUNCT
ejpam-4675	23	56	·	·	PUNCT
ejpam-4675	23	57	,	,	PUNCT
ejpam-4675	23	58	1	1	NUM
ejpam-4675	23	59	)	)	PUNCT
ejpam-4675	23	60	is	be	AUX
ejpam-4675	23	61	a	a	DET
ejpam-4675	23	62	db	db	NOUN
ejpam-4675	23	63	-	-	PUNCT
ejpam-4675	23	64	algebra	algebra	NOUN
ejpam-4675	23	65	.	.	PUNCT
ejpam-4675	24	1	lemma	lemma	PROPN
ejpam-4675	24	2	1	1	NUM
ejpam-4675	24	3	.	.	PUNCT
ejpam-4675	25	1	[	[	X
ejpam-4675	25	2	2	2	NUM
ejpam-4675	25	3	]	]	X
ejpam-4675	25	4	let	let	VERB
ejpam-4675	25	5	(	(	PUNCT
ejpam-4675	25	6	x	x	NOUN
ejpam-4675	25	7	,	,	PUNCT
ejpam-4675	25	8	·	·	PUNCT
ejpam-4675	25	9	,	,	PUNCT
ejpam-4675	25	10	1	1	X
ejpam-4675	25	11	)	)	PUNCT
ejpam-4675	25	12	be	be	AUX
ejpam-4675	25	13	a	a	DET
ejpam-4675	25	14	db	db	NOUN
ejpam-4675	25	15	-	-	PUNCT
ejpam-4675	25	16	algebra	algebra	NOUN
ejpam-4675	25	17	,	,	PUNCT
ejpam-4675	25	18	then	then	ADV
ejpam-4675	25	19	for	for	ADP
ejpam-4675	25	20	any	any	DET
ejpam-4675	25	21	x	x	NOUN
ejpam-4675	25	22	,	,	PUNCT
ejpam-4675	25	23	y	y	PROPN
ejpam-4675	25	24	∈	∈	PROPN
ejpam-4675	25	25	x	x	X
ejpam-4675	25	26	,	,	PUNCT
ejpam-4675	25	27	x	x	X
ejpam-4675	25	28	·	·	PUNCT
ejpam-4675	25	29	y	y	SYM
ejpam-4675	25	30	=	=	SYM
ejpam-4675	25	31	1	1	NUM
ejpam-4675	25	32	implies	imply	VERB
ejpam-4675	25	33	x	x	PUNCT
ejpam-4675	25	34	=	=	SYM
ejpam-4675	25	35	y	y	PROPN
ejpam-4675	25	36	definition	definition	NOUN
ejpam-4675	25	37	2	2	NUM
ejpam-4675	25	38	.	.	PUNCT
ejpam-4675	26	1	[	[	X
ejpam-4675	26	2	1	1	X
ejpam-4675	26	3	]	]	PUNCT
ejpam-4675	26	4	let	let	VERB
ejpam-4675	26	5	x	x	PRON
ejpam-4675	26	6	be	be	AUX
ejpam-4675	26	7	a	a	DET
ejpam-4675	26	8	db	db	NOUN
ejpam-4675	26	9	-	-	PUNCT
ejpam-4675	26	10	algebra	algebra	NOUN
ejpam-4675	26	11	and	and	CCONJ
ejpam-4675	26	12	s	s	VERB
ejpam-4675	26	13	a	a	DET
ejpam-4675	26	14	nonempty	nonempty	ADJ
ejpam-4675	26	15	subset	subset	NOUN
ejpam-4675	26	16	of	of	ADP
ejpam-4675	26	17	x.	x.	NOUN
ejpam-4675	26	18	then	then	ADV
ejpam-4675	26	19	s	s	VERB
ejpam-4675	26	20	is	be	AUX
ejpam-4675	26	21	called	call	VERB
ejpam-4675	26	22	a	a	DET
ejpam-4675	26	23	dual	dual	ADJ
ejpam-4675	26	24	b	b	NOUN
ejpam-4675	26	25	-	-	PUNCT
ejpam-4675	26	26	subalgebra	subalgebra	NOUN
ejpam-4675	26	27	,	,	PUNCT
ejpam-4675	26	28	(	(	PUNCT
ejpam-4675	26	29	or	or	CCONJ
ejpam-4675	26	30	db	db	NOUN
ejpam-4675	26	31	-	-	PUNCT
ejpam-4675	26	32	subalgebra	subalgebra	NOUN
ejpam-4675	26	33	)	)	PUNCT
ejpam-4675	26	34	,	,	PUNCT
ejpam-4675	26	35	of	of	ADP
ejpam-4675	26	36	x	x	PRON
ejpam-4675	26	37	if	if	SCONJ
ejpam-4675	26	38	s	s	PRON
ejpam-4675	26	39	itself	itself	PRON
ejpam-4675	26	40	is	be	AUX
ejpam-4675	26	41	a	a	DET
ejpam-4675	26	42	db	db	NOUN
ejpam-4675	26	43	-	-	PUNCT
ejpam-4675	26	44	algebra	algebra	NOUN
ejpam-4675	26	45	with	with	ADP
ejpam-4675	26	46	binary	binary	ADJ
ejpam-4675	26	47	operation	operation	NOUN
ejpam-4675	26	48	of	of	ADP
ejpam-4675	26	49	x	x	PUNCT
ejpam-4675	26	50	on	on	ADP
ejpam-4675	26	51	s.	s.	PROPN
ejpam-4675	26	52	remark	remark	PROPN
ejpam-4675	26	53	1	1	NUM
ejpam-4675	26	54	.	.	PUNCT
ejpam-4675	27	1	[	[	X
ejpam-4675	27	2	1	1	X
ejpam-4675	27	3	]	]	X
ejpam-4675	27	4	if	if	SCONJ
ejpam-4675	27	5	s	s	PROPN
ejpam-4675	27	6	is	be	AUX
ejpam-4675	27	7	a	a	DET
ejpam-4675	27	8	db	db	NOUN
ejpam-4675	27	9	-	-	PUNCT
ejpam-4675	27	10	subalgebra	subalgebra	NOUN
ejpam-4675	27	11	of	of	ADP
ejpam-4675	27	12	x	x	PRON
ejpam-4675	27	13	,	,	PUNCT
ejpam-4675	27	14	then	then	ADV
ejpam-4675	27	15	1	1	NUM
ejpam-4675	27	16	∈	∈	PROPN
ejpam-4675	27	17	s.	s.	PROPN
ejpam-4675	27	18	theorem	theorem	VERB
ejpam-4675	27	19	1	1	NUM
ejpam-4675	27	20	.	.	PUNCT
ejpam-4675	28	1	[	[	X
ejpam-4675	28	2	1	1	X
ejpam-4675	28	3	]	]	X
ejpam-4675	28	4	s	s	VERB
ejpam-4675	28	5	is	be	AUX
ejpam-4675	28	6	a	a	DET
ejpam-4675	28	7	db	db	NOUN
ejpam-4675	28	8	-	-	PUNCT
ejpam-4675	28	9	subalgebra	subalgebra	NOUN
ejpam-4675	28	10	if	if	SCONJ
ejpam-4675	28	11	and	and	CCONJ
ejpam-4675	28	12	only	only	ADV
ejpam-4675	28	13	if	if	SCONJ
ejpam-4675	28	14	for	for	ADP
ejpam-4675	28	15	any	any	DET
ejpam-4675	28	16	x	x	NOUN
ejpam-4675	28	17	,	,	PUNCT
ejpam-4675	28	18	y	y	PROPN
ejpam-4675	28	19	∈	∈	PROPN
ejpam-4675	28	20	s	s	PROPN
ejpam-4675	28	21	,	,	PUNCT
ejpam-4675	28	22	x	x	PUNCT
ejpam-4675	28	23	·	·	PUNCT
ejpam-4675	28	24	y	y	PROPN
ejpam-4675	28	25	∈	∈	PROPN
ejpam-4675	28	26	s.	s.	PROPN
ejpam-4675	28	27	example	example	NOUN
ejpam-4675	28	28	2	2	X
ejpam-4675	28	29	.	.	X
ejpam-4675	28	30	consider	consider	VERB
ejpam-4675	28	31	the	the	DET
ejpam-4675	28	32	db	db	NOUN
ejpam-4675	28	33	-	-	PUNCT
ejpam-4675	28	34	algebra	algebra	NOUN
ejpam-4675	28	35	x	x	PUNCT
ejpam-4675	28	36	=	=	SYM
ejpam-4675	28	37	{	{	PUNCT
ejpam-4675	28	38	1	1	NUM
ejpam-4675	28	39	,	,	PUNCT
ejpam-4675	28	40	a	a	DET
ejpam-4675	28	41	,	,	PUNCT
ejpam-4675	28	42	b	b	NOUN
ejpam-4675	28	43	,	,	PUNCT
ejpam-4675	28	44	c	c	NOUN
ejpam-4675	28	45	}	}	PUNCT
ejpam-4675	28	46	with	with	ADP
ejpam-4675	28	47	the	the	DET
ejpam-4675	28	48	binary	binary	PROPN
ejpam-4675	28	49	operation	operation	NOUN
ejpam-4675	28	50	·	·	PUNCT
ejpam-4675	28	51	as	as	SCONJ
ejpam-4675	28	52	defined	define	VERB
ejpam-4675	28	53	in	in	ADP
ejpam-4675	28	54	the	the	DET
ejpam-4675	28	55	table	table	NOUN
ejpam-4675	28	56	:	:	PUNCT
ejpam-4675	28	57	·	·	PUNCT
ejpam-4675	28	58	1	1	X
ejpam-4675	28	59	a	a	DET
ejpam-4675	28	60	b	b	NOUN
ejpam-4675	28	61	c	c	NOUN
ejpam-4675	28	62	1	1	NUM
ejpam-4675	28	63	1	1	NUM
ejpam-4675	28	64	a	a	DET
ejpam-4675	28	65	b	b	NOUN
ejpam-4675	28	66	c	c	ADP
ejpam-4675	28	67	a	a	DET
ejpam-4675	28	68	a	a	DET
ejpam-4675	28	69	1	1	NUM
ejpam-4675	28	70	c	c	NOUN
ejpam-4675	28	71	b	b	PROPN
ejpam-4675	28	72	b	b	PROPN
ejpam-4675	28	73	b	b	PROPN
ejpam-4675	28	74	c	c	PROPN
ejpam-4675	28	75	1	1	NUM
ejpam-4675	28	76	a	a	DET
ejpam-4675	28	77	c	c	NOUN
ejpam-4675	28	78	c	c	NOUN
ejpam-4675	28	79	b	b	PROPN
ejpam-4675	28	80	a	a	DET
ejpam-4675	28	81	1	1	NUM
ejpam-4675	28	82	by	by	ADP
ejpam-4675	28	83	remark	remark	NOUN
ejpam-4675	28	84	2.6	2.6	NUM
ejpam-4675	28	85	,	,	PUNCT
ejpam-4675	28	86	a	a	DET
ejpam-4675	28	87	=	=	X
ejpam-4675	28	88	(	(	PUNCT
ejpam-4675	28	89	1	1	NUM
ejpam-4675	28	90	,	,	PUNCT
ejpam-4675	28	91	a	a	PRON
ejpam-4675	28	92	)	)	PUNCT
ejpam-4675	28	93	is	be	AUX
ejpam-4675	28	94	a	a	DET
ejpam-4675	28	95	db	db	NOUN
ejpam-4675	28	96	-	-	PUNCT
ejpam-4675	28	97	subalgebra	subalgebra	NOUN
ejpam-4675	28	98	of	of	ADP
ejpam-4675	28	99	x	x	SYM
ejpam-4675	28	100	but	but	CCONJ
ejpam-4675	28	101	b	b	X
ejpam-4675	28	102	=	=	SYM
ejpam-4675	28	103	(	(	PUNCT
ejpam-4675	28	104	1	1	NUM
ejpam-4675	28	105	,	,	PUNCT
ejpam-4675	28	106	a	a	DET
ejpam-4675	28	107	,	,	PUNCT
ejpam-4675	28	108	c	c	NOUN
ejpam-4675	28	109	)	)	PUNCT
ejpam-4675	28	110	is	be	AUX
ejpam-4675	28	111	not	not	PART
ejpam-4675	28	112	a	a	DET
ejpam-4675	28	113	db	db	NOUN
ejpam-4675	28	114	-	-	PUNCT
ejpam-4675	28	115	subalgebra	subalgebra	NOUN
ejpam-4675	28	116	of	of	ADP
ejpam-4675	28	117	x	x	PRON
ejpam-4675	28	118	since	since	SCONJ
ejpam-4675	28	119	a	a	DET
ejpam-4675	28	120	·	·	PUNCT
ejpam-4675	28	121	c	c	X
ejpam-4675	28	122	=	=	SYM
ejpam-4675	28	123	b	b	PROPN
ejpam-4675	28	124	̸∈	̸∈	PROPN
ejpam-4675	28	125	b.	b.	PROPN
ejpam-4675	28	126	definition	definition	NOUN
ejpam-4675	28	127	3	3	NUM
ejpam-4675	28	128	.	.	PUNCT
ejpam-4675	29	1	[	[	X
ejpam-4675	29	2	1	1	X
ejpam-4675	29	3	]	]	PUNCT
ejpam-4675	29	4	let	let	VERB
ejpam-4675	29	5	x	x	PRON
ejpam-4675	29	6	be	be	AUX
ejpam-4675	29	7	a	a	DET
ejpam-4675	29	8	db	db	NOUN
ejpam-4675	29	9	-	-	PUNCT
ejpam-4675	29	10	algebra	algebra	NOUN
ejpam-4675	29	11	.	.	PUNCT
ejpam-4675	30	1	a	a	DET
ejpam-4675	30	2	subset	subset	NOUN
ejpam-4675	30	3	f	f	NOUN
ejpam-4675	30	4	of	of	ADP
ejpam-4675	30	5	x	x	PROPN
ejpam-4675	30	6	is	be	AUX
ejpam-4675	30	7	called	call	VERB
ejpam-4675	30	8	a	a	DET
ejpam-4675	30	9	dual	dual	ADJ
ejpam-4675	30	10	b	b	NOUN
ejpam-4675	30	11	-	-	NOUN
ejpam-4675	30	12	filter	filter	NOUN
ejpam-4675	30	13	,	,	PUNCT
ejpam-4675	30	14	(	(	PUNCT
ejpam-4675	30	15	or	or	CCONJ
ejpam-4675	30	16	db	db	NOUN
ejpam-4675	30	17	-	-	PUNCT
ejpam-4675	30	18	filter	filter	NOUN
ejpam-4675	30	19	)	)	PUNCT
ejpam-4675	30	20	,	,	PUNCT
ejpam-4675	30	21	if	if	SCONJ
ejpam-4675	30	22	it	it	PRON
ejpam-4675	30	23	satisfies	satisfy	VERB
ejpam-4675	30	24	the	the	DET
ejpam-4675	30	25	following	following	NOUN
ejpam-4675	30	26	:	:	PUNCT
ejpam-4675	30	27	(	(	PUNCT
ejpam-4675	30	28	i.	i.	NOUN
ejpam-4675	30	29	)	)	PUNCT
ejpam-4675	30	30	1	1	NUM
ejpam-4675	30	31	∈	∈	PROPN
ejpam-4675	30	32	f	f	NOUN
ejpam-4675	30	33	;	;	PUNCT
ejpam-4675	30	34	(	(	PUNCT
ejpam-4675	30	35	ii	ii	NOUN
ejpam-4675	30	36	.	.	PUNCT
ejpam-4675	30	37	)	)	PUNCT
ejpam-4675	30	38	for	for	ADP
ejpam-4675	30	39	each	each	DET
ejpam-4675	30	40	x	x	NOUN
ejpam-4675	30	41	,	,	PUNCT
ejpam-4675	30	42	y	y	PROPN
ejpam-4675	30	43	∈	∈	PROPN
ejpam-4675	30	44	x	x	X
ejpam-4675	30	45	,	,	PUNCT
ejpam-4675	30	46	x	x	X
ejpam-4675	30	47	·	·	PUNCT
ejpam-4675	30	48	y	y	PROPN
ejpam-4675	30	49	∈	∈	PROPN
ejpam-4675	30	50	f	f	PROPN
ejpam-4675	30	51	and	and	CCONJ
ejpam-4675	30	52	x	x	PROPN
ejpam-4675	30	53	∈	∈	NOUN
ejpam-4675	31	1	f	f	X
ejpam-4675	31	2	imply	imply	VERB
ejpam-4675	31	3	y	y	PROPN
ejpam-4675	31	4	∈	∈	PROPN
ejpam-4675	32	1	f	f	X
ejpam-4675	32	2	.	.	PUNCT
ejpam-4675	33	1	j.e	j.e	PROPN
ejpam-4675	33	2	.	.	PROPN
ejpam-4675	33	3	bolima	bolima	PROPN
ejpam-4675	33	4	,	,	PUNCT
ejpam-4675	33	5	k.b	k.b	PROPN
ejpam-4675	33	6	.	.	PUNCT
ejpam-4675	33	7	fuentes	fuentes	PROPN
ejpam-4675	33	8	/	/	SYM
ejpam-4675	33	9	eur	eur	PROPN
ejpam-4675	33	10	.	.	PUNCT
ejpam-4675	34	1	j.	j.	PROPN
ejpam-4675	34	2	pure	pure	PROPN
ejpam-4675	34	3	appl	appl	PROPN
ejpam-4675	34	4	.	.	PROPN
ejpam-4675	34	5	math	math	PROPN
ejpam-4675	34	6	,	,	PUNCT
ejpam-4675	34	7	16	16	NUM
ejpam-4675	34	8	(	(	PUNCT
ejpam-4675	34	9	1	1	NUM
ejpam-4675	34	10	)	)	PUNCT
ejpam-4675	34	11	(	(	PUNCT
ejpam-4675	34	12	2023	2023	NUM
ejpam-4675	34	13	)	)	PUNCT
ejpam-4675	34	14	,	,	PUNCT
ejpam-4675	34	15	577	577	NUM
ejpam-4675	34	16	-	-	SYM
ejpam-4675	34	17	586	586	NUM
ejpam-4675	34	18	579	579	NUM
ejpam-4675	34	19	proposition	proposition	NOUN
ejpam-4675	34	20	1	1	NUM
ejpam-4675	34	21	.	.	PUNCT
ejpam-4675	35	1	[	[	X
ejpam-4675	35	2	1	1	X
ejpam-4675	35	3	]	]	X
ejpam-4675	35	4	if	if	SCONJ
ejpam-4675	35	5	f	f	PROPN
ejpam-4675	35	6	is	be	AUX
ejpam-4675	35	7	a	a	DET
ejpam-4675	35	8	db	db	NOUN
ejpam-4675	35	9	-	-	PUNCT
ejpam-4675	35	10	filter	filter	NOUN
ejpam-4675	35	11	of	of	ADP
ejpam-4675	35	12	a	a	DET
ejpam-4675	35	13	db	db	NOUN
ejpam-4675	35	14	-	-	PUNCT
ejpam-4675	35	15	algebra	algebra	NOUN
ejpam-4675	35	16	x	x	NOUN
ejpam-4675	35	17	,	,	PUNCT
ejpam-4675	35	18	then	then	ADV
ejpam-4675	35	19	f	f	PROPN
ejpam-4675	35	20	is	be	AUX
ejpam-4675	35	21	a	a	DET
ejpam-4675	35	22	db	db	NOUN
ejpam-4675	35	23	-	-	PUNCT
ejpam-4675	35	24	subalgebra	subalgebra	NOUN
ejpam-4675	35	25	of	of	ADP
ejpam-4675	35	26	x.	x.	NOUN
ejpam-4675	35	27	definition	definition	NOUN
ejpam-4675	35	28	4	4	NUM
ejpam-4675	35	29	.	.	PUNCT
ejpam-4675	36	1	[	[	X
ejpam-4675	36	2	1	1	X
ejpam-4675	36	3	]	]	PUNCT
ejpam-4675	36	4	let	let	VERB
ejpam-4675	36	5	x	x	PRON
ejpam-4675	36	6	be	be	AUX
ejpam-4675	36	7	a	a	DET
ejpam-4675	36	8	db	db	NOUN
ejpam-4675	36	9	-	-	PUNCT
ejpam-4675	36	10	algebra	algebra	NOUN
ejpam-4675	36	11	and	and	CCONJ
ejpam-4675	36	12	n	n	DET
ejpam-4675	36	13	a	a	DET
ejpam-4675	36	14	nonempty	nonempty	NOUN
ejpam-4675	36	15	subset	subset	NOUN
ejpam-4675	36	16	of	of	ADP
ejpam-4675	36	17	x.	x.	NOUN
ejpam-4675	36	18	then	then	ADV
ejpam-4675	36	19	n	n	PRON
ejpam-4675	36	20	is	be	AUX
ejpam-4675	36	21	a	a	DET
ejpam-4675	36	22	normal	normal	ADJ
ejpam-4675	36	23	subset	subset	NOUN
ejpam-4675	36	24	of	of	ADP
ejpam-4675	36	25	x	x	PRON
ejpam-4675	36	26	if	if	SCONJ
ejpam-4675	36	27	for	for	ADP
ejpam-4675	36	28	any	any	DET
ejpam-4675	36	29	a	a	DET
ejpam-4675	36	30	·	·	SYM
ejpam-4675	36	31	b	b	NOUN
ejpam-4675	36	32	,	,	PUNCT
ejpam-4675	36	33	x	x	X
ejpam-4675	36	34	·	·	PUNCT
ejpam-4675	36	35	y	y	PROPN
ejpam-4675	36	36	∈	∈	PROPN
ejpam-4675	36	37	n	n	CCONJ
ejpam-4675	36	38	,	,	PUNCT
ejpam-4675	36	39	(	(	PUNCT
ejpam-4675	36	40	a	a	DET
ejpam-4675	36	41	·	·	PUNCT
ejpam-4675	36	42	x	x	X
ejpam-4675	36	43	)	)	PUNCT
ejpam-4675	36	44	·	·	PUNCT
ejpam-4675	36	45	(	(	PUNCT
ejpam-4675	36	46	b	b	X
ejpam-4675	36	47	·	·	PUNCT
ejpam-4675	36	48	y	y	X
ejpam-4675	36	49	)	)	PUNCT
ejpam-4675	36	50	∈	∈	PROPN
ejpam-4675	36	51	n	n	NOUN
ejpam-4675	36	52	.	.	PUNCT
ejpam-4675	37	1	a	a	DET
ejpam-4675	37	2	db	db	ADJ
ejpam-4675	37	3	-	-	PUNCT
ejpam-4675	37	4	filter	filter	NOUN
ejpam-4675	37	5	f	f	NOUN
ejpam-4675	37	6	of	of	ADP
ejpam-4675	37	7	a	a	DET
ejpam-4675	37	8	db	db	NOUN
ejpam-4675	37	9	-	-	PUNCT
ejpam-4675	37	10	algebra	algebra	NOUN
ejpam-4675	37	11	x	x	PUNCT
ejpam-4675	37	12	is	be	AUX
ejpam-4675	37	13	called	call	VERB
ejpam-4675	37	14	a	a	DET
ejpam-4675	37	15	normal	normal	ADJ
ejpam-4675	37	16	db	db	NOUN
ejpam-4675	37	17	-	-	PUNCT
ejpam-4675	37	18	filter	filter	NOUN
ejpam-4675	37	19	if	if	SCONJ
ejpam-4675	37	20	f	f	PROPN
ejpam-4675	37	21	is	be	AUX
ejpam-4675	37	22	a	a	DET
ejpam-4675	37	23	normal	normal	ADJ
ejpam-4675	37	24	subset	subset	NOUN
ejpam-4675	37	25	of	of	ADP
ejpam-4675	37	26	x.	x.	PROPN
ejpam-4675	37	27	a	a	DET
ejpam-4675	37	28	db	db	ADJ
ejpam-4675	37	29	-	-	PUNCT
ejpam-4675	37	30	subalgebra	subalgebra	NOUN
ejpam-4675	37	31	s	s	NOUN
ejpam-4675	37	32	of	of	ADP
ejpam-4675	37	33	a	a	DET
ejpam-4675	37	34	db	db	NOUN
ejpam-4675	37	35	-	-	PUNCT
ejpam-4675	37	36	algebra	algebra	NOUN
ejpam-4675	37	37	x	x	PUNCT
ejpam-4675	37	38	is	be	AUX
ejpam-4675	37	39	called	call	VERB
ejpam-4675	37	40	a	a	DET
ejpam-4675	37	41	normal	normal	ADJ
ejpam-4675	37	42	db	db	NOUN
ejpam-4675	37	43	-	-	PUNCT
ejpam-4675	37	44	subalgebra	subalgebra	NOUN
ejpam-4675	37	45	if	if	SCONJ
ejpam-4675	37	46	s	s	VERB
ejpam-4675	37	47	is	be	AUX
ejpam-4675	37	48	a	a	DET
ejpam-4675	37	49	normal	normal	ADJ
ejpam-4675	37	50	subset	subset	NOUN
ejpam-4675	37	51	of	of	ADP
ejpam-4675	37	52	x.	x.	PROPN
ejpam-4675	37	53	example	example	NOUN
ejpam-4675	38	1	3	3	NUM
ejpam-4675	38	2	.	.	PUNCT
ejpam-4675	39	1	[	[	X
ejpam-4675	39	2	1	1	X
ejpam-4675	39	3	]	]	PUNCT
ejpam-4675	39	4	let	let	VERB
ejpam-4675	39	5	x	x	PUNCT
ejpam-4675	39	6	=	=	PRON
ejpam-4675	39	7	{	{	PUNCT
ejpam-4675	39	8	1	1	NUM
ejpam-4675	39	9	,	,	PUNCT
ejpam-4675	39	10	a	a	DET
ejpam-4675	39	11	,	,	PUNCT
ejpam-4675	39	12	b	b	NOUN
ejpam-4675	39	13	,	,	PUNCT
ejpam-4675	39	14	c	c	NOUN
ejpam-4675	39	15	,	,	PUNCT
ejpam-4675	39	16	d	d	NOUN
ejpam-4675	39	17	,	,	PUNCT
ejpam-4675	39	18	e	e	NOUN
ejpam-4675	39	19	}	}	PUNCT
ejpam-4675	39	20	with	with	ADP
ejpam-4675	39	21	the	the	DET
ejpam-4675	39	22	binary	binary	PROPN
ejpam-4675	39	23	operation	operation	NOUN
ejpam-4675	39	24	·	·	PUNCT
ejpam-4675	39	25	as	as	SCONJ
ejpam-4675	39	26	defined	define	VERB
ejpam-4675	39	27	in	in	ADP
ejpam-4675	39	28	the	the	DET
ejpam-4675	39	29	table	table	NOUN
ejpam-4675	39	30	:	:	PUNCT
ejpam-4675	39	31	·	·	PUNCT
ejpam-4675	39	32	1	1	X
ejpam-4675	39	33	a	a	DET
ejpam-4675	39	34	b	b	NOUN
ejpam-4675	39	35	c	c	NOUN
ejpam-4675	39	36	d	d	X
ejpam-4675	39	37	e	e	PROPN
ejpam-4675	39	38	1	1	NUM
ejpam-4675	39	39	1	1	NUM
ejpam-4675	39	40	a	a	DET
ejpam-4675	39	41	b	b	NOUN
ejpam-4675	39	42	c	c	NOUN
ejpam-4675	39	43	d	d	PROPN
ejpam-4675	39	44	e	e	PROPN
ejpam-4675	39	45	a	a	PRON
ejpam-4675	39	46	b	b	PROPN
ejpam-4675	39	47	1	1	NUM
ejpam-4675	39	48	a	a	PRON
ejpam-4675	39	49	d	d	X
ejpam-4675	39	50	e	e	NOUN
ejpam-4675	39	51	c	c	NOUN
ejpam-4675	39	52	b	b	PROPN
ejpam-4675	39	53	a	a	DET
ejpam-4675	39	54	b	b	NOUN
ejpam-4675	39	55	1	1	NUM
ejpam-4675	39	56	e	e	NOUN
ejpam-4675	39	57	c	c	NOUN
ejpam-4675	39	58	d	d	NOUN
ejpam-4675	39	59	c	c	NOUN
ejpam-4675	39	60	c	c	NOUN
ejpam-4675	39	61	d	d	X
ejpam-4675	39	62	e	e	PROPN
ejpam-4675	39	63	1	1	NUM
ejpam-4675	39	64	a	a	DET
ejpam-4675	39	65	b	b	NOUN
ejpam-4675	39	66	d	d	X
ejpam-4675	39	67	d	d	PROPN
ejpam-4675	39	68	e	e	PROPN
ejpam-4675	39	69	c	c	NOUN
ejpam-4675	39	70	b	b	PROPN
ejpam-4675	39	71	1	1	NUM
ejpam-4675	39	72	a	a	DET
ejpam-4675	39	73	e	e	NOUN
ejpam-4675	39	74	e	e	NOUN
ejpam-4675	39	75	c	c	NOUN
ejpam-4675	39	76	d	d	X
ejpam-4675	39	77	a	a	PRON
ejpam-4675	39	78	b	b	NOUN
ejpam-4675	39	79	1	1	NUM
ejpam-4675	39	80	then	then	ADV
ejpam-4675	39	81	(	(	PUNCT
ejpam-4675	39	82	x	x	NOUN
ejpam-4675	39	83	,	,	PUNCT
ejpam-4675	39	84	·	·	PUNCT
ejpam-4675	39	85	,	,	PUNCT
ejpam-4675	39	86	1	1	NUM
ejpam-4675	39	87	)	)	PUNCT
ejpam-4675	39	88	is	be	AUX
ejpam-4675	39	89	a	a	DET
ejpam-4675	39	90	db	db	NOUN
ejpam-4675	39	91	-	-	PUNCT
ejpam-4675	39	92	algebra	algebra	NOUN
ejpam-4675	39	93	.	.	PUNCT
ejpam-4675	40	1	so	so	ADV
ejpam-4675	40	2	,	,	PUNCT
ejpam-4675	40	3	(	(	PUNCT
ejpam-4675	40	4	a	a	X
ejpam-4675	40	5	)	)	PUNCT
ejpam-4675	40	6	the	the	DET
ejpam-4675	40	7	set	set	NOUN
ejpam-4675	40	8	a={1	a={1	PROPN
ejpam-4675	40	9	,	,	PUNCT
ejpam-4675	40	10	a	a	PRON
ejpam-4675	40	11	,	,	PUNCT
ejpam-4675	40	12	e	e	NOUN
ejpam-4675	40	13	}	}	PUNCT
ejpam-4675	40	14	is	be	AUX
ejpam-4675	40	15	not	not	PART
ejpam-4675	40	16	a	a	DET
ejpam-4675	40	17	db	db	NOUN
ejpam-4675	40	18	-	-	NOUN
ejpam-4675	40	19	filter	filter	NOUN
ejpam-4675	40	20	since	since	SCONJ
ejpam-4675	40	21	∃e	∃e	NUM
ejpam-4675	40	22	·	·	PUNCT
ejpam-4675	40	23	c	c	X
ejpam-4675	40	24	=	=	PUNCT
ejpam-4675	40	25	a	a	PROPN
ejpam-4675	40	26	but	but	CCONJ
ejpam-4675	40	27	c	c	AUX
ejpam-4675	40	28	̸∈	̸∈	PROPN
ejpam-4675	40	29	a	a	DET
ejpam-4675	40	30	(	(	PUNCT
ejpam-4675	40	31	b	b	NOUN
ejpam-4675	40	32	)	)	PUNCT
ejpam-4675	40	33	the	the	DET
ejpam-4675	40	34	set	set	NOUN
ejpam-4675	40	35	b={1	b={1	ADJ
ejpam-4675	40	36	,	,	PUNCT
ejpam-4675	40	37	c	c	NOUN
ejpam-4675	40	38	}	}	PUNCT
ejpam-4675	40	39	is	be	AUX
ejpam-4675	40	40	a	a	DET
ejpam-4675	40	41	db	db	NOUN
ejpam-4675	40	42	-	-	PUNCT
ejpam-4675	40	43	filter	filter	NOUN
ejpam-4675	40	44	but	but	CCONJ
ejpam-4675	40	45	is	be	AUX
ejpam-4675	40	46	not	not	PART
ejpam-4675	40	47	normal	normal	ADJ
ejpam-4675	40	48	since	since	SCONJ
ejpam-4675	40	49	∃c	∃c	PROPN
ejpam-4675	40	50	·	·	PUNCT
ejpam-4675	40	51	1	1	NUM
ejpam-4675	40	52	=	=	SYM
ejpam-4675	40	53	a	a	PRON
ejpam-4675	40	54	·	·	PUNCT
ejpam-4675	40	55	e	e	X
ejpam-4675	40	56	=	=	PUNCT
ejpam-4675	40	57	c	c	PROPN
ejpam-4675	40	58	∈	∈	PROPN
ejpam-4675	40	59	b	b	PROPN
ejpam-4675	40	60	but	but	CCONJ
ejpam-4675	40	61	(	(	PUNCT
ejpam-4675	40	62	c	c	X
ejpam-4675	40	63	·	·	PUNCT
ejpam-4675	40	64	a	a	X
ejpam-4675	40	65	)	)	PUNCT
ejpam-4675	40	66	·	·	PUNCT
ejpam-4675	40	67	(	(	PUNCT
ejpam-4675	40	68	1	1	NUM
ejpam-4675	40	69	·	·	PUNCT
ejpam-4675	40	70	e	e	X
ejpam-4675	40	71	)	)	PUNCT
ejpam-4675	40	72	=	=	SYM
ejpam-4675	40	73	d	d	NOUN
ejpam-4675	40	74	·	·	PUNCT
ejpam-4675	40	75	e	e	X
ejpam-4675	40	76	=	=	PUNCT
ejpam-4675	40	77	a	a	DET
ejpam-4675	40	78	̸∈	̸∈	PROPN
ejpam-4675	40	79	b	b	PROPN
ejpam-4675	40	80	(	(	PUNCT
ejpam-4675	40	81	c	c	NOUN
ejpam-4675	40	82	)	)	PUNCT
ejpam-4675	40	83	the	the	DET
ejpam-4675	40	84	set	set	ADJ
ejpam-4675	40	85	c={1	c={1	PROPN
ejpam-4675	40	86	,	,	PUNCT
ejpam-4675	40	87	a	a	PRON
ejpam-4675	40	88	,	,	PUNCT
ejpam-4675	40	89	b	b	NOUN
ejpam-4675	40	90	}	}	PUNCT
ejpam-4675	40	91	is	be	AUX
ejpam-4675	40	92	a	a	DET
ejpam-4675	40	93	normal	normal	ADJ
ejpam-4675	40	94	db	db	NOUN
ejpam-4675	40	95	-	-	PUNCT
ejpam-4675	40	96	filter	filter	NOUN
ejpam-4675	40	97	.	.	PUNCT
ejpam-4675	41	1	theorem	theorem	NOUN
ejpam-4675	41	2	2	2	NUM
ejpam-4675	41	3	.	.	PUNCT
ejpam-4675	42	1	[	[	X
ejpam-4675	42	2	1	1	X
ejpam-4675	42	3	]	]	X
ejpam-4675	42	4	let	let	VERB
ejpam-4675	42	5	(	(	PUNCT
ejpam-4675	42	6	x	x	NOUN
ejpam-4675	42	7	,	,	PUNCT
ejpam-4675	42	8	·	·	PUNCT
ejpam-4675	42	9	,	,	PUNCT
ejpam-4675	42	10	1	1	X
ejpam-4675	42	11	)	)	PUNCT
ejpam-4675	42	12	be	be	AUX
ejpam-4675	42	13	a	a	DET
ejpam-4675	42	14	db	db	NOUN
ejpam-4675	42	15	-	-	PUNCT
ejpam-4675	42	16	algebra	algebra	NOUN
ejpam-4675	42	17	and	and	CCONJ
ejpam-4675	42	18	s	s	VERB
ejpam-4675	42	19	a	a	DET
ejpam-4675	42	20	normal	normal	ADJ
ejpam-4675	42	21	db	db	NOUN
ejpam-4675	42	22	-	-	PUNCT
ejpam-4675	42	23	subalgebra	subalgebra	NOUN
ejpam-4675	42	24	of	of	ADP
ejpam-4675	42	25	x.	x.	NOUN
ejpam-4675	42	26	the	the	DET
ejpam-4675	42	27	relation	relation	NOUN
ejpam-4675	42	28	defined	define	VERB
ejpam-4675	42	29	by	by	ADP
ejpam-4675	42	30	x	x	X
ejpam-4675	42	31	∼	∼	NOUN
ejpam-4675	42	32	y	y	NOUN
ejpam-4675	42	33	if	if	SCONJ
ejpam-4675	42	34	and	and	CCONJ
ejpam-4675	42	35	only	only	ADV
ejpam-4675	42	36	if	if	SCONJ
ejpam-4675	42	37	x	x	X
ejpam-4675	42	38	·	·	PUNCT
ejpam-4675	42	39	y	y	X
ejpam-4675	42	40	,	,	PUNCT
ejpam-4675	42	41	y	y	PROPN
ejpam-4675	42	42	·	·	PUNCT
ejpam-4675	42	43	x	x	PUNCT
ejpam-4675	43	1	∈	∈	NOUN
ejpam-4675	43	2	s	s	VERB
ejpam-4675	43	3	is	be	AUX
ejpam-4675	43	4	a	a	DET
ejpam-4675	43	5	congruence	congruence	NOUN
ejpam-4675	43	6	relation	relation	NOUN
ejpam-4675	43	7	on	on	ADP
ejpam-4675	43	8	x	x	PUNCT
ejpam-4675	43	9	for	for	ADP
ejpam-4675	43	10	any	any	DET
ejpam-4675	43	11	x	x	NOUN
ejpam-4675	43	12	,	,	PUNCT
ejpam-4675	43	13	y	y	PROPN
ejpam-4675	43	14	∈	∈	PROPN
ejpam-4675	43	15	x.	x.	NOUN
ejpam-4675	43	16	definition	definition	NOUN
ejpam-4675	43	17	5	5	NUM
ejpam-4675	43	18	.	.	PUNCT
ejpam-4675	44	1	[	[	X
ejpam-4675	44	2	1	1	X
ejpam-4675	44	3	]	]	X
ejpam-4675	44	4	let	let	VERB
ejpam-4675	44	5	(	(	PUNCT
ejpam-4675	44	6	x	x	NOUN
ejpam-4675	44	7	,	,	PUNCT
ejpam-4675	44	8	·	·	PUNCT
ejpam-4675	44	9	,	,	PUNCT
ejpam-4675	44	10	1	1	X
ejpam-4675	44	11	)	)	PUNCT
ejpam-4675	44	12	be	be	AUX
ejpam-4675	44	13	a	a	DET
ejpam-4675	44	14	db	db	NOUN
ejpam-4675	44	15	-	-	PUNCT
ejpam-4675	44	16	algebra	algebra	NOUN
ejpam-4675	44	17	and	and	CCONJ
ejpam-4675	44	18	s	s	VERB
ejpam-4675	44	19	a	a	DET
ejpam-4675	44	20	normal	normal	ADJ
ejpam-4675	44	21	db	db	NOUN
ejpam-4675	44	22	-	-	PUNCT
ejpam-4675	44	23	subalgebra	subalgebra	NOUN
ejpam-4675	44	24	of	of	ADP
ejpam-4675	44	25	x.	x.	NOUN
ejpam-4675	44	26	define	define	VERB
ejpam-4675	44	27	a	a	DET
ejpam-4675	44	28	congruence	congruence	ADJ
ejpam-4675	44	29	class	class	NOUN
ejpam-4675	45	1	[	[	X
ejpam-4675	45	2	x]s	x]s	NOUN
ejpam-4675	45	3	by	by	ADP
ejpam-4675	45	4	[	[	X
ejpam-4675	45	5	x]s	x]s	PROPN
ejpam-4675	45	6	=	=	SYM
ejpam-4675	45	7	{	{	PUNCT
ejpam-4675	45	8	y	y	PROPN
ejpam-4675	45	9	∈	∈	PROPN
ejpam-4675	45	10	x|y	x|y	PUNCT
ejpam-4675	46	1	∼	∼	NOUN
ejpam-4675	46	2	x	x	SYM
ejpam-4675	46	3	}	}	PUNCT
ejpam-4675	46	4	and	and	CCONJ
ejpam-4675	46	5	define	define	VERB
ejpam-4675	46	6	x	x	NOUN
ejpam-4675	46	7	/	/	SYM
ejpam-4675	46	8	s	s	VERB
ejpam-4675	46	9	to	to	PART
ejpam-4675	46	10	be	be	AUX
ejpam-4675	46	11	the	the	DET
ejpam-4675	46	12	set	set	NOUN
ejpam-4675	46	13	of	of	ADP
ejpam-4675	46	14	all	all	DET
ejpam-4675	46	15	congruence	congruence	NOUN
ejpam-4675	46	16	classes	class	NOUN
ejpam-4675	46	17	of	of	ADP
ejpam-4675	46	18	x	x	PRON
ejpam-4675	46	19	,	,	PUNCT
ejpam-4675	46	20	that	that	PRON
ejpam-4675	46	21	is	be	AUX
ejpam-4675	46	22	x	x	X
ejpam-4675	46	23	/	/	SYM
ejpam-4675	46	24	s	s	PART
ejpam-4675	46	25	=	=	X
ejpam-4675	46	26	{	{	PUNCT
ejpam-4675	46	27	[	[	X
ejpam-4675	46	28	x]s	x]s	PROPN
ejpam-4675	46	29	|x	|x	X
ejpam-4675	46	30	∈	∈	PROPN
ejpam-4675	46	31	x	x	PUNCT
ejpam-4675	46	32	}	}	PUNCT
ejpam-4675	46	33	.	.	PUNCT
ejpam-4675	47	1	3	3	X
ejpam-4675	47	2	.	.	X
ejpam-4675	47	3	results	result	NOUN
ejpam-4675	47	4	lemma	lemma	PROPN
ejpam-4675	47	5	2	2	X
ejpam-4675	47	6	.	.	PUNCT
ejpam-4675	48	1	let	let	VERB
ejpam-4675	48	2	s	s	PRON
ejpam-4675	48	3	be	be	AUX
ejpam-4675	48	4	a	a	DET
ejpam-4675	48	5	normal	normal	ADJ
ejpam-4675	48	6	db	db	NOUN
ejpam-4675	48	7	-	-	PUNCT
ejpam-4675	48	8	subalgebra	subalgebra	NOUN
ejpam-4675	48	9	of	of	ADP
ejpam-4675	48	10	a	a	DET
ejpam-4675	48	11	db	db	NOUN
ejpam-4675	48	12	-	-	PUNCT
ejpam-4675	48	13	algebra	algebra	NOUN
ejpam-4675	48	14	(	(	PUNCT
ejpam-4675	48	15	x	x	X
ejpam-4675	48	16	,	,	PUNCT
ejpam-4675	48	17	·	·	PUNCT
ejpam-4675	48	18	,	,	PUNCT
ejpam-4675	48	19	1	1	NUM
ejpam-4675	48	20	)	)	PUNCT
ejpam-4675	48	21	and	and	CCONJ
ejpam-4675	48	22	x	x	X
ejpam-4675	48	23	,	,	PUNCT
ejpam-4675	48	24	y	y	PROPN
ejpam-4675	48	25	∈	∈	PROPN
ejpam-4675	48	26	x.	x.	NOUN
ejpam-4675	49	1	then	then	ADV
ejpam-4675	49	2	[	[	X
ejpam-4675	49	3	x]s	x]s	NOUN
ejpam-4675	49	4	=	=	PUNCT
ejpam-4675	50	1	[	[	X
ejpam-4675	50	2	y]s	y]s	X
ejpam-4675	50	3	if	if	SCONJ
ejpam-4675	50	4	and	and	CCONJ
ejpam-4675	50	5	only	only	ADV
ejpam-4675	50	6	if	if	SCONJ
ejpam-4675	50	7	x	x	PUNCT
ejpam-4675	50	8	∼	∼	NOUN
ejpam-4675	50	9	y.	y.	NOUN
ejpam-4675	50	10	proof	proof	NOUN
ejpam-4675	50	11	.	.	PUNCT
ejpam-4675	51	1	suppose	suppose	VERB
ejpam-4675	52	1	[	[	X
ejpam-4675	52	2	x]s	x]s	PROPN
ejpam-4675	52	3	=	=	PUNCT
ejpam-4675	53	1	[	[	X
ejpam-4675	53	2	y]s	y]s	X
ejpam-4675	53	3	.	.	PUNCT
ejpam-4675	54	1	then	then	ADV
ejpam-4675	54	2	z	z	PROPN
ejpam-4675	54	3	∈	∈	PROPN
ejpam-4675	55	1	[	[	X
ejpam-4675	55	2	x]s	x]s	PROPN
ejpam-4675	55	3	implies	imply	VERB
ejpam-4675	55	4	that	that	SCONJ
ejpam-4675	55	5	z	z	PROPN
ejpam-4675	55	6	∈	∈	PROPN
ejpam-4675	56	1	[	[	X
ejpam-4675	56	2	y]s	y]s	X
ejpam-4675	56	3	.	.	PUNCT
ejpam-4675	57	1	we	we	PRON
ejpam-4675	57	2	have	have	VERB
ejpam-4675	57	3	that	that	DET
ejpam-4675	57	4	z	z	NOUN
ejpam-4675	57	5	∼	∼	NOUN
ejpam-4675	57	6	x	x	NOUN
ejpam-4675	57	7	,	,	PUNCT
ejpam-4675	57	8	z	z	NOUN
ejpam-4675	57	9	∼	∼	NOUN
ejpam-4675	57	10	y	y	NOUN
ejpam-4675	57	11	and	and	CCONJ
ejpam-4675	57	12	since	since	SCONJ
ejpam-4675	57	13	∼	∼	NOUN
ejpam-4675	57	14	is	be	AUX
ejpam-4675	57	15	symmetric	symmetric	ADJ
ejpam-4675	57	16	and	and	CCONJ
ejpam-4675	57	17	transitive	transitive	ADJ
ejpam-4675	57	18	by	by	ADP
ejpam-4675	57	19	theorem	theorem	NOUN
ejpam-4675	57	20	2	2	NUM
ejpam-4675	57	21	,	,	PUNCT
ejpam-4675	57	22	then	then	ADV
ejpam-4675	57	23	z	z	NOUN
ejpam-4675	57	24	∼	∼	NOUN
ejpam-4675	57	25	x	x	NOUN
ejpam-4675	57	26	,	,	PUNCT
ejpam-4675	57	27	z	z	NOUN
ejpam-4675	57	28	∼	∼	NOUN
ejpam-4675	57	29	y	y	PROPN
ejpam-4675	57	30	implies	imply	VERB
ejpam-4675	57	31	x	x	PUNCT
ejpam-4675	57	32	∼	∼	NOUN
ejpam-4675	57	33	z	z	NOUN
ejpam-4675	57	34	,	,	PUNCT
ejpam-4675	57	35	z	z	NOUN
ejpam-4675	57	36	∼	∼	NOUN
ejpam-4675	57	37	y	y	PROPN
ejpam-4675	57	38	which	which	PRON
ejpam-4675	57	39	implies	imply	VERB
ejpam-4675	57	40	that	that	SCONJ
ejpam-4675	57	41	x	x	PUNCT
ejpam-4675	57	42	∼	∼	NOUN
ejpam-4675	57	43	y.	y.	NOUN
ejpam-4675	57	44	now	now	ADV
ejpam-4675	57	45	,	,	PUNCT
ejpam-4675	57	46	suppose	suppose	VERB
ejpam-4675	57	47	x	x	PUNCT
ejpam-4675	57	48	∼	∼	NOUN
ejpam-4675	57	49	y.	y.	NOUN
ejpam-4675	57	50	then	then	ADV
ejpam-4675	57	51	x	x	X
ejpam-4675	57	52	·	·	PUNCT
ejpam-4675	57	53	y	y	X
ejpam-4675	57	54	,	,	PUNCT
ejpam-4675	57	55	y	y	PROPN
ejpam-4675	57	56	·	·	PUNCT
ejpam-4675	57	57	x	x	SYM
ejpam-4675	57	58	∈	∈	PROPN
ejpam-4675	57	59	s.	s.	PROPN
ejpam-4675	57	60	let	let	VERB
ejpam-4675	57	61	z	z	PROPN
ejpam-4675	57	62	∈	∈	PROPN
ejpam-4675	58	1	[	[	X
ejpam-4675	58	2	x]s	x]s	PROPN
ejpam-4675	58	3	,	,	PUNCT
ejpam-4675	58	4	then	then	ADV
ejpam-4675	58	5	z	z	NOUN
ejpam-4675	58	6	∼	∼	NOUN
ejpam-4675	58	7	x.	x.	NOUN
ejpam-4675	59	1	we	we	PRON
ejpam-4675	59	2	have	have	VERB
ejpam-4675	59	3	that	that	DET
ejpam-4675	59	4	z	z	NOUN
ejpam-4675	59	5	∼	∼	NOUN
ejpam-4675	59	6	x	x	NOUN
ejpam-4675	59	7	,	,	PUNCT
ejpam-4675	59	8	x	x	SYM
ejpam-4675	59	9	∼	∼	NOUN
ejpam-4675	59	10	y	y	PROPN
ejpam-4675	59	11	implies	imply	VERB
ejpam-4675	59	12	z	z	NOUN
ejpam-4675	59	13	∼	∼	NOUN
ejpam-4675	59	14	y	y	PROPN
ejpam-4675	59	15	which	which	PRON
ejpam-4675	59	16	implies	imply	VERB
ejpam-4675	59	17	that	that	SCONJ
ejpam-4675	59	18	z	z	PROPN
ejpam-4675	59	19	∈	∈	PROPN
ejpam-4675	60	1	[	[	X
ejpam-4675	60	2	y]s	y]s	X
ejpam-4675	60	3	.	.	PUNCT
ejpam-4675	61	1	hence	hence	ADV
ejpam-4675	61	2	,	,	PUNCT
ejpam-4675	61	3	[	[	X
ejpam-4675	61	4	x]s	x]s	NOUN
ejpam-4675	61	5	⊆	⊆	NUM
ejpam-4675	61	6	[	[	X
ejpam-4675	61	7	y]s	y]s	X
ejpam-4675	61	8	.	.	PUNCT
ejpam-4675	62	1	similarly	similarly	ADV
ejpam-4675	62	2	,	,	PUNCT
ejpam-4675	62	3	let	let	VERB
ejpam-4675	62	4	a	a	DET
ejpam-4675	62	5	∈	∈	NOUN
ejpam-4675	63	1	[	[	X
ejpam-4675	63	2	y]s	y]s	X
ejpam-4675	63	3	,	,	PUNCT
ejpam-4675	63	4	then	then	ADV
ejpam-4675	63	5	a	a	DET
ejpam-4675	63	6	∼	∼	NOUN
ejpam-4675	63	7	y.	y.	NOUN
ejpam-4675	63	8	we	we	PRON
ejpam-4675	63	9	have	have	VERB
ejpam-4675	63	10	that	that	PRON
ejpam-4675	63	11	a	a	DET
ejpam-4675	63	12	∼	∼	NOUN
ejpam-4675	63	13	y	y	NOUN
ejpam-4675	63	14	,	,	PUNCT
ejpam-4675	63	15	x	x	PUNCT
ejpam-4675	63	16	∼	∼	NOUN
ejpam-4675	63	17	y	y	PROPN
ejpam-4675	63	18	implies	imply	VERB
ejpam-4675	63	19	a	a	DET
ejpam-4675	63	20	∼	∼	NOUN
ejpam-4675	63	21	y	y	NOUN
ejpam-4675	63	22	,	,	PUNCT
ejpam-4675	63	23	y	y	PROPN
ejpam-4675	63	24	∼	∼	NOUN
ejpam-4675	63	25	x	x	PUNCT
ejpam-4675	63	26	which	which	PRON
ejpam-4675	63	27	implies	imply	VERB
ejpam-4675	63	28	that	that	SCONJ
ejpam-4675	63	29	a	a	DET
ejpam-4675	63	30	∼	∼	NOUN
ejpam-4675	63	31	x	x	PUNCT
ejpam-4675	63	32	and	and	CCONJ
ejpam-4675	63	33	so	so	ADV
ejpam-4675	63	34	a	a	DET
ejpam-4675	63	35	∈	∈	PROPN
ejpam-4675	63	36	[	[	X
ejpam-4675	63	37	x]s	x]s	PROPN
ejpam-4675	63	38	.	.	PUNCT
ejpam-4675	64	1	thus	thus	ADV
ejpam-4675	64	2	[	[	X
ejpam-4675	64	3	y]s	y]s	X
ejpam-4675	64	4	⊆	⊆	NUM
ejpam-4675	64	5	[	[	X
ejpam-4675	64	6	x]s	x]s	NOUN
ejpam-4675	64	7	and	and	CCONJ
ejpam-4675	64	8	it	it	PRON
ejpam-4675	64	9	follows	follow	VERB
ejpam-4675	64	10	that	that	SCONJ
ejpam-4675	65	1	[	[	X
ejpam-4675	65	2	x]s	x]s	NOUN
ejpam-4675	65	3	=	=	PUNCT
ejpam-4675	66	1	[	[	X
ejpam-4675	66	2	y]s	y]s	X
ejpam-4675	66	3	.	.	PUNCT
ejpam-4675	67	1	j.e	j.e	PROPN
ejpam-4675	67	2	.	.	PROPN
ejpam-4675	67	3	bolima	bolima	PROPN
ejpam-4675	67	4	,	,	PUNCT
ejpam-4675	67	5	k.b	k.b	PROPN
ejpam-4675	67	6	.	.	PUNCT
ejpam-4675	67	7	fuentes	fuentes	PROPN
ejpam-4675	67	8	/	/	SYM
ejpam-4675	67	9	eur	eur	PROPN
ejpam-4675	67	10	.	.	PUNCT
ejpam-4675	68	1	j.	j.	PROPN
ejpam-4675	68	2	pure	pure	PROPN
ejpam-4675	68	3	appl	appl	PROPN
ejpam-4675	68	4	.	.	PROPN
ejpam-4675	68	5	math	math	PROPN
ejpam-4675	68	6	,	,	PUNCT
ejpam-4675	68	7	16	16	NUM
ejpam-4675	68	8	(	(	PUNCT
ejpam-4675	68	9	1	1	NUM
ejpam-4675	68	10	)	)	PUNCT
ejpam-4675	68	11	(	(	PUNCT
ejpam-4675	68	12	2023	2023	NUM
ejpam-4675	68	13	)	)	PUNCT
ejpam-4675	68	14	,	,	PUNCT
ejpam-4675	68	15	577	577	NUM
ejpam-4675	68	16	-	-	SYM
ejpam-4675	68	17	586	586	NUM
ejpam-4675	68	18	580	580	NUM
ejpam-4675	68	19	theorem	theorem	NOUN
ejpam-4675	68	20	3	3	X
ejpam-4675	68	21	.	.	PUNCT
ejpam-4675	69	1	let	let	VERB
ejpam-4675	69	2	s	s	PRON
ejpam-4675	69	3	be	be	AUX
ejpam-4675	69	4	a	a	DET
ejpam-4675	69	5	normal	normal	ADJ
ejpam-4675	69	6	db	db	NOUN
ejpam-4675	69	7	-	-	PUNCT
ejpam-4675	69	8	subalgebra	subalgebra	NOUN
ejpam-4675	69	9	of	of	ADP
ejpam-4675	69	10	a	a	DET
ejpam-4675	69	11	db	db	NOUN
ejpam-4675	69	12	-	-	PUNCT
ejpam-4675	69	13	algebra	algebra	NOUN
ejpam-4675	69	14	(	(	PUNCT
ejpam-4675	69	15	x	x	X
ejpam-4675	69	16	,	,	PUNCT
ejpam-4675	69	17	·	·	PUNCT
ejpam-4675	69	18	,	,	PUNCT
ejpam-4675	69	19	1x	1x	NUM
ejpam-4675	69	20	)	)	PUNCT
ejpam-4675	69	21	.	.	PUNCT
ejpam-4675	70	1	then	then	ADV
ejpam-4675	70	2	(	(	PUNCT
ejpam-4675	70	3	x	x	X
ejpam-4675	70	4	/	/	SYM
ejpam-4675	70	5	s	s	PROPN
ejpam-4675	70	6	,	,	PUNCT
ejpam-4675	70	7	∗	∗	NOUN
ejpam-4675	70	8	,	,	PUNCT
ejpam-4675	70	9	[	[	X
ejpam-4675	70	10	1]s	1]s	NOUN
ejpam-4675	70	11	)	)	PUNCT
ejpam-4675	70	12	with	with	ADP
ejpam-4675	70	13	the	the	DET
ejpam-4675	70	14	binary	binary	PROPN
ejpam-4675	70	15	operation	operation	NOUN
ejpam-4675	70	16	∗	∗	NOUN
ejpam-4675	70	17	on	on	ADP
ejpam-4675	70	18	x	x	X
ejpam-4675	70	19	/	/	SYM
ejpam-4675	70	20	s	s	AUX
ejpam-4675	70	21	defined	define	VERB
ejpam-4675	70	22	by	by	ADP
ejpam-4675	70	23	[	[	X
ejpam-4675	70	24	x]s	x]s	PROPN
ejpam-4675	70	25	∗	∗	PROPN
ejpam-4675	70	26	[	[	X
ejpam-4675	70	27	y]s	y]s	X
ejpam-4675	70	28	=	=	PUNCT
ejpam-4675	71	1	[	[	X
ejpam-4675	71	2	x	x	X
ejpam-4675	71	3	·	·	PUNCT
ejpam-4675	71	4	y]s	y]	VERB
ejpam-4675	71	5	for	for	ADP
ejpam-4675	71	6	all	all	DET
ejpam-4675	71	7	x	x	NOUN
ejpam-4675	71	8	,	,	PUNCT
ejpam-4675	71	9	y	y	PROPN
ejpam-4675	71	10	∈	∈	PROPN
ejpam-4675	71	11	x	x	X
ejpam-4675	71	12	is	be	AUX
ejpam-4675	71	13	a	a	DET
ejpam-4675	71	14	db	db	NOUN
ejpam-4675	71	15	-	-	PUNCT
ejpam-4675	71	16	algebra	algebra	NOUN
ejpam-4675	71	17	.	.	PUNCT
ejpam-4675	72	1	x	x	X
ejpam-4675	72	2	/	/	SYM
ejpam-4675	72	3	s	s	VERB
ejpam-4675	72	4	is	be	AUX
ejpam-4675	72	5	called	call	VERB
ejpam-4675	72	6	the	the	DET
ejpam-4675	72	7	quotient	quotient	NOUN
ejpam-4675	72	8	db	db	NOUN
ejpam-4675	72	9	-	-	PUNCT
ejpam-4675	72	10	algebra	algebra	NOUN
ejpam-4675	72	11	of	of	ADP
ejpam-4675	72	12	x	x	PUNCT
ejpam-4675	72	13	by	by	ADP
ejpam-4675	72	14	s.	s.	PROPN
ejpam-4675	72	15	proof	proof	PROPN
ejpam-4675	72	16	.	.	PUNCT
ejpam-4675	73	1	let	let	VERB
ejpam-4675	73	2	x1	x1	NUM
ejpam-4675	73	3	,	,	PUNCT
ejpam-4675	73	4	x2	x2	PROPN
ejpam-4675	73	5	,	,	PUNCT
ejpam-4675	73	6	y1	y1	NOUN
ejpam-4675	73	7	,	,	PUNCT
ejpam-4675	73	8	y2	y2	NOUN
ejpam-4675	73	9	∈	∈	PROPN
ejpam-4675	73	10	x	x	PUNCT
ejpam-4675	74	1	such	such	ADJ
ejpam-4675	74	2	that	that	SCONJ
ejpam-4675	74	3	[	[	X
ejpam-4675	74	4	x1]s	x1]s	X
ejpam-4675	74	5	=	=	PUNCT
ejpam-4675	75	1	[	[	X
ejpam-4675	75	2	x2]s	x2]s	X
ejpam-4675	75	3	and	and	CCONJ
ejpam-4675	75	4	[	[	X
ejpam-4675	75	5	y1]s	y1]s	X
ejpam-4675	75	6	=	=	PUNCT
ejpam-4675	76	1	[	[	X
ejpam-4675	76	2	y2]s	y2]s	X
ejpam-4675	76	3	.	.	PUNCT
ejpam-4675	77	1	then	then	ADV
ejpam-4675	77	2	x1	x1	NUM
ejpam-4675	77	3	∼	∼	NOUN
ejpam-4675	77	4	x2	x2	NOUN
ejpam-4675	77	5	and	and	CCONJ
ejpam-4675	77	6	y1	y1	ADJ
ejpam-4675	77	7	∼	∼	NOUN
ejpam-4675	77	8	y2	y2	NOUN
ejpam-4675	77	9	.	.	PUNCT
ejpam-4675	78	1	since	since	SCONJ
ejpam-4675	78	2	∼	∼	NOUN
ejpam-4675	78	3	is	be	AUX
ejpam-4675	78	4	a	a	DET
ejpam-4675	78	5	congruence	congruence	NOUN
ejpam-4675	78	6	relation	relation	NOUN
ejpam-4675	78	7	,	,	PUNCT
ejpam-4675	78	8	we	we	PRON
ejpam-4675	78	9	have	have	VERB
ejpam-4675	78	10	that	that	PRON
ejpam-4675	78	11	x1	x1	PRON
ejpam-4675	78	12	·	·	PUNCT
ejpam-4675	78	13	y1	y1	INTJ
ejpam-4675	78	14	∼	∼	X
ejpam-4675	78	15	x2	x2	X
ejpam-4675	78	16	·	·	PUNCT
ejpam-4675	78	17	y2	y2	INTJ
ejpam-4675	78	18	and	and	CCONJ
ejpam-4675	78	19	by	by	ADP
ejpam-4675	78	20	lemma	lemma	PROPN
ejpam-4675	78	21	2	2	NUM
ejpam-4675	78	22	,	,	PUNCT
ejpam-4675	78	23	[	[	X
ejpam-4675	78	24	x1	x1	X
ejpam-4675	78	25	·	·	PUNCT
ejpam-4675	78	26	y1]s	y1]s	PUNCT
ejpam-4675	78	27	=	=	PUNCT
ejpam-4675	79	1	[	[	X
ejpam-4675	79	2	x2	x2	X
ejpam-4675	79	3	·	·	PUNCT
ejpam-4675	79	4	y2]s	y2]s	X
ejpam-4675	79	5	which	which	PRON
ejpam-4675	79	6	implies	imply	VERB
ejpam-4675	79	7	that	that	SCONJ
ejpam-4675	79	8	[	[	X
ejpam-4675	79	9	x1]s	x1]s	X
ejpam-4675	79	10	∗	∗	VERB
ejpam-4675	80	1	[	[	X
ejpam-4675	80	2	y1]s	y1]s	X
ejpam-4675	80	3	=	=	PUNCT
ejpam-4675	81	1	[	[	X
ejpam-4675	81	2	x2]s	x2]s	X
ejpam-4675	81	3	∗	∗	X
ejpam-4675	82	1	[	[	X
ejpam-4675	82	2	y2]s	y2]s	X
ejpam-4675	82	3	.	.	PUNCT
ejpam-4675	82	4	hence	hence	ADV
ejpam-4675	82	5	∗	∗	NOUN
ejpam-4675	82	6	is	be	AUX
ejpam-4675	82	7	well	well	ADV
ejpam-4675	82	8	-	-	PUNCT
ejpam-4675	82	9	defined	define	VERB
ejpam-4675	82	10	.	.	PUNCT
ejpam-4675	83	1	now	now	ADV
ejpam-4675	83	2	,	,	PUNCT
ejpam-4675	83	3	for	for	ADP
ejpam-4675	83	4	all	all	DET
ejpam-4675	83	5	x	x	NOUN
ejpam-4675	83	6	,	,	PUNCT
ejpam-4675	83	7	y	y	PROPN
ejpam-4675	83	8	,	,	PUNCT
ejpam-4675	83	9	z	z	PROPN
ejpam-4675	83	10	∈	∈	PROPN
ejpam-4675	83	11	x	x	X
ejpam-4675	83	12	,	,	PUNCT
ejpam-4675	83	13	[	[	X
ejpam-4675	83	14	x]s	x]s	PROPN
ejpam-4675	83	15	∗	∗	PROPN
ejpam-4675	83	16	[	[	X
ejpam-4675	83	17	x]s	x]s	NOUN
ejpam-4675	83	18	=	=	PUNCT
ejpam-4675	84	1	[	[	X
ejpam-4675	84	2	x	x	X
ejpam-4675	84	3	·	·	PUNCT
ejpam-4675	84	4	x]s	x]s	PUNCT
ejpam-4675	85	1	=	=	PUNCT
ejpam-4675	86	1	[	[	X
ejpam-4675	86	2	1]s	1]s	NUM
ejpam-4675	86	3	(	(	PUNCT
ejpam-4675	86	4	db1	db1	NOUN
ejpam-4675	86	5	)	)	PUNCT
ejpam-4675	86	6	[	[	X
ejpam-4675	86	7	1]s	1]s	NUM
ejpam-4675	86	8	∗	∗	NOUN
ejpam-4675	86	9	[	[	X
ejpam-4675	86	10	x]s	x]s	NOUN
ejpam-4675	86	11	=	=	PUNCT
ejpam-4675	87	1	[	[	X
ejpam-4675	87	2	1	1	NUM
ejpam-4675	87	3	·	·	PUNCT
ejpam-4675	87	4	x]s	x]s	PUNCT
ejpam-4675	88	1	=	=	PUNCT
ejpam-4675	89	1	[	[	X
ejpam-4675	89	2	x]s	x]s	PROPN
ejpam-4675	89	3	(	(	PUNCT
ejpam-4675	89	4	db2	db2	PROPN
ejpam-4675	89	5	)	)	PUNCT
ejpam-4675	89	6	[	[	X
ejpam-4675	89	7	x]s	x]s	PROPN
ejpam-4675	89	8	∗	∗	X
ejpam-4675	89	9	(	(	PUNCT
ejpam-4675	89	10	[	[	X
ejpam-4675	89	11	y]s	y]s	X
ejpam-4675	89	12	∗	∗	VERB
ejpam-4675	89	13	[	[	X
ejpam-4675	89	14	z]s	z]s	NOUN
ejpam-4675	89	15	)	)	PUNCT
ejpam-4675	89	16	=	=	PUNCT
ejpam-4675	90	1	[	[	X
ejpam-4675	90	2	x]s	x]s	PROPN
ejpam-4675	90	3	∗	∗	X
ejpam-4675	90	4	(	(	PUNCT
ejpam-4675	90	5	[	[	X
ejpam-4675	90	6	y	y	X
ejpam-4675	90	7	·	·	PUNCT
ejpam-4675	90	8	z]s	z]s	PROPN
ejpam-4675	90	9	)	)	PUNCT
ejpam-4675	90	10	=	=	PUNCT
ejpam-4675	91	1	[	[	X
ejpam-4675	91	2	x	x	X
ejpam-4675	91	3	·	·	PUNCT
ejpam-4675	91	4	(	(	PUNCT
ejpam-4675	91	5	y	y	X
ejpam-4675	91	6	·	·	PUNCT
ejpam-4675	91	7	z)]s	z)]s	X
ejpam-4675	91	8	=	=	PUNCT
ejpam-4675	92	1	[	[	X
ejpam-4675	92	2	(	(	PUNCT
ejpam-4675	92	3	(	(	PUNCT
ejpam-4675	92	4	y	y	PROPN
ejpam-4675	92	5	·	·	PUNCT
ejpam-4675	92	6	1	1	NUM
ejpam-4675	92	7	)	)	PUNCT
ejpam-4675	92	8	·	·	PUNCT
ejpam-4675	92	9	x	x	X
ejpam-4675	92	10	)	)	PUNCT
ejpam-4675	92	11	·	·	PUNCT
ejpam-4675	92	12	z]s	z]s	X
ejpam-4675	93	1	=	=	PUNCT
ejpam-4675	93	2	[	[	X
ejpam-4675	93	3	(	(	PUNCT
ejpam-4675	93	4	y	y	PROPN
ejpam-4675	93	5	·	·	PUNCT
ejpam-4675	93	6	1	1	NUM
ejpam-4675	93	7	)	)	PUNCT
ejpam-4675	93	8	·	·	PUNCT
ejpam-4675	93	9	x]s	x]s	PUNCT
ejpam-4675	93	10	∗	∗	PROPN
ejpam-4675	94	1	[	[	X
ejpam-4675	94	2	z]s	z]s	X
ejpam-4675	94	3	=	=	SYM
ejpam-4675	94	4	(	(	PUNCT
ejpam-4675	94	5	[	[	X
ejpam-4675	94	6	y	y	X
ejpam-4675	94	7	·	·	PUNCT
ejpam-4675	94	8	1]s	1]s	NUM
ejpam-4675	94	9	∗	∗	NOUN
ejpam-4675	94	10	[	[	X
ejpam-4675	94	11	x]s	x]s	NOUN
ejpam-4675	94	12	)	)	PUNCT
ejpam-4675	94	13	∗	∗	NOUN
ejpam-4675	95	1	[	[	X
ejpam-4675	95	2	z]s	z]s	X
ejpam-4675	95	3	=	=	SYM
ejpam-4675	95	4	(	(	PUNCT
ejpam-4675	95	5	(	(	PUNCT
ejpam-4675	95	6	[	[	X
ejpam-4675	95	7	y]s	y]s	X
ejpam-4675	95	8	∗	∗	NOUN
ejpam-4675	95	9	[	[	X
ejpam-4675	95	10	1]s	1]s	NUM
ejpam-4675	95	11	)	)	PUNCT
ejpam-4675	95	12	∗	∗	NOUN
ejpam-4675	96	1	[	[	X
ejpam-4675	96	2	x]s	x]s	NOUN
ejpam-4675	96	3	)	)	PUNCT
ejpam-4675	96	4	∗	∗	NOUN
ejpam-4675	97	1	[	[	X
ejpam-4675	97	2	z]s	z]s	X
ejpam-4675	97	3	(	(	PUNCT
ejpam-4675	97	4	db3	db3	PROPN
ejpam-4675	97	5	)	)	PUNCT
ejpam-4675	97	6	hence	hence	ADV
ejpam-4675	97	7	,	,	PUNCT
ejpam-4675	97	8	(	(	PUNCT
ejpam-4675	97	9	x	x	X
ejpam-4675	97	10	/	/	SYM
ejpam-4675	97	11	s	s	PROPN
ejpam-4675	97	12	,	,	PUNCT
ejpam-4675	97	13	∗	∗	NOUN
ejpam-4675	97	14	,	,	PUNCT
ejpam-4675	97	15	[	[	X
ejpam-4675	97	16	1]s	1]s	NOUN
ejpam-4675	97	17	)	)	PUNCT
ejpam-4675	97	18	is	be	AUX
ejpam-4675	97	19	a	a	DET
ejpam-4675	97	20	db	db	NOUN
ejpam-4675	97	21	-	-	PUNCT
ejpam-4675	97	22	algebra	algebra	NOUN
ejpam-4675	97	23	.	.	PUNCT
ejpam-4675	98	1	proposition	proposition	NOUN
ejpam-4675	98	2	2	2	NUM
ejpam-4675	98	3	.	.	PUNCT
ejpam-4675	99	1	let	let	AUX
ejpam-4675	99	2	(	(	PUNCT
ejpam-4675	99	3	x	x	NOUN
ejpam-4675	99	4	,	,	PUNCT
ejpam-4675	99	5	·	·	PUNCT
ejpam-4675	99	6	,	,	PUNCT
ejpam-4675	99	7	1	1	X
ejpam-4675	99	8	)	)	PUNCT
ejpam-4675	99	9	be	be	AUX
ejpam-4675	99	10	a	a	DET
ejpam-4675	99	11	db	db	NOUN
ejpam-4675	99	12	-	-	PUNCT
ejpam-4675	99	13	algebra	algebra	NOUN
ejpam-4675	99	14	and	and	CCONJ
ejpam-4675	99	15	s	s	AUX
ejpam-4675	99	16	be	be	AUX
ejpam-4675	99	17	a	a	DET
ejpam-4675	99	18	subset	subset	NOUN
ejpam-4675	99	19	of	of	ADP
ejpam-4675	99	20	x.	x.	NOUN
ejpam-4675	100	1	then	then	ADV
ejpam-4675	100	2	s	s	VERB
ejpam-4675	100	3	is	be	AUX
ejpam-4675	100	4	a	a	DET
ejpam-4675	100	5	normal	normal	ADJ
ejpam-4675	100	6	db	db	NOUN
ejpam-4675	100	7	-	-	PUNCT
ejpam-4675	100	8	subalgebra	subalgebra	NOUN
ejpam-4675	100	9	of	of	ADP
ejpam-4675	100	10	x	x	PRON
ejpam-4675	100	11	if	if	SCONJ
ejpam-4675	100	12	and	and	CCONJ
ejpam-4675	100	13	only	only	ADV
ejpam-4675	100	14	if	if	SCONJ
ejpam-4675	100	15	s	s	NOUN
ejpam-4675	100	16	is	be	AUX
ejpam-4675	100	17	a	a	DET
ejpam-4675	100	18	normal	normal	ADJ
ejpam-4675	100	19	db	db	NOUN
ejpam-4675	100	20	-	-	PUNCT
ejpam-4675	100	21	filter	filter	NOUN
ejpam-4675	100	22	of	of	ADP
ejpam-4675	100	23	x.	x.	NOUN
ejpam-4675	100	24	proof	proof	PROPN
ejpam-4675	100	25	.	.	PUNCT
ejpam-4675	101	1	suppose	suppose	VERB
ejpam-4675	101	2	s	s	PRON
ejpam-4675	101	3	is	be	AUX
ejpam-4675	101	4	a	a	DET
ejpam-4675	101	5	normal	normal	ADJ
ejpam-4675	101	6	db	db	NOUN
ejpam-4675	101	7	-	-	PUNCT
ejpam-4675	101	8	filter	filter	NOUN
ejpam-4675	101	9	of	of	ADP
ejpam-4675	101	10	x.	x.	NOUN
ejpam-4675	101	11	it	it	PRON
ejpam-4675	101	12	follows	follow	VERB
ejpam-4675	101	13	from	from	ADP
ejpam-4675	101	14	proposition	proposition	NOUN
ejpam-4675	101	15	1	1	NUM
ejpam-4675	101	16	and	and	CCONJ
ejpam-4675	101	17	s	s	PRON
ejpam-4675	101	18	as	as	ADP
ejpam-4675	101	19	a	a	DET
ejpam-4675	101	20	normal	normal	ADJ
ejpam-4675	101	21	subset	subset	NOUN
ejpam-4675	101	22	of	of	ADP
ejpam-4675	101	23	x	x	PRON
ejpam-4675	101	24	that	that	PRON
ejpam-4675	101	25	s	s	VERB
ejpam-4675	101	26	is	be	AUX
ejpam-4675	101	27	a	a	DET
ejpam-4675	101	28	normal	normal	ADJ
ejpam-4675	101	29	db	db	NOUN
ejpam-4675	101	30	-	-	PUNCT
ejpam-4675	101	31	subalgebra	subalgebra	NOUN
ejpam-4675	101	32	of	of	ADP
ejpam-4675	101	33	x.	x.	NOUN
ejpam-4675	101	34	now	now	ADV
ejpam-4675	101	35	,	,	PUNCT
ejpam-4675	101	36	suppose	suppose	VERB
ejpam-4675	101	37	s	s	NOUN
ejpam-4675	101	38	is	be	AUX
ejpam-4675	101	39	a	a	DET
ejpam-4675	101	40	normal	normal	ADJ
ejpam-4675	101	41	db	db	NOUN
ejpam-4675	101	42	-	-	PUNCT
ejpam-4675	101	43	subalgebra	subalgebra	NOUN
ejpam-4675	101	44	of	of	ADP
ejpam-4675	101	45	x.	x.	NOUN
ejpam-4675	101	46	let	let	VERB
ejpam-4675	101	47	x	x	PRON
ejpam-4675	101	48	,	,	PUNCT
ejpam-4675	101	49	y	y	PROPN
ejpam-4675	101	50	∈	∈	PROPN
ejpam-4675	101	51	x	x	PUNCT
ejpam-4675	101	52	such	such	ADJ
ejpam-4675	101	53	that	that	SCONJ
ejpam-4675	101	54	x	x	X
ejpam-4675	101	55	·	·	PUNCT
ejpam-4675	101	56	y	y	X
ejpam-4675	101	57	∈	∈	PROPN
ejpam-4675	101	58	s	s	PART
ejpam-4675	101	59	and	and	CCONJ
ejpam-4675	101	60	x	x	PROPN
ejpam-4675	101	61	∈	∈	PROPN
ejpam-4675	101	62	s.	s.	PROPN
ejpam-4675	101	63	since	since	SCONJ
ejpam-4675	101	64	s	s	PROPN
ejpam-4675	101	65	is	be	AUX
ejpam-4675	101	66	a	a	DET
ejpam-4675	101	67	db	db	NOUN
ejpam-4675	101	68	-	-	PUNCT
ejpam-4675	101	69	subalgebra	subalgebra	NOUN
ejpam-4675	101	70	,	,	PUNCT
ejpam-4675	101	71	then	then	ADV
ejpam-4675	101	72	1	1	NUM
ejpam-4675	101	73	∈	∈	PROPN
ejpam-4675	101	74	s.	s.	PROPN
ejpam-4675	101	75	since	since	SCONJ
ejpam-4675	101	76	1	1	NUM
ejpam-4675	101	77	,	,	PUNCT
ejpam-4675	101	78	x	x	PUNCT
ejpam-4675	101	79	∈	∈	NOUN
ejpam-4675	101	80	s	s	X
ejpam-4675	101	81	and	and	CCONJ
ejpam-4675	101	82	s	s	VERB
ejpam-4675	101	83	is	be	AUX
ejpam-4675	101	84	closed	close	VERB
ejpam-4675	101	85	by	by	ADP
ejpam-4675	101	86	theorem	theorem	NOUN
ejpam-4675	101	87	1	1	NUM
ejpam-4675	101	88	,	,	PUNCT
ejpam-4675	101	89	we	we	PRON
ejpam-4675	101	90	have	have	VERB
ejpam-4675	101	91	that	that	PRON
ejpam-4675	101	92	x	x	SYM
ejpam-4675	101	93	·	·	PUNCT
ejpam-4675	101	94	1	1	NUM
ejpam-4675	101	95	∈	∈	NOUN
ejpam-4675	101	96	s	s	X
ejpam-4675	101	97	and	and	CCONJ
ejpam-4675	101	98	since	since	SCONJ
ejpam-4675	101	99	x	x	X
ejpam-4675	101	100	·	·	PUNCT
ejpam-4675	101	101	y	y	PROPN
ejpam-4675	101	102	∈	∈	PROPN
ejpam-4675	101	103	s	s	X
ejpam-4675	101	104	,	,	PUNCT
ejpam-4675	101	105	it	it	PRON
ejpam-4675	101	106	follows	follow	VERB
ejpam-4675	101	107	that	that	SCONJ
ejpam-4675	101	108	(	(	PUNCT
ejpam-4675	101	109	x	x	X
ejpam-4675	101	110	·	·	PUNCT
ejpam-4675	101	111	x	x	X
ejpam-4675	101	112	)	)	PUNCT
ejpam-4675	101	113	·	·	PUNCT
ejpam-4675	101	114	(	(	PUNCT
ejpam-4675	101	115	1	1	NUM
ejpam-4675	101	116	·	·	SYM
ejpam-4675	101	117	y	y	X
ejpam-4675	101	118	)	)	PUNCT
ejpam-4675	101	119	∈	∈	PROPN
ejpam-4675	101	120	s	s	PART
ejpam-4675	101	121	since	since	SCONJ
ejpam-4675	101	122	s	s	NOUN
ejpam-4675	101	123	is	be	AUX
ejpam-4675	101	124	normal	normal	ADJ
ejpam-4675	101	125	.	.	PUNCT
ejpam-4675	102	1	then	then	ADV
ejpam-4675	102	2	,	,	PUNCT
ejpam-4675	102	3	y	y	PROPN
ejpam-4675	102	4	=	=	SYM
ejpam-4675	102	5	1	1	NUM
ejpam-4675	102	6	·	·	SYM
ejpam-4675	102	7	y	y	NOUN
ejpam-4675	102	8	=	=	SYM
ejpam-4675	102	9	1	1	X
ejpam-4675	102	10	·	·	PUNCT
ejpam-4675	102	11	(	(	PUNCT
ejpam-4675	102	12	1	1	NUM
ejpam-4675	102	13	·	·	SYM
ejpam-4675	102	14	y	y	NOUN
ejpam-4675	102	15	)	)	PUNCT
ejpam-4675	102	16	=	=	SYM
ejpam-4675	102	17	(	(	PUNCT
ejpam-4675	102	18	x	x	SYM
ejpam-4675	102	19	·	·	PUNCT
ejpam-4675	102	20	x	x	X
ejpam-4675	102	21	)	)	PUNCT
ejpam-4675	102	22	·	·	PUNCT
ejpam-4675	102	23	(	(	PUNCT
ejpam-4675	102	24	1	1	NUM
ejpam-4675	102	25	·	·	SYM
ejpam-4675	102	26	y	y	X
ejpam-4675	102	27	)	)	PUNCT
ejpam-4675	102	28	∈	∈	PROPN
ejpam-4675	102	29	s.	s.	PROPN
ejpam-4675	102	30	hence	hence	ADV
ejpam-4675	102	31	,	,	PUNCT
ejpam-4675	102	32	s	s	VERB
ejpam-4675	102	33	is	be	AUX
ejpam-4675	102	34	a	a	DET
ejpam-4675	102	35	normal	normal	ADJ
ejpam-4675	102	36	db	db	NOUN
ejpam-4675	102	37	-	-	PUNCT
ejpam-4675	102	38	filter	filter	NOUN
ejpam-4675	102	39	.	.	PUNCT
ejpam-4675	103	1	definition	definition	NOUN
ejpam-4675	103	2	6	6	NUM
ejpam-4675	103	3	.	.	PUNCT
ejpam-4675	104	1	let	let	VERB
ejpam-4675	104	2	(	(	PUNCT
ejpam-4675	104	3	x	x	NOUN
ejpam-4675	104	4	,	,	PUNCT
ejpam-4675	104	5	·	·	PUNCT
ejpam-4675	104	6	,	,	PUNCT
ejpam-4675	104	7	1x	1x	NUM
ejpam-4675	104	8	)	)	PUNCT
ejpam-4675	104	9	and	and	CCONJ
ejpam-4675	104	10	(	(	PUNCT
ejpam-4675	104	11	y	y	PROPN
ejpam-4675	104	12	,	,	PUNCT
ejpam-4675	104	13	∗	∗	NOUN
ejpam-4675	104	14	,	,	PUNCT
ejpam-4675	104	15	1y	1y	NOUN
ejpam-4675	104	16	)	)	PUNCT
ejpam-4675	104	17	be	be	AUX
ejpam-4675	104	18	db	db	NOUN
ejpam-4675	104	19	-	-	PUNCT
ejpam-4675	104	20	algebras	algebras	PROPN
ejpam-4675	104	21	.	.	PUNCT
ejpam-4675	105	1	a	a	DET
ejpam-4675	105	2	mapping	mapping	NOUN
ejpam-4675	105	3	φ	φ	NOUN
ejpam-4675	105	4	:	:	PUNCT
ejpam-4675	105	5	x	x	X
ejpam-4675	105	6	→	→	SYM
ejpam-4675	105	7	y	y	PROPN
ejpam-4675	105	8	is	be	AUX
ejpam-4675	105	9	called	call	VERB
ejpam-4675	105	10	a	a	DET
ejpam-4675	105	11	dual	dual	ADJ
ejpam-4675	105	12	b	b	NOUN
ejpam-4675	105	13	-	-	PUNCT
ejpam-4675	105	14	homomorphism	homomorphism	NOUN
ejpam-4675	105	15	(	(	PUNCT
ejpam-4675	105	16	or	or	CCONJ
ejpam-4675	105	17	db	db	NOUN
ejpam-4675	105	18	-	-	PUNCT
ejpam-4675	105	19	homomorphism	homomorphism	NOUN
ejpam-4675	105	20	)	)	PUNCT
ejpam-4675	105	21	,	,	PUNCT
ejpam-4675	105	22	from	from	ADP
ejpam-4675	105	23	x	x	PUNCT
ejpam-4675	105	24	into	into	ADP
ejpam-4675	105	25	y	y	PRON
ejpam-4675	105	26	if	if	SCONJ
ejpam-4675	105	27	φ(x	φ(x	PROPN
ejpam-4675	105	28	·	·	PUNCT
ejpam-4675	105	29	y	y	X
ejpam-4675	105	30	)	)	PUNCT
ejpam-4675	105	31	=	=	SYM
ejpam-4675	105	32	φ(x	φ(x	NOUN
ejpam-4675	105	33	)	)	PUNCT
ejpam-4675	105	34	∗	∗	NOUN
ejpam-4675	105	35	φ(y	φ(y	NOUN
ejpam-4675	105	36	)	)	PUNCT
ejpam-4675	105	37	for	for	ADP
ejpam-4675	105	38	any	any	DET
ejpam-4675	105	39	x	x	NOUN
ejpam-4675	105	40	,	,	PUNCT
ejpam-4675	105	41	y	y	PROPN
ejpam-4675	105	42	∈	∈	PROPN
ejpam-4675	105	43	x.	x.	NOUN
ejpam-4675	105	44	a	a	DET
ejpam-4675	105	45	db	db	PROPN
ejpam-4675	105	46	-	-	PUNCT
ejpam-4675	105	47	homomorphism	homomorphism	NOUN
ejpam-4675	105	48	φ	φ	PROPN
ejpam-4675	105	49	is	be	AUX
ejpam-4675	105	50	called	call	VERB
ejpam-4675	105	51	db	db	NOUN
ejpam-4675	105	52	-	-	PUNCT
ejpam-4675	105	53	monomorphism	monomorphism	NOUN
ejpam-4675	105	54	,	,	PUNCT
ejpam-4675	105	55	db	db	NOUN
ejpam-4675	105	56	-	-	PUNCT
ejpam-4675	105	57	epimorphism	epimorphism	NOUN
ejpam-4675	105	58	,	,	PUNCT
ejpam-4675	105	59	or	or	CCONJ
ejpam-4675	105	60	db	db	PROPN
ejpam-4675	105	61	-	-	PUNCT
ejpam-4675	105	62	isomorphism	isomorphism	NOUN
ejpam-4675	105	63	(	(	PUNCT
ejpam-4675	105	64	denoted	denote	VERB
ejpam-4675	105	65	by	by	ADP
ejpam-4675	105	66	x	x	SYM
ejpam-4675	105	67	∼=	∼=	PROPN
ejpam-4675	105	68	y	y	NOUN
ejpam-4675	105	69	)	)	PUNCT
ejpam-4675	105	70	,	,	PUNCT
ejpam-4675	105	71	if	if	SCONJ
ejpam-4675	105	72	φ	φ	PROPN
ejpam-4675	105	73	is	be	AUX
ejpam-4675	105	74	one	one	NUM
ejpam-4675	105	75	-	-	PUNCT
ejpam-4675	105	76	to	to	ADP
ejpam-4675	105	77	-	-	PUNCT
ejpam-4675	105	78	one	one	NUM
ejpam-4675	105	79	,	,	PUNCT
ejpam-4675	105	80	onto	onto	ADP
ejpam-4675	105	81	,	,	PUNCT
ejpam-4675	105	82	or	or	CCONJ
ejpam-4675	105	83	a	a	DET
ejpam-4675	105	84	bijection	bijection	NOUN
ejpam-4675	105	85	,	,	PUNCT
ejpam-4675	105	86	respectively	respectively	ADV
ejpam-4675	105	87	.	.	PUNCT
ejpam-4675	106	1	an	an	DET
ejpam-4675	106	2	isomorphism	isomorphism	NOUN
ejpam-4675	106	3	φ	φ	NOUN
ejpam-4675	106	4	:	:	PUNCT
ejpam-4675	106	5	x	x	X
ejpam-4675	106	6	→	→	PUNCT
ejpam-4675	106	7	x	x	X
ejpam-4675	106	8	is	be	AUX
ejpam-4675	106	9	called	call	VERB
ejpam-4675	106	10	db	db	NOUN
ejpam-4675	106	11	-	-	NOUN
ejpam-4675	106	12	automorphism	automorphism	NOUN
ejpam-4675	106	13	.	.	PUNCT
ejpam-4675	107	1	the	the	DET
ejpam-4675	107	2	kernel	kernel	NOUN
ejpam-4675	107	3	of	of	ADP
ejpam-4675	107	4	the	the	DET
ejpam-4675	107	5	db	db	PROPN
ejpam-4675	107	6	-	-	PUNCT
ejpam-4675	107	7	homomorphism	homomorphism	NOUN
ejpam-4675	107	8	φ	φ	NOUN
ejpam-4675	107	9	,	,	PUNCT
ejpam-4675	107	10	denoted	denote	VERB
ejpam-4675	107	11	by	by	ADP
ejpam-4675	107	12	kerφ	kerφ	PROPN
ejpam-4675	107	13	,	,	PUNCT
ejpam-4675	107	14	is	be	AUX
ejpam-4675	107	15	the	the	DET
ejpam-4675	107	16	set	set	NOUN
ejpam-4675	107	17	whose	whose	DET
ejpam-4675	107	18	elements	element	NOUN
ejpam-4675	107	19	of	of	ADP
ejpam-4675	107	20	x	x	SYM
ejpam-4675	107	21	are	be	AUX
ejpam-4675	107	22	mapped	map	VERB
ejpam-4675	107	23	to	to	ADP
ejpam-4675	107	24	1y	1y	PROPN
ejpam-4675	107	25	.	.	PUNCT
ejpam-4675	108	1	j.e	j.e	PROPN
ejpam-4675	108	2	.	.	PROPN
ejpam-4675	108	3	bolima	bolima	PROPN
ejpam-4675	108	4	,	,	PUNCT
ejpam-4675	108	5	k.b	k.b	PROPN
ejpam-4675	108	6	.	.	PUNCT
ejpam-4675	108	7	fuentes	fuentes	PROPN
ejpam-4675	108	8	/	/	SYM
ejpam-4675	108	9	eur	eur	PROPN
ejpam-4675	108	10	.	.	PUNCT
ejpam-4675	109	1	j.	j.	PROPN
ejpam-4675	109	2	pure	pure	PROPN
ejpam-4675	109	3	appl	appl	PROPN
ejpam-4675	109	4	.	.	PROPN
ejpam-4675	109	5	math	math	PROPN
ejpam-4675	109	6	,	,	PUNCT
ejpam-4675	109	7	16	16	NUM
ejpam-4675	109	8	(	(	PUNCT
ejpam-4675	109	9	1	1	NUM
ejpam-4675	109	10	)	)	PUNCT
ejpam-4675	109	11	(	(	PUNCT
ejpam-4675	109	12	2023	2023	NUM
ejpam-4675	109	13	)	)	PUNCT
ejpam-4675	109	14	,	,	PUNCT
ejpam-4675	109	15	577	577	NUM
ejpam-4675	109	16	-	-	SYM
ejpam-4675	109	17	586	586	NUM
ejpam-4675	109	18	581	581	NUM
ejpam-4675	109	19	example	example	NOUN
ejpam-4675	109	20	4	4	NUM
ejpam-4675	109	21	.	.	X
ejpam-4675	110	1	let	let	AUX
ejpam-4675	110	2	(	(	PUNCT
ejpam-4675	110	3	r+	r+	X
ejpam-4675	110	4	,	,	PUNCT
ejpam-4675	110	5	·	·	PUNCT
ejpam-4675	110	6	,	,	PUNCT
ejpam-4675	110	7	1	1	X
ejpam-4675	110	8	)	)	PUNCT
ejpam-4675	110	9	be	be	AUX
ejpam-4675	110	10	a	a	DET
ejpam-4675	110	11	db	db	NOUN
ejpam-4675	110	12	-	-	PUNCT
ejpam-4675	110	13	algebra	algebra	NOUN
ejpam-4675	110	14	with	with	ADP
ejpam-4675	110	15	the	the	DET
ejpam-4675	110	16	binary	binary	ADJ
ejpam-4675	110	17	operator	operator	NOUN
ejpam-4675	110	18	·	·	PUNCT
ejpam-4675	110	19	be	be	AUX
ejpam-4675	110	20	defined	define	VERB
ejpam-4675	110	21	as	as	ADP
ejpam-4675	110	22	x·y	x·y	PROPN
ejpam-4675	110	23	=	=	SYM
ejpam-4675	110	24	y	y	PROPN
ejpam-4675	110	25	x	x	PUNCT
ejpam-4675	110	26	for	for	ADP
ejpam-4675	110	27	all	all	DET
ejpam-4675	110	28	x	x	NOUN
ejpam-4675	110	29	,	,	PUNCT
ejpam-4675	110	30	y	y	PROPN
ejpam-4675	110	31	in	in	ADP
ejpam-4675	110	32	r+	r+	X
ejpam-4675	110	33	.	.	PUNCT
ejpam-4675	111	1	define	define	VERB
ejpam-4675	111	2	φ	φ	NOUN
ejpam-4675	111	3	:	:	PUNCT
ejpam-4675	111	4	r+	r+	NOUN
ejpam-4675	111	5	→	→	SYM
ejpam-4675	111	6	r+	r+	NOUN
ejpam-4675	111	7	by	by	ADP
ejpam-4675	111	8	φ(x	φ(x	NOUN
ejpam-4675	111	9	)	)	PUNCT
ejpam-4675	111	10	=	=	SYM
ejpam-4675	112	1	x2	x2	PROPN
ejpam-4675	112	2	for	for	ADP
ejpam-4675	112	3	all	all	DET
ejpam-4675	112	4	x	x	SYM
ejpam-4675	112	5	∈	∈	PROPN
ejpam-4675	112	6	r+	r+	NOUN
ejpam-4675	112	7	.	.	PUNCT
ejpam-4675	113	1	for	for	ADP
ejpam-4675	113	2	all	all	DET
ejpam-4675	113	3	x	x	NOUN
ejpam-4675	113	4	,	,	PUNCT
ejpam-4675	113	5	y	y	PROPN
ejpam-4675	113	6	∈	∈	PROPN
ejpam-4675	113	7	r+	r+	X
ejpam-4675	113	8	,	,	PUNCT
ejpam-4675	113	9	x	x	SYM
ejpam-4675	113	10	=	=	SYM
ejpam-4675	113	11	y	y	PROPN
ejpam-4675	113	12	implies	imply	VERB
ejpam-4675	113	13	x2	x2	X
ejpam-4675	114	1	=	=	PUNCT
ejpam-4675	114	2	y2	y2	INTJ
ejpam-4675	114	3	which	which	PRON
ejpam-4675	114	4	implies	imply	VERB
ejpam-4675	114	5	that	that	SCONJ
ejpam-4675	114	6	φ(x	φ(x	NOUN
ejpam-4675	114	7	)	)	PUNCT
ejpam-4675	114	8	=	=	SYM
ejpam-4675	114	9	φ(y	φ(y	NOUN
ejpam-4675	114	10	)	)	PUNCT
ejpam-4675	114	11	.	.	PUNCT
ejpam-4675	115	1	hence	hence	ADV
ejpam-4675	115	2	,	,	PUNCT
ejpam-4675	115	3	φ	φ	PROPN
ejpam-4675	115	4	is	be	AUX
ejpam-4675	115	5	well	well	ADV
ejpam-4675	115	6	-	-	PUNCT
ejpam-4675	115	7	defined	define	VERB
ejpam-4675	115	8	.	.	PUNCT
ejpam-4675	116	1	now	now	ADV
ejpam-4675	116	2	,	,	PUNCT
ejpam-4675	116	3	φ(x	φ(x	PROPN
ejpam-4675	116	4	·	·	PUNCT
ejpam-4675	116	5	y	y	X
ejpam-4675	116	6	)	)	PUNCT
ejpam-4675	116	7	=	=	SYM
ejpam-4675	116	8	φ	φ	PROPN
ejpam-4675	116	9	(	(	PUNCT
ejpam-4675	116	10	y	y	NOUN
ejpam-4675	116	11	x	x	PROPN
ejpam-4675	116	12	)	)	PUNCT
ejpam-4675	117	1	=	=	PUNCT
ejpam-4675	117	2	y2	y2	NOUN
ejpam-4675	118	1	x2	x2	NOUN
ejpam-4675	119	1	=	=	PUNCT
ejpam-4675	120	1	x2	x2	PROPN
ejpam-4675	120	2	·	·	PUNCT
ejpam-4675	120	3	y2	y2	X
ejpam-4675	120	4	=	=	SYM
ejpam-4675	120	5	φ(x	φ(x	PROPN
ejpam-4675	120	6	)	)	PUNCT
ejpam-4675	120	7	·	·	PUNCT
ejpam-4675	120	8	φ(y	φ(y	NOUN
ejpam-4675	120	9	)	)	PUNCT
ejpam-4675	120	10	for	for	ADP
ejpam-4675	120	11	all	all	DET
ejpam-4675	120	12	x	x	NOUN
ejpam-4675	120	13	,	,	PUNCT
ejpam-4675	120	14	y	y	PROPN
ejpam-4675	120	15	∈	∈	PROPN
ejpam-4675	120	16	r+	r+	NOUN
ejpam-4675	120	17	.	.	PUNCT
ejpam-4675	121	1	hence	hence	ADV
ejpam-4675	121	2	,	,	PUNCT
ejpam-4675	121	3	φ	φ	PROPN
ejpam-4675	121	4	is	be	AUX
ejpam-4675	121	5	a	a	DET
ejpam-4675	121	6	db	db	NOUN
ejpam-4675	121	7	-	-	PUNCT
ejpam-4675	121	8	homomorphism	homomorphism	NOUN
ejpam-4675	121	9	.	.	PUNCT
ejpam-4675	122	1	suppose	suppose	VERB
ejpam-4675	122	2	that	that	SCONJ
ejpam-4675	122	3	φ(x	φ(x	NOUN
ejpam-4675	122	4	)	)	PUNCT
ejpam-4675	122	5	=	=	SYM
ejpam-4675	122	6	φ(y	φ(y	NOUN
ejpam-4675	122	7	)	)	PUNCT
ejpam-4675	122	8	for	for	ADP
ejpam-4675	122	9	all	all	DET
ejpam-4675	122	10	x	x	NOUN
ejpam-4675	122	11	,	,	PUNCT
ejpam-4675	122	12	y	y	PROPN
ejpam-4675	122	13	∈	∈	PROPN
ejpam-4675	122	14	r+	r+	ADV
ejpam-4675	122	15	,	,	PUNCT
ejpam-4675	122	16	then	then	ADV
ejpam-4675	122	17	x2	x2	PROPN
ejpam-4675	122	18	=	=	PUNCT
ejpam-4675	122	19	y2	y2	PROPN
ejpam-4675	122	20	implies	imply	VERB
ejpam-4675	122	21	that	that	SCONJ
ejpam-4675	122	22	x	x	X
ejpam-4675	122	23	=	=	SYM
ejpam-4675	122	24	y	y	PROPN
ejpam-4675	122	25	which	which	PRON
ejpam-4675	122	26	means	mean	VERB
ejpam-4675	122	27	φ	φ	PROPN
ejpam-4675	122	28	is	be	AUX
ejpam-4675	122	29	one	one	NUM
ejpam-4675	122	30	-	-	PUNCT
ejpam-4675	122	31	to	to	ADP
ejpam-4675	122	32	-	-	PUNCT
ejpam-4675	122	33	one	one	NUM
ejpam-4675	122	34	.	.	PUNCT
ejpam-4675	123	1	now	now	ADV
ejpam-4675	123	2	,	,	PUNCT
ejpam-4675	123	3	for	for	ADP
ejpam-4675	123	4	all	all	DET
ejpam-4675	123	5	y	y	PROPN
ejpam-4675	123	6	∈	∈	PROPN
ejpam-4675	123	7	r+	r+	NOUN
ejpam-4675	123	8	,	,	PUNCT
ejpam-4675	123	9	∃x	∃x	PROPN
ejpam-4675	123	10	∈	∈	PROPN
ejpam-4675	123	11	r+	r+	NOUN
ejpam-4675	123	12	such	such	ADJ
ejpam-4675	123	13	that	that	SCONJ
ejpam-4675	123	14	x	x	X
ejpam-4675	123	15	=	=	PUNCT
ejpam-4675	123	16	√	√	NUM
ejpam-4675	123	17	y	y	PROPN
ejpam-4675	123	18	implies	imply	VERB
ejpam-4675	123	19	x2	x2	PROPN
ejpam-4675	124	1	=	=	SYM
ejpam-4675	124	2	y	y	PROPN
ejpam-4675	124	3	which	which	PRON
ejpam-4675	124	4	implies	imply	VERB
ejpam-4675	124	5	that	that	SCONJ
ejpam-4675	124	6	φ(x	φ(x	NOUN
ejpam-4675	124	7	)	)	PUNCT
ejpam-4675	124	8	=	=	SYM
ejpam-4675	124	9	y	y	PROPN
ejpam-4675	125	1	and	and	CCONJ
ejpam-4675	125	2	so	so	ADV
ejpam-4675	125	3	φ	φ	PROPN
ejpam-4675	125	4	is	be	AUX
ejpam-4675	125	5	onto	onto	ADP
ejpam-4675	125	6	.	.	PUNCT
ejpam-4675	126	1	consequently	consequently	ADV
ejpam-4675	126	2	,	,	PUNCT
ejpam-4675	126	3	φ	φ	PROPN
ejpam-4675	126	4	is	be	AUX
ejpam-4675	126	5	a	a	DET
ejpam-4675	126	6	db	db	NOUN
ejpam-4675	126	7	-	-	NOUN
ejpam-4675	126	8	automorphism	automorphism	NOUN
ejpam-4675	126	9	.	.	PUNCT
ejpam-4675	127	1	the	the	DET
ejpam-4675	127	2	kernel	kernel	NOUN
ejpam-4675	127	3	of	of	ADP
ejpam-4675	127	4	this	this	DET
ejpam-4675	127	5	db	db	NOUN
ejpam-4675	127	6	-	-	PUNCT
ejpam-4675	127	7	automorphism	automorphism	NOUN
ejpam-4675	127	8	is	be	AUX
ejpam-4675	127	9	kerφ	kerφ	NOUN
ejpam-4675	127	10	=	=	PUNCT
ejpam-4675	127	11	{	{	PUNCT
ejpam-4675	127	12	x	x	PUNCT
ejpam-4675	127	13	∈	∈	PROPN
ejpam-4675	127	14	r+|φ(x	r+|φ(x	NOUN
ejpam-4675	127	15	)	)	PUNCT
ejpam-4675	127	16	=	=	SYM
ejpam-4675	127	17	1	1	X
ejpam-4675	127	18	}	}	PUNCT
ejpam-4675	127	19	=	=	PRON
ejpam-4675	127	20	{	{	PUNCT
ejpam-4675	127	21	x	x	SYM
ejpam-4675	127	22	∈	∈	PROPN
ejpam-4675	127	23	r+|x2	r+|x2	NOUN
ejpam-4675	127	24	=	=	NOUN
ejpam-4675	127	25	1	1	NUM
ejpam-4675	127	26	}	}	PUNCT
ejpam-4675	127	27	=	=	PRON
ejpam-4675	127	28	{	{	PUNCT
ejpam-4675	127	29	x	x	SYM
ejpam-4675	127	30	∈	∈	PROPN
ejpam-4675	127	31	r+|x	r+|x	ADJ
ejpam-4675	127	32	=	=	SYM
ejpam-4675	127	33	1	1	NUM
ejpam-4675	127	34	}	}	PUNCT
ejpam-4675	127	35	=	=	SYM
ejpam-4675	127	36	{	{	PUNCT
ejpam-4675	127	37	1	1	NUM
ejpam-4675	127	38	}	}	PUNCT
ejpam-4675	127	39	the	the	DET
ejpam-4675	127	40	next	next	ADJ
ejpam-4675	127	41	corollary	corollary	NOUN
ejpam-4675	127	42	,	,	PUNCT
ejpam-4675	127	43	which	which	PRON
ejpam-4675	127	44	is	be	AUX
ejpam-4675	127	45	needed	need	VERB
ejpam-4675	127	46	for	for	ADP
ejpam-4675	127	47	the	the	DET
ejpam-4675	127	48	following	follow	VERB
ejpam-4675	127	49	results	result	NOUN
ejpam-4675	127	50	,	,	PUNCT
ejpam-4675	127	51	is	be	AUX
ejpam-4675	127	52	immediate	immediate	ADJ
ejpam-4675	127	53	from	from	ADP
ejpam-4675	127	54	lemma	lemma	PROPN
ejpam-4675	127	55	1	1	NUM
ejpam-4675	127	56	and	and	CCONJ
ejpam-4675	127	57	db1	db1	NOUN
ejpam-4675	127	58	.	.	PUNCT
ejpam-4675	128	1	corollary	corollary	ADJ
ejpam-4675	128	2	1	1	NUM
ejpam-4675	128	3	.	.	PUNCT
ejpam-4675	129	1	let	let	AUX
ejpam-4675	129	2	(	(	PUNCT
ejpam-4675	129	3	x	x	NOUN
ejpam-4675	129	4	,	,	PUNCT
ejpam-4675	129	5	·	·	PUNCT
ejpam-4675	129	6	,	,	PUNCT
ejpam-4675	129	7	1	1	X
ejpam-4675	129	8	)	)	PUNCT
ejpam-4675	129	9	be	be	AUX
ejpam-4675	129	10	a	a	DET
ejpam-4675	129	11	db	db	NOUN
ejpam-4675	129	12	-	-	PUNCT
ejpam-4675	129	13	algebra	algebra	NOUN
ejpam-4675	129	14	,	,	PUNCT
ejpam-4675	129	15	then	then	ADV
ejpam-4675	129	16	for	for	ADP
ejpam-4675	129	17	any	any	DET
ejpam-4675	129	18	x	x	NOUN
ejpam-4675	129	19	,	,	PUNCT
ejpam-4675	129	20	y	y	PROPN
ejpam-4675	129	21	∈	∈	PROPN
ejpam-4675	129	22	x	x	X
ejpam-4675	129	23	,	,	PUNCT
ejpam-4675	129	24	x	x	SYM
ejpam-4675	129	25	=	=	SYM
ejpam-4675	129	26	y	y	PROPN
ejpam-4675	129	27	implies	imply	VERB
ejpam-4675	129	28	that	that	SCONJ
ejpam-4675	129	29	x	x	X
ejpam-4675	129	30	·	·	PUNCT
ejpam-4675	129	31	y	y	SYM
ejpam-4675	129	32	=	=	SYM
ejpam-4675	129	33	1	1	X
ejpam-4675	129	34	.	.	PUNCT
ejpam-4675	129	35	theorem	theorem	NOUN
ejpam-4675	129	36	4	4	NUM
ejpam-4675	129	37	.	.	PUNCT
ejpam-4675	130	1	let	let	VERB
ejpam-4675	130	2	φ	φ	NOUN
ejpam-4675	130	3	:	:	PUNCT
ejpam-4675	130	4	x	x	X
ejpam-4675	130	5	→	→	SYM
ejpam-4675	130	6	y	y	X
ejpam-4675	130	7	be	be	AUX
ejpam-4675	130	8	a	a	DET
ejpam-4675	130	9	db	db	NOUN
ejpam-4675	130	10	-	-	PUNCT
ejpam-4675	130	11	homomorphism	homomorphism	NOUN
ejpam-4675	130	12	,	,	PUNCT
ejpam-4675	130	13	(	(	PUNCT
ejpam-4675	130	14	x	x	X
ejpam-4675	130	15	,	,	PUNCT
ejpam-4675	130	16	·	·	PUNCT
ejpam-4675	130	17	,	,	PUNCT
ejpam-4675	130	18	1x	1x	NUM
ejpam-4675	130	19	)	)	PUNCT
ejpam-4675	130	20	,	,	PUNCT
ejpam-4675	130	21	(	(	PUNCT
ejpam-4675	130	22	y	y	NOUN
ejpam-4675	130	23	,	,	PUNCT
ejpam-4675	130	24	∗	∗	NOUN
ejpam-4675	130	25	,	,	PUNCT
ejpam-4675	130	26	1y	1y	NUM
ejpam-4675	130	27	)	)	PUNCT
ejpam-4675	130	28	be	be	VERB
ejpam-4675	130	29	dbalgebras	dbalgebra	NOUN
ejpam-4675	130	30	,	,	PUNCT
ejpam-4675	130	31	and	and	CCONJ
ejpam-4675	130	32	s	s	VERB
ejpam-4675	130	33	⊆	⊆	NUM
ejpam-4675	130	34	x	x	NOUN
ejpam-4675	130	35	,	,	PUNCT
ejpam-4675	130	36	then	then	ADV
ejpam-4675	130	37	(	(	PUNCT
ejpam-4675	130	38	i	i	NOUN
ejpam-4675	130	39	)	)	PUNCT
ejpam-4675	130	40	φ(1x	φ(1x	PROPN
ejpam-4675	130	41	)	)	PUNCT
ejpam-4675	131	1	=	=	SYM
ejpam-4675	131	2	1y	1y	PROPN
ejpam-4675	131	3	(	(	PUNCT
ejpam-4675	131	4	ii	ii	NOUN
ejpam-4675	131	5	)	)	PUNCT
ejpam-4675	131	6	φ	φ	PROPN
ejpam-4675	131	7	is	be	AUX
ejpam-4675	131	8	a	a	DET
ejpam-4675	131	9	db	db	NOUN
ejpam-4675	131	10	-	-	PUNCT
ejpam-4675	131	11	monomorphism	monomorphism	NOUN
ejpam-4675	131	12	,	,	PUNCT
ejpam-4675	131	13	if	if	SCONJ
ejpam-4675	131	14	and	and	CCONJ
ejpam-4675	131	15	only	only	ADV
ejpam-4675	131	16	if	if	SCONJ
ejpam-4675	131	17	kerφ	kerφ	PROPN
ejpam-4675	131	18	=	=	PUNCT
ejpam-4675	131	19	{	{	PUNCT
ejpam-4675	131	20	1x	1x	NUM
ejpam-4675	131	21	}	}	PUNCT
ejpam-4675	131	22	(	(	PUNCT
ejpam-4675	131	23	iii	iii	NOUN
ejpam-4675	131	24	)	)	PUNCT
ejpam-4675	131	25	im(φ	im(φ	NUM
ejpam-4675	131	26	)	)	PUNCT
ejpam-4675	131	27	is	be	AUX
ejpam-4675	131	28	a	a	DET
ejpam-4675	131	29	db	db	NOUN
ejpam-4675	131	30	-	-	PUNCT
ejpam-4675	131	31	subalgebra	subalgebra	NOUN
ejpam-4675	131	32	of	of	ADP
ejpam-4675	131	33	y	y	PROPN
ejpam-4675	131	34	.	.	PUNCT
ejpam-4675	132	1	(	(	PUNCT
ejpam-4675	132	2	iv	iv	X
ejpam-4675	132	3	)	)	PUNCT
ejpam-4675	132	4	kerφ	kerφ	PROPN
ejpam-4675	132	5	is	be	AUX
ejpam-4675	132	6	a	a	DET
ejpam-4675	132	7	db	db	NOUN
ejpam-4675	132	8	-	-	PUNCT
ejpam-4675	132	9	filter	filter	NOUN
ejpam-4675	132	10	of	of	ADP
ejpam-4675	132	11	x	x	X
ejpam-4675	132	12	and	and	CCONJ
ejpam-4675	132	13	consequently	consequently	ADV
ejpam-4675	132	14	a	a	DET
ejpam-4675	132	15	db	db	NOUN
ejpam-4675	132	16	-	-	PUNCT
ejpam-4675	132	17	subalgebra	subalgebra	NOUN
ejpam-4675	132	18	of	of	ADP
ejpam-4675	132	19	x.	x.	PROPN
ejpam-4675	132	20	(	(	PUNCT
ejpam-4675	132	21	v	v	NOUN
ejpam-4675	132	22	)	)	PUNCT
ejpam-4675	132	23	if	if	SCONJ
ejpam-4675	132	24	s	s	VERB
ejpam-4675	132	25	is	be	AUX
ejpam-4675	132	26	a	a	DET
ejpam-4675	132	27	db	db	NOUN
ejpam-4675	132	28	-	-	PUNCT
ejpam-4675	132	29	filter	filter	NOUN
ejpam-4675	132	30	of	of	ADP
ejpam-4675	132	31	x	x	NOUN
ejpam-4675	132	32	,	,	PUNCT
ejpam-4675	132	33	then	then	ADV
ejpam-4675	132	34	φ(s	φ(s	NOUN
ejpam-4675	132	35	)	)	PUNCT
ejpam-4675	132	36	is	be	AUX
ejpam-4675	132	37	a	a	DET
ejpam-4675	132	38	db	db	NOUN
ejpam-4675	132	39	-	-	PUNCT
ejpam-4675	132	40	filter	filter	NOUN
ejpam-4675	132	41	of	of	ADP
ejpam-4675	132	42	y	y	PROPN
ejpam-4675	132	43	and	and	CCONJ
ejpam-4675	132	44	consequently	consequently	ADV
ejpam-4675	132	45	a	a	DET
ejpam-4675	132	46	dbsubalgebra	dbsubalgebra	NOUN
ejpam-4675	132	47	of	of	ADP
ejpam-4675	132	48	y	y	PROPN
ejpam-4675	132	49	.	.	PUNCT
ejpam-4675	133	1	proof	proof	NOUN
ejpam-4675	133	2	.	.	PUNCT
ejpam-4675	134	1	suppose	suppose	VERB
ejpam-4675	135	1	φ	φ	X
ejpam-4675	135	2	:	:	PUNCT
ejpam-4675	135	3	x	x	X
ejpam-4675	135	4	→	→	SYM
ejpam-4675	135	5	y	y	X
ejpam-4675	135	6	be	be	AUX
ejpam-4675	135	7	a	a	DET
ejpam-4675	135	8	db	db	NOUN
ejpam-4675	135	9	-	-	PUNCT
ejpam-4675	135	10	homomorphism	homomorphism	NOUN
ejpam-4675	135	11	and	and	CCONJ
ejpam-4675	135	12	s	s	VERB
ejpam-4675	135	13	⊆	⊆	NUM
ejpam-4675	135	14	x	x	X
ejpam-4675	135	15	,	,	PUNCT
ejpam-4675	135	16	(	(	PUNCT
ejpam-4675	135	17	i	i	NOUN
ejpam-4675	135	18	)	)	PUNCT
ejpam-4675	135	19	since	since	SCONJ
ejpam-4675	135	20	φ	φ	PROPN
ejpam-4675	135	21	is	be	AUX
ejpam-4675	135	22	a	a	DET
ejpam-4675	135	23	db	db	NOUN
ejpam-4675	135	24	-	-	PUNCT
ejpam-4675	135	25	homomorphism	homomorphism	NOUN
ejpam-4675	135	26	and	and	CCONJ
ejpam-4675	135	27	by	by	ADP
ejpam-4675	135	28	db1	db1	NOUN
ejpam-4675	135	29	,	,	PUNCT
ejpam-4675	135	30	φ(1x	φ(1x	PROPN
ejpam-4675	135	31	)	)	PUNCT
ejpam-4675	135	32	=	=	PUNCT
ejpam-4675	136	1	φ(1x	φ(1x	PROPN
ejpam-4675	136	2	·	·	PUNCT
ejpam-4675	136	3	1x	1x	NUM
ejpam-4675	136	4	)	)	PUNCT
ejpam-4675	136	5	=	=	SYM
ejpam-4675	137	1	φ(1x	φ(1x	PROPN
ejpam-4675	137	2	)	)	PUNCT
ejpam-4675	137	3	∗	∗	NOUN
ejpam-4675	137	4	φ(1x	φ(1x	PROPN
ejpam-4675	137	5	)	)	PUNCT
ejpam-4675	138	1	=	=	SYM
ejpam-4675	138	2	1y	1y	X
ejpam-4675	138	3	.	.	PUNCT
ejpam-4675	139	1	j.e	j.e	PROPN
ejpam-4675	139	2	.	.	PROPN
ejpam-4675	139	3	bolima	bolima	PROPN
ejpam-4675	139	4	,	,	PUNCT
ejpam-4675	139	5	k.b	k.b	PROPN
ejpam-4675	139	6	.	.	PUNCT
ejpam-4675	139	7	fuentes	fuentes	PROPN
ejpam-4675	139	8	/	/	SYM
ejpam-4675	139	9	eur	eur	PROPN
ejpam-4675	139	10	.	.	PUNCT
ejpam-4675	140	1	j.	j.	PROPN
ejpam-4675	140	2	pure	pure	PROPN
ejpam-4675	140	3	appl	appl	PROPN
ejpam-4675	140	4	.	.	PROPN
ejpam-4675	140	5	math	math	PROPN
ejpam-4675	140	6	,	,	PUNCT
ejpam-4675	140	7	16	16	NUM
ejpam-4675	140	8	(	(	PUNCT
ejpam-4675	140	9	1	1	NUM
ejpam-4675	140	10	)	)	PUNCT
ejpam-4675	140	11	(	(	PUNCT
ejpam-4675	140	12	2023	2023	NUM
ejpam-4675	140	13	)	)	PUNCT
ejpam-4675	140	14	,	,	PUNCT
ejpam-4675	140	15	577	577	NUM
ejpam-4675	140	16	-	-	SYM
ejpam-4675	140	17	586	586	NUM
ejpam-4675	140	18	582	582	NUM
ejpam-4675	140	19	(	(	PUNCT
ejpam-4675	140	20	ii	ii	NOUN
ejpam-4675	140	21	)	)	PUNCT
ejpam-4675	140	22	suppose	suppose	VERB
ejpam-4675	140	23	φ	φ	PROPN
ejpam-4675	140	24	is	be	AUX
ejpam-4675	140	25	a	a	DET
ejpam-4675	140	26	db	db	NOUN
ejpam-4675	140	27	-	-	PUNCT
ejpam-4675	140	28	monomorphism	monomorphism	NOUN
ejpam-4675	140	29	.	.	PUNCT
ejpam-4675	141	1	it	it	PRON
ejpam-4675	141	2	follows	follow	VERB
ejpam-4675	141	3	from	from	ADP
ejpam-4675	141	4	(	(	PUNCT
ejpam-4675	141	5	i.	i.	NOUN
ejpam-4675	141	6	)	)	PUNCT
ejpam-4675	142	1	that	that	PRON
ejpam-4675	142	2	1x	1x	PROPN
ejpam-4675	142	3	∈	∈	PROPN
ejpam-4675	142	4	kerφ	kerφ	PROPN
ejpam-4675	142	5	.	.	PUNCT
ejpam-4675	142	6	let	let	VERB
ejpam-4675	142	7	x	x	SYM
ejpam-4675	142	8	∈	∈	PROPN
ejpam-4675	142	9	kerφ	kerφ	PROPN
ejpam-4675	142	10	.	.	PUNCT
ejpam-4675	143	1	then	then	ADV
ejpam-4675	143	2	φ(x	φ(x	NOUN
ejpam-4675	143	3	)	)	PUNCT
ejpam-4675	143	4	=	=	SYM
ejpam-4675	143	5	1y	1y	NUM
ejpam-4675	143	6	=	=	SYM
ejpam-4675	143	7	φ(1x	φ(1x	NOUN
ejpam-4675	143	8	)	)	PUNCT
ejpam-4675	143	9	.	.	PUNCT
ejpam-4675	144	1	since	since	SCONJ
ejpam-4675	144	2	φ	φ	PROPN
ejpam-4675	144	3	is	be	AUX
ejpam-4675	144	4	one	one	NUM
ejpam-4675	144	5	-	-	PUNCT
ejpam-4675	144	6	to	to	ADP
ejpam-4675	144	7	-	-	PUNCT
ejpam-4675	144	8	one	one	NUM
ejpam-4675	144	9	,	,	PUNCT
ejpam-4675	144	10	φ(x	φ(x	PROPN
ejpam-4675	144	11	)	)	PUNCT
ejpam-4675	144	12	=	=	SYM
ejpam-4675	144	13	φ(1x	φ(1x	PROPN
ejpam-4675	144	14	)	)	PUNCT
ejpam-4675	144	15	implies	imply	VERB
ejpam-4675	144	16	x	x	PUNCT
ejpam-4675	144	17	=	=	SYM
ejpam-4675	144	18	1x	1x	NUM
ejpam-4675	144	19	.	.	PUNCT
ejpam-4675	145	1	hence	hence	ADV
ejpam-4675	145	2	,	,	PUNCT
ejpam-4675	145	3	kerφ	kerφ	PROPN
ejpam-4675	145	4	=	=	PUNCT
ejpam-4675	145	5	{	{	PUNCT
ejpam-4675	145	6	1x	1x	NUM
ejpam-4675	145	7	}	}	PUNCT
ejpam-4675	145	8	.	.	PUNCT
ejpam-4675	146	1	conversely	conversely	ADV
ejpam-4675	146	2	,	,	PUNCT
ejpam-4675	146	3	suppose	suppose	VERB
ejpam-4675	146	4	kerφ	kerφ	PROPN
ejpam-4675	146	5	=	=	SYM
ejpam-4675	146	6	{	{	PUNCT
ejpam-4675	146	7	1x	1x	NUM
ejpam-4675	146	8	}	}	PUNCT
ejpam-4675	146	9	and	and	CCONJ
ejpam-4675	146	10	x	x	X
ejpam-4675	146	11	,	,	PUNCT
ejpam-4675	146	12	y	y	PROPN
ejpam-4675	146	13	∈	∈	PROPN
ejpam-4675	146	14	x	x	PUNCT
ejpam-4675	146	15	such	such	ADJ
ejpam-4675	146	16	that	that	SCONJ
ejpam-4675	146	17	φ(x	φ(x	NOUN
ejpam-4675	146	18	)	)	PUNCT
ejpam-4675	146	19	=	=	SYM
ejpam-4675	146	20	φ(y	φ(y	NOUN
ejpam-4675	146	21	)	)	PUNCT
ejpam-4675	146	22	.	.	PUNCT
ejpam-4675	147	1	by	by	ADP
ejpam-4675	147	2	corollary	corollary	ADJ
ejpam-4675	147	3	1	1	NUM
ejpam-4675	147	4	,	,	PUNCT
ejpam-4675	147	5	φ(x	φ(x	NOUN
ejpam-4675	147	6	)	)	PUNCT
ejpam-4675	147	7	∗	∗	NOUN
ejpam-4675	147	8	φ(y	φ(y	NOUN
ejpam-4675	147	9	)	)	PUNCT
ejpam-4675	147	10	=	=	SYM
ejpam-4675	147	11	1y	1y	NUM
ejpam-4675	147	12	=	=	SYM
ejpam-4675	147	13	φ(x	φ(x	PROPN
ejpam-4675	147	14	·	·	PUNCT
ejpam-4675	147	15	y	y	X
ejpam-4675	147	16	)	)	PUNCT
ejpam-4675	147	17	.	.	PUNCT
ejpam-4675	148	1	then	then	ADV
ejpam-4675	148	2	x	x	X
ejpam-4675	148	3	·	·	PUNCT
ejpam-4675	148	4	y	y	PROPN
ejpam-4675	148	5	∈	∈	PROPN
ejpam-4675	148	6	kerφ	kerφ	PROPN
ejpam-4675	148	7	.	.	PUNCT
ejpam-4675	149	1	since	since	SCONJ
ejpam-4675	149	2	kerφ	kerφ	PROPN
ejpam-4675	149	3	=	=	PUNCT
ejpam-4675	149	4	{	{	PUNCT
ejpam-4675	149	5	1x	1x	NUM
ejpam-4675	149	6	}	}	PUNCT
ejpam-4675	149	7	,	,	PUNCT
ejpam-4675	149	8	x	x	X
ejpam-4675	149	9	·	·	PUNCT
ejpam-4675	149	10	y	y	X
ejpam-4675	149	11	=	=	PUNCT
ejpam-4675	149	12	1x	1x	PROPN
ejpam-4675	149	13	and	and	CCONJ
ejpam-4675	149	14	it	it	PRON
ejpam-4675	149	15	follows	follow	VERB
ejpam-4675	149	16	that	that	SCONJ
ejpam-4675	149	17	x	x	X
ejpam-4675	149	18	=	=	SYM
ejpam-4675	149	19	y	y	PROPN
ejpam-4675	149	20	by	by	ADP
ejpam-4675	149	21	lemma	lemma	PROPN
ejpam-4675	149	22	1	1	NUM
ejpam-4675	149	23	.	.	PUNCT
ejpam-4675	150	1	hence	hence	ADV
ejpam-4675	150	2	,	,	PUNCT
ejpam-4675	150	3	φ	φ	PROPN
ejpam-4675	150	4	is	be	AUX
ejpam-4675	150	5	one	one	NUM
ejpam-4675	150	6	-	-	PUNCT
ejpam-4675	150	7	to	to	ADP
ejpam-4675	150	8	-	-	PUNCT
ejpam-4675	150	9	one	one	NUM
ejpam-4675	150	10	i.e.	i.e.	X
ejpam-4675	150	11	φ	φ	PROPN
ejpam-4675	150	12	is	be	AUX
ejpam-4675	150	13	a	a	DET
ejpam-4675	150	14	db	db	NOUN
ejpam-4675	150	15	-	-	PUNCT
ejpam-4675	150	16	monomorphism	monomorphism	NOUN
ejpam-4675	150	17	.	.	PUNCT
ejpam-4675	151	1	(	(	PUNCT
ejpam-4675	151	2	iii	iii	X
ejpam-4675	151	3	)	)	PUNCT
ejpam-4675	151	4	let	let	VERB
ejpam-4675	151	5	x	x	PRON
ejpam-4675	151	6	,	,	PUNCT
ejpam-4675	151	7	y	y	PROPN
ejpam-4675	151	8	∈	∈	PROPN
ejpam-4675	151	9	im(φ	im(φ	PROPN
ejpam-4675	151	10	)	)	PUNCT
ejpam-4675	151	11	.	.	PUNCT
ejpam-4675	152	1	then	then	ADV
ejpam-4675	152	2	there	there	PRON
ejpam-4675	152	3	exists	exist	VERB
ejpam-4675	152	4	a	a	DET
ejpam-4675	152	5	,	,	PUNCT
ejpam-4675	152	6	b	b	X
ejpam-4675	152	7	∈	∈	PROPN
ejpam-4675	152	8	x	x	X
ejpam-4675	152	9	such	such	ADJ
ejpam-4675	152	10	that	that	SCONJ
ejpam-4675	152	11	x	x	SYM
ejpam-4675	152	12	=	=	SYM
ejpam-4675	152	13	φ(a	φ(a	PROPN
ejpam-4675	152	14	)	)	PUNCT
ejpam-4675	152	15	,	,	PUNCT
ejpam-4675	152	16	y	y	PROPN
ejpam-4675	152	17	=	=	PUNCT
ejpam-4675	152	18	φ(b	φ(b	PROPN
ejpam-4675	152	19	)	)	PUNCT
ejpam-4675	152	20	.	.	PUNCT
ejpam-4675	153	1	this	this	PRON
ejpam-4675	153	2	implies	imply	VERB
ejpam-4675	153	3	that	that	SCONJ
ejpam-4675	153	4	x	x	SYM
ejpam-4675	153	5	∗	∗	VERB
ejpam-4675	153	6	y	y	NOUN
ejpam-4675	153	7	=	=	PUNCT
ejpam-4675	153	8	φ(a	φ(a	ADJ
ejpam-4675	153	9	)	)	PUNCT
ejpam-4675	153	10	∗	∗	NOUN
ejpam-4675	153	11	φ(b	φ(b	ADP
ejpam-4675	153	12	)	)	PUNCT
ejpam-4675	153	13	=	=	SYM
ejpam-4675	153	14	φ(a	φ(a	PROPN
ejpam-4675	153	15	·	·	PUNCT
ejpam-4675	153	16	b	b	X
ejpam-4675	153	17	)	)	PUNCT
ejpam-4675	153	18	∈	∈	PROPN
ejpam-4675	153	19	im(φ	im(φ	NUM
ejpam-4675	153	20	)	)	PUNCT
ejpam-4675	153	21	since	since	SCONJ
ejpam-4675	153	22	a	a	DET
ejpam-4675	153	23	·	·	SYM
ejpam-4675	153	24	b	b	SYM
ejpam-4675	153	25	∈	∈	PROPN
ejpam-4675	153	26	x.	x.	NOUN
ejpam-4675	153	27	thus	thus	ADV
ejpam-4675	153	28	,	,	PUNCT
ejpam-4675	153	29	im(φ	im(φ	PRON
ejpam-4675	153	30	)	)	PUNCT
ejpam-4675	153	31	is	be	AUX
ejpam-4675	153	32	a	a	DET
ejpam-4675	153	33	db	db	NOUN
ejpam-4675	153	34	-	-	PUNCT
ejpam-4675	153	35	subalgebra	subalgebra	NOUN
ejpam-4675	153	36	of	of	ADP
ejpam-4675	153	37	y	y	PROPN
ejpam-4675	153	38	.	.	PUNCT
ejpam-4675	154	1	(	(	PUNCT
ejpam-4675	154	2	iv	iv	X
ejpam-4675	154	3	)	)	PUNCT
ejpam-4675	154	4	by	by	ADP
ejpam-4675	154	5	definition	definition	NOUN
ejpam-4675	154	6	6	6	NUM
ejpam-4675	154	7	,	,	PUNCT
ejpam-4675	154	8	kerφ	kerφ	VERB
ejpam-4675	154	9	⊆	⊆	X
ejpam-4675	154	10	x	x	PUNCT
ejpam-4675	154	11	and	and	CCONJ
ejpam-4675	154	12	by	by	ADP
ejpam-4675	154	13	(	(	PUNCT
ejpam-4675	154	14	i.	i.	PROPN
ejpam-4675	154	15	)	)	PUNCT
ejpam-4675	154	16	,	,	PUNCT
ejpam-4675	154	17	1x	1x	PROPN
ejpam-4675	154	18	∈	∈	PROPN
ejpam-4675	154	19	kerφ	kerφ	PROPN
ejpam-4675	154	20	which	which	PRON
ejpam-4675	154	21	also	also	ADV
ejpam-4675	154	22	implies	imply	VERB
ejpam-4675	154	23	that	that	SCONJ
ejpam-4675	154	24	kerφ	kerφ	PROPN
ejpam-4675	154	25	̸=	̸=	PROPN
ejpam-4675	154	26	∅.	∅.	ADV
ejpam-4675	154	27	let	let	VERB
ejpam-4675	154	28	x	x	X
ejpam-4675	154	29	·	·	PUNCT
ejpam-4675	154	30	y	y	PROPN
ejpam-4675	154	31	∈	∈	PROPN
ejpam-4675	154	32	kerφ	kerφ	PROPN
ejpam-4675	154	33	and	and	CCONJ
ejpam-4675	154	34	x	x	PROPN
ejpam-4675	154	35	∈	∈	PROPN
ejpam-4675	154	36	kerφ	kerφ	PROPN
ejpam-4675	154	37	.	.	PUNCT
ejpam-4675	155	1	then	then	ADV
ejpam-4675	155	2	for	for	ADP
ejpam-4675	155	3	all	all	DET
ejpam-4675	155	4	y	y	PROPN
ejpam-4675	155	5	∈	∈	PROPN
ejpam-4675	155	6	x	x	NOUN
ejpam-4675	155	7	,	,	PUNCT
ejpam-4675	155	8	φ(y	φ(y	ADJ
ejpam-4675	155	9	)	)	PUNCT
ejpam-4675	155	10	=	=	SYM
ejpam-4675	155	11	1y	1y	PROPN
ejpam-4675	155	12	∗	∗	NOUN
ejpam-4675	155	13	φ(y	φ(y	NOUN
ejpam-4675	155	14	)	)	PUNCT
ejpam-4675	155	15	=	=	SYM
ejpam-4675	155	16	φ(x	φ(x	NOUN
ejpam-4675	155	17	)	)	PUNCT
ejpam-4675	155	18	∗	∗	NOUN
ejpam-4675	155	19	φ(y	φ(y	NOUN
ejpam-4675	155	20	)	)	PUNCT
ejpam-4675	155	21	=	=	SYM
ejpam-4675	155	22	φ(x	φ(x	PROPN
ejpam-4675	155	23	·	·	PUNCT
ejpam-4675	155	24	y	y	X
ejpam-4675	155	25	)	)	PUNCT
ejpam-4675	155	26	=	=	SYM
ejpam-4675	155	27	1y	1y	NOUN
ejpam-4675	155	28	.	.	PUNCT
ejpam-4675	156	1	hence	hence	ADV
ejpam-4675	156	2	,	,	PUNCT
ejpam-4675	156	3	y	y	PROPN
ejpam-4675	156	4	∈	∈	PROPN
ejpam-4675	156	5	kerφ	kerφ	PROPN
ejpam-4675	156	6	and	and	CCONJ
ejpam-4675	156	7	it	it	PRON
ejpam-4675	156	8	follows	follow	VERB
ejpam-4675	156	9	that	that	SCONJ
ejpam-4675	156	10	kerφ	kerφ	PROPN
ejpam-4675	156	11	is	be	AUX
ejpam-4675	156	12	a	a	DET
ejpam-4675	156	13	db	db	NOUN
ejpam-4675	156	14	-	-	PUNCT
ejpam-4675	156	15	filter	filter	NOUN
ejpam-4675	156	16	of	of	ADP
ejpam-4675	156	17	x.	x.	NOUN
ejpam-4675	156	18	consequently	consequently	ADV
ejpam-4675	156	19	,	,	PUNCT
ejpam-4675	156	20	by	by	ADP
ejpam-4675	156	21	theorem	theorem	NOUN
ejpam-4675	156	22	1	1	NUM
ejpam-4675	156	23	,	,	PUNCT
ejpam-4675	156	24	kerφ	kerφ	PROPN
ejpam-4675	156	25	is	be	AUX
ejpam-4675	156	26	a	a	DET
ejpam-4675	156	27	db	db	NOUN
ejpam-4675	156	28	-	-	PUNCT
ejpam-4675	156	29	subalgebra	subalgebra	NOUN
ejpam-4675	156	30	of	of	ADP
ejpam-4675	156	31	x.	x.	PROPN
ejpam-4675	156	32	(	(	PUNCT
ejpam-4675	156	33	v	v	NOUN
ejpam-4675	156	34	)	)	PUNCT
ejpam-4675	156	35	let	let	VERB
ejpam-4675	156	36	s	s	PRON
ejpam-4675	156	37	be	be	AUX
ejpam-4675	156	38	a	a	DET
ejpam-4675	156	39	db	db	NOUN
ejpam-4675	156	40	-	-	PUNCT
ejpam-4675	156	41	filter	filter	NOUN
ejpam-4675	156	42	of	of	ADP
ejpam-4675	156	43	x	x	NOUN
ejpam-4675	156	44	,	,	PUNCT
ejpam-4675	156	45	then	then	ADV
ejpam-4675	156	46	1x	1x	PROPN
ejpam-4675	156	47	∈	∈	PROPN
ejpam-4675	156	48	s	s	X
ejpam-4675	156	49	and	and	CCONJ
ejpam-4675	156	50	by	by	ADP
ejpam-4675	156	51	(	(	PUNCT
ejpam-4675	156	52	i.	i.	NOUN
ejpam-4675	156	53	)	)	PUNCT
ejpam-4675	156	54	,	,	PUNCT
ejpam-4675	156	55	φ(1x	φ(1x	PROPN
ejpam-4675	156	56	)	)	PUNCT
ejpam-4675	157	1	=	=	SYM
ejpam-4675	157	2	1y	1y	NUM
ejpam-4675	157	3	∈	∈	PROPN
ejpam-4675	157	4	φ(s	φ(s	NOUN
ejpam-4675	157	5	)	)	PUNCT
ejpam-4675	157	6	.	.	PUNCT
ejpam-4675	158	1	now	now	ADV
ejpam-4675	158	2	,	,	PUNCT
ejpam-4675	158	3	for	for	ADP
ejpam-4675	158	4	all	all	DET
ejpam-4675	158	5	x	x	NOUN
ejpam-4675	158	6	,	,	PUNCT
ejpam-4675	158	7	y	y	PROPN
ejpam-4675	158	8	∈	∈	PROPN
ejpam-4675	158	9	x	x	PUNCT
ejpam-4675	158	10	such	such	ADJ
ejpam-4675	158	11	that	that	SCONJ
ejpam-4675	158	12	x	x	SYM
ejpam-4675	158	13	∈	∈	NOUN
ejpam-4675	158	14	s	s	X
ejpam-4675	158	15	and	and	CCONJ
ejpam-4675	158	16	x	x	SYM
ejpam-4675	158	17	·	·	PUNCT
ejpam-4675	158	18	y	y	X
ejpam-4675	158	19	∈	∈	PROPN
ejpam-4675	158	20	s	s	PART
ejpam-4675	158	21	implies	imply	VERB
ejpam-4675	158	22	that	that	SCONJ
ejpam-4675	158	23	φ(x	φ(x	NOUN
ejpam-4675	158	24	)	)	PUNCT
ejpam-4675	158	25	∈	∈	PROPN
ejpam-4675	158	26	φ(s	φ(s	NOUN
ejpam-4675	158	27	)	)	PUNCT
ejpam-4675	158	28	and	and	CCONJ
ejpam-4675	158	29	φ(x	φ(x	NOUN
ejpam-4675	158	30	)	)	PUNCT
ejpam-4675	158	31	∗φ(y	∗φ(y	NOUN
ejpam-4675	158	32	)	)	PUNCT
ejpam-4675	158	33	=	=	SYM
ejpam-4675	158	34	φ(x	φ(x	PROPN
ejpam-4675	158	35	·	·	PUNCT
ejpam-4675	158	36	y	y	X
ejpam-4675	158	37	)	)	PUNCT
ejpam-4675	158	38	∈	∈	PROPN
ejpam-4675	158	39	s.	s.	PROPN
ejpam-4675	158	40	since	since	SCONJ
ejpam-4675	158	41	s	s	PROPN
ejpam-4675	158	42	is	be	AUX
ejpam-4675	158	43	a	a	DET
ejpam-4675	158	44	db	db	NOUN
ejpam-4675	158	45	-	-	PUNCT
ejpam-4675	158	46	filter	filter	NOUN
ejpam-4675	158	47	of	of	ADP
ejpam-4675	158	48	x	x	NOUN
ejpam-4675	158	49	,	,	PUNCT
ejpam-4675	158	50	then	then	ADV
ejpam-4675	158	51	y	y	PROPN
ejpam-4675	158	52	∈	∈	PROPN
ejpam-4675	158	53	s	s	VERB
ejpam-4675	158	54	also	also	ADV
ejpam-4675	158	55	implies	imply	VERB
ejpam-4675	158	56	that	that	SCONJ
ejpam-4675	158	57	φ(y	φ(y	NOUN
ejpam-4675	158	58	)	)	PUNCT
ejpam-4675	158	59	∈	∈	PROPN
ejpam-4675	158	60	φ(s	φ(s	NOUN
ejpam-4675	158	61	)	)	PUNCT
ejpam-4675	158	62	.	.	PUNCT
ejpam-4675	159	1	hence	hence	ADV
ejpam-4675	159	2	,	,	PUNCT
ejpam-4675	159	3	φ(s	φ(s	NOUN
ejpam-4675	159	4	)	)	PUNCT
ejpam-4675	159	5	is	be	AUX
ejpam-4675	159	6	a	a	DET
ejpam-4675	159	7	db	db	NOUN
ejpam-4675	159	8	-	-	PUNCT
ejpam-4675	159	9	filter	filter	NOUN
ejpam-4675	159	10	of	of	ADP
ejpam-4675	159	11	y	y	PROPN
ejpam-4675	159	12	.	.	PUNCT
ejpam-4675	160	1	consequently	consequently	ADV
ejpam-4675	160	2	,	,	PUNCT
ejpam-4675	160	3	by	by	ADP
ejpam-4675	160	4	theorem	theorem	NOUN
ejpam-4675	160	5	1	1	NUM
ejpam-4675	160	6	,	,	PUNCT
ejpam-4675	160	7	φ(s	φ(s	NOUN
ejpam-4675	160	8	)	)	PUNCT
ejpam-4675	160	9	is	be	AUX
ejpam-4675	160	10	a	a	DET
ejpam-4675	160	11	db	db	NOUN
ejpam-4675	160	12	-	-	PUNCT
ejpam-4675	160	13	subalgebra	subalgebra	NOUN
ejpam-4675	160	14	of	of	ADP
ejpam-4675	160	15	y	y	PROPN
ejpam-4675	160	16	.	.	PUNCT
ejpam-4675	161	1	theorem	theorem	ADJ
ejpam-4675	161	2	5	5	NUM
ejpam-4675	161	3	.	.	PUNCT
ejpam-4675	162	1	let	let	VERB
ejpam-4675	162	2	s	s	PRON
ejpam-4675	162	3	be	be	AUX
ejpam-4675	162	4	a	a	DET
ejpam-4675	162	5	normal	normal	ADJ
ejpam-4675	162	6	db	db	NOUN
ejpam-4675	162	7	-	-	PUNCT
ejpam-4675	162	8	subalgebra	subalgebra	NOUN
ejpam-4675	162	9	(	(	PUNCT
ejpam-4675	162	10	normal	normal	ADJ
ejpam-4675	162	11	db	db	NOUN
ejpam-4675	162	12	-	-	PUNCT
ejpam-4675	162	13	filter	filter	NOUN
ejpam-4675	162	14	)	)	PUNCT
ejpam-4675	162	15	of	of	ADP
ejpam-4675	162	16	a	a	DET
ejpam-4675	162	17	db	db	NOUN
ejpam-4675	162	18	-	-	PUNCT
ejpam-4675	162	19	algebra	algebra	NOUN
ejpam-4675	162	20	(	(	PUNCT
ejpam-4675	162	21	x	x	X
ejpam-4675	162	22	,	,	PUNCT
ejpam-4675	162	23	·	·	PUNCT
ejpam-4675	162	24	,	,	PUNCT
ejpam-4675	162	25	1	1	NUM
ejpam-4675	162	26	)	)	PUNCT
ejpam-4675	162	27	.	.	PUNCT
ejpam-4675	163	1	then	then	ADV
ejpam-4675	163	2	the	the	DET
ejpam-4675	163	3	mapping	mapping	NOUN
ejpam-4675	163	4	φ	φ	NOUN
ejpam-4675	163	5	:	:	PUNCT
ejpam-4675	163	6	(	(	PUNCT
ejpam-4675	163	7	x	x	X
ejpam-4675	163	8	,	,	PUNCT
ejpam-4675	163	9	·	·	PUNCT
ejpam-4675	163	10	,	,	PUNCT
ejpam-4675	163	11	1	1	NUM
ejpam-4675	163	12	)	)	PUNCT
ejpam-4675	163	13	→	→	SYM
ejpam-4675	163	14	(	(	PUNCT
ejpam-4675	163	15	x	x	X
ejpam-4675	163	16	/	/	SYM
ejpam-4675	163	17	s	s	PROPN
ejpam-4675	163	18	,	,	PUNCT
ejpam-4675	163	19	∗	∗	NOUN
ejpam-4675	163	20	,	,	PUNCT
ejpam-4675	163	21	[	[	X
ejpam-4675	163	22	1]s	1]s	NOUN
ejpam-4675	163	23	)	)	PUNCT
ejpam-4675	163	24	given	give	VERB
ejpam-4675	163	25	by	by	ADP
ejpam-4675	163	26	φ(x	φ(x	NOUN
ejpam-4675	163	27	)	)	PUNCT
ejpam-4675	163	28	=	=	PUNCT
ejpam-4675	164	1	[	[	X
ejpam-4675	164	2	x]s	x]s	NOUN
ejpam-4675	164	3	for	for	ADP
ejpam-4675	164	4	all	all	DET
ejpam-4675	164	5	x	x	SYM
ejpam-4675	164	6	∈	∈	NOUN
ejpam-4675	164	7	x	x	X
ejpam-4675	164	8	is	be	AUX
ejpam-4675	164	9	a	a	DET
ejpam-4675	164	10	db	db	NOUN
ejpam-4675	164	11	-	-	PUNCT
ejpam-4675	164	12	epimorphism	epimorphism	NOUN
ejpam-4675	164	13	and	and	CCONJ
ejpam-4675	164	14	kerφ	kerφ	PROPN
ejpam-4675	164	15	=	=	PUNCT
ejpam-4675	164	16	s.	s.	PROPN
ejpam-4675	164	17	the	the	DET
ejpam-4675	164	18	mapping	mapping	NOUN
ejpam-4675	164	19	φ	φ	PROPN
ejpam-4675	164	20	in	in	ADP
ejpam-4675	164	21	this	this	DET
ejpam-4675	164	22	case	case	NOUN
ejpam-4675	164	23	is	be	AUX
ejpam-4675	164	24	called	call	VERB
ejpam-4675	164	25	the	the	DET
ejpam-4675	164	26	natural	natural	ADJ
ejpam-4675	164	27	dbhomomorphism	dbhomomorphism	NOUN
ejpam-4675	164	28	of	of	ADP
ejpam-4675	164	29	x	x	PUNCT
ejpam-4675	164	30	onto	onto	ADP
ejpam-4675	164	31	x	x	PROPN
ejpam-4675	164	32	/	/	SYM
ejpam-4675	164	33	s.	s.	PROPN
ejpam-4675	164	34	proof	proof	NOUN
ejpam-4675	164	35	.	.	PUNCT
ejpam-4675	165	1	let	let	VERB
ejpam-4675	165	2	x	x	PRON
ejpam-4675	165	3	,	,	PUNCT
ejpam-4675	165	4	y	y	PROPN
ejpam-4675	165	5	∈	∈	PROPN
ejpam-4675	165	6	x	x	PUNCT
ejpam-4675	165	7	such	such	ADJ
ejpam-4675	165	8	that	that	SCONJ
ejpam-4675	165	9	x	x	X
ejpam-4675	165	10	=	=	PUNCT
ejpam-4675	165	11	y	y	PROPN
ejpam-4675	165	12	which	which	PRON
ejpam-4675	165	13	by	by	ADP
ejpam-4675	165	14	corollary	corollary	ADJ
ejpam-4675	165	15	1	1	NUM
ejpam-4675	165	16	,	,	PUNCT
ejpam-4675	165	17	x	x	X
ejpam-4675	165	18	·	·	PUNCT
ejpam-4675	165	19	y	y	X
ejpam-4675	165	20	=	=	SYM
ejpam-4675	165	21	1	1	NUM
ejpam-4675	165	22	∈	∈	PROPN
ejpam-4675	165	23	s	s	X
ejpam-4675	165	24	and	and	CCONJ
ejpam-4675	165	25	y	y	PROPN
ejpam-4675	165	26	·	·	PUNCT
ejpam-4675	165	27	x	x	PUNCT
ejpam-4675	166	1	=	=	SYM
ejpam-4675	166	2	1	1	NUM
ejpam-4675	166	3	∈	∈	PROPN
ejpam-4675	166	4	s.	s.	PROPN
ejpam-4675	166	5	then	then	ADV
ejpam-4675	166	6	x	x	ADP
ejpam-4675	166	7	∼	∼	NOUN
ejpam-4675	166	8	y	y	PROPN
ejpam-4675	166	9	implies	imply	VERB
ejpam-4675	166	10	[	[	X
ejpam-4675	166	11	x]s	x]s	PROPN
ejpam-4675	166	12	=	=	SYM
ejpam-4675	167	1	[	[	X
ejpam-4675	167	2	y]s	y]s	X
ejpam-4675	167	3	which	which	PRON
ejpam-4675	167	4	implies	imply	VERB
ejpam-4675	167	5	that	that	SCONJ
ejpam-4675	167	6	φ(x	φ(x	NOUN
ejpam-4675	167	7	)	)	PUNCT
ejpam-4675	167	8	=	=	SYM
ejpam-4675	167	9	φ(y	φ(y	NOUN
ejpam-4675	167	10	)	)	PUNCT
ejpam-4675	167	11	.	.	PUNCT
ejpam-4675	168	1	hence	hence	ADV
ejpam-4675	168	2	,	,	PUNCT
ejpam-4675	168	3	φ	φ	PROPN
ejpam-4675	168	4	is	be	AUX
ejpam-4675	168	5	well	well	ADV
ejpam-4675	168	6	-	-	PUNCT
ejpam-4675	168	7	defined	define	VERB
ejpam-4675	168	8	.	.	PUNCT
ejpam-4675	169	1	now	now	ADV
ejpam-4675	169	2	,	,	PUNCT
ejpam-4675	169	3	let	let	VERB
ejpam-4675	169	4	a	a	DET
ejpam-4675	169	5	,	,	PUNCT
ejpam-4675	169	6	b	b	X
ejpam-4675	169	7	∈	∈	PROPN
ejpam-4675	169	8	x.	x.	NOUN
ejpam-4675	169	9	then	then	ADV
ejpam-4675	169	10	φ(a	φ(a	PROPN
ejpam-4675	169	11	·	·	PUNCT
ejpam-4675	170	1	b	b	X
ejpam-4675	170	2	)	)	PUNCT
ejpam-4675	170	3	=	=	PUNCT
ejpam-4675	171	1	[	[	X
ejpam-4675	171	2	a	a	DET
ejpam-4675	171	3	·	·	PUNCT
ejpam-4675	171	4	b]s	b]s	NOUN
ejpam-4675	171	5	=	=	PUNCT
ejpam-4675	172	1	[	[	X
ejpam-4675	172	2	a]s	a]s	ADJ
ejpam-4675	172	3	∗	∗	NOUN
ejpam-4675	172	4	[	[	X
ejpam-4675	172	5	b]s	b]s	NOUN
ejpam-4675	172	6	=	=	SYM
ejpam-4675	172	7	φ(a	φ(a	ADJ
ejpam-4675	172	8	)	)	PUNCT
ejpam-4675	172	9	∗φ(b	∗φ(b	PROPN
ejpam-4675	172	10	)	)	PUNCT
ejpam-4675	172	11	.	.	PUNCT
ejpam-4675	173	1	this	this	PRON
ejpam-4675	173	2	shows	show	VERB
ejpam-4675	173	3	that	that	SCONJ
ejpam-4675	173	4	φ	φ	PROPN
ejpam-4675	173	5	is	be	AUX
ejpam-4675	173	6	a	a	DET
ejpam-4675	173	7	db	db	NOUN
ejpam-4675	173	8	-	-	PUNCT
ejpam-4675	173	9	homomorphism	homomorphism	NOUN
ejpam-4675	173	10	.	.	PUNCT
ejpam-4675	174	1	since	since	SCONJ
ejpam-4675	174	2	φ(x	φ(x	NOUN
ejpam-4675	174	3	)	)	PUNCT
ejpam-4675	174	4	=	=	PRON
ejpam-4675	174	5	{	{	PUNCT
ejpam-4675	174	6	φ(a	φ(a	ADJ
ejpam-4675	174	7	)	)	PUNCT
ejpam-4675	174	8	:	:	PUNCT
ejpam-4675	174	9	a	a	DET
ejpam-4675	174	10	∈	∈	NOUN
ejpam-4675	174	11	x	x	PUNCT
ejpam-4675	174	12	}	}	PUNCT
ejpam-4675	174	13	=	=	SYM
ejpam-4675	174	14	{	{	PUNCT
ejpam-4675	175	1	[	[	X
ejpam-4675	175	2	a]s	a]s	NOUN
ejpam-4675	175	3	:	:	PUNCT
ejpam-4675	175	4	a	a	DET
ejpam-4675	175	5	∈	∈	NOUN
ejpam-4675	175	6	x	x	PUNCT
ejpam-4675	175	7	}	}	PUNCT
ejpam-4675	175	8	=	=	PUNCT
ejpam-4675	175	9	x	x	X
ejpam-4675	175	10	/	/	SYM
ejpam-4675	175	11	s	s	PROPN
ejpam-4675	175	12	,	,	PUNCT
ejpam-4675	175	13	it	it	PRON
ejpam-4675	175	14	shows	show	VERB
ejpam-4675	175	15	that	that	SCONJ
ejpam-4675	175	16	φ	φ	PROPN
ejpam-4675	175	17	is	be	AUX
ejpam-4675	175	18	onto	onto	ADP
ejpam-4675	175	19	and	and	CCONJ
ejpam-4675	175	20	so	so	ADV
ejpam-4675	175	21	φ	φ	PROPN
ejpam-4675	175	22	is	be	AUX
ejpam-4675	175	23	a	a	DET
ejpam-4675	175	24	db	db	NOUN
ejpam-4675	175	25	-	-	PUNCT
ejpam-4675	175	26	epimorphism	epimorphism	NOUN
ejpam-4675	175	27	.	.	PUNCT
ejpam-4675	176	1	to	to	PART
ejpam-4675	176	2	show	show	VERB
ejpam-4675	176	3	that	that	SCONJ
ejpam-4675	176	4	kerφ	kerφ	PROPN
ejpam-4675	176	5	=	=	SYM
ejpam-4675	176	6	s	s	PROPN
ejpam-4675	176	7	,	,	PUNCT
ejpam-4675	176	8	let	let	VERB
ejpam-4675	176	9	x	x	X
ejpam-4675	176	10	∈	∈	PROPN
ejpam-4675	176	11	kerφ	kerφ	PROPN
ejpam-4675	176	12	.	.	PUNCT
ejpam-4675	177	1	then	then	ADV
ejpam-4675	177	2	[	[	X
ejpam-4675	177	3	x]s	x]s	NOUN
ejpam-4675	177	4	=	=	SYM
ejpam-4675	177	5	φ(x	φ(x	NOUN
ejpam-4675	177	6	)	)	PUNCT
ejpam-4675	177	7	=	=	PUNCT
ejpam-4675	178	1	[	[	X
ejpam-4675	178	2	1]s	1]s	NUM
ejpam-4675	178	3	and	and	CCONJ
ejpam-4675	178	4	so	so	ADV
ejpam-4675	178	5	x	x	PUNCT
ejpam-4675	178	6	∼	∼	NOUN
ejpam-4675	178	7	1	1	NUM
ejpam-4675	178	8	.	.	PUNCT
ejpam-4675	179	1	it	it	PRON
ejpam-4675	179	2	follows	follow	VERB
ejpam-4675	179	3	that	that	SCONJ
ejpam-4675	179	4	x	x	X
ejpam-4675	179	5	·	·	PUNCT
ejpam-4675	179	6	1	1	NUM
ejpam-4675	179	7	∈	∈	NOUN
ejpam-4675	179	8	s	s	X
ejpam-4675	179	9	and	and	CCONJ
ejpam-4675	179	10	1	1	NUM
ejpam-4675	179	11	·	·	PUNCT
ejpam-4675	179	12	x	x	SYM
ejpam-4675	179	13	∈	∈	PROPN
ejpam-4675	179	14	s.	s.	PROPN
ejpam-4675	179	15	since	since	SCONJ
ejpam-4675	179	16	1	1	NUM
ejpam-4675	179	17	∈	∈	PROPN
ejpam-4675	179	18	s	s	NOUN
ejpam-4675	179	19	and	and	CCONJ
ejpam-4675	179	20	s	s	VERB
ejpam-4675	179	21	is	be	AUX
ejpam-4675	179	22	also	also	ADV
ejpam-4675	179	23	a	a	DET
ejpam-4675	179	24	db	db	NOUN
ejpam-4675	179	25	-	-	PUNCT
ejpam-4675	179	26	filter	filter	NOUN
ejpam-4675	179	27	by	by	ADP
ejpam-4675	179	28	proposition	proposition	NOUN
ejpam-4675	179	29	2	2	NUM
ejpam-4675	179	30	,	,	PUNCT
ejpam-4675	179	31	then	then	ADV
ejpam-4675	179	32	x	x	PART
ejpam-4675	179	33	∈	∈	PROPN
ejpam-4675	179	34	s	s	X
ejpam-4675	179	35	and	and	CCONJ
ejpam-4675	179	36	so	so	ADV
ejpam-4675	179	37	kerφ	kerφ	PROPN
ejpam-4675	179	38	⊆	⊆	NUM
ejpam-4675	179	39	s.	s.	PROPN
ejpam-4675	179	40	now	now	ADV
ejpam-4675	179	41	,	,	PUNCT
ejpam-4675	179	42	let	let	VERB
ejpam-4675	179	43	x	x	X
ejpam-4675	179	44	∈	∈	PROPN
ejpam-4675	179	45	s.	s.	PROPN
ejpam-4675	179	46	by	by	ADP
ejpam-4675	179	47	remark	remark	NOUN
ejpam-4675	179	48	1	1	NUM
ejpam-4675	179	49	,	,	PUNCT
ejpam-4675	179	50	1	1	NUM
ejpam-4675	179	51	∈	∈	NOUN
ejpam-4675	179	52	s	s	NOUN
ejpam-4675	179	53	,	,	PUNCT
ejpam-4675	179	54	and	and	CCONJ
ejpam-4675	179	55	since	since	SCONJ
ejpam-4675	179	56	s	s	NOUN
ejpam-4675	179	57	is	be	AUX
ejpam-4675	179	58	closed	close	VERB
ejpam-4675	179	59	by	by	ADP
ejpam-4675	179	60	theorem	theorem	NOUN
ejpam-4675	179	61	1	1	NUM
ejpam-4675	179	62	,	,	PUNCT
ejpam-4675	179	63	1	1	NUM
ejpam-4675	180	1	·	·	PUNCT
ejpam-4675	180	2	x	x	PUNCT
ejpam-4675	180	3	∈	∈	NOUN
ejpam-4675	180	4	s	s	X
ejpam-4675	180	5	and	and	CCONJ
ejpam-4675	180	6	x	x	SYM
ejpam-4675	180	7	·	·	PUNCT
ejpam-4675	180	8	1	1	NUM
ejpam-4675	180	9	∈	∈	PROPN
ejpam-4675	180	10	s.	s.	PROPN
ejpam-4675	180	11	then	then	ADV
ejpam-4675	180	12	x	x	PUNCT
ejpam-4675	180	13	∼	∼	NOUN
ejpam-4675	180	14	1	1	NUM
ejpam-4675	180	15	,	,	PUNCT
ejpam-4675	180	16	and	and	CCONJ
ejpam-4675	180	17	so	so	ADV
ejpam-4675	180	18	[	[	X
ejpam-4675	180	19	x]s	x]s	NOUN
ejpam-4675	180	20	=	=	PUNCT
ejpam-4675	181	1	[	[	X
ejpam-4675	181	2	1]s	1]s	NOUN
ejpam-4675	181	3	.	.	PUNCT
ejpam-4675	182	1	since	since	SCONJ
ejpam-4675	182	2	φ(x	φ(x	NOUN
ejpam-4675	182	3	)	)	PUNCT
ejpam-4675	182	4	=	=	PUNCT
ejpam-4675	183	1	[	[	X
ejpam-4675	183	2	x]s	x]s	NOUN
ejpam-4675	183	3	=	=	PUNCT
ejpam-4675	184	1	[	[	X
ejpam-4675	184	2	1]s	1]s	NOUN
ejpam-4675	184	3	,	,	PUNCT
ejpam-4675	184	4	then	then	ADV
ejpam-4675	184	5	x	x	PROPN
ejpam-4675	184	6	∈	∈	PROPN
ejpam-4675	184	7	kerφ	kerφ	PROPN
ejpam-4675	184	8	.	.	PUNCT
ejpam-4675	185	1	this	this	PRON
ejpam-4675	185	2	implies	imply	VERB
ejpam-4675	185	3	that	that	SCONJ
ejpam-4675	185	4	s	s	VERB
ejpam-4675	185	5	⊆	⊆	NUM
ejpam-4675	185	6	kerφ	kerφ	PROPN
ejpam-4675	186	1	and	and	CCONJ
ejpam-4675	186	2	it	it	PRON
ejpam-4675	186	3	follows	follow	VERB
ejpam-4675	186	4	that	that	SCONJ
ejpam-4675	186	5	kerφ	kerφ	PROPN
ejpam-4675	186	6	=	=	PUNCT
ejpam-4675	186	7	s.	s.	PROPN
ejpam-4675	186	8	lemma	lemma	PROPN
ejpam-4675	187	1	3	3	X
ejpam-4675	187	2	.	.	PUNCT
ejpam-4675	187	3	let	let	VERB
ejpam-4675	187	4	f	f	NOUN
ejpam-4675	187	5	:	:	PUNCT
ejpam-4675	187	6	(	(	PUNCT
ejpam-4675	187	7	x	x	X
ejpam-4675	187	8	,	,	PUNCT
ejpam-4675	187	9	·	·	PUNCT
ejpam-4675	187	10	,	,	PUNCT
ejpam-4675	187	11	1x	1x	NUM
ejpam-4675	187	12	)	)	PUNCT
ejpam-4675	187	13	→	→	SYM
ejpam-4675	187	14	(	(	PUNCT
ejpam-4675	187	15	y	y	PROPN
ejpam-4675	187	16	,	,	PUNCT
ejpam-4675	187	17	∗	∗	NOUN
ejpam-4675	187	18	,	,	PUNCT
ejpam-4675	187	19	1y	1y	NUM
ejpam-4675	187	20	)	)	PUNCT
ejpam-4675	187	21	and	and	CCONJ
ejpam-4675	187	22	g	g	NOUN
ejpam-4675	187	23	:	:	PUNCT
ejpam-4675	187	24	(	(	PUNCT
ejpam-4675	187	25	y	y	NOUN
ejpam-4675	187	26	,	,	PUNCT
ejpam-4675	187	27	∗	∗	NOUN
ejpam-4675	187	28	,	,	PUNCT
ejpam-4675	187	29	1y	1y	NOUN
ejpam-4675	187	30	)	)	PUNCT
ejpam-4675	187	31	→	→	SYM
ejpam-4675	187	32	(	(	PUNCT
ejpam-4675	187	33	z	z	NOUN
ejpam-4675	187	34	,	,	PUNCT
ejpam-4675	187	35	∗′	∗′	ADJ
ejpam-4675	187	36	,	,	PUNCT
ejpam-4675	187	37	1z	1z	NOUN
ejpam-4675	187	38	)	)	PUNCT
ejpam-4675	187	39	be	be	VERB
ejpam-4675	187	40	dbhomomorphisms	dbhomomorphism	NOUN
ejpam-4675	187	41	,	,	PUNCT
ejpam-4675	187	42	then	then	ADV
ejpam-4675	187	43	g	g	PROPN
ejpam-4675	187	44	◦	◦	NOUN
ejpam-4675	188	1	f	f	X
ejpam-4675	188	2	:	:	PUNCT
ejpam-4675	188	3	(	(	PUNCT
ejpam-4675	188	4	x	x	X
ejpam-4675	188	5	,	,	PUNCT
ejpam-4675	188	6	·	·	PUNCT
ejpam-4675	188	7	,	,	PUNCT
ejpam-4675	188	8	1x	1x	NUM
ejpam-4675	188	9	)	)	PUNCT
ejpam-4675	188	10	→	→	PUNCT
ejpam-4675	188	11	(	(	PUNCT
ejpam-4675	188	12	z	z	NOUN
ejpam-4675	188	13	,	,	PUNCT
ejpam-4675	188	14	∗′	∗′	ADJ
ejpam-4675	188	15	,	,	PUNCT
ejpam-4675	188	16	1z	1z	NOUN
ejpam-4675	188	17	)	)	PUNCT
ejpam-4675	188	18	is	be	AUX
ejpam-4675	188	19	also	also	ADV
ejpam-4675	188	20	a	a	DET
ejpam-4675	188	21	db	db	NOUN
ejpam-4675	188	22	-	-	PUNCT
ejpam-4675	188	23	homomorphism	homomorphism	NOUN
ejpam-4675	188	24	(	(	PUNCT
ejpam-4675	188	25	◦	◦	NOUN
ejpam-4675	188	26	is	be	AUX
ejpam-4675	188	27	the	the	DET
ejpam-4675	188	28	usual	usual	ADJ
ejpam-4675	188	29	composition	composition	NOUN
ejpam-4675	188	30	of	of	ADP
ejpam-4675	188	31	functions	function	NOUN
ejpam-4675	188	32	)	)	PUNCT
ejpam-4675	188	33	.	.	PUNCT
ejpam-4675	189	1	j.e	j.e	PROPN
ejpam-4675	189	2	.	.	PROPN
ejpam-4675	189	3	bolima	bolima	PROPN
ejpam-4675	189	4	,	,	PUNCT
ejpam-4675	189	5	k.b	k.b	PROPN
ejpam-4675	189	6	.	.	PUNCT
ejpam-4675	189	7	fuentes	fuentes	PROPN
ejpam-4675	189	8	/	/	SYM
ejpam-4675	189	9	eur	eur	PROPN
ejpam-4675	189	10	.	.	PUNCT
ejpam-4675	190	1	j.	j.	PROPN
ejpam-4675	190	2	pure	pure	PROPN
ejpam-4675	190	3	appl	appl	PROPN
ejpam-4675	190	4	.	.	PROPN
ejpam-4675	190	5	math	math	PROPN
ejpam-4675	190	6	,	,	PUNCT
ejpam-4675	190	7	16	16	NUM
ejpam-4675	190	8	(	(	PUNCT
ejpam-4675	190	9	1	1	NUM
ejpam-4675	190	10	)	)	PUNCT
ejpam-4675	190	11	(	(	PUNCT
ejpam-4675	190	12	2023	2023	NUM
ejpam-4675	190	13	)	)	PUNCT
ejpam-4675	190	14	,	,	PUNCT
ejpam-4675	190	15	577	577	NUM
ejpam-4675	190	16	-	-	SYM
ejpam-4675	190	17	586	586	NUM
ejpam-4675	190	18	583	583	NUM
ejpam-4675	190	19	proof	proof	NOUN
ejpam-4675	190	20	.	.	PUNCT
ejpam-4675	191	1	let	let	VERB
ejpam-4675	191	2	x	x	PRON
ejpam-4675	191	3	,	,	PUNCT
ejpam-4675	191	4	y	y	PROPN
ejpam-4675	191	5	∈	∈	PROPN
ejpam-4675	191	6	x.	x.	NOUN
ejpam-4675	191	7	since	since	SCONJ
ejpam-4675	191	8	f	f	PROPN
ejpam-4675	191	9	and	and	CCONJ
ejpam-4675	191	10	g	g	PROPN
ejpam-4675	191	11	are	be	AUX
ejpam-4675	191	12	db	db	NOUN
ejpam-4675	191	13	-	-	PUNCT
ejpam-4675	191	14	homomorphisms	homomorphism	NOUN
ejpam-4675	191	15	,	,	PUNCT
ejpam-4675	191	16	then	then	ADV
ejpam-4675	191	17	(	(	PUNCT
ejpam-4675	191	18	g	g	NOUN
ejpam-4675	191	19	◦	◦	NOUN
ejpam-4675	191	20	f)(x	f)(x	X
ejpam-4675	191	21	·	·	PUNCT
ejpam-4675	191	22	y	y	X
ejpam-4675	191	23	)	)	PUNCT
ejpam-4675	192	1	=	=	SYM
ejpam-4675	192	2	g	g	PROPN
ejpam-4675	192	3	(	(	PUNCT
ejpam-4675	192	4	f(x	f(x	PROPN
ejpam-4675	192	5	·	·	PUNCT
ejpam-4675	192	6	y	y	X
ejpam-4675	192	7	)	)	PUNCT
ejpam-4675	192	8	)	)	PUNCT
ejpam-4675	193	1	=	=	SYM
ejpam-4675	193	2	g	g	PROPN
ejpam-4675	193	3	(	(	PUNCT
ejpam-4675	193	4	f(x	f(x	PROPN
ejpam-4675	193	5	)	)	PUNCT
ejpam-4675	193	6	∗	∗	NOUN
ejpam-4675	193	7	f(y	f(y	NOUN
ejpam-4675	193	8	)	)	PUNCT
ejpam-4675	193	9	)	)	PUNCT
ejpam-4675	194	1	=	=	SYM
ejpam-4675	194	2	g	g	PROPN
ejpam-4675	194	3	(	(	PUNCT
ejpam-4675	194	4	f(x	f(x	PROPN
ejpam-4675	194	5	)	)	PUNCT
ejpam-4675	194	6	)	)	PUNCT
ejpam-4675	195	1	∗′	∗′	PROPN
ejpam-4675	195	2	g	g	NOUN
ejpam-4675	195	3	(	(	PUNCT
ejpam-4675	195	4	f(y	f(y	NOUN
ejpam-4675	195	5	)	)	PUNCT
ejpam-4675	195	6	)	)	PUNCT
ejpam-4675	196	1	=	=	PUNCT
ejpam-4675	196	2	(	(	PUNCT
ejpam-4675	196	3	g	g	PROPN
ejpam-4675	196	4	◦	◦	NOUN
ejpam-4675	196	5	f)(x	f)(x	NOUN
ejpam-4675	196	6	)	)	PUNCT
ejpam-4675	196	7	∗′	∗′	PROPN
ejpam-4675	196	8	(	(	PUNCT
ejpam-4675	196	9	g	g	PROPN
ejpam-4675	196	10	◦	◦	NOUN
ejpam-4675	196	11	f)(y	f)(y	NOUN
ejpam-4675	196	12	)	)	PUNCT
ejpam-4675	196	13	.	.	PUNCT
ejpam-4675	197	1	hence	hence	ADV
ejpam-4675	197	2	,	,	PUNCT
ejpam-4675	197	3	g	g	PROPN
ejpam-4675	197	4	◦	◦	NOUN
ejpam-4675	197	5	f	f	PROPN
ejpam-4675	197	6	is	be	AUX
ejpam-4675	197	7	a	a	DET
ejpam-4675	197	8	db	db	NOUN
ejpam-4675	197	9	-	-	PUNCT
ejpam-4675	197	10	homomorphism	homomorphism	NOUN
ejpam-4675	197	11	.	.	PUNCT
ejpam-4675	198	1	theorem	theorem	ADJ
ejpam-4675	198	2	6	6	NUM
ejpam-4675	198	3	.	.	PUNCT
ejpam-4675	198	4	fundamental	fundamental	ADJ
ejpam-4675	198	5	theorem	theorem	NOUN
ejpam-4675	198	6	of	of	ADP
ejpam-4675	198	7	db	db	NOUN
ejpam-4675	198	8	-	-	PUNCT
ejpam-4675	198	9	homomorphism	homomorphism	NOUN
ejpam-4675	198	10	for	for	ADP
ejpam-4675	198	11	db	db	PROPN
ejpam-4675	198	12	-	-	PUNCT
ejpam-4675	198	13	algebras	algebras	PROPN
ejpam-4675	198	14	let	let	VERB
ejpam-4675	198	15	φ	φ	PROPN
ejpam-4675	198	16	be	be	AUX
ejpam-4675	198	17	a	a	DET
ejpam-4675	198	18	db	db	NOUN
ejpam-4675	198	19	-	-	PUNCT
ejpam-4675	198	20	homomorphism	homomorphism	NOUN
ejpam-4675	198	21	of	of	ADP
ejpam-4675	198	22	a	a	DET
ejpam-4675	198	23	db	db	NOUN
ejpam-4675	198	24	-	-	PUNCT
ejpam-4675	198	25	algebra	algebra	NOUN
ejpam-4675	198	26	(	(	PUNCT
ejpam-4675	198	27	x	x	X
ejpam-4675	198	28	,	,	PUNCT
ejpam-4675	198	29	·	·	PUNCT
ejpam-4675	198	30	,	,	PUNCT
ejpam-4675	198	31	1x	1x	NUM
ejpam-4675	198	32	)	)	PUNCT
ejpam-4675	198	33	onto	onto	ADP
ejpam-4675	198	34	a	a	DET
ejpam-4675	198	35	db	db	NOUN
ejpam-4675	198	36	-	-	PUNCT
ejpam-4675	198	37	algebra	algebra	NOUN
ejpam-4675	198	38	(	(	PUNCT
ejpam-4675	198	39	y	y	PROPN
ejpam-4675	198	40	,	,	PUNCT
ejpam-4675	198	41	∗	∗	NOUN
ejpam-4675	198	42	,	,	PUNCT
ejpam-4675	198	43	1y	1y	NOUN
ejpam-4675	198	44	)	)	PUNCT
ejpam-4675	198	45	,	,	PUNCT
ejpam-4675	198	46	s	s	PROPN
ejpam-4675	198	47	⊆	⊆	NUM
ejpam-4675	198	48	kerφ	kerφ	PROPN
ejpam-4675	198	49	be	be	AUX
ejpam-4675	198	50	a	a	DET
ejpam-4675	198	51	normal	normal	ADJ
ejpam-4675	198	52	db	db	NOUN
ejpam-4675	198	53	-	-	PUNCT
ejpam-4675	198	54	subalgebra	subalgebra	NOUN
ejpam-4675	198	55	(	(	PUNCT
ejpam-4675	198	56	normal	normal	ADJ
ejpam-4675	198	57	db	db	NOUN
ejpam-4675	198	58	-	-	PUNCT
ejpam-4675	198	59	filter	filter	NOUN
ejpam-4675	198	60	)	)	PUNCT
ejpam-4675	198	61	of	of	ADP
ejpam-4675	198	62	x	x	NOUN
ejpam-4675	198	63	,	,	PUNCT
ejpam-4675	198	64	and	and	CCONJ
ejpam-4675	198	65	g	g	PROPN
ejpam-4675	198	66	be	be	AUX
ejpam-4675	198	67	the	the	DET
ejpam-4675	198	68	natural	natural	ADJ
ejpam-4675	198	69	dbhomomorphism	dbhomomorphism	NOUN
ejpam-4675	198	70	of	of	ADP
ejpam-4675	198	71	x	x	PUNCT
ejpam-4675	198	72	onto	onto	ADP
ejpam-4675	198	73	(	(	PUNCT
ejpam-4675	198	74	x	x	NOUN
ejpam-4675	198	75	/	/	SYM
ejpam-4675	198	76	s	s	PROPN
ejpam-4675	198	77	,	,	PUNCT
ejpam-4675	198	78	θ	θ	PROPN
ejpam-4675	198	79	,	,	PUNCT
ejpam-4675	198	80	[	[	X
ejpam-4675	198	81	1]s	1]s	NUM
ejpam-4675	198	82	)	)	PUNCT
ejpam-4675	198	83	.	.	PUNCT
ejpam-4675	199	1	then	then	ADV
ejpam-4675	199	2	there	there	PRON
ejpam-4675	199	3	exists	exist	VERB
ejpam-4675	199	4	a	a	DET
ejpam-4675	199	5	unique	unique	ADJ
ejpam-4675	199	6	db	db	NOUN
ejpam-4675	199	7	-	-	PUNCT
ejpam-4675	199	8	homomorphism	homomorphism	ADJ
ejpam-4675	199	9	h	h	NOUN
ejpam-4675	199	10	of	of	ADP
ejpam-4675	199	11	x	x	PROPN
ejpam-4675	199	12	/	/	SYM
ejpam-4675	199	13	s	s	X
ejpam-4675	199	14	onto	onto	ADP
ejpam-4675	199	15	y	y	PROPN
ejpam-4675	199	16	such	such	ADJ
ejpam-4675	199	17	that	that	SCONJ
ejpam-4675	199	18	φ	φ	PROPN
ejpam-4675	199	19	=	=	SYM
ejpam-4675	199	20	h	h	PROPN
ejpam-4675	199	21	◦	◦	NOUN
ejpam-4675	199	22	g.	g.	PROPN
ejpam-4675	199	23	furthermore	furthermore	ADV
ejpam-4675	199	24	,	,	PUNCT
ejpam-4675	199	25	h	h	NOUN
ejpam-4675	199	26	is	be	AUX
ejpam-4675	199	27	one	one	NUM
ejpam-4675	199	28	-	-	PUNCT
ejpam-4675	199	29	to	to	ADP
ejpam-4675	199	30	-	-	PUNCT
ejpam-4675	199	31	one	one	NOUN
ejpam-4675	199	32	if	if	SCONJ
ejpam-4675	200	1	and	and	CCONJ
ejpam-4675	200	2	only	only	ADV
ejpam-4675	200	3	if	if	SCONJ
ejpam-4675	200	4	s	s	NOUN
ejpam-4675	200	5	=	=	VERB
ejpam-4675	200	6	kerφ	kerφ	PROPN
ejpam-4675	200	7	.	.	PUNCT
ejpam-4675	201	1	proof	proof	NOUN
ejpam-4675	201	2	.	.	PUNCT
ejpam-4675	202	1	define	define	VERB
ejpam-4675	202	2	the	the	DET
ejpam-4675	202	3	map	map	NOUN
ejpam-4675	202	4	h	h	NOUN
ejpam-4675	202	5	:	:	PUNCT
ejpam-4675	202	6	x	x	X
ejpam-4675	202	7	/	/	SYM
ejpam-4675	202	8	s	s	X
ejpam-4675	202	9	→	→	SYM
ejpam-4675	202	10	y	y	PROPN
ejpam-4675	202	11	by	by	ADP
ejpam-4675	202	12	h	h	PROPN
ejpam-4675	202	13	(	(	PUNCT
ejpam-4675	202	14	[	[	X
ejpam-4675	202	15	x]s	x]s	NOUN
ejpam-4675	202	16	)	)	PUNCT
ejpam-4675	203	1	=	=	SYM
ejpam-4675	203	2	φ(x	φ(x	NOUN
ejpam-4675	203	3	)	)	PUNCT
ejpam-4675	203	4	for	for	SCONJ
ejpam-4675	203	5	all	all	DET
ejpam-4675	203	6	[	[	X
ejpam-4675	203	7	x]s	x]s	PROPN
ejpam-4675	203	8	∈	∈	PROPN
ejpam-4675	203	9	x	x	X
ejpam-4675	203	10	/	/	SYM
ejpam-4675	203	11	s.	s.	PROPN
ejpam-4675	203	12	let	let	VERB
ejpam-4675	203	13	[	[	X
ejpam-4675	203	14	x]s	x]s	PROPN
ejpam-4675	203	15	,	,	PUNCT
ejpam-4675	204	1	[	[	X
ejpam-4675	204	2	y]s	y]s	X
ejpam-4675	204	3	∈	∈	NOUN
ejpam-4675	204	4	x	x	PRON
ejpam-4675	204	5	/	/	SYM
ejpam-4675	204	6	s	s	VERB
ejpam-4675	204	7	such	such	ADJ
ejpam-4675	204	8	that	that	SCONJ
ejpam-4675	204	9	[	[	X
ejpam-4675	204	10	x]s	x]s	NOUN
ejpam-4675	204	11	=	=	PUNCT
ejpam-4675	205	1	[	[	X
ejpam-4675	205	2	y]s	y]s	X
ejpam-4675	205	3	.	.	PUNCT
ejpam-4675	206	1	then	then	ADV
ejpam-4675	206	2	x	x	PUNCT
ejpam-4675	206	3	∼	∼	NOUN
ejpam-4675	206	4	y	y	NOUN
ejpam-4675	206	5	,	,	PUNCT
ejpam-4675	206	6	so	so	ADV
ejpam-4675	206	7	x	x	SYM
ejpam-4675	206	8	·	·	PUNCT
ejpam-4675	206	9	y	y	X
ejpam-4675	206	10	∈	∈	PROPN
ejpam-4675	206	11	s	s	X
ejpam-4675	206	12	and	and	CCONJ
ejpam-4675	206	13	y	y	PROPN
ejpam-4675	206	14	·	·	PUNCT
ejpam-4675	206	15	x	x	SYM
ejpam-4675	206	16	∈	∈	PROPN
ejpam-4675	206	17	s.	s.	PROPN
ejpam-4675	206	18	since	since	SCONJ
ejpam-4675	206	19	s	s	PROPN
ejpam-4675	206	20	⊆	⊆	NUM
ejpam-4675	206	21	kerφ	kerφ	PROPN
ejpam-4675	206	22	,	,	PUNCT
ejpam-4675	206	23	x	x	X
ejpam-4675	206	24	·	·	PUNCT
ejpam-4675	206	25	y	y	PROPN
ejpam-4675	206	26	∈	∈	PROPN
ejpam-4675	206	27	kerφ	kerφ	PROPN
ejpam-4675	206	28	and	and	CCONJ
ejpam-4675	206	29	y	y	PROPN
ejpam-4675	206	30	·	·	PUNCT
ejpam-4675	206	31	x	x	SYM
ejpam-4675	206	32	∈	∈	PROPN
ejpam-4675	206	33	kerφ	kerφ	PROPN
ejpam-4675	206	34	.	.	PUNCT
ejpam-4675	207	1	thus	thus	ADV
ejpam-4675	207	2	φ(x	φ(x	NOUN
ejpam-4675	207	3	)	)	PUNCT
ejpam-4675	207	4	∗	∗	NOUN
ejpam-4675	207	5	φ(y	φ(y	NOUN
ejpam-4675	207	6	)	)	PUNCT
ejpam-4675	207	7	=	=	SYM
ejpam-4675	207	8	φ(x	φ(x	PROPN
ejpam-4675	207	9	·	·	PUNCT
ejpam-4675	207	10	y	y	X
ejpam-4675	207	11	)	)	PUNCT
ejpam-4675	207	12	=	=	SYM
ejpam-4675	207	13	1y	1y	PROPN
ejpam-4675	207	14	and	and	CCONJ
ejpam-4675	207	15	φ(y	φ(y	ADJ
ejpam-4675	207	16	)	)	PUNCT
ejpam-4675	207	17	∗φ(x	∗φ(x	PROPN
ejpam-4675	207	18	)	)	PUNCT
ejpam-4675	207	19	=	=	PUNCT
ejpam-4675	208	1	φ(y	φ(y	ADJ
ejpam-4675	208	2	·	·	PUNCT
ejpam-4675	208	3	x	x	X
ejpam-4675	208	4	)	)	PUNCT
ejpam-4675	208	5	=	=	SYM
ejpam-4675	208	6	1y	1y	NOUN
ejpam-4675	208	7	.	.	PUNCT
ejpam-4675	209	1	by	by	ADP
ejpam-4675	209	2	lemma	lemma	PROPN
ejpam-4675	209	3	1	1	NUM
ejpam-4675	209	4	,	,	PUNCT
ejpam-4675	209	5	φ(x	φ(x	NOUN
ejpam-4675	209	6	)	)	PUNCT
ejpam-4675	209	7	=	=	SYM
ejpam-4675	209	8	φ(y	φ(y	NOUN
ejpam-4675	209	9	)	)	PUNCT
ejpam-4675	209	10	and	and	CCONJ
ejpam-4675	209	11	so	so	ADV
ejpam-4675	209	12	h	h	NOUN
ejpam-4675	209	13	(	(	PUNCT
ejpam-4675	209	14	[	[	X
ejpam-4675	209	15	x]s	x]s	NOUN
ejpam-4675	209	16	)	)	PUNCT
ejpam-4675	210	1	=	=	SYM
ejpam-4675	210	2	h	h	NOUN
ejpam-4675	210	3	(	(	PUNCT
ejpam-4675	210	4	[	[	X
ejpam-4675	210	5	y]s	y]s	X
ejpam-4675	210	6	)	)	PUNCT
ejpam-4675	210	7	.	.	PUNCT
ejpam-4675	211	1	hence	hence	ADV
ejpam-4675	211	2	,	,	PUNCT
ejpam-4675	211	3	h	h	NOUN
ejpam-4675	211	4	is	be	AUX
ejpam-4675	211	5	well	well	ADV
ejpam-4675	211	6	-	-	PUNCT
ejpam-4675	211	7	defined	define	VERB
ejpam-4675	211	8	.	.	PUNCT
ejpam-4675	212	1	let	let	VERB
ejpam-4675	212	2	[	[	X
ejpam-4675	212	3	x]s	x]s	PROPN
ejpam-4675	212	4	,	,	PUNCT
ejpam-4675	212	5	[	[	X
ejpam-4675	212	6	y]s	y]s	X
ejpam-4675	212	7	∈	∈	PROPN
ejpam-4675	212	8	x	x	PRON
ejpam-4675	212	9	/	/	SYM
ejpam-4675	212	10	s.	s.	PROPN
ejpam-4675	213	1	then	then	ADV
ejpam-4675	213	2	h	h	VERB
ejpam-4675	213	3	(	(	PUNCT
ejpam-4675	213	4	[	[	X
ejpam-4675	213	5	x]sθ[y]s	x]sθ[y]s	X
ejpam-4675	213	6	)	)	PUNCT
ejpam-4675	214	1	=	=	SYM
ejpam-4675	214	2	h	h	NOUN
ejpam-4675	214	3	(	(	PUNCT
ejpam-4675	214	4	[	[	X
ejpam-4675	214	5	x	x	X
ejpam-4675	214	6	·	·	PUNCT
ejpam-4675	214	7	y]s	y]s	NUM
ejpam-4675	214	8	)	)	PUNCT
ejpam-4675	215	1	=	=	PUNCT
ejpam-4675	216	1	φ(x	φ(x	PROPN
ejpam-4675	216	2	·	·	PUNCT
ejpam-4675	216	3	y	y	X
ejpam-4675	216	4	)	)	PUNCT
ejpam-4675	216	5	=	=	SYM
ejpam-4675	216	6	φ(x	φ(x	NOUN
ejpam-4675	216	7	)	)	PUNCT
ejpam-4675	216	8	∗	∗	NOUN
ejpam-4675	216	9	φ(y	φ(y	NOUN
ejpam-4675	216	10	)	)	PUNCT
ejpam-4675	217	1	=	=	SYM
ejpam-4675	217	2	h	h	NOUN
ejpam-4675	217	3	(	(	PUNCT
ejpam-4675	217	4	[	[	X
ejpam-4675	217	5	x]s	x]s	NOUN
ejpam-4675	217	6	)	)	PUNCT
ejpam-4675	217	7	∗	∗	NOUN
ejpam-4675	217	8	h	h	NOUN
ejpam-4675	217	9	(	(	PUNCT
ejpam-4675	217	10	[	[	X
ejpam-4675	217	11	y]s	y]s	X
ejpam-4675	217	12	)	)	PUNCT
ejpam-4675	217	13	.	.	PUNCT
ejpam-4675	218	1	thus	thus	ADV
ejpam-4675	218	2	,	,	PUNCT
ejpam-4675	218	3	h	h	NOUN
ejpam-4675	218	4	is	be	AUX
ejpam-4675	218	5	a	a	DET
ejpam-4675	218	6	db	db	NOUN
ejpam-4675	218	7	-	-	PUNCT
ejpam-4675	218	8	homomorphism	homomorphism	NOUN
ejpam-4675	218	9	.	.	PUNCT
ejpam-4675	219	1	since	since	SCONJ
ejpam-4675	219	2	φ	φ	PROPN
ejpam-4675	219	3	is	be	AUX
ejpam-4675	219	4	onto	onto	ADP
ejpam-4675	219	5	,	,	PUNCT
ejpam-4675	219	6	for	for	ADP
ejpam-4675	219	7	all	all	DET
ejpam-4675	219	8	y	y	PROPN
ejpam-4675	219	9	∈	∈	PROPN
ejpam-4675	219	10	y	y	NOUN
ejpam-4675	219	11	there	there	PRON
ejpam-4675	219	12	exists	exist	VERB
ejpam-4675	219	13	x	x	X
ejpam-4675	219	14	∈	∈	PROPN
ejpam-4675	219	15	x	x	X
ejpam-4675	219	16	such	such	ADJ
ejpam-4675	219	17	that	that	SCONJ
ejpam-4675	219	18	φ(x	φ(x	NOUN
ejpam-4675	219	19	)	)	PUNCT
ejpam-4675	219	20	=	=	SYM
ejpam-4675	220	1	y.	y.	NOUN
ejpam-4675	220	2	as	as	ADP
ejpam-4675	220	3	h	h	NOUN
ejpam-4675	220	4	(	(	PUNCT
ejpam-4675	220	5	[	[	X
ejpam-4675	220	6	x]s	x]s	NOUN
ejpam-4675	220	7	)	)	PUNCT
ejpam-4675	221	1	=	=	SYM
ejpam-4675	221	2	φ(x	φ(x	NOUN
ejpam-4675	221	3	)	)	PUNCT
ejpam-4675	221	4	for	for	ADP
ejpam-4675	221	5	all	all	DET
ejpam-4675	221	6	[	[	X
ejpam-4675	221	7	x]s	x]s	PROPN
ejpam-4675	221	8	∈	∈	PROPN
ejpam-4675	221	9	x	x	SYM
ejpam-4675	221	10	/	/	SYM
ejpam-4675	221	11	s	s	PROPN
ejpam-4675	221	12	,	,	PUNCT
ejpam-4675	221	13	it	it	PRON
ejpam-4675	221	14	follows	follow	VERB
ejpam-4675	221	15	that	that	SCONJ
ejpam-4675	221	16	there	there	PRON
ejpam-4675	221	17	exists	exist	VERB
ejpam-4675	222	1	[	[	X
ejpam-4675	222	2	x]s	x]s	PROPN
ejpam-4675	222	3	∈	∈	PROPN
ejpam-4675	222	4	x	x	X
ejpam-4675	222	5	/	/	SYM
ejpam-4675	222	6	s	s	VERB
ejpam-4675	222	7	such	such	ADJ
ejpam-4675	222	8	that	that	DET
ejpam-4675	222	9	h	h	NOUN
ejpam-4675	222	10	(	(	PUNCT
ejpam-4675	222	11	[	[	X
ejpam-4675	222	12	x]s	x]s	NOUN
ejpam-4675	222	13	)	)	PUNCT
ejpam-4675	223	1	=	=	SYM
ejpam-4675	223	2	y	y	PROPN
ejpam-4675	223	3	for	for	ADP
ejpam-4675	223	4	all	all	DET
ejpam-4675	223	5	y	y	PROPN
ejpam-4675	223	6	∈	∈	PROPN
ejpam-4675	223	7	y	y	PROPN
ejpam-4675	223	8	.	.	PUNCT
ejpam-4675	224	1	hence	hence	ADV
ejpam-4675	224	2	,	,	PUNCT
ejpam-4675	224	3	h	h	PROPN
ejpam-4675	224	4	is	be	AUX
ejpam-4675	224	5	onto	onto	ADP
ejpam-4675	224	6	.	.	PUNCT
ejpam-4675	225	1	suppose	suppose	VERB
ejpam-4675	225	2	h′	h′	PROPN
ejpam-4675	225	3	:	:	PUNCT
ejpam-4675	225	4	x	x	X
ejpam-4675	225	5	/	/	SYM
ejpam-4675	225	6	s	s	X
ejpam-4675	225	7	→	→	SYM
ejpam-4675	225	8	y	y	PROPN
ejpam-4675	225	9	is	be	AUX
ejpam-4675	225	10	another	another	DET
ejpam-4675	225	11	function	function	NOUN
ejpam-4675	225	12	such	such	ADJ
ejpam-4675	225	13	that	that	SCONJ
ejpam-4675	225	14	φ	φ	PROPN
ejpam-4675	225	15	=	=	SYM
ejpam-4675	225	16	h′	h′	PROPN
ejpam-4675	225	17	◦	◦	NOUN
ejpam-4675	225	18	g.	g.	PROPN
ejpam-4675	225	19	let	let	VERB
ejpam-4675	226	1	[	[	PUNCT
ejpam-4675	226	2	x]s	x]s	PROPN
ejpam-4675	226	3	∈	∈	PROPN
ejpam-4675	226	4	x	x	SYM
ejpam-4675	226	5	/	/	SYM
ejpam-4675	226	6	s	s	PROPN
ejpam-4675	226	7	,	,	PUNCT
ejpam-4675	226	8	then	then	ADV
ejpam-4675	226	9	h′	h′	PROPN
ejpam-4675	226	10	(	(	PUNCT
ejpam-4675	226	11	[	[	X
ejpam-4675	226	12	x]s	x]s	NOUN
ejpam-4675	226	13	)	)	PUNCT
ejpam-4675	226	14	=	=	SYM
ejpam-4675	226	15	h′	h′	X
ejpam-4675	226	16	(	(	PUNCT
ejpam-4675	226	17	g(x	g(x	NOUN
ejpam-4675	226	18	)	)	PUNCT
ejpam-4675	226	19	)	)	PUNCT
ejpam-4675	226	20	=	=	SYM
ejpam-4675	226	21	(	(	PUNCT
ejpam-4675	226	22	h′	h′	PROPN
ejpam-4675	226	23	◦	◦	PROPN
ejpam-4675	226	24	g)(x	g)(x	PROPN
ejpam-4675	226	25	)	)	PUNCT
ejpam-4675	226	26	=	=	SYM
ejpam-4675	226	27	φ(x	φ(x	NOUN
ejpam-4675	226	28	)	)	PUNCT
ejpam-4675	226	29	=	=	SYM
ejpam-4675	226	30	h	h	NOUN
ejpam-4675	226	31	(	(	PUNCT
ejpam-4675	226	32	[	[	X
ejpam-4675	226	33	x]s	x]s	PROPN
ejpam-4675	226	34	)	)	PUNCT
ejpam-4675	226	35	.	.	PUNCT
ejpam-4675	227	1	thus	thus	ADV
ejpam-4675	227	2	,	,	PUNCT
ejpam-4675	227	3	h′	h′	PROPN
ejpam-4675	227	4	(	(	PUNCT
ejpam-4675	227	5	[	[	X
ejpam-4675	227	6	x]s	x]s	NOUN
ejpam-4675	227	7	)	)	PUNCT
ejpam-4675	227	8	=	=	SYM
ejpam-4675	227	9	h	h	NOUN
ejpam-4675	227	10	(	(	PUNCT
ejpam-4675	227	11	[	[	X
ejpam-4675	227	12	x]s	x]s	PROPN
ejpam-4675	227	13	)	)	PUNCT
ejpam-4675	227	14	for	for	ADP
ejpam-4675	227	15	all	all	PRON
ejpam-4675	227	16	[	[	X
ejpam-4675	227	17	a]s	a]s	ADJ
ejpam-4675	227	18	∈	∈	PROPN
ejpam-4675	227	19	x	x	PROPN
ejpam-4675	227	20	/	/	SYM
ejpam-4675	227	21	s	s	PROPN
ejpam-4675	227	22	,	,	PUNCT
ejpam-4675	227	23	i.e.	i.e.	X
ejpam-4675	227	24	h	h	NOUN
ejpam-4675	227	25	is	be	AUX
ejpam-4675	227	26	unique	unique	ADJ
ejpam-4675	227	27	.	.	PUNCT
ejpam-4675	228	1	now	now	ADV
ejpam-4675	228	2	,	,	PUNCT
ejpam-4675	228	3	to	to	PART
ejpam-4675	228	4	show	show	VERB
ejpam-4675	228	5	that	that	SCONJ
ejpam-4675	228	6	h	h	NOUN
ejpam-4675	228	7	is	be	AUX
ejpam-4675	228	8	one	one	NUM
ejpam-4675	228	9	-	-	PUNCT
ejpam-4675	228	10	to	to	ADP
ejpam-4675	228	11	-	-	PUNCT
ejpam-4675	228	12	one	one	NOUN
ejpam-4675	228	13	if	if	SCONJ
ejpam-4675	228	14	and	and	CCONJ
ejpam-4675	228	15	only	only	ADV
ejpam-4675	228	16	if	if	SCONJ
ejpam-4675	228	17	s	s	PROPN
ejpam-4675	228	18	=	=	SYM
ejpam-4675	228	19	kerφ	kerφ	PROPN
ejpam-4675	228	20	,	,	PUNCT
ejpam-4675	228	21	suppose	suppose	VERB
ejpam-4675	228	22	h	h	NOUN
ejpam-4675	228	23	is	be	AUX
ejpam-4675	228	24	one	one	NUM
ejpam-4675	228	25	-	-	PUNCT
ejpam-4675	228	26	to	to	ADP
ejpam-4675	228	27	-	-	PUNCT
ejpam-4675	228	28	one	one	NUM
ejpam-4675	228	29	and	and	CCONJ
ejpam-4675	228	30	x	x	SYM
ejpam-4675	228	31	∈	∈	PROPN
ejpam-4675	228	32	kerφ	kerφ	PROPN
ejpam-4675	228	33	.	.	PUNCT
ejpam-4675	229	1	then	then	ADV
ejpam-4675	229	2	h	h	NOUN
ejpam-4675	229	3	(	(	PUNCT
ejpam-4675	229	4	[	[	X
ejpam-4675	229	5	x]s	x]s	NOUN
ejpam-4675	229	6	)	)	PUNCT
ejpam-4675	230	1	=	=	SYM
ejpam-4675	230	2	φ(x	φ(x	X
ejpam-4675	230	3	)	)	PUNCT
ejpam-4675	230	4	=	=	SYM
ejpam-4675	230	5	1y	1y	NUM
ejpam-4675	230	6	=	=	SYM
ejpam-4675	230	7	h	h	NOUN
ejpam-4675	230	8	(	(	PUNCT
ejpam-4675	230	9	[	[	X
ejpam-4675	230	10	1]s	1]s	NUM
ejpam-4675	230	11	)	)	PUNCT
ejpam-4675	230	12	and	and	CCONJ
ejpam-4675	230	13	since	since	SCONJ
ejpam-4675	230	14	h	h	NOUN
ejpam-4675	230	15	is	be	AUX
ejpam-4675	230	16	one	one	NUM
ejpam-4675	230	17	-	-	PUNCT
ejpam-4675	230	18	to	to	ADP
ejpam-4675	230	19	-	-	PUNCT
ejpam-4675	230	20	one	one	NOUN
ejpam-4675	230	21	,	,	PUNCT
ejpam-4675	230	22	[	[	X
ejpam-4675	230	23	x]s	x]s	NOUN
ejpam-4675	230	24	=	=	PUNCT
ejpam-4675	231	1	[	[	X
ejpam-4675	231	2	1]s	1]s	NUM
ejpam-4675	231	3	.	.	PUNCT
ejpam-4675	232	1	it	it	PRON
ejpam-4675	232	2	follows	follow	VERB
ejpam-4675	232	3	that	that	SCONJ
ejpam-4675	232	4	x	x	PUNCT
ejpam-4675	232	5	∼	∼	NOUN
ejpam-4675	232	6	1x	1x	NUM
ejpam-4675	232	7	,	,	PUNCT
ejpam-4675	232	8	and	and	CCONJ
ejpam-4675	232	9	so	so	ADV
ejpam-4675	232	10	x	x	X
ejpam-4675	232	11	·	·	PUNCT
ejpam-4675	232	12	1x	1x	NUM
ejpam-4675	232	13	∈	∈	PROPN
ejpam-4675	232	14	s	s	X
ejpam-4675	232	15	and	and	CCONJ
ejpam-4675	232	16	1x	1x	NUM
ejpam-4675	232	17	·	·	PUNCT
ejpam-4675	233	1	x	x	SYM
ejpam-4675	233	2	∈	∈	PROPN
ejpam-4675	233	3	s.	s.	PROPN
ejpam-4675	233	4	since	since	SCONJ
ejpam-4675	233	5	1x	1x	PROPN
ejpam-4675	233	6	∈	∈	PROPN
ejpam-4675	233	7	s	s	PART
ejpam-4675	233	8	and	and	CCONJ
ejpam-4675	233	9	s	s	VERB
ejpam-4675	233	10	is	be	AUX
ejpam-4675	233	11	a	a	DET
ejpam-4675	233	12	db	db	NOUN
ejpam-4675	233	13	-	-	PUNCT
ejpam-4675	233	14	filter	filter	NOUN
ejpam-4675	233	15	,	,	PUNCT
ejpam-4675	233	16	x	x	PROPN
ejpam-4675	233	17	∈	∈	PROPN
ejpam-4675	233	18	s.	s.	PROPN
ejpam-4675	233	19	thus	thus	ADV
ejpam-4675	233	20	,	,	PUNCT
ejpam-4675	233	21	kerφ	kerφ	VERB
ejpam-4675	233	22	⊆	⊆	NUM
ejpam-4675	233	23	s	s	NOUN
ejpam-4675	233	24	and	and	CCONJ
ejpam-4675	233	25	since	since	SCONJ
ejpam-4675	233	26	s	s	NOUN
ejpam-4675	233	27	⊆	⊆	NUM
ejpam-4675	233	28	kerφ	kerφ	NOUN
ejpam-4675	233	29	by	by	ADP
ejpam-4675	233	30	hypothesis	hypothesis	NOUN
ejpam-4675	233	31	,	,	PUNCT
ejpam-4675	233	32	kerφ	kerφ	PROPN
ejpam-4675	233	33	=	=	PUNCT
ejpam-4675	233	34	s.	s.	PROPN
ejpam-4675	233	35	suppose	suppose	VERB
ejpam-4675	233	36	that	that	SCONJ
ejpam-4675	233	37	kerφ	kerφ	PROPN
ejpam-4675	233	38	=	=	PROPN
ejpam-4675	233	39	s	s	PROPN
ejpam-4675	233	40	and	and	CCONJ
ejpam-4675	233	41	[	[	X
ejpam-4675	233	42	x]s	x]s	PROPN
ejpam-4675	233	43	,	,	PUNCT
ejpam-4675	233	44	[	[	X
ejpam-4675	233	45	y]s	y]s	X
ejpam-4675	233	46	∈	∈	NOUN
ejpam-4675	233	47	x	x	PRON
ejpam-4675	233	48	/	/	SYM
ejpam-4675	233	49	s	s	VERB
ejpam-4675	233	50	such	such	ADJ
ejpam-4675	233	51	that	that	DET
ejpam-4675	233	52	h	h	NOUN
ejpam-4675	233	53	(	(	PUNCT
ejpam-4675	233	54	[	[	X
ejpam-4675	233	55	x]s	x]s	NOUN
ejpam-4675	233	56	)	)	PUNCT
ejpam-4675	234	1	=	=	SYM
ejpam-4675	234	2	h	h	NOUN
ejpam-4675	234	3	(	(	PUNCT
ejpam-4675	234	4	[	[	X
ejpam-4675	234	5	y]s	y]s	X
ejpam-4675	234	6	)	)	PUNCT
ejpam-4675	234	7	.	.	PUNCT
ejpam-4675	235	1	then	then	ADV
ejpam-4675	235	2	φ(x	φ(x	NOUN
ejpam-4675	235	3	)	)	PUNCT
ejpam-4675	235	4	=	=	SYM
ejpam-4675	235	5	φ(y	φ(y	NOUN
ejpam-4675	235	6	)	)	PUNCT
ejpam-4675	235	7	.	.	PUNCT
ejpam-4675	236	1	by	by	ADP
ejpam-4675	236	2	corollary	corollary	ADJ
ejpam-4675	236	3	1	1	NUM
ejpam-4675	236	4	,	,	PUNCT
ejpam-4675	236	5	1y	1y	NOUN
ejpam-4675	236	6	=	=	SYM
ejpam-4675	236	7	φ(x	φ(x	NOUN
ejpam-4675	236	8	)	)	PUNCT
ejpam-4675	236	9	∗	∗	NOUN
ejpam-4675	236	10	φ(y	φ(y	NOUN
ejpam-4675	236	11	)	)	PUNCT
ejpam-4675	236	12	=	=	SYM
ejpam-4675	236	13	φ(x	φ(x	PROPN
ejpam-4675	236	14	·	·	PUNCT
ejpam-4675	236	15	y	y	X
ejpam-4675	236	16	)	)	PUNCT
ejpam-4675	236	17	which	which	PRON
ejpam-4675	236	18	implies	imply	VERB
ejpam-4675	236	19	that	that	SCONJ
ejpam-4675	236	20	x	x	X
ejpam-4675	236	21	·	·	PUNCT
ejpam-4675	236	22	y	y	PROPN
ejpam-4675	236	23	∈	∈	PROPN
ejpam-4675	236	24	kerφ	kerφ	PROPN
ejpam-4675	236	25	=	=	SYM
ejpam-4675	236	26	s.	s.	PROPN
ejpam-4675	236	27	similarly	similarly	ADV
ejpam-4675	236	28	,	,	PUNCT
ejpam-4675	236	29	1y	1y	PROPN
ejpam-4675	236	30	=	=	SYM
ejpam-4675	236	31	φ(y	φ(y	ADJ
ejpam-4675	236	32	)	)	PUNCT
ejpam-4675	236	33	∗φ(x	∗φ(x	PROPN
ejpam-4675	236	34	)	)	PUNCT
ejpam-4675	236	35	=	=	PUNCT
ejpam-4675	236	36	φ(y	φ(y	NOUN
ejpam-4675	236	37	·	·	PUNCT
ejpam-4675	236	38	x	x	X
ejpam-4675	236	39	)	)	PUNCT
ejpam-4675	236	40	implies	imply	VERB
ejpam-4675	236	41	that	that	SCONJ
ejpam-4675	236	42	y	y	PROPN
ejpam-4675	236	43	·	·	PUNCT
ejpam-4675	236	44	x	x	PROPN
ejpam-4675	236	45	∈	∈	PROPN
ejpam-4675	236	46	s.	s.	PROPN
ejpam-4675	236	47	hence	hence	ADV
ejpam-4675	236	48	,	,	PUNCT
ejpam-4675	236	49	x	x	PUNCT
ejpam-4675	236	50	∼	∼	NOUN
ejpam-4675	236	51	y	y	NOUN
ejpam-4675	236	52	and	and	CCONJ
ejpam-4675	236	53	it	it	PRON
ejpam-4675	236	54	follows	follow	VERB
ejpam-4675	236	55	that	that	SCONJ
ejpam-4675	237	1	[	[	X
ejpam-4675	237	2	x]s	x]s	NOUN
ejpam-4675	237	3	=	=	PUNCT
ejpam-4675	238	1	[	[	X
ejpam-4675	238	2	y]s	y]s	X
ejpam-4675	238	3	,	,	PUNCT
ejpam-4675	238	4	showing	show	VERB
ejpam-4675	238	5	that	that	SCONJ
ejpam-4675	238	6	h	h	NOUN
ejpam-4675	238	7	is	be	AUX
ejpam-4675	238	8	one	one	NUM
ejpam-4675	238	9	-	-	PUNCT
ejpam-4675	238	10	to	to	ADP
ejpam-4675	238	11	-	-	PUNCT
ejpam-4675	238	12	one	one	NUM
ejpam-4675	238	13	.	.	PUNCT
ejpam-4675	239	1	theorem	theorem	VERB
ejpam-4675	239	2	7	7	NUM
ejpam-4675	239	3	.	.	PUNCT
ejpam-4675	240	1	first	first	PROPN
ejpam-4675	240	2	isomorphism	isomorphism	PROPN
ejpam-4675	240	3	theorem	theorem	NOUN
ejpam-4675	240	4	for	for	ADP
ejpam-4675	240	5	the	the	DET
ejpam-4675	240	6	db	db	PROPN
ejpam-4675	240	7	-	-	PUNCT
ejpam-4675	240	8	algebra	algebra	NOUN
ejpam-4675	240	9	let	let	VERB
ejpam-4675	240	10	φ	φ	PROPN
ejpam-4675	240	11	be	be	AUX
ejpam-4675	240	12	a	a	DET
ejpam-4675	240	13	db	db	NOUN
ejpam-4675	240	14	-	-	PUNCT
ejpam-4675	240	15	homomorphism	homomorphism	NOUN
ejpam-4675	240	16	of	of	ADP
ejpam-4675	240	17	a	a	DET
ejpam-4675	240	18	db	db	NOUN
ejpam-4675	240	19	-	-	PUNCT
ejpam-4675	240	20	algebra	algebra	NOUN
ejpam-4675	240	21	(	(	PUNCT
ejpam-4675	240	22	x	x	X
ejpam-4675	240	23	,	,	PUNCT
ejpam-4675	240	24	·	·	PUNCT
ejpam-4675	240	25	,	,	PUNCT
ejpam-4675	240	26	1x	1x	NUM
ejpam-4675	240	27	)	)	PUNCT
ejpam-4675	240	28	into	into	ADP
ejpam-4675	240	29	a	a	DET
ejpam-4675	240	30	db	db	NOUN
ejpam-4675	240	31	-	-	PUNCT
ejpam-4675	240	32	algebra	algebra	NOUN
ejpam-4675	240	33	(	(	PUNCT
ejpam-4675	240	34	y	y	PROPN
ejpam-4675	240	35	,	,	PUNCT
ejpam-4675	240	36	∗	∗	NOUN
ejpam-4675	240	37	,	,	PUNCT
ejpam-4675	240	38	1y	1y	PROPN
ejpam-4675	240	39	)	)	PUNCT
ejpam-4675	240	40	,	,	PUNCT
ejpam-4675	240	41	then	then	ADV
ejpam-4675	240	42	(	(	PUNCT
ejpam-4675	240	43	x/	x/	PROPN
ejpam-4675	240	44	kerφ	kerφ	PROPN
ejpam-4675	240	45	,	,	PUNCT
ejpam-4675	240	46	θ	θ	PROPN
ejpam-4675	240	47	,	,	PUNCT
ejpam-4675	240	48	[	[	X
ejpam-4675	240	49	1]kerφ	1]kerφ	NUM
ejpam-4675	240	50	)	)	PUNCT
ejpam-4675	240	51	∼=	∼=	PART
ejpam-4675	240	52	φ(x	φ(x	NOUN
ejpam-4675	240	53	)	)	PUNCT
ejpam-4675	240	54	.	.	PUNCT
ejpam-4675	241	1	proof	proof	NOUN
ejpam-4675	241	2	.	.	PUNCT
ejpam-4675	242	1	let	let	VERB
ejpam-4675	242	2	s	s	PROPN
ejpam-4675	242	3	=	=	SYM
ejpam-4675	242	4	kerφ	kerφ	PROPN
ejpam-4675	242	5	,	,	PUNCT
ejpam-4675	242	6	g	g	PROPN
ejpam-4675	242	7	be	be	AUX
ejpam-4675	242	8	the	the	DET
ejpam-4675	242	9	natural	natural	ADJ
ejpam-4675	242	10	db	db	NOUN
ejpam-4675	242	11	-	-	PUNCT
ejpam-4675	242	12	homomorphism	homomorphism	NOUN
ejpam-4675	242	13	from	from	ADP
ejpam-4675	242	14	x	x	PRON
ejpam-4675	242	15	onto	onto	ADP
ejpam-4675	242	16	x	x	PROPN
ejpam-4675	242	17	/	/	SYM
ejpam-4675	242	18	s	s	PROPN
ejpam-4675	242	19	,	,	PUNCT
ejpam-4675	242	20	the	the	DET
ejpam-4675	242	21	mapping	mapping	NOUN
ejpam-4675	242	22	f	f	X
ejpam-4675	242	23	:	:	PUNCT
ejpam-4675	242	24	x	x	X
ejpam-4675	242	25	/	/	SYM
ejpam-4675	242	26	s	s	X
ejpam-4675	242	27	→	→	SYM
ejpam-4675	242	28	φ(x	φ(x	X
ejpam-4675	242	29	)	)	PUNCT
ejpam-4675	242	30	be	be	AUX
ejpam-4675	242	31	defined	define	VERB
ejpam-4675	242	32	by	by	ADP
ejpam-4675	242	33	f	f	PROPN
ejpam-4675	242	34	(	(	PUNCT
ejpam-4675	242	35	[	[	X
ejpam-4675	242	36	x]s	x]s	NOUN
ejpam-4675	242	37	)	)	PUNCT
ejpam-4675	243	1	=	=	SYM
ejpam-4675	243	2	φ(x	φ(x	NOUN
ejpam-4675	243	3	)	)	PUNCT
ejpam-4675	243	4	for	for	ADP
ejpam-4675	243	5	all	all	DET
ejpam-4675	243	6	[	[	X
ejpam-4675	243	7	x]s	x]s	PROPN
ejpam-4675	243	8	∈	∈	PROPN
ejpam-4675	243	9	x	x	SYM
ejpam-4675	243	10	/	/	SYM
ejpam-4675	243	11	s	s	PROPN
ejpam-4675	243	12	,	,	PUNCT
ejpam-4675	243	13	and	and	CCONJ
ejpam-4675	243	14	recall	recall	VERB
ejpam-4675	243	15	that	that	SCONJ
ejpam-4675	243	16	φ(x	φ(x	NOUN
ejpam-4675	243	17	)	)	PUNCT
ejpam-4675	243	18	is	be	AUX
ejpam-4675	243	19	a	a	DET
ejpam-4675	243	20	db	db	NOUN
ejpam-4675	243	21	-	-	PUNCT
ejpam-4675	243	22	subalgebra	subalgebra	NOUN
ejpam-4675	243	23	of	of	ADP
ejpam-4675	243	24	y	y	PROPN
ejpam-4675	243	25	by	by	ADP
ejpam-4675	243	26	theorem	theorem	VERB
ejpam-4675	243	27	4	4	NUM
ejpam-4675	243	28	(	(	PUNCT
ejpam-4675	243	29	iii	iii	NOUN
ejpam-4675	243	30	)	)	PUNCT
ejpam-4675	243	31	which	which	PRON
ejpam-4675	243	32	implies	imply	VERB
ejpam-4675	243	33	that	that	SCONJ
ejpam-4675	243	34	φ(x	φ(x	NOUN
ejpam-4675	243	35	)	)	PUNCT
ejpam-4675	243	36	has	have	VERB
ejpam-4675	243	37	the	the	DET
ejpam-4675	243	38	same	same	ADJ
ejpam-4675	243	39	binary	binary	NOUN
ejpam-4675	243	40	operator	operator	NOUN
ejpam-4675	243	41	as	as	ADP
ejpam-4675	243	42	y	y	PROPN
ejpam-4675	243	43	.	.	PUNCT
ejpam-4675	244	1	j.e	j.e	PROPN
ejpam-4675	244	2	.	.	PROPN
ejpam-4675	244	3	bolima	bolima	PROPN
ejpam-4675	244	4	,	,	PUNCT
ejpam-4675	244	5	k.b	k.b	PROPN
ejpam-4675	244	6	.	.	PUNCT
ejpam-4675	244	7	fuentes	fuentes	PROPN
ejpam-4675	244	8	/	/	SYM
ejpam-4675	244	9	eur	eur	PROPN
ejpam-4675	244	10	.	.	PUNCT
ejpam-4675	245	1	j.	j.	PROPN
ejpam-4675	245	2	pure	pure	PROPN
ejpam-4675	245	3	appl	appl	PROPN
ejpam-4675	245	4	.	.	PROPN
ejpam-4675	245	5	math	math	PROPN
ejpam-4675	245	6	,	,	PUNCT
ejpam-4675	245	7	16	16	NUM
ejpam-4675	245	8	(	(	PUNCT
ejpam-4675	245	9	1	1	NUM
ejpam-4675	245	10	)	)	PUNCT
ejpam-4675	245	11	(	(	PUNCT
ejpam-4675	245	12	2023	2023	NUM
ejpam-4675	245	13	)	)	PUNCT
ejpam-4675	245	14	,	,	PUNCT
ejpam-4675	245	15	577	577	NUM
ejpam-4675	245	16	-	-	SYM
ejpam-4675	245	17	586	586	NUM
ejpam-4675	245	18	584	584	NUM
ejpam-4675	245	19	let	let	VERB
ejpam-4675	245	20	[	[	X
ejpam-4675	245	21	x]s	x]s	NOUN
ejpam-4675	245	22	,	,	PUNCT
ejpam-4675	245	23	[	[	X
ejpam-4675	245	24	y]s	y]s	X
ejpam-4675	245	25	∈	∈	NOUN
ejpam-4675	245	26	x	x	PRON
ejpam-4675	245	27	/	/	SYM
ejpam-4675	245	28	s	s	VERB
ejpam-4675	245	29	such	such	ADJ
ejpam-4675	245	30	that	that	SCONJ
ejpam-4675	246	1	[	[	X
ejpam-4675	246	2	x]s	x]s	NOUN
ejpam-4675	246	3	=	=	PUNCT
ejpam-4675	247	1	[	[	X
ejpam-4675	247	2	y]s	y]s	X
ejpam-4675	247	3	.	.	PUNCT
ejpam-4675	248	1	then	then	ADV
ejpam-4675	248	2	x	x	PUNCT
ejpam-4675	248	3	∼	∼	NOUN
ejpam-4675	248	4	y	y	NOUN
ejpam-4675	249	1	and	and	CCONJ
ejpam-4675	249	2	it	it	PRON
ejpam-4675	249	3	follows	follow	VERB
ejpam-4675	249	4	that	that	SCONJ
ejpam-4675	249	5	x	x	X
ejpam-4675	249	6	·	·	PUNCT
ejpam-4675	249	7	y	y	X
ejpam-4675	249	8	∈	∈	PROPN
ejpam-4675	249	9	s	s	X
ejpam-4675	249	10	and	and	CCONJ
ejpam-4675	249	11	y	y	PROPN
ejpam-4675	249	12	·	·	PUNCT
ejpam-4675	250	1	x	x	SYM
ejpam-4675	250	2	∈	∈	PROPN
ejpam-4675	250	3	s.	s.	PROPN
ejpam-4675	250	4	since	since	SCONJ
ejpam-4675	250	5	s	s	PROPN
ejpam-4675	250	6	=	=	SYM
ejpam-4675	250	7	kerφ	kerφ	PROPN
ejpam-4675	250	8	,	,	PUNCT
ejpam-4675	250	9	φ(x	φ(x	PROPN
ejpam-4675	250	10	·	·	PUNCT
ejpam-4675	250	11	y	y	X
ejpam-4675	250	12	)	)	PUNCT
ejpam-4675	250	13	=	=	SYM
ejpam-4675	250	14	φ(x	φ(x	NOUN
ejpam-4675	250	15	)	)	PUNCT
ejpam-4675	250	16	∗	∗	NOUN
ejpam-4675	250	17	φ(y	φ(y	NOUN
ejpam-4675	250	18	)	)	PUNCT
ejpam-4675	250	19	=	=	SYM
ejpam-4675	250	20	1y	1y	NUM
ejpam-4675	250	21	=	=	SYM
ejpam-4675	250	22	φ(y	φ(y	NOUN
ejpam-4675	250	23	)	)	PUNCT
ejpam-4675	250	24	∗	∗	NOUN
ejpam-4675	250	25	φ(x	φ(x	PROPN
ejpam-4675	250	26	)	)	PUNCT
ejpam-4675	250	27	=	=	PUNCT
ejpam-4675	250	28	φ(y	φ(y	NOUN
ejpam-4675	250	29	·	·	PUNCT
ejpam-4675	250	30	x	x	X
ejpam-4675	250	31	)	)	PUNCT
ejpam-4675	250	32	and	and	CCONJ
ejpam-4675	250	33	by	by	ADP
ejpam-4675	250	34	lemma	lemma	PROPN
ejpam-4675	250	35	1	1	NUM
ejpam-4675	250	36	,	,	PUNCT
ejpam-4675	250	37	φ(x	φ(x	NOUN
ejpam-4675	250	38	)	)	PUNCT
ejpam-4675	250	39	=	=	SYM
ejpam-4675	250	40	φ(y	φ(y	NOUN
ejpam-4675	250	41	)	)	PUNCT
ejpam-4675	250	42	which	which	PRON
ejpam-4675	250	43	is	be	AUX
ejpam-4675	250	44	f	f	X
ejpam-4675	250	45	(	(	PUNCT
ejpam-4675	250	46	[	[	X
ejpam-4675	250	47	x]s	x]s	NOUN
ejpam-4675	250	48	)	)	PUNCT
ejpam-4675	251	1	=	=	SYM
ejpam-4675	251	2	f	f	X
ejpam-4675	251	3	(	(	PUNCT
ejpam-4675	251	4	[	[	X
ejpam-4675	251	5	y]s	y]s	X
ejpam-4675	251	6	)	)	PUNCT
ejpam-4675	251	7	.	.	PUNCT
ejpam-4675	252	1	hence	hence	ADV
ejpam-4675	252	2	,	,	PUNCT
ejpam-4675	252	3	f	f	PROPN
ejpam-4675	252	4	is	be	AUX
ejpam-4675	252	5	well	well	ADV
ejpam-4675	252	6	-	-	PUNCT
ejpam-4675	252	7	defined	define	VERB
ejpam-4675	252	8	.	.	PUNCT
ejpam-4675	253	1	let	let	VERB
ejpam-4675	253	2	[	[	X
ejpam-4675	253	3	x]s	x]s	PROPN
ejpam-4675	253	4	,	,	PUNCT
ejpam-4675	253	5	[	[	X
ejpam-4675	253	6	y]s	y]s	X
ejpam-4675	253	7	∈	∈	PROPN
ejpam-4675	253	8	x	x	X
ejpam-4675	253	9	/	/	SYM
ejpam-4675	253	10	s.	s.	PROPN
ejpam-4675	254	1	then	then	ADV
ejpam-4675	254	2	f	f	X
ejpam-4675	254	3	(	(	PUNCT
ejpam-4675	254	4	[	[	X
ejpam-4675	254	5	x]sθ[y]s	x]sθ[y]s	X
ejpam-4675	254	6	)	)	PUNCT
ejpam-4675	255	1	=	=	SYM
ejpam-4675	255	2	f	f	X
ejpam-4675	255	3	(	(	PUNCT
ejpam-4675	255	4	[	[	X
ejpam-4675	255	5	x	x	X
ejpam-4675	255	6	·	·	PUNCT
ejpam-4675	255	7	y]s	y]s	NUM
ejpam-4675	255	8	)	)	PUNCT
ejpam-4675	256	1	=	=	PUNCT
ejpam-4675	257	1	φ(x	φ(x	PROPN
ejpam-4675	257	2	·	·	PUNCT
ejpam-4675	257	3	y	y	X
ejpam-4675	257	4	)	)	PUNCT
ejpam-4675	257	5	=	=	SYM
ejpam-4675	257	6	φ(x	φ(x	NOUN
ejpam-4675	257	7	)	)	PUNCT
ejpam-4675	257	8	∗	∗	NOUN
ejpam-4675	257	9	φ(y	φ(y	NOUN
ejpam-4675	257	10	)	)	PUNCT
ejpam-4675	257	11	=	=	SYM
ejpam-4675	257	12	f	f	X
ejpam-4675	257	13	(	(	PUNCT
ejpam-4675	257	14	[	[	X
ejpam-4675	257	15	x]s	x]s	NOUN
ejpam-4675	257	16	)	)	PUNCT
ejpam-4675	257	17	∗	∗	PROPN
ejpam-4675	257	18	f	f	PROPN
ejpam-4675	257	19	(	(	PUNCT
ejpam-4675	257	20	[	[	X
ejpam-4675	257	21	y]s	y]s	X
ejpam-4675	257	22	)	)	PUNCT
ejpam-4675	257	23	thus	thus	ADV
ejpam-4675	257	24	,	,	PUNCT
ejpam-4675	257	25	f	f	PROPN
ejpam-4675	257	26	is	be	AUX
ejpam-4675	257	27	a	a	DET
ejpam-4675	257	28	db	db	NOUN
ejpam-4675	257	29	-	-	PUNCT
ejpam-4675	257	30	homomorphism	homomorphism	NOUN
ejpam-4675	257	31	.	.	PUNCT
ejpam-4675	258	1	let	let	VERB
ejpam-4675	258	2	[	[	X
ejpam-4675	258	3	x]s	x]s	PROPN
ejpam-4675	258	4	,	,	PUNCT
ejpam-4675	258	5	[	[	X
ejpam-4675	258	6	y]s	y]s	X
ejpam-4675	258	7	∈	∈	NOUN
ejpam-4675	258	8	x	x	PRON
ejpam-4675	258	9	/	/	SYM
ejpam-4675	258	10	s	s	VERB
ejpam-4675	258	11	such	such	ADJ
ejpam-4675	258	12	that	that	SCONJ
ejpam-4675	258	13	f	f	PROPN
ejpam-4675	258	14	(	(	PUNCT
ejpam-4675	258	15	[	[	X
ejpam-4675	258	16	x]s	x]s	NOUN
ejpam-4675	258	17	)	)	PUNCT
ejpam-4675	259	1	=	=	SYM
ejpam-4675	259	2	f	f	X
ejpam-4675	259	3	(	(	PUNCT
ejpam-4675	259	4	[	[	X
ejpam-4675	259	5	y]s	y]s	X
ejpam-4675	259	6	)	)	PUNCT
ejpam-4675	259	7	.	.	PUNCT
ejpam-4675	260	1	then	then	ADV
ejpam-4675	260	2	φ(x	φ(x	NOUN
ejpam-4675	260	3	)	)	PUNCT
ejpam-4675	260	4	=	=	SYM
ejpam-4675	260	5	φ(y	φ(y	NOUN
ejpam-4675	260	6	)	)	PUNCT
ejpam-4675	260	7	.	.	PUNCT
ejpam-4675	261	1	it	it	PRON
ejpam-4675	261	2	follows	follow	VERB
ejpam-4675	261	3	that	that	SCONJ
ejpam-4675	261	4	1y	1y	NOUN
ejpam-4675	261	5	=	=	SYM
ejpam-4675	261	6	φ(x	φ(x	NOUN
ejpam-4675	261	7	)	)	PUNCT
ejpam-4675	261	8	∗	∗	NOUN
ejpam-4675	261	9	φ(y	φ(y	NOUN
ejpam-4675	261	10	)	)	PUNCT
ejpam-4675	262	1	=	=	SYM
ejpam-4675	262	2	φ(x	φ(x	PROPN
ejpam-4675	262	3	·	·	PUNCT
ejpam-4675	262	4	y	y	X
ejpam-4675	262	5	)	)	PUNCT
ejpam-4675	262	6	which	which	PRON
ejpam-4675	262	7	implies	imply	VERB
ejpam-4675	262	8	that	that	SCONJ
ejpam-4675	262	9	x	x	X
ejpam-4675	262	10	·	·	PUNCT
ejpam-4675	262	11	y	y	PROPN
ejpam-4675	262	12	∈	∈	PROPN
ejpam-4675	262	13	kerφ	kerφ	PROPN
ejpam-4675	262	14	=	=	SYM
ejpam-4675	262	15	s.	s.	PROPN
ejpam-4675	262	16	similarly	similarly	ADV
ejpam-4675	262	17	,	,	PUNCT
ejpam-4675	262	18	1y	1y	PROPN
ejpam-4675	262	19	=	=	SYM
ejpam-4675	262	20	φ(y	φ(y	NOUN
ejpam-4675	262	21	)	)	PUNCT
ejpam-4675	262	22	∗	∗	NOUN
ejpam-4675	262	23	φ(x	φ(x	PROPN
ejpam-4675	262	24	)	)	PUNCT
ejpam-4675	262	25	=	=	PUNCT
ejpam-4675	263	1	φ(y	φ(y	NOUN
ejpam-4675	263	2	·	·	PUNCT
ejpam-4675	263	3	x	x	X
ejpam-4675	263	4	)	)	PUNCT
ejpam-4675	263	5	implies	imply	VERB
ejpam-4675	263	6	that	that	SCONJ
ejpam-4675	263	7	y	y	PROPN
ejpam-4675	263	8	·	·	PUNCT
ejpam-4675	263	9	x	x	SYM
ejpam-4675	263	10	∈	∈	PROPN
ejpam-4675	263	11	s.	s.	PROPN
ejpam-4675	263	12	thus	thus	ADV
ejpam-4675	263	13	,	,	PUNCT
ejpam-4675	263	14	x	x	PUNCT
ejpam-4675	263	15	∼	∼	NOUN
ejpam-4675	263	16	y	y	PROPN
ejpam-4675	263	17	which	which	PRON
ejpam-4675	263	18	implies	imply	VERB
ejpam-4675	263	19	that	that	SCONJ
ejpam-4675	263	20	[	[	X
ejpam-4675	263	21	x]s	x]s	NOUN
ejpam-4675	263	22	=	=	PUNCT
ejpam-4675	264	1	[	[	X
ejpam-4675	264	2	y]s	y]s	X
ejpam-4675	264	3	,	,	PUNCT
ejpam-4675	264	4	so	so	CCONJ
ejpam-4675	264	5	f	f	PROPN
ejpam-4675	264	6	is	be	AUX
ejpam-4675	264	7	one	one	NUM
ejpam-4675	264	8	-	-	PUNCT
ejpam-4675	264	9	to	to	ADP
ejpam-4675	264	10	-	-	PUNCT
ejpam-4675	264	11	one	one	NUM
ejpam-4675	264	12	.	.	PUNCT
ejpam-4675	265	1	let	let	VERB
ejpam-4675	265	2	y	y	PRON
ejpam-4675	265	3	∈	∈	PROPN
ejpam-4675	265	4	φ(x	φ(x	PROPN
ejpam-4675	265	5	)	)	PUNCT
ejpam-4675	265	6	,	,	PUNCT
ejpam-4675	265	7	then	then	ADV
ejpam-4675	265	8	there	there	PRON
ejpam-4675	265	9	exists	exist	VERB
ejpam-4675	265	10	x	x	X
ejpam-4675	265	11	∈	∈	PROPN
ejpam-4675	265	12	x	x	PUNCT
ejpam-4675	265	13	such	such	ADJ
ejpam-4675	265	14	that	that	SCONJ
ejpam-4675	265	15	y	y	NOUN
ejpam-4675	265	16	=	=	SYM
ejpam-4675	265	17	φ(x	φ(x	PROPN
ejpam-4675	265	18	)	)	PUNCT
ejpam-4675	265	19	and	and	CCONJ
ejpam-4675	265	20	[	[	X
ejpam-4675	265	21	x]s	x]s	PROPN
ejpam-4675	265	22	∈	∈	PROPN
ejpam-4675	265	23	x	x	X
ejpam-4675	265	24	/	/	SYM
ejpam-4675	265	25	s.	s.	PROPN
ejpam-4675	266	1	then	then	ADV
ejpam-4675	266	2	f	f	X
ejpam-4675	266	3	(	(	PUNCT
ejpam-4675	266	4	[	[	X
ejpam-4675	266	5	x]s	x]s	NOUN
ejpam-4675	266	6	)	)	PUNCT
ejpam-4675	266	7	=	=	SYM
ejpam-4675	266	8	φ(x	φ(x	NOUN
ejpam-4675	266	9	)	)	PUNCT
ejpam-4675	266	10	=	=	SYM
ejpam-4675	267	1	y.	y.	PROPN
ejpam-4675	267	2	hence	hence	ADV
ejpam-4675	267	3	,	,	PUNCT
ejpam-4675	267	4	f	f	PROPN
ejpam-4675	267	5	is	be	AUX
ejpam-4675	267	6	onto	onto	ADP
ejpam-4675	267	7	and	and	CCONJ
ejpam-4675	267	8	consequently	consequently	ADV
ejpam-4675	267	9	,	,	PUNCT
ejpam-4675	267	10	f	f	PROPN
ejpam-4675	267	11	is	be	AUX
ejpam-4675	267	12	a	a	DET
ejpam-4675	267	13	db	db	NOUN
ejpam-4675	267	14	-	-	PUNCT
ejpam-4675	267	15	isomorphism	isomorphism	NOUN
ejpam-4675	267	16	.	.	PUNCT
ejpam-4675	267	17	.	.	PUNCT
ejpam-4675	268	1	proposition	proposition	NOUN
ejpam-4675	268	2	3	3	X
ejpam-4675	268	3	.	.	PUNCT
ejpam-4675	268	4	suppose	suppose	VERB
ejpam-4675	268	5	f	f	X
ejpam-4675	268	6	:	:	PUNCT
ejpam-4675	268	7	(	(	PUNCT
ejpam-4675	268	8	g	g	NOUN
ejpam-4675	268	9	,	,	PUNCT
ejpam-4675	268	10	·	·	PUNCT
ejpam-4675	268	11	,	,	PUNCT
ejpam-4675	268	12	1	1	NUM
ejpam-4675	268	13	g	g	NOUN
ejpam-4675	268	14	)	)	PUNCT
ejpam-4675	268	15	→	→	SYM
ejpam-4675	268	16	(	(	PUNCT
ejpam-4675	268	17	g	g	NOUN
ejpam-4675	268	18	/	/	SYM
ejpam-4675	268	19	h1	h1	PROPN
ejpam-4675	268	20	,	,	PUNCT
ejpam-4675	268	21	∗	∗	NOUN
ejpam-4675	268	22	,	,	PUNCT
ejpam-4675	268	23	[	[	X
ejpam-4675	268	24	1]h1	1]h1	NUM
ejpam-4675	268	25	)	)	PUNCT
ejpam-4675	268	26	is	be	AUX
ejpam-4675	268	27	a	a	DET
ejpam-4675	268	28	db	db	NOUN
ejpam-4675	268	29	-	-	PUNCT
ejpam-4675	268	30	epimorphism	epimorphism	NOUN
ejpam-4675	268	31	of	of	ADP
ejpam-4675	268	32	dbalgebras	dbalgebra	NOUN
ejpam-4675	268	33	.	.	PUNCT
ejpam-4675	269	1	if	if	SCONJ
ejpam-4675	269	2	h2	h2	PROPN
ejpam-4675	269	3	is	be	AUX
ejpam-4675	269	4	a	a	DET
ejpam-4675	269	5	normal	normal	ADJ
ejpam-4675	269	6	db	db	NOUN
ejpam-4675	269	7	-	-	PUNCT
ejpam-4675	269	8	subalgebra	subalgebra	NOUN
ejpam-4675	269	9	of	of	ADP
ejpam-4675	269	10	g	g	NOUN
ejpam-4675	269	11	,	,	PUNCT
ejpam-4675	269	12	then	then	ADV
ejpam-4675	269	13	f(h2	f(h2	NOUN
ejpam-4675	269	14	)	)	PUNCT
ejpam-4675	269	15	is	be	AUX
ejpam-4675	269	16	a	a	DET
ejpam-4675	269	17	normal	normal	ADJ
ejpam-4675	269	18	db	db	NOUN
ejpam-4675	269	19	-	-	PUNCT
ejpam-4675	269	20	subalgebra	subalgebra	NOUN
ejpam-4675	269	21	of	of	ADP
ejpam-4675	269	22	g	g	NOUN
ejpam-4675	269	23	/	/	SYM
ejpam-4675	269	24	h1	h1	PROPN
ejpam-4675	269	25	.	.	PUNCT
ejpam-4675	270	1	proof	proof	NOUN
ejpam-4675	270	2	.	.	PUNCT
ejpam-4675	271	1	it	it	PRON
ejpam-4675	271	2	follows	follow	VERB
ejpam-4675	271	3	from	from	ADP
ejpam-4675	271	4	theorem	theorem	ADJ
ejpam-4675	271	5	4	4	NUM
ejpam-4675	271	6	(	(	PUNCT
ejpam-4675	271	7	iii	iii	NOUN
ejpam-4675	271	8	)	)	PUNCT
ejpam-4675	271	9	that	that	DET
ejpam-4675	271	10	f(h2	f(h2	NOUN
ejpam-4675	271	11	)	)	PUNCT
ejpam-4675	271	12	is	be	AUX
ejpam-4675	271	13	a	a	DET
ejpam-4675	271	14	db	db	NOUN
ejpam-4675	271	15	-	-	PUNCT
ejpam-4675	271	16	subalgebra	subalgebra	NOUN
ejpam-4675	271	17	of	of	ADP
ejpam-4675	271	18	g	g	NOUN
ejpam-4675	271	19	/	/	SYM
ejpam-4675	271	20	h1	h1	PROPN
ejpam-4675	271	21	.	.	PUNCT
ejpam-4675	272	1	now	now	ADV
ejpam-4675	272	2	to	to	PART
ejpam-4675	272	3	show	show	VERB
ejpam-4675	272	4	that	that	DET
ejpam-4675	272	5	f(h2	f(h2	NOUN
ejpam-4675	272	6	)	)	PUNCT
ejpam-4675	272	7	is	be	AUX
ejpam-4675	272	8	normal	normal	ADJ
ejpam-4675	272	9	,	,	PUNCT
ejpam-4675	272	10	let	let	VERB
ejpam-4675	272	11	[	[	X
ejpam-4675	272	12	x]h1	x]h1	INTJ
ejpam-4675	272	13	∗	∗	NOUN
ejpam-4675	272	14	[	[	X
ejpam-4675	272	15	y]h1	y]h1	NOUN
ejpam-4675	272	16	,	,	PUNCT
ejpam-4675	272	17	[	[	X
ejpam-4675	272	18	a]h1	a]h1	NOUN
ejpam-4675	272	19	∗	∗	NOUN
ejpam-4675	272	20	[	[	X
ejpam-4675	272	21	b]h1	b]h1	NOUN
ejpam-4675	272	22	∈	∈	NOUN
ejpam-4675	272	23	f(h2	f(h2	NOUN
ejpam-4675	272	24	)	)	PUNCT
ejpam-4675	272	25	for	for	ADP
ejpam-4675	272	26	any	any	DET
ejpam-4675	272	27	[	[	X
ejpam-4675	272	28	x]h1	x]h1	ADJ
ejpam-4675	272	29	,	,	PUNCT
ejpam-4675	272	30	[	[	X
ejpam-4675	272	31	y]h1	y]h1	NOUN
ejpam-4675	272	32	,	,	PUNCT
ejpam-4675	272	33	[	[	X
ejpam-4675	272	34	a]h1	a]h1	NOUN
ejpam-4675	272	35	,	,	PUNCT
ejpam-4675	272	36	and	and	CCONJ
ejpam-4675	272	37	[	[	X
ejpam-4675	272	38	b]h1	b]h1	NOUN
ejpam-4675	272	39	∈	∈	X
ejpam-4675	272	40	g	g	NOUN
ejpam-4675	272	41	/	/	SYM
ejpam-4675	272	42	h1	h1	PROPN
ejpam-4675	272	43	.	.	PUNCT
ejpam-4675	273	1	since	since	SCONJ
ejpam-4675	273	2	f	f	PROPN
ejpam-4675	273	3	is	be	AUX
ejpam-4675	273	4	onto	onto	ADP
ejpam-4675	273	5	,	,	PUNCT
ejpam-4675	273	6	then	then	ADV
ejpam-4675	273	7	there	there	PRON
ejpam-4675	273	8	exists	exist	VERB
ejpam-4675	273	9	j	j	PROPN
ejpam-4675	273	10	,	,	PUNCT
ejpam-4675	273	11	k	k	PROPN
ejpam-4675	273	12	,	,	PUNCT
ejpam-4675	273	13	l	l	NOUN
ejpam-4675	273	14	,	,	PUNCT
ejpam-4675	273	15	m	m	VERB
ejpam-4675	273	16	∈	∈	NOUN
ejpam-4675	273	17	g	g	NOUN
ejpam-4675	273	18	such	such	ADJ
ejpam-4675	273	19	that	that	DET
ejpam-4675	273	20	f(j	f(j	NOUN
ejpam-4675	273	21	)	)	PUNCT
ejpam-4675	274	1	=	=	PUNCT
ejpam-4675	275	1	[	[	X
ejpam-4675	275	2	x]h1	x]h1	INTJ
ejpam-4675	275	3	,	,	PUNCT
ejpam-4675	275	4	f(k	f(k	ADJ
ejpam-4675	275	5	)	)	PUNCT
ejpam-4675	275	6	=	=	PUNCT
ejpam-4675	276	1	[	[	X
ejpam-4675	276	2	y]h1	y]h1	NOUN
ejpam-4675	276	3	,	,	PUNCT
ejpam-4675	276	4	f(l	f(l	PROPN
ejpam-4675	276	5	)	)	PUNCT
ejpam-4675	276	6	=	=	PUNCT
ejpam-4675	277	1	[	[	X
ejpam-4675	277	2	a]h1	a]h1	NOUN
ejpam-4675	277	3	,	,	PUNCT
ejpam-4675	277	4	f(m	f(m	PROPN
ejpam-4675	277	5	)	)	PUNCT
ejpam-4675	277	6	=	=	PUNCT
ejpam-4675	278	1	[	[	X
ejpam-4675	278	2	b]h1	b]h1	X
ejpam-4675	278	3	.	.	PUNCT
ejpam-4675	278	4	suppose	suppose	VERB
ejpam-4675	278	5	j	j	PROPN
ejpam-4675	278	6	·	·	SYM
ejpam-4675	278	7	k	k	PROPN
ejpam-4675	278	8	,	,	PUNCT
ejpam-4675	278	9	l·m	l·m	PROPN
ejpam-4675	278	10	∈	∈	PROPN
ejpam-4675	278	11	h2	h2	PROPN
ejpam-4675	278	12	.	.	PUNCT
ejpam-4675	279	1	then	then	ADV
ejpam-4675	279	2	(	(	PUNCT
ejpam-4675	279	3	j	j	NOUN
ejpam-4675	279	4	·	·	PUNCT
ejpam-4675	279	5	l)·(k	l)·(k	X
ejpam-4675	279	6	·	·	SYM
ejpam-4675	279	7	m	m	X
ejpam-4675	279	8	)	)	PUNCT
ejpam-4675	279	9	∈	∈	PROPN
ejpam-4675	279	10	h2	h2	NOUN
ejpam-4675	279	11	since	since	SCONJ
ejpam-4675	279	12	h2	h2	NOUN
ejpam-4675	279	13	is	be	AUX
ejpam-4675	279	14	normal	normal	ADJ
ejpam-4675	279	15	,	,	PUNCT
ejpam-4675	279	16	which	which	PRON
ejpam-4675	279	17	then	then	ADV
ejpam-4675	279	18	implies	imply	VERB
ejpam-4675	279	19	that	that	SCONJ
ejpam-4675	279	20	f	f	PROPN
ejpam-4675	279	21	(	(	PUNCT
ejpam-4675	279	22	(	(	PUNCT
ejpam-4675	279	23	j	j	X
ejpam-4675	279	24	·	·	PUNCT
ejpam-4675	279	25	l	l	NOUN
ejpam-4675	279	26	)	)	PUNCT
ejpam-4675	279	27	·	·	PUNCT
ejpam-4675	279	28	(	(	PUNCT
ejpam-4675	279	29	k	k	X
ejpam-4675	279	30	·	·	PUNCT
ejpam-4675	279	31	m	m	NOUN
ejpam-4675	279	32	)	)	PUNCT
ejpam-4675	279	33	)	)	PUNCT
ejpam-4675	280	1	∈	∈	PROPN
ejpam-4675	280	2	f(h2	f(h2	NOUN
ejpam-4675	280	3	)	)	PUNCT
ejpam-4675	280	4	.	.	PUNCT
ejpam-4675	281	1	it	it	PRON
ejpam-4675	281	2	follows	follow	VERB
ejpam-4675	281	3	that	that	SCONJ
ejpam-4675	282	1	f	f	PROPN
ejpam-4675	282	2	(	(	PUNCT
ejpam-4675	282	3	(	(	PUNCT
ejpam-4675	282	4	j	j	X
ejpam-4675	282	5	·	·	PUNCT
ejpam-4675	282	6	l	l	NOUN
ejpam-4675	282	7	)	)	PUNCT
ejpam-4675	282	8	·	·	PUNCT
ejpam-4675	282	9	(	(	PUNCT
ejpam-4675	282	10	k	k	X
ejpam-4675	282	11	·	·	PUNCT
ejpam-4675	282	12	m	m	NOUN
ejpam-4675	282	13	)	)	PUNCT
ejpam-4675	282	14	)	)	PUNCT
ejpam-4675	283	1	=	=	PUNCT
ejpam-4675	284	1	f(j	f(j	NOUN
ejpam-4675	284	2	·	·	PUNCT
ejpam-4675	284	3	l	l	X
ejpam-4675	284	4	)	)	PUNCT
ejpam-4675	284	5	∗	∗	NOUN
ejpam-4675	284	6	f(k	f(k	VERB
ejpam-4675	284	7	·	·	PUNCT
ejpam-4675	284	8	m	m	X
ejpam-4675	284	9	)	)	PUNCT
ejpam-4675	284	10	=	=	SYM
ejpam-4675	284	11	(	(	PUNCT
ejpam-4675	284	12	f(j	f(j	NOUN
ejpam-4675	284	13	)	)	PUNCT
ejpam-4675	284	14	∗	∗	NOUN
ejpam-4675	284	15	f(l	f(l	PROPN
ejpam-4675	284	16	)	)	PUNCT
ejpam-4675	284	17	)	)	PUNCT
ejpam-4675	284	18	∗	∗	NOUN
ejpam-4675	284	19	(	(	PUNCT
ejpam-4675	284	20	f(k	f(k	VERB
ejpam-4675	284	21	)	)	PUNCT
ejpam-4675	284	22	∗	∗	NOUN
ejpam-4675	284	23	f(m	f(m	PROPN
ejpam-4675	284	24	)	)	PUNCT
ejpam-4675	284	25	)	)	PUNCT
ejpam-4675	285	1	=	=	PUNCT
ejpam-4675	286	1	(	(	PUNCT
ejpam-4675	286	2	[	[	X
ejpam-4675	286	3	x]h1	x]h1	INTJ
ejpam-4675	286	4	∗	∗	X
ejpam-4675	286	5	[	[	X
ejpam-4675	286	6	a]h1	a]h1	NOUN
ejpam-4675	286	7	)	)	PUNCT
ejpam-4675	286	8	∗	∗	NOUN
ejpam-4675	286	9	(	(	PUNCT
ejpam-4675	286	10	[	[	X
ejpam-4675	286	11	y]h1	y]h1	NOUN
ejpam-4675	286	12	∗	∗	NOUN
ejpam-4675	286	13	[	[	X
ejpam-4675	286	14	b]h1	b]h1	NOUN
ejpam-4675	286	15	)	)	PUNCT
ejpam-4675	286	16	thus	thus	ADV
ejpam-4675	286	17	,	,	PUNCT
ejpam-4675	286	18	f(h2	f(h2	NOUN
ejpam-4675	286	19	)	)	PUNCT
ejpam-4675	286	20	is	be	AUX
ejpam-4675	286	21	normal	normal	ADJ
ejpam-4675	286	22	and	and	CCONJ
ejpam-4675	286	23	consequently	consequently	ADV
ejpam-4675	286	24	,	,	PUNCT
ejpam-4675	286	25	f(h2	f(h2	NOUN
ejpam-4675	286	26	)	)	PUNCT
ejpam-4675	286	27	is	be	AUX
ejpam-4675	286	28	a	a	DET
ejpam-4675	286	29	normal	normal	ADJ
ejpam-4675	286	30	db	db	NOUN
ejpam-4675	286	31	-	-	PUNCT
ejpam-4675	286	32	subalgebra	subalgebra	NOUN
ejpam-4675	286	33	of	of	ADP
ejpam-4675	286	34	g	g	NOUN
ejpam-4675	286	35	/	/	SYM
ejpam-4675	286	36	h1	h1	PROPN
ejpam-4675	286	37	.	.	PUNCT
ejpam-4675	287	1	theorem	theorem	ADJ
ejpam-4675	287	2	8	8	NUM
ejpam-4675	287	3	.	.	PUNCT
ejpam-4675	287	4	third	third	ADJ
ejpam-4675	287	5	isomorphism	isomorphism	PROPN
ejpam-4675	287	6	theorem	theorem	NOUN
ejpam-4675	287	7	for	for	ADP
ejpam-4675	287	8	the	the	DET
ejpam-4675	287	9	db	db	PROPN
ejpam-4675	287	10	-	-	PUNCT
ejpam-4675	287	11	algebra	algebra	NOUN
ejpam-4675	287	12	let	let	VERB
ejpam-4675	287	13	f	f	PRON
ejpam-4675	287	14	be	be	AUX
ejpam-4675	287	15	a	a	DET
ejpam-4675	287	16	natural	natural	ADJ
ejpam-4675	287	17	db	db	NOUN
ejpam-4675	287	18	-	-	PUNCT
ejpam-4675	287	19	homomorphism	homomorphism	NOUN
ejpam-4675	287	20	of	of	ADP
ejpam-4675	287	21	a	a	DET
ejpam-4675	287	22	db	db	NOUN
ejpam-4675	287	23	-	-	PUNCT
ejpam-4675	287	24	algebra	algebra	NOUN
ejpam-4675	287	25	(	(	PUNCT
ejpam-4675	287	26	g	g	NOUN
ejpam-4675	287	27	,	,	PUNCT
ejpam-4675	287	28	·	·	PUNCT
ejpam-4675	287	29	,	,	PUNCT
ejpam-4675	287	30	1	1	NUM
ejpam-4675	287	31	g	g	NOUN
ejpam-4675	287	32	)	)	PUNCT
ejpam-4675	287	33	onto	onto	ADP
ejpam-4675	287	34	a	a	DET
ejpam-4675	287	35	db	db	NOUN
ejpam-4675	287	36	-	-	PUNCT
ejpam-4675	287	37	algebra	algebra	NOUN
ejpam-4675	287	38	(	(	PUNCT
ejpam-4675	287	39	g	g	NOUN
ejpam-4675	287	40	/	/	SYM
ejpam-4675	287	41	h1	h1	PROPN
ejpam-4675	287	42	,	,	PUNCT
ejpam-4675	287	43	∗	∗	NOUN
ejpam-4675	287	44	,	,	PUNCT
ejpam-4675	287	45	[	[	X
ejpam-4675	287	46	1]h1	1]h1	NUM
ejpam-4675	287	47	)	)	PUNCT
ejpam-4675	287	48	,	,	PUNCT
ejpam-4675	287	49	h2	h2	PROPN
ejpam-4675	287	50	be	be	AUX
ejpam-4675	287	51	a	a	DET
ejpam-4675	287	52	normal	normal	ADJ
ejpam-4675	287	53	db	db	NOUN
ejpam-4675	287	54	-	-	PUNCT
ejpam-4675	287	55	subalgebra	subalgebra	NOUN
ejpam-4675	287	56	of	of	ADP
ejpam-4675	287	57	g	g	NOUN
ejpam-4675	287	58	such	such	ADJ
ejpam-4675	287	59	that	that	DET
ejpam-4675	287	60	ker	ker	NOUN
ejpam-4675	288	1	f	f	PROPN
ejpam-4675	288	2	=	=	PRON
ejpam-4675	288	3	h1	h1	PROPN
ejpam-4675	288	4	⊆	⊆	NUM
ejpam-4675	288	5	h2	h2	NOUN
ejpam-4675	288	6	,	,	PUNCT
ejpam-4675	288	7	and	and	CCONJ
ejpam-4675	288	8	g	g	NOUN
ejpam-4675	288	9	,	,	PUNCT
ejpam-4675	288	10	g′	g′	NOUN
ejpam-4675	288	11	be	be	AUX
ejpam-4675	288	12	the	the	DET
ejpam-4675	288	13	natural	natural	ADJ
ejpam-4675	288	14	db	db	NOUN
ejpam-4675	288	15	-	-	PUNCT
ejpam-4675	288	16	homomorphisms	homomorphism	NOUN
ejpam-4675	288	17	of	of	ADP
ejpam-4675	288	18	g	g	NOUN
ejpam-4675	288	19	onto	onto	ADP
ejpam-4675	288	20	(	(	PUNCT
ejpam-4675	288	21	g	g	NOUN
ejpam-4675	288	22	/	/	SYM
ejpam-4675	288	23	h2	h2	NOUN
ejpam-4675	288	24	,	,	PUNCT
ejpam-4675	288	25	·	·	PUNCT
ejpam-4675	288	26	′	′	NUM
ejpam-4675	288	27	,	,	PUNCT
ejpam-4675	288	28	[	[	X
ejpam-4675	288	29	1]h2	1]h2	NUM
ejpam-4675	288	30	)	)	PUNCT
ejpam-4675	288	31	and	and	CCONJ
ejpam-4675	288	32	g	g	NOUN
ejpam-4675	288	33	/	/	SYM
ejpam-4675	288	34	h1	h1	NOUN
ejpam-4675	288	35	onto	onto	ADP
ejpam-4675	288	36	(	(	PUNCT
ejpam-4675	288	37	(	(	PUNCT
ejpam-4675	288	38	g	g	NOUN
ejpam-4675	288	39	/	/	SYM
ejpam-4675	288	40	h1)/(h2	h1)/(h2	NOUN
ejpam-4675	288	41	/	/	SYM
ejpam-4675	288	42	h1	h1	PROPN
ejpam-4675	288	43	)	)	PUNCT
ejpam-4675	288	44	,	,	PUNCT
ejpam-4675	288	45	∗′	∗′	PROPN
ejpam-4675	288	46	,	,	PUNCT
ejpam-4675	288	47	[	[	X
ejpam-4675	288	48	1]h2	1]h2	NUM
ejpam-4675	288	49	/	/	SYM
ejpam-4675	288	50	h1	h1	NOUN
ejpam-4675	288	51	)	)	PUNCT
ejpam-4675	288	52	,	,	PUNCT
ejpam-4675	288	53	respectively	respectively	ADV
ejpam-4675	288	54	.	.	PUNCT
ejpam-4675	289	1	then	then	ADV
ejpam-4675	289	2	there	there	PRON
ejpam-4675	289	3	exists	exist	VERB
ejpam-4675	289	4	a	a	DET
ejpam-4675	289	5	unique	unique	ADJ
ejpam-4675	289	6	db	db	NOUN
ejpam-4675	289	7	-	-	PUNCT
ejpam-4675	289	8	isomorphism	isomorphism	NOUN
ejpam-4675	289	9	h	h	NOUN
ejpam-4675	289	10	of	of	ADP
ejpam-4675	289	11	g	g	PROPN
ejpam-4675	289	12	/	/	SYM
ejpam-4675	289	13	h2	h2	NOUN
ejpam-4675	289	14	onto	onto	ADP
ejpam-4675	289	15	(	(	PUNCT
ejpam-4675	289	16	g	g	NOUN
ejpam-4675	289	17	/	/	SYM
ejpam-4675	289	18	h1)/(h2	h1)/(h2	NOUN
ejpam-4675	289	19	/	/	SYM
ejpam-4675	289	20	h1	h1	PROPN
ejpam-4675	289	21	)	)	PUNCT
ejpam-4675	289	22	,	,	PUNCT
ejpam-4675	289	23	that	that	PRON
ejpam-4675	289	24	is	be	AUX
ejpam-4675	289	25	g	g	NOUN
ejpam-4675	289	26	/	/	SYM
ejpam-4675	289	27	h2	h2	NOUN
ejpam-4675	289	28	∼=	∼=	PROPN
ejpam-4675	289	29	(	(	PUNCT
ejpam-4675	289	30	g	g	NOUN
ejpam-4675	289	31	/	/	SYM
ejpam-4675	289	32	h1)/(h2	h1)/(h2	NOUN
ejpam-4675	289	33	/	/	SYM
ejpam-4675	289	34	h1	h1	PROPN
ejpam-4675	289	35	)	)	PUNCT
ejpam-4675	289	36	,	,	PUNCT
ejpam-4675	289	37	where	where	SCONJ
ejpam-4675	289	38	g	g	PROPN
ejpam-4675	289	39	′	′	NUM
ejpam-4675	290	1	◦	◦	NOUN
ejpam-4675	291	1	f	f	X
ejpam-4675	292	1	=	=	SYM
ejpam-4675	292	2	h	h	PROPN
ejpam-4675	292	3	◦	◦	NOUN
ejpam-4675	292	4	g.	g.	NOUN
ejpam-4675	292	5	proof	proof	NOUN
ejpam-4675	292	6	.	.	PUNCT
ejpam-4675	293	1	since	since	SCONJ
ejpam-4675	293	2	f(h2	f(h2	NOUN
ejpam-4675	293	3	)	)	PUNCT
ejpam-4675	293	4	is	be	AUX
ejpam-4675	293	5	a	a	DET
ejpam-4675	293	6	normal	normal	ADJ
ejpam-4675	293	7	db	db	NOUN
ejpam-4675	293	8	-	-	PUNCT
ejpam-4675	293	9	subalgebra	subalgebra	NOUN
ejpam-4675	293	10	of	of	ADP
ejpam-4675	293	11	g	g	NOUN
ejpam-4675	293	12	/	/	SYM
ejpam-4675	293	13	h1	h1	NOUN
ejpam-4675	293	14	by	by	ADP
ejpam-4675	293	15	proposition	proposition	NOUN
ejpam-4675	293	16	3	3	NUM
ejpam-4675	293	17	,	,	PUNCT
ejpam-4675	293	18	we	we	PRON
ejpam-4675	293	19	have	have	VERB
ejpam-4675	293	20	that	that	DET
ejpam-4675	293	21	f(h2	f(h2	NOUN
ejpam-4675	293	22	)	)	PUNCT
ejpam-4675	293	23	=	=	PUNCT
ejpam-4675	293	24	ker	ker	NOUN
ejpam-4675	293	25	g′	g′	NOUN
ejpam-4675	293	26	by	by	ADP
ejpam-4675	293	27	theorem	theorem	NOUN
ejpam-4675	293	28	5	5	NUM
ejpam-4675	293	29	.	.	PUNCT
ejpam-4675	293	30	suppose	suppose	VERB
ejpam-4675	293	31	a	a	DET
ejpam-4675	293	32	∈	∈	PROPN
ejpam-4675	293	33	h2	h2	NOUN
ejpam-4675	293	34	,	,	PUNCT
ejpam-4675	293	35	then	then	ADV
ejpam-4675	293	36	f(a	f(a	PROPN
ejpam-4675	293	37	)	)	PUNCT
ejpam-4675	293	38	∈	∈	PROPN
ejpam-4675	293	39	f(h2	f(h2	NOUN
ejpam-4675	293	40	)	)	PUNCT
ejpam-4675	293	41	which	which	PRON
ejpam-4675	293	42	implies	imply	VERB
ejpam-4675	293	43	that	that	SCONJ
ejpam-4675	293	44	f(a	f(a	NOUN
ejpam-4675	293	45	)	)	PUNCT
ejpam-4675	293	46	∈	∈	PROPN
ejpam-4675	293	47	ker	ker	NOUN
ejpam-4675	294	1	g′.	g′.	X
ejpam-4675	294	2	then	then	ADV
ejpam-4675	294	3	(	(	PUNCT
ejpam-4675	294	4	g′	g′	NOUN
ejpam-4675	294	5	◦	◦	NOUN
ejpam-4675	294	6	f)(a	f)(a	NUM
ejpam-4675	294	7	)	)	PUNCT
ejpam-4675	294	8	=	=	SYM
ejpam-4675	294	9	g′	g′	NOUN
ejpam-4675	294	10	(	(	PUNCT
ejpam-4675	294	11	f(a	f(a	NOUN
ejpam-4675	294	12	)	)	PUNCT
ejpam-4675	294	13	)	)	PUNCT
ejpam-4675	295	1	=	=	PUNCT
ejpam-4675	295	2	g′	g′	NOUN
ejpam-4675	295	3	(	(	PUNCT
ejpam-4675	296	1	[	[	X
ejpam-4675	296	2	1]h1	1]h1	NUM
ejpam-4675	296	3	)	)	PUNCT
ejpam-4675	296	4	=	=	PUNCT
ejpam-4675	297	1	[	[	PUNCT
ejpam-4675	297	2	[	[	X
ejpam-4675	297	3	1]h1	1]h1	NUM
ejpam-4675	297	4	]	]	X
ejpam-4675	297	5	h2	h2	PROPN
ejpam-4675	297	6	/	/	SYM
ejpam-4675	297	7	h1	h1	PROPN
ejpam-4675	297	8	by	by	ADP
ejpam-4675	297	9	theorem	theorem	NOUN
ejpam-4675	297	10	4	4	NUM
ejpam-4675	297	11	(	(	PUNCT
ejpam-4675	297	12	i	i	NOUN
ejpam-4675	297	13	)	)	PUNCT
ejpam-4675	297	14	.	.	PUNCT
ejpam-4675	298	1	this	this	PRON
ejpam-4675	298	2	implies	imply	VERB
ejpam-4675	298	3	that	that	SCONJ
ejpam-4675	298	4	a	a	DET
ejpam-4675	298	5	∈	∈	NOUN
ejpam-4675	298	6	ker(g′	ker(g′	VERB
ejpam-4675	298	7	◦	◦	NOUN
ejpam-4675	298	8	f	f	X
ejpam-4675	298	9	)	)	PUNCT
ejpam-4675	298	10	and	and	CCONJ
ejpam-4675	298	11	so	so	ADV
ejpam-4675	298	12	,	,	PUNCT
ejpam-4675	298	13	h2	h2	PROPN
ejpam-4675	298	14	⊆	⊆	NUM
ejpam-4675	298	15	ker(g′	ker(g′	NOUN
ejpam-4675	298	16	◦	◦	NOUN
ejpam-4675	298	17	f	f	NUM
ejpam-4675	298	18	)	)	PUNCT
ejpam-4675	298	19	.	.	PUNCT
ejpam-4675	299	1	references	reference	NOUN
ejpam-4675	299	2	585	585	NUM
ejpam-4675	299	3	conversely	conversely	ADV
ejpam-4675	299	4	,	,	PUNCT
ejpam-4675	299	5	suppose	suppose	VERB
ejpam-4675	299	6	a	a	DET
ejpam-4675	299	7	∈	∈	NOUN
ejpam-4675	299	8	ker(g′	ker(g′	VERB
ejpam-4675	299	9	◦	◦	NOUN
ejpam-4675	299	10	f	f	X
ejpam-4675	299	11	)	)	PUNCT
ejpam-4675	299	12	,	,	PUNCT
ejpam-4675	299	13	then	then	ADV
ejpam-4675	299	14	(	(	PUNCT
ejpam-4675	299	15	g′	g′	NOUN
ejpam-4675	299	16	◦	◦	NOUN
ejpam-4675	299	17	f)(a	f)(a	NUM
ejpam-4675	299	18	)	)	PUNCT
ejpam-4675	300	1	=	=	SYM
ejpam-4675	300	2	g′	g′	NOUN
ejpam-4675	300	3	(	(	PUNCT
ejpam-4675	300	4	f(a	f(a	NOUN
ejpam-4675	300	5	)	)	PUNCT
ejpam-4675	300	6	)	)	PUNCT
ejpam-4675	301	1	=	=	PUNCT
ejpam-4675	301	2	g′	g′	NOUN
ejpam-4675	301	3	(	(	PUNCT
ejpam-4675	301	4	[	[	X
ejpam-4675	301	5	a]h1	a]h1	NOUN
ejpam-4675	301	6	)	)	PUNCT
ejpam-4675	301	7	=	=	PUNCT
ejpam-4675	302	1	[	[	PUNCT
ejpam-4675	302	2	[	[	X
ejpam-4675	302	3	a]h1	a]h1	NOUN
ejpam-4675	302	4	]	]	X
ejpam-4675	302	5	h2	h2	NOUN
ejpam-4675	302	6	/	/	SYM
ejpam-4675	302	7	h1	h1	PROPN
ejpam-4675	302	8	=	=	PUNCT
ejpam-4675	303	1	[	[	X
ejpam-4675	303	2	1]h2	1]h2	NUM
ejpam-4675	303	3	/	/	SYM
ejpam-4675	303	4	h1	h1	NOUN
ejpam-4675	303	5	.	.	PUNCT
ejpam-4675	304	1	by	by	ADP
ejpam-4675	304	2	theorem	theorem	NOUN
ejpam-4675	304	3	4	4	NUM
ejpam-4675	304	4	(	(	PUNCT
ejpam-4675	304	5	i	i	NOUN
ejpam-4675	304	6	)	)	PUNCT
ejpam-4675	304	7	,	,	PUNCT
ejpam-4675	304	8	we	we	PRON
ejpam-4675	304	9	have	have	VERB
ejpam-4675	304	10	that	that	DET
ejpam-4675	304	11	g′	g′	NOUN
ejpam-4675	304	12	(	(	PUNCT
ejpam-4675	304	13	[	[	X
ejpam-4675	304	14	1]h1	1]h1	NUM
ejpam-4675	304	15	)	)	PUNCT
ejpam-4675	304	16	=	=	PUNCT
ejpam-4675	305	1	[	[	PUNCT
ejpam-4675	305	2	[	[	X
ejpam-4675	305	3	1]h1	1]h1	NUM
ejpam-4675	305	4	]	]	X
ejpam-4675	305	5	h2	h2	NOUN
ejpam-4675	305	6	/	/	SYM
ejpam-4675	305	7	h1	h1	PROPN
ejpam-4675	305	8	=	=	PUNCT
ejpam-4675	306	1	[	[	X
ejpam-4675	306	2	1]h2	1]h2	NUM
ejpam-4675	306	3	/	/	SYM
ejpam-4675	306	4	h1	h1	NOUN
ejpam-4675	306	5	.	.	PUNCT
ejpam-4675	307	1	then	then	ADV
ejpam-4675	307	2	[	[	X
ejpam-4675	307	3	1]h1	1]h1	NUM
ejpam-4675	307	4	∼	∼	NOUN
ejpam-4675	307	5	[	[	X
ejpam-4675	307	6	a]h1	a]h1	NOUN
ejpam-4675	307	7	.	.	PUNCT
ejpam-4675	308	1	this	this	PRON
ejpam-4675	308	2	implies	imply	VERB
ejpam-4675	308	3	that	that	SCONJ
ejpam-4675	308	4	[	[	X
ejpam-4675	308	5	a]h1	a]h1	X
ejpam-4675	308	6	∗′	∗′	ADJ
ejpam-4675	308	7	[	[	X
ejpam-4675	308	8	1]h1	1]h1	NUM
ejpam-4675	308	9	∈	∈	PROPN
ejpam-4675	308	10	h2	h2	NOUN
ejpam-4675	308	11	/	/	SYM
ejpam-4675	308	12	h1	h1	PROPN
ejpam-4675	308	13	and	and	CCONJ
ejpam-4675	308	14	[	[	X
ejpam-4675	308	15	1]h1	1]h1	NUM
ejpam-4675	308	16	∗′	∗′	PROPN
ejpam-4675	308	17	[	[	X
ejpam-4675	308	18	a]h1	a]h1	NOUN
ejpam-4675	308	19	∈	∈	PROPN
ejpam-4675	308	20	h2	h2	NOUN
ejpam-4675	308	21	/	/	SYM
ejpam-4675	308	22	h1	h1	PROPN
ejpam-4675	308	23	which	which	PRON
ejpam-4675	308	24	by	by	ADP
ejpam-4675	308	25	db2	db2	PROPN
ejpam-4675	308	26	implies	imply	VERB
ejpam-4675	308	27	that	that	SCONJ
ejpam-4675	308	28	[	[	X
ejpam-4675	308	29	a]h1	a]h1	NOUN
ejpam-4675	308	30	∈	∈	PROPN
ejpam-4675	308	31	h2	h2	NOUN
ejpam-4675	308	32	/	/	SYM
ejpam-4675	308	33	h1	h1	PROPN
ejpam-4675	308	34	.	.	PUNCT
ejpam-4675	309	1	it	it	PRON
ejpam-4675	309	2	follows	follow	VERB
ejpam-4675	309	3	that	that	SCONJ
ejpam-4675	309	4	f(a	f(a	NOUN
ejpam-4675	309	5	)	)	PUNCT
ejpam-4675	309	6	∈	∈	PROPN
ejpam-4675	309	7	h2	h2	PROPN
ejpam-4675	309	8	/	/	SYM
ejpam-4675	309	9	h1	h1	PROPN
ejpam-4675	309	10	=	=	PUNCT
ejpam-4675	309	11	ker	ker	PROPN
ejpam-4675	309	12	g′	g′	NOUN
ejpam-4675	309	13	by	by	ADP
ejpam-4675	309	14	theorem	theorem	NOUN
ejpam-4675	309	15	5	5	NUM
ejpam-4675	309	16	and	and	CCONJ
ejpam-4675	309	17	so	so	ADV
ejpam-4675	309	18	,	,	PUNCT
ejpam-4675	309	19	f(a	f(a	NOUN
ejpam-4675	309	20	)	)	PUNCT
ejpam-4675	309	21	∈	∈	PROPN
ejpam-4675	309	22	f(h2	f(h2	NOUN
ejpam-4675	309	23	)	)	PUNCT
ejpam-4675	309	24	.	.	PUNCT
ejpam-4675	310	1	since	since	SCONJ
ejpam-4675	310	2	f	f	PROPN
ejpam-4675	310	3	is	be	AUX
ejpam-4675	310	4	onto	onto	ADP
ejpam-4675	310	5	,	,	PUNCT
ejpam-4675	310	6	there	there	PRON
ejpam-4675	310	7	exists	exist	VERB
ejpam-4675	310	8	x	x	X
ejpam-4675	310	9	∈	∈	PROPN
ejpam-4675	310	10	h2	h2	NOUN
ejpam-4675	310	11	such	such	ADJ
ejpam-4675	310	12	that	that	SCONJ
ejpam-4675	310	13	f(x	f(x	NOUN
ejpam-4675	310	14	)	)	PUNCT
ejpam-4675	310	15	=	=	SYM
ejpam-4675	310	16	f(a	f(a	PROPN
ejpam-4675	310	17	)	)	PUNCT
ejpam-4675	310	18	implies	imply	VERB
ejpam-4675	311	1	[	[	X
ejpam-4675	311	2	x]h1	x]h1	X
ejpam-4675	311	3	=	=	PUNCT
ejpam-4675	312	1	[	[	X
ejpam-4675	312	2	a]h1	a]h1	NOUN
ejpam-4675	312	3	which	which	PRON
ejpam-4675	312	4	implies	imply	VERB
ejpam-4675	312	5	that	that	SCONJ
ejpam-4675	312	6	x	x	PUNCT
ejpam-4675	312	7	∼	∼	NOUN
ejpam-4675	312	8	a.	a.	NOUN
ejpam-4675	313	1	so	so	ADV
ejpam-4675	313	2	,	,	PUNCT
ejpam-4675	313	3	x	x	X
ejpam-4675	313	4	·	·	PUNCT
ejpam-4675	313	5	a	a	DET
ejpam-4675	313	6	∈	∈	PROPN
ejpam-4675	313	7	h1	h1	NOUN
ejpam-4675	313	8	and	and	CCONJ
ejpam-4675	313	9	a	a	DET
ejpam-4675	313	10	·	·	PUNCT
ejpam-4675	313	11	x	x	SYM
ejpam-4675	313	12	∈	∈	PROPN
ejpam-4675	313	13	h1	h1	PROPN
ejpam-4675	313	14	.	.	PUNCT
ejpam-4675	314	1	since	since	SCONJ
ejpam-4675	314	2	h1	h1	PROPN
ejpam-4675	314	3	⊆	⊆	NUM
ejpam-4675	314	4	h2	h2	NOUN
ejpam-4675	314	5	,	,	PUNCT
ejpam-4675	314	6	x	x	X
ejpam-4675	314	7	·	·	PUNCT
ejpam-4675	314	8	a	a	DET
ejpam-4675	314	9	∈	∈	PROPN
ejpam-4675	314	10	h2	h2	NOUN
ejpam-4675	314	11	and	and	CCONJ
ejpam-4675	314	12	a	a	DET
ejpam-4675	314	13	·	·	PUNCT
ejpam-4675	314	14	x	x	SYM
ejpam-4675	314	15	∈	∈	PROPN
ejpam-4675	314	16	h2	h2	NOUN
ejpam-4675	314	17	and	and	CCONJ
ejpam-4675	314	18	it	it	PRON
ejpam-4675	314	19	follows	follow	VERB
ejpam-4675	314	20	that	that	SCONJ
ejpam-4675	314	21	since	since	SCONJ
ejpam-4675	314	22	h2	h2	PROPN
ejpam-4675	314	23	is	be	AUX
ejpam-4675	314	24	also	also	ADV
ejpam-4675	314	25	a	a	DET
ejpam-4675	314	26	normal	normal	ADJ
ejpam-4675	314	27	db	db	NOUN
ejpam-4675	314	28	-	-	PUNCT
ejpam-4675	314	29	filter	filter	NOUN
ejpam-4675	314	30	by	by	ADP
ejpam-4675	314	31	proposition	proposition	NOUN
ejpam-4675	314	32	2	2	NUM
ejpam-4675	314	33	,	,	PUNCT
ejpam-4675	314	34	a	a	DET
ejpam-4675	314	35	∈	∈	PROPN
ejpam-4675	314	36	h2	h2	NOUN
ejpam-4675	314	37	.	.	PUNCT
ejpam-4675	315	1	this	this	PRON
ejpam-4675	315	2	implies	imply	VERB
ejpam-4675	315	3	that	that	PRON
ejpam-4675	315	4	ker(g′	ker(g′	AUX
ejpam-4675	315	5	◦	◦	NOUN
ejpam-4675	315	6	f	f	X
ejpam-4675	315	7	)	)	PUNCT
ejpam-4675	315	8	⊆	⊆	NUM
ejpam-4675	315	9	h2	h2	NOUN
ejpam-4675	315	10	,	,	PUNCT
ejpam-4675	315	11	and	and	CCONJ
ejpam-4675	315	12	consequently	consequently	ADV
ejpam-4675	315	13	ker(g′	ker(g′	AUX
ejpam-4675	315	14	◦	◦	NOUN
ejpam-4675	315	15	f	f	X
ejpam-4675	315	16	)	)	PUNCT
ejpam-4675	315	17	=	=	SYM
ejpam-4675	315	18	h2	h2	NOUN
ejpam-4675	315	19	.	.	PUNCT
ejpam-4675	316	1	by	by	ADP
ejpam-4675	316	2	theorem	theorem	NOUN
ejpam-4675	316	3	6	6	NUM
ejpam-4675	316	4	,	,	PUNCT
ejpam-4675	316	5	there	there	PRON
ejpam-4675	316	6	exists	exist	VERB
ejpam-4675	316	7	a	a	DET
ejpam-4675	316	8	unique	unique	ADJ
ejpam-4675	316	9	db	db	NOUN
ejpam-4675	316	10	-	-	PUNCT
ejpam-4675	316	11	isomorphism	isomorphism	NOUN
ejpam-4675	316	12	h	h	NOUN
ejpam-4675	316	13	of	of	ADP
ejpam-4675	316	14	g	g	PROPN
ejpam-4675	316	15	/	/	SYM
ejpam-4675	316	16	h2	h2	NOUN
ejpam-4675	316	17	onto	onto	ADP
ejpam-4675	316	18	(	(	PUNCT
ejpam-4675	316	19	g	g	NOUN
ejpam-4675	316	20	/	/	SYM
ejpam-4675	316	21	h1)/(h2	h1)/(h2	NOUN
ejpam-4675	316	22	/	/	SYM
ejpam-4675	316	23	h1	h1	PROPN
ejpam-4675	316	24	)	)	PUNCT
ejpam-4675	317	1	such	such	ADJ
ejpam-4675	317	2	that	that	DET
ejpam-4675	317	3	g′	g′	NOUN
ejpam-4675	317	4	◦	◦	NOUN
ejpam-4675	317	5	f	f	X
ejpam-4675	318	1	=	=	SYM
ejpam-4675	318	2	h	h	PROPN
ejpam-4675	318	3	◦	◦	NOUN
ejpam-4675	318	4	g.	g.	PROPN
ejpam-4675	318	5	4	4	NUM
ejpam-4675	318	6	.	.	PUNCT
ejpam-4675	318	7	conclusion	conclusion	NOUN
ejpam-4675	318	8	in	in	ADP
ejpam-4675	318	9	this	this	DET
ejpam-4675	318	10	paper	paper	NOUN
ejpam-4675	318	11	,	,	PUNCT
ejpam-4675	318	12	it	it	PRON
ejpam-4675	318	13	is	be	AUX
ejpam-4675	318	14	shown	show	VERB
ejpam-4675	318	15	that	that	SCONJ
ejpam-4675	318	16	the	the	DET
ejpam-4675	318	17	necessary	necessary	ADJ
ejpam-4675	318	18	and	and	CCONJ
ejpam-4675	318	19	sufficient	sufficient	ADJ
ejpam-4675	318	20	condition	condition	NOUN
ejpam-4675	318	21	for	for	ADP
ejpam-4675	318	22	a	a	DET
ejpam-4675	318	23	db	db	NOUN
ejpam-4675	318	24	-	-	PUNCT
ejpam-4675	318	25	filter	filter	NOUN
ejpam-4675	318	26	to	to	PART
ejpam-4675	318	27	be	be	AUX
ejpam-4675	318	28	a	a	DET
ejpam-4675	318	29	db	db	ADJ
ejpam-4675	318	30	-	-	PUNCT
ejpam-4675	318	31	subalgebra	subalgebra	NOUN
ejpam-4675	318	32	and	and	CCONJ
ejpam-4675	318	33	vice	vice	NOUN
ejpam-4675	318	34	versa	versa	ADV
ejpam-4675	318	35	is	be	AUX
ejpam-4675	318	36	normality	normality	NOUN
ejpam-4675	318	37	.	.	PUNCT
ejpam-4675	319	1	using	use	VERB
ejpam-4675	319	2	the	the	DET
ejpam-4675	319	3	quotient	quotient	NOUN
ejpam-4675	319	4	db	db	NOUN
ejpam-4675	319	5	-	-	PUNCT
ejpam-4675	319	6	algebra	algebra	NOUN
ejpam-4675	319	7	,	,	PUNCT
ejpam-4675	319	8	along	along	ADP
ejpam-4675	319	9	with	with	ADP
ejpam-4675	319	10	some	some	DET
ejpam-4675	319	11	properties	property	NOUN
ejpam-4675	319	12	(	(	PUNCT
ejpam-4675	319	13	such	such	ADJ
ejpam-4675	319	14	as	as	ADP
ejpam-4675	319	15	normality	normality	NOUN
ejpam-4675	319	16	)	)	PUNCT
ejpam-4675	319	17	of	of	ADP
ejpam-4675	319	18	the	the	DET
ejpam-4675	319	19	db	db	NOUN
ejpam-4675	319	20	-	-	PUNCT
ejpam-4675	319	21	filter	filter	NOUN
ejpam-4675	319	22	,	,	PUNCT
ejpam-4675	319	23	db	db	NOUN
ejpam-4675	319	24	-	-	PUNCT
ejpam-4675	319	25	subalgebra	subalgebra	NOUN
ejpam-4675	319	26	,	,	PUNCT
ejpam-4675	319	27	and	and	CCONJ
ejpam-4675	319	28	db	db	PROPN
ejpam-4675	319	29	-	-	PUNCT
ejpam-4675	319	30	homomorphism	homomorphism	NOUN
ejpam-4675	319	31	presented	present	VERB
ejpam-4675	319	32	in	in	ADP
ejpam-4675	319	33	the	the	DET
ejpam-4675	319	34	paper	paper	NOUN
ejpam-4675	319	35	,	,	PUNCT
ejpam-4675	319	36	the	the	DET
ejpam-4675	319	37	natural	natural	ADJ
ejpam-4675	319	38	db	db	NOUN
ejpam-4675	319	39	-	-	PUNCT
ejpam-4675	319	40	homomorphism	homomorphism	NOUN
ejpam-4675	319	41	is	be	AUX
ejpam-4675	319	42	determined	determine	VERB
ejpam-4675	319	43	;	;	PUNCT
ejpam-4675	319	44	this	this	PRON
ejpam-4675	319	45	then	then	ADV
ejpam-4675	319	46	led	lead	VERB
ejpam-4675	319	47	to	to	ADP
ejpam-4675	319	48	the	the	DET
ejpam-4675	319	49	creation	creation	NOUN
ejpam-4675	319	50	of	of	ADP
ejpam-4675	319	51	the	the	DET
ejpam-4675	319	52	fundamental	fundamental	ADJ
ejpam-4675	319	53	theorem	theorem	NOUN
ejpam-4675	319	54	of	of	ADP
ejpam-4675	319	55	db	db	NOUN
ejpam-4675	319	56	-	-	PUNCT
ejpam-4675	319	57	homomorphisms	homomorphism	NOUN
ejpam-4675	319	58	for	for	ADP
ejpam-4675	319	59	db	db	NOUN
ejpam-4675	319	60	-	-	PUNCT
ejpam-4675	319	61	algebras	algebras	PROPN
ejpam-4675	319	62	.	.	PUNCT
ejpam-4675	320	1	following	follow	VERB
ejpam-4675	320	2	the	the	DET
ejpam-4675	320	3	aforementioned	aforementioned	ADJ
ejpam-4675	320	4	theorem	theorem	NOUN
ejpam-4675	320	5	,	,	PUNCT
ejpam-4675	320	6	the	the	DET
ejpam-4675	320	7	first	first	ADJ
ejpam-4675	320	8	and	and	CCONJ
ejpam-4675	320	9	third	third	ADJ
ejpam-4675	320	10	isomorphism	isomorphism	NOUN
ejpam-4675	320	11	theorems	theorem	NOUN
ejpam-4675	320	12	for	for	SCONJ
ejpam-4675	320	13	the	the	DET
ejpam-4675	320	14	db	db	PROPN
ejpam-4675	320	15	-	-	PUNCT
ejpam-4675	320	16	algebra	algebra	NOUN
ejpam-4675	320	17	are	be	AUX
ejpam-4675	320	18	constructed	construct	VERB
ejpam-4675	320	19	.	.	PUNCT
ejpam-4675	321	1	acknowledgements	acknowledgement	NOUN
ejpam-4675	321	2	the	the	DET
ejpam-4675	321	3	authors	author	NOUN
ejpam-4675	321	4	would	would	AUX
ejpam-4675	321	5	like	like	VERB
ejpam-4675	321	6	to	to	PART
ejpam-4675	321	7	thank	thank	VERB
ejpam-4675	321	8	the	the	DET
ejpam-4675	321	9	department	department	NOUN
ejpam-4675	321	10	of	of	ADP
ejpam-4675	321	11	science	science	NOUN
ejpam-4675	321	12	and	and	CCONJ
ejpam-4675	321	13	technology	technology	NOUN
ejpam-4675	321	14	accelerated	accelerate	VERB
ejpam-4675	321	15	science	science	NOUN
ejpam-4675	321	16	and	and	CCONJ
ejpam-4675	321	17	technology	technology	NOUN
ejpam-4675	321	18	human	human	ADJ
ejpam-4675	321	19	resource	resource	NOUN
ejpam-4675	321	20	development	development	NOUN
ejpam-4675	321	21	program	program	NOUN
ejpam-4675	321	22	(	(	PUNCT
ejpam-4675	321	23	dost	dost	NOUN
ejpam-4675	321	24	-	-	PUNCT
ejpam-4675	321	25	asthrdp	asthrdp	NOUN
ejpam-4675	321	26	)	)	PUNCT
ejpam-4675	321	27	and	and	CCONJ
ejpam-4675	321	28	the	the	DET
ejpam-4675	321	29	university	university	NOUN
ejpam-4675	321	30	of	of	ADP
ejpam-4675	321	31	san	san	PROPN
ejpam-4675	321	32	carlos	carlos	PROPN
ejpam-4675	321	33	for	for	ADP
ejpam-4675	321	34	funding	fund	VERB
ejpam-4675	321	35	this	this	DET
ejpam-4675	321	36	research	research	NOUN
ejpam-4675	321	37	.	.	PUNCT
ejpam-4675	322	1	references	reference	NOUN
ejpam-4675	322	2	[	[	X
ejpam-4675	322	3	1	1	X
ejpam-4675	322	4	]	]	X
ejpam-4675	322	5	katrina	katrina	PROPN
ejpam-4675	322	6	belleza	belleza	PROPN
ejpam-4675	322	7	and	and	CCONJ
ejpam-4675	322	8	jimboy	jimboy	PROPN
ejpam-4675	322	9	albaracin	albaracin	PROPN
ejpam-4675	322	10	.	.	PUNCT
ejpam-4675	323	1	on	on	ADP
ejpam-4675	323	2	dual	dual	ADJ
ejpam-4675	323	3	b	b	NOUN
ejpam-4675	323	4	-	-	PUNCT
ejpam-4675	323	5	filters	filter	NOUN
ejpam-4675	323	6	and	and	CCONJ
ejpam-4675	323	7	dual	dual	ADJ
ejpam-4675	323	8	b	b	NOUN
ejpam-4675	323	9	-	-	PUNCT
ejpam-4675	323	10	subalgebras	subalgebras	PROPN
ejpam-4675	323	11	in	in	ADP
ejpam-4675	323	12	a	a	DET
ejpam-4675	323	13	topological	topological	ADJ
ejpam-4675	323	14	dual	dual	ADJ
ejpam-4675	323	15	b	b	NOUN
ejpam-4675	323	16	-	-	PUNCT
ejpam-4675	323	17	algebra	algebra	NOUN
ejpam-4675	323	18	.	.	PUNCT
ejpam-4675	324	1	journal	journal	NOUN
ejpam-4675	324	2	of	of	ADP
ejpam-4675	324	3	mathematics	mathematic	NOUN
ejpam-4675	324	4	and	and	CCONJ
ejpam-4675	324	5	computer	computer	NOUN
ejpam-4675	324	6	science	science	NOUN
ejpam-4675	324	7	,	,	PUNCT
ejpam-4675	324	8	28:1–10	28:1–10	NUM
ejpam-4675	324	9	,	,	PUNCT
ejpam-4675	324	10	04	04	NUM
ejpam-4675	324	11	2022	2022	NUM
ejpam-4675	324	12	.	.	PUNCT
ejpam-4675	325	1	[	[	X
ejpam-4675	325	2	2	2	NUM
ejpam-4675	325	3	]	]	X
ejpam-4675	325	4	katrina	katrina	PROPN
ejpam-4675	325	5	belleza	belleza	PROPN
ejpam-4675	325	6	and	and	CCONJ
ejpam-4675	325	7	jocelyn	jocelyn	PROPN
ejpam-4675	325	8	p	p	PROPN
ejpam-4675	325	9	vilela	vilela	PROPN
ejpam-4675	325	10	.	.	PUNCT
ejpam-4675	326	1	the	the	DET
ejpam-4675	326	2	dual	dual	ADJ
ejpam-4675	326	3	b	b	NOUN
ejpam-4675	326	4	-	-	PUNCT
ejpam-4675	326	5	algebra	algebra	NOUN
ejpam-4675	326	6	.	.	PUNCT
ejpam-4675	327	1	european	european	ADJ
ejpam-4675	327	2	journal	journal	PROPN
ejpam-4675	327	3	of	of	ADP
ejpam-4675	327	4	pure	pure	ADJ
ejpam-4675	327	5	and	and	CCONJ
ejpam-4675	327	6	applied	applied	ADJ
ejpam-4675	327	7	mathematics	mathematic	NOUN
ejpam-4675	327	8	,	,	PUNCT
ejpam-4675	327	9	12(4):1497–1507	12(4):1497–1507	NUM
ejpam-4675	327	10	,	,	PUNCT
ejpam-4675	327	11	2019	2019	NUM
ejpam-4675	327	12	.	.	PUNCT
ejpam-4675	328	1	references	reference	NOUN
ejpam-4675	328	2	586	586	NUM
ejpam-4675	328	3	[	[	X
ejpam-4675	328	4	3	3	NUM
ejpam-4675	328	5	]	]	X
ejpam-4675	328	6	muhammad	muhammad	PROPN
ejpam-4675	328	7	chaudhry	chaudhry	PROPN
ejpam-4675	328	8	,	,	PUNCT
ejpam-4675	328	9	muhammad	muhammad	PROPN
ejpam-4675	328	10	qureshi	qureshi	PROPN
ejpam-4675	328	11	,	,	PUNCT
ejpam-4675	328	12	asfand	asfand	PROPN
ejpam-4675	328	13	fahad	fahad	PROPN
ejpam-4675	328	14	,	,	PUNCT
ejpam-4675	328	15	and	and	CCONJ
ejpam-4675	328	16	muhammad	muhammad	PROPN
ejpam-4675	328	17	bashir	bashir	PROPN
ejpam-4675	328	18	.	.	PUNCT
ejpam-4675	329	1	isomorphism	isomorphism	NOUN
ejpam-4675	329	2	theorems	theorem	NOUN
ejpam-4675	329	3	in	in	ADP
ejpam-4675	329	4	generalized	generalized	ADJ
ejpam-4675	329	5	d	d	NOUN
ejpam-4675	329	6	-	-	PUNCT
ejpam-4675	329	7	algebras	algebras	PROPN
ejpam-4675	329	8	.	.	PUNCT
ejpam-4675	330	1	journal	journal	PROPN
ejpam-4675	330	2	of	of	ADP
ejpam-4675	330	3	prime	prime	ADJ
ejpam-4675	330	4	research	research	NOUN
ejpam-4675	330	5	in	in	ADP
ejpam-4675	330	6	mathematics	mathematic	NOUN
ejpam-4675	330	7	,	,	PUNCT
ejpam-4675	330	8	17:149–158	17:149–158	PROPN
ejpam-4675	330	9	,	,	PUNCT
ejpam-4675	330	10	06	06	NUM
ejpam-4675	330	11	2022	2022	NUM
ejpam-4675	330	12	.	.	PUNCT
ejpam-4675	331	1	[	[	X
ejpam-4675	331	2	4	4	X
ejpam-4675	331	3	]	]	PUNCT
ejpam-4675	331	4	joemar	joemar	PROPN
ejpam-4675	331	5	c	c	PROPN
ejpam-4675	331	6	endam	endam	PROPN
ejpam-4675	331	7	and	and	CCONJ
ejpam-4675	331	8	jocelyn	jocelyn	PROPN
ejpam-4675	331	9	p	p	PROPN
ejpam-4675	331	10	vilela	vilela	PROPN
ejpam-4675	331	11	.	.	PUNCT
ejpam-4675	332	1	the	the	DET
ejpam-4675	332	2	second	second	ADJ
ejpam-4675	332	3	isomorphism	isomorphism	NOUN
ejpam-4675	332	4	theorem	theorem	NOUN
ejpam-4675	332	5	for	for	ADP
ejpam-4675	332	6	balgebras	balgebras	PROPN
ejpam-4675	332	7	.	.	PROPN
ejpam-4675	332	8	applied	apply	VERB
ejpam-4675	332	9	mathematical	mathematical	ADJ
ejpam-4675	332	10	sciences	science	NOUN
ejpam-4675	332	11	,	,	PUNCT
ejpam-4675	332	12	8(38):1865–1872	8(38):1865–1872	NUM
ejpam-4675	332	13	,	,	PUNCT
ejpam-4675	332	14	2014	2014	NUM
ejpam-4675	332	15	.	.	PUNCT
ejpam-4675	333	1	[	[	X
ejpam-4675	333	2	5	5	X
ejpam-4675	333	3	]	]	PUNCT
ejpam-4675	333	4	aiyared	aiyare	VERB
ejpam-4675	333	5	iampan	iampan	PROPN
ejpam-4675	333	6	.	.	PUNCT
ejpam-4675	334	1	the	the	DET
ejpam-4675	334	2	up	up	ADP
ejpam-4675	334	3	-	-	PUNCT
ejpam-4675	334	4	isomorphism	isomorphism	NOUN
ejpam-4675	334	5	theorems	theorem	NOUN
ejpam-4675	334	6	for	for	ADP
ejpam-4675	334	7	up	up	ADV
ejpam-4675	334	8	-	-	PUNCT
ejpam-4675	334	9	algebras	algebras	X
ejpam-4675	334	10	.	.	PUNCT
ejpam-4675	335	1	arxiv	arxiv	PROPN
ejpam-4675	335	2	preprint	preprint	PROPN
ejpam-4675	335	3	arxiv:1808.07370	arxiv:1808.07370	NUM
ejpam-4675	335	4	,	,	PUNCT
ejpam-4675	335	5	2018	2018	NUM
ejpam-4675	335	6	.	.	PUNCT
ejpam-4675	336	1	[	[	X
ejpam-4675	336	2	6	6	NUM
ejpam-4675	336	3	]	]	PUNCT
ejpam-4675	336	4	yb	yb	PROPN
ejpam-4675	336	5	jun	jun	PROPN
ejpam-4675	336	6	,	,	PUNCT
ejpam-4675	336	7	sm	sm	PROPN
ejpam-4675	336	8	hong	hong	PROPN
ejpam-4675	336	9	,	,	PUNCT
ejpam-4675	336	10	xl	xl	PROPN
ejpam-4675	336	11	xin	xin	PROPN
ejpam-4675	336	12	,	,	PUNCT
ejpam-4675	336	13	and	and	CCONJ
ejpam-4675	336	14	eh	eh	INTJ
ejpam-4675	336	15	roh	roh	PROPN
ejpam-4675	336	16	.	.	PUNCT
ejpam-4675	337	1	chinese	chinese	ADJ
ejpam-4675	337	2	remainder	remainder	NOUN
ejpam-4675	337	3	theorems	theorem	NOUN
ejpam-4675	337	4	in	in	ADP
ejpam-4675	337	5	bci	bci	NOUN
ejpam-4675	337	6	-	-	PUNCT
ejpam-4675	337	7	algebras	algebras	PROPN
ejpam-4675	337	8	.	.	PUNCT
ejpam-4675	338	1	soochow	soochow	PROPN
ejpam-4675	338	2	journal	journal	PROPN
ejpam-4675	338	3	of	of	ADP
ejpam-4675	338	4	mathematics	mathematic	NOUN
ejpam-4675	338	5	,	,	PUNCT
ejpam-4675	338	6	24(3):219–230	24(3):219–230	NUM
ejpam-4675	338	7	,	,	PUNCT
ejpam-4675	338	8	1998	1998	NUM
ejpam-4675	338	9	.	.	PUNCT
ejpam-4675	339	1	[	[	X
ejpam-4675	339	2	7	7	X
ejpam-4675	339	3	]	]	X
ejpam-4675	339	4	joseph	joseph	PROPN
ejpam-4675	339	5	neggers	neggers	PROPN
ejpam-4675	339	6	and	and	CCONJ
ejpam-4675	339	7	hee	hee	PROPN
ejpam-4675	339	8	sik	sik	PROPN
ejpam-4675	339	9	kim	kim	PROPN
ejpam-4675	339	10	.	.	PUNCT
ejpam-4675	340	1	a	a	DET
ejpam-4675	340	2	fundamental	fundamental	ADJ
ejpam-4675	340	3	theorem	theorem	NOUN
ejpam-4675	340	4	of	of	ADP
ejpam-4675	340	5	b	b	NOUN
ejpam-4675	340	6	-	-	PUNCT
ejpam-4675	340	7	homomorphism	homomorphism	NOUN
ejpam-4675	340	8	for	for	ADP
ejpam-4675	340	9	b	b	NOUN
ejpam-4675	340	10	-	-	PUNCT
ejpam-4675	340	11	algebras	algebras	PROPN
ejpam-4675	340	12	.	.	PUNCT
ejpam-4675	341	1	int	int	NOUN
ejpam-4675	341	2	.	.	PUNCT
ejpam-4675	342	1	math	math	NOUN
ejpam-4675	342	2	.	.	PUNCT
ejpam-4675	343	1	j.	j.	PROPN
ejpam-4675	343	2	,	,	PUNCT
ejpam-4675	343	3	2	2	NUM
ejpam-4675	343	4	,	,	PUNCT
ejpam-4675	343	5	3:207–214	3:207–214	NUM
ejpam-4675	343	6	,	,	PUNCT
ejpam-4675	343	7	2002	2002	NUM
ejpam-4675	343	8	.	.	PUNCT