id	sid	tid	token	lemma	pos
ejpam-3966	1	1	european	european	PROPN
ejpam-3966	1	2	journal	journal	PROPN
ejpam-3966	1	3	of	of	ADP
ejpam-3966	1	4	pure	pure	ADJ
ejpam-3966	1	5	and	and	CCONJ
ejpam-3966	1	6	applied	apply	VERB
ejpam-3966	1	7	mathematics	mathematic	NOUN
ejpam-3966	1	8	vol	vol	NOUN
ejpam-3966	1	9	.	.	PUNCT
ejpam-3966	2	1	14	14	NUM
ejpam-3966	2	2	,	,	PUNCT
ejpam-3966	2	3	no	no	INTJ
ejpam-3966	2	4	.	.	NOUN
ejpam-3966	2	5	2	2	NUM
ejpam-3966	2	6	,	,	PUNCT
ejpam-3966	2	7	2021	2021	NUM
ejpam-3966	2	8	,	,	PUNCT
ejpam-3966	2	9	423	423	NUM
ejpam-3966	2	10	-	-	SYM
ejpam-3966	2	11	430	430	NUM
ejpam-3966	2	12	issn	issn	PROPN
ejpam-3966	2	13	1307	1307	NUM
ejpam-3966	2	14	-	-	SYM
ejpam-3966	2	15	5543	5543	NUM
ejpam-3966	2	16	–	–	PUNCT
ejpam-3966	3	1	ejpam.com	ejpam.com	X
ejpam-3966	3	2	published	publish	VERB
ejpam-3966	3	3	by	by	ADP
ejpam-3966	3	4	new	new	PROPN
ejpam-3966	3	5	york	york	PROPN
ejpam-3966	3	6	business	business	PROPN
ejpam-3966	3	7	global	global	ADJ
ejpam-3966	3	8	inverse	inverse	NOUN
ejpam-3966	3	9	limit	limit	NOUN
ejpam-3966	3	10	of	of	ADP
ejpam-3966	3	11	an	an	DET
ejpam-3966	3	12	inverse	inverse	NOUN
ejpam-3966	3	13	system	system	NOUN
ejpam-3966	3	14	of	of	ADP
ejpam-3966	3	15	be	be	AUX
ejpam-3966	3	16	-	-	PUNCT
ejpam-3966	3	17	algebras	algebras	X
ejpam-3966	3	18	jimboy	jimboy	PROPN
ejpam-3966	3	19	r.	r.	PROPN
ejpam-3966	3	20	albaracin1,∗	albaracin1,∗	PROPN
ejpam-3966	3	21	,	,	PUNCT
ejpam-3966	3	22	jocelyn	jocelyn	PROPN
ejpam-3966	3	23	p.	p.	PROPN
ejpam-3966	3	24	vilela2	vilela2	NOUN
ejpam-3966	3	25	1	1	NUM
ejpam-3966	3	26	mathematics	mathematic	NOUN
ejpam-3966	3	27	program	program	NOUN
ejpam-3966	3	28	,	,	PUNCT
ejpam-3966	3	29	college	college	NOUN
ejpam-3966	3	30	of	of	ADP
ejpam-3966	3	31	science	science	NOUN
ejpam-3966	3	32	,	,	PUNCT
ejpam-3966	3	33	university	university	NOUN
ejpam-3966	3	34	of	of	ADP
ejpam-3966	3	35	the	the	DET
ejpam-3966	3	36	philippines	philippine	NOUN
ejpam-3966	3	37	cebu	cebu	NOUN
ejpam-3966	3	38	,	,	PUNCT
ejpam-3966	3	39	6000	6000	NUM
ejpam-3966	3	40	cebu	cebu	NOUN
ejpam-3966	3	41	city	city	NOUN
ejpam-3966	3	42	,	,	PUNCT
ejpam-3966	3	43	philippines	philippines	PROPN
ejpam-3966	3	44	2	2	NUM
ejpam-3966	3	45	department	department	NOUN
ejpam-3966	3	46	of	of	ADP
ejpam-3966	3	47	mathematics	mathematic	NOUN
ejpam-3966	3	48	and	and	CCONJ
ejpam-3966	3	49	statistics	statistic	NOUN
ejpam-3966	3	50	,	,	PUNCT
ejpam-3966	3	51	college	college	NOUN
ejpam-3966	3	52	of	of	ADP
ejpam-3966	3	53	science	science	NOUN
ejpam-3966	3	54	and	and	CCONJ
ejpam-3966	3	55	mathematics	mathematic	NOUN
ejpam-3966	3	56	,	,	PUNCT
ejpam-3966	3	57	mindanao	mindanao	PROPN
ejpam-3966	3	58	state	state	PROPN
ejpam-3966	3	59	university	university	PROPN
ejpam-3966	3	60	-	-	PUNCT
ejpam-3966	3	61	iligan	iligan	PROPN
ejpam-3966	3	62	institute	institute	PROPN
ejpam-3966	3	63	of	of	ADP
ejpam-3966	3	64	technology	technology	PROPN
ejpam-3966	3	65	,	,	PUNCT
ejpam-3966	3	66	9200	9200	NUM
ejpam-3966	3	67	iligan	iligan	ADJ
ejpam-3966	3	68	city	city	NOUN
ejpam-3966	3	69	,	,	PUNCT
ejpam-3966	3	70	philippines	philippine	NOUN
ejpam-3966	3	71	abstract	abstract	ADJ
ejpam-3966	3	72	.	.	PUNCT
ejpam-3966	4	1	this	this	DET
ejpam-3966	4	2	paper	paper	NOUN
ejpam-3966	4	3	covers	cover	VERB
ejpam-3966	4	4	the	the	DET
ejpam-3966	4	5	notion	notion	NOUN
ejpam-3966	4	6	of	of	ADP
ejpam-3966	4	7	the	the	DET
ejpam-3966	4	8	inverse	inverse	NOUN
ejpam-3966	4	9	limit	limit	NOUN
ejpam-3966	4	10	of	of	ADP
ejpam-3966	4	11	an	an	DET
ejpam-3966	4	12	inverse	inverse	NOUN
ejpam-3966	4	13	system	system	NOUN
ejpam-3966	4	14	of	of	ADP
ejpam-3966	4	15	be	be	AUX
ejpam-3966	4	16	-	-	PUNCT
ejpam-3966	4	17	algebras	algebra	VERB
ejpam-3966	4	18	and	and	CCONJ
ejpam-3966	4	19	investigates	investigate	VERB
ejpam-3966	4	20	some	some	PRON
ejpam-3966	4	21	of	of	ADP
ejpam-3966	4	22	its	its	PRON
ejpam-3966	4	23	properties	property	NOUN
ejpam-3966	4	24	.	.	PUNCT
ejpam-3966	5	1	moreover	moreover	ADV
ejpam-3966	5	2	,	,	PUNCT
ejpam-3966	5	3	this	this	DET
ejpam-3966	5	4	study	study	NOUN
ejpam-3966	5	5	deals	deal	VERB
ejpam-3966	5	6	with	with	ADP
ejpam-3966	5	7	the	the	DET
ejpam-3966	5	8	completion	completion	NOUN
ejpam-3966	5	9	of	of	ADP
ejpam-3966	5	10	a	a	DET
ejpam-3966	5	11	bealgebra	bealgebra	NOUN
ejpam-3966	5	12	.	.	PUNCT
ejpam-3966	6	1	2020	2020	NUM
ejpam-3966	6	2	mathematics	mathematic	NOUN
ejpam-3966	6	3	subject	subject	NOUN
ejpam-3966	6	4	classifications	classification	NOUN
ejpam-3966	6	5	:	:	PUNCT
ejpam-3966	6	6	06f35	06f35	NUM
ejpam-3966	6	7	,	,	PUNCT
ejpam-3966	6	8	03g25	03g25	NOUN
ejpam-3966	6	9	key	key	ADJ
ejpam-3966	6	10	words	word	NOUN
ejpam-3966	6	11	and	and	CCONJ
ejpam-3966	6	12	phrases	phrase	NOUN
ejpam-3966	6	13	:	:	PUNCT
ejpam-3966	6	14	be	be	AUX
ejpam-3966	6	15	-	-	PUNCT
ejpam-3966	6	16	algebra	algebra	NOUN
ejpam-3966	6	17	,	,	PUNCT
ejpam-3966	6	18	inverse	inverse	NOUN
ejpam-3966	6	19	limit	limit	NOUN
ejpam-3966	6	20	,	,	PUNCT
ejpam-3966	6	21	inverse	inverse	NOUN
ejpam-3966	6	22	system	system	NOUN
ejpam-3966	6	23	,	,	PUNCT
ejpam-3966	6	24	completion	completion	NOUN
ejpam-3966	6	25	1	1	NUM
ejpam-3966	6	26	.	.	PUNCT
ejpam-3966	7	1	introduction	introduction	NOUN
ejpam-3966	7	2	the	the	DET
ejpam-3966	7	3	notion	notion	NOUN
ejpam-3966	7	4	of	of	ADP
ejpam-3966	7	5	bck	bck	PROPN
ejpam-3966	7	6	-	-	PUNCT
ejpam-3966	7	7	algebras	algebras	PROPN
ejpam-3966	7	8	was	be	AUX
ejpam-3966	7	9	initiated	initiate	VERB
ejpam-3966	7	10	by	by	ADP
ejpam-3966	7	11	y.	y.	PROPN
ejpam-3966	7	12	imai	imai	PROPN
ejpam-3966	7	13	and	and	CCONJ
ejpam-3966	7	14	k.	k.	PROPN
ejpam-3966	7	15	iséki	iséki	PROPN
ejpam-3966	8	1	[	[	X
ejpam-3966	8	2	1	1	X
ejpam-3966	8	3	]	]	PUNCT
ejpam-3966	8	4	in	in	ADP
ejpam-3966	8	5	1966	1966	NUM
ejpam-3966	8	6	as	as	ADP
ejpam-3966	8	7	a	a	DET
ejpam-3966	8	8	generalization	generalization	NOUN
ejpam-3966	8	9	of	of	ADP
ejpam-3966	8	10	the	the	DET
ejpam-3966	8	11	concept	concept	NOUN
ejpam-3966	8	12	of	of	ADP
ejpam-3966	8	13	set	set	VERB
ejpam-3966	8	14	theoretic	theoretic	ADJ
ejpam-3966	8	15	difference	difference	NOUN
ejpam-3966	8	16	and	and	CCONJ
ejpam-3966	8	17	propositional	propositional	ADJ
ejpam-3966	8	18	calculi	calculi	NOUN
ejpam-3966	8	19	.	.	PUNCT
ejpam-3966	9	1	in	in	ADP
ejpam-3966	9	2	[	[	X
ejpam-3966	9	3	3	3	NUM
ejpam-3966	9	4	]	]	PUNCT
ejpam-3966	9	5	,	,	PUNCT
ejpam-3966	9	6	k.	k.	PROPN
ejpam-3966	9	7	h.	h.	PROPN
ejpam-3966	9	8	kim	kim	PROPN
ejpam-3966	9	9	and	and	CCONJ
ejpam-3966	9	10	y.	y.	PROPN
ejpam-3966	9	11	h.	h.	PROPN
ejpam-3966	9	12	yon	yon	PROPN
ejpam-3966	9	13	introduced	introduce	VERB
ejpam-3966	9	14	the	the	DET
ejpam-3966	9	15	dual	dual	ADJ
ejpam-3966	9	16	bck	bck	NOUN
ejpam-3966	9	17	-	-	PUNCT
ejpam-3966	9	18	algebra	algebra	NOUN
ejpam-3966	9	19	and	and	CCONJ
ejpam-3966	9	20	study	study	VERB
ejpam-3966	9	21	its	its	PRON
ejpam-3966	9	22	relation	relation	NOUN
ejpam-3966	9	23	to	to	ADP
ejpam-3966	9	24	mv	mv	NOUN
ejpam-3966	9	25	-	-	NOUN
ejpam-3966	9	26	algebra	algebra	NOUN
ejpam-3966	9	27	.	.	PUNCT
ejpam-3966	10	1	as	as	ADP
ejpam-3966	10	2	a	a	DET
ejpam-3966	10	3	generalization	generalization	NOUN
ejpam-3966	10	4	of	of	ADP
ejpam-3966	10	5	dual	dual	ADJ
ejpam-3966	10	6	bck	bck	NOUN
ejpam-3966	10	7	-	-	PUNCT
ejpam-3966	10	8	algebra	algebra	NOUN
ejpam-3966	10	9	,	,	PUNCT
ejpam-3966	10	10	h.	h.	PROPN
ejpam-3966	10	11	s.	s.	PROPN
ejpam-3966	10	12	kim	kim	PROPN
ejpam-3966	10	13	and	and	CCONJ
ejpam-3966	10	14	y.	y.	PROPN
ejpam-3966	10	15	h.	h.	PROPN
ejpam-3966	10	16	kim	kim	PROPN
ejpam-3966	11	1	[	[	X
ejpam-3966	11	2	2	2	NUM
ejpam-3966	11	3	]	]	PUNCT
ejpam-3966	11	4	introduced	introduce	VERB
ejpam-3966	11	5	the	the	DET
ejpam-3966	11	6	be	be	NOUN
ejpam-3966	11	7	-	-	PUNCT
ejpam-3966	11	8	algebra	algebra	NOUN
ejpam-3966	11	9	.	.	PUNCT
ejpam-3966	12	1	today	today	NOUN
ejpam-3966	12	2	,	,	PUNCT
ejpam-3966	12	3	be	be	AUX
ejpam-3966	12	4	-	-	PUNCT
ejpam-3966	12	5	algebras	algebra	NOUN
ejpam-3966	12	6	have	have	AUX
ejpam-3966	12	7	been	be	AUX
ejpam-3966	12	8	studied	study	VERB
ejpam-3966	12	9	by	by	ADP
ejpam-3966	12	10	many	many	ADJ
ejpam-3966	12	11	authors	author	NOUN
ejpam-3966	12	12	and	and	CCONJ
ejpam-3966	12	13	many	many	ADJ
ejpam-3966	12	14	branches	branch	NOUN
ejpam-3966	12	15	of	of	ADP
ejpam-3966	12	16	mathematics	mathematic	NOUN
ejpam-3966	12	17	have	have	AUX
ejpam-3966	12	18	been	be	AUX
ejpam-3966	12	19	applied	apply	VERB
ejpam-3966	12	20	to	to	PART
ejpam-3966	12	21	be	be	AUX
ejpam-3966	12	22	-	-	PUNCT
ejpam-3966	12	23	algebras	algebra	NOUN
ejpam-3966	12	24	,	,	PUNCT
ejpam-3966	12	25	such	such	ADJ
ejpam-3966	12	26	as	as	ADP
ejpam-3966	12	27	probability	probability	NOUN
ejpam-3966	12	28	theory	theory	NOUN
ejpam-3966	12	29	,	,	PUNCT
ejpam-3966	12	30	topology	topology	NOUN
ejpam-3966	12	31	,	,	PUNCT
ejpam-3966	12	32	fuzzy	fuzzy	ADJ
ejpam-3966	12	33	set	set	NOUN
ejpam-3966	12	34	theory	theory	NOUN
ejpam-3966	12	35	and	and	CCONJ
ejpam-3966	12	36	so	so	ADV
ejpam-3966	12	37	on	on	ADV
ejpam-3966	12	38	.	.	PUNCT
ejpam-3966	13	1	in	in	ADP
ejpam-3966	13	2	this	this	DET
ejpam-3966	13	3	paper	paper	NOUN
ejpam-3966	13	4	we	we	PRON
ejpam-3966	13	5	will	will	AUX
ejpam-3966	13	6	apply	apply	VERB
ejpam-3966	13	7	the	the	DET
ejpam-3966	13	8	concept	concept	NOUN
ejpam-3966	13	9	of	of	ADP
ejpam-3966	13	10	inverse	inverse	NOUN
ejpam-3966	13	11	limit	limit	NOUN
ejpam-3966	13	12	in	in	ADP
ejpam-3966	13	13	the	the	DET
ejpam-3966	13	14	sense	sense	NOUN
ejpam-3966	13	15	of	of	ADP
ejpam-3966	13	16	category	category	NOUN
ejpam-3966	13	17	theory	theory	NOUN
ejpam-3966	13	18	to	to	ADP
ejpam-3966	13	19	some	some	DET
ejpam-3966	13	20	collections	collection	NOUN
ejpam-3966	13	21	of	of	ADP
ejpam-3966	13	22	be	be	NOUN
ejpam-3966	13	23	-	-	PUNCT
ejpam-3966	13	24	algebras	algebras	X
ejpam-3966	13	25	.	.	PUNCT
ejpam-3966	14	1	this	this	DET
ejpam-3966	14	2	notion	notion	NOUN
ejpam-3966	14	3	in	in	ADP
ejpam-3966	14	4	category	category	NOUN
ejpam-3966	14	5	theory	theory	NOUN
ejpam-3966	14	6	has	have	AUX
ejpam-3966	14	7	been	be	AUX
ejpam-3966	14	8	studied	study	VERB
ejpam-3966	14	9	in	in	ADP
ejpam-3966	14	10	different	different	ADJ
ejpam-3966	14	11	kinds	kind	NOUN
ejpam-3966	14	12	of	of	ADP
ejpam-3966	14	13	categories	category	NOUN
ejpam-3966	14	14	.	.	PUNCT
ejpam-3966	15	1	this	this	DET
ejpam-3966	15	2	study	study	NOUN
ejpam-3966	15	3	introduces	introduce	VERB
ejpam-3966	15	4	the	the	DET
ejpam-3966	15	5	inverse	inverse	NOUN
ejpam-3966	15	6	limit	limit	NOUN
ejpam-3966	15	7	of	of	ADP
ejpam-3966	15	8	an	an	DET
ejpam-3966	15	9	inverse	inverse	NOUN
ejpam-3966	15	10	system	system	NOUN
ejpam-3966	15	11	of	of	ADP
ejpam-3966	15	12	be	be	AUX
ejpam-3966	15	13	-	-	PUNCT
ejpam-3966	15	14	algebras	algebra	VERB
ejpam-3966	15	15	and	and	CCONJ
ejpam-3966	15	16	investigates	investigate	VERB
ejpam-3966	15	17	some	some	PRON
ejpam-3966	15	18	of	of	ADP
ejpam-3966	15	19	its	its	PRON
ejpam-3966	15	20	properties	property	NOUN
ejpam-3966	15	21	.	.	PUNCT
ejpam-3966	16	1	through	through	ADP
ejpam-3966	16	2	this	this	DET
ejpam-3966	16	3	concept	concept	NOUN
ejpam-3966	16	4	,	,	PUNCT
ejpam-3966	16	5	we	we	PRON
ejpam-3966	16	6	present	present	VERB
ejpam-3966	16	7	the	the	DET
ejpam-3966	16	8	idea	idea	NOUN
ejpam-3966	16	9	of	of	ADP
ejpam-3966	16	10	the	the	DET
ejpam-3966	16	11	completion	completion	NOUN
ejpam-3966	16	12	of	of	ADP
ejpam-3966	16	13	any	any	DET
ejpam-3966	16	14	be	be	NOUN
ejpam-3966	16	15	-	-	PUNCT
ejpam-3966	16	16	algebra	algebra	NOUN
ejpam-3966	16	17	.	.	PUNCT
ejpam-3966	17	1	an	an	DET
ejpam-3966	17	2	algebra	algebra	NOUN
ejpam-3966	17	3	(	(	PUNCT
ejpam-3966	17	4	x	x	NOUN
ejpam-3966	17	5	;	;	PUNCT
ejpam-3966	17	6	∗	∗	NOUN
ejpam-3966	17	7	,	,	PUNCT
ejpam-3966	17	8	1x	1x	NUM
ejpam-3966	17	9	)	)	PUNCT
ejpam-3966	17	10	is	be	AUX
ejpam-3966	17	11	called	call	VERB
ejpam-3966	17	12	a	a	DET
ejpam-3966	17	13	be	be	NOUN
ejpam-3966	17	14	-	-	PUNCT
ejpam-3966	17	15	algebra	algebra	NOUN
ejpam-3966	17	16	if	if	SCONJ
ejpam-3966	17	17	the	the	DET
ejpam-3966	17	18	following	follow	VERB
ejpam-3966	17	19	hold	hold	NOUN
ejpam-3966	17	20	:	:	PUNCT
ejpam-3966	17	21	for	for	ADP
ejpam-3966	17	22	all	all	DET
ejpam-3966	17	23	x	x	NOUN
ejpam-3966	17	24	,	,	PUNCT
ejpam-3966	17	25	y	y	PROPN
ejpam-3966	17	26	,	,	PUNCT
ejpam-3966	17	27	z	z	PROPN
ejpam-3966	17	28	∈	∈	PROPN
ejpam-3966	17	29	x	x	X
ejpam-3966	17	30	,	,	PUNCT
ejpam-3966	17	31	(	(	PUNCT
ejpam-3966	17	32	be1	be1	NOUN
ejpam-3966	17	33	)	)	PUNCT
ejpam-3966	17	34	x∗x	x∗x	PUNCT
ejpam-3966	18	1	=	=	X
ejpam-3966	18	2	1x	1x	NUM
ejpam-3966	18	3	;	;	PUNCT
ejpam-3966	18	4	(	(	PUNCT
ejpam-3966	18	5	be2	be2	NOUN
ejpam-3966	18	6	)	)	PUNCT
ejpam-3966	18	7	x∗1x	x∗1x	X
ejpam-3966	19	1	=	=	PUNCT
ejpam-3966	19	2	1x	1x	NUM
ejpam-3966	19	3	;	;	PUNCT
ejpam-3966	19	4	(	(	PUNCT
ejpam-3966	19	5	be3	be3	PROPN
ejpam-3966	19	6	)	)	PUNCT
ejpam-3966	19	7	1x	1x	NUM
ejpam-3966	20	1	∗x	∗x	NOUN
ejpam-3966	20	2	=	=	SYM
ejpam-3966	20	3	x	x	X
ejpam-3966	20	4	;	;	PUNCT
ejpam-3966	20	5	and	and	CCONJ
ejpam-3966	20	6	(	(	PUNCT
ejpam-3966	20	7	be4	be4	NOUN
ejpam-3966	20	8	)	)	PUNCT
ejpam-3966	20	9	x∗	x∗	PROPN
ejpam-3966	20	10	(	(	PUNCT
ejpam-3966	20	11	y	y	PROPN
ejpam-3966	20	12	∗z	∗z	PROPN
ejpam-3966	20	13	)	)	PUNCT
ejpam-3966	21	1	=	=	SYM
ejpam-3966	21	2	y	y	PROPN
ejpam-3966	21	3	∗	∗	NOUN
ejpam-3966	21	4	(	(	PUNCT
ejpam-3966	21	5	x∗z	x∗z	NOUN
ejpam-3966	21	6	)	)	PUNCT
ejpam-3966	21	7	.	.	PUNCT
ejpam-3966	22	1	a	a	DET
ejpam-3966	22	2	relation	relation	NOUN
ejpam-3966	22	3	“	"	PUNCT
ejpam-3966	22	4	≤	≤	NOUN
ejpam-3966	22	5	”	"	PUNCT
ejpam-3966	22	6	on	on	ADP
ejpam-3966	22	7	x	x	PRON
ejpam-3966	22	8	,	,	PUNCT
ejpam-3966	22	9	called	call	VERB
ejpam-3966	22	10	be	be	NOUN
ejpam-3966	22	11	-	-	PUNCT
ejpam-3966	22	12	ordering	ordering	NOUN
ejpam-3966	22	13	,	,	PUNCT
ejpam-3966	22	14	is	be	AUX
ejpam-3966	22	15	defined	define	VERB
ejpam-3966	22	16	by	by	ADP
ejpam-3966	22	17	x	x	PROPN
ejpam-3966	22	18	≤	≤	NUM
ejpam-3966	22	19	y	y	NOUN
ejpam-3966	22	20	if	if	SCONJ
ejpam-3966	23	1	and	and	CCONJ
ejpam-3966	23	2	only	only	ADV
ejpam-3966	23	3	if	if	SCONJ
ejpam-3966	23	4	x	x	X
ejpam-3966	23	5	∗	∗	VERB
ejpam-3966	23	6	y	y	NOUN
ejpam-3966	23	7	=	=	SYM
ejpam-3966	23	8	1x	1x	PROPN
ejpam-3966	23	9	.	.	PUNCT
ejpam-3966	24	1	throughout	throughout	ADP
ejpam-3966	24	2	this	this	DET
ejpam-3966	24	3	paper	paper	NOUN
ejpam-3966	24	4	,	,	PUNCT
ejpam-3966	24	5	we	we	PRON
ejpam-3966	24	6	denote	denote	VERB
ejpam-3966	24	7	a	a	DET
ejpam-3966	24	8	be	be	NOUN
ejpam-3966	24	9	-	-	PUNCT
ejpam-3966	24	10	algebra	algebra	NOUN
ejpam-3966	24	11	(	(	PUNCT
ejpam-3966	24	12	x	x	X
ejpam-3966	24	13	,	,	PUNCT
ejpam-3966	24	14	∗	∗	NOUN
ejpam-3966	24	15	,	,	PUNCT
ejpam-3966	24	16	1x	1x	NUM
ejpam-3966	24	17	)	)	PUNCT
ejpam-3966	24	18	simply	simply	ADV
ejpam-3966	24	19	by	by	ADP
ejpam-3966	24	20	x	x	PRON
ejpam-3966	24	21	if	if	SCONJ
ejpam-3966	24	22	no	no	DET
ejpam-3966	24	23	confusion	confusion	NOUN
ejpam-3966	24	24	arises	arise	VERB
ejpam-3966	24	25	.	.	PUNCT
ejpam-3966	25	1	a	a	DET
ejpam-3966	25	2	non	non	ADJ
ejpam-3966	25	3	-	-	ADJ
ejpam-3966	25	4	empty	empty	ADJ
ejpam-3966	25	5	subset	subset	NOUN
ejpam-3966	25	6	s	s	NOUN
ejpam-3966	25	7	of	of	ADP
ejpam-3966	25	8	x	x	VERB
ejpam-3966	25	9	is	be	AUX
ejpam-3966	25	10	said	say	VERB
ejpam-3966	25	11	to	to	PART
ejpam-3966	25	12	be	be	AUX
ejpam-3966	25	13	a	a	DET
ejpam-3966	25	14	subalgebra	subalgebra	NOUN
ejpam-3966	25	15	of	of	ADP
ejpam-3966	25	16	x	x	PRON
ejpam-3966	25	17	if	if	SCONJ
ejpam-3966	25	18	x	x	PROPN
ejpam-3966	25	19	∗	∗	VERB
ejpam-3966	25	20	y	y	PROPN
ejpam-3966	25	21	∈	∈	PROPN
ejpam-3966	25	22	s	s	X
ejpam-3966	25	23	for	for	ADP
ejpam-3966	25	24	all	all	PRON
ejpam-3966	25	25	∗corresponding	∗corresponde	VERB
ejpam-3966	25	26	author	author	NOUN
ejpam-3966	25	27	.	.	PUNCT
ejpam-3966	26	1	doi	doi	NOUN
ejpam-3966	26	2	:	:	PUNCT
ejpam-3966	26	3	https://doi.org/10.29020/nybg.ejpam.v14i2.3966	https://doi.org/10.29020/nybg.ejpam.v14i2.3966	ADJ
ejpam-3966	26	4	email	email	NOUN
ejpam-3966	26	5	addresses	address	VERB
ejpam-3966	26	6	:	:	PUNCT
ejpam-3966	26	7	jralbaracin@up.edu.ph	jralbaracin@up.edu.ph	PROPN
ejpam-3966	26	8	(	(	PUNCT
ejpam-3966	26	9	j.	j.	PROPN
ejpam-3966	26	10	albaracin	albaracin	PROPN
ejpam-3966	26	11	)	)	PUNCT
ejpam-3966	26	12	,	,	PUNCT
ejpam-3966	26	13	jocelyn.vilela@g.msuiit.edu.ph	jocelyn.vilela@g.msuiit.edu.ph	PROPN
ejpam-3966	26	14	(	(	PUNCT
ejpam-3966	26	15	j.	j.	PROPN
ejpam-3966	26	16	vilela	vilela	PROPN
ejpam-3966	26	17	)	)	PUNCT
ejpam-3966	26	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3966	27	1	423	423	NUM
ejpam-3966	27	2	c	c	X
ejpam-3966	27	3	©	©	PROPN
ejpam-3966	27	4	2021	2021	NUM
ejpam-3966	27	5	ejpam	ejpam	VERB
ejpam-3966	27	6	all	all	DET
ejpam-3966	27	7	rights	right	NOUN
ejpam-3966	27	8	reserved	reserve	VERB
ejpam-3966	27	9	.	.	PUNCT
ejpam-3966	28	1	j.	j.	PROPN
ejpam-3966	28	2	albaracin	albaracin	PROPN
ejpam-3966	28	3	,	,	PUNCT
ejpam-3966	28	4	j.	j.	PROPN
ejpam-3966	28	5	vilela	vilela	PROPN
ejpam-3966	28	6	/	/	SYM
ejpam-3966	28	7	eur	eur	PROPN
ejpam-3966	28	8	.	.	PUNCT
ejpam-3966	29	1	j.	j.	PROPN
ejpam-3966	29	2	pure	pure	PROPN
ejpam-3966	29	3	appl	appl	PROPN
ejpam-3966	29	4	.	.	PROPN
ejpam-3966	29	5	math	math	PROPN
ejpam-3966	29	6	,	,	PUNCT
ejpam-3966	29	7	14	14	NUM
ejpam-3966	29	8	(	(	PUNCT
ejpam-3966	29	9	2	2	NUM
ejpam-3966	29	10	)	)	PUNCT
ejpam-3966	29	11	(	(	PUNCT
ejpam-3966	29	12	2021	2021	NUM
ejpam-3966	29	13	)	)	PUNCT
ejpam-3966	29	14	,	,	PUNCT
ejpam-3966	29	15	423	423	NUM
ejpam-3966	29	16	-	-	SYM
ejpam-3966	29	17	430	430	NUM
ejpam-3966	29	18	424	424	NUM
ejpam-3966	29	19	x	x	NOUN
ejpam-3966	29	20	,	,	PUNCT
ejpam-3966	29	21	y	y	PROPN
ejpam-3966	29	22	∈	∈	PROPN
ejpam-3966	29	23	s.	s.	PROPN
ejpam-3966	29	24	a	a	DET
ejpam-3966	29	25	non	non	ADJ
ejpam-3966	29	26	-	-	ADJ
ejpam-3966	29	27	empty	empty	ADJ
ejpam-3966	29	28	subset	subset	NOUN
ejpam-3966	29	29	f	f	PROPN
ejpam-3966	29	30	of	of	ADP
ejpam-3966	29	31	x	x	PROPN
ejpam-3966	29	32	is	be	AUX
ejpam-3966	29	33	said	say	VERB
ejpam-3966	29	34	to	to	PART
ejpam-3966	29	35	be	be	AUX
ejpam-3966	29	36	a	a	DET
ejpam-3966	29	37	filter	filter	NOUN
ejpam-3966	29	38	of	of	ADP
ejpam-3966	29	39	x	x	SYM
ejpam-3966	29	40	if	if	SCONJ
ejpam-3966	29	41	:	:	PUNCT
ejpam-3966	29	42	(	(	PUNCT
ejpam-3966	29	43	f1	f1	NOUN
ejpam-3966	29	44	)	)	PUNCT
ejpam-3966	29	45	1x	1x	NOUN
ejpam-3966	30	1	∈	∈	PROPN
ejpam-3966	30	2	f	f	X
ejpam-3966	30	3	;	;	PUNCT
ejpam-3966	30	4	and	and	CCONJ
ejpam-3966	30	5	(	(	PUNCT
ejpam-3966	30	6	f2	f2	PROPN
ejpam-3966	30	7	)	)	PUNCT
ejpam-3966	30	8	x	x	SYM
ejpam-3966	30	9	∗	∗	NOUN
ejpam-3966	30	10	y	y	PROPN
ejpam-3966	30	11	∈	∈	PROPN
ejpam-3966	30	12	f	f	PROPN
ejpam-3966	30	13	and	and	CCONJ
ejpam-3966	30	14	x	x	PROPN
ejpam-3966	30	15	∈	∈	NOUN
ejpam-3966	31	1	f	f	X
ejpam-3966	31	2	imply	imply	VERB
ejpam-3966	31	3	y	y	PROPN
ejpam-3966	31	4	∈	∈	PROPN
ejpam-3966	32	1	f	f	PROPN
ejpam-3966	32	2	.	.	PUNCT
ejpam-3966	33	1	a	a	DET
ejpam-3966	33	2	filter	filter	NOUN
ejpam-3966	33	3	f	f	NOUN
ejpam-3966	33	4	of	of	ADP
ejpam-3966	33	5	x	x	PROPN
ejpam-3966	33	6	is	be	AUX
ejpam-3966	33	7	said	say	VERB
ejpam-3966	33	8	to	to	PART
ejpam-3966	33	9	be	be	AUX
ejpam-3966	33	10	normal	normal	ADJ
ejpam-3966	33	11	if	if	SCONJ
ejpam-3966	33	12	it	it	PRON
ejpam-3966	33	13	satisfies	satisfy	VERB
ejpam-3966	33	14	the	the	DET
ejpam-3966	33	15	following	follow	VERB
ejpam-3966	33	16	condition	condition	NOUN
ejpam-3966	33	17	:	:	PUNCT
ejpam-3966	33	18	for	for	SCONJ
ejpam-3966	33	19	all	all	DET
ejpam-3966	33	20	x	x	NOUN
ejpam-3966	33	21	,	,	PUNCT
ejpam-3966	33	22	y	y	PROPN
ejpam-3966	33	23	,	,	PUNCT
ejpam-3966	33	24	z	z	PROPN
ejpam-3966	33	25	∈	∈	PROPN
ejpam-3966	33	26	x	x	X
ejpam-3966	33	27	,	,	PUNCT
ejpam-3966	33	28	x	x	SYM
ejpam-3966	33	29	∗	∗	NOUN
ejpam-3966	33	30	y	y	PROPN
ejpam-3966	33	31	∈	∈	PROPN
ejpam-3966	33	32	f	f	PROPN
ejpam-3966	33	33	implies	imply	VERB
ejpam-3966	33	34	(	(	PUNCT
ejpam-3966	33	35	z	z	NOUN
ejpam-3966	33	36	∗	∗	NOUN
ejpam-3966	33	37	x	x	NOUN
ejpam-3966	33	38	)	)	PUNCT
ejpam-3966	33	39	∗	∗	NOUN
ejpam-3966	33	40	(	(	PUNCT
ejpam-3966	33	41	z	z	NOUN
ejpam-3966	33	42	∗	∗	PROPN
ejpam-3966	33	43	y	y	PROPN
ejpam-3966	33	44	)	)	PUNCT
ejpam-3966	33	45	∈	∈	PROPN
ejpam-3966	33	46	f	f	PROPN
ejpam-3966	33	47	and	and	CCONJ
ejpam-3966	33	48	(	(	PUNCT
ejpam-3966	33	49	y∗z)∗(x∗z	y∗z)∗(x∗z	NOUN
ejpam-3966	33	50	)	)	PUNCT
ejpam-3966	33	51	∈	∈	PROPN
ejpam-3966	34	1	f	f	PROPN
ejpam-3966	34	2	.	.	PUNCT
ejpam-3966	35	1	a	a	DET
ejpam-3966	35	2	be	be	NOUN
ejpam-3966	35	3	-	-	PUNCT
ejpam-3966	35	4	algebra	algebra	NOUN
ejpam-3966	35	5	x	x	PUNCT
ejpam-3966	35	6	is	be	AUX
ejpam-3966	35	7	said	say	VERB
ejpam-3966	35	8	to	to	PART
ejpam-3966	35	9	be	be	AUX
ejpam-3966	35	10	self	self	NOUN
ejpam-3966	35	11	distributive	distributive	ADJ
ejpam-3966	35	12	if	if	SCONJ
ejpam-3966	35	13	x∗(y∗z	x∗(y∗z	NUM
ejpam-3966	35	14	)	)	PUNCT
ejpam-3966	36	1	=	=	SYM
ejpam-3966	36	2	(	(	PUNCT
ejpam-3966	36	3	x∗y)∗(x∗z	x∗y)∗(x∗z	PROPN
ejpam-3966	36	4	)	)	PUNCT
ejpam-3966	36	5	for	for	ADP
ejpam-3966	36	6	all	all	DET
ejpam-3966	36	7	x	x	NOUN
ejpam-3966	36	8	,	,	PUNCT
ejpam-3966	36	9	y	y	PROPN
ejpam-3966	36	10	,	,	PUNCT
ejpam-3966	36	11	z	z	NOUN
ejpam-3966	36	12	∈	∈	PROPN
ejpam-3966	36	13	x.	x.	NOUN
ejpam-3966	36	14	it	it	PRON
ejpam-3966	36	15	is	be	AUX
ejpam-3966	36	16	called	call	VERB
ejpam-3966	36	17	commutative	commutative	ADJ
ejpam-3966	36	18	if	if	SCONJ
ejpam-3966	36	19	satisfies	satisfie	NOUN
ejpam-3966	36	20	(	(	PUNCT
ejpam-3966	36	21	x∗y)∗y	x∗y)∗y	SYM
ejpam-3966	36	22	=	=	SYM
ejpam-3966	36	23	(	(	PUNCT
ejpam-3966	36	24	y∗x)∗x	y∗x)∗x	PROPN
ejpam-3966	36	25	for	for	ADP
ejpam-3966	36	26	all	all	DET
ejpam-3966	36	27	x	x	NOUN
ejpam-3966	36	28	,	,	PUNCT
ejpam-3966	36	29	y	y	PROPN
ejpam-3966	36	30	∈	∈	PROPN
ejpam-3966	36	31	x.	x.	NOUN
ejpam-3966	37	1	it	it	PRON
ejpam-3966	37	2	is	be	AUX
ejpam-3966	37	3	said	say	VERB
ejpam-3966	37	4	to	to	PART
ejpam-3966	37	5	be	be	AUX
ejpam-3966	37	6	a	a	DET
ejpam-3966	37	7	transitive	transitive	ADJ
ejpam-3966	37	8	be	be	NOUN
ejpam-3966	37	9	-	-	PUNCT
ejpam-3966	37	10	algebra	algebra	NOUN
ejpam-3966	37	11	if	if	SCONJ
ejpam-3966	37	12	it	it	PRON
ejpam-3966	37	13	satisfies	satisfy	VERB
ejpam-3966	37	14	the	the	DET
ejpam-3966	37	15	condition	condition	NOUN
ejpam-3966	37	16	:	:	PUNCT
ejpam-3966	37	17	y∗z	y∗z	PROPN
ejpam-3966	37	18	≤	≤	NUM
ejpam-3966	37	19	(	(	PUNCT
ejpam-3966	37	20	x∗y)∗(x∗z	x∗y)∗(x∗z	PROPN
ejpam-3966	37	21	)	)	PUNCT
ejpam-3966	37	22	for	for	ADP
ejpam-3966	37	23	all	all	DET
ejpam-3966	37	24	x	x	NOUN
ejpam-3966	37	25	,	,	PUNCT
ejpam-3966	37	26	y	y	PROPN
ejpam-3966	37	27	,	,	PUNCT
ejpam-3966	37	28	z	z	NOUN
ejpam-3966	37	29	∈	∈	PROPN
ejpam-3966	37	30	x.	x.	NOUN
ejpam-3966	38	1	if	if	SCONJ
ejpam-3966	38	2	x	x	PRON
ejpam-3966	38	3	is	be	AUX
ejpam-3966	38	4	a	a	DET
ejpam-3966	38	5	transitive	transitive	ADJ
ejpam-3966	38	6	be	be	NOUN
ejpam-3966	38	7	-	-	PUNCT
ejpam-3966	38	8	algebra	algebra	NOUN
ejpam-3966	38	9	,	,	PUNCT
ejpam-3966	38	10	then	then	ADV
ejpam-3966	38	11	the	the	DET
ejpam-3966	38	12	relation	relation	NOUN
ejpam-3966	38	13	“	"	PUNCT
ejpam-3966	38	14	≤	≤	NUM
ejpam-3966	38	15	”	"	PUNCT
ejpam-3966	38	16	is	be	AUX
ejpam-3966	38	17	transitive	transitive	ADJ
ejpam-3966	38	18	.	.	PUNCT
ejpam-3966	39	1	let	let	VERB
ejpam-3966	39	2	x	x	PRON
ejpam-3966	39	3	and	and	CCONJ
ejpam-3966	39	4	y	y	PROPN
ejpam-3966	39	5	be	be	AUX
ejpam-3966	39	6	be	be	AUX
ejpam-3966	39	7	-	-	PUNCT
ejpam-3966	39	8	algebras	algebras	X
ejpam-3966	39	9	.	.	PUNCT
ejpam-3966	40	1	a	a	DET
ejpam-3966	40	2	mapping	mapping	NOUN
ejpam-3966	40	3	f	f	NOUN
ejpam-3966	40	4	:	:	PUNCT
ejpam-3966	40	5	x	x	X
ejpam-3966	40	6	→	→	SYM
ejpam-3966	40	7	y	y	PROPN
ejpam-3966	40	8	is	be	AUX
ejpam-3966	40	9	a	a	DET
ejpam-3966	40	10	homomorphism	homomorphism	NOUN
ejpam-3966	40	11	if	if	SCONJ
ejpam-3966	40	12	f(x∗y	f(x∗y	PROPN
ejpam-3966	40	13	)	)	PUNCT
ejpam-3966	41	1	=	=	SYM
ejpam-3966	41	2	f(x)∗f(y	f(x)∗f(y	PROPN
ejpam-3966	41	3	)	)	PUNCT
ejpam-3966	41	4	for	for	ADP
ejpam-3966	41	5	all	all	DET
ejpam-3966	41	6	x	x	NOUN
ejpam-3966	41	7	,	,	PUNCT
ejpam-3966	41	8	y	y	PROPN
ejpam-3966	41	9	∈	∈	PROPN
ejpam-3966	41	10	x	x	AUX
ejpam-3966	41	11	,	,	PUNCT
ejpam-3966	41	12	see	see	VERB
ejpam-3966	41	13	[	[	X
ejpam-3966	41	14	4	4	NUM
ejpam-3966	41	15	]	]	PUNCT
ejpam-3966	41	16	.	.	PUNCT
ejpam-3966	42	1	theorem	theorem	NOUN
ejpam-3966	42	2	1	1	NUM
ejpam-3966	42	3	.	.	PUNCT
ejpam-3966	43	1	[	[	X
ejpam-3966	43	2	4	4	X
ejpam-3966	43	3	]	]	AUX
ejpam-3966	43	4	let	let	VERB
ejpam-3966	43	5	x	x	PRON
ejpam-3966	43	6	and	and	CCONJ
ejpam-3966	43	7	y	y	PROPN
ejpam-3966	43	8	be	be	AUX
ejpam-3966	43	9	be	be	AUX
ejpam-3966	43	10	-	-	PUNCT
ejpam-3966	43	11	algebras	algebra	NOUN
ejpam-3966	43	12	.	.	PUNCT
ejpam-3966	44	1	if	if	SCONJ
ejpam-3966	44	2	f	f	PROPN
ejpam-3966	44	3	:	:	PUNCT
ejpam-3966	44	4	x	x	X
ejpam-3966	44	5	→	→	SYM
ejpam-3966	44	6	y	y	PROPN
ejpam-3966	44	7	is	be	AUX
ejpam-3966	44	8	a	a	DET
ejpam-3966	44	9	homomorphism	homomorphism	NOUN
ejpam-3966	44	10	,	,	PUNCT
ejpam-3966	44	11	then	then	ADV
ejpam-3966	44	12	f(1x	f(1x	X
ejpam-3966	44	13	)	)	PUNCT
ejpam-3966	44	14	=	=	SYM
ejpam-3966	44	15	1y	1y	PROPN
ejpam-3966	44	16	.	.	PUNCT
ejpam-3966	45	1	theorem	theorem	NOUN
ejpam-3966	45	2	2	2	NUM
ejpam-3966	45	3	.	.	PUNCT
ejpam-3966	46	1	[	[	X
ejpam-3966	46	2	4	4	X
ejpam-3966	46	3	]	]	PUNCT
ejpam-3966	46	4	every	every	DET
ejpam-3966	46	5	commutative	commutative	ADJ
ejpam-3966	46	6	be	be	AUX
ejpam-3966	46	7	-	-	PUNCT
ejpam-3966	46	8	algebra	algebra	NOUN
ejpam-3966	46	9	x	x	PUNCT
ejpam-3966	46	10	is	be	AUX
ejpam-3966	46	11	transitive	transitive	ADJ
ejpam-3966	46	12	.	.	PUNCT
ejpam-3966	47	1	proposition	proposition	NOUN
ejpam-3966	47	2	1	1	NUM
ejpam-3966	47	3	.	.	PUNCT
ejpam-3966	48	1	[	[	X
ejpam-3966	48	2	6	6	NUM
ejpam-3966	48	3	]	]	PUNCT
ejpam-3966	48	4	if	if	SCONJ
ejpam-3966	48	5	x	x	PRON
ejpam-3966	48	6	is	be	AUX
ejpam-3966	48	7	a	a	DET
ejpam-3966	48	8	transitive	transitive	ADJ
ejpam-3966	48	9	be	be	NOUN
ejpam-3966	48	10	-	-	PUNCT
ejpam-3966	48	11	algebra	algebra	NOUN
ejpam-3966	48	12	,	,	PUNCT
ejpam-3966	48	13	then	then	ADV
ejpam-3966	48	14	every	every	DET
ejpam-3966	48	15	filter	filter	NOUN
ejpam-3966	48	16	of	of	ADP
ejpam-3966	48	17	x	x	PUNCT
ejpam-3966	48	18	is	be	AUX
ejpam-3966	48	19	normal	normal	ADJ
ejpam-3966	48	20	.	.	PUNCT
ejpam-3966	49	1	theorem	theorem	NOUN
ejpam-3966	49	2	3	3	NUM
ejpam-3966	49	3	.	.	PUNCT
ejpam-3966	50	1	[	[	X
ejpam-3966	50	2	6	6	NUM
ejpam-3966	50	3	]	]	PUNCT
ejpam-3966	50	4	let	let	VERB
ejpam-3966	50	5	x	x	PRON
ejpam-3966	50	6	be	be	AUX
ejpam-3966	50	7	a	a	DET
ejpam-3966	50	8	commutative	commutative	ADJ
ejpam-3966	50	9	be	be	NOUN
ejpam-3966	50	10	-	-	PUNCT
ejpam-3966	50	11	algebra	algebra	NOUN
ejpam-3966	50	12	.	.	PUNCT
ejpam-3966	51	1	there	there	PRON
ejpam-3966	51	2	is	be	VERB
ejpam-3966	51	3	a	a	DET
ejpam-3966	51	4	bijection	bijection	NOUN
ejpam-3966	51	5	between	between	ADP
ejpam-3966	51	6	congruence	congruence	NOUN
ejpam-3966	51	7	relations	relation	NOUN
ejpam-3966	51	8	and	and	CCONJ
ejpam-3966	51	9	filters	filter	NOUN
ejpam-3966	51	10	of	of	ADP
ejpam-3966	51	11	x.	x.	NOUN
ejpam-3966	51	12	definition	definition	NOUN
ejpam-3966	51	13	1	1	NUM
ejpam-3966	51	14	.	.	PUNCT
ejpam-3966	52	1	[	[	X
ejpam-3966	52	2	5	5	X
ejpam-3966	52	3	]	]	PUNCT
ejpam-3966	52	4	let	let	VERB
ejpam-3966	52	5	i	i	PRON
ejpam-3966	52	6	be	be	AUX
ejpam-3966	52	7	a	a	DET
ejpam-3966	52	8	set	set	NOUN
ejpam-3966	52	9	and	and	CCONJ
ejpam-3966	52	10	≤	≤	NUM
ejpam-3966	52	11	be	be	VERB
ejpam-3966	52	12	a	a	DET
ejpam-3966	52	13	binary	binary	ADJ
ejpam-3966	52	14	operation	operation	NOUN
ejpam-3966	52	15	on	on	ADP
ejpam-3966	52	16	i.	i.	NOUN
ejpam-3966	52	17	we	we	PRON
ejpam-3966	52	18	call	call	VERB
ejpam-3966	52	19	i	i	PRON
ejpam-3966	52	20	=	=	SYM
ejpam-3966	52	21	(	(	PUNCT
ejpam-3966	52	22	i,≤	i,≤	X
ejpam-3966	52	23	)	)	PUNCT
ejpam-3966	52	24	a	a	DET
ejpam-3966	52	25	directed	direct	VERB
ejpam-3966	52	26	partially	partially	ADV
ejpam-3966	52	27	ordered	order	VERB
ejpam-3966	52	28	set	set	NOUN
ejpam-3966	52	29	or	or	CCONJ
ejpam-3966	52	30	directed	direct	VERB
ejpam-3966	52	31	poset	poset	NOUN
ejpam-3966	52	32	if	if	SCONJ
ejpam-3966	52	33	it	it	PRON
ejpam-3966	52	34	satisfies	satisfy	VERB
ejpam-3966	52	35	the	the	DET
ejpam-3966	52	36	following	follow	VERB
ejpam-3966	52	37	conditions	condition	NOUN
ejpam-3966	52	38	:	:	PUNCT
ejpam-3966	52	39	(	(	PUNCT
ejpam-3966	52	40	i	i	NOUN
ejpam-3966	52	41	)	)	PUNCT
ejpam-3966	53	1	i	i	PRON
ejpam-3966	53	2	≤	≤	PUNCT
ejpam-3966	54	1	i	i	PRON
ejpam-3966	54	2	,	,	PUNCT
ejpam-3966	54	3	for	for	ADP
ejpam-3966	54	4	i	i	PRON
ejpam-3966	54	5	∈	∈	PROPN
ejpam-3966	55	1	i	i	PRON
ejpam-3966	55	2	;	;	PUNCT
ejpam-3966	55	3	(	(	PUNCT
ejpam-3966	55	4	ii	ii	NOUN
ejpam-3966	55	5	)	)	PUNCT
ejpam-3966	55	6	i	i	PROPN
ejpam-3966	55	7	≤	≤	NUM
ejpam-3966	55	8	j	j	PROPN
ejpam-3966	55	9	and	and	CCONJ
ejpam-3966	55	10	j	j	PROPN
ejpam-3966	56	1	≤	≤	PROPN
ejpam-3966	56	2	k	k	NOUN
ejpam-3966	56	3	imply	imply	VERB
ejpam-3966	56	4	i	i	PRON
ejpam-3966	56	5	≤	≤	ADJ
ejpam-3966	57	1	k	k	NOUN
ejpam-3966	57	2	,	,	PUNCT
ejpam-3966	57	3	for	for	ADP
ejpam-3966	57	4	i	i	PROPN
ejpam-3966	57	5	,	,	PUNCT
ejpam-3966	57	6	j	j	PROPN
ejpam-3966	57	7	,	,	PUNCT
ejpam-3966	57	8	k	k	PROPN
ejpam-3966	57	9	∈	∈	PROPN
ejpam-3966	58	1	i	i	PRON
ejpam-3966	58	2	;	;	PUNCT
ejpam-3966	58	3	(	(	PUNCT
ejpam-3966	58	4	iii	iii	X
ejpam-3966	58	5	)	)	PUNCT
ejpam-3966	58	6	i	i	PROPN
ejpam-3966	58	7	≤	≤	NUM
ejpam-3966	58	8	j	j	PROPN
ejpam-3966	58	9	and	and	CCONJ
ejpam-3966	58	10	j	j	PROPN
ejpam-3966	58	11	≤	≤	ADV
ejpam-3966	59	1	i	i	PRON
ejpam-3966	59	2	imply	imply	VERB
ejpam-3966	59	3	i	i	PRON
ejpam-3966	59	4	=	=	SYM
ejpam-3966	59	5	j	j	PROPN
ejpam-3966	59	6	,	,	PUNCT
ejpam-3966	59	7	for	for	ADP
ejpam-3966	59	8	i	i	PRON
ejpam-3966	59	9	,	,	PUNCT
ejpam-3966	59	10	j	j	PROPN
ejpam-3966	59	11	∈	∈	PROPN
ejpam-3966	59	12	i	i	PRON
ejpam-3966	59	13	;	;	PUNCT
ejpam-3966	59	14	and	and	CCONJ
ejpam-3966	59	15	(	(	PUNCT
ejpam-3966	59	16	iv	iv	X
ejpam-3966	59	17	)	)	PUNCT
ejpam-3966	59	18	if	if	SCONJ
ejpam-3966	59	19	i	i	PRON
ejpam-3966	59	20	,	,	PUNCT
ejpam-3966	59	21	j	j	PROPN
ejpam-3966	59	22	∈	∈	PROPN
ejpam-3966	60	1	i	i	PRON
ejpam-3966	60	2	,	,	PUNCT
ejpam-3966	60	3	there	there	PRON
ejpam-3966	60	4	exists	exist	VERB
ejpam-3966	60	5	some	some	DET
ejpam-3966	60	6	k	k	PROPN
ejpam-3966	60	7	∈	∈	PROPN
ejpam-3966	60	8	i	i	PRON
ejpam-3966	60	9	such	such	ADJ
ejpam-3966	60	10	that	that	SCONJ
ejpam-3966	60	11	i	i	PRON
ejpam-3966	60	12	,	,	PUNCT
ejpam-3966	60	13	j	j	PROPN
ejpam-3966	60	14	≤	≤	PROPN
ejpam-3966	60	15	k.	k.	PROPN
ejpam-3966	60	16	definition	definition	NOUN
ejpam-3966	60	17	2	2	NUM
ejpam-3966	60	18	.	.	PUNCT
ejpam-3966	60	19	an	an	DET
ejpam-3966	60	20	inverse	inverse	NOUN
ejpam-3966	60	21	or	or	CCONJ
ejpam-3966	60	22	projective	projective	ADJ
ejpam-3966	60	23	system	system	NOUN
ejpam-3966	60	24	of	of	ADP
ejpam-3966	60	25	be	be	AUX
ejpam-3966	60	26	-	-	PUNCT
ejpam-3966	60	27	algebras	algebras	ADJ
ejpam-3966	60	28	over	over	ADP
ejpam-3966	60	29	a	a	DET
ejpam-3966	60	30	directed	direct	VERB
ejpam-3966	60	31	poset	poset	NOUN
ejpam-3966	60	32	i	i	PRON
ejpam-3966	60	33	,	,	PUNCT
ejpam-3966	60	34	consists	consist	VERB
ejpam-3966	60	35	of	of	ADP
ejpam-3966	60	36	a	a	DET
ejpam-3966	60	37	collection	collection	NOUN
ejpam-3966	60	38	{	{	PUNCT
ejpam-3966	61	1	xi	xi	X
ejpam-3966	62	1	|	|	ADV
ejpam-3966	63	1	i	i	PRON
ejpam-3966	63	2	∈	∈	VERB
ejpam-3966	64	1	i	i	PRON
ejpam-3966	64	2	}	}	PUNCT
ejpam-3966	64	3	of	of	ADP
ejpam-3966	64	4	be	be	AUX
ejpam-3966	64	5	-	-	PUNCT
ejpam-3966	64	6	algebras	algebra	VERB
ejpam-3966	64	7	indexed	index	VERB
ejpam-3966	64	8	by	by	ADP
ejpam-3966	64	9	i	i	PROPN
ejpam-3966	64	10	,	,	PUNCT
ejpam-3966	64	11	and	and	CCONJ
ejpam-3966	64	12	a	a	DET
ejpam-3966	64	13	collection	collection	NOUN
ejpam-3966	64	14	of	of	ADP
ejpam-3966	64	15	homomorphisms	homomorphism	NOUN
ejpam-3966	64	16	ϕij	ϕij	NOUN
ejpam-3966	64	17	:	:	PUNCT
ejpam-3966	64	18	xi	xi	PROPN
ejpam-3966	64	19	→	→	SYM
ejpam-3966	64	20	xj	xj	PROPN
ejpam-3966	64	21	,	,	PUNCT
ejpam-3966	64	22	defined	define	VERB
ejpam-3966	64	23	whenever	whenever	SCONJ
ejpam-3966	64	24	i	i	PRON
ejpam-3966	64	25	≥	≥	VERB
ejpam-3966	64	26	j	j	PROPN
ejpam-3966	64	27	,	,	PUNCT
ejpam-3966	64	28	such	such	ADJ
ejpam-3966	64	29	that	that	DET
ejpam-3966	64	30	ϕjkϕij	ϕjkϕij	NOUN
ejpam-3966	64	31	=	=	PUNCT
ejpam-3966	65	1	ϕik	ϕik	INTJ
ejpam-3966	65	2	whenever	whenever	SCONJ
ejpam-3966	65	3	i	i	PRON
ejpam-3966	65	4	,	,	PUNCT
ejpam-3966	65	5	j	j	PROPN
ejpam-3966	65	6	,	,	PUNCT
ejpam-3966	65	7	k	k	PROPN
ejpam-3966	65	8	∈	∈	PROPN
ejpam-3966	66	1	i	i	PRON
ejpam-3966	66	2	and	and	CCONJ
ejpam-3966	66	3	i	i	PRON
ejpam-3966	66	4	≥	≥	VERB
ejpam-3966	66	5	j	j	PROPN
ejpam-3966	66	6	≥	≥	X
ejpam-3966	66	7	k.	k.	INTJ
ejpam-3966	67	1	in	in	ADP
ejpam-3966	67	2	addition	addition	NOUN
ejpam-3966	67	3	,	,	PUNCT
ejpam-3966	67	4	we	we	PRON
ejpam-3966	67	5	assume	assume	VERB
ejpam-3966	67	6	that	that	SCONJ
ejpam-3966	67	7	ϕii	ϕii	PROPN
ejpam-3966	67	8	is	be	AUX
ejpam-3966	67	9	the	the	DET
ejpam-3966	67	10	identity	identity	NOUN
ejpam-3966	67	11	mapping	map	VERB
ejpam-3966	67	12	idxi	idxi	NOUN
ejpam-3966	67	13	on	on	ADP
ejpam-3966	67	14	xi	xi	PROPN
ejpam-3966	67	15	.	.	PUNCT
ejpam-3966	68	1	we	we	PRON
ejpam-3966	68	2	shall	shall	AUX
ejpam-3966	68	3	denote	denote	VERB
ejpam-3966	68	4	such	such	DET
ejpam-3966	68	5	a	a	DET
ejpam-3966	68	6	system	system	NOUN
ejpam-3966	68	7	by	by	ADP
ejpam-3966	68	8	{	{	PUNCT
ejpam-3966	68	9	xi	xi	PROPN
ejpam-3966	68	10	,	,	PUNCT
ejpam-3966	68	11	ϕij	ϕij	NOUN
ejpam-3966	68	12	,	,	PUNCT
ejpam-3966	68	13	i	i	NOUN
ejpam-3966	68	14	}	}	PUNCT
ejpam-3966	68	15	,	,	PUNCT
ejpam-3966	68	16	or	or	CCONJ
ejpam-3966	68	17	by	by	ADP
ejpam-3966	68	18	{	{	PUNCT
ejpam-3966	68	19	xi	xi	PROPN
ejpam-3966	68	20	,	,	PUNCT
ejpam-3966	68	21	ϕij	ϕij	NOUN
ejpam-3966	68	22	}	}	PUNCT
ejpam-3966	68	23	if	if	SCONJ
ejpam-3966	68	24	the	the	DET
ejpam-3966	68	25	index	index	NOUN
ejpam-3966	68	26	set	set	VERB
ejpam-3966	68	27	i	i	PRON
ejpam-3966	68	28	is	be	AUX
ejpam-3966	68	29	clearly	clearly	ADV
ejpam-3966	68	30	understood	understand	VERB
ejpam-3966	68	31	.	.	PUNCT
ejpam-3966	69	1	definition	definition	NOUN
ejpam-3966	69	2	3	3	NUM
ejpam-3966	69	3	.	.	PUNCT
ejpam-3966	70	1	let	let	VERB
ejpam-3966	70	2	y	y	PRON
ejpam-3966	70	3	be	be	AUX
ejpam-3966	70	4	a	a	DET
ejpam-3966	70	5	be	be	NOUN
ejpam-3966	70	6	-	-	PUNCT
ejpam-3966	70	7	algebra	algebra	NOUN
ejpam-3966	70	8	,	,	PUNCT
ejpam-3966	70	9	{	{	PUNCT
ejpam-3966	70	10	xi	xi	PROPN
ejpam-3966	70	11	,	,	PUNCT
ejpam-3966	70	12	ϕij	ϕij	NOUN
ejpam-3966	70	13	,	,	PUNCT
ejpam-3966	70	14	i	i	NOUN
ejpam-3966	70	15	}	}	PUNCT
ejpam-3966	70	16	an	an	DET
ejpam-3966	70	17	inverse	inverse	NOUN
ejpam-3966	70	18	system	system	NOUN
ejpam-3966	70	19	of	of	ADP
ejpam-3966	70	20	be	be	AUX
ejpam-3966	70	21	-	-	PUNCT
ejpam-3966	70	22	algebras	algebras	ADJ
ejpam-3966	70	23	over	over	ADP
ejpam-3966	70	24	a	a	DET
ejpam-3966	70	25	directed	direct	VERB
ejpam-3966	70	26	poset	poset	NOUN
ejpam-3966	70	27	i	i	PRON
ejpam-3966	70	28	,	,	PUNCT
ejpam-3966	70	29	and	and	CCONJ
ejpam-3966	70	30	let	let	VERB
ejpam-3966	70	31	ψi	ψi	VERB
ejpam-3966	70	32	:	:	PUNCT
ejpam-3966	70	33	y	y	PROPN
ejpam-3966	70	34	→	→	PUNCT
ejpam-3966	70	35	xi	xi	X
ejpam-3966	70	36	be	be	AUX
ejpam-3966	70	37	a	a	DET
ejpam-3966	70	38	homomorphism	homomorphism	NOUN
ejpam-3966	70	39	for	for	ADP
ejpam-3966	70	40	each	each	DET
ejpam-3966	70	41	i	i	PRON
ejpam-3966	70	42	∈	∈	PROPN
ejpam-3966	70	43	i.	i.	NOUN
ejpam-3966	70	44	these	these	DET
ejpam-3966	70	45	mappings	mapping	NOUN
ejpam-3966	70	46	ψi	ψi	ADV
ejpam-3966	70	47	are	be	AUX
ejpam-3966	70	48	said	say	VERB
ejpam-3966	70	49	to	to	PART
ejpam-3966	70	50	be	be	AUX
ejpam-3966	70	51	compatible	compatible	ADJ
ejpam-3966	70	52	if	if	SCONJ
ejpam-3966	70	53	ϕijψi	ϕijψi	ADP
ejpam-3966	70	54	=	=	NOUN
ejpam-3966	70	55	ψj	ψj	ADV
ejpam-3966	70	56	whenever	whenever	SCONJ
ejpam-3966	70	57	j	j	PROPN
ejpam-3966	70	58	≤	≤	PROPN
ejpam-3966	70	59	i.	i.	NOUN
ejpam-3966	70	60	definition	definition	NOUN
ejpam-3966	70	61	4	4	X
ejpam-3966	70	62	.	.	PUNCT
ejpam-3966	71	1	let	let	VERB
ejpam-3966	71	2	{	{	PUNCT
ejpam-3966	71	3	xi	xi	PROPN
ejpam-3966	71	4	,	,	PUNCT
ejpam-3966	71	5	ϕij	ϕij	NOUN
ejpam-3966	71	6	,	,	PUNCT
ejpam-3966	71	7	i	i	PRON
ejpam-3966	71	8	}	}	PUNCT
ejpam-3966	71	9	be	be	VERB
ejpam-3966	71	10	an	an	DET
ejpam-3966	71	11	inverse	inverse	NOUN
ejpam-3966	71	12	system	system	NOUN
ejpam-3966	71	13	of	of	ADP
ejpam-3966	71	14	be	be	AUX
ejpam-3966	71	15	-	-	PUNCT
ejpam-3966	71	16	algebras	algebras	ADJ
ejpam-3966	71	17	over	over	ADP
ejpam-3966	71	18	a	a	DET
ejpam-3966	71	19	directed	direct	VERB
ejpam-3966	71	20	poset	poset	NOUN
ejpam-3966	71	21	i.	i.	NOUN
ejpam-3966	71	22	a	a	DET
ejpam-3966	71	23	subalgebra	subalgebra	NOUN
ejpam-3966	71	24	x	x	PUNCT
ejpam-3966	71	25	of	of	ADP
ejpam-3966	71	26	∏	∏	PROPN
ejpam-3966	71	27	i∈i	i∈i	NOUN
ejpam-3966	71	28	xi	xi	INTJ
ejpam-3966	71	29	together	together	ADV
ejpam-3966	71	30	with	with	ADP
ejpam-3966	71	31	compatible	compatible	ADJ
ejpam-3966	71	32	homomorphisms	homomorphism	NOUN
ejpam-3966	71	33	ϕi	ϕi	ADP
ejpam-3966	71	34	:	:	PUNCT
ejpam-3966	71	35	x	x	X
ejpam-3966	71	36	→	→	SYM
ejpam-3966	71	37	xi	xi	X
ejpam-3966	71	38	where	where	SCONJ
ejpam-3966	71	39	i	i	PRON
ejpam-3966	71	40	∈	∈	VERB
ejpam-3966	71	41	i	i	PRON
ejpam-3966	71	42	is	be	AUX
ejpam-3966	71	43	an	an	DET
ejpam-3966	71	44	inverse	inverse	NOUN
ejpam-3966	71	45	limit	limit	NOUN
ejpam-3966	71	46	or	or	CCONJ
ejpam-3966	71	47	a	a	DET
ejpam-3966	71	48	projective	projective	ADJ
ejpam-3966	71	49	limit	limit	NOUN
ejpam-3966	71	50	of	of	ADP
ejpam-3966	71	51	the	the	DET
ejpam-3966	71	52	inverse	inverse	NOUN
ejpam-3966	71	53	system	system	NOUN
ejpam-3966	71	54	{	{	PUNCT
ejpam-3966	71	55	xi	xi	PROPN
ejpam-3966	71	56	,	,	PUNCT
ejpam-3966	71	57	ϕij	ϕij	NOUN
ejpam-3966	71	58	,	,	PUNCT
ejpam-3966	71	59	i	i	PRON
ejpam-3966	71	60	}	}	PUNCT
ejpam-3966	71	61	if	if	SCONJ
ejpam-3966	71	62	the	the	DET
ejpam-3966	71	63	following	follow	VERB
ejpam-3966	71	64	universal	universal	ADJ
ejpam-3966	71	65	property	property	NOUN
ejpam-3966	71	66	is	be	AUX
ejpam-3966	71	67	satisfied	satisfied	ADJ
ejpam-3966	71	68	:	:	PUNCT
ejpam-3966	71	69	whenever	whenever	SCONJ
ejpam-3966	71	70	y	y	PROPN
ejpam-3966	71	71	is	be	AUX
ejpam-3966	71	72	a	a	DET
ejpam-3966	71	73	be	be	NOUN
ejpam-3966	71	74	-	-	PUNCT
ejpam-3966	71	75	algebra	algebra	NOUN
ejpam-3966	71	76	and	and	CCONJ
ejpam-3966	71	77	{	{	PUNCT
ejpam-3966	71	78	ψi	ψi	ADP
ejpam-3966	71	79	:	:	PUNCT
ejpam-3966	71	80	y	y	PROPN
ejpam-3966	71	81	→	→	SYM
ejpam-3966	71	82	xi	xi	X
ejpam-3966	71	83	(	(	PUNCT
ejpam-3966	72	1	i	i	NOUN
ejpam-3966	72	2	∈	∈	PROPN
ejpam-3966	72	3	i	i	X
ejpam-3966	72	4	)	)	PUNCT
ejpam-3966	72	5	}	}	PUNCT
ejpam-3966	72	6	is	be	AUX
ejpam-3966	72	7	a	a	DET
ejpam-3966	72	8	set	set	NOUN
ejpam-3966	72	9	of	of	ADP
ejpam-3966	72	10	compatible	compatible	ADJ
ejpam-3966	72	11	homomorphisms	homomorphism	NOUN
ejpam-3966	72	12	,	,	PUNCT
ejpam-3966	72	13	then	then	ADV
ejpam-3966	72	14	there	there	PRON
ejpam-3966	72	15	is	be	VERB
ejpam-3966	72	16	a	a	DET
ejpam-3966	72	17	unique	unique	ADJ
ejpam-3966	72	18	homomorphism	homomorphism	NOUN
ejpam-3966	72	19	ψ	ψ	X
ejpam-3966	72	20	:	:	PUNCT
ejpam-3966	72	21	y	y	PROPN
ejpam-3966	72	22	→	→	PUNCT
ejpam-3966	72	23	x	x	PROPN
ejpam-3966	72	24	such	such	ADJ
ejpam-3966	72	25	that	that	SCONJ
ejpam-3966	72	26	ϕiψ	ϕiψ	ADV
ejpam-3966	72	27	=	=	X
ejpam-3966	72	28	ψi	ψi	ADP
ejpam-3966	72	29	for	for	ADP
ejpam-3966	72	30	all	all	DET
ejpam-3966	72	31	i	i	PRON
ejpam-3966	72	32	∈	∈	PROPN
ejpam-3966	72	33	i.	i.	NOUN
ejpam-3966	72	34	we	we	PRON
ejpam-3966	72	35	say	say	VERB
ejpam-3966	72	36	that	that	SCONJ
ejpam-3966	72	37	ψ	ψ	NOUN
ejpam-3966	72	38	is	be	AUX
ejpam-3966	72	39	“	"	PUNCT
ejpam-3966	72	40	induced	induce	VERB
ejpam-3966	72	41	”	"	PUNCT
ejpam-3966	72	42	or	or	CCONJ
ejpam-3966	72	43	“	"	PUNCT
ejpam-3966	72	44	determined	determine	VERB
ejpam-3966	72	45	”	"	PUNCT
ejpam-3966	72	46	by	by	ADP
ejpam-3966	72	47	the	the	DET
ejpam-3966	72	48	compatible	compatible	ADJ
ejpam-3966	72	49	homomorphisms	homomorphism	NOUN
ejpam-3966	72	50	ψi	ψi	ADP
ejpam-3966	72	51	.	.	PUNCT
ejpam-3966	73	1	the	the	DET
ejpam-3966	73	2	maps	map	NOUN
ejpam-3966	73	3	ϕi	ϕi	ADP
ejpam-3966	73	4	:	:	PUNCT
ejpam-3966	73	5	x	x	X
ejpam-3966	73	6	→	→	SYM
ejpam-3966	73	7	xi	xi	X
ejpam-3966	73	8	are	be	AUX
ejpam-3966	73	9	called	call	VERB
ejpam-3966	73	10	projections	projection	NOUN
ejpam-3966	73	11	.	.	PUNCT
ejpam-3966	74	1	we	we	PRON
ejpam-3966	74	2	shall	shall	AUX
ejpam-3966	74	3	denote	denote	VERB
ejpam-3966	74	4	the	the	DET
ejpam-3966	74	5	inverse	inverse	NOUN
ejpam-3966	74	6	limit	limit	NOUN
ejpam-3966	74	7	of	of	ADP
ejpam-3966	74	8	the	the	DET
ejpam-3966	74	9	inverse	inverse	NOUN
ejpam-3966	74	10	system	system	NOUN
ejpam-3966	74	11	{	{	PUNCT
ejpam-3966	74	12	xi	xi	PROPN
ejpam-3966	74	13	,	,	PUNCT
ejpam-3966	74	14	ϕij	ϕij	NOUN
ejpam-3966	74	15	,	,	PUNCT
ejpam-3966	74	16	i	i	PRON
ejpam-3966	74	17	}	}	PUNCT
ejpam-3966	74	18	by	by	ADP
ejpam-3966	74	19	lim←−i∈ixi	lim←−i∈ixi	NOUN
ejpam-3966	74	20	,	,	PUNCT
ejpam-3966	74	21	lim←−xi	lim←−xi	ADJ
ejpam-3966	74	22	,	,	PUNCT
ejpam-3966	74	23	(	(	PUNCT
ejpam-3966	74	24	lim←−xi	lim←−xi	ADV
ejpam-3966	74	25	,	,	PUNCT
ejpam-3966	74	26	ϕi	ϕi	ADJ
ejpam-3966	74	27	)	)	PUNCT
ejpam-3966	74	28	or	or	CCONJ
ejpam-3966	74	29	(	(	PUNCT
ejpam-3966	74	30	x,ϕi	x,ϕi	NUM
ejpam-3966	74	31	)	)	PUNCT
ejpam-3966	74	32	.	.	PUNCT
ejpam-3966	75	1	j.	j.	PROPN
ejpam-3966	75	2	albaracin	albaracin	PROPN
ejpam-3966	75	3	,	,	PUNCT
ejpam-3966	75	4	j.	j.	PROPN
ejpam-3966	75	5	vilela	vilela	PROPN
ejpam-3966	75	6	/	/	SYM
ejpam-3966	75	7	eur	eur	PROPN
ejpam-3966	75	8	.	.	PUNCT
ejpam-3966	76	1	j.	j.	PROPN
ejpam-3966	76	2	pure	pure	PROPN
ejpam-3966	76	3	appl	appl	PROPN
ejpam-3966	76	4	.	.	PROPN
ejpam-3966	76	5	math	math	PROPN
ejpam-3966	76	6	,	,	PUNCT
ejpam-3966	76	7	14	14	NUM
ejpam-3966	76	8	(	(	PUNCT
ejpam-3966	76	9	2	2	NUM
ejpam-3966	76	10	)	)	PUNCT
ejpam-3966	76	11	(	(	PUNCT
ejpam-3966	76	12	2021	2021	NUM
ejpam-3966	76	13	)	)	PUNCT
ejpam-3966	76	14	,	,	PUNCT
ejpam-3966	76	15	423	423	NUM
ejpam-3966	76	16	-	-	SYM
ejpam-3966	76	17	430	430	NUM
ejpam-3966	76	18	425	425	NUM
ejpam-3966	76	19	2	2	NUM
ejpam-3966	76	20	.	.	PUNCT
ejpam-3966	77	1	some	some	DET
ejpam-3966	77	2	properties	property	NOUN
ejpam-3966	77	3	of	of	ADP
ejpam-3966	77	4	inverse	inverse	NOUN
ejpam-3966	77	5	limit	limit	NOUN
ejpam-3966	77	6	of	of	ADP
ejpam-3966	77	7	be	be	AUX
ejpam-3966	77	8	-	-	PUNCT
ejpam-3966	77	9	algebras	algebras	NOUN
ejpam-3966	77	10	theorem	theorem	ADJ
ejpam-3966	77	11	4	4	NUM
ejpam-3966	77	12	.	.	PUNCT
ejpam-3966	78	1	let	let	VERB
ejpam-3966	78	2	{	{	PUNCT
ejpam-3966	78	3	xi	xi	PROPN
ejpam-3966	78	4	,	,	PUNCT
ejpam-3966	78	5	ϕij	ϕij	NOUN
ejpam-3966	78	6	,	,	PUNCT
ejpam-3966	78	7	i	i	PRON
ejpam-3966	78	8	}	}	PUNCT
ejpam-3966	78	9	be	be	VERB
ejpam-3966	78	10	an	an	DET
ejpam-3966	78	11	inverse	inverse	NOUN
ejpam-3966	78	12	system	system	NOUN
ejpam-3966	78	13	of	of	ADP
ejpam-3966	78	14	be	be	AUX
ejpam-3966	78	15	-	-	PUNCT
ejpam-3966	78	16	algebras	algebras	ADJ
ejpam-3966	78	17	over	over	ADP
ejpam-3966	78	18	a	a	DET
ejpam-3966	78	19	directed	direct	VERB
ejpam-3966	78	20	poset	poset	NOUN
ejpam-3966	78	21	i.	i.	NOUN
ejpam-3966	78	22	then	then	ADV
ejpam-3966	78	23	(	(	PUNCT
ejpam-3966	78	24	x,ϕi	x,ϕi	X
ejpam-3966	78	25	)	)	PUNCT
ejpam-3966	78	26	is	be	AUX
ejpam-3966	78	27	an	an	DET
ejpam-3966	78	28	inverse	inverse	NOUN
ejpam-3966	78	29	limit	limit	NOUN
ejpam-3966	78	30	of	of	ADP
ejpam-3966	78	31	the	the	DET
ejpam-3966	78	32	inverse	inverse	NOUN
ejpam-3966	78	33	system	system	NOUN
ejpam-3966	78	34	{	{	PUNCT
ejpam-3966	78	35	xi	xi	PROPN
ejpam-3966	78	36	,	,	PUNCT
ejpam-3966	78	37	ϕij	ϕij	NOUN
ejpam-3966	78	38	,	,	PUNCT
ejpam-3966	78	39	i	i	PRON
ejpam-3966	78	40	}	}	PUNCT
ejpam-3966	78	41	,	,	PUNCT
ejpam-3966	78	42	where	where	SCONJ
ejpam-3966	78	43	x	x	X
ejpam-3966	78	44	=	=	PRON
ejpam-3966	78	45	{	{	PUNCT
ejpam-3966	78	46	(	(	PUNCT
ejpam-3966	78	47	xi	xi	NOUN
ejpam-3966	78	48	)	)	PUNCT
ejpam-3966	78	49	∈	∈	PROPN
ejpam-3966	78	50	∏	∏	PROPN
ejpam-3966	78	51	i∈i	i∈i	NOUN
ejpam-3966	78	52	xi	xi	X
ejpam-3966	78	53	|	|	ADV
ejpam-3966	78	54	for	for	ADP
ejpam-3966	78	55	all	all	DET
ejpam-3966	78	56	i	i	PRON
ejpam-3966	78	57	,	,	PUNCT
ejpam-3966	78	58	j	j	PROPN
ejpam-3966	78	59	∈	∈	PROPN
ejpam-3966	78	60	i	i	PRON
ejpam-3966	78	61	such	such	ADJ
ejpam-3966	78	62	that	that	SCONJ
ejpam-3966	78	63	i	i	PRON
ejpam-3966	78	64	≥	≥	VERB
ejpam-3966	78	65	j	j	PROPN
ejpam-3966	78	66	,	,	PUNCT
ejpam-3966	78	67	ϕij(xi	ϕij(xi	NUM
ejpam-3966	78	68	)	)	PUNCT
ejpam-3966	78	69	=	=	SYM
ejpam-3966	78	70	xj	xj	PROPN
ejpam-3966	78	71	}	}	PUNCT
ejpam-3966	78	72	and	and	CCONJ
ejpam-3966	78	73	ϕi	ϕi	ADP
ejpam-3966	78	74	:	:	PUNCT
ejpam-3966	78	75	x	x	X
ejpam-3966	78	76	→	→	SYM
ejpam-3966	78	77	xi	xi	X
ejpam-3966	78	78	is	be	AUX
ejpam-3966	78	79	the	the	DET
ejpam-3966	78	80	restriction	restriction	NOUN
ejpam-3966	78	81	of	of	ADP
ejpam-3966	78	82	the	the	DET
ejpam-3966	78	83	natural	natural	ADJ
ejpam-3966	78	84	projection	projection	NOUN
ejpam-3966	78	85	ρi	ρi	NOUN
ejpam-3966	78	86	:	:	PUNCT
ejpam-3966	78	87	∏	∏	PROPN
ejpam-3966	78	88	i∈i	i∈i	NOUN
ejpam-3966	78	89	xi	xi	X
ejpam-3966	78	90	→	→	SYM
ejpam-3966	78	91	xi	xi	PROPN
ejpam-3966	78	92	,	,	PUNCT
ejpam-3966	78	93	that	that	ADV
ejpam-3966	78	94	is	is	ADV
ejpam-3966	78	95	,	,	PUNCT
ejpam-3966	78	96	ϕi	ϕi	ADP
ejpam-3966	78	97	=	=	PUNCT
ejpam-3966	78	98	ρi|x	ρi|x	PROPN
ejpam-3966	78	99	.	.	PUNCT
ejpam-3966	79	1	proof	proof	NOUN
ejpam-3966	79	2	.	.	PUNCT
ejpam-3966	80	1	let	let	VERB
ejpam-3966	80	2	(	(	PUNCT
ejpam-3966	80	3	xi	xi	PROPN
ejpam-3966	80	4	)	)	PUNCT
ejpam-3966	80	5	,	,	PUNCT
ejpam-3966	80	6	(	(	PUNCT
ejpam-3966	80	7	yi	yi	NOUN
ejpam-3966	80	8	)	)	PUNCT
ejpam-3966	80	9	∈	∈	PROPN
ejpam-3966	80	10	x.	x.	NOUN
ejpam-3966	80	11	then	then	ADV
ejpam-3966	80	12	ϕij(xi	ϕij(xi	PUNCT
ejpam-3966	80	13	)	)	PUNCT
ejpam-3966	81	1	=	=	SYM
ejpam-3966	81	2	xj	xj	PROPN
ejpam-3966	81	3	and	and	CCONJ
ejpam-3966	81	4	ϕij(yi	ϕij(yi	NUM
ejpam-3966	81	5	)	)	PUNCT
ejpam-3966	82	1	=	=	VERB
ejpam-3966	82	2	yj	yj	NOUN
ejpam-3966	82	3	whenever	whenever	SCONJ
ejpam-3966	82	4	i	i	PRON
ejpam-3966	82	5	≥	≥	VERB
ejpam-3966	82	6	j.	j.	PROPN
ejpam-3966	82	7	thus	thus	ADV
ejpam-3966	82	8	,	,	PUNCT
ejpam-3966	82	9	ϕij(xi	ϕij(xi	PROPN
ejpam-3966	82	10	∗	∗	NOUN
ejpam-3966	82	11	yi	yi	NOUN
ejpam-3966	82	12	)	)	PUNCT
ejpam-3966	82	13	=	=	SYM
ejpam-3966	82	14	ϕij(xi	ϕij(xi	X
ejpam-3966	82	15	)	)	PUNCT
ejpam-3966	82	16	∗	∗	NOUN
ejpam-3966	82	17	ϕij(yi	ϕij(yi	NUM
ejpam-3966	82	18	)	)	PUNCT
ejpam-3966	82	19	=	=	SYM
ejpam-3966	82	20	xj	xj	PROPN
ejpam-3966	82	21	∗	∗	PROPN
ejpam-3966	82	22	yj	yj	PROPN
ejpam-3966	82	23	whenever	whenever	SCONJ
ejpam-3966	82	24	i	i	PRON
ejpam-3966	82	25	≥	≥	VERB
ejpam-3966	82	26	j.	j.	PROPN
ejpam-3966	82	27	since	since	SCONJ
ejpam-3966	82	28	(	(	PUNCT
ejpam-3966	82	29	xi	xi	PROPN
ejpam-3966	82	30	)	)	PUNCT
ejpam-3966	82	31	∗	∗	NOUN
ejpam-3966	82	32	(	(	PUNCT
ejpam-3966	82	33	yi	yi	NOUN
ejpam-3966	82	34	)	)	PUNCT
ejpam-3966	82	35	=	=	PUNCT
ejpam-3966	82	36	(	(	PUNCT
ejpam-3966	82	37	xi	xi	X
ejpam-3966	82	38	∗	∗	PROPN
ejpam-3966	82	39	yi	yi	PROPN
ejpam-3966	82	40	)	)	PUNCT
ejpam-3966	82	41	,	,	PUNCT
ejpam-3966	82	42	(	(	PUNCT
ejpam-3966	82	43	xi	xi	X
ejpam-3966	82	44	)	)	PUNCT
ejpam-3966	82	45	∗	∗	NOUN
ejpam-3966	82	46	(	(	PUNCT
ejpam-3966	82	47	yi	yi	NOUN
ejpam-3966	82	48	)	)	PUNCT
ejpam-3966	82	49	∈	∈	PROPN
ejpam-3966	82	50	x.	x.	NOUN
ejpam-3966	82	51	hence	hence	ADV
ejpam-3966	82	52	,	,	PUNCT
ejpam-3966	82	53	x	x	X
ejpam-3966	82	54	is	be	AUX
ejpam-3966	82	55	a	a	DET
ejpam-3966	82	56	subalgebra	subalgebra	NOUN
ejpam-3966	82	57	of	of	ADP
ejpam-3966	82	58	∏	∏	NUM
ejpam-3966	82	59	i∈i	i∈i	ADJ
ejpam-3966	82	60	xi	xi	PROPN
ejpam-3966	82	61	.	.	PUNCT
ejpam-3966	83	1	let	let	VERB
ejpam-3966	83	2	ϕi	ϕi	ADP
ejpam-3966	83	3	:	:	PUNCT
ejpam-3966	83	4	x	x	X
ejpam-3966	83	5	→	→	SYM
ejpam-3966	83	6	xi	xi	X
ejpam-3966	83	7	be	be	AUX
ejpam-3966	83	8	the	the	DET
ejpam-3966	83	9	restriction	restriction	NOUN
ejpam-3966	83	10	of	of	ADP
ejpam-3966	83	11	the	the	DET
ejpam-3966	83	12	natural	natural	ADJ
ejpam-3966	83	13	projection	projection	NOUN
ejpam-3966	83	14	ρi	ρi	NOUN
ejpam-3966	83	15	:	:	PUNCT
ejpam-3966	83	16	∏	∏	PROPN
ejpam-3966	83	17	i∈i	i∈i	NOUN
ejpam-3966	83	18	xi	xi	X
ejpam-3966	83	19	→	→	SYM
ejpam-3966	83	20	xi	xi	PROPN
ejpam-3966	83	21	.	.	PUNCT
ejpam-3966	84	1	we	we	PRON
ejpam-3966	84	2	will	will	AUX
ejpam-3966	84	3	show	show	VERB
ejpam-3966	84	4	that	that	SCONJ
ejpam-3966	84	5	the	the	DET
ejpam-3966	84	6	be	be	NOUN
ejpam-3966	84	7	-	-	PUNCT
ejpam-3966	84	8	algebra	algebra	NOUN
ejpam-3966	84	9	x	x	PUNCT
ejpam-3966	84	10	together	together	ADV
ejpam-3966	84	11	with	with	ADP
ejpam-3966	84	12	ϕi	ϕi	ADP
ejpam-3966	84	13	is	be	AUX
ejpam-3966	84	14	the	the	DET
ejpam-3966	84	15	inverse	inverse	ADJ
ejpam-3966	84	16	limit	limit	NOUN
ejpam-3966	84	17	of	of	ADP
ejpam-3966	84	18	{	{	PUNCT
ejpam-3966	84	19	xi	xi	PROPN
ejpam-3966	84	20	,	,	PUNCT
ejpam-3966	84	21	ϕij	ϕij	NOUN
ejpam-3966	84	22	,	,	PUNCT
ejpam-3966	84	23	i	i	NOUN
ejpam-3966	84	24	}	}	PUNCT
ejpam-3966	84	25	.	.	PUNCT
ejpam-3966	85	1	let	let	VERB
ejpam-3966	85	2	(	(	PUNCT
ejpam-3966	85	3	xi	xi	NOUN
ejpam-3966	85	4	)	)	PUNCT
ejpam-3966	85	5	∈	∈	PROPN
ejpam-3966	85	6	x.	x.	NOUN
ejpam-3966	85	7	then	then	ADV
ejpam-3966	85	8	ϕijϕi((xi	ϕijϕi((xi	PROPN
ejpam-3966	85	9	)	)	PUNCT
ejpam-3966	85	10	)	)	PUNCT
ejpam-3966	86	1	=	=	SYM
ejpam-3966	86	2	ϕij(xi	ϕij(xi	X
ejpam-3966	86	3	)	)	PUNCT
ejpam-3966	87	1	=	=	SYM
ejpam-3966	87	2	xj	xj	PROPN
ejpam-3966	87	3	=	=	SYM
ejpam-3966	87	4	ϕj((xi	ϕj((xi	PROPN
ejpam-3966	87	5	)	)	PUNCT
ejpam-3966	87	6	)	)	PUNCT
ejpam-3966	88	1	whenever	whenever	SCONJ
ejpam-3966	88	2	i	i	PRON
ejpam-3966	88	3	≥	≥	VERB
ejpam-3966	88	4	j.	j.	PROPN
ejpam-3966	88	5	thus	thus	ADV
ejpam-3966	88	6	,	,	PUNCT
ejpam-3966	88	7	ϕijϕi	ϕijϕi	PROPN
ejpam-3966	88	8	=	=	PUNCT
ejpam-3966	88	9	ϕj	ϕj	INTJ
ejpam-3966	88	10	whenever	whenever	SCONJ
ejpam-3966	88	11	i	i	PRON
ejpam-3966	88	12	≥	≥	VERB
ejpam-3966	89	1	j.	j.	PROPN
ejpam-3966	89	2	this	this	PRON
ejpam-3966	89	3	implies	imply	VERB
ejpam-3966	89	4	that	that	SCONJ
ejpam-3966	89	5	ϕi	ϕi	INTJ
ejpam-3966	89	6	’s	’	NOUN
ejpam-3966	89	7	are	be	AUX
ejpam-3966	89	8	compatible	compatible	ADJ
ejpam-3966	89	9	.	.	PUNCT
ejpam-3966	90	1	let	let	VERB
ejpam-3966	90	2	y	y	PRON
ejpam-3966	90	3	be	be	AUX
ejpam-3966	90	4	a	a	DET
ejpam-3966	90	5	be	be	NOUN
ejpam-3966	90	6	-	-	PUNCT
ejpam-3966	90	7	algebra	algebra	NOUN
ejpam-3966	90	8	and	and	CCONJ
ejpam-3966	90	9	{	{	PUNCT
ejpam-3966	90	10	ψi	ψi	ADP
ejpam-3966	90	11	:	:	PUNCT
ejpam-3966	90	12	y	y	PROPN
ejpam-3966	90	13	→	→	SYM
ejpam-3966	90	14	xi	xi	PROPN
ejpam-3966	90	15	}	}	PUNCT
ejpam-3966	90	16	be	be	AUX
ejpam-3966	90	17	a	a	DET
ejpam-3966	90	18	set	set	NOUN
ejpam-3966	90	19	of	of	ADP
ejpam-3966	90	20	compatible	compatible	ADJ
ejpam-3966	90	21	homomorphisms	homomorphism	NOUN
ejpam-3966	90	22	.	.	PUNCT
ejpam-3966	91	1	consider	consider	VERB
ejpam-3966	91	2	the	the	DET
ejpam-3966	91	3	mapping	mapping	NOUN
ejpam-3966	91	4	ψ	ψ	X
ejpam-3966	91	5	:	:	PUNCT
ejpam-3966	91	6	y	y	PROPN
ejpam-3966	91	7	→	→	SYM
ejpam-3966	91	8	x	x	PUNCT
ejpam-3966	91	9	defined	define	VERB
ejpam-3966	91	10	by	by	ADP
ejpam-3966	91	11	ψ(y	ψ(y	NOUN
ejpam-3966	91	12	)	)	PUNCT
ejpam-3966	91	13	=	=	PRON
ejpam-3966	91	14	(	(	PUNCT
ejpam-3966	91	15	ψi(y	ψi(y	NUM
ejpam-3966	91	16	)	)	PUNCT
ejpam-3966	91	17	)	)	PUNCT
ejpam-3966	91	18	for	for	ADP
ejpam-3966	91	19	each	each	DET
ejpam-3966	91	20	y	y	PROPN
ejpam-3966	91	21	∈	∈	PROPN
ejpam-3966	91	22	y	y	PROPN
ejpam-3966	91	23	.	.	PUNCT
ejpam-3966	92	1	since	since	SCONJ
ejpam-3966	92	2	ψi	ψi	NOUN
ejpam-3966	92	3	’s	’s	PART
ejpam-3966	92	4	are	be	AUX
ejpam-3966	92	5	compatible	compatible	ADJ
ejpam-3966	92	6	,	,	PUNCT
ejpam-3966	92	7	ϕijψi	ϕijψi	PUNCT
ejpam-3966	93	1	=	=	PRON
ejpam-3966	93	2	ψj	ψj	ADV
ejpam-3966	93	3	whenever	whenever	SCONJ
ejpam-3966	93	4	i	i	PRON
ejpam-3966	93	5	≥	≥	VERB
ejpam-3966	93	6	j.	j.	PROPN
ejpam-3966	93	7	thus	thus	ADV
ejpam-3966	93	8	,	,	PUNCT
ejpam-3966	93	9	ϕij(ψi(y	ϕij(ψi(y	NOUN
ejpam-3966	93	10	)	)	PUNCT
ejpam-3966	93	11	)	)	PUNCT
ejpam-3966	94	1	=	=	SYM
ejpam-3966	94	2	ψj(y	ψj(y	X
ejpam-3966	94	3	)	)	PUNCT
ejpam-3966	94	4	whenever	whenever	SCONJ
ejpam-3966	94	5	i	i	PRON
ejpam-3966	94	6	≥	≥	VERB
ejpam-3966	94	7	j	j	PROPN
ejpam-3966	94	8	and	and	CCONJ
ejpam-3966	94	9	for	for	ADP
ejpam-3966	94	10	y	y	PROPN
ejpam-3966	94	11	∈	∈	PROPN
ejpam-3966	94	12	y	y	PROPN
ejpam-3966	94	13	.	.	PUNCT
ejpam-3966	95	1	hence	hence	ADV
ejpam-3966	95	2	,	,	PUNCT
ejpam-3966	95	3	(	(	PUNCT
ejpam-3966	95	4	ψi(y	ψi(y	NUM
ejpam-3966	95	5	)	)	PUNCT
ejpam-3966	95	6	)	)	PUNCT
ejpam-3966	96	1	∈	∈	PROPN
ejpam-3966	96	2	x.	x.	NOUN
ejpam-3966	96	3	let	let	VERB
ejpam-3966	96	4	y	y	PROPN
ejpam-3966	96	5	∈	∈	PROPN
ejpam-3966	96	6	y	y	PROPN
ejpam-3966	96	7	.	.	PUNCT
ejpam-3966	97	1	then	then	ADV
ejpam-3966	97	2	ϕiψ(y	ϕiψ(y	PROPN
ejpam-3966	97	3	)	)	PUNCT
ejpam-3966	97	4	=	=	SYM
ejpam-3966	97	5	ϕi((ψi(y	ϕi((ψi(y	PROPN
ejpam-3966	97	6	)	)	PUNCT
ejpam-3966	97	7	)	)	PUNCT
ejpam-3966	98	1	=	=	PRON
ejpam-3966	98	2	ψi(y	ψi(y	X
ejpam-3966	98	3	)	)	PUNCT
ejpam-3966	98	4	for	for	ADP
ejpam-3966	98	5	all	all	DET
ejpam-3966	98	6	i	i	PRON
ejpam-3966	98	7	∈	∈	PROPN
ejpam-3966	98	8	i.	i.	NOUN
ejpam-3966	98	9	thus	thus	ADV
ejpam-3966	98	10	,	,	PUNCT
ejpam-3966	98	11	ϕiψ	ϕiψ	ADP
ejpam-3966	98	12	=	=	PUNCT
ejpam-3966	98	13	ψi	ψi	ADP
ejpam-3966	98	14	for	for	ADP
ejpam-3966	98	15	all	all	PRON
ejpam-3966	98	16	i	i	PRON
ejpam-3966	98	17	∈	∈	PROPN
ejpam-3966	98	18	i.	i.	NOUN
ejpam-3966	98	19	now	now	ADV
ejpam-3966	98	20	,	,	PUNCT
ejpam-3966	98	21	we	we	PRON
ejpam-3966	98	22	will	will	AUX
ejpam-3966	98	23	show	show	VERB
ejpam-3966	98	24	that	that	SCONJ
ejpam-3966	98	25	ψ	ψ	NOUN
ejpam-3966	98	26	is	be	AUX
ejpam-3966	98	27	unique	unique	ADJ
ejpam-3966	98	28	.	.	PUNCT
ejpam-3966	98	29	suppose	suppose	VERB
ejpam-3966	98	30	that	that	SCONJ
ejpam-3966	98	31	φ	φ	PROPN
ejpam-3966	98	32	:	:	PUNCT
ejpam-3966	98	33	y	y	PROPN
ejpam-3966	98	34	→	→	PUNCT
ejpam-3966	98	35	x	x	X
ejpam-3966	98	36	is	be	AUX
ejpam-3966	98	37	another	another	DET
ejpam-3966	98	38	homomorphism	homomorphism	NOUN
ejpam-3966	98	39	such	such	ADJ
ejpam-3966	98	40	that	that	DET
ejpam-3966	98	41	ϕiφ	ϕiφ	NOUN
ejpam-3966	98	42	=	=	PUNCT
ejpam-3966	98	43	ψi	ψi	ADP
ejpam-3966	98	44	for	for	ADP
ejpam-3966	98	45	all	all	PRON
ejpam-3966	98	46	i	i	PRON
ejpam-3966	98	47	∈	∈	PROPN
ejpam-3966	98	48	i.	i.	NOUN
ejpam-3966	98	49	suppose	suppose	VERB
ejpam-3966	98	50	further	far	ADV
ejpam-3966	98	51	that	that	SCONJ
ejpam-3966	98	52	there	there	PRON
ejpam-3966	98	53	exists	exist	VERB
ejpam-3966	98	54	y	y	PROPN
ejpam-3966	98	55	∈	∈	PROPN
ejpam-3966	98	56	y	y	PROPN
ejpam-3966	98	57	such	such	ADJ
ejpam-3966	98	58	that	that	PRON
ejpam-3966	98	59	ψ(y	ψ(y	NOUN
ejpam-3966	98	60	)	)	PUNCT
ejpam-3966	98	61	6=	6=	NUM
ejpam-3966	98	62	φ(y	φ(y	NOUN
ejpam-3966	98	63	)	)	PUNCT
ejpam-3966	98	64	.	.	PUNCT
ejpam-3966	99	1	by	by	ADP
ejpam-3966	99	2	the	the	DET
ejpam-3966	99	3	definition	definition	NOUN
ejpam-3966	99	4	of	of	ADP
ejpam-3966	99	5	x	x	PRON
ejpam-3966	99	6	,	,	PUNCT
ejpam-3966	99	7	there	there	PRON
ejpam-3966	99	8	exists	exist	VERB
ejpam-3966	99	9	i	i	PRON
ejpam-3966	99	10	∈	∈	VERB
ejpam-3966	100	1	i	i	PRON
ejpam-3966	100	2	such	such	ADJ
ejpam-3966	100	3	that	that	SCONJ
ejpam-3966	100	4	ϕi(ψ(y	ϕi(ψ(y	PROPN
ejpam-3966	100	5	)	)	PUNCT
ejpam-3966	100	6	)	)	PUNCT
ejpam-3966	101	1	=	=	PRON
ejpam-3966	101	2	ψi(y	ψi(y	NOUN
ejpam-3966	101	3	)	)	PUNCT
ejpam-3966	101	4	6=	6=	NUM
ejpam-3966	101	5	ϕi(φ(y	ϕi(φ(y	NOUN
ejpam-3966	101	6	)	)	PUNCT
ejpam-3966	101	7	)	)	PUNCT
ejpam-3966	101	8	.	.	PUNCT
ejpam-3966	102	1	this	this	PRON
ejpam-3966	102	2	is	be	AUX
ejpam-3966	102	3	a	a	DET
ejpam-3966	102	4	contradiction	contradiction	NOUN
ejpam-3966	102	5	.	.	PUNCT
ejpam-3966	103	1	hence	hence	ADV
ejpam-3966	103	2	,	,	PUNCT
ejpam-3966	103	3	ψ(y	ψ(y	PROPN
ejpam-3966	103	4	)	)	PUNCT
ejpam-3966	103	5	=	=	SYM
ejpam-3966	103	6	φ(y	φ(y	NOUN
ejpam-3966	103	7	)	)	PUNCT
ejpam-3966	103	8	for	for	ADP
ejpam-3966	103	9	all	all	DET
ejpam-3966	103	10	y	y	PROPN
ejpam-3966	103	11	∈	∈	PROPN
ejpam-3966	103	12	y	y	PROPN
ejpam-3966	103	13	.	.	PUNCT
ejpam-3966	104	1	therefore	therefore	ADV
ejpam-3966	104	2	,	,	PUNCT
ejpam-3966	104	3	ψ	ψ	NOUN
ejpam-3966	104	4	is	be	AUX
ejpam-3966	104	5	unique	unique	ADJ
ejpam-3966	104	6	.	.	PUNCT
ejpam-3966	105	1	consequently	consequently	ADV
ejpam-3966	105	2	,	,	PUNCT
ejpam-3966	105	3	x	x	PRON
ejpam-3966	105	4	is	be	AUX
ejpam-3966	105	5	an	an	DET
ejpam-3966	105	6	inverse	inverse	NOUN
ejpam-3966	105	7	limit	limit	NOUN
ejpam-3966	105	8	of	of	ADP
ejpam-3966	105	9	{	{	PUNCT
ejpam-3966	105	10	xi	xi	PROPN
ejpam-3966	105	11	,	,	PUNCT
ejpam-3966	105	12	ϕij	ϕij	NOUN
ejpam-3966	105	13	,	,	PUNCT
ejpam-3966	105	14	i	i	NOUN
ejpam-3966	105	15	}	}	PUNCT
ejpam-3966	105	16	.	.	PUNCT
ejpam-3966	106	1	let	let	AUX
ejpam-3966	106	2	(	(	PUNCT
ejpam-3966	106	3	x,ϕi	x,ϕi	X
ejpam-3966	106	4	)	)	PUNCT
ejpam-3966	106	5	be	be	VERB
ejpam-3966	106	6	an	an	DET
ejpam-3966	106	7	inverse	inverse	NOUN
ejpam-3966	106	8	limit	limit	NOUN
ejpam-3966	106	9	of	of	ADP
ejpam-3966	106	10	the	the	DET
ejpam-3966	106	11	inverse	inverse	NOUN
ejpam-3966	106	12	system	system	NOUN
ejpam-3966	106	13	of	of	ADP
ejpam-3966	106	14	be	be	AUX
ejpam-3966	106	15	-	-	PUNCT
ejpam-3966	106	16	algebras	algebras	X
ejpam-3966	106	17	{	{	PUNCT
ejpam-3966	106	18	xi	xi	PROPN
ejpam-3966	106	19	,	,	PUNCT
ejpam-3966	106	20	ϕij	ϕij	NOUN
ejpam-3966	106	21	,	,	PUNCT
ejpam-3966	106	22	i	i	NOUN
ejpam-3966	106	23	}	}	PUNCT
ejpam-3966	106	24	.	.	PUNCT
ejpam-3966	107	1	by	by	ADP
ejpam-3966	107	2	definition	definition	NOUN
ejpam-3966	107	3	,	,	PUNCT
ejpam-3966	107	4	the	the	DET
ejpam-3966	107	5	maps	map	NOUN
ejpam-3966	107	6	ϕi	ϕi	ADP
ejpam-3966	107	7	:	:	PUNCT
ejpam-3966	107	8	x	x	X
ejpam-3966	107	9	→	→	SYM
ejpam-3966	107	10	xi	xi	NOUN
ejpam-3966	107	11	are	be	AUX
ejpam-3966	107	12	compatible	compatible	ADJ
ejpam-3966	107	13	.	.	PUNCT
ejpam-3966	108	1	thus	thus	ADV
ejpam-3966	108	2	,	,	PUNCT
ejpam-3966	108	3	the	the	DET
ejpam-3966	108	4	universal	universal	ADJ
ejpam-3966	108	5	property	property	NOUN
ejpam-3966	108	6	of	of	ADP
ejpam-3966	108	7	the	the	DET
ejpam-3966	108	8	inverse	inverse	NOUN
ejpam-3966	108	9	limit	limit	NOUN
ejpam-3966	108	10	shows	show	VERB
ejpam-3966	108	11	that	that	SCONJ
ejpam-3966	108	12	there	there	PRON
ejpam-3966	108	13	exists	exist	VERB
ejpam-3966	108	14	a	a	DET
ejpam-3966	108	15	unique	unique	ADJ
ejpam-3966	108	16	homomorphism	homomorphism	NOUN
ejpam-3966	108	17	ϕ	ϕ	NOUN
ejpam-3966	108	18	:	:	PUNCT
ejpam-3966	108	19	x	x	SYM
ejpam-3966	108	20	→	→	SYM
ejpam-3966	108	21	x	x	X
ejpam-3966	108	22	such	such	ADJ
ejpam-3966	108	23	that	that	DET
ejpam-3966	108	24	ϕiϕ	ϕiϕ	NOUN
ejpam-3966	108	25	=	=	NOUN
ejpam-3966	108	26	ϕi	ϕi	ADP
ejpam-3966	108	27	for	for	ADP
ejpam-3966	108	28	all	all	PRON
ejpam-3966	108	29	i	i	PRON
ejpam-3966	108	30	∈	∈	PROPN
ejpam-3966	108	31	i.	i.	NOUN
ejpam-3966	108	32	since	since	SCONJ
ejpam-3966	108	33	ϕiidx	ϕiidx	NOUN
ejpam-3966	108	34	=	=	PUNCT
ejpam-3966	108	35	ϕi	ϕi	ADP
ejpam-3966	108	36	for	for	ADP
ejpam-3966	108	37	all	all	PRON
ejpam-3966	108	38	i	i	PRON
ejpam-3966	108	39	∈	∈	VERB
ejpam-3966	109	1	i	i	PRON
ejpam-3966	109	2	and	and	CCONJ
ejpam-3966	109	3	ϕ	ϕ	NOUN
ejpam-3966	109	4	is	be	AUX
ejpam-3966	109	5	unique	unique	ADJ
ejpam-3966	109	6	,	,	PUNCT
ejpam-3966	109	7	ϕ	ϕ	NOUN
ejpam-3966	109	8	=	=	X
ejpam-3966	109	9	idx	idx	PROPN
ejpam-3966	109	10	.	.	PUNCT
ejpam-3966	110	1	this	this	DET
ejpam-3966	110	2	observation	observation	NOUN
ejpam-3966	110	3	is	be	AUX
ejpam-3966	110	4	stated	state	VERB
ejpam-3966	110	5	in	in	ADP
ejpam-3966	110	6	the	the	DET
ejpam-3966	110	7	following	follow	VERB
ejpam-3966	110	8	remark	remark	NOUN
ejpam-3966	110	9	.	.	PUNCT
ejpam-3966	111	1	remark	remark	PROPN
ejpam-3966	111	2	1	1	NUM
ejpam-3966	111	3	.	.	PUNCT
ejpam-3966	112	1	let	let	VERB
ejpam-3966	112	2	{	{	PUNCT
ejpam-3966	112	3	xi	xi	PROPN
ejpam-3966	112	4	,	,	PUNCT
ejpam-3966	112	5	ϕij	ϕij	NOUN
ejpam-3966	112	6	,	,	PUNCT
ejpam-3966	112	7	i	i	PRON
ejpam-3966	112	8	}	}	PUNCT
ejpam-3966	112	9	be	be	VERB
ejpam-3966	112	10	an	an	DET
ejpam-3966	112	11	inverse	inverse	NOUN
ejpam-3966	112	12	system	system	NOUN
ejpam-3966	112	13	of	of	ADP
ejpam-3966	112	14	be	be	AUX
ejpam-3966	112	15	-	-	PUNCT
ejpam-3966	112	16	algebras	algebras	ADJ
ejpam-3966	112	17	over	over	ADP
ejpam-3966	112	18	a	a	DET
ejpam-3966	112	19	directed	direct	VERB
ejpam-3966	112	20	poset	poset	NOUN
ejpam-3966	112	21	i	i	PRON
ejpam-3966	112	22	and	and	CCONJ
ejpam-3966	112	23	let	let	VERB
ejpam-3966	112	24	(	(	PUNCT
ejpam-3966	112	25	x,ϕi	x,ϕi	X
ejpam-3966	112	26	)	)	PUNCT
ejpam-3966	112	27	be	be	VERB
ejpam-3966	112	28	an	an	DET
ejpam-3966	112	29	inverse	inverse	NOUN
ejpam-3966	112	30	limit	limit	NOUN
ejpam-3966	112	31	of	of	ADP
ejpam-3966	112	32	{	{	PUNCT
ejpam-3966	112	33	xi	xi	PROPN
ejpam-3966	112	34	,	,	PUNCT
ejpam-3966	112	35	ϕij	ϕij	NOUN
ejpam-3966	112	36	,	,	PUNCT
ejpam-3966	112	37	i	i	NOUN
ejpam-3966	112	38	}	}	PUNCT
ejpam-3966	112	39	.	.	PUNCT
ejpam-3966	113	1	then	then	ADV
ejpam-3966	113	2	the	the	DET
ejpam-3966	113	3	homomorphism	homomorphism	PROPN
ejpam-3966	113	4	idx	idx	NOUN
ejpam-3966	113	5	:	:	PUNCT
ejpam-3966	113	6	x	x	X
ejpam-3966	113	7	→	→	SYM
ejpam-3966	113	8	x	x	NUM
ejpam-3966	113	9	satisfies	satisfie	NOUN
ejpam-3966	113	10	ϕiidx	ϕiidx	VERB
ejpam-3966	113	11	=	=	PUNCT
ejpam-3966	113	12	ϕi	ϕi	ADP
ejpam-3966	113	13	for	for	ADP
ejpam-3966	113	14	all	all	PRON
ejpam-3966	113	15	i	i	PRON
ejpam-3966	113	16	∈	∈	VERB
ejpam-3966	114	1	i	i	PRON
ejpam-3966	114	2	and	and	CCONJ
ejpam-3966	114	3	is	be	AUX
ejpam-3966	114	4	the	the	DET
ejpam-3966	114	5	only	only	ADJ
ejpam-3966	114	6	homomorphism	homomorphism	NOUN
ejpam-3966	114	7	with	with	ADP
ejpam-3966	114	8	this	this	DET
ejpam-3966	114	9	property	property	NOUN
ejpam-3966	114	10	.	.	PUNCT
ejpam-3966	115	1	theorem	theorem	NOUN
ejpam-3966	115	2	5	5	NUM
ejpam-3966	115	3	.	.	PUNCT
ejpam-3966	116	1	let	let	VERB
ejpam-3966	116	2	{	{	PUNCT
ejpam-3966	116	3	xi	xi	PROPN
ejpam-3966	116	4	,	,	PUNCT
ejpam-3966	116	5	ϕij	ϕij	NOUN
ejpam-3966	116	6	,	,	PUNCT
ejpam-3966	116	7	i	i	PRON
ejpam-3966	116	8	}	}	PUNCT
ejpam-3966	116	9	be	be	VERB
ejpam-3966	116	10	an	an	DET
ejpam-3966	116	11	inverse	inverse	NOUN
ejpam-3966	116	12	system	system	NOUN
ejpam-3966	116	13	of	of	ADP
ejpam-3966	116	14	be	be	AUX
ejpam-3966	116	15	-	-	PUNCT
ejpam-3966	116	16	algebras	algebras	ADJ
ejpam-3966	116	17	over	over	ADP
ejpam-3966	116	18	a	a	DET
ejpam-3966	116	19	directed	direct	VERB
ejpam-3966	116	20	poset	poset	NOUN
ejpam-3966	116	21	i.	i.	NOUN
ejpam-3966	116	22	then	then	ADV
ejpam-3966	116	23	the	the	DET
ejpam-3966	116	24	inverse	inverse	NOUN
ejpam-3966	116	25	limit	limit	NOUN
ejpam-3966	116	26	is	be	AUX
ejpam-3966	116	27	unique	unique	ADJ
ejpam-3966	116	28	up	up	ADP
ejpam-3966	116	29	to	to	ADP
ejpam-3966	116	30	isomorphism	isomorphism	NOUN
ejpam-3966	116	31	,	,	PUNCT
ejpam-3966	116	32	that	that	ADV
ejpam-3966	116	33	is	is	ADV
ejpam-3966	116	34	,	,	PUNCT
ejpam-3966	116	35	if	if	SCONJ
ejpam-3966	116	36	(	(	PUNCT
ejpam-3966	116	37	x,ϕi	x,ϕi	NUM
ejpam-3966	116	38	)	)	PUNCT
ejpam-3966	116	39	and	and	CCONJ
ejpam-3966	116	40	(	(	PUNCT
ejpam-3966	116	41	y	y	NOUN
ejpam-3966	116	42	,	,	PUNCT
ejpam-3966	116	43	ψi	ψi	NOUN
ejpam-3966	116	44	)	)	PUNCT
ejpam-3966	116	45	are	be	AUX
ejpam-3966	116	46	two	two	NUM
ejpam-3966	116	47	limits	limit	NOUN
ejpam-3966	116	48	of	of	ADP
ejpam-3966	116	49	the	the	DET
ejpam-3966	116	50	inverse	inverse	NOUN
ejpam-3966	116	51	system	system	NOUN
ejpam-3966	116	52	{	{	PUNCT
ejpam-3966	116	53	xi	xi	PROPN
ejpam-3966	116	54	,	,	PUNCT
ejpam-3966	116	55	ϕij	ϕij	NOUN
ejpam-3966	116	56	,	,	PUNCT
ejpam-3966	116	57	i	i	PRON
ejpam-3966	116	58	}	}	PUNCT
ejpam-3966	116	59	,	,	PUNCT
ejpam-3966	116	60	then	then	ADV
ejpam-3966	116	61	there	there	PRON
ejpam-3966	116	62	is	be	VERB
ejpam-3966	116	63	a	a	DET
ejpam-3966	116	64	unique	unique	ADJ
ejpam-3966	116	65	isomorphism	isomorphism	NOUN
ejpam-3966	116	66	ϕ	ϕ	NOUN
ejpam-3966	116	67	:	:	PUNCT
ejpam-3966	116	68	x	x	X
ejpam-3966	116	69	→	→	SYM
ejpam-3966	116	70	y	y	PROPN
ejpam-3966	116	71	such	such	ADJ
ejpam-3966	116	72	that	that	SCONJ
ejpam-3966	116	73	ψiϕ	ψiϕ	ADV
ejpam-3966	117	1	=	=	X
ejpam-3966	117	2	ϕi	ϕi	ADP
ejpam-3966	117	3	for	for	ADP
ejpam-3966	117	4	each	each	DET
ejpam-3966	117	5	i	i	PROPN
ejpam-3966	117	6	∈	∈	PROPN
ejpam-3966	117	7	i.	i.	NOUN
ejpam-3966	117	8	proof	proof	PROPN
ejpam-3966	117	9	.	.	PUNCT
ejpam-3966	117	10	suppose	suppose	VERB
ejpam-3966	117	11	that	that	SCONJ
ejpam-3966	117	12	(	(	PUNCT
ejpam-3966	117	13	x,ϕi	x,ϕi	NUM
ejpam-3966	117	14	)	)	PUNCT
ejpam-3966	117	15	and	and	CCONJ
ejpam-3966	117	16	(	(	PUNCT
ejpam-3966	117	17	y	y	NOUN
ejpam-3966	117	18	,	,	PUNCT
ejpam-3966	117	19	ψi	ψi	NOUN
ejpam-3966	117	20	)	)	PUNCT
ejpam-3966	117	21	are	be	AUX
ejpam-3966	117	22	two	two	NUM
ejpam-3966	117	23	inverse	inverse	NOUN
ejpam-3966	117	24	limits	limit	NOUN
ejpam-3966	117	25	of	of	ADP
ejpam-3966	117	26	the	the	DET
ejpam-3966	117	27	inverse	inverse	NOUN
ejpam-3966	117	28	system	system	NOUN
ejpam-3966	117	29	{	{	PUNCT
ejpam-3966	117	30	xi	xi	PROPN
ejpam-3966	117	31	,	,	PUNCT
ejpam-3966	117	32	ϕij	ϕij	NOUN
ejpam-3966	117	33	,	,	PUNCT
ejpam-3966	117	34	i	i	NOUN
ejpam-3966	117	35	}	}	PUNCT
ejpam-3966	117	36	.	.	PUNCT
ejpam-3966	118	1	since	since	SCONJ
ejpam-3966	118	2	the	the	DET
ejpam-3966	118	3	maps	map	NOUN
ejpam-3966	118	4	ψi	ψi	ADP
ejpam-3966	118	5	:	:	PUNCT
ejpam-3966	118	6	y	y	X
ejpam-3966	118	7	→	→	SYM
ejpam-3966	118	8	xi	xi	PROPN
ejpam-3966	118	9	are	be	AUX
ejpam-3966	118	10	compatible	compatible	ADJ
ejpam-3966	118	11	,	,	PUNCT
ejpam-3966	118	12	the	the	DET
ejpam-3966	118	13	universal	universal	ADJ
ejpam-3966	118	14	property	property	NOUN
ejpam-3966	118	15	of	of	ADP
ejpam-3966	118	16	the	the	DET
ejpam-3966	118	17	inverse	inverse	NOUN
ejpam-3966	118	18	limit	limit	NOUN
ejpam-3966	118	19	(	(	PUNCT
ejpam-3966	118	20	x,ϕi	x,ϕi	PROPN
ejpam-3966	118	21	)	)	PUNCT
ejpam-3966	118	22	shows	show	VERB
ejpam-3966	118	23	that	that	SCONJ
ejpam-3966	118	24	there	there	PRON
ejpam-3966	118	25	exists	exist	VERB
ejpam-3966	118	26	a	a	DET
ejpam-3966	118	27	unique	unique	ADJ
ejpam-3966	118	28	homomorphism	homomorphism	NOUN
ejpam-3966	118	29	ψ	ψ	X
ejpam-3966	118	30	:	:	PUNCT
ejpam-3966	118	31	y	y	PROPN
ejpam-3966	118	32	→	→	PUNCT
ejpam-3966	118	33	x	x	PROPN
ejpam-3966	118	34	such	such	ADJ
ejpam-3966	118	35	that	that	SCONJ
ejpam-3966	118	36	ϕiψ	ϕiψ	ADV
ejpam-3966	118	37	=	=	X
ejpam-3966	118	38	ψi	ψi	ADP
ejpam-3966	118	39	for	for	ADP
ejpam-3966	118	40	all	all	PRON
ejpam-3966	118	41	i	i	PRON
ejpam-3966	118	42	∈	∈	PROPN
ejpam-3966	118	43	i.	i.	NOUN
ejpam-3966	118	44	similarly	similarly	ADV
ejpam-3966	118	45	,	,	PUNCT
ejpam-3966	118	46	there	there	PRON
ejpam-3966	118	47	exists	exist	VERB
ejpam-3966	118	48	a	a	DET
ejpam-3966	118	49	unique	unique	ADJ
ejpam-3966	118	50	homomorphism	homomorphism	NOUN
ejpam-3966	118	51	ϕ	ϕ	NOUN
ejpam-3966	118	52	:	:	PUNCT
ejpam-3966	118	53	y	y	PROPN
ejpam-3966	118	54	→	→	PUNCT
ejpam-3966	118	55	x	x	X
ejpam-3966	118	56	such	such	ADJ
ejpam-3966	118	57	that	that	SCONJ
ejpam-3966	118	58	ψiϕ	ψiϕ	ADV
ejpam-3966	119	1	=	=	X
ejpam-3966	119	2	ϕi	ϕi	ADP
ejpam-3966	119	3	for	for	ADP
ejpam-3966	119	4	all	all	PRON
ejpam-3966	119	5	i	i	PRON
ejpam-3966	119	6	∈	∈	PROPN
ejpam-3966	119	7	i.	i.	NOUN
ejpam-3966	119	8	it	it	PRON
ejpam-3966	119	9	follows	follow	VERB
ejpam-3966	119	10	that	that	PRON
ejpam-3966	119	11	ψi	ψi	ADP
ejpam-3966	119	12	=	=	PUNCT
ejpam-3966	119	13	ϕiψ	ϕiψ	NOUN
ejpam-3966	119	14	=	=	VERB
ejpam-3966	119	15	ψiϕψ	ψiϕψ	NOUN
ejpam-3966	119	16	for	for	ADP
ejpam-3966	119	17	all	all	PRON
ejpam-3966	119	18	i	i	PRON
ejpam-3966	119	19	∈	∈	PROPN
ejpam-3966	119	20	i.	i.	NOUN
ejpam-3966	119	21	thus	thus	ADV
ejpam-3966	119	22	,	,	PUNCT
ejpam-3966	119	23	by	by	ADP
ejpam-3966	119	24	remark	remark	NOUN
ejpam-3966	119	25	1	1	NUM
ejpam-3966	119	26	,	,	PUNCT
ejpam-3966	119	27	ϕψ	ϕψ	ADP
ejpam-3966	119	28	=	=	SYM
ejpam-3966	119	29	idy	idy	PROPN
ejpam-3966	119	30	.	.	PUNCT
ejpam-3966	120	1	similarly	similarly	ADV
ejpam-3966	120	2	,	,	PUNCT
ejpam-3966	120	3	ψϕ	ψϕ	NOUN
ejpam-3966	120	4	=	=	PUNCT
ejpam-3966	120	5	idx	idx	NOUN
ejpam-3966	120	6	.	.	PUNCT
ejpam-3966	121	1	therefore	therefore	ADV
ejpam-3966	121	2	,	,	PUNCT
ejpam-3966	121	3	ϕ	ϕ	PROPN
ejpam-3966	121	4	is	be	AUX
ejpam-3966	121	5	an	an	DET
ejpam-3966	121	6	isomorphism	isomorphism	NOUN
ejpam-3966	121	7	.	.	PUNCT
ejpam-3966	122	1	j.	j.	PROPN
ejpam-3966	122	2	albaracin	albaracin	PROPN
ejpam-3966	122	3	,	,	PUNCT
ejpam-3966	122	4	j.	j.	PROPN
ejpam-3966	122	5	vilela	vilela	PROPN
ejpam-3966	122	6	/	/	SYM
ejpam-3966	122	7	eur	eur	PROPN
ejpam-3966	122	8	.	.	PUNCT
ejpam-3966	123	1	j.	j.	PROPN
ejpam-3966	123	2	pure	pure	PROPN
ejpam-3966	123	3	appl	appl	PROPN
ejpam-3966	123	4	.	.	PROPN
ejpam-3966	123	5	math	math	PROPN
ejpam-3966	123	6	,	,	PUNCT
ejpam-3966	123	7	14	14	NUM
ejpam-3966	123	8	(	(	PUNCT
ejpam-3966	123	9	2	2	NUM
ejpam-3966	123	10	)	)	PUNCT
ejpam-3966	123	11	(	(	PUNCT
ejpam-3966	123	12	2021	2021	NUM
ejpam-3966	123	13	)	)	PUNCT
ejpam-3966	123	14	,	,	PUNCT
ejpam-3966	123	15	423	423	NUM
ejpam-3966	123	16	-	-	SYM
ejpam-3966	123	17	430	430	NUM
ejpam-3966	123	18	426	426	NUM
ejpam-3966	123	19	note	note	NOUN
ejpam-3966	123	20	that	that	SCONJ
ejpam-3966	123	21	if	if	SCONJ
ejpam-3966	123	22	s	s	NOUN
ejpam-3966	123	23	is	be	AUX
ejpam-3966	123	24	a	a	DET
ejpam-3966	123	25	subalgebra	subalgebra	NOUN
ejpam-3966	123	26	of	of	ADP
ejpam-3966	123	27	a	a	DET
ejpam-3966	123	28	transitive	transitive	ADJ
ejpam-3966	123	29	be	be	NOUN
ejpam-3966	123	30	-	-	PUNCT
ejpam-3966	123	31	algebra	algebra	NOUN
ejpam-3966	123	32	x	x	NOUN
ejpam-3966	123	33	,	,	PUNCT
ejpam-3966	123	34	then	then	ADV
ejpam-3966	123	35	for	for	ADP
ejpam-3966	123	36	all	all	DET
ejpam-3966	123	37	x	x	NOUN
ejpam-3966	123	38	,	,	PUNCT
ejpam-3966	123	39	y	y	PROPN
ejpam-3966	123	40	,	,	PUNCT
ejpam-3966	123	41	z	z	PROPN
ejpam-3966	123	42	∈	∈	PROPN
ejpam-3966	123	43	s	s	PART
ejpam-3966	123	44	,	,	PUNCT
ejpam-3966	123	45	y	y	PROPN
ejpam-3966	123	46	∗	∗	NOUN
ejpam-3966	123	47	z	z	NOUN
ejpam-3966	123	48	≤	≤	NOUN
ejpam-3966	123	49	(	(	PUNCT
ejpam-3966	123	50	x	x	X
ejpam-3966	123	51	∗	∗	PROPN
ejpam-3966	123	52	y	y	NOUN
ejpam-3966	123	53	)	)	PUNCT
ejpam-3966	123	54	∗	∗	NOUN
ejpam-3966	123	55	(	(	PUNCT
ejpam-3966	123	56	x	x	X
ejpam-3966	123	57	∗	∗	PROPN
ejpam-3966	123	58	z	z	NOUN
ejpam-3966	123	59	)	)	PUNCT
ejpam-3966	123	60	.	.	PUNCT
ejpam-3966	124	1	thus	thus	ADV
ejpam-3966	124	2	,	,	PUNCT
ejpam-3966	124	3	s	s	X
ejpam-3966	124	4	is	be	AUX
ejpam-3966	124	5	also	also	ADV
ejpam-3966	124	6	transitive	transitive	ADJ
ejpam-3966	124	7	.	.	PUNCT
ejpam-3966	125	1	also	also	ADV
ejpam-3966	125	2	,	,	PUNCT
ejpam-3966	125	3	in	in	ADP
ejpam-3966	125	4	[	[	PUNCT
ejpam-3966	125	5	4	4	NUM
ejpam-3966	125	6	]	]	PUNCT
ejpam-3966	125	7	,	,	PUNCT
ejpam-3966	125	8	the	the	DET
ejpam-3966	125	9	direct	direct	ADJ
ejpam-3966	125	10	product	product	NOUN
ejpam-3966	125	11	of	of	ADP
ejpam-3966	125	12	transitive	transitive	ADJ
ejpam-3966	125	13	be	be	AUX
ejpam-3966	125	14	-	-	PUNCT
ejpam-3966	125	15	algebras	algebras	NOUN
ejpam-3966	125	16	is	be	AUX
ejpam-3966	125	17	transitive	transitive	ADJ
ejpam-3966	125	18	and	and	CCONJ
ejpam-3966	125	19	every	every	DET
ejpam-3966	125	20	commutative	commutative	ADJ
ejpam-3966	125	21	and	and	CCONJ
ejpam-3966	125	22	self	self	NOUN
ejpam-3966	125	23	-	-	PUNCT
ejpam-3966	125	24	distributive	distributive	ADJ
ejpam-3966	125	25	bealgebra	bealgebra	NOUN
ejpam-3966	125	26	is	be	AUX
ejpam-3966	125	27	transitive	transitive	ADJ
ejpam-3966	125	28	.	.	PUNCT
ejpam-3966	126	1	thus	thus	ADV
ejpam-3966	126	2	,	,	PUNCT
ejpam-3966	126	3	we	we	PRON
ejpam-3966	126	4	have	have	VERB
ejpam-3966	126	5	the	the	DET
ejpam-3966	126	6	following	follow	VERB
ejpam-3966	126	7	result	result	NOUN
ejpam-3966	126	8	.	.	PUNCT
ejpam-3966	127	1	proposition	proposition	NOUN
ejpam-3966	127	2	2	2	NUM
ejpam-3966	127	3	.	.	PUNCT
ejpam-3966	128	1	let	let	VERB
ejpam-3966	128	2	{	{	PUNCT
ejpam-3966	128	3	xi	xi	PROPN
ejpam-3966	128	4	,	,	PUNCT
ejpam-3966	128	5	ϕij	ϕij	NOUN
ejpam-3966	128	6	,	,	PUNCT
ejpam-3966	128	7	i	i	PRON
ejpam-3966	128	8	}	}	PUNCT
ejpam-3966	128	9	be	be	VERB
ejpam-3966	128	10	an	an	DET
ejpam-3966	128	11	inverse	inverse	NOUN
ejpam-3966	128	12	system	system	NOUN
ejpam-3966	128	13	of	of	ADP
ejpam-3966	128	14	be	be	NOUN
ejpam-3966	128	15	-	-	PUNCT
ejpam-3966	128	16	algebras	algebra	NOUN
ejpam-3966	128	17	.	.	PUNCT
ejpam-3966	129	1	if	if	SCONJ
ejpam-3966	129	2	each	each	PRON
ejpam-3966	129	3	xi	xi	X
ejpam-3966	129	4	is	be	AUX
ejpam-3966	129	5	transitive	transitive	ADJ
ejpam-3966	129	6	(	(	PUNCT
ejpam-3966	129	7	resp	resp	NOUN
ejpam-3966	129	8	.	.	PUNCT
ejpam-3966	130	1	commutative	commutative	ADJ
ejpam-3966	130	2	,	,	PUNCT
ejpam-3966	130	3	self	self	NOUN
ejpam-3966	130	4	-	-	PUNCT
ejpam-3966	130	5	distributive	distributive	ADJ
ejpam-3966	130	6	)	)	PUNCT
ejpam-3966	130	7	for	for	ADP
ejpam-3966	130	8	all	all	PRON
ejpam-3966	130	9	i	i	PRON
ejpam-3966	130	10	∈	∈	PROPN
ejpam-3966	131	1	i	i	PRON
ejpam-3966	131	2	,	,	PUNCT
ejpam-3966	131	3	then	then	ADV
ejpam-3966	131	4	lim←−xi	lim←−xi	ADV
ejpam-3966	131	5	is	be	AUX
ejpam-3966	131	6	transitive	transitive	ADJ
ejpam-3966	131	7	(	(	PUNCT
ejpam-3966	131	8	resp	resp	NOUN
ejpam-3966	131	9	.	.	PUNCT
ejpam-3966	132	1	commutative	commutative	ADJ
ejpam-3966	132	2	,	,	PUNCT
ejpam-3966	132	3	self	self	NOUN
ejpam-3966	132	4	-	-	PUNCT
ejpam-3966	132	5	distributive	distributive	ADJ
ejpam-3966	132	6	)	)	PUNCT
ejpam-3966	132	7	.	.	PUNCT
ejpam-3966	132	8	proposition	proposition	NOUN
ejpam-3966	132	9	3	3	X
ejpam-3966	132	10	.	.	PUNCT
ejpam-3966	133	1	let	let	VERB
ejpam-3966	133	2	{	{	PUNCT
ejpam-3966	133	3	xi	xi	PROPN
ejpam-3966	133	4	,	,	PUNCT
ejpam-3966	133	5	ϕij	ϕij	NOUN
ejpam-3966	133	6	,	,	PUNCT
ejpam-3966	133	7	i	i	PRON
ejpam-3966	133	8	}	}	PUNCT
ejpam-3966	133	9	be	be	VERB
ejpam-3966	133	10	an	an	DET
ejpam-3966	133	11	inverse	inverse	NOUN
ejpam-3966	133	12	system	system	NOUN
ejpam-3966	133	13	of	of	ADP
ejpam-3966	133	14	be	be	AUX
ejpam-3966	133	15	-	-	PUNCT
ejpam-3966	133	16	algebras	algebra	VERB
ejpam-3966	133	17	and	and	CCONJ
ejpam-3966	133	18	let	let	VERB
ejpam-3966	133	19	x	x	PUNCT
ejpam-3966	133	20	=	=	PRON
ejpam-3966	133	21	lim←−xi	lim←−xi	ADV
ejpam-3966	133	22	be	be	AUX
ejpam-3966	133	23	its	its	PRON
ejpam-3966	133	24	corresponding	corresponding	ADJ
ejpam-3966	133	25	inverse	inverse	NOUN
ejpam-3966	133	26	limit	limit	NOUN
ejpam-3966	133	27	.	.	PUNCT
ejpam-3966	134	1	suppose	suppose	VERB
ejpam-3966	134	2	that	that	SCONJ
ejpam-3966	134	3	i0	i0	PROPN
ejpam-3966	134	4	∈	∈	PROPN
ejpam-3966	135	1	i	i	PRON
ejpam-3966	135	2	such	such	ADJ
ejpam-3966	135	3	that	that	SCONJ
ejpam-3966	135	4	i0	i0	PROPN
ejpam-3966	135	5	≥	≥	PROPN
ejpam-3966	135	6	i1	i1	PROPN
ejpam-3966	135	7	,	,	PUNCT
ejpam-3966	135	8	.	.	PUNCT
ejpam-3966	135	9	.	.	PUNCT
ejpam-3966	136	1	.	.	PUNCT
ejpam-3966	137	1	,	,	PUNCT
ejpam-3966	137	2	it	it	PRON
ejpam-3966	137	3	and	and	CCONJ
ejpam-3966	137	4	ϕi0ik(ai0	ϕi0ik(ai0	NUM
ejpam-3966	137	5	)	)	PUNCT
ejpam-3966	138	1	⊆	⊆	NUM
ejpam-3966	138	2	aik	aik	NOUN
ejpam-3966	138	3	where	where	SCONJ
ejpam-3966	138	4	aik	aik	NOUN
ejpam-3966	138	5	⊆	⊆	NUM
ejpam-3966	138	6	xik	xik	NOUN
ejpam-3966	138	7	for	for	ADP
ejpam-3966	138	8	all	all	PRON
ejpam-3966	138	9	k	k	NOUN
ejpam-3966	138	10	=	=	SYM
ejpam-3966	138	11	0	0	NUM
ejpam-3966	138	12	,	,	PUNCT
ejpam-3966	138	13	1	1	NUM
ejpam-3966	138	14	,	,	PUNCT
ejpam-3966	138	15	.	.	PUNCT
ejpam-3966	138	16	.	.	PUNCT
ejpam-3966	138	17	.	.	PUNCT
ejpam-3966	139	1	,	,	PUNCT
ejpam-3966	139	2	t.	t.	PROPN
ejpam-3966	139	3	then	then	ADV
ejpam-3966	139	4	x	x	X
ejpam-3966	139	5	∩	∩	X
ejpam-3966	139	6	[	[	X
ejpam-3966	139	7	(	(	PUNCT
ejpam-3966	139	8	∏	∏	X
ejpam-3966	139	9	i	i	PRON
ejpam-3966	139	10	6	6	NUM
ejpam-3966	139	11	=	=	X
ejpam-3966	139	12	i0	i0	PROPN
ejpam-3966	139	13	xi	xi	PUNCT
ejpam-3966	139	14	)	)	PUNCT
ejpam-3966	139	15	×ai0	×ai0	PUNCT
ejpam-3966	139	16	]	]	PUNCT
ejpam-3966	140	1	=	=	PUNCT
ejpam-3966	140	2	x	x	SYM
ejpam-3966	140	3	∩	∩	X
ejpam-3966	140	4	[	[	X
ejpam-3966	140	5	(	(	PUNCT
ejpam-3966	140	6	∏	∏	X
ejpam-3966	140	7	i	i	NOUN
ejpam-3966	140	8	6	6	NUM
ejpam-3966	140	9	=	=	SYM
ejpam-3966	140	10	i0,	i0,	NOUN
ejpam-3966	140	11	...	...	PUNCT
ejpam-3966	140	12	,it	,it	PUNCT
ejpam-3966	140	13	xi	xi	X
ejpam-3966	140	14	)	)	PUNCT
ejpam-3966	140	15	×ai0	×ai0	SYM
ejpam-3966	140	16	×	×	NOUN
ejpam-3966	140	17	·	·	PUNCT
ejpam-3966	140	18	·	·	PUNCT
ejpam-3966	140	19	·	·	PUNCT
ejpam-3966	140	20	×ait	×ait	NUM
ejpam-3966	140	21	]	]	PUNCT
ejpam-3966	140	22	.	.	PUNCT
ejpam-3966	141	1	proof	proof	NOUN
ejpam-3966	141	2	.	.	PUNCT
ejpam-3966	142	1	let	let	VERB
ejpam-3966	142	2	(	(	PUNCT
ejpam-3966	142	3	xi	xi	NOUN
ejpam-3966	142	4	)	)	PUNCT
ejpam-3966	142	5	∈	∈	PROPN
ejpam-3966	142	6	x	x	SYM
ejpam-3966	142	7	∩	∩	X
ejpam-3966	142	8	[	[	X
ejpam-3966	142	9	(	(	PUNCT
ejpam-3966	142	10	∏	∏	X
ejpam-3966	142	11	i	i	PRON
ejpam-3966	142	12	6	6	NUM
ejpam-3966	142	13	=	=	X
ejpam-3966	142	14	i0	i0	PROPN
ejpam-3966	142	15	xi	xi	PUNCT
ejpam-3966	142	16	)	)	PUNCT
ejpam-3966	142	17	×ai0	×ai0	PUNCT
ejpam-3966	142	18	]	]	PUNCT
ejpam-3966	142	19	.	.	PUNCT
ejpam-3966	143	1	then	then	ADV
ejpam-3966	143	2	(	(	PUNCT
ejpam-3966	143	3	xi	xi	X
ejpam-3966	143	4	)	)	PUNCT
ejpam-3966	143	5	∈	∈	PROPN
ejpam-3966	143	6	x	x	X
ejpam-3966	143	7	and	and	CCONJ
ejpam-3966	143	8	(	(	PUNCT
ejpam-3966	143	9	xi	xi	NOUN
ejpam-3966	143	10	)	)	PUNCT
ejpam-3966	143	11	∈	∈	PROPN
ejpam-3966	143	12	(	(	PUNCT
ejpam-3966	143	13	∏	∏	X
ejpam-3966	143	14	i	i	PRON
ejpam-3966	143	15	6	6	NUM
ejpam-3966	143	16	=	=	X
ejpam-3966	143	17	i0	i0	PROPN
ejpam-3966	143	18	xi	xi	X
ejpam-3966	143	19	)	)	PUNCT
ejpam-3966	143	20	×ai0	×ai0	PUNCT
ejpam-3966	143	21	.	.	PUNCT
ejpam-3966	144	1	thus	thus	ADV
ejpam-3966	144	2	,	,	PUNCT
ejpam-3966	144	3	ϕij(xi	ϕij(xi	NUM
ejpam-3966	144	4	)	)	PUNCT
ejpam-3966	144	5	=	=	SYM
ejpam-3966	144	6	xj	xj	PROPN
ejpam-3966	144	7	for	for	ADP
ejpam-3966	144	8	all	all	DET
ejpam-3966	144	9	i	i	PRON
ejpam-3966	144	10	≥	≥	VERB
ejpam-3966	144	11	j	j	NOUN
ejpam-3966	144	12	and	and	CCONJ
ejpam-3966	144	13	xi0	xi0	PROPN
ejpam-3966	144	14	∈	∈	PROPN
ejpam-3966	144	15	ai0	ai0	PROPN
ejpam-3966	144	16	.	.	PUNCT
ejpam-3966	145	1	hence	hence	ADV
ejpam-3966	145	2	,	,	PUNCT
ejpam-3966	145	3	ϕi0j(xi0	ϕi0j(xi0	X
ejpam-3966	145	4	)	)	PUNCT
ejpam-3966	145	5	=	=	PUNCT
ejpam-3966	145	6	xj	xj	PROPN
ejpam-3966	145	7	for	for	ADP
ejpam-3966	145	8	all	all	DET
ejpam-3966	145	9	j	j	PROPN
ejpam-3966	145	10	≤	≤	PROPN
ejpam-3966	145	11	i0	i0	PROPN
ejpam-3966	145	12	.	.	PUNCT
ejpam-3966	146	1	since	since	SCONJ
ejpam-3966	146	2	i0	i0	PROPN
ejpam-3966	146	3	≥	≥	PROPN
ejpam-3966	146	4	i1	i1	PROPN
ejpam-3966	146	5	,	,	PUNCT
ejpam-3966	146	6	.	.	PUNCT
ejpam-3966	146	7	.	.	PUNCT
ejpam-3966	146	8	.	.	PUNCT
ejpam-3966	146	9	,	,	PUNCT
ejpam-3966	146	10	it	it	PRON
ejpam-3966	146	11	,	,	PUNCT
ejpam-3966	146	12	ϕi0ik(xi0	ϕi0ik(xi0	PROPN
ejpam-3966	146	13	)	)	PUNCT
ejpam-3966	147	1	=	=	PUNCT
ejpam-3966	148	1	xik	xik	PROPN
ejpam-3966	148	2	for	for	ADP
ejpam-3966	148	3	all	all	PRON
ejpam-3966	148	4	k	k	NOUN
ejpam-3966	148	5	=	=	SYM
ejpam-3966	148	6	1	1	NUM
ejpam-3966	148	7	,	,	PUNCT
ejpam-3966	148	8	.	.	PUNCT
ejpam-3966	148	9	.	.	PUNCT
ejpam-3966	148	10	.	.	PUNCT
ejpam-3966	149	1	,	,	PUNCT
ejpam-3966	149	2	t.	t.	PROPN
ejpam-3966	149	3	since	since	SCONJ
ejpam-3966	149	4	ϕi0ik(ai0	ϕi0ik(ai0	PROPN
ejpam-3966	149	5	)	)	PUNCT
ejpam-3966	150	1	⊆	⊆	NUM
ejpam-3966	150	2	aik	aik	NOUN
ejpam-3966	150	3	for	for	ADP
ejpam-3966	150	4	all	all	PRON
ejpam-3966	150	5	k	k	NOUN
ejpam-3966	150	6	=	=	SYM
ejpam-3966	150	7	1	1	NUM
ejpam-3966	150	8	,	,	PUNCT
ejpam-3966	150	9	.	.	PUNCT
ejpam-3966	150	10	.	.	PUNCT
ejpam-3966	150	11	.	.	PUNCT
ejpam-3966	151	1	,	,	PUNCT
ejpam-3966	151	2	t	t	PROPN
ejpam-3966	151	3	,	,	PUNCT
ejpam-3966	151	4	we	we	PRON
ejpam-3966	151	5	have	have	VERB
ejpam-3966	151	6	xik	xik	PROPN
ejpam-3966	151	7	∈	∈	PROPN
ejpam-3966	151	8	aik	aik	NOUN
ejpam-3966	151	9	for	for	ADP
ejpam-3966	151	10	all	all	PRON
ejpam-3966	151	11	k	k	NOUN
ejpam-3966	152	1	=	=	SYM
ejpam-3966	153	1	1	1	NUM
ejpam-3966	153	2	,	,	PUNCT
ejpam-3966	153	3	.	.	PUNCT
ejpam-3966	153	4	.	.	PUNCT
ejpam-3966	153	5	.	.	PUNCT
ejpam-3966	154	1	,	,	PUNCT
ejpam-3966	154	2	t.	t.	NOUN
ejpam-3966	154	3	this	this	PRON
ejpam-3966	154	4	implies	imply	VERB
ejpam-3966	154	5	that	that	SCONJ
ejpam-3966	154	6	(	(	PUNCT
ejpam-3966	154	7	xi	xi	X
ejpam-3966	154	8	)	)	PUNCT
ejpam-3966	154	9	∈	∈	PROPN
ejpam-3966	154	10	(	(	PUNCT
ejpam-3966	154	11	∏	∏	X
ejpam-3966	154	12	i	i	NOUN
ejpam-3966	154	13	6	6	NUM
ejpam-3966	154	14	=	=	SYM
ejpam-3966	154	15	i0,	i0,	NOUN
ejpam-3966	154	16	...	...	PUNCT
ejpam-3966	154	17	,it	,it	PUNCT
ejpam-3966	154	18	xi	xi	X
ejpam-3966	154	19	)	)	PUNCT
ejpam-3966	154	20	×	×	PROPN
ejpam-3966	154	21	ai0	ai0	INTJ
ejpam-3966	154	22	×	×	NOUN
ejpam-3966	154	23	·	·	PUNCT
ejpam-3966	154	24	·	·	PUNCT
ejpam-3966	154	25	·	·	PUNCT
ejpam-3966	155	1	×ait	×ait	NUM
ejpam-3966	155	2	.	.	PUNCT
ejpam-3966	156	1	since	since	SCONJ
ejpam-3966	156	2	(	(	PUNCT
ejpam-3966	156	3	xi	xi	NOUN
ejpam-3966	156	4	)	)	PUNCT
ejpam-3966	156	5	∈	∈	PROPN
ejpam-3966	157	1	x	x	NOUN
ejpam-3966	157	2	,	,	PUNCT
ejpam-3966	157	3	we	we	PRON
ejpam-3966	157	4	get	get	VERB
ejpam-3966	157	5	(	(	PUNCT
ejpam-3966	157	6	xi	xi	NOUN
ejpam-3966	157	7	)	)	PUNCT
ejpam-3966	157	8	∈	∈	PROPN
ejpam-3966	157	9	x	x	SYM
ejpam-3966	157	10	∩	∩	X
ejpam-3966	157	11	[	[	X
ejpam-3966	157	12	(	(	PUNCT
ejpam-3966	157	13	∏	∏	X
ejpam-3966	157	14	i	i	NOUN
ejpam-3966	157	15	6	6	NUM
ejpam-3966	157	16	=	=	SYM
ejpam-3966	157	17	i0,	i0,	NOUN
ejpam-3966	157	18	...	...	PUNCT
ejpam-3966	157	19	,it	,it	PUNCT
ejpam-3966	157	20	xi	xi	X
ejpam-3966	157	21	)	)	PUNCT
ejpam-3966	157	22	×ai0	×ai0	SYM
ejpam-3966	157	23	×	×	NOUN
ejpam-3966	157	24	·	·	PUNCT
ejpam-3966	157	25	·	·	PUNCT
ejpam-3966	157	26	·	·	PUNCT
ejpam-3966	157	27	×ait	×ait	NUM
ejpam-3966	157	28	]	]	PUNCT
ejpam-3966	157	29	.	.	PUNCT
ejpam-3966	158	1	the	the	DET
ejpam-3966	158	2	other	other	ADJ
ejpam-3966	158	3	inclusion	inclusion	NOUN
ejpam-3966	158	4	is	be	AUX
ejpam-3966	158	5	easy	easy	ADJ
ejpam-3966	158	6	to	to	PART
ejpam-3966	158	7	show	show	VERB
ejpam-3966	158	8	.	.	PUNCT
ejpam-3966	159	1	corollary	corollary	ADJ
ejpam-3966	159	2	1	1	NUM
ejpam-3966	159	3	.	.	PUNCT
ejpam-3966	160	1	let	let	VERB
ejpam-3966	160	2	{	{	PUNCT
ejpam-3966	160	3	xi	xi	PROPN
ejpam-3966	160	4	,	,	PUNCT
ejpam-3966	160	5	ϕij	ϕij	NOUN
ejpam-3966	160	6	,	,	PUNCT
ejpam-3966	160	7	i	i	PRON
ejpam-3966	160	8	}	}	PUNCT
ejpam-3966	160	9	be	be	VERB
ejpam-3966	160	10	an	an	DET
ejpam-3966	160	11	inverse	inverse	NOUN
ejpam-3966	160	12	system	system	NOUN
ejpam-3966	160	13	of	of	ADP
ejpam-3966	160	14	be	be	AUX
ejpam-3966	160	15	-	-	PUNCT
ejpam-3966	160	16	algebras	algebra	VERB
ejpam-3966	160	17	and	and	CCONJ
ejpam-3966	160	18	let	let	VERB
ejpam-3966	160	19	x	x	PUNCT
ejpam-3966	160	20	=	=	PRON
ejpam-3966	160	21	lim←−xi	lim←−xi	ADV
ejpam-3966	160	22	be	be	AUX
ejpam-3966	160	23	its	its	PRON
ejpam-3966	160	24	corresponding	corresponding	ADJ
ejpam-3966	160	25	inverse	inverse	NOUN
ejpam-3966	160	26	limit	limit	NOUN
ejpam-3966	160	27	.	.	PUNCT
ejpam-3966	161	1	then	then	ADV
ejpam-3966	161	2	x	x	X
ejpam-3966	161	3	∩	∩	ADJ
ejpam-3966	161	4	[	[	X
ejpam-3966	161	5	(	(	PUNCT
ejpam-3966	161	6	∏	∏	X
ejpam-3966	161	7	i	i	PRON
ejpam-3966	161	8	6	6	NUM
ejpam-3966	161	9	=	=	X
ejpam-3966	161	10	i0	i0	PROPN
ejpam-3966	161	11	xi	xi	PUNCT
ejpam-3966	161	12	)	)	PUNCT
ejpam-3966	161	13	×	×	PROPN
ejpam-3966	161	14	{	{	PUNCT
ejpam-3966	161	15	1xi0	1xi0	NUM
ejpam-3966	161	16	}	}	PUNCT
ejpam-3966	161	17	]	]	PUNCT
ejpam-3966	162	1	=	=	PUNCT
ejpam-3966	162	2	x	x	SYM
ejpam-3966	162	3	∩	∩	X
ejpam-3966	162	4	[	[	X
ejpam-3966	162	5	(	(	PUNCT
ejpam-3966	162	6	∏	∏	X
ejpam-3966	162	7	i	i	NOUN
ejpam-3966	162	8	6	6	NUM
ejpam-3966	162	9	=	=	SYM
ejpam-3966	162	10	i0,	i0,	NOUN
ejpam-3966	162	11	...	...	PUNCT
ejpam-3966	162	12	,it	,it	PUNCT
ejpam-3966	162	13	xi	xi	X
ejpam-3966	162	14	)	)	PUNCT
ejpam-3966	162	15	×	×	PROPN
ejpam-3966	162	16	{	{	PUNCT
ejpam-3966	162	17	1xi0	1xi0	NUM
ejpam-3966	162	18	}	}	PUNCT
ejpam-3966	162	19	×	×	PROPN
ejpam-3966	162	20	·	·	PUNCT
ejpam-3966	162	21	·	·	PUNCT
ejpam-3966	162	22	·	·	PUNCT
ejpam-3966	163	1	×	×	NOUN
ejpam-3966	163	2	{	{	PUNCT
ejpam-3966	163	3	1xit	1xit	PROPN
ejpam-3966	163	4	}	}	PUNCT
ejpam-3966	163	5	]	]	PUNCT
ejpam-3966	163	6	where	where	SCONJ
ejpam-3966	163	7	i0	i0	PROPN
ejpam-3966	163	8	≥	≥	PROPN
ejpam-3966	163	9	i1	i1	PROPN
ejpam-3966	163	10	,	,	PUNCT
ejpam-3966	163	11	.	.	PUNCT
ejpam-3966	163	12	.	.	PUNCT
ejpam-3966	163	13	.	.	PUNCT
ejpam-3966	164	1	,	,	PUNCT
ejpam-3966	164	2	it	it	PRON
ejpam-3966	164	3	.	.	PUNCT
ejpam-3966	165	1	proof	proof	NOUN
ejpam-3966	165	2	.	.	PUNCT
ejpam-3966	166	1	since	since	SCONJ
ejpam-3966	166	2	ϕi0ik	ϕi0ik	NOUN
ejpam-3966	166	3	is	be	AUX
ejpam-3966	166	4	a	a	DET
ejpam-3966	166	5	homomorphism	homomorphism	NOUN
ejpam-3966	166	6	for	for	ADP
ejpam-3966	166	7	all	all	DET
ejpam-3966	166	8	i0	i0	PROPN
ejpam-3966	166	9	≥	≥	PROPN
ejpam-3966	166	10	i1	i1	PROPN
ejpam-3966	166	11	,	,	PUNCT
ejpam-3966	166	12	.	.	PUNCT
ejpam-3966	166	13	.	.	PUNCT
ejpam-3966	167	1	.	.	PUNCT
ejpam-3966	168	1	,	,	PUNCT
ejpam-3966	168	2	it	it	PRON
ejpam-3966	168	3	and	and	CCONJ
ejpam-3966	168	4	for	for	ADP
ejpam-3966	168	5	all	all	PRON
ejpam-3966	168	6	k	k	NOUN
ejpam-3966	168	7	=	=	SYM
ejpam-3966	168	8	1	1	NUM
ejpam-3966	168	9	,	,	PUNCT
ejpam-3966	168	10	.	.	PUNCT
ejpam-3966	168	11	.	.	PUNCT
ejpam-3966	168	12	.	.	PUNCT
ejpam-3966	169	1	,	,	PUNCT
ejpam-3966	169	2	t	t	PROPN
ejpam-3966	169	3	,	,	PUNCT
ejpam-3966	169	4	by	by	ADP
ejpam-3966	169	5	theorem	theorem	NOUN
ejpam-3966	169	6	1	1	NUM
ejpam-3966	169	7	,	,	PUNCT
ejpam-3966	169	8	ϕi0ik(1xi0	ϕi0ik(1xi0	NOUN
ejpam-3966	169	9	)	)	PUNCT
ejpam-3966	170	1	=	=	PUNCT
ejpam-3966	170	2	1xik	1xik	NUM
ejpam-3966	170	3	for	for	ADP
ejpam-3966	170	4	all	all	PRON
ejpam-3966	170	5	k	k	NOUN
ejpam-3966	170	6	=	=	SYM
ejpam-3966	170	7	1	1	NUM
ejpam-3966	170	8	,	,	PUNCT
ejpam-3966	170	9	.	.	PUNCT
ejpam-3966	170	10	.	.	PUNCT
ejpam-3966	170	11	.	.	PUNCT
ejpam-3966	171	1	,	,	PUNCT
ejpam-3966	172	1	t.	t.	PROPN
ejpam-3966	172	2	thus	thus	ADV
ejpam-3966	172	3	,	,	PUNCT
ejpam-3966	172	4	ϕi0ik({1xi0	ϕi0ik({1xi0	NOUN
ejpam-3966	172	5	}	}	PUNCT
ejpam-3966	172	6	)	)	PUNCT
ejpam-3966	173	1	=	=	PRON
ejpam-3966	173	2	{	{	PUNCT
ejpam-3966	173	3	1xik	1xik	NOUN
ejpam-3966	173	4	}	}	PUNCT
ejpam-3966	173	5	for	for	ADP
ejpam-3966	173	6	all	all	DET
ejpam-3966	173	7	i0	i0	PROPN
ejpam-3966	173	8	≥	≥	PROPN
ejpam-3966	173	9	i1	i1	PROPN
ejpam-3966	173	10	,	,	PUNCT
ejpam-3966	173	11	.	.	PUNCT
ejpam-3966	173	12	.	.	PUNCT
ejpam-3966	174	1	.	.	PUNCT
ejpam-3966	175	1	,	,	PUNCT
ejpam-3966	175	2	it	it	PRON
ejpam-3966	175	3	and	and	CCONJ
ejpam-3966	175	4	for	for	ADP
ejpam-3966	175	5	all	all	PRON
ejpam-3966	175	6	k	k	NOUN
ejpam-3966	175	7	=	=	SYM
ejpam-3966	175	8	1	1	NUM
ejpam-3966	175	9	,	,	PUNCT
ejpam-3966	175	10	.	.	PUNCT
ejpam-3966	175	11	.	.	PUNCT
ejpam-3966	175	12	.	.	PUNCT
ejpam-3966	176	1	,	,	PUNCT
ejpam-3966	176	2	t.	t.	NOUN
ejpam-3966	176	3	by	by	ADP
ejpam-3966	176	4	proposition	proposition	NOUN
ejpam-3966	176	5	3	3	NUM
ejpam-3966	176	6	,	,	PUNCT
ejpam-3966	176	7	the	the	DET
ejpam-3966	176	8	result	result	NOUN
ejpam-3966	176	9	holds	hold	VERB
ejpam-3966	176	10	.	.	PUNCT
ejpam-3966	177	1	theorem	theorem	NOUN
ejpam-3966	177	2	6	6	NUM
ejpam-3966	177	3	.	.	PUNCT
ejpam-3966	178	1	let	let	VERB
ejpam-3966	178	2	{	{	PUNCT
ejpam-3966	178	3	xi	xi	PROPN
ejpam-3966	178	4	,	,	PUNCT
ejpam-3966	178	5	ϕij	ϕij	NOUN
ejpam-3966	178	6	,	,	PUNCT
ejpam-3966	178	7	i	i	PRON
ejpam-3966	178	8	}	}	PUNCT
ejpam-3966	178	9	be	be	VERB
ejpam-3966	178	10	an	an	DET
ejpam-3966	178	11	inverse	inverse	NOUN
ejpam-3966	178	12	system	system	NOUN
ejpam-3966	178	13	of	of	ADP
ejpam-3966	178	14	be	be	AUX
ejpam-3966	178	15	-	-	PUNCT
ejpam-3966	178	16	algebras	algebra	VERB
ejpam-3966	178	17	and	and	CCONJ
ejpam-3966	178	18	let	let	VERB
ejpam-3966	178	19	(	(	PUNCT
ejpam-3966	178	20	x	x	SYM
ejpam-3966	178	21	=	=	SYM
ejpam-3966	178	22	lim←−xi	lim←−xi	ADJ
ejpam-3966	178	23	,	,	PUNCT
ejpam-3966	178	24	ϕi	ϕi	ADJ
ejpam-3966	178	25	)	)	PUNCT
ejpam-3966	178	26	be	be	AUX
ejpam-3966	178	27	its	its	PRON
ejpam-3966	178	28	corresponding	corresponding	ADJ
ejpam-3966	178	29	inverse	inverse	NOUN
ejpam-3966	178	30	limit	limit	NOUN
ejpam-3966	178	31	where	where	SCONJ
ejpam-3966	178	32	ϕi	ϕi	ADP
ejpam-3966	178	33	:	:	PUNCT
ejpam-3966	178	34	x	x	X
ejpam-3966	178	35	→	→	SYM
ejpam-3966	178	36	xi	xi	X
ejpam-3966	178	37	is	be	AUX
ejpam-3966	178	38	the	the	DET
ejpam-3966	178	39	restriction	restriction	NOUN
ejpam-3966	178	40	of	of	ADP
ejpam-3966	178	41	the	the	DET
ejpam-3966	178	42	natural	natural	ADJ
ejpam-3966	178	43	projection	projection	NOUN
ejpam-3966	178	44	ρi	ρi	NOUN
ejpam-3966	178	45	:	:	PUNCT
ejpam-3966	178	46	∏	∏	PROPN
ejpam-3966	178	47	i∈i	i∈i	NOUN
ejpam-3966	178	48	xi	xi	X
ejpam-3966	178	49	→	→	SYM
ejpam-3966	178	50	xi	xi	PROPN
ejpam-3966	178	51	.	.	PUNCT
ejpam-3966	179	1	then	then	ADV
ejpam-3966	179	2	for	for	SCONJ
ejpam-3966	179	3	all	all	DET
ejpam-3966	179	4	j	j	PROPN
ejpam-3966	179	5	∈	∈	PROPN
ejpam-3966	179	6	i	i	PRON
ejpam-3966	179	7	,	,	PUNCT
ejpam-3966	179	8	x	x	X
ejpam-3966	179	9	∩	∩	NOUN
ejpam-3966	179	10	[	[	X
ejpam-3966	179	11	(	(	PUNCT
ejpam-3966	179	12	∏	∏	X
ejpam-3966	179	13	i	i	PRON
ejpam-3966	179	14	6	6	NUM
ejpam-3966	179	15	=	=	SYM
ejpam-3966	179	16	j	j	PROPN
ejpam-3966	179	17	xi	xi	INTJ
ejpam-3966	179	18	)	)	PUNCT
ejpam-3966	179	19	×	×	PROPN
ejpam-3966	179	20	{	{	PUNCT
ejpam-3966	179	21	1xj	1xj	ADV
ejpam-3966	179	22	}	}	PUNCT
ejpam-3966	179	23	]	]	PUNCT
ejpam-3966	179	24	=	=	PUNCT
ejpam-3966	179	25	kerϕj	kerϕj	PROPN
ejpam-3966	179	26	.	.	PUNCT
ejpam-3966	180	1	j.	j.	PROPN
ejpam-3966	180	2	albaracin	albaracin	PROPN
ejpam-3966	180	3	,	,	PUNCT
ejpam-3966	180	4	j.	j.	PROPN
ejpam-3966	180	5	vilela	vilela	PROPN
ejpam-3966	180	6	/	/	SYM
ejpam-3966	180	7	eur	eur	PROPN
ejpam-3966	180	8	.	.	PUNCT
ejpam-3966	181	1	j.	j.	PROPN
ejpam-3966	181	2	pure	pure	PROPN
ejpam-3966	181	3	appl	appl	PROPN
ejpam-3966	181	4	.	.	PROPN
ejpam-3966	181	5	math	math	PROPN
ejpam-3966	181	6	,	,	PUNCT
ejpam-3966	181	7	14	14	NUM
ejpam-3966	181	8	(	(	PUNCT
ejpam-3966	181	9	2	2	NUM
ejpam-3966	181	10	)	)	PUNCT
ejpam-3966	181	11	(	(	PUNCT
ejpam-3966	181	12	2021	2021	NUM
ejpam-3966	181	13	)	)	PUNCT
ejpam-3966	181	14	,	,	PUNCT
ejpam-3966	181	15	423	423	NUM
ejpam-3966	181	16	-	-	SYM
ejpam-3966	181	17	430	430	NUM
ejpam-3966	181	18	427	427	NUM
ejpam-3966	181	19	proof	proof	NOUN
ejpam-3966	181	20	.	.	PUNCT
ejpam-3966	182	1	for	for	ADP
ejpam-3966	182	2	any	any	DET
ejpam-3966	182	3	j	j	PROPN
ejpam-3966	182	4	∈	∈	PROPN
ejpam-3966	183	1	i	i	PRON
ejpam-3966	183	2	,	,	PUNCT
ejpam-3966	183	3	we	we	PRON
ejpam-3966	183	4	have	have	VERB
ejpam-3966	183	5	kerϕj	kerϕj	NOUN
ejpam-3966	183	6	=	=	X
ejpam-3966	183	7	{	{	PUNCT
ejpam-3966	183	8	(	(	PUNCT
ejpam-3966	183	9	xi	xi	NOUN
ejpam-3966	183	10	)	)	PUNCT
ejpam-3966	183	11	∈	∈	PROPN
ejpam-3966	183	12	x	x	X
ejpam-3966	184	1	|	|	ADV
ejpam-3966	184	2	ϕj((xi	ϕj((xi	ADJ
ejpam-3966	184	3	)	)	PUNCT
ejpam-3966	184	4	)	)	PUNCT
ejpam-3966	185	1	=	=	PUNCT
ejpam-3966	185	2	ρj((xi	ρj((xi	NOUN
ejpam-3966	185	3	)	)	PUNCT
ejpam-3966	185	4	)	)	PUNCT
ejpam-3966	186	1	=	=	SYM
ejpam-3966	186	2	xj	xj	PROPN
ejpam-3966	186	3	=	=	SYM
ejpam-3966	186	4	1xj	1xj	PROPN
ejpam-3966	186	5	}	}	PUNCT
ejpam-3966	186	6	=	=	SYM
ejpam-3966	186	7	{	{	PUNCT
ejpam-3966	186	8	(	(	PUNCT
ejpam-3966	186	9	xi	xi	NOUN
ejpam-3966	186	10	)	)	PUNCT
ejpam-3966	186	11	∈	∈	PROPN
ejpam-3966	186	12	x	x	X
ejpam-3966	186	13	|	|	ADV
ejpam-3966	186	14	xj	xj	NOUN
ejpam-3966	186	15	=	=	SYM
ejpam-3966	186	16	1xj	1xj	ADJ
ejpam-3966	186	17	}	}	PUNCT
ejpam-3966	186	18	=	=	SYM
ejpam-3966	187	1	x	x	NOUN
ejpam-3966	187	2	∩	∩	NOUN
ejpam-3966	187	3	∏	∏	PROPN
ejpam-3966	187	4	i	i	PRON
ejpam-3966	187	5	6	6	NUM
ejpam-3966	187	6	=	=	SYM
ejpam-3966	187	7	j	j	PROPN
ejpam-3966	187	8	xi	xi	PROPN
ejpam-3966	187	9	×	×	PROPN
ejpam-3966	187	10	{	{	PUNCT
ejpam-3966	187	11	1xj	1xj	ADV
ejpam-3966	187	12	}	}	PUNCT
ejpam-3966	187	13			NOUN
ejpam-3966	187	14	.	.	PUNCT
ejpam-3966	188	1	3	3	X
ejpam-3966	188	2	.	.	X
ejpam-3966	188	3	completion	completion	NOUN
ejpam-3966	188	4	of	of	ADP
ejpam-3966	188	5	a	a	DET
ejpam-3966	188	6	be	be	NOUN
ejpam-3966	188	7	-	-	PUNCT
ejpam-3966	188	8	algebra	algebra	ADJ
ejpam-3966	188	9	proposition	proposition	NOUN
ejpam-3966	188	10	4	4	NUM
ejpam-3966	188	11	.	.	PUNCT
ejpam-3966	189	1	let	let	VERB
ejpam-3966	189	2	x	x	PRON
ejpam-3966	189	3	be	be	AUX
ejpam-3966	189	4	a	a	DET
ejpam-3966	189	5	be	be	NOUN
ejpam-3966	189	6	-	-	PUNCT
ejpam-3966	189	7	algebra	algebra	NOUN
ejpam-3966	189	8	and	and	CCONJ
ejpam-3966	189	9	i	i	PRON
ejpam-3966	189	10	be	be	VERB
ejpam-3966	189	11	the	the	DET
ejpam-3966	189	12	set	set	NOUN
ejpam-3966	189	13	of	of	ADP
ejpam-3966	189	14	congruences	congruence	NOUN
ejpam-3966	189	15	of	of	ADP
ejpam-3966	189	16	x.	x.	NOUN
ejpam-3966	189	17	then	then	ADV
ejpam-3966	189	18	(	(	PUNCT
ejpam-3966	189	19	i,≤	i,≤	X
ejpam-3966	189	20	)	)	PUNCT
ejpam-3966	189	21	is	be	AUX
ejpam-3966	189	22	a	a	DET
ejpam-3966	189	23	directed	direct	VERB
ejpam-3966	189	24	poset	poset	NOUN
ejpam-3966	189	25	where	where	SCONJ
ejpam-3966	189	26	the	the	DET
ejpam-3966	189	27	binary	binary	PROPN
ejpam-3966	189	28	operation	operation	NOUN
ejpam-3966	189	29	≤	≤	PROPN
ejpam-3966	189	30	on	on	ADP
ejpam-3966	189	31	i	i	PRON
ejpam-3966	189	32	is	be	AUX
ejpam-3966	189	33	defined	define	VERB
ejpam-3966	189	34	by	by	ADP
ejpam-3966	189	35	θ	θ	PROPN
ejpam-3966	189	36	≤	≤	PROPN
ejpam-3966	189	37	φ	φ	NUM
ejpam-3966	189	38	whenever	whenever	SCONJ
ejpam-3966	189	39	φ	φ	PROPN
ejpam-3966	189	40	⊆	⊆	NUM
ejpam-3966	189	41	θ	θ	NOUN
ejpam-3966	189	42	for	for	ADP
ejpam-3966	189	43	all	all	DET
ejpam-3966	189	44	θ	θ	PROPN
ejpam-3966	189	45	,	,	PUNCT
ejpam-3966	189	46	φ	φ	PROPN
ejpam-3966	189	47	∈	∈	PROPN
ejpam-3966	189	48	i.	i.	NOUN
ejpam-3966	189	49	theorem	theorem	VERB
ejpam-3966	189	50	7	7	NUM
ejpam-3966	189	51	.	.	PUNCT
ejpam-3966	190	1	let	let	VERB
ejpam-3966	190	2	x	x	PRON
ejpam-3966	190	3	be	be	AUX
ejpam-3966	190	4	a	a	DET
ejpam-3966	190	5	be	be	NOUN
ejpam-3966	190	6	-	-	PUNCT
ejpam-3966	190	7	algebra	algebra	NOUN
ejpam-3966	190	8	and	and	CCONJ
ejpam-3966	190	9	i	i	PRON
ejpam-3966	190	10	be	be	VERB
ejpam-3966	190	11	the	the	DET
ejpam-3966	190	12	set	set	NOUN
ejpam-3966	190	13	of	of	ADP
ejpam-3966	190	14	congruences	congruence	NOUN
ejpam-3966	190	15	of	of	ADP
ejpam-3966	190	16	x.	x.	NOUN
ejpam-3966	190	17	then	then	ADV
ejpam-3966	190	18	{	{	PUNCT
ejpam-3966	190	19	x	x	X
ejpam-3966	190	20	/	/	SYM
ejpam-3966	190	21	φ	φ	PROPN
ejpam-3966	190	22	,	,	PUNCT
ejpam-3966	190	23	ϕφθ	ϕφθ	PROPN
ejpam-3966	190	24	,	,	PUNCT
ejpam-3966	191	1	i	i	PRON
ejpam-3966	191	2	}	}	PUNCT
ejpam-3966	191	3	is	be	AUX
ejpam-3966	191	4	an	an	DET
ejpam-3966	191	5	inverse	inverse	NOUN
ejpam-3966	191	6	system	system	NOUN
ejpam-3966	191	7	where	where	SCONJ
ejpam-3966	191	8	θ	θ	PROPN
ejpam-3966	191	9	≤	≤	PROPN
ejpam-3966	191	10	φ	φ	NUM
ejpam-3966	192	1	whenever	whenever	SCONJ
ejpam-3966	192	2	φ	φ	PROPN
ejpam-3966	192	3	⊆	⊆	NUM
ejpam-3966	192	4	θ	θ	NOUN
ejpam-3966	192	5	for	for	ADP
ejpam-3966	192	6	all	all	DET
ejpam-3966	192	7	θ	θ	PROPN
ejpam-3966	192	8	,	,	PUNCT
ejpam-3966	192	9	φ	φ	PROPN
ejpam-3966	192	10	∈	∈	PROPN
ejpam-3966	192	11	i	i	PRON
ejpam-3966	192	12	and	and	CCONJ
ejpam-3966	192	13	ϕφθ	ϕφθ	PRON
ejpam-3966	192	14	:	:	PUNCT
ejpam-3966	192	15	x	x	X
ejpam-3966	192	16	/	/	SYM
ejpam-3966	192	17	φ→	φ→	PROPN
ejpam-3966	192	18	x	x	NOUN
ejpam-3966	192	19	/	/	SYM
ejpam-3966	192	20	θ	θ	PROPN
ejpam-3966	192	21	is	be	AUX
ejpam-3966	192	22	the	the	DET
ejpam-3966	192	23	epimorphism	epimorphism	NOUN
ejpam-3966	192	24	defined	define	VERB
ejpam-3966	192	25	by	by	ADP
ejpam-3966	192	26	ϕφθ([x]φ	ϕφθ([x]φ	PROPN
ejpam-3966	192	27	)	)	PUNCT
ejpam-3966	193	1	=	=	PUNCT
ejpam-3966	194	1	[	[	X
ejpam-3966	194	2	x]θ	x]θ	X
ejpam-3966	194	3	.	.	PUNCT
ejpam-3966	195	1	proof	proof	NOUN
ejpam-3966	195	2	.	.	PUNCT
ejpam-3966	196	1	by	by	ADP
ejpam-3966	196	2	proposition	proposition	NOUN
ejpam-3966	196	3	4	4	NUM
ejpam-3966	196	4	,	,	PUNCT
ejpam-3966	196	5	(	(	PUNCT
ejpam-3966	196	6	i,≤	i,≤	X
ejpam-3966	196	7	)	)	PUNCT
ejpam-3966	196	8	is	be	AUX
ejpam-3966	196	9	a	a	DET
ejpam-3966	196	10	directed	direct	VERB
ejpam-3966	196	11	poset	poset	NOUN
ejpam-3966	196	12	.	.	PUNCT
ejpam-3966	197	1	we	we	PRON
ejpam-3966	197	2	will	will	AUX
ejpam-3966	197	3	show	show	VERB
ejpam-3966	197	4	that	that	SCONJ
ejpam-3966	197	5	{	{	PUNCT
ejpam-3966	197	6	x	x	X
ejpam-3966	197	7	/	/	SYM
ejpam-3966	197	8	φ	φ	PROPN
ejpam-3966	197	9	,	,	PUNCT
ejpam-3966	197	10	ϕφθ	ϕφθ	PROPN
ejpam-3966	197	11	,	,	PUNCT
ejpam-3966	197	12	i	i	PRON
ejpam-3966	197	13	}	}	PUNCT
ejpam-3966	197	14	is	be	AUX
ejpam-3966	197	15	an	an	DET
ejpam-3966	197	16	inverse	inverse	NOUN
ejpam-3966	197	17	system	system	NOUN
ejpam-3966	197	18	,	,	PUNCT
ejpam-3966	198	1	that	that	ADV
ejpam-3966	198	2	is	is	ADV
ejpam-3966	198	3	,	,	PUNCT
ejpam-3966	198	4	ϕθλϕφθ	ϕθλϕφθ	NOUN
ejpam-3966	198	5	=	=	PUNCT
ejpam-3966	198	6	ϕφλ	ϕφλ	NOUN
ejpam-3966	199	1	whenever	whenever	SCONJ
ejpam-3966	199	2	φ	φ	PROPN
ejpam-3966	199	3	≥	≥	PROPN
ejpam-3966	199	4	θ	θ	PROPN
ejpam-3966	199	5	≥	≥	NUM
ejpam-3966	199	6	λ	λ	X
ejpam-3966	199	7	.	.	PUNCT
ejpam-3966	199	8	now	now	ADV
ejpam-3966	199	9	,	,	PUNCT
ejpam-3966	199	10	ϕθλϕφθ([x]φ	ϕθλϕφθ([x]φ	PROPN
ejpam-3966	199	11	)	)	PUNCT
ejpam-3966	200	1	=	=	SYM
ejpam-3966	200	2	ϕθλ(ϕφθ([x]φ	ϕθλ(ϕφθ([x]φ	NOUN
ejpam-3966	200	3	)	)	PUNCT
ejpam-3966	200	4	)	)	PUNCT
ejpam-3966	201	1	=	=	PUNCT
ejpam-3966	201	2	ϕθλ([x]θ	ϕθλ([x]θ	PROPN
ejpam-3966	201	3	)	)	PUNCT
ejpam-3966	201	4	=	=	PUNCT
ejpam-3966	202	1	[	[	X
ejpam-3966	202	2	x]λ	x]λ	X
ejpam-3966	202	3	=	=	SYM
ejpam-3966	202	4	ϕφλ([x]φ	ϕφλ([x]φ	PROPN
ejpam-3966	202	5	)	)	PUNCT
ejpam-3966	202	6	.	.	PUNCT
ejpam-3966	203	1	therefore	therefore	ADV
ejpam-3966	203	2	,	,	PUNCT
ejpam-3966	203	3	ϕθλϕφθ	ϕθλϕφθ	NOUN
ejpam-3966	203	4	=	=	PUNCT
ejpam-3966	203	5	ϕφλ	ϕφλ	NOUN
ejpam-3966	203	6	whenever	whenever	SCONJ
ejpam-3966	203	7	φ	φ	PROPN
ejpam-3966	203	8	≥	≥	PROPN
ejpam-3966	203	9	θ	θ	PROPN
ejpam-3966	203	10	≥	≥	NUM
ejpam-3966	203	11	λ	λ	X
ejpam-3966	203	12	.	.	PUNCT
ejpam-3966	203	13	note	note	VERB
ejpam-3966	203	14	that	that	DET
ejpam-3966	203	15	ϕθθ	ϕθθ	NOUN
ejpam-3966	203	16	:	:	PUNCT
ejpam-3966	203	17	x	x	X
ejpam-3966	203	18	/	/	SYM
ejpam-3966	203	19	θ	θ	X
ejpam-3966	203	20	→	→	SYM
ejpam-3966	203	21	x	x	SYM
ejpam-3966	203	22	/	/	SYM
ejpam-3966	203	23	θ	θ	PROPN
ejpam-3966	203	24	is	be	AUX
ejpam-3966	203	25	defined	define	VERB
ejpam-3966	203	26	by	by	ADP
ejpam-3966	203	27	ϕθθ([x]θ	ϕθθ([x]θ	PROPN
ejpam-3966	203	28	)	)	PUNCT
ejpam-3966	203	29	=	=	PUNCT
ejpam-3966	204	1	[	[	X
ejpam-3966	204	2	x]θ	x]θ	X
ejpam-3966	204	3	.	.	PUNCT
ejpam-3966	205	1	thus	thus	ADV
ejpam-3966	205	2	,	,	PUNCT
ejpam-3966	205	3	ϕθθ	ϕθθ	PROPN
ejpam-3966	205	4	=	=	SYM
ejpam-3966	205	5	idx	idx	PROPN
ejpam-3966	205	6	/	/	SYM
ejpam-3966	205	7	θ	θ	NOUN
ejpam-3966	205	8	.	.	PUNCT
ejpam-3966	206	1	therefore	therefore	ADV
ejpam-3966	206	2	,	,	PUNCT
ejpam-3966	206	3	{	{	PUNCT
ejpam-3966	206	4	x	x	X
ejpam-3966	206	5	/	/	SYM
ejpam-3966	206	6	φ	φ	PROPN
ejpam-3966	206	7	,	,	PUNCT
ejpam-3966	206	8	ϕφθ	ϕφθ	PROPN
ejpam-3966	206	9	,	,	PUNCT
ejpam-3966	206	10	i	i	PRON
ejpam-3966	206	11	}	}	PUNCT
ejpam-3966	206	12	is	be	AUX
ejpam-3966	206	13	an	an	DET
ejpam-3966	206	14	inverse	inverse	NOUN
ejpam-3966	206	15	system	system	NOUN
ejpam-3966	206	16	.	.	PUNCT
ejpam-3966	207	1	theorem	theorem	ADJ
ejpam-3966	207	2	8	8	NUM
ejpam-3966	207	3	.	.	PUNCT
ejpam-3966	208	1	let	let	VERB
ejpam-3966	208	2	x	x	PRON
ejpam-3966	208	3	be	be	AUX
ejpam-3966	208	4	a	a	DET
ejpam-3966	208	5	be	be	NOUN
ejpam-3966	208	6	-	-	PUNCT
ejpam-3966	208	7	algebra	algebra	NOUN
ejpam-3966	208	8	and	and	CCONJ
ejpam-3966	208	9	i	i	PRON
ejpam-3966	208	10	be	be	VERB
ejpam-3966	208	11	the	the	DET
ejpam-3966	208	12	set	set	NOUN
ejpam-3966	208	13	of	of	ADP
ejpam-3966	208	14	congruences	congruence	NOUN
ejpam-3966	208	15	on	on	ADP
ejpam-3966	208	16	x.	x.	NOUN
ejpam-3966	208	17	consider	consider	VERB
ejpam-3966	208	18	the	the	DET
ejpam-3966	208	19	inverse	inverse	NOUN
ejpam-3966	208	20	system	system	NOUN
ejpam-3966	208	21	{	{	PUNCT
ejpam-3966	208	22	x	x	NOUN
ejpam-3966	208	23	/	/	SYM
ejpam-3966	208	24	φ	φ	PROPN
ejpam-3966	208	25	,	,	PUNCT
ejpam-3966	208	26	ϕφθ	ϕφθ	PROPN
ejpam-3966	208	27	,	,	PUNCT
ejpam-3966	208	28	i	i	PROPN
ejpam-3966	208	29	}	}	PUNCT
ejpam-3966	208	30	.	.	PUNCT
ejpam-3966	209	1	then	then	ADV
ejpam-3966	209	2	x̂	x̂	PUNCT
ejpam-3966	210	1	=	=	PRON
ejpam-3966	210	2	{	{	PUNCT
ejpam-3966	210	3	(	(	PUNCT
ejpam-3966	210	4	[	[	X
ejpam-3966	210	5	x]φ	x]φ	X
ejpam-3966	210	6	)	)	PUNCT
ejpam-3966	210	7	∈	∈	PROPN
ejpam-3966	210	8	∏	∏	NOUN
ejpam-3966	210	9	φ∈i	φ∈i	NOUN
ejpam-3966	210	10	x	x	X
ejpam-3966	210	11	/	/	SYM
ejpam-3966	210	12	φ	φ	PROPN
ejpam-3966	210	13	|	|	INTJ
ejpam-3966	210	14	for	for	ADP
ejpam-3966	210	15	all	all	DET
ejpam-3966	210	16	φ	φ	NOUN
ejpam-3966	210	17	,	,	PUNCT
ejpam-3966	210	18	θ	θ	PROPN
ejpam-3966	210	19	∈	∈	PROPN
ejpam-3966	210	20	i	i	PRON
ejpam-3966	210	21	such	such	ADJ
ejpam-3966	210	22	that	that	SCONJ
ejpam-3966	210	23	φ	φ	PROPN
ejpam-3966	210	24	≥	≥	PROPN
ejpam-3966	210	25	θ	θ	PROPN
ejpam-3966	210	26	,	,	PUNCT
ejpam-3966	210	27	ϕφθ([x]φ	ϕφθ([x]φ	NUM
ejpam-3966	210	28	)	)	PUNCT
ejpam-3966	210	29	=	=	PUNCT
ejpam-3966	211	1	[	[	X
ejpam-3966	211	2	x]θ	x]θ	ADP
ejpam-3966	211	3	}	}	PUNCT
ejpam-3966	211	4	together	together	ADV
ejpam-3966	211	5	with	with	ADP
ejpam-3966	211	6	the	the	DET
ejpam-3966	211	7	projections	projection	NOUN
ejpam-3966	211	8	ϕφ	ϕφ	ADP
ejpam-3966	211	9	:	:	PUNCT
ejpam-3966	211	10	x̂	x̂	PUNCT
ejpam-3966	211	11	→	→	PUNCT
ejpam-3966	211	12	x	x	X
ejpam-3966	211	13	/	/	SYM
ejpam-3966	211	14	φ	φ	PROPN
ejpam-3966	211	15	for	for	ADP
ejpam-3966	211	16	all	all	DET
ejpam-3966	211	17	φ	φ	PROPN
ejpam-3966	211	18	∈	∈	PROPN
ejpam-3966	211	19	i	i	PRON
ejpam-3966	211	20	is	be	AUX
ejpam-3966	211	21	an	an	DET
ejpam-3966	211	22	inverse	inverse	NOUN
ejpam-3966	211	23	limit	limit	NOUN
ejpam-3966	211	24	of	of	ADP
ejpam-3966	211	25	{	{	PUNCT
ejpam-3966	211	26	x	x	PROPN
ejpam-3966	211	27	/	/	SYM
ejpam-3966	211	28	φ	φ	PROPN
ejpam-3966	211	29	,	,	PUNCT
ejpam-3966	211	30	ϕφθ	ϕφθ	PROPN
ejpam-3966	211	31	,	,	PUNCT
ejpam-3966	211	32	i	i	PROPN
ejpam-3966	211	33	}	}	PUNCT
ejpam-3966	211	34	.	.	PUNCT
ejpam-3966	212	1	proof	proof	NOUN
ejpam-3966	212	2	.	.	PUNCT
ejpam-3966	213	1	the	the	DET
ejpam-3966	213	2	result	result	NOUN
ejpam-3966	213	3	follows	follow	VERB
ejpam-3966	213	4	from	from	ADP
ejpam-3966	213	5	theorem	theorem	ADJ
ejpam-3966	213	6	4	4	NUM
ejpam-3966	213	7	.	.	PUNCT
ejpam-3966	213	8	we	we	PRON
ejpam-3966	213	9	call	call	VERB
ejpam-3966	213	10	x̂	x̂	NOUN
ejpam-3966	213	11	of	of	ADP
ejpam-3966	213	12	theorem	theorem	NOUN
ejpam-3966	213	13	8	8	NUM
ejpam-3966	213	14	as	as	ADP
ejpam-3966	213	15	the	the	DET
ejpam-3966	213	16	completion	completion	NOUN
ejpam-3966	213	17	of	of	ADP
ejpam-3966	213	18	the	the	DET
ejpam-3966	213	19	be	be	NOUN
ejpam-3966	213	20	-	-	PUNCT
ejpam-3966	213	21	algebra	algebra	NOUN
ejpam-3966	213	22	x.	x.	NOUN
ejpam-3966	213	23	lemma	lemma	PROPN
ejpam-3966	214	1	1	1	X
ejpam-3966	214	2	.	.	PUNCT
ejpam-3966	215	1	let	let	VERB
ejpam-3966	215	2	x	x	PRON
ejpam-3966	215	3	be	be	AUX
ejpam-3966	215	4	a	a	DET
ejpam-3966	215	5	be	be	NOUN
ejpam-3966	215	6	-	-	PUNCT
ejpam-3966	215	7	algebra	algebra	NOUN
ejpam-3966	215	8	and	and	CCONJ
ejpam-3966	215	9	{	{	PUNCT
ejpam-3966	215	10	x	x	X
ejpam-3966	215	11	/	/	SYM
ejpam-3966	215	12	φ	φ	PROPN
ejpam-3966	215	13	,	,	PUNCT
ejpam-3966	215	14	ϕφθ	ϕφθ	PROPN
ejpam-3966	215	15	,	,	PUNCT
ejpam-3966	215	16	i	i	PRON
ejpam-3966	215	17	}	}	PUNCT
ejpam-3966	215	18	be	be	VERB
ejpam-3966	215	19	the	the	DET
ejpam-3966	215	20	defining	define	VERB
ejpam-3966	215	21	inverse	inverse	NOUN
ejpam-3966	215	22	system	system	NOUN
ejpam-3966	215	23	of	of	ADP
ejpam-3966	215	24	the	the	DET
ejpam-3966	215	25	completion	completion	NOUN
ejpam-3966	215	26	x̂	x̂	NUM
ejpam-3966	215	27	of	of	ADP
ejpam-3966	215	28	x.	x.	NOUN
ejpam-3966	215	29	then	then	ADV
ejpam-3966	216	1	the	the	DET
ejpam-3966	216	2	canonical	canonical	ADJ
ejpam-3966	216	3	epimorphisms	epimorphism	NOUN
ejpam-3966	216	4	ϕθ	ϕθ	INTJ
ejpam-3966	216	5	:	:	PUNCT
ejpam-3966	216	6	x	x	X
ejpam-3966	216	7	→	→	SYM
ejpam-3966	216	8	x	x	SYM
ejpam-3966	216	9	/	/	SYM
ejpam-3966	216	10	θ	θ	NOUN
ejpam-3966	216	11	are	be	AUX
ejpam-3966	216	12	compatible	compatible	ADJ
ejpam-3966	216	13	where	where	SCONJ
ejpam-3966	216	14	θ	θ	PROPN
ejpam-3966	216	15	∈	∈	PROPN
ejpam-3966	216	16	i.	i.	NOUN
ejpam-3966	216	17	proof	proof	NOUN
ejpam-3966	216	18	.	.	PUNCT
ejpam-3966	217	1	let	let	VERB
ejpam-3966	217	2	x	x	SYM
ejpam-3966	217	3	∈	∈	PROPN
ejpam-3966	217	4	x.	x.	NOUN
ejpam-3966	217	5	then	then	ADV
ejpam-3966	217	6	ϕφθ(ϕφ(x	ϕφθ(ϕφ(x	PROPN
ejpam-3966	217	7	)	)	PUNCT
ejpam-3966	217	8	)	)	PUNCT
ejpam-3966	218	1	=	=	PUNCT
ejpam-3966	218	2	ϕφθ([x]φ	ϕφθ([x]φ	X
ejpam-3966	218	3	)	)	PUNCT
ejpam-3966	218	4	=	=	PUNCT
ejpam-3966	219	1	[	[	X
ejpam-3966	219	2	x]θ	x]θ	X
ejpam-3966	219	3	=	=	SYM
ejpam-3966	219	4	ϕθ(x	ϕθ(x	X
ejpam-3966	219	5	)	)	PUNCT
ejpam-3966	219	6	whenever	whenever	SCONJ
ejpam-3966	219	7	φ	φ	PROPN
ejpam-3966	219	8	≥	≥	PROPN
ejpam-3966	219	9	θ	θ	PROPN
ejpam-3966	219	10	.	.	PUNCT
ejpam-3966	219	11	therefore	therefore	ADV
ejpam-3966	219	12	,	,	PUNCT
ejpam-3966	219	13	the	the	DET
ejpam-3966	219	14	canonical	canonical	ADJ
ejpam-3966	219	15	epimorphisms	epimorphism	NOUN
ejpam-3966	219	16	ϕθ	ϕθ	NOUN
ejpam-3966	219	17	’s	’	VERB
ejpam-3966	219	18	are	be	AUX
ejpam-3966	219	19	compatible	compatible	ADJ
ejpam-3966	219	20	.	.	PUNCT
ejpam-3966	220	1	theorem	theorem	NOUN
ejpam-3966	220	2	9	9	NUM
ejpam-3966	220	3	.	.	PUNCT
ejpam-3966	221	1	let	let	VERB
ejpam-3966	221	2	x	x	PRON
ejpam-3966	221	3	be	be	AUX
ejpam-3966	221	4	a	a	DET
ejpam-3966	221	5	be	be	NOUN
ejpam-3966	221	6	-	-	PUNCT
ejpam-3966	221	7	algebra	algebra	NOUN
ejpam-3966	221	8	and	and	CCONJ
ejpam-3966	221	9	{	{	PUNCT
ejpam-3966	221	10	x	x	X
ejpam-3966	221	11	/	/	SYM
ejpam-3966	221	12	φ	φ	PROPN
ejpam-3966	221	13	,	,	PUNCT
ejpam-3966	221	14	ϕφθ	ϕφθ	PROPN
ejpam-3966	221	15	,	,	PUNCT
ejpam-3966	221	16	i	i	PRON
ejpam-3966	221	17	}	}	PUNCT
ejpam-3966	221	18	be	be	VERB
ejpam-3966	221	19	the	the	DET
ejpam-3966	221	20	defining	define	VERB
ejpam-3966	221	21	inverse	inverse	NOUN
ejpam-3966	221	22	system	system	NOUN
ejpam-3966	221	23	of	of	ADP
ejpam-3966	221	24	the	the	DET
ejpam-3966	221	25	completion	completion	NOUN
ejpam-3966	221	26	x̂	x̂	NUM
ejpam-3966	221	27	of	of	ADP
ejpam-3966	221	28	x.	x.	NOUN
ejpam-3966	221	29	then	then	ADV
ejpam-3966	222	1	the	the	DET
ejpam-3966	222	2	canonical	canonical	ADJ
ejpam-3966	222	3	epimorphisms	epimorphism	NOUN
ejpam-3966	222	4	ϕθ	ϕθ	INTJ
ejpam-3966	222	5	:	:	PUNCT
ejpam-3966	222	6	x	x	X
ejpam-3966	222	7	→	→	SYM
ejpam-3966	222	8	x	x	SYM
ejpam-3966	222	9	/	/	SYM
ejpam-3966	222	10	θ	θ	NOUN
ejpam-3966	222	11	induce	induce	VERB
ejpam-3966	222	12	a	a	DET
ejpam-3966	222	13	homomorphism	homomorphism	NOUN
ejpam-3966	222	14	γ	γ	X
ejpam-3966	222	15	:	:	PUNCT
ejpam-3966	222	16	x	x	SYM
ejpam-3966	222	17	→	→	SYM
ejpam-3966	222	18	x̂	x̂	NUM
ejpam-3966	222	19	defined	define	VERB
ejpam-3966	222	20	by	by	ADP
ejpam-3966	222	21	γ(x	γ(x	NOUN
ejpam-3966	222	22	)	)	PUNCT
ejpam-3966	222	23	=	=	SYM
ejpam-3966	222	24	(	(	PUNCT
ejpam-3966	222	25	ϕθ(x	ϕθ(x	NUM
ejpam-3966	222	26	)	)	PUNCT
ejpam-3966	222	27	)	)	PUNCT
ejpam-3966	223	1	=	=	PUNCT
ejpam-3966	223	2	(	(	PUNCT
ejpam-3966	223	3	[	[	X
ejpam-3966	223	4	x]θ	x]θ	NOUN
ejpam-3966	223	5	)	)	PUNCT
ejpam-3966	223	6	.	.	PUNCT
ejpam-3966	224	1	j.	j.	PROPN
ejpam-3966	224	2	albaracin	albaracin	PROPN
ejpam-3966	224	3	,	,	PUNCT
ejpam-3966	224	4	j.	j.	PROPN
ejpam-3966	224	5	vilela	vilela	PROPN
ejpam-3966	224	6	/	/	SYM
ejpam-3966	224	7	eur	eur	PROPN
ejpam-3966	224	8	.	.	PUNCT
ejpam-3966	225	1	j.	j.	PROPN
ejpam-3966	225	2	pure	pure	PROPN
ejpam-3966	225	3	appl	appl	PROPN
ejpam-3966	225	4	.	.	PROPN
ejpam-3966	225	5	math	math	PROPN
ejpam-3966	225	6	,	,	PUNCT
ejpam-3966	225	7	14	14	NUM
ejpam-3966	225	8	(	(	PUNCT
ejpam-3966	225	9	2	2	NUM
ejpam-3966	225	10	)	)	PUNCT
ejpam-3966	225	11	(	(	PUNCT
ejpam-3966	225	12	2021	2021	NUM
ejpam-3966	225	13	)	)	PUNCT
ejpam-3966	225	14	,	,	PUNCT
ejpam-3966	225	15	423	423	NUM
ejpam-3966	225	16	-	-	SYM
ejpam-3966	225	17	430	430	NUM
ejpam-3966	225	18	428	428	NUM
ejpam-3966	225	19	proof	proof	NOUN
ejpam-3966	225	20	.	.	PUNCT
ejpam-3966	226	1	by	by	ADP
ejpam-3966	226	2	lemma	lemma	PROPN
ejpam-3966	226	3	1	1	NUM
ejpam-3966	226	4	,	,	PUNCT
ejpam-3966	226	5	{	{	PUNCT
ejpam-3966	226	6	ϕθ	ϕθ	NOUN
ejpam-3966	226	7	:	:	PUNCT
ejpam-3966	226	8	x	x	X
ejpam-3966	226	9	→	→	SYM
ejpam-3966	226	10	x	x	SYM
ejpam-3966	226	11	/	/	SYM
ejpam-3966	226	12	θ	θ	NOUN
ejpam-3966	226	13	}	}	PUNCT
ejpam-3966	226	14	is	be	AUX
ejpam-3966	226	15	a	a	DET
ejpam-3966	226	16	set	set	NOUN
ejpam-3966	226	17	of	of	ADP
ejpam-3966	226	18	compatible	compatible	ADJ
ejpam-3966	226	19	homomorphism	homomorphism	NOUN
ejpam-3966	226	20	.	.	PUNCT
ejpam-3966	227	1	since	since	SCONJ
ejpam-3966	227	2	x	x	PRON
ejpam-3966	227	3	is	be	AUX
ejpam-3966	227	4	a	a	DET
ejpam-3966	227	5	be	be	NOUN
ejpam-3966	227	6	-	-	PUNCT
ejpam-3966	227	7	algebra	algebra	NOUN
ejpam-3966	227	8	and	and	CCONJ
ejpam-3966	227	9	x̂	x̂	PUNCT
ejpam-3966	228	1	=	=	PUNCT
ejpam-3966	228	2	lim←−x	lim←−x	PROPN
ejpam-3966	228	3	/	/	SYM
ejpam-3966	228	4	θ	θ	PROPN
ejpam-3966	228	5	,	,	PUNCT
ejpam-3966	228	6	by	by	ADP
ejpam-3966	228	7	definition	definition	NOUN
ejpam-3966	228	8	4	4	NUM
ejpam-3966	228	9	and	and	CCONJ
ejpam-3966	228	10	from	from	ADP
ejpam-3966	228	11	the	the	DET
ejpam-3966	228	12	proof	proof	NOUN
ejpam-3966	228	13	of	of	ADP
ejpam-3966	228	14	theorem	theorem	NOUN
ejpam-3966	228	15	4	4	NUM
ejpam-3966	228	16	,	,	PUNCT
ejpam-3966	228	17	there	there	PRON
ejpam-3966	228	18	exists	exist	VERB
ejpam-3966	228	19	a	a	DET
ejpam-3966	228	20	homomorphism	homomorphism	NOUN
ejpam-3966	228	21	γ	γ	X
ejpam-3966	228	22	:	:	PUNCT
ejpam-3966	228	23	x	x	SYM
ejpam-3966	228	24	→	→	SYM
ejpam-3966	228	25	x̂	x̂	NUM
ejpam-3966	228	26	with	with	ADP
ejpam-3966	228	27	γ(x	γ(x	NOUN
ejpam-3966	228	28	)	)	PUNCT
ejpam-3966	228	29	=	=	SYM
ejpam-3966	228	30	(	(	PUNCT
ejpam-3966	228	31	ϕθ(x	ϕθ(x	NUM
ejpam-3966	228	32	)	)	PUNCT
ejpam-3966	228	33	)	)	PUNCT
ejpam-3966	229	1	=	=	PUNCT
ejpam-3966	229	2	(	(	PUNCT
ejpam-3966	229	3	[	[	X
ejpam-3966	229	4	x]θ	x]θ	X
ejpam-3966	229	5	)	)	PUNCT
ejpam-3966	229	6	for	for	ADP
ejpam-3966	229	7	each	each	PRON
ejpam-3966	229	8	x	x	SYM
ejpam-3966	229	9	∈	∈	PROPN
ejpam-3966	229	10	x.	x.	NOUN
ejpam-3966	229	11	theorem	theorem	VERB
ejpam-3966	229	12	10	10	NUM
ejpam-3966	229	13	.	.	PUNCT
ejpam-3966	230	1	let	let	VERB
ejpam-3966	230	2	x	x	PRON
ejpam-3966	230	3	be	be	AUX
ejpam-3966	230	4	a	a	DET
ejpam-3966	230	5	be	be	NOUN
ejpam-3966	230	6	-	-	PUNCT
ejpam-3966	230	7	algebra	algebra	NOUN
ejpam-3966	230	8	and	and	CCONJ
ejpam-3966	230	9	{	{	PUNCT
ejpam-3966	230	10	x	x	X
ejpam-3966	230	11	/	/	SYM
ejpam-3966	230	12	φ	φ	PROPN
ejpam-3966	230	13	,	,	PUNCT
ejpam-3966	230	14	ϕφθ	ϕφθ	PROPN
ejpam-3966	230	15	,	,	PUNCT
ejpam-3966	230	16	i	i	PRON
ejpam-3966	230	17	}	}	PUNCT
ejpam-3966	230	18	be	be	VERB
ejpam-3966	230	19	the	the	DET
ejpam-3966	230	20	defining	define	VERB
ejpam-3966	230	21	inverse	inverse	NOUN
ejpam-3966	230	22	system	system	NOUN
ejpam-3966	230	23	of	of	ADP
ejpam-3966	230	24	the	the	DET
ejpam-3966	230	25	completion	completion	NOUN
ejpam-3966	230	26	x̂	x̂	NUM
ejpam-3966	230	27	of	of	ADP
ejpam-3966	230	28	x.	x.	PROPN
ejpam-3966	230	29	then	then	ADV
ejpam-3966	230	30	γ−1(([x]θ	γ−1(([x]θ	PROPN
ejpam-3966	230	31	)	)	PUNCT
ejpam-3966	230	32	)	)	PUNCT
ejpam-3966	231	1	=	=	SYM
ejpam-3966	231	2	⋂	⋂	PROPN
ejpam-3966	231	3	θ∈i	θ∈i	X
ejpam-3966	231	4	[	[	X
ejpam-3966	231	5	x]θ	x]θ	ADV
ejpam-3966	231	6	for	for	ADP
ejpam-3966	231	7	all	all	DET
ejpam-3966	231	8	(	(	PUNCT
ejpam-3966	231	9	[	[	X
ejpam-3966	231	10	x]θ	x]θ	ADJ
ejpam-3966	231	11	)	)	PUNCT
ejpam-3966	231	12	∈	∈	NOUN
ejpam-3966	231	13	x̂.	x̂.	NOUN
ejpam-3966	231	14	proof	proof	NOUN
ejpam-3966	231	15	.	.	PUNCT
ejpam-3966	232	1	let	let	VERB
ejpam-3966	232	2	y	y	PROPN
ejpam-3966	232	3	∈	∈	PROPN
ejpam-3966	232	4	γ−1(([x]θ	γ−1(([x]θ	PROPN
ejpam-3966	232	5	)	)	PUNCT
ejpam-3966	232	6	)	)	PUNCT
ejpam-3966	232	7	.	.	PUNCT
ejpam-3966	233	1	then	then	ADV
ejpam-3966	233	2	γ(y	γ(y	PROPN
ejpam-3966	233	3	)	)	PUNCT
ejpam-3966	234	1	=	=	PUNCT
ejpam-3966	235	1	(	(	PUNCT
ejpam-3966	235	2	[	[	X
ejpam-3966	235	3	x]θ	x]θ	NOUN
ejpam-3966	235	4	)	)	PUNCT
ejpam-3966	235	5	.	.	PUNCT
ejpam-3966	236	1	by	by	ADP
ejpam-3966	236	2	the	the	DET
ejpam-3966	236	3	definition	definition	NOUN
ejpam-3966	236	4	of	of	ADP
ejpam-3966	236	5	γ	γ	PROPN
ejpam-3966	236	6	,	,	PUNCT
ejpam-3966	236	7	γ(y	γ(y	PROPN
ejpam-3966	236	8	)	)	PUNCT
ejpam-3966	236	9	=	=	PUNCT
ejpam-3966	237	1	(	(	PUNCT
ejpam-3966	237	2	[	[	X
ejpam-3966	237	3	y]θ	y]θ	NOUN
ejpam-3966	237	4	)	)	PUNCT
ejpam-3966	237	5	.	.	PUNCT
ejpam-3966	238	1	thus	thus	ADV
ejpam-3966	238	2	,	,	PUNCT
ejpam-3966	238	3	(	(	PUNCT
ejpam-3966	238	4	[	[	X
ejpam-3966	238	5	y]θ	y]θ	NOUN
ejpam-3966	238	6	)	)	PUNCT
ejpam-3966	238	7	=	=	SYM
ejpam-3966	238	8	(	(	PUNCT
ejpam-3966	238	9	[	[	X
ejpam-3966	238	10	x]θ	x]θ	NOUN
ejpam-3966	238	11	)	)	PUNCT
ejpam-3966	238	12	.	.	PUNCT
ejpam-3966	239	1	hence	hence	ADV
ejpam-3966	239	2	,	,	PUNCT
ejpam-3966	240	1	[	[	X
ejpam-3966	240	2	y]θ	y]θ	NOUN
ejpam-3966	240	3	=	=	PUNCT
ejpam-3966	241	1	[	[	X
ejpam-3966	241	2	x]θ	x]θ	ADV
ejpam-3966	241	3	for	for	ADP
ejpam-3966	241	4	all	all	DET
ejpam-3966	241	5	θ	θ	PROPN
ejpam-3966	241	6	∈	∈	PROPN
ejpam-3966	241	7	i.	i.	NOUN
ejpam-3966	241	8	this	this	PRON
ejpam-3966	241	9	implies	imply	VERB
ejpam-3966	241	10	that	that	SCONJ
ejpam-3966	241	11	y	y	PROPN
ejpam-3966	241	12	∈	∈	PROPN
ejpam-3966	241	13	⋂	⋂	PROPN
ejpam-3966	241	14	θ∈i	θ∈i	NOUN
ejpam-3966	241	15	[	[	X
ejpam-3966	241	16	x]θ	x]θ	NOUN
ejpam-3966	241	17	.	.	PUNCT
ejpam-3966	242	1	it	it	PRON
ejpam-3966	242	2	follows	follow	VERB
ejpam-3966	242	3	that	that	PRON
ejpam-3966	242	4	γ−1(([x]θ	γ−1(([x]θ	NOUN
ejpam-3966	242	5	)	)	PUNCT
ejpam-3966	242	6	)	)	PUNCT
ejpam-3966	243	1	⊆	⊆	NUM
ejpam-3966	243	2	⋂	⋂	PROPN
ejpam-3966	243	3	θ∈i	θ∈i	NOUN
ejpam-3966	243	4	[	[	X
ejpam-3966	243	5	x]θ	x]θ	X
ejpam-3966	243	6	.	.	PUNCT
ejpam-3966	244	1	let	let	VERB
ejpam-3966	244	2	y	y	PROPN
ejpam-3966	244	3	∈	∈	PROPN
ejpam-3966	244	4	⋂	⋂	PROPN
ejpam-3966	244	5	θ∈i	θ∈i	NOUN
ejpam-3966	244	6	[	[	X
ejpam-3966	244	7	x]θ	x]θ	NOUN
ejpam-3966	244	8	.	.	PUNCT
ejpam-3966	245	1	then	then	ADV
ejpam-3966	245	2	y	y	PROPN
ejpam-3966	245	3	∈	∈	PROPN
ejpam-3966	246	1	[	[	X
ejpam-3966	246	2	x]θ	x]θ	ADV
ejpam-3966	246	3	for	for	ADP
ejpam-3966	246	4	all	all	DET
ejpam-3966	246	5	θ	θ	PROPN
ejpam-3966	246	6	∈	∈	PROPN
ejpam-3966	246	7	i.	i.	NOUN
ejpam-3966	246	8	thus	thus	ADV
ejpam-3966	246	9	,	,	PUNCT
ejpam-3966	247	1	[	[	X
ejpam-3966	247	2	y]θ	y]θ	NOUN
ejpam-3966	247	3	=	=	PUNCT
ejpam-3966	248	1	[	[	X
ejpam-3966	248	2	x]θ	x]θ	ADV
ejpam-3966	248	3	for	for	ADP
ejpam-3966	248	4	all	all	DET
ejpam-3966	248	5	θ	θ	PROPN
ejpam-3966	248	6	∈	∈	PROPN
ejpam-3966	248	7	i.	i.	NOUN
ejpam-3966	248	8	hence	hence	ADV
ejpam-3966	248	9	,	,	PUNCT
ejpam-3966	248	10	(	(	PUNCT
ejpam-3966	248	11	[	[	X
ejpam-3966	248	12	y]θ	y]θ	NOUN
ejpam-3966	248	13	)	)	PUNCT
ejpam-3966	248	14	=	=	SYM
ejpam-3966	249	1	(	(	PUNCT
ejpam-3966	249	2	[	[	X
ejpam-3966	249	3	x]θ	x]θ	NOUN
ejpam-3966	249	4	)	)	PUNCT
ejpam-3966	249	5	.	.	PUNCT
ejpam-3966	250	1	since	since	SCONJ
ejpam-3966	250	2	γ(y	γ(y	PROPN
ejpam-3966	250	3	)	)	PUNCT
ejpam-3966	250	4	=	=	PUNCT
ejpam-3966	251	1	(	(	PUNCT
ejpam-3966	251	2	[	[	X
ejpam-3966	251	3	y]θ	y]θ	NOUN
ejpam-3966	251	4	)	)	PUNCT
ejpam-3966	251	5	,	,	PUNCT
ejpam-3966	251	6	it	it	PRON
ejpam-3966	251	7	follows	follow	VERB
ejpam-3966	251	8	that	that	SCONJ
ejpam-3966	251	9	γ(y	γ(y	NOUN
ejpam-3966	251	10	)	)	PUNCT
ejpam-3966	252	1	=	=	PUNCT
ejpam-3966	252	2	(	(	PUNCT
ejpam-3966	252	3	[	[	X
ejpam-3966	252	4	x]θ	x]θ	NOUN
ejpam-3966	252	5	)	)	PUNCT
ejpam-3966	252	6	.	.	PUNCT
ejpam-3966	253	1	hence	hence	ADV
ejpam-3966	253	2	,	,	PUNCT
ejpam-3966	253	3	y	y	PROPN
ejpam-3966	253	4	∈	∈	PROPN
ejpam-3966	253	5	γ−1(([x]θ	γ−1(([x]θ	PROPN
ejpam-3966	253	6	)	)	PUNCT
ejpam-3966	253	7	)	)	PUNCT
ejpam-3966	253	8	.	.	PUNCT
ejpam-3966	254	1	therefore	therefore	ADV
ejpam-3966	254	2	,	,	PUNCT
ejpam-3966	254	3	⋂	⋂	PROPN
ejpam-3966	254	4	θ∈i	θ∈i	NOUN
ejpam-3966	254	5	[	[	X
ejpam-3966	254	6	x]θ	x]θ	ADP
ejpam-3966	254	7	⊆	⊆	NUM
ejpam-3966	254	8	γ−1(([x]θ	γ−1(([x]θ	NOUN
ejpam-3966	254	9	)	)	PUNCT
ejpam-3966	254	10	)	)	PUNCT
ejpam-3966	254	11	.	.	PUNCT
ejpam-3966	255	1	suppose	suppose	VERB
ejpam-3966	255	2	x	x	PRON
ejpam-3966	255	3	is	be	AUX
ejpam-3966	255	4	commutative	commutative	ADJ
ejpam-3966	255	5	be	be	AUX
ejpam-3966	255	6	-	-	PUNCT
ejpam-3966	255	7	algebra	algebra	NOUN
ejpam-3966	255	8	.	.	PUNCT
ejpam-3966	256	1	by	by	ADP
ejpam-3966	256	2	theorem	theorem	NOUN
ejpam-3966	256	3	3	3	NUM
ejpam-3966	256	4	,	,	PUNCT
ejpam-3966	256	5	there	there	PRON
ejpam-3966	256	6	is	be	VERB
ejpam-3966	256	7	a	a	DET
ejpam-3966	256	8	one	one	NUM
ejpam-3966	256	9	to	to	ADP
ejpam-3966	256	10	one	one	NUM
ejpam-3966	256	11	correspondence	correspondence	NOUN
ejpam-3966	256	12	between	between	ADP
ejpam-3966	256	13	the	the	DET
ejpam-3966	256	14	set	set	NOUN
ejpam-3966	256	15	of	of	ADP
ejpam-3966	256	16	congruences	congruence	NOUN
ejpam-3966	256	17	of	of	ADP
ejpam-3966	256	18	x	x	X
ejpam-3966	256	19	and	and	CCONJ
ejpam-3966	256	20	the	the	DET
ejpam-3966	256	21	set	set	NOUN
ejpam-3966	256	22	of	of	ADP
ejpam-3966	256	23	filters	filter	NOUN
ejpam-3966	256	24	of	of	ADP
ejpam-3966	256	25	x.	x.	NOUN
ejpam-3966	256	26	for	for	ADP
ejpam-3966	256	27	every	every	DET
ejpam-3966	256	28	congruence	congruence	ADJ
ejpam-3966	256	29	θ	θ	NOUN
ejpam-3966	256	30	,	,	PUNCT
ejpam-3966	256	31	there	there	PRON
ejpam-3966	256	32	is	be	VERB
ejpam-3966	256	33	a	a	DET
ejpam-3966	256	34	corresponding	corresponding	ADJ
ejpam-3966	256	35	≡f	≡f	NOUN
ejpam-3966	256	36	,	,	PUNCT
ejpam-3966	256	37	where	where	SCONJ
ejpam-3966	256	38	f	f	PROPN
ejpam-3966	256	39	is	be	AUX
ejpam-3966	256	40	a	a	DET
ejpam-3966	256	41	filter	filter	NOUN
ejpam-3966	256	42	,	,	PUNCT
ejpam-3966	256	43	such	such	ADJ
ejpam-3966	256	44	that	that	SCONJ
ejpam-3966	256	45	θ	θ	PROPN
ejpam-3966	256	46	=	=	SYM
ejpam-3966	256	47	≡f	≡f	NOUN
ejpam-3966	256	48	.	.	PUNCT
ejpam-3966	257	1	with	with	ADP
ejpam-3966	257	2	this	this	PRON
ejpam-3966	257	3	,	,	PUNCT
ejpam-3966	257	4	we	we	PRON
ejpam-3966	257	5	can	can	AUX
ejpam-3966	257	6	just	just	ADV
ejpam-3966	257	7	write	write	VERB
ejpam-3966	257	8	every	every	DET
ejpam-3966	257	9	congruence	congruence	ADJ
ejpam-3966	257	10	θ	θ	PROPN
ejpam-3966	257	11	as	as	ADP
ejpam-3966	257	12	a	a	DET
ejpam-3966	257	13	filter	filter	NOUN
ejpam-3966	257	14	f	f	NOUN
ejpam-3966	257	15	in	in	ADP
ejpam-3966	257	16	x.	x.	PROPN
ejpam-3966	257	17	theorem	theorem	VERB
ejpam-3966	257	18	11	11	NUM
ejpam-3966	257	19	.	.	PUNCT
ejpam-3966	258	1	let	let	VERB
ejpam-3966	258	2	x	x	PRON
ejpam-3966	258	3	be	be	AUX
ejpam-3966	258	4	a	a	DET
ejpam-3966	258	5	commutative	commutative	ADJ
ejpam-3966	258	6	be	be	NOUN
ejpam-3966	258	7	-	-	PUNCT
ejpam-3966	258	8	algebra	algebra	NOUN
ejpam-3966	258	9	and	and	CCONJ
ejpam-3966	258	10	let	let	VERB
ejpam-3966	258	11	{	{	PUNCT
ejpam-3966	258	12	fi	fi	NOUN
ejpam-3966	259	1	|	|	INTJ
ejpam-3966	259	2	i	i	PRON
ejpam-3966	259	3	∈	∈	PROPN
ejpam-3966	259	4	i	i	PRON
ejpam-3966	259	5	}	}	PUNCT
ejpam-3966	259	6	be	be	VERB
ejpam-3966	259	7	the	the	DET
ejpam-3966	259	8	family	family	NOUN
ejpam-3966	259	9	of	of	ADP
ejpam-3966	259	10	filters	filter	NOUN
ejpam-3966	259	11	of	of	ADP
ejpam-3966	259	12	x	x	INTJ
ejpam-3966	259	13	such	such	ADJ
ejpam-3966	259	14	that	that	DET
ejpam-3966	259	15	fi	fi	NOUN
ejpam-3966	259	16	⊆	⊆	NUM
ejpam-3966	259	17	fj	fj	INTJ
ejpam-3966	260	1	whenever	whenever	SCONJ
ejpam-3966	260	2	i	i	PRON
ejpam-3966	260	3	≥	≥	VERB
ejpam-3966	260	4	j.	j.	PROPN
ejpam-3966	260	5	then	then	ADV
ejpam-3966	260	6	kerγ	kerγ	VERB
ejpam-3966	261	1	=	=	PUNCT
ejpam-3966	261	2	⋂	⋂	PROPN
ejpam-3966	261	3	i∈i	i∈i	ADJ
ejpam-3966	261	4	fi	fi	NOUN
ejpam-3966	261	5	.	.	PUNCT
ejpam-3966	262	1	proof	proof	NOUN
ejpam-3966	262	2	.	.	PUNCT
ejpam-3966	263	1	let	let	VERB
ejpam-3966	263	2	x	x	PRON
ejpam-3966	263	3	be	be	AUX
ejpam-3966	263	4	a	a	DET
ejpam-3966	263	5	commutative	commutative	ADJ
ejpam-3966	263	6	be	be	NOUN
ejpam-3966	263	7	-	-	PUNCT
ejpam-3966	263	8	algebra	algebra	NOUN
ejpam-3966	263	9	.	.	PUNCT
ejpam-3966	264	1	then	then	ADV
ejpam-3966	264	2	kerγ	kerγ	VERB
ejpam-3966	264	3	=	=	PUNCT
ejpam-3966	264	4	{	{	PUNCT
ejpam-3966	264	5	x	x	SYM
ejpam-3966	264	6	∈	∈	PROPN
ejpam-3966	264	7	x	x	X
ejpam-3966	264	8	|	|	ADV
ejpam-3966	264	9	γ(x	γ(x	VERB
ejpam-3966	264	10	)	)	PUNCT
ejpam-3966	264	11	=	=	SYM
ejpam-3966	265	1	(	(	PUNCT
ejpam-3966	265	2	[	[	X
ejpam-3966	265	3	1x	1x	X
ejpam-3966	265	4	]	]	SYM
ejpam-3966	265	5	fi	fi	NOUN
ejpam-3966	265	6	)	)	PUNCT
ejpam-3966	265	7	∀i	∀i	NOUN
ejpam-3966	265	8	∈	∈	NOUN
ejpam-3966	265	9	i	i	NOUN
ejpam-3966	265	10	}	}	PUNCT
ejpam-3966	265	11	=	=	PUNCT
ejpam-3966	265	12	{	{	PUNCT
ejpam-3966	265	13	x	x	PUNCT
ejpam-3966	265	14	∈	∈	NOUN
ejpam-3966	265	15	x	x	INTJ
ejpam-3966	265	16	|	|	INTJ
ejpam-3966	265	17	(	(	PUNCT
ejpam-3966	265	18	[	[	X
ejpam-3966	265	19	x]fi	x]fi	X
ejpam-3966	265	20	)	)	PUNCT
ejpam-3966	265	21	=	=	SYM
ejpam-3966	265	22	(	(	PUNCT
ejpam-3966	265	23	[	[	X
ejpam-3966	265	24	1x	1x	X
ejpam-3966	265	25	]	]	SYM
ejpam-3966	265	26	fi	fi	NOUN
ejpam-3966	265	27	)	)	PUNCT
ejpam-3966	265	28	∀i	∀i	NOUN
ejpam-3966	265	29	∈	∈	NOUN
ejpam-3966	265	30	i	i	NOUN
ejpam-3966	265	31	}	}	PUNCT
ejpam-3966	265	32	=	=	PUNCT
ejpam-3966	265	33	{	{	PUNCT
ejpam-3966	265	34	x	x	PUNCT
ejpam-3966	265	35	∈	∈	NOUN
ejpam-3966	265	36	x	x	PUNCT
ejpam-3966	265	37	|	|	ADV
ejpam-3966	265	38	x	x	X
ejpam-3966	265	39	∈	∈	PROPN
ejpam-3966	266	1	[	[	X
ejpam-3966	266	2	1x	1x	X
ejpam-3966	266	3	]	]	X
ejpam-3966	266	4	fi	fi	NOUN
ejpam-3966	266	5	=	=	NOUN
ejpam-3966	266	6	fi	fi	NOUN
ejpam-3966	266	7	∀i	∀i	NOUN
ejpam-3966	266	8	∈	∈	NOUN
ejpam-3966	266	9	i	i	NOUN
ejpam-3966	266	10	}	}	PUNCT
ejpam-3966	266	11	=	=	SYM
ejpam-3966	266	12	⋂	⋂	PROPN
ejpam-3966	266	13	i∈i	i∈i	ADJ
ejpam-3966	266	14	fi	fi	NOUN
ejpam-3966	266	15	.	.	PUNCT
ejpam-3966	267	1	lemma	lemma	PROPN
ejpam-3966	267	2	2	2	X
ejpam-3966	267	3	.	.	PUNCT
ejpam-3966	268	1	let	let	VERB
ejpam-3966	268	2	x	x	PRON
ejpam-3966	268	3	be	be	AUX
ejpam-3966	268	4	a	a	DET
ejpam-3966	268	5	be	be	NOUN
ejpam-3966	268	6	-	-	PUNCT
ejpam-3966	268	7	algebra	algebra	NOUN
ejpam-3966	268	8	.	.	PUNCT
ejpam-3966	269	1	if	if	SCONJ
ejpam-3966	269	2	f	f	PROPN
ejpam-3966	269	3	and	and	CCONJ
ejpam-3966	269	4	g	g	PROPN
ejpam-3966	269	5	are	be	AUX
ejpam-3966	269	6	normal	normal	ADJ
ejpam-3966	269	7	filters	filter	NOUN
ejpam-3966	269	8	of	of	ADP
ejpam-3966	269	9	x	x	NOUN
ejpam-3966	269	10	,	,	PUNCT
ejpam-3966	269	11	then	then	ADV
ejpam-3966	269	12	f	f	PROPN
ejpam-3966	269	13	∩	∩	PROPN
ejpam-3966	269	14	g	g	PROPN
ejpam-3966	269	15	is	be	AUX
ejpam-3966	269	16	also	also	ADV
ejpam-3966	269	17	a	a	DET
ejpam-3966	269	18	normal	normal	ADJ
ejpam-3966	269	19	filter	filter	NOUN
ejpam-3966	269	20	of	of	ADP
ejpam-3966	269	21	x.	x.	PROPN
ejpam-3966	269	22	theorem	theorem	VERB
ejpam-3966	269	23	12	12	NUM
ejpam-3966	269	24	.	.	PUNCT
ejpam-3966	270	1	let	let	VERB
ejpam-3966	270	2	x	x	PRON
ejpam-3966	270	3	be	be	AUX
ejpam-3966	270	4	a	a	DET
ejpam-3966	270	5	be	be	NOUN
ejpam-3966	270	6	-	-	PUNCT
ejpam-3966	270	7	algebra	algebra	NOUN
ejpam-3966	270	8	and	and	CCONJ
ejpam-3966	270	9	let	let	VERB
ejpam-3966	270	10	i	i	PRON
ejpam-3966	270	11	be	be	AUX
ejpam-3966	270	12	a	a	DET
ejpam-3966	270	13	family	family	NOUN
ejpam-3966	270	14	of	of	ADP
ejpam-3966	270	15	normal	normal	ADJ
ejpam-3966	270	16	filters	filter	NOUN
ejpam-3966	270	17	of	of	ADP
ejpam-3966	270	18	x	x	SYM
ejpam-3966	270	19	such	such	ADJ
ejpam-3966	270	20	that	that	SCONJ
ejpam-3966	270	21	f	f	PROPN
ejpam-3966	270	22	∩	∩	PROPN
ejpam-3966	270	23	g	g	PROPN
ejpam-3966	270	24	∈	∈	PROPN
ejpam-3966	270	25	i	i	PRON
ejpam-3966	270	26	for	for	ADP
ejpam-3966	270	27	every	every	DET
ejpam-3966	270	28	f	f	PROPN
ejpam-3966	270	29	,	,	PUNCT
ejpam-3966	270	30	g	g	PROPN
ejpam-3966	270	31	∈	∈	PROPN
ejpam-3966	270	32	i.	i.	NOUN
ejpam-3966	270	33	then	then	ADV
ejpam-3966	270	34	{	{	PUNCT
ejpam-3966	270	35	x	x	X
ejpam-3966	270	36	/	/	SYM
ejpam-3966	270	37	f,ϕfg	f,ϕfg	PROPN
ejpam-3966	270	38	,	,	PUNCT
ejpam-3966	270	39	i	i	PRON
ejpam-3966	270	40	}	}	PUNCT
ejpam-3966	270	41	is	be	AUX
ejpam-3966	270	42	an	an	DET
ejpam-3966	270	43	inverse	inverse	NOUN
ejpam-3966	270	44	system	system	NOUN
ejpam-3966	270	45	of	of	ADP
ejpam-3966	270	46	be	be	AUX
ejpam-3966	270	47	-	-	PUNCT
ejpam-3966	270	48	algebras	algebra	NOUN
ejpam-3966	270	49	where	where	SCONJ
ejpam-3966	270	50	ϕfg	ϕfg	NOUN
ejpam-3966	270	51	:	:	PUNCT
ejpam-3966	270	52	x	x	X
ejpam-3966	270	53	/	/	SYM
ejpam-3966	270	54	f	f	X
ejpam-3966	270	55	→	→	SYM
ejpam-3966	270	56	x	x	X
ejpam-3966	270	57	/	/	SYM
ejpam-3966	270	58	g	g	PROPN
ejpam-3966	270	59	is	be	AUX
ejpam-3966	270	60	the	the	DET
ejpam-3966	270	61	epimorphism	epimorphism	NOUN
ejpam-3966	270	62	defined	define	VERB
ejpam-3966	270	63	by	by	ADP
ejpam-3966	270	64	ϕfg([x]f	ϕfg([x]f	PROPN
ejpam-3966	270	65	)	)	PUNCT
ejpam-3966	271	1	=	=	SYM
ejpam-3966	271	2	(	(	PUNCT
ejpam-3966	271	3	[	[	X
ejpam-3966	271	4	x]g	x]g	X
ejpam-3966	271	5	)	)	PUNCT
ejpam-3966	272	1	whenever	whenever	SCONJ
ejpam-3966	272	2	f	f	PROPN
ejpam-3966	272	3	⊆	⊆	NUM
ejpam-3966	272	4	g.	g.	PROPN
ejpam-3966	272	5	j.	j.	PROPN
ejpam-3966	272	6	albaracin	albaracin	PROPN
ejpam-3966	272	7	,	,	PUNCT
ejpam-3966	272	8	j.	j.	PROPN
ejpam-3966	272	9	vilela	vilela	PROPN
ejpam-3966	272	10	/	/	SYM
ejpam-3966	272	11	eur	eur	PROPN
ejpam-3966	272	12	.	.	PUNCT
ejpam-3966	273	1	j.	j.	PROPN
ejpam-3966	273	2	pure	pure	PROPN
ejpam-3966	273	3	appl	appl	PROPN
ejpam-3966	273	4	.	.	PROPN
ejpam-3966	273	5	math	math	PROPN
ejpam-3966	273	6	,	,	PUNCT
ejpam-3966	273	7	14	14	NUM
ejpam-3966	273	8	(	(	PUNCT
ejpam-3966	273	9	2	2	NUM
ejpam-3966	273	10	)	)	PUNCT
ejpam-3966	273	11	(	(	PUNCT
ejpam-3966	273	12	2021	2021	NUM
ejpam-3966	273	13	)	)	PUNCT
ejpam-3966	273	14	,	,	PUNCT
ejpam-3966	273	15	423	423	NUM
ejpam-3966	273	16	-	-	SYM
ejpam-3966	273	17	430	430	NUM
ejpam-3966	273	18	429	429	NUM
ejpam-3966	273	19	proof	proof	NOUN
ejpam-3966	273	20	.	.	PUNCT
ejpam-3966	274	1	we	we	PRON
ejpam-3966	274	2	will	will	AUX
ejpam-3966	274	3	denote	denote	VERB
ejpam-3966	274	4	by	by	ADP
ejpam-3966	274	5	f	f	PROPN
ejpam-3966	274	6	≥	≥	NUM
ejpam-3966	274	7	g	g	NOUN
ejpam-3966	275	1	whenever	whenever	SCONJ
ejpam-3966	275	2	f	f	PROPN
ejpam-3966	275	3	⊆	⊆	NUM
ejpam-3966	275	4	g.	g.	NOUN
ejpam-3966	275	5	we	we	PRON
ejpam-3966	275	6	will	will	AUX
ejpam-3966	275	7	show	show	VERB
ejpam-3966	275	8	that	that	SCONJ
ejpam-3966	275	9	(	(	PUNCT
ejpam-3966	275	10	i,≤	i,≤	X
ejpam-3966	275	11	)	)	PUNCT
ejpam-3966	275	12	is	be	AUX
ejpam-3966	275	13	a	a	DET
ejpam-3966	275	14	directed	direct	VERB
ejpam-3966	275	15	poset	poset	NOUN
ejpam-3966	275	16	.	.	PUNCT
ejpam-3966	276	1	let	let	VERB
ejpam-3966	276	2	f	f	X
ejpam-3966	276	3	,	,	PUNCT
ejpam-3966	276	4	g	g	PROPN
ejpam-3966	276	5	,	,	PUNCT
ejpam-3966	276	6	h	h	PROPN
ejpam-3966	276	7	∈	∈	PROPN
ejpam-3966	276	8	i.	i.	NOUN
ejpam-3966	276	9	since	since	SCONJ
ejpam-3966	276	10	f	f	PROPN
ejpam-3966	276	11	⊆	⊆	NUM
ejpam-3966	276	12	f	f	PROPN
ejpam-3966	276	13	for	for	ADP
ejpam-3966	276	14	all	all	DET
ejpam-3966	276	15	f	f	PROPN
ejpam-3966	276	16	∈	∈	PROPN
ejpam-3966	276	17	i	i	PRON
ejpam-3966	276	18	,	,	PUNCT
ejpam-3966	276	19	f	f	PROPN
ejpam-3966	276	20	≤	≤	PROPN
ejpam-3966	276	21	f	f	PROPN
ejpam-3966	276	22	for	for	ADP
ejpam-3966	276	23	all	all	DET
ejpam-3966	276	24	f	f	PROPN
ejpam-3966	276	25	∈	∈	PROPN
ejpam-3966	276	26	i.	i.	NOUN
ejpam-3966	276	27	suppose	suppose	VERB
ejpam-3966	276	28	that	that	SCONJ
ejpam-3966	276	29	f	f	PROPN
ejpam-3966	276	30	≤	≤	X
ejpam-3966	276	31	g	g	PROPN
ejpam-3966	276	32	and	and	CCONJ
ejpam-3966	276	33	g	g	PROPN
ejpam-3966	276	34	≤	≤	PROPN
ejpam-3966	276	35	h.	h.	NOUN
ejpam-3966	276	36	then	then	ADV
ejpam-3966	276	37	g	g	PROPN
ejpam-3966	276	38	⊆	⊆	NUM
ejpam-3966	276	39	f	f	PROPN
ejpam-3966	276	40	and	and	CCONJ
ejpam-3966	276	41	h	h	PROPN
ejpam-3966	276	42	⊆	⊆	NUM
ejpam-3966	276	43	g.	g.	NOUN
ejpam-3966	276	44	by	by	ADP
ejpam-3966	276	45	set	set	NOUN
ejpam-3966	276	46	inclusion	inclusion	NOUN
ejpam-3966	276	47	,	,	PUNCT
ejpam-3966	276	48	h	h	NOUN
ejpam-3966	276	49	⊆	⊆	NUM
ejpam-3966	276	50	f	f	NOUN
ejpam-3966	276	51	.	.	PUNCT
ejpam-3966	277	1	hence	hence	ADV
ejpam-3966	277	2	,	,	PUNCT
ejpam-3966	277	3	f	f	PROPN
ejpam-3966	277	4	≤	≤	PROPN
ejpam-3966	277	5	h.	h.	PROPN
ejpam-3966	277	6	suppose	suppose	VERB
ejpam-3966	277	7	that	that	SCONJ
ejpam-3966	277	8	f	f	PROPN
ejpam-3966	277	9	≤	≤	X
ejpam-3966	277	10	g	g	PROPN
ejpam-3966	277	11	and	and	CCONJ
ejpam-3966	277	12	g	g	NOUN
ejpam-3966	277	13	≤	≤	ADJ
ejpam-3966	277	14	f	f	NOUN
ejpam-3966	277	15	.	.	PUNCT
ejpam-3966	278	1	then	then	ADV
ejpam-3966	278	2	g	g	PROPN
ejpam-3966	278	3	⊆	⊆	NUM
ejpam-3966	278	4	f	f	PROPN
ejpam-3966	278	5	and	and	CCONJ
ejpam-3966	278	6	f	f	PROPN
ejpam-3966	278	7	⊆	⊆	NUM
ejpam-3966	278	8	g.	g.	NOUN
ejpam-3966	278	9	by	by	ADP
ejpam-3966	278	10	set	set	NOUN
ejpam-3966	278	11	inclusion	inclusion	NOUN
ejpam-3966	278	12	,	,	PUNCT
ejpam-3966	278	13	f	f	PROPN
ejpam-3966	278	14	=	=	PUNCT
ejpam-3966	278	15	g.	g.	PROPN
ejpam-3966	278	16	note	note	VERB
ejpam-3966	278	17	that	that	SCONJ
ejpam-3966	278	18	f	f	PROPN
ejpam-3966	279	1	∩g	∩g	NOUN
ejpam-3966	280	1	⊆	⊆	NUM
ejpam-3966	280	2	f	f	NOUN
ejpam-3966	280	3	,	,	PUNCT
ejpam-3966	280	4	f	f	PROPN
ejpam-3966	280	5	∩g	∩g	NOUN
ejpam-3966	280	6	⊆	⊆	NUM
ejpam-3966	280	7	g	g	NOUN
ejpam-3966	280	8	and	and	CCONJ
ejpam-3966	280	9	f	f	PROPN
ejpam-3966	280	10	∩g	∩g	PROPN
ejpam-3966	280	11	∈	∈	PROPN
ejpam-3966	280	12	i.	i.	NOUN
ejpam-3966	280	13	thus	thus	ADV
ejpam-3966	280	14	,	,	PUNCT
ejpam-3966	280	15	f	f	PROPN
ejpam-3966	280	16	≤	≤	PROPN
ejpam-3966	280	17	f	f	PROPN
ejpam-3966	280	18	∩g	∩g	NOUN
ejpam-3966	280	19	and	and	CCONJ
ejpam-3966	280	20	g	g	NOUN
ejpam-3966	280	21	≤	≤	NUM
ejpam-3966	280	22	f	f	PROPN
ejpam-3966	280	23	∩g	∩g	PROPN
ejpam-3966	280	24	.	.	PUNCT
ejpam-3966	281	1	hence	hence	ADV
ejpam-3966	281	2	,	,	PUNCT
ejpam-3966	281	3	for	for	ADP
ejpam-3966	281	4	every	every	DET
ejpam-3966	281	5	f	f	PROPN
ejpam-3966	281	6	,	,	PUNCT
ejpam-3966	281	7	g	g	PROPN
ejpam-3966	281	8	∈	∈	PROPN
ejpam-3966	281	9	i	i	PRON
ejpam-3966	281	10	,	,	PUNCT
ejpam-3966	281	11	there	there	PRON
ejpam-3966	281	12	exists	exist	VERB
ejpam-3966	281	13	h	h	NOUN
ejpam-3966	281	14	=	=	SYM
ejpam-3966	281	15	f	f	PROPN
ejpam-3966	281	16	∩	∩	PROPN
ejpam-3966	281	17	g	g	PROPN
ejpam-3966	281	18	∈	∈	PROPN
ejpam-3966	281	19	i	i	PRON
ejpam-3966	281	20	such	such	ADJ
ejpam-3966	281	21	that	that	SCONJ
ejpam-3966	281	22	f	f	X
ejpam-3966	281	23	,	,	PUNCT
ejpam-3966	281	24	g	g	PROPN
ejpam-3966	281	25	≤	≤	PROPN
ejpam-3966	281	26	h.	h.	NOUN
ejpam-3966	281	27	therefore	therefore	ADV
ejpam-3966	281	28	,	,	PUNCT
ejpam-3966	281	29	(	(	PUNCT
ejpam-3966	281	30	i,≤	i,≤	X
ejpam-3966	281	31	)	)	PUNCT
ejpam-3966	281	32	is	be	AUX
ejpam-3966	281	33	a	a	DET
ejpam-3966	281	34	directed	direct	VERB
ejpam-3966	281	35	poset	poset	NOUN
ejpam-3966	281	36	.	.	PUNCT
ejpam-3966	282	1	we	we	PRON
ejpam-3966	282	2	will	will	AUX
ejpam-3966	282	3	show	show	VERB
ejpam-3966	282	4	that	that	SCONJ
ejpam-3966	282	5	{	{	PUNCT
ejpam-3966	282	6	x	x	X
ejpam-3966	282	7	/	/	SYM
ejpam-3966	282	8	f,ϕfg	f,ϕfg	PROPN
ejpam-3966	282	9	,	,	PUNCT
ejpam-3966	282	10	i	i	PRON
ejpam-3966	282	11	}	}	PUNCT
ejpam-3966	282	12	is	be	AUX
ejpam-3966	282	13	an	an	DET
ejpam-3966	282	14	inverse	inverse	NOUN
ejpam-3966	282	15	system	system	NOUN
ejpam-3966	282	16	,	,	PUNCT
ejpam-3966	282	17	that	that	ADV
ejpam-3966	282	18	is	is	ADV
ejpam-3966	282	19	,	,	PUNCT
ejpam-3966	282	20	ϕghϕfg	ϕghϕfg	NOUN
ejpam-3966	282	21	=	=	PUNCT
ejpam-3966	282	22	ϕfh	ϕfh	PROPN
ejpam-3966	282	23	whenever	whenever	SCONJ
ejpam-3966	282	24	f	f	PROPN
ejpam-3966	282	25	≥	≥	AUX
ejpam-3966	282	26	g	g	PROPN
ejpam-3966	282	27	≥	≥	PROPN
ejpam-3966	282	28	h.	h.	PROPN
ejpam-3966	283	1	now	now	ADV
ejpam-3966	283	2	,	,	PUNCT
ejpam-3966	283	3	ϕghϕfg([x]f	ϕghϕfg([x]f	ADJ
ejpam-3966	283	4	)	)	PUNCT
ejpam-3966	284	1	=	=	SYM
ejpam-3966	284	2	ϕgh(ϕfg([x]f	ϕgh(ϕfg([x]f	ADJ
ejpam-3966	284	3	)	)	PUNCT
ejpam-3966	284	4	)	)	PUNCT
ejpam-3966	285	1	=	=	PUNCT
ejpam-3966	285	2	ϕgh([x]g	ϕgh([x]g	X
ejpam-3966	285	3	)	)	PUNCT
ejpam-3966	285	4	=	=	PUNCT
ejpam-3966	286	1	[	[	X
ejpam-3966	286	2	x]h	x]h	NOUN
ejpam-3966	286	3	=	=	SYM
ejpam-3966	286	4	ϕfh([x]f	ϕfh([x]f	PROPN
ejpam-3966	286	5	)	)	PUNCT
ejpam-3966	286	6	.	.	PUNCT
ejpam-3966	287	1	therefore	therefore	ADV
ejpam-3966	287	2	,	,	PUNCT
ejpam-3966	287	3	ϕghϕfg	ϕghϕfg	NOUN
ejpam-3966	287	4	=	=	PUNCT
ejpam-3966	287	5	ϕfh	ϕfh	PROPN
ejpam-3966	287	6	whenever	whenever	SCONJ
ejpam-3966	287	7	f	f	PROPN
ejpam-3966	287	8	≥	≥	NUM
ejpam-3966	287	9	g	g	PROPN
ejpam-3966	287	10	≥	≥	PROPN
ejpam-3966	287	11	h.	h.	PROPN
ejpam-3966	287	12	note	note	NOUN
ejpam-3966	287	13	that	that	PRON
ejpam-3966	287	14	ϕff	ϕff	ADV
ejpam-3966	287	15	:	:	PUNCT
ejpam-3966	287	16	x	x	X
ejpam-3966	287	17	/	/	SYM
ejpam-3966	287	18	f	f	X
ejpam-3966	287	19	→	→	SYM
ejpam-3966	287	20	x	x	X
ejpam-3966	287	21	/	/	SYM
ejpam-3966	287	22	f	f	PROPN
ejpam-3966	287	23	is	be	AUX
ejpam-3966	287	24	defined	define	VERB
ejpam-3966	287	25	by	by	ADP
ejpam-3966	287	26	ϕff	ϕff	NOUN
ejpam-3966	287	27	(	(	PUNCT
ejpam-3966	287	28	[	[	X
ejpam-3966	287	29	x]f	x]f	NOUN
ejpam-3966	287	30	)	)	PUNCT
ejpam-3966	288	1	=	=	PUNCT
ejpam-3966	289	1	[	[	X
ejpam-3966	289	2	x]f	x]f	NOUN
ejpam-3966	289	3	.	.	PUNCT
ejpam-3966	290	1	thus	thus	ADV
ejpam-3966	290	2	,	,	PUNCT
ejpam-3966	290	3	ϕff	ϕff	NOUN
ejpam-3966	290	4	=	=	PUNCT
ejpam-3966	290	5	idx	idx	PROPN
ejpam-3966	290	6	/	/	SYM
ejpam-3966	290	7	f	f	PROPN
ejpam-3966	290	8	.	.	PUNCT
ejpam-3966	291	1	therefore	therefore	ADV
ejpam-3966	291	2	,	,	PUNCT
ejpam-3966	291	3	{	{	PUNCT
ejpam-3966	291	4	x	x	X
ejpam-3966	291	5	/	/	SYM
ejpam-3966	291	6	f,ϕfg	f,ϕfg	PROPN
ejpam-3966	291	7	,	,	PUNCT
ejpam-3966	291	8	i	i	PRON
ejpam-3966	291	9	}	}	PUNCT
ejpam-3966	291	10	is	be	AUX
ejpam-3966	291	11	an	an	DET
ejpam-3966	291	12	inverse	inverse	NOUN
ejpam-3966	291	13	system	system	NOUN
ejpam-3966	291	14	.	.	PUNCT
ejpam-3966	292	1	if	if	SCONJ
ejpam-3966	292	2	i	i	PRON
ejpam-3966	292	3	is	be	AUX
ejpam-3966	292	4	the	the	DET
ejpam-3966	292	5	family	family	NOUN
ejpam-3966	292	6	of	of	ADP
ejpam-3966	292	7	all	all	DET
ejpam-3966	292	8	normal	normal	ADJ
ejpam-3966	292	9	filters	filter	NOUN
ejpam-3966	292	10	of	of	ADP
ejpam-3966	292	11	x	x	SYM
ejpam-3966	292	12	such	such	ADJ
ejpam-3966	292	13	that	that	SCONJ
ejpam-3966	292	14	x	x	X
ejpam-3966	292	15	/	/	SYM
ejpam-3966	292	16	f	f	PROPN
ejpam-3966	292	17	is	be	AUX
ejpam-3966	292	18	finite	finite	ADJ
ejpam-3966	292	19	for	for	ADP
ejpam-3966	292	20	all	all	DET
ejpam-3966	292	21	f	f	PROPN
ejpam-3966	292	22	∈	∈	PROPN
ejpam-3966	293	1	i	i	PRON
ejpam-3966	293	2	,	,	PUNCT
ejpam-3966	293	3	then	then	ADV
ejpam-3966	293	4	we	we	PRON
ejpam-3966	293	5	call	call	VERB
ejpam-3966	293	6	the	the	DET
ejpam-3966	293	7	inverse	inverse	NOUN
ejpam-3966	293	8	limit	limit	NOUN
ejpam-3966	293	9	of	of	ADP
ejpam-3966	293	10	the	the	DET
ejpam-3966	293	11	inverse	inverse	NOUN
ejpam-3966	293	12	system	system	NOUN
ejpam-3966	293	13	{	{	PUNCT
ejpam-3966	293	14	x	x	X
ejpam-3966	293	15	/	/	SYM
ejpam-3966	293	16	f,ϕfg	f,ϕfg	PROPN
ejpam-3966	293	17	,	,	PUNCT
ejpam-3966	293	18	i	i	NOUN
ejpam-3966	293	19	}	}	PUNCT
ejpam-3966	293	20	the	the	DET
ejpam-3966	293	21	normal	normal	ADJ
ejpam-3966	293	22	completion	completion	NOUN
ejpam-3966	293	23	of	of	ADP
ejpam-3966	293	24	x.	x.	NOUN
ejpam-3966	293	25	example	example	NOUN
ejpam-3966	293	26	1	1	X
ejpam-3966	293	27	.	.	PUNCT
ejpam-3966	294	1	consider	consider	VERB
ejpam-3966	294	2	the	the	DET
ejpam-3966	294	3	commutative	commutative	ADJ
ejpam-3966	294	4	be	be	AUX
ejpam-3966	294	5	-	-	PUNCT
ejpam-3966	294	6	algebra	algebra	NOUN
ejpam-3966	294	7	x	x	PUNCT
ejpam-3966	294	8	=	=	SYM
ejpam-3966	294	9	{	{	PUNCT
ejpam-3966	294	10	1	1	NUM
ejpam-3966	294	11	,	,	PUNCT
ejpam-3966	294	12	a	a	DET
ejpam-3966	294	13	,	,	PUNCT
ejpam-3966	294	14	b	b	NOUN
ejpam-3966	294	15	,	,	PUNCT
ejpam-3966	294	16	c	c	NOUN
ejpam-3966	294	17	,	,	PUNCT
ejpam-3966	294	18	}	}	PUNCT
ejpam-3966	294	19	with	with	ADP
ejpam-3966	294	20	the	the	DET
ejpam-3966	294	21	operation	operation	NOUN
ejpam-3966	294	22	∗	∗	NOUN
ejpam-3966	294	23	defined	define	VERB
ejpam-3966	294	24	by	by	ADP
ejpam-3966	294	25	the	the	DET
ejpam-3966	294	26	cayley	cayley	ADJ
ejpam-3966	294	27	table	table	NOUN
ejpam-3966	294	28	shown	show	VERB
ejpam-3966	294	29	below	below	ADV
ejpam-3966	294	30	.	.	PUNCT
ejpam-3966	295	1	∗	∗	NOUN
ejpam-3966	295	2	1	1	NUM
ejpam-3966	295	3	a	a	DET
ejpam-3966	295	4	b	b	NOUN
ejpam-3966	295	5	c	c	NOUN
ejpam-3966	295	6	1	1	NUM
ejpam-3966	295	7	1	1	NUM
ejpam-3966	295	8	a	a	DET
ejpam-3966	295	9	b	b	NOUN
ejpam-3966	295	10	c	c	NOUN
ejpam-3966	295	11	a	a	DET
ejpam-3966	295	12	1	1	NUM
ejpam-3966	295	13	1	1	NUM
ejpam-3966	295	14	b	b	NOUN
ejpam-3966	295	15	c	c	NOUN
ejpam-3966	295	16	b	b	PROPN
ejpam-3966	295	17	1	1	NUM
ejpam-3966	295	18	a	a	DET
ejpam-3966	295	19	1	1	NUM
ejpam-3966	295	20	c	c	NOUN
ejpam-3966	295	21	c	c	NOUN
ejpam-3966	295	22	1	1	NUM
ejpam-3966	295	23	a	a	DET
ejpam-3966	295	24	b	b	NOUN
ejpam-3966	295	25	1	1	NUM
ejpam-3966	295	26	by	by	ADP
ejpam-3966	295	27	theorem	theorem	NOUN
ejpam-3966	295	28	3	3	NUM
ejpam-3966	295	29	,	,	PUNCT
ejpam-3966	295	30	there	there	PRON
ejpam-3966	295	31	is	be	VERB
ejpam-3966	295	32	a	a	DET
ejpam-3966	295	33	bijection	bijection	NOUN
ejpam-3966	295	34	between	between	ADP
ejpam-3966	295	35	the	the	DET
ejpam-3966	295	36	congruence	congruence	PROPN
ejpam-3966	295	37	relations	relation	NOUN
ejpam-3966	295	38	and	and	CCONJ
ejpam-3966	295	39	filters	filter	NOUN
ejpam-3966	295	40	of	of	ADP
ejpam-3966	295	41	x.	x.	NOUN
ejpam-3966	295	42	thus	thus	ADV
ejpam-3966	295	43	,	,	PUNCT
ejpam-3966	295	44	the	the	DET
ejpam-3966	295	45	set	set	NOUN
ejpam-3966	295	46	i	i	PRON
ejpam-3966	295	47	of	of	ADP
ejpam-3966	295	48	congruence	congruence	PROPN
ejpam-3966	295	49	relations	relation	NOUN
ejpam-3966	295	50	of	of	ADP
ejpam-3966	295	51	x	x	PRON
ejpam-3966	295	52	is	be	AUX
ejpam-3966	295	53	completely	completely	ADV
ejpam-3966	295	54	determined	determine	VERB
ejpam-3966	295	55	by	by	ADP
ejpam-3966	295	56	the	the	DET
ejpam-3966	295	57	set	set	NOUN
ejpam-3966	295	58	of	of	ADP
ejpam-3966	295	59	all	all	DET
ejpam-3966	295	60	filters	filter	NOUN
ejpam-3966	295	61	of	of	ADP
ejpam-3966	295	62	x.	x.	NOUN
ejpam-3966	295	63	the	the	DET
ejpam-3966	295	64	filters	filter	NOUN
ejpam-3966	295	65	of	of	ADP
ejpam-3966	295	66	x	x	SYM
ejpam-3966	295	67	are	be	AUX
ejpam-3966	295	68	f1	f1	NOUN
ejpam-3966	295	69	=	=	SYM
ejpam-3966	295	70	{	{	PUNCT
ejpam-3966	295	71	1	1	NUM
ejpam-3966	295	72	}	}	PUNCT
ejpam-3966	295	73	,	,	PUNCT
ejpam-3966	295	74	f2	f2	PROPN
ejpam-3966	295	75	=	=	SYM
ejpam-3966	295	76	{	{	PUNCT
ejpam-3966	295	77	1	1	NUM
ejpam-3966	295	78	,	,	PUNCT
ejpam-3966	295	79	a	a	PRON
ejpam-3966	295	80	}	}	PUNCT
ejpam-3966	295	81	,	,	PUNCT
ejpam-3966	295	82	f3	f3	PROPN
ejpam-3966	295	83	=	=	SYM
ejpam-3966	295	84	{	{	PUNCT
ejpam-3966	295	85	1	1	NUM
ejpam-3966	295	86	,	,	PUNCT
ejpam-3966	295	87	b	b	NOUN
ejpam-3966	295	88	}	}	PUNCT
ejpam-3966	295	89	,	,	PUNCT
ejpam-3966	295	90	f4	f4	NOUN
ejpam-3966	295	91	=	=	SYM
ejpam-3966	295	92	{	{	PUNCT
ejpam-3966	295	93	1	1	NUM
ejpam-3966	295	94	,	,	PUNCT
ejpam-3966	295	95	c	c	NOUN
ejpam-3966	295	96	}	}	PUNCT
ejpam-3966	295	97	,	,	PUNCT
ejpam-3966	295	98	f5	f5	PROPN
ejpam-3966	295	99	=	=	SYM
ejpam-3966	295	100	{	{	PUNCT
ejpam-3966	295	101	1	1	NUM
ejpam-3966	295	102	,	,	PUNCT
ejpam-3966	295	103	a	a	DET
ejpam-3966	295	104	,	,	PUNCT
ejpam-3966	295	105	b	b	NOUN
ejpam-3966	295	106	}	}	PUNCT
ejpam-3966	295	107	,	,	PUNCT
ejpam-3966	295	108	f6	f6	PROPN
ejpam-3966	295	109	=	=	PUNCT
ejpam-3966	295	110	{	{	PUNCT
ejpam-3966	295	111	1	1	NUM
ejpam-3966	295	112	,	,	PUNCT
ejpam-3966	295	113	a	a	DET
ejpam-3966	295	114	,	,	PUNCT
ejpam-3966	295	115	c	c	NOUN
ejpam-3966	295	116	}	}	PUNCT
ejpam-3966	295	117	,	,	PUNCT
ejpam-3966	295	118	f7	f7	PROPN
ejpam-3966	295	119	=	=	PUNCT
ejpam-3966	295	120	{	{	PUNCT
ejpam-3966	295	121	1	1	NUM
ejpam-3966	295	122	,	,	PUNCT
ejpam-3966	295	123	b	b	NOUN
ejpam-3966	295	124	,	,	PUNCT
ejpam-3966	295	125	c	c	NOUN
ejpam-3966	295	126	}	}	PUNCT
ejpam-3966	295	127	and	and	CCONJ
ejpam-3966	295	128	f8	f8	PROPN
ejpam-3966	295	129	=	=	PUNCT
ejpam-3966	296	1	x.	x.	NOUN
ejpam-3966	296	2	since	since	SCONJ
ejpam-3966	296	3	x	x	PROPN
ejpam-3966	296	4	is	be	AUX
ejpam-3966	296	5	commutative	commutative	ADJ
ejpam-3966	296	6	,	,	PUNCT
ejpam-3966	296	7	by	by	ADP
ejpam-3966	296	8	theorem	theorem	NOUN
ejpam-3966	296	9	2	2	NUM
ejpam-3966	296	10	,	,	PUNCT
ejpam-3966	296	11	x	x	X
ejpam-3966	296	12	is	be	AUX
ejpam-3966	296	13	transitive	transitive	ADJ
ejpam-3966	296	14	.	.	PUNCT
ejpam-3966	297	1	by	by	ADP
ejpam-3966	297	2	proposition	proposition	NOUN
ejpam-3966	297	3	1	1	NUM
ejpam-3966	297	4	,	,	PUNCT
ejpam-3966	297	5	all	all	DET
ejpam-3966	297	6	filters	filter	NOUN
ejpam-3966	297	7	of	of	ADP
ejpam-3966	297	8	x	x	SYM
ejpam-3966	297	9	are	be	AUX
ejpam-3966	297	10	normal	normal	ADJ
ejpam-3966	297	11	.	.	PUNCT
ejpam-3966	298	1	hence	hence	ADV
ejpam-3966	298	2	,	,	PUNCT
ejpam-3966	298	3	≡fi	≡fi	X
ejpam-3966	298	4	is	be	AUX
ejpam-3966	298	5	a	a	DET
ejpam-3966	298	6	congruence	congruence	NOUN
ejpam-3966	298	7	relation	relation	NOUN
ejpam-3966	298	8	on	on	ADP
ejpam-3966	298	9	x	x	SYM
ejpam-3966	298	10	where	where	SCONJ
ejpam-3966	298	11	i	i	PRON
ejpam-3966	298	12	=	=	NOUN
ejpam-3966	298	13	1	1	NUM
ejpam-3966	298	14	,	,	PUNCT
ejpam-3966	298	15	.	.	PUNCT
ejpam-3966	298	16	.	.	PUNCT
ejpam-3966	299	1	.	.	PUNCT
ejpam-3966	300	1	,	,	PUNCT
ejpam-3966	300	2	8	8	X
ejpam-3966	300	3	.	.	PUNCT
ejpam-3966	301	1	thus	thus	ADV
ejpam-3966	301	2	,	,	PUNCT
ejpam-3966	301	3	i	i	PRON
ejpam-3966	301	4	=	=	PUNCT
ejpam-3966	301	5	{	{	PUNCT
ejpam-3966	301	6	≡fi	≡fi	X
ejpam-3966	301	7	|	|	ADV
ejpam-3966	301	8	i	i	PRON
ejpam-3966	301	9	=	=	NOUN
ejpam-3966	301	10	1	1	NUM
ejpam-3966	301	11	,	,	PUNCT
ejpam-3966	301	12	.	.	PUNCT
ejpam-3966	301	13	.	.	PUNCT
ejpam-3966	301	14	.	.	PUNCT
ejpam-3966	302	1	,	,	PUNCT
ejpam-3966	302	2	8	8	NUM
ejpam-3966	302	3	}	}	PUNCT
ejpam-3966	302	4	.	.	PUNCT
ejpam-3966	303	1	we	we	PRON
ejpam-3966	303	2	will	will	AUX
ejpam-3966	303	3	just	just	ADV
ejpam-3966	303	4	denote	denote	VERB
ejpam-3966	303	5	≡fi	≡fi	X
ejpam-3966	303	6	by	by	ADP
ejpam-3966	303	7	fi	fi	NOUN
ejpam-3966	303	8	for	for	ADP
ejpam-3966	303	9	all	all	PRON
ejpam-3966	303	10	i	i	PRON
ejpam-3966	303	11	∈	∈	PROPN
ejpam-3966	303	12	i.	i.	NOUN
ejpam-3966	303	13	note	note	VERB
ejpam-3966	303	14	that	that	SCONJ
ejpam-3966	303	15	≡fi⊆≡fj	≡fi⊆≡fj	VERB
ejpam-3966	303	16	if	if	SCONJ
ejpam-3966	303	17	fi	fi	NOUN
ejpam-3966	303	18	⊆	⊆	NUM
ejpam-3966	303	19	fj	fj	NOUN
ejpam-3966	303	20	.	.	PUNCT
ejpam-3966	304	1	now	now	ADV
ejpam-3966	304	2	,	,	PUNCT
ejpam-3966	304	3	x	x	X
ejpam-3966	304	4	/	/	SYM
ejpam-3966	304	5	f1	f1	NOUN
ejpam-3966	304	6	=	=	SYM
ejpam-3966	304	7	{	{	PUNCT
ejpam-3966	305	1	[	[	X
ejpam-3966	305	2	1]f1	1]f1	NUM
ejpam-3966	305	3	,	,	PUNCT
ejpam-3966	305	4	[	[	X
ejpam-3966	305	5	a]f1	a]f1	X
ejpam-3966	305	6	,	,	PUNCT
ejpam-3966	306	1	[	[	X
ejpam-3966	306	2	b]f1	b]f1	X
ejpam-3966	306	3	,	,	PUNCT
ejpam-3966	306	4	[	[	X
ejpam-3966	306	5	c]f1	c]f1	X
ejpam-3966	306	6	}	}	PUNCT
ejpam-3966	306	7	where	where	SCONJ
ejpam-3966	306	8	[	[	X
ejpam-3966	306	9	1]f1	1]f1	NUM
ejpam-3966	306	10	=	=	SYM
ejpam-3966	306	11	{	{	PUNCT
ejpam-3966	306	12	1	1	NUM
ejpam-3966	306	13	}	}	PUNCT
ejpam-3966	306	14	,	,	PUNCT
ejpam-3966	306	15	[	[	X
ejpam-3966	306	16	a]f1	a]f1	X
ejpam-3966	306	17	=	=	SYM
ejpam-3966	306	18	{	{	PUNCT
ejpam-3966	306	19	a	a	NOUN
ejpam-3966	306	20	}	}	PUNCT
ejpam-3966	306	21	,	,	PUNCT
ejpam-3966	306	22	[	[	X
ejpam-3966	306	23	b]f1	b]f1	X
ejpam-3966	306	24	=	=	PRON
ejpam-3966	306	25	{	{	PUNCT
ejpam-3966	306	26	b	b	NOUN
ejpam-3966	306	27	}	}	PUNCT
ejpam-3966	306	28	and	and	CCONJ
ejpam-3966	306	29	[	[	X
ejpam-3966	306	30	c]f1	c]f1	X
ejpam-3966	306	31	=	=	X
ejpam-3966	306	32	{	{	PUNCT
ejpam-3966	306	33	c	c	NOUN
ejpam-3966	306	34	}	}	PUNCT
ejpam-3966	306	35	;	;	PUNCT
ejpam-3966	306	36	x	x	X
ejpam-3966	306	37	/	/	SYM
ejpam-3966	306	38	f2	f2	PROPN
ejpam-3966	306	39	=	=	SYM
ejpam-3966	306	40	{	{	PUNCT
ejpam-3966	306	41	[	[	X
ejpam-3966	306	42	1]f2	1]f2	NUM
ejpam-3966	306	43	,	,	PUNCT
ejpam-3966	306	44	[	[	X
ejpam-3966	306	45	b]f2	b]f2	X
ejpam-3966	306	46	,	,	PUNCT
ejpam-3966	306	47	[	[	X
ejpam-3966	306	48	c]f2	c]f2	NOUN
ejpam-3966	306	49	}	}	PUNCT
ejpam-3966	306	50	where	where	SCONJ
ejpam-3966	306	51	[	[	X
ejpam-3966	306	52	1]f2	1]f2	X
ejpam-3966	306	53	=	=	SYM
ejpam-3966	306	54	f2	f2	PROPN
ejpam-3966	306	55	,	,	PUNCT
ejpam-3966	306	56	[	[	X
ejpam-3966	306	57	b]f2	b]f2	X
ejpam-3966	306	58	=	=	PUNCT
ejpam-3966	306	59	{	{	PUNCT
ejpam-3966	306	60	b	b	NOUN
ejpam-3966	306	61	}	}	PUNCT
ejpam-3966	306	62	and	and	CCONJ
ejpam-3966	307	1	[	[	X
ejpam-3966	307	2	c]f2	c]f2	X
ejpam-3966	307	3	=	=	X
ejpam-3966	307	4	{	{	PUNCT
ejpam-3966	307	5	c	c	NOUN
ejpam-3966	307	6	}	}	PUNCT
ejpam-3966	307	7	;	;	PUNCT
ejpam-3966	307	8	x	x	X
ejpam-3966	307	9	/	/	SYM
ejpam-3966	307	10	f3	f3	ADJ
ejpam-3966	307	11	=	=	SYM
ejpam-3966	307	12	{	{	PUNCT
ejpam-3966	307	13	[	[	X
ejpam-3966	307	14	1]f3	1]f3	NUM
ejpam-3966	307	15	,	,	PUNCT
ejpam-3966	307	16	[	[	X
ejpam-3966	307	17	a]f3	a]f3	X
ejpam-3966	307	18	,	,	PUNCT
ejpam-3966	307	19	[	[	X
ejpam-3966	307	20	c]f3	c]f3	NOUN
ejpam-3966	307	21	}	}	PUNCT
ejpam-3966	307	22	where	where	SCONJ
ejpam-3966	307	23	[	[	X
ejpam-3966	307	24	1]f3	1]f3	NUM
ejpam-3966	307	25	=	=	SYM
ejpam-3966	307	26	f3	f3	NOUN
ejpam-3966	307	27	,	,	PUNCT
ejpam-3966	307	28	[	[	X
ejpam-3966	307	29	a]f3	a]f3	X
ejpam-3966	307	30	=	=	SYM
ejpam-3966	307	31	{	{	PUNCT
ejpam-3966	307	32	a	a	NOUN
ejpam-3966	307	33	}	}	PUNCT
ejpam-3966	307	34	and	and	CCONJ
ejpam-3966	307	35	[	[	X
ejpam-3966	307	36	c]f3	c]f3	X
ejpam-3966	307	37	=	=	SYM
ejpam-3966	307	38	{	{	PUNCT
ejpam-3966	307	39	c	c	NOUN
ejpam-3966	307	40	}	}	PUNCT
ejpam-3966	307	41	;	;	PUNCT
ejpam-3966	307	42	x	x	X
ejpam-3966	307	43	/	/	SYM
ejpam-3966	307	44	f4	f4	NOUN
ejpam-3966	307	45	=	=	PUNCT
ejpam-3966	307	46	{	{	PUNCT
ejpam-3966	307	47	[	[	X
ejpam-3966	307	48	1]f4	1]f4	NUM
ejpam-3966	307	49	,	,	PUNCT
ejpam-3966	307	50	[	[	X
ejpam-3966	307	51	a]f4	a]f4	ADJ
ejpam-3966	307	52	,	,	PUNCT
ejpam-3966	307	53	[	[	X
ejpam-3966	307	54	b]f4	b]f4	ADP
ejpam-3966	307	55	}	}	PUNCT
ejpam-3966	307	56	where	where	SCONJ
ejpam-3966	307	57	[	[	X
ejpam-3966	307	58	1]f4	1]f4	NUM
ejpam-3966	307	59	=	=	SYM
ejpam-3966	307	60	f4	f4	PROPN
ejpam-3966	307	61	,	,	PUNCT
ejpam-3966	307	62	[	[	X
ejpam-3966	307	63	a]f4	a]f4	NOUN
ejpam-3966	307	64	=	=	SYM
ejpam-3966	307	65	{	{	PUNCT
ejpam-3966	307	66	a	a	NOUN
ejpam-3966	307	67	}	}	PUNCT
ejpam-3966	307	68	and	and	CCONJ
ejpam-3966	307	69	[	[	X
ejpam-3966	307	70	b]f4	b]f4	PROPN
ejpam-3966	307	71	=	=	SYM
ejpam-3966	307	72	{	{	PUNCT
ejpam-3966	307	73	b	b	NOUN
ejpam-3966	307	74	}	}	PUNCT
ejpam-3966	307	75	;	;	PUNCT
ejpam-3966	307	76	x	x	X
ejpam-3966	307	77	/	/	SYM
ejpam-3966	307	78	f5	f5	NOUN
ejpam-3966	307	79	=	=	SYM
ejpam-3966	307	80	{	{	PUNCT
ejpam-3966	308	1	[	[	X
ejpam-3966	308	2	1]f5	1]f5	X
ejpam-3966	308	3	,	,	PUNCT
ejpam-3966	308	4	[	[	X
ejpam-3966	308	5	c]f5	c]f5	NOUN
ejpam-3966	308	6	}	}	PUNCT
ejpam-3966	308	7	where	where	SCONJ
ejpam-3966	308	8	[	[	X
ejpam-3966	308	9	1]f5	1]f5	X
ejpam-3966	308	10	=	=	SYM
ejpam-3966	308	11	f5	f5	NOUN
ejpam-3966	308	12	and	and	CCONJ
ejpam-3966	308	13	[	[	X
ejpam-3966	308	14	c]f5	c]f5	NOUN
ejpam-3966	308	15	=	=	X
ejpam-3966	308	16	{	{	PUNCT
ejpam-3966	308	17	c	c	NOUN
ejpam-3966	308	18	}	}	PUNCT
ejpam-3966	308	19	;	;	PUNCT
ejpam-3966	308	20	x	x	X
ejpam-3966	308	21	/	/	SYM
ejpam-3966	308	22	f6	f6	PROPN
ejpam-3966	308	23	=	=	PUNCT
ejpam-3966	308	24	{	{	PUNCT
ejpam-3966	308	25	[	[	X
ejpam-3966	308	26	1]f6	1]f6	NUM
ejpam-3966	308	27	,	,	PUNCT
ejpam-3966	308	28	[	[	X
ejpam-3966	308	29	b]f6	b]f6	NOUN
ejpam-3966	308	30	}	}	PUNCT
ejpam-3966	308	31	where	where	SCONJ
ejpam-3966	309	1	[	[	X
ejpam-3966	309	2	1]f6	1]f6	NUM
ejpam-3966	309	3	=	=	SYM
ejpam-3966	309	4	f6	f6	PROPN
ejpam-3966	309	5	and	and	CCONJ
ejpam-3966	309	6	[	[	X
ejpam-3966	309	7	b]f6	b]f6	NOUN
ejpam-3966	309	8	=	=	SYM
ejpam-3966	309	9	{	{	PUNCT
ejpam-3966	309	10	b	b	NOUN
ejpam-3966	309	11	}	}	PUNCT
ejpam-3966	309	12	;	;	PUNCT
ejpam-3966	309	13	x	x	X
ejpam-3966	309	14	/	/	SYM
ejpam-3966	309	15	f7	f7	PROPN
ejpam-3966	309	16	=	=	PUNCT
ejpam-3966	309	17	{	{	PUNCT
ejpam-3966	309	18	[	[	X
ejpam-3966	309	19	1]f7	1]f7	NUM
ejpam-3966	309	20	,	,	PUNCT
ejpam-3966	309	21	[	[	X
ejpam-3966	309	22	a]f7	a]f7	ADP
ejpam-3966	309	23	}	}	PUNCT
ejpam-3966	309	24	where	where	SCONJ
ejpam-3966	309	25	[	[	X
ejpam-3966	309	26	1]f7	1]f7	X
ejpam-3966	309	27	=	=	SYM
ejpam-3966	309	28	f7	f7	PROPN
ejpam-3966	309	29	and	and	CCONJ
ejpam-3966	309	30	[	[	X
ejpam-3966	309	31	a]f7	a]f7	X
ejpam-3966	309	32	=	=	PRON
ejpam-3966	309	33	{	{	PUNCT
ejpam-3966	309	34	a	a	NOUN
ejpam-3966	309	35	}	}	PUNCT
ejpam-3966	309	36	;	;	PUNCT
ejpam-3966	309	37	and	and	CCONJ
ejpam-3966	309	38	references	reference	NOUN
ejpam-3966	309	39	430	430	NUM
ejpam-3966	309	40	x	x	SYM
ejpam-3966	309	41	/	/	SYM
ejpam-3966	309	42	f8	f8	PROPN
ejpam-3966	309	43	=	=	SYM
ejpam-3966	309	44	{	{	PUNCT
ejpam-3966	309	45	[	[	X
ejpam-3966	309	46	1]f8	1]f8	NUM
ejpam-3966	309	47	}	}	PUNCT
ejpam-3966	309	48	where	where	SCONJ
ejpam-3966	309	49	[	[	X
ejpam-3966	309	50	1]f8	1]f8	NUM
ejpam-3966	309	51	=	=	SYM
ejpam-3966	309	52	x.	x.	NOUN
ejpam-3966	309	53	therefore	therefore	ADV
ejpam-3966	309	54	,	,	PUNCT
ejpam-3966	309	55	{	{	PUNCT
ejpam-3966	309	56	x	x	NOUN
ejpam-3966	309	57	/	/	SYM
ejpam-3966	309	58	fi	fi	NOUN
ejpam-3966	309	59	,	,	PUNCT
ejpam-3966	309	60	ϕfifj	ϕfifj	PROPN
ejpam-3966	309	61	,	,	PUNCT
ejpam-3966	309	62	i	i	PRON
ejpam-3966	309	63	}	}	PUNCT
ejpam-3966	309	64	is	be	AUX
ejpam-3966	309	65	an	an	DET
ejpam-3966	309	66	inverse	inverse	NOUN
ejpam-3966	309	67	system	system	NOUN
ejpam-3966	309	68	of	of	ADP
ejpam-3966	309	69	be	be	AUX
ejpam-3966	309	70	-	-	PUNCT
ejpam-3966	309	71	algebras	algebras	X
ejpam-3966	309	72	where	where	SCONJ
ejpam-3966	309	73	ϕfifj	ϕfifj	NOUN
ejpam-3966	309	74	:	:	PUNCT
ejpam-3966	309	75	x	x	X
ejpam-3966	309	76	/	/	SYM
ejpam-3966	309	77	fi	fi	NOUN
ejpam-3966	309	78	→	→	SYM
ejpam-3966	309	79	x	x	SYM
ejpam-3966	309	80	/	/	SYM
ejpam-3966	309	81	fj	fj	PROPN
ejpam-3966	309	82	is	be	AUX
ejpam-3966	309	83	the	the	DET
ejpam-3966	309	84	canonical	canonical	ADJ
ejpam-3966	309	85	epimorphism	epimorphism	NOUN
ejpam-3966	309	86	whenever	whenever	SCONJ
ejpam-3966	309	87	fi	fi	PROPN
ejpam-3966	309	88	≥	≥	X
ejpam-3966	309	89	fj	fj	INTJ
ejpam-3966	309	90	,	,	PUNCT
ejpam-3966	309	91	that	that	ADV
ejpam-3966	309	92	is	is	ADV
ejpam-3966	309	93	,	,	PUNCT
ejpam-3966	309	94	fi	fi	NOUN
ejpam-3966	309	95	⊆	⊆	NUM
ejpam-3966	309	96	fj	fj	X
ejpam-3966	309	97	.	.	PUNCT
ejpam-3966	310	1	in	in	ADP
ejpam-3966	310	2	particular	particular	ADJ
ejpam-3966	310	3	,	,	PUNCT
ejpam-3966	310	4	{	{	PUNCT
ejpam-3966	310	5	x	x	NOUN
ejpam-3966	310	6	/	/	SYM
ejpam-3966	310	7	fi	fi	NOUN
ejpam-3966	310	8	,	,	PUNCT
ejpam-3966	310	9	ϕfifj	ϕfifj	PROPN
ejpam-3966	310	10	,	,	PUNCT
ejpam-3966	310	11	i	i	PRON
ejpam-3966	310	12	}	}	PUNCT
ejpam-3966	310	13	is	be	AUX
ejpam-3966	310	14	a	a	DET
ejpam-3966	310	15	normal	normal	ADJ
ejpam-3966	310	16	completion	completion	NOUN
ejpam-3966	310	17	of	of	ADP
ejpam-3966	310	18	x.	x.	NOUN
ejpam-3966	310	19	example	example	NOUN
ejpam-3966	310	20	2	2	X
ejpam-3966	310	21	.	.	X
ejpam-3966	310	22	consider	consider	VERB
ejpam-3966	310	23	the	the	DET
ejpam-3966	310	24	inverse	inverse	NOUN
ejpam-3966	310	25	system	system	NOUN
ejpam-3966	310	26	{	{	PUNCT
ejpam-3966	310	27	x	x	NOUN
ejpam-3966	310	28	/	/	SYM
ejpam-3966	310	29	fi	fi	NOUN
ejpam-3966	310	30	,	,	PUNCT
ejpam-3966	310	31	ϕfifj	ϕfifj	PROPN
ejpam-3966	310	32	,	,	PUNCT
ejpam-3966	310	33	i	i	PRON
ejpam-3966	310	34	}	}	PUNCT
ejpam-3966	310	35	in	in	ADP
ejpam-3966	310	36	example	example	NOUN
ejpam-3966	311	1	1	1	X
ejpam-3966	311	2	.	.	PUNCT
ejpam-3966	311	3	then	then	ADV
ejpam-3966	311	4	lim←−x	lim←−x	PROPN
ejpam-3966	311	5	/	/	SYM
ejpam-3966	311	6	fi	fi	NOUN
ejpam-3966	311	7	=	=	PUNCT
ejpam-3966	311	8	{	{	PUNCT
ejpam-3966	311	9	(	(	PUNCT
ejpam-3966	311	10	[	[	X
ejpam-3966	311	11	x]fi	x]fi	X
ejpam-3966	311	12	)	)	PUNCT
ejpam-3966	311	13	∈	∈	PROPN
ejpam-3966	311	14	∏8	∏8	ADJ
ejpam-3966	311	15	i=1x	i=1x	ADJ
ejpam-3966	311	16	/	/	SYM
ejpam-3966	311	17	fi	fi	NOUN
ejpam-3966	311	18	|	|	NOUN
ejpam-3966	311	19	∀	∀	NOUN
ejpam-3966	311	20	fi	fi	NOUN
ejpam-3966	311	21	,	,	PUNCT
ejpam-3966	311	22	fj	fj	PROPN
ejpam-3966	311	23	∈	∈	PROPN
ejpam-3966	312	1	i	i	PRON
ejpam-3966	312	2	such	such	ADJ
ejpam-3966	312	3	that	that	DET
ejpam-3966	312	4	fi	fi	NOUN
ejpam-3966	312	5	≥	≥	X
ejpam-3966	312	6	fj	fj	INTJ
ejpam-3966	312	7	,	,	PUNCT
ejpam-3966	312	8	ϕfifj	ϕfifj	PROPN
ejpam-3966	312	9	(	(	PUNCT
ejpam-3966	312	10	[	[	X
ejpam-3966	312	11	x]fi	x]fi	X
ejpam-3966	312	12	)	)	PUNCT
ejpam-3966	312	13	=	=	PUNCT
ejpam-3966	313	1	[	[	X
ejpam-3966	313	2	x]fj	x]fj	X
ejpam-3966	313	3	}	}	PUNCT
ejpam-3966	313	4	.	.	PUNCT
ejpam-3966	314	1	now	now	ADV
ejpam-3966	314	2	,	,	PUNCT
ejpam-3966	314	3	the	the	DET
ejpam-3966	314	4	elements	element	NOUN
ejpam-3966	314	5	α1	α1	PROPN
ejpam-3966	314	6	=	=	SYM
ejpam-3966	314	7	(	(	PUNCT
ejpam-3966	314	8	[	[	X
ejpam-3966	314	9	1]f1	1]f1	NUM
ejpam-3966	314	10	,	,	PUNCT
ejpam-3966	314	11	[	[	X
ejpam-3966	314	12	1]f2	1]f2	NUM
ejpam-3966	314	13	,	,	PUNCT
ejpam-3966	314	14	[	[	X
ejpam-3966	314	15	1]f3	1]f3	NUM
ejpam-3966	314	16	,	,	PUNCT
ejpam-3966	314	17	[	[	X
ejpam-3966	314	18	1]f4	1]f4	NUM
ejpam-3966	314	19	,	,	PUNCT
ejpam-3966	314	20	[	[	X
ejpam-3966	314	21	1]f5	1]f5	NUM
ejpam-3966	314	22	,	,	PUNCT
ejpam-3966	314	23	[	[	X
ejpam-3966	314	24	1]f6	1]f6	NUM
ejpam-3966	314	25	,	,	PUNCT
ejpam-3966	314	26	[	[	X
ejpam-3966	314	27	1]f7	1]f7	NUM
ejpam-3966	314	28	,	,	PUNCT
ejpam-3966	314	29	[	[	X
ejpam-3966	314	30	1]f8	1]f8	NUM
ejpam-3966	314	31	)	)	PUNCT
ejpam-3966	314	32	,	,	PUNCT
ejpam-3966	314	33	α2	α2	PROPN
ejpam-3966	314	34	=	=	SYM
ejpam-3966	314	35	(	(	PUNCT
ejpam-3966	314	36	[	[	X
ejpam-3966	314	37	a]f1	a]f1	X
ejpam-3966	314	38	,	,	PUNCT
ejpam-3966	314	39	[	[	X
ejpam-3966	314	40	1]f2	1]f2	NUM
ejpam-3966	314	41	,	,	PUNCT
ejpam-3966	314	42	[	[	X
ejpam-3966	314	43	a]f3	a]f3	X
ejpam-3966	314	44	,	,	PUNCT
ejpam-3966	314	45	[	[	X
ejpam-3966	314	46	a]f4	a]f4	ADV
ejpam-3966	314	47	,	,	PUNCT
ejpam-3966	314	48	[	[	X
ejpam-3966	314	49	1]f5	1]f5	X
ejpam-3966	314	50	,	,	PUNCT
ejpam-3966	314	51	[	[	X
ejpam-3966	314	52	1]f6	1]f6	NUM
ejpam-3966	314	53	,	,	PUNCT
ejpam-3966	314	54	[	[	X
ejpam-3966	314	55	a]f7	a]f7	X
ejpam-3966	314	56	,	,	PUNCT
ejpam-3966	314	57	[	[	X
ejpam-3966	314	58	1]f8	1]f8	NUM
ejpam-3966	314	59	)	)	PUNCT
ejpam-3966	314	60	,	,	PUNCT
ejpam-3966	314	61	α3	α3	NOUN
ejpam-3966	314	62	=	=	SYM
ejpam-3966	314	63	(	(	PUNCT
ejpam-3966	314	64	[	[	X
ejpam-3966	314	65	b]f1	b]f1	X
ejpam-3966	314	66	,	,	PUNCT
ejpam-3966	314	67	[	[	X
ejpam-3966	314	68	b]f2	b]f2	X
ejpam-3966	314	69	,	,	PUNCT
ejpam-3966	315	1	[	[	X
ejpam-3966	315	2	1]f3	1]f3	NUM
ejpam-3966	315	3	,	,	PUNCT
ejpam-3966	315	4	[	[	X
ejpam-3966	315	5	b]f4	b]f4	X
ejpam-3966	315	6	,	,	PUNCT
ejpam-3966	315	7	[	[	X
ejpam-3966	315	8	1]f5	1]f5	X
ejpam-3966	315	9	,	,	PUNCT
ejpam-3966	315	10	[	[	X
ejpam-3966	315	11	b]f6	b]f6	NOUN
ejpam-3966	315	12	,	,	PUNCT
ejpam-3966	315	13	[	[	X
ejpam-3966	315	14	1]f7	1]f7	NUM
ejpam-3966	315	15	,	,	PUNCT
ejpam-3966	315	16	[	[	X
ejpam-3966	315	17	1]f8	1]f8	NUM
ejpam-3966	315	18	)	)	PUNCT
ejpam-3966	315	19	,	,	PUNCT
ejpam-3966	315	20	and	and	CCONJ
ejpam-3966	315	21	α4	α4	NOUN
ejpam-3966	315	22	=	=	SYM
ejpam-3966	315	23	(	(	PUNCT
ejpam-3966	315	24	[	[	X
ejpam-3966	315	25	c]f1	c]f1	X
ejpam-3966	315	26	,	,	PUNCT
ejpam-3966	315	27	[	[	X
ejpam-3966	315	28	c]f2	c]f2	X
ejpam-3966	315	29	,	,	PUNCT
ejpam-3966	315	30	[	[	X
ejpam-3966	315	31	c]f3	c]f3	X
ejpam-3966	315	32	,	,	PUNCT
ejpam-3966	315	33	[	[	X
ejpam-3966	315	34	1]f4	1]f4	NUM
ejpam-3966	315	35	,	,	PUNCT
ejpam-3966	315	36	[	[	X
ejpam-3966	315	37	c]f5	c]f5	X
ejpam-3966	315	38	,	,	PUNCT
ejpam-3966	315	39	[	[	X
ejpam-3966	315	40	1]f6	1]f6	NUM
ejpam-3966	315	41	,	,	PUNCT
ejpam-3966	315	42	[	[	X
ejpam-3966	315	43	1]f7	1]f7	NUM
ejpam-3966	315	44	,	,	PUNCT
ejpam-3966	315	45	[	[	X
ejpam-3966	315	46	1]f8	1]f8	NUM
ejpam-3966	315	47	)	)	PUNCT
ejpam-3966	315	48	of	of	ADP
ejpam-3966	315	49	∏8	∏8	ADJ
ejpam-3966	315	50	i=1x	i=1x	ADJ
ejpam-3966	315	51	/	/	SYM
ejpam-3966	315	52	fi	fi	NOUN
ejpam-3966	315	53	are	be	AUX
ejpam-3966	315	54	the	the	DET
ejpam-3966	315	55	only	only	ADJ
ejpam-3966	315	56	elements	element	NOUN
ejpam-3966	315	57	that	that	PRON
ejpam-3966	315	58	satisfies	satisfy	VERB
ejpam-3966	315	59	the	the	DET
ejpam-3966	315	60	condition	condition	NOUN
ejpam-3966	315	61	of	of	ADP
ejpam-3966	315	62	lim←−x	lim←−x	PROPN
ejpam-3966	315	63	/	/	SYM
ejpam-3966	315	64	fi	fi	NOUN
ejpam-3966	315	65	.	.	PUNCT
ejpam-3966	316	1	thus	thus	ADV
ejpam-3966	316	2	,	,	PUNCT
ejpam-3966	316	3	lim←−x	lim←−x	PROPN
ejpam-3966	316	4	/	/	SYM
ejpam-3966	316	5	fi	fi	NOUN
ejpam-3966	316	6	=	=	NOUN
ejpam-3966	316	7	{	{	PUNCT
ejpam-3966	316	8	α1	α1	PROPN
ejpam-3966	316	9	,	,	PUNCT
ejpam-3966	316	10	α2	α2	ADJ
ejpam-3966	316	11	,	,	PUNCT
ejpam-3966	316	12	α3	α3	NOUN
ejpam-3966	316	13	,	,	PUNCT
ejpam-3966	316	14	α4	α4	NOUN
ejpam-3966	316	15	}	}	PUNCT
ejpam-3966	316	16	.	.	PUNCT
ejpam-3966	317	1	references	reference	NOUN
ejpam-3966	317	2	[	[	X
ejpam-3966	317	3	1	1	NUM
ejpam-3966	317	4	]	]	X
ejpam-3966	317	5	y.	y.	PROPN
ejpam-3966	317	6	imai	imai	PROPN
ejpam-3966	317	7	and	and	CCONJ
ejpam-3966	317	8	k.	k.	PROPN
ejpam-3966	317	9	iséki	iséki	PROPN
ejpam-3966	317	10	.	.	PROPN
ejpam-3966	318	1	on	on	ADP
ejpam-3966	318	2	axiom	axiom	NOUN
ejpam-3966	318	3	systems	system	NOUN
ejpam-3966	318	4	of	of	ADP
ejpam-3966	318	5	propositional	propositional	ADJ
ejpam-3966	318	6	calculi	calculi	PROPN
ejpam-3966	318	7	xiv	xiv	PROPN
ejpam-3966	318	8	.	.	PUNCT
ejpam-3966	319	1	proceedings	proceeding	NOUN
ejpam-3966	319	2	of	of	ADP
ejpam-3966	319	3	the	the	DET
ejpam-3966	319	4	japan	japan	PROPN
ejpam-3966	319	5	academy	academy	PROPN
ejpam-3966	319	6	,	,	PUNCT
ejpam-3966	319	7	42:19–22	42:19–22	NUM
ejpam-3966	319	8	,	,	PUNCT
ejpam-3966	319	9	1996	1996	NUM
ejpam-3966	319	10	.	.	PUNCT
ejpam-3966	320	1	[	[	X
ejpam-3966	320	2	2	2	NUM
ejpam-3966	320	3	]	]	X
ejpam-3966	320	4	h.s	h.s	PROPN
ejpam-3966	320	5	.	.	PROPN
ejpam-3966	320	6	kim	kim	PROPN
ejpam-3966	320	7	and	and	CCONJ
ejpam-3966	320	8	y.h	y.h	PROPN
ejpam-3966	320	9	.	.	PROPN
ejpam-3966	320	10	kim	kim	PROPN
ejpam-3966	320	11	.	.	PUNCT
ejpam-3966	321	1	on	on	ADP
ejpam-3966	321	2	be	be	AUX
ejpam-3966	321	3	-	-	PUNCT
ejpam-3966	321	4	algebras	algebra	NOUN
ejpam-3966	321	5	.	.	PUNCT
ejpam-3966	322	1	scientiae	scientiae	PROPN
ejpam-3966	322	2	mathematicae	mathematicae	VERB
ejpam-3966	322	3	japonicae	japonicae	PROPN
ejpam-3966	322	4	online	online	ADV
ejpam-3966	322	5	,	,	PUNCT
ejpam-3966	322	6	pages	page	NOUN
ejpam-3966	322	7	1299–1302	1299–1302	NUM
ejpam-3966	322	8	,	,	PUNCT
ejpam-3966	322	9	2004	2004	NUM
ejpam-3966	322	10	.	.	PUNCT
ejpam-3966	323	1	[	[	X
ejpam-3966	323	2	3	3	X
ejpam-3966	323	3	]	]	X
ejpam-3966	323	4	k.h	k.h	PROPN
ejpam-3966	323	5	.	.	PROPN
ejpam-3966	323	6	kim	kim	PROPN
ejpam-3966	323	7	and	and	CCONJ
ejpam-3966	323	8	y.h	y.h	PROPN
ejpam-3966	323	9	.	.	PROPN
ejpam-3966	323	10	yon	yon	PROPN
ejpam-3966	323	11	.	.	PUNCT
ejpam-3966	324	1	dual	dual	ADJ
ejpam-3966	324	2	bck	bck	NOUN
ejpam-3966	324	3	-	-	PUNCT
ejpam-3966	324	4	algebra	algebra	PROPN
ejpam-3966	324	5	and	and	CCONJ
ejpam-3966	324	6	mv	mv	NOUN
ejpam-3966	324	7	-	-	NOUN
ejpam-3966	324	8	algebra	algebra	NOUN
ejpam-3966	324	9	.	.	PUNCT
ejpam-3966	325	1	scientiae	scientiae	PROPN
ejpam-3966	325	2	mathematicae	mathematicae	VERB
ejpam-3966	325	3	japonicae	japonicae	PROPN
ejpam-3966	325	4	online	online	ADV
ejpam-3966	325	5	,	,	PUNCT
ejpam-3966	325	6	pages	page	NOUN
ejpam-3966	325	7	393–399	393–399	NUM
ejpam-3966	325	8	,	,	PUNCT
ejpam-3966	325	9	2007	2007	NUM
ejpam-3966	325	10	.	.	PUNCT
ejpam-3966	326	1	[	[	X
ejpam-3966	326	2	4	4	X
ejpam-3966	326	3	]	]	X
ejpam-3966	326	4	s.r	s.r	PROPN
ejpam-3966	326	5	.	.	PROPN
ejpam-3966	326	6	mukkamala	mukkamala	PROPN
ejpam-3966	326	7	.	.	PUNCT
ejpam-3966	327	1	a	a	DET
ejpam-3966	327	2	course	course	NOUN
ejpam-3966	327	3	in	in	ADP
ejpam-3966	327	4	be	be	NOUN
ejpam-3966	327	5	-	-	PUNCT
ejpam-3966	327	6	algebra	algebra	NOUN
ejpam-3966	327	7	.	.	PUNCT
ejpam-3966	328	1	springer	springer	NOUN
ejpam-3966	328	2	nature	nature	PROPN
ejpam-3966	328	3	singapore	singapore	PROPN
ejpam-3966	328	4	pte	pte	PROPN
ejpam-3966	328	5	ltd	ltd	PROPN
ejpam-3966	328	6	.	.	PROPN
ejpam-3966	328	7	,	,	PUNCT
ejpam-3966	328	8	singapore	singapore	PROPN
ejpam-3966	328	9	,	,	PUNCT
ejpam-3966	328	10	2018	2018	NUM
ejpam-3966	328	11	.	.	PUNCT
ejpam-3966	329	1	[	[	X
ejpam-3966	329	2	5	5	X
ejpam-3966	329	3	]	]	PUNCT
ejpam-3966	329	4	l.	l.	NOUN
ejpam-3966	329	5	ribes	ribes	PROPN
ejpam-3966	329	6	and	and	CCONJ
ejpam-3966	329	7	p.	p.	PROPN
ejpam-3966	329	8	zalesskii	zalesskii	PROPN
ejpam-3966	329	9	.	.	PUNCT
ejpam-3966	330	1	profinite	profinite	NOUN
ejpam-3966	330	2	groups	group	NOUN
ejpam-3966	330	3	.	.	PUNCT
ejpam-3966	331	1	springer	springer	NOUN
ejpam-3966	331	2	,	,	PUNCT
ejpam-3966	331	3	verlag	verlag	PROPN
ejpam-3966	331	4	berlin	berlin	PROPN
ejpam-3966	331	5	heidelberg	heidelberg	PROPN
ejpam-3966	331	6	,	,	PUNCT
ejpam-3966	331	7	2010	2010	NUM
ejpam-3966	331	8	.	.	PUNCT
ejpam-3966	332	1	[	[	X
ejpam-3966	332	2	6	6	NUM
ejpam-3966	332	3	]	]	PUNCT
ejpam-3966	332	4	a.	a.	NOUN
ejpam-3966	332	5	walendziak	walendziak	PROPN
ejpam-3966	332	6	.	.	PUNCT
ejpam-3966	333	1	on	on	ADP
ejpam-3966	333	2	normal	normal	ADJ
ejpam-3966	333	3	filters	filter	NOUN
ejpam-3966	333	4	and	and	CCONJ
ejpam-3966	333	5	congruence	congruence	NOUN
ejpam-3966	333	6	relations	relation	NOUN
ejpam-3966	333	7	in	in	ADP
ejpam-3966	333	8	be	be	NOUN
ejpam-3966	333	9	-	-	PUNCT
ejpam-3966	333	10	algebras	algebra	NOUN
ejpam-3966	333	11	.	.	PUNCT
ejpam-3966	334	1	commentationes	commentatione	NOUN
ejpam-3966	334	2	mathematicae	mathematicae	PROPN
ejpam-3966	334	3	,	,	PUNCT
ejpam-3966	334	4	52:199–205	52:199–205	PROPN
ejpam-3966	334	5	,	,	PUNCT
ejpam-3966	334	6	2012	2012	NUM
ejpam-3966	334	7	.	.	PUNCT