id	sid	tid	token	lemma	pos
ejpam-6131	1	1	european	european	PROPN
ejpam-6131	1	2	journal	journal	PROPN
ejpam-6131	1	3	of	of	ADP
ejpam-6131	1	4	pure	pure	ADJ
ejpam-6131	1	5	and	and	CCONJ
ejpam-6131	1	6	applied	applied	ADJ
ejpam-6131	1	7	mathematics	mathematic	NOUN
ejpam-6131	1	8	2025	2025	NUM
ejpam-6131	1	9	,	,	PUNCT
ejpam-6131	1	10	vol	vol	NOUN
ejpam-6131	1	11	.	.	PROPN
ejpam-6131	1	12	18	18	NUM
ejpam-6131	1	13	,	,	PUNCT
ejpam-6131	1	14	issue	issue	NOUN
ejpam-6131	1	15	2	2	NUM
ejpam-6131	1	16	,	,	PUNCT
ejpam-6131	1	17	article	article	NOUN
ejpam-6131	1	18	number	number	NOUN
ejpam-6131	1	19	6131	6131	NUM
ejpam-6131	1	20	issn	issn	PROPN
ejpam-6131	1	21	1307	1307	NUM
ejpam-6131	1	22	-	-	SYM
ejpam-6131	1	23	5543	5543	NUM
ejpam-6131	1	24	–	–	PUNCT
ejpam-6131	2	1	ejpam.com	ejpam.com	X
ejpam-6131	2	2	published	publish	VERB
ejpam-6131	2	3	by	by	ADP
ejpam-6131	2	4	new	new	PROPN
ejpam-6131	2	5	york	york	PROPN
ejpam-6131	2	6	business	business	PROPN
ejpam-6131	2	7	global	global	ADJ
ejpam-6131	2	8	uniqueness	uniqueness	NOUN
ejpam-6131	2	9	of	of	ADP
ejpam-6131	2	10	stationary	stationary	ADJ
ejpam-6131	2	11	distribution	distribution	NOUN
ejpam-6131	2	12	in	in	ADP
ejpam-6131	2	13	markov	markov	NOUN
ejpam-6131	2	14	processes	process	NOUN
ejpam-6131	2	15	:	:	PUNCT
ejpam-6131	2	16	a	a	DET
ejpam-6131	2	17	quintuple	quintuple	ADV
ejpam-6131	2	18	fixed	fix	VERB
ejpam-6131	2	19	point	point	NOUN
ejpam-6131	2	20	and	and	CCONJ
ejpam-6131	2	21	coincidence	coincidence	NOUN
ejpam-6131	2	22	point	point	NOUN
ejpam-6131	2	23	approach	approach	NOUN
ejpam-6131	2	24	samina	samina	PROPN
ejpam-6131	2	25	batul1,∗	batul1,∗	PROPN
ejpam-6131	2	26	,	,	PUNCT
ejpam-6131	2	27	sidra	sidra	PROPN
ejpam-6131	2	28	fida1	fida1	PROPN
ejpam-6131	2	29	,	,	PUNCT
ejpam-6131	2	30	dur	dur	PROPN
ejpam-6131	2	31	-	-	PUNCT
ejpam-6131	2	32	e	e	ADJ
ejpam-6131	2	33	-	-	ADJ
ejpam-6131	2	34	shehwar	shehwar	ADJ
ejpam-6131	2	35	sagheer1	sagheer1	NOUN
ejpam-6131	2	36	,	,	PUNCT
ejpam-6131	2	37	,	,	PUNCT
ejpam-6131	2	38	hassen	hassen	PROPN
ejpam-6131	2	39	aydi2,3	aydi2,3	PROPN
ejpam-6131	2	40	,	,	PUNCT
ejpam-6131	2	41	saber	saber	NOUN
ejpam-6131	2	42	mansour4	mansour4	PROPN
ejpam-6131	2	43	1	1	NUM
ejpam-6131	2	44	department	department	NOUN
ejpam-6131	2	45	of	of	ADP
ejpam-6131	2	46	mathematics	mathematic	NOUN
ejpam-6131	2	47	,	,	PUNCT
ejpam-6131	2	48	capital	capital	NOUN
ejpam-6131	2	49	university	university	PROPN
ejpam-6131	2	50	of	of	ADP
ejpam-6131	2	51	science	science	NOUN
ejpam-6131	2	52	and	and	CCONJ
ejpam-6131	2	53	technology	technology	NOUN
ejpam-6131	2	54	,	,	PUNCT
ejpam-6131	2	55	islamabad	islamabad	PROPN
ejpam-6131	2	56	,	,	PUNCT
ejpam-6131	2	57	pakistan	pakistan	PROPN
ejpam-6131	2	58	2	2	NUM
ejpam-6131	2	59	université	université	NOUN
ejpam-6131	2	60	de	de	X
ejpam-6131	2	61	sousse	sousse	PROPN
ejpam-6131	2	62	,	,	PUNCT
ejpam-6131	2	63	institut	institut	PROPN
ejpam-6131	2	64	supérieur	supérieur	PROPN
ejpam-6131	2	65	d’informatique	d’informatique	PROPN
ejpam-6131	2	66	et	et	NOUN
ejpam-6131	2	67	des	des	X
ejpam-6131	2	68	techniques	techniques	X
ejpam-6131	2	69	de	de	X
ejpam-6131	2	70	communication	communication	NOUN
ejpam-6131	2	71	,	,	PUNCT
ejpam-6131	2	72	h.	h.	PROPN
ejpam-6131	2	73	sousse	sousse	PROPN
ejpam-6131	2	74	4000	4000	NUM
ejpam-6131	2	75	,	,	PUNCT
ejpam-6131	2	76	tunisia	tunisia	PROPN
ejpam-6131	2	77	3department	3department	NUM
ejpam-6131	2	78	of	of	ADP
ejpam-6131	2	79	mathematics	mathematic	NOUN
ejpam-6131	2	80	,	,	PUNCT
ejpam-6131	2	81	sefako	sefako	VERB
ejpam-6131	2	82	makgatho	makgatho	PROPN
ejpam-6131	2	83	health	health	PROPN
ejpam-6131	2	84	sciences	sciences	PROPN
ejpam-6131	2	85	university	university	PROPN
ejpam-6131	2	86	,	,	PUNCT
ejpam-6131	2	87	ga	ga	PROPN
ejpam-6131	2	88	-	-	NOUN
ejpam-6131	2	89	rankuwa	rankuwa	PROPN
ejpam-6131	2	90	,	,	PUNCT
ejpam-6131	2	91	south	south	PROPN
ejpam-6131	2	92	africa	africa	PROPN
ejpam-6131	2	93	4	4	NUM
ejpam-6131	2	94	department	department	NOUN
ejpam-6131	2	95	of	of	ADP
ejpam-6131	2	96	mathematics	mathematic	NOUN
ejpam-6131	2	97	,	,	PUNCT
ejpam-6131	2	98	umm	umm	INTJ
ejpam-6131	2	99	al	al	PROPN
ejpam-6131	2	100	-	-	PUNCT
ejpam-6131	2	101	qura	qura	PROPN
ejpam-6131	2	102	university	university	NOUN
ejpam-6131	2	103	,	,	PUNCT
ejpam-6131	2	104	faculty	faculty	NOUN
ejpam-6131	2	105	of	of	ADP
ejpam-6131	2	106	sciences	sciences	PROPN
ejpam-6131	2	107	,	,	PUNCT
ejpam-6131	2	108	p.o	p.o	PROPN
ejpam-6131	2	109	.	.	PROPN
ejpam-6131	2	110	box	box	PROPN
ejpam-6131	2	111	14035	14035	NUM
ejpam-6131	2	112	,	,	PUNCT
ejpam-6131	2	113	holly	holly	PROPN
ejpam-6131	2	114	makkah	makkah	PROPN
ejpam-6131	2	115	21955	21955	NUM
ejpam-6131	2	116	,	,	PUNCT
ejpam-6131	2	117	saudi	saudi	PROPN
ejpam-6131	2	118	arabia	arabia	PROPN
ejpam-6131	2	119	abstract	abstract	NOUN
ejpam-6131	2	120	.	.	PUNCT
ejpam-6131	3	1	this	this	DET
ejpam-6131	3	2	article	article	NOUN
ejpam-6131	3	3	introduces	introduce	VERB
ejpam-6131	3	4	the	the	DET
ejpam-6131	3	5	concept	concept	NOUN
ejpam-6131	3	6	of	of	ADP
ejpam-6131	3	7	quintuple	quintuple	ADV
ejpam-6131	3	8	fixed	fix	VERB
ejpam-6131	3	9	points	point	NOUN
ejpam-6131	3	10	and	and	CCONJ
ejpam-6131	3	11	coincidence	coincidence	NOUN
ejpam-6131	3	12	points	point	NOUN
ejpam-6131	3	13	for	for	ADP
ejpam-6131	3	14	matrix	matrix	NOUN
ejpam-6131	3	15	-	-	PUNCT
ejpam-6131	3	16	related	relate	VERB
ejpam-6131	3	17	mappings	mapping	NOUN
ejpam-6131	3	18	in	in	ADP
ejpam-6131	3	19	generalized	generalized	ADJ
ejpam-6131	3	20	metric	metric	ADJ
ejpam-6131	3	21	spaces	space	NOUN
ejpam-6131	3	22	.	.	PUNCT
ejpam-6131	4	1	furthermore	furthermore	ADV
ejpam-6131	4	2	,	,	PUNCT
ejpam-6131	4	3	the	the	DET
ejpam-6131	4	4	existence	existence	NOUN
ejpam-6131	4	5	of	of	ADP
ejpam-6131	4	6	quintuple	quintuple	ADJ
ejpam-6131	4	7	coincidence	coincidence	NOUN
ejpam-6131	4	8	points	point	NOUN
ejpam-6131	4	9	is	be	AUX
ejpam-6131	4	10	established	establish	VERB
ejpam-6131	4	11	.	.	PUNCT
ejpam-6131	5	1	this	this	DET
ejpam-6131	5	2	task	task	NOUN
ejpam-6131	5	3	is	be	AUX
ejpam-6131	5	4	achieved	achieve	VERB
ejpam-6131	5	5	by	by	ADP
ejpam-6131	5	6	leveraging	leverage	VERB
ejpam-6131	5	7	the	the	DET
ejpam-6131	5	8	structure	structure	NOUN
ejpam-6131	5	9	of	of	ADP
ejpam-6131	5	10	matrices	matrix	NOUN
ejpam-6131	5	11	.	.	PUNCT
ejpam-6131	6	1	we	we	PRON
ejpam-6131	6	2	derive	derive	VERB
ejpam-6131	6	3	several	several	ADJ
ejpam-6131	6	4	corollaries	corollary	NOUN
ejpam-6131	6	5	as	as	ADP
ejpam-6131	6	6	special	special	ADJ
ejpam-6131	6	7	cases	case	NOUN
ejpam-6131	6	8	of	of	ADP
ejpam-6131	6	9	our	our	PRON
ejpam-6131	6	10	main	main	ADJ
ejpam-6131	6	11	results	result	NOUN
ejpam-6131	6	12	.	.	PUNCT
ejpam-6131	7	1	these	these	DET
ejpam-6131	7	2	corollaries	corollary	NOUN
ejpam-6131	7	3	provide	provide	VERB
ejpam-6131	7	4	evidence	evidence	NOUN
ejpam-6131	7	5	for	for	ADP
ejpam-6131	7	6	the	the	DET
ejpam-6131	7	7	authentication	authentication	NOUN
ejpam-6131	7	8	of	of	ADP
ejpam-6131	7	9	the	the	DET
ejpam-6131	7	10	proven	prove	VERB
ejpam-6131	7	11	results	result	NOUN
ejpam-6131	7	12	.	.	PUNCT
ejpam-6131	8	1	to	to	PART
ejpam-6131	8	2	validate	validate	VERB
ejpam-6131	8	3	the	the	DET
ejpam-6131	8	4	significance	significance	NOUN
ejpam-6131	8	5	of	of	ADP
ejpam-6131	8	6	our	our	PRON
ejpam-6131	8	7	findings	finding	NOUN
ejpam-6131	8	8	,	,	PUNCT
ejpam-6131	8	9	we	we	PRON
ejpam-6131	8	10	provide	provide	VERB
ejpam-6131	8	11	a	a	DET
ejpam-6131	8	12	selection	selection	NOUN
ejpam-6131	8	13	of	of	ADP
ejpam-6131	8	14	non	non	ADJ
ejpam-6131	8	15	-	-	ADJ
ejpam-6131	8	16	trivial	trivial	ADJ
ejpam-6131	8	17	examples	example	NOUN
ejpam-6131	8	18	.	.	PUNCT
ejpam-6131	9	1	eventually	eventually	ADV
ejpam-6131	9	2	,	,	PUNCT
ejpam-6131	9	3	we	we	PRON
ejpam-6131	9	4	demonstrate	demonstrate	VERB
ejpam-6131	9	5	the	the	DET
ejpam-6131	9	6	practical	practical	ADJ
ejpam-6131	9	7	applicability	applicability	NOUN
ejpam-6131	9	8	of	of	ADP
ejpam-6131	9	9	our	our	PRON
ejpam-6131	9	10	established	establish	VERB
ejpam-6131	9	11	results	result	NOUN
ejpam-6131	9	12	by	by	ADP
ejpam-6131	9	13	applying	apply	VERB
ejpam-6131	9	14	them	they	PRON
ejpam-6131	9	15	to	to	PART
ejpam-6131	9	16	determine	determine	VERB
ejpam-6131	9	17	the	the	DET
ejpam-6131	9	18	stationary	stationary	ADJ
ejpam-6131	9	19	distribution	distribution	NOUN
ejpam-6131	9	20	of	of	ADP
ejpam-6131	9	21	a	a	DET
ejpam-6131	9	22	markov	markov	NOUN
ejpam-6131	9	23	process	process	NOUN
ejpam-6131	9	24	.	.	PUNCT
ejpam-6131	10	1	2020	2020	NUM
ejpam-6131	10	2	mathematics	mathematic	NOUN
ejpam-6131	10	3	subject	subject	NOUN
ejpam-6131	10	4	classifications	classification	NOUN
ejpam-6131	10	5	:	:	PUNCT
ejpam-6131	10	6	47h10	47h10	NUM
ejpam-6131	10	7	,	,	PUNCT
ejpam-6131	10	8	54h25	54h25	NUM
ejpam-6131	10	9	key	key	ADJ
ejpam-6131	10	10	words	word	NOUN
ejpam-6131	10	11	and	and	CCONJ
ejpam-6131	10	12	phrases	phrase	NOUN
ejpam-6131	10	13	:	:	PUNCT
ejpam-6131	10	14	generalized	generalize	VERB
ejpam-6131	10	15	metric	metric	ADJ
ejpam-6131	10	16	space	space	NOUN
ejpam-6131	10	17	(	(	PUNCT
ejpam-6131	10	18	gms	gms	NOUN
ejpam-6131	10	19	)	)	PUNCT
ejpam-6131	10	20	,	,	PUNCT
ejpam-6131	10	21	markov	markov	NOUN
ejpam-6131	10	22	process	process	NOUN
ejpam-6131	10	23	,	,	PUNCT
ejpam-6131	10	24	partially	partially	ADV
ejpam-6131	10	25	ordered	order	VERB
ejpam-6131	10	26	metric	metric	ADJ
ejpam-6131	10	27	spaces	space	NOUN
ejpam-6131	10	28	(	(	PUNCT
ejpam-6131	10	29	pom	pom	NOUN
ejpam-6131	10	30	)	)	PUNCT
ejpam-6131	10	31	,	,	PUNCT
ejpam-6131	10	32	tripled	triple	VERB
ejpam-6131	10	33	fixed	fix	VERB
ejpam-6131	10	34	point	point	NOUN
ejpam-6131	10	35	(	(	PUNCT
ejpam-6131	10	36	tfp	tfp	PROPN
ejpam-6131	10	37	)	)	PUNCT
ejpam-6131	10	38	,	,	PUNCT
ejpam-6131	10	39	quintuple	quintuple	ADV
ejpam-6131	10	40	fixed	fix	VERB
ejpam-6131	10	41	point(qfp	point(qfp	NOUN
ejpam-6131	10	42	)	)	PUNCT
ejpam-6131	10	43	1	1	NUM
ejpam-6131	10	44	.	.	X
ejpam-6131	11	1	introduction	introduction	NOUN
ejpam-6131	11	2	functional	functional	ADJ
ejpam-6131	11	3	analysis	analysis	NOUN
ejpam-6131	11	4	has	have	VERB
ejpam-6131	11	5	far	far	ADV
ejpam-6131	11	6	-	-	PUNCT
ejpam-6131	11	7	reaching	reach	VERB
ejpam-6131	11	8	applications	application	NOUN
ejpam-6131	11	9	in	in	ADP
ejpam-6131	11	10	various	various	ADJ
ejpam-6131	11	11	fields	field	NOUN
ejpam-6131	11	12	,	,	PUNCT
ejpam-6131	11	13	including	include	VERB
ejpam-6131	11	14	linear	linear	ADJ
ejpam-6131	11	15	and	and	CCONJ
ejpam-6131	11	16	nonlinear	nonlinear	ADJ
ejpam-6131	11	17	analysis	analysis	NOUN
ejpam-6131	11	18	,	,	PUNCT
ejpam-6131	11	19	calculus	calculus	NOUN
ejpam-6131	11	20	of	of	ADP
ejpam-6131	11	21	variations	variation	NOUN
ejpam-6131	11	22	,	,	PUNCT
ejpam-6131	11	23	approximation	approximation	NOUN
ejpam-6131	11	24	theory	theory	NOUN
ejpam-6131	11	25	,	,	PUNCT
ejpam-6131	11	26	numerical	numerical	ADJ
ejpam-6131	11	27	analysis	analysis	NOUN
ejpam-6131	11	28	,	,	PUNCT
ejpam-6131	11	29	and	and	CCONJ
ejpam-6131	11	30	differential	differential	ADJ
ejpam-6131	11	31	and	and	CCONJ
ejpam-6131	11	32	integral	integral	ADJ
ejpam-6131	11	33	equations	equation	NOUN
ejpam-6131	11	34	.	.	PUNCT
ejpam-6131	12	1	in	in	ADP
ejpam-6131	12	2	nonlinear	nonlinear	ADJ
ejpam-6131	12	3	analysis	analysis	NOUN
ejpam-6131	12	4	,	,	PUNCT
ejpam-6131	12	5	metric	metric	ADJ
ejpam-6131	12	6	fixed	fix	VERB
ejpam-6131	12	7	point	point	NOUN
ejpam-6131	12	8	theory	theory	NOUN
ejpam-6131	12	9	is	be	AUX
ejpam-6131	12	10	a	a	DET
ejpam-6131	12	11	fundamental	fundamental	ADJ
ejpam-6131	12	12	tool	tool	NOUN
ejpam-6131	12	13	.	.	PUNCT
ejpam-6131	13	1	currently	currently	ADV
ejpam-6131	13	2	,	,	PUNCT
ejpam-6131	13	3	finding	find	VERB
ejpam-6131	13	4	solutions	solution	NOUN
ejpam-6131	13	5	to	to	PART
ejpam-6131	13	6	differential	differential	VERB
ejpam-6131	13	7	and	and	CCONJ
ejpam-6131	13	8	integral	integral	ADJ
ejpam-6131	13	9	equations	equation	NOUN
ejpam-6131	13	10	is	be	AUX
ejpam-6131	13	11	a	a	DET
ejpam-6131	13	12	∗corresponding	∗corresponde	VERB
ejpam-6131	13	13	author	author	NOUN
ejpam-6131	13	14	.	.	PUNCT
ejpam-6131	14	1	doi	doi	NOUN
ejpam-6131	14	2	:	:	PUNCT
ejpam-6131	14	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6131	https://doi.org/10.29020/nybg.ejpam.v18i2.6131	X
ejpam-6131	14	4	email	email	NOUN
ejpam-6131	14	5	addresses	address	NOUN
ejpam-6131	14	6	:	:	PUNCT
ejpam-6131	15	1	samina.batul@cust.edu.pk	samina.batul@cust.edu.pk	PROPN
ejpam-6131	15	2	(	(	PUNCT
ejpam-6131	15	3	s.	s.	PROPN
ejpam-6131	15	4	batul	batul	PROPN
ejpam-6131	15	5	)	)	PUNCT
ejpam-6131	15	6	,	,	PUNCT
ejpam-6131	15	7	mmt221005@cust.pk	mmt221005@cust.pk	PROPN
ejpam-6131	15	8	(	(	PUNCT
ejpam-6131	15	9	s.	s.	PROPN
ejpam-6131	15	10	fida	fida	PROPN
ejpam-6131	15	11	)	)	PUNCT
ejpam-6131	15	12	,	,	PUNCT
ejpam-6131	15	13	d.e.shehwar@cust.edu.pk	d.e.shehwar@cust.edu.pk	PROPN
ejpam-6131	15	14	(	(	PUNCT
ejpam-6131	15	15	d.	d.	PROPN
ejpam-6131	15	16	sagheer	sagheer	PROPN
ejpam-6131	15	17	)	)	PUNCT
ejpam-6131	15	18	,	,	PUNCT
ejpam-6131	15	19	hassen.aydi@isima.rnu.tn	hassen.aydi@isima.rnu.tn	INTJ
ejpam-6131	15	20	(	(	PUNCT
ejpam-6131	15	21	h.	h.	PROPN
ejpam-6131	15	22	aydi	aydi	VERB
ejpam-6131	15	23	)	)	PUNCT
ejpam-6131	15	24	,	,	PUNCT
ejpam-6131	15	25	samansour@uqu.edu.sa	samansour@uqu.edu.sa	PROPN
ejpam-6131	15	26	(	(	PUNCT
ejpam-6131	15	27	s.	s.	PROPN
ejpam-6131	15	28	mansour	mansour	PROPN
ejpam-6131	15	29	)	)	PUNCT
ejpam-6131	15	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6131	15	31	1	1	NUM
ejpam-6131	15	32	copyright	copyright	NOUN
ejpam-6131	15	33	:	:	PUNCT
ejpam-6131	16	1	©	©	PROPN
ejpam-6131	16	2	2025	2025	NUM
ejpam-6131	16	3	the	the	DET
ejpam-6131	16	4	author(s	author(s	NOUN
ejpam-6131	16	5	)	)	PUNCT
ejpam-6131	16	6	.	.	PUNCT
ejpam-6131	17	1	(	(	PUNCT
ejpam-6131	17	2	cc	cc	NOUN
ejpam-6131	17	3	by	by	ADP
ejpam-6131	17	4	-	-	PUNCT
ejpam-6131	17	5	nc	nc	PROPN
ejpam-6131	17	6	4.0	4.0	NUM
ejpam-6131	17	7	)	)	PUNCT
ejpam-6131	17	8	s.	s.	PROPN
ejpam-6131	17	9	batul	batul	PROPN
ejpam-6131	17	10	et	et	PROPN
ejpam-6131	17	11	a.	a.	PROPN
ejpam-6131	17	12	/	/	PUNCT
ejpam-6131	17	13	eur	eur	PROPN
ejpam-6131	17	14	.	.	PUNCT
ejpam-6131	18	1	j.	j.	PROPN
ejpam-6131	18	2	pure	pure	PROPN
ejpam-6131	18	3	appl	appl	PROPN
ejpam-6131	18	4	.	.	PROPN
ejpam-6131	18	5	math	math	PROPN
ejpam-6131	18	6	,	,	PUNCT
ejpam-6131	18	7	18	18	NUM
ejpam-6131	18	8	(	(	PUNCT
ejpam-6131	18	9	2	2	NUM
ejpam-6131	18	10	)	)	PUNCT
ejpam-6131	18	11	(	(	PUNCT
ejpam-6131	18	12	2025	2025	NUM
ejpam-6131	18	13	)	)	PUNCT
ejpam-6131	18	14	,	,	PUNCT
ejpam-6131	18	15	6131	6131	NUM
ejpam-6131	18	16	2	2	NUM
ejpam-6131	18	17	of	of	ADP
ejpam-6131	18	18	22	22	NUM
ejpam-6131	18	19	crucial	crucial	ADJ
ejpam-6131	18	20	research	research	NOUN
ejpam-6131	18	21	area	area	NOUN
ejpam-6131	18	22	.	.	PUNCT
ejpam-6131	19	1	this	this	DET
ejpam-6131	19	2	task	task	NOUN
ejpam-6131	19	3	can	can	AUX
ejpam-6131	19	4	be	be	AUX
ejpam-6131	19	5	achieved	achieve	VERB
ejpam-6131	19	6	by	by	ADP
ejpam-6131	19	7	converting	convert	VERB
ejpam-6131	19	8	the	the	DET
ejpam-6131	19	9	equation	equation	NOUN
ejpam-6131	19	10	into	into	ADP
ejpam-6131	19	11	a	a	DET
ejpam-6131	19	12	fixed	fix	VERB
ejpam-6131	19	13	point	point	NOUN
ejpam-6131	19	14	problem	problem	NOUN
ejpam-6131	19	15	for	for	ADP
ejpam-6131	19	16	a	a	DET
ejpam-6131	19	17	suitable	suitable	ADJ
ejpam-6131	19	18	mapping	mapping	NOUN
ejpam-6131	19	19	and	and	CCONJ
ejpam-6131	19	20	an	an	DET
ejpam-6131	19	21	appropriate	appropriate	ADJ
ejpam-6131	19	22	domain	domain	NOUN
ejpam-6131	19	23	.	.	PUNCT
ejpam-6131	20	1	in	in	ADP
ejpam-6131	20	2	1922	1922	NUM
ejpam-6131	20	3	,	,	PUNCT
ejpam-6131	20	4	stephan	stephan	PROPN
ejpam-6131	20	5	banach	banach	NOUN
ejpam-6131	20	6	[	[	X
ejpam-6131	20	7	1	1	X
ejpam-6131	20	8	]	]	PUNCT
ejpam-6131	20	9	presented	present	VERB
ejpam-6131	20	10	a	a	DET
ejpam-6131	20	11	vital	vital	ADJ
ejpam-6131	20	12	result	result	NOUN
ejpam-6131	20	13	known	know	VERB
ejpam-6131	20	14	as	as	ADP
ejpam-6131	20	15	the	the	DET
ejpam-6131	20	16	banach	banach	NOUN
ejpam-6131	20	17	contraction	contraction	NOUN
ejpam-6131	20	18	principle	principle	NOUN
ejpam-6131	20	19	(	(	PUNCT
ejpam-6131	20	20	bcp	bcp	PROPN
ejpam-6131	20	21	)	)	PUNCT
ejpam-6131	20	22	,	,	PUNCT
ejpam-6131	20	23	which	which	PRON
ejpam-6131	20	24	erected	erect	VERB
ejpam-6131	20	25	a	a	DET
ejpam-6131	20	26	base	base	NOUN
ejpam-6131	20	27	for	for	ADP
ejpam-6131	20	28	metric	metric	ADJ
ejpam-6131	20	29	fixed	fix	VERB
ejpam-6131	20	30	-	-	PUNCT
ejpam-6131	20	31	point	point	NOUN
ejpam-6131	20	32	theory	theory	NOUN
ejpam-6131	20	33	.	.	PUNCT
ejpam-6131	21	1	in	in	ADP
ejpam-6131	21	2	1964	1964	NUM
ejpam-6131	21	3	,	,	PUNCT
ejpam-6131	21	4	perov	perov	VERB
ejpam-6131	22	1	[	[	X
ejpam-6131	22	2	2	2	NUM
ejpam-6131	22	3	]	]	PUNCT
ejpam-6131	22	4	extended	extend	VERB
ejpam-6131	22	5	the	the	DET
ejpam-6131	22	6	classical	classical	ADJ
ejpam-6131	22	7	bcp	bcp	NOUN
ejpam-6131	22	8	on	on	ADP
ejpam-6131	22	9	generalized	generalized	ADJ
ejpam-6131	22	10	metric	metric	ADJ
ejpam-6131	22	11	spaces	space	NOUN
ejpam-6131	22	12	for	for	ADP
ejpam-6131	22	13	contraction	contraction	NOUN
ejpam-6131	22	14	mappings	mapping	NOUN
ejpam-6131	22	15	.	.	PUNCT
ejpam-6131	23	1	filip	filip	NOUN
ejpam-6131	23	2	and	and	CCONJ
ejpam-6131	23	3	petrusel	petrusel	NOUN
ejpam-6131	23	4	[	[	X
ejpam-6131	23	5	3	3	NUM
ejpam-6131	23	6	]	]	PUNCT
ejpam-6131	23	7	further	far	ADV
ejpam-6131	23	8	generalized	generalize	VERB
ejpam-6131	23	9	these	these	DET
ejpam-6131	23	10	results	result	NOUN
ejpam-6131	23	11	on	on	ADP
ejpam-6131	23	12	vector	vector	NOUN
ejpam-6131	23	13	-	-	PUNCT
ejpam-6131	23	14	valued	value	VERB
ejpam-6131	23	15	metric	metric	ADJ
ejpam-6131	23	16	spaces	space	NOUN
ejpam-6131	23	17	for	for	ADP
ejpam-6131	23	18	self	self	NOUN
ejpam-6131	23	19	-	-	PUNCT
ejpam-6131	23	20	mappings	mapping	NOUN
ejpam-6131	23	21	.	.	PUNCT
ejpam-6131	24	1	a	a	DET
ejpam-6131	24	2	deeper	deep	ADJ
ejpam-6131	24	3	concept	concept	NOUN
ejpam-6131	24	4	of	of	ADP
ejpam-6131	24	5	perov	perov	NOUN
ejpam-6131	24	6	-	-	PUNCT
ejpam-6131	24	7	type	type	NOUN
ejpam-6131	24	8	contractions	contraction	NOUN
ejpam-6131	24	9	can	can	AUX
ejpam-6131	24	10	be	be	AUX
ejpam-6131	24	11	perceived	perceive	VERB
ejpam-6131	24	12	from	from	ADP
ejpam-6131	24	13	[	[	X
ejpam-6131	24	14	4	4	NUM
ejpam-6131	24	15	]	]	PUNCT
ejpam-6131	24	16	.	.	PUNCT
ejpam-6131	25	1	later	later	ADV
ejpam-6131	25	2	on	on	ADV
ejpam-6131	25	3	,	,	PUNCT
ejpam-6131	25	4	authors	author	NOUN
ejpam-6131	25	5	proved	prove	VERB
ejpam-6131	25	6	further	further	ADJ
ejpam-6131	25	7	extensions	extension	NOUN
ejpam-6131	25	8	of	of	ADP
ejpam-6131	25	9	bcp	bcp	NOUN
ejpam-6131	25	10	on	on	ADP
ejpam-6131	25	11	generalized	generalized	ADJ
ejpam-6131	25	12	structures	structure	NOUN
ejpam-6131	25	13	of	of	ADP
ejpam-6131	25	14	metric	metric	ADJ
ejpam-6131	25	15	spaces	space	NOUN
ejpam-6131	25	16	[	[	X
ejpam-6131	25	17	5–7	5–7	X
ejpam-6131	25	18	]	]	PUNCT
ejpam-6131	25	19	.	.	PUNCT
ejpam-6131	26	1	working	work	VERB
ejpam-6131	26	2	on	on	ADP
ejpam-6131	26	3	a	a	DET
ejpam-6131	26	4	new	new	ADJ
ejpam-6131	26	5	track	track	NOUN
ejpam-6131	26	6	,	,	PUNCT
ejpam-6131	26	7	bhaskar	bhaskar	NOUN
ejpam-6131	26	8	and	and	CCONJ
ejpam-6131	26	9	lakshmikantham	lakshmikantham	VERB
ejpam-6131	26	10	[	[	X
ejpam-6131	26	11	8	8	NUM
ejpam-6131	26	12	]	]	PUNCT
ejpam-6131	26	13	established	establish	VERB
ejpam-6131	26	14	the	the	DET
ejpam-6131	26	15	coupled	couple	VERB
ejpam-6131	26	16	fixed	fix	VERB
ejpam-6131	26	17	point	point	NOUN
ejpam-6131	26	18	for	for	ADP
ejpam-6131	26	19	mixed	mixed	ADJ
ejpam-6131	26	20	-	-	PUNCT
ejpam-6131	26	21	monotone	monotone	NOUN
ejpam-6131	26	22	mappings	mapping	NOUN
ejpam-6131	26	23	under	under	ADP
ejpam-6131	26	24	partially	partially	ADV
ejpam-6131	26	25	ordered	order	VERB
ejpam-6131	26	26	metric	metric	ADJ
ejpam-6131	26	27	spaces	space	NOUN
ejpam-6131	26	28	(	(	PUNCT
ejpam-6131	26	29	pom	pom	NOUN
ejpam-6131	26	30	)	)	PUNCT
ejpam-6131	26	31	.	.	PUNCT
ejpam-6131	27	1	furthermore	furthermore	ADV
ejpam-6131	27	2	,	,	PUNCT
ejpam-6131	27	3	a	a	DET
ejpam-6131	27	4	few	few	ADJ
ejpam-6131	27	5	important	important	ADJ
ejpam-6131	27	6	partial	partial	ADJ
ejpam-6131	27	7	-	-	PUNCT
ejpam-6131	27	8	order	order	NOUN
ejpam-6131	27	9	metric	metric	ADJ
ejpam-6131	27	10	space	space	NOUN
ejpam-6131	27	11	results	result	NOUN
ejpam-6131	27	12	were	be	AUX
ejpam-6131	27	13	presented	present	VERB
ejpam-6131	27	14	in	in	ADP
ejpam-6131	27	15	[	[	PUNCT
ejpam-6131	27	16	9	9	NUM
ejpam-6131	27	17	]	]	PUNCT
ejpam-6131	27	18	.	.	PUNCT
ejpam-6131	28	1	in	in	ADP
ejpam-6131	28	2	2011	2011	NUM
ejpam-6131	28	3	,	,	PUNCT
ejpam-6131	28	4	berinde	berinde	NOUN
ejpam-6131	28	5	and	and	CCONJ
ejpam-6131	28	6	borcut	borcut	VERB
ejpam-6131	28	7	[	[	PUNCT
ejpam-6131	28	8	10	10	NUM
ejpam-6131	28	9	]	]	PUNCT
ejpam-6131	28	10	extended	extend	VERB
ejpam-6131	28	11	the	the	DET
ejpam-6131	28	12	idea	idea	NOUN
ejpam-6131	28	13	of	of	ADP
ejpam-6131	28	14	coupled	couple	VERB
ejpam-6131	28	15	fixed	fix	VERB
ejpam-6131	28	16	point	point	NOUN
ejpam-6131	28	17	to	to	PART
ejpam-6131	28	18	tripled	triple	VERB
ejpam-6131	28	19	fixed	fix	VERB
ejpam-6131	28	20	point	point	NOUN
ejpam-6131	28	21	(	(	PUNCT
ejpam-6131	28	22	tfp	tfp	PROPN
ejpam-6131	28	23	)	)	PUNCT
ejpam-6131	28	24	for	for	ADP
ejpam-6131	28	25	self	self	NOUN
ejpam-6131	28	26	-	-	PUNCT
ejpam-6131	28	27	mappings	mapping	NOUN
ejpam-6131	28	28	and	and	CCONJ
ejpam-6131	28	29	set	set	VERB
ejpam-6131	28	30	up	up	ADP
ejpam-6131	28	31	some	some	DET
ejpam-6131	28	32	significant	significant	ADJ
ejpam-6131	28	33	results	result	NOUN
ejpam-6131	28	34	in	in	ADP
ejpam-6131	28	35	poms	pom	NOUN
ejpam-6131	28	36	.	.	PUNCT
ejpam-6131	29	1	one	one	PRON
ejpam-6131	29	2	can	can	AUX
ejpam-6131	29	3	refer	refer	VERB
ejpam-6131	29	4	to	to	ADP
ejpam-6131	29	5	[	[	X
ejpam-6131	29	6	11	11	NUM
ejpam-6131	29	7	]	]	PUNCT
ejpam-6131	29	8	and	and	CCONJ
ejpam-6131	29	9	[	[	X
ejpam-6131	29	10	12	12	NUM
ejpam-6131	29	11	]	]	PUNCT
ejpam-6131	29	12	for	for	ADP
ejpam-6131	29	13	a	a	DET
ejpam-6131	29	14	detailed	detailed	ADJ
ejpam-6131	29	15	review	review	NOUN
ejpam-6131	29	16	of	of	ADP
ejpam-6131	29	17	these	these	DET
ejpam-6131	29	18	ideas	idea	NOUN
ejpam-6131	29	19	.	.	PUNCT
ejpam-6131	30	1	subsequently	subsequently	ADV
ejpam-6131	30	2	,	,	PUNCT
ejpam-6131	30	3	generalizing	generalize	VERB
ejpam-6131	30	4	the	the	DET
ejpam-6131	30	5	concept	concept	NOUN
ejpam-6131	30	6	of	of	ADP
ejpam-6131	30	7	tfp	tfp	PROPN
ejpam-6131	30	8	in	in	ADP
ejpam-6131	30	9	2012	2012	NUM
ejpam-6131	30	10	,	,	PUNCT
ejpam-6131	30	11	karapınar	karapınar	PROPN
ejpam-6131	30	12	[	[	X
ejpam-6131	30	13	13	13	NUM
ejpam-6131	30	14	]	]	PUNCT
ejpam-6131	30	15	opened	open	VERB
ejpam-6131	30	16	a	a	DET
ejpam-6131	30	17	gateway	gateway	NOUN
ejpam-6131	30	18	for	for	ADP
ejpam-6131	30	19	researchers	researcher	NOUN
ejpam-6131	30	20	in	in	ADP
ejpam-6131	30	21	a	a	DET
ejpam-6131	30	22	new	new	ADJ
ejpam-6131	30	23	direction	direction	NOUN
ejpam-6131	30	24	by	by	ADP
ejpam-6131	30	25	proposing	propose	VERB
ejpam-6131	30	26	the	the	DET
ejpam-6131	30	27	theory	theory	NOUN
ejpam-6131	30	28	of	of	ADP
ejpam-6131	30	29	quadruple	quadruple	NOUN
ejpam-6131	30	30	fixed	fix	VERB
ejpam-6131	30	31	point	point	NOUN
ejpam-6131	30	32	of	of	ADP
ejpam-6131	30	33	mappings	mapping	NOUN
ejpam-6131	30	34	and	and	CCONJ
ejpam-6131	30	35	established	establish	VERB
ejpam-6131	30	36	exciting	exciting	ADJ
ejpam-6131	30	37	consequences	consequence	NOUN
ejpam-6131	30	38	in	in	ADP
ejpam-6131	30	39	this	this	DET
ejpam-6131	30	40	regard	regard	NOUN
ejpam-6131	30	41	,	,	PUNCT
ejpam-6131	30	42	see	see	VERB
ejpam-6131	30	43	also	also	ADV
ejpam-6131	30	44	[	[	X
ejpam-6131	30	45	14	14	NUM
ejpam-6131	30	46	]	]	PUNCT
ejpam-6131	30	47	and	and	CCONJ
ejpam-6131	30	48	[	[	X
ejpam-6131	30	49	15	15	NUM
ejpam-6131	30	50	]	]	PUNCT
ejpam-6131	30	51	.	.	PUNCT
ejpam-6131	31	1	working	work	VERB
ejpam-6131	31	2	on	on	ADP
ejpam-6131	31	3	a	a	DET
ejpam-6131	31	4	similar	similar	ADJ
ejpam-6131	31	5	track	track	NOUN
ejpam-6131	31	6	,	,	PUNCT
ejpam-6131	31	7	we	we	PRON
ejpam-6131	31	8	extend	extend	VERB
ejpam-6131	31	9	the	the	DET
ejpam-6131	31	10	idea	idea	NOUN
ejpam-6131	31	11	of	of	ADP
ejpam-6131	31	12	a	a	DET
ejpam-6131	31	13	quadruple	quadruple	NOUN
ejpam-6131	31	14	fixed	fix	VERB
ejpam-6131	31	15	point	point	NOUN
ejpam-6131	31	16	and	and	CCONJ
ejpam-6131	31	17	introduced	introduce	VERB
ejpam-6131	31	18	the	the	DET
ejpam-6131	31	19	notion	notion	NOUN
ejpam-6131	31	20	of	of	ADP
ejpam-6131	31	21	a	a	DET
ejpam-6131	31	22	quintuple	quintuple	ADV
ejpam-6131	31	23	fixed	fix	VERB
ejpam-6131	31	24	point(qfp	point(qfp	NOUN
ejpam-6131	31	25	)	)	PUNCT
ejpam-6131	31	26	.	.	PUNCT
ejpam-6131	32	1	motivated	motivate	VERB
ejpam-6131	32	2	by	by	ADP
ejpam-6131	32	3	the	the	DET
ejpam-6131	32	4	work	work	NOUN
ejpam-6131	32	5	of	of	ADP
ejpam-6131	32	6	hammad	hammad	PROPN
ejpam-6131	33	1	[	[	X
ejpam-6131	33	2	16	16	NUM
ejpam-6131	33	3	]	]	PUNCT
ejpam-6131	33	4	in	in	ADP
ejpam-6131	33	5	2022	2022	NUM
ejpam-6131	33	6	,	,	PUNCT
ejpam-6131	33	7	we	we	PRON
ejpam-6131	33	8	generalize	generalize	VERB
ejpam-6131	33	9	crucial	crucial	ADJ
ejpam-6131	33	10	results	result	NOUN
ejpam-6131	33	11	for	for	ADP
ejpam-6131	33	12	the	the	DET
ejpam-6131	33	13	existence	existence	NOUN
ejpam-6131	33	14	of	of	ADP
ejpam-6131	33	15	qfps	qfps	NOUN
ejpam-6131	33	16	in	in	ADP
ejpam-6131	33	17	generalized	generalized	ADJ
ejpam-6131	33	18	metric	metric	ADJ
ejpam-6131	33	19	spaces	space	NOUN
ejpam-6131	33	20	and	and	CCONJ
ejpam-6131	33	21	provide	provide	VERB
ejpam-6131	33	22	supportive	supportive	ADJ
ejpam-6131	33	23	examples	example	NOUN
ejpam-6131	33	24	and	and	CCONJ
ejpam-6131	33	25	applications	application	NOUN
ejpam-6131	33	26	related	relate	VERB
ejpam-6131	33	27	to	to	ADP
ejpam-6131	33	28	markov	markov	NOUN
ejpam-6131	33	29	process	process	NOUN
ejpam-6131	33	30	stationary	stationary	ADJ
ejpam-6131	33	31	distribution	distribution	NOUN
ejpam-6131	33	32	analysis	analysis	NOUN
ejpam-6131	33	33	.	.	PUNCT
ejpam-6131	34	1	2	2	X
ejpam-6131	34	2	.	.	X
ejpam-6131	34	3	preliminaries	preliminary	NOUN
ejpam-6131	34	4	now	now	ADV
ejpam-6131	34	5	,	,	PUNCT
ejpam-6131	34	6	onward	onward	ADV
ejpam-6131	34	7	in	in	ADP
ejpam-6131	34	8	this	this	DET
ejpam-6131	34	9	manuscript	manuscript	NOUN
ejpam-6131	34	10	,	,	PUNCT
ejpam-6131	34	11	mn	mn	PROPN
ejpam-6131	34	12	,	,	PUNCT
ejpam-6131	34	13	n(r+	n(r+	NOUN
ejpam-6131	34	14	)	)	PUNCT
ejpam-6131	34	15	,	,	PUNCT
ejpam-6131	34	16	i	i	PRON
ejpam-6131	34	17	,	,	PUNCT
ejpam-6131	34	18	o	o	PROPN
ejpam-6131	34	19	are	be	AUX
ejpam-6131	34	20	the	the	DET
ejpam-6131	34	21	symbol	symbol	NOUN
ejpam-6131	34	22	representations	representation	NOUN
ejpam-6131	34	23	for	for	ADP
ejpam-6131	34	24	the	the	DET
ejpam-6131	34	25	set	set	NOUN
ejpam-6131	34	26	of	of	ADP
ejpam-6131	34	27	all	all	DET
ejpam-6131	34	28	n	n	PRON
ejpam-6131	34	29	×	×	NOUN
ejpam-6131	34	30	n	n	PRON
ejpam-6131	34	31	matrices	matrice	VERB
ejpam-6131	34	32	over	over	ADP
ejpam-6131	34	33	r+	r+	NOUN
ejpam-6131	34	34	,	,	PUNCT
ejpam-6131	34	35	identity	identity	NOUN
ejpam-6131	34	36	and	and	CCONJ
ejpam-6131	34	37	zero	zero	NUM
ejpam-6131	34	38	matrices	matrix	NOUN
ejpam-6131	34	39	respectively	respectively	ADV
ejpam-6131	34	40	,	,	PUNCT
ejpam-6131	34	41	and	and	CCONJ
ejpam-6131	34	42	w	w	X
ejpam-6131	34	43	=	=	PUNCT
ejpam-6131	34	44	{	{	PUNCT
ejpam-6131	34	45	0	0	NUM
ejpam-6131	34	46	,	,	PUNCT
ejpam-6131	34	47	1	1	NUM
ejpam-6131	34	48	,	,	PUNCT
ejpam-6131	34	49	2	2	NUM
ejpam-6131	34	50	,	,	PUNCT
ejpam-6131	34	51	3	3	NUM
ejpam-6131	34	52	,	,	PUNCT
ejpam-6131	34	53	·	·	PUNCT
ejpam-6131	34	54	·	·	PUNCT
ejpam-6131	34	55	·	·	PUNCT
ejpam-6131	34	56	}	}	PUNCT
ejpam-6131	34	57	is	be	AUX
ejpam-6131	34	58	the	the	DET
ejpam-6131	34	59	set	set	NOUN
ejpam-6131	34	60	of	of	ADP
ejpam-6131	34	61	inetgers	inetger	NOUN
ejpam-6131	34	62	.	.	PUNCT
ejpam-6131	35	1	suppose	suppose	VERB
ejpam-6131	35	2	that	that	SCONJ
ejpam-6131	35	3	γ̃	γ̃	PROPN
ejpam-6131	35	4	∈	∈	PROPN
ejpam-6131	35	5	mn	mn	PROPN
ejpam-6131	35	6	,	,	PUNCT
ejpam-6131	35	7	n(r+	n(r+	NOUN
ejpam-6131	35	8	)	)	PUNCT
ejpam-6131	35	9	,	,	PUNCT
ejpam-6131	35	10	then	then	ADV
ejpam-6131	35	11	γ̃	γ̃	PROPN
ejpam-6131	35	12	is	be	AUX
ejpam-6131	35	13	said	say	VERB
ejpam-6131	35	14	a	a	DET
ejpam-6131	35	15	convergent	convergent	NOUN
ejpam-6131	35	16	matrix	matrix	NOUN
ejpam-6131	35	17	,	,	PUNCT
ejpam-6131	35	18	i.e	i.e	PRON
ejpam-6131	35	19	,	,	PUNCT
ejpam-6131	35	20	converges	converge	VERB
ejpam-6131	35	21	to	to	ADP
ejpam-6131	35	22	zero	zero	NUM
ejpam-6131	35	23	matrix	matrix	NOUN
ejpam-6131	35	24	o	o	NOUN
ejpam-6131	36	1	if	if	SCONJ
ejpam-6131	36	2	and	and	CCONJ
ejpam-6131	36	3	only	only	ADV
ejpam-6131	37	1	if	if	SCONJ
ejpam-6131	37	2	lim	lim	PROPN
ejpam-6131	37	3	n→∞	n→∞	PRON
ejpam-6131	37	4	γ̃n	γ̃n	PROPN
ejpam-6131	37	5	=	=	SYM
ejpam-6131	37	6	o.	o.	NOUN
ejpam-6131	37	7	a	a	DET
ejpam-6131	37	8	deeper	deep	ADJ
ejpam-6131	37	9	concept	concept	NOUN
ejpam-6131	37	10	can	can	AUX
ejpam-6131	37	11	be	be	AUX
ejpam-6131	37	12	built	build	VERB
ejpam-6131	37	13	through	through	ADP
ejpam-6131	37	14	[	[	X
ejpam-6131	37	15	17	17	NUM
ejpam-6131	37	16	]	]	PUNCT
ejpam-6131	37	17	.	.	PUNCT
ejpam-6131	38	1	denote	denote	VERB
ejpam-6131	38	2	a	a	DET
ejpam-6131	38	3	set	set	NOUN
ejpam-6131	38	4	of	of	ADP
ejpam-6131	38	5	all	all	DET
ejpam-6131	38	6	n×n	n×n	PROPN
ejpam-6131	38	7	matrices	matrice	VERB
ejpam-6131	38	8	γ̃	γ̃	PROPN
ejpam-6131	38	9	∈	∈	PROPN
ejpam-6131	38	10	mn	mn	PROPN
ejpam-6131	38	11	,	,	PUNCT
ejpam-6131	38	12	n(r+	n(r+	NOUN
ejpam-6131	38	13	)	)	PUNCT
ejpam-6131	38	14	,	,	PUNCT
ejpam-6131	38	15	with	with	ADP
ejpam-6131	38	16	γ̃n	γ̃n	PROPN
ejpam-6131	38	17	→	→	SYM
ejpam-6131	39	1	o	o	X
ejpam-6131	39	2	,	,	PUNCT
ejpam-6131	39	3	whenever	whenever	SCONJ
ejpam-6131	39	4	n	n	X
ejpam-6131	39	5	→	→	SYM
ejpam-6131	39	6	∞	∞	PROPN
ejpam-6131	39	7	by	by	ADP
ejpam-6131	39	8	zm	zm	PROPN
ejpam-6131	39	9	.	.	PUNCT
ejpam-6131	40	1	example	example	NOUN
ejpam-6131	41	1	1	1	NUM
ejpam-6131	41	2	.	.	PUNCT
ejpam-6131	41	3	let	let	VERB
ejpam-6131	41	4	γ̃	γ̃	PROPN
ejpam-6131	41	5	=	=	PUNCT
ejpam-6131	41	6	(	(	PUNCT
ejpam-6131	41	7	ξ1	ξ1	NOUN
ejpam-6131	41	8	ξ2	ξ2	ADJ
ejpam-6131	41	9	ξ1	ξ1	NOUN
ejpam-6131	41	10	ξ2	ξ2	NOUN
ejpam-6131	41	11	)	)	PUNCT
ejpam-6131	41	12	be	be	AUX
ejpam-6131	41	13	a	a	DET
ejpam-6131	41	14	matrix	matrix	NOUN
ejpam-6131	41	15	in	in	ADP
ejpam-6131	41	16	m2,2(r+	m2,2(r+	NOUN
ejpam-6131	41	17	)	)	PUNCT
ejpam-6131	41	18	with	with	ADP
ejpam-6131	41	19	the	the	DET
ejpam-6131	41	20	condition	condition	NOUN
ejpam-6131	41	21	that	that	SCONJ
ejpam-6131	41	22	ξ1+ξ2	ξ1+ξ2	PROPN
ejpam-6131	41	23	<	<	X
ejpam-6131	41	24	1	1	NUM
ejpam-6131	41	25	,	,	PUNCT
ejpam-6131	41	26	for	for	ADP
ejpam-6131	41	27	some	some	DET
ejpam-6131	41	28	ξ1	ξ1	NOUN
ejpam-6131	41	29	,	,	PUNCT
ejpam-6131	41	30	ξ2	ξ2	PROPN
ejpam-6131	41	31	∈	∈	PROPN
ejpam-6131	41	32	r+	r+	NOUN
ejpam-6131	41	33	,	,	PUNCT
ejpam-6131	41	34	then	then	ADV
ejpam-6131	41	35	γ̃	γ̃	PROPN
ejpam-6131	41	36	∈zm	∈zm	PROPN
ejpam-6131	41	37	.	.	PUNCT
ejpam-6131	41	38	example	example	NOUN
ejpam-6131	42	1	2	2	NUM
ejpam-6131	42	2	.	.	PUNCT
ejpam-6131	42	3	suppose	suppose	VERB
ejpam-6131	42	4	a	a	DET
ejpam-6131	42	5	matrix	matrix	NOUN
ejpam-6131	42	6	υ̃	υ̃	NOUN
ejpam-6131	42	7	=	=	PUNCT
ejpam-6131	42	8	(	(	PUNCT
ejpam-6131	42	9	ξ1	ξ1	NOUN
ejpam-6131	42	10	ξ2	ξ2	ADJ
ejpam-6131	42	11	ξ1	ξ1	NOUN
ejpam-6131	42	12	ξ2	ξ2	NOUN
ejpam-6131	42	13	)	)	PUNCT
ejpam-6131	42	14	∈	∈	PROPN
ejpam-6131	42	15	m2,2(r+	m2,2(r+	PROPN
ejpam-6131	42	16	)	)	PUNCT
ejpam-6131	42	17	,	,	PUNCT
ejpam-6131	42	18	such	such	ADJ
ejpam-6131	42	19	that	that	DET
ejpam-6131	42	20	ξ1	ξ1	NOUN
ejpam-6131	42	21	+	+	CCONJ
ejpam-6131	42	22	ξ2	ξ2	ADJ
ejpam-6131	42	23	≥	≥	NUM
ejpam-6131	42	24	1	1	NUM
ejpam-6131	42	25	,	,	PUNCT
ejpam-6131	42	26	for	for	ADP
ejpam-6131	42	27	some	some	DET
ejpam-6131	42	28	ξ1	ξ1	NOUN
ejpam-6131	42	29	,	,	PUNCT
ejpam-6131	42	30	ξ2	ξ2	PROPN
ejpam-6131	42	31	∈	∈	PROPN
ejpam-6131	42	32	r+	r+	NOUN
ejpam-6131	42	33	,	,	PUNCT
ejpam-6131	42	34	then	then	ADV
ejpam-6131	42	35	υ̃	υ̃	PROPN
ejpam-6131	42	36	does	do	AUX
ejpam-6131	42	37	not	not	PART
ejpam-6131	42	38	belong	belong	VERB
ejpam-6131	42	39	to	to	ADP
ejpam-6131	42	40	zm	zm	PROPN
ejpam-6131	42	41	.	.	PUNCT
ejpam-6131	43	1	for	for	ADP
ejpam-6131	43	2	a	a	DET
ejpam-6131	43	3	k	k	PROPN
ejpam-6131	43	4	dimensional	dimensional	ADJ
ejpam-6131	43	5	vector	vector	NOUN
ejpam-6131	43	6	space	space	NOUN
ejpam-6131	43	7	rk	rk	NOUN
ejpam-6131	43	8	,	,	PUNCT
ejpam-6131	43	9	let	let	VERB
ejpam-6131	43	10	0	0	NUM
ejpam-6131	43	11	,	,	PUNCT
ejpam-6131	43	12	1	1	NUM
ejpam-6131	43	13	be	be	AUX
ejpam-6131	43	14	the	the	DET
ejpam-6131	43	15	zero	zero	NUM
ejpam-6131	43	16	vector	vector	NOUN
ejpam-6131	43	17	and	and	CCONJ
ejpam-6131	43	18	identity	identity	NOUN
ejpam-6131	43	19	vector	vector	NOUN
ejpam-6131	43	20	,	,	PUNCT
ejpam-6131	43	21	respectively	respectively	ADV
ejpam-6131	43	22	.	.	PUNCT
ejpam-6131	44	1	also	also	ADV
ejpam-6131	44	2	,	,	PUNCT
ejpam-6131	44	3	addition	addition	NOUN
ejpam-6131	44	4	and	and	CCONJ
ejpam-6131	44	5	multiplication	multiplication	NOUN
ejpam-6131	44	6	in	in	ADP
ejpam-6131	44	7	rk	rk	NOUN
ejpam-6131	44	8	are	be	AUX
ejpam-6131	44	9	defined	define	VERB
ejpam-6131	44	10	as	as	ADP
ejpam-6131	44	11	under	under	ADV
ejpam-6131	44	12	:	:	PUNCT
ejpam-6131	44	13	ξ	ξ	PROPN
ejpam-6131	44	14	+	+	NUM
ejpam-6131	44	15	ξ∗	ξ∗	NOUN
ejpam-6131	44	16	=	=	SYM
ejpam-6131	44	17	(	(	PUNCT
ejpam-6131	44	18	ξ1	ξ1	NOUN
ejpam-6131	44	19	+	+	CCONJ
ejpam-6131	44	20	ξ∗1	ξ∗1	ADJ
ejpam-6131	44	21	,	,	PUNCT
ejpam-6131	44	22	ξ2	ξ2	NOUN
ejpam-6131	44	23	+	+	CCONJ
ejpam-6131	44	24	ξ∗2	ξ∗2	NOUN
ejpam-6131	44	25	,	,	PUNCT
ejpam-6131	44	26	ξ3	ξ3	PROPN
ejpam-6131	44	27	+	+	CCONJ
ejpam-6131	44	28	ξ∗3	ξ∗3	NOUN
ejpam-6131	44	29	,	,	PUNCT
ejpam-6131	44	30	·	·	PUNCT
ejpam-6131	44	31	·	·	PUNCT
ejpam-6131	44	32	·	·	PUNCT
ejpam-6131	44	33	,	,	PUNCT
ejpam-6131	44	34	ξk	ξk	ADP
ejpam-6131	44	35	+	+	ADJ
ejpam-6131	44	36	ξ∗k	ξ∗k	NOUN
ejpam-6131	44	37	)	)	PUNCT
ejpam-6131	44	38	and	and	CCONJ
ejpam-6131	44	39	ξ.ξ∗	ξ.ξ∗	PROPN
ejpam-6131	44	40	=	=	SYM
ejpam-6131	44	41	(	(	PUNCT
ejpam-6131	44	42	ξ1.ξ	ξ1.ξ	NOUN
ejpam-6131	44	43	∗	∗	NOUN
ejpam-6131	44	44	1	1	NUM
ejpam-6131	44	45	,	,	PUNCT
ejpam-6131	44	46	ξ2.ξ	ξ2.ξ	NUM
ejpam-6131	44	47	∗	∗	NOUN
ejpam-6131	44	48	2	2	NUM
ejpam-6131	44	49	,	,	PUNCT
ejpam-6131	44	50	·	·	PUNCT
ejpam-6131	44	51	·	·	PUNCT
ejpam-6131	44	52	·	·	PUNCT
ejpam-6131	44	53	,	,	PUNCT
ejpam-6131	44	54	ξk.ξ∗k	ξk.ξ∗k	PROPN
ejpam-6131	44	55	)	)	PUNCT
ejpam-6131	44	56	,	,	PUNCT
ejpam-6131	44	57	s.	s.	PROPN
ejpam-6131	44	58	batul	batul	PROPN
ejpam-6131	44	59	et	et	PROPN
ejpam-6131	44	60	a.	a.	PROPN
ejpam-6131	44	61	/	/	PUNCT
ejpam-6131	44	62	eur	eur	PROPN
ejpam-6131	44	63	.	.	PUNCT
ejpam-6131	45	1	j.	j.	PROPN
ejpam-6131	45	2	pure	pure	PROPN
ejpam-6131	45	3	appl	appl	PROPN
ejpam-6131	45	4	.	.	PROPN
ejpam-6131	45	5	math	math	PROPN
ejpam-6131	45	6	,	,	PUNCT
ejpam-6131	45	7	18	18	NUM
ejpam-6131	45	8	(	(	PUNCT
ejpam-6131	45	9	2	2	NUM
ejpam-6131	45	10	)	)	PUNCT
ejpam-6131	45	11	(	(	PUNCT
ejpam-6131	45	12	2025	2025	NUM
ejpam-6131	45	13	)	)	PUNCT
ejpam-6131	45	14	,	,	PUNCT
ejpam-6131	45	15	6131	6131	NUM
ejpam-6131	45	16	3	3	NUM
ejpam-6131	45	17	of	of	ADP
ejpam-6131	45	18	22	22	NUM
ejpam-6131	45	19	for	for	ADP
ejpam-6131	45	20	any	any	DET
ejpam-6131	45	21	ξ	ξ	PROPN
ejpam-6131	45	22	,	,	PUNCT
ejpam-6131	45	23	ξ∗	ξ∗	PROPN
ejpam-6131	45	24	∈	∈	PROPN
ejpam-6131	45	25	rk	rk	NOUN
ejpam-6131	45	26	,	,	PUNCT
ejpam-6131	45	27	where	where	SCONJ
ejpam-6131	45	28	ξ	ξ	X
ejpam-6131	45	29	=	=	SYM
ejpam-6131	45	30	(	(	PUNCT
ejpam-6131	45	31	ξ1	ξ1	PROPN
ejpam-6131	45	32	,	,	PUNCT
ejpam-6131	45	33	ξ2	ξ2	ADJ
ejpam-6131	45	34	,	,	PUNCT
ejpam-6131	45	35	ξ3	ξ3	NOUN
ejpam-6131	45	36	,	,	PUNCT
ejpam-6131	45	37	·	·	PUNCT
ejpam-6131	45	38	·	·	PUNCT
ejpam-6131	45	39	·	·	PUNCT
ejpam-6131	45	40	,	,	PUNCT
ejpam-6131	45	41	ξk	ξk	ADP
ejpam-6131	45	42	)	)	PUNCT
ejpam-6131	45	43	and	and	CCONJ
ejpam-6131	45	44	ξ∗	ξ∗	PROPN
ejpam-6131	45	45	=	=	SYM
ejpam-6131	45	46	(	(	PUNCT
ejpam-6131	45	47	ξ∗1	ξ∗1	NOUN
ejpam-6131	45	48	,	,	PUNCT
ejpam-6131	45	49	ξ	ξ	PROPN
ejpam-6131	45	50	∗	∗	NOUN
ejpam-6131	45	51	2	2	NUM
ejpam-6131	45	52	,	,	PUNCT
ejpam-6131	45	53	ξ	ξ	PROPN
ejpam-6131	45	54	∗	∗	NOUN
ejpam-6131	45	55	3	3	NUM
ejpam-6131	45	56	,	,	PUNCT
ejpam-6131	45	57	·	·	PUNCT
ejpam-6131	45	58	·	·	PUNCT
ejpam-6131	45	59	·	·	PUNCT
ejpam-6131	45	60	,	,	PUNCT
ejpam-6131	45	61	ξ∗k	ξ∗k	NOUN
ejpam-6131	45	62	)	)	PUNCT
ejpam-6131	45	63	.	.	PUNCT
ejpam-6131	46	1	one	one	PRON
ejpam-6131	46	2	can	can	AUX
ejpam-6131	46	3	have	have	VERB
ejpam-6131	46	4	a	a	DET
ejpam-6131	46	5	detailed	detailed	ADJ
ejpam-6131	46	6	study	study	NOUN
ejpam-6131	46	7	from	from	ADP
ejpam-6131	46	8	[	[	X
ejpam-6131	46	9	3	3	NUM
ejpam-6131	46	10	]	]	PUNCT
ejpam-6131	46	11	.	.	PUNCT
ejpam-6131	47	1	the	the	DET
ejpam-6131	47	2	proof	proof	NOUN
ejpam-6131	47	3	of	of	ADP
ejpam-6131	47	4	the	the	DET
ejpam-6131	47	5	subsequent	subsequent	ADJ
ejpam-6131	47	6	lemma	lemma	PROPN
ejpam-6131	47	7	is	be	AUX
ejpam-6131	47	8	discussed	discuss	VERB
ejpam-6131	47	9	in	in	ADP
ejpam-6131	47	10	matrix	matrix	NOUN
ejpam-6131	47	11	analysis	analysis	NOUN
ejpam-6131	47	12	in	in	ADP
ejpam-6131	47	13	[	[	X
ejpam-6131	47	14	3	3	NUM
ejpam-6131	47	15	]	]	PUNCT
ejpam-6131	47	16	.	.	PUNCT
ejpam-6131	48	1	lemma	lemma	PROPN
ejpam-6131	48	2	1	1	X
ejpam-6131	48	3	.	.	PUNCT
ejpam-6131	48	4	suppose	suppose	VERB
ejpam-6131	48	5	that	that	SCONJ
ejpam-6131	48	6	γ̃	γ̃	PROPN
ejpam-6131	48	7	is	be	AUX
ejpam-6131	48	8	a	a	DET
ejpam-6131	48	9	square	square	ADJ
ejpam-6131	48	10	matrix	matrix	NOUN
ejpam-6131	48	11	with	with	ADP
ejpam-6131	48	12	entries	entry	NOUN
ejpam-6131	48	13	from	from	ADP
ejpam-6131	48	14	r+	r+	PROPN
ejpam-6131	48	15	,	,	PUNCT
ejpam-6131	48	16	then	then	ADV
ejpam-6131	48	17	the	the	DET
ejpam-6131	48	18	following	following	ADJ
ejpam-6131	48	19	statements	statement	NOUN
ejpam-6131	48	20	are	be	AUX
ejpam-6131	48	21	equivalent	equivalent	ADJ
ejpam-6131	48	22	:	:	PUNCT
ejpam-6131	48	23	(	(	PUNCT
ejpam-6131	48	24	l1	l1	PROPN
ejpam-6131	48	25	)	)	PUNCT
ejpam-6131	48	26	γ̃	γ̃	PROPN
ejpam-6131	48	27	→	→	SYM
ejpam-6131	48	28	o	o	PROPN
ejpam-6131	48	29	;	;	PUNCT
ejpam-6131	48	30	(	(	PUNCT
ejpam-6131	48	31	l2	l2	NOUN
ejpam-6131	48	32	)	)	PUNCT
ejpam-6131	48	33	γ̃n	γ̃n	PROPN
ejpam-6131	48	34	→	→	SYM
ejpam-6131	48	35	o	o	PROPN
ejpam-6131	48	36	as	as	ADP
ejpam-6131	48	37	n	n	PROPN
ejpam-6131	48	38	→	→	SYM
ejpam-6131	48	39	∞	∞	PROPN
ejpam-6131	48	40	;	;	PUNCT
ejpam-6131	48	41	(	(	PUNCT
ejpam-6131	48	42	l3	l3	NOUN
ejpam-6131	48	43	)	)	PUNCT
ejpam-6131	48	44	for	for	ADP
ejpam-6131	48	45	each	each	DET
ejpam-6131	48	46	z	z	NOUN
ejpam-6131	48	47	∈	∈	PROPN
ejpam-6131	48	48	c	c	NOUN
ejpam-6131	48	49	,	,	PUNCT
ejpam-6131	48	50	|z|	|z|	VERB
ejpam-6131	48	51	<	<	X
ejpam-6131	48	52	1	1	NUM
ejpam-6131	48	53	with	with	ADP
ejpam-6131	48	54	det(γ̃−	det(γ̃−	PROPN
ejpam-6131	48	55	zi	zi	NOUN
ejpam-6131	48	56	)	)	PUNCT
ejpam-6131	48	57	=	=	PUNCT
ejpam-6131	48	58	0	0	NUM
ejpam-6131	48	59	;	;	PUNCT
ejpam-6131	48	60	(	(	PUNCT
ejpam-6131	48	61	l4	l4	PROPN
ejpam-6131	48	62	)	)	PUNCT
ejpam-6131	48	63	for	for	ADP
ejpam-6131	48	64	a	a	DET
ejpam-6131	48	65	non	non	ADJ
ejpam-6131	48	66	-	-	ADJ
ejpam-6131	48	67	singular	singular	ADJ
ejpam-6131	48	68	matrix	matrix	NOUN
ejpam-6131	48	69	i	i	PRON
ejpam-6131	49	1	−	−	PROPN
ejpam-6131	49	2	γ̃	γ̃	PROPN
ejpam-6131	49	3	(	(	PUNCT
ejpam-6131	49	4	i	i	PRON
ejpam-6131	49	5	−	−	PROPN
ejpam-6131	49	6	γ̃)−1	γ̃)−1	NOUN
ejpam-6131	49	7	=	=	PUNCT
ejpam-6131	49	8	i	i	NOUN
ejpam-6131	49	9	+	+	NUM
ejpam-6131	49	10	γ̃	γ̃	PROPN
ejpam-6131	49	11	+	+	CCONJ
ejpam-6131	49	12	·	·	PUNCT
ejpam-6131	49	13	·	·	PUNCT
ejpam-6131	49	14	·	·	PUNCT
ejpam-6131	49	15	+	+	NUM
ejpam-6131	49	16	γ̃n	γ̃n	PROPN
ejpam-6131	49	17	+	+	CCONJ
ejpam-6131	49	18	·	·	PUNCT
ejpam-6131	49	19	·	·	PUNCT
ejpam-6131	49	20	·	·	PUNCT
ejpam-6131	49	21	;	;	PUNCT
ejpam-6131	49	22	(	(	PUNCT
ejpam-6131	49	23	l5	l5	PROPN
ejpam-6131	49	24	)	)	PUNCT
ejpam-6131	49	25	two	two	NUM
ejpam-6131	49	26	matrices	matrix	NOUN
ejpam-6131	49	27	γ̃nw	γ̃nw	PROPN
ejpam-6131	49	28	and	and	CCONJ
ejpam-6131	49	29	wγ̃n	wγ̃n	PROPN
ejpam-6131	49	30	tend	tend	VERB
ejpam-6131	49	31	to	to	ADP
ejpam-6131	49	32	zero	zero	NUM
ejpam-6131	49	33	as	as	ADP
ejpam-6131	49	34	n	n	PROPN
ejpam-6131	49	35	→	→	SYM
ejpam-6131	49	36	∞	∞	PROPN
ejpam-6131	49	37	,	,	PUNCT
ejpam-6131	49	38	for	for	ADP
ejpam-6131	49	39	some	some	DET
ejpam-6131	49	40	w	w	PROPN
ejpam-6131	49	41	∈	∈	PROPN
ejpam-6131	49	42	rk	rk	NOUN
ejpam-6131	49	43	.	.	PUNCT
ejpam-6131	49	44	definition	definition	NOUN
ejpam-6131	49	45	1	1	NUM
ejpam-6131	49	46	.	.	PUNCT
ejpam-6131	50	1	a	a	DET
ejpam-6131	50	2	mapping	mapping	NOUN
ejpam-6131	50	3	t	t	NOUN
ejpam-6131	50	4	:	:	PUNCT
ejpam-6131	50	5	g2	g2	PROPN
ejpam-6131	50	6	→	→	SYM
ejpam-6131	50	7	rk	rk	PROPN
ejpam-6131	50	8	,	,	PUNCT
ejpam-6131	50	9	where	where	SCONJ
ejpam-6131	50	10	g	g	PROPN
ejpam-6131	50	11	̸=	̸=	PROPN
ejpam-6131	50	12	∅	∅	NOUN
ejpam-6131	50	13	,	,	PUNCT
ejpam-6131	50	14	is	be	AUX
ejpam-6131	50	15	named	name	VERB
ejpam-6131	50	16	as	as	ADP
ejpam-6131	50	17	a	a	DET
ejpam-6131	50	18	vector	vector	NOUN
ejpam-6131	50	19	-	-	PUNCT
ejpam-6131	50	20	valued	value	VERB
ejpam-6131	50	21	metric	metric	NOUN
ejpam-6131	50	22	over	over	ADP
ejpam-6131	50	23	g	g	PROPN
ejpam-6131	50	24	,	,	PUNCT
ejpam-6131	50	25	whenever	whenever	SCONJ
ejpam-6131	50	26	the	the	DET
ejpam-6131	50	27	conditions	condition	NOUN
ejpam-6131	50	28	below	below	ADV
ejpam-6131	50	29	are	be	AUX
ejpam-6131	50	30	fulfilled	fulfil	VERB
ejpam-6131	50	31	,	,	PUNCT
ejpam-6131	50	32	that	that	ADV
ejpam-6131	50	33	is	is	ADV
ejpam-6131	50	34	,	,	PUNCT
ejpam-6131	50	35	for	for	ADP
ejpam-6131	50	36	each	each	DET
ejpam-6131	50	37	ξ1	ξ1	NOUN
ejpam-6131	50	38	,	,	PUNCT
ejpam-6131	50	39	ξ2	ξ2	NOUN
ejpam-6131	50	40	,	,	PUNCT
ejpam-6131	50	41	ξ3	ξ3	PROPN
ejpam-6131	50	42	∈	∈	PROPN
ejpam-6131	50	43	g	g	PROPN
ejpam-6131	50	44	,	,	PUNCT
ejpam-6131	50	45	(	(	PUNCT
ejpam-6131	50	46	g1	g1	PROPN
ejpam-6131	50	47	)	)	PUNCT
ejpam-6131	50	48	t(ξ1	t(ξ1	NUM
ejpam-6131	50	49	,	,	PUNCT
ejpam-6131	50	50	ξ2	ξ2	NOUN
ejpam-6131	50	51	)	)	PUNCT
ejpam-6131	50	52	≥	≥	NOUN
ejpam-6131	50	53	0	0	NUM
ejpam-6131	50	54	,	,	PUNCT
ejpam-6131	50	55	t(ξ1	t(ξ1	NUM
ejpam-6131	50	56	,	,	PUNCT
ejpam-6131	50	57	ξ2	ξ2	NOUN
ejpam-6131	50	58	)	)	PUNCT
ejpam-6131	50	59	=	=	SYM
ejpam-6131	50	60	0	0	NUM
ejpam-6131	50	61	⇔	⇔	PROPN
ejpam-6131	50	62	ξ1	ξ1	PROPN
ejpam-6131	50	63	=	=	SYM
ejpam-6131	50	64	ξ2	ξ2	PROPN
ejpam-6131	50	65	,	,	PUNCT
ejpam-6131	50	66	(	(	PUNCT
ejpam-6131	50	67	g2	g2	PROPN
ejpam-6131	50	68	)	)	PUNCT
ejpam-6131	50	69	t(ξ1	t(ξ1	NUM
ejpam-6131	50	70	,	,	PUNCT
ejpam-6131	50	71	ξ2	ξ2	NOUN
ejpam-6131	50	72	)	)	PUNCT
ejpam-6131	50	73	=	=	SYM
ejpam-6131	50	74	t(ξ2	t(ξ2	NOUN
ejpam-6131	50	75	,	,	PUNCT
ejpam-6131	50	76	ξ1	ξ1	NOUN
ejpam-6131	50	77	)	)	PUNCT
ejpam-6131	50	78	,	,	PUNCT
ejpam-6131	50	79	(	(	PUNCT
ejpam-6131	50	80	g3	g3	NOUN
ejpam-6131	50	81	)	)	PUNCT
ejpam-6131	50	82	t(ξ1	t(ξ1	NUM
ejpam-6131	50	83	,	,	PUNCT
ejpam-6131	50	84	ξ2	ξ2	NOUN
ejpam-6131	50	85	)	)	PUNCT
ejpam-6131	50	86	≤	≤	NOUN
ejpam-6131	50	87	t(ξ1	t(ξ1	NUM
ejpam-6131	50	88	,	,	PUNCT
ejpam-6131	50	89	ξ3	ξ3	NOUN
ejpam-6131	50	90	)	)	PUNCT
ejpam-6131	50	91	+	+	NUM
ejpam-6131	50	92	t(ξ3	t(ξ3	NOUN
ejpam-6131	50	93	,	,	PUNCT
ejpam-6131	50	94	ξ2	ξ2	NOUN
ejpam-6131	50	95	)	)	PUNCT
ejpam-6131	50	96	.	.	PUNCT
ejpam-6131	51	1	if	if	SCONJ
ejpam-6131	51	2	ξ1	ξ1	NOUN
ejpam-6131	51	3	,	,	PUNCT
ejpam-6131	51	4	ξ2	ξ2	PROPN
ejpam-6131	51	5	∈	∈	PROPN
ejpam-6131	51	6	rk	rk	NOUN
ejpam-6131	51	7	,	,	PUNCT
ejpam-6131	51	8	where	where	SCONJ
ejpam-6131	51	9	ξ1	ξ1	NOUN
ejpam-6131	51	10	=	=	SYM
ejpam-6131	51	11	(	(	PUNCT
ejpam-6131	51	12	ξ11	ξ11	NOUN
ejpam-6131	51	13	,	,	PUNCT
ejpam-6131	51	14	ξ	ξ	PROPN
ejpam-6131	51	15	2	2	NUM
ejpam-6131	51	16	1	1	NUM
ejpam-6131	51	17	,	,	PUNCT
ejpam-6131	51	18	·	·	PUNCT
ejpam-6131	51	19	·	·	PUNCT
ejpam-6131	51	20	·	·	PUNCT
ejpam-6131	51	21	,	,	PUNCT
ejpam-6131	51	22	ξk1	ξk1	NOUN
ejpam-6131	51	23	)	)	PUNCT
ejpam-6131	51	24	and	and	CCONJ
ejpam-6131	51	25	ξ2	ξ2	NOUN
ejpam-6131	51	26	=	=	SYM
ejpam-6131	51	27	(	(	PUNCT
ejpam-6131	51	28	ξ12	ξ12	X
ejpam-6131	51	29	,	,	PUNCT
ejpam-6131	51	30	ξ	ξ	PROPN
ejpam-6131	51	31	2	2	NUM
ejpam-6131	51	32	2	2	NUM
ejpam-6131	51	33	,	,	PUNCT
ejpam-6131	51	34	·	·	PUNCT
ejpam-6131	51	35	·	·	PUNCT
ejpam-6131	51	36	·	·	PUNCT
ejpam-6131	51	37	,	,	PUNCT
ejpam-6131	51	38	ξk2	ξk2	X
ejpam-6131	51	39	)	)	PUNCT
ejpam-6131	51	40	,	,	PUNCT
ejpam-6131	51	41	then	then	ADV
ejpam-6131	51	42	ξ1	ξ1	VERB
ejpam-6131	51	43	≤	≤	PROPN
ejpam-6131	51	44	ξ2	ξ2	PROPN
ejpam-6131	51	45	if	if	SCONJ
ejpam-6131	51	46	and	and	CCONJ
ejpam-6131	51	47	only	only	ADV
ejpam-6131	51	48	if	if	SCONJ
ejpam-6131	51	49	ξi1	ξi1	NOUN
ejpam-6131	51	50	≤	≤	NUM
ejpam-6131	51	51	ξi2	ξi2	VERB
ejpam-6131	51	52	,	,	PUNCT
ejpam-6131	51	53	for	for	ADP
ejpam-6131	51	54	1	1	NUM
ejpam-6131	51	55	≤	≤	NUM
ejpam-6131	51	56	i	i	PRON
ejpam-6131	51	57	≤	≤	PROPN
ejpam-6131	51	58	k.	k.	PROPN
ejpam-6131	52	1	thus	thus	ADV
ejpam-6131	52	2	,	,	PUNCT
ejpam-6131	52	3	(	(	PUNCT
ejpam-6131	52	4	g	g	NOUN
ejpam-6131	52	5	,	,	PUNCT
ejpam-6131	52	6	t	t	PROPN
ejpam-6131	52	7	)	)	PUNCT
ejpam-6131	52	8	is	be	AUX
ejpam-6131	52	9	a	a	DET
ejpam-6131	52	10	generalized	generalized	ADJ
ejpam-6131	52	11	metric	metric	ADJ
ejpam-6131	52	12	space	space	NOUN
ejpam-6131	52	13	.	.	PUNCT
ejpam-6131	53	1	[	[	X
ejpam-6131	53	2	3	3	X
ejpam-6131	53	3	]	]	X
ejpam-6131	53	4	bhaskar	bhaskar	NOUN
ejpam-6131	53	5	and	and	CCONJ
ejpam-6131	53	6	lakshmikantham	lakshmikantham	VERB
ejpam-6131	53	7	[	[	X
ejpam-6131	53	8	8	8	NUM
ejpam-6131	53	9	]	]	PUNCT
ejpam-6131	53	10	established	establish	VERB
ejpam-6131	53	11	the	the	DET
ejpam-6131	53	12	following	following	ADJ
ejpam-6131	53	13	concepts	concept	NOUN
ejpam-6131	53	14	.	.	PUNCT
ejpam-6131	54	1	definition	definition	NOUN
ejpam-6131	54	2	2	2	NUM
ejpam-6131	54	3	.	.	PUNCT
ejpam-6131	55	1	an	an	DET
ejpam-6131	55	2	element	element	NOUN
ejpam-6131	55	3	(	(	PUNCT
ejpam-6131	55	4	ξ1	ξ1	NOUN
ejpam-6131	55	5	,	,	PUNCT
ejpam-6131	55	6	ξ2	ξ2	ADJ
ejpam-6131	55	7	)	)	PUNCT
ejpam-6131	55	8	∈	∈	PROPN
ejpam-6131	55	9	g2	g2	PROPN
ejpam-6131	55	10	is	be	AUX
ejpam-6131	55	11	named	name	VERB
ejpam-6131	55	12	as	as	ADP
ejpam-6131	55	13	a	a	DET
ejpam-6131	55	14	coupled	couple	VERB
ejpam-6131	55	15	fixed	fix	VERB
ejpam-6131	55	16	point	point	NOUN
ejpam-6131	55	17	of	of	ADP
ejpam-6131	55	18	the	the	DET
ejpam-6131	55	19	mapping	mapping	NOUN
ejpam-6131	55	20	p	p	NOUN
ejpam-6131	55	21	:	:	PUNCT
ejpam-6131	55	22	g2	g2	PROPN
ejpam-6131	55	23	→	→	SYM
ejpam-6131	55	24	g	g	PROPN
ejpam-6131	55	25	if	if	SCONJ
ejpam-6131	55	26	p	p	PROPN
ejpam-6131	55	27	(	(	PUNCT
ejpam-6131	55	28	ξ1	ξ1	NOUN
ejpam-6131	55	29	,	,	PUNCT
ejpam-6131	55	30	ξ2	ξ2	ADJ
ejpam-6131	55	31	)	)	PUNCT
ejpam-6131	56	1	=	=	SYM
ejpam-6131	56	2	ξ1	ξ1	NOUN
ejpam-6131	56	3	and	and	CCONJ
ejpam-6131	56	4	p	p	PROPN
ejpam-6131	56	5	(	(	PUNCT
ejpam-6131	56	6	ξ2	ξ2	ADJ
ejpam-6131	56	7	,	,	PUNCT
ejpam-6131	56	8	ξ1	ξ1	NOUN
ejpam-6131	56	9	)	)	PUNCT
ejpam-6131	56	10	=	=	SYM
ejpam-6131	56	11	ξ2	ξ2	NOUN
ejpam-6131	56	12	.	.	PUNCT
ejpam-6131	57	1	definition	definition	NOUN
ejpam-6131	57	2	3	3	NUM
ejpam-6131	57	3	.	.	PUNCT
ejpam-6131	57	4	two	two	NUM
ejpam-6131	57	5	mappings	mapping	NOUN
ejpam-6131	58	1	p	p	NOUN
ejpam-6131	58	2	:	:	PUNCT
ejpam-6131	58	3	g2	g2	PROPN
ejpam-6131	58	4	→	→	SYM
ejpam-6131	58	5	g	g	PROPN
ejpam-6131	58	6	and	and	CCONJ
ejpam-6131	58	7	p	p	X
ejpam-6131	58	8	:	:	PUNCT
ejpam-6131	58	9	g	g	PROPN
ejpam-6131	58	10	→	→	SYM
ejpam-6131	58	11	g	g	PROPN
ejpam-6131	58	12	have	have	VERB
ejpam-6131	58	13	a	a	DET
ejpam-6131	58	14	couple	couple	NOUN
ejpam-6131	58	15	fixed	fix	VERB
ejpam-6131	58	16	point	point	NOUN
ejpam-6131	58	17	(	(	PUNCT
ejpam-6131	58	18	ξ1	ξ1	NOUN
ejpam-6131	58	19	,	,	PUNCT
ejpam-6131	58	20	ξ2	ξ2	ADJ
ejpam-6131	58	21	)	)	PUNCT
ejpam-6131	58	22	∈	∈	PROPN
ejpam-6131	58	23	g2	g2	PROPN
ejpam-6131	59	1	if	if	SCONJ
ejpam-6131	59	2	p	p	PROPN
ejpam-6131	59	3	(	(	PUNCT
ejpam-6131	59	4	ξ1	ξ1	NOUN
ejpam-6131	59	5	,	,	PUNCT
ejpam-6131	59	6	ξ2	ξ2	NOUN
ejpam-6131	59	7	)	)	PUNCT
ejpam-6131	59	8	=	=	SYM
ejpam-6131	59	9	p(ξ1	p(ξ1	NOUN
ejpam-6131	59	10	)	)	PUNCT
ejpam-6131	59	11	and	and	CCONJ
ejpam-6131	59	12	p	p	X
ejpam-6131	59	13	(	(	PUNCT
ejpam-6131	59	14	ξ2	ξ2	ADJ
ejpam-6131	59	15	,	,	PUNCT
ejpam-6131	59	16	ξ1	ξ1	NOUN
ejpam-6131	59	17	)	)	PUNCT
ejpam-6131	59	18	=	=	SYM
ejpam-6131	59	19	p(ξ2	p(ξ2	NOUN
ejpam-6131	59	20	)	)	PUNCT
ejpam-6131	59	21	.	.	PUNCT
ejpam-6131	60	1	definition	definition	NOUN
ejpam-6131	60	2	4	4	NUM
ejpam-6131	60	3	.	.	PUNCT
ejpam-6131	61	1	a	a	DET
ejpam-6131	61	2	mapping	mapping	NOUN
ejpam-6131	61	3	p	p	NOUN
ejpam-6131	61	4	:	:	PUNCT
ejpam-6131	61	5	g2	g2	PROPN
ejpam-6131	61	6	→	→	SYM
ejpam-6131	61	7	g	g	PROPN
ejpam-6131	61	8	on	on	ADP
ejpam-6131	61	9	a	a	DET
ejpam-6131	61	10	partially	partially	ADV
ejpam-6131	61	11	ordered	order	VERB
ejpam-6131	61	12	set	set	NOUN
ejpam-6131	61	13	(	(	PUNCT
ejpam-6131	61	14	g,⪯	g,⪯	X
ejpam-6131	61	15	)	)	PUNCT
ejpam-6131	61	16	possesses	possess	VERB
ejpam-6131	61	17	the	the	DET
ejpam-6131	61	18	mixed	mix	VERB
ejpam-6131	61	19	-	-	PUNCT
ejpam-6131	61	20	monotone	monotone	NOUN
ejpam-6131	61	21	property	property	NOUN
ejpam-6131	61	22	(	(	PUNCT
ejpam-6131	61	23	mmp	mmp	PROPN
ejpam-6131	61	24	)	)	PUNCT
ejpam-6131	61	25	if	if	SCONJ
ejpam-6131	61	26	p	p	PROPN
ejpam-6131	61	27	(	(	PUNCT
ejpam-6131	61	28	ξ1	ξ1	NOUN
ejpam-6131	61	29	,	,	PUNCT
ejpam-6131	61	30	ξ2	ξ2	NOUN
ejpam-6131	61	31	)	)	PUNCT
ejpam-6131	61	32	is	be	AUX
ejpam-6131	61	33	non	non	ADJ
ejpam-6131	61	34	-	-	ADJ
ejpam-6131	61	35	decreasing	decrease	VERB
ejpam-6131	61	36	in	in	ADP
ejpam-6131	61	37	ξ1	ξ1	NOUN
ejpam-6131	61	38	and	and	CCONJ
ejpam-6131	61	39	non	non	ADJ
ejpam-6131	61	40	-	-	ADJ
ejpam-6131	61	41	increasing	increase	VERB
ejpam-6131	61	42	in	in	ADP
ejpam-6131	61	43	ξ2	ξ2	PROPN
ejpam-6131	61	44	,	,	PUNCT
ejpam-6131	61	45	i.e	i.e	X
ejpam-6131	61	46	,	,	PUNCT
ejpam-6131	61	47	for	for	ADP
ejpam-6131	61	48	any	any	DET
ejpam-6131	61	49	ξ1	ξ1	NOUN
ejpam-6131	61	50	,	,	PUNCT
ejpam-6131	61	51	ξ2	ξ2	NOUN
ejpam-6131	61	52	∈	∈	PROPN
ejpam-6131	61	53	g	g	PROPN
ejpam-6131	61	54	,	,	PUNCT
ejpam-6131	61	55	ξ11	ξ11	PROPN
ejpam-6131	61	56	,	,	PUNCT
ejpam-6131	61	57	ξ	ξ	PROPN
ejpam-6131	61	58	2	2	NUM
ejpam-6131	61	59	1	1	NUM
ejpam-6131	61	60	∈	∈	NOUN
ejpam-6131	61	61	g	g	NOUN
ejpam-6131	61	62	,	,	PUNCT
ejpam-6131	61	63	ξ11	ξ11	PROPN
ejpam-6131	61	64	⪯	⪯	VERB
ejpam-6131	61	65	ξ21	ξ21	PROPN
ejpam-6131	61	66	⇒	⇒	PROPN
ejpam-6131	61	67	p	p	PROPN
ejpam-6131	61	68	(	(	PUNCT
ejpam-6131	61	69	ξ11	ξ11	NOUN
ejpam-6131	61	70	,	,	PUNCT
ejpam-6131	61	71	ξ2	ξ2	NOUN
ejpam-6131	61	72	)	)	PUNCT
ejpam-6131	61	73	⪯	⪯	NOUN
ejpam-6131	61	74	p	p	NOUN
ejpam-6131	61	75	(	(	PUNCT
ejpam-6131	61	76	ξ21	ξ21	NOUN
ejpam-6131	61	77	,	,	PUNCT
ejpam-6131	61	78	ξ2	ξ2	NOUN
ejpam-6131	61	79	)	)	PUNCT
ejpam-6131	61	80	ξ12	ξ12	X
ejpam-6131	61	81	,	,	PUNCT
ejpam-6131	61	82	ξ	ξ	PROPN
ejpam-6131	61	83	2	2	NUM
ejpam-6131	61	84	2	2	NUM
ejpam-6131	61	85	∈	∈	NOUN
ejpam-6131	61	86	g	g	NOUN
ejpam-6131	61	87	,	,	PUNCT
ejpam-6131	62	1	ξ12	ξ12	PRON
ejpam-6131	62	2	⪯	⪯	NOUN
ejpam-6131	62	3	ξ22	ξ22	VERB
ejpam-6131	62	4	⇒	⇒	PROPN
ejpam-6131	62	5	p	p	PROPN
ejpam-6131	62	6	(	(	PUNCT
ejpam-6131	62	7	ξ1	ξ1	PROPN
ejpam-6131	62	8	,	,	PUNCT
ejpam-6131	62	9	ξ	ξ	PROPN
ejpam-6131	62	10	1	1	NUM
ejpam-6131	62	11	2	2	NUM
ejpam-6131	62	12	)	)	PUNCT
ejpam-6131	62	13	⪰	⪰	NOUN
ejpam-6131	62	14	p	p	X
ejpam-6131	62	15	(	(	PUNCT
ejpam-6131	62	16	ξ1	ξ1	PROPN
ejpam-6131	62	17	,	,	PUNCT
ejpam-6131	62	18	ξ	ξ	PROPN
ejpam-6131	62	19	2	2	NUM
ejpam-6131	62	20	2	2	NUM
ejpam-6131	62	21	)	)	PUNCT
ejpam-6131	62	22	.	.	PUNCT
ejpam-6131	63	1	berinde	berinde	NOUN
ejpam-6131	63	2	and	and	CCONJ
ejpam-6131	63	3	borcut	borcut	VERB
ejpam-6131	63	4	[	[	PUNCT
ejpam-6131	63	5	10	10	NUM
ejpam-6131	63	6	]	]	PUNCT
ejpam-6131	63	7	constructed	construct	VERB
ejpam-6131	63	8	the	the	DET
ejpam-6131	63	9	idea	idea	NOUN
ejpam-6131	63	10	of	of	ADP
ejpam-6131	63	11	a	a	DET
ejpam-6131	63	12	tripled	triple	VERB
ejpam-6131	63	13	fixed	fix	VERB
ejpam-6131	63	14	point	point	NOUN
ejpam-6131	63	15	by	by	ADP
ejpam-6131	63	16	generalizing	generalize	VERB
ejpam-6131	63	17	the	the	DET
ejpam-6131	63	18	term	term	NOUN
ejpam-6131	63	19	of	of	ADP
ejpam-6131	63	20	a	a	DET
ejpam-6131	63	21	coupled	couple	VERB
ejpam-6131	63	22	fixed	fix	VERB
ejpam-6131	63	23	point	point	NOUN
ejpam-6131	63	24	.	.	PUNCT
ejpam-6131	64	1	s.	s.	PROPN
ejpam-6131	64	2	batul	batul	PROPN
ejpam-6131	64	3	et	et	PROPN
ejpam-6131	64	4	a.	a.	PROPN
ejpam-6131	64	5	/	/	PUNCT
ejpam-6131	64	6	eur	eur	PROPN
ejpam-6131	64	7	.	.	PUNCT
ejpam-6131	65	1	j.	j.	PROPN
ejpam-6131	65	2	pure	pure	PROPN
ejpam-6131	65	3	appl	appl	PROPN
ejpam-6131	65	4	.	.	PROPN
ejpam-6131	65	5	math	math	PROPN
ejpam-6131	65	6	,	,	PUNCT
ejpam-6131	65	7	18	18	NUM
ejpam-6131	65	8	(	(	PUNCT
ejpam-6131	65	9	2	2	NUM
ejpam-6131	65	10	)	)	PUNCT
ejpam-6131	65	11	(	(	PUNCT
ejpam-6131	65	12	2025	2025	NUM
ejpam-6131	65	13	)	)	PUNCT
ejpam-6131	65	14	,	,	PUNCT
ejpam-6131	65	15	6131	6131	NUM
ejpam-6131	65	16	4	4	NUM
ejpam-6131	65	17	of	of	ADP
ejpam-6131	65	18	22	22	NUM
ejpam-6131	65	19	definition	definition	NOUN
ejpam-6131	65	20	5	5	NUM
ejpam-6131	65	21	.	.	PUNCT
ejpam-6131	66	1	an	an	DET
ejpam-6131	66	2	element	element	NOUN
ejpam-6131	66	3	(	(	PUNCT
ejpam-6131	66	4	ξ1	ξ1	NOUN
ejpam-6131	66	5	,	,	PUNCT
ejpam-6131	66	6	ξ2	ξ2	ADJ
ejpam-6131	66	7	,	,	PUNCT
ejpam-6131	66	8	ξ3	ξ3	NOUN
ejpam-6131	66	9	)	)	PUNCT
ejpam-6131	66	10	∈	∈	PROPN
ejpam-6131	66	11	g3	g3	NOUN
ejpam-6131	66	12	is	be	AUX
ejpam-6131	66	13	termed	term	VERB
ejpam-6131	66	14	as	as	ADP
ejpam-6131	66	15	a	a	DET
ejpam-6131	66	16	triple	triple	ADJ
ejpam-6131	66	17	fixed	fix	VERB
ejpam-6131	66	18	point	point	NOUN
ejpam-6131	66	19	of	of	ADP
ejpam-6131	66	20	the	the	DET
ejpam-6131	66	21	mapping	mapping	NOUN
ejpam-6131	66	22	p	p	X
ejpam-6131	66	23	:	:	PUNCT
ejpam-6131	66	24	g3	g3	PROPN
ejpam-6131	66	25	→	→	SYM
ejpam-6131	66	26	g	g	NOUN
ejpam-6131	67	1	if	if	SCONJ
ejpam-6131	67	2	p	p	PROPN
ejpam-6131	67	3	(	(	PUNCT
ejpam-6131	67	4	ξ1	ξ1	NOUN
ejpam-6131	67	5	,	,	PUNCT
ejpam-6131	67	6	ξ2	ξ2	ADJ
ejpam-6131	67	7	,	,	PUNCT
ejpam-6131	67	8	ξ3	ξ3	NOUN
ejpam-6131	67	9	)	)	PUNCT
ejpam-6131	67	10	=	=	SYM
ejpam-6131	67	11	ξ1	ξ1	NOUN
ejpam-6131	67	12	,	,	PUNCT
ejpam-6131	67	13	p	p	X
ejpam-6131	67	14	(	(	PUNCT
ejpam-6131	67	15	ξ2	ξ2	ADJ
ejpam-6131	67	16	,	,	PUNCT
ejpam-6131	67	17	ξ3	ξ3	NOUN
ejpam-6131	67	18	,	,	PUNCT
ejpam-6131	67	19	ξ1	ξ1	NOUN
ejpam-6131	67	20	)	)	PUNCT
ejpam-6131	68	1	=	=	SYM
ejpam-6131	68	2	ξ2,p	ξ2,p	PROPN
ejpam-6131	68	3	(	(	PUNCT
ejpam-6131	68	4	ξ3	ξ3	PROPN
ejpam-6131	68	5	,	,	PUNCT
ejpam-6131	68	6	ξ1	ξ1	NOUN
ejpam-6131	68	7	,	,	PUNCT
ejpam-6131	68	8	ξ2	ξ2	ADJ
ejpam-6131	68	9	)	)	PUNCT
ejpam-6131	68	10	=	=	SYM
ejpam-6131	68	11	ξ3	ξ3	NOUN
ejpam-6131	68	12	.	.	PUNCT
ejpam-6131	69	1	the	the	DET
ejpam-6131	69	2	definition	definition	NOUN
ejpam-6131	69	3	of	of	ADP
ejpam-6131	69	4	a	a	DET
ejpam-6131	69	5	quadruple	quadruple	NOUN
ejpam-6131	69	6	fixed	fix	VERB
ejpam-6131	69	7	point	point	NOUN
ejpam-6131	69	8	introduced	introduce	VERB
ejpam-6131	69	9	by	by	ADP
ejpam-6131	69	10	karapınar	karapınar	PROPN
ejpam-6131	69	11	[	[	X
ejpam-6131	69	12	18	18	NUM
ejpam-6131	69	13	]	]	PUNCT
ejpam-6131	69	14	is	be	AUX
ejpam-6131	69	15	stated	state	VERB
ejpam-6131	69	16	as	as	SCONJ
ejpam-6131	69	17	follows	follow	VERB
ejpam-6131	69	18	:	:	PUNCT
ejpam-6131	69	19	definition	definition	NOUN
ejpam-6131	69	20	6	6	NUM
ejpam-6131	69	21	.	.	PUNCT
ejpam-6131	70	1	[	[	X
ejpam-6131	70	2	18	18	NUM
ejpam-6131	70	3	]	]	PUNCT
ejpam-6131	70	4	let	let	VERB
ejpam-6131	70	5	g	g	PROPN
ejpam-6131	70	6	̸=	̸=	PROPN
ejpam-6131	70	7	∅.	∅.	ADP
ejpam-6131	70	8	an	an	DET
ejpam-6131	70	9	element	element	NOUN
ejpam-6131	70	10	(	(	PUNCT
ejpam-6131	70	11	ξ1	ξ1	NOUN
ejpam-6131	70	12	,	,	PUNCT
ejpam-6131	70	13	ξ2	ξ2	ADJ
ejpam-6131	70	14	,	,	PUNCT
ejpam-6131	70	15	ξ3	ξ3	NOUN
ejpam-6131	70	16	,	,	PUNCT
ejpam-6131	70	17	ξ4	ξ4	NOUN
ejpam-6131	70	18	)	)	PUNCT
ejpam-6131	70	19	∈	∈	NOUN
ejpam-6131	70	20	g4	g4	NOUN
ejpam-6131	70	21	is	be	AUX
ejpam-6131	70	22	stated	state	VERB
ejpam-6131	70	23	as	as	ADP
ejpam-6131	70	24	the	the	DET
ejpam-6131	70	25	quadruple	quadruple	NOUN
ejpam-6131	70	26	fixed	fix	VERB
ejpam-6131	70	27	point	point	NOUN
ejpam-6131	70	28	of	of	ADP
ejpam-6131	70	29	the	the	DET
ejpam-6131	70	30	mapping	mapping	NOUN
ejpam-6131	70	31	p	p	NOUN
ejpam-6131	70	32	:	:	PUNCT
ejpam-6131	70	33	g4	g4	NOUN
ejpam-6131	70	34	→	→	SYM
ejpam-6131	70	35	g	g	NOUN
ejpam-6131	71	1	if	if	SCONJ
ejpam-6131	71	2	p	p	PROPN
ejpam-6131	71	3	(	(	PUNCT
ejpam-6131	71	4	ξ1	ξ1	NOUN
ejpam-6131	71	5	,	,	PUNCT
ejpam-6131	71	6	ξ2	ξ2	ADJ
ejpam-6131	71	7	,	,	PUNCT
ejpam-6131	71	8	ξ3	ξ3	NOUN
ejpam-6131	71	9	,	,	PUNCT
ejpam-6131	71	10	ξ4	ξ4	NOUN
ejpam-6131	71	11	)	)	PUNCT
ejpam-6131	71	12	=	=	SYM
ejpam-6131	71	13	ξ1	ξ1	NOUN
ejpam-6131	71	14	,	,	PUNCT
ejpam-6131	71	15	p	p	X
ejpam-6131	71	16	(	(	PUNCT
ejpam-6131	71	17	ξ2	ξ2	ADJ
ejpam-6131	71	18	,	,	PUNCT
ejpam-6131	71	19	ξ3	ξ3	PROPN
ejpam-6131	71	20	,	,	PUNCT
ejpam-6131	71	21	ξ4	ξ4	NOUN
ejpam-6131	71	22	,	,	PUNCT
ejpam-6131	71	23	ξ1	ξ1	NOUN
ejpam-6131	71	24	)	)	PUNCT
ejpam-6131	71	25	=	=	SYM
ejpam-6131	72	1	ξ2	ξ2	NOUN
ejpam-6131	72	2	,	,	PUNCT
ejpam-6131	72	3	p	p	X
ejpam-6131	72	4	(	(	PUNCT
ejpam-6131	72	5	ξ3	ξ3	NOUN
ejpam-6131	72	6	,	,	PUNCT
ejpam-6131	72	7	ξ4	ξ4	NOUN
ejpam-6131	72	8	,	,	PUNCT
ejpam-6131	72	9	ξ1	ξ1	NOUN
ejpam-6131	72	10	,	,	PUNCT
ejpam-6131	72	11	ξ2	ξ2	ADJ
ejpam-6131	72	12	)	)	PUNCT
ejpam-6131	72	13	=	=	SYM
ejpam-6131	72	14	ξ3	ξ3	NOUN
ejpam-6131	72	15	,	,	PUNCT
ejpam-6131	72	16	p	p	X
ejpam-6131	72	17	(	(	PUNCT
ejpam-6131	72	18	ξ4	ξ4	PROPN
ejpam-6131	72	19	,	,	PUNCT
ejpam-6131	72	20	ξ1	ξ1	NOUN
ejpam-6131	72	21	,	,	PUNCT
ejpam-6131	72	22	ξ2	ξ2	ADJ
ejpam-6131	72	23	,	,	PUNCT
ejpam-6131	72	24	ξ3	ξ3	NOUN
ejpam-6131	72	25	)	)	PUNCT
ejpam-6131	72	26	=	=	SYM
ejpam-6131	72	27	ξ4	ξ4	NOUN
ejpam-6131	72	28	.	.	PUNCT
ejpam-6131	73	1	berinde	berinde	NOUN
ejpam-6131	73	2	extended	extend	VERB
ejpam-6131	73	3	the	the	DET
ejpam-6131	73	4	idea	idea	NOUN
ejpam-6131	73	5	of	of	ADP
ejpam-6131	73	6	mixed	mixed	ADJ
ejpam-6131	73	7	monotone	monotone	ADJ
ejpam-6131	73	8	property	property	NOUN
ejpam-6131	73	9	(	(	PUNCT
ejpam-6131	73	10	mmp	mmp	PROPN
ejpam-6131	73	11	)	)	PUNCT
ejpam-6131	74	1	[	[	X
ejpam-6131	74	2	10	10	NUM
ejpam-6131	74	3	]	]	X
ejpam-6131	74	4	on	on	ADP
ejpam-6131	74	5	g3	g3	PROPN
ejpam-6131	74	6	,	,	PUNCT
ejpam-6131	74	7	whereas	whereas	SCONJ
ejpam-6131	74	8	karapınar	karapınar	PROPN
ejpam-6131	75	1	[	[	X
ejpam-6131	75	2	18	18	NUM
ejpam-6131	75	3	]	]	PUNCT
ejpam-6131	75	4	introduced	introduce	VERB
ejpam-6131	75	5	the	the	DET
ejpam-6131	75	6	concept	concept	NOUN
ejpam-6131	75	7	of	of	ADP
ejpam-6131	75	8	mmp	mmp	PROPN
ejpam-6131	75	9	on	on	ADP
ejpam-6131	75	10	g4	g4	NOUN
ejpam-6131	75	11	.	.	PUNCT
ejpam-6131	76	1	definition	definition	NOUN
ejpam-6131	76	2	7	7	NUM
ejpam-6131	76	3	.	.	PUNCT
ejpam-6131	77	1	a	a	DET
ejpam-6131	77	2	partially	partially	ADV
ejpam-6131	77	3	ordered	order	VERB
ejpam-6131	77	4	set	set	NOUN
ejpam-6131	77	5	(	(	PUNCT
ejpam-6131	77	6	g,⪯	g,⪯	X
ejpam-6131	77	7	)	)	PUNCT
ejpam-6131	77	8	is	be	AUX
ejpam-6131	77	9	termed	term	VERB
ejpam-6131	77	10	as	as	ADV
ejpam-6131	77	11	regular	regular	ADJ
ejpam-6131	77	12	if	if	SCONJ
ejpam-6131	77	13	the	the	DET
ejpam-6131	77	14	conditions	condition	NOUN
ejpam-6131	77	15	below	below	ADV
ejpam-6131	77	16	are	be	AUX
ejpam-6131	77	17	satisfied	satisfied	ADJ
ejpam-6131	77	18	:	:	PUNCT
ejpam-6131	77	19	(	(	PUNCT
ejpam-6131	77	20	a	a	X
ejpam-6131	77	21	)	)	PUNCT
ejpam-6131	77	22	for	for	ADP
ejpam-6131	77	23	m	m	PROPN
ejpam-6131	77	24	≥	≥	NOUN
ejpam-6131	77	25	0	0	NUM
ejpam-6131	77	26	,	,	PUNCT
ejpam-6131	77	27	ξm1	ξm1	PROPN
ejpam-6131	77	28	⪯	⪯	NOUN
ejpam-6131	77	29	ξ1	ξ1	PROPN
ejpam-6131	77	30	if	if	SCONJ
ejpam-6131	77	31	a	a	DET
ejpam-6131	77	32	non	non	ADJ
ejpam-6131	77	33	-	-	ADJ
ejpam-6131	77	34	decreasing	decrease	VERB
ejpam-6131	77	35	sequence	sequence	NOUN
ejpam-6131	77	36	ξm1	ξm1	NOUN
ejpam-6131	77	37	→	→	SYM
ejpam-6131	77	38	ξ1	ξ1	NOUN
ejpam-6131	77	39	,	,	PUNCT
ejpam-6131	77	40	(	(	PUNCT
ejpam-6131	77	41	b	b	NOUN
ejpam-6131	77	42	)	)	PUNCT
ejpam-6131	77	43	for	for	ADP
ejpam-6131	77	44	m	m	PROPN
ejpam-6131	77	45	≥	≥	NOUN
ejpam-6131	77	46	0	0	NUM
ejpam-6131	77	47	,	,	PUNCT
ejpam-6131	77	48	ξ2	ξ2	ADJ
ejpam-6131	77	49	≤	≤	NOUN
ejpam-6131	78	1	ξm2	ξm2	ADV
ejpam-6131	78	2	if	if	SCONJ
ejpam-6131	78	3	a	a	DET
ejpam-6131	78	4	non	non	ADJ
ejpam-6131	78	5	-	-	ADJ
ejpam-6131	78	6	increasing	increase	VERB
ejpam-6131	78	7	sequence	sequence	NOUN
ejpam-6131	78	8	ξm2	ξm2	ADV
ejpam-6131	78	9	→	→	SYM
ejpam-6131	78	10	ξ2	ξ2	ADJ
ejpam-6131	78	11	.	.	PUNCT
ejpam-6131	79	1	[	[	X
ejpam-6131	79	2	19	19	NUM
ejpam-6131	79	3	]	]	SYM
ejpam-6131	79	4	3	3	NUM
ejpam-6131	79	5	.	.	X
ejpam-6131	79	6	main	main	ADJ
ejpam-6131	79	7	results	result	NOUN
ejpam-6131	79	8	inspired	inspire	VERB
ejpam-6131	79	9	by	by	ADP
ejpam-6131	79	10	the	the	DET
ejpam-6131	79	11	results	result	NOUN
ejpam-6131	79	12	on	on	ADP
ejpam-6131	79	13	couple	couple	NOUN
ejpam-6131	79	14	,	,	PUNCT
ejpam-6131	79	15	triple	triple	ADJ
ejpam-6131	79	16	and	and	CCONJ
ejpam-6131	79	17	quadruple	quadruple	ADJ
ejpam-6131	79	18	fixed	fix	VERB
ejpam-6131	79	19	points	point	NOUN
ejpam-6131	79	20	,	,	PUNCT
ejpam-6131	79	21	we	we	PRON
ejpam-6131	79	22	initiate	initiate	VERB
ejpam-6131	79	23	the	the	DET
ejpam-6131	79	24	term	term	NOUN
ejpam-6131	79	25	of	of	ADP
ejpam-6131	79	26	quintuple	quintuple	ADV
ejpam-6131	79	27	fixed	fix	VERB
ejpam-6131	79	28	points	point	NOUN
ejpam-6131	79	29	to	to	PART
ejpam-6131	79	30	present	present	VERB
ejpam-6131	79	31	some	some	DET
ejpam-6131	79	32	related	related	ADJ
ejpam-6131	79	33	fixed	fix	VERB
ejpam-6131	79	34	point	point	NOUN
ejpam-6131	79	35	results	result	NOUN
ejpam-6131	79	36	in	in	ADP
ejpam-6131	79	37	the	the	DET
ejpam-6131	79	38	partially	partially	ADV
ejpam-6131	79	39	ordered	order	VERB
ejpam-6131	79	40	complete	complete	ADJ
ejpam-6131	79	41	generalized	generalized	ADJ
ejpam-6131	79	42	metric	metric	ADJ
ejpam-6131	79	43	space	space	NOUN
ejpam-6131	79	44	(	(	PUNCT
ejpam-6131	79	45	pocgms	pocgms	PROPN
ejpam-6131	79	46	)	)	PUNCT
ejpam-6131	79	47	(	(	PUNCT
ejpam-6131	79	48	g	g	NOUN
ejpam-6131	79	49	,	,	PUNCT
ejpam-6131	79	50	t,⪯	t,⪯	NOUN
ejpam-6131	79	51	)	)	PUNCT
ejpam-6131	79	52	.	.	PUNCT
ejpam-6131	80	1	definition	definition	NOUN
ejpam-6131	80	2	8	8	NUM
ejpam-6131	80	3	.	.	PUNCT
ejpam-6131	81	1	let	let	VERB
ejpam-6131	81	2	p	p	NOUN
ejpam-6131	81	3	:	:	PUNCT
ejpam-6131	81	4	g5	g5	NOUN
ejpam-6131	81	5	→	→	SYM
ejpam-6131	81	6	g	g	NOUN
ejpam-6131	81	7	be	be	AUX
ejpam-6131	81	8	a	a	DET
ejpam-6131	81	9	mapping	mapping	NOUN
ejpam-6131	81	10	.	.	PUNCT
ejpam-6131	82	1	if	if	SCONJ
ejpam-6131	82	2	p	p	NOUN
ejpam-6131	82	3	is	be	AUX
ejpam-6131	82	4	monotonically	monotonically	ADV
ejpam-6131	82	5	non	non	ADJ
ejpam-6131	82	6	-	-	ADJ
ejpam-6131	82	7	increasing	increase	VERB
ejpam-6131	82	8	in	in	ADP
ejpam-6131	82	9	ξ2	ξ2	NOUN
ejpam-6131	82	10	,	,	PUNCT
ejpam-6131	82	11	ξ4	ξ4	ADJ
ejpam-6131	82	12	and	and	CCONJ
ejpam-6131	82	13	non	non	ADJ
ejpam-6131	82	14	-	-	ADJ
ejpam-6131	82	15	decreasing	decrease	VERB
ejpam-6131	82	16	in	in	ADP
ejpam-6131	82	17	ξ1	ξ1	NOUN
ejpam-6131	82	18	,	,	PUNCT
ejpam-6131	82	19	ξ3	ξ3	NOUN
ejpam-6131	82	20	,	,	PUNCT
ejpam-6131	82	21	ξ5	ξ5	NOUN
ejpam-6131	82	22	,	,	PUNCT
ejpam-6131	82	23	then	then	ADV
ejpam-6131	82	24	p	p	NOUN
ejpam-6131	82	25	is	be	AUX
ejpam-6131	82	26	said	say	VERB
ejpam-6131	82	27	to	to	PART
ejpam-6131	82	28	have	have	VERB
ejpam-6131	82	29	mmp	mmp	PROPN
ejpam-6131	82	30	.	.	PUNCT
ejpam-6131	83	1	in	in	ADP
ejpam-6131	83	2	other	other	ADJ
ejpam-6131	83	3	words	word	NOUN
ejpam-6131	83	4	,	,	PUNCT
ejpam-6131	83	5	for	for	ADP
ejpam-6131	83	6	any	any	DET
ejpam-6131	83	7	ξ1	ξ1	NOUN
ejpam-6131	83	8	,	,	PUNCT
ejpam-6131	83	9	ξ2	ξ2	NOUN
ejpam-6131	83	10	,	,	PUNCT
ejpam-6131	83	11	ξ3	ξ3	NOUN
ejpam-6131	83	12	,	,	PUNCT
ejpam-6131	83	13	ξ4	ξ4	NOUN
ejpam-6131	83	14	,	,	PUNCT
ejpam-6131	83	15	ξ5	ξ5	NOUN
ejpam-6131	83	16	∈	∈	PROPN
ejpam-6131	83	17	g	g	PROPN
ejpam-6131	83	18	,	,	PUNCT
ejpam-6131	83	19	ξ11	ξ11	PROPN
ejpam-6131	83	20	,	,	PUNCT
ejpam-6131	83	21	ξ	ξ	PROPN
ejpam-6131	83	22	2	2	NUM
ejpam-6131	83	23	1	1	NUM
ejpam-6131	83	24	∈	∈	NOUN
ejpam-6131	83	25	g	g	NOUN
ejpam-6131	83	26	,	,	PUNCT
ejpam-6131	83	27	ξ11	ξ11	PROPN
ejpam-6131	83	28	⪯	⪯	VERB
ejpam-6131	83	29	ξ21	ξ21	PROPN
ejpam-6131	83	30	⇒	⇒	PROPN
ejpam-6131	83	31	p	p	PROPN
ejpam-6131	83	32	(	(	PUNCT
ejpam-6131	83	33	ξ11	ξ11	NOUN
ejpam-6131	83	34	,	,	PUNCT
ejpam-6131	83	35	ξ2	ξ2	NOUN
ejpam-6131	83	36	,	,	PUNCT
ejpam-6131	83	37	ξ3	ξ3	NOUN
ejpam-6131	83	38	,	,	PUNCT
ejpam-6131	83	39	ξ4	ξ4	NOUN
ejpam-6131	83	40	,	,	PUNCT
ejpam-6131	83	41	ξ5	ξ5	NOUN
ejpam-6131	83	42	)	)	PUNCT
ejpam-6131	83	43	⪯	⪯	NOUN
ejpam-6131	83	44	p	p	NOUN
ejpam-6131	83	45	(	(	PUNCT
ejpam-6131	83	46	ξ21	ξ21	NOUN
ejpam-6131	83	47	,	,	PUNCT
ejpam-6131	83	48	ξ2	ξ2	NOUN
ejpam-6131	83	49	,	,	PUNCT
ejpam-6131	83	50	ξ3	ξ3	NOUN
ejpam-6131	83	51	,	,	PUNCT
ejpam-6131	83	52	ξ4	ξ4	NOUN
ejpam-6131	83	53	,	,	PUNCT
ejpam-6131	83	54	ξ5	ξ5	NOUN
ejpam-6131	83	55	)	)	PUNCT
ejpam-6131	83	56	,	,	PUNCT
ejpam-6131	83	57	ξ12	ξ12	VERB
ejpam-6131	83	58	,	,	PUNCT
ejpam-6131	83	59	ξ	ξ	PROPN
ejpam-6131	83	60	2	2	NUM
ejpam-6131	83	61	2	2	NUM
ejpam-6131	83	62	∈	∈	NOUN
ejpam-6131	83	63	g	g	NOUN
ejpam-6131	83	64	,	,	PUNCT
ejpam-6131	83	65	ξ12	ξ12	PRON
ejpam-6131	83	66	⪯	⪯	NOUN
ejpam-6131	83	67	ξ22	ξ22	VERB
ejpam-6131	83	68	⇒	⇒	PROPN
ejpam-6131	83	69	p	p	PROPN
ejpam-6131	83	70	(	(	PUNCT
ejpam-6131	83	71	ξ1	ξ1	PROPN
ejpam-6131	83	72	,	,	PUNCT
ejpam-6131	83	73	ξ	ξ	PROPN
ejpam-6131	83	74	1	1	NUM
ejpam-6131	83	75	2	2	NUM
ejpam-6131	83	76	,	,	PUNCT
ejpam-6131	83	77	ξ3	ξ3	NOUN
ejpam-6131	83	78	,	,	PUNCT
ejpam-6131	83	79	ξ4	ξ4	NOUN
ejpam-6131	83	80	,	,	PUNCT
ejpam-6131	83	81	ξ5	ξ5	NOUN
ejpam-6131	83	82	)	)	PUNCT
ejpam-6131	83	83	⪰	⪰	NOUN
ejpam-6131	83	84	p	p	X
ejpam-6131	83	85	(	(	PUNCT
ejpam-6131	83	86	ξ1	ξ1	PROPN
ejpam-6131	83	87	,	,	PUNCT
ejpam-6131	83	88	ξ	ξ	PROPN
ejpam-6131	83	89	2	2	NUM
ejpam-6131	83	90	2	2	NUM
ejpam-6131	83	91	,	,	PUNCT
ejpam-6131	83	92	ξ3	ξ3	NOUN
ejpam-6131	83	93	,	,	PUNCT
ejpam-6131	83	94	ξ4	ξ4	NOUN
ejpam-6131	83	95	,	,	PUNCT
ejpam-6131	83	96	ξ5	ξ5	NOUN
ejpam-6131	83	97	)	)	PUNCT
ejpam-6131	83	98	,	,	PUNCT
ejpam-6131	83	99	ξ13	ξ13	NOUN
ejpam-6131	83	100	,	,	PUNCT
ejpam-6131	83	101	ξ	ξ	PROPN
ejpam-6131	83	102	2	2	NUM
ejpam-6131	83	103	3	3	NUM
ejpam-6131	83	104	∈	∈	NOUN
ejpam-6131	83	105	g	g	NOUN
ejpam-6131	83	106	,	,	PUNCT
ejpam-6131	83	107	ξ13	ξ13	ADJ
ejpam-6131	83	108	⪯	⪯	NOUN
ejpam-6131	83	109	ξ23	ξ23	PROPN
ejpam-6131	83	110	⇒	⇒	PROPN
ejpam-6131	83	111	p	p	PROPN
ejpam-6131	83	112	(	(	PUNCT
ejpam-6131	83	113	ξ1	ξ1	PROPN
ejpam-6131	83	114	,	,	PUNCT
ejpam-6131	83	115	ξ2	ξ2	NUM
ejpam-6131	83	116	,	,	PUNCT
ejpam-6131	83	117	ξ	ξ	PROPN
ejpam-6131	83	118	1	1	NUM
ejpam-6131	83	119	3	3	NUM
ejpam-6131	83	120	,	,	PUNCT
ejpam-6131	83	121	ξ4	ξ4	NOUN
ejpam-6131	83	122	,	,	PUNCT
ejpam-6131	83	123	ξ5	ξ5	NOUN
ejpam-6131	83	124	)	)	PUNCT
ejpam-6131	83	125	⪯	⪯	NOUN
ejpam-6131	83	126	p	p	NOUN
ejpam-6131	83	127	(	(	PUNCT
ejpam-6131	83	128	ξ1	ξ1	PROPN
ejpam-6131	83	129	,	,	PUNCT
ejpam-6131	83	130	ξ2	ξ2	NOUN
ejpam-6131	83	131	,	,	PUNCT
ejpam-6131	83	132	ξ	ξ	PROPN
ejpam-6131	83	133	2	2	NUM
ejpam-6131	83	134	3	3	NUM
ejpam-6131	83	135	,	,	PUNCT
ejpam-6131	83	136	ξ4	ξ4	NOUN
ejpam-6131	83	137	,	,	PUNCT
ejpam-6131	83	138	ξ5	ξ5	NOUN
ejpam-6131	83	139	)	)	PUNCT
ejpam-6131	83	140	,	,	PUNCT
ejpam-6131	83	141	ξ14	ξ14	PROPN
ejpam-6131	83	142	,	,	PUNCT
ejpam-6131	83	143	ξ	ξ	PROPN
ejpam-6131	83	144	2	2	NUM
ejpam-6131	83	145	4	4	NUM
ejpam-6131	83	146	∈	∈	NOUN
ejpam-6131	83	147	g	g	NOUN
ejpam-6131	83	148	,	,	PUNCT
ejpam-6131	83	149	ξ14	ξ14	PROPN
ejpam-6131	83	150	⪯	⪯	VERB
ejpam-6131	83	151	ξ24	ξ24	ADJ
ejpam-6131	83	152	⇒	⇒	NOUN
ejpam-6131	83	153	p	p	X
ejpam-6131	83	154	(	(	PUNCT
ejpam-6131	83	155	ξ1	ξ1	PROPN
ejpam-6131	83	156	,	,	PUNCT
ejpam-6131	83	157	ξ2	ξ2	ADJ
ejpam-6131	83	158	,	,	PUNCT
ejpam-6131	83	159	ξ3	ξ3	PROPN
ejpam-6131	83	160	,	,	PUNCT
ejpam-6131	83	161	ξ	ξ	PROPN
ejpam-6131	83	162	1	1	NUM
ejpam-6131	83	163	4	4	NUM
ejpam-6131	83	164	,	,	PUNCT
ejpam-6131	83	165	ξ5	ξ5	NOUN
ejpam-6131	83	166	)	)	PUNCT
ejpam-6131	83	167	⪰	⪰	NOUN
ejpam-6131	83	168	p	p	X
ejpam-6131	83	169	(	(	PUNCT
ejpam-6131	83	170	ξ1	ξ1	NOUN
ejpam-6131	83	171	,	,	PUNCT
ejpam-6131	83	172	ξ2	ξ2	ADJ
ejpam-6131	83	173	,	,	PUNCT
ejpam-6131	83	174	ξ3	ξ3	PROPN
ejpam-6131	83	175	,	,	PUNCT
ejpam-6131	83	176	ξ	ξ	PROPN
ejpam-6131	83	177	2	2	NUM
ejpam-6131	83	178	4	4	NUM
ejpam-6131	83	179	,	,	PUNCT
ejpam-6131	83	180	ξ5	ξ5	NOUN
ejpam-6131	83	181	)	)	PUNCT
ejpam-6131	83	182	,	,	PUNCT
ejpam-6131	83	183	ξ15	ξ15	NOUN
ejpam-6131	83	184	,	,	PUNCT
ejpam-6131	83	185	ξ	ξ	PROPN
ejpam-6131	83	186	2	2	NUM
ejpam-6131	83	187	5	5	NUM
ejpam-6131	83	188	∈	∈	NOUN
ejpam-6131	83	189	g	g	NOUN
ejpam-6131	83	190	,	,	PUNCT
ejpam-6131	83	191	ξ15	ξ15	NOUN
ejpam-6131	83	192	⪯	⪯	VERB
ejpam-6131	83	193	ξ25	ξ25	ADJ
ejpam-6131	83	194	⇒	⇒	PROPN
ejpam-6131	83	195	p	p	PROPN
ejpam-6131	83	196	(	(	PUNCT
ejpam-6131	83	197	ξ1	ξ1	PROPN
ejpam-6131	83	198	,	,	PUNCT
ejpam-6131	83	199	ξ2	ξ2	ADJ
ejpam-6131	83	200	,	,	PUNCT
ejpam-6131	83	201	ξ3	ξ3	PROPN
ejpam-6131	83	202	,	,	PUNCT
ejpam-6131	83	203	ξ4	ξ4	PROPN
ejpam-6131	83	204	,	,	PUNCT
ejpam-6131	83	205	ξ	ξ	PROPN
ejpam-6131	83	206	1	1	NUM
ejpam-6131	83	207	5	5	NUM
ejpam-6131	83	208	)	)	PUNCT
ejpam-6131	83	209	⪯	⪯	NOUN
ejpam-6131	83	210	p	p	NOUN
ejpam-6131	83	211	(	(	PUNCT
ejpam-6131	83	212	ξ1	ξ1	PROPN
ejpam-6131	83	213	,	,	PUNCT
ejpam-6131	83	214	ξ2	ξ2	ADJ
ejpam-6131	83	215	,	,	PUNCT
ejpam-6131	83	216	ξ3	ξ3	PROPN
ejpam-6131	83	217	,	,	PUNCT
ejpam-6131	83	218	ξ4	ξ4	PROPN
ejpam-6131	83	219	,	,	PUNCT
ejpam-6131	83	220	ξ	ξ	PROPN
ejpam-6131	83	221	2	2	NUM
ejpam-6131	83	222	5	5	NUM
ejpam-6131	83	223	)	)	PUNCT
ejpam-6131	83	224	.	.	PUNCT
ejpam-6131	84	1	the	the	DET
ejpam-6131	84	2	above	above	ADJ
ejpam-6131	84	3	definition	definition	NOUN
ejpam-6131	84	4	can	can	AUX
ejpam-6131	84	5	be	be	AUX
ejpam-6131	84	6	generalized	generalize	VERB
ejpam-6131	84	7	for	for	ADP
ejpam-6131	84	8	two	two	NUM
ejpam-6131	84	9	mappings	mapping	NOUN
ejpam-6131	84	10	as	as	SCONJ
ejpam-6131	84	11	follows	follow	VERB
ejpam-6131	84	12	:	:	PUNCT
ejpam-6131	84	13	definition	definition	NOUN
ejpam-6131	84	14	9	9	NUM
ejpam-6131	84	15	.	.	PUNCT
ejpam-6131	85	1	let	let	VERB
ejpam-6131	85	2	p	p	NOUN
ejpam-6131	85	3	:	:	PUNCT
ejpam-6131	85	4	g5	g5	NOUN
ejpam-6131	85	5	→	→	SYM
ejpam-6131	85	6	g	g	PROPN
ejpam-6131	85	7	and	and	CCONJ
ejpam-6131	85	8	p	p	X
ejpam-6131	85	9	:	:	PUNCT
ejpam-6131	85	10	g	g	PROPN
ejpam-6131	85	11	→	→	SYM
ejpam-6131	85	12	g	g	NOUN
ejpam-6131	85	13	be	be	AUX
ejpam-6131	85	14	two	two	NUM
ejpam-6131	85	15	mappings	mapping	NOUN
ejpam-6131	85	16	.	.	PUNCT
ejpam-6131	86	1	then	then	ADV
ejpam-6131	86	2	,	,	PUNCT
ejpam-6131	86	3	p	p	NOUN
ejpam-6131	86	4	exhibits	exhibit	VERB
ejpam-6131	86	5	mixed	mixed	ADJ
ejpam-6131	86	6	p	p	NOUN
ejpam-6131	86	7	-	-	PUNCT
ejpam-6131	86	8	monotone	monotone	NOUN
ejpam-6131	86	9	property	property	NOUN
ejpam-6131	86	10	(	(	PUNCT
ejpam-6131	86	11	mpmp	mpmp	NOUN
ejpam-6131	86	12	)	)	PUNCT
ejpam-6131	86	13	if	if	SCONJ
ejpam-6131	86	14	,	,	PUNCT
ejpam-6131	86	15	for	for	ADP
ejpam-6131	86	16	any	any	DET
ejpam-6131	86	17	ξ1	ξ1	NOUN
ejpam-6131	86	18	,	,	PUNCT
ejpam-6131	86	19	ξ2	ξ2	NOUN
ejpam-6131	86	20	,	,	PUNCT
ejpam-6131	86	21	ξ3	ξ3	NOUN
ejpam-6131	86	22	,	,	PUNCT
ejpam-6131	86	23	ξ4	ξ4	NOUN
ejpam-6131	86	24	,	,	PUNCT
ejpam-6131	86	25	ξ5	ξ5	NOUN
ejpam-6131	86	26	∈	∈	PROPN
ejpam-6131	86	27	g	g	PROPN
ejpam-6131	86	28	,	,	PUNCT
ejpam-6131	86	29	ξ11	ξ11	PROPN
ejpam-6131	86	30	,	,	PUNCT
ejpam-6131	86	31	ξ	ξ	PROPN
ejpam-6131	86	32	2	2	NUM
ejpam-6131	86	33	1	1	NUM
ejpam-6131	86	34	∈	∈	NOUN
ejpam-6131	86	35	g	g	NOUN
ejpam-6131	86	36	,	,	PUNCT
ejpam-6131	86	37	p(ξ11	p(ξ11	NOUN
ejpam-6131	86	38	)	)	PUNCT
ejpam-6131	86	39	⪯	⪯	PROPN
ejpam-6131	86	40	p(ξ21	p(ξ21	NOUN
ejpam-6131	86	41	)	)	PUNCT
ejpam-6131	86	42	⇒	⇒	PROPN
ejpam-6131	86	43	p	p	PROPN
ejpam-6131	86	44	(	(	PUNCT
ejpam-6131	86	45	ξ11	ξ11	NOUN
ejpam-6131	86	46	,	,	PUNCT
ejpam-6131	86	47	ξ2	ξ2	NOUN
ejpam-6131	86	48	,	,	PUNCT
ejpam-6131	86	49	ξ3	ξ3	NOUN
ejpam-6131	86	50	,	,	PUNCT
ejpam-6131	86	51	ξ4	ξ4	NOUN
ejpam-6131	86	52	,	,	PUNCT
ejpam-6131	86	53	ξ5	ξ5	NOUN
ejpam-6131	86	54	)	)	PUNCT
ejpam-6131	86	55	⪯	⪯	NOUN
ejpam-6131	86	56	p	p	NOUN
ejpam-6131	86	57	(	(	PUNCT
ejpam-6131	86	58	ξ21	ξ21	NOUN
ejpam-6131	86	59	,	,	PUNCT
ejpam-6131	86	60	ξ2	ξ2	NOUN
ejpam-6131	86	61	,	,	PUNCT
ejpam-6131	86	62	ξ3	ξ3	NOUN
ejpam-6131	86	63	,	,	PUNCT
ejpam-6131	86	64	ξ4	ξ4	NOUN
ejpam-6131	86	65	,	,	PUNCT
ejpam-6131	86	66	ξ5	ξ5	NOUN
ejpam-6131	86	67	)	)	PUNCT
ejpam-6131	86	68	,	,	PUNCT
ejpam-6131	86	69	ξ12	ξ12	VERB
ejpam-6131	86	70	,	,	PUNCT
ejpam-6131	86	71	ξ	ξ	PROPN
ejpam-6131	86	72	2	2	NUM
ejpam-6131	86	73	2	2	NUM
ejpam-6131	86	74	∈	∈	NOUN
ejpam-6131	86	75	g	g	NOUN
ejpam-6131	86	76	,	,	PUNCT
ejpam-6131	86	77	p(ξ12	p(ξ12	NUM
ejpam-6131	86	78	)	)	PUNCT
ejpam-6131	86	79	⪯	⪯	NOUN
ejpam-6131	86	80	p(ξ22	p(ξ22	NOUN
ejpam-6131	86	81	)	)	PUNCT
ejpam-6131	86	82	⇒	⇒	NOUN
ejpam-6131	86	83	p	p	PROPN
ejpam-6131	86	84	(	(	PUNCT
ejpam-6131	86	85	ξ1	ξ1	PROPN
ejpam-6131	86	86	,	,	PUNCT
ejpam-6131	86	87	ξ	ξ	PROPN
ejpam-6131	86	88	1	1	NUM
ejpam-6131	86	89	2	2	NUM
ejpam-6131	86	90	,	,	PUNCT
ejpam-6131	86	91	ξ3	ξ3	NOUN
ejpam-6131	86	92	,	,	PUNCT
ejpam-6131	86	93	ξ4	ξ4	NOUN
ejpam-6131	86	94	,	,	PUNCT
ejpam-6131	86	95	ξ5	ξ5	NOUN
ejpam-6131	86	96	)	)	PUNCT
ejpam-6131	86	97	⪰	⪰	NOUN
ejpam-6131	86	98	p	p	X
ejpam-6131	86	99	(	(	PUNCT
ejpam-6131	86	100	ξ1	ξ1	PROPN
ejpam-6131	86	101	,	,	PUNCT
ejpam-6131	86	102	ξ	ξ	PROPN
ejpam-6131	86	103	2	2	NUM
ejpam-6131	86	104	2	2	NUM
ejpam-6131	86	105	,	,	PUNCT
ejpam-6131	86	106	ξ3	ξ3	NOUN
ejpam-6131	86	107	,	,	PUNCT
ejpam-6131	86	108	ξ4	ξ4	NOUN
ejpam-6131	86	109	,	,	PUNCT
ejpam-6131	86	110	ξ5	ξ5	NOUN
ejpam-6131	86	111	)	)	PUNCT
ejpam-6131	86	112	,	,	PUNCT
ejpam-6131	86	113	ξ13	ξ13	NOUN
ejpam-6131	86	114	,	,	PUNCT
ejpam-6131	86	115	ξ	ξ	PROPN
ejpam-6131	86	116	2	2	NUM
ejpam-6131	86	117	3	3	NUM
ejpam-6131	86	118	∈	∈	NOUN
ejpam-6131	86	119	g	g	NOUN
ejpam-6131	86	120	,	,	PUNCT
ejpam-6131	86	121	p(ξ13	p(ξ13	NOUN
ejpam-6131	86	122	)	)	PUNCT
ejpam-6131	86	123	⪯	⪯	NOUN
ejpam-6131	86	124	p(ξ23	p(ξ23	NOUN
ejpam-6131	86	125	)	)	PUNCT
ejpam-6131	86	126	⇒	⇒	VERB
ejpam-6131	86	127	p	p	PROPN
ejpam-6131	86	128	(	(	PUNCT
ejpam-6131	86	129	ξ1	ξ1	PROPN
ejpam-6131	86	130	,	,	PUNCT
ejpam-6131	86	131	ξ2	ξ2	NUM
ejpam-6131	86	132	,	,	PUNCT
ejpam-6131	86	133	ξ	ξ	PROPN
ejpam-6131	86	134	1	1	NUM
ejpam-6131	86	135	3	3	NUM
ejpam-6131	86	136	,	,	PUNCT
ejpam-6131	86	137	ξ4	ξ4	NOUN
ejpam-6131	86	138	,	,	PUNCT
ejpam-6131	86	139	ξ5	ξ5	NOUN
ejpam-6131	86	140	)	)	PUNCT
ejpam-6131	86	141	⪯	⪯	NOUN
ejpam-6131	86	142	p	p	NOUN
ejpam-6131	86	143	(	(	PUNCT
ejpam-6131	86	144	ξ1	ξ1	PROPN
ejpam-6131	86	145	,	,	PUNCT
ejpam-6131	86	146	ξ2	ξ2	NOUN
ejpam-6131	86	147	,	,	PUNCT
ejpam-6131	86	148	ξ	ξ	PROPN
ejpam-6131	86	149	2	2	NUM
ejpam-6131	86	150	3	3	NUM
ejpam-6131	86	151	,	,	PUNCT
ejpam-6131	86	152	ξ4	ξ4	NOUN
ejpam-6131	86	153	,	,	PUNCT
ejpam-6131	86	154	ξ5	ξ5	NOUN
ejpam-6131	86	155	)	)	PUNCT
ejpam-6131	86	156	,	,	PUNCT
ejpam-6131	86	157	ξ14	ξ14	PROPN
ejpam-6131	86	158	,	,	PUNCT
ejpam-6131	86	159	ξ	ξ	PROPN
ejpam-6131	86	160	2	2	NUM
ejpam-6131	86	161	4	4	NUM
ejpam-6131	86	162	∈	∈	NOUN
ejpam-6131	86	163	g	g	NOUN
ejpam-6131	86	164	,	,	PUNCT
ejpam-6131	86	165	p(ξ14	p(ξ14	NOUN
ejpam-6131	86	166	)	)	PUNCT
ejpam-6131	86	167	⪯	⪯	NOUN
ejpam-6131	86	168	p(ξ24	p(ξ24	NOUN
ejpam-6131	86	169	)	)	PUNCT
ejpam-6131	87	1	⇒	⇒	VERB
ejpam-6131	87	2	p	p	PROPN
ejpam-6131	87	3	(	(	PUNCT
ejpam-6131	87	4	ξ1	ξ1	PROPN
ejpam-6131	87	5	,	,	PUNCT
ejpam-6131	87	6	ξ2	ξ2	ADJ
ejpam-6131	87	7	,	,	PUNCT
ejpam-6131	87	8	ξ3	ξ3	PROPN
ejpam-6131	87	9	,	,	PUNCT
ejpam-6131	87	10	ξ	ξ	PROPN
ejpam-6131	87	11	1	1	NUM
ejpam-6131	87	12	4	4	NUM
ejpam-6131	87	13	,	,	PUNCT
ejpam-6131	87	14	ξ5	ξ5	NOUN
ejpam-6131	87	15	)	)	PUNCT
ejpam-6131	87	16	⪰	⪰	NOUN
ejpam-6131	87	17	p	p	X
ejpam-6131	87	18	(	(	PUNCT
ejpam-6131	87	19	ξ1	ξ1	NOUN
ejpam-6131	87	20	,	,	PUNCT
ejpam-6131	87	21	ξ2	ξ2	ADJ
ejpam-6131	87	22	,	,	PUNCT
ejpam-6131	87	23	ξ3	ξ3	PROPN
ejpam-6131	87	24	,	,	PUNCT
ejpam-6131	87	25	ξ	ξ	PROPN
ejpam-6131	87	26	2	2	NUM
ejpam-6131	87	27	4	4	NUM
ejpam-6131	87	28	,	,	PUNCT
ejpam-6131	87	29	ξ5	ξ5	NOUN
ejpam-6131	87	30	)	)	PUNCT
ejpam-6131	87	31	,	,	PUNCT
ejpam-6131	87	32	ξ15	ξ15	NOUN
ejpam-6131	87	33	,	,	PUNCT
ejpam-6131	87	34	ξ	ξ	PROPN
ejpam-6131	87	35	2	2	NUM
ejpam-6131	87	36	5	5	NUM
ejpam-6131	87	37	∈	∈	NOUN
ejpam-6131	87	38	g	g	NOUN
ejpam-6131	87	39	,	,	PUNCT
ejpam-6131	87	40	p(ξ15	p(ξ15	ADV
ejpam-6131	87	41	)	)	PUNCT
ejpam-6131	87	42	⪯	⪯	NOUN
ejpam-6131	87	43	p(ξ25	p(ξ25	NOUN
ejpam-6131	87	44	)	)	PUNCT
ejpam-6131	87	45	⇒	⇒	PROPN
ejpam-6131	87	46	p	p	PROPN
ejpam-6131	87	47	(	(	PUNCT
ejpam-6131	87	48	ξ1	ξ1	PROPN
ejpam-6131	87	49	,	,	PUNCT
ejpam-6131	87	50	ξ2	ξ2	ADJ
ejpam-6131	87	51	,	,	PUNCT
ejpam-6131	87	52	ξ3	ξ3	PROPN
ejpam-6131	87	53	,	,	PUNCT
ejpam-6131	87	54	ξ4	ξ4	PROPN
ejpam-6131	87	55	,	,	PUNCT
ejpam-6131	87	56	ξ	ξ	PROPN
ejpam-6131	87	57	1	1	NUM
ejpam-6131	87	58	5	5	NUM
ejpam-6131	87	59	)	)	PUNCT
ejpam-6131	87	60	⪯	⪯	NOUN
ejpam-6131	87	61	p	p	NOUN
ejpam-6131	87	62	(	(	PUNCT
ejpam-6131	87	63	ξ1	ξ1	PROPN
ejpam-6131	87	64	,	,	PUNCT
ejpam-6131	87	65	ξ2	ξ2	ADJ
ejpam-6131	87	66	,	,	PUNCT
ejpam-6131	87	67	ξ3	ξ3	PROPN
ejpam-6131	87	68	,	,	PUNCT
ejpam-6131	87	69	ξ4	ξ4	PROPN
ejpam-6131	87	70	,	,	PUNCT
ejpam-6131	87	71	ξ	ξ	PROPN
ejpam-6131	87	72	2	2	NUM
ejpam-6131	87	73	5	5	NUM
ejpam-6131	87	74	)	)	PUNCT
ejpam-6131	87	75	.	.	PUNCT
ejpam-6131	88	1	s.	s.	PROPN
ejpam-6131	88	2	batul	batul	PROPN
ejpam-6131	88	3	et	et	PROPN
ejpam-6131	88	4	a.	a.	PROPN
ejpam-6131	88	5	/	/	PUNCT
ejpam-6131	88	6	eur	eur	PROPN
ejpam-6131	88	7	.	.	PUNCT
ejpam-6131	89	1	j.	j.	PROPN
ejpam-6131	89	2	pure	pure	PROPN
ejpam-6131	89	3	appl	appl	PROPN
ejpam-6131	89	4	.	.	PROPN
ejpam-6131	89	5	math	math	PROPN
ejpam-6131	89	6	,	,	PUNCT
ejpam-6131	89	7	18	18	NUM
ejpam-6131	89	8	(	(	PUNCT
ejpam-6131	89	9	2	2	NUM
ejpam-6131	89	10	)	)	PUNCT
ejpam-6131	89	11	(	(	PUNCT
ejpam-6131	89	12	2025	2025	NUM
ejpam-6131	89	13	)	)	PUNCT
ejpam-6131	89	14	,	,	PUNCT
ejpam-6131	89	15	6131	6131	NUM
ejpam-6131	89	16	5	5	NUM
ejpam-6131	89	17	of	of	ADP
ejpam-6131	89	18	22	22	NUM
ejpam-6131	89	19	definition	definition	NOUN
ejpam-6131	89	20	10	10	NUM
ejpam-6131	89	21	.	.	PUNCT
ejpam-6131	90	1	an	an	DET
ejpam-6131	90	2	element	element	NOUN
ejpam-6131	90	3	(	(	PUNCT
ejpam-6131	90	4	ξ1	ξ1	NOUN
ejpam-6131	90	5	,	,	PUNCT
ejpam-6131	90	6	ξ2	ξ2	ADJ
ejpam-6131	90	7	,	,	PUNCT
ejpam-6131	90	8	ξ3	ξ3	NOUN
ejpam-6131	90	9	,	,	PUNCT
ejpam-6131	90	10	ξ4	ξ4	NOUN
ejpam-6131	90	11	,	,	PUNCT
ejpam-6131	90	12	ξ5	ξ5	NOUN
ejpam-6131	90	13	)	)	PUNCT
ejpam-6131	90	14	∈	∈	PROPN
ejpam-6131	90	15	g	g	PROPN
ejpam-6131	90	16	is	be	AUX
ejpam-6131	90	17	called	call	VERB
ejpam-6131	90	18	a	a	DET
ejpam-6131	90	19	quintuple	quintuple	ADV
ejpam-6131	90	20	fixed	fix	VERB
ejpam-6131	90	21	point	point	NOUN
ejpam-6131	90	22	(	(	PUNCT
ejpam-6131	90	23	qfp	qfp	PROPN
ejpam-6131	90	24	)	)	PUNCT
ejpam-6131	90	25	of	of	ADP
ejpam-6131	90	26	the	the	DET
ejpam-6131	90	27	mapping	mapping	NOUN
ejpam-6131	90	28	p	p	NOUN
ejpam-6131	90	29	:	:	PUNCT
ejpam-6131	90	30	g5	g5	NOUN
ejpam-6131	90	31	→	→	SYM
ejpam-6131	90	32	g	g	PROPN
ejpam-6131	90	33	if	if	SCONJ
ejpam-6131	90	34	p	p	PROPN
ejpam-6131	90	35	(	(	PUNCT
ejpam-6131	90	36	ξ1	ξ1	NOUN
ejpam-6131	90	37	,	,	PUNCT
ejpam-6131	90	38	ξ2	ξ2	ADJ
ejpam-6131	90	39	,	,	PUNCT
ejpam-6131	90	40	ξ3	ξ3	NOUN
ejpam-6131	90	41	,	,	PUNCT
ejpam-6131	90	42	ξ4	ξ4	NOUN
ejpam-6131	90	43	,	,	PUNCT
ejpam-6131	90	44	ξ5	ξ5	NOUN
ejpam-6131	90	45	)	)	PUNCT
ejpam-6131	90	46	=	=	SYM
ejpam-6131	90	47	ξ1	ξ1	NOUN
ejpam-6131	90	48	,	,	PUNCT
ejpam-6131	90	49	p	p	X
ejpam-6131	90	50	(	(	PUNCT
ejpam-6131	90	51	ξ2	ξ2	ADJ
ejpam-6131	90	52	,	,	PUNCT
ejpam-6131	90	53	ξ3	ξ3	PROPN
ejpam-6131	90	54	,	,	PUNCT
ejpam-6131	90	55	ξ4	ξ4	NOUN
ejpam-6131	90	56	,	,	PUNCT
ejpam-6131	90	57	ξ5	ξ5	NOUN
ejpam-6131	90	58	,	,	PUNCT
ejpam-6131	90	59	ξ1	ξ1	NOUN
ejpam-6131	90	60	)	)	PUNCT
ejpam-6131	90	61	=	=	SYM
ejpam-6131	91	1	ξ2	ξ2	NOUN
ejpam-6131	91	2	,	,	PUNCT
ejpam-6131	91	3	p	p	X
ejpam-6131	91	4	(	(	PUNCT
ejpam-6131	91	5	ξ3	ξ3	NOUN
ejpam-6131	91	6	,	,	PUNCT
ejpam-6131	91	7	ξ4	ξ4	NOUN
ejpam-6131	91	8	,	,	PUNCT
ejpam-6131	91	9	ξ5	ξ5	NOUN
ejpam-6131	91	10	,	,	PUNCT
ejpam-6131	91	11	ξ1	ξ1	NOUN
ejpam-6131	91	12	,	,	PUNCT
ejpam-6131	91	13	ξ2	ξ2	ADJ
ejpam-6131	91	14	)	)	PUNCT
ejpam-6131	91	15	=	=	SYM
ejpam-6131	91	16	ξ3	ξ3	NOUN
ejpam-6131	91	17	,	,	PUNCT
ejpam-6131	91	18	p	p	X
ejpam-6131	91	19	(	(	PUNCT
ejpam-6131	91	20	ξ4	ξ4	NOUN
ejpam-6131	91	21	,	,	PUNCT
ejpam-6131	91	22	ξ5	ξ5	NOUN
ejpam-6131	91	23	,	,	PUNCT
ejpam-6131	91	24	ξ1	ξ1	NOUN
ejpam-6131	91	25	,	,	PUNCT
ejpam-6131	91	26	ξ2	ξ2	ADJ
ejpam-6131	91	27	,	,	PUNCT
ejpam-6131	91	28	ξ3	ξ3	NOUN
ejpam-6131	91	29	)	)	PUNCT
ejpam-6131	91	30	=	=	SYM
ejpam-6131	91	31	ξ4	ξ4	PROPN
ejpam-6131	91	32	,	,	PUNCT
ejpam-6131	91	33	p	p	X
ejpam-6131	91	34	(	(	PUNCT
ejpam-6131	91	35	ξ5	ξ5	NOUN
ejpam-6131	91	36	,	,	PUNCT
ejpam-6131	91	37	ξ1	ξ1	NOUN
ejpam-6131	91	38	,	,	PUNCT
ejpam-6131	91	39	ξ2	ξ2	NOUN
ejpam-6131	91	40	,	,	PUNCT
ejpam-6131	91	41	ξ3	ξ3	NOUN
ejpam-6131	91	42	,	,	PUNCT
ejpam-6131	91	43	ξ4	ξ4	NOUN
ejpam-6131	91	44	)	)	PUNCT
ejpam-6131	91	45	=	=	SYM
ejpam-6131	91	46	ξ5	ξ5	NOUN
ejpam-6131	91	47	.	.	PUNCT
ejpam-6131	92	1	for	for	ADP
ejpam-6131	92	2	a	a	DET
ejpam-6131	92	3	generalized	generalized	ADJ
ejpam-6131	92	4	metric	metric	ADJ
ejpam-6131	92	5	space	space	NOUN
ejpam-6131	92	6	(	(	PUNCT
ejpam-6131	92	7	g	g	PROPN
ejpam-6131	92	8	,	,	PUNCT
ejpam-6131	92	9	t	t	PROPN
ejpam-6131	92	10	)	)	PUNCT
ejpam-6131	92	11	,	,	PUNCT
ejpam-6131	92	12	a	a	DET
ejpam-6131	92	13	function	function	NOUN
ejpam-6131	92	14	t̄	t̄	NOUN
ejpam-6131	92	15	:	:	PUNCT
ejpam-6131	92	16	g5	g5	VERB
ejpam-6131	92	17	×	×	NOUN
ejpam-6131	92	18	g5	g5	NOUN
ejpam-6131	92	19	→	→	PUNCT
ejpam-6131	92	20	rk	rk	NOUN
ejpam-6131	92	21	,	,	PUNCT
ejpam-6131	92	22	given	give	VERB
ejpam-6131	92	23	by	by	ADP
ejpam-6131	92	24	t̄((ξ1	t̄((ξ1	PRON
ejpam-6131	92	25	,	,	PUNCT
ejpam-6131	92	26	ξ2	ξ2	ADJ
ejpam-6131	92	27	,	,	PUNCT
ejpam-6131	92	28	ξ3	ξ3	NOUN
ejpam-6131	92	29	,	,	PUNCT
ejpam-6131	92	30	ξ4	ξ4	NOUN
ejpam-6131	92	31	,	,	PUNCT
ejpam-6131	92	32	ξ5	ξ5	NOUN
ejpam-6131	92	33	)	)	PUNCT
ejpam-6131	92	34	,	,	PUNCT
ejpam-6131	92	35	(	(	PUNCT
ejpam-6131	92	36	q1	q1	PROPN
ejpam-6131	92	37	,	,	PUNCT
ejpam-6131	92	38	q2	q2	NOUN
ejpam-6131	92	39	,	,	PUNCT
ejpam-6131	92	40	q3	q3	PROPN
ejpam-6131	92	41	,	,	PUNCT
ejpam-6131	92	42	q4	q4	PROPN
ejpam-6131	92	43	,	,	PUNCT
ejpam-6131	92	44	q5	q5	PROPN
ejpam-6131	92	45	)	)	PUNCT
ejpam-6131	92	46	)	)	PUNCT
ejpam-6131	93	1	=	=	SYM
ejpam-6131	93	2	t(ξ1	t(ξ1	NUM
ejpam-6131	93	3	,	,	PUNCT
ejpam-6131	93	4	q1)+t(ξ2	q1)+t(ξ2	NOUN
ejpam-6131	93	5	,	,	PUNCT
ejpam-6131	93	6	q2)+t(ξ3	q2)+t(ξ3	NOUN
ejpam-6131	93	7	,	,	PUNCT
ejpam-6131	93	8	q3)+t(ξ4	q3)+t(ξ4	NOUN
ejpam-6131	93	9	,	,	PUNCT
ejpam-6131	93	10	q4)+t(ξ5	q4)+t(ξ5	NOUN
ejpam-6131	93	11	,	,	PUNCT
ejpam-6131	93	12	q5	q5	PROPN
ejpam-6131	93	13	)	)	PUNCT
ejpam-6131	93	14	,	,	PUNCT
ejpam-6131	93	15	is	be	AUX
ejpam-6131	93	16	a	a	DET
ejpam-6131	93	17	gms	gms	NOUN
ejpam-6131	93	18	on	on	ADP
ejpam-6131	93	19	g5	g5	PROPN
ejpam-6131	93	20	,	,	PUNCT
ejpam-6131	93	21	that	that	ADV
ejpam-6131	93	22	is	is	ADV
ejpam-6131	93	23	,	,	PUNCT
ejpam-6131	93	24	(	(	PUNCT
ejpam-6131	93	25	g5	g5	NOUN
ejpam-6131	93	26	,	,	PUNCT
ejpam-6131	93	27	t̄	t̄	PROPN
ejpam-6131	93	28	)	)	PUNCT
ejpam-6131	93	29	is	be	AUX
ejpam-6131	93	30	a	a	DET
ejpam-6131	93	31	gms	gms	NOUN
ejpam-6131	93	32	induced	induce	VERB
ejpam-6131	93	33	by	by	ADP
ejpam-6131	93	34	t.	t.	ADJ
ejpam-6131	93	35	definition	definition	NOUN
ejpam-6131	93	36	11	11	NUM
ejpam-6131	93	37	.	.	PUNCT
ejpam-6131	94	1	an	an	DET
ejpam-6131	94	2	element	element	NOUN
ejpam-6131	94	3	(	(	PUNCT
ejpam-6131	94	4	ξ1	ξ1	NOUN
ejpam-6131	94	5	,	,	PUNCT
ejpam-6131	94	6	ξ2	ξ2	ADJ
ejpam-6131	94	7	,	,	PUNCT
ejpam-6131	94	8	ξ3	ξ3	NOUN
ejpam-6131	94	9	,	,	PUNCT
ejpam-6131	94	10	ξ4	ξ4	NOUN
ejpam-6131	94	11	,	,	PUNCT
ejpam-6131	94	12	ξ5	ξ5	NOUN
ejpam-6131	94	13	)	)	PUNCT
ejpam-6131	94	14	∈	∈	PROPN
ejpam-6131	94	15	g5	g5	NOUN
ejpam-6131	94	16	is	be	AUX
ejpam-6131	94	17	called	call	VERB
ejpam-6131	94	18	a	a	DET
ejpam-6131	94	19	quintuple	quintuple	ADJ
ejpam-6131	94	20	coincidence	coincidence	NOUN
ejpam-6131	94	21	point	point	NOUN
ejpam-6131	94	22	(	(	PUNCT
ejpam-6131	94	23	qcp	qcp	INTJ
ejpam-6131	94	24	)	)	PUNCT
ejpam-6131	94	25	or	or	CCONJ
ejpam-6131	94	26	a	a	DET
ejpam-6131	94	27	common	common	ADJ
ejpam-6131	94	28	quintuple	quintuple	ADJ
ejpam-6131	94	29	fixed	fix	VERB
ejpam-6131	94	30	point	point	NOUN
ejpam-6131	94	31	of	of	ADP
ejpam-6131	94	32	the	the	DET
ejpam-6131	94	33	mappings	mapping	NOUN
ejpam-6131	94	34	p	p	NOUN
ejpam-6131	94	35	:	:	PUNCT
ejpam-6131	94	36	g5	g5	NOUN
ejpam-6131	94	37	→	→	SYM
ejpam-6131	94	38	g	g	PROPN
ejpam-6131	94	39	and	and	CCONJ
ejpam-6131	94	40	p	p	X
ejpam-6131	94	41	:	:	PUNCT
ejpam-6131	94	42	g	g	PROPN
ejpam-6131	94	43	→	→	SYM
ejpam-6131	94	44	g	g	PROPN
ejpam-6131	94	45	if	if	SCONJ
ejpam-6131	94	46	p	p	PROPN
ejpam-6131	94	47	(	(	PUNCT
ejpam-6131	94	48	ξ1	ξ1	NOUN
ejpam-6131	94	49	,	,	PUNCT
ejpam-6131	94	50	ξ2	ξ2	ADJ
ejpam-6131	94	51	,	,	PUNCT
ejpam-6131	94	52	ξ3	ξ3	NOUN
ejpam-6131	94	53	,	,	PUNCT
ejpam-6131	94	54	ξ4	ξ4	NOUN
ejpam-6131	94	55	,	,	PUNCT
ejpam-6131	94	56	ξ5	ξ5	NOUN
ejpam-6131	94	57	)	)	PUNCT
ejpam-6131	94	58	=	=	SYM
ejpam-6131	94	59	p(ξ1	p(ξ1	NOUN
ejpam-6131	94	60	)	)	PUNCT
ejpam-6131	94	61	,	,	PUNCT
ejpam-6131	94	62	p	p	X
ejpam-6131	94	63	(	(	PUNCT
ejpam-6131	94	64	ξ2	ξ2	ADJ
ejpam-6131	94	65	,	,	PUNCT
ejpam-6131	94	66	ξ3	ξ3	PROPN
ejpam-6131	94	67	,	,	PUNCT
ejpam-6131	94	68	ξ4	ξ4	NOUN
ejpam-6131	94	69	,	,	PUNCT
ejpam-6131	94	70	ξ5	ξ5	NOUN
ejpam-6131	94	71	,	,	PUNCT
ejpam-6131	94	72	ξ1	ξ1	NOUN
ejpam-6131	94	73	)	)	PUNCT
ejpam-6131	94	74	=	=	SYM
ejpam-6131	94	75	p(ξ2	p(ξ2	NOUN
ejpam-6131	94	76	)	)	PUNCT
ejpam-6131	94	77	,	,	PUNCT
ejpam-6131	94	78	p	p	X
ejpam-6131	94	79	(	(	PUNCT
ejpam-6131	94	80	ξ3	ξ3	NOUN
ejpam-6131	94	81	,	,	PUNCT
ejpam-6131	94	82	ξ4	ξ4	NOUN
ejpam-6131	94	83	,	,	PUNCT
ejpam-6131	94	84	ξ5	ξ5	NOUN
ejpam-6131	94	85	,	,	PUNCT
ejpam-6131	94	86	ξ1	ξ1	NOUN
ejpam-6131	94	87	,	,	PUNCT
ejpam-6131	94	88	ξ2	ξ2	ADJ
ejpam-6131	94	89	)	)	PUNCT
ejpam-6131	94	90	=	=	SYM
ejpam-6131	94	91	p(ξ3	p(ξ3	NOUN
ejpam-6131	94	92	)	)	PUNCT
ejpam-6131	94	93	,	,	PUNCT
ejpam-6131	94	94	p	p	X
ejpam-6131	94	95	(	(	PUNCT
ejpam-6131	94	96	ξ4	ξ4	NOUN
ejpam-6131	94	97	,	,	PUNCT
ejpam-6131	94	98	ξ5	ξ5	NOUN
ejpam-6131	94	99	,	,	PUNCT
ejpam-6131	94	100	ξ1	ξ1	NOUN
ejpam-6131	94	101	,	,	PUNCT
ejpam-6131	94	102	ξ2	ξ2	ADJ
ejpam-6131	94	103	,	,	PUNCT
ejpam-6131	94	104	ξ3	ξ3	NOUN
ejpam-6131	94	105	)	)	PUNCT
ejpam-6131	94	106	=	=	SYM
ejpam-6131	94	107	p(ξ4	p(ξ4	NOUN
ejpam-6131	94	108	)	)	PUNCT
ejpam-6131	94	109	,	,	PUNCT
ejpam-6131	94	110	p	p	X
ejpam-6131	94	111	(	(	PUNCT
ejpam-6131	94	112	ξ5	ξ5	NOUN
ejpam-6131	94	113	,	,	PUNCT
ejpam-6131	94	114	ξ1	ξ1	NOUN
ejpam-6131	94	115	,	,	PUNCT
ejpam-6131	94	116	ξ2	ξ2	NOUN
ejpam-6131	94	117	,	,	PUNCT
ejpam-6131	94	118	ξ3	ξ3	NOUN
ejpam-6131	94	119	,	,	PUNCT
ejpam-6131	94	120	ξ4	ξ4	NOUN
ejpam-6131	94	121	)	)	PUNCT
ejpam-6131	94	122	=	=	SYM
ejpam-6131	94	123	p(ξ5	p(ξ5	NOUN
ejpam-6131	94	124	)	)	PUNCT
ejpam-6131	94	125	.	.	PUNCT
ejpam-6131	95	1	moreover	moreover	ADV
ejpam-6131	95	2	,	,	PUNCT
ejpam-6131	95	3	for	for	ADP
ejpam-6131	95	4	p	p	X
ejpam-6131	95	5	:	:	PUNCT
ejpam-6131	95	6	g	g	PROPN
ejpam-6131	95	7	→	→	SYM
ejpam-6131	95	8	g	g	PROPN
ejpam-6131	95	9	being	be	AUX
ejpam-6131	95	10	the	the	DET
ejpam-6131	95	11	identity	identity	NOUN
ejpam-6131	95	12	map	map	NOUN
ejpam-6131	95	13	,	,	PUNCT
ejpam-6131	95	14	definition	definition	NOUN
ejpam-6131	95	15	9	9	NUM
ejpam-6131	95	16	and	and	CCONJ
ejpam-6131	95	17	definition	definition	NOUN
ejpam-6131	95	18	11	11	NUM
ejpam-6131	95	19	reduce	reduce	VERB
ejpam-6131	95	20	into	into	ADP
ejpam-6131	95	21	definition	definition	NOUN
ejpam-6131	95	22	8	8	NUM
ejpam-6131	95	23	and	and	CCONJ
ejpam-6131	95	24	definition	definition	NOUN
ejpam-6131	95	25	10	10	NUM
ejpam-6131	95	26	,	,	PUNCT
ejpam-6131	95	27	respectively	respectively	ADV
ejpam-6131	95	28	.	.	PUNCT
ejpam-6131	96	1	definition	definition	NOUN
ejpam-6131	96	2	12	12	NUM
ejpam-6131	96	3	.	.	PUNCT
ejpam-6131	97	1	let	let	VERB
ejpam-6131	97	2	p	p	NOUN
ejpam-6131	97	3	:	:	PUNCT
ejpam-6131	97	4	g5	g5	NOUN
ejpam-6131	97	5	→	→	SYM
ejpam-6131	97	6	g	g	PROPN
ejpam-6131	97	7	and	and	CCONJ
ejpam-6131	97	8	p	p	X
ejpam-6131	97	9	:	:	PUNCT
ejpam-6131	97	10	g	g	PROPN
ejpam-6131	97	11	→	→	SYM
ejpam-6131	97	12	g	g	NOUN
ejpam-6131	97	13	be	be	AUX
ejpam-6131	97	14	two	two	NUM
ejpam-6131	97	15	mappings	mapping	NOUN
ejpam-6131	97	16	.	.	PUNCT
ejpam-6131	98	1	then	then	ADV
ejpam-6131	98	2	,	,	PUNCT
ejpam-6131	98	3	p	p	PROPN
ejpam-6131	98	4	and	and	CCONJ
ejpam-6131	98	5	p	p	NOUN
ejpam-6131	98	6	are	be	AUX
ejpam-6131	98	7	said	say	VERB
ejpam-6131	98	8	to	to	PART
ejpam-6131	98	9	be	be	AUX
ejpam-6131	98	10	commutable	commutable	ADJ
ejpam-6131	98	11	if	if	SCONJ
ejpam-6131	98	12	p(p	p(p	ADV
ejpam-6131	98	13	(	(	PUNCT
ejpam-6131	98	14	ξ1	ξ1	NOUN
ejpam-6131	98	15	,	,	PUNCT
ejpam-6131	98	16	ξ2	ξ2	ADJ
ejpam-6131	98	17	,	,	PUNCT
ejpam-6131	98	18	ξ3	ξ3	NOUN
ejpam-6131	98	19	,	,	PUNCT
ejpam-6131	98	20	ξ4	ξ4	NOUN
ejpam-6131	98	21	,	,	PUNCT
ejpam-6131	98	22	ξ5	ξ5	NOUN
ejpam-6131	98	23	)	)	PUNCT
ejpam-6131	98	24	)	)	PUNCT
ejpam-6131	99	1	=	=	SYM
ejpam-6131	99	2	p	p	X
ejpam-6131	99	3	(	(	PUNCT
ejpam-6131	99	4	p(ξ1	p(ξ1	NOUN
ejpam-6131	99	5	)	)	PUNCT
ejpam-6131	99	6	,	,	PUNCT
ejpam-6131	99	7	p(ξ2	p(ξ2	NOUN
ejpam-6131	99	8	)	)	PUNCT
ejpam-6131	99	9	,	,	PUNCT
ejpam-6131	99	10	p(ξ3	p(ξ3	NOUN
ejpam-6131	99	11	)	)	PUNCT
ejpam-6131	99	12	,	,	PUNCT
ejpam-6131	99	13	p(ξ4	p(ξ4	PROPN
ejpam-6131	99	14	)	)	PUNCT
ejpam-6131	99	15	,	,	PUNCT
ejpam-6131	99	16	p(ξ5	p(ξ5	NOUN
ejpam-6131	99	17	)	)	PUNCT
ejpam-6131	99	18	)	)	PUNCT
ejpam-6131	99	19	,	,	PUNCT
ejpam-6131	99	20	for	for	ADP
ejpam-6131	99	21	all	all	DET
ejpam-6131	99	22	ξ1	ξ1	NOUN
ejpam-6131	99	23	,	,	PUNCT
ejpam-6131	99	24	ξ2	ξ2	NOUN
ejpam-6131	99	25	,	,	PUNCT
ejpam-6131	99	26	ξ3	ξ3	NOUN
ejpam-6131	99	27	,	,	PUNCT
ejpam-6131	99	28	ξ4	ξ4	NOUN
ejpam-6131	99	29	,	,	PUNCT
ejpam-6131	99	30	ξ5	ξ5	PROPN
ejpam-6131	99	31	∈	∈	PROPN
ejpam-6131	99	32	g.	g.	NOUN
ejpam-6131	99	33	definition	definition	NOUN
ejpam-6131	99	34	13	13	NUM
ejpam-6131	99	35	.	.	PUNCT
ejpam-6131	100	1	the	the	DET
ejpam-6131	100	2	mappings	mapping	NOUN
ejpam-6131	100	3	p	p	NOUN
ejpam-6131	100	4	:	:	PUNCT
ejpam-6131	100	5	g5	g5	NOUN
ejpam-6131	100	6	→	→	SYM
ejpam-6131	100	7	g	g	PROPN
ejpam-6131	100	8	and	and	CCONJ
ejpam-6131	100	9	p	p	X
ejpam-6131	100	10	:	:	PUNCT
ejpam-6131	100	11	g	g	PROPN
ejpam-6131	100	12	→	→	SYM
ejpam-6131	100	13	g	g	NOUN
ejpam-6131	100	14	over	over	ADP
ejpam-6131	100	15	a	a	DET
ejpam-6131	100	16	metric	metric	ADJ
ejpam-6131	100	17	space	space	NOUN
ejpam-6131	100	18	(	(	PUNCT
ejpam-6131	100	19	g	g	PROPN
ejpam-6131	100	20	,	,	PUNCT
ejpam-6131	100	21	t	t	PROPN
ejpam-6131	100	22	)	)	PUNCT
ejpam-6131	100	23	are	be	AUX
ejpam-6131	100	24	compatible	compatible	ADJ
ejpam-6131	100	25	if	if	SCONJ
ejpam-6131	100	26	the	the	DET
ejpam-6131	100	27	following	follow	VERB
ejpam-6131	100	28	conditions	condition	NOUN
ejpam-6131	100	29	hold	hold	VERB
ejpam-6131	100	30	:	:	PUNCT
ejpam-6131	100	31	lim	lim	PROPN
ejpam-6131	100	32	n→+∞	n→+∞	VERB
ejpam-6131	100	33	t(p(u1	t(p(u1	PROPN
ejpam-6131	100	34	)	)	PUNCT
ejpam-6131	100	35	,	,	PUNCT
ejpam-6131	100	36	p	p	X
ejpam-6131	100	37	(	(	PUNCT
ejpam-6131	100	38	v	v	NOUN
ejpam-6131	100	39	1	1	NUM
ejpam-6131	100	40	)	)	PUNCT
ejpam-6131	100	41	)	)	PUNCT
ejpam-6131	101	1	=	=	SYM
ejpam-6131	101	2	0	0	NUM
ejpam-6131	101	3	,	,	PUNCT
ejpam-6131	101	4	where	where	SCONJ
ejpam-6131	101	5	u1	u1	NOUN
ejpam-6131	101	6	=	=	SYM
ejpam-6131	101	7	p	p	X
ejpam-6131	101	8	(	(	PUNCT
ejpam-6131	101	9	ξn1	ξn1	PROPN
ejpam-6131	101	10	,	,	PUNCT
ejpam-6131	101	11	ξ	ξ	PROPN
ejpam-6131	101	12	n	n	NUM
ejpam-6131	101	13	2	2	NUM
ejpam-6131	101	14	,	,	PUNCT
ejpam-6131	101	15	ξ	ξ	PROPN
ejpam-6131	101	16	n	n	PRON
ejpam-6131	101	17	3	3	NUM
ejpam-6131	101	18	,	,	PUNCT
ejpam-6131	101	19	ξ	ξ	PROPN
ejpam-6131	101	20	n	n	PRON
ejpam-6131	101	21	4	4	NUM
ejpam-6131	101	22	,	,	PUNCT
ejpam-6131	101	23	ξ	ξ	PROPN
ejpam-6131	101	24	n	n	PRON
ejpam-6131	101	25	5	5	NUM
ejpam-6131	101	26	)	)	PUNCT
ejpam-6131	101	27	and	and	CCONJ
ejpam-6131	101	28	v	v	X
ejpam-6131	101	29	1	1	NUM
ejpam-6131	101	30	=	=	SYM
ejpam-6131	101	31	(	(	PUNCT
ejpam-6131	101	32	p(ξn1	p(ξn1	PROPN
ejpam-6131	101	33	)	)	PUNCT
ejpam-6131	101	34	,	,	PUNCT
ejpam-6131	101	35	p(ξ	p(ξ	NOUN
ejpam-6131	101	36	n	n	PRON
ejpam-6131	101	37	2	2	NUM
ejpam-6131	101	38	)	)	PUNCT
ejpam-6131	101	39	,	,	PUNCT
ejpam-6131	101	40	p(ξ	p(ξ	NOUN
ejpam-6131	101	41	n	n	PRON
ejpam-6131	101	42	3	3	NUM
ejpam-6131	101	43	)	)	PUNCT
ejpam-6131	101	44	,	,	PUNCT
ejpam-6131	101	45	p(ξ	p(ξ	NOUN
ejpam-6131	101	46	n	n	PRON
ejpam-6131	101	47	4	4	NUM
ejpam-6131	101	48	)	)	PUNCT
ejpam-6131	101	49	,	,	PUNCT
ejpam-6131	101	50	p(ξ	p(ξ	NOUN
ejpam-6131	101	51	n	n	PRON
ejpam-6131	101	52	5	5	NUM
ejpam-6131	101	53	)	)	PUNCT
ejpam-6131	101	54	)	)	PUNCT
ejpam-6131	101	55	,	,	PUNCT
ejpam-6131	101	56	lim	lim	PROPN
ejpam-6131	101	57	n→+∞	n→+∞	PROPN
ejpam-6131	101	58	t(p(u2	t(p(u2	PROPN
ejpam-6131	101	59	)	)	PUNCT
ejpam-6131	101	60	,	,	PUNCT
ejpam-6131	101	61	p	p	X
ejpam-6131	101	62	(	(	PUNCT
ejpam-6131	101	63	v	v	NOUN
ejpam-6131	101	64	2	2	NUM
ejpam-6131	101	65	)	)	PUNCT
ejpam-6131	101	66	)	)	PUNCT
ejpam-6131	102	1	=	=	SYM
ejpam-6131	102	2	0	0	NUM
ejpam-6131	102	3	,	,	PUNCT
ejpam-6131	102	4	where	where	SCONJ
ejpam-6131	102	5	u2	u2	NOUN
ejpam-6131	102	6	=	=	PROPN
ejpam-6131	102	7	p	p	X
ejpam-6131	102	8	(	(	PUNCT
ejpam-6131	102	9	ξn2	ξn2	NOUN
ejpam-6131	102	10	,	,	PUNCT
ejpam-6131	102	11	ξ	ξ	PROPN
ejpam-6131	102	12	n	n	NUM
ejpam-6131	102	13	3	3	NUM
ejpam-6131	102	14	,	,	PUNCT
ejpam-6131	102	15	ξ	ξ	PROPN
ejpam-6131	102	16	n	n	PRON
ejpam-6131	102	17	4	4	NUM
ejpam-6131	102	18	,	,	PUNCT
ejpam-6131	102	19	ξ	ξ	PROPN
ejpam-6131	102	20	n	n	NUM
ejpam-6131	102	21	5	5	NUM
ejpam-6131	102	22	,	,	PUNCT
ejpam-6131	102	23	ξ	ξ	PROPN
ejpam-6131	102	24	n	n	PRON
ejpam-6131	102	25	1	1	NUM
ejpam-6131	102	26	)	)	PUNCT
ejpam-6131	102	27	and	and	CCONJ
ejpam-6131	102	28	v	v	ADP
ejpam-6131	102	29	2	2	NUM
ejpam-6131	102	30	=	=	SYM
ejpam-6131	102	31	(	(	PUNCT
ejpam-6131	102	32	p(ξn2	p(ξn2	NOUN
ejpam-6131	102	33	)	)	PUNCT
ejpam-6131	102	34	,	,	PUNCT
ejpam-6131	102	35	p(ξ	p(ξ	NOUN
ejpam-6131	102	36	n	n	PRON
ejpam-6131	102	37	3	3	NUM
ejpam-6131	102	38	)	)	PUNCT
ejpam-6131	102	39	,	,	PUNCT
ejpam-6131	102	40	p(ξ	p(ξ	NOUN
ejpam-6131	102	41	n	n	PRON
ejpam-6131	102	42	4	4	NUM
ejpam-6131	102	43	)	)	PUNCT
ejpam-6131	102	44	,	,	PUNCT
ejpam-6131	102	45	p(ξ	p(ξ	NOUN
ejpam-6131	102	46	n	n	PRON
ejpam-6131	102	47	5	5	NUM
ejpam-6131	102	48	)	)	PUNCT
ejpam-6131	102	49	,	,	PUNCT
ejpam-6131	102	50	p(ξ	p(ξ	NOUN
ejpam-6131	102	51	n	n	PRON
ejpam-6131	102	52	1	1	NUM
ejpam-6131	102	53	)	)	PUNCT
ejpam-6131	102	54	)	)	PUNCT
ejpam-6131	102	55	,	,	PUNCT
ejpam-6131	102	56	lim	lim	PROPN
ejpam-6131	102	57	n→+∞	n→+∞	VERB
ejpam-6131	102	58	t(p(u3	t(p(u3	PROPN
ejpam-6131	102	59	)	)	PUNCT
ejpam-6131	102	60	,	,	PUNCT
ejpam-6131	102	61	p	p	X
ejpam-6131	102	62	(	(	PUNCT
ejpam-6131	102	63	v	v	NOUN
ejpam-6131	102	64	3	3	NUM
ejpam-6131	102	65	)	)	PUNCT
ejpam-6131	102	66	)	)	PUNCT
ejpam-6131	103	1	=	=	SYM
ejpam-6131	103	2	0	0	NUM
ejpam-6131	103	3	,	,	PUNCT
ejpam-6131	103	4	where	where	SCONJ
ejpam-6131	103	5	u3	u3	NOUN
ejpam-6131	103	6	=	=	PROPN
ejpam-6131	103	7	p	p	X
ejpam-6131	103	8	(	(	PUNCT
ejpam-6131	103	9	ξn3	ξn3	PROPN
ejpam-6131	103	10	,	,	PUNCT
ejpam-6131	103	11	ξ	ξ	PROPN
ejpam-6131	103	12	n	n	NUM
ejpam-6131	103	13	4	4	NUM
ejpam-6131	103	14	,	,	PUNCT
ejpam-6131	103	15	ξ	ξ	PROPN
ejpam-6131	103	16	n	n	NUM
ejpam-6131	103	17	5	5	NUM
ejpam-6131	103	18	,	,	PUNCT
ejpam-6131	103	19	ξ	ξ	PROPN
ejpam-6131	103	20	n	n	NUM
ejpam-6131	103	21	1	1	NUM
ejpam-6131	103	22	,	,	PUNCT
ejpam-6131	103	23	ξ	ξ	PROPN
ejpam-6131	103	24	n	n	PRON
ejpam-6131	103	25	2	2	NUM
ejpam-6131	103	26	)	)	PUNCT
ejpam-6131	103	27	and	and	CCONJ
ejpam-6131	103	28	v	v	ADP
ejpam-6131	103	29	3	3	NUM
ejpam-6131	103	30	=	=	SYM
ejpam-6131	103	31	(	(	PUNCT
ejpam-6131	103	32	p(ξn3	p(ξn3	PROPN
ejpam-6131	103	33	)	)	PUNCT
ejpam-6131	103	34	,	,	PUNCT
ejpam-6131	103	35	p(ξ	p(ξ	NOUN
ejpam-6131	103	36	n	n	PRON
ejpam-6131	103	37	4	4	NUM
ejpam-6131	103	38	)	)	PUNCT
ejpam-6131	103	39	,	,	PUNCT
ejpam-6131	103	40	p(ξ	p(ξ	NOUN
ejpam-6131	103	41	n	n	PRON
ejpam-6131	103	42	5	5	NUM
ejpam-6131	103	43	)	)	PUNCT
ejpam-6131	103	44	,	,	PUNCT
ejpam-6131	103	45	p(ξ	p(ξ	NOUN
ejpam-6131	103	46	n	n	PRON
ejpam-6131	103	47	1	1	NUM
ejpam-6131	103	48	)	)	PUNCT
ejpam-6131	103	49	,	,	PUNCT
ejpam-6131	103	50	p(ξ	p(ξ	NOUN
ejpam-6131	103	51	n	n	PRON
ejpam-6131	103	52	2	2	NUM
ejpam-6131	103	53	)	)	PUNCT
ejpam-6131	103	54	)	)	PUNCT
ejpam-6131	103	55	,	,	PUNCT
ejpam-6131	103	56	lim	lim	PROPN
ejpam-6131	103	57	n→+∞	n→+∞	PROPN
ejpam-6131	103	58	t(p(u4	t(p(u4	PROPN
ejpam-6131	103	59	)	)	PUNCT
ejpam-6131	103	60	,	,	PUNCT
ejpam-6131	103	61	p	p	X
ejpam-6131	103	62	(	(	PUNCT
ejpam-6131	103	63	v	v	NOUN
ejpam-6131	103	64	4	4	NUM
ejpam-6131	103	65	)	)	PUNCT
ejpam-6131	103	66	)	)	PUNCT
ejpam-6131	104	1	=	=	PUNCT
ejpam-6131	104	2	0	0	NUM
ejpam-6131	104	3	,	,	PUNCT
ejpam-6131	104	4	where	where	SCONJ
ejpam-6131	104	5	u4	u4	PROPN
ejpam-6131	104	6	=	=	PROPN
ejpam-6131	104	7	p	p	X
ejpam-6131	104	8	(	(	PUNCT
ejpam-6131	104	9	ξn4	ξn4	PROPN
ejpam-6131	104	10	,	,	PUNCT
ejpam-6131	104	11	ξ	ξ	PROPN
ejpam-6131	104	12	n	n	NUM
ejpam-6131	104	13	5	5	NUM
ejpam-6131	104	14	,	,	PUNCT
ejpam-6131	104	15	ξ	ξ	PROPN
ejpam-6131	104	16	n	n	NUM
ejpam-6131	104	17	1	1	NUM
ejpam-6131	104	18	,	,	PUNCT
ejpam-6131	104	19	ξ	ξ	PROPN
ejpam-6131	104	20	n	n	PRON
ejpam-6131	104	21	2	2	NUM
ejpam-6131	104	22	,	,	PUNCT
ejpam-6131	104	23	ξ	ξ	PROPN
ejpam-6131	104	24	n	n	PRON
ejpam-6131	104	25	3	3	NUM
ejpam-6131	104	26	)	)	PUNCT
ejpam-6131	104	27	and	and	CCONJ
ejpam-6131	104	28	v	v	ADP
ejpam-6131	104	29	4	4	NUM
ejpam-6131	104	30	=	=	SYM
ejpam-6131	104	31	(	(	PUNCT
ejpam-6131	104	32	p(ξn4	p(ξn4	PROPN
ejpam-6131	104	33	)	)	PUNCT
ejpam-6131	104	34	,	,	PUNCT
ejpam-6131	104	35	p(ξ	p(ξ	NOUN
ejpam-6131	104	36	n	n	PRON
ejpam-6131	104	37	5	5	NUM
ejpam-6131	104	38	)	)	PUNCT
ejpam-6131	104	39	,	,	PUNCT
ejpam-6131	104	40	p(ξ	p(ξ	NOUN
ejpam-6131	104	41	n	n	PRON
ejpam-6131	104	42	1	1	NUM
ejpam-6131	104	43	)	)	PUNCT
ejpam-6131	104	44	,	,	PUNCT
ejpam-6131	104	45	p(ξ	p(ξ	NOUN
ejpam-6131	104	46	n	n	PRON
ejpam-6131	104	47	2	2	NUM
ejpam-6131	104	48	)	)	PUNCT
ejpam-6131	104	49	,	,	PUNCT
ejpam-6131	104	50	p(ξ	p(ξ	NOUN
ejpam-6131	104	51	n	n	PRON
ejpam-6131	104	52	3	3	NUM
ejpam-6131	104	53	)	)	PUNCT
ejpam-6131	104	54	)	)	PUNCT
ejpam-6131	104	55	,	,	PUNCT
ejpam-6131	104	56	lim	lim	PROPN
ejpam-6131	104	57	n→+∞	n→+∞	PROPN
ejpam-6131	104	58	t(p(u5	t(p(u5	PROPN
ejpam-6131	104	59	)	)	PUNCT
ejpam-6131	104	60	,	,	PUNCT
ejpam-6131	104	61	p	p	X
ejpam-6131	104	62	(	(	PUNCT
ejpam-6131	104	63	v	v	NOUN
ejpam-6131	104	64	5	5	NUM
ejpam-6131	104	65	)	)	PUNCT
ejpam-6131	104	66	)	)	PUNCT
ejpam-6131	105	1	=	=	PUNCT
ejpam-6131	105	2	0	0	NUM
ejpam-6131	105	3	,	,	PUNCT
ejpam-6131	105	4	where	where	SCONJ
ejpam-6131	105	5	u5	u5	NOUN
ejpam-6131	105	6	=	=	SYM
ejpam-6131	105	7	p	p	X
ejpam-6131	105	8	(	(	PUNCT
ejpam-6131	105	9	ξn5	ξn5	NOUN
ejpam-6131	105	10	,	,	PUNCT
ejpam-6131	105	11	ξ	ξ	PROPN
ejpam-6131	105	12	n	n	NUM
ejpam-6131	105	13	1	1	NUM
ejpam-6131	105	14	,	,	PUNCT
ejpam-6131	105	15	ξ	ξ	PROPN
ejpam-6131	105	16	n	n	PRON
ejpam-6131	105	17	2	2	NUM
ejpam-6131	105	18	,	,	PUNCT
ejpam-6131	105	19	ξ	ξ	PROPN
ejpam-6131	105	20	n	n	PRON
ejpam-6131	105	21	3	3	NUM
ejpam-6131	105	22	,	,	PUNCT
ejpam-6131	105	23	ξ	ξ	PROPN
ejpam-6131	105	24	n	n	PRON
ejpam-6131	105	25	4	4	NUM
ejpam-6131	105	26	)	)	PUNCT
ejpam-6131	105	27	and	and	CCONJ
ejpam-6131	105	28	v	v	ADP
ejpam-6131	105	29	5	5	NUM
ejpam-6131	105	30	=	=	SYM
ejpam-6131	105	31	(	(	PUNCT
ejpam-6131	105	32	p(ξn5	p(ξn5	NOUN
ejpam-6131	105	33	)	)	PUNCT
ejpam-6131	105	34	,	,	PUNCT
ejpam-6131	105	35	p(ξ	p(ξ	NOUN
ejpam-6131	105	36	n	n	PRON
ejpam-6131	105	37	1	1	NUM
ejpam-6131	105	38	)	)	PUNCT
ejpam-6131	105	39	,	,	PUNCT
ejpam-6131	105	40	p(ξ	p(ξ	NOUN
ejpam-6131	105	41	n	n	PRON
ejpam-6131	105	42	2	2	NUM
ejpam-6131	105	43	)	)	PUNCT
ejpam-6131	105	44	,	,	PUNCT
ejpam-6131	105	45	p(ξ	p(ξ	NOUN
ejpam-6131	105	46	n	n	PRON
ejpam-6131	105	47	3	3	NUM
ejpam-6131	105	48	)	)	PUNCT
ejpam-6131	105	49	,	,	PUNCT
ejpam-6131	105	50	p(ξ	p(ξ	NOUN
ejpam-6131	105	51	n	n	PRON
ejpam-6131	105	52	4	4	NUM
ejpam-6131	105	53	)	)	PUNCT
ejpam-6131	105	54	)	)	PUNCT
ejpam-6131	105	55	,	,	PUNCT
ejpam-6131	105	56	s.	s.	PROPN
ejpam-6131	105	57	batul	batul	PROPN
ejpam-6131	105	58	et	et	PROPN
ejpam-6131	105	59	a.	a.	PROPN
ejpam-6131	105	60	/	/	PUNCT
ejpam-6131	105	61	eur	eur	PROPN
ejpam-6131	105	62	.	.	PUNCT
ejpam-6131	106	1	j.	j.	PROPN
ejpam-6131	106	2	pure	pure	PROPN
ejpam-6131	106	3	appl	appl	PROPN
ejpam-6131	106	4	.	.	PROPN
ejpam-6131	106	5	math	math	PROPN
ejpam-6131	106	6	,	,	PUNCT
ejpam-6131	106	7	18	18	NUM
ejpam-6131	106	8	(	(	PUNCT
ejpam-6131	106	9	2	2	NUM
ejpam-6131	106	10	)	)	PUNCT
ejpam-6131	106	11	(	(	PUNCT
ejpam-6131	106	12	2025	2025	NUM
ejpam-6131	106	13	)	)	PUNCT
ejpam-6131	106	14	,	,	PUNCT
ejpam-6131	106	15	6131	6131	NUM
ejpam-6131	106	16	6	6	NUM
ejpam-6131	106	17	of	of	ADP
ejpam-6131	106	18	22	22	NUM
ejpam-6131	106	19	whenever	whenever	SCONJ
ejpam-6131	106	20	{	{	PUNCT
ejpam-6131	106	21	ξn1	ξn1	NOUN
ejpam-6131	106	22	}	}	PUNCT
ejpam-6131	106	23	,	,	PUNCT
ejpam-6131	106	24	{	{	PUNCT
ejpam-6131	106	25	ξn2	ξn2	NOUN
ejpam-6131	106	26	}	}	PUNCT
ejpam-6131	106	27	,	,	PUNCT
ejpam-6131	106	28	{	{	PUNCT
ejpam-6131	106	29	ξn3	ξn3	NOUN
ejpam-6131	106	30	}	}	PUNCT
ejpam-6131	106	31	,	,	PUNCT
ejpam-6131	106	32	{	{	PUNCT
ejpam-6131	106	33	ξn4	ξn4	NOUN
ejpam-6131	106	34	}	}	PUNCT
ejpam-6131	106	35	and	and	CCONJ
ejpam-6131	106	36	{	{	PUNCT
ejpam-6131	106	37	ξn5	ξn5	NOUN
ejpam-6131	106	38	}	}	PUNCT
ejpam-6131	106	39	are	be	AUX
ejpam-6131	106	40	sequences	sequence	NOUN
ejpam-6131	106	41	in	in	ADP
ejpam-6131	106	42	g	g	NOUN
ejpam-6131	106	43	in	in	ADP
ejpam-6131	106	44	such	such	DET
ejpam-6131	106	45	a	a	DET
ejpam-6131	106	46	way	way	NOUN
ejpam-6131	106	47	that	that	PRON
ejpam-6131	106	48	lim	lim	PROPN
ejpam-6131	106	49	n→+∞	n→+∞	PROPN
ejpam-6131	106	50	u1	u1	NOUN
ejpam-6131	106	51	=	=	PROPN
ejpam-6131	106	52	lim	lim	PROPN
ejpam-6131	106	53	n→+∞	n→+∞	VERB
ejpam-6131	106	54	p(ξn1	p(ξn1	PROPN
ejpam-6131	106	55	)	)	PUNCT
ejpam-6131	107	1	=	=	SYM
ejpam-6131	107	2	ξ1	ξ1	PROPN
ejpam-6131	107	3	,	,	PUNCT
ejpam-6131	107	4	lim	lim	PROPN
ejpam-6131	107	5	n→+∞	n→+∞	VERB
ejpam-6131	107	6	u2	u2	PROPN
ejpam-6131	107	7	=	=	PROPN
ejpam-6131	107	8	lim	lim	PROPN
ejpam-6131	107	9	n→+∞	n→+∞	VERB
ejpam-6131	107	10	p(ξn2	p(ξn2	NOUN
ejpam-6131	107	11	)	)	PUNCT
ejpam-6131	108	1	=	=	SYM
ejpam-6131	108	2	ξ2	ξ2	NOUN
ejpam-6131	108	3	,	,	PUNCT
ejpam-6131	108	4	lim	lim	PROPN
ejpam-6131	108	5	n→+∞	n→+∞	VERB
ejpam-6131	108	6	u3	u3	PROPN
ejpam-6131	108	7	=	=	PROPN
ejpam-6131	108	8	lim	lim	PROPN
ejpam-6131	108	9	n→+∞	n→+∞	PROPN
ejpam-6131	108	10	p(ξn3	p(ξn3	PROPN
ejpam-6131	108	11	)	)	PUNCT
ejpam-6131	109	1	=	=	SYM
ejpam-6131	109	2	ξ3	ξ3	PROPN
ejpam-6131	109	3	,	,	PUNCT
ejpam-6131	109	4	lim	lim	PROPN
ejpam-6131	109	5	n→+∞	n→+∞	VERB
ejpam-6131	109	6	u4	u4	PROPN
ejpam-6131	109	7	=	=	PROPN
ejpam-6131	109	8	lim	lim	PROPN
ejpam-6131	109	9	n→+∞	n→+∞	VERB
ejpam-6131	109	10	p(ξn4	p(ξn4	PROPN
ejpam-6131	109	11	)	)	PUNCT
ejpam-6131	109	12	=	=	SYM
ejpam-6131	109	13	ξ4	ξ4	PROPN
ejpam-6131	109	14	,	,	PUNCT
ejpam-6131	109	15	lim	lim	PROPN
ejpam-6131	109	16	n→+∞	n→+∞	PROPN
ejpam-6131	109	17	u5	u5	PROPN
ejpam-6131	110	1	=	=	PROPN
ejpam-6131	110	2	lim	lim	PROPN
ejpam-6131	110	3	n→+∞	n→+∞	VERB
ejpam-6131	110	4	p(ξn5	p(ξn5	NOUN
ejpam-6131	110	5	)	)	PUNCT
ejpam-6131	111	1	=	=	SYM
ejpam-6131	111	2	ξ5	ξ5	NOUN
ejpam-6131	111	3	,	,	PUNCT
ejpam-6131	111	4	for	for	ADP
ejpam-6131	111	5	some	some	DET
ejpam-6131	111	6	ξ1	ξ1	NOUN
ejpam-6131	111	7	,	,	PUNCT
ejpam-6131	111	8	ξ2	ξ2	NOUN
ejpam-6131	111	9	,	,	PUNCT
ejpam-6131	111	10	ξ3	ξ3	NOUN
ejpam-6131	111	11	,	,	PUNCT
ejpam-6131	111	12	ξ4	ξ4	NOUN
ejpam-6131	111	13	,	,	PUNCT
ejpam-6131	111	14	ξ5	ξ5	PROPN
ejpam-6131	111	15	∈	∈	PROPN
ejpam-6131	111	16	g.	g.	NOUN
ejpam-6131	111	17	definition	definition	NOUN
ejpam-6131	111	18	14	14	NUM
ejpam-6131	111	19	.	.	PUNCT
ejpam-6131	112	1	the	the	DET
ejpam-6131	112	2	mappings	mapping	NOUN
ejpam-6131	112	3	p	p	NOUN
ejpam-6131	112	4	:	:	PUNCT
ejpam-6131	112	5	g5	g5	NOUN
ejpam-6131	112	6	→	→	SYM
ejpam-6131	112	7	g	g	PROPN
ejpam-6131	112	8	and	and	CCONJ
ejpam-6131	112	9	p	p	X
ejpam-6131	112	10	:	:	PUNCT
ejpam-6131	112	11	g	g	NOUN
ejpam-6131	112	12	→	→	SYM
ejpam-6131	112	13	g	g	PROPN
ejpam-6131	112	14	are	be	AUX
ejpam-6131	112	15	termed	term	VERB
ejpam-6131	112	16	as	as	ADP
ejpam-6131	112	17	reciprocally	reciprocally	ADV
ejpam-6131	112	18	continuous	continuous	ADJ
ejpam-6131	112	19	if	if	SCONJ
ejpam-6131	112	20	for	for	ADP
ejpam-6131	112	21	some	some	DET
ejpam-6131	112	22	ξi	ξi	NOUN
ejpam-6131	112	23	∈	∈	NOUN
ejpam-6131	112	24	g	g	NOUN
ejpam-6131	112	25	,	,	PUNCT
ejpam-6131	112	26	where	where	SCONJ
ejpam-6131	112	27	1	1	NUM
ejpam-6131	112	28	≤	≤	NUM
ejpam-6131	112	29	i	i	X
ejpam-6131	112	30	≤	≤	NOUN
ejpam-6131	112	31	5	5	NUM
ejpam-6131	112	32	,	,	PUNCT
ejpam-6131	112	33	we	we	PRON
ejpam-6131	112	34	have	have	VERB
ejpam-6131	112	35	lim	lim	PROPN
ejpam-6131	112	36	n→+∞	n→+∞	PROPN
ejpam-6131	112	37	p(u1	p(u1	NOUN
ejpam-6131	112	38	)	)	PUNCT
ejpam-6131	112	39	=	=	SYM
ejpam-6131	112	40	p(ξ1	p(ξ1	NOUN
ejpam-6131	112	41	)	)	PUNCT
ejpam-6131	112	42	and	and	CCONJ
ejpam-6131	112	43	lim	lim	PROPN
ejpam-6131	112	44	n→+∞	n→+∞	VERB
ejpam-6131	112	45	p	p	X
ejpam-6131	112	46	(	(	PUNCT
ejpam-6131	112	47	v	v	NOUN
ejpam-6131	112	48	1	1	NUM
ejpam-6131	112	49	)	)	PUNCT
ejpam-6131	113	1	=	=	SYM
ejpam-6131	113	2	p	p	X
ejpam-6131	113	3	(	(	PUNCT
ejpam-6131	113	4	ξ1	ξ1	PROPN
ejpam-6131	113	5	,	,	PUNCT
ejpam-6131	113	6	ξ2	ξ2	ADJ
ejpam-6131	113	7	,	,	PUNCT
ejpam-6131	113	8	ξ3	ξ3	NOUN
ejpam-6131	113	9	,	,	PUNCT
ejpam-6131	113	10	ξ4	ξ4	NOUN
ejpam-6131	113	11	,	,	PUNCT
ejpam-6131	113	12	ξ5	ξ5	NOUN
ejpam-6131	113	13	)	)	PUNCT
ejpam-6131	113	14	,	,	PUNCT
ejpam-6131	113	15	lim	lim	PROPN
ejpam-6131	113	16	n→+∞	n→+∞	PROPN
ejpam-6131	113	17	p(u2	p(u2	PROPN
ejpam-6131	113	18	)	)	PUNCT
ejpam-6131	113	19	=	=	SYM
ejpam-6131	113	20	p(ξ2	p(ξ2	NOUN
ejpam-6131	113	21	)	)	PUNCT
ejpam-6131	113	22	and	and	CCONJ
ejpam-6131	113	23	lim	lim	PROPN
ejpam-6131	113	24	n→+∞	n→+∞	VERB
ejpam-6131	113	25	p	p	X
ejpam-6131	113	26	(	(	PUNCT
ejpam-6131	113	27	v	v	NOUN
ejpam-6131	113	28	2	2	NUM
ejpam-6131	113	29	)	)	PUNCT
ejpam-6131	113	30	=	=	SYM
ejpam-6131	114	1	p	p	X
ejpam-6131	114	2	(	(	PUNCT
ejpam-6131	114	3	ξ2	ξ2	ADJ
ejpam-6131	114	4	,	,	PUNCT
ejpam-6131	114	5	ξ3	ξ3	PROPN
ejpam-6131	114	6	,	,	PUNCT
ejpam-6131	114	7	ξ4	ξ4	NOUN
ejpam-6131	114	8	,	,	PUNCT
ejpam-6131	114	9	ξ5	ξ5	NOUN
ejpam-6131	114	10	,	,	PUNCT
ejpam-6131	114	11	ξ1	ξ1	NOUN
ejpam-6131	114	12	)	)	PUNCT
ejpam-6131	114	13	,	,	PUNCT
ejpam-6131	114	14	lim	lim	PROPN
ejpam-6131	114	15	n→+∞	n→+∞	PROPN
ejpam-6131	114	16	p(u3	p(u3	PROPN
ejpam-6131	114	17	)	)	PUNCT
ejpam-6131	114	18	=	=	SYM
ejpam-6131	114	19	p(ξ3	p(ξ3	NOUN
ejpam-6131	114	20	)	)	PUNCT
ejpam-6131	114	21	and	and	CCONJ
ejpam-6131	114	22	lim	lim	PROPN
ejpam-6131	114	23	n→+∞	n→+∞	VERB
ejpam-6131	114	24	p	p	X
ejpam-6131	114	25	(	(	PUNCT
ejpam-6131	114	26	v	v	NOUN
ejpam-6131	114	27	3	3	NUM
ejpam-6131	114	28	)	)	PUNCT
ejpam-6131	114	29	=	=	SYM
ejpam-6131	115	1	p	p	X
ejpam-6131	115	2	(	(	PUNCT
ejpam-6131	115	3	ξ3	ξ3	NOUN
ejpam-6131	115	4	,	,	PUNCT
ejpam-6131	115	5	ξ4	ξ4	NOUN
ejpam-6131	115	6	,	,	PUNCT
ejpam-6131	115	7	ξ5	ξ5	NOUN
ejpam-6131	115	8	,	,	PUNCT
ejpam-6131	115	9	ξ1	ξ1	NOUN
ejpam-6131	115	10	,	,	PUNCT
ejpam-6131	115	11	ξ2	ξ2	NOUN
ejpam-6131	115	12	)	)	PUNCT
ejpam-6131	115	13	,	,	PUNCT
ejpam-6131	115	14	lim	lim	PROPN
ejpam-6131	115	15	n→+∞	n→+∞	PROPN
ejpam-6131	115	16	p(u4	p(u4	NOUN
ejpam-6131	115	17	)	)	PUNCT
ejpam-6131	115	18	=	=	SYM
ejpam-6131	115	19	p(ξ4	p(ξ4	NOUN
ejpam-6131	115	20	)	)	PUNCT
ejpam-6131	115	21	and	and	CCONJ
ejpam-6131	115	22	lim	lim	PROPN
ejpam-6131	115	23	n→+∞	n→+∞	VERB
ejpam-6131	115	24	p	p	X
ejpam-6131	115	25	(	(	PUNCT
ejpam-6131	115	26	v	v	NOUN
ejpam-6131	115	27	4	4	NUM
ejpam-6131	115	28	)	)	PUNCT
ejpam-6131	116	1	=	=	SYM
ejpam-6131	116	2	p	p	X
ejpam-6131	116	3	(	(	PUNCT
ejpam-6131	116	4	ξ4	ξ4	NOUN
ejpam-6131	116	5	,	,	PUNCT
ejpam-6131	116	6	ξ5	ξ5	NOUN
ejpam-6131	116	7	,	,	PUNCT
ejpam-6131	116	8	ξ1	ξ1	NOUN
ejpam-6131	116	9	,	,	PUNCT
ejpam-6131	116	10	ξ2	ξ2	NOUN
ejpam-6131	116	11	,	,	PUNCT
ejpam-6131	116	12	ξ3	ξ3	PROPN
ejpam-6131	116	13	)	)	PUNCT
ejpam-6131	116	14	,	,	PUNCT
ejpam-6131	116	15	lim	lim	PROPN
ejpam-6131	116	16	n→+∞	n→+∞	PROPN
ejpam-6131	116	17	p(u5	p(u5	NOUN
ejpam-6131	116	18	)	)	PUNCT
ejpam-6131	116	19	=	=	SYM
ejpam-6131	116	20	p(ξ5	p(ξ5	NOUN
ejpam-6131	116	21	)	)	PUNCT
ejpam-6131	116	22	and	and	CCONJ
ejpam-6131	116	23	lim	lim	PROPN
ejpam-6131	116	24	n→+∞	n→+∞	VERB
ejpam-6131	116	25	p	p	X
ejpam-6131	116	26	(	(	PUNCT
ejpam-6131	116	27	v	v	NOUN
ejpam-6131	116	28	5	5	NUM
ejpam-6131	116	29	)	)	PUNCT
ejpam-6131	116	30	=	=	SYM
ejpam-6131	117	1	p	p	X
ejpam-6131	117	2	(	(	PUNCT
ejpam-6131	117	3	ξ5	ξ5	NOUN
ejpam-6131	117	4	,	,	PUNCT
ejpam-6131	117	5	ξ1	ξ1	NOUN
ejpam-6131	117	6	,	,	PUNCT
ejpam-6131	117	7	ξ2	ξ2	NOUN
ejpam-6131	117	8	,	,	PUNCT
ejpam-6131	117	9	ξ3	ξ3	NOUN
ejpam-6131	117	10	,	,	PUNCT
ejpam-6131	117	11	ξ4	ξ4	NOUN
ejpam-6131	117	12	)	)	PUNCT
ejpam-6131	117	13	,	,	PUNCT
ejpam-6131	117	14	whenever	whenever	SCONJ
ejpam-6131	117	15	{	{	PUNCT
ejpam-6131	117	16	ξn1	ξn1	NOUN
ejpam-6131	117	17	}	}	PUNCT
ejpam-6131	117	18	,	,	PUNCT
ejpam-6131	117	19	{	{	PUNCT
ejpam-6131	117	20	ξn2	ξn2	NOUN
ejpam-6131	117	21	}	}	PUNCT
ejpam-6131	117	22	,	,	PUNCT
ejpam-6131	117	23	{	{	PUNCT
ejpam-6131	117	24	ξn3	ξn3	NOUN
ejpam-6131	117	25	}	}	PUNCT
ejpam-6131	117	26	,	,	PUNCT
ejpam-6131	117	27	{	{	PUNCT
ejpam-6131	117	28	ξn4	ξn4	NOUN
ejpam-6131	117	29	}	}	PUNCT
ejpam-6131	117	30	and	and	CCONJ
ejpam-6131	117	31	{	{	PUNCT
ejpam-6131	117	32	ξn5	ξn5	NOUN
ejpam-6131	117	33	}	}	PUNCT
ejpam-6131	117	34	are	be	AUX
ejpam-6131	117	35	sequences	sequence	NOUN
ejpam-6131	117	36	in	in	ADP
ejpam-6131	117	37	g	g	PROPN
ejpam-6131	117	38	such	such	ADJ
ejpam-6131	117	39	that	that	SCONJ
ejpam-6131	117	40	lim	lim	PROPN
ejpam-6131	117	41	n→+∞	n→+∞	PROPN
ejpam-6131	117	42	u1	u1	NOUN
ejpam-6131	117	43	=	=	PROPN
ejpam-6131	117	44	lim	lim	PROPN
ejpam-6131	117	45	n→+∞	n→+∞	VERB
ejpam-6131	117	46	p(ξn1	p(ξn1	PROPN
ejpam-6131	117	47	)	)	PUNCT
ejpam-6131	118	1	=	=	SYM
ejpam-6131	118	2	ξ1	ξ1	PROPN
ejpam-6131	118	3	,	,	PUNCT
ejpam-6131	118	4	lim	lim	PROPN
ejpam-6131	118	5	n→+∞	n→+∞	VERB
ejpam-6131	118	6	u2	u2	PROPN
ejpam-6131	118	7	=	=	PROPN
ejpam-6131	118	8	lim	lim	PROPN
ejpam-6131	118	9	n→+∞	n→+∞	VERB
ejpam-6131	118	10	p(ξn2	p(ξn2	NOUN
ejpam-6131	118	11	)	)	PUNCT
ejpam-6131	118	12	=	=	SYM
ejpam-6131	118	13	ξ2	ξ2	NOUN
ejpam-6131	118	14	,	,	PUNCT
ejpam-6131	118	15	,	,	PUNCT
ejpam-6131	118	16	lim	lim	PROPN
ejpam-6131	118	17	n→+∞	n→+∞	VERB
ejpam-6131	118	18	u3	u3	PROPN
ejpam-6131	118	19	=	=	PROPN
ejpam-6131	118	20	lim	lim	PROPN
ejpam-6131	118	21	n→+∞	n→+∞	PROPN
ejpam-6131	118	22	p(ξn3	p(ξn3	PROPN
ejpam-6131	118	23	)	)	PUNCT
ejpam-6131	119	1	=	=	SYM
ejpam-6131	119	2	ξ3	ξ3	PROPN
ejpam-6131	119	3	,	,	PUNCT
ejpam-6131	119	4	lim	lim	PROPN
ejpam-6131	119	5	n→+∞	n→+∞	VERB
ejpam-6131	119	6	u4	u4	PROPN
ejpam-6131	119	7	=	=	PROPN
ejpam-6131	119	8	lim	lim	PROPN
ejpam-6131	119	9	n→+∞	n→+∞	VERB
ejpam-6131	119	10	p(ξn4	p(ξn4	PROPN
ejpam-6131	119	11	)	)	PUNCT
ejpam-6131	119	12	=	=	SYM
ejpam-6131	119	13	ξ4	ξ4	PROPN
ejpam-6131	119	14	,	,	PUNCT
ejpam-6131	119	15	lim	lim	PROPN
ejpam-6131	119	16	n→+∞	n→+∞	PROPN
ejpam-6131	119	17	u5	u5	PROPN
ejpam-6131	120	1	=	=	PROPN
ejpam-6131	120	2	lim	lim	PROPN
ejpam-6131	120	3	n→+∞	n→+∞	VERB
ejpam-6131	120	4	p(ξn5	p(ξn5	NOUN
ejpam-6131	120	5	)	)	PUNCT
ejpam-6131	121	1	=	=	SYM
ejpam-6131	121	2	ξ5	ξ5	NOUN
ejpam-6131	121	3	,	,	PUNCT
ejpam-6131	121	4	for	for	ADP
ejpam-6131	121	5	some	some	DET
ejpam-6131	121	6	ξ1	ξ1	NOUN
ejpam-6131	121	7	,	,	PUNCT
ejpam-6131	121	8	ξ2	ξ2	NOUN
ejpam-6131	121	9	,	,	PUNCT
ejpam-6131	121	10	ξ3	ξ3	NOUN
ejpam-6131	121	11	,	,	PUNCT
ejpam-6131	121	12	ξ4	ξ4	NOUN
ejpam-6131	121	13	,	,	PUNCT
ejpam-6131	121	14	ξ5	ξ5	PROPN
ejpam-6131	121	15	∈	∈	PROPN
ejpam-6131	121	16	g.	g.	NOUN
ejpam-6131	121	17	definition	definition	NOUN
ejpam-6131	121	18	15	15	NUM
ejpam-6131	121	19	.	.	PUNCT
ejpam-6131	122	1	two	two	NUM
ejpam-6131	122	2	mappings	mapping	NOUN
ejpam-6131	122	3	p	p	NOUN
ejpam-6131	122	4	:	:	PUNCT
ejpam-6131	122	5	g5	g5	NOUN
ejpam-6131	122	6	→	→	SYM
ejpam-6131	122	7	g	g	PROPN
ejpam-6131	122	8	and	and	CCONJ
ejpam-6131	122	9	p	p	X
ejpam-6131	122	10	:	:	PUNCT
ejpam-6131	122	11	g	g	NOUN
ejpam-6131	122	12	→	→	SYM
ejpam-6131	122	13	g	g	PROPN
ejpam-6131	122	14	are	be	AUX
ejpam-6131	122	15	known	know	VERB
ejpam-6131	122	16	as	as	ADP
ejpam-6131	122	17	weakly	weakly	ADV
ejpam-6131	122	18	reciprocally	reciprocally	ADV
ejpam-6131	122	19	continuous	continuous	ADJ
ejpam-6131	122	20	if	if	SCONJ
ejpam-6131	122	21	for	for	ADP
ejpam-6131	122	22	some	some	DET
ejpam-6131	122	23	ξi	ξi	NOUN
ejpam-6131	122	24	∈	∈	NOUN
ejpam-6131	122	25	g	g	NOUN
ejpam-6131	122	26	,	,	PUNCT
ejpam-6131	122	27	where	where	SCONJ
ejpam-6131	122	28	1	1	NUM
ejpam-6131	122	29	≤	≤	NUM
ejpam-6131	122	30	i	i	X
ejpam-6131	122	31	≤	≤	NOUN
ejpam-6131	122	32	5	5	NUM
ejpam-6131	122	33	,	,	PUNCT
ejpam-6131	122	34	we	we	PRON
ejpam-6131	122	35	have	have	VERB
ejpam-6131	122	36	lim	lim	PROPN
ejpam-6131	122	37	n→+∞	n→+∞	PROPN
ejpam-6131	122	38	p(u1	p(u1	NOUN
ejpam-6131	122	39	)	)	PUNCT
ejpam-6131	122	40	=	=	SYM
ejpam-6131	122	41	p(ξ1	p(ξ1	NOUN
ejpam-6131	122	42	)	)	PUNCT
ejpam-6131	122	43	or	or	CCONJ
ejpam-6131	122	44	lim	lim	PROPN
ejpam-6131	122	45	n→+∞	n→+∞	VERB
ejpam-6131	122	46	p	p	X
ejpam-6131	122	47	(	(	PUNCT
ejpam-6131	122	48	v	v	NOUN
ejpam-6131	122	49	1	1	NUM
ejpam-6131	122	50	)	)	PUNCT
ejpam-6131	123	1	=	=	SYM
ejpam-6131	123	2	p	p	X
ejpam-6131	123	3	(	(	PUNCT
ejpam-6131	123	4	ξ1	ξ1	PROPN
ejpam-6131	123	5	,	,	PUNCT
ejpam-6131	123	6	ξ2	ξ2	ADJ
ejpam-6131	123	7	,	,	PUNCT
ejpam-6131	123	8	ξ3	ξ3	NOUN
ejpam-6131	123	9	,	,	PUNCT
ejpam-6131	123	10	ξ4	ξ4	NOUN
ejpam-6131	123	11	,	,	PUNCT
ejpam-6131	123	12	ξ5	ξ5	NOUN
ejpam-6131	123	13	)	)	PUNCT
ejpam-6131	123	14	,	,	PUNCT
ejpam-6131	123	15	lim	lim	PROPN
ejpam-6131	123	16	n→+∞	n→+∞	PROPN
ejpam-6131	123	17	p(u2	p(u2	PROPN
ejpam-6131	123	18	)	)	PUNCT
ejpam-6131	123	19	=	=	SYM
ejpam-6131	123	20	p(ξ2	p(ξ2	NOUN
ejpam-6131	123	21	)	)	PUNCT
ejpam-6131	123	22	or	or	CCONJ
ejpam-6131	123	23	lim	lim	PROPN
ejpam-6131	123	24	n→+∞	n→+∞	VERB
ejpam-6131	123	25	p	p	X
ejpam-6131	123	26	(	(	PUNCT
ejpam-6131	123	27	v	v	NOUN
ejpam-6131	123	28	2	2	NUM
ejpam-6131	123	29	)	)	PUNCT
ejpam-6131	123	30	=	=	SYM
ejpam-6131	124	1	p	p	X
ejpam-6131	124	2	(	(	PUNCT
ejpam-6131	124	3	ξ2	ξ2	ADJ
ejpam-6131	124	4	,	,	PUNCT
ejpam-6131	124	5	ξ3	ξ3	PROPN
ejpam-6131	124	6	,	,	PUNCT
ejpam-6131	124	7	ξ4	ξ4	NOUN
ejpam-6131	124	8	,	,	PUNCT
ejpam-6131	124	9	ξ5	ξ5	NOUN
ejpam-6131	124	10	,	,	PUNCT
ejpam-6131	124	11	ξ1	ξ1	NOUN
ejpam-6131	124	12	)	)	PUNCT
ejpam-6131	124	13	,	,	PUNCT
ejpam-6131	124	14	lim	lim	PROPN
ejpam-6131	124	15	n→+∞	n→+∞	PROPN
ejpam-6131	124	16	p(u3	p(u3	PROPN
ejpam-6131	124	17	)	)	PUNCT
ejpam-6131	124	18	=	=	SYM
ejpam-6131	124	19	p(ξ3	p(ξ3	NOUN
ejpam-6131	124	20	)	)	PUNCT
ejpam-6131	124	21	or	or	CCONJ
ejpam-6131	124	22	lim	lim	PROPN
ejpam-6131	124	23	n→+∞	n→+∞	VERB
ejpam-6131	124	24	p	p	X
ejpam-6131	124	25	(	(	PUNCT
ejpam-6131	124	26	v	v	NOUN
ejpam-6131	124	27	3	3	NUM
ejpam-6131	124	28	)	)	PUNCT
ejpam-6131	124	29	=	=	SYM
ejpam-6131	125	1	p	p	X
ejpam-6131	125	2	(	(	PUNCT
ejpam-6131	125	3	ξ3	ξ3	NOUN
ejpam-6131	125	4	,	,	PUNCT
ejpam-6131	125	5	ξ4	ξ4	NOUN
ejpam-6131	125	6	,	,	PUNCT
ejpam-6131	125	7	ξ5	ξ5	NOUN
ejpam-6131	125	8	,	,	PUNCT
ejpam-6131	125	9	ξ1	ξ1	NOUN
ejpam-6131	125	10	,	,	PUNCT
ejpam-6131	125	11	ξ2	ξ2	NOUN
ejpam-6131	125	12	)	)	PUNCT
ejpam-6131	125	13	,	,	PUNCT
ejpam-6131	125	14	lim	lim	PROPN
ejpam-6131	125	15	n→+∞	n→+∞	PROPN
ejpam-6131	125	16	p(u4	p(u4	NOUN
ejpam-6131	125	17	)	)	PUNCT
ejpam-6131	125	18	=	=	SYM
ejpam-6131	125	19	p(ξ4	p(ξ4	NOUN
ejpam-6131	125	20	)	)	PUNCT
ejpam-6131	125	21	or	or	CCONJ
ejpam-6131	125	22	lim	lim	PROPN
ejpam-6131	125	23	n→+∞	n→+∞	VERB
ejpam-6131	125	24	p	p	X
ejpam-6131	125	25	(	(	PUNCT
ejpam-6131	125	26	v	v	NOUN
ejpam-6131	125	27	4	4	NUM
ejpam-6131	125	28	)	)	PUNCT
ejpam-6131	125	29	=	=	SYM
ejpam-6131	126	1	p	p	X
ejpam-6131	126	2	(	(	PUNCT
ejpam-6131	126	3	ξ4	ξ4	NOUN
ejpam-6131	126	4	,	,	PUNCT
ejpam-6131	126	5	ξ5	ξ5	NOUN
ejpam-6131	126	6	,	,	PUNCT
ejpam-6131	126	7	ξ1	ξ1	NOUN
ejpam-6131	126	8	,	,	PUNCT
ejpam-6131	126	9	ξ2	ξ2	NOUN
ejpam-6131	126	10	,	,	PUNCT
ejpam-6131	126	11	ξ3	ξ3	PROPN
ejpam-6131	126	12	)	)	PUNCT
ejpam-6131	126	13	,	,	PUNCT
ejpam-6131	126	14	lim	lim	PROPN
ejpam-6131	126	15	n→+∞	n→+∞	PROPN
ejpam-6131	126	16	p(u5	p(u5	NOUN
ejpam-6131	126	17	)	)	PUNCT
ejpam-6131	126	18	=	=	SYM
ejpam-6131	126	19	p(ξ5	p(ξ5	NOUN
ejpam-6131	126	20	)	)	PUNCT
ejpam-6131	126	21	or	or	CCONJ
ejpam-6131	126	22	lim	lim	PROPN
ejpam-6131	126	23	n→+∞	n→+∞	VERB
ejpam-6131	126	24	p	p	X
ejpam-6131	126	25	(	(	PUNCT
ejpam-6131	126	26	v	v	NOUN
ejpam-6131	126	27	5	5	NUM
ejpam-6131	126	28	)	)	PUNCT
ejpam-6131	126	29	=	=	SYM
ejpam-6131	127	1	p	p	X
ejpam-6131	127	2	(	(	PUNCT
ejpam-6131	127	3	ξ5	ξ5	NOUN
ejpam-6131	127	4	,	,	PUNCT
ejpam-6131	127	5	ξ1	ξ1	NOUN
ejpam-6131	127	6	,	,	PUNCT
ejpam-6131	127	7	ξ2	ξ2	NOUN
ejpam-6131	127	8	,	,	PUNCT
ejpam-6131	127	9	ξ3	ξ3	NOUN
ejpam-6131	127	10	,	,	PUNCT
ejpam-6131	127	11	ξ4	ξ4	NOUN
ejpam-6131	127	12	)	)	PUNCT
ejpam-6131	127	13	,	,	PUNCT
ejpam-6131	127	14	whenever	whenever	SCONJ
ejpam-6131	127	15	{	{	PUNCT
ejpam-6131	127	16	ξn1	ξn1	NOUN
ejpam-6131	127	17	}	}	PUNCT
ejpam-6131	127	18	,	,	PUNCT
ejpam-6131	127	19	{	{	PUNCT
ejpam-6131	127	20	ξn2	ξn2	NOUN
ejpam-6131	127	21	}	}	PUNCT
ejpam-6131	127	22	,	,	PUNCT
ejpam-6131	127	23	{	{	PUNCT
ejpam-6131	127	24	ξn3	ξn3	NOUN
ejpam-6131	127	25	}	}	PUNCT
ejpam-6131	127	26	,	,	PUNCT
ejpam-6131	127	27	{	{	PUNCT
ejpam-6131	127	28	ξn4	ξn4	NOUN
ejpam-6131	127	29	}	}	PUNCT
ejpam-6131	127	30	and	and	CCONJ
ejpam-6131	127	31	{	{	PUNCT
ejpam-6131	127	32	ξn5	ξn5	NOUN
ejpam-6131	127	33	}	}	PUNCT
ejpam-6131	127	34	are	be	AUX
ejpam-6131	127	35	few	few	ADJ
ejpam-6131	127	36	sequences	sequence	NOUN
ejpam-6131	127	37	within	within	ADP
ejpam-6131	127	38	the	the	DET
ejpam-6131	127	39	set	set	NOUN
ejpam-6131	127	40	g	g	NOUN
ejpam-6131	127	41	in	in	ADP
ejpam-6131	127	42	such	such	DET
ejpam-6131	127	43	a	a	DET
ejpam-6131	127	44	way	way	NOUN
ejpam-6131	127	45	that	that	PRON
ejpam-6131	127	46	lim	lim	PROPN
ejpam-6131	127	47	n→+∞	n→+∞	PROPN
ejpam-6131	127	48	u1	u1	NOUN
ejpam-6131	127	49	=	=	PROPN
ejpam-6131	127	50	lim	lim	PROPN
ejpam-6131	127	51	n→+∞	n→+∞	VERB
ejpam-6131	127	52	p(ξn1	p(ξn1	PROPN
ejpam-6131	127	53	)	)	PUNCT
ejpam-6131	128	1	=	=	SYM
ejpam-6131	128	2	ξ1	ξ1	PROPN
ejpam-6131	128	3	,	,	PUNCT
ejpam-6131	128	4	lim	lim	PROPN
ejpam-6131	128	5	n→+∞	n→+∞	VERB
ejpam-6131	128	6	u2	u2	PROPN
ejpam-6131	128	7	=	=	PROPN
ejpam-6131	128	8	lim	lim	PROPN
ejpam-6131	128	9	n→+∞	n→+∞	VERB
ejpam-6131	128	10	p(ξn2	p(ξn2	NOUN
ejpam-6131	128	11	)	)	PUNCT
ejpam-6131	128	12	=	=	SYM
ejpam-6131	128	13	ξ2	ξ2	NOUN
ejpam-6131	128	14	,	,	PUNCT
ejpam-6131	128	15	,	,	PUNCT
ejpam-6131	128	16	lim	lim	PROPN
ejpam-6131	128	17	n→+∞	n→+∞	VERB
ejpam-6131	128	18	u3	u3	PROPN
ejpam-6131	128	19	=	=	PROPN
ejpam-6131	128	20	lim	lim	PROPN
ejpam-6131	128	21	n→+∞	n→+∞	PROPN
ejpam-6131	128	22	p(ξn3	p(ξn3	PROPN
ejpam-6131	128	23	)	)	PUNCT
ejpam-6131	129	1	=	=	SYM
ejpam-6131	129	2	ξ3	ξ3	PROPN
ejpam-6131	129	3	,	,	PUNCT
ejpam-6131	129	4	lim	lim	PROPN
ejpam-6131	129	5	n→+∞	n→+∞	VERB
ejpam-6131	129	6	u4	u4	PROPN
ejpam-6131	129	7	=	=	PROPN
ejpam-6131	129	8	lim	lim	PROPN
ejpam-6131	129	9	n→+∞	n→+∞	VERB
ejpam-6131	129	10	p(ξn4	p(ξn4	PROPN
ejpam-6131	129	11	)	)	PUNCT
ejpam-6131	129	12	=	=	SYM
ejpam-6131	129	13	ξ4	ξ4	PROPN
ejpam-6131	129	14	,	,	PUNCT
ejpam-6131	129	15	lim	lim	PROPN
ejpam-6131	129	16	n→+∞	n→+∞	PROPN
ejpam-6131	129	17	u5	u5	PROPN
ejpam-6131	130	1	=	=	PROPN
ejpam-6131	130	2	lim	lim	PROPN
ejpam-6131	130	3	n→+∞	n→+∞	VERB
ejpam-6131	130	4	p(ξn5	p(ξn5	NOUN
ejpam-6131	130	5	)	)	PUNCT
ejpam-6131	131	1	=	=	SYM
ejpam-6131	131	2	ξ5	ξ5	NOUN
ejpam-6131	131	3	,	,	PUNCT
ejpam-6131	131	4	for	for	ADP
ejpam-6131	131	5	some	some	DET
ejpam-6131	131	6	ξ1	ξ1	NOUN
ejpam-6131	131	7	,	,	PUNCT
ejpam-6131	131	8	ξ2	ξ2	NOUN
ejpam-6131	131	9	,	,	PUNCT
ejpam-6131	131	10	ξ3	ξ3	NOUN
ejpam-6131	131	11	,	,	PUNCT
ejpam-6131	131	12	ξ4	ξ4	NOUN
ejpam-6131	131	13	,	,	PUNCT
ejpam-6131	131	14	ξ5	ξ5	PROPN
ejpam-6131	131	15	∈	∈	PROPN
ejpam-6131	131	16	g.	g.	PROPN
ejpam-6131	131	17	s.	s.	PROPN
ejpam-6131	131	18	batul	batul	PROPN
ejpam-6131	131	19	et	et	PROPN
ejpam-6131	131	20	a.	a.	PROPN
ejpam-6131	131	21	/	/	PUNCT
ejpam-6131	131	22	eur	eur	PROPN
ejpam-6131	131	23	.	.	PUNCT
ejpam-6131	132	1	j.	j.	PROPN
ejpam-6131	132	2	pure	pure	PROPN
ejpam-6131	132	3	appl	appl	PROPN
ejpam-6131	132	4	.	.	PROPN
ejpam-6131	132	5	math	math	PROPN
ejpam-6131	132	6	,	,	PUNCT
ejpam-6131	132	7	18	18	NUM
ejpam-6131	132	8	(	(	PUNCT
ejpam-6131	132	9	2	2	NUM
ejpam-6131	132	10	)	)	PUNCT
ejpam-6131	132	11	(	(	PUNCT
ejpam-6131	132	12	2025	2025	NUM
ejpam-6131	132	13	)	)	PUNCT
ejpam-6131	132	14	,	,	PUNCT
ejpam-6131	132	15	6131	6131	NUM
ejpam-6131	132	16	7	7	NUM
ejpam-6131	132	17	of	of	ADP
ejpam-6131	132	18	22	22	NUM
ejpam-6131	132	19	example	example	NOUN
ejpam-6131	132	20	3	3	NUM
ejpam-6131	132	21	.	.	PUNCT
ejpam-6131	133	1	let	let	VERB
ejpam-6131	133	2	g	g	NOUN
ejpam-6131	133	3	=	=	PUNCT
ejpam-6131	134	1	[	[	X
ejpam-6131	134	2	0	0	NUM
ejpam-6131	134	3	,	,	PUNCT
ejpam-6131	134	4	1	1	NUM
ejpam-6131	134	5	]	]	PUNCT
ejpam-6131	134	6	.	.	PUNCT
ejpam-6131	135	1	let	let	VERB
ejpam-6131	135	2	t(ξ1	t(ξ1	NOUN
ejpam-6131	135	3	,	,	PUNCT
ejpam-6131	135	4	ξ2	ξ2	NOUN
ejpam-6131	135	5	)	)	PUNCT
ejpam-6131	135	6	=	=	SYM
ejpam-6131	135	7	|ξ1	|ξ1	NOUN
ejpam-6131	135	8	−	−	NUM
ejpam-6131	135	9	ξ2|	ξ2|	NOUN
ejpam-6131	135	10	and	and	CCONJ
ejpam-6131	135	11	“	"	PUNCT
ejpam-6131	135	12	⪯	⪯	NOUN
ejpam-6131	135	13	”	"	PUNCT
ejpam-6131	135	14	be	be	AUX
ejpam-6131	135	15	the	the	DET
ejpam-6131	135	16	partial	partial	ADJ
ejpam-6131	135	17	order	order	NOUN
ejpam-6131	135	18	on	on	ADP
ejpam-6131	135	19	g	g	PROPN
ejpam-6131	135	20	defined	define	VERB
ejpam-6131	135	21	for	for	ADP
ejpam-6131	135	22	all	all	DET
ejpam-6131	135	23	ξ1	ξ1	NOUN
ejpam-6131	135	24	,	,	PUNCT
ejpam-6131	135	25	ξ2	ξ2	NOUN
ejpam-6131	135	26	∈	∈	PROPN
ejpam-6131	135	27	g	g	NOUN
ejpam-6131	135	28	,	,	PUNCT
ejpam-6131	135	29	ξ1	ξ1	PROPN
ejpam-6131	135	30	⪯	⪯	NOUN
ejpam-6131	135	31	ξ2	ξ2	PROPN
ejpam-6131	135	32	⇔	⇔	PROPN
ejpam-6131	135	33	ξ1	ξ1	PROPN
ejpam-6131	135	34	≤	≤	PROPN
ejpam-6131	135	35	ξ2	ξ2	NOUN
ejpam-6131	135	36	.	.	PUNCT
ejpam-6131	136	1	let	let	VERB
ejpam-6131	136	2	p	p	NOUN
ejpam-6131	136	3	:	:	PUNCT
ejpam-6131	136	4	g5	g5	NOUN
ejpam-6131	136	5	→	→	SYM
ejpam-6131	136	6	g	g	PROPN
ejpam-6131	136	7	and	and	CCONJ
ejpam-6131	136	8	p	p	X
ejpam-6131	136	9	:	:	PUNCT
ejpam-6131	136	10	g	g	PROPN
ejpam-6131	136	11	→	→	SYM
ejpam-6131	136	12	g	g	NOUN
ejpam-6131	136	13	be	be	VERB
ejpam-6131	136	14	two	two	NUM
ejpam-6131	136	15	mappings	mapping	NOUN
ejpam-6131	136	16	defined	define	VERB
ejpam-6131	136	17	as	as	ADP
ejpam-6131	136	18	p	p	PROPN
ejpam-6131	136	19	(	(	PUNCT
ejpam-6131	136	20	ξ1	ξ1	NOUN
ejpam-6131	136	21	,	,	PUNCT
ejpam-6131	136	22	ξ2	ξ2	ADJ
ejpam-6131	136	23	,	,	PUNCT
ejpam-6131	136	24	ξ3	ξ3	NOUN
ejpam-6131	136	25	,	,	PUNCT
ejpam-6131	136	26	ξ4	ξ4	NOUN
ejpam-6131	136	27	,	,	PUNCT
ejpam-6131	136	28	ξ5	ξ5	NOUN
ejpam-6131	136	29	)	)	PUNCT
ejpam-6131	136	30	=	=	SYM
ejpam-6131	137	1	ξ1ξ2	ξ1ξ2	ADP
ejpam-6131	137	2	−	−	NOUN
ejpam-6131	137	3	ξ3ξ4	ξ3ξ4	NOUN
ejpam-6131	138	1	+	+	NUM
ejpam-6131	138	2	ξ5	ξ5	NOUN
ejpam-6131	138	3	5	5	NUM
ejpam-6131	138	4	and	and	CCONJ
ejpam-6131	138	5	p(ξ1	p(ξ1	NOUN
ejpam-6131	138	6	)	)	PUNCT
ejpam-6131	138	7	=	=	SYM
ejpam-6131	138	8	ξ1	ξ1	NOUN
ejpam-6131	138	9	,	,	PUNCT
ejpam-6131	138	10	∀	∀	NOUN
ejpam-6131	138	11	ξ1	ξ1	NOUN
ejpam-6131	138	12	,	,	PUNCT
ejpam-6131	138	13	ξ2	ξ2	ADJ
ejpam-6131	138	14	,	,	PUNCT
ejpam-6131	138	15	ξ3	ξ3	NOUN
ejpam-6131	138	16	,	,	PUNCT
ejpam-6131	138	17	ξ4	ξ4	NOUN
ejpam-6131	138	18	,	,	PUNCT
ejpam-6131	138	19	ξ5	ξ5	PROPN
ejpam-6131	138	20	∈	∈	PROPN
ejpam-6131	138	21	g.	g.	NOUN
ejpam-6131	138	22	consider	consider	VERB
ejpam-6131	138	23	the	the	DET
ejpam-6131	138	24	sequences	sequence	NOUN
ejpam-6131	138	25	{	{	PUNCT
ejpam-6131	138	26	ξn1	ξn1	PROPN
ejpam-6131	138	27	}	}	PUNCT
ejpam-6131	138	28	,	,	PUNCT
ejpam-6131	138	29	{	{	PUNCT
ejpam-6131	138	30	ξn2	ξn2	NOUN
ejpam-6131	138	31	}	}	PUNCT
ejpam-6131	138	32	,	,	PUNCT
ejpam-6131	138	33	{	{	PUNCT
ejpam-6131	138	34	ξn3	ξn3	NOUN
ejpam-6131	138	35	}	}	PUNCT
ejpam-6131	138	36	,	,	PUNCT
ejpam-6131	138	37	{	{	PUNCT
ejpam-6131	138	38	ξn4	ξn4	NOUN
ejpam-6131	138	39	}	}	PUNCT
ejpam-6131	138	40	and	and	CCONJ
ejpam-6131	138	41	{	{	PUNCT
ejpam-6131	138	42	ξn5	ξn5	NOUN
ejpam-6131	138	43	}	}	PUNCT
ejpam-6131	138	44	defined	define	VERB
ejpam-6131	138	45	by	by	ADP
ejpam-6131	138	46	ξn1	ξn1	PROPN
ejpam-6131	138	47	=	=	SYM
ejpam-6131	138	48	1	1	NUM
ejpam-6131	138	49	n	n	NOUN
ejpam-6131	138	50	,	,	PUNCT
ejpam-6131	138	51	ξn2	ξn2	NOUN
ejpam-6131	138	52	=	=	SYM
ejpam-6131	138	53	1	1	NUM
ejpam-6131	138	54	n3	n3	NOUN
ejpam-6131	138	55	+	+	CCONJ
ejpam-6131	138	56	1	1	NUM
ejpam-6131	138	57	,	,	PUNCT
ejpam-6131	138	58	ξn3	ξn3	PROPN
ejpam-6131	138	59	=	=	SYM
ejpam-6131	138	60	1√	1√	PROPN
ejpam-6131	138	61	n3	n3	NOUN
ejpam-6131	138	62	+	+	CCONJ
ejpam-6131	138	63	1	1	NUM
ejpam-6131	138	64	,	,	PUNCT
ejpam-6131	138	65	ξn4	ξn4	NOUN
ejpam-6131	138	66	=	=	SYM
ejpam-6131	138	67	1	1	NUM
ejpam-6131	138	68	n3	n3	NOUN
ejpam-6131	138	69	,	,	PUNCT
ejpam-6131	138	70	and	and	CCONJ
ejpam-6131	138	71	ξn5	ξn5	NOUN
ejpam-6131	138	72	=	=	SYM
ejpam-6131	138	73	1	1	NUM
ejpam-6131	138	74	n3	n3	NOUN
ejpam-6131	138	75	+	+	CCONJ
ejpam-6131	138	76	2	2	NUM
ejpam-6131	138	77	∀	∀	NOUN
ejpam-6131	138	78	n	n	PRON
ejpam-6131	138	79	∈	∈	PROPN
ejpam-6131	138	80	n.	n.	NOUN
ejpam-6131	138	81	clearly	clearly	ADV
ejpam-6131	138	82	,	,	PUNCT
ejpam-6131	138	83	(	(	PUNCT
ejpam-6131	138	84	g	g	NOUN
ejpam-6131	138	85	,	,	PUNCT
ejpam-6131	138	86	t	t	PROPN
ejpam-6131	138	87	)	)	PUNCT
ejpam-6131	138	88	is	be	AUX
ejpam-6131	138	89	a	a	DET
ejpam-6131	138	90	partially	partially	ADV
ejpam-6131	138	91	ordered	order	VERB
ejpam-6131	138	92	metric	metric	ADJ
ejpam-6131	138	93	space	space	NOUN
ejpam-6131	138	94	and	and	CCONJ
ejpam-6131	138	95	g	g	NOUN
ejpam-6131	138	96	is	be	AUX
ejpam-6131	138	97	complete	complete	ADJ
ejpam-6131	138	98	.	.	PUNCT
ejpam-6131	139	1	in	in	ADP
ejpam-6131	139	2	addition	addition	NOUN
ejpam-6131	139	3	,	,	PUNCT
ejpam-6131	139	4	lim	lim	PROPN
ejpam-6131	139	5	n→+∞	n→+∞	PROPN
ejpam-6131	139	6	u1	u1	NOUN
ejpam-6131	139	7	=	=	PROPN
ejpam-6131	139	8	lim	lim	PROPN
ejpam-6131	139	9	n→+∞	n→+∞	VERB
ejpam-6131	139	10	p(ξn1	p(ξn1	PROPN
ejpam-6131	139	11	)	)	PUNCT
ejpam-6131	139	12	=	=	SYM
ejpam-6131	139	13	0	0	PROPN
ejpam-6131	139	14	,	,	PUNCT
ejpam-6131	139	15	lim	lim	PROPN
ejpam-6131	139	16	n→+∞	n→+∞	VERB
ejpam-6131	139	17	u2	u2	PROPN
ejpam-6131	139	18	=	=	PROPN
ejpam-6131	139	19	lim	lim	PROPN
ejpam-6131	139	20	n→+∞	n→+∞	VERB
ejpam-6131	139	21	p(ξn2	p(ξn2	NOUN
ejpam-6131	139	22	)	)	PUNCT
ejpam-6131	140	1	=	=	SYM
ejpam-6131	140	2	0	0	NUM
ejpam-6131	140	3	,	,	PUNCT
ejpam-6131	140	4	lim	lim	PROPN
ejpam-6131	140	5	n→+∞	n→+∞	VERB
ejpam-6131	140	6	u3	u3	PROPN
ejpam-6131	140	7	=	=	PROPN
ejpam-6131	140	8	lim	lim	PROPN
ejpam-6131	140	9	n→+∞	n→+∞	PROPN
ejpam-6131	140	10	p(ξn3	p(ξn3	PROPN
ejpam-6131	140	11	)	)	PUNCT
ejpam-6131	141	1	=	=	SYM
ejpam-6131	141	2	0	0	PROPN
ejpam-6131	141	3	,	,	PUNCT
ejpam-6131	141	4	lim	lim	PROPN
ejpam-6131	141	5	n→+∞	n→+∞	VERB
ejpam-6131	141	6	u4	u4	PROPN
ejpam-6131	141	7	=	=	PROPN
ejpam-6131	141	8	lim	lim	PROPN
ejpam-6131	141	9	n→+∞	n→+∞	VERB
ejpam-6131	141	10	p(ξn4	p(ξn4	PROPN
ejpam-6131	141	11	)	)	PUNCT
ejpam-6131	141	12	=	=	SYM
ejpam-6131	142	1	0	0	PROPN
ejpam-6131	142	2	,	,	PUNCT
ejpam-6131	142	3	lim	lim	PROPN
ejpam-6131	142	4	n→+∞	n→+∞	PROPN
ejpam-6131	142	5	u5	u5	PROPN
ejpam-6131	142	6	=	=	PROPN
ejpam-6131	142	7	lim	lim	PROPN
ejpam-6131	142	8	n→+∞	n→+∞	VERB
ejpam-6131	142	9	p(ξn5	p(ξn5	X
ejpam-6131	142	10	)	)	PUNCT
ejpam-6131	143	1	=	=	SYM
ejpam-6131	143	2	0	0	X
ejpam-6131	143	3	.	.	PUNCT
ejpam-6131	144	1	moreover	moreover	ADV
ejpam-6131	144	2	,	,	PUNCT
ejpam-6131	144	3	defined	define	VERB
ejpam-6131	144	4	sequences	sequence	NOUN
ejpam-6131	144	5	,	,	PUNCT
ejpam-6131	144	6	functions	function	NOUN
ejpam-6131	144	7	and	and	CCONJ
ejpam-6131	144	8	metrics	metric	NOUN
ejpam-6131	144	9	satisfy	satisfy	VERB
ejpam-6131	144	10	compatibility	compatibility	NOUN
ejpam-6131	144	11	conditions	condition	NOUN
ejpam-6131	144	12	,	,	PUNCT
ejpam-6131	144	13	reciprocal	reciprocal	ADJ
ejpam-6131	144	14	continuity	continuity	NOUN
ejpam-6131	144	15	and	and	CCONJ
ejpam-6131	144	16	weakly	weakly	ADJ
ejpam-6131	144	17	reciprocal	reciprocal	ADJ
ejpam-6131	144	18	continuity	continuity	NOUN
ejpam-6131	144	19	for	for	ADP
ejpam-6131	144	20	p	p	PROPN
ejpam-6131	144	21	and	and	CCONJ
ejpam-6131	144	22	p.	p.	NOUN
ejpam-6131	144	23	in	in	ADP
ejpam-6131	144	24	light	light	NOUN
ejpam-6131	144	25	of	of	ADP
ejpam-6131	144	26	this	this	PRON
ejpam-6131	144	27	,	,	PUNCT
ejpam-6131	144	28	both	both	CCONJ
ejpam-6131	144	29	p	p	NOUN
ejpam-6131	144	30	and	and	CCONJ
ejpam-6131	144	31	p	p	NOUN
ejpam-6131	144	32	exhibit	exhibit	NOUN
ejpam-6131	144	33	compatibility	compatibility	NOUN
ejpam-6131	144	34	,	,	PUNCT
ejpam-6131	144	35	reciprocal	reciprocal	ADJ
ejpam-6131	144	36	continuity	continuity	NOUN
ejpam-6131	144	37	and	and	CCONJ
ejpam-6131	144	38	weak	weak	ADJ
ejpam-6131	144	39	reciprocal	reciprocal	ADJ
ejpam-6131	144	40	continuity	continuity	NOUN
ejpam-6131	144	41	.	.	PUNCT
ejpam-6131	145	1	definition	definition	NOUN
ejpam-6131	145	2	16	16	NUM
ejpam-6131	145	3	.	.	PUNCT
ejpam-6131	146	1	for	for	ADP
ejpam-6131	146	2	two	two	NUM
ejpam-6131	146	3	mappings	mapping	NOUN
ejpam-6131	146	4	ζn	ζn	DET
ejpam-6131	146	5	:	:	PUNCT
ejpam-6131	146	6	g5	g5	NOUN
ejpam-6131	146	7	→	→	SYM
ejpam-6131	146	8	g	g	PROPN
ejpam-6131	146	9	and	and	CCONJ
ejpam-6131	146	10	p	p	X
ejpam-6131	146	11	:	:	PUNCT
ejpam-6131	146	12	g	g	PROPN
ejpam-6131	146	13	→	→	SYM
ejpam-6131	146	14	g	g	NOUN
ejpam-6131	146	15	defined	define	VERB
ejpam-6131	146	16	on	on	ADP
ejpam-6131	146	17	the	the	DET
ejpam-6131	146	18	metric	metric	ADJ
ejpam-6131	146	19	space	space	NOUN
ejpam-6131	146	20	(	(	PUNCT
ejpam-6131	146	21	g	g	PROPN
ejpam-6131	146	22	,	,	PUNCT
ejpam-6131	146	23	t	t	PROPN
ejpam-6131	146	24	)	)	PUNCT
ejpam-6131	146	25	,	,	PUNCT
ejpam-6131	146	26	the	the	DET
ejpam-6131	146	27	sequence	sequence	NOUN
ejpam-6131	146	28	{	{	PUNCT
ejpam-6131	146	29	ζn}n∈w	ζn}n∈w	NUM
ejpam-6131	146	30	and	and	CCONJ
ejpam-6131	146	31	p	p	NOUN
ejpam-6131	146	32	are	be	AUX
ejpam-6131	146	33	known	know	VERB
ejpam-6131	146	34	as	as	ADP
ejpam-6131	146	35	compatible	compatible	ADJ
ejpam-6131	146	36	if	if	SCONJ
ejpam-6131	146	37	lim	lim	PROPN
ejpam-6131	146	38	n→+∞	n→+∞	PROPN
ejpam-6131	146	39	t(p(ū1	t(p(ū1	PROPN
ejpam-6131	146	40	)	)	PUNCT
ejpam-6131	146	41	,	,	PUNCT
ejpam-6131	146	42	ζn(v̄	ζn(v̄	NOUN
ejpam-6131	146	43	1	1	NUM
ejpam-6131	146	44	)	)	PUNCT
ejpam-6131	146	45	)	)	PUNCT
ejpam-6131	147	1	=	=	PUNCT
ejpam-6131	147	2	0	0	NUM
ejpam-6131	147	3	,	,	PUNCT
ejpam-6131	147	4	where	where	SCONJ
ejpam-6131	147	5	ū1	ū1	ADP
ejpam-6131	147	6	=	=	SYM
ejpam-6131	147	7	ζn(ξn1	ζn(ξn1	PROPN
ejpam-6131	147	8	,	,	PUNCT
ejpam-6131	147	9	ξ	ξ	PROPN
ejpam-6131	147	10	n	n	PRON
ejpam-6131	147	11	2	2	NUM
ejpam-6131	147	12	,	,	PUNCT
ejpam-6131	147	13	ξ	ξ	PROPN
ejpam-6131	147	14	n	n	PRON
ejpam-6131	147	15	3	3	NUM
ejpam-6131	147	16	,	,	PUNCT
ejpam-6131	147	17	ξ	ξ	PROPN
ejpam-6131	147	18	n	n	PRON
ejpam-6131	147	19	4	4	NUM
ejpam-6131	147	20	,	,	PUNCT
ejpam-6131	147	21	ξ	ξ	PROPN
ejpam-6131	147	22	n	n	PRON
ejpam-6131	147	23	5	5	NUM
ejpam-6131	147	24	)	)	PUNCT
ejpam-6131	147	25	and	and	CCONJ
ejpam-6131	147	26	v̄	v̄	NOUN
ejpam-6131	147	27	1	1	NUM
ejpam-6131	147	28	=	=	SYM
ejpam-6131	147	29	(	(	PUNCT
ejpam-6131	147	30	p(ξn1	p(ξn1	PROPN
ejpam-6131	147	31	)	)	PUNCT
ejpam-6131	147	32	,	,	PUNCT
ejpam-6131	147	33	p(ξ	p(ξ	NOUN
ejpam-6131	147	34	n	n	PRON
ejpam-6131	147	35	2	2	NUM
ejpam-6131	147	36	)	)	PUNCT
ejpam-6131	147	37	,	,	PUNCT
ejpam-6131	147	38	p(ξ	p(ξ	NOUN
ejpam-6131	147	39	n	n	PRON
ejpam-6131	147	40	3	3	NUM
ejpam-6131	147	41	)	)	PUNCT
ejpam-6131	147	42	,	,	PUNCT
ejpam-6131	147	43	p(ξ	p(ξ	NOUN
ejpam-6131	147	44	n	n	PRON
ejpam-6131	147	45	4	4	NUM
ejpam-6131	147	46	)	)	PUNCT
ejpam-6131	147	47	,	,	PUNCT
ejpam-6131	147	48	p(ξ	p(ξ	NOUN
ejpam-6131	147	49	n	n	PRON
ejpam-6131	147	50	5	5	NUM
ejpam-6131	147	51	)	)	PUNCT
ejpam-6131	147	52	)	)	PUNCT
ejpam-6131	147	53	,	,	PUNCT
ejpam-6131	147	54	lim	lim	PROPN
ejpam-6131	147	55	n→+∞	n→+∞	PROPN
ejpam-6131	147	56	t(p(ū2	t(p(ū2	PROPN
ejpam-6131	147	57	)	)	PUNCT
ejpam-6131	147	58	,	,	PUNCT
ejpam-6131	147	59	ζn(v̄	ζn(v̄	NOUN
ejpam-6131	147	60	2	2	NUM
ejpam-6131	147	61	)	)	PUNCT
ejpam-6131	147	62	)	)	PUNCT
ejpam-6131	148	1	=	=	SYM
ejpam-6131	148	2	0	0	NUM
ejpam-6131	148	3	,	,	PUNCT
ejpam-6131	148	4	where	where	SCONJ
ejpam-6131	148	5	ū2	ū2	ADJ
ejpam-6131	148	6	=	=	SYM
ejpam-6131	148	7	ζn(ξn2	ζn(ξn2	PROPN
ejpam-6131	148	8	,	,	PUNCT
ejpam-6131	148	9	ξ	ξ	PROPN
ejpam-6131	148	10	n	n	NUM
ejpam-6131	148	11	3	3	NUM
ejpam-6131	148	12	,	,	PUNCT
ejpam-6131	148	13	ξ	ξ	PROPN
ejpam-6131	148	14	n	n	PRON
ejpam-6131	148	15	4	4	NUM
ejpam-6131	148	16	,	,	PUNCT
ejpam-6131	148	17	ξ	ξ	PROPN
ejpam-6131	148	18	n	n	NUM
ejpam-6131	148	19	5	5	NUM
ejpam-6131	148	20	,	,	PUNCT
ejpam-6131	148	21	ξ	ξ	PROPN
ejpam-6131	148	22	n	n	PRON
ejpam-6131	148	23	1	1	NUM
ejpam-6131	148	24	)	)	PUNCT
ejpam-6131	148	25	and	and	CCONJ
ejpam-6131	148	26	v̄	v̄	NOUN
ejpam-6131	148	27	2	2	NUM
ejpam-6131	148	28	=	=	SYM
ejpam-6131	148	29	(	(	PUNCT
ejpam-6131	148	30	p(ξn2	p(ξn2	NOUN
ejpam-6131	148	31	)	)	PUNCT
ejpam-6131	148	32	,	,	PUNCT
ejpam-6131	148	33	p(ξ	p(ξ	NOUN
ejpam-6131	148	34	n	n	PRON
ejpam-6131	148	35	3	3	NUM
ejpam-6131	148	36	)	)	PUNCT
ejpam-6131	148	37	,	,	PUNCT
ejpam-6131	148	38	p(ξ	p(ξ	NOUN
ejpam-6131	148	39	n	n	PRON
ejpam-6131	148	40	4	4	NUM
ejpam-6131	148	41	)	)	PUNCT
ejpam-6131	148	42	,	,	PUNCT
ejpam-6131	148	43	p(ξ	p(ξ	NOUN
ejpam-6131	148	44	n	n	PRON
ejpam-6131	148	45	5	5	NUM
ejpam-6131	148	46	)	)	PUNCT
ejpam-6131	148	47	,	,	PUNCT
ejpam-6131	148	48	p(ξ	p(ξ	NOUN
ejpam-6131	148	49	n	n	PRON
ejpam-6131	148	50	1	1	NUM
ejpam-6131	148	51	)	)	PUNCT
ejpam-6131	148	52	)	)	PUNCT
ejpam-6131	148	53	,	,	PUNCT
ejpam-6131	148	54	lim	lim	PROPN
ejpam-6131	148	55	n→+∞	n→+∞	PROPN
ejpam-6131	148	56	t(p(ū3	t(p(ū3	PROPN
ejpam-6131	148	57	)	)	PUNCT
ejpam-6131	148	58	,	,	PUNCT
ejpam-6131	148	59	ζn(v̄	ζn(v̄	NOUN
ejpam-6131	148	60	3	3	NUM
ejpam-6131	148	61	)	)	PUNCT
ejpam-6131	148	62	)	)	PUNCT
ejpam-6131	148	63	=	=	SYM
ejpam-6131	149	1	0	0	NUM
ejpam-6131	149	2	,	,	PUNCT
ejpam-6131	149	3	where	where	SCONJ
ejpam-6131	149	4	ū3	ū3	ADJ
ejpam-6131	149	5	=	=	SYM
ejpam-6131	149	6	ζn(ξn3	ζn(ξn3	PROPN
ejpam-6131	149	7	,	,	PUNCT
ejpam-6131	149	8	ξ	ξ	PROPN
ejpam-6131	149	9	n	n	NUM
ejpam-6131	149	10	4	4	NUM
ejpam-6131	149	11	,	,	PUNCT
ejpam-6131	149	12	ξ	ξ	PROPN
ejpam-6131	149	13	n	n	NUM
ejpam-6131	149	14	5	5	NUM
ejpam-6131	149	15	,	,	PUNCT
ejpam-6131	149	16	ξ	ξ	PROPN
ejpam-6131	149	17	n	n	NUM
ejpam-6131	149	18	1	1	NUM
ejpam-6131	149	19	,	,	PUNCT
ejpam-6131	149	20	ξ	ξ	PROPN
ejpam-6131	149	21	n	n	PRON
ejpam-6131	149	22	2	2	NUM
ejpam-6131	149	23	)	)	PUNCT
ejpam-6131	149	24	and	and	CCONJ
ejpam-6131	149	25	v̄	v̄	NOUN
ejpam-6131	149	26	3	3	NUM
ejpam-6131	149	27	=	=	SYM
ejpam-6131	149	28	(	(	PUNCT
ejpam-6131	149	29	p(ξn3	p(ξn3	PROPN
ejpam-6131	149	30	)	)	PUNCT
ejpam-6131	149	31	,	,	PUNCT
ejpam-6131	149	32	p(ξ	p(ξ	NOUN
ejpam-6131	149	33	n	n	PRON
ejpam-6131	149	34	4	4	NUM
ejpam-6131	149	35	)	)	PUNCT
ejpam-6131	149	36	,	,	PUNCT
ejpam-6131	149	37	p(ξ	p(ξ	NOUN
ejpam-6131	149	38	n	n	PRON
ejpam-6131	149	39	5	5	NUM
ejpam-6131	149	40	)	)	PUNCT
ejpam-6131	149	41	,	,	PUNCT
ejpam-6131	149	42	p(ξ	p(ξ	NOUN
ejpam-6131	149	43	n	n	PRON
ejpam-6131	149	44	1	1	NUM
ejpam-6131	149	45	)	)	PUNCT
ejpam-6131	149	46	,	,	PUNCT
ejpam-6131	149	47	p(ξ	p(ξ	NOUN
ejpam-6131	149	48	n	n	PRON
ejpam-6131	149	49	2	2	NUM
ejpam-6131	149	50	)	)	PUNCT
ejpam-6131	149	51	)	)	PUNCT
ejpam-6131	149	52	,	,	PUNCT
ejpam-6131	149	53	lim	lim	PROPN
ejpam-6131	149	54	n→∞	n→∞	NUM
ejpam-6131	149	55	t(p(ū4	t(p(ū4	PROPN
ejpam-6131	149	56	)	)	PUNCT
ejpam-6131	149	57	,	,	PUNCT
ejpam-6131	149	58	ζn(v̄	ζn(v̄	NOUN
ejpam-6131	149	59	4	4	NUM
ejpam-6131	149	60	)	)	PUNCT
ejpam-6131	149	61	)	)	PUNCT
ejpam-6131	150	1	=	=	SYM
ejpam-6131	150	2	0	0	NUM
ejpam-6131	150	3	,	,	PUNCT
ejpam-6131	150	4	where	where	SCONJ
ejpam-6131	150	5	ū4	ū4	X
ejpam-6131	150	6	=	=	SYM
ejpam-6131	150	7	ζn(ξn4	ζn(ξn4	X
ejpam-6131	150	8	,	,	PUNCT
ejpam-6131	150	9	ξ	ξ	PROPN
ejpam-6131	150	10	n	n	NUM
ejpam-6131	150	11	5	5	NUM
ejpam-6131	150	12	,	,	PUNCT
ejpam-6131	150	13	ξ	ξ	PROPN
ejpam-6131	150	14	n	n	NUM
ejpam-6131	150	15	1	1	NUM
ejpam-6131	150	16	,	,	PUNCT
ejpam-6131	150	17	ξ	ξ	PROPN
ejpam-6131	150	18	n	n	PRON
ejpam-6131	150	19	2	2	NUM
ejpam-6131	150	20	,	,	PUNCT
ejpam-6131	150	21	ξ	ξ	PROPN
ejpam-6131	150	22	n	n	PRON
ejpam-6131	150	23	3	3	NUM
ejpam-6131	150	24	)	)	PUNCT
ejpam-6131	150	25	and	and	CCONJ
ejpam-6131	150	26	v̄	v̄	NOUN
ejpam-6131	150	27	4	4	NUM
ejpam-6131	150	28	=	=	SYM
ejpam-6131	150	29	(	(	PUNCT
ejpam-6131	150	30	p(ξn4	p(ξn4	PROPN
ejpam-6131	150	31	)	)	PUNCT
ejpam-6131	150	32	,	,	PUNCT
ejpam-6131	150	33	p(ξ	p(ξ	NOUN
ejpam-6131	150	34	n	n	PRON
ejpam-6131	150	35	5	5	NUM
ejpam-6131	150	36	)	)	PUNCT
ejpam-6131	150	37	,	,	PUNCT
ejpam-6131	150	38	p(ξ	p(ξ	NOUN
ejpam-6131	150	39	n	n	PRON
ejpam-6131	150	40	1	1	NUM
ejpam-6131	150	41	)	)	PUNCT
ejpam-6131	150	42	,	,	PUNCT
ejpam-6131	150	43	p(ξ	p(ξ	NOUN
ejpam-6131	150	44	n	n	PRON
ejpam-6131	150	45	2	2	NUM
ejpam-6131	150	46	)	)	PUNCT
ejpam-6131	150	47	,	,	PUNCT
ejpam-6131	150	48	p(ξ	p(ξ	NOUN
ejpam-6131	150	49	n	n	PRON
ejpam-6131	150	50	3	3	NUM
ejpam-6131	150	51	)	)	PUNCT
ejpam-6131	150	52	)	)	PUNCT
ejpam-6131	150	53	,	,	PUNCT
ejpam-6131	150	54	lim	lim	PROPN
ejpam-6131	150	55	n→∞	n→∞	X
ejpam-6131	150	56	t(p(ū5	t(p(ū5	NOUN
ejpam-6131	150	57	)	)	PUNCT
ejpam-6131	150	58	,	,	PUNCT
ejpam-6131	150	59	ζn(v̄	ζn(v̄	NOUN
ejpam-6131	150	60	5	5	NUM
ejpam-6131	150	61	)	)	PUNCT
ejpam-6131	150	62	)	)	PUNCT
ejpam-6131	151	1	=	=	PUNCT
ejpam-6131	151	2	0	0	NUM
ejpam-6131	151	3	,	,	PUNCT
ejpam-6131	151	4	where	where	SCONJ
ejpam-6131	151	5	ū5	ū5	NOUN
ejpam-6131	151	6	=	=	SYM
ejpam-6131	151	7	ζn(ξn5	ζn(ξn5	X
ejpam-6131	151	8	,	,	PUNCT
ejpam-6131	151	9	ξ	ξ	PROPN
ejpam-6131	151	10	n	n	NUM
ejpam-6131	151	11	1	1	NUM
ejpam-6131	151	12	,	,	PUNCT
ejpam-6131	151	13	ξ	ξ	PROPN
ejpam-6131	151	14	n	n	PRON
ejpam-6131	151	15	2	2	NUM
ejpam-6131	151	16	,	,	PUNCT
ejpam-6131	151	17	ξ	ξ	PROPN
ejpam-6131	151	18	n	n	PRON
ejpam-6131	151	19	3	3	NUM
ejpam-6131	151	20	,	,	PUNCT
ejpam-6131	151	21	ξ	ξ	PROPN
ejpam-6131	151	22	n	n	PRON
ejpam-6131	151	23	4	4	NUM
ejpam-6131	151	24	)	)	PUNCT
ejpam-6131	151	25	and	and	CCONJ
ejpam-6131	151	26	v̄	v̄	NOUN
ejpam-6131	151	27	5	5	NUM
ejpam-6131	151	28	=	=	SYM
ejpam-6131	151	29	(	(	PUNCT
ejpam-6131	151	30	p(ξn5	p(ξn5	NOUN
ejpam-6131	151	31	)	)	PUNCT
ejpam-6131	151	32	,	,	PUNCT
ejpam-6131	151	33	p(ξ	p(ξ	NOUN
ejpam-6131	151	34	n	n	PRON
ejpam-6131	151	35	1	1	NUM
ejpam-6131	151	36	)	)	PUNCT
ejpam-6131	151	37	,	,	PUNCT
ejpam-6131	151	38	p(ξ	p(ξ	NOUN
ejpam-6131	151	39	n	n	PRON
ejpam-6131	151	40	2	2	NUM
ejpam-6131	151	41	)	)	PUNCT
ejpam-6131	151	42	,	,	PUNCT
ejpam-6131	151	43	p(ξ	p(ξ	NOUN
ejpam-6131	151	44	n	n	PRON
ejpam-6131	151	45	3	3	NUM
ejpam-6131	151	46	)	)	PUNCT
ejpam-6131	151	47	,	,	PUNCT
ejpam-6131	151	48	p(ξ	p(ξ	NOUN
ejpam-6131	151	49	n	n	PRON
ejpam-6131	151	50	4	4	NUM
ejpam-6131	151	51	)	)	PUNCT
ejpam-6131	151	52	)	)	PUNCT
ejpam-6131	151	53	,	,	PUNCT
ejpam-6131	151	54	whenever	whenever	SCONJ
ejpam-6131	151	55	{	{	PUNCT
ejpam-6131	151	56	ξn1	ξn1	NOUN
ejpam-6131	151	57	}	}	PUNCT
ejpam-6131	151	58	,	,	PUNCT
ejpam-6131	151	59	{	{	PUNCT
ejpam-6131	151	60	ξn2	ξn2	NOUN
ejpam-6131	151	61	}	}	PUNCT
ejpam-6131	151	62	,	,	PUNCT
ejpam-6131	151	63	{	{	PUNCT
ejpam-6131	151	64	ξn3	ξn3	NOUN
ejpam-6131	151	65	}	}	PUNCT
ejpam-6131	151	66	,	,	PUNCT
ejpam-6131	151	67	{	{	PUNCT
ejpam-6131	151	68	ξn4	ξn4	NOUN
ejpam-6131	151	69	}	}	PUNCT
ejpam-6131	151	70	and	and	CCONJ
ejpam-6131	151	71	{	{	PUNCT
ejpam-6131	151	72	ξn5	ξn5	NOUN
ejpam-6131	151	73	}	}	PUNCT
ejpam-6131	151	74	are	be	AUX
ejpam-6131	151	75	sequences	sequence	NOUN
ejpam-6131	151	76	in	in	ADP
ejpam-6131	151	77	g	g	PROPN
ejpam-6131	151	78	such	such	ADJ
ejpam-6131	151	79	that	that	SCONJ
ejpam-6131	151	80	lim	lim	PROPN
ejpam-6131	151	81	n→+∞	n→+∞	VERB
ejpam-6131	151	82	ū1	ū1	NOUN
ejpam-6131	152	1	=	=	PROPN
ejpam-6131	152	2	lim	lim	PROPN
ejpam-6131	152	3	n→∞	n→∞	X
ejpam-6131	152	4	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	152	5	1	1	NUM
ejpam-6131	152	6	)	)	PUNCT
ejpam-6131	152	7	=	=	SYM
ejpam-6131	152	8	ξ1	ξ1	PROPN
ejpam-6131	152	9	,	,	PUNCT
ejpam-6131	152	10	lim	lim	PROPN
ejpam-6131	152	11	n→+∞	n→+∞	VERB
ejpam-6131	152	12	ū2	ū2	ADJ
ejpam-6131	153	1	=	=	SYM
ejpam-6131	153	2	lim	lim	PROPN
ejpam-6131	153	3	n→∞	n→∞	X
ejpam-6131	153	4	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	153	5	2	2	NUM
ejpam-6131	153	6	)	)	PUNCT
ejpam-6131	153	7	=	=	SYM
ejpam-6131	153	8	ξ2	ξ2	NOUN
ejpam-6131	153	9	,	,	PUNCT
ejpam-6131	153	10	lim	lim	PROPN
ejpam-6131	153	11	n→+∞	n→+∞	VERB
ejpam-6131	153	12	ū3	ū3	PROPN
ejpam-6131	154	1	=	=	SYM
ejpam-6131	154	2	lim	lim	PROPN
ejpam-6131	154	3	n→∞	n→∞	X
ejpam-6131	154	4	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	154	5	3	3	NUM
ejpam-6131	154	6	)	)	PUNCT
ejpam-6131	154	7	=	=	SYM
ejpam-6131	154	8	ξ3	ξ3	PROPN
ejpam-6131	154	9	lim	lim	PROPN
ejpam-6131	154	10	n→+∞	n→+∞	VERB
ejpam-6131	154	11	ū4	ū4	X
ejpam-6131	155	1	=	=	PUNCT
ejpam-6131	155	2	lim	lim	PROPN
ejpam-6131	155	3	n→∞	n→∞	X
ejpam-6131	156	1	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	156	2	4	4	NUM
ejpam-6131	156	3	)	)	PUNCT
ejpam-6131	156	4	=	=	SYM
ejpam-6131	156	5	ξ4	ξ4	PROPN
ejpam-6131	156	6	,	,	PUNCT
ejpam-6131	156	7	lim	lim	PROPN
ejpam-6131	156	8	n→+∞	n→+∞	VERB
ejpam-6131	156	9	ū5	ū5	NOUN
ejpam-6131	156	10	=	=	PUNCT
ejpam-6131	156	11	lim	lim	PROPN
ejpam-6131	156	12	n→∞	n→∞	X
ejpam-6131	157	1	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	157	2	5	5	NUM
ejpam-6131	157	3	)	)	PUNCT
ejpam-6131	157	4	=	=	SYM
ejpam-6131	157	5	ξ5	ξ5	NOUN
ejpam-6131	157	6	,	,	PUNCT
ejpam-6131	157	7	for	for	ADP
ejpam-6131	157	8	some	some	DET
ejpam-6131	157	9	ξ1	ξ1	NOUN
ejpam-6131	157	10	,	,	PUNCT
ejpam-6131	157	11	ξ2	ξ2	NOUN
ejpam-6131	157	12	,	,	PUNCT
ejpam-6131	157	13	ξ3	ξ3	NOUN
ejpam-6131	157	14	,	,	PUNCT
ejpam-6131	157	15	ξ4	ξ4	NOUN
ejpam-6131	157	16	,	,	PUNCT
ejpam-6131	157	17	ξ5	ξ5	PROPN
ejpam-6131	157	18	∈	∈	PROPN
ejpam-6131	157	19	g.	g.	PROPN
ejpam-6131	157	20	s.	s.	PROPN
ejpam-6131	157	21	batul	batul	PROPN
ejpam-6131	157	22	et	et	PROPN
ejpam-6131	157	23	a.	a.	PROPN
ejpam-6131	157	24	/	/	PUNCT
ejpam-6131	157	25	eur	eur	PROPN
ejpam-6131	157	26	.	.	PUNCT
ejpam-6131	158	1	j.	j.	PROPN
ejpam-6131	158	2	pure	pure	PROPN
ejpam-6131	158	3	appl	appl	PROPN
ejpam-6131	158	4	.	.	PROPN
ejpam-6131	158	5	math	math	PROPN
ejpam-6131	158	6	,	,	PUNCT
ejpam-6131	158	7	18	18	NUM
ejpam-6131	158	8	(	(	PUNCT
ejpam-6131	158	9	2	2	NUM
ejpam-6131	158	10	)	)	PUNCT
ejpam-6131	158	11	(	(	PUNCT
ejpam-6131	158	12	2025	2025	NUM
ejpam-6131	158	13	)	)	PUNCT
ejpam-6131	158	14	,	,	PUNCT
ejpam-6131	158	15	6131	6131	NUM
ejpam-6131	158	16	8	8	NUM
ejpam-6131	158	17	of	of	ADP
ejpam-6131	158	18	22	22	NUM
ejpam-6131	158	19	definition	definition	NOUN
ejpam-6131	158	20	17	17	NUM
ejpam-6131	158	21	.	.	PUNCT
ejpam-6131	159	1	let	let	VERB
ejpam-6131	159	2	ζn	ζn	NOUN
ejpam-6131	159	3	:	:	PUNCT
ejpam-6131	159	4	g5	g5	NOUN
ejpam-6131	159	5	→	→	SYM
ejpam-6131	159	6	g	g	PROPN
ejpam-6131	159	7	and	and	CCONJ
ejpam-6131	159	8	p	p	X
ejpam-6131	159	9	:	:	PUNCT
ejpam-6131	159	10	g	g	PROPN
ejpam-6131	159	11	→	→	SYM
ejpam-6131	159	12	g	g	NOUN
ejpam-6131	159	13	be	be	AUX
ejpam-6131	159	14	two	two	NUM
ejpam-6131	159	15	mappings	mapping	NOUN
ejpam-6131	159	16	on	on	ADP
ejpam-6131	159	17	a	a	DET
ejpam-6131	159	18	metric	metric	ADJ
ejpam-6131	159	19	space	space	NOUN
ejpam-6131	159	20	(	(	PUNCT
ejpam-6131	159	21	g	g	PROPN
ejpam-6131	159	22	,	,	PUNCT
ejpam-6131	159	23	t	t	PROPN
ejpam-6131	159	24	)	)	PUNCT
ejpam-6131	159	25	,	,	PUNCT
ejpam-6131	159	26	then	then	ADV
ejpam-6131	159	27	the	the	DET
ejpam-6131	159	28	following	follow	VERB
ejpam-6131	159	29	conditions	condition	NOUN
ejpam-6131	159	30	describe	describe	VERB
ejpam-6131	159	31	weak	weak	ADJ
ejpam-6131	159	32	reciprocal	reciprocal	ADJ
ejpam-6131	159	33	continuity	continuity	NOUN
ejpam-6131	159	34	of	of	ADP
ejpam-6131	159	35	{	{	PUNCT
ejpam-6131	159	36	ζn}n∈n	ζn}n∈n	PROPN
ejpam-6131	159	37	and	and	CCONJ
ejpam-6131	159	38	p.	p.	PROPN
ejpam-6131	159	39	lim	lim	PROPN
ejpam-6131	160	1	n→+∞	n→+∞	PROPN
ejpam-6131	160	2	p(ū1	p(ū1	X
ejpam-6131	160	3	)	)	PUNCT
ejpam-6131	160	4	=	=	SYM
ejpam-6131	160	5	p(ξ1	p(ξ1	NOUN
ejpam-6131	160	6	)	)	PUNCT
ejpam-6131	160	7	,	,	PUNCT
ejpam-6131	160	8	lim	lim	PROPN
ejpam-6131	160	9	n→+∞	n→+∞	VERB
ejpam-6131	160	10	p(ū2	p(ū2	NOUN
ejpam-6131	160	11	)	)	PUNCT
ejpam-6131	160	12	=	=	SYM
ejpam-6131	160	13	p(ξ2	p(ξ2	NOUN
ejpam-6131	160	14	)	)	PUNCT
ejpam-6131	160	15	,	,	PUNCT
ejpam-6131	160	16	lim	lim	PROPN
ejpam-6131	160	17	n→+∞	n→+∞	VERB
ejpam-6131	160	18	p(ū3	p(ū3	NOUN
ejpam-6131	160	19	)	)	PUNCT
ejpam-6131	160	20	=	=	SYM
ejpam-6131	160	21	p(ξ3	p(ξ3	NOUN
ejpam-6131	160	22	)	)	PUNCT
ejpam-6131	160	23	lim	lim	PROPN
ejpam-6131	160	24	n→+∞	n→+∞	VERB
ejpam-6131	160	25	p(ū4	p(ū4	PRON
ejpam-6131	160	26	)	)	PUNCT
ejpam-6131	160	27	=	=	SYM
ejpam-6131	160	28	p(ξ4	p(ξ4	NOUN
ejpam-6131	160	29	)	)	PUNCT
ejpam-6131	160	30	,	,	PUNCT
ejpam-6131	160	31	lim	lim	PROPN
ejpam-6131	160	32	n→+∞	n→+∞	VERB
ejpam-6131	160	33	p(ū5	p(ū5	NOUN
ejpam-6131	160	34	)	)	PUNCT
ejpam-6131	160	35	=	=	SYM
ejpam-6131	160	36	p(ξ5	p(ξ5	NOUN
ejpam-6131	160	37	)	)	PUNCT
ejpam-6131	160	38	,	,	PUNCT
ejpam-6131	160	39	whenever	whenever	SCONJ
ejpam-6131	160	40	{	{	PUNCT
ejpam-6131	160	41	ξn1	ξn1	NOUN
ejpam-6131	160	42	}	}	PUNCT
ejpam-6131	160	43	,	,	PUNCT
ejpam-6131	160	44	{	{	PUNCT
ejpam-6131	160	45	ξn2	ξn2	NOUN
ejpam-6131	160	46	}	}	PUNCT
ejpam-6131	160	47	,	,	PUNCT
ejpam-6131	160	48	{	{	PUNCT
ejpam-6131	160	49	ξn3	ξn3	NOUN
ejpam-6131	160	50	}	}	PUNCT
ejpam-6131	160	51	,	,	PUNCT
ejpam-6131	160	52	{	{	PUNCT
ejpam-6131	160	53	ξn4	ξn4	NOUN
ejpam-6131	160	54	}	}	PUNCT
ejpam-6131	160	55	and	and	CCONJ
ejpam-6131	160	56	{	{	PUNCT
ejpam-6131	160	57	ξn5	ξn5	NOUN
ejpam-6131	160	58	}	}	PUNCT
ejpam-6131	160	59	are	be	AUX
ejpam-6131	160	60	sequences	sequence	NOUN
ejpam-6131	160	61	in	in	ADP
ejpam-6131	160	62	g	g	PROPN
ejpam-6131	160	63	such	such	ADJ
ejpam-6131	160	64	that	that	SCONJ
ejpam-6131	160	65	lim	lim	PROPN
ejpam-6131	160	66	n→+∞	n→+∞	VERB
ejpam-6131	160	67	ū1	ū1	NOUN
ejpam-6131	161	1	=	=	PROPN
ejpam-6131	161	2	lim	lim	PROPN
ejpam-6131	161	3	n→∞	n→∞	X
ejpam-6131	161	4	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	161	5	1	1	NUM
ejpam-6131	161	6	)	)	PUNCT
ejpam-6131	161	7	=	=	SYM
ejpam-6131	161	8	ξ1	ξ1	PROPN
ejpam-6131	161	9	,	,	PUNCT
ejpam-6131	161	10	lim	lim	PROPN
ejpam-6131	161	11	n→+∞	n→+∞	VERB
ejpam-6131	161	12	ū2	ū2	ADJ
ejpam-6131	162	1	=	=	SYM
ejpam-6131	162	2	lim	lim	PROPN
ejpam-6131	162	3	n→∞	n→∞	X
ejpam-6131	162	4	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	162	5	2	2	NUM
ejpam-6131	162	6	)	)	PUNCT
ejpam-6131	162	7	=	=	SYM
ejpam-6131	162	8	ξ2	ξ2	NOUN
ejpam-6131	162	9	,	,	PUNCT
ejpam-6131	162	10	lim	lim	PROPN
ejpam-6131	162	11	n→+∞	n→+∞	VERB
ejpam-6131	162	12	ū3	ū3	PROPN
ejpam-6131	163	1	=	=	SYM
ejpam-6131	163	2	lim	lim	PROPN
ejpam-6131	163	3	n→∞	n→∞	X
ejpam-6131	163	4	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	163	5	3	3	NUM
ejpam-6131	163	6	)	)	PUNCT
ejpam-6131	163	7	=	=	SYM
ejpam-6131	163	8	ξ3	ξ3	PROPN
ejpam-6131	163	9	lim	lim	PROPN
ejpam-6131	163	10	n→+∞	n→+∞	VERB
ejpam-6131	163	11	ū4	ū4	X
ejpam-6131	164	1	=	=	PUNCT
ejpam-6131	164	2	lim	lim	PROPN
ejpam-6131	164	3	n→∞	n→∞	X
ejpam-6131	165	1	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	165	2	4	4	NUM
ejpam-6131	165	3	)	)	PUNCT
ejpam-6131	165	4	=	=	SYM
ejpam-6131	165	5	ξ4	ξ4	PROPN
ejpam-6131	165	6	,	,	PUNCT
ejpam-6131	165	7	lim	lim	PROPN
ejpam-6131	165	8	n→+∞	n→+∞	VERB
ejpam-6131	165	9	ū5	ū5	NOUN
ejpam-6131	165	10	=	=	PUNCT
ejpam-6131	165	11	lim	lim	PROPN
ejpam-6131	165	12	n→∞	n→∞	X
ejpam-6131	166	1	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	166	2	5	5	NUM
ejpam-6131	166	3	)	)	PUNCT
ejpam-6131	166	4	=	=	SYM
ejpam-6131	166	5	ξ5	ξ5	NOUN
ejpam-6131	166	6	,	,	PUNCT
ejpam-6131	166	7	for	for	ADP
ejpam-6131	166	8	some	some	DET
ejpam-6131	166	9	ξi	ξi	NOUN
ejpam-6131	166	10	in	in	ADP
ejpam-6131	166	11	g	g	PROPN
ejpam-6131	166	12	,	,	PUNCT
ejpam-6131	166	13	where	where	SCONJ
ejpam-6131	166	14	1	1	NUM
ejpam-6131	166	15	≤	≤	NUM
ejpam-6131	166	16	i	i	X
ejpam-6131	166	17	≤	≤	ADJ
ejpam-6131	166	18	5	5	NUM
ejpam-6131	166	19	.	.	PUNCT
ejpam-6131	166	20	example	example	NOUN
ejpam-6131	167	1	4	4	NUM
ejpam-6131	167	2	.	.	PUNCT
ejpam-6131	167	3	let	let	VERB
ejpam-6131	167	4	g	g	NOUN
ejpam-6131	167	5	=	=	PUNCT
ejpam-6131	168	1	[	[	X
ejpam-6131	168	2	0	0	NUM
ejpam-6131	168	3	,	,	PUNCT
ejpam-6131	168	4	1	1	NUM
ejpam-6131	168	5	]	]	PUNCT
ejpam-6131	168	6	be	be	AUX
ejpam-6131	168	7	endowed	endow	VERB
ejpam-6131	168	8	with	with	ADP
ejpam-6131	168	9	the	the	DET
ejpam-6131	168	10	metric	metric	ADJ
ejpam-6131	168	11	t(ξ1	t(ξ1	NOUN
ejpam-6131	168	12	,	,	PUNCT
ejpam-6131	168	13	ξ2	ξ2	NOUN
ejpam-6131	168	14	)	)	PUNCT
ejpam-6131	168	15	=	=	PUNCT
ejpam-6131	168	16	|ξ1−ξ2|	|ξ1−ξ2|	NOUN
ejpam-6131	168	17	.	.	PUNCT
ejpam-6131	169	1	let	let	VERB
ejpam-6131	169	2	ζn	ζn	NOUN
ejpam-6131	169	3	:	:	PUNCT
ejpam-6131	169	4	g5	g5	NOUN
ejpam-6131	169	5	→	→	SYM
ejpam-6131	169	6	g	g	PROPN
ejpam-6131	169	7	and	and	CCONJ
ejpam-6131	169	8	p	p	X
ejpam-6131	169	9	:	:	PUNCT
ejpam-6131	169	10	g	g	PROPN
ejpam-6131	169	11	→	→	SYM
ejpam-6131	169	12	g	g	NOUN
ejpam-6131	169	13	be	be	VERB
ejpam-6131	169	14	two	two	NUM
ejpam-6131	169	15	mappings	mapping	NOUN
ejpam-6131	169	16	defined	define	VERB
ejpam-6131	169	17	as	as	ADP
ejpam-6131	169	18	ζn(ξ1	ζn(ξ1	ADJ
ejpam-6131	169	19	,	,	PUNCT
ejpam-6131	169	20	ξ2	ξ2	ADJ
ejpam-6131	169	21	,	,	PUNCT
ejpam-6131	169	22	ξ3	ξ3	NOUN
ejpam-6131	169	23	,	,	PUNCT
ejpam-6131	169	24	ξ4	ξ4	NOUN
ejpam-6131	169	25	,	,	PUNCT
ejpam-6131	169	26	ξ5	ξ5	NOUN
ejpam-6131	169	27	)	)	PUNCT
ejpam-6131	169	28	=	=	SYM
ejpam-6131	169	29	1	1	NUM
ejpam-6131	169	30	5n	5n	NOUN
ejpam-6131	169	31	−	−	NOUN
ejpam-6131	169	32	ξ1ξ2ξ3ξ4ξ5	ξ1ξ2ξ3ξ4ξ5	PROPN
ejpam-6131	169	33	5	5	NUM
ejpam-6131	169	34	and	and	CCONJ
ejpam-6131	169	35	p(ξ1	p(ξ1	NOUN
ejpam-6131	169	36	)	)	PUNCT
ejpam-6131	169	37	=	=	SYM
ejpam-6131	169	38	ξ1	ξ1	NOUN
ejpam-6131	169	39	,	,	PUNCT
ejpam-6131	169	40	∀	∀	NOUN
ejpam-6131	169	41	ξ1	ξ1	NOUN
ejpam-6131	169	42	,	,	PUNCT
ejpam-6131	169	43	ξ2	ξ2	ADJ
ejpam-6131	169	44	,	,	PUNCT
ejpam-6131	169	45	ξ3	ξ3	NOUN
ejpam-6131	169	46	,	,	PUNCT
ejpam-6131	169	47	ξ4	ξ4	NOUN
ejpam-6131	169	48	,	,	PUNCT
ejpam-6131	169	49	ξ5	ξ5	PROPN
ejpam-6131	169	50	∈	∈	PROPN
ejpam-6131	169	51	g.	g.	NOUN
ejpam-6131	169	52	consider	consider	VERB
ejpam-6131	169	53	the	the	DET
ejpam-6131	169	54	five	five	NUM
ejpam-6131	169	55	sequences	sequence	NOUN
ejpam-6131	169	56	{	{	PUNCT
ejpam-6131	169	57	ξn1	ξn1	PROPN
ejpam-6131	169	58	}	}	PUNCT
ejpam-6131	169	59	,	,	PUNCT
ejpam-6131	169	60	{	{	PUNCT
ejpam-6131	169	61	ξn2	ξn2	NOUN
ejpam-6131	169	62	}	}	PUNCT
ejpam-6131	169	63	,	,	PUNCT
ejpam-6131	169	64	{	{	PUNCT
ejpam-6131	169	65	ξn3	ξn3	NOUN
ejpam-6131	169	66	}	}	PUNCT
ejpam-6131	169	67	,	,	PUNCT
ejpam-6131	169	68	{	{	PUNCT
ejpam-6131	169	69	ξn4	ξn4	NOUN
ejpam-6131	169	70	}	}	PUNCT
ejpam-6131	169	71	and	and	CCONJ
ejpam-6131	169	72	{	{	PUNCT
ejpam-6131	169	73	ξn5	ξn5	NOUN
ejpam-6131	169	74	}	}	PUNCT
ejpam-6131	169	75	∈	∈	PROPN
ejpam-6131	169	76	g	g	NOUN
ejpam-6131	169	77	defined	define	VERB
ejpam-6131	169	78	as	as	ADP
ejpam-6131	169	79	ξn1	ξn1	NOUN
ejpam-6131	169	80	=	=	SYM
ejpam-6131	169	81	1	1	NUM
ejpam-6131	169	82	n2	n2	NOUN
ejpam-6131	169	83	+	+	CCONJ
ejpam-6131	169	84	1	1	NUM
ejpam-6131	169	85	,	,	PUNCT
ejpam-6131	169	86	ξn2	ξn2	NOUN
ejpam-6131	169	87	=	=	SYM
ejpam-6131	169	88	1√	1√	PROPN
ejpam-6131	169	89	n2	n2	NOUN
ejpam-6131	169	90	+	+	CCONJ
ejpam-6131	169	91	1	1	NUM
ejpam-6131	169	92	,	,	PUNCT
ejpam-6131	169	93	ξn3	ξn3	NOUN
ejpam-6131	169	94	=	=	SYM
ejpam-6131	169	95	1	1	NUM
ejpam-6131	169	96	n+	n+	NUM
ejpam-6131	169	97	1	1	NUM
ejpam-6131	169	98	,	,	PUNCT
ejpam-6131	169	99	ξn4	ξn4	NOUN
ejpam-6131	169	100	=	=	SYM
ejpam-6131	169	101	1√	1√	PROPN
ejpam-6131	169	102	n+	n+	NUM
ejpam-6131	169	103	1	1	NUM
ejpam-6131	169	104	and	and	CCONJ
ejpam-6131	169	105	ξn5	ξn5	NOUN
ejpam-6131	169	106	=	=	SYM
ejpam-6131	169	107	1	1	NUM
ejpam-6131	169	108	n3	n3	NOUN
ejpam-6131	169	109	+	+	CCONJ
ejpam-6131	169	110	1	1	NUM
ejpam-6131	169	111	,	,	PUNCT
ejpam-6131	169	112	∀	∀	NOUN
ejpam-6131	169	113	n	n	PRON
ejpam-6131	169	114	∈	∈	PROPN
ejpam-6131	169	115	n.	n.	NOUN
ejpam-6131	169	116	then	then	ADV
ejpam-6131	169	117	,	,	PUNCT
ejpam-6131	169	118	lim	lim	PROPN
ejpam-6131	169	119	n→+∞	n→+∞	VERB
ejpam-6131	169	120	ū1	ū1	NOUN
ejpam-6131	170	1	=	=	PROPN
ejpam-6131	170	2	lim	lim	PROPN
ejpam-6131	170	3	n→∞	n→∞	X
ejpam-6131	170	4	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	170	5	1	1	NUM
ejpam-6131	170	6	)	)	PUNCT
ejpam-6131	170	7	=	=	SYM
ejpam-6131	170	8	0	0	PROPN
ejpam-6131	170	9	,	,	PUNCT
ejpam-6131	170	10	lim	lim	PROPN
ejpam-6131	170	11	n→+∞	n→+∞	VERB
ejpam-6131	170	12	ū2	ū2	ADJ
ejpam-6131	171	1	=	=	SYM
ejpam-6131	171	2	lim	lim	PROPN
ejpam-6131	171	3	n→∞	n→∞	X
ejpam-6131	171	4	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	171	5	2	2	NUM
ejpam-6131	171	6	)	)	PUNCT
ejpam-6131	171	7	=	=	SYM
ejpam-6131	171	8	0	0	PROPN
ejpam-6131	171	9	,	,	PUNCT
ejpam-6131	171	10	lim	lim	PROPN
ejpam-6131	171	11	n→+∞	n→+∞	VERB
ejpam-6131	171	12	ū3	ū3	PROPN
ejpam-6131	171	13	=	=	SYM
ejpam-6131	171	14	lim	lim	PROPN
ejpam-6131	171	15	n→∞	n→∞	X
ejpam-6131	172	1	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	172	2	3	3	NUM
ejpam-6131	172	3	)	)	PUNCT
ejpam-6131	172	4	=	=	SYM
ejpam-6131	172	5	0	0	PROPN
ejpam-6131	172	6	,	,	PUNCT
ejpam-6131	172	7	lim	lim	PROPN
ejpam-6131	172	8	n→+∞	n→+∞	VERB
ejpam-6131	172	9	ū4	ū4	X
ejpam-6131	173	1	=	=	PUNCT
ejpam-6131	173	2	lim	lim	PROPN
ejpam-6131	173	3	n→∞	n→∞	X
ejpam-6131	174	1	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	174	2	4	4	NUM
ejpam-6131	174	3	)	)	PUNCT
ejpam-6131	174	4	=	=	SYM
ejpam-6131	174	5	0	0	PROPN
ejpam-6131	174	6	,	,	PUNCT
ejpam-6131	174	7	lim	lim	PROPN
ejpam-6131	174	8	n→+∞	n→+∞	VERB
ejpam-6131	174	9	ū5	ū5	NOUN
ejpam-6131	174	10	=	=	PUNCT
ejpam-6131	174	11	lim	lim	PROPN
ejpam-6131	174	12	n→∞	n→∞	X
ejpam-6131	175	1	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	175	2	5	5	NUM
ejpam-6131	175	3	)	)	PUNCT
ejpam-6131	175	4	=	=	SYM
ejpam-6131	176	1	0	0	X
ejpam-6131	176	2	.	.	PUNCT
ejpam-6131	177	1	also	also	ADV
ejpam-6131	177	2	,	,	PUNCT
ejpam-6131	177	3	lim	lim	PROPN
ejpam-6131	177	4	n→+∞	n→+∞	PROPN
ejpam-6131	177	5	t(p(ū1	t(p(ū1	PROPN
ejpam-6131	177	6	)	)	PUNCT
ejpam-6131	177	7	,	,	PUNCT
ejpam-6131	177	8	ζn(v̄	ζn(v̄	NOUN
ejpam-6131	177	9	1	1	NUM
ejpam-6131	177	10	)	)	PUNCT
ejpam-6131	177	11	)	)	PUNCT
ejpam-6131	178	1	=	=	SYM
ejpam-6131	178	2	0	0	NUM
ejpam-6131	178	3	,	,	PUNCT
ejpam-6131	178	4	lim	lim	PROPN
ejpam-6131	178	5	n→+∞	n→+∞	PROPN
ejpam-6131	178	6	t(p(ū2	t(p(ū2	PROPN
ejpam-6131	178	7	)	)	PUNCT
ejpam-6131	178	8	,	,	PUNCT
ejpam-6131	178	9	ζn(v̄	ζn(v̄	NOUN
ejpam-6131	178	10	2	2	NUM
ejpam-6131	178	11	)	)	PUNCT
ejpam-6131	178	12	)	)	PUNCT
ejpam-6131	179	1	=	=	SYM
ejpam-6131	179	2	0	0	NUM
ejpam-6131	179	3	,	,	PUNCT
ejpam-6131	179	4	lim	lim	PROPN
ejpam-6131	179	5	n→+∞	n→+∞	PROPN
ejpam-6131	179	6	t(p(ū3	t(p(ū3	PROPN
ejpam-6131	179	7	)	)	PUNCT
ejpam-6131	179	8	,	,	PUNCT
ejpam-6131	179	9	ζn(v̄	ζn(v̄	NOUN
ejpam-6131	179	10	3	3	NUM
ejpam-6131	179	11	)	)	PUNCT
ejpam-6131	179	12	)	)	PUNCT
ejpam-6131	180	1	=	=	SYM
ejpam-6131	180	2	0	0	NUM
ejpam-6131	180	3	,	,	PUNCT
ejpam-6131	180	4	lim	lim	PROPN
ejpam-6131	180	5	n→+∞	n→+∞	VERB
ejpam-6131	180	6	t(p(ū4	t(p(ū4	PROPN
ejpam-6131	180	7	)	)	PUNCT
ejpam-6131	180	8	,	,	PUNCT
ejpam-6131	180	9	ζn(v̄	ζn(v̄	NOUN
ejpam-6131	180	10	4	4	NUM
ejpam-6131	180	11	)	)	PUNCT
ejpam-6131	180	12	)	)	PUNCT
ejpam-6131	181	1	=	=	SYM
ejpam-6131	181	2	0	0	NUM
ejpam-6131	181	3	,	,	PUNCT
ejpam-6131	181	4	lim	lim	PROPN
ejpam-6131	181	5	n→+∞	n→+∞	VERB
ejpam-6131	181	6	t(p(ū5	t(p(ū5	PROPN
ejpam-6131	181	7	)	)	PUNCT
ejpam-6131	181	8	,	,	PUNCT
ejpam-6131	181	9	ζn(v̄	ζn(v̄	NOUN
ejpam-6131	181	10	5	5	NUM
ejpam-6131	181	11	)	)	PUNCT
ejpam-6131	181	12	)	)	PUNCT
ejpam-6131	182	1	=	=	PUNCT
ejpam-6131	182	2	0	0	NUM
ejpam-6131	182	3	,	,	PUNCT
ejpam-6131	182	4	and	and	CCONJ
ejpam-6131	182	5	lim	lim	PROPN
ejpam-6131	182	6	n→+∞	n→+∞	PROPN
ejpam-6131	182	7	p(ū1	p(ū1	X
ejpam-6131	182	8	)	)	PUNCT
ejpam-6131	182	9	=	=	SYM
ejpam-6131	182	10	p(ξ1	p(ξ1	NOUN
ejpam-6131	182	11	)	)	PUNCT
ejpam-6131	182	12	=	=	SYM
ejpam-6131	182	13	0	0	NUM
ejpam-6131	182	14	,	,	PUNCT
ejpam-6131	182	15	lim	lim	PROPN
ejpam-6131	182	16	n→+∞	n→+∞	VERB
ejpam-6131	182	17	p(ū2	p(ū2	NOUN
ejpam-6131	182	18	)	)	PUNCT
ejpam-6131	182	19	=	=	SYM
ejpam-6131	182	20	p(ξ2	p(ξ2	NOUN
ejpam-6131	182	21	)	)	PUNCT
ejpam-6131	182	22	=	=	SYM
ejpam-6131	183	1	0	0	NUM
ejpam-6131	183	2	,	,	PUNCT
ejpam-6131	183	3	lim	lim	PROPN
ejpam-6131	183	4	n→+∞	n→+∞	VERB
ejpam-6131	183	5	p(ū3	p(ū3	NOUN
ejpam-6131	183	6	)	)	PUNCT
ejpam-6131	183	7	=	=	SYM
ejpam-6131	183	8	p(ξ3	p(ξ3	NOUN
ejpam-6131	183	9	)	)	PUNCT
ejpam-6131	183	10	=	=	SYM
ejpam-6131	184	1	0	0	NUM
ejpam-6131	185	1	lim	lim	PROPN
ejpam-6131	185	2	n→+∞	n→+∞	VERB
ejpam-6131	185	3	p(ū4	p(ū4	PRON
ejpam-6131	185	4	)	)	PUNCT
ejpam-6131	185	5	=	=	SYM
ejpam-6131	185	6	p(ξ4	p(ξ4	NOUN
ejpam-6131	185	7	)	)	PUNCT
ejpam-6131	185	8	=	=	SYM
ejpam-6131	186	1	0	0	PROPN
ejpam-6131	186	2	,	,	PUNCT
ejpam-6131	186	3	lim	lim	PROPN
ejpam-6131	186	4	n→+∞	n→+∞	VERB
ejpam-6131	186	5	p(ū5	p(ū5	NOUN
ejpam-6131	186	6	)	)	PUNCT
ejpam-6131	186	7	=	=	SYM
ejpam-6131	186	8	p(ξ5	p(ξ5	NOUN
ejpam-6131	186	9	)	)	PUNCT
ejpam-6131	186	10	=	=	SYM
ejpam-6131	187	1	0	0	NUM
ejpam-6131	187	2	,	,	PUNCT
ejpam-6131	187	3	which	which	PRON
ejpam-6131	187	4	proves	prove	VERB
ejpam-6131	187	5	the	the	DET
ejpam-6131	187	6	compatibility	compatibility	NOUN
ejpam-6131	187	7	and	and	CCONJ
ejpam-6131	187	8	weak	weak	ADJ
ejpam-6131	187	9	reciprocal	reciprocal	ADJ
ejpam-6131	187	10	continuity	continuity	NOUN
ejpam-6131	187	11	of	of	ADP
ejpam-6131	187	12	{	{	PUNCT
ejpam-6131	187	13	ζn}n∈n	ζn}n∈n	PROPN
ejpam-6131	187	14	and	and	CCONJ
ejpam-6131	187	15	p.	p.	PROPN
ejpam-6131	187	16	s.	s.	PROPN
ejpam-6131	187	17	batul	batul	PROPN
ejpam-6131	187	18	et	et	PROPN
ejpam-6131	187	19	a.	a.	PROPN
ejpam-6131	187	20	/	/	PUNCT
ejpam-6131	187	21	eur	eur	PROPN
ejpam-6131	187	22	.	.	PUNCT
ejpam-6131	188	1	j.	j.	PROPN
ejpam-6131	188	2	pure	pure	PROPN
ejpam-6131	188	3	appl	appl	PROPN
ejpam-6131	188	4	.	.	PROPN
ejpam-6131	188	5	math	math	PROPN
ejpam-6131	188	6	,	,	PUNCT
ejpam-6131	188	7	18	18	NUM
ejpam-6131	188	8	(	(	PUNCT
ejpam-6131	188	9	2	2	NUM
ejpam-6131	188	10	)	)	PUNCT
ejpam-6131	188	11	(	(	PUNCT
ejpam-6131	188	12	2025	2025	NUM
ejpam-6131	188	13	)	)	PUNCT
ejpam-6131	188	14	,	,	PUNCT
ejpam-6131	188	15	6131	6131	NUM
ejpam-6131	188	16	9	9	NUM
ejpam-6131	188	17	of	of	ADP
ejpam-6131	188	18	22	22	NUM
ejpam-6131	188	19	definition	definition	NOUN
ejpam-6131	188	20	18	18	NUM
ejpam-6131	188	21	.	.	PUNCT
ejpam-6131	189	1	let	let	AUX
ejpam-6131	189	2	(	(	PUNCT
ejpam-6131	189	3	g,⪯	g,⪯	X
ejpam-6131	189	4	)	)	PUNCT
ejpam-6131	189	5	be	be	AUX
ejpam-6131	189	6	a	a	DET
ejpam-6131	189	7	partially	partially	ADV
ejpam-6131	189	8	ordered	order	VERB
ejpam-6131	189	9	set	set	NOUN
ejpam-6131	189	10	(	(	PUNCT
ejpam-6131	189	11	pos	pos	NOUN
ejpam-6131	189	12	)	)	PUNCT
ejpam-6131	189	13	and	and	CCONJ
ejpam-6131	189	14	ζn	ζn	INTJ
ejpam-6131	189	15	:	:	PUNCT
ejpam-6131	189	16	g5	g5	NOUN
ejpam-6131	189	17	→	→	SYM
ejpam-6131	189	18	g	g	PROPN
ejpam-6131	189	19	and	and	CCONJ
ejpam-6131	189	20	p	p	X
ejpam-6131	189	21	:	:	PUNCT
ejpam-6131	189	22	g	g	PROPN
ejpam-6131	189	23	→	→	SYM
ejpam-6131	189	24	g	g	NOUN
ejpam-6131	189	25	be	be	AUX
ejpam-6131	189	26	two	two	NUM
ejpam-6131	189	27	mappings	mapping	NOUN
ejpam-6131	189	28	on	on	ADP
ejpam-6131	189	29	g	g	NOUN
ejpam-6131	189	30	,	,	PUNCT
ejpam-6131	189	31	then	then	ADV
ejpam-6131	189	32	{	{	PUNCT
ejpam-6131	189	33	ζn}n∈w	ζn}n∈w	NOUN
ejpam-6131	189	34	is	be	AUX
ejpam-6131	189	35	said	say	VERB
ejpam-6131	189	36	to	to	PART
ejpam-6131	189	37	have	have	VERB
ejpam-6131	189	38	mpmp	mpmp	PRON
ejpam-6131	189	39	if	if	SCONJ
ejpam-6131	189	40	for	for	ADP
ejpam-6131	189	41	any	any	DET
ejpam-6131	189	42	ξ1	ξ1	NOUN
ejpam-6131	189	43	,	,	PUNCT
ejpam-6131	189	44	ξ2	ξ2	NOUN
ejpam-6131	189	45	,	,	PUNCT
ejpam-6131	189	46	ξ3	ξ3	NOUN
ejpam-6131	189	47	,	,	PUNCT
ejpam-6131	189	48	ξ4	ξ4	NOUN
ejpam-6131	189	49	,	,	PUNCT
ejpam-6131	189	50	ξ5	ξ5	NOUN
ejpam-6131	189	51	,	,	PUNCT
ejpam-6131	189	52	q1	q1	PROPN
ejpam-6131	189	53	,	,	PUNCT
ejpam-6131	189	54	q2	q2	NOUN
ejpam-6131	189	55	,	,	PUNCT
ejpam-6131	189	56	q3	q3	PROPN
ejpam-6131	189	57	,	,	PUNCT
ejpam-6131	189	58	q4	q4	PROPN
ejpam-6131	189	59	,	,	PUNCT
ejpam-6131	189	60	q5	q5	PROPN
ejpam-6131	189	61	∈	∈	PROPN
ejpam-6131	189	62	g	g	PROPN
ejpam-6131	189	63	,	,	PUNCT
ejpam-6131	189	64	p(ξ1	p(ξ1	NOUN
ejpam-6131	189	65	)	)	PUNCT
ejpam-6131	189	66	⪯	⪯	PROPN
ejpam-6131	189	67	p(q1	p(q1	PROPN
ejpam-6131	189	68	)	)	PUNCT
ejpam-6131	189	69	⇒	⇒	PROPN
ejpam-6131	189	70	ζn(ξ1	ζn(ξ1	ADJ
ejpam-6131	189	71	,	,	PUNCT
ejpam-6131	189	72	ξ2	ξ2	ADJ
ejpam-6131	189	73	,	,	PUNCT
ejpam-6131	189	74	ξ3	ξ3	NOUN
ejpam-6131	189	75	,	,	PUNCT
ejpam-6131	189	76	ξ4	ξ4	NOUN
ejpam-6131	189	77	,	,	PUNCT
ejpam-6131	189	78	ξ5	ξ5	NOUN
ejpam-6131	189	79	)	)	PUNCT
ejpam-6131	189	80	⪯	⪯	NOUN
ejpam-6131	189	81	ζn+1(q1	ζn+1(q1	NUM
ejpam-6131	189	82	,	,	PUNCT
ejpam-6131	189	83	q2	q2	NOUN
ejpam-6131	189	84	,	,	PUNCT
ejpam-6131	189	85	q3	q3	PROPN
ejpam-6131	189	86	,	,	PUNCT
ejpam-6131	189	87	q4	q4	PROPN
ejpam-6131	189	88	,	,	PUNCT
ejpam-6131	189	89	q5	q5	PROPN
ejpam-6131	189	90	)	)	PUNCT
ejpam-6131	189	91	,	,	PUNCT
ejpam-6131	189	92	p(ξ2	p(ξ2	NOUN
ejpam-6131	189	93	)	)	PUNCT
ejpam-6131	189	94	⪰	⪰	NOUN
ejpam-6131	189	95	p(q2	p(q2	NOUN
ejpam-6131	189	96	)	)	PUNCT
ejpam-6131	189	97	⇒	⇒	NOUN
ejpam-6131	189	98	ζn(ξ2	ζn(ξ2	NOUN
ejpam-6131	189	99	,	,	PUNCT
ejpam-6131	189	100	ξ3	ξ3	NOUN
ejpam-6131	189	101	,	,	PUNCT
ejpam-6131	189	102	ξ4	ξ4	NOUN
ejpam-6131	189	103	,	,	PUNCT
ejpam-6131	189	104	ξ5	ξ5	NOUN
ejpam-6131	189	105	,	,	PUNCT
ejpam-6131	189	106	ξ1	ξ1	NOUN
ejpam-6131	189	107	)	)	PUNCT
ejpam-6131	189	108	⪰	⪰	NOUN
ejpam-6131	189	109	ζn+1(q2	ζn+1(q2	NOUN
ejpam-6131	189	110	,	,	PUNCT
ejpam-6131	189	111	q3	q3	PROPN
ejpam-6131	189	112	,	,	PUNCT
ejpam-6131	189	113	q4	q4	PROPN
ejpam-6131	189	114	,	,	PUNCT
ejpam-6131	189	115	q5	q5	PROPN
ejpam-6131	189	116	,	,	PUNCT
ejpam-6131	189	117	q1	q1	PROPN
ejpam-6131	189	118	)	)	PUNCT
ejpam-6131	189	119	,	,	PUNCT
ejpam-6131	189	120	p(ξ3	p(ξ3	NUM
ejpam-6131	189	121	)	)	PUNCT
ejpam-6131	189	122	⪯	⪯	PROPN
ejpam-6131	189	123	p(q3	p(q3	NOUN
ejpam-6131	189	124	)	)	PUNCT
ejpam-6131	189	125	⇒	⇒	PROPN
ejpam-6131	189	126	ζn(ξ3	ζn(ξ3	PROPN
ejpam-6131	189	127	,	,	PUNCT
ejpam-6131	189	128	ξ4	ξ4	PROPN
ejpam-6131	189	129	,	,	PUNCT
ejpam-6131	189	130	ξ5	ξ5	NOUN
ejpam-6131	189	131	,	,	PUNCT
ejpam-6131	189	132	ξ1	ξ1	NOUN
ejpam-6131	189	133	,	,	PUNCT
ejpam-6131	189	134	ξ2	ξ2	NOUN
ejpam-6131	189	135	)	)	PUNCT
ejpam-6131	189	136	⪯	⪯	NOUN
ejpam-6131	189	137	ζn+1(q3	ζn+1(q3	NOUN
ejpam-6131	189	138	,	,	PUNCT
ejpam-6131	189	139	q4	q4	PROPN
ejpam-6131	189	140	,	,	PUNCT
ejpam-6131	189	141	q5	q5	PROPN
ejpam-6131	189	142	,	,	PUNCT
ejpam-6131	189	143	q1	q1	PROPN
ejpam-6131	189	144	,	,	PUNCT
ejpam-6131	189	145	q2	q2	NOUN
ejpam-6131	189	146	)	)	PUNCT
ejpam-6131	189	147	,	,	PUNCT
ejpam-6131	189	148	p(ξ4	p(ξ4	NOUN
ejpam-6131	189	149	)	)	PUNCT
ejpam-6131	189	150	⪰	⪰	NOUN
ejpam-6131	189	151	p(q4	p(q4	NOUN
ejpam-6131	189	152	)	)	PUNCT
ejpam-6131	189	153	⇒	⇒	PROPN
ejpam-6131	189	154	ζn(ξ4	ζn(ξ4	PROPN
ejpam-6131	189	155	,	,	PUNCT
ejpam-6131	189	156	ξ5	ξ5	NOUN
ejpam-6131	189	157	,	,	PUNCT
ejpam-6131	189	158	ξ1	ξ1	NOUN
ejpam-6131	189	159	,	,	PUNCT
ejpam-6131	189	160	ξ2	ξ2	ADJ
ejpam-6131	189	161	,	,	PUNCT
ejpam-6131	189	162	ξ3	ξ3	NOUN
ejpam-6131	189	163	)	)	PUNCT
ejpam-6131	189	164	⪰	⪰	NOUN
ejpam-6131	189	165	ζn+1(q4	ζn+1(q4	NOUN
ejpam-6131	189	166	,	,	PUNCT
ejpam-6131	189	167	q5	q5	PROPN
ejpam-6131	189	168	,	,	PUNCT
ejpam-6131	189	169	q1	q1	PROPN
ejpam-6131	189	170	,	,	PUNCT
ejpam-6131	189	171	q2	q2	NOUN
ejpam-6131	189	172	,	,	PUNCT
ejpam-6131	189	173	q3	q3	PROPN
ejpam-6131	189	174	)	)	PUNCT
ejpam-6131	189	175	,	,	PUNCT
ejpam-6131	189	176	p(ξ5	p(ξ5	NOUN
ejpam-6131	189	177	)	)	PUNCT
ejpam-6131	189	178	⪯	⪯	NOUN
ejpam-6131	189	179	p(q5	p(q5	NOUN
ejpam-6131	189	180	)	)	PUNCT
ejpam-6131	189	181	⇒	⇒	PROPN
ejpam-6131	189	182	ζn(ξ5	ζn(ξ5	NOUN
ejpam-6131	189	183	,	,	PUNCT
ejpam-6131	189	184	ξ1	ξ1	NOUN
ejpam-6131	189	185	,	,	PUNCT
ejpam-6131	189	186	ξ2	ξ2	ADJ
ejpam-6131	189	187	,	,	PUNCT
ejpam-6131	189	188	ξ3	ξ3	NOUN
ejpam-6131	189	189	,	,	PUNCT
ejpam-6131	189	190	ξ4	ξ4	NOUN
ejpam-6131	189	191	)	)	PUNCT
ejpam-6131	189	192	⪯	⪯	NOUN
ejpam-6131	189	193	ζn+1(q5	ζn+1(q5	NUM
ejpam-6131	189	194	,	,	PUNCT
ejpam-6131	189	195	q1	q1	PROPN
ejpam-6131	189	196	,	,	PUNCT
ejpam-6131	189	197	q2	q2	NOUN
ejpam-6131	189	198	,	,	PUNCT
ejpam-6131	189	199	q3	q3	PROPN
ejpam-6131	189	200	,	,	PUNCT
ejpam-6131	189	201	q4	q4	PROPN
ejpam-6131	189	202	)	)	PUNCT
ejpam-6131	189	203	.	.	PUNCT
ejpam-6131	190	1	definition	definition	NOUN
ejpam-6131	190	2	19	19	NUM
ejpam-6131	190	3	.	.	PUNCT
ejpam-6131	191	1	let	let	VERB
ejpam-6131	191	2	ζi	ζi	PRON
ejpam-6131	191	3	:	:	PUNCT
ejpam-6131	191	4	g5	g5	NOUN
ejpam-6131	191	5	→	→	SYM
ejpam-6131	191	6	g	g	PROPN
ejpam-6131	191	7	and	and	CCONJ
ejpam-6131	191	8	p	p	X
ejpam-6131	191	9	:	:	PUNCT
ejpam-6131	191	10	g	g	PROPN
ejpam-6131	191	11	→	→	SYM
ejpam-6131	191	12	g	g	NOUN
ejpam-6131	191	13	be	be	AUX
ejpam-6131	191	14	two	two	NUM
ejpam-6131	191	15	mappings	mapping	NOUN
ejpam-6131	191	16	.	.	PUNCT
ejpam-6131	192	1	then	then	ADV
ejpam-6131	192	2	,	,	PUNCT
ejpam-6131	192	3	{	{	PUNCT
ejpam-6131	192	4	ζi}i∈w	ζi}i∈w	X
ejpam-6131	192	5	and	and	CCONJ
ejpam-6131	192	6	p	p	NOUN
ejpam-6131	192	7	are	be	AUX
ejpam-6131	192	8	said	say	VERB
ejpam-6131	192	9	to	to	PART
ejpam-6131	192	10	satisfy	satisfy	VERB
ejpam-6131	192	11	the	the	DET
ejpam-6131	192	12	(	(	PUNCT
ejpam-6131	192	13	c	c	NOUN
ejpam-6131	192	14	)	)	PUNCT
ejpam-6131	192	15	condition	condition	NOUN
ejpam-6131	192	16	if	if	SCONJ
ejpam-6131	192	17	t(ζi(ξ1	t(ζi(ξ1	ADJ
ejpam-6131	192	18	,	,	PUNCT
ejpam-6131	192	19	ξ2	ξ2	ADJ
ejpam-6131	192	20	,	,	PUNCT
ejpam-6131	192	21	ξ3	ξ3	NOUN
ejpam-6131	192	22	,	,	PUNCT
ejpam-6131	192	23	ξ4	ξ4	NOUN
ejpam-6131	192	24	,	,	PUNCT
ejpam-6131	192	25	ξ5	ξ5	NOUN
ejpam-6131	192	26	)	)	PUNCT
ejpam-6131	192	27	,	,	PUNCT
ejpam-6131	192	28	ζ	ζ	NOUN
ejpam-6131	192	29	j(q1	j(q1	NOUN
ejpam-6131	192	30	,	,	PUNCT
ejpam-6131	192	31	q2	q2	PROPN
ejpam-6131	192	32	,	,	PUNCT
ejpam-6131	192	33	q3	q3	PROPN
ejpam-6131	192	34	,	,	PUNCT
ejpam-6131	192	35	q4	q4	PROPN
ejpam-6131	192	36	,	,	PUNCT
ejpam-6131	192	37	q5	q5	PROPN
ejpam-6131	192	38	)	)	PUNCT
ejpam-6131	192	39	)	)	PUNCT
ejpam-6131	192	40	≤	≤	NUM
ejpam-6131	192	41	γ̃[t(p(ξ1	γ̃[t(p(ξ1	NOUN
ejpam-6131	192	42	)	)	PUNCT
ejpam-6131	192	43	,	,	PUNCT
ejpam-6131	192	44	ζ	ζ	NOUN
ejpam-6131	192	45	i(ξ1	i(ξ1	NOUN
ejpam-6131	192	46	,	,	PUNCT
ejpam-6131	192	47	ξ2	ξ2	NOUN
ejpam-6131	192	48	,	,	PUNCT
ejpam-6131	192	49	ξ3	ξ3	NOUN
ejpam-6131	192	50	,	,	PUNCT
ejpam-6131	192	51	ξ4	ξ4	NOUN
ejpam-6131	192	52	,	,	PUNCT
ejpam-6131	192	53	ξ5	ξ5	NOUN
ejpam-6131	192	54	)	)	PUNCT
ejpam-6131	192	55	)	)	PUNCT
ejpam-6131	193	1	+	+	CCONJ
ejpam-6131	193	2	t(p(q1	t(p(q1	X
ejpam-6131	193	3	)	)	PUNCT
ejpam-6131	193	4	,	,	PUNCT
ejpam-6131	193	5	ζ	ζ	NOUN
ejpam-6131	193	6	j(q1	j(q1	NOUN
ejpam-6131	193	7	,	,	PUNCT
ejpam-6131	193	8	q2	q2	PROPN
ejpam-6131	193	9	,	,	PUNCT
ejpam-6131	193	10	q3	q3	PROPN
ejpam-6131	193	11	,	,	PUNCT
ejpam-6131	193	12	q4	q4	PROPN
ejpam-6131	193	13	,	,	PUNCT
ejpam-6131	193	14	q5	q5	PROPN
ejpam-6131	193	15	)	)	PUNCT
ejpam-6131	193	16	)	)	PUNCT
ejpam-6131	193	17	]	]	PUNCT
ejpam-6131	194	1	+	+	CCONJ
ejpam-6131	194	2	υ̃[t(p(ξ1	υ̃[t(p(ξ1	NOUN
ejpam-6131	194	3	)	)	PUNCT
ejpam-6131	194	4	,	,	PUNCT
ejpam-6131	194	5	p(q1	p(q1	NOUN
ejpam-6131	194	6	)	)	PUNCT
ejpam-6131	194	7	)	)	PUNCT
ejpam-6131	194	8	]	]	PUNCT
ejpam-6131	194	9	,	,	PUNCT
ejpam-6131	194	10	(	(	PUNCT
ejpam-6131	194	11	1	1	X
ejpam-6131	194	12	)	)	PUNCT
ejpam-6131	194	13	for	for	ADP
ejpam-6131	194	14	some	some	DET
ejpam-6131	194	15	ξi	ξi	NOUN
ejpam-6131	194	16	,	,	PUNCT
ejpam-6131	194	17	qi	qi	PROPN
ejpam-6131	194	18	∈	∈	PROPN
ejpam-6131	194	19	g	g	PROPN
ejpam-6131	194	20	,	,	PUNCT
ejpam-6131	194	21	where	where	SCONJ
ejpam-6131	194	22	1	1	NUM
ejpam-6131	194	23	≤	≤	NUM
ejpam-6131	194	24	i	i	X
ejpam-6131	194	25	≤	≤	NOUN
ejpam-6131	194	26	5	5	NUM
ejpam-6131	194	27	,	,	PUNCT
ejpam-6131	194	28	provided	provide	VERB
ejpam-6131	194	29	that	that	SCONJ
ejpam-6131	194	30	p(ξi	p(ξi	ADJ
ejpam-6131	194	31	)	)	PUNCT
ejpam-6131	194	32	⪯	⪯	NOUN
ejpam-6131	194	33	p(qi	p(qi	PROPN
ejpam-6131	194	34	)	)	PUNCT
ejpam-6131	194	35	,	,	PUNCT
ejpam-6131	194	36	for	for	ADP
ejpam-6131	194	37	1	1	NUM
ejpam-6131	194	38	≤	≤	NUM
ejpam-6131	194	39	i	i	PRON
ejpam-6131	194	40	≤	≤	NOUN
ejpam-6131	194	41	5	5	NUM
ejpam-6131	194	42	,	,	PUNCT
ejpam-6131	194	43	or	or	CCONJ
ejpam-6131	194	44	p(ξi	p(ξi	ADJ
ejpam-6131	194	45	)	)	PUNCT
ejpam-6131	194	46	⪰	⪰	NOUN
ejpam-6131	194	47	p(qi	p(qi	PROPN
ejpam-6131	194	48	)	)	PUNCT
ejpam-6131	194	49	,	,	PUNCT
ejpam-6131	194	50	for	for	ADP
ejpam-6131	194	51	1	1	NUM
ejpam-6131	194	52	≤	≤	NUM
ejpam-6131	194	53	i	i	PRON
ejpam-6131	194	54	≤	≤	NOUN
ejpam-6131	194	55	5	5	NUM
ejpam-6131	194	56	.	.	PUNCT
ejpam-6131	195	1	in	in	ADP
ejpam-6131	195	2	addition	addition	NOUN
ejpam-6131	195	3	,	,	PUNCT
ejpam-6131	195	4	i	i	PRON
ejpam-6131	195	5	=	=	NOUN
ejpam-6131	195	6	̸	̸	PUNCT
ejpam-6131	195	7	γ̃	γ̃	PROPN
ejpam-6131	195	8	=	=	SYM
ejpam-6131	195	9	(	(	PUNCT
ejpam-6131	195	10	γ̃ij	γ̃ij	PROPN
ejpam-6131	195	11	)	)	PUNCT
ejpam-6131	195	12	and	and	CCONJ
ejpam-6131	195	13	i	i	PRON
ejpam-6131	195	14	=	=	PUNCT
ejpam-6131	195	15	̸	̸	X
ejpam-6131	195	16	υ̃	υ̃	PROPN
ejpam-6131	195	17	=	=	SYM
ejpam-6131	195	18	(	(	PUNCT
ejpam-6131	195	19	υ̃ij	υ̃ij	PROPN
ejpam-6131	195	20	)	)	PUNCT
ejpam-6131	195	21	∈	∈	PROPN
ejpam-6131	195	22	zm	zm	PROPN
ejpam-6131	195	23	satisfy	satisfy	VERB
ejpam-6131	195	24	the	the	DET
ejpam-6131	195	25	condition	condition	NOUN
ejpam-6131	195	26	that	that	SCONJ
ejpam-6131	195	27	(	(	PUNCT
ejpam-6131	195	28	γ̃	γ̃	PROPN
ejpam-6131	195	29	+	+	NUM
ejpam-6131	195	30	υ̃)(i	υ̃)(i	NOUN
ejpam-6131	195	31	−	−	NOUN
ejpam-6131	195	32	γ̃)−1	γ̃)−1	NOUN
ejpam-6131	195	33	∈	∈	PROPN
ejpam-6131	195	34	zm	zm	PROPN
ejpam-6131	195	35	.	.	PUNCT
ejpam-6131	195	36	example	example	NOUN
ejpam-6131	196	1	5	5	NUM
ejpam-6131	196	2	.	.	PUNCT
ejpam-6131	197	1	let	let	VERB
ejpam-6131	197	2	g	g	NOUN
ejpam-6131	197	3	=	=	PUNCT
ejpam-6131	198	1	[	[	X
ejpam-6131	198	2	0	0	NUM
ejpam-6131	198	3	,	,	PUNCT
ejpam-6131	198	4	1	1	NUM
ejpam-6131	198	5	]	]	PUNCT
ejpam-6131	198	6	be	be	AUX
ejpam-6131	198	7	equipped	equip	VERB
ejpam-6131	198	8	with	with	ADP
ejpam-6131	198	9	metric	metric	ADJ
ejpam-6131	198	10	t(ξ1	t(ξ1	NUM
ejpam-6131	198	11	,	,	PUNCT
ejpam-6131	198	12	ξ2	ξ2	NOUN
ejpam-6131	198	13	)	)	PUNCT
ejpam-6131	198	14	=	=	SYM
ejpam-6131	198	15	|ξ1	|ξ1	NOUN
ejpam-6131	198	16	−	−	NUM
ejpam-6131	198	17	ξ2|	ξ2|	NOUN
ejpam-6131	198	18	,	,	PUNCT
ejpam-6131	198	19	for	for	ADP
ejpam-6131	198	20	all	all	DET
ejpam-6131	198	21	ξ1	ξ1	NOUN
ejpam-6131	198	22	,	,	PUNCT
ejpam-6131	198	23	ξ2	ξ2	PROPN
ejpam-6131	198	24	∈	∈	PROPN
ejpam-6131	198	25	g.	g.	NOUN
ejpam-6131	198	26	(	(	PUNCT
ejpam-6131	198	27	1	1	X
ejpam-6131	198	28	)	)	PUNCT
ejpam-6131	198	29	let	let	VERB
ejpam-6131	198	30	γ̃	γ̃	PROPN
ejpam-6131	198	31	=	=	PUNCT
ejpam-6131	198	32	(	(	PUNCT
ejpam-6131	198	33	1	1	NUM
ejpam-6131	198	34	5	5	NUM
ejpam-6131	198	35	0	0	NUM
ejpam-6131	198	36	0	0	NUM
ejpam-6131	198	37	1	1	NUM
ejpam-6131	198	38	5	5	NUM
ejpam-6131	198	39	)	)	PUNCT
ejpam-6131	198	40	and	and	CCONJ
ejpam-6131	199	1	υ̃	υ̃	PROPN
ejpam-6131	199	2	=	=	PUNCT
ejpam-6131	199	3	(	(	PUNCT
ejpam-6131	199	4	0	0	NUM
ejpam-6131	199	5	1	1	NUM
ejpam-6131	199	6	5	5	NUM
ejpam-6131	199	7	1	1	NUM
ejpam-6131	199	8	5	5	NUM
ejpam-6131	199	9	0	0	NUM
ejpam-6131	199	10	)	)	PUNCT
ejpam-6131	199	11	∈	∈	PROPN
ejpam-6131	200	1	zm	zm	PROPN
ejpam-6131	200	2	.	.	PUNCT
ejpam-6131	201	1	then	then	ADV
ejpam-6131	201	2	,	,	PUNCT
ejpam-6131	201	3	(	(	PUNCT
ejpam-6131	201	4	γ̃	γ̃	PROPN
ejpam-6131	201	5	+	+	NUM
ejpam-6131	201	6	υ̃)(i	υ̃)(i	NOUN
ejpam-6131	201	7	−	−	NOUN
ejpam-6131	201	8	γ̃)−1	γ̃)−1	NOUN
ejpam-6131	201	9	∈;zm	∈;zm	PROPN
ejpam-6131	201	10	.	.	PUNCT
ejpam-6131	202	1	(	(	PUNCT
ejpam-6131	202	2	2	2	X
ejpam-6131	202	3	)	)	PUNCT
ejpam-6131	202	4	let	let	VERB
ejpam-6131	202	5	γ̃	γ̃	PROPN
ejpam-6131	202	6	=	=	SYM
ejpam-6131	202	7	ξi	ξi	NOUN
ejpam-6131	202	8	,	,	PUNCT
ejpam-6131	202	9	and	and	CCONJ
ejpam-6131	202	10	υ̃	υ̃	PROPN
ejpam-6131	203	1	=	=	SYM
ejpam-6131	203	2	(	(	PUNCT
ejpam-6131	203	3	(	(	PUNCT
ejpam-6131	203	4	1−ξ)3−ξ)i	1−ξ)3−ξ)i	NUM
ejpam-6131	203	5	∈	∈	NOUN
ejpam-6131	203	6	zm	zm	NOUN
ejpam-6131	203	7	such	such	ADJ
ejpam-6131	203	8	that	that	SCONJ
ejpam-6131	203	9	ξ	ξ	X
ejpam-6131	203	10	=	=	SYM
ejpam-6131	203	11	1	1	NUM
ejpam-6131	203	12	4	4	NUM
ejpam-6131	203	13	,	,	PUNCT
ejpam-6131	203	14	1	1	NUM
ejpam-6131	203	15	5	5	NUM
ejpam-6131	203	16	,	,	PUNCT
ejpam-6131	203	17	1	1	NUM
ejpam-6131	203	18	7	7	NUM
ejpam-6131	203	19	,	,	PUNCT
ejpam-6131	203	20	1	1	NUM
ejpam-6131	203	21	8	8	NUM
ejpam-6131	203	22	,	,	PUNCT
ejpam-6131	203	23	then	then	ADV
ejpam-6131	203	24	(	(	PUNCT
ejpam-6131	203	25	γ̃+υ̃)(i−	γ̃+υ̃)(i−	NUM
ejpam-6131	203	26	γ̃)−1	γ̃)−1	NOUN
ejpam-6131	203	27	∈	∈	PROPN
ejpam-6131	203	28	zm	zm	PROPN
ejpam-6131	203	29	.	.	PUNCT
ejpam-6131	204	1	definition	definition	NOUN
ejpam-6131	204	2	20	20	NUM
ejpam-6131	204	3	.	.	PUNCT
ejpam-6131	205	1	let	let	VERB
ejpam-6131	205	2	ζo	ζo	ADP
ejpam-6131	205	3	:	:	PUNCT
ejpam-6131	205	4	g5	g5	NOUN
ejpam-6131	205	5	→	→	SYM
ejpam-6131	205	6	g	g	PROPN
ejpam-6131	205	7	and	and	CCONJ
ejpam-6131	205	8	p	p	X
ejpam-6131	205	9	:	:	PUNCT
ejpam-6131	205	10	g	g	PROPN
ejpam-6131	205	11	→	→	SYM
ejpam-6131	205	12	g	g	NOUN
ejpam-6131	205	13	be	be	AUX
ejpam-6131	205	14	two	two	NUM
ejpam-6131	205	15	mappings	mapping	NOUN
ejpam-6131	205	16	,	,	PUNCT
ejpam-6131	205	17	then	then	ADV
ejpam-6131	205	18	ζo	ζo	ADP
ejpam-6131	205	19	and	and	CCONJ
ejpam-6131	205	20	p	p	NOUN
ejpam-6131	205	21	are	be	AUX
ejpam-6131	205	22	said	say	VERB
ejpam-6131	205	23	to	to	PART
ejpam-6131	205	24	have	have	VERB
ejpam-6131	205	25	mixed	mixed	ADJ
ejpam-6131	205	26	quintuple	quintuple	ADJ
ejpam-6131	205	27	transcendence	transcendence	NOUN
ejpam-6131	205	28	point	point	NOUN
ejpam-6131	205	29	(	(	PUNCT
ejpam-6131	205	30	mqtp	mqtp	NOUN
ejpam-6131	205	31	)	)	PUNCT
ejpam-6131	205	32	if	if	SCONJ
ejpam-6131	205	33	there	there	PRON
ejpam-6131	205	34	exists	exist	VERB
ejpam-6131	205	35	some	some	DET
ejpam-6131	205	36	ξo1	ξo1	PROPN
ejpam-6131	205	37	,	,	PUNCT
ejpam-6131	205	38	ξ	ξ	X
ejpam-6131	205	39	o	o	PROPN
ejpam-6131	205	40	2	2	NUM
ejpam-6131	205	41	,	,	PUNCT
ejpam-6131	205	42	ξ	ξ	PROPN
ejpam-6131	205	43	o	o	NOUN
ejpam-6131	205	44	3	3	NUM
ejpam-6131	205	45	,	,	PUNCT
ejpam-6131	205	46	ξ	ξ	PROPN
ejpam-6131	205	47	o	o	NOUN
ejpam-6131	205	48	4	4	NUM
ejpam-6131	205	49	,	,	PUNCT
ejpam-6131	205	50	ξ	ξ	PROPN
ejpam-6131	205	51	o	o	NOUN
ejpam-6131	205	52	5	5	NUM
ejpam-6131	205	53	∈	∈	NOUN
ejpam-6131	205	54	g	g	NOUN
ejpam-6131	205	55	such	such	ADJ
ejpam-6131	205	56	that	that	DET
ejpam-6131	205	57	ζo(ξo1	ζo(ξo1	PROPN
ejpam-6131	205	58	,	,	PUNCT
ejpam-6131	205	59	ξ	ξ	X
ejpam-6131	205	60	o	o	PROPN
ejpam-6131	205	61	2	2	NUM
ejpam-6131	205	62	,	,	PUNCT
ejpam-6131	205	63	ξ	ξ	PROPN
ejpam-6131	205	64	o	o	NOUN
ejpam-6131	205	65	3	3	NUM
ejpam-6131	205	66	,	,	PUNCT
ejpam-6131	205	67	ξ	ξ	PROPN
ejpam-6131	205	68	o	o	NOUN
ejpam-6131	205	69	4	4	NUM
ejpam-6131	205	70	,	,	PUNCT
ejpam-6131	205	71	ξ	ξ	X
ejpam-6131	205	72	o	o	NOUN
ejpam-6131	205	73	5	5	NUM
ejpam-6131	205	74	)	)	PUNCT
ejpam-6131	205	75	⪰	⪰	NOUN
ejpam-6131	205	76	p(ξo1	p(ξo1	NOUN
ejpam-6131	205	77	)	)	PUNCT
ejpam-6131	205	78	,	,	PUNCT
ejpam-6131	205	79	ζo(ξo2	ζo(ξo2	NUM
ejpam-6131	205	80	,	,	PUNCT
ejpam-6131	205	81	ξ	ξ	X
ejpam-6131	205	82	o	o	PROPN
ejpam-6131	205	83	3	3	NUM
ejpam-6131	205	84	,	,	PUNCT
ejpam-6131	205	85	ξ	ξ	PROPN
ejpam-6131	205	86	o	o	NOUN
ejpam-6131	205	87	4	4	NUM
ejpam-6131	205	88	,	,	PUNCT
ejpam-6131	205	89	ξ	ξ	X
ejpam-6131	205	90	o	o	NOUN
ejpam-6131	205	91	5	5	NUM
ejpam-6131	205	92	,	,	PUNCT
ejpam-6131	205	93	ξ	ξ	PROPN
ejpam-6131	205	94	o	o	PROPN
ejpam-6131	205	95	1	1	X
ejpam-6131	205	96	)	)	PUNCT
ejpam-6131	205	97	⪯	⪯	NOUN
ejpam-6131	205	98	p(ξo2	p(ξo2	NUM
ejpam-6131	205	99	)	)	PUNCT
ejpam-6131	205	100	,	,	PUNCT
ejpam-6131	205	101	ζo(ξo3	ζo(ξo3	PROPN
ejpam-6131	205	102	,	,	PUNCT
ejpam-6131	205	103	ξ	ξ	PROPN
ejpam-6131	205	104	o	o	PROPN
ejpam-6131	205	105	4	4	NUM
ejpam-6131	205	106	,	,	PUNCT
ejpam-6131	205	107	ξ	ξ	X
ejpam-6131	205	108	o	o	NOUN
ejpam-6131	205	109	5	5	NUM
ejpam-6131	205	110	,	,	PUNCT
ejpam-6131	205	111	ξ	ξ	PROPN
ejpam-6131	205	112	o	o	PROPN
ejpam-6131	205	113	1	1	NUM
ejpam-6131	205	114	,	,	PUNCT
ejpam-6131	205	115	ξ	ξ	PROPN
ejpam-6131	205	116	o	o	NOUN
ejpam-6131	205	117	2	2	X
ejpam-6131	205	118	)	)	PUNCT
ejpam-6131	205	119	⪰	⪰	NOUN
ejpam-6131	205	120	p(ξo3	p(ξo3	NOUN
ejpam-6131	205	121	)	)	PUNCT
ejpam-6131	205	122	,	,	PUNCT
ejpam-6131	205	123	ζo(ξo4	ζo(ξo4	PROPN
ejpam-6131	205	124	,	,	PUNCT
ejpam-6131	205	125	ξ	ξ	X
ejpam-6131	205	126	o	o	PROPN
ejpam-6131	205	127	5	5	NUM
ejpam-6131	205	128	,	,	PUNCT
ejpam-6131	205	129	ξ	ξ	PROPN
ejpam-6131	205	130	o	o	PROPN
ejpam-6131	205	131	1	1	NUM
ejpam-6131	205	132	,	,	PUNCT
ejpam-6131	205	133	ξ	ξ	PROPN
ejpam-6131	205	134	o	o	NOUN
ejpam-6131	205	135	2	2	NUM
ejpam-6131	205	136	,	,	PUNCT
ejpam-6131	205	137	ξ	ξ	PROPN
ejpam-6131	205	138	o	o	NOUN
ejpam-6131	205	139	3	3	X
ejpam-6131	205	140	)	)	PUNCT
ejpam-6131	205	141	⪯	⪯	NOUN
ejpam-6131	205	142	p(ξo4	p(ξo4	NOUN
ejpam-6131	205	143	)	)	PUNCT
ejpam-6131	205	144	,	,	PUNCT
ejpam-6131	205	145	ζo(ξo5	ζo(ξo5	NUM
ejpam-6131	205	146	,	,	PUNCT
ejpam-6131	205	147	ξ	ξ	PROPN
ejpam-6131	205	148	o	o	PROPN
ejpam-6131	205	149	1	1	NUM
ejpam-6131	205	150	,	,	PUNCT
ejpam-6131	205	151	ξ	ξ	PROPN
ejpam-6131	205	152	o	o	NOUN
ejpam-6131	205	153	2	2	NUM
ejpam-6131	205	154	,	,	PUNCT
ejpam-6131	205	155	ξ	ξ	PROPN
ejpam-6131	205	156	o	o	NOUN
ejpam-6131	205	157	3	3	NUM
ejpam-6131	205	158	,	,	PUNCT
ejpam-6131	205	159	ξ	ξ	X
ejpam-6131	205	160	o	o	NOUN
ejpam-6131	205	161	4	4	X
ejpam-6131	205	162	)	)	PUNCT
ejpam-6131	205	163	⪰	⪰	NOUN
ejpam-6131	205	164	p(ξo5	p(ξo5	PROPN
ejpam-6131	205	165	)	)	PUNCT
ejpam-6131	205	166	,	,	PUNCT
ejpam-6131	205	167	(	(	PUNCT
ejpam-6131	205	168	2	2	X
ejpam-6131	205	169	)	)	PUNCT
ejpam-6131	205	170	given	give	VERB
ejpam-6131	205	171	that	that	DET
ejpam-6131	205	172	ζo	ζo	NOUN
ejpam-6131	205	173	and	and	CCONJ
ejpam-6131	205	174	p	p	NOUN
ejpam-6131	205	175	have	have	VERB
ejpam-6131	205	176	non	non	ADJ
ejpam-6131	205	177	-	-	ADJ
ejpam-6131	205	178	decreasing	decrease	VERB
ejpam-6131	205	179	transcendent	transcendent	NOUN
ejpam-6131	205	180	point	point	NOUN
ejpam-6131	205	181	in	in	ADP
ejpam-6131	205	182	ξo1	ξo1	PROPN
ejpam-6131	205	183	,	,	PUNCT
ejpam-6131	205	184	ξ	ξ	X
ejpam-6131	205	185	o	o	NOUN
ejpam-6131	205	186	3	3	NUM
ejpam-6131	205	187	,	,	PUNCT
ejpam-6131	205	188	ξ	ξ	PROPN
ejpam-6131	205	189	o	o	NOUN
ejpam-6131	205	190	5	5	NUM
ejpam-6131	205	191	and	and	CCONJ
ejpam-6131	205	192	a	a	DET
ejpam-6131	205	193	non	non	ADJ
ejpam-6131	205	194	-	-	ADJ
ejpam-6131	205	195	increasing	increase	VERB
ejpam-6131	205	196	transcendence	transcendence	NOUN
ejpam-6131	205	197	point	point	NOUN
ejpam-6131	205	198	in	in	ADP
ejpam-6131	205	199	ξo2	ξo2	PROPN
ejpam-6131	205	200	,	,	PUNCT
ejpam-6131	205	201	ξ	ξ	X
ejpam-6131	205	202	o	o	PROPN
ejpam-6131	205	203	4	4	X
ejpam-6131	205	204	.	.	PUNCT
ejpam-6131	206	1	lemma	lemma	PROPN
ejpam-6131	206	2	2	2	X
ejpam-6131	206	3	.	.	PUNCT
ejpam-6131	207	1	let	let	VERB
ejpam-6131	207	2	ζi	ζi	PRON
ejpam-6131	207	3	:	:	PUNCT
ejpam-6131	207	4	g5	g5	NOUN
ejpam-6131	207	5	→	→	SYM
ejpam-6131	207	6	g	g	PROPN
ejpam-6131	207	7	and	and	CCONJ
ejpam-6131	207	8	p	p	X
ejpam-6131	207	9	:	:	PUNCT
ejpam-6131	207	10	g	g	PROPN
ejpam-6131	207	11	→	→	SYM
ejpam-6131	207	12	g	g	NOUN
ejpam-6131	207	13	be	be	AUX
ejpam-6131	207	14	two	two	NUM
ejpam-6131	207	15	mappings	mapping	NOUN
ejpam-6131	207	16	in	in	ADP
ejpam-6131	207	17	the	the	DET
ejpam-6131	207	18	setting	setting	NOUN
ejpam-6131	207	19	of	of	ADP
ejpam-6131	207	20	a	a	DET
ejpam-6131	207	21	partially	partially	ADV
ejpam-6131	207	22	ordered	order	VERB
ejpam-6131	207	23	complete	complete	ADJ
ejpam-6131	207	24	generalized	generalized	ADJ
ejpam-6131	207	25	metric	metric	ADJ
ejpam-6131	207	26	space	space	NOUN
ejpam-6131	207	27	(	(	PUNCT
ejpam-6131	207	28	pocgms	pocgms	PROPN
ejpam-6131	207	29	)	)	PUNCT
ejpam-6131	207	30	(	(	PUNCT
ejpam-6131	207	31	g	g	NOUN
ejpam-6131	207	32	,	,	PUNCT
ejpam-6131	207	33	t,⪯	t,⪯	NOUN
ejpam-6131	207	34	)	)	PUNCT
ejpam-6131	207	35	.	.	PUNCT
ejpam-6131	208	1	suppose	suppose	VERB
ejpam-6131	208	2	that	that	SCONJ
ejpam-6131	208	3	{	{	PUNCT
ejpam-6131	208	4	ζi}i∈w	ζi}i∈w	AUX
ejpam-6131	208	5	have	have	VERB
ejpam-6131	208	6	mpmp	mpmp	NOUN
ejpam-6131	208	7	such	such	ADJ
ejpam-6131	208	8	that	that	DET
ejpam-6131	208	9	ζi(g5	ζi(g5	NOUN
ejpam-6131	208	10	)	)	PUNCT
ejpam-6131	208	11	⊆	⊆	NUM
ejpam-6131	208	12	p(g	p(g	NOUN
ejpam-6131	208	13	)	)	PUNCT
ejpam-6131	208	14	.	.	PUNCT
ejpam-6131	209	1	if	if	SCONJ
ejpam-6131	209	2	ζo	ζo	ADP
ejpam-6131	209	3	and	and	CCONJ
ejpam-6131	209	4	p	p	NOUN
ejpam-6131	209	5	have	have	AUX
ejpam-6131	209	6	mqtp	mqtp	VERB
ejpam-6131	209	7	,	,	PUNCT
ejpam-6131	209	8	then	then	ADV
ejpam-6131	209	9	s.	s.	PROPN
ejpam-6131	209	10	batul	batul	PROPN
ejpam-6131	209	11	et	et	PROPN
ejpam-6131	209	12	a.	a.	PROPN
ejpam-6131	209	13	/	/	PUNCT
ejpam-6131	209	14	eur	eur	PROPN
ejpam-6131	209	15	.	.	PUNCT
ejpam-6131	210	1	j.	j.	PROPN
ejpam-6131	210	2	pure	pure	PROPN
ejpam-6131	210	3	appl	appl	PROPN
ejpam-6131	210	4	.	.	PROPN
ejpam-6131	210	5	math	math	PROPN
ejpam-6131	210	6	,	,	PUNCT
ejpam-6131	210	7	18	18	NUM
ejpam-6131	210	8	(	(	PUNCT
ejpam-6131	210	9	2	2	NUM
ejpam-6131	210	10	)	)	PUNCT
ejpam-6131	210	11	(	(	PUNCT
ejpam-6131	210	12	2025	2025	NUM
ejpam-6131	210	13	)	)	PUNCT
ejpam-6131	210	14	,	,	PUNCT
ejpam-6131	210	15	6131	6131	NUM
ejpam-6131	210	16	10	10	NUM
ejpam-6131	210	17	of	of	ADP
ejpam-6131	210	18	22	22	NUM
ejpam-6131	210	19	(	(	PUNCT
ejpam-6131	210	20	a	a	X
ejpam-6131	210	21	):	):	PUNCT
ejpam-6131	210	22	∃	∃	PROPN
ejpam-6131	210	23	sequences	sequence	NOUN
ejpam-6131	210	24	{	{	PUNCT
ejpam-6131	210	25	ξn1	ξn1	PROPN
ejpam-6131	210	26	}	}	PUNCT
ejpam-6131	210	27	,	,	PUNCT
ejpam-6131	210	28	{	{	PUNCT
ejpam-6131	210	29	ξn2	ξn2	NOUN
ejpam-6131	210	30	}	}	PUNCT
ejpam-6131	210	31	,	,	PUNCT
ejpam-6131	210	32	{	{	PUNCT
ejpam-6131	210	33	ξn3	ξn3	NOUN
ejpam-6131	210	34	}	}	PUNCT
ejpam-6131	210	35	,	,	PUNCT
ejpam-6131	210	36	{	{	PUNCT
ejpam-6131	210	37	ξn4	ξn4	NOUN
ejpam-6131	210	38	}	}	PUNCT
ejpam-6131	210	39	and	and	CCONJ
ejpam-6131	210	40	{	{	PUNCT
ejpam-6131	210	41	ξn5	ξn5	NOUN
ejpam-6131	210	42	}	}	PUNCT
ejpam-6131	210	43	∈	∈	PROPN
ejpam-6131	211	1	g	g	NOUN
ejpam-6131	211	2	such	such	ADJ
ejpam-6131	211	3	that	that	DET
ejpam-6131	211	4	p(ξn1	p(ξn1	ADJ
ejpam-6131	211	5	)	)	PUNCT
ejpam-6131	212	1	=	=	PUNCT
ejpam-6131	212	2	ζn−1(ξn−1	ζn−1(ξn−1	PROPN
ejpam-6131	212	3	1	1	NUM
ejpam-6131	212	4	,	,	PUNCT
ejpam-6131	212	5	ξn−1	ξn−1	PROPN
ejpam-6131	212	6	2	2	NUM
ejpam-6131	212	7	,	,	PUNCT
ejpam-6131	212	8	ξn−1	ξn−1	PROPN
ejpam-6131	212	9	3	3	NUM
ejpam-6131	212	10	,	,	PUNCT
ejpam-6131	212	11	ξn−1	ξn−1	PROPN
ejpam-6131	212	12	4	4	NUM
ejpam-6131	212	13	,	,	PUNCT
ejpam-6131	212	14	ξn−1	ξn−1	ADV
ejpam-6131	212	15	5	5	NUM
ejpam-6131	212	16	)	)	PUNCT
ejpam-6131	212	17	,	,	PUNCT
ejpam-6131	212	18	p(ξn2	p(ξn2	NOUN
ejpam-6131	212	19	)	)	PUNCT
ejpam-6131	212	20	=	=	PUNCT
ejpam-6131	212	21	ζn−1(ξn−1	ζn−1(ξn−1	PROPN
ejpam-6131	212	22	2	2	NUM
ejpam-6131	212	23	,	,	PUNCT
ejpam-6131	212	24	ξn−1	ξn−1	PROPN
ejpam-6131	212	25	3	3	NUM
ejpam-6131	212	26	,	,	PUNCT
ejpam-6131	212	27	ξn−1	ξn−1	PROPN
ejpam-6131	212	28	4	4	NUM
ejpam-6131	212	29	,	,	PUNCT
ejpam-6131	212	30	ξn−1	ξn−1	ADV
ejpam-6131	212	31	5	5	NUM
ejpam-6131	212	32	,	,	PUNCT
ejpam-6131	212	33	ξn−1	ξn−1	PROPN
ejpam-6131	212	34	1	1	NUM
ejpam-6131	212	35	)	)	PUNCT
ejpam-6131	212	36	,	,	PUNCT
ejpam-6131	212	37	p(ξn3	p(ξn3	PROPN
ejpam-6131	212	38	)	)	PUNCT
ejpam-6131	212	39	=	=	PUNCT
ejpam-6131	212	40	ζn−1(ξn−1	ζn−1(ξn−1	PROPN
ejpam-6131	212	41	3	3	NUM
ejpam-6131	212	42	,	,	PUNCT
ejpam-6131	212	43	ξn−1	ξn−1	PROPN
ejpam-6131	212	44	4	4	NUM
ejpam-6131	212	45	,	,	PUNCT
ejpam-6131	212	46	ξn−1	ξn−1	ADV
ejpam-6131	212	47	5	5	NUM
ejpam-6131	212	48	,	,	PUNCT
ejpam-6131	212	49	ξn−1	ξn−1	PROPN
ejpam-6131	212	50	1	1	NUM
ejpam-6131	212	51	,	,	PUNCT
ejpam-6131	212	52	ξn−1	ξn−1	PROPN
ejpam-6131	212	53	2	2	NUM
ejpam-6131	212	54	)	)	PUNCT
ejpam-6131	212	55	,	,	PUNCT
ejpam-6131	212	56	p(ξn4	p(ξn4	NOUN
ejpam-6131	212	57	)	)	PUNCT
ejpam-6131	212	58	=	=	PUNCT
ejpam-6131	212	59	ζn−1(ξn−1	ζn−1(ξn−1	PROPN
ejpam-6131	212	60	4	4	NUM
ejpam-6131	212	61	,	,	PUNCT
ejpam-6131	212	62	ξn−1	ξn−1	ADV
ejpam-6131	212	63	5	5	NUM
ejpam-6131	212	64	,	,	PUNCT
ejpam-6131	212	65	ξn−1	ξn−1	PROPN
ejpam-6131	212	66	1	1	NUM
ejpam-6131	212	67	,	,	PUNCT
ejpam-6131	212	68	ξn−1	ξn−1	PROPN
ejpam-6131	212	69	2	2	NUM
ejpam-6131	212	70	,	,	PUNCT
ejpam-6131	212	71	ξn−1	ξn−1	PROPN
ejpam-6131	212	72	3	3	NUM
ejpam-6131	212	73	)	)	PUNCT
ejpam-6131	212	74	,	,	PUNCT
ejpam-6131	212	75	p(ξn5	p(ξn5	NOUN
ejpam-6131	212	76	)	)	PUNCT
ejpam-6131	213	1	=	=	PUNCT
ejpam-6131	213	2	ζn−1(ξn−1	ζn−1(ξn−1	PROPN
ejpam-6131	213	3	5	5	NUM
ejpam-6131	213	4	,	,	PUNCT
ejpam-6131	213	5	ξn−1	ξn−1	PROPN
ejpam-6131	213	6	1	1	NUM
ejpam-6131	213	7	,	,	PUNCT
ejpam-6131	213	8	ξn−1	ξn−1	PROPN
ejpam-6131	213	9	2	2	NUM
ejpam-6131	213	10	,	,	PUNCT
ejpam-6131	213	11	ξn−1	ξn−1	PROPN
ejpam-6131	213	12	3	3	NUM
ejpam-6131	213	13	,	,	PUNCT
ejpam-6131	213	14	ξn−1	ξn−1	ADV
ejpam-6131	213	15	4	4	NUM
ejpam-6131	213	16	)	)	PUNCT
ejpam-6131	213	17	.	.	PUNCT
ejpam-6131	214	1	(	(	PUNCT
ejpam-6131	214	2	b	b	X
ejpam-6131	214	3	):	):	PUNCT
ejpam-6131	214	4	{	{	PUNCT
ejpam-6131	214	5	p(ξn1	p(ξn1	ADJ
ejpam-6131	214	6	)	)	PUNCT
ejpam-6131	214	7	}	}	PUNCT
ejpam-6131	214	8	,	,	PUNCT
ejpam-6131	214	9	{	{	PUNCT
ejpam-6131	214	10	p(ξn3	p(ξn3	PROPN
ejpam-6131	214	11	)	)	PUNCT
ejpam-6131	214	12	}	}	PUNCT
ejpam-6131	214	13	,	,	PUNCT
ejpam-6131	214	14	{	{	PUNCT
ejpam-6131	214	15	p(ξn5	p(ξn5	NOUN
ejpam-6131	214	16	)	)	PUNCT
ejpam-6131	214	17	}	}	PUNCT
ejpam-6131	214	18	are	be	AUX
ejpam-6131	214	19	non	non	ADJ
ejpam-6131	214	20	-	-	ADJ
ejpam-6131	214	21	decreasing	decrease	VERB
ejpam-6131	214	22	sequences	sequence	NOUN
ejpam-6131	214	23	and	and	CCONJ
ejpam-6131	214	24	{	{	PUNCT
ejpam-6131	214	25	p(ξn2	p(ξn2	NOUN
ejpam-6131	214	26	)	)	PUNCT
ejpam-6131	214	27	}	}	PUNCT
ejpam-6131	214	28	,	,	PUNCT
ejpam-6131	214	29	{	{	PUNCT
ejpam-6131	214	30	p(ξn4	p(ξn4	NOUN
ejpam-6131	214	31	)	)	PUNCT
ejpam-6131	214	32	}	}	PUNCT
ejpam-6131	214	33	are	be	AUX
ejpam-6131	214	34	nonincreasing	nonincrease	VERB
ejpam-6131	214	35	sequences	sequence	NOUN
ejpam-6131	214	36	.	.	PUNCT
ejpam-6131	215	1	proof	proof	NOUN
ejpam-6131	215	2	.	.	PUNCT
ejpam-6131	216	1	(	(	PUNCT
ejpam-6131	216	2	a	a	X
ejpam-6131	216	3	):	):	PUNCT
ejpam-6131	216	4	suppose	suppose	VERB
ejpam-6131	216	5	that	that	SCONJ
ejpam-6131	216	6	condition	condition	NOUN
ejpam-6131	216	7	in	in	ADP
ejpam-6131	216	8	(	(	PUNCT
ejpam-6131	216	9	2	2	X
ejpam-6131	216	10	)	)	PUNCT
ejpam-6131	216	11	is	be	AUX
ejpam-6131	216	12	fulfilled	fulfil	VERB
ejpam-6131	216	13	for	for	ADP
ejpam-6131	216	14	some	some	DET
ejpam-6131	216	15	ξo1	ξo1	PROPN
ejpam-6131	216	16	,	,	PUNCT
ejpam-6131	216	17	ξ	ξ	X
ejpam-6131	216	18	o	o	PROPN
ejpam-6131	216	19	2	2	NUM
ejpam-6131	216	20	,	,	PUNCT
ejpam-6131	216	21	ξ	ξ	PROPN
ejpam-6131	216	22	o	o	NOUN
ejpam-6131	216	23	3	3	NUM
ejpam-6131	216	24	,	,	PUNCT
ejpam-6131	216	25	ξ	ξ	PROPN
ejpam-6131	216	26	o	o	NOUN
ejpam-6131	216	27	4	4	NUM
ejpam-6131	216	28	,	,	PUNCT
ejpam-6131	216	29	ξ	ξ	PROPN
ejpam-6131	216	30	o	o	PROPN
ejpam-6131	216	31	5	5	NUM
ejpam-6131	216	32	∈	∈	PROPN
ejpam-6131	216	33	g.	g.	NOUN
ejpam-6131	216	34	since	since	SCONJ
ejpam-6131	216	35	ζo(g5	ζo(g5	NOUN
ejpam-6131	216	36	)	)	PUNCT
ejpam-6131	216	37	⊆	⊆	NUM
ejpam-6131	216	38	p(g	p(g	NOUN
ejpam-6131	216	39	)	)	PUNCT
ejpam-6131	216	40	,	,	PUNCT
ejpam-6131	216	41	then	then	ADV
ejpam-6131	216	42	some	some	DET
ejpam-6131	216	43	elements	element	NOUN
ejpam-6131	216	44	ξ11	ξ11	NOUN
ejpam-6131	216	45	,	,	PUNCT
ejpam-6131	216	46	ξ	ξ	PROPN
ejpam-6131	216	47	1	1	NUM
ejpam-6131	216	48	2	2	NUM
ejpam-6131	216	49	,	,	PUNCT
ejpam-6131	216	50	ξ	ξ	PROPN
ejpam-6131	216	51	1	1	NUM
ejpam-6131	216	52	3	3	NUM
ejpam-6131	216	53	,	,	PUNCT
ejpam-6131	216	54	ξ	ξ	PROPN
ejpam-6131	216	55	1	1	NUM
ejpam-6131	216	56	4	4	NUM
ejpam-6131	216	57	,	,	PUNCT
ejpam-6131	216	58	ξ	ξ	PROPN
ejpam-6131	216	59	1	1	NUM
ejpam-6131	216	60	5	5	NUM
ejpam-6131	216	61	∈	∈	PROPN
ejpam-6131	216	62	g	g	PROPN
ejpam-6131	216	63	p(ξ11	p(ξ11	NOUN
ejpam-6131	216	64	)	)	PUNCT
ejpam-6131	217	1	=	=	SYM
ejpam-6131	217	2	ζo(ξo1	ζo(ξo1	PROPN
ejpam-6131	217	3	,	,	PUNCT
ejpam-6131	217	4	ξ	ξ	X
ejpam-6131	217	5	o	o	PROPN
ejpam-6131	217	6	2	2	NUM
ejpam-6131	217	7	,	,	PUNCT
ejpam-6131	217	8	ξ	ξ	PROPN
ejpam-6131	217	9	o	o	NOUN
ejpam-6131	217	10	3	3	NUM
ejpam-6131	217	11	,	,	PUNCT
ejpam-6131	217	12	ξ	ξ	PROPN
ejpam-6131	217	13	o	o	NOUN
ejpam-6131	217	14	4	4	NUM
ejpam-6131	217	15	,	,	PUNCT
ejpam-6131	217	16	ξ	ξ	X
ejpam-6131	217	17	o	o	NOUN
ejpam-6131	217	18	5	5	NUM
ejpam-6131	217	19	)	)	PUNCT
ejpam-6131	217	20	,	,	PUNCT
ejpam-6131	217	21	p(ξ12	p(ξ12	NUM
ejpam-6131	217	22	)	)	PUNCT
ejpam-6131	217	23	=	=	PUNCT
ejpam-6131	218	1	ζo(ξo2	ζo(ξo2	PROPN
ejpam-6131	218	2	,	,	PUNCT
ejpam-6131	218	3	ξ	ξ	X
ejpam-6131	218	4	o	o	PROPN
ejpam-6131	218	5	3	3	NUM
ejpam-6131	218	6	,	,	PUNCT
ejpam-6131	218	7	ξ	ξ	PROPN
ejpam-6131	218	8	o	o	NOUN
ejpam-6131	218	9	4	4	NUM
ejpam-6131	218	10	,	,	PUNCT
ejpam-6131	218	11	ξ	ξ	X
ejpam-6131	218	12	o	o	NOUN
ejpam-6131	218	13	5	5	NUM
ejpam-6131	218	14	,	,	PUNCT
ejpam-6131	218	15	ξ	ξ	X
ejpam-6131	218	16	o	o	NOUN
ejpam-6131	218	17	1	1	NUM
ejpam-6131	218	18	)	)	PUNCT
ejpam-6131	218	19	,	,	PUNCT
ejpam-6131	218	20	p(ξ13	p(ξ13	NOUN
ejpam-6131	218	21	)	)	PUNCT
ejpam-6131	219	1	=	=	SYM
ejpam-6131	219	2	ζo(ξo3	ζo(ξo3	PROPN
ejpam-6131	219	3	,	,	PUNCT
ejpam-6131	219	4	ξ	ξ	PROPN
ejpam-6131	219	5	o	o	PROPN
ejpam-6131	219	6	4	4	NUM
ejpam-6131	219	7	,	,	PUNCT
ejpam-6131	219	8	ξ	ξ	X
ejpam-6131	219	9	o	o	NOUN
ejpam-6131	219	10	5	5	NUM
ejpam-6131	219	11	,	,	PUNCT
ejpam-6131	219	12	ξ	ξ	PROPN
ejpam-6131	219	13	o	o	PROPN
ejpam-6131	219	14	1	1	NUM
ejpam-6131	219	15	,	,	PUNCT
ejpam-6131	219	16	ξ	ξ	PROPN
ejpam-6131	219	17	o	o	NOUN
ejpam-6131	219	18	2	2	NUM
ejpam-6131	219	19	)	)	PUNCT
ejpam-6131	219	20	,	,	PUNCT
ejpam-6131	219	21	p(ξ14	p(ξ14	NOUN
ejpam-6131	219	22	)	)	PUNCT
ejpam-6131	219	23	=	=	SYM
ejpam-6131	219	24	ζo(ξo4	ζo(ξo4	PROPN
ejpam-6131	219	25	,	,	PUNCT
ejpam-6131	219	26	ξ	ξ	X
ejpam-6131	219	27	o	o	PROPN
ejpam-6131	219	28	5	5	NUM
ejpam-6131	219	29	,	,	PUNCT
ejpam-6131	219	30	ξ	ξ	PROPN
ejpam-6131	219	31	o	o	PROPN
ejpam-6131	219	32	1	1	NUM
ejpam-6131	219	33	,	,	PUNCT
ejpam-6131	219	34	ξ	ξ	PROPN
ejpam-6131	219	35	o	o	NOUN
ejpam-6131	219	36	2	2	NUM
ejpam-6131	219	37	,	,	PUNCT
ejpam-6131	219	38	ξ	ξ	PROPN
ejpam-6131	219	39	o	o	NOUN
ejpam-6131	219	40	3	3	NUM
ejpam-6131	219	41	)	)	PUNCT
ejpam-6131	219	42	,	,	PUNCT
ejpam-6131	219	43	p(ξ15	p(ξ15	ADV
ejpam-6131	219	44	)	)	PUNCT
ejpam-6131	220	1	=	=	SYM
ejpam-6131	220	2	ζo(ξo5	ζo(ξo5	NOUN
ejpam-6131	220	3	,	,	PUNCT
ejpam-6131	220	4	ξ	ξ	PROPN
ejpam-6131	220	5	o	o	PROPN
ejpam-6131	220	6	1	1	NUM
ejpam-6131	220	7	,	,	PUNCT
ejpam-6131	220	8	ξ	ξ	PROPN
ejpam-6131	220	9	o	o	NOUN
ejpam-6131	220	10	2	2	NUM
ejpam-6131	220	11	,	,	PUNCT
ejpam-6131	220	12	ξ	ξ	PROPN
ejpam-6131	220	13	o	o	NOUN
ejpam-6131	220	14	3	3	NUM
ejpam-6131	220	15	,	,	PUNCT
ejpam-6131	220	16	ξ	ξ	X
ejpam-6131	220	17	o	o	NOUN
ejpam-6131	220	18	4	4	NUM
ejpam-6131	220	19	)	)	PUNCT
ejpam-6131	220	20	.	.	PUNCT
ejpam-6131	221	1	(	(	PUNCT
ejpam-6131	221	2	3	3	X
ejpam-6131	221	3	)	)	PUNCT
ejpam-6131	221	4	since	since	SCONJ
ejpam-6131	221	5	ζo(g5	ζo(g5	NOUN
ejpam-6131	221	6	)	)	PUNCT
ejpam-6131	221	7	⊆	⊆	NUM
ejpam-6131	221	8	p(g	p(g	NOUN
ejpam-6131	221	9	)	)	PUNCT
ejpam-6131	221	10	,	,	PUNCT
ejpam-6131	221	11	then	then	ADV
ejpam-6131	221	12	some	some	DET
ejpam-6131	221	13	elements	element	NOUN
ejpam-6131	221	14	can	can	AUX
ejpam-6131	221	15	be	be	AUX
ejpam-6131	221	16	set	set	VERB
ejpam-6131	221	17	as	as	ADP
ejpam-6131	221	18	ξ21	ξ21	NOUN
ejpam-6131	221	19	,	,	PUNCT
ejpam-6131	221	20	ξ	ξ	PROPN
ejpam-6131	221	21	2	2	NUM
ejpam-6131	221	22	2	2	NUM
ejpam-6131	221	23	,	,	PUNCT
ejpam-6131	221	24	ξ	ξ	PROPN
ejpam-6131	221	25	2	2	NUM
ejpam-6131	221	26	3	3	NUM
ejpam-6131	221	27	,	,	PUNCT
ejpam-6131	221	28	ξ	ξ	PROPN
ejpam-6131	221	29	2	2	NUM
ejpam-6131	221	30	4	4	NUM
ejpam-6131	221	31	,	,	PUNCT
ejpam-6131	221	32	ξ	ξ	PROPN
ejpam-6131	221	33	2	2	NUM
ejpam-6131	221	34	5	5	NUM
ejpam-6131	221	35	∈	∈	NOUN
ejpam-6131	221	36	g	g	NOUN
ejpam-6131	221	37	such	such	ADJ
ejpam-6131	221	38	that	that	PRON
ejpam-6131	221	39	p(ξ21	p(ξ21	NOUN
ejpam-6131	221	40	)	)	PUNCT
ejpam-6131	221	41	=	=	SYM
ejpam-6131	221	42	ζ1(ξ11	ζ1(ξ11	PROPN
ejpam-6131	221	43	,	,	PUNCT
ejpam-6131	221	44	ξ	ξ	PROPN
ejpam-6131	221	45	1	1	NUM
ejpam-6131	221	46	2	2	NUM
ejpam-6131	221	47	,	,	PUNCT
ejpam-6131	221	48	ξ	ξ	PROPN
ejpam-6131	221	49	1	1	NUM
ejpam-6131	221	50	3	3	NUM
ejpam-6131	221	51	,	,	PUNCT
ejpam-6131	221	52	ξ	ξ	PROPN
ejpam-6131	221	53	1	1	NUM
ejpam-6131	221	54	4	4	NUM
ejpam-6131	221	55	,	,	PUNCT
ejpam-6131	221	56	ξ	ξ	PROPN
ejpam-6131	221	57	1	1	NUM
ejpam-6131	221	58	5	5	NUM
ejpam-6131	221	59	)	)	PUNCT
ejpam-6131	221	60	,	,	PUNCT
ejpam-6131	221	61	p(ξ22	p(ξ22	ADJ
ejpam-6131	221	62	)	)	PUNCT
ejpam-6131	221	63	=	=	SYM
ejpam-6131	221	64	ζ1(ξ12	ζ1(ξ12	PROPN
ejpam-6131	221	65	,	,	PUNCT
ejpam-6131	221	66	ξ	ξ	PROPN
ejpam-6131	221	67	1	1	NUM
ejpam-6131	221	68	3	3	NUM
ejpam-6131	221	69	,	,	PUNCT
ejpam-6131	221	70	ξ	ξ	PROPN
ejpam-6131	221	71	1	1	NUM
ejpam-6131	221	72	4	4	NUM
ejpam-6131	221	73	,	,	PUNCT
ejpam-6131	221	74	ξ	ξ	PROPN
ejpam-6131	221	75	1	1	NUM
ejpam-6131	221	76	5	5	NUM
ejpam-6131	221	77	,	,	PUNCT
ejpam-6131	221	78	ξ	ξ	PROPN
ejpam-6131	221	79	1	1	NUM
ejpam-6131	221	80	1	1	NUM
ejpam-6131	221	81	)	)	PUNCT
ejpam-6131	221	82	,	,	PUNCT
ejpam-6131	221	83	p(ξ23	p(ξ23	NOUN
ejpam-6131	221	84	)	)	PUNCT
ejpam-6131	222	1	=	=	NOUN
ejpam-6131	222	2	ζ1(ξ13	ζ1(ξ13	X
ejpam-6131	222	3	,	,	PUNCT
ejpam-6131	222	4	ξ	ξ	PROPN
ejpam-6131	222	5	1	1	NUM
ejpam-6131	222	6	4	4	NUM
ejpam-6131	222	7	,	,	PUNCT
ejpam-6131	222	8	ξ	ξ	PROPN
ejpam-6131	222	9	1	1	NUM
ejpam-6131	222	10	5	5	NUM
ejpam-6131	222	11	,	,	PUNCT
ejpam-6131	222	12	ξ	ξ	PROPN
ejpam-6131	222	13	1	1	NUM
ejpam-6131	222	14	1	1	NUM
ejpam-6131	222	15	,	,	PUNCT
ejpam-6131	222	16	ξ	ξ	PROPN
ejpam-6131	222	17	1	1	NUM
ejpam-6131	222	18	2	2	NUM
ejpam-6131	222	19	)	)	PUNCT
ejpam-6131	222	20	,	,	PUNCT
ejpam-6131	222	21	p(ξ24	p(ξ24	ADJ
ejpam-6131	222	22	)	)	PUNCT
ejpam-6131	223	1	=	=	SYM
ejpam-6131	223	2	ζ1(ξ14	ζ1(ξ14	NOUN
ejpam-6131	223	3	,	,	PUNCT
ejpam-6131	223	4	ξ	ξ	PROPN
ejpam-6131	223	5	1	1	NUM
ejpam-6131	223	6	5	5	NUM
ejpam-6131	223	7	,	,	PUNCT
ejpam-6131	223	8	ξ	ξ	PROPN
ejpam-6131	223	9	1	1	NUM
ejpam-6131	223	10	1	1	NUM
ejpam-6131	223	11	,	,	PUNCT
ejpam-6131	223	12	ξ	ξ	PROPN
ejpam-6131	223	13	1	1	NUM
ejpam-6131	223	14	2	2	NUM
ejpam-6131	223	15	,	,	PUNCT
ejpam-6131	223	16	ξ	ξ	PROPN
ejpam-6131	223	17	1	1	NUM
ejpam-6131	223	18	3	3	NUM
ejpam-6131	223	19	)	)	PUNCT
ejpam-6131	223	20	,	,	PUNCT
ejpam-6131	223	21	p(ξ25	p(ξ25	NOUN
ejpam-6131	223	22	)	)	PUNCT
ejpam-6131	224	1	=	=	NOUN
ejpam-6131	224	2	ζ1(ξ15	ζ1(ξ15	NOUN
ejpam-6131	224	3	,	,	PUNCT
ejpam-6131	224	4	ξ	ξ	PROPN
ejpam-6131	224	5	1	1	NUM
ejpam-6131	224	6	1	1	NUM
ejpam-6131	224	7	,	,	PUNCT
ejpam-6131	224	8	ξ	ξ	PROPN
ejpam-6131	224	9	1	1	NUM
ejpam-6131	224	10	2	2	NUM
ejpam-6131	224	11	,	,	PUNCT
ejpam-6131	224	12	ξ	ξ	PROPN
ejpam-6131	224	13	1	1	NUM
ejpam-6131	224	14	3	3	NUM
ejpam-6131	224	15	,	,	PUNCT
ejpam-6131	224	16	ξ	ξ	PROPN
ejpam-6131	224	17	1	1	NUM
ejpam-6131	224	18	4	4	NUM
ejpam-6131	224	19	)	)	PUNCT
ejpam-6131	224	20	.	.	PUNCT
ejpam-6131	225	1	proceeding	proceed	VERB
ejpam-6131	225	2	similarly	similarly	ADV
ejpam-6131	225	3	,	,	PUNCT
ejpam-6131	225	4	we	we	PRON
ejpam-6131	225	5	obtain	obtain	VERB
ejpam-6131	225	6	p(ξn1	p(ξn1	ADJ
ejpam-6131	225	7	)	)	PUNCT
ejpam-6131	226	1	=	=	PUNCT
ejpam-6131	226	2	ζn−1(ξn−1	ζn−1(ξn−1	PROPN
ejpam-6131	226	3	1	1	NUM
ejpam-6131	226	4	,	,	PUNCT
ejpam-6131	226	5	ξn−1	ξn−1	PROPN
ejpam-6131	226	6	2	2	NUM
ejpam-6131	226	7	,	,	PUNCT
ejpam-6131	226	8	ξn−1	ξn−1	PROPN
ejpam-6131	226	9	3	3	NUM
ejpam-6131	226	10	,	,	PUNCT
ejpam-6131	226	11	ξn−1	ξn−1	PROPN
ejpam-6131	226	12	4	4	NUM
ejpam-6131	226	13	,	,	PUNCT
ejpam-6131	226	14	ξn−1	ξn−1	ADV
ejpam-6131	226	15	5	5	NUM
ejpam-6131	226	16	)	)	PUNCT
ejpam-6131	226	17	,	,	PUNCT
ejpam-6131	226	18	p(ξn2	p(ξn2	NOUN
ejpam-6131	226	19	)	)	PUNCT
ejpam-6131	226	20	=	=	PUNCT
ejpam-6131	226	21	ζn−1(ξn−1	ζn−1(ξn−1	PROPN
ejpam-6131	226	22	2	2	NUM
ejpam-6131	226	23	,	,	PUNCT
ejpam-6131	226	24	ξn−1	ξn−1	PROPN
ejpam-6131	226	25	3	3	NUM
ejpam-6131	226	26	,	,	PUNCT
ejpam-6131	226	27	ξn−1	ξn−1	PROPN
ejpam-6131	226	28	4	4	NUM
ejpam-6131	226	29	,	,	PUNCT
ejpam-6131	226	30	ξn−1	ξn−1	ADV
ejpam-6131	226	31	5	5	NUM
ejpam-6131	226	32	,	,	PUNCT
ejpam-6131	226	33	ξn−1	ξn−1	PROPN
ejpam-6131	226	34	1	1	NUM
ejpam-6131	226	35	)	)	PUNCT
ejpam-6131	226	36	,	,	PUNCT
ejpam-6131	226	37	p(ξn3	p(ξn3	PROPN
ejpam-6131	226	38	)	)	PUNCT
ejpam-6131	226	39	=	=	PUNCT
ejpam-6131	226	40	ζn−1(ξn−1	ζn−1(ξn−1	PROPN
ejpam-6131	226	41	3	3	NUM
ejpam-6131	226	42	,	,	PUNCT
ejpam-6131	226	43	ξn−1	ξn−1	PROPN
ejpam-6131	226	44	4	4	NUM
ejpam-6131	226	45	,	,	PUNCT
ejpam-6131	226	46	ξn−1	ξn−1	ADV
ejpam-6131	226	47	5	5	NUM
ejpam-6131	226	48	,	,	PUNCT
ejpam-6131	226	49	ξn−1	ξn−1	PROPN
ejpam-6131	226	50	1	1	NUM
ejpam-6131	226	51	,	,	PUNCT
ejpam-6131	226	52	ξn−1	ξn−1	PROPN
ejpam-6131	226	53	2	2	NUM
ejpam-6131	226	54	)	)	PUNCT
ejpam-6131	226	55	,	,	PUNCT
ejpam-6131	226	56	p(ξn4	p(ξn4	NOUN
ejpam-6131	226	57	)	)	PUNCT
ejpam-6131	226	58	=	=	PUNCT
ejpam-6131	226	59	ζn−1(ξn−1	ζn−1(ξn−1	PROPN
ejpam-6131	226	60	4	4	NUM
ejpam-6131	226	61	,	,	PUNCT
ejpam-6131	226	62	ξn−1	ξn−1	ADV
ejpam-6131	226	63	5	5	NUM
ejpam-6131	226	64	,	,	PUNCT
ejpam-6131	226	65	ξn−1	ξn−1	PROPN
ejpam-6131	226	66	1	1	NUM
ejpam-6131	226	67	,	,	PUNCT
ejpam-6131	226	68	ξn−1	ξn−1	PROPN
ejpam-6131	226	69	2	2	NUM
ejpam-6131	226	70	,	,	PUNCT
ejpam-6131	226	71	ξn−1	ξn−1	PROPN
ejpam-6131	226	72	3	3	NUM
ejpam-6131	226	73	)	)	PUNCT
ejpam-6131	226	74	,	,	PUNCT
ejpam-6131	226	75	p(ξn5	p(ξn5	NOUN
ejpam-6131	226	76	)	)	PUNCT
ejpam-6131	227	1	=	=	PUNCT
ejpam-6131	227	2	ζn−1(ξn−1	ζn−1(ξn−1	PROPN
ejpam-6131	227	3	5	5	NUM
ejpam-6131	227	4	,	,	PUNCT
ejpam-6131	227	5	ξn−1	ξn−1	PROPN
ejpam-6131	227	6	1	1	NUM
ejpam-6131	227	7	,	,	PUNCT
ejpam-6131	227	8	ξn−1	ξn−1	PROPN
ejpam-6131	227	9	2	2	NUM
ejpam-6131	227	10	,	,	PUNCT
ejpam-6131	227	11	ξn−1	ξn−1	PROPN
ejpam-6131	227	12	3	3	NUM
ejpam-6131	227	13	,	,	PUNCT
ejpam-6131	227	14	ξn−1	ξn−1	ADV
ejpam-6131	227	15	4	4	NUM
ejpam-6131	227	16	)	)	PUNCT
ejpam-6131	227	17	.	.	PUNCT
ejpam-6131	228	1	(	(	PUNCT
ejpam-6131	228	2	4	4	NUM
ejpam-6131	228	3	)	)	PUNCT
ejpam-6131	228	4	(	(	PUNCT
ejpam-6131	228	5	b	b	NOUN
ejpam-6131	228	6	):	):	PUNCT
ejpam-6131	228	7	now	now	ADV
ejpam-6131	228	8	,	,	PUNCT
ejpam-6131	228	9	from	from	ADP
ejpam-6131	228	10	(	(	PUNCT
ejpam-6131	228	11	2	2	NUM
ejpam-6131	228	12	)	)	PUNCT
ejpam-6131	228	13	and	and	CCONJ
ejpam-6131	228	14	(	(	PUNCT
ejpam-6131	228	15	3	3	NUM
ejpam-6131	228	16	)	)	PUNCT
ejpam-6131	228	17	,	,	PUNCT
ejpam-6131	228	18	p(ξo1	p(ξo1	NUM
ejpam-6131	228	19	)	)	PUNCT
ejpam-6131	228	20	⪯	⪯	NOUN
ejpam-6131	228	21	p(ξ11	p(ξ11	NOUN
ejpam-6131	228	22	)	)	PUNCT
ejpam-6131	228	23	,	,	PUNCT
ejpam-6131	228	24	p(ξo3	p(ξo3	NOUN
ejpam-6131	228	25	)	)	PUNCT
ejpam-6131	228	26	⪯	⪯	NOUN
ejpam-6131	228	27	p(ξ13	p(ξ13	NOUN
ejpam-6131	228	28	)	)	PUNCT
ejpam-6131	228	29	,	,	PUNCT
ejpam-6131	228	30	p(ξo5	p(ξo5	PROPN
ejpam-6131	228	31	)	)	PUNCT
ejpam-6131	228	32	⪯	⪯	NOUN
ejpam-6131	228	33	p(ξ15	p(ξ15	NOUN
ejpam-6131	228	34	)	)	PUNCT
ejpam-6131	228	35	,	,	PUNCT
ejpam-6131	228	36	p(ξo2	p(ξo2	NUM
ejpam-6131	228	37	)	)	PUNCT
ejpam-6131	228	38	⪰	⪰	NOUN
ejpam-6131	228	39	s(ξ12	s(ξ12	NOUN
ejpam-6131	228	40	)	)	PUNCT
ejpam-6131	228	41	and	and	CCONJ
ejpam-6131	228	42	s(ξo4	s(ξo4	NOUN
ejpam-6131	228	43	)	)	PUNCT
ejpam-6131	228	44	⪰	⪰	NOUN
ejpam-6131	228	45	s(ξ14	s(ξ14	NOUN
ejpam-6131	228	46	)	)	PUNCT
ejpam-6131	228	47	.	.	PUNCT
ejpam-6131	229	1	then	then	ADV
ejpam-6131	229	2	,	,	PUNCT
ejpam-6131	229	3	∀	∀	X
ejpam-6131	229	4	n	n	PRON
ejpam-6131	229	5	≥	≥	NOUN
ejpam-6131	229	6	0	0	NUM
ejpam-6131	229	7	,	,	PUNCT
ejpam-6131	229	8	by	by	ADP
ejpam-6131	229	9	mathematical	mathematical	ADJ
ejpam-6131	229	10	induction	induction	NOUN
ejpam-6131	229	11	,	,	PUNCT
ejpam-6131	229	12	it	it	PRON
ejpam-6131	229	13	is	be	AUX
ejpam-6131	229	14	obtained	obtain	VERB
ejpam-6131	229	15	that	that	DET
ejpam-6131	229	16	p(ξn1	p(ξn1	PROPN
ejpam-6131	229	17	)	)	PUNCT
ejpam-6131	229	18	⪯	⪯	VERB
ejpam-6131	229	19	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	229	20	1	1	NUM
ejpam-6131	229	21	)	)	PUNCT
ejpam-6131	229	22	,	,	PUNCT
ejpam-6131	229	23	p(ξn3	p(ξn3	PROPN
ejpam-6131	229	24	)	)	PUNCT
ejpam-6131	229	25	⪯	⪯	VERB
ejpam-6131	229	26	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	229	27	3	3	NUM
ejpam-6131	229	28	)	)	PUNCT
ejpam-6131	229	29	,	,	PUNCT
ejpam-6131	229	30	p(ξn5	p(ξn5	NOUN
ejpam-6131	229	31	)	)	PUNCT
ejpam-6131	229	32	⪯	⪯	VERB
ejpam-6131	229	33	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	229	34	5	5	NUM
ejpam-6131	229	35	)	)	PUNCT
ejpam-6131	229	36	,	,	PUNCT
ejpam-6131	229	37	p(ξn2	p(ξn2	NOUN
ejpam-6131	229	38	)	)	PUNCT
ejpam-6131	229	39	⪰	⪰	VERB
ejpam-6131	229	40	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	229	41	2	2	NUM
ejpam-6131	229	42	)	)	PUNCT
ejpam-6131	229	43	,	,	PUNCT
ejpam-6131	229	44	and	and	CCONJ
ejpam-6131	229	45	p(ξn4	p(ξn4	NOUN
ejpam-6131	229	46	)	)	PUNCT
ejpam-6131	229	47	⪰	⪰	NOUN
ejpam-6131	229	48	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	229	49	4	4	NUM
ejpam-6131	229	50	)	)	PUNCT
ejpam-6131	229	51	.	.	PUNCT
ejpam-6131	230	1	(	(	PUNCT
ejpam-6131	230	2	5	5	NUM
ejpam-6131	230	3	)	)	PUNCT
ejpam-6131	230	4	hence	hence	ADV
ejpam-6131	230	5	,	,	PUNCT
ejpam-6131	230	6	(	(	PUNCT
ejpam-6131	230	7	4	4	NUM
ejpam-6131	230	8	)	)	PUNCT
ejpam-6131	230	9	and	and	CCONJ
ejpam-6131	230	10	(	(	PUNCT
ejpam-6131	230	11	5	5	X
ejpam-6131	230	12	)	)	PUNCT
ejpam-6131	230	13	complete	complete	VERB
ejpam-6131	230	14	the	the	DET
ejpam-6131	230	15	required	require	VERB
ejpam-6131	230	16	result	result	NOUN
ejpam-6131	230	17	.	.	PUNCT
ejpam-6131	231	1	our	our	PRON
ejpam-6131	231	2	next	next	ADJ
ejpam-6131	231	3	theorem	theorem	NOUN
ejpam-6131	231	4	is	be	AUX
ejpam-6131	231	5	the	the	DET
ejpam-6131	231	6	core	core	ADJ
ejpam-6131	231	7	part	part	NOUN
ejpam-6131	231	8	of	of	ADP
ejpam-6131	231	9	this	this	DET
ejpam-6131	231	10	section	section	NOUN
ejpam-6131	231	11	.	.	PUNCT
ejpam-6131	232	1	s.	s.	PROPN
ejpam-6131	232	2	batul	batul	PROPN
ejpam-6131	232	3	et	et	PROPN
ejpam-6131	232	4	a.	a.	PROPN
ejpam-6131	232	5	/	/	PUNCT
ejpam-6131	232	6	eur	eur	PROPN
ejpam-6131	232	7	.	.	PUNCT
ejpam-6131	233	1	j.	j.	PROPN
ejpam-6131	233	2	pure	pure	PROPN
ejpam-6131	233	3	appl	appl	PROPN
ejpam-6131	233	4	.	.	PROPN
ejpam-6131	233	5	math	math	PROPN
ejpam-6131	233	6	,	,	PUNCT
ejpam-6131	233	7	18	18	NUM
ejpam-6131	233	8	(	(	PUNCT
ejpam-6131	233	9	2	2	NUM
ejpam-6131	233	10	)	)	PUNCT
ejpam-6131	233	11	(	(	PUNCT
ejpam-6131	233	12	2025	2025	NUM
ejpam-6131	233	13	)	)	PUNCT
ejpam-6131	233	14	,	,	PUNCT
ejpam-6131	233	15	6131	6131	NUM
ejpam-6131	233	16	11	11	NUM
ejpam-6131	233	17	of	of	ADP
ejpam-6131	233	18	22	22	NUM
ejpam-6131	233	19	theorem	theorem	NOUN
ejpam-6131	233	20	1	1	NUM
ejpam-6131	233	21	.	.	PUNCT
ejpam-6131	233	22	suppose	suppose	VERB
ejpam-6131	233	23	that	that	SCONJ
ejpam-6131	233	24	all	all	DET
ejpam-6131	233	25	suppositions	supposition	NOUN
ejpam-6131	233	26	of	of	ADP
ejpam-6131	233	27	lemma	lemma	PROPN
ejpam-6131	233	28	2	2	NUM
ejpam-6131	233	29	hold	hold	NOUN
ejpam-6131	233	30	,	,	PUNCT
ejpam-6131	233	31	let	let	VERB
ejpam-6131	233	32	{	{	PUNCT
ejpam-6131	233	33	ζi}i∈w	ζi}i∈w	X
ejpam-6131	233	34	and	and	CCONJ
ejpam-6131	233	35	p	p	PROPN
ejpam-6131	233	36	be	be	AUX
ejpam-6131	233	37	two	two	NUM
ejpam-6131	233	38	monotonically	monotonically	ADV
ejpam-6131	233	39	decreasing	decrease	VERB
ejpam-6131	233	40	mappings	mapping	NOUN
ejpam-6131	233	41	such	such	ADJ
ejpam-6131	233	42	that	that	SCONJ
ejpam-6131	233	43	they	they	PRON
ejpam-6131	233	44	satisfy	satisfy	VERB
ejpam-6131	233	45	(	(	PUNCT
ejpam-6131	233	46	c	c	NOUN
ejpam-6131	233	47	)	)	PUNCT
ejpam-6131	233	48	condition	condition	NOUN
ejpam-6131	233	49	.	.	PUNCT
ejpam-6131	234	1	in	in	ADP
ejpam-6131	234	2	addition	addition	NOUN
ejpam-6131	234	3	,	,	PUNCT
ejpam-6131	234	4	suppose	suppose	VERB
ejpam-6131	234	5	that	that	SCONJ
ejpam-6131	234	6	both	both	DET
ejpam-6131	234	7	mappings	mapping	NOUN
ejpam-6131	234	8	are	be	AUX
ejpam-6131	234	9	compatible	compatible	ADJ
ejpam-6131	234	10	and	and	CCONJ
ejpam-6131	234	11	weakly	weakly	ADV
ejpam-6131	234	12	reciprocally	reciprocally	ADV
ejpam-6131	234	13	continuous	continuous	ADJ
ejpam-6131	234	14	and	and	CCONJ
ejpam-6131	234	15	p	p	NOUN
ejpam-6131	234	16	is	be	AUX
ejpam-6131	234	17	continuous	continuous	ADJ
ejpam-6131	234	18	.	.	PUNCT
ejpam-6131	235	1	if	if	SCONJ
ejpam-6131	235	2	p(g	p(g	NOUN
ejpam-6131	235	3	)	)	PUNCT
ejpam-6131	235	4	⊆	⊆	NUM
ejpam-6131	235	5	g	g	NOUN
ejpam-6131	235	6	is	be	AUX
ejpam-6131	235	7	complete	complete	ADJ
ejpam-6131	235	8	and	and	CCONJ
ejpam-6131	235	9	regular	regular	ADJ
ejpam-6131	235	10	,	,	PUNCT
ejpam-6131	235	11	then	then	ADV
ejpam-6131	235	12	there	there	PRON
ejpam-6131	235	13	exists	exist	VERB
ejpam-6131	235	14	a	a	DET
ejpam-6131	235	15	quintuple	quintuple	ADJ
ejpam-6131	235	16	coincidence	coincidence	NOUN
ejpam-6131	235	17	point	point	NOUN
ejpam-6131	235	18	(	(	PUNCT
ejpam-6131	235	19	qcp	qcp	INTJ
ejpam-6131	235	20	)	)	PUNCT
ejpam-6131	235	21	of	of	ADP
ejpam-6131	235	22	{	{	PUNCT
ejpam-6131	235	23	ζi}i∈w	ζi}i∈w	X
ejpam-6131	235	24	and	and	CCONJ
ejpam-6131	235	25	p	p	NOUN
ejpam-6131	235	26	provided	provide	VERB
ejpam-6131	235	27	that	that	SCONJ
ejpam-6131	235	28	γ̃	γ̃	PROPN
ejpam-6131	235	29	,	,	PUNCT
ejpam-6131	235	30	υ̃	υ̃	PROPN
ejpam-6131	235	31	̸=	̸=	PROPN
ejpam-6131	235	32	o	o	PROPN
ejpam-6131	235	33	belongs	belong	VERB
ejpam-6131	235	34	to	to	ADP
ejpam-6131	235	35	zm	zm	PROPN
ejpam-6131	235	36	.	.	PUNCT
ejpam-6131	236	1	proof	proof	NOUN
ejpam-6131	236	2	.	.	PUNCT
ejpam-6131	237	1	let	let	VERB
ejpam-6131	237	2	{	{	PUNCT
ejpam-6131	237	3	ξn1	ξn1	PROPN
ejpam-6131	237	4	}	}	PUNCT
ejpam-6131	237	5	,	,	PUNCT
ejpam-6131	237	6	{	{	PUNCT
ejpam-6131	237	7	ξn2	ξn2	NOUN
ejpam-6131	237	8	}	}	PUNCT
ejpam-6131	237	9	,	,	PUNCT
ejpam-6131	237	10	{	{	PUNCT
ejpam-6131	237	11	ξn3	ξn3	NOUN
ejpam-6131	237	12	}	}	PUNCT
ejpam-6131	237	13	,	,	PUNCT
ejpam-6131	237	14	{	{	PUNCT
ejpam-6131	237	15	ξn4	ξn4	NOUN
ejpam-6131	237	16	}	}	PUNCT
ejpam-6131	237	17	and	and	CCONJ
ejpam-6131	237	18	{	{	PUNCT
ejpam-6131	237	19	ξn5	ξn5	NOUN
ejpam-6131	237	20	}	}	PUNCT
ejpam-6131	237	21	be	be	AUX
ejpam-6131	237	22	the	the	DET
ejpam-6131	237	23	sequences	sequence	NOUN
ejpam-6131	237	24	in	in	ADP
ejpam-6131	237	25	g	g	PROPN
ejpam-6131	237	26	constructed	construct	VERB
ejpam-6131	237	27	by	by	ADP
ejpam-6131	237	28	lemma	lemma	PROPN
ejpam-6131	237	29	2	2	NUM
ejpam-6131	237	30	,	,	PUNCT
ejpam-6131	237	31	then	then	ADV
ejpam-6131	237	32	from	from	ADP
ejpam-6131	237	33	(	(	PUNCT
ejpam-6131	237	34	2	2	X
ejpam-6131	237	35	)	)	PUNCT
ejpam-6131	237	36	it	it	PRON
ejpam-6131	237	37	follows	follow	VERB
ejpam-6131	237	38	that	that	SCONJ
ejpam-6131	237	39	t(p(ξn1	t(p(ξn1	PROPN
ejpam-6131	237	40	)	)	PUNCT
ejpam-6131	237	41	,	,	PUNCT
ejpam-6131	237	42	(	(	PUNCT
ejpam-6131	237	43	ξ	ξ	X
ejpam-6131	237	44	n+1	n+1	PROPN
ejpam-6131	237	45	1	1	NUM
ejpam-6131	237	46	)	)	PUNCT
ejpam-6131	237	47	)	)	PUNCT
ejpam-6131	238	1	=	=	PUNCT
ejpam-6131	238	2	t(ζn−1(ξn−1	t(ζn−1(ξn−1	PROPN
ejpam-6131	238	3	1	1	NUM
ejpam-6131	238	4	,	,	PUNCT
ejpam-6131	238	5	ξn−1	ξn−1	PROPN
ejpam-6131	238	6	2	2	NUM
ejpam-6131	238	7	,	,	PUNCT
ejpam-6131	238	8	ξn−1	ξn−1	PROPN
ejpam-6131	238	9	3	3	NUM
ejpam-6131	238	10	,	,	PUNCT
ejpam-6131	238	11	ξn−1	ξn−1	PROPN
ejpam-6131	238	12	4	4	NUM
ejpam-6131	238	13	,	,	PUNCT
ejpam-6131	238	14	ξn−1	ξn−1	ADV
ejpam-6131	238	15	5	5	NUM
ejpam-6131	238	16	)	)	PUNCT
ejpam-6131	238	17	,	,	PUNCT
ejpam-6131	238	18	ζn(ξn1	ζn(ξn1	PROPN
ejpam-6131	238	19	,	,	PUNCT
ejpam-6131	238	20	ξ	ξ	PROPN
ejpam-6131	238	21	n	n	PRON
ejpam-6131	238	22	2	2	NUM
ejpam-6131	238	23	,	,	PUNCT
ejpam-6131	238	24	ξ	ξ	PROPN
ejpam-6131	238	25	n	n	PRON
ejpam-6131	238	26	3	3	NUM
ejpam-6131	238	27	,	,	PUNCT
ejpam-6131	238	28	ξ	ξ	PROPN
ejpam-6131	238	29	n	n	PRON
ejpam-6131	238	30	4	4	NUM
ejpam-6131	238	31	,	,	PUNCT
ejpam-6131	238	32	ξ	ξ	PROPN
ejpam-6131	238	33	n	n	PRON
ejpam-6131	238	34	5	5	NUM
ejpam-6131	238	35	)	)	PUNCT
ejpam-6131	238	36	)	)	PUNCT
ejpam-6131	238	37	≤	≤	NOUN
ejpam-6131	238	38	γ̃[t(p(ξn−1	γ̃[t(p(ξn−1	PRON
ejpam-6131	238	39	1	1	NUM
ejpam-6131	238	40	)	)	PUNCT
ejpam-6131	238	41	,	,	PUNCT
ejpam-6131	238	42	ζn−1(ξn−1	ζn−1(ξn−1	PROPN
ejpam-6131	238	43	1	1	NUM
ejpam-6131	238	44	,	,	PUNCT
ejpam-6131	238	45	ξn−1	ξn−1	PROPN
ejpam-6131	238	46	2	2	NUM
ejpam-6131	238	47	,	,	PUNCT
ejpam-6131	238	48	ξn−1	ξn−1	PROPN
ejpam-6131	238	49	3	3	NUM
ejpam-6131	238	50	,	,	PUNCT
ejpam-6131	238	51	ξn−1	ξn−1	PROPN
ejpam-6131	238	52	4	4	NUM
ejpam-6131	238	53	,	,	PUNCT
ejpam-6131	238	54	ξn−1	ξn−1	ADV
ejpam-6131	238	55	5	5	NUM
ejpam-6131	238	56	)	)	PUNCT
ejpam-6131	238	57	)	)	PUNCT
ejpam-6131	239	1	+	+	CCONJ
ejpam-6131	239	2	t(p(ξn1	t(p(ξn1	X
ejpam-6131	239	3	)	)	PUNCT
ejpam-6131	239	4	,	,	PUNCT
ejpam-6131	239	5	ζ	ζ	PROPN
ejpam-6131	239	6	n(ξn1	n(ξn1	PROPN
ejpam-6131	239	7	,	,	PUNCT
ejpam-6131	239	8	ξ	ξ	PROPN
ejpam-6131	239	9	n	n	NUM
ejpam-6131	239	10	2	2	NUM
ejpam-6131	239	11	,	,	PUNCT
ejpam-6131	239	12	ξ	ξ	PROPN
ejpam-6131	239	13	n	n	PRON
ejpam-6131	239	14	3	3	NUM
ejpam-6131	239	15	,	,	PUNCT
ejpam-6131	239	16	ξ	ξ	PROPN
ejpam-6131	239	17	n	n	PRON
ejpam-6131	239	18	4	4	NUM
ejpam-6131	239	19	,	,	PUNCT
ejpam-6131	239	20	ξ	ξ	PROPN
ejpam-6131	239	21	n	n	PRON
ejpam-6131	239	22	5	5	NUM
ejpam-6131	239	23	)	)	PUNCT
ejpam-6131	239	24	)	)	PUNCT
ejpam-6131	239	25	]	]	PUNCT
ejpam-6131	240	1	+	+	CCONJ
ejpam-6131	240	2	υ̃(t(p(ξn−1	υ̃(t(p(ξn−1	PROPN
ejpam-6131	240	3	1	1	NUM
ejpam-6131	240	4	)	)	PUNCT
ejpam-6131	240	5	,	,	PUNCT
ejpam-6131	240	6	p(ξn1	p(ξn1	PROPN
ejpam-6131	240	7	)	)	PUNCT
ejpam-6131	240	8	)	)	PUNCT
ejpam-6131	240	9	)	)	PUNCT
ejpam-6131	241	1	=	=	SYM
ejpam-6131	241	2	(	(	PUNCT
ejpam-6131	241	3	γ̃	γ̃	PROPN
ejpam-6131	241	4	+	+	CCONJ
ejpam-6131	241	5	υ̃)t(p(ξn−1	υ̃)t(p(ξn−1	PROPN
ejpam-6131	241	6	1	1	NUM
ejpam-6131	241	7	)	)	PUNCT
ejpam-6131	241	8	,	,	PUNCT
ejpam-6131	241	9	p(ξn1	p(ξn1	PROPN
ejpam-6131	241	10	)	)	PUNCT
ejpam-6131	241	11	)	)	PUNCT
ejpam-6131	242	1	+	+	CCONJ
ejpam-6131	242	2	γ̃t(p(ξn1	γ̃t(p(ξn1	ADJ
ejpam-6131	242	3	)	)	PUNCT
ejpam-6131	242	4	,	,	PUNCT
ejpam-6131	242	5	p(ξ	p(ξ	PROPN
ejpam-6131	242	6	n+1	n+1	ADV
ejpam-6131	242	7	1	1	NUM
ejpam-6131	242	8	)	)	PUNCT
ejpam-6131	242	9	)	)	PUNCT
ejpam-6131	242	10	.	.	PUNCT
ejpam-6131	243	1	it	it	PRON
ejpam-6131	243	2	results	result	VERB
ejpam-6131	243	3	in	in	ADP
ejpam-6131	243	4	t(p(ξn1	t(p(ξn1	PROPN
ejpam-6131	243	5	)	)	PUNCT
ejpam-6131	243	6	,	,	PUNCT
ejpam-6131	243	7	p(ξ	p(ξ	PROPN
ejpam-6131	243	8	n+1	n+1	ADV
ejpam-6131	243	9	1	1	NUM
ejpam-6131	243	10	)	)	PUNCT
ejpam-6131	243	11	)	)	PUNCT
ejpam-6131	243	12	≤	≤	NOUN
ejpam-6131	243	13	(	(	PUNCT
ejpam-6131	243	14	γ̃	γ̃	PROPN
ejpam-6131	243	15	+	+	CCONJ
ejpam-6131	243	16	υ̃)(i	υ̃)(i	NOUN
ejpam-6131	243	17	−	−	PROPN
ejpam-6131	243	18	γ̃)−1t(p(ξn−1	γ̃)−1t(p(ξn−1	PROPN
ejpam-6131	243	19	1	1	NUM
ejpam-6131	243	20	)	)	PUNCT
ejpam-6131	243	21	,	,	PUNCT
ejpam-6131	243	22	p(ξn1	p(ξn1	PROPN
ejpam-6131	243	23	)	)	PUNCT
ejpam-6131	243	24	)	)	PUNCT
ejpam-6131	243	25	.	.	PUNCT
ejpam-6131	244	1	(	(	PUNCT
ejpam-6131	244	2	6	6	NUM
ejpam-6131	244	3	)	)	PUNCT
ejpam-6131	244	4	similar	similar	ADJ
ejpam-6131	244	5	operations	operation	NOUN
ejpam-6131	244	6	generate	generate	VERB
ejpam-6131	244	7	t(p(ξn2	t(p(ξn2	NOUN
ejpam-6131	244	8	)	)	PUNCT
ejpam-6131	244	9	,	,	PUNCT
ejpam-6131	244	10	p(ξ	p(ξ	PROPN
ejpam-6131	244	11	n+1	n+1	ADV
ejpam-6131	244	12	2	2	NUM
ejpam-6131	244	13	)	)	PUNCT
ejpam-6131	244	14	)	)	PUNCT
ejpam-6131	244	15	≤	≤	NOUN
ejpam-6131	244	16	(	(	PUNCT
ejpam-6131	244	17	γ̃	γ̃	PROPN
ejpam-6131	244	18	+	+	CCONJ
ejpam-6131	244	19	υ̃)(i	υ̃)(i	NOUN
ejpam-6131	244	20	−	−	PROPN
ejpam-6131	244	21	γ̃)−1t(p(ξn−1	γ̃)−1t(p(ξn−1	PROPN
ejpam-6131	244	22	2	2	NUM
ejpam-6131	244	23	)	)	PUNCT
ejpam-6131	244	24	,	,	PUNCT
ejpam-6131	244	25	p(ξn2	p(ξn2	NOUN
ejpam-6131	244	26	)	)	PUNCT
ejpam-6131	244	27	)	)	PUNCT
ejpam-6131	244	28	,	,	PUNCT
ejpam-6131	244	29	t(p(ξn3	t(p(ξn3	PROPN
ejpam-6131	244	30	)	)	PUNCT
ejpam-6131	244	31	,	,	PUNCT
ejpam-6131	245	1	p(ξ	p(ξ	PROPN
ejpam-6131	245	2	n+1	n+1	ADV
ejpam-6131	245	3	3	3	NUM
ejpam-6131	245	4	)	)	PUNCT
ejpam-6131	245	5	)	)	PUNCT
ejpam-6131	246	1	≤	≤	NOUN
ejpam-6131	246	2	(	(	PUNCT
ejpam-6131	246	3	γ̃	γ̃	PROPN
ejpam-6131	246	4	+	+	CCONJ
ejpam-6131	246	5	υ̃)(i	υ̃)(i	NOUN
ejpam-6131	246	6	−	−	PROPN
ejpam-6131	246	7	γ̃)−1t(p(ξn−1	γ̃)−1t(p(ξn−1	PROPN
ejpam-6131	246	8	3	3	NUM
ejpam-6131	246	9	)	)	PUNCT
ejpam-6131	246	10	,	,	PUNCT
ejpam-6131	246	11	p(ξn3	p(ξn3	PROPN
ejpam-6131	246	12	)	)	PUNCT
ejpam-6131	246	13	)	)	PUNCT
ejpam-6131	246	14	,	,	PUNCT
ejpam-6131	246	15	t(p(ξn4	t(p(ξn4	PROPN
ejpam-6131	246	16	)	)	PUNCT
ejpam-6131	246	17	,	,	PUNCT
ejpam-6131	246	18	p(ξ	p(ξ	PROPN
ejpam-6131	246	19	n+1	n+1	ADV
ejpam-6131	246	20	4	4	NUM
ejpam-6131	246	21	)	)	PUNCT
ejpam-6131	246	22	)	)	PUNCT
ejpam-6131	246	23	≤	≤	NOUN
ejpam-6131	246	24	(	(	PUNCT
ejpam-6131	246	25	γ̃	γ̃	PROPN
ejpam-6131	246	26	+	+	CCONJ
ejpam-6131	246	27	υ̃)(i	υ̃)(i	NOUN
ejpam-6131	246	28	−	−	PROPN
ejpam-6131	246	29	γ̃)−1t(p(ξn−1	γ̃)−1t(p(ξn−1	PROPN
ejpam-6131	246	30	4	4	NUM
ejpam-6131	246	31	)	)	PUNCT
ejpam-6131	246	32	,	,	PUNCT
ejpam-6131	246	33	p(ξn4	p(ξn4	NOUN
ejpam-6131	246	34	)	)	PUNCT
ejpam-6131	246	35	)	)	PUNCT
ejpam-6131	246	36	,	,	PUNCT
ejpam-6131	246	37	(	(	PUNCT
ejpam-6131	246	38	7	7	X
ejpam-6131	246	39	)	)	PUNCT
ejpam-6131	246	40	and	and	CCONJ
ejpam-6131	246	41	t(p(ξn5	t(p(ξn5	PROPN
ejpam-6131	246	42	)	)	PUNCT
ejpam-6131	246	43	,	,	PUNCT
ejpam-6131	246	44	p(ξ	p(ξ	PROPN
ejpam-6131	246	45	n+1	n+1	ADV
ejpam-6131	246	46	5	5	NUM
ejpam-6131	246	47	)	)	PUNCT
ejpam-6131	246	48	)	)	PUNCT
ejpam-6131	246	49	≤	≤	NOUN
ejpam-6131	246	50	(	(	PUNCT
ejpam-6131	246	51	γ̃	γ̃	PROPN
ejpam-6131	246	52	+	+	CCONJ
ejpam-6131	246	53	υ̃)(i	υ̃)(i	NOUN
ejpam-6131	246	54	−	−	PROPN
ejpam-6131	246	55	γ̃)−1t(p(ξn−1	γ̃)−1t(p(ξn−1	PROPN
ejpam-6131	246	56	5	5	NUM
ejpam-6131	246	57	)	)	PUNCT
ejpam-6131	246	58	,	,	PUNCT
ejpam-6131	246	59	p(ξn5	p(ξn5	NOUN
ejpam-6131	246	60	)	)	PUNCT
ejpam-6131	246	61	)	)	PUNCT
ejpam-6131	246	62	.	.	PUNCT
ejpam-6131	247	1	(	(	PUNCT
ejpam-6131	247	2	8)	8)	NUM
ejpam-6131	247	3	adding	add	VERB
ejpam-6131	247	4	(	(	PUNCT
ejpam-6131	247	5	3.6	3.6	NUM
ejpam-6131	247	6	)	)	PUNCT
ejpam-6131	247	7	(	(	PUNCT
ejpam-6131	247	8	3.8	3.8	NUM
ejpam-6131	247	9	)	)	PUNCT
ejpam-6131	247	10	,	,	PUNCT
ejpam-6131	247	11	one	one	NUM
ejpam-6131	247	12	writes	write	VERB
ejpam-6131	247	13	µn	µn	NOUN
ejpam-6131	247	14	=	=	SYM
ejpam-6131	247	15	t(p(ξn1	t(p(ξn1	PROPN
ejpam-6131	247	16	)	)	PUNCT
ejpam-6131	247	17	,	,	PUNCT
ejpam-6131	247	18	p(ξ	p(ξ	PROPN
ejpam-6131	247	19	n+1	n+1	ADV
ejpam-6131	247	20	1	1	NUM
ejpam-6131	247	21	)	)	PUNCT
ejpam-6131	247	22	)	)	PUNCT
ejpam-6131	248	1	+	+	CCONJ
ejpam-6131	248	2	t(p(ξn2	t(p(ξn2	NOUN
ejpam-6131	248	3	)	)	PUNCT
ejpam-6131	248	4	,	,	PUNCT
ejpam-6131	248	5	p(ξ	p(ξ	PROPN
ejpam-6131	248	6	n+1	n+1	ADV
ejpam-6131	248	7	2	2	NUM
ejpam-6131	248	8	)	)	PUNCT
ejpam-6131	248	9	)	)	PUNCT
ejpam-6131	249	1	+	+	CCONJ
ejpam-6131	249	2	t(p(ξn3	t(p(ξn3	PROPN
ejpam-6131	249	3	)	)	PUNCT
ejpam-6131	249	4	,	,	PUNCT
ejpam-6131	249	5	p(ξ	p(ξ	PROPN
ejpam-6131	249	6	n+1	n+1	ADV
ejpam-6131	249	7	3	3	NUM
ejpam-6131	249	8	)	)	PUNCT
ejpam-6131	249	9	)	)	PUNCT
ejpam-6131	250	1	+	+	CCONJ
ejpam-6131	250	2	t(p(ξn4	t(p(ξn4	NOUN
ejpam-6131	250	3	)	)	PUNCT
ejpam-6131	250	4	,	,	PUNCT
ejpam-6131	250	5	p(ξ	p(ξ	PROPN
ejpam-6131	250	6	n+1	n+1	ADV
ejpam-6131	250	7	4	4	NUM
ejpam-6131	250	8	)	)	PUNCT
ejpam-6131	250	9	)	)	PUNCT
ejpam-6131	251	1	+	+	CCONJ
ejpam-6131	251	2	t(p(ξn5	t(p(ξn5	PROPN
ejpam-6131	251	3	)	)	PUNCT
ejpam-6131	251	4	,	,	PUNCT
ejpam-6131	251	5	p(ξ	p(ξ	PROPN
ejpam-6131	251	6	n+1	n+1	ADV
ejpam-6131	251	7	5	5	NUM
ejpam-6131	251	8	)	)	PUNCT
ejpam-6131	251	9	)	)	PUNCT
ejpam-6131	251	10	≤	≤	NOUN
ejpam-6131	251	11	(	(	PUNCT
ejpam-6131	251	12	γ̃	γ̃	PROPN
ejpam-6131	251	13	+	+	CCONJ
ejpam-6131	251	14	υ̃)(i	υ̃)(i	NOUN
ejpam-6131	252	1	−	−	NOUN
ejpam-6131	252	2	γ̃)−1[t(p(ξn−1	γ̃)−1[t(p(ξn−1	PROPN
ejpam-6131	252	3	1	1	NUM
ejpam-6131	252	4	)	)	PUNCT
ejpam-6131	252	5	,	,	PUNCT
ejpam-6131	252	6	p(ξn1	p(ξn1	PROPN
ejpam-6131	252	7	)	)	PUNCT
ejpam-6131	252	8	)	)	PUNCT
ejpam-6131	253	1	+	+	CCONJ
ejpam-6131	253	2	t(p(ξn−1	t(p(ξn−1	PROPN
ejpam-6131	253	3	2	2	NUM
ejpam-6131	253	4	)	)	PUNCT
ejpam-6131	253	5	,	,	PUNCT
ejpam-6131	253	6	p(ξn2	p(ξn2	NOUN
ejpam-6131	253	7	)	)	PUNCT
ejpam-6131	253	8	)	)	PUNCT
ejpam-6131	254	1	+	+	CCONJ
ejpam-6131	254	2	t(p(ξn−1	t(p(ξn−1	INTJ
ejpam-6131	254	3	3	3	NUM
ejpam-6131	254	4	)	)	PUNCT
ejpam-6131	254	5	,	,	PUNCT
ejpam-6131	254	6	p(ξn3	p(ξn3	PROPN
ejpam-6131	254	7	)	)	PUNCT
ejpam-6131	254	8	)	)	PUNCT
ejpam-6131	255	1	+	+	CCONJ
ejpam-6131	255	2	t(p(ξn−1	t(p(ξn−1	PROPN
ejpam-6131	255	3	4	4	NUM
ejpam-6131	255	4	)	)	PUNCT
ejpam-6131	255	5	,	,	PUNCT
ejpam-6131	255	6	p	p	X
ejpam-6131	255	7	(	(	PUNCT
ejpam-6131	255	8	ξn4	ξn4	NOUN
ejpam-6131	255	9	)	)	PUNCT
ejpam-6131	255	10	)	)	PUNCT
ejpam-6131	256	1	+	+	CCONJ
ejpam-6131	256	2	t(p(ξn−1	t(p(ξn−1	INTJ
ejpam-6131	256	3	5	5	NUM
ejpam-6131	256	4	)	)	PUNCT
ejpam-6131	256	5	,	,	PUNCT
ejpam-6131	256	6	p	p	X
ejpam-6131	256	7	(	(	PUNCT
ejpam-6131	256	8	ξn5	ξn5	NOUN
ejpam-6131	256	9	)	)	PUNCT
ejpam-6131	256	10	)	)	PUNCT
ejpam-6131	256	11	]	]	PUNCT
ejpam-6131	257	1	=	=	PUNCT
ejpam-6131	257	2	(	(	PUNCT
ejpam-6131	257	3	γ̃	γ̃	PROPN
ejpam-6131	257	4	+	+	CCONJ
ejpam-6131	257	5	υ̃)(i	υ̃)(i	NOUN
ejpam-6131	257	6	−	−	NOUN
ejpam-6131	257	7	γ̃)−1µn−1	γ̃)−1µn−1	PROPN
ejpam-6131	257	8	.	.	PUNCT
ejpam-6131	258	1	take	take	VERB
ejpam-6131	258	2	(	(	PUNCT
ejpam-6131	258	3	γ̃	γ̃	PROPN
ejpam-6131	258	4	+	+	CCONJ
ejpam-6131	258	5	υ̃)(i	υ̃)(i	NOUN
ejpam-6131	258	6	−	−	NOUN
ejpam-6131	258	7	γ̃)−1	γ̃)−1	NOUN
ejpam-6131	258	8	=	=	SYM
ejpam-6131	258	9	q	q	NOUN
ejpam-6131	258	10	,	,	PUNCT
ejpam-6131	258	11	hence	hence	ADV
ejpam-6131	258	12	for	for	ADP
ejpam-6131	258	13	n	n	PRON
ejpam-6131	258	14	∈	∈	PROPN
ejpam-6131	258	15	n	n	CCONJ
ejpam-6131	258	16	,	,	PUNCT
ejpam-6131	258	17	o	o	NOUN
ejpam-6131	258	18	≤	≤	NUM
ejpam-6131	258	19	µn	µn	NOUN
ejpam-6131	258	20	≤	≤	NUM
ejpam-6131	259	1	qµn−1	qµn−1	PROPN
ejpam-6131	259	2	≤	≤	NOUN
ejpam-6131	259	3	q2µn−2	q2µn−2	NUM
ejpam-6131	259	4	≤	≤	NOUN
ejpam-6131	259	5	·	·	PUNCT
ejpam-6131	259	6	·	·	PUNCT
ejpam-6131	259	7	·	·	PUNCT
ejpam-6131	260	1	≤	≤	NUM
ejpam-6131	260	2	qnµo	qnµo	ADJ
ejpam-6131	260	3	.	.	PUNCT
ejpam-6131	261	1	in	in	ADP
ejpam-6131	261	2	light	light	NOUN
ejpam-6131	261	3	of	of	ADP
ejpam-6131	261	4	triangular	triangular	NOUN
ejpam-6131	261	5	inequality	inequality	NOUN
ejpam-6131	261	6	,	,	PUNCT
ejpam-6131	261	7	for	for	ADP
ejpam-6131	261	8	m	m	PROPN
ejpam-6131	261	9	>	>	X
ejpam-6131	261	10	0	0	NUM
ejpam-6131	261	11	,	,	PUNCT
ejpam-6131	261	12	t(p(ξn1	t(p(ξn1	PROPN
ejpam-6131	261	13	)	)	PUNCT
ejpam-6131	261	14	,	,	PUNCT
ejpam-6131	261	15	p(ξ	p(ξ	PROPN
ejpam-6131	261	16	n+m	n+m	NUM
ejpam-6131	261	17	1	1	NUM
ejpam-6131	261	18	)	)	PUNCT
ejpam-6131	261	19	)	)	PUNCT
ejpam-6131	262	1	+	+	CCONJ
ejpam-6131	262	2	t(p(ξn2	t(p(ξn2	NOUN
ejpam-6131	262	3	)	)	PUNCT
ejpam-6131	262	4	,	,	PUNCT
ejpam-6131	262	5	p(ξ	p(ξ	PROPN
ejpam-6131	262	6	n+m	n+m	NUM
ejpam-6131	262	7	2	2	NUM
ejpam-6131	262	8	)	)	PUNCT
ejpam-6131	262	9	)	)	PUNCT
ejpam-6131	263	1	+	+	CCONJ
ejpam-6131	263	2	t(p(ξn3	t(p(ξn3	PROPN
ejpam-6131	263	3	)	)	PUNCT
ejpam-6131	263	4	,	,	PUNCT
ejpam-6131	263	5	p(ξ	p(ξ	PROPN
ejpam-6131	263	6	n+m	n+m	NUM
ejpam-6131	263	7	3	3	NUM
ejpam-6131	263	8	)	)	PUNCT
ejpam-6131	263	9	)	)	PUNCT
ejpam-6131	264	1	+	+	CCONJ
ejpam-6131	264	2	t(p(ξn4	t(p(ξn4	NOUN
ejpam-6131	264	3	)	)	PUNCT
ejpam-6131	264	4	,	,	PUNCT
ejpam-6131	264	5	p(ξ	p(ξ	PROPN
ejpam-6131	264	6	n+m	n+m	NUM
ejpam-6131	264	7	4	4	NUM
ejpam-6131	264	8	)	)	PUNCT
ejpam-6131	264	9	)	)	PUNCT
ejpam-6131	265	1	+	+	CCONJ
ejpam-6131	265	2	t(p(ξn5	t(p(ξn5	PROPN
ejpam-6131	265	3	)	)	PUNCT
ejpam-6131	265	4	,	,	PUNCT
ejpam-6131	265	5	p(ξ	p(ξ	PROPN
ejpam-6131	265	6	n+m	n+m	NUM
ejpam-6131	265	7	5	5	NUM
ejpam-6131	265	8	)	)	PUNCT
ejpam-6131	265	9	)	)	PUNCT
ejpam-6131	266	1	s.	s.	PROPN
ejpam-6131	266	2	batul	batul	PROPN
ejpam-6131	266	3	et	et	PROPN
ejpam-6131	266	4	a.	a.	PROPN
ejpam-6131	266	5	/	/	PUNCT
ejpam-6131	266	6	eur	eur	PROPN
ejpam-6131	266	7	.	.	PUNCT
ejpam-6131	267	1	j.	j.	PROPN
ejpam-6131	267	2	pure	pure	PROPN
ejpam-6131	267	3	appl	appl	PROPN
ejpam-6131	267	4	.	.	PROPN
ejpam-6131	267	5	math	math	PROPN
ejpam-6131	267	6	,	,	PUNCT
ejpam-6131	267	7	18	18	NUM
ejpam-6131	267	8	(	(	PUNCT
ejpam-6131	267	9	2	2	NUM
ejpam-6131	267	10	)	)	PUNCT
ejpam-6131	267	11	(	(	PUNCT
ejpam-6131	267	12	2025	2025	NUM
ejpam-6131	267	13	)	)	PUNCT
ejpam-6131	267	14	,	,	PUNCT
ejpam-6131	267	15	6131	6131	NUM
ejpam-6131	267	16	12	12	NUM
ejpam-6131	267	17	of	of	ADP
ejpam-6131	267	18	22	22	NUM
ejpam-6131	267	19	≤	≤	NOUN
ejpam-6131	267	20	t(p(ξn1	t(p(ξn1	PROPN
ejpam-6131	267	21	)	)	PUNCT
ejpam-6131	267	22	,	,	PUNCT
ejpam-6131	267	23	p(ξ	p(ξ	PROPN
ejpam-6131	267	24	n+1	n+1	ADV
ejpam-6131	267	25	1	1	NUM
ejpam-6131	267	26	)	)	PUNCT
ejpam-6131	267	27	)	)	PUNCT
ejpam-6131	268	1	+	+	CCONJ
ejpam-6131	268	2	t(p(ξn2	t(p(ξn2	NOUN
ejpam-6131	268	3	)	)	PUNCT
ejpam-6131	268	4	,	,	PUNCT
ejpam-6131	268	5	(	(	PUNCT
ejpam-6131	268	6	ξ	ξ	X
ejpam-6131	268	7	n+1	n+1	PROPN
ejpam-6131	268	8	2	2	NUM
ejpam-6131	268	9	)	)	PUNCT
ejpam-6131	268	10	)	)	PUNCT
ejpam-6131	269	1	+	+	CCONJ
ejpam-6131	269	2	t(p(ξn3	t(p(ξn3	PROPN
ejpam-6131	269	3	)	)	PUNCT
ejpam-6131	269	4	,	,	PUNCT
ejpam-6131	269	5	p(ξ	p(ξ	PROPN
ejpam-6131	269	6	n+1	n+1	ADV
ejpam-6131	269	7	3	3	NUM
ejpam-6131	269	8	)	)	PUNCT
ejpam-6131	269	9	)	)	PUNCT
ejpam-6131	270	1	+	+	CCONJ
ejpam-6131	270	2	t(p(ξn4	t(p(ξn4	NOUN
ejpam-6131	270	3	)	)	PUNCT
ejpam-6131	270	4	,	,	PUNCT
ejpam-6131	270	5	p(ξ	p(ξ	PROPN
ejpam-6131	270	6	n+1	n+1	ADV
ejpam-6131	270	7	4	4	NUM
ejpam-6131	270	8	)	)	PUNCT
ejpam-6131	270	9	)	)	PUNCT
ejpam-6131	271	1	+	+	CCONJ
ejpam-6131	271	2	t(p(ξn5	t(p(ξn5	PROPN
ejpam-6131	271	3	)	)	PUNCT
ejpam-6131	271	4	,	,	PUNCT
ejpam-6131	271	5	p(ξ	p(ξ	PROPN
ejpam-6131	271	6	n+1	n+1	ADV
ejpam-6131	271	7	5	5	NUM
ejpam-6131	271	8	)	)	PUNCT
ejpam-6131	271	9	)	)	PUNCT
ejpam-6131	272	1	+	+	CCONJ
ejpam-6131	272	2	t(p(ξn+1	t(p(ξn+1	NOUN
ejpam-6131	272	3	1	1	NUM
ejpam-6131	272	4	)	)	PUNCT
ejpam-6131	272	5	,	,	PUNCT
ejpam-6131	272	6	p(ξn+2	p(ξn+2	PRON
ejpam-6131	272	7	1	1	NUM
ejpam-6131	272	8	)	)	PUNCT
ejpam-6131	272	9	)	)	PUNCT
ejpam-6131	273	1	+	+	NUM
ejpam-6131	273	2	t(p(ξn+1	t(p(ξn+1	NOUN
ejpam-6131	273	3	2	2	NUM
ejpam-6131	273	4	)	)	PUNCT
ejpam-6131	273	5	,	,	PUNCT
ejpam-6131	273	6	p(ξn+2	p(ξn+2	PRON
ejpam-6131	273	7	2	2	NUM
ejpam-6131	273	8	)	)	PUNCT
ejpam-6131	273	9	)	)	PUNCT
ejpam-6131	274	1	+	+	CCONJ
ejpam-6131	274	2	t(p(ξn+1	t(p(ξn+1	NOUN
ejpam-6131	274	3	3	3	NUM
ejpam-6131	274	4	)	)	PUNCT
ejpam-6131	274	5	,	,	PUNCT
ejpam-6131	274	6	p(ξn+2	p(ξn+2	PRON
ejpam-6131	274	7	3	3	NUM
ejpam-6131	274	8	)	)	PUNCT
ejpam-6131	274	9	)	)	PUNCT
ejpam-6131	275	1	+	+	CCONJ
ejpam-6131	275	2	t(p(ξn5	t(p(ξn5	PROPN
ejpam-6131	275	3	)	)	PUNCT
ejpam-6131	275	4	,	,	PUNCT
ejpam-6131	276	1	p(ξ	p(ξ	NOUN
ejpam-6131	276	2	n+2	n+2	PRON
ejpam-6131	276	3	5	5	NUM
ejpam-6131	276	4	)	)	PUNCT
ejpam-6131	276	5	)	)	PUNCT
ejpam-6131	277	1	+	+	CCONJ
ejpam-6131	277	2	t(p(ξn+1	t(p(ξn+1	NOUN
ejpam-6131	277	3	4	4	NUM
ejpam-6131	277	4	)	)	PUNCT
ejpam-6131	277	5	,	,	PUNCT
ejpam-6131	277	6	p(aξ+2	p(aξ+2	ADJ
ejpam-6131	277	7	4	4	NUM
ejpam-6131	277	8	)	)	PUNCT
ejpam-6131	277	9	)	)	PUNCT
ejpam-6131	278	1	+	+	CCONJ
ejpam-6131	278	2	·	·	PUNCT
ejpam-6131	278	3	·	·	PUNCT
ejpam-6131	278	4	·	·	PUNCT
ejpam-6131	278	5	+	+	NUM
ejpam-6131	278	6	t(p(ξn+m−1	t(p(ξn+m−1	NOUN
ejpam-6131	278	7	1	1	NUM
ejpam-6131	278	8	)	)	PUNCT
ejpam-6131	278	9	,	,	PUNCT
ejpam-6131	278	10	p(ξn+m	p(ξn+m	PROPN
ejpam-6131	278	11	1	1	NUM
ejpam-6131	278	12	)	)	PUNCT
ejpam-6131	278	13	)	)	PUNCT
ejpam-6131	279	1	+	+	CCONJ
ejpam-6131	279	2	t(p(ξn+m−1	t(p(ξn+m−1	NOUN
ejpam-6131	279	3	2	2	NUM
ejpam-6131	279	4	)	)	PUNCT
ejpam-6131	279	5	,	,	PUNCT
ejpam-6131	279	6	p(ξn+m	p(ξn+m	PROPN
ejpam-6131	279	7	2	2	NUM
ejpam-6131	279	8	)	)	PUNCT
ejpam-6131	279	9	)	)	PUNCT
ejpam-6131	280	1	+	+	NUM
ejpam-6131	280	2	t(p(ξn+m−1	t(p(ξn+m−1	NOUN
ejpam-6131	280	3	3	3	NUM
ejpam-6131	280	4	)	)	PUNCT
ejpam-6131	280	5	,	,	PUNCT
ejpam-6131	280	6	p(ξn+m	p(ξn+m	PROPN
ejpam-6131	280	7	3	3	NUM
ejpam-6131	280	8	)	)	PUNCT
ejpam-6131	280	9	)	)	PUNCT
ejpam-6131	281	1	+	+	CCONJ
ejpam-6131	281	2	t(p(ξn+m−1	t(p(ξn+m−1	NOUN
ejpam-6131	281	3	4	4	NUM
ejpam-6131	281	4	)	)	PUNCT
ejpam-6131	281	5	,	,	PUNCT
ejpam-6131	281	6	p(ξn+m	p(ξn+m	PROPN
ejpam-6131	281	7	4	4	NUM
ejpam-6131	281	8	)	)	PUNCT
ejpam-6131	281	9	)	)	PUNCT
ejpam-6131	282	1	+	+	CCONJ
ejpam-6131	282	2	t(p(ξn+m−1	t(p(ξn+m−1	NOUN
ejpam-6131	282	3	5	5	NUM
ejpam-6131	282	4	)	)	PUNCT
ejpam-6131	282	5	,	,	PUNCT
ejpam-6131	282	6	p(ξn+m	p(ξn+m	PROPN
ejpam-6131	282	7	5	5	NUM
ejpam-6131	282	8	)	)	PUNCT
ejpam-6131	282	9	)	)	PUNCT
ejpam-6131	283	1	=	=	SYM
ejpam-6131	283	2	µn	µn	PROPN
ejpam-6131	283	3	+	+	NOUN
ejpam-6131	283	4	µn+1	µn+1	NUM
ejpam-6131	283	5	+	+	NOUN
ejpam-6131	283	6	·	·	PUNCT
ejpam-6131	283	7	·	·	PUNCT
ejpam-6131	283	8	·	·	PUNCT
ejpam-6131	283	9	+	+	NUM
ejpam-6131	283	10	µn+m−1	µn+m−1	NOUN
ejpam-6131	283	11	≤	≤	NUM
ejpam-6131	283	12	(	(	PUNCT
ejpam-6131	283	13	qn	qn	NOUN
ejpam-6131	283	14	+	+	NOUN
ejpam-6131	283	15	qn+1	qn+1	NUM
ejpam-6131	283	16	+	+	X
ejpam-6131	283	17	·	·	PUNCT
ejpam-6131	283	18	·	·	PUNCT
ejpam-6131	283	19	·	·	PUNCT
ejpam-6131	283	20	+	+	PROPN
ejpam-6131	283	21	qn+m−1)µo	qn+m−1)µo	X
ejpam-6131	283	22	=	=	SYM
ejpam-6131	283	23	qn(i	qn(i	X
ejpam-6131	283	24	+	+	ADJ
ejpam-6131	283	25	q+	q+	ADV
ejpam-6131	283	26	·	·	PUNCT
ejpam-6131	283	27	·	·	PUNCT
ejpam-6131	283	28	·	·	PUNCT
ejpam-6131	284	1	+	+	PUNCT
ejpam-6131	284	2	qm−1	qm−1	NOUN
ejpam-6131	284	3	+	+	X
ejpam-6131	284	4	·	·	PUNCT
ejpam-6131	284	5	·	·	PUNCT
ejpam-6131	284	6	·	·	PUNCT
ejpam-6131	284	7	)	)	PUNCT
ejpam-6131	284	8	µo	µo	X
ejpam-6131	284	9	=	=	PUNCT
ejpam-6131	284	10	qn(i	qn(i	X
ejpam-6131	284	11	−q)−1µo	−q)−1µo	NUM
ejpam-6131	284	12	.	.	PUNCT
ejpam-6131	285	1	this	this	PRON
ejpam-6131	285	2	implies	imply	VERB
ejpam-6131	285	3	that	that	SCONJ
ejpam-6131	285	4	lim	lim	PROPN
ejpam-6131	285	5	n→+∞	n→+∞	VERB
ejpam-6131	286	1	[	[	X
ejpam-6131	286	2	t(p(ξn1	t(p(ξn1	X
ejpam-6131	286	3	)	)	PUNCT
ejpam-6131	286	4	,	,	PUNCT
ejpam-6131	286	5	p(ξ	p(ξ	PROPN
ejpam-6131	286	6	n+m	n+m	NUM
ejpam-6131	286	7	1	1	NUM
ejpam-6131	286	8	)	)	PUNCT
ejpam-6131	286	9	)	)	PUNCT
ejpam-6131	287	1	+	+	CCONJ
ejpam-6131	287	2	t(p(ξn2	t(p(ξn2	NOUN
ejpam-6131	287	3	)	)	PUNCT
ejpam-6131	287	4	,	,	PUNCT
ejpam-6131	287	5	p(ξ	p(ξ	PROPN
ejpam-6131	287	6	n+m	n+m	NUM
ejpam-6131	287	7	2	2	NUM
ejpam-6131	287	8	)	)	PUNCT
ejpam-6131	287	9	)	)	PUNCT
ejpam-6131	288	1	+	+	CCONJ
ejpam-6131	288	2	t(p(ξn3	t(p(ξn3	PROPN
ejpam-6131	288	3	)	)	PUNCT
ejpam-6131	288	4	,	,	PUNCT
ejpam-6131	288	5	p(ξ	p(ξ	PROPN
ejpam-6131	288	6	n+m	n+m	NUM
ejpam-6131	288	7	3	3	NUM
ejpam-6131	288	8	)	)	PUNCT
ejpam-6131	288	9	)	)	PUNCT
ejpam-6131	289	1	+	+	CCONJ
ejpam-6131	289	2	t(p(ξn4	t(p(ξn4	NOUN
ejpam-6131	289	3	)	)	PUNCT
ejpam-6131	289	4	,	,	PUNCT
ejpam-6131	289	5	p(ξ	p(ξ	PROPN
ejpam-6131	289	6	n+m	n+m	NUM
ejpam-6131	289	7	4	4	NUM
ejpam-6131	289	8	)	)	PUNCT
ejpam-6131	289	9	)	)	PUNCT
ejpam-6131	290	1	+	+	CCONJ
ejpam-6131	290	2	t(p(ξn5	t(p(ξn5	PROPN
ejpam-6131	290	3	)	)	PUNCT
ejpam-6131	290	4	,	,	PUNCT
ejpam-6131	290	5	p(ξ	p(ξ	PROPN
ejpam-6131	290	6	n+m	n+m	NUM
ejpam-6131	290	7	5	5	NUM
ejpam-6131	290	8	)	)	PUNCT
ejpam-6131	290	9	)	)	PUNCT
ejpam-6131	290	10	]	]	PUNCT
ejpam-6131	290	11	≤	≤	X
ejpam-6131	291	1	[	[	X
ejpam-6131	291	2	(	(	PUNCT
ejpam-6131	291	3	γ̃	γ̃	PROPN
ejpam-6131	291	4	+	+	NUM
ejpam-6131	291	5	υ̃)(i	υ̃)(i	NOUN
ejpam-6131	291	6	−	−	NOUN
ejpam-6131	291	7	γ̃)−1]n[i	γ̃)−1]n[i	NOUN
ejpam-6131	291	8	−	−	PROPN
ejpam-6131	292	1	(	(	PUNCT
ejpam-6131	292	2	γ̃	γ̃	PROPN
ejpam-6131	292	3	+	+	CCONJ
ejpam-6131	292	4	υ̃)(i	υ̃)(i	NOUN
ejpam-6131	292	5	−	−	NOUN
ejpam-6131	292	6	γ̃)−1]−1µo	γ̃)−1]−1µo	PROPN
ejpam-6131	292	7	=	=	SYM
ejpam-6131	293	1	[	[	X
ejpam-6131	293	2	(	(	PUNCT
ejpam-6131	293	3	γ̃	γ̃	PROPN
ejpam-6131	293	4	+	+	NUM
ejpam-6131	293	5	υ̃)(i	υ̃)(i	NOUN
ejpam-6131	293	6	−	−	NOUN
ejpam-6131	293	7	γ̃)−1]n[i	γ̃)−1]n[i	NOUN
ejpam-6131	293	8	−	−	PROPN
ejpam-6131	293	9	(	(	PUNCT
ejpam-6131	293	10	γ̃	γ̃	PROPN
ejpam-6131	293	11	+	+	NUM
ejpam-6131	293	12	υ̃)(i	υ̃)(i	NOUN
ejpam-6131	293	13	−	−	NOUN
ejpam-6131	293	14	γ̃)−1]−1µo	γ̃)−1]−1µo	AUX
ejpam-6131	293	15	.	.	PUNCT
ejpam-6131	293	16	applying	apply	VERB
ejpam-6131	293	17	lim	lim	PROPN
ejpam-6131	293	18	n→+∞	n→+∞	VERB
ejpam-6131	293	19	on	on	ADP
ejpam-6131	293	20	both	both	DET
ejpam-6131	293	21	sides	side	NOUN
ejpam-6131	293	22	yields	yield	VERB
ejpam-6131	293	23	that	that	SCONJ
ejpam-6131	293	24	lim	lim	PROPN
ejpam-6131	293	25	n→+∞	n→+∞	VERB
ejpam-6131	294	1	[	[	X
ejpam-6131	294	2	t(p(ξn1	t(p(ξn1	X
ejpam-6131	294	3	)	)	PUNCT
ejpam-6131	294	4	,	,	PUNCT
ejpam-6131	294	5	p(ξ	p(ξ	PROPN
ejpam-6131	294	6	n+m	n+m	NUM
ejpam-6131	294	7	1	1	NUM
ejpam-6131	294	8	)	)	PUNCT
ejpam-6131	294	9	)	)	PUNCT
ejpam-6131	295	1	+	+	CCONJ
ejpam-6131	295	2	t(p(ξn2	t(p(ξn2	NOUN
ejpam-6131	295	3	)	)	PUNCT
ejpam-6131	295	4	,	,	PUNCT
ejpam-6131	295	5	p(ξ	p(ξ	PROPN
ejpam-6131	295	6	n+m	n+m	NUM
ejpam-6131	295	7	2	2	NUM
ejpam-6131	295	8	)	)	PUNCT
ejpam-6131	295	9	)	)	PUNCT
ejpam-6131	296	1	+	+	CCONJ
ejpam-6131	296	2	t(p(ξn3	t(p(ξn3	PROPN
ejpam-6131	296	3	)	)	PUNCT
ejpam-6131	296	4	,	,	PUNCT
ejpam-6131	296	5	p(ξ	p(ξ	PROPN
ejpam-6131	296	6	n+m	n+m	NUM
ejpam-6131	296	7	3	3	NUM
ejpam-6131	296	8	)	)	PUNCT
ejpam-6131	296	9	)	)	PUNCT
ejpam-6131	297	1	+	+	CCONJ
ejpam-6131	297	2	t(p(ξn4	t(p(ξn4	NOUN
ejpam-6131	297	3	)	)	PUNCT
ejpam-6131	297	4	,	,	PUNCT
ejpam-6131	297	5	p(ξ	p(ξ	PROPN
ejpam-6131	297	6	n+m	n+m	NUM
ejpam-6131	297	7	4	4	NUM
ejpam-6131	297	8	)	)	PUNCT
ejpam-6131	297	9	)	)	PUNCT
ejpam-6131	298	1	+	+	CCONJ
ejpam-6131	298	2	t(p(ξn5	t(p(ξn5	PROPN
ejpam-6131	298	3	)	)	PUNCT
ejpam-6131	298	4	,	,	PUNCT
ejpam-6131	298	5	p(ξ	p(ξ	PROPN
ejpam-6131	298	6	n+m	n+m	NUM
ejpam-6131	298	7	5	5	NUM
ejpam-6131	298	8	)	)	PUNCT
ejpam-6131	298	9	)	)	PUNCT
ejpam-6131	298	10	]	]	PUNCT
ejpam-6131	299	1	=	=	PUNCT
ejpam-6131	299	2	0	0	NUM
ejpam-6131	299	3	,	,	PUNCT
ejpam-6131	299	4	or	or	CCONJ
ejpam-6131	299	5	lim	lim	PROPN
ejpam-6131	299	6	n→+∞	n→+∞	VERB
ejpam-6131	299	7	t(p(ξn1	t(p(ξn1	PROPN
ejpam-6131	299	8	)	)	PUNCT
ejpam-6131	299	9	,	,	PUNCT
ejpam-6131	299	10	p(ξ	p(ξ	PROPN
ejpam-6131	299	11	n+m	n+m	NUM
ejpam-6131	299	12	1	1	NUM
ejpam-6131	299	13	)	)	PUNCT
ejpam-6131	299	14	)	)	PUNCT
ejpam-6131	300	1	=	=	VERB
ejpam-6131	300	2	lim	lim	PROPN
ejpam-6131	300	3	n→+∞	n→+∞	VERB
ejpam-6131	300	4	t(p(ξn2	t(p(ξn2	NOUN
ejpam-6131	300	5	)	)	PUNCT
ejpam-6131	300	6	,	,	PUNCT
ejpam-6131	300	7	p(ξ	p(ξ	PROPN
ejpam-6131	300	8	n+m	n+m	NUM
ejpam-6131	300	9	2	2	NUM
ejpam-6131	300	10	)	)	PUNCT
ejpam-6131	300	11	)	)	PUNCT
ejpam-6131	301	1	=	=	SYM
ejpam-6131	301	2	lim	lim	PROPN
ejpam-6131	301	3	n→+∞	n→+∞	PROPN
ejpam-6131	301	4	t(p(ξn3	t(p(ξn3	PROPN
ejpam-6131	301	5	)	)	PUNCT
ejpam-6131	301	6	,	,	PUNCT
ejpam-6131	301	7	p(ξ	p(ξ	PROPN
ejpam-6131	301	8	n+m	n+m	NUM
ejpam-6131	301	9	3	3	NUM
ejpam-6131	301	10	)	)	PUNCT
ejpam-6131	301	11	)	)	PUNCT
ejpam-6131	302	1	=	=	PUNCT
ejpam-6131	303	1	=	=	SYM
ejpam-6131	303	2	lim	lim	PROPN
ejpam-6131	303	3	n→+∞	n→+∞	PROPN
ejpam-6131	303	4	t(p(ξn4	t(p(ξn4	PROPN
ejpam-6131	303	5	)	)	PUNCT
ejpam-6131	303	6	,	,	PUNCT
ejpam-6131	303	7	p(ξ	p(ξ	PROPN
ejpam-6131	303	8	n+m	n+m	NUM
ejpam-6131	303	9	4	4	NUM
ejpam-6131	303	10	)	)	PUNCT
ejpam-6131	303	11	)	)	PUNCT
ejpam-6131	303	12	]	]	PUNCT
ejpam-6131	304	1	=	=	SYM
ejpam-6131	304	2	lim	lim	PROPN
ejpam-6131	304	3	n→+∞	n→+∞	VERB
ejpam-6131	304	4	t(p(ξn5	t(p(ξn5	PROPN
ejpam-6131	304	5	)	)	PUNCT
ejpam-6131	304	6	,	,	PUNCT
ejpam-6131	304	7	p(ξ	p(ξ	PROPN
ejpam-6131	304	8	n+m	n+m	NUM
ejpam-6131	304	9	5	5	NUM
ejpam-6131	304	10	)	)	PUNCT
ejpam-6131	304	11	)	)	PUNCT
ejpam-6131	304	12	]	]	PUNCT
ejpam-6131	305	1	=	=	PUNCT
ejpam-6131	305	2	0	0	X
ejpam-6131	305	3	.	.	PUNCT
ejpam-6131	306	1	hence	hence	ADV
ejpam-6131	306	2	,	,	PUNCT
ejpam-6131	306	3	{	{	PUNCT
ejpam-6131	306	4	p(ξn1	p(ξn1	ADJ
ejpam-6131	306	5	)	)	PUNCT
ejpam-6131	306	6	}	}	PUNCT
ejpam-6131	306	7	,	,	PUNCT
ejpam-6131	306	8	{	{	PUNCT
ejpam-6131	306	9	p(ξn2	p(ξn2	NOUN
ejpam-6131	306	10	)	)	PUNCT
ejpam-6131	306	11	}	}	PUNCT
ejpam-6131	306	12	,	,	PUNCT
ejpam-6131	306	13	{	{	PUNCT
ejpam-6131	306	14	p(ξn3	p(ξn3	PROPN
ejpam-6131	306	15	)	)	PUNCT
ejpam-6131	306	16	}	}	PUNCT
ejpam-6131	306	17	,	,	PUNCT
ejpam-6131	306	18	{	{	PUNCT
ejpam-6131	306	19	p(ξn4	p(ξn4	NOUN
ejpam-6131	306	20	)	)	PUNCT
ejpam-6131	306	21	}	}	PUNCT
ejpam-6131	306	22	and	and	CCONJ
ejpam-6131	306	23	{	{	PUNCT
ejpam-6131	306	24	p(ξn5	p(ξn5	NOUN
ejpam-6131	306	25	)	)	PUNCT
ejpam-6131	306	26	}	}	PUNCT
ejpam-6131	306	27	are	be	AUX
ejpam-6131	306	28	cauchy	cauchy	ADJ
ejpam-6131	306	29	sequences	sequence	NOUN
ejpam-6131	306	30	within	within	ADP
ejpam-6131	306	31	the	the	DET
ejpam-6131	306	32	set	set	NOUN
ejpam-6131	306	33	g.	g.	PROPN
ejpam-6131	306	34	moreover	moreover	ADV
ejpam-6131	306	35	,	,	PUNCT
ejpam-6131	306	36	by	by	ADP
ejpam-6131	306	37	completeness	completeness	NOUN
ejpam-6131	306	38	of	of	ADP
ejpam-6131	306	39	p(g	p(g	PROPN
ejpam-6131	306	40	)	)	PUNCT
ejpam-6131	306	41	,	,	PUNCT
ejpam-6131	306	42	there	there	PRON
ejpam-6131	306	43	must	must	AUX
ejpam-6131	306	44	exist	exist	VERB
ejpam-6131	306	45	(	(	PUNCT
ejpam-6131	306	46	ξ∗1	ξ∗1	NOUN
ejpam-6131	306	47	,	,	PUNCT
ejpam-6131	306	48	ξ	ξ	PROPN
ejpam-6131	306	49	∗	∗	NOUN
ejpam-6131	306	50	2	2	NUM
ejpam-6131	306	51	,	,	PUNCT
ejpam-6131	306	52	ξ	ξ	PROPN
ejpam-6131	306	53	∗	∗	NOUN
ejpam-6131	306	54	3	3	NUM
ejpam-6131	306	55	,	,	PUNCT
ejpam-6131	306	56	ξ	ξ	PROPN
ejpam-6131	306	57	∗	∗	NOUN
ejpam-6131	306	58	4	4	NUM
ejpam-6131	306	59	,	,	PUNCT
ejpam-6131	306	60	ξ	ξ	PROPN
ejpam-6131	306	61	∗	∗	NOUN
ejpam-6131	306	62	5	5	NUM
ejpam-6131	306	63	)	)	PUNCT
ejpam-6131	306	64	∈	∈	NOUN
ejpam-6131	306	65	g5	g5	NOUN
ejpam-6131	306	66	such	such	ADJ
ejpam-6131	306	67	that	that	SCONJ
ejpam-6131	306	68	lim	lim	PROPN
ejpam-6131	306	69	n→+∞	n→+∞	VERB
ejpam-6131	306	70	p(ξn1	p(ξn1	PROPN
ejpam-6131	306	71	)	)	PUNCT
ejpam-6131	307	1	=	=	SYM
ejpam-6131	307	2	p(ξ∗1	p(ξ∗1	NOUN
ejpam-6131	307	3	)	)	PUNCT
ejpam-6131	307	4	=	=	SYM
ejpam-6131	307	5	ξ1	ξ1	NOUN
ejpam-6131	307	6	,	,	PUNCT
ejpam-6131	307	7	lim	lim	PROPN
ejpam-6131	307	8	n→+∞	n→+∞	VERB
ejpam-6131	307	9	p(ξn2	p(ξn2	NOUN
ejpam-6131	307	10	)	)	PUNCT
ejpam-6131	308	1	=	=	SYM
ejpam-6131	308	2	p(ξ∗2	p(ξ∗2	NOUN
ejpam-6131	308	3	)	)	PUNCT
ejpam-6131	308	4	=	=	SYM
ejpam-6131	308	5	ξ2	ξ2	NOUN
ejpam-6131	308	6	,	,	PUNCT
ejpam-6131	308	7	lim	lim	PROPN
ejpam-6131	308	8	n→+∞	n→+∞	VERB
ejpam-6131	308	9	p(ξn3	p(ξn3	PROPN
ejpam-6131	308	10	)	)	PUNCT
ejpam-6131	309	1	=	=	PUNCT
ejpam-6131	309	2	p(ξ∗3	p(ξ∗3	NOUN
ejpam-6131	309	3	)	)	PUNCT
ejpam-6131	309	4	=	=	SYM
ejpam-6131	309	5	ξ3	ξ3	NOUN
ejpam-6131	309	6	,	,	PUNCT
ejpam-6131	309	7	lim	lim	PROPN
ejpam-6131	309	8	n→+∞	n→+∞	VERB
ejpam-6131	309	9	p(ξn4	p(ξn4	PROPN
ejpam-6131	309	10	)	)	PUNCT
ejpam-6131	309	11	=	=	SYM
ejpam-6131	309	12	p(ξ∗4	p(ξ∗4	NOUN
ejpam-6131	309	13	)	)	PUNCT
ejpam-6131	309	14	=	=	SYM
ejpam-6131	309	15	ξ4	ξ4	PROPN
ejpam-6131	309	16	,	,	PUNCT
ejpam-6131	309	17	lim	lim	PROPN
ejpam-6131	309	18	n→+∞	n→+∞	VERB
ejpam-6131	309	19	p(ξn5	p(ξn5	NOUN
ejpam-6131	309	20	)	)	PUNCT
ejpam-6131	309	21	=	=	SYM
ejpam-6131	310	1	p(ξ∗5	p(ξ∗5	NOUN
ejpam-6131	310	2	)	)	PUNCT
ejpam-6131	310	3	=	=	SYM
ejpam-6131	310	4	ξ5	ξ5	NOUN
ejpam-6131	310	5	,	,	PUNCT
ejpam-6131	310	6	which	which	PRON
ejpam-6131	310	7	results	result	VERB
ejpam-6131	310	8	in	in	ADP
ejpam-6131	310	9	lim	lim	PROPN
ejpam-6131	310	10	n→+∞	n→+∞	PROPN
ejpam-6131	310	11	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	310	12	1	1	NUM
ejpam-6131	310	13	)	)	PUNCT
ejpam-6131	311	1	=	=	VERB
ejpam-6131	311	2	lim	lim	PROPN
ejpam-6131	311	3	n→+∞	n→+∞	VERB
ejpam-6131	311	4	ζn(ξn1	ζn(ξn1	PROPN
ejpam-6131	311	5	,	,	PUNCT
ejpam-6131	311	6	ξ	ξ	PROPN
ejpam-6131	311	7	n	n	PRON
ejpam-6131	311	8	2	2	NUM
ejpam-6131	311	9	,	,	PUNCT
ejpam-6131	311	10	ξ	ξ	PROPN
ejpam-6131	311	11	n	n	PRON
ejpam-6131	311	12	3	3	NUM
ejpam-6131	311	13	,	,	PUNCT
ejpam-6131	311	14	ξ	ξ	PROPN
ejpam-6131	311	15	n	n	PRON
ejpam-6131	311	16	4	4	NUM
ejpam-6131	311	17	,	,	PUNCT
ejpam-6131	311	18	ξ	ξ	PROPN
ejpam-6131	311	19	n	n	PRON
ejpam-6131	311	20	5	5	NUM
ejpam-6131	311	21	)	)	PUNCT
ejpam-6131	311	22	,	,	PUNCT
ejpam-6131	311	23	lim	lim	PROPN
ejpam-6131	311	24	n→+∞	n→+∞	VERB
ejpam-6131	311	25	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	311	26	2	2	NUM
ejpam-6131	311	27	)	)	PUNCT
ejpam-6131	311	28	=	=	NOUN
ejpam-6131	311	29	lim	lim	PROPN
ejpam-6131	311	30	n→+∞	n→+∞	PROPN
ejpam-6131	311	31	ζn(ξn2	ζn(ξn2	PUNCT
ejpam-6131	311	32	,	,	PUNCT
ejpam-6131	311	33	ξ	ξ	PROPN
ejpam-6131	311	34	n	n	NUM
ejpam-6131	311	35	3	3	NUM
ejpam-6131	311	36	,	,	PUNCT
ejpam-6131	311	37	ξ	ξ	PROPN
ejpam-6131	311	38	n	n	PRON
ejpam-6131	311	39	4	4	NUM
ejpam-6131	311	40	,	,	PUNCT
ejpam-6131	311	41	ξ	ξ	PROPN
ejpam-6131	311	42	n	n	NUM
ejpam-6131	311	43	5	5	NUM
ejpam-6131	311	44	,	,	PUNCT
ejpam-6131	311	45	ξ	ξ	PROPN
ejpam-6131	311	46	n	n	PRON
ejpam-6131	311	47	1	1	NUM
ejpam-6131	311	48	)	)	PUNCT
ejpam-6131	311	49	,	,	PUNCT
ejpam-6131	311	50	lim	lim	PROPN
ejpam-6131	311	51	n→+∞	n→+∞	VERB
ejpam-6131	311	52	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	311	53	3	3	NUM
ejpam-6131	311	54	)	)	PUNCT
ejpam-6131	311	55	=	=	VERB
ejpam-6131	311	56	lim	lim	PROPN
ejpam-6131	311	57	n→+∞	n→+∞	PROPN
ejpam-6131	311	58	ζn(ξn3	ζn(ξn3	PROPN
ejpam-6131	311	59	,	,	PUNCT
ejpam-6131	311	60	ξ	ξ	PROPN
ejpam-6131	311	61	n	n	NUM
ejpam-6131	311	62	4	4	NUM
ejpam-6131	311	63	,	,	PUNCT
ejpam-6131	311	64	ξ	ξ	PROPN
ejpam-6131	311	65	n	n	NUM
ejpam-6131	311	66	5	5	NUM
ejpam-6131	311	67	,	,	PUNCT
ejpam-6131	311	68	ξ	ξ	PROPN
ejpam-6131	311	69	n	n	NUM
ejpam-6131	311	70	1	1	NUM
ejpam-6131	311	71	,	,	PUNCT
ejpam-6131	311	72	ξ	ξ	PROPN
ejpam-6131	311	73	n	n	PRON
ejpam-6131	311	74	2	2	NUM
ejpam-6131	311	75	)	)	PUNCT
ejpam-6131	311	76	,	,	PUNCT
ejpam-6131	311	77	lim	lim	PROPN
ejpam-6131	311	78	n→+∞	n→+∞	VERB
ejpam-6131	311	79	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	311	80	4	4	NUM
ejpam-6131	311	81	)	)	PUNCT
ejpam-6131	311	82	=	=	VERB
ejpam-6131	311	83	lim	lim	PROPN
ejpam-6131	311	84	n→+∞	n→+∞	PROPN
ejpam-6131	311	85	ζn(ξn4	ζn(ξn4	NUM
ejpam-6131	311	86	,	,	PUNCT
ejpam-6131	311	87	ξ	ξ	PROPN
ejpam-6131	311	88	n	n	NUM
ejpam-6131	311	89	5	5	NUM
ejpam-6131	311	90	,	,	PUNCT
ejpam-6131	311	91	ξ	ξ	PROPN
ejpam-6131	311	92	n	n	NUM
ejpam-6131	311	93	1	1	NUM
ejpam-6131	311	94	,	,	PUNCT
ejpam-6131	311	95	ξ	ξ	PROPN
ejpam-6131	311	96	n	n	PRON
ejpam-6131	311	97	2	2	NUM
ejpam-6131	311	98	,	,	PUNCT
ejpam-6131	311	99	ξ	ξ	PROPN
ejpam-6131	311	100	n	n	PRON
ejpam-6131	311	101	3	3	NUM
ejpam-6131	311	102	)	)	PUNCT
ejpam-6131	311	103	,	,	PUNCT
ejpam-6131	311	104	lim	lim	PROPN
ejpam-6131	311	105	n→+∞	n→+∞	VERB
ejpam-6131	311	106	p(ξn+1	p(ξn+1	PROPN
ejpam-6131	311	107	5	5	NUM
ejpam-6131	311	108	)	)	PUNCT
ejpam-6131	311	109	=	=	SYM
ejpam-6131	311	110	lim	lim	PROPN
ejpam-6131	311	111	n→+∞	n→+∞	PROPN
ejpam-6131	311	112	ζn(ξn5	ζn(ξn5	PUNCT
ejpam-6131	311	113	,	,	PUNCT
ejpam-6131	311	114	ξ	ξ	PROPN
ejpam-6131	311	115	n	n	NUM
ejpam-6131	311	116	1	1	NUM
ejpam-6131	311	117	,	,	PUNCT
ejpam-6131	311	118	ξ	ξ	PROPN
ejpam-6131	311	119	n	n	PRON
ejpam-6131	311	120	2	2	NUM
ejpam-6131	311	121	,	,	PUNCT
ejpam-6131	311	122	ξ	ξ	PROPN
ejpam-6131	311	123	n	n	PRON
ejpam-6131	311	124	3	3	NUM
ejpam-6131	311	125	,	,	PUNCT
ejpam-6131	311	126	ξ	ξ	PROPN
ejpam-6131	311	127	n	n	PRON
ejpam-6131	311	128	4	4	NUM
ejpam-6131	311	129	)	)	PUNCT
ejpam-6131	311	130	.	.	PUNCT
ejpam-6131	312	1	s.	s.	PROPN
ejpam-6131	312	2	batul	batul	PROPN
ejpam-6131	312	3	et	et	PROPN
ejpam-6131	312	4	a.	a.	PROPN
ejpam-6131	312	5	/	/	PUNCT
ejpam-6131	312	6	eur	eur	PROPN
ejpam-6131	312	7	.	.	PUNCT
ejpam-6131	313	1	j.	j.	PROPN
ejpam-6131	313	2	pure	pure	PROPN
ejpam-6131	313	3	appl	appl	PROPN
ejpam-6131	313	4	.	.	PROPN
ejpam-6131	313	5	math	math	PROPN
ejpam-6131	313	6	,	,	PUNCT
ejpam-6131	313	7	18	18	NUM
ejpam-6131	313	8	(	(	PUNCT
ejpam-6131	313	9	2	2	NUM
ejpam-6131	313	10	)	)	PUNCT
ejpam-6131	313	11	(	(	PUNCT
ejpam-6131	313	12	2025	2025	NUM
ejpam-6131	313	13	)	)	PUNCT
ejpam-6131	313	14	,	,	PUNCT
ejpam-6131	313	15	6131	6131	NUM
ejpam-6131	313	16	13	13	NUM
ejpam-6131	313	17	of	of	ADP
ejpam-6131	313	18	22	22	NUM
ejpam-6131	313	19	also	also	ADV
ejpam-6131	313	20	,	,	PUNCT
ejpam-6131	313	21	from	from	ADP
ejpam-6131	313	22	the	the	DET
ejpam-6131	313	23	weak	weak	ADJ
ejpam-6131	313	24	reciprocal	reciprocal	ADJ
ejpam-6131	313	25	continuity	continuity	NOUN
ejpam-6131	313	26	and	and	CCONJ
ejpam-6131	313	27	compatibility	compatibility	NOUN
ejpam-6131	313	28	of	of	ADP
ejpam-6131	313	29	{	{	PUNCT
ejpam-6131	313	30	ζi}i∈w	ζi}i∈w	X
ejpam-6131	313	31	and	and	CCONJ
ejpam-6131	313	32	p	p	X
ejpam-6131	313	33	,	,	PUNCT
ejpam-6131	313	34	it	it	PRON
ejpam-6131	313	35	is	be	AUX
ejpam-6131	313	36	derived	derive	VERB
ejpam-6131	313	37	that	that	SCONJ
ejpam-6131	313	38	lim	lim	PROPN
ejpam-6131	313	39	n→+∞	n→+∞	VERB
ejpam-6131	313	40	ζn(p(ξn1	ζn(p(ξn1	PROPN
ejpam-6131	313	41	)	)	PUNCT
ejpam-6131	313	42	,	,	PUNCT
ejpam-6131	313	43	p(ξ	p(ξ	NOUN
ejpam-6131	313	44	n	n	PRON
ejpam-6131	313	45	2	2	NUM
ejpam-6131	313	46	)	)	PUNCT
ejpam-6131	313	47	,	,	PUNCT
ejpam-6131	313	48	p(ξ	p(ξ	NOUN
ejpam-6131	313	49	n	n	PRON
ejpam-6131	313	50	3	3	NUM
ejpam-6131	313	51	)	)	PUNCT
ejpam-6131	313	52	,	,	PUNCT
ejpam-6131	313	53	p(ξ	p(ξ	NOUN
ejpam-6131	313	54	n	n	PRON
ejpam-6131	313	55	4	4	NUM
ejpam-6131	313	56	)	)	PUNCT
ejpam-6131	313	57	,	,	PUNCT
ejpam-6131	313	58	p(ξ	p(ξ	NOUN
ejpam-6131	313	59	n	n	PRON
ejpam-6131	313	60	5	5	NUM
ejpam-6131	313	61	)	)	PUNCT
ejpam-6131	313	62	)	)	PUNCT
ejpam-6131	314	1	=	=	SYM
ejpam-6131	314	2	p(ξ1	p(ξ1	NOUN
ejpam-6131	314	3	)	)	PUNCT
ejpam-6131	314	4	,	,	PUNCT
ejpam-6131	314	5	lim	lim	PROPN
ejpam-6131	314	6	n→+∞	n→+∞	VERB
ejpam-6131	314	7	ζn(p(ξn2	ζn(p(ξn2	PROPN
ejpam-6131	314	8	)	)	PUNCT
ejpam-6131	314	9	,	,	PUNCT
ejpam-6131	314	10	p(ξ	p(ξ	NOUN
ejpam-6131	314	11	n	n	PRON
ejpam-6131	314	12	3	3	NUM
ejpam-6131	314	13	)	)	PUNCT
ejpam-6131	314	14	,	,	PUNCT
ejpam-6131	314	15	p(ξ	p(ξ	NOUN
ejpam-6131	314	16	n	n	PRON
ejpam-6131	314	17	4	4	NUM
ejpam-6131	314	18	)	)	PUNCT
ejpam-6131	314	19	,	,	PUNCT
ejpam-6131	314	20	p(ξ	p(ξ	NOUN
ejpam-6131	314	21	n	n	PRON
ejpam-6131	314	22	5	5	NUM
ejpam-6131	314	23	)	)	PUNCT
ejpam-6131	314	24	,	,	PUNCT
ejpam-6131	314	25	p(ξ	p(ξ	NOUN
ejpam-6131	314	26	n	n	PRON
ejpam-6131	314	27	1	1	NUM
ejpam-6131	314	28	)	)	PUNCT
ejpam-6131	314	29	)	)	PUNCT
ejpam-6131	315	1	=	=	SYM
ejpam-6131	315	2	p(ξ2	p(ξ2	NOUN
ejpam-6131	315	3	)	)	PUNCT
ejpam-6131	315	4	,	,	PUNCT
ejpam-6131	315	5	lim	lim	PROPN
ejpam-6131	315	6	n→+∞	n→+∞	VERB
ejpam-6131	315	7	ζn(p(ξn3	ζn(p(ξn3	PROPN
ejpam-6131	315	8	)	)	PUNCT
ejpam-6131	315	9	,	,	PUNCT
ejpam-6131	315	10	p(ξ	p(ξ	NOUN
ejpam-6131	315	11	n	n	PRON
ejpam-6131	315	12	4	4	NUM
ejpam-6131	315	13	)	)	PUNCT
ejpam-6131	315	14	,	,	PUNCT
ejpam-6131	315	15	p(ξ	p(ξ	NOUN
ejpam-6131	315	16	n	n	PRON
ejpam-6131	315	17	5	5	NUM
ejpam-6131	315	18	)	)	PUNCT
ejpam-6131	315	19	,	,	PUNCT
ejpam-6131	315	20	p(ξ	p(ξ	NOUN
ejpam-6131	315	21	n	n	PRON
ejpam-6131	315	22	1	1	NUM
ejpam-6131	315	23	)	)	PUNCT
ejpam-6131	315	24	,	,	PUNCT
ejpam-6131	315	25	p(ξ	p(ξ	NOUN
ejpam-6131	315	26	n	n	PRON
ejpam-6131	315	27	2	2	NUM
ejpam-6131	315	28	)	)	PUNCT
ejpam-6131	315	29	)	)	PUNCT
ejpam-6131	316	1	=	=	SYM
ejpam-6131	316	2	p(ξ3	p(ξ3	NOUN
ejpam-6131	316	3	)	)	PUNCT
ejpam-6131	316	4	,	,	PUNCT
ejpam-6131	316	5	lim	lim	PROPN
ejpam-6131	316	6	n→+∞	n→+∞	PROPN
ejpam-6131	316	7	ζn(p(ξn4	ζn(p(ξn4	PROPN
ejpam-6131	316	8	)	)	PUNCT
ejpam-6131	316	9	,	,	PUNCT
ejpam-6131	316	10	p(ξ	p(ξ	NOUN
ejpam-6131	316	11	n	n	PRON
ejpam-6131	316	12	5	5	NUM
ejpam-6131	316	13	)	)	PUNCT
ejpam-6131	316	14	,	,	PUNCT
ejpam-6131	316	15	p(ξ	p(ξ	NOUN
ejpam-6131	316	16	n	n	PRON
ejpam-6131	316	17	1	1	NUM
ejpam-6131	316	18	)	)	PUNCT
ejpam-6131	316	19	,	,	PUNCT
ejpam-6131	316	20	p(ξ	p(ξ	NOUN
ejpam-6131	316	21	n	n	PRON
ejpam-6131	316	22	2	2	NUM
ejpam-6131	316	23	)	)	PUNCT
ejpam-6131	316	24	,	,	PUNCT
ejpam-6131	316	25	p(ξ	p(ξ	NOUN
ejpam-6131	316	26	n	n	PRON
ejpam-6131	316	27	3	3	NUM
ejpam-6131	316	28	)	)	PUNCT
ejpam-6131	316	29	)	)	PUNCT
ejpam-6131	317	1	=	=	SYM
ejpam-6131	317	2	p(ξ4	p(ξ4	NOUN
ejpam-6131	317	3	)	)	PUNCT
ejpam-6131	317	4	,	,	PUNCT
ejpam-6131	317	5	lim	lim	PROPN
ejpam-6131	317	6	n→+∞	n→+∞	VERB
ejpam-6131	317	7	ζn(p(ξn5	ζn(p(ξn5	PROPN
ejpam-6131	317	8	)	)	PUNCT
ejpam-6131	317	9	,	,	PUNCT
ejpam-6131	317	10	p(ξ	p(ξ	NOUN
ejpam-6131	317	11	n	n	PRON
ejpam-6131	317	12	1	1	NUM
ejpam-6131	317	13	)	)	PUNCT
ejpam-6131	317	14	,	,	PUNCT
ejpam-6131	317	15	p(ξ	p(ξ	NOUN
ejpam-6131	317	16	n	n	PRON
ejpam-6131	317	17	2	2	NUM
ejpam-6131	317	18	)	)	PUNCT
ejpam-6131	317	19	,	,	PUNCT
ejpam-6131	317	20	s(ξ	s(ξ	PROPN
ejpam-6131	317	21	n	n	PRON
ejpam-6131	317	22	3	3	NUM
ejpam-6131	317	23	)	)	PUNCT
ejpam-6131	317	24	,	,	PUNCT
ejpam-6131	317	25	p(ξ	p(ξ	NOUN
ejpam-6131	317	26	n	n	PRON
ejpam-6131	317	27	4	4	NUM
ejpam-6131	317	28	)	)	PUNCT
ejpam-6131	317	29	)	)	PUNCT
ejpam-6131	318	1	=	=	SYM
ejpam-6131	318	2	p(ξ5	p(ξ5	NOUN
ejpam-6131	318	3	)	)	PUNCT
ejpam-6131	318	4	.	.	PUNCT
ejpam-6131	319	1	since	since	SCONJ
ejpam-6131	319	2	{	{	PUNCT
ejpam-6131	319	3	p(ξn1	p(ξn1	ADJ
ejpam-6131	319	4	)	)	PUNCT
ejpam-6131	319	5	}	}	PUNCT
ejpam-6131	319	6	,	,	PUNCT
ejpam-6131	319	7	{	{	PUNCT
ejpam-6131	319	8	p(ξn3	p(ξn3	PROPN
ejpam-6131	319	9	)	)	PUNCT
ejpam-6131	319	10	}	}	PUNCT
ejpam-6131	319	11	,	,	PUNCT
ejpam-6131	319	12	{	{	PUNCT
ejpam-6131	319	13	p(ξn5	p(ξn5	NOUN
ejpam-6131	319	14	)	)	PUNCT
ejpam-6131	319	15	}	}	PUNCT
ejpam-6131	319	16	are	be	AUX
ejpam-6131	319	17	non	non	ADJ
ejpam-6131	319	18	-	-	ADJ
ejpam-6131	319	19	decreasing	decrease	VERB
ejpam-6131	319	20	sequences	sequence	NOUN
ejpam-6131	319	21	and	and	CCONJ
ejpam-6131	319	22	{	{	PUNCT
ejpam-6131	319	23	p(ξn2	p(ξn2	NOUN
ejpam-6131	319	24	)	)	PUNCT
ejpam-6131	319	25	}	}	PUNCT
ejpam-6131	319	26	,	,	PUNCT
ejpam-6131	319	27	{	{	PUNCT
ejpam-6131	319	28	p(ξn4	p(ξn4	NOUN
ejpam-6131	319	29	)	)	PUNCT
ejpam-6131	319	30	}	}	PUNCT
ejpam-6131	319	31	are	be	AUX
ejpam-6131	319	32	non	non	ADJ
ejpam-6131	319	33	-	-	ADJ
ejpam-6131	319	34	increasing	increase	VERB
ejpam-6131	319	35	sequences	sequence	NOUN
ejpam-6131	319	36	,	,	PUNCT
ejpam-6131	319	37	from	from	ADP
ejpam-6131	319	38	the	the	DET
ejpam-6131	319	39	regularity	regularity	NOUN
ejpam-6131	319	40	of	of	ADP
ejpam-6131	319	41	g	g	NOUN
ejpam-6131	319	42	,	,	PUNCT
ejpam-6131	319	43	for	for	ADP
ejpam-6131	319	44	all	all	DET
ejpam-6131	319	45	n	n	PRON
ejpam-6131	319	46	≥	≥	NOUN
ejpam-6131	319	47	0	0	NUM
ejpam-6131	319	48	,	,	PUNCT
ejpam-6131	319	49	it	it	PRON
ejpam-6131	319	50	is	be	AUX
ejpam-6131	319	51	obtained	obtain	VERB
ejpam-6131	319	52	that	that	DET
ejpam-6131	319	53	p(ξn1	p(ξn1	PROPN
ejpam-6131	319	54	)	)	PUNCT
ejpam-6131	319	55	⪯	⪯	PROPN
ejpam-6131	319	56	ξ1	ξ1	NOUN
ejpam-6131	319	57	,	,	PUNCT
ejpam-6131	319	58	ξ2	ξ2	NOUN
ejpam-6131	319	59	⪯	⪯	NOUN
ejpam-6131	319	60	p(ξn2	p(ξn2	NOUN
ejpam-6131	319	61	)	)	PUNCT
ejpam-6131	319	62	,	,	PUNCT
ejpam-6131	319	63	p(ξ	p(ξ	NOUN
ejpam-6131	319	64	n	n	PRON
ejpam-6131	319	65	3	3	X
ejpam-6131	319	66	)	)	PUNCT
ejpam-6131	319	67	⪯	⪯	NOUN
ejpam-6131	319	68	ξ3	ξ3	NOUN
ejpam-6131	319	69	,	,	PUNCT
ejpam-6131	319	70	ξ4	ξ4	NOUN
ejpam-6131	319	71	⪯	⪯	NOUN
ejpam-6131	319	72	p(ξn4	p(ξn4	PROPN
ejpam-6131	319	73	)	)	PUNCT
ejpam-6131	319	74	,	,	PUNCT
ejpam-6131	319	75	p(ξ	p(ξ	NOUN
ejpam-6131	319	76	n	n	PRON
ejpam-6131	319	77	5	5	NUM
ejpam-6131	319	78	)	)	PUNCT
ejpam-6131	319	79	⪯	⪯	NOUN
ejpam-6131	319	80	ξ5	ξ5	NOUN
ejpam-6131	319	81	.	.	PUNCT
ejpam-6131	320	1	then	then	ADV
ejpam-6131	320	2	,	,	PUNCT
ejpam-6131	320	3	from	from	ADP
ejpam-6131	320	4	(	(	PUNCT
ejpam-6131	320	5	1	1	NUM
ejpam-6131	320	6	)	)	PUNCT
ejpam-6131	320	7	,	,	PUNCT
ejpam-6131	320	8	it	it	PRON
ejpam-6131	320	9	is	be	AUX
ejpam-6131	320	10	computed	compute	VERB
ejpam-6131	320	11	as	as	ADP
ejpam-6131	320	12	t(ζi(ξ1	t(ζi(ξ1	ADJ
ejpam-6131	320	13	,	,	PUNCT
ejpam-6131	320	14	ξ2	ξ2	ADJ
ejpam-6131	320	15	,	,	PUNCT
ejpam-6131	320	16	ξ3	ξ3	NOUN
ejpam-6131	320	17	,	,	PUNCT
ejpam-6131	320	18	ξ4	ξ4	NOUN
ejpam-6131	320	19	,	,	PUNCT
ejpam-6131	320	20	ξ5	ξ5	NOUN
ejpam-6131	320	21	)	)	PUNCT
ejpam-6131	320	22	,	,	PUNCT
ejpam-6131	320	23	ζ	ζ	PROPN
ejpam-6131	320	24	n(p(ξn1	n(p(ξn1	PROPN
ejpam-6131	320	25	)	)	PUNCT
ejpam-6131	320	26	,	,	PUNCT
ejpam-6131	320	27	p(ξ	p(ξ	NOUN
ejpam-6131	320	28	n	n	PRON
ejpam-6131	320	29	2	2	NUM
ejpam-6131	320	30	)	)	PUNCT
ejpam-6131	320	31	,	,	PUNCT
ejpam-6131	320	32	p(ξ	p(ξ	NOUN
ejpam-6131	320	33	n	n	PRON
ejpam-6131	320	34	3	3	NUM
ejpam-6131	320	35	)	)	PUNCT
ejpam-6131	320	36	,	,	PUNCT
ejpam-6131	320	37	p(ξ	p(ξ	NOUN
ejpam-6131	320	38	n	n	PRON
ejpam-6131	320	39	4	4	NUM
ejpam-6131	320	40	)	)	PUNCT
ejpam-6131	320	41	,	,	PUNCT
ejpam-6131	320	42	p(ξ	p(ξ	NOUN
ejpam-6131	320	43	n	n	PRON
ejpam-6131	320	44	5	5	NUM
ejpam-6131	320	45	)	)	PUNCT
ejpam-6131	320	46	)	)	PUNCT
ejpam-6131	320	47	≤	≤	NUM
ejpam-6131	320	48	γ̃[t(p(ξ1	γ̃[t(p(ξ1	NOUN
ejpam-6131	320	49	)	)	PUNCT
ejpam-6131	320	50	,	,	PUNCT
ejpam-6131	320	51	ζ	ζ	NOUN
ejpam-6131	320	52	i(ξ1	i(ξ1	NOUN
ejpam-6131	320	53	,	,	PUNCT
ejpam-6131	320	54	ξ2	ξ2	NOUN
ejpam-6131	320	55	,	,	PUNCT
ejpam-6131	320	56	ξ3	ξ3	NOUN
ejpam-6131	320	57	,	,	PUNCT
ejpam-6131	320	58	ξ4	ξ4	NOUN
ejpam-6131	320	59	,	,	PUNCT
ejpam-6131	320	60	ξ5	ξ5	NOUN
ejpam-6131	320	61	)	)	PUNCT
ejpam-6131	320	62	)	)	PUNCT
ejpam-6131	321	1	+	+	CCONJ
ejpam-6131	321	2	t(p(p(ξn1	t(p(p(ξn1	PROPN
ejpam-6131	321	3	)	)	PUNCT
ejpam-6131	321	4	)	)	PUNCT
ejpam-6131	321	5	,	,	PUNCT
ejpam-6131	321	6	ζ	ζ	PROPN
ejpam-6131	321	7	n(p(ξn1	n(p(ξn1	PROPN
ejpam-6131	321	8	)	)	PUNCT
ejpam-6131	321	9	,	,	PUNCT
ejpam-6131	321	10	p(ξ	p(ξ	NOUN
ejpam-6131	321	11	n	n	PRON
ejpam-6131	321	12	2	2	NUM
ejpam-6131	321	13	)	)	PUNCT
ejpam-6131	321	14	,	,	PUNCT
ejpam-6131	321	15	p(ξ	p(ξ	NOUN
ejpam-6131	321	16	n	n	PRON
ejpam-6131	321	17	3	3	NUM
ejpam-6131	321	18	)	)	PUNCT
ejpam-6131	321	19	,	,	PUNCT
ejpam-6131	321	20	p(ξ	p(ξ	NOUN
ejpam-6131	321	21	n	n	PRON
ejpam-6131	321	22	4	4	NUM
ejpam-6131	321	23	)	)	PUNCT
ejpam-6131	321	24	,	,	PUNCT
ejpam-6131	321	25	p(ξ	p(ξ	NOUN
ejpam-6131	321	26	n	n	PRON
ejpam-6131	321	27	5	5	NUM
ejpam-6131	321	28	)	)	PUNCT
ejpam-6131	321	29	)	)	PUNCT
ejpam-6131	321	30	]	]	PUNCT
ejpam-6131	322	1	+	+	CCONJ
ejpam-6131	322	2	υ̃t(p(ξ1	υ̃t(p(ξ1	NOUN
ejpam-6131	322	3	)	)	PUNCT
ejpam-6131	322	4	,	,	PUNCT
ejpam-6131	322	5	p(p(ξ	p(p(ξ	NOUN
ejpam-6131	322	6	n	n	CCONJ
ejpam-6131	322	7	1	1	NUM
ejpam-6131	322	8	)	)	PUNCT
ejpam-6131	322	9	)	)	PUNCT
ejpam-6131	322	10	)	)	PUNCT
ejpam-6131	322	11	.	.	PUNCT
ejpam-6131	323	1	hence	hence	ADV
ejpam-6131	323	2	,	,	PUNCT
ejpam-6131	323	3	taking	take	VERB
ejpam-6131	323	4	n	n	PRON
ejpam-6131	323	5	→	→	SYM
ejpam-6131	323	6	+	+	PROPN
ejpam-6131	323	7	∞	∞	PROPN
ejpam-6131	323	8	,	,	PUNCT
ejpam-6131	323	9	one	one	PRON
ejpam-6131	323	10	gets	get	VERB
ejpam-6131	323	11	t(ζi(ξ1	t(ζi(ξ1	ADJ
ejpam-6131	323	12	,	,	PUNCT
ejpam-6131	323	13	ξ2	ξ2	ADJ
ejpam-6131	323	14	,	,	PUNCT
ejpam-6131	323	15	ξ3	ξ3	NOUN
ejpam-6131	323	16	,	,	PUNCT
ejpam-6131	323	17	ξ4	ξ4	NOUN
ejpam-6131	323	18	,	,	PUNCT
ejpam-6131	323	19	ξ5	ξ5	NOUN
ejpam-6131	323	20	)	)	PUNCT
ejpam-6131	323	21	,	,	PUNCT
ejpam-6131	323	22	p(ξ1	p(ξ1	NOUN
ejpam-6131	323	23	)	)	PUNCT
ejpam-6131	323	24	)	)	PUNCT
ejpam-6131	323	25	≤	≤	NOUN
ejpam-6131	323	26	γ̃t(p(ξ1	γ̃t(p(ξ1	NOUN
ejpam-6131	323	27	)	)	PUNCT
ejpam-6131	323	28	,	,	PUNCT
ejpam-6131	323	29	ζ	ζ	NOUN
ejpam-6131	323	30	i(ξ1	i(ξ1	NOUN
ejpam-6131	323	31	,	,	PUNCT
ejpam-6131	323	32	ξ2	ξ2	NOUN
ejpam-6131	323	33	,	,	PUNCT
ejpam-6131	323	34	ξ3	ξ3	NOUN
ejpam-6131	323	35	,	,	PUNCT
ejpam-6131	323	36	ξ4	ξ4	NOUN
ejpam-6131	323	37	,	,	PUNCT
ejpam-6131	323	38	ξ5	ξ5	NOUN
ejpam-6131	323	39	)	)	PUNCT
ejpam-6131	323	40	)	)	PUNCT
ejpam-6131	323	41	,	,	PUNCT
ejpam-6131	323	42	which	which	PRON
ejpam-6131	323	43	only	only	ADV
ejpam-6131	323	44	holds	hold	VERB
ejpam-6131	323	45	if	if	SCONJ
ejpam-6131	323	46	t(ζi(ξ1	t(ζi(ξ1	ADJ
ejpam-6131	323	47	,	,	PUNCT
ejpam-6131	323	48	ξ2	ξ2	ADJ
ejpam-6131	323	49	,	,	PUNCT
ejpam-6131	323	50	ξ3	ξ3	NOUN
ejpam-6131	323	51	,	,	PUNCT
ejpam-6131	323	52	ξ4	ξ4	NOUN
ejpam-6131	323	53	,	,	PUNCT
ejpam-6131	323	54	ξ5	ξ5	NOUN
ejpam-6131	323	55	)	)	PUNCT
ejpam-6131	323	56	,	,	PUNCT
ejpam-6131	323	57	p(ξ1	p(ξ1	NOUN
ejpam-6131	323	58	)	)	PUNCT
ejpam-6131	323	59	)	)	PUNCT
ejpam-6131	324	1	=	=	SYM
ejpam-6131	324	2	0	0	NUM
ejpam-6131	324	3	⇒	⇒	PROPN
ejpam-6131	324	4	ζi(ξ1	ζi(ξ1	NUM
ejpam-6131	324	5	,	,	PUNCT
ejpam-6131	324	6	ξ2	ξ2	ADJ
ejpam-6131	324	7	,	,	PUNCT
ejpam-6131	324	8	ξ3	ξ3	NOUN
ejpam-6131	324	9	,	,	PUNCT
ejpam-6131	324	10	ξ4	ξ4	NOUN
ejpam-6131	324	11	,	,	PUNCT
ejpam-6131	324	12	ξ5	ξ5	NOUN
ejpam-6131	324	13	)	)	PUNCT
ejpam-6131	324	14	=	=	SYM
ejpam-6131	324	15	p(ξ1	p(ξ1	NOUN
ejpam-6131	324	16	)	)	PUNCT
ejpam-6131	324	17	.	.	PUNCT
ejpam-6131	325	1	similar	similar	ADJ
ejpam-6131	325	2	operation	operation	NOUN
ejpam-6131	325	3	generates	generate	VERB
ejpam-6131	325	4	ζi(ξ2	ζi(ξ2	NOUN
ejpam-6131	325	5	,	,	PUNCT
ejpam-6131	325	6	ξ3	ξ3	NOUN
ejpam-6131	325	7	,	,	PUNCT
ejpam-6131	325	8	ξ4	ξ4	NOUN
ejpam-6131	325	9	,	,	PUNCT
ejpam-6131	325	10	ξ5	ξ5	NOUN
ejpam-6131	325	11	,	,	PUNCT
ejpam-6131	325	12	ξ1	ξ1	NOUN
ejpam-6131	325	13	)	)	PUNCT
ejpam-6131	325	14	=	=	SYM
ejpam-6131	325	15	p(ξ2	p(ξ2	NOUN
ejpam-6131	325	16	)	)	PUNCT
ejpam-6131	325	17	,	,	PUNCT
ejpam-6131	325	18	ζi(ξ3	ζi(ξ3	NOUN
ejpam-6131	325	19	,	,	PUNCT
ejpam-6131	325	20	ξ4	ξ4	NOUN
ejpam-6131	325	21	,	,	PUNCT
ejpam-6131	325	22	ξ5	ξ5	NOUN
ejpam-6131	325	23	,	,	PUNCT
ejpam-6131	325	24	ξ1	ξ1	NOUN
ejpam-6131	325	25	,	,	PUNCT
ejpam-6131	325	26	ξ2	ξ2	ADJ
ejpam-6131	325	27	)	)	PUNCT
ejpam-6131	325	28	=	=	SYM
ejpam-6131	325	29	p(ξ3	p(ξ3	NOUN
ejpam-6131	325	30	)	)	PUNCT
ejpam-6131	325	31	,	,	PUNCT
ejpam-6131	325	32	ζi(ξ4	ζi(ξ4	ADV
ejpam-6131	325	33	,	,	PUNCT
ejpam-6131	325	34	ξ5	ξ5	NOUN
ejpam-6131	325	35	,	,	PUNCT
ejpam-6131	325	36	ξ1	ξ1	NOUN
ejpam-6131	325	37	,	,	PUNCT
ejpam-6131	325	38	ξ2	ξ2	ADJ
ejpam-6131	325	39	,	,	PUNCT
ejpam-6131	325	40	ξ3	ξ3	NOUN
ejpam-6131	325	41	)	)	PUNCT
ejpam-6131	325	42	=	=	SYM
ejpam-6131	325	43	p(ξ4	p(ξ4	NOUN
ejpam-6131	325	44	)	)	PUNCT
ejpam-6131	325	45	and	and	CCONJ
ejpam-6131	325	46	ζi(ξ5	ζi(ξ5	NOUN
ejpam-6131	325	47	,	,	PUNCT
ejpam-6131	325	48	ξ1	ξ1	NOUN
ejpam-6131	325	49	,	,	PUNCT
ejpam-6131	325	50	ξ2	ξ2	ADJ
ejpam-6131	325	51	,	,	PUNCT
ejpam-6131	325	52	ξ3	ξ3	NOUN
ejpam-6131	325	53	,	,	PUNCT
ejpam-6131	325	54	ξ4	ξ4	NOUN
ejpam-6131	325	55	)	)	PUNCT
ejpam-6131	325	56	=	=	SYM
ejpam-6131	325	57	p(ξ5	p(ξ5	NOUN
ejpam-6131	325	58	)	)	PUNCT
ejpam-6131	325	59	.	.	PUNCT
ejpam-6131	326	1	hence	hence	ADV
ejpam-6131	326	2	,	,	PUNCT
ejpam-6131	326	3	(	(	PUNCT
ejpam-6131	326	4	ξ1	ξ1	NOUN
ejpam-6131	326	5	,	,	PUNCT
ejpam-6131	326	6	ξ2	ξ2	ADJ
ejpam-6131	326	7	,	,	PUNCT
ejpam-6131	326	8	ξ3	ξ3	NOUN
ejpam-6131	326	9	,	,	PUNCT
ejpam-6131	326	10	ξ4	ξ4	NOUN
ejpam-6131	326	11	,	,	PUNCT
ejpam-6131	326	12	ξ5	ξ5	NOUN
ejpam-6131	326	13	)	)	PUNCT
ejpam-6131	326	14	is	be	AUX
ejpam-6131	326	15	a	a	DET
ejpam-6131	326	16	qcp	qcp	NOUN
ejpam-6131	326	17	of	of	ADP
ejpam-6131	326	18	{	{	PUNCT
ejpam-6131	326	19	ζi}i∈w	ζi}i∈w	X
ejpam-6131	326	20	and	and	CCONJ
ejpam-6131	326	21	p.	p.	NOUN
ejpam-6131	326	22	the	the	DET
ejpam-6131	326	23	next	next	ADJ
ejpam-6131	326	24	result	result	NOUN
ejpam-6131	326	25	is	be	AUX
ejpam-6131	326	26	an	an	DET
ejpam-6131	326	27	extension	extension	NOUN
ejpam-6131	326	28	of	of	ADP
ejpam-6131	326	29	theorem	theorem	NOUN
ejpam-6131	326	30	1	1	NUM
ejpam-6131	326	31	by	by	ADP
ejpam-6131	326	32	introducing	introduce	VERB
ejpam-6131	326	33	s	s	PART
ejpam-6131	326	34	=	=	PUNCT
ejpam-6131	326	35	i	i	PROPN
ejpam-6131	326	36	d	d	PROPN
ejpam-6131	326	37	as	as	ADP
ejpam-6131	326	38	an	an	DET
ejpam-6131	326	39	identity	identity	NOUN
ejpam-6131	326	40	map	map	NOUN
ejpam-6131	326	41	.	.	PUNCT
ejpam-6131	327	1	corollary	corollary	ADJ
ejpam-6131	327	2	1	1	NUM
ejpam-6131	327	3	.	.	PUNCT
ejpam-6131	328	1	let	let	VERB
ejpam-6131	328	2	{	{	PUNCT
ejpam-6131	328	3	ζi}i∈w	ζi}i∈w	X
ejpam-6131	328	4	:	:	PUNCT
ejpam-6131	328	5	g5	g5	NOUN
ejpam-6131	328	6	→	→	SYM
ejpam-6131	328	7	g	g	NOUN
ejpam-6131	328	8	be	be	AUX
ejpam-6131	328	9	a	a	DET
ejpam-6131	328	10	mixed	mixed	ADJ
ejpam-6131	328	11	-	-	PUNCT
ejpam-6131	328	12	monotone	monotone	NOUN
ejpam-6131	328	13	sequence	sequence	NOUN
ejpam-6131	328	14	over	over	ADP
ejpam-6131	328	15	a	a	DET
ejpam-6131	328	16	pocgms	pocgms	NOUN
ejpam-6131	328	17	(	(	PUNCT
ejpam-6131	328	18	g	g	NOUN
ejpam-6131	328	19	,	,	PUNCT
ejpam-6131	328	20	t,⪯	t,⪯	NOUN
ejpam-6131	328	21	)	)	PUNCT
ejpam-6131	329	1	such	such	ADJ
ejpam-6131	329	2	that	that	SCONJ
ejpam-6131	329	3	{	{	PUNCT
ejpam-6131	329	4	ζi}i∈w	ζi}i∈w	X
ejpam-6131	329	5	and	and	CCONJ
ejpam-6131	329	6	i	i	PROPN
ejpam-6131	329	7	d	d	PROPN
ejpam-6131	329	8	:	:	PUNCT
ejpam-6131	329	9	g	g	NOUN
ejpam-6131	329	10	→	→	SYM
ejpam-6131	329	11	g	g	NOUN
ejpam-6131	329	12	satisfy	satisfy	NOUN
ejpam-6131	329	13	(	(	PUNCT
ejpam-6131	329	14	c	c	NOUN
ejpam-6131	329	15	)	)	PUNCT
ejpam-6131	329	16	condition	condition	NOUN
ejpam-6131	329	17	and	and	CCONJ
ejpam-6131	329	18	id(ℵ	id(ℵ	NOUN
ejpam-6131	329	19	)	)	PUNCT
ejpam-6131	329	20	is	be	AUX
ejpam-6131	329	21	regular	regular	ADJ
ejpam-6131	329	22	.	.	PUNCT
ejpam-6131	330	1	if	if	SCONJ
ejpam-6131	330	2	i	i	PROPN
ejpam-6131	330	3	d	d	PROPN
ejpam-6131	330	4	and	and	CCONJ
ejpam-6131	330	5	ζo	ζo	AUX
ejpam-6131	330	6	have	have	AUX
ejpam-6131	330	7	mqtp	mqtp	VERB
ejpam-6131	330	8	,	,	PUNCT
ejpam-6131	330	9	then	then	ADV
ejpam-6131	330	10	∃	∃	PROPN
ejpam-6131	330	11	(	(	PUNCT
ejpam-6131	330	12	ξ1	ξ1	PROPN
ejpam-6131	330	13	,	,	PUNCT
ejpam-6131	330	14	ξ2	ξ2	ADJ
ejpam-6131	330	15	,	,	PUNCT
ejpam-6131	330	16	ξ3	ξ3	NOUN
ejpam-6131	330	17	,	,	PUNCT
ejpam-6131	330	18	ξ4	ξ4	NOUN
ejpam-6131	330	19	,	,	PUNCT
ejpam-6131	330	20	ξ5	ξ5	NOUN
ejpam-6131	330	21	)	)	PUNCT
ejpam-6131	330	22	∈	∈	PROPN
ejpam-6131	330	23	g5	g5	NOUN
ejpam-6131	330	24	such	such	ADJ
ejpam-6131	330	25	that	that	SCONJ
ejpam-6131	330	26	ζi(ξ1	ζi(ξ1	NUM
ejpam-6131	330	27	,	,	PUNCT
ejpam-6131	330	28	ξ2	ξ2	ADJ
ejpam-6131	330	29	,	,	PUNCT
ejpam-6131	330	30	ξ3	ξ3	NOUN
ejpam-6131	330	31	,	,	PUNCT
ejpam-6131	330	32	ξ4	ξ4	NOUN
ejpam-6131	330	33	,	,	PUNCT
ejpam-6131	330	34	ξ5	ξ5	NOUN
ejpam-6131	330	35	)	)	PUNCT
ejpam-6131	330	36	=	=	SYM
ejpam-6131	330	37	ξ1	ξ1	NOUN
ejpam-6131	330	38	,	,	PUNCT
ejpam-6131	330	39	ζi(ξ2	ζi(ξ2	NOUN
ejpam-6131	330	40	,	,	PUNCT
ejpam-6131	330	41	ξ3	ξ3	NOUN
ejpam-6131	330	42	,	,	PUNCT
ejpam-6131	330	43	ξ4	ξ4	NOUN
ejpam-6131	330	44	,	,	PUNCT
ejpam-6131	330	45	ξ5	ξ5	NOUN
ejpam-6131	330	46	,	,	PUNCT
ejpam-6131	330	47	ξ1	ξ1	NOUN
ejpam-6131	330	48	)	)	PUNCT
ejpam-6131	330	49	=	=	SYM
ejpam-6131	330	50	ξ2	ξ2	NOUN
ejpam-6131	330	51	,	,	PUNCT
ejpam-6131	330	52	ζi(ξ3	ζi(ξ3	NOUN
ejpam-6131	330	53	,	,	PUNCT
ejpam-6131	330	54	ξ4	ξ4	NOUN
ejpam-6131	330	55	,	,	PUNCT
ejpam-6131	330	56	ξ5	ξ5	NOUN
ejpam-6131	330	57	,	,	PUNCT
ejpam-6131	330	58	ξ1	ξ1	NOUN
ejpam-6131	330	59	,	,	PUNCT
ejpam-6131	330	60	ξ2	ξ2	ADJ
ejpam-6131	330	61	)	)	PUNCT
ejpam-6131	330	62	=	=	SYM
ejpam-6131	330	63	ξ3	ξ3	NOUN
ejpam-6131	330	64	,	,	PUNCT
ejpam-6131	330	65	ζi(ξ4	ζi(ξ4	ADV
ejpam-6131	330	66	,	,	PUNCT
ejpam-6131	330	67	ξ5	ξ5	NOUN
ejpam-6131	330	68	,	,	PUNCT
ejpam-6131	330	69	ξ1	ξ1	NOUN
ejpam-6131	330	70	,	,	PUNCT
ejpam-6131	330	71	ξ2	ξ2	ADJ
ejpam-6131	330	72	,	,	PUNCT
ejpam-6131	330	73	ξ3	ξ3	NOUN
ejpam-6131	330	74	)	)	PUNCT
ejpam-6131	330	75	=	=	SYM
ejpam-6131	330	76	ξ4	ξ4	PROPN
ejpam-6131	330	77	,	,	PUNCT
ejpam-6131	330	78	and	and	CCONJ
ejpam-6131	330	79	ζi(ξ5	ζi(ξ5	NOUN
ejpam-6131	330	80	,	,	PUNCT
ejpam-6131	330	81	ξ1	ξ1	NOUN
ejpam-6131	330	82	,	,	PUNCT
ejpam-6131	330	83	ξ2	ξ2	ADJ
ejpam-6131	330	84	,	,	PUNCT
ejpam-6131	330	85	ξ3	ξ3	NOUN
ejpam-6131	330	86	,	,	PUNCT
ejpam-6131	330	87	ξ4	ξ4	NOUN
ejpam-6131	330	88	)	)	PUNCT
ejpam-6131	330	89	=	=	SYM
ejpam-6131	330	90	ξ5	ξ5	NOUN
ejpam-6131	330	91	.	.	PUNCT
ejpam-6131	331	1	for	for	ADP
ejpam-6131	331	2	i	i	PROPN
ejpam-6131	331	3	∈	∈	PROPN
ejpam-6131	331	4	w.	w.	PROPN
ejpam-6131	331	5	s.	s.	PROPN
ejpam-6131	331	6	batul	batul	PROPN
ejpam-6131	331	7	et	et	PROPN
ejpam-6131	331	8	a.	a.	PROPN
ejpam-6131	331	9	/	/	PUNCT
ejpam-6131	331	10	eur	eur	PROPN
ejpam-6131	331	11	.	.	PUNCT
ejpam-6131	332	1	j.	j.	PROPN
ejpam-6131	332	2	pure	pure	PROPN
ejpam-6131	332	3	appl	appl	PROPN
ejpam-6131	332	4	.	.	PROPN
ejpam-6131	332	5	math	math	PROPN
ejpam-6131	332	6	,	,	PUNCT
ejpam-6131	332	7	18	18	NUM
ejpam-6131	332	8	(	(	PUNCT
ejpam-6131	332	9	2	2	NUM
ejpam-6131	332	10	)	)	PUNCT
ejpam-6131	332	11	(	(	PUNCT
ejpam-6131	332	12	2025	2025	NUM
ejpam-6131	332	13	)	)	PUNCT
ejpam-6131	332	14	,	,	PUNCT
ejpam-6131	332	15	6131	6131	NUM
ejpam-6131	332	16	14	14	NUM
ejpam-6131	332	17	of	of	ADP
ejpam-6131	332	18	22	22	NUM
ejpam-6131	332	19	by	by	ADP
ejpam-6131	332	20	excluding	exclude	VERB
ejpam-6131	332	21	some	some	PRON
ejpam-6131	332	22	of	of	ADP
ejpam-6131	332	23	the	the	DET
ejpam-6131	332	24	conditions	condition	NOUN
ejpam-6131	332	25	from	from	ADP
ejpam-6131	332	26	corollary	corollary	ADJ
ejpam-6131	332	27	1	1	NUM
ejpam-6131	332	28	,	,	PUNCT
ejpam-6131	332	29	taking	take	VERB
ejpam-6131	332	30	γ̃	γ̃	PROPN
ejpam-6131	332	31	as	as	ADP
ejpam-6131	332	32	a	a	DET
ejpam-6131	332	33	zero	zero	NUM
ejpam-6131	332	34	matrix	matrix	NOUN
ejpam-6131	332	35	and	and	CCONJ
ejpam-6131	332	36	expanding	expand	VERB
ejpam-6131	332	37	the	the	DET
ejpam-6131	332	38	distance	distance	NOUN
ejpam-6131	332	39	t(ξ1	t(ξ1	NUM
ejpam-6131	332	40	,	,	PUNCT
ejpam-6131	332	41	ξ2	ξ2	NOUN
ejpam-6131	332	42	)	)	PUNCT
ejpam-6131	333	1	,	,	PUNCT
ejpam-6131	333	2	we	we	PRON
ejpam-6131	333	3	conclude	conclude	VERB
ejpam-6131	333	4	an	an	DET
ejpam-6131	333	5	important	important	ADJ
ejpam-6131	333	6	outcome	outcome	NOUN
ejpam-6131	333	7	.	.	PUNCT
ejpam-6131	334	1	corollary	corollary	ADJ
ejpam-6131	334	2	2	2	NUM
ejpam-6131	334	3	.	.	PUNCT
ejpam-6131	335	1	let	let	VERB
ejpam-6131	335	2	f	f	NOUN
ejpam-6131	335	3	:	:	PUNCT
ejpam-6131	335	4	g5	g5	NOUN
ejpam-6131	335	5	→	→	SYM
ejpam-6131	335	6	g	g	NOUN
ejpam-6131	335	7	be	be	AUX
ejpam-6131	335	8	a	a	DET
ejpam-6131	335	9	mixed	mixed	ADJ
ejpam-6131	335	10	-	-	PUNCT
ejpam-6131	335	11	monotone	monotone	NOUN
ejpam-6131	335	12	mapping	mapping	NOUN
ejpam-6131	335	13	in	in	ADP
ejpam-6131	335	14	the	the	DET
ejpam-6131	335	15	setting	setting	NOUN
ejpam-6131	335	16	of	of	ADP
ejpam-6131	335	17	a	a	DET
ejpam-6131	335	18	pocgms	pocgms	NOUN
ejpam-6131	335	19	(	(	PUNCT
ejpam-6131	335	20	g	g	NOUN
ejpam-6131	335	21	,	,	PUNCT
ejpam-6131	335	22	t,⪯	t,⪯	NOUN
ejpam-6131	335	23	)	)	PUNCT
ejpam-6131	335	24	such	such	ADJ
ejpam-6131	335	25	that	that	SCONJ
ejpam-6131	335	26	f	f	PROPN
ejpam-6131	335	27	has	have	VERB
ejpam-6131	335	28	a	a	DET
ejpam-6131	335	29	mqtp	mqtp	NOUN
ejpam-6131	335	30	and	and	CCONJ
ejpam-6131	335	31	f	f	PROPN
ejpam-6131	335	32	satisfy	satisfy	VERB
ejpam-6131	335	33	the	the	DET
ejpam-6131	335	34	condition	condition	NOUN
ejpam-6131	335	35	t(f(ξ1	t(f(ξ1	NOUN
ejpam-6131	335	36	,	,	PUNCT
ejpam-6131	335	37	ξ2	ξ2	ADJ
ejpam-6131	335	38	,	,	PUNCT
ejpam-6131	335	39	ξ3	ξ3	PROPN
ejpam-6131	335	40	,	,	PUNCT
ejpam-6131	335	41	ξ4	ξ4	PROPN
ejpam-6131	335	42	,	,	PUNCT
ejpam-6131	335	43	ξ5),f(q1	ξ5),f(q1	PROPN
ejpam-6131	335	44	,	,	PUNCT
ejpam-6131	335	45	q2	q2	PROPN
ejpam-6131	335	46	,	,	PUNCT
ejpam-6131	335	47	q3	q3	PROPN
ejpam-6131	335	48	,	,	PUNCT
ejpam-6131	335	49	q4	q4	PROPN
ejpam-6131	335	50	,	,	PUNCT
ejpam-6131	335	51	q5	q5	PROPN
ejpam-6131	335	52	)	)	PUNCT
ejpam-6131	335	53	)	)	PUNCT
ejpam-6131	336	1	≤	≤	PROPN
ejpam-6131	336	2	υ̃(t((ξ1	υ̃(t((ξ1	NUM
ejpam-6131	336	3	,	,	PUNCT
ejpam-6131	336	4	ξ2	ξ2	NOUN
ejpam-6131	336	5	,	,	PUNCT
ejpam-6131	336	6	ξ3	ξ3	NOUN
ejpam-6131	336	7	,	,	PUNCT
ejpam-6131	336	8	ξ4	ξ4	NOUN
ejpam-6131	336	9	,	,	PUNCT
ejpam-6131	336	10	ξ5	ξ5	NOUN
ejpam-6131	336	11	)	)	PUNCT
ejpam-6131	336	12	,	,	PUNCT
ejpam-6131	336	13	(	(	PUNCT
ejpam-6131	336	14	q1	q1	PROPN
ejpam-6131	336	15	,	,	PUNCT
ejpam-6131	336	16	q2	q2	NOUN
ejpam-6131	336	17	,	,	PUNCT
ejpam-6131	336	18	q3	q3	PROPN
ejpam-6131	336	19	,	,	PUNCT
ejpam-6131	336	20	q4	q4	PROPN
ejpam-6131	336	21	,	,	PUNCT
ejpam-6131	336	22	q5	q5	PROPN
ejpam-6131	336	23	)	)	PUNCT
ejpam-6131	336	24	)	)	PUNCT
ejpam-6131	336	25	)	)	PUNCT
ejpam-6131	336	26	.	.	PUNCT
ejpam-6131	337	1	then	then	ADV
ejpam-6131	337	2	,	,	PUNCT
ejpam-6131	337	3	their	their	PRON
ejpam-6131	337	4	exists	exist	VERB
ejpam-6131	337	5	a	a	DET
ejpam-6131	337	6	qfp	qfp	NOUN
ejpam-6131	337	7	of	of	ADP
ejpam-6131	337	8	f	f	PROPN
ejpam-6131	337	9	in	in	ADP
ejpam-6131	337	10	g.	g.	PROPN
ejpam-6131	337	11	definition	definition	NOUN
ejpam-6131	337	12	21	21	NUM
ejpam-6131	337	13	.	.	PUNCT
ejpam-6131	338	1	two	two	NUM
ejpam-6131	338	2	points	point	NOUN
ejpam-6131	338	3	(	(	PUNCT
ejpam-6131	338	4	ξ1	ξ1	NOUN
ejpam-6131	338	5	,	,	PUNCT
ejpam-6131	338	6	ξ2	ξ2	ADJ
ejpam-6131	338	7	,	,	PUNCT
ejpam-6131	338	8	ξ3	ξ3	NOUN
ejpam-6131	338	9	,	,	PUNCT
ejpam-6131	338	10	ξ4	ξ4	NOUN
ejpam-6131	338	11	,	,	PUNCT
ejpam-6131	338	12	ξ5	ξ5	NOUN
ejpam-6131	338	13	)	)	PUNCT
ejpam-6131	338	14	and	and	CCONJ
ejpam-6131	338	15	(	(	PUNCT
ejpam-6131	338	16	q1	q1	PROPN
ejpam-6131	338	17	,	,	PUNCT
ejpam-6131	338	18	q2	q2	NOUN
ejpam-6131	338	19	,	,	PUNCT
ejpam-6131	338	20	q3	q3	PROPN
ejpam-6131	338	21	,	,	PUNCT
ejpam-6131	338	22	q4	q4	PROPN
ejpam-6131	338	23	,	,	PUNCT
ejpam-6131	338	24	q5	q5	PROPN
ejpam-6131	338	25	)	)	PUNCT
ejpam-6131	338	26	∈	∈	PROPN
ejpam-6131	338	27	g	g	PROPN
ejpam-6131	338	28	are	be	AUX
ejpam-6131	338	29	called	call	VERB
ejpam-6131	338	30	quintuple	quintuple	ADV
ejpam-6131	338	31	comparable	comparable	ADJ
ejpam-6131	338	32	(	(	PUNCT
ejpam-6131	338	33	qc	qc	PROPN
ejpam-6131	338	34	)	)	PUNCT
ejpam-6131	338	35	if	if	SCONJ
ejpam-6131	339	1	and	and	CCONJ
ejpam-6131	339	2	only	only	ADV
ejpam-6131	339	3	if	if	SCONJ
ejpam-6131	339	4	ξ1	ξ1	PROPN
ejpam-6131	339	5	⪯	⪯	PROPN
ejpam-6131	339	6	q1	q1	PROPN
ejpam-6131	339	7	,	,	PUNCT
ejpam-6131	339	8	ξ2	ξ2	ADJ
ejpam-6131	339	9	⪰	⪰	NOUN
ejpam-6131	339	10	q2	q2	NOUN
ejpam-6131	339	11	,	,	PUNCT
ejpam-6131	339	12	ξ3	ξ3	PROPN
ejpam-6131	339	13	⪯	⪯	PROPN
ejpam-6131	339	14	q3	q3	PROPN
ejpam-6131	339	15	,	,	PUNCT
ejpam-6131	339	16	ξ4	ξ4	NOUN
ejpam-6131	339	17	⪰	⪰	NOUN
ejpam-6131	339	18	q4	q4	PROPN
ejpam-6131	339	19	,	,	PUNCT
ejpam-6131	339	20	ξ5	ξ5	PROPN
ejpam-6131	339	21	⪯	⪯	PROPN
ejpam-6131	339	22	q5	q5	PROPN
ejpam-6131	339	23	or	or	CCONJ
ejpam-6131	339	24	ξ1	ξ1	PROPN
ejpam-6131	339	25	⪰	⪰	PROPN
ejpam-6131	339	26	q1	q1	PROPN
ejpam-6131	339	27	,	,	PUNCT
ejpam-6131	339	28	ξ2	ξ2	PROPN
ejpam-6131	339	29	⪯	⪯	PROPN
ejpam-6131	339	30	q2	q2	PROPN
ejpam-6131	339	31	,	,	PUNCT
ejpam-6131	339	32	ξ3	ξ3	PROPN
ejpam-6131	339	33	⪰	⪰	NOUN
ejpam-6131	339	34	q3	q3	NOUN
ejpam-6131	339	35	,	,	PUNCT
ejpam-6131	339	36	ξ4	ξ4	PROPN
ejpam-6131	339	37	⪯	⪯	NOUN
ejpam-6131	339	38	q4	q4	PROPN
ejpam-6131	339	39	,	,	PUNCT
ejpam-6131	339	40	ξ5	ξ5	PROPN
ejpam-6131	339	41	⪰	⪰	PROPN
ejpam-6131	339	42	q5	q5	PROPN
ejpam-6131	339	43	or	or	CCONJ
ejpam-6131	339	44	ξ1	ξ1	PROPN
ejpam-6131	339	45	⪯	⪯	PROPN
ejpam-6131	339	46	q2	q2	PROPN
ejpam-6131	339	47	,	,	PUNCT
ejpam-6131	339	48	ξ2	ξ2	ADJ
ejpam-6131	339	49	⪰	⪰	NOUN
ejpam-6131	339	50	q3	q3	NOUN
ejpam-6131	339	51	,	,	PUNCT
ejpam-6131	339	52	ξ3	ξ3	PROPN
ejpam-6131	339	53	⪯	⪯	PROPN
ejpam-6131	339	54	q4	q4	PROPN
ejpam-6131	339	55	,	,	PUNCT
ejpam-6131	339	56	ξ4	ξ4	NOUN
ejpam-6131	339	57	⪰	⪰	PROPN
ejpam-6131	339	58	q5	q5	PROPN
ejpam-6131	339	59	,	,	PUNCT
ejpam-6131	339	60	ξ5	ξ5	PROPN
ejpam-6131	339	61	⪯	⪯	NOUN
ejpam-6131	339	62	q1	q1	PROPN
ejpam-6131	339	63	or	or	CCONJ
ejpam-6131	339	64	ξ1	ξ1	PROPN
ejpam-6131	339	65	⪰	⪰	PROPN
ejpam-6131	339	66	q2	q2	NOUN
ejpam-6131	339	67	,	,	PUNCT
ejpam-6131	339	68	ξ2	ξ2	PROPN
ejpam-6131	339	69	⪯	⪯	PROPN
ejpam-6131	339	70	q3	q3	PROPN
ejpam-6131	339	71	,	,	PUNCT
ejpam-6131	339	72	ξ3	ξ3	PROPN
ejpam-6131	339	73	⪰	⪰	NOUN
ejpam-6131	339	74	q4	q4	PROPN
ejpam-6131	339	75	,	,	PUNCT
ejpam-6131	339	76	ξ4	ξ4	PROPN
ejpam-6131	339	77	⪯	⪯	PROPN
ejpam-6131	339	78	q5	q5	PROPN
ejpam-6131	339	79	,	,	PUNCT
ejpam-6131	339	80	ξ5	ξ5	PROPN
ejpam-6131	339	81	⪰	⪰	NOUN
ejpam-6131	339	82	q1	q1	NOUN
ejpam-6131	339	83	or	or	CCONJ
ejpam-6131	339	84	ξ1	ξ1	PROPN
ejpam-6131	339	85	⪯	⪯	PROPN
ejpam-6131	339	86	q3	q3	PROPN
ejpam-6131	339	87	,	,	PUNCT
ejpam-6131	339	88	ξ2	ξ2	ADJ
ejpam-6131	339	89	⪰	⪰	NOUN
ejpam-6131	339	90	q4	q4	PROPN
ejpam-6131	339	91	,	,	PUNCT
ejpam-6131	339	92	ξ3	ξ3	PROPN
ejpam-6131	339	93	⪯	⪯	PROPN
ejpam-6131	339	94	q5	q5	PROPN
ejpam-6131	339	95	,	,	PUNCT
ejpam-6131	339	96	ξ4	ξ4	NOUN
ejpam-6131	339	97	⪰	⪰	NOUN
ejpam-6131	339	98	q1	q1	NOUN
ejpam-6131	339	99	,	,	PUNCT
ejpam-6131	339	100	ξ5	ξ5	PROPN
ejpam-6131	339	101	⪯	⪯	NOUN
ejpam-6131	339	102	q2	q2	NOUN
ejpam-6131	339	103	or	or	CCONJ
ejpam-6131	339	104	ξ1	ξ1	PROPN
ejpam-6131	339	105	⪰	⪰	PROPN
ejpam-6131	339	106	q3	q3	NOUN
ejpam-6131	339	107	,	,	PUNCT
ejpam-6131	339	108	ξ2	ξ2	PROPN
ejpam-6131	339	109	⪯	⪯	PROPN
ejpam-6131	339	110	q4	q4	PROPN
ejpam-6131	339	111	,	,	PUNCT
ejpam-6131	339	112	ξ3	ξ3	PROPN
ejpam-6131	339	113	⪰	⪰	PROPN
ejpam-6131	339	114	q5	q5	PROPN
ejpam-6131	339	115	,	,	PUNCT
ejpam-6131	339	116	ξ4	ξ4	PROPN
ejpam-6131	339	117	⪯	⪯	PROPN
ejpam-6131	339	118	q1	q1	PROPN
ejpam-6131	339	119	,	,	PUNCT
ejpam-6131	339	120	ξ5	ξ5	NOUN
ejpam-6131	339	121	⪰	⪰	NOUN
ejpam-6131	339	122	q2	q2	NOUN
ejpam-6131	339	123	or	or	CCONJ
ejpam-6131	339	124	ξ1	ξ1	PROPN
ejpam-6131	339	125	⪯	⪯	PROPN
ejpam-6131	339	126	q4	q4	PROPN
ejpam-6131	339	127	,	,	PUNCT
ejpam-6131	339	128	ξ2	ξ2	NOUN
ejpam-6131	339	129	⪰	⪰	PROPN
ejpam-6131	339	130	q5	q5	PROPN
ejpam-6131	339	131	,	,	PUNCT
ejpam-6131	339	132	ξ3	ξ3	PROPN
ejpam-6131	339	133	⪯	⪯	PROPN
ejpam-6131	339	134	q1	q1	PROPN
ejpam-6131	339	135	,	,	PUNCT
ejpam-6131	339	136	ξ4	ξ4	NOUN
ejpam-6131	339	137	⪰	⪰	NOUN
ejpam-6131	339	138	q2	q2	NOUN
ejpam-6131	339	139	,	,	PUNCT
ejpam-6131	339	140	ξ5	ξ5	PROPN
ejpam-6131	339	141	⪯	⪯	NOUN
ejpam-6131	339	142	q3	q3	NOUN
ejpam-6131	339	143	or	or	CCONJ
ejpam-6131	339	144	ξ1	ξ1	PROPN
ejpam-6131	339	145	⪰	⪰	NOUN
ejpam-6131	339	146	q4	q4	PROPN
ejpam-6131	339	147	,	,	PUNCT
ejpam-6131	339	148	ξ2	ξ2	PROPN
ejpam-6131	339	149	⪯	⪯	PROPN
ejpam-6131	339	150	q5	q5	PROPN
ejpam-6131	339	151	,	,	PUNCT
ejpam-6131	339	152	ξ3	ξ3	PROPN
ejpam-6131	339	153	⪰	⪰	NOUN
ejpam-6131	339	154	q1	q1	NOUN
ejpam-6131	339	155	,	,	PUNCT
ejpam-6131	339	156	ξ5	ξ5	PROPN
ejpam-6131	339	157	⪯	⪯	NOUN
ejpam-6131	339	158	q2	q2	NOUN
ejpam-6131	339	159	,	,	PUNCT
ejpam-6131	339	160	ξ5	ξ5	NOUN
ejpam-6131	339	161	⪰	⪰	NOUN
ejpam-6131	339	162	q3	q3	NOUN
ejpam-6131	339	163	or	or	CCONJ
ejpam-6131	339	164	ξ1	ξ1	PROPN
ejpam-6131	339	165	⪯	⪯	PROPN
ejpam-6131	339	166	q5	q5	PROPN
ejpam-6131	339	167	,	,	PUNCT
ejpam-6131	339	168	ξ2	ξ2	ADJ
ejpam-6131	339	169	⪰	⪰	NOUN
ejpam-6131	339	170	q1	q1	NOUN
ejpam-6131	339	171	,	,	PUNCT
ejpam-6131	339	172	ξ3	ξ3	PROPN
ejpam-6131	339	173	⪯	⪯	PROPN
ejpam-6131	339	174	q2	q2	NOUN
ejpam-6131	339	175	,	,	PUNCT
ejpam-6131	339	176	ξ4	ξ4	VERB
ejpam-6131	339	177	⪰	⪰	NOUN
ejpam-6131	339	178	q3	q3	NOUN
ejpam-6131	339	179	,	,	PUNCT
ejpam-6131	339	180	ξ5	ξ5	PROPN
ejpam-6131	339	181	⪯	⪯	NOUN
ejpam-6131	339	182	q4	q4	PROPN
ejpam-6131	339	183	or	or	CCONJ
ejpam-6131	339	184	ξ1	ξ1	PROPN
ejpam-6131	339	185	⪰	⪰	PROPN
ejpam-6131	339	186	q5	q5	PROPN
ejpam-6131	339	187	,	,	PUNCT
ejpam-6131	339	188	ξ2	ξ2	PROPN
ejpam-6131	339	189	⪯	⪯	PROPN
ejpam-6131	339	190	q1	q1	PROPN
ejpam-6131	339	191	,	,	PUNCT
ejpam-6131	339	192	ξ3	ξ3	PROPN
ejpam-6131	339	193	⪰	⪰	NOUN
ejpam-6131	339	194	q2	q2	NOUN
ejpam-6131	339	195	,	,	PUNCT
ejpam-6131	339	196	ξ4	ξ4	PROPN
ejpam-6131	339	197	⪯	⪯	PROPN
ejpam-6131	339	198	q3	q3	PROPN
ejpam-6131	339	199	,	,	PUNCT
ejpam-6131	339	200	ξ5	ξ5	NOUN
ejpam-6131	339	201	⪰	⪰	NOUN
ejpam-6131	339	202	q4	q4	PROPN
ejpam-6131	339	203	.	.	PUNCT
ejpam-6131	340	1	if	if	SCONJ
ejpam-6131	340	2	we	we	PRON
ejpam-6131	340	3	replace	replace	VERB
ejpam-6131	340	4	(	(	PUNCT
ejpam-6131	340	5	ξ1	ξ1	NOUN
ejpam-6131	340	6	,	,	PUNCT
ejpam-6131	340	7	ξ2	ξ2	ADJ
ejpam-6131	340	8	,	,	PUNCT
ejpam-6131	340	9	ξ3	ξ3	NOUN
ejpam-6131	340	10	,	,	PUNCT
ejpam-6131	340	11	ξ4	ξ4	NOUN
ejpam-6131	340	12	,	,	PUNCT
ejpam-6131	340	13	ξ5	ξ5	NOUN
ejpam-6131	340	14	)	)	PUNCT
ejpam-6131	340	15	and	and	CCONJ
ejpam-6131	340	16	(	(	PUNCT
ejpam-6131	340	17	q1	q1	PROPN
ejpam-6131	340	18	,	,	PUNCT
ejpam-6131	340	19	q2	q2	NOUN
ejpam-6131	340	20	,	,	PUNCT
ejpam-6131	340	21	q3	q3	PROPN
ejpam-6131	340	22	,	,	PUNCT
ejpam-6131	340	23	q4	q4	PROPN
ejpam-6131	340	24	,	,	PUNCT
ejpam-6131	340	25	q5	q5	PROPN
ejpam-6131	340	26	)	)	PUNCT
ejpam-6131	340	27	with	with	ADP
ejpam-6131	340	28	(	(	PUNCT
ejpam-6131	340	29	p(ξ1	p(ξ1	NOUN
ejpam-6131	340	30	)	)	PUNCT
ejpam-6131	340	31	,	,	PUNCT
ejpam-6131	340	32	p(ξ2	p(ξ2	NOUN
ejpam-6131	340	33	)	)	PUNCT
ejpam-6131	340	34	,	,	PUNCT
ejpam-6131	340	35	p(ξ3	p(ξ3	NOUN
ejpam-6131	340	36	)	)	PUNCT
ejpam-6131	340	37	,	,	PUNCT
ejpam-6131	340	38	p(ξ4	p(ξ4	PROPN
ejpam-6131	340	39	)	)	PUNCT
ejpam-6131	340	40	,	,	PUNCT
ejpam-6131	340	41	p(ξ5	p(ξ5	NOUN
ejpam-6131	340	42	)	)	PUNCT
ejpam-6131	340	43	)	)	PUNCT
ejpam-6131	341	1	and	and	CCONJ
ejpam-6131	341	2	(	(	PUNCT
ejpam-6131	341	3	p(q1	p(q1	PROPN
ejpam-6131	341	4	)	)	PUNCT
ejpam-6131	341	5	,	,	PUNCT
ejpam-6131	341	6	p(q2	p(q2	NOUN
ejpam-6131	341	7	)	)	PUNCT
ejpam-6131	341	8	,	,	PUNCT
ejpam-6131	341	9	p(q3	p(q3	NOUN
ejpam-6131	341	10	)	)	PUNCT
ejpam-6131	341	11	,	,	PUNCT
ejpam-6131	341	12	p(q4	p(q4	NOUN
ejpam-6131	341	13	)	)	PUNCT
ejpam-6131	341	14	,	,	PUNCT
ejpam-6131	341	15	p(q5	p(q5	NOUN
ejpam-6131	341	16	)	)	PUNCT
ejpam-6131	341	17	)	)	PUNCT
ejpam-6131	341	18	in	in	ADP
ejpam-6131	341	19	above	above	ADP
ejpam-6131	341	20	definition	definition	NOUN
ejpam-6131	341	21	,	,	PUNCT
ejpam-6131	341	22	then	then	ADV
ejpam-6131	341	23	we	we	PRON
ejpam-6131	341	24	say	say	VERB
ejpam-6131	341	25	that	that	PRON
ejpam-6131	341	26	(	(	PUNCT
ejpam-6131	341	27	ξ1	ξ1	NOUN
ejpam-6131	341	28	,	,	PUNCT
ejpam-6131	341	29	ξ2	ξ2	ADJ
ejpam-6131	341	30	,	,	PUNCT
ejpam-6131	341	31	ξ3	ξ3	NOUN
ejpam-6131	341	32	,	,	PUNCT
ejpam-6131	341	33	ξ4	ξ4	NOUN
ejpam-6131	341	34	,	,	PUNCT
ejpam-6131	341	35	ξ5	ξ5	NOUN
ejpam-6131	341	36	)	)	PUNCT
ejpam-6131	341	37	a	a	DET
ejpam-6131	341	38	qc	qc	NOUN
ejpam-6131	341	39	with	with	ADP
ejpam-6131	341	40	(	(	PUNCT
ejpam-6131	341	41	q	q	ADJ
ejpam-6131	341	42	,	,	PUNCT
ejpam-6131	341	43	q2	q2	NOUN
ejpam-6131	341	44	,	,	PUNCT
ejpam-6131	341	45	q3	q3	PROPN
ejpam-6131	341	46	,	,	PUNCT
ejpam-6131	341	47	q4	q4	PROPN
ejpam-6131	341	48	,	,	PUNCT
ejpam-6131	341	49	q5	q5	PROPN
ejpam-6131	341	50	)	)	PUNCT
ejpam-6131	341	51	with	with	ADP
ejpam-6131	341	52	respect	respect	NOUN
ejpam-6131	341	53	to	to	ADP
ejpam-6131	341	54	(	(	PUNCT
ejpam-6131	341	55	w.r.t	w.r.t	NOUN
ejpam-6131	341	56	)	)	PUNCT
ejpam-6131	341	57	p.	p.	NOUN
ejpam-6131	341	58	theorem	theorem	NOUN
ejpam-6131	341	59	2	2	X
ejpam-6131	341	60	.	.	PUNCT
ejpam-6131	342	1	let	let	VERB
ejpam-6131	342	2	{	{	PUNCT
ejpam-6131	342	3	ζi}i∈w	ζi}i∈w	X
ejpam-6131	342	4	:	:	PUNCT
ejpam-6131	342	5	g5	g5	NOUN
ejpam-6131	342	6	→	→	SYM
ejpam-6131	342	7	g	g	PROPN
ejpam-6131	343	1	and	and	CCONJ
ejpam-6131	343	2	p	p	X
ejpam-6131	343	3	:	:	PUNCT
ejpam-6131	343	4	g	g	PROPN
ejpam-6131	343	5	→	→	SYM
ejpam-6131	343	6	g	g	NOUN
ejpam-6131	343	7	be	be	AUX
ejpam-6131	343	8	two	two	NUM
ejpam-6131	343	9	mappings	mapping	NOUN
ejpam-6131	343	10	over	over	ADP
ejpam-6131	343	11	a	a	DET
ejpam-6131	343	12	pocgms	pocgms	NOUN
ejpam-6131	343	13	(	(	PUNCT
ejpam-6131	343	14	g	g	NOUN
ejpam-6131	343	15	,	,	PUNCT
ejpam-6131	343	16	t,⪯	t,⪯	NOUN
ejpam-6131	343	17	)	)	PUNCT
ejpam-6131	343	18	such	such	ADJ
ejpam-6131	343	19	that	that	SCONJ
ejpam-6131	343	20	{	{	PUNCT
ejpam-6131	343	21	ζi}i∈w	ζi}i∈w	X
ejpam-6131	343	22	and	and	CCONJ
ejpam-6131	343	23	p	p	PROPN
ejpam-6131	343	24	have	have	VERB
ejpam-6131	343	25	quintuple	quintuple	ADJ
ejpam-6131	343	26	coincidence	coincidence	NOUN
ejpam-6131	343	27	point	point	NOUN
ejpam-6131	343	28	with	with	ADP
ejpam-6131	343	29	quintuple	quintuple	ADV
ejpam-6131	343	30	comparable	comparable	ADJ
ejpam-6131	343	31	(	(	PUNCT
ejpam-6131	343	32	w.r.t	w.r.t	NOUN
ejpam-6131	343	33	)	)	PUNCT
ejpam-6131	343	34	p	p	NOUN
ejpam-6131	343	35	and	and	CCONJ
ejpam-6131	343	36	satisfy	satisfy	VERB
ejpam-6131	343	37	(	(	PUNCT
ejpam-6131	343	38	c	c	NOUN
ejpam-6131	343	39	)	)	PUNCT
ejpam-6131	343	40	condition	condition	NOUN
ejpam-6131	343	41	.	.	PUNCT
ejpam-6131	344	1	then	then	ADV
ejpam-6131	344	2	,	,	PUNCT
ejpam-6131	344	3	there	there	PRON
ejpam-6131	344	4	is	be	VERB
ejpam-6131	344	5	a	a	DET
ejpam-6131	344	6	unique	unique	ADJ
ejpam-6131	344	7	quintuple	quintuple	NOUN
ejpam-6131	344	8	coincidence	coincidence	NOUN
ejpam-6131	344	9	point	point	NOUN
ejpam-6131	344	10	{	{	PUNCT
ejpam-6131	344	11	ζi}i∈w	ζi}i∈w	X
ejpam-6131	344	12	and	and	CCONJ
ejpam-6131	344	13	p.	p.	NOUN
ejpam-6131	344	14	proof	proof	NOUN
ejpam-6131	344	15	.	.	PUNCT
ejpam-6131	345	1	theorem	theorem	ADJ
ejpam-6131	345	2	1	1	NUM
ejpam-6131	345	3	shows	show	VERB
ejpam-6131	345	4	that	that	SCONJ
ejpam-6131	345	5	the	the	DET
ejpam-6131	345	6	existence	existence	NOUN
ejpam-6131	345	7	of	of	ADP
ejpam-6131	345	8	a	a	DET
ejpam-6131	345	9	qcp	qcp	NOUN
ejpam-6131	345	10	s	s	NOUN
ejpam-6131	345	11	of	of	ADP
ejpam-6131	345	12	mappings	mapping	NOUN
ejpam-6131	345	13	is	be	AUX
ejpam-6131	345	14	ensured	ensure	VERB
ejpam-6131	345	15	.	.	PUNCT
ejpam-6131	346	1	let	let	VERB
ejpam-6131	346	2	(	(	PUNCT
ejpam-6131	346	3	ξ1	ξ1	NOUN
ejpam-6131	346	4	,	,	PUNCT
ejpam-6131	346	5	ξ2	ξ2	ADJ
ejpam-6131	346	6	,	,	PUNCT
ejpam-6131	346	7	ξ3	ξ3	NOUN
ejpam-6131	346	8	,	,	PUNCT
ejpam-6131	346	9	ξ4	ξ4	NOUN
ejpam-6131	346	10	,	,	PUNCT
ejpam-6131	346	11	ξ5	ξ5	NOUN
ejpam-6131	346	12	)	)	PUNCT
ejpam-6131	346	13	and	and	CCONJ
ejpam-6131	346	14	(	(	PUNCT
ejpam-6131	346	15	(	(	PUNCT
ejpam-6131	346	16	q1	q1	PROPN
ejpam-6131	346	17	,	,	PUNCT
ejpam-6131	346	18	q2	q2	NOUN
ejpam-6131	346	19	,	,	PUNCT
ejpam-6131	346	20	q3	q3	PROPN
ejpam-6131	346	21	,	,	PUNCT
ejpam-6131	346	22	q4	q4	PROPN
ejpam-6131	346	23	,	,	PUNCT
ejpam-6131	346	24	q5	q5	PROPN
ejpam-6131	346	25	)	)	PUNCT
ejpam-6131	346	26	be	be	AUX
ejpam-6131	346	27	qcp	qcp	NOUN
ejpam-6131	346	28	s	s	NOUN
ejpam-6131	346	29	,	,	PUNCT
ejpam-6131	346	30	that	that	ADV
ejpam-6131	346	31	is	is	ADV
ejpam-6131	346	32	,	,	PUNCT
ejpam-6131	346	33	if	if	SCONJ
ejpam-6131	346	34	p(ξ1	p(ξ1	VERB
ejpam-6131	346	35	)	)	PUNCT
ejpam-6131	346	36	=	=	SYM
ejpam-6131	346	37	ζi(ξ1	ζi(ξ1	NOUN
ejpam-6131	346	38	,	,	PUNCT
ejpam-6131	346	39	ξ2	ξ2	ADJ
ejpam-6131	346	40	,	,	PUNCT
ejpam-6131	346	41	ξ3	ξ3	NOUN
ejpam-6131	346	42	,	,	PUNCT
ejpam-6131	346	43	ξ4	ξ4	NOUN
ejpam-6131	346	44	,	,	PUNCT
ejpam-6131	346	45	ξ5	ξ5	NOUN
ejpam-6131	346	46	)	)	PUNCT
ejpam-6131	346	47	,	,	PUNCT
ejpam-6131	346	48	p(ξ2	p(ξ2	NOUN
ejpam-6131	346	49	)	)	PUNCT
ejpam-6131	346	50	=	=	SYM
ejpam-6131	346	51	ζi(ξ2	ζi(ξ2	NOUN
ejpam-6131	346	52	,	,	PUNCT
ejpam-6131	346	53	ξ3	ξ3	NOUN
ejpam-6131	346	54	,	,	PUNCT
ejpam-6131	346	55	ξ4	ξ4	NOUN
ejpam-6131	346	56	,	,	PUNCT
ejpam-6131	346	57	ξ5	ξ5	NOUN
ejpam-6131	346	58	,	,	PUNCT
ejpam-6131	346	59	ξ1	ξ1	NOUN
ejpam-6131	346	60	)	)	PUNCT
ejpam-6131	346	61	,	,	PUNCT
ejpam-6131	346	62	p(ξ3	p(ξ3	NOUN
ejpam-6131	346	63	)	)	PUNCT
ejpam-6131	346	64	=	=	SYM
ejpam-6131	346	65	ζi(ξ3	ζi(ξ3	NOUN
ejpam-6131	346	66	,	,	PUNCT
ejpam-6131	346	67	ξ4	ξ4	NOUN
ejpam-6131	346	68	,	,	PUNCT
ejpam-6131	346	69	ξ5	ξ5	NOUN
ejpam-6131	346	70	,	,	PUNCT
ejpam-6131	346	71	ξ1	ξ1	NOUN
ejpam-6131	346	72	,	,	PUNCT
ejpam-6131	346	73	ξ2	ξ2	NOUN
ejpam-6131	346	74	)	)	PUNCT
ejpam-6131	346	75	,	,	PUNCT
ejpam-6131	346	76	p(ξ4	p(ξ4	NOUN
ejpam-6131	346	77	)	)	PUNCT
ejpam-6131	346	78	=	=	SYM
ejpam-6131	347	1	ζi(ξ4	ζi(ξ4	NOUN
ejpam-6131	347	2	,	,	PUNCT
ejpam-6131	347	3	ξ5	ξ5	NOUN
ejpam-6131	347	4	,	,	PUNCT
ejpam-6131	347	5	ξ1	ξ1	NOUN
ejpam-6131	347	6	,	,	PUNCT
ejpam-6131	347	7	ξ2	ξ2	NOUN
ejpam-6131	347	8	,	,	PUNCT
ejpam-6131	347	9	ξ3	ξ3	NOUN
ejpam-6131	347	10	)	)	PUNCT
ejpam-6131	347	11	,	,	PUNCT
ejpam-6131	347	12	p(ξ5	p(ξ5	NOUN
ejpam-6131	347	13	)	)	PUNCT
ejpam-6131	347	14	=	=	SYM
ejpam-6131	347	15	ζi(ξ5	ζi(ξ5	NOUN
ejpam-6131	347	16	,	,	PUNCT
ejpam-6131	347	17	ξ1	ξ1	NOUN
ejpam-6131	347	18	,	,	PUNCT
ejpam-6131	347	19	ξ2	ξ2	ADJ
ejpam-6131	347	20	,	,	PUNCT
ejpam-6131	347	21	ξ3	ξ3	NOUN
ejpam-6131	347	22	,	,	PUNCT
ejpam-6131	347	23	ξ4	ξ4	PROPN
ejpam-6131	347	24	)	)	PUNCT
ejpam-6131	347	25	,	,	PUNCT
ejpam-6131	347	26	p(q1	p(q1	NOUN
ejpam-6131	347	27	)	)	PUNCT
ejpam-6131	347	28	=	=	SYM
ejpam-6131	347	29	ζi((q1	ζi((q1	PROPN
ejpam-6131	347	30	,	,	PUNCT
ejpam-6131	347	31	q2	q2	PROPN
ejpam-6131	347	32	,	,	PUNCT
ejpam-6131	347	33	q3	q3	PROPN
ejpam-6131	347	34	,	,	PUNCT
ejpam-6131	347	35	q4	q4	PROPN
ejpam-6131	347	36	,	,	PUNCT
ejpam-6131	347	37	q5	q5	PROPN
ejpam-6131	347	38	)	)	PUNCT
ejpam-6131	347	39	,	,	PUNCT
ejpam-6131	347	40	p(q2	p(q2	NOUN
ejpam-6131	347	41	)	)	PUNCT
ejpam-6131	347	42	=	=	SYM
ejpam-6131	347	43	ζi(q2	ζi(q2	PROPN
ejpam-6131	347	44	,	,	PUNCT
ejpam-6131	347	45	q3	q3	PROPN
ejpam-6131	347	46	,	,	PUNCT
ejpam-6131	347	47	q4	q4	PROPN
ejpam-6131	347	48	,	,	PUNCT
ejpam-6131	347	49	q5	q5	PROPN
ejpam-6131	347	50	,	,	PUNCT
ejpam-6131	347	51	q1	q1	PROPN
ejpam-6131	347	52	)	)	PUNCT
ejpam-6131	347	53	,	,	PUNCT
ejpam-6131	347	54	p(q3	p(q3	NOUN
ejpam-6131	347	55	)	)	PUNCT
ejpam-6131	347	56	=	=	SYM
ejpam-6131	347	57	ζi(q3	ζi(q3	PROPN
ejpam-6131	347	58	,	,	PUNCT
ejpam-6131	347	59	q4	q4	PROPN
ejpam-6131	347	60	,	,	PUNCT
ejpam-6131	347	61	q5	q5	PROPN
ejpam-6131	347	62	,	,	PUNCT
ejpam-6131	347	63	q1	q1	PROPN
ejpam-6131	347	64	,	,	PUNCT
ejpam-6131	347	65	q2	q2	NOUN
ejpam-6131	347	66	)	)	PUNCT
ejpam-6131	347	67	,	,	PUNCT
ejpam-6131	347	68	p(q4	p(q4	NOUN
ejpam-6131	347	69	)	)	PUNCT
ejpam-6131	347	70	=	=	PUNCT
ejpam-6131	347	71	ζi(q4	ζi(q4	X
ejpam-6131	347	72	,	,	PUNCT
ejpam-6131	347	73	q5	q5	PROPN
ejpam-6131	347	74	,	,	PUNCT
ejpam-6131	347	75	q1	q1	PROPN
ejpam-6131	347	76	,	,	PUNCT
ejpam-6131	347	77	q2	q2	NOUN
ejpam-6131	347	78	,	,	PUNCT
ejpam-6131	347	79	q3	q3	PROPN
ejpam-6131	347	80	)	)	PUNCT
ejpam-6131	347	81	,	,	PUNCT
ejpam-6131	347	82	p(q5	p(q5	NOUN
ejpam-6131	347	83	)	)	PUNCT
ejpam-6131	347	84	=	=	SYM
ejpam-6131	347	85	ζi(q5	ζi(q5	NOUN
ejpam-6131	347	86	,	,	PUNCT
ejpam-6131	347	87	q1	q1	PROPN
ejpam-6131	347	88	,	,	PUNCT
ejpam-6131	347	89	q2	q2	NOUN
ejpam-6131	347	90	,	,	PUNCT
ejpam-6131	347	91	q3	q3	PROPN
ejpam-6131	347	92	,	,	PUNCT
ejpam-6131	347	93	q4	q4	PROPN
ejpam-6131	347	94	)	)	PUNCT
ejpam-6131	347	95	,	,	PUNCT
ejpam-6131	347	96	then	then	ADV
ejpam-6131	347	97	,	,	PUNCT
ejpam-6131	347	98	p(ξ1	p(ξ1	NOUN
ejpam-6131	347	99	)	)	PUNCT
ejpam-6131	347	100	=	=	SYM
ejpam-6131	347	101	p(q1	p(q1	NOUN
ejpam-6131	347	102	)	)	PUNCT
ejpam-6131	347	103	,	,	PUNCT
ejpam-6131	347	104	p(ξ2	p(ξ2	NOUN
ejpam-6131	347	105	)	)	PUNCT
ejpam-6131	347	106	=	=	SYM
ejpam-6131	347	107	p(q2	p(q2	NOUN
ejpam-6131	347	108	)	)	PUNCT
ejpam-6131	347	109	,	,	PUNCT
ejpam-6131	347	110	p(ξ3	p(ξ3	NOUN
ejpam-6131	347	111	)	)	PUNCT
ejpam-6131	347	112	=	=	SYM
ejpam-6131	347	113	p(q3	p(q3	NOUN
ejpam-6131	347	114	)	)	PUNCT
ejpam-6131	347	115	,	,	PUNCT
ejpam-6131	347	116	p(ξ4	p(ξ4	NOUN
ejpam-6131	347	117	)	)	PUNCT
ejpam-6131	347	118	=	=	SYM
ejpam-6131	347	119	p(q4	p(q4	X
ejpam-6131	347	120	)	)	PUNCT
ejpam-6131	347	121	and	and	CCONJ
ejpam-6131	347	122	p(ξ5	p(ξ5	ADJ
ejpam-6131	347	123	)	)	PUNCT
ejpam-6131	347	124	=	=	SYM
ejpam-6131	347	125	p(q5	p(q5	NOUN
ejpam-6131	347	126	)	)	PUNCT
ejpam-6131	347	127	.	.	PUNCT
ejpam-6131	348	1	since	since	SCONJ
ejpam-6131	348	2	,	,	PUNCT
ejpam-6131	348	3	qcp	qcp	PROPN
ejpam-6131	348	4	s	s	X
ejpam-6131	348	5	are	be	AUX
ejpam-6131	348	6	also	also	ADV
ejpam-6131	348	7	qc	qc	PROPN
ejpam-6131	348	8	,	,	PUNCT
ejpam-6131	348	9	then	then	ADV
ejpam-6131	348	10	from	from	ADP
ejpam-6131	348	11	(	(	PUNCT
ejpam-6131	348	12	1	1	NUM
ejpam-6131	348	13	)	)	PUNCT
ejpam-6131	348	14	,	,	PUNCT
ejpam-6131	348	15	it	it	PRON
ejpam-6131	348	16	is	be	AUX
ejpam-6131	348	17	obtained	obtain	VERB
ejpam-6131	348	18	that	that	SCONJ
ejpam-6131	348	19	t(p(ξ1	t(p(ξ1	NOUN
ejpam-6131	348	20	)	)	PUNCT
ejpam-6131	348	21	,	,	PUNCT
ejpam-6131	348	22	p(q1	p(q1	NOUN
ejpam-6131	348	23	)	)	PUNCT
ejpam-6131	348	24	)	)	PUNCT
ejpam-6131	349	1	=	=	PUNCT
ejpam-6131	349	2	t(ζi(ξ1	t(ζi(ξ1	ADJ
ejpam-6131	349	3	,	,	PUNCT
ejpam-6131	349	4	ξ2	ξ2	ADJ
ejpam-6131	349	5	,	,	PUNCT
ejpam-6131	349	6	ξ3	ξ3	NOUN
ejpam-6131	349	7	,	,	PUNCT
ejpam-6131	349	8	ξ4	ξ4	NOUN
ejpam-6131	349	9	,	,	PUNCT
ejpam-6131	349	10	ξ5	ξ5	NOUN
ejpam-6131	349	11	)	)	PUNCT
ejpam-6131	349	12	,	,	PUNCT
ejpam-6131	349	13	ζ	ζ	NOUN
ejpam-6131	349	14	j(q1	j(q1	NOUN
ejpam-6131	349	15	,	,	PUNCT
ejpam-6131	349	16	q2	q2	PROPN
ejpam-6131	349	17	,	,	PUNCT
ejpam-6131	349	18	q3	q3	PROPN
ejpam-6131	349	19	,	,	PUNCT
ejpam-6131	349	20	q4	q4	PROPN
ejpam-6131	349	21	,	,	PUNCT
ejpam-6131	349	22	q5	q5	PROPN
ejpam-6131	349	23	)	)	PUNCT
ejpam-6131	349	24	)	)	PUNCT
ejpam-6131	349	25	≤	≤	NUM
ejpam-6131	349	26	γ̃[t(p(ξ1	γ̃[t(p(ξ1	NOUN
ejpam-6131	349	27	)	)	PUNCT
ejpam-6131	349	28	,	,	PUNCT
ejpam-6131	349	29	ζ	ζ	NOUN
ejpam-6131	349	30	i(ξ1	i(ξ1	NOUN
ejpam-6131	349	31	,	,	PUNCT
ejpam-6131	349	32	ξ2	ξ2	NOUN
ejpam-6131	349	33	,	,	PUNCT
ejpam-6131	349	34	ξ3	ξ3	NOUN
ejpam-6131	349	35	,	,	PUNCT
ejpam-6131	349	36	ξ4	ξ4	NOUN
ejpam-6131	349	37	,	,	PUNCT
ejpam-6131	349	38	ξ5	ξ5	NOUN
ejpam-6131	349	39	)	)	PUNCT
ejpam-6131	349	40	)	)	PUNCT
ejpam-6131	350	1	+	+	CCONJ
ejpam-6131	350	2	t(p(q1	t(p(q1	X
ejpam-6131	350	3	)	)	PUNCT
ejpam-6131	350	4	,	,	PUNCT
ejpam-6131	350	5	ζ	ζ	NOUN
ejpam-6131	350	6	j(q1	j(q1	NOUN
ejpam-6131	350	7	,	,	PUNCT
ejpam-6131	350	8	q2	q2	PROPN
ejpam-6131	350	9	,	,	PUNCT
ejpam-6131	350	10	q3	q3	PROPN
ejpam-6131	350	11	,	,	PUNCT
ejpam-6131	350	12	q4	q4	PROPN
ejpam-6131	350	13	,	,	PUNCT
ejpam-6131	350	14	q5	q5	PROPN
ejpam-6131	350	15	)	)	PUNCT
ejpam-6131	350	16	)	)	PUNCT
ejpam-6131	350	17	]	]	PUNCT
ejpam-6131	351	1	+	+	CCONJ
ejpam-6131	351	2	υ̃[t(p(ξ1	υ̃[t(p(ξ1	NOUN
ejpam-6131	351	3	)	)	PUNCT
ejpam-6131	351	4	,	,	PUNCT
ejpam-6131	351	5	p(q1	p(q1	NOUN
ejpam-6131	351	6	)	)	PUNCT
ejpam-6131	351	7	)	)	PUNCT
ejpam-6131	351	8	]	]	PUNCT
ejpam-6131	351	9	,	,	PUNCT
ejpam-6131	351	10	⇒	⇒	PROPN
ejpam-6131	351	11	t(p(ξ1	t(p(ξ1	NOUN
ejpam-6131	351	12	)	)	PUNCT
ejpam-6131	351	13	,	,	PUNCT
ejpam-6131	351	14	p(q1	p(q1	NOUN
ejpam-6131	351	15	)	)	PUNCT
ejpam-6131	351	16	)	)	PUNCT
ejpam-6131	352	1	≤	≤	NUM
ejpam-6131	352	2	υ̃[t(p(ξ1	υ̃[t(p(ξ1	NOUN
ejpam-6131	352	3	)	)	PUNCT
ejpam-6131	352	4	,	,	PUNCT
ejpam-6131	352	5	p(q1	p(q1	NOUN
ejpam-6131	352	6	)	)	PUNCT
ejpam-6131	352	7	)	)	PUNCT
ejpam-6131	352	8	]	]	PUNCT
ejpam-6131	352	9	.	.	PUNCT
ejpam-6131	353	1	s.	s.	PROPN
ejpam-6131	353	2	batul	batul	PROPN
ejpam-6131	353	3	et	et	PROPN
ejpam-6131	353	4	a.	a.	PROPN
ejpam-6131	353	5	/	/	PUNCT
ejpam-6131	353	6	eur	eur	PROPN
ejpam-6131	353	7	.	.	PUNCT
ejpam-6131	354	1	j.	j.	PROPN
ejpam-6131	354	2	pure	pure	PROPN
ejpam-6131	354	3	appl	appl	PROPN
ejpam-6131	354	4	.	.	PROPN
ejpam-6131	354	5	math	math	PROPN
ejpam-6131	354	6	,	,	PUNCT
ejpam-6131	354	7	18	18	NUM
ejpam-6131	354	8	(	(	PUNCT
ejpam-6131	354	9	2	2	NUM
ejpam-6131	354	10	)	)	PUNCT
ejpam-6131	354	11	(	(	PUNCT
ejpam-6131	354	12	2025	2025	NUM
ejpam-6131	354	13	)	)	PUNCT
ejpam-6131	354	14	,	,	PUNCT
ejpam-6131	354	15	6131	6131	NUM
ejpam-6131	354	16	15	15	NUM
ejpam-6131	354	17	of	of	ADP
ejpam-6131	354	18	22	22	NUM
ejpam-6131	354	19	since	since	SCONJ
ejpam-6131	354	20	i	i	PRON
ejpam-6131	354	21	̸=	̸=	PROPN
ejpam-6131	354	22	υ̃	υ̃	PROPN
ejpam-6131	354	23	∈	∈	PROPN
ejpam-6131	354	24	zm	zm	PROPN
ejpam-6131	354	25	,	,	PUNCT
ejpam-6131	354	26	then	then	ADV
ejpam-6131	354	27	t(p(ξ1	t(p(ξ1	NOUN
ejpam-6131	354	28	)	)	PUNCT
ejpam-6131	354	29	,	,	PUNCT
ejpam-6131	354	30	p(q1	p(q1	NOUN
ejpam-6131	354	31	)	)	PUNCT
ejpam-6131	354	32	)	)	PUNCT
ejpam-6131	355	1	=	=	PUNCT
ejpam-6131	355	2	0	0	NUM
ejpam-6131	355	3	,	,	PUNCT
ejpam-6131	355	4	or	or	CCONJ
ejpam-6131	355	5	p(ξ1	p(ξ1	NOUN
ejpam-6131	355	6	)	)	PUNCT
ejpam-6131	355	7	=	=	SYM
ejpam-6131	355	8	p(q1	p(q1	NOUN
ejpam-6131	355	9	)	)	PUNCT
ejpam-6131	355	10	.	.	PUNCT
ejpam-6131	356	1	similarly	similarly	ADV
ejpam-6131	356	2	,	,	PUNCT
ejpam-6131	356	3	it	it	PRON
ejpam-6131	356	4	is	be	AUX
ejpam-6131	356	5	obtained	obtain	VERB
ejpam-6131	356	6	that	that	DET
ejpam-6131	356	7	p(ξ2	p(ξ2	NOUN
ejpam-6131	356	8	)	)	PUNCT
ejpam-6131	356	9	=	=	SYM
ejpam-6131	356	10	p(q2	p(q2	NOUN
ejpam-6131	356	11	)	)	PUNCT
ejpam-6131	356	12	,	,	PUNCT
ejpam-6131	356	13	p(ξ3	p(ξ3	NOUN
ejpam-6131	356	14	)	)	PUNCT
ejpam-6131	356	15	=	=	SYM
ejpam-6131	356	16	p(q3	p(q3	NOUN
ejpam-6131	356	17	)	)	PUNCT
ejpam-6131	356	18	,	,	PUNCT
ejpam-6131	356	19	p(ξ4	p(ξ4	NOUN
ejpam-6131	356	20	)	)	PUNCT
ejpam-6131	356	21	=	=	SYM
ejpam-6131	356	22	p(q4	p(q4	X
ejpam-6131	356	23	)	)	PUNCT
ejpam-6131	356	24	and	and	CCONJ
ejpam-6131	356	25	p(ξ5	p(ξ5	ADJ
ejpam-6131	356	26	)	)	PUNCT
ejpam-6131	356	27	=	=	SYM
ejpam-6131	356	28	p(q5	p(q5	NOUN
ejpam-6131	356	29	)	)	PUNCT
ejpam-6131	356	30	.	.	PUNCT
ejpam-6131	357	1	hence	hence	ADV
ejpam-6131	357	2	,	,	PUNCT
ejpam-6131	357	3	p(ξ1	p(ξ1	NOUN
ejpam-6131	357	4	)	)	PUNCT
ejpam-6131	357	5	=	=	SYM
ejpam-6131	357	6	p(ξ2	p(ξ2	NOUN
ejpam-6131	357	7	)	)	PUNCT
ejpam-6131	357	8	=	=	SYM
ejpam-6131	357	9	p(ξ3	p(ξ3	NOUN
ejpam-6131	357	10	)	)	PUNCT
ejpam-6131	357	11	=	=	SYM
ejpam-6131	357	12	p(ξ4	p(ξ4	NOUN
ejpam-6131	357	13	)	)	PUNCT
ejpam-6131	357	14	=	=	SYM
ejpam-6131	357	15	p(ξ5	p(ξ5	NOUN
ejpam-6131	357	16	)	)	PUNCT
ejpam-6131	357	17	=	=	SYM
ejpam-6131	357	18	p(q1	p(q1	NOUN
ejpam-6131	357	19	)	)	PUNCT
ejpam-6131	357	20	=	=	SYM
ejpam-6131	357	21	p(q2	p(q2	NOUN
ejpam-6131	357	22	)	)	PUNCT
ejpam-6131	357	23	=	=	SYM
ejpam-6131	357	24	p(q3	p(q3	NOUN
ejpam-6131	357	25	)	)	PUNCT
ejpam-6131	357	26	=	=	SYM
ejpam-6131	358	1	p(q4	p(q4	X
ejpam-6131	358	2	)	)	PUNCT
ejpam-6131	358	3	=	=	SYM
ejpam-6131	358	4	p(q5	p(q5	NOUN
ejpam-6131	358	5	)	)	PUNCT
ejpam-6131	358	6	.	.	PUNCT
ejpam-6131	359	1	which	which	PRON
ejpam-6131	359	2	shows	show	VERB
ejpam-6131	359	3	that	that	SCONJ
ejpam-6131	359	4	(	(	PUNCT
ejpam-6131	359	5	p(ξ1	p(ξ1	NOUN
ejpam-6131	359	6	)	)	PUNCT
ejpam-6131	359	7	,	,	PUNCT
ejpam-6131	359	8	p(ξ2	p(ξ2	NOUN
ejpam-6131	359	9	)	)	PUNCT
ejpam-6131	359	10	,	,	PUNCT
ejpam-6131	359	11	p(ξ3	p(ξ3	NOUN
ejpam-6131	359	12	)	)	PUNCT
ejpam-6131	359	13	,	,	PUNCT
ejpam-6131	359	14	p(ξ4	p(ξ4	PROPN
ejpam-6131	359	15	)	)	PUNCT
ejpam-6131	359	16	,	,	PUNCT
ejpam-6131	359	17	p(ξ5	p(ξ5	NOUN
ejpam-6131	359	18	)	)	PUNCT
ejpam-6131	359	19	)	)	PUNCT
ejpam-6131	360	1	is	be	AUX
ejpam-6131	360	2	a	a	DET
ejpam-6131	360	3	unique	unique	ADJ
ejpam-6131	360	4	quintuple	quintuple	NOUN
ejpam-6131	360	5	coincidence	coincidence	NOUN
ejpam-6131	360	6	point	point	NOUN
ejpam-6131	360	7	of	of	ADP
ejpam-6131	360	8	{	{	PUNCT
ejpam-6131	360	9	ζi}i∈w	ζi}i∈w	X
ejpam-6131	360	10	and	and	CCONJ
ejpam-6131	360	11	p.	p.	PROPN
ejpam-6131	360	12	moreover	moreover	ADV
ejpam-6131	360	13	,	,	PUNCT
ejpam-6131	360	14	{	{	PUNCT
ejpam-6131	360	15	ζi}i∈w	ζi}i∈w	X
ejpam-6131	360	16	and	and	CCONJ
ejpam-6131	360	17	p	p	NOUN
ejpam-6131	360	18	being	be	AUX
ejpam-6131	360	19	compatible	compatible	ADJ
ejpam-6131	360	20	are	be	AUX
ejpam-6131	360	21	also	also	ADV
ejpam-6131	360	22	commutable	commutable	ADJ
ejpam-6131	360	23	,	,	PUNCT
ejpam-6131	360	24	which	which	PRON
ejpam-6131	360	25	proves	prove	VERB
ejpam-6131	360	26	the	the	DET
ejpam-6131	360	27	uniqueness	uniqueness	NOUN
ejpam-6131	360	28	of	of	ADP
ejpam-6131	360	29	the	the	DET
ejpam-6131	360	30	qfp	qfp	PROPN
ejpam-6131	360	31	(	(	PUNCT
ejpam-6131	360	32	ξ1	ξ1	PROPN
ejpam-6131	360	33	,	,	PUNCT
ejpam-6131	360	34	ξ2	ξ2	ADJ
ejpam-6131	360	35	,	,	PUNCT
ejpam-6131	360	36	ξ3	ξ3	NOUN
ejpam-6131	360	37	,	,	PUNCT
ejpam-6131	360	38	ξ4	ξ4	NOUN
ejpam-6131	360	39	,	,	PUNCT
ejpam-6131	360	40	ξ5	ξ5	NOUN
ejpam-6131	360	41	)	)	PUNCT
ejpam-6131	360	42	of	of	ADP
ejpam-6131	360	43	{	{	PUNCT
ejpam-6131	360	44	ζi}i∈w	ζi}i∈w	X
ejpam-6131	360	45	and	and	CCONJ
ejpam-6131	360	46	p.	p.	PROPN
ejpam-6131	360	47	example	example	NOUN
ejpam-6131	361	1	6	6	NUM
ejpam-6131	361	2	.	.	PUNCT
ejpam-6131	361	3	let	let	VERB
ejpam-6131	361	4	g	g	NOUN
ejpam-6131	361	5	=	=	PUNCT
ejpam-6131	362	1	[	[	X
ejpam-6131	362	2	0	0	NUM
ejpam-6131	362	3	,	,	PUNCT
ejpam-6131	362	4	1	1	NUM
ejpam-6131	362	5	]	]	PUNCT
ejpam-6131	362	6	be	be	AUX
ejpam-6131	362	7	the	the	DET
ejpam-6131	362	8	non	non	ADJ
ejpam-6131	362	9	-	-	ADJ
ejpam-6131	362	10	empty	empty	ADJ
ejpam-6131	362	11	set	set	NOUN
ejpam-6131	362	12	equipped	equip	VERB
ejpam-6131	362	13	with	with	ADP
ejpam-6131	362	14	the	the	DET
ejpam-6131	362	15	metric	metric	ADJ
ejpam-6131	362	16	t(ξ1	t(ξ1	NOUN
ejpam-6131	362	17	,	,	PUNCT
ejpam-6131	362	18	ξ2	ξ2	ADJ
ejpam-6131	362	19	)	)	PUNCT
ejpam-6131	362	20	=(	=(	NOUN
ejpam-6131	362	21	|ξ1	|ξ1	NOUN
ejpam-6131	362	22	−	−	NUM
ejpam-6131	362	23	ξ2|	ξ2|	PROPN
ejpam-6131	362	24	|ξ1	|ξ1	VERB
ejpam-6131	362	25	−	−	NUM
ejpam-6131	362	26	ξ2|	ξ2|	NOUN
ejpam-6131	362	27	)	)	PUNCT
ejpam-6131	362	28	and	and	CCONJ
ejpam-6131	362	29	γ̃	γ̃	PROPN
ejpam-6131	362	30	=	=	PUNCT
ejpam-6131	362	31	(	(	PUNCT
ejpam-6131	362	32	1	1	NUM
ejpam-6131	362	33	5	5	NUM
ejpam-6131	362	34	0	0	NUM
ejpam-6131	362	35	0	0	NUM
ejpam-6131	362	36	1	1	NUM
ejpam-6131	362	37	5	5	NUM
ejpam-6131	362	38	)	)	PUNCT
ejpam-6131	362	39	,	,	PUNCT
ejpam-6131	362	40	υ̃	υ̃	PROPN
ejpam-6131	362	41	=	=	PUNCT
ejpam-6131	362	42	(	(	PUNCT
ejpam-6131	362	43	0	0	NUM
ejpam-6131	362	44	1	1	NUM
ejpam-6131	362	45	25	25	NUM
ejpam-6131	362	46	1	1	NUM
ejpam-6131	362	47	25	25	NUM
ejpam-6131	362	48	0	0	NUM
ejpam-6131	362	49	)	)	PUNCT
ejpam-6131	362	50	∈	∈	PROPN
ejpam-6131	363	1	zm	zm	PROPN
ejpam-6131	363	2	.	.	PUNCT
ejpam-6131	364	1	hence	hence	ADV
ejpam-6131	364	2	,	,	PUNCT
ejpam-6131	364	3	(	(	PUNCT
ejpam-6131	364	4	g	g	NOUN
ejpam-6131	364	5	,	,	PUNCT
ejpam-6131	364	6	t,≤	t,≤	NOUN
ejpam-6131	364	7	)	)	PUNCT
ejpam-6131	364	8	is	be	AUX
ejpam-6131	364	9	clearly	clearly	ADV
ejpam-6131	364	10	a	a	DET
ejpam-6131	364	11	pocgms	pocgms	NOUN
ejpam-6131	364	12	.	.	PUNCT
ejpam-6131	365	1	let	let	VERB
ejpam-6131	365	2	ζi	ζi	PRON
ejpam-6131	365	3	:	:	PUNCT
ejpam-6131	365	4	g5	g5	NOUN
ejpam-6131	365	5	→	→	SYM
ejpam-6131	365	6	g	g	PROPN
ejpam-6131	365	7	and	and	CCONJ
ejpam-6131	365	8	s	s	VERB
ejpam-6131	365	9	:	:	PUNCT
ejpam-6131	365	10	g	g	NOUN
ejpam-6131	365	11	→	→	SYM
ejpam-6131	365	12	g	g	NOUN
ejpam-6131	365	13	be	be	VERB
ejpam-6131	365	14	two	two	NUM
ejpam-6131	365	15	mappings	mapping	NOUN
ejpam-6131	365	16	defined	define	VERB
ejpam-6131	365	17	as	as	ADP
ejpam-6131	365	18	ζi(ξ1	ζi(ξ1	NOUN
ejpam-6131	365	19	,	,	PUNCT
ejpam-6131	365	20	ξ2	ξ2	ADJ
ejpam-6131	365	21	,	,	PUNCT
ejpam-6131	365	22	ξ3	ξ3	NOUN
ejpam-6131	365	23	,	,	PUNCT
ejpam-6131	365	24	ξ4	ξ4	NOUN
ejpam-6131	365	25	,	,	PUNCT
ejpam-6131	365	26	ξ5	ξ5	NOUN
ejpam-6131	365	27	)	)	PUNCT
ejpam-6131	365	28	=	=	SYM
ejpam-6131	366	1	ξ1	ξ1	NOUN
ejpam-6131	366	2	5i	5i	NUM
ejpam-6131	366	3	and	and	CCONJ
ejpam-6131	366	4	p(ξ1	p(ξ1	NOUN
ejpam-6131	366	5	)	)	PUNCT
ejpam-6131	366	6	=	=	NUM
ejpam-6131	366	7	5ξ1	5ξ1	NUM
ejpam-6131	366	8	respectively	respectively	ADV
ejpam-6131	366	9	.	.	PUNCT
ejpam-6131	367	1	then	then	ADV
ejpam-6131	367	2	,	,	PUNCT
ejpam-6131	367	3	t(ζi(ξ1	t(ζi(ξ1	ADJ
ejpam-6131	367	4	,	,	PUNCT
ejpam-6131	367	5	ξ2	ξ2	ADJ
ejpam-6131	367	6	,	,	PUNCT
ejpam-6131	367	7	ξ3	ξ3	NOUN
ejpam-6131	367	8	,	,	PUNCT
ejpam-6131	367	9	ξ4	ξ4	NOUN
ejpam-6131	367	10	,	,	PUNCT
ejpam-6131	367	11	ξ5	ξ5	NOUN
ejpam-6131	367	12	)	)	PUNCT
ejpam-6131	367	13	,	,	PUNCT
ejpam-6131	367	14	ζ	ζ	NOUN
ejpam-6131	367	15	j(q1	j(q1	NOUN
ejpam-6131	367	16	,	,	PUNCT
ejpam-6131	367	17	q2	q2	PROPN
ejpam-6131	367	18	,	,	PUNCT
ejpam-6131	367	19	q3	q3	PROPN
ejpam-6131	367	20	,	,	PUNCT
ejpam-6131	367	21	q4	q4	PROPN
ejpam-6131	367	22	,	,	PUNCT
ejpam-6131	367	23	q5	q5	PROPN
ejpam-6131	367	24	)	)	PUNCT
ejpam-6131	367	25	)	)	PUNCT
ejpam-6131	368	1	=	=	PRON
ejpam-6131	368	2	(	(	PUNCT
ejpam-6131	368	3	|	|	ADV
ejpam-6131	368	4	ξ1	ξ1	PROPN
ejpam-6131	368	5	5i	5i	NUM
ejpam-6131	368	6	−	−	PROPN
ejpam-6131	368	7	q1	q1	PROPN
ejpam-6131	368	8	5j	5j	NUM
ejpam-6131	369	1	|	|	CCONJ
ejpam-6131	369	2	|	|	ADV
ejpam-6131	369	3	ξ1	ξ1	PROPN
ejpam-6131	369	4	5i	5i	NUM
ejpam-6131	369	5	−	−	PROPN
ejpam-6131	369	6	q1	q1	PROPN
ejpam-6131	369	7	5j	5j	NUM
ejpam-6131	369	8	|	|	ADV
ejpam-6131	369	9	)	)	PUNCT
ejpam-6131	369	10	=	=	SYM
ejpam-6131	369	11	1	1	NUM
ejpam-6131	369	12	5	5	NUM
ejpam-6131	369	13	(	(	PUNCT
ejpam-6131	369	14	|(6ξ1	|(6ξ1	NUM
ejpam-6131	369	15	5i	5i	NUM
ejpam-6131	369	16	−	−	PROPN
ejpam-6131	369	17	ξ1	ξ1	NOUN
ejpam-6131	369	18	5i	5i	NUM
ejpam-6131	369	19	)	)	PUNCT
ejpam-6131	370	1	+	+	CCONJ
ejpam-6131	370	2	(	(	PUNCT
ejpam-6131	370	3	q1	q1	PROPN
ejpam-6131	370	4	4j	4j	NOUN
ejpam-6131	370	5	−	−	PROPN
ejpam-6131	370	6	6q1	6q1	NUM
ejpam-6131	370	7	5j	5j	NUM
ejpam-6131	370	8	)	)	PUNCT
ejpam-6131	370	9	|	|	ADV
ejpam-6131	370	10	|(6ξ1	|(6ξ1	PUNCT
ejpam-6131	370	11	5i	5i	NUM
ejpam-6131	370	12	−	−	PROPN
ejpam-6131	370	13	ξ1	ξ1	NOUN
ejpam-6131	370	14	5i	5i	NUM
ejpam-6131	370	15	)	)	PUNCT
ejpam-6131	371	1	+	+	CCONJ
ejpam-6131	371	2	(	(	PUNCT
ejpam-6131	371	3	q1	q1	PROPN
ejpam-6131	371	4	4j	4j	NOUN
ejpam-6131	371	5	−	−	PROPN
ejpam-6131	371	6	6q1	6q1	NUM
ejpam-6131	371	7	5j	5j	NUM
ejpam-6131	371	8	)	)	PUNCT
ejpam-6131	371	9	|	|	CCONJ
ejpam-6131	371	10	)	)	PUNCT
ejpam-6131	371	11	≤	≤	NOUN
ejpam-6131	371	12	1	1	NUM
ejpam-6131	371	13	5	5	NUM
ejpam-6131	371	14	(	(	PUNCT
ejpam-6131	371	15	|(5ξ1	|(5ξ1	NUM
ejpam-6131	371	16	−	−	PROPN
ejpam-6131	371	17	ξ1	ξ1	PROPN
ejpam-6131	371	18	5i	5i	NUM
ejpam-6131	371	19	)	)	PUNCT
ejpam-6131	372	1	+	+	CCONJ
ejpam-6131	372	2	(	(	PUNCT
ejpam-6131	372	3	q1	q1	PROPN
ejpam-6131	372	4	5j	5j	NUM
ejpam-6131	372	5	−	−	PROPN
ejpam-6131	372	6	5q1	5q1	NUM
ejpam-6131	372	7	)	)	PUNCT
ejpam-6131	373	1	+	+	CCONJ
ejpam-6131	373	2	(	(	PUNCT
ejpam-6131	373	3	ξ1	ξ1	PROPN
ejpam-6131	373	4	−	−	PROPN
ejpam-6131	373	5	q1)|	q1)|	PROPN
ejpam-6131	373	6	|(5ξ1	|(5ξ1	PUNCT
ejpam-6131	374	1	−	−	PROPN
ejpam-6131	374	2	ξ1	ξ1	PROPN
ejpam-6131	374	3	5i	5i	NUM
ejpam-6131	374	4	)	)	PUNCT
ejpam-6131	375	1	+	+	CCONJ
ejpam-6131	375	2	(	(	PUNCT
ejpam-6131	375	3	q1	q1	PROPN
ejpam-6131	375	4	4j	4j	NOUN
ejpam-6131	375	5	−	−	ADV
ejpam-6131	375	6	4q1	4q1	NUM
ejpam-6131	375	7	)	)	PUNCT
ejpam-6131	376	1	+	+	CCONJ
ejpam-6131	376	2	(	(	PUNCT
ejpam-6131	376	3	ξ1	ξ1	PROPN
ejpam-6131	376	4	−	−	PROPN
ejpam-6131	376	5	q1)|	q1)|	PROPN
ejpam-6131	376	6	)	)	PUNCT
ejpam-6131	376	7	≤	≤	NOUN
ejpam-6131	376	8	1	1	NUM
ejpam-6131	376	9	5	5	NUM
ejpam-6131	376	10	(	(	PUNCT
ejpam-6131	376	11	(	(	PUNCT
ejpam-6131	376	12	|5ξ1	|5ξ1	NOUN
ejpam-6131	376	13	−	−	PROPN
ejpam-6131	376	14	ξ1	ξ1	PROPN
ejpam-6131	376	15	5i	5i	NUM
ejpam-6131	376	16	|	|	ADV
ejpam-6131	376	17	|5ξ1	|5ξ1	NOUN
ejpam-6131	376	18	−	−	PROPN
ejpam-6131	376	19	ξ1	ξ1	NOUN
ejpam-6131	376	20	5i	5i	NUM
ejpam-6131	376	21	|	|	ADV
ejpam-6131	376	22	)	)	PUNCT
ejpam-6131	377	1	+	+	CCONJ
ejpam-6131	377	2	(	(	PUNCT
ejpam-6131	377	3	|5q1	|5q1	ADJ
ejpam-6131	377	4	−	−	PROPN
ejpam-6131	377	5	q1	q1	NOUN
ejpam-6131	377	6	5j	5j	NUM
ejpam-6131	377	7	|	|	NOUN
ejpam-6131	377	8	|q1	|q1	NOUN
ejpam-6131	377	9	−	−	PROPN
ejpam-6131	377	10	q1	q1	PROPN
ejpam-6131	377	11	5j	5j	NUM
ejpam-6131	377	12	|	|	NOUN
ejpam-6131	377	13	)	)	PUNCT
ejpam-6131	377	14	)	)	PUNCT
ejpam-6131	378	1	+	+	CCONJ
ejpam-6131	378	2	1	1	NUM
ejpam-6131	378	3	25	25	NUM
ejpam-6131	378	4	(	(	PUNCT
ejpam-6131	378	5	|5ξ1	|5ξ1	NOUN
ejpam-6131	378	6	−	−	PROPN
ejpam-6131	378	7	5q1|	5q1|	NUM
ejpam-6131	378	8	|5ξ1	|5ξ1	NOUN
ejpam-6131	378	9	−	−	PROPN
ejpam-6131	378	10	5q1|	5q1|	NUM
ejpam-6131	378	11	)	)	PUNCT
ejpam-6131	378	12	=	=	PUNCT
ejpam-6131	379	1	(	(	PUNCT
ejpam-6131	379	2	1	1	NUM
ejpam-6131	379	3	5	5	NUM
ejpam-6131	379	4	0	0	NUM
ejpam-6131	379	5	0	0	NUM
ejpam-6131	379	6	1	1	NUM
ejpam-6131	379	7	5	5	NUM
ejpam-6131	379	8	)	)	PUNCT
ejpam-6131	379	9	(	(	PUNCT
ejpam-6131	379	10	t(p(ξ1	t(p(ξ1	NOUN
ejpam-6131	379	11	)	)	PUNCT
ejpam-6131	379	12	,	,	PUNCT
ejpam-6131	379	13	ζ	ζ	NOUN
ejpam-6131	379	14	i(ξ1	i(ξ1	NOUN
ejpam-6131	379	15	,	,	PUNCT
ejpam-6131	379	16	ξ2	ξ2	NOUN
ejpam-6131	379	17	,	,	PUNCT
ejpam-6131	379	18	ξ3	ξ3	NOUN
ejpam-6131	379	19	,	,	PUNCT
ejpam-6131	379	20	ξ4	ξ4	NOUN
ejpam-6131	379	21	,	,	PUNCT
ejpam-6131	379	22	ξ5	ξ5	NOUN
ejpam-6131	379	23	)	)	PUNCT
ejpam-6131	379	24	)	)	PUNCT
ejpam-6131	380	1	+	+	CCONJ
ejpam-6131	380	2	t(p(q1	t(p(q1	X
ejpam-6131	380	3	)	)	PUNCT
ejpam-6131	380	4	,	,	PUNCT
ejpam-6131	380	5	ζ	ζ	NOUN
ejpam-6131	380	6	j(q1	j(q1	NOUN
ejpam-6131	380	7	,	,	PUNCT
ejpam-6131	380	8	q2	q2	PROPN
ejpam-6131	380	9	,	,	PUNCT
ejpam-6131	380	10	q3	q3	PROPN
ejpam-6131	380	11	,	,	PUNCT
ejpam-6131	380	12	q4	q4	PROPN
ejpam-6131	380	13	,	,	PUNCT
ejpam-6131	380	14	q5	q5	PROPN
ejpam-6131	380	15	)	)	PUNCT
ejpam-6131	380	16	)	)	PUNCT
ejpam-6131	380	17	)	)	PUNCT
ejpam-6131	381	1	+	+	CCONJ
ejpam-6131	381	2	(	(	PUNCT
ejpam-6131	381	3	0	0	NUM
ejpam-6131	381	4	1	1	NUM
ejpam-6131	381	5	25	25	NUM
ejpam-6131	381	6	1	1	NUM
ejpam-6131	381	7	25	25	NUM
ejpam-6131	381	8	0	0	NUM
ejpam-6131	381	9	)	)	PUNCT
ejpam-6131	381	10	t(p(ξ1	t(p(ξ1	NOUN
ejpam-6131	381	11	)	)	PUNCT
ejpam-6131	381	12	,	,	PUNCT
ejpam-6131	381	13	p(q1	p(q1	NOUN
ejpam-6131	381	14	)	)	PUNCT
ejpam-6131	381	15	)	)	PUNCT
ejpam-6131	381	16	.	.	PUNCT
ejpam-6131	382	1	consequently	consequently	ADV
ejpam-6131	382	2	,	,	PUNCT
ejpam-6131	382	3	t(ζi(ξ1	t(ζi(ξ1	ADJ
ejpam-6131	382	4	,	,	PUNCT
ejpam-6131	382	5	ξ2	ξ2	ADJ
ejpam-6131	382	6	,	,	PUNCT
ejpam-6131	382	7	ξ3	ξ3	NOUN
ejpam-6131	382	8	,	,	PUNCT
ejpam-6131	382	9	ξ4	ξ4	NOUN
ejpam-6131	382	10	,	,	PUNCT
ejpam-6131	382	11	ξ5	ξ5	NOUN
ejpam-6131	382	12	)	)	PUNCT
ejpam-6131	382	13	,	,	PUNCT
ejpam-6131	382	14	ζ	ζ	NOUN
ejpam-6131	382	15	j(q1	j(q1	NOUN
ejpam-6131	382	16	,	,	PUNCT
ejpam-6131	382	17	q2	q2	PROPN
ejpam-6131	382	18	,	,	PUNCT
ejpam-6131	382	19	q3	q3	PROPN
ejpam-6131	382	20	,	,	PUNCT
ejpam-6131	382	21	q4	q4	PROPN
ejpam-6131	382	22	,	,	PUNCT
ejpam-6131	382	23	q5	q5	PROPN
ejpam-6131	382	24	)	)	PUNCT
ejpam-6131	382	25	)	)	PUNCT
ejpam-6131	382	26	≤	≤	NUM
ejpam-6131	382	27	γ̃[t(p(ξ1	γ̃[t(p(ξ1	NOUN
ejpam-6131	382	28	)	)	PUNCT
ejpam-6131	382	29	,	,	PUNCT
ejpam-6131	382	30	ζ	ζ	NOUN
ejpam-6131	382	31	i(ξ1	i(ξ1	NOUN
ejpam-6131	382	32	,	,	PUNCT
ejpam-6131	382	33	ξ2	ξ2	NOUN
ejpam-6131	382	34	,	,	PUNCT
ejpam-6131	382	35	ξ3	ξ3	NOUN
ejpam-6131	382	36	,	,	PUNCT
ejpam-6131	382	37	ξ4	ξ4	NOUN
ejpam-6131	382	38	,	,	PUNCT
ejpam-6131	382	39	ξ5	ξ5	NOUN
ejpam-6131	382	40	)	)	PUNCT
ejpam-6131	382	41	)	)	PUNCT
ejpam-6131	383	1	+	+	CCONJ
ejpam-6131	383	2	t(p(q1	t(p(q1	X
ejpam-6131	383	3	)	)	PUNCT
ejpam-6131	383	4	,	,	PUNCT
ejpam-6131	383	5	ζ	ζ	NOUN
ejpam-6131	383	6	j(q1	j(q1	NOUN
ejpam-6131	383	7	,	,	PUNCT
ejpam-6131	383	8	q2	q2	PROPN
ejpam-6131	383	9	,	,	PUNCT
ejpam-6131	383	10	q3	q3	PROPN
ejpam-6131	383	11	,	,	PUNCT
ejpam-6131	383	12	q4	q4	PROPN
ejpam-6131	383	13	,	,	PUNCT
ejpam-6131	383	14	q5	q5	PROPN
ejpam-6131	383	15	)	)	PUNCT
ejpam-6131	383	16	)	)	PUNCT
ejpam-6131	383	17	]	]	PUNCT
ejpam-6131	384	1	+	+	CCONJ
ejpam-6131	384	2	υ̃t(p(ξ1	υ̃t(p(ξ1	NOUN
ejpam-6131	384	3	)	)	PUNCT
ejpam-6131	384	4	,	,	PUNCT
ejpam-6131	384	5	p(q1	p(q1	NOUN
ejpam-6131	384	6	)	)	PUNCT
ejpam-6131	384	7	)	)	PUNCT
ejpam-6131	384	8	.	.	PUNCT
ejpam-6131	385	1	hence	hence	ADV
ejpam-6131	385	2	,	,	PUNCT
ejpam-6131	385	3	the	the	DET
ejpam-6131	385	4	(	(	PUNCT
ejpam-6131	385	5	c	c	NOUN
ejpam-6131	385	6	)	)	PUNCT
ejpam-6131	385	7	condition	condition	NOUN
ejpam-6131	385	8	is	be	AUX
ejpam-6131	385	9	fulfilled	fulfil	VERB
ejpam-6131	385	10	.	.	PUNCT
ejpam-6131	386	1	all	all	DET
ejpam-6131	386	2	the	the	DET
ejpam-6131	386	3	conditions	condition	NOUN
ejpam-6131	386	4	of	of	ADP
ejpam-6131	386	5	theorem	theorem	NOUN
ejpam-6131	386	6	1	1	NUM
ejpam-6131	386	7	are	be	AUX
ejpam-6131	386	8	accomplished	accomplish	VERB
ejpam-6131	386	9	.	.	PUNCT
ejpam-6131	387	1	moreover	moreover	ADV
ejpam-6131	387	2	,	,	PUNCT
ejpam-6131	387	3	(	(	PUNCT
ejpam-6131	387	4	0	0	NUM
ejpam-6131	387	5	,	,	PUNCT
ejpam-6131	387	6	0	0	NUM
ejpam-6131	387	7	,	,	PUNCT
ejpam-6131	387	8	0	0	NUM
ejpam-6131	387	9	,	,	PUNCT
ejpam-6131	387	10	0	0	NUM
ejpam-6131	387	11	,	,	PUNCT
ejpam-6131	387	12	0	0	NUM
ejpam-6131	387	13	)	)	PUNCT
ejpam-6131	387	14	being	be	AUX
ejpam-6131	387	15	a	a	DET
ejpam-6131	387	16	qcp	qcp	NOUN
ejpam-6131	387	17	of	of	ADP
ejpam-6131	387	18	{	{	PUNCT
ejpam-6131	387	19	ζi}i∈w	ζi}i∈w	X
ejpam-6131	387	20	and	and	CCONJ
ejpam-6131	387	21	p	p	NOUN
ejpam-6131	387	22	is	be	AUX
ejpam-6131	387	23	also	also	ADV
ejpam-6131	387	24	a	a	DET
ejpam-6131	387	25	unique	unique	ADJ
ejpam-6131	387	26	quintuple	quintuple	NOUN
ejpam-6131	387	27	coincidence	coincidence	NOUN
ejpam-6131	387	28	point	point	NOUN
ejpam-6131	387	29	of	of	ADP
ejpam-6131	387	30	both	both	DET
ejpam-6131	387	31	mappings	mapping	NOUN
ejpam-6131	387	32	according	accord	VERB
ejpam-6131	387	33	to	to	ADP
ejpam-6131	387	34	theorem	theorem	ADJ
ejpam-6131	387	35	2	2	NUM
ejpam-6131	387	36	.	.	PUNCT
ejpam-6131	387	37	s.	s.	PROPN
ejpam-6131	387	38	batul	batul	PROPN
ejpam-6131	387	39	et	et	PROPN
ejpam-6131	387	40	a.	a.	PROPN
ejpam-6131	387	41	/	/	PUNCT
ejpam-6131	387	42	eur	eur	PROPN
ejpam-6131	387	43	.	.	PUNCT
ejpam-6131	388	1	j.	j.	PROPN
ejpam-6131	388	2	pure	pure	PROPN
ejpam-6131	388	3	appl	appl	PROPN
ejpam-6131	388	4	.	.	PROPN
ejpam-6131	388	5	math	math	PROPN
ejpam-6131	388	6	,	,	PUNCT
ejpam-6131	388	7	18	18	NUM
ejpam-6131	388	8	(	(	PUNCT
ejpam-6131	388	9	2	2	NUM
ejpam-6131	388	10	)	)	PUNCT
ejpam-6131	388	11	(	(	PUNCT
ejpam-6131	388	12	2025	2025	NUM
ejpam-6131	388	13	)	)	PUNCT
ejpam-6131	388	14	,	,	PUNCT
ejpam-6131	388	15	6131	6131	NUM
ejpam-6131	388	16	16	16	NUM
ejpam-6131	388	17	of	of	ADP
ejpam-6131	388	18	22	22	NUM
ejpam-6131	388	19	4	4	NUM
ejpam-6131	388	20	.	.	PUNCT
ejpam-6131	389	1	application	application	NOUN
ejpam-6131	389	2	suppose	suppose	VERB
ejpam-6131	389	3	that	that	SCONJ
ejpam-6131	389	4	rn	rn	PROPN
ejpam-6131	389	5	+	+	CCONJ
ejpam-6131	389	6	=	=	SYM
ejpam-6131	389	7	{	{	PUNCT
ejpam-6131	389	8	ξ1	ξ1	NOUN
ejpam-6131	389	9	=	=	SYM
ejpam-6131	389	10	(	(	PUNCT
ejpam-6131	389	11	ξ11	ξ11	NOUN
ejpam-6131	389	12	,	,	PUNCT
ejpam-6131	389	13	ξ	ξ	PROPN
ejpam-6131	389	14	2	2	NUM
ejpam-6131	389	15	1	1	NUM
ejpam-6131	389	16	,	,	PUNCT
ejpam-6131	389	17	ξ	ξ	PROPN
ejpam-6131	389	18	3	3	NUM
ejpam-6131	389	19	1	1	NUM
ejpam-6131	389	20	,	,	PUNCT
ejpam-6131	389	21	·	·	PUNCT
ejpam-6131	389	22	·	·	PUNCT
ejpam-6131	389	23	·	·	PUNCT
ejpam-6131	389	24	,	,	PUNCT
ejpam-6131	389	25	ξn1	ξn1	PROPN
ejpam-6131	389	26	)	)	PUNCT
ejpam-6131	389	27	:	:	PUNCT
ejpam-6131	390	1	ξi	ξi	NOUN
ejpam-6131	390	2	≥	≥	NOUN
ejpam-6131	390	3	,	,	PUNCT
ejpam-6131	390	4	i	i	PRON
ejpam-6131	390	5	≥	≥	VERB
ejpam-6131	390	6	1	1	NUM
ejpam-6131	390	7	}	}	PUNCT
ejpam-6131	390	8	and	and	CCONJ
ejpam-6131	390	9	θ5	θ5	PROPN
ejpam-6131	390	10	n−1	n−1	PROPN
ejpam-6131	390	11	being	be	AUX
ejpam-6131	390	12	5(n	5(n	NUM
ejpam-6131	390	13	−	−	NOUN
ejpam-6131	390	14	1	1	X
ejpam-6131	390	15	)	)	PUNCT
ejpam-6131	390	16	dimensional	dimensional	ADJ
ejpam-6131	390	17	unit	unit	NOUN
ejpam-6131	390	18	simplex	simplex	NOUN
ejpam-6131	390	19	defined	define	VERB
ejpam-6131	390	20	as	as	ADP
ejpam-6131	390	21	θ5	θ5	PROPN
ejpam-6131	390	22	n−1	n−1	PROPN
ejpam-6131	390	23	=	=	SYM
ejpam-6131	390	24	{	{	PUNCT
ejpam-6131	390	25	θ	θ	NOUN
ejpam-6131	390	26	=	=	PUNCT
ejpam-6131	390	27	(	(	PUNCT
ejpam-6131	390	28	ξ1	ξ1	PROPN
ejpam-6131	390	29	,	,	PUNCT
ejpam-6131	390	30	ξ2	ξ2	ADJ
ejpam-6131	390	31	,	,	PUNCT
ejpam-6131	390	32	ξ3	ξ3	NOUN
ejpam-6131	390	33	,	,	PUNCT
ejpam-6131	390	34	ξ4	ξ4	NOUN
ejpam-6131	390	35	,	,	PUNCT
ejpam-6131	390	36	ξ5	ξ5	NOUN
ejpam-6131	390	37	)	)	PUNCT
ejpam-6131	390	38	∈	∈	PROPN
ejpam-6131	390	39	rn	rn	PROPN
ejpam-6131	391	1	+	+	CCONJ
ejpam-6131	391	2	×	×	PROPN
ejpam-6131	391	3	rn	rn	PROPN
ejpam-6131	391	4	+	+	PROPN
ejpam-6131	391	5	×	×	PROPN
ejpam-6131	391	6	rn	rn	PROPN
ejpam-6131	391	7	+	+	PROPN
ejpam-6131	391	8	×	×	PROPN
ejpam-6131	391	9	rn	rn	PROPN
ejpam-6131	391	10	+	+	PROPN
ejpam-6131	391	11	×	×	PROPN
ejpam-6131	391	12	rn	rn	PROPN
ejpam-6131	391	13	+	+	NOUN
ejpam-6131	391	14	:	:	PUNCT
ejpam-6131	391	15	n∑	n∑	PROPN
ejpam-6131	391	16	i=1	i=1	PROPN
ejpam-6131	391	17	θi	θi	ADP
ejpam-6131	391	18	=	=	SYM
ejpam-6131	391	19	n∑	n∑	PROPN
ejpam-6131	391	20	i=1	i=1	PROPN
ejpam-6131	391	21	(	(	PUNCT
ejpam-6131	391	22	ξi1	ξi1	NOUN
ejpam-6131	391	23	+	+	CCONJ
ejpam-6131	391	24	ξi2	ξi2	VERB
ejpam-6131	391	25	+	+	CCONJ
ejpam-6131	391	26	ξi3	ξi3	NOUN
ejpam-6131	391	27	+	+	CCONJ
ejpam-6131	391	28	ξi4	ξi4	NOUN
ejpam-6131	391	29	+	+	CCONJ
ejpam-6131	391	30	ξi5	ξi5	NOUN
ejpam-6131	391	31	)	)	PUNCT
ejpam-6131	391	32	=	=	SYM
ejpam-6131	391	33	1	1	NUM
ejpam-6131	391	34	}	}	PUNCT
ejpam-6131	391	35	.	.	PUNCT
ejpam-6131	392	1	let	let	VERB
ejpam-6131	392	2	θ	θ	PROPN
ejpam-6131	392	3	∈	∈	PROPN
ejpam-6131	392	4	θ5	θ5	PROPN
ejpam-6131	392	5	n−1	n−1	PROPN
ejpam-6131	392	6	be	be	AUX
ejpam-6131	392	7	the	the	DET
ejpam-6131	392	8	probability	probability	NOUN
ejpam-6131	392	9	over	over	ADP
ejpam-6131	392	10	5n	5n	NUM
ejpam-6131	392	11	prospective	prospective	ADJ
ejpam-6131	392	12	states	state	NOUN
ejpam-6131	392	13	.	.	PUNCT
ejpam-6131	393	1	as	as	ADP
ejpam-6131	393	2	a	a	DET
ejpam-6131	393	3	stochastic	stochastic	ADJ
ejpam-6131	393	4	process	process	NOUN
ejpam-6131	393	5	,	,	PUNCT
ejpam-6131	393	6	the	the	DET
ejpam-6131	393	7	markov	markov	NOUN
ejpam-6131	393	8	process	process	NOUN
ejpam-6131	393	9	asserts	assert	VERB
ejpam-6131	393	10	that	that	SCONJ
ejpam-6131	393	11	5n	5n	NUM
ejpam-6131	393	12	states	state	NOUN
ejpam-6131	393	13	are	be	AUX
ejpam-6131	393	14	achieved	achieve	VERB
ejpam-6131	393	15	in	in	ADP
ejpam-6131	393	16	each	each	DET
ejpam-6131	393	17	period	period	NOUN
ejpam-6131	393	18	π	π	X
ejpam-6131	393	19	=	=	SYM
ejpam-6131	393	20	1	1	NUM
ejpam-6131	393	21	,	,	PUNCT
ejpam-6131	393	22	2	2	NUM
ejpam-6131	393	23	,	,	PUNCT
ejpam-6131	393	24	3	3	NUM
ejpam-6131	393	25	,	,	PUNCT
ejpam-6131	393	26	·	·	PUNCT
ejpam-6131	393	27	·	·	PUNCT
ejpam-6131	393	28	·	·	PUNCT
ejpam-6131	393	29	with	with	ADP
ejpam-6131	393	30	the	the	DET
ejpam-6131	393	31	probability	probability	NOUN
ejpam-6131	393	32	events	event	NOUN
ejpam-6131	393	33	over	over	ADP
ejpam-6131	393	34	the	the	DET
ejpam-6131	393	35	currently	currently	ADV
ejpam-6131	393	36	attained	attain	VERB
ejpam-6131	393	37	states	state	NOUN
ejpam-6131	393	38	.	.	PUNCT
ejpam-6131	394	1	for	for	ADP
ejpam-6131	394	2	each	each	DET
ejpam-6131	394	3	π	π	PROPN
ejpam-6131	394	4	=	=	SYM
ejpam-6131	394	5	1	1	NUM
ejpam-6131	394	6	,	,	PUNCT
ejpam-6131	394	7	2	2	NUM
ejpam-6131	394	8	,	,	PUNCT
ejpam-6131	394	9	3	3	NUM
ejpam-6131	394	10	,	,	PUNCT
ejpam-6131	394	11	·	·	PUNCT
ejpam-6131	394	12	·	·	PUNCT
ejpam-6131	394	13	·	·	PUNCT
ejpam-6131	394	14	,	,	PUNCT
ejpam-6131	394	15	eij	eij	PROPN
ejpam-6131	394	16	shows	show	VERB
ejpam-6131	394	17	the	the	DET
ejpam-6131	394	18	probability	probability	NOUN
ejpam-6131	394	19	event	event	NOUN
ejpam-6131	394	20	achieved	achieve	VERB
ejpam-6131	394	21	by	by	ADP
ejpam-6131	394	22	state	state	NOUN
ejpam-6131	394	23	i	i	PRON
ejpam-6131	394	24	in	in	ADP
ejpam-6131	394	25	the	the	DET
ejpam-6131	394	26	next	next	ADJ
ejpam-6131	394	27	period	period	NOUN
ejpam-6131	394	28	starting	start	VERB
ejpam-6131	394	29	from	from	ADP
ejpam-6131	394	30	state	state	PROPN
ejpam-6131	394	31	j.	j.	PROPN
ejpam-6131	394	32	then	then	ADV
ejpam-6131	394	33	,	,	PUNCT
ejpam-6131	394	34	the	the	DET
ejpam-6131	394	35	preceding	precede	VERB
ejpam-6131	394	36	probability	probability	NOUN
ejpam-6131	394	37	vector	vector	NOUN
ejpam-6131	394	38	θπ	θπ	NOUN
ejpam-6131	394	39	and	and	CCONJ
ejpam-6131	394	40	the	the	DET
ejpam-6131	394	41	succeeding	succeed	VERB
ejpam-6131	394	42	probability	probability	NOUN
ejpam-6131	394	43	vector	vector	NOUN
ejpam-6131	394	44	θπ+1	θπ+1	NUM
ejpam-6131	394	45	in	in	ADP
ejpam-6131	394	46	the	the	DET
ejpam-6131	394	47	period	period	NOUN
ejpam-6131	394	48	π	π	NOUN
ejpam-6131	394	49	and	and	CCONJ
ejpam-6131	394	50	π	π	PROPN
ejpam-6131	394	51	+	+	CCONJ
ejpam-6131	394	52	1	1	NUM
ejpam-6131	394	53	respectively	respectively	ADV
ejpam-6131	394	54	,	,	PUNCT
ejpam-6131	394	55	written	write	VERB
ejpam-6131	394	56	as	as	ADP
ejpam-6131	394	57	θπ+1	θπ+1	X
ejpam-6131	394	58	i	i	NOUN
ejpam-6131	394	59	=	=	PUNCT
ejpam-6131	394	60	∑	∑	PUNCT
ejpam-6131	394	61	j	j	PROPN
ejpam-6131	394	62	eijθ	eijθ	PROPN
ejpam-6131	394	63	π	π	PROPN
ejpam-6131	394	64	j	j	PROPN
ejpam-6131	394	65	,	,	PUNCT
ejpam-6131	394	66	for	for	ADP
ejpam-6131	394	67	each	each	DET
ejpam-6131	394	68	j	j	PROPN
ejpam-6131	394	69	≥	≥	PROPN
ejpam-6131	394	70	1	1	NUM
ejpam-6131	394	71	.	.	PUNCT
ejpam-6131	395	1	let	let	VERB
ejpam-6131	395	2	θπ	θπ	PART
ejpam-6131	395	3	be	be	AUX
ejpam-6131	395	4	a	a	DET
ejpam-6131	395	5	column	column	NOUN
ejpam-6131	395	6	vector	vector	NOUN
ejpam-6131	395	7	,	,	PUNCT
ejpam-6131	395	8	then	then	ADV
ejpam-6131	395	9	to	to	PART
ejpam-6131	395	10	obtain	obtain	VERB
ejpam-6131	395	11	matrix	matrix	NOUN
ejpam-6131	395	12	form	form	NOUN
ejpam-6131	395	13	,	,	PUNCT
ejpam-6131	395	14	consider	consider	VERB
ejpam-6131	395	15	the	the	DET
ejpam-6131	395	16	mapping	mapping	NOUN
ejpam-6131	395	17	θπ+1	θπ+1	NUM
ejpam-6131	395	18	=	=	SYM
ejpam-6131	395	19	fθπ	fθπ	PROPN
ejpam-6131	395	20	.	.	PUNCT
ejpam-6131	396	1	in	in	ADP
ejpam-6131	396	2	addition	addition	NOUN
ejpam-6131	396	3	with	with	ADP
ejpam-6131	396	4	that	that	PRON
ejpam-6131	396	5	for	for	ADP
ejpam-6131	396	6	all	all	DET
ejpam-6131	396	7	eij	eij	PROPN
ejpam-6131	396	8	≥	≥	PROPN
ejpam-6131	396	9	0	0	NUM
ejpam-6131	396	10	,	,	PUNCT
ejpam-6131	396	11	∑n	∑n	PROPN
ejpam-6131	396	12	i=1	i=1	PROPN
ejpam-6131	396	13	eij	eij	PROPN
ejpam-6131	396	14	=	=	SYM
ejpam-6131	396	15	1	1	PROPN
ejpam-6131	396	16	,	,	PUNCT
ejpam-6131	396	17	required	require	VERB
ejpam-6131	396	18	for	for	ADP
ejpam-6131	396	19	conditional	conditional	ADJ
ejpam-6131	396	20	probability	probability	NOUN
ejpam-6131	396	21	.	.	PUNCT
ejpam-6131	397	1	finding	find	VERB
ejpam-6131	397	2	the	the	DET
ejpam-6131	397	3	stationary	stationary	ADJ
ejpam-6131	397	4	distribution	distribution	NOUN
ejpam-6131	397	5	for	for	ADP
ejpam-6131	397	6	the	the	DET
ejpam-6131	397	7	markov	markov	NOUN
ejpam-6131	397	8	process	process	NOUN
ejpam-6131	397	9	is	be	AUX
ejpam-6131	397	10	the	the	DET
ejpam-6131	397	11	same	same	ADJ
ejpam-6131	397	12	as	as	ADP
ejpam-6131	397	13	finding	find	VERB
ejpam-6131	397	14	the	the	DET
ejpam-6131	397	15	fixed	fix	VERB
ejpam-6131	397	16	point	point	NOUN
ejpam-6131	397	17	of	of	ADP
ejpam-6131	397	18	f	f	PROPN
ejpam-6131	397	19	,	,	PUNCT
ejpam-6131	397	20	i.e.	i.e.	X
ejpam-6131	397	21	,	,	PUNCT
ejpam-6131	397	22	there	there	PRON
ejpam-6131	397	23	exists	exist	VERB
ejpam-6131	397	24	some	some	DET
ejpam-6131	397	25	θ	θ	PROPN
ejpam-6131	397	26	∈	∈	PROPN
ejpam-6131	397	27	θ5	θ5	PROPN
ejpam-6131	397	28	n−1	n−1	PROPN
ejpam-6131	397	29	such	such	ADJ
ejpam-6131	397	30	that	that	DET
ejpam-6131	397	31	fθπ	fθπ	NOUN
ejpam-6131	397	32	=	=	PUNCT
ejpam-6131	397	33	θπ	θπ	NOUN
ejpam-6131	397	34	,	,	PUNCT
ejpam-6131	397	35	whenever	whenever	SCONJ
ejpam-6131	397	36	θπ+1	θπ+1	NUM
ejpam-6131	397	37	=	=	SYM
ejpam-6131	397	38	θπ	θπ	PROPN
ejpam-6131	397	39	.	.	PUNCT
ejpam-6131	398	1	the	the	DET
ejpam-6131	398	2	period	period	NOUN
ejpam-6131	398	3	θπ	θπ	ADP
ejpam-6131	398	4	is	be	AUX
ejpam-6131	398	5	called	call	VERB
ejpam-6131	398	6	the	the	DET
ejpam-6131	398	7	stationary	stationary	ADJ
ejpam-6131	398	8	distribution	distribution	NOUN
ejpam-6131	398	9	of	of	ADP
ejpam-6131	398	10	the	the	DET
ejpam-6131	398	11	markov	markov	NOUN
ejpam-6131	398	12	process	process	NOUN
ejpam-6131	398	13	.	.	PUNCT
ejpam-6131	399	1	suppose	suppose	VERB
ejpam-6131	399	2	that	that	SCONJ
ejpam-6131	399	3	ϕi	ϕi	ADP
ejpam-6131	399	4	=	=	X
ejpam-6131	399	5	minj	minj	NOUN
ejpam-6131	399	6	eij	eij	PROPN
ejpam-6131	399	7	,	,	PUNCT
ejpam-6131	399	8	for	for	ADP
ejpam-6131	399	9	each	each	DET
ejpam-6131	399	10	i	i	PRON
ejpam-6131	399	11	and	and	CCONJ
ejpam-6131	399	12	ϕ	ϕ	X
ejpam-6131	399	13	=	=	PUNCT
ejpam-6131	399	14	∑n	∑n	PROPN
ejpam-6131	399	15	i=1	i=1	X
ejpam-6131	399	16	ϕi	ϕi	INTJ
ejpam-6131	399	17	.	.	PUNCT
ejpam-6131	400	1	now	now	ADV
ejpam-6131	400	2	,	,	PUNCT
ejpam-6131	400	3	the	the	DET
ejpam-6131	400	4	major	major	ADJ
ejpam-6131	400	5	part	part	NOUN
ejpam-6131	400	6	of	of	ADP
ejpam-6131	400	7	this	this	DET
ejpam-6131	400	8	section	section	NOUN
ejpam-6131	400	9	is	be	AUX
ejpam-6131	400	10	stated	state	VERB
ejpam-6131	400	11	here	here	ADV
ejpam-6131	400	12	.	.	PUNCT
ejpam-6131	401	1	theorem	theorem	VERB
ejpam-6131	401	2	3	3	NUM
ejpam-6131	401	3	.	.	PUNCT
ejpam-6131	401	4	by	by	ADP
ejpam-6131	401	5	supposition	supposition	PROPN
ejpam-6131	401	6	eij	eij	PROPN
ejpam-6131	401	7	≥	≥	PROPN
ejpam-6131	401	8	0	0	NUM
ejpam-6131	401	9	,	,	PUNCT
ejpam-6131	401	10	the	the	DET
ejpam-6131	401	11	markov	markov	NOUN
ejpam-6131	401	12	process	process	NOUN
ejpam-6131	401	13	has	have	VERB
ejpam-6131	401	14	a	a	DET
ejpam-6131	401	15	unique	unique	ADJ
ejpam-6131	401	16	stationary	stationary	ADJ
ejpam-6131	401	17	distribution	distribution	NOUN
ejpam-6131	401	18	.	.	PUNCT
ejpam-6131	402	1	proof	proof	NOUN
ejpam-6131	402	2	.	.	PUNCT
ejpam-6131	403	1	let	let	VERB
ejpam-6131	403	2	t	t	NOUN
ejpam-6131	403	3	:	:	PUNCT
ejpam-6131	403	4	θ5	θ5	PROPN
ejpam-6131	403	5	n−1	n−1	PROPN
ejpam-6131	403	6	×θ5	×θ5	PROPN
ejpam-6131	403	7	n−1	n−1	PROPN
ejpam-6131	403	8	→	→	SYM
ejpam-6131	403	9	r2	r2	PROPN
ejpam-6131	403	10	be	be	AUX
ejpam-6131	403	11	a	a	DET
ejpam-6131	403	12	mapping	mapping	NOUN
ejpam-6131	403	13	defined	define	VERB
ejpam-6131	403	14	as	as	ADP
ejpam-6131	403	15	t(m	t(m	PROPN
ejpam-6131	403	16	,	,	PUNCT
ejpam-6131	403	17	n	n	CCONJ
ejpam-6131	403	18	)	)	PUNCT
ejpam-6131	403	19	=	=	NOUN
ejpam-6131	403	20	t((ξ1	t((ξ1	NOUN
ejpam-6131	403	21	,	,	PUNCT
ejpam-6131	403	22	ξ2	ξ2	ADJ
ejpam-6131	403	23	,	,	PUNCT
ejpam-6131	403	24	ξ3	ξ3	NOUN
ejpam-6131	403	25	,	,	PUNCT
ejpam-6131	403	26	ξ4	ξ4	NOUN
ejpam-6131	403	27	,	,	PUNCT
ejpam-6131	403	28	ξ5	ξ5	NOUN
ejpam-6131	403	29	)	)	PUNCT
ejpam-6131	403	30	,	,	PUNCT
ejpam-6131	403	31	(	(	PUNCT
ejpam-6131	403	32	q1	q1	PROPN
ejpam-6131	403	33	,	,	PUNCT
ejpam-6131	403	34	q2	q2	NOUN
ejpam-6131	403	35	,	,	PUNCT
ejpam-6131	403	36	q3	q3	PROPN
ejpam-6131	403	37	,	,	PUNCT
ejpam-6131	403	38	q4	q4	PROPN
ejpam-6131	403	39	,	,	PUNCT
ejpam-6131	403	40	q5	q5	PROPN
ejpam-6131	403	41	)	)	PUNCT
ejpam-6131	403	42	)	)	PUNCT
ejpam-6131	404	1	=	=	PRON
ejpam-6131	405	1	(	(	PUNCT
ejpam-6131	405	2	n∑	n∑	INTJ
ejpam-6131	405	3	i=1	i=1	PROPN
ejpam-6131	405	4	(	(	PUNCT
ejpam-6131	405	5	|ξi1	|ξi1	PROPN
ejpam-6131	405	6	−	−	NOUN
ejpam-6131	405	7	qi1|+	qi1|+	NOUN
ejpam-6131	406	1	|ξi2	|ξi2	CCONJ
ejpam-6131	406	2	−	−	PROPN
ejpam-6131	406	3	qi2|+	qi2|+	PROPN
ejpam-6131	406	4	|ξi3	|ξi3	SYM
ejpam-6131	406	5	−	−	PROPN
ejpam-6131	406	6	qi3|+	qi3|+	NOUN
ejpam-6131	406	7	|ξi4	|ξi4	PROPN
ejpam-6131	406	8	−	−	PROPN
ejpam-6131	406	9	qi4|+	qi4|+	X
ejpam-6131	406	10	|ξi5	|ξi5	ADP
ejpam-6131	406	11	−	−	NOUN
ejpam-6131	406	12	qi5|	qi5|	ADV
ejpam-6131	406	13	)	)	PUNCT
ejpam-6131	406	14	,	,	PUNCT
ejpam-6131	406	15	n∑	n∑	NOUN
ejpam-6131	406	16	i=1	i=1	PROPN
ejpam-6131	406	17	(	(	PUNCT
ejpam-6131	406	18	|ξi1	|ξi1	PROPN
ejpam-6131	406	19	−	−	NOUN
ejpam-6131	406	20	qi1|+	qi1|+	NOUN
ejpam-6131	407	1	|ξi2	|ξi2	CCONJ
ejpam-6131	407	2	−	−	PROPN
ejpam-6131	407	3	qi2|+	qi2|+	PROPN
ejpam-6131	407	4	|ξi3	|ξi3	SYM
ejpam-6131	407	5	−	−	PROPN
ejpam-6131	407	6	qi3|+	qi3|+	NOUN
ejpam-6131	407	7	|ξi4	|ξi4	PROPN
ejpam-6131	407	8	−	−	PROPN
ejpam-6131	407	9	qi4|+	qi4|+	X
ejpam-6131	407	10	|ξi5	|ξi5	ADP
ejpam-6131	407	11	−	−	NOUN
ejpam-6131	407	12	qi5|	qi5|	ADV
ejpam-6131	407	13	)	)	PUNCT
ejpam-6131	407	14	)	)	PUNCT
ejpam-6131	407	15	,	,	PUNCT
ejpam-6131	407	16	where	where	SCONJ
ejpam-6131	407	17	m	m	VERB
ejpam-6131	407	18	=	=	SYM
ejpam-6131	407	19	(	(	PUNCT
ejpam-6131	407	20	ξ1	ξ1	PROPN
ejpam-6131	407	21	,	,	PUNCT
ejpam-6131	407	22	ξ2	ξ2	ADJ
ejpam-6131	407	23	,	,	PUNCT
ejpam-6131	407	24	ξ3	ξ3	NOUN
ejpam-6131	407	25	,	,	PUNCT
ejpam-6131	407	26	ξ4	ξ4	NOUN
ejpam-6131	407	27	,	,	PUNCT
ejpam-6131	407	28	ξ5	ξ5	NOUN
ejpam-6131	407	29	)	)	PUNCT
ejpam-6131	407	30	and	and	CCONJ
ejpam-6131	407	31	n	n	CCONJ
ejpam-6131	407	32	=	=	SYM
ejpam-6131	407	33	(	(	PUNCT
ejpam-6131	407	34	q1	q1	PROPN
ejpam-6131	407	35	,	,	PUNCT
ejpam-6131	407	36	q2	q2	NOUN
ejpam-6131	407	37	,	,	PUNCT
ejpam-6131	407	38	q3	q3	PROPN
ejpam-6131	407	39	,	,	PUNCT
ejpam-6131	407	40	q4	q4	PROPN
ejpam-6131	407	41	,	,	PUNCT
ejpam-6131	407	42	q5	q5	PROPN
ejpam-6131	407	43	)	)	PUNCT
ejpam-6131	407	44	belongs	belong	VERB
ejpam-6131	407	45	to	to	ADP
ejpam-6131	407	46	θ5	θ5	PROPN
ejpam-6131	407	47	n−1	n−1	PROPN
ejpam-6131	407	48	.	.	PUNCT
ejpam-6131	408	1	since	since	SCONJ
ejpam-6131	408	2	,	,	PUNCT
ejpam-6131	408	3	t(m	t(m	PROPN
ejpam-6131	408	4	,	,	PUNCT
ejpam-6131	408	5	n	n	CCONJ
ejpam-6131	408	6	)	)	PUNCT
ejpam-6131	408	7	≥	≥	X
ejpam-6131	408	8	(	(	PUNCT
ejpam-6131	408	9	0	0	NUM
ejpam-6131	408	10	,	,	PUNCT
ejpam-6131	408	11	0	0	NUM
ejpam-6131	408	12	)	)	PUNCT
ejpam-6131	408	13	for	for	ADP
ejpam-6131	408	14	all	all	DET
ejpam-6131	408	15	m	m	ADJ
ejpam-6131	408	16	and	and	CCONJ
ejpam-6131	408	17	n	n	ADV
ejpam-6131	408	18	in	in	ADP
ejpam-6131	408	19	θ5	θ5	PROPN
ejpam-6131	408	20	n−1	n−1	PROPN
ejpam-6131	408	21	.	.	PUNCT
ejpam-6131	409	1	also	also	ADV
ejpam-6131	409	2	,	,	PUNCT
ejpam-6131	409	3	if	if	SCONJ
ejpam-6131	409	4	t(m	t(m	PROPN
ejpam-6131	409	5	,	,	PUNCT
ejpam-6131	409	6	n	n	CCONJ
ejpam-6131	409	7	)	)	PUNCT
ejpam-6131	409	8	=	=	SYM
ejpam-6131	409	9	(	(	PUNCT
ejpam-6131	409	10	0	0	NUM
ejpam-6131	409	11	,	,	PUNCT
ejpam-6131	409	12	0	0	NUM
ejpam-6131	409	13	)	)	PUNCT
ejpam-6131	409	14	,	,	PUNCT
ejpam-6131	409	15	then	then	ADV
ejpam-6131	409	16	this	this	PRON
ejpam-6131	409	17	implies	imply	VERB
ejpam-6131	409	18	that	that	SCONJ
ejpam-6131	409	19	(	(	PUNCT
ejpam-6131	409	20	n∑	n∑	NOUN
ejpam-6131	409	21	i=1	i=1	PROPN
ejpam-6131	409	22	(	(	PUNCT
ejpam-6131	409	23	|ξi1	|ξi1	PROPN
ejpam-6131	409	24	−	−	NOUN
ejpam-6131	409	25	qi1|+	qi1|+	NOUN
ejpam-6131	409	26	|ξi2	|ξi2	CCONJ
ejpam-6131	409	27	−	−	PROPN
ejpam-6131	409	28	qi2|+	qi2|+	PROPN
ejpam-6131	409	29	|ξi3	|ξi3	SYM
ejpam-6131	409	30	−	−	PROPN
ejpam-6131	409	31	qi3|+	qi3|+	NOUN
ejpam-6131	409	32	|ξi4	|ξi4	PROPN
ejpam-6131	409	33	−	−	PROPN
ejpam-6131	409	34	qi4|+	qi4|+	X
ejpam-6131	409	35	|ξi5	|ξi5	ADP
ejpam-6131	409	36	−	−	NOUN
ejpam-6131	409	37	qi5|	qi5|	ADV
ejpam-6131	409	38	)	)	PUNCT
ejpam-6131	409	39	,	,	PUNCT
ejpam-6131	410	1	n∑	n∑	NOUN
ejpam-6131	410	2	i=1	i=1	PROPN
ejpam-6131	411	1	(	(	PUNCT
ejpam-6131	411	2	|ξi1	|ξi1	PROPN
ejpam-6131	411	3	−	−	NOUN
ejpam-6131	411	4	qi1|+	qi1|+	NOUN
ejpam-6131	412	1	|ξi2	|ξi2	CCONJ
ejpam-6131	412	2	−	−	PROPN
ejpam-6131	412	3	qi2|+	qi2|+	PROPN
ejpam-6131	412	4	|ξi3	|ξi3	SYM
ejpam-6131	412	5	−	−	PROPN
ejpam-6131	412	6	qi3|+	qi3|+	NOUN
ejpam-6131	412	7	|ξi4	|ξi4	PROPN
ejpam-6131	412	8	−	−	PROPN
ejpam-6131	412	9	qi4|+	qi4|+	X
ejpam-6131	412	10	|ξi5	|ξi5	ADP
ejpam-6131	412	11	−	−	NOUN
ejpam-6131	412	12	qi5|	qi5|	ADV
ejpam-6131	412	13	)	)	PUNCT
ejpam-6131	412	14	)	)	PUNCT
ejpam-6131	413	1	=	=	PUNCT
ejpam-6131	413	2	(	(	PUNCT
ejpam-6131	413	3	0	0	NUM
ejpam-6131	413	4	,	,	PUNCT
ejpam-6131	413	5	0	0	NUM
ejpam-6131	413	6	)	)	PUNCT
ejpam-6131	413	7	,	,	PUNCT
ejpam-6131	413	8	s.	s.	PROPN
ejpam-6131	413	9	batul	batul	PROPN
ejpam-6131	413	10	et	et	PROPN
ejpam-6131	413	11	a.	a.	PROPN
ejpam-6131	413	12	/	/	PUNCT
ejpam-6131	413	13	eur	eur	PROPN
ejpam-6131	413	14	.	.	PUNCT
ejpam-6131	414	1	j.	j.	PROPN
ejpam-6131	414	2	pure	pure	PROPN
ejpam-6131	414	3	appl	appl	PROPN
ejpam-6131	414	4	.	.	PROPN
ejpam-6131	414	5	math	math	PROPN
ejpam-6131	414	6	,	,	PUNCT
ejpam-6131	414	7	18	18	NUM
ejpam-6131	414	8	(	(	PUNCT
ejpam-6131	414	9	2	2	NUM
ejpam-6131	414	10	)	)	PUNCT
ejpam-6131	414	11	(	(	PUNCT
ejpam-6131	414	12	2025	2025	NUM
ejpam-6131	414	13	)	)	PUNCT
ejpam-6131	414	14	,	,	PUNCT
ejpam-6131	414	15	6131	6131	NUM
ejpam-6131	414	16	17	17	NUM
ejpam-6131	414	17	of	of	ADP
ejpam-6131	414	18	22	22	NUM
ejpam-6131	414	19	or	or	CCONJ
ejpam-6131	414	20	|ξi1	|ξi1	PROPN
ejpam-6131	414	21	−	−	PROPN
ejpam-6131	414	22	qi1|+	qi1|+	NOUN
ejpam-6131	415	1	|ξi2	|ξi2	CCONJ
ejpam-6131	415	2	−	−	PROPN
ejpam-6131	415	3	qi2|+	qi2|+	PROPN
ejpam-6131	415	4	|ξi3	|ξi3	SYM
ejpam-6131	415	5	−	−	PROPN
ejpam-6131	415	6	qi3|+	qi3|+	NOUN
ejpam-6131	415	7	|ξi4	|ξi4	PROPN
ejpam-6131	415	8	−	−	PROPN
ejpam-6131	415	9	qi4|+	qi4|+	X
ejpam-6131	415	10	|ξi5	|ξi5	NOUN
ejpam-6131	415	11	−	−	NOUN
ejpam-6131	415	12	qi5|	qi5|	PUNCT
ejpam-6131	415	13	=	=	SYM
ejpam-6131	415	14	0	0	NUM
ejpam-6131	415	15	,	,	PUNCT
ejpam-6131	415	16	⇒	⇒	PROPN
ejpam-6131	415	17	|ξi1	|ξi1	VERB
ejpam-6131	415	18	−	−	PROPN
ejpam-6131	415	19	qi1|	qi1|	VERB
ejpam-6131	415	20	=	=	PUNCT
ejpam-6131	416	1	|ξi2	|ξi2	NOUN
ejpam-6131	416	2	−	−	X
ejpam-6131	417	1	qi2|	qi2|	X
ejpam-6131	417	2	=	=	SYM
ejpam-6131	417	3	|ξi3	|ξi3	SYM
ejpam-6131	417	4	−	−	PROPN
ejpam-6131	417	5	qi3|	qi3|	NOUN
ejpam-6131	417	6	=	=	SYM
ejpam-6131	417	7	|ξi4	|ξi4	PROPN
ejpam-6131	417	8	−	−	PROPN
ejpam-6131	417	9	qi4|+	qi4|+	X
ejpam-6131	417	10	|ξi5	|ξi5	NOUN
ejpam-6131	417	11	−	−	NOUN
ejpam-6131	417	12	qi5|	qi5|	PUNCT
ejpam-6131	418	1	=	=	SYM
ejpam-6131	418	2	0	0	NUM
ejpam-6131	418	3	,	,	PUNCT
ejpam-6131	418	4	⇒	⇒	VERB
ejpam-6131	418	5	ξi1	ξi1	NOUN
ejpam-6131	418	6	=	=	SYM
ejpam-6131	418	7	qi1	qi1	PROPN
ejpam-6131	418	8	,	,	PUNCT
ejpam-6131	418	9	ξi2	ξi2	VERB
ejpam-6131	419	1	=	=	SYM
ejpam-6131	420	1	qi2	qi2	ADV
ejpam-6131	420	2	,	,	PUNCT
ejpam-6131	420	3	ξi3	ξi3	NOUN
ejpam-6131	420	4	=	=	PUNCT
ejpam-6131	420	5	qi3	qi3	ADJ
ejpam-6131	420	6	,	,	PUNCT
ejpam-6131	420	7	ξi4	ξi4	NOUN
ejpam-6131	420	8	=	=	NOUN
ejpam-6131	420	9	qi4	qi4	NOUN
ejpam-6131	420	10	,	,	PUNCT
ejpam-6131	420	11	ξi5	ξi5	NOUN
ejpam-6131	420	12	=	=	SYM
ejpam-6131	420	13	qi5	qi5	NOUN
ejpam-6131	420	14	.	.	PUNCT
ejpam-6131	421	1	hence	hence	ADV
ejpam-6131	421	2	,	,	PUNCT
ejpam-6131	421	3	m	m	VERB
ejpam-6131	421	4	=	=	SYM
ejpam-6131	421	5	n	n	X
ejpam-6131	421	6	.	.	PUNCT
ejpam-6131	422	1	conversely	conversely	ADV
ejpam-6131	422	2	,	,	PUNCT
ejpam-6131	422	3	let	let	VERB
ejpam-6131	422	4	m	m	VERB
ejpam-6131	422	5	=	=	SYM
ejpam-6131	422	6	n	n	PROPN
ejpam-6131	422	7	,	,	PUNCT
ejpam-6131	422	8	then	then	ADV
ejpam-6131	422	9	ξi1	ξi1	NOUN
ejpam-6131	422	10	=	=	SYM
ejpam-6131	422	11	qi1	qi1	PROPN
ejpam-6131	422	12	,	,	PUNCT
ejpam-6131	422	13	ξi2	ξi2	VERB
ejpam-6131	422	14	=	=	SYM
ejpam-6131	423	1	qi2	qi2	ADV
ejpam-6131	423	2	,	,	PUNCT
ejpam-6131	423	3	ξi3	ξi3	NOUN
ejpam-6131	423	4	=	=	PUNCT
ejpam-6131	423	5	qi3	qi3	ADJ
ejpam-6131	423	6	,	,	PUNCT
ejpam-6131	423	7	ξi4	ξi4	NOUN
ejpam-6131	423	8	=	=	NOUN
ejpam-6131	423	9	qi4	qi4	NOUN
ejpam-6131	423	10	,	,	PUNCT
ejpam-6131	423	11	ξi5	ξi5	NOUN
ejpam-6131	423	12	=	=	SYM
ejpam-6131	423	13	qi5	qi5	PROPN
ejpam-6131	423	14	,	,	PUNCT
ejpam-6131	423	15	⇒	⇒	PROPN
ejpam-6131	423	16	|ξi1	|ξi1	PROPN
ejpam-6131	423	17	−	−	PROPN
ejpam-6131	423	18	qi1|	qi1|	VERB
ejpam-6131	423	19	=	=	PUNCT
ejpam-6131	424	1	|ξi2	|ξi2	NOUN
ejpam-6131	424	2	−	−	X
ejpam-6131	424	3	qi2|	qi2|	X
ejpam-6131	424	4	=	=	SYM
ejpam-6131	424	5	|ξi3	|ξi3	SYM
ejpam-6131	424	6	−	−	PROPN
ejpam-6131	424	7	qi3|	qi3|	NOUN
ejpam-6131	424	8	=	=	SYM
ejpam-6131	424	9	|ξi4	|ξi4	ADP
ejpam-6131	424	10	−	−	PROPN
ejpam-6131	424	11	qi4|	qi4|	NOUN
ejpam-6131	424	12	=	=	PUNCT
ejpam-6131	424	13	|ξi5	|ξi5	NOUN
ejpam-6131	424	14	−	−	NOUN
ejpam-6131	424	15	qi5|	qi5|	PUNCT
ejpam-6131	425	1	=	=	NOUN
ejpam-6131	425	2	0	0	X
ejpam-6131	425	3	.	.	PUNCT
ejpam-6131	426	1	hence	hence	ADV
ejpam-6131	426	2	,	,	PUNCT
ejpam-6131	426	3	(	(	PUNCT
ejpam-6131	426	4	n∑	n∑	INTJ
ejpam-6131	426	5	i=1	i=1	PROPN
ejpam-6131	426	6	(	(	PUNCT
ejpam-6131	426	7	|ξi1	|ξi1	PROPN
ejpam-6131	426	8	−	−	NOUN
ejpam-6131	426	9	qi1|+	qi1|+	NOUN
ejpam-6131	427	1	|ξi2	|ξi2	CCONJ
ejpam-6131	427	2	−	−	PROPN
ejpam-6131	427	3	qi2|+	qi2|+	PROPN
ejpam-6131	427	4	|ξi3	|ξi3	SYM
ejpam-6131	427	5	−	−	PROPN
ejpam-6131	427	6	qi3|+	qi3|+	NOUN
ejpam-6131	427	7	|ξi4	|ξi4	PROPN
ejpam-6131	427	8	−	−	PROPN
ejpam-6131	427	9	qi4|+	qi4|+	X
ejpam-6131	427	10	|ξ5i	|ξ5i	PROPN
ejpam-6131	427	11	−	−	PROPN
ejpam-6131	427	12	qi5|	qi5|	PROPN
ejpam-6131	427	13	)	)	PUNCT
ejpam-6131	427	14	,	,	PUNCT
ejpam-6131	427	15	n∑	n∑	NOUN
ejpam-6131	427	16	i=1	i=1	PROPN
ejpam-6131	427	17	(	(	PUNCT
ejpam-6131	427	18	|ξi1	|ξi1	PROPN
ejpam-6131	427	19	−	−	NOUN
ejpam-6131	427	20	qi1|+	qi1|+	NOUN
ejpam-6131	428	1	|ξi2	|ξi2	CCONJ
ejpam-6131	428	2	−	−	PROPN
ejpam-6131	428	3	qi2|+	qi2|+	PROPN
ejpam-6131	428	4	|ξi3	|ξi3	SYM
ejpam-6131	428	5	−	−	PROPN
ejpam-6131	428	6	qi3|+	qi3|+	NOUN
ejpam-6131	428	7	|ξi4	|ξi4	PROPN
ejpam-6131	428	8	−	−	PROPN
ejpam-6131	428	9	qi4|+	qi4|+	X
ejpam-6131	428	10	|ξi5	|ξi5	ADP
ejpam-6131	428	11	−	−	NOUN
ejpam-6131	428	12	qi5|	qi5|	ADV
ejpam-6131	428	13	)	)	PUNCT
ejpam-6131	428	14	)	)	PUNCT
ejpam-6131	429	1	=	=	PUNCT
ejpam-6131	429	2	(	(	PUNCT
ejpam-6131	429	3	0	0	NUM
ejpam-6131	429	4	,	,	PUNCT
ejpam-6131	429	5	0	0	NUM
ejpam-6131	429	6	)	)	PUNCT
ejpam-6131	429	7	⇒	⇒	NOUN
ejpam-6131	429	8	t(m	t(m	PROPN
ejpam-6131	429	9	,	,	PUNCT
ejpam-6131	429	10	n	n	CCONJ
ejpam-6131	429	11	)	)	PUNCT
ejpam-6131	429	12	=	=	SYM
ejpam-6131	429	13	(	(	PUNCT
ejpam-6131	429	14	0	0	NUM
ejpam-6131	429	15	,	,	PUNCT
ejpam-6131	429	16	0	0	NUM
ejpam-6131	429	17	)	)	PUNCT
ejpam-6131	429	18	.	.	PUNCT
ejpam-6131	430	1	moreover	moreover	ADV
ejpam-6131	430	2	,	,	PUNCT
ejpam-6131	430	3	t(m	t(m	PROPN
ejpam-6131	430	4	,	,	PUNCT
ejpam-6131	430	5	n	n	CCONJ
ejpam-6131	430	6	)	)	PUNCT
ejpam-6131	430	7	=	=	SYM
ejpam-6131	431	1	(	(	PUNCT
ejpam-6131	431	2	n∑	n∑	INTJ
ejpam-6131	431	3	i=1	i=1	PROPN
ejpam-6131	431	4	(	(	PUNCT
ejpam-6131	431	5	|ξi1	|ξi1	PROPN
ejpam-6131	431	6	−	−	NOUN
ejpam-6131	431	7	qi1|+	qi1|+	NOUN
ejpam-6131	432	1	|ξi2	|ξi2	CCONJ
ejpam-6131	432	2	−	−	PROPN
ejpam-6131	432	3	qi2|+	qi2|+	PROPN
ejpam-6131	432	4	|ξi3	|ξi3	SYM
ejpam-6131	432	5	−	−	PROPN
ejpam-6131	432	6	qi3|+	qi3|+	NOUN
ejpam-6131	432	7	|ξi4	|ξi4	PROPN
ejpam-6131	432	8	−	−	PROPN
ejpam-6131	432	9	qi4|+	qi4|+	X
ejpam-6131	432	10	|ξi5	|ξi5	ADP
ejpam-6131	432	11	−	−	NOUN
ejpam-6131	432	12	qi5|	qi5|	ADV
ejpam-6131	432	13	)	)	PUNCT
ejpam-6131	432	14	,	,	PUNCT
ejpam-6131	432	15	n∑	n∑	NOUN
ejpam-6131	432	16	i=1	i=1	PROPN
ejpam-6131	432	17	(	(	PUNCT
ejpam-6131	432	18	|ξi1	|ξi1	PROPN
ejpam-6131	432	19	−	−	NOUN
ejpam-6131	432	20	qi1|+	qi1|+	NOUN
ejpam-6131	433	1	|ξi2	|ξi2	CCONJ
ejpam-6131	433	2	−	−	PROPN
ejpam-6131	433	3	qi2|+	qi2|+	PROPN
ejpam-6131	433	4	|ξi3	|ξi3	SYM
ejpam-6131	433	5	−	−	PROPN
ejpam-6131	433	6	qi3|+	qi3|+	NOUN
ejpam-6131	433	7	|ξi4	|ξi4	PROPN
ejpam-6131	433	8	−	−	PROPN
ejpam-6131	433	9	qi4|+	qi4|+	X
ejpam-6131	433	10	|ξi5	|ξi5	ADP
ejpam-6131	433	11	−	−	NOUN
ejpam-6131	433	12	qi5|	qi5|	ADV
ejpam-6131	433	13	)	)	PUNCT
ejpam-6131	433	14	)	)	PUNCT
ejpam-6131	434	1	=	=	PUNCT
ejpam-6131	435	1	(	(	PUNCT
ejpam-6131	435	2	n∑	n∑	INTJ
ejpam-6131	435	3	i=1	i=1	PROPN
ejpam-6131	436	1	(	(	PUNCT
ejpam-6131	436	2	|qi1	|qi1	PROPN
ejpam-6131	436	3	−	−	PROPN
ejpam-6131	436	4	ξi1|+	ξi1|+	PROPN
ejpam-6131	437	1	|qi2	|qi2	CCONJ
ejpam-6131	438	1	−	−	PROPN
ejpam-6131	438	2	ξi2|+	ξi2|+	NOUN
ejpam-6131	438	3	|qi3	|qi3	VERB
ejpam-6131	438	4	−	−	PROPN
ejpam-6131	438	5	ξi3|+	ξi3|+	ADP
ejpam-6131	438	6	|qi4	|qi4	PUNCT
ejpam-6131	438	7	−	−	NOUN
ejpam-6131	438	8	ξi4|+	ξi4|+	NOUN
ejpam-6131	438	9	|qi5	|qi5	PROPN
ejpam-6131	438	10	−	−	PROPN
ejpam-6131	438	11	ξi5|	ξi5|	PROPN
ejpam-6131	438	12	)	)	PUNCT
ejpam-6131	438	13	,	,	PUNCT
ejpam-6131	438	14	n∑	n∑	NOUN
ejpam-6131	438	15	i=1	i=1	PROPN
ejpam-6131	439	1	(	(	PUNCT
ejpam-6131	439	2	|qi1	|qi1	PROPN
ejpam-6131	439	3	−	−	PROPN
ejpam-6131	439	4	ξi1|+	ξi1|+	PROPN
ejpam-6131	440	1	|qi2	|qi2	CCONJ
ejpam-6131	441	1	−	−	PROPN
ejpam-6131	441	2	ξi2|+	ξi2|+	NOUN
ejpam-6131	441	3	|qi3	|qi3	VERB
ejpam-6131	441	4	−	−	PROPN
ejpam-6131	441	5	ξi3|+	ξi3|+	ADP
ejpam-6131	441	6	|qi4	|qi4	PUNCT
ejpam-6131	441	7	−	−	NOUN
ejpam-6131	441	8	ξi4|+	ξi4|+	NOUN
ejpam-6131	441	9	|qi5	|qi5	PROPN
ejpam-6131	441	10	−	−	PROPN
ejpam-6131	441	11	ξi5|	ξi5|	PROPN
ejpam-6131	441	12	)	)	PUNCT
ejpam-6131	441	13	)	)	PUNCT
ejpam-6131	442	1	=	=	PUNCT
ejpam-6131	442	2	t(n	t(n	PROPN
ejpam-6131	442	3	,	,	PUNCT
ejpam-6131	442	4	m	m	NOUN
ejpam-6131	442	5	)	)	PUNCT
ejpam-6131	442	6	.	.	PUNCT
ejpam-6131	443	1	now	now	ADV
ejpam-6131	443	2	,	,	PUNCT
ejpam-6131	443	3	t(m	t(m	PROPN
ejpam-6131	443	4	,	,	PUNCT
ejpam-6131	443	5	n	n	CCONJ
ejpam-6131	443	6	)	)	PUNCT
ejpam-6131	443	7	=	=	SYM
ejpam-6131	444	1	(	(	PUNCT
ejpam-6131	444	2	n∑	n∑	NOUN
ejpam-6131	444	3	i−1	i−1	PROPN
ejpam-6131	444	4	(	(	PUNCT
ejpam-6131	444	5	|ξi1	|ξi1	PROPN
ejpam-6131	444	6	−	−	NOUN
ejpam-6131	444	7	qi1|+	qi1|+	NOUN
ejpam-6131	445	1	|ξi2	|ξi2	CCONJ
ejpam-6131	445	2	−	−	PROPN
ejpam-6131	445	3	qi2|+	qi2|+	PROPN
ejpam-6131	445	4	|ξi3	|ξi3	SYM
ejpam-6131	445	5	−	−	PROPN
ejpam-6131	445	6	qi3|+	qi3|+	NOUN
ejpam-6131	445	7	|ξi4	|ξi4	PROPN
ejpam-6131	445	8	−	−	PROPN
ejpam-6131	445	9	qi4|+	qi4|+	X
ejpam-6131	445	10	|ξi5	|ξi5	ADP
ejpam-6131	445	11	−	−	NOUN
ejpam-6131	445	12	qi5|	qi5|	ADV
ejpam-6131	445	13	)	)	PUNCT
ejpam-6131	445	14	,	,	PUNCT
ejpam-6131	445	15	n∑	n∑	NOUN
ejpam-6131	445	16	i=1	i=1	PROPN
ejpam-6131	445	17	(	(	PUNCT
ejpam-6131	445	18	|ξi1	|ξi1	PROPN
ejpam-6131	445	19	−	−	NOUN
ejpam-6131	445	20	qi1|+	qi1|+	NOUN
ejpam-6131	446	1	|ξi2	|ξi2	CCONJ
ejpam-6131	446	2	−	−	PROPN
ejpam-6131	446	3	qi2|+	qi2|+	PROPN
ejpam-6131	446	4	|ξi3	|ξi3	SYM
ejpam-6131	446	5	−	−	PROPN
ejpam-6131	446	6	qi3|+	qi3|+	NOUN
ejpam-6131	446	7	|ξi4	|ξi4	PROPN
ejpam-6131	446	8	−	−	PROPN
ejpam-6131	446	9	qi4|+	qi4|+	X
ejpam-6131	446	10	|ξi5	|ξi5	ADP
ejpam-6131	446	11	−	−	NOUN
ejpam-6131	446	12	qi5|	qi5|	ADV
ejpam-6131	446	13	)	)	PUNCT
ejpam-6131	446	14	)	)	PUNCT
ejpam-6131	447	1	=	=	PUNCT
ejpam-6131	448	1	(	(	PUNCT
ejpam-6131	448	2	n∑	n∑	INTJ
ejpam-6131	448	3	i=1	i=1	PROPN
ejpam-6131	449	1	(	(	PUNCT
ejpam-6131	449	2	|(ξi1	|(ξi1	NOUN
ejpam-6131	449	3	−	−	PROPN
ejpam-6131	449	4	κi1	κi1	PROPN
ejpam-6131	449	5	)	)	PUNCT
ejpam-6131	450	1	+	+	CCONJ
ejpam-6131	450	2	(	(	PUNCT
ejpam-6131	450	3	κi1	κi1	PROPN
ejpam-6131	450	4	−	−	PROPN
ejpam-6131	450	5	qi1)|+	qi1)|+	NOUN
ejpam-6131	450	6	|(ξi2	|(ξi2	ADP
ejpam-6131	450	7	−	−	PROPN
ejpam-6131	450	8	κi2	κi2	NOUN
ejpam-6131	450	9	)	)	PUNCT
ejpam-6131	451	1	+	+	CCONJ
ejpam-6131	451	2	(	(	PUNCT
ejpam-6131	451	3	κi2	κi2	NOUN
ejpam-6131	451	4	−	−	PROPN
ejpam-6131	451	5	qi2)|+	qi2)|+	NOUN
ejpam-6131	451	6	|(ξi3	|(ξi3	DET
ejpam-6131	451	7	−	−	NOUN
ejpam-6131	451	8	κi3	κi3	NUM
ejpam-6131	451	9	)	)	PUNCT
ejpam-6131	452	1	+	+	ADV
ejpam-6131	452	2	(	(	PUNCT
ejpam-6131	452	3	κi3	κi3	ADJ
ejpam-6131	452	4	−	−	ADP
ejpam-6131	452	5	qi3)|+	qi3)|+	VERB
ejpam-6131	452	6	|(ξi4	|(ξi4	NOUN
ejpam-6131	452	7	−	−	NOUN
ejpam-6131	452	8	κi4	κi4	NOUN
ejpam-6131	452	9	)	)	PUNCT
ejpam-6131	452	10	+	+	CCONJ
ejpam-6131	452	11	(	(	PUNCT
ejpam-6131	452	12	κi4	κi4	NOUN
ejpam-6131	452	13	−	−	PROPN
ejpam-6131	452	14	qi4)|+	qi4)|+	NOUN
ejpam-6131	452	15	|(ξi5	|(ξi5	ADV
ejpam-6131	452	16	−	−	PROPN
ejpam-6131	452	17	κi5	κi5	NOUN
ejpam-6131	452	18	)	)	PUNCT
ejpam-6131	452	19	+	+	CCONJ
ejpam-6131	452	20	(	(	PUNCT
ejpam-6131	452	21	κi5	κi5	NOUN
ejpam-6131	452	22	−	−	PROPN
ejpam-6131	452	23	qi5)|	qi5)|	PROPN
ejpam-6131	452	24	)	)	PUNCT
ejpam-6131	452	25	,	,	PUNCT
ejpam-6131	452	26	s.	s.	PROPN
ejpam-6131	452	27	batul	batul	PROPN
ejpam-6131	452	28	et	et	PROPN
ejpam-6131	452	29	a.	a.	PROPN
ejpam-6131	452	30	/	/	PUNCT
ejpam-6131	452	31	eur	eur	PROPN
ejpam-6131	452	32	.	.	PUNCT
ejpam-6131	453	1	j.	j.	PROPN
ejpam-6131	453	2	pure	pure	PROPN
ejpam-6131	453	3	appl	appl	PROPN
ejpam-6131	453	4	.	.	PROPN
ejpam-6131	453	5	math	math	PROPN
ejpam-6131	453	6	,	,	PUNCT
ejpam-6131	453	7	18	18	NUM
ejpam-6131	453	8	(	(	PUNCT
ejpam-6131	453	9	2	2	NUM
ejpam-6131	453	10	)	)	PUNCT
ejpam-6131	453	11	(	(	PUNCT
ejpam-6131	453	12	2025	2025	NUM
ejpam-6131	453	13	)	)	PUNCT
ejpam-6131	453	14	,	,	PUNCT
ejpam-6131	453	15	6131	6131	NUM
ejpam-6131	453	16	18	18	NUM
ejpam-6131	453	17	of	of	ADP
ejpam-6131	453	18	22	22	NUM
ejpam-6131	453	19	n∑	n∑	NOUN
ejpam-6131	453	20	i=1	i=1	PROPN
ejpam-6131	453	21	(	(	PUNCT
ejpam-6131	453	22	|(ξi1	|(ξi1	NOUN
ejpam-6131	453	23	−	−	PROPN
ejpam-6131	453	24	κi1	κi1	PROPN
ejpam-6131	453	25	)	)	PUNCT
ejpam-6131	454	1	+	+	CCONJ
ejpam-6131	454	2	(	(	PUNCT
ejpam-6131	454	3	κi1	κi1	PROPN
ejpam-6131	454	4	−	−	PROPN
ejpam-6131	454	5	qi1)|+	qi1)|+	NOUN
ejpam-6131	454	6	|(ξi2	|(ξi2	ADP
ejpam-6131	454	7	−	−	PROPN
ejpam-6131	454	8	κi2	κi2	NOUN
ejpam-6131	454	9	)	)	PUNCT
ejpam-6131	455	1	+	+	CCONJ
ejpam-6131	455	2	(	(	PUNCT
ejpam-6131	455	3	κi2	κi2	NOUN
ejpam-6131	455	4	−	−	PROPN
ejpam-6131	455	5	qi2)|+	qi2)|+	NOUN
ejpam-6131	455	6	|(ξi3	|(ξi3	DET
ejpam-6131	455	7	−	−	NOUN
ejpam-6131	455	8	κi3	κi3	NUM
ejpam-6131	455	9	)	)	PUNCT
ejpam-6131	456	1	+	+	ADV
ejpam-6131	456	2	(	(	PUNCT
ejpam-6131	456	3	κi3	κi3	ADJ
ejpam-6131	456	4	−	−	ADP
ejpam-6131	456	5	qi3)|+	qi3)|+	VERB
ejpam-6131	456	6	|(ξi4	|(ξi4	NOUN
ejpam-6131	456	7	−	−	NOUN
ejpam-6131	456	8	κi4	κi4	NOUN
ejpam-6131	456	9	)	)	PUNCT
ejpam-6131	456	10	+	+	CCONJ
ejpam-6131	456	11	(	(	PUNCT
ejpam-6131	456	12	κi4	κi4	NOUN
ejpam-6131	456	13	−	−	PROPN
ejpam-6131	456	14	qi4)|+	qi4)|+	NOUN
ejpam-6131	456	15	|(ξi5	|(ξi5	ADV
ejpam-6131	456	16	−	−	PROPN
ejpam-6131	456	17	κi5	κi5	NOUN
ejpam-6131	456	18	)	)	PUNCT
ejpam-6131	456	19	+	+	CCONJ
ejpam-6131	456	20	(	(	PUNCT
ejpam-6131	456	21	κi5	κi5	NOUN
ejpam-6131	456	22	−	−	PROPN
ejpam-6131	456	23	qi5)|	qi5)|	PROPN
ejpam-6131	456	24	)	)	PUNCT
ejpam-6131	456	25	)	)	PUNCT
ejpam-6131	456	26	≤	≤	NOUN
ejpam-6131	457	1	(	(	PUNCT
ejpam-6131	457	2	n∑	n∑	NOUN
ejpam-6131	457	3	i−1	i−1	PROPN
ejpam-6131	457	4	(	(	PUNCT
ejpam-6131	457	5	|ξi1	|ξi1	PROPN
ejpam-6131	457	6	−	−	PROPN
ejpam-6131	457	7	κi1|+	κi1|+	NOUN
ejpam-6131	458	1	|κi1	|κi1	DET
ejpam-6131	458	2	−	−	PROPN
ejpam-6131	458	3	qi1|+	qi1|+	NOUN
ejpam-6131	459	1	|ξi2	|ξi2	NOUN
ejpam-6131	459	2	−	−	PROPN
ejpam-6131	460	1	κi2|+	κi2|+	PROPN
ejpam-6131	460	2	|κi2	|κi2	PROPN
ejpam-6131	460	3	−	−	PROPN
ejpam-6131	460	4	qi2|+	qi2|+	NOUN
ejpam-6131	460	5	|ξi3	|ξi3	PUNCT
ejpam-6131	460	6	−	−	NOUN
ejpam-6131	460	7	κi3|	κi3|	PUNCT
ejpam-6131	461	1	+	+	ADJ
ejpam-6131	461	2	|κi3	|κi3	NOUN
ejpam-6131	461	3	−	−	ADP
ejpam-6131	461	4	qi3|+	qi3|+	NOUN
ejpam-6131	461	5	|ξi4	|ξi4	NOUN
ejpam-6131	461	6	−	−	NOUN
ejpam-6131	461	7	κi4|+	κi4|+	X
ejpam-6131	461	8	|κi4	|κi4	ADJ
ejpam-6131	461	9	−	−	NOUN
ejpam-6131	461	10	qi4|+	qi4|+	X
ejpam-6131	461	11	|ξi5	|ξi5	NOUN
ejpam-6131	461	12	−	−	PROPN
ejpam-6131	461	13	κi5|+	κi5|+	NOUN
ejpam-6131	461	14	|κi5	|κi5	PUNCT
ejpam-6131	461	15	−	−	PROPN
ejpam-6131	461	16	qi5|	qi5|	ADV
ejpam-6131	461	17	)	)	PUNCT
ejpam-6131	461	18	,	,	PUNCT
ejpam-6131	461	19	n∑	n∑	NOUN
ejpam-6131	461	20	i=1	i=1	PROPN
ejpam-6131	461	21	(	(	PUNCT
ejpam-6131	461	22	|ξi1	|ξi1	NOUN
ejpam-6131	461	23	−	−	PROPN
ejpam-6131	461	24	κi1|+	κi1|+	NOUN
ejpam-6131	461	25	|κi1	|κi1	PRON
ejpam-6131	461	26	−	−	PROPN
ejpam-6131	461	27	qi1|+	qi1|+	NOUN
ejpam-6131	462	1	|ξi2	|ξi2	NOUN
ejpam-6131	462	2	−	−	PROPN
ejpam-6131	463	1	κi2|+	κi2|+	PROPN
ejpam-6131	463	2	|κi2	|κi2	PROPN
ejpam-6131	463	3	−	−	PROPN
ejpam-6131	463	4	qi2|+	qi2|+	NOUN
ejpam-6131	463	5	|ξi3	|ξi3	PUNCT
ejpam-6131	463	6	−	−	NOUN
ejpam-6131	463	7	κi3|	κi3|	PUNCT
ejpam-6131	464	1	+	+	ADJ
ejpam-6131	464	2	|κi3	|κi3	NOUN
ejpam-6131	464	3	−	−	ADP
ejpam-6131	464	4	qi3|+	qi3|+	NOUN
ejpam-6131	464	5	|ξi4	|ξi4	NOUN
ejpam-6131	464	6	−	−	NOUN
ejpam-6131	464	7	κi4|+	κi4|+	X
ejpam-6131	464	8	|κi4	|κi4	ADJ
ejpam-6131	464	9	−	−	NOUN
ejpam-6131	464	10	qi4|+	qi4|+	X
ejpam-6131	464	11	|ξi5	|ξi5	NOUN
ejpam-6131	464	12	−	−	PROPN
ejpam-6131	464	13	κi5|+	κi5|+	NOUN
ejpam-6131	464	14	|κi5	|κi5	PUNCT
ejpam-6131	464	15	−	−	PROPN
ejpam-6131	464	16	qi5|	qi5|	NOUN
ejpam-6131	464	17	)	)	PUNCT
ejpam-6131	464	18	)	)	PUNCT
ejpam-6131	465	1	=	=	PRON
ejpam-6131	465	2	{	{	PUNCT
ejpam-6131	465	3	(	(	PUNCT
ejpam-6131	465	4	n∑	n∑	INTJ
ejpam-6131	465	5	i=1	i=1	PROPN
ejpam-6131	465	6	(	(	PUNCT
ejpam-6131	465	7	|ξi1	|ξi1	PROPN
ejpam-6131	465	8	−	−	PROPN
ejpam-6131	465	9	κi1|+|ξi2	κi1|+|ξi2	NOUN
ejpam-6131	465	10	−	−	NOUN
ejpam-6131	465	11	κi2|+	κi2|+	ADJ
ejpam-6131	465	12	|ξi3	|ξi3	SYM
ejpam-6131	465	13	−	−	PROPN
ejpam-6131	465	14	κi3|+	κi3|+	NOUN
ejpam-6131	465	15	|ξi4	|ξi4	NOUN
ejpam-6131	465	16	−	−	NOUN
ejpam-6131	465	17	κi4|+	κi4|+	X
ejpam-6131	465	18	|ξi5	|ξi5	NOUN
ejpam-6131	465	19	−	−	PROPN
ejpam-6131	465	20	κi5|	κi5|	PROPN
ejpam-6131	465	21	)	)	PUNCT
ejpam-6131	465	22	,	,	PUNCT
ejpam-6131	466	1	n∑	n∑	NOUN
ejpam-6131	466	2	i=1	i=1	PROPN
ejpam-6131	466	3	(	(	PUNCT
ejpam-6131	466	4	|ξi1	|ξi1	PROPN
ejpam-6131	466	5	−	−	PROPN
ejpam-6131	466	6	κi1|+|ξi2	κi1|+|ξi2	NOUN
ejpam-6131	466	7	−	−	NOUN
ejpam-6131	466	8	κi2|+	κi2|+	ADJ
ejpam-6131	466	9	|ξi3	|ξi3	SYM
ejpam-6131	466	10	−	−	PROPN
ejpam-6131	466	11	κi3|+	κi3|+	NOUN
ejpam-6131	466	12	|ξi4	|ξi4	NOUN
ejpam-6131	466	13	−	−	NOUN
ejpam-6131	466	14	κi4|+	κi4|+	X
ejpam-6131	466	15	|ξi5	|ξi5	NOUN
ejpam-6131	466	16	−	−	PROPN
ejpam-6131	466	17	κi5|	κi5|	NOUN
ejpam-6131	466	18	)	)	PUNCT
ejpam-6131	466	19	)	)	PUNCT
ejpam-6131	467	1	+	+	CCONJ
ejpam-6131	467	2	(	(	PUNCT
ejpam-6131	467	3	n∑	n∑	INTJ
ejpam-6131	467	4	i=1	i=1	PROPN
ejpam-6131	467	5	(	(	PUNCT
ejpam-6131	467	6	|κi1	|κi1	PROPN
ejpam-6131	467	7	−	−	PROPN
ejpam-6131	467	8	qi1|+	qi1|+	PROPN
ejpam-6131	467	9	|κi2	|κi2	PROPN
ejpam-6131	467	10	−	−	PROPN
ejpam-6131	467	11	qi2|+	qi2|+	NOUN
ejpam-6131	467	12	|κi3	|κi3	NOUN
ejpam-6131	467	13	−	−	NOUN
ejpam-6131	467	14	qi3|+	qi3|+	NOUN
ejpam-6131	467	15	|κi4	|κi4	NOUN
ejpam-6131	467	16	−	−	NOUN
ejpam-6131	467	17	qi4|+	qi4|+	NOUN
ejpam-6131	467	18	|κi5	|κi5	PUNCT
ejpam-6131	467	19	−	−	PROPN
ejpam-6131	467	20	qi5|	qi5|	ADV
ejpam-6131	467	21	)	)	PUNCT
ejpam-6131	467	22	,	,	PUNCT
ejpam-6131	467	23	n∑	n∑	NOUN
ejpam-6131	467	24	i=1	i=1	PROPN
ejpam-6131	468	1	(	(	PUNCT
ejpam-6131	468	2	|κi1	|κi1	PROPN
ejpam-6131	468	3	−	−	PROPN
ejpam-6131	468	4	qi1|+	qi1|+	PROPN
ejpam-6131	468	5	|κi2	|κi2	PROPN
ejpam-6131	468	6	−	−	PROPN
ejpam-6131	468	7	qi2|+	qi2|+	NOUN
ejpam-6131	468	8	|κi3	|κi3	NOUN
ejpam-6131	468	9	−	−	NOUN
ejpam-6131	468	10	qi3|+	qi3|+	NOUN
ejpam-6131	468	11	|κi4	|κi4	NOUN
ejpam-6131	468	12	−	−	NOUN
ejpam-6131	468	13	qi4|+	qi4|+	NOUN
ejpam-6131	468	14	|κi5	|κi5	PUNCT
ejpam-6131	469	1	−	−	PROPN
ejpam-6131	469	2	qi5|	qi5|	ADV
ejpam-6131	469	3	)	)	PUNCT
ejpam-6131	469	4	)	)	PUNCT
ejpam-6131	469	5	}	}	PUNCT
ejpam-6131	470	1	=	=	SYM
ejpam-6131	470	2	t(m	t(m	PROPN
ejpam-6131	470	3	,	,	PUNCT
ejpam-6131	470	4	l	l	NOUN
ejpam-6131	470	5	)	)	PUNCT
ejpam-6131	470	6	+	+	CCONJ
ejpam-6131	470	7	t(l	t(l	PROPN
ejpam-6131	470	8	,	,	PUNCT
ejpam-6131	470	9	n	n	CCONJ
ejpam-6131	470	10	)	)	PUNCT
ejpam-6131	470	11	,	,	PUNCT
ejpam-6131	470	12	where	where	SCONJ
ejpam-6131	470	13	,	,	PUNCT
ejpam-6131	470	14	l	l	NOUN
ejpam-6131	470	15	=	=	SYM
ejpam-6131	470	16	(	(	PUNCT
ejpam-6131	470	17	κ1	κ1	NOUN
ejpam-6131	470	18	,	,	PUNCT
ejpam-6131	470	19	κ2	κ2	PROPN
ejpam-6131	470	20	,	,	PUNCT
ejpam-6131	470	21	κ3	κ3	PROPN
ejpam-6131	470	22	,	,	PUNCT
ejpam-6131	470	23	κ4	κ4	NOUN
ejpam-6131	470	24	,	,	PUNCT
ejpam-6131	470	25	κ5	κ5	NOUN
ejpam-6131	470	26	)	)	PUNCT
ejpam-6131	470	27	∈	∈	PROPN
ejpam-6131	470	28	θ5	θ5	PROPN
ejpam-6131	470	29	n−1	n−1	PROPN
ejpam-6131	470	30	.	.	PUNCT
ejpam-6131	471	1	hence	hence	ADV
ejpam-6131	471	2	,	,	PUNCT
ejpam-6131	471	3	(	(	PUNCT
ejpam-6131	471	4	θ	θ	PROPN
ejpam-6131	471	5	5	5	NUM
ejpam-6131	471	6	n−1	n−1	PROPN
ejpam-6131	471	7	,	,	PUNCT
ejpam-6131	471	8	t	t	PROPN
ejpam-6131	471	9	)	)	PUNCT
ejpam-6131	471	10	is	be	AUX
ejpam-6131	471	11	a	a	DET
ejpam-6131	471	12	generalized	generalized	ADJ
ejpam-6131	471	13	metric	metric	ADJ
ejpam-6131	471	14	space	space	NOUN
ejpam-6131	471	15	.	.	PUNCT
ejpam-6131	472	1	completeness	completeness	NOUN
ejpam-6131	472	2	of	of	ADP
ejpam-6131	472	3	θ5	θ5	PROPN
ejpam-6131	472	4	n−1	n−1	PROPN
ejpam-6131	472	5	can	can	AUX
ejpam-6131	472	6	be	be	AUX
ejpam-6131	472	7	easily	easily	ADV
ejpam-6131	472	8	proved	prove	VERB
ejpam-6131	472	9	.	.	PUNCT
ejpam-6131	473	1	moreover	moreover	ADV
ejpam-6131	473	2	,	,	PUNCT
ejpam-6131	473	3	define	define	VERB
ejpam-6131	473	4	the	the	DET
ejpam-6131	473	5	partial	partial	ADJ
ejpam-6131	473	6	order	order	NOUN
ejpam-6131	473	7	on	on	ADP
ejpam-6131	473	8	θ5	θ5	PROPN
ejpam-6131	473	9	n−1	n−1	PROPN
ejpam-6131	473	10	as	as	ADP
ejpam-6131	473	11	for	for	ADP
ejpam-6131	473	12	all	all	DET
ejpam-6131	473	13	(	(	PUNCT
ejpam-6131	473	14	ξ1	ξ1	NOUN
ejpam-6131	473	15	,	,	PUNCT
ejpam-6131	473	16	ξ2	ξ2	ADJ
ejpam-6131	473	17	,	,	PUNCT
ejpam-6131	473	18	ξ3	ξ3	NOUN
ejpam-6131	473	19	,	,	PUNCT
ejpam-6131	473	20	ξ4	ξ4	NOUN
ejpam-6131	473	21	,	,	PUNCT
ejpam-6131	473	22	ξ5	ξ5	NOUN
ejpam-6131	473	23	)	)	PUNCT
ejpam-6131	473	24	,	,	PUNCT
ejpam-6131	473	25	(	(	PUNCT
ejpam-6131	473	26	q1	q1	PROPN
ejpam-6131	473	27	,	,	PUNCT
ejpam-6131	473	28	q2	q2	NOUN
ejpam-6131	473	29	,	,	PUNCT
ejpam-6131	473	30	q3	q3	PROPN
ejpam-6131	473	31	,	,	PUNCT
ejpam-6131	473	32	q4	q4	PROPN
ejpam-6131	473	33	,	,	PUNCT
ejpam-6131	473	34	q5	q5	PROPN
ejpam-6131	473	35	)	)	PUNCT
ejpam-6131	473	36	∈	∈	PROPN
ejpam-6131	473	37	θ5	θ5	PROPN
ejpam-6131	473	38	n−1	n−1	PROPN
ejpam-6131	473	39	,	,	PUNCT
ejpam-6131	473	40	(	(	PUNCT
ejpam-6131	473	41	ξ1	ξ1	NOUN
ejpam-6131	473	42	,	,	PUNCT
ejpam-6131	473	43	ξ2	ξ2	ADJ
ejpam-6131	473	44	,	,	PUNCT
ejpam-6131	473	45	ξ3	ξ3	NOUN
ejpam-6131	473	46	,	,	PUNCT
ejpam-6131	473	47	ξ4	ξ4	NOUN
ejpam-6131	473	48	,	,	PUNCT
ejpam-6131	473	49	ξ5	ξ5	NOUN
ejpam-6131	473	50	)	)	PUNCT
ejpam-6131	473	51	⪯	⪯	NOUN
ejpam-6131	473	52	(	(	PUNCT
ejpam-6131	473	53	q1	q1	PROPN
ejpam-6131	473	54	,	,	PUNCT
ejpam-6131	473	55	q2	q2	NOUN
ejpam-6131	473	56	,	,	PUNCT
ejpam-6131	473	57	q3	q3	PROPN
ejpam-6131	473	58	,	,	PUNCT
ejpam-6131	473	59	q4	q4	PROPN
ejpam-6131	473	60	,	,	PUNCT
ejpam-6131	473	61	q5	q5	PROPN
ejpam-6131	473	62	)	)	PUNCT
ejpam-6131	473	63	⇐	⇐	ADJ
ejpam-6131	473	64	⇒	⇒	PROPN
ejpam-6131	473	65	ξ1	ξ1	PROPN
ejpam-6131	473	66	⪯	⪯	PROPN
ejpam-6131	473	67	q1	q1	PROPN
ejpam-6131	473	68	,	,	PUNCT
ejpam-6131	473	69	ξ2	ξ2	ADJ
ejpam-6131	473	70	⪰	⪰	NOUN
ejpam-6131	473	71	q2	q2	NOUN
ejpam-6131	473	72	,	,	PUNCT
ejpam-6131	473	73	ξ3	ξ3	PROPN
ejpam-6131	473	74	⪯	⪯	PROPN
ejpam-6131	473	75	q3	q3	PROPN
ejpam-6131	473	76	,	,	PUNCT
ejpam-6131	473	77	ξ4	ξ4	NOUN
ejpam-6131	473	78	⪰	⪰	NOUN
ejpam-6131	473	79	q4	q4	PROPN
ejpam-6131	473	80	,	,	PUNCT
ejpam-6131	473	81	ξ5	ξ5	PROPN
ejpam-6131	473	82	⪯	⪯	PROPN
ejpam-6131	473	83	q5	q5	PROPN
ejpam-6131	473	84	.	.	PUNCT
ejpam-6131	474	1	hence	hence	ADV
ejpam-6131	474	2	,	,	PUNCT
ejpam-6131	474	3	(	(	PUNCT
ejpam-6131	474	4	θ5	θ5	PROPN
ejpam-6131	474	5	n−1	n−1	PROPN
ejpam-6131	474	6	,	,	PUNCT
ejpam-6131	474	7	t	t	PROPN
ejpam-6131	474	8	,	,	PUNCT
ejpam-6131	474	9	⪯	⪯	PROPN
ejpam-6131	474	10	)	)	PUNCT
ejpam-6131	474	11	is	be	AUX
ejpam-6131	474	12	a	a	DET
ejpam-6131	474	13	pocgms	pocgms	NOUN
ejpam-6131	474	14	.	.	PUNCT
ejpam-6131	475	1	let	let	VERB
ejpam-6131	475	2	f	f	NOUN
ejpam-6131	475	3	:	:	PUNCT
ejpam-6131	475	4	θ5	θ5	PROPN
ejpam-6131	475	5	n−1	n−1	PROPN
ejpam-6131	475	6	→	→	SYM
ejpam-6131	475	7	θ5	θ5	PROPN
ejpam-6131	475	8	n−1	n−1	PROPN
ejpam-6131	475	9	be	be	AUX
ejpam-6131	475	10	a	a	DET
ejpam-6131	475	11	mapping	mapping	NOUN
ejpam-6131	475	12	defined	define	VERB
ejpam-6131	475	13	as	as	ADP
ejpam-6131	475	14	for	for	ADP
ejpam-6131	475	15	all	all	DET
ejpam-6131	475	16	θ	θ	PROPN
ejpam-6131	475	17	∈	∈	PROPN
ejpam-6131	475	18	θ5	θ5	PROPN
ejpam-6131	475	19	n−1	n−1	PROPN
ejpam-6131	475	20	,	,	PUNCT
ejpam-6131	475	21	fθ	fθ	X
ejpam-6131	475	22	=	=	SYM
ejpam-6131	475	23	αj	αj	ADP
ejpam-6131	475	24	such	such	ADJ
ejpam-6131	475	25	that	that	PRON
ejpam-6131	475	26	for	for	ADP
ejpam-6131	475	27	each	each	DET
ejpam-6131	475	28	j	j	NOUN
ejpam-6131	475	29	,	,	PUNCT
ejpam-6131	475	30	αj	αj	X
ejpam-6131	476	1	=	=	SYM
ejpam-6131	477	1	∑n	∑n	PROPN
ejpam-6131	478	1	i=1	i=1	PROPN
ejpam-6131	479	1	eijθj	eijθj	PROPN
ejpam-6131	479	2	.	.	PUNCT
ejpam-6131	480	1	as	as	ADP
ejpam-6131	480	2	,	,	PUNCT
ejpam-6131	480	3	n∑	n∑	NOUN
ejpam-6131	480	4	j=1	j=1	NOUN
ejpam-6131	480	5	αj	αj	X
ejpam-6131	480	6	=	=	SYM
ejpam-6131	481	1	n∑	n∑	PROPN
ejpam-6131	481	2	j=1	j=1	PROPN
ejpam-6131	482	1	n∑	n∑	PROPN
ejpam-6131	482	2	i=1	i=1	PROPN
ejpam-6131	483	1	eijθj	eijθj	PROPN
ejpam-6131	484	1	=	=	SYM
ejpam-6131	484	2	n∑	n∑	PROPN
ejpam-6131	484	3	i=1	i=1	PROPN
ejpam-6131	485	1	eij	eij	PROPN
ejpam-6131	485	2	n∑	n∑	PROPN
ejpam-6131	486	1	j=1	j=1	PROPN
ejpam-6131	486	2	(	(	PUNCT
ejpam-6131	486	3	ξj1	ξj1	NOUN
ejpam-6131	486	4	+	+	CCONJ
ejpam-6131	486	5	ξj2	ξj2	NOUN
ejpam-6131	486	6	+	+	CCONJ
ejpam-6131	486	7	ξj3	ξj3	PROPN
ejpam-6131	486	8	+	+	CCONJ
ejpam-6131	486	9	ξj4	ξj4	VERB
ejpam-6131	486	10	,	,	PUNCT
ejpam-6131	486	11	ξ	ξ	PROPN
ejpam-6131	486	12	j	j	PROPN
ejpam-6131	486	13	5	5	NUM
ejpam-6131	486	14	)	)	PUNCT
ejpam-6131	486	15	=	=	SYM
ejpam-6131	487	1	n∑	n∑	NOUN
ejpam-6131	487	2	j=1	j=1	NOUN
ejpam-6131	487	3	(	(	PUNCT
ejpam-6131	487	4	ξj1	ξj1	NOUN
ejpam-6131	487	5	+	+	CCONJ
ejpam-6131	487	6	ξj2	ξj2	NOUN
ejpam-6131	487	7	+	+	CCONJ
ejpam-6131	487	8	ξj3	ξj3	PROPN
ejpam-6131	487	9	+	+	CCONJ
ejpam-6131	487	10	ξj4	ξj4	VERB
ejpam-6131	487	11	,	,	PUNCT
ejpam-6131	487	12	ξ	ξ	PROPN
ejpam-6131	487	13	j	j	PROPN
ejpam-6131	487	14	5	5	NUM
ejpam-6131	487	15	)	)	PUNCT
ejpam-6131	487	16	=	=	SYM
ejpam-6131	487	17	1	1	NUM
ejpam-6131	487	18	,	,	PUNCT
ejpam-6131	487	19	therefore	therefore	ADV
ejpam-6131	487	20	,	,	PUNCT
ejpam-6131	487	21	αj	αj	PROPN
ejpam-6131	487	22	∈	∈	PROPN
ejpam-6131	487	23	θ5	θ5	PROPN
ejpam-6131	487	24	n−1	n−1	PROPN
ejpam-6131	487	25	,	,	PUNCT
ejpam-6131	487	26	so	so	ADV
ejpam-6131	487	27	mapping	mapping	NOUN
ejpam-6131	487	28	is	be	AUX
ejpam-6131	487	29	defined	define	VERB
ejpam-6131	487	30	.	.	PUNCT
ejpam-6131	488	1	now	now	ADV
ejpam-6131	488	2	,	,	PUNCT
ejpam-6131	488	3	we	we	PRON
ejpam-6131	488	4	have	have	VERB
ejpam-6131	488	5	to	to	PART
ejpam-6131	488	6	show	show	VERB
ejpam-6131	488	7	that	that	SCONJ
ejpam-6131	488	8	f	f	PROPN
ejpam-6131	488	9	satisfies	satisfy	VERB
ejpam-6131	488	10	the	the	DET
ejpam-6131	488	11	contraction	contraction	NOUN
ejpam-6131	488	12	condition	condition	NOUN
ejpam-6131	488	13	.	.	PUNCT
ejpam-6131	489	1	for	for	ADP
ejpam-6131	489	2	this	this	PRON
ejpam-6131	489	3	,	,	PUNCT
ejpam-6131	489	4	let	let	VERB
ejpam-6131	489	5	αi	αi	PRON
ejpam-6131	489	6	be	be	AUX
ejpam-6131	489	7	the	the	DET
ejpam-6131	489	8	ith	ith	NOUN
ejpam-6131	489	9	row	row	NOUN
ejpam-6131	489	10	of	of	ADP
ejpam-6131	489	11	α	α	PROPN
ejpam-6131	489	12	.	.	PUNCT
ejpam-6131	490	1	then	then	ADV
ejpam-6131	490	2	,	,	PUNCT
ejpam-6131	490	3	for	for	ADP
ejpam-6131	490	4	all	all	DET
ejpam-6131	490	5	(	(	PUNCT
ejpam-6131	490	6	ξ1	ξ1	NOUN
ejpam-6131	490	7	,	,	PUNCT
ejpam-6131	490	8	ξ2	ξ2	ADJ
ejpam-6131	490	9	,	,	PUNCT
ejpam-6131	490	10	ξ3	ξ3	NOUN
ejpam-6131	490	11	,	,	PUNCT
ejpam-6131	490	12	ξ4	ξ4	NOUN
ejpam-6131	490	13	,	,	PUNCT
ejpam-6131	490	14	ξ5	ξ5	NOUN
ejpam-6131	490	15	)	)	PUNCT
ejpam-6131	490	16	,	,	PUNCT
ejpam-6131	490	17	(	(	PUNCT
ejpam-6131	490	18	q1	q1	PROPN
ejpam-6131	490	19	,	,	PUNCT
ejpam-6131	490	20	q2	q2	NOUN
ejpam-6131	490	21	,	,	PUNCT
ejpam-6131	490	22	q3	q3	PROPN
ejpam-6131	490	23	,	,	PUNCT
ejpam-6131	490	24	q4	q4	PROPN
ejpam-6131	490	25	,	,	PUNCT
ejpam-6131	490	26	q5	q5	PROPN
ejpam-6131	490	27	)	)	PUNCT
ejpam-6131	490	28	in	in	ADP
ejpam-6131	490	29	θ5	θ5	PROPN
ejpam-6131	490	30	n−1	n−1	PROPN
ejpam-6131	490	31	,	,	PUNCT
ejpam-6131	490	32	we	we	PRON
ejpam-6131	490	33	have	have	VERB
ejpam-6131	490	34	t(f(ξ1	t(f(ξ1	VERB
ejpam-6131	490	35	,	,	PUNCT
ejpam-6131	490	36	ξ2	ξ2	ADJ
ejpam-6131	490	37	,	,	PUNCT
ejpam-6131	490	38	ξ3	ξ3	PROPN
ejpam-6131	490	39	,	,	PUNCT
ejpam-6131	490	40	ξ4	ξ4	PROPN
ejpam-6131	490	41	,	,	PUNCT
ejpam-6131	490	42	ξ5),f(q1	ξ5),f(q1	PROPN
ejpam-6131	490	43	,	,	PUNCT
ejpam-6131	490	44	q2	q2	PROPN
ejpam-6131	490	45	,	,	PUNCT
ejpam-6131	490	46	q3	q3	PROPN
ejpam-6131	490	47	,	,	PUNCT
ejpam-6131	490	48	q4	q4	PROPN
ejpam-6131	490	49	,	,	PUNCT
ejpam-6131	490	50	q5	q5	PROPN
ejpam-6131	490	51	)	)	PUNCT
ejpam-6131	490	52	)	)	PUNCT
ejpam-6131	491	1	=	=	PUNCT
ejpam-6131	492	1			PROPN
ejpam-6131	492	2	n∑	n∑	PROPN
ejpam-6131	492	3	i=1	i=1	PROPN
ejpam-6131	492	4	∣∣∣∣∣∣	∣∣∣∣∣∣	NOUN
ejpam-6131	492	5	n∑	n∑	NOUN
ejpam-6131	492	6	j=1	j=1	NOUN
ejpam-6131	492	7	(	(	PUNCT
ejpam-6131	492	8	eij(ξ	eij(ξ	PROPN
ejpam-6131	492	9	j	j	PROPN
ejpam-6131	492	10	1	1	NUM
ejpam-6131	492	11	+	+	NUM
ejpam-6131	492	12	ξj2	ξj2	NOUN
ejpam-6131	492	13	+	+	CCONJ
ejpam-6131	492	14	ξj3	ξj3	PROPN
ejpam-6131	492	15	+	+	CCONJ
ejpam-6131	492	16	ξj4	ξj4	VERB
ejpam-6131	492	17	+	+	SYM
ejpam-6131	492	18	ξj5)−	ξj5)−	NOUN
ejpam-6131	492	19	eij(q	eij(q	PROPN
ejpam-6131	492	20	j	j	PROPN
ejpam-6131	492	21	1	1	NUM
ejpam-6131	492	22	+	+	CCONJ
ejpam-6131	492	23	qj2	qj2	ADJ
ejpam-6131	492	24	+	+	CCONJ
ejpam-6131	492	25	qj3	qj3	NOUN
ejpam-6131	492	26	+	+	CCONJ
ejpam-6131	492	27	qj4	qj4	NOUN
ejpam-6131	492	28	+	+	CCONJ
ejpam-6131	492	29	qj5	qj5	NOUN
ejpam-6131	492	30	)	)	PUNCT
ejpam-6131	492	31	∣∣∣∣∣∣	∣∣∣∣∣∣	PUNCT
ejpam-6131	493	1			PROPN
ejpam-6131	493	2	,	,	PUNCT
ejpam-6131	493	3	s.	s.	PROPN
ejpam-6131	493	4	batul	batul	PROPN
ejpam-6131	493	5	et	et	PROPN
ejpam-6131	493	6	a.	a.	PROPN
ejpam-6131	493	7	/	/	PUNCT
ejpam-6131	493	8	eur	eur	PROPN
ejpam-6131	493	9	.	.	PUNCT
ejpam-6131	494	1	j.	j.	PROPN
ejpam-6131	494	2	pure	pure	PROPN
ejpam-6131	494	3	appl	appl	PROPN
ejpam-6131	494	4	.	.	PROPN
ejpam-6131	494	5	math	math	PROPN
ejpam-6131	494	6	,	,	PUNCT
ejpam-6131	494	7	18	18	NUM
ejpam-6131	494	8	(	(	PUNCT
ejpam-6131	494	9	2	2	NUM
ejpam-6131	494	10	)	)	PUNCT
ejpam-6131	494	11	(	(	PUNCT
ejpam-6131	494	12	2025	2025	NUM
ejpam-6131	494	13	)	)	PUNCT
ejpam-6131	494	14	,	,	PUNCT
ejpam-6131	494	15	6131	6131	NUM
ejpam-6131	494	16	19	19	NUM
ejpam-6131	494	17	of	of	ADP
ejpam-6131	494	18	22	22	NUM
ejpam-6131	494	19	n∑	n∑	NOUN
ejpam-6131	494	20	i=1	i=1	PROPN
ejpam-6131	495	1	∣∣∣∣∣∣	∣∣∣∣∣∣	NOUN
ejpam-6131	496	1	n∑	n∑	NOUN
ejpam-6131	496	2	j=1	j=1	NOUN
ejpam-6131	496	3	(	(	PUNCT
ejpam-6131	496	4	eij(ξ	eij(ξ	PROPN
ejpam-6131	496	5	j	j	PROPN
ejpam-6131	496	6	1	1	NUM
ejpam-6131	496	7	+	+	NUM
ejpam-6131	496	8	ξj2	ξj2	NOUN
ejpam-6131	496	9	+	+	CCONJ
ejpam-6131	496	10	ξj3	ξj3	PROPN
ejpam-6131	496	11	+	+	CCONJ
ejpam-6131	496	12	ξj4	ξj4	VERB
ejpam-6131	496	13	+	+	SYM
ejpam-6131	496	14	ξj5)−	ξj5)−	NOUN
ejpam-6131	496	15	eij(q	eij(q	PROPN
ejpam-6131	496	16	j	j	PROPN
ejpam-6131	496	17	1	1	NUM
ejpam-6131	496	18	+	+	CCONJ
ejpam-6131	496	19	qj2	qj2	ADJ
ejpam-6131	496	20	+	+	CCONJ
ejpam-6131	496	21	qj3	qj3	NOUN
ejpam-6131	496	22	+	+	CCONJ
ejpam-6131	496	23	qj4	qj4	NOUN
ejpam-6131	496	24	+	+	CCONJ
ejpam-6131	496	25	qj5	qj5	NOUN
ejpam-6131	496	26	)	)	PUNCT
ejpam-6131	496	27	)	)	PUNCT
ejpam-6131	496	28	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6131	496	29			PROPN
ejpam-6131	496	30	)	)	PUNCT
ejpam-6131	496	31	=	=	PUNCT
ejpam-6131	497	1	(	(	PUNCT
ejpam-6131	497	2	n∑	n∑	INTJ
ejpam-6131	497	3	i=1	i=1	PROPN
ejpam-6131	498	1	(	(	PUNCT
ejpam-6131	498	2	|	|	INTJ
ejpam-6131	498	3	n∑	n∑	INTJ
ejpam-6131	498	4	j=1	j=1	NOUN
ejpam-6131	498	5	(	(	PUNCT
ejpam-6131	498	6	eij	eij	PROPN
ejpam-6131	498	7	−	−	PROPN
ejpam-6131	498	8	ϕi){(ξj1	ϕi){(ξj1	PROPN
ejpam-6131	498	9	+	+	CCONJ
ejpam-6131	498	10	ξj2	ξj2	NOUN
ejpam-6131	499	1	+	+	CCONJ
ejpam-6131	499	2	ξj3	ξj3	PROPN
ejpam-6131	499	3	+	+	CCONJ
ejpam-6131	499	4	ξj4	ξj4	VERB
ejpam-6131	499	5	+	+	SYM
ejpam-6131	499	6	ξj5)−	ξj5)−	NOUN
ejpam-6131	499	7	(	(	PUNCT
ejpam-6131	499	8	qj1	qj1	NOUN
ejpam-6131	499	9	+	+	CCONJ
ejpam-6131	499	10	qj2	qj2	ADJ
ejpam-6131	499	11	+	+	CCONJ
ejpam-6131	499	12	qj3	qj3	NOUN
ejpam-6131	499	13	+	+	CCONJ
ejpam-6131	499	14	qj4	qj4	NOUN
ejpam-6131	500	1	+	+	CCONJ
ejpam-6131	500	2	qj5	qj5	NOUN
ejpam-6131	500	3	)	)	PUNCT
ejpam-6131	500	4	}	}	PUNCT
ejpam-6131	501	1	+	+	CCONJ
ejpam-6131	501	2	ϕi{(ξj1	ϕi{(ξj1	X
ejpam-6131	501	3	+	+	CCONJ
ejpam-6131	501	4	ξj2	ξj2	NOUN
ejpam-6131	501	5	+	+	CCONJ
ejpam-6131	501	6	ξj3	ξj3	PROPN
ejpam-6131	501	7	+	+	CCONJ
ejpam-6131	501	8	ξj4	ξj4	VERB
ejpam-6131	501	9	,	,	PUNCT
ejpam-6131	501	10	ξ	ξ	X
ejpam-6131	501	11	j	j	PROPN
ejpam-6131	501	12	5)−	5)−	NUM
ejpam-6131	501	13	(	(	PUNCT
ejpam-6131	501	14	qj1	qj1	NOUN
ejpam-6131	501	15	+	+	CCONJ
ejpam-6131	501	16	qj2	qj2	ADJ
ejpam-6131	501	17	+	+	CCONJ
ejpam-6131	501	18	qj3	qj3	NOUN
ejpam-6131	501	19	+	+	CCONJ
ejpam-6131	501	20	qj4	qj4	NOUN
ejpam-6131	501	21	+	+	CCONJ
ejpam-6131	501	22	qj5)}|	qj5)}|	NOUN
ejpam-6131	501	23	)	)	PUNCT
ejpam-6131	501	24	,	,	PUNCT
ejpam-6131	502	1	n∑	n∑	NOUN
ejpam-6131	502	2	i=1	i=1	PROPN
ejpam-6131	503	1	(	(	PUNCT
ejpam-6131	503	2	|	|	INTJ
ejpam-6131	503	3	n∑	n∑	INTJ
ejpam-6131	503	4	j=1	j=1	NOUN
ejpam-6131	503	5	(	(	PUNCT
ejpam-6131	503	6	eij	eij	PROPN
ejpam-6131	503	7	−	−	PROPN
ejpam-6131	503	8	ϕi){(ξj1	ϕi){(ξj1	PROPN
ejpam-6131	503	9	+	+	CCONJ
ejpam-6131	503	10	ξj2	ξj2	NOUN
ejpam-6131	504	1	+	+	CCONJ
ejpam-6131	504	2	ξj3	ξj3	PROPN
ejpam-6131	504	3	+	+	CCONJ
ejpam-6131	504	4	ξj4	ξj4	VERB
ejpam-6131	504	5	+	+	SYM
ejpam-6131	504	6	ξj5)−	ξj5)−	NOUN
ejpam-6131	504	7	(	(	PUNCT
ejpam-6131	504	8	qj1	qj1	NOUN
ejpam-6131	504	9	+	+	CCONJ
ejpam-6131	504	10	qj2	qj2	ADJ
ejpam-6131	504	11	+	+	CCONJ
ejpam-6131	504	12	qj3	qj3	NOUN
ejpam-6131	504	13	+	+	CCONJ
ejpam-6131	504	14	qj4	qj4	NOUN
ejpam-6131	505	1	+	+	CCONJ
ejpam-6131	505	2	qj5	qj5	NOUN
ejpam-6131	505	3	)	)	PUNCT
ejpam-6131	505	4	}	}	PUNCT
ejpam-6131	506	1	+	+	CCONJ
ejpam-6131	506	2	ϕi{(ξj1	ϕi{(ξj1	X
ejpam-6131	506	3	+	+	CCONJ
ejpam-6131	506	4	ξj2	ξj2	NOUN
ejpam-6131	506	5	+	+	CCONJ
ejpam-6131	506	6	ξj3	ξj3	PROPN
ejpam-6131	506	7	+	+	CCONJ
ejpam-6131	506	8	ξj4	ξj4	VERB
ejpam-6131	506	9	+	+	SYM
ejpam-6131	506	10	ξj5)−	ξj5)−	NOUN
ejpam-6131	506	11	(	(	PUNCT
ejpam-6131	506	12	qj1	qj1	NOUN
ejpam-6131	506	13	+	+	CCONJ
ejpam-6131	506	14	qj2	qj2	ADJ
ejpam-6131	506	15	+	+	CCONJ
ejpam-6131	506	16	qj3	qj3	NOUN
ejpam-6131	506	17	+	+	CCONJ
ejpam-6131	506	18	qj4	qj4	NOUN
ejpam-6131	506	19	+	+	CCONJ
ejpam-6131	506	20	qj5)}|	qj5)}|	NOUN
ejpam-6131	506	21	)	)	PUNCT
ejpam-6131	506	22	)	)	PUNCT
ejpam-6131	506	23	≤	≤	NOUN
ejpam-6131	506	24	(	(	PUNCT
ejpam-6131	506	25	(	(	PUNCT
ejpam-6131	506	26	n∑	n∑	NOUN
ejpam-6131	506	27	i=1	i=1	PROPN
ejpam-6131	506	28	n∑	n∑	PROPN
ejpam-6131	507	1	j=1	j=1	PROPN
ejpam-6131	508	1	|(eij	|(eij	NUM
ejpam-6131	508	2	−	−	PROPN
ejpam-6131	508	3	ϕi){(ξj1	ϕi){(ξj1	NOUN
ejpam-6131	508	4	+	+	CCONJ
ejpam-6131	508	5	ξj2	ξj2	NOUN
ejpam-6131	508	6	+	+	CCONJ
ejpam-6131	508	7	ξj3	ξj3	PROPN
ejpam-6131	508	8	+	+	CCONJ
ejpam-6131	508	9	ξj4	ξj4	VERB
ejpam-6131	508	10	+	+	SYM
ejpam-6131	508	11	ξj5)−	ξj5)−	NOUN
ejpam-6131	508	12	(	(	PUNCT
ejpam-6131	508	13	qj1	qj1	NOUN
ejpam-6131	508	14	+	+	CCONJ
ejpam-6131	508	15	qj2	qj2	ADJ
ejpam-6131	508	16	+	+	CCONJ
ejpam-6131	508	17	qj3	qj3	NOUN
ejpam-6131	508	18	+	+	CCONJ
ejpam-6131	508	19	qj4	qj4	NOUN
ejpam-6131	508	20	+	+	CCONJ
ejpam-6131	508	21	qj5)}|	qj5)}|	NOUN
ejpam-6131	508	22	+	+	CCONJ
ejpam-6131	508	23	n∑	n∑	PROPN
ejpam-6131	508	24	i=1	i=1	PROPN
ejpam-6131	508	25	∣∣∣∣∣∣ϕi	∣∣∣∣∣∣ϕi	NOUN
ejpam-6131	508	26	n∑	n∑	PROPN
ejpam-6131	508	27	j=1	j=1	PROPN
ejpam-6131	508	28	{	{	PUNCT
ejpam-6131	508	29	(	(	PUNCT
ejpam-6131	508	30	ξj1	ξj1	NOUN
ejpam-6131	508	31	+	+	CCONJ
ejpam-6131	508	32	ξj2	ξj2	NOUN
ejpam-6131	508	33	+	+	CCONJ
ejpam-6131	508	34	ξj3	ξj3	PROPN
ejpam-6131	508	35	+	+	CCONJ
ejpam-6131	508	36	ξj4	ξj4	VERB
ejpam-6131	508	37	+	+	SYM
ejpam-6131	508	38	ξj5)−	ξj5)−	NOUN
ejpam-6131	508	39	(	(	PUNCT
ejpam-6131	508	40	qj1	qj1	NOUN
ejpam-6131	508	41	+	+	CCONJ
ejpam-6131	508	42	qj2	qj2	ADJ
ejpam-6131	508	43	+	+	CCONJ
ejpam-6131	508	44	qj3	qj3	NOUN
ejpam-6131	508	45	+	+	CCONJ
ejpam-6131	508	46	qj4	qj4	NOUN
ejpam-6131	509	1	+	+	CCONJ
ejpam-6131	509	2	qj5	qj5	NOUN
ejpam-6131	509	3	)	)	PUNCT
ejpam-6131	509	4	}	}	PUNCT
ejpam-6131	509	5	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6131	509	6	)	)	PUNCT
ejpam-6131	509	7	,	,	PUNCT
ejpam-6131	509	8	(	(	PUNCT
ejpam-6131	509	9	n∑	n∑	NOUN
ejpam-6131	509	10	i=1	i=1	PROPN
ejpam-6131	509	11	n∑	n∑	PROPN
ejpam-6131	510	1	j=1	j=1	ADJ
ejpam-6131	510	2	∣∣∣(eij	∣∣∣(eij	NOUN
ejpam-6131	510	3	−	−	PROPN
ejpam-6131	510	4	ϕi){(ξj1	ϕi){(ξj1	NOUN
ejpam-6131	510	5	+	+	CCONJ
ejpam-6131	510	6	ξj2	ξj2	NOUN
ejpam-6131	511	1	+	+	CCONJ
ejpam-6131	511	2	ξj3	ξj3	PROPN
ejpam-6131	511	3	+	+	CCONJ
ejpam-6131	511	4	ξj4	ξj4	VERB
ejpam-6131	511	5	+	+	SYM
ejpam-6131	511	6	ξj5)−	ξj5)−	NOUN
ejpam-6131	511	7	(	(	PUNCT
ejpam-6131	511	8	qj1	qj1	NOUN
ejpam-6131	511	9	+	+	CCONJ
ejpam-6131	511	10	qj2	qj2	ADJ
ejpam-6131	511	11	+	+	CCONJ
ejpam-6131	511	12	qj3	qj3	NOUN
ejpam-6131	511	13	+	+	CCONJ
ejpam-6131	511	14	qj4	qj4	NOUN
ejpam-6131	512	1	+	+	CCONJ
ejpam-6131	512	2	qj5	qj5	NOUN
ejpam-6131	512	3	)	)	PUNCT
ejpam-6131	512	4	}	}	PUNCT
ejpam-6131	512	5	∣∣∣	∣∣∣	NOUN
ejpam-6131	513	1	+	+	CCONJ
ejpam-6131	513	2	n∑	n∑	PROPN
ejpam-6131	513	3	i=1	i=1	PROPN
ejpam-6131	513	4	∣∣∣∣∣∣ϕi	∣∣∣∣∣∣ϕi	NOUN
ejpam-6131	513	5	n∑	n∑	PROPN
ejpam-6131	513	6	j=1	j=1	PROPN
ejpam-6131	513	7	{	{	PUNCT
ejpam-6131	513	8	(	(	PUNCT
ejpam-6131	513	9	ξj1	ξj1	NOUN
ejpam-6131	513	10	+	+	CCONJ
ejpam-6131	513	11	ξj2	ξj2	NOUN
ejpam-6131	513	12	+	+	CCONJ
ejpam-6131	513	13	ξj3	ξj3	PROPN
ejpam-6131	513	14	+	+	CCONJ
ejpam-6131	513	15	ξj4	ξj4	VERB
ejpam-6131	513	16	+	+	SYM
ejpam-6131	513	17	ξj5)−	ξj5)−	NOUN
ejpam-6131	513	18	(	(	PUNCT
ejpam-6131	513	19	qj1	qj1	NOUN
ejpam-6131	513	20	+	+	CCONJ
ejpam-6131	513	21	qj2	qj2	ADJ
ejpam-6131	513	22	+	+	CCONJ
ejpam-6131	513	23	qj3	qj3	NOUN
ejpam-6131	513	24	+	+	CCONJ
ejpam-6131	513	25	qj4	qj4	NOUN
ejpam-6131	514	1	+	+	CCONJ
ejpam-6131	514	2	qj5	qj5	NOUN
ejpam-6131	514	3	)	)	PUNCT
ejpam-6131	514	4	}	}	PUNCT
ejpam-6131	514	5	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6131	514	6	)	)	PUNCT
ejpam-6131	514	7	)	)	PUNCT
ejpam-6131	514	8	≤	≤	NOUN
ejpam-6131	514	9	(	(	PUNCT
ejpam-6131	514	10	∑n	∑n	PROPN
ejpam-6131	514	11	i=1	i=1	PROPN
ejpam-6131	514	12	∑n	∑n	PROPN
ejpam-6131	514	13	j=1(|ξ	j=1(|ξ	NOUN
ejpam-6131	514	14	j	j	NOUN
ejpam-6131	514	15	1	1	NUM
ejpam-6131	514	16	−	−	NOUN
ejpam-6131	514	17	qj1|+	qj1|+	NOUN
ejpam-6131	515	1	|ξj2	|ξj2	PRON
ejpam-6131	515	2	−	−	PUNCT
ejpam-6131	516	1	qj2|+	qj2|+	PROPN
ejpam-6131	517	1	|ξj3	|ξj3	PROPN
ejpam-6131	517	2	−	−	PROPN
ejpam-6131	517	3	qj3|+	qj3|+	PROPN
ejpam-6131	517	4	|ξj4	|ξj4	NUM
ejpam-6131	517	5	−	−	PROPN
ejpam-6131	517	6	qj4|+	qj4|+	PRON
ejpam-6131	517	7	|ξj5	|ξj5	PUNCT
ejpam-6131	517	8	−	−	NOUN
ejpam-6131	517	9	qj5|)×	qj5|)×	NOUN
ejpam-6131	517	10	|eij	|eij	ADP
ejpam-6131	517	11	−	−	PUNCT
ejpam-6131	518	1	ϕi|),∑n	ϕi|),∑n	VERB
ejpam-6131	518	2	i=1	i=1	VERB
ejpam-6131	518	3	∑n	∑n	PROPN
ejpam-6131	518	4	j=1(|ξ	j=1(|ξ	NOUN
ejpam-6131	518	5	j	j	NOUN
ejpam-6131	518	6	1	1	NUM
ejpam-6131	518	7	−	−	NOUN
ejpam-6131	518	8	qj1|+	qj1|+	NOUN
ejpam-6131	519	1	|ξj2	|ξj2	PRON
ejpam-6131	519	2	−	−	PUNCT
ejpam-6131	520	1	qj2|+	qj2|+	PROPN
ejpam-6131	521	1	|ξj3	|ξj3	PROPN
ejpam-6131	521	2	−	−	PROPN
ejpam-6131	521	3	qj3|+	qj3|+	PROPN
ejpam-6131	521	4	|ξj4	|ξj4	NUM
ejpam-6131	521	5	−	−	PROPN
ejpam-6131	521	6	qj4|+	qj4|+	PRON
ejpam-6131	521	7	|ξj5	|ξj5	PUNCT
ejpam-6131	521	8	−	−	PROPN
ejpam-6131	521	9	qj5|	qj5|	NOUN
ejpam-6131	521	10	×	×	VERB
ejpam-6131	521	11	|eij	|eij	PRON
ejpam-6131	521	12	−	−	PROPN
ejpam-6131	521	13	ϕi|	ϕi|	NOUN
ejpam-6131	521	14	)	)	PUNCT
ejpam-6131	521	15	)	)	PUNCT
ejpam-6131	522	1	=	=	PUNCT
ejpam-6131	522	2	(	(	PUNCT
ejpam-6131	522	3	i	i	PRON
ejpam-6131	522	4	−	−	PROPN
ejpam-6131	522	5	ϕ	ϕ	NOUN
ejpam-6131	522	6	)	)	PUNCT
ejpam-6131	522	7	(	(	PUNCT
ejpam-6131	522	8	∑n	∑n	PROPN
ejpam-6131	522	9	j=1(|ξ	j=1(|ξ	NOUN
ejpam-6131	522	10	j	j	NOUN
ejpam-6131	522	11	1	1	NUM
ejpam-6131	522	12	−	−	NOUN
ejpam-6131	522	13	qj1|+	qj1|+	NOUN
ejpam-6131	522	14	|ξj2	|ξj2	PRON
ejpam-6131	522	15	−	−	PUNCT
ejpam-6131	522	16	qj2|+	qj2|+	PROPN
ejpam-6131	523	1	|ξj3	|ξj3	PROPN
ejpam-6131	523	2	−	−	PROPN
ejpam-6131	523	3	qj3|+	qj3|+	PROPN
ejpam-6131	523	4	|ξj4	|ξj4	NUM
ejpam-6131	523	5	−	−	PROPN
ejpam-6131	523	6	qj4|+	qj4|+	PRON
ejpam-6131	523	7	|ξj5	|ξj5	PUNCT
ejpam-6131	523	8	−	−	NOUN
ejpam-6131	523	9	qj5|),∑n	qj5|),∑n	VERB
ejpam-6131	523	10	j=1(|ξ	j=1(|ξ	NOUN
ejpam-6131	523	11	j	j	NOUN
ejpam-6131	523	12	1	1	NUM
ejpam-6131	523	13	−	−	NOUN
ejpam-6131	523	14	qj1|+	qj1|+	NOUN
ejpam-6131	524	1	|ξj2	|ξj2	PRON
ejpam-6131	524	2	−	−	PUNCT
ejpam-6131	525	1	qj2|+	qj2|+	PROPN
ejpam-6131	525	2	|ξj3	|ξj3	PROPN
ejpam-6131	526	1	−	−	PROPN
ejpam-6131	526	2	qj3|2	qj3|2	NOUN
ejpam-6131	526	3	+	+	CCONJ
ejpam-6131	526	4	|ξj4	|ξj4	NUM
ejpam-6131	526	5	−	−	NOUN
ejpam-6131	526	6	qj4|+	qj4|+	PRON
ejpam-6131	526	7	|ξj5	|ξj5	PUNCT
ejpam-6131	526	8	−	−	PROPN
ejpam-6131	526	9	qj5|	qj5|	NOUN
ejpam-6131	526	10	)	)	PUNCT
ejpam-6131	526	11	)	)	PUNCT
ejpam-6131	527	1	=	=	PUNCT
ejpam-6131	527	2	υ̃t((ξ1	υ̃t((ξ1	ADJ
ejpam-6131	527	3	,	,	PUNCT
ejpam-6131	527	4	ξ2	ξ2	ADJ
ejpam-6131	527	5	,	,	PUNCT
ejpam-6131	527	6	ξ3	ξ3	NOUN
ejpam-6131	527	7	,	,	PUNCT
ejpam-6131	527	8	ξ4	ξ4	NOUN
ejpam-6131	527	9	,	,	PUNCT
ejpam-6131	527	10	ξ5	ξ5	NOUN
ejpam-6131	527	11	)	)	PUNCT
ejpam-6131	527	12	,	,	PUNCT
ejpam-6131	527	13	(	(	PUNCT
ejpam-6131	527	14	q1	q1	PROPN
ejpam-6131	527	15	,	,	PUNCT
ejpam-6131	527	16	q2	q2	NOUN
ejpam-6131	527	17	,	,	PUNCT
ejpam-6131	527	18	q3	q3	PROPN
ejpam-6131	527	19	,	,	PUNCT
ejpam-6131	527	20	q4	q4	PROPN
ejpam-6131	527	21	,	,	PUNCT
ejpam-6131	527	22	q5	q5	PROPN
ejpam-6131	527	23	)	)	PUNCT
ejpam-6131	527	24	)	)	PUNCT
ejpam-6131	527	25	,	,	PUNCT
ejpam-6131	527	26	where	where	SCONJ
ejpam-6131	527	27	(	(	PUNCT
ejpam-6131	527	28	i	i	PRON
ejpam-6131	527	29	−	−	PROPN
ejpam-6131	527	30	ϕ	ϕ	NOUN
ejpam-6131	527	31	)	)	PUNCT
ejpam-6131	527	32	=	=	PUNCT
ejpam-6131	527	33	υ̃	υ̃	PROPN
ejpam-6131	527	34	∈	∈	PROPN
ejpam-6131	527	35	zm	zm	PROPN
ejpam-6131	527	36	,	,	PUNCT
ejpam-6131	527	37	therefore	therefore	ADV
ejpam-6131	527	38	all	all	DET
ejpam-6131	527	39	conditions	condition	NOUN
ejpam-6131	527	40	of	of	ADP
ejpam-6131	527	41	corollary	corollary	ADJ
ejpam-6131	527	42	2	2	NUM
ejpam-6131	527	43	have	have	AUX
ejpam-6131	527	44	been	be	AUX
ejpam-6131	527	45	met	meet	VERB
ejpam-6131	527	46	.	.	PUNCT
ejpam-6131	528	1	then	then	ADV
ejpam-6131	528	2	,	,	PUNCT
ejpam-6131	528	3	there	there	PRON
ejpam-6131	528	4	is	be	VERB
ejpam-6131	528	5	a	a	DET
ejpam-6131	528	6	unique	unique	ADJ
ejpam-6131	528	7	quintuple	quintuple	ADV
ejpam-6131	528	8	fixed	fix	VERB
ejpam-6131	528	9	point	point	NOUN
ejpam-6131	528	10	for	for	ADP
ejpam-6131	528	11	f	f	PROPN
ejpam-6131	528	12	or	or	CCONJ
ejpam-6131	528	13	,	,	PUNCT
ejpam-6131	528	14	in	in	ADP
ejpam-6131	528	15	other	other	ADJ
ejpam-6131	528	16	words	word	NOUN
ejpam-6131	528	17	,	,	PUNCT
ejpam-6131	528	18	a	a	DET
ejpam-6131	528	19	unique	unique	ADJ
ejpam-6131	528	20	stationary	stationary	ADJ
ejpam-6131	528	21	distribution	distribution	NOUN
ejpam-6131	528	22	of	of	ADP
ejpam-6131	528	23	the	the	DET
ejpam-6131	528	24	markov	markov	NOUN
ejpam-6131	528	25	process	process	NOUN
ejpam-6131	528	26	.	.	PUNCT
ejpam-6131	529	1	moreover	moreover	ADV
ejpam-6131	529	2	,	,	PUNCT
ejpam-6131	529	3	the	the	DET
ejpam-6131	529	4	sequence	sequence	NOUN
ejpam-6131	529	5	{	{	PUNCT
ejpam-6131	529	6	fnθk	fnθk	NOUN
ejpam-6131	529	7	}	}	PUNCT
ejpam-6131	529	8	converges	converge	NOUN
ejpam-6131	529	9	to	to	ADP
ejpam-6131	529	10	a	a	DET
ejpam-6131	529	11	unique	unique	ADJ
ejpam-6131	529	12	stationary	stationary	ADJ
ejpam-6131	529	13	distribution	distribution	NOUN
ejpam-6131	529	14	for	for	ADP
ejpam-6131	529	15	any	any	DET
ejpam-6131	529	16	θk	θk	NOUN
ejpam-6131	529	17	∈	∈	PROPN
ejpam-6131	529	18	θ5	θ5	PROPN
ejpam-6131	529	19	n−1	n−1	PROPN
ejpam-6131	529	20	.	.	PROPN
ejpam-6131	529	21	5	5	NUM
ejpam-6131	529	22	.	.	X
ejpam-6131	529	23	conclusion	conclusion	NOUN
ejpam-6131	529	24	in	in	ADP
ejpam-6131	529	25	this	this	DET
ejpam-6131	529	26	work	work	NOUN
ejpam-6131	529	27	,	,	PUNCT
ejpam-6131	529	28	we	we	PRON
ejpam-6131	529	29	found	find	VERB
ejpam-6131	529	30	some	some	DET
ejpam-6131	529	31	quadruple	quadruple	NOUN
ejpam-6131	529	32	fixed	fix	VERB
ejpam-6131	529	33	point	point	NOUN
ejpam-6131	529	34	theorems	theorem	NOUN
ejpam-6131	529	35	for	for	ADP
ejpam-6131	529	36	solving	solve	VERB
ejpam-6131	529	37	integral	integral	ADJ
ejpam-6131	529	38	equations	equation	NOUN
ejpam-6131	529	39	involved	involve	VERB
ejpam-6131	529	40	with	with	ADP
ejpam-6131	529	41	matrices	matrix	NOUN
ejpam-6131	529	42	and	and	CCONJ
ejpam-6131	529	43	the	the	DET
ejpam-6131	529	44	markov	markov	NOUN
ejpam-6131	529	45	process	process	NOUN
ejpam-6131	529	46	in	in	ADP
ejpam-6131	529	47	generalized	generalized	ADJ
ejpam-6131	529	48	metric	metric	ADJ
ejpam-6131	529	49	spaces	space	NOUN
ejpam-6131	529	50	.	.	PUNCT
ejpam-6131	530	1	in	in	ADP
ejpam-6131	530	2	this	this	DET
ejpam-6131	530	3	study	study	NOUN
ejpam-6131	530	4	,	,	PUNCT
ejpam-6131	530	5	the	the	DET
ejpam-6131	530	6	notions	notion	NOUN
ejpam-6131	530	7	introduced	introduce	VERB
ejpam-6131	530	8	in	in	ADP
ejpam-6131	530	9	[	[	X
ejpam-6131	530	10	16	16	NUM
ejpam-6131	530	11	]	]	PUNCT
ejpam-6131	530	12	are	be	AUX
ejpam-6131	530	13	structured	structure	VERB
ejpam-6131	530	14	with	with	ADP
ejpam-6131	530	15	a	a	DET
ejpam-6131	530	16	mapping	mapping	NOUN
ejpam-6131	530	17	defined	define	VERB
ejpam-6131	530	18	on	on	ADP
ejpam-6131	530	19	quintuples	quintuple	NOUN
ejpam-6131	530	20	.	.	PUNCT
ejpam-6131	531	1	s.	s.	PROPN
ejpam-6131	531	2	batul	batul	PROPN
ejpam-6131	531	3	et	et	PROPN
ejpam-6131	531	4	a.	a.	PROPN
ejpam-6131	531	5	/	/	PUNCT
ejpam-6131	531	6	eur	eur	PROPN
ejpam-6131	531	7	.	.	PUNCT
ejpam-6131	532	1	j.	j.	PROPN
ejpam-6131	532	2	pure	pure	PROPN
ejpam-6131	532	3	appl	appl	PROPN
ejpam-6131	532	4	.	.	PROPN
ejpam-6131	532	5	math	math	PROPN
ejpam-6131	532	6	,	,	PUNCT
ejpam-6131	532	7	18	18	NUM
ejpam-6131	532	8	(	(	PUNCT
ejpam-6131	532	9	2	2	NUM
ejpam-6131	532	10	)	)	PUNCT
ejpam-6131	532	11	(	(	PUNCT
ejpam-6131	532	12	2025	2025	NUM
ejpam-6131	532	13	)	)	PUNCT
ejpam-6131	532	14	,	,	PUNCT
ejpam-6131	532	15	6131	6131	NUM
ejpam-6131	532	16	20	20	NUM
ejpam-6131	532	17	of	of	ADP
ejpam-6131	532	18	22	22	NUM
ejpam-6131	532	19	the	the	DET
ejpam-6131	532	20	research	research	NOUN
ejpam-6131	532	21	study	study	NOUN
ejpam-6131	532	22	investigated	investigate	VERB
ejpam-6131	532	23	the	the	DET
ejpam-6131	532	24	existence	existence	NOUN
ejpam-6131	532	25	of	of	ADP
ejpam-6131	532	26	quintuple	quintuple	ADV
ejpam-6131	532	27	fixed	fix	VERB
ejpam-6131	532	28	points	point	NOUN
ejpam-6131	532	29	(	(	PUNCT
ejpam-6131	532	30	qfps	qfps	NOUN
ejpam-6131	532	31	)	)	PUNCT
ejpam-6131	532	32	for	for	ADP
ejpam-6131	532	33	mappings	mapping	NOUN
ejpam-6131	532	34	in	in	ADP
ejpam-6131	532	35	generalized	generalized	ADJ
ejpam-6131	532	36	metric	metric	ADJ
ejpam-6131	532	37	spaces	space	NOUN
ejpam-6131	532	38	,	,	PUNCT
ejpam-6131	532	39	utilizing	utilize	VERB
ejpam-6131	532	40	matrix	matrix	NOUN
ejpam-6131	532	41	-	-	PUNCT
ejpam-6131	532	42	based	base	VERB
ejpam-6131	532	43	methods	method	NOUN
ejpam-6131	532	44	.	.	PUNCT
ejpam-6131	533	1	several	several	ADJ
ejpam-6131	533	2	definitions	definition	NOUN
ejpam-6131	533	3	of	of	ADP
ejpam-6131	533	4	(	(	PUNCT
ejpam-6131	533	5	qfps	qfps	NOUN
ejpam-6131	533	6	)	)	PUNCT
ejpam-6131	533	7	are	be	AUX
ejpam-6131	533	8	formulated	formulate	VERB
ejpam-6131	533	9	,	,	PUNCT
ejpam-6131	533	10	and	and	CCONJ
ejpam-6131	533	11	new	new	ADJ
ejpam-6131	533	12	fixed	fix	VERB
ejpam-6131	533	13	point	point	NOUN
ejpam-6131	533	14	theorems	theorem	NOUN
ejpam-6131	533	15	is	be	AUX
ejpam-6131	533	16	established	establish	VERB
ejpam-6131	533	17	.	.	PUNCT
ejpam-6131	534	1	to	to	PART
ejpam-6131	534	2	illustrate	illustrate	VERB
ejpam-6131	534	3	the	the	DET
ejpam-6131	534	4	findings	finding	NOUN
ejpam-6131	534	5	,	,	PUNCT
ejpam-6131	534	6	an	an	DET
ejpam-6131	534	7	example	example	NOUN
ejpam-6131	534	8	is	be	AUX
ejpam-6131	534	9	provided	provide	VERB
ejpam-6131	534	10	.	.	PUNCT
ejpam-6131	535	1	additionally	additionally	ADV
ejpam-6131	535	2	,	,	PUNCT
ejpam-6131	535	3	an	an	DET
ejpam-6131	535	4	application	application	NOUN
ejpam-6131	535	5	was	be	AUX
ejpam-6131	535	6	developed	develop	VERB
ejpam-6131	535	7	to	to	PART
ejpam-6131	535	8	verify	verify	VERB
ejpam-6131	535	9	the	the	DET
ejpam-6131	535	10	results	result	NOUN
ejpam-6131	535	11	by	by	ADP
ejpam-6131	535	12	determining	determine	VERB
ejpam-6131	535	13	the	the	DET
ejpam-6131	535	14	stationary	stationary	ADJ
ejpam-6131	535	15	distribution	distribution	NOUN
ejpam-6131	535	16	of	of	ADP
ejpam-6131	535	17	a	a	DET
ejpam-6131	535	18	markov	markov	NOUN
ejpam-6131	535	19	process	process	NOUN
ejpam-6131	535	20	.	.	PUNCT
ejpam-6131	536	1	future	future	ADJ
ejpam-6131	536	2	research	research	NOUN
ejpam-6131	536	3	on	on	ADP
ejpam-6131	536	4	quintuple	quintuple	ADV
ejpam-6131	536	5	fixed	fix	VERB
ejpam-6131	536	6	points	point	NOUN
ejpam-6131	536	7	could	could	AUX
ejpam-6131	536	8	explore	explore	VERB
ejpam-6131	536	9	alternative	alternative	ADJ
ejpam-6131	536	10	approaches	approach	NOUN
ejpam-6131	536	11	,	,	PUNCT
ejpam-6131	536	12	such	such	ADJ
ejpam-6131	536	13	as	as	ADP
ejpam-6131	536	14	:	:	PUNCT
ejpam-6131	536	15	(	(	PUNCT
ejpam-6131	536	16	a	a	X
ejpam-6131	536	17	):	):	PUNCT
ejpam-6131	536	18	by	by	ADP
ejpam-6131	536	19	working	work	VERB
ejpam-6131	536	20	on	on	ADP
ejpam-6131	536	21	different	different	ADJ
ejpam-6131	536	22	structures	structure	NOUN
ejpam-6131	536	23	,	,	PUNCT
ejpam-6131	536	24	e.g.	e.g.	ADV
ejpam-6131	536	25	,	,	PUNCT
ejpam-6131	536	26	by	by	ADP
ejpam-6131	536	27	generalizing	generalize	VERB
ejpam-6131	536	28	the	the	DET
ejpam-6131	536	29	obtained	obtain	VERB
ejpam-6131	536	30	results	result	NOUN
ejpam-6131	536	31	in	in	ADP
ejpam-6131	536	32	the	the	DET
ejpam-6131	536	33	setting	setting	NOUN
ejpam-6131	536	34	of	of	ADP
ejpam-6131	536	35	“	"	PUNCT
ejpam-6131	536	36	b	b	X
ejpam-6131	536	37	-	-	PUNCT
ejpam-6131	536	38	metric	metric	ADJ
ejpam-6131	536	39	spaces	space	NOUN
ejpam-6131	536	40	”	"	PUNCT
ejpam-6131	536	41	.	.	PUNCT
ejpam-6131	537	1	(	(	PUNCT
ejpam-6131	537	2	b	b	X
ejpam-6131	537	3	):	):	PUNCT
ejpam-6131	537	4	different	different	ADJ
ejpam-6131	537	5	contraction	contraction	NOUN
ejpam-6131	537	6	conditions	condition	NOUN
ejpam-6131	537	7	can	can	AUX
ejpam-6131	537	8	be	be	AUX
ejpam-6131	537	9	adopted	adopt	VERB
ejpam-6131	537	10	by	by	ADP
ejpam-6131	537	11	involving	involve	VERB
ejpam-6131	537	12	new	new	ADJ
ejpam-6131	537	13	parameters	parameter	NOUN
ejpam-6131	537	14	and	and	CCONJ
ejpam-6131	537	15	introducing	introduce	VERB
ejpam-6131	537	16	more	more	ADJ
ejpam-6131	537	17	properties	property	NOUN
ejpam-6131	537	18	of	of	ADP
ejpam-6131	537	19	contraction	contraction	NOUN
ejpam-6131	537	20	mappings	mapping	NOUN
ejpam-6131	537	21	.	.	PUNCT
ejpam-6131	538	1	acknowledgements	acknowledgement	NOUN
ejpam-6131	538	2	the	the	DET
ejpam-6131	538	3	authors	author	NOUN
ejpam-6131	538	4	extend	extend	VERB
ejpam-6131	538	5	their	their	PRON
ejpam-6131	538	6	appreciation	appreciation	NOUN
ejpam-6131	538	7	to	to	ADP
ejpam-6131	538	8	umm	umm	INTJ
ejpam-6131	538	9	al	al	PROPN
ejpam-6131	538	10	-	-	PUNCT
ejpam-6131	538	11	qura	qura	PROPN
ejpam-6131	538	12	university	university	PROPN
ejpam-6131	538	13	,	,	PUNCT
ejpam-6131	538	14	saudi	saudi	PROPN
ejpam-6131	538	15	arabia	arabia	PROPN
ejpam-6131	538	16	for	for	ADP
ejpam-6131	538	17	funding	fund	VERB
ejpam-6131	538	18	this	this	DET
ejpam-6131	538	19	research	research	NOUN
ejpam-6131	538	20	work	work	NOUN
ejpam-6131	538	21	through	through	ADP
ejpam-6131	538	22	grant	grant	NOUN
ejpam-6131	538	23	number	number	NOUN
ejpam-6131	538	24	:	:	PUNCT
ejpam-6131	538	25	25uqu4331214gssr04	25uqu4331214gssr04	NUM
ejpam-6131	538	26	.	.	PUNCT
ejpam-6131	539	1	declarations	declaration	NOUN
ejpam-6131	539	2	availability	availability	NOUN
ejpam-6131	539	3	of	of	ADP
ejpam-6131	539	4	data	datum	NOUN
ejpam-6131	539	5	and	and	CCONJ
ejpam-6131	539	6	materials	material	NOUN
ejpam-6131	539	7	data	datum	NOUN
ejpam-6131	539	8	sharing	share	VERB
ejpam-6131	539	9	not	not	PART
ejpam-6131	539	10	applicable	applicable	ADJ
ejpam-6131	539	11	to	to	ADP
ejpam-6131	539	12	this	this	DET
ejpam-6131	539	13	article	article	NOUN
ejpam-6131	539	14	as	as	SCONJ
ejpam-6131	539	15	no	no	DET
ejpam-6131	539	16	data	data	NOUN
ejpam-6131	539	17	sets	set	NOUN
ejpam-6131	539	18	were	be	AUX
ejpam-6131	539	19	generated	generate	VERB
ejpam-6131	539	20	or	or	CCONJ
ejpam-6131	539	21	analyzed	analyze	VERB
ejpam-6131	539	22	during	during	ADP
ejpam-6131	539	23	the	the	DET
ejpam-6131	539	24	current	current	ADJ
ejpam-6131	539	25	study	study	NOUN
ejpam-6131	539	26	.	.	PUNCT
ejpam-6131	540	1	funding	fund	VERB
ejpam-6131	540	2	this	this	DET
ejpam-6131	540	3	research	research	NOUN
ejpam-6131	540	4	work	work	NOUN
ejpam-6131	540	5	was	be	AUX
ejpam-6131	540	6	funded	fund	VERB
ejpam-6131	540	7	by	by	ADP
ejpam-6131	540	8	umm	umm	INTJ
ejpam-6131	540	9	al	al	PROPN
ejpam-6131	540	10	-	-	PUNCT
ejpam-6131	540	11	qura	qura	PROPN
ejpam-6131	540	12	university	university	NOUN
ejpam-6131	540	13	,	,	PUNCT
ejpam-6131	540	14	saudi	saudi	PROPN
ejpam-6131	540	15	arabia	arabia	PROPN
ejpam-6131	540	16	under	under	ADP
ejpam-6131	540	17	grant	grant	NOUN
ejpam-6131	540	18	number	number	NOUN
ejpam-6131	540	19	:	:	PUNCT
ejpam-6131	540	20	25uqu4331214gssr04	25uqu4331214gssr04	NUM
ejpam-6131	540	21	.	.	PUNCT
ejpam-6131	541	1	authors	author	NOUN
ejpam-6131	541	2	’	'	PUNCT
ejpam-6131	541	3	contributions	contribution	NOUN
ejpam-6131	541	4	the	the	DET
ejpam-6131	541	5	authors	author	NOUN
ejpam-6131	541	6	declare	declare	VERB
ejpam-6131	541	7	that	that	SCONJ
ejpam-6131	541	8	the	the	DET
ejpam-6131	541	9	study	study	NOUN
ejpam-6131	541	10	was	be	AUX
ejpam-6131	541	11	realized	realize	VERB
ejpam-6131	541	12	in	in	ADP
ejpam-6131	541	13	collaboration	collaboration	NOUN
ejpam-6131	541	14	with	with	ADP
ejpam-6131	541	15	equal	equal	ADJ
ejpam-6131	541	16	responsibility	responsibility	NOUN
ejpam-6131	541	17	.	.	PUNCT
ejpam-6131	542	1	all	all	DET
ejpam-6131	542	2	authors	author	NOUN
ejpam-6131	542	3	read	read	VERB
ejpam-6131	542	4	and	and	CCONJ
ejpam-6131	542	5	approved	approve	VERB
ejpam-6131	542	6	the	the	DET
ejpam-6131	542	7	final	final	ADJ
ejpam-6131	542	8	manuscript	manuscript	NOUN
ejpam-6131	542	9	.	.	PUNCT
ejpam-6131	543	1	competing	compete	VERB
ejpam-6131	543	2	interests	interest	NOUN
ejpam-6131	543	3	the	the	DET
ejpam-6131	543	4	authors	author	NOUN
ejpam-6131	543	5	declare	declare	VERB
ejpam-6131	543	6	that	that	SCONJ
ejpam-6131	543	7	they	they	PRON
ejpam-6131	543	8	have	have	VERB
ejpam-6131	543	9	no	no	DET
ejpam-6131	543	10	competing	compete	VERB
ejpam-6131	543	11	interests	interest	NOUN
ejpam-6131	543	12	.	.	PUNCT
ejpam-6131	544	1	references	reference	NOUN
ejpam-6131	544	2	[	[	X
ejpam-6131	544	3	1	1	X
ejpam-6131	544	4	]	]	X
ejpam-6131	544	5	stefan	stefan	PROPN
ejpam-6131	544	6	banach	banach	PROPN
ejpam-6131	544	7	.	.	PUNCT
ejpam-6131	545	1	sur	sur	PROPN
ejpam-6131	545	2	les	les	X
ejpam-6131	545	3	opérations	opération	NOUN
ejpam-6131	545	4	dans	dan	NOUN
ejpam-6131	545	5	les	les	X
ejpam-6131	545	6	ensembles	ensemble	NOUN
ejpam-6131	545	7	abstraits	abstrait	NOUN
ejpam-6131	545	8	et	et	PROPN
ejpam-6131	545	9	leur	leur	X
ejpam-6131	545	10	application	application	PROPN
ejpam-6131	545	11	aux	aux	PROPN
ejpam-6131	545	12	équations	équations	PROPN
ejpam-6131	545	13	intégrales	intégrale	NOUN
ejpam-6131	545	14	.	.	PUNCT
ejpam-6131	546	1	fundamenta	fundamenta	PROPN
ejpam-6131	546	2	mathematicae	mathematicae	PROPN
ejpam-6131	546	3	,	,	PUNCT
ejpam-6131	546	4	3(1):133–181	3(1):133–181	NUM
ejpam-6131	546	5	,	,	PUNCT
ejpam-6131	546	6	1992	1992	NUM
ejpam-6131	546	7	.	.	PUNCT
ejpam-6131	547	1	s.	s.	PROPN
ejpam-6131	547	2	batul	batul	PROPN
ejpam-6131	547	3	et	et	PROPN
ejpam-6131	547	4	a.	a.	PROPN
ejpam-6131	547	5	/	/	PUNCT
ejpam-6131	547	6	eur	eur	PROPN
ejpam-6131	547	7	.	.	PUNCT
ejpam-6131	548	1	j.	j.	PROPN
ejpam-6131	548	2	pure	pure	PROPN
ejpam-6131	548	3	appl	appl	PROPN
ejpam-6131	548	4	.	.	PROPN
ejpam-6131	548	5	math	math	PROPN
ejpam-6131	548	6	,	,	PUNCT
ejpam-6131	548	7	18	18	NUM
ejpam-6131	548	8	(	(	PUNCT
ejpam-6131	548	9	2	2	NUM
ejpam-6131	548	10	)	)	PUNCT
ejpam-6131	548	11	(	(	PUNCT
ejpam-6131	548	12	2025	2025	NUM
ejpam-6131	548	13	)	)	PUNCT
ejpam-6131	548	14	,	,	PUNCT
ejpam-6131	548	15	6131	6131	NUM
ejpam-6131	548	16	21	21	NUM
ejpam-6131	548	17	of	of	ADP
ejpam-6131	548	18	22	22	NUM
ejpam-6131	549	1	[	[	X
ejpam-6131	549	2	2	2	NUM
ejpam-6131	549	3	]	]	PUNCT
ejpam-6131	549	4	ai	ai	AUX
ejpam-6131	549	5	perov	perov	NOUN
ejpam-6131	549	6	.	.	PUNCT
ejpam-6131	550	1	on	on	ADP
ejpam-6131	550	2	the	the	DET
ejpam-6131	550	3	cauchy	cauchy	ADJ
ejpam-6131	550	4	problem	problem	NOUN
ejpam-6131	550	5	for	for	ADP
ejpam-6131	550	6	a	a	DET
ejpam-6131	550	7	system	system	NOUN
ejpam-6131	550	8	of	of	ADP
ejpam-6131	550	9	ordinary	ordinary	ADJ
ejpam-6131	550	10	differential	differential	ADJ
ejpam-6131	550	11	equations	equation	NOUN
ejpam-6131	550	12	.	.	PUNCT
ejpam-6131	551	1	pviblizhen	pviblizhen	ADV
ejpam-6131	551	2	.	.	PUNCT
ejpam-6131	552	1	met	meet	VERB
ejpam-6131	552	2	.	.	PUNCT
ejpam-6131	553	1	reshen	reshen	NOUN
ejpam-6131	553	2	.	.	PUNCT
ejpam-6131	554	1	differ	differ	VERB
ejpam-6131	554	2	.	.	PUNCT
ejpam-6131	555	1	uvavn	uvavn	PROPN
ejpam-6131	555	2	,	,	PUNCT
ejpam-6131	555	3	2(1964):115–134	2(1964):115–134	NUM
ejpam-6131	555	4	,	,	PUNCT
ejpam-6131	555	5	1964	1964	NUM
ejpam-6131	555	6	.	.	PUNCT
ejpam-6131	556	1	[	[	X
ejpam-6131	556	2	3	3	X
ejpam-6131	556	3	]	]	X
ejpam-6131	556	4	alexandru	alexandru	PROPN
ejpam-6131	556	5	-	-	PUNCT
ejpam-6131	556	6	darius	darius	PROPN
ejpam-6131	556	7	filip	filip	PROPN
ejpam-6131	556	8	and	and	CCONJ
ejpam-6131	556	9	adrian	adrian	PROPN
ejpam-6131	556	10	petruşel	petruşel	PROPN
ejpam-6131	556	11	.	.	PUNCT
ejpam-6131	557	1	fixed	fix	VERB
ejpam-6131	557	2	point	point	NOUN
ejpam-6131	557	3	theorems	theorem	NOUN
ejpam-6131	557	4	on	on	ADP
ejpam-6131	557	5	spaces	space	NOUN
ejpam-6131	557	6	endowed	endow	VERB
ejpam-6131	557	7	with	with	ADP
ejpam-6131	557	8	vector	vector	NOUN
ejpam-6131	557	9	-	-	PUNCT
ejpam-6131	557	10	valued	value	VERB
ejpam-6131	557	11	metrics	metric	NOUN
ejpam-6131	557	12	.	.	PUNCT
ejpam-6131	558	1	fixed	fix	VERB
ejpam-6131	558	2	point	point	NOUN
ejpam-6131	558	3	theory	theory	NOUN
ejpam-6131	558	4	and	and	CCONJ
ejpam-6131	558	5	applications	application	NOUN
ejpam-6131	558	6	,	,	PUNCT
ejpam-6131	558	7	2010:1–15	2010:1–15	NUM
ejpam-6131	558	8	,	,	PUNCT
ejpam-6131	558	9	2010	2010	NUM
ejpam-6131	558	10	.	.	PUNCT
ejpam-6131	559	1	[	[	X
ejpam-6131	559	2	4	4	NUM
ejpam-6131	559	3	]	]	PUNCT
ejpam-6131	559	4	dejan	dejan	NOUN
ejpam-6131	559	5	ilić	ilić	PROPN
ejpam-6131	559	6	,	,	PUNCT
ejpam-6131	559	7	marija	marija	PROPN
ejpam-6131	559	8	cvetković	cvetković	PROPN
ejpam-6131	559	9	,	,	PUNCT
ejpam-6131	559	10	ljiljana	ljiljana	PROPN
ejpam-6131	559	11	gajić	gajić	PROPN
ejpam-6131	559	12	,	,	PUNCT
ejpam-6131	559	13	and	and	CCONJ
ejpam-6131	559	14	vladimir	vladimir	PROPN
ejpam-6131	559	15	rakočević.	rakočević.	PROPN
ejpam-6131	559	16	fixed	fix	VERB
ejpam-6131	559	17	points	point	NOUN
ejpam-6131	559	18	of	of	ADP
ejpam-6131	559	19	sequence	sequence	NOUN
ejpam-6131	559	20	of	of	ADP
ejpam-6131	559	21	ćirić	ćirić	PROPN
ejpam-6131	559	22	generalized	generalize	VERB
ejpam-6131	559	23	contractions	contraction	NOUN
ejpam-6131	559	24	of	of	ADP
ejpam-6131	559	25	perov	perov	PROPN
ejpam-6131	559	26	type	type	NOUN
ejpam-6131	559	27	.	.	PUNCT
ejpam-6131	560	1	mediterranean	mediterranean	PROPN
ejpam-6131	560	2	journal	journal	PROPN
ejpam-6131	560	3	of	of	ADP
ejpam-6131	560	4	mathematics	mathematic	NOUN
ejpam-6131	560	5	,	,	PUNCT
ejpam-6131	560	6	13:3921–3937	13:3921–3937	NUM
ejpam-6131	560	7	,	,	PUNCT
ejpam-6131	560	8	2016	2016	NUM
ejpam-6131	560	9	.	.	PUNCT
ejpam-6131	561	1	[	[	X
ejpam-6131	561	2	5	5	X
ejpam-6131	561	3	]	]	X
ejpam-6131	561	4	stefan	stefan	PROPN
ejpam-6131	561	5	czerwik	czerwik	PROPN
ejpam-6131	561	6	.	.	PUNCT
ejpam-6131	562	1	contraction	contraction	NOUN
ejpam-6131	562	2	mappings	mapping	NOUN
ejpam-6131	562	3	in	in	ADP
ejpam-6131	562	4	b	b	NOUN
ejpam-6131	562	5	-	-	ADJ
ejpam-6131	562	6	metric	metric	ADJ
ejpam-6131	562	7	spaces	space	NOUN
ejpam-6131	562	8	.	.	PUNCT
ejpam-6131	563	1	acta	acta	PROPN
ejpam-6131	563	2	mathematica	mathematica	PROPN
ejpam-6131	563	3	et	et	PROPN
ejpam-6131	563	4	informatica	informatica	PROPN
ejpam-6131	563	5	universitatis	universitatis	PROPN
ejpam-6131	563	6	ostraviensis	ostraviensis	PROPN
ejpam-6131	563	7	,	,	PUNCT
ejpam-6131	563	8	1(1):5–11	1(1):5–11	NUM
ejpam-6131	563	9	,	,	PUNCT
ejpam-6131	563	10	1993	1993	NUM
ejpam-6131	563	11	.	.	PUNCT
ejpam-6131	564	1	[	[	X
ejpam-6131	564	2	6	6	NUM
ejpam-6131	564	3	]	]	X
ejpam-6131	564	4	hassen	hassen	PROPN
ejpam-6131	564	5	aydi	aydi	VERB
ejpam-6131	564	6	,	,	PUNCT
ejpam-6131	564	7	muhammad	muhammad	PROPN
ejpam-6131	564	8	aslam	aslam	PROPN
ejpam-6131	564	9	,	,	PUNCT
ejpam-6131	564	10	dur	dur	PROPN
ejpam-6131	564	11	-	-	PUNCT
ejpam-6131	564	12	e	e	ADJ
ejpam-6131	564	13	-	-	ADJ
ejpam-6131	564	14	shehwar	shehwar	ADJ
ejpam-6131	564	15	sagheer	sagheer	NOUN
ejpam-6131	564	16	,	,	PUNCT
ejpam-6131	564	17	samina	samina	PROPN
ejpam-6131	564	18	batul	batul	PROPN
ejpam-6131	564	19	,	,	PUNCT
ejpam-6131	564	20	rashid	rashid	PROPN
ejpam-6131	564	21	ali	ali	PROPN
ejpam-6131	564	22	,	,	PUNCT
ejpam-6131	564	23	and	and	CCONJ
ejpam-6131	564	24	eskandar	eskandar	PROPN
ejpam-6131	564	25	ameer	ameer	PROPN
ejpam-6131	564	26	.	.	PUNCT
ejpam-6131	565	1	kannan	kannan	PROPN
ejpam-6131	565	2	-	-	PUNCT
ejpam-6131	565	3	type	type	NOUN
ejpam-6131	565	4	contractions	contraction	NOUN
ejpam-6131	565	5	on	on	ADP
ejpam-6131	565	6	new	new	ADJ
ejpam-6131	565	7	extended	extended	ADJ
ejpam-6131	565	8	b	b	NOUN
ejpam-6131	565	9	-	-	ADJ
ejpam-6131	565	10	metric	metric	ADJ
ejpam-6131	565	11	spaces	space	NOUN
ejpam-6131	565	12	.	.	PUNCT
ejpam-6131	566	1	journal	journal	NOUN
ejpam-6131	566	2	of	of	ADP
ejpam-6131	566	3	function	function	NOUN
ejpam-6131	566	4	spaces	space	NOUN
ejpam-6131	566	5	,	,	PUNCT
ejpam-6131	566	6	2021(1):7613684	2021(1):7613684	NUM
ejpam-6131	566	7	,	,	PUNCT
ejpam-6131	566	8	2021	2021	NUM
ejpam-6131	566	9	.	.	PUNCT
ejpam-6131	567	1	[	[	X
ejpam-6131	567	2	7	7	X
ejpam-6131	567	3	]	]	X
ejpam-6131	567	4	samina	samina	PROPN
ejpam-6131	567	5	batul	batul	PROPN
ejpam-6131	567	6	,	,	PUNCT
ejpam-6131	567	7	hassen	hassen	PROPN
ejpam-6131	567	8	aydi	aydi	PROPN
ejpam-6131	567	9	,	,	PUNCT
ejpam-6131	567	10	aiman	aiman	PROPN
ejpam-6131	567	11	mukheimer	mukheimer	PROPN
ejpam-6131	567	12	,	,	PUNCT
ejpam-6131	567	13	suhad	suhad	ADJ
ejpam-6131	567	14	subhi	subhi	PROPN
ejpam-6131	567	15	aiadi	aiadi	PROPN
ejpam-6131	567	16	,	,	PUNCT
ejpam-6131	567	17	dur	dur	PROPN
ejpam-6131	567	18	-	-	PUNCT
ejpam-6131	567	19	e	e	ADJ
ejpam-6131	567	20	-	-	ADJ
ejpam-6131	567	21	shehwar	shehwar	ADJ
ejpam-6131	567	22	sagheer	sagheer	NOUN
ejpam-6131	567	23	,	,	PUNCT
ejpam-6131	567	24	et	et	PROPN
ejpam-6131	567	25	al	al	PROPN
ejpam-6131	567	26	.	.	PUNCT
ejpam-6131	568	1	best	good	ADJ
ejpam-6131	568	2	proximity	proximity	NOUN
ejpam-6131	568	3	point	point	NOUN
ejpam-6131	568	4	results	result	NOUN
ejpam-6131	568	5	for	for	ADP
ejpam-6131	568	6	prešić	prešić	NOUN
ejpam-6131	568	7	type	type	PROPN
ejpam-6131	568	8	nonself	nonself	PROPN
ejpam-6131	568	9	operators	operator	NOUN
ejpam-6131	568	10	in	in	ADP
ejpam-6131	568	11	bmetric	bmetric	ADJ
ejpam-6131	568	12	spaces	space	NOUN
ejpam-6131	568	13	.	.	PUNCT
ejpam-6131	569	1	aims	aim	VERB
ejpam-6131	569	2	mathematics	mathematic	NOUN
ejpam-6131	569	3	,	,	PUNCT
ejpam-6131	569	4	7(6):10711–10730	7(6):10711–10730	NUM
ejpam-6131	569	5	,	,	PUNCT
ejpam-6131	569	6	2022	2022	NUM
ejpam-6131	569	7	.	.	PUNCT
ejpam-6131	570	1	[	[	X
ejpam-6131	570	2	8	8	NUM
ejpam-6131	570	3	]	]	PUNCT
ejpam-6131	570	4	t	t	PROPN
ejpam-6131	570	5	gnana	gnana	NOUN
ejpam-6131	570	6	bhaskar	bhaskar	NOUN
ejpam-6131	570	7	and	and	CCONJ
ejpam-6131	570	8	vangipuram	vangipuram	PROPN
ejpam-6131	570	9	lakshmikantham	lakshmikantham	VERB
ejpam-6131	570	10	.	.	PUNCT
ejpam-6131	571	1	fixed	fix	VERB
ejpam-6131	571	2	point	point	NOUN
ejpam-6131	571	3	theorems	theorem	NOUN
ejpam-6131	571	4	in	in	ADP
ejpam-6131	571	5	partially	partially	ADV
ejpam-6131	571	6	ordered	order	VERB
ejpam-6131	571	7	metric	metric	ADJ
ejpam-6131	571	8	spaces	space	NOUN
ejpam-6131	571	9	and	and	CCONJ
ejpam-6131	571	10	applications	application	NOUN
ejpam-6131	571	11	.	.	PUNCT
ejpam-6131	572	1	nonlinear	nonlinear	ADJ
ejpam-6131	572	2	analysis	analysis	NOUN
ejpam-6131	572	3	:	:	PUNCT
ejpam-6131	572	4	theory	theory	NOUN
ejpam-6131	572	5	,	,	PUNCT
ejpam-6131	572	6	methods	method	NOUN
ejpam-6131	572	7	&	&	CCONJ
ejpam-6131	572	8	applications	application	NOUN
ejpam-6131	572	9	,	,	PUNCT
ejpam-6131	572	10	65(7):1379–1393	65(7):1379–1393	NUM
ejpam-6131	572	11	,	,	PUNCT
ejpam-6131	572	12	2006	2006	NUM
ejpam-6131	572	13	.	.	PUNCT
ejpam-6131	573	1	[	[	X
ejpam-6131	573	2	9	9	NUM
ejpam-6131	573	3	]	]	PUNCT
ejpam-6131	573	4	mujahid	mujahid	NOUN
ejpam-6131	573	5	abbas	abbas	PROPN
ejpam-6131	573	6	,	,	PUNCT
ejpam-6131	573	7	m	m	PROPN
ejpam-6131	573	8	ali	ali	PROPN
ejpam-6131	573	9	khan	khan	PROPN
ejpam-6131	573	10	,	,	PUNCT
ejpam-6131	573	11	and	and	CCONJ
ejpam-6131	573	12	s	s	VERB
ejpam-6131	573	13	radenović.	radenović.	PROPN
ejpam-6131	573	14	common	common	ADJ
ejpam-6131	573	15	coupled	couple	VERB
ejpam-6131	573	16	fixed	fix	VERB
ejpam-6131	573	17	point	point	NOUN
ejpam-6131	573	18	theorems	theorem	NOUN
ejpam-6131	573	19	in	in	ADP
ejpam-6131	573	20	cone	cone	NOUN
ejpam-6131	573	21	metric	metric	ADJ
ejpam-6131	573	22	spaces	space	NOUN
ejpam-6131	573	23	for	for	ADP
ejpam-6131	573	24	w	w	ADJ
ejpam-6131	573	25	-	-	PUNCT
ejpam-6131	573	26	compatible	compatible	ADJ
ejpam-6131	573	27	mappings	mapping	NOUN
ejpam-6131	573	28	.	.	PUNCT
ejpam-6131	574	1	applied	apply	VERB
ejpam-6131	574	2	mathematics	mathematic	NOUN
ejpam-6131	574	3	and	and	CCONJ
ejpam-6131	574	4	computation	computation	NOUN
ejpam-6131	574	5	,	,	PUNCT
ejpam-6131	574	6	217(1):195–202	217(1):195–202	PROPN
ejpam-6131	574	7	,	,	PUNCT
ejpam-6131	574	8	2010	2010	NUM
ejpam-6131	574	9	.	.	PUNCT
ejpam-6131	575	1	[	[	X
ejpam-6131	575	2	10	10	NUM
ejpam-6131	575	3	]	]	X
ejpam-6131	575	4	vasile	vasile	NOUN
ejpam-6131	575	5	berinde	berinde	NOUN
ejpam-6131	575	6	and	and	CCONJ
ejpam-6131	575	7	marin	marin	NOUN
ejpam-6131	575	8	borcut	borcut	VERB
ejpam-6131	575	9	.	.	PUNCT
ejpam-6131	576	1	tripled	triple	VERB
ejpam-6131	576	2	fixed	fix	VERB
ejpam-6131	576	3	point	point	NOUN
ejpam-6131	576	4	theorems	theorem	NOUN
ejpam-6131	576	5	for	for	ADP
ejpam-6131	576	6	contractive	contractive	ADJ
ejpam-6131	576	7	type	type	NOUN
ejpam-6131	576	8	mappings	mapping	NOUN
ejpam-6131	576	9	in	in	ADP
ejpam-6131	576	10	partially	partially	ADV
ejpam-6131	576	11	ordered	order	VERB
ejpam-6131	576	12	metric	metric	ADJ
ejpam-6131	576	13	spaces	space	NOUN
ejpam-6131	576	14	.	.	PUNCT
ejpam-6131	577	1	nonlinear	nonlinear	ADJ
ejpam-6131	577	2	analysis	analysis	NOUN
ejpam-6131	577	3	:	:	PUNCT
ejpam-6131	577	4	theory	theory	NOUN
ejpam-6131	577	5	,	,	PUNCT
ejpam-6131	577	6	methods	method	NOUN
ejpam-6131	577	7	&	&	CCONJ
ejpam-6131	577	8	applications	application	NOUN
ejpam-6131	577	9	,	,	PUNCT
ejpam-6131	577	10	74(15):4889–4897	74(15):4889–4897	NUM
ejpam-6131	577	11	,	,	PUNCT
ejpam-6131	577	12	2011	2011	NUM
ejpam-6131	577	13	.	.	PUNCT
ejpam-6131	578	1	[	[	X
ejpam-6131	578	2	11	11	NUM
ejpam-6131	578	3	]	]	X
ejpam-6131	578	4	marin	marin	NOUN
ejpam-6131	578	5	borcut	borcut	VERB
ejpam-6131	578	6	.	.	PUNCT
ejpam-6131	579	1	tripled	triple	VERB
ejpam-6131	579	2	coincidence	coincidence	NOUN
ejpam-6131	579	3	theorems	theorem	NOUN
ejpam-6131	579	4	for	for	ADP
ejpam-6131	579	5	contractive	contractive	ADJ
ejpam-6131	579	6	type	type	NOUN
ejpam-6131	579	7	mappings	mapping	NOUN
ejpam-6131	579	8	in	in	ADP
ejpam-6131	579	9	partially	partially	ADV
ejpam-6131	579	10	ordered	order	VERB
ejpam-6131	579	11	metric	metric	ADJ
ejpam-6131	579	12	spaces	space	NOUN
ejpam-6131	579	13	.	.	PUNCT
ejpam-6131	580	1	applied	apply	VERB
ejpam-6131	580	2	mathematics	mathematic	NOUN
ejpam-6131	580	3	and	and	CCONJ
ejpam-6131	580	4	computation	computation	NOUN
ejpam-6131	580	5	,	,	PUNCT
ejpam-6131	580	6	218(14):7339–7346	218(14):7339–7346	NUM
ejpam-6131	580	7	,	,	PUNCT
ejpam-6131	580	8	2012	2012	NUM
ejpam-6131	580	9	.	.	PUNCT
ejpam-6131	581	1	[	[	X
ejpam-6131	581	2	12	12	NUM
ejpam-6131	581	3	]	]	PUNCT
ejpam-6131	581	4	zoran	zoran	PROPN
ejpam-6131	581	5	kadelburg	kadelburg	PROPN
ejpam-6131	581	6	and	and	CCONJ
ejpam-6131	581	7	stojan	stojan	ADJ
ejpam-6131	581	8	radenovic	radenovic	PROPN
ejpam-6131	581	9	.	.	PUNCT
ejpam-6131	582	1	fixed	fix	VERB
ejpam-6131	582	2	point	point	NOUN
ejpam-6131	582	3	and	and	CCONJ
ejpam-6131	582	4	tripled	triple	VERB
ejpam-6131	582	5	fixed	fix	VERB
ejpam-6131	582	6	point	point	NOUN
ejpam-6131	582	7	theorems	theorem	NOUN
ejpam-6131	582	8	under	under	ADP
ejpam-6131	582	9	pata	pata	NOUN
ejpam-6131	582	10	-	-	PUNCT
ejpam-6131	582	11	type	type	NOUN
ejpam-6131	582	12	conditions	condition	NOUN
ejpam-6131	582	13	in	in	ADP
ejpam-6131	582	14	ordered	order	VERB
ejpam-6131	582	15	metric	metric	ADJ
ejpam-6131	582	16	spaces	space	NOUN
ejpam-6131	582	17	.	.	PUNCT
ejpam-6131	583	1	international	international	ADJ
ejpam-6131	583	2	journal	journal	NOUN
ejpam-6131	583	3	of	of	ADP
ejpam-6131	583	4	analysis	analysis	NOUN
ejpam-6131	583	5	and	and	CCONJ
ejpam-6131	583	6	applications	application	NOUN
ejpam-6131	583	7	,	,	PUNCT
ejpam-6131	583	8	6(1):113–122	6(1):113–122	NUM
ejpam-6131	583	9	,	,	PUNCT
ejpam-6131	583	10	2014	2014	NUM
ejpam-6131	583	11	.	.	PUNCT
ejpam-6131	584	1	[	[	X
ejpam-6131	584	2	13	13	NUM
ejpam-6131	584	3	]	]	PUNCT
ejpam-6131	584	4	erdal	erdal	PROPN
ejpam-6131	584	5	karapınar	karapınar	PROPN
ejpam-6131	584	6	.	.	PUNCT
ejpam-6131	585	1	quartet	quartet	NOUN
ejpam-6131	585	2	fixed	fix	VERB
ejpam-6131	585	3	point	point	NOUN
ejpam-6131	585	4	for	for	ADP
ejpam-6131	585	5	nonlinear	nonlinear	ADJ
ejpam-6131	585	6	contraction	contraction	NOUN
ejpam-6131	585	7	.	.	PUNCT
ejpam-6131	586	1	arxiv	arxiv	PROPN
ejpam-6131	586	2	preprint	preprint	NOUN
ejpam-6131	586	3	arxiv:1106.5472	arxiv:1106.5472	PROPN
ejpam-6131	586	4	,	,	PUNCT
ejpam-6131	586	5	2011	2011	NUM
ejpam-6131	586	6	.	.	PUNCT
ejpam-6131	587	1	[	[	X
ejpam-6131	587	2	14	14	NUM
ejpam-6131	587	3	]	]	X
ejpam-6131	587	4	erdal	erdal	PROPN
ejpam-6131	587	5	karapınar	karapınar	PROPN
ejpam-6131	587	6	and	and	CCONJ
ejpam-6131	587	7	nguyen	nguyen	PROPN
ejpam-6131	587	8	van	van	PROPN
ejpam-6131	587	9	luong	luong	PROPN
ejpam-6131	587	10	.	.	PUNCT
ejpam-6131	588	1	quadruple	quadruple	PROPN
ejpam-6131	588	2	fixed	fix	VERB
ejpam-6131	588	3	point	point	NOUN
ejpam-6131	588	4	theorems	theorem	NOUN
ejpam-6131	588	5	for	for	ADP
ejpam-6131	588	6	nonlinear	nonlinear	ADJ
ejpam-6131	588	7	contractions	contraction	NOUN
ejpam-6131	588	8	.	.	PUNCT
ejpam-6131	589	1	computers	computer	NOUN
ejpam-6131	589	2	&	&	CCONJ
ejpam-6131	589	3	mathematics	mathematics	PROPN
ejpam-6131	589	4	with	with	ADP
ejpam-6131	589	5	applications	application	NOUN
ejpam-6131	589	6	,	,	PUNCT
ejpam-6131	589	7	64(6):1839–1848	64(6):1839–1848	NUM
ejpam-6131	589	8	,	,	PUNCT
ejpam-6131	589	9	2012	2012	NUM
ejpam-6131	589	10	.	.	PUNCT
ejpam-6131	590	1	[	[	X
ejpam-6131	590	2	15	15	NUM
ejpam-6131	590	3	]	]	X
ejpam-6131	590	4	xiao	xiao	PROPN
ejpam-6131	590	5	-	-	PUNCT
ejpam-6131	590	6	lan	lan	PROPN
ejpam-6131	590	7	liu	liu	PROPN
ejpam-6131	590	8	.	.	PROPN
ejpam-6131	591	1	quadruple	quadruple	PROPN
ejpam-6131	591	2	fixed	fix	VERB
ejpam-6131	591	3	point	point	NOUN
ejpam-6131	591	4	theorems	theorem	NOUN
ejpam-6131	591	5	in	in	ADP
ejpam-6131	591	6	partially	partially	ADV
ejpam-6131	591	7	ordered	order	VERB
ejpam-6131	591	8	metric	metric	ADJ
ejpam-6131	591	9	spaces	space	NOUN
ejpam-6131	591	10	with	with	ADP
ejpam-6131	591	11	mixed	mixed	ADJ
ejpam-6131	591	12	g	g	NOUN
ejpam-6131	591	13	-	-	PUNCT
ejpam-6131	591	14	monotone	monotone	NOUN
ejpam-6131	591	15	property	property	NOUN
ejpam-6131	591	16	.	.	PUNCT
ejpam-6131	592	1	fixed	fix	VERB
ejpam-6131	592	2	point	point	NOUN
ejpam-6131	592	3	theory	theory	NOUN
ejpam-6131	592	4	and	and	CCONJ
ejpam-6131	592	5	applications	application	NOUN
ejpam-6131	592	6	,	,	PUNCT
ejpam-6131	592	7	2013:1–18	2013:1–18	NUM
ejpam-6131	592	8	,	,	PUNCT
ejpam-6131	592	9	2013	2013	NUM
ejpam-6131	592	10	.	.	PUNCT
ejpam-6131	593	1	[	[	X
ejpam-6131	593	2	16	16	NUM
ejpam-6131	593	3	]	]	X
ejpam-6131	593	4	hasanen	hasanen	NOUN
ejpam-6131	593	5	a	a	DET
ejpam-6131	593	6	hammad	hammad	PROPN
ejpam-6131	593	7	and	and	CCONJ
ejpam-6131	593	8	thabet	thabet	ADJ
ejpam-6131	593	9	abdeljawad	abdeljawad	NOUN
ejpam-6131	593	10	.	.	PUNCT
ejpam-6131	594	1	quadruple	quadruple	PROPN
ejpam-6131	594	2	fixed	fix	VERB
ejpam-6131	594	3	-	-	PUNCT
ejpam-6131	594	4	point	point	NOUN
ejpam-6131	594	5	techniques	technique	NOUN
ejpam-6131	594	6	for	for	ADP
ejpam-6131	594	7	solving	solve	VERB
ejpam-6131	594	8	integral	integral	ADJ
ejpam-6131	594	9	equations	equation	NOUN
ejpam-6131	594	10	involved	involve	VERB
ejpam-6131	594	11	with	with	ADP
ejpam-6131	594	12	matrices	matrix	NOUN
ejpam-6131	594	13	and	and	CCONJ
ejpam-6131	594	14	the	the	DET
ejpam-6131	594	15	markov	markov	NOUN
ejpam-6131	594	16	process	process	NOUN
ejpam-6131	594	17	in	in	ADP
ejpam-6131	594	18	generalized	generalized	ADJ
ejpam-6131	594	19	metric	metric	ADJ
ejpam-6131	594	20	spaces	space	NOUN
ejpam-6131	594	21	.	.	PUNCT
ejpam-6131	595	1	journal	journal	PROPN
ejpam-6131	595	2	of	of	ADP
ejpam-6131	595	3	inequalities	inequality	NOUN
ejpam-6131	595	4	and	and	CCONJ
ejpam-6131	595	5	applications	application	NOUN
ejpam-6131	595	6	,	,	PUNCT
ejpam-6131	595	7	2022(1):44	2022(1):44	NUM
ejpam-6131	595	8	,	,	PUNCT
ejpam-6131	595	9	2022	2022	NUM
ejpam-6131	595	10	.	.	PUNCT
ejpam-6131	596	1	[	[	X
ejpam-6131	596	2	17	17	NUM
ejpam-6131	596	3	]	]	X
ejpam-6131	596	4	j	j	PROPN
ejpam-6131	596	5	west	west	PROPN
ejpam-6131	596	6	and	and	CCONJ
ejpam-6131	596	7	linster	linster	PROPN
ejpam-6131	596	8	.	.	PUNCT
ejpam-6131	597	1	matrix	matrix	NOUN
ejpam-6131	597	2	iterative	iterative	NOUN
ejpam-6131	597	3	analysis	analysis	NOUN
ejpam-6131	597	4	.	.	PUNCT
ejpam-6131	598	1	southern	southern	ADJ
ejpam-6131	598	2	economic	economic	ADJ
ejpam-6131	598	3	journal	journal	NOUN
ejpam-6131	598	4	,	,	PUNCT
ejpam-6131	598	5	27(3):705	27(3):705	NUM
ejpam-6131	598	6	–	–	PUNCT
ejpam-6131	598	7	717	717	NUM
ejpam-6131	598	8	,	,	PUNCT
ejpam-6131	598	9	1999	1999	NUM
ejpam-6131	598	10	.	.	PUNCT
ejpam-6131	599	1	[	[	X
ejpam-6131	599	2	18	18	NUM
ejpam-6131	599	3	]	]	PUNCT
ejpam-6131	599	4	erdal	erdal	PROPN
ejpam-6131	599	5	karapınar	karapınar	PROPN
ejpam-6131	599	6	and	and	CCONJ
ejpam-6131	599	7	nguyen	nguyen	PROPN
ejpam-6131	599	8	van	van	PROPN
ejpam-6131	599	9	luong	luong	PROPN
ejpam-6131	599	10	.	.	PUNCT
ejpam-6131	600	1	quadruple	quadruple	PROPN
ejpam-6131	600	2	fixed	fix	VERB
ejpam-6131	600	3	point	point	NOUN
ejpam-6131	600	4	theorems	theorem	NOUN
ejpam-6131	600	5	for	for	ADP
ejpam-6131	600	6	nons	non	NOUN
ejpam-6131	600	7	.	.	PUNCT
ejpam-6131	601	1	batul	batul	PROPN
ejpam-6131	601	2	et	et	PROPN
ejpam-6131	601	3	a.	a.	PROPN
ejpam-6131	601	4	/	/	PUNCT
ejpam-6131	601	5	eur	eur	PROPN
ejpam-6131	601	6	.	.	PUNCT
ejpam-6131	602	1	j.	j.	PROPN
ejpam-6131	602	2	pure	pure	PROPN
ejpam-6131	602	3	appl	appl	PROPN
ejpam-6131	602	4	.	.	PROPN
ejpam-6131	602	5	math	math	PROPN
ejpam-6131	602	6	,	,	PUNCT
ejpam-6131	602	7	18	18	NUM
ejpam-6131	602	8	(	(	PUNCT
ejpam-6131	602	9	2	2	NUM
ejpam-6131	602	10	)	)	PUNCT
ejpam-6131	602	11	(	(	PUNCT
ejpam-6131	602	12	2025	2025	NUM
ejpam-6131	602	13	)	)	PUNCT
ejpam-6131	602	14	,	,	PUNCT
ejpam-6131	602	15	6131	6131	NUM
ejpam-6131	602	16	22	22	NUM
ejpam-6131	602	17	of	of	ADP
ejpam-6131	602	18	22	22	NUM
ejpam-6131	602	19	linear	linear	ADJ
ejpam-6131	602	20	contractions	contraction	NOUN
ejpam-6131	602	21	.	.	PUNCT
ejpam-6131	603	1	computers	computer	NOUN
ejpam-6131	603	2	&	&	CCONJ
ejpam-6131	603	3	mathematics	mathematics	PROPN
ejpam-6131	603	4	with	with	ADP
ejpam-6131	603	5	applications	application	NOUN
ejpam-6131	603	6	,	,	PUNCT
ejpam-6131	603	7	64(6):1839–1848	64(6):1839–1848	NUM
ejpam-6131	603	8	,	,	PUNCT
ejpam-6131	603	9	2012	2012	NUM
ejpam-6131	603	10	.	.	PUNCT
ejpam-6131	604	1	[	[	X
ejpam-6131	604	2	19	19	NUM
ejpam-6131	604	3	]	]	X
ejpam-6131	604	4	ramesh	ramesh	PROPN
ejpam-6131	604	5	kumar	kumar	PROPN
ejpam-6131	604	6	vats	vats	PROPN
ejpam-6131	604	7	,	,	PUNCT
ejpam-6131	604	8	kenan	kenan	PROPN
ejpam-6131	604	9	tas	tas	PROPN
ejpam-6131	604	10	,	,	PUNCT
ejpam-6131	604	11	vizender	vizender	NOUN
ejpam-6131	604	12	sihag	sihag	NOUN
ejpam-6131	604	13	,	,	PUNCT
ejpam-6131	604	14	and	and	CCONJ
ejpam-6131	604	15	amit	amit	PROPN
ejpam-6131	604	16	kumar	kumar	PROPN
ejpam-6131	604	17	.	.	PUNCT
ejpam-6131	605	1	triple	triple	ADJ
ejpam-6131	605	2	fixed	fix	VERB
ejpam-6131	605	3	point	point	NOUN
ejpam-6131	605	4	theorems	theorem	NOUN
ejpam-6131	605	5	via	via	ADP
ejpam-6131	605	6	α	α	NOUN
ejpam-6131	605	7	-	-	PUNCT
ejpam-6131	605	8	series	series	NOUN
ejpam-6131	605	9	in	in	ADP
ejpam-6131	605	10	partially	partially	ADV
ejpam-6131	605	11	ordered	order	VERB
ejpam-6131	605	12	metric	metric	ADJ
ejpam-6131	605	13	spaces	space	NOUN
ejpam-6131	605	14	.	.	PUNCT
ejpam-6131	606	1	journal	journal	PROPN
ejpam-6131	606	2	of	of	ADP
ejpam-6131	606	3	inequalities	inequality	NOUN
ejpam-6131	606	4	and	and	CCONJ
ejpam-6131	606	5	applications	application	NOUN
ejpam-6131	606	6	,	,	PUNCT
ejpam-6131	606	7	2014:1–12	2014:1–12	NUM
ejpam-6131	606	8	,	,	PUNCT
ejpam-6131	606	9	2014	2014	NUM
ejpam-6131	606	10	.	.	PUNCT