id	sid	tid	token	lemma	pos
ejpam-6931	1	1	european	european	PROPN
ejpam-6931	1	2	journal	journal	PROPN
ejpam-6931	1	3	of	of	ADP
ejpam-6931	1	4	pure	pure	ADJ
ejpam-6931	1	5	and	and	CCONJ
ejpam-6931	1	6	applied	applied	ADJ
ejpam-6931	1	7	mathematics	mathematic	NOUN
ejpam-6931	1	8	2025	2025	NUM
ejpam-6931	1	9	,	,	PUNCT
ejpam-6931	1	10	vol	vol	NOUN
ejpam-6931	1	11	.	.	PROPN
ejpam-6931	1	12	18	18	NUM
ejpam-6931	1	13	,	,	PUNCT
ejpam-6931	1	14	issue	issue	NOUN
ejpam-6931	1	15	4	4	NUM
ejpam-6931	1	16	,	,	PUNCT
ejpam-6931	1	17	article	article	NOUN
ejpam-6931	1	18	number	number	NOUN
ejpam-6931	1	19	6931	6931	NUM
ejpam-6931	1	20	issn	issn	VERB
ejpam-6931	1	21	1307	1307	NUM
ejpam-6931	1	22	-	-	SYM
ejpam-6931	1	23	5543	5543	NUM
ejpam-6931	1	24	–	–	PUNCT
ejpam-6931	1	25	ejpam.com	ejpam.com	X
ejpam-6931	1	26	published	publish	VERB
ejpam-6931	1	27	by	by	ADP
ejpam-6931	1	28	new	new	PROPN
ejpam-6931	1	29	york	york	PROPN
ejpam-6931	1	30	business	business	PROPN
ejpam-6931	1	31	global	global	ADJ
ejpam-6931	1	32	fixed	fix	VERB
ejpam-6931	1	33	point	point	NOUN
ejpam-6931	1	34	results	result	NOUN
ejpam-6931	1	35	in	in	ADP
ejpam-6931	1	36	complex	complex	ADV
ejpam-6931	1	37	-	-	PUNCT
ejpam-6931	1	38	valued	value	VERB
ejpam-6931	1	39	neutrosophic	neutrosophic	ADJ
ejpam-6931	1	40	metric	metric	ADJ
ejpam-6931	1	41	spaces	space	NOUN
ejpam-6931	1	42	with	with	ADP
ejpam-6931	1	43	application	application	NOUN
ejpam-6931	1	44	to	to	ADP
ejpam-6931	1	45	integral	integral	ADJ
ejpam-6931	1	46	equations	equation	NOUN
ejpam-6931	1	47	syed	sye	VERB
ejpam-6931	1	48	muhammad	muhammad	PROPN
ejpam-6931	1	49	umair	umair	PROPN
ejpam-6931	1	50	ud	ud	PROPN
ejpam-6931	1	51	-	-	PUNCT
ejpam-6931	1	52	din1	din1	PROPN
ejpam-6931	1	53	,	,	PUNCT
ejpam-6931	1	54	umar	umar	PROPN
ejpam-6931	1	55	ishtiaq2	ishtiaq2	PROPN
ejpam-6931	1	56	,	,	PUNCT
ejpam-6931	1	57	hafiz	hafiz	PROPN
ejpam-6931	1	58	fukhar	fukhar	VERB
ejpam-6931	1	59	ud	ud	PROPN
ejpam-6931	1	60	-	-	PUNCT
ejpam-6931	1	61	din1	din1	PROPN
ejpam-6931	1	62	,	,	PUNCT
ejpam-6931	1	63	ibrahim	ibrahim	PROPN
ejpam-6931	1	64	alraddadi3,∗	alraddadi3,∗	PROPN
ejpam-6931	1	65	,	,	PUNCT
ejpam-6931	1	66	dragan	dragan	NOUN
ejpam-6931	1	67	pamucar4	pamucar4	PROPN
ejpam-6931	1	68	1	1	NUM
ejpam-6931	1	69	department	department	NOUN
ejpam-6931	1	70	of	of	ADP
ejpam-6931	1	71	mathematics	mathematic	NOUN
ejpam-6931	1	72	,	,	PUNCT
ejpam-6931	1	73	the	the	DET
ejpam-6931	1	74	islamia	islamia	PROPN
ejpam-6931	1	75	university	university	PROPN
ejpam-6931	1	76	of	of	ADP
ejpam-6931	1	77	bahawalpur	bahawalpur	PROPN
ejpam-6931	1	78	,	,	PUNCT
ejpam-6931	1	79	bahawalpur	bahawalpur	NOUN
ejpam-6931	1	80	63100	63100	NUM
ejpam-6931	1	81	,	,	PUNCT
ejpam-6931	1	82	pakistan	pakistan	PROPN
ejpam-6931	1	83	2	2	NUM
ejpam-6931	1	84	office	office	NOUN
ejpam-6931	1	85	of	of	ADP
ejpam-6931	1	86	research	research	NOUN
ejpam-6931	1	87	innovation	innovation	NOUN
ejpam-6931	1	88	and	and	CCONJ
ejpam-6931	1	89	commercialization	commercialization	NOUN
ejpam-6931	1	90	,	,	PUNCT
ejpam-6931	1	91	university	university	NOUN
ejpam-6931	1	92	of	of	ADP
ejpam-6931	1	93	management	management	NOUN
ejpam-6931	1	94	and	and	CCONJ
ejpam-6931	1	95	technology	technology	NOUN
ejpam-6931	1	96	,	,	PUNCT
ejpam-6931	1	97	lahore	lahore	NOUN
ejpam-6931	1	98	54770	54770	NUM
ejpam-6931	1	99	,	,	PUNCT
ejpam-6931	1	100	pakistan	pakistan	PROPN
ejpam-6931	1	101	3	3	NUM
ejpam-6931	1	102	department	department	NOUN
ejpam-6931	1	103	of	of	ADP
ejpam-6931	1	104	mathematics	mathematic	NOUN
ejpam-6931	1	105	,	,	PUNCT
ejpam-6931	1	106	faculty	faculty	NOUN
ejpam-6931	1	107	of	of	ADP
ejpam-6931	1	108	science	science	NOUN
ejpam-6931	1	109	,	,	PUNCT
ejpam-6931	1	110	islamic	islamic	PROPN
ejpam-6931	1	111	university	university	PROPN
ejpam-6931	1	112	of	of	ADP
ejpam-6931	1	113	madinah	madinah	PROPN
ejpam-6931	1	114	,	,	PUNCT
ejpam-6931	1	115	madinah	madinah	PROPN
ejpam-6931	1	116	,	,	PUNCT
ejpam-6931	1	117	saudi	saudi	PROPN
ejpam-6931	1	118	arabia	arabia	PROPN
ejpam-6931	1	119	4	4	NUM
ejpam-6931	1	120	széchenyi	széchenyi	PROPN
ejpam-6931	1	121	istván	istván	PROPN
ejpam-6931	1	122	university	university	NOUN
ejpam-6931	1	123	,	,	PUNCT
ejpam-6931	1	124	győr	győr	PROPN
ejpam-6931	1	125	,	,	PUNCT
ejpam-6931	1	126	hungary	hungary	PROPN
ejpam-6931	1	127	abstract	abstract	NOUN
ejpam-6931	1	128	.	.	PUNCT
ejpam-6931	2	1	this	this	DET
ejpam-6931	2	2	work	work	NOUN
ejpam-6931	2	3	presents	present	VERB
ejpam-6931	2	4	the	the	DET
ejpam-6931	2	5	notion	notion	NOUN
ejpam-6931	2	6	of	of	ADP
ejpam-6931	2	7	complex	complex	NOUN
ejpam-6931	2	8	-	-	PUNCT
ejpam-6931	2	9	valued	value	VERB
ejpam-6931	2	10	neutrosophic	neutrosophic	ADJ
ejpam-6931	2	11	metric	metric	ADJ
ejpam-6931	2	12	spaces	space	NOUN
ejpam-6931	2	13	(	(	PUNCT
ejpam-6931	2	14	cvnmss	cvnmss	NOUN
ejpam-6931	2	15	)	)	PUNCT
ejpam-6931	2	16	and	and	CCONJ
ejpam-6931	2	17	provides	provide	VERB
ejpam-6931	2	18	a	a	DET
ejpam-6931	2	19	fresh	fresh	ADJ
ejpam-6931	2	20	mathematical	mathematical	ADJ
ejpam-6931	2	21	framework	framework	NOUN
ejpam-6931	2	22	extending	extend	VERB
ejpam-6931	2	23	conventional	conventional	ADJ
ejpam-6931	2	24	fuzzy	fuzzy	ADJ
ejpam-6931	2	25	and	and	CCONJ
ejpam-6931	2	26	intuitionistic	intuitionistic	ADJ
ejpam-6931	2	27	fuzzy	fuzzy	ADJ
ejpam-6931	2	28	metric	metric	ADJ
ejpam-6931	2	29	spaces	space	NOUN
ejpam-6931	2	30	(	(	PUNCT
ejpam-6931	2	31	ifmss	ifmss	PROPN
ejpam-6931	2	32	)	)	PUNCT
ejpam-6931	2	33	.	.	PUNCT
ejpam-6931	3	1	this	this	DET
ejpam-6931	3	2	new	new	ADJ
ejpam-6931	3	3	method	method	NOUN
ejpam-6931	3	4	is	be	AUX
ejpam-6931	3	5	especially	especially	ADV
ejpam-6931	3	6	appropriate	appropriate	ADJ
ejpam-6931	3	7	for	for	ADP
ejpam-6931	3	8	studying	study	VERB
ejpam-6931	3	9	complicated	complicated	ADJ
ejpam-6931	3	10	mathematical	mathematical	ADJ
ejpam-6931	3	11	structures	structure	NOUN
ejpam-6931	3	12	since	since	SCONJ
ejpam-6931	3	13	it	it	PRON
ejpam-6931	3	14	helps	help	VERB
ejpam-6931	3	15	to	to	PART
ejpam-6931	3	16	better	well	ADV
ejpam-6931	3	17	depict	depict	VERB
ejpam-6931	3	18	uncertainty	uncertainty	NOUN
ejpam-6931	3	19	and	and	CCONJ
ejpam-6931	3	20	imprecision	imprecision	NOUN
ejpam-6931	3	21	by	by	ADP
ejpam-6931	3	22	including	include	VERB
ejpam-6931	3	23	neutrosophic	neutrosophic	ADJ
ejpam-6931	3	24	sets	set	NOUN
ejpam-6931	3	25	.	.	PUNCT
ejpam-6931	4	1	we	we	PRON
ejpam-6931	4	2	determine	determine	VERB
ejpam-6931	4	3	the	the	DET
ejpam-6931	4	4	existence	existence	NOUN
ejpam-6931	4	5	and	and	CCONJ
ejpam-6931	4	6	uniqueness	uniqueness	NOUN
ejpam-6931	4	7	of	of	ADP
ejpam-6931	4	8	fixed	fix	VERB
ejpam-6931	4	9	points	point	NOUN
ejpam-6931	4	10	under	under	ADP
ejpam-6931	4	11	several	several	ADJ
ejpam-6931	4	12	contractive	contractive	ADJ
ejpam-6931	4	13	mappings	mapping	NOUN
ejpam-6931	4	14	in	in	ADP
ejpam-6931	4	15	this	this	DET
ejpam-6931	4	16	newly	newly	ADV
ejpam-6931	4	17	defined	define	VERB
ejpam-6931	4	18	metric	metric	ADJ
ejpam-6931	4	19	space	space	NOUN
ejpam-6931	4	20	.	.	PUNCT
ejpam-6931	5	1	our	our	PRON
ejpam-6931	5	2	results	result	NOUN
ejpam-6931	5	3	extend	extend	VERB
ejpam-6931	5	4	the	the	DET
ejpam-6931	5	5	classical	classical	ADJ
ejpam-6931	5	6	banach	banach	NOUN
ejpam-6931	5	7	contraction	contraction	NOUN
ejpam-6931	5	8	ideas	idea	NOUN
ejpam-6931	5	9	and	and	CCONJ
ejpam-6931	5	10	modify	modify	VERB
ejpam-6931	5	11	them	they	PRON
ejpam-6931	5	12	for	for	ADP
ejpam-6931	5	13	the	the	DET
ejpam-6931	5	14	neutrosophic	neutrosophic	ADJ
ejpam-6931	5	15	environment	environment	NOUN
ejpam-6931	5	16	.	.	PUNCT
ejpam-6931	6	1	we	we	PRON
ejpam-6931	6	2	demonstrate	demonstrate	VERB
ejpam-6931	6	3	several	several	ADJ
ejpam-6931	6	4	fixed	fix	VERB
ejpam-6931	6	5	-	-	PUNCT
ejpam-6931	6	6	point	point	NOUN
ejpam-6931	6	7	theorems	theorem	NOUN
ejpam-6931	6	8	,	,	PUNCT
ejpam-6931	6	9	expanding	expand	VERB
ejpam-6931	6	10	the	the	DET
ejpam-6931	6	11	applicability	applicability	NOUN
ejpam-6931	6	12	of	of	ADP
ejpam-6931	6	13	current	current	ADJ
ejpam-6931	6	14	fixed	fix	VERB
ejpam-6931	6	15	-	-	PUNCT
ejpam-6931	6	16	point	point	NOUN
ejpam-6931	6	17	results	result	NOUN
ejpam-6931	6	18	in	in	ADP
ejpam-6931	6	19	non	non	ADJ
ejpam-6931	6	20	-	-	ADJ
ejpam-6931	6	21	classical	classical	ADJ
ejpam-6931	6	22	metric	metric	ADJ
ejpam-6931	6	23	spaces	space	NOUN
ejpam-6931	6	24	.	.	PUNCT
ejpam-6931	7	1	we	we	PRON
ejpam-6931	7	2	use	use	VERB
ejpam-6931	7	3	our	our	PRON
ejpam-6931	7	4	results	result	NOUN
ejpam-6931	7	5	to	to	PART
ejpam-6931	7	6	solve	solve	VERB
ejpam-6931	7	7	fredholm	fredholm	ADJ
ejpam-6931	7	8	integral	integral	ADJ
ejpam-6931	7	9	equations	equation	NOUN
ejpam-6931	7	10	and	and	CCONJ
ejpam-6931	7	11	show	show	VERB
ejpam-6931	7	12	the	the	DET
ejpam-6931	7	13	efficiency	efficiency	NOUN
ejpam-6931	7	14	of	of	ADP
ejpam-6931	7	15	cvnmss	cvnmss	NOUN
ejpam-6931	7	16	in	in	ADP
ejpam-6931	7	17	tackling	tackle	VERB
ejpam-6931	7	18	real	real	ADJ
ejpam-6931	7	19	-	-	PUNCT
ejpam-6931	7	20	world	world	NOUN
ejpam-6931	7	21	mathematical	mathematical	ADJ
ejpam-6931	7	22	problems	problem	NOUN
ejpam-6931	7	23	by	by	ADP
ejpam-6931	7	24	illustrating	illustrate	VERB
ejpam-6931	7	25	the	the	DET
ejpam-6931	7	26	pragmatic	pragmatic	ADJ
ejpam-6931	7	27	relevance	relevance	NOUN
ejpam-6931	7	28	of	of	ADP
ejpam-6931	7	29	our	our	PRON
ejpam-6931	7	30	results	result	NOUN
ejpam-6931	7	31	.	.	PUNCT
ejpam-6931	8	1	furthermore	furthermore	ADV
ejpam-6931	8	2	,	,	PUNCT
ejpam-6931	8	3	comprehensive	comprehensive	ADJ
ejpam-6931	8	4	cases	case	NOUN
ejpam-6931	8	5	are	be	AUX
ejpam-6931	8	6	included	include	VERB
ejpam-6931	8	7	to	to	PART
ejpam-6931	8	8	show	show	VERB
ejpam-6931	8	9	the	the	DET
ejpam-6931	8	10	relevance	relevance	NOUN
ejpam-6931	8	11	of	of	ADP
ejpam-6931	8	12	our	our	PRON
ejpam-6931	8	13	findings	finding	NOUN
ejpam-6931	8	14	.	.	PUNCT
ejpam-6931	9	1	this	this	DET
ejpam-6931	9	2	work	work	NOUN
ejpam-6931	9	3	also	also	ADV
ejpam-6931	9	4	extends	extend	VERB
ejpam-6931	9	5	the	the	DET
ejpam-6931	9	6	fixed	fix	VERB
ejpam-6931	9	7	-	-	PUNCT
ejpam-6931	9	8	point	point	NOUN
ejpam-6931	9	9	theory	theory	NOUN
ejpam-6931	9	10	in	in	ADP
ejpam-6931	9	11	neutrosophic	neutrosophic	ADJ
ejpam-6931	9	12	environments	environment	NOUN
ejpam-6931	9	13	and	and	CCONJ
ejpam-6931	9	14	provides	provide	VERB
ejpam-6931	9	15	fresh	fresh	ADJ
ejpam-6931	9	16	directions	direction	NOUN
ejpam-6931	9	17	for	for	ADP
ejpam-6931	9	18	investigation	investigation	NOUN
ejpam-6931	9	19	in	in	ADP
ejpam-6931	9	20	integral	integral	ADJ
ejpam-6931	9	21	equations	equation	NOUN
ejpam-6931	9	22	and	and	CCONJ
ejpam-6931	9	23	contractive	contractive	ADJ
ejpam-6931	9	24	mappings	mapping	NOUN
ejpam-6931	9	25	.	.	PUNCT
ejpam-6931	10	1	2020	2020	NUM
ejpam-6931	10	2	mathematics	mathematic	NOUN
ejpam-6931	10	3	subject	subject	NOUN
ejpam-6931	10	4	classifications	classification	NOUN
ejpam-6931	10	5	:	:	PUNCT
ejpam-6931	10	6	47h10	47h10	NUM
ejpam-6931	10	7	,	,	PUNCT
ejpam-6931	10	8	54h25	54h25	NUM
ejpam-6931	10	9	key	key	ADJ
ejpam-6931	10	10	words	word	NOUN
ejpam-6931	10	11	and	and	CCONJ
ejpam-6931	10	12	phrases	phrase	NOUN
ejpam-6931	10	13	:	:	PUNCT
ejpam-6931	10	14	fixed	fix	VERB
ejpam-6931	10	15	point	point	NOUN
ejpam-6931	10	16	,	,	PUNCT
ejpam-6931	10	17	neutrosophic	neutrosophic	ADJ
ejpam-6931	10	18	sets	set	NOUN
ejpam-6931	10	19	,	,	PUNCT
ejpam-6931	10	20	existence	existence	NOUN
ejpam-6931	10	21	and	and	CCONJ
ejpam-6931	10	22	uniqueness	uniqueness	NOUN
ejpam-6931	10	23	,	,	PUNCT
ejpam-6931	10	24	metric	metric	ADJ
ejpam-6931	10	25	spaces	space	NOUN
ejpam-6931	10	26	,	,	PUNCT
ejpam-6931	10	27	contraction	contraction	NOUN
ejpam-6931	10	28	mappings	mapping	NOUN
ejpam-6931	10	29	∗corresponding	∗corresponde	VERB
ejpam-6931	10	30	author	author	NOUN
ejpam-6931	10	31	.	.	PUNCT
ejpam-6931	11	1	doi	doi	NOUN
ejpam-6931	11	2	:	:	PUNCT
ejpam-6931	11	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6931	https://doi.org/10.29020/nybg.ejpam.v18i4.6931	ADJ
ejpam-6931	11	4	email	email	NOUN
ejpam-6931	11	5	addresses	address	NOUN
ejpam-6931	11	6	:	:	PUNCT
ejpam-6931	11	7	m.umairuddin@iub.edu.pk	m.umairuddin@iub.edu.pk	PROPN
ejpam-6931	11	8	(	(	PUNCT
ejpam-6931	11	9	s.	s.	PROPN
ejpam-6931	11	10	m.	m.	PROPN
ejpam-6931	11	11	u.	u.	PROPN
ejpam-6931	11	12	ud	ud	AUX
ejpam-6931	11	13	-	-	PUNCT
ejpam-6931	11	14	din	din	NOUN
ejpam-6931	11	15	)	)	PUNCT
ejpam-6931	11	16	,	,	PUNCT
ejpam-6931	11	17	hfdin@yahoo.com	hfdin@yahoo.com	X
ejpam-6931	11	18	(	(	PUNCT
ejpam-6931	11	19	h.	h.	PROPN
ejpam-6931	11	20	f.	f.	PROPN
ejpam-6931	11	21	ud	ud	PROPN
ejpam-6931	11	22	-	-	PUNCT
ejpam-6931	11	23	din	din	NOUN
ejpam-6931	11	24	)	)	PUNCT
ejpam-6931	11	25	,	,	PUNCT
ejpam-6931	11	26	umarishtiaq@umt.edu.pk	umarishtiaq@umt.edu.pk	PROPN
ejpam-6931	11	27	(	(	PUNCT
ejpam-6931	11	28	u.	u.	PROPN
ejpam-6931	11	29	ishtiaq	ishtiaq	PROPN
ejpam-6931	11	30	)	)	PUNCT
ejpam-6931	11	31	,	,	PUNCT
ejpam-6931	11	32	ialraddadi@iu.edu.sa	ialraddadi@iu.edu.sa	PROPN
ejpam-6931	11	33	(	(	PUNCT
ejpam-6931	11	34	i.	i.	NOUN
ejpam-6931	11	35	alraddadi	alraddadi	PROPN
ejpam-6931	11	36	)	)	PUNCT
ejpam-6931	11	37	,	,	PUNCT
ejpam-6931	11	38	pamucar.dragan@sze.hu	pamucar.dragan@sze.hu	PROPN
ejpam-6931	11	39	(	(	PUNCT
ejpam-6931	11	40	d.	d.	PROPN
ejpam-6931	11	41	pamucar	pamucar	PROPN
ejpam-6931	11	42	)	)	PUNCT
ejpam-6931	11	43	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6931	12	1	1	1	NUM
ejpam-6931	12	2	copyright	copyright	NOUN
ejpam-6931	12	3	:	:	PUNCT
ejpam-6931	12	4	©	©	PROPN
ejpam-6931	12	5	2025	2025	NUM
ejpam-6931	12	6	the	the	DET
ejpam-6931	12	7	author(s	author(s	NOUN
ejpam-6931	12	8	)	)	PUNCT
ejpam-6931	12	9	.	.	PUNCT
ejpam-6931	13	1	(	(	PUNCT
ejpam-6931	13	2	cc	cc	NOUN
ejpam-6931	13	3	by	by	ADP
ejpam-6931	13	4	-	-	PUNCT
ejpam-6931	13	5	nc	nc	PROPN
ejpam-6931	13	6	4.0	4.0	NUM
ejpam-6931	13	7	)	)	PUNCT
ejpam-6931	13	8	s.	s.	PROPN
ejpam-6931	13	9	m.	m.	PROPN
ejpam-6931	13	10	u.	u.	PROPN
ejpam-6931	14	1	ud	ud	AUX
ejpam-6931	14	2	-	-	PUNCT
ejpam-6931	14	3	din	din	VERB
ejpam-6931	14	4	et	et	PROPN
ejpam-6931	14	5	al	al	PROPN
ejpam-6931	14	6	.	.	PUNCT
ejpam-6931	14	7	/	/	SYM
ejpam-6931	14	8	eur	eur	PROPN
ejpam-6931	14	9	.	.	PUNCT
ejpam-6931	15	1	j.	j.	PROPN
ejpam-6931	15	2	pure	pure	PROPN
ejpam-6931	15	3	appl	appl	PROPN
ejpam-6931	15	4	.	.	PROPN
ejpam-6931	15	5	math	math	PROPN
ejpam-6931	15	6	,	,	PUNCT
ejpam-6931	15	7	18	18	NUM
ejpam-6931	15	8	(	(	PUNCT
ejpam-6931	15	9	4	4	NUM
ejpam-6931	15	10	)	)	PUNCT
ejpam-6931	15	11	(	(	PUNCT
ejpam-6931	15	12	2025	2025	NUM
ejpam-6931	15	13	)	)	PUNCT
ejpam-6931	15	14	,	,	PUNCT
ejpam-6931	15	15	6931	6931	NUM
ejpam-6931	15	16	2	2	NUM
ejpam-6931	15	17	of	of	ADP
ejpam-6931	15	18	38	38	NUM
ejpam-6931	15	19	1	1	NUM
ejpam-6931	15	20	.	.	PUNCT
ejpam-6931	16	1	introduction	introduction	NOUN
ejpam-6931	16	2	a	a	DET
ejpam-6931	16	3	neutrosophic	neutrosophic	ADJ
ejpam-6931	16	4	metric	metric	ADJ
ejpam-6931	16	5	space	space	NOUN
ejpam-6931	16	6	expands	expand	VERB
ejpam-6931	16	7	on	on	ADP
ejpam-6931	16	8	the	the	DET
ejpam-6931	16	9	traditional	traditional	ADJ
ejpam-6931	16	10	notion	notion	NOUN
ejpam-6931	16	11	of	of	ADP
ejpam-6931	16	12	metric	metric	ADJ
ejpam-6931	16	13	spaces	space	NOUN
ejpam-6931	16	14	by	by	ADP
ejpam-6931	16	15	including	include	VERB
ejpam-6931	16	16	the	the	DET
ejpam-6931	16	17	concept	concept	NOUN
ejpam-6931	16	18	of	of	ADP
ejpam-6931	16	19	neutrosophy	neutrosophy	NOUN
ejpam-6931	16	20	,	,	PUNCT
ejpam-6931	16	21	which	which	PRON
ejpam-6931	16	22	deals	deal	VERB
ejpam-6931	16	23	with	with	ADP
ejpam-6931	16	24	uncertainty	uncertainty	NOUN
ejpam-6931	16	25	and	and	CCONJ
ejpam-6931	16	26	indeterminacy	indeterminacy	NOUN
ejpam-6931	16	27	.	.	PUNCT
ejpam-6931	17	1	the	the	DET
ejpam-6931	17	2	distances	distance	NOUN
ejpam-6931	17	3	between	between	ADP
ejpam-6931	17	4	points	point	NOUN
ejpam-6931	17	5	in	in	ADP
ejpam-6931	17	6	a	a	DET
ejpam-6931	17	7	typical	typical	ADJ
ejpam-6931	17	8	metric	metric	ADJ
ejpam-6931	17	9	space	space	NOUN
ejpam-6931	17	10	are	be	AUX
ejpam-6931	17	11	well	well	ADV
ejpam-6931	17	12	defined	define	VERB
ejpam-6931	17	13	and	and	CCONJ
ejpam-6931	17	14	accurate	accurate	ADJ
ejpam-6931	17	15	;	;	PUNCT
ejpam-6931	17	16	however	however	ADV
ejpam-6931	17	17	,	,	PUNCT
ejpam-6931	17	18	in	in	ADP
ejpam-6931	17	19	a	a	DET
ejpam-6931	17	20	neutrosophic	neutrosophic	ADJ
ejpam-6931	17	21	metric	metric	ADJ
ejpam-6931	17	22	space	space	NOUN
ejpam-6931	17	23	,	,	PUNCT
ejpam-6931	17	24	the	the	DET
ejpam-6931	17	25	distance	distance	NOUN
ejpam-6931	17	26	between	between	ADP
ejpam-6931	17	27	points	point	NOUN
ejpam-6931	17	28	is	be	AUX
ejpam-6931	17	29	specified	specify	VERB
ejpam-6931	17	30	by	by	ADP
ejpam-6931	17	31	three	three	NUM
ejpam-6931	17	32	distinct	distinct	ADJ
ejpam-6931	17	33	functions	function	NOUN
ejpam-6931	17	34	that	that	PRON
ejpam-6931	17	35	indicate	indicate	VERB
ejpam-6931	17	36	the	the	DET
ejpam-6931	17	37	degree	degree	NOUN
ejpam-6931	17	38	of	of	ADP
ejpam-6931	17	39	truth	truth	NOUN
ejpam-6931	17	40	,	,	PUNCT
ejpam-6931	17	41	indeterminacy	indeterminacy	NOUN
ejpam-6931	17	42	,	,	PUNCT
ejpam-6931	17	43	and	and	CCONJ
ejpam-6931	17	44	falsity	falsity	NOUN
ejpam-6931	17	45	.	.	PUNCT
ejpam-6931	18	1	this	this	DET
ejpam-6931	18	2	approach	approach	NOUN
ejpam-6931	18	3	enables	enable	VERB
ejpam-6931	18	4	more	more	ADV
ejpam-6931	18	5	sophisticated	sophisticated	ADJ
ejpam-6931	18	6	modeling	modeling	NOUN
ejpam-6931	18	7	of	of	ADP
ejpam-6931	18	8	complicated	complicated	ADJ
ejpam-6931	18	9	,	,	PUNCT
ejpam-6931	18	10	uncertain	uncertain	ADJ
ejpam-6931	18	11	,	,	PUNCT
ejpam-6931	18	12	or	or	CCONJ
ejpam-6931	18	13	ambiguous	ambiguous	ADJ
ejpam-6931	18	14	processes	process	NOUN
ejpam-6931	18	15	in	in	ADP
ejpam-6931	18	16	which	which	PRON
ejpam-6931	18	17	information	information	NOUN
ejpam-6931	18	18	may	may	AUX
ejpam-6931	18	19	be	be	AUX
ejpam-6931	18	20	inadequate	inadequate	ADJ
ejpam-6931	18	21	or	or	CCONJ
ejpam-6931	18	22	inconsistent	inconsistent	ADJ
ejpam-6931	18	23	.	.	PUNCT
ejpam-6931	19	1	essentially	essentially	ADV
ejpam-6931	19	2	,	,	PUNCT
ejpam-6931	19	3	it	it	PRON
ejpam-6931	19	4	provides	provide	VERB
ejpam-6931	19	5	a	a	DET
ejpam-6931	19	6	mathematical	mathematical	ADJ
ejpam-6931	19	7	structure	structure	NOUN
ejpam-6931	19	8	for	for	ADP
ejpam-6931	19	9	analyzing	analyze	VERB
ejpam-6931	19	10	environments	environment	NOUN
ejpam-6931	19	11	where	where	SCONJ
ejpam-6931	19	12	traditional	traditional	ADJ
ejpam-6931	19	13	metrics	metric	NOUN
ejpam-6931	19	14	fall	fall	VERB
ejpam-6931	19	15	short	short	ADJ
ejpam-6931	19	16	,	,	PUNCT
ejpam-6931	19	17	allowing	allow	VERB
ejpam-6931	19	18	more	more	ADV
ejpam-6931	19	19	adaptable	adaptable	ADJ
ejpam-6931	19	20	and	and	CCONJ
ejpam-6931	19	21	resilient	resilient	ADJ
ejpam-6931	19	22	approaches	approach	NOUN
ejpam-6931	19	23	to	to	ADP
ejpam-6931	19	24	problems	problem	NOUN
ejpam-6931	19	25	in	in	ADP
ejpam-6931	19	26	fields	field	NOUN
ejpam-6931	19	27	such	such	ADJ
ejpam-6931	19	28	as	as	ADP
ejpam-6931	19	29	fuzzy	fuzzy	ADJ
ejpam-6931	19	30	logic	logic	NOUN
ejpam-6931	19	31	,	,	PUNCT
ejpam-6931	19	32	decision	decision	NOUN
ejpam-6931	19	33	making	making	NOUN
ejpam-6931	19	34	,	,	PUNCT
ejpam-6931	19	35	and	and	CCONJ
ejpam-6931	19	36	applied	apply	VERB
ejpam-6931	19	37	research	research	NOUN
ejpam-6931	19	38	.	.	PUNCT
ejpam-6931	20	1	neutrosophic	neutrosophic	ADJ
ejpam-6931	20	2	metric	metric	ADJ
ejpam-6931	20	3	spaces	space	NOUN
ejpam-6931	20	4	allow	allow	VERB
ejpam-6931	20	5	for	for	ADP
ejpam-6931	20	6	a	a	DET
ejpam-6931	20	7	more	more	ADJ
ejpam-6931	20	8	in	in	ADP
ejpam-6931	20	9	-	-	PUNCT
ejpam-6931	20	10	depth	depth	NOUN
ejpam-6931	20	11	examination	examination	NOUN
ejpam-6931	20	12	of	of	ADP
ejpam-6931	20	13	phenomena	phenomenon	NOUN
ejpam-6931	20	14	that	that	SCONJ
ejpam-6931	20	15	classical	classical	ADJ
ejpam-6931	20	16	approaches	approach	NOUN
ejpam-6931	20	17	can	can	AUX
ejpam-6931	20	18	not	not	PART
ejpam-6931	20	19	fully	fully	ADV
ejpam-6931	20	20	represent	represent	VERB
ejpam-6931	20	21	.	.	PUNCT
ejpam-6931	21	1	in	in	ADP
ejpam-6931	21	2	mathematical	mathematical	ADJ
ejpam-6931	21	3	analysis	analysis	NOUN
ejpam-6931	21	4	,	,	PUNCT
ejpam-6931	21	5	fixed	fix	VERB
ejpam-6931	21	6	-	-	PUNCT
ejpam-6931	21	7	point	point	NOUN
ejpam-6931	21	8	theory	theory	NOUN
ejpam-6931	21	9	is	be	AUX
ejpam-6931	21	10	a	a	DET
ejpam-6931	21	11	powerful	powerful	ADJ
ejpam-6931	21	12	tool	tool	NOUN
ejpam-6931	21	13	with	with	ADP
ejpam-6931	21	14	wide	wide	ADV
ejpam-6931	21	15	-	-	PUNCT
ejpam-6931	21	16	ranging	range	VERB
ejpam-6931	21	17	applications	application	NOUN
ejpam-6931	21	18	.	.	PUNCT
ejpam-6931	22	1	the	the	DET
ejpam-6931	22	2	most	most	ADV
ejpam-6931	22	3	applicable	applicable	ADJ
ejpam-6931	22	4	fixed	fix	VERB
ejpam-6931	22	5	point	point	NOUN
ejpam-6931	22	6	theorem	theorem	VERB
ejpam-6931	22	7	in	in	ADP
ejpam-6931	22	8	metric	metric	ADJ
ejpam-6931	22	9	spaces	space	NOUN
ejpam-6931	22	10	is	be	AUX
ejpam-6931	22	11	the	the	DET
ejpam-6931	22	12	banach	banach	NOUN
ejpam-6931	22	13	contraction	contraction	NOUN
ejpam-6931	22	14	mapping	mapping	NOUN
ejpam-6931	22	15	theorem	theorem	VERB
ejpam-6931	22	16	,	,	PUNCT
ejpam-6931	22	17	which	which	PRON
ejpam-6931	22	18	was	be	AUX
ejpam-6931	22	19	introduced	introduce	VERB
ejpam-6931	22	20	in	in	ADP
ejpam-6931	22	21	[	[	X
ejpam-6931	22	22	1	1	NUM
ejpam-6931	22	23	]	]	PUNCT
ejpam-6931	22	24	.	.	PUNCT
ejpam-6931	23	1	it	it	PRON
ejpam-6931	23	2	has	have	AUX
ejpam-6931	23	3	been	be	AUX
ejpam-6931	23	4	generalized	generalize	VERB
ejpam-6931	23	5	into	into	ADP
ejpam-6931	23	6	several	several	ADJ
ejpam-6931	23	7	versions	version	NOUN
ejpam-6931	23	8	of	of	ADP
ejpam-6931	23	9	fixed	fix	VERB
ejpam-6931	23	10	-	-	PUNCT
ejpam-6931	23	11	point	point	NOUN
ejpam-6931	23	12	theorems	theorem	NOUN
ejpam-6931	23	13	and	and	CCONJ
ejpam-6931	23	14	has	have	AUX
ejpam-6931	23	15	been	be	AUX
ejpam-6931	23	16	advanced	advance	VERB
ejpam-6931	23	17	through	through	ADP
ejpam-6931	23	18	numerous	numerous	ADJ
ejpam-6931	23	19	methodologies	methodology	NOUN
ejpam-6931	23	20	.	.	PUNCT
ejpam-6931	24	1	mathematical	mathematical	ADJ
ejpam-6931	24	2	models	model	NOUN
ejpam-6931	24	3	based	base	VERB
ejpam-6931	24	4	on	on	ADP
ejpam-6931	24	5	classical	classical	ADJ
ejpam-6931	24	6	set	set	NOUN
ejpam-6931	24	7	theory	theory	NOUN
ejpam-6931	24	8	can	can	AUX
ejpam-6931	24	9	not	not	PART
ejpam-6931	24	10	always	always	ADV
ejpam-6931	24	11	capture	capture	VERB
ejpam-6931	24	12	ambiguous	ambiguous	ADJ
ejpam-6931	24	13	circumstances	circumstance	NOUN
ejpam-6931	24	14	in	in	ADP
ejpam-6931	24	15	nature	nature	NOUN
ejpam-6931	24	16	or	or	CCONJ
ejpam-6931	24	17	real	real	ADJ
ejpam-6931	24	18	-	-	PUNCT
ejpam-6931	24	19	world	world	NOUN
ejpam-6931	24	20	challenges	challenge	NOUN
ejpam-6931	24	21	.	.	PUNCT
ejpam-6931	25	1	to	to	PART
ejpam-6931	25	2	overcome	overcome	VERB
ejpam-6931	25	3	this	this	DET
ejpam-6931	25	4	challenge	challenge	NOUN
ejpam-6931	25	5	,	,	PUNCT
ejpam-6931	25	6	zadeh	zadeh	PROPN
ejpam-6931	26	1	[	[	X
ejpam-6931	26	2	2	2	NUM
ejpam-6931	26	3	]	]	PUNCT
ejpam-6931	26	4	introduced	introduce	VERB
ejpam-6931	26	5	fuzzy	fuzzy	ADJ
ejpam-6931	26	6	sets	set	NOUN
ejpam-6931	26	7	to	to	PART
ejpam-6931	26	8	represent	represent	VERB
ejpam-6931	26	9	an	an	DET
ejpam-6931	26	10	element	element	NOUN
ejpam-6931	26	11	’s	’s	PART
ejpam-6931	26	12	membership	membership	NOUN
ejpam-6931	26	13	by	by	ADP
ejpam-6931	26	14	designating	designate	VERB
ejpam-6931	26	15	an	an	DET
ejpam-6931	26	16	element	element	NOUN
ejpam-6931	26	17	’s	’s	PART
ejpam-6931	26	18	inclusion	inclusion	NOUN
ejpam-6931	26	19	in	in	ADP
ejpam-6931	26	20	a	a	DET
ejpam-6931	26	21	set	set	NOUN
ejpam-6931	26	22	by	by	ADP
ejpam-6931	26	23	allocating	allocate	VERB
ejpam-6931	26	24	a	a	DET
ejpam-6931	26	25	value	value	NOUN
ejpam-6931	26	26	within	within	ADP
ejpam-6931	26	27	the	the	DET
ejpam-6931	26	28	interval	interval	NOUN
ejpam-6931	26	29	[	[	X
ejpam-6931	26	30	0	0	NUM
ejpam-6931	26	31	,	,	PUNCT
ejpam-6931	26	32	1	1	NUM
ejpam-6931	26	33	]	]	PUNCT
ejpam-6931	26	34	.	.	PUNCT
ejpam-6931	27	1	afterward	afterward	ADV
ejpam-6931	27	2	,	,	PUNCT
ejpam-6931	27	3	atanassov	atanassov	VERB
ejpam-6931	27	4	[	[	X
ejpam-6931	27	5	3	3	NUM
ejpam-6931	27	6	]	]	PUNCT
ejpam-6931	27	7	presented	present	VERB
ejpam-6931	27	8	intuitionistic	intuitionistic	ADJ
ejpam-6931	27	9	fuzzy	fuzzy	ADJ
ejpam-6931	27	10	sets	set	NOUN
ejpam-6931	27	11	,	,	PUNCT
ejpam-6931	27	12	which	which	PRON
ejpam-6931	27	13	facilitates	facilitate	VERB
ejpam-6931	27	14	the	the	DET
ejpam-6931	27	15	representation	representation	NOUN
ejpam-6931	27	16	of	of	ADP
ejpam-6931	27	17	level	level	NOUN
ejpam-6931	27	18	of	of	ADP
ejpam-6931	27	19	ambiguity	ambiguity	NOUN
ejpam-6931	27	20	when	when	SCONJ
ejpam-6931	27	21	determining	determine	VERB
ejpam-6931	27	22	whether	whether	SCONJ
ejpam-6931	27	23	an	an	DET
ejpam-6931	27	24	element	element	NOUN
ejpam-6931	27	25	in	in	ADP
ejpam-6931	27	26	a	a	DET
ejpam-6931	27	27	set	set	NOUN
ejpam-6931	27	28	is	be	AUX
ejpam-6931	27	29	a	a	DET
ejpam-6931	27	30	member	member	NOUN
ejpam-6931	27	31	or	or	CCONJ
ejpam-6931	27	32	not	not	PART
ejpam-6931	27	33	.	.	PUNCT
ejpam-6931	28	1	kramosil	kramosil	NOUN
ejpam-6931	28	2	and	and	CCONJ
ejpam-6931	28	3	michalek	michalek	VERB
ejpam-6931	28	4	[	[	X
ejpam-6931	28	5	4	4	X
ejpam-6931	28	6	]	]	PUNCT
ejpam-6931	28	7	proposed	propose	VERB
ejpam-6931	28	8	fuzzy	fuzzy	ADJ
ejpam-6931	28	9	metric	metric	ADJ
ejpam-6931	28	10	spaces	space	NOUN
ejpam-6931	28	11	(	(	PUNCT
ejpam-6931	28	12	fmss	fmss	NOUN
ejpam-6931	28	13	)	)	PUNCT
ejpam-6931	28	14	,	,	PUNCT
ejpam-6931	28	15	which	which	PRON
ejpam-6931	28	16	extend	extend	VERB
ejpam-6931	28	17	probabilistic	probabilistic	ADJ
ejpam-6931	28	18	metric	metric	ADJ
ejpam-6931	28	19	spaces	space	NOUN
ejpam-6931	28	20	.	.	PUNCT
ejpam-6931	29	1	grabiec	grabiec	PROPN
ejpam-6931	30	1	[	[	X
ejpam-6931	30	2	5	5	NUM
ejpam-6931	30	3	]	]	PUNCT
ejpam-6931	30	4	was	be	AUX
ejpam-6931	30	5	the	the	DET
ejpam-6931	30	6	first	first	ADJ
ejpam-6931	30	7	to	to	PART
ejpam-6931	30	8	research	research	VERB
ejpam-6931	30	9	the	the	DET
ejpam-6931	30	10	ideology	ideology	NOUN
ejpam-6931	30	11	of	of	ADP
ejpam-6931	30	12	fuzzy	fuzzy	ADJ
ejpam-6931	30	13	metric	metric	ADJ
ejpam-6931	30	14	fixed	fix	VERB
ejpam-6931	30	15	-	-	PUNCT
ejpam-6931	30	16	point	point	NOUN
ejpam-6931	30	17	theory	theory	NOUN
ejpam-6931	30	18	(	(	PUNCT
ejpam-6931	30	19	fmfpt	fmfpt	NOUN
ejpam-6931	30	20	)	)	PUNCT
ejpam-6931	30	21	.	.	PUNCT
ejpam-6931	31	1	by	by	ADP
ejpam-6931	31	2	introducing	introduce	VERB
ejpam-6931	31	3	g	g	NOUN
ejpam-6931	31	4	-	-	PUNCT
ejpam-6931	31	5	completeness	completeness	NOUN
ejpam-6931	31	6	and	and	CCONJ
ejpam-6931	31	7	g	g	NOUN
ejpam-6931	31	8	-	-	PUNCT
ejpam-6931	31	9	cauchy	cauchy	ADJ
ejpam-6931	31	10	sequences	sequence	NOUN
ejpam-6931	31	11	,	,	PUNCT
ejpam-6931	31	12	he	he	PRON
ejpam-6931	31	13	established	establish	VERB
ejpam-6931	31	14	a	a	DET
ejpam-6931	31	15	fuzzy	fuzzy	ADJ
ejpam-6931	31	16	counterpart	counterpart	NOUN
ejpam-6931	31	17	to	to	ADP
ejpam-6931	31	18	the	the	DET
ejpam-6931	31	19	banach	banach	NOUN
ejpam-6931	31	20	contraction	contraction	NOUN
ejpam-6931	31	21	principle	principle	NOUN
ejpam-6931	31	22	on	on	ADP
ejpam-6931	31	23	fmss	fmss	PROPN
ejpam-6931	31	24	inspired	inspire	VERB
ejpam-6931	31	25	by	by	ADP
ejpam-6931	31	26	[	[	X
ejpam-6931	31	27	4	4	NUM
ejpam-6931	31	28	]	]	PUNCT
ejpam-6931	31	29	.	.	PUNCT
ejpam-6931	32	1	in	in	ADP
ejpam-6931	32	2	1994	1994	NUM
ejpam-6931	32	3	,	,	PUNCT
ejpam-6931	32	4	george	george	NOUN
ejpam-6931	32	5	and	and	CCONJ
ejpam-6931	32	6	veeramani	veeramani	NOUN
ejpam-6931	33	1	[	[	X
ejpam-6931	33	2	6	6	NUM
ejpam-6931	33	3	]	]	PUNCT
ejpam-6931	33	4	developed	develop	VERB
ejpam-6931	33	5	a	a	DET
ejpam-6931	33	6	hausdorff	hausdorff	NOUN
ejpam-6931	33	7	topology	topology	NOUN
ejpam-6931	33	8	for	for	ADP
ejpam-6931	33	9	fmss	fmss	NOUN
ejpam-6931	33	10	.	.	PUNCT
ejpam-6931	34	1	additionally	additionally	ADV
ejpam-6931	34	2	,	,	PUNCT
ejpam-6931	34	3	they	they	PRON
ejpam-6931	34	4	showed	show	VERB
ejpam-6931	34	5	several	several	ADJ
ejpam-6931	34	6	fixed	fix	VERB
ejpam-6931	34	7	-	-	PUNCT
ejpam-6931	34	8	point	point	NOUN
ejpam-6931	34	9	outcomes	outcome	NOUN
ejpam-6931	34	10	on	on	ADP
ejpam-6931	34	11	the	the	DET
ejpam-6931	34	12	modified	modify	VERB
ejpam-6931	34	13	spaces	space	NOUN
ejpam-6931	34	14	and	and	CCONJ
ejpam-6931	34	15	suggested	suggest	VERB
ejpam-6931	34	16	changes	change	NOUN
ejpam-6931	34	17	to	to	ADP
ejpam-6931	34	18	grabiec	grabiec	PROPN
ejpam-6931	34	19	’s	’s	PART
ejpam-6931	34	20	cauchy	cauchy	PROPN
ejpam-6931	34	21	sequence	sequence	NOUN
ejpam-6931	34	22	concept	concept	NOUN
ejpam-6931	34	23	.	.	PUNCT
ejpam-6931	35	1	in	in	ADP
ejpam-6931	35	2	2004	2004	NUM
ejpam-6931	35	3	,	,	PUNCT
ejpam-6931	35	4	park	park	NOUN
ejpam-6931	35	5	[	[	X
ejpam-6931	35	6	7	7	NUM
ejpam-6931	35	7	]	]	PUNCT
ejpam-6931	35	8	proposed	propose	VERB
ejpam-6931	35	9	the	the	DET
ejpam-6931	35	10	framework	framework	NOUN
ejpam-6931	35	11	of	of	ADP
ejpam-6931	35	12	ifmss	ifmss	PROPN
ejpam-6931	35	13	,	,	PUNCT
ejpam-6931	35	14	which	which	PRON
ejpam-6931	35	15	increased	increase	VERB
ejpam-6931	35	16	the	the	DET
ejpam-6931	35	17	scope	scope	NOUN
ejpam-6931	35	18	of	of	ADP
ejpam-6931	35	19	fuzzy	fuzzy	ADJ
ejpam-6931	35	20	metrics	metric	NOUN
ejpam-6931	35	21	.	.	PUNCT
ejpam-6931	36	1	researchers	researcher	NOUN
ejpam-6931	36	2	are	be	AUX
ejpam-6931	36	3	still	still	ADV
ejpam-6931	36	4	delving	delve	VERB
ejpam-6931	36	5	deeper	deeply	ADV
ejpam-6931	36	6	into	into	ADP
ejpam-6931	36	7	fmfpt	fmfpt	NOUN
ejpam-6931	36	8	.	.	PUNCT
ejpam-6931	37	1	the	the	DET
ejpam-6931	37	2	study	study	NOUN
ejpam-6931	37	3	mostly	mostly	ADV
ejpam-6931	37	4	goes	go	VERB
ejpam-6931	37	5	in	in	ADP
ejpam-6931	37	6	two	two	NUM
ejpam-6931	37	7	different	different	ADJ
ejpam-6931	37	8	directions	direction	NOUN
ejpam-6931	37	9	:	:	PUNCT
ejpam-6931	37	10	expanding	expand	VERB
ejpam-6931	37	11	the	the	DET
ejpam-6931	37	12	scope	scope	NOUN
ejpam-6931	37	13	of	of	ADP
ejpam-6931	37	14	fmss	fmss	PROPN
ejpam-6931	37	15	(	(	PUNCT
ejpam-6931	37	16	comprehensive	comprehensive	ADJ
ejpam-6931	37	17	analysis	analysis	NOUN
ejpam-6931	37	18	provided	provide	VERB
ejpam-6931	37	19	in	in	ADP
ejpam-6931	37	20	[	[	PUNCT
ejpam-6931	37	21	8–13	8–13	NOUN
ejpam-6931	37	22	]	]	PUNCT
ejpam-6931	37	23	)	)	PUNCT
ejpam-6931	37	24	and	and	CCONJ
ejpam-6931	37	25	examining	examine	VERB
ejpam-6931	37	26	the	the	DET
ejpam-6931	37	27	existence	existence	NOUN
ejpam-6931	37	28	of	of	ADP
ejpam-6931	37	29	fixed	fix	VERB
ejpam-6931	37	30	points	point	NOUN
ejpam-6931	37	31	for	for	ADP
ejpam-6931	37	32	mappings	mapping	NOUN
ejpam-6931	37	33	adhering	adhere	VERB
ejpam-6931	37	34	to	to	ADP
ejpam-6931	37	35	various	various	ADJ
ejpam-6931	37	36	contractive	contractive	ADJ
ejpam-6931	37	37	conditions	condition	NOUN
ejpam-6931	37	38	(	(	PUNCT
ejpam-6931	37	39	for	for	ADP
ejpam-6931	37	40	comprehensive	comprehensive	ADJ
ejpam-6931	37	41	information	information	NOUN
ejpam-6931	37	42	,	,	PUNCT
ejpam-6931	37	43	refer	refer	VERB
ejpam-6931	37	44	to	to	ADP
ejpam-6931	37	45	[	[	X
ejpam-6931	37	46	14–17	14–17	NUM
ejpam-6931	37	47	]	]	PUNCT
ejpam-6931	37	48	.	.	PUNCT
ejpam-6931	38	1	azam	azam	PROPN
ejpam-6931	38	2	et	et	PROPN
ejpam-6931	38	3	al	al	PROPN
ejpam-6931	38	4	.	.	PUNCT
ejpam-6931	39	1	[	[	X
ejpam-6931	39	2	18	18	NUM
ejpam-6931	39	3	]	]	PUNCT
ejpam-6931	39	4	introduced	introduce	VERB
ejpam-6931	39	5	complex	complex	ADV
ejpam-6931	39	6	-	-	PUNCT
ejpam-6931	39	7	valued	value	VERB
ejpam-6931	39	8	metric	metric	ADJ
ejpam-6931	39	9	spaces	space	NOUN
ejpam-6931	39	10	to	to	ADP
ejpam-6931	39	11	metric	metric	ADJ
ejpam-6931	39	12	fixed	fix	VERB
ejpam-6931	39	13	-	-	PUNCT
ejpam-6931	39	14	point	point	NOUN
ejpam-6931	39	15	theory	theory	NOUN
ejpam-6931	39	16	in	in	ADP
ejpam-6931	39	17	2011	2011	NUM
ejpam-6931	39	18	.	.	PUNCT
ejpam-6931	40	1	instead	instead	ADV
ejpam-6931	40	2	of	of	ADP
ejpam-6931	40	3	using	use	VERB
ejpam-6931	40	4	non	non	ADJ
ejpam-6931	40	5	-	-	ADJ
ejpam-6931	40	6	negative	negative	ADJ
ejpam-6931	40	7	real	real	ADJ
ejpam-6931	40	8	numbers	number	NOUN
ejpam-6931	40	9	,	,	PUNCT
ejpam-6931	40	10	they	they	PRON
ejpam-6931	40	11	used	use	VERB
ejpam-6931	40	12	ordered	order	VERB
ejpam-6931	40	13	complex	complex	ADJ
ejpam-6931	40	14	numbers	number	NOUN
ejpam-6931	40	15	to	to	PART
ejpam-6931	40	16	provide	provide	VERB
ejpam-6931	40	17	fixed	fix	VERB
ejpam-6931	40	18	-	-	PUNCT
ejpam-6931	40	19	point	point	NOUN
ejpam-6931	40	20	results	result	NOUN
ejpam-6931	40	21	for	for	ADP
ejpam-6931	40	22	translations	translation	NOUN
ejpam-6931	40	23	that	that	PRON
ejpam-6931	40	24	meet	meet	VERB
ejpam-6931	40	25	logical	logical	ADJ
ejpam-6931	40	26	inequality	inequality	NOUN
ejpam-6931	40	27	criteria	criterion	NOUN
ejpam-6931	40	28	.	.	PUNCT
ejpam-6931	41	1	shukla	shukla	NOUN
ejpam-6931	41	2	et	et	PROPN
ejpam-6931	41	3	al	al	PROPN
ejpam-6931	41	4	.	.	PUNCT
ejpam-6931	42	1	[	[	X
ejpam-6931	42	2	19	19	NUM
ejpam-6931	42	3	]	]	PUNCT
ejpam-6931	42	4	used	use	VERB
ejpam-6931	42	5	this	this	DET
ejpam-6931	42	6	notion	notion	NOUN
ejpam-6931	42	7	in	in	ADP
ejpam-6931	42	8	fmfpt	fmfpt	NOUN
ejpam-6931	42	9	.	.	PUNCT
ejpam-6931	43	1	the	the	DET
ejpam-6931	43	2	authors	author	NOUN
ejpam-6931	43	3	defined	define	VERB
ejpam-6931	43	4	complex	complex	ADV
ejpam-6931	43	5	-	-	PUNCT
ejpam-6931	43	6	valued	value	VERB
ejpam-6931	43	7	fuzzy	fuzzy	ADJ
ejpam-6931	43	8	metric	metric	ADJ
ejpam-6931	43	9	spaces	space	NOUN
ejpam-6931	43	10	(	(	PUNCT
ejpam-6931	43	11	cvfmss	cvfmss	NOUN
ejpam-6931	43	12	)	)	PUNCT
ejpam-6931	43	13	and	and	CCONJ
ejpam-6931	43	14	identified	identify	VERB
ejpam-6931	43	15	fixed	fix	VERB
ejpam-6931	43	16	-	-	PUNCT
ejpam-6931	43	17	point	point	NOUN
ejpam-6931	43	18	transformations	transformation	NOUN
ejpam-6931	43	19	that	that	PRON
ejpam-6931	43	20	meet	meet	VERB
ejpam-6931	43	21	contractive	contractive	ADJ
ejpam-6931	43	22	conditions	condition	NOUN
ejpam-6931	43	23	.	.	PUNCT
ejpam-6931	44	1	umar	umar	PROPN
ejpam-6931	44	2	et	et	PROPN
ejpam-6931	44	3	al	al	PROPN
ejpam-6931	44	4	.	.	PUNCT
ejpam-6931	45	1	[	[	X
ejpam-6931	45	2	20	20	NUM
ejpam-6931	45	3	]	]	PUNCT
ejpam-6931	45	4	worked	work	VERB
ejpam-6931	45	5	on	on	ADP
ejpam-6931	45	6	some	some	DET
ejpam-6931	45	7	common	common	ADJ
ejpam-6931	45	8	fixed	fix	VERB
ejpam-6931	45	9	-	-	PUNCT
ejpam-6931	45	10	point	point	NOUN
ejpam-6931	45	11	theorems	theorem	NOUN
ejpam-6931	45	12	in	in	ADP
ejpam-6931	45	13	neutrosophic	neutrosophic	ADJ
ejpam-6931	45	14	metric	metric	ADJ
ejpam-6931	45	15	spaces	space	NOUN
ejpam-6931	45	16	(	(	PUNCT
ejpam-6931	45	17	nmss	nmss	ADJ
ejpam-6931	45	18	)	)	PUNCT
ejpam-6931	45	19	.	.	PUNCT
ejpam-6931	46	1	current	current	ADJ
ejpam-6931	46	2	research	research	NOUN
ejpam-6931	46	3	focuses	focus	VERB
ejpam-6931	46	4	on	on	ADP
ejpam-6931	46	5	analyzing	analyze	VERB
ejpam-6931	46	6	fixed	fix	VERB
ejpam-6931	46	7	-	-	PUNCT
ejpam-6931	46	8	point	point	NOUN
ejpam-6931	46	9	translations	translation	NOUN
ejpam-6931	46	10	using	use	VERB
ejpam-6931	46	11	cvfmss	cvfmss	NOUN
ejpam-6931	46	12	.	.	PUNCT
ejpam-6931	47	1	examples	example	NOUN
ejpam-6931	47	2	of	of	ADP
ejpam-6931	47	3	relevant	relevant	ADJ
ejpam-6931	47	4	research	research	NOUN
ejpam-6931	47	5	include	include	VERB
ejpam-6931	47	6	publications	publication	NOUN
ejpam-6931	47	7	by	by	ADP
ejpam-6931	47	8	[	[	X
ejpam-6931	47	9	21	21	NUM
ejpam-6931	47	10	,	,	PUNCT
ejpam-6931	47	11	22	22	NUM
ejpam-6931	47	12	]	]	PUNCT
ejpam-6931	47	13	and	and	CCONJ
ejpam-6931	47	14	humaira	humaira	PROPN
ejpam-6931	47	15	et	et	PROPN
ejpam-6931	47	16	al	al	PROPN
ejpam-6931	47	17	.	.	PUNCT
ejpam-6931	48	1	[	[	X
ejpam-6931	48	2	23–27	23–27	NUM
ejpam-6931	48	3	]	]	X
ejpam-6931	48	4	,	,	PUNCT
ejpam-6931	48	5	which	which	PRON
ejpam-6931	48	6	provide	provide	VERB
ejpam-6931	48	7	practical	practical	ADJ
ejpam-6931	48	8	applications	application	NOUN
ejpam-6931	48	9	.	.	PUNCT
ejpam-6931	49	1	kiri̧	kiri̧	PROPN
ejpam-6931	49	2	sci	sci	PROPN
ejpam-6931	49	3	s.	s.	PROPN
ejpam-6931	49	4	m.	m.	PROPN
ejpam-6931	49	5	u.	u.	PROPN
ejpam-6931	49	6	ud	ud	AUX
ejpam-6931	49	7	-	-	PUNCT
ejpam-6931	49	8	din	din	VERB
ejpam-6931	49	9	et	et	PROPN
ejpam-6931	49	10	al	al	PROPN
ejpam-6931	49	11	.	.	PUNCT
ejpam-6931	49	12	/	/	SYM
ejpam-6931	49	13	eur	eur	PROPN
ejpam-6931	49	14	.	.	PUNCT
ejpam-6931	50	1	j.	j.	PROPN
ejpam-6931	50	2	pure	pure	PROPN
ejpam-6931	50	3	appl	appl	PROPN
ejpam-6931	50	4	.	.	PROPN
ejpam-6931	50	5	math	math	PROPN
ejpam-6931	50	6	,	,	PUNCT
ejpam-6931	50	7	18	18	NUM
ejpam-6931	50	8	(	(	PUNCT
ejpam-6931	50	9	4	4	NUM
ejpam-6931	50	10	)	)	PUNCT
ejpam-6931	50	11	(	(	PUNCT
ejpam-6931	50	12	2025	2025	NUM
ejpam-6931	50	13	)	)	PUNCT
ejpam-6931	50	14	,	,	PUNCT
ejpam-6931	50	15	6931	6931	NUM
ejpam-6931	50	16	3	3	NUM
ejpam-6931	50	17	of	of	ADP
ejpam-6931	50	18	38	38	NUM
ejpam-6931	50	19	and	and	CCONJ
ejpam-6931	50	20	simsek	simsek	VERB
ejpam-6931	50	21	[	[	X
ejpam-6931	50	22	28	28	NUM
ejpam-6931	50	23	]	]	PUNCT
ejpam-6931	50	24	proposed	propose	VERB
ejpam-6931	50	25	nmss	nmss	PROPN
ejpam-6931	50	26	for	for	ADP
ejpam-6931	50	27	membership	membership	NOUN
ejpam-6931	50	28	,	,	PUNCT
ejpam-6931	50	29	nonmembership	nonmembership	NOUN
ejpam-6931	50	30	,	,	PUNCT
ejpam-6931	50	31	and	and	CCONJ
ejpam-6931	50	32	naturalness	naturalness	NOUN
ejpam-6931	50	33	functions	function	NOUN
ejpam-6931	50	34	.	.	PUNCT
ejpam-6931	51	1	the	the	DET
ejpam-6931	51	2	authors	author	NOUN
ejpam-6931	51	3	in	in	ADP
ejpam-6931	51	4	[	[	X
ejpam-6931	51	5	29	29	NUM
ejpam-6931	51	6	,	,	PUNCT
ejpam-6931	51	7	30	30	NUM
ejpam-6931	51	8	]	]	PUNCT
ejpam-6931	51	9	and	and	CCONJ
ejpam-6931	51	10	sowndrarajan	sowndrarajan	PROPN
ejpam-6931	51	11	et	et	PROPN
ejpam-6931	51	12	al	al	PROPN
ejpam-6931	51	13	.	.	PUNCT
ejpam-6931	52	1	[	[	X
ejpam-6931	52	2	31	31	NUM
ejpam-6931	52	3	]	]	PUNCT
ejpam-6931	52	4	demonstrated	demonstrate	VERB
ejpam-6931	52	5	fixed	fix	VERB
ejpam-6931	52	6	point	point	NOUN
ejpam-6931	52	7	findings	finding	NOUN
ejpam-6931	52	8	in	in	ADP
ejpam-6931	52	9	nmss	nmss	PROPN
ejpam-6931	52	10	.	.	PUNCT
ejpam-6931	53	1	umar	umar	PROPN
ejpam-6931	53	2	et	et	PROPN
ejpam-6931	53	3	al	al	PROPN
ejpam-6931	53	4	.	.	PUNCT
ejpam-6931	54	1	[	[	X
ejpam-6931	54	2	32	32	NUM
ejpam-6931	54	3	]	]	PUNCT
ejpam-6931	54	4	worked	work	VERB
ejpam-6931	54	5	on	on	ADP
ejpam-6931	54	6	fixed	fix	VERB
ejpam-6931	54	7	point	point	NOUN
ejpam-6931	54	8	results	result	NOUN
ejpam-6931	54	9	in	in	ADP
ejpam-6931	54	10	orthogonal	orthogonal	ADJ
ejpam-6931	54	11	nmss	nmss	PROPN
ejpam-6931	54	12	.	.	PUNCT
ejpam-6931	55	1	see	see	VERB
ejpam-6931	55	2	[	[	X
ejpam-6931	55	3	33	33	NUM
ejpam-6931	55	4	,	,	PUNCT
ejpam-6931	55	5	34	34	NUM
ejpam-6931	55	6	]	]	PUNCT
ejpam-6931	55	7	for	for	ADP
ejpam-6931	55	8	applications	application	NOUN
ejpam-6931	55	9	and	and	CCONJ
ejpam-6931	55	10	research	research	NOUN
ejpam-6931	55	11	direction	direction	NOUN
ejpam-6931	55	12	.	.	PUNCT
ejpam-6931	56	1	this	this	DET
ejpam-6931	56	2	paper	paper	NOUN
ejpam-6931	56	3	introduces	introduce	NOUN
ejpam-6931	56	4	cvnmss	cvnmss	NOUN
ejpam-6931	56	5	(	(	PUNCT
ejpam-6931	56	6	cvnmss	cvnmss	NOUN
ejpam-6931	56	7	)	)	PUNCT
ejpam-6931	56	8	as	as	ADP
ejpam-6931	56	9	a	a	DET
ejpam-6931	56	10	new	new	ADJ
ejpam-6931	56	11	type	type	NOUN
ejpam-6931	56	12	of	of	ADP
ejpam-6931	56	13	fuzzy	fuzzy	ADJ
ejpam-6931	56	14	metric	metric	ADJ
ejpam-6931	56	15	space	space	NOUN
ejpam-6931	56	16	.	.	PUNCT
ejpam-6931	57	1	this	this	DET
ejpam-6931	57	2	novel	novel	ADJ
ejpam-6931	57	3	idea	idea	NOUN
ejpam-6931	57	4	encompasses	encompass	VERB
ejpam-6931	57	5	both	both	DET
ejpam-6931	57	6	cvfmss	cvfmss	NOUN
ejpam-6931	57	7	by	by	ADP
ejpam-6931	57	8	[	[	X
ejpam-6931	57	9	19	19	NUM
ejpam-6931	57	10	]	]	PUNCT
ejpam-6931	57	11	and	and	CCONJ
ejpam-6931	57	12	ifmss	ifmss	VERB
ejpam-6931	57	13	by	by	ADP
ejpam-6931	57	14	[	[	X
ejpam-6931	57	15	7	7	NUM
ejpam-6931	57	16	]	]	PUNCT
ejpam-6931	57	17	.	.	PUNCT
ejpam-6931	58	1	we	we	PRON
ejpam-6931	58	2	give	give	VERB
ejpam-6931	58	3	some	some	DET
ejpam-6931	58	4	fixed	fix	VERB
ejpam-6931	58	5	-	-	PUNCT
ejpam-6931	58	6	point	point	NOUN
ejpam-6931	58	7	outcomes	outcome	NOUN
ejpam-6931	58	8	for	for	ADP
ejpam-6931	58	9	transformations	transformation	NOUN
ejpam-6931	58	10	with	with	ADP
ejpam-6931	58	11	contractive	contractive	ADJ
ejpam-6931	58	12	constraints	constraint	NOUN
ejpam-6931	58	13	in	in	ADP
ejpam-6931	58	14	freshly	freshly	ADV
ejpam-6931	58	15	formed	form	VERB
ejpam-6931	58	16	spaces	space	NOUN
ejpam-6931	58	17	.	.	PUNCT
ejpam-6931	59	1	we	we	PRON
ejpam-6931	59	2	apply	apply	VERB
ejpam-6931	59	3	banach	banach	NOUN
ejpam-6931	59	4	’s	’s	PART
ejpam-6931	59	5	fuzzy	fuzzy	ADJ
ejpam-6931	59	6	variation	variation	NOUN
ejpam-6931	59	7	to	to	ADP
ejpam-6931	59	8	intuitionistic	intuitionistic	ADJ
ejpam-6931	59	9	fuzzy	fuzzy	ADJ
ejpam-6931	59	10	spaces	space	NOUN
ejpam-6931	59	11	,	,	PUNCT
ejpam-6931	59	12	resulting	result	VERB
ejpam-6931	59	13	in	in	ADP
ejpam-6931	59	14	common	common	ADJ
ejpam-6931	59	15	fixedpoint	fixedpoint	NOUN
ejpam-6931	59	16	outcomes	outcome	NOUN
ejpam-6931	59	17	in	in	ADP
ejpam-6931	59	18	cvfmss	cvfmss	NOUN
ejpam-6931	59	19	.	.	PUNCT
ejpam-6931	60	1	our	our	PRON
ejpam-6931	60	2	findings	finding	NOUN
ejpam-6931	60	3	are	be	AUX
ejpam-6931	60	4	demonstrated	demonstrate	VERB
ejpam-6931	60	5	through	through	ADP
ejpam-6931	60	6	practical	practical	ADJ
ejpam-6931	60	7	examples	example	NOUN
ejpam-6931	60	8	and	and	CCONJ
ejpam-6931	60	9	applications	application	NOUN
ejpam-6931	60	10	.	.	PUNCT
ejpam-6931	61	1	2	2	X
ejpam-6931	61	2	.	.	X
ejpam-6931	61	3	preliminaries	preliminary	NOUN
ejpam-6931	61	4	this	this	DET
ejpam-6931	61	5	section	section	NOUN
ejpam-6931	61	6	summarizes	summarize	VERB
ejpam-6931	61	7	key	key	ADJ
ejpam-6931	61	8	concepts	concept	NOUN
ejpam-6931	61	9	in	in	ADP
ejpam-6931	61	10	cvfmss	cvfmss	NOUN
ejpam-6931	61	11	,	,	PUNCT
ejpam-6931	61	12	as	as	SCONJ
ejpam-6931	61	13	defined	define	VERB
ejpam-6931	61	14	in	in	ADP
ejpam-6931	61	15	previous	previous	ADJ
ejpam-6931	61	16	work	work	NOUN
ejpam-6931	61	17	by	by	ADP
ejpam-6931	61	18	[	[	X
ejpam-6931	61	19	19	19	NUM
ejpam-6931	61	20	]	]	PUNCT
ejpam-6931	61	21	.	.	PUNCT
ejpam-6931	62	1	throughout	throughout	ADP
ejpam-6931	62	2	the	the	DET
ejpam-6931	62	3	paper	paper	NOUN
ejpam-6931	62	4	,	,	PUNCT
ejpam-6931	62	5	we	we	PRON
ejpam-6931	62	6	denote	denote	VERB
ejpam-6931	62	7	the	the	DET
ejpam-6931	62	8	set	set	NOUN
ejpam-6931	62	9	of	of	ADP
ejpam-6931	62	10	positive	positive	ADJ
ejpam-6931	62	11	integers	integer	NOUN
ejpam-6931	62	12	by	by	ADP
ejpam-6931	62	13	m	m	PRON
ejpam-6931	62	14	and	and	CCONJ
ejpam-6931	62	15	the	the	DET
ejpam-6931	62	16	set	set	NOUN
ejpam-6931	62	17	of	of	ADP
ejpam-6931	62	18	nonnegative	nonnegative	ADJ
ejpam-6931	62	19	integers	integer	NOUN
ejpam-6931	62	20	by	by	ADP
ejpam-6931	62	21	m0	m0	NOUN
ejpam-6931	62	22	.	.	PUNCT
ejpam-6931	63	1	we	we	PRON
ejpam-6931	63	2	represent	represent	VERB
ejpam-6931	63	3	any	any	DET
ejpam-6931	63	4	complex	complex	ADJ
ejpam-6931	63	5	number	number	NOUN
ejpam-6931	63	6	z	z	NOUN
ejpam-6931	64	1	=	=	SYM
ejpam-6931	64	2	c	c	PROPN
ejpam-6931	65	1	+	+	CCONJ
ejpam-6931	65	2	i	i	PROPN
ejpam-6931	65	3	d	d	NOUN
ejpam-6931	65	4	by	by	ADP
ejpam-6931	65	5	(	(	PUNCT
ejpam-6931	65	6	c	c	X
ejpam-6931	65	7	,	,	PUNCT
ejpam-6931	65	8	d	d	NOUN
ejpam-6931	65	9	)	)	PUNCT
ejpam-6931	65	10	.	.	PUNCT
ejpam-6931	65	11	assume	assume	VERB
ejpam-6931	65	12	that	that	SCONJ
ejpam-6931	65	13	s	s	VERB
ejpam-6931	65	14	=	=	X
ejpam-6931	65	15	{	{	PUNCT
ejpam-6931	65	16	(	(	PUNCT
ejpam-6931	65	17	c	c	NOUN
ejpam-6931	65	18	,	,	PUNCT
ejpam-6931	65	19	d	d	NOUN
ejpam-6931	65	20	)	)	PUNCT
ejpam-6931	65	21	:	:	PUNCT
ejpam-6931	65	22	0	0	NUM
ejpam-6931	65	23	≤	≤	NUM
ejpam-6931	65	24	c	c	X
ejpam-6931	65	25	<	<	X
ejpam-6931	65	26	∞	∞	PROPN
ejpam-6931	65	27	,	,	PUNCT
ejpam-6931	65	28	0	0	NUM
ejpam-6931	65	29	≤	≤	NUM
ejpam-6931	66	1	d	d	X
ejpam-6931	66	2	<	<	X
ejpam-6931	66	3	∞	∞	NUM
ejpam-6931	66	4	}	}	PUNCT
ejpam-6931	66	5	⊂	⊂	PROPN
ejpam-6931	67	1	c	c	X
ejpam-6931	67	2	,	,	PUNCT
ejpam-6931	67	3	where	where	SCONJ
ejpam-6931	67	4	c	c	PROPN
ejpam-6931	67	5	is	be	AUX
ejpam-6931	67	6	the	the	DET
ejpam-6931	67	7	set	set	NOUN
ejpam-6931	67	8	of	of	ADP
ejpam-6931	67	9	complex	complex	ADJ
ejpam-6931	67	10	numbers	number	NOUN
ejpam-6931	67	11	.	.	PUNCT
ejpam-6931	68	1	we	we	PRON
ejpam-6931	68	2	express	express	VERB
ejpam-6931	68	3	(	(	PUNCT
ejpam-6931	68	4	0,0),(1,1	0,0),(1,1	PROPN
ejpam-6931	68	5	)	)	PUNCT
ejpam-6931	68	6	and	and	CCONJ
ejpam-6931	68	7	(	(	PUNCT
ejpam-6931	68	8	3,1	3,1	NOUN
ejpam-6931	68	9	)	)	PUNCT
ejpam-6931	68	10	in	in	ADP
ejpam-6931	68	11	c	c	PROPN
ejpam-6931	68	12	as	as	ADP
ejpam-6931	68	13	∅,ℑ′	∅,ℑ′	NOUN
ejpam-6931	68	14	and	and	CCONJ
ejpam-6931	68	15	ℑ	ℑ	PROPN
ejpam-6931	68	16	respectively	respectively	ADV
ejpam-6931	68	17	.	.	PUNCT
ejpam-6931	69	1	we	we	PRON
ejpam-6931	69	2	denote	denote	VERB
ejpam-6931	69	3	the	the	DET
ejpam-6931	69	4	closed	closed	ADJ
ejpam-6931	69	5	unit	unit	NOUN
ejpam-6931	69	6	complex	complex	ADJ
ejpam-6931	69	7	interval	interval	NOUN
ejpam-6931	69	8	by	by	ADP
ejpam-6931	69	9	t	t	PROPN
ejpam-6931	69	10	=	=	SYM
ejpam-6931	69	11	{	{	PUNCT
ejpam-6931	69	12	(	(	PUNCT
ejpam-6931	69	13	c	c	NOUN
ejpam-6931	69	14	,	,	PUNCT
ejpam-6931	69	15	d	d	NOUN
ejpam-6931	69	16	)	)	PUNCT
ejpam-6931	69	17	:	:	PUNCT
ejpam-6931	69	18	0	0	NUM
ejpam-6931	70	1	≤	≤	NUM
ejpam-6931	70	2	c	c	NOUN
ejpam-6931	70	3	≤	≤	NUM
ejpam-6931	70	4	1	1	NUM
ejpam-6931	70	5	,	,	PUNCT
ejpam-6931	70	6	0	0	NUM
ejpam-6931	70	7	≤	≤	NUM
ejpam-6931	70	8	d	d	NOUN
ejpam-6931	70	9	≤	≤	NUM
ejpam-6931	70	10	1	1	NUM
ejpam-6931	70	11	}	}	PUNCT
ejpam-6931	70	12	,	,	PUNCT
ejpam-6931	70	13	the	the	DET
ejpam-6931	70	14	open	open	ADJ
ejpam-6931	70	15	unit	unit	NOUN
ejpam-6931	70	16	complex	complex	ADJ
ejpam-6931	70	17	interval	interval	NOUN
ejpam-6931	70	18	by	by	ADP
ejpam-6931	70	19	t0	t0	PROPN
ejpam-6931	70	20	=	=	SYM
ejpam-6931	70	21	{	{	PUNCT
ejpam-6931	70	22	(	(	PUNCT
ejpam-6931	70	23	c	c	NOUN
ejpam-6931	70	24	,	,	PUNCT
ejpam-6931	70	25	d	d	NOUN
ejpam-6931	70	26	)	)	PUNCT
ejpam-6931	70	27	:	:	PUNCT
ejpam-6931	70	28	0	0	PUNCT
ejpam-6931	70	29	<	<	X
ejpam-6931	70	30	c	c	X
ejpam-6931	70	31	<	<	X
ejpam-6931	70	32	1	1	NUM
ejpam-6931	70	33	,	,	PUNCT
ejpam-6931	70	34	0	0	PUNCT
ejpam-6931	70	35	<	<	X
ejpam-6931	70	36	d	d	X
ejpam-6931	70	37	<	<	X
ejpam-6931	70	38	1	1	NUM
ejpam-6931	70	39	}	}	PUNCT
ejpam-6931	70	40	,	,	PUNCT
ejpam-6931	70	41	and	and	CCONJ
ejpam-6931	70	42	s0	s0	PROPN
ejpam-6931	70	43	=	=	SYM
ejpam-6931	70	44	{	{	PUNCT
ejpam-6931	70	45	(	(	PUNCT
ejpam-6931	70	46	c	c	NOUN
ejpam-6931	70	47	,	,	PUNCT
ejpam-6931	70	48	d	d	NOUN
ejpam-6931	70	49	)	)	PUNCT
ejpam-6931	70	50	:	:	PUNCT
ejpam-6931	70	51	0	0	PUNCT
ejpam-6931	70	52	<	<	X
ejpam-6931	70	53	c	c	X
ejpam-6931	70	54	<	<	X
ejpam-6931	70	55	∞	∞	PROPN
ejpam-6931	70	56	,	,	PUNCT
ejpam-6931	70	57	0	0	PUNCT
ejpam-6931	70	58	<	<	X
ejpam-6931	70	59	d	d	X
ejpam-6931	70	60	<	<	X
ejpam-6931	70	61	∞	∞	NUM
ejpam-6931	70	62	}	}	PUNCT
ejpam-6931	70	63	.	.	PUNCT
ejpam-6931	71	1	assume	assume	VERB
ejpam-6931	71	2	that	that	SCONJ
ejpam-6931	71	3	⪯	⪯	NOUN
ejpam-6931	71	4	is	be	AUX
ejpam-6931	71	5	a	a	DET
ejpam-6931	71	6	partial	partial	ADJ
ejpam-6931	71	7	order	order	NOUN
ejpam-6931	71	8	in	in	ADP
ejpam-6931	71	9	c	c	PROPN
ejpam-6931	71	10	,	,	PUNCT
ejpam-6931	71	11	e2	e2	PROPN
ejpam-6931	71	12	−	−	PROPN
ejpam-6931	71	13	e1	e1	PROPN
ejpam-6931	71	14	∈	∈	PROPN
ejpam-6931	71	15	s	s	VERB
ejpam-6931	71	16	if	if	SCONJ
ejpam-6931	71	17	and	and	CCONJ
ejpam-6931	71	18	only	only	ADV
ejpam-6931	71	19	if	if	SCONJ
ejpam-6931	71	20	e1	e1	PROPN
ejpam-6931	71	21	⪯	⪯	PROPN
ejpam-6931	71	22	e2	e2	PROPN
ejpam-6931	71	23	,	,	PUNCT
ejpam-6931	71	24	where	where	SCONJ
ejpam-6931	71	25	e1	e1	NOUN
ejpam-6931	71	26	,	,	PUNCT
ejpam-6931	71	27	e2	e2	PROPN
ejpam-6931	71	28	∈	∈	PROPN
ejpam-6931	71	29	c.	c.	NOUN
ejpam-6931	71	30	we	we	PRON
ejpam-6931	71	31	write	write	VERB
ejpam-6931	71	32	e1	e1	PROPN
ejpam-6931	71	33	≺	≺	NOUN
ejpam-6931	71	34	e2	e2	PROPN
ejpam-6931	71	35	to	to	PART
ejpam-6931	71	36	express	express	VERB
ejpam-6931	71	37	re(e2	re(e2	NOUN
ejpam-6931	71	38	)	)	PUNCT
ejpam-6931	71	39	>	>	PUNCT
ejpam-6931	72	1	re(e1	re(e1	NOUN
ejpam-6931	72	2	)	)	PUNCT
ejpam-6931	72	3	and	and	CCONJ
ejpam-6931	72	4	im(e2	im(e2	NOUN
ejpam-6931	72	5	)	)	PUNCT
ejpam-6931	72	6	>	>	X
ejpam-6931	72	7	im(e1	im(e1	NOUN
ejpam-6931	72	8	)	)	PUNCT
ejpam-6931	72	9	.	.	PUNCT
ejpam-6931	73	1	it	it	PRON
ejpam-6931	73	2	is	be	AUX
ejpam-6931	73	3	obvious	obvious	ADJ
ejpam-6931	73	4	that	that	SCONJ
ejpam-6931	73	5	e1	e1	NOUN
ejpam-6931	73	6	≺	≺	NOUN
ejpam-6931	73	7	e2	e2	PROPN
ejpam-6931	73	8	if	if	SCONJ
ejpam-6931	73	9	and	and	CCONJ
ejpam-6931	73	10	only	only	ADV
ejpam-6931	73	11	if	if	SCONJ
ejpam-6931	73	12	e2	e2	PROPN
ejpam-6931	73	13	−	−	PROPN
ejpam-6931	73	14	e1	e1	PROPN
ejpam-6931	73	15	∈	∈	PROPN
ejpam-6931	73	16	s0	s0	PROPN
ejpam-6931	73	17	.	.	PUNCT
ejpam-6931	73	18	assume	assume	VERB
ejpam-6931	73	19	that	that	SCONJ
ejpam-6931	73	20	{	{	PUNCT
ejpam-6931	73	21	en	en	X
ejpam-6931	73	22	}	}	PUNCT
ejpam-6931	73	23	is	be	AUX
ejpam-6931	73	24	a	a	DET
ejpam-6931	73	25	sequence	sequence	NOUN
ejpam-6931	73	26	in	in	ADP
ejpam-6931	73	27	c.	c.	NOUN
ejpam-6931	73	28	if	if	SCONJ
ejpam-6931	73	29	for	for	ADP
ejpam-6931	73	30	each	each	DET
ejpam-6931	73	31	n	n	PRON
ejpam-6931	73	32	∈	∈	PROPN
ejpam-6931	73	33	m	m	PROPN
ejpam-6931	73	34	,	,	PUNCT
ejpam-6931	73	35	cn+1	cn+1	VERB
ejpam-6931	73	36	⪯	⪯	NOUN
ejpam-6931	73	37	en	en	ADV
ejpam-6931	73	38	or	or	CCONJ
ejpam-6931	73	39	en	en	ADP
ejpam-6931	73	40	⪯	⪯	NOUN
ejpam-6931	73	41	en+1	en+1	PROPN
ejpam-6931	73	42	hold	hold	VERB
ejpam-6931	73	43	,	,	PUNCT
ejpam-6931	73	44	then	then	ADV
ejpam-6931	73	45	{	{	PUNCT
ejpam-6931	73	46	en	en	X
ejpam-6931	73	47	}	}	PUNCT
ejpam-6931	73	48	is	be	AUX
ejpam-6931	73	49	called	call	VERB
ejpam-6931	73	50	a	a	DET
ejpam-6931	73	51	monotonic	monotonic	ADJ
ejpam-6931	73	52	sequence	sequence	NOUN
ejpam-6931	73	53	in	in	ADP
ejpam-6931	73	54	relation	relation	NOUN
ejpam-6931	73	55	to	to	PART
ejpam-6931	73	56	⪯	⪯	VERB
ejpam-6931	73	57	.	.	PUNCT
ejpam-6931	74	1	remark	remark	VERB
ejpam-6931	74	2	1	1	NUM
ejpam-6931	74	3	.	.	PUNCT
ejpam-6931	75	1	[	[	X
ejpam-6931	75	2	19	19	NUM
ejpam-6931	75	3	]	]	PUNCT
ejpam-6931	75	4	let	let	VERB
ejpam-6931	75	5	en	en	X
ejpam-6931	75	6	∈	∈	NOUN
ejpam-6931	75	7	s	s	PART
ejpam-6931	75	8	for	for	ADP
ejpam-6931	75	9	every	every	DET
ejpam-6931	75	10	n	n	PRON
ejpam-6931	75	11	∈	∈	PROPN
ejpam-6931	75	12	m	m	NOUN
ejpam-6931	75	13	,	,	PUNCT
ejpam-6931	75	14	all	all	PRON
ejpam-6931	75	15	of	of	ADP
ejpam-6931	75	16	the	the	DET
ejpam-6931	75	17	following	follow	VERB
ejpam-6931	75	18	propositions	proposition	NOUN
ejpam-6931	75	19	are	be	AUX
ejpam-6931	75	20	true	true	ADJ
ejpam-6931	75	21	:	:	PUNCT
ejpam-6931	75	22	(	(	PUNCT
ejpam-6931	75	23	1	1	X
ejpam-6931	75	24	)	)	PUNCT
ejpam-6931	75	25	if	if	SCONJ
ejpam-6931	75	26	{	{	PUNCT
ejpam-6931	75	27	en	en	X
ejpam-6931	75	28	}	}	PUNCT
ejpam-6931	75	29	is	be	AUX
ejpam-6931	75	30	a	a	DET
ejpam-6931	75	31	monotonic	monotonic	ADJ
ejpam-6931	75	32	sequence	sequence	NOUN
ejpam-6931	75	33	with	with	ADP
ejpam-6931	75	34	respect	respect	NOUN
ejpam-6931	75	35	to	to	ADP
ejpam-6931	75	36	⪯	⪯	NOUN
ejpam-6931	75	37	and	and	CCONJ
ejpam-6931	75	38	for	for	ADP
ejpam-6931	75	39	some	some	DET
ejpam-6931	75	40	x́	x́	PROPN
ejpam-6931	75	41	,	,	PUNCT
ejpam-6931	75	42	ý	ý	PROPN
ejpam-6931	75	43	∈	∈	PROPN
ejpam-6931	75	44	s	s	PART
ejpam-6931	75	45	fulfil	fulfil	NOUN
ejpam-6931	75	46	x́	x́	PROPN
ejpam-6931	75	47	⪯	⪯	AUX
ejpam-6931	75	48	en	en	PROPN
ejpam-6931	75	49	⪯	⪯	PROPN
ejpam-6931	75	50	ý	ý	ADJ
ejpam-6931	75	51	for	for	ADP
ejpam-6931	75	52	each	each	DET
ejpam-6931	75	53	n	n	PRON
ejpam-6931	75	54	∈	∈	PROPN
ejpam-6931	75	55	m	m	NOUN
ejpam-6931	75	56	,	,	PUNCT
ejpam-6931	75	57	then	then	ADV
ejpam-6931	75	58	there	there	PRON
ejpam-6931	75	59	exists	exist	VERB
ejpam-6931	75	60	e	e	X
ejpam-6931	75	61	∈	∈	PROPN
ejpam-6931	75	62	s	s	VERB
ejpam-6931	75	63	such	such	ADJ
ejpam-6931	75	64	that	that	SCONJ
ejpam-6931	75	65	limn→∞	limn→∞	PROPN
ejpam-6931	75	66	en	en	X
ejpam-6931	75	67	=	=	PROPN
ejpam-6931	75	68	e.	e.	PROPN
ejpam-6931	75	69	(	(	PUNCT
ejpam-6931	75	70	2	2	X
ejpam-6931	75	71	)	)	PUNCT
ejpam-6931	75	72	⪯	⪯	NOUN
ejpam-6931	75	73	creates	create	VERB
ejpam-6931	75	74	a	a	DET
ejpam-6931	75	75	lattice	lattice	NOUN
ejpam-6931	75	76	structure	structure	NOUN
ejpam-6931	75	77	on	on	ADP
ejpam-6931	75	78	set	set	NOUN
ejpam-6931	75	79	of	of	ADP
ejpam-6931	75	80	complex	complex	ADJ
ejpam-6931	75	81	numbers	number	NOUN
ejpam-6931	75	82	c	c	NOUN
ejpam-6931	75	83	,	,	PUNCT
ejpam-6931	75	84	but	but	CCONJ
ejpam-6931	75	85	does	do	AUX
ejpam-6931	75	86	not	not	PART
ejpam-6931	75	87	create	create	VERB
ejpam-6931	75	88	a	a	DET
ejpam-6931	75	89	total	total	ADJ
ejpam-6931	75	90	ordering	ordering	NOUN
ejpam-6931	75	91	on	on	ADP
ejpam-6931	75	92	c.	c.	PROPN
ejpam-6931	75	93	(	(	PUNCT
ejpam-6931	75	94	3	3	X
ejpam-6931	75	95	)	)	PUNCT
ejpam-6931	75	96	if	if	SCONJ
ejpam-6931	75	97	for	for	ADP
ejpam-6931	75	98	each	each	DET
ejpam-6931	75	99	k	k	PROPN
ejpam-6931	75	100	∈	∈	PROPN
ejpam-6931	75	101	l	l	NOUN
ejpam-6931	75	102	satisfies	satisfie	NOUN
ejpam-6931	75	103	x́	x́	PUNCT
ejpam-6931	76	1	⪯	⪯	PROPN
ejpam-6931	77	1	k	k	PROPN
ejpam-6931	77	2	⪯	⪯	VERB
ejpam-6931	77	3	ý	ý	ADJ
ejpam-6931	77	4	for	for	ADP
ejpam-6931	77	5	some	some	DET
ejpam-6931	77	6	x́	x́	PROPN
ejpam-6931	77	7	,	,	PUNCT
ejpam-6931	77	8	ý	ý	PROPN
ejpam-6931	77	9	∈	∈	PROPN
ejpam-6931	77	10	c	c	X
ejpam-6931	77	11	,	,	PUNCT
ejpam-6931	77	12	then	then	ADV
ejpam-6931	77	13	infimum	infimum	ADJ
ejpam-6931	77	14	of	of	ADP
ejpam-6931	77	15	l	l	NOUN
ejpam-6931	77	16	and	and	CCONJ
ejpam-6931	77	17	supremum	supremum	NOUN
ejpam-6931	77	18	of	of	ADP
ejpam-6931	77	19	l	l	NOUN
ejpam-6931	77	20	are	be	AUX
ejpam-6931	77	21	exists	exist	NOUN
ejpam-6931	77	22	.	.	PUNCT
ejpam-6931	78	1	remark	remark	NOUN
ejpam-6931	78	2	2	2	NUM
ejpam-6931	78	3	.	.	PUNCT
ejpam-6931	79	1	[	[	X
ejpam-6931	79	2	19	19	NUM
ejpam-6931	79	3	]	]	PUNCT
ejpam-6931	79	4	considering	consider	VERB
ejpam-6931	79	5	that	that	SCONJ
ejpam-6931	79	6	the	the	DET
ejpam-6931	79	7	following	follow	VERB
ejpam-6931	79	8	criteria	criterion	NOUN
ejpam-6931	79	9	hold	hold	VERB
ejpam-6931	79	10	for	for	ADP
ejpam-6931	79	11	each	each	DET
ejpam-6931	79	12	n	n	PRON
ejpam-6931	79	13	∈	∈	PROPN
ejpam-6931	79	14	m	m	PROPN
ejpam-6931	79	15	,	,	PUNCT
ejpam-6931	79	16	en	en	X
ejpam-6931	79	17	,	,	PUNCT
ejpam-6931	79	18	e	e	NOUN
ejpam-6931	79	19	′	′	NUM
ejpam-6931	79	20	n	n	CCONJ
ejpam-6931	79	21	∈	∈	PROPN
ejpam-6931	79	22	s	s	NOUN
ejpam-6931	79	23	,	,	PUNCT
ejpam-6931	79	24	(	(	PUNCT
ejpam-6931	79	25	1	1	X
ejpam-6931	79	26	)	)	PUNCT
ejpam-6931	79	27	if	if	SCONJ
ejpam-6931	79	28	for	for	ADP
ejpam-6931	79	29	each	each	DET
ejpam-6931	79	30	n	n	PRON
ejpam-6931	79	31	∈	∈	PROPN
ejpam-6931	79	32	m	m	NOUN
ejpam-6931	79	33	,	,	PUNCT
ejpam-6931	79	34	we	we	PRON
ejpam-6931	79	35	have	have	VERB
ejpam-6931	79	36	en	en	ADP
ejpam-6931	79	37	⪯	⪯	PROPN
ejpam-6931	79	38	e′n	e′n	PROPN
ejpam-6931	79	39	⪯	⪯	NOUN
ejpam-6931	79	40	ℑ′	ℑ′	PROPN
ejpam-6931	79	41	in	in	ADP
ejpam-6931	79	42	addition	addition	NOUN
ejpam-6931	79	43	to	to	ADP
ejpam-6931	79	44	en	en	PROPN
ejpam-6931	79	45	→	→	SYM
ejpam-6931	79	46	ℑ′	ℑ′	PROPN
ejpam-6931	79	47	as	as	ADP
ejpam-6931	79	48	n	n	PRON
ejpam-6931	79	49	approaches	approach	NOUN
ejpam-6931	79	50	to	to	ADP
ejpam-6931	79	51	infinity	infinity	NOUN
ejpam-6931	79	52	,	,	PUNCT
ejpam-6931	79	53	it	it	PRON
ejpam-6931	79	54	follows	follow	VERB
ejpam-6931	79	55	that	that	PRON
ejpam-6931	79	56	e′n	e′n	NOUN
ejpam-6931	80	1	=	=	PUNCT
ejpam-6931	80	2	ℑ′.	ℑ′.	NUM
ejpam-6931	80	3	(	(	PUNCT
ejpam-6931	80	4	2	2	NUM
ejpam-6931	80	5	)	)	PUNCT
ejpam-6931	80	6	if	if	SCONJ
ejpam-6931	80	7	every	every	DET
ejpam-6931	80	8	element	element	NOUN
ejpam-6931	80	9	en	en	ADV
ejpam-6931	80	10	in	in	ADP
ejpam-6931	80	11	a	a	DET
ejpam-6931	80	12	sequence	sequence	NOUN
ejpam-6931	80	13	satisfies	satisfie	NOUN
ejpam-6931	80	14	en	en	ADP
ejpam-6931	80	15	⪯	⪯	PROPN
ejpam-6931	80	16	z	z	PROPN
ejpam-6931	80	17	,	,	PUNCT
ejpam-6931	80	18	and	and	CCONJ
ejpam-6931	80	19	if	if	SCONJ
ejpam-6931	80	20	the	the	DET
ejpam-6931	80	21	sequence	sequence	NOUN
ejpam-6931	80	22	en	en	ADV
ejpam-6931	80	23	has	have	VERB
ejpam-6931	80	24	a	a	DET
ejpam-6931	80	25	limit	limit	NOUN
ejpam-6931	80	26	e	e	X
ejpam-6931	80	27	∈	∈	NOUN
ejpam-6931	80	28	s	s	NOUN
ejpam-6931	80	29	,	,	PUNCT
ejpam-6931	80	30	then	then	ADV
ejpam-6931	80	31	the	the	DET
ejpam-6931	80	32	limit	limit	NOUN
ejpam-6931	80	33	e	e	NOUN
ejpam-6931	80	34	also	also	ADV
ejpam-6931	80	35	satisfies	satisfy	VERB
ejpam-6931	80	36	e	e	X
ejpam-6931	80	37	⪯	⪯	PROPN
ejpam-6931	80	38	z.	z.	PROPN
ejpam-6931	80	39	(	(	PUNCT
ejpam-6931	80	40	3	3	NUM
ejpam-6931	80	41	)	)	PUNCT
ejpam-6931	80	42	if	if	SCONJ
ejpam-6931	80	43	every	every	DET
ejpam-6931	80	44	element	element	NOUN
ejpam-6931	80	45	en	en	ADV
ejpam-6931	80	46	in	in	ADP
ejpam-6931	80	47	a	a	DET
ejpam-6931	80	48	sequence	sequence	NOUN
ejpam-6931	80	49	satisfies	satisfie	NOUN
ejpam-6931	80	50	z	z	X
ejpam-6931	80	51	⪯	⪯	PROPN
ejpam-6931	80	52	en	en	ADP
ejpam-6931	80	53	,	,	PUNCT
ejpam-6931	80	54	and	and	CCONJ
ejpam-6931	80	55	if	if	SCONJ
ejpam-6931	80	56	the	the	DET
ejpam-6931	80	57	sequence	sequence	NOUN
ejpam-6931	80	58	en	en	ADV
ejpam-6931	80	59	has	have	VERB
ejpam-6931	80	60	a	a	DET
ejpam-6931	80	61	limit	limit	NOUN
ejpam-6931	80	62	e	e	X
ejpam-6931	80	63	∈	∈	NOUN
ejpam-6931	80	64	s	s	NOUN
ejpam-6931	80	65	,	,	PUNCT
ejpam-6931	80	66	then	then	ADV
ejpam-6931	80	67	the	the	DET
ejpam-6931	80	68	limit	limit	NOUN
ejpam-6931	80	69	e	e	NOUN
ejpam-6931	80	70	also	also	ADV
ejpam-6931	80	71	satisfies	satisfy	VERB
ejpam-6931	80	72	z	z	PROPN
ejpam-6931	80	73	⪯	⪯	PROPN
ejpam-6931	80	74	e.	e.	PROPN
ejpam-6931	80	75	s.	s.	PROPN
ejpam-6931	80	76	m.	m.	PROPN
ejpam-6931	80	77	u.	u.	PROPN
ejpam-6931	80	78	ud	ud	AUX
ejpam-6931	80	79	-	-	PUNCT
ejpam-6931	80	80	din	din	VERB
ejpam-6931	80	81	et	et	PROPN
ejpam-6931	80	82	al	al	PROPN
ejpam-6931	80	83	.	.	PUNCT
ejpam-6931	80	84	/	/	SYM
ejpam-6931	80	85	eur	eur	PROPN
ejpam-6931	80	86	.	.	PUNCT
ejpam-6931	81	1	j.	j.	PROPN
ejpam-6931	81	2	pure	pure	PROPN
ejpam-6931	81	3	appl	appl	PROPN
ejpam-6931	81	4	.	.	PROPN
ejpam-6931	81	5	math	math	PROPN
ejpam-6931	81	6	,	,	PUNCT
ejpam-6931	81	7	18	18	NUM
ejpam-6931	81	8	(	(	PUNCT
ejpam-6931	81	9	4	4	NUM
ejpam-6931	81	10	)	)	PUNCT
ejpam-6931	81	11	(	(	PUNCT
ejpam-6931	81	12	2025	2025	NUM
ejpam-6931	81	13	)	)	PUNCT
ejpam-6931	81	14	,	,	PUNCT
ejpam-6931	81	15	6931	6931	NUM
ejpam-6931	81	16	4	4	NUM
ejpam-6931	81	17	of	of	ADP
ejpam-6931	81	18	38	38	NUM
ejpam-6931	81	19	definition	definition	NOUN
ejpam-6931	81	20	1	1	NUM
ejpam-6931	81	21	.	.	PUNCT
ejpam-6931	82	1	[	[	X
ejpam-6931	82	2	19	19	NUM
ejpam-6931	82	3	]	]	PUNCT
ejpam-6931	82	4	assume	assume	VERB
ejpam-6931	82	5	that	that	SCONJ
ejpam-6931	82	6	v	v	NOUN
ejpam-6931	82	7	is	be	AUX
ejpam-6931	82	8	a	a	DET
ejpam-6931	82	9	set	set	NOUN
ejpam-6931	82	10	that	that	PRON
ejpam-6931	82	11	is	be	AUX
ejpam-6931	82	12	not	not	PART
ejpam-6931	82	13	empty	empty	ADJ
ejpam-6931	82	14	.	.	PUNCT
ejpam-6931	83	1	complex	complex	ADJ
ejpam-6931	83	2	fuzzy	fuzzy	ADJ
ejpam-6931	83	3	set	set	NOUN
ejpam-6931	83	4	(	(	PUNCT
ejpam-6931	83	5	cfs	cfs	PROPN
ejpam-6931	83	6	)	)	PUNCT
ejpam-6931	83	7	e	e	NOUN
ejpam-6931	83	8	is	be	AUX
ejpam-6931	83	9	defined	define	VERB
ejpam-6931	83	10	as	as	ADP
ejpam-6931	83	11	the	the	DET
ejpam-6931	83	12	mapping	mapping	NOUN
ejpam-6931	83	13	from	from	ADP
ejpam-6931	83	14	v	v	NUM
ejpam-6931	83	15	to	to	ADP
ejpam-6931	83	16	the	the	DET
ejpam-6931	83	17	closed	closed	ADJ
ejpam-6931	83	18	unit	unit	NOUN
ejpam-6931	83	19	complex	complex	ADJ
ejpam-6931	83	20	interval	interval	NOUN
ejpam-6931	83	21	t.	t.	NOUN
ejpam-6931	83	22	definition	definition	NOUN
ejpam-6931	83	23	2	2	NUM
ejpam-6931	83	24	.	.	PUNCT
ejpam-6931	84	1	[	[	X
ejpam-6931	84	2	19	19	NUM
ejpam-6931	84	3	]	]	X
ejpam-6931	84	4	a	a	DET
ejpam-6931	84	5	binary	binary	ADJ
ejpam-6931	84	6	operation	operation	NOUN
ejpam-6931	84	7	⋆	⋆	VERB
ejpam-6931	84	8	:	:	PUNCT
ejpam-6931	84	9	t×t	t×t	NUM
ejpam-6931	84	10	→	→	SYM
ejpam-6931	84	11	t	t	PROPN
ejpam-6931	84	12	is	be	AUX
ejpam-6931	84	13	called	call	VERB
ejpam-6931	84	14	a	a	DET
ejpam-6931	84	15	complex	complex	ADV
ejpam-6931	84	16	-	-	PUNCT
ejpam-6931	84	17	valued	value	VERB
ejpam-6931	84	18	t	t	NOUN
ejpam-6931	84	19	-	-	PUNCT
ejpam-6931	84	20	norm	norm	NOUN
ejpam-6931	84	21	if	if	SCONJ
ejpam-6931	84	22	it	it	PRON
ejpam-6931	84	23	meets	meet	VERB
ejpam-6931	84	24	the	the	DET
ejpam-6931	84	25	following	following	ADJ
ejpam-6931	84	26	conditions	condition	NOUN
ejpam-6931	84	27	:	:	PUNCT
ejpam-6931	84	28	(	(	PUNCT
ejpam-6931	84	29	1	1	X
ejpam-6931	84	30	)	)	PUNCT
ejpam-6931	84	31	∅	∅	NOUN
ejpam-6931	85	1	⋆	⋆	PUNCT
ejpam-6931	85	2	e	e	X
ejpam-6931	85	3	=	=	PUNCT
ejpam-6931	85	4	∅,ℑ′	∅,ℑ′	PROPN
ejpam-6931	85	5	⋆	⋆	PUNCT
ejpam-6931	85	6	e	e	NOUN
ejpam-6931	85	7	=	=	SYM
ejpam-6931	85	8	e	e	PROPN
ejpam-6931	85	9	for	for	ADP
ejpam-6931	85	10	every	every	DET
ejpam-6931	85	11	e	e	PROPN
ejpam-6931	85	12	∈	∈	PROPN
ejpam-6931	85	13	t	t	PROPN
ejpam-6931	85	14	;	;	PUNCT
ejpam-6931	85	15	(	(	PUNCT
ejpam-6931	85	16	2	2	X
ejpam-6931	85	17	)	)	PUNCT
ejpam-6931	85	18	⋆	⋆	VERB
ejpam-6931	85	19	is	be	AUX
ejpam-6931	85	20	associative	associative	ADJ
ejpam-6931	85	21	and	and	CCONJ
ejpam-6931	85	22	commutative	commutative	ADJ
ejpam-6931	85	23	(	(	PUNCT
ejpam-6931	85	24	3	3	NUM
ejpam-6931	85	25	)	)	PUNCT
ejpam-6931	85	26	e3	e3	PROPN
ejpam-6931	85	27	⋆	⋆	PUNCT
ejpam-6931	85	28	e4	e4	PROPN
ejpam-6931	85	29	⪰	⪰	NOUN
ejpam-6931	85	30	e2	e2	PROPN
ejpam-6931	85	31	⋆	⋆	PUNCT
ejpam-6931	85	32	e1	e1	PROPN
ejpam-6931	85	33	given	give	VERB
ejpam-6931	85	34	that	that	SCONJ
ejpam-6931	85	35	e3	e3	NOUN
ejpam-6931	85	36	⪰	⪰	NOUN
ejpam-6931	85	37	e1	e1	NOUN
ejpam-6931	85	38	,	,	PUNCT
ejpam-6931	85	39	e4	e4	PROPN
ejpam-6931	85	40	⪰	⪰	NOUN
ejpam-6931	85	41	e2	e2	PROPN
ejpam-6931	85	42	for	for	ADP
ejpam-6931	85	43	each	each	DET
ejpam-6931	85	44	e1	e1	NOUN
ejpam-6931	85	45	,	,	PUNCT
ejpam-6931	85	46	e2	e2	PROPN
ejpam-6931	85	47	,	,	PUNCT
ejpam-6931	85	48	e3	e3	NOUN
ejpam-6931	85	49	,	,	PUNCT
ejpam-6931	85	50	e4	e4	PROPN
ejpam-6931	85	51	∈	∈	PROPN
ejpam-6931	85	52	t.	t.	NOUN
ejpam-6931	85	53	example	example	NOUN
ejpam-6931	86	1	1	1	NUM
ejpam-6931	86	2	.	.	PUNCT
ejpam-6931	87	1	[	[	X
ejpam-6931	87	2	19	19	NUM
ejpam-6931	87	3	]	]	PUNCT
ejpam-6931	87	4	suppose	suppose	VERB
ejpam-6931	87	5	that	that	SCONJ
ejpam-6931	87	6	ei	ei	NOUN
ejpam-6931	87	7	=	=	PUNCT
ejpam-6931	87	8	(	(	PUNCT
ejpam-6931	87	9	τi	τi	ADP
ejpam-6931	87	10	,	,	PUNCT
ejpam-6931	87	11	ξi	ξi	NOUN
ejpam-6931	87	12	)	)	PUNCT
ejpam-6931	87	13	∈	∈	PROPN
ejpam-6931	87	14	t	t	PROPN
ejpam-6931	87	15	for	for	ADP
ejpam-6931	87	16	i	i	PROPN
ejpam-6931	87	17	=	=	NOUN
ejpam-6931	87	18	1	1	NUM
ejpam-6931	87	19	,	,	PUNCT
ejpam-6931	87	20	2	2	NUM
ejpam-6931	87	21	,	,	PUNCT
ejpam-6931	87	22	binary	binary	ADJ
ejpam-6931	87	23	operations	operation	NOUN
ejpam-6931	87	24	⋆x	⋆x	PROPN
ejpam-6931	87	25	,	,	PUNCT
ejpam-6931	87	26	⋆y	⋆y	PROPN
ejpam-6931	87	27	,	,	PUNCT
ejpam-6931	87	28	⋆z	⋆z	PROPN
ejpam-6931	87	29	:	:	PUNCT
ejpam-6931	87	30	t×	t×	NUM
ejpam-6931	87	31	t	t	PROPN
ejpam-6931	87	32	→	→	SYM
ejpam-6931	87	33	t	t	PROPN
ejpam-6931	87	34	are	be	AUX
ejpam-6931	87	35	defined	define	VERB
ejpam-6931	87	36	below	below	ADP
ejpam-6931	87	37	:	:	PUNCT
ejpam-6931	87	38	(	(	PUNCT
ejpam-6931	87	39	1	1	X
ejpam-6931	87	40	)	)	PUNCT
ejpam-6931	87	41	e1	e1	PROPN
ejpam-6931	87	42	⋆x	⋆x	PROPN
ejpam-6931	87	43	e2	e2	PROPN
ejpam-6931	87	44	=	=	SYM
ejpam-6931	87	45	(	(	PUNCT
ejpam-6931	87	46	τ1τ2	τ1τ2	X
ejpam-6931	87	47	,	,	PUNCT
ejpam-6931	87	48	ξ1ξ2	ξ1ξ2	NOUN
ejpam-6931	87	49	)	)	PUNCT
ejpam-6931	87	50	;	;	PUNCT
ejpam-6931	87	51	(	(	PUNCT
ejpam-6931	87	52	2	2	X
ejpam-6931	87	53	)	)	PUNCT
ejpam-6931	87	54	e1	e1	NOUN
ejpam-6931	87	55	⋆y	⋆y	PROPN
ejpam-6931	87	56	e2	e2	PROPN
ejpam-6931	87	57	=	=	PUNCT
ejpam-6931	87	58	(	(	PUNCT
ejpam-6931	87	59	min{τ1	min{τ1	PROPN
ejpam-6931	87	60	,	,	PUNCT
ejpam-6931	87	61	τ2},min{ξ1	τ2},min{ξ1	PROPN
ejpam-6931	87	62	,	,	PUNCT
ejpam-6931	87	63	ξ2	ξ2	NOUN
ejpam-6931	87	64	}	}	PUNCT
ejpam-6931	87	65	)	)	PUNCT
ejpam-6931	87	66	;	;	PUNCT
ejpam-6931	87	67	(	(	PUNCT
ejpam-6931	87	68	3	3	X
ejpam-6931	87	69	)	)	PUNCT
ejpam-6931	87	70	e1	e1	PROPN
ejpam-6931	87	71	⋆z	⋆z	PROPN
ejpam-6931	87	72	e2	e2	PROPN
ejpam-6931	87	73	=	=	SYM
ejpam-6931	87	74	(	(	PUNCT
ejpam-6931	87	75	max{τ1	max{τ1	X
ejpam-6931	87	76	+	+	X
ejpam-6931	87	77	τ2	τ2	VERB
ejpam-6931	87	78	−	−	NOUN
ejpam-6931	87	79	1	1	NUM
ejpam-6931	87	80	,	,	PUNCT
ejpam-6931	87	81	0},max{ξ1	0},max{ξ1	NOUN
ejpam-6931	87	82	+	+	CCONJ
ejpam-6931	87	83	ξ2	ξ2	ADJ
ejpam-6931	87	84	−	−	NUM
ejpam-6931	87	85	1	1	NUM
ejpam-6931	87	86	,	,	PUNCT
ejpam-6931	87	87	0	0	NUM
ejpam-6931	87	88	}	}	PUNCT
ejpam-6931	87	89	)	)	PUNCT
ejpam-6931	87	90	.	.	PUNCT
ejpam-6931	88	1	therefore	therefore	ADV
ejpam-6931	88	2	,	,	PUNCT
ejpam-6931	88	3	⋆x	⋆x	PROPN
ejpam-6931	88	4	,	,	PUNCT
ejpam-6931	88	5	⋆y	⋆y	PROPN
ejpam-6931	88	6	,	,	PUNCT
ejpam-6931	88	7	⋆z	⋆z	PROPN
ejpam-6931	88	8	are	be	AUX
ejpam-6931	88	9	complex	complex	ADV
ejpam-6931	88	10	-	-	PUNCT
ejpam-6931	88	11	valued	value	VERB
ejpam-6931	88	12	t	t	NOUN
ejpam-6931	88	13	-	-	PUNCT
ejpam-6931	88	14	norms	norm	NOUN
ejpam-6931	88	15	.	.	PUNCT
ejpam-6931	89	1	definition	definition	NOUN
ejpam-6931	89	2	3	3	NUM
ejpam-6931	89	3	.	.	PUNCT
ejpam-6931	90	1	[	[	X
ejpam-6931	90	2	19	19	NUM
ejpam-6931	90	3	]	]	PUNCT
ejpam-6931	90	4	let	let	VERB
ejpam-6931	90	5	v	v	ADP
ejpam-6931	90	6	̸=	̸=	PROPN
ejpam-6931	90	7	0	0	NUM
ejpam-6931	90	8	,	,	PUNCT
ejpam-6931	90	9	⋆	⋆	ADJ
ejpam-6931	90	10	be	be	AUX
ejpam-6931	90	11	a	a	DET
ejpam-6931	90	12	continuous	continuous	ADJ
ejpam-6931	90	13	complex	complex	ADV
ejpam-6931	90	14	-	-	PUNCT
ejpam-6931	90	15	valued	value	VERB
ejpam-6931	90	16	t	t	NOUN
ejpam-6931	90	17	-	-	PUNCT
ejpam-6931	90	18	norms	norm	NOUN
ejpam-6931	90	19	and	and	CCONJ
ejpam-6931	90	20	e	e	PRON
ejpam-6931	90	21	be	be	AUX
ejpam-6931	90	22	a	a	DET
ejpam-6931	90	23	cfs	cfs	NOUN
ejpam-6931	90	24	defined	define	VERB
ejpam-6931	90	25	on	on	ADP
ejpam-6931	90	26	v2	v2	PROPN
ejpam-6931	90	27	×	×	PROPN
ejpam-6931	90	28	s0	s0	NOUN
ejpam-6931	90	29	whereby	whereby	SCONJ
ejpam-6931	90	30	the	the	DET
ejpam-6931	90	31	criteria	criterion	NOUN
ejpam-6931	90	32	following	follow	VERB
ejpam-6931	90	33	hold	hold	NOUN
ejpam-6931	90	34	:	:	PUNCT
ejpam-6931	90	35	(	(	PUNCT
ejpam-6931	90	36	1	1	X
ejpam-6931	90	37	)	)	PUNCT
ejpam-6931	90	38	e(ϱo	e(ϱo	NOUN
ejpam-6931	90	39	,	,	PUNCT
ejpam-6931	90	40	ν	ν	NOUN
ejpam-6931	90	41	,	,	PUNCT
ejpam-6931	90	42	e	e	NOUN
ejpam-6931	90	43	)	)	PUNCT
ejpam-6931	90	44	≻	≻	NOUN
ejpam-6931	90	45	∅	∅	NOUN
ejpam-6931	90	46	;	;	PUNCT
ejpam-6931	90	47	(	(	PUNCT
ejpam-6931	90	48	2	2	X
ejpam-6931	90	49	)	)	PUNCT
ejpam-6931	90	50	e(ϱo	e(ϱo	NOUN
ejpam-6931	90	51	,	,	PUNCT
ejpam-6931	90	52	ν	ν	NOUN
ejpam-6931	90	53	,	,	PUNCT
ejpam-6931	90	54	e	e	NOUN
ejpam-6931	90	55	)	)	PUNCT
ejpam-6931	90	56	=	=	SYM
ejpam-6931	91	1	ℑ′	ℑ′	PROPN
ejpam-6931	91	2	for	for	ADP
ejpam-6931	91	3	each	each	DET
ejpam-6931	91	4	e	e	PROPN
ejpam-6931	91	5	∈	∈	PROPN
ejpam-6931	91	6	s0	s0	NOUN
ejpam-6931	91	7	if	if	SCONJ
ejpam-6931	91	8	and	and	CCONJ
ejpam-6931	91	9	only	only	ADV
ejpam-6931	91	10	if	if	SCONJ
ejpam-6931	91	11	ϱo	ϱo	PROPN
ejpam-6931	91	12	=	=	SYM
ejpam-6931	91	13	ν	ν	NOUN
ejpam-6931	91	14	;	;	PUNCT
ejpam-6931	91	15	(	(	PUNCT
ejpam-6931	91	16	3	3	X
ejpam-6931	91	17	)	)	PUNCT
ejpam-6931	91	18	e(ϱo	e(ϱo	NOUN
ejpam-6931	91	19	,	,	PUNCT
ejpam-6931	91	20	ν	ν	NOUN
ejpam-6931	91	21	,	,	PUNCT
ejpam-6931	91	22	e	e	NOUN
ejpam-6931	91	23	)	)	PUNCT
ejpam-6931	91	24	=	=	SYM
ejpam-6931	91	25	e(ν	e(ν	PROPN
ejpam-6931	91	26	,	,	PUNCT
ejpam-6931	91	27	ϱo	ϱo	NOUN
ejpam-6931	91	28	,	,	PUNCT
ejpam-6931	91	29	e	e	NOUN
ejpam-6931	91	30	)	)	PUNCT
ejpam-6931	91	31	;	;	PUNCT
ejpam-6931	91	32	(	(	PUNCT
ejpam-6931	91	33	4	4	X
ejpam-6931	91	34	)	)	PUNCT
ejpam-6931	91	35	e(ϱo	e(ϱo	NOUN
ejpam-6931	91	36	,	,	PUNCT
ejpam-6931	91	37	ς	ς	PROPN
ejpam-6931	91	38	,	,	PUNCT
ejpam-6931	91	39	e+	e+	ADJ
ejpam-6931	91	40	e′	e′	NOUN
ejpam-6931	91	41	)	)	PUNCT
ejpam-6931	91	42	⪰	⪰	NOUN
ejpam-6931	91	43	e(ϱo	e(ϱo	NOUN
ejpam-6931	91	44	,	,	PUNCT
ejpam-6931	91	45	ν	ν	NOUN
ejpam-6931	91	46	,	,	PUNCT
ejpam-6931	91	47	e	e	NOUN
ejpam-6931	91	48	)	)	PUNCT
ejpam-6931	91	49	⋆	⋆	PROPN
ejpam-6931	91	50	e(ν	e(ν	PROPN
ejpam-6931	91	51	,	,	PUNCT
ejpam-6931	91	52	ς	ς	PROPN
ejpam-6931	91	53	,	,	PUNCT
ejpam-6931	91	54	e′	e′	ADJ
ejpam-6931	91	55	)	)	PUNCT
ejpam-6931	91	56	;	;	PUNCT
ejpam-6931	91	57	(	(	PUNCT
ejpam-6931	91	58	5	5	X
ejpam-6931	91	59	)	)	PUNCT
ejpam-6931	91	60	e(ϱo	e(ϱo	NOUN
ejpam-6931	91	61	,	,	PUNCT
ejpam-6931	91	62	ν	ν	NOUN
ejpam-6931	91	63	,	,	PUNCT
ejpam-6931	91	64	·	·	PUNCT
ejpam-6931	91	65	)	)	PUNCT
ejpam-6931	91	66	:	:	PUNCT
ejpam-6931	91	67	s0	s0	PROPN
ejpam-6931	91	68	→	→	SYM
ejpam-6931	91	69	t	t	PROPN
ejpam-6931	91	70	is	be	AUX
ejpam-6931	91	71	continuous	continuous	ADJ
ejpam-6931	91	72	;	;	PUNCT
ejpam-6931	91	73	for	for	ADP
ejpam-6931	91	74	every	every	DET
ejpam-6931	91	75	ϱo	ϱo	PROPN
ejpam-6931	91	76	,	,	PUNCT
ejpam-6931	91	77	ν	ν	PROPN
ejpam-6931	91	78	,	,	PUNCT
ejpam-6931	91	79	ς	ς	PROPN
ejpam-6931	91	80	∈	∈	PROPN
ejpam-6931	91	81	v	v	NOUN
ejpam-6931	91	82	and	and	CCONJ
ejpam-6931	91	83	e	e	NOUN
ejpam-6931	91	84	,	,	PUNCT
ejpam-6931	91	85	e′	e′	PROPN
ejpam-6931	91	86	∈	∈	PROPN
ejpam-6931	91	87	s0	s0	PROPN
ejpam-6931	91	88	.	.	PUNCT
ejpam-6931	92	1	then	then	ADV
ejpam-6931	92	2	e	e	PROPN
ejpam-6931	92	3	is	be	AUX
ejpam-6931	92	4	called	call	VERB
ejpam-6931	92	5	a	a	DET
ejpam-6931	92	6	complex	complex	ADV
ejpam-6931	92	7	-	-	PUNCT
ejpam-6931	92	8	valued	value	VERB
ejpam-6931	92	9	fuzzy	fuzzy	ADJ
ejpam-6931	92	10	metric	metric	ADJ
ejpam-6931	92	11	on	on	ADP
ejpam-6931	92	12	v	v	NOUN
ejpam-6931	92	13	,	,	PUNCT
ejpam-6931	92	14	and	and	CCONJ
ejpam-6931	92	15	(	(	PUNCT
ejpam-6931	92	16	v	v	NOUN
ejpam-6931	92	17	,	,	PUNCT
ejpam-6931	92	18	e	e	NOUN
ejpam-6931	92	19	,	,	PUNCT
ejpam-6931	92	20	⋆	⋆	CCONJ
ejpam-6931	92	21	)	)	PUNCT
ejpam-6931	92	22	is	be	AUX
ejpam-6931	92	23	called	call	VERB
ejpam-6931	92	24	a	a	DET
ejpam-6931	92	25	complexvalued	complexvalue	VERB
ejpam-6931	92	26	fuzzy	fuzzy	ADJ
ejpam-6931	92	27	metric	metric	ADJ
ejpam-6931	92	28	space	space	NOUN
ejpam-6931	92	29	.	.	PUNCT
ejpam-6931	93	1	a	a	DET
ejpam-6931	93	2	cvfm	cvfm	PROPN
ejpam-6931	93	3	e	e	NOUN
ejpam-6931	93	4	characterizes	characterize	VERB
ejpam-6931	93	5	the	the	DET
ejpam-6931	93	6	degree	degree	NOUN
ejpam-6931	93	7	of	of	ADP
ejpam-6931	93	8	nearness	nearness	NOUN
ejpam-6931	93	9	between	between	ADP
ejpam-6931	93	10	two	two	NUM
ejpam-6931	93	11	points	point	NOUN
ejpam-6931	93	12	of	of	ADP
ejpam-6931	93	13	the	the	DET
ejpam-6931	93	14	set	set	NOUN
ejpam-6931	93	15	v	v	NOUN
ejpam-6931	93	16	relative	relative	ADJ
ejpam-6931	93	17	to	to	ADP
ejpam-6931	93	18	a	a	DET
ejpam-6931	93	19	complex	complex	ADJ
ejpam-6931	93	20	factor	factor	NOUN
ejpam-6931	93	21	e	e	NOUN
ejpam-6931	93	22	∈	∈	PROPN
ejpam-6931	93	23	s0	s0	PROPN
ejpam-6931	93	24	.	.	PUNCT
ejpam-6931	94	1	definition	definition	NOUN
ejpam-6931	94	2	4	4	NUM
ejpam-6931	94	3	.	.	PUNCT
ejpam-6931	95	1	a	a	DET
ejpam-6931	95	2	binary	binary	ADJ
ejpam-6931	95	3	operation	operation	NOUN
ejpam-6931	95	4	△	△	PROPN
ejpam-6931	95	5	:	:	PUNCT
ejpam-6931	95	6	t×	t×	NOUN
ejpam-6931	95	7	t	t	PROPN
ejpam-6931	95	8	→	→	SYM
ejpam-6931	95	9	t	t	PROPN
ejpam-6931	95	10	is	be	AUX
ejpam-6931	95	11	called	call	VERB
ejpam-6931	95	12	complex	complex	ADV
ejpam-6931	95	13	-	-	PUNCT
ejpam-6931	95	14	valued	value	VERB
ejpam-6931	95	15	t	t	NOUN
ejpam-6931	95	16	-	-	PUNCT
ejpam-6931	95	17	conorm	conorm	NOUN
ejpam-6931	95	18	if	if	SCONJ
ejpam-6931	95	19	it	it	PRON
ejpam-6931	95	20	meets	meet	VERB
ejpam-6931	95	21	the	the	DET
ejpam-6931	95	22	following	following	ADJ
ejpam-6931	95	23	conditions	condition	NOUN
ejpam-6931	95	24	:	:	PUNCT
ejpam-6931	95	25	(	(	PUNCT
ejpam-6931	95	26	1	1	X
ejpam-6931	95	27	)	)	PUNCT
ejpam-6931	95	28	e	e	NOUN
ejpam-6931	95	29	△	△	NOUN
ejpam-6931	95	30	∅	∅	NOUN
ejpam-6931	95	31	=	=	SYM
ejpam-6931	95	32	e	e	NOUN
ejpam-6931	95	33	,	,	PUNCT
ejpam-6931	95	34	e	e	NOUN
ejpam-6931	95	35	△	△	X
ejpam-6931	95	36	ℑ′	ℑ′	X
ejpam-6931	95	37	=	=	SYM
ejpam-6931	95	38	ℑ′	ℑ′	PROPN
ejpam-6931	95	39	for	for	ADP
ejpam-6931	95	40	every	every	DET
ejpam-6931	95	41	e	e	PROPN
ejpam-6931	95	42	∈	∈	PROPN
ejpam-6931	95	43	t	t	PROPN
ejpam-6931	95	44	;	;	PUNCT
ejpam-6931	95	45	(	(	PUNCT
ejpam-6931	95	46	2	2	X
ejpam-6931	95	47	)	)	PUNCT
ejpam-6931	95	48	△	△	X
ejpam-6931	95	49	is	be	AUX
ejpam-6931	95	50	associative	associative	ADJ
ejpam-6931	95	51	and	and	CCONJ
ejpam-6931	95	52	commutative	commutative	ADJ
ejpam-6931	95	53	;	;	PUNCT
ejpam-6931	95	54	(	(	PUNCT
ejpam-6931	95	55	3	3	X
ejpam-6931	95	56	)	)	PUNCT
ejpam-6931	95	57	e3	e3	NOUN
ejpam-6931	95	58	△	△	NOUN
ejpam-6931	95	59	e4	e4	PROPN
ejpam-6931	95	60	⪰	⪰	NOUN
ejpam-6931	95	61	e1	e1	PROPN
ejpam-6931	95	62	△	△	PROPN
ejpam-6931	95	63	e2	e2	PROPN
ejpam-6931	95	64	given	give	VERB
ejpam-6931	95	65	that	that	SCONJ
ejpam-6931	95	66	e3	e3	NOUN
ejpam-6931	95	67	⪰	⪰	NOUN
ejpam-6931	95	68	e1	e1	NOUN
ejpam-6931	95	69	,	,	PUNCT
ejpam-6931	95	70	e4	e4	PROPN
ejpam-6931	95	71	⪰	⪰	NOUN
ejpam-6931	95	72	e2	e2	PROPN
ejpam-6931	95	73	for	for	ADP
ejpam-6931	95	74	each	each	DET
ejpam-6931	95	75	e1	e1	NOUN
ejpam-6931	95	76	,	,	PUNCT
ejpam-6931	95	77	e2	e2	PROPN
ejpam-6931	95	78	,	,	PUNCT
ejpam-6931	95	79	e3	e3	NOUN
ejpam-6931	95	80	,	,	PUNCT
ejpam-6931	95	81	e4	e4	PROPN
ejpam-6931	95	82	∈	∈	PROPN
ejpam-6931	95	83	t.	t.	PROPN
ejpam-6931	95	84	s.	s.	PROPN
ejpam-6931	95	85	m.	m.	PROPN
ejpam-6931	95	86	u.	u.	PROPN
ejpam-6931	95	87	ud	ud	AUX
ejpam-6931	95	88	-	-	PUNCT
ejpam-6931	95	89	din	din	VERB
ejpam-6931	95	90	et	et	PROPN
ejpam-6931	95	91	al	al	PROPN
ejpam-6931	95	92	.	.	PUNCT
ejpam-6931	95	93	/	/	SYM
ejpam-6931	95	94	eur	eur	PROPN
ejpam-6931	95	95	.	.	PUNCT
ejpam-6931	96	1	j.	j.	PROPN
ejpam-6931	96	2	pure	pure	PROPN
ejpam-6931	96	3	appl	appl	PROPN
ejpam-6931	96	4	.	.	PROPN
ejpam-6931	96	5	math	math	PROPN
ejpam-6931	96	6	,	,	PUNCT
ejpam-6931	96	7	18	18	NUM
ejpam-6931	96	8	(	(	PUNCT
ejpam-6931	96	9	4	4	NUM
ejpam-6931	96	10	)	)	PUNCT
ejpam-6931	96	11	(	(	PUNCT
ejpam-6931	96	12	2025	2025	NUM
ejpam-6931	96	13	)	)	PUNCT
ejpam-6931	96	14	,	,	PUNCT
ejpam-6931	96	15	6931	6931	NUM
ejpam-6931	96	16	5	5	NUM
ejpam-6931	96	17	of	of	ADP
ejpam-6931	96	18	38	38	NUM
ejpam-6931	96	19	example	example	NOUN
ejpam-6931	96	20	2	2	NUM
ejpam-6931	96	21	.	.	PUNCT
ejpam-6931	96	22	suppose	suppose	VERB
ejpam-6931	96	23	that	that	SCONJ
ejpam-6931	96	24	ei	ei	NOUN
ejpam-6931	96	25	=	=	PUNCT
ejpam-6931	96	26	(	(	PUNCT
ejpam-6931	96	27	τi	τi	ADP
ejpam-6931	96	28	,	,	PUNCT
ejpam-6931	96	29	ξi	ξi	NOUN
ejpam-6931	96	30	)	)	PUNCT
ejpam-6931	96	31	∈	∈	PROPN
ejpam-6931	96	32	t	t	PROPN
ejpam-6931	96	33	for	for	ADP
ejpam-6931	96	34	i	i	PROPN
ejpam-6931	96	35	=	=	NOUN
ejpam-6931	96	36	1	1	NUM
ejpam-6931	96	37	,	,	PUNCT
ejpam-6931	96	38	2	2	NUM
ejpam-6931	96	39	,	,	PUNCT
ejpam-6931	96	40	binary	binary	ADJ
ejpam-6931	96	41	operations	operation	NOUN
ejpam-6931	96	42	△	△	PROPN
ejpam-6931	96	43	x,	x,	PROPN
ejpam-6931	96	44	△	△	X
ejpam-6931	96	45	y,	y,	X
ejpam-6931	96	46	△	△	PROPN
ejpam-6931	96	47	z	z	NOUN
ejpam-6931	96	48	:	:	PUNCT
ejpam-6931	96	49	t×	t×	NOUN
ejpam-6931	96	50	t	t	PROPN
ejpam-6931	96	51	→	→	SYM
ejpam-6931	96	52	t	t	PROPN
ejpam-6931	96	53	are	be	AUX
ejpam-6931	96	54	defined	define	VERB
ejpam-6931	96	55	as	as	ADP
ejpam-6931	96	56	below	below	ADV
ejpam-6931	96	57	:	:	PUNCT
ejpam-6931	96	58	(	(	PUNCT
ejpam-6931	96	59	1	1	X
ejpam-6931	96	60	)	)	PUNCT
ejpam-6931	96	61	e1	e1	VERB
ejpam-6931	96	62	△	△	NOUN
ejpam-6931	96	63	x	x	X
ejpam-6931	96	64	e2	e2	PROPN
ejpam-6931	96	65	=	=	PUNCT
ejpam-6931	96	66	(	(	PUNCT
ejpam-6931	96	67	τ1	τ1	NOUN
ejpam-6931	96	68	+	+	CCONJ
ejpam-6931	96	69	τ2	τ2	ADJ
ejpam-6931	96	70	,	,	PUNCT
ejpam-6931	96	71	ξ1	ξ1	NOUN
ejpam-6931	96	72	+	+	CCONJ
ejpam-6931	96	73	ξ2)−	ξ2)−	NOUN
ejpam-6931	96	74	(	(	PUNCT
ejpam-6931	96	75	τ1τ2	τ1τ2	NOUN
ejpam-6931	96	76	,	,	PUNCT
ejpam-6931	96	77	ξ1ξ2	ξ1ξ2	NOUN
ejpam-6931	96	78	)	)	PUNCT
ejpam-6931	96	79	;	;	PUNCT
ejpam-6931	96	80	(	(	PUNCT
ejpam-6931	96	81	2	2	X
ejpam-6931	96	82	)	)	PUNCT
ejpam-6931	96	83	e1	e1	PROPN
ejpam-6931	96	84	△	△	NOUN
ejpam-6931	96	85	y	y	PROPN
ejpam-6931	96	86	e2	e2	PROPN
ejpam-6931	96	87	=	=	PUNCT
ejpam-6931	96	88	(	(	PUNCT
ejpam-6931	96	89	max{τ1	max{τ1	PROPN
ejpam-6931	96	90	,	,	PUNCT
ejpam-6931	96	91	τ2},max{ξ1	τ2},max{ξ1	NUM
ejpam-6931	96	92	,	,	PUNCT
ejpam-6931	96	93	ξ2	ξ2	NOUN
ejpam-6931	96	94	}	}	PUNCT
ejpam-6931	96	95	)	)	PUNCT
ejpam-6931	96	96	;	;	PUNCT
ejpam-6931	96	97	(	(	PUNCT
ejpam-6931	96	98	3	3	X
ejpam-6931	96	99	)	)	PUNCT
ejpam-6931	96	100	e1	e1	PROPN
ejpam-6931	96	101	△	△	NOUN
ejpam-6931	96	102	z	z	PROPN
ejpam-6931	96	103	e2	e2	NOUN
ejpam-6931	96	104	=	=	SYM
ejpam-6931	96	105	(	(	PUNCT
ejpam-6931	96	106	min{τ1	min{τ1	X
ejpam-6931	96	107	+	+	CCONJ
ejpam-6931	96	108	τ2	τ2	ADJ
ejpam-6931	96	109	,	,	PUNCT
ejpam-6931	96	110	1},min{ξ1	1},min{ξ1	NUM
ejpam-6931	96	111	+	+	CCONJ
ejpam-6931	96	112	ξ2	ξ2	ADJ
ejpam-6931	96	113	,	,	PUNCT
ejpam-6931	96	114	1	1	NUM
ejpam-6931	96	115	}	}	PUNCT
ejpam-6931	96	116	)	)	PUNCT
ejpam-6931	96	117	.	.	PUNCT
ejpam-6931	97	1	therefore	therefore	ADV
ejpam-6931	97	2	,	,	PUNCT
ejpam-6931	97	3	△	△	PROPN
ejpam-6931	97	4	x,	x,	PROPN
ejpam-6931	97	5	△	△	X
ejpam-6931	97	6	y	y	PROPN
ejpam-6931	97	7	and	and	CCONJ
ejpam-6931	97	8	△	△	PROPN
ejpam-6931	97	9	z	z	X
ejpam-6931	97	10	are	be	AUX
ejpam-6931	97	11	complex	complex	ADV
ejpam-6931	97	12	-	-	PUNCT
ejpam-6931	97	13	valued	value	VERB
ejpam-6931	97	14	triangular	triangular	NOUN
ejpam-6931	97	15	-	-	PUNCT
ejpam-6931	97	16	conorms	conorm	NOUN
ejpam-6931	97	17	.	.	PUNCT
ejpam-6931	98	1	remark	remark	VERB
ejpam-6931	98	2	3	3	NUM
ejpam-6931	98	3	.	.	PUNCT
ejpam-6931	99	1	both	both	DET
ejpam-6931	99	2	binary	binary	ADJ
ejpam-6931	99	3	operations	operation	NOUN
ejpam-6931	99	4	,	,	PUNCT
ejpam-6931	99	5	triangular	triangular	NOUN
ejpam-6931	99	6	-	-	PUNCT
ejpam-6931	99	7	norm	norm	NOUN
ejpam-6931	99	8	,	,	PUNCT
ejpam-6931	99	9	and	and	CCONJ
ejpam-6931	99	10	triangular	triangular	NOUN
ejpam-6931	99	11	-	-	PUNCT
ejpam-6931	99	12	conorm	conorm	NOUN
ejpam-6931	99	13	,	,	PUNCT
ejpam-6931	99	14	are	be	AUX
ejpam-6931	99	15	frequently	frequently	ADV
ejpam-6931	99	16	employed	employ	VERB
ejpam-6931	99	17	in	in	ADP
ejpam-6931	99	18	fuzzy	fuzzy	ADJ
ejpam-6931	99	19	set	set	NOUN
ejpam-6931	99	20	theory	theory	NOUN
ejpam-6931	99	21	,	,	PUNCT
ejpam-6931	99	22	especially	especially	ADV
ejpam-6931	99	23	within	within	ADP
ejpam-6931	99	24	the	the	DET
ejpam-6931	99	25	contexts	contexts	NOUN
ejpam-6931	99	26	of	of	ADP
ejpam-6931	99	27	[	[	X
ejpam-6931	99	28	0	0	NUM
ejpam-6931	99	29	,	,	PUNCT
ejpam-6931	99	30	1	1	NUM
ejpam-6931	99	31	]	]	PUNCT
ejpam-6931	99	32	and	and	CCONJ
ejpam-6931	99	33	lattices	lattice	NOUN
ejpam-6931	99	34	.	.	PUNCT
ejpam-6931	100	1	the	the	DET
ejpam-6931	100	2	former	former	ADJ
ejpam-6931	100	3	denotes	denote	NOUN
ejpam-6931	100	4	the	the	DET
ejpam-6931	100	5	shared	share	VERB
ejpam-6931	100	6	area	area	NOUN
ejpam-6931	100	7	between	between	ADP
ejpam-6931	100	8	two	two	NUM
ejpam-6931	100	9	fuzzy	fuzzy	ADJ
ejpam-6931	100	10	sets	set	NOUN
ejpam-6931	100	11	,	,	PUNCT
ejpam-6931	100	12	sometimes	sometimes	ADV
ejpam-6931	100	13	expressed	express	VERB
ejpam-6931	100	14	as	as	ADP
ejpam-6931	100	15	a	a	DET
ejpam-6931	100	16	conjunction	conjunction	NOUN
ejpam-6931	100	17	in	in	ADP
ejpam-6931	100	18	fuzzy	fuzzy	ADJ
ejpam-6931	100	19	logic	logic	NOUN
ejpam-6931	100	20	.	.	PUNCT
ejpam-6931	101	1	the	the	DET
ejpam-6931	101	2	t	t	NOUN
ejpam-6931	101	3	-	-	PUNCT
ejpam-6931	101	4	conorm	conorm	NOUN
ejpam-6931	101	5	,	,	PUNCT
ejpam-6931	101	6	which	which	PRON
ejpam-6931	101	7	is	be	AUX
ejpam-6931	101	8	the	the	DET
ejpam-6931	101	9	dual	dual	ADJ
ejpam-6931	101	10	of	of	ADP
ejpam-6931	101	11	the	the	DET
ejpam-6931	101	12	t	t	NOUN
ejpam-6931	101	13	-	-	PUNCT
ejpam-6931	101	14	norm	norm	NOUN
ejpam-6931	101	15	,	,	PUNCT
ejpam-6931	101	16	is	be	AUX
ejpam-6931	101	17	seen	see	VERB
ejpam-6931	101	18	as	as	ADP
ejpam-6931	101	19	the	the	DET
ejpam-6931	101	20	area	area	NOUN
ejpam-6931	101	21	where	where	SCONJ
ejpam-6931	101	22	two	two	NUM
ejpam-6931	101	23	fuzzy	fuzzy	ADJ
ejpam-6931	101	24	sets	set	NOUN
ejpam-6931	101	25	meet	meet	VERB
ejpam-6931	101	26	,	,	PUNCT
ejpam-6931	101	27	or	or	CCONJ
ejpam-6931	101	28	,	,	PUNCT
ejpam-6931	101	29	in	in	ADP
ejpam-6931	101	30	other	other	ADJ
ejpam-6931	101	31	words	word	NOUN
ejpam-6931	101	32	,	,	PUNCT
ejpam-6931	101	33	a	a	DET
ejpam-6931	101	34	disjunction	disjunction	NOUN
ejpam-6931	101	35	in	in	ADP
ejpam-6931	101	36	fuzzy	fuzzy	ADJ
ejpam-6931	101	37	logic	logic	NOUN
ejpam-6931	101	38	.	.	PUNCT
ejpam-6931	102	1	for	for	ADP
ejpam-6931	102	2	additional	additional	ADJ
ejpam-6931	102	3	insights	insight	NOUN
ejpam-6931	102	4	into	into	ADP
ejpam-6931	102	5	the	the	DET
ejpam-6931	102	6	ideas	idea	NOUN
ejpam-6931	102	7	of	of	ADP
ejpam-6931	102	8	t	t	NOUN
ejpam-6931	102	9	-	-	PUNCT
ejpam-6931	102	10	norm	norm	NOUN
ejpam-6931	102	11	and	and	CCONJ
ejpam-6931	102	12	t	t	PROPN
ejpam-6931	102	13	-	-	PUNCT
ejpam-6931	102	14	conorm	conorm	NOUN
ejpam-6931	102	15	are	be	AUX
ejpam-6931	102	16	encouraged	encourage	VERB
ejpam-6931	102	17	to	to	PART
ejpam-6931	102	18	refer	refer	VERB
ejpam-6931	102	19	to	to	ADP
ejpam-6931	102	20	[	[	X
ejpam-6931	102	21	35	35	NUM
ejpam-6931	102	22	]	]	PUNCT
ejpam-6931	102	23	and	and	CCONJ
ejpam-6931	102	24	[	[	X
ejpam-6931	102	25	36	36	NUM
ejpam-6931	102	26	]	]	PUNCT
ejpam-6931	102	27	.	.	PUNCT
ejpam-6931	103	1	definition	definition	NOUN
ejpam-6931	103	2	5	5	NUM
ejpam-6931	103	3	.	.	PUNCT
ejpam-6931	103	4	assume	assume	VERB
ejpam-6931	103	5	that	that	SCONJ
ejpam-6931	103	6	v	v	ADP
ejpam-6931	103	7	̸=	̸=	PROPN
ejpam-6931	103	8	0	0	NUM
ejpam-6931	103	9	,	,	PUNCT
ejpam-6931	103	10	⋆	⋆	VERB
ejpam-6931	103	11	and	and	CCONJ
ejpam-6931	103	12	△	△	PROPN
ejpam-6931	103	13	are	be	AUX
ejpam-6931	103	14	continuous	continuous	ADJ
ejpam-6931	103	15	complex	complex	ADV
ejpam-6931	103	16	-	-	PUNCT
ejpam-6931	103	17	valued	value	VERB
ejpam-6931	103	18	t	t	NOUN
ejpam-6931	103	19	-	-	PUNCT
ejpam-6931	103	20	norm	norm	NOUN
ejpam-6931	103	21	and	and	CCONJ
ejpam-6931	103	22	t	t	NOUN
ejpam-6931	103	23	-	-	PUNCT
ejpam-6931	103	24	conorm	conorm	NOUN
ejpam-6931	103	25	,	,	PUNCT
ejpam-6931	103	26	respectively	respectively	ADV
ejpam-6931	103	27	,	,	PUNCT
ejpam-6931	103	28	and	and	CCONJ
ejpam-6931	103	29	e	e	NOUN
ejpam-6931	103	30	,	,	PUNCT
ejpam-6931	103	31	g	g	PROPN
ejpam-6931	103	32	are	be	AUX
ejpam-6931	103	33	complex	complex	ADJ
ejpam-6931	103	34	fuzzy	fuzzy	ADJ
ejpam-6931	103	35	sets	set	NOUN
ejpam-6931	103	36	(	(	PUNCT
ejpam-6931	103	37	cfss	cfss	ADJ
ejpam-6931	103	38	)	)	PUNCT
ejpam-6931	103	39	defined	define	VERB
ejpam-6931	103	40	on	on	ADP
ejpam-6931	103	41	v2×s0	v2×s0	NOUN
ejpam-6931	103	42	in	in	ADP
ejpam-6931	103	43	which	which	PRON
ejpam-6931	103	44	the	the	DET
ejpam-6931	103	45	following	follow	VERB
ejpam-6931	103	46	conditions	condition	NOUN
ejpam-6931	103	47	are	be	AUX
ejpam-6931	103	48	satisfied	satisfied	ADJ
ejpam-6931	103	49	:	:	PUNCT
ejpam-6931	103	50	(	(	PUNCT
ejpam-6931	103	51	1	1	X
ejpam-6931	103	52	)	)	PUNCT
ejpam-6931	103	53	e(ϱo	e(ϱo	NOUN
ejpam-6931	103	54	,	,	PUNCT
ejpam-6931	103	55	ν	ν	NOUN
ejpam-6931	103	56	,	,	PUNCT
ejpam-6931	103	57	e	e	NOUN
ejpam-6931	103	58	)	)	PUNCT
ejpam-6931	104	1	+	+	X
ejpam-6931	104	2	g(ϱo	g(ϱo	PROPN
ejpam-6931	104	3	,	,	PUNCT
ejpam-6931	104	4	ν	ν	NOUN
ejpam-6931	104	5	,	,	PUNCT
ejpam-6931	104	6	e	e	NOUN
ejpam-6931	104	7	)	)	PUNCT
ejpam-6931	104	8	⪯	⪯	NOUN
ejpam-6931	104	9	ℑ′	ℑ′	NOUN
ejpam-6931	104	10	;	;	PUNCT
ejpam-6931	104	11	(	(	PUNCT
ejpam-6931	104	12	2	2	X
ejpam-6931	104	13	)	)	PUNCT
ejpam-6931	104	14	e(ϱo	e(ϱo	NOUN
ejpam-6931	104	15	,	,	PUNCT
ejpam-6931	104	16	ν	ν	NOUN
ejpam-6931	104	17	,	,	PUNCT
ejpam-6931	104	18	e	e	NOUN
ejpam-6931	104	19	)	)	PUNCT
ejpam-6931	104	20	≻	≻	NOUN
ejpam-6931	104	21	∅	∅	NOUN
ejpam-6931	104	22	;	;	PUNCT
ejpam-6931	104	23	(	(	PUNCT
ejpam-6931	104	24	3	3	X
ejpam-6931	104	25	)	)	PUNCT
ejpam-6931	104	26	e(ϱo	e(ϱo	NOUN
ejpam-6931	104	27	,	,	PUNCT
ejpam-6931	104	28	ν	ν	NOUN
ejpam-6931	104	29	,	,	PUNCT
ejpam-6931	104	30	e	e	NOUN
ejpam-6931	104	31	)	)	PUNCT
ejpam-6931	104	32	=	=	SYM
ejpam-6931	105	1	ℑ′	ℑ′	PROPN
ejpam-6931	105	2	for	for	ADP
ejpam-6931	105	3	each	each	DET
ejpam-6931	105	4	e	e	PROPN
ejpam-6931	105	5	∈	∈	PROPN
ejpam-6931	105	6	s0	s0	NOUN
ejpam-6931	105	7	if	if	SCONJ
ejpam-6931	105	8	and	and	CCONJ
ejpam-6931	105	9	only	only	ADV
ejpam-6931	105	10	if	if	SCONJ
ejpam-6931	105	11	ϱo	ϱo	PROPN
ejpam-6931	105	12	=	=	SYM
ejpam-6931	105	13	ν	ν	NOUN
ejpam-6931	105	14	;	;	PUNCT
ejpam-6931	105	15	(	(	PUNCT
ejpam-6931	105	16	4	4	X
ejpam-6931	105	17	)	)	PUNCT
ejpam-6931	105	18	e(ϱo	e(ϱo	NOUN
ejpam-6931	105	19	,	,	PUNCT
ejpam-6931	105	20	ν	ν	NOUN
ejpam-6931	105	21	,	,	PUNCT
ejpam-6931	105	22	e	e	NOUN
ejpam-6931	105	23	)	)	PUNCT
ejpam-6931	105	24	=	=	SYM
ejpam-6931	105	25	e(ν	e(ν	PROPN
ejpam-6931	105	26	,	,	PUNCT
ejpam-6931	105	27	ϱo	ϱo	NOUN
ejpam-6931	105	28	,	,	PUNCT
ejpam-6931	105	29	e	e	NOUN
ejpam-6931	105	30	)	)	PUNCT
ejpam-6931	105	31	;	;	PUNCT
ejpam-6931	105	32	(	(	PUNCT
ejpam-6931	105	33	5	5	X
ejpam-6931	105	34	)	)	PUNCT
ejpam-6931	105	35	e(ϱo	e(ϱo	NOUN
ejpam-6931	105	36	,	,	PUNCT
ejpam-6931	105	37	ς	ς	PROPN
ejpam-6931	105	38	,	,	PUNCT
ejpam-6931	105	39	e+	e+	ADJ
ejpam-6931	105	40	e′	e′	NOUN
ejpam-6931	105	41	)	)	PUNCT
ejpam-6931	105	42	⪰	⪰	NOUN
ejpam-6931	105	43	e(ϱo	e(ϱo	NOUN
ejpam-6931	105	44	,	,	PUNCT
ejpam-6931	105	45	ν	ν	NOUN
ejpam-6931	105	46	,	,	PUNCT
ejpam-6931	105	47	e	e	NOUN
ejpam-6931	105	48	)	)	PUNCT
ejpam-6931	105	49	⋆	⋆	PROPN
ejpam-6931	105	50	e(ν	e(ν	PROPN
ejpam-6931	105	51	,	,	PUNCT
ejpam-6931	105	52	ς	ς	PROPN
ejpam-6931	105	53	,	,	PUNCT
ejpam-6931	105	54	e′	e′	ADJ
ejpam-6931	105	55	)	)	PUNCT
ejpam-6931	105	56	;	;	PUNCT
ejpam-6931	105	57	(	(	PUNCT
ejpam-6931	105	58	6	6	X
ejpam-6931	105	59	)	)	PUNCT
ejpam-6931	105	60	e(ϱo	e(ϱo	NOUN
ejpam-6931	105	61	,	,	PUNCT
ejpam-6931	105	62	ν	ν	NOUN
ejpam-6931	105	63	,	,	PUNCT
ejpam-6931	105	64	·	·	PUNCT
ejpam-6931	105	65	)	)	PUNCT
ejpam-6931	105	66	:	:	PUNCT
ejpam-6931	105	67	s0	s0	PROPN
ejpam-6931	105	68	→	→	SYM
ejpam-6931	105	69	t	t	PROPN
ejpam-6931	105	70	is	be	AUX
ejpam-6931	105	71	continuous	continuous	ADJ
ejpam-6931	105	72	;	;	PUNCT
ejpam-6931	105	73	(	(	PUNCT
ejpam-6931	105	74	7	7	X
ejpam-6931	105	75	)	)	PUNCT
ejpam-6931	105	76	g(ϱo	g(ϱo	NOUN
ejpam-6931	105	77	,	,	PUNCT
ejpam-6931	105	78	ν	ν	NOUN
ejpam-6931	105	79	,	,	PUNCT
ejpam-6931	105	80	e	e	NOUN
ejpam-6931	105	81	)	)	PUNCT
ejpam-6931	105	82	≺	≺	NOUN
ejpam-6931	105	83	ℑ′	ℑ′	PROPN
ejpam-6931	105	84	;	;	PUNCT
ejpam-6931	105	85	(	(	PUNCT
ejpam-6931	105	86	8)	8)	NUM
ejpam-6931	105	87	g(ϱo	g(ϱo	NUM
ejpam-6931	105	88	,	,	PUNCT
ejpam-6931	105	89	ν	ν	NOUN
ejpam-6931	105	90	,	,	PUNCT
ejpam-6931	105	91	e	e	NOUN
ejpam-6931	105	92	)	)	PUNCT
ejpam-6931	105	93	=	=	NOUN
ejpam-6931	105	94	∅	∅	NOUN
ejpam-6931	105	95	for	for	ADP
ejpam-6931	105	96	each	each	DET
ejpam-6931	105	97	e	e	PROPN
ejpam-6931	105	98	∈	∈	PROPN
ejpam-6931	105	99	s0	s0	NOUN
ejpam-6931	105	100	if	if	SCONJ
ejpam-6931	105	101	and	and	CCONJ
ejpam-6931	105	102	only	only	ADV
ejpam-6931	105	103	if	if	SCONJ
ejpam-6931	105	104	ϱo	ϱo	PROPN
ejpam-6931	105	105	=	=	SYM
ejpam-6931	105	106	ν	ν	NOUN
ejpam-6931	105	107	;	;	PUNCT
ejpam-6931	105	108	(	(	PUNCT
ejpam-6931	105	109	9	9	X
ejpam-6931	105	110	)	)	PUNCT
ejpam-6931	105	111	g(ϱo	g(ϱo	NOUN
ejpam-6931	105	112	,	,	PUNCT
ejpam-6931	105	113	ν	ν	NOUN
ejpam-6931	105	114	,	,	PUNCT
ejpam-6931	105	115	e	e	NOUN
ejpam-6931	105	116	)	)	PUNCT
ejpam-6931	105	117	=	=	SYM
ejpam-6931	105	118	g(ν	g(ν	PROPN
ejpam-6931	105	119	,	,	PUNCT
ejpam-6931	105	120	ϱo	ϱo	NOUN
ejpam-6931	105	121	,	,	PUNCT
ejpam-6931	105	122	e	e	NOUN
ejpam-6931	105	123	)	)	PUNCT
ejpam-6931	105	124	;	;	PUNCT
ejpam-6931	105	125	(	(	PUNCT
ejpam-6931	105	126	10	10	NUM
ejpam-6931	105	127	)	)	PUNCT
ejpam-6931	105	128	g(ϱo	g(ϱo	NOUN
ejpam-6931	105	129	,	,	PUNCT
ejpam-6931	105	130	ς	ς	PROPN
ejpam-6931	105	131	,	,	PUNCT
ejpam-6931	105	132	e+	e+	ADJ
ejpam-6931	105	133	e′	e′	NOUN
ejpam-6931	105	134	)	)	PUNCT
ejpam-6931	105	135	⪯	⪯	NOUN
ejpam-6931	105	136	g(ϱo	g(ϱo	PROPN
ejpam-6931	105	137	,	,	PUNCT
ejpam-6931	105	138	ν	ν	NOUN
ejpam-6931	105	139	,	,	PUNCT
ejpam-6931	105	140	e)	e)	PROPN
ejpam-6931	105	141	△	△	NOUN
ejpam-6931	105	142	g(ν	g(ν	PROPN
ejpam-6931	105	143	,	,	PUNCT
ejpam-6931	105	144	ς	ς	NOUN
ejpam-6931	105	145	,	,	PUNCT
ejpam-6931	105	146	e′	e′	ADJ
ejpam-6931	105	147	)	)	PUNCT
ejpam-6931	105	148	;	;	PUNCT
ejpam-6931	105	149	(	(	PUNCT
ejpam-6931	105	150	11	11	NUM
ejpam-6931	105	151	)	)	PUNCT
ejpam-6931	105	152	g(ϱo	g(ϱo	PROPN
ejpam-6931	105	153	,	,	PUNCT
ejpam-6931	105	154	ν	ν	NOUN
ejpam-6931	105	155	,	,	PUNCT
ejpam-6931	105	156	·	·	PUNCT
ejpam-6931	105	157	)	)	PUNCT
ejpam-6931	105	158	:	:	PUNCT
ejpam-6931	106	1	s0	s0	PROPN
ejpam-6931	106	2	→	→	SYM
ejpam-6931	106	3	t	t	PROPN
ejpam-6931	106	4	is	be	AUX
ejpam-6931	106	5	continuous	continuous	ADJ
ejpam-6931	106	6	;	;	PUNCT
ejpam-6931	106	7	for	for	ADP
ejpam-6931	106	8	every	every	DET
ejpam-6931	106	9	ϱo	ϱo	PROPN
ejpam-6931	106	10	,	,	PUNCT
ejpam-6931	106	11	ν	ν	PROPN
ejpam-6931	106	12	,	,	PUNCT
ejpam-6931	106	13	ς	ς	PROPN
ejpam-6931	106	14	∈	∈	PROPN
ejpam-6931	106	15	v	v	NOUN
ejpam-6931	106	16	and	and	CCONJ
ejpam-6931	106	17	e	e	NOUN
ejpam-6931	106	18	,	,	PUNCT
ejpam-6931	106	19	e′	e′	PROPN
ejpam-6931	106	20	∈	∈	PROPN
ejpam-6931	106	21	s0	s0	PROPN
ejpam-6931	106	22	.	.	PUNCT
ejpam-6931	107	1	the	the	DET
ejpam-6931	107	2	pair	pair	NOUN
ejpam-6931	107	3	(	(	PUNCT
ejpam-6931	107	4	e	e	NOUN
ejpam-6931	107	5	,	,	PUNCT
ejpam-6931	107	6	g	g	NOUN
ejpam-6931	107	7	)	)	PUNCT
ejpam-6931	107	8	is	be	AUX
ejpam-6931	107	9	called	call	VERB
ejpam-6931	107	10	complex	complex	ADV
ejpam-6931	107	11	-	-	PUNCT
ejpam-6931	107	12	valued	value	VERB
ejpam-6931	107	13	intuitionistic	intuitionistic	ADJ
ejpam-6931	107	14	fuzzy	fuzzy	ADJ
ejpam-6931	107	15	metric	metric	NOUN
ejpam-6931	107	16	on	on	ADP
ejpam-6931	107	17	v	v	NUM
ejpam-6931	107	18	and	and	CCONJ
ejpam-6931	107	19	(	(	PUNCT
ejpam-6931	107	20	v	v	NOUN
ejpam-6931	107	21	,	,	PUNCT
ejpam-6931	107	22	e	e	NOUN
ejpam-6931	107	23	,	,	PUNCT
ejpam-6931	107	24	g	g	PROPN
ejpam-6931	107	25	,	,	PUNCT
ejpam-6931	107	26	⋆	⋆	NOUN
ejpam-6931	107	27	,	,	PUNCT
ejpam-6931	107	28	△	△	NOUN
ejpam-6931	107	29	)	)	PUNCT
ejpam-6931	107	30	is	be	AUX
ejpam-6931	107	31	called	call	VERB
ejpam-6931	107	32	complex	complex	ADV
ejpam-6931	107	33	-	-	PUNCT
ejpam-6931	107	34	valued	value	VERB
ejpam-6931	107	35	intuitionistic	intuitionistic	ADJ
ejpam-6931	107	36	fuzzy	fuzzy	ADJ
ejpam-6931	107	37	metric	metric	ADJ
ejpam-6931	107	38	space	space	NOUN
ejpam-6931	107	39	.	.	PUNCT
ejpam-6931	108	1	the	the	DET
ejpam-6931	108	2	pair	pair	NOUN
ejpam-6931	108	3	(	(	PUNCT
ejpam-6931	108	4	e	e	NOUN
ejpam-6931	108	5	,	,	PUNCT
ejpam-6931	108	6	g	g	NOUN
ejpam-6931	108	7	)	)	PUNCT
ejpam-6931	108	8	denotes	denote	VERB
ejpam-6931	108	9	the	the	DET
ejpam-6931	108	10	degree	degree	NOUN
ejpam-6931	108	11	of	of	ADP
ejpam-6931	108	12	nearness	nearness	NOUN
ejpam-6931	108	13	and	and	CCONJ
ejpam-6931	108	14	the	the	DET
ejpam-6931	108	15	degree	degree	NOUN
ejpam-6931	108	16	of	of	ADP
ejpam-6931	108	17	non	non	NOUN
ejpam-6931	108	18	-	-	NOUN
ejpam-6931	108	19	nearness	nearness	NOUN
ejpam-6931	108	20	between	between	ADP
ejpam-6931	108	21	two	two	NUM
ejpam-6931	108	22	points	point	NOUN
ejpam-6931	108	23	of	of	ADP
ejpam-6931	108	24	the	the	DET
ejpam-6931	108	25	set	set	NOUN
ejpam-6931	108	26	v	v	NOUN
ejpam-6931	108	27	with	with	ADP
ejpam-6931	108	28	respect	respect	NOUN
ejpam-6931	108	29	to	to	ADP
ejpam-6931	108	30	a	a	DET
ejpam-6931	108	31	complex	complex	ADJ
ejpam-6931	108	32	parameter	parameter	NOUN
ejpam-6931	108	33	e	e	PROPN
ejpam-6931	108	34	∈	∈	PROPN
ejpam-6931	108	35	s0	s0	PROPN
ejpam-6931	108	36	.	.	PUNCT
ejpam-6931	109	1	s.	s.	PROPN
ejpam-6931	109	2	m.	m.	PROPN
ejpam-6931	109	3	u.	u.	PROPN
ejpam-6931	109	4	ud	ud	AUX
ejpam-6931	109	5	-	-	PUNCT
ejpam-6931	109	6	din	din	VERB
ejpam-6931	109	7	et	et	PROPN
ejpam-6931	109	8	al	al	PROPN
ejpam-6931	109	9	.	.	PUNCT
ejpam-6931	109	10	/	/	SYM
ejpam-6931	109	11	eur	eur	PROPN
ejpam-6931	109	12	.	.	PUNCT
ejpam-6931	110	1	j.	j.	PROPN
ejpam-6931	110	2	pure	pure	PROPN
ejpam-6931	110	3	appl	appl	PROPN
ejpam-6931	110	4	.	.	PROPN
ejpam-6931	110	5	math	math	PROPN
ejpam-6931	110	6	,	,	PUNCT
ejpam-6931	110	7	18	18	NUM
ejpam-6931	110	8	(	(	PUNCT
ejpam-6931	110	9	4	4	NUM
ejpam-6931	110	10	)	)	PUNCT
ejpam-6931	110	11	(	(	PUNCT
ejpam-6931	110	12	2025	2025	NUM
ejpam-6931	110	13	)	)	PUNCT
ejpam-6931	110	14	,	,	PUNCT
ejpam-6931	110	15	6931	6931	NUM
ejpam-6931	110	16	6	6	NUM
ejpam-6931	110	17	of	of	ADP
ejpam-6931	110	18	38	38	NUM
ejpam-6931	110	19	3	3	NUM
ejpam-6931	110	20	.	.	PUNCT
ejpam-6931	110	21	main	main	ADJ
ejpam-6931	110	22	results	result	NOUN
ejpam-6931	110	23	in	in	ADP
ejpam-6931	110	24	this	this	DET
ejpam-6931	110	25	section	section	NOUN
ejpam-6931	110	26	,	,	PUNCT
ejpam-6931	110	27	we	we	PRON
ejpam-6931	110	28	introduce	introduce	VERB
ejpam-6931	110	29	the	the	DET
ejpam-6931	110	30	concept	concept	NOUN
ejpam-6931	110	31	of	of	ADP
ejpam-6931	110	32	complex	complex	ADV
ejpam-6931	110	33	-	-	PUNCT
ejpam-6931	110	34	valued	value	VERB
ejpam-6931	110	35	neutrosophic	neutrosophic	ADJ
ejpam-6931	110	36	metric	metric	ADJ
ejpam-6931	110	37	space	space	NOUN
ejpam-6931	110	38	(	(	PUNCT
ejpam-6931	110	39	cvnms	cvnms	NOUN
ejpam-6931	110	40	)	)	PUNCT
ejpam-6931	110	41	.	.	PUNCT
ejpam-6931	111	1	definition	definition	NOUN
ejpam-6931	111	2	6	6	NUM
ejpam-6931	111	3	.	.	PUNCT
ejpam-6931	112	1	[	[	X
ejpam-6931	112	2	28	28	NUM
ejpam-6931	112	3	]	]	PUNCT
ejpam-6931	112	4	assume	assume	VERB
ejpam-6931	112	5	that	that	SCONJ
ejpam-6931	112	6	v	v	ADP
ejpam-6931	112	7	̸=	̸=	PROPN
ejpam-6931	112	8	0	0	NUM
ejpam-6931	112	9	,	,	PUNCT
ejpam-6931	112	10	and	and	CCONJ
ejpam-6931	112	11	let	let	VERB
ejpam-6931	112	12	⋆	⋆	VERB
ejpam-6931	112	13	and	and	CCONJ
ejpam-6931	112	14	△	△	PROPN
ejpam-6931	112	15	represent	represent	VERB
ejpam-6931	112	16	continuous	continuous	ADJ
ejpam-6931	112	17	triangular	triangular	NOUN
ejpam-6931	112	18	norm	norm	NOUN
ejpam-6931	112	19	and	and	CCONJ
ejpam-6931	112	20	continuous	continuous	ADJ
ejpam-6931	112	21	triangular	triangular	NOUN
ejpam-6931	112	22	conorm	conorm	NOUN
ejpam-6931	112	23	,	,	PUNCT
ejpam-6931	112	24	respectively	respectively	ADV
ejpam-6931	112	25	,	,	PUNCT
ejpam-6931	112	26	and	and	CCONJ
ejpam-6931	112	27	e	e	NOUN
ejpam-6931	112	28	,	,	PUNCT
ejpam-6931	112	29	g	g	PROPN
ejpam-6931	112	30	,	,	PUNCT
ejpam-6931	112	31	h	h	PROPN
ejpam-6931	112	32	are	be	AUX
ejpam-6931	112	33	the	the	DET
ejpam-6931	112	34	neutrosophic	neutrosophic	ADJ
ejpam-6931	112	35	sets	set	NOUN
ejpam-6931	112	36	defined	define	VERB
ejpam-6931	112	37	on	on	ADP
ejpam-6931	112	38	v×	v×	NUM
ejpam-6931	112	39	v×	v×	NOUN
ejpam-6931	112	40	(	(	PUNCT
ejpam-6931	112	41	0,∞	0,∞	NUM
ejpam-6931	112	42	)	)	PUNCT
ejpam-6931	112	43	in	in	ADP
ejpam-6931	112	44	which	which	PRON
ejpam-6931	112	45	the	the	DET
ejpam-6931	112	46	following	follow	VERB
ejpam-6931	112	47	conditions	condition	NOUN
ejpam-6931	112	48	are	be	AUX
ejpam-6931	112	49	satisfied	satisfied	ADJ
ejpam-6931	112	50	:	:	PUNCT
ejpam-6931	112	51	(	(	PUNCT
ejpam-6931	112	52	1	1	X
ejpam-6931	112	53	)	)	PUNCT
ejpam-6931	112	54	e(ϱo	e(ϱo	NOUN
ejpam-6931	112	55	,	,	PUNCT
ejpam-6931	112	56	ν	ν	NOUN
ejpam-6931	112	57	,	,	PUNCT
ejpam-6931	112	58	e	e	NOUN
ejpam-6931	112	59	)	)	PUNCT
ejpam-6931	113	1	+	+	X
ejpam-6931	113	2	g(ϱo	g(ϱo	PROPN
ejpam-6931	113	3	,	,	PUNCT
ejpam-6931	113	4	ν	ν	NOUN
ejpam-6931	113	5	,	,	PUNCT
ejpam-6931	113	6	e	e	NOUN
ejpam-6931	113	7	)	)	PUNCT
ejpam-6931	113	8	+	+	VERB
ejpam-6931	113	9	h(ϱo	h(ϱo	ADJ
ejpam-6931	113	10	,	,	PUNCT
ejpam-6931	113	11	ν	ν	NOUN
ejpam-6931	113	12	,	,	PUNCT
ejpam-6931	113	13	e	e	NOUN
ejpam-6931	113	14	)	)	PUNCT
ejpam-6931	113	15	≤	≤	NOUN
ejpam-6931	113	16	3	3	NUM
ejpam-6931	113	17	;	;	PUNCT
ejpam-6931	113	18	(	(	PUNCT
ejpam-6931	113	19	2	2	X
ejpam-6931	113	20	)	)	PUNCT
ejpam-6931	113	21	e(ϱo	e(ϱo	NOUN
ejpam-6931	113	22	,	,	PUNCT
ejpam-6931	113	23	ν	ν	NOUN
ejpam-6931	113	24	,	,	PUNCT
ejpam-6931	113	25	e	e	NOUN
ejpam-6931	113	26	)	)	PUNCT
ejpam-6931	113	27	>	>	X
ejpam-6931	113	28	0	0	NUM
ejpam-6931	113	29	;	;	PUNCT
ejpam-6931	113	30	(	(	PUNCT
ejpam-6931	113	31	3	3	X
ejpam-6931	113	32	)	)	PUNCT
ejpam-6931	113	33	e(ϱo	e(ϱo	NOUN
ejpam-6931	113	34	,	,	PUNCT
ejpam-6931	113	35	ν	ν	NOUN
ejpam-6931	113	36	,	,	PUNCT
ejpam-6931	113	37	e	e	NOUN
ejpam-6931	113	38	)	)	PUNCT
ejpam-6931	113	39	=	=	SYM
ejpam-6931	113	40	1	1	NUM
ejpam-6931	113	41	if	if	SCONJ
ejpam-6931	113	42	and	and	CCONJ
ejpam-6931	113	43	only	only	ADV
ejpam-6931	113	44	if	if	SCONJ
ejpam-6931	113	45	ϱo	ϱo	PROPN
ejpam-6931	113	46	=	=	SYM
ejpam-6931	113	47	ν	ν	NOUN
ejpam-6931	113	48	;	;	PUNCT
ejpam-6931	113	49	(	(	PUNCT
ejpam-6931	113	50	4	4	X
ejpam-6931	113	51	)	)	PUNCT
ejpam-6931	113	52	e(ϱo	e(ϱo	NOUN
ejpam-6931	113	53	,	,	PUNCT
ejpam-6931	113	54	ν	ν	NOUN
ejpam-6931	113	55	,	,	PUNCT
ejpam-6931	113	56	e	e	NOUN
ejpam-6931	113	57	)	)	PUNCT
ejpam-6931	113	58	=	=	SYM
ejpam-6931	113	59	e(ν	e(ν	PROPN
ejpam-6931	113	60	,	,	PUNCT
ejpam-6931	113	61	ϱo	ϱo	NOUN
ejpam-6931	113	62	,	,	PUNCT
ejpam-6931	113	63	e	e	NOUN
ejpam-6931	113	64	)	)	PUNCT
ejpam-6931	113	65	;	;	PUNCT
ejpam-6931	113	66	(	(	PUNCT
ejpam-6931	113	67	5	5	X
ejpam-6931	113	68	)	)	PUNCT
ejpam-6931	113	69	e(ϱo	e(ϱo	NOUN
ejpam-6931	113	70	,	,	PUNCT
ejpam-6931	113	71	ς	ς	PROPN
ejpam-6931	113	72	,	,	PUNCT
ejpam-6931	113	73	e+	e+	ADJ
ejpam-6931	113	74	e′	e′	ADJ
ejpam-6931	113	75	)	)	PUNCT
ejpam-6931	113	76	≥	≥	NOUN
ejpam-6931	113	77	e(ϱo	e(ϱo	NOUN
ejpam-6931	113	78	,	,	PUNCT
ejpam-6931	113	79	ν	ν	NOUN
ejpam-6931	113	80	,	,	PUNCT
ejpam-6931	113	81	e	e	NOUN
ejpam-6931	113	82	)	)	PUNCT
ejpam-6931	113	83	⋆	⋆	PROPN
ejpam-6931	113	84	e(ν	e(ν	PROPN
ejpam-6931	113	85	,	,	PUNCT
ejpam-6931	113	86	ς	ς	PROPN
ejpam-6931	113	87	,	,	PUNCT
ejpam-6931	113	88	e′	e′	ADJ
ejpam-6931	113	89	)	)	PUNCT
ejpam-6931	113	90	;	;	PUNCT
ejpam-6931	113	91	(	(	PUNCT
ejpam-6931	113	92	6	6	X
ejpam-6931	113	93	)	)	PUNCT
ejpam-6931	113	94	e(ϱo	e(ϱo	NOUN
ejpam-6931	113	95	,	,	PUNCT
ejpam-6931	113	96	ν	ν	NOUN
ejpam-6931	113	97	,	,	PUNCT
ejpam-6931	113	98	△	△	NOUN
ejpam-6931	113	99	)	)	PUNCT
ejpam-6931	113	100	is	be	AUX
ejpam-6931	113	101	a	a	DET
ejpam-6931	113	102	non	non	ADJ
ejpam-6931	113	103	decreasing	decrease	VERB
ejpam-6931	113	104	function	function	NOUN
ejpam-6931	113	105	of	of	ADP
ejpam-6931	113	106	r+	r+	NOUN
ejpam-6931	113	107	and	and	CCONJ
ejpam-6931	113	108	lime→∞	lime→∞	PROPN
ejpam-6931	113	109	e(ϱo	e(ϱo	PROPN
ejpam-6931	113	110	,	,	PUNCT
ejpam-6931	113	111	ν	ν	NOUN
ejpam-6931	113	112	,	,	PUNCT
ejpam-6931	113	113	e	e	NOUN
ejpam-6931	113	114	)	)	PUNCT
ejpam-6931	113	115	=	=	SYM
ejpam-6931	113	116	1	1	NUM
ejpam-6931	113	117	;	;	PUNCT
ejpam-6931	113	118	(	(	PUNCT
ejpam-6931	113	119	7	7	X
ejpam-6931	113	120	)	)	PUNCT
ejpam-6931	113	121	g(ϱo	g(ϱo	NOUN
ejpam-6931	113	122	,	,	PUNCT
ejpam-6931	113	123	ν	ν	NOUN
ejpam-6931	113	124	,	,	PUNCT
ejpam-6931	113	125	e	e	NOUN
ejpam-6931	113	126	)	)	PUNCT
ejpam-6931	113	127	<	<	X
ejpam-6931	113	128	1	1	NUM
ejpam-6931	113	129	;	;	PUNCT
ejpam-6931	113	130	(	(	PUNCT
ejpam-6931	113	131	8)	8)	NUM
ejpam-6931	113	132	g(ϱo	g(ϱo	NUM
ejpam-6931	113	133	,	,	PUNCT
ejpam-6931	113	134	ν	ν	NOUN
ejpam-6931	113	135	,	,	PUNCT
ejpam-6931	113	136	e	e	NOUN
ejpam-6931	113	137	)	)	PUNCT
ejpam-6931	113	138	=	=	SYM
ejpam-6931	113	139	0	0	PUNCT
ejpam-6931	114	1	if	if	SCONJ
ejpam-6931	114	2	and	and	CCONJ
ejpam-6931	114	3	only	only	ADV
ejpam-6931	114	4	if	if	SCONJ
ejpam-6931	114	5	ϱo	ϱo	PROPN
ejpam-6931	114	6	=	=	SYM
ejpam-6931	114	7	ν	ν	NOUN
ejpam-6931	114	8	;	;	PUNCT
ejpam-6931	114	9	(	(	PUNCT
ejpam-6931	114	10	9	9	X
ejpam-6931	114	11	)	)	PUNCT
ejpam-6931	114	12	g(ϱo	g(ϱo	NOUN
ejpam-6931	114	13	,	,	PUNCT
ejpam-6931	114	14	ν	ν	NOUN
ejpam-6931	114	15	,	,	PUNCT
ejpam-6931	114	16	e	e	NOUN
ejpam-6931	114	17	)	)	PUNCT
ejpam-6931	114	18	=	=	SYM
ejpam-6931	114	19	g(ν	g(ν	PROPN
ejpam-6931	114	20	,	,	PUNCT
ejpam-6931	114	21	ϱo	ϱo	NOUN
ejpam-6931	114	22	,	,	PUNCT
ejpam-6931	114	23	e	e	NOUN
ejpam-6931	114	24	)	)	PUNCT
ejpam-6931	114	25	;	;	PUNCT
ejpam-6931	114	26	(	(	PUNCT
ejpam-6931	114	27	10	10	NUM
ejpam-6931	114	28	)	)	PUNCT
ejpam-6931	114	29	g(ϱo	g(ϱo	NOUN
ejpam-6931	114	30	,	,	PUNCT
ejpam-6931	114	31	ς	ς	PROPN
ejpam-6931	114	32	,	,	PUNCT
ejpam-6931	114	33	e+	e+	ADJ
ejpam-6931	114	34	e′	e′	NOUN
ejpam-6931	114	35	)	)	PUNCT
ejpam-6931	114	36	≤	≤	NOUN
ejpam-6931	114	37	g(ϱo	g(ϱo	NOUN
ejpam-6931	114	38	,	,	PUNCT
ejpam-6931	114	39	ν	ν	NOUN
ejpam-6931	114	40	,	,	PUNCT
ejpam-6931	114	41	e)	e)	PROPN
ejpam-6931	114	42	△	△	NOUN
ejpam-6931	114	43	g(ν	g(ν	PROPN
ejpam-6931	114	44	,	,	PUNCT
ejpam-6931	114	45	ς	ς	NOUN
ejpam-6931	114	46	,	,	PUNCT
ejpam-6931	114	47	e′	e′	ADJ
ejpam-6931	114	48	)	)	PUNCT
ejpam-6931	114	49	;	;	PUNCT
ejpam-6931	114	50	(	(	PUNCT
ejpam-6931	114	51	11	11	NUM
ejpam-6931	114	52	)	)	PUNCT
ejpam-6931	114	53	g(ϱo	g(ϱo	PROPN
ejpam-6931	114	54	,	,	PUNCT
ejpam-6931	114	55	ν	ν	NOUN
ejpam-6931	114	56	,	,	PUNCT
ejpam-6931	114	57	△	△	NOUN
ejpam-6931	114	58	)	)	PUNCT
ejpam-6931	114	59	is	be	AUX
ejpam-6931	114	60	a	a	DET
ejpam-6931	114	61	non	non	ADJ
ejpam-6931	114	62	increasing	increase	VERB
ejpam-6931	114	63	function	function	NOUN
ejpam-6931	114	64	of	of	ADP
ejpam-6931	114	65	r+	r+	NOUN
ejpam-6931	114	66	and	and	CCONJ
ejpam-6931	114	67	lime→∞	lime→∞	PROPN
ejpam-6931	114	68	g(ϱo	g(ϱo	PROPN
ejpam-6931	114	69	,	,	PUNCT
ejpam-6931	114	70	ν	ν	NOUN
ejpam-6931	114	71	,	,	PUNCT
ejpam-6931	114	72	e	e	NOUN
ejpam-6931	114	73	)	)	PUNCT
ejpam-6931	114	74	=	=	SYM
ejpam-6931	114	75	0	0	NUM
ejpam-6931	114	76	;	;	PUNCT
ejpam-6931	114	77	(	(	PUNCT
ejpam-6931	114	78	12	12	NUM
ejpam-6931	114	79	)	)	PUNCT
ejpam-6931	114	80	h(ϱo	h(ϱo	ADJ
ejpam-6931	114	81	,	,	PUNCT
ejpam-6931	114	82	ν	ν	NOUN
ejpam-6931	114	83	,	,	PUNCT
ejpam-6931	114	84	e	e	NOUN
ejpam-6931	114	85	)	)	PUNCT
ejpam-6931	114	86	<	<	X
ejpam-6931	114	87	1	1	NUM
ejpam-6931	114	88	;	;	PUNCT
ejpam-6931	114	89	(	(	PUNCT
ejpam-6931	114	90	13	13	NUM
ejpam-6931	114	91	)	)	PUNCT
ejpam-6931	114	92	h(ϱo	h(ϱo	ADJ
ejpam-6931	114	93	,	,	PUNCT
ejpam-6931	114	94	ν	ν	NOUN
ejpam-6931	114	95	,	,	PUNCT
ejpam-6931	114	96	e	e	NOUN
ejpam-6931	114	97	)	)	PUNCT
ejpam-6931	114	98	=	=	SYM
ejpam-6931	114	99	0	0	PUNCT
ejpam-6931	115	1	if	if	SCONJ
ejpam-6931	115	2	and	and	CCONJ
ejpam-6931	115	3	only	only	ADV
ejpam-6931	115	4	if	if	SCONJ
ejpam-6931	115	5	ϱo	ϱo	PROPN
ejpam-6931	115	6	=	=	SYM
ejpam-6931	115	7	ν	ν	NOUN
ejpam-6931	115	8	;	;	PUNCT
ejpam-6931	115	9	(	(	PUNCT
ejpam-6931	115	10	14	14	NUM
ejpam-6931	115	11	)	)	PUNCT
ejpam-6931	115	12	h(ϱo	h(ϱo	ADJ
ejpam-6931	115	13	,	,	PUNCT
ejpam-6931	115	14	ν	ν	NOUN
ejpam-6931	115	15	,	,	PUNCT
ejpam-6931	115	16	e	e	NOUN
ejpam-6931	115	17	)	)	PUNCT
ejpam-6931	115	18	=	=	SYM
ejpam-6931	115	19	h(ν	h(ν	PROPN
ejpam-6931	115	20	,	,	PUNCT
ejpam-6931	115	21	ϱo	ϱo	NOUN
ejpam-6931	115	22	,	,	PUNCT
ejpam-6931	115	23	e	e	NOUN
ejpam-6931	115	24	)	)	PUNCT
ejpam-6931	115	25	;	;	PUNCT
ejpam-6931	115	26	(	(	PUNCT
ejpam-6931	115	27	15	15	X
ejpam-6931	115	28	)	)	PUNCT
ejpam-6931	115	29	h(ϱo	h(ϱo	ADJ
ejpam-6931	115	30	,	,	PUNCT
ejpam-6931	115	31	ς	ς	NOUN
ejpam-6931	115	32	,	,	PUNCT
ejpam-6931	115	33	e+	e+	ADJ
ejpam-6931	115	34	e′	e′	NOUN
ejpam-6931	115	35	)	)	PUNCT
ejpam-6931	115	36	⪯	⪯	NOUN
ejpam-6931	115	37	h(ϱo	h(ϱo	ADJ
ejpam-6931	115	38	,	,	PUNCT
ejpam-6931	115	39	ν	ν	NOUN
ejpam-6931	115	40	,	,	PUNCT
ejpam-6931	115	41	c)	c)	X
ejpam-6931	115	42	△	△	X
ejpam-6931	115	43	h(ν	h(ν	PROPN
ejpam-6931	115	44	,	,	PUNCT
ejpam-6931	115	45	ς	ς	NOUN
ejpam-6931	115	46	,	,	PUNCT
ejpam-6931	115	47	e′	e′	ADJ
ejpam-6931	115	48	)	)	PUNCT
ejpam-6931	115	49	;	;	PUNCT
ejpam-6931	115	50	(	(	PUNCT
ejpam-6931	115	51	16	16	NUM
ejpam-6931	115	52	)	)	PUNCT
ejpam-6931	115	53	h(ϱo	h(ϱo	ADJ
ejpam-6931	115	54	,	,	PUNCT
ejpam-6931	115	55	ν	ν	NOUN
ejpam-6931	115	56	,	,	PUNCT
ejpam-6931	115	57	△	△	NOUN
ejpam-6931	115	58	)	)	PUNCT
ejpam-6931	115	59	is	be	AUX
ejpam-6931	115	60	a	a	DET
ejpam-6931	115	61	non	non	ADJ
ejpam-6931	115	62	increasing	increase	VERB
ejpam-6931	115	63	function	function	NOUN
ejpam-6931	115	64	of	of	ADP
ejpam-6931	115	65	r+	r+	NOUN
ejpam-6931	115	66	and	and	CCONJ
ejpam-6931	115	67	lime→∞h(ϱo	lime→∞h(ϱo	ADJ
ejpam-6931	115	68	,	,	PUNCT
ejpam-6931	115	69	ν	ν	NOUN
ejpam-6931	115	70	,	,	PUNCT
ejpam-6931	115	71	e	e	NOUN
ejpam-6931	115	72	)	)	PUNCT
ejpam-6931	115	73	=	=	SYM
ejpam-6931	115	74	0	0	NUM
ejpam-6931	115	75	;	;	PUNCT
ejpam-6931	115	76	(	(	PUNCT
ejpam-6931	115	77	17	17	NUM
ejpam-6931	115	78	)	)	PUNCT
ejpam-6931	115	79	if	if	SCONJ
ejpam-6931	115	80	e	e	NOUN
ejpam-6931	115	81	≤	≤	X
ejpam-6931	115	82	0	0	NUM
ejpam-6931	115	83	then	then	ADV
ejpam-6931	115	84	e(ϱo	e(ϱo	NOUN
ejpam-6931	115	85	,	,	PUNCT
ejpam-6931	115	86	ν	ν	NOUN
ejpam-6931	115	87	,	,	PUNCT
ejpam-6931	115	88	e	e	NOUN
ejpam-6931	115	89	)	)	PUNCT
ejpam-6931	115	90	=	=	SYM
ejpam-6931	115	91	0,g(ϱo	0,g(ϱo	NOUN
ejpam-6931	115	92	,	,	PUNCT
ejpam-6931	115	93	ν	ν	NOUN
ejpam-6931	115	94	,	,	PUNCT
ejpam-6931	115	95	e	e	NOUN
ejpam-6931	115	96	)	)	PUNCT
ejpam-6931	115	97	=	=	SYM
ejpam-6931	115	98	1	1	NUM
ejpam-6931	115	99	and	and	CCONJ
ejpam-6931	115	100	h(ϱo	h(ϱo	ADJ
ejpam-6931	115	101	,	,	PUNCT
ejpam-6931	115	102	ν	ν	NOUN
ejpam-6931	115	103	,	,	PUNCT
ejpam-6931	115	104	e	e	NOUN
ejpam-6931	115	105	)	)	PUNCT
ejpam-6931	115	106	=	=	SYM
ejpam-6931	115	107	1	1	NUM
ejpam-6931	115	108	;	;	PUNCT
ejpam-6931	115	109	for	for	ADP
ejpam-6931	115	110	every	every	DET
ejpam-6931	115	111	ϱo	ϱo	PROPN
ejpam-6931	115	112	,	,	PUNCT
ejpam-6931	115	113	ν	ν	PROPN
ejpam-6931	115	114	,	,	PUNCT
ejpam-6931	115	115	ς	ς	PROPN
ejpam-6931	115	116	∈	∈	PROPN
ejpam-6931	115	117	v	v	NOUN
ejpam-6931	115	118	and	and	CCONJ
ejpam-6931	115	119	e	e	NOUN
ejpam-6931	115	120	,	,	PUNCT
ejpam-6931	115	121	e′	e′	PROPN
ejpam-6931	115	122	∈	∈	PROPN
ejpam-6931	115	123	(	(	PUNCT
ejpam-6931	115	124	0,∞	0,∞	NUM
ejpam-6931	115	125	)	)	PUNCT
ejpam-6931	115	126	.	.	PUNCT
ejpam-6931	116	1	the	the	DET
ejpam-6931	116	2	triplet	triplet	NOUN
ejpam-6931	116	3	(	(	PUNCT
ejpam-6931	116	4	e	e	NOUN
ejpam-6931	116	5	,	,	PUNCT
ejpam-6931	116	6	g	g	PROPN
ejpam-6931	116	7	,	,	PUNCT
ejpam-6931	116	8	h	h	NOUN
ejpam-6931	116	9	)	)	PUNCT
ejpam-6931	116	10	is	be	AUX
ejpam-6931	116	11	called	call	VERB
ejpam-6931	116	12	neutrosophic	neutrosophic	ADJ
ejpam-6931	116	13	metric	metric	NOUN
ejpam-6931	116	14	on	on	ADP
ejpam-6931	116	15	v	v	NUM
ejpam-6931	116	16	and	and	CCONJ
ejpam-6931	116	17	(	(	PUNCT
ejpam-6931	116	18	v	v	NOUN
ejpam-6931	116	19	,	,	PUNCT
ejpam-6931	116	20	e	e	NOUN
ejpam-6931	116	21	,	,	PUNCT
ejpam-6931	116	22	g	g	PROPN
ejpam-6931	116	23	,	,	PUNCT
ejpam-6931	116	24	h	h	NOUN
ejpam-6931	116	25	,	,	PUNCT
ejpam-6931	116	26	⋆	⋆	NOUN
ejpam-6931	116	27	,	,	PUNCT
ejpam-6931	116	28	△	△	NOUN
ejpam-6931	116	29	)	)	PUNCT
ejpam-6931	116	30	is	be	AUX
ejpam-6931	116	31	called	call	VERB
ejpam-6931	116	32	cvnms	cvnms	NOUN
ejpam-6931	116	33	.	.	PUNCT
ejpam-6931	117	1	the	the	DET
ejpam-6931	117	2	triplet	triplet	NOUN
ejpam-6931	117	3	(	(	PUNCT
ejpam-6931	117	4	e	e	NOUN
ejpam-6931	117	5	,	,	PUNCT
ejpam-6931	117	6	g	g	PROPN
ejpam-6931	117	7	,	,	PUNCT
ejpam-6931	117	8	h	h	NOUN
ejpam-6931	117	9	)	)	PUNCT
ejpam-6931	117	10	indicates	indicate	VERB
ejpam-6931	117	11	the	the	DET
ejpam-6931	117	12	closeness	closeness	NOUN
ejpam-6931	117	13	degree	degree	NOUN
ejpam-6931	117	14	,	,	PUNCT
ejpam-6931	117	15	the	the	DET
ejpam-6931	117	16	non	non	ADJ
ejpam-6931	117	17	-	-	ADJ
ejpam-6931	117	18	closeness	closeness	ADJ
ejpam-6931	117	19	degree	degree	NOUN
ejpam-6931	117	20	,	,	PUNCT
ejpam-6931	117	21	and	and	CCONJ
ejpam-6931	117	22	the	the	DET
ejpam-6931	117	23	neutralness	neutralness	NOUN
ejpam-6931	117	24	degree	degree	NOUN
ejpam-6931	117	25	between	between	ADP
ejpam-6931	117	26	two	two	NUM
ejpam-6931	117	27	points	point	NOUN
ejpam-6931	117	28	of	of	ADP
ejpam-6931	117	29	the	the	DET
ejpam-6931	117	30	set	set	NOUN
ejpam-6931	117	31	v	v	NOUN
ejpam-6931	117	32	with	with	ADP
ejpam-6931	117	33	respect	respect	NOUN
ejpam-6931	117	34	to	to	ADP
ejpam-6931	117	35	a	a	DET
ejpam-6931	117	36	parameter	parameter	NOUN
ejpam-6931	117	37	e	e	X
ejpam-6931	117	38	∈	∈	PROPN
ejpam-6931	117	39	(	(	PUNCT
ejpam-6931	117	40	0,∞	0,∞	NOUN
ejpam-6931	117	41	)	)	PUNCT
ejpam-6931	117	42	.	.	PUNCT
ejpam-6931	118	1	s.	s.	PROPN
ejpam-6931	118	2	m.	m.	PROPN
ejpam-6931	118	3	u.	u.	PROPN
ejpam-6931	118	4	ud	ud	AUX
ejpam-6931	118	5	-	-	PUNCT
ejpam-6931	118	6	din	din	VERB
ejpam-6931	118	7	et	et	PROPN
ejpam-6931	118	8	al	al	PROPN
ejpam-6931	118	9	.	.	PUNCT
ejpam-6931	118	10	/	/	SYM
ejpam-6931	118	11	eur	eur	PROPN
ejpam-6931	118	12	.	.	PUNCT
ejpam-6931	119	1	j.	j.	PROPN
ejpam-6931	119	2	pure	pure	PROPN
ejpam-6931	119	3	appl	appl	PROPN
ejpam-6931	119	4	.	.	PROPN
ejpam-6931	119	5	math	math	PROPN
ejpam-6931	119	6	,	,	PUNCT
ejpam-6931	119	7	18	18	NUM
ejpam-6931	119	8	(	(	PUNCT
ejpam-6931	119	9	4	4	NUM
ejpam-6931	119	10	)	)	PUNCT
ejpam-6931	119	11	(	(	PUNCT
ejpam-6931	119	12	2025	2025	NUM
ejpam-6931	119	13	)	)	PUNCT
ejpam-6931	119	14	,	,	PUNCT
ejpam-6931	119	15	6931	6931	NUM
ejpam-6931	119	16	7	7	NUM
ejpam-6931	119	17	of	of	ADP
ejpam-6931	119	18	38	38	NUM
ejpam-6931	119	19	definition	definition	NOUN
ejpam-6931	119	20	7	7	NUM
ejpam-6931	119	21	.	.	PUNCT
ejpam-6931	119	22	assume	assume	VERB
ejpam-6931	119	23	that	that	SCONJ
ejpam-6931	119	24	v	v	ADP
ejpam-6931	119	25	̸=	̸=	PROPN
ejpam-6931	119	26	0	0	NUM
ejpam-6931	119	27	,	,	PUNCT
ejpam-6931	119	28	⋆	⋆	VERB
ejpam-6931	119	29	and	and	CCONJ
ejpam-6931	119	30	△	△	PROPN
ejpam-6931	119	31	represent	represent	VERB
ejpam-6931	119	32	continuous	continuous	ADJ
ejpam-6931	119	33	complex	complex	ADV
ejpam-6931	119	34	-	-	PUNCT
ejpam-6931	119	35	valued	value	VERB
ejpam-6931	119	36	triangular	triangular	NOUN
ejpam-6931	119	37	norm	norm	NOUN
ejpam-6931	119	38	and	and	CCONJ
ejpam-6931	119	39	continuous	continuous	ADJ
ejpam-6931	119	40	complex	complex	ADV
ejpam-6931	119	41	-	-	PUNCT
ejpam-6931	119	42	valued	value	VERB
ejpam-6931	119	43	triangular	triangular	NOUN
ejpam-6931	119	44	conorm	conorm	NOUN
ejpam-6931	119	45	,	,	PUNCT
ejpam-6931	119	46	respectively	respectively	ADV
ejpam-6931	119	47	,	,	PUNCT
ejpam-6931	119	48	and	and	CCONJ
ejpam-6931	119	49	e	e	NOUN
ejpam-6931	119	50	,	,	PUNCT
ejpam-6931	119	51	g	g	PROPN
ejpam-6931	119	52	,	,	PUNCT
ejpam-6931	119	53	h	h	NOUN
ejpam-6931	119	54	are	be	AUX
ejpam-6931	119	55	cfss	cfss	ADV
ejpam-6931	119	56	defined	define	VERB
ejpam-6931	119	57	on	on	ADP
ejpam-6931	119	58	v2	v2	PROPN
ejpam-6931	119	59	×	×	NOUN
ejpam-6931	119	60	s0	s0	NOUN
ejpam-6931	119	61	in	in	ADP
ejpam-6931	119	62	which	which	PRON
ejpam-6931	119	63	the	the	DET
ejpam-6931	119	64	following	follow	VERB
ejpam-6931	119	65	conditions	condition	NOUN
ejpam-6931	119	66	are	be	AUX
ejpam-6931	119	67	satisfied	satisfied	ADJ
ejpam-6931	119	68	:	:	PUNCT
ejpam-6931	119	69	(	(	PUNCT
ejpam-6931	119	70	1	1	X
ejpam-6931	119	71	)	)	PUNCT
ejpam-6931	119	72	e(ϱo	e(ϱo	NOUN
ejpam-6931	119	73	,	,	PUNCT
ejpam-6931	119	74	ν	ν	NOUN
ejpam-6931	119	75	,	,	PUNCT
ejpam-6931	119	76	e	e	NOUN
ejpam-6931	119	77	)	)	PUNCT
ejpam-6931	120	1	+	+	X
ejpam-6931	120	2	g(ϱo	g(ϱo	PROPN
ejpam-6931	120	3	,	,	PUNCT
ejpam-6931	120	4	ν	ν	NOUN
ejpam-6931	120	5	,	,	PUNCT
ejpam-6931	120	6	e	e	NOUN
ejpam-6931	120	7	)	)	PUNCT
ejpam-6931	120	8	+	+	VERB
ejpam-6931	120	9	h(ϱo	h(ϱo	ADJ
ejpam-6931	120	10	,	,	PUNCT
ejpam-6931	120	11	ν	ν	NOUN
ejpam-6931	120	12	,	,	PUNCT
ejpam-6931	120	13	e	e	NOUN
ejpam-6931	120	14	)	)	PUNCT
ejpam-6931	120	15	⪯	⪯	PROPN
ejpam-6931	120	16	ℑ	ℑ	PROPN
ejpam-6931	120	17	;	;	PUNCT
ejpam-6931	120	18	(	(	PUNCT
ejpam-6931	120	19	2	2	X
ejpam-6931	120	20	)	)	PUNCT
ejpam-6931	120	21	e(ϱo	e(ϱo	NOUN
ejpam-6931	120	22	,	,	PUNCT
ejpam-6931	120	23	ν	ν	NOUN
ejpam-6931	120	24	,	,	PUNCT
ejpam-6931	120	25	e	e	NOUN
ejpam-6931	120	26	)	)	PUNCT
ejpam-6931	120	27	≻	≻	NOUN
ejpam-6931	120	28	∅	∅	NOUN
ejpam-6931	120	29	;	;	PUNCT
ejpam-6931	120	30	(	(	PUNCT
ejpam-6931	120	31	3	3	X
ejpam-6931	120	32	)	)	PUNCT
ejpam-6931	120	33	e(ϱo	e(ϱo	NOUN
ejpam-6931	120	34	,	,	PUNCT
ejpam-6931	120	35	ν	ν	NOUN
ejpam-6931	120	36	,	,	PUNCT
ejpam-6931	120	37	e	e	NOUN
ejpam-6931	120	38	)	)	PUNCT
ejpam-6931	120	39	=	=	SYM
ejpam-6931	120	40	ℑ	ℑ	NOUN
ejpam-6931	120	41	for	for	ADP
ejpam-6931	120	42	each	each	DET
ejpam-6931	120	43	e	e	PROPN
ejpam-6931	120	44	∈	∈	PROPN
ejpam-6931	120	45	s0	s0	NOUN
ejpam-6931	120	46	if	if	SCONJ
ejpam-6931	120	47	and	and	CCONJ
ejpam-6931	120	48	only	only	ADV
ejpam-6931	120	49	if	if	SCONJ
ejpam-6931	120	50	ϱo	ϱo	PROPN
ejpam-6931	120	51	=	=	SYM
ejpam-6931	120	52	ν	ν	NOUN
ejpam-6931	120	53	;	;	PUNCT
ejpam-6931	120	54	(	(	PUNCT
ejpam-6931	120	55	4	4	X
ejpam-6931	120	56	)	)	PUNCT
ejpam-6931	120	57	e(ϱo	e(ϱo	NOUN
ejpam-6931	120	58	,	,	PUNCT
ejpam-6931	120	59	ν	ν	NOUN
ejpam-6931	120	60	,	,	PUNCT
ejpam-6931	120	61	e	e	NOUN
ejpam-6931	120	62	)	)	PUNCT
ejpam-6931	120	63	=	=	SYM
ejpam-6931	120	64	e(ν	e(ν	PROPN
ejpam-6931	120	65	,	,	PUNCT
ejpam-6931	120	66	ϱo	ϱo	NOUN
ejpam-6931	120	67	,	,	PUNCT
ejpam-6931	120	68	e	e	NOUN
ejpam-6931	120	69	)	)	PUNCT
ejpam-6931	120	70	;	;	PUNCT
ejpam-6931	120	71	(	(	PUNCT
ejpam-6931	120	72	5	5	X
ejpam-6931	120	73	)	)	PUNCT
ejpam-6931	120	74	e(ϱo	e(ϱo	NOUN
ejpam-6931	120	75	,	,	PUNCT
ejpam-6931	120	76	ς	ς	PROPN
ejpam-6931	120	77	,	,	PUNCT
ejpam-6931	120	78	e+	e+	ADJ
ejpam-6931	120	79	e′	e′	NOUN
ejpam-6931	120	80	)	)	PUNCT
ejpam-6931	120	81	⪰	⪰	NOUN
ejpam-6931	120	82	e(ϱo	e(ϱo	NOUN
ejpam-6931	120	83	,	,	PUNCT
ejpam-6931	120	84	ν	ν	NOUN
ejpam-6931	120	85	,	,	PUNCT
ejpam-6931	120	86	e	e	NOUN
ejpam-6931	120	87	)	)	PUNCT
ejpam-6931	120	88	⋆	⋆	PROPN
ejpam-6931	120	89	e(ν	e(ν	PROPN
ejpam-6931	120	90	,	,	PUNCT
ejpam-6931	120	91	ς	ς	PROPN
ejpam-6931	120	92	,	,	PUNCT
ejpam-6931	120	93	c′	c′	NUM
ejpam-6931	120	94	)	)	PUNCT
ejpam-6931	120	95	;	;	PUNCT
ejpam-6931	120	96	(	(	PUNCT
ejpam-6931	120	97	6	6	X
ejpam-6931	120	98	)	)	PUNCT
ejpam-6931	120	99	e(ϱo	e(ϱo	NOUN
ejpam-6931	120	100	,	,	PUNCT
ejpam-6931	120	101	ν	ν	NOUN
ejpam-6931	120	102	,	,	PUNCT
ejpam-6931	120	103	·	·	PUNCT
ejpam-6931	120	104	)	)	PUNCT
ejpam-6931	120	105	:	:	PUNCT
ejpam-6931	121	1	s0	s0	PROPN
ejpam-6931	121	2	→	→	SYM
ejpam-6931	121	3	t	t	PROPN
ejpam-6931	121	4	is	be	AUX
ejpam-6931	121	5	continuous	continuous	ADJ
ejpam-6931	121	6	;	;	PUNCT
ejpam-6931	121	7	(	(	PUNCT
ejpam-6931	121	8	7	7	X
ejpam-6931	121	9	)	)	PUNCT
ejpam-6931	121	10	g(ϱo	g(ϱo	NOUN
ejpam-6931	121	11	,	,	PUNCT
ejpam-6931	121	12	ν	ν	NOUN
ejpam-6931	121	13	,	,	PUNCT
ejpam-6931	121	14	e	e	NOUN
ejpam-6931	121	15	)	)	PUNCT
ejpam-6931	121	16	≺	≺	NOUN
ejpam-6931	121	17	ℑ	ℑ	NOUN
ejpam-6931	121	18	;	;	PUNCT
ejpam-6931	121	19	(	(	PUNCT
ejpam-6931	121	20	8)	8)	NUM
ejpam-6931	121	21	g(ϱo	g(ϱo	NUM
ejpam-6931	121	22	,	,	PUNCT
ejpam-6931	121	23	ν	ν	NOUN
ejpam-6931	121	24	,	,	PUNCT
ejpam-6931	121	25	e	e	NOUN
ejpam-6931	121	26	)	)	PUNCT
ejpam-6931	121	27	=	=	NOUN
ejpam-6931	121	28	∅	∅	NOUN
ejpam-6931	121	29	for	for	ADP
ejpam-6931	121	30	each	each	DET
ejpam-6931	121	31	e	e	PROPN
ejpam-6931	121	32	∈	∈	PROPN
ejpam-6931	121	33	s0	s0	NOUN
ejpam-6931	121	34	if	if	SCONJ
ejpam-6931	121	35	and	and	CCONJ
ejpam-6931	121	36	only	only	ADV
ejpam-6931	121	37	if	if	SCONJ
ejpam-6931	121	38	ϱo	ϱo	PROPN
ejpam-6931	121	39	=	=	SYM
ejpam-6931	121	40	ν	ν	NOUN
ejpam-6931	121	41	;	;	PUNCT
ejpam-6931	121	42	(	(	PUNCT
ejpam-6931	121	43	9	9	X
ejpam-6931	121	44	)	)	PUNCT
ejpam-6931	121	45	g(ϱo	g(ϱo	NOUN
ejpam-6931	121	46	,	,	PUNCT
ejpam-6931	121	47	ν	ν	NOUN
ejpam-6931	121	48	,	,	PUNCT
ejpam-6931	121	49	e	e	NOUN
ejpam-6931	121	50	)	)	PUNCT
ejpam-6931	121	51	=	=	SYM
ejpam-6931	121	52	g(ν	g(ν	PROPN
ejpam-6931	121	53	,	,	PUNCT
ejpam-6931	121	54	ϱo	ϱo	NOUN
ejpam-6931	121	55	,	,	PUNCT
ejpam-6931	121	56	e	e	NOUN
ejpam-6931	121	57	)	)	PUNCT
ejpam-6931	121	58	;	;	PUNCT
ejpam-6931	121	59	(	(	PUNCT
ejpam-6931	121	60	10	10	NUM
ejpam-6931	121	61	)	)	PUNCT
ejpam-6931	121	62	g(ϱo	g(ϱo	NOUN
ejpam-6931	121	63	,	,	PUNCT
ejpam-6931	121	64	ς	ς	PROPN
ejpam-6931	121	65	,	,	PUNCT
ejpam-6931	121	66	e+	e+	ADJ
ejpam-6931	121	67	e′	e′	NOUN
ejpam-6931	121	68	)	)	PUNCT
ejpam-6931	121	69	⪯	⪯	NOUN
ejpam-6931	121	70	g(ϱo	g(ϱo	PROPN
ejpam-6931	121	71	,	,	PUNCT
ejpam-6931	121	72	ν	ν	NOUN
ejpam-6931	121	73	,	,	PUNCT
ejpam-6931	121	74	e)	e)	PROPN
ejpam-6931	121	75	△	△	NOUN
ejpam-6931	121	76	g(ν	g(ν	PROPN
ejpam-6931	121	77	,	,	PUNCT
ejpam-6931	121	78	ς	ς	NOUN
ejpam-6931	121	79	,	,	PUNCT
ejpam-6931	121	80	e′	e′	ADJ
ejpam-6931	121	81	)	)	PUNCT
ejpam-6931	121	82	;	;	PUNCT
ejpam-6931	121	83	(	(	PUNCT
ejpam-6931	121	84	11	11	NUM
ejpam-6931	121	85	)	)	PUNCT
ejpam-6931	121	86	g(ϱo	g(ϱo	PROPN
ejpam-6931	121	87	,	,	PUNCT
ejpam-6931	121	88	ν	ν	NOUN
ejpam-6931	121	89	,	,	PUNCT
ejpam-6931	121	90	·	·	PUNCT
ejpam-6931	121	91	)	)	PUNCT
ejpam-6931	121	92	:	:	PUNCT
ejpam-6931	122	1	s0	s0	PROPN
ejpam-6931	122	2	→	→	SYM
ejpam-6931	122	3	t	t	PROPN
ejpam-6931	122	4	is	be	AUX
ejpam-6931	122	5	continuous	continuous	ADJ
ejpam-6931	122	6	;	;	PUNCT
ejpam-6931	122	7	(	(	PUNCT
ejpam-6931	122	8	12	12	NUM
ejpam-6931	122	9	)	)	PUNCT
ejpam-6931	122	10	h(ϱo	h(ϱo	ADJ
ejpam-6931	122	11	,	,	PUNCT
ejpam-6931	122	12	ν	ν	NOUN
ejpam-6931	122	13	,	,	PUNCT
ejpam-6931	122	14	e	e	NOUN
ejpam-6931	122	15	)	)	PUNCT
ejpam-6931	122	16	≺	≺	NOUN
ejpam-6931	122	17	ℑ	ℑ	NOUN
ejpam-6931	122	18	;	;	PUNCT
ejpam-6931	122	19	(	(	PUNCT
ejpam-6931	122	20	13	13	NUM
ejpam-6931	122	21	)	)	PUNCT
ejpam-6931	122	22	h(ϱo	h(ϱo	ADJ
ejpam-6931	122	23	,	,	PUNCT
ejpam-6931	122	24	ν	ν	NOUN
ejpam-6931	122	25	,	,	PUNCT
ejpam-6931	122	26	e	e	NOUN
ejpam-6931	122	27	)	)	PUNCT
ejpam-6931	122	28	=	=	NOUN
ejpam-6931	122	29	∅	∅	NOUN
ejpam-6931	122	30	for	for	ADP
ejpam-6931	122	31	each	each	DET
ejpam-6931	122	32	e	e	PROPN
ejpam-6931	122	33	∈	∈	PROPN
ejpam-6931	122	34	s0	s0	NOUN
ejpam-6931	123	1	if	if	SCONJ
ejpam-6931	123	2	and	and	CCONJ
ejpam-6931	123	3	only	only	ADV
ejpam-6931	123	4	if	if	SCONJ
ejpam-6931	123	5	ϱo	ϱo	PROPN
ejpam-6931	123	6	=	=	SYM
ejpam-6931	123	7	ν	ν	NOUN
ejpam-6931	123	8	;	;	PUNCT
ejpam-6931	123	9	(	(	PUNCT
ejpam-6931	123	10	14	14	NUM
ejpam-6931	123	11	)	)	PUNCT
ejpam-6931	123	12	h(ϱo	h(ϱo	ADJ
ejpam-6931	123	13	,	,	PUNCT
ejpam-6931	123	14	ν	ν	NOUN
ejpam-6931	123	15	,	,	PUNCT
ejpam-6931	123	16	e	e	NOUN
ejpam-6931	123	17	)	)	PUNCT
ejpam-6931	123	18	=	=	SYM
ejpam-6931	123	19	h(ν	h(ν	PROPN
ejpam-6931	123	20	,	,	PUNCT
ejpam-6931	123	21	ϱo	ϱo	NOUN
ejpam-6931	123	22	,	,	PUNCT
ejpam-6931	123	23	e	e	NOUN
ejpam-6931	123	24	)	)	PUNCT
ejpam-6931	123	25	;	;	PUNCT
ejpam-6931	123	26	(	(	PUNCT
ejpam-6931	123	27	15	15	X
ejpam-6931	123	28	)	)	PUNCT
ejpam-6931	123	29	h(ϱo	h(ϱo	ADJ
ejpam-6931	123	30	,	,	PUNCT
ejpam-6931	123	31	ς	ς	NOUN
ejpam-6931	123	32	,	,	PUNCT
ejpam-6931	123	33	e+	e+	ADJ
ejpam-6931	123	34	e′	e′	NOUN
ejpam-6931	123	35	)	)	PUNCT
ejpam-6931	123	36	⪯	⪯	NOUN
ejpam-6931	123	37	h(ϱo	h(ϱo	ADJ
ejpam-6931	123	38	,	,	PUNCT
ejpam-6931	123	39	ν	ν	NOUN
ejpam-6931	123	40	,	,	PUNCT
ejpam-6931	123	41	e)	e)	PROPN
ejpam-6931	123	42	△	△	X
ejpam-6931	123	43	h(ν	h(ν	PROPN
ejpam-6931	123	44	,	,	PUNCT
ejpam-6931	123	45	ς	ς	NOUN
ejpam-6931	123	46	,	,	PUNCT
ejpam-6931	123	47	e′	e′	ADJ
ejpam-6931	123	48	)	)	PUNCT
ejpam-6931	123	49	;	;	PUNCT
ejpam-6931	123	50	(	(	PUNCT
ejpam-6931	123	51	16	16	NUM
ejpam-6931	123	52	)	)	PUNCT
ejpam-6931	123	53	h(ϱo	h(ϱo	ADJ
ejpam-6931	123	54	,	,	PUNCT
ejpam-6931	123	55	ν	ν	NOUN
ejpam-6931	123	56	,	,	PUNCT
ejpam-6931	123	57	·	·	PUNCT
ejpam-6931	123	58	)	)	PUNCT
ejpam-6931	123	59	:	:	PUNCT
ejpam-6931	123	60	s0	s0	PROPN
ejpam-6931	123	61	→	→	SYM
ejpam-6931	123	62	t	t	PROPN
ejpam-6931	123	63	is	be	AUX
ejpam-6931	123	64	continuous	continuous	ADJ
ejpam-6931	123	65	;	;	PUNCT
ejpam-6931	123	66	for	for	ADP
ejpam-6931	123	67	every	every	DET
ejpam-6931	123	68	ϱo	ϱo	PROPN
ejpam-6931	123	69	,	,	PUNCT
ejpam-6931	123	70	ν	ν	PROPN
ejpam-6931	123	71	,	,	PUNCT
ejpam-6931	123	72	ς	ς	PROPN
ejpam-6931	123	73	∈	∈	PROPN
ejpam-6931	123	74	v	v	NOUN
ejpam-6931	123	75	and	and	CCONJ
ejpam-6931	123	76	e	e	NOUN
ejpam-6931	123	77	,	,	PUNCT
ejpam-6931	123	78	e′	e′	PROPN
ejpam-6931	123	79	∈	∈	PROPN
ejpam-6931	123	80	s0	s0	PROPN
ejpam-6931	123	81	.	.	PUNCT
ejpam-6931	124	1	then	then	ADV
ejpam-6931	124	2	the	the	DET
ejpam-6931	124	3	triplet	triplet	NOUN
ejpam-6931	124	4	(	(	PUNCT
ejpam-6931	124	5	e	e	NOUN
ejpam-6931	124	6	,	,	PUNCT
ejpam-6931	124	7	g	g	PROPN
ejpam-6931	124	8	,	,	PUNCT
ejpam-6931	124	9	h	h	NOUN
ejpam-6931	124	10	)	)	PUNCT
ejpam-6931	124	11	is	be	AUX
ejpam-6931	124	12	called	call	VERB
ejpam-6931	124	13	complex	complex	ADV
ejpam-6931	124	14	-	-	PUNCT
ejpam-6931	124	15	valued	value	VERB
ejpam-6931	124	16	neutrosophic	neutrosophic	ADJ
ejpam-6931	124	17	metric	metric	NOUN
ejpam-6931	124	18	on	on	ADP
ejpam-6931	124	19	v	v	NUM
ejpam-6931	124	20	and	and	CCONJ
ejpam-6931	124	21	(	(	PUNCT
ejpam-6931	124	22	v	v	NOUN
ejpam-6931	124	23	,	,	PUNCT
ejpam-6931	124	24	e	e	NOUN
ejpam-6931	124	25	,	,	PUNCT
ejpam-6931	124	26	g	g	PROPN
ejpam-6931	124	27	,	,	PUNCT
ejpam-6931	124	28	h	h	NOUN
ejpam-6931	124	29	,	,	PUNCT
ejpam-6931	124	30	⋆	⋆	NOUN
ejpam-6931	124	31	,	,	PUNCT
ejpam-6931	124	32	△	△	NOUN
ejpam-6931	124	33	)	)	PUNCT
ejpam-6931	124	34	is	be	AUX
ejpam-6931	124	35	called	call	VERB
ejpam-6931	124	36	cvnms	cvnms	NOUN
ejpam-6931	124	37	.	.	PUNCT
ejpam-6931	125	1	the	the	DET
ejpam-6931	125	2	triplet	triplet	NOUN
ejpam-6931	125	3	(	(	PUNCT
ejpam-6931	125	4	e	e	NOUN
ejpam-6931	125	5	,	,	PUNCT
ejpam-6931	125	6	g	g	PROPN
ejpam-6931	125	7	,	,	PUNCT
ejpam-6931	125	8	h	h	NOUN
ejpam-6931	125	9	)	)	PUNCT
ejpam-6931	125	10	characterizes	characterize	VERB
ejpam-6931	125	11	the	the	DET
ejpam-6931	125	12	degree	degree	NOUN
ejpam-6931	125	13	of	of	ADP
ejpam-6931	125	14	nearness	nearness	NOUN
ejpam-6931	125	15	,	,	PUNCT
ejpam-6931	125	16	the	the	DET
ejpam-6931	125	17	degree	degree	NOUN
ejpam-6931	125	18	of	of	ADP
ejpam-6931	125	19	non	non	NOUN
ejpam-6931	125	20	-	-	NOUN
ejpam-6931	125	21	nearness	nearness	NOUN
ejpam-6931	125	22	,	,	PUNCT
ejpam-6931	125	23	and	and	CCONJ
ejpam-6931	125	24	the	the	DET
ejpam-6931	125	25	neutralness	neutralness	NOUN
ejpam-6931	125	26	degree	degree	NOUN
ejpam-6931	125	27	between	between	ADP
ejpam-6931	125	28	two	two	NUM
ejpam-6931	125	29	points	point	NOUN
ejpam-6931	125	30	of	of	ADP
ejpam-6931	125	31	the	the	DET
ejpam-6931	125	32	set	set	NOUN
ejpam-6931	125	33	v	v	NOUN
ejpam-6931	125	34	relative	relative	ADJ
ejpam-6931	125	35	to	to	ADP
ejpam-6931	125	36	a	a	DET
ejpam-6931	125	37	complex	complex	ADJ
ejpam-6931	125	38	parameter	parameter	NOUN
ejpam-6931	125	39	e	e	PROPN
ejpam-6931	125	40	∈	∈	PROPN
ejpam-6931	125	41	s0	s0	PROPN
ejpam-6931	125	42	.	.	PUNCT
ejpam-6931	125	43	example	example	NOUN
ejpam-6931	126	1	3	3	X
ejpam-6931	126	2	.	.	X
ejpam-6931	126	3	consider	consider	VERB
ejpam-6931	126	4	the	the	DET
ejpam-6931	126	5	metric	metric	ADJ
ejpam-6931	126	6	space	space	NOUN
ejpam-6931	126	7	(	(	PUNCT
ejpam-6931	126	8	v	v	NOUN
ejpam-6931	126	9	,	,	PUNCT
ejpam-6931	126	10	d	d	NOUN
ejpam-6931	126	11	)	)	PUNCT
ejpam-6931	126	12	.	.	PUNCT
ejpam-6931	127	1	two	two	NUM
ejpam-6931	127	2	binary	binary	ADJ
ejpam-6931	127	3	operations	operation	NOUN
ejpam-6931	127	4	,	,	PUNCT
ejpam-6931	127	5	⋆y	⋆y	PROPN
ejpam-6931	127	6	and	and	CCONJ
ejpam-6931	127	7	△	△	PROPN
ejpam-6931	127	8	y	y	PROPN
ejpam-6931	127	9	,	,	PUNCT
ejpam-6931	127	10	are	be	AUX
ejpam-6931	127	11	defined	define	VERB
ejpam-6931	127	12	for	for	ADP
ejpam-6931	127	13	ei	ei	NOUN
ejpam-6931	127	14	=	=	SYM
ejpam-6931	127	15	(	(	PUNCT
ejpam-6931	127	16	τi	τi	ADP
ejpam-6931	127	17	,	,	PUNCT
ejpam-6931	127	18	ξi	ξi	NOUN
ejpam-6931	127	19	)	)	PUNCT
ejpam-6931	127	20	∈	∈	PROPN
ejpam-6931	127	21	t	t	PROPN
ejpam-6931	127	22	,	,	PUNCT
ejpam-6931	127	23	where	where	SCONJ
ejpam-6931	127	24	i=1,2	i=1,2	ADJ
ejpam-6931	127	25	,	,	PUNCT
ejpam-6931	127	26	as	as	SCONJ
ejpam-6931	127	27	follows	follow	VERB
ejpam-6931	127	28	:	:	PUNCT
ejpam-6931	127	29	e1	e1	VERB
ejpam-6931	128	1	⋆y	⋆y	PROPN
ejpam-6931	128	2	e2	e2	PROPN
ejpam-6931	128	3	=	=	PUNCT
ejpam-6931	128	4	(	(	PUNCT
ejpam-6931	128	5	min{τ1	min{τ1	PROPN
ejpam-6931	128	6	,	,	PUNCT
ejpam-6931	128	7	τ2},min{ξ1	τ2},min{ξ1	PROPN
ejpam-6931	128	8	,	,	PUNCT
ejpam-6931	128	9	ξ2	ξ2	NOUN
ejpam-6931	128	10	}	}	PUNCT
ejpam-6931	128	11	)	)	PUNCT
ejpam-6931	128	12	and	and	CCONJ
ejpam-6931	128	13	e1	e1	PROPN
ejpam-6931	128	14	△	△	PROPN
ejpam-6931	128	15	y	y	PROPN
ejpam-6931	128	16	e2	e2	PROPN
ejpam-6931	128	17	=	=	PUNCT
ejpam-6931	128	18	(	(	PUNCT
ejpam-6931	128	19	max{τ1	max{τ1	PROPN
ejpam-6931	128	20	,	,	PUNCT
ejpam-6931	128	21	τ2},max{ξ1	τ2},max{ξ1	NUM
ejpam-6931	128	22	,	,	PUNCT
ejpam-6931	128	23	ξ2	ξ2	NOUN
ejpam-6931	128	24	}	}	PUNCT
ejpam-6931	128	25	)	)	PUNCT
ejpam-6931	128	26	.	.	PUNCT
ejpam-6931	129	1	the	the	DET
ejpam-6931	129	2	cfss	cfss	PROPN
ejpam-6931	129	3	e	e	PROPN
ejpam-6931	129	4	,	,	PUNCT
ejpam-6931	129	5	g	g	PROPN
ejpam-6931	129	6	,	,	PUNCT
ejpam-6931	129	7	and	and	CCONJ
ejpam-6931	129	8	h	h	NOUN
ejpam-6931	129	9	are	be	AUX
ejpam-6931	129	10	defined	define	VERB
ejpam-6931	129	11	as	as	SCONJ
ejpam-6931	129	12	follows	follow	VERB
ejpam-6931	129	13	:	:	PUNCT
ejpam-6931	129	14	e(ϱo	e(ϱo	NOUN
ejpam-6931	129	15	,	,	PUNCT
ejpam-6931	129	16	ν	ν	NOUN
ejpam-6931	129	17	,	,	PUNCT
ejpam-6931	129	18	e	e	NOUN
ejpam-6931	129	19	)	)	PUNCT
ejpam-6931	129	20	=	=	SYM
ejpam-6931	130	1	τ	τ	PROPN
ejpam-6931	130	2	+	+	NUM
ejpam-6931	130	3	ξ	ξ	X
ejpam-6931	130	4	τ	τ	PROPN
ejpam-6931	130	5	+	+	NUM
ejpam-6931	130	6	ξ	ξ	PROPN
ejpam-6931	130	7	+	+	SYM
ejpam-6931	130	8	d(ϱo	d(ϱo	PROPN
ejpam-6931	130	9	,	,	PUNCT
ejpam-6931	130	10	ν	ν	NOUN
ejpam-6931	130	11	)	)	PUNCT
ejpam-6931	130	12	ℑ	ℑ	PROPN
ejpam-6931	130	13	,	,	PUNCT
ejpam-6931	130	14	g(ϱo	g(ϱo	PROPN
ejpam-6931	130	15	,	,	PUNCT
ejpam-6931	130	16	ν	ν	NOUN
ejpam-6931	130	17	,	,	PUNCT
ejpam-6931	130	18	e	e	NOUN
ejpam-6931	130	19	)	)	PUNCT
ejpam-6931	130	20	=	=	SYM
ejpam-6931	130	21	d(ϱo	d(ϱo	PROPN
ejpam-6931	130	22	,	,	PUNCT
ejpam-6931	130	23	ν	ν	NOUN
ejpam-6931	130	24	)	)	PUNCT
ejpam-6931	130	25	τ	τ	PROPN
ejpam-6931	130	26	+	+	NUM
ejpam-6931	130	27	ξ	ξ	PROPN
ejpam-6931	130	28	+	+	SYM
ejpam-6931	130	29	d(ϱo	d(ϱo	PROPN
ejpam-6931	130	30	,	,	PUNCT
ejpam-6931	130	31	ν	ν	NOUN
ejpam-6931	130	32	)	)	PUNCT
ejpam-6931	130	33	ℑ	ℑ	PROPN
ejpam-6931	130	34	,	,	PUNCT
ejpam-6931	130	35	h(ϱo	h(ϱo	ADJ
ejpam-6931	130	36	,	,	PUNCT
ejpam-6931	130	37	ν	ν	NOUN
ejpam-6931	130	38	,	,	PUNCT
ejpam-6931	130	39	e	e	NOUN
ejpam-6931	130	40	)	)	PUNCT
ejpam-6931	130	41	=	=	SYM
ejpam-6931	130	42	d(ϱo	d(ϱo	PROPN
ejpam-6931	130	43	,	,	PUNCT
ejpam-6931	130	44	ν	ν	NOUN
ejpam-6931	130	45	)	)	PUNCT
ejpam-6931	130	46	τ	τ	PROPN
ejpam-6931	130	47	+	+	NUM
ejpam-6931	130	48	ξ	ξ	PROPN
ejpam-6931	130	49	ℑ	ℑ	PROPN
ejpam-6931	130	50	for	for	ADP
ejpam-6931	130	51	each	each	DET
ejpam-6931	130	52	ϱo	ϱo	NOUN
ejpam-6931	130	53	,	,	PUNCT
ejpam-6931	130	54	ν	ν	PROPN
ejpam-6931	130	55	∈	∈	PROPN
ejpam-6931	130	56	v	v	NOUN
ejpam-6931	130	57	and	and	CCONJ
ejpam-6931	130	58	e	e	NOUN
ejpam-6931	130	59	=	=	SYM
ejpam-6931	130	60	(	(	PUNCT
ejpam-6931	130	61	τ	τ	PROPN
ejpam-6931	130	62	,	,	PUNCT
ejpam-6931	130	63	ξ	ξ	X
ejpam-6931	130	64	)	)	PUNCT
ejpam-6931	130	65	∈	∈	PROPN
ejpam-6931	130	66	s0	s0	NOUN
ejpam-6931	130	67	.	.	PUNCT
ejpam-6931	131	1	consequently	consequently	ADV
ejpam-6931	131	2	,	,	PUNCT
ejpam-6931	131	3	(	(	PUNCT
ejpam-6931	131	4	v	v	NOUN
ejpam-6931	131	5	,	,	PUNCT
ejpam-6931	131	6	e	e	NOUN
ejpam-6931	131	7	,	,	PUNCT
ejpam-6931	131	8	g	g	PROPN
ejpam-6931	131	9	,	,	PUNCT
ejpam-6931	131	10	h	h	NOUN
ejpam-6931	131	11	,	,	PUNCT
ejpam-6931	131	12	⋆y,	⋆y,	PROPN
ejpam-6931	131	13	△	△	PROPN
ejpam-6931	131	14	y	y	NOUN
ejpam-6931	131	15	)	)	PUNCT
ejpam-6931	131	16	is	be	AUX
ejpam-6931	131	17	a	a	DET
ejpam-6931	131	18	cvnms	cvnms	NOUN
ejpam-6931	131	19	.	.	PUNCT
ejpam-6931	132	1	s.	s.	PROPN
ejpam-6931	132	2	m.	m.	PROPN
ejpam-6931	132	3	u.	u.	PROPN
ejpam-6931	132	4	ud	ud	AUX
ejpam-6931	132	5	-	-	PUNCT
ejpam-6931	132	6	din	din	VERB
ejpam-6931	132	7	et	et	PROPN
ejpam-6931	132	8	al	al	PROPN
ejpam-6931	132	9	.	.	PUNCT
ejpam-6931	132	10	/	/	SYM
ejpam-6931	132	11	eur	eur	PROPN
ejpam-6931	132	12	.	.	PUNCT
ejpam-6931	133	1	j.	j.	PROPN
ejpam-6931	133	2	pure	pure	PROPN
ejpam-6931	133	3	appl	appl	PROPN
ejpam-6931	133	4	.	.	PROPN
ejpam-6931	133	5	math	math	PROPN
ejpam-6931	133	6	,	,	PUNCT
ejpam-6931	133	7	18	18	NUM
ejpam-6931	133	8	(	(	PUNCT
ejpam-6931	133	9	4	4	NUM
ejpam-6931	133	10	)	)	PUNCT
ejpam-6931	133	11	(	(	PUNCT
ejpam-6931	133	12	2025	2025	NUM
ejpam-6931	133	13	)	)	PUNCT
ejpam-6931	133	14	,	,	PUNCT
ejpam-6931	133	15	6931	6931	NUM
ejpam-6931	133	16	8	8	NUM
ejpam-6931	133	17	of	of	ADP
ejpam-6931	133	18	38	38	NUM
ejpam-6931	133	19	lemma	lemma	PROPN
ejpam-6931	133	20	1	1	NUM
ejpam-6931	133	21	.	.	PUNCT
ejpam-6931	134	1	given	give	VERB
ejpam-6931	134	2	that	that	SCONJ
ejpam-6931	134	3	(	(	PUNCT
ejpam-6931	134	4	v	v	NOUN
ejpam-6931	134	5	,	,	PUNCT
ejpam-6931	134	6	e	e	NOUN
ejpam-6931	134	7	,	,	PUNCT
ejpam-6931	134	8	g	g	PROPN
ejpam-6931	134	9	,	,	PUNCT
ejpam-6931	134	10	h	h	NOUN
ejpam-6931	134	11	,	,	PUNCT
ejpam-6931	134	12	⋆	⋆	NOUN
ejpam-6931	134	13	,	,	PUNCT
ejpam-6931	134	14	△	△	NOUN
ejpam-6931	134	15	)	)	PUNCT
ejpam-6931	134	16	is	be	AUX
ejpam-6931	134	17	a	a	DET
ejpam-6931	134	18	cvnms	cvnms	NOUN
ejpam-6931	134	19	,	,	PUNCT
ejpam-6931	134	20	e(ϱo	e(ϱo	NOUN
ejpam-6931	134	21	,	,	PUNCT
ejpam-6931	134	22	ν	ν	NOUN
ejpam-6931	134	23	,	,	PUNCT
ejpam-6931	134	24	·	·	PUNCT
ejpam-6931	134	25	)	)	PUNCT
ejpam-6931	134	26	is	be	AUX
ejpam-6931	134	27	non	non	ADJ
ejpam-6931	134	28	-	-	ADJ
ejpam-6931	134	29	decreasing	decrease	VERB
ejpam-6931	134	30	,	,	PUNCT
ejpam-6931	134	31	g(ϱo	g(ϱo	PROPN
ejpam-6931	134	32	,	,	PUNCT
ejpam-6931	134	33	ν	ν	NOUN
ejpam-6931	134	34	,	,	PUNCT
ejpam-6931	134	35	·	·	PUNCT
ejpam-6931	134	36	)	)	PUNCT
ejpam-6931	134	37	is	be	AUX
ejpam-6931	134	38	non	non	ADJ
ejpam-6931	134	39	-	-	ADJ
ejpam-6931	134	40	increasing	increasing	ADJ
ejpam-6931	134	41	,	,	PUNCT
ejpam-6931	134	42	and	and	CCONJ
ejpam-6931	134	43	h(ϱo	h(ϱo	ADJ
ejpam-6931	134	44	,	,	PUNCT
ejpam-6931	134	45	ν	ν	NOUN
ejpam-6931	134	46	,	,	PUNCT
ejpam-6931	134	47	·	·	PUNCT
ejpam-6931	134	48	)	)	PUNCT
ejpam-6931	135	1	is	be	AUX
ejpam-6931	135	2	non	non	ADJ
ejpam-6931	135	3	-	-	ADJ
ejpam-6931	135	4	increasing	increase	VERB
ejpam-6931	135	5	,	,	PUNCT
ejpam-6931	135	6	that	that	ADV
ejpam-6931	135	7	is	is	ADV
ejpam-6931	135	8	,	,	PUNCT
ejpam-6931	135	9	for	for	ADP
ejpam-6931	135	10	any	any	DET
ejpam-6931	135	11	e	e	NOUN
ejpam-6931	135	12	,	,	PUNCT
ejpam-6931	135	13	e′	e′	X
ejpam-6931	135	14	∈	∈	PROPN
ejpam-6931	135	15	s0	s0	PROPN
ejpam-6931	135	16	with	with	ADP
ejpam-6931	135	17	e	e	NOUN
ejpam-6931	135	18	≺	≺	NOUN
ejpam-6931	135	19	e′	e′	PROPN
ejpam-6931	135	20	,	,	PUNCT
ejpam-6931	135	21	it	it	PRON
ejpam-6931	135	22	follows	follow	VERB
ejpam-6931	135	23	that	that	SCONJ
ejpam-6931	135	24	e(ϱo	e(ϱo	NOUN
ejpam-6931	135	25	,	,	PUNCT
ejpam-6931	135	26	ν	ν	NOUN
ejpam-6931	135	27	,	,	PUNCT
ejpam-6931	135	28	e	e	NOUN
ejpam-6931	135	29	)	)	PUNCT
ejpam-6931	135	30	⪯	⪯	NOUN
ejpam-6931	135	31	e(ϱo	e(ϱo	NOUN
ejpam-6931	135	32	,	,	PUNCT
ejpam-6931	135	33	ν	ν	NOUN
ejpam-6931	135	34	,	,	PUNCT
ejpam-6931	135	35	e′),g(ϱo	e′),g(ϱo	NUM
ejpam-6931	135	36	,	,	PUNCT
ejpam-6931	135	37	ν	ν	NOUN
ejpam-6931	135	38	,	,	PUNCT
ejpam-6931	135	39	e	e	NOUN
ejpam-6931	135	40	)	)	PUNCT
ejpam-6931	135	41	⪰	⪰	NOUN
ejpam-6931	135	42	g(ϱo	g(ϱo	NOUN
ejpam-6931	135	43	,	,	PUNCT
ejpam-6931	135	44	ν	ν	NOUN
ejpam-6931	135	45	,	,	PUNCT
ejpam-6931	135	46	e′	e′	ADJ
ejpam-6931	135	47	)	)	PUNCT
ejpam-6931	135	48	and	and	CCONJ
ejpam-6931	135	49	h(ϱo	h(ϱo	ADJ
ejpam-6931	135	50	,	,	PUNCT
ejpam-6931	135	51	ν	ν	NOUN
ejpam-6931	135	52	,	,	PUNCT
ejpam-6931	135	53	e	e	NOUN
ejpam-6931	135	54	)	)	PUNCT
ejpam-6931	135	55	⪰	⪰	VERB
ejpam-6931	135	56	h(ϱo	h(ϱo	ADV
ejpam-6931	135	57	,	,	PUNCT
ejpam-6931	135	58	ν	ν	NOUN
ejpam-6931	135	59	,	,	PUNCT
ejpam-6931	135	60	e′	e′	NOUN
ejpam-6931	135	61	)	)	PUNCT
ejpam-6931	135	62	for	for	ADP
ejpam-6931	135	63	each	each	DET
ejpam-6931	135	64	ϱo	ϱo	NOUN
ejpam-6931	135	65	,	,	PUNCT
ejpam-6931	135	66	ν	ν	PROPN
ejpam-6931	135	67	∈	∈	NOUN
ejpam-6931	135	68	v.	v.	ADP
ejpam-6931	135	69	proof	proof	NOUN
ejpam-6931	135	70	.	.	PUNCT
ejpam-6931	136	1	consider	consider	VERB
ejpam-6931	136	2	e	e	NOUN
ejpam-6931	136	3	,	,	PUNCT
ejpam-6931	136	4	e′	e′	X
ejpam-6931	136	5	∈	∈	PROPN
ejpam-6931	136	6	s0	s0	PROPN
ejpam-6931	136	7	where	where	SCONJ
ejpam-6931	136	8	e	e	NOUN
ejpam-6931	136	9	≺	≺	NOUN
ejpam-6931	136	10	e′	e′	PROPN
ejpam-6931	136	11	,	,	PUNCT
ejpam-6931	136	12	this	this	PRON
ejpam-6931	136	13	implies	imply	VERB
ejpam-6931	136	14	that	that	SCONJ
ejpam-6931	136	15	e′	e′	PROPN
ejpam-6931	136	16	−	−	PROPN
ejpam-6931	136	17	e	e	PROPN
ejpam-6931	136	18	∈	∈	PROPN
ejpam-6931	136	19	s0	s0	PROPN
ejpam-6931	136	20	.	.	PUNCT
ejpam-6931	137	1	by	by	ADP
ejpam-6931	137	2	using	use	VERB
ejpam-6931	137	3	condition	condition	NOUN
ejpam-6931	137	4	(	(	PUNCT
ejpam-6931	137	5	5	5	NUM
ejpam-6931	137	6	)	)	PUNCT
ejpam-6931	137	7	from	from	ADP
ejpam-6931	137	8	definition	definition	NOUN
ejpam-6931	137	9	7	7	NUM
ejpam-6931	137	10	,	,	PUNCT
ejpam-6931	137	11	we	we	PRON
ejpam-6931	137	12	obtain	obtain	VERB
ejpam-6931	137	13	e(ϱo	e(ϱo	NOUN
ejpam-6931	137	14	,	,	PUNCT
ejpam-6931	137	15	ν	ν	NOUN
ejpam-6931	137	16	,	,	PUNCT
ejpam-6931	137	17	e′	e′	ADJ
ejpam-6931	137	18	)	)	PUNCT
ejpam-6931	137	19	=	=	PUNCT
ejpam-6931	138	1	e(ϱo	e(ϱo	NOUN
ejpam-6931	138	2	,	,	PUNCT
ejpam-6931	138	3	ν	ν	NOUN
ejpam-6931	138	4	,	,	PUNCT
ejpam-6931	138	5	e′	e′	X
ejpam-6931	138	6	−	−	PROPN
ejpam-6931	138	7	e+	e+	VERB
ejpam-6931	138	8	e	e	NOUN
ejpam-6931	138	9	)	)	PUNCT
ejpam-6931	138	10	⪰	⪰	NOUN
ejpam-6931	138	11	e(ϱo	e(ϱo	NOUN
ejpam-6931	138	12	,	,	PUNCT
ejpam-6931	138	13	ϱo	ϱo	INTJ
ejpam-6931	138	14	,	,	PUNCT
ejpam-6931	138	15	e′	e′	X
ejpam-6931	138	16	−	−	PROPN
ejpam-6931	138	17	e	e	X
ejpam-6931	138	18	)	)	PUNCT
ejpam-6931	138	19	⋆	⋆	VERB
ejpam-6931	138	20	e(ϱo	e(ϱo	NOUN
ejpam-6931	138	21	,	,	PUNCT
ejpam-6931	138	22	ν	ν	NOUN
ejpam-6931	138	23	,	,	PUNCT
ejpam-6931	138	24	e	e	NOUN
ejpam-6931	138	25	)	)	PUNCT
ejpam-6931	138	26	=	=	SYM
ejpam-6931	138	27	ℑ	ℑ	NOUN
ejpam-6931	138	28	⋆	⋆	VERB
ejpam-6931	138	29	e(ϱo	e(ϱo	NOUN
ejpam-6931	138	30	,	,	PUNCT
ejpam-6931	138	31	ν	ν	NOUN
ejpam-6931	138	32	,	,	PUNCT
ejpam-6931	138	33	e	e	NOUN
ejpam-6931	138	34	)	)	PUNCT
ejpam-6931	138	35	=	=	SYM
ejpam-6931	138	36	e(ϱo	e(ϱo	NOUN
ejpam-6931	138	37	,	,	PUNCT
ejpam-6931	138	38	ν	ν	NOUN
ejpam-6931	138	39	,	,	PUNCT
ejpam-6931	138	40	e	e	NOUN
ejpam-6931	138	41	)	)	PUNCT
ejpam-6931	138	42	.	.	PUNCT
ejpam-6931	139	1	hence	hence	ADV
ejpam-6931	139	2	e(ϱo	e(ϱo	NOUN
ejpam-6931	139	3	,	,	PUNCT
ejpam-6931	139	4	ν	ν	NOUN
ejpam-6931	139	5	,	,	PUNCT
ejpam-6931	139	6	e′	e′	ADJ
ejpam-6931	139	7	)	)	PUNCT
ejpam-6931	139	8	⪰	⪰	NOUN
ejpam-6931	139	9	e(ϱo	e(ϱo	NOUN
ejpam-6931	139	10	,	,	PUNCT
ejpam-6931	139	11	ν	ν	NOUN
ejpam-6931	139	12	,	,	PUNCT
ejpam-6931	139	13	e	e	NOUN
ejpam-6931	139	14	)	)	PUNCT
ejpam-6931	139	15	.	.	PUNCT
ejpam-6931	140	1	alternatively	alternatively	ADV
ejpam-6931	140	2	by	by	ADP
ejpam-6931	140	3	using	use	VERB
ejpam-6931	140	4	condition	condition	NOUN
ejpam-6931	140	5	(	(	PUNCT
ejpam-6931	140	6	10	10	NUM
ejpam-6931	140	7	)	)	PUNCT
ejpam-6931	140	8	from	from	ADP
ejpam-6931	140	9	definition	definition	NOUN
ejpam-6931	140	10	7	7	NUM
ejpam-6931	140	11	,	,	PUNCT
ejpam-6931	140	12	we	we	PRON
ejpam-6931	140	13	have	have	VERB
ejpam-6931	140	14	g(ϱo	g(ϱo	NOUN
ejpam-6931	140	15	,	,	PUNCT
ejpam-6931	140	16	ν	ν	NOUN
ejpam-6931	140	17	,	,	PUNCT
ejpam-6931	140	18	e′	e′	ADJ
ejpam-6931	140	19	)	)	PUNCT
ejpam-6931	140	20	=	=	SYM
ejpam-6931	140	21	g(ϱo	g(ϱo	NOUN
ejpam-6931	140	22	,	,	PUNCT
ejpam-6931	140	23	ν	ν	NOUN
ejpam-6931	140	24	,	,	PUNCT
ejpam-6931	140	25	e′	e′	X
ejpam-6931	140	26	−	−	PROPN
ejpam-6931	140	27	e+	e+	ADJ
ejpam-6931	140	28	e	e	NOUN
ejpam-6931	140	29	)	)	PUNCT
ejpam-6931	140	30	⪯	⪯	NOUN
ejpam-6931	140	31	g(ϱo	g(ϱo	PROPN
ejpam-6931	140	32	,	,	PUNCT
ejpam-6931	140	33	ϱo	ϱo	PROPN
ejpam-6931	140	34	,	,	PUNCT
ejpam-6931	140	35	e′	e′	X
ejpam-6931	140	36	−	−	PROPN
ejpam-6931	140	37	e	e	NOUN
ejpam-6931	140	38	)	)	PUNCT
ejpam-6931	140	39	△	△	X
ejpam-6931	140	40	g(ϱo	g(ϱo	PROPN
ejpam-6931	140	41	,	,	PUNCT
ejpam-6931	140	42	ν	ν	NOUN
ejpam-6931	140	43	,	,	PUNCT
ejpam-6931	140	44	e	e	NOUN
ejpam-6931	140	45	)	)	PUNCT
ejpam-6931	140	46	=	=	SYM
ejpam-6931	140	47	∅	∅	NOUN
ejpam-6931	140	48	△	△	NOUN
ejpam-6931	140	49	g(ϱo	g(ϱo	NOUN
ejpam-6931	140	50	,	,	PUNCT
ejpam-6931	140	51	ν	ν	NOUN
ejpam-6931	140	52	,	,	PUNCT
ejpam-6931	140	53	e	e	NOUN
ejpam-6931	140	54	)	)	PUNCT
ejpam-6931	140	55	=	=	SYM
ejpam-6931	140	56	g(ϱo	g(ϱo	NOUN
ejpam-6931	140	57	,	,	PUNCT
ejpam-6931	140	58	ν	ν	NOUN
ejpam-6931	140	59	,	,	PUNCT
ejpam-6931	140	60	e	e	NOUN
ejpam-6931	140	61	)	)	PUNCT
ejpam-6931	140	62	.	.	PUNCT
ejpam-6931	141	1	hence	hence	ADV
ejpam-6931	141	2	g(ϱo	g(ϱo	PROPN
ejpam-6931	141	3	,	,	PUNCT
ejpam-6931	141	4	ν	ν	NOUN
ejpam-6931	141	5	,	,	PUNCT
ejpam-6931	141	6	e′	e′	NOUN
ejpam-6931	141	7	)	)	PUNCT
ejpam-6931	141	8	⪯	⪯	PROPN
ejpam-6931	141	9	g(ϱo	g(ϱo	PROPN
ejpam-6931	141	10	,	,	PUNCT
ejpam-6931	141	11	ν	ν	PROPN
ejpam-6931	141	12	,	,	PUNCT
ejpam-6931	141	13	e	e	NOUN
ejpam-6931	141	14	)	)	PUNCT
ejpam-6931	141	15	.	.	PUNCT
ejpam-6931	142	1	similarly	similarly	ADV
ejpam-6931	142	2	by	by	ADP
ejpam-6931	142	3	using	use	VERB
ejpam-6931	142	4	condition	condition	NOUN
ejpam-6931	142	5	(	(	PUNCT
ejpam-6931	142	6	15	15	NUM
ejpam-6931	142	7	)	)	PUNCT
ejpam-6931	142	8	from	from	ADP
ejpam-6931	142	9	definition	definition	NOUN
ejpam-6931	142	10	7	7	NUM
ejpam-6931	142	11	,	,	PUNCT
ejpam-6931	142	12	we	we	PRON
ejpam-6931	142	13	have	have	VERB
ejpam-6931	142	14	h(ϱo	h(ϱo	ADJ
ejpam-6931	142	15	,	,	PUNCT
ejpam-6931	142	16	ν	ν	NOUN
ejpam-6931	142	17	,	,	PUNCT
ejpam-6931	142	18	e′	e′	ADJ
ejpam-6931	142	19	)	)	PUNCT
ejpam-6931	142	20	=	=	PUNCT
ejpam-6931	142	21	h(ϱo	h(ϱo	ADJ
ejpam-6931	142	22	,	,	PUNCT
ejpam-6931	142	23	ν	ν	NOUN
ejpam-6931	142	24	,	,	PUNCT
ejpam-6931	142	25	e′	e′	X
ejpam-6931	142	26	−	−	PROPN
ejpam-6931	142	27	e+	e+	VERB
ejpam-6931	142	28	e	e	NOUN
ejpam-6931	142	29	)	)	PUNCT
ejpam-6931	142	30	⪯	⪯	NOUN
ejpam-6931	142	31	h(ϱo	h(ϱo	ADJ
ejpam-6931	142	32	,	,	PUNCT
ejpam-6931	142	33	ϱo	ϱo	NOUN
ejpam-6931	142	34	,	,	PUNCT
ejpam-6931	142	35	e′	e′	NOUN
ejpam-6931	142	36	−	−	X
ejpam-6931	142	37	e)	e)	PROPN
ejpam-6931	142	38	△	△	NOUN
ejpam-6931	142	39	h(ϱo	h(ϱo	ADJ
ejpam-6931	142	40	,	,	PUNCT
ejpam-6931	142	41	ν	ν	NOUN
ejpam-6931	142	42	,	,	PUNCT
ejpam-6931	142	43	e	e	NOUN
ejpam-6931	142	44	)	)	PUNCT
ejpam-6931	142	45	=	=	SYM
ejpam-6931	142	46	∅	∅	NOUN
ejpam-6931	142	47	△	△	NOUN
ejpam-6931	142	48	h(ϱo	h(ϱo	ADJ
ejpam-6931	142	49	,	,	PUNCT
ejpam-6931	142	50	ν	ν	NOUN
ejpam-6931	142	51	,	,	PUNCT
ejpam-6931	142	52	e	e	NOUN
ejpam-6931	142	53	)	)	PUNCT
ejpam-6931	142	54	=	=	SYM
ejpam-6931	142	55	h(ϱo	h(ϱo	ADJ
ejpam-6931	142	56	,	,	PUNCT
ejpam-6931	142	57	ν	ν	NOUN
ejpam-6931	142	58	,	,	PUNCT
ejpam-6931	142	59	e	e	NOUN
ejpam-6931	142	60	)	)	PUNCT
ejpam-6931	142	61	.	.	PUNCT
ejpam-6931	143	1	hence	hence	ADV
ejpam-6931	143	2	h(ϱo	h(ϱo	ADV
ejpam-6931	143	3	,	,	PUNCT
ejpam-6931	143	4	ν	ν	NOUN
ejpam-6931	143	5	,	,	PUNCT
ejpam-6931	143	6	e′	e′	NOUN
ejpam-6931	143	7	)	)	PUNCT
ejpam-6931	143	8	⪯	⪯	NOUN
ejpam-6931	143	9	h(ϱo	h(ϱo	ADV
ejpam-6931	143	10	,	,	PUNCT
ejpam-6931	143	11	ν	ν	NOUN
ejpam-6931	143	12	,	,	PUNCT
ejpam-6931	143	13	e	e	NOUN
ejpam-6931	143	14	)	)	PUNCT
ejpam-6931	143	15	.	.	PUNCT
ejpam-6931	144	1	definition	definition	NOUN
ejpam-6931	144	2	8	8	NUM
ejpam-6931	144	3	.	.	PUNCT
ejpam-6931	145	1	let	let	VERB
ejpam-6931	145	2	(	(	PUNCT
ejpam-6931	145	3	v	v	NOUN
ejpam-6931	145	4	,	,	PUNCT
ejpam-6931	145	5	e	e	NOUN
ejpam-6931	145	6	,	,	PUNCT
ejpam-6931	145	7	g	g	PROPN
ejpam-6931	145	8	,	,	PUNCT
ejpam-6931	145	9	h	h	NOUN
ejpam-6931	145	10	,	,	PUNCT
ejpam-6931	145	11	⋆	⋆	NOUN
ejpam-6931	145	12	,	,	PUNCT
ejpam-6931	145	13	△	△	X
ejpam-6931	145	14	)	)	PUNCT
ejpam-6931	145	15	be	be	AUX
ejpam-6931	145	16	a	a	DET
ejpam-6931	145	17	cvnms	cvnms	NOUN
ejpam-6931	145	18	.	.	PUNCT
ejpam-6931	146	1	a	a	DET
ejpam-6931	146	2	sequence	sequence	NOUN
ejpam-6931	146	3	{	{	PUNCT
ejpam-6931	146	4	ϱon	ϱon	NOUN
ejpam-6931	146	5	}	}	PUNCT
ejpam-6931	146	6	in	in	ADP
ejpam-6931	146	7	v	v	NUM
ejpam-6931	146	8	converges	converge	NOUN
ejpam-6931	146	9	to	to	ADP
ejpam-6931	146	10	ϱo	ϱo	DET
ejpam-6931	146	11	∈	∈	PROPN
ejpam-6931	146	12	v	v	NOUN
ejpam-6931	146	13	provided	provide	VERB
ejpam-6931	146	14	that	that	SCONJ
ejpam-6931	146	15	all	all	DET
ejpam-6931	146	16	r	r	NOUN
ejpam-6931	146	17	∈	∈	PROPN
ejpam-6931	146	18	t0	t0	PROPN
ejpam-6931	146	19	as	as	ADV
ejpam-6931	146	20	well	well	ADV
ejpam-6931	146	21	as	as	ADP
ejpam-6931	146	22	e	e	PROPN
ejpam-6931	146	23	∈	∈	PROPN
ejpam-6931	146	24	s0	s0	PROPN
ejpam-6931	146	25	,	,	PUNCT
ejpam-6931	146	26	for	for	ADP
ejpam-6931	146	27	some	some	DET
ejpam-6931	146	28	n0	n0	NOUN
ejpam-6931	146	29	∈	∈	PROPN
ejpam-6931	146	30	m	m	VERB
ejpam-6931	146	31	if	if	SCONJ
ejpam-6931	146	32	it	it	PRON
ejpam-6931	146	33	meets	meet	VERB
ejpam-6931	146	34	the	the	DET
ejpam-6931	146	35	following	follow	VERB
ejpam-6931	146	36	criteria	criterion	NOUN
ejpam-6931	146	37	:	:	PUNCT
ejpam-6931	146	38	e(ϱon	e(ϱon	PROPN
ejpam-6931	146	39	,	,	PUNCT
ejpam-6931	146	40	ϱo	ϱo	NOUN
ejpam-6931	146	41	,	,	PUNCT
ejpam-6931	146	42	e	e	NOUN
ejpam-6931	146	43	)	)	PUNCT
ejpam-6931	146	44	≻	≻	VERB
ejpam-6931	146	45	ℑ−	ℑ−	ADJ
ejpam-6931	146	46	r	r	NOUN
ejpam-6931	146	47	,	,	PUNCT
ejpam-6931	146	48	g(ϱon	g(ϱon	PROPN
ejpam-6931	146	49	,	,	PUNCT
ejpam-6931	146	50	ϱo	ϱo	NOUN
ejpam-6931	146	51	,	,	PUNCT
ejpam-6931	146	52	e	e	NOUN
ejpam-6931	146	53	)	)	PUNCT
ejpam-6931	146	54	≺	≺	NOUN
ejpam-6931	146	55	r	r	NOUN
ejpam-6931	146	56	and	and	CCONJ
ejpam-6931	146	57	h(ϱon	h(ϱon	PROPN
ejpam-6931	146	58	,	,	PUNCT
ejpam-6931	146	59	ϱ	ϱ	ADP
ejpam-6931	146	60	o	o	PROPN
ejpam-6931	146	61	,	,	PUNCT
ejpam-6931	146	62	e	e	NOUN
ejpam-6931	146	63	)	)	PUNCT
ejpam-6931	146	64	≺	≺	NOUN
ejpam-6931	146	65	r	r	NOUN
ejpam-6931	146	66	for	for	ADP
ejpam-6931	146	67	each	each	DET
ejpam-6931	146	68	n	n	PROPN
ejpam-6931	146	69	>	>	X
ejpam-6931	146	70	n0	n0	PROPN
ejpam-6931	146	71	.	.	PUNCT
ejpam-6931	147	1	definition	definition	NOUN
ejpam-6931	147	2	9	9	NUM
ejpam-6931	147	3	.	.	PUNCT
ejpam-6931	148	1	let	let	VERB
ejpam-6931	148	2	(	(	PUNCT
ejpam-6931	148	3	v	v	NOUN
ejpam-6931	148	4	,	,	PUNCT
ejpam-6931	148	5	e	e	NOUN
ejpam-6931	148	6	,	,	PUNCT
ejpam-6931	148	7	g	g	PROPN
ejpam-6931	148	8	,	,	PUNCT
ejpam-6931	148	9	h	h	NOUN
ejpam-6931	148	10	,	,	PUNCT
ejpam-6931	148	11	⋆	⋆	NOUN
ejpam-6931	148	12	,	,	PUNCT
ejpam-6931	148	13	△	△	X
ejpam-6931	148	14	)	)	PUNCT
ejpam-6931	148	15	be	be	AUX
ejpam-6931	148	16	a	a	DET
ejpam-6931	148	17	cvnms	cvnms	NOUN
ejpam-6931	148	18	.	.	PUNCT
ejpam-6931	149	1	a	a	DET
ejpam-6931	149	2	cauchy	cauchy	ADJ
ejpam-6931	149	3	sequence	sequence	NOUN
ejpam-6931	149	4	is	be	AUX
ejpam-6931	149	5	a	a	DET
ejpam-6931	149	6	sequence	sequence	NOUN
ejpam-6931	149	7	{	{	PUNCT
ejpam-6931	149	8	ϱon	ϱon	NOUN
ejpam-6931	149	9	}	}	PUNCT
ejpam-6931	149	10	in	in	ADP
ejpam-6931	149	11	v	v	NUM
ejpam-6931	149	12	that	that	PRON
ejpam-6931	149	13	satisfies	satisfy	VERB
ejpam-6931	149	14	the	the	DET
ejpam-6931	149	15	following	follow	VERB
ejpam-6931	149	16	criteria	criterion	NOUN
ejpam-6931	149	17	:	:	PUNCT
ejpam-6931	149	18	lim	lim	PROPN
ejpam-6931	149	19	n→∞	n→∞	NUM
ejpam-6931	149	20	inf	inf	PROPN
ejpam-6931	149	21	m	m	PROPN
ejpam-6931	149	22	>	>	PROPN
ejpam-6931	149	23	n	n	PRON
ejpam-6931	149	24	e(ϱon	e(ϱon	PROPN
ejpam-6931	149	25	,	,	PUNCT
ejpam-6931	149	26	ϱom	ϱom	NOUN
ejpam-6931	149	27	,	,	PUNCT
ejpam-6931	149	28	e	e	NOUN
ejpam-6931	149	29	)	)	PUNCT
ejpam-6931	149	30	=	=	SYM
ejpam-6931	149	31	ℑ	ℑ	PROPN
ejpam-6931	149	32	,	,	PUNCT
ejpam-6931	149	33	lim	lim	PROPN
ejpam-6931	149	34	n→∞	n→∞	NUM
ejpam-6931	149	35	sup	sup	PROPN
ejpam-6931	149	36	m	m	PROPN
ejpam-6931	149	37	>	>	NOUN
ejpam-6931	149	38	n	n	PRON
ejpam-6931	149	39	g(ϱon	g(ϱon	NOUN
ejpam-6931	149	40	,	,	PUNCT
ejpam-6931	149	41	ϱom	ϱom	NOUN
ejpam-6931	149	42	,	,	PUNCT
ejpam-6931	149	43	e	e	NOUN
ejpam-6931	149	44	)	)	PUNCT
ejpam-6931	149	45	=	=	NOUN
ejpam-6931	149	46	∅	∅	NOUN
ejpam-6931	149	47	,	,	PUNCT
ejpam-6931	149	48	lim	lim	PROPN
ejpam-6931	149	49	n→∞	n→∞	NUM
ejpam-6931	149	50	sup	sup	PROPN
ejpam-6931	149	51	m	m	PROPN
ejpam-6931	149	52	>	>	X
ejpam-6931	149	53	n	n	PROPN
ejpam-6931	149	54	h(ϱon	h(ϱon	NOUN
ejpam-6931	149	55	,	,	PUNCT
ejpam-6931	149	56	ϱ	ϱ	ADP
ejpam-6931	149	57	o	o	PROPN
ejpam-6931	149	58	m	m	NOUN
ejpam-6931	149	59	,	,	PUNCT
ejpam-6931	149	60	e	e	NOUN
ejpam-6931	149	61	)	)	PUNCT
ejpam-6931	149	62	=	=	NOUN
ejpam-6931	149	63	∅	∅	NOUN
ejpam-6931	149	64	,	,	PUNCT
ejpam-6931	149	65	for	for	ADP
ejpam-6931	149	66	each	each	DET
ejpam-6931	149	67	e	e	PROPN
ejpam-6931	149	68	∈	∈	PROPN
ejpam-6931	149	69	s0	s0	PROPN
ejpam-6931	149	70	.	.	PUNCT
ejpam-6931	150	1	s.	s.	PROPN
ejpam-6931	150	2	m.	m.	PROPN
ejpam-6931	150	3	u.	u.	PROPN
ejpam-6931	150	4	ud	ud	AUX
ejpam-6931	150	5	-	-	PUNCT
ejpam-6931	150	6	din	din	VERB
ejpam-6931	150	7	et	et	PROPN
ejpam-6931	150	8	al	al	PROPN
ejpam-6931	150	9	.	.	PUNCT
ejpam-6931	150	10	/	/	SYM
ejpam-6931	150	11	eur	eur	PROPN
ejpam-6931	150	12	.	.	PUNCT
ejpam-6931	151	1	j.	j.	PROPN
ejpam-6931	151	2	pure	pure	PROPN
ejpam-6931	151	3	appl	appl	PROPN
ejpam-6931	151	4	.	.	PROPN
ejpam-6931	151	5	math	math	PROPN
ejpam-6931	151	6	,	,	PUNCT
ejpam-6931	151	7	18	18	NUM
ejpam-6931	151	8	(	(	PUNCT
ejpam-6931	151	9	4	4	NUM
ejpam-6931	151	10	)	)	PUNCT
ejpam-6931	151	11	(	(	PUNCT
ejpam-6931	151	12	2025	2025	NUM
ejpam-6931	151	13	)	)	PUNCT
ejpam-6931	151	14	,	,	PUNCT
ejpam-6931	151	15	6931	6931	NUM
ejpam-6931	151	16	9	9	NUM
ejpam-6931	151	17	of	of	ADP
ejpam-6931	151	18	38	38	NUM
ejpam-6931	151	19	a	a	DET
ejpam-6931	151	20	cvnms	cvnms	NOUN
ejpam-6931	151	21	is	be	AUX
ejpam-6931	151	22	said	say	VERB
ejpam-6931	151	23	to	to	PART
ejpam-6931	151	24	be	be	AUX
ejpam-6931	151	25	complete	complete	ADJ
ejpam-6931	151	26	if	if	SCONJ
ejpam-6931	151	27	every	every	DET
ejpam-6931	151	28	cauchy	cauchy	ADJ
ejpam-6931	151	29	sequence	sequence	NOUN
ejpam-6931	151	30	in	in	ADP
ejpam-6931	151	31	v	v	NOUN
ejpam-6931	151	32	converges	converge	NOUN
ejpam-6931	151	33	.	.	PUNCT
ejpam-6931	152	1	the	the	DET
ejpam-6931	152	2	examples	example	NOUN
ejpam-6931	152	3	below	below	ADP
ejpam-6931	152	4	help	help	NOUN
ejpam-6931	152	5	to	to	PART
ejpam-6931	152	6	clarify	clarify	VERB
ejpam-6931	152	7	the	the	DET
ejpam-6931	152	8	ideas	idea	NOUN
ejpam-6931	152	9	covered	cover	VERB
ejpam-6931	152	10	in	in	ADP
ejpam-6931	152	11	definitions	definition	NOUN
ejpam-6931	152	12	8	8	NUM
ejpam-6931	152	13	and	and	CCONJ
ejpam-6931	152	14	9	9	NUM
ejpam-6931	152	15	.	.	NOUN
ejpam-6931	152	16	example	example	NOUN
ejpam-6931	152	17	4	4	NUM
ejpam-6931	152	18	.	.	X
ejpam-6931	152	19	observe	observe	VERB
ejpam-6931	152	20	the	the	DET
ejpam-6931	152	21	cvnms	cvnms	NOUN
ejpam-6931	152	22	,	,	PUNCT
ejpam-6931	152	23	denoted	denote	VERB
ejpam-6931	152	24	as	as	ADP
ejpam-6931	152	25	(	(	PUNCT
ejpam-6931	152	26	v	v	NOUN
ejpam-6931	152	27	,	,	PUNCT
ejpam-6931	152	28	e	e	NOUN
ejpam-6931	152	29	,	,	PUNCT
ejpam-6931	152	30	g	g	PROPN
ejpam-6931	152	31	,	,	PUNCT
ejpam-6931	152	32	h	h	NOUN
ejpam-6931	152	33	,	,	PUNCT
ejpam-6931	152	34	⋆y,	⋆y,	PROPN
ejpam-6931	152	35	△	△	PROPN
ejpam-6931	152	36	y	y	NOUN
ejpam-6931	152	37	)	)	PUNCT
ejpam-6931	152	38	in	in	ADP
ejpam-6931	152	39	example	example	NOUN
ejpam-6931	153	1	3	3	X
ejpam-6931	153	2	.	.	PUNCT
ejpam-6931	154	1	furthermore	furthermore	ADV
ejpam-6931	154	2	,	,	PUNCT
ejpam-6931	154	3	set	set	VERB
ejpam-6931	154	4	v	v	NOUN
ejpam-6931	154	5	=	=	PUNCT
ejpam-6931	155	1	[	[	X
ejpam-6931	155	2	4	4	NUM
ejpam-6931	155	3	,	,	PUNCT
ejpam-6931	155	4	5	5	NUM
ejpam-6931	155	5	]	]	PUNCT
ejpam-6931	155	6	and	and	CCONJ
ejpam-6931	155	7	define	define	VERB
ejpam-6931	155	8	d	d	NOUN
ejpam-6931	155	9	as	as	ADP
ejpam-6931	155	10	d(ϱo	d(ϱo	PROPN
ejpam-6931	155	11	,	,	PUNCT
ejpam-6931	155	12	ν	ν	NOUN
ejpam-6931	155	13	)	)	PUNCT
ejpam-6931	155	14	=	=	SYM
ejpam-6931	155	15	|ϱo	|ϱo	PRON
ejpam-6931	155	16	−	−	PROPN
ejpam-6931	155	17	ν|	ν|	NOUN
ejpam-6931	155	18	for	for	ADP
ejpam-6931	155	19	all	all	DET
ejpam-6931	155	20	ϱo	ϱo	NOUN
ejpam-6931	155	21	,	,	PUNCT
ejpam-6931	155	22	ν	ν	PROPN
ejpam-6931	155	23	∈	∈	PROPN
ejpam-6931	155	24	v.	v.	CCONJ
ejpam-6931	155	25	let	let	VERB
ejpam-6931	155	26	the	the	DET
ejpam-6931	155	27	sequence	sequence	NOUN
ejpam-6931	155	28	{	{	PUNCT
ejpam-6931	155	29	ϱon	ϱon	NOUN
ejpam-6931	155	30	}	}	PUNCT
ejpam-6931	155	31	=	=	PUNCT
ejpam-6931	155	32	{	{	PUNCT
ejpam-6931	155	33	4	4	NUM
ejpam-6931	155	34	+	+	SYM
ejpam-6931	155	35	1	1	NUM
ejpam-6931	155	36	n	n	CCONJ
ejpam-6931	155	37	}	}	PUNCT
ejpam-6931	155	38	and	and	CCONJ
ejpam-6931	155	39	ϱo	ϱo	X
ejpam-6931	155	40	=	=	ADJ
ejpam-6931	155	41	4	4	X
ejpam-6931	155	42	.	.	PUNCT
ejpam-6931	156	1	now	now	ADV
ejpam-6931	156	2	we	we	PRON
ejpam-6931	156	3	verify	verify	VERB
ejpam-6931	156	4	that	that	SCONJ
ejpam-6931	156	5	e(ϱon	e(ϱon	PROPN
ejpam-6931	156	6	,	,	PUNCT
ejpam-6931	156	7	ϱo	ϱo	NOUN
ejpam-6931	156	8	,	,	PUNCT
ejpam-6931	156	9	e	e	NOUN
ejpam-6931	156	10	)	)	PUNCT
ejpam-6931	156	11	≻	≻	VERB
ejpam-6931	156	12	ℑ−	ℑ−	PROPN
ejpam-6931	156	13	s	s	NOUN
ejpam-6931	156	14	for	for	ADP
ejpam-6931	156	15	each	each	DET
ejpam-6931	156	16	s	s	PART
ejpam-6931	156	17	=	=	SYM
ejpam-6931	156	18	(	(	PUNCT
ejpam-6931	156	19	s1	s1	NOUN
ejpam-6931	156	20	,	,	PUNCT
ejpam-6931	156	21	s2	s2	PROPN
ejpam-6931	156	22	)	)	PUNCT
ejpam-6931	156	23	∈	∈	PROPN
ejpam-6931	156	24	t0	t0	PROPN
ejpam-6931	156	25	and	and	CCONJ
ejpam-6931	156	26	e	e	PROPN
ejpam-6931	156	27	∈	∈	PROPN
ejpam-6931	156	28	s0	s0	PROPN
ejpam-6931	156	29	.	.	PUNCT
ejpam-6931	157	1	for	for	ADP
ejpam-6931	157	2	the	the	DET
ejpam-6931	157	3	real	real	ADJ
ejpam-6931	157	4	part	part	NOUN
ejpam-6931	157	5	,	,	PUNCT
ejpam-6931	157	6	re(e(ϱon	re(e(ϱon	PROPN
ejpam-6931	157	7	,	,	PUNCT
ejpam-6931	157	8	ϱo	ϱo	PROPN
ejpam-6931	157	9	,	,	PUNCT
ejpam-6931	157	10	e)−ℑ+	e)−ℑ+	NOUN
ejpam-6931	157	11	s	s	PART
ejpam-6931	157	12	)	)	PUNCT
ejpam-6931	157	13	=	=	SYM
ejpam-6931	157	14	τ	τ	PROPN
ejpam-6931	157	15	+	+	NUM
ejpam-6931	157	16	ξ	ξ	X
ejpam-6931	157	17	τ	τ	PROPN
ejpam-6931	157	18	+	+	NUM
ejpam-6931	157	19	ξ	ξ	PROPN
ejpam-6931	157	20	+	+	SYM
ejpam-6931	157	21	d(ϱon	d(ϱon	PROPN
ejpam-6931	157	22	,	,	PUNCT
ejpam-6931	157	23	ϱ	ϱ	ADP
ejpam-6931	157	24	o	o	NOUN
ejpam-6931	157	25	)	)	PUNCT
ejpam-6931	157	26	−	−	PROPN
ejpam-6931	157	27	1	1	NUM
ejpam-6931	157	28	+	+	NUM
ejpam-6931	157	29	s1	s1	NOUN
ejpam-6931	157	30	=	=	PUNCT
ejpam-6931	157	31	τ	τ	PROPN
ejpam-6931	157	32	+	+	NUM
ejpam-6931	157	33	ξ	ξ	X
ejpam-6931	157	34	τ	τ	PROPN
ejpam-6931	157	35	+	+	NUM
ejpam-6931	157	36	ξ	ξ	X
ejpam-6931	157	37	+	+	NUM
ejpam-6931	157	38	|4	|4	NUM
ejpam-6931	157	39	+	+	SYM
ejpam-6931	157	40	1	1	NUM
ejpam-6931	157	41	n	n	NUM
ejpam-6931	157	42	−	−	PROPN
ejpam-6931	157	43	4|	4|	NUM
ejpam-6931	157	44	−	−	NOUN
ejpam-6931	157	45	1	1	NUM
ejpam-6931	157	46	+	+	NUM
ejpam-6931	157	47	s1	s1	NOUN
ejpam-6931	157	48	=	=	PUNCT
ejpam-6931	157	49	τ	τ	PROPN
ejpam-6931	157	50	+	+	NUM
ejpam-6931	157	51	ξ	ξ	X
ejpam-6931	157	52	τ	τ	PROPN
ejpam-6931	157	53	+	+	NUM
ejpam-6931	157	54	ξ	ξ	X
ejpam-6931	157	55	+	+	SYM
ejpam-6931	157	56	1	1	NUM
ejpam-6931	157	57	n	n	NUM
ejpam-6931	157	58	−	−	NUM
ejpam-6931	157	59	1	1	NUM
ejpam-6931	157	60	+	+	NUM
ejpam-6931	157	61	s1	s1	NOUN
ejpam-6931	157	62	.	.	PUNCT
ejpam-6931	158	1	as	as	ADP
ejpam-6931	158	2	n	n	PROPN
ejpam-6931	158	3	→	→	SYM
ejpam-6931	158	4	∞	∞	PROPN
ejpam-6931	158	5	,	,	PUNCT
ejpam-6931	158	6	then	then	ADV
ejpam-6931	158	7	re(e(ϱon	re(e(ϱon	PROPN
ejpam-6931	158	8	,	,	PUNCT
ejpam-6931	158	9	ϱo	ϱo	NOUN
ejpam-6931	158	10	,	,	PUNCT
ejpam-6931	158	11	e	e	NOUN
ejpam-6931	158	12	)	)	PUNCT
ejpam-6931	159	1	−	−	PROPN
ejpam-6931	159	2	ℑ	ℑ	PROPN
ejpam-6931	159	3	+	+	CCONJ
ejpam-6931	159	4	s	s	X
ejpam-6931	159	5	)	)	PUNCT
ejpam-6931	159	6	→	→	SYM
ejpam-6931	159	7	s1	s1	PROPN
ejpam-6931	159	8	.	.	PUNCT
ejpam-6931	160	1	therefore	therefore	ADV
ejpam-6931	160	2	,	,	PUNCT
ejpam-6931	160	3	for	for	ADP
ejpam-6931	160	4	each	each	DET
ejpam-6931	160	5	s	s	PROPN
ejpam-6931	160	6	∈	∈	PROPN
ejpam-6931	160	7	t0	t0	PROPN
ejpam-6931	160	8	together	together	ADV
ejpam-6931	160	9	with	with	ADP
ejpam-6931	160	10	e	e	PROPN
ejpam-6931	160	11	∈	∈	PROPN
ejpam-6931	160	12	s0	s0	NOUN
ejpam-6931	160	13	,	,	PUNCT
ejpam-6931	160	14	there	there	PRON
ejpam-6931	160	15	is	be	VERB
ejpam-6931	160	16	always	always	ADV
ejpam-6931	160	17	an	an	DET
ejpam-6931	160	18	m1	m1	PROPN
ejpam-6931	160	19	∈	∈	PROPN
ejpam-6931	160	20	m	m	NOUN
ejpam-6931	160	21	in	in	ADP
ejpam-6931	160	22	which	which	PRON
ejpam-6931	160	23	re(e(ϱon	re(e(ϱon	PROPN
ejpam-6931	160	24	,	,	PUNCT
ejpam-6931	160	25	ϱo	ϱo	NOUN
ejpam-6931	160	26	,	,	PUNCT
ejpam-6931	160	27	e	e	NOUN
ejpam-6931	160	28	)	)	PUNCT
ejpam-6931	160	29	−	−	PROPN
ejpam-6931	160	30	ℑ	ℑ	PROPN
ejpam-6931	160	31	+	+	CCONJ
ejpam-6931	160	32	s	s	X
ejpam-6931	160	33	)	)	PUNCT
ejpam-6931	160	34	>	>	X
ejpam-6931	160	35	0	0	NUM
ejpam-6931	160	36	holds	hold	VERB
ejpam-6931	160	37	for	for	ADP
ejpam-6931	160	38	all	all	PRON
ejpam-6931	160	39	n	n	PRON
ejpam-6931	160	40	>	>	X
ejpam-6931	160	41	m1	m1	PROPN
ejpam-6931	160	42	.	.	PUNCT
ejpam-6931	161	1	the	the	DET
ejpam-6931	161	2	approach	approach	NOUN
ejpam-6931	161	3	for	for	ADP
ejpam-6931	161	4	determining	determine	VERB
ejpam-6931	161	5	the	the	DET
ejpam-6931	161	6	imaginary	imaginary	ADJ
ejpam-6931	161	7	part	part	NOUN
ejpam-6931	161	8	is	be	AUX
ejpam-6931	161	9	the	the	DET
ejpam-6931	161	10	same	same	ADJ
ejpam-6931	161	11	,	,	PUNCT
ejpam-6931	161	12	leading	lead	VERB
ejpam-6931	161	13	to	to	ADP
ejpam-6931	161	14	im(e(ϱon	im(e(ϱon	ADJ
ejpam-6931	161	15	,	,	PUNCT
ejpam-6931	161	16	ϱo	ϱo	INTJ
ejpam-6931	161	17	,	,	PUNCT
ejpam-6931	161	18	e)−	e)−	PROPN
ejpam-6931	161	19	ℑ	ℑ	NOUN
ejpam-6931	161	20	+	+	CCONJ
ejpam-6931	161	21	s	s	X
ejpam-6931	161	22	)	)	PUNCT
ejpam-6931	161	23	→	→	SYM
ejpam-6931	161	24	s2	s2	NOUN
ejpam-6931	161	25	as	as	ADP
ejpam-6931	161	26	n	n	PROPN
ejpam-6931	161	27	→	→	SYM
ejpam-6931	161	28	∞.	∞.	PROPN
ejpam-6931	161	29	therefore	therefore	ADV
ejpam-6931	161	30	,	,	PUNCT
ejpam-6931	161	31	for	for	ADP
ejpam-6931	161	32	every	every	DET
ejpam-6931	161	33	s	s	PROPN
ejpam-6931	161	34	∈	∈	PROPN
ejpam-6931	161	35	t0	t0	PROPN
ejpam-6931	161	36	and	and	CCONJ
ejpam-6931	161	37	e	e	PROPN
ejpam-6931	161	38	∈	∈	PROPN
ejpam-6931	161	39	s0	s0	PROPN
ejpam-6931	161	40	,	,	PUNCT
ejpam-6931	161	41	always	always	ADV
ejpam-6931	161	42	there	there	PRON
ejpam-6931	161	43	is	be	VERB
ejpam-6931	161	44	a	a	DET
ejpam-6931	161	45	m2	m2	PROPN
ejpam-6931	161	46	∈	∈	PROPN
ejpam-6931	161	47	m	m	VERB
ejpam-6931	161	48	such	such	ADJ
ejpam-6931	161	49	that	that	SCONJ
ejpam-6931	161	50	im(e(ϱon	im(e(ϱon	ADJ
ejpam-6931	161	51	,	,	PUNCT
ejpam-6931	161	52	ϱo	ϱo	NOUN
ejpam-6931	161	53	,	,	PUNCT
ejpam-6931	161	54	e	e	NOUN
ejpam-6931	161	55	)	)	PUNCT
ejpam-6931	161	56	)	)	PUNCT
ejpam-6931	161	57	>	>	X
ejpam-6931	162	1	0	0	NUM
ejpam-6931	162	2	holds	hold	VERB
ejpam-6931	162	3	for	for	ADP
ejpam-6931	162	4	all	all	PRON
ejpam-6931	162	5	n	n	PROPN
ejpam-6931	162	6	>	>	PUNCT
ejpam-6931	162	7	m2	m2	PROPN
ejpam-6931	162	8	.	.	PUNCT
ejpam-6931	163	1	therefore	therefore	ADV
ejpam-6931	163	2	,	,	PUNCT
ejpam-6931	163	3	for	for	ADP
ejpam-6931	163	4	every	every	DET
ejpam-6931	163	5	s	s	PROPN
ejpam-6931	163	6	∈	∈	PROPN
ejpam-6931	163	7	t0	t0	PROPN
ejpam-6931	163	8	and	and	CCONJ
ejpam-6931	163	9	e	e	NOUN
ejpam-6931	163	10	∈	∈	PROPN
ejpam-6931	163	11	s0	s0	PROPN
ejpam-6931	163	12	,	,	PUNCT
ejpam-6931	163	13	by	by	ADP
ejpam-6931	163	14	taking	take	VERB
ejpam-6931	163	15	n0	n0	ADJ
ejpam-6931	163	16	=	=	PUNCT
ejpam-6931	163	17	max{m1,m2	max{m1,m2	PROPN
ejpam-6931	163	18	}	}	PUNCT
ejpam-6931	163	19	,	,	PUNCT
ejpam-6931	163	20	we	we	PRON
ejpam-6931	163	21	establish	establish	VERB
ejpam-6931	163	22	e(ϱon	e(ϱon	PROPN
ejpam-6931	163	23	,	,	PUNCT
ejpam-6931	163	24	ϱo	ϱo	NOUN
ejpam-6931	163	25	,	,	PUNCT
ejpam-6931	163	26	e	e	NOUN
ejpam-6931	163	27	)	)	PUNCT
ejpam-6931	163	28	>	>	PUNCT
ejpam-6931	163	29	ℑ	ℑ	PROPN
ejpam-6931	163	30	−	−	PROPN
ejpam-6931	163	31	s	s	PART
ejpam-6931	163	32	foe	foe	NOUN
ejpam-6931	163	33	each	each	DET
ejpam-6931	163	34	n	n	PROPN
ejpam-6931	163	35	>	>	X
ejpam-6931	163	36	n0	n0	PROPN
ejpam-6931	163	37	.	.	PUNCT
ejpam-6931	164	1	now	now	ADV
ejpam-6931	164	2	we	we	PRON
ejpam-6931	164	3	verify	verify	VERB
ejpam-6931	164	4	that	that	SCONJ
ejpam-6931	164	5	g(ϱon	g(ϱon	PROPN
ejpam-6931	164	6	,	,	PUNCT
ejpam-6931	164	7	ϱo	ϱo	NOUN
ejpam-6931	164	8	,	,	PUNCT
ejpam-6931	164	9	e	e	NOUN
ejpam-6931	164	10	)	)	PUNCT
ejpam-6931	164	11	<	<	X
ejpam-6931	164	12	s	s	X
ejpam-6931	164	13	for	for	ADP
ejpam-6931	164	14	every	every	DET
ejpam-6931	164	15	(	(	PUNCT
ejpam-6931	164	16	s1	s1	NOUN
ejpam-6931	164	17	,	,	PUNCT
ejpam-6931	164	18	s2	s2	PROPN
ejpam-6931	164	19	)	)	PUNCT
ejpam-6931	164	20	∈	∈	PROPN
ejpam-6931	164	21	t0	t0	PROPN
ejpam-6931	164	22	and	and	CCONJ
ejpam-6931	164	23	e	e	PROPN
ejpam-6931	164	24	∈	∈	PROPN
ejpam-6931	164	25	s0	s0	PROPN
ejpam-6931	164	26	.	.	PUNCT
ejpam-6931	165	1	for	for	ADP
ejpam-6931	165	2	the	the	DET
ejpam-6931	165	3	real	real	ADJ
ejpam-6931	165	4	part	part	NOUN
ejpam-6931	165	5	,	,	PUNCT
ejpam-6931	165	6	re(s−	re(s−	PROPN
ejpam-6931	165	7	g(ϱon	g(ϱon	PROPN
ejpam-6931	165	8	,	,	PUNCT
ejpam-6931	165	9	ϱo	ϱo	NOUN
ejpam-6931	165	10	,	,	PUNCT
ejpam-6931	165	11	e	e	NOUN
ejpam-6931	165	12	)	)	PUNCT
ejpam-6931	165	13	)	)	PUNCT
ejpam-6931	165	14	=	=	SYM
ejpam-6931	165	15	s1	s1	PROPN
ejpam-6931	165	16	−	−	PROPN
ejpam-6931	165	17	d(ϱon	d(ϱon	PROPN
ejpam-6931	165	18	,	,	PUNCT
ejpam-6931	165	19	ϱ	ϱ	ADP
ejpam-6931	165	20	o	o	NOUN
ejpam-6931	165	21	)	)	PUNCT
ejpam-6931	165	22	τ	τ	PROPN
ejpam-6931	165	23	+	+	NUM
ejpam-6931	165	24	ξ	ξ	X
ejpam-6931	165	25	+	+	SYM
ejpam-6931	165	26	d(ϱon	d(ϱon	PROPN
ejpam-6931	165	27	,	,	PUNCT
ejpam-6931	165	28	ϱ	ϱ	ADP
ejpam-6931	165	29	o	o	NOUN
ejpam-6931	165	30	)	)	PUNCT
ejpam-6931	165	31	=	=	SYM
ejpam-6931	165	32	s1	s1	PROPN
ejpam-6931	165	33	−	−	PROPN
ejpam-6931	165	34	|4	|4	SYM
ejpam-6931	165	35	+	+	CCONJ
ejpam-6931	165	36	1	1	NUM
ejpam-6931	165	37	n	n	NUM
ejpam-6931	165	38	−	−	PROPN
ejpam-6931	165	39	4|	4|	NUM
ejpam-6931	165	40	τ	τ	X
ejpam-6931	165	41	+	+	SYM
ejpam-6931	165	42	ξ	ξ	X
ejpam-6931	165	43	+	+	NUM
ejpam-6931	165	44	|4	|4	NUM
ejpam-6931	165	45	+	+	SYM
ejpam-6931	165	46	1	1	NUM
ejpam-6931	165	47	n	n	NUM
ejpam-6931	165	48	−	−	PROPN
ejpam-6931	165	49	4|	4|	NUM
ejpam-6931	165	50	=	=	SYM
ejpam-6931	165	51	s1	s1	NOUN
ejpam-6931	165	52	−	−	PROPN
ejpam-6931	165	53	1	1	NUM
ejpam-6931	165	54	n	n	NOUN
ejpam-6931	165	55	τ	τ	PROPN
ejpam-6931	165	56	+	+	NUM
ejpam-6931	165	57	ξ	ξ	X
ejpam-6931	165	58	+	+	SYM
ejpam-6931	165	59	1	1	NUM
ejpam-6931	165	60	n	n	NOUN
ejpam-6931	165	61	.	.	PUNCT
ejpam-6931	166	1	as	as	ADP
ejpam-6931	166	2	n	n	PROPN
ejpam-6931	166	3	→	→	SYM
ejpam-6931	166	4	∞	∞	PROPN
ejpam-6931	166	5	,	,	PUNCT
ejpam-6931	166	6	then	then	ADV
ejpam-6931	166	7	re(s	re(s	ADJ
ejpam-6931	166	8	−	−	PROPN
ejpam-6931	166	9	g(ϱon	g(ϱon	NOUN
ejpam-6931	166	10	,	,	PUNCT
ejpam-6931	166	11	ϱo	ϱo	NOUN
ejpam-6931	166	12	,	,	PUNCT
ejpam-6931	166	13	e	e	NOUN
ejpam-6931	166	14	)	)	PUNCT
ejpam-6931	166	15	)	)	PUNCT
ejpam-6931	167	1	→	→	SYM
ejpam-6931	167	2	s1	s1	PROPN
ejpam-6931	167	3	.	.	PUNCT
ejpam-6931	168	1	therefore	therefore	ADV
ejpam-6931	168	2	,	,	PUNCT
ejpam-6931	168	3	for	for	ADP
ejpam-6931	168	4	each	each	DET
ejpam-6931	168	5	s	s	PROPN
ejpam-6931	168	6	∈	∈	PROPN
ejpam-6931	168	7	t0	t0	PROPN
ejpam-6931	168	8	and	and	CCONJ
ejpam-6931	168	9	e	e	PROPN
ejpam-6931	168	10	∈	∈	PROPN
ejpam-6931	168	11	s0	s0	PROPN
ejpam-6931	168	12	,	,	PUNCT
ejpam-6931	168	13	there	there	PRON
ejpam-6931	168	14	is	be	VERB
ejpam-6931	168	15	always	always	ADV
ejpam-6931	168	16	an	an	DET
ejpam-6931	168	17	m1	m1	PROPN
ejpam-6931	168	18	∈	∈	PROPN
ejpam-6931	168	19	m	m	NOUN
ejpam-6931	168	20	in	in	ADP
ejpam-6931	168	21	which	which	PRON
ejpam-6931	168	22	re(g(ϱon	re(g(ϱon	PROPN
ejpam-6931	168	23	,	,	PUNCT
ejpam-6931	168	24	ϱo	ϱo	NOUN
ejpam-6931	168	25	,	,	PUNCT
ejpam-6931	168	26	e	e	NOUN
ejpam-6931	168	27	)	)	PUNCT
ejpam-6931	168	28	−	−	PROPN
ejpam-6931	168	29	ℑ	ℑ	PROPN
ejpam-6931	168	30	+	+	CCONJ
ejpam-6931	168	31	s	s	X
ejpam-6931	168	32	)	)	PUNCT
ejpam-6931	168	33	>	>	X
ejpam-6931	168	34	0	0	NUM
ejpam-6931	168	35	holds	hold	VERB
ejpam-6931	168	36	for	for	ADP
ejpam-6931	168	37	each	each	DET
ejpam-6931	168	38	n	n	PROPN
ejpam-6931	168	39	>	>	X
ejpam-6931	168	40	m1	m1	PROPN
ejpam-6931	168	41	.	.	PUNCT
ejpam-6931	169	1	the	the	DET
ejpam-6931	169	2	approach	approach	NOUN
ejpam-6931	169	3	for	for	ADP
ejpam-6931	169	4	determining	determine	VERB
ejpam-6931	169	5	the	the	DET
ejpam-6931	169	6	imaginary	imaginary	ADJ
ejpam-6931	169	7	part	part	NOUN
ejpam-6931	169	8	is	be	AUX
ejpam-6931	169	9	the	the	DET
ejpam-6931	169	10	same	same	ADJ
ejpam-6931	169	11	,	,	PUNCT
ejpam-6931	169	12	this	this	PRON
ejpam-6931	169	13	leads	lead	VERB
ejpam-6931	169	14	to	to	PART
ejpam-6931	169	15	im(s	im(s	VERB
ejpam-6931	169	16	−	−	PROPN
ejpam-6931	169	17	g(ϱon	g(ϱon	PROPN
ejpam-6931	169	18	,	,	PUNCT
ejpam-6931	169	19	ϱo	ϱo	NOUN
ejpam-6931	169	20	,	,	PUNCT
ejpam-6931	169	21	e	e	NOUN
ejpam-6931	169	22	)	)	PUNCT
ejpam-6931	169	23	)	)	PUNCT
ejpam-6931	170	1	→	→	SYM
ejpam-6931	170	2	s2	s2	PROPN
ejpam-6931	170	3	as	as	ADP
ejpam-6931	170	4	n	n	PROPN
ejpam-6931	170	5	→	→	SYM
ejpam-6931	170	6	∞.	∞.	PROPN
ejpam-6931	170	7	therefore	therefore	ADV
ejpam-6931	170	8	,	,	PUNCT
ejpam-6931	170	9	for	for	ADP
ejpam-6931	170	10	each	each	DET
ejpam-6931	170	11	r	r	NOUN
ejpam-6931	170	12	∈	∈	PROPN
ejpam-6931	170	13	t0	t0	PROPN
ejpam-6931	170	14	and	and	CCONJ
ejpam-6931	170	15	e	e	PROPN
ejpam-6931	170	16	∈	∈	PROPN
ejpam-6931	170	17	s0	s0	PROPN
ejpam-6931	170	18	,	,	PUNCT
ejpam-6931	170	19	there	there	PRON
ejpam-6931	170	20	is	be	VERB
ejpam-6931	170	21	always	always	ADV
ejpam-6931	170	22	an	an	DET
ejpam-6931	170	23	m2	m2	PROPN
ejpam-6931	170	24	∈	∈	PROPN
ejpam-6931	170	25	m	m	VERB
ejpam-6931	170	26	in	in	ADP
ejpam-6931	170	27	which	which	PRON
ejpam-6931	170	28	im(s	im(s	NOUN
ejpam-6931	170	29	−	−	PROPN
ejpam-6931	170	30	g(ϱon	g(ϱon	PROPN
ejpam-6931	170	31	,	,	PUNCT
ejpam-6931	170	32	ϱo	ϱo	NOUN
ejpam-6931	170	33	,	,	PUNCT
ejpam-6931	170	34	e	e	NOUN
ejpam-6931	170	35	)	)	PUNCT
ejpam-6931	170	36	)	)	PUNCT
ejpam-6931	170	37	>	>	X
ejpam-6931	170	38	0	0	NUM
ejpam-6931	170	39	holds	hold	VERB
ejpam-6931	170	40	for	for	ADP
ejpam-6931	170	41	all	all	PRON
ejpam-6931	170	42	n	n	PROPN
ejpam-6931	170	43	>	>	PUNCT
ejpam-6931	170	44	m2	m2	PROPN
ejpam-6931	170	45	.	.	PUNCT
ejpam-6931	171	1	therefore	therefore	ADV
ejpam-6931	171	2	,	,	PUNCT
ejpam-6931	171	3	for	for	ADP
ejpam-6931	171	4	every	every	DET
ejpam-6931	171	5	s	s	PROPN
ejpam-6931	171	6	∈	∈	PROPN
ejpam-6931	171	7	t0	t0	PROPN
ejpam-6931	171	8	and	and	CCONJ
ejpam-6931	171	9	e	e	NOUN
ejpam-6931	171	10	∈	∈	PROPN
ejpam-6931	171	11	s0	s0	PROPN
ejpam-6931	171	12	,	,	PUNCT
ejpam-6931	171	13	by	by	ADP
ejpam-6931	171	14	taking	take	VERB
ejpam-6931	171	15	n0	n0	ADJ
ejpam-6931	171	16	=	=	PUNCT
ejpam-6931	171	17	max{m1,m2	max{m1,m2	PROPN
ejpam-6931	171	18	}	}	PUNCT
ejpam-6931	171	19	,	,	PUNCT
ejpam-6931	171	20	we	we	PRON
ejpam-6931	171	21	establish	establish	VERB
ejpam-6931	171	22	g(ϱon	g(ϱon	PROPN
ejpam-6931	171	23	,	,	PUNCT
ejpam-6931	171	24	ϱo	ϱo	NOUN
ejpam-6931	171	25	,	,	PUNCT
ejpam-6931	171	26	e	e	NOUN
ejpam-6931	171	27	)	)	PUNCT
ejpam-6931	171	28	<	<	X
ejpam-6931	171	29	s	s	X
ejpam-6931	171	30	for	for	ADP
ejpam-6931	171	31	each	each	DET
ejpam-6931	171	32	n	n	PROPN
ejpam-6931	171	33	>	>	X
ejpam-6931	171	34	n0	n0	PROPN
ejpam-6931	171	35	.	.	PUNCT
ejpam-6931	172	1	now	now	ADV
ejpam-6931	172	2	we	we	PRON
ejpam-6931	172	3	verify	verify	VERB
ejpam-6931	172	4	that	that	SCONJ
ejpam-6931	172	5	h(ϱon	h(ϱon	PROPN
ejpam-6931	172	6	,	,	PUNCT
ejpam-6931	172	7	ϱ	ϱ	ADP
ejpam-6931	172	8	o	o	PROPN
ejpam-6931	172	9	,	,	PUNCT
ejpam-6931	172	10	e	e	NOUN
ejpam-6931	172	11	)	)	PUNCT
ejpam-6931	172	12	<	<	X
ejpam-6931	172	13	s	s	X
ejpam-6931	172	14	for	for	ADP
ejpam-6931	172	15	every	every	DET
ejpam-6931	172	16	(	(	PUNCT
ejpam-6931	172	17	s1	s1	NOUN
ejpam-6931	172	18	,	,	PUNCT
ejpam-6931	172	19	s2	s2	PROPN
ejpam-6931	172	20	)	)	PUNCT
ejpam-6931	172	21	∈	∈	PROPN
ejpam-6931	172	22	t0	t0	PROPN
ejpam-6931	172	23	and	and	CCONJ
ejpam-6931	172	24	e	e	PROPN
ejpam-6931	172	25	∈	∈	PROPN
ejpam-6931	172	26	s0	s0	PROPN
ejpam-6931	172	27	.	.	PUNCT
ejpam-6931	173	1	for	for	ADP
ejpam-6931	173	2	the	the	DET
ejpam-6931	173	3	real	real	ADJ
ejpam-6931	173	4	part	part	NOUN
ejpam-6931	173	5	,	,	PUNCT
ejpam-6931	173	6	re(s−h(ϱon	re(s−h(ϱon	PROPN
ejpam-6931	173	7	,	,	PUNCT
ejpam-6931	173	8	ϱ	ϱ	ADP
ejpam-6931	173	9	o	o	PROPN
ejpam-6931	173	10	,	,	PUNCT
ejpam-6931	173	11	e	e	NOUN
ejpam-6931	173	12	)	)	PUNCT
ejpam-6931	173	13	)	)	PUNCT
ejpam-6931	173	14	=	=	SYM
ejpam-6931	173	15	s1	s1	PROPN
ejpam-6931	173	16	−	−	PROPN
ejpam-6931	173	17	d(ϱon	d(ϱon	PROPN
ejpam-6931	173	18	,	,	PUNCT
ejpam-6931	173	19	ϱ	ϱ	ADP
ejpam-6931	173	20	o	o	NOUN
ejpam-6931	173	21	)	)	PUNCT
ejpam-6931	173	22	τ	τ	PROPN
ejpam-6931	173	23	+	+	NUM
ejpam-6931	173	24	ξ	ξ	PROPN
ejpam-6931	173	25	s.	s.	PROPN
ejpam-6931	173	26	m.	m.	PROPN
ejpam-6931	173	27	u.	u.	PROPN
ejpam-6931	173	28	ud	ud	PROPN
ejpam-6931	173	29	-	-	PUNCT
ejpam-6931	173	30	din	din	VERB
ejpam-6931	173	31	et	et	PROPN
ejpam-6931	173	32	al	al	PROPN
ejpam-6931	173	33	.	.	PUNCT
ejpam-6931	173	34	/	/	SYM
ejpam-6931	173	35	eur	eur	PROPN
ejpam-6931	173	36	.	.	PUNCT
ejpam-6931	174	1	j.	j.	PROPN
ejpam-6931	174	2	pure	pure	PROPN
ejpam-6931	174	3	appl	appl	PROPN
ejpam-6931	174	4	.	.	PROPN
ejpam-6931	174	5	math	math	PROPN
ejpam-6931	174	6	,	,	PUNCT
ejpam-6931	174	7	18	18	NUM
ejpam-6931	174	8	(	(	PUNCT
ejpam-6931	174	9	4	4	NUM
ejpam-6931	174	10	)	)	PUNCT
ejpam-6931	174	11	(	(	PUNCT
ejpam-6931	174	12	2025	2025	NUM
ejpam-6931	174	13	)	)	PUNCT
ejpam-6931	174	14	,	,	PUNCT
ejpam-6931	174	15	6931	6931	NUM
ejpam-6931	174	16	10	10	NUM
ejpam-6931	174	17	of	of	ADP
ejpam-6931	174	18	38	38	NUM
ejpam-6931	174	19	=	=	SYM
ejpam-6931	174	20	s1	s1	NOUN
ejpam-6931	174	21	−	−	PROPN
ejpam-6931	174	22	|4	|4	SYM
ejpam-6931	175	1	+	+	CCONJ
ejpam-6931	175	2	1	1	NUM
ejpam-6931	175	3	n	n	NUM
ejpam-6931	175	4	−	−	PROPN
ejpam-6931	175	5	4|	4|	NUM
ejpam-6931	175	6	τ	τ	X
ejpam-6931	176	1	+	+	NUM
ejpam-6931	176	2	ξ	ξ	X
ejpam-6931	176	3	=	=	SYM
ejpam-6931	176	4	s1	s1	PROPN
ejpam-6931	176	5	−	−	PROPN
ejpam-6931	176	6	1	1	NUM
ejpam-6931	176	7	n	n	NOUN
ejpam-6931	176	8	τ	τ	PROPN
ejpam-6931	176	9	+	+	X
ejpam-6931	176	10	ξ	ξ	PROPN
ejpam-6931	176	11	.	.	PUNCT
ejpam-6931	177	1	as	as	SCONJ
ejpam-6931	177	2	n	n	NUM
ejpam-6931	177	3	→	→	SYM
ejpam-6931	177	4	∞	∞	PROPN
ejpam-6931	177	5	,	,	PUNCT
ejpam-6931	177	6	then	then	ADV
ejpam-6931	177	7	re(s	re(s	ADJ
ejpam-6931	177	8	−	−	PROPN
ejpam-6931	177	9	h(ϱon	h(ϱon	PROPN
ejpam-6931	177	10	,	,	PUNCT
ejpam-6931	177	11	ϱ	ϱ	ADP
ejpam-6931	177	12	o	o	PROPN
ejpam-6931	177	13	,	,	PUNCT
ejpam-6931	177	14	e	e	NOUN
ejpam-6931	177	15	)	)	PUNCT
ejpam-6931	177	16	)	)	PUNCT
ejpam-6931	178	1	→	→	SYM
ejpam-6931	178	2	s1	s1	PROPN
ejpam-6931	178	3	.	.	PUNCT
ejpam-6931	179	1	therefore	therefore	ADV
ejpam-6931	179	2	,	,	PUNCT
ejpam-6931	179	3	for	for	ADP
ejpam-6931	179	4	each	each	DET
ejpam-6931	179	5	s	s	PROPN
ejpam-6931	179	6	∈	∈	PROPN
ejpam-6931	179	7	t0	t0	PROPN
ejpam-6931	179	8	and	and	CCONJ
ejpam-6931	179	9	e	e	PROPN
ejpam-6931	179	10	∈	∈	PROPN
ejpam-6931	179	11	s0	s0	PROPN
ejpam-6931	179	12	,	,	PUNCT
ejpam-6931	179	13	there	there	PRON
ejpam-6931	179	14	is	be	VERB
ejpam-6931	179	15	always	always	ADV
ejpam-6931	179	16	an	an	DET
ejpam-6931	179	17	m1	m1	PROPN
ejpam-6931	179	18	∈	∈	PROPN
ejpam-6931	179	19	m	m	NOUN
ejpam-6931	179	20	in	in	ADP
ejpam-6931	179	21	which	which	PRON
ejpam-6931	179	22	re(h(ϱon	re(h(ϱon	PROPN
ejpam-6931	179	23	,	,	PUNCT
ejpam-6931	179	24	ϱ	ϱ	ADP
ejpam-6931	179	25	o	o	PROPN
ejpam-6931	179	26	,	,	PUNCT
ejpam-6931	179	27	e	e	NOUN
ejpam-6931	179	28	)	)	PUNCT
ejpam-6931	179	29	−	−	PROPN
ejpam-6931	179	30	ℑ	ℑ	PROPN
ejpam-6931	179	31	+	+	CCONJ
ejpam-6931	179	32	s	s	X
ejpam-6931	179	33	)	)	PUNCT
ejpam-6931	179	34	>	>	X
ejpam-6931	179	35	0	0	NUM
ejpam-6931	179	36	holds	hold	VERB
ejpam-6931	179	37	for	for	ADP
ejpam-6931	179	38	each	each	DET
ejpam-6931	179	39	n	n	PROPN
ejpam-6931	179	40	>	>	X
ejpam-6931	179	41	m1	m1	PROPN
ejpam-6931	179	42	.	.	PUNCT
ejpam-6931	180	1	the	the	DET
ejpam-6931	180	2	approach	approach	NOUN
ejpam-6931	180	3	for	for	ADP
ejpam-6931	180	4	determining	determine	VERB
ejpam-6931	180	5	the	the	DET
ejpam-6931	180	6	imaginary	imaginary	ADJ
ejpam-6931	180	7	part	part	NOUN
ejpam-6931	180	8	is	be	AUX
ejpam-6931	180	9	the	the	DET
ejpam-6931	180	10	same	same	ADJ
ejpam-6931	180	11	,	,	PUNCT
ejpam-6931	180	12	this	this	PRON
ejpam-6931	180	13	leads	lead	VERB
ejpam-6931	180	14	to	to	PART
ejpam-6931	180	15	im(s	im(s	VERB
ejpam-6931	180	16	−	−	PROPN
ejpam-6931	180	17	h(ϱon	h(ϱon	PROPN
ejpam-6931	180	18	,	,	PUNCT
ejpam-6931	180	19	ϱ	ϱ	ADP
ejpam-6931	180	20	o	o	PROPN
ejpam-6931	180	21	,	,	PUNCT
ejpam-6931	180	22	e	e	NOUN
ejpam-6931	180	23	)	)	PUNCT
ejpam-6931	180	24	)	)	PUNCT
ejpam-6931	181	1	→	→	SYM
ejpam-6931	181	2	s2	s2	PROPN
ejpam-6931	181	3	as	as	ADP
ejpam-6931	181	4	n	n	PROPN
ejpam-6931	181	5	→	→	SYM
ejpam-6931	181	6	∞.	∞.	PROPN
ejpam-6931	181	7	therefore	therefore	ADV
ejpam-6931	181	8	,	,	PUNCT
ejpam-6931	181	9	for	for	ADP
ejpam-6931	181	10	each	each	DET
ejpam-6931	181	11	s	s	PROPN
ejpam-6931	181	12	∈	∈	PROPN
ejpam-6931	181	13	t0	t0	PROPN
ejpam-6931	181	14	and	and	CCONJ
ejpam-6931	181	15	e	e	PROPN
ejpam-6931	181	16	∈	∈	PROPN
ejpam-6931	181	17	s0	s0	PROPN
ejpam-6931	181	18	,	,	PUNCT
ejpam-6931	181	19	there	there	PRON
ejpam-6931	181	20	is	be	VERB
ejpam-6931	181	21	always	always	ADV
ejpam-6931	181	22	an	an	DET
ejpam-6931	181	23	m2	m2	PROPN
ejpam-6931	181	24	∈	∈	PROPN
ejpam-6931	181	25	m	m	VERB
ejpam-6931	181	26	in	in	ADP
ejpam-6931	181	27	which	which	PRON
ejpam-6931	181	28	im(s	im(s	VERB
ejpam-6931	181	29	−	−	PROPN
ejpam-6931	181	30	h(ϱon	h(ϱon	PROPN
ejpam-6931	181	31	,	,	PUNCT
ejpam-6931	181	32	ϱ	ϱ	ADP
ejpam-6931	181	33	o	o	PROPN
ejpam-6931	181	34	,	,	PUNCT
ejpam-6931	181	35	e	e	NOUN
ejpam-6931	181	36	)	)	PUNCT
ejpam-6931	181	37	)	)	PUNCT
ejpam-6931	181	38	>	>	X
ejpam-6931	181	39	0	0	NUM
ejpam-6931	181	40	holds	hold	VERB
ejpam-6931	181	41	for	for	ADP
ejpam-6931	181	42	all	all	PRON
ejpam-6931	181	43	n	n	PROPN
ejpam-6931	181	44	>	>	PUNCT
ejpam-6931	181	45	m2	m2	PROPN
ejpam-6931	181	46	.	.	PUNCT
ejpam-6931	182	1	therefore	therefore	ADV
ejpam-6931	182	2	,	,	PUNCT
ejpam-6931	182	3	for	for	ADP
ejpam-6931	182	4	every	every	DET
ejpam-6931	182	5	s	s	PROPN
ejpam-6931	182	6	∈	∈	PROPN
ejpam-6931	182	7	t0	t0	PROPN
ejpam-6931	182	8	and	and	CCONJ
ejpam-6931	182	9	e	e	NOUN
ejpam-6931	182	10	∈	∈	PROPN
ejpam-6931	182	11	s0	s0	PROPN
ejpam-6931	182	12	,	,	PUNCT
ejpam-6931	182	13	by	by	ADP
ejpam-6931	182	14	taking	take	VERB
ejpam-6931	182	15	n0	n0	ADJ
ejpam-6931	182	16	=	=	PUNCT
ejpam-6931	182	17	max{m1,m2	max{m1,m2	PROPN
ejpam-6931	182	18	}	}	PUNCT
ejpam-6931	182	19	,	,	PUNCT
ejpam-6931	182	20	we	we	PRON
ejpam-6931	182	21	establish	establish	VERB
ejpam-6931	182	22	h(ϱon	h(ϱon	PROPN
ejpam-6931	182	23	,	,	PUNCT
ejpam-6931	182	24	ϱ	ϱ	ADP
ejpam-6931	182	25	o	o	PROPN
ejpam-6931	182	26	,	,	PUNCT
ejpam-6931	182	27	e	e	NOUN
ejpam-6931	182	28	)	)	PUNCT
ejpam-6931	182	29	<	<	X
ejpam-6931	182	30	s	s	X
ejpam-6931	182	31	for	for	ADP
ejpam-6931	182	32	each	each	DET
ejpam-6931	182	33	n	n	PROPN
ejpam-6931	182	34	>	>	X
ejpam-6931	182	35	n0	n0	PROPN
ejpam-6931	182	36	.	.	PUNCT
ejpam-6931	183	1	every	every	DET
ejpam-6931	183	2	requirement	requirement	NOUN
ejpam-6931	183	3	of	of	ADP
ejpam-6931	183	4	definition	definition	NOUN
ejpam-6931	183	5	8	8	NUM
ejpam-6931	183	6	is	be	AUX
ejpam-6931	183	7	fulfilled	fulfil	VERB
ejpam-6931	183	8	.	.	PUNCT
ejpam-6931	184	1	we	we	PRON
ejpam-6931	184	2	may	may	AUX
ejpam-6931	184	3	therefore	therefore	ADV
ejpam-6931	184	4	say	say	VERB
ejpam-6931	184	5	that	that	SCONJ
ejpam-6931	184	6	{	{	PUNCT
ejpam-6931	184	7	4	4	NUM
ejpam-6931	184	8	+	+	SYM
ejpam-6931	184	9	1	1	NUM
ejpam-6931	184	10	n	n	CCONJ
ejpam-6931	184	11	}	}	PUNCT
ejpam-6931	184	12	converges	converge	VERB
ejpam-6931	184	13	to	to	ADP
ejpam-6931	184	14	4	4	NUM
ejpam-6931	184	15	.	.	PUNCT
ejpam-6931	184	16	example	example	NOUN
ejpam-6931	184	17	5	5	NUM
ejpam-6931	184	18	.	.	PUNCT
ejpam-6931	184	19	using	use	VERB
ejpam-6931	184	20	the	the	DET
ejpam-6931	184	21	same	same	ADJ
ejpam-6931	184	22	conditions	condition	NOUN
ejpam-6931	184	23	as	as	ADP
ejpam-6931	184	24	the	the	DET
ejpam-6931	184	25	previous	previous	ADJ
ejpam-6931	184	26	example	example	NOUN
ejpam-6931	184	27	,	,	PUNCT
ejpam-6931	184	28	we	we	PRON
ejpam-6931	184	29	will	will	AUX
ejpam-6931	184	30	demonstrate	demonstrate	VERB
ejpam-6931	184	31	that	that	SCONJ
ejpam-6931	184	32	{	{	PUNCT
ejpam-6931	184	33	4	4	NUM
ejpam-6931	184	34	+	+	SYM
ejpam-6931	184	35	1	1	NUM
ejpam-6931	184	36	n	n	CCONJ
ejpam-6931	184	37	}	}	PUNCT
ejpam-6931	184	38	is	be	AUX
ejpam-6931	184	39	a	a	DET
ejpam-6931	184	40	cauchy	cauchy	ADJ
ejpam-6931	184	41	sequence	sequence	NOUN
ejpam-6931	184	42	.	.	PUNCT
ejpam-6931	185	1	for	for	ADP
ejpam-6931	185	2	all	all	DET
ejpam-6931	185	3	e	e	PROPN
ejpam-6931	185	4	∈	∈	PROPN
ejpam-6931	185	5	s	s	X
ejpam-6931	185	6	for	for	ADP
ejpam-6931	185	7	any	any	DET
ejpam-6931	185	8	n	n	CCONJ
ejpam-6931	185	9	,	,	PUNCT
ejpam-6931	185	10	m	m	VERB
ejpam-6931	185	11	∈	∈	NOUN
ejpam-6931	185	12	m	m	VERB
ejpam-6931	185	13	where	where	SCONJ
ejpam-6931	185	14	m	m	VERB
ejpam-6931	185	15	>	>	X
ejpam-6931	185	16	n	n	CCONJ
ejpam-6931	185	17	,	,	PUNCT
ejpam-6931	185	18	e(ϱon	e(ϱon	PROPN
ejpam-6931	185	19	,	,	PUNCT
ejpam-6931	185	20	ϱom	ϱom	NOUN
ejpam-6931	185	21	,	,	PUNCT
ejpam-6931	185	22	e	e	NOUN
ejpam-6931	185	23	)	)	PUNCT
ejpam-6931	185	24	=	=	SYM
ejpam-6931	185	25	τ	τ	PROPN
ejpam-6931	185	26	+	+	NUM
ejpam-6931	185	27	ξ	ξ	X
ejpam-6931	185	28	τ	τ	PROPN
ejpam-6931	185	29	+	+	NUM
ejpam-6931	185	30	ξ	ξ	PROPN
ejpam-6931	185	31	+	+	SYM
ejpam-6931	185	32	d(ϱon	d(ϱon	PROPN
ejpam-6931	185	33	,	,	PUNCT
ejpam-6931	185	34	ϱ	ϱ	ADP
ejpam-6931	185	35	o	o	PROPN
ejpam-6931	185	36	m	m	NOUN
ejpam-6931	185	37	)	)	PUNCT
ejpam-6931	185	38	ℑ	ℑ	PROPN
ejpam-6931	185	39	=	=	SYM
ejpam-6931	185	40	τ	τ	PROPN
ejpam-6931	185	41	+	+	NUM
ejpam-6931	185	42	ξ	ξ	X
ejpam-6931	185	43	τ	τ	PROPN
ejpam-6931	185	44	+	+	NUM
ejpam-6931	185	45	ξ	ξ	X
ejpam-6931	185	46	+	+	NUM
ejpam-6931	185	47	|4	|4	NUM
ejpam-6931	185	48	+	+	SYM
ejpam-6931	185	49	1	1	NUM
ejpam-6931	185	50	n	n	NUM
ejpam-6931	185	51	−	−	PROPN
ejpam-6931	185	52	(	(	PUNCT
ejpam-6931	185	53	4	4	NUM
ejpam-6931	185	54	+	+	SYM
ejpam-6931	185	55	1	1	NUM
ejpam-6931	185	56	m)|	m)|	ADJ
ejpam-6931	185	57	ℑ	ℑ	NOUN
ejpam-6931	185	58	=	=	SYM
ejpam-6931	185	59	τ	τ	PROPN
ejpam-6931	185	60	+	+	NUM
ejpam-6931	185	61	ξ	ξ	X
ejpam-6931	185	62	τ	τ	PROPN
ejpam-6931	185	63	+	+	NUM
ejpam-6931	185	64	ξ	ξ	PROPN
ejpam-6931	185	65	+	+	CCONJ
ejpam-6931	185	66	|	|	ADV
ejpam-6931	185	67	1n	1n	NUM
ejpam-6931	185	68	−	−	NUM
ejpam-6931	185	69	1	1	NUM
ejpam-6931	185	70	m	m	VERB
ejpam-6931	185	71	|	|	ADV
ejpam-6931	185	72	ℑ	ℑ	NOUN
ejpam-6931	185	73	,	,	PUNCT
ejpam-6931	185	74	g(ϱon	g(ϱon	PROPN
ejpam-6931	185	75	,	,	PUNCT
ejpam-6931	185	76	ϱom	ϱom	NOUN
ejpam-6931	185	77	,	,	PUNCT
ejpam-6931	185	78	e	e	NOUN
ejpam-6931	185	79	)	)	PUNCT
ejpam-6931	185	80	=	=	SYM
ejpam-6931	185	81	d(ϱon	d(ϱon	PROPN
ejpam-6931	185	82	,	,	PUNCT
ejpam-6931	185	83	ϱ	ϱ	ADP
ejpam-6931	185	84	o	o	PROPN
ejpam-6931	185	85	m	m	NOUN
ejpam-6931	185	86	)	)	PUNCT
ejpam-6931	185	87	τ	τ	PROPN
ejpam-6931	186	1	+	+	NUM
ejpam-6931	186	2	ξ	ξ	X
ejpam-6931	186	3	+	+	SYM
ejpam-6931	186	4	d(ϱon	d(ϱon	PROPN
ejpam-6931	186	5	,	,	PUNCT
ejpam-6931	186	6	ϱ	ϱ	ADP
ejpam-6931	186	7	o	o	PROPN
ejpam-6931	186	8	m	m	NOUN
ejpam-6931	186	9	)	)	PUNCT
ejpam-6931	186	10	ℑ	ℑ	NOUN
ejpam-6931	186	11	=	=	PUNCT
ejpam-6931	186	12	|4	|4	NUM
ejpam-6931	186	13	+	+	SYM
ejpam-6931	186	14	1	1	NUM
ejpam-6931	186	15	n	n	NUM
ejpam-6931	186	16	−	−	PROPN
ejpam-6931	186	17	(	(	PUNCT
ejpam-6931	186	18	4	4	NUM
ejpam-6931	186	19	+	+	SYM
ejpam-6931	186	20	1	1	NUM
ejpam-6931	186	21	m)|	m)|	NOUN
ejpam-6931	186	22	τ	τ	PROPN
ejpam-6931	186	23	+	+	NUM
ejpam-6931	186	24	ξ	ξ	PROPN
ejpam-6931	186	25	+	+	PUNCT
ejpam-6931	186	26	|4	|4	NUM
ejpam-6931	186	27	+	+	SYM
ejpam-6931	186	28	1	1	NUM
ejpam-6931	186	29	n	n	NUM
ejpam-6931	186	30	−	−	PROPN
ejpam-6931	186	31	(	(	PUNCT
ejpam-6931	186	32	4	4	NUM
ejpam-6931	186	33	+	+	SYM
ejpam-6931	186	34	1	1	NUM
ejpam-6931	186	35	m)|	m)|	ADJ
ejpam-6931	186	36	ℑ	ℑ	NOUN
ejpam-6931	186	37	=	=	PUNCT
ejpam-6931	187	1	|	|	ADV
ejpam-6931	187	2	1n	1n	NUM
ejpam-6931	188	1	−	−	NUM
ejpam-6931	188	2	1	1	NUM
ejpam-6931	188	3	m	m	VERB
ejpam-6931	188	4	|	|	ADV
ejpam-6931	188	5	τ	τ	PROPN
ejpam-6931	188	6	+	+	SYM
ejpam-6931	188	7	ξ	ξ	PROPN
ejpam-6931	189	1	+	+	CCONJ
ejpam-6931	189	2	|	|	ADV
ejpam-6931	189	3	1n	1n	NUM
ejpam-6931	190	1	−	−	NUM
ejpam-6931	190	2	1	1	NUM
ejpam-6931	190	3	m	m	NOUN
ejpam-6931	190	4	|	|	ADV
ejpam-6931	190	5	ℑ	ℑ	PROPN
ejpam-6931	190	6	and	and	CCONJ
ejpam-6931	190	7	h(ϱon	h(ϱon	PROPN
ejpam-6931	190	8	,	,	PUNCT
ejpam-6931	190	9	ϱ	ϱ	ADP
ejpam-6931	190	10	o	o	PROPN
ejpam-6931	190	11	m	m	NOUN
ejpam-6931	190	12	,	,	PUNCT
ejpam-6931	190	13	e	e	NOUN
ejpam-6931	190	14	)	)	PUNCT
ejpam-6931	190	15	=	=	SYM
ejpam-6931	190	16	d(ϱon	d(ϱon	PROPN
ejpam-6931	190	17	,	,	PUNCT
ejpam-6931	190	18	ϱ	ϱ	ADP
ejpam-6931	190	19	o	o	PROPN
ejpam-6931	190	20	m	m	NOUN
ejpam-6931	190	21	)	)	PUNCT
ejpam-6931	190	22	τ	τ	PROPN
ejpam-6931	191	1	+	+	NUM
ejpam-6931	191	2	ξ	ξ	PROPN
ejpam-6931	191	3	ℑ	ℑ	NOUN
ejpam-6931	191	4	=	=	SYM
ejpam-6931	191	5	|4	|4	NUM
ejpam-6931	191	6	+	+	SYM
ejpam-6931	191	7	1	1	NUM
ejpam-6931	191	8	n	n	NUM
ejpam-6931	191	9	−	−	PROPN
ejpam-6931	191	10	(	(	PUNCT
ejpam-6931	191	11	4	4	NUM
ejpam-6931	191	12	+	+	SYM
ejpam-6931	191	13	1	1	NUM
ejpam-6931	191	14	m)|	m)|	NOUN
ejpam-6931	191	15	τ	τ	PROPN
ejpam-6931	191	16	+	+	NUM
ejpam-6931	191	17	ξ	ξ	PROPN
ejpam-6931	191	18	ℑ	ℑ	NOUN
ejpam-6931	191	19	=	=	PUNCT
ejpam-6931	192	1	|	|	ADV
ejpam-6931	192	2	1n	1n	NUM
ejpam-6931	193	1	−	−	NUM
ejpam-6931	193	2	1	1	NUM
ejpam-6931	193	3	m	m	VERB
ejpam-6931	193	4	|	|	ADV
ejpam-6931	193	5	τ	τ	X
ejpam-6931	194	1	+	+	CCONJ
ejpam-6931	194	2	ξ	ξ	X
ejpam-6931	194	3	ℑ.	ℑ.	NOUN
ejpam-6931	194	4	as	as	ADP
ejpam-6931	194	5	m	m	PROPN
ejpam-6931	194	6	,	,	PUNCT
ejpam-6931	194	7	n	n	PROPN
ejpam-6931	194	8	→	→	SYM
ejpam-6931	194	9	∞	∞	PROPN
ejpam-6931	194	10	,	,	PUNCT
ejpam-6931	194	11	we	we	PRON
ejpam-6931	194	12	observe	observe	VERB
ejpam-6931	194	13	that	that	SCONJ
ejpam-6931	194	14	e(ϱon	e(ϱon	PROPN
ejpam-6931	194	15	,	,	PUNCT
ejpam-6931	194	16	ϱom	ϱom	NOUN
ejpam-6931	194	17	,	,	PUNCT
ejpam-6931	194	18	e	e	NOUN
ejpam-6931	194	19	)	)	PUNCT
ejpam-6931	194	20	→	→	SYM
ejpam-6931	194	21	ℑ,g(ϱon	ℑ,g(ϱon	PROPN
ejpam-6931	194	22	,	,	PUNCT
ejpam-6931	194	23	ϱom	ϱom	NOUN
ejpam-6931	194	24	,	,	PUNCT
ejpam-6931	194	25	e	e	NOUN
ejpam-6931	194	26	)	)	PUNCT
ejpam-6931	194	27	→	→	SYM
ejpam-6931	194	28	∅	∅	NOUN
ejpam-6931	194	29	and	and	CCONJ
ejpam-6931	194	30	h(ϱon	h(ϱon	PROPN
ejpam-6931	194	31	,	,	PUNCT
ejpam-6931	194	32	ϱ	ϱ	ADP
ejpam-6931	194	33	o	o	PROPN
ejpam-6931	194	34	m	m	NOUN
ejpam-6931	194	35	,	,	PUNCT
ejpam-6931	194	36	e	e	NOUN
ejpam-6931	194	37	)	)	PUNCT
ejpam-6931	194	38	→	→	SYM
ejpam-6931	194	39	∅	∅	NOUN
ejpam-6931	194	40	,	,	PUNCT
ejpam-6931	194	41	which	which	PRON
ejpam-6931	194	42	leads	lead	VERB
ejpam-6931	194	43	to	to	ADP
ejpam-6931	194	44	limn→∞	limn→∞	PROPN
ejpam-6931	194	45	infm	infm	NOUN
ejpam-6931	194	46	>	>	X
ejpam-6931	194	47	n	n	PROPN
ejpam-6931	194	48	e(ϱon	e(ϱon	PROPN
ejpam-6931	194	49	,	,	PUNCT
ejpam-6931	194	50	ϱom	ϱom	NOUN
ejpam-6931	194	51	,	,	PUNCT
ejpam-6931	194	52	e	e	NOUN
ejpam-6931	194	53	)	)	PUNCT
ejpam-6931	194	54	=	=	SYM
ejpam-6931	194	55	ℑ	ℑ	PROPN
ejpam-6931	194	56	,	,	PUNCT
ejpam-6931	194	57	limn→∞	limn→∞	PROPN
ejpam-6931	194	58	supm	supm	PROPN
ejpam-6931	194	59	>	>	SYM
ejpam-6931	194	60	n	n	PRON
ejpam-6931	194	61	g(ϱon	g(ϱon	NOUN
ejpam-6931	194	62	,	,	PUNCT
ejpam-6931	194	63	ϱom	ϱom	NOUN
ejpam-6931	194	64	,	,	PUNCT
ejpam-6931	194	65	e	e	NOUN
ejpam-6931	194	66	)	)	PUNCT
ejpam-6931	194	67	=	=	SYM
ejpam-6931	194	68	∅	∅	NOUN
ejpam-6931	194	69	and	and	CCONJ
ejpam-6931	194	70	limn→∞	limn→∞	PROPN
ejpam-6931	194	71	supm	supm	PROPN
ejpam-6931	194	72	>	>	SYM
ejpam-6931	194	73	nh(ϱon	nh(ϱon	PROPN
ejpam-6931	194	74	,	,	PUNCT
ejpam-6931	194	75	ϱ	ϱ	ADP
ejpam-6931	194	76	o	o	PROPN
ejpam-6931	194	77	m	m	NOUN
ejpam-6931	194	78	,	,	PUNCT
ejpam-6931	194	79	e	e	NOUN
ejpam-6931	194	80	)	)	PUNCT
ejpam-6931	194	81	=	=	VERB
ejpam-6931	194	82	∅.	∅.	NOUN
ejpam-6931	194	83	hence	hence	ADV
ejpam-6931	194	84	show	show	VERB
ejpam-6931	194	85	that	that	SCONJ
ejpam-6931	194	86	4	4	NUM
ejpam-6931	194	87	+	+	SYM
ejpam-6931	194	88	1	1	NUM
ejpam-6931	194	89	n	n	NOUN
ejpam-6931	194	90	is	be	AUX
ejpam-6931	194	91	a	a	DET
ejpam-6931	194	92	cauchy	cauchy	ADJ
ejpam-6931	194	93	sequence	sequence	NOUN
ejpam-6931	194	94	.	.	PUNCT
ejpam-6931	195	1	s.	s.	PROPN
ejpam-6931	195	2	m.	m.	PROPN
ejpam-6931	195	3	u.	u.	PROPN
ejpam-6931	195	4	ud	ud	AUX
ejpam-6931	195	5	-	-	PUNCT
ejpam-6931	195	6	din	din	VERB
ejpam-6931	195	7	et	et	PROPN
ejpam-6931	195	8	al	al	PROPN
ejpam-6931	195	9	.	.	PUNCT
ejpam-6931	195	10	/	/	SYM
ejpam-6931	195	11	eur	eur	PROPN
ejpam-6931	195	12	.	.	PUNCT
ejpam-6931	196	1	j.	j.	PROPN
ejpam-6931	196	2	pure	pure	PROPN
ejpam-6931	196	3	appl	appl	PROPN
ejpam-6931	196	4	.	.	PROPN
ejpam-6931	196	5	math	math	PROPN
ejpam-6931	196	6	,	,	PUNCT
ejpam-6931	196	7	18	18	NUM
ejpam-6931	196	8	(	(	PUNCT
ejpam-6931	196	9	4	4	NUM
ejpam-6931	196	10	)	)	PUNCT
ejpam-6931	196	11	(	(	PUNCT
ejpam-6931	196	12	2025	2025	NUM
ejpam-6931	196	13	)	)	PUNCT
ejpam-6931	196	14	,	,	PUNCT
ejpam-6931	196	15	6931	6931	NUM
ejpam-6931	196	16	11	11	NUM
ejpam-6931	196	17	of	of	ADP
ejpam-6931	196	18	38	38	NUM
ejpam-6931	196	19	lemma	lemma	PROPN
ejpam-6931	196	20	2	2	NUM
ejpam-6931	196	21	.	.	PUNCT
ejpam-6931	197	1	let	let	VERB
ejpam-6931	197	2	(	(	PUNCT
ejpam-6931	197	3	v	v	NOUN
ejpam-6931	197	4	,	,	PUNCT
ejpam-6931	197	5	e	e	NOUN
ejpam-6931	197	6	,	,	PUNCT
ejpam-6931	197	7	g	g	PROPN
ejpam-6931	197	8	,	,	PUNCT
ejpam-6931	197	9	h	h	NOUN
ejpam-6931	197	10	,	,	PUNCT
ejpam-6931	197	11	⋆	⋆	NOUN
ejpam-6931	197	12	,	,	PUNCT
ejpam-6931	197	13	△	△	X
ejpam-6931	197	14	)	)	PUNCT
ejpam-6931	197	15	be	be	AUX
ejpam-6931	197	16	a	a	DET
ejpam-6931	197	17	cvnms	cvnms	NOUN
ejpam-6931	197	18	.	.	PUNCT
ejpam-6931	198	1	the	the	DET
ejpam-6931	198	2	sequence	sequence	NOUN
ejpam-6931	198	3	{	{	PUNCT
ejpam-6931	198	4	ϱon	ϱon	NOUN
ejpam-6931	198	5	}	}	PUNCT
ejpam-6931	198	6	∈	∈	NOUN
ejpam-6931	198	7	v	v	ADP
ejpam-6931	198	8	converges	converge	NOUN
ejpam-6931	198	9	to	to	ADP
ejpam-6931	198	10	ϱo	ϱo	PROPN
ejpam-6931	198	11	∈	∈	PROPN
ejpam-6931	198	12	v	v	NOUN
ejpam-6931	198	13	if	if	SCONJ
ejpam-6931	198	14	and	and	CCONJ
ejpam-6931	198	15	only	only	ADV
ejpam-6931	198	16	if	if	SCONJ
ejpam-6931	198	17	limn→∞	limn→∞	PROPN
ejpam-6931	198	18	e(ϱon	e(ϱon	PROPN
ejpam-6931	198	19	,	,	PUNCT
ejpam-6931	198	20	ϱo	ϱo	NOUN
ejpam-6931	198	21	,	,	PUNCT
ejpam-6931	198	22	e	e	NOUN
ejpam-6931	198	23	)	)	PUNCT
ejpam-6931	198	24	=	=	SYM
ejpam-6931	198	25	ℑ	ℑ	PROPN
ejpam-6931	198	26	,	,	PUNCT
ejpam-6931	198	27	limn→∞	limn→∞	PROPN
ejpam-6931	198	28	g(ϱon	g(ϱon	NOUN
ejpam-6931	198	29	,	,	PUNCT
ejpam-6931	198	30	ϱo	ϱo	NOUN
ejpam-6931	198	31	,	,	PUNCT
ejpam-6931	198	32	e	e	NOUN
ejpam-6931	198	33	)	)	PUNCT
ejpam-6931	198	34	=	=	SYM
ejpam-6931	198	35	∅	∅	NOUN
ejpam-6931	198	36	and	and	CCONJ
ejpam-6931	198	37	limn→∞h(ϱon	limn→∞h(ϱon	PROPN
ejpam-6931	198	38	,	,	PUNCT
ejpam-6931	198	39	ϱ	ϱ	ADP
ejpam-6931	198	40	o	o	PROPN
ejpam-6931	198	41	,	,	PUNCT
ejpam-6931	198	42	e	e	NOUN
ejpam-6931	198	43	)	)	PUNCT
ejpam-6931	198	44	=	=	NOUN
ejpam-6931	198	45	∅	∅	NOUN
ejpam-6931	198	46	are	be	AUX
ejpam-6931	198	47	satisfied	satisfied	ADJ
ejpam-6931	198	48	for	for	ADP
ejpam-6931	198	49	each	each	DET
ejpam-6931	198	50	e	e	PROPN
ejpam-6931	198	51	∈	∈	PROPN
ejpam-6931	198	52	s0	s0	PROPN
ejpam-6931	198	53	.	.	PUNCT
ejpam-6931	199	1	proof	proof	NOUN
ejpam-6931	199	2	.	.	PUNCT
ejpam-6931	200	1	assume	assume	VERB
ejpam-6931	200	2	that	that	SCONJ
ejpam-6931	200	3	limn→∞	limn→∞	PROPN
ejpam-6931	200	4	e(ϱon	e(ϱon	PROPN
ejpam-6931	200	5	,	,	PUNCT
ejpam-6931	200	6	ϱo	ϱo	NOUN
ejpam-6931	200	7	,	,	PUNCT
ejpam-6931	200	8	e	e	NOUN
ejpam-6931	200	9	)	)	PUNCT
ejpam-6931	200	10	=	=	SYM
ejpam-6931	200	11	ℑ	ℑ	PROPN
ejpam-6931	200	12	,	,	PUNCT
ejpam-6931	200	13	limn→∞	limn→∞	PROPN
ejpam-6931	200	14	g(ϱon	g(ϱon	NOUN
ejpam-6931	200	15	,	,	PUNCT
ejpam-6931	200	16	ϱo	ϱo	NOUN
ejpam-6931	200	17	,	,	PUNCT
ejpam-6931	200	18	e	e	NOUN
ejpam-6931	200	19	)	)	PUNCT
ejpam-6931	200	20	=	=	SYM
ejpam-6931	200	21	∅	∅	NOUN
ejpam-6931	200	22	and	and	CCONJ
ejpam-6931	200	23	limn→∞h(ϱon	limn→∞h(ϱon	PROPN
ejpam-6931	200	24	,	,	PUNCT
ejpam-6931	200	25	ϱ	ϱ	ADP
ejpam-6931	200	26	o	o	PROPN
ejpam-6931	200	27	,	,	PUNCT
ejpam-6931	200	28	e	e	NOUN
ejpam-6931	200	29	)	)	PUNCT
ejpam-6931	200	30	=	=	NOUN
ejpam-6931	200	31	∅	∅	NOUN
ejpam-6931	200	32	for	for	ADP
ejpam-6931	200	33	every	every	DET
ejpam-6931	200	34	e	e	PROPN
ejpam-6931	200	35	∈	∈	PROPN
ejpam-6931	200	36	s0	s0	PROPN
ejpam-6931	200	37	.	.	PUNCT
ejpam-6931	200	38	assume	assume	VERB
ejpam-6931	200	39	that	that	SCONJ
ejpam-6931	200	40	e	e	PRON
ejpam-6931	200	41	be	be	AUX
ejpam-6931	200	42	a	a	DET
ejpam-6931	200	43	fixed	fix	VERB
ejpam-6931	200	44	element	element	NOUN
ejpam-6931	200	45	from	from	ADP
ejpam-6931	200	46	s0	s0	PROPN
ejpam-6931	200	47	.	.	PUNCT
ejpam-6931	201	1	it	it	PRON
ejpam-6931	201	2	is	be	AUX
ejpam-6931	201	3	feasible	feasible	ADJ
ejpam-6931	201	4	to	to	PART
ejpam-6931	201	5	identify	identify	VERB
ejpam-6931	201	6	a	a	DET
ejpam-6931	201	7	real	real	ADJ
ejpam-6931	201	8	number	number	NOUN
ejpam-6931	201	9	ϵ	ϵ	X
ejpam-6931	201	10	>	>	X
ejpam-6931	201	11	0	0	NUM
ejpam-6931	202	1	such	such	ADJ
ejpam-6931	202	2	that	that	SCONJ
ejpam-6931	202	3	z	z	NOUN
ejpam-6931	202	4	≺	≺	NOUN
ejpam-6931	202	5	r	r	NOUN
ejpam-6931	202	6	for	for	ADP
ejpam-6931	202	7	all	all	DET
ejpam-6931	202	8	z	z	NOUN
ejpam-6931	202	9	∈	∈	PROPN
ejpam-6931	202	10	c	c	NOUN
ejpam-6931	202	11	and	and	CCONJ
ejpam-6931	202	12	|z|	|z|	VERB
ejpam-6931	202	13	<	<	X
ejpam-6931	202	14	ϵ	ϵ	NOUN
ejpam-6931	202	15	for	for	ADP
ejpam-6931	202	16	any	any	DET
ejpam-6931	202	17	r	r	NOUN
ejpam-6931	202	18	∈	∈	PROPN
ejpam-6931	202	19	t0	t0	NOUN
ejpam-6931	202	20	.	.	PUNCT
ejpam-6931	203	1	considering	consider	VERB
ejpam-6931	203	2	this	this	DET
ejpam-6931	203	3	particular	particular	ADJ
ejpam-6931	203	4	ϵ	ϵ	NOUN
ejpam-6931	203	5	,	,	PUNCT
ejpam-6931	203	6	we	we	PRON
ejpam-6931	203	7	may	may	AUX
ejpam-6931	203	8	find	find	VERB
ejpam-6931	203	9	a	a	DET
ejpam-6931	203	10	n0	n0	NUM
ejpam-6931	203	11	∈	∈	NOUN
ejpam-6931	203	12	m	m	VERB
ejpam-6931	203	13	such	such	ADJ
ejpam-6931	203	14	that	that	SCONJ
ejpam-6931	203	15	|ℑ	|ℑ	NOUN
ejpam-6931	203	16	−	−	PROPN
ejpam-6931	203	17	e(ϱon	e(ϱon	PROPN
ejpam-6931	203	18	,	,	PUNCT
ejpam-6931	203	19	ϱo	ϱo	PROPN
ejpam-6931	203	20	,	,	PUNCT
ejpam-6931	203	21	e)|	e)|	NOUN
ejpam-6931	203	22	<	<	X
ejpam-6931	203	23	ϵ	ϵ	X
ejpam-6931	203	24	,	,	PUNCT
ejpam-6931	203	25	|g(ϱon	|g(ϱon	NUM
ejpam-6931	203	26	,	,	PUNCT
ejpam-6931	203	27	ϱo	ϱo	NOUN
ejpam-6931	203	28	,	,	PUNCT
ejpam-6931	203	29	e)|	e)|	NOUN
ejpam-6931	203	30	<	<	X
ejpam-6931	203	31	ϵ	ϵ	X
ejpam-6931	203	32	and|h(ϱon	and|h(ϱon	NOUN
ejpam-6931	203	33	,	,	PUNCT
ejpam-6931	203	34	ϱ	ϱ	ADP
ejpam-6931	203	35	o	o	PROPN
ejpam-6931	203	36	,	,	PUNCT
ejpam-6931	203	37	e)|	e)|	NOUN
ejpam-6931	203	38	<	<	X
ejpam-6931	203	39	ϵ	ϵ	X
ejpam-6931	203	40	for	for	ADP
ejpam-6931	203	41	each	each	DET
ejpam-6931	203	42	n	n	PRON
ejpam-6931	203	43	∈	∈	PROPN
ejpam-6931	203	44	n0	n0	PROPN
ejpam-6931	203	45	.	.	PUNCT
ejpam-6931	204	1	these	these	DET
ejpam-6931	204	2	two	two	NUM
ejpam-6931	204	3	inequalities	inequality	NOUN
ejpam-6931	204	4	indicate	indicate	VERB
ejpam-6931	204	5	that	that	SCONJ
ejpam-6931	204	6	ℑ−	ℑ−	PROPN
ejpam-6931	204	7	e(ϱon	e(ϱon	PROPN
ejpam-6931	204	8	,	,	PUNCT
ejpam-6931	204	9	ϱo	ϱo	NOUN
ejpam-6931	204	10	,	,	PUNCT
ejpam-6931	204	11	e	e	NOUN
ejpam-6931	204	12	)	)	PUNCT
ejpam-6931	204	13	≺	≺	NOUN
ejpam-6931	204	14	s	s	VERB
ejpam-6931	204	15	−e(ϱon	−e(ϱon	PROPN
ejpam-6931	204	16	,	,	PUNCT
ejpam-6931	204	17	ϱo	ϱo	NOUN
ejpam-6931	204	18	,	,	PUNCT
ejpam-6931	204	19	e	e	NOUN
ejpam-6931	204	20	)	)	PUNCT
ejpam-6931	204	21	≺	≺	NOUN
ejpam-6931	204	22	s−ℑ	s−ℑ	PROPN
ejpam-6931	204	23	e(ϱon	e(ϱon	PROPN
ejpam-6931	204	24	,	,	PUNCT
ejpam-6931	204	25	ϱo	ϱo	NOUN
ejpam-6931	204	26	,	,	PUNCT
ejpam-6931	204	27	e	e	NOUN
ejpam-6931	204	28	)	)	PUNCT
ejpam-6931	204	29	≻	≻	VERB
ejpam-6931	204	30	ℑ−	ℑ−	NOUN
ejpam-6931	204	31	s	s	NOUN
ejpam-6931	204	32	as	as	ADV
ejpam-6931	204	33	well	well	ADV
ejpam-6931	204	34	as	as	ADP
ejpam-6931	204	35	g(ϱon	g(ϱon	PROPN
ejpam-6931	204	36	,	,	PUNCT
ejpam-6931	204	37	ϱo	ϱo	NOUN
ejpam-6931	204	38	,	,	PUNCT
ejpam-6931	204	39	e	e	NOUN
ejpam-6931	204	40	)	)	PUNCT
ejpam-6931	204	41	≺	≺	NOUN
ejpam-6931	204	42	s	s	PART
ejpam-6931	204	43	also	also	ADV
ejpam-6931	204	44	h(ϱon	h(ϱon	PROPN
ejpam-6931	204	45	,	,	PUNCT
ejpam-6931	204	46	ϱ	ϱ	ADP
ejpam-6931	204	47	o	o	PROPN
ejpam-6931	204	48	,	,	PUNCT
ejpam-6931	204	49	e	e	NOUN
ejpam-6931	204	50	)	)	PUNCT
ejpam-6931	204	51	≺	≺	NOUN
ejpam-6931	204	52	s	s	PART
ejpam-6931	204	53	for	for	ADP
ejpam-6931	204	54	all	all	PRON
ejpam-6931	204	55	n	n	PRON
ejpam-6931	204	56	>	>	X
ejpam-6931	204	57	n0	n0	NUM
ejpam-6931	204	58	respectively	respectively	ADV
ejpam-6931	204	59	.	.	PUNCT
ejpam-6931	205	1	consequently	consequently	ADV
ejpam-6931	205	2	,	,	PUNCT
ejpam-6931	205	3	{	{	PUNCT
ejpam-6931	205	4	ϱon	ϱon	NOUN
ejpam-6931	205	5	}	}	PUNCT
ejpam-6931	205	6	is	be	AUX
ejpam-6931	205	7	convergent	convergent	ADJ
ejpam-6931	205	8	to	to	ADP
ejpam-6931	205	9	ϱo	ϱo	DET
ejpam-6931	205	10	∈	∈	PROPN
ejpam-6931	205	11	v.	v.	ADP
ejpam-6931	205	12	conversely	conversely	ADV
ejpam-6931	205	13	,	,	PUNCT
ejpam-6931	205	14	assume	assume	VERB
ejpam-6931	205	15	that	that	SCONJ
ejpam-6931	205	16	e	e	PROPN
ejpam-6931	205	17	∈	∈	PROPN
ejpam-6931	205	18	s0	s0	PROPN
ejpam-6931	205	19	is	be	AUX
ejpam-6931	205	20	fixed	fix	VERB
ejpam-6931	205	21	and	and	CCONJ
ejpam-6931	205	22	a	a	DET
ejpam-6931	205	23	real	real	ADJ
ejpam-6931	205	24	value	value	NOUN
ejpam-6931	206	1	ϵ	ϵ	X
ejpam-6931	206	2	>	>	X
ejpam-6931	206	3	0	0	NUM
ejpam-6931	206	4	is	be	AUX
ejpam-6931	206	5	specified	specify	VERB
ejpam-6931	206	6	.	.	PUNCT
ejpam-6931	207	1	assume	assume	VERB
ejpam-6931	207	2	that	that	SCONJ
ejpam-6931	207	3	a	a	DET
ejpam-6931	207	4	sequence	sequence	NOUN
ejpam-6931	207	5	{	{	PUNCT
ejpam-6931	207	6	ϱon	ϱon	NOUN
ejpam-6931	207	7	}	}	PUNCT
ejpam-6931	207	8	is	be	AUX
ejpam-6931	207	9	converges	converge	NOUN
ejpam-6931	207	10	to	to	ADP
ejpam-6931	207	11	ϱo	ϱo	PROPN
ejpam-6931	207	12	∈	∈	PROPN
ejpam-6931	207	13	v	v	NOUN
ejpam-6931	207	14	that	that	PRON
ejpam-6931	207	15	is	be	AUX
ejpam-6931	207	16	,	,	PUNCT
ejpam-6931	207	17	for	for	ADP
ejpam-6931	207	18	each	each	DET
ejpam-6931	207	19	element	element	NOUN
ejpam-6931	207	20	s	s	PART
ejpam-6931	207	21	in	in	ADP
ejpam-6931	207	22	the	the	DET
ejpam-6931	207	23	set	set	NOUN
ejpam-6931	207	24	t0	t0	PROPN
ejpam-6931	207	25	and	and	CCONJ
ejpam-6931	207	26	every	every	DET
ejpam-6931	207	27	element	element	NOUN
ejpam-6931	207	28	no	no	INTJ
ejpam-6931	207	29	in	in	ADP
ejpam-6931	207	30	the	the	DET
ejpam-6931	207	31	set	set	NOUN
ejpam-6931	207	32	m	m	NOUN
ejpam-6931	207	33	,	,	PUNCT
ejpam-6931	207	34	it	it	PRON
ejpam-6931	207	35	is	be	AUX
ejpam-6931	207	36	possible	possible	ADJ
ejpam-6931	207	37	to	to	PART
ejpam-6931	207	38	select	select	VERB
ejpam-6931	207	39	a	a	DET
ejpam-6931	207	40	value	value	NOUN
ejpam-6931	207	41	such	such	ADJ
ejpam-6931	207	42	that	that	SCONJ
ejpam-6931	207	43	e(ϱon	e(ϱon	PROPN
ejpam-6931	207	44	,	,	PUNCT
ejpam-6931	207	45	ϱo	ϱo	NOUN
ejpam-6931	207	46	,	,	PUNCT
ejpam-6931	207	47	e	e	NOUN
ejpam-6931	207	48	)	)	PUNCT
ejpam-6931	208	1	>	>	PUNCT
ejpam-6931	208	2	ℑ	ℑ	PROPN
ejpam-6931	208	3	−	−	PROPN
ejpam-6931	208	4	s	s	PROPN
ejpam-6931	208	5	,	,	PUNCT
ejpam-6931	208	6	g(ϱon	g(ϱon	PROPN
ejpam-6931	208	7	,	,	PUNCT
ejpam-6931	208	8	ϱo	ϱo	NOUN
ejpam-6931	208	9	,	,	PUNCT
ejpam-6931	208	10	e	e	NOUN
ejpam-6931	208	11	)	)	PUNCT
ejpam-6931	208	12	<	<	X
ejpam-6931	208	13	s	s	X
ejpam-6931	208	14	and	and	CCONJ
ejpam-6931	208	15	h(ϱon	h(ϱon	PROPN
ejpam-6931	208	16	,	,	PUNCT
ejpam-6931	208	17	ϱ	ϱ	ADP
ejpam-6931	208	18	o	o	PROPN
ejpam-6931	208	19	,	,	PUNCT
ejpam-6931	208	20	e	e	NOUN
ejpam-6931	208	21	)	)	PUNCT
ejpam-6931	208	22	<	<	X
ejpam-6931	208	23	s	s	X
ejpam-6931	208	24	for	for	ADP
ejpam-6931	208	25	each	each	DET
ejpam-6931	208	26	n	n	PROPN
ejpam-6931	208	27	>	>	X
ejpam-6931	208	28	n0	n0	PROPN
ejpam-6931	208	29	.	.	PUNCT
ejpam-6931	209	1	a	a	DET
ejpam-6931	209	2	complex	complex	ADJ
ejpam-6931	209	3	number	number	NOUN
ejpam-6931	209	4	s	s	PART
ejpam-6931	209	5	is	be	AUX
ejpam-6931	209	6	selected	select	VERB
ejpam-6931	209	7	from	from	ADP
ejpam-6931	209	8	the	the	DET
ejpam-6931	209	9	set	set	NOUN
ejpam-6931	209	10	t0	t0	PROPN
ejpam-6931	209	11	such	such	ADJ
ejpam-6931	209	12	that	that	SCONJ
ejpam-6931	209	13	|s|	|s|	PROPN
ejpam-6931	209	14	<	<	X
ejpam-6931	209	15	ϵ.	ϵ.	NOUN
ejpam-6931	209	16	therefore	therefore	ADV
ejpam-6931	209	17	|ℑ	|ℑ	X
ejpam-6931	209	18	−	−	PROPN
ejpam-6931	209	19	e(ϱon	e(ϱon	PROPN
ejpam-6931	209	20	,	,	PUNCT
ejpam-6931	209	21	ϱo	ϱo	PROPN
ejpam-6931	209	22	,	,	PUNCT
ejpam-6931	209	23	e)|	e)|	NOUN
ejpam-6931	209	24	<	<	X
ejpam-6931	209	25	|s|	|s|	PROPN
ejpam-6931	209	26	,	,	PUNCT
ejpam-6931	209	27	|g(ϱon	|g(ϱon	NUM
ejpam-6931	209	28	,	,	PUNCT
ejpam-6931	209	29	ϱo	ϱo	NOUN
ejpam-6931	209	30	,	,	PUNCT
ejpam-6931	209	31	e)|	e)|	NOUN
ejpam-6931	209	32	<	<	X
ejpam-6931	209	33	|s|	|s|	PROPN
ejpam-6931	209	34	<	<	X
ejpam-6931	209	35	ϵ	ϵ	PROPN
ejpam-6931	209	36	and	and	CCONJ
ejpam-6931	209	37	|h(ϱon	|h(ϱon	NUM
ejpam-6931	209	38	,	,	PUNCT
ejpam-6931	209	39	ϱ	ϱ	ADP
ejpam-6931	209	40	o	o	PROPN
ejpam-6931	209	41	,	,	PUNCT
ejpam-6931	209	42	e)|	e)|	INTJ
ejpam-6931	209	43	<	<	X
ejpam-6931	209	44	|s|	|s|	PROPN
ejpam-6931	209	45	<	<	X
ejpam-6931	209	46	ϵ	ϵ	NOUN
ejpam-6931	209	47	for	for	ADP
ejpam-6931	209	48	any	any	DET
ejpam-6931	209	49	n	n	PROPN
ejpam-6931	209	50	>	>	X
ejpam-6931	209	51	n0	n0	PROPN
ejpam-6931	209	52	.	.	PUNCT
ejpam-6931	210	1	therefore	therefore	ADV
ejpam-6931	210	2	,	,	PUNCT
ejpam-6931	210	3	limn→∞	limn→∞	PROPN
ejpam-6931	210	4	e(ϱon	e(ϱon	PROPN
ejpam-6931	210	5	,	,	PUNCT
ejpam-6931	210	6	ϱo	ϱo	NOUN
ejpam-6931	210	7	,	,	PUNCT
ejpam-6931	210	8	e	e	NOUN
ejpam-6931	210	9	)	)	PUNCT
ejpam-6931	210	10	=	=	SYM
ejpam-6931	210	11	ℑ	ℑ	PROPN
ejpam-6931	210	12	,	,	PUNCT
ejpam-6931	210	13	limn→∞	limn→∞	PROPN
ejpam-6931	210	14	g(ϱon	g(ϱon	NOUN
ejpam-6931	210	15	,	,	PUNCT
ejpam-6931	210	16	ϱo	ϱo	NOUN
ejpam-6931	210	17	,	,	PUNCT
ejpam-6931	210	18	e	e	NOUN
ejpam-6931	210	19	)	)	PUNCT
ejpam-6931	210	20	=	=	SYM
ejpam-6931	210	21	∅	∅	NOUN
ejpam-6931	210	22	and	and	CCONJ
ejpam-6931	210	23	limn→∞h(ϱon	limn→∞h(ϱon	PROPN
ejpam-6931	210	24	,	,	PUNCT
ejpam-6931	210	25	ϱ	ϱ	ADP
ejpam-6931	210	26	o	o	PROPN
ejpam-6931	210	27	,	,	PUNCT
ejpam-6931	210	28	e	e	NOUN
ejpam-6931	210	29	)	)	PUNCT
ejpam-6931	210	30	=	=	NOUN
ejpam-6931	210	31	∅	∅	NOUN
ejpam-6931	210	32	is	be	AUX
ejpam-6931	210	33	satisfied	satisfied	ADJ
ejpam-6931	210	34	for	for	ADP
ejpam-6931	210	35	every	every	DET
ejpam-6931	210	36	e	e	PROPN
ejpam-6931	210	37	∈	∈	PROPN
ejpam-6931	210	38	s0	s0	PROPN
ejpam-6931	210	39	.	.	PUNCT
ejpam-6931	211	1	lemma	lemma	PROPN
ejpam-6931	211	2	3	3	X
ejpam-6931	211	3	.	.	PUNCT
ejpam-6931	212	1	let	let	VERB
ejpam-6931	212	2	(	(	PUNCT
ejpam-6931	212	3	v	v	NOUN
ejpam-6931	212	4	,	,	PUNCT
ejpam-6931	212	5	e	e	NOUN
ejpam-6931	212	6	,	,	PUNCT
ejpam-6931	212	7	g	g	PROPN
ejpam-6931	212	8	,	,	PUNCT
ejpam-6931	212	9	h	h	NOUN
ejpam-6931	212	10	,	,	PUNCT
ejpam-6931	212	11	⋆	⋆	NOUN
ejpam-6931	212	12	,	,	PUNCT
ejpam-6931	212	13	△	△	X
ejpam-6931	212	14	)	)	PUNCT
ejpam-6931	212	15	be	be	AUX
ejpam-6931	212	16	a	a	DET
ejpam-6931	212	17	cvnms	cvnms	NOUN
ejpam-6931	212	18	.	.	PUNCT
ejpam-6931	213	1	a	a	DET
ejpam-6931	213	2	sequence	sequence	NOUN
ejpam-6931	213	3	{	{	PUNCT
ejpam-6931	213	4	ϱon	ϱon	NOUN
ejpam-6931	213	5	}	}	PUNCT
ejpam-6931	213	6	∈	∈	NOUN
ejpam-6931	213	7	v	v	NOUN
ejpam-6931	213	8	is	be	AUX
ejpam-6931	213	9	classified	classify	VERB
ejpam-6931	213	10	as	as	ADP
ejpam-6931	213	11	a	a	DET
ejpam-6931	213	12	cauchy	cauchy	ADJ
ejpam-6931	213	13	sequence	sequence	NOUN
ejpam-6931	213	14	if	if	SCONJ
ejpam-6931	213	15	and	and	CCONJ
ejpam-6931	213	16	only	only	ADV
ejpam-6931	213	17	if	if	SCONJ
ejpam-6931	213	18	for	for	ADP
ejpam-6931	213	19	every	every	DET
ejpam-6931	213	20	s	s	PROPN
ejpam-6931	213	21	∈	∈	PROPN
ejpam-6931	213	22	t0	t0	PROPN
ejpam-6931	213	23	and	and	CCONJ
ejpam-6931	213	24	e	e	PROPN
ejpam-6931	213	25	∈	∈	PROPN
ejpam-6931	213	26	s0	s0	PROPN
ejpam-6931	213	27	,	,	PUNCT
ejpam-6931	213	28	one	one	PRON
ejpam-6931	213	29	can	can	AUX
ejpam-6931	213	30	find	find	VERB
ejpam-6931	213	31	n0	n0	NUM
ejpam-6931	213	32	∈	∈	PROPN
ejpam-6931	213	33	m	m	VERB
ejpam-6931	213	34	satisfying	satisfy	VERB
ejpam-6931	213	35	e(ϱon	e(ϱon	PROPN
ejpam-6931	213	36	,	,	PUNCT
ejpam-6931	213	37	ϱo	ϱo	NOUN
ejpam-6931	213	38	,	,	PUNCT
ejpam-6931	213	39	e	e	NOUN
ejpam-6931	213	40	)	)	PUNCT
ejpam-6931	213	41	≻	≻	VERB
ejpam-6931	213	42	ℑ−	ℑ−	PROPN
ejpam-6931	213	43	s	s	PROPN
ejpam-6931	213	44	,	,	PUNCT
ejpam-6931	213	45	g(ϱon	g(ϱon	PROPN
ejpam-6931	213	46	,	,	PUNCT
ejpam-6931	213	47	ϱo	ϱo	NOUN
ejpam-6931	213	48	,	,	PUNCT
ejpam-6931	213	49	e	e	NOUN
ejpam-6931	213	50	)	)	PUNCT
ejpam-6931	213	51	≺	≺	NOUN
ejpam-6931	213	52	s	s	PART
ejpam-6931	213	53	and	and	CCONJ
ejpam-6931	213	54	h(ϱon	h(ϱon	PROPN
ejpam-6931	213	55	,	,	PUNCT
ejpam-6931	213	56	ϱ	ϱ	ADP
ejpam-6931	213	57	o	o	PROPN
ejpam-6931	213	58	,	,	PUNCT
ejpam-6931	213	59	e	e	NOUN
ejpam-6931	213	60	)	)	PUNCT
ejpam-6931	213	61	≺	≺	NOUN
ejpam-6931	213	62	s	s	PRON
ejpam-6931	213	63	for	for	ADP
ejpam-6931	213	64	each	each	DET
ejpam-6931	213	65	n	n	CCONJ
ejpam-6931	213	66	,	,	PUNCT
ejpam-6931	213	67	m	m	VERB
ejpam-6931	213	68	>	>	X
ejpam-6931	213	69	n0	n0	X
ejpam-6931	213	70	.	.	PUNCT
ejpam-6931	214	1	proof	proof	NOUN
ejpam-6931	214	2	.	.	PUNCT
ejpam-6931	215	1	assume	assume	VERB
ejpam-6931	215	2	that	that	SCONJ
ejpam-6931	215	3	{	{	PUNCT
ejpam-6931	215	4	ϱon	ϱon	NOUN
ejpam-6931	215	5	}	}	PUNCT
ejpam-6931	215	6	is	be	AUX
ejpam-6931	215	7	cauchy	cauchy	ADJ
ejpam-6931	215	8	sequence	sequence	NOUN
ejpam-6931	215	9	.	.	PUNCT
ejpam-6931	216	1	suppose	suppose	VERB
ejpam-6931	216	2	e	e	NOUN
ejpam-6931	216	3	is	be	AUX
ejpam-6931	216	4	a	a	DET
ejpam-6931	216	5	fixed	fix	VERB
ejpam-6931	216	6	element	element	NOUN
ejpam-6931	216	7	from	from	ADP
ejpam-6931	216	8	s0	s0	PROPN
ejpam-6931	216	9	,	,	PUNCT
ejpam-6931	216	10	then	then	ADV
ejpam-6931	216	11	,	,	PUNCT
ejpam-6931	216	12	for	for	ADP
ejpam-6931	216	13	each	each	DET
ejpam-6931	216	14	s	s	PROPN
ejpam-6931	216	15	∈	∈	PROPN
ejpam-6931	216	16	t0	t0	PROPN
ejpam-6931	216	17	,	,	PUNCT
ejpam-6931	216	18	it	it	PRON
ejpam-6931	216	19	is	be	AUX
ejpam-6931	216	20	possible	possible	ADJ
ejpam-6931	216	21	to	to	PART
ejpam-6931	216	22	identify	identify	VERB
ejpam-6931	216	23	n0	n0	NUM
ejpam-6931	216	24	∈	∈	PROPN
ejpam-6931	216	25	m	m	VERB
ejpam-6931	216	26	that	that	PRON
ejpam-6931	216	27	satisfies	satisfy	VERB
ejpam-6931	216	28	the	the	DET
ejpam-6931	216	29	conditions	condition	NOUN
ejpam-6931	216	30	ℑ	ℑ	PROPN
ejpam-6931	216	31	−	−	PROPN
ejpam-6931	216	32	infm	infm	NOUN
ejpam-6931	216	33	>	>	X
ejpam-6931	216	34	n	n	PROPN
ejpam-6931	216	35	e(ϱon	e(ϱon	PROPN
ejpam-6931	216	36	,	,	PUNCT
ejpam-6931	216	37	ϱom	ϱom	NOUN
ejpam-6931	216	38	,	,	PUNCT
ejpam-6931	216	39	e	e	NOUN
ejpam-6931	216	40	)	)	PUNCT
ejpam-6931	216	41	≺	≺	NOUN
ejpam-6931	216	42	s	s	SYM
ejpam-6931	216	43	,	,	PUNCT
ejpam-6931	216	44	supm	supm	PROPN
ejpam-6931	216	45	>	>	SYM
ejpam-6931	216	46	n	n	PRON
ejpam-6931	216	47	g(ϱon	g(ϱon	NOUN
ejpam-6931	216	48	,	,	PUNCT
ejpam-6931	216	49	ϱom	ϱom	NOUN
ejpam-6931	216	50	,	,	PUNCT
ejpam-6931	216	51	e	e	NOUN
ejpam-6931	216	52	)	)	PUNCT
ejpam-6931	216	53	≺	≺	NOUN
ejpam-6931	216	54	s	s	PART
ejpam-6931	216	55	,	,	PUNCT
ejpam-6931	216	56	and	and	CCONJ
ejpam-6931	216	57	supm	supm	PROPN
ejpam-6931	216	58	>	>	SYM
ejpam-6931	216	59	nh(ϱon	nh(ϱon	PROPN
ejpam-6931	216	60	,	,	PUNCT
ejpam-6931	216	61	ϱ	ϱ	ADP
ejpam-6931	216	62	o	o	PROPN
ejpam-6931	216	63	m	m	NOUN
ejpam-6931	216	64	,	,	PUNCT
ejpam-6931	216	65	e	e	NOUN
ejpam-6931	216	66	)	)	PUNCT
ejpam-6931	216	67	≺	≺	NOUN
ejpam-6931	216	68	s	s	PRON
ejpam-6931	216	69	for	for	ADP
ejpam-6931	216	70	each	each	DET
ejpam-6931	216	71	n	n	PROPN
ejpam-6931	216	72	>	>	X
ejpam-6931	216	73	n0	n0	PROPN
ejpam-6931	216	74	.	.	PUNCT
ejpam-6931	217	1	here	here	ADV
ejpam-6931	217	2	,	,	PUNCT
ejpam-6931	217	3	we	we	PRON
ejpam-6931	217	4	look	look	VERB
ejpam-6931	217	5	at	at	ADP
ejpam-6931	217	6	three	three	NUM
ejpam-6931	217	7	situations	situation	NOUN
ejpam-6931	217	8	.	.	PUNCT
ejpam-6931	218	1	for	for	ADP
ejpam-6931	218	2	the	the	DET
ejpam-6931	218	3	situation	situation	NOUN
ejpam-6931	218	4	where	where	SCONJ
ejpam-6931	218	5	m	m	VERB
ejpam-6931	218	6	>	>	X
ejpam-6931	218	7	n	n	PROPN
ejpam-6931	218	8	>	>	X
ejpam-6931	218	9	n0	n0	PROPN
ejpam-6931	218	10	,	,	PUNCT
ejpam-6931	218	11	this	this	PRON
ejpam-6931	218	12	leads	lead	VERB
ejpam-6931	218	13	to	to	ADP
ejpam-6931	218	14	ℑ−s	ℑ−	VERB
ejpam-6931	218	15	≺	≺	NOUN
ejpam-6931	218	16	infm	infm	NOUN
ejpam-6931	218	17	>	>	X
ejpam-6931	218	18	n	n	PROPN
ejpam-6931	218	19	e(ϱon	e(ϱon	PROPN
ejpam-6931	218	20	,	,	PUNCT
ejpam-6931	218	21	ϱom	ϱom	NOUN
ejpam-6931	218	22	,	,	PUNCT
ejpam-6931	218	23	e	e	NOUN
ejpam-6931	218	24	)	)	PUNCT
ejpam-6931	218	25	≺	≺	NOUN
ejpam-6931	218	26	e(ϱon	e(ϱon	PROPN
ejpam-6931	218	27	,	,	PUNCT
ejpam-6931	218	28	ϱom	ϱom	NOUN
ejpam-6931	218	29	,	,	PUNCT
ejpam-6931	218	30	e	e	NOUN
ejpam-6931	218	31	)	)	PUNCT
ejpam-6931	218	32	,	,	PUNCT
ejpam-6931	218	33	g(ϱon	g(ϱon	PROPN
ejpam-6931	218	34	,	,	PUNCT
ejpam-6931	218	35	ϱom	ϱom	NOUN
ejpam-6931	218	36	,	,	PUNCT
ejpam-6931	218	37	e	e	NOUN
ejpam-6931	218	38	)	)	PUNCT
ejpam-6931	218	39	≺	≺	NOUN
ejpam-6931	218	40	supm	supm	PROPN
ejpam-6931	218	41	>	>	SYM
ejpam-6931	218	42	n	n	X
ejpam-6931	218	43	g(ϱon	g(ϱon	NOUN
ejpam-6931	218	44	,	,	PUNCT
ejpam-6931	218	45	ϱom	ϱom	NOUN
ejpam-6931	218	46	,	,	PUNCT
ejpam-6931	218	47	e	e	NOUN
ejpam-6931	218	48	)	)	PUNCT
ejpam-6931	218	49	≺	≺	NOUN
ejpam-6931	218	50	s	s	PART
ejpam-6931	218	51	and	and	CCONJ
ejpam-6931	218	52	h(ϱon	h(ϱon	PROPN
ejpam-6931	218	53	,	,	PUNCT
ejpam-6931	218	54	ϱ	ϱ	ADP
ejpam-6931	218	55	o	o	PROPN
ejpam-6931	218	56	m	m	NOUN
ejpam-6931	218	57	,	,	PUNCT
ejpam-6931	218	58	e	e	NOUN
ejpam-6931	218	59	)	)	PUNCT
ejpam-6931	218	60	≺	≺	NOUN
ejpam-6931	218	61	supm	supm	PROPN
ejpam-6931	218	62	>	>	SYM
ejpam-6931	218	63	nh(ϱon	nh(ϱon	PROPN
ejpam-6931	218	64	,	,	PUNCT
ejpam-6931	218	65	ϱ	ϱ	ADP
ejpam-6931	218	66	o	o	PROPN
ejpam-6931	218	67	m	m	NOUN
ejpam-6931	218	68	,	,	PUNCT
ejpam-6931	218	69	e	e	NOUN
ejpam-6931	218	70	)	)	PUNCT
ejpam-6931	218	71	≺.	≺.	NOUN
ejpam-6931	218	72	now	now	ADV
ejpam-6931	218	73	if	if	SCONJ
ejpam-6931	218	74	m	m	VERB
ejpam-6931	218	75	=	=	SYM
ejpam-6931	218	76	n	n	PROPN
ejpam-6931	218	77	>	>	X
ejpam-6931	218	78	n0	n0	PROPN
ejpam-6931	218	79	,	,	PUNCT
ejpam-6931	218	80	then	then	ADV
ejpam-6931	218	81	ℑ	ℑ	PROPN
ejpam-6931	218	82	−	−	PROPN
ejpam-6931	218	83	s	s	NOUN
ejpam-6931	218	84	≺	≺	NOUN
ejpam-6931	218	85	ℑ	ℑ	PROPN
ejpam-6931	218	86	=	=	SYM
ejpam-6931	218	87	e(ϱon	e(ϱon	PROPN
ejpam-6931	218	88	,	,	PUNCT
ejpam-6931	218	89	ϱom	ϱom	NOUN
ejpam-6931	218	90	,	,	PUNCT
ejpam-6931	218	91	e	e	NOUN
ejpam-6931	218	92	)	)	PUNCT
ejpam-6931	218	93	,	,	PUNCT
ejpam-6931	218	94	g(ϱon	g(ϱon	PROPN
ejpam-6931	218	95	,	,	PUNCT
ejpam-6931	218	96	ϱom	ϱom	NOUN
ejpam-6931	218	97	,	,	PUNCT
ejpam-6931	218	98	e	e	NOUN
ejpam-6931	218	99	)	)	PUNCT
ejpam-6931	218	100	=	=	NOUN
ejpam-6931	218	101	∅	∅	NOUN
ejpam-6931	218	102	≺	≺	NOUN
ejpam-6931	218	103	s	s	PART
ejpam-6931	218	104	and	and	CCONJ
ejpam-6931	218	105	h(ϱon	h(ϱon	PROPN
ejpam-6931	218	106	,	,	PUNCT
ejpam-6931	218	107	ϱ	ϱ	ADP
ejpam-6931	218	108	o	o	PROPN
ejpam-6931	218	109	m	m	NOUN
ejpam-6931	218	110	,	,	PUNCT
ejpam-6931	218	111	e	e	NOUN
ejpam-6931	218	112	)	)	PUNCT
ejpam-6931	218	113	=	=	NOUN
ejpam-6931	218	114	∅	∅	NOUN
ejpam-6931	218	115	≺	≺	NOUN
ejpam-6931	218	116	s.	s.	PROPN
ejpam-6931	218	117	finally	finally	ADV
ejpam-6931	218	118	,	,	PUNCT
ejpam-6931	218	119	but	but	CCONJ
ejpam-6931	218	120	not	not	PART
ejpam-6931	218	121	least	least	ADJ
ejpam-6931	218	122	,	,	PUNCT
ejpam-6931	218	123	given	give	VERB
ejpam-6931	218	124	s.	s.	PROPN
ejpam-6931	218	125	m.	m.	PROPN
ejpam-6931	218	126	u.	u.	PROPN
ejpam-6931	218	127	ud	ud	AUX
ejpam-6931	218	128	-	-	PUNCT
ejpam-6931	218	129	din	din	VERB
ejpam-6931	218	130	et	et	PROPN
ejpam-6931	218	131	al	al	PROPN
ejpam-6931	218	132	.	.	PUNCT
ejpam-6931	218	133	/	/	SYM
ejpam-6931	218	134	eur	eur	PROPN
ejpam-6931	218	135	.	.	PUNCT
ejpam-6931	219	1	j.	j.	PROPN
ejpam-6931	219	2	pure	pure	PROPN
ejpam-6931	219	3	appl	appl	PROPN
ejpam-6931	219	4	.	.	PROPN
ejpam-6931	219	5	math	math	PROPN
ejpam-6931	219	6	,	,	PUNCT
ejpam-6931	219	7	18	18	NUM
ejpam-6931	219	8	(	(	PUNCT
ejpam-6931	219	9	4	4	NUM
ejpam-6931	219	10	)	)	PUNCT
ejpam-6931	219	11	(	(	PUNCT
ejpam-6931	219	12	2025	2025	NUM
ejpam-6931	219	13	)	)	PUNCT
ejpam-6931	219	14	,	,	PUNCT
ejpam-6931	219	15	6931	6931	NUM
ejpam-6931	219	16	12	12	NUM
ejpam-6931	219	17	of	of	ADP
ejpam-6931	219	18	38	38	NUM
ejpam-6931	219	19	the	the	DET
ejpam-6931	219	20	situation	situation	NOUN
ejpam-6931	219	21	when	when	SCONJ
ejpam-6931	219	22	n	n	X
ejpam-6931	219	23	>	>	X
ejpam-6931	219	24	m	m	VERB
ejpam-6931	219	25	>	>	X
ejpam-6931	219	26	n0	n0	PROPN
ejpam-6931	219	27	,	,	PUNCT
ejpam-6931	219	28	it	it	PRON
ejpam-6931	219	29	follows	follow	VERB
ejpam-6931	219	30	that	that	SCONJ
ejpam-6931	219	31	ℑ−s	ℑ−s	ADJ
ejpam-6931	219	32	≺	≺	VERB
ejpam-6931	219	33	infn	infn	PROPN
ejpam-6931	219	34	>	>	X
ejpam-6931	219	35	m	m	PROPN
ejpam-6931	219	36	e(ϱom	e(ϱom	PROPN
ejpam-6931	219	37	,	,	PUNCT
ejpam-6931	219	38	ϱon	ϱon	PROPN
ejpam-6931	219	39	,	,	PUNCT
ejpam-6931	219	40	e	e	NOUN
ejpam-6931	219	41	)	)	PUNCT
ejpam-6931	219	42	⪯	⪯	PROPN
ejpam-6931	219	43	e(ϱom	e(ϱom	PROPN
ejpam-6931	219	44	,	,	PUNCT
ejpam-6931	219	45	ϱon	ϱon	PROPN
ejpam-6931	219	46	,	,	PUNCT
ejpam-6931	219	47	e	e	NOUN
ejpam-6931	219	48	)	)	PUNCT
ejpam-6931	219	49	=	=	SYM
ejpam-6931	219	50	e(ϱon	e(ϱon	PROPN
ejpam-6931	219	51	,	,	PUNCT
ejpam-6931	219	52	ϱom	ϱom	NOUN
ejpam-6931	219	53	,	,	PUNCT
ejpam-6931	219	54	e	e	NOUN
ejpam-6931	219	55	)	)	PUNCT
ejpam-6931	219	56	,	,	PUNCT
ejpam-6931	219	57	g(ϱom	g(ϱom	PROPN
ejpam-6931	219	58	,	,	PUNCT
ejpam-6931	219	59	ϱon	ϱon	PROPN
ejpam-6931	219	60	,	,	PUNCT
ejpam-6931	219	61	e	e	NOUN
ejpam-6931	219	62	)	)	PUNCT
ejpam-6931	219	63	=	=	SYM
ejpam-6931	219	64	g(ϱon	g(ϱon	PROPN
ejpam-6931	219	65	,	,	PUNCT
ejpam-6931	219	66	ϱom	ϱom	NOUN
ejpam-6931	219	67	,	,	PUNCT
ejpam-6931	219	68	e	e	NOUN
ejpam-6931	219	69	)	)	PUNCT
ejpam-6931	219	70	⪯	⪯	PROPN
ejpam-6931	219	71	supn	supn	PROPN
ejpam-6931	219	72	>	>	PROPN
ejpam-6931	219	73	m	m	PROPN
ejpam-6931	219	74	g(ϱon	g(ϱon	NOUN
ejpam-6931	219	75	,	,	PUNCT
ejpam-6931	219	76	ϱom	ϱom	NOUN
ejpam-6931	219	77	,	,	PUNCT
ejpam-6931	219	78	e	e	NOUN
ejpam-6931	219	79	)	)	PUNCT
ejpam-6931	219	80	≺	≺	NOUN
ejpam-6931	219	81	s	s	PART
ejpam-6931	219	82	and	and	CCONJ
ejpam-6931	219	83	h(ϱom	h(ϱom	PROPN
ejpam-6931	219	84	,	,	PUNCT
ejpam-6931	219	85	ϱon	ϱon	PROPN
ejpam-6931	219	86	,	,	PUNCT
ejpam-6931	219	87	e	e	NOUN
ejpam-6931	219	88	)	)	PUNCT
ejpam-6931	219	89	=	=	SYM
ejpam-6931	219	90	h(ϱon	h(ϱon	PROPN
ejpam-6931	219	91	,	,	PUNCT
ejpam-6931	219	92	ϱ	ϱ	ADP
ejpam-6931	219	93	o	o	PROPN
ejpam-6931	219	94	m	m	NOUN
ejpam-6931	219	95	,	,	PUNCT
ejpam-6931	219	96	e	e	NOUN
ejpam-6931	219	97	)	)	PUNCT
ejpam-6931	219	98	⪯	⪯	PROPN
ejpam-6931	219	99	supn	supn	PROPN
ejpam-6931	219	100	>	>	PROPN
ejpam-6931	219	101	mh(ϱon	mh(ϱon	PROPN
ejpam-6931	219	102	,	,	PUNCT
ejpam-6931	219	103	ϱ	ϱ	ADP
ejpam-6931	219	104	o	o	PROPN
ejpam-6931	219	105	m	m	NOUN
ejpam-6931	219	106	,	,	PUNCT
ejpam-6931	219	107	e	e	NOUN
ejpam-6931	219	108	)	)	PUNCT
ejpam-6931	219	109	≺	≺	NOUN
ejpam-6931	219	110	s.	s.	PROPN
ejpam-6931	219	111	thus	thus	ADV
ejpam-6931	219	112	,	,	PUNCT
ejpam-6931	219	113	we	we	PRON
ejpam-6931	219	114	deduce	deduce	VERB
ejpam-6931	219	115	that	that	SCONJ
ejpam-6931	219	116	e(ϱon	e(ϱon	PROPN
ejpam-6931	219	117	,	,	PUNCT
ejpam-6931	219	118	ϱom	ϱom	NOUN
ejpam-6931	219	119	,	,	PUNCT
ejpam-6931	219	120	e	e	NOUN
ejpam-6931	219	121	)	)	PUNCT
ejpam-6931	219	122	≻	≻	X
ejpam-6931	219	123	ℑ−s	ℑ−	VERB
ejpam-6931	219	124	,	,	PUNCT
ejpam-6931	219	125	g(ϱon	g(ϱon	PROPN
ejpam-6931	219	126	,	,	PUNCT
ejpam-6931	219	127	ϱom	ϱom	NOUN
ejpam-6931	219	128	,	,	PUNCT
ejpam-6931	219	129	e	e	NOUN
ejpam-6931	219	130	)	)	PUNCT
ejpam-6931	219	131	≺	≺	NOUN
ejpam-6931	219	132	s	s	PRON
ejpam-6931	219	133	as	as	ADV
ejpam-6931	219	134	well	well	ADV
ejpam-6931	219	135	as	as	ADP
ejpam-6931	219	136	h(ϱon	h(ϱon	PROPN
ejpam-6931	219	137	,	,	PUNCT
ejpam-6931	219	138	ϱ	ϱ	ADP
ejpam-6931	219	139	o	o	PROPN
ejpam-6931	219	140	m	m	NOUN
ejpam-6931	219	141	,	,	PUNCT
ejpam-6931	219	142	e	e	NOUN
ejpam-6931	219	143	)	)	PUNCT
ejpam-6931	219	144	≺	≺	NOUN
ejpam-6931	219	145	s	s	PRON
ejpam-6931	219	146	for	for	ADP
ejpam-6931	219	147	any	any	DET
ejpam-6931	219	148	n	n	CCONJ
ejpam-6931	219	149	,	,	PUNCT
ejpam-6931	219	150	m	m	VERB
ejpam-6931	219	151	>	>	X
ejpam-6931	219	152	n0	n0	PROPN
ejpam-6931	219	153	.	.	PUNCT
ejpam-6931	220	1	conversely	conversely	ADV
ejpam-6931	220	2	,	,	PUNCT
ejpam-6931	220	3	let	let	VERB
ejpam-6931	220	4	e	e	X
ejpam-6931	220	5	∈	∈	NOUN
ejpam-6931	220	6	s	s	AUX
ejpam-6931	220	7	be	be	AUX
ejpam-6931	220	8	fixed	fix	VERB
ejpam-6931	220	9	,	,	PUNCT
ejpam-6931	220	10	and	and	CCONJ
ejpam-6931	220	11	a	a	DET
ejpam-6931	220	12	real	real	ADJ
ejpam-6931	220	13	number	number	NOUN
ejpam-6931	220	14	ϵ	ϵ	ADP
ejpam-6931	220	15	>	>	X
ejpam-6931	220	16	0	0	NUM
ejpam-6931	220	17	be	be	AUX
ejpam-6931	220	18	given	give	VERB
ejpam-6931	220	19	.	.	PUNCT
ejpam-6931	220	20	suppose	suppose	VERB
ejpam-6931	220	21	that	that	SCONJ
ejpam-6931	220	22	for	for	ADP
ejpam-6931	220	23	each	each	DET
ejpam-6931	220	24	s	s	PROPN
ejpam-6931	220	25	∈	∈	PROPN
ejpam-6931	220	26	t0	t0	PROPN
ejpam-6931	220	27	,	,	PUNCT
ejpam-6931	220	28	one	one	PRON
ejpam-6931	220	29	can	can	AUX
ejpam-6931	220	30	identify	identify	VERB
ejpam-6931	220	31	an	an	DET
ejpam-6931	220	32	n0	n0	NUM
ejpam-6931	220	33	∈	∈	PROPN
ejpam-6931	220	34	m	m	VERB
ejpam-6931	220	35	in	in	ADP
ejpam-6931	220	36	which	which	PRON
ejpam-6931	220	37	e(ϱon	e(ϱon	PROPN
ejpam-6931	220	38	,	,	PUNCT
ejpam-6931	220	39	ϱom	ϱom	NOUN
ejpam-6931	220	40	,	,	PUNCT
ejpam-6931	220	41	e	e	NOUN
ejpam-6931	220	42	)	)	PUNCT
ejpam-6931	220	43	>	>	PUNCT
ejpam-6931	221	1	ℑ	ℑ	PROPN
ejpam-6931	221	2	−	−	PROPN
ejpam-6931	221	3	s	s	PROPN
ejpam-6931	221	4	,	,	PUNCT
ejpam-6931	221	5	g(ϱon	g(ϱon	PROPN
ejpam-6931	221	6	,	,	PUNCT
ejpam-6931	221	7	ϱom	ϱom	NOUN
ejpam-6931	221	8	,	,	PUNCT
ejpam-6931	221	9	e	e	NOUN
ejpam-6931	221	10	)	)	PUNCT
ejpam-6931	221	11	≺	≺	NOUN
ejpam-6931	221	12	s	s	PART
ejpam-6931	221	13	and	and	CCONJ
ejpam-6931	221	14	h(ϱon	h(ϱon	PROPN
ejpam-6931	221	15	,	,	PUNCT
ejpam-6931	221	16	ϱ	ϱ	ADP
ejpam-6931	221	17	o	o	PROPN
ejpam-6931	221	18	m	m	NOUN
ejpam-6931	221	19	,	,	PUNCT
ejpam-6931	221	20	e	e	NOUN
ejpam-6931	221	21	)	)	PUNCT
ejpam-6931	221	22	≺	≺	NOUN
ejpam-6931	221	23	s	s	PRON
ejpam-6931	221	24	for	for	ADP
ejpam-6931	221	25	each	each	DET
ejpam-6931	221	26	n	n	NOUN
ejpam-6931	221	27	>	>	X
ejpam-6931	221	28	m	m	VERB
ejpam-6931	221	29	>	>	X
ejpam-6931	221	30	n0	n0	PROPN
ejpam-6931	221	31	.	.	PUNCT
ejpam-6931	222	1	consequently	consequently	ADV
ejpam-6931	222	2	ℑ−	ℑ−	NUM
ejpam-6931	222	3	2s	2s	NUM
ejpam-6931	222	4	≺	≺	NOUN
ejpam-6931	222	5	ℑ−	ℑ−	NOUN
ejpam-6931	222	6	s	s	PART
ejpam-6931	222	7	⪯	⪯	PROPN
ejpam-6931	222	8	inf	inf	PROPN
ejpam-6931	222	9	m	m	PROPN
ejpam-6931	222	10	>	>	PROPN
ejpam-6931	222	11	n	n	PRON
ejpam-6931	222	12	e(ϱon	e(ϱon	PROPN
ejpam-6931	222	13	,	,	PUNCT
ejpam-6931	222	14	ϱom	ϱom	NOUN
ejpam-6931	222	15	,	,	PUNCT
ejpam-6931	222	16	e	e	NOUN
ejpam-6931	222	17	)	)	PUNCT
ejpam-6931	222	18	sup	sup	PROPN
ejpam-6931	222	19	m	m	PROPN
ejpam-6931	222	20	>	>	NOUN
ejpam-6931	222	21	n	n	PRON
ejpam-6931	222	22	g(ϱon	g(ϱon	NOUN
ejpam-6931	222	23	,	,	PUNCT
ejpam-6931	222	24	ϱom	ϱom	NOUN
ejpam-6931	222	25	,	,	PUNCT
ejpam-6931	222	26	e	e	NOUN
ejpam-6931	222	27	)	)	PUNCT
ejpam-6931	222	28	⪯	⪯	NOUN
ejpam-6931	222	29	s	s	PART
ejpam-6931	222	30	≺	≺	NOUN
ejpam-6931	222	31	2s	2s	PROPN
ejpam-6931	222	32	and	and	CCONJ
ejpam-6931	222	33	sup	sup	NOUN
ejpam-6931	222	34	m	m	PROPN
ejpam-6931	222	35	>	>	X
ejpam-6931	222	36	n	n	PROPN
ejpam-6931	222	37	h(ϱon	h(ϱon	NOUN
ejpam-6931	222	38	,	,	PUNCT
ejpam-6931	222	39	ϱ	ϱ	ADP
ejpam-6931	222	40	o	o	PROPN
ejpam-6931	222	41	m	m	NOUN
ejpam-6931	222	42	,	,	PUNCT
ejpam-6931	222	43	e	e	NOUN
ejpam-6931	222	44	)	)	PUNCT
ejpam-6931	222	45	⪯	⪯	NOUN
ejpam-6931	222	46	s	s	PART
ejpam-6931	222	47	≺	≺	NOUN
ejpam-6931	222	48	2s	2s	PROPN
ejpam-6931	222	49	for	for	ADP
ejpam-6931	222	50	every	every	DET
ejpam-6931	222	51	n	n	PROPN
ejpam-6931	222	52	>	>	X
ejpam-6931	222	53	n0	n0	PROPN
ejpam-6931	222	54	.	.	PUNCT
ejpam-6931	223	1	select	select	VERB
ejpam-6931	223	2	a	a	DET
ejpam-6931	223	3	complex	complex	ADJ
ejpam-6931	223	4	number	number	NOUN
ejpam-6931	223	5	s	s	PART
ejpam-6931	223	6	∈	∈	PROPN
ejpam-6931	223	7	t0	t0	NOUN
ejpam-6931	223	8	that	that	PRON
ejpam-6931	223	9	fulfils	fulfil	VERB
ejpam-6931	223	10	|s|	|s|	VERB
ejpam-6931	223	11	<	<	X
ejpam-6931	223	12	ϵ	ϵ	ADP
ejpam-6931	223	13	2	2	NUM
ejpam-6931	223	14	,	,	PUNCT
ejpam-6931	223	15	then	then	ADV
ejpam-6931	223	16	we	we	PRON
ejpam-6931	223	17	get	get	VERB
ejpam-6931	223	18	|ℑ−	|ℑ−	NOUN
ejpam-6931	223	19	inf	inf	PROPN
ejpam-6931	223	20	m	m	PROPN
ejpam-6931	223	21	>	>	PROPN
ejpam-6931	223	22	n	n	PRON
ejpam-6931	223	23	e(ϱon	e(ϱon	PROPN
ejpam-6931	223	24	,	,	PUNCT
ejpam-6931	223	25	ϱom	ϱom	NOUN
ejpam-6931	223	26	,	,	PUNCT
ejpam-6931	223	27	e)|	e)|	NOUN
ejpam-6931	223	28	<	<	X
ejpam-6931	223	29	2|s|	2|s|	NUM
ejpam-6931	223	30	<	<	X
ejpam-6931	223	31	ϵ	ϵ	X
ejpam-6931	223	32	,	,	PUNCT
ejpam-6931	223	33	|	|	ADV
ejpam-6931	223	34	sup	sup	NOUN
ejpam-6931	223	35	m	m	PROPN
ejpam-6931	223	36	>	>	X
ejpam-6931	223	37	n	n	PRON
ejpam-6931	223	38	g(ϱon	g(ϱon	NOUN
ejpam-6931	223	39	,	,	PUNCT
ejpam-6931	223	40	ϱom	ϱom	NOUN
ejpam-6931	223	41	,	,	PUNCT
ejpam-6931	223	42	e)|	e)|	NOUN
ejpam-6931	223	43	<	<	X
ejpam-6931	223	44	2|s|	2|s|	NUM
ejpam-6931	223	45	<	<	X
ejpam-6931	223	46	ϵ	ϵ	NOUN
ejpam-6931	224	1	and	and	CCONJ
ejpam-6931	225	1	|	|	ADV
ejpam-6931	225	2	sup	sup	NOUN
ejpam-6931	225	3	m	m	PROPN
ejpam-6931	225	4	>	>	X
ejpam-6931	225	5	n	n	PROPN
ejpam-6931	225	6	h(ϱon	h(ϱon	NOUN
ejpam-6931	225	7	,	,	PUNCT
ejpam-6931	225	8	ϱ	ϱ	ADP
ejpam-6931	225	9	o	o	PROPN
ejpam-6931	225	10	m	m	NOUN
ejpam-6931	225	11	,	,	PUNCT
ejpam-6931	225	12	e)|	e)|	ADJ
ejpam-6931	225	13	<	<	X
ejpam-6931	225	14	2|s|	2|s|	NUM
ejpam-6931	225	15	<	<	X
ejpam-6931	225	16	ϵ	ϵ	NOUN
ejpam-6931	225	17	for	for	ADP
ejpam-6931	225	18	each	each	DET
ejpam-6931	225	19	n	n	PROPN
ejpam-6931	225	20	>	>	X
ejpam-6931	225	21	n0	n0	PROPN
ejpam-6931	225	22	.	.	PUNCT
ejpam-6931	226	1	thus	thus	ADV
ejpam-6931	226	2	,	,	PUNCT
ejpam-6931	226	3	we	we	PRON
ejpam-6931	226	4	have	have	VERB
ejpam-6931	226	5	limn→∞	limn→∞	PROPN
ejpam-6931	226	6	infm	infm	NOUN
ejpam-6931	226	7	>	>	X
ejpam-6931	226	8	n	n	PROPN
ejpam-6931	226	9	e(ϱon	e(ϱon	PROPN
ejpam-6931	226	10	,	,	PUNCT
ejpam-6931	226	11	ϱom	ϱom	NOUN
ejpam-6931	226	12	,	,	PUNCT
ejpam-6931	226	13	e	e	NOUN
ejpam-6931	226	14	)	)	PUNCT
ejpam-6931	226	15	=	=	SYM
ejpam-6931	226	16	ℑ	ℑ	PROPN
ejpam-6931	226	17	,	,	PUNCT
ejpam-6931	226	18	limn→∞	limn→∞	PROPN
ejpam-6931	226	19	supm	supm	PROPN
ejpam-6931	226	20	>	>	SYM
ejpam-6931	226	21	n	n	PRON
ejpam-6931	226	22	g(ϱon	g(ϱon	NOUN
ejpam-6931	226	23	,	,	PUNCT
ejpam-6931	226	24	ϱom	ϱom	NOUN
ejpam-6931	226	25	,	,	PUNCT
ejpam-6931	226	26	e	e	NOUN
ejpam-6931	226	27	)	)	PUNCT
ejpam-6931	226	28	=	=	SYM
ejpam-6931	226	29	∅	∅	NOUN
ejpam-6931	226	30	,	,	PUNCT
ejpam-6931	226	31	and	and	CCONJ
ejpam-6931	226	32	limn→∞	limn→∞	PROPN
ejpam-6931	226	33	supm	supm	PROPN
ejpam-6931	226	34	>	>	SYM
ejpam-6931	226	35	nh(ϱon	nh(ϱon	PROPN
ejpam-6931	226	36	,	,	PUNCT
ejpam-6931	226	37	ϱ	ϱ	ADP
ejpam-6931	226	38	o	o	PROPN
ejpam-6931	226	39	m	m	NOUN
ejpam-6931	226	40	,	,	PUNCT
ejpam-6931	226	41	e	e	NOUN
ejpam-6931	226	42	)	)	PUNCT
ejpam-6931	226	43	=	=	NOUN
ejpam-6931	226	44	∅	∅	NOUN
ejpam-6931	226	45	,	,	PUNCT
ejpam-6931	226	46	this	this	PRON
ejpam-6931	226	47	demonstrates	demonstrate	VERB
ejpam-6931	226	48	that	that	SCONJ
ejpam-6931	226	49	the	the	DET
ejpam-6931	226	50	sequence	sequence	NOUN
ejpam-6931	226	51	{	{	PUNCT
ejpam-6931	226	52	ϱo}n	ϱo}n	PROPN
ejpam-6931	226	53	is	be	AUX
ejpam-6931	226	54	cauchy	cauchy	NOUN
ejpam-6931	226	55	.	.	PUNCT
ejpam-6931	227	1	4	4	NUM
ejpam-6931	227	2	.	.	NUM
ejpam-6931	227	3	fixed	fix	VERB
ejpam-6931	227	4	-	-	PUNCT
ejpam-6931	227	5	point	point	NOUN
ejpam-6931	227	6	results	result	NOUN
ejpam-6931	227	7	we	we	PRON
ejpam-6931	227	8	will	will	AUX
ejpam-6931	227	9	now	now	ADV
ejpam-6931	227	10	examine	examine	VERB
ejpam-6931	227	11	the	the	DET
ejpam-6931	227	12	existence	existence	NOUN
ejpam-6931	227	13	and	and	CCONJ
ejpam-6931	227	14	uniqueness	uniqueness	NOUN
ejpam-6931	227	15	of	of	ADP
ejpam-6931	227	16	fixed	fix	VERB
ejpam-6931	227	17	points	point	NOUN
ejpam-6931	227	18	for	for	ADP
ejpam-6931	227	19	self	self	NOUN
ejpam-6931	227	20	-	-	PUNCT
ejpam-6931	227	21	mappings	mapping	NOUN
ejpam-6931	227	22	that	that	PRON
ejpam-6931	227	23	satisfy	satisfy	VERB
ejpam-6931	227	24	the	the	DET
ejpam-6931	227	25	specified	specified	ADJ
ejpam-6931	227	26	contractive	contractive	ADJ
ejpam-6931	227	27	requirements	requirement	NOUN
ejpam-6931	227	28	in	in	ADP
ejpam-6931	227	29	cvnms	cvnms	NOUN
ejpam-6931	227	30	.	.	PUNCT
ejpam-6931	228	1	let	let	AUX
ejpam-6931	228	2	{	{	PUNCT
ejpam-6931	228	3	en	en	PART
ejpam-6931	228	4	}	}	PUNCT
ejpam-6931	228	5	be	be	AUX
ejpam-6931	228	6	a	a	DET
ejpam-6931	228	7	sequence	sequence	NOUN
ejpam-6931	228	8	from	from	ADP
ejpam-6931	228	9	c.	c.	PROPN
ejpam-6931	228	10	it	it	PRON
ejpam-6931	228	11	is	be	AUX
ejpam-6931	228	12	said	say	VERB
ejpam-6931	228	13	that	that	SCONJ
ejpam-6931	228	14	limn→∞	limn→∞	PROPN
ejpam-6931	228	15	en	en	X
ejpam-6931	228	16	=	=	SYM
ejpam-6931	228	17	∞	∞	PROPN
ejpam-6931	228	18	=	=	SYM
ejpam-6931	228	19	(	(	PUNCT
ejpam-6931	228	20	∞,∞	∞,∞	NOUN
ejpam-6931	228	21	)	)	PUNCT
ejpam-6931	228	22	if	if	SCONJ
ejpam-6931	228	23	for	for	ADP
ejpam-6931	228	24	every	every	DET
ejpam-6931	228	25	c	c	PROPN
ejpam-6931	228	26	∈	∈	PROPN
ejpam-6931	228	27	c	c	NOUN
ejpam-6931	228	28	,	,	PUNCT
ejpam-6931	228	29	there	there	PRON
ejpam-6931	228	30	is	be	VERB
ejpam-6931	228	31	a	a	DET
ejpam-6931	228	32	n0	n0	NUM
ejpam-6931	228	33	∈	∈	NOUN
ejpam-6931	228	34	m	m	VERB
ejpam-6931	228	35	such	such	ADJ
ejpam-6931	228	36	that	that	SCONJ
ejpam-6931	228	37	en	en	ADP
ejpam-6931	228	38	⪰	⪰	NOUN
ejpam-6931	228	39	e	e	NOUN
ejpam-6931	228	40	for	for	ADP
ejpam-6931	228	41	all	all	DET
ejpam-6931	228	42	n	n	PRON
ejpam-6931	228	43	>	>	X
ejpam-6931	228	44	n0	n0	X
ejpam-6931	228	45	theorem	theorem	NOUN
ejpam-6931	228	46	1	1	X
ejpam-6931	228	47	.	.	PUNCT
ejpam-6931	229	1	let	let	VERB
ejpam-6931	229	2	(	(	PUNCT
ejpam-6931	229	3	v	v	NOUN
ejpam-6931	229	4	,	,	PUNCT
ejpam-6931	229	5	e	e	NOUN
ejpam-6931	229	6	,	,	PUNCT
ejpam-6931	229	7	g	g	PROPN
ejpam-6931	229	8	,	,	PUNCT
ejpam-6931	229	9	h	h	NOUN
ejpam-6931	229	10	,	,	PUNCT
ejpam-6931	229	11	⋆	⋆	NOUN
ejpam-6931	229	12	,	,	PUNCT
ejpam-6931	229	13	△	△	X
ejpam-6931	229	14	)	)	PUNCT
ejpam-6931	229	15	be	be	AUX
ejpam-6931	229	16	a	a	DET
ejpam-6931	229	17	complete	complete	ADJ
ejpam-6931	229	18	cvnms	cvnms	NOUN
ejpam-6931	229	19	with	with	ADP
ejpam-6931	229	20	the	the	DET
ejpam-6931	229	21	characteristic	characteristic	NOUN
ejpam-6931	229	22	that	that	SCONJ
ejpam-6931	229	23	any	any	DET
ejpam-6931	229	24	sequence	sequence	NOUN
ejpam-6931	229	25	{	{	PUNCT
ejpam-6931	229	26	en	en	ADP
ejpam-6931	229	27	}	}	PUNCT
ejpam-6931	229	28	∈	∈	PROPN
ejpam-6931	229	29	s0	s0	PROPN
ejpam-6931	229	30	fulfills	fulfill	VERB
ejpam-6931	229	31	limn→∞	limn→∞	PROPN
ejpam-6931	229	32	en	en	X
ejpam-6931	229	33	=	=	SYM
ejpam-6931	229	34	∞	∞	PROPN
ejpam-6931	229	35	implies	imply	VERB
ejpam-6931	229	36	lim	lim	PROPN
ejpam-6931	229	37	n→∞	n→∞	NUM
ejpam-6931	229	38	inf	inf	PROPN
ejpam-6931	229	39	ν∈v	ν∈v	ADV
ejpam-6931	229	40	e(ϱo	e(ϱo	NOUN
ejpam-6931	229	41	,	,	PUNCT
ejpam-6931	229	42	ν	ν	NOUN
ejpam-6931	229	43	,	,	PUNCT
ejpam-6931	229	44	en	en	ADJ
ejpam-6931	229	45	)	)	PUNCT
ejpam-6931	229	46	=	=	SYM
ejpam-6931	229	47	ℑ	ℑ	PROPN
ejpam-6931	229	48	,	,	PUNCT
ejpam-6931	229	49	lim	lim	PROPN
ejpam-6931	229	50	n→∞	n→∞	NUM
ejpam-6931	229	51	sup	sup	NOUN
ejpam-6931	229	52	ν∈v	ν∈v	ADV
ejpam-6931	229	53	g(ϱo	g(ϱo	NOUN
ejpam-6931	229	54	,	,	PUNCT
ejpam-6931	229	55	ν	ν	NOUN
ejpam-6931	229	56	,	,	PUNCT
ejpam-6931	229	57	en	en	ADJ
ejpam-6931	229	58	)	)	PUNCT
ejpam-6931	229	59	=	=	NOUN
ejpam-6931	229	60	∅	∅	NOUN
ejpam-6931	229	61	,	,	PUNCT
ejpam-6931	229	62	lim	lim	PROPN
ejpam-6931	229	63	n→∞	n→∞	NUM
ejpam-6931	229	64	sup	sup	NOUN
ejpam-6931	229	65	ν∈v	ν∈v	ADV
ejpam-6931	229	66	h(ϱo	h(ϱo	ADV
ejpam-6931	229	67	,	,	PUNCT
ejpam-6931	229	68	ν	ν	NOUN
ejpam-6931	229	69	,	,	PUNCT
ejpam-6931	229	70	en	en	ADJ
ejpam-6931	229	71	)	)	PUNCT
ejpam-6931	229	72	=	=	NOUN
ejpam-6931	229	73	∅	∅	NOUN
ejpam-6931	229	74	,	,	PUNCT
ejpam-6931	229	75	for	for	ADP
ejpam-6931	229	76	any	any	DET
ejpam-6931	229	77	ϱo	ϱo	PROPN
ejpam-6931	229	78	∈	∈	PROPN
ejpam-6931	229	79	v.	v.	CCONJ
ejpam-6931	229	80	consider	consider	VERB
ejpam-6931	229	81	a	a	DET
ejpam-6931	229	82	self	self	NOUN
ejpam-6931	229	83	-	-	PUNCT
ejpam-6931	229	84	mapping	mapping	NOUN
ejpam-6931	229	85	h	h	NOUN
ejpam-6931	229	86	:	:	PUNCT
ejpam-6931	229	87	v	v	X
ejpam-6931	229	88	→	→	SYM
ejpam-6931	229	89	v	v	X
ejpam-6931	229	90	meets	meet	VERB
ejpam-6931	229	91	the	the	DET
ejpam-6931	229	92	following	follow	VERB
ejpam-6931	229	93	condition	condition	NOUN
ejpam-6931	229	94	:	:	PUNCT
ejpam-6931	229	95	e(hϱo	e(hϱo	PROPN
ejpam-6931	229	96	,	,	PUNCT
ejpam-6931	229	97	hν	hν	NOUN
ejpam-6931	229	98	,	,	PUNCT
ejpam-6931	229	99	ke	ke	NOUN
ejpam-6931	229	100	)	)	PUNCT
ejpam-6931	229	101	⪰	⪰	NOUN
ejpam-6931	229	102	e(ϱo	e(ϱo	NOUN
ejpam-6931	229	103	,	,	PUNCT
ejpam-6931	229	104	ν	ν	NOUN
ejpam-6931	229	105	,	,	PUNCT
ejpam-6931	229	106	e	e	NOUN
ejpam-6931	229	107	)	)	PUNCT
ejpam-6931	229	108	,	,	PUNCT
ejpam-6931	229	109	g(hϱo	g(hϱo	PROPN
ejpam-6931	229	110	,	,	PUNCT
ejpam-6931	229	111	hν	hν	NOUN
ejpam-6931	229	112	,	,	PUNCT
ejpam-6931	229	113	ke	ke	PROPN
ejpam-6931	229	114	)	)	PUNCT
ejpam-6931	229	115	⪯	⪯	NOUN
ejpam-6931	229	116	g(ϱo	g(ϱo	PROPN
ejpam-6931	229	117	,	,	PUNCT
ejpam-6931	229	118	ν	ν	PROPN
ejpam-6931	229	119	,	,	PUNCT
ejpam-6931	229	120	e	e	NOUN
ejpam-6931	229	121	)	)	PUNCT
ejpam-6931	229	122	and	and	CCONJ
ejpam-6931	229	123	h(hϱo	h(hϱo	VERB
ejpam-6931	229	124	,	,	PUNCT
ejpam-6931	229	125	hν	hν	NOUN
ejpam-6931	229	126	,	,	PUNCT
ejpam-6931	229	127	ke	ke	PROPN
ejpam-6931	229	128	)	)	PUNCT
ejpam-6931	229	129	⪯	⪯	NOUN
ejpam-6931	229	130	h(ϱo	h(ϱo	ADJ
ejpam-6931	229	131	,	,	PUNCT
ejpam-6931	229	132	ν	ν	NOUN
ejpam-6931	229	133	,	,	PUNCT
ejpam-6931	229	134	e	e	NOUN
ejpam-6931	229	135	)	)	PUNCT
ejpam-6931	229	136	(	(	PUNCT
ejpam-6931	229	137	1	1	X
ejpam-6931	229	138	)	)	PUNCT
ejpam-6931	229	139	for	for	ADP
ejpam-6931	229	140	each	each	DET
ejpam-6931	229	141	ϱo	ϱo	NOUN
ejpam-6931	229	142	,	,	PUNCT
ejpam-6931	229	143	ν	ν	PROPN
ejpam-6931	229	144	∈	∈	PROPN
ejpam-6931	229	145	v	v	NOUN
ejpam-6931	229	146	and	and	CCONJ
ejpam-6931	229	147	e	e	NOUN
ejpam-6931	229	148	∈	∈	PROPN
ejpam-6931	229	149	s0	s0	PROPN
ejpam-6931	229	150	,	,	PUNCT
ejpam-6931	229	151	where	where	SCONJ
ejpam-6931	229	152	k	k	PROPN
ejpam-6931	229	153	∈	∈	PROPN
ejpam-6931	229	154	(	(	PUNCT
ejpam-6931	229	155	0	0	NUM
ejpam-6931	229	156	,	,	PUNCT
ejpam-6931	229	157	1	1	NUM
ejpam-6931	229	158	)	)	PUNCT
ejpam-6931	229	159	.	.	PUNCT
ejpam-6931	230	1	then	then	ADV
ejpam-6931	230	2	,	,	PUNCT
ejpam-6931	230	3	there	there	PRON
ejpam-6931	230	4	is	be	VERB
ejpam-6931	230	5	a	a	DET
ejpam-6931	230	6	unique	unique	ADJ
ejpam-6931	230	7	fixed	fix	VERB
ejpam-6931	230	8	point	point	NOUN
ejpam-6931	230	9	of	of	ADP
ejpam-6931	230	10	the	the	DET
ejpam-6931	230	11	mapping	mapping	NOUN
ejpam-6931	230	12	h	h	NOUN
ejpam-6931	230	13	that	that	PRON
ejpam-6931	230	14	is	be	AUX
ejpam-6931	230	15	located	locate	VERB
ejpam-6931	230	16	in	in	ADP
ejpam-6931	230	17	v.	v.	ADP
ejpam-6931	230	18	proof	proof	NOUN
ejpam-6931	230	19	.	.	PUNCT
ejpam-6931	231	1	let	let	VERB
ejpam-6931	231	2	ϱo	ϱo	PRON
ejpam-6931	231	3	∈	∈	PROPN
ejpam-6931	231	4	v	v	AUX
ejpam-6931	231	5	be	be	AUX
ejpam-6931	231	6	an	an	DET
ejpam-6931	231	7	arbitrarily	arbitrarily	ADV
ejpam-6931	231	8	chosen	choose	VERB
ejpam-6931	231	9	point	point	NOUN
ejpam-6931	231	10	.	.	PUNCT
ejpam-6931	232	1	in	in	ADP
ejpam-6931	232	2	v	v	NUM
ejpam-6931	232	3	,	,	PUNCT
ejpam-6931	232	4	a	a	DET
ejpam-6931	232	5	sequence	sequence	NOUN
ejpam-6931	232	6	{	{	PUNCT
ejpam-6931	232	7	ϱon	ϱon	NOUN
ejpam-6931	232	8	}	}	PUNCT
ejpam-6931	232	9	is	be	AUX
ejpam-6931	232	10	defined	define	VERB
ejpam-6931	232	11	by	by	ADP
ejpam-6931	232	12	ϱon	ϱon	PROPN
ejpam-6931	232	13	=	=	PROPN
ejpam-6931	232	14	hϱon−1	hϱon−1	PROPN
ejpam-6931	232	15	for	for	ADP
ejpam-6931	232	16	all	all	DET
ejpam-6931	232	17	n	n	DET
ejpam-6931	232	18	∈	∈	NOUN
ejpam-6931	232	19	m.	m.	NOUN
ejpam-6931	232	20	the	the	DET
ejpam-6931	232	21	existence	existence	NOUN
ejpam-6931	232	22	of	of	ADP
ejpam-6931	232	23	a	a	DET
ejpam-6931	232	24	n0	n0	NUM
ejpam-6931	232	25	∈	∈	NOUN
ejpam-6931	232	26	m	m	VERB
ejpam-6931	232	27	such	such	ADJ
ejpam-6931	232	28	that	that	PRON
ejpam-6931	232	29	ϱon0	ϱon0	PROPN
ejpam-6931	232	30	=	=	SYM
ejpam-6931	232	31	ϱon0−1	ϱon0−1	PROPN
ejpam-6931	232	32	guarantees	guarantee	VERB
ejpam-6931	232	33	that	that	SCONJ
ejpam-6931	232	34	ϱon0	ϱon0	PROPN
ejpam-6931	232	35	is	be	AUX
ejpam-6931	232	36	a	a	DET
ejpam-6931	232	37	fixed	fix	VERB
ejpam-6931	232	38	point	point	NOUN
ejpam-6931	232	39	of	of	ADP
ejpam-6931	232	40	h.	h.	NOUN
ejpam-6931	232	41	to	to	PART
ejpam-6931	232	42	prove	prove	VERB
ejpam-6931	232	43	that	that	SCONJ
ejpam-6931	232	44	the	the	DET
ejpam-6931	232	45	sequence	sequence	NOUN
ejpam-6931	232	46	{	{	PUNCT
ejpam-6931	232	47	ϱon	ϱon	NOUN
ejpam-6931	232	48	}	}	PUNCT
ejpam-6931	232	49	is	be	AUX
ejpam-6931	232	50	cauchy	cauchy	PROPN
ejpam-6931	232	51	,	,	PUNCT
ejpam-6931	232	52	we	we	PRON
ejpam-6931	232	53	see	see	VERB
ejpam-6931	232	54	that	that	SCONJ
ejpam-6931	232	55	ϱon	ϱon	PROPN
ejpam-6931	232	56	̸=	̸=	PROPN
ejpam-6931	232	57	ϱon−1	ϱon−1	PROPN
ejpam-6931	232	58	for	for	ADP
ejpam-6931	232	59	each	each	DET
ejpam-6931	232	60	n	n	PRON
ejpam-6931	232	61	∈	∈	PROPN
ejpam-6931	232	62	m.	m.	NOUN
ejpam-6931	233	1	s.	s.	PROPN
ejpam-6931	233	2	m.	m.	PROPN
ejpam-6931	233	3	u.	u.	PROPN
ejpam-6931	233	4	ud	ud	AUX
ejpam-6931	233	5	-	-	PUNCT
ejpam-6931	233	6	din	din	VERB
ejpam-6931	233	7	et	et	PROPN
ejpam-6931	233	8	al	al	PROPN
ejpam-6931	233	9	.	.	PUNCT
ejpam-6931	233	10	/	/	SYM
ejpam-6931	233	11	eur	eur	PROPN
ejpam-6931	233	12	.	.	PUNCT
ejpam-6931	234	1	j.	j.	PROPN
ejpam-6931	234	2	pure	pure	PROPN
ejpam-6931	234	3	appl	appl	PROPN
ejpam-6931	234	4	.	.	PROPN
ejpam-6931	234	5	math	math	PROPN
ejpam-6931	234	6	,	,	PUNCT
ejpam-6931	234	7	18	18	NUM
ejpam-6931	234	8	(	(	PUNCT
ejpam-6931	234	9	4	4	NUM
ejpam-6931	234	10	)	)	PUNCT
ejpam-6931	234	11	(	(	PUNCT
ejpam-6931	234	12	2025	2025	NUM
ejpam-6931	234	13	)	)	PUNCT
ejpam-6931	234	14	,	,	PUNCT
ejpam-6931	234	15	6931	6931	NUM
ejpam-6931	234	16	13	13	NUM
ejpam-6931	234	17	of	of	ADP
ejpam-6931	234	18	38	38	NUM
ejpam-6931	234	19	for	for	ADP
ejpam-6931	234	20	every	every	DET
ejpam-6931	234	21	n	n	NOUN
ejpam-6931	234	22	∈	∈	NOUN
ejpam-6931	234	23	m	m	NOUN
ejpam-6931	234	24	and	and	CCONJ
ejpam-6931	234	25	a	a	DET
ejpam-6931	234	26	fixed	fix	VERB
ejpam-6931	234	27	e	e	NOUN
ejpam-6931	234	28	∈	∈	PROPN
ejpam-6931	234	29	s0	s0	PROPN
ejpam-6931	234	30	,	,	PUNCT
ejpam-6931	234	31	we	we	PRON
ejpam-6931	234	32	define	define	VERB
ejpam-6931	234	33	an	an	PRON
ejpam-6931	234	34	:	:	PUNCT
ejpam-6931	234	35	=	=	SYM
ejpam-6931	234	36	{	{	PUNCT
ejpam-6931	234	37	e(ϱon	e(ϱon	PROPN
ejpam-6931	234	38	,	,	PUNCT
ejpam-6931	234	39	ϱom	ϱom	NOUN
ejpam-6931	234	40	,	,	PUNCT
ejpam-6931	234	41	e	e	NOUN
ejpam-6931	234	42	)	)	PUNCT
ejpam-6931	234	43	:	:	PUNCT
ejpam-6931	234	44	m	m	VERB
ejpam-6931	234	45	>	>	X
ejpam-6931	234	46	n	n	CCONJ
ejpam-6931	234	47	}	}	PUNCT
ejpam-6931	234	48	⊂	⊂	PROPN
ejpam-6931	234	49	t	t	PROPN
ejpam-6931	234	50	,	,	PUNCT
ejpam-6931	234	51	bn	bn	ADV
ejpam-6931	234	52	:	:	PUNCT
ejpam-6931	234	53	=	=	PRON
ejpam-6931	234	54	{	{	PUNCT
ejpam-6931	234	55	g(ϱon	g(ϱon	NOUN
ejpam-6931	234	56	,	,	PUNCT
ejpam-6931	234	57	ϱom	ϱom	NOUN
ejpam-6931	234	58	,	,	PUNCT
ejpam-6931	234	59	e	e	NOUN
ejpam-6931	234	60	)	)	PUNCT
ejpam-6931	234	61	:	:	PUNCT
ejpam-6931	234	62	m	m	VERB
ejpam-6931	234	63	>	>	X
ejpam-6931	234	64	n	n	CCONJ
ejpam-6931	234	65	}	}	PUNCT
ejpam-6931	234	66	⊂	⊂	PROPN
ejpam-6931	234	67	t	t	PROPN
ejpam-6931	234	68	,	,	PUNCT
ejpam-6931	234	69	cn	cn	PROPN
ejpam-6931	234	70	:	:	PUNCT
ejpam-6931	234	71	=	=	SYM
ejpam-6931	234	72	{	{	PUNCT
ejpam-6931	234	73	h(ϱon	h(ϱon	PROPN
ejpam-6931	234	74	,	,	PUNCT
ejpam-6931	234	75	ϱ	ϱ	ADP
ejpam-6931	234	76	o	o	PROPN
ejpam-6931	234	77	m	m	NOUN
ejpam-6931	234	78	,	,	PUNCT
ejpam-6931	234	79	e	e	NOUN
ejpam-6931	234	80	)	)	PUNCT
ejpam-6931	234	81	:	:	PUNCT
ejpam-6931	234	82	m	m	VERB
ejpam-6931	234	83	>	>	X
ejpam-6931	234	84	n	n	CCONJ
ejpam-6931	234	85	}	}	PUNCT
ejpam-6931	234	86	⊂	⊂	PROPN
ejpam-6931	234	87	t.	t.	NOUN
ejpam-6931	234	88	as	as	ADP
ejpam-6931	234	89	∅	∅	NOUN
ejpam-6931	234	90	<	<	X
ejpam-6931	234	91	e(ϱon	e(ϱon	PROPN
ejpam-6931	234	92	,	,	PUNCT
ejpam-6931	234	93	ϱom	ϱom	NOUN
ejpam-6931	234	94	,	,	PUNCT
ejpam-6931	234	95	e	e	NOUN
ejpam-6931	234	96	)	)	PUNCT
ejpam-6931	234	97	⪯	⪯	NOUN
ejpam-6931	234	98	ℑ	ℑ	PROPN
ejpam-6931	234	99	for	for	ADP
ejpam-6931	234	100	every	every	DET
ejpam-6931	234	101	n	n	NOUN
ejpam-6931	234	102	∈	∈	NOUN
ejpam-6931	234	103	m	m	NOUN
ejpam-6931	234	104	and	and	CCONJ
ejpam-6931	234	105	n	n	CCONJ
ejpam-6931	234	106	<	<	X
ejpam-6931	234	107	m	m	PROPN
ejpam-6931	234	108	,	,	PUNCT
ejpam-6931	234	109	subsequent	subsequent	ADJ
ejpam-6931	234	110	to	to	ADP
ejpam-6931	234	111	the	the	DET
ejpam-6931	234	112	remarks	remark	NOUN
ejpam-6931	234	113	1	1	NUM
ejpam-6931	234	114	,	,	PUNCT
ejpam-6931	234	115	the	the	DET
ejpam-6931	234	116	greatest	greatest	ADV
ejpam-6931	234	117	lower	low	ADJ
ejpam-6931	234	118	bound	bind	VERB
ejpam-6931	234	119	of	of	ADP
ejpam-6931	234	120	the	the	DET
ejpam-6931	234	121	set	set	NOUN
ejpam-6931	234	122	an	an	NOUN
ejpam-6931	234	123	,	,	PUNCT
ejpam-6931	234	124	denoted	denote	VERB
ejpam-6931	234	125	as	as	ADP
ejpam-6931	234	126	inf	inf	NOUN
ejpam-6931	234	127	an	an	PRON
ejpam-6931	234	128	=	=	SYM
ejpam-6931	234	129	x́n	x́n	PROPN
ejpam-6931	234	130	,	,	PUNCT
ejpam-6931	234	131	exist	exist	VERB
ejpam-6931	234	132	for	for	ADP
ejpam-6931	234	133	every	every	DET
ejpam-6931	234	134	n	n	PRON
ejpam-6931	234	135	∈	∈	NOUN
ejpam-6931	234	136	m.	m.	NOUN
ejpam-6931	234	137	in	in	ADP
ejpam-6931	234	138	the	the	DET
ejpam-6931	234	139	same	same	ADJ
ejpam-6931	234	140	way	way	NOUN
ejpam-6931	234	141	,	,	PUNCT
ejpam-6931	234	142	since	since	SCONJ
ejpam-6931	234	143	∅	∅	NOUN
ejpam-6931	234	144	⪯	⪯	PROPN
ejpam-6931	234	145	g(ϱon	g(ϱon	PROPN
ejpam-6931	234	146	,	,	PUNCT
ejpam-6931	234	147	ϱom	ϱom	NOUN
ejpam-6931	234	148	,	,	PUNCT
ejpam-6931	234	149	e	e	NOUN
ejpam-6931	234	150	)	)	PUNCT
ejpam-6931	234	151	≺	≺	VERB
ejpam-6931	234	152	ℑ	ℑ	PROPN
ejpam-6931	234	153	for	for	ADP
ejpam-6931	234	154	all	all	DET
ejpam-6931	234	155	n	n	PRON
ejpam-6931	234	156	∈	∈	NOUN
ejpam-6931	234	157	m	m	VERB
ejpam-6931	234	158	such	such	ADJ
ejpam-6931	234	159	that	that	SCONJ
ejpam-6931	234	160	n	n	PROPN
ejpam-6931	234	161	<	<	X
ejpam-6931	234	162	m	m	PROPN
ejpam-6931	234	163	,	,	PUNCT
ejpam-6931	234	164	subsequent	subsequent	ADJ
ejpam-6931	234	165	to	to	ADP
ejpam-6931	234	166	the	the	DET
ejpam-6931	234	167	remarks	remark	NOUN
ejpam-6931	234	168	1	1	NUM
ejpam-6931	234	169	,	,	PUNCT
ejpam-6931	234	170	the	the	DET
ejpam-6931	234	171	least	least	ADV
ejpam-6931	234	172	upper	upper	ADJ
ejpam-6931	234	173	bound	bind	VERB
ejpam-6931	234	174	of	of	ADP
ejpam-6931	234	175	the	the	DET
ejpam-6931	234	176	set	set	NOUN
ejpam-6931	234	177	bn	bn	NOUN
ejpam-6931	234	178	,	,	PUNCT
ejpam-6931	234	179	denoted	denote	VERB
ejpam-6931	234	180	as	as	ADP
ejpam-6931	234	181	supbn	supbn	NOUN
ejpam-6931	234	182	=	=	SYM
ejpam-6931	234	183	ýn	ýn	NOUN
ejpam-6931	234	184	,	,	PUNCT
ejpam-6931	234	185	exists	exist	VERB
ejpam-6931	234	186	for	for	ADP
ejpam-6931	234	187	every	every	DET
ejpam-6931	234	188	n	n	PRON
ejpam-6931	234	189	∈	∈	NOUN
ejpam-6931	234	190	m.	m.	NOUN
ejpam-6931	234	191	and	and	CCONJ
ejpam-6931	234	192	also	also	ADV
ejpam-6931	234	193	,	,	PUNCT
ejpam-6931	234	194	since	since	SCONJ
ejpam-6931	234	195	∅	∅	NOUN
ejpam-6931	234	196	⪯	⪯	PROPN
ejpam-6931	234	197	h(ϱon	h(ϱon	PROPN
ejpam-6931	234	198	,	,	PUNCT
ejpam-6931	234	199	ϱ	ϱ	ADP
ejpam-6931	234	200	o	o	PROPN
ejpam-6931	234	201	m	m	NOUN
ejpam-6931	234	202	,	,	PUNCT
ejpam-6931	234	203	c	c	NOUN
ejpam-6931	234	204	)	)	PUNCT
ejpam-6931	234	205	≺	≺	NOUN
ejpam-6931	234	206	ℑ	ℑ	PROPN
ejpam-6931	234	207	for	for	ADP
ejpam-6931	234	208	all	all	DET
ejpam-6931	234	209	n	n	PRON
ejpam-6931	234	210	∈	∈	NOUN
ejpam-6931	234	211	m	m	VERB
ejpam-6931	234	212	where	where	SCONJ
ejpam-6931	234	213	n	n	X
ejpam-6931	234	214	<	<	X
ejpam-6931	234	215	m	m	PROPN
ejpam-6931	234	216	,	,	PUNCT
ejpam-6931	234	217	subsequent	subsequent	ADJ
ejpam-6931	234	218	to	to	ADP
ejpam-6931	234	219	the	the	DET
ejpam-6931	234	220	remarks	remark	NOUN
ejpam-6931	234	221	1	1	NUM
ejpam-6931	234	222	,	,	PUNCT
ejpam-6931	234	223	the	the	DET
ejpam-6931	234	224	supremum	supremum	NOUN
ejpam-6931	234	225	of	of	ADP
ejpam-6931	234	226	the	the	DET
ejpam-6931	234	227	set	set	NOUN
ejpam-6931	234	228	cn	cn	PROPN
ejpam-6931	234	229	,	,	PUNCT
ejpam-6931	234	230	denoted	denote	VERB
ejpam-6931	234	231	as	as	ADP
ejpam-6931	234	232	supcn	supcn	NOUN
ejpam-6931	234	233	=	=	SYM
ejpam-6931	234	234	ćn	ćn	PROPN
ejpam-6931	234	235	,	,	PUNCT
ejpam-6931	234	236	exists	exist	VERB
ejpam-6931	234	237	for	for	ADP
ejpam-6931	234	238	every	every	DET
ejpam-6931	234	239	n	n	ADP
ejpam-6931	234	240	belonging	belong	VERB
ejpam-6931	234	241	to	to	ADP
ejpam-6931	234	242	the	the	DET
ejpam-6931	234	243	set	set	VERB
ejpam-6931	234	244	m.	m.	NOUN
ejpam-6931	234	245	for	for	ADP
ejpam-6931	234	246	c	c	PROPN
ejpam-6931	234	247	∈	∈	PROPN
ejpam-6931	234	248	s0	s0	PROPN
ejpam-6931	234	249	and	and	CCONJ
ejpam-6931	234	250	n	n	CCONJ
ejpam-6931	234	251	,	,	PUNCT
ejpam-6931	234	252	m	m	VERB
ejpam-6931	234	253	∈	∈	NOUN
ejpam-6931	234	254	m	m	VERB
ejpam-6931	234	255	where	where	SCONJ
ejpam-6931	234	256	m	m	VERB
ejpam-6931	234	257	>	>	X
ejpam-6931	234	258	n	n	CCONJ
ejpam-6931	234	259	,	,	PUNCT
ejpam-6931	234	260	using	use	VERB
ejpam-6931	234	261	equation	equation	NOUN
ejpam-6931	234	262	(	(	PUNCT
ejpam-6931	234	263	1	1	NUM
ejpam-6931	234	264	)	)	PUNCT
ejpam-6931	234	265	,	,	PUNCT
ejpam-6931	234	266	we	we	PRON
ejpam-6931	234	267	obtain	obtain	VERB
ejpam-6931	234	268	e(ϱon+1	e(ϱon+1	NOUN
ejpam-6931	234	269	,	,	PUNCT
ejpam-6931	234	270	ϱ	ϱ	ADP
ejpam-6931	234	271	o	o	NOUN
ejpam-6931	234	272	m+1	m+1	X
ejpam-6931	234	273	,	,	PUNCT
ejpam-6931	234	274	e	e	NOUN
ejpam-6931	234	275	)	)	PUNCT
ejpam-6931	234	276	=	=	SYM
ejpam-6931	234	277	e(hϱon+1	e(hϱon+1	PROPN
ejpam-6931	234	278	,	,	PUNCT
ejpam-6931	234	279	hϱ	hϱ	INTJ
ejpam-6931	234	280	o	o	NOUN
ejpam-6931	234	281	m	m	PROPN
ejpam-6931	234	282	,	,	PUNCT
ejpam-6931	234	283	e	e	NOUN
ejpam-6931	234	284	)	)	PUNCT
ejpam-6931	234	285	⪰	⪰	NOUN
ejpam-6931	234	286	e	e	X
ejpam-6931	234	287	(	(	PUNCT
ejpam-6931	234	288	ϱon	ϱon	PROPN
ejpam-6931	234	289	,	,	PUNCT
ejpam-6931	234	290	ϱ	ϱ	ADP
ejpam-6931	234	291	o	o	NOUN
ejpam-6931	234	292	m	m	PROPN
ejpam-6931	234	293	,	,	PUNCT
ejpam-6931	234	294	e	e	PROPN
ejpam-6931	234	295	k	k	X
ejpam-6931	234	296	)	)	PUNCT
ejpam-6931	234	297	(	(	PUNCT
ejpam-6931	234	298	2	2	X
ejpam-6931	234	299	)	)	PUNCT
ejpam-6931	234	300	g(ϱon+1	g(ϱon+1	NOUN
ejpam-6931	234	301	,	,	PUNCT
ejpam-6931	234	302	ϱ	ϱ	ADP
ejpam-6931	234	303	o	o	NOUN
ejpam-6931	234	304	m+1	m+1	X
ejpam-6931	234	305	,	,	PUNCT
ejpam-6931	234	306	e	e	NOUN
ejpam-6931	234	307	)	)	PUNCT
ejpam-6931	234	308	=	=	SYM
ejpam-6931	234	309	g(hϱon	g(hϱon	NOUN
ejpam-6931	234	310	,	,	PUNCT
ejpam-6931	234	311	hϱom	hϱom	NOUN
ejpam-6931	234	312	,	,	PUNCT
ejpam-6931	234	313	e	e	NOUN
ejpam-6931	234	314	)	)	PUNCT
ejpam-6931	234	315	⪯	⪯	NOUN
ejpam-6931	234	316	g	g	PROPN
ejpam-6931	234	317	(	(	PUNCT
ejpam-6931	234	318	ϱon	ϱon	PROPN
ejpam-6931	234	319	,	,	PUNCT
ejpam-6931	234	320	ϱ	ϱ	ADP
ejpam-6931	234	321	o	o	NOUN
ejpam-6931	234	322	m	m	PROPN
ejpam-6931	234	323	,	,	PUNCT
ejpam-6931	234	324	e	e	PROPN
ejpam-6931	234	325	k	k	X
ejpam-6931	234	326	)	)	PUNCT
ejpam-6931	234	327	(	(	PUNCT
ejpam-6931	234	328	3	3	X
ejpam-6931	234	329	)	)	PUNCT
ejpam-6931	234	330	and	and	CCONJ
ejpam-6931	234	331	h(ϱon+1	h(ϱon+1	PROPN
ejpam-6931	234	332	,	,	PUNCT
ejpam-6931	234	333	ϱ	ϱ	ADP
ejpam-6931	234	334	o	o	NOUN
ejpam-6931	234	335	m+1	m+1	X
ejpam-6931	234	336	,	,	PUNCT
ejpam-6931	234	337	e	e	NOUN
ejpam-6931	234	338	)	)	PUNCT
ejpam-6931	234	339	=	=	SYM
ejpam-6931	234	340	h(hϱon	h(hϱon	NOUN
ejpam-6931	234	341	,	,	PUNCT
ejpam-6931	234	342	hϱ	hϱ	INTJ
ejpam-6931	234	343	o	o	NOUN
ejpam-6931	234	344	m	m	PROPN
ejpam-6931	234	345	,	,	PUNCT
ejpam-6931	234	346	e	e	NOUN
ejpam-6931	234	347	)	)	PUNCT
ejpam-6931	234	348	⪯	⪯	PROPN
ejpam-6931	234	349	h	h	PROPN
ejpam-6931	234	350	(	(	PUNCT
ejpam-6931	234	351	ϱon	ϱon	PROPN
ejpam-6931	234	352	,	,	PUNCT
ejpam-6931	234	353	ϱ	ϱ	ADP
ejpam-6931	234	354	o	o	NOUN
ejpam-6931	234	355	m	m	PROPN
ejpam-6931	234	356	,	,	PUNCT
ejpam-6931	234	357	e	e	PROPN
ejpam-6931	234	358	k	k	X
ejpam-6931	234	359	)	)	PUNCT
ejpam-6931	234	360	(	(	PUNCT
ejpam-6931	234	361	4	4	X
ejpam-6931	234	362	)	)	PUNCT
ejpam-6931	234	363	since	since	SCONJ
ejpam-6931	234	364	k	k	PROPN
ejpam-6931	234	365	∈	∈	PROPN
ejpam-6931	234	366	(	(	PUNCT
ejpam-6931	234	367	0	0	NUM
ejpam-6931	234	368	,	,	PUNCT
ejpam-6931	234	369	1	1	NUM
ejpam-6931	234	370	)	)	PUNCT
ejpam-6931	234	371	,	,	PUNCT
ejpam-6931	234	372	according	accord	VERB
ejpam-6931	234	373	to	to	ADP
ejpam-6931	234	374	lemma	lemma	PROPN
ejpam-6931	234	375	1	1	NUM
ejpam-6931	234	376	,	,	PUNCT
ejpam-6931	234	377	this	this	PRON
ejpam-6931	234	378	implies	imply	VERB
ejpam-6931	234	379	that	that	SCONJ
ejpam-6931	234	380	e	e	PROPN
ejpam-6931	234	381	(	(	PUNCT
ejpam-6931	234	382	ϱon	ϱon	PROPN
ejpam-6931	234	383	,	,	PUNCT
ejpam-6931	234	384	ϱ	ϱ	ADP
ejpam-6931	234	385	o	o	NOUN
ejpam-6931	234	386	m	m	PROPN
ejpam-6931	234	387	,	,	PUNCT
ejpam-6931	234	388	e	e	PROPN
ejpam-6931	234	389	k	k	X
ejpam-6931	234	390	)	)	PUNCT
ejpam-6931	234	391	⪰	⪰	PROPN
ejpam-6931	234	392	e(ϱon	e(ϱon	PROPN
ejpam-6931	234	393	,	,	PUNCT
ejpam-6931	234	394	ϱom	ϱom	NOUN
ejpam-6931	234	395	,	,	PUNCT
ejpam-6931	234	396	e	e	NOUN
ejpam-6931	234	397	)	)	PUNCT
ejpam-6931	234	398	,	,	PUNCT
ejpam-6931	234	399	g	g	PROPN
ejpam-6931	234	400	(	(	PUNCT
ejpam-6931	234	401	ϱon	ϱon	PROPN
ejpam-6931	234	402	,	,	PUNCT
ejpam-6931	234	403	ϱ	ϱ	ADP
ejpam-6931	234	404	o	o	NOUN
ejpam-6931	234	405	m	m	PROPN
ejpam-6931	234	406	,	,	PUNCT
ejpam-6931	234	407	e	e	PROPN
ejpam-6931	234	408	k	k	X
ejpam-6931	234	409	)	)	PUNCT
ejpam-6931	234	410	⪯	⪯	PROPN
ejpam-6931	234	411	g(ϱon	g(ϱon	PROPN
ejpam-6931	234	412	,	,	PUNCT
ejpam-6931	234	413	ϱom	ϱom	NOUN
ejpam-6931	234	414	,	,	PUNCT
ejpam-6931	234	415	e	e	NOUN
ejpam-6931	234	416	)	)	PUNCT
ejpam-6931	234	417	and	and	CCONJ
ejpam-6931	234	418	h	h	PROPN
ejpam-6931	234	419	(	(	PUNCT
ejpam-6931	234	420	ϱon	ϱon	PROPN
ejpam-6931	234	421	,	,	PUNCT
ejpam-6931	234	422	ϱ	ϱ	ADP
ejpam-6931	234	423	o	o	NOUN
ejpam-6931	234	424	m	m	PROPN
ejpam-6931	234	425	,	,	PUNCT
ejpam-6931	234	426	e	e	PROPN
ejpam-6931	234	427	k	k	X
ejpam-6931	234	428	)	)	PUNCT
ejpam-6931	234	429	⪯	⪯	PROPN
ejpam-6931	234	430	h(ϱon	h(ϱon	PROPN
ejpam-6931	234	431	,	,	PUNCT
ejpam-6931	234	432	ϱ	ϱ	ADP
ejpam-6931	234	433	o	o	PROPN
ejpam-6931	234	434	m	m	NOUN
ejpam-6931	234	435	,	,	PUNCT
ejpam-6931	234	436	e	e	NOUN
ejpam-6931	234	437	)	)	PUNCT
ejpam-6931	234	438	.	.	PUNCT
ejpam-6931	235	1	this	this	PRON
ejpam-6931	235	2	ultimately	ultimately	ADV
ejpam-6931	235	3	results	result	VERB
ejpam-6931	235	4	in	in	ADP
ejpam-6931	235	5	e(ϱon+1	e(ϱon+1	NOUN
ejpam-6931	235	6	,	,	PUNCT
ejpam-6931	235	7	ϱ	ϱ	ADP
ejpam-6931	235	8	o	o	NOUN
ejpam-6931	235	9	m+1	m+1	X
ejpam-6931	235	10	,	,	PUNCT
ejpam-6931	235	11	e	e	NOUN
ejpam-6931	235	12	)	)	PUNCT
ejpam-6931	235	13	⪰	⪰	PROPN
ejpam-6931	235	14	e(ϱon	e(ϱon	PROPN
ejpam-6931	235	15	,	,	PUNCT
ejpam-6931	235	16	ϱom	ϱom	NOUN
ejpam-6931	235	17	,	,	PUNCT
ejpam-6931	235	18	e	e	NOUN
ejpam-6931	235	19	)	)	PUNCT
ejpam-6931	235	20	g(ϱon+1	g(ϱon+1	NOUN
ejpam-6931	235	21	,	,	PUNCT
ejpam-6931	235	22	ϱ	ϱ	ADP
ejpam-6931	235	23	o	o	NOUN
ejpam-6931	235	24	m+1	m+1	X
ejpam-6931	235	25	,	,	PUNCT
ejpam-6931	235	26	e	e	NOUN
ejpam-6931	235	27	)	)	PUNCT
ejpam-6931	235	28	⪯	⪯	PROPN
ejpam-6931	235	29	g(ϱon	g(ϱon	PROPN
ejpam-6931	235	30	,	,	PUNCT
ejpam-6931	235	31	ϱom	ϱom	NOUN
ejpam-6931	235	32	,	,	PUNCT
ejpam-6931	235	33	e	e	NOUN
ejpam-6931	235	34	)	)	PUNCT
ejpam-6931	235	35	and	and	CCONJ
ejpam-6931	235	36	h(ϱon+1	h(ϱon+1	PROPN
ejpam-6931	235	37	,	,	PUNCT
ejpam-6931	235	38	ϱ	ϱ	ADP
ejpam-6931	235	39	o	o	NOUN
ejpam-6931	235	40	m+1	m+1	X
ejpam-6931	235	41	,	,	PUNCT
ejpam-6931	235	42	e	e	NOUN
ejpam-6931	235	43	)	)	PUNCT
ejpam-6931	235	44	⪯	⪯	NOUN
ejpam-6931	235	45	h(ϱon	h(ϱon	PROPN
ejpam-6931	235	46	,	,	PUNCT
ejpam-6931	235	47	ϱ	ϱ	ADP
ejpam-6931	235	48	o	o	PROPN
ejpam-6931	235	49	m	m	NOUN
ejpam-6931	235	50	,	,	PUNCT
ejpam-6931	235	51	e	e	NOUN
ejpam-6931	235	52	)	)	PUNCT
ejpam-6931	235	53	for	for	ADP
ejpam-6931	235	54	every	every	DET
ejpam-6931	235	55	n	n	CCONJ
ejpam-6931	235	56	,	,	PUNCT
ejpam-6931	235	57	m	m	VERB
ejpam-6931	235	58	∈	∈	NOUN
ejpam-6931	235	59	m	m	NOUN
ejpam-6931	235	60	and	and	CCONJ
ejpam-6931	235	61	m	m	VERB
ejpam-6931	235	62	>	>	X
ejpam-6931	235	63	n.after	n.after	NOUN
ejpam-6931	235	64	verifying	verify	VERB
ejpam-6931	235	65	the	the	DET
ejpam-6931	235	66	inf(e	inf(e	PROPN
ejpam-6931	235	67	)	)	PUNCT
ejpam-6931	235	68	,	,	PUNCT
ejpam-6931	235	69	sup(g	sup(g	NOUN
ejpam-6931	235	70	)	)	PUNCT
ejpam-6931	235	71	and	and	CCONJ
ejpam-6931	235	72	sup(h	sup(h	PROPN
ejpam-6931	235	73	)	)	PUNCT
ejpam-6931	235	74	above	above	ADV
ejpam-6931	235	75	,	,	PUNCT
ejpam-6931	235	76	we	we	PRON
ejpam-6931	235	77	may	may	AUX
ejpam-6931	235	78	conclude	conclude	VERB
ejpam-6931	235	79	that	that	DET
ejpam-6931	235	80	∅	∅	NOUN
ejpam-6931	235	81	⪯	⪯	NOUN
ejpam-6931	235	82	x́n	x́n	PUNCT
ejpam-6931	235	83	⪯	⪯	X
ejpam-6931	235	84	x́n+1	x́n+1	PROPN
ejpam-6931	235	85	⪯	⪯	PROPN
ejpam-6931	235	86	ℑ	ℑ	PROPN
ejpam-6931	235	87	,	,	PUNCT
ejpam-6931	235	88	∅	∅	NOUN
ejpam-6931	235	89	⪯	⪯	NOUN
ejpam-6931	235	90	ýn+1	ýn+1	PROPN
ejpam-6931	235	91	⪯	⪯	PROPN
ejpam-6931	235	92	ýn	ýn	NOUN
ejpam-6931	235	93	⪯	⪯	NOUN
ejpam-6931	235	94	ℑ	ℑ	PROPN
ejpam-6931	235	95	,	,	PUNCT
ejpam-6931	235	96	∅	∅	NOUN
ejpam-6931	235	97	⪯	⪯	NOUN
ejpam-6931	235	98	ćn+1	ćn+1	PROPN
ejpam-6931	235	99	⪯	⪯	X
ejpam-6931	235	100	ćn	ćn	PROPN
ejpam-6931	235	101	⪯	⪯	VERB
ejpam-6931	235	102	ℑ	ℑ	PROPN
ejpam-6931	235	103	for	for	ADP
ejpam-6931	235	104	any	any	DET
ejpam-6931	235	105	n	n	PRON
ejpam-6931	235	106	∈	∈	NOUN
ejpam-6931	235	107	m.	m.	NOUN
ejpam-6931	235	108	thus	thus	ADV
ejpam-6931	235	109	{	{	PUNCT
ejpam-6931	235	110	x́n	x́n	NOUN
ejpam-6931	235	111	}	}	PUNCT
ejpam-6931	235	112	,	,	PUNCT
ejpam-6931	235	113	{	{	PUNCT
ejpam-6931	235	114	ýn	ýn	NOUN
ejpam-6931	235	115	}	}	PUNCT
ejpam-6931	235	116	and	and	CCONJ
ejpam-6931	235	117	{	{	PUNCT
ejpam-6931	235	118	ćn	ćn	ADV
ejpam-6931	235	119	}	}	PUNCT
ejpam-6931	235	120	are	be	AUX
ejpam-6931	235	121	monotonic	monotonic	ADJ
ejpam-6931	235	122	sequences	sequence	NOUN
ejpam-6931	235	123	in	in	ADP
ejpam-6931	235	124	s.	s.	PROPN
ejpam-6931	235	125	according	accord	VERB
ejpam-6931	235	126	to	to	ADP
ejpam-6931	235	127	remarks	remark	NOUN
ejpam-6931	235	128	1	1	NUM
ejpam-6931	235	129	,	,	PUNCT
ejpam-6931	235	130	there	there	PRON
ejpam-6931	235	131	are	be	VERB
ejpam-6931	235	132	complex	complex	ADJ
ejpam-6931	235	133	numbers	number	NOUN
ejpam-6931	235	134	x́	x́	PROPN
ejpam-6931	235	135	,	,	PUNCT
ejpam-6931	235	136	ý	ý	ADJ
ejpam-6931	235	137	,	,	PUNCT
ejpam-6931	235	138	ć	ć	PROPN
ejpam-6931	235	139	∈	∈	PROPN
ejpam-6931	235	140	s	s	AUX
ejpam-6931	235	141	satisfying	satisfy	VERB
ejpam-6931	235	142	limn→∞	limn→∞	X
ejpam-6931	236	1	x́n	x́n	NOUN
ejpam-6931	236	2	=	=	SYM
ejpam-6931	236	3	x́	x́	PROPN
ejpam-6931	236	4	,	,	PUNCT
ejpam-6931	236	5	limn→∞	limn→∞	PRON
ejpam-6931	236	6	ýn	ýn	NOUN
ejpam-6931	236	7	=	=	SYM
ejpam-6931	236	8	ý	ý	ADJ
ejpam-6931	236	9	and	and	CCONJ
ejpam-6931	236	10	limn→∞	limn→∞	ADJ
ejpam-6931	236	11	ćn	ćn	PROPN
ejpam-6931	236	12	=	=	SYM
ejpam-6931	236	13	ć.	ć.	NOUN
ejpam-6931	236	14	by	by	ADP
ejpam-6931	236	15	using	use	VERB
ejpam-6931	236	16	equations	equation	NOUN
ejpam-6931	236	17	(	(	PUNCT
ejpam-6931	236	18	2	2	NUM
ejpam-6931	236	19	)	)	PUNCT
ejpam-6931	236	20	,	,	PUNCT
ejpam-6931	236	21	(	(	PUNCT
ejpam-6931	236	22	3	3	NUM
ejpam-6931	236	23	)	)	PUNCT
ejpam-6931	236	24	,	,	PUNCT
ejpam-6931	236	25	and	and	CCONJ
ejpam-6931	236	26	(	(	PUNCT
ejpam-6931	236	27	4	4	NUM
ejpam-6931	236	28	)	)	PUNCT
ejpam-6931	236	29	,	,	PUNCT
ejpam-6931	236	30	we	we	PRON
ejpam-6931	236	31	have	have	VERB
ejpam-6931	236	32	x́n+1	x́n+1	PROPN
ejpam-6931	236	33	=	=	SYM
ejpam-6931	236	34	inf	inf	PROPN
ejpam-6931	236	35	m	m	PROPN
ejpam-6931	236	36	>	>	PROPN
ejpam-6931	236	37	n	n	PRON
ejpam-6931	236	38	e(ϱon+1	e(ϱon+1	NOUN
ejpam-6931	236	39	,	,	PUNCT
ejpam-6931	236	40	ϱ	ϱ	ADP
ejpam-6931	236	41	o	o	NOUN
ejpam-6931	236	42	m+1	m+1	X
ejpam-6931	236	43	,	,	PUNCT
ejpam-6931	236	44	e	e	NOUN
ejpam-6931	236	45	)	)	PUNCT
ejpam-6931	236	46	⪰	⪰	NOUN
ejpam-6931	236	47	inf	inf	PROPN
ejpam-6931	236	48	m	m	PROPN
ejpam-6931	236	49	>	>	X
ejpam-6931	236	50	n	n	PRON
ejpam-6931	236	51	e	e	X
ejpam-6931	236	52	(	(	PUNCT
ejpam-6931	236	53	ϱon	ϱon	PROPN
ejpam-6931	236	54	,	,	PUNCT
ejpam-6931	236	55	ϱ	ϱ	ADP
ejpam-6931	236	56	o	o	NOUN
ejpam-6931	236	57	m	m	PROPN
ejpam-6931	236	58	,	,	PUNCT
ejpam-6931	236	59	e	e	PROPN
ejpam-6931	236	60	k	k	X
ejpam-6931	236	61	)	)	PUNCT
ejpam-6931	236	62	s.	s.	PROPN
ejpam-6931	236	63	m.	m.	PROPN
ejpam-6931	236	64	u.	u.	PROPN
ejpam-6931	236	65	ud	ud	AUX
ejpam-6931	236	66	-	-	PUNCT
ejpam-6931	236	67	din	din	VERB
ejpam-6931	236	68	et	et	PROPN
ejpam-6931	236	69	al	al	PROPN
ejpam-6931	236	70	.	.	PUNCT
ejpam-6931	236	71	/	/	SYM
ejpam-6931	236	72	eur	eur	PROPN
ejpam-6931	236	73	.	.	PUNCT
ejpam-6931	237	1	j.	j.	PROPN
ejpam-6931	237	2	pure	pure	PROPN
ejpam-6931	237	3	appl	appl	PROPN
ejpam-6931	237	4	.	.	PROPN
ejpam-6931	237	5	math	math	PROPN
ejpam-6931	237	6	,	,	PUNCT
ejpam-6931	237	7	18	18	NUM
ejpam-6931	237	8	(	(	PUNCT
ejpam-6931	237	9	4	4	NUM
ejpam-6931	237	10	)	)	PUNCT
ejpam-6931	237	11	(	(	PUNCT
ejpam-6931	237	12	2025	2025	NUM
ejpam-6931	237	13	)	)	PUNCT
ejpam-6931	237	14	,	,	PUNCT
ejpam-6931	237	15	6931	6931	NUM
ejpam-6931	237	16	14	14	NUM
ejpam-6931	237	17	of	of	ADP
ejpam-6931	237	18	38	38	NUM
ejpam-6931	237	19	ýn+1	ýn+1	NOUN
ejpam-6931	237	20	=	=	SYM
ejpam-6931	237	21	sup	sup	NOUN
ejpam-6931	237	22	m	m	PROPN
ejpam-6931	237	23	>	>	NOUN
ejpam-6931	237	24	n	n	PRON
ejpam-6931	237	25	g(ϱon+1	g(ϱon+1	NOUN
ejpam-6931	237	26	,	,	PUNCT
ejpam-6931	237	27	ϱ	ϱ	ADP
ejpam-6931	237	28	o	o	NOUN
ejpam-6931	237	29	m+1	m+1	X
ejpam-6931	237	30	,	,	PUNCT
ejpam-6931	237	31	e	e	NOUN
ejpam-6931	237	32	)	)	PUNCT
ejpam-6931	237	33	⪯	⪯	NOUN
ejpam-6931	237	34	sup	sup	PROPN
ejpam-6931	237	35	m	m	PROPN
ejpam-6931	237	36	>	>	PROPN
ejpam-6931	237	37	n	n	PROPN
ejpam-6931	237	38	g	g	PROPN
ejpam-6931	237	39	(	(	PUNCT
ejpam-6931	237	40	ϱon	ϱon	PROPN
ejpam-6931	237	41	,	,	PUNCT
ejpam-6931	237	42	ϱ	ϱ	ADP
ejpam-6931	237	43	o	o	NOUN
ejpam-6931	237	44	m	m	PROPN
ejpam-6931	237	45	,	,	PUNCT
ejpam-6931	237	46	e	e	PROPN
ejpam-6931	237	47	k	k	X
ejpam-6931	237	48	)	)	PUNCT
ejpam-6931	237	49	and	and	CCONJ
ejpam-6931	237	50	ćn+1	ćn+1	PROPN
ejpam-6931	237	51	=	=	SYM
ejpam-6931	237	52	sup	sup	NOUN
ejpam-6931	237	53	m	m	PROPN
ejpam-6931	237	54	>	>	X
ejpam-6931	237	55	n	n	X
ejpam-6931	237	56	h(ϱon+1	h(ϱon+1	PROPN
ejpam-6931	237	57	,	,	PUNCT
ejpam-6931	237	58	ϱ	ϱ	ADP
ejpam-6931	237	59	o	o	NOUN
ejpam-6931	237	60	m+1	m+1	X
ejpam-6931	237	61	,	,	PUNCT
ejpam-6931	237	62	e	e	NOUN
ejpam-6931	237	63	)	)	PUNCT
ejpam-6931	237	64	⪯	⪯	NOUN
ejpam-6931	237	65	sup	sup	PROPN
ejpam-6931	237	66	m	m	PROPN
ejpam-6931	237	67	>	>	PROPN
ejpam-6931	237	68	n	n	PROPN
ejpam-6931	237	69	h	h	PROPN
ejpam-6931	237	70	(	(	PUNCT
ejpam-6931	237	71	ϱon	ϱon	PROPN
ejpam-6931	237	72	,	,	PUNCT
ejpam-6931	237	73	ϱ	ϱ	ADP
ejpam-6931	237	74	o	o	NOUN
ejpam-6931	237	75	m	m	PROPN
ejpam-6931	237	76	,	,	PUNCT
ejpam-6931	237	77	e	e	PROPN
ejpam-6931	237	78	k	k	PROPN
ejpam-6931	237	79	)	)	PUNCT
ejpam-6931	237	80	for	for	ADP
ejpam-6931	237	81	c	c	PROPN
ejpam-6931	237	82	∈	∈	PROPN
ejpam-6931	237	83	s0	s0	NOUN
ejpam-6931	237	84	and	and	CCONJ
ejpam-6931	237	85	n	n	PRON
ejpam-6931	237	86	∈	∈	NOUN
ejpam-6931	237	87	m.	m.	NOUN
ejpam-6931	237	88	by	by	ADP
ejpam-6931	237	89	successively	successively	ADV
ejpam-6931	237	90	applying	apply	VERB
ejpam-6931	237	91	equation	equation	NOUN
ejpam-6931	237	92	(	(	PUNCT
ejpam-6931	237	93	1	1	NUM
ejpam-6931	237	94	)	)	PUNCT
ejpam-6931	237	95	to	to	ADP
ejpam-6931	237	96	the	the	DET
ejpam-6931	237	97	inequalities	inequality	NOUN
ejpam-6931	237	98	mentioned	mention	VERB
ejpam-6931	237	99	above	above	ADV
ejpam-6931	237	100	,	,	PUNCT
ejpam-6931	237	101	we	we	PRON
ejpam-6931	237	102	obtain	obtain	VERB
ejpam-6931	237	103	x́n+1	x́n+1	PROPN
ejpam-6931	237	104	⪰	⪰	PROPN
ejpam-6931	237	105	inf	inf	PROPN
ejpam-6931	237	106	m	m	PROPN
ejpam-6931	237	107	>	>	PROPN
ejpam-6931	237	108	n	n	PRON
ejpam-6931	237	109	e(ϱon	e(ϱon	PROPN
ejpam-6931	237	110	,	,	PUNCT
ejpam-6931	237	111	ϱom	ϱom	NOUN
ejpam-6931	237	112	,	,	PUNCT
ejpam-6931	237	113	e	e	PROPN
ejpam-6931	237	114	k	k	X
ejpam-6931	237	115	)	)	PUNCT
ejpam-6931	237	116	⪰	⪰	VERB
ejpam-6931	237	117	inf	inf	PROPN
ejpam-6931	237	118	m	m	PROPN
ejpam-6931	237	119	>	>	X
ejpam-6931	237	120	n	n	X
ejpam-6931	237	121	e(ϱon−1	e(ϱon−1	PROPN
ejpam-6931	237	122	,	,	PUNCT
ejpam-6931	237	123	ϱ	ϱ	ADP
ejpam-6931	237	124	o	o	X
ejpam-6931	237	125	m−1	m−1	PROPN
ejpam-6931	237	126	,	,	PUNCT
ejpam-6931	237	127	e	e	PROPN
ejpam-6931	237	128	k2	k2	X
ejpam-6931	237	129	)	)	PUNCT
ejpam-6931	237	130	⪰	⪰	PROPN
ejpam-6931	237	131	inf	inf	PROPN
ejpam-6931	237	132	m	m	PROPN
ejpam-6931	237	133	>	>	NOUN
ejpam-6931	237	134	n	n	PRON
ejpam-6931	237	135	e(ϱon−2	e(ϱon−2	PROPN
ejpam-6931	237	136	,	,	PUNCT
ejpam-6931	237	137	ϱ	ϱ	ADP
ejpam-6931	237	138	o	o	NOUN
ejpam-6931	237	139	m−2	m−2	PROPN
ejpam-6931	237	140	,	,	PUNCT
ejpam-6931	237	141	e	e	NOUN
ejpam-6931	237	142	k3	k3	VERB
ejpam-6931	237	143	)	)	PUNCT
ejpam-6931	237	144	.	.	PUNCT
ejpam-6931	237	145	.	.	PUNCT
ejpam-6931	237	146	.	.	PUNCT
ejpam-6931	238	1	⪰	⪰	VERB
ejpam-6931	238	2	inf	inf	PROPN
ejpam-6931	238	3	m	m	PROPN
ejpam-6931	238	4	>	>	PROPN
ejpam-6931	238	5	n	n	PROPN
ejpam-6931	238	6	e(ϱo0	e(ϱo0	PROPN
ejpam-6931	238	7	,	,	PUNCT
ejpam-6931	238	8	ϱom−n	ϱom−n	PROPN
ejpam-6931	238	9	,	,	PUNCT
ejpam-6931	238	10	e	e	X
ejpam-6931	238	11	kn+1	kn+1	PROPN
ejpam-6931	238	12	)	)	PUNCT
ejpam-6931	239	1	ýn+1	ýn+1	PROPN
ejpam-6931	239	2	⪯	⪯	NOUN
ejpam-6931	239	3	sup	sup	NOUN
ejpam-6931	239	4	m	m	PROPN
ejpam-6931	239	5	>	>	PROPN
ejpam-6931	239	6	n	n	PRON
ejpam-6931	239	7	g(ϱon	g(ϱon	NOUN
ejpam-6931	239	8	,	,	PUNCT
ejpam-6931	239	9	ϱom	ϱom	NOUN
ejpam-6931	239	10	,	,	PUNCT
ejpam-6931	239	11	e	e	PROPN
ejpam-6931	239	12	k	k	X
ejpam-6931	239	13	)	)	PUNCT
ejpam-6931	239	14	⪯	⪯	NOUN
ejpam-6931	239	15	sup	sup	PROPN
ejpam-6931	239	16	m	m	PROPN
ejpam-6931	239	17	>	>	NOUN
ejpam-6931	239	18	n	n	X
ejpam-6931	239	19	g(ϱon−1	g(ϱon−1	ADJ
ejpam-6931	239	20	,	,	PUNCT
ejpam-6931	239	21	ϱ	ϱ	ADP
ejpam-6931	239	22	o	o	X
ejpam-6931	239	23	m−1	m−1	PROPN
ejpam-6931	239	24	,	,	PUNCT
ejpam-6931	239	25	e	e	PROPN
ejpam-6931	239	26	k2	k2	X
ejpam-6931	239	27	)	)	PUNCT
ejpam-6931	239	28	⪯	⪯	NOUN
ejpam-6931	239	29	sup	sup	PROPN
ejpam-6931	239	30	m	m	PROPN
ejpam-6931	239	31	>	>	NOUN
ejpam-6931	239	32	n	n	PRON
ejpam-6931	239	33	g(ϱon−2	g(ϱon−2	PROPN
ejpam-6931	239	34	,	,	PUNCT
ejpam-6931	239	35	ϱ	ϱ	ADP
ejpam-6931	239	36	o	o	NOUN
ejpam-6931	239	37	m−2	m−2	PROPN
ejpam-6931	239	38	,	,	PUNCT
ejpam-6931	239	39	e	e	NOUN
ejpam-6931	239	40	k3	k3	VERB
ejpam-6931	239	41	)	)	PUNCT
ejpam-6931	239	42	.	.	PUNCT
ejpam-6931	239	43	.	.	PUNCT
ejpam-6931	240	1	.	.	PUNCT
ejpam-6931	241	1	⪯	⪯	PROPN
ejpam-6931	241	2	sup	sup	PROPN
ejpam-6931	241	3	m	m	PROPN
ejpam-6931	241	4	>	>	PROPN
ejpam-6931	241	5	n	n	PROPN
ejpam-6931	241	6	g(ϱo0	g(ϱo0	PROPN
ejpam-6931	241	7	,	,	PUNCT
ejpam-6931	241	8	ϱom−n	ϱom−n	PROPN
ejpam-6931	241	9	,	,	PUNCT
ejpam-6931	241	10	e	e	X
ejpam-6931	241	11	kn+1	kn+1	PROPN
ejpam-6931	241	12	)	)	PUNCT
ejpam-6931	241	13	and	and	CCONJ
ejpam-6931	241	14	ćn+1	ćn+1	PROPN
ejpam-6931	241	15	⪯	⪯	NOUN
ejpam-6931	241	16	sup	sup	NOUN
ejpam-6931	241	17	m	m	PROPN
ejpam-6931	241	18	>	>	X
ejpam-6931	241	19	n	n	PROPN
ejpam-6931	241	20	h(ϱon	h(ϱon	NOUN
ejpam-6931	241	21	,	,	PUNCT
ejpam-6931	241	22	ϱ	ϱ	ADP
ejpam-6931	241	23	o	o	NOUN
ejpam-6931	241	24	m	m	PROPN
ejpam-6931	241	25	,	,	PUNCT
ejpam-6931	241	26	e	e	PROPN
ejpam-6931	241	27	k	k	X
ejpam-6931	241	28	)	)	PUNCT
ejpam-6931	241	29	⪯	⪯	NOUN
ejpam-6931	241	30	sup	sup	NOUN
ejpam-6931	241	31	m	m	PROPN
ejpam-6931	241	32	>	>	X
ejpam-6931	241	33	n	n	PROPN
ejpam-6931	241	34	h(ϱon−1	h(ϱon−1	PROPN
ejpam-6931	241	35	,	,	PUNCT
ejpam-6931	241	36	ϱ	ϱ	ADP
ejpam-6931	241	37	o	o	X
ejpam-6931	241	38	m−1	m−1	PROPN
ejpam-6931	241	39	,	,	PUNCT
ejpam-6931	241	40	e	e	PROPN
ejpam-6931	241	41	k2	k2	X
ejpam-6931	241	42	)	)	PUNCT
ejpam-6931	241	43	⪯	⪯	NOUN
ejpam-6931	241	44	sup	sup	PROPN
ejpam-6931	241	45	m	m	PROPN
ejpam-6931	241	46	>	>	NOUN
ejpam-6931	241	47	n	n	PRON
ejpam-6931	241	48	h(ϱon−2	h(ϱon−2	PROPN
ejpam-6931	241	49	,	,	PUNCT
ejpam-6931	241	50	ϱ	ϱ	ADP
ejpam-6931	241	51	o	o	NOUN
ejpam-6931	241	52	m−2	m−2	PROPN
ejpam-6931	241	53	,	,	PUNCT
ejpam-6931	241	54	e	e	NOUN
ejpam-6931	241	55	k3	k3	VERB
ejpam-6931	241	56	)	)	PUNCT
ejpam-6931	241	57	.	.	PUNCT
ejpam-6931	241	58	.	.	PUNCT
ejpam-6931	241	59	.	.	PUNCT
ejpam-6931	242	1	s.	s.	PROPN
ejpam-6931	242	2	m.	m.	PROPN
ejpam-6931	242	3	u.	u.	PROPN
ejpam-6931	242	4	ud	ud	AUX
ejpam-6931	242	5	-	-	PUNCT
ejpam-6931	242	6	din	din	VERB
ejpam-6931	242	7	et	et	PROPN
ejpam-6931	242	8	al	al	PROPN
ejpam-6931	242	9	.	.	PUNCT
ejpam-6931	242	10	/	/	SYM
ejpam-6931	242	11	eur	eur	PROPN
ejpam-6931	242	12	.	.	PUNCT
ejpam-6931	243	1	j.	j.	PROPN
ejpam-6931	243	2	pure	pure	PROPN
ejpam-6931	243	3	appl	appl	PROPN
ejpam-6931	243	4	.	.	PROPN
ejpam-6931	243	5	math	math	PROPN
ejpam-6931	243	6	,	,	PUNCT
ejpam-6931	243	7	18	18	NUM
ejpam-6931	243	8	(	(	PUNCT
ejpam-6931	243	9	4	4	NUM
ejpam-6931	243	10	)	)	PUNCT
ejpam-6931	243	11	(	(	PUNCT
ejpam-6931	243	12	2025	2025	NUM
ejpam-6931	243	13	)	)	PUNCT
ejpam-6931	243	14	,	,	PUNCT
ejpam-6931	243	15	6931	6931	NUM
ejpam-6931	243	16	15	15	NUM
ejpam-6931	243	17	of	of	ADP
ejpam-6931	243	18	38	38	NUM
ejpam-6931	243	19	⪯	⪯	NOUN
ejpam-6931	243	20	sup	sup	PROPN
ejpam-6931	243	21	m	m	PROPN
ejpam-6931	243	22	>	>	PROPN
ejpam-6931	243	23	n	n	DET
ejpam-6931	243	24	h(ϱo0	h(ϱo0	PROPN
ejpam-6931	243	25	,	,	PUNCT
ejpam-6931	243	26	ϱ	ϱ	ADP
ejpam-6931	243	27	o	o	PROPN
ejpam-6931	243	28	m−n	m−n	PROPN
ejpam-6931	243	29	,	,	PUNCT
ejpam-6931	243	30	e	e	X
ejpam-6931	243	31	kn+1	kn+1	PROPN
ejpam-6931	243	32	)	)	PUNCT
ejpam-6931	243	33	for	for	ADP
ejpam-6931	243	34	any	any	DET
ejpam-6931	243	35	e	e	PROPN
ejpam-6931	243	36	∈	∈	PROPN
ejpam-6931	243	37	s0	s0	NOUN
ejpam-6931	243	38	and	and	CCONJ
ejpam-6931	243	39	n	n	CCONJ
ejpam-6931	243	40	∈	∈	NOUN
ejpam-6931	243	41	m.	m.	NOUN
ejpam-6931	243	42	in	in	ADP
ejpam-6931	243	43	addition	addition	NOUN
ejpam-6931	243	44	,	,	PUNCT
ejpam-6931	243	45	we	we	PRON
ejpam-6931	243	46	obtain	obtain	VERB
ejpam-6931	243	47	x́n+1	x́n+1	PROPN
ejpam-6931	243	48	⪰	⪰	PROPN
ejpam-6931	243	49	inf	inf	PROPN
ejpam-6931	243	50	m	m	PROPN
ejpam-6931	243	51	>	>	X
ejpam-6931	243	52	n	n	PRON
ejpam-6931	243	53	e	e	X
ejpam-6931	243	54	(	(	PUNCT
ejpam-6931	243	55	ϱo0	ϱo0	PROPN
ejpam-6931	243	56	,	,	PUNCT
ejpam-6931	243	57	ϱ	ϱ	ADP
ejpam-6931	243	58	o	o	PROPN
ejpam-6931	243	59	m−n	m−n	PROPN
ejpam-6931	243	60	,	,	PUNCT
ejpam-6931	243	61	e	e	X
ejpam-6931	243	62	kn+1	kn+1	PROPN
ejpam-6931	243	63	)	)	PUNCT
ejpam-6931	243	64	⪰	⪰	VERB
ejpam-6931	243	65	inf	inf	NOUN
ejpam-6931	243	66	ν∈v	ν∈v	NOUN
ejpam-6931	244	1	e	e	NOUN
ejpam-6931	244	2	(	(	PUNCT
ejpam-6931	244	3	ϱo0	ϱo0	PROPN
ejpam-6931	244	4	,	,	PUNCT
ejpam-6931	244	5	ν	ν	PROPN
ejpam-6931	244	6	,	,	PUNCT
ejpam-6931	244	7	e	e	X
ejpam-6931	244	8	kn+1	kn+1	PROPN
ejpam-6931	244	9	)	)	PUNCT
ejpam-6931	245	1	ýn+1	ýn+1	PROPN
ejpam-6931	245	2	⪯	⪯	NOUN
ejpam-6931	245	3	sup	sup	NOUN
ejpam-6931	245	4	m	m	PROPN
ejpam-6931	245	5	>	>	PROPN
ejpam-6931	245	6	n	n	PROPN
ejpam-6931	245	7	g	g	PROPN
ejpam-6931	245	8	(	(	PUNCT
ejpam-6931	245	9	ϱo0	ϱo0	PROPN
ejpam-6931	245	10	,	,	PUNCT
ejpam-6931	245	11	ϱ	ϱ	ADP
ejpam-6931	245	12	o	o	PROPN
ejpam-6931	245	13	m−n	m−n	PROPN
ejpam-6931	245	14	,	,	PUNCT
ejpam-6931	245	15	e	e	X
ejpam-6931	245	16	kn+1	kn+1	PROPN
ejpam-6931	245	17	)	)	PUNCT
ejpam-6931	245	18	⪯	⪯	NOUN
ejpam-6931	245	19	sup	sup	NOUN
ejpam-6931	245	20	ν∈v	ν∈v	ADV
ejpam-6931	245	21	g	g	PROPN
ejpam-6931	245	22	(	(	PUNCT
ejpam-6931	245	23	ϱo0	ϱo0	PROPN
ejpam-6931	245	24	,	,	PUNCT
ejpam-6931	245	25	ν	ν	PROPN
ejpam-6931	245	26	,	,	PUNCT
ejpam-6931	245	27	e	e	X
ejpam-6931	245	28	kn+1	kn+1	PROPN
ejpam-6931	245	29	)	)	PUNCT
ejpam-6931	245	30	and	and	CCONJ
ejpam-6931	245	31	ćn+1	ćn+1	PROPN
ejpam-6931	245	32	⪯	⪯	NOUN
ejpam-6931	245	33	sup	sup	NOUN
ejpam-6931	245	34	m	m	PROPN
ejpam-6931	245	35	>	>	PROPN
ejpam-6931	245	36	n	n	PROPN
ejpam-6931	245	37	h	h	NOUN
ejpam-6931	245	38	(	(	PUNCT
ejpam-6931	245	39	ϱo0	ϱo0	PROPN
ejpam-6931	245	40	,	,	PUNCT
ejpam-6931	245	41	ϱ	ϱ	ADP
ejpam-6931	245	42	o	o	PROPN
ejpam-6931	245	43	m−n	m−n	PROPN
ejpam-6931	245	44	,	,	PUNCT
ejpam-6931	245	45	e	e	X
ejpam-6931	245	46	kn+1	kn+1	PROPN
ejpam-6931	245	47	)	)	PUNCT
ejpam-6931	245	48	⪯	⪯	NOUN
ejpam-6931	245	49	sup	sup	NOUN
ejpam-6931	245	50	ν∈v	ν∈v	ADJ
ejpam-6931	245	51	h	h	NOUN
ejpam-6931	245	52	(	(	PUNCT
ejpam-6931	245	53	ϱo0	ϱo0	PROPN
ejpam-6931	245	54	,	,	PUNCT
ejpam-6931	245	55	ν	ν	PROPN
ejpam-6931	245	56	,	,	PUNCT
ejpam-6931	245	57	e	e	X
ejpam-6931	245	58	kn+1	kn+1	PROPN
ejpam-6931	245	59	)	)	PUNCT
ejpam-6931	245	60	for	for	ADP
ejpam-6931	245	61	each	each	DET
ejpam-6931	245	62	e	e	PROPN
ejpam-6931	245	63	∈	∈	PROPN
ejpam-6931	245	64	s0	s0	NOUN
ejpam-6931	245	65	and	and	CCONJ
ejpam-6931	245	66	n	n	CCONJ
ejpam-6931	245	67	∈	∈	NOUN
ejpam-6931	245	68	m.	m.	NOUN
ejpam-6931	245	69	as	as	ADP
ejpam-6931	245	70	n	n	PROPN
ejpam-6931	245	71	→	→	SYM
ejpam-6931	245	72	∞	∞	NUM
ejpam-6931	245	73	on	on	ADP
ejpam-6931	245	74	both	both	DET
ejpam-6931	245	75	sides	side	NOUN
ejpam-6931	245	76	of	of	ADP
ejpam-6931	245	77	the	the	DET
ejpam-6931	245	78	given	give	VERB
ejpam-6931	245	79	inequality	inequality	NOUN
ejpam-6931	245	80	,	,	PUNCT
ejpam-6931	245	81	the	the	DET
ejpam-6931	245	82	hypothesis	hypothesis	NOUN
ejpam-6931	245	83	yields	yield	VERB
ejpam-6931	245	84	x́	x́	PUNCT
ejpam-6931	246	1	=	=	PRON
ejpam-6931	246	2	lim	lim	PROPN
ejpam-6931	246	3	n→∞	n→∞	X
ejpam-6931	247	1	x́n+1	x́n+1	PROPN
ejpam-6931	247	2	⪰	⪰	PROPN
ejpam-6931	247	3	lim	lim	PROPN
ejpam-6931	247	4	n→∞	n→∞	NUM
ejpam-6931	247	5	inf	inf	PROPN
ejpam-6931	247	6	ν∈v	ν∈v	NOUN
ejpam-6931	247	7	e	e	NOUN
ejpam-6931	247	8	(	(	PUNCT
ejpam-6931	247	9	ϱo0	ϱo0	PROPN
ejpam-6931	247	10	,	,	PUNCT
ejpam-6931	247	11	ν	ν	PROPN
ejpam-6931	247	12	,	,	PUNCT
ejpam-6931	247	13	e	e	X
ejpam-6931	247	14	kn+1	kn+1	PROPN
ejpam-6931	247	15	)	)	PUNCT
ejpam-6931	248	1	=	=	SYM
ejpam-6931	248	2	ℑ	ℑ	NOUN
ejpam-6931	248	3	ý	ý	ADJ
ejpam-6931	248	4	=	=	PUNCT
ejpam-6931	248	5	lim	lim	PROPN
ejpam-6931	248	6	n→∞	n→∞	NUM
ejpam-6931	249	1	ýn+1	ýn+1	PROPN
ejpam-6931	249	2	⪯	⪯	PROPN
ejpam-6931	249	3	lim	lim	PROPN
ejpam-6931	249	4	n→∞	n→∞	NUM
ejpam-6931	249	5	sup	sup	NOUN
ejpam-6931	249	6	ν∈v	ν∈v	ADJ
ejpam-6931	249	7	g	g	PROPN
ejpam-6931	249	8	(	(	PUNCT
ejpam-6931	249	9	ϱo0	ϱo0	PROPN
ejpam-6931	249	10	,	,	PUNCT
ejpam-6931	249	11	ν	ν	PROPN
ejpam-6931	249	12	,	,	PUNCT
ejpam-6931	249	13	e	e	X
ejpam-6931	249	14	kn+1	kn+1	PROPN
ejpam-6931	249	15	)	)	PUNCT
ejpam-6931	250	1	=	=	NOUN
ejpam-6931	250	2	∅	∅	NOUN
ejpam-6931	250	3	and	and	CCONJ
ejpam-6931	250	4	ć	ć	PROPN
ejpam-6931	250	5	=	=	PROPN
ejpam-6931	250	6	lim	lim	PROPN
ejpam-6931	250	7	n→∞	n→∞	X
ejpam-6931	250	8	ćn+1	ćn+1	PROPN
ejpam-6931	250	9	⪯	⪯	PROPN
ejpam-6931	250	10	lim	lim	PROPN
ejpam-6931	250	11	n→∞	n→∞	NUM
ejpam-6931	250	12	sup	sup	ADV
ejpam-6931	250	13	ν∈v	ν∈v	ADJ
ejpam-6931	250	14	h	h	NOUN
ejpam-6931	250	15	(	(	PUNCT
ejpam-6931	250	16	ϱo0	ϱo0	PROPN
ejpam-6931	250	17	,	,	PUNCT
ejpam-6931	250	18	ν	ν	PROPN
ejpam-6931	250	19	,	,	PUNCT
ejpam-6931	250	20	e	e	X
ejpam-6931	250	21	kn+1	kn+1	PROPN
ejpam-6931	250	22	)	)	PUNCT
ejpam-6931	250	23	=	=	NOUN
ejpam-6931	250	24	∅	∅	NOUN
ejpam-6931	250	25	which	which	PRON
ejpam-6931	250	26	imply	imply	VERB
ejpam-6931	250	27	x́	x́	PUNCT
ejpam-6931	250	28	=	=	SYM
ejpam-6931	250	29	ℑ	ℑ	PROPN
ejpam-6931	250	30	,	,	PUNCT
ejpam-6931	250	31	ý	ý	ADJ
ejpam-6931	250	32	=	=	NOUN
ejpam-6931	250	33	∅	∅	NOUN
ejpam-6931	250	34	and	and	CCONJ
ejpam-6931	250	35	ć	ć	NOUN
ejpam-6931	250	36	=	=	PUNCT
ejpam-6931	250	37	∅.	∅.	VERB
ejpam-6931	250	38	thus	thus	ADV
ejpam-6931	250	39	,	,	PUNCT
ejpam-6931	250	40	lim	lim	PROPN
ejpam-6931	250	41	n→∞	n→∞	NUM
ejpam-6931	250	42	inf	inf	PROPN
ejpam-6931	250	43	m	m	PROPN
ejpam-6931	250	44	>	>	PROPN
ejpam-6931	250	45	n	n	PRON
ejpam-6931	250	46	e(ϱon+1	e(ϱon+1	NOUN
ejpam-6931	250	47	,	,	PUNCT
ejpam-6931	250	48	ϱ	ϱ	ADP
ejpam-6931	250	49	o	o	NOUN
ejpam-6931	250	50	m+1	m+1	X
ejpam-6931	250	51	,	,	PUNCT
ejpam-6931	250	52	e	e	NOUN
ejpam-6931	250	53	)	)	PUNCT
ejpam-6931	250	54	=	=	SYM
ejpam-6931	250	55	lim	lim	NOUN
ejpam-6931	250	56	n→∞	n→∞	X
ejpam-6931	250	57	x́n	x́n	SYM
ejpam-6931	250	58	=	=	SYM
ejpam-6931	250	59	ℑ	ℑ	PROPN
ejpam-6931	250	60	,	,	PUNCT
ejpam-6931	250	61	lim	lim	PROPN
ejpam-6931	250	62	n→∞	n→∞	NUM
ejpam-6931	250	63	sup	sup	PROPN
ejpam-6931	250	64	m	m	PROPN
ejpam-6931	250	65	>	>	NOUN
ejpam-6931	250	66	n	n	PRON
ejpam-6931	250	67	g(ϱon+1	g(ϱon+1	NOUN
ejpam-6931	250	68	,	,	PUNCT
ejpam-6931	250	69	ϱ	ϱ	ADP
ejpam-6931	250	70	o	o	NOUN
ejpam-6931	250	71	m+1	m+1	X
ejpam-6931	250	72	,	,	PUNCT
ejpam-6931	250	73	e	e	NOUN
ejpam-6931	250	74	)	)	PUNCT
ejpam-6931	250	75	=	=	SYM
ejpam-6931	250	76	lim	lim	PROPN
ejpam-6931	250	77	n→∞	n→∞	NUM
ejpam-6931	250	78	ýn	ýn	NOUN
ejpam-6931	250	79	=	=	SYM
ejpam-6931	250	80	∅	∅	NOUN
ejpam-6931	250	81	,	,	PUNCT
ejpam-6931	250	82	lim	lim	PROPN
ejpam-6931	250	83	n→∞	n→∞	NUM
ejpam-6931	250	84	sup	sup	PROPN
ejpam-6931	250	85	m	m	PROPN
ejpam-6931	250	86	>	>	X
ejpam-6931	250	87	n	n	PROPN
ejpam-6931	250	88	h(ϱon+1	h(ϱon+1	PROPN
ejpam-6931	250	89	,	,	PUNCT
ejpam-6931	250	90	ϱ	ϱ	ADP
ejpam-6931	250	91	o	o	NOUN
ejpam-6931	250	92	m+1	m+1	X
ejpam-6931	250	93	,	,	PUNCT
ejpam-6931	250	94	e	e	NOUN
ejpam-6931	250	95	)	)	PUNCT
ejpam-6931	250	96	=	=	SYM
ejpam-6931	250	97	lim	lim	PROPN
ejpam-6931	250	98	n→∞	n→∞	NUM
ejpam-6931	250	99	ćn	ćn	NOUN
ejpam-6931	250	100	=	=	NOUN
ejpam-6931	250	101	∅	∅	NOUN
ejpam-6931	250	102	,	,	PUNCT
ejpam-6931	250	103	for	for	ADP
ejpam-6931	250	104	all	all	DET
ejpam-6931	250	105	e	e	X
ejpam-6931	250	106	∈	∈	PROPN
ejpam-6931	250	107	s0	s0	NOUN
ejpam-6931	250	108	which	which	PRON
ejpam-6931	250	109	show	show	VERB
ejpam-6931	250	110	sequence	sequence	NOUN
ejpam-6931	250	111	{	{	PUNCT
ejpam-6931	250	112	ϱon	ϱon	NOUN
ejpam-6931	250	113	}	}	PUNCT
ejpam-6931	250	114	is	be	AUX
ejpam-6931	250	115	cauchy	cauchy	NOUN
ejpam-6931	250	116	.	.	PUNCT
ejpam-6931	251	1	given	give	VERB
ejpam-6931	251	2	that	that	SCONJ
ejpam-6931	251	3	(	(	PUNCT
ejpam-6931	251	4	v	v	NOUN
ejpam-6931	251	5	,	,	PUNCT
ejpam-6931	251	6	e	e	NOUN
ejpam-6931	251	7	,	,	PUNCT
ejpam-6931	251	8	g	g	PROPN
ejpam-6931	251	9	,	,	PUNCT
ejpam-6931	251	10	h	h	NOUN
ejpam-6931	251	11	,	,	PUNCT
ejpam-6931	251	12	⋆	⋆	NOUN
ejpam-6931	251	13	,	,	PUNCT
ejpam-6931	251	14	△	△	NOUN
ejpam-6931	251	15	)	)	PUNCT
ejpam-6931	251	16	is	be	AUX
ejpam-6931	251	17	complete	complete	ADJ
ejpam-6931	251	18	,	,	PUNCT
ejpam-6931	251	19	2	2	NUM
ejpam-6931	251	20	implies	imply	VERB
ejpam-6931	251	21	the	the	DET
ejpam-6931	251	22	existence	existence	NOUN
ejpam-6931	251	23	of	of	ADP
ejpam-6931	251	24	ϱo	ϱo	PROPN
ejpam-6931	251	25	∈	∈	PROPN
ejpam-6931	251	26	v	v	NOUN
ejpam-6931	251	27	satisfying	satisfy	VERB
ejpam-6931	251	28	lim	lim	PROPN
ejpam-6931	251	29	n→∞	n→∞	NUM
ejpam-6931	251	30	e(ϱon	e(ϱon	PROPN
ejpam-6931	251	31	,	,	PUNCT
ejpam-6931	251	32	ϱo	ϱo	NOUN
ejpam-6931	251	33	,	,	PUNCT
ejpam-6931	251	34	e	e	NOUN
ejpam-6931	251	35	)	)	PUNCT
ejpam-6931	251	36	=	=	SYM
ejpam-6931	251	37	ℑ	ℑ	PROPN
ejpam-6931	251	38	,	,	PUNCT
ejpam-6931	251	39	lim	lim	PROPN
ejpam-6931	251	40	n→∞	n→∞	NUM
ejpam-6931	251	41	g(ϱon	g(ϱon	PROPN
ejpam-6931	251	42	,	,	PUNCT
ejpam-6931	251	43	ϱom	ϱom	NOUN
ejpam-6931	251	44	,	,	PUNCT
ejpam-6931	251	45	e	e	NOUN
ejpam-6931	251	46	)	)	PUNCT
ejpam-6931	251	47	=	=	SYM
ejpam-6931	251	48	∅	∅	NOUN
ejpam-6931	251	49	and	and	CCONJ
ejpam-6931	251	50	lim	lim	PROPN
ejpam-6931	251	51	n→∞	n→∞	PROPN
ejpam-6931	252	1	h(ϱon	h(ϱon	PROPN
ejpam-6931	252	2	,	,	PUNCT
ejpam-6931	252	3	ϱ	ϱ	ADP
ejpam-6931	252	4	o	o	PROPN
ejpam-6931	252	5	m	m	NOUN
ejpam-6931	252	6	,	,	PUNCT
ejpam-6931	252	7	e	e	NOUN
ejpam-6931	252	8	)	)	PUNCT
ejpam-6931	252	9	=	=	NOUN
ejpam-6931	252	10	∅	∅	NOUN
ejpam-6931	252	11	for	for	ADP
ejpam-6931	252	12	any	any	DET
ejpam-6931	252	13	e	e	PROPN
ejpam-6931	252	14	∈	∈	PROPN
ejpam-6931	252	15	s0	s0	NOUN
ejpam-6931	252	16	(	(	PUNCT
ejpam-6931	252	17	5	5	NUM
ejpam-6931	252	18	)	)	PUNCT
ejpam-6931	252	19	as	as	ADP
ejpam-6931	252	20	a	a	DET
ejpam-6931	252	21	result	result	NOUN
ejpam-6931	252	22	of	of	ADP
ejpam-6931	252	23	equation	equation	NOUN
ejpam-6931	252	24	(	(	PUNCT
ejpam-6931	252	25	1	1	NUM
ejpam-6931	252	26	)	)	PUNCT
ejpam-6931	252	27	,	,	PUNCT
ejpam-6931	252	28	and	and	CCONJ
ejpam-6931	252	29	conditions	condition	NOUN
ejpam-6931	252	30	(	(	PUNCT
ejpam-6931	252	31	5	5	NUM
ejpam-6931	252	32	)	)	PUNCT
ejpam-6931	252	33	,	,	PUNCT
ejpam-6931	252	34	(	(	PUNCT
ejpam-6931	252	35	10	10	NUM
ejpam-6931	252	36	)	)	PUNCT
ejpam-6931	252	37	,	,	PUNCT
ejpam-6931	252	38	(	(	PUNCT
ejpam-6931	252	39	15	15	NUM
ejpam-6931	252	40	)	)	PUNCT
ejpam-6931	252	41	of	of	ADP
ejpam-6931	252	42	definition	definition	NOUN
ejpam-6931	252	43	7	7	NUM
ejpam-6931	252	44	for	for	ADP
ejpam-6931	252	45	any	any	DET
ejpam-6931	252	46	e	e	PROPN
ejpam-6931	252	47	∈	∈	PROPN
ejpam-6931	252	48	s0	s0	NOUN
ejpam-6931	252	49	,	,	PUNCT
ejpam-6931	252	50	lead	lead	VERB
ejpam-6931	252	51	us	we	PRON
ejpam-6931	252	52	to	to	ADP
ejpam-6931	252	53	the	the	DET
ejpam-6931	252	54	conclusion	conclusion	NOUN
ejpam-6931	252	55	that	that	SCONJ
ejpam-6931	252	56	e(ϱo	e(ϱo	NOUN
ejpam-6931	252	57	,	,	PUNCT
ejpam-6931	252	58	hϱo	hϱo	INTJ
ejpam-6931	252	59	,	,	PUNCT
ejpam-6931	252	60	e	e	NOUN
ejpam-6931	252	61	)	)	PUNCT
ejpam-6931	252	62	⪰	⪰	NOUN
ejpam-6931	252	63	e	e	X
ejpam-6931	252	64	(	(	PUNCT
ejpam-6931	252	65	ϱo	ϱo	PROPN
ejpam-6931	252	66	,	,	PUNCT
ejpam-6931	252	67	ϱon+1	ϱon+1	PROPN
ejpam-6931	252	68	,	,	PUNCT
ejpam-6931	252	69	e	e	X
ejpam-6931	252	70	2	2	NUM
ejpam-6931	252	71	)	)	PUNCT
ejpam-6931	252	72	∗	∗	NOUN
ejpam-6931	252	73	e	e	X
ejpam-6931	252	74	(	(	PUNCT
ejpam-6931	252	75	ϱon+1	ϱon+1	PROPN
ejpam-6931	252	76	,	,	PUNCT
ejpam-6931	252	77	hϱ	hϱ	PRON
ejpam-6931	252	78	o	o	NOUN
ejpam-6931	252	79	,	,	PUNCT
ejpam-6931	252	80	e	e	X
ejpam-6931	252	81	2	2	NUM
ejpam-6931	252	82	)	)	PUNCT
ejpam-6931	252	83	=	=	SYM
ejpam-6931	252	84	e	e	X
ejpam-6931	252	85	(	(	PUNCT
ejpam-6931	252	86	ϱo	ϱo	PROPN
ejpam-6931	252	87	,	,	PUNCT
ejpam-6931	252	88	ϱon+1	ϱon+1	PROPN
ejpam-6931	252	89	,	,	PUNCT
ejpam-6931	252	90	c	c	PROPN
ejpam-6931	252	91	2	2	NUM
ejpam-6931	252	92	)	)	PUNCT
ejpam-6931	252	93	∗	∗	NOUN
ejpam-6931	252	94	e	e	NOUN
ejpam-6931	252	95	(	(	PUNCT
ejpam-6931	252	96	hϱon	hϱon	PROPN
ejpam-6931	252	97	,	,	PUNCT
ejpam-6931	252	98	hϱ	hϱ	PRON
ejpam-6931	252	99	o	o	NOUN
ejpam-6931	252	100	,	,	PUNCT
ejpam-6931	252	101	c	c	PROPN
ejpam-6931	252	102	2	2	NUM
ejpam-6931	252	103	)	)	PUNCT
ejpam-6931	252	104	⪰	⪰	NOUN
ejpam-6931	252	105	e	e	X
ejpam-6931	252	106	(	(	PUNCT
ejpam-6931	252	107	ϱo	ϱo	PROPN
ejpam-6931	252	108	,	,	PUNCT
ejpam-6931	252	109	ϱon+1	ϱon+1	PROPN
ejpam-6931	252	110	,	,	PUNCT
ejpam-6931	252	111	e	e	X
ejpam-6931	252	112	2	2	NUM
ejpam-6931	252	113	)	)	PUNCT
ejpam-6931	252	114	∗	∗	NOUN
ejpam-6931	252	115	e	e	X
ejpam-6931	252	116	(	(	PUNCT
ejpam-6931	252	117	ϱon	ϱon	PROPN
ejpam-6931	252	118	,	,	PUNCT
ejpam-6931	252	119	ϱ	ϱ	ADP
ejpam-6931	252	120	o	o	PROPN
ejpam-6931	252	121	,	,	PUNCT
ejpam-6931	252	122	e	e	PROPN
ejpam-6931	252	123	2k	2k	NUM
ejpam-6931	252	124	)	)	PUNCT
ejpam-6931	252	125	,	,	PUNCT
ejpam-6931	252	126	g(ϱo	g(ϱo	PROPN
ejpam-6931	252	127	,	,	PUNCT
ejpam-6931	252	128	hϱo	hϱo	ADJ
ejpam-6931	252	129	,	,	PUNCT
ejpam-6931	252	130	e	e	NOUN
ejpam-6931	252	131	)	)	PUNCT
ejpam-6931	252	132	⪯	⪯	NOUN
ejpam-6931	252	133	g	g	PROPN
ejpam-6931	252	134	(	(	PUNCT
ejpam-6931	252	135	ϱo	ϱo	PROPN
ejpam-6931	252	136	,	,	PUNCT
ejpam-6931	252	137	ϱon+1	ϱon+1	PROPN
ejpam-6931	252	138	,	,	PUNCT
ejpam-6931	252	139	e	e	X
ejpam-6931	252	140	2	2	NUM
ejpam-6931	252	141	)	)	PUNCT
ejpam-6931	252	142	△	△	PROPN
ejpam-6931	252	143	g	g	PROPN
ejpam-6931	252	144	(	(	PUNCT
ejpam-6931	252	145	ϱon+1	ϱon+1	PROPN
ejpam-6931	252	146	,	,	PUNCT
ejpam-6931	252	147	hϱ	hϱ	PRON
ejpam-6931	252	148	o	o	NOUN
ejpam-6931	252	149	,	,	PUNCT
ejpam-6931	252	150	e	e	X
ejpam-6931	252	151	2	2	NUM
ejpam-6931	252	152	)	)	PUNCT
ejpam-6931	252	153	s.	s.	PROPN
ejpam-6931	252	154	m.	m.	PROPN
ejpam-6931	252	155	u.	u.	PROPN
ejpam-6931	252	156	ud	ud	AUX
ejpam-6931	252	157	-	-	PUNCT
ejpam-6931	252	158	din	din	VERB
ejpam-6931	252	159	et	et	PROPN
ejpam-6931	252	160	al	al	PROPN
ejpam-6931	252	161	.	.	PUNCT
ejpam-6931	252	162	/	/	SYM
ejpam-6931	252	163	eur	eur	PROPN
ejpam-6931	252	164	.	.	PUNCT
ejpam-6931	253	1	j.	j.	PROPN
ejpam-6931	253	2	pure	pure	PROPN
ejpam-6931	253	3	appl	appl	PROPN
ejpam-6931	253	4	.	.	PROPN
ejpam-6931	253	5	math	math	PROPN
ejpam-6931	253	6	,	,	PUNCT
ejpam-6931	253	7	18	18	NUM
ejpam-6931	253	8	(	(	PUNCT
ejpam-6931	253	9	4	4	NUM
ejpam-6931	253	10	)	)	PUNCT
ejpam-6931	253	11	(	(	PUNCT
ejpam-6931	253	12	2025	2025	NUM
ejpam-6931	253	13	)	)	PUNCT
ejpam-6931	253	14	,	,	PUNCT
ejpam-6931	253	15	6931	6931	NUM
ejpam-6931	253	16	16	16	NUM
ejpam-6931	253	17	of	of	ADP
ejpam-6931	253	18	38	38	NUM
ejpam-6931	253	19	=	=	SYM
ejpam-6931	253	20	g	g	PROPN
ejpam-6931	253	21	(	(	PUNCT
ejpam-6931	253	22	ϱo	ϱo	PROPN
ejpam-6931	253	23	,	,	PUNCT
ejpam-6931	253	24	ϱon+1	ϱon+1	PROPN
ejpam-6931	253	25	,	,	PUNCT
ejpam-6931	253	26	e	e	X
ejpam-6931	253	27	2	2	NUM
ejpam-6931	253	28	)	)	PUNCT
ejpam-6931	253	29	△	△	PROPN
ejpam-6931	253	30	g	g	PROPN
ejpam-6931	253	31	(	(	PUNCT
ejpam-6931	253	32	hϱon	hϱon	PROPN
ejpam-6931	253	33	,	,	PUNCT
ejpam-6931	253	34	hϱ	hϱ	NOUN
ejpam-6931	253	35	o	o	NOUN
ejpam-6931	253	36	,	,	PUNCT
ejpam-6931	253	37	e	e	X
ejpam-6931	253	38	2	2	X
ejpam-6931	253	39	)	)	PUNCT
ejpam-6931	253	40	⪯	⪯	NOUN
ejpam-6931	253	41	g	g	PROPN
ejpam-6931	253	42	(	(	PUNCT
ejpam-6931	253	43	ϱo	ϱo	PROPN
ejpam-6931	253	44	,	,	PUNCT
ejpam-6931	253	45	ϱon+1	ϱon+1	PROPN
ejpam-6931	253	46	,	,	PUNCT
ejpam-6931	253	47	e	e	X
ejpam-6931	253	48	2	2	NUM
ejpam-6931	253	49	)	)	PUNCT
ejpam-6931	253	50	△	△	PROPN
ejpam-6931	253	51	g	g	PROPN
ejpam-6931	253	52	(	(	PUNCT
ejpam-6931	253	53	ϱon	ϱon	PROPN
ejpam-6931	253	54	,	,	PUNCT
ejpam-6931	253	55	ϱ	ϱ	ADP
ejpam-6931	253	56	o	o	PROPN
ejpam-6931	253	57	,	,	PUNCT
ejpam-6931	253	58	e	e	PROPN
ejpam-6931	253	59	2k	2k	NUM
ejpam-6931	253	60	)	)	PUNCT
ejpam-6931	253	61	,	,	PUNCT
ejpam-6931	253	62	and	and	CCONJ
ejpam-6931	253	63	h(ϱo	h(ϱo	ADJ
ejpam-6931	253	64	,	,	PUNCT
ejpam-6931	253	65	hϱo	hϱo	ADJ
ejpam-6931	253	66	,	,	PUNCT
ejpam-6931	253	67	e	e	NOUN
ejpam-6931	253	68	)	)	PUNCT
ejpam-6931	254	1	⪯	⪯	NOUN
ejpam-6931	254	2	h	h	PROPN
ejpam-6931	254	3	(	(	PUNCT
ejpam-6931	254	4	ϱo	ϱo	PROPN
ejpam-6931	254	5	,	,	PUNCT
ejpam-6931	254	6	ϱon+1	ϱon+1	PROPN
ejpam-6931	254	7	,	,	PUNCT
ejpam-6931	254	8	e	e	X
ejpam-6931	254	9	2	2	NUM
ejpam-6931	254	10	)	)	PUNCT
ejpam-6931	254	11	△	△	PROPN
ejpam-6931	254	12	h	h	NOUN
ejpam-6931	254	13	(	(	PUNCT
ejpam-6931	254	14	ϱon+1	ϱon+1	PROPN
ejpam-6931	254	15	,	,	PUNCT
ejpam-6931	254	16	hϱ	hϱ	PRON
ejpam-6931	254	17	o	o	NOUN
ejpam-6931	254	18	,	,	PUNCT
ejpam-6931	254	19	e	e	X
ejpam-6931	254	20	2	2	NUM
ejpam-6931	254	21	)	)	PUNCT
ejpam-6931	255	1	=	=	SYM
ejpam-6931	255	2	h	h	NOUN
ejpam-6931	255	3	(	(	PUNCT
ejpam-6931	255	4	ϱo	ϱo	PROPN
ejpam-6931	255	5	,	,	PUNCT
ejpam-6931	255	6	ϱon+1	ϱon+1	PROPN
ejpam-6931	255	7	,	,	PUNCT
ejpam-6931	255	8	e	e	X
ejpam-6931	255	9	2	2	NUM
ejpam-6931	255	10	)	)	PUNCT
ejpam-6931	255	11	△	△	PROPN
ejpam-6931	255	12	h	h	NOUN
ejpam-6931	255	13	(	(	PUNCT
ejpam-6931	255	14	hϱon	hϱon	PROPN
ejpam-6931	255	15	,	,	PUNCT
ejpam-6931	255	16	hϱ	hϱ	ADJ
ejpam-6931	255	17	o	o	NOUN
ejpam-6931	255	18	,	,	PUNCT
ejpam-6931	255	19	e	e	X
ejpam-6931	255	20	2	2	X
ejpam-6931	255	21	)	)	PUNCT
ejpam-6931	255	22	⪯	⪯	NOUN
ejpam-6931	255	23	h	h	PROPN
ejpam-6931	255	24	(	(	PUNCT
ejpam-6931	255	25	ϱo	ϱo	PROPN
ejpam-6931	255	26	,	,	PUNCT
ejpam-6931	255	27	ϱon+1	ϱon+1	PROPN
ejpam-6931	255	28	,	,	PUNCT
ejpam-6931	255	29	e	e	X
ejpam-6931	255	30	2	2	NUM
ejpam-6931	255	31	)	)	PUNCT
ejpam-6931	255	32	△	△	PROPN
ejpam-6931	255	33	h	h	NOUN
ejpam-6931	255	34	(	(	PUNCT
ejpam-6931	255	35	ϱon	ϱon	PROPN
ejpam-6931	255	36	,	,	PUNCT
ejpam-6931	255	37	ϱ	ϱ	ADP
ejpam-6931	255	38	o	o	PROPN
ejpam-6931	255	39	,	,	PUNCT
ejpam-6931	255	40	e	e	PROPN
ejpam-6931	255	41	2k	2k	NUM
ejpam-6931	255	42	)	)	PUNCT
ejpam-6931	255	43	.	.	PUNCT
ejpam-6931	256	1	now	now	ADV
ejpam-6931	256	2	considering	consider	VERB
ejpam-6931	256	3	the	the	DET
ejpam-6931	256	4	limit	limit	NOUN
ejpam-6931	256	5	as	as	ADP
ejpam-6931	256	6	n	n	PROPN
ejpam-6931	256	7	→	→	SYM
ejpam-6931	256	8	∞	∞	NUM
ejpam-6931	256	9	for	for	ADP
ejpam-6931	256	10	both	both	DET
ejpam-6931	256	11	given	give	VERB
ejpam-6931	256	12	inequalities	inequality	NOUN
ejpam-6931	256	13	,	,	PUNCT
ejpam-6931	256	14	utilizing	utilize	VERB
ejpam-6931	256	15	equation	equation	NOUN
ejpam-6931	256	16	(	(	PUNCT
ejpam-6931	256	17	5	5	NUM
ejpam-6931	256	18	)	)	PUNCT
ejpam-6931	256	19	together	together	ADV
ejpam-6931	256	20	with	with	ADP
ejpam-6931	256	21	remarks	remark	NOUN
ejpam-6931	256	22	2	2	NUM
ejpam-6931	256	23	,	,	PUNCT
ejpam-6931	256	24	for	for	ADP
ejpam-6931	256	25	any	any	DET
ejpam-6931	256	26	e	e	PROPN
ejpam-6931	256	27	∈	∈	PROPN
ejpam-6931	256	28	s0	s0	PROPN
ejpam-6931	256	29	,	,	PUNCT
ejpam-6931	256	30	it	it	PRON
ejpam-6931	256	31	follows	follow	VERB
ejpam-6931	256	32	that	that	SCONJ
ejpam-6931	256	33	e(ϱo	e(ϱo	NOUN
ejpam-6931	256	34	,	,	PUNCT
ejpam-6931	256	35	hϱo	hϱo	INTJ
ejpam-6931	256	36	,	,	PUNCT
ejpam-6931	256	37	e	e	NOUN
ejpam-6931	256	38	)	)	PUNCT
ejpam-6931	256	39	=	=	SYM
ejpam-6931	256	40	ℑ	ℑ	PROPN
ejpam-6931	256	41	,	,	PUNCT
ejpam-6931	256	42	g(ϱo	g(ϱo	PROPN
ejpam-6931	256	43	,	,	PUNCT
ejpam-6931	256	44	hϱo	hϱo	ADJ
ejpam-6931	256	45	,	,	PUNCT
ejpam-6931	256	46	e	e	NOUN
ejpam-6931	256	47	)	)	PUNCT
ejpam-6931	256	48	=	=	SYM
ejpam-6931	256	49	∅	∅	NOUN
ejpam-6931	256	50	and	and	CCONJ
ejpam-6931	256	51	h(ϱo	h(ϱo	ADJ
ejpam-6931	256	52	,	,	PUNCT
ejpam-6931	256	53	hϱo	hϱo	ADJ
ejpam-6931	256	54	,	,	PUNCT
ejpam-6931	256	55	e	e	NOUN
ejpam-6931	256	56	)	)	PUNCT
ejpam-6931	256	57	=	=	PUNCT
ejpam-6931	256	58	∅.	∅.	NOUN
ejpam-6931	256	59	by	by	ADP
ejpam-6931	256	60	conditions	condition	NOUN
ejpam-6931	256	61	(	(	PUNCT
ejpam-6931	256	62	3	3	NUM
ejpam-6931	256	63	)	)	PUNCT
ejpam-6931	256	64	,	,	PUNCT
ejpam-6931	256	65	(	(	PUNCT
ejpam-6931	256	66	8)	8)	NUM
ejpam-6931	256	67	,	,	PUNCT
ejpam-6931	256	68	and	and	CCONJ
ejpam-6931	256	69	(	(	PUNCT
ejpam-6931	256	70	11	11	NUM
ejpam-6931	256	71	)	)	PUNCT
ejpam-6931	256	72	of	of	ADP
ejpam-6931	256	73	definition	definition	NOUN
ejpam-6931	256	74	7	7	NUM
ejpam-6931	256	75	,	,	PUNCT
ejpam-6931	256	76	it	it	PRON
ejpam-6931	256	77	can	can	AUX
ejpam-6931	256	78	be	be	AUX
ejpam-6931	256	79	concluded	conclude	VERB
ejpam-6931	256	80	that	that	SCONJ
ejpam-6931	256	81	ϱo	ϱo	PROPN
ejpam-6931	256	82	is	be	AUX
ejpam-6931	256	83	equal	equal	ADJ
ejpam-6931	256	84	to	to	ADP
ejpam-6931	256	85	hϱo	hϱo	VERB
ejpam-6931	256	86	,	,	PUNCT
ejpam-6931	256	87	indicating	indicate	VERB
ejpam-6931	256	88	that	that	SCONJ
ejpam-6931	256	89	ϱo	ϱo	PROPN
ejpam-6931	256	90	is	be	AUX
ejpam-6931	256	91	a	a	DET
ejpam-6931	256	92	fixed	fixed	ADJ
ejpam-6931	256	93	point	point	NOUN
ejpam-6931	256	94	of	of	ADP
ejpam-6931	256	95	h.	h.	NOUN
ejpam-6931	256	96	to	to	PART
ejpam-6931	256	97	demonstrate	demonstrate	VERB
ejpam-6931	256	98	uniqueness	uniqueness	NOUN
ejpam-6931	256	99	,	,	PUNCT
ejpam-6931	256	100	let	let	VERB
ejpam-6931	256	101	us	we	PRON
ejpam-6931	256	102	assume	assume	VERB
ejpam-6931	256	103	that	that	SCONJ
ejpam-6931	256	104	z	z	PROPN
ejpam-6931	256	105	and	and	CCONJ
ejpam-6931	256	106	ϱo	ϱo	PROPN
ejpam-6931	256	107	are	be	AUX
ejpam-6931	256	108	two	two	NUM
ejpam-6931	256	109	distinct	distinct	ADJ
ejpam-6931	256	110	fixed	fix	VERB
ejpam-6931	256	111	points	point	NOUN
ejpam-6931	256	112	of	of	ADP
ejpam-6931	256	113	h.	h.	PROPN
ejpam-6931	256	114	this	this	PRON
ejpam-6931	256	115	indicates	indicate	VERB
ejpam-6931	256	116	that	that	SCONJ
ejpam-6931	256	117	there	there	PRON
ejpam-6931	256	118	are	be	VERB
ejpam-6931	256	119	some	some	DET
ejpam-6931	256	120	elements	element	NOUN
ejpam-6931	256	121	e′	e′	X
ejpam-6931	256	122	∈	∈	PROPN
ejpam-6931	256	123	s0	s0	PROPN
ejpam-6931	256	124	for	for	ADP
ejpam-6931	256	125	which	which	PRON
ejpam-6931	256	126	e(ϱo	e(ϱo	SYM
ejpam-6931	256	127	,	,	PUNCT
ejpam-6931	256	128	z	z	NOUN
ejpam-6931	256	129	,	,	PUNCT
ejpam-6931	256	130	e′	e′	ADJ
ejpam-6931	256	131	)	)	PUNCT
ejpam-6931	256	132	̸=	̸=	PROPN
ejpam-6931	256	133	ℑ,g(ϱo	ℑ,g(ϱo	NUM
ejpam-6931	256	134	,	,	PUNCT
ejpam-6931	256	135	z	z	NOUN
ejpam-6931	256	136	,	,	PUNCT
ejpam-6931	256	137	e′	e′	ADJ
ejpam-6931	256	138	)	)	PUNCT
ejpam-6931	256	139	̸=	̸=	NOUN
ejpam-6931	256	140	∅	∅	NOUN
ejpam-6931	256	141	and	and	CCONJ
ejpam-6931	256	142	h(ϱo	h(ϱo	ADJ
ejpam-6931	256	143	,	,	PUNCT
ejpam-6931	256	144	z	z	NOUN
ejpam-6931	256	145	,	,	PUNCT
ejpam-6931	256	146	e′	e′	ADJ
ejpam-6931	256	147	)	)	PUNCT
ejpam-6931	257	1	̸=	̸=	PROPN
ejpam-6931	257	2	∅.	∅.	ADV
ejpam-6931	257	3	by	by	ADP
ejpam-6931	257	4	iteratively	iteratively	ADV
ejpam-6931	257	5	applying	apply	VERB
ejpam-6931	257	6	equation	equation	NOUN
ejpam-6931	257	7	(	(	PUNCT
ejpam-6931	257	8	1	1	NUM
ejpam-6931	257	9	)	)	PUNCT
ejpam-6931	257	10	,	,	PUNCT
ejpam-6931	257	11	for	for	ADP
ejpam-6931	257	12	every	every	DET
ejpam-6931	257	13	n	n	NOUN
ejpam-6931	257	14	∈	∈	NOUN
ejpam-6931	257	15	m	m	VERB
ejpam-6931	257	16	we	we	PRON
ejpam-6931	257	17	obtain	obtain	VERB
ejpam-6931	257	18	e(ϱo	e(ϱo	NOUN
ejpam-6931	257	19	,	,	PUNCT
ejpam-6931	257	20	z	z	NOUN
ejpam-6931	257	21	,	,	PUNCT
ejpam-6931	257	22	e′	e′	ADJ
ejpam-6931	257	23	)	)	PUNCT
ejpam-6931	257	24	=	=	SYM
ejpam-6931	257	25	e(hϱo	e(hϱo	PROPN
ejpam-6931	257	26	,	,	PUNCT
ejpam-6931	257	27	hz	hz	VERB
ejpam-6931	257	28	,	,	PUNCT
ejpam-6931	257	29	e′	e′	ADJ
ejpam-6931	257	30	)	)	PUNCT
ejpam-6931	257	31	⪰	⪰	NOUN
ejpam-6931	257	32	e(ϱo	e(ϱo	NOUN
ejpam-6931	257	33	,	,	PUNCT
ejpam-6931	257	34	z	z	NOUN
ejpam-6931	257	35	,	,	PUNCT
ejpam-6931	257	36	e	e	NOUN
ejpam-6931	257	37	′	′	NUM
ejpam-6931	257	38	k	k	NOUN
ejpam-6931	257	39	)	)	PUNCT
ejpam-6931	257	40	⪰	⪰	NOUN
ejpam-6931	257	41	e(ϱo	e(ϱo	NOUN
ejpam-6931	257	42	,	,	PUNCT
ejpam-6931	257	43	z	z	NOUN
ejpam-6931	257	44	,	,	PUNCT
ejpam-6931	257	45	e	e	NOUN
ejpam-6931	257	46	′	′	NUM
ejpam-6931	257	47	k2	k2	PROPN
ejpam-6931	257	48	)	)	PUNCT
ejpam-6931	257	49	.	.	PUNCT
ejpam-6931	257	50	.	.	PUNCT
ejpam-6931	257	51	.	.	PUNCT
ejpam-6931	258	1	⪰	⪰	ADJ
ejpam-6931	258	2	e(ϱo	e(ϱo	NOUN
ejpam-6931	258	3	,	,	PUNCT
ejpam-6931	258	4	z	z	NOUN
ejpam-6931	258	5	,	,	PUNCT
ejpam-6931	258	6	e	e	NOUN
ejpam-6931	258	7	′	′	NUM
ejpam-6931	258	8	kn	kn	PROPN
ejpam-6931	258	9	)	)	PUNCT
ejpam-6931	258	10	g(ϱo	g(ϱo	PROPN
ejpam-6931	258	11	,	,	PUNCT
ejpam-6931	258	12	z	z	NOUN
ejpam-6931	258	13	,	,	PUNCT
ejpam-6931	258	14	e′	e′	ADJ
ejpam-6931	258	15	)	)	PUNCT
ejpam-6931	258	16	=	=	SYM
ejpam-6931	258	17	g(hϱo	g(hϱo	PROPN
ejpam-6931	258	18	,	,	PUNCT
ejpam-6931	258	19	hz	hz	VERB
ejpam-6931	258	20	,	,	PUNCT
ejpam-6931	258	21	e′	e′	ADJ
ejpam-6931	258	22	)	)	PUNCT
ejpam-6931	258	23	⪯	⪯	NOUN
ejpam-6931	258	24	g(ϱo	g(ϱo	PROPN
ejpam-6931	258	25	,	,	PUNCT
ejpam-6931	258	26	z	z	NOUN
ejpam-6931	258	27	,	,	PUNCT
ejpam-6931	258	28	e	e	NOUN
ejpam-6931	258	29	′	′	NUM
ejpam-6931	258	30	k	k	X
ejpam-6931	258	31	)	)	PUNCT
ejpam-6931	258	32	⪯	⪯	PROPN
ejpam-6931	258	33	g(ϱo	g(ϱo	PROPN
ejpam-6931	258	34	,	,	PUNCT
ejpam-6931	258	35	z	z	NOUN
ejpam-6931	258	36	,	,	PUNCT
ejpam-6931	258	37	e	e	NOUN
ejpam-6931	258	38	′	′	NUM
ejpam-6931	258	39	k2	k2	PROPN
ejpam-6931	258	40	)	)	PUNCT
ejpam-6931	258	41	.	.	PUNCT
ejpam-6931	258	42	.	.	PUNCT
ejpam-6931	258	43	.	.	PUNCT
ejpam-6931	259	1	⪯	⪯	PROPN
ejpam-6931	259	2	g(ϱo	g(ϱo	PROPN
ejpam-6931	259	3	,	,	PUNCT
ejpam-6931	259	4	z	z	PROPN
ejpam-6931	259	5	,	,	PUNCT
ejpam-6931	259	6	e	e	NOUN
ejpam-6931	259	7	′	′	NOUN
ejpam-6931	259	8	kn	kn	PROPN
ejpam-6931	259	9	)	)	PUNCT
ejpam-6931	260	1	s.	s.	PROPN
ejpam-6931	260	2	m.	m.	PROPN
ejpam-6931	260	3	u.	u.	PROPN
ejpam-6931	260	4	ud	ud	AUX
ejpam-6931	260	5	-	-	PUNCT
ejpam-6931	260	6	din	din	VERB
ejpam-6931	260	7	et	et	PROPN
ejpam-6931	260	8	al	al	PROPN
ejpam-6931	260	9	.	.	PUNCT
ejpam-6931	260	10	/	/	SYM
ejpam-6931	260	11	eur	eur	PROPN
ejpam-6931	260	12	.	.	PUNCT
ejpam-6931	261	1	j.	j.	PROPN
ejpam-6931	261	2	pure	pure	PROPN
ejpam-6931	261	3	appl	appl	PROPN
ejpam-6931	261	4	.	.	PROPN
ejpam-6931	261	5	math	math	PROPN
ejpam-6931	261	6	,	,	PUNCT
ejpam-6931	261	7	18	18	NUM
ejpam-6931	261	8	(	(	PUNCT
ejpam-6931	261	9	4	4	NUM
ejpam-6931	261	10	)	)	PUNCT
ejpam-6931	261	11	(	(	PUNCT
ejpam-6931	261	12	2025	2025	NUM
ejpam-6931	261	13	)	)	PUNCT
ejpam-6931	261	14	,	,	PUNCT
ejpam-6931	261	15	6931	6931	NUM
ejpam-6931	261	16	17	17	NUM
ejpam-6931	261	17	of	of	ADP
ejpam-6931	261	18	38	38	NUM
ejpam-6931	261	19	and	and	CCONJ
ejpam-6931	261	20	h(ϱo	h(ϱo	ADJ
ejpam-6931	261	21	,	,	PUNCT
ejpam-6931	261	22	z	z	NOUN
ejpam-6931	261	23	,	,	PUNCT
ejpam-6931	261	24	e′	e′	ADJ
ejpam-6931	261	25	)	)	PUNCT
ejpam-6931	261	26	=	=	SYM
ejpam-6931	261	27	ẃ(hϱo	ẃ(hϱo	PROPN
ejpam-6931	261	28	,	,	PUNCT
ejpam-6931	261	29	hz	hz	VERB
ejpam-6931	261	30	,	,	PUNCT
ejpam-6931	261	31	e′	e′	ADJ
ejpam-6931	261	32	)	)	PUNCT
ejpam-6931	261	33	⪯	⪯	NOUN
ejpam-6931	261	34	h(ϱo	h(ϱo	NOUN
ejpam-6931	261	35	,	,	PUNCT
ejpam-6931	261	36	z	z	NOUN
ejpam-6931	261	37	,	,	PUNCT
ejpam-6931	261	38	e′	e′	PROPN
ejpam-6931	261	39	k	k	X
ejpam-6931	261	40	)	)	PUNCT
ejpam-6931	261	41	⪯	⪯	PROPN
ejpam-6931	261	42	h(ϱo	h(ϱo	NOUN
ejpam-6931	261	43	,	,	PUNCT
ejpam-6931	261	44	z	z	PROPN
ejpam-6931	261	45	,	,	PUNCT
ejpam-6931	261	46	e′	e′	PROPN
ejpam-6931	261	47	k2	k2	PROPN
ejpam-6931	261	48	)	)	PUNCT
ejpam-6931	261	49	.	.	PUNCT
ejpam-6931	261	50	.	.	PUNCT
ejpam-6931	261	51	.	.	PUNCT
ejpam-6931	262	1	⪯	⪯	PROPN
ejpam-6931	262	2	h(ϱo	h(ϱo	PROPN
ejpam-6931	262	3	,	,	PUNCT
ejpam-6931	262	4	z	z	PROPN
ejpam-6931	262	5	,	,	PUNCT
ejpam-6931	262	6	e′	e′	PROPN
ejpam-6931	262	7	kn	kn	PROPN
ejpam-6931	262	8	)	)	PUNCT
ejpam-6931	262	9	.	.	PUNCT
ejpam-6931	263	1	consequently	consequently	ADV
ejpam-6931	263	2	,	,	PUNCT
ejpam-6931	263	3	we	we	PRON
ejpam-6931	263	4	derive	derive	VERB
ejpam-6931	263	5	that	that	SCONJ
ejpam-6931	263	6	e(ϱo	e(ϱo	NOUN
ejpam-6931	263	7	,	,	PUNCT
ejpam-6931	263	8	z	z	NOUN
ejpam-6931	263	9	,	,	PUNCT
ejpam-6931	263	10	e′	e′	ADJ
ejpam-6931	263	11	)	)	PUNCT
ejpam-6931	263	12	⪰	⪰	NOUN
ejpam-6931	263	13	e(ϱo	e(ϱo	NOUN
ejpam-6931	264	1	,	,	PUNCT
ejpam-6931	264	2	z	z	NOUN
ejpam-6931	264	3	,	,	PUNCT
ejpam-6931	264	4	e	e	NOUN
ejpam-6931	264	5	′	′	NOUN
ejpam-6931	264	6	kn	kn	NOUN
ejpam-6931	264	7	)	)	PUNCT
ejpam-6931	264	8	⪰	⪰	PROPN
ejpam-6931	264	9	inf	inf	PROPN
ejpam-6931	264	10	ν∈v	ν∈v	ADV
ejpam-6931	264	11	e(ϱo	e(ϱo	NOUN
ejpam-6931	264	12	,	,	PUNCT
ejpam-6931	264	13	z	z	NOUN
ejpam-6931	264	14	,	,	PUNCT
ejpam-6931	264	15	e	e	NOUN
ejpam-6931	264	16	′	′	NUM
ejpam-6931	264	17	kn	kn	PROPN
ejpam-6931	264	18	)	)	PUNCT
ejpam-6931	264	19	g(ϱo	g(ϱo	PROPN
ejpam-6931	264	20	,	,	PUNCT
ejpam-6931	264	21	z	z	NOUN
ejpam-6931	264	22	,	,	PUNCT
ejpam-6931	264	23	e′	e′	ADJ
ejpam-6931	264	24	)	)	PUNCT
ejpam-6931	264	25	⪯	⪯	NOUN
ejpam-6931	264	26	g(ϱo	g(ϱo	PROPN
ejpam-6931	264	27	,	,	PUNCT
ejpam-6931	264	28	z	z	NOUN
ejpam-6931	264	29	,	,	PUNCT
ejpam-6931	264	30	e	e	NOUN
ejpam-6931	264	31	′	′	NOUN
ejpam-6931	264	32	kn	kn	PROPN
ejpam-6931	264	33	)	)	PUNCT
ejpam-6931	264	34	⪯	⪯	NOUN
ejpam-6931	264	35	sup	sup	NOUN
ejpam-6931	264	36	ν∈v	ν∈v	ADV
ejpam-6931	264	37	g(ϱo	g(ϱo	NOUN
ejpam-6931	264	38	,	,	PUNCT
ejpam-6931	264	39	z	z	NOUN
ejpam-6931	264	40	,	,	PUNCT
ejpam-6931	264	41	e	e	NOUN
ejpam-6931	264	42	′	′	NUM
ejpam-6931	264	43	kn	kn	PROPN
ejpam-6931	264	44	)	)	PUNCT
ejpam-6931	264	45	and	and	CCONJ
ejpam-6931	264	46	h(ϱo	h(ϱo	ADJ
ejpam-6931	264	47	,	,	PUNCT
ejpam-6931	264	48	z	z	NOUN
ejpam-6931	264	49	,	,	PUNCT
ejpam-6931	264	50	e′	e′	ADJ
ejpam-6931	264	51	)	)	PUNCT
ejpam-6931	264	52	⪯	⪯	NOUN
ejpam-6931	264	53	h(ϱo	h(ϱo	NOUN
ejpam-6931	264	54	,	,	PUNCT
ejpam-6931	264	55	z	z	PROPN
ejpam-6931	264	56	,	,	PUNCT
ejpam-6931	264	57	e′	e′	PROPN
ejpam-6931	264	58	kn	kn	PROPN
ejpam-6931	264	59	)	)	PUNCT
ejpam-6931	264	60	⪯	⪯	NOUN
ejpam-6931	264	61	sup	sup	NOUN
ejpam-6931	264	62	ν∈v	ν∈v	ADV
ejpam-6931	264	63	h(ϱo	h(ϱo	ADV
ejpam-6931	264	64	,	,	PUNCT
ejpam-6931	264	65	z	z	NOUN
ejpam-6931	264	66	,	,	PUNCT
ejpam-6931	264	67	e′	e′	PROPN
ejpam-6931	264	68	kn	kn	PROPN
ejpam-6931	264	69	)	)	PUNCT
ejpam-6931	264	70	.	.	PUNCT
ejpam-6931	265	1	as	as	ADP
ejpam-6931	265	2	k	k	PROPN
ejpam-6931	265	3	∈	∈	PROPN
ejpam-6931	265	4	(	(	PUNCT
ejpam-6931	265	5	0	0	NUM
ejpam-6931	265	6	,	,	PUNCT
ejpam-6931	265	7	1	1	NUM
ejpam-6931	265	8	)	)	PUNCT
ejpam-6931	265	9	,	,	PUNCT
ejpam-6931	265	10	it	it	PRON
ejpam-6931	265	11	is	be	AUX
ejpam-6931	265	12	obvious	obvious	ADJ
ejpam-6931	265	13	that	that	SCONJ
ejpam-6931	265	14	limn→∞	limn→∞	PROPN
ejpam-6931	265	15	e′	e′	PROPN
ejpam-6931	265	16	kn	kn	PROPN
ejpam-6931	265	17	=	=	PUNCT
ejpam-6931	265	18	∞.	∞.	PROPN
ejpam-6931	265	19	so	so	ADV
ejpam-6931	265	20	by	by	ADP
ejpam-6931	265	21	assuming	assume	VERB
ejpam-6931	265	22	the	the	DET
ejpam-6931	265	23	limit	limit	NOUN
ejpam-6931	265	24	as	as	ADP
ejpam-6931	265	25	n	n	NOUN
ejpam-6931	265	26	approaches	approach	NOUN
ejpam-6931	265	27	infinity	infinity	NOUN
ejpam-6931	265	28	for	for	ADP
ejpam-6931	265	29	the	the	DET
ejpam-6931	265	30	above	above	ADJ
ejpam-6931	265	31	inequalities	inequality	NOUN
ejpam-6931	265	32	,	,	PUNCT
ejpam-6931	265	33	it	it	PRON
ejpam-6931	265	34	implies	imply	VERB
ejpam-6931	265	35	e(ϱo	e(ϱo	NOUN
ejpam-6931	265	36	,	,	PUNCT
ejpam-6931	265	37	z	z	NOUN
ejpam-6931	265	38	,	,	PUNCT
ejpam-6931	265	39	e′	e′	ADJ
ejpam-6931	265	40	)	)	PUNCT
ejpam-6931	265	41	=	=	SYM
ejpam-6931	265	42	ℑ	ℑ	PROPN
ejpam-6931	265	43	,	,	PUNCT
ejpam-6931	265	44	g(ϱo	g(ϱo	PROPN
ejpam-6931	265	45	,	,	PUNCT
ejpam-6931	265	46	z	z	NOUN
ejpam-6931	265	47	,	,	PUNCT
ejpam-6931	265	48	e′	e′	ADJ
ejpam-6931	265	49	)	)	PUNCT
ejpam-6931	265	50	=	=	SYM
ejpam-6931	265	51	∅	∅	NOUN
ejpam-6931	265	52	and	and	CCONJ
ejpam-6931	265	53	h(ϱo	h(ϱo	ADJ
ejpam-6931	265	54	,	,	PUNCT
ejpam-6931	265	55	z	z	NOUN
ejpam-6931	265	56	,	,	PUNCT
ejpam-6931	265	57	e′	e′	ADJ
ejpam-6931	265	58	)	)	PUNCT
ejpam-6931	266	1	=	=	NOUN
ejpam-6931	266	2	∅	∅	NOUN
ejpam-6931	266	3	which	which	PRON
ejpam-6931	266	4	is	be	AUX
ejpam-6931	266	5	a	a	DET
ejpam-6931	266	6	contradiction	contradiction	NOUN
ejpam-6931	266	7	.	.	PUNCT
ejpam-6931	267	1	thus	thus	ADV
ejpam-6931	267	2	e(ϱo	e(ϱo	ADV
ejpam-6931	267	3	,	,	PUNCT
ejpam-6931	267	4	z	z	NOUN
ejpam-6931	267	5	,	,	PUNCT
ejpam-6931	267	6	e	e	NOUN
ejpam-6931	267	7	)	)	PUNCT
ejpam-6931	267	8	=	=	SYM
ejpam-6931	267	9	ℑ,g(ϱo	ℑ,g(ϱo	ADJ
ejpam-6931	267	10	,	,	PUNCT
ejpam-6931	267	11	z	z	NOUN
ejpam-6931	267	12	,	,	PUNCT
ejpam-6931	267	13	e	e	NOUN
ejpam-6931	267	14	)	)	PUNCT
ejpam-6931	267	15	=	=	SYM
ejpam-6931	267	16	∅	∅	NOUN
ejpam-6931	267	17	and	and	CCONJ
ejpam-6931	267	18	h(ϱo	h(ϱo	ADJ
ejpam-6931	267	19	,	,	PUNCT
ejpam-6931	267	20	z	z	NOUN
ejpam-6931	267	21	,	,	PUNCT
ejpam-6931	267	22	e	e	NOUN
ejpam-6931	267	23	)	)	PUNCT
ejpam-6931	267	24	=	=	NOUN
ejpam-6931	267	25	∅	∅	NOUN
ejpam-6931	267	26	for	for	ADP
ejpam-6931	267	27	each	each	DET
ejpam-6931	267	28	e	e	PROPN
ejpam-6931	267	29	∈	∈	PROPN
ejpam-6931	267	30	s0	s0	PROPN
ejpam-6931	267	31	.	.	PUNCT
ejpam-6931	268	1	the	the	DET
ejpam-6931	268	2	uniqueness	uniqueness	NOUN
ejpam-6931	268	3	of	of	ADP
ejpam-6931	268	4	the	the	DET
ejpam-6931	268	5	fixed	fix	VERB
ejpam-6931	268	6	points	point	NOUN
ejpam-6931	268	7	of	of	ADP
ejpam-6931	268	8	h	h	NOUN
ejpam-6931	268	9	is	be	AUX
ejpam-6931	268	10	confirmed	confirm	VERB
ejpam-6931	268	11	by	by	ADP
ejpam-6931	268	12	the	the	DET
ejpam-6931	268	13	fact	fact	NOUN
ejpam-6931	268	14	that	that	SCONJ
ejpam-6931	268	15	ϱo	ϱo	PROPN
ejpam-6931	268	16	=	=	SYM
ejpam-6931	268	17	z	z	PROPN
ejpam-6931	268	18	,	,	PUNCT
ejpam-6931	268	19	as	as	SCONJ
ejpam-6931	268	20	deduced	deduce	VERB
ejpam-6931	268	21	from	from	ADP
ejpam-6931	268	22	the	the	DET
ejpam-6931	268	23	conditions	condition	NOUN
ejpam-6931	268	24	(	(	PUNCT
ejpam-6931	268	25	3	3	NUM
ejpam-6931	268	26	)	)	PUNCT
ejpam-6931	268	27	,	,	PUNCT
ejpam-6931	268	28	(	(	PUNCT
ejpam-6931	268	29	8)	8)	NUM
ejpam-6931	268	30	,	,	PUNCT
ejpam-6931	268	31	and	and	CCONJ
ejpam-6931	268	32	(	(	PUNCT
ejpam-6931	268	33	11	11	NUM
ejpam-6931	268	34	)	)	PUNCT
ejpam-6931	268	35	of	of	ADP
ejpam-6931	268	36	definitions	definition	NOUN
ejpam-6931	268	37	7	7	NUM
ejpam-6931	268	38	.	.	PUNCT
ejpam-6931	268	39	remark	remark	PROPN
ejpam-6931	268	40	4	4	NUM
ejpam-6931	268	41	.	.	PUNCT
ejpam-6931	269	1	the	the	DET
ejpam-6931	269	2	proof	proof	NOUN
ejpam-6931	269	3	of	of	ADP
ejpam-6931	269	4	theorem	theorem	ADJ
ejpam-6931	269	5	1	1	NUM
ejpam-6931	269	6	remains	remain	VERB
ejpam-6931	269	7	the	the	DET
ejpam-6931	269	8	same	same	ADJ
ejpam-6931	269	9	by	by	ADP
ejpam-6931	269	10	substituting	substitute	VERB
ejpam-6931	269	11	equation	equation	NOUN
ejpam-6931	269	12	(	(	PUNCT
ejpam-6931	269	13	1	1	NUM
ejpam-6931	269	14	)	)	PUNCT
ejpam-6931	269	15	with	with	ADP
ejpam-6931	269	16	the	the	DET
ejpam-6931	269	17	subsequently	subsequently	ADV
ejpam-6931	269	18	contractive	contractive	ADJ
ejpam-6931	269	19	condition	condition	NOUN
ejpam-6931	269	20	of	of	ADP
ejpam-6931	269	21	mapping	mapping	NOUN
ejpam-6931	269	22	h	h	NOUN
ejpam-6931	269	23	:	:	PUNCT
ejpam-6931	269	24	e(hϱo	e(hϱo	PROPN
ejpam-6931	269	25	,	,	PUNCT
ejpam-6931	269	26	hν	hν	NOUN
ejpam-6931	269	27	,	,	PUNCT
ejpam-6931	269	28	κ(e)e	κ(e)e	NOUN
ejpam-6931	269	29	)	)	PUNCT
ejpam-6931	269	30	⪰	⪰	NOUN
ejpam-6931	269	31	e(ϱo	e(ϱo	NOUN
ejpam-6931	269	32	,	,	PUNCT
ejpam-6931	269	33	ν	ν	NOUN
ejpam-6931	269	34	,	,	PUNCT
ejpam-6931	269	35	e	e	NOUN
ejpam-6931	269	36	)	)	PUNCT
ejpam-6931	269	37	,	,	PUNCT
ejpam-6931	269	38	g(hϱo	g(hϱo	PROPN
ejpam-6931	269	39	,	,	PUNCT
ejpam-6931	269	40	hν	hν	NOUN
ejpam-6931	269	41	,	,	PUNCT
ejpam-6931	269	42	κ(e)e	κ(e)e	PROPN
ejpam-6931	269	43	)	)	PUNCT
ejpam-6931	269	44	⪯	⪯	NOUN
ejpam-6931	269	45	g(ϱo	g(ϱo	PROPN
ejpam-6931	269	46	,	,	PUNCT
ejpam-6931	269	47	ν	ν	PROPN
ejpam-6931	269	48	,	,	PUNCT
ejpam-6931	269	49	e	e	NOUN
ejpam-6931	269	50	)	)	PUNCT
ejpam-6931	269	51	and	and	CCONJ
ejpam-6931	269	52	h(hϱo	h(hϱo	VERB
ejpam-6931	269	53	,	,	PUNCT
ejpam-6931	269	54	hν	hν	NOUN
ejpam-6931	269	55	,	,	PUNCT
ejpam-6931	269	56	κ(e)e	κ(e)e	PROPN
ejpam-6931	269	57	)	)	PUNCT
ejpam-6931	269	58	⪯	⪯	NOUN
ejpam-6931	269	59	h(ϱo	h(ϱo	NOUN
ejpam-6931	269	60	,	,	PUNCT
ejpam-6931	269	61	ν	ν	NOUN
ejpam-6931	269	62	,	,	PUNCT
ejpam-6931	269	63	e	e	NOUN
ejpam-6931	269	64	)	)	PUNCT
ejpam-6931	269	65	.	.	PUNCT
ejpam-6931	270	1	for	for	ADP
ejpam-6931	270	2	each	each	DET
ejpam-6931	270	3	e	e	PROPN
ejpam-6931	270	4	∈	∈	PROPN
ejpam-6931	270	5	s0	s0	PROPN
ejpam-6931	270	6	and	and	CCONJ
ejpam-6931	270	7	ϱo	ϱo	PROPN
ejpam-6931	270	8	,	,	PUNCT
ejpam-6931	270	9	ν	ν	PROPN
ejpam-6931	270	10	∈	∈	PROPN
ejpam-6931	270	11	v	v	NOUN
ejpam-6931	270	12	,	,	PUNCT
ejpam-6931	270	13	κ	κ	PROPN
ejpam-6931	270	14	denotes	denote	VERB
ejpam-6931	270	15	a	a	DET
ejpam-6931	270	16	mapping	mapping	NOUN
ejpam-6931	270	17	from	from	ADP
ejpam-6931	270	18	s0	s0	PROPN
ejpam-6931	270	19	to	to	ADP
ejpam-6931	270	20	(	(	PUNCT
ejpam-6931	270	21	0	0	NUM
ejpam-6931	270	22	,	,	PUNCT
ejpam-6931	270	23	1	1	NUM
ejpam-6931	270	24	)	)	PUNCT
ejpam-6931	270	25	.	.	PUNCT
ejpam-6931	271	1	example	example	NOUN
ejpam-6931	272	1	6	6	NUM
ejpam-6931	272	2	.	.	PUNCT
ejpam-6931	272	3	assume	assume	VERB
ejpam-6931	272	4	that	that	SCONJ
ejpam-6931	272	5	(	(	PUNCT
ejpam-6931	272	6	v	v	NOUN
ejpam-6931	272	7	,	,	PUNCT
ejpam-6931	272	8	d	d	NOUN
ejpam-6931	272	9	)	)	PUNCT
ejpam-6931	272	10	is	be	AUX
ejpam-6931	272	11	a	a	DET
ejpam-6931	272	12	metric	metric	ADJ
ejpam-6931	272	13	space	space	NOUN
ejpam-6931	272	14	and	and	CCONJ
ejpam-6931	272	15	v	v	NOUN
ejpam-6931	272	16	=	=	SYM
ejpam-6931	273	1	[	[	X
ejpam-6931	273	2	0	0	NUM
ejpam-6931	273	3	,	,	PUNCT
ejpam-6931	273	4	1	1	NUM
ejpam-6931	273	5	]	]	PUNCT
ejpam-6931	273	6	combined	combine	VERB
ejpam-6931	273	7	with	with	ADP
ejpam-6931	273	8	d(ϱo	d(ϱo	PROPN
ejpam-6931	273	9	,	,	PUNCT
ejpam-6931	273	10	ν	ν	NOUN
ejpam-6931	273	11	)	)	PUNCT
ejpam-6931	273	12	=	=	SYM
ejpam-6931	273	13	|ϱo	|ϱo	PRON
ejpam-6931	273	14	−	−	PROPN
ejpam-6931	273	15	ν|	ν|	NOUN
ejpam-6931	273	16	for	for	ADP
ejpam-6931	273	17	each	each	DET
ejpam-6931	273	18	ϱo	ϱo	NOUN
ejpam-6931	273	19	,	,	PUNCT
ejpam-6931	273	20	ν	ν	PROPN
ejpam-6931	273	21	∈	∈	NOUN
ejpam-6931	273	22	v.	v.	CCONJ
ejpam-6931	273	23	define	define	VERB
ejpam-6931	273	24	the	the	DET
ejpam-6931	273	25	complex	complex	ADV
ejpam-6931	273	26	-	-	PUNCT
ejpam-6931	273	27	valued	value	VERB
ejpam-6931	273	28	t	t	NOUN
ejpam-6931	273	29	-	-	PUNCT
ejpam-6931	273	30	norm	norm	NOUN
ejpam-6931	273	31	∗	∗	NOUN
ejpam-6931	273	32	and	and	CCONJ
ejpam-6931	273	33	the	the	DET
ejpam-6931	273	34	complex	complex	ADV
ejpam-6931	273	35	-	-	PUNCT
ejpam-6931	273	36	valued	value	VERB
ejpam-6931	273	37	t	t	NOUN
ejpam-6931	273	38	-	-	PUNCT
ejpam-6931	273	39	conorm	conorm	NOUN
ejpam-6931	273	40	△	△	PROPN
ejpam-6931	273	41	by	by	ADP
ejpam-6931	273	42	ẃ1	ẃ1	NOUN
ejpam-6931	273	43	∗	∗	NOUN
ejpam-6931	273	44	ẃ2	ẃ2	NOUN
ejpam-6931	274	1	=	=	PUNCT
ejpam-6931	274	2	(	(	PUNCT
ejpam-6931	274	3	µ1µ2,κ1κ2	µ1µ2,κ1κ2	ADJ
ejpam-6931	274	4	)	)	PUNCT
ejpam-6931	274	5	and	and	CCONJ
ejpam-6931	274	6	ẃ1	ẃ1	NOUN
ejpam-6931	274	7	△	△	NOUN
ejpam-6931	274	8	ẃ2	ẃ2	NOUN
ejpam-6931	274	9	=	=	PUNCT
ejpam-6931	274	10	(	(	PUNCT
ejpam-6931	274	11	max{µ1	max{µ1	PROPN
ejpam-6931	274	12	,	,	PUNCT
ejpam-6931	274	13	µ2},max{κ1,κ2	µ2},max{κ1,κ2	NOUN
ejpam-6931	274	14	}	}	PUNCT
ejpam-6931	274	15	)	)	PUNCT
ejpam-6931	274	16	for	for	ADP
ejpam-6931	274	17	all	all	DET
ejpam-6931	274	18	ẃ1	ẃ1	NOUN
ejpam-6931	274	19	=	=	SYM
ejpam-6931	274	20	(	(	PUNCT
ejpam-6931	274	21	µ1,κ1	µ1,κ1	PROPN
ejpam-6931	274	22	)	)	PUNCT
ejpam-6931	274	23	,	,	PUNCT
ejpam-6931	274	24	ẃ2	ẃ2	NOUN
ejpam-6931	274	25	=	=	SYM
ejpam-6931	274	26	(	(	PUNCT
ejpam-6931	274	27	µ2,κ2	µ2,κ2	PROPN
ejpam-6931	274	28	)	)	PUNCT
ejpam-6931	274	29	∈	∈	PROPN
ejpam-6931	274	30	t	t	NOUN
ejpam-6931	274	31	respectively	respectively	ADV
ejpam-6931	274	32	.	.	PUNCT
ejpam-6931	275	1	define	define	VERB
ejpam-6931	275	2	complex	complex	ADV
ejpam-6931	275	3	-	-	PUNCT
ejpam-6931	275	4	valued	value	VERB
ejpam-6931	275	5	fuzzy	fuzzy	ADJ
ejpam-6931	275	6	sets	set	NOUN
ejpam-6931	275	7	e	e	NOUN
ejpam-6931	275	8	,	,	PUNCT
ejpam-6931	275	9	g	g	NOUN
ejpam-6931	275	10	,	,	PUNCT
ejpam-6931	275	11	and	and	CCONJ
ejpam-6931	275	12	h	h	NOUN
ejpam-6931	275	13	as	as	ADP
ejpam-6931	275	14	:	:	PUNCT
ejpam-6931	275	15	e(ϱo	e(ϱo	NOUN
ejpam-6931	275	16	,	,	PUNCT
ejpam-6931	275	17	ν	ν	NOUN
ejpam-6931	275	18	,	,	PUNCT
ejpam-6931	275	19	e	e	NOUN
ejpam-6931	275	20	)	)	PUNCT
ejpam-6931	276	1	=	=	NOUN
ejpam-6931	276	2	τξ	τξ	ADP
ejpam-6931	276	3	τξ	τξ	X
ejpam-6931	276	4	+	+	CCONJ
ejpam-6931	276	5	d(ϱo	d(ϱo	ADV
ejpam-6931	276	6	,	,	PUNCT
ejpam-6931	276	7	ν	ν	NOUN
ejpam-6931	276	8	)	)	PUNCT
ejpam-6931	276	9	ℑ	ℑ	PROPN
ejpam-6931	276	10	,	,	PUNCT
ejpam-6931	276	11	g(ϱo	g(ϱo	PROPN
ejpam-6931	276	12	,	,	PUNCT
ejpam-6931	276	13	ν	ν	NOUN
ejpam-6931	276	14	,	,	PUNCT
ejpam-6931	276	15	e	e	NOUN
ejpam-6931	276	16	)	)	PUNCT
ejpam-6931	276	17	=	=	SYM
ejpam-6931	276	18	d(ϱo	d(ϱo	PROPN
ejpam-6931	276	19	,	,	PUNCT
ejpam-6931	276	20	ν	ν	NOUN
ejpam-6931	276	21	)	)	PUNCT
ejpam-6931	276	22	τξ	τξ	NOUN
ejpam-6931	277	1	+	+	CCONJ
ejpam-6931	277	2	d(ϱo	d(ϱo	ADV
ejpam-6931	277	3	,	,	PUNCT
ejpam-6931	277	4	ν	ν	NOUN
ejpam-6931	277	5	)	)	PUNCT
ejpam-6931	277	6	ℑ	ℑ	PROPN
ejpam-6931	277	7	,	,	PUNCT
ejpam-6931	277	8	h(ϱo	h(ϱo	ADJ
ejpam-6931	277	9	,	,	PUNCT
ejpam-6931	277	10	ν	ν	NOUN
ejpam-6931	277	11	,	,	PUNCT
ejpam-6931	277	12	e	e	NOUN
ejpam-6931	277	13	)	)	PUNCT
ejpam-6931	277	14	=	=	SYM
ejpam-6931	277	15	d(ϱo	d(ϱo	PROPN
ejpam-6931	277	16	,	,	PUNCT
ejpam-6931	277	17	ν	ν	NOUN
ejpam-6931	277	18	)	)	PUNCT
ejpam-6931	277	19	τξ	τξ	ADJ
ejpam-6931	277	20	ℑ	ℑ	PROPN
ejpam-6931	277	21	,	,	PUNCT
ejpam-6931	277	22	s.	s.	PROPN
ejpam-6931	277	23	m.	m.	PROPN
ejpam-6931	277	24	u.	u.	PROPN
ejpam-6931	277	25	ud	ud	AUX
ejpam-6931	277	26	-	-	PUNCT
ejpam-6931	277	27	din	din	VERB
ejpam-6931	277	28	et	et	PROPN
ejpam-6931	277	29	al	al	PROPN
ejpam-6931	277	30	.	.	PUNCT
ejpam-6931	277	31	/	/	SYM
ejpam-6931	277	32	eur	eur	PROPN
ejpam-6931	277	33	.	.	PUNCT
ejpam-6931	278	1	j.	j.	PROPN
ejpam-6931	278	2	pure	pure	PROPN
ejpam-6931	278	3	appl	appl	PROPN
ejpam-6931	278	4	.	.	PROPN
ejpam-6931	278	5	math	math	PROPN
ejpam-6931	278	6	,	,	PUNCT
ejpam-6931	278	7	18	18	NUM
ejpam-6931	278	8	(	(	PUNCT
ejpam-6931	278	9	4	4	NUM
ejpam-6931	278	10	)	)	PUNCT
ejpam-6931	278	11	(	(	PUNCT
ejpam-6931	278	12	2025	2025	NUM
ejpam-6931	278	13	)	)	PUNCT
ejpam-6931	278	14	,	,	PUNCT
ejpam-6931	278	15	6931	6931	NUM
ejpam-6931	278	16	18	18	NUM
ejpam-6931	278	17	of	of	ADP
ejpam-6931	278	18	38	38	NUM
ejpam-6931	278	19	for	for	ADP
ejpam-6931	278	20	each	each	DET
ejpam-6931	278	21	ϱo	ϱo	NOUN
ejpam-6931	278	22	,	,	PUNCT
ejpam-6931	278	23	ν	ν	PROPN
ejpam-6931	278	24	∈	∈	PROPN
ejpam-6931	278	25	v	v	NOUN
ejpam-6931	278	26	and	and	CCONJ
ejpam-6931	278	27	e	e	NOUN
ejpam-6931	278	28	=	=	SYM
ejpam-6931	278	29	(	(	PUNCT
ejpam-6931	278	30	τ	τ	PROPN
ejpam-6931	278	31	,	,	PUNCT
ejpam-6931	278	32	ξ	ξ	X
ejpam-6931	278	33	)	)	PUNCT
ejpam-6931	278	34	∈	∈	PROPN
ejpam-6931	278	35	s0	s0	NOUN
ejpam-6931	278	36	.	.	PUNCT
ejpam-6931	279	1	it	it	PRON
ejpam-6931	279	2	is	be	AUX
ejpam-6931	279	3	simple	simple	ADJ
ejpam-6931	279	4	to	to	PART
ejpam-6931	279	5	prove	prove	VERB
ejpam-6931	279	6	that	that	SCONJ
ejpam-6931	279	7	(	(	PUNCT
ejpam-6931	279	8	v	v	NOUN
ejpam-6931	279	9	,	,	PUNCT
ejpam-6931	279	10	e	e	NOUN
ejpam-6931	279	11	,	,	PUNCT
ejpam-6931	279	12	g	g	PROPN
ejpam-6931	279	13	,	,	PUNCT
ejpam-6931	279	14	h	h	NOUN
ejpam-6931	279	15	,	,	PUNCT
ejpam-6931	279	16	⋆	⋆	NOUN
ejpam-6931	279	17	,	,	PUNCT
ejpam-6931	279	18	△	△	NOUN
ejpam-6931	279	19	)	)	PUNCT
ejpam-6931	279	20	is	be	AUX
ejpam-6931	279	21	a	a	DET
ejpam-6931	279	22	complete	complete	ADJ
ejpam-6931	279	23	cvnms	cvnms	NOUN
ejpam-6931	279	24	induced	induce	VERB
ejpam-6931	279	25	by	by	ADP
ejpam-6931	279	26	metric	metric	PROPN
ejpam-6931	279	27	d.	d.	PROPN
ejpam-6931	279	28	let	let	VERB
ejpam-6931	279	29	us	we	PRON
ejpam-6931	279	30	consider	consider	VERB
ejpam-6931	279	31	a	a	DET
ejpam-6931	279	32	sequence	sequence	NOUN
ejpam-6931	279	33	{	{	PUNCT
ejpam-6931	279	34	en	en	NOUN
ejpam-6931	279	35	}	}	PUNCT
ejpam-6931	279	36	∈	∈	NOUN
ejpam-6931	279	37	s0	s0	NOUN
ejpam-6931	279	38	where	where	SCONJ
ejpam-6931	279	39	each	each	DET
ejpam-6931	279	40	element	element	NOUN
ejpam-6931	279	41	en	en	X
ejpam-6931	279	42	=	=	SYM
ejpam-6931	279	43	(	(	PUNCT
ejpam-6931	279	44	τn	τn	PROPN
ejpam-6931	279	45	,	,	PUNCT
ejpam-6931	279	46	ξn	ξn	NOUN
ejpam-6931	279	47	)	)	PUNCT
ejpam-6931	279	48	for	for	ADP
ejpam-6931	279	49	n	n	DET
ejpam-6931	279	50	∈	∈	NOUN
ejpam-6931	279	51	m	m	VERB
ejpam-6931	279	52	is	be	AUX
ejpam-6931	279	53	arbitrary	arbitrary	ADJ
ejpam-6931	279	54	,	,	PUNCT
ejpam-6931	279	55	along	along	ADP
ejpam-6931	279	56	with	with	ADP
ejpam-6931	279	57	the	the	DET
ejpam-6931	279	58	fact	fact	NOUN
ejpam-6931	279	59	that	that	SCONJ
ejpam-6931	279	60	for	for	ADP
ejpam-6931	279	61	all	all	DET
ejpam-6931	279	62	ν	ν	PRON
ejpam-6931	279	63	∈	∈	PROPN
ejpam-6931	279	64	v	v	NOUN
ejpam-6931	279	65	,	,	PUNCT
ejpam-6931	279	66	0	0	NUM
ejpam-6931	279	67	≤	≤	NOUN
ejpam-6931	279	68	d(ϱo	d(ϱo	PROPN
ejpam-6931	279	69	,	,	PUNCT
ejpam-6931	279	70	ν	ν	NOUN
ejpam-6931	279	71	)	)	PUNCT
ejpam-6931	279	72	≤	≤	NUM
ejpam-6931	279	73	1	1	NUM
ejpam-6931	279	74	,	,	PUNCT
ejpam-6931	279	75	this	this	PRON
ejpam-6931	279	76	means	mean	VERB
ejpam-6931	279	77	that	that	SCONJ
ejpam-6931	279	78	ℑ	ℑ	PROPN
ejpam-6931	279	79	⪰	⪰	VERB
ejpam-6931	279	80	inf	inf	NOUN
ejpam-6931	279	81	ν∈v	ν∈v	ADV
ejpam-6931	279	82	e(ϱo	e(ϱo	NOUN
ejpam-6931	279	83	,	,	PUNCT
ejpam-6931	279	84	ν	ν	NOUN
ejpam-6931	279	85	,	,	PUNCT
ejpam-6931	279	86	en	en	ADJ
ejpam-6931	279	87	)	)	PUNCT
ejpam-6931	279	88	=	=	SYM
ejpam-6931	279	89	inf	inf	PROPN
ejpam-6931	279	90	ν∈v	ν∈v	ADV
ejpam-6931	279	91	τnξn	τnξn	AUX
ejpam-6931	279	92	τnξn	τnξn	VERB
ejpam-6931	279	93	+	+	X
ejpam-6931	279	94	d(ϱo	d(ϱo	ADJ
ejpam-6931	279	95	,	,	PUNCT
ejpam-6931	279	96	ν	ν	NOUN
ejpam-6931	279	97	)	)	PUNCT
ejpam-6931	279	98	ℑ	ℑ	NOUN
ejpam-6931	279	99	=	=	PUNCT
ejpam-6931	279	100	τnξn	τnξn	AUX
ejpam-6931	279	101	τnξn	τnξn	VERB
ejpam-6931	279	102	+	+	CCONJ
ejpam-6931	280	1	supν∈v	supν∈v	NOUN
ejpam-6931	280	2	d(ϱo	d(ϱo	PROPN
ejpam-6931	280	3	,	,	PUNCT
ejpam-6931	280	4	ν	ν	NOUN
ejpam-6931	280	5	)	)	PUNCT
ejpam-6931	280	6	ℑ	ℑ	PROPN
ejpam-6931	280	7	⪰	⪰	NOUN
ejpam-6931	280	8	τnξn	τnξn	VERB
ejpam-6931	280	9	τnξn	τnξn	VERB
ejpam-6931	280	10	+	+	X
ejpam-6931	280	11	1	1	NUM
ejpam-6931	280	12	ℑ.	ℑ.	NOUN
ejpam-6931	280	13	as	as	ADP
ejpam-6931	280	14	n	n	NUM
ejpam-6931	280	15	approaches	approach	NOUN
ejpam-6931	280	16	infinity	infinity	NOUN
ejpam-6931	280	17	,	,	PUNCT
ejpam-6931	280	18	we	we	PRON
ejpam-6931	280	19	have	have	VERB
ejpam-6931	280	20	ℑ	ℑ	PROPN
ejpam-6931	280	21	⪰	⪰	NOUN
ejpam-6931	280	22	lim	lim	PROPN
ejpam-6931	280	23	n→∞	n→∞	NUM
ejpam-6931	280	24	inf	inf	PROPN
ejpam-6931	280	25	ν∈v	ν∈v	NOUN
ejpam-6931	280	26	e(ϱo	e(ϱo	NOUN
ejpam-6931	280	27	,	,	PUNCT
ejpam-6931	280	28	ν	ν	NOUN
ejpam-6931	280	29	,	,	PUNCT
ejpam-6931	280	30	en	en	NOUN
ejpam-6931	280	31	)	)	PUNCT
ejpam-6931	280	32	⪰	⪰	NOUN
ejpam-6931	280	33	lim	lim	PROPN
ejpam-6931	280	34	n∈∞	n∈∞	PROPN
ejpam-6931	280	35	τnξn	τnξn	AUX
ejpam-6931	280	36	τnξn	τnξn	VERB
ejpam-6931	280	37	+	+	NUM
ejpam-6931	280	38	1	1	NUM
ejpam-6931	280	39	ℑ	ℑ	NOUN
ejpam-6931	280	40	=	=	SYM
ejpam-6931	280	41	ℑ	ℑ	VERB
ejpam-6931	280	42	the	the	DET
ejpam-6931	280	43	given	give	VERB
ejpam-6931	280	44	expression	expression	NOUN
ejpam-6931	280	45	implies	imply	VERB
ejpam-6931	280	46	that	that	SCONJ
ejpam-6931	280	47	limn→∞	limn→∞	PROPN
ejpam-6931	280	48	infν∈v	infν∈v	ADV
ejpam-6931	280	49	e(ϱo	e(ϱo	NOUN
ejpam-6931	280	50	,	,	PUNCT
ejpam-6931	280	51	ν	ν	NOUN
ejpam-6931	280	52	,	,	PUNCT
ejpam-6931	280	53	en	en	ADJ
ejpam-6931	280	54	)	)	PUNCT
ejpam-6931	280	55	=	=	SYM
ejpam-6931	280	56	ℑ.	ℑ.	NOUN
ejpam-6931	280	57	furthermore	furthermore	ADV
ejpam-6931	280	58	,	,	PUNCT
ejpam-6931	280	59	we	we	PRON
ejpam-6931	280	60	obtain	obtain	VERB
ejpam-6931	280	61	∅	∅	NOUN
ejpam-6931	280	62	⪯	⪯	NOUN
ejpam-6931	280	63	sup	sup	NOUN
ejpam-6931	280	64	ν∈v	ν∈v	ADV
ejpam-6931	280	65	g(ϱo	g(ϱo	NOUN
ejpam-6931	280	66	,	,	PUNCT
ejpam-6931	280	67	ν	ν	NOUN
ejpam-6931	280	68	,	,	PUNCT
ejpam-6931	280	69	en	en	ADJ
ejpam-6931	280	70	)	)	PUNCT
ejpam-6931	280	71	=	=	SYM
ejpam-6931	280	72	sup	sup	NOUN
ejpam-6931	280	73	ν∈v	ν∈v	ADV
ejpam-6931	280	74	d(ϱo	d(ϱo	NOUN
ejpam-6931	280	75	,	,	PUNCT
ejpam-6931	280	76	ν	ν	NOUN
ejpam-6931	280	77	)	)	PUNCT
ejpam-6931	280	78	τnξn	τnξn	VERB
ejpam-6931	280	79	+	+	X
ejpam-6931	280	80	d(ϱo	d(ϱo	ADJ
ejpam-6931	280	81	,	,	PUNCT
ejpam-6931	280	82	ν	ν	NOUN
ejpam-6931	280	83	)	)	PUNCT
ejpam-6931	280	84	ℑ	ℑ	NOUN
ejpam-6931	280	85	=	=	SYM
ejpam-6931	280	86	supν∈v	supν∈v	VERB
ejpam-6931	280	87	d(ϱo	d(ϱo	SYM
ejpam-6931	280	88	,	,	PUNCT
ejpam-6931	280	89	ν	ν	NOUN
ejpam-6931	280	90	)	)	PUNCT
ejpam-6931	280	91	τnξn	τnξn	VERB
ejpam-6931	280	92	+	+	X
ejpam-6931	280	93	infν∈v	infν∈v	ADV
ejpam-6931	280	94	d(ϱo	d(ϱo	PROPN
ejpam-6931	280	95	,	,	PUNCT
ejpam-6931	280	96	ν	ν	NOUN
ejpam-6931	280	97	)	)	PUNCT
ejpam-6931	280	98	ℑ	ℑ	NOUN
ejpam-6931	280	99	⪯	⪯	VERB
ejpam-6931	280	100	1	1	NUM
ejpam-6931	280	101	τnξn	τnξn	VERB
ejpam-6931	280	102	ℑ.	ℑ.	NOUN
ejpam-6931	280	103	as	as	ADP
ejpam-6931	280	104	n	n	NUM
ejpam-6931	280	105	approaches	approach	NOUN
ejpam-6931	280	106	infinity	infinity	NOUN
ejpam-6931	280	107	,	,	PUNCT
ejpam-6931	280	108	we	we	PRON
ejpam-6931	280	109	have	have	VERB
ejpam-6931	280	110	∅	∅	NOUN
ejpam-6931	280	111	⪯	⪯	PROPN
ejpam-6931	280	112	lim	lim	PROPN
ejpam-6931	280	113	n→∞	n→∞	NUM
ejpam-6931	280	114	sup	sup	NOUN
ejpam-6931	280	115	ν∈v	ν∈v	ADV
ejpam-6931	280	116	g(ϱo	g(ϱo	NOUN
ejpam-6931	280	117	,	,	PUNCT
ejpam-6931	280	118	ν	ν	NOUN
ejpam-6931	280	119	,	,	PUNCT
ejpam-6931	280	120	en	en	X
ejpam-6931	280	121	)	)	PUNCT
ejpam-6931	280	122	⪯	⪯	PROPN
ejpam-6931	280	123	lim	lim	PROPN
ejpam-6931	280	124	n∈∞	n∈∞	VERB
ejpam-6931	280	125	1	1	NUM
ejpam-6931	280	126	τnξn	τnξn	ADJ
ejpam-6931	280	127	ℑ	ℑ	NOUN
ejpam-6931	280	128	=	=	NOUN
ejpam-6931	280	129	∅	∅	VERB
ejpam-6931	280	130	the	the	DET
ejpam-6931	280	131	given	give	VERB
ejpam-6931	280	132	expression	expression	NOUN
ejpam-6931	280	133	implies	imply	VERB
ejpam-6931	280	134	that	that	SCONJ
ejpam-6931	280	135	limn→∞	limn→∞	PROPN
ejpam-6931	280	136	supν∈v	supν∈v	NOUN
ejpam-6931	280	137	g(ϱo	g(ϱo	ADJ
ejpam-6931	280	138	,	,	PUNCT
ejpam-6931	280	139	ν	ν	NOUN
ejpam-6931	280	140	,	,	PUNCT
ejpam-6931	280	141	en	en	X
ejpam-6931	280	142	)	)	PUNCT
ejpam-6931	280	143	=	=	PUNCT
ejpam-6931	280	144	∅.	∅.	NOUN
ejpam-6931	280	145	in	in	ADP
ejpam-6931	280	146	a	a	DET
ejpam-6931	280	147	similar	similar	ADJ
ejpam-6931	280	148	way	way	NOUN
ejpam-6931	280	149	,	,	PUNCT
ejpam-6931	280	150	we	we	PRON
ejpam-6931	280	151	have	have	VERB
ejpam-6931	280	152	∅	∅	NOUN
ejpam-6931	280	153	⪯	⪯	NOUN
ejpam-6931	280	154	sup	sup	VERB
ejpam-6931	280	155	ν∈v	ν∈v	ADV
ejpam-6931	280	156	h(ϱo	h(ϱo	ADV
ejpam-6931	280	157	,	,	PUNCT
ejpam-6931	280	158	ν	ν	NOUN
ejpam-6931	280	159	,	,	PUNCT
ejpam-6931	280	160	en	en	ADJ
ejpam-6931	280	161	)	)	PUNCT
ejpam-6931	280	162	=	=	SYM
ejpam-6931	280	163	sup	sup	NOUN
ejpam-6931	280	164	ν∈v	ν∈v	ADV
ejpam-6931	280	165	d(ϱo	d(ϱo	NOUN
ejpam-6931	280	166	,	,	PUNCT
ejpam-6931	280	167	ν	ν	NOUN
ejpam-6931	280	168	)	)	PUNCT
ejpam-6931	280	169	τnξn	τnξn	VERB
ejpam-6931	280	170	ℑ	ℑ	NOUN
ejpam-6931	280	171	=	=	SYM
ejpam-6931	280	172	supν∈v	supν∈v	VERB
ejpam-6931	280	173	d(ϱo	d(ϱo	SYM
ejpam-6931	280	174	,	,	PUNCT
ejpam-6931	280	175	ν	ν	NOUN
ejpam-6931	280	176	)	)	PUNCT
ejpam-6931	280	177	τnξn	τnξn	VERB
ejpam-6931	280	178	ℑ	ℑ	PROPN
ejpam-6931	280	179	⪯	⪯	VERB
ejpam-6931	280	180	1	1	NUM
ejpam-6931	280	181	τnξn	τnξn	VERB
ejpam-6931	280	182	ℑ.	ℑ.	PROPN
ejpam-6931	280	183	s.	s.	PROPN
ejpam-6931	280	184	m.	m.	PROPN
ejpam-6931	280	185	u.	u.	PROPN
ejpam-6931	280	186	ud	ud	AUX
ejpam-6931	280	187	-	-	PUNCT
ejpam-6931	280	188	din	din	VERB
ejpam-6931	280	189	et	et	PROPN
ejpam-6931	280	190	al	al	PROPN
ejpam-6931	280	191	.	.	PUNCT
ejpam-6931	280	192	/	/	SYM
ejpam-6931	280	193	eur	eur	PROPN
ejpam-6931	280	194	.	.	PUNCT
ejpam-6931	281	1	j.	j.	PROPN
ejpam-6931	281	2	pure	pure	PROPN
ejpam-6931	281	3	appl	appl	PROPN
ejpam-6931	281	4	.	.	PROPN
ejpam-6931	281	5	math	math	PROPN
ejpam-6931	281	6	,	,	PUNCT
ejpam-6931	281	7	18	18	NUM
ejpam-6931	281	8	(	(	PUNCT
ejpam-6931	281	9	4	4	NUM
ejpam-6931	281	10	)	)	PUNCT
ejpam-6931	281	11	(	(	PUNCT
ejpam-6931	281	12	2025	2025	NUM
ejpam-6931	281	13	)	)	PUNCT
ejpam-6931	281	14	,	,	PUNCT
ejpam-6931	281	15	6931	6931	NUM
ejpam-6931	281	16	19	19	NUM
ejpam-6931	281	17	of	of	ADP
ejpam-6931	281	18	38	38	NUM
ejpam-6931	281	19	as	as	ADP
ejpam-6931	281	20	n	n	NUM
ejpam-6931	281	21	approaches	approach	NOUN
ejpam-6931	281	22	infinity	infinity	NOUN
ejpam-6931	281	23	,	,	PUNCT
ejpam-6931	281	24	we	we	PRON
ejpam-6931	281	25	have	have	VERB
ejpam-6931	281	26	∅	∅	NOUN
ejpam-6931	281	27	⪯	⪯	PROPN
ejpam-6931	281	28	lim	lim	PROPN
ejpam-6931	281	29	n→∞	n→∞	NUM
ejpam-6931	281	30	sup	sup	NOUN
ejpam-6931	281	31	ν∈v	ν∈v	ADV
ejpam-6931	281	32	h(ϱo	h(ϱo	ADV
ejpam-6931	281	33	,	,	PUNCT
ejpam-6931	281	34	ν	ν	NOUN
ejpam-6931	281	35	,	,	PUNCT
ejpam-6931	281	36	en	en	X
ejpam-6931	281	37	)	)	PUNCT
ejpam-6931	281	38	⪯	⪯	PROPN
ejpam-6931	281	39	lim	lim	PROPN
ejpam-6931	281	40	n∈∞	n∈∞	VERB
ejpam-6931	281	41	1	1	NUM
ejpam-6931	281	42	τnξn	τnξn	ADJ
ejpam-6931	281	43	ℑ	ℑ	NOUN
ejpam-6931	281	44	=	=	NOUN
ejpam-6931	281	45	∅	∅	VERB
ejpam-6931	281	46	the	the	DET
ejpam-6931	281	47	given	give	VERB
ejpam-6931	281	48	expression	expression	NOUN
ejpam-6931	281	49	implies	imply	VERB
ejpam-6931	281	50	that	that	SCONJ
ejpam-6931	281	51	limn→∞	limn→∞	PROPN
ejpam-6931	281	52	supν∈vh(ϱo	supν∈vh(ϱo	NUM
ejpam-6931	281	53	,	,	PUNCT
ejpam-6931	281	54	ν	ν	NOUN
ejpam-6931	281	55	,	,	PUNCT
ejpam-6931	281	56	en	en	X
ejpam-6931	281	57	)	)	PUNCT
ejpam-6931	281	58	=	=	VERB
ejpam-6931	281	59	∅.	∅.	AUX
ejpam-6931	281	60	let	let	VERB
ejpam-6931	281	61	k	k	PROPN
ejpam-6931	281	62	be	be	AUX
ejpam-6931	281	63	a	a	DET
ejpam-6931	281	64	mapping	mapping	NOUN
ejpam-6931	281	65	from	from	ADP
ejpam-6931	281	66	v	v	NUM
ejpam-6931	281	67	to	to	ADP
ejpam-6931	281	68	v	v	ADP
ejpam-6931	281	69	which	which	PRON
ejpam-6931	281	70	defined	define	VERB
ejpam-6931	281	71	as	as	ADP
ejpam-6931	281	72	kϱo	kϱo	NOUN
ejpam-6931	281	73	=	=	NOUN
ejpam-6931	281	74	ϱo	ϱo	PRON
ejpam-6931	281	75	2	2	NUM
ejpam-6931	281	76	for	for	ADP
ejpam-6931	281	77	each	each	DET
ejpam-6931	281	78	ϱo	ϱo	PROPN
ejpam-6931	281	79	∈	∈	PROPN
ejpam-6931	282	1	v.	v.	CCONJ
ejpam-6931	282	2	if	if	SCONJ
ejpam-6931	282	3	we	we	PRON
ejpam-6931	282	4	choose	choose	VERB
ejpam-6931	282	5	a	a	DET
ejpam-6931	282	6	number	number	NOUN
ejpam-6931	282	7	k	k	PROPN
ejpam-6931	282	8	∈	∈	PROPN
ejpam-6931	283	1	[	[	X
ejpam-6931	283	2	1/2	1/2	NUM
ejpam-6931	283	3	,	,	PUNCT
ejpam-6931	283	4	1	1	NUM
ejpam-6931	283	5	)	)	PUNCT
ejpam-6931	283	6	⊂	⊂	PROPN
ejpam-6931	283	7	(	(	PUNCT
ejpam-6931	283	8	0	0	NUM
ejpam-6931	283	9	,	,	PUNCT
ejpam-6931	283	10	1	1	NUM
ejpam-6931	283	11	)	)	PUNCT
ejpam-6931	283	12	,	,	PUNCT
ejpam-6931	283	13	then	then	ADV
ejpam-6931	283	14	for	for	ADP
ejpam-6931	283	15	all	all	DET
ejpam-6931	283	16	ϱo	ϱo	PROPN
ejpam-6931	283	17	,	,	PUNCT
ejpam-6931	283	18	ν	ν	PROPN
ejpam-6931	283	19	∈	∈	PROPN
ejpam-6931	283	20	v	v	NOUN
ejpam-6931	283	21	and	and	CCONJ
ejpam-6931	283	22	e	e	NOUN
ejpam-6931	283	23	∈	∈	PROPN
ejpam-6931	283	24	s0	s0	PROPN
ejpam-6931	283	25	,	,	PUNCT
ejpam-6931	283	26	fulfills	fulfill	VERB
ejpam-6931	283	27	equation	equation	NOUN
ejpam-6931	283	28	(	(	PUNCT
ejpam-6931	283	29	1	1	NUM
ejpam-6931	283	30	)	)	PUNCT
ejpam-6931	283	31	.	.	PUNCT
ejpam-6931	284	1	however	however	ADV
ejpam-6931	284	2	,	,	PUNCT
ejpam-6931	284	3	since	since	SCONJ
ejpam-6931	284	4	2k	2k	PROPN
ejpam-6931	284	5	>	>	X
ejpam-6931	284	6	1	1	NUM
ejpam-6931	284	7	,	,	PUNCT
ejpam-6931	284	8	we	we	PRON
ejpam-6931	284	9	have	have	VERB
ejpam-6931	284	10	e(kϱo	e(kϱo	PROPN
ejpam-6931	284	11	,	,	PUNCT
ejpam-6931	284	12	kν	kν	PROPN
ejpam-6931	284	13	,	,	PUNCT
ejpam-6931	284	14	ke	ke	NOUN
ejpam-6931	284	15	)	)	PUNCT
ejpam-6931	284	16	=	=	SYM
ejpam-6931	285	1	kτξ	kτξ	PROPN
ejpam-6931	285	2	kτξ	kτξ	PROPN
ejpam-6931	285	3	+	+	CCONJ
ejpam-6931	285	4	d(kϱo	d(kϱo	PROPN
ejpam-6931	285	5	,	,	PUNCT
ejpam-6931	285	6	kν	kν	ADJ
ejpam-6931	285	7	)	)	PUNCT
ejpam-6931	285	8	ℑ	ℑ	NOUN
ejpam-6931	285	9	=	=	SYM
ejpam-6931	285	10	kτξ	kτξ	PROPN
ejpam-6931	285	11	kτξ	kτξ	NOUN
ejpam-6931	286	1	+	+	CCONJ
ejpam-6931	286	2	|ϱo2	|ϱo2	ADJ
ejpam-6931	286	3	−	−	NOUN
ejpam-6931	286	4	ν	ν	NOUN
ejpam-6931	286	5	2	2	NUM
ejpam-6931	286	6	|	|	ADV
ejpam-6931	286	7	ℑ	ℑ	PROPN
ejpam-6931	286	8	=	=	SYM
ejpam-6931	286	9	kτξ	kτξ	PROPN
ejpam-6931	287	1	kτξ	kτξ	NOUN
ejpam-6931	288	1	+	+	CCONJ
ejpam-6931	288	2	1	1	NUM
ejpam-6931	288	3	2	2	NUM
ejpam-6931	288	4	|ϱo	|ϱo	PRON
ejpam-6931	288	5	−	−	PROPN
ejpam-6931	288	6	ν|	ν|	PROPN
ejpam-6931	288	7	ℑ	ℑ	NOUN
ejpam-6931	288	8	=	=	SYM
ejpam-6931	289	1	2kτξ	2kτξ	NUM
ejpam-6931	289	2	2kτξ	2kτξ	NUM
ejpam-6931	289	3	+	+	CCONJ
ejpam-6931	289	4	|ϱo	|ϱo	NUM
ejpam-6931	289	5	−	−	PROPN
ejpam-6931	289	6	ν|	ν|	PROPN
ejpam-6931	289	7	ℑ	ℑ	PROPN
ejpam-6931	289	8	⪰	⪰	VERB
ejpam-6931	289	9	τξ	τξ	SCONJ
ejpam-6931	289	10	τξ	τξ	ADP
ejpam-6931	289	11	+	+	NUM
ejpam-6931	289	12	|ϱo	|ϱo	CCONJ
ejpam-6931	289	13	−	−	PROPN
ejpam-6931	289	14	ν|	ν|	ADJ
ejpam-6931	289	15	ℑ	ℑ	NOUN
ejpam-6931	289	16	=	=	SYM
ejpam-6931	289	17	e(ϱo	e(ϱo	X
ejpam-6931	289	18	,	,	PUNCT
ejpam-6931	289	19	ν	ν	NOUN
ejpam-6931	289	20	,	,	PUNCT
ejpam-6931	289	21	e	e	NOUN
ejpam-6931	289	22	)	)	PUNCT
ejpam-6931	289	23	for	for	ADP
ejpam-6931	289	24	any	any	DET
ejpam-6931	289	25	ϱo	ϱo	NOUN
ejpam-6931	289	26	,	,	PUNCT
ejpam-6931	289	27	ν	ν	PROPN
ejpam-6931	289	28	∈	∈	PROPN
ejpam-6931	289	29	v	v	NOUN
ejpam-6931	289	30	and	and	CCONJ
ejpam-6931	289	31	e	e	NOUN
ejpam-6931	289	32	=	=	SYM
ejpam-6931	289	33	(	(	PUNCT
ejpam-6931	289	34	τ	τ	PROPN
ejpam-6931	289	35	,	,	PUNCT
ejpam-6931	289	36	ξ	ξ	X
ejpam-6931	289	37	)	)	PUNCT
ejpam-6931	289	38	∈	∈	PROPN
ejpam-6931	289	39	s0	s0	PROPN
ejpam-6931	289	40	.	.	PUNCT
ejpam-6931	290	1	g(kϱo	g(kϱo	PROPN
ejpam-6931	290	2	,	,	PUNCT
ejpam-6931	290	3	kν	kν	PROPN
ejpam-6931	290	4	,	,	PUNCT
ejpam-6931	290	5	ke	ke	NOUN
ejpam-6931	290	6	)	)	PUNCT
ejpam-6931	290	7	=	=	PUNCT
ejpam-6931	291	1	d(kϱo	d(kϱo	PROPN
ejpam-6931	291	2	,	,	PUNCT
ejpam-6931	291	3	kν	kν	PROPN
ejpam-6931	291	4	)	)	PUNCT
ejpam-6931	291	5	kτξ	kτξ	PROPN
ejpam-6931	292	1	+	+	CCONJ
ejpam-6931	292	2	d(kϱo	d(kϱo	PROPN
ejpam-6931	292	3	,	,	PUNCT
ejpam-6931	292	4	kν	kν	ADJ
ejpam-6931	292	5	)	)	PUNCT
ejpam-6931	292	6	ℑ	ℑ	NOUN
ejpam-6931	292	7	=	=	SYM
ejpam-6931	292	8	|ϱ	|ϱ	ADJ
ejpam-6931	292	9	o	o	NOUN
ejpam-6931	292	10	2	2	NUM
ejpam-6931	292	11	−	−	NOUN
ejpam-6931	292	12	ν	ν	NOUN
ejpam-6931	292	13	2	2	NUM
ejpam-6931	292	14	|	|	ADV
ejpam-6931	292	15	kτξ	kτξ	NOUN
ejpam-6931	293	1	+	+	CCONJ
ejpam-6931	293	2	|ϱo2	|ϱo2	ADJ
ejpam-6931	293	3	−	−	NOUN
ejpam-6931	293	4	ν	ν	NOUN
ejpam-6931	293	5	2	2	NUM
ejpam-6931	293	6	|	|	NOUN
ejpam-6931	293	7	ℑ	ℑ	NOUN
ejpam-6931	293	8	=	=	SYM
ejpam-6931	293	9	1	1	NUM
ejpam-6931	293	10	2	2	NUM
ejpam-6931	293	11	|ϱ	|ϱ	ADJ
ejpam-6931	293	12	o	o	NOUN
ejpam-6931	293	13	−	−	PROPN
ejpam-6931	293	14	ν|	ν|	PROPN
ejpam-6931	293	15	kτξ	kτξ	NOUN
ejpam-6931	294	1	+	+	CCONJ
ejpam-6931	294	2	1	1	NUM
ejpam-6931	294	3	2	2	NUM
ejpam-6931	294	4	|ϱo	|ϱo	PRON
ejpam-6931	294	5	−	−	PROPN
ejpam-6931	294	6	ν|	ν|	PROPN
ejpam-6931	294	7	ℑ	ℑ	NOUN
ejpam-6931	294	8	=	=	SYM
ejpam-6931	294	9	|ϱo	|ϱo	PRON
ejpam-6931	294	10	−	−	PROPN
ejpam-6931	294	11	ν|	ν|	PROPN
ejpam-6931	294	12	2kτξ	2kτξ	NUM
ejpam-6931	294	13	+	+	CCONJ
ejpam-6931	294	14	|ϱo	|ϱo	NUM
ejpam-6931	294	15	−	−	PROPN
ejpam-6931	294	16	ν|	ν|	PROPN
ejpam-6931	294	17	ℑ	ℑ	PROPN
ejpam-6931	294	18	⪯	⪯	VERB
ejpam-6931	294	19	|ϱo	|ϱo	PRON
ejpam-6931	294	20	−	−	PROPN
ejpam-6931	294	21	ν|	ν|	NOUN
ejpam-6931	294	22	τξ	τξ	X
ejpam-6931	294	23	+	+	CCONJ
ejpam-6931	294	24	|ϱo	|ϱo	X
ejpam-6931	294	25	−	−	PROPN
ejpam-6931	294	26	ν|	ν|	PROPN
ejpam-6931	294	27	ℑ	ℑ	PROPN
ejpam-6931	294	28	=	=	SYM
ejpam-6931	294	29	g(ϱo	g(ϱo	PROPN
ejpam-6931	294	30	,	,	PUNCT
ejpam-6931	294	31	ν	ν	NOUN
ejpam-6931	294	32	,	,	PUNCT
ejpam-6931	294	33	e	e	NOUN
ejpam-6931	294	34	)	)	PUNCT
ejpam-6931	294	35	for	for	ADP
ejpam-6931	294	36	any	any	DET
ejpam-6931	294	37	ϱo	ϱo	NOUN
ejpam-6931	294	38	,	,	PUNCT
ejpam-6931	294	39	ν	ν	PROPN
ejpam-6931	294	40	∈	∈	PROPN
ejpam-6931	294	41	v	v	NOUN
ejpam-6931	294	42	and	and	CCONJ
ejpam-6931	294	43	e	e	NOUN
ejpam-6931	294	44	=	=	SYM
ejpam-6931	294	45	(	(	PUNCT
ejpam-6931	294	46	τ	τ	PROPN
ejpam-6931	294	47	,	,	PUNCT
ejpam-6931	294	48	ξ	ξ	X
ejpam-6931	294	49	)	)	PUNCT
ejpam-6931	294	50	∈	∈	PROPN
ejpam-6931	294	51	s0	s0	PROPN
ejpam-6931	294	52	.	.	PUNCT
ejpam-6931	295	1	h(kϱo	h(kϱo	PROPN
ejpam-6931	295	2	,	,	PUNCT
ejpam-6931	295	3	kν	kν	PROPN
ejpam-6931	295	4	,	,	PUNCT
ejpam-6931	295	5	ke	ke	NOUN
ejpam-6931	295	6	)	)	PUNCT
ejpam-6931	295	7	=	=	PUNCT
ejpam-6931	295	8	d(kϱo	d(kϱo	PROPN
ejpam-6931	295	9	,	,	PUNCT
ejpam-6931	295	10	kν	kν	PROPN
ejpam-6931	295	11	)	)	PUNCT
ejpam-6931	295	12	kτξ	kτξ	NOUN
ejpam-6931	295	13	ℑ	ℑ	PROPN
ejpam-6931	295	14	=	=	SYM
ejpam-6931	295	15	|ϱ	|ϱ	ADJ
ejpam-6931	295	16	o	o	NOUN
ejpam-6931	295	17	2	2	NUM
ejpam-6931	295	18	−	−	NOUN
ejpam-6931	295	19	ν	ν	NOUN
ejpam-6931	295	20	2	2	NUM
ejpam-6931	295	21	|	|	ADV
ejpam-6931	295	22	kτξ	kτξ	NOUN
ejpam-6931	296	1	ℑ	ℑ	PROPN
ejpam-6931	296	2	s.	s.	PROPN
ejpam-6931	296	3	m.	m.	PROPN
ejpam-6931	296	4	u.	u.	PROPN
ejpam-6931	296	5	ud	ud	AUX
ejpam-6931	296	6	-	-	PUNCT
ejpam-6931	296	7	din	din	VERB
ejpam-6931	296	8	et	et	PROPN
ejpam-6931	296	9	al	al	PROPN
ejpam-6931	296	10	.	.	PUNCT
ejpam-6931	296	11	/	/	SYM
ejpam-6931	296	12	eur	eur	PROPN
ejpam-6931	296	13	.	.	PUNCT
ejpam-6931	297	1	j.	j.	PROPN
ejpam-6931	297	2	pure	pure	PROPN
ejpam-6931	297	3	appl	appl	PROPN
ejpam-6931	297	4	.	.	PROPN
ejpam-6931	297	5	math	math	PROPN
ejpam-6931	297	6	,	,	PUNCT
ejpam-6931	297	7	18	18	NUM
ejpam-6931	297	8	(	(	PUNCT
ejpam-6931	297	9	4	4	NUM
ejpam-6931	297	10	)	)	PUNCT
ejpam-6931	297	11	(	(	PUNCT
ejpam-6931	297	12	2025	2025	NUM
ejpam-6931	297	13	)	)	PUNCT
ejpam-6931	297	14	,	,	PUNCT
ejpam-6931	297	15	6931	6931	NUM
ejpam-6931	297	16	20	20	NUM
ejpam-6931	297	17	of	of	ADP
ejpam-6931	297	18	38	38	NUM
ejpam-6931	297	19	=	=	SYM
ejpam-6931	297	20	1	1	NUM
ejpam-6931	297	21	2	2	NUM
ejpam-6931	297	22	|ϱ	|ϱ	ADJ
ejpam-6931	297	23	o	o	NOUN
ejpam-6931	297	24	−	−	ADP
ejpam-6931	297	25	ν|	ν|	ADJ
ejpam-6931	297	26	kτξ	kτξ	NOUN
ejpam-6931	297	27	ℑ	ℑ	PROPN
ejpam-6931	297	28	=	=	SYM
ejpam-6931	297	29	|ϱo	|ϱo	PRON
ejpam-6931	297	30	−	−	PROPN
ejpam-6931	297	31	ν|	ν|	NOUN
ejpam-6931	297	32	2kτξ	2kτξ	NUM
ejpam-6931	297	33	ℑ	ℑ	NOUN
ejpam-6931	297	34	⪯	⪯	VERB
ejpam-6931	297	35	|ϱo	|ϱo	PRON
ejpam-6931	297	36	−	−	PROPN
ejpam-6931	297	37	ν|	ν|	ADJ
ejpam-6931	297	38	τξ	τξ	ADJ
ejpam-6931	297	39	ℑ	ℑ	PROPN
ejpam-6931	297	40	=	=	SYM
ejpam-6931	297	41	h(ϱo	h(ϱo	ADJ
ejpam-6931	297	42	,	,	PUNCT
ejpam-6931	297	43	ν	ν	NOUN
ejpam-6931	297	44	,	,	PUNCT
ejpam-6931	297	45	c	c	NOUN
ejpam-6931	297	46	)	)	PUNCT
ejpam-6931	297	47	for	for	ADP
ejpam-6931	297	48	each	each	DET
ejpam-6931	297	49	e	e	NOUN
ejpam-6931	297	50	=	=	SYM
ejpam-6931	297	51	(	(	PUNCT
ejpam-6931	297	52	τ	τ	PROPN
ejpam-6931	297	53	,	,	PUNCT
ejpam-6931	297	54	ξ	ξ	X
ejpam-6931	297	55	)	)	PUNCT
ejpam-6931	297	56	∈	∈	PROPN
ejpam-6931	297	57	s0	s0	NOUN
ejpam-6931	297	58	and	and	CCONJ
ejpam-6931	297	59	ϱo	ϱo	PROPN
ejpam-6931	297	60	,	,	PUNCT
ejpam-6931	297	61	ν	ν	PROPN
ejpam-6931	297	62	∈	∈	PROPN
ejpam-6931	297	63	v.	v.	CCONJ
ejpam-6931	297	64	consequently	consequently	ADV
ejpam-6931	297	65	,	,	PUNCT
ejpam-6931	297	66	all	all	DET
ejpam-6931	297	67	the	the	DET
ejpam-6931	297	68	conditions	condition	NOUN
ejpam-6931	297	69	given	give	VERB
ejpam-6931	297	70	in	in	ADP
ejpam-6931	297	71	theorem	theorem	ADJ
ejpam-6931	297	72	1	1	NUM
ejpam-6931	297	73	are	be	AUX
ejpam-6931	297	74	met	meet	VERB
ejpam-6931	297	75	.	.	PUNCT
ejpam-6931	298	1	hence	hence	ADV
ejpam-6931	298	2	in	in	ADP
ejpam-6931	298	3	k	k	PROPN
ejpam-6931	298	4	,	,	PUNCT
ejpam-6931	298	5	0	0	NUM
ejpam-6931	298	6	is	be	AUX
ejpam-6931	298	7	the	the	DET
ejpam-6931	298	8	only	only	ADJ
ejpam-6931	298	9	fixed	fix	VERB
ejpam-6931	298	10	point	point	NOUN
ejpam-6931	298	11	.	.	PUNCT
ejpam-6931	299	1	the	the	DET
ejpam-6931	299	2	following	follow	VERB
ejpam-6931	299	3	example	example	NOUN
ejpam-6931	299	4	demonstrates	demonstrate	VERB
ejpam-6931	299	5	that	that	SCONJ
ejpam-6931	299	6	theorem	theorem	NOUN
ejpam-6931	299	7	1	1	NUM
ejpam-6931	299	8	is	be	AUX
ejpam-6931	299	9	not	not	PART
ejpam-6931	299	10	unnecessary	unnecessary	ADJ
ejpam-6931	299	11	.	.	PUNCT
ejpam-6931	299	12	example	example	NOUN
ejpam-6931	300	1	7	7	NUM
ejpam-6931	300	2	.	.	PUNCT
ejpam-6931	300	3	suppose	suppose	VERB
ejpam-6931	300	4	that	that	SCONJ
ejpam-6931	300	5	v	v	NOUN
ejpam-6931	300	6	is	be	AUX
ejpam-6931	300	7	equal	equal	ADJ
ejpam-6931	300	8	to	to	ADP
ejpam-6931	300	9	m.	m.	NOUN
ejpam-6931	300	10	we	we	PRON
ejpam-6931	300	11	define	define	VERB
ejpam-6931	300	12	two	two	NUM
ejpam-6931	300	13	binary	binary	ADJ
ejpam-6931	300	14	operations	operation	NOUN
ejpam-6931	300	15	,	,	PUNCT
ejpam-6931	300	16	⋆	⋆	NOUN
ejpam-6931	300	17	and	and	CCONJ
ejpam-6931	300	18	△	△	X
ejpam-6931	300	19	,	,	PUNCT
ejpam-6931	300	20	as	as	SCONJ
ejpam-6931	300	21	e1	e1	PROPN
ejpam-6931	300	22	⋆	⋆	NOUN
ejpam-6931	300	23	e2	e2	PROPN
ejpam-6931	300	24	=	=	SYM
ejpam-6931	300	25	(	(	PUNCT
ejpam-6931	300	26	τ1τ2	τ1τ2	X
ejpam-6931	300	27	,	,	PUNCT
ejpam-6931	300	28	ξ1ξ2	ξ1ξ2	PUNCT
ejpam-6931	300	29	)	)	PUNCT
ejpam-6931	300	30	and	and	CCONJ
ejpam-6931	300	31	e1	e1	PROPN
ejpam-6931	300	32	△	△	PROPN
ejpam-6931	300	33	e2	e2	PROPN
ejpam-6931	300	34	=	=	SYM
ejpam-6931	300	35	(	(	PUNCT
ejpam-6931	300	36	τ1	τ1	NOUN
ejpam-6931	300	37	+	+	CCONJ
ejpam-6931	300	38	τ2	τ2	ADJ
ejpam-6931	300	39	,	,	PUNCT
ejpam-6931	300	40	ξ1	ξ1	NOUN
ejpam-6931	300	41	+	+	CCONJ
ejpam-6931	300	42	ξ2)−	ξ2)−	NOUN
ejpam-6931	300	43	(	(	PUNCT
ejpam-6931	300	44	τ1τ2	τ1τ2	NOUN
ejpam-6931	300	45	,	,	PUNCT
ejpam-6931	300	46	ξ1ξ2	ξ1ξ2	NOUN
ejpam-6931	300	47	)	)	PUNCT
ejpam-6931	300	48	for	for	ADP
ejpam-6931	300	49	any	any	DET
ejpam-6931	300	50	ei	ei	NOUN
ejpam-6931	300	51	=	=	PUNCT
ejpam-6931	300	52	(	(	PUNCT
ejpam-6931	300	53	τi	τi	ADP
ejpam-6931	300	54	,	,	PUNCT
ejpam-6931	300	55	ξi	ξi	NOUN
ejpam-6931	300	56	)	)	PUNCT
ejpam-6931	300	57	∈	∈	PROPN
ejpam-6931	300	58	t	t	PROPN
ejpam-6931	300	59	for	for	ADP
ejpam-6931	300	60	i=1,2	i=1,2	PROPN
ejpam-6931	300	61	.	.	PUNCT
ejpam-6931	300	62	consider	consider	VERB
ejpam-6931	300	63	the	the	DET
ejpam-6931	300	64	cfss	cfss	ADJ
ejpam-6931	300	65	e	e	NOUN
ejpam-6931	300	66	,	,	PUNCT
ejpam-6931	300	67	g	g	NOUN
ejpam-6931	300	68	,	,	PUNCT
ejpam-6931	300	69	and	and	CCONJ
ejpam-6931	300	70	h	h	NOUN
ejpam-6931	300	71	,	,	PUNCT
ejpam-6931	300	72	which	which	PRON
ejpam-6931	300	73	are	be	AUX
ejpam-6931	300	74	defined	define	VERB
ejpam-6931	300	75	as	as	ADP
ejpam-6931	300	76	follows	follow	VERB
ejpam-6931	300	77	:	:	PUNCT
ejpam-6931	300	78	e(ϱo	e(ϱo	NOUN
ejpam-6931	300	79	,	,	PUNCT
ejpam-6931	300	80	ν	ν	NOUN
ejpam-6931	300	81	,	,	PUNCT
ejpam-6931	300	82	e	e	NOUN
ejpam-6931	300	83	)	)	PUNCT
ejpam-6931	300	84	=	=	SYM
ejpam-6931	300	85	min{ϱo	min{ϱo	NOUN
ejpam-6931	300	86	,	,	PUNCT
ejpam-6931	300	87	ν	ν	NOUN
ejpam-6931	300	88	}	}	PUNCT
ejpam-6931	300	89	max{ϱo	max{ϱo	NOUN
ejpam-6931	300	90	,	,	PUNCT
ejpam-6931	300	91	ν	ν	NOUN
ejpam-6931	300	92	}	}	PUNCT
ejpam-6931	300	93	ℑ	ℑ	PROPN
ejpam-6931	300	94	,	,	PUNCT
ejpam-6931	300	95	g(ϱo	g(ϱo	PROPN
ejpam-6931	300	96	,	,	PUNCT
ejpam-6931	300	97	ν	ν	NOUN
ejpam-6931	300	98	,	,	PUNCT
ejpam-6931	300	99	e	e	NOUN
ejpam-6931	300	100	)	)	PUNCT
ejpam-6931	300	101	=	=	SYM
ejpam-6931	300	102	(	(	PUNCT
ejpam-6931	300	103	1−	1−	NUM
ejpam-6931	300	104	min{ϱo	min{ϱo	NUM
ejpam-6931	300	105	,	,	PUNCT
ejpam-6931	300	106	ν	ν	NOUN
ejpam-6931	300	107	}	}	PUNCT
ejpam-6931	300	108	max{ϱo	max{ϱo	NOUN
ejpam-6931	300	109	,	,	PUNCT
ejpam-6931	300	110	ν	ν	NOUN
ejpam-6931	300	111	}	}	PUNCT
ejpam-6931	300	112	)	)	PUNCT
ejpam-6931	300	113	ℑ	ℑ	PROPN
ejpam-6931	300	114	,	,	PUNCT
ejpam-6931	300	115	h(ϱo	h(ϱo	ADJ
ejpam-6931	300	116	,	,	PUNCT
ejpam-6931	300	117	ν	ν	NOUN
ejpam-6931	300	118	,	,	PUNCT
ejpam-6931	300	119	e	e	NOUN
ejpam-6931	300	120	)	)	PUNCT
ejpam-6931	300	121	=	=	SYM
ejpam-6931	300	122	(	(	PUNCT
ejpam-6931	300	123	1−	1−	NUM
ejpam-6931	300	124	2min{ϱo	2min{ϱo	NUM
ejpam-6931	300	125	,	,	PUNCT
ejpam-6931	300	126	ν	ν	NOUN
ejpam-6931	300	127	}	}	PUNCT
ejpam-6931	300	128	min{ϱo	min{ϱo	NUM
ejpam-6931	300	129	,	,	PUNCT
ejpam-6931	300	130	ν}+max{ϱo	ν}+max{ϱo	ADV
ejpam-6931	300	131	,	,	PUNCT
ejpam-6931	300	132	ν	ν	NOUN
ejpam-6931	300	133	}	}	PUNCT
ejpam-6931	300	134	)	)	PUNCT
ejpam-6931	300	135	ℑ	ℑ	PROPN
ejpam-6931	300	136	,	,	PUNCT
ejpam-6931	300	137	for	for	ADP
ejpam-6931	300	138	each	each	DET
ejpam-6931	300	139	ϱo	ϱo	NOUN
ejpam-6931	300	140	,	,	PUNCT
ejpam-6931	300	141	ν	ν	PROPN
ejpam-6931	300	142	∈	∈	PROPN
ejpam-6931	300	143	v	v	NOUN
ejpam-6931	300	144	and	and	CCONJ
ejpam-6931	300	145	e	e	NOUN
ejpam-6931	300	146	=	=	SYM
ejpam-6931	300	147	(	(	PUNCT
ejpam-6931	300	148	τ	τ	PROPN
ejpam-6931	300	149	,	,	PUNCT
ejpam-6931	300	150	ξ	ξ	X
ejpam-6931	300	151	)	)	PUNCT
ejpam-6931	300	152	∈	∈	PROPN
ejpam-6931	300	153	s0	s0	NOUN
ejpam-6931	300	154	.	.	PUNCT
ejpam-6931	301	1	it	it	PRON
ejpam-6931	301	2	is	be	AUX
ejpam-6931	301	3	simple	simple	ADJ
ejpam-6931	301	4	to	to	PART
ejpam-6931	301	5	prove	prove	VERB
ejpam-6931	301	6	that	that	SCONJ
ejpam-6931	301	7	(	(	PUNCT
ejpam-6931	301	8	v	v	NOUN
ejpam-6931	301	9	,	,	PUNCT
ejpam-6931	301	10	e	e	NOUN
ejpam-6931	301	11	,	,	PUNCT
ejpam-6931	301	12	g	g	PROPN
ejpam-6931	301	13	,	,	PUNCT
ejpam-6931	301	14	h	h	NOUN
ejpam-6931	301	15	,	,	PUNCT
ejpam-6931	301	16	⋆	⋆	NOUN
ejpam-6931	301	17	,	,	PUNCT
ejpam-6931	301	18	△	△	NOUN
ejpam-6931	301	19	)	)	PUNCT
ejpam-6931	301	20	is	be	AUX
ejpam-6931	301	21	a	a	DET
ejpam-6931	301	22	complete	complete	ADJ
ejpam-6931	301	23	cvnms	cvnms	NOUN
ejpam-6931	301	24	.	.	PUNCT
ejpam-6931	302	1	for	for	ADP
ejpam-6931	302	2	any	any	DET
ejpam-6931	302	3	ϱo	ϱo	PROPN
ejpam-6931	302	4	∈	∈	PROPN
ejpam-6931	302	5	v	v	NOUN
ejpam-6931	302	6	,	,	PUNCT
ejpam-6931	302	7	consider	consider	VERB
ejpam-6931	302	8	a	a	DET
ejpam-6931	302	9	mapping	mapping	NOUN
ejpam-6931	302	10	k	k	NOUN
ejpam-6931	302	11	:	:	PUNCT
ejpam-6931	302	12	v	v	X
ejpam-6931	302	13	→	→	SYM
ejpam-6931	302	14	v	v	NUM
ejpam-6931	302	15	represented	represent	VERB
ejpam-6931	302	16	by	by	ADP
ejpam-6931	302	17	ϱo2	ϱo2	PROPN
ejpam-6931	302	18	+	+	PROPN
ejpam-6931	302	19	5	5	NUM
ejpam-6931	302	20	.	.	PUNCT
ejpam-6931	302	21	consider	consider	VERB
ejpam-6931	302	22	the	the	DET
ejpam-6931	302	23	sequence	sequence	NOUN
ejpam-6931	302	24	{	{	PUNCT
ejpam-6931	302	25	en	en	X
ejpam-6931	302	26	}	}	PUNCT
ejpam-6931	302	27	,	,	PUNCT
ejpam-6931	302	28	defined	define	VERB
ejpam-6931	302	29	as	as	ADP
ejpam-6931	302	30	en	en	X
ejpam-6931	302	31	=	=	SYM
ejpam-6931	302	32	(	(	PUNCT
ejpam-6931	302	33	n	n	CCONJ
ejpam-6931	302	34	,	,	PUNCT
ejpam-6931	302	35	n	n	CCONJ
ejpam-6931	302	36	)	)	PUNCT
ejpam-6931	302	37	for	for	ADP
ejpam-6931	302	38	all	all	DET
ejpam-6931	302	39	n	n	DET
ejpam-6931	302	40	∈	∈	NOUN
ejpam-6931	302	41	m.	m.	NOUN
ejpam-6931	302	42	the	the	DET
ejpam-6931	302	43	construction	construction	NOUN
ejpam-6931	302	44	of	of	ADP
ejpam-6931	302	45	en	en	X
ejpam-6931	302	46	ensures	ensure	NOUN
ejpam-6931	302	47	that	that	SCONJ
ejpam-6931	302	48	there	there	PRON
ejpam-6931	302	49	is	be	VERB
ejpam-6931	302	50	no	no	DET
ejpam-6931	302	51	ambiguity	ambiguity	NOUN
ejpam-6931	302	52	in	in	ADP
ejpam-6931	302	53	the	the	DET
ejpam-6931	302	54	expression	expression	NOUN
ejpam-6931	302	55	limn→∞	limn→∞	X
ejpam-6931	302	56	=	=	SYM
ejpam-6931	302	57	∞.	∞.	PROPN
ejpam-6931	302	58	for	for	ADP
ejpam-6931	302	59	every	every	DET
ejpam-6931	302	60	element	element	NOUN
ejpam-6931	302	61	ϱo	ϱo	NOUN
ejpam-6931	302	62	in	in	ADP
ejpam-6931	302	63	the	the	DET
ejpam-6931	302	64	set	set	NOUN
ejpam-6931	302	65	v	v	NOUN
ejpam-6931	302	66	,	,	PUNCT
ejpam-6931	302	67	with	with	ADP
ejpam-6931	302	68	a	a	DET
ejpam-6931	302	69	fixed	fix	VERB
ejpam-6931	302	70	element	element	NOUN
ejpam-6931	302	71	ν	ν	X
ejpam-6931	302	72	∈	∈	PROPN
ejpam-6931	302	73	v	v	ADP
ejpam-6931	302	74	such	such	ADJ
ejpam-6931	302	75	that	that	SCONJ
ejpam-6931	302	76	ϱo	ϱo	PROPN
ejpam-6931	302	77	is	be	AUX
ejpam-6931	302	78	not	not	PART
ejpam-6931	302	79	equal	equal	ADJ
ejpam-6931	302	80	to	to	ADP
ejpam-6931	302	81	ν	ν	NOUN
ejpam-6931	302	82	,	,	PUNCT
ejpam-6931	302	83	and	and	CCONJ
ejpam-6931	302	84	for	for	ADP
ejpam-6931	302	85	all	all	PRON
ejpam-6931	302	86	n	n	PRON
ejpam-6931	302	87	∈	∈	PROPN
ejpam-6931	302	88	m	m	NOUN
ejpam-6931	302	89	,	,	PUNCT
ejpam-6931	302	90	we	we	PRON
ejpam-6931	302	91	may	may	AUX
ejpam-6931	302	92	prove	prove	VERB
ejpam-6931	302	93	that	that	DET
ejpam-6931	302	94	inf	inf	NOUN
ejpam-6931	302	95	ν∈v	ν∈v	ADV
ejpam-6931	302	96	e(ϱo	e(ϱo	NOUN
ejpam-6931	302	97	,	,	PUNCT
ejpam-6931	302	98	ν	ν	NOUN
ejpam-6931	302	99	,	,	PUNCT
ejpam-6931	302	100	en	en	ADJ
ejpam-6931	302	101	)	)	PUNCT
ejpam-6931	302	102	=	=	SYM
ejpam-6931	302	103	inf	inf	PROPN
ejpam-6931	302	104	min{ϱo	min{ϱo	NOUN
ejpam-6931	302	105	,	,	PUNCT
ejpam-6931	302	106	ν	ν	NOUN
ejpam-6931	302	107	}	}	PUNCT
ejpam-6931	302	108	max{ϱo	max{ϱo	NOUN
ejpam-6931	302	109	,	,	PUNCT
ejpam-6931	302	110	ν	ν	NOUN
ejpam-6931	302	111	}	}	PUNCT
ejpam-6931	302	112	ℑ	ℑ	NOUN
ejpam-6931	302	113	=	=	NOUN
ejpam-6931	302	114	∅	∅	NOUN
ejpam-6931	302	115	sup	sup	X
ejpam-6931	302	116	ν∈v	ν∈v	ADV
ejpam-6931	302	117	g(ϱo	g(ϱo	NOUN
ejpam-6931	302	118	,	,	PUNCT
ejpam-6931	302	119	ν	ν	NOUN
ejpam-6931	302	120	,	,	PUNCT
ejpam-6931	302	121	en	en	ADJ
ejpam-6931	302	122	)	)	PUNCT
ejpam-6931	302	123	=	=	SYM
ejpam-6931	302	124	sup	sup	NOUN
ejpam-6931	302	125	(	(	PUNCT
ejpam-6931	302	126	1−	1−	NUM
ejpam-6931	302	127	min{ϱo	min{ϱo	NUM
ejpam-6931	302	128	,	,	PUNCT
ejpam-6931	302	129	ν	ν	NOUN
ejpam-6931	302	130	}	}	PUNCT
ejpam-6931	302	131	max{ϱo	max{ϱo	NOUN
ejpam-6931	302	132	,	,	PUNCT
ejpam-6931	302	133	ν	ν	NOUN
ejpam-6931	302	134	}	}	PUNCT
ejpam-6931	302	135	)	)	PUNCT
ejpam-6931	302	136	ℑ	ℑ	PROPN
ejpam-6931	302	137	=	=	SYM
ejpam-6931	302	138	ℑ	ℑ	PROPN
ejpam-6931	302	139	and	and	CCONJ
ejpam-6931	302	140	sup	sup	NOUN
ejpam-6931	302	141	ν∈v	ν∈v	ADV
ejpam-6931	302	142	h(ϱo	h(ϱo	ADV
ejpam-6931	302	143	,	,	PUNCT
ejpam-6931	302	144	ν	ν	NOUN
ejpam-6931	302	145	,	,	PUNCT
ejpam-6931	302	146	en	en	ADJ
ejpam-6931	302	147	)	)	PUNCT
ejpam-6931	302	148	=	=	SYM
ejpam-6931	302	149	sup	sup	NOUN
ejpam-6931	302	150	(	(	PUNCT
ejpam-6931	302	151	1−	1−	NUM
ejpam-6931	302	152	2min{ϱo	2min{ϱo	NUM
ejpam-6931	302	153	,	,	PUNCT
ejpam-6931	302	154	ν	ν	NOUN
ejpam-6931	302	155	}	}	PUNCT
ejpam-6931	302	156	min{ϱo	min{ϱo	NUM
ejpam-6931	302	157	,	,	PUNCT
ejpam-6931	302	158	ν}+max{ϱo	ν}+max{ϱo	ADV
ejpam-6931	302	159	,	,	PUNCT
ejpam-6931	302	160	ν	ν	NOUN
ejpam-6931	302	161	}	}	PUNCT
ejpam-6931	302	162	)	)	PUNCT
ejpam-6931	302	163	ℑ	ℑ	NOUN
ejpam-6931	302	164	=	=	SYM
ejpam-6931	302	165	ℑ.	ℑ.	PROPN
ejpam-6931	302	166	therefore	therefore	ADV
ejpam-6931	302	167	,	,	PUNCT
ejpam-6931	302	168	we	we	PRON
ejpam-6931	302	169	get	get	VERB
ejpam-6931	302	170	lim	lim	PROPN
ejpam-6931	302	171	n→∞	n→∞	NUM
ejpam-6931	302	172	inf	inf	PROPN
ejpam-6931	302	173	ν∈v	ν∈v	NOUN
ejpam-6931	302	174	e(ϱo	e(ϱo	NOUN
ejpam-6931	302	175	,	,	PUNCT
ejpam-6931	302	176	ν	ν	NOUN
ejpam-6931	302	177	,	,	PUNCT
ejpam-6931	302	178	en	en	ADJ
ejpam-6931	302	179	)	)	PUNCT
ejpam-6931	302	180	=	=	NOUN
ejpam-6931	302	181	∅	∅	NOUN
ejpam-6931	302	182	̸=	̸=	PROPN
ejpam-6931	302	183	ℑ	ℑ	PROPN
ejpam-6931	302	184	lim	lim	NOUN
ejpam-6931	302	185	n→∞	n→∞	NUM
ejpam-6931	302	186	sup	sup	NOUN
ejpam-6931	302	187	ν∈v	ν∈v	ADV
ejpam-6931	302	188	g(ϱo	g(ϱo	NOUN
ejpam-6931	302	189	,	,	PUNCT
ejpam-6931	302	190	ν	ν	NOUN
ejpam-6931	302	191	,	,	PUNCT
ejpam-6931	302	192	en	en	ADJ
ejpam-6931	302	193	)	)	PUNCT
ejpam-6931	302	194	=	=	SYM
ejpam-6931	302	195	ℑ	ℑ	PROPN
ejpam-6931	302	196	̸=	̸=	PROPN
ejpam-6931	302	197	∅	∅	NOUN
ejpam-6931	302	198	and	and	CCONJ
ejpam-6931	302	199	lim	lim	PROPN
ejpam-6931	302	200	n→∞	n→∞	NUM
ejpam-6931	302	201	sup	sup	NOUN
ejpam-6931	302	202	ν∈v	ν∈v	ADV
ejpam-6931	302	203	h(ϱo	h(ϱo	ADV
ejpam-6931	302	204	,	,	PUNCT
ejpam-6931	302	205	ν	ν	NOUN
ejpam-6931	302	206	,	,	PUNCT
ejpam-6931	302	207	en	en	ADJ
ejpam-6931	302	208	)	)	PUNCT
ejpam-6931	302	209	=	=	SYM
ejpam-6931	303	1	ℑ	ℑ	PROPN
ejpam-6931	303	2	̸=	̸=	PROPN
ejpam-6931	303	3	∅	∅	NOUN
ejpam-6931	303	4	for	for	ADP
ejpam-6931	303	5	each	each	DET
ejpam-6931	303	6	ϱo	ϱo	PROPN
ejpam-6931	303	7	∈	∈	PROPN
ejpam-6931	303	8	v.	v.	ADV
ejpam-6931	303	9	for	for	ADP
ejpam-6931	303	10	every	every	DET
ejpam-6931	303	11	k	k	PROPN
ejpam-6931	303	12	∈	∈	PROPN
ejpam-6931	303	13	(	(	PUNCT
ejpam-6931	303	14	0	0	NUM
ejpam-6931	303	15	,	,	PUNCT
ejpam-6931	303	16	1	1	NUM
ejpam-6931	303	17	)	)	PUNCT
ejpam-6931	303	18	,	,	PUNCT
ejpam-6931	303	19	ϱo	ϱo	NOUN
ejpam-6931	303	20	,	,	PUNCT
ejpam-6931	303	21	ν	ν	PROPN
ejpam-6931	303	22	∈	∈	PROPN
ejpam-6931	303	23	v	v	NOUN
ejpam-6931	303	24	and	and	CCONJ
ejpam-6931	303	25	e	e	NOUN
ejpam-6931	303	26	∈	∈	PROPN
ejpam-6931	303	27	s0	s0	PROPN
ejpam-6931	303	28	,	,	PUNCT
ejpam-6931	303	29	note	note	VERB
ejpam-6931	303	30	that	that	SCONJ
ejpam-6931	303	31	e(kϱo	e(kϱo	PROPN
ejpam-6931	303	32	,	,	PUNCT
ejpam-6931	303	33	kν	kν	PROPN
ejpam-6931	303	34	,	,	PUNCT
ejpam-6931	303	35	ke	ke	NOUN
ejpam-6931	303	36	)	)	PUNCT
ejpam-6931	303	37	=	=	PUNCT
ejpam-6931	304	1	min{ϱo2	min{ϱo2	PROPN
ejpam-6931	305	1	+	+	CCONJ
ejpam-6931	305	2	5	5	NUM
ejpam-6931	305	3	,	,	PUNCT
ejpam-6931	305	4	ν2	ν2	NOUN
ejpam-6931	305	5	+	+	CCONJ
ejpam-6931	305	6	5	5	NUM
ejpam-6931	305	7	}	}	PUNCT
ejpam-6931	305	8	max{ϱo2	max{ϱo2	NOUN
ejpam-6931	305	9	+	+	CCONJ
ejpam-6931	305	10	5	5	NUM
ejpam-6931	305	11	,	,	PUNCT
ejpam-6931	305	12	ν2	ν2	NOUN
ejpam-6931	305	13	+	+	CCONJ
ejpam-6931	305	14	5	5	NUM
ejpam-6931	305	15	}	}	SYM
ejpam-6931	305	16	ℑ	ℑ	PROPN
ejpam-6931	305	17	s.	s.	PROPN
ejpam-6931	305	18	m.	m.	PROPN
ejpam-6931	305	19	u.	u.	PROPN
ejpam-6931	305	20	ud	ud	AUX
ejpam-6931	305	21	-	-	PUNCT
ejpam-6931	305	22	din	din	VERB
ejpam-6931	306	1	et	et	PROPN
ejpam-6931	306	2	al	al	PROPN
ejpam-6931	306	3	.	.	PUNCT
ejpam-6931	306	4	/	/	SYM
ejpam-6931	306	5	eur	eur	PROPN
ejpam-6931	306	6	.	.	PUNCT
ejpam-6931	307	1	j.	j.	PROPN
ejpam-6931	307	2	pure	pure	PROPN
ejpam-6931	307	3	appl	appl	PROPN
ejpam-6931	307	4	.	.	PROPN
ejpam-6931	307	5	math	math	PROPN
ejpam-6931	307	6	,	,	PUNCT
ejpam-6931	307	7	18	18	NUM
ejpam-6931	307	8	(	(	PUNCT
ejpam-6931	307	9	4	4	NUM
ejpam-6931	307	10	)	)	PUNCT
ejpam-6931	307	11	(	(	PUNCT
ejpam-6931	307	12	2025	2025	NUM
ejpam-6931	307	13	)	)	PUNCT
ejpam-6931	307	14	,	,	PUNCT
ejpam-6931	307	15	6931	6931	NUM
ejpam-6931	307	16	21	21	NUM
ejpam-6931	307	17	of	of	ADP
ejpam-6931	307	18	38	38	NUM
ejpam-6931	307	19	⪰	⪰	NOUN
ejpam-6931	307	20	min{ϱo	min{ϱo	NOUN
ejpam-6931	307	21	,	,	PUNCT
ejpam-6931	307	22	ν	ν	NOUN
ejpam-6931	307	23	}	}	PUNCT
ejpam-6931	307	24	max{ϱo	max{ϱo	NOUN
ejpam-6931	307	25	,	,	PUNCT
ejpam-6931	307	26	ν	ν	NOUN
ejpam-6931	307	27	}	}	PUNCT
ejpam-6931	307	28	ℑ	ℑ	NOUN
ejpam-6931	307	29	=	=	PUNCT
ejpam-6931	307	30	e(ϱo	e(ϱo	X
ejpam-6931	307	31	,	,	PUNCT
ejpam-6931	307	32	ν	ν	NOUN
ejpam-6931	307	33	,	,	PUNCT
ejpam-6931	307	34	e	e	NOUN
ejpam-6931	307	35	)	)	PUNCT
ejpam-6931	307	36	g(kϱo	g(kϱo	PROPN
ejpam-6931	307	37	,	,	PUNCT
ejpam-6931	307	38	kν	kν	PROPN
ejpam-6931	307	39	,	,	PUNCT
ejpam-6931	307	40	ke	ke	NOUN
ejpam-6931	307	41	)	)	PUNCT
ejpam-6931	307	42	=	=	PUNCT
ejpam-6931	307	43	(	(	PUNCT
ejpam-6931	307	44	1−	1−	NUM
ejpam-6931	307	45	min{ϱo2	min{ϱo2	NOUN
ejpam-6931	307	46	+	+	CCONJ
ejpam-6931	307	47	5	5	NUM
ejpam-6931	307	48	,	,	PUNCT
ejpam-6931	307	49	ν2	ν2	NOUN
ejpam-6931	307	50	+	+	CCONJ
ejpam-6931	307	51	5	5	NUM
ejpam-6931	307	52	}	}	PUNCT
ejpam-6931	307	53	max{ϱo2	max{ϱo2	NOUN
ejpam-6931	307	54	+	+	CCONJ
ejpam-6931	307	55	5	5	NUM
ejpam-6931	307	56	,	,	PUNCT
ejpam-6931	307	57	ν2	ν2	NOUN
ejpam-6931	307	58	+	+	CCONJ
ejpam-6931	307	59	5	5	NUM
ejpam-6931	307	60	}	}	PUNCT
ejpam-6931	307	61	)	)	PUNCT
ejpam-6931	307	62	ℑ	ℑ	PROPN
ejpam-6931	307	63	⪯	⪯	NOUN
ejpam-6931	307	64	(	(	PUNCT
ejpam-6931	307	65	1−	1−	NUM
ejpam-6931	307	66	min{ϱo	min{ϱo	NUM
ejpam-6931	307	67	,	,	PUNCT
ejpam-6931	307	68	ν	ν	NOUN
ejpam-6931	307	69	}	}	PUNCT
ejpam-6931	307	70	max{ϱo	max{ϱo	NOUN
ejpam-6931	307	71	,	,	PUNCT
ejpam-6931	307	72	ν	ν	NOUN
ejpam-6931	307	73	}	}	PUNCT
ejpam-6931	307	74	)	)	PUNCT
ejpam-6931	307	75	ℑ	ℑ	PROPN
ejpam-6931	307	76	=	=	SYM
ejpam-6931	307	77	g(ϱo	g(ϱo	PROPN
ejpam-6931	307	78	,	,	PUNCT
ejpam-6931	307	79	ν	ν	NOUN
ejpam-6931	307	80	,	,	PUNCT
ejpam-6931	307	81	e	e	NOUN
ejpam-6931	307	82	)	)	PUNCT
ejpam-6931	307	83	and	and	CCONJ
ejpam-6931	307	84	h(kϱo	h(kϱo	PROPN
ejpam-6931	307	85	,	,	PUNCT
ejpam-6931	307	86	kν	kν	PROPN
ejpam-6931	307	87	,	,	PUNCT
ejpam-6931	307	88	ke	ke	NOUN
ejpam-6931	307	89	)	)	PUNCT
ejpam-6931	307	90	=	=	PUNCT
ejpam-6931	307	91	(	(	PUNCT
ejpam-6931	307	92	1−	1−	NUM
ejpam-6931	307	93	2min{ϱo2	2min{ϱo2	NUM
ejpam-6931	307	94	+	+	CCONJ
ejpam-6931	307	95	5	5	NUM
ejpam-6931	307	96	,	,	PUNCT
ejpam-6931	307	97	ν2	ν2	NOUN
ejpam-6931	307	98	+	+	CCONJ
ejpam-6931	307	99	5	5	NUM
ejpam-6931	307	100	}	}	PUNCT
ejpam-6931	307	101	min{ϱo2	min{ϱo2	NOUN
ejpam-6931	308	1	+	+	CCONJ
ejpam-6931	308	2	5	5	NUM
ejpam-6931	308	3	,	,	PUNCT
ejpam-6931	308	4	ν2	ν2	NOUN
ejpam-6931	308	5	+	+	NOUN
ejpam-6931	308	6	5}+max{ϱo2	5}+max{ϱo2	NUM
ejpam-6931	308	7	+	+	NUM
ejpam-6931	308	8	5	5	NUM
ejpam-6931	308	9	,	,	PUNCT
ejpam-6931	308	10	ν2	ν2	NOUN
ejpam-6931	308	11	+	+	CCONJ
ejpam-6931	308	12	5	5	NUM
ejpam-6931	308	13	}	}	PUNCT
ejpam-6931	308	14	)	)	PUNCT
ejpam-6931	308	15	ℑ	ℑ	PROPN
ejpam-6931	308	16	⪯	⪯	NOUN
ejpam-6931	308	17	(	(	PUNCT
ejpam-6931	308	18	1−	1−	NUM
ejpam-6931	308	19	2min{ϱo	2min{ϱo	NUM
ejpam-6931	308	20	,	,	PUNCT
ejpam-6931	308	21	ν	ν	NOUN
ejpam-6931	308	22	}	}	PUNCT
ejpam-6931	308	23	min{ϱo	min{ϱo	NUM
ejpam-6931	308	24	,	,	PUNCT
ejpam-6931	308	25	ν}+max{ϱo	ν}+max{ϱo	ADV
ejpam-6931	308	26	,	,	PUNCT
ejpam-6931	308	27	ν	ν	NOUN
ejpam-6931	308	28	}	}	PUNCT
ejpam-6931	308	29	)	)	PUNCT
ejpam-6931	308	30	ℑ	ℑ	PROPN
ejpam-6931	308	31	=	=	SYM
ejpam-6931	308	32	h(ϱo	h(ϱo	ADJ
ejpam-6931	308	33	,	,	PUNCT
ejpam-6931	308	34	ν	ν	NOUN
ejpam-6931	308	35	,	,	PUNCT
ejpam-6931	308	36	e	e	NOUN
ejpam-6931	308	37	)	)	PUNCT
ejpam-6931	308	38	.	.	PUNCT
ejpam-6931	309	1	equation	equation	NOUN
ejpam-6931	309	2	(	(	PUNCT
ejpam-6931	309	3	1	1	X
ejpam-6931	309	4	)	)	PUNCT
ejpam-6931	309	5	is	be	AUX
ejpam-6931	309	6	satisfied	satisfied	ADJ
ejpam-6931	309	7	by	by	ADP
ejpam-6931	309	8	the	the	DET
ejpam-6931	309	9	mapping	mapping	NOUN
ejpam-6931	310	1	k	k	NOUN
ejpam-6931	310	2	,	,	PUNCT
ejpam-6931	310	3	however	however	ADV
ejpam-6931	310	4	,	,	PUNCT
ejpam-6931	310	5	v	v	NOUN
ejpam-6931	310	6	has	have	VERB
ejpam-6931	310	7	no	no	DET
ejpam-6931	310	8	fixed	fix	VERB
ejpam-6931	310	9	point	point	NOUN
ejpam-6931	310	10	.	.	PUNCT
ejpam-6931	311	1	in	in	ADP
ejpam-6931	311	2	order	order	NOUN
ejpam-6931	311	3	to	to	PART
ejpam-6931	311	4	obtain	obtain	VERB
ejpam-6931	311	5	the	the	DET
ejpam-6931	311	6	next	next	ADJ
ejpam-6931	311	7	result	result	NOUN
ejpam-6931	311	8	,	,	PUNCT
ejpam-6931	311	9	ω	ω	PROPN
ejpam-6931	311	10	is	be	AUX
ejpam-6931	311	11	defined	define	VERB
ejpam-6931	311	12	as	as	ADP
ejpam-6931	311	13	the	the	DET
ejpam-6931	311	14	set	set	NOUN
ejpam-6931	311	15	of	of	ADP
ejpam-6931	311	16	all	all	DET
ejpam-6931	311	17	mappings	mapping	NOUN
ejpam-6931	311	18	φ	φ	NOUN
ejpam-6931	311	19	:	:	PUNCT
ejpam-6931	311	20	t	t	PROPN
ejpam-6931	311	21	→	→	SYM
ejpam-6931	311	22	t	t	PROPN
ejpam-6931	311	23	,	,	PUNCT
ejpam-6931	311	24	where	where	SCONJ
ejpam-6931	311	25	φ	φ	PROPN
ejpam-6931	311	26	is	be	AUX
ejpam-6931	311	27	continuous	continuous	ADJ
ejpam-6931	311	28	,	,	PUNCT
ejpam-6931	311	29	φ(ℑ	φ(ℑ	PROPN
ejpam-6931	311	30	)	)	PUNCT
ejpam-6931	311	31	=	=	SYM
ejpam-6931	311	32	ℑ	ℑ	PROPN
ejpam-6931	311	33	,	,	PUNCT
ejpam-6931	311	34	φ(c	φ(c	NOUN
ejpam-6931	311	35	)	)	PUNCT
ejpam-6931	311	36	≻	≻	PROPN
ejpam-6931	312	1	c	c	NOUN
ejpam-6931	312	2	for	for	ADP
ejpam-6931	312	3	every	every	DET
ejpam-6931	312	4	e	e	PROPN
ejpam-6931	312	5	∈	∈	PROPN
ejpam-6931	312	6	t0	t0	PROPN
ejpam-6931	312	7	,	,	PUNCT
ejpam-6931	312	8	and	and	CCONJ
ejpam-6931	312	9	limn→	limn→	ADV
ejpam-6931	312	10	φn(e	φn(e	X
ejpam-6931	312	11	)	)	PUNCT
ejpam-6931	312	12	=	=	SYM
ejpam-6931	312	13	ℑ	ℑ	NOUN
ejpam-6931	312	14	for	for	ADP
ejpam-6931	312	15	every	every	DET
ejpam-6931	312	16	e	e	PROPN
ejpam-6931	312	17	∈	∈	PROPN
ejpam-6931	312	18	t0	t0	PROPN
ejpam-6931	312	19	.	.	PUNCT
ejpam-6931	313	1	similarly	similarly	ADV
ejpam-6931	313	2	,	,	PUNCT
ejpam-6931	313	3	𭟋	𭟋	PROPN
ejpam-6931	313	4	is	be	AUX
ejpam-6931	313	5	defined	define	VERB
ejpam-6931	313	6	as	as	ADP
ejpam-6931	313	7	the	the	DET
ejpam-6931	313	8	set	set	NOUN
ejpam-6931	313	9	of	of	ADP
ejpam-6931	313	10	all	all	DET
ejpam-6931	313	11	mappings	mapping	NOUN
ejpam-6931	313	12	σ	σ	NOUN
ejpam-6931	313	13	:	:	PUNCT
ejpam-6931	313	14	t	t	PROPN
ejpam-6931	313	15	→	→	SYM
ejpam-6931	313	16	t	t	PROPN
ejpam-6931	313	17	in	in	ADP
ejpam-6931	313	18	which	which	PRON
ejpam-6931	313	19	σ	σ	PROPN
ejpam-6931	313	20	is	be	AUX
ejpam-6931	313	21	continuous	continuous	ADJ
ejpam-6931	313	22	,	,	PUNCT
ejpam-6931	313	23	σ(∅	σ(∅	ADJ
ejpam-6931	313	24	)	)	PUNCT
ejpam-6931	313	25	=	=	SYM
ejpam-6931	313	26	∅	∅	NOUN
ejpam-6931	313	27	,	,	PUNCT
ejpam-6931	313	28	σ(e	σ(e	PROPN
ejpam-6931	313	29	)	)	PUNCT
ejpam-6931	313	30	≺	≺	NOUN
ejpam-6931	313	31	e	e	X
ejpam-6931	313	32	for	for	ADP
ejpam-6931	313	33	every	every	DET
ejpam-6931	313	34	e	e	PROPN
ejpam-6931	313	35	∈	∈	PROPN
ejpam-6931	313	36	t	t	PROPN
ejpam-6931	313	37	,	,	PUNCT
ejpam-6931	313	38	and	and	CCONJ
ejpam-6931	313	39	limn→	limn→	ADV
ejpam-6931	313	40	σn(e	σn(e	X
ejpam-6931	313	41	)	)	PUNCT
ejpam-6931	314	1	=	=	NOUN
ejpam-6931	314	2	∅	∅	NOUN
ejpam-6931	314	3	for	for	ADP
ejpam-6931	314	4	every	every	DET
ejpam-6931	314	5	e	e	PROPN
ejpam-6931	314	6	∈	∈	PROPN
ejpam-6931	314	7	t.	t.	NOUN
ejpam-6931	314	8	theorem	theorem	NOUN
ejpam-6931	314	9	2	2	PROPN
ejpam-6931	314	10	.	.	X
ejpam-6931	314	11	assume	assume	VERB
ejpam-6931	314	12	that	that	SCONJ
ejpam-6931	314	13	the	the	DET
ejpam-6931	314	14	cvnms	cvnms	NOUN
ejpam-6931	314	15	(	(	PUNCT
ejpam-6931	314	16	v	v	NOUN
ejpam-6931	314	17	,	,	PUNCT
ejpam-6931	314	18	e	e	NOUN
ejpam-6931	314	19	,	,	PUNCT
ejpam-6931	314	20	g	g	PROPN
ejpam-6931	314	21	,	,	PUNCT
ejpam-6931	314	22	h	h	NOUN
ejpam-6931	314	23	,	,	PUNCT
ejpam-6931	314	24	⋆	⋆	NOUN
ejpam-6931	314	25	,	,	PUNCT
ejpam-6931	314	26	△	△	NOUN
ejpam-6931	314	27	)	)	PUNCT
ejpam-6931	314	28	is	be	AUX
ejpam-6931	314	29	complete	complete	ADJ
ejpam-6931	314	30	.	.	PUNCT
ejpam-6931	315	1	if	if	SCONJ
ejpam-6931	315	2	the	the	DET
ejpam-6931	315	3	following	follow	VERB
ejpam-6931	315	4	conditions	condition	NOUN
ejpam-6931	315	5	are	be	AUX
ejpam-6931	315	6	satisfied	satisfied	ADJ
ejpam-6931	315	7	by	by	ADP
ejpam-6931	315	8	a	a	DET
ejpam-6931	315	9	mapping	mapping	NOUN
ejpam-6931	315	10	k	k	NOUN
ejpam-6931	315	11	:	:	PUNCT
ejpam-6931	315	12	v	v	X
ejpam-6931	315	13	→	→	SYM
ejpam-6931	315	14	v	v	NOUN
ejpam-6931	315	15	:	:	PUNCT
ejpam-6931	315	16	e(kϱo	e(kϱo	PROPN
ejpam-6931	315	17	,	,	PUNCT
ejpam-6931	315	18	kν	kν	PROPN
ejpam-6931	315	19	,	,	PUNCT
ejpam-6931	315	20	e	e	NOUN
ejpam-6931	315	21	)	)	PUNCT
ejpam-6931	315	22	⪰	⪰	NOUN
ejpam-6931	315	23	φ(e(ϱo	φ(e(ϱo	ADJ
ejpam-6931	315	24	,	,	PUNCT
ejpam-6931	315	25	ν	ν	NOUN
ejpam-6931	315	26	,	,	PUNCT
ejpam-6931	315	27	e	e	NOUN
ejpam-6931	315	28	)	)	PUNCT
ejpam-6931	315	29	)	)	PUNCT
ejpam-6931	315	30	,	,	PUNCT
ejpam-6931	315	31	g(kϱo	g(kϱo	PROPN
ejpam-6931	315	32	,	,	PUNCT
ejpam-6931	315	33	kν	kν	PROPN
ejpam-6931	315	34	,	,	PUNCT
ejpam-6931	315	35	e	e	NOUN
ejpam-6931	315	36	)	)	PUNCT
ejpam-6931	315	37	⪯	⪯	NOUN
ejpam-6931	315	38	σ(g(ϱo	σ(g(ϱo	NOUN
ejpam-6931	315	39	,	,	PUNCT
ejpam-6931	315	40	ν	ν	NOUN
ejpam-6931	315	41	,	,	PUNCT
ejpam-6931	315	42	e	e	NOUN
ejpam-6931	315	43	)	)	PUNCT
ejpam-6931	315	44	)	)	PUNCT
ejpam-6931	315	45	and	and	CCONJ
ejpam-6931	315	46	h(kϱo	h(kϱo	PROPN
ejpam-6931	315	47	,	,	PUNCT
ejpam-6931	315	48	kν	kν	PROPN
ejpam-6931	315	49	,	,	PUNCT
ejpam-6931	315	50	e	e	NOUN
ejpam-6931	315	51	)	)	PUNCT
ejpam-6931	315	52	⪯	⪯	NOUN
ejpam-6931	315	53	σ(h(ϱo	σ(h(ϱo	ADJ
ejpam-6931	315	54	,	,	PUNCT
ejpam-6931	315	55	ν	ν	NOUN
ejpam-6931	315	56	,	,	PUNCT
ejpam-6931	315	57	e	e	NOUN
ejpam-6931	315	58	)	)	PUNCT
ejpam-6931	315	59	)	)	PUNCT
ejpam-6931	315	60	(	(	PUNCT
ejpam-6931	315	61	6	6	NUM
ejpam-6931	315	62	)	)	PUNCT
ejpam-6931	315	63	for	for	ADP
ejpam-6931	315	64	each	each	DET
ejpam-6931	315	65	ϱo	ϱo	NOUN
ejpam-6931	315	66	,	,	PUNCT
ejpam-6931	315	67	ν	ν	PROPN
ejpam-6931	315	68	∈	∈	PROPN
ejpam-6931	315	69	v	v	NOUN
ejpam-6931	315	70	and	and	CCONJ
ejpam-6931	315	71	e	e	NOUN
ejpam-6931	315	72	∈	∈	PROPN
ejpam-6931	315	73	s0	s0	PROPN
ejpam-6931	315	74	,	,	PUNCT
ejpam-6931	315	75	with	with	ADP
ejpam-6931	315	76	σ	σ	PROPN
ejpam-6931	315	77	∈	∈	PROPN
ejpam-6931	315	78	𭟋	𭟋	PROPN
ejpam-6931	315	79	and	and	CCONJ
ejpam-6931	315	80	φ	φ	PROPN
ejpam-6931	315	81	∈	∈	PROPN
ejpam-6931	315	82	ω	ω	PROPN
ejpam-6931	315	83	.	.	PUNCT
ejpam-6931	316	1	then	then	ADV
ejpam-6931	316	2	the	the	DET
ejpam-6931	316	3	mapping	mapping	NOUN
ejpam-6931	316	4	k	k	PROPN
ejpam-6931	316	5	has	have	VERB
ejpam-6931	316	6	a	a	DET
ejpam-6931	316	7	fixed	fix	VERB
ejpam-6931	316	8	point	point	NOUN
ejpam-6931	316	9	in	in	ADP
ejpam-6931	316	10	the	the	DET
ejpam-6931	316	11	set	set	NOUN
ejpam-6931	316	12	v.	v.	ADP
ejpam-6931	316	13	proof	proof	NOUN
ejpam-6931	316	14	.	.	PUNCT
ejpam-6931	317	1	let	let	VERB
ejpam-6931	317	2	ϱo0	ϱo0	PROPN
ejpam-6931	317	3	∈	∈	PROPN
ejpam-6931	317	4	v	v	AUX
ejpam-6931	317	5	be	be	AUX
ejpam-6931	317	6	any	any	DET
ejpam-6931	317	7	given	give	VERB
ejpam-6931	317	8	point	point	NOUN
ejpam-6931	317	9	.	.	PUNCT
ejpam-6931	318	1	in	in	ADP
ejpam-6931	318	2	v	v	NUM
ejpam-6931	318	3	,	,	PUNCT
ejpam-6931	318	4	a	a	DET
ejpam-6931	318	5	sequence	sequence	NOUN
ejpam-6931	318	6	{	{	PUNCT
ejpam-6931	318	7	ϱon	ϱon	NOUN
ejpam-6931	318	8	}	}	PUNCT
ejpam-6931	318	9	is	be	AUX
ejpam-6931	318	10	defined	define	VERB
ejpam-6931	318	11	by	by	ADP
ejpam-6931	318	12	ϱon	ϱon	PROPN
ejpam-6931	318	13	=	=	PROPN
ejpam-6931	318	14	hϱon−1	hϱon−1	PROPN
ejpam-6931	318	15	for	for	ADP
ejpam-6931	318	16	all	all	DET
ejpam-6931	318	17	n	n	DET
ejpam-6931	318	18	∈	∈	NOUN
ejpam-6931	318	19	m.	m.	NOUN
ejpam-6931	318	20	the	the	DET
ejpam-6931	318	21	existence	existence	NOUN
ejpam-6931	318	22	of	of	ADP
ejpam-6931	318	23	an	an	DET
ejpam-6931	318	24	element	element	NOUN
ejpam-6931	318	25	n0	n0	PROPN
ejpam-6931	318	26	∈	∈	PROPN
ejpam-6931	318	27	m	m	VERB
ejpam-6931	319	1	such	such	ADJ
ejpam-6931	319	2	that	that	DET
ejpam-6931	319	3	ϱon0	ϱon0	PROPN
ejpam-6931	320	1	=	=	PROPN
ejpam-6931	321	1	ϱon0−1	ϱon0−1	PROPN
ejpam-6931	321	2	makes	make	VERB
ejpam-6931	321	3	sure	sure	ADJ
ejpam-6931	321	4	that	that	SCONJ
ejpam-6931	321	5	ϱon0	ϱon0	PROPN
ejpam-6931	321	6	is	be	AUX
ejpam-6931	321	7	a	a	DET
ejpam-6931	321	8	fixed	fix	VERB
ejpam-6931	321	9	point	point	NOUN
ejpam-6931	321	10	in	in	ADP
ejpam-6931	321	11	k.	k.	PROPN
ejpam-6931	321	12	now	now	ADV
ejpam-6931	321	13	,	,	PUNCT
ejpam-6931	321	14	we	we	PRON
ejpam-6931	321	15	assume	assume	VERB
ejpam-6931	321	16	that	that	SCONJ
ejpam-6931	321	17	ϱon	ϱon	PROPN
ejpam-6931	321	18	is	be	AUX
ejpam-6931	321	19	not	not	PART
ejpam-6931	321	20	equal	equal	ADJ
ejpam-6931	321	21	to	to	ADP
ejpam-6931	321	22	ϱon−1	ϱon−1	PROPN
ejpam-6931	321	23	for	for	ADP
ejpam-6931	321	24	every	every	DET
ejpam-6931	321	25	nm	nm	NOUN
ejpam-6931	321	26	,	,	PUNCT
ejpam-6931	321	27	and	and	CCONJ
ejpam-6931	321	28	we	we	PRON
ejpam-6931	321	29	prove	prove	VERB
ejpam-6931	321	30	that	that	SCONJ
ejpam-6931	321	31	the	the	DET
ejpam-6931	321	32	sequence	sequence	NOUN
ejpam-6931	321	33	{	{	PUNCT
ejpam-6931	321	34	ϱon	ϱon	NOUN
ejpam-6931	321	35	}	}	PUNCT
ejpam-6931	321	36	is	be	AUX
ejpam-6931	321	37	cauchy	cauchy	PROPN
ejpam-6931	321	38	.	.	PUNCT
ejpam-6931	322	1	for	for	ADP
ejpam-6931	322	2	each	each	DET
ejpam-6931	322	3	n	n	PRON
ejpam-6931	322	4	∈	∈	NOUN
ejpam-6931	322	5	m	m	NOUN
ejpam-6931	322	6	and	and	CCONJ
ejpam-6931	322	7	a	a	DET
ejpam-6931	322	8	given	give	VERB
ejpam-6931	322	9	e	e	PROPN
ejpam-6931	322	10	∈	∈	PROPN
ejpam-6931	322	11	s0	s0	NOUN
ejpam-6931	322	12	,	,	PUNCT
ejpam-6931	322	13	let	let	VERB
ejpam-6931	322	14	us	we	PRON
ejpam-6931	322	15	define	define	VERB
ejpam-6931	322	16	an	an	DET
ejpam-6931	322	17	:	:	PUNCT
ejpam-6931	322	18	=	=	SYM
ejpam-6931	322	19	{	{	PUNCT
ejpam-6931	322	20	e(ϱon	e(ϱon	PROPN
ejpam-6931	322	21	,	,	PUNCT
ejpam-6931	322	22	ϱom	ϱom	NOUN
ejpam-6931	322	23	,	,	PUNCT
ejpam-6931	322	24	e	e	NOUN
ejpam-6931	322	25	)	)	PUNCT
ejpam-6931	322	26	:	:	PUNCT
ejpam-6931	322	27	m	m	VERB
ejpam-6931	322	28	>	>	X
ejpam-6931	322	29	n	n	CCONJ
ejpam-6931	322	30	}	}	PUNCT
ejpam-6931	322	31	⊂	⊂	PROPN
ejpam-6931	322	32	t	t	PROPN
ejpam-6931	322	33	,	,	PUNCT
ejpam-6931	322	34	bn	bn	ADV
ejpam-6931	322	35	:	:	PUNCT
ejpam-6931	322	36	=	=	PRON
ejpam-6931	322	37	{	{	PUNCT
ejpam-6931	322	38	g(ϱon	g(ϱon	NOUN
ejpam-6931	322	39	,	,	PUNCT
ejpam-6931	322	40	ϱom	ϱom	NOUN
ejpam-6931	322	41	,	,	PUNCT
ejpam-6931	322	42	e	e	NOUN
ejpam-6931	322	43	)	)	PUNCT
ejpam-6931	322	44	:	:	PUNCT
ejpam-6931	322	45	m	m	VERB
ejpam-6931	322	46	>	>	X
ejpam-6931	322	47	n	n	CCONJ
ejpam-6931	322	48	}	}	PUNCT
ejpam-6931	322	49	⊂	⊂	PROPN
ejpam-6931	322	50	t	t	PROPN
ejpam-6931	322	51	,	,	PUNCT
ejpam-6931	322	52	cn	cn	PROPN
ejpam-6931	322	53	:	:	PUNCT
ejpam-6931	322	54	=	=	SYM
ejpam-6931	322	55	{	{	PUNCT
ejpam-6931	322	56	h(ϱon	h(ϱon	PROPN
ejpam-6931	322	57	,	,	PUNCT
ejpam-6931	322	58	ϱ	ϱ	ADP
ejpam-6931	322	59	o	o	PROPN
ejpam-6931	322	60	m	m	NOUN
ejpam-6931	322	61	,	,	PUNCT
ejpam-6931	322	62	e	e	NOUN
ejpam-6931	322	63	)	)	PUNCT
ejpam-6931	322	64	:	:	PUNCT
ejpam-6931	322	65	m	m	VERB
ejpam-6931	322	66	>	>	X
ejpam-6931	322	67	n	n	CCONJ
ejpam-6931	322	68	}	}	PUNCT
ejpam-6931	322	69	⊂	⊂	PROPN
ejpam-6931	322	70	t.	t.	PROPN
ejpam-6931	322	71	s.	s.	PROPN
ejpam-6931	322	72	m.	m.	PROPN
ejpam-6931	322	73	u.	u.	PROPN
ejpam-6931	322	74	ud	ud	AUX
ejpam-6931	322	75	-	-	PUNCT
ejpam-6931	322	76	din	din	VERB
ejpam-6931	322	77	et	et	PROPN
ejpam-6931	322	78	al	al	PROPN
ejpam-6931	322	79	.	.	PUNCT
ejpam-6931	322	80	/	/	SYM
ejpam-6931	322	81	eur	eur	PROPN
ejpam-6931	322	82	.	.	PUNCT
ejpam-6931	323	1	j.	j.	PROPN
ejpam-6931	323	2	pure	pure	PROPN
ejpam-6931	323	3	appl	appl	PROPN
ejpam-6931	323	4	.	.	PROPN
ejpam-6931	323	5	math	math	PROPN
ejpam-6931	323	6	,	,	PUNCT
ejpam-6931	323	7	18	18	NUM
ejpam-6931	323	8	(	(	PUNCT
ejpam-6931	323	9	4	4	NUM
ejpam-6931	323	10	)	)	PUNCT
ejpam-6931	323	11	(	(	PUNCT
ejpam-6931	323	12	2025	2025	NUM
ejpam-6931	323	13	)	)	PUNCT
ejpam-6931	323	14	,	,	PUNCT
ejpam-6931	323	15	6931	6931	NUM
ejpam-6931	323	16	22	22	NUM
ejpam-6931	323	17	of	of	ADP
ejpam-6931	323	18	38	38	NUM
ejpam-6931	323	19	as	as	ADP
ejpam-6931	323	20	∅	∅	NOUN
ejpam-6931	323	21	≺	≺	NOUN
ejpam-6931	323	22	e(ϱon	e(ϱon	PROPN
ejpam-6931	323	23	,	,	PUNCT
ejpam-6931	323	24	ϱom	ϱom	NOUN
ejpam-6931	323	25	,	,	PUNCT
ejpam-6931	323	26	e	e	NOUN
ejpam-6931	323	27	)	)	PUNCT
ejpam-6931	323	28	⪯	⪯	NOUN
ejpam-6931	323	29	ℑ	ℑ	PROPN
ejpam-6931	323	30	according	accord	VERB
ejpam-6931	323	31	to	to	ADP
ejpam-6931	323	32	remarks	remark	NOUN
ejpam-6931	323	33	1	1	NUM
ejpam-6931	323	34	,	,	PUNCT
ejpam-6931	323	35	the	the	DET
ejpam-6931	323	36	greatest	greatest	ADV
ejpam-6931	323	37	lower	low	ADJ
ejpam-6931	323	38	bound	bind	VERB
ejpam-6931	323	39	of	of	ADP
ejpam-6931	323	40	an	an	PRON
ejpam-6931	323	41	,	,	PUNCT
ejpam-6931	323	42	that	that	ADV
ejpam-6931	323	43	is	is	ADV
ejpam-6931	323	44	,	,	PUNCT
ejpam-6931	323	45	inf	inf	VERB
ejpam-6931	323	46	an	an	DET
ejpam-6931	323	47	=	=	SYM
ejpam-6931	323	48	x́n	x́n	PROPN
ejpam-6931	323	49	,	,	PUNCT
ejpam-6931	323	50	exists	exist	VERB
ejpam-6931	323	51	for	for	ADP
ejpam-6931	323	52	any	any	DET
ejpam-6931	323	53	n	n	PRON
ejpam-6931	323	54	∈	∈	NOUN
ejpam-6931	323	55	n	n	PRON
ejpam-6931	323	56	such	such	ADJ
ejpam-6931	323	57	that	that	SCONJ
ejpam-6931	323	58	n	n	NOUN
ejpam-6931	323	59	<	<	X
ejpam-6931	323	60	m.	m.	NOUN
ejpam-6931	323	61	in	in	ADP
ejpam-6931	323	62	the	the	DET
ejpam-6931	323	63	same	same	ADJ
ejpam-6931	323	64	way	way	NOUN
ejpam-6931	323	65	,	,	PUNCT
ejpam-6931	323	66	since	since	SCONJ
ejpam-6931	323	67	∅	∅	NOUN
ejpam-6931	323	68	⪯	⪯	PROPN
ejpam-6931	323	69	g(ϱon	g(ϱon	PROPN
ejpam-6931	323	70	,	,	PUNCT
ejpam-6931	323	71	ϱom	ϱom	NOUN
ejpam-6931	323	72	,	,	PUNCT
ejpam-6931	323	73	e	e	NOUN
ejpam-6931	323	74	)	)	PUNCT
ejpam-6931	323	75	≺	≺	VERB
ejpam-6931	323	76	ℑ	ℑ	PROPN
ejpam-6931	323	77	for	for	ADP
ejpam-6931	323	78	each	each	DET
ejpam-6931	323	79	n	n	PRON
ejpam-6931	323	80	∈	∈	NOUN
ejpam-6931	323	81	m	m	VERB
ejpam-6931	323	82	such	such	ADJ
ejpam-6931	323	83	that	that	SCONJ
ejpam-6931	323	84	n	n	PROPN
ejpam-6931	323	85	<	<	X
ejpam-6931	323	86	m	m	PROPN
ejpam-6931	323	87	,	,	PUNCT
ejpam-6931	323	88	according	accord	VERB
ejpam-6931	323	89	to	to	ADP
ejpam-6931	323	90	remarks	remark	NOUN
ejpam-6931	323	91	1	1	NUM
ejpam-6931	323	92	,	,	PUNCT
ejpam-6931	323	93	the	the	DET
ejpam-6931	323	94	least	least	ADV
ejpam-6931	323	95	upper	upper	ADJ
ejpam-6931	323	96	bound	bind	VERB
ejpam-6931	323	97	bn	bn	NOUN
ejpam-6931	323	98	,	,	PUNCT
ejpam-6931	323	99	that	that	ADV
ejpam-6931	323	100	is	is	ADV
ejpam-6931	323	101	,	,	PUNCT
ejpam-6931	323	102	supbn	supbn	ADJ
ejpam-6931	323	103	=	=	SYM
ejpam-6931	323	104	ýn	ýn	NOUN
ejpam-6931	323	105	exist	exist	VERB
ejpam-6931	323	106	for	for	ADP
ejpam-6931	323	107	any	any	DET
ejpam-6931	323	108	n	n	PRON
ejpam-6931	323	109	∈	∈	PROPN
ejpam-6931	323	110	n.	n.	NOUN
ejpam-6931	323	111	also	also	ADV
ejpam-6931	323	112	,	,	PUNCT
ejpam-6931	323	113	since	since	SCONJ
ejpam-6931	323	114	∅	∅	NOUN
ejpam-6931	323	115	⪯	⪯	PROPN
ejpam-6931	323	116	h(ϱon	h(ϱon	PROPN
ejpam-6931	323	117	,	,	PUNCT
ejpam-6931	323	118	ϱ	ϱ	ADP
ejpam-6931	323	119	o	o	PROPN
ejpam-6931	323	120	m	m	NOUN
ejpam-6931	323	121	,	,	PUNCT
ejpam-6931	323	122	e	e	NOUN
ejpam-6931	323	123	)	)	PUNCT
ejpam-6931	323	124	≺	≺	VERB
ejpam-6931	323	125	ℑ	ℑ	PROPN
ejpam-6931	323	126	for	for	ADP
ejpam-6931	323	127	each	each	DET
ejpam-6931	323	128	n	n	PRON
ejpam-6931	323	129	∈	∈	NOUN
ejpam-6931	323	130	m	m	VERB
ejpam-6931	323	131	such	such	ADJ
ejpam-6931	323	132	that	that	SCONJ
ejpam-6931	323	133	n	n	PROPN
ejpam-6931	323	134	<	<	X
ejpam-6931	323	135	m	m	PROPN
ejpam-6931	323	136	,	,	PUNCT
ejpam-6931	323	137	according	accord	VERB
ejpam-6931	323	138	to	to	ADP
ejpam-6931	323	139	remarks	remark	NOUN
ejpam-6931	323	140	1	1	NUM
ejpam-6931	323	141	,	,	PUNCT
ejpam-6931	323	142	the	the	DET
ejpam-6931	323	143	sup(cn	sup(cn	NOUN
ejpam-6931	323	144	)	)	PUNCT
ejpam-6931	323	145	,	,	PUNCT
ejpam-6931	323	146	that	that	ADV
ejpam-6931	323	147	is	is	ADV
ejpam-6931	323	148	,	,	PUNCT
ejpam-6931	323	149	supcn	supcn	NOUN
ejpam-6931	323	150	=	=	SYM
ejpam-6931	323	151	ćn	ćn	NOUN
ejpam-6931	323	152	exist	exist	VERB
ejpam-6931	323	153	for	for	ADP
ejpam-6931	323	154	any	any	DET
ejpam-6931	323	155	n	n	PRON
ejpam-6931	323	156	∈	∈	PROPN
ejpam-6931	323	157	n.	n.	NOUN
ejpam-6931	323	158	according	accord	VERB
ejpam-6931	323	159	to	to	ADP
ejpam-6931	323	160	equation	equation	NOUN
ejpam-6931	323	161	(	(	PUNCT
ejpam-6931	323	162	6	6	NUM
ejpam-6931	323	163	)	)	PUNCT
ejpam-6931	323	164	,	,	PUNCT
ejpam-6931	323	165	for	for	ADP
ejpam-6931	323	166	each	each	DET
ejpam-6931	323	167	n	n	NOUN
ejpam-6931	323	168	,	,	PUNCT
ejpam-6931	323	169	m	m	PROPN
ejpam-6931	323	170	∈	∈	NOUN
ejpam-6931	323	171	m	m	VERB
ejpam-6931	323	172	such	such	ADJ
ejpam-6931	323	173	that	that	SCONJ
ejpam-6931	323	174	m	m	VERB
ejpam-6931	323	175	>	>	X
ejpam-6931	323	176	n	n	CCONJ
ejpam-6931	323	177	,	,	PUNCT
ejpam-6931	323	178	this	this	PRON
ejpam-6931	323	179	implies	imply	VERB
ejpam-6931	323	180	that	that	SCONJ
ejpam-6931	323	181	e(ϱon+1	e(ϱon+1	NOUN
ejpam-6931	323	182	,	,	PUNCT
ejpam-6931	323	183	ϱ	ϱ	ADP
ejpam-6931	323	184	o	o	NOUN
ejpam-6931	323	185	m+1	m+1	X
ejpam-6931	323	186	,	,	PUNCT
ejpam-6931	323	187	e	e	NOUN
ejpam-6931	323	188	)	)	PUNCT
ejpam-6931	323	189	=	=	SYM
ejpam-6931	323	190	e(kϱon	e(kϱon	PROPN
ejpam-6931	323	191	,	,	PUNCT
ejpam-6931	323	192	kϱom	kϱom	NOUN
ejpam-6931	323	193	,	,	PUNCT
ejpam-6931	323	194	e	e	NOUN
ejpam-6931	323	195	)	)	PUNCT
ejpam-6931	323	196	⪰	⪰	NOUN
ejpam-6931	323	197	φ(e(ϱon	φ(e(ϱon	NUM
ejpam-6931	323	198	,	,	PUNCT
ejpam-6931	323	199	ϱom	ϱom	NOUN
ejpam-6931	323	200	,	,	PUNCT
ejpam-6931	323	201	e	e	NOUN
ejpam-6931	323	202	)	)	PUNCT
ejpam-6931	323	203	)	)	PUNCT
ejpam-6931	323	204	≻	≻	PROPN
ejpam-6931	324	1	e(ϱon	e(ϱon	PROPN
ejpam-6931	324	2	,	,	PUNCT
ejpam-6931	324	3	ϱom	ϱom	NOUN
ejpam-6931	324	4	,	,	PUNCT
ejpam-6931	324	5	e	e	NOUN
ejpam-6931	324	6	)	)	PUNCT
ejpam-6931	324	7	(	(	PUNCT
ejpam-6931	324	8	7	7	X
ejpam-6931	324	9	)	)	PUNCT
ejpam-6931	324	10	g(ϱon+1	g(ϱon+1	NOUN
ejpam-6931	324	11	,	,	PUNCT
ejpam-6931	324	12	ϱ	ϱ	ADP
ejpam-6931	324	13	o	o	NOUN
ejpam-6931	324	14	m+1	m+1	X
ejpam-6931	324	15	,	,	PUNCT
ejpam-6931	324	16	e	e	NOUN
ejpam-6931	324	17	)	)	PUNCT
ejpam-6931	324	18	=	=	SYM
ejpam-6931	324	19	g(kϱon	g(kϱon	PROPN
ejpam-6931	324	20	,	,	PUNCT
ejpam-6931	324	21	kϱom	kϱom	NOUN
ejpam-6931	324	22	,	,	PUNCT
ejpam-6931	324	23	e	e	NOUN
ejpam-6931	324	24	)	)	PUNCT
ejpam-6931	324	25	⪯	⪯	NOUN
ejpam-6931	324	26	σ(g(ϱon	σ(g(ϱon	PROPN
ejpam-6931	324	27	,	,	PUNCT
ejpam-6931	324	28	ϱom	ϱom	NOUN
ejpam-6931	324	29	,	,	PUNCT
ejpam-6931	324	30	e	e	NOUN
ejpam-6931	324	31	)	)	PUNCT
ejpam-6931	324	32	≺	≺	NOUN
ejpam-6931	324	33	g(ϱon	g(ϱon	NOUN
ejpam-6931	324	34	,	,	PUNCT
ejpam-6931	324	35	ϱom	ϱom	NOUN
ejpam-6931	324	36	,	,	PUNCT
ejpam-6931	324	37	e	e	NOUN
ejpam-6931	324	38	)	)	PUNCT
ejpam-6931	324	39	(	(	PUNCT
ejpam-6931	324	40	8)	8)	NUM
ejpam-6931	324	41	and	and	CCONJ
ejpam-6931	324	42	h(ϱon+1	h(ϱon+1	PROPN
ejpam-6931	324	43	,	,	PUNCT
ejpam-6931	324	44	ϱ	ϱ	ADP
ejpam-6931	324	45	o	o	NOUN
ejpam-6931	324	46	m+1	m+1	X
ejpam-6931	324	47	,	,	PUNCT
ejpam-6931	324	48	e	e	NOUN
ejpam-6931	324	49	)	)	PUNCT
ejpam-6931	324	50	=	=	SYM
ejpam-6931	324	51	h(kϱon	h(kϱon	ADJ
ejpam-6931	324	52	,	,	PUNCT
ejpam-6931	324	53	kϱom	kϱom	NOUN
ejpam-6931	324	54	,	,	PUNCT
ejpam-6931	324	55	e	e	X
ejpam-6931	324	56	)	)	PUNCT
ejpam-6931	324	57	⪯	⪯	PROPN
ejpam-6931	324	58	σ(h(ϱon	σ(h(ϱon	PROPN
ejpam-6931	324	59	,	,	PUNCT
ejpam-6931	324	60	ϱ	ϱ	ADP
ejpam-6931	324	61	o	o	PROPN
ejpam-6931	324	62	m	m	NOUN
ejpam-6931	324	63	,	,	PUNCT
ejpam-6931	324	64	e	e	NOUN
ejpam-6931	324	65	)	)	PUNCT
ejpam-6931	324	66	≺	≺	NOUN
ejpam-6931	324	67	h(ϱon	h(ϱon	PROPN
ejpam-6931	324	68	,	,	PUNCT
ejpam-6931	324	69	ϱ	ϱ	ADP
ejpam-6931	324	70	o	o	PROPN
ejpam-6931	324	71	m	m	NOUN
ejpam-6931	324	72	,	,	PUNCT
ejpam-6931	324	73	e	e	NOUN
ejpam-6931	324	74	)	)	PUNCT
ejpam-6931	324	75	.	.	PUNCT
ejpam-6931	325	1	(	(	PUNCT
ejpam-6931	325	2	9	9	NUM
ejpam-6931	325	3	)	)	PUNCT
ejpam-6931	325	4	from	from	ADP
ejpam-6931	325	5	this	this	PRON
ejpam-6931	325	6	,	,	PUNCT
ejpam-6931	325	7	we	we	PRON
ejpam-6931	325	8	can	can	AUX
ejpam-6931	325	9	conclude	conclude	VERB
ejpam-6931	325	10	that	that	DET
ejpam-6931	325	11	e(ϱon+1	e(ϱon+1	NOUN
ejpam-6931	325	12	,	,	PUNCT
ejpam-6931	325	13	ϱ	ϱ	ADP
ejpam-6931	325	14	o	o	NOUN
ejpam-6931	325	15	m+1	m+1	X
ejpam-6931	325	16	,	,	PUNCT
ejpam-6931	325	17	e	e	NOUN
ejpam-6931	325	18	)	)	PUNCT
ejpam-6931	325	19	≻	≻	PROPN
ejpam-6931	326	1	e(ϱon	e(ϱon	PROPN
ejpam-6931	326	2	,	,	PUNCT
ejpam-6931	326	3	ϱom	ϱom	NOUN
ejpam-6931	326	4	,	,	PUNCT
ejpam-6931	326	5	e	e	NOUN
ejpam-6931	326	6	)	)	PUNCT
ejpam-6931	326	7	g(ϱon+1	g(ϱon+1	NOUN
ejpam-6931	326	8	,	,	PUNCT
ejpam-6931	326	9	ϱ	ϱ	ADP
ejpam-6931	326	10	o	o	NOUN
ejpam-6931	326	11	m+1	m+1	X
ejpam-6931	326	12	,	,	PUNCT
ejpam-6931	326	13	e	e	NOUN
ejpam-6931	326	14	)	)	PUNCT
ejpam-6931	326	15	≺	≺	NOUN
ejpam-6931	326	16	g(ϱon	g(ϱon	NOUN
ejpam-6931	326	17	,	,	PUNCT
ejpam-6931	326	18	ϱom	ϱom	NOUN
ejpam-6931	326	19	,	,	PUNCT
ejpam-6931	326	20	e	e	NOUN
ejpam-6931	326	21	)	)	PUNCT
ejpam-6931	326	22	and	and	CCONJ
ejpam-6931	326	23	h(ϱon+1	h(ϱon+1	PROPN
ejpam-6931	326	24	,	,	PUNCT
ejpam-6931	326	25	ϱ	ϱ	ADP
ejpam-6931	326	26	o	o	NOUN
ejpam-6931	326	27	m+1	m+1	X
ejpam-6931	326	28	,	,	PUNCT
ejpam-6931	326	29	e	e	NOUN
ejpam-6931	326	30	)	)	PUNCT
ejpam-6931	326	31	≺	≺	NOUN
ejpam-6931	326	32	h(ϱon	h(ϱon	PROPN
ejpam-6931	326	33	,	,	PUNCT
ejpam-6931	326	34	ϱ	ϱ	ADP
ejpam-6931	326	35	o	o	PROPN
ejpam-6931	326	36	m	m	NOUN
ejpam-6931	326	37	,	,	PUNCT
ejpam-6931	326	38	e	e	NOUN
ejpam-6931	326	39	)	)	PUNCT
ejpam-6931	326	40	for	for	ADP
ejpam-6931	326	41	all	all	DET
ejpam-6931	326	42	n	n	CCONJ
ejpam-6931	326	43	,	,	PUNCT
ejpam-6931	326	44	m	m	VERB
ejpam-6931	326	45	∈	∈	NOUN
ejpam-6931	326	46	m	m	VERB
ejpam-6931	326	47	such	such	ADJ
ejpam-6931	326	48	that	that	SCONJ
ejpam-6931	326	49	m	m	VERB
ejpam-6931	326	50	>	>	X
ejpam-6931	326	51	n	n	X
ejpam-6931	326	52	with	with	ADP
ejpam-6931	326	53	e	e	PROPN
ejpam-6931	326	54	∈	∈	PROPN
ejpam-6931	326	55	s0	s0	PROPN
ejpam-6931	326	56	.	.	PUNCT
ejpam-6931	327	1	by	by	ADP
ejpam-6931	327	2	taking	take	VERB
ejpam-6931	327	3	the	the	DET
ejpam-6931	327	4	inf(e	inf(e	NOUN
ejpam-6931	327	5	)	)	PUNCT
ejpam-6931	327	6	,	,	PUNCT
ejpam-6931	327	7	sup(g	sup(g	NOUN
ejpam-6931	327	8	)	)	PUNCT
ejpam-6931	327	9	,	,	PUNCT
ejpam-6931	327	10	and	and	CCONJ
ejpam-6931	327	11	sup(h	sup(h	PROPN
ejpam-6931	327	12	)	)	PUNCT
ejpam-6931	327	13	,	,	PUNCT
ejpam-6931	327	14	we	we	PRON
ejpam-6931	327	15	obtain	obtain	VERB
ejpam-6931	327	16	∅	∅	NOUN
ejpam-6931	327	17	⪯	⪯	NOUN
ejpam-6931	327	18	x́n	x́n	PUNCT
ejpam-6931	327	19	⪯	⪯	X
ejpam-6931	327	20	x́n+1	x́n+1	PROPN
ejpam-6931	327	21	⪯	⪯	PROPN
ejpam-6931	327	22	ℑ	ℑ	PROPN
ejpam-6931	327	23	,	,	PUNCT
ejpam-6931	327	24	∅	∅	NOUN
ejpam-6931	327	25	⪯	⪯	NOUN
ejpam-6931	327	26	ýn+1	ýn+1	PROPN
ejpam-6931	327	27	⪯	⪯	PROPN
ejpam-6931	327	28	ýn	ýn	NOUN
ejpam-6931	327	29	⪯	⪯	NOUN
ejpam-6931	327	30	ℑ	ℑ	PROPN
ejpam-6931	327	31	,	,	PUNCT
ejpam-6931	327	32	∅	∅	NOUN
ejpam-6931	327	33	⪯	⪯	NOUN
ejpam-6931	327	34	ćn+1	ćn+1	PROPN
ejpam-6931	327	35	⪯	⪯	X
ejpam-6931	327	36	ćn	ćn	PROPN
ejpam-6931	327	37	⪯	⪯	VERB
ejpam-6931	327	38	ℑ	ℑ	PROPN
ejpam-6931	327	39	for	for	ADP
ejpam-6931	327	40	any	any	DET
ejpam-6931	327	41	n	n	PRON
ejpam-6931	327	42	∈	∈	NOUN
ejpam-6931	327	43	m.	m.	NOUN
ejpam-6931	327	44	thus	thus	ADV
ejpam-6931	327	45	{	{	PUNCT
ejpam-6931	327	46	x́n	x́n	NOUN
ejpam-6931	327	47	}	}	PUNCT
ejpam-6931	327	48	,	,	PUNCT
ejpam-6931	327	49	{	{	PUNCT
ejpam-6931	327	50	ýn	ýn	NOUN
ejpam-6931	327	51	}	}	PUNCT
ejpam-6931	327	52	and	and	CCONJ
ejpam-6931	327	53	{	{	PUNCT
ejpam-6931	327	54	ćn	ćn	ADV
ejpam-6931	327	55	}	}	PUNCT
ejpam-6931	327	56	are	be	AUX
ejpam-6931	327	57	monotonic	monotonic	ADJ
ejpam-6931	327	58	sequences	sequence	NOUN
ejpam-6931	327	59	in	in	ADP
ejpam-6931	327	60	s.	s.	PROPN
ejpam-6931	327	61	according	accord	VERB
ejpam-6931	327	62	to	to	ADP
ejpam-6931	327	63	remarks	remark	NOUN
ejpam-6931	327	64	1	1	NUM
ejpam-6931	327	65	,	,	PUNCT
ejpam-6931	327	66	there	there	PRON
ejpam-6931	327	67	are	be	VERB
ejpam-6931	327	68	complex	complex	ADJ
ejpam-6931	327	69	numbers	number	NOUN
ejpam-6931	327	70	x́	x́	PROPN
ejpam-6931	327	71	,	,	PUNCT
ejpam-6931	327	72	ý	ý	ADJ
ejpam-6931	327	73	,	,	PUNCT
ejpam-6931	327	74	ć	ć	PROPN
ejpam-6931	327	75	∈	∈	PROPN
ejpam-6931	327	76	s	s	AUX
ejpam-6931	327	77	satisfying	satisfy	VERB
ejpam-6931	327	78	limn→∞	limn→∞	X
ejpam-6931	328	1	x́n	x́n	NOUN
ejpam-6931	328	2	=	=	SYM
ejpam-6931	328	3	x́	x́	PROPN
ejpam-6931	328	4	,	,	PUNCT
ejpam-6931	328	5	limn→∞	limn→∞	PRON
ejpam-6931	328	6	ýn	ýn	NOUN
ejpam-6931	328	7	=	=	SYM
ejpam-6931	328	8	ý	ý	ADJ
ejpam-6931	328	9	and	and	CCONJ
ejpam-6931	328	10	limn→∞	limn→∞	ADJ
ejpam-6931	328	11	ćn	ćn	PROPN
ejpam-6931	328	12	=	=	SYM
ejpam-6931	328	13	ć.	ć.	NOUN
ejpam-6931	328	14	by	by	ADP
ejpam-6931	328	15	using	use	VERB
ejpam-6931	328	16	equations	equation	NOUN
ejpam-6931	328	17	(	(	PUNCT
ejpam-6931	328	18	7	7	NUM
ejpam-6931	328	19	)	)	PUNCT
ejpam-6931	328	20	,	,	PUNCT
ejpam-6931	328	21	(	(	PUNCT
ejpam-6931	328	22	8)	8)	NUM
ejpam-6931	328	23	,	,	PUNCT
ejpam-6931	328	24	and	and	CCONJ
ejpam-6931	328	25	(	(	PUNCT
ejpam-6931	328	26	9	9	NUM
ejpam-6931	328	27	)	)	PUNCT
ejpam-6931	328	28	,	,	PUNCT
ejpam-6931	328	29	and	and	CCONJ
ejpam-6931	328	30	employing	employ	VERB
ejpam-6931	328	31	equation	equation	NOUN
ejpam-6931	328	32	(	(	PUNCT
ejpam-6931	328	33	6	6	NUM
ejpam-6931	328	34	)	)	PUNCT
ejpam-6931	328	35	gradually	gradually	ADV
ejpam-6931	328	36	,	,	PUNCT
ejpam-6931	328	37	we	we	PRON
ejpam-6931	328	38	have	have	VERB
ejpam-6931	328	39	e(ϱon+1	e(ϱon+1	NOUN
ejpam-6931	328	40	,	,	PUNCT
ejpam-6931	328	41	ϱ	ϱ	ADP
ejpam-6931	328	42	o	o	NOUN
ejpam-6931	328	43	m+1	m+1	X
ejpam-6931	328	44	,	,	PUNCT
ejpam-6931	328	45	e	e	NOUN
ejpam-6931	328	46	)	)	PUNCT
ejpam-6931	328	47	⪰	⪰	NOUN
ejpam-6931	328	48	φ(e(ϱon	φ(e(ϱon	NUM
ejpam-6931	328	49	,	,	PUNCT
ejpam-6931	328	50	ϱom	ϱom	NOUN
ejpam-6931	328	51	,	,	PUNCT
ejpam-6931	328	52	e	e	NOUN
ejpam-6931	328	53	)	)	PUNCT
ejpam-6931	328	54	)	)	PUNCT
ejpam-6931	328	55	⪰	⪰	NOUN
ejpam-6931	328	56	φ2(e(ϱon−1	φ2(e(ϱon−1	PROPN
ejpam-6931	328	57	,	,	PUNCT
ejpam-6931	328	58	ϱ	ϱ	ADP
ejpam-6931	328	59	o	o	X
ejpam-6931	328	60	m−1	m−1	PROPN
ejpam-6931	328	61	,	,	PUNCT
ejpam-6931	328	62	e	e	NOUN
ejpam-6931	328	63	)	)	PUNCT
ejpam-6931	328	64	)	)	PUNCT
ejpam-6931	328	65	.	.	PUNCT
ejpam-6931	328	66	.	.	PUNCT
ejpam-6931	328	67	.	.	PUNCT
ejpam-6931	329	1	⪰	⪰	PROPN
ejpam-6931	329	2	φ(e(ϱo0	φ(e(ϱo0	PROPN
ejpam-6931	329	3	,	,	PUNCT
ejpam-6931	329	4	ϱom−n	ϱom−n	PROPN
ejpam-6931	329	5	,	,	PUNCT
ejpam-6931	329	6	e	e	NOUN
ejpam-6931	329	7	)	)	PUNCT
ejpam-6931	329	8	)	)	PUNCT
ejpam-6931	329	9	g(ϱon+1	g(ϱon+1	NOUN
ejpam-6931	329	10	,	,	PUNCT
ejpam-6931	329	11	ϱ	ϱ	ADP
ejpam-6931	329	12	o	o	NOUN
ejpam-6931	329	13	m+1	m+1	X
ejpam-6931	329	14	,	,	PUNCT
ejpam-6931	329	15	e	e	NOUN
ejpam-6931	329	16	)	)	PUNCT
ejpam-6931	329	17	⪯	⪯	NOUN
ejpam-6931	329	18	σ(g(ϱon	σ(g(ϱon	PROPN
ejpam-6931	329	19	,	,	PUNCT
ejpam-6931	329	20	ϱom	ϱom	NOUN
ejpam-6931	329	21	,	,	PUNCT
ejpam-6931	329	22	e	e	NOUN
ejpam-6931	329	23	)	)	PUNCT
ejpam-6931	329	24	)	)	PUNCT
ejpam-6931	329	25	⪯	⪯	NOUN
ejpam-6931	329	26	σ2(g(ϱon−1	σ2(g(ϱon−1	PROPN
ejpam-6931	329	27	,	,	PUNCT
ejpam-6931	329	28	ϱ	ϱ	ADP
ejpam-6931	329	29	o	o	X
ejpam-6931	329	30	m−1	m−1	PROPN
ejpam-6931	329	31	,	,	PUNCT
ejpam-6931	329	32	e	e	NOUN
ejpam-6931	329	33	)	)	PUNCT
ejpam-6931	329	34	)	)	PUNCT
ejpam-6931	330	1	s.	s.	PROPN
ejpam-6931	330	2	m.	m.	PROPN
ejpam-6931	330	3	u.	u.	PROPN
ejpam-6931	330	4	ud	ud	AUX
ejpam-6931	330	5	-	-	PUNCT
ejpam-6931	330	6	din	din	VERB
ejpam-6931	330	7	et	et	PROPN
ejpam-6931	330	8	al	al	PROPN
ejpam-6931	330	9	.	.	PUNCT
ejpam-6931	330	10	/	/	SYM
ejpam-6931	330	11	eur	eur	PROPN
ejpam-6931	330	12	.	.	PUNCT
ejpam-6931	331	1	j.	j.	PROPN
ejpam-6931	331	2	pure	pure	PROPN
ejpam-6931	331	3	appl	appl	PROPN
ejpam-6931	331	4	.	.	PROPN
ejpam-6931	331	5	math	math	PROPN
ejpam-6931	331	6	,	,	PUNCT
ejpam-6931	331	7	18	18	NUM
ejpam-6931	331	8	(	(	PUNCT
ejpam-6931	331	9	4	4	NUM
ejpam-6931	331	10	)	)	PUNCT
ejpam-6931	331	11	(	(	PUNCT
ejpam-6931	331	12	2025	2025	NUM
ejpam-6931	331	13	)	)	PUNCT
ejpam-6931	331	14	,	,	PUNCT
ejpam-6931	331	15	6931	6931	NUM
ejpam-6931	331	16	23	23	NUM
ejpam-6931	331	17	of	of	ADP
ejpam-6931	331	18	38	38	NUM
ejpam-6931	331	19	.	.	PUNCT
ejpam-6931	331	20	.	.	PUNCT
ejpam-6931	331	21	.	.	PUNCT
ejpam-6931	332	1	⪯	⪯	PROPN
ejpam-6931	332	2	σ(g(ϱo0	σ(g(ϱo0	PROPN
ejpam-6931	332	3	,	,	PUNCT
ejpam-6931	332	4	ϱom−n	ϱom−n	PROPN
ejpam-6931	332	5	,	,	PUNCT
ejpam-6931	332	6	e	e	NOUN
ejpam-6931	332	7	)	)	PUNCT
ejpam-6931	332	8	)	)	PUNCT
ejpam-6931	332	9	and	and	CCONJ
ejpam-6931	332	10	h(ϱon+1	h(ϱon+1	PROPN
ejpam-6931	332	11	,	,	PUNCT
ejpam-6931	332	12	ϱ	ϱ	ADP
ejpam-6931	332	13	o	o	NOUN
ejpam-6931	332	14	m+1	m+1	X
ejpam-6931	332	15	,	,	PUNCT
ejpam-6931	332	16	e	e	NOUN
ejpam-6931	332	17	)	)	PUNCT
ejpam-6931	332	18	⪯	⪯	PROPN
ejpam-6931	332	19	σ(h(ϱon	σ(h(ϱon	PROPN
ejpam-6931	332	20	,	,	PUNCT
ejpam-6931	332	21	ϱ	ϱ	ADP
ejpam-6931	332	22	o	o	PROPN
ejpam-6931	332	23	m	m	NOUN
ejpam-6931	332	24	,	,	PUNCT
ejpam-6931	332	25	e	e	NOUN
ejpam-6931	332	26	)	)	PUNCT
ejpam-6931	332	27	)	)	PUNCT
ejpam-6931	333	1	⪯	⪯	PROPN
ejpam-6931	333	2	σ2(h(ϱon−1	σ2(h(ϱon−1	PROPN
ejpam-6931	333	3	,	,	PUNCT
ejpam-6931	333	4	ϱ	ϱ	ADP
ejpam-6931	333	5	o	o	X
ejpam-6931	333	6	m−1	m−1	PROPN
ejpam-6931	333	7	,	,	PUNCT
ejpam-6931	333	8	e	e	NOUN
ejpam-6931	333	9	)	)	PUNCT
ejpam-6931	333	10	)	)	PUNCT
ejpam-6931	333	11	.	.	PUNCT
ejpam-6931	333	12	.	.	PUNCT
ejpam-6931	333	13	.	.	PUNCT
ejpam-6931	334	1	⪯	⪯	PROPN
ejpam-6931	334	2	σ(h(ϱo0	σ(h(ϱo0	PROPN
ejpam-6931	334	3	,	,	PUNCT
ejpam-6931	334	4	ϱ	ϱ	ADP
ejpam-6931	334	5	o	o	PROPN
ejpam-6931	334	6	m−n	m−n	PROPN
ejpam-6931	334	7	,	,	PUNCT
ejpam-6931	334	8	e	e	NOUN
ejpam-6931	334	9	)	)	PUNCT
ejpam-6931	334	10	)	)	PUNCT
ejpam-6931	334	11	for	for	ADP
ejpam-6931	334	12	every	every	DET
ejpam-6931	334	13	n	n	NOUN
ejpam-6931	334	14	∈	∈	NOUN
ejpam-6931	334	15	m	m	VERB
ejpam-6931	334	16	such	such	ADJ
ejpam-6931	334	17	that	that	SCONJ
ejpam-6931	334	18	m	m	VERB
ejpam-6931	334	19	>	>	X
ejpam-6931	334	20	n	n	PROPN
ejpam-6931	334	21	and	and	CCONJ
ejpam-6931	334	22	e	e	PROPN
ejpam-6931	334	23	∈	∈	PROPN
ejpam-6931	334	24	s0	s0	PROPN
ejpam-6931	334	25	.	.	PUNCT
ejpam-6931	335	1	this	this	PRON
ejpam-6931	335	2	implies	imply	VERB
ejpam-6931	335	3	that	that	SCONJ
ejpam-6931	335	4	x́n+1	x́n+1	PROPN
ejpam-6931	335	5	⪰	⪰	VERB
ejpam-6931	335	6	inf	inf	PROPN
ejpam-6931	335	7	m	m	PROPN
ejpam-6931	335	8	>	>	NOUN
ejpam-6931	335	9	n	n	PRON
ejpam-6931	335	10	φn(e(ϱo0	φn(e(ϱo0	NUM
ejpam-6931	335	11	,	,	PUNCT
ejpam-6931	335	12	ϱom−n	ϱom−n	PROPN
ejpam-6931	335	13	,	,	PUNCT
ejpam-6931	335	14	e	e	NOUN
ejpam-6931	335	15	)	)	PUNCT
ejpam-6931	335	16	ýn+1	ýn+1	NOUN
ejpam-6931	335	17	⪯	⪯	NOUN
ejpam-6931	335	18	sup	sup	NOUN
ejpam-6931	335	19	m	m	PROPN
ejpam-6931	335	20	>	>	PROPN
ejpam-6931	335	21	n	n	PROPN
ejpam-6931	335	22	σn(g(ϱo0	σn(g(ϱo0	PROPN
ejpam-6931	335	23	,	,	PUNCT
ejpam-6931	335	24	ϱom−n	ϱom−n	PROPN
ejpam-6931	335	25	,	,	PUNCT
ejpam-6931	335	26	e	e	NOUN
ejpam-6931	335	27	)	)	PUNCT
ejpam-6931	335	28	and	and	CCONJ
ejpam-6931	335	29	ćn+1	ćn+1	PROPN
ejpam-6931	335	30	⪯	⪯	NOUN
ejpam-6931	335	31	sup	sup	NOUN
ejpam-6931	335	32	m	m	PROPN
ejpam-6931	335	33	>	>	PROPN
ejpam-6931	335	34	n	n	PROPN
ejpam-6931	335	35	σn(h(ϱo0	σn(h(ϱo0	PROPN
ejpam-6931	335	36	,	,	PUNCT
ejpam-6931	335	37	ϱ	ϱ	ADP
ejpam-6931	335	38	o	o	PROPN
ejpam-6931	335	39	m−n	m−n	PROPN
ejpam-6931	335	40	,	,	PUNCT
ejpam-6931	335	41	e	e	NOUN
ejpam-6931	335	42	)	)	PUNCT
ejpam-6931	335	43	,	,	PUNCT
ejpam-6931	335	44	for	for	SCONJ
ejpam-6931	335	45	every	every	DET
ejpam-6931	335	46	n	n	NOUN
ejpam-6931	335	47	∈	∈	NOUN
ejpam-6931	335	48	m	m	VERB
ejpam-6931	335	49	along	along	ADP
ejpam-6931	335	50	with	with	ADP
ejpam-6931	335	51	c	c	PROPN
ejpam-6931	335	52	∈	∈	PROPN
ejpam-6931	335	53	s0	s0	PROPN
ejpam-6931	335	54	.	.	PUNCT
ejpam-6931	336	1	on	on	ADP
ejpam-6931	336	2	both	both	DET
ejpam-6931	336	3	sides	side	NOUN
ejpam-6931	336	4	of	of	ADP
ejpam-6931	336	5	the	the	DET
ejpam-6931	336	6	above	above	ADJ
ejpam-6931	336	7	inequality	inequality	NOUN
ejpam-6931	336	8	,	,	PUNCT
ejpam-6931	336	9	as	as	SCONJ
ejpam-6931	336	10	n	n	NOUN
ejpam-6931	336	11	approaches	approach	NOUN
ejpam-6931	336	12	infinity	infinity	NOUN
ejpam-6931	336	13	,	,	PUNCT
ejpam-6931	336	14	we	we	PRON
ejpam-6931	336	15	deduce	deduce	VERB
ejpam-6931	336	16	that	that	PRON
ejpam-6931	336	17	x́	x́	PROPN
ejpam-6931	337	1	⪰	⪰	PROPN
ejpam-6931	337	2	lim	lim	PROPN
ejpam-6931	337	3	n→∞	n→∞	PROPN
ejpam-6931	337	4	inf	inf	PROPN
ejpam-6931	337	5	m	m	PROPN
ejpam-6931	337	6	>	>	PROPN
ejpam-6931	337	7	n	n	PRON
ejpam-6931	337	8	φn(e(ϱo0	φn(e(ϱo0	NUM
ejpam-6931	337	9	,	,	PUNCT
ejpam-6931	337	10	ϱom−n	ϱom−n	PROPN
ejpam-6931	337	11	,	,	PUNCT
ejpam-6931	337	12	e	e	NOUN
ejpam-6931	337	13	)	)	PUNCT
ejpam-6931	337	14	)	)	PUNCT
ejpam-6931	338	1	=	=	SYM
ejpam-6931	338	2	lim	lim	PROPN
ejpam-6931	338	3	n→∞	n→∞	NUM
ejpam-6931	338	4	φn(e(ϱo0	φn(e(ϱo0	PROPN
ejpam-6931	338	5	,	,	PUNCT
ejpam-6931	338	6	ϱom−n	ϱom−n	PROPN
ejpam-6931	338	7	,	,	PUNCT
ejpam-6931	338	8	e	e	NOUN
ejpam-6931	338	9	)	)	PUNCT
ejpam-6931	338	10	)	)	PUNCT
ejpam-6931	339	1	=	=	PUNCT
ejpam-6931	339	2	ℑ	ℑ	NOUN
ejpam-6931	339	3	ý	ý	ADJ
ejpam-6931	339	4	⪯	⪯	NOUN
ejpam-6931	339	5	lim	lim	PROPN
ejpam-6931	339	6	n→∞	n→∞	NUM
ejpam-6931	339	7	sup	sup	PROPN
ejpam-6931	339	8	m	m	PROPN
ejpam-6931	339	9	>	>	PROPN
ejpam-6931	339	10	n	n	PROPN
ejpam-6931	339	11	σn(g(ϱo0	σn(g(ϱo0	PROPN
ejpam-6931	339	12	,	,	PUNCT
ejpam-6931	339	13	ϱom−n	ϱom−n	PROPN
ejpam-6931	339	14	,	,	PUNCT
ejpam-6931	339	15	e	e	NOUN
ejpam-6931	339	16	)	)	PUNCT
ejpam-6931	339	17	)	)	PUNCT
ejpam-6931	340	1	=	=	SYM
ejpam-6931	340	2	lim	lim	PROPN
ejpam-6931	340	3	n→∞	n→∞	NUM
ejpam-6931	341	1	σn(g(ϱo0	σn(g(ϱo0	PROPN
ejpam-6931	341	2	,	,	PUNCT
ejpam-6931	341	3	ϱom−n	ϱom−n	PROPN
ejpam-6931	341	4	,	,	PUNCT
ejpam-6931	341	5	e	e	NOUN
ejpam-6931	341	6	)	)	PUNCT
ejpam-6931	341	7	)	)	PUNCT
ejpam-6931	342	1	=	=	NOUN
ejpam-6931	342	2	∅	∅	NOUN
ejpam-6931	342	3	and	and	CCONJ
ejpam-6931	342	4	ć	ć	PROPN
ejpam-6931	342	5	⪯	⪯	PROPN
ejpam-6931	342	6	lim	lim	PROPN
ejpam-6931	342	7	n→∞	n→∞	NUM
ejpam-6931	342	8	sup	sup	PROPN
ejpam-6931	342	9	m	m	PROPN
ejpam-6931	342	10	>	>	X
ejpam-6931	342	11	n	n	PROPN
ejpam-6931	342	12	σn(h(ϱo0	σn(h(ϱo0	PROPN
ejpam-6931	342	13	,	,	PUNCT
ejpam-6931	342	14	ϱ	ϱ	ADP
ejpam-6931	342	15	o	o	PROPN
ejpam-6931	342	16	m−n	m−n	PROPN
ejpam-6931	342	17	,	,	PUNCT
ejpam-6931	342	18	e	e	NOUN
ejpam-6931	342	19	)	)	PUNCT
ejpam-6931	342	20	)	)	PUNCT
ejpam-6931	343	1	s.	s.	PROPN
ejpam-6931	343	2	m.	m.	PROPN
ejpam-6931	343	3	u.	u.	PROPN
ejpam-6931	343	4	ud	ud	AUX
ejpam-6931	343	5	-	-	PUNCT
ejpam-6931	343	6	din	din	VERB
ejpam-6931	343	7	et	et	PROPN
ejpam-6931	343	8	al	al	PROPN
ejpam-6931	343	9	.	.	PUNCT
ejpam-6931	343	10	/	/	SYM
ejpam-6931	343	11	eur	eur	PROPN
ejpam-6931	343	12	.	.	PUNCT
ejpam-6931	344	1	j.	j.	PROPN
ejpam-6931	344	2	pure	pure	PROPN
ejpam-6931	344	3	appl	appl	PROPN
ejpam-6931	344	4	.	.	PROPN
ejpam-6931	344	5	math	math	PROPN
ejpam-6931	344	6	,	,	PUNCT
ejpam-6931	344	7	18	18	NUM
ejpam-6931	344	8	(	(	PUNCT
ejpam-6931	344	9	4	4	NUM
ejpam-6931	344	10	)	)	PUNCT
ejpam-6931	344	11	(	(	PUNCT
ejpam-6931	344	12	2025	2025	NUM
ejpam-6931	344	13	)	)	PUNCT
ejpam-6931	344	14	,	,	PUNCT
ejpam-6931	344	15	6931	6931	NUM
ejpam-6931	344	16	24	24	NUM
ejpam-6931	344	17	of	of	ADP
ejpam-6931	344	18	38	38	NUM
ejpam-6931	344	19	=	=	SYM
ejpam-6931	344	20	lim	lim	PROPN
ejpam-6931	344	21	n→∞	n→∞	NUM
ejpam-6931	344	22	σn(h(ϱo0	σn(h(ϱo0	PROPN
ejpam-6931	344	23	,	,	PUNCT
ejpam-6931	344	24	ϱ	ϱ	ADP
ejpam-6931	344	25	o	o	PROPN
ejpam-6931	344	26	m−n	m−n	PROPN
ejpam-6931	344	27	,	,	PUNCT
ejpam-6931	344	28	e	e	NOUN
ejpam-6931	344	29	)	)	PUNCT
ejpam-6931	344	30	)	)	PUNCT
ejpam-6931	345	1	=	=	PUNCT
ejpam-6931	345	2	∅.	∅.	VERB
ejpam-6931	345	3	hence	hence	ADV
ejpam-6931	345	4	,	,	PUNCT
ejpam-6931	345	5	x́	x́	PUNCT
ejpam-6931	345	6	=	=	SYM
ejpam-6931	345	7	ℑ	ℑ	PROPN
ejpam-6931	345	8	,	,	PUNCT
ejpam-6931	345	9	ý	ý	ADJ
ejpam-6931	345	10	=	=	NOUN
ejpam-6931	345	11	∅	∅	NOUN
ejpam-6931	345	12	and	and	CCONJ
ejpam-6931	345	13	ć	ć	NOUN
ejpam-6931	345	14	=	=	PUNCT
ejpam-6931	345	15	∅.	∅.	VERB
ejpam-6931	345	16	thus	thus	ADV
ejpam-6931	345	17	,	,	PUNCT
ejpam-6931	345	18	lim	lim	PROPN
ejpam-6931	345	19	n→∞	n→∞	NUM
ejpam-6931	345	20	inf	inf	PROPN
ejpam-6931	345	21	m	m	PROPN
ejpam-6931	345	22	>	>	PROPN
ejpam-6931	345	23	n	n	PRON
ejpam-6931	345	24	e(ϱon+1	e(ϱon+1	NOUN
ejpam-6931	345	25	,	,	PUNCT
ejpam-6931	345	26	ϱ	ϱ	ADP
ejpam-6931	345	27	o	o	NOUN
ejpam-6931	345	28	m+1	m+1	X
ejpam-6931	345	29	,	,	PUNCT
ejpam-6931	345	30	e	e	NOUN
ejpam-6931	345	31	)	)	PUNCT
ejpam-6931	345	32	=	=	SYM
ejpam-6931	345	33	lim	lim	NOUN
ejpam-6931	345	34	n→∞	n→∞	X
ejpam-6931	345	35	x́n	x́n	SYM
ejpam-6931	345	36	=	=	SYM
ejpam-6931	345	37	ℑ	ℑ	PROPN
ejpam-6931	345	38	,	,	PUNCT
ejpam-6931	345	39	lim	lim	PROPN
ejpam-6931	345	40	n→∞	n→∞	NUM
ejpam-6931	345	41	sup	sup	PROPN
ejpam-6931	345	42	m	m	PROPN
ejpam-6931	345	43	>	>	NOUN
ejpam-6931	345	44	n	n	PRON
ejpam-6931	345	45	g(ϱon+1	g(ϱon+1	NOUN
ejpam-6931	345	46	,	,	PUNCT
ejpam-6931	345	47	ϱ	ϱ	ADP
ejpam-6931	345	48	o	o	NOUN
ejpam-6931	345	49	m+1	m+1	X
ejpam-6931	345	50	,	,	PUNCT
ejpam-6931	345	51	e	e	NOUN
ejpam-6931	345	52	)	)	PUNCT
ejpam-6931	345	53	=	=	SYM
ejpam-6931	345	54	lim	lim	PROPN
ejpam-6931	345	55	n→∞	n→∞	NUM
ejpam-6931	345	56	ýn	ýn	NOUN
ejpam-6931	345	57	=	=	SYM
ejpam-6931	345	58	∅	∅	NOUN
ejpam-6931	345	59	,	,	PUNCT
ejpam-6931	345	60	lim	lim	PROPN
ejpam-6931	345	61	n→∞	n→∞	NUM
ejpam-6931	345	62	sup	sup	PROPN
ejpam-6931	345	63	m	m	PROPN
ejpam-6931	345	64	>	>	X
ejpam-6931	345	65	n	n	PROPN
ejpam-6931	345	66	h(ϱon+1	h(ϱon+1	PROPN
ejpam-6931	345	67	,	,	PUNCT
ejpam-6931	345	68	ϱ	ϱ	ADP
ejpam-6931	345	69	o	o	NOUN
ejpam-6931	345	70	m+1	m+1	X
ejpam-6931	345	71	,	,	PUNCT
ejpam-6931	345	72	e	e	NOUN
ejpam-6931	345	73	)	)	PUNCT
ejpam-6931	345	74	=	=	SYM
ejpam-6931	345	75	lim	lim	PROPN
ejpam-6931	345	76	n→∞	n→∞	NUM
ejpam-6931	345	77	ýn	ýn	NOUN
ejpam-6931	345	78	=	=	SYM
ejpam-6931	345	79	∅	∅	NOUN
ejpam-6931	345	80	,	,	PUNCT
ejpam-6931	345	81	for	for	ADP
ejpam-6931	345	82	all	all	DET
ejpam-6931	345	83	e	e	X
ejpam-6931	345	84	∈	∈	PROPN
ejpam-6931	345	85	s0	s0	NOUN
ejpam-6931	345	86	which	which	PRON
ejpam-6931	345	87	show	show	VERB
ejpam-6931	345	88	sequence	sequence	NOUN
ejpam-6931	345	89	{	{	PUNCT
ejpam-6931	345	90	ϱon	ϱon	NOUN
ejpam-6931	345	91	}	}	PUNCT
ejpam-6931	345	92	is	be	AUX
ejpam-6931	345	93	cauchy	cauchy	NOUN
ejpam-6931	345	94	.	.	PUNCT
ejpam-6931	346	1	given	give	VERB
ejpam-6931	346	2	that	that	SCONJ
ejpam-6931	346	3	(	(	PUNCT
ejpam-6931	346	4	v	v	NOUN
ejpam-6931	346	5	,	,	PUNCT
ejpam-6931	346	6	e	e	NOUN
ejpam-6931	346	7	,	,	PUNCT
ejpam-6931	346	8	g	g	PROPN
ejpam-6931	346	9	,	,	PUNCT
ejpam-6931	346	10	h	h	NOUN
ejpam-6931	346	11	,	,	PUNCT
ejpam-6931	346	12	⋆	⋆	NOUN
ejpam-6931	346	13	,	,	PUNCT
ejpam-6931	346	14	△	△	NOUN
ejpam-6931	346	15	)	)	PUNCT
ejpam-6931	346	16	is	be	AUX
ejpam-6931	346	17	complete	complete	ADJ
ejpam-6931	346	18	,	,	PUNCT
ejpam-6931	346	19	2	2	NUM
ejpam-6931	346	20	implies	imply	VERB
ejpam-6931	346	21	the	the	DET
ejpam-6931	346	22	existence	existence	NOUN
ejpam-6931	346	23	of	of	ADP
ejpam-6931	346	24	ϱo	ϱo	PROPN
ejpam-6931	346	25	∈	∈	PROPN
ejpam-6931	346	26	v	v	NOUN
ejpam-6931	346	27	satisfying	satisfy	VERB
ejpam-6931	346	28	lim	lim	PROPN
ejpam-6931	346	29	n→∞	n→∞	NUM
ejpam-6931	346	30	e(ϱon	e(ϱon	PROPN
ejpam-6931	346	31	,	,	PUNCT
ejpam-6931	346	32	ϱo	ϱo	NOUN
ejpam-6931	346	33	,	,	PUNCT
ejpam-6931	346	34	e	e	NOUN
ejpam-6931	346	35	)	)	PUNCT
ejpam-6931	346	36	=	=	SYM
ejpam-6931	346	37	ℑ	ℑ	PROPN
ejpam-6931	346	38	,	,	PUNCT
ejpam-6931	346	39	lim	lim	PROPN
ejpam-6931	346	40	n→∞	n→∞	NUM
ejpam-6931	346	41	g(ϱon	g(ϱon	PROPN
ejpam-6931	346	42	,	,	PUNCT
ejpam-6931	346	43	ϱom	ϱom	NOUN
ejpam-6931	346	44	,	,	PUNCT
ejpam-6931	346	45	e	e	NOUN
ejpam-6931	346	46	)	)	PUNCT
ejpam-6931	346	47	=	=	SYM
ejpam-6931	346	48	∅	∅	NOUN
ejpam-6931	346	49	and	and	CCONJ
ejpam-6931	346	50	lim	lim	PROPN
ejpam-6931	346	51	n→∞	n→∞	PROPN
ejpam-6931	347	1	h(ϱon	h(ϱon	PROPN
ejpam-6931	347	2	,	,	PUNCT
ejpam-6931	347	3	ϱ	ϱ	ADP
ejpam-6931	347	4	o	o	PROPN
ejpam-6931	347	5	m	m	NOUN
ejpam-6931	347	6	,	,	PUNCT
ejpam-6931	347	7	e	e	NOUN
ejpam-6931	347	8	)	)	PUNCT
ejpam-6931	347	9	=	=	NOUN
ejpam-6931	347	10	∅	∅	NOUN
ejpam-6931	347	11	(	(	PUNCT
ejpam-6931	347	12	10	10	NUM
ejpam-6931	347	13	)	)	PUNCT
ejpam-6931	347	14	for	for	ADP
ejpam-6931	347	15	any	any	DET
ejpam-6931	347	16	e	e	PROPN
ejpam-6931	347	17	∈	∈	PROPN
ejpam-6931	347	18	s0	s0	PROPN
ejpam-6931	347	19	.	.	PUNCT
ejpam-6931	348	1	as	as	ADP
ejpam-6931	348	2	a	a	DET
ejpam-6931	348	3	result	result	NOUN
ejpam-6931	348	4	of	of	ADP
ejpam-6931	348	5	the	the	DET
ejpam-6931	348	6	conditions	condition	NOUN
ejpam-6931	348	7	(	(	PUNCT
ejpam-6931	348	8	5	5	NUM
ejpam-6931	348	9	)	)	PUNCT
ejpam-6931	348	10	,	,	PUNCT
ejpam-6931	348	11	(	(	PUNCT
ejpam-6931	348	12	10	10	NUM
ejpam-6931	348	13	)	)	PUNCT
ejpam-6931	348	14	and	and	CCONJ
ejpam-6931	348	15	(	(	PUNCT
ejpam-6931	348	16	15	15	NUM
ejpam-6931	348	17	)	)	PUNCT
ejpam-6931	348	18	of	of	ADP
ejpam-6931	348	19	definition	definition	NOUN
ejpam-6931	348	20	7	7	NUM
ejpam-6931	348	21	and	and	CCONJ
ejpam-6931	348	22	equation	equation	NOUN
ejpam-6931	348	23	(	(	PUNCT
ejpam-6931	348	24	6	6	NUM
ejpam-6931	348	25	)	)	PUNCT
ejpam-6931	348	26	,	,	PUNCT
ejpam-6931	348	27	for	for	ADP
ejpam-6931	348	28	any	any	DET
ejpam-6931	348	29	e	e	PROPN
ejpam-6931	348	30	∈	∈	PROPN
ejpam-6931	348	31	s0	s0	PROPN
ejpam-6931	348	32	,	,	PUNCT
ejpam-6931	348	33	we	we	PRON
ejpam-6931	348	34	can	can	AUX
ejpam-6931	348	35	conclude	conclude	VERB
ejpam-6931	348	36	that	that	SCONJ
ejpam-6931	348	37	e(ϱo	e(ϱo	NOUN
ejpam-6931	348	38	,	,	PUNCT
ejpam-6931	348	39	hϱo	hϱo	INTJ
ejpam-6931	348	40	,	,	PUNCT
ejpam-6931	348	41	e	e	NOUN
ejpam-6931	348	42	)	)	PUNCT
ejpam-6931	348	43	⪰	⪰	NOUN
ejpam-6931	348	44	e	e	X
ejpam-6931	348	45	(	(	PUNCT
ejpam-6931	348	46	ϱo	ϱo	PROPN
ejpam-6931	348	47	,	,	PUNCT
ejpam-6931	348	48	ϱon+1	ϱon+1	PROPN
ejpam-6931	348	49	,	,	PUNCT
ejpam-6931	348	50	e	e	X
ejpam-6931	348	51	2	2	NUM
ejpam-6931	348	52	)	)	PUNCT
ejpam-6931	348	53	∗	∗	NOUN
ejpam-6931	348	54	e	e	NOUN
ejpam-6931	348	55	(	(	PUNCT
ejpam-6931	348	56	ϱon+1,kϱo	ϱon+1,kϱo	ADV
ejpam-6931	348	57	,	,	PUNCT
ejpam-6931	348	58	e	e	X
ejpam-6931	348	59	2	2	NUM
ejpam-6931	348	60	)	)	PUNCT
ejpam-6931	348	61	=	=	SYM
ejpam-6931	348	62	ea	ea	X
ejpam-6931	348	63	(	(	PUNCT
ejpam-6931	348	64	ϱo	ϱo	PROPN
ejpam-6931	348	65	,	,	PUNCT
ejpam-6931	348	66	ϱon+1	ϱon+1	PROPN
ejpam-6931	348	67	,	,	PUNCT
ejpam-6931	348	68	e	e	X
ejpam-6931	348	69	2	2	NUM
ejpam-6931	348	70	)	)	PUNCT
ejpam-6931	348	71	∗	∗	NOUN
ejpam-6931	348	72	e	e	NOUN
ejpam-6931	348	73	(	(	PUNCT
ejpam-6931	348	74	kϱon	kϱon	PROPN
ejpam-6931	348	75	,	,	PUNCT
ejpam-6931	348	76	kϱo	kϱo	NOUN
ejpam-6931	348	77	,	,	PUNCT
ejpam-6931	348	78	e	e	X
ejpam-6931	348	79	2	2	X
ejpam-6931	348	80	)	)	PUNCT
ejpam-6931	348	81	⪰	⪰	NOUN
ejpam-6931	348	82	e	e	X
ejpam-6931	348	83	(	(	PUNCT
ejpam-6931	348	84	ϱo	ϱo	PROPN
ejpam-6931	348	85	,	,	PUNCT
ejpam-6931	348	86	ϱon+1	ϱon+1	PROPN
ejpam-6931	348	87	,	,	PUNCT
ejpam-6931	348	88	e	e	X
ejpam-6931	348	89	2	2	X
ejpam-6931	348	90	)	)	PUNCT
ejpam-6931	348	91	∗	∗	NOUN
ejpam-6931	348	92	φ	φ	PROPN
ejpam-6931	348	93	(	(	PUNCT
ejpam-6931	348	94	e	e	X
ejpam-6931	348	95	(	(	PUNCT
ejpam-6931	348	96	ϱon	ϱon	PROPN
ejpam-6931	348	97	,	,	PUNCT
ejpam-6931	348	98	ϱ	ϱ	ADP
ejpam-6931	348	99	o	o	PROPN
ejpam-6931	348	100	,	,	PUNCT
ejpam-6931	348	101	e	e	PROPN
ejpam-6931	348	102	2	2	NUM
ejpam-6931	348	103	)	)	PUNCT
ejpam-6931	348	104	)	)	PUNCT
ejpam-6931	348	105	≻	≻	PROPN
ejpam-6931	349	1	e	e	X
ejpam-6931	349	2	(	(	PUNCT
ejpam-6931	349	3	ϱo	ϱo	PROPN
ejpam-6931	349	4	,	,	PUNCT
ejpam-6931	349	5	ϱon+1	ϱon+1	PROPN
ejpam-6931	349	6	,	,	PUNCT
ejpam-6931	349	7	e	e	X
ejpam-6931	349	8	2	2	NUM
ejpam-6931	349	9	)	)	PUNCT
ejpam-6931	349	10	∗	∗	NOUN
ejpam-6931	349	11	e	e	X
ejpam-6931	349	12	(	(	PUNCT
ejpam-6931	349	13	ϱon	ϱon	PROPN
ejpam-6931	349	14	,	,	PUNCT
ejpam-6931	349	15	ϱ	ϱ	ADP
ejpam-6931	349	16	o	o	PROPN
ejpam-6931	349	17	,	,	PUNCT
ejpam-6931	349	18	e	e	X
ejpam-6931	349	19	2	2	NUM
ejpam-6931	349	20	)	)	PUNCT
ejpam-6931	349	21	g(ϱo	g(ϱo	PROPN
ejpam-6931	349	22	,	,	PUNCT
ejpam-6931	349	23	kϱo	kϱo	NOUN
ejpam-6931	349	24	,	,	PUNCT
ejpam-6931	349	25	e	e	NOUN
ejpam-6931	349	26	)	)	PUNCT
ejpam-6931	349	27	⪯	⪯	NOUN
ejpam-6931	349	28	g	g	PROPN
ejpam-6931	349	29	(	(	PUNCT
ejpam-6931	349	30	ϱo	ϱo	PROPN
ejpam-6931	349	31	,	,	PUNCT
ejpam-6931	349	32	ϱon+1	ϱon+1	PROPN
ejpam-6931	349	33	,	,	PUNCT
ejpam-6931	349	34	e	e	X
ejpam-6931	349	35	2	2	NUM
ejpam-6931	349	36	)	)	PUNCT
ejpam-6931	349	37	△	△	PROPN
ejpam-6931	349	38	g	g	NOUN
ejpam-6931	349	39	(	(	PUNCT
ejpam-6931	349	40	ϱon+1,kϱo	ϱon+1,kϱo	PROPN
ejpam-6931	349	41	,	,	PUNCT
ejpam-6931	349	42	e	e	X
ejpam-6931	349	43	2	2	NUM
ejpam-6931	349	44	)	)	PUNCT
ejpam-6931	349	45	=	=	SYM
ejpam-6931	349	46	g	g	PROPN
ejpam-6931	349	47	(	(	PUNCT
ejpam-6931	349	48	ϱo	ϱo	PROPN
ejpam-6931	349	49	,	,	PUNCT
ejpam-6931	349	50	ϱon+1	ϱon+1	PROPN
ejpam-6931	349	51	,	,	PUNCT
ejpam-6931	349	52	e	e	X
ejpam-6931	349	53	2	2	NUM
ejpam-6931	349	54	)	)	PUNCT
ejpam-6931	349	55	△	△	PROPN
ejpam-6931	349	56	g	g	PROPN
ejpam-6931	349	57	(	(	PUNCT
ejpam-6931	349	58	kϱon	kϱon	PROPN
ejpam-6931	349	59	,	,	PUNCT
ejpam-6931	349	60	kϱo	kϱo	NOUN
ejpam-6931	349	61	,	,	PUNCT
ejpam-6931	349	62	e	e	X
ejpam-6931	349	63	2	2	X
ejpam-6931	349	64	)	)	PUNCT
ejpam-6931	349	65	⪯	⪯	NOUN
ejpam-6931	349	66	g	g	PROPN
ejpam-6931	349	67	(	(	PUNCT
ejpam-6931	349	68	ϱo	ϱo	PROPN
ejpam-6931	349	69	,	,	PUNCT
ejpam-6931	349	70	ϱon+1	ϱon+1	PROPN
ejpam-6931	349	71	,	,	PUNCT
ejpam-6931	349	72	e	e	X
ejpam-6931	349	73	2	2	NUM
ejpam-6931	349	74	)	)	PUNCT
ejpam-6931	350	1	△	△	PROPN
ejpam-6931	351	1	σ	σ	PROPN
ejpam-6931	352	1	(	(	PUNCT
ejpam-6931	352	2	g	g	PROPN
ejpam-6931	352	3	(	(	PUNCT
ejpam-6931	352	4	ϱon	ϱon	PROPN
ejpam-6931	352	5	,	,	PUNCT
ejpam-6931	352	6	ϱ	ϱ	ADP
ejpam-6931	352	7	o	o	PROPN
ejpam-6931	352	8	,	,	PUNCT
ejpam-6931	352	9	e	e	PROPN
ejpam-6931	352	10	2	2	NUM
ejpam-6931	352	11	)	)	PUNCT
ejpam-6931	352	12	)	)	PUNCT
ejpam-6931	353	1	≺	≺	VERB
ejpam-6931	353	2	g	g	PROPN
ejpam-6931	353	3	(	(	PUNCT
ejpam-6931	353	4	ϱo	ϱo	PROPN
ejpam-6931	353	5	,	,	PUNCT
ejpam-6931	353	6	ϱon+1	ϱon+1	PROPN
ejpam-6931	353	7	,	,	PUNCT
ejpam-6931	353	8	e	e	X
ejpam-6931	353	9	2	2	NUM
ejpam-6931	353	10	)	)	PUNCT
ejpam-6931	353	11	△	△	PROPN
ejpam-6931	353	12	g	g	PROPN
ejpam-6931	353	13	(	(	PUNCT
ejpam-6931	353	14	ϱon	ϱon	PROPN
ejpam-6931	353	15	,	,	PUNCT
ejpam-6931	353	16	ϱ	ϱ	ADP
ejpam-6931	353	17	o	o	PROPN
ejpam-6931	353	18	,	,	PUNCT
ejpam-6931	353	19	e	e	X
ejpam-6931	353	20	2	2	NUM
ejpam-6931	353	21	)	)	PUNCT
ejpam-6931	353	22	and	and	CCONJ
ejpam-6931	353	23	h(ϱo	h(ϱo	ADJ
ejpam-6931	353	24	,	,	PUNCT
ejpam-6931	353	25	kϱo	kϱo	NOUN
ejpam-6931	353	26	,	,	PUNCT
ejpam-6931	353	27	e	e	NOUN
ejpam-6931	353	28	)	)	PUNCT
ejpam-6931	353	29	⪯	⪯	PROPN
ejpam-6931	353	30	h	h	PROPN
ejpam-6931	353	31	(	(	PUNCT
ejpam-6931	353	32	ϱo	ϱo	PROPN
ejpam-6931	353	33	,	,	PUNCT
ejpam-6931	353	34	ϱon+1	ϱon+1	PROPN
ejpam-6931	353	35	,	,	PUNCT
ejpam-6931	353	36	e	e	X
ejpam-6931	353	37	2	2	NUM
ejpam-6931	353	38	)	)	PUNCT
ejpam-6931	353	39	△	△	PROPN
ejpam-6931	353	40	h	h	NOUN
ejpam-6931	353	41	(	(	PUNCT
ejpam-6931	353	42	ϱon+1	ϱon+1	PROPN
ejpam-6931	353	43	,	,	PUNCT
ejpam-6931	353	44	hϱ	hϱ	PRON
ejpam-6931	353	45	o	o	NOUN
ejpam-6931	353	46	,	,	PUNCT
ejpam-6931	353	47	e	e	X
ejpam-6931	353	48	2	2	NUM
ejpam-6931	353	49	)	)	PUNCT
ejpam-6931	354	1	=	=	SYM
ejpam-6931	354	2	h	h	NOUN
ejpam-6931	354	3	(	(	PUNCT
ejpam-6931	354	4	ϱo	ϱo	PROPN
ejpam-6931	354	5	,	,	PUNCT
ejpam-6931	354	6	ϱon+1	ϱon+1	PROPN
ejpam-6931	354	7	,	,	PUNCT
ejpam-6931	354	8	e	e	X
ejpam-6931	354	9	2	2	NUM
ejpam-6931	354	10	)	)	PUNCT
ejpam-6931	354	11	△	△	PROPN
ejpam-6931	354	12	h	h	NOUN
ejpam-6931	354	13	(	(	PUNCT
ejpam-6931	354	14	kϱon	kϱon	PROPN
ejpam-6931	354	15	,	,	PUNCT
ejpam-6931	354	16	kϱo	kϱo	NOUN
ejpam-6931	354	17	,	,	PUNCT
ejpam-6931	354	18	e	e	X
ejpam-6931	354	19	2	2	X
ejpam-6931	354	20	)	)	PUNCT
ejpam-6931	354	21	⪯	⪯	NOUN
ejpam-6931	354	22	h	h	PROPN
ejpam-6931	354	23	(	(	PUNCT
ejpam-6931	354	24	ϱo	ϱo	PROPN
ejpam-6931	354	25	,	,	PUNCT
ejpam-6931	354	26	ϱon+1	ϱon+1	PROPN
ejpam-6931	354	27	,	,	PUNCT
ejpam-6931	354	28	e	e	X
ejpam-6931	354	29	2	2	NUM
ejpam-6931	354	30	)	)	PUNCT
ejpam-6931	354	31	△	△	PROPN
ejpam-6931	354	32	σ	σ	PROPN
ejpam-6931	354	33	(	(	PUNCT
ejpam-6931	354	34	h	h	PROPN
ejpam-6931	354	35	(	(	PUNCT
ejpam-6931	354	36	ϱon	ϱon	PROPN
ejpam-6931	354	37	,	,	PUNCT
ejpam-6931	354	38	ϱ	ϱ	ADP
ejpam-6931	354	39	o	o	PROPN
ejpam-6931	354	40	,	,	PUNCT
ejpam-6931	354	41	e	e	PROPN
ejpam-6931	354	42	2	2	NUM
ejpam-6931	354	43	)	)	PUNCT
ejpam-6931	354	44	)	)	PUNCT
ejpam-6931	354	45	≺	≺	NOUN
ejpam-6931	354	46	h	h	NOUN
ejpam-6931	354	47	(	(	PUNCT
ejpam-6931	354	48	ϱo	ϱo	PROPN
ejpam-6931	354	49	,	,	PUNCT
ejpam-6931	354	50	ϱon+1	ϱon+1	PROPN
ejpam-6931	354	51	,	,	PUNCT
ejpam-6931	354	52	e	e	X
ejpam-6931	354	53	2	2	NUM
ejpam-6931	354	54	)	)	PUNCT
ejpam-6931	354	55	△	△	PROPN
ejpam-6931	354	56	h	h	NOUN
ejpam-6931	354	57	(	(	PUNCT
ejpam-6931	354	58	ϱon	ϱon	PROPN
ejpam-6931	354	59	,	,	PUNCT
ejpam-6931	354	60	ϱ	ϱ	ADP
ejpam-6931	354	61	o	o	PROPN
ejpam-6931	354	62	,	,	PUNCT
ejpam-6931	354	63	e	e	X
ejpam-6931	354	64	2	2	NUM
ejpam-6931	354	65	)	)	PUNCT
ejpam-6931	354	66	.	.	PUNCT
ejpam-6931	355	1	s.	s.	PROPN
ejpam-6931	355	2	m.	m.	PROPN
ejpam-6931	355	3	u.	u.	PROPN
ejpam-6931	355	4	ud	ud	AUX
ejpam-6931	355	5	-	-	PUNCT
ejpam-6931	355	6	din	din	VERB
ejpam-6931	355	7	et	et	PROPN
ejpam-6931	355	8	al	al	PROPN
ejpam-6931	355	9	.	.	PUNCT
ejpam-6931	355	10	/	/	SYM
ejpam-6931	355	11	eur	eur	PROPN
ejpam-6931	355	12	.	.	PUNCT
ejpam-6931	356	1	j.	j.	PROPN
ejpam-6931	356	2	pure	pure	PROPN
ejpam-6931	356	3	appl	appl	PROPN
ejpam-6931	356	4	.	.	PROPN
ejpam-6931	356	5	math	math	PROPN
ejpam-6931	356	6	,	,	PUNCT
ejpam-6931	356	7	18	18	NUM
ejpam-6931	356	8	(	(	PUNCT
ejpam-6931	356	9	4	4	NUM
ejpam-6931	356	10	)	)	PUNCT
ejpam-6931	356	11	(	(	PUNCT
ejpam-6931	356	12	2025	2025	NUM
ejpam-6931	356	13	)	)	PUNCT
ejpam-6931	356	14	,	,	PUNCT
ejpam-6931	356	15	6931	6931	NUM
ejpam-6931	356	16	25	25	NUM
ejpam-6931	356	17	of	of	ADP
ejpam-6931	356	18	38	38	NUM
ejpam-6931	356	19	considering	consider	VERB
ejpam-6931	356	20	the	the	DET
ejpam-6931	356	21	preceding	precede	VERB
ejpam-6931	356	22	inequalities	inequality	NOUN
ejpam-6931	356	23	and	and	CCONJ
ejpam-6931	356	24	applying	apply	VERB
ejpam-6931	356	25	limn→∞	limn→∞	PROPN
ejpam-6931	356	26	,	,	PUNCT
ejpam-6931	356	27	by	by	ADP
ejpam-6931	356	28	using	use	VERB
ejpam-6931	356	29	equation	equation	NOUN
ejpam-6931	356	30	(	(	PUNCT
ejpam-6931	356	31	10	10	NUM
ejpam-6931	356	32	)	)	PUNCT
ejpam-6931	357	1	,	,	PUNCT
ejpam-6931	357	2	we	we	PRON
ejpam-6931	357	3	can	can	AUX
ejpam-6931	357	4	conclude	conclude	VERB
ejpam-6931	357	5	that	that	SCONJ
ejpam-6931	357	6	e(ϱo	e(ϱo	NOUN
ejpam-6931	357	7	,	,	PUNCT
ejpam-6931	357	8	kϱo	kϱo	NOUN
ejpam-6931	357	9	,	,	PUNCT
ejpam-6931	357	10	e	e	NOUN
ejpam-6931	357	11	)	)	PUNCT
ejpam-6931	357	12	=	=	SYM
ejpam-6931	357	13	ℑ	ℑ	PROPN
ejpam-6931	357	14	,	,	PUNCT
ejpam-6931	357	15	g(ϱo	g(ϱo	PROPN
ejpam-6931	357	16	,	,	PUNCT
ejpam-6931	357	17	kϱo	kϱo	NOUN
ejpam-6931	357	18	,	,	PUNCT
ejpam-6931	357	19	e	e	NOUN
ejpam-6931	357	20	)	)	PUNCT
ejpam-6931	357	21	=	=	SYM
ejpam-6931	357	22	∅	∅	NOUN
ejpam-6931	357	23	and	and	CCONJ
ejpam-6931	357	24	h(ϱo	h(ϱo	ADJ
ejpam-6931	357	25	,	,	PUNCT
ejpam-6931	357	26	kϱo	kϱo	NOUN
ejpam-6931	357	27	,	,	PUNCT
ejpam-6931	357	28	e	e	NOUN
ejpam-6931	357	29	)	)	PUNCT
ejpam-6931	357	30	=	=	NOUN
ejpam-6931	357	31	∅	∅	NOUN
ejpam-6931	357	32	for	for	ADP
ejpam-6931	357	33	any	any	DET
ejpam-6931	357	34	e	e	PROPN
ejpam-6931	357	35	∈	∈	PROPN
ejpam-6931	357	36	s0	s0	PROPN
ejpam-6931	357	37	.	.	PUNCT
ejpam-6931	358	1	by	by	ADP
ejpam-6931	358	2	applying	apply	VERB
ejpam-6931	358	3	the	the	DET
ejpam-6931	358	4	conditions	condition	NOUN
ejpam-6931	358	5	(	(	PUNCT
ejpam-6931	358	6	3	3	NUM
ejpam-6931	358	7	)	)	PUNCT
ejpam-6931	358	8	,	,	PUNCT
ejpam-6931	358	9	(	(	PUNCT
ejpam-6931	358	10	8)	8)	NUM
ejpam-6931	358	11	and	and	CCONJ
ejpam-6931	358	12	(	(	PUNCT
ejpam-6931	358	13	13	13	NUM
ejpam-6931	358	14	)	)	PUNCT
ejpam-6931	358	15	of	of	ADP
ejpam-6931	358	16	definition	definition	NOUN
ejpam-6931	358	17	7	7	NUM
ejpam-6931	358	18	,	,	PUNCT
ejpam-6931	358	19	it	it	PRON
ejpam-6931	358	20	can	can	AUX
ejpam-6931	358	21	be	be	AUX
ejpam-6931	358	22	derived	derive	VERB
ejpam-6931	358	23	that	that	PRON
ejpam-6931	358	24	ϱo	ϱo	PROPN
ejpam-6931	358	25	=	=	PUNCT
ejpam-6931	358	26	kϱo	kϱo	NOUN
ejpam-6931	358	27	,	,	PUNCT
ejpam-6931	358	28	that	that	ADV
ejpam-6931	358	29	is	is	ADV
ejpam-6931	358	30	,	,	PUNCT
ejpam-6931	358	31	ϱois	ϱois	VERB
ejpam-6931	358	32	a	a	DET
ejpam-6931	358	33	fixed	fix	VERB
ejpam-6931	358	34	point	point	NOUN
ejpam-6931	358	35	of	of	ADP
ejpam-6931	358	36	k.	k.	PROPN
ejpam-6931	358	37	to	to	PART
ejpam-6931	358	38	prove	prove	VERB
ejpam-6931	358	39	the	the	DET
ejpam-6931	358	40	uniqueness	uniqueness	NOUN
ejpam-6931	358	41	of	of	ADP
ejpam-6931	358	42	fixed	fix	VERB
ejpam-6931	358	43	point	point	NOUN
ejpam-6931	358	44	,	,	PUNCT
ejpam-6931	358	45	suppose	suppose	VERB
ejpam-6931	358	46	that	that	SCONJ
ejpam-6931	358	47	z	z	PROPN
ejpam-6931	358	48	and	and	CCONJ
ejpam-6931	358	49	ϱo	ϱo	PROPN
ejpam-6931	358	50	are	be	AUX
ejpam-6931	358	51	two	two	NUM
ejpam-6931	358	52	distinct	distinct	ADJ
ejpam-6931	358	53	fixed	fix	VERB
ejpam-6931	358	54	points	point	NOUN
ejpam-6931	358	55	of	of	ADP
ejpam-6931	358	56	k.	k.	NOUN
ejpam-6931	358	57	according	accord	VERB
ejpam-6931	358	58	to	to	ADP
ejpam-6931	358	59	equation	equation	NOUN
ejpam-6931	358	60	(	(	PUNCT
ejpam-6931	358	61	6	6	NUM
ejpam-6931	358	62	)	)	PUNCT
ejpam-6931	358	63	for	for	ADP
ejpam-6931	358	64	every	every	DET
ejpam-6931	358	65	c	c	PROPN
ejpam-6931	358	66	∈	∈	PROPN
ejpam-6931	358	67	s0	s0	PROPN
ejpam-6931	358	68	,	,	PUNCT
ejpam-6931	358	69	it	it	PRON
ejpam-6931	358	70	implies	imply	VERB
ejpam-6931	358	71	e(ϱo	e(ϱo	NOUN
ejpam-6931	358	72	,	,	PUNCT
ejpam-6931	358	73	z	z	NOUN
ejpam-6931	358	74	,	,	PUNCT
ejpam-6931	358	75	e	e	NOUN
ejpam-6931	358	76	)	)	PUNCT
ejpam-6931	358	77	=	=	SYM
ejpam-6931	358	78	e(kϱo	e(kϱo	PROPN
ejpam-6931	358	79	,	,	PUNCT
ejpam-6931	358	80	kz	kz	PROPN
ejpam-6931	358	81	,	,	PUNCT
ejpam-6931	358	82	e	e	NOUN
ejpam-6931	358	83	)	)	PUNCT
ejpam-6931	358	84	⪰	⪰	NOUN
ejpam-6931	358	85	φ(e(ϱo	φ(e(ϱo	ADJ
ejpam-6931	358	86	,	,	PUNCT
ejpam-6931	358	87	z	z	NOUN
ejpam-6931	358	88	,	,	PUNCT
ejpam-6931	358	89	e	e	NOUN
ejpam-6931	358	90	)	)	PUNCT
ejpam-6931	358	91	)	)	PUNCT
ejpam-6931	358	92	≻	≻	VERB
ejpam-6931	359	1	e(ϱo	e(ϱo	PROPN
ejpam-6931	359	2	,	,	PUNCT
ejpam-6931	359	3	z	z	NOUN
ejpam-6931	359	4	,	,	PUNCT
ejpam-6931	359	5	e	e	NOUN
ejpam-6931	359	6	)	)	PUNCT
ejpam-6931	359	7	g(ϱo	g(ϱo	PROPN
ejpam-6931	359	8	,	,	PUNCT
ejpam-6931	359	9	z	z	NOUN
ejpam-6931	359	10	,	,	PUNCT
ejpam-6931	359	11	e	e	NOUN
ejpam-6931	359	12	)	)	PUNCT
ejpam-6931	359	13	=	=	SYM
ejpam-6931	359	14	g(kϱo	g(kϱo	PROPN
ejpam-6931	359	15	,	,	PUNCT
ejpam-6931	359	16	kz	kz	PROPN
ejpam-6931	359	17	,	,	PUNCT
ejpam-6931	359	18	e	e	NOUN
ejpam-6931	359	19	)	)	PUNCT
ejpam-6931	359	20	⪯	⪯	NOUN
ejpam-6931	359	21	σ(g(ϱo	σ(g(ϱo	NOUN
ejpam-6931	359	22	,	,	PUNCT
ejpam-6931	359	23	z	z	NOUN
ejpam-6931	359	24	,	,	PUNCT
ejpam-6931	359	25	e	e	NOUN
ejpam-6931	359	26	)	)	PUNCT
ejpam-6931	359	27	)	)	PUNCT
ejpam-6931	359	28	≺	≺	NOUN
ejpam-6931	359	29	g(ϱo	g(ϱo	NOUN
ejpam-6931	359	30	,	,	PUNCT
ejpam-6931	359	31	z	z	NOUN
ejpam-6931	359	32	,	,	PUNCT
ejpam-6931	359	33	e	e	NOUN
ejpam-6931	359	34	)	)	PUNCT
ejpam-6931	359	35	and	and	CCONJ
ejpam-6931	359	36	h(ϱo	h(ϱo	ADJ
ejpam-6931	359	37	,	,	PUNCT
ejpam-6931	359	38	z	z	NOUN
ejpam-6931	359	39	,	,	PUNCT
ejpam-6931	359	40	e	e	NOUN
ejpam-6931	359	41	)	)	PUNCT
ejpam-6931	359	42	=	=	SYM
ejpam-6931	359	43	h(kϱo	h(kϱo	PROPN
ejpam-6931	359	44	,	,	PUNCT
ejpam-6931	359	45	kz	kz	PROPN
ejpam-6931	359	46	,	,	PUNCT
ejpam-6931	359	47	e	e	NOUN
ejpam-6931	359	48	)	)	PUNCT
ejpam-6931	359	49	⪯	⪯	NOUN
ejpam-6931	359	50	σ(h(ϱo	σ(h(ϱo	ADJ
ejpam-6931	359	51	,	,	PUNCT
ejpam-6931	359	52	z	z	NOUN
ejpam-6931	359	53	,	,	PUNCT
ejpam-6931	359	54	e	e	NOUN
ejpam-6931	359	55	)	)	PUNCT
ejpam-6931	359	56	)	)	PUNCT
ejpam-6931	359	57	≺	≺	NOUN
ejpam-6931	359	58	h(ϱo	h(ϱo	ADJ
ejpam-6931	359	59	,	,	PUNCT
ejpam-6931	359	60	z	z	NOUN
ejpam-6931	359	61	,	,	PUNCT
ejpam-6931	359	62	e	e	X
ejpam-6931	359	63	)	)	PUNCT
ejpam-6931	359	64	it	it	PRON
ejpam-6931	359	65	is	be	AUX
ejpam-6931	359	66	a	a	DET
ejpam-6931	359	67	contradiction	contradiction	NOUN
ejpam-6931	359	68	.	.	PUNCT
ejpam-6931	360	1	consequently	consequently	ADV
ejpam-6931	360	2	,	,	PUNCT
ejpam-6931	360	3	x	x	PROPN
ejpam-6931	360	4	=	=	SYM
ejpam-6931	360	5	z	z	PROPN
ejpam-6931	360	6	,	,	PUNCT
ejpam-6931	360	7	which	which	PRON
ejpam-6931	360	8	shows	show	VERB
ejpam-6931	360	9	that	that	SCONJ
ejpam-6931	360	10	fixed	fix	VERB
ejpam-6931	360	11	point	point	NOUN
ejpam-6931	360	12	is	be	AUX
ejpam-6931	360	13	unique	unique	ADJ
ejpam-6931	360	14	.	.	PUNCT
ejpam-6931	361	1	5	5	X
ejpam-6931	361	2	.	.	X
ejpam-6931	361	3	common	common	ADJ
ejpam-6931	361	4	fixed	fix	VERB
ejpam-6931	361	5	-	-	PUNCT
ejpam-6931	361	6	point	point	NOUN
ejpam-6931	361	7	results	result	NOUN
ejpam-6931	361	8	this	this	DET
ejpam-6931	361	9	section	section	NOUN
ejpam-6931	361	10	investigates	investigate	VERB
ejpam-6931	361	11	several	several	ADJ
ejpam-6931	361	12	standard	standard	ADJ
ejpam-6931	361	13	fixed	fix	VERB
ejpam-6931	361	14	-	-	PUNCT
ejpam-6931	361	15	point	point	NOUN
ejpam-6931	361	16	theorems	theorem	NOUN
ejpam-6931	361	17	for	for	ADP
ejpam-6931	361	18	two	two	NUM
ejpam-6931	361	19	mappings	mapping	NOUN
ejpam-6931	361	20	that	that	PRON
ejpam-6931	361	21	satisfy	satisfy	VERB
ejpam-6931	361	22	the	the	DET
ejpam-6931	361	23	given	give	VERB
ejpam-6931	361	24	contraction	contraction	NOUN
ejpam-6931	361	25	condition	condition	NOUN
ejpam-6931	361	26	on	on	ADP
ejpam-6931	361	27	cvnmss	cvnmss	NOUN
ejpam-6931	361	28	.	.	PUNCT
ejpam-6931	362	1	it	it	PRON
ejpam-6931	362	2	extends	extend	VERB
ejpam-6931	362	3	the	the	DET
ejpam-6931	362	4	concept	concept	NOUN
ejpam-6931	362	5	of	of	ADP
ejpam-6931	362	6	fuzzy	fuzzy	ADJ
ejpam-6931	362	7	banach	banach	NOUN
ejpam-6931	362	8	contraction	contraction	NOUN
ejpam-6931	362	9	to	to	ADP
ejpam-6931	362	10	these	these	DET
ejpam-6931	362	11	spaces	space	NOUN
ejpam-6931	362	12	.	.	PUNCT
ejpam-6931	363	1	definition	definition	NOUN
ejpam-6931	363	2	10	10	NUM
ejpam-6931	363	3	.	.	PUNCT
ejpam-6931	364	1	let	let	VERB
ejpam-6931	364	2	(	(	PUNCT
ejpam-6931	364	3	v	v	NOUN
ejpam-6931	364	4	,	,	PUNCT
ejpam-6931	364	5	e	e	NOUN
ejpam-6931	364	6	,	,	PUNCT
ejpam-6931	364	7	g	g	PROPN
ejpam-6931	364	8	,	,	PUNCT
ejpam-6931	364	9	h	h	NOUN
ejpam-6931	364	10	,	,	PUNCT
ejpam-6931	364	11	⋆	⋆	NOUN
ejpam-6931	364	12	,	,	PUNCT
ejpam-6931	364	13	△	△	X
ejpam-6931	364	14	)	)	PUNCT
ejpam-6931	364	15	be	be	AUX
ejpam-6931	364	16	a	a	DET
ejpam-6931	364	17	cvnms	cvnms	NOUN
ejpam-6931	364	18	.	.	PUNCT
ejpam-6931	365	1	a	a	DET
ejpam-6931	365	2	neutrosophic	neutrosophic	ADJ
ejpam-6931	365	3	banach	banach	NOUN
ejpam-6931	365	4	contraction	contraction	NOUN
ejpam-6931	365	5	is	be	AUX
ejpam-6931	365	6	defined	define	VERB
ejpam-6931	365	7	as	as	ADP
ejpam-6931	365	8	a	a	DET
ejpam-6931	365	9	pair	pair	NOUN
ejpam-6931	365	10	of	of	ADP
ejpam-6931	365	11	two	two	NUM
ejpam-6931	365	12	mappings	mapping	NOUN
ejpam-6931	365	13	,	,	PUNCT
ejpam-6931	365	14	i	i	PRON
ejpam-6931	365	15	and	and	CCONJ
ejpam-6931	365	16	j	j	PROPN
ejpam-6931	365	17	,	,	PUNCT
ejpam-6931	365	18	both	both	DET
ejpam-6931	365	19	mapping	mapping	NOUN
ejpam-6931	365	20	from	from	ADP
ejpam-6931	365	21	v	v	NUM
ejpam-6931	365	22	to	to	ADP
ejpam-6931	365	23	v	v	NOUN
ejpam-6931	365	24	,	,	PUNCT
ejpam-6931	365	25	such	such	ADJ
ejpam-6931	365	26	that	that	SCONJ
ejpam-6931	365	27	there	there	PRON
ejpam-6931	365	28	exists	exist	VERB
ejpam-6931	365	29	a	a	DET
ejpam-6931	365	30	real	real	ADJ
ejpam-6931	365	31	number	number	NOUN
ejpam-6931	365	32	k	k	NOUN
ejpam-6931	365	33	in	in	ADP
ejpam-6931	365	34	the	the	DET
ejpam-6931	365	35	interval	interval	NOUN
ejpam-6931	365	36	(	(	PUNCT
ejpam-6931	365	37	0	0	NUM
ejpam-6931	365	38	,	,	PUNCT
ejpam-6931	365	39	1	1	NUM
ejpam-6931	365	40	)	)	PUNCT
ejpam-6931	365	41	where	where	SCONJ
ejpam-6931	365	42	ℑ−	ℑ−	PROPN
ejpam-6931	365	43	e(iϱo	e(iϱo	PROPN
ejpam-6931	365	44	,	,	PUNCT
ejpam-6931	365	45	j	j	PROPN
ejpam-6931	365	46	ν	ν	PROPN
ejpam-6931	365	47	,	,	PUNCT
ejpam-6931	365	48	e	e	NOUN
ejpam-6931	365	49	)	)	PUNCT
ejpam-6931	365	50	⪯	⪯	NOUN
ejpam-6931	365	51	k(ℑ−	k(ℑ−	PROPN
ejpam-6931	365	52	e(iϱo	e(iϱo	PROPN
ejpam-6931	365	53	,	,	PUNCT
ejpam-6931	365	54	j	j	PROPN
ejpam-6931	365	55	ν	ν	PROPN
ejpam-6931	365	56	,	,	PUNCT
ejpam-6931	365	57	e	e	NOUN
ejpam-6931	365	58	)	)	PUNCT
ejpam-6931	365	59	,	,	PUNCT
ejpam-6931	365	60	g(iϱo	g(iϱo	PROPN
ejpam-6931	365	61	,	,	PUNCT
ejpam-6931	365	62	j	j	PROPN
ejpam-6931	365	63	ν	ν	PROPN
ejpam-6931	365	64	,	,	PUNCT
ejpam-6931	365	65	e	e	NOUN
ejpam-6931	365	66	)	)	PUNCT
ejpam-6931	365	67	⪯	⪯	PROPN
ejpam-6931	365	68	kg(iϱo	kg(iϱo	PROPN
ejpam-6931	365	69	,	,	PUNCT
ejpam-6931	365	70	j	j	PROPN
ejpam-6931	365	71	ν	ν	PROPN
ejpam-6931	365	72	,	,	PUNCT
ejpam-6931	365	73	e	e	NOUN
ejpam-6931	365	74	)	)	PUNCT
ejpam-6931	365	75	,	,	PUNCT
ejpam-6931	365	76	(	(	PUNCT
ejpam-6931	365	77	11	11	X
ejpam-6931	365	78	)	)	PUNCT
ejpam-6931	365	79	h(iϱo	h(iϱo	PROPN
ejpam-6931	365	80	,	,	PUNCT
ejpam-6931	365	81	j	j	PROPN
ejpam-6931	365	82	ν	ν	PROPN
ejpam-6931	365	83	,	,	PUNCT
ejpam-6931	365	84	e	e	NOUN
ejpam-6931	365	85	)	)	PUNCT
ejpam-6931	365	86	⪯	⪯	PROPN
ejpam-6931	365	87	kh(iϱo	kh(iϱo	PROPN
ejpam-6931	365	88	,	,	PUNCT
ejpam-6931	365	89	j	j	PROPN
ejpam-6931	365	90	ν	ν	PROPN
ejpam-6931	365	91	,	,	PUNCT
ejpam-6931	365	92	e	e	NOUN
ejpam-6931	365	93	)	)	PUNCT
ejpam-6931	365	94	holds	hold	VERB
ejpam-6931	365	95	for	for	ADP
ejpam-6931	365	96	any	any	DET
ejpam-6931	365	97	ϱo	ϱo	NOUN
ejpam-6931	365	98	,	,	PUNCT
ejpam-6931	365	99	ν	ν	PROPN
ejpam-6931	365	100	∈	∈	PROPN
ejpam-6931	365	101	v	v	NOUN
ejpam-6931	365	102	and	and	CCONJ
ejpam-6931	365	103	e	e	NOUN
ejpam-6931	365	104	∈	∈	PROPN
ejpam-6931	365	105	s0	s0	PROPN
ejpam-6931	365	106	.	.	PUNCT
ejpam-6931	366	1	theorem	theorem	NOUN
ejpam-6931	366	2	3	3	X
ejpam-6931	366	3	.	.	PUNCT
ejpam-6931	366	4	suppose	suppose	VERB
ejpam-6931	366	5	that	that	SCONJ
ejpam-6931	366	6	(	(	PUNCT
ejpam-6931	366	7	v	v	NOUN
ejpam-6931	366	8	,	,	PUNCT
ejpam-6931	366	9	e	e	NOUN
ejpam-6931	366	10	,	,	PUNCT
ejpam-6931	366	11	g	g	PROPN
ejpam-6931	366	12	,	,	PUNCT
ejpam-6931	366	13	h	h	NOUN
ejpam-6931	366	14	,	,	PUNCT
ejpam-6931	366	15	⋆	⋆	NOUN
ejpam-6931	366	16	,	,	PUNCT
ejpam-6931	366	17	△	△	NOUN
ejpam-6931	366	18	)	)	PUNCT
ejpam-6931	366	19	is	be	AUX
ejpam-6931	366	20	a	a	DET
ejpam-6931	366	21	complete	complete	ADJ
ejpam-6931	366	22	cvnms	cvnms	NOUN
ejpam-6931	366	23	and	and	CCONJ
ejpam-6931	366	24	a	a	DET
ejpam-6931	366	25	pair	pair	NOUN
ejpam-6931	366	26	of	of	ADP
ejpam-6931	366	27	two	two	NUM
ejpam-6931	366	28	mappings	mapping	NOUN
ejpam-6931	366	29	i	i	PRON
ejpam-6931	366	30	,	,	PUNCT
ejpam-6931	366	31	j	j	PROPN
ejpam-6931	366	32	:	:	PUNCT
ejpam-6931	366	33	v	v	X
ejpam-6931	366	34	→	→	SYM
ejpam-6931	366	35	v	v	PROPN
ejpam-6931	366	36	is	be	AUX
ejpam-6931	366	37	a	a	DET
ejpam-6931	366	38	neutrosophic	neutrosophic	ADJ
ejpam-6931	366	39	banach	banach	NOUN
ejpam-6931	366	40	contraction	contraction	NOUN
ejpam-6931	366	41	.	.	PUNCT
ejpam-6931	367	1	then	then	ADV
ejpam-6931	367	2	both	both	CCONJ
ejpam-6931	367	3	the	the	DET
ejpam-6931	367	4	mappings	mapping	NOUN
ejpam-6931	367	5	i	i	PRON
ejpam-6931	367	6	and	and	CCONJ
ejpam-6931	367	7	j	j	PROPN
ejpam-6931	367	8	have	have	VERB
ejpam-6931	367	9	a	a	DET
ejpam-6931	367	10	unique	unique	ADJ
ejpam-6931	367	11	shared	share	VERB
ejpam-6931	367	12	fixed	fix	VERB
ejpam-6931	367	13	point	point	NOUN
ejpam-6931	367	14	that	that	PRON
ejpam-6931	367	15	belongs	belong	VERB
ejpam-6931	367	16	to	to	ADP
ejpam-6931	367	17	v.	v.	ADP
ejpam-6931	367	18	proof	proof	NOUN
ejpam-6931	367	19	.	.	PUNCT
ejpam-6931	368	1	take	take	VERB
ejpam-6931	368	2	an	an	DET
ejpam-6931	368	3	arbitrarily	arbitrarily	ADV
ejpam-6931	368	4	selected	select	VERB
ejpam-6931	368	5	point	point	NOUN
ejpam-6931	368	6	ϱo	ϱo	ADP
ejpam-6931	368	7	∈	∈	PROPN
ejpam-6931	368	8	v.	v.	ADV
ejpam-6931	368	9	for	for	ADP
ejpam-6931	368	10	any	any	DET
ejpam-6931	368	11	n	n	PRON
ejpam-6931	368	12	∈	∈	PROPN
ejpam-6931	368	13	m0	m0	NOUN
ejpam-6931	368	14	,	,	PUNCT
ejpam-6931	368	15	a	a	DET
ejpam-6931	368	16	sequence	sequence	NOUN
ejpam-6931	368	17	{	{	PUNCT
ejpam-6931	368	18	ϱon	ϱon	NOUN
ejpam-6931	368	19	}	}	PUNCT
ejpam-6931	368	20	is	be	AUX
ejpam-6931	368	21	defined	define	VERB
ejpam-6931	368	22	in	in	ADP
ejpam-6931	368	23	v	v	NOUN
ejpam-6931	368	24	as	as	ADP
ejpam-6931	368	25	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	368	26	=	=	SYM
ejpam-6931	368	27	iϱo2n	iϱo2n	PROPN
ejpam-6931	368	28	,	,	PUNCT
ejpam-6931	368	29	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	369	1	=	=	PUNCT
ejpam-6931	369	2	j	j	PROPN
ejpam-6931	369	3	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	369	4	.	.	PUNCT
ejpam-6931	370	1	it	it	PRON
ejpam-6931	370	2	is	be	AUX
ejpam-6931	370	3	guaranteed	guarantee	VERB
ejpam-6931	370	4	that	that	SCONJ
ejpam-6931	370	5	ϱon0	ϱon0	PROPN
ejpam-6931	370	6	is	be	AUX
ejpam-6931	370	7	a	a	DET
ejpam-6931	370	8	common	common	ADJ
ejpam-6931	370	9	fixed	fix	VERB
ejpam-6931	370	10	point	point	NOUN
ejpam-6931	370	11	of	of	ADP
ejpam-6931	370	12	i	i	PRON
ejpam-6931	370	13	,	,	PUNCT
ejpam-6931	370	14	if	if	SCONJ
ejpam-6931	370	15	there	there	PRON
ejpam-6931	370	16	is	be	VERB
ejpam-6931	370	17	a	a	DET
ejpam-6931	370	18	n0	n0	NUM
ejpam-6931	370	19	∈	∈	NOUN
ejpam-6931	370	20	m	m	VERB
ejpam-6931	370	21	such	such	ADJ
ejpam-6931	370	22	that	that	DET
ejpam-6931	370	23	ϱon0	ϱon0	PROPN
ejpam-6931	370	24	=	=	SYM
ejpam-6931	371	1	ϱon0	ϱon0	PROPN
ejpam-6931	371	2	+	+	PROPN
ejpam-6931	371	3	1	1	NUM
ejpam-6931	371	4	.	.	PUNCT
ejpam-6931	372	1	using	use	VERB
ejpam-6931	372	2	the	the	DET
ejpam-6931	372	3	equation	equation	NOUN
ejpam-6931	372	4	(	(	PUNCT
ejpam-6931	372	5	11	11	NUM
ejpam-6931	372	6	)	)	PUNCT
ejpam-6931	372	7	,	,	PUNCT
ejpam-6931	372	8	we	we	PRON
ejpam-6931	372	9	also	also	ADV
ejpam-6931	372	10	have	have	VERB
ejpam-6931	372	11	ℑ−	ℑ−	NOUN
ejpam-6931	372	12	e(ϱo2n+1	e(ϱo2n+1	ADJ
ejpam-6931	372	13	,	,	PUNCT
ejpam-6931	372	14	ϱ	ϱ	ADP
ejpam-6931	372	15	o	o	NOUN
ejpam-6931	372	16	2n+2	2n+2	PROPN
ejpam-6931	372	17	,	,	PUNCT
ejpam-6931	372	18	e	e	NOUN
ejpam-6931	372	19	)	)	PUNCT
ejpam-6931	372	20	=	=	NUM
ejpam-6931	372	21	ℑ−	ℑ−	NOUN
ejpam-6931	372	22	e(iϱo2n	e(iϱo2n	NOUN
ejpam-6931	372	23	,	,	PUNCT
ejpam-6931	372	24	j	j	PROPN
ejpam-6931	372	25	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	372	26	,	,	PUNCT
ejpam-6931	372	27	e	e	NOUN
ejpam-6931	372	28	)	)	PUNCT
ejpam-6931	372	29	s.	s.	PROPN
ejpam-6931	372	30	m.	m.	PROPN
ejpam-6931	372	31	u.	u.	PROPN
ejpam-6931	372	32	ud	ud	AUX
ejpam-6931	372	33	-	-	PUNCT
ejpam-6931	372	34	din	din	VERB
ejpam-6931	372	35	et	et	PROPN
ejpam-6931	372	36	al	al	PROPN
ejpam-6931	372	37	.	.	PUNCT
ejpam-6931	372	38	/	/	SYM
ejpam-6931	372	39	eur	eur	PROPN
ejpam-6931	372	40	.	.	PUNCT
ejpam-6931	373	1	j.	j.	PROPN
ejpam-6931	373	2	pure	pure	PROPN
ejpam-6931	373	3	appl	appl	PROPN
ejpam-6931	373	4	.	.	PROPN
ejpam-6931	373	5	math	math	PROPN
ejpam-6931	373	6	,	,	PUNCT
ejpam-6931	373	7	18	18	NUM
ejpam-6931	373	8	(	(	PUNCT
ejpam-6931	373	9	4	4	NUM
ejpam-6931	373	10	)	)	PUNCT
ejpam-6931	373	11	(	(	PUNCT
ejpam-6931	373	12	2025	2025	NUM
ejpam-6931	373	13	)	)	PUNCT
ejpam-6931	373	14	,	,	PUNCT
ejpam-6931	373	15	6931	6931	NUM
ejpam-6931	373	16	26	26	NUM
ejpam-6931	373	17	of	of	ADP
ejpam-6931	373	18	38	38	NUM
ejpam-6931	373	19	⪯	⪯	NOUN
ejpam-6931	373	20	k(ℑ−	k(ℑ−	X
ejpam-6931	373	21	e(ϱo2n	e(ϱo2n	X
ejpam-6931	373	22	,	,	PUNCT
ejpam-6931	373	23	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	373	24	,	,	PUNCT
ejpam-6931	373	25	e	e	NOUN
ejpam-6931	373	26	)	)	PUNCT
ejpam-6931	373	27	)	)	PUNCT
ejpam-6931	374	1	=	=	PUNCT
ejpam-6931	374	2	k(ℑ−	k(ℑ−	NUM
ejpam-6931	374	3	ℑ	ℑ	PROPN
ejpam-6931	374	4	)	)	PUNCT
ejpam-6931	374	5	=	=	SYM
ejpam-6931	374	6	∅	∅	NOUN
ejpam-6931	374	7	g(ϱo2n+1	g(ϱo2n+1	ADJ
ejpam-6931	374	8	,	,	PUNCT
ejpam-6931	374	9	ϱ	ϱ	ADP
ejpam-6931	374	10	o	o	NOUN
ejpam-6931	374	11	2n+2	2n+2	PROPN
ejpam-6931	374	12	,	,	PUNCT
ejpam-6931	374	13	e	e	NOUN
ejpam-6931	374	14	)	)	PUNCT
ejpam-6931	374	15	=	=	SYM
ejpam-6931	374	16	g(iϱo2n	g(iϱo2n	NOUN
ejpam-6931	374	17	,	,	PUNCT
ejpam-6931	374	18	j	j	PROPN
ejpam-6931	374	19	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	374	20	,	,	PUNCT
ejpam-6931	374	21	e	e	NOUN
ejpam-6931	374	22	)	)	PUNCT
ejpam-6931	374	23	⪯	⪯	PROPN
ejpam-6931	374	24	kg(ϱo2n	kg(ϱo2n	PROPN
ejpam-6931	374	25	,	,	PUNCT
ejpam-6931	374	26	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	374	27	,	,	PUNCT
ejpam-6931	374	28	e	e	NOUN
ejpam-6931	374	29	)	)	PUNCT
ejpam-6931	374	30	=	=	SYM
ejpam-6931	374	31	k(∅	k(∅	NOUN
ejpam-6931	374	32	)	)	PUNCT
ejpam-6931	374	33	=	=	NOUN
ejpam-6931	374	34	∅	∅	NOUN
ejpam-6931	374	35	and	and	CCONJ
ejpam-6931	374	36	h(ϱo2n+1	h(ϱo2n+1	PROPN
ejpam-6931	374	37	,	,	PUNCT
ejpam-6931	374	38	ϱ	ϱ	ADP
ejpam-6931	374	39	o	o	NOUN
ejpam-6931	374	40	2n+2	2n+2	PROPN
ejpam-6931	374	41	,	,	PUNCT
ejpam-6931	374	42	e	e	X
ejpam-6931	374	43	)	)	PUNCT
ejpam-6931	374	44	=	=	SYM
ejpam-6931	374	45	h(iϱo2n	h(iϱo2n	PROPN
ejpam-6931	374	46	,	,	PUNCT
ejpam-6931	374	47	j	j	PROPN
ejpam-6931	374	48	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	374	49	,	,	PUNCT
ejpam-6931	374	50	e	e	NOUN
ejpam-6931	374	51	)	)	PUNCT
ejpam-6931	374	52	⪯	⪯	PROPN
ejpam-6931	374	53	kh(ϱo2n	kh(ϱo2n	PROPN
ejpam-6931	374	54	,	,	PUNCT
ejpam-6931	374	55	ϱ	ϱ	ADP
ejpam-6931	374	56	o	o	PROPN
ejpam-6931	374	57	2n+1	2n+1	PROPN
ejpam-6931	374	58	,	,	PUNCT
ejpam-6931	374	59	e	e	NOUN
ejpam-6931	374	60	)	)	PUNCT
ejpam-6931	374	61	=	=	SYM
ejpam-6931	374	62	k(∅	k(∅	NOUN
ejpam-6931	374	63	)	)	PUNCT
ejpam-6931	374	64	=	=	NOUN
ejpam-6931	374	65	∅	∅	NOUN
ejpam-6931	374	66	for	for	ADP
ejpam-6931	374	67	each	each	DET
ejpam-6931	374	68	e	e	PROPN
ejpam-6931	374	69	∈	∈	PROPN
ejpam-6931	374	70	s0	s0	PROPN
ejpam-6931	374	71	.	.	PUNCT
ejpam-6931	375	1	consequently	consequently	ADV
ejpam-6931	375	2	,	,	PUNCT
ejpam-6931	375	3	e(ϱo2n+1	e(ϱo2n+1	ADJ
ejpam-6931	375	4	,	,	PUNCT
ejpam-6931	375	5	ϱ	ϱ	ADP
ejpam-6931	375	6	o	o	NOUN
ejpam-6931	375	7	2n+2	2n+2	PROPN
ejpam-6931	375	8	,	,	PUNCT
ejpam-6931	375	9	e	e	NOUN
ejpam-6931	375	10	)	)	PUNCT
ejpam-6931	375	11	=	=	SYM
ejpam-6931	375	12	ℑ,g(ϱo2n+1	ℑ,g(ϱo2n+1	PROPN
ejpam-6931	375	13	,	,	PUNCT
ejpam-6931	375	14	ϱ	ϱ	ADP
ejpam-6931	375	15	o	o	NOUN
ejpam-6931	375	16	2n+2	2n+2	PROPN
ejpam-6931	375	17	,	,	PUNCT
ejpam-6931	375	18	e	e	NOUN
ejpam-6931	375	19	)	)	PUNCT
ejpam-6931	375	20	=	=	NOUN
ejpam-6931	375	21	∅	∅	NOUN
ejpam-6931	375	22	and	and	CCONJ
ejpam-6931	375	23	h(ϱo2n+1	h(ϱo2n+1	PROPN
ejpam-6931	375	24	,	,	PUNCT
ejpam-6931	375	25	ϱ	ϱ	ADP
ejpam-6931	375	26	o	o	NOUN
ejpam-6931	375	27	2n+2	2n+2	PROPN
ejpam-6931	375	28	,	,	PUNCT
ejpam-6931	375	29	e	e	X
ejpam-6931	375	30	)	)	PUNCT
ejpam-6931	375	31	=	=	PUNCT
ejpam-6931	375	32	∅.	∅.	NOUN
ejpam-6931	375	33	by	by	ADP
ejpam-6931	375	34	conditions	condition	NOUN
ejpam-6931	375	35	(	(	PUNCT
ejpam-6931	375	36	3	3	NUM
ejpam-6931	375	37	)	)	PUNCT
ejpam-6931	375	38	,	,	PUNCT
ejpam-6931	375	39	(	(	PUNCT
ejpam-6931	375	40	8)	8)	NUM
ejpam-6931	375	41	and	and	CCONJ
ejpam-6931	375	42	(	(	PUNCT
ejpam-6931	375	43	13	13	NUM
ejpam-6931	375	44	)	)	PUNCT
ejpam-6931	375	45	of	of	ADP
ejpam-6931	375	46	definition	definition	NOUN
ejpam-6931	375	47	7	7	NUM
ejpam-6931	375	48	,	,	PUNCT
ejpam-6931	375	49	ϱo2n+1	ϱo2n+1	PUNCT
ejpam-6931	375	50	=	=	SYM
ejpam-6931	375	51	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	376	1	=	=	SYM
ejpam-6931	376	2	j	j	PROPN
ejpam-6931	376	3	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	376	4	,	,	PUNCT
ejpam-6931	376	5	this	this	PRON
ejpam-6931	376	6	shows	show	VERB
ejpam-6931	376	7	that	that	SCONJ
ejpam-6931	376	8	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	376	9	is	be	AUX
ejpam-6931	376	10	a	a	DET
ejpam-6931	376	11	fixed	fix	VERB
ejpam-6931	376	12	point	point	NOUN
ejpam-6931	376	13	of	of	ADP
ejpam-6931	376	14	j	j	PROPN
ejpam-6931	376	15	.	.	PUNCT
ejpam-6931	377	1	we	we	PRON
ejpam-6931	377	2	can	can	AUX
ejpam-6931	377	3	infer	infer	VERB
ejpam-6931	377	4	that	that	SCONJ
ejpam-6931	377	5	ϱo2n	ϱo2n	PROPN
ejpam-6931	377	6	is	be	AUX
ejpam-6931	377	7	a	a	DET
ejpam-6931	377	8	common	common	ADJ
ejpam-6931	377	9	fixed	fix	VERB
ejpam-6931	377	10	point	point	NOUN
ejpam-6931	377	11	of	of	ADP
ejpam-6931	377	12	i	i	PRON
ejpam-6931	377	13	and	and	CCONJ
ejpam-6931	377	14	j	j	PROPN
ejpam-6931	377	15	because	because	SCONJ
ejpam-6931	377	16	ϱo2n	ϱo2n	PROPN
ejpam-6931	377	17	=	=	SYM
ejpam-6931	377	18	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	377	19	.	.	PUNCT
ejpam-6931	378	1	similarly	similarly	ADV
ejpam-6931	378	2	,	,	PUNCT
ejpam-6931	378	3	if	if	SCONJ
ejpam-6931	378	4	there	there	PRON
ejpam-6931	378	5	exists	exist	VERB
ejpam-6931	378	6	an	an	DET
ejpam-6931	378	7	element	element	NOUN
ejpam-6931	378	8	n	n	CCONJ
ejpam-6931	378	9	∈	∈	NOUN
ejpam-6931	378	10	m0	m0	NOUN
ejpam-6931	378	11	such	such	ADJ
ejpam-6931	378	12	that	that	DET
ejpam-6931	378	13	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	378	14	=	=	SYM
ejpam-6931	378	15	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	378	16	,	,	PUNCT
ejpam-6931	378	17	we	we	PRON
ejpam-6931	378	18	can	can	AUX
ejpam-6931	378	19	demonstrate	demonstrate	VERB
ejpam-6931	378	20	using	use	VERB
ejpam-6931	378	21	equation	equation	NOUN
ejpam-6931	378	22	(	(	PUNCT
ejpam-6931	378	23	11	11	NUM
ejpam-6931	378	24	)	)	PUNCT
ejpam-6931	378	25	that	that	PRON
ejpam-6931	378	26	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	378	27	is	be	AUX
ejpam-6931	378	28	a	a	DET
ejpam-6931	378	29	shared	share	VERB
ejpam-6931	378	30	fixed	fix	VERB
ejpam-6931	378	31	point	point	NOUN
ejpam-6931	378	32	of	of	ADP
ejpam-6931	378	33	i	i	PRON
ejpam-6931	378	34	and	and	CCONJ
ejpam-6931	378	35	j	j	PROPN
ejpam-6931	378	36	.	.	PUNCT
ejpam-6931	379	1	suppose	suppose	VERB
ejpam-6931	379	2	that	that	SCONJ
ejpam-6931	379	3	ϱon	ϱon	PROPN
ejpam-6931	379	4	̸=	̸=	PROPN
ejpam-6931	379	5	ϱon+1	ϱon+1	VERB
ejpam-6931	379	6	for	for	ADP
ejpam-6931	379	7	every	every	DET
ejpam-6931	379	8	n	n	PRON
ejpam-6931	379	9	∈	∈	PROPN
ejpam-6931	379	10	m0	m0	NOUN
ejpam-6931	379	11	.	.	PUNCT
ejpam-6931	380	1	there	there	PRON
ejpam-6931	380	2	are	be	VERB
ejpam-6931	380	3	two	two	NUM
ejpam-6931	380	4	scenarios	scenario	NOUN
ejpam-6931	380	5	that	that	SCONJ
ejpam-6931	380	6	we	we	PRON
ejpam-6931	380	7	will	will	AUX
ejpam-6931	380	8	examine	examine	VERB
ejpam-6931	380	9	.	.	PUNCT
ejpam-6931	381	1	suppose	suppose	VERB
ejpam-6931	381	2	that	that	SCONJ
ejpam-6931	381	3	n	n	PRON
ejpam-6931	381	4	is	be	AUX
ejpam-6931	381	5	an	an	DET
ejpam-6931	381	6	odd	odd	ADJ
ejpam-6931	381	7	number	number	NOUN
ejpam-6931	381	8	in	in	ADP
ejpam-6931	381	9	the	the	DET
ejpam-6931	381	10	first	first	ADJ
ejpam-6931	381	11	case	case	NOUN
ejpam-6931	381	12	.	.	PUNCT
ejpam-6931	382	1	by	by	ADP
ejpam-6931	382	2	substituting	substitute	VERB
ejpam-6931	382	3	ϱo	ϱo	PROPN
ejpam-6931	382	4	=	=	SYM
ejpam-6931	382	5	ϱon−1	ϱon−1	PROPN
ejpam-6931	382	6	and	and	CCONJ
ejpam-6931	382	7	ν	ν	X
ejpam-6931	382	8	=	=	SYM
ejpam-6931	382	9	ϱon	ϱon	PROPN
ejpam-6931	382	10	into	into	ADP
ejpam-6931	382	11	equation	equation	NOUN
ejpam-6931	382	12	(	(	PUNCT
ejpam-6931	382	13	11	11	NUM
ejpam-6931	382	14	)	)	PUNCT
ejpam-6931	382	15	,	,	PUNCT
ejpam-6931	382	16	for	for	ADP
ejpam-6931	382	17	every	every	DET
ejpam-6931	382	18	e	e	PROPN
ejpam-6931	382	19	∈	∈	PROPN
ejpam-6931	382	20	s0	s0	PROPN
ejpam-6931	382	21	,	,	PUNCT
ejpam-6931	382	22	we	we	PRON
ejpam-6931	382	23	obtain	obtain	VERB
ejpam-6931	382	24	ℑ−	ℑ−	NUM
ejpam-6931	382	25	e(ϱon	e(ϱon	PROPN
ejpam-6931	382	26	,	,	PUNCT
ejpam-6931	382	27	ϱon+1	ϱon+1	X
ejpam-6931	382	28	,	,	PUNCT
ejpam-6931	382	29	e	e	NOUN
ejpam-6931	382	30	)	)	PUNCT
ejpam-6931	382	31	=	=	SYM
ejpam-6931	382	32	ℑ−	ℑ−	NUM
ejpam-6931	382	33	e(iϱon−1,j	e(iϱon−1,j	ADP
ejpam-6931	382	34	ϱon	ϱon	PROPN
ejpam-6931	382	35	,	,	PUNCT
ejpam-6931	382	36	e	e	NOUN
ejpam-6931	382	37	)	)	PUNCT
ejpam-6931	382	38	⪯	⪯	NOUN
ejpam-6931	382	39	k(ℑ−	k(ℑ−	X
ejpam-6931	382	40	e(ϱon−1	e(ϱon−1	PROPN
ejpam-6931	382	41	,	,	PUNCT
ejpam-6931	382	42	ϱ	ϱ	ADP
ejpam-6931	382	43	o	o	PROPN
ejpam-6931	382	44	n	n	CCONJ
ejpam-6931	382	45	,	,	PUNCT
ejpam-6931	382	46	e	e	NOUN
ejpam-6931	382	47	)	)	PUNCT
ejpam-6931	382	48	)	)	PUNCT
ejpam-6931	382	49	≺	≺	NOUN
ejpam-6931	382	50	ℑ−	ℑ−	ADV
ejpam-6931	382	51	e(ϱon−1	e(ϱon−1	PROPN
ejpam-6931	382	52	,	,	PUNCT
ejpam-6931	382	53	ϱ	ϱ	ADP
ejpam-6931	382	54	o	o	PROPN
ejpam-6931	382	55	n	n	CCONJ
ejpam-6931	382	56	,	,	PUNCT
ejpam-6931	382	57	e	e	NOUN
ejpam-6931	382	58	)	)	PUNCT
ejpam-6931	382	59	,	,	PUNCT
ejpam-6931	382	60	g(ϱon	g(ϱon	NOUN
ejpam-6931	382	61	,	,	PUNCT
ejpam-6931	382	62	ϱon+1	ϱon+1	PROPN
ejpam-6931	382	63	,	,	PUNCT
ejpam-6931	382	64	e	e	NOUN
ejpam-6931	382	65	)	)	PUNCT
ejpam-6931	382	66	=	=	SYM
ejpam-6931	382	67	g(iϱon−1,j	g(iϱon−1,j	NUM
ejpam-6931	382	68	ϱon	ϱon	PROPN
ejpam-6931	382	69	,	,	PUNCT
ejpam-6931	382	70	e	e	NOUN
ejpam-6931	382	71	)	)	PUNCT
ejpam-6931	382	72	⪯	⪯	PROPN
ejpam-6931	382	73	kg(ϱon−1	kg(ϱon−1	PROPN
ejpam-6931	382	74	,	,	PUNCT
ejpam-6931	382	75	ϱ	ϱ	ADP
ejpam-6931	382	76	o	o	PROPN
ejpam-6931	382	77	n	n	CCONJ
ejpam-6931	382	78	,	,	PUNCT
ejpam-6931	382	79	e	e	NOUN
ejpam-6931	382	80	)	)	PUNCT
ejpam-6931	382	81	≺	≺	NOUN
ejpam-6931	382	82	g(ϱon−1	g(ϱon−1	PROPN
ejpam-6931	382	83	,	,	PUNCT
ejpam-6931	382	84	ϱ	ϱ	ADP
ejpam-6931	382	85	o	o	NOUN
ejpam-6931	382	86	n	n	CCONJ
ejpam-6931	382	87	,	,	PUNCT
ejpam-6931	382	88	e	e	NOUN
ejpam-6931	382	89	)	)	PUNCT
ejpam-6931	382	90	and	and	CCONJ
ejpam-6931	382	91	h(ϱon	h(ϱon	PROPN
ejpam-6931	382	92	,	,	PUNCT
ejpam-6931	382	93	ϱ	ϱ	ADP
ejpam-6931	382	94	o	o	PROPN
ejpam-6931	382	95	n+1	n+1	NOUN
ejpam-6931	382	96	,	,	PUNCT
ejpam-6931	382	97	e	e	NOUN
ejpam-6931	382	98	)	)	PUNCT
ejpam-6931	382	99	=	=	SYM
ejpam-6931	382	100	h(iϱon−1,j	h(iϱon−1,j	NUM
ejpam-6931	382	101	ϱon	ϱon	PROPN
ejpam-6931	382	102	,	,	PUNCT
ejpam-6931	382	103	e	e	NOUN
ejpam-6931	382	104	)	)	PUNCT
ejpam-6931	382	105	⪯	⪯	NOUN
ejpam-6931	382	106	kh(ϱon−1	kh(ϱon−1	PROPN
ejpam-6931	382	107	,	,	PUNCT
ejpam-6931	382	108	ϱ	ϱ	ADP
ejpam-6931	382	109	o	o	PROPN
ejpam-6931	382	110	n	n	CCONJ
ejpam-6931	382	111	,	,	PUNCT
ejpam-6931	382	112	e	e	NOUN
ejpam-6931	382	113	)	)	PUNCT
ejpam-6931	382	114	≺	≺	NOUN
ejpam-6931	382	115	h(ϱon−1	h(ϱon−1	PROPN
ejpam-6931	382	116	,	,	PUNCT
ejpam-6931	382	117	ϱ	ϱ	ADP
ejpam-6931	382	118	o	o	PROPN
ejpam-6931	382	119	n	n	CCONJ
ejpam-6931	382	120	,	,	PUNCT
ejpam-6931	382	121	e	e	NOUN
ejpam-6931	382	122	)	)	PUNCT
ejpam-6931	382	123	.	.	PUNCT
ejpam-6931	383	1	s.	s.	PROPN
ejpam-6931	383	2	m.	m.	PROPN
ejpam-6931	383	3	u.	u.	PROPN
ejpam-6931	383	4	ud	ud	AUX
ejpam-6931	383	5	-	-	PUNCT
ejpam-6931	383	6	din	din	VERB
ejpam-6931	383	7	et	et	PROPN
ejpam-6931	383	8	al	al	PROPN
ejpam-6931	383	9	.	.	PUNCT
ejpam-6931	383	10	/	/	SYM
ejpam-6931	383	11	eur	eur	PROPN
ejpam-6931	383	12	.	.	PUNCT
ejpam-6931	384	1	j.	j.	PROPN
ejpam-6931	384	2	pure	pure	PROPN
ejpam-6931	384	3	appl	appl	PROPN
ejpam-6931	384	4	.	.	PROPN
ejpam-6931	384	5	math	math	PROPN
ejpam-6931	384	6	,	,	PUNCT
ejpam-6931	384	7	18	18	NUM
ejpam-6931	384	8	(	(	PUNCT
ejpam-6931	384	9	4	4	NUM
ejpam-6931	384	10	)	)	PUNCT
ejpam-6931	384	11	(	(	PUNCT
ejpam-6931	384	12	2025	2025	NUM
ejpam-6931	384	13	)	)	PUNCT
ejpam-6931	384	14	,	,	PUNCT
ejpam-6931	384	15	6931	6931	NUM
ejpam-6931	384	16	27	27	NUM
ejpam-6931	384	17	of	of	ADP
ejpam-6931	384	18	38	38	NUM
ejpam-6931	384	19	it	it	PRON
ejpam-6931	384	20	follows	follow	VERB
ejpam-6931	384	21	that	that	SCONJ
ejpam-6931	384	22	e(ϱon	e(ϱon	PROPN
ejpam-6931	384	23	,	,	PUNCT
ejpam-6931	384	24	ϱon+1	ϱon+1	X
ejpam-6931	384	25	,	,	PUNCT
ejpam-6931	384	26	e	e	NOUN
ejpam-6931	384	27	)	)	PUNCT
ejpam-6931	384	28	≻	≻	X
ejpam-6931	385	1	e(ϱon−1	e(ϱon−1	PROPN
ejpam-6931	385	2	,	,	PUNCT
ejpam-6931	385	3	ϱ	ϱ	ADP
ejpam-6931	385	4	o	o	PROPN
ejpam-6931	385	5	n	n	CCONJ
ejpam-6931	385	6	,	,	PUNCT
ejpam-6931	385	7	e	e	NOUN
ejpam-6931	385	8	)	)	PUNCT
ejpam-6931	385	9	g(ϱon	g(ϱon	NOUN
ejpam-6931	385	10	,	,	PUNCT
ejpam-6931	385	11	ϱon+1	ϱon+1	PROPN
ejpam-6931	385	12	,	,	PUNCT
ejpam-6931	385	13	e	e	NOUN
ejpam-6931	385	14	)	)	PUNCT
ejpam-6931	385	15	≺	≺	NOUN
ejpam-6931	385	16	g(ϱon−1	g(ϱon−1	PROPN
ejpam-6931	385	17	,	,	PUNCT
ejpam-6931	385	18	ϱ	ϱ	ADP
ejpam-6931	385	19	o	o	NOUN
ejpam-6931	385	20	n	n	CCONJ
ejpam-6931	385	21	,	,	PUNCT
ejpam-6931	385	22	e	e	NOUN
ejpam-6931	385	23	)	)	PUNCT
ejpam-6931	385	24	and	and	CCONJ
ejpam-6931	385	25	h(ϱon	h(ϱon	PROPN
ejpam-6931	385	26	,	,	PUNCT
ejpam-6931	385	27	ϱ	ϱ	ADP
ejpam-6931	385	28	o	o	PROPN
ejpam-6931	385	29	n+1	n+1	NOUN
ejpam-6931	385	30	,	,	PUNCT
ejpam-6931	385	31	e	e	NOUN
ejpam-6931	385	32	)	)	PUNCT
ejpam-6931	385	33	≺	≺	NOUN
ejpam-6931	385	34	h(ϱon−1	h(ϱon−1	PROPN
ejpam-6931	385	35	,	,	PUNCT
ejpam-6931	385	36	ϱ	ϱ	ADP
ejpam-6931	385	37	o	o	PROPN
ejpam-6931	385	38	n	n	CCONJ
ejpam-6931	385	39	,	,	PUNCT
ejpam-6931	385	40	e	e	NOUN
ejpam-6931	385	41	)	)	PUNCT
ejpam-6931	385	42	for	for	ADP
ejpam-6931	385	43	any	any	DET
ejpam-6931	385	44	e	e	PROPN
ejpam-6931	385	45	∈	∈	PROPN
ejpam-6931	385	46	s.	s.	PROPN
ejpam-6931	385	47	for	for	ADP
ejpam-6931	385	48	the	the	DET
ejpam-6931	385	49	second	second	ADJ
ejpam-6931	385	50	case	case	NOUN
ejpam-6931	385	51	,	,	PUNCT
ejpam-6931	385	52	let	let	VERB
ejpam-6931	385	53	us	we	PRON
ejpam-6931	385	54	assume	assume	VERB
ejpam-6931	385	55	that	that	SCONJ
ejpam-6931	385	56	n	n	PRON
ejpam-6931	385	57	is	be	AUX
ejpam-6931	385	58	an	an	DET
ejpam-6931	385	59	even	even	ADJ
ejpam-6931	385	60	number	number	NOUN
ejpam-6931	385	61	.	.	PUNCT
ejpam-6931	386	1	by	by	ADP
ejpam-6931	386	2	substituting	substitute	VERB
ejpam-6931	386	3	ϱo	ϱo	PROPN
ejpam-6931	386	4	=	=	SYM
ejpam-6931	386	5	ϱon	ϱon	PROPN
ejpam-6931	386	6	and	and	CCONJ
ejpam-6931	386	7	ν	ν	X
ejpam-6931	386	8	=	=	PUNCT
ejpam-6931	386	9	ϱon−1	ϱon−1	PROPN
ejpam-6931	386	10	into	into	ADP
ejpam-6931	386	11	equation	equation	NOUN
ejpam-6931	386	12	(	(	PUNCT
ejpam-6931	386	13	11	11	NUM
ejpam-6931	386	14	)	)	PUNCT
ejpam-6931	386	15	,	,	PUNCT
ejpam-6931	386	16	for	for	ADP
ejpam-6931	386	17	every	every	DET
ejpam-6931	386	18	e	e	PROPN
ejpam-6931	386	19	∈	∈	PROPN
ejpam-6931	386	20	s0	s0	PROPN
ejpam-6931	386	21	,	,	PUNCT
ejpam-6931	386	22	we	we	PRON
ejpam-6931	386	23	obtain	obtain	VERB
ejpam-6931	386	24	ℑ−	ℑ−	NUM
ejpam-6931	386	25	e(ϱon+1	e(ϱon+1	NOUN
ejpam-6931	386	26	,	,	PUNCT
ejpam-6931	386	27	ϱ	ϱ	ADP
ejpam-6931	386	28	o	o	PROPN
ejpam-6931	386	29	n	n	CCONJ
ejpam-6931	386	30	,	,	PUNCT
ejpam-6931	386	31	e	e	NOUN
ejpam-6931	386	32	)	)	PUNCT
ejpam-6931	386	33	=	=	SYM
ejpam-6931	386	34	ℑ−	ℑ−	NUM
ejpam-6931	386	35	e(iϱon	e(iϱon	PROPN
ejpam-6931	386	36	,	,	PUNCT
ejpam-6931	386	37	j	j	PROPN
ejpam-6931	386	38	ϱon−1	ϱon−1	PROPN
ejpam-6931	386	39	,	,	PUNCT
ejpam-6931	386	40	e	e	NOUN
ejpam-6931	386	41	)	)	PUNCT
ejpam-6931	386	42	⪯	⪯	NOUN
ejpam-6931	386	43	k(ℑ−	k(ℑ−	PROPN
ejpam-6931	386	44	e(ϱon	e(ϱon	PROPN
ejpam-6931	386	45	,	,	PUNCT
ejpam-6931	386	46	ϱon−1	ϱon−1	PROPN
ejpam-6931	386	47	,	,	PUNCT
ejpam-6931	386	48	e	e	NOUN
ejpam-6931	386	49	)	)	PUNCT
ejpam-6931	386	50	)	)	PUNCT
ejpam-6931	386	51	≺	≺	NOUN
ejpam-6931	386	52	ℑ−	ℑ−	NUM
ejpam-6931	386	53	e(ϱon	e(ϱon	PROPN
ejpam-6931	386	54	,	,	PUNCT
ejpam-6931	386	55	ϱon−1	ϱon−1	PROPN
ejpam-6931	386	56	,	,	PUNCT
ejpam-6931	386	57	e	e	NOUN
ejpam-6931	386	58	)	)	PUNCT
ejpam-6931	386	59	,	,	PUNCT
ejpam-6931	386	60	g(ϱon+1	g(ϱon+1	PROPN
ejpam-6931	386	61	,	,	PUNCT
ejpam-6931	386	62	ϱ	ϱ	ADP
ejpam-6931	386	63	o	o	NOUN
ejpam-6931	386	64	n	n	CCONJ
ejpam-6931	386	65	,	,	PUNCT
ejpam-6931	386	66	e	e	NOUN
ejpam-6931	386	67	)	)	PUNCT
ejpam-6931	386	68	=	=	SYM
ejpam-6931	386	69	g(iϱon	g(iϱon	PROPN
ejpam-6931	386	70	,	,	PUNCT
ejpam-6931	386	71	j	j	PROPN
ejpam-6931	386	72	ϱon−1	ϱon−1	PROPN
ejpam-6931	386	73	,	,	PUNCT
ejpam-6931	386	74	e	e	NOUN
ejpam-6931	386	75	)	)	PUNCT
ejpam-6931	386	76	⪯	⪯	PROPN
ejpam-6931	386	77	kg(ϱon	kg(ϱon	PROPN
ejpam-6931	386	78	,	,	PUNCT
ejpam-6931	386	79	ϱon−1	ϱon−1	PROPN
ejpam-6931	386	80	,	,	PUNCT
ejpam-6931	386	81	e	e	NOUN
ejpam-6931	386	82	)	)	PUNCT
ejpam-6931	386	83	≺	≺	NOUN
ejpam-6931	386	84	g(ϱon	g(ϱon	PROPN
ejpam-6931	386	85	,	,	PUNCT
ejpam-6931	386	86	ϱon−1	ϱon−1	PROPN
ejpam-6931	386	87	,	,	PUNCT
ejpam-6931	386	88	e	e	NOUN
ejpam-6931	386	89	)	)	PUNCT
ejpam-6931	386	90	and	and	CCONJ
ejpam-6931	386	91	h(ϱon+1	h(ϱon+1	PROPN
ejpam-6931	386	92	,	,	PUNCT
ejpam-6931	386	93	ϱ	ϱ	ADP
ejpam-6931	386	94	o	o	PROPN
ejpam-6931	386	95	n	n	CCONJ
ejpam-6931	386	96	,	,	PUNCT
ejpam-6931	386	97	e	e	NOUN
ejpam-6931	386	98	)	)	PUNCT
ejpam-6931	386	99	=	=	SYM
ejpam-6931	386	100	h(iϱon	h(iϱon	PROPN
ejpam-6931	386	101	,	,	PUNCT
ejpam-6931	386	102	j	j	PROPN
ejpam-6931	386	103	ϱon−1	ϱon−1	PROPN
ejpam-6931	386	104	,	,	PUNCT
ejpam-6931	386	105	e	e	NOUN
ejpam-6931	386	106	)	)	PUNCT
ejpam-6931	386	107	⪯	⪯	PROPN
ejpam-6931	386	108	kh(ϱon	kh(ϱon	PROPN
ejpam-6931	386	109	,	,	PUNCT
ejpam-6931	386	110	ϱ	ϱ	ADP
ejpam-6931	386	111	o	o	PROPN
ejpam-6931	386	112	n−1	n−1	PROPN
ejpam-6931	386	113	,	,	PUNCT
ejpam-6931	386	114	e	e	NOUN
ejpam-6931	386	115	)	)	PUNCT
ejpam-6931	386	116	≺	≺	NOUN
ejpam-6931	386	117	h(ϱon	h(ϱon	PROPN
ejpam-6931	386	118	,	,	PUNCT
ejpam-6931	386	119	ϱ	ϱ	ADP
ejpam-6931	386	120	o	o	PROPN
ejpam-6931	386	121	n−1	n−1	PROPN
ejpam-6931	386	122	,	,	PUNCT
ejpam-6931	386	123	e	e	NOUN
ejpam-6931	386	124	)	)	PUNCT
ejpam-6931	386	125	.	.	PUNCT
ejpam-6931	387	1	it	it	PRON
ejpam-6931	387	2	follows	follow	VERB
ejpam-6931	387	3	that	that	SCONJ
ejpam-6931	387	4	e(ϱon	e(ϱon	PROPN
ejpam-6931	387	5	,	,	PUNCT
ejpam-6931	387	6	ϱon+1	ϱon+1	X
ejpam-6931	387	7	,	,	PUNCT
ejpam-6931	387	8	e	e	NOUN
ejpam-6931	387	9	)	)	PUNCT
ejpam-6931	387	10	≻	≻	X
ejpam-6931	387	11	e(ϱon−1	e(ϱon−1	PROPN
ejpam-6931	387	12	,	,	PUNCT
ejpam-6931	387	13	ϱ	ϱ	ADP
ejpam-6931	387	14	o	o	PROPN
ejpam-6931	387	15	n	n	CCONJ
ejpam-6931	387	16	,	,	PUNCT
ejpam-6931	387	17	e	e	NOUN
ejpam-6931	387	18	)	)	PUNCT
ejpam-6931	387	19	g(ϱon	g(ϱon	NOUN
ejpam-6931	387	20	,	,	PUNCT
ejpam-6931	387	21	ϱon+1	ϱon+1	PROPN
ejpam-6931	387	22	,	,	PUNCT
ejpam-6931	387	23	e	e	NOUN
ejpam-6931	387	24	)	)	PUNCT
ejpam-6931	387	25	≺	≺	NOUN
ejpam-6931	387	26	g(ϱon	g(ϱon	PROPN
ejpam-6931	387	27	,	,	PUNCT
ejpam-6931	387	28	ϱon−1	ϱon−1	PROPN
ejpam-6931	387	29	,	,	PUNCT
ejpam-6931	387	30	e	e	NOUN
ejpam-6931	387	31	)	)	PUNCT
ejpam-6931	387	32	and	and	CCONJ
ejpam-6931	387	33	h(ϱon	h(ϱon	PROPN
ejpam-6931	387	34	,	,	PUNCT
ejpam-6931	387	35	ϱ	ϱ	ADP
ejpam-6931	387	36	o	o	PROPN
ejpam-6931	387	37	n+1	n+1	NOUN
ejpam-6931	387	38	,	,	PUNCT
ejpam-6931	387	39	e	e	NOUN
ejpam-6931	387	40	)	)	PUNCT
ejpam-6931	387	41	≺	≺	NOUN
ejpam-6931	387	42	h(ϱon	h(ϱon	PROPN
ejpam-6931	387	43	,	,	PUNCT
ejpam-6931	387	44	ϱ	ϱ	ADP
ejpam-6931	387	45	o	o	PROPN
ejpam-6931	387	46	n−1	n−1	PROPN
ejpam-6931	387	47	,	,	PUNCT
ejpam-6931	387	48	e	e	NOUN
ejpam-6931	387	49	)	)	PUNCT
ejpam-6931	387	50	for	for	ADP
ejpam-6931	387	51	any	any	DET
ejpam-6931	387	52	e	e	PROPN
ejpam-6931	387	53	∈	∈	PROPN
ejpam-6931	387	54	s.	s.	PROPN
ejpam-6931	387	55	therefore	therefore	ADV
ejpam-6931	387	56	,	,	PUNCT
ejpam-6931	387	57	we	we	PRON
ejpam-6931	387	58	conclude	conclude	VERB
ejpam-6931	387	59	that	that	SCONJ
ejpam-6931	387	60	e(ϱon	e(ϱon	PROPN
ejpam-6931	387	61	,	,	PUNCT
ejpam-6931	387	62	ϱon+1	ϱon+1	X
ejpam-6931	387	63	,	,	PUNCT
ejpam-6931	387	64	e	e	NOUN
ejpam-6931	387	65	)	)	PUNCT
ejpam-6931	387	66	≻	≻	X
ejpam-6931	387	67	e(ϱon−1	e(ϱon−1	PROPN
ejpam-6931	387	68	,	,	PUNCT
ejpam-6931	387	69	ϱ	ϱ	ADP
ejpam-6931	387	70	o	o	PROPN
ejpam-6931	387	71	n	n	CCONJ
ejpam-6931	387	72	,	,	PUNCT
ejpam-6931	387	73	e	e	NOUN
ejpam-6931	387	74	)	)	PUNCT
ejpam-6931	387	75	,	,	PUNCT
ejpam-6931	387	76	g(ϱon	g(ϱon	NOUN
ejpam-6931	387	77	,	,	PUNCT
ejpam-6931	387	78	ϱon+1	ϱon+1	PROPN
ejpam-6931	387	79	,	,	PUNCT
ejpam-6931	387	80	e	e	NOUN
ejpam-6931	387	81	)	)	PUNCT
ejpam-6931	387	82	≺	≺	NOUN
ejpam-6931	387	83	g(ϱon	g(ϱon	PROPN
ejpam-6931	387	84	,	,	PUNCT
ejpam-6931	387	85	ϱon−1	ϱon−1	PROPN
ejpam-6931	387	86	,	,	PUNCT
ejpam-6931	387	87	e	e	NOUN
ejpam-6931	387	88	)	)	PUNCT
ejpam-6931	387	89	,	,	PUNCT
ejpam-6931	387	90	h(ϱon	h(ϱon	PROPN
ejpam-6931	387	91	,	,	PUNCT
ejpam-6931	387	92	ϱ	ϱ	ADP
ejpam-6931	387	93	o	o	PROPN
ejpam-6931	387	94	n+1	n+1	NOUN
ejpam-6931	387	95	,	,	PUNCT
ejpam-6931	387	96	e	e	NOUN
ejpam-6931	387	97	)	)	PUNCT
ejpam-6931	387	98	≺	≺	NOUN
ejpam-6931	387	99	h(ϱon	h(ϱon	PROPN
ejpam-6931	387	100	,	,	PUNCT
ejpam-6931	387	101	ϱ	ϱ	ADP
ejpam-6931	387	102	o	o	PROPN
ejpam-6931	387	103	n−1	n−1	PROPN
ejpam-6931	387	104	,	,	PUNCT
ejpam-6931	387	105	e	e	NOUN
ejpam-6931	387	106	)	)	PUNCT
ejpam-6931	387	107	for	for	ADP
ejpam-6931	387	108	every	every	DET
ejpam-6931	387	109	n	n	CCONJ
ejpam-6931	387	110	∈	∈	NOUN
ejpam-6931	387	111	m0	m0	NOUN
ejpam-6931	387	112	and	and	CCONJ
ejpam-6931	387	113	e	e	NOUN
ejpam-6931	387	114	∈	∈	PROPN
ejpam-6931	387	115	s0	s0	PROPN
ejpam-6931	387	116	.	.	PROPN
ejpam-6931	388	1	denote	denote	PROPN
ejpam-6931	388	2	e(ϱon	e(ϱon	PROPN
ejpam-6931	388	3	,	,	PUNCT
ejpam-6931	388	4	ϱon+1	ϱon+1	X
ejpam-6931	388	5	,	,	PUNCT
ejpam-6931	388	6	e	e	NOUN
ejpam-6931	388	7	)	)	PUNCT
ejpam-6931	388	8	=	=	SYM
ejpam-6931	388	9	an	an	PROPN
ejpam-6931	388	10	,	,	PUNCT
ejpam-6931	388	11	g(ϱon	g(ϱon	NOUN
ejpam-6931	388	12	,	,	PUNCT
ejpam-6931	388	13	ϱon+1	ϱon+1	PROPN
ejpam-6931	388	14	,	,	PUNCT
ejpam-6931	388	15	e	e	NOUN
ejpam-6931	388	16	)	)	PUNCT
ejpam-6931	388	17	=	=	SYM
ejpam-6931	389	1	bn	bn	NOUN
ejpam-6931	389	2	and	and	CCONJ
ejpam-6931	389	3	h(ϱon	h(ϱon	PROPN
ejpam-6931	389	4	,	,	PUNCT
ejpam-6931	389	5	ϱ	ϱ	ADP
ejpam-6931	389	6	o	o	PROPN
ejpam-6931	389	7	n+1	n+1	NOUN
ejpam-6931	389	8	,	,	PUNCT
ejpam-6931	389	9	e	e	NOUN
ejpam-6931	389	10	)	)	PUNCT
ejpam-6931	389	11	=	=	SYM
ejpam-6931	389	12	cn	cn	PROPN
ejpam-6931	389	13	for	for	ADP
ejpam-6931	389	14	each	each	DET
ejpam-6931	389	15	n	n	PRON
ejpam-6931	389	16	∈	∈	PROPN
ejpam-6931	389	17	m0	m0	NOUN
ejpam-6931	389	18	.	.	PUNCT
ejpam-6931	390	1	since	since	SCONJ
ejpam-6931	390	2	ℑ	ℑ	PRON
ejpam-6931	390	3	⪰	⪰	VERB
ejpam-6931	390	4	an	an	DET
ejpam-6931	390	5	≻	≻	NOUN
ejpam-6931	390	6	an−1	an−1	PROPN
ejpam-6931	390	7	≻	≻	PROPN
ejpam-6931	390	8	∅	∅	NOUN
ejpam-6931	390	9	∅	∅	NOUN
ejpam-6931	390	10	⪯	⪯	PROPN
ejpam-6931	390	11	bn	bn	ADP
ejpam-6931	390	12	≺	≺	NOUN
ejpam-6931	390	13	bn−1	bn−1	NOUN
ejpam-6931	390	14	≺	≺	NOUN
ejpam-6931	390	15	ℑ	ℑ	PROPN
ejpam-6931	390	16	∅	∅	AUX
ejpam-6931	390	17	⪯	⪯	NOUN
ejpam-6931	390	18	cn	cn	PROPN
ejpam-6931	390	19	≺	≺	NOUN
ejpam-6931	390	20	cn−1	cn−1	PROPN
ejpam-6931	390	21	≺	≺	NOUN
ejpam-6931	390	22	ℑ	ℑ	PROPN
ejpam-6931	390	23	s.	s.	PROPN
ejpam-6931	390	24	m.	m.	PROPN
ejpam-6931	390	25	u.	u.	PROPN
ejpam-6931	390	26	ud	ud	AUX
ejpam-6931	390	27	-	-	PUNCT
ejpam-6931	390	28	din	din	VERB
ejpam-6931	390	29	et	et	PROPN
ejpam-6931	390	30	al	al	PROPN
ejpam-6931	390	31	.	.	PUNCT
ejpam-6931	390	32	/	/	SYM
ejpam-6931	390	33	eur	eur	PROPN
ejpam-6931	390	34	.	.	PUNCT
ejpam-6931	391	1	j.	j.	PROPN
ejpam-6931	391	2	pure	pure	PROPN
ejpam-6931	391	3	appl	appl	PROPN
ejpam-6931	391	4	.	.	PROPN
ejpam-6931	391	5	math	math	PROPN
ejpam-6931	391	6	,	,	PUNCT
ejpam-6931	391	7	18	18	NUM
ejpam-6931	391	8	(	(	PUNCT
ejpam-6931	391	9	4	4	NUM
ejpam-6931	391	10	)	)	PUNCT
ejpam-6931	391	11	(	(	PUNCT
ejpam-6931	391	12	2025	2025	NUM
ejpam-6931	391	13	)	)	PUNCT
ejpam-6931	391	14	,	,	PUNCT
ejpam-6931	391	15	6931	6931	NUM
ejpam-6931	391	16	28	28	NUM
ejpam-6931	391	17	of	of	ADP
ejpam-6931	391	18	38	38	NUM
ejpam-6931	391	19	for	for	ADP
ejpam-6931	391	20	every	every	DET
ejpam-6931	391	21	n	n	PRON
ejpam-6931	391	22	∈	∈	NOUN
ejpam-6931	391	23	m0	m0	NOUN
ejpam-6931	392	1	,	,	PUNCT
ejpam-6931	392	2	it	it	PRON
ejpam-6931	392	3	concludes	conclude	VERB
ejpam-6931	392	4	that	that	SCONJ
ejpam-6931	392	5	sequences	sequence	NOUN
ejpam-6931	392	6	{	{	PUNCT
ejpam-6931	392	7	an	an	X
ejpam-6931	392	8	}	}	PUNCT
ejpam-6931	392	9	,	,	PUNCT
ejpam-6931	392	10	{	{	PUNCT
ejpam-6931	392	11	bn	bn	NOUN
ejpam-6931	392	12	}	}	PUNCT
ejpam-6931	392	13	and	and	CCONJ
ejpam-6931	392	14	{	{	PUNCT
ejpam-6931	392	15	cn	cn	NOUN
ejpam-6931	392	16	}	}	PUNCT
ejpam-6931	392	17	are	be	AUX
ejpam-6931	392	18	monotonic	monotonic	ADJ
ejpam-6931	392	19	in	in	ADP
ejpam-6931	392	20	s.	s.	PROPN
ejpam-6931	392	21	by	by	ADP
ejpam-6931	392	22	remarks	remark	NOUN
ejpam-6931	392	23	1	1	NUM
ejpam-6931	392	24	,	,	PUNCT
ejpam-6931	392	25	one	one	PRON
ejpam-6931	392	26	is	be	AUX
ejpam-6931	392	27	possible	possible	ADJ
ejpam-6931	392	28	to	to	PART
ejpam-6931	392	29	locate	locate	VERB
ejpam-6931	392	30	x́	x́	PROPN
ejpam-6931	392	31	,	,	PUNCT
ejpam-6931	392	32	ý	ý	PROPN
ejpam-6931	392	33	,	,	PUNCT
ejpam-6931	392	34	ć	ć	PROPN
ejpam-6931	392	35	∈	∈	PROPN
ejpam-6931	392	36	s	s	PART
ejpam-6931	392	37	satisfying	satisfy	VERB
ejpam-6931	392	38	lim	lim	PROPN
ejpam-6931	392	39	n→∞	n→∞	PRON
ejpam-6931	392	40	an	an	DET
ejpam-6931	392	41	=	=	SYM
ejpam-6931	392	42	x́	x́	PROPN
ejpam-6931	392	43	,	,	PUNCT
ejpam-6931	392	44	lim	lim	PROPN
ejpam-6931	392	45	n→∞	n→∞	NUM
ejpam-6931	392	46	bn	bn	NOUN
ejpam-6931	392	47	=	=	SYM
ejpam-6931	392	48	ý	ý	PROPN
ejpam-6931	392	49	,	,	PUNCT
ejpam-6931	392	50	lim	lim	PROPN
ejpam-6931	392	51	n→∞	n→∞	NUM
ejpam-6931	392	52	cn	cn	PROPN
ejpam-6931	392	53	=	=	NOUN
ejpam-6931	392	54	ć.	ć.	PROPN
ejpam-6931	392	55	by	by	ADP
ejpam-6931	392	56	using	use	VERB
ejpam-6931	392	57	equation	equation	NOUN
ejpam-6931	392	58	equation	equation	NOUN
ejpam-6931	392	59	(	(	PUNCT
ejpam-6931	392	60	11	11	NUM
ejpam-6931	392	61	)	)	PUNCT
ejpam-6931	392	62	,	,	PUNCT
ejpam-6931	392	63	for	for	ADP
ejpam-6931	392	64	n	n	PRON
ejpam-6931	392	65	∈	∈	PROPN
ejpam-6931	392	66	m0	m0	NOUN
ejpam-6931	392	67	and	and	CCONJ
ejpam-6931	392	68	c	c	NOUN
ejpam-6931	392	69	∈	∈	PROPN
ejpam-6931	392	70	s0	s0	NOUN
ejpam-6931	392	71	we	we	PRON
ejpam-6931	392	72	obtain	obtain	VERB
ejpam-6931	392	73	ℑ−	ℑ−	NUM
ejpam-6931	392	74	e(ϱon	e(ϱon	PROPN
ejpam-6931	392	75	,	,	PUNCT
ejpam-6931	392	76	ϱon+1	ϱon+1	X
ejpam-6931	392	77	,	,	PUNCT
ejpam-6931	392	78	e	e	X
ejpam-6931	392	79	)	)	PUNCT
ejpam-6931	392	80	⪯	⪯	NOUN
ejpam-6931	392	81	k(ℑ−	k(ℑ−	X
ejpam-6931	392	82	e(ϱon−1	e(ϱon−1	PROPN
ejpam-6931	392	83	,	,	PUNCT
ejpam-6931	392	84	ϱ	ϱ	ADP
ejpam-6931	392	85	o	o	PROPN
ejpam-6931	392	86	n	n	CCONJ
ejpam-6931	392	87	,	,	PUNCT
ejpam-6931	392	88	e	e	NOUN
ejpam-6931	392	89	)	)	PUNCT
ejpam-6931	392	90	)	)	PUNCT
ejpam-6931	392	91	ℑ−	ℑ−	VERB
ejpam-6931	392	92	an	an	DET
ejpam-6931	392	93	⪯	⪯	NOUN
ejpam-6931	392	94	k(ℑ−	k(ℑ−	X
ejpam-6931	392	95	an−1	an−1	ADJ
ejpam-6931	392	96	)	)	PUNCT
ejpam-6931	392	97	g(ϱon	g(ϱon	NOUN
ejpam-6931	392	98	,	,	PUNCT
ejpam-6931	392	99	ϱon+1	ϱon+1	PROPN
ejpam-6931	392	100	,	,	PUNCT
ejpam-6931	392	101	e	e	X
ejpam-6931	392	102	)	)	PUNCT
ejpam-6931	392	103	⪯	⪯	PROPN
ejpam-6931	392	104	kg(ϱon−1	kg(ϱon−1	PROPN
ejpam-6931	392	105	,	,	PUNCT
ejpam-6931	392	106	ϱ	ϱ	ADP
ejpam-6931	392	107	o	o	PROPN
ejpam-6931	392	108	n	n	CCONJ
ejpam-6931	392	109	,	,	PUNCT
ejpam-6931	392	110	e	e	NOUN
ejpam-6931	392	111	)	)	PUNCT
ejpam-6931	392	112	bn	bn	NOUN
ejpam-6931	392	113	⪯	⪯	NOUN
ejpam-6931	392	114	k(bn−1	k(bn−1	PROPN
ejpam-6931	392	115	)	)	PUNCT
ejpam-6931	392	116	and	and	CCONJ
ejpam-6931	392	117	h(ϱon	h(ϱon	PROPN
ejpam-6931	392	118	,	,	PUNCT
ejpam-6931	392	119	ϱ	ϱ	ADP
ejpam-6931	392	120	o	o	PROPN
ejpam-6931	392	121	n+1	n+1	NOUN
ejpam-6931	392	122	,	,	PUNCT
ejpam-6931	392	123	e	e	NOUN
ejpam-6931	392	124	)	)	PUNCT
ejpam-6931	392	125	⪯	⪯	NOUN
ejpam-6931	392	126	kh(ϱon−1	kh(ϱon−1	PROPN
ejpam-6931	392	127	,	,	PUNCT
ejpam-6931	392	128	ϱ	ϱ	ADP
ejpam-6931	392	129	o	o	PROPN
ejpam-6931	392	130	n	n	CCONJ
ejpam-6931	392	131	,	,	PUNCT
ejpam-6931	392	132	e	e	X
ejpam-6931	392	133	)	)	PUNCT
ejpam-6931	392	134	cn	cn	PROPN
ejpam-6931	392	135	⪯	⪯	PROPN
ejpam-6931	392	136	k(cn−1	k(cn−1	PROPN
ejpam-6931	392	137	)	)	PUNCT
ejpam-6931	392	138	.	.	PUNCT
ejpam-6931	393	1	as	as	SCONJ
ejpam-6931	393	2	the	the	DET
ejpam-6931	393	3	value	value	NOUN
ejpam-6931	393	4	of	of	ADP
ejpam-6931	393	5	n	n	NOUN
ejpam-6931	393	6	approaches	approach	NOUN
ejpam-6931	393	7	infinity	infinity	NOUN
ejpam-6931	393	8	for	for	ADP
ejpam-6931	393	9	inequalities	inequality	NOUN
ejpam-6931	393	10	,	,	PUNCT
ejpam-6931	393	11	we	we	PRON
ejpam-6931	393	12	get	get	VERB
ejpam-6931	393	13	ℑ−	ℑ−	NUM
ejpam-6931	393	14	x́	x́	PROPN
ejpam-6931	394	1	⪯	⪯	VERB
ejpam-6931	394	2	k(ℑ−	k(ℑ−	PROPN
ejpam-6931	394	3	x́	x́	PROPN
ejpam-6931	394	4	)	)	PUNCT
ejpam-6931	395	1	ý	ý	ADJ
ejpam-6931	395	2	⪯	⪯	NOUN
ejpam-6931	395	3	ký	ký	PROPN
ejpam-6931	395	4	and	and	CCONJ
ejpam-6931	395	5	ć	ć	PROPN
ejpam-6931	395	6	⪯	⪯	PROPN
ejpam-6931	396	1	kć.	kć.	PROPN
ejpam-6931	396	2	as	as	ADP
ejpam-6931	396	3	k	k	PROPN
ejpam-6931	396	4	∈	∈	PROPN
ejpam-6931	396	5	(	(	PUNCT
ejpam-6931	396	6	0	0	NUM
ejpam-6931	396	7	,	,	PUNCT
ejpam-6931	396	8	1	1	NUM
ejpam-6931	396	9	)	)	PUNCT
ejpam-6931	396	10	,	,	PUNCT
ejpam-6931	396	11	if	if	SCONJ
ejpam-6931	396	12	x́	x́	PROPN
ejpam-6931	396	13	≺	≺	VERB
ejpam-6931	396	14	ℑ	ℑ	PROPN
ejpam-6931	396	15	,	,	PUNCT
ejpam-6931	396	16	ý	ý	ADJ
ejpam-6931	396	17	≻	≻	NOUN
ejpam-6931	396	18	∅	∅	NOUN
ejpam-6931	396	19	,	,	PUNCT
ejpam-6931	396	20	and	and	CCONJ
ejpam-6931	396	21	ć	ć	PROPN
ejpam-6931	396	22	≻	≻	PROPN
ejpam-6931	396	23	∅	∅	NOUN
ejpam-6931	396	24	,	,	PUNCT
ejpam-6931	396	25	it	it	PRON
ejpam-6931	396	26	is	be	AUX
ejpam-6931	396	27	a	a	DET
ejpam-6931	396	28	contradiction	contradiction	NOUN
ejpam-6931	396	29	.	.	PUNCT
ejpam-6931	397	1	therefore	therefore	ADV
ejpam-6931	397	2	x́	x́	PUNCT
ejpam-6931	398	1	=	=	SYM
ejpam-6931	398	2	ℑ	ℑ	PROPN
ejpam-6931	398	3	,	,	PUNCT
ejpam-6931	398	4	ý	ý	ADJ
ejpam-6931	398	5	=	=	NOUN
ejpam-6931	398	6	∅	∅	NOUN
ejpam-6931	398	7	and	and	CCONJ
ejpam-6931	398	8	ć	ć	NOUN
ejpam-6931	398	9	=	=	NOUN
ejpam-6931	398	10	∅	∅	NOUN
ejpam-6931	398	11	it	it	PRON
ejpam-6931	398	12	indicates	indicate	VERB
ejpam-6931	398	13	that	that	SCONJ
ejpam-6931	398	14	lim	lim	PROPN
ejpam-6931	398	15	n→∞	n→∞	NUM
ejpam-6931	398	16	e(ϱon	e(ϱon	PROPN
ejpam-6931	398	17	,	,	PUNCT
ejpam-6931	398	18	ϱon+1	ϱon+1	X
ejpam-6931	398	19	,	,	PUNCT
ejpam-6931	398	20	e	e	NOUN
ejpam-6931	398	21	)	)	PUNCT
ejpam-6931	398	22	=	=	SYM
ejpam-6931	398	23	ℑ	ℑ	PROPN
ejpam-6931	398	24	,	,	PUNCT
ejpam-6931	398	25	lim	lim	PROPN
ejpam-6931	398	26	n→∞	n→∞	NUM
ejpam-6931	398	27	g(ϱon	g(ϱon	PROPN
ejpam-6931	398	28	,	,	PUNCT
ejpam-6931	398	29	ϱon+1	ϱon+1	PROPN
ejpam-6931	398	30	,	,	PUNCT
ejpam-6931	398	31	e	e	NOUN
ejpam-6931	398	32	)	)	PUNCT
ejpam-6931	398	33	=	=	NOUN
ejpam-6931	398	34	∅	∅	NOUN
ejpam-6931	398	35	,	,	PUNCT
ejpam-6931	398	36	lim	lim	PROPN
ejpam-6931	398	37	n→∞	n→∞	NUM
ejpam-6931	398	38	h(ϱon	h(ϱon	PROPN
ejpam-6931	398	39	,	,	PUNCT
ejpam-6931	398	40	ϱ	ϱ	ADP
ejpam-6931	398	41	o	o	PROPN
ejpam-6931	398	42	n+1	n+1	NOUN
ejpam-6931	398	43	,	,	PUNCT
ejpam-6931	398	44	e	e	NOUN
ejpam-6931	398	45	)	)	PUNCT
ejpam-6931	398	46	=	=	NOUN
ejpam-6931	398	47	∅	∅	NOUN
ejpam-6931	398	48	for	for	ADP
ejpam-6931	398	49	every	every	DET
ejpam-6931	398	50	n	n	PRON
ejpam-6931	398	51	∈	∈	NOUN
ejpam-6931	398	52	m0	m0	NOUN
ejpam-6931	398	53	and	and	CCONJ
ejpam-6931	398	54	e	e	NOUN
ejpam-6931	398	55	∈	∈	PROPN
ejpam-6931	398	56	s0	s0	PROPN
ejpam-6931	398	57	.	.	PUNCT
ejpam-6931	399	1	now	now	ADV
ejpam-6931	399	2	we	we	PRON
ejpam-6931	399	3	will	will	AUX
ejpam-6931	399	4	show	show	VERB
ejpam-6931	399	5	that	that	SCONJ
ejpam-6931	399	6	the	the	DET
ejpam-6931	399	7	{	{	PUNCT
ejpam-6931	399	8	ϱon	ϱon	NOUN
ejpam-6931	399	9	}	}	PUNCT
ejpam-6931	399	10	is	be	AUX
ejpam-6931	399	11	a	a	DET
ejpam-6931	399	12	cauchy	cauchy	ADJ
ejpam-6931	399	13	sequence	sequence	NOUN
ejpam-6931	399	14	.	.	PUNCT
ejpam-6931	400	1	for	for	ADP
ejpam-6931	400	2	every	every	DET
ejpam-6931	400	3	n	n	PRON
ejpam-6931	400	4	∈	∈	NOUN
ejpam-6931	400	5	m0	m0	NOUN
ejpam-6931	400	6	as	as	ADV
ejpam-6931	400	7	well	well	ADV
ejpam-6931	400	8	as	as	ADP
ejpam-6931	400	9	fixed	fix	VERB
ejpam-6931	400	10	e	e	PROPN
ejpam-6931	400	11	∈	∈	PROPN
ejpam-6931	400	12	s0	s0	PROPN
ejpam-6931	400	13	,	,	PUNCT
ejpam-6931	400	14	consider	consider	VERB
ejpam-6931	400	15	dn	dn	NOUN
ejpam-6931	400	16	=	=	PUNCT
ejpam-6931	400	17	{	{	PUNCT
ejpam-6931	400	18	e(ϱon	e(ϱon	PROPN
ejpam-6931	400	19	,	,	PUNCT
ejpam-6931	400	20	ϱom	ϱom	NOUN
ejpam-6931	400	21	,	,	PUNCT
ejpam-6931	400	22	e	e	NOUN
ejpam-6931	400	23	)	)	PUNCT
ejpam-6931	400	24	:	:	PUNCT
ejpam-6931	400	25	m	m	VERB
ejpam-6931	400	26	>	>	X
ejpam-6931	400	27	n	n	CCONJ
ejpam-6931	400	28	}	}	PUNCT
ejpam-6931	400	29	⊆	⊆	NUM
ejpam-6931	400	30	t	t	NOUN
ejpam-6931	400	31	,	,	PUNCT
ejpam-6931	400	32	en	en	X
ejpam-6931	400	33	=	=	SYM
ejpam-6931	400	34	{	{	PUNCT
ejpam-6931	400	35	g(ϱon	g(ϱon	PROPN
ejpam-6931	400	36	,	,	PUNCT
ejpam-6931	400	37	ϱom	ϱom	NOUN
ejpam-6931	400	38	,	,	PUNCT
ejpam-6931	400	39	e	e	NOUN
ejpam-6931	400	40	)	)	PUNCT
ejpam-6931	400	41	:	:	PUNCT
ejpam-6931	401	1	m	m	VERB
ejpam-6931	401	2	>	>	X
ejpam-6931	401	3	n	n	CCONJ
ejpam-6931	401	4	}	}	PUNCT
ejpam-6931	401	5	⊆	⊆	NUM
ejpam-6931	401	6	t	t	NOUN
ejpam-6931	401	7	,	,	PUNCT
ejpam-6931	401	8	fn	fn	NOUN
ejpam-6931	401	9	=	=	SYM
ejpam-6931	401	10	{	{	PUNCT
ejpam-6931	401	11	h(ϱon	h(ϱon	PROPN
ejpam-6931	401	12	,	,	PUNCT
ejpam-6931	401	13	ϱ	ϱ	ADP
ejpam-6931	401	14	o	o	PROPN
ejpam-6931	401	15	m	m	NOUN
ejpam-6931	401	16	,	,	PUNCT
ejpam-6931	401	17	e	e	NOUN
ejpam-6931	401	18	)	)	PUNCT
ejpam-6931	401	19	:	:	PUNCT
ejpam-6931	401	20	m	m	VERB
ejpam-6931	401	21	>	>	X
ejpam-6931	401	22	n	n	CCONJ
ejpam-6931	401	23	}	}	PUNCT
ejpam-6931	401	24	⊆	⊆	NUM
ejpam-6931	401	25	t.	t.	NOUN
ejpam-6931	401	26	since	since	SCONJ
ejpam-6931	401	27	∅	∅	NOUN
ejpam-6931	401	28	≺	≺	NOUN
ejpam-6931	401	29	e(ϱon	e(ϱon	PROPN
ejpam-6931	401	30	,	,	PUNCT
ejpam-6931	401	31	ϱom	ϱom	NOUN
ejpam-6931	401	32	,	,	PUNCT
ejpam-6931	401	33	e	e	NOUN
ejpam-6931	401	34	)	)	PUNCT
ejpam-6931	401	35	⪯	⪯	NOUN
ejpam-6931	401	36	ℑ,∅	ℑ,∅	PROPN
ejpam-6931	401	37	⪯	⪯	PROPN
ejpam-6931	401	38	g(ϱom	g(ϱom	PROPN
ejpam-6931	401	39	,	,	PUNCT
ejpam-6931	401	40	ϱon	ϱon	PROPN
ejpam-6931	401	41	,	,	PUNCT
ejpam-6931	401	42	e	e	NOUN
ejpam-6931	401	43	)	)	PUNCT
ejpam-6931	401	44	≺	≺	NOUN
ejpam-6931	401	45	ℑ	ℑ	PROPN
ejpam-6931	401	46	and	and	CCONJ
ejpam-6931	401	47	∅	∅	NOUN
ejpam-6931	401	48	⪯	⪯	PROPN
ejpam-6931	401	49	h(ϱom	h(ϱom	PROPN
ejpam-6931	401	50	,	,	PUNCT
ejpam-6931	401	51	ϱon	ϱon	PROPN
ejpam-6931	401	52	,	,	PUNCT
ejpam-6931	401	53	e	e	NOUN
ejpam-6931	401	54	)	)	PUNCT
ejpam-6931	401	55	≺	≺	NOUN
ejpam-6931	401	56	ℑ	ℑ	PROPN
ejpam-6931	401	57	,	,	PUNCT
ejpam-6931	401	58	by	by	ADP
ejpam-6931	401	59	remarks	remark	NOUN
ejpam-6931	401	60	1	1	NUM
ejpam-6931	401	61	,	,	PUNCT
ejpam-6931	401	62	the	the	DET
ejpam-6931	401	63	infimum	infimum	NOUN
ejpam-6931	401	64	of	of	ADP
ejpam-6931	401	65	the	the	DET
ejpam-6931	401	66	cfs	cfs	PROPN
ejpam-6931	401	67	e(ϱon	e(ϱon	PROPN
ejpam-6931	401	68	,	,	PUNCT
ejpam-6931	401	69	ϱom	ϱom	NOUN
ejpam-6931	401	70	,	,	PUNCT
ejpam-6931	401	71	e	e	NOUN
ejpam-6931	401	72	)	)	PUNCT
ejpam-6931	401	73	,	,	PUNCT
ejpam-6931	401	74	the	the	DET
ejpam-6931	401	75	supremum	supremum	NOUN
ejpam-6931	401	76	of	of	ADP
ejpam-6931	401	77	the	the	DET
ejpam-6931	401	78	cfs	cfs	PROPN
ejpam-6931	401	79	g(ϱon	g(ϱon	PROPN
ejpam-6931	401	80	,	,	PUNCT
ejpam-6931	401	81	ϱom	ϱom	NOUN
ejpam-6931	401	82	,	,	PUNCT
ejpam-6931	401	83	e	e	NOUN
ejpam-6931	401	84	)	)	PUNCT
ejpam-6931	401	85	,	,	PUNCT
ejpam-6931	401	86	and	and	CCONJ
ejpam-6931	401	87	the	the	DET
ejpam-6931	401	88	s.	s.	PROPN
ejpam-6931	401	89	m.	m.	PROPN
ejpam-6931	401	90	u.	u.	PROPN
ejpam-6931	401	91	ud	ud	AUX
ejpam-6931	401	92	-	-	PUNCT
ejpam-6931	401	93	din	din	VERB
ejpam-6931	401	94	et	et	PROPN
ejpam-6931	401	95	al	al	PROPN
ejpam-6931	401	96	.	.	PUNCT
ejpam-6931	401	97	/	/	SYM
ejpam-6931	401	98	eur	eur	PROPN
ejpam-6931	401	99	.	.	PUNCT
ejpam-6931	402	1	j.	j.	PROPN
ejpam-6931	402	2	pure	pure	PROPN
ejpam-6931	402	3	appl	appl	PROPN
ejpam-6931	402	4	.	.	PROPN
ejpam-6931	402	5	math	math	PROPN
ejpam-6931	402	6	,	,	PUNCT
ejpam-6931	402	7	18	18	NUM
ejpam-6931	402	8	(	(	PUNCT
ejpam-6931	402	9	4	4	NUM
ejpam-6931	402	10	)	)	PUNCT
ejpam-6931	402	11	(	(	PUNCT
ejpam-6931	402	12	2025	2025	NUM
ejpam-6931	402	13	)	)	PUNCT
ejpam-6931	402	14	,	,	PUNCT
ejpam-6931	402	15	6931	6931	NUM
ejpam-6931	402	16	29	29	NUM
ejpam-6931	402	17	of	of	ADP
ejpam-6931	402	18	38	38	NUM
ejpam-6931	402	19	supremum	supremum	NOUN
ejpam-6931	402	20	of	of	ADP
ejpam-6931	402	21	the	the	DET
ejpam-6931	402	22	cfs	cfs	PROPN
ejpam-6931	402	23	h(ϱon	h(ϱon	PROPN
ejpam-6931	402	24	,	,	PUNCT
ejpam-6931	402	25	ϱ	ϱ	ADP
ejpam-6931	402	26	o	o	PROPN
ejpam-6931	402	27	m	m	NOUN
ejpam-6931	402	28	,	,	PUNCT
ejpam-6931	402	29	e	e	NOUN
ejpam-6931	402	30	)	)	PUNCT
ejpam-6931	402	31	all	all	PRON
ejpam-6931	402	32	exist	exist	VERB
ejpam-6931	402	33	.	.	PUNCT
ejpam-6931	403	1	by	by	ADP
ejpam-6931	403	2	iteratively	iteratively	ADV
ejpam-6931	403	3	applying	apply	VERB
ejpam-6931	403	4	the	the	DET
ejpam-6931	403	5	condition	condition	NOUN
ejpam-6931	403	6	(	(	PUNCT
ejpam-6931	403	7	5	5	NUM
ejpam-6931	403	8	)	)	PUNCT
ejpam-6931	403	9	of	of	ADP
ejpam-6931	403	10	definition	definition	NOUN
ejpam-6931	403	11	7	7	NUM
ejpam-6931	403	12	for	for	ADP
ejpam-6931	403	13	any	any	DET
ejpam-6931	403	14	positive	positive	ADJ
ejpam-6931	403	15	integers	integer	NOUN
ejpam-6931	403	16	m	m	VERB
ejpam-6931	403	17	>	>	X
ejpam-6931	403	18	n	n	CCONJ
ejpam-6931	403	19	,	,	PUNCT
ejpam-6931	403	20	we	we	PRON
ejpam-6931	403	21	can	can	AUX
ejpam-6931	403	22	obtain	obtain	VERB
ejpam-6931	403	23	e(ϱon	e(ϱon	PROPN
ejpam-6931	403	24	,	,	PUNCT
ejpam-6931	403	25	ϱom	ϱom	NOUN
ejpam-6931	403	26	,	,	PUNCT
ejpam-6931	403	27	e	e	NOUN
ejpam-6931	403	28	)	)	PUNCT
ejpam-6931	403	29	⪰	⪰	NOUN
ejpam-6931	403	30	e	e	X
ejpam-6931	403	31	(	(	PUNCT
ejpam-6931	403	32	ϱon	ϱon	PROPN
ejpam-6931	403	33	,	,	PUNCT
ejpam-6931	403	34	ϱ	ϱ	ADP
ejpam-6931	403	35	o	o	PROPN
ejpam-6931	403	36	n+1	n+1	PROPN
ejpam-6931	403	37	,	,	PUNCT
ejpam-6931	403	38	e	e	NOUN
ejpam-6931	403	39	m−	m−	PROPN
ejpam-6931	403	40	n	n	PROPN
ejpam-6931	403	41	)	)	PUNCT
ejpam-6931	403	42	⋆e	⋆e	PROPN
ejpam-6931	403	43	(	(	PUNCT
ejpam-6931	403	44	ϱon+1	ϱon+1	PROPN
ejpam-6931	403	45	,	,	PUNCT
ejpam-6931	403	46	ϱ	ϱ	ADP
ejpam-6931	403	47	o	o	NOUN
ejpam-6931	403	48	n+2	n+2	PROPN
ejpam-6931	403	49	,	,	PUNCT
ejpam-6931	403	50	e	e	NOUN
ejpam-6931	403	51	m−	m−	PROPN
ejpam-6931	403	52	n	n	PROPN
ejpam-6931	403	53	)	)	PUNCT
ejpam-6931	403	54	⋆	⋆	VERB
ejpam-6931	403	55	...	...	PUNCT
ejpam-6931	404	1	⋆e	⋆e	PROPN
ejpam-6931	404	2	(	(	PUNCT
ejpam-6931	404	3	ϱom−1	ϱom−1	PROPN
ejpam-6931	404	4	,	,	PUNCT
ejpam-6931	404	5	ϱ	ϱ	ADP
ejpam-6931	404	6	o	o	NOUN
ejpam-6931	404	7	m	m	PROPN
ejpam-6931	404	8	,	,	PUNCT
ejpam-6931	404	9	e	e	VERB
ejpam-6931	404	10	m−	m−	PROPN
ejpam-6931	404	11	n	n	PROPN
ejpam-6931	404	12	)	)	PUNCT
ejpam-6931	404	13	.	.	PUNCT
ejpam-6931	405	1	consequently	consequently	ADV
ejpam-6931	405	2	,	,	PUNCT
ejpam-6931	405	3	lim	lim	PROPN
ejpam-6931	405	4	n→∞	n→∞	NUM
ejpam-6931	405	5	inf	inf	PROPN
ejpam-6931	405	6	m	m	PROPN
ejpam-6931	405	7	>	>	PROPN
ejpam-6931	405	8	n	n	PRON
ejpam-6931	405	9	e(ϱon	e(ϱon	PROPN
ejpam-6931	405	10	,	,	PUNCT
ejpam-6931	405	11	ϱom	ϱom	NOUN
ejpam-6931	405	12	,	,	PUNCT
ejpam-6931	405	13	e	e	NOUN
ejpam-6931	405	14	)	)	PUNCT
ejpam-6931	405	15	⪰	⪰	NOUN
ejpam-6931	405	16	ℑ	ℑ	PROPN
ejpam-6931	405	17	⋆	⋆	VERB
ejpam-6931	405	18	ℑ	ℑ	PROPN
ejpam-6931	405	19	⋆	⋆	VERB
ejpam-6931	405	20	...	...	PUNCT
ejpam-6931	405	21	⋆	⋆	PUNCT
ejpam-6931	405	22	ℑ	ℑ	PROPN
ejpam-6931	405	23	=	=	SYM
ejpam-6931	405	24	ℑ	ℑ	NOUN
ejpam-6931	405	25	which	which	PRON
ejpam-6931	405	26	leads	lead	VERB
ejpam-6931	405	27	to	to	ADP
ejpam-6931	405	28	lim	lim	PROPN
ejpam-6931	405	29	n→∞	n→∞	PROPN
ejpam-6931	405	30	inf	inf	PROPN
ejpam-6931	405	31	m	m	PROPN
ejpam-6931	405	32	>	>	PROPN
ejpam-6931	405	33	n	n	PRON
ejpam-6931	405	34	e(ϱon	e(ϱon	PROPN
ejpam-6931	405	35	,	,	PUNCT
ejpam-6931	405	36	ϱom	ϱom	NOUN
ejpam-6931	405	37	,	,	PUNCT
ejpam-6931	405	38	e	e	NOUN
ejpam-6931	405	39	)	)	PUNCT
ejpam-6931	405	40	=	=	SYM
ejpam-6931	405	41	ℑ	ℑ	NOUN
ejpam-6931	405	42	for	for	ADP
ejpam-6931	405	43	every	every	DET
ejpam-6931	405	44	e	e	PROPN
ejpam-6931	405	45	∈	∈	PROPN
ejpam-6931	405	46	s0	s0	NOUN
ejpam-6931	405	47	.	.	PUNCT
ejpam-6931	406	1	furthermore	furthermore	ADV
ejpam-6931	406	2	,	,	PUNCT
ejpam-6931	406	3	by	by	ADP
ejpam-6931	406	4	iteratively	iteratively	ADV
ejpam-6931	406	5	applying	apply	VERB
ejpam-6931	406	6	the	the	DET
ejpam-6931	406	7	condition	condition	NOUN
ejpam-6931	406	8	(	(	PUNCT
ejpam-6931	406	9	10	10	NUM
ejpam-6931	406	10	)	)	PUNCT
ejpam-6931	406	11	of	of	ADP
ejpam-6931	406	12	definition	definition	NOUN
ejpam-6931	406	13	7	7	NUM
ejpam-6931	406	14	for	for	ADP
ejpam-6931	406	15	any	any	DET
ejpam-6931	406	16	positive	positive	ADJ
ejpam-6931	406	17	integers	integer	NOUN
ejpam-6931	406	18	m	m	VERB
ejpam-6931	406	19	>	>	X
ejpam-6931	406	20	n	n	CCONJ
ejpam-6931	406	21	,	,	PUNCT
ejpam-6931	406	22	we	we	PRON
ejpam-6931	406	23	can	can	AUX
ejpam-6931	406	24	obtain	obtain	VERB
ejpam-6931	406	25	g(ϱon	g(ϱon	PROPN
ejpam-6931	406	26	,	,	PUNCT
ejpam-6931	406	27	ϱom	ϱom	NOUN
ejpam-6931	406	28	,	,	PUNCT
ejpam-6931	406	29	e	e	NOUN
ejpam-6931	406	30	)	)	PUNCT
ejpam-6931	406	31	⪯	⪯	NOUN
ejpam-6931	406	32	g	g	PROPN
ejpam-6931	406	33	(	(	PUNCT
ejpam-6931	406	34	ϱon	ϱon	PROPN
ejpam-6931	406	35	,	,	PUNCT
ejpam-6931	406	36	ϱ	ϱ	ADP
ejpam-6931	406	37	o	o	PROPN
ejpam-6931	406	38	n+1	n+1	PROPN
ejpam-6931	406	39	,	,	PUNCT
ejpam-6931	406	40	c	c	PROPN
ejpam-6931	406	41	m−	m−	PROPN
ejpam-6931	406	42	n	n	PROPN
ejpam-6931	406	43	)	)	PUNCT
ejpam-6931	406	44	△	△	PROPN
ejpam-6931	406	45	g	g	PROPN
ejpam-6931	406	46	(	(	PUNCT
ejpam-6931	406	47	ϱon+1	ϱon+1	PROPN
ejpam-6931	406	48	,	,	PUNCT
ejpam-6931	406	49	ϱ	ϱ	ADP
ejpam-6931	406	50	o	o	NOUN
ejpam-6931	406	51	n+2	n+2	PROPN
ejpam-6931	406	52	,	,	PUNCT
ejpam-6931	406	53	e	e	NOUN
ejpam-6931	406	54	m−	m−	PROPN
ejpam-6931	406	55	n	n	PROPN
ejpam-6931	406	56	)	)	PUNCT
ejpam-6931	406	57	△	△	X
ejpam-6931	406	58	...	...	PUNCT
ejpam-6931	406	59	△	△	PROPN
ejpam-6931	406	60	g	g	PROPN
ejpam-6931	406	61	(	(	PUNCT
ejpam-6931	406	62	ϱom−1	ϱom−1	PROPN
ejpam-6931	406	63	,	,	PUNCT
ejpam-6931	406	64	ϱ	ϱ	ADP
ejpam-6931	406	65	o	o	NOUN
ejpam-6931	406	66	m	m	PROPN
ejpam-6931	406	67	,	,	PUNCT
ejpam-6931	406	68	e	e	VERB
ejpam-6931	406	69	m−	m−	PROPN
ejpam-6931	406	70	n	n	PROPN
ejpam-6931	406	71	)	)	PUNCT
ejpam-6931	406	72	.	.	PUNCT
ejpam-6931	407	1	consequently	consequently	ADV
ejpam-6931	407	2	,	,	PUNCT
ejpam-6931	407	3	lim	lim	PROPN
ejpam-6931	407	4	n→∞	n→∞	NUM
ejpam-6931	407	5	sup	sup	PROPN
ejpam-6931	407	6	m	m	PROPN
ejpam-6931	407	7	>	>	NOUN
ejpam-6931	407	8	n	n	PRON
ejpam-6931	407	9	g(ϱon	g(ϱon	NOUN
ejpam-6931	407	10	,	,	PUNCT
ejpam-6931	407	11	ϱom	ϱom	NOUN
ejpam-6931	407	12	,	,	PUNCT
ejpam-6931	407	13	e	e	NOUN
ejpam-6931	407	14	)	)	PUNCT
ejpam-6931	407	15	⪯	⪯	NOUN
ejpam-6931	407	16	∅	∅	NOUN
ejpam-6931	407	17	△	△	NOUN
ejpam-6931	407	18	∅	∅	NOUN
ejpam-6931	407	19	△	△	X
ejpam-6931	407	20	...	...	PUNCT
ejpam-6931	407	21	△	△	NOUN
ejpam-6931	407	22	∅	∅	NOUN
ejpam-6931	407	23	=	=	SYM
ejpam-6931	407	24	∅	∅	NOUN
ejpam-6931	407	25	which	which	PRON
ejpam-6931	407	26	leads	lead	VERB
ejpam-6931	407	27	to	to	ADP
ejpam-6931	407	28	lim	lim	PROPN
ejpam-6931	407	29	n→∞	n→∞	NUM
ejpam-6931	407	30	sup	sup	PROPN
ejpam-6931	407	31	m	m	PROPN
ejpam-6931	407	32	>	>	NOUN
ejpam-6931	407	33	n	n	PRON
ejpam-6931	407	34	g(ϱon	g(ϱon	NOUN
ejpam-6931	407	35	,	,	PUNCT
ejpam-6931	407	36	ϱom	ϱom	NOUN
ejpam-6931	407	37	,	,	PUNCT
ejpam-6931	407	38	e	e	NOUN
ejpam-6931	407	39	)	)	PUNCT
ejpam-6931	407	40	=	=	NOUN
ejpam-6931	407	41	∅	∅	NOUN
ejpam-6931	407	42	for	for	ADP
ejpam-6931	407	43	every	every	DET
ejpam-6931	407	44	e	e	PROPN
ejpam-6931	407	45	∈	∈	PROPN
ejpam-6931	407	46	s0	s0	PROPN
ejpam-6931	407	47	.	.	PUNCT
ejpam-6931	408	1	also	also	ADV
ejpam-6931	408	2	by	by	ADP
ejpam-6931	408	3	iteratively	iteratively	ADV
ejpam-6931	408	4	applying	apply	VERB
ejpam-6931	408	5	the	the	DET
ejpam-6931	408	6	condition	condition	NOUN
ejpam-6931	408	7	(	(	PUNCT
ejpam-6931	408	8	15	15	NUM
ejpam-6931	408	9	)	)	PUNCT
ejpam-6931	408	10	of	of	ADP
ejpam-6931	408	11	definition	definition	NOUN
ejpam-6931	408	12	7	7	NUM
ejpam-6931	408	13	for	for	ADP
ejpam-6931	408	14	any	any	DET
ejpam-6931	408	15	positive	positive	ADJ
ejpam-6931	408	16	integers	integer	NOUN
ejpam-6931	408	17	m	m	VERB
ejpam-6931	408	18	>	>	X
ejpam-6931	408	19	n	n	CCONJ
ejpam-6931	408	20	,	,	PUNCT
ejpam-6931	408	21	we	we	PRON
ejpam-6931	408	22	can	can	AUX
ejpam-6931	408	23	obtain	obtain	VERB
ejpam-6931	408	24	h(ϱon	h(ϱon	PROPN
ejpam-6931	408	25	,	,	PUNCT
ejpam-6931	408	26	ϱ	ϱ	ADP
ejpam-6931	408	27	o	o	PROPN
ejpam-6931	408	28	m	m	NOUN
ejpam-6931	408	29	,	,	PUNCT
ejpam-6931	408	30	e	e	NOUN
ejpam-6931	408	31	)	)	PUNCT
ejpam-6931	408	32	⪯	⪯	PROPN
ejpam-6931	408	33	h	h	PROPN
ejpam-6931	408	34	(	(	PUNCT
ejpam-6931	408	35	ϱon	ϱon	PROPN
ejpam-6931	408	36	,	,	PUNCT
ejpam-6931	408	37	ϱ	ϱ	ADP
ejpam-6931	408	38	o	o	PROPN
ejpam-6931	408	39	n+1	n+1	PROPN
ejpam-6931	408	40	,	,	PUNCT
ejpam-6931	408	41	e	e	NOUN
ejpam-6931	408	42	m−	m−	PROPN
ejpam-6931	408	43	n	n	PROPN
ejpam-6931	408	44	)	)	PUNCT
ejpam-6931	408	45	△	△	PROPN
ejpam-6931	408	46	h	h	NOUN
ejpam-6931	408	47	(	(	PUNCT
ejpam-6931	408	48	ϱon+1	ϱon+1	PROPN
ejpam-6931	408	49	,	,	PUNCT
ejpam-6931	408	50	ϱ	ϱ	ADP
ejpam-6931	408	51	o	o	NOUN
ejpam-6931	408	52	n+2	n+2	PROPN
ejpam-6931	408	53	,	,	PUNCT
ejpam-6931	408	54	e	e	NOUN
ejpam-6931	408	55	m−	m−	PROPN
ejpam-6931	408	56	n	n	PROPN
ejpam-6931	408	57	)	)	PUNCT
ejpam-6931	408	58	△	△	PROPN
ejpam-6931	408	59	...	...	PUNCT
ejpam-6931	408	60	△	△	X
ejpam-6931	408	61	h	h	NOUN
ejpam-6931	408	62	(	(	PUNCT
ejpam-6931	408	63	ϱom−1	ϱom−1	PROPN
ejpam-6931	408	64	,	,	PUNCT
ejpam-6931	408	65	ϱ	ϱ	ADP
ejpam-6931	408	66	o	o	NOUN
ejpam-6931	408	67	m	m	PROPN
ejpam-6931	408	68	,	,	PUNCT
ejpam-6931	408	69	e	e	VERB
ejpam-6931	408	70	m−	m−	PROPN
ejpam-6931	408	71	n	n	PROPN
ejpam-6931	408	72	)	)	PUNCT
ejpam-6931	408	73	.	.	PUNCT
ejpam-6931	409	1	consequently	consequently	ADV
ejpam-6931	409	2	,	,	PUNCT
ejpam-6931	409	3	lim	lim	PROPN
ejpam-6931	409	4	n→∞	n→∞	NUM
ejpam-6931	409	5	sup	sup	PROPN
ejpam-6931	409	6	m	m	PROPN
ejpam-6931	409	7	>	>	X
ejpam-6931	409	8	n	n	PROPN
ejpam-6931	409	9	h(ϱon	h(ϱon	NOUN
ejpam-6931	409	10	,	,	PUNCT
ejpam-6931	409	11	ϱ	ϱ	ADP
ejpam-6931	409	12	o	o	PROPN
ejpam-6931	409	13	m	m	NOUN
ejpam-6931	409	14	,	,	PUNCT
ejpam-6931	409	15	e	e	NOUN
ejpam-6931	409	16	)	)	PUNCT
ejpam-6931	409	17	⪯	⪯	NOUN
ejpam-6931	409	18	∅	∅	NOUN
ejpam-6931	409	19	△	△	NOUN
ejpam-6931	409	20	∅	∅	NOUN
ejpam-6931	409	21	△	△	X
ejpam-6931	409	22	...	...	PUNCT
ejpam-6931	409	23	△	△	NOUN
ejpam-6931	409	24	∅	∅	NOUN
ejpam-6931	409	25	=	=	SYM
ejpam-6931	409	26	∅	∅	NOUN
ejpam-6931	409	27	which	which	PRON
ejpam-6931	409	28	leads	lead	VERB
ejpam-6931	409	29	to	to	ADP
ejpam-6931	409	30	lim	lim	PROPN
ejpam-6931	409	31	n→∞	n→∞	NUM
ejpam-6931	409	32	sup	sup	PROPN
ejpam-6931	409	33	m	m	PROPN
ejpam-6931	409	34	>	>	X
ejpam-6931	409	35	n	n	PROPN
ejpam-6931	409	36	h(ϱon	h(ϱon	NOUN
ejpam-6931	409	37	,	,	PUNCT
ejpam-6931	409	38	ϱ	ϱ	ADP
ejpam-6931	409	39	o	o	PROPN
ejpam-6931	409	40	m	m	NOUN
ejpam-6931	409	41	,	,	PUNCT
ejpam-6931	409	42	e	e	NOUN
ejpam-6931	409	43	)	)	PUNCT
ejpam-6931	409	44	=	=	NOUN
ejpam-6931	409	45	∅	∅	NOUN
ejpam-6931	409	46	for	for	ADP
ejpam-6931	409	47	every	every	DET
ejpam-6931	409	48	e	e	PROPN
ejpam-6931	409	49	∈	∈	PROPN
ejpam-6931	409	50	s0	s0	PROPN
ejpam-6931	409	51	.	.	PUNCT
ejpam-6931	410	1	hence	hence	ADV
ejpam-6931	410	2	,	,	PUNCT
ejpam-6931	410	3	sequence	sequence	NOUN
ejpam-6931	410	4	{	{	PUNCT
ejpam-6931	410	5	ϱon	ϱon	NOUN
ejpam-6931	410	6	}	}	PUNCT
ejpam-6931	410	7	is	be	AUX
ejpam-6931	410	8	cauchy	cauchy	PROPN
ejpam-6931	410	9	.	.	PUNCT
ejpam-6931	411	1	s.	s.	PROPN
ejpam-6931	411	2	m.	m.	PROPN
ejpam-6931	411	3	u.	u.	PROPN
ejpam-6931	411	4	ud	ud	AUX
ejpam-6931	411	5	-	-	PUNCT
ejpam-6931	411	6	din	din	VERB
ejpam-6931	411	7	et	et	PROPN
ejpam-6931	411	8	al	al	PROPN
ejpam-6931	411	9	.	.	PUNCT
ejpam-6931	411	10	/	/	SYM
ejpam-6931	411	11	eur	eur	PROPN
ejpam-6931	411	12	.	.	PUNCT
ejpam-6931	412	1	j.	j.	PROPN
ejpam-6931	412	2	pure	pure	PROPN
ejpam-6931	412	3	appl	appl	PROPN
ejpam-6931	412	4	.	.	PROPN
ejpam-6931	412	5	math	math	PROPN
ejpam-6931	412	6	,	,	PUNCT
ejpam-6931	412	7	18	18	NUM
ejpam-6931	412	8	(	(	PUNCT
ejpam-6931	412	9	4	4	NUM
ejpam-6931	412	10	)	)	PUNCT
ejpam-6931	412	11	(	(	PUNCT
ejpam-6931	412	12	2025	2025	NUM
ejpam-6931	412	13	)	)	PUNCT
ejpam-6931	412	14	,	,	PUNCT
ejpam-6931	412	15	6931	6931	NUM
ejpam-6931	412	16	30	30	NUM
ejpam-6931	412	17	of	of	ADP
ejpam-6931	412	18	38	38	NUM
ejpam-6931	412	19	given	give	VERB
ejpam-6931	412	20	that	that	SCONJ
ejpam-6931	412	21	(	(	PUNCT
ejpam-6931	412	22	v	v	NOUN
ejpam-6931	412	23	,	,	PUNCT
ejpam-6931	412	24	e	e	NOUN
ejpam-6931	412	25	,	,	PUNCT
ejpam-6931	412	26	g	g	PROPN
ejpam-6931	412	27	,	,	PUNCT
ejpam-6931	412	28	h	h	NOUN
ejpam-6931	412	29	,	,	PUNCT
ejpam-6931	412	30	⋆	⋆	NOUN
ejpam-6931	412	31	,	,	PUNCT
ejpam-6931	412	32	△	△	NOUN
ejpam-6931	412	33	)	)	PUNCT
ejpam-6931	412	34	is	be	AUX
ejpam-6931	412	35	complete	complete	ADJ
ejpam-6931	412	36	,	,	PUNCT
ejpam-6931	412	37	lemma	lemma	PROPN
ejpam-6931	412	38	2	2	NUM
ejpam-6931	412	39	implies	imply	VERB
ejpam-6931	412	40	the	the	DET
ejpam-6931	412	41	existence	existence	NOUN
ejpam-6931	412	42	of	of	ADP
ejpam-6931	412	43	u	u	PROPN
ejpam-6931	412	44	∈	∈	PROPN
ejpam-6931	412	45	v	v	ADP
ejpam-6931	412	46	satisfying	satisfy	VERB
ejpam-6931	412	47	lim	lim	PROPN
ejpam-6931	412	48	n→∞	n→∞	NUM
ejpam-6931	412	49	e(ϱon	e(ϱon	PROPN
ejpam-6931	412	50	,	,	PUNCT
ejpam-6931	412	51	u	u	NOUN
ejpam-6931	412	52	,	,	PUNCT
ejpam-6931	412	53	e	e	NOUN
ejpam-6931	412	54	)	)	PUNCT
ejpam-6931	412	55	=	=	SYM
ejpam-6931	412	56	ℑ	ℑ	PROPN
ejpam-6931	412	57	,	,	PUNCT
ejpam-6931	412	58	lim	lim	PROPN
ejpam-6931	412	59	n→∞	n→∞	NUM
ejpam-6931	413	1	g(ϱon	g(ϱon	PROPN
ejpam-6931	413	2	,	,	PUNCT
ejpam-6931	413	3	u	u	NOUN
ejpam-6931	413	4	,	,	PUNCT
ejpam-6931	413	5	e	e	NOUN
ejpam-6931	413	6	)	)	PUNCT
ejpam-6931	413	7	=	=	SYM
ejpam-6931	413	8	∅	∅	NOUN
ejpam-6931	413	9	and	and	CCONJ
ejpam-6931	413	10	lim	lim	PROPN
ejpam-6931	413	11	n→∞	n→∞	PROPN
ejpam-6931	413	12	h(ϱon	h(ϱon	PROPN
ejpam-6931	413	13	,	,	PUNCT
ejpam-6931	413	14	u	u	NOUN
ejpam-6931	413	15	,	,	PUNCT
ejpam-6931	413	16	e	e	NOUN
ejpam-6931	413	17	)	)	PUNCT
ejpam-6931	413	18	=	=	NOUN
ejpam-6931	413	19	∅	∅	NOUN
ejpam-6931	413	20	for	for	ADP
ejpam-6931	413	21	all	all	DET
ejpam-6931	413	22	e	e	PROPN
ejpam-6931	413	23	∈	∈	PROPN
ejpam-6931	413	24	s0	s0	PROPN
ejpam-6931	413	25	.	.	PUNCT
ejpam-6931	414	1	for	for	ADP
ejpam-6931	414	2	any	any	DET
ejpam-6931	414	3	n	n	PRON
ejpam-6931	414	4	∈	∈	NOUN
ejpam-6931	414	5	m0	m0	NOUN
ejpam-6931	414	6	and	and	CCONJ
ejpam-6931	414	7	e	e	NOUN
ejpam-6931	414	8	∈	∈	PROPN
ejpam-6931	414	9	s0	s0	PROPN
ejpam-6931	414	10	,	,	PUNCT
ejpam-6931	414	11	by	by	ADP
ejpam-6931	414	12	equation	equation	NOUN
ejpam-6931	414	13	(	(	PUNCT
ejpam-6931	414	14	11	11	NUM
ejpam-6931	414	15	)	)	PUNCT
ejpam-6931	414	16	we	we	PRON
ejpam-6931	414	17	yield	yield	VERB
ejpam-6931	414	18	ℑ−	ℑ−	NUM
ejpam-6931	414	19	e(fu	e(fu	PROPN
ejpam-6931	414	20	,	,	PUNCT
ejpam-6931	414	21	gϱo2n+1	gϱo2n+1	NOUN
ejpam-6931	414	22	,	,	PUNCT
ejpam-6931	414	23	e	e	NOUN
ejpam-6931	414	24	)	)	PUNCT
ejpam-6931	414	25	⪯	⪯	NOUN
ejpam-6931	414	26	k(ℑ−	k(ℑ−	PROPN
ejpam-6931	414	27	e(u	e(u	PROPN
ejpam-6931	414	28	,	,	PUNCT
ejpam-6931	414	29	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	414	30	,	,	PUNCT
ejpam-6931	414	31	e	e	NOUN
ejpam-6931	414	32	)	)	PUNCT
ejpam-6931	414	33	)	)	PUNCT
ejpam-6931	414	34	≺	≺	NOUN
ejpam-6931	414	35	ℑ−	ℑ−	NUM
ejpam-6931	414	36	e(u	e(u	PROPN
ejpam-6931	414	37	,	,	PUNCT
ejpam-6931	414	38	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	414	39	,	,	PUNCT
ejpam-6931	414	40	e	e	NOUN
ejpam-6931	414	41	)	)	PUNCT
ejpam-6931	414	42	g(iu	g(iu	PROPN
ejpam-6931	414	43	,	,	PUNCT
ejpam-6931	414	44	j	j	PROPN
ejpam-6931	414	45	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	414	46	,	,	PUNCT
ejpam-6931	414	47	e	e	NOUN
ejpam-6931	414	48	)	)	PUNCT
ejpam-6931	414	49	⪯	⪯	NOUN
ejpam-6931	414	50	kg(u	kg(u	X
ejpam-6931	414	51	,	,	PUNCT
ejpam-6931	414	52	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	414	53	,	,	PUNCT
ejpam-6931	414	54	e	e	NOUN
ejpam-6931	414	55	)	)	PUNCT
ejpam-6931	414	56	≺	≺	NOUN
ejpam-6931	414	57	g(u	g(u	PROPN
ejpam-6931	414	58	,	,	PUNCT
ejpam-6931	414	59	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	414	60	,	,	PUNCT
ejpam-6931	414	61	e	e	NOUN
ejpam-6931	414	62	)	)	PUNCT
ejpam-6931	414	63	and	and	CCONJ
ejpam-6931	414	64	h(iu	h(iu	PROPN
ejpam-6931	414	65	,	,	PUNCT
ejpam-6931	414	66	j	j	PROPN
ejpam-6931	414	67	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	414	68	,	,	PUNCT
ejpam-6931	414	69	e	e	NOUN
ejpam-6931	414	70	)	)	PUNCT
ejpam-6931	414	71	⪯	⪯	NOUN
ejpam-6931	414	72	kh(u	kh(u	PROPN
ejpam-6931	414	73	,	,	PUNCT
ejpam-6931	414	74	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	414	75	,	,	PUNCT
ejpam-6931	414	76	e	e	NOUN
ejpam-6931	414	77	)	)	PUNCT
ejpam-6931	414	78	≺	≺	NOUN
ejpam-6931	414	79	h(u	h(u	PROPN
ejpam-6931	414	80	,	,	PUNCT
ejpam-6931	414	81	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	414	82	,	,	PUNCT
ejpam-6931	414	83	e	e	NOUN
ejpam-6931	414	84	)	)	PUNCT
ejpam-6931	414	85	.	.	PUNCT
ejpam-6931	415	1	this	this	PRON
ejpam-6931	415	2	implies	imply	VERB
ejpam-6931	415	3	that	that	SCONJ
ejpam-6931	415	4	e(iu	e(iu	PROPN
ejpam-6931	415	5	,	,	PUNCT
ejpam-6931	415	6	j	j	PROPN
ejpam-6931	415	7	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	415	8	,	,	PUNCT
ejpam-6931	415	9	e	e	NOUN
ejpam-6931	415	10	)	)	PUNCT
ejpam-6931	415	11	≻	≻	PROPN
ejpam-6931	415	12	e(u	e(u	PROPN
ejpam-6931	415	13	,	,	PUNCT
ejpam-6931	415	14	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	415	15	,	,	PUNCT
ejpam-6931	415	16	e	e	NOUN
ejpam-6931	415	17	)	)	PUNCT
ejpam-6931	415	18	(	(	PUNCT
ejpam-6931	415	19	12	12	NUM
ejpam-6931	415	20	)	)	PUNCT
ejpam-6931	415	21	g(iu	g(iu	NOUN
ejpam-6931	415	22	,	,	PUNCT
ejpam-6931	415	23	j	j	PROPN
ejpam-6931	415	24	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	415	25	,	,	PUNCT
ejpam-6931	415	26	e	e	NOUN
ejpam-6931	415	27	)	)	PUNCT
ejpam-6931	415	28	≺	≺	NOUN
ejpam-6931	415	29	g(u	g(u	PROPN
ejpam-6931	415	30	,	,	PUNCT
ejpam-6931	415	31	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	415	32	,	,	PUNCT
ejpam-6931	415	33	e	e	NOUN
ejpam-6931	415	34	)	)	PUNCT
ejpam-6931	415	35	(	(	PUNCT
ejpam-6931	415	36	13	13	NUM
ejpam-6931	415	37	)	)	PUNCT
ejpam-6931	415	38	and	and	CCONJ
ejpam-6931	415	39	h(iu	h(iu	PROPN
ejpam-6931	415	40	,	,	PUNCT
ejpam-6931	415	41	j	j	PROPN
ejpam-6931	415	42	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	415	43	,	,	PUNCT
ejpam-6931	415	44	e	e	NOUN
ejpam-6931	415	45	)	)	PUNCT
ejpam-6931	415	46	≺	≺	NOUN
ejpam-6931	415	47	h(u	h(u	PROPN
ejpam-6931	415	48	,	,	PUNCT
ejpam-6931	415	49	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	415	50	,	,	PUNCT
ejpam-6931	415	51	e	e	NOUN
ejpam-6931	415	52	)	)	PUNCT
ejpam-6931	415	53	(	(	PUNCT
ejpam-6931	415	54	14	14	NUM
ejpam-6931	415	55	)	)	PUNCT
ejpam-6931	415	56	for	for	ADP
ejpam-6931	415	57	each	each	DET
ejpam-6931	415	58	n	n	PRON
ejpam-6931	415	59	∈	∈	NOUN
ejpam-6931	415	60	m0	m0	NOUN
ejpam-6931	415	61	and	and	CCONJ
ejpam-6931	415	62	e	e	NOUN
ejpam-6931	415	63	∈	∈	PROPN
ejpam-6931	415	64	s0	s0	PROPN
ejpam-6931	415	65	.	.	PUNCT
ejpam-6931	416	1	as	as	ADP
ejpam-6931	416	2	a	a	DET
ejpam-6931	416	3	result	result	NOUN
ejpam-6931	416	4	of	of	ADP
ejpam-6931	416	5	conditions	condition	NOUN
ejpam-6931	416	6	(	(	PUNCT
ejpam-6931	416	7	5	5	NUM
ejpam-6931	416	8	)	)	PUNCT
ejpam-6931	416	9	,	,	PUNCT
ejpam-6931	416	10	(	(	PUNCT
ejpam-6931	416	11	10	10	NUM
ejpam-6931	416	12	)	)	PUNCT
ejpam-6931	416	13	and	and	CCONJ
ejpam-6931	416	14	(	(	PUNCT
ejpam-6931	416	15	15	15	NUM
ejpam-6931	416	16	)	)	PUNCT
ejpam-6931	416	17	of	of	ADP
ejpam-6931	416	18	definition	definition	NOUN
ejpam-6931	416	19	7	7	NUM
ejpam-6931	416	20	,	,	PUNCT
ejpam-6931	416	21	equations	equation	NOUN
ejpam-6931	416	22	(	(	PUNCT
ejpam-6931	416	23	12	12	NUM
ejpam-6931	416	24	)	)	PUNCT
ejpam-6931	416	25	,	,	PUNCT
ejpam-6931	416	26	(	(	PUNCT
ejpam-6931	416	27	13	13	NUM
ejpam-6931	416	28	)	)	PUNCT
ejpam-6931	416	29	and	and	CCONJ
ejpam-6931	416	30	(	(	PUNCT
ejpam-6931	416	31	14	14	NUM
ejpam-6931	416	32	)	)	PUNCT
ejpam-6931	416	33	,	,	PUNCT
ejpam-6931	416	34	for	for	ADP
ejpam-6931	416	35	each	each	DET
ejpam-6931	416	36	n	n	PRON
ejpam-6931	416	37	∈	∈	NOUN
ejpam-6931	416	38	m0	m0	NOUN
ejpam-6931	416	39	and	and	CCONJ
ejpam-6931	416	40	e	e	NOUN
ejpam-6931	416	41	∈	∈	PROPN
ejpam-6931	416	42	s0	s0	PROPN
ejpam-6931	416	43	,	,	PUNCT
ejpam-6931	416	44	we	we	PRON
ejpam-6931	416	45	may	may	AUX
ejpam-6931	416	46	deduce	deduce	VERB
ejpam-6931	416	47	that	that	SCONJ
ejpam-6931	416	48	e(u	e(u	PROPN
ejpam-6931	416	49	,	,	PUNCT
ejpam-6931	416	50	iu	iu	ADP
ejpam-6931	416	51	,	,	PUNCT
ejpam-6931	416	52	e	e	NOUN
ejpam-6931	416	53	)	)	PUNCT
ejpam-6931	416	54	⪰	⪰	NOUN
ejpam-6931	416	55	e	e	X
ejpam-6931	416	56	(	(	PUNCT
ejpam-6931	416	57	u	u	NOUN
ejpam-6931	416	58	,	,	PUNCT
ejpam-6931	416	59	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	416	60	,	,	PUNCT
ejpam-6931	416	61	e	e	X
ejpam-6931	416	62	2	2	NUM
ejpam-6931	416	63	)	)	PUNCT
ejpam-6931	416	64	⋆	⋆	X
ejpam-6931	416	65	e	e	X
ejpam-6931	416	66	(	(	PUNCT
ejpam-6931	416	67	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	416	68	,	,	PUNCT
ejpam-6931	416	69	iu	iu	ADP
ejpam-6931	416	70	,	,	PUNCT
ejpam-6931	416	71	e	e	X
ejpam-6931	416	72	2	2	NUM
ejpam-6931	416	73	)	)	PUNCT
ejpam-6931	416	74	=	=	SYM
ejpam-6931	417	1	e	e	X
ejpam-6931	417	2	(	(	PUNCT
ejpam-6931	417	3	u	u	NOUN
ejpam-6931	417	4	,	,	PUNCT
ejpam-6931	417	5	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	417	6	,	,	PUNCT
ejpam-6931	417	7	e	e	X
ejpam-6931	417	8	2	2	NUM
ejpam-6931	417	9	)	)	PUNCT
ejpam-6931	417	10	⋆	⋆	X
ejpam-6931	417	11	e	e	X
ejpam-6931	417	12	(	(	PUNCT
ejpam-6931	417	13	j	j	PROPN
ejpam-6931	417	14	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	417	15	,	,	PUNCT
ejpam-6931	417	16	iu	iu	ADP
ejpam-6931	417	17	,	,	PUNCT
ejpam-6931	417	18	e	e	X
ejpam-6931	417	19	2	2	NUM
ejpam-6931	417	20	)	)	PUNCT
ejpam-6931	417	21	=	=	SYM
ejpam-6931	417	22	e	e	X
ejpam-6931	417	23	(	(	PUNCT
ejpam-6931	417	24	u	u	NOUN
ejpam-6931	417	25	,	,	PUNCT
ejpam-6931	417	26	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	417	27	,	,	PUNCT
ejpam-6931	417	28	e	e	X
ejpam-6931	417	29	2	2	NUM
ejpam-6931	417	30	)	)	PUNCT
ejpam-6931	417	31	⋆	⋆	X
ejpam-6931	417	32	e	e	X
ejpam-6931	417	33	(	(	PUNCT
ejpam-6931	417	34	iu	iu	PROPN
ejpam-6931	417	35	,	,	PUNCT
ejpam-6931	417	36	j	j	PROPN
ejpam-6931	417	37	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	417	38	,	,	PUNCT
ejpam-6931	417	39	e	e	X
ejpam-6931	417	40	2	2	NUM
ejpam-6931	417	41	)	)	PUNCT
ejpam-6931	417	42	⪰	⪰	NOUN
ejpam-6931	417	43	e	e	X
ejpam-6931	417	44	(	(	PUNCT
ejpam-6931	417	45	u	u	NOUN
ejpam-6931	417	46	,	,	PUNCT
ejpam-6931	417	47	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	417	48	,	,	PUNCT
ejpam-6931	417	49	e	e	X
ejpam-6931	417	50	2	2	NUM
ejpam-6931	417	51	)	)	PUNCT
ejpam-6931	417	52	⋆	⋆	X
ejpam-6931	417	53	e	e	X
ejpam-6931	417	54	(	(	PUNCT
ejpam-6931	417	55	u	u	NOUN
ejpam-6931	417	56	,	,	PUNCT
ejpam-6931	417	57	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	417	58	,	,	PUNCT
ejpam-6931	417	59	e	e	X
ejpam-6931	417	60	2	2	NUM
ejpam-6931	417	61	)	)	PUNCT
ejpam-6931	417	62	g(u	g(u	PROPN
ejpam-6931	417	63	,	,	PUNCT
ejpam-6931	417	64	iu	iu	ADP
ejpam-6931	417	65	,	,	PUNCT
ejpam-6931	417	66	e	e	NOUN
ejpam-6931	417	67	)	)	PUNCT
ejpam-6931	417	68	⪯	⪯	NOUN
ejpam-6931	417	69	g	g	PROPN
ejpam-6931	417	70	(	(	PUNCT
ejpam-6931	417	71	u	u	PROPN
ejpam-6931	417	72	,	,	PUNCT
ejpam-6931	417	73	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	417	74	,	,	PUNCT
ejpam-6931	417	75	e	e	X
ejpam-6931	417	76	2	2	NUM
ejpam-6931	417	77	)	)	PUNCT
ejpam-6931	417	78	△	△	PROPN
ejpam-6931	417	79	g	g	PROPN
ejpam-6931	417	80	(	(	PUNCT
ejpam-6931	417	81	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	417	82	,	,	PUNCT
ejpam-6931	417	83	iu	iu	ADP
ejpam-6931	417	84	,	,	PUNCT
ejpam-6931	417	85	e	e	X
ejpam-6931	417	86	2	2	NUM
ejpam-6931	417	87	)	)	PUNCT
ejpam-6931	417	88	=	=	SYM
ejpam-6931	417	89	g	g	PROPN
ejpam-6931	417	90	(	(	PUNCT
ejpam-6931	417	91	u	u	PROPN
ejpam-6931	417	92	,	,	PUNCT
ejpam-6931	417	93	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	417	94	,	,	PUNCT
ejpam-6931	417	95	e	e	X
ejpam-6931	417	96	2	2	NUM
ejpam-6931	417	97	)	)	PUNCT
ejpam-6931	417	98	△	△	PROPN
ejpam-6931	417	99	g	g	PROPN
ejpam-6931	417	100	(	(	PUNCT
ejpam-6931	417	101	j	j	PROPN
ejpam-6931	417	102	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	417	103	,	,	PUNCT
ejpam-6931	417	104	iu	iu	ADP
ejpam-6931	417	105	,	,	PUNCT
ejpam-6931	417	106	e	e	X
ejpam-6931	417	107	2	2	NUM
ejpam-6931	417	108	)	)	PUNCT
ejpam-6931	417	109	=	=	SYM
ejpam-6931	417	110	g	g	PROPN
ejpam-6931	417	111	(	(	PUNCT
ejpam-6931	417	112	u	u	PROPN
ejpam-6931	417	113	,	,	PUNCT
ejpam-6931	417	114	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	417	115	,	,	PUNCT
ejpam-6931	417	116	e	e	X
ejpam-6931	417	117	2	2	NUM
ejpam-6931	417	118	)	)	PUNCT
ejpam-6931	417	119	△	△	PROPN
ejpam-6931	417	120	g	g	PROPN
ejpam-6931	417	121	(	(	PUNCT
ejpam-6931	417	122	iu	iu	PROPN
ejpam-6931	417	123	,	,	PUNCT
ejpam-6931	417	124	j	j	PROPN
ejpam-6931	417	125	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	417	126	,	,	PUNCT
ejpam-6931	417	127	e	e	X
ejpam-6931	417	128	2	2	NUM
ejpam-6931	417	129	)	)	PUNCT
ejpam-6931	417	130	⪯	⪯	NOUN
ejpam-6931	417	131	g	g	PROPN
ejpam-6931	417	132	(	(	PUNCT
ejpam-6931	417	133	u	u	PROPN
ejpam-6931	417	134	,	,	PUNCT
ejpam-6931	417	135	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	417	136	,	,	PUNCT
ejpam-6931	417	137	e	e	X
ejpam-6931	417	138	2	2	NUM
ejpam-6931	417	139	)	)	PUNCT
ejpam-6931	417	140	△	△	PROPN
ejpam-6931	417	141	g	g	PROPN
ejpam-6931	417	142	(	(	PUNCT
ejpam-6931	417	143	u	u	PROPN
ejpam-6931	417	144	,	,	PUNCT
ejpam-6931	417	145	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	417	146	,	,	PUNCT
ejpam-6931	417	147	e	e	X
ejpam-6931	417	148	2	2	NUM
ejpam-6931	417	149	)	)	PUNCT
ejpam-6931	417	150	s.	s.	PROPN
ejpam-6931	417	151	m.	m.	PROPN
ejpam-6931	417	152	u.	u.	PROPN
ejpam-6931	417	153	ud	ud	AUX
ejpam-6931	417	154	-	-	PUNCT
ejpam-6931	417	155	din	din	VERB
ejpam-6931	417	156	et	et	PROPN
ejpam-6931	417	157	al	al	PROPN
ejpam-6931	417	158	.	.	PUNCT
ejpam-6931	417	159	/	/	SYM
ejpam-6931	417	160	eur	eur	PROPN
ejpam-6931	417	161	.	.	PUNCT
ejpam-6931	418	1	j.	j.	PROPN
ejpam-6931	418	2	pure	pure	PROPN
ejpam-6931	418	3	appl	appl	PROPN
ejpam-6931	418	4	.	.	PROPN
ejpam-6931	418	5	math	math	PROPN
ejpam-6931	418	6	,	,	PUNCT
ejpam-6931	418	7	18	18	NUM
ejpam-6931	418	8	(	(	PUNCT
ejpam-6931	418	9	4	4	NUM
ejpam-6931	418	10	)	)	PUNCT
ejpam-6931	418	11	(	(	PUNCT
ejpam-6931	418	12	2025	2025	NUM
ejpam-6931	418	13	)	)	PUNCT
ejpam-6931	418	14	,	,	PUNCT
ejpam-6931	418	15	6931	6931	NUM
ejpam-6931	418	16	31	31	NUM
ejpam-6931	418	17	of	of	ADP
ejpam-6931	418	18	38	38	NUM
ejpam-6931	418	19	and	and	CCONJ
ejpam-6931	418	20	h(u	h(u	PROPN
ejpam-6931	418	21	,	,	PUNCT
ejpam-6931	418	22	iu	iu	ADP
ejpam-6931	418	23	,	,	PUNCT
ejpam-6931	418	24	e	e	NOUN
ejpam-6931	418	25	)	)	PUNCT
ejpam-6931	418	26	⪯	⪯	PROPN
ejpam-6931	418	27	h	h	PROPN
ejpam-6931	418	28	(	(	PUNCT
ejpam-6931	418	29	u	u	PROPN
ejpam-6931	418	30	,	,	PUNCT
ejpam-6931	418	31	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	418	32	,	,	PUNCT
ejpam-6931	418	33	e	e	X
ejpam-6931	418	34	2	2	NUM
ejpam-6931	418	35	)	)	PUNCT
ejpam-6931	418	36	△	△	PROPN
ejpam-6931	418	37	h	h	NOUN
ejpam-6931	418	38	(	(	PUNCT
ejpam-6931	418	39	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	418	40	,	,	PUNCT
ejpam-6931	418	41	iu	iu	ADP
ejpam-6931	418	42	,	,	PUNCT
ejpam-6931	418	43	e	e	X
ejpam-6931	418	44	2	2	NUM
ejpam-6931	418	45	)	)	PUNCT
ejpam-6931	419	1	=	=	SYM
ejpam-6931	419	2	h	h	NOUN
ejpam-6931	419	3	(	(	PUNCT
ejpam-6931	419	4	u	u	NOUN
ejpam-6931	419	5	,	,	PUNCT
ejpam-6931	419	6	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	419	7	,	,	PUNCT
ejpam-6931	419	8	e	e	X
ejpam-6931	419	9	2	2	NUM
ejpam-6931	419	10	)	)	PUNCT
ejpam-6931	419	11	△	△	PROPN
ejpam-6931	419	12	h	h	NOUN
ejpam-6931	419	13	(	(	PUNCT
ejpam-6931	419	14	j	j	PROPN
ejpam-6931	419	15	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	419	16	,	,	PUNCT
ejpam-6931	419	17	iu	iu	ADP
ejpam-6931	419	18	,	,	PUNCT
ejpam-6931	419	19	e	e	X
ejpam-6931	419	20	2	2	NUM
ejpam-6931	419	21	)	)	PUNCT
ejpam-6931	419	22	=	=	SYM
ejpam-6931	419	23	h	h	NOUN
ejpam-6931	419	24	(	(	PUNCT
ejpam-6931	419	25	u	u	NOUN
ejpam-6931	419	26	,	,	PUNCT
ejpam-6931	419	27	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	419	28	,	,	PUNCT
ejpam-6931	419	29	e	e	X
ejpam-6931	419	30	2	2	NUM
ejpam-6931	419	31	)	)	PUNCT
ejpam-6931	419	32	△	△	PROPN
ejpam-6931	419	33	h	h	NOUN
ejpam-6931	419	34	(	(	PUNCT
ejpam-6931	419	35	iu	iu	PROPN
ejpam-6931	419	36	,	,	PUNCT
ejpam-6931	419	37	j	j	PROPN
ejpam-6931	419	38	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	419	39	,	,	PUNCT
ejpam-6931	419	40	e	e	X
ejpam-6931	419	41	2	2	NUM
ejpam-6931	419	42	)	)	PUNCT
ejpam-6931	419	43	⪯	⪯	NOUN
ejpam-6931	419	44	h	h	PROPN
ejpam-6931	419	45	(	(	PUNCT
ejpam-6931	419	46	u	u	PROPN
ejpam-6931	419	47	,	,	PUNCT
ejpam-6931	419	48	ϱo2n+2	ϱo2n+2	PROPN
ejpam-6931	419	49	,	,	PUNCT
ejpam-6931	419	50	e	e	X
ejpam-6931	419	51	2	2	NUM
ejpam-6931	419	52	)	)	PUNCT
ejpam-6931	419	53	△	△	PROPN
ejpam-6931	419	54	h	h	NOUN
ejpam-6931	419	55	(	(	PUNCT
ejpam-6931	419	56	u	u	PROPN
ejpam-6931	419	57	,	,	PUNCT
ejpam-6931	419	58	ϱo2n+1	ϱo2n+1	PROPN
ejpam-6931	419	59	,	,	PUNCT
ejpam-6931	419	60	e	e	X
ejpam-6931	419	61	2	2	NUM
ejpam-6931	419	62	)	)	PUNCT
ejpam-6931	419	63	as	as	ADP
ejpam-6931	419	64	the	the	DET
ejpam-6931	419	65	value	value	NOUN
ejpam-6931	419	66	of	of	ADP
ejpam-6931	419	67	n	n	NOUN
ejpam-6931	419	68	approaches	approach	NOUN
ejpam-6931	419	69	infinity	infinity	NOUN
ejpam-6931	419	70	for	for	ADP
ejpam-6931	419	71	inequalities	inequality	NOUN
ejpam-6931	419	72	,	,	PUNCT
ejpam-6931	419	73	we	we	PRON
ejpam-6931	419	74	get	get	VERB
ejpam-6931	419	75	e(u	e(u	PROPN
ejpam-6931	419	76	,	,	PUNCT
ejpam-6931	419	77	iu	iu	ADP
ejpam-6931	419	78	,	,	PUNCT
ejpam-6931	419	79	e	e	NOUN
ejpam-6931	419	80	)	)	PUNCT
ejpam-6931	419	81	=	=	SYM
ejpam-6931	419	82	ℑ	ℑ	PROPN
ejpam-6931	419	83	,	,	PUNCT
ejpam-6931	419	84	g(u	g(u	PROPN
ejpam-6931	419	85	,	,	PUNCT
ejpam-6931	419	86	iu	iu	ADP
ejpam-6931	419	87	,	,	PUNCT
ejpam-6931	419	88	e	e	NOUN
ejpam-6931	419	89	)	)	PUNCT
ejpam-6931	419	90	=	=	SYM
ejpam-6931	419	91	∅	∅	NOUN
ejpam-6931	419	92	and	and	CCONJ
ejpam-6931	419	93	h(u	h(u	PROPN
ejpam-6931	419	94	,	,	PUNCT
ejpam-6931	419	95	iu	iu	ADP
ejpam-6931	419	96	,	,	PUNCT
ejpam-6931	419	97	e	e	NOUN
ejpam-6931	419	98	)	)	PUNCT
ejpam-6931	419	99	=	=	NOUN
ejpam-6931	419	100	∅	∅	NOUN
ejpam-6931	419	101	for	for	ADP
ejpam-6931	419	102	every	every	DET
ejpam-6931	419	103	e	e	PROPN
ejpam-6931	419	104	∈	∈	PROPN
ejpam-6931	419	105	s0	s0	PROPN
ejpam-6931	419	106	.	.	PUNCT
ejpam-6931	420	1	under	under	ADP
ejpam-6931	420	2	conditions	condition	NOUN
ejpam-6931	420	3	(	(	PUNCT
ejpam-6931	420	4	3	3	NUM
ejpam-6931	420	5	)	)	PUNCT
ejpam-6931	420	6	,	,	PUNCT
ejpam-6931	420	7	(	(	PUNCT
ejpam-6931	420	8	8)	8)	NUM
ejpam-6931	420	9	and	and	CCONJ
ejpam-6931	420	10	(	(	PUNCT
ejpam-6931	420	11	13	13	NUM
ejpam-6931	420	12	)	)	PUNCT
ejpam-6931	420	13	of	of	ADP
ejpam-6931	420	14	definition	definition	NOUN
ejpam-6931	420	15	7	7	NUM
ejpam-6931	420	16	,	,	PUNCT
ejpam-6931	420	17	it	it	PRON
ejpam-6931	420	18	indicates	indicate	VERB
ejpam-6931	420	19	that	that	SCONJ
ejpam-6931	420	20	u	u	PRON
ejpam-6931	420	21	is	be	AUX
ejpam-6931	420	22	equal	equal	ADJ
ejpam-6931	420	23	to	to	PART
ejpam-6931	420	24	iu	iu	VERB
ejpam-6931	420	25	.	.	PUNCT
ejpam-6931	421	1	by	by	ADP
ejpam-6931	421	2	applying	apply	VERB
ejpam-6931	421	3	the	the	DET
ejpam-6931	421	4	same	same	ADJ
ejpam-6931	421	5	methods	method	NOUN
ejpam-6931	421	6	as	as	ADP
ejpam-6931	421	7	previously	previously	ADV
ejpam-6931	421	8	,	,	PUNCT
ejpam-6931	421	9	one	one	PRON
ejpam-6931	421	10	can	can	AUX
ejpam-6931	421	11	establish	establish	VERB
ejpam-6931	421	12	that	that	SCONJ
ejpam-6931	421	13	e(u	e(u	PROPN
ejpam-6931	421	14	,	,	PUNCT
ejpam-6931	421	15	j	j	PROPN
ejpam-6931	421	16	u	u	PROPN
ejpam-6931	421	17	,	,	PUNCT
ejpam-6931	421	18	e	e	NOUN
ejpam-6931	421	19	)	)	PUNCT
ejpam-6931	421	20	=	=	SYM
ejpam-6931	421	21	ℑ	ℑ	PROPN
ejpam-6931	421	22	,	,	PUNCT
ejpam-6931	421	23	g(u	g(u	PROPN
ejpam-6931	421	24	,	,	PUNCT
ejpam-6931	421	25	j	j	PROPN
ejpam-6931	421	26	u	u	PROPN
ejpam-6931	421	27	,	,	PUNCT
ejpam-6931	421	28	e	e	NOUN
ejpam-6931	421	29	)	)	PUNCT
ejpam-6931	421	30	=	=	SYM
ejpam-6931	421	31	∅	∅	NOUN
ejpam-6931	421	32	and	and	CCONJ
ejpam-6931	421	33	h(u	h(u	PROPN
ejpam-6931	421	34	,	,	PUNCT
ejpam-6931	421	35	j	j	PROPN
ejpam-6931	421	36	u	u	PROPN
ejpam-6931	421	37	,	,	PUNCT
ejpam-6931	421	38	e	e	NOUN
ejpam-6931	421	39	)	)	PUNCT
ejpam-6931	421	40	=	=	NOUN
ejpam-6931	421	41	∅	∅	NOUN
ejpam-6931	421	42	for	for	ADP
ejpam-6931	421	43	every	every	DET
ejpam-6931	421	44	e	e	PROPN
ejpam-6931	421	45	∈	∈	PROPN
ejpam-6931	421	46	s0	s0	PROPN
ejpam-6931	421	47	.	.	PUNCT
ejpam-6931	422	1	by	by	ADP
ejpam-6931	422	2	the	the	DET
ejpam-6931	422	3	conditions	condition	NOUN
ejpam-6931	422	4	(	(	PUNCT
ejpam-6931	422	5	3	3	NUM
ejpam-6931	422	6	)	)	PUNCT
ejpam-6931	422	7	,	,	PUNCT
ejpam-6931	422	8	(	(	PUNCT
ejpam-6931	422	9	8)	8)	NUM
ejpam-6931	422	10	and	and	CCONJ
ejpam-6931	422	11	(	(	PUNCT
ejpam-6931	422	12	13	13	NUM
ejpam-6931	422	13	)	)	PUNCT
ejpam-6931	422	14	of	of	ADP
ejpam-6931	422	15	definition	definition	NOUN
ejpam-6931	422	16	7	7	NUM
ejpam-6931	422	17	,	,	PUNCT
ejpam-6931	422	18	imply	imply	VERB
ejpam-6931	422	19	that	that	SCONJ
ejpam-6931	422	20	u	u	NOUN
ejpam-6931	422	21	is	be	AUX
ejpam-6931	422	22	equal	equal	ADJ
ejpam-6931	422	23	to	to	ADP
ejpam-6931	422	24	j	j	PROPN
ejpam-6931	422	25	u.	u.	PROPN
ejpam-6931	422	26	consequently	consequently	ADV
ejpam-6931	422	27	,	,	PUNCT
ejpam-6931	422	28	it	it	PRON
ejpam-6931	422	29	follows	follow	VERB
ejpam-6931	422	30	that	that	SCONJ
ejpam-6931	422	31	u	u	NOUN
ejpam-6931	422	32	=	=	NOUN
ejpam-6931	422	33	iu	iu	PROPN
ejpam-6931	422	34	=	=	PROPN
ejpam-6931	422	35	j	j	PROPN
ejpam-6931	422	36	u	u	NOUN
ejpam-6931	422	37	which	which	PRON
ejpam-6931	422	38	shows	show	VERB
ejpam-6931	422	39	that	that	SCONJ
ejpam-6931	422	40	u	u	PRON
ejpam-6931	422	41	is	be	AUX
ejpam-6931	422	42	a	a	PRON
ejpam-6931	422	43	is	be	AUX
ejpam-6931	422	44	common	common	ADJ
ejpam-6931	422	45	fixed	fix	VERB
ejpam-6931	422	46	point	point	NOUN
ejpam-6931	422	47	of	of	ADP
ejpam-6931	422	48	both	both	DET
ejpam-6931	422	49	functions	function	NOUN
ejpam-6931	422	50	i	i	PRON
ejpam-6931	422	51	and	and	CCONJ
ejpam-6931	422	52	j	j	PROPN
ejpam-6931	422	53	.	.	PUNCT
ejpam-6931	423	1	in	in	ADP
ejpam-6931	423	2	order	order	NOUN
ejpam-6931	423	3	to	to	PART
ejpam-6931	423	4	prove	prove	VERB
ejpam-6931	423	5	uniqueness	uniqueness	NOUN
ejpam-6931	423	6	,	,	PUNCT
ejpam-6931	423	7	assume	assume	VERB
ejpam-6931	423	8	that	that	SCONJ
ejpam-6931	423	9	u	u	PROPN
ejpam-6931	423	10	and	and	CCONJ
ejpam-6931	423	11	v	v	NOUN
ejpam-6931	423	12	are	be	AUX
ejpam-6931	423	13	two	two	NUM
ejpam-6931	423	14	distinct	distinct	ADJ
ejpam-6931	423	15	fixed	fix	VERB
ejpam-6931	423	16	points	point	NOUN
ejpam-6931	423	17	of	of	ADP
ejpam-6931	423	18	k	k	NOUN
ejpam-6931	423	19	,	,	PUNCT
ejpam-6931	423	20	it	it	PRON
ejpam-6931	423	21	is	be	AUX
ejpam-6931	423	22	possible	possible	ADJ
ejpam-6931	423	23	to	to	PART
ejpam-6931	423	24	locate	locate	VERB
ejpam-6931	423	25	e	e	PROPN
ejpam-6931	423	26	∈	∈	PROPN
ejpam-6931	423	27	s0	s0	PROPN
ejpam-6931	423	28	satisfying	satisfy	VERB
ejpam-6931	423	29	e(u	e(u	PROPN
ejpam-6931	423	30	,	,	PUNCT
ejpam-6931	423	31	v	v	NOUN
ejpam-6931	423	32	,	,	PUNCT
ejpam-6931	423	33	e	e	NOUN
ejpam-6931	423	34	)	)	PUNCT
ejpam-6931	423	35	̸=	̸=	PROPN
ejpam-6931	423	36	ℑ,g(u	ℑ,g(u	NUM
ejpam-6931	423	37	,	,	PUNCT
ejpam-6931	423	38	v	v	NOUN
ejpam-6931	423	39	,	,	PUNCT
ejpam-6931	423	40	e	e	NOUN
ejpam-6931	423	41	)	)	PUNCT
ejpam-6931	423	42	̸=	̸=	PROPN
ejpam-6931	423	43	∅	∅	NOUN
ejpam-6931	423	44	and	and	CCONJ
ejpam-6931	423	45	h(u	h(u	PROPN
ejpam-6931	423	46	,	,	PUNCT
ejpam-6931	423	47	v	v	NOUN
ejpam-6931	423	48	,	,	PUNCT
ejpam-6931	423	49	e	e	NOUN
ejpam-6931	423	50	)	)	PUNCT
ejpam-6931	423	51	̸=	̸=	PROPN
ejpam-6931	423	52	∅	∅	NOUN
ejpam-6931	423	53	by	by	ADP
ejpam-6931	423	54	equation	equation	NOUN
ejpam-6931	423	55	(	(	PUNCT
ejpam-6931	423	56	11	11	NUM
ejpam-6931	423	57	)	)	PUNCT
ejpam-6931	423	58	,	,	PUNCT
ejpam-6931	423	59	ℑ−	ℑ−	NUM
ejpam-6931	423	60	e(u	e(u	PROPN
ejpam-6931	423	61	,	,	PUNCT
ejpam-6931	423	62	v	v	NOUN
ejpam-6931	423	63	,	,	PUNCT
ejpam-6931	423	64	e	e	NOUN
ejpam-6931	423	65	)	)	PUNCT
ejpam-6931	423	66	=	=	SYM
ejpam-6931	423	67	ℑ−	ℑ−	NUM
ejpam-6931	423	68	e(iu	e(iu	PROPN
ejpam-6931	423	69	,	,	PUNCT
ejpam-6931	423	70	j	j	PROPN
ejpam-6931	423	71	v	v	NOUN
ejpam-6931	423	72	,	,	PUNCT
ejpam-6931	423	73	e	e	NOUN
ejpam-6931	423	74	)	)	PUNCT
ejpam-6931	423	75	⪯	⪯	NOUN
ejpam-6931	423	76	k(ℑ−	k(ℑ−	PROPN
ejpam-6931	423	77	e(u	e(u	PROPN
ejpam-6931	423	78	,	,	PUNCT
ejpam-6931	423	79	v	v	NOUN
ejpam-6931	423	80	,	,	PUNCT
ejpam-6931	423	81	e	e	NOUN
ejpam-6931	423	82	)	)	PUNCT
ejpam-6931	423	83	)	)	PUNCT
ejpam-6931	423	84	≺	≺	NOUN
ejpam-6931	423	85	ℑ−	ℑ−	NUM
ejpam-6931	423	86	e(u	e(u	PROPN
ejpam-6931	423	87	,	,	PUNCT
ejpam-6931	423	88	v	v	NOUN
ejpam-6931	423	89	,	,	PUNCT
ejpam-6931	423	90	e	e	NOUN
ejpam-6931	423	91	)	)	PUNCT
ejpam-6931	423	92	g(u	g(u	PROPN
ejpam-6931	423	93	,	,	PUNCT
ejpam-6931	423	94	v	v	NOUN
ejpam-6931	423	95	,	,	PUNCT
ejpam-6931	423	96	e	e	NOUN
ejpam-6931	423	97	)	)	PUNCT
ejpam-6931	424	1	=	=	SYM
ejpam-6931	424	2	g(iu	g(iu	PROPN
ejpam-6931	424	3	,	,	PUNCT
ejpam-6931	424	4	j	j	PROPN
ejpam-6931	424	5	v	v	NOUN
ejpam-6931	424	6	,	,	PUNCT
ejpam-6931	424	7	e	e	NOUN
ejpam-6931	424	8	)	)	PUNCT
ejpam-6931	424	9	⪯	⪯	NOUN
ejpam-6931	424	10	k(g(u	k(g(u	PROPN
ejpam-6931	424	11	,	,	PUNCT
ejpam-6931	424	12	v	v	NOUN
ejpam-6931	424	13	,	,	PUNCT
ejpam-6931	424	14	e	e	NOUN
ejpam-6931	424	15	)	)	PUNCT
ejpam-6931	424	16	)	)	PUNCT
ejpam-6931	424	17	≺	≺	NOUN
ejpam-6931	424	18	g(u	g(u	PROPN
ejpam-6931	424	19	,	,	PUNCT
ejpam-6931	424	20	v	v	NOUN
ejpam-6931	424	21	,	,	PUNCT
ejpam-6931	424	22	e	e	NOUN
ejpam-6931	424	23	)	)	PUNCT
ejpam-6931	424	24	and	and	CCONJ
ejpam-6931	424	25	h(u	h(u	PROPN
ejpam-6931	424	26	,	,	PUNCT
ejpam-6931	424	27	v	v	NOUN
ejpam-6931	424	28	,	,	PUNCT
ejpam-6931	424	29	e	e	NOUN
ejpam-6931	424	30	)	)	PUNCT
ejpam-6931	424	31	=	=	SYM
ejpam-6931	425	1	h(iu	h(iu	NOUN
ejpam-6931	425	2	,	,	PUNCT
ejpam-6931	425	3	j	j	PROPN
ejpam-6931	425	4	v	v	NOUN
ejpam-6931	425	5	,	,	PUNCT
ejpam-6931	425	6	e	e	NOUN
ejpam-6931	425	7	)	)	PUNCT
ejpam-6931	425	8	⪯	⪯	PROPN
ejpam-6931	425	9	k(h(u	k(h(u	PROPN
ejpam-6931	425	10	,	,	PUNCT
ejpam-6931	425	11	v	v	NOUN
ejpam-6931	425	12	,	,	PUNCT
ejpam-6931	425	13	e	e	NOUN
ejpam-6931	425	14	)	)	PUNCT
ejpam-6931	425	15	)	)	PUNCT
ejpam-6931	425	16	≺	≺	NOUN
ejpam-6931	425	17	h(u	h(u	PROPN
ejpam-6931	425	18	,	,	PUNCT
ejpam-6931	425	19	v	v	NOUN
ejpam-6931	425	20	,	,	PUNCT
ejpam-6931	425	21	e	e	NOUN
ejpam-6931	425	22	)	)	PUNCT
ejpam-6931	425	23	which	which	PRON
ejpam-6931	425	24	contradicts	contradict	VERB
ejpam-6931	425	25	our	our	PRON
ejpam-6931	425	26	assumption	assumption	NOUN
ejpam-6931	425	27	.	.	PUNCT
ejpam-6931	426	1	thus	thus	ADV
ejpam-6931	426	2	e(u	e(u	PROPN
ejpam-6931	426	3	,	,	PUNCT
ejpam-6931	426	4	v	v	NOUN
ejpam-6931	426	5	,	,	PUNCT
ejpam-6931	426	6	e	e	NOUN
ejpam-6931	426	7	)	)	PUNCT
ejpam-6931	426	8	=	=	SYM
ejpam-6931	426	9	ℑ,g(u	ℑ,g(u	NUM
ejpam-6931	426	10	,	,	PUNCT
ejpam-6931	426	11	v	v	NOUN
ejpam-6931	426	12	,	,	PUNCT
ejpam-6931	426	13	e	e	NOUN
ejpam-6931	426	14	)	)	PUNCT
ejpam-6931	426	15	=	=	SYM
ejpam-6931	426	16	∅	∅	NOUN
ejpam-6931	426	17	and	and	CCONJ
ejpam-6931	426	18	h(u	h(u	PROPN
ejpam-6931	426	19	,	,	PUNCT
ejpam-6931	426	20	v	v	NOUN
ejpam-6931	426	21	,	,	PUNCT
ejpam-6931	426	22	e	e	NOUN
ejpam-6931	426	23	)	)	PUNCT
ejpam-6931	426	24	=	=	NOUN
ejpam-6931	426	25	∅	∅	NOUN
ejpam-6931	426	26	for	for	ADP
ejpam-6931	426	27	all	all	DET
ejpam-6931	426	28	e	e	PROPN
ejpam-6931	426	29	∈	∈	PROPN
ejpam-6931	426	30	s0	s0	PROPN
ejpam-6931	426	31	.	.	PUNCT
ejpam-6931	427	1	by	by	ADP
ejpam-6931	427	2	the	the	DET
ejpam-6931	427	3	conditions	condition	NOUN
ejpam-6931	427	4	(	(	PUNCT
ejpam-6931	427	5	3	3	NUM
ejpam-6931	427	6	)	)	PUNCT
ejpam-6931	427	7	,	,	PUNCT
ejpam-6931	427	8	(	(	PUNCT
ejpam-6931	427	9	8)	8)	NUM
ejpam-6931	427	10	and	and	CCONJ
ejpam-6931	427	11	(	(	PUNCT
ejpam-6931	427	12	13	13	NUM
ejpam-6931	427	13	)	)	PUNCT
ejpam-6931	427	14	of	of	ADP
ejpam-6931	427	15	definition	definition	NOUN
ejpam-6931	427	16	7	7	NUM
ejpam-6931	427	17	,	,	PUNCT
ejpam-6931	427	18	we	we	PRON
ejpam-6931	427	19	may	may	AUX
ejpam-6931	427	20	deduce	deduce	VERB
ejpam-6931	427	21	that	that	SCONJ
ejpam-6931	427	22	u	u	NOUN
ejpam-6931	427	23	is	be	AUX
ejpam-6931	427	24	equal	equal	ADJ
ejpam-6931	427	25	to	to	ADP
ejpam-6931	427	26	v	v	ADP
ejpam-6931	427	27	which	which	PRON
ejpam-6931	427	28	show	show	VERB
ejpam-6931	427	29	that	that	SCONJ
ejpam-6931	427	30	the	the	DET
ejpam-6931	427	31	k	k	PROPN
ejpam-6931	427	32	has	have	VERB
ejpam-6931	427	33	a	a	DET
ejpam-6931	427	34	unique	unique	ADJ
ejpam-6931	427	35	fixed	fix	VERB
ejpam-6931	427	36	point	point	NOUN
ejpam-6931	427	37	.	.	PUNCT
ejpam-6931	428	1	s.	s.	PROPN
ejpam-6931	428	2	m.	m.	PROPN
ejpam-6931	428	3	u.	u.	PROPN
ejpam-6931	428	4	ud	ud	AUX
ejpam-6931	428	5	-	-	PUNCT
ejpam-6931	428	6	din	din	VERB
ejpam-6931	428	7	et	et	PROPN
ejpam-6931	428	8	al	al	PROPN
ejpam-6931	428	9	.	.	PUNCT
ejpam-6931	428	10	/	/	SYM
ejpam-6931	428	11	eur	eur	PROPN
ejpam-6931	428	12	.	.	PUNCT
ejpam-6931	429	1	j.	j.	PROPN
ejpam-6931	429	2	pure	pure	PROPN
ejpam-6931	429	3	appl	appl	PROPN
ejpam-6931	429	4	.	.	PROPN
ejpam-6931	429	5	math	math	PROPN
ejpam-6931	429	6	,	,	PUNCT
ejpam-6931	429	7	18	18	NUM
ejpam-6931	429	8	(	(	PUNCT
ejpam-6931	429	9	4	4	NUM
ejpam-6931	429	10	)	)	PUNCT
ejpam-6931	429	11	(	(	PUNCT
ejpam-6931	429	12	2025	2025	NUM
ejpam-6931	429	13	)	)	PUNCT
ejpam-6931	429	14	,	,	PUNCT
ejpam-6931	429	15	6931	6931	NUM
ejpam-6931	429	16	32	32	NUM
ejpam-6931	429	17	of	of	ADP
ejpam-6931	429	18	38	38	NUM
ejpam-6931	429	19	corollary	corollary	ADJ
ejpam-6931	429	20	1	1	NUM
ejpam-6931	429	21	.	.	PUNCT
ejpam-6931	429	22	suppose	suppose	VERB
ejpam-6931	429	23	that	that	SCONJ
ejpam-6931	429	24	(	(	PUNCT
ejpam-6931	429	25	v	v	NOUN
ejpam-6931	429	26	,	,	PUNCT
ejpam-6931	429	27	e	e	NOUN
ejpam-6931	429	28	,	,	PUNCT
ejpam-6931	429	29	g	g	PROPN
ejpam-6931	429	30	,	,	PUNCT
ejpam-6931	429	31	h	h	NOUN
ejpam-6931	429	32	,	,	PUNCT
ejpam-6931	429	33	⋆	⋆	NOUN
ejpam-6931	429	34	,	,	PUNCT
ejpam-6931	429	35	△	△	NOUN
ejpam-6931	429	36	)	)	PUNCT
ejpam-6931	429	37	is	be	AUX
ejpam-6931	429	38	a	a	DET
ejpam-6931	429	39	complete	complete	ADJ
ejpam-6931	429	40	cvnms	cvnms	NOUN
ejpam-6931	429	41	.	.	PUNCT
ejpam-6931	430	1	a	a	DET
ejpam-6931	430	2	mapping	mapping	NOUN
ejpam-6931	430	3	i	i	PRON
ejpam-6931	430	4	:	:	PUNCT
ejpam-6931	430	5	v	v	X
ejpam-6931	430	6	→	→	SYM
ejpam-6931	430	7	v	v	NOUN
ejpam-6931	430	8	satisfying	satisfy	VERB
ejpam-6931	430	9	ℑ−	ℑ−	NUM
ejpam-6931	430	10	e(iϱo	e(iϱo	PROPN
ejpam-6931	430	11	,	,	PUNCT
ejpam-6931	430	12	iν	iν	NOUN
ejpam-6931	430	13	,	,	PUNCT
ejpam-6931	430	14	e	e	NOUN
ejpam-6931	430	15	)	)	PUNCT
ejpam-6931	430	16	⪯	⪯	NOUN
ejpam-6931	430	17	k(ℑ−	k(ℑ−	X
ejpam-6931	430	18	e(ϱo	e(ϱo	PROPN
ejpam-6931	430	19	,	,	PUNCT
ejpam-6931	430	20	ν	ν	NOUN
ejpam-6931	430	21	,	,	PUNCT
ejpam-6931	430	22	e	e	NOUN
ejpam-6931	430	23	)	)	PUNCT
ejpam-6931	430	24	)	)	PUNCT
ejpam-6931	430	25	,	,	PUNCT
ejpam-6931	430	26	g(iϱo	g(iϱo	PROPN
ejpam-6931	430	27	,	,	PUNCT
ejpam-6931	430	28	iν	iν	NOUN
ejpam-6931	430	29	,	,	PUNCT
ejpam-6931	430	30	e	e	NOUN
ejpam-6931	430	31	)	)	PUNCT
ejpam-6931	430	32	⪯	⪯	NOUN
ejpam-6931	430	33	kg(ϱo	kg(ϱo	NOUN
ejpam-6931	430	34	,	,	PUNCT
ejpam-6931	430	35	ν	ν	NOUN
ejpam-6931	430	36	,	,	PUNCT
ejpam-6931	430	37	e	e	NOUN
ejpam-6931	430	38	)	)	PUNCT
ejpam-6931	430	39	,	,	PUNCT
ejpam-6931	430	40	h(iϱo	h(iϱo	PROPN
ejpam-6931	430	41	,	,	PUNCT
ejpam-6931	430	42	iν	iν	NOUN
ejpam-6931	430	43	,	,	PUNCT
ejpam-6931	430	44	e	e	NOUN
ejpam-6931	430	45	)	)	PUNCT
ejpam-6931	430	46	⪯	⪯	NOUN
ejpam-6931	430	47	kh(ϱo	kh(ϱo	PROPN
ejpam-6931	430	48	,	,	PUNCT
ejpam-6931	430	49	ν	ν	X
ejpam-6931	430	50	,	,	PUNCT
ejpam-6931	430	51	e	e	NOUN
ejpam-6931	430	52	)	)	PUNCT
ejpam-6931	430	53	for	for	ADP
ejpam-6931	430	54	each	each	DET
ejpam-6931	430	55	ϱo	ϱo	NOUN
ejpam-6931	430	56	,	,	PUNCT
ejpam-6931	430	57	ν	ν	PROPN
ejpam-6931	430	58	∈	∈	PROPN
ejpam-6931	430	59	v	v	NOUN
ejpam-6931	430	60	and	and	CCONJ
ejpam-6931	430	61	e	e	NOUN
ejpam-6931	430	62	∈	∈	PROPN
ejpam-6931	430	63	s0	s0	PROPN
ejpam-6931	430	64	,	,	PUNCT
ejpam-6931	430	65	where	where	SCONJ
ejpam-6931	430	66	k	k	PROPN
ejpam-6931	430	67	∈	∈	PROPN
ejpam-6931	430	68	(	(	PUNCT
ejpam-6931	430	69	0	0	NUM
ejpam-6931	430	70	,	,	PUNCT
ejpam-6931	430	71	1	1	NUM
ejpam-6931	430	72	)	)	PUNCT
ejpam-6931	430	73	.	.	PUNCT
ejpam-6931	431	1	in	in	ADP
ejpam-6931	431	2	that	that	DET
ejpam-6931	431	3	case	case	NOUN
ejpam-6931	431	4	,	,	PUNCT
ejpam-6931	431	5	the	the	DET
ejpam-6931	431	6	mapping	mapping	NOUN
ejpam-6931	431	7	i	i	PRON
ejpam-6931	431	8	has	have	VERB
ejpam-6931	431	9	a	a	DET
ejpam-6931	431	10	single	single	ADJ
ejpam-6931	431	11	fixed	fix	VERB
ejpam-6931	431	12	point	point	NOUN
ejpam-6931	431	13	in	in	ADP
ejpam-6931	431	14	v.	v.	ADP
ejpam-6931	431	15	proof	proof	NOUN
ejpam-6931	431	16	.	.	PUNCT
ejpam-6931	432	1	the	the	DET
ejpam-6931	432	2	desired	desire	VERB
ejpam-6931	432	3	outcome	outcome	NOUN
ejpam-6931	432	4	may	may	AUX
ejpam-6931	432	5	be	be	AUX
ejpam-6931	432	6	obtained	obtain	VERB
ejpam-6931	432	7	by	by	ADP
ejpam-6931	432	8	replacing	replace	VERB
ejpam-6931	432	9	i	i	PRON
ejpam-6931	432	10	=	=	PUNCT
ejpam-6931	432	11	j	j	PROPN
ejpam-6931	432	12	into	into	ADP
ejpam-6931	432	13	theorem	theorem	NOUN
ejpam-6931	432	14	3	3	NUM
ejpam-6931	432	15	.	.	PUNCT
ejpam-6931	433	1	an	an	DET
ejpam-6931	433	2	example	example	NOUN
ejpam-6931	433	3	of	of	ADP
ejpam-6931	433	4	the	the	DET
ejpam-6931	433	5	idea	idea	NOUN
ejpam-6931	433	6	presented	present	VERB
ejpam-6931	433	7	in	in	ADP
ejpam-6931	433	8	corollary	corollary	ADJ
ejpam-6931	433	9	1	1	NUM
ejpam-6931	433	10	is	be	AUX
ejpam-6931	433	11	shown	show	VERB
ejpam-6931	433	12	below	below	ADP
ejpam-6931	433	13	.	.	PUNCT
ejpam-6931	434	1	example	example	NOUN
ejpam-6931	434	2	8	8	NUM
ejpam-6931	434	3	.	.	PUNCT
ejpam-6931	435	1	consider	consider	VERB
ejpam-6931	435	2	v	v	NOUN
ejpam-6931	435	3	=	=	PUNCT
ejpam-6931	436	1	[	[	X
ejpam-6931	436	2	0	0	NUM
ejpam-6931	436	3	,	,	PUNCT
ejpam-6931	436	4	1	1	NUM
ejpam-6931	436	5	]	]	PUNCT
ejpam-6931	436	6	.	.	PUNCT
ejpam-6931	437	1	define	define	VERB
ejpam-6931	437	2	two	two	NUM
ejpam-6931	437	3	binary	binary	ADJ
ejpam-6931	437	4	operations	operation	NOUN
ejpam-6931	437	5	⋆	⋆	VERB
ejpam-6931	437	6	and	and	CCONJ
ejpam-6931	437	7	△	△	PROPN
ejpam-6931	437	8	by	by	ADP
ejpam-6931	437	9	e1	e1	PROPN
ejpam-6931	437	10	⋆	⋆	PROPN
ejpam-6931	437	11	e2	e2	PROPN
ejpam-6931	437	12	=	=	SYM
ejpam-6931	437	13	(	(	PUNCT
ejpam-6931	437	14	τ1τ2	τ1τ2	X
ejpam-6931	437	15	,	,	PUNCT
ejpam-6931	437	16	ξ1ξ2	ξ1ξ2	PUNCT
ejpam-6931	437	17	)	)	PUNCT
ejpam-6931	437	18	and	and	CCONJ
ejpam-6931	437	19	e1	e1	PROPN
ejpam-6931	437	20	△	△	PROPN
ejpam-6931	437	21	e2	e2	PROPN
ejpam-6931	437	22	=	=	SYM
ejpam-6931	437	23	(	(	PUNCT
ejpam-6931	437	24	max(τ1	max(τ1	PROPN
ejpam-6931	437	25	,	,	PUNCT
ejpam-6931	437	26	τ2),max(ξ1	τ2),max(ξ1	NOUN
ejpam-6931	437	27	,	,	PUNCT
ejpam-6931	437	28	ξ2	ξ2	NOUN
ejpam-6931	437	29	)	)	PUNCT
ejpam-6931	437	30	)	)	PUNCT
ejpam-6931	437	31	for	for	ADP
ejpam-6931	437	32	any	any	DET
ejpam-6931	437	33	ei	ei	NOUN
ejpam-6931	437	34	=	=	PUNCT
ejpam-6931	437	35	(	(	PUNCT
ejpam-6931	437	36	τi	τi	ADP
ejpam-6931	437	37	,	,	PUNCT
ejpam-6931	437	38	ξi	ξi	NOUN
ejpam-6931	437	39	)	)	PUNCT
ejpam-6931	437	40	∈	∈	PROPN
ejpam-6931	437	41	t	t	NOUN
ejpam-6931	437	42	where	where	SCONJ
ejpam-6931	437	43	i=1,2	i=1,2	ADJ
ejpam-6931	437	44	.	.	PUNCT
ejpam-6931	438	1	let	let	VERB
ejpam-6931	438	2	cfss	cfss	ADV
ejpam-6931	438	3	e	e	NOUN
ejpam-6931	438	4	,	,	PUNCT
ejpam-6931	438	5	g	g	PROPN
ejpam-6931	438	6	and	and	CCONJ
ejpam-6931	438	7	h	h	NOUN
ejpam-6931	438	8	be	be	AUX
ejpam-6931	438	9	defined	define	VERB
ejpam-6931	438	10	as	as	SCONJ
ejpam-6931	438	11	follows	follow	VERB
ejpam-6931	438	12	:	:	PUNCT
ejpam-6931	439	1	e(ϱo	e(ϱo	NOUN
ejpam-6931	439	2	,	,	PUNCT
ejpam-6931	439	3	ν	ν	NOUN
ejpam-6931	439	4	,	,	PUNCT
ejpam-6931	439	5	e	e	NOUN
ejpam-6931	439	6	)	)	PUNCT
ejpam-6931	439	7	=	=	SYM
ejpam-6931	439	8	(	(	PUNCT
ejpam-6931	439	9	τξ	τξ	X
ejpam-6931	439	10	+	+	ADJ
ejpam-6931	439	11	min{ϱo	min{ϱo	NUM
ejpam-6931	439	12	,	,	PUNCT
ejpam-6931	439	13	ν	ν	NOUN
ejpam-6931	439	14	}	}	PUNCT
ejpam-6931	439	15	τξ	τξ	ADJ
ejpam-6931	439	16	+	+	ADJ
ejpam-6931	439	17	max(ϱo	max(ϱo	ADJ
ejpam-6931	439	18	,	,	PUNCT
ejpam-6931	439	19	ν	ν	NOUN
ejpam-6931	439	20	)	)	PUNCT
ejpam-6931	439	21	)	)	PUNCT
ejpam-6931	439	22	ℑ	ℑ	PROPN
ejpam-6931	439	23	,	,	PUNCT
ejpam-6931	439	24	g(ϱo	g(ϱo	PROPN
ejpam-6931	439	25	,	,	PUNCT
ejpam-6931	439	26	ν	ν	NOUN
ejpam-6931	439	27	,	,	PUNCT
ejpam-6931	439	28	e	e	NOUN
ejpam-6931	439	29	)	)	PUNCT
ejpam-6931	439	30	=	=	SYM
ejpam-6931	439	31	1−	1−	NUM
ejpam-6931	439	32	(	(	PUNCT
ejpam-6931	439	33	τξ	τξ	X
ejpam-6931	439	34	+	+	ADJ
ejpam-6931	439	35	min{ϱo	min{ϱo	NUM
ejpam-6931	439	36	,	,	PUNCT
ejpam-6931	439	37	ν	ν	NOUN
ejpam-6931	439	38	}	}	PUNCT
ejpam-6931	439	39	τξ	τξ	ADJ
ejpam-6931	439	40	+	+	ADJ
ejpam-6931	439	41	max(ϱo	max(ϱo	ADJ
ejpam-6931	439	42	,	,	PUNCT
ejpam-6931	439	43	ν	ν	NOUN
ejpam-6931	439	44	)	)	PUNCT
ejpam-6931	439	45	)	)	PUNCT
ejpam-6931	439	46	ℑ	ℑ	PROPN
ejpam-6931	439	47	,	,	PUNCT
ejpam-6931	439	48	h(ϱo	h(ϱo	ADJ
ejpam-6931	439	49	,	,	PUNCT
ejpam-6931	439	50	ν	ν	NOUN
ejpam-6931	439	51	,	,	PUNCT
ejpam-6931	439	52	e	e	NOUN
ejpam-6931	439	53	)	)	PUNCT
ejpam-6931	439	54	=	=	SYM
ejpam-6931	439	55	(	(	PUNCT
ejpam-6931	439	56	max{ϱo	max{ϱo	INTJ
ejpam-6931	439	57	,	,	PUNCT
ejpam-6931	439	58	ν	ν	NOUN
ejpam-6931	439	59	}	}	PUNCT
ejpam-6931	439	60	−min{ϱo	−min{ϱo	PROPN
ejpam-6931	439	61	,	,	PUNCT
ejpam-6931	439	62	ν	ν	NOUN
ejpam-6931	439	63	}	}	PUNCT
ejpam-6931	439	64	τξ	τξ	NOUN
ejpam-6931	439	65	+	+	PROPN
ejpam-6931	439	66	max{ϱo	max{ϱo	NOUN
ejpam-6931	439	67	,	,	PUNCT
ejpam-6931	439	68	ν	ν	NOUN
ejpam-6931	439	69	}	}	PUNCT
ejpam-6931	439	70	)	)	PUNCT
ejpam-6931	439	71	ℑ	ℑ	NOUN
ejpam-6931	439	72	for	for	ADP
ejpam-6931	439	73	all	all	DET
ejpam-6931	439	74	ϱo	ϱo	PROPN
ejpam-6931	439	75	,	,	PUNCT
ejpam-6931	439	76	ν	ν	PROPN
ejpam-6931	439	77	∈	∈	PROPN
ejpam-6931	439	78	v	v	NOUN
ejpam-6931	439	79	and	and	CCONJ
ejpam-6931	439	80	e	e	NOUN
ejpam-6931	439	81	=	=	SYM
ejpam-6931	439	82	(	(	PUNCT
ejpam-6931	439	83	τ	τ	PROPN
ejpam-6931	439	84	,	,	PUNCT
ejpam-6931	439	85	ξ	ξ	X
ejpam-6931	439	86	)	)	PUNCT
ejpam-6931	439	87	∈	∈	PROPN
ejpam-6931	439	88	s0	s0	NOUN
ejpam-6931	439	89	.	.	PUNCT
ejpam-6931	440	1	it	it	PRON
ejpam-6931	440	2	is	be	AUX
ejpam-6931	440	3	not	not	PART
ejpam-6931	440	4	difficult	difficult	ADJ
ejpam-6931	440	5	to	to	PART
ejpam-6931	440	6	show	show	VERB
ejpam-6931	440	7	that	that	SCONJ
ejpam-6931	440	8	(	(	PUNCT
ejpam-6931	440	9	v	v	NOUN
ejpam-6931	440	10	,	,	PUNCT
ejpam-6931	440	11	e	e	NOUN
ejpam-6931	440	12	,	,	PUNCT
ejpam-6931	440	13	g	g	PROPN
ejpam-6931	440	14	,	,	PUNCT
ejpam-6931	440	15	h	h	NOUN
ejpam-6931	440	16	,	,	PUNCT
ejpam-6931	440	17	⋆	⋆	NOUN
ejpam-6931	440	18	,	,	PUNCT
ejpam-6931	440	19	△	△	NOUN
ejpam-6931	440	20	)	)	PUNCT
ejpam-6931	440	21	is	be	AUX
ejpam-6931	440	22	a	a	DET
ejpam-6931	440	23	complete	complete	ADJ
ejpam-6931	440	24	cvnms	cvnms	NOUN
ejpam-6931	440	25	.	.	PUNCT
ejpam-6931	441	1	consider	consider	VERB
ejpam-6931	441	2	a	a	DET
ejpam-6931	441	3	mapping	mapping	NOUN
ejpam-6931	442	1	i	i	PRON
ejpam-6931	442	2	:	:	PUNCT
ejpam-6931	442	3	v	v	X
ejpam-6931	442	4	→	→	SYM
ejpam-6931	442	5	v	v	NUM
ejpam-6931	442	6	expressed	express	VERB
ejpam-6931	442	7	by	by	ADP
ejpam-6931	442	8	ϱo	ϱo	PRON
ejpam-6931	442	9	2	2	NUM
ejpam-6931	442	10	for	for	ADP
ejpam-6931	442	11	all	all	PRON
ejpam-6931	442	12	ϱo	ϱo	PRON
ejpam-6931	442	13	∈	∈	PROPN
ejpam-6931	442	14	v.	v.	ADV
ejpam-6931	442	15	for	for	ADP
ejpam-6931	442	16	any	any	DET
ejpam-6931	442	17	ϱo	ϱo	NOUN
ejpam-6931	442	18	,	,	PUNCT
ejpam-6931	442	19	ν	ν	PROPN
ejpam-6931	442	20	∈	∈	NOUN
ejpam-6931	442	21	v	v	ADP
ejpam-6931	442	22	satisfying	satisfy	VERB
ejpam-6931	442	23	ϱo	ϱo	PRON
ejpam-6931	442	24	≤	≤	ADJ
ejpam-6931	442	25	ν	ν	NOUN
ejpam-6931	442	26	,	,	PUNCT
ejpam-6931	442	27	it	it	PRON
ejpam-6931	442	28	is	be	AUX
ejpam-6931	442	29	clear	clear	ADJ
ejpam-6931	442	30	that	that	SCONJ
ejpam-6931	442	31	iϱo	iϱo	VERB
ejpam-6931	442	32	≤	≤	ADJ
ejpam-6931	442	33	iν	iν	NOUN
ejpam-6931	442	34	.	.	PUNCT
ejpam-6931	443	1	it	it	PRON
ejpam-6931	443	2	follows	follow	VERB
ejpam-6931	443	3	that	that	SCONJ
ejpam-6931	443	4	e(iϱo	e(iϱo	PROPN
ejpam-6931	443	5	,	,	PUNCT
ejpam-6931	443	6	iν	iν	NOUN
ejpam-6931	443	7	,	,	PUNCT
ejpam-6931	443	8	e	e	NOUN
ejpam-6931	443	9	)	)	PUNCT
ejpam-6931	443	10	=	=	SYM
ejpam-6931	443	11	(	(	PUNCT
ejpam-6931	443	12	τξ	τξ	X
ejpam-6931	444	1	+	+	ADP
ejpam-6931	444	2	min{iϱo	min{iϱo	NOUN
ejpam-6931	444	3	,	,	PUNCT
ejpam-6931	444	4	iν	iν	NOUN
ejpam-6931	444	5	}	}	PUNCT
ejpam-6931	444	6	τξ	τξ	NOUN
ejpam-6931	444	7	+	+	PROPN
ejpam-6931	444	8	max(iϱo	max(iϱo	PROPN
ejpam-6931	444	9	,	,	PUNCT
ejpam-6931	444	10	iν	iν	NOUN
ejpam-6931	444	11	)	)	PUNCT
ejpam-6931	444	12	)	)	PUNCT
ejpam-6931	444	13	ℑ	ℑ	PROPN
ejpam-6931	444	14	,	,	PUNCT
ejpam-6931	444	15	=	=	SYM
ejpam-6931	444	16	(	(	PUNCT
ejpam-6931	444	17	τξ	τξ	ADP
ejpam-6931	444	18	+	+	CCONJ
ejpam-6931	444	19	iϱo	iϱo	VERB
ejpam-6931	444	20	τξ	τξ	X
ejpam-6931	444	21	+	+	ADJ
ejpam-6931	444	22	iν	iν	NOUN
ejpam-6931	444	23	)	)	PUNCT
ejpam-6931	444	24	ℑ	ℑ	PROPN
ejpam-6931	444	25	,	,	PUNCT
ejpam-6931	444	26	⪰	⪰	NOUN
ejpam-6931	444	27	(	(	PUNCT
ejpam-6931	444	28	τξ	τξ	ADP
ejpam-6931	445	1	+	+	CCONJ
ejpam-6931	445	2	ϱo	ϱo	PRON
ejpam-6931	445	3	τξ	τξ	ADJ
ejpam-6931	445	4	+	+	CCONJ
ejpam-6931	445	5	ν	ν	X
ejpam-6931	445	6	)	)	PUNCT
ejpam-6931	445	7	ℑ	ℑ	PROPN
ejpam-6931	445	8	,	,	PUNCT
ejpam-6931	445	9	=	=	PUNCT
ejpam-6931	445	10	e(ϱo	e(ϱo	NOUN
ejpam-6931	445	11	,	,	PUNCT
ejpam-6931	445	12	ν	ν	NOUN
ejpam-6931	445	13	,	,	PUNCT
ejpam-6931	445	14	e	e	NOUN
ejpam-6931	445	15	)	)	PUNCT
ejpam-6931	445	16	.	.	PUNCT
ejpam-6931	446	1	if	if	SCONJ
ejpam-6931	446	2	we	we	PRON
ejpam-6931	446	3	choose	choose	VERB
ejpam-6931	446	4	any	any	DET
ejpam-6931	446	5	k	k	PROPN
ejpam-6931	446	6	∈	∈	PROPN
ejpam-6931	446	7	(	(	PUNCT
ejpam-6931	446	8	12	12	NUM
ejpam-6931	446	9	,	,	PUNCT
ejpam-6931	446	10	1	1	NUM
ejpam-6931	446	11	)	)	PUNCT
ejpam-6931	446	12	,	,	PUNCT
ejpam-6931	446	13	we	we	PRON
ejpam-6931	446	14	have	have	VERB
ejpam-6931	446	15	ℑ−	ℑ−	NUM
ejpam-6931	446	16	e(iϱo	e(iϱo	PROPN
ejpam-6931	446	17	,	,	PUNCT
ejpam-6931	446	18	iν	iν	NOUN
ejpam-6931	446	19	,	,	PUNCT
ejpam-6931	446	20	e	e	NOUN
ejpam-6931	446	21	)	)	PUNCT
ejpam-6931	446	22	⪯	⪯	NOUN
ejpam-6931	446	23	k(ℑ−	k(ℑ−	X
ejpam-6931	446	24	e(ϱo	e(ϱo	PROPN
ejpam-6931	446	25	,	,	PUNCT
ejpam-6931	446	26	ν	ν	NOUN
ejpam-6931	446	27	,	,	PUNCT
ejpam-6931	446	28	e	e	NOUN
ejpam-6931	446	29	)	)	PUNCT
ejpam-6931	446	30	)	)	PUNCT
ejpam-6931	446	31	for	for	ADP
ejpam-6931	446	32	every	every	DET
ejpam-6931	446	33	ϱo	ϱo	NOUN
ejpam-6931	446	34	,	,	PUNCT
ejpam-6931	446	35	ν	ν	PROPN
ejpam-6931	446	36	∈	∈	PROPN
ejpam-6931	446	37	v	v	NOUN
ejpam-6931	446	38	and	and	CCONJ
ejpam-6931	446	39	e	e	NOUN
ejpam-6931	446	40	=	=	SYM
ejpam-6931	446	41	(	(	PUNCT
ejpam-6931	446	42	τ	τ	PROPN
ejpam-6931	446	43	,	,	PUNCT
ejpam-6931	446	44	ξ	ξ	X
ejpam-6931	446	45	)	)	PUNCT
ejpam-6931	446	46	∈	∈	PROPN
ejpam-6931	446	47	s0	s0	PROPN
ejpam-6931	446	48	.	.	PUNCT
ejpam-6931	447	1	similarly	similarly	ADV
ejpam-6931	447	2	,	,	PUNCT
ejpam-6931	447	3	we	we	PRON
ejpam-6931	447	4	can	can	AUX
ejpam-6931	447	5	deduce	deduce	VERB
ejpam-6931	447	6	that	that	DET
ejpam-6931	447	7	g(iϱo	g(iϱo	PROPN
ejpam-6931	447	8	,	,	PUNCT
ejpam-6931	447	9	iν	iν	NOUN
ejpam-6931	447	10	,	,	PUNCT
ejpam-6931	447	11	e	e	NOUN
ejpam-6931	447	12	)	)	PUNCT
ejpam-6931	447	13	⪯	⪯	NOUN
ejpam-6931	447	14	kg(ϱo	kg(ϱo	NOUN
ejpam-6931	447	15	,	,	PUNCT
ejpam-6931	447	16	ν	ν	NOUN
ejpam-6931	447	17	,	,	PUNCT
ejpam-6931	447	18	e	e	NOUN
ejpam-6931	447	19	)	)	PUNCT
ejpam-6931	447	20	and	and	CCONJ
ejpam-6931	447	21	h(iϱo	h(iϱo	PROPN
ejpam-6931	447	22	,	,	PUNCT
ejpam-6931	447	23	iν	iν	NOUN
ejpam-6931	447	24	,	,	PUNCT
ejpam-6931	447	25	e	e	NOUN
ejpam-6931	447	26	)	)	PUNCT
ejpam-6931	447	27	⪯	⪯	NOUN
ejpam-6931	447	28	kh(ϱo	kh(ϱo	PROPN
ejpam-6931	447	29	,	,	PUNCT
ejpam-6931	447	30	ν	ν	X
ejpam-6931	447	31	,	,	PUNCT
ejpam-6931	447	32	e	e	NOUN
ejpam-6931	447	33	)	)	PUNCT
ejpam-6931	447	34	for	for	ADP
ejpam-6931	447	35	all	all	DET
ejpam-6931	447	36	ϱo	ϱo	PROPN
ejpam-6931	447	37	,	,	PUNCT
ejpam-6931	447	38	ν	ν	PROPN
ejpam-6931	447	39	∈	∈	PROPN
ejpam-6931	447	40	v	v	NOUN
ejpam-6931	447	41	and	and	CCONJ
ejpam-6931	447	42	e	e	NOUN
ejpam-6931	447	43	=	=	SYM
ejpam-6931	447	44	(	(	PUNCT
ejpam-6931	447	45	τ	τ	PROPN
ejpam-6931	447	46	,	,	PUNCT
ejpam-6931	447	47	ξ	ξ	X
ejpam-6931	447	48	)	)	PUNCT
ejpam-6931	447	49	∈	∈	PROPN
ejpam-6931	447	50	s0	s0	NOUN
ejpam-6931	447	51	.	.	PUNCT
ejpam-6931	448	1	thus	thus	ADV
ejpam-6931	448	2	,	,	PUNCT
ejpam-6931	448	3	all	all	DET
ejpam-6931	448	4	the	the	DET
ejpam-6931	448	5	requirements	requirement	NOUN
ejpam-6931	448	6	stated	state	VERB
ejpam-6931	448	7	in	in	ADP
ejpam-6931	448	8	corollary	corollary	ADJ
ejpam-6931	448	9	1	1	NUM
ejpam-6931	448	10	are	be	AUX
ejpam-6931	448	11	satisfied	satisfied	ADJ
ejpam-6931	448	12	.	.	PUNCT
ejpam-6931	449	1	specifically	specifically	ADV
ejpam-6931	449	2	,	,	PUNCT
ejpam-6931	449	3	the	the	DET
ejpam-6931	449	4	number	number	NOUN
ejpam-6931	449	5	0	0	NUM
ejpam-6931	449	6	is	be	AUX
ejpam-6931	449	7	the	the	DET
ejpam-6931	449	8	only	only	ADJ
ejpam-6931	449	9	fixed	fix	VERB
ejpam-6931	449	10	point	point	NOUN
ejpam-6931	449	11	of	of	ADP
ejpam-6931	449	12	i.	i.	PROPN
ejpam-6931	449	13	s.	s.	PROPN
ejpam-6931	449	14	m.	m.	PROPN
ejpam-6931	449	15	u.	u.	PROPN
ejpam-6931	449	16	ud	ud	AUX
ejpam-6931	449	17	-	-	PUNCT
ejpam-6931	449	18	din	din	VERB
ejpam-6931	449	19	et	et	PROPN
ejpam-6931	449	20	al	al	PROPN
ejpam-6931	449	21	.	.	PUNCT
ejpam-6931	449	22	/	/	SYM
ejpam-6931	449	23	eur	eur	PROPN
ejpam-6931	449	24	.	.	PUNCT
ejpam-6931	450	1	j.	j.	PROPN
ejpam-6931	450	2	pure	pure	PROPN
ejpam-6931	450	3	appl	appl	PROPN
ejpam-6931	450	4	.	.	PROPN
ejpam-6931	450	5	math	math	PROPN
ejpam-6931	450	6	,	,	PUNCT
ejpam-6931	450	7	18	18	NUM
ejpam-6931	450	8	(	(	PUNCT
ejpam-6931	450	9	4	4	NUM
ejpam-6931	450	10	)	)	PUNCT
ejpam-6931	450	11	(	(	PUNCT
ejpam-6931	450	12	2025	2025	NUM
ejpam-6931	450	13	)	)	PUNCT
ejpam-6931	450	14	,	,	PUNCT
ejpam-6931	450	15	6931	6931	NUM
ejpam-6931	450	16	33	33	NUM
ejpam-6931	450	17	of	of	ADP
ejpam-6931	450	18	38	38	NUM
ejpam-6931	450	19	theorem	theorem	NOUN
ejpam-6931	450	20	4	4	NUM
ejpam-6931	450	21	.	.	PUNCT
ejpam-6931	451	1	let	let	VERB
ejpam-6931	451	2	(	(	PUNCT
ejpam-6931	451	3	v	v	NOUN
ejpam-6931	451	4	,	,	PUNCT
ejpam-6931	451	5	e	e	NOUN
ejpam-6931	451	6	,	,	PUNCT
ejpam-6931	451	7	g	g	PROPN
ejpam-6931	451	8	,	,	PUNCT
ejpam-6931	451	9	h	h	NOUN
ejpam-6931	451	10	,	,	PUNCT
ejpam-6931	451	11	⋆	⋆	NOUN
ejpam-6931	451	12	,	,	PUNCT
ejpam-6931	451	13	△	△	X
ejpam-6931	451	14	)	)	PUNCT
ejpam-6931	451	15	be	be	AUX
ejpam-6931	451	16	a	a	DET
ejpam-6931	451	17	cvnms	cvnms	NOUN
ejpam-6931	451	18	.	.	PUNCT
ejpam-6931	452	1	if	if	SCONJ
ejpam-6931	452	2	there	there	PRON
ejpam-6931	452	3	is	be	VERB
ejpam-6931	452	4	a	a	DET
ejpam-6931	452	5	commuting	commute	VERB
ejpam-6931	452	6	pair	pair	NOUN
ejpam-6931	452	7	of	of	ADP
ejpam-6931	452	8	selfmappings	selfmapping	NOUN
ejpam-6931	452	9	,	,	PUNCT
ejpam-6931	452	10	i	i	PRON
ejpam-6931	452	11	,	,	PUNCT
ejpam-6931	452	12	j	j	PROPN
ejpam-6931	452	13	:	:	PUNCT
ejpam-6931	452	14	v	v	X
ejpam-6931	452	15	→	→	SYM
ejpam-6931	452	16	v	v	NOUN
ejpam-6931	452	17	satisfying	satisfy	VERB
ejpam-6931	452	18	ℑ−	ℑ−	NUM
ejpam-6931	452	19	e(inϱo	e(inϱo	PROPN
ejpam-6931	452	20	,	,	PUNCT
ejpam-6931	452	21	j	j	PROPN
ejpam-6931	452	22	nν	nν	PROPN
ejpam-6931	452	23	,	,	PUNCT
ejpam-6931	452	24	e	e	NOUN
ejpam-6931	452	25	)	)	PUNCT
ejpam-6931	452	26	⪯	⪯	NOUN
ejpam-6931	452	27	k(ℑ−	k(ℑ−	X
ejpam-6931	452	28	e(ϱo	e(ϱo	PROPN
ejpam-6931	452	29	,	,	PUNCT
ejpam-6931	452	30	ν	ν	NOUN
ejpam-6931	452	31	,	,	PUNCT
ejpam-6931	452	32	e	e	NOUN
ejpam-6931	452	33	)	)	PUNCT
ejpam-6931	452	34	)	)	PUNCT
ejpam-6931	452	35	,	,	PUNCT
ejpam-6931	452	36	g(inϱo	g(inϱo	PROPN
ejpam-6931	452	37	,	,	PUNCT
ejpam-6931	452	38	j	j	PROPN
ejpam-6931	452	39	nν	nν	PROPN
ejpam-6931	452	40	,	,	PUNCT
ejpam-6931	452	41	e	e	NOUN
ejpam-6931	452	42	)	)	PUNCT
ejpam-6931	452	43	⪯	⪯	NOUN
ejpam-6931	452	44	kg(ϱo	kg(ϱo	NOUN
ejpam-6931	452	45	,	,	PUNCT
ejpam-6931	452	46	ν	ν	NOUN
ejpam-6931	452	47	,	,	PUNCT
ejpam-6931	452	48	e	e	NOUN
ejpam-6931	452	49	)	)	PUNCT
ejpam-6931	452	50	,	,	PUNCT
ejpam-6931	452	51	h(inϱo	h(inϱo	PROPN
ejpam-6931	452	52	,	,	PUNCT
ejpam-6931	452	53	j	j	PROPN
ejpam-6931	452	54	nν	nν	PROPN
ejpam-6931	452	55	,	,	PUNCT
ejpam-6931	452	56	e	e	NOUN
ejpam-6931	452	57	)	)	PUNCT
ejpam-6931	452	58	⪯	⪯	NOUN
ejpam-6931	452	59	kh(ϱo	kh(ϱo	PROPN
ejpam-6931	452	60	,	,	PUNCT
ejpam-6931	452	61	ν	ν	X
ejpam-6931	452	62	,	,	PUNCT
ejpam-6931	452	63	e	e	NOUN
ejpam-6931	452	64	)	)	PUNCT
ejpam-6931	452	65	for	for	ADP
ejpam-6931	452	66	every	every	DET
ejpam-6931	452	67	ϱo	ϱo	NOUN
ejpam-6931	452	68	,	,	PUNCT
ejpam-6931	452	69	ν	ν	PROPN
ejpam-6931	452	70	∈	∈	PROPN
ejpam-6931	452	71	v	v	NOUN
ejpam-6931	452	72	,	,	PUNCT
ejpam-6931	452	73	e	e	PROPN
ejpam-6931	452	74	∈	∈	PROPN
ejpam-6931	452	75	s0	s0	NOUN
ejpam-6931	452	76	and	and	CCONJ
ejpam-6931	452	77	n	n	CCONJ
ejpam-6931	452	78	∈	∈	PROPN
ejpam-6931	452	79	m	m	NOUN
ejpam-6931	452	80	,	,	PUNCT
ejpam-6931	452	81	where	where	SCONJ
ejpam-6931	452	82	k	k	PROPN
ejpam-6931	452	83	is	be	AUX
ejpam-6931	452	84	any	any	DET
ejpam-6931	452	85	real	real	ADJ
ejpam-6931	452	86	number	number	NOUN
ejpam-6931	452	87	from	from	ADP
ejpam-6931	452	88	(	(	PUNCT
ejpam-6931	452	89	0	0	NUM
ejpam-6931	452	90	,	,	PUNCT
ejpam-6931	452	91	1	1	NUM
ejpam-6931	452	92	)	)	PUNCT
ejpam-6931	452	93	.	.	PUNCT
ejpam-6931	453	1	then	then	ADV
ejpam-6931	453	2	there	there	PRON
ejpam-6931	453	3	is	be	VERB
ejpam-6931	453	4	a	a	DET
ejpam-6931	453	5	single	single	ADJ
ejpam-6931	453	6	shared	share	VERB
ejpam-6931	453	7	fixed	fix	VERB
ejpam-6931	453	8	point	point	NOUN
ejpam-6931	453	9	of	of	ADP
ejpam-6931	453	10	mappings	mapping	NOUN
ejpam-6931	454	1	i	i	PRON
ejpam-6931	454	2	and	and	CCONJ
ejpam-6931	454	3	j	j	PROPN
ejpam-6931	454	4	inside	inside	ADV
ejpam-6931	454	5	v.	v.	ADP
ejpam-6931	454	6	proof	proof	NOUN
ejpam-6931	454	7	.	.	PUNCT
ejpam-6931	455	1	both	both	CCONJ
ejpam-6931	455	2	in	in	ADP
ejpam-6931	455	3	and	and	CCONJ
ejpam-6931	455	4	j	j	PROPN
ejpam-6931	455	5	n	n	PRON
ejpam-6931	455	6	satisfy	satisfy	VERB
ejpam-6931	455	7	all	all	DET
ejpam-6931	455	8	the	the	DET
ejpam-6931	455	9	conditions	condition	NOUN
ejpam-6931	455	10	stated	state	VERB
ejpam-6931	455	11	in	in	ADP
ejpam-6931	455	12	theorem	theorem	NOUN
ejpam-6931	455	13	3	3	NUM
ejpam-6931	455	14	.	.	PUNCT
ejpam-6931	456	1	thus	thus	ADV
ejpam-6931	456	2	,	,	PUNCT
ejpam-6931	456	3	they	they	PRON
ejpam-6931	456	4	have	have	VERB
ejpam-6931	456	5	a	a	DET
ejpam-6931	456	6	shared	share	VERB
ejpam-6931	456	7	fixed	fix	VERB
ejpam-6931	456	8	point	point	NOUN
ejpam-6931	456	9	µ	µ	X
ejpam-6931	456	10	in	in	ADP
ejpam-6931	456	11	v	v	NOUN
ejpam-6931	456	12	,	,	PUNCT
ejpam-6931	456	13	for	for	ADP
ejpam-6931	456	14	instance	instance	NOUN
ejpam-6931	456	15	,	,	PUNCT
ejpam-6931	456	16	inµ	inµ	VERB
ejpam-6931	456	17	=	=	PUNCT
ejpam-6931	456	18	j	j	PROPN
ejpam-6931	456	19	nµ	nµ	ADV
ejpam-6931	456	20	=	=	PUNCT
ejpam-6931	456	21	µ.	µ.	PROPN
ejpam-6931	456	22	according	accord	VERB
ejpam-6931	456	23	to	to	ADP
ejpam-6931	456	24	the	the	DET
ejpam-6931	456	25	provided	provide	VERB
ejpam-6931	456	26	information	information	NOUN
ejpam-6931	456	27	iniµ	iniµ	NOUN
ejpam-6931	456	28	=	=	NOUN
ejpam-6931	456	29	iinµ	iinµ	NOUN
ejpam-6931	457	1	=	=	NOUN
ejpam-6931	457	2	iµ	iµ	ADV
ejpam-6931	457	3	,	,	PUNCT
ejpam-6931	457	4	it	it	PRON
ejpam-6931	457	5	may	may	AUX
ejpam-6931	457	6	be	be	AUX
ejpam-6931	457	7	deduced	deduce	VERB
ejpam-6931	457	8	that	that	SCONJ
ejpam-6931	457	9	iµ	iµ	NOUN
ejpam-6931	457	10	is	be	AUX
ejpam-6931	457	11	a	a	DET
ejpam-6931	457	12	point	point	NOUN
ejpam-6931	457	13	fixed	fix	VERB
ejpam-6931	457	14	by	by	ADP
ejpam-6931	457	15	in	in	ADP
ejpam-6931	457	16	.	.	PUNCT
ejpam-6931	458	1	since	since	SCONJ
ejpam-6931	458	2	both	both	CCONJ
ejpam-6931	458	3	the	the	DET
ejpam-6931	458	4	mappings	mapping	NOUN
ejpam-6931	458	5	i	i	PRON
ejpam-6931	458	6	and	and	CCONJ
ejpam-6931	458	7	j	j	PROPN
ejpam-6931	458	8	commute	commute	NOUN
ejpam-6931	458	9	,	,	PUNCT
ejpam-6931	458	10	we	we	PRON
ejpam-6931	458	11	may	may	AUX
ejpam-6931	458	12	express	express	VERB
ejpam-6931	458	13	the	the	DET
ejpam-6931	458	14	equation	equation	NOUN
ejpam-6931	458	15	as	as	SCONJ
ejpam-6931	458	16	follows	follow	VERB
ejpam-6931	458	17	:	:	PUNCT
ejpam-6931	458	18	j	j	PROPN
ejpam-6931	458	19	niµ	niµ	PROPN
ejpam-6931	458	20	=	=	NOUN
ejpam-6931	459	1	ij	ij	NOUN
ejpam-6931	459	2	nµ	nµ	ADV
ejpam-6931	459	3	=	=	X
ejpam-6931	459	4	iµ	iµ	ADP
ejpam-6931	459	5	this	this	PRON
ejpam-6931	459	6	demonstrates	demonstrate	VERB
ejpam-6931	459	7	that	that	SCONJ
ejpam-6931	459	8	iµ	iµ	NOUN
ejpam-6931	459	9	is	be	AUX
ejpam-6931	459	10	a	a	DET
ejpam-6931	459	11	point	point	NOUN
ejpam-6931	459	12	fixed	fix	VERB
ejpam-6931	459	13	by	by	ADP
ejpam-6931	459	14	j	j	PROPN
ejpam-6931	459	15	n.	n.	PROPN
ejpam-6931	459	16	thus	thus	ADV
ejpam-6931	459	17	,	,	PUNCT
ejpam-6931	459	18	iµ	iµ	PROPN
ejpam-6931	459	19	acts	act	NOUN
ejpam-6931	459	20	as	as	ADP
ejpam-6931	459	21	a	a	DET
ejpam-6931	459	22	common	common	ADJ
ejpam-6931	459	23	fixed	fix	VERB
ejpam-6931	459	24	point	point	NOUN
ejpam-6931	459	25	of	of	ADP
ejpam-6931	459	26	in	in	ADP
ejpam-6931	459	27	and	and	CCONJ
ejpam-6931	459	28	j	j	PROPN
ejpam-6931	459	29	n.	n.	PROPN
ejpam-6931	459	30	similarly	similarly	ADV
ejpam-6931	459	31	,	,	PUNCT
ejpam-6931	459	32	according	accord	VERB
ejpam-6931	459	33	to	to	ADP
ejpam-6931	459	34	the	the	DET
ejpam-6931	459	35	provided	provide	VERB
ejpam-6931	459	36	information	information	NOUN
ejpam-6931	459	37	j	j	PROPN
ejpam-6931	459	38	nj	nj	PROPN
ejpam-6931	459	39	µ	µ	PROPN
ejpam-6931	459	40	=	=	PUNCT
ejpam-6931	459	41	jj	jj	PROPN
ejpam-6931	459	42	nµ	nµ	NOUN
ejpam-6931	459	43	=	=	PROPN
ejpam-6931	459	44	j	j	PROPN
ejpam-6931	459	45	µ	µ	NUM
ejpam-6931	459	46	,	,	PUNCT
ejpam-6931	459	47	it	it	PRON
ejpam-6931	459	48	may	may	AUX
ejpam-6931	459	49	be	be	AUX
ejpam-6931	459	50	deduced	deduce	VERB
ejpam-6931	459	51	that	that	SCONJ
ejpam-6931	459	52	j	j	PROPN
ejpam-6931	459	53	µ	µ	PROPN
ejpam-6931	459	54	is	be	AUX
ejpam-6931	459	55	a	a	DET
ejpam-6931	459	56	point	point	NOUN
ejpam-6931	459	57	fixed	fix	VERB
ejpam-6931	459	58	by	by	ADP
ejpam-6931	459	59	j	j	PROPN
ejpam-6931	459	60	n.	n.	PROPN
ejpam-6931	459	61	since	since	SCONJ
ejpam-6931	459	62	both	both	CCONJ
ejpam-6931	459	63	the	the	DET
ejpam-6931	459	64	mappings	mapping	NOUN
ejpam-6931	459	65	i	i	PRON
ejpam-6931	459	66	and	and	CCONJ
ejpam-6931	459	67	j	j	PROPN
ejpam-6931	459	68	commute	commute	NOUN
ejpam-6931	459	69	,	,	PUNCT
ejpam-6931	459	70	we	we	PRON
ejpam-6931	459	71	may	may	AUX
ejpam-6931	459	72	express	express	VERB
ejpam-6931	459	73	the	the	DET
ejpam-6931	459	74	equation	equation	NOUN
ejpam-6931	459	75	as	as	SCONJ
ejpam-6931	459	76	follows	follow	VERB
ejpam-6931	459	77	:	:	PUNCT
ejpam-6931	459	78	inj	inj	VERB
ejpam-6931	459	79	µ	µ	PROPN
ejpam-6931	459	80	=	=	SYM
ejpam-6931	459	81	j	j	PROPN
ejpam-6931	459	82	inµ	inµ	NOUN
ejpam-6931	459	83	=	=	PUNCT
ejpam-6931	459	84	j	j	PROPN
ejpam-6931	459	85	µ	µ	NOUN
ejpam-6931	459	86	this	this	PRON
ejpam-6931	459	87	demonstrates	demonstrate	VERB
ejpam-6931	459	88	that	that	SCONJ
ejpam-6931	459	89	j	j	PROPN
ejpam-6931	459	90	µ	µ	PROPN
ejpam-6931	459	91	is	be	AUX
ejpam-6931	459	92	a	a	DET
ejpam-6931	459	93	point	point	NOUN
ejpam-6931	459	94	fixed	fix	VERB
ejpam-6931	459	95	by	by	ADP
ejpam-6931	459	96	in	in	ADV
ejpam-6931	459	97	.	.	PUNCT
ejpam-6931	460	1	thus	thus	ADV
ejpam-6931	460	2	,	,	PUNCT
ejpam-6931	460	3	j	j	PROPN
ejpam-6931	460	4	µ	µ	PROPN
ejpam-6931	460	5	acts	act	VERB
ejpam-6931	460	6	as	as	ADP
ejpam-6931	460	7	a	a	DET
ejpam-6931	460	8	common	common	ADJ
ejpam-6931	460	9	fixed	fix	VERB
ejpam-6931	460	10	point	point	NOUN
ejpam-6931	460	11	of	of	ADP
ejpam-6931	460	12	in	in	ADP
ejpam-6931	460	13	and	and	CCONJ
ejpam-6931	460	14	j	j	PROPN
ejpam-6931	460	15	n.	n.	PROPN
ejpam-6931	460	16	given	give	VERB
ejpam-6931	460	17	that	that	SCONJ
ejpam-6931	460	18	the	the	DET
ejpam-6931	460	19	common	common	ADJ
ejpam-6931	460	20	fixed	fix	VERB
ejpam-6931	460	21	point	point	NOUN
ejpam-6931	460	22	of	of	ADP
ejpam-6931	460	23	in	in	ADP
ejpam-6931	460	24	and	and	CCONJ
ejpam-6931	460	25	j	j	PROPN
ejpam-6931	460	26	n	n	PRON
ejpam-6931	460	27	is	be	AUX
ejpam-6931	460	28	unique	unique	ADJ
ejpam-6931	460	29	,	,	PUNCT
ejpam-6931	460	30	it	it	PRON
ejpam-6931	460	31	follows	follow	VERB
ejpam-6931	460	32	that	that	SCONJ
ejpam-6931	460	33	µ	µ	PROPN
ejpam-6931	460	34	=	=	SYM
ejpam-6931	460	35	j	j	PROPN
ejpam-6931	460	36	µ	µ	X
ejpam-6931	460	37	=	=	SYM
ejpam-6931	460	38	iµ.	iµ.	PROPN
ejpam-6931	460	39	consequently	consequently	ADV
ejpam-6931	460	40	,	,	PUNCT
ejpam-6931	460	41	µ	µ	X
ejpam-6931	460	42	as	as	ADP
ejpam-6931	460	43	the	the	DET
ejpam-6931	460	44	common	common	ADJ
ejpam-6931	460	45	fixed	fix	VERB
ejpam-6931	460	46	point	point	NOUN
ejpam-6931	460	47	for	for	ADP
ejpam-6931	460	48	both	both	DET
ejpam-6931	460	49	i	i	PROPN
ejpam-6931	460	50	and	and	CCONJ
ejpam-6931	460	51	j	j	PROPN
ejpam-6931	460	52	.	.	PUNCT
ejpam-6931	461	1	if	if	SCONJ
ejpam-6931	461	2	i	i	PRON
ejpam-6931	461	3	and	and	CCONJ
ejpam-6931	461	4	j	j	PROPN
ejpam-6931	461	5	have	have	VERB
ejpam-6931	461	6	any	any	DET
ejpam-6931	461	7	common	common	ADJ
ejpam-6931	461	8	fixed	fix	VERB
ejpam-6931	461	9	point	point	NOUN
ejpam-6931	461	10	,	,	PUNCT
ejpam-6931	461	11	that	that	DET
ejpam-6931	461	12	point	point	NOUN
ejpam-6931	461	13	will	will	AUX
ejpam-6931	461	14	also	also	ADV
ejpam-6931	461	15	be	be	AUX
ejpam-6931	461	16	a	a	DET
ejpam-6931	461	17	fixed	fix	VERB
ejpam-6931	461	18	point	point	NOUN
ejpam-6931	461	19	of	of	ADP
ejpam-6931	461	20	in	in	ADP
ejpam-6931	461	21	and	and	CCONJ
ejpam-6931	461	22	j	j	PROPN
ejpam-6931	461	23	n.	n.	NOUN
ejpam-6931	461	24	the	the	DET
ejpam-6931	461	25	common	common	ADJ
ejpam-6931	461	26	fixed	fix	VERB
ejpam-6931	461	27	point	point	NOUN
ejpam-6931	461	28	of	of	ADP
ejpam-6931	461	29	i	i	PRON
ejpam-6931	461	30	and	and	CCONJ
ejpam-6931	461	31	j	j	PROPN
ejpam-6931	461	32	is	be	AUX
ejpam-6931	461	33	uniquely	uniquely	ADV
ejpam-6931	461	34	defined	define	VERB
ejpam-6931	461	35	for	for	ADP
ejpam-6931	461	36	this	this	DET
ejpam-6931	461	37	purpose	purpose	NOUN
ejpam-6931	461	38	.	.	PUNCT
ejpam-6931	462	1	corollary	corollary	ADJ
ejpam-6931	462	2	2	2	NUM
ejpam-6931	462	3	.	.	PUNCT
ejpam-6931	463	1	let	let	VERB
ejpam-6931	463	2	(	(	PUNCT
ejpam-6931	463	3	v	v	NOUN
ejpam-6931	463	4	,	,	PUNCT
ejpam-6931	463	5	e	e	NOUN
ejpam-6931	463	6	,	,	PUNCT
ejpam-6931	463	7	g	g	PROPN
ejpam-6931	463	8	,	,	PUNCT
ejpam-6931	463	9	h	h	NOUN
ejpam-6931	463	10	,	,	PUNCT
ejpam-6931	463	11	⋆	⋆	NOUN
ejpam-6931	463	12	,	,	PUNCT
ejpam-6931	463	13	△	△	X
ejpam-6931	463	14	)	)	PUNCT
ejpam-6931	463	15	be	be	AUX
ejpam-6931	463	16	a	a	DET
ejpam-6931	463	17	cvnms	cvnms	NOUN
ejpam-6931	463	18	.	.	PUNCT
ejpam-6931	464	1	if	if	SCONJ
ejpam-6931	464	2	there	there	PRON
ejpam-6931	464	3	is	be	VERB
ejpam-6931	464	4	a	a	DET
ejpam-6931	464	5	mapping	mapping	NOUN
ejpam-6931	464	6	i	i	PRON
ejpam-6931	464	7	:	:	PUNCT
ejpam-6931	464	8	v	v	X
ejpam-6931	464	9	→	→	SYM
ejpam-6931	464	10	v	v	NOUN
ejpam-6931	464	11	satisfying	satisfy	VERB
ejpam-6931	464	12	ℑ−	ℑ−	NUM
ejpam-6931	464	13	e(inϱo	e(inϱo	PROPN
ejpam-6931	464	14	,	,	PUNCT
ejpam-6931	464	15	inν	inν	PROPN
ejpam-6931	464	16	,	,	PUNCT
ejpam-6931	464	17	e	e	NOUN
ejpam-6931	464	18	)	)	PUNCT
ejpam-6931	464	19	⪯	⪯	NOUN
ejpam-6931	464	20	k(ℑ−	k(ℑ−	X
ejpam-6931	464	21	e(ϱo	e(ϱo	PROPN
ejpam-6931	464	22	,	,	PUNCT
ejpam-6931	464	23	ν	ν	NOUN
ejpam-6931	464	24	,	,	PUNCT
ejpam-6931	464	25	e	e	NOUN
ejpam-6931	464	26	)	)	PUNCT
ejpam-6931	464	27	)	)	PUNCT
ejpam-6931	464	28	,	,	PUNCT
ejpam-6931	464	29	g(inϱo	g(inϱo	PROPN
ejpam-6931	464	30	,	,	PUNCT
ejpam-6931	464	31	inν	inν	PROPN
ejpam-6931	464	32	,	,	PUNCT
ejpam-6931	464	33	e	e	NOUN
ejpam-6931	464	34	)	)	PUNCT
ejpam-6931	464	35	⪯	⪯	NOUN
ejpam-6931	464	36	kg(ϱo	kg(ϱo	NOUN
ejpam-6931	464	37	,	,	PUNCT
ejpam-6931	464	38	ν	ν	NOUN
ejpam-6931	464	39	,	,	PUNCT
ejpam-6931	464	40	e	e	NOUN
ejpam-6931	464	41	)	)	PUNCT
ejpam-6931	464	42	,	,	PUNCT
ejpam-6931	464	43	h(inϱo	h(inϱo	PROPN
ejpam-6931	464	44	,	,	PUNCT
ejpam-6931	464	45	inν	inν	ADJ
ejpam-6931	464	46	,	,	PUNCT
ejpam-6931	464	47	e	e	NOUN
ejpam-6931	464	48	)	)	PUNCT
ejpam-6931	464	49	⪯	⪯	NOUN
ejpam-6931	464	50	kh(ϱo	kh(ϱo	PROPN
ejpam-6931	464	51	,	,	PUNCT
ejpam-6931	464	52	ν	ν	X
ejpam-6931	464	53	,	,	PUNCT
ejpam-6931	464	54	e	e	NOUN
ejpam-6931	464	55	)	)	PUNCT
ejpam-6931	464	56	for	for	ADP
ejpam-6931	464	57	each	each	DET
ejpam-6931	464	58	ϱo	ϱo	NOUN
ejpam-6931	464	59	,	,	PUNCT
ejpam-6931	464	60	ν	ν	PROPN
ejpam-6931	464	61	∈	∈	PROPN
ejpam-6931	464	62	v	v	NOUN
ejpam-6931	464	63	,	,	PUNCT
ejpam-6931	464	64	e	e	PROPN
ejpam-6931	464	65	∈	∈	PROPN
ejpam-6931	464	66	s0	s0	NOUN
ejpam-6931	464	67	and	and	CCONJ
ejpam-6931	464	68	n	n	CCONJ
ejpam-6931	464	69	∈	∈	PROPN
ejpam-6931	464	70	m	m	NOUN
ejpam-6931	464	71	,	,	PUNCT
ejpam-6931	465	1	where	where	SCONJ
ejpam-6931	465	2	0	0	X
ejpam-6931	465	3	<	<	X
ejpam-6931	465	4	k	k	X
ejpam-6931	465	5	<	<	X
ejpam-6931	465	6	1	1	NUM
ejpam-6931	465	7	.	.	PUNCT
ejpam-6931	466	1	then	then	ADV
ejpam-6931	466	2	mapping	mapping	NOUN
ejpam-6931	466	3	i	i	PRON
ejpam-6931	466	4	has	have	VERB
ejpam-6931	466	5	a	a	DET
ejpam-6931	466	6	single	single	ADJ
ejpam-6931	466	7	common	common	ADJ
ejpam-6931	466	8	fixed	fix	VERB
ejpam-6931	466	9	point	point	NOUN
ejpam-6931	466	10	within	within	ADP
ejpam-6931	466	11	v.	v.	ADP
ejpam-6931	466	12	proof	proof	NOUN
ejpam-6931	466	13	.	.	PUNCT
ejpam-6931	467	1	the	the	DET
ejpam-6931	467	2	desired	desire	VERB
ejpam-6931	467	3	outcome	outcome	NOUN
ejpam-6931	467	4	may	may	AUX
ejpam-6931	467	5	be	be	AUX
ejpam-6931	467	6	obtained	obtain	VERB
ejpam-6931	467	7	by	by	ADP
ejpam-6931	467	8	replacing	replace	VERB
ejpam-6931	467	9	i	i	PRON
ejpam-6931	467	10	=	=	SYM
ejpam-6931	467	11	j	j	PROPN
ejpam-6931	467	12	in	in	ADP
ejpam-6931	467	13	theorem	theorem	PROPN
ejpam-6931	467	14	4	4	NUM
ejpam-6931	467	15	.	.	PUNCT
ejpam-6931	468	1	s.	s.	PROPN
ejpam-6931	468	2	m.	m.	PROPN
ejpam-6931	468	3	u.	u.	PROPN
ejpam-6931	468	4	ud	ud	AUX
ejpam-6931	468	5	-	-	PUNCT
ejpam-6931	468	6	din	din	VERB
ejpam-6931	468	7	et	et	PROPN
ejpam-6931	468	8	al	al	PROPN
ejpam-6931	468	9	.	.	PUNCT
ejpam-6931	468	10	/	/	SYM
ejpam-6931	468	11	eur	eur	PROPN
ejpam-6931	468	12	.	.	PUNCT
ejpam-6931	469	1	j.	j.	PROPN
ejpam-6931	469	2	pure	pure	PROPN
ejpam-6931	469	3	appl	appl	PROPN
ejpam-6931	469	4	.	.	PROPN
ejpam-6931	469	5	math	math	PROPN
ejpam-6931	469	6	,	,	PUNCT
ejpam-6931	469	7	18	18	NUM
ejpam-6931	469	8	(	(	PUNCT
ejpam-6931	469	9	4	4	NUM
ejpam-6931	469	10	)	)	PUNCT
ejpam-6931	469	11	(	(	PUNCT
ejpam-6931	469	12	2025	2025	NUM
ejpam-6931	469	13	)	)	PUNCT
ejpam-6931	469	14	,	,	PUNCT
ejpam-6931	469	15	6931	6931	NUM
ejpam-6931	469	16	34	34	NUM
ejpam-6931	469	17	of	of	ADP
ejpam-6931	469	18	38	38	NUM
ejpam-6931	469	19	6	6	NUM
ejpam-6931	469	20	.	.	PUNCT
ejpam-6931	470	1	application	application	NOUN
ejpam-6931	470	2	to	to	PART
ejpam-6931	470	3	fredholm	fredholm	VERB
ejpam-6931	470	4	integral	integral	ADJ
ejpam-6931	470	5	equations	equation	NOUN
ejpam-6931	470	6	of	of	ADP
ejpam-6931	470	7	the	the	DET
ejpam-6931	470	8	second	second	ADJ
ejpam-6931	470	9	kind	kind	NOUN
ejpam-6931	470	10	in	in	ADP
ejpam-6931	470	11	this	this	DET
ejpam-6931	470	12	section	section	NOUN
ejpam-6931	471	1	,	,	PUNCT
ejpam-6931	471	2	we	we	PRON
ejpam-6931	471	3	use	use	VERB
ejpam-6931	471	4	theorem	theorem	NOUN
ejpam-6931	471	5	1	1	NUM
ejpam-6931	471	6	to	to	PART
ejpam-6931	471	7	show	show	VERB
ejpam-6931	471	8	that	that	SCONJ
ejpam-6931	471	9	fredholm	fredholm	ADJ
ejpam-6931	471	10	integral	integral	ADJ
ejpam-6931	471	11	equations	equation	NOUN
ejpam-6931	471	12	have	have	VERB
ejpam-6931	471	13	a	a	DET
ejpam-6931	471	14	unique	unique	ADJ
ejpam-6931	471	15	solution	solution	NOUN
ejpam-6931	471	16	.	.	PUNCT
ejpam-6931	472	1	the	the	DET
ejpam-6931	472	2	collection	collection	NOUN
ejpam-6931	472	3	of	of	ADP
ejpam-6931	472	4	all	all	DET
ejpam-6931	472	5	continuous	continuous	ADJ
ejpam-6931	472	6	functions	function	NOUN
ejpam-6931	472	7	mapping	map	VERB
ejpam-6931	472	8	the	the	DET
ejpam-6931	472	9	interval	interval	NOUN
ejpam-6931	472	10	[	[	X
ejpam-6931	472	11	0	0	NUM
ejpam-6931	472	12	,	,	PUNCT
ejpam-6931	472	13	1	1	NUM
ejpam-6931	472	14	]	]	PUNCT
ejpam-6931	472	15	to	to	ADP
ejpam-6931	472	16	r	r	NOUN
ejpam-6931	472	17	is	be	AUX
ejpam-6931	472	18	represented	represent	VERB
ejpam-6931	472	19	by	by	ADP
ejpam-6931	472	20	the	the	DET
ejpam-6931	472	21	set	set	NOUN
ejpam-6931	472	22	c([0	c([0	NOUN
ejpam-6931	472	23	,	,	PUNCT
ejpam-6931	472	24	1],r	1],r	NUM
ejpam-6931	472	25	)	)	PUNCT
ejpam-6931	472	26	.	.	PUNCT
ejpam-6931	473	1	an	an	DET
ejpam-6931	473	2	illustration	illustration	NOUN
ejpam-6931	473	3	of	of	ADP
ejpam-6931	473	4	a	a	DET
ejpam-6931	473	5	second	second	ADJ
ejpam-6931	473	6	-	-	PUNCT
ejpam-6931	473	7	kind	kind	NOUN
ejpam-6931	473	8	nonlinear	nonlinear	ADJ
ejpam-6931	473	9	fredholm	fredholm	ADJ
ejpam-6931	473	10	integral	integral	ADJ
ejpam-6931	473	11	equation	equation	NOUN
ejpam-6931	473	12	is	be	AUX
ejpam-6931	473	13	given	give	VERB
ejpam-6931	473	14	below	below	ADP
ejpam-6931	473	15	:	:	PUNCT
ejpam-6931	473	16	φ(q	φ(q	NUM
ejpam-6931	473	17	)	)	PUNCT
ejpam-6931	473	18	=	=	SYM
ejpam-6931	473	19	q(q	q(q	PROPN
ejpam-6931	473	20	)	)	PUNCT
ejpam-6931	474	1	+	+	CCONJ
ejpam-6931	474	2	ć	ć	PROPN
ejpam-6931	474	3	∫	∫	PROPN
ejpam-6931	474	4	1	1	NUM
ejpam-6931	474	5	0	0	NUM
ejpam-6931	474	6	ẃ(q	ẃ(q	NOUN
ejpam-6931	474	7	,	,	PUNCT
ejpam-6931	474	8	r)ϖ(r	r)ϖ(r	VERB
ejpam-6931	474	9	,	,	PUNCT
ejpam-6931	474	10	φ(r))dr	φ(r))dr	NOUN
ejpam-6931	474	11	(	(	PUNCT
ejpam-6931	474	12	15	15	NUM
ejpam-6931	474	13	)	)	PUNCT
ejpam-6931	474	14	where	where	SCONJ
ejpam-6931	474	15	q	q	NOUN
ejpam-6931	474	16	denotes	denote	NOUN
ejpam-6931	474	17	is	be	AUX
ejpam-6931	474	18	a	a	DET
ejpam-6931	474	19	continuous	continuous	ADJ
ejpam-6931	474	20	real	real	ADV
ejpam-6931	474	21	-	-	PUNCT
ejpam-6931	474	22	valued	value	VERB
ejpam-6931	474	23	function	function	NOUN
ejpam-6931	474	24	on	on	ADP
ejpam-6931	474	25	[	[	X
ejpam-6931	474	26	0	0	NUM
ejpam-6931	474	27	,	,	PUNCT
ejpam-6931	474	28	1	1	NUM
ejpam-6931	474	29	]	]	PUNCT
ejpam-6931	474	30	,	,	PUNCT
ejpam-6931	474	31	ẃ(q	ẃ(q	PROPN
ejpam-6931	474	32	,	,	PUNCT
ejpam-6931	474	33	r	r	NOUN
ejpam-6931	474	34	)	)	PUNCT
ejpam-6931	474	35	denotes	denote	VERB
ejpam-6931	474	36	the	the	DET
ejpam-6931	474	37	kernel	kernel	NOUN
ejpam-6931	474	38	of	of	ADP
ejpam-6931	474	39	the	the	DET
ejpam-6931	474	40	integral	integral	ADJ
ejpam-6931	474	41	function,ϖ(r	function,ϖ(r	NOUN
ejpam-6931	474	42	,	,	PUNCT
ejpam-6931	474	43	φ(r	φ(r	ADJ
ejpam-6931	474	44	)	)	PUNCT
ejpam-6931	474	45	)	)	PUNCT
ejpam-6931	474	46	denotes	denote	VERB
ejpam-6931	474	47	nonlinear	nonlinear	ADJ
ejpam-6931	474	48	and	and	CCONJ
ejpam-6931	474	49	continuous	continuous	ADJ
ejpam-6931	474	50	function	function	NOUN
ejpam-6931	474	51	defined	define	VERB
ejpam-6931	474	52	on	on	ADP
ejpam-6931	474	53	[	[	X
ejpam-6931	474	54	0	0	NUM
ejpam-6931	474	55	,	,	PUNCT
ejpam-6931	474	56	1]×	1]×	NUM
ejpam-6931	474	57	r	r	NOUN
ejpam-6931	474	58	and	and	CCONJ
ejpam-6931	474	59	φ(q	φ(q	NUM
ejpam-6931	474	60	)	)	PUNCT
ejpam-6931	474	61	symbolizes	symbolize	VERB
ejpam-6931	474	62	the	the	DET
ejpam-6931	474	63	function	function	NOUN
ejpam-6931	474	64	we	we	PRON
ejpam-6931	474	65	want	want	VERB
ejpam-6931	474	66	to	to	PART
ejpam-6931	474	67	be	be	AUX
ejpam-6931	474	68	identified	identify	VERB
ejpam-6931	474	69	.	.	PUNCT
ejpam-6931	475	1	theorem	theorem	ADJ
ejpam-6931	475	2	5	5	NUM
ejpam-6931	475	3	.	.	PUNCT
ejpam-6931	476	1	assume	assume	VERB
ejpam-6931	476	2	that	that	SCONJ
ejpam-6931	476	3	the	the	DET
ejpam-6931	476	4	set	set	NOUN
ejpam-6931	476	5	v	v	X
ejpam-6931	476	6	=	=	SYM
ejpam-6931	476	7	c([0	c([0	NOUN
ejpam-6931	476	8	,	,	PUNCT
ejpam-6931	476	9	1	1	NUM
ejpam-6931	476	10	]	]	X
ejpam-6931	476	11	×	×	PROPN
ejpam-6931	476	12	r	r	NOUN
ejpam-6931	476	13	)	)	PUNCT
ejpam-6931	476	14	.	.	PUNCT
ejpam-6931	477	1	assume	assume	VERB
ejpam-6931	477	2	that	that	SCONJ
ejpam-6931	477	3	the	the	DET
ejpam-6931	477	4	following	follow	VERB
ejpam-6931	477	5	circumstances	circumstance	NOUN
ejpam-6931	477	6	are	be	AUX
ejpam-6931	477	7	fulfilled	fulfil	VERB
ejpam-6931	477	8	:	:	PUNCT
ejpam-6931	477	9	(	(	PUNCT
ejpam-6931	477	10	1	1	X
ejpam-6931	477	11	)	)	PUNCT
ejpam-6931	477	12	a	a	DET
ejpam-6931	477	13	member	member	NOUN
ejpam-6931	477	14	x́	x́	PROPN
ejpam-6931	477	15	∈	∈	PROPN
ejpam-6931	477	16	(	(	PUNCT
ejpam-6931	477	17	0	0	NUM
ejpam-6931	477	18	,	,	PUNCT
ejpam-6931	477	19	1	1	NUM
ejpam-6931	477	20	)	)	PUNCT
ejpam-6931	477	21	can	can	AUX
ejpam-6931	477	22	be	be	AUX
ejpam-6931	477	23	identified	identify	VERB
ejpam-6931	477	24	in	in	ADP
ejpam-6931	477	25	the	the	DET
ejpam-6931	477	26	following	following	NOUN
ejpam-6931	477	27	:	:	PUNCT
ejpam-6931	478	1	|ϖ(r	|ϖ(r	ADJ
ejpam-6931	478	2	,	,	PUNCT
ejpam-6931	478	3	φ(r))−ϖ(r	φ(r))−ϖ(r	ADV
ejpam-6931	478	4	,	,	PUNCT
ejpam-6931	478	5	σ(r))|	σ(r))|	PROPN
ejpam-6931	478	6	≤	≤	VERB
ejpam-6931	478	7	x́|φ(r)−	x́|φ(r)−	PROPN
ejpam-6931	478	8	σ(r)|	σ(r)|	PROPN
ejpam-6931	478	9	for	for	ADP
ejpam-6931	478	10	any	any	DET
ejpam-6931	478	11	φ	φ	PROPN
ejpam-6931	478	12	,	,	PUNCT
ejpam-6931	478	13	σ	σ	PROPN
ejpam-6931	478	14	∈	∈	PROPN
ejpam-6931	478	15	v	v	NOUN
ejpam-6931	478	16	and	and	CCONJ
ejpam-6931	478	17	r	r	NOUN
ejpam-6931	478	18	∈	∈	PROPN
ejpam-6931	479	1	[	[	X
ejpam-6931	479	2	0	0	NUM
ejpam-6931	479	3	,	,	PUNCT
ejpam-6931	479	4	1	1	NUM
ejpam-6931	479	5	]	]	PUNCT
ejpam-6931	479	6	;	;	PUNCT
ejpam-6931	479	7	(	(	PUNCT
ejpam-6931	479	8	2	2	X
ejpam-6931	479	9	)	)	PUNCT
ejpam-6931	479	10	∫	∫	NOUN
ejpam-6931	479	11	1	1	NUM
ejpam-6931	479	12	0	0	NUM
ejpam-6931	479	13	ẃ(q	ẃ(q	NOUN
ejpam-6931	479	14	,	,	PUNCT
ejpam-6931	479	15	r)dr	r)dr	PROPN
ejpam-6931	479	16	≤	≤	NOUN
ejpam-6931	479	17	ý	ý	ADJ
ejpam-6931	479	18	;	;	PUNCT
ejpam-6931	479	19	(	(	PUNCT
ejpam-6931	479	20	3	3	X
ejpam-6931	479	21	)	)	PUNCT
ejpam-6931	479	22	ć2ý2x́2	ć2ý2x́2	PROPN
ejpam-6931	479	23	≤	≤	NOUN
ejpam-6931	479	24	k	k	X
ejpam-6931	479	25	<	<	X
ejpam-6931	479	26	1	1	X
ejpam-6931	479	27	.	.	PUNCT
ejpam-6931	480	1	as	as	ADP
ejpam-6931	480	2	a	a	DET
ejpam-6931	480	3	result	result	NOUN
ejpam-6931	480	4	,	,	PUNCT
ejpam-6931	480	5	the	the	DET
ejpam-6931	480	6	integral	integral	ADJ
ejpam-6931	480	7	equation	equation	NOUN
ejpam-6931	480	8	(	(	PUNCT
ejpam-6931	480	9	15	15	NUM
ejpam-6931	480	10	)	)	PUNCT
ejpam-6931	480	11	possesses	possess	VERB
ejpam-6931	480	12	a	a	DET
ejpam-6931	480	13	unique	unique	ADJ
ejpam-6931	480	14	solution	solution	NOUN
ejpam-6931	480	15	inside	inside	ADP
ejpam-6931	480	16	the	the	DET
ejpam-6931	480	17	set	set	NOUN
ejpam-6931	480	18	v.	v.	ADP
ejpam-6931	480	19	proof	proof	NOUN
ejpam-6931	480	20	.	.	PUNCT
ejpam-6931	481	1	consider	consider	VERB
ejpam-6931	481	2	a	a	DET
ejpam-6931	481	3	mapping	mapping	NOUN
ejpam-6931	482	1	i	i	PRON
ejpam-6931	482	2	:	:	PUNCT
ejpam-6931	482	3	v	v	X
ejpam-6931	482	4	→	→	SYM
ejpam-6931	482	5	v	v	NOUN
ejpam-6931	482	6	defined	define	VERB
ejpam-6931	482	7	as	as	ADP
ejpam-6931	482	8	iφ(q	iφ(q	NOUN
ejpam-6931	482	9	)	)	PUNCT
ejpam-6931	482	10	=	=	SYM
ejpam-6931	482	11	q(q	q(q	PROPN
ejpam-6931	482	12	)	)	PUNCT
ejpam-6931	482	13	+	+	CCONJ
ejpam-6931	483	1	ć	ć	PROPN
ejpam-6931	483	2	∫	∫	PROPN
ejpam-6931	483	3	1	1	NUM
ejpam-6931	483	4	0	0	NUM
ejpam-6931	483	5	ẃ(q	ẃ(q	NOUN
ejpam-6931	483	6	,	,	PUNCT
ejpam-6931	483	7	r)ϖ(r	r)ϖ(r	VERB
ejpam-6931	483	8	,	,	PUNCT
ejpam-6931	483	9	φ(r))dr	φ(r))dr	NOUN
ejpam-6931	483	10	for	for	ADP
ejpam-6931	483	11	each	each	DET
ejpam-6931	483	12	φ(q	φ(q	NUM
ejpam-6931	483	13	)	)	PUNCT
ejpam-6931	483	14	∈	∈	PROPN
ejpam-6931	483	15	v	v	NOUN
ejpam-6931	483	16	and	and	CCONJ
ejpam-6931	483	17	q	q	NOUN
ejpam-6931	483	18	∈	∈	PROPN
ejpam-6931	484	1	[	[	X
ejpam-6931	484	2	0	0	NUM
ejpam-6931	484	3	,	,	PUNCT
ejpam-6931	484	4	1	1	NUM
ejpam-6931	484	5	]	]	PUNCT
ejpam-6931	484	6	.	.	PUNCT
ejpam-6931	485	1	the	the	DET
ejpam-6931	485	2	complex	complex	ADV
ejpam-6931	485	3	-	-	PUNCT
ejpam-6931	485	4	valued	value	VERB
ejpam-6931	485	5	t	t	NOUN
ejpam-6931	485	6	-	-	PUNCT
ejpam-6931	485	7	norm	norm	NOUN
ejpam-6931	485	8	is	be	AUX
ejpam-6931	485	9	defined	define	VERB
ejpam-6931	485	10	as	as	ADP
ejpam-6931	485	11	⋆x	⋆x	PROPN
ejpam-6931	485	12	,	,	PUNCT
ejpam-6931	485	13	whereas	whereas	SCONJ
ejpam-6931	485	14	the	the	DET
ejpam-6931	485	15	complex	complex	ADV
ejpam-6931	485	16	-	-	PUNCT
ejpam-6931	485	17	valued	value	VERB
ejpam-6931	485	18	t	t	PROPN
ejpam-6931	485	19	-	-	PUNCT
ejpam-6931	485	20	conorm	conorm	NOUN
ejpam-6931	485	21	is	be	AUX
ejpam-6931	485	22	defined	define	VERB
ejpam-6931	485	23	as	as	ADP
ejpam-6931	485	24	△	△	NOUN
ejpam-6931	485	25	x.	x.	NOUN
ejpam-6931	485	26	moreover	moreover	ADV
ejpam-6931	485	27	,	,	PUNCT
ejpam-6931	485	28	e(ϱo	e(ϱo	NOUN
ejpam-6931	485	29	,	,	PUNCT
ejpam-6931	485	30	ν	ν	NOUN
ejpam-6931	485	31	,	,	PUNCT
ejpam-6931	485	32	e),g(ϱo	e),g(ϱo	ADV
ejpam-6931	485	33	,	,	PUNCT
ejpam-6931	485	34	ν	ν	NOUN
ejpam-6931	485	35	,	,	PUNCT
ejpam-6931	485	36	e	e	NOUN
ejpam-6931	485	37	)	)	PUNCT
ejpam-6931	485	38	and	and	CCONJ
ejpam-6931	485	39	h(ϱo	h(ϱo	ADJ
ejpam-6931	485	40	,	,	PUNCT
ejpam-6931	485	41	ν	ν	NOUN
ejpam-6931	485	42	,	,	PUNCT
ejpam-6931	485	43	e	e	NOUN
ejpam-6931	485	44	)	)	PUNCT
ejpam-6931	485	45	defined	define	VERB
ejpam-6931	485	46	by	by	ADP
ejpam-6931	485	47	e(φ(q	e(φ(q	PROPN
ejpam-6931	485	48	)	)	PUNCT
ejpam-6931	485	49	,	,	PUNCT
ejpam-6931	485	50	σ(q	σ(q	PROPN
ejpam-6931	485	51	)	)	PUNCT
ejpam-6931	485	52	,	,	PUNCT
ejpam-6931	486	1	e	e	X
ejpam-6931	486	2	)	)	PUNCT
ejpam-6931	486	3	=	=	SYM
ejpam-6931	486	4	τ	τ	PROPN
ejpam-6931	486	5	+	+	NUM
ejpam-6931	487	1	ξ	ξ	X
ejpam-6931	487	2	τ	τ	PROPN
ejpam-6931	487	3	+	+	NUM
ejpam-6931	487	4	ξ	ξ	X
ejpam-6931	487	5	+	+	CCONJ
ejpam-6931	487	6	|φ(q)−	|φ(q)−	VERB
ejpam-6931	487	7	σ(q)|2	σ(q)|2	PROPN
ejpam-6931	487	8	ℑ	ℑ	PROPN
ejpam-6931	487	9	,	,	PUNCT
ejpam-6931	487	10	g(φ(q	g(φ(q	ADV
ejpam-6931	487	11	)	)	PUNCT
ejpam-6931	487	12	,	,	PUNCT
ejpam-6931	487	13	σ(q	σ(q	PROPN
ejpam-6931	487	14	)	)	PUNCT
ejpam-6931	487	15	,	,	PUNCT
ejpam-6931	487	16	e	e	X
ejpam-6931	487	17	)	)	PUNCT
ejpam-6931	487	18	=	=	SYM
ejpam-6931	487	19	|φ(q)−	|φ(q)−	VERB
ejpam-6931	487	20	σ(q)|2	σ(q)|2	PROPN
ejpam-6931	487	21	τ	τ	X
ejpam-6931	487	22	+	+	PROPN
ejpam-6931	487	23	ξ	ξ	X
ejpam-6931	487	24	+	+	CCONJ
ejpam-6931	487	25	|φ(q)−	|φ(q)−	VERB
ejpam-6931	487	26	σ(q)|2	σ(q)|2	PROPN
ejpam-6931	487	27	ℑ	ℑ	PROPN
ejpam-6931	487	28	,	,	PUNCT
ejpam-6931	487	29	h(φ(q	h(φ(q	PROPN
ejpam-6931	487	30	)	)	PUNCT
ejpam-6931	487	31	,	,	PUNCT
ejpam-6931	487	32	σ(q	σ(q	PROPN
ejpam-6931	487	33	)	)	PUNCT
ejpam-6931	487	34	,	,	PUNCT
ejpam-6931	487	35	e	e	X
ejpam-6931	487	36	)	)	PUNCT
ejpam-6931	487	37	=	=	SYM
ejpam-6931	487	38	|φ(q)−	|φ(q)−	VERB
ejpam-6931	487	39	σ(q)|2	σ(q)|2	PROPN
ejpam-6931	487	40	τ	τ	X
ejpam-6931	487	41	+	+	NUM
ejpam-6931	487	42	ξ	ξ	PROPN
ejpam-6931	487	43	ℑ	ℑ	PROPN
ejpam-6931	487	44	for	for	ADP
ejpam-6931	487	45	each	each	DET
ejpam-6931	487	46	φ	φ	PROPN
ejpam-6931	487	47	,	,	PUNCT
ejpam-6931	487	48	σ	σ	PROPN
ejpam-6931	487	49	∈	∈	PROPN
ejpam-6931	487	50	v	v	NOUN
ejpam-6931	487	51	,	,	PUNCT
ejpam-6931	487	52	e	e	X
ejpam-6931	487	53	=	=	SYM
ejpam-6931	487	54	(	(	PUNCT
ejpam-6931	487	55	τ	τ	PROPN
ejpam-6931	487	56	,	,	PUNCT
ejpam-6931	487	57	ξ	ξ	X
ejpam-6931	487	58	)	)	PUNCT
ejpam-6931	487	59	>	>	X
ejpam-6931	487	60	0	0	PUNCT
ejpam-6931	487	61	and	and	CCONJ
ejpam-6931	487	62	q	q	ADJ
ejpam-6931	487	63	∈	∈	PROPN
ejpam-6931	488	1	[	[	X
ejpam-6931	488	2	0	0	NUM
ejpam-6931	488	3	,	,	PUNCT
ejpam-6931	488	4	1	1	NUM
ejpam-6931	488	5	]	]	PUNCT
ejpam-6931	488	6	.	.	PUNCT
ejpam-6931	489	1	it	it	PRON
ejpam-6931	489	2	is	be	AUX
ejpam-6931	489	3	easily	easily	ADV
ejpam-6931	489	4	established	establish	VERB
ejpam-6931	489	5	that	that	SCONJ
ejpam-6931	489	6	(	(	PUNCT
ejpam-6931	489	7	v	v	NOUN
ejpam-6931	489	8	,	,	PUNCT
ejpam-6931	489	9	e	e	NOUN
ejpam-6931	489	10	,	,	PUNCT
ejpam-6931	489	11	g	g	PROPN
ejpam-6931	489	12	,	,	PUNCT
ejpam-6931	489	13	h	h	NOUN
ejpam-6931	489	14	,	,	PUNCT
ejpam-6931	489	15	⋆	⋆	NOUN
ejpam-6931	489	16	,	,	PUNCT
ejpam-6931	489	17	△	△	NOUN
ejpam-6931	489	18	)	)	PUNCT
ejpam-6931	489	19	is	be	AUX
ejpam-6931	489	20	a	a	DET
ejpam-6931	489	21	cvnms	cvnms	NOUN
ejpam-6931	489	22	.	.	PUNCT
ejpam-6931	490	1	s.	s.	PROPN
ejpam-6931	490	2	m.	m.	PROPN
ejpam-6931	490	3	u.	u.	PROPN
ejpam-6931	490	4	ud	ud	AUX
ejpam-6931	490	5	-	-	PUNCT
ejpam-6931	490	6	din	din	VERB
ejpam-6931	490	7	et	et	PROPN
ejpam-6931	490	8	al	al	PROPN
ejpam-6931	490	9	.	.	PUNCT
ejpam-6931	490	10	/	/	SYM
ejpam-6931	490	11	eur	eur	PROPN
ejpam-6931	490	12	.	.	PUNCT
ejpam-6931	491	1	j.	j.	PROPN
ejpam-6931	491	2	pure	pure	PROPN
ejpam-6931	491	3	appl	appl	PROPN
ejpam-6931	491	4	.	.	PROPN
ejpam-6931	491	5	math	math	PROPN
ejpam-6931	491	6	,	,	PUNCT
ejpam-6931	491	7	18	18	NUM
ejpam-6931	491	8	(	(	PUNCT
ejpam-6931	491	9	4	4	NUM
ejpam-6931	491	10	)	)	PUNCT
ejpam-6931	491	11	(	(	PUNCT
ejpam-6931	491	12	2025	2025	NUM
ejpam-6931	491	13	)	)	PUNCT
ejpam-6931	491	14	,	,	PUNCT
ejpam-6931	491	15	6931	6931	NUM
ejpam-6931	491	16	35	35	NUM
ejpam-6931	491	17	of	of	ADP
ejpam-6931	491	18	38	38	NUM
ejpam-6931	491	19	for	for	ADP
ejpam-6931	491	20	each	each	DET
ejpam-6931	491	21	φ	φ	PROPN
ejpam-6931	491	22	,	,	PUNCT
ejpam-6931	491	23	σ	σ	PROPN
ejpam-6931	491	24	∈	∈	PROPN
ejpam-6931	491	25	v	v	NOUN
ejpam-6931	491	26	and	and	CCONJ
ejpam-6931	491	27	q	q	NOUN
ejpam-6931	491	28	∈	∈	PROPN
ejpam-6931	492	1	[	[	X
ejpam-6931	492	2	0	0	NUM
ejpam-6931	492	3	,	,	PUNCT
ejpam-6931	492	4	1	1	NUM
ejpam-6931	492	5	]	]	PUNCT
ejpam-6931	492	6	,	,	PUNCT
ejpam-6931	492	7	it	it	PRON
ejpam-6931	492	8	follows	follow	VERB
ejpam-6931	492	9	that	that	PRON
ejpam-6931	492	10	|iφ(q)−	|iφ(q)−	VERB
ejpam-6931	492	11	iσ(q)|2	iσ(q)|2	NOUN
ejpam-6931	492	12	=	=	SYM
ejpam-6931	492	13	|q(q	|q(q	PROPN
ejpam-6931	492	14	)	)	PUNCT
ejpam-6931	493	1	+	+	CCONJ
ejpam-6931	494	1	ć	ć	PROPN
ejpam-6931	494	2	∫	∫	PROPN
ejpam-6931	494	3	1	1	NUM
ejpam-6931	494	4	0	0	NUM
ejpam-6931	494	5	ẃ(q	ẃ(q	NOUN
ejpam-6931	494	6	,	,	PUNCT
ejpam-6931	494	7	r)ϖ(r	r)ϖ(r	VERB
ejpam-6931	494	8	,	,	PUNCT
ejpam-6931	494	9	φ(r))dr	φ(r))dr	ADJ
ejpam-6931	494	10	−q(q)−	−q(q)−	NOUN
ejpam-6931	495	1	ć	ć	INTJ
ejpam-6931	495	2	∫	∫	PROPN
ejpam-6931	495	3	1	1	NUM
ejpam-6931	495	4	0	0	NUM
ejpam-6931	495	5	ẃ(q	ẃ(q	NOUN
ejpam-6931	495	6	,	,	PUNCT
ejpam-6931	495	7	r)ϖ(r	r)ϖ(r	VERB
ejpam-6931	495	8	,	,	PUNCT
ejpam-6931	495	9	σ(r))dr|2	σ(r))dr|2	PROPN
ejpam-6931	495	10	=	=	SYM
ejpam-6931	496	1	ć2|	ć2|	PROPN
ejpam-6931	496	2	∫	∫	PROPN
ejpam-6931	496	3	1	1	NUM
ejpam-6931	496	4	0	0	NUM
ejpam-6931	496	5	ẃ(q	ẃ(q	NOUN
ejpam-6931	496	6	,	,	PUNCT
ejpam-6931	496	7	r)ϖ(r	r)ϖ(r	VERB
ejpam-6931	496	8	,	,	PUNCT
ejpam-6931	496	9	φ(r))dr	φ(r))dr	NOUN
ejpam-6931	496	10	−	−	PROPN
ejpam-6931	496	11	∫	∫	PROPN
ejpam-6931	496	12	1	1	NUM
ejpam-6931	496	13	0	0	NUM
ejpam-6931	496	14	ẃ(q	ẃ(q	NOUN
ejpam-6931	496	15	,	,	PUNCT
ejpam-6931	496	16	r)ϖ(r	r)ϖ(r	VERB
ejpam-6931	496	17	,	,	PUNCT
ejpam-6931	496	18	σ(r))dr|2	σ(r))dr|2	PROPN
ejpam-6931	496	19	≤	≤	PROPN
ejpam-6931	496	20	ć2	ć2	PROPN
ejpam-6931	496	21	(	(	PUNCT
ejpam-6931	496	22	∫	∫	PROPN
ejpam-6931	496	23	1	1	NUM
ejpam-6931	496	24	0	0	NUM
ejpam-6931	496	25	ẃ(q	ẃ(q	NOUN
ejpam-6931	496	26	,	,	PUNCT
ejpam-6931	496	27	r)dr	r)dr	PROPN
ejpam-6931	496	28	)	)	PUNCT
ejpam-6931	496	29	2	2	NUM
ejpam-6931	496	30	|ϖ(r	|ϖ(r	ADJ
ejpam-6931	496	31	,	,	PUNCT
ejpam-6931	496	32	φ(r))−ϖ(r	φ(r))−ϖ(r	ADV
ejpam-6931	496	33	,	,	PUNCT
ejpam-6931	496	34	σ(r))|2	σ(r))|2	VERB
ejpam-6931	496	35	≤	≤	NUM
ejpam-6931	496	36	ć2ý2x́2|φ(r)−	ć2ý2x́2|φ(r)−	PROPN
ejpam-6931	496	37	σ(r)|2	σ(r)|2	PROPN
ejpam-6931	496	38	≤	≤	NOUN
ejpam-6931	496	39	k|φ(r)−	k|φ(r)−	VERB
ejpam-6931	497	1	σ(r)|2	σ(r)|2	PROPN
ejpam-6931	497	2	.	.	PUNCT
ejpam-6931	498	1	now	now	ADV
ejpam-6931	498	2	,	,	PUNCT
ejpam-6931	498	3	for	for	ADP
ejpam-6931	498	4	each	each	DET
ejpam-6931	498	5	φ	φ	PROPN
ejpam-6931	498	6	,	,	PUNCT
ejpam-6931	498	7	σ	σ	PROPN
ejpam-6931	498	8	∈	∈	PROPN
ejpam-6931	498	9	v	v	NOUN
ejpam-6931	498	10	and	and	CCONJ
ejpam-6931	498	11	e	e	NOUN
ejpam-6931	498	12	∈	∈	PROPN
ejpam-6931	498	13	s0	s0	PROPN
ejpam-6931	498	14	,	,	PUNCT
ejpam-6931	498	15	it	it	PRON
ejpam-6931	498	16	leads	lead	VERB
ejpam-6931	498	17	to	to	ADP
ejpam-6931	498	18	e(iφ(q	e(iφ(q	PROPN
ejpam-6931	498	19	)	)	PUNCT
ejpam-6931	498	20	,	,	PUNCT
ejpam-6931	498	21	iσ(q	iσ(q	NUM
ejpam-6931	498	22	)	)	PUNCT
ejpam-6931	498	23	,	,	PUNCT
ejpam-6931	498	24	ke	ke	PROPN
ejpam-6931	498	25	)	)	PUNCT
ejpam-6931	499	1	=	=	SYM
ejpam-6931	499	2	k(τ	k(τ	PROPN
ejpam-6931	499	3	+	+	CCONJ
ejpam-6931	499	4	ξ	ξ	X
ejpam-6931	499	5	)	)	PUNCT
ejpam-6931	499	6	k(τ	k(τ	PROPN
ejpam-6931	499	7	+	+	CCONJ
ejpam-6931	499	8	ξ	ξ	X
ejpam-6931	499	9	)	)	PUNCT
ejpam-6931	499	10	+	+	CCONJ
ejpam-6931	499	11	|iφ(q)−	|iφ(q)−	VERB
ejpam-6931	499	12	iσ(q)|2	iσ(q)|2	VERB
ejpam-6931	499	13	ℑ	ℑ	NOUN
ejpam-6931	499	14	⪰	⪰	VERB
ejpam-6931	499	15	k(τ	k(τ	PROPN
ejpam-6931	499	16	+	+	CCONJ
ejpam-6931	499	17	ξ	ξ	PROPN
ejpam-6931	499	18	)	)	PUNCT
ejpam-6931	499	19	k(τ	k(τ	PROPN
ejpam-6931	499	20	+	+	CCONJ
ejpam-6931	499	21	ξ	ξ	X
ejpam-6931	499	22	)	)	PUNCT
ejpam-6931	500	1	+	+	CCONJ
ejpam-6931	500	2	k|φ(q)−	k|φ(q)−	VERB
ejpam-6931	500	3	σ(q)|2	σ(q)|2	PROPN
ejpam-6931	500	4	ℑ	ℑ	NOUN
ejpam-6931	500	5	=	=	SYM
ejpam-6931	500	6	(	(	PUNCT
ejpam-6931	500	7	τ	τ	X
ejpam-6931	500	8	+	+	NUM
ejpam-6931	500	9	ξ	ξ	X
ejpam-6931	500	10	)	)	PUNCT
ejpam-6931	500	11	(	(	PUNCT
ejpam-6931	500	12	τ	τ	X
ejpam-6931	500	13	+	+	NUM
ejpam-6931	500	14	ξ	ξ	X
ejpam-6931	500	15	)	)	PUNCT
ejpam-6931	500	16	+	+	PUNCT
ejpam-6931	500	17	|φ(q)−	|φ(q)−	VERB
ejpam-6931	500	18	σ(q)|2	σ(q)|2	PROPN
ejpam-6931	500	19	ℑ	ℑ	PROPN
ejpam-6931	500	20	=	=	SYM
ejpam-6931	500	21	e(φ(q	e(φ(q	PROPN
ejpam-6931	500	22	)	)	PUNCT
ejpam-6931	500	23	,	,	PUNCT
ejpam-6931	500	24	σ(q	σ(q	PROPN
ejpam-6931	500	25	)	)	PUNCT
ejpam-6931	500	26	,	,	PUNCT
ejpam-6931	500	27	e	e	X
ejpam-6931	500	28	)	)	PUNCT
ejpam-6931	500	29	g(iφ(q	g(iφ(q	NOUN
ejpam-6931	500	30	)	)	PUNCT
ejpam-6931	500	31	,	,	PUNCT
ejpam-6931	500	32	iσ(q	iσ(q	NUM
ejpam-6931	500	33	)	)	PUNCT
ejpam-6931	500	34	,	,	PUNCT
ejpam-6931	500	35	ke	ke	PROPN
ejpam-6931	500	36	)	)	PUNCT
ejpam-6931	500	37	=	=	PUNCT
ejpam-6931	500	38	|iφ(q)−	|iφ(q)−	VERB
ejpam-6931	500	39	iσ(q)|2	iσ(q)|2	VERB
ejpam-6931	500	40	k(τ	k(τ	PROPN
ejpam-6931	500	41	+	+	CCONJ
ejpam-6931	500	42	ξ	ξ	X
ejpam-6931	500	43	)	)	PUNCT
ejpam-6931	501	1	+	+	CCONJ
ejpam-6931	501	2	|iφ(q)−	|iφ(q)−	VERB
ejpam-6931	501	3	iσ(q)|2	iσ(q)|2	VERB
ejpam-6931	501	4	ℑ	ℑ	NOUN
ejpam-6931	501	5	=	=	SYM
ejpam-6931	501	6	(	(	PUNCT
ejpam-6931	501	7	1−	1−	NUM
ejpam-6931	501	8	k(τ	k(τ	PROPN
ejpam-6931	501	9	+	+	CCONJ
ejpam-6931	501	10	ξ	ξ	X
ejpam-6931	501	11	)	)	PUNCT
ejpam-6931	501	12	k(τ	k(τ	PROPN
ejpam-6931	501	13	+	+	CCONJ
ejpam-6931	501	14	ξ	ξ	X
ejpam-6931	501	15	)	)	PUNCT
ejpam-6931	502	1	+	+	CCONJ
ejpam-6931	502	2	|iφ(q)−	|iφ(q)−	VERB
ejpam-6931	502	3	iσ(q)|2	iσ(q)|2	NOUN
ejpam-6931	502	4	)	)	PUNCT
ejpam-6931	502	5	ℑ	ℑ	NOUN
ejpam-6931	502	6	⪯	⪯	NOUN
ejpam-6931	502	7	(	(	PUNCT
ejpam-6931	502	8	1−	1−	NUM
ejpam-6931	502	9	k(τ	k(τ	PROPN
ejpam-6931	502	10	+	+	CCONJ
ejpam-6931	502	11	ξ	ξ	X
ejpam-6931	502	12	)	)	PUNCT
ejpam-6931	502	13	k(τ	k(τ	PROPN
ejpam-6931	502	14	+	+	CCONJ
ejpam-6931	502	15	ξ	ξ	X
ejpam-6931	502	16	)	)	PUNCT
ejpam-6931	502	17	+	+	CCONJ
ejpam-6931	502	18	k|φ(q)−	k|φ(q)−	VERB
ejpam-6931	502	19	σ(q)|2	σ(q)|2	PROPN
ejpam-6931	502	20	)	)	PUNCT
ejpam-6931	502	21	ℑ	ℑ	PROPN
ejpam-6931	502	22	=	=	SYM
ejpam-6931	502	23	(	(	PUNCT
ejpam-6931	502	24	1−	1−	NUM
ejpam-6931	502	25	k(τ	k(τ	PROPN
ejpam-6931	502	26	+	+	CCONJ
ejpam-6931	502	27	ξ	ξ	X
ejpam-6931	502	28	)	)	PUNCT
ejpam-6931	502	29	k(τ	k(τ	PROPN
ejpam-6931	502	30	+	+	CCONJ
ejpam-6931	502	31	ξ	ξ	X
ejpam-6931	502	32	)	)	PUNCT
ejpam-6931	502	33	+	+	CCONJ
ejpam-6931	502	34	k|φ(q)−	k|φ(q)−	VERB
ejpam-6931	502	35	σ(q)|2	σ(q)|2	PROPN
ejpam-6931	502	36	)	)	PUNCT
ejpam-6931	502	37	ℑ	ℑ	NOUN
ejpam-6931	502	38	=	=	SYM
ejpam-6931	502	39	|φ(q)−	|φ(q)−	VERB
ejpam-6931	502	40	σ(q)|2	σ(q)|2	PROPN
ejpam-6931	502	41	τ	τ	X
ejpam-6931	502	42	+	+	PROPN
ejpam-6931	502	43	ξ	ξ	X
ejpam-6931	502	44	+	+	CCONJ
ejpam-6931	502	45	|φ(q)−	|φ(q)−	ADP
ejpam-6931	502	46	σ(q)|2	σ(q)|2	PROPN
ejpam-6931	502	47	ℑ	ℑ	PROPN
ejpam-6931	502	48	=	=	SYM
ejpam-6931	502	49	g(φ(q	g(φ(q	ADV
ejpam-6931	502	50	)	)	PUNCT
ejpam-6931	502	51	,	,	PUNCT
ejpam-6931	502	52	σ(q	σ(q	PROPN
ejpam-6931	502	53	)	)	PUNCT
ejpam-6931	502	54	,	,	PUNCT
ejpam-6931	502	55	e	e	NOUN
ejpam-6931	502	56	)	)	PUNCT
ejpam-6931	502	57	,	,	PUNCT
ejpam-6931	502	58	and	and	CCONJ
ejpam-6931	502	59	h(iφ(q	h(iφ(q	NUM
ejpam-6931	502	60	)	)	PUNCT
ejpam-6931	502	61	,	,	PUNCT
ejpam-6931	502	62	iσ(q	iσ(q	NUM
ejpam-6931	502	63	)	)	PUNCT
ejpam-6931	502	64	,	,	PUNCT
ejpam-6931	502	65	ke	ke	PROPN
ejpam-6931	502	66	)	)	PUNCT
ejpam-6931	502	67	=	=	PUNCT
ejpam-6931	502	68	|iφ(q)−	|iφ(q)−	VERB
ejpam-6931	502	69	iσ(q)|2	iσ(q)|2	VERB
ejpam-6931	502	70	k(τ	k(τ	PROPN
ejpam-6931	502	71	+	+	CCONJ
ejpam-6931	502	72	ξ	ξ	X
ejpam-6931	502	73	)	)	PUNCT
ejpam-6931	502	74	ℑ	ℑ	NOUN
ejpam-6931	502	75	⪯	⪯	NOUN
ejpam-6931	502	76	|iφ(q)−	|iφ(q)−	VERB
ejpam-6931	502	77	iσ(q)|2	iσ(q)|2	NOUN
ejpam-6931	502	78	(	(	PUNCT
ejpam-6931	502	79	τ	τ	X
ejpam-6931	502	80	+	+	NUM
ejpam-6931	502	81	ξ	ξ	X
ejpam-6931	502	82	)	)	PUNCT
ejpam-6931	502	83	ℑ	ℑ	NOUN
ejpam-6931	502	84	=	=	SYM
ejpam-6931	502	85	h(φ(q	h(φ(q	PROPN
ejpam-6931	502	86	)	)	PUNCT
ejpam-6931	502	87	,	,	PUNCT
ejpam-6931	502	88	σ(q	σ(q	PROPN
ejpam-6931	502	89	)	)	PUNCT
ejpam-6931	502	90	,	,	PUNCT
ejpam-6931	502	91	e	e	NOUN
ejpam-6931	502	92	)	)	PUNCT
ejpam-6931	502	93	.	.	PUNCT
ejpam-6931	503	1	consequently	consequently	ADV
ejpam-6931	503	2	,	,	PUNCT
ejpam-6931	503	3	every	every	DET
ejpam-6931	503	4	condition	condition	NOUN
ejpam-6931	503	5	listed	list	VERB
ejpam-6931	503	6	in	in	ADP
ejpam-6931	503	7	theorem	theorem	NOUN
ejpam-6931	503	8	1	1	NUM
ejpam-6931	503	9	is	be	AUX
ejpam-6931	503	10	satisfied	satisfied	ADJ
ejpam-6931	503	11	,	,	PUNCT
ejpam-6931	503	12	suggesting	suggest	VERB
ejpam-6931	503	13	that	that	SCONJ
ejpam-6931	503	14	there	there	PRON
ejpam-6931	503	15	is	be	VERB
ejpam-6931	503	16	only	only	ADV
ejpam-6931	503	17	one	one	NUM
ejpam-6931	503	18	solution	solution	NOUN
ejpam-6931	503	19	to	to	ADP
ejpam-6931	503	20	the	the	DET
ejpam-6931	503	21	equation	equation	NOUN
ejpam-6931	503	22	(	(	PUNCT
ejpam-6931	503	23	15	15	NUM
ejpam-6931	503	24	)	)	PUNCT
ejpam-6931	503	25	exists	exist	VERB
ejpam-6931	503	26	in	in	ADP
ejpam-6931	503	27	the	the	DET
ejpam-6931	503	28	set	set	NOUN
ejpam-6931	503	29	c([0	c([0	NOUN
ejpam-6931	503	30	,	,	PUNCT
ejpam-6931	503	31	1],r	1],r	NUM
ejpam-6931	503	32	)	)	PUNCT
ejpam-6931	503	33	.	.	PUNCT
ejpam-6931	504	1	s.	s.	PROPN
ejpam-6931	504	2	m.	m.	PROPN
ejpam-6931	504	3	u.	u.	PROPN
ejpam-6931	504	4	ud	ud	AUX
ejpam-6931	504	5	-	-	PUNCT
ejpam-6931	504	6	din	din	VERB
ejpam-6931	504	7	et	et	PROPN
ejpam-6931	504	8	al	al	PROPN
ejpam-6931	504	9	.	.	PUNCT
ejpam-6931	504	10	/	/	SYM
ejpam-6931	504	11	eur	eur	PROPN
ejpam-6931	504	12	.	.	PUNCT
ejpam-6931	505	1	j.	j.	PROPN
ejpam-6931	505	2	pure	pure	PROPN
ejpam-6931	505	3	appl	appl	PROPN
ejpam-6931	505	4	.	.	PROPN
ejpam-6931	505	5	math	math	PROPN
ejpam-6931	505	6	,	,	PUNCT
ejpam-6931	505	7	18	18	NUM
ejpam-6931	505	8	(	(	PUNCT
ejpam-6931	505	9	4	4	NUM
ejpam-6931	505	10	)	)	PUNCT
ejpam-6931	505	11	(	(	PUNCT
ejpam-6931	505	12	2025	2025	NUM
ejpam-6931	505	13	)	)	PUNCT
ejpam-6931	505	14	,	,	PUNCT
ejpam-6931	505	15	6931	6931	NUM
ejpam-6931	505	16	36	36	NUM
ejpam-6931	505	17	of	of	ADP
ejpam-6931	505	18	38	38	NUM
ejpam-6931	505	19	7	7	NUM
ejpam-6931	505	20	.	.	PUNCT
ejpam-6931	505	21	conclusion	conclusion	NOUN
ejpam-6931	505	22	in	in	ADP
ejpam-6931	505	23	this	this	DET
ejpam-6931	505	24	paper	paper	NOUN
ejpam-6931	506	1	,	,	PUNCT
ejpam-6931	506	2	we	we	PRON
ejpam-6931	506	3	introduced	introduce	VERB
ejpam-6931	506	4	the	the	DET
ejpam-6931	506	5	concept	concept	NOUN
ejpam-6931	506	6	of	of	ADP
ejpam-6931	506	7	cvnmss	cvnmss	NOUN
ejpam-6931	506	8	as	as	ADP
ejpam-6931	506	9	a	a	DET
ejpam-6931	506	10	generalization	generalization	NOUN
ejpam-6931	506	11	of	of	ADP
ejpam-6931	506	12	cvfmss	cvfmss	NOUN
ejpam-6931	506	13	,	,	PUNCT
ejpam-6931	506	14	complex	complex	NOUN
ejpam-6931	506	15	-	-	PUNCT
ejpam-6931	506	16	valued	value	VERB
ejpam-6931	506	17	ifmss	ifmss	NOUN
ejpam-6931	506	18	,	,	PUNCT
ejpam-6931	506	19	and	and	CCONJ
ejpam-6931	506	20	nmss	nmss	NOUN
ejpam-6931	506	21	.	.	PUNCT
ejpam-6931	507	1	further	far	ADV
ejpam-6931	507	2	,	,	PUNCT
ejpam-6931	507	3	we	we	PRON
ejpam-6931	507	4	proved	prove	VERB
ejpam-6931	507	5	the	the	DET
ejpam-6931	507	6	banach	banach	NOUN
ejpam-6931	507	7	contraction	contraction	NOUN
ejpam-6931	507	8	theorem	theorem	ADJ
ejpam-6931	507	9	and	and	CCONJ
ejpam-6931	507	10	common	common	ADJ
ejpam-6931	507	11	fixed	fix	VERB
ejpam-6931	507	12	point	point	NOUN
ejpam-6931	507	13	theorems	theorem	NOUN
ejpam-6931	507	14	in	in	ADP
ejpam-6931	507	15	the	the	DET
ejpam-6931	507	16	setting	setting	NOUN
ejpam-6931	507	17	of	of	ADP
ejpam-6931	507	18	cvnmss	cvnmss	NOUN
ejpam-6931	507	19	.	.	PUNCT
ejpam-6931	508	1	we	we	PRON
ejpam-6931	508	2	provide	provide	VERB
ejpam-6931	508	3	several	several	ADJ
ejpam-6931	508	4	non	non	ADJ
ejpam-6931	508	5	-	-	ADJ
ejpam-6931	508	6	trivial	trivial	ADJ
ejpam-6931	508	7	examples	example	NOUN
ejpam-6931	508	8	to	to	PART
ejpam-6931	508	9	demonstrate	demonstrate	VERB
ejpam-6931	508	10	how	how	SCONJ
ejpam-6931	508	11	the	the	DET
ejpam-6931	508	12	new	new	ADJ
ejpam-6931	508	13	strategy	strategy	NOUN
ejpam-6931	508	14	outperforms	outperform	VERB
ejpam-6931	508	15	literature	literature	NOUN
ejpam-6931	508	16	-	-	PUNCT
ejpam-6931	508	17	based	base	VERB
ejpam-6931	508	18	methods	method	NOUN
ejpam-6931	508	19	.	.	PUNCT
ejpam-6931	509	1	furthermore	furthermore	ADV
ejpam-6931	509	2	,	,	PUNCT
ejpam-6931	509	3	we	we	PRON
ejpam-6931	509	4	find	find	VERB
ejpam-6931	509	5	the	the	DET
ejpam-6931	509	6	existence	existence	NOUN
ejpam-6931	509	7	and	and	CCONJ
ejpam-6931	509	8	uniqueness	uniqueness	NOUN
ejpam-6931	509	9	of	of	ADP
ejpam-6931	509	10	the	the	DET
ejpam-6931	509	11	solution	solution	NOUN
ejpam-6931	509	12	of	of	ADP
ejpam-6931	509	13	the	the	DET
ejpam-6931	509	14	integral	integral	ADJ
ejpam-6931	509	15	equation	equation	NOUN
ejpam-6931	509	16	by	by	ADP
ejpam-6931	509	17	applying	apply	VERB
ejpam-6931	509	18	the	the	DET
ejpam-6931	509	19	main	main	ADJ
ejpam-6931	509	20	result	result	NOUN
ejpam-6931	509	21	.	.	PUNCT
ejpam-6931	510	1	our	our	PRON
ejpam-6931	510	2	findings	finding	NOUN
ejpam-6931	510	3	broaden	broaden	VERB
ejpam-6931	510	4	the	the	DET
ejpam-6931	510	5	scope	scope	NOUN
ejpam-6931	510	6	of	of	ADP
ejpam-6931	510	7	previous	previous	ADJ
ejpam-6931	510	8	research	research	NOUN
ejpam-6931	510	9	beyond	beyond	ADP
ejpam-6931	510	10	fuzzy	fuzzy	ADJ
ejpam-6931	510	11	metric	metric	ADJ
ejpam-6931	510	12	,	,	PUNCT
ejpam-6931	510	13	intuitionistic	intuitionistic	ADJ
ejpam-6931	510	14	fuzzy	fuzzy	ADJ
ejpam-6931	510	15	metric	metric	NOUN
ejpam-6931	510	16	,	,	PUNCT
ejpam-6931	510	17	and	and	CCONJ
ejpam-6931	510	18	nmss	nmss	NOUN
ejpam-6931	510	19	.	.	PUNCT
ejpam-6931	511	1	this	this	DET
ejpam-6931	511	2	work	work	NOUN
ejpam-6931	511	3	is	be	AUX
ejpam-6931	511	4	extendable	extendable	ADJ
ejpam-6931	511	5	in	in	ADP
ejpam-6931	511	6	the	the	DET
ejpam-6931	511	7	context	context	NOUN
ejpam-6931	511	8	of	of	ADP
ejpam-6931	511	9	complex	complex	NOUN
ejpam-6931	511	10	-	-	PUNCT
ejpam-6931	511	11	valued	value	VERB
ejpam-6931	511	12	neutrosophic	neutrosophic	ADJ
ejpam-6931	511	13	b	b	X
ejpam-6931	511	14	-	-	PUNCT
ejpam-6931	511	15	metric	metric	ADJ
ejpam-6931	511	16	spaces	space	NOUN
ejpam-6931	511	17	,	,	PUNCT
ejpam-6931	511	18	complex	complex	ADV
ejpam-6931	511	19	-	-	PUNCT
ejpam-6931	511	20	valued	value	VERB
ejpam-6931	511	21	neutrosophic	neutrosophic	PROPN
ejpam-6931	511	22	controlled	control	VERB
ejpam-6931	511	23	metric	metric	ADJ
ejpam-6931	511	24	spaces	space	NOUN
ejpam-6931	511	25	,	,	PUNCT
ejpam-6931	511	26	complex	complex	ADV
ejpam-6931	511	27	-	-	PUNCT
ejpam-6931	511	28	valued	value	VERB
ejpam-6931	511	29	neutrosophic	neutrosophic	ADJ
ejpam-6931	511	30	partial	partial	ADJ
ejpam-6931	511	31	metric	metric	ADJ
ejpam-6931	511	32	spaces	space	NOUN
ejpam-6931	511	33	,	,	PUNCT
ejpam-6931	511	34	and	and	CCONJ
ejpam-6931	511	35	many	many	ADJ
ejpam-6931	511	36	other	other	ADJ
ejpam-6931	511	37	structures	structure	NOUN
ejpam-6931	511	38	.	.	PUNCT
ejpam-6931	512	1	conflict	conflict	NOUN
ejpam-6931	512	2	of	of	ADP
ejpam-6931	512	3	interest	interest	NOUN
ejpam-6931	512	4	the	the	DET
ejpam-6931	512	5	authors	author	NOUN
ejpam-6931	512	6	declare	declare	VERB
ejpam-6931	512	7	that	that	SCONJ
ejpam-6931	512	8	they	they	PRON
ejpam-6931	512	9	have	have	VERB
ejpam-6931	512	10	no	no	DET
ejpam-6931	512	11	conflicts	conflict	NOUN
ejpam-6931	512	12	of	of	ADP
ejpam-6931	512	13	interest	interest	NOUN
ejpam-6931	512	14	.	.	PUNCT
ejpam-6931	513	1	authors	author	NOUN
ejpam-6931	513	2	contribution	contribution	VERB
ejpam-6931	513	3	all	all	DET
ejpam-6931	513	4	authors	author	NOUN
ejpam-6931	513	5	contributed	contribute	VERB
ejpam-6931	513	6	equally	equally	ADV
ejpam-6931	513	7	in	in	ADP
ejpam-6931	513	8	this	this	DET
ejpam-6931	513	9	manuscript	manuscript	NOUN
ejpam-6931	513	10	.	.	PUNCT
ejpam-6931	514	1	references	reference	NOUN
ejpam-6931	514	2	[	[	X
ejpam-6931	514	3	1	1	X
ejpam-6931	514	4	]	]	PUNCT
ejpam-6931	514	5	s.	s.	PROPN
ejpam-6931	514	6	banach	banach	PROPN
ejpam-6931	514	7	.	.	PUNCT
ejpam-6931	515	1	sur	sur	PROPN
ejpam-6931	515	2	les	les	X
ejpam-6931	515	3	opérations	opération	NOUN
ejpam-6931	515	4	dans	dan	NOUN
ejpam-6931	515	5	les	les	X
ejpam-6931	515	6	ensembles	ensemble	NOUN
ejpam-6931	515	7	abstraits	abstrait	NOUN
ejpam-6931	515	8	et	et	PROPN
ejpam-6931	515	9	leur	leur	X
ejpam-6931	515	10	application	application	PROPN
ejpam-6931	515	11	aux	aux	PROPN
ejpam-6931	515	12	équations	équations	PROPN
ejpam-6931	515	13	intégrales	intégrale	NOUN
ejpam-6931	515	14	.	.	PUNCT
ejpam-6931	516	1	fundamenta	fundamenta	PROPN
ejpam-6931	516	2	mathematicae	mathematicae	PROPN
ejpam-6931	516	3	,	,	PUNCT
ejpam-6931	516	4	3(1):133–181	3(1):133–181	NUM
ejpam-6931	516	5	,	,	PUNCT
ejpam-6931	516	6	1922	1922	NUM
ejpam-6931	516	7	.	.	PUNCT
ejpam-6931	517	1	[	[	X
ejpam-6931	517	2	2	2	NUM
ejpam-6931	517	3	]	]	PUNCT
ejpam-6931	517	4	l.	l.	PROPN
ejpam-6931	517	5	a.	a.	PROPN
ejpam-6931	517	6	zadeh	zadeh	PROPN
ejpam-6931	517	7	.	.	PUNCT
ejpam-6931	517	8	fuzzy	fuzzy	ADJ
ejpam-6931	517	9	sets	set	NOUN
ejpam-6931	517	10	.	.	PUNCT
ejpam-6931	518	1	information	information	NOUN
ejpam-6931	518	2	and	and	CCONJ
ejpam-6931	518	3	control	control	NOUN
ejpam-6931	518	4	,	,	PUNCT
ejpam-6931	518	5	8(3):338–353	8(3):338–353	NUM
ejpam-6931	518	6	,	,	PUNCT
ejpam-6931	518	7	1965	1965	NUM
ejpam-6931	518	8	.	.	PUNCT
ejpam-6931	519	1	[	[	X
ejpam-6931	519	2	3	3	X
ejpam-6931	519	3	]	]	PUNCT
ejpam-6931	519	4	k.	k.	PROPN
ejpam-6931	519	5	t.	t.	PROPN
ejpam-6931	519	6	atanassov	atanassov	PROPN
ejpam-6931	519	7	.	.	PUNCT
ejpam-6931	520	1	on	on	ADP
ejpam-6931	520	2	intuitionistic	intuitionistic	ADJ
ejpam-6931	520	3	fuzzy	fuzzy	ADJ
ejpam-6931	520	4	sets	set	NOUN
ejpam-6931	520	5	theory	theory	NOUN
ejpam-6931	520	6	,	,	PUNCT
ejpam-6931	520	7	volume	volume	NOUN
ejpam-6931	520	8	283	283	NUM
ejpam-6931	520	9	of	of	ADP
ejpam-6931	520	10	studies	study	NOUN
ejpam-6931	520	11	in	in	ADP
ejpam-6931	520	12	fuzziness	fuzziness	NOUN
ejpam-6931	520	13	and	and	CCONJ
ejpam-6931	520	14	soft	soft	ADJ
ejpam-6931	520	15	computing	computing	NOUN
ejpam-6931	520	16	.	.	PUNCT
ejpam-6931	521	1	springer	springer	NOUN
ejpam-6931	521	2	,	,	PUNCT
ejpam-6931	521	3	2012	2012	NUM
ejpam-6931	521	4	.	.	PUNCT
ejpam-6931	522	1	[	[	X
ejpam-6931	522	2	4	4	X
ejpam-6931	522	3	]	]	X
ejpam-6931	522	4	u.	u.	PROPN
ejpam-6931	522	5	saeed	saeed	PROPN
ejpam-6931	522	6	and	and	CCONJ
ejpam-6931	522	7	m.	m.	NOUN
ejpam-6931	522	8	umair	umair	NOUN
ejpam-6931	522	9	.	.	PUNCT
ejpam-6931	523	1	a	a	DET
ejpam-6931	523	2	modified	modify	VERB
ejpam-6931	523	3	method	method	NOUN
ejpam-6931	523	4	for	for	ADP
ejpam-6931	523	5	solving	solve	VERB
ejpam-6931	523	6	non	non	ADJ
ejpam-6931	523	7	-	-	ADJ
ejpam-6931	523	8	linear	linear	ADJ
ejpam-6931	523	9	time	time	NOUN
ejpam-6931	523	10	and	and	CCONJ
ejpam-6931	523	11	space	space	NOUN
ejpam-6931	523	12	fractional	fractional	ADJ
ejpam-6931	523	13	partial	partial	ADJ
ejpam-6931	523	14	differential	differential	NOUN
ejpam-6931	523	15	equations	equation	NOUN
ejpam-6931	523	16	.	.	PUNCT
ejpam-6931	524	1	engineering	engineering	NOUN
ejpam-6931	524	2	computations	computation	NOUN
ejpam-6931	524	3	,	,	PUNCT
ejpam-6931	524	4	36(7):2162–2178	36(7):2162–2178	NUM
ejpam-6931	524	5	,	,	PUNCT
ejpam-6931	524	6	2019	2019	NUM
ejpam-6931	524	7	.	.	PUNCT
ejpam-6931	525	1	[	[	X
ejpam-6931	525	2	5	5	NUM
ejpam-6931	525	3	]	]	PUNCT
ejpam-6931	525	4	m.	m.	NOUN
ejpam-6931	525	5	grabiec	grabiec	PROPN
ejpam-6931	525	6	.	.	PUNCT
ejpam-6931	526	1	fixed	fix	VERB
ejpam-6931	526	2	points	point	NOUN
ejpam-6931	526	3	in	in	ADP
ejpam-6931	526	4	fuzzy	fuzzy	ADJ
ejpam-6931	526	5	metric	metric	ADJ
ejpam-6931	526	6	spaces	space	NOUN
ejpam-6931	526	7	.	.	PUNCT
ejpam-6931	527	1	fuzzy	fuzzy	ADJ
ejpam-6931	527	2	sets	set	NOUN
ejpam-6931	527	3	and	and	CCONJ
ejpam-6931	527	4	systems	system	NOUN
ejpam-6931	527	5	,	,	PUNCT
ejpam-6931	527	6	27(3):385	27(3):385	NUM
ejpam-6931	527	7	–	–	PUNCT
ejpam-6931	527	8	389	389	NUM
ejpam-6931	527	9	,	,	PUNCT
ejpam-6931	527	10	1988	1988	NUM
ejpam-6931	527	11	.	.	PUNCT
ejpam-6931	528	1	[	[	X
ejpam-6931	528	2	6	6	NUM
ejpam-6931	528	3	]	]	PUNCT
ejpam-6931	528	4	a.	a.	NOUN
ejpam-6931	528	5	george	george	PROPN
ejpam-6931	528	6	and	and	CCONJ
ejpam-6931	528	7	p.	p.	PROPN
ejpam-6931	528	8	veeramani	veeramani	PROPN
ejpam-6931	528	9	.	.	PUNCT
ejpam-6931	529	1	on	on	ADP
ejpam-6931	529	2	some	some	DET
ejpam-6931	529	3	results	result	NOUN
ejpam-6931	529	4	in	in	ADP
ejpam-6931	529	5	fuzzy	fuzzy	ADJ
ejpam-6931	529	6	metric	metric	ADJ
ejpam-6931	529	7	spaces	space	NOUN
ejpam-6931	529	8	.	.	PUNCT
ejpam-6931	530	1	fuzzy	fuzzy	ADJ
ejpam-6931	530	2	sets	set	NOUN
ejpam-6931	530	3	and	and	CCONJ
ejpam-6931	530	4	systems	system	NOUN
ejpam-6931	530	5	,	,	PUNCT
ejpam-6931	530	6	64(3):395–399	64(3):395–399	PROPN
ejpam-6931	530	7	,	,	PUNCT
ejpam-6931	530	8	1994	1994	NUM
ejpam-6931	530	9	.	.	PUNCT
ejpam-6931	531	1	[	[	X
ejpam-6931	531	2	7	7	X
ejpam-6931	531	3	]	]	PUNCT
ejpam-6931	531	4	j.	j.	PROPN
ejpam-6931	531	5	h.	h.	PROPN
ejpam-6931	531	6	park	park	PROPN
ejpam-6931	531	7	.	.	PUNCT
ejpam-6931	532	1	intuitionistic	intuitionistic	ADJ
ejpam-6931	532	2	fuzzy	fuzzy	ADJ
ejpam-6931	532	3	metric	metric	ADJ
ejpam-6931	532	4	spaces	space	NOUN
ejpam-6931	532	5	.	.	PUNCT
ejpam-6931	533	1	chaos	chaos	NOUN
ejpam-6931	533	2	,	,	PUNCT
ejpam-6931	533	3	solitons	soliton	NOUN
ejpam-6931	533	4	&	&	CCONJ
ejpam-6931	533	5	fractals	fractal	NOUN
ejpam-6931	533	6	,	,	PUNCT
ejpam-6931	533	7	22(5):1039	22(5):1039	NUM
ejpam-6931	533	8	–	–	PUNCT
ejpam-6931	533	9	1046	1046	NUM
ejpam-6931	533	10	,	,	PUNCT
ejpam-6931	533	11	2004	2004	NUM
ejpam-6931	533	12	.	.	PUNCT
ejpam-6931	534	1	[	[	X
ejpam-6931	534	2	8	8	NUM
ejpam-6931	534	3	]	]	PUNCT
ejpam-6931	534	4	a.	a.	NOUN
ejpam-6931	534	5	bartwal	bartwal	PROPN
ejpam-6931	534	6	,	,	PUNCT
ejpam-6931	534	7	r.	r.	PROPN
ejpam-6931	534	8	c.	c.	PROPN
ejpam-6931	534	9	dimri	dimri	PROPN
ejpam-6931	534	10	,	,	PUNCT
ejpam-6931	534	11	and	and	CCONJ
ejpam-6931	534	12	g.	g.	PROPN
ejpam-6931	534	13	prasad	prasad	PROPN
ejpam-6931	534	14	.	.	PUNCT
ejpam-6931	535	1	some	some	DET
ejpam-6931	535	2	fixed	fix	VERB
ejpam-6931	535	3	point	point	NOUN
ejpam-6931	535	4	theorems	theorem	NOUN
ejpam-6931	535	5	in	in	ADP
ejpam-6931	535	6	fuzzy	fuzzy	ADJ
ejpam-6931	535	7	bipolar	bipolar	ADJ
ejpam-6931	535	8	metric	metric	ADJ
ejpam-6931	535	9	spaces	space	NOUN
ejpam-6931	535	10	.	.	PUNCT
ejpam-6931	536	1	journal	journal	PROPN
ejpam-6931	536	2	of	of	ADP
ejpam-6931	536	3	nonlinear	nonlinear	PROPN
ejpam-6931	536	4	sciences	sciences	PROPN
ejpam-6931	536	5	and	and	CCONJ
ejpam-6931	536	6	applications	application	NOUN
ejpam-6931	536	7	,	,	PUNCT
ejpam-6931	536	8	13:196–204	13:196–204	NUM
ejpam-6931	536	9	,	,	PUNCT
ejpam-6931	536	10	2020	2020	NUM
ejpam-6931	536	11	.	.	PUNCT
ejpam-6931	537	1	[	[	X
ejpam-6931	537	2	9	9	NUM
ejpam-6931	537	3	]	]	X
ejpam-6931	537	4	r.	r.	NOUN
ejpam-6931	537	5	chugh	chugh	NOUN
ejpam-6931	537	6	and	and	CCONJ
ejpam-6931	537	7	s.	s.	PROPN
ejpam-6931	537	8	kumar	kumar	PROPN
ejpam-6931	537	9	.	.	PUNCT
ejpam-6931	538	1	weakly	weakly	ADJ
ejpam-6931	538	2	compatible	compatible	ADJ
ejpam-6931	538	3	maps	map	NOUN
ejpam-6931	538	4	in	in	ADP
ejpam-6931	538	5	generalized	generalized	ADJ
ejpam-6931	538	6	fuzzy	fuzzy	ADJ
ejpam-6931	538	7	metric	metric	ADJ
ejpam-6931	538	8	spaces	space	NOUN
ejpam-6931	538	9	.	.	PUNCT
ejpam-6931	539	1	journal	journal	NOUN
ejpam-6931	539	2	of	of	ADP
ejpam-6931	539	3	analysis	analysis	NOUN
ejpam-6931	539	4	,	,	PUNCT
ejpam-6931	539	5	10:65–74	10:65–74	NUM
ejpam-6931	539	6	,	,	PUNCT
ejpam-6931	539	7	2002	2002	NUM
ejpam-6931	539	8	.	.	PUNCT
ejpam-6931	540	1	s.	s.	PROPN
ejpam-6931	540	2	m.	m.	PROPN
ejpam-6931	540	3	u.	u.	PROPN
ejpam-6931	540	4	ud	ud	AUX
ejpam-6931	540	5	-	-	PUNCT
ejpam-6931	540	6	din	din	VERB
ejpam-6931	540	7	et	et	PROPN
ejpam-6931	540	8	al	al	PROPN
ejpam-6931	540	9	.	.	PUNCT
ejpam-6931	540	10	/	/	SYM
ejpam-6931	540	11	eur	eur	PROPN
ejpam-6931	540	12	.	.	PUNCT
ejpam-6931	541	1	j.	j.	PROPN
ejpam-6931	541	2	pure	pure	PROPN
ejpam-6931	541	3	appl	appl	PROPN
ejpam-6931	541	4	.	.	PROPN
ejpam-6931	541	5	math	math	PROPN
ejpam-6931	541	6	,	,	PUNCT
ejpam-6931	541	7	18	18	NUM
ejpam-6931	541	8	(	(	PUNCT
ejpam-6931	541	9	4	4	NUM
ejpam-6931	541	10	)	)	PUNCT
ejpam-6931	541	11	(	(	PUNCT
ejpam-6931	541	12	2025	2025	NUM
ejpam-6931	541	13	)	)	PUNCT
ejpam-6931	541	14	,	,	PUNCT
ejpam-6931	541	15	6931	6931	NUM
ejpam-6931	541	16	37	37	NUM
ejpam-6931	541	17	of	of	ADP
ejpam-6931	541	18	38	38	NUM
ejpam-6931	541	19	[	[	SYM
ejpam-6931	541	20	10	10	NUM
ejpam-6931	541	21	]	]	X
ejpam-6931	541	22	f.	f.	PROPN
ejpam-6931	541	23	mehmood	mehmood	PROPN
ejpam-6931	541	24	,	,	PUNCT
ejpam-6931	541	25	r.	r.	PROPN
ejpam-6931	541	26	ali	ali	PROPN
ejpam-6931	541	27	,	,	PUNCT
ejpam-6931	541	28	and	and	CCONJ
ejpam-6931	541	29	n.	n.	PROPN
ejpam-6931	541	30	hussain	hussain	PROPN
ejpam-6931	541	31	.	.	PUNCT
ejpam-6931	542	1	contractions	contraction	NOUN
ejpam-6931	542	2	in	in	ADP
ejpam-6931	542	3	fuzzy	fuzzy	ADJ
ejpam-6931	542	4	rectangular	rectangular	ADJ
ejpam-6931	542	5	b	b	X
ejpam-6931	542	6	-	-	ADJ
ejpam-6931	542	7	metric	metric	ADJ
ejpam-6931	542	8	spaces	space	NOUN
ejpam-6931	542	9	with	with	ADP
ejpam-6931	542	10	application	application	NOUN
ejpam-6931	542	11	.	.	PUNCT
ejpam-6931	543	1	journal	journal	NOUN
ejpam-6931	543	2	of	of	ADP
ejpam-6931	543	3	intelligent	intelligent	ADJ
ejpam-6931	543	4	&	&	CCONJ
ejpam-6931	543	5	fuzzy	fuzzy	ADJ
ejpam-6931	543	6	systems	system	NOUN
ejpam-6931	543	7	,	,	PUNCT
ejpam-6931	543	8	37(1):1275–1285	37(1):1275–1285	NUM
ejpam-6931	543	9	,	,	PUNCT
ejpam-6931	543	10	2019	2019	NUM
ejpam-6931	543	11	.	.	PUNCT
ejpam-6931	544	1	[	[	X
ejpam-6931	544	2	11	11	NUM
ejpam-6931	544	3	]	]	PUNCT
ejpam-6931	544	4	s.	s.	PROPN
ejpam-6931	544	5	nădăban	nădăban	PROPN
ejpam-6931	544	6	.	.	PUNCT
ejpam-6931	545	1	fuzzy	fuzzy	ADJ
ejpam-6931	545	2	b	b	X
ejpam-6931	545	3	-	-	PUNCT
ejpam-6931	545	4	metric	metric	ADJ
ejpam-6931	545	5	spaces	space	NOUN
ejpam-6931	545	6	.	.	PUNCT
ejpam-6931	546	1	international	international	ADJ
ejpam-6931	546	2	journal	journal	PROPN
ejpam-6931	546	3	of	of	ADP
ejpam-6931	546	4	computers	computer	NOUN
ejpam-6931	546	5	communications	communication	NOUN
ejpam-6931	546	6	&	&	CCONJ
ejpam-6931	546	7	control	control	PROPN
ejpam-6931	546	8	,	,	PUNCT
ejpam-6931	546	9	11(2):273–281	11(2):273–281	PROPN
ejpam-6931	546	10	,	,	PUNCT
ejpam-6931	546	11	2016	2016	NUM
ejpam-6931	546	12	.	.	PUNCT
ejpam-6931	547	1	[	[	X
ejpam-6931	547	2	12	12	NUM
ejpam-6931	547	3	]	]	X
ejpam-6931	547	4	r.	r.	PROPN
ejpam-6931	547	5	saadati	saadati	PROPN
ejpam-6931	547	6	,	,	PUNCT
ejpam-6931	547	7	s.	s.	PROPN
ejpam-6931	547	8	sedghi	sedghi	PROPN
ejpam-6931	547	9	,	,	PUNCT
ejpam-6931	547	10	and	and	CCONJ
ejpam-6931	547	11	n.	n.	PROPN
ejpam-6931	547	12	shobe	shobe	PROPN
ejpam-6931	547	13	.	.	PUNCT
ejpam-6931	548	1	modified	modify	VERB
ejpam-6931	548	2	intuitionistic	intuitionistic	ADJ
ejpam-6931	548	3	fuzzy	fuzzy	ADJ
ejpam-6931	548	4	metric	metric	ADJ
ejpam-6931	548	5	spaces	space	NOUN
ejpam-6931	548	6	and	and	CCONJ
ejpam-6931	548	7	some	some	DET
ejpam-6931	548	8	fixed	fix	VERB
ejpam-6931	548	9	point	point	NOUN
ejpam-6931	548	10	theorems	theorem	NOUN
ejpam-6931	548	11	.	.	PUNCT
ejpam-6931	548	12	chaos	chaos	NOUN
ejpam-6931	548	13	,	,	PUNCT
ejpam-6931	548	14	solitons	soliton	NOUN
ejpam-6931	548	15	&	&	CCONJ
ejpam-6931	548	16	fractals	fractal	NOUN
ejpam-6931	548	17	,	,	PUNCT
ejpam-6931	548	18	38(1):36–47	38(1):36–47	NUM
ejpam-6931	548	19	,	,	PUNCT
ejpam-6931	548	20	2008	2008	NUM
ejpam-6931	548	21	.	.	PUNCT
ejpam-6931	549	1	[	[	X
ejpam-6931	549	2	13	13	NUM
ejpam-6931	549	3	]	]	PUNCT
ejpam-6931	549	4	k.	k.	PROPN
ejpam-6931	549	5	s.	s.	PROPN
ejpam-6931	549	6	wong	wong	PROPN
ejpam-6931	549	7	,	,	PUNCT
ejpam-6931	549	8	z.	z.	PROPN
ejpam-6931	549	9	salleh	salleh	PROPN
ejpam-6931	549	10	,	,	PUNCT
ejpam-6931	549	11	c.	c.	PROPN
ejpam-6931	549	12	m.	m.	PROPN
ejpam-6931	549	13	i.	i.	PROPN
ejpam-6931	549	14	c.	c.	PROPN
ejpam-6931	549	15	taib	taib	PROPN
ejpam-6931	549	16	,	,	PUNCT
ejpam-6931	549	17	and	and	CCONJ
ejpam-6931	549	18	i.	i.	PROPN
ejpam-6931	549	19	abdullah	abdullah	PROPN
ejpam-6931	549	20	.	.	PUNCT
ejpam-6931	550	1	some	some	DET
ejpam-6931	550	2	fixed	fix	VERB
ejpam-6931	550	3	point	point	NOUN
ejpam-6931	550	4	results	result	NOUN
ejpam-6931	550	5	on	on	ADP
ejpam-6931	550	6	fuzzy	fuzzy	ADJ
ejpam-6931	550	7	extended	extend	VERB
ejpam-6931	550	8	rectangular	rectangular	ADJ
ejpam-6931	550	9	b	b	X
ejpam-6931	550	10	-	-	ADJ
ejpam-6931	550	11	metric	metric	ADJ
ejpam-6931	550	12	spaces	space	NOUN
ejpam-6931	550	13	.	.	PUNCT
ejpam-6931	551	1	in	in	ADP
ejpam-6931	551	2	american	american	PROPN
ejpam-6931	551	3	institute	institute	PROPN
ejpam-6931	551	4	of	of	ADP
ejpam-6931	551	5	physics	physics	PROPN
ejpam-6931	551	6	conference	conference	PROPN
ejpam-6931	551	7	series	series	PROPN
ejpam-6931	551	8	,	,	PUNCT
ejpam-6931	551	9	volume	volume	NOUN
ejpam-6931	551	10	2746	2746	NUM
ejpam-6931	551	11	,	,	PUNCT
ejpam-6931	551	12	page	page	NOUN
ejpam-6931	551	13	060004	060004	NUM
ejpam-6931	551	14	,	,	PUNCT
ejpam-6931	551	15	october	october	PROPN
ejpam-6931	551	16	2023	2023	NUM
ejpam-6931	551	17	.	.	PUNCT
ejpam-6931	552	1	[	[	X
ejpam-6931	552	2	14	14	NUM
ejpam-6931	552	3	]	]	PUNCT
ejpam-6931	552	4	m.	m.	NOUN
ejpam-6931	552	5	s.	s.	PROPN
ejpam-6931	552	6	ashraf	ashraf	PROPN
ejpam-6931	552	7	,	,	PUNCT
ejpam-6931	552	8	r.	r.	PROPN
ejpam-6931	552	9	ali	ali	PROPN
ejpam-6931	552	10	,	,	PUNCT
ejpam-6931	552	11	and	and	CCONJ
ejpam-6931	552	12	n.	n.	PROPN
ejpam-6931	552	13	hussain	hussain	PROPN
ejpam-6931	552	14	.	.	PUNCT
ejpam-6931	553	1	geraghty	geraghty	PROPN
ejpam-6931	553	2	type	type	NOUN
ejpam-6931	553	3	contractions	contraction	NOUN
ejpam-6931	553	4	in	in	ADP
ejpam-6931	553	5	fuzzy	fuzzy	ADJ
ejpam-6931	553	6	b	b	X
ejpam-6931	553	7	-	-	ADJ
ejpam-6931	553	8	metric	metric	ADJ
ejpam-6931	553	9	spaces	space	NOUN
ejpam-6931	553	10	with	with	ADP
ejpam-6931	553	11	application	application	NOUN
ejpam-6931	553	12	to	to	ADP
ejpam-6931	553	13	integral	integral	ADJ
ejpam-6931	553	14	equations	equation	NOUN
ejpam-6931	553	15	.	.	PUNCT
ejpam-6931	554	1	filomat	filomat	PROPN
ejpam-6931	554	2	,	,	PUNCT
ejpam-6931	554	3	34(9):3083–3098	34(9):3083–3098	NUM
ejpam-6931	554	4	,	,	PUNCT
ejpam-6931	554	5	2020	2020	NUM
ejpam-6931	554	6	.	.	PUNCT
ejpam-6931	555	1	[	[	X
ejpam-6931	555	2	15	15	NUM
ejpam-6931	555	3	]	]	X
ejpam-6931	555	4	d.	d.	PROPN
ejpam-6931	555	5	gopal	gopal	PROPN
ejpam-6931	555	6	.	.	PUNCT
ejpam-6931	556	1	contributions	contribution	NOUN
ejpam-6931	556	2	to	to	ADP
ejpam-6931	556	3	fixed	fix	VERB
ejpam-6931	556	4	point	point	NOUN
ejpam-6931	556	5	theory	theory	NOUN
ejpam-6931	556	6	of	of	ADP
ejpam-6931	556	7	fuzzy	fuzzy	ADJ
ejpam-6931	556	8	contractive	contractive	ADJ
ejpam-6931	556	9	mappings	mapping	NOUN
ejpam-6931	556	10	.	.	PUNCT
ejpam-6931	557	1	advances	advance	NOUN
ejpam-6931	557	2	in	in	ADP
ejpam-6931	557	3	metric	metric	ADJ
ejpam-6931	557	4	fixed	fix	VERB
ejpam-6931	557	5	point	point	NOUN
ejpam-6931	557	6	theory	theory	NOUN
ejpam-6931	557	7	and	and	CCONJ
ejpam-6931	557	8	applications	application	NOUN
ejpam-6931	557	9	,	,	PUNCT
ejpam-6931	557	10	pages	page	NOUN
ejpam-6931	557	11	241–282	241–282	NUM
ejpam-6931	557	12	,	,	PUNCT
ejpam-6931	557	13	2021	2021	NUM
ejpam-6931	557	14	.	.	PUNCT
ejpam-6931	558	1	[	[	X
ejpam-6931	558	2	16	16	NUM
ejpam-6931	558	3	]	]	X
ejpam-6931	558	4	d.	d.	PROPN
ejpam-6931	558	5	gopal	gopal	PROPN
ejpam-6931	558	6	,	,	PUNCT
ejpam-6931	558	7	p.	p.	PROPN
ejpam-6931	558	8	kumam	kumam	PROPN
ejpam-6931	558	9	,	,	PUNCT
ejpam-6931	558	10	and	and	CCONJ
ejpam-6931	558	11	m.	m.	NOUN
ejpam-6931	558	12	abbas	abbas	PROPN
ejpam-6931	558	13	.	.	PUNCT
ejpam-6931	559	1	background	background	NOUN
ejpam-6931	559	2	and	and	CCONJ
ejpam-6931	559	3	recent	recent	ADJ
ejpam-6931	559	4	developments	development	NOUN
ejpam-6931	559	5	of	of	ADP
ejpam-6931	559	6	metric	metric	ADJ
ejpam-6931	559	7	fixed	fix	VERB
ejpam-6931	559	8	point	point	NOUN
ejpam-6931	559	9	theory	theory	NOUN
ejpam-6931	559	10	.	.	PUNCT
ejpam-6931	560	1	2017	2017	NUM
ejpam-6931	560	2	.	.	PUNCT
ejpam-6931	561	1	[	[	X
ejpam-6931	561	2	17	17	NUM
ejpam-6931	561	3	]	]	X
ejpam-6931	561	4	n.	n.	PROPN
ejpam-6931	561	5	saleem	saleem	PROPN
ejpam-6931	561	6	,	,	PUNCT
ejpam-6931	561	7	b.	b.	PROPN
ejpam-6931	561	8	ali	ali	PROPN
ejpam-6931	561	9	,	,	PUNCT
ejpam-6931	561	10	m.	m.	NOUN
ejpam-6931	561	11	abbas	abbas	PROPN
ejpam-6931	561	12	,	,	PUNCT
ejpam-6931	561	13	and	and	CCONJ
ejpam-6931	561	14	z.	z.	PROPN
ejpam-6931	561	15	raza	raza	PROPN
ejpam-6931	561	16	.	.	PUNCT
ejpam-6931	562	1	fixed	fix	VERB
ejpam-6931	562	2	points	point	NOUN
ejpam-6931	562	3	of	of	ADP
ejpam-6931	562	4	suzuki	suzuki	NOUN
ejpam-6931	562	5	type	type	NOUN
ejpam-6931	562	6	generalized	generalize	VERB
ejpam-6931	562	7	multivalued	multivalue	VERB
ejpam-6931	562	8	mappings	mapping	NOUN
ejpam-6931	562	9	in	in	ADP
ejpam-6931	562	10	fuzzy	fuzzy	ADJ
ejpam-6931	562	11	metric	metric	ADJ
ejpam-6931	562	12	spaces	space	NOUN
ejpam-6931	562	13	with	with	ADP
ejpam-6931	562	14	applications	application	NOUN
ejpam-6931	562	15	.	.	PUNCT
ejpam-6931	563	1	fixed	fix	VERB
ejpam-6931	563	2	point	point	NOUN
ejpam-6931	563	3	theory	theory	NOUN
ejpam-6931	563	4	and	and	CCONJ
ejpam-6931	563	5	applications	application	NOUN
ejpam-6931	563	6	,	,	PUNCT
ejpam-6931	563	7	pages	page	NOUN
ejpam-6931	563	8	1–18	1–18	NUM
ejpam-6931	563	9	,	,	PUNCT
ejpam-6931	563	10	2015	2015	NUM
ejpam-6931	563	11	.	.	PUNCT
ejpam-6931	564	1	[	[	X
ejpam-6931	564	2	18	18	NUM
ejpam-6931	564	3	]	]	X
ejpam-6931	564	4	a.	a.	PROPN
ejpam-6931	564	5	azam	azam	PROPN
ejpam-6931	564	6	,	,	PUNCT
ejpam-6931	564	7	b.	b.	PROPN
ejpam-6931	564	8	fisher	fisher	PROPN
ejpam-6931	564	9	,	,	PUNCT
ejpam-6931	564	10	and	and	CCONJ
ejpam-6931	564	11	m.	m.	PROPN
ejpam-6931	564	12	khan	khan	PROPN
ejpam-6931	564	13	.	.	PUNCT
ejpam-6931	565	1	common	common	ADJ
ejpam-6931	565	2	fixed	fix	VERB
ejpam-6931	565	3	point	point	NOUN
ejpam-6931	565	4	theorems	theorem	NOUN
ejpam-6931	565	5	in	in	ADP
ejpam-6931	565	6	complex	complex	ADV
ejpam-6931	565	7	-	-	PUNCT
ejpam-6931	565	8	valued	value	VERB
ejpam-6931	565	9	metric	metric	ADJ
ejpam-6931	565	10	spaces	space	NOUN
ejpam-6931	565	11	.	.	PUNCT
ejpam-6931	566	1	numerical	numerical	ADJ
ejpam-6931	566	2	functional	functional	ADJ
ejpam-6931	566	3	analysis	analysis	NOUN
ejpam-6931	566	4	and	and	CCONJ
ejpam-6931	566	5	optimization	optimization	NOUN
ejpam-6931	566	6	,	,	PUNCT
ejpam-6931	566	7	32(3):243–253	32(3):243–253	NUM
ejpam-6931	566	8	,	,	PUNCT
ejpam-6931	566	9	2011	2011	NUM
ejpam-6931	566	10	.	.	PUNCT
ejpam-6931	567	1	[	[	X
ejpam-6931	567	2	19	19	NUM
ejpam-6931	567	3	]	]	X
ejpam-6931	567	4	s.	s.	PROPN
ejpam-6931	567	5	shukla	shukla	PROPN
ejpam-6931	567	6	,	,	PUNCT
ejpam-6931	567	7	r.	r.	PROPN
ejpam-6931	567	8	rodriguez	rodriguez	PROPN
ejpam-6931	567	9	-	-	PUNCT
ejpam-6931	567	10	lopez	lopez	NOUN
ejpam-6931	567	11	,	,	PUNCT
ejpam-6931	567	12	and	and	CCONJ
ejpam-6931	567	13	m.	m.	NOUN
ejpam-6931	567	14	abbas	abbas	PROPN
ejpam-6931	567	15	.	.	PUNCT
ejpam-6931	568	1	fixed	fix	VERB
ejpam-6931	568	2	point	point	NOUN
ejpam-6931	568	3	results	result	NOUN
ejpam-6931	568	4	for	for	ADP
ejpam-6931	568	5	contractive	contractive	ADJ
ejpam-6931	568	6	mappings	mapping	NOUN
ejpam-6931	568	7	in	in	ADP
ejpam-6931	568	8	complex	complex	ADV
ejpam-6931	568	9	-	-	PUNCT
ejpam-6931	568	10	valued	value	VERB
ejpam-6931	568	11	fuzzy	fuzzy	ADJ
ejpam-6931	568	12	metric	metric	ADJ
ejpam-6931	568	13	spaces	space	NOUN
ejpam-6931	568	14	.	.	PUNCT
ejpam-6931	569	1	fixed	fix	VERB
ejpam-6931	569	2	point	point	NOUN
ejpam-6931	569	3	theory	theory	NOUN
ejpam-6931	569	4	,	,	PUNCT
ejpam-6931	569	5	19(2):751–774	19(2):751–774	NOUN
ejpam-6931	569	6	,	,	PUNCT
ejpam-6931	569	7	2018	2018	NUM
ejpam-6931	569	8	.	.	PUNCT
ejpam-6931	570	1	[	[	X
ejpam-6931	570	2	20	20	NUM
ejpam-6931	570	3	]	]	PUNCT
ejpam-6931	570	4	k.	k.	PROPN
ejpam-6931	571	1	p.	p.	PROPN
ejpam-6931	571	2	patel	patel	PROPN
ejpam-6931	571	3	and	and	CCONJ
ejpam-6931	571	4	g.	g.	PROPN
ejpam-6931	571	5	m.	m.	PROPN
ejpam-6931	571	6	deheri	deheri	PROPN
ejpam-6931	571	7	.	.	PUNCT
ejpam-6931	572	1	extension	extension	NOUN
ejpam-6931	572	2	of	of	ADP
ejpam-6931	572	3	some	some	DET
ejpam-6931	572	4	common	common	ADJ
ejpam-6931	572	5	fixed	fix	VERB
ejpam-6931	572	6	point	point	NOUN
ejpam-6931	572	7	theorems	theorem	NOUN
ejpam-6931	572	8	.	.	PUNCT
ejpam-6931	573	1	international	international	ADJ
ejpam-6931	573	2	journal	journal	NOUN
ejpam-6931	573	3	of	of	ADP
ejpam-6931	573	4	applied	apply	VERB
ejpam-6931	573	5	physics	physics	NOUN
ejpam-6931	573	6	and	and	CCONJ
ejpam-6931	573	7	mathematics	mathematic	NOUN
ejpam-6931	573	8	,	,	PUNCT
ejpam-6931	573	9	3(5):329	3(5):329	NUM
ejpam-6931	573	10	,	,	PUNCT
ejpam-6931	573	11	2013	2013	NUM
ejpam-6931	573	12	.	.	PUNCT
ejpam-6931	574	1	[	[	X
ejpam-6931	574	2	21	21	NUM
ejpam-6931	574	3	]	]	X
ejpam-6931	574	4	i.	i.	PROPN
ejpam-6931	574	5	demir	demir	PROPN
ejpam-6931	574	6	.	.	PROPN
ejpam-6931	575	1	fixed	fix	VERB
ejpam-6931	575	2	point	point	NOUN
ejpam-6931	575	3	theorems	theorem	NOUN
ejpam-6931	575	4	in	in	ADP
ejpam-6931	575	5	complex	complex	ADV
ejpam-6931	575	6	-	-	PUNCT
ejpam-6931	575	7	valued	value	VERB
ejpam-6931	575	8	fuzzy	fuzzy	ADJ
ejpam-6931	575	9	b	b	X
ejpam-6931	575	10	-	-	PUNCT
ejpam-6931	575	11	metric	metric	ADJ
ejpam-6931	575	12	spaces	space	NOUN
ejpam-6931	575	13	with	with	ADP
ejpam-6931	575	14	application	application	NOUN
ejpam-6931	575	15	to	to	ADP
ejpam-6931	575	16	integral	integral	ADJ
ejpam-6931	575	17	equations	equation	NOUN
ejpam-6931	575	18	.	.	PUNCT
ejpam-6931	576	1	miskolc	miskolc	ADJ
ejpam-6931	576	2	mathematical	mathematical	ADJ
ejpam-6931	576	3	notes	note	NOUN
ejpam-6931	576	4	,	,	PUNCT
ejpam-6931	576	5	22(1):153–171	22(1):153–171	PROPN
ejpam-6931	576	6	,	,	PUNCT
ejpam-6931	576	7	2021	2021	NUM
ejpam-6931	576	8	.	.	PUNCT
ejpam-6931	577	1	[	[	X
ejpam-6931	577	2	22	22	NUM
ejpam-6931	577	3	]	]	PUNCT
ejpam-6931	577	4	s.	s.	PROPN
ejpam-6931	577	5	t.	t.	PROPN
ejpam-6931	577	6	zubair	zubair	PROPN
ejpam-6931	577	7	,	,	PUNCT
ejpam-6931	577	8	k.	k.	PROPN
ejpam-6931	577	9	gopalan	gopalan	PROPN
ejpam-6931	577	10	,	,	PUNCT
ejpam-6931	577	11	t.	t.	NOUN
ejpam-6931	577	12	abdeljawad	abdeljawad	NOUN
ejpam-6931	577	13	,	,	PUNCT
ejpam-6931	577	14	and	and	CCONJ
ejpam-6931	577	15	n.	n.	PROPN
ejpam-6931	577	16	mlaiki	mlaiki	PROPN
ejpam-6931	577	17	.	.	PUNCT
ejpam-6931	578	1	novel	novel	ADJ
ejpam-6931	578	2	fixed	fix	VERB
ejpam-6931	578	3	point	point	NOUN
ejpam-6931	578	4	technique	technique	NOUN
ejpam-6931	578	5	to	to	ADP
ejpam-6931	578	6	coupled	couple	VERB
ejpam-6931	578	7	system	system	NOUN
ejpam-6931	578	8	of	of	ADP
ejpam-6931	578	9	nonlinear	nonlinear	ADJ
ejpam-6931	578	10	implicit	implicit	ADJ
ejpam-6931	578	11	fractional	fractional	ADJ
ejpam-6931	578	12	differential	differential	ADJ
ejpam-6931	578	13	equations	equation	NOUN
ejpam-6931	578	14	in	in	ADP
ejpam-6931	578	15	complexvalued	complexvalue	VERB
ejpam-6931	578	16	fuzzy	fuzzy	ADJ
ejpam-6931	578	17	rectangular	rectangular	ADJ
ejpam-6931	578	18	b	b	X
ejpam-6931	578	19	-	-	ADJ
ejpam-6931	578	20	metric	metric	ADJ
ejpam-6931	578	21	spaces	space	NOUN
ejpam-6931	578	22	.	.	PUNCT
ejpam-6931	579	1	aims	aim	VERB
ejpam-6931	579	2	mathematics	mathematic	NOUN
ejpam-6931	579	3	,	,	PUNCT
ejpam-6931	579	4	7(6):10867–10891	7(6):10867–10891	PROPN
ejpam-6931	579	5	,	,	PUNCT
ejpam-6931	579	6	2022	2022	NUM
ejpam-6931	579	7	.	.	PUNCT
ejpam-6931	580	1	[	[	X
ejpam-6931	580	2	23	23	NUM
ejpam-6931	580	3	]	]	X
ejpam-6931	580	4	humaira	humaira	PROPN
ejpam-6931	580	5	,	,	PUNCT
ejpam-6931	580	6	h.	h.	PROPN
ejpam-6931	580	7	a.	a.	PROPN
ejpam-6931	580	8	hammad	hammad	PROPN
ejpam-6931	580	9	,	,	PUNCT
ejpam-6931	580	10	m.	m.	NOUN
ejpam-6931	580	11	sarwar	sarwar	PROPN
ejpam-6931	580	12	,	,	PUNCT
ejpam-6931	580	13	and	and	CCONJ
ejpam-6931	580	14	m.	m.	PROPN
ejpam-6931	580	15	de	de	PROPN
ejpam-6931	580	16	la	la	PROPN
ejpam-6931	580	17	sen	sen	PROPN
ejpam-6931	580	18	.	.	PROPN
ejpam-6931	580	19	existence	existence	PROPN
ejpam-6931	580	20	theorem	theorem	VERB
ejpam-6931	580	21	for	for	ADP
ejpam-6931	580	22	a	a	DET
ejpam-6931	580	23	unique	unique	ADJ
ejpam-6931	580	24	solution	solution	NOUN
ejpam-6931	580	25	to	to	ADP
ejpam-6931	580	26	a	a	DET
ejpam-6931	580	27	coupled	couple	VERB
ejpam-6931	580	28	system	system	NOUN
ejpam-6931	580	29	of	of	ADP
ejpam-6931	580	30	impulsive	impulsive	ADJ
ejpam-6931	580	31	fractional	fractional	ADJ
ejpam-6931	580	32	differential	differential	ADJ
ejpam-6931	580	33	equations	equation	NOUN
ejpam-6931	580	34	in	in	ADP
ejpam-6931	580	35	complex	complex	ADV
ejpam-6931	580	36	-	-	PUNCT
ejpam-6931	580	37	valued	value	VERB
ejpam-6931	580	38	fuzzy	fuzzy	ADJ
ejpam-6931	580	39	metric	metric	ADJ
ejpam-6931	580	40	spaces	space	NOUN
ejpam-6931	580	41	.	.	PUNCT
ejpam-6931	581	1	advances	advance	NOUN
ejpam-6931	581	2	in	in	ADP
ejpam-6931	581	3	difference	difference	NOUN
ejpam-6931	581	4	equations	equation	NOUN
ejpam-6931	581	5	,	,	PUNCT
ejpam-6931	581	6	2021(1):242	2021(1):242	NUM
ejpam-6931	581	7	,	,	PUNCT
ejpam-6931	581	8	2021	2021	NUM
ejpam-6931	581	9	.	.	PUNCT
ejpam-6931	582	1	[	[	X
ejpam-6931	582	2	24	24	NUM
ejpam-6931	582	3	]	]	PUNCT
ejpam-6931	582	4	m.	m.	NOUN
ejpam-6931	582	5	sarwar	sarwar	NOUN
ejpam-6931	582	6	and	and	CCONJ
ejpam-6931	582	7	t.	t.	PROPN
ejpam-6931	582	8	abdeljawad	abdeljawad	NOUN
ejpam-6931	582	9	.	.	PUNCT
ejpam-6931	583	1	existence	existence	NOUN
ejpam-6931	583	2	of	of	ADP
ejpam-6931	583	3	unique	unique	ADJ
ejpam-6931	583	4	solution	solution	NOUN
ejpam-6931	583	5	to	to	ADP
ejpam-6931	583	6	nonlinear	nonlinear	ADJ
ejpam-6931	583	7	mixed	mixed	PROPN
ejpam-6931	583	8	volterra	volterra	PROPN
ejpam-6931	583	9	fredholm	fredholm	PROPN
ejpam-6931	583	10	-	-	PUNCT
ejpam-6931	583	11	hammerstein	hammerstein	NOUN
ejpam-6931	583	12	integral	integral	ADJ
ejpam-6931	583	13	equations	equation	NOUN
ejpam-6931	583	14	in	in	ADP
ejpam-6931	583	15	complex	complex	ADV
ejpam-6931	583	16	-	-	PUNCT
ejpam-6931	583	17	valued	value	VERB
ejpam-6931	583	18	fuzzy	fuzzy	ADJ
ejpam-6931	583	19	metric	metric	ADJ
ejpam-6931	583	20	spaces	space	NOUN
ejpam-6931	583	21	.	.	PUNCT
ejpam-6931	584	1	journal	journal	NOUN
ejpam-6931	584	2	of	of	ADP
ejpam-6931	584	3	intelligent	intelligent	ADJ
ejpam-6931	584	4	&	&	CCONJ
ejpam-6931	584	5	fuzzy	fuzzy	ADJ
ejpam-6931	584	6	systems	system	NOUN
ejpam-6931	584	7	,	,	PUNCT
ejpam-6931	584	8	40(3):4065–4074	40(3):4065–4074	PROPN
ejpam-6931	584	9	,	,	PUNCT
ejpam-6931	584	10	2021	2021	NUM
ejpam-6931	584	11	.	.	PUNCT
ejpam-6931	585	1	[	[	X
ejpam-6931	585	2	25	25	NUM
ejpam-6931	585	3	]	]	X
ejpam-6931	585	4	humaira	humaira	PROPN
ejpam-6931	585	5	,	,	PUNCT
ejpam-6931	585	6	m.	m.	NOUN
ejpam-6931	585	7	sarwar	sarwar	PROPN
ejpam-6931	585	8	,	,	PUNCT
ejpam-6931	585	9	and	and	CCONJ
ejpam-6931	585	10	t.	t.	PROPN
ejpam-6931	585	11	abdeljawad	abdeljawad	NOUN
ejpam-6931	585	12	.	.	PUNCT
ejpam-6931	586	1	existence	existence	NOUN
ejpam-6931	586	2	of	of	ADP
ejpam-6931	586	3	solutions	solution	NOUN
ejpam-6931	586	4	for	for	ADP
ejpam-6931	586	5	nonlinear	nonlinear	ADJ
ejpam-6931	586	6	impulsive	impulsive	ADJ
ejpam-6931	586	7	fractional	fractional	ADJ
ejpam-6931	586	8	differential	differential	ADJ
ejpam-6931	586	9	equations	equation	NOUN
ejpam-6931	586	10	via	via	ADP
ejpam-6931	586	11	common	common	ADJ
ejpam-6931	586	12	fixed	fix	VERB
ejpam-6931	586	13	-	-	PUNCT
ejpam-6931	586	14	point	point	NOUN
ejpam-6931	586	15	techniques	technique	NOUN
ejpam-6931	586	16	in	in	ADP
ejpam-6931	586	17	complexvalued	complexvalue	VERB
ejpam-6931	586	18	fuzzy	fuzzy	ADJ
ejpam-6931	586	19	metric	metric	ADJ
ejpam-6931	586	20	spaces	space	NOUN
ejpam-6931	586	21	.	.	PUNCT
ejpam-6931	587	1	mathematical	mathematical	ADJ
ejpam-6931	587	2	problems	problem	NOUN
ejpam-6931	587	3	in	in	ADP
ejpam-6931	587	4	engineering	engineering	NOUN
ejpam-6931	587	5	,	,	PUNCT
ejpam-6931	587	6	2020(1):7042715	2020(1):7042715	NOUN
ejpam-6931	587	7	,	,	PUNCT
ejpam-6931	587	8	2020	2020	NUM
ejpam-6931	587	9	.	.	PUNCT
ejpam-6931	588	1	s.	s.	PROPN
ejpam-6931	588	2	m.	m.	PROPN
ejpam-6931	588	3	u.	u.	PROPN
ejpam-6931	588	4	ud	ud	AUX
ejpam-6931	588	5	-	-	PUNCT
ejpam-6931	588	6	din	din	VERB
ejpam-6931	588	7	et	et	PROPN
ejpam-6931	588	8	al	al	PROPN
ejpam-6931	588	9	.	.	PUNCT
ejpam-6931	588	10	/	/	SYM
ejpam-6931	588	11	eur	eur	PROPN
ejpam-6931	588	12	.	.	PUNCT
ejpam-6931	589	1	j.	j.	PROPN
ejpam-6931	589	2	pure	pure	PROPN
ejpam-6931	589	3	appl	appl	PROPN
ejpam-6931	589	4	.	.	PROPN
ejpam-6931	589	5	math	math	PROPN
ejpam-6931	589	6	,	,	PUNCT
ejpam-6931	589	7	18	18	NUM
ejpam-6931	589	8	(	(	PUNCT
ejpam-6931	589	9	4	4	NUM
ejpam-6931	589	10	)	)	PUNCT
ejpam-6931	589	11	(	(	PUNCT
ejpam-6931	589	12	2025	2025	NUM
ejpam-6931	589	13	)	)	PUNCT
ejpam-6931	589	14	,	,	PUNCT
ejpam-6931	589	15	6931	6931	NUM
ejpam-6931	589	16	38	38	NUM
ejpam-6931	589	17	of	of	ADP
ejpam-6931	589	18	38	38	NUM
ejpam-6931	589	19	[	[	SYM
ejpam-6931	589	20	26	26	NUM
ejpam-6931	589	21	]	]	PUNCT
ejpam-6931	589	22	m.	m.	NOUN
ejpam-6931	589	23	sarwar	sarwar	PROPN
ejpam-6931	589	24	,	,	PUNCT
ejpam-6931	589	25	t.	t.	NOUN
ejpam-6931	589	26	abdeljawad	abdeljawad	NOUN
ejpam-6931	589	27	,	,	PUNCT
ejpam-6931	589	28	and	and	CCONJ
ejpam-6931	589	29	n.	n.	PROPN
ejpam-6931	589	30	mlaiki	mlaiki	PROPN
ejpam-6931	589	31	.	.	PUNCT
ejpam-6931	590	1	fixed	fix	VERB
ejpam-6931	590	2	point	point	NOUN
ejpam-6931	590	3	results	result	NOUN
ejpam-6931	590	4	via	via	ADP
ejpam-6931	590	5	least	least	ADJ
ejpam-6931	590	6	upper	upper	ADJ
ejpam-6931	590	7	bound	bind	VERB
ejpam-6931	590	8	property	property	NOUN
ejpam-6931	590	9	and	and	CCONJ
ejpam-6931	590	10	its	its	PRON
ejpam-6931	590	11	applications	application	NOUN
ejpam-6931	590	12	to	to	ADP
ejpam-6931	590	13	fuzzy	fuzzy	ADJ
ejpam-6931	590	14	caputo	caputo	PROPN
ejpam-6931	590	15	fractional	fractional	PROPN
ejpam-6931	590	16	volterra	volterra	PROPN
ejpam-6931	590	17	–	–	PUNCT
ejpam-6931	590	18	fredholm	fredholm	NOUN
ejpam-6931	590	19	integrodifferential	integrodifferential	ADJ
ejpam-6931	590	20	equations	equation	NOUN
ejpam-6931	590	21	.	.	PUNCT
ejpam-6931	591	1	mathematics	mathematic	NOUN
ejpam-6931	591	2	,	,	PUNCT
ejpam-6931	591	3	9(16):1969	9(16):1969	NOUN
ejpam-6931	591	4	,	,	PUNCT
ejpam-6931	591	5	2021	2021	NUM
ejpam-6931	591	6	.	.	PUNCT
ejpam-6931	592	1	[	[	X
ejpam-6931	592	2	27	27	NUM
ejpam-6931	592	3	]	]	X
ejpam-6931	592	4	u.	u.	PROPN
ejpam-6931	592	5	saeed	saeed	PROPN
ejpam-6931	592	6	and	and	CCONJ
ejpam-6931	592	7	m.	m.	NOUN
ejpam-6931	592	8	umair	umair	NOUN
ejpam-6931	592	9	.	.	PUNCT
ejpam-6931	593	1	a	a	DET
ejpam-6931	593	2	modified	modify	VERB
ejpam-6931	593	3	method	method	NOUN
ejpam-6931	593	4	for	for	ADP
ejpam-6931	593	5	solving	solve	VERB
ejpam-6931	593	6	non	non	ADJ
ejpam-6931	593	7	-	-	ADJ
ejpam-6931	593	8	linear	linear	ADJ
ejpam-6931	593	9	time	time	NOUN
ejpam-6931	593	10	and	and	CCONJ
ejpam-6931	593	11	space	space	NOUN
ejpam-6931	593	12	fractional	fractional	ADJ
ejpam-6931	593	13	partial	partial	ADJ
ejpam-6931	593	14	differential	differential	NOUN
ejpam-6931	593	15	equations	equation	NOUN
ejpam-6931	593	16	.	.	PUNCT
ejpam-6931	594	1	engineering	engineering	NOUN
ejpam-6931	594	2	computations	computation	NOUN
ejpam-6931	594	3	,	,	PUNCT
ejpam-6931	594	4	36(7):2162–2178	36(7):2162–2178	NUM
ejpam-6931	594	5	,	,	PUNCT
ejpam-6931	594	6	2019	2019	NUM
ejpam-6931	594	7	.	.	PUNCT
ejpam-6931	595	1	[	[	X
ejpam-6931	595	2	28	28	NUM
ejpam-6931	595	3	]	]	X
ejpam-6931	595	4	m.	m.	NOUN
ejpam-6931	595	5	kirişci	kirişci	PROPN
ejpam-6931	595	6	and	and	CCONJ
ejpam-6931	595	7	n.	n.	PROPN
ejpam-6931	595	8	şimşek	şimşek	PROPN
ejpam-6931	595	9	.	.	PUNCT
ejpam-6931	596	1	neutrosophic	neutrosophic	ADJ
ejpam-6931	596	2	metric	metric	ADJ
ejpam-6931	596	3	spaces	space	NOUN
ejpam-6931	596	4	.	.	PUNCT
ejpam-6931	597	1	mathematical	mathematical	ADJ
ejpam-6931	597	2	sciences	science	NOUN
ejpam-6931	597	3	,	,	PUNCT
ejpam-6931	597	4	14(3):241–248	14(3):241–248	NUM
ejpam-6931	597	5	,	,	PUNCT
ejpam-6931	597	6	2020	2020	NUM
ejpam-6931	597	7	.	.	PUNCT
ejpam-6931	598	1	[	[	X
ejpam-6931	598	2	29	29	NUM
ejpam-6931	598	3	]	]	X
ejpam-6931	598	4	a.	a.	NOUN
ejpam-6931	598	5	asghar	asghar	PROPN
ejpam-6931	598	6	,	,	PUNCT
ejpam-6931	598	7	a.	a.	PROPN
ejpam-6931	598	8	hussain	hussain	PROPN
ejpam-6931	598	9	,	,	PUNCT
ejpam-6931	598	10	k.	k.	PROPN
ejpam-6931	598	11	ahmad	ahmad	PROPN
ejpam-6931	598	12	,	,	PUNCT
ejpam-6931	598	13	u.	u.	PROPN
ejpam-6931	598	14	ishtiaq	ishtiaq	PROPN
ejpam-6931	598	15	,	,	PUNCT
ejpam-6931	598	16	h.	h.	PROPN
ejpam-6931	598	17	al	al	PROPN
ejpam-6931	598	18	sulami	sulami	PROPN
ejpam-6931	598	19	,	,	PUNCT
ejpam-6931	598	20	and	and	CCONJ
ejpam-6931	598	21	n.	n.	PROPN
ejpam-6931	598	22	hussain	hussain	PROPN
ejpam-6931	598	23	.	.	PUNCT
ejpam-6931	599	1	on	on	ADP
ejpam-6931	599	2	neutrosophic	neutrosophic	ADJ
ejpam-6931	599	3	2	2	NUM
ejpam-6931	599	4	-	-	PUNCT
ejpam-6931	599	5	metric	metric	ADJ
ejpam-6931	599	6	spaces	space	NOUN
ejpam-6931	599	7	with	with	ADP
ejpam-6931	599	8	application	application	NOUN
ejpam-6931	599	9	.	.	PUNCT
ejpam-6931	600	1	journal	journal	NOUN
ejpam-6931	600	2	of	of	ADP
ejpam-6931	600	3	function	function	NOUN
ejpam-6931	600	4	spaces	space	NOUN
ejpam-6931	600	5	,	,	PUNCT
ejpam-6931	600	6	2023(1):9057107	2023(1):9057107	NOUN
ejpam-6931	600	7	,	,	PUNCT
ejpam-6931	600	8	2023	2023	NUM
ejpam-6931	600	9	.	.	PUNCT
ejpam-6931	601	1	[	[	X
ejpam-6931	601	2	30	30	NUM
ejpam-6931	601	3	]	]	X
ejpam-6931	601	4	m.	m.	NOUN
ejpam-6931	601	5	akram	akram	PROPN
ejpam-6931	601	6	,	,	PUNCT
ejpam-6931	601	7	u.	u.	PROPN
ejpam-6931	601	8	ishtiaq	ishtiaq	PROPN
ejpam-6931	601	9	,	,	PUNCT
ejpam-6931	601	10	k.	k.	PROPN
ejpam-6931	601	11	ahmad	ahmad	PROPN
ejpam-6931	601	12	,	,	PUNCT
ejpam-6931	601	13	t.	t.	PROPN
ejpam-6931	601	14	a.	a.	PROPN
ejpam-6931	601	15	lazăr	lazăr	PROPN
ejpam-6931	601	16	,	,	PUNCT
ejpam-6931	601	17	v.	v.	PROPN
ejpam-6931	601	18	l.	l.	PROPN
ejpam-6931	601	19	lazăr	lazăr	PROPN
ejpam-6931	601	20	,	,	PUNCT
ejpam-6931	601	21	and	and	CCONJ
ejpam-6931	601	22	l.	l.	PROPN
ejpam-6931	601	23	guran	guran	PROPN
ejpam-6931	601	24	.	.	PUNCT
ejpam-6931	602	1	some	some	DET
ejpam-6931	602	2	generalized	generalize	VERB
ejpam-6931	602	3	neutrosophic	neutrosophic	ADJ
ejpam-6931	602	4	metric	metric	ADJ
ejpam-6931	602	5	spaces	space	NOUN
ejpam-6931	602	6	and	and	CCONJ
ejpam-6931	602	7	fixed	fix	VERB
ejpam-6931	602	8	point	point	NOUN
ejpam-6931	602	9	results	result	NOUN
ejpam-6931	602	10	with	with	ADP
ejpam-6931	602	11	applications	application	NOUN
ejpam-6931	602	12	.	.	PUNCT
ejpam-6931	603	1	symmetry	symmetry	NOUN
ejpam-6931	603	2	,	,	PUNCT
ejpam-6931	603	3	16(8):965	16(8):965	NUM
ejpam-6931	603	4	,	,	PUNCT
ejpam-6931	603	5	2024	2024	NUM
ejpam-6931	603	6	.	.	PUNCT
ejpam-6931	604	1	[	[	X
ejpam-6931	604	2	31	31	NUM
ejpam-6931	604	3	]	]	PUNCT
ejpam-6931	604	4	s.	s.	PROPN
ejpam-6931	604	5	sowndrarajan	sowndrarajan	PROPN
ejpam-6931	604	6	,	,	PUNCT
ejpam-6931	604	7	m.	m.	NOUN
ejpam-6931	604	8	jeyaraman	jeyaraman	PROPN
ejpam-6931	604	9	,	,	PUNCT
ejpam-6931	604	10	and	and	CCONJ
ejpam-6931	604	11	f.	f.	PROPN
ejpam-6931	604	12	smarandache	smarandache	PROPN
ejpam-6931	604	13	.	.	PUNCT
ejpam-6931	605	1	fixed	fix	VERB
ejpam-6931	605	2	point	point	NOUN
ejpam-6931	605	3	results	result	NOUN
ejpam-6931	605	4	for	for	ADP
ejpam-6931	605	5	contraction	contraction	NOUN
ejpam-6931	605	6	theorems	theorem	NOUN
ejpam-6931	605	7	in	in	ADP
ejpam-6931	605	8	neutrosophic	neutrosophic	ADJ
ejpam-6931	605	9	metric	metric	ADJ
ejpam-6931	605	10	spaces	space	NOUN
ejpam-6931	605	11	,	,	PUNCT
ejpam-6931	605	12	volume	volume	NOUN
ejpam-6931	605	13	36	36	NUM
ejpam-6931	605	14	.	.	PUNCT
ejpam-6931	606	1	infinite	infinite	ADJ
ejpam-6931	606	2	study	study	NOUN
ejpam-6931	606	3	,	,	PUNCT
ejpam-6931	606	4	2020	2020	NUM
ejpam-6931	606	5	.	.	PUNCT
ejpam-6931	607	1	[	[	X
ejpam-6931	607	2	32	32	NUM
ejpam-6931	607	3	]	]	X
ejpam-6931	607	4	u.	u.	PROPN
ejpam-6931	607	5	ishtiaq	ishtiaq	PROPN
ejpam-6931	607	6	,	,	PUNCT
ejpam-6931	607	7	k.	k.	PROPN
ejpam-6931	607	8	javed	javed	PROPN
ejpam-6931	607	9	,	,	PUNCT
ejpam-6931	607	10	f.	f.	PROPN
ejpam-6931	607	11	uddin	uddin	PROPN
ejpam-6931	607	12	,	,	PUNCT
ejpam-6931	607	13	m.	m.	PROPN
ejpam-6931	607	14	d.	d.	PROPN
ejpam-6931	607	15	l.	l.	PROPN
ejpam-6931	607	16	sen	sen	PROPN
ejpam-6931	607	17	,	,	PUNCT
ejpam-6931	607	18	k.	k.	PROPN
ejpam-6931	607	19	ahmed	ahmed	PROPN
ejpam-6931	607	20	,	,	PUNCT
ejpam-6931	607	21	and	and	CCONJ
ejpam-6931	607	22	m.	m.	PROPN
ejpam-6931	607	23	u.	u.	PROPN
ejpam-6931	607	24	ali	ali	PROPN
ejpam-6931	607	25	.	.	PUNCT
ejpam-6931	607	26	fixed	fix	VERB
ejpam-6931	607	27	point	point	NOUN
ejpam-6931	607	28	results	result	NOUN
ejpam-6931	607	29	in	in	ADP
ejpam-6931	607	30	orthogonal	orthogonal	ADJ
ejpam-6931	607	31	neutrosophic	neutrosophic	ADJ
ejpam-6931	607	32	metric	metric	ADJ
ejpam-6931	607	33	spaces	space	NOUN
ejpam-6931	607	34	.	.	PUNCT
ejpam-6931	608	1	complexity	complexity	NOUN
ejpam-6931	608	2	,	,	PUNCT
ejpam-6931	608	3	2021(1):2809657	2021(1):2809657	NOUN
ejpam-6931	608	4	,	,	PUNCT
ejpam-6931	608	5	2021	2021	NUM
ejpam-6931	608	6	.	.	PUNCT
ejpam-6931	609	1	[	[	X
ejpam-6931	609	2	33	33	NUM
ejpam-6931	609	3	]	]	PUNCT
ejpam-6931	609	4	m.	m.	PROPN
ejpam-6931	609	5	e.	e.	PROPN
ejpam-6931	609	6	m.	m.	PROPN
ejpam-6931	609	7	abdalla	abdalla	PROPN
ejpam-6931	609	8	,	,	PUNCT
ejpam-6931	609	9	a.	a.	PROPN
ejpam-6931	609	10	uzair	uzair	PROPN
ejpam-6931	609	11	,	,	PUNCT
ejpam-6931	609	12	a.	a.	NOUN
ejpam-6931	609	13	ishtiaq	ishtiaq	PROPN
ejpam-6931	609	14	,	,	PUNCT
ejpam-6931	609	15	m.	m.	NOUN
ejpam-6931	609	16	tahir	tahir	PROPN
ejpam-6931	609	17	,	,	PUNCT
ejpam-6931	609	18	and	and	CCONJ
ejpam-6931	609	19	m.	m.	PROPN
ejpam-6931	609	20	kamran	kamran	PROPN
ejpam-6931	609	21	.	.	PUNCT
ejpam-6931	610	1	algebraic	algebraic	ADJ
ejpam-6931	610	2	structures	structure	NOUN
ejpam-6931	610	3	and	and	CCONJ
ejpam-6931	610	4	practical	practical	ADJ
ejpam-6931	610	5	implications	implication	NOUN
ejpam-6931	610	6	of	of	ADP
ejpam-6931	610	7	interval	interval	NOUN
ejpam-6931	610	8	-	-	PUNCT
ejpam-6931	610	9	valued	value	VERB
ejpam-6931	610	10	fermatean	fermatean	NOUN
ejpam-6931	610	11	neutrosophic	neutrosophic	PROPN
ejpam-6931	610	12	super	super	PROPN
ejpam-6931	610	13	hypersoft	hypersoft	PROPN
ejpam-6931	610	14	sets	set	NOUN
ejpam-6931	610	15	in	in	ADP
ejpam-6931	610	16	healthcare	healthcare	PROPN
ejpam-6931	610	17	.	.	PUNCT
ejpam-6931	611	1	spectrum	spectrum	NOUN
ejpam-6931	611	2	of	of	ADP
ejpam-6931	611	3	operational	operational	ADJ
ejpam-6931	611	4	research	research	NOUN
ejpam-6931	611	5	,	,	PUNCT
ejpam-6931	611	6	2(1):199–218	2(1):199–218	NOUN
ejpam-6931	611	7	,	,	PUNCT
ejpam-6931	611	8	2025	2025	NUM
ejpam-6931	611	9	.	.	PUNCT
ejpam-6931	612	1	[	[	X
ejpam-6931	612	2	34	34	NUM
ejpam-6931	612	3	]	]	X
ejpam-6931	612	4	t.	t.	PROPN
ejpam-6931	612	5	fujita	fujita	PROPN
ejpam-6931	612	6	.	.	PUNCT
ejpam-6931	613	1	shadowed	shadow	VERB
ejpam-6931	613	2	offset	offset	VERB
ejpam-6931	613	3	:	:	PUNCT
ejpam-6931	613	4	integrating	integrate	VERB
ejpam-6931	613	5	offset	offset	NOUN
ejpam-6931	613	6	and	and	CCONJ
ejpam-6931	613	7	shadowed	shadow	VERB
ejpam-6931	613	8	set	set	VERB
ejpam-6931	613	9	frameworks	framework	NOUN
ejpam-6931	613	10	for	for	ADP
ejpam-6931	613	11	enhanced	enhanced	ADJ
ejpam-6931	613	12	uncertainty	uncertainty	NOUN
ejpam-6931	613	13	modeling	modeling	NOUN
ejpam-6931	613	14	.	.	PUNCT
ejpam-6931	614	1	spectrum	spectrum	NOUN
ejpam-6931	614	2	of	of	ADP
ejpam-6931	614	3	operational	operational	ADJ
ejpam-6931	614	4	research	research	NOUN
ejpam-6931	614	5	,	,	PUNCT
ejpam-6931	614	6	4(1):1–17	4(1):1–17	NUM
ejpam-6931	614	7	,	,	PUNCT
ejpam-6931	614	8	2025	2025	NUM
ejpam-6931	614	9	.	.	PUNCT
ejpam-6931	615	1	[	[	X
ejpam-6931	615	2	35	35	NUM
ejpam-6931	615	3	]	]	PUNCT
ejpam-6931	615	4	e.	e.	PROPN
ejpam-6931	615	5	p.	p.	PROPN
ejpam-6931	615	6	klement	klement	PROPN
ejpam-6931	615	7	,	,	PUNCT
ejpam-6931	615	8	r.	r.	PROPN
ejpam-6931	615	9	mesiar	mesiar	PROPN
ejpam-6931	615	10	,	,	PUNCT
ejpam-6931	615	11	and	and	CCONJ
ejpam-6931	615	12	e.	e.	PROPN
ejpam-6931	615	13	pap	pap	PROPN
ejpam-6931	615	14	.	.	PUNCT
ejpam-6931	616	1	triangular	triangular	NOUN
ejpam-6931	616	2	norms	norm	NOUN
ejpam-6931	616	3	.	.	PUNCT
ejpam-6931	617	1	position	position	NOUN
ejpam-6931	617	2	paper	paper	PROPN
ejpam-6931	617	3	ii	ii	PROPN
ejpam-6931	617	4	:	:	PUNCT
ejpam-6931	617	5	general	general	ADJ
ejpam-6931	617	6	constructions	construction	NOUN
ejpam-6931	617	7	and	and	CCONJ
ejpam-6931	617	8	parameterized	parameterized	ADJ
ejpam-6931	617	9	families	family	NOUN
ejpam-6931	617	10	.	.	PUNCT
ejpam-6931	618	1	fuzzy	fuzzy	ADJ
ejpam-6931	618	2	sets	set	NOUN
ejpam-6931	618	3	and	and	CCONJ
ejpam-6931	618	4	systems	system	NOUN
ejpam-6931	618	5	,	,	PUNCT
ejpam-6931	618	6	145(3):411–438	145(3):411–438	NUM
ejpam-6931	618	7	,	,	PUNCT
ejpam-6931	618	8	2004	2004	NUM
ejpam-6931	618	9	.	.	PUNCT
ejpam-6931	619	1	[	[	X
ejpam-6931	619	2	36	36	NUM
ejpam-6931	619	3	]	]	X
ejpam-6931	619	4	o.	o.	PROPN
ejpam-6931	619	5	yazdanbakhsh	yazdanbakhsh	PROPN
ejpam-6931	619	6	and	and	CCONJ
ejpam-6931	619	7	s.	s.	PROPN
ejpam-6931	619	8	dick	dick	PROPN
ejpam-6931	619	9	.	.	PUNCT
ejpam-6931	620	1	a	a	DET
ejpam-6931	620	2	systematic	systematic	ADJ
ejpam-6931	620	3	review	review	NOUN
ejpam-6931	620	4	of	of	ADP
ejpam-6931	620	5	complex	complex	ADJ
ejpam-6931	620	6	fuzzy	fuzzy	ADJ
ejpam-6931	620	7	sets	set	NOUN
ejpam-6931	620	8	and	and	CCONJ
ejpam-6931	620	9	logic	logic	NOUN
ejpam-6931	620	10	.	.	PUNCT
ejpam-6931	621	1	fuzzy	fuzzy	ADJ
ejpam-6931	621	2	sets	set	NOUN
ejpam-6931	621	3	and	and	CCONJ
ejpam-6931	621	4	systems	system	NOUN
ejpam-6931	621	5	,	,	PUNCT
ejpam-6931	621	6	338:1–22	338:1–22	NUM
ejpam-6931	621	7	,	,	PUNCT
ejpam-6931	621	8	2018	2018	NUM
ejpam-6931	621	9	.	.	PUNCT