id	sid	tid	token	lemma	pos
ejpam-3096	1	1	european	european	PROPN
ejpam-3096	1	2	journal	journal	PROPN
ejpam-3096	1	3	of	of	ADP
ejpam-3096	1	4	pure	pure	ADJ
ejpam-3096	1	5	and	and	CCONJ
ejpam-3096	1	6	applied	apply	VERB
ejpam-3096	1	7	mathematics	mathematic	NOUN
ejpam-3096	1	8	vol	vol	NOUN
ejpam-3096	1	9	.	.	PROPN
ejpam-3096	2	1	10	10	NUM
ejpam-3096	2	2	,	,	PUNCT
ejpam-3096	2	3	no	no	INTJ
ejpam-3096	2	4	.	.	NOUN
ejpam-3096	2	5	5	5	NUM
ejpam-3096	2	6	,	,	PUNCT
ejpam-3096	2	7	2017	2017	NUM
ejpam-3096	2	8	,	,	PUNCT
ejpam-3096	2	9	1023	1023	NUM
ejpam-3096	2	10	-	-	SYM
ejpam-3096	2	11	1034	1034	NUM
ejpam-3096	2	12	issn	issn	PROPN
ejpam-3096	2	13	1307	1307	NUM
ejpam-3096	2	14	-	-	SYM
ejpam-3096	2	15	5543	5543	NUM
ejpam-3096	2	16	–	–	PUNCT
ejpam-3096	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3096	2	18	published	publish	VERB
ejpam-3096	2	19	by	by	ADP
ejpam-3096	3	1	new	new	PROPN
ejpam-3096	3	2	york	york	PROPN
ejpam-3096	3	3	business	business	PROPN
ejpam-3096	3	4	global	global	PROPN
ejpam-3096	3	5	some	some	DET
ejpam-3096	3	6	coincidence	coincidence	NOUN
ejpam-3096	3	7	and	and	CCONJ
ejpam-3096	3	8	fixed	fix	VERB
ejpam-3096	3	9	point	point	NOUN
ejpam-3096	3	10	results	result	NOUN
ejpam-3096	3	11	in	in	ADP
ejpam-3096	3	12	partially	partially	ADV
ejpam-3096	3	13	ordered	order	VERB
ejpam-3096	3	14	complete	complete	ADJ
ejpam-3096	3	15	generalized	generalized	ADJ
ejpam-3096	3	16	d∗-metric	d∗-metric	ADJ
ejpam-3096	3	17	spaces	space	NOUN
ejpam-3096	3	18	alaa	alaa	PROPN
ejpam-3096	3	19	.	.	PUNCT
ejpam-3096	4	1	m.	m.	PROPN
ejpam-3096	4	2	f.	f.	PROPN
ejpam-3096	4	3	al	al	PROPN
ejpam-3096	4	4	.	.	PROPN
ejpam-3096	5	1	jumaili	jumaili	PROPN
ejpam-3096	5	2	department	department	PROPN
ejpam-3096	5	3	of	of	ADP
ejpam-3096	5	4	mathematics	mathematics	PROPN
ejpam-3096	5	5	,	,	PUNCT
ejpam-3096	5	6	university	university	NOUN
ejpam-3096	5	7	of	of	ADP
ejpam-3096	5	8	anbar	anbar	NOUN
ejpam-3096	5	9	,	,	PUNCT
ejpam-3096	5	10	college	college	NOUN
ejpam-3096	5	11	of	of	ADP
ejpam-3096	5	12	education	education	NOUN
ejpam-3096	5	13	for	for	ADP
ejpam-3096	5	14	pure	pure	ADJ
ejpam-3096	5	15	sciences	science	NOUN
ejpam-3096	5	16	,	,	PUNCT
ejpam-3096	5	17	iraq	iraq	PROPN
ejpam-3096	5	18	abstract	abstract	NOUN
ejpam-3096	5	19	.	.	PUNCT
ejpam-3096	6	1	in	in	ADP
ejpam-3096	6	2	the	the	DET
ejpam-3096	6	3	present	present	ADJ
ejpam-3096	6	4	paper	paper	NOUN
ejpam-3096	6	5	,	,	PUNCT
ejpam-3096	6	6	several	several	ADJ
ejpam-3096	6	7	coincidence	coincidence	NOUN
ejpam-3096	6	8	fixed	fix	VERB
ejpam-3096	6	9	point	point	NOUN
ejpam-3096	6	10	theorems	theorem	NOUN
ejpam-3096	6	11	established	establish	VERB
ejpam-3096	6	12	for	for	ADP
ejpam-3096	6	13	mappings	mapping	NOUN
ejpam-3096	6	14	satisfying	satisfy	VERB
ejpam-3096	6	15	contractive	contractive	ADJ
ejpam-3096	6	16	conditions	condition	NOUN
ejpam-3096	6	17	related	relate	VERB
ejpam-3096	6	18	to	to	ADP
ejpam-3096	6	19	a	a	DET
ejpam-3096	6	20	non	non	ADJ
ejpam-3096	6	21	-	-	ADJ
ejpam-3096	6	22	decreasing	decrease	VERB
ejpam-3096	6	23	φ	φ	NOUN
ejpam-3096	6	24	-	-	NOUN
ejpam-3096	6	25	maps	map	NOUN
ejpam-3096	6	26	in	in	ADP
ejpam-3096	6	27	partially	partially	ADV
ejpam-3096	6	28	ordered	order	VERB
ejpam-3096	6	29	complete	complete	ADJ
ejpam-3096	6	30	generalized	generalized	ADJ
ejpam-3096	6	31	d∗-metric	d∗-metric	ADJ
ejpam-3096	6	32	spaces	space	NOUN
ejpam-3096	6	33	where	where	SCONJ
ejpam-3096	6	34	the	the	DET
ejpam-3096	6	35	cone	cone	NOUN
ejpam-3096	6	36	is	be	AUX
ejpam-3096	6	37	not	not	PART
ejpam-3096	6	38	necessarily	necessarily	ADV
ejpam-3096	6	39	normal	normal	ADJ
ejpam-3096	6	40	which	which	PRON
ejpam-3096	6	41	is	be	AUX
ejpam-3096	6	42	the	the	DET
ejpam-3096	6	43	main	main	ADJ
ejpam-3096	6	44	result	result	NOUN
ejpam-3096	6	45	of	of	ADP
ejpam-3096	6	46	our	our	PRON
ejpam-3096	6	47	article	article	NOUN
ejpam-3096	6	48	.	.	PUNCT
ejpam-3096	7	1	2010	2010	NUM
ejpam-3096	7	2	mathematics	mathematic	NOUN
ejpam-3096	7	3	subject	subject	NOUN
ejpam-3096	7	4	classifications	classification	NOUN
ejpam-3096	7	5	:	:	PUNCT
ejpam-3096	7	6	primary	primary	ADJ
ejpam-3096	7	7	47h10	47h10	NOUN
ejpam-3096	7	8	;	;	PUNCT
ejpam-3096	7	9	secondary	secondary	ADJ
ejpam-3096	7	10	54h25	54h25	NUM
ejpam-3096	7	11	key	key	ADJ
ejpam-3096	7	12	words	word	NOUN
ejpam-3096	7	13	and	and	CCONJ
ejpam-3096	7	14	phrases	phrase	NOUN
ejpam-3096	7	15	:	:	PUNCT
ejpam-3096	7	16	coincidence	coincidence	NOUN
ejpam-3096	7	17	point	point	NOUN
ejpam-3096	7	18	(	(	PUNCT
ejpam-3096	7	19	c.p	c.p	PROPN
ejpam-3096	7	20	)	)	PUNCT
ejpam-3096	7	21	,	,	PUNCT
ejpam-3096	7	22	d∗-metric	d∗-metric	ADJ
ejpam-3096	7	23	spaces	space	NOUN
ejpam-3096	7	24	,	,	PUNCT
ejpam-3096	7	25	generalized	generalized	ADJ
ejpam-3096	7	26	d∗-metric	d∗-metric	ADJ
ejpam-3096	7	27	spaces	space	NOUN
ejpam-3096	7	28	1	1	NUM
ejpam-3096	7	29	.	.	X
ejpam-3096	7	30	introduction	introduction	NOUN
ejpam-3096	7	31	the	the	DET
ejpam-3096	7	32	fixed	fix	VERB
ejpam-3096	7	33	point	point	NOUN
ejpam-3096	7	34	theorems	theorem	NOUN
ejpam-3096	7	35	in	in	ADP
ejpam-3096	7	36	metric	metric	ADJ
ejpam-3096	7	37	spaces	space	NOUN
ejpam-3096	7	38	are	be	AUX
ejpam-3096	7	39	playing	play	VERB
ejpam-3096	7	40	a	a	DET
ejpam-3096	7	41	fundamental	fundamental	ADJ
ejpam-3096	7	42	role	role	NOUN
ejpam-3096	7	43	to	to	PART
ejpam-3096	7	44	construct	construct	VERB
ejpam-3096	7	45	methods	method	NOUN
ejpam-3096	7	46	in	in	ADP
ejpam-3096	7	47	mathematical	mathematical	ADJ
ejpam-3096	7	48	sciences	science	NOUN
ejpam-3096	7	49	.	.	PUNCT
ejpam-3096	8	1	so	so	ADV
ejpam-3096	8	2	the	the	DET
ejpam-3096	8	3	metric	metric	ADJ
ejpam-3096	8	4	fixed	fix	VERB
ejpam-3096	8	5	point	point	NOUN
ejpam-3096	8	6	theorems	theorem	NOUN
ejpam-3096	8	7	(	(	PUNCT
ejpam-3096	8	8	f.p.ths	f.p.th	NOUN
ejpam-3096	8	9	.	.	PUNCT
ejpam-3096	8	10	)	)	PUNCT
ejpam-3096	8	11	has	have	AUX
ejpam-3096	8	12	been	be	AUX
ejpam-3096	8	13	researched	research	VERB
ejpam-3096	8	14	extensively	extensively	ADV
ejpam-3096	8	15	in	in	ADP
ejpam-3096	8	16	the	the	DET
ejpam-3096	8	17	past	past	ADJ
ejpam-3096	8	18	two	two	NUM
ejpam-3096	8	19	decades	decade	NOUN
ejpam-3096	8	20	.	.	PUNCT
ejpam-3096	9	1	the	the	DET
ejpam-3096	9	2	concept	concept	NOUN
ejpam-3096	9	3	of	of	ADP
ejpam-3096	9	4	cone	cone	NOUN
ejpam-3096	9	5	metric	metric	ADJ
ejpam-3096	9	6	spaces	space	NOUN
ejpam-3096	9	7	is	be	AUX
ejpam-3096	9	8	a	a	DET
ejpam-3096	9	9	generalization	generalization	NOUN
ejpam-3096	9	10	of	of	ADP
ejpam-3096	9	11	metric	metric	ADJ
ejpam-3096	9	12	spaces	space	NOUN
ejpam-3096	9	13	(	(	PUNCT
ejpam-3096	9	14	m.sps	m.sp	NOUN
ejpam-3096	9	15	)	)	PUNCT
ejpam-3096	9	16	.	.	PUNCT
ejpam-3096	10	1	the	the	DET
ejpam-3096	10	2	banach	banach	ADV
ejpam-3096	10	3	fixed	fix	VERB
ejpam-3096	10	4	point	point	NOUN
ejpam-3096	10	5	theorems	theorem	NOUN
ejpam-3096	10	6	[	[	X
ejpam-3096	10	7	5	5	NUM
ejpam-3096	10	8	]	]	PUNCT
ejpam-3096	10	9	provides	provide	VERB
ejpam-3096	10	10	a	a	DET
ejpam-3096	10	11	technique	technique	NOUN
ejpam-3096	10	12	for	for	ADP
ejpam-3096	10	13	solving	solve	VERB
ejpam-3096	10	14	variety	variety	NOUN
ejpam-3096	10	15	problems	problem	NOUN
ejpam-3096	10	16	in	in	ADP
ejpam-3096	10	17	mathematical	mathematical	ADJ
ejpam-3096	10	18	science	science	NOUN
ejpam-3096	10	19	and	and	CCONJ
ejpam-3096	10	20	engineering	engineering	NOUN
ejpam-3096	10	21	.	.	PUNCT
ejpam-3096	11	1	in	in	ADP
ejpam-3096	11	2	the	the	DET
ejpam-3096	11	3	literature	literature	NOUN
ejpam-3096	11	4	there	there	PRON
ejpam-3096	11	5	are	be	VERB
ejpam-3096	11	6	several	several	ADJ
ejpam-3096	11	7	generalizations	generalization	NOUN
ejpam-3096	11	8	of	of	ADP
ejpam-3096	11	9	the	the	DET
ejpam-3096	11	10	banach	banach	NOUN
ejpam-3096	11	11	’s	’s	PART
ejpam-3096	11	12	contraction	contraction	NOUN
ejpam-3096	11	13	principle	principle	NOUN
ejpam-3096	11	14	,	,	PUNCT
ejpam-3096	11	15	for	for	ADP
ejpam-3096	11	16	some	some	PRON
ejpam-3096	11	17	of	of	ADP
ejpam-3096	11	18	these	these	DET
ejpam-3096	11	19	generalizations	generalization	NOUN
ejpam-3096	11	20	of	of	ADP
ejpam-3096	11	21	the	the	DET
ejpam-3096	11	22	banach	banach	NOUN
ejpam-3096	11	23	’s	’s	PART
ejpam-3096	11	24	fixed	fix	VERB
ejpam-3096	11	25	point	point	NOUN
ejpam-3096	11	26	theorems	theorem	NOUN
ejpam-3096	11	27	and	and	CCONJ
ejpam-3096	11	28	various	various	ADJ
ejpam-3096	11	29	contractive	contractive	ADJ
ejpam-3096	11	30	definitions	definition	NOUN
ejpam-3096	11	31	that	that	PRON
ejpam-3096	11	32	have	have	AUX
ejpam-3096	11	33	been	be	AUX
ejpam-3096	11	34	employed	employ	VERB
ejpam-3096	11	35	;	;	PUNCT
ejpam-3096	11	36	we	we	PRON
ejpam-3096	11	37	refer	refer	VERB
ejpam-3096	11	38	the	the	DET
ejpam-3096	11	39	readers	reader	NOUN
ejpam-3096	11	40	to	to	ADP
ejpam-3096	11	41	[	[	PUNCT
ejpam-3096	11	42	1,6	1,6	NUM
ejpam-3096	11	43	-	-	PUNCT
ejpam-3096	11	44	8,11	8,11	NUM
ejpam-3096	11	45	-	-	NUM
ejpam-3096	11	46	14,17,21	14,17,21	NUM
ejpam-3096	11	47	]	]	PUNCT
ejpam-3096	11	48	,	,	PUNCT
ejpam-3096	11	49	and	and	CCONJ
ejpam-3096	11	50	other	other	ADJ
ejpam-3096	11	51	references	reference	NOUN
ejpam-3096	11	52	listed	list	VERB
ejpam-3096	11	53	in	in	ADP
ejpam-3096	11	54	the	the	DET
ejpam-3096	11	55	reference	reference	NOUN
ejpam-3096	11	56	section	section	NOUN
ejpam-3096	11	57	of	of	ADP
ejpam-3096	11	58	this	this	DET
ejpam-3096	11	59	article	article	NOUN
ejpam-3096	11	60	.	.	PUNCT
ejpam-3096	12	1	recently,(f.p.th	recently,(f.p.th	PROPN
ejpam-3096	12	2	.	.	PUNCT
ejpam-3096	12	3	)	)	PUNCT
ejpam-3096	12	4	has	have	AUX
ejpam-3096	12	5	developed	develop	VERB
ejpam-3096	12	6	rapidly	rapidly	ADV
ejpam-3096	12	7	in	in	ADP
ejpam-3096	12	8	partially	partially	ADV
ejpam-3096	12	9	ordered	order	VERB
ejpam-3096	12	10	metric	metric	ADJ
ejpam-3096	12	11	spaces	space	NOUN
ejpam-3096	12	12	such	such	ADJ
ejpam-3096	12	13	as	as	ADP
ejpam-3096	12	14	[	[	X
ejpam-3096	12	15	17	17	NUM
ejpam-3096	12	16	,	,	PUNCT
ejpam-3096	12	17	18	18	NUM
ejpam-3096	12	18	]	]	PUNCT
ejpam-3096	12	19	,	,	PUNCT
ejpam-3096	12	20	ran	run	VERB
ejpam-3096	12	21	and	and	CCONJ
ejpam-3096	12	22	reurings	reuring	NOUN
ejpam-3096	13	1	[	[	X
ejpam-3096	13	2	23	23	NUM
ejpam-3096	13	3	]	]	PUNCT
ejpam-3096	13	4	and	and	CCONJ
ejpam-3096	13	5	[	[	X
ejpam-3096	13	6	22	22	NUM
ejpam-3096	13	7	]	]	PUNCT
ejpam-3096	13	8	studied	study	VERB
ejpam-3096	13	9	several	several	ADJ
ejpam-3096	13	10	new	new	ADJ
ejpam-3096	13	11	facts	fact	NOUN
ejpam-3096	13	12	for	for	ADP
ejpam-3096	13	13	contractions	contraction	NOUN
ejpam-3096	13	14	in	in	ADP
ejpam-3096	13	15	partially	partially	ADV
ejpam-3096	13	16	ordered	order	VERB
ejpam-3096	13	17	metric	metric	ADJ
ejpam-3096	13	18	spaces	space	NOUN
ejpam-3096	13	19	.	.	PUNCT
ejpam-3096	14	1	the	the	DET
ejpam-3096	14	2	authors	author	NOUN
ejpam-3096	14	3	in	in	ADP
ejpam-3096	14	4	[	[	X
ejpam-3096	14	5	15	15	NUM
ejpam-3096	14	6	]	]	X
ejpam-3096	14	7	generalized	generalize	VERB
ejpam-3096	14	8	the	the	DET
ejpam-3096	14	9	conception	conception	NOUN
ejpam-3096	14	10	of	of	ADP
ejpam-3096	14	11	(	(	PUNCT
ejpam-3096	14	12	m.sps	m.sp	NOUN
ejpam-3096	14	13	)	)	PUNCT
ejpam-3096	14	14	,	,	PUNCT
ejpam-3096	14	15	substitute	substitute	VERB
ejpam-3096	14	16	the	the	DET
ejpam-3096	14	17	r	r	NOUN
ejpam-3096	14	18	by	by	ADP
ejpam-3096	14	19	an	an	DET
ejpam-3096	14	20	ordered	order	VERB
ejpam-3096	14	21	banach	banach	NOUN
ejpam-3096	14	22	spaces	space	NOUN
ejpam-3096	14	23	(	(	PUNCT
ejpam-3096	14	24	b.s	b.s	NOUN
ejpam-3096	14	25	)	)	PUNCT
ejpam-3096	14	26	and	and	CCONJ
ejpam-3096	14	27	defined	define	VERB
ejpam-3096	14	28	cone	cone	NOUN
ejpam-3096	14	29	-	-	PUNCT
ejpam-3096	14	30	metric	metric	ADJ
ejpam-3096	14	31	spaces	space	NOUN
ejpam-3096	14	32	.	.	PUNCT
ejpam-3096	15	1	b.c.dhage	b.c.dhage	NOUN
ejpam-3096	15	2	,	,	PUNCT
ejpam-3096	15	3	[	[	X
ejpam-3096	15	4	9	9	NUM
ejpam-3096	15	5	]	]	PUNCT
ejpam-3096	15	6	in	in	ADP
ejpam-3096	15	7	1992	1992	NUM
ejpam-3096	15	8	,	,	PUNCT
ejpam-3096	15	9	defined	define	VERB
ejpam-3096	15	10	d	d	ADJ
ejpam-3096	15	11	-	-	ADJ
ejpam-3096	15	12	metric	metric	ADJ
ejpam-3096	15	13	spaces	space	NOUN
ejpam-3096	15	14	as	as	ADP
ejpam-3096	15	15	a	a	DET
ejpam-3096	15	16	generalization	generalization	NOUN
ejpam-3096	15	17	of	of	ADP
ejpam-3096	15	18	(	(	PUNCT
ejpam-3096	15	19	m.sps	m.sp	NOUN
ejpam-3096	15	20	)	)	PUNCT
ejpam-3096	15	21	and	and	CCONJ
ejpam-3096	15	22	he	he	PRON
ejpam-3096	15	23	proved	prove	VERB
ejpam-3096	15	24	the	the	DET
ejpam-3096	15	25	existence	existence	NOUN
ejpam-3096	15	26	of	of	ADP
ejpam-3096	15	27	unique	unique	ADJ
ejpam-3096	15	28	fixed	fix	VERB
ejpam-3096	15	29	point	point	NOUN
ejpam-3096	15	30	of	of	ADP
ejpam-3096	15	31	a	a	DET
ejpam-3096	15	32	self	self	NOUN
ejpam-3096	15	33	-	-	PUNCT
ejpam-3096	15	34	map	map	NOUN
ejpam-3096	15	35	satisfying	satisfy	VERB
ejpam-3096	15	36	a	a	DET
ejpam-3096	15	37	contractive	contractive	ADJ
ejpam-3096	15	38	condition	condition	NOUN
ejpam-3096	15	39	in	in	ADP
ejpam-3096	15	40	complete	complete	ADJ
ejpam-3096	15	41	and	and	CCONJ
ejpam-3096	15	42	bounded	bound	VERB
ejpam-3096	15	43	d	d	X
ejpam-3096	15	44	-	-	ADJ
ejpam-3096	15	45	metric	metric	ADJ
ejpam-3096	15	46	spaces	space	NOUN
ejpam-3096	15	47	.	.	PUNCT
ejpam-3096	16	1	in	in	ADP
ejpam-3096	16	2	2007	2007	NUM
ejpam-3096	16	3	,	,	PUNCT
ejpam-3096	16	4	s.	s.	PROPN
ejpam-3096	16	5	shaban	shaban	PROPN
ejpam-3096	16	6	,	,	PUNCT
ejpam-3096	16	7	etal	etal	NOUN
ejpam-3096	16	8	[	[	X
ejpam-3096	16	9	24	24	NUM
ejpam-3096	16	10	]	]	PUNCT
ejpam-3096	16	11	have	have	AUX
ejpam-3096	16	12	been	be	AUX
ejpam-3096	16	13	established	establish	VERB
ejpam-3096	16	14	the	the	DET
ejpam-3096	16	15	meaning	meaning	NOUN
ejpam-3096	16	16	of	of	ADP
ejpam-3096	16	17	d∗-metric	d∗-metric	ADJ
ejpam-3096	16	18	spaces	space	NOUN
ejpam-3096	16	19	which	which	PRON
ejpam-3096	16	20	as	as	ADP
ejpam-3096	16	21	a	a	DET
ejpam-3096	16	22	probable	probable	ADJ
ejpam-3096	16	23	modification	modification	NOUN
ejpam-3096	16	24	of	of	ADP
ejpam-3096	16	25	the	the	DET
ejpam-3096	16	26	definition	definition	NOUN
ejpam-3096	16	27	of	of	ADP
ejpam-3096	16	28	(	(	PUNCT
ejpam-3096	16	29	d	d	NOUN
ejpam-3096	16	30	-	-	ADJ
ejpam-3096	16	31	metric	metric	ADJ
ejpam-3096	16	32	)	)	PUNCT
ejpam-3096	16	33	established	establish	VERB
ejpam-3096	16	34	via	via	ADP
ejpam-3096	16	35	the	the	DET
ejpam-3096	16	36	author	author	NOUN
ejpam-3096	16	37	in	in	ADP
ejpam-3096	16	38	[	[	X
ejpam-3096	16	39	9	9	NUM
ejpam-3096	16	40	]	]	PUNCT
ejpam-3096	16	41	,	,	PUNCT
ejpam-3096	16	42	and	and	CCONJ
ejpam-3096	16	43	proved	prove	VERB
ejpam-3096	16	44	several	several	ADJ
ejpam-3096	16	45	basic	basic	ADJ
ejpam-3096	16	46	properties	property	NOUN
ejpam-3096	16	47	in	in	ADP
ejpam-3096	16	48	email	email	NOUN
ejpam-3096	16	49	addresses	address	NOUN
ejpam-3096	16	50	:	:	PUNCT
ejpam-3096	16	51	alaa−mf1970@yahoo.com	alaa−mf1970@yahoo.com	X
ejpam-3096	16	52	(	(	PUNCT
ejpam-3096	16	53	alaa	alaa	PROPN
ejpam-3096	16	54	.	.	PUNCT
ejpam-3096	17	1	m.	m.	PROPN
ejpam-3096	17	2	f.	f.	PROPN
ejpam-3096	17	3	al	al	PROPN
ejpam-3096	17	4	.	.	PROPN
ejpam-3096	17	5	jumaili	jumaili	PROPN
ejpam-3096	17	6	)	)	PUNCT
ejpam-3096	17	7	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3096	18	1	1023	1023	NUM
ejpam-3096	18	2	c	c	X
ejpam-3096	18	3	©	©	PROPN
ejpam-3096	18	4	2017	2017	NUM
ejpam-3096	18	5	ejpam	ejpam	VERB
ejpam-3096	18	6	all	all	DET
ejpam-3096	18	7	rights	right	NOUN
ejpam-3096	18	8	reserved	reserve	VERB
ejpam-3096	18	9	.	.	PUNCT
ejpam-3096	19	1	a.	a.	PROPN
ejpam-3096	19	2	m.	m.	PROPN
ejpam-3096	19	3	al	al	PROPN
ejpam-3096	19	4	.	.	PROPN
ejpam-3096	19	5	jumaili	jumaili	PROPN
ejpam-3096	19	6	/	/	SYM
ejpam-3096	19	7	eur	eur	PROPN
ejpam-3096	19	8	.	.	PUNCT
ejpam-3096	20	1	j.	j.	PROPN
ejpam-3096	20	2	pure	pure	PROPN
ejpam-3096	20	3	appl	appl	PROPN
ejpam-3096	20	4	.	.	PROPN
ejpam-3096	20	5	math	math	PROPN
ejpam-3096	20	6	,	,	PUNCT
ejpam-3096	20	7	10	10	NUM
ejpam-3096	20	8	(	(	PUNCT
ejpam-3096	20	9	5	5	NUM
ejpam-3096	20	10	)	)	PUNCT
ejpam-3096	20	11	(	(	PUNCT
ejpam-3096	20	12	2017	2017	NUM
ejpam-3096	20	13	)	)	PUNCT
ejpam-3096	20	14	,	,	PUNCT
ejpam-3096	20	15	1023	1023	NUM
ejpam-3096	20	16	-	-	SYM
ejpam-3096	20	17	1034	1034	NUM
ejpam-3096	20	18	1024	1024	NUM
ejpam-3096	20	19	d∗-metric	d∗-metric	ADJ
ejpam-3096	20	20	spaces	space	NOUN
ejpam-3096	20	21	.	.	PUNCT
ejpam-3096	21	1	afterwards	afterwards	ADV
ejpam-3096	21	2	,	,	PUNCT
ejpam-3096	21	3	many	many	ADJ
ejpam-3096	21	4	authors	author	NOUN
ejpam-3096	21	5	[	[	X
ejpam-3096	21	6	25,26,16	25,26,16	NUM
ejpam-3096	21	7	]	]	PUNCT
ejpam-3096	21	8	proved	prove	VERB
ejpam-3096	21	9	several	several	ADJ
ejpam-3096	21	10	(	(	PUNCT
ejpam-3096	21	11	f.p.ths	f.p.th	NOUN
ejpam-3096	21	12	.	.	PUNCT
ejpam-3096	21	13	)	)	PUNCT
ejpam-3096	22	1	in	in	ADP
ejpam-3096	22	2	these	these	DET
ejpam-3096	22	3	spaces	space	NOUN
ejpam-3096	22	4	.	.	PUNCT
ejpam-3096	23	1	fixed	fix	VERB
ejpam-3096	23	2	point	point	NOUN
ejpam-3096	23	3	problems	problem	NOUN
ejpam-3096	23	4	have	have	AUX
ejpam-3096	23	5	as	as	ADV
ejpam-3096	23	6	well	well	ADV
ejpam-3096	23	7	been	be	AUX
ejpam-3096	23	8	considered	consider	VERB
ejpam-3096	23	9	partially	partially	ADV
ejpam-3096	23	10	ordered	order	VERB
ejpam-3096	23	11	d∗-m.sps	d∗-m.sp	NOUN
ejpam-3096	23	12	,	,	PUNCT
ejpam-3096	23	13	in	in	ADP
ejpam-3096	23	14	[	[	X
ejpam-3096	23	15	4	4	NUM
ejpam-3096	23	16	]	]	X
ejpam-3096	23	17	alaa.m	alaa.m	PROPN
ejpam-3096	23	18	.	.	PUNCT
ejpam-3096	24	1	al	al	PROPN
ejpam-3096	24	2	.	.	PROPN
ejpam-3096	24	3	jumaili	jumaili	PROPN
ejpam-3096	24	4	and	and	CCONJ
ejpam-3096	24	5	xiao	xiao	PROPN
ejpam-3096	24	6	-	-	PUNCT
ejpam-3096	24	7	song	song	PROPN
ejpam-3096	24	8	yang	yang	PROPN
ejpam-3096	24	9	,	,	PUNCT
ejpam-3096	24	10	they	they	PRON
ejpam-3096	24	11	used	use	VERB
ejpam-3096	24	12	the	the	DET
ejpam-3096	24	13	meaning	meaning	NOUN
ejpam-3096	24	14	of	of	ADP
ejpam-3096	24	15	d∗-metric	d∗-metric	ADJ
ejpam-3096	24	16	spaces	space	NOUN
ejpam-3096	24	17	presented	present	VERB
ejpam-3096	24	18	a	a	DET
ejpam-3096	24	19	new	new	ADJ
ejpam-3096	24	20	notion	notion	NOUN
ejpam-3096	24	21	of	of	ADP
ejpam-3096	24	22	the	the	DET
ejpam-3096	24	23	∇∗-distance	∇∗-distance	NOUN
ejpam-3096	24	24	on	on	ADP
ejpam-3096	24	25	a	a	DET
ejpam-3096	24	26	complete	complete	ADJ
ejpam-3096	24	27	d∗-metric	d∗-metric	ADJ
ejpam-3096	24	28	spaces	space	NOUN
ejpam-3096	24	29	and	and	CCONJ
ejpam-3096	24	30	established	establish	VERB
ejpam-3096	24	31	several	several	ADJ
ejpam-3096	24	32	(	(	PUNCT
ejpam-3096	24	33	f.p.ths	f.p.th	NOUN
ejpam-3096	24	34	.	.	PUNCT
ejpam-3096	24	35	)	)	PUNCT
ejpam-3096	25	1	in	in	ADP
ejpam-3096	25	2	partially	partially	ADV
ejpam-3096	25	3	ordered	order	VERB
ejpam-3096	25	4	d∗-metric	d∗-metric	ADJ
ejpam-3096	25	5	spaces	space	NOUN
ejpam-3096	25	6	.	.	PUNCT
ejpam-3096	26	1	recently	recently	ADV
ejpam-3096	26	2	,	,	PUNCT
ejpam-3096	26	3	the	the	DET
ejpam-3096	26	4	authors	author	NOUN
ejpam-3096	26	5	in	in	ADP
ejpam-3096	26	6	[	[	X
ejpam-3096	26	7	2	2	NUM
ejpam-3096	26	8	]	]	PUNCT
ejpam-3096	26	9	extension	extension	NOUN
ejpam-3096	26	10	the	the	DET
ejpam-3096	26	11	concept	concept	NOUN
ejpam-3096	26	12	of	of	ADP
ejpam-3096	26	13	d∗-metric	d∗-metric	ADJ
ejpam-3096	26	14	spaces	space	NOUN
ejpam-3096	26	15	by	by	ADP
ejpam-3096	26	16	changing	change	VERB
ejpam-3096	26	17	r	r	NOUN
ejpam-3096	26	18	by	by	ADP
ejpam-3096	26	19	a	a	DET
ejpam-3096	26	20	real-(b.s	real-(b.	NOUN
ejpam-3096	26	21	)	)	PUNCT
ejpam-3096	26	22	in	in	ADP
ejpam-3096	26	23	d∗-metric	d∗-metric	ADJ
ejpam-3096	26	24	spaces	space	NOUN
ejpam-3096	26	25	,	,	PUNCT
ejpam-3096	26	26	they	they	PRON
ejpam-3096	26	27	established	establish	VERB
ejpam-3096	26	28	several	several	ADJ
ejpam-3096	26	29	(	(	PUNCT
ejpam-3096	26	30	f.p.th	f.p.th	PROPN
ejpam-3096	26	31	.	.	PUNCT
ejpam-3096	26	32	)	)	PUNCT
ejpam-3096	26	33	under	under	ADP
ejpam-3096	26	34	certain	certain	ADJ
ejpam-3096	26	35	contractive	contractive	ADJ
ejpam-3096	26	36	conditions	condition	NOUN
ejpam-3096	26	37	.	.	PUNCT
ejpam-3096	27	1	the	the	DET
ejpam-3096	27	2	motivation	motivation	NOUN
ejpam-3096	27	3	of	of	ADP
ejpam-3096	27	4	this	this	DET
ejpam-3096	27	5	article	article	NOUN
ejpam-3096	27	6	is	be	AUX
ejpam-3096	27	7	to	to	PART
ejpam-3096	27	8	study	study	VERB
ejpam-3096	27	9	several	several	ADJ
ejpam-3096	27	10	coincidence	coincidence	NOUN
ejpam-3096	27	11	(	(	PUNCT
ejpam-3096	27	12	f.p.ths	f.p.th	NOUN
ejpam-3096	27	13	.	.	PUNCT
ejpam-3096	27	14	)	)	PUNCT
ejpam-3096	28	1	for	for	ADP
ejpam-3096	28	2	functions	function	NOUN
ejpam-3096	28	3	satisfying	satisfy	VERB
ejpam-3096	28	4	contractive	contractive	ADJ
ejpam-3096	28	5	conditions	condition	NOUN
ejpam-3096	28	6	concerning	concern	VERB
ejpam-3096	28	7	to	to	ADP
ejpam-3096	28	8	a	a	DET
ejpam-3096	28	9	non	non	ADJ
ejpam-3096	28	10	-	-	ADJ
ejpam-3096	28	11	decreasing	decrease	VERB
ejpam-3096	28	12	φ	φ	NOUN
ejpam-3096	28	13	-	-	NOUN
ejpam-3096	28	14	maps	map	NOUN
ejpam-3096	28	15	[	[	X
ejpam-3096	28	16	3,10	3,10	X
ejpam-3096	28	17	]	]	PUNCT
ejpam-3096	28	18	partially	partially	ADV
ejpam-3096	28	19	ordered	order	VERB
ejpam-3096	28	20	complete	complete	ADJ
ejpam-3096	28	21	generalized	generalized	ADJ
ejpam-3096	28	22	d∗-m.sps	d∗-m.sp	NOUN
ejpam-3096	28	23	,	,	PUNCT
ejpam-3096	28	24	where	where	SCONJ
ejpam-3096	28	25	the	the	DET
ejpam-3096	28	26	cone	cone	NOUN
ejpam-3096	28	27	is	be	AUX
ejpam-3096	28	28	not	not	PART
ejpam-3096	28	29	necessarily	necessarily	ADV
ejpam-3096	28	30	normal	normal	ADJ
ejpam-3096	28	31	.	.	PUNCT
ejpam-3096	29	1	2	2	X
ejpam-3096	29	2	.	.	X
ejpam-3096	29	3	preliminaries	preliminary	NOUN
ejpam-3096	29	4	assume	assume	VERB
ejpam-3096	29	5	e	e	NOUN
ejpam-3096	29	6	is	be	AUX
ejpam-3096	29	7	real-(b.s	real-(b.	NOUN
ejpam-3096	29	8	)	)	PUNCT
ejpam-3096	29	9	and	and	CCONJ
ejpam-3096	29	10	p	p	NOUN
ejpam-3096	29	11	is	be	AUX
ejpam-3096	29	12	proper	proper	ADJ
ejpam-3096	29	13	sub	sub	NOUN
ejpam-3096	29	14	set	set	NOUN
ejpam-3096	29	15	of	of	ADP
ejpam-3096	29	16	e.	e.	PROPN
ejpam-3096	29	17	p	p	PROPN
ejpam-3096	29	18	is	be	AUX
ejpam-3096	29	19	called	call	VERB
ejpam-3096	29	20	an	an	DET
ejpam-3096	29	21	order	order	NOUN
ejpam-3096	29	22	cone	cone	NOUN
ejpam-3096	29	23	(	(	PUNCT
ejpam-3096	29	24	o.c	o.c	PROPN
ejpam-3096	29	25	)	)	PUNCT
ejpam-3096	29	26	if	if	SCONJ
ejpam-3096	29	27	:	:	PUNCT
ejpam-3096	29	28	a	a	X
ejpam-3096	29	29	)	)	PUNCT
ejpam-3096	29	30	p	p	NOUN
ejpam-3096	29	31	is	be	AUX
ejpam-3096	29	32	closed	closed	ADJ
ejpam-3096	29	33	,	,	PUNCT
ejpam-3096	29	34	p	p	PROPN
ejpam-3096	29	35	6=	6=	PROPN
ejpam-3096	29	36	φ	φ	PROPN
ejpam-3096	29	37	and	and	CCONJ
ejpam-3096	29	38	p	p	PROPN
ejpam-3096	29	39	6=	6=	PROPN
ejpam-3096	29	40	{	{	PUNCT
ejpam-3096	29	41	0	0	NUM
ejpam-3096	29	42	}	}	PUNCT
ejpam-3096	29	43	,	,	PUNCT
ejpam-3096	29	44	b	b	X
ejpam-3096	29	45	)	)	PUNCT
ejpam-3096	29	46	ax+	ax+	NOUN
ejpam-3096	29	47	by	by	ADP
ejpam-3096	29	48	∈	∈	PROPN
ejpam-3096	29	49	p	p	NOUN
ejpam-3096	29	50	∀	∀	NOUN
ejpam-3096	29	51	x	x	NOUN
ejpam-3096	29	52	,	,	PUNCT
ejpam-3096	29	53	y	y	PROPN
ejpam-3096	29	54	∈	∈	PROPN
ejpam-3096	29	55	p	p	PROPN
ejpam-3096	29	56	and	and	CCONJ
ejpam-3096	29	57	a	a	DET
ejpam-3096	29	58	,	,	PUNCT
ejpam-3096	29	59	b	b	PROPN
ejpam-3096	29	60	∈	∈	PROPN
ejpam-3096	29	61	r+	r+	NOUN
ejpam-3096	29	62	,	,	PUNCT
ejpam-3096	29	63	c	c	NOUN
ejpam-3096	29	64	)	)	PUNCT
ejpam-3096	29	65	x	x	SYM
ejpam-3096	29	66	∈	∈	PROPN
ejpam-3096	29	67	p	p	NOUN
ejpam-3096	29	68	and	and	CCONJ
ejpam-3096	29	69	−x	−x	NUM
ejpam-3096	29	70	∈	∈	PROPN
ejpam-3096	29	71	p	p	NOUN
ejpam-3096	29	72	implies	imply	VERB
ejpam-3096	29	73	x	x	PUNCT
ejpam-3096	29	74	=	=	SYM
ejpam-3096	29	75	0	0	NUM
ejpam-3096	29	76	.	.	PUNCT
ejpam-3096	30	1	for	for	ADP
ejpam-3096	30	2	an	an	DET
ejpam-3096	30	3	(	(	PUNCT
ejpam-3096	30	4	o.c	o.c	PROPN
ejpam-3096	30	5	)	)	PUNCT
ejpam-3096	30	6	p	p	NOUN
ejpam-3096	30	7	⊂	⊂	PROPN
ejpam-3096	30	8	e	e	NOUN
ejpam-3096	30	9	,	,	PUNCT
ejpam-3096	30	10	we	we	PRON
ejpam-3096	30	11	define	define	VERB
ejpam-3096	30	12	a	a	DET
ejpam-3096	30	13	partial	partial	ADJ
ejpam-3096	30	14	ordering	ordering	NOUN
ejpam-3096	30	15	4	4	NUM
ejpam-3096	30	16	on	on	ADP
ejpam-3096	30	17	e	e	NOUN
ejpam-3096	30	18	with	with	ADP
ejpam-3096	30	19	respect	respect	NOUN
ejpam-3096	30	20	to	to	ADP
ejpam-3096	30	21	p	p	NOUN
ejpam-3096	30	22	via	via	ADP
ejpam-3096	30	23	x	x	SYM
ejpam-3096	30	24	4	4	NUM
ejpam-3096	30	25	y	y	PROPN
ejpam-3096	30	26	iff	iff	NOUN
ejpam-3096	31	1	y	y	PROPN
ejpam-3096	31	2	−	−	PROPN
ejpam-3096	31	3	x	x	PUNCT
ejpam-3096	31	4	∈	∈	PROPN
ejpam-3096	31	5	p	p	NOUN
ejpam-3096	31	6	.	.	PUNCT
ejpam-3096	32	1	we	we	PRON
ejpam-3096	32	2	shall	shall	AUX
ejpam-3096	32	3	using	use	VERB
ejpam-3096	32	4	x	x	PUNCT
ejpam-3096	32	5	≺	≺	NOUN
ejpam-3096	32	6	y	y	PROPN
ejpam-3096	32	7	to	to	PART
ejpam-3096	32	8	indicate	indicate	VERB
ejpam-3096	32	9	that	that	SCONJ
ejpam-3096	32	10	x	x	PROPN
ejpam-3096	32	11	4	4	NUM
ejpam-3096	32	12	y	y	NOUN
ejpam-3096	32	13	but	but	CCONJ
ejpam-3096	32	14	x	x	SYM
ejpam-3096	32	15	6=	6=	NUM
ejpam-3096	32	16	y	y	PROPN
ejpam-3096	32	17	,	,	PUNCT
ejpam-3096	32	18	while	while	SCONJ
ejpam-3096	32	19	x	x	PROPN
ejpam-3096	32	20	�	�	PROPN
ejpam-3096	32	21	y	y	PROPN
ejpam-3096	32	22	for	for	ADP
ejpam-3096	32	23	y	y	PROPN
ejpam-3096	32	24	−	−	PROPN
ejpam-3096	32	25	x	x	SYM
ejpam-3096	32	26	∈	∈	PROPN
ejpam-3096	32	27	intp	intp	NOUN
ejpam-3096	32	28	,	,	PUNCT
ejpam-3096	32	29	where	where	SCONJ
ejpam-3096	32	30	intp	intp	NOUN
ejpam-3096	32	31	refer	refer	VERB
ejpam-3096	32	32	to	to	ADP
ejpam-3096	32	33	the	the	DET
ejpam-3096	32	34	interior	interior	NOUN
ejpam-3096	32	35	of	of	ADP
ejpam-3096	32	36	p.	p.	PROPN
ejpam-3096	32	37	the	the	DET
ejpam-3096	32	38	(	(	PUNCT
ejpam-3096	32	39	o.c	o.c	PROPN
ejpam-3096	32	40	)	)	PUNCT
ejpam-3096	32	41	p	p	NOUN
ejpam-3096	32	42	is	be	AUX
ejpam-3096	32	43	called	call	VERB
ejpam-3096	32	44	normal	normal	ADJ
ejpam-3096	32	45	if	if	SCONJ
ejpam-3096	32	46	∃	∃	PROPN
ejpam-3096	32	47	a	a	DET
ejpam-3096	32	48	number	number	NOUN
ejpam-3096	32	49	k	k	PROPN
ejpam-3096	32	50	>	>	X
ejpam-3096	32	51	0	0	PUNCT
ejpam-3096	33	1	(	(	PUNCT
ejpam-3096	33	2	s.t	s.t	PROPN
ejpam-3096	33	3	)	)	PUNCT
ejpam-3096	33	4	∀x	∀x	NUM
ejpam-3096	33	5	,	,	PUNCT
ejpam-3096	33	6	y	y	PROPN
ejpam-3096	33	7	∈	∈	PROPN
ejpam-3096	33	8	e	e	PROPN
ejpam-3096	33	9	,	,	PUNCT
ejpam-3096	33	10	0	0	NUM
ejpam-3096	33	11	≤	≤	NUM
ejpam-3096	33	12	x	x	X
ejpam-3096	33	13	≤	≤	NUM
ejpam-3096	33	14	y	y	PROPN
ejpam-3096	33	15	⇒	⇒	NOUN
ejpam-3096	33	16	,	,	PUNCT
ejpam-3096	33	17	‖x‖	‖x‖	PROPN
ejpam-3096	33	18	≤	≤	PROPN
ejpam-3096	33	19	k‖y‖	k‖y‖	PROPN
ejpam-3096	33	20	..................................	..................................	PUNCT
ejpam-3096	33	21	(	(	PUNCT
ejpam-3096	33	22	2.1	2.1	NUM
ejpam-3096	33	23	)	)	PUNCT
ejpam-3096	33	24	or	or	CCONJ
ejpam-3096	33	25	equivalently	equivalently	ADV
ejpam-3096	33	26	,	,	PUNCT
ejpam-3096	33	27	inf{‖x+	inf{‖x+	PROPN
ejpam-3096	33	28	y‖	y‖	NOUN
ejpam-3096	33	29	:	:	PUNCT
ejpam-3096	34	1	x	x	X
ejpam-3096	34	2	,	,	PUNCT
ejpam-3096	34	3	y	y	PROPN
ejpam-3096	34	4	∈	∈	PROPN
ejpam-3096	34	5	p	p	PROPN
ejpam-3096	34	6	and	and	CCONJ
ejpam-3096	34	7	‖x‖	‖x‖	PROPN
ejpam-3096	34	8	=	=	SYM
ejpam-3096	34	9	‖y‖	‖y‖	PROPN
ejpam-3096	34	10	=	=	NOUN
ejpam-3096	34	11	1	1	NUM
ejpam-3096	34	12	}	}	PUNCT
ejpam-3096	34	13	>	>	X
ejpam-3096	34	14	0	0	NUM
ejpam-3096	34	15	...................................	...................................	PUNCT
ejpam-3096	34	16	(	(	PUNCT
ejpam-3096	34	17	2.2	2.2	NUM
ejpam-3096	34	18	)	)	PUNCT
ejpam-3096	34	19	we	we	PRON
ejpam-3096	34	20	name	name	VERB
ejpam-3096	34	21	the	the	DET
ejpam-3096	34	22	positive	positive	ADJ
ejpam-3096	34	23	element	element	NOUN
ejpam-3096	34	24	k	k	PROPN
ejpam-3096	34	25	which	which	PRON
ejpam-3096	34	26	satisfying	satisfy	VERB
ejpam-3096	34	27	(	(	PUNCT
ejpam-3096	34	28	2.1	2.1	NUM
ejpam-3096	34	29	)	)	PUNCT
ejpam-3096	34	30	normal	normal	ADJ
ejpam-3096	34	31	constant	constant	NOUN
ejpam-3096	34	32	of	of	ADP
ejpam-3096	34	33	p.	p.	NOUN
ejpam-3096	34	34	from	from	ADP
ejpam-3096	34	35	(	(	PUNCT
ejpam-3096	34	36	2.2	2.2	NUM
ejpam-3096	34	37	)	)	PUNCT
ejpam-3096	34	38	we	we	PRON
ejpam-3096	34	39	can	can	AUX
ejpam-3096	34	40	deduce	deduce	VERB
ejpam-3096	34	41	that	that	SCONJ
ejpam-3096	34	42	p	p	NOUN
ejpam-3096	34	43	is	be	AUX
ejpam-3096	34	44	non	non	ADJ
ejpam-3096	34	45	-	-	ADJ
ejpam-3096	34	46	normal	normal	ADJ
ejpam-3096	34	47	iff	iff	PROPN
ejpam-3096	34	48	∃	∃	PROPN
ejpam-3096	34	49	sequences	sequences	PROPN
ejpam-3096	34	50	{	{	PUNCT
ejpam-3096	34	51	xs	xs	PROPN
ejpam-3096	34	52	}	}	PUNCT
ejpam-3096	34	53	,	,	PUNCT
ejpam-3096	34	54	{	{	PUNCT
ejpam-3096	34	55	ys	ys	NOUN
ejpam-3096	34	56	}	}	PUNCT
ejpam-3096	34	57	∈	∈	PROPN
ejpam-3096	34	58	p	p	X
ejpam-3096	34	59	(	(	PUNCT
ejpam-3096	34	60	s.t	s.t	PROPN
ejpam-3096	34	61	)	)	PUNCT
ejpam-3096	34	62	,	,	PUNCT
ejpam-3096	34	63	0	0	NUM
ejpam-3096	34	64	≤	≤	NUM
ejpam-3096	34	65	{	{	PUNCT
ejpam-3096	34	66	xs	xs	NOUN
ejpam-3096	34	67	}	}	PUNCT
ejpam-3096	34	68	≤	≤	NOUN
ejpam-3096	34	69	{	{	PUNCT
ejpam-3096	34	70	xs}+	xs}+	PROPN
ejpam-3096	34	71	{	{	PUNCT
ejpam-3096	34	72	ys	ys	NOUN
ejpam-3096	34	73	}	}	PUNCT
ejpam-3096	34	74	,	,	PUNCT
ejpam-3096	34	75	lims→∞({xs}+	lims→∞({xs}+	PROPN
ejpam-3096	34	76	{	{	PUNCT
ejpam-3096	34	77	ys	ys	NOUN
ejpam-3096	34	78	}	}	PUNCT
ejpam-3096	34	79	)	)	PUNCT
ejpam-3096	34	80	=	=	SYM
ejpam-3096	34	81	0	0	NUM
ejpam-3096	34	82	,	,	PUNCT
ejpam-3096	34	83	but	but	CCONJ
ejpam-3096	34	84	lims→∞{xs	lims→∞{xs	ADJ
ejpam-3096	34	85	}	}	PUNCT
ejpam-3096	34	86	6=	6=	ADP
ejpam-3096	34	87	0	0	NUM
ejpam-3096	34	88	.	.	PUNCT
ejpam-3096	35	1	in	in	ADP
ejpam-3096	35	2	this	this	DET
ejpam-3096	35	3	paper	paper	NOUN
ejpam-3096	35	4	,	,	PUNCT
ejpam-3096	35	5	e	e	PROPN
ejpam-3096	35	6	stands	stand	VERB
ejpam-3096	35	7	for	for	ADP
ejpam-3096	35	8	a	a	DET
ejpam-3096	35	9	real-(b.s	real-(b.	NOUN
ejpam-3096	35	10	)	)	PUNCT
ejpam-3096	35	11	,	,	PUNCT
ejpam-3096	35	12	p	p	PROPN
ejpam-3096	35	13	is	be	AUX
ejpam-3096	35	14	a	a	DET
ejpam-3096	35	15	cone	cone	NOUN
ejpam-3096	35	16	in	in	ADP
ejpam-3096	35	17	e	e	PROPN
ejpam-3096	35	18	with	with	ADP
ejpam-3096	35	19	intp	intp	PROPN
ejpam-3096	35	20	6=	6=	X
ejpam-3096	35	21	{	{	PUNCT
ejpam-3096	35	22	0	0	NUM
ejpam-3096	35	23	}	}	PUNCT
ejpam-3096	35	24	(	(	PUNCT
ejpam-3096	35	25	such	such	ADJ
ejpam-3096	35	26	cones	cone	NOUN
ejpam-3096	35	27	are	be	AUX
ejpam-3096	35	28	called	call	VERB
ejpam-3096	35	29	solid	solid	ADJ
ejpam-3096	35	30	)	)	PUNCT
ejpam-3096	35	31	and	and	CCONJ
ejpam-3096	35	32	4	4	NUM
ejpam-3096	35	33	is	be	AUX
ejpam-3096	35	34	a	a	DET
ejpam-3096	35	35	partial	partial	ADJ
ejpam-3096	35	36	-	-	PUNCT
ejpam-3096	35	37	ordering	order	VERB
ejpam-3096	35	38	(	(	PUNCT
ejpam-3096	35	39	p	p	NOUN
ejpam-3096	35	40	-	-	PUNCT
ejpam-3096	35	41	o	o	NOUN
ejpam-3096	35	42	)	)	PUNCT
ejpam-3096	35	43	with	with	ADP
ejpam-3096	35	44	respect	respect	NOUN
ejpam-3096	35	45	to	to	ADP
ejpam-3096	35	46	p	p	PRON
ejpam-3096	35	47	,	,	PUNCT
ejpam-3096	35	48	where	where	SCONJ
ejpam-3096	35	49	the	the	DET
ejpam-3096	35	50	cone	cone	NOUN
ejpam-3096	35	51	is	be	AUX
ejpam-3096	35	52	not	not	PART
ejpam-3096	35	53	necessarily	necessarily	ADV
ejpam-3096	35	54	normal	normal	ADJ
ejpam-3096	35	55	unless	unless	SCONJ
ejpam-3096	35	56	otherwise	otherwise	ADV
ejpam-3096	35	57	stated	state	VERB
ejpam-3096	35	58	.	.	PUNCT
ejpam-3096	36	1	now	now	ADV
ejpam-3096	36	2	,	,	PUNCT
ejpam-3096	36	3	recall	recall	VERB
ejpam-3096	36	4	several	several	ADJ
ejpam-3096	36	5	basic	basic	ADJ
ejpam-3096	36	6	definitions	definition	NOUN
ejpam-3096	36	7	and	and	CCONJ
ejpam-3096	36	8	results	result	NOUN
ejpam-3096	36	9	of	of	ADP
ejpam-3096	36	10	generalizedd∗-metric	generalizedd∗-metric	ADJ
ejpam-3096	36	11	spaces	space	NOUN
ejpam-3096	36	12	,	,	PUNCT
ejpam-3096	36	13	and	and	CCONJ
ejpam-3096	36	14	for	for	ADP
ejpam-3096	36	15	more	more	ADJ
ejpam-3096	36	16	details	detail	NOUN
ejpam-3096	36	17	on	on	ADP
ejpam-3096	36	18	d∗-metric	d∗-metric	ADJ
ejpam-3096	36	19	spaces	space	NOUN
ejpam-3096	36	20	and	and	CCONJ
ejpam-3096	36	21	generalized	generalized	ADJ
ejpam-3096	36	22	d∗-metric	d∗-metric	ADJ
ejpam-3096	36	23	spaces	space	NOUN
ejpam-3096	36	24	,	,	PUNCT
ejpam-3096	36	25	we	we	PRON
ejpam-3096	36	26	refer	refer	VERB
ejpam-3096	36	27	the	the	DET
ejpam-3096	36	28	authors	author	NOUN
ejpam-3096	36	29	for	for	ADP
ejpam-3096	36	30	review	review	NOUN
ejpam-3096	36	31	[	[	X
ejpam-3096	36	32	24	24	NUM
ejpam-3096	36	33	]	]	PUNCT
ejpam-3096	36	34	and	and	CCONJ
ejpam-3096	36	35	[	[	X
ejpam-3096	36	36	2	2	NUM
ejpam-3096	36	37	]	]	PUNCT
ejpam-3096	36	38	respectively	respectively	ADV
ejpam-3096	36	39	.	.	PUNCT
ejpam-3096	37	1	definition	definition	NOUN
ejpam-3096	37	2	1	1	NUM
ejpam-3096	37	3	.	.	PUNCT
ejpam-3096	38	1	[	[	X
ejpam-3096	38	2	2	2	X
ejpam-3096	38	3	]	]	PUNCT
ejpam-3096	38	4	let	let	VERB
ejpam-3096	38	5	x	x	PRON
ejpam-3096	38	6	be	be	AUX
ejpam-3096	38	7	a	a	DET
ejpam-3096	38	8	non	non	X
ejpam-3096	38	9	empty	empty	ADJ
ejpam-3096	38	10	set	set	NOUN
ejpam-3096	38	11	.	.	PUNCT
ejpam-3096	39	1	a	a	DET
ejpam-3096	39	2	generalized	generalize	VERB
ejpam-3096	39	3	d∗-m.sp	d∗-m.sp	X
ejpam-3096	39	4	on	on	ADP
ejpam-3096	39	5	a	a	DET
ejpam-3096	39	6	set	set	NOUN
ejpam-3096	39	7	x	x	PUNCT
ejpam-3096	39	8	is	be	AUX
ejpam-3096	39	9	a	a	DET
ejpam-3096	39	10	function	function	NOUN
ejpam-3096	39	11	,	,	PUNCT
ejpam-3096	39	12	d∗	d∗	PROPN
ejpam-3096	39	13	:	:	PUNCT
ejpam-3096	39	14	x	x	X
ejpam-3096	39	15	×x	×x	X
ejpam-3096	39	16	×x	×x	X
ejpam-3096	39	17	→	→	SYM
ejpam-3096	39	18	e	e	NOUN
ejpam-3096	39	19	,	,	PUNCT
ejpam-3096	39	20	that	that	PRON
ejpam-3096	39	21	satisfies	satisfy	VERB
ejpam-3096	39	22	the	the	DET
ejpam-3096	39	23	following	follow	VERB
ejpam-3096	39	24	conditions	condition	NOUN
ejpam-3096	39	25	∀x	∀x	NUM
ejpam-3096	39	26	,	,	PUNCT
ejpam-3096	39	27	y	y	PROPN
ejpam-3096	39	28	,	,	PUNCT
ejpam-3096	39	29	z	z	PROPN
ejpam-3096	39	30	,	,	PUNCT
ejpam-3096	39	31	a	a	DET
ejpam-3096	39	32	∈	∈	NOUN
ejpam-3096	39	33	x	x	NOUN
ejpam-3096	39	34	:	:	PUNCT
ejpam-3096	39	35	a.	a.	NOUN
ejpam-3096	39	36	d∗(x	d∗(x	PROPN
ejpam-3096	39	37	,	,	PUNCT
ejpam-3096	39	38	y	y	PROPN
ejpam-3096	39	39	,	,	PUNCT
ejpam-3096	39	40	z	z	NOUN
ejpam-3096	39	41	)	)	PUNCT
ejpam-3096	39	42	≥	≥	NOUN
ejpam-3096	39	43	0	0	NUM
ejpam-3096	39	44	,	,	PUNCT
ejpam-3096	39	45	a.	a.	PROPN
ejpam-3096	39	46	m.	m.	PROPN
ejpam-3096	40	1	al	al	PROPN
ejpam-3096	40	2	.	.	PROPN
ejpam-3096	40	3	jumaili	jumaili	PROPN
ejpam-3096	40	4	/	/	SYM
ejpam-3096	40	5	eur	eur	PROPN
ejpam-3096	40	6	.	.	PUNCT
ejpam-3096	41	1	j.	j.	PROPN
ejpam-3096	41	2	pure	pure	PROPN
ejpam-3096	41	3	appl	appl	PROPN
ejpam-3096	41	4	.	.	PROPN
ejpam-3096	41	5	math	math	PROPN
ejpam-3096	41	6	,	,	PUNCT
ejpam-3096	41	7	10	10	NUM
ejpam-3096	41	8	(	(	PUNCT
ejpam-3096	41	9	5	5	NUM
ejpam-3096	41	10	)	)	PUNCT
ejpam-3096	41	11	(	(	PUNCT
ejpam-3096	41	12	2017	2017	NUM
ejpam-3096	41	13	)	)	PUNCT
ejpam-3096	41	14	,	,	PUNCT
ejpam-3096	41	15	1023	1023	NUM
ejpam-3096	41	16	-	-	SYM
ejpam-3096	41	17	1034	1034	NUM
ejpam-3096	41	18	1025	1025	NUM
ejpam-3096	41	19	b.	b.	PROPN
ejpam-3096	41	20	d∗(x	d∗(x	PROPN
ejpam-3096	41	21	,	,	PUNCT
ejpam-3096	41	22	y	y	PROPN
ejpam-3096	41	23	,	,	PUNCT
ejpam-3096	41	24	z	z	NOUN
ejpam-3096	41	25	)	)	PUNCT
ejpam-3096	41	26	=	=	SYM
ejpam-3096	42	1	0	0	NUM
ejpam-3096	42	2	⇔	⇔	NOUN
ejpam-3096	42	3	x	x	X
ejpam-3096	42	4	=	=	PUNCT
ejpam-3096	42	5	y	y	PROPN
ejpam-3096	42	6	=	=	SYM
ejpam-3096	42	7	z	z	PROPN
ejpam-3096	42	8	,	,	PUNCT
ejpam-3096	42	9	c.	c.	PROPN
ejpam-3096	42	10	d∗(x	d∗(x	PROPN
ejpam-3096	42	11	,	,	PUNCT
ejpam-3096	42	12	y	y	PROPN
ejpam-3096	42	13	,	,	PUNCT
ejpam-3096	42	14	z	z	NOUN
ejpam-3096	42	15	)	)	PUNCT
ejpam-3096	42	16	=	=	PUNCT
ejpam-3096	42	17	d∗(p{x	d∗(p{x	PROPN
ejpam-3096	42	18	,	,	PUNCT
ejpam-3096	42	19	y	y	PROPN
ejpam-3096	42	20	,	,	PUNCT
ejpam-3096	42	21	z}),(symmetry	z}),(symmetry	PROPN
ejpam-3096	42	22	)	)	PUNCT
ejpam-3096	42	23	where	where	SCONJ
ejpam-3096	42	24	p	p	NOUN
ejpam-3096	42	25	is	be	AUX
ejpam-3096	42	26	a	a	DET
ejpam-3096	42	27	permutation	permutation	NOUN
ejpam-3096	42	28	function	function	NOUN
ejpam-3096	42	29	,	,	PUNCT
ejpam-3096	42	30	d.	d.	PROPN
ejpam-3096	42	31	d∗(x	d∗(x	PROPN
ejpam-3096	42	32	,	,	PUNCT
ejpam-3096	42	33	y	y	PROPN
ejpam-3096	42	34	,	,	PUNCT
ejpam-3096	42	35	z	z	NOUN
ejpam-3096	42	36	)	)	PUNCT
ejpam-3096	42	37	≤	≤	NOUN
ejpam-3096	43	1	d∗(x	d∗(x	PROPN
ejpam-3096	43	2	,	,	PUNCT
ejpam-3096	43	3	y	y	PROPN
ejpam-3096	43	4	,	,	PUNCT
ejpam-3096	43	5	a	a	PRON
ejpam-3096	43	6	)	)	PUNCT
ejpam-3096	43	7	+	+	ADJ
ejpam-3096	43	8	d∗(a	d∗(a	PROPN
ejpam-3096	43	9	,	,	PUNCT
ejpam-3096	43	10	z	z	NOUN
ejpam-3096	43	11	,	,	PUNCT
ejpam-3096	43	12	z	z	NOUN
ejpam-3096	43	13	)	)	PUNCT
ejpam-3096	43	14	.	.	PUNCT
ejpam-3096	44	1	in	in	ADP
ejpam-3096	44	2	that	that	DET
ejpam-3096	44	3	case	case	NOUN
ejpam-3096	44	4	d∗	d∗	NOUN
ejpam-3096	44	5	is	be	AUX
ejpam-3096	44	6	called	call	VERB
ejpam-3096	44	7	a	a	DET
ejpam-3096	44	8	generalized	generalized	ADJ
ejpam-3096	44	9	d∗-metric	d∗-metric	NOUN
ejpam-3096	44	10	(	(	PUNCT
ejpam-3096	44	11	d∗-cone	d∗-cone	NOUN
ejpam-3096	44	12	metric	metric	NOUN
ejpam-3096	44	13	)	)	PUNCT
ejpam-3096	44	14	and	and	CCONJ
ejpam-3096	44	15	(	(	PUNCT
ejpam-3096	44	16	x	x	NOUN
ejpam-3096	44	17	,	,	PUNCT
ejpam-3096	44	18	d∗	d∗	PROPN
ejpam-3096	44	19	)	)	PUNCT
ejpam-3096	44	20	is	be	AUX
ejpam-3096	44	21	called	call	VERB
ejpam-3096	44	22	a	a	DET
ejpam-3096	44	23	generalized	generalize	VERB
ejpam-3096	44	24	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	44	25	(	(	PUNCT
ejpam-3096	44	26	d∗-cone	d∗-cone	NUM
ejpam-3096	44	27	metric	metric	ADJ
ejpam-3096	44	28	space	space	NOUN
ejpam-3096	44	29	)	)	PUNCT
ejpam-3096	44	30	.	.	PUNCT
ejpam-3096	45	1	remark	remark	PROPN
ejpam-3096	45	2	1	1	NUM
ejpam-3096	45	3	.	.	PUNCT
ejpam-3096	46	1	it	it	PRON
ejpam-3096	46	2	is	be	AUX
ejpam-3096	46	3	obvious	obvious	ADJ
ejpam-3096	46	4	that	that	SCONJ
ejpam-3096	46	5	the	the	DET
ejpam-3096	46	6	concept	concept	NOUN
ejpam-3096	46	7	of	of	ADP
ejpam-3096	46	8	a	a	DET
ejpam-3096	46	9	generalized	generalize	VERB
ejpam-3096	46	10	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	46	11	(	(	PUNCT
ejpam-3096	46	12	d∗-cone	d∗-cone	NUM
ejpam-3096	46	13	metric	metric	ADJ
ejpam-3096	46	14	space	space	NOUN
ejpam-3096	46	15	)	)	PUNCT
ejpam-3096	46	16	is	be	AUX
ejpam-3096	46	17	more	more	ADV
ejpam-3096	46	18	general	general	ADJ
ejpam-3096	46	19	than	than	ADP
ejpam-3096	46	20	that	that	PRON
ejpam-3096	46	21	of	of	ADP
ejpam-3096	46	22	d∗-m.sp	d∗-m.sp	X
ejpam-3096	46	23	or	or	CCONJ
ejpam-3096	46	24	cone	cone	NOUN
ejpam-3096	46	25	metric	metric	ADJ
ejpam-3096	46	26	space	space	NOUN
ejpam-3096	46	27	.	.	PUNCT
ejpam-3096	47	1	if	if	SCONJ
ejpam-3096	47	2	e	e	NOUN
ejpam-3096	47	3	=	=	SYM
ejpam-3096	47	4	r	r	NOUN
ejpam-3096	47	5	and	and	CCONJ
ejpam-3096	47	6	p	p	NOUN
ejpam-3096	47	7	=	=	PROPN
ejpam-3096	48	1	[	[	X
ejpam-3096	48	2	0,+∞	0,+∞	NUM
ejpam-3096	48	3	)	)	PUNCT
ejpam-3096	49	1	after	after	ADP
ejpam-3096	49	2	that	that	PRON
ejpam-3096	49	3	a	a	DET
ejpam-3096	49	4	generalized	generalize	VERB
ejpam-3096	49	5	d∗-m.sp	d∗-m.sp	X
ejpam-3096	49	6	becomes	become	VERB
ejpam-3096	49	7	d∗-m.sp	d∗-m.sp	X
ejpam-3096	49	8	.	.	NOUN
ejpam-3096	49	9	example	example	NOUN
ejpam-3096	49	10	1	1	NUM
ejpam-3096	49	11	.	.	PUNCT
ejpam-3096	49	12	suppose	suppose	VERB
ejpam-3096	49	13	e	e	NOUN
ejpam-3096	49	14	=	=	NOUN
ejpam-3096	49	15	r2	r2	PROPN
ejpam-3096	49	16	,	,	PUNCT
ejpam-3096	49	17	p	p	NOUN
ejpam-3096	49	18	=	=	X
ejpam-3096	49	19	{	{	PUNCT
ejpam-3096	49	20	(	(	PUNCT
ejpam-3096	49	21	x	x	NOUN
ejpam-3096	49	22	,	,	PUNCT
ejpam-3096	49	23	y	y	NOUN
ejpam-3096	49	24	)	)	PUNCT
ejpam-3096	49	25	∈	∈	PROPN
ejpam-3096	49	26	e	e	NOUN
ejpam-3096	49	27	:	:	PUNCT
ejpam-3096	49	28	x	x	X
ejpam-3096	49	29	,	,	PUNCT
ejpam-3096	49	30	y	y	PROPN
ejpam-3096	49	31	≥	≥	NUM
ejpam-3096	49	32	0	0	NUM
ejpam-3096	49	33	}	}	PUNCT
ejpam-3096	49	34	,	,	PUNCT
ejpam-3096	49	35	x	x	X
ejpam-3096	49	36	=	=	SYM
ejpam-3096	49	37	r	r	NOUN
ejpam-3096	49	38	,	,	PUNCT
ejpam-3096	49	39	defined	define	VERB
ejpam-3096	49	40	a	a	DET
ejpam-3096	49	41	function	function	NOUN
ejpam-3096	49	42	,	,	PUNCT
ejpam-3096	49	43	d∗	d∗	PROPN
ejpam-3096	49	44	:	:	PUNCT
ejpam-3096	50	1	x3	x3	ADJ
ejpam-3096	50	2	→	→	SYM
ejpam-3096	50	3	e	e	NOUN
ejpam-3096	50	4	via	via	ADP
ejpam-3096	50	5	:	:	PUNCT
ejpam-3096	50	6	d∗(x	d∗(x	PROPN
ejpam-3096	50	7	,	,	PUNCT
ejpam-3096	50	8	y	y	PROPN
ejpam-3096	50	9	,	,	PUNCT
ejpam-3096	50	10	z	z	NOUN
ejpam-3096	50	11	)	)	PUNCT
ejpam-3096	50	12	=	=	SYM
ejpam-3096	50	13	(	(	PUNCT
ejpam-3096	50	14	|x−	|x−	NOUN
ejpam-3096	50	15	y|+	y|+	PROPN
ejpam-3096	50	16	|y−	|y−	NOUN
ejpam-3096	50	17	z|+	z|+	PROPN
ejpam-3096	50	18	|x−	|x−	PROPN
ejpam-3096	50	19	z|	z|	PROPN
ejpam-3096	50	20	,	,	PUNCT
ejpam-3096	50	21	α(|x−	α(|x−	PROPN
ejpam-3096	50	22	y|+	y|+	PROPN
ejpam-3096	50	23	|y−	|y−	NOUN
ejpam-3096	50	24	z|+	z|+	PROPN
ejpam-3096	50	25	|x−	|x−	PROPN
ejpam-3096	50	26	z|	z|	PROPN
ejpam-3096	50	27	)	)	PUNCT
ejpam-3096	50	28	)	)	PUNCT
ejpam-3096	50	29	3	3	NUM
ejpam-3096	50	30	α	α	PRON
ejpam-3096	50	31	≥	≥	NOUN
ejpam-3096	50	32	0	0	NUM
ejpam-3096	50	33	is	be	AUX
ejpam-3096	50	34	a	a	DET
ejpam-3096	50	35	constant	constant	ADJ
ejpam-3096	50	36	(	(	PUNCT
ejpam-3096	50	37	see[2	see[2	NUM
ejpam-3096	50	38	]	]	PUNCT
ejpam-3096	50	39	)	)	PUNCT
ejpam-3096	50	40	.	.	PUNCT
ejpam-3096	51	1	in	in	ADP
ejpam-3096	51	2	that	that	DET
ejpam-3096	51	3	case	case	NOUN
ejpam-3096	51	4	(	(	PUNCT
ejpam-3096	51	5	x	x	X
ejpam-3096	51	6	,	,	PUNCT
ejpam-3096	51	7	d∗	d∗	PROPN
ejpam-3096	51	8	)	)	PUNCT
ejpam-3096	51	9	is	be	AUX
ejpam-3096	51	10	a	a	DET
ejpam-3096	51	11	generalized	generalized	ADJ
ejpam-3096	51	12	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	51	13	(	(	PUNCT
ejpam-3096	51	14	d∗-cone	d∗-cone	NUM
ejpam-3096	51	15	metric	metric	ADJ
ejpam-3096	51	16	space	space	NOUN
ejpam-3096	51	17	)	)	PUNCT
ejpam-3096	51	18	.	.	PUNCT
ejpam-3096	52	1	over	over	ADP
ejpam-3096	52	2	the	the	DET
ejpam-3096	52	3	normal	normal	ADJ
ejpam-3096	52	4	cone	cone	NOUN
ejpam-3096	52	5	p.	p.	NOUN
ejpam-3096	52	6	example	example	NOUN
ejpam-3096	52	7	2	2	X
ejpam-3096	52	8	.	.	PUNCT
ejpam-3096	52	9	let	let	VERB
ejpam-3096	52	10	e	e	PROPN
ejpam-3096	52	11	=	=	PROPN
ejpam-3096	52	12	c1	c1	PROPN
ejpam-3096	52	13	r[0	r[0	PROPN
ejpam-3096	52	14	,	,	PUNCT
ejpam-3096	52	15	1	1	NUM
ejpam-3096	52	16	]	]	PUNCT
ejpam-3096	52	17	with	with	ADP
ejpam-3096	52	18	‖u‖	‖u‖	PROPN
ejpam-3096	52	19	=	=	PUNCT
ejpam-3096	53	1	‖u‖∞	‖u‖∞	PROPN
ejpam-3096	53	2	+	+	CCONJ
ejpam-3096	53	3	‖u′‖∞	‖u′‖∞	X
ejpam-3096	53	4	and	and	CCONJ
ejpam-3096	53	5	p	p	NOUN
ejpam-3096	53	6	=	=	PUNCT
ejpam-3096	53	7	{	{	PUNCT
ejpam-3096	53	8	u	u	NOUN
ejpam-3096	53	9	∈	∈	PROPN
ejpam-3096	53	10	e	e	NOUN
ejpam-3096	53	11	:	:	PUNCT
ejpam-3096	53	12	u(t	u(t	NOUN
ejpam-3096	53	13	)	)	PUNCT
ejpam-3096	53	14	≥	≥	NOUN
ejpam-3096	53	15	0	0	NUM
ejpam-3096	53	16	on	on	ADP
ejpam-3096	53	17	[	[	X
ejpam-3096	53	18	0	0	NUM
ejpam-3096	53	19	,	,	PUNCT
ejpam-3096	53	20	1	1	NUM
ejpam-3096	53	21	]	]	PUNCT
ejpam-3096	53	22	}	}	PUNCT
ejpam-3096	53	23	(	(	PUNCT
ejpam-3096	53	24	see	see	VERB
ejpam-3096	53	25	,	,	PUNCT
ejpam-3096	53	26	e.g.	e.g.	ADV
ejpam-3096	53	27	,	,	PUNCT
ejpam-3096	53	28	[	[	X
ejpam-3096	53	29	27	27	NUM
ejpam-3096	53	30	]	]	PUNCT
ejpam-3096	53	31	)	)	PUNCT
ejpam-3096	53	32	.	.	PUNCT
ejpam-3096	54	1	let	let	VERB
ejpam-3096	54	2	x	x	PUNCT
ejpam-3096	54	3	=	=	PUNCT
ejpam-3096	55	1	[	[	X
ejpam-3096	55	2	0,+∞	0,+∞	NUM
ejpam-3096	55	3	)	)	PUNCT
ejpam-3096	56	1	and	and	CCONJ
ejpam-3096	56	2	,	,	PUNCT
ejpam-3096	56	3	d(x	d(x	PROPN
ejpam-3096	56	4	,	,	PUNCT
ejpam-3096	56	5	y	y	NOUN
ejpam-3096	56	6	)	)	PUNCT
ejpam-3096	56	7	=	=	PUNCT
ejpam-3096	56	8	|x−	|x−	NOUN
ejpam-3096	56	9	y|	y|	NOUN
ejpam-3096	56	10	,	,	PUNCT
ejpam-3096	56	11	g(x	g(x	PROPN
ejpam-3096	56	12	,	,	PUNCT
ejpam-3096	56	13	y	y	PROPN
ejpam-3096	56	14	,	,	PUNCT
ejpam-3096	56	15	z	z	NOUN
ejpam-3096	56	16	)	)	PUNCT
ejpam-3096	56	17	=	=	SYM
ejpam-3096	56	18	d(x	d(x	PROPN
ejpam-3096	56	19	,	,	PUNCT
ejpam-3096	56	20	y	y	NOUN
ejpam-3096	56	21	)	)	PUNCT
ejpam-3096	57	1	+	+	CCONJ
ejpam-3096	57	2	d(y	d(y	NOUN
ejpam-3096	57	3	,	,	PUNCT
ejpam-3096	57	4	z	z	NOUN
ejpam-3096	57	5	)	)	PUNCT
ejpam-3096	58	1	+	+	CCONJ
ejpam-3096	58	2	d(z	d(z	PROPN
ejpam-3096	58	3	,	,	PUNCT
ejpam-3096	58	4	x	x	NOUN
ejpam-3096	58	5	)	)	PUNCT
ejpam-3096	58	6	∀x	∀x	NUM
ejpam-3096	58	7	,	,	PUNCT
ejpam-3096	58	8	y	y	PROPN
ejpam-3096	58	9	,	,	PUNCT
ejpam-3096	58	10	z	z	PROPN
ejpam-3096	58	11	∈	∈	PROPN
ejpam-3096	58	12	x	x	X
ejpam-3096	58	13	,	,	PUNCT
ejpam-3096	58	14	defined	define	VERB
ejpam-3096	58	15	a	a	DET
ejpam-3096	58	16	function	function	NOUN
ejpam-3096	58	17	d∗	d∗	NOUN
ejpam-3096	58	18	:	:	PUNCT
ejpam-3096	58	19	x3	x3	ADJ
ejpam-3096	58	20	→	→	SYM
ejpam-3096	58	21	p	p	NOUN
ejpam-3096	58	22	via	via	ADP
ejpam-3096	58	23	d∗	d∗	PROPN
ejpam-3096	58	24	(	(	PUNCT
ejpam-3096	58	25	x	x	X
ejpam-3096	58	26	,	,	PUNCT
ejpam-3096	58	27	y	y	PROPN
ejpam-3096	58	28	,	,	PUNCT
ejpam-3096	58	29	z	z	NOUN
ejpam-3096	58	30	)	)	PUNCT
ejpam-3096	58	31	=	=	SYM
ejpam-3096	58	32	g	g	PROPN
ejpam-3096	58	33	(	(	PUNCT
ejpam-3096	58	34	x	x	PROPN
ejpam-3096	58	35	,	,	PUNCT
ejpam-3096	58	36	y	y	PROPN
ejpam-3096	58	37	,	,	PUNCT
ejpam-3096	58	38	z)u	z)u	X
ejpam-3096	58	39	where	where	SCONJ
ejpam-3096	58	40	u	u	PROPN
ejpam-3096	58	41	∈	∈	PROPN
ejpam-3096	58	42	p	p	NOUN
ejpam-3096	58	43	is	be	AUX
ejpam-3096	58	44	fixed	fix	VERB
ejpam-3096	58	45	.	.	PUNCT
ejpam-3096	59	1	in	in	ADP
ejpam-3096	59	2	that	that	DET
ejpam-3096	59	3	case	case	NOUN
ejpam-3096	59	4	(	(	PUNCT
ejpam-3096	59	5	x	x	X
ejpam-3096	59	6	,	,	PUNCT
ejpam-3096	59	7	d∗	d∗	PROPN
ejpam-3096	59	8	)	)	PUNCT
ejpam-3096	59	9	is	be	AUX
ejpam-3096	59	10	a	a	DET
ejpam-3096	59	11	generalized	generalized	ADJ
ejpam-3096	59	12	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	59	13	over	over	ADP
ejpam-3096	59	14	the	the	DET
ejpam-3096	59	15	non	non	ADJ
ejpam-3096	59	16	-	-	ADJ
ejpam-3096	59	17	normal	normal	ADJ
ejpam-3096	59	18	cone	cone	NOUN
ejpam-3096	59	19	p.	p.	NOUN
ejpam-3096	59	20	lemma	lemma	PROPN
ejpam-3096	60	1	1	1	NUM
ejpam-3096	60	2	.	.	PUNCT
ejpam-3096	61	1	[	[	X
ejpam-3096	61	2	2	2	X
ejpam-3096	61	3	]	]	X
ejpam-3096	61	4	assume	assume	VERB
ejpam-3096	61	5	(	(	PUNCT
ejpam-3096	61	6	x	x	X
ejpam-3096	61	7	,	,	PUNCT
ejpam-3096	61	8	d∗	d∗	PROPN
ejpam-3096	61	9	)	)	PUNCT
ejpam-3096	61	10	is	be	AUX
ejpam-3096	61	11	a	a	DET
ejpam-3096	61	12	generalized	generalized	ADJ
ejpam-3096	61	13	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	61	14	,	,	PUNCT
ejpam-3096	61	15	in	in	ADP
ejpam-3096	61	16	that	that	DET
ejpam-3096	61	17	case	case	NOUN
ejpam-3096	61	18	∀x	∀x	NUM
ejpam-3096	61	19	,	,	PUNCT
ejpam-3096	61	20	y	y	PROPN
ejpam-3096	61	21	∈	∈	PROPN
ejpam-3096	61	22	x	x	X
ejpam-3096	61	23	,	,	PUNCT
ejpam-3096	61	24	obtain	obtain	VERB
ejpam-3096	61	25	d∗(x	d∗(x	PROPN
ejpam-3096	61	26	,	,	PUNCT
ejpam-3096	61	27	x	x	NOUN
ejpam-3096	61	28	,	,	PUNCT
ejpam-3096	61	29	y	y	NOUN
ejpam-3096	61	30	)	)	PUNCT
ejpam-3096	61	31	equal	equal	ADJ
ejpam-3096	61	32	to	to	ADP
ejpam-3096	61	33	d∗(x	d∗(x	PROPN
ejpam-3096	61	34	,	,	PUNCT
ejpam-3096	61	35	y	y	PROPN
ejpam-3096	61	36	,	,	PUNCT
ejpam-3096	61	37	y	y	PROPN
ejpam-3096	61	38	)	)	PUNCT
ejpam-3096	61	39	.	.	PUNCT
ejpam-3096	62	1	remark	remark	PROPN
ejpam-3096	62	2	2	2	NUM
ejpam-3096	62	3	.	.	PUNCT
ejpam-3096	63	1	for	for	ADP
ejpam-3096	63	2	the	the	DET
ejpam-3096	63	3	case	case	NOUN
ejpam-3096	63	4	of	of	ADP
ejpam-3096	63	5	non	non	ADJ
ejpam-3096	63	6	-	-	ADJ
ejpam-3096	63	7	normal	normal	ADJ
ejpam-3096	63	8	cones	cone	NOUN
ejpam-3096	63	9	,	,	PUNCT
ejpam-3096	63	10	the	the	DET
ejpam-3096	63	11	following	follow	VERB
ejpam-3096	63	12	remarks	remark	NOUN
ejpam-3096	63	13	holed	holed	ADJ
ejpam-3096	63	14	and	and	CCONJ
ejpam-3096	63	15	useful	useful	ADJ
ejpam-3096	63	16	in	in	ADP
ejpam-3096	63	17	the	the	DET
ejpam-3096	63	18	sequel	sequel	NOUN
ejpam-3096	63	19	for	for	ADP
ejpam-3096	63	20	elements	element	NOUN
ejpam-3096	63	21	u	u	NOUN
ejpam-3096	63	22	,	,	PUNCT
ejpam-3096	63	23	v	v	NOUN
ejpam-3096	63	24	,	,	PUNCT
ejpam-3096	63	25	w	w	PROPN
ejpam-3096	63	26	∈	∈	PROPN
ejpam-3096	63	27	p	p	X
ejpam-3096	63	28	:	:	PUNCT
ejpam-3096	63	29	(	(	PUNCT
ejpam-3096	63	30	r1)−	r1)−	NOUN
ejpam-3096	63	31	if	if	SCONJ
ejpam-3096	63	32	u	u	NOUN
ejpam-3096	63	33	≤	≤	X
ejpam-3096	63	34	v	v	NOUN
ejpam-3096	63	35	and	and	CCONJ
ejpam-3096	63	36	v	v	ADP
ejpam-3096	63	37	�	�	PROPN
ejpam-3096	63	38	w	w	PROPN
ejpam-3096	63	39	,	,	PUNCT
ejpam-3096	63	40	in	in	ADP
ejpam-3096	63	41	that	that	DET
ejpam-3096	63	42	case	case	NOUN
ejpam-3096	63	43	u	u	NOUN
ejpam-3096	63	44	�	�	PROPN
ejpam-3096	63	45	w.	w.	PROPN
ejpam-3096	63	46	(	(	PUNCT
ejpam-3096	63	47	r2)−	r2)−	VERB
ejpam-3096	63	48	if	if	SCONJ
ejpam-3096	63	49	u	u	NOUN
ejpam-3096	63	50	�	�	PROPN
ejpam-3096	63	51	v	v	NOUN
ejpam-3096	63	52	and	and	CCONJ
ejpam-3096	63	53	v	v	ADP
ejpam-3096	63	54	≤	≤	NUM
ejpam-3096	63	55	w	w	ADP
ejpam-3096	63	56	,	,	PUNCT
ejpam-3096	63	57	in	in	ADP
ejpam-3096	63	58	that	that	DET
ejpam-3096	63	59	case	case	NOUN
ejpam-3096	63	60	u	u	NOUN
ejpam-3096	63	61	�	�	PROPN
ejpam-3096	63	62	w.	w.	PROPN
ejpam-3096	63	63	(	(	PUNCT
ejpam-3096	63	64	r3)−	r3)−	ADJ
ejpam-3096	63	65	if	if	SCONJ
ejpam-3096	63	66	0	0	NUM
ejpam-3096	63	67	≤	≤	NUM
ejpam-3096	63	68	u	u	NOUN
ejpam-3096	63	69	�	�	PROPN
ejpam-3096	63	70	d	d	X
ejpam-3096	63	71	∀	∀	X
ejpam-3096	63	72	d	d	X
ejpam-3096	63	73	∈	∈	NOUN
ejpam-3096	63	74	intp	intp	NOUN
ejpam-3096	63	75	,	,	PUNCT
ejpam-3096	63	76	in	in	ADP
ejpam-3096	63	77	that	that	DET
ejpam-3096	63	78	case	case	NOUN
ejpam-3096	63	79	u	u	NOUN
ejpam-3096	63	80	=	=	NOUN
ejpam-3096	63	81	0	0	PROPN
ejpam-3096	63	82	.	.	PUNCT
ejpam-3096	64	1	definition	definition	NOUN
ejpam-3096	64	2	2	2	NUM
ejpam-3096	64	3	.	.	PUNCT
ejpam-3096	65	1	[	[	X
ejpam-3096	65	2	2	2	X
ejpam-3096	65	3	]	]	PUNCT
ejpam-3096	65	4	suppose	suppose	VERB
ejpam-3096	65	5	(	(	PUNCT
ejpam-3096	65	6	x	x	X
ejpam-3096	65	7	,	,	PUNCT
ejpam-3096	65	8	d∗	d∗	PROPN
ejpam-3096	65	9	)	)	PUNCT
ejpam-3096	65	10	is	be	AUX
ejpam-3096	65	11	a	a	DET
ejpam-3096	65	12	generalized	generalized	ADJ
ejpam-3096	65	13	d∗-m.sp	d∗-m.sp	X
ejpam-3096	65	14	in	in	ADP
ejpam-3096	65	15	that	that	DET
ejpam-3096	65	16	case	case	NOUN
ejpam-3096	65	17	:	:	PUNCT
ejpam-3096	65	18	a	a	X
ejpam-3096	65	19	)	)	PUNCT
ejpam-3096	65	20	a	a	DET
ejpam-3096	65	21	sequence{xs	sequence{xs	NOUN
ejpam-3096	65	22	}	}	PUNCT
ejpam-3096	65	23	in	in	ADP
ejpam-3096	65	24	x	x	PROPN
ejpam-3096	65	25	is	be	AUX
ejpam-3096	65	26	called	call	VERB
ejpam-3096	65	27	cauchy	cauchy	ADJ
ejpam-3096	65	28	sequence	sequence	NOUN
ejpam-3096	65	29	if	if	SCONJ
ejpam-3096	65	30	∀	∀	NOUN
ejpam-3096	65	31	d	d	AUX
ejpam-3096	65	32	belong	belong	VERB
ejpam-3096	65	33	to	to	ADP
ejpam-3096	65	34	e	e	NOUN
ejpam-3096	65	35	with	with	ADP
ejpam-3096	65	36	0	0	NUM
ejpam-3096	65	37	�	�	PROPN
ejpam-3096	65	38	d	d	PROPN
ejpam-3096	65	39	,	,	PUNCT
ejpam-3096	65	40	there	there	PRON
ejpam-3096	65	41	exist	exist	VERB
ejpam-3096	65	42	h	h	NOUN
ejpam-3096	65	43	(	(	PUNCT
ejpam-3096	65	44	s.t	s.t	PROPN
ejpam-3096	65	45	)	)	PUNCT
ejpam-3096	65	46	∀	∀	PUNCT
ejpam-3096	66	1	r	r	NOUN
ejpam-3096	66	2	,	,	PUNCT
ejpam-3096	66	3	s	s	X
ejpam-3096	66	4	,	,	PUNCT
ejpam-3096	66	5	l	l	PROPN
ejpam-3096	66	6	≥	≥	NOUN
ejpam-3096	66	7	h	h	NOUN
ejpam-3096	66	8	,	,	PUNCT
ejpam-3096	66	9	d∗(xr	d∗(xr	PROPN
ejpam-3096	66	10	,	,	PUNCT
ejpam-3096	66	11	xs	xs	PROPN
ejpam-3096	66	12	,	,	PUNCT
ejpam-3096	66	13	xl	xl	PROPN
ejpam-3096	66	14	)	)	PUNCT
ejpam-3096	66	15	�	�	PROPN
ejpam-3096	66	16	d.	d.	PROPN
ejpam-3096	66	17	b	b	PROPN
ejpam-3096	66	18	)	)	PUNCT
ejpam-3096	66	19	if	if	SCONJ
ejpam-3096	66	20	each	each	DET
ejpam-3096	66	21	cauchy	cauchy	ADJ
ejpam-3096	66	22	sequence	sequence	NOUN
ejpam-3096	66	23	is	be	AUX
ejpam-3096	66	24	convergent	convergent	ADJ
ejpam-3096	66	25	in	in	ADP
ejpam-3096	66	26	x	x	NOUN
ejpam-3096	66	27	,	,	PUNCT
ejpam-3096	66	28	in	in	ADP
ejpam-3096	66	29	that	that	DET
ejpam-3096	66	30	case	case	NOUN
ejpam-3096	66	31	x	x	PUNCT
ejpam-3096	66	32	is	be	AUX
ejpam-3096	66	33	called	call	VERB
ejpam-3096	66	34	complete	complete	ADJ
ejpam-3096	66	35	generalized	generalized	ADJ
ejpam-3096	66	36	d∗-metric	d∗-metric	NOUN
ejpam-3096	66	37	.	.	PUNCT
ejpam-3096	67	1	c	c	X
ejpam-3096	67	2	)	)	PUNCT
ejpam-3096	67	3	a	a	DET
ejpam-3096	67	4	sequence{xs	sequence{x	VERB
ejpam-3096	67	5	}	}	PUNCT
ejpam-3096	67	6	→	→	SYM
ejpam-3096	67	7	x	x	SYM
ejpam-3096	67	8	∈	∈	NOUN
ejpam-3096	67	9	x	x	NOUN
ejpam-3096	67	10	,	,	PUNCT
ejpam-3096	67	11	if	if	SCONJ
ejpam-3096	67	12	∀	∀	NUM
ejpam-3096	67	13	d	d	X
ejpam-3096	67	14	∈	∈	PROPN
ejpam-3096	67	15	e	e	X
ejpam-3096	67	16	with	with	ADP
ejpam-3096	67	17	0	0	NUM
ejpam-3096	67	18	�	�	PROPN
ejpam-3096	67	19	d	d	NOUN
ejpam-3096	67	20	there	there	PRON
ejpam-3096	67	21	exist	exist	VERB
ejpam-3096	67	22	h	h	NOUN
ejpam-3096	67	23	(	(	PUNCT
ejpam-3096	67	24	s.t	s.t	PROPN
ejpam-3096	67	25	)	)	PUNCT
ejpam-3096	67	26	∀	∀	PUNCT
ejpam-3096	68	1	r	r	NOUN
ejpam-3096	68	2	,	,	PUNCT
ejpam-3096	68	3	s	s	PART
ejpam-3096	68	4	≥	≥	NOUN
ejpam-3096	68	5	h	h	NOUN
ejpam-3096	68	6	,	,	PUNCT
ejpam-3096	68	7	d∗(xr	d∗(xr	PROPN
ejpam-3096	68	8	,	,	PUNCT
ejpam-3096	68	9	xs	xs	PROPN
ejpam-3096	68	10	,	,	PUNCT
ejpam-3096	68	11	x	x	NOUN
ejpam-3096	68	12	)	)	PUNCT
ejpam-3096	68	13	�	�	PROPN
ejpam-3096	68	14	d	d	PROPN
ejpam-3096	68	15	,	,	PUNCT
ejpam-3096	68	16	and	and	CCONJ
ejpam-3096	68	17	x	x	X
ejpam-3096	68	18	is	be	AUX
ejpam-3096	68	19	the	the	DET
ejpam-3096	68	20	limit	limit	NOUN
ejpam-3096	68	21	point	point	NOUN
ejpam-3096	68	22	of	of	ADP
ejpam-3096	68	23	{	{	PUNCT
ejpam-3096	68	24	xs	xs	PROPN
ejpam-3096	68	25	}	}	PUNCT
ejpam-3096	68	26	with	with	ADP
ejpam-3096	68	27	indicate	indicate	NOUN
ejpam-3096	68	28	via	via	ADP
ejpam-3096	68	29	xs	xs	PROPN
ejpam-3096	68	30	→	→	SYM
ejpam-3096	68	31	x	x	X
ejpam-3096	68	32	,	,	PUNCT
ejpam-3096	68	33	as	as	ADP
ejpam-3096	68	34	(	(	PUNCT
ejpam-3096	68	35	s→∞	s→∞	NOUN
ejpam-3096	68	36	)	)	PUNCT
ejpam-3096	68	37	.	.	PUNCT
ejpam-3096	69	1	proposition	proposition	NOUN
ejpam-3096	69	2	1	1	NUM
ejpam-3096	69	3	.	.	PUNCT
ejpam-3096	70	1	[	[	X
ejpam-3096	70	2	2	2	X
ejpam-3096	70	3	]	]	X
ejpam-3096	70	4	assume	assume	VERB
ejpam-3096	70	5	(	(	PUNCT
ejpam-3096	70	6	x	x	X
ejpam-3096	70	7	,	,	PUNCT
ejpam-3096	70	8	d∗	d∗	PROPN
ejpam-3096	70	9	)	)	PUNCT
ejpam-3096	70	10	is	be	AUX
ejpam-3096	70	11	a	a	DET
ejpam-3096	70	12	generalized	generalized	ADJ
ejpam-3096	70	13	d∗-m.sp	d∗-m.sp	X
ejpam-3096	70	14	in	in	ADP
ejpam-3096	70	15	x	x	SYM
ejpam-3096	70	16	,	,	PUNCT
ejpam-3096	70	17	if	if	SCONJ
ejpam-3096	70	18	xs	xs	PROPN
ejpam-3096	70	19	→	→	SYM
ejpam-3096	70	20	x	x	X
ejpam-3096	70	21	,	,	PUNCT
ejpam-3096	70	22	in	in	ADP
ejpam-3096	70	23	that	that	DET
ejpam-3096	70	24	case	case	NOUN
ejpam-3096	70	25	{	{	PUNCT
ejpam-3096	70	26	xs	xs	NOUN
ejpam-3096	70	27	}	}	PUNCT
ejpam-3096	70	28	is	be	AUX
ejpam-3096	70	29	a	a	DET
ejpam-3096	70	30	cauchy	cauchy	ADJ
ejpam-3096	70	31	sequence	sequence	NOUN
ejpam-3096	70	32	.	.	PUNCT
ejpam-3096	71	1	proposition	proposition	NOUN
ejpam-3096	71	2	2	2	NUM
ejpam-3096	71	3	.	.	PUNCT
ejpam-3096	72	1	[	[	X
ejpam-3096	72	2	2	2	X
ejpam-3096	72	3	]	]	X
ejpam-3096	72	4	assume	assume	VERB
ejpam-3096	72	5	(	(	PUNCT
ejpam-3096	72	6	x	x	X
ejpam-3096	72	7	,	,	PUNCT
ejpam-3096	72	8	d∗	d∗	PROPN
ejpam-3096	72	9	)	)	PUNCT
ejpam-3096	72	10	is	be	AUX
ejpam-3096	72	11	a	a	DET
ejpam-3096	72	12	generalized	generalized	ADJ
ejpam-3096	72	13	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	72	14	,	,	PUNCT
ejpam-3096	72	15	and	and	CCONJ
ejpam-3096	72	16	p	p	NOUN
ejpam-3096	72	17	is	be	AUX
ejpam-3096	72	18	normal	normal	ADJ
ejpam-3096	72	19	cone	cone	NOUN
ejpam-3096	72	20	with	with	ADP
ejpam-3096	72	21	normal	normal	ADJ
ejpam-3096	72	22	constant	constant	ADJ
ejpam-3096	72	23	k.	k.	PROPN
ejpam-3096	72	24	suppose	suppose	VERB
ejpam-3096	72	25	{	{	PUNCT
ejpam-3096	72	26	xs	xs	NOUN
ejpam-3096	72	27	}	}	PUNCT
ejpam-3096	72	28	in	in	ADP
ejpam-3096	72	29	x	x	NOUN
ejpam-3096	72	30	,	,	PUNCT
ejpam-3096	72	31	in	in	ADP
ejpam-3096	72	32	that	that	DET
ejpam-3096	72	33	case	case	NOUN
ejpam-3096	72	34	{	{	PUNCT
ejpam-3096	72	35	xs	xs	PROPN
ejpam-3096	72	36	}	}	PUNCT
ejpam-3096	72	37	converges	converge	VERB
ejpam-3096	72	38	to	to	ADP
ejpam-3096	72	39	x⇔	x⇔	PROPN
ejpam-3096	72	40	d∗(xr	d∗(xr	PROPN
ejpam-3096	72	41	,	,	PUNCT
ejpam-3096	72	42	xs	xs	PROPN
ejpam-3096	72	43	,	,	PUNCT
ejpam-3096	72	44	x)→	x)→	PROPN
ejpam-3096	72	45	0	0	NUM
ejpam-3096	72	46	,	,	PUNCT
ejpam-3096	72	47	as	as	ADP
ejpam-3096	72	48	(	(	PUNCT
ejpam-3096	72	49	r	r	NOUN
ejpam-3096	72	50	,	,	PUNCT
ejpam-3096	72	51	s→∞	s→∞	NUM
ejpam-3096	72	52	)	)	PUNCT
ejpam-3096	72	53	.	.	PUNCT
ejpam-3096	73	1	a.	a.	PROPN
ejpam-3096	73	2	m.	m.	PROPN
ejpam-3096	73	3	al	al	PROPN
ejpam-3096	73	4	.	.	PROPN
ejpam-3096	73	5	jumaili	jumaili	PROPN
ejpam-3096	73	6	/	/	SYM
ejpam-3096	73	7	eur	eur	PROPN
ejpam-3096	73	8	.	.	PUNCT
ejpam-3096	74	1	j.	j.	PROPN
ejpam-3096	74	2	pure	pure	PROPN
ejpam-3096	74	3	appl	appl	PROPN
ejpam-3096	74	4	.	.	PROPN
ejpam-3096	74	5	math	math	PROPN
ejpam-3096	74	6	,	,	PUNCT
ejpam-3096	74	7	10	10	NUM
ejpam-3096	74	8	(	(	PUNCT
ejpam-3096	74	9	5	5	NUM
ejpam-3096	74	10	)	)	PUNCT
ejpam-3096	74	11	(	(	PUNCT
ejpam-3096	74	12	2017	2017	NUM
ejpam-3096	74	13	)	)	PUNCT
ejpam-3096	74	14	,	,	PUNCT
ejpam-3096	74	15	1023	1023	NUM
ejpam-3096	74	16	-	-	SYM
ejpam-3096	74	17	1034	1034	NUM
ejpam-3096	74	18	1026	1026	NUM
ejpam-3096	74	19	proposition	proposition	NOUN
ejpam-3096	74	20	3	3	NUM
ejpam-3096	74	21	.	.	PUNCT
ejpam-3096	75	1	[	[	X
ejpam-3096	75	2	2	2	X
ejpam-3096	75	3	]	]	X
ejpam-3096	75	4	assume	assume	VERB
ejpam-3096	75	5	(	(	PUNCT
ejpam-3096	75	6	x	x	X
ejpam-3096	75	7	,	,	PUNCT
ejpam-3096	75	8	d∗	d∗	PROPN
ejpam-3096	75	9	)	)	PUNCT
ejpam-3096	75	10	is	be	AUX
ejpam-3096	75	11	a	a	DET
ejpam-3096	75	12	generalized	generalized	ADJ
ejpam-3096	75	13	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	75	14	,	,	PUNCT
ejpam-3096	75	15	and	and	CCONJ
ejpam-3096	75	16	p	p	NOUN
ejpam-3096	75	17	is	be	AUX
ejpam-3096	75	18	normal	normal	ADJ
ejpam-3096	75	19	cone	cone	NOUN
ejpam-3096	75	20	.	.	PUNCT
ejpam-3096	76	1	suppose	suppose	VERB
ejpam-3096	76	2	{	{	PUNCT
ejpam-3096	76	3	xs	xs	NOUN
ejpam-3096	76	4	}	}	PUNCT
ejpam-3096	76	5	in	in	ADP
ejpam-3096	76	6	x	x	X
ejpam-3096	76	7	and	and	CCONJ
ejpam-3096	76	8	x	x	SYM
ejpam-3096	76	9	∈	∈	NOUN
ejpam-3096	76	10	x.	x.	NOUN
ejpam-3096	76	11	in	in	ADP
ejpam-3096	76	12	that	that	DET
ejpam-3096	76	13	case	case	NOUN
ejpam-3096	76	14	the	the	DET
ejpam-3096	76	15	following	follow	VERB
ejpam-3096	76	16	equivalent	equivalent	NOUN
ejpam-3096	76	17	:	:	PUNCT
ejpam-3096	76	18	a	a	X
ejpam-3096	76	19	)	)	PUNCT
ejpam-3096	76	20	{	{	PUNCT
ejpam-3096	76	21	xs	xs	NOUN
ejpam-3096	76	22	}	}	PUNCT
ejpam-3096	76	23	is	be	AUX
ejpam-3096	76	24	d∗-convergent	d∗-convergent	ADJ
ejpam-3096	76	25	to	to	ADP
ejpam-3096	76	26	x	x	SYM
ejpam-3096	76	27	;	;	PUNCT
ejpam-3096	76	28	b	b	X
ejpam-3096	76	29	)	)	PUNCT
ejpam-3096	76	30	d∗(xs	d∗(xs	PROPN
ejpam-3096	76	31	,	,	PUNCT
ejpam-3096	76	32	xs	xs	PROPN
ejpam-3096	76	33	,	,	PUNCT
ejpam-3096	76	34	x	x	X
ejpam-3096	76	35	)	)	PUNCT
ejpam-3096	76	36	convergent	convergent	NOUN
ejpam-3096	76	37	to	to	ADP
ejpam-3096	76	38	0	0	NUM
ejpam-3096	76	39	,	,	PUNCT
ejpam-3096	76	40	when	when	SCONJ
ejpam-3096	76	41	(	(	PUNCT
ejpam-3096	76	42	s→∞	s→∞	NOUN
ejpam-3096	76	43	)	)	PUNCT
ejpam-3096	76	44	;	;	PUNCT
ejpam-3096	77	1	c	c	X
ejpam-3096	77	2	)	)	PUNCT
ejpam-3096	77	3	d∗(xs	d∗(x	NOUN
ejpam-3096	77	4	,	,	PUNCT
ejpam-3096	77	5	x	x	X
ejpam-3096	77	6	,	,	PUNCT
ejpam-3096	77	7	x	x	NOUN
ejpam-3096	77	8	)	)	PUNCT
ejpam-3096	77	9	convergent	convergent	NOUN
ejpam-3096	77	10	to	to	ADP
ejpam-3096	77	11	0	0	NUM
ejpam-3096	77	12	,	,	PUNCT
ejpam-3096	77	13	when	when	SCONJ
ejpam-3096	77	14	(	(	PUNCT
ejpam-3096	77	15	s→∞	s→∞	NOUN
ejpam-3096	77	16	)	)	PUNCT
ejpam-3096	77	17	.	.	PUNCT
ejpam-3096	78	1	definition	definition	NOUN
ejpam-3096	78	2	3	3	X
ejpam-3096	78	3	.	.	PUNCT
ejpam-3096	78	4	suppose	suppose	VERB
ejpam-3096	78	5	x	x	PUNCT
ejpam-3096	79	1	6=	6=	ADP
ejpam-3096	79	2	φ	φ	NUM
ejpam-3096	79	3	,	,	PUNCT
ejpam-3096	79	4	in	in	ADP
ejpam-3096	79	5	that	that	DET
ejpam-3096	79	6	case	case	NOUN
ejpam-3096	79	7	(	(	PUNCT
ejpam-3096	79	8	x	x	X
ejpam-3096	79	9	,	,	PUNCT
ejpam-3096	79	10	d∗,4	d∗,4	PROPN
ejpam-3096	79	11	)	)	PUNCT
ejpam-3096	79	12	is	be	AUX
ejpam-3096	79	13	said	say	VERB
ejpam-3096	79	14	to	to	PART
ejpam-3096	79	15	be	be	AUX
ejpam-3096	79	16	an	an	DET
ejpam-3096	79	17	ordered	order	VERB
ejpam-3096	79	18	generalized	generalize	VERB
ejpam-3096	79	19	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	79	20	if	if	SCONJ
ejpam-3096	79	21	the	the	DET
ejpam-3096	79	22	following	follow	VERB
ejpam-3096	79	23	hold	hold	NOUN
ejpam-3096	79	24	:	:	PUNCT
ejpam-3096	79	25	a	a	X
ejpam-3096	79	26	)	)	PUNCT
ejpam-3096	79	27	(	(	PUNCT
ejpam-3096	79	28	x	x	X
ejpam-3096	79	29	,	,	PUNCT
ejpam-3096	79	30	d∗	d∗	PROPN
ejpam-3096	79	31	)	)	PUNCT
ejpam-3096	79	32	is	be	AUX
ejpam-3096	79	33	a	a	DET
ejpam-3096	79	34	generalized	generalized	ADJ
ejpam-3096	79	35	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	79	36	,	,	PUNCT
ejpam-3096	79	37	b	b	NOUN
ejpam-3096	79	38	)	)	PUNCT
ejpam-3096	79	39	(	(	PUNCT
ejpam-3096	79	40	x,4	x,4	X
ejpam-3096	79	41	)	)	PUNCT
ejpam-3096	79	42	is	be	AUX
ejpam-3096	79	43	a	a	DET
ejpam-3096	79	44	partially	partially	ADV
ejpam-3096	79	45	ordered	order	VERB
ejpam-3096	79	46	set	set	NOUN
ejpam-3096	79	47	(	(	PUNCT
ejpam-3096	79	48	p.o.s	p.o.s	NOUN
ejpam-3096	79	49	)	)	PUNCT
ejpam-3096	79	50	.	.	PUNCT
ejpam-3096	80	1	recall	recall	VERB
ejpam-3096	80	2	that	that	SCONJ
ejpam-3096	80	3	if	if	SCONJ
ejpam-3096	80	4	(	(	PUNCT
ejpam-3096	80	5	x,4	x,4	X
ejpam-3096	80	6	)	)	PUNCT
ejpam-3096	80	7	is	be	AUX
ejpam-3096	80	8	a	a	DET
ejpam-3096	80	9	(	(	PUNCT
ejpam-3096	80	10	p.o.s	p.o.s	NOUN
ejpam-3096	80	11	)	)	PUNCT
ejpam-3096	80	12	,	,	PUNCT
ejpam-3096	80	13	in	in	ADP
ejpam-3096	80	14	that	that	DET
ejpam-3096	80	15	case	case	NOUN
ejpam-3096	80	16	x	x	X
ejpam-3096	80	17	,	,	PUNCT
ejpam-3096	80	18	y	y	PROPN
ejpam-3096	80	19	∈	∈	PROPN
ejpam-3096	80	20	x	x	PRON
ejpam-3096	80	21	are	be	AUX
ejpam-3096	80	22	said	say	VERB
ejpam-3096	80	23	to	to	PART
ejpam-3096	80	24	be	be	AUX
ejpam-3096	80	25	comparable	comparable	ADJ
ejpam-3096	80	26	[	[	X
ejpam-3096	80	27	19	19	NUM
ejpam-3096	80	28	]	]	PUNCT
ejpam-3096	80	29	when	when	SCONJ
ejpam-3096	80	30	x	x	X
ejpam-3096	80	31	4	4	NUM
ejpam-3096	80	32	y	y	NOUN
ejpam-3096	80	33	or	or	CCONJ
ejpam-3096	80	34	y	y	PROPN
ejpam-3096	80	35	4	4	NUM
ejpam-3096	80	36	x	x	NOUN
ejpam-3096	80	37	satisfies	satisfie	NOUN
ejpam-3096	80	38	.	.	PUNCT
ejpam-3096	81	1	also	also	ADV
ejpam-3096	81	2	nashine	nashine	NOUN
ejpam-3096	81	3	and	and	CCONJ
ejpam-3096	81	4	samet	samet	PROPN
ejpam-3096	81	5	,	,	PUNCT
ejpam-3096	81	6	in	in	ADP
ejpam-3096	81	7	[	[	X
ejpam-3096	81	8	20	20	NUM
ejpam-3096	81	9	]	]	PUNCT
ejpam-3096	81	10	introduced	introduce	VERB
ejpam-3096	81	11	the	the	DET
ejpam-3096	81	12	following	follow	VERB
ejpam-3096	81	13	concept	concept	NOUN
ejpam-3096	81	14	:	:	PUNCT
ejpam-3096	81	15	let	let	VERB
ejpam-3096	81	16	x	x	PROPN
ejpam-3096	81	17	6=	6=	ADP
ejpam-3096	81	18	φ	φ	NUM
ejpam-3096	81	19	and	and	CCONJ
ejpam-3096	81	20	let	let	VERB
ejpam-3096	81	21	£	£	NOUN
ejpam-3096	81	22	:	:	PUNCT
ejpam-3096	81	23	x	x	SYM
ejpam-3096	81	24	→	→	SYM
ejpam-3096	81	25	x	x	SYM
ejpam-3096	81	26	,	,	PUNCT
ejpam-3096	81	27	∀x	∀x	X
ejpam-3096	81	28	∈	∈	PROPN
ejpam-3096	81	29	x	x	PRON
ejpam-3096	81	30	,	,	PUNCT
ejpam-3096	81	31	we	we	PRON
ejpam-3096	81	32	denoted	denote	VERB
ejpam-3096	81	33	via	via	ADP
ejpam-3096	81	34	£	£	SYM
ejpam-3096	81	35	−1(x	−1(x	NOUN
ejpam-3096	81	36	)	)	PUNCT
ejpam-3096	81	37	the	the	DET
ejpam-3096	81	38	sub	sub	NOUN
ejpam-3096	81	39	set	set	NOUN
ejpam-3096	81	40	of	of	ADP
ejpam-3096	81	41	x	x	PUNCT
ejpam-3096	81	42	given	give	VERB
ejpam-3096	81	43	through	through	ADP
ejpam-3096	81	44	£	£	SYM
ejpam-3096	81	45	−1(x	−1(x	NOUN
ejpam-3096	81	46	)	)	PUNCT
ejpam-3096	81	47	:	:	PUNCT
ejpam-3096	82	1	=	=	SYM
ejpam-3096	82	2	{	{	PUNCT
ejpam-3096	82	3	u	u	NOUN
ejpam-3096	82	4	∈	∈	PROPN
ejpam-3096	82	5	x	x	X
ejpam-3096	82	6	:	:	PUNCT
ejpam-3096	82	7	£	£	SYM
ejpam-3096	82	8	u	u	NOUN
ejpam-3096	82	9	=	=	NOUN
ejpam-3096	82	10	x	x	NOUN
ejpam-3096	82	11	}	}	PUNCT
ejpam-3096	82	12	.	.	PUNCT
ejpam-3096	83	1	definition	definition	NOUN
ejpam-3096	83	2	4	4	NUM
ejpam-3096	83	3	.	.	PUNCT
ejpam-3096	84	1	[	[	X
ejpam-3096	84	2	19	19	NUM
ejpam-3096	84	3	]	]	X
ejpam-3096	84	4	assume	assume	PROPN
ejpam-3096	84	5	(	(	PUNCT
ejpam-3096	84	6	x,4	x,4	X
ejpam-3096	84	7	)	)	PUNCT
ejpam-3096	84	8	is	be	AUX
ejpam-3096	84	9	a	a	DET
ejpam-3096	84	10	(	(	PUNCT
ejpam-3096	84	11	p.o.s	p.o.s	NOUN
ejpam-3096	84	12	)	)	PUNCT
ejpam-3096	84	13	and	and	CCONJ
ejpam-3096	84	14	let	let	VERB
ejpam-3096	84	15	t	t	PROPN
ejpam-3096	84	16	,	,	PUNCT
ejpam-3096	84	17	g,£	g,£	NOUN
ejpam-3096	84	18	:	:	PUNCT
ejpam-3096	84	19	x	x	SYM
ejpam-3096	84	20	→	→	PUNCT
ejpam-3096	84	21	x	x	PART
ejpam-3096	84	22	be	be	AUX
ejpam-3096	84	23	given	give	VERB
ejpam-3096	84	24	mappings	mapping	NOUN
ejpam-3096	84	25	(	(	PUNCT
ejpam-3096	84	26	s.t	s.t	PROPN
ejpam-3096	84	27	)	)	PUNCT
ejpam-3096	84	28	tx	tx	VERB
ejpam-3096	84	29	⊆	⊆	NUM
ejpam-3096	84	30	£	£	SYM
ejpam-3096	84	31	x	x	NUM
ejpam-3096	84	32	and	and	CCONJ
ejpam-3096	84	33	gx	gx	PROPN
ejpam-3096	84	34	⊆	⊆	NUM
ejpam-3096	85	1	£	£	PROPN
ejpam-3096	85	2	x.	x.	NOUN
ejpam-3096	85	3	describe	describe	VERB
ejpam-3096	85	4	that	that	PRON
ejpam-3096	85	5	g	g	PROPN
ejpam-3096	85	6	and	and	CCONJ
ejpam-3096	85	7	t	t	PROPN
ejpam-3096	85	8	are	be	AUX
ejpam-3096	85	9	weakly	weakly	ADV
ejpam-3096	85	10	increasing	increase	VERB
ejpam-3096	85	11	with	with	ADP
ejpam-3096	85	12	respect	respect	NOUN
ejpam-3096	85	13	to	to	ADP
ejpam-3096	85	14	£	£	NOUN
ejpam-3096	85	15	if	if	SCONJ
ejpam-3096	85	16	for	for	ADP
ejpam-3096	85	17	each	each	DET
ejpam-3096	85	18	x	x	SYM
ejpam-3096	85	19	∈	∈	PROPN
ejpam-3096	85	20	x	x	X
ejpam-3096	85	21	,	,	PUNCT
ejpam-3096	85	22	we	we	PRON
ejpam-3096	85	23	obtain	obtain	VERB
ejpam-3096	85	24	:	:	PUNCT
ejpam-3096	85	25	tx	tx	PROPN
ejpam-3096	85	26	4	4	NUM
ejpam-3096	85	27	gy,∀	gy,∀	NOUN
ejpam-3096	85	28	y	y	PROPN
ejpam-3096	85	29	∈	∈	PROPN
ejpam-3096	86	1	£	£	SYM
ejpam-3096	86	2	−1(tx	−1(tx	NOUN
ejpam-3096	86	3	)	)	PUNCT
ejpam-3096	86	4	and	and	CCONJ
ejpam-3096	86	5	gx	gx	PROPN
ejpam-3096	86	6	4	4	NUM
ejpam-3096	86	7	ty,∀	ty,∀	NOUN
ejpam-3096	86	8	y	y	PROPN
ejpam-3096	86	9	∈	∈	PROPN
ejpam-3096	86	10	£	£	SYM
ejpam-3096	86	11	−1(gx	−1(gx	NOUN
ejpam-3096	86	12	)	)	PUNCT
ejpam-3096	86	13	.	.	PUNCT
ejpam-3096	87	1	if	if	SCONJ
ejpam-3096	87	2	t	t	NOUN
ejpam-3096	87	3	=	=	SYM
ejpam-3096	87	4	g	g	NOUN
ejpam-3096	87	5	,	,	PUNCT
ejpam-3096	87	6	we	we	PRON
ejpam-3096	87	7	say	say	VERB
ejpam-3096	87	8	that	that	SCONJ
ejpam-3096	87	9	t	t	PROPN
ejpam-3096	87	10	is	be	AUX
ejpam-3096	87	11	weakly	weakly	ADV
ejpam-3096	87	12	increasing	increase	VERB
ejpam-3096	87	13	with	with	ADP
ejpam-3096	87	14	related	related	ADJ
ejpam-3096	87	15	to	to	ADP
ejpam-3096	87	16	£	£	PROPN
ejpam-3096	87	17	.	.	NOUN
ejpam-3096	88	1	remark	remark	NOUN
ejpam-3096	88	2	3	3	NUM
ejpam-3096	88	3	.	.	PUNCT
ejpam-3096	89	1	if	if	SCONJ
ejpam-3096	89	2	£	£	NUM
ejpam-3096	89	3	:	:	PUNCT
ejpam-3096	89	4	x	x	SYM
ejpam-3096	89	5	→	→	PUNCT
ejpam-3096	89	6	x	x	SYM
ejpam-3096	89	7	is	be	AUX
ejpam-3096	89	8	the	the	DET
ejpam-3096	89	9	identity	identity	NOUN
ejpam-3096	89	10	mapping	mapping	NOUN
ejpam-3096	89	11	(	(	PUNCT
ejpam-3096	89	12	£	£	NOUN
ejpam-3096	89	13	x	x	SYM
ejpam-3096	89	14	=	=	SYM
ejpam-3096	89	15	x	x	SYM
ejpam-3096	89	16	∀x	∀x	X
ejpam-3096	89	17	∈	∈	PROPN
ejpam-3096	89	18	x	x	NOUN
ejpam-3096	89	19	)	)	PUNCT
ejpam-3096	89	20	,	,	PUNCT
ejpam-3096	89	21	in	in	ADP
ejpam-3096	89	22	that	that	DET
ejpam-3096	89	23	case	case	NOUN
ejpam-3096	89	24	g	g	PROPN
ejpam-3096	89	25	and	and	CCONJ
ejpam-3096	89	26	t	t	PROPN
ejpam-3096	89	27	are	be	AUX
ejpam-3096	89	28	weakly	weakly	ADV
ejpam-3096	89	29	increasing	increase	VERB
ejpam-3096	89	30	with	with	ADP
ejpam-3096	89	31	respect	respect	NOUN
ejpam-3096	89	32	to	to	ADP
ejpam-3096	89	33	£	£	SYM
ejpam-3096	89	34	⇔	⇔	NUM
ejpam-3096	89	35	g	g	PROPN
ejpam-3096	89	36	and	and	CCONJ
ejpam-3096	89	37	t	t	PROPN
ejpam-3096	89	38	are	be	AUX
ejpam-3096	89	39	weakly	weakly	ADV
ejpam-3096	89	40	increasing	increase	VERB
ejpam-3096	89	41	mappings	mapping	NOUN
ejpam-3096	89	42	[	[	X
ejpam-3096	89	43	19	19	NUM
ejpam-3096	89	44	]	]	PUNCT
ejpam-3096	89	45	,	,	PUNCT
ejpam-3096	89	46	i.e.	i.e.	X
ejpam-3096	89	47	,	,	PUNCT
ejpam-3096	89	48	tx	tx	PROPN
ejpam-3096	89	49	4	4	NUM
ejpam-3096	89	50	g(tx	g(tx	NOUN
ejpam-3096	89	51	)	)	PUNCT
ejpam-3096	89	52	and	and	CCONJ
ejpam-3096	89	53	gx	gx	PROPN
ejpam-3096	89	54	4	4	NUM
ejpam-3096	89	55	t	t	PROPN
ejpam-3096	89	56	(	(	PUNCT
ejpam-3096	89	57	gx	gx	PROPN
ejpam-3096	89	58	)	)	PUNCT
ejpam-3096	89	59	hold	hold	VERB
ejpam-3096	89	60	∀x	∀x	PUNCT
ejpam-3096	89	61	∈	∈	PROPN
ejpam-3096	89	62	x.	x.	NOUN
ejpam-3096	89	63	definition	definition	NOUN
ejpam-3096	89	64	5	5	NUM
ejpam-3096	89	65	.	.	PUNCT
ejpam-3096	90	1	let	let	AUX
ejpam-3096	90	2	(	(	PUNCT
ejpam-3096	90	3	x,4	x,4	X
ejpam-3096	90	4	)	)	PUNCT
ejpam-3096	90	5	be	be	VERB
ejpam-3096	90	6	an	an	DET
ejpam-3096	90	7	ordered	order	VERB
ejpam-3096	90	8	generalized	generalized	ADJ
ejpam-3096	90	9	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	90	10	,	,	PUNCT
ejpam-3096	90	11	x	x	PRON
ejpam-3096	90	12	is	be	AUX
ejpam-3096	90	13	called	call	VERB
ejpam-3096	90	14	regular	regular	ADV
ejpam-3096	90	15	[	[	X
ejpam-3096	90	16	19	19	NUM
ejpam-3096	90	17	]	]	X
ejpam-3096	90	18	if	if	SCONJ
ejpam-3096	90	19	the	the	DET
ejpam-3096	90	20	next	next	ADJ
ejpam-3096	90	21	condition	condition	NOUN
ejpam-3096	90	22	holds	hold	VERB
ejpam-3096	90	23	:	:	PUNCT
ejpam-3096	90	24	if	if	SCONJ
ejpam-3096	90	25	{	{	PUNCT
ejpam-3096	90	26	zs	zs	NOUN
ejpam-3096	90	27	}	}	PUNCT
ejpam-3096	90	28	is	be	AUX
ejpam-3096	90	29	a	a	DET
ejpam-3096	90	30	non	non	ADJ
ejpam-3096	90	31	-	-	ADJ
ejpam-3096	90	32	decreasing	decrease	VERB
ejpam-3096	90	33	sequence	sequence	NOUN
ejpam-3096	90	34	in	in	ADP
ejpam-3096	90	35	(	(	PUNCT
ejpam-3096	90	36	x,4	x,4	NUM
ejpam-3096	90	37	)	)	PUNCT
ejpam-3096	90	38	(	(	PUNCT
ejpam-3096	90	39	s.t	s.t	PROPN
ejpam-3096	90	40	)	)	PUNCT
ejpam-3096	90	41	zs	zs	PROPN
ejpam-3096	90	42	→	→	SYM
ejpam-3096	90	43	z	z	NOUN
ejpam-3096	90	44	∈	∈	PROPN
ejpam-3096	90	45	x	x	X
ejpam-3096	90	46	,	,	PUNCT
ejpam-3096	90	47	when	when	SCONJ
ejpam-3096	90	48	(	(	PUNCT
ejpam-3096	90	49	s	s	X
ejpam-3096	90	50	→	→	SYM
ejpam-3096	90	51	∞	∞	NUM
ejpam-3096	90	52	)	)	PUNCT
ejpam-3096	90	53	,	,	PUNCT
ejpam-3096	90	54	in	in	ADP
ejpam-3096	90	55	that	that	DET
ejpam-3096	90	56	case	case	NOUN
ejpam-3096	90	57	zs	zs	NOUN
ejpam-3096	90	58	4	4	NUM
ejpam-3096	90	59	z	z	PROPN
ejpam-3096	90	60	,	,	PUNCT
ejpam-3096	90	61	for	for	ADP
ejpam-3096	90	62	each	each	DET
ejpam-3096	90	63	s	s	NOUN
ejpam-3096	90	64	belong	belong	VERB
ejpam-3096	90	65	to	to	ADP
ejpam-3096	90	66	n.	n.	NOUN
ejpam-3096	90	67	3	3	NUM
ejpam-3096	90	68	.	.	PUNCT
ejpam-3096	90	69	coincidence	coincidence	NOUN
ejpam-3096	90	70	fixed	fix	VERB
ejpam-3096	90	71	point	point	NOUN
ejpam-3096	90	72	theorems	theorem	NOUN
ejpam-3096	90	73	in	in	ADP
ejpam-3096	90	74	partially	partially	ADV
ejpam-3096	90	75	ordered	order	VERB
ejpam-3096	90	76	complete	complete	ADJ
ejpam-3096	90	77	generalized	generalize	VERB
ejpam-3096	90	78	d∗-m.sps	d∗-m.sp	NOUN
ejpam-3096	90	79	in	in	ADP
ejpam-3096	90	80	this	this	DET
ejpam-3096	90	81	section	section	NOUN
ejpam-3096	90	82	,	,	PUNCT
ejpam-3096	90	83	we	we	PRON
ejpam-3096	90	84	establish	establish	VERB
ejpam-3096	90	85	several	several	ADJ
ejpam-3096	90	86	coincidence	coincidence	NOUN
ejpam-3096	90	87	(	(	PUNCT
ejpam-3096	90	88	f.p.ths	f.p.th	NOUN
ejpam-3096	90	89	.	.	PUNCT
ejpam-3096	90	90	)	)	PUNCT
ejpam-3096	90	91	in	in	ADP
ejpam-3096	90	92	partially	partially	ADV
ejpam-3096	90	93	ordered	order	VERB
ejpam-3096	90	94	complete	complete	ADJ
ejpam-3096	90	95	generalized	generalized	ADJ
ejpam-3096	90	96	d∗-m.sps	d∗-m.sp	NOUN
ejpam-3096	90	97	.	.	PUNCT
ejpam-3096	91	1	we	we	PRON
ejpam-3096	91	2	start	start	VERB
ejpam-3096	91	3	with	with	ADP
ejpam-3096	91	4	the	the	DET
ejpam-3096	91	5	following	follow	VERB
ejpam-3096	91	6	definition	definition	NOUN
ejpam-3096	91	7	(	(	PUNCT
ejpam-3096	91	8	φ	φ	NOUN
ejpam-3096	91	9	-	-	NOUN
ejpam-3096	91	10	maps	map	NOUN
ejpam-3096	91	11	)	)	PUNCT
ejpam-3096	91	12	.	.	PUNCT
ejpam-3096	92	1	definition	definition	NOUN
ejpam-3096	92	2	6	6	NUM
ejpam-3096	92	3	.	.	PUNCT
ejpam-3096	93	1	[	[	X
ejpam-3096	93	2	3	3	NUM
ejpam-3096	93	3	,	,	PUNCT
ejpam-3096	93	4	10	10	NUM
ejpam-3096	93	5	]	]	PUNCT
ejpam-3096	93	6	.	.	PUNCT
ejpam-3096	94	1	let	let	VERB
ejpam-3096	94	2	p	p	PRON
ejpam-3096	94	3	be	be	AUX
ejpam-3096	94	4	(	(	PUNCT
ejpam-3096	94	5	o.c	o.c	PROPN
ejpam-3096	94	6	)	)	PUNCT
ejpam-3096	94	7	.	.	PUNCT
ejpam-3096	95	1	a	a	DET
ejpam-3096	95	2	non	non	ADJ
ejpam-3096	95	3	-	-	ADJ
ejpam-3096	95	4	decreasing	decrease	VERB
ejpam-3096	95	5	function	function	NOUN
ejpam-3096	95	6	φ	φ	NOUN
ejpam-3096	95	7	:	:	PUNCT
ejpam-3096	95	8	p	p	X
ejpam-3096	95	9	→	→	PUNCT
ejpam-3096	95	10	p	p	X
ejpam-3096	95	11	is	be	AUX
ejpam-3096	95	12	called	call	VERB
ejpam-3096	95	13	an	an	DET
ejpam-3096	95	14	φ	φ	NUM
ejpam-3096	95	15	-	-	PUNCT
ejpam-3096	95	16	maps	map	NOUN
ejpam-3096	95	17	if	if	SCONJ
ejpam-3096	95	18	:	:	PUNCT
ejpam-3096	95	19	a	a	X
ejpam-3096	95	20	)	)	PUNCT
ejpam-3096	95	21	φ(0	φ(0	ADJ
ejpam-3096	95	22	)	)	PUNCT
ejpam-3096	95	23	=	=	SYM
ejpam-3096	95	24	0	0	NUM
ejpam-3096	95	25	and	and	CCONJ
ejpam-3096	95	26	0	0	NUM
ejpam-3096	95	27	<	<	X
ejpam-3096	95	28	φ(w	φ(w	PROPN
ejpam-3096	95	29	)	)	PUNCT
ejpam-3096	95	30	<	<	X
ejpam-3096	95	31	w	w	NOUN
ejpam-3096	95	32	for	for	ADP
ejpam-3096	95	33	w	w	PROPN
ejpam-3096	95	34	∈	∈	PROPN
ejpam-3096	95	35	p\{0	p\{0	PROPN
ejpam-3096	95	36	}	}	PUNCT
ejpam-3096	95	37	,	,	PUNCT
ejpam-3096	95	38	b	b	X
ejpam-3096	95	39	)	)	PUNCT
ejpam-3096	95	40	w	w	PROPN
ejpam-3096	95	41	∈	∈	PROPN
ejpam-3096	95	42	intp	intp	NOUN
ejpam-3096	95	43	implies	imply	VERB
ejpam-3096	95	44	w	w	ADP
ejpam-3096	95	45	−	−	PUNCT
ejpam-3096	95	46	φ(w	φ(w	PROPN
ejpam-3096	95	47	)	)	PUNCT
ejpam-3096	95	48	∈	∈	PROPN
ejpam-3096	95	49	intp	intp	NOUN
ejpam-3096	95	50	,	,	PUNCT
ejpam-3096	95	51	c	c	NOUN
ejpam-3096	95	52	)	)	PUNCT
ejpam-3096	95	53	if	if	SCONJ
ejpam-3096	95	54	w	w	PROPN
ejpam-3096	95	55	∈	∈	PROPN
ejpam-3096	95	56	p\{0	p\{0	NOUN
ejpam-3096	95	57	}	}	PUNCT
ejpam-3096	95	58	and	and	CCONJ
ejpam-3096	95	59	d	d	PROPN
ejpam-3096	95	60	∈	∈	PROPN
ejpam-3096	95	61	intp	intp	NOUN
ejpam-3096	95	62	,	,	PUNCT
ejpam-3096	95	63	so	so	ADV
ejpam-3096	96	1	∃	∃	PROPN
ejpam-3096	96	2	s0	s0	PROPN
ejpam-3096	96	3	∈	∈	PROPN
ejpam-3096	96	4	n	n	CCONJ
ejpam-3096	96	5	(	(	PUNCT
ejpam-3096	96	6	s.t	s.t	PROPN
ejpam-3096	96	7	)	)	PUNCT
ejpam-3096	96	8	φs(w	φs(w	ADV
ejpam-3096	96	9	)	)	PUNCT
ejpam-3096	96	10	�	�	PROPN
ejpam-3096	96	11	d	d	PROPN
ejpam-3096	96	12	for	for	ADP
ejpam-3096	96	13	each	each	DET
ejpam-3096	96	14	s	s	PART
ejpam-3096	96	15	≥	≥	NOUN
ejpam-3096	96	16	s0	s0	PROPN
ejpam-3096	96	17	.	.	PROPN
ejpam-3096	96	18	example	example	NOUN
ejpam-3096	97	1	3	3	NUM
ejpam-3096	97	2	(	(	PUNCT
ejpam-3096	97	3	3	3	NUM
ejpam-3096	97	4	)	)	PUNCT
ejpam-3096	97	5	.	.	PUNCT
ejpam-3096	98	1	(	(	PUNCT
ejpam-3096	98	2	a	a	X
ejpam-3096	98	3	)	)	PUNCT
ejpam-3096	98	4	if	if	SCONJ
ejpam-3096	98	5	p	p	NOUN
ejpam-3096	98	6	is	be	AUX
ejpam-3096	98	7	an	an	DET
ejpam-3096	98	8	arbitrary	arbitrary	ADJ
ejpam-3096	98	9	cone	cone	NOUN
ejpam-3096	98	10	in	in	ADP
ejpam-3096	98	11	(	(	PUNCT
ejpam-3096	98	12	b.s	b.s	NOUN
ejpam-3096	98	13	)	)	PUNCT
ejpam-3096	98	14	e	e	PROPN
ejpam-3096	98	15	and	and	CCONJ
ejpam-3096	98	16	δ	δ	PROPN
ejpam-3096	98	17	∈	∈	PROPN
ejpam-3096	98	18	(	(	PUNCT
ejpam-3096	98	19	0	0	NUM
ejpam-3096	98	20	,	,	PUNCT
ejpam-3096	98	21	1	1	NUM
ejpam-3096	98	22	)	)	PUNCT
ejpam-3096	98	23	,	,	PUNCT
ejpam-3096	98	24	in	in	ADP
ejpam-3096	98	25	that	that	DET
ejpam-3096	98	26	case	case	NOUN
ejpam-3096	98	27	φ	φ	X
ejpam-3096	98	28	:	:	PUNCT
ejpam-3096	98	29	p	p	X
ejpam-3096	98	30	→	→	SYM
ejpam-3096	98	31	p	p	X
ejpam-3096	98	32	,	,	PUNCT
ejpam-3096	98	33	defined	define	VERB
ejpam-3096	98	34	by	by	ADP
ejpam-3096	98	35	φ(w	φ(w	PROPN
ejpam-3096	98	36	)	)	PUNCT
ejpam-3096	98	37	=	=	SYM
ejpam-3096	98	38	δw	δw	VERB
ejpam-3096	98	39	for	for	ADP
ejpam-3096	98	40	w	w	PROPN
ejpam-3096	98	41	∈	∈	PROPN
ejpam-3096	98	42	p	p	NOUN
ejpam-3096	98	43	,	,	PUNCT
ejpam-3096	98	44	is	be	AUX
ejpam-3096	98	45	a	a	DET
ejpam-3096	98	46	φ	φ	NOUN
ejpam-3096	98	47	-	-	PUNCT
ejpam-3096	98	48	maps	map	NOUN
ejpam-3096	98	49	.	.	PUNCT
ejpam-3096	99	1	a.	a.	PROPN
ejpam-3096	99	2	m.	m.	PROPN
ejpam-3096	99	3	al	al	PROPN
ejpam-3096	99	4	.	.	PROPN
ejpam-3096	99	5	jumaili	jumaili	PROPN
ejpam-3096	99	6	/	/	SYM
ejpam-3096	99	7	eur	eur	PROPN
ejpam-3096	99	8	.	.	PUNCT
ejpam-3096	100	1	j.	j.	PROPN
ejpam-3096	100	2	pure	pure	PROPN
ejpam-3096	100	3	appl	appl	PROPN
ejpam-3096	100	4	.	.	PROPN
ejpam-3096	100	5	math	math	PROPN
ejpam-3096	100	6	,	,	PUNCT
ejpam-3096	100	7	10	10	NUM
ejpam-3096	100	8	(	(	PUNCT
ejpam-3096	100	9	5	5	NUM
ejpam-3096	100	10	)	)	PUNCT
ejpam-3096	100	11	(	(	PUNCT
ejpam-3096	100	12	2017	2017	NUM
ejpam-3096	100	13	)	)	PUNCT
ejpam-3096	100	14	,	,	PUNCT
ejpam-3096	100	15	1023	1023	NUM
ejpam-3096	100	16	-	-	SYM
ejpam-3096	100	17	1034	1034	NUM
ejpam-3096	100	18	1027	1027	NUM
ejpam-3096	100	19	(	(	PUNCT
ejpam-3096	100	20	b	b	X
ejpam-3096	100	21	)	)	PUNCT
ejpam-3096	100	22	let	let	VERB
ejpam-3096	100	23	ψ	ψ	X
ejpam-3096	100	24	:	:	PUNCT
ejpam-3096	101	1	[	[	X
ejpam-3096	101	2	0,+∞	0,+∞	NUM
ejpam-3096	101	3	)	)	PUNCT
ejpam-3096	101	4	→	→	PUNCT
ejpam-3096	102	1	[	[	X
ejpam-3096	102	2	0,+∞	0,+∞	NUM
ejpam-3096	102	3	)	)	PUNCT
ejpam-3096	102	4	be	be	VERB
ejpam-3096	102	5	any	any	PRON
ejpam-3096	102	6	real	real	ADV
ejpam-3096	102	7	valued	value	VERB
ejpam-3096	102	8	φ	φ	NOUN
ejpam-3096	102	9	-	-	NOUN
ejpam-3096	102	10	map	map	NOUN
ejpam-3096	102	11	and	and	CCONJ
ejpam-3096	102	12	let	let	VERB
ejpam-3096	102	13	p	p	PRON
ejpam-3096	102	14	be	be	AUX
ejpam-3096	102	15	a	a	DET
ejpam-3096	102	16	cone	cone	NOUN
ejpam-3096	102	17	in	in	ADP
ejpam-3096	102	18	(	(	PUNCT
ejpam-3096	102	19	b.s	b.s	NOUN
ejpam-3096	102	20	)	)	PUNCT
ejpam-3096	102	21	e	e	PROPN
ejpam-3096	102	22	and	and	CCONJ
ejpam-3096	102	23	δ	δ	PROPN
ejpam-3096	102	24	∈	∈	PROPN
ejpam-3096	102	25	(	(	PUNCT
ejpam-3096	102	26	0	0	NUM
ejpam-3096	102	27	,	,	PUNCT
ejpam-3096	102	28	1	1	NUM
ejpam-3096	102	29	)	)	PUNCT
ejpam-3096	102	30	,	,	PUNCT
ejpam-3096	102	31	be	be	AUX
ejpam-3096	102	32	fixed	fix	VERB
ejpam-3096	102	33	.	.	PUNCT
ejpam-3096	103	1	in	in	ADP
ejpam-3096	103	2	that	that	DET
ejpam-3096	103	3	case	case	NOUN
ejpam-3096	103	4	the	the	DET
ejpam-3096	103	5	function	function	NOUN
ejpam-3096	103	6	φδ	φδ	VERB
ejpam-3096	103	7	:	:	PUNCT
ejpam-3096	103	8	p	p	X
ejpam-3096	103	9	→	→	PUNCT
ejpam-3096	103	10	p	p	NOUN
ejpam-3096	103	11	defined	define	VERB
ejpam-3096	103	12	by	by	ADP
ejpam-3096	103	13	:	:	PUNCT
ejpam-3096	103	14	φδ(w	φδ(w	X
ejpam-3096	103	15	)	)	PUNCT
ejpam-3096	103	16	=	=	SYM
ejpam-3096	103	17	ψ(δ)w	ψ(δ)w	PROPN
ejpam-3096	103	18	,	,	PUNCT
ejpam-3096	103	19	is	be	AUX
ejpam-3096	103	20	a	a	DET
ejpam-3096	103	21	φ	φ	NOUN
ejpam-3096	103	22	-	-	PUNCT
ejpam-3096	103	23	maps	map	NOUN
ejpam-3096	103	24	.	.	PUNCT
ejpam-3096	104	1	examples	example	NOUN
ejpam-3096	104	2	of	of	ADP
ejpam-3096	104	3	this	this	DET
ejpam-3096	104	4	type	type	NOUN
ejpam-3096	104	5	are	be	AUX
ejpam-3096	104	6	of	of	ADP
ejpam-3096	104	7	particular	particular	ADJ
ejpam-3096	104	8	interest	interest	NOUN
ejpam-3096	104	9	in	in	ADP
ejpam-3096	104	10	the	the	DET
ejpam-3096	104	11	case	case	NOUN
ejpam-3096	104	12	when	when	SCONJ
ejpam-3096	104	13	the	the	DET
ejpam-3096	104	14	cone	cone	NOUN
ejpam-3096	104	15	p	p	NOUN
ejpam-3096	104	16	is	be	AUX
ejpam-3096	104	17	non	non	ADJ
ejpam-3096	104	18	-	-	ADJ
ejpam-3096	104	19	normal	normal	ADJ
ejpam-3096	104	20	.	.	PUNCT
ejpam-3096	105	1	(	(	PUNCT
ejpam-3096	105	2	see	see	VERB
ejpam-3096	105	3	example	example	NOUN
ejpam-3096	105	4	2	2	NUM
ejpam-3096	105	5	)	)	PUNCT
ejpam-3096	105	6	,	,	PUNCT
ejpam-3096	105	7	one	one	PRON
ejpam-3096	105	8	can	can	AUX
ejpam-3096	105	9	take	take	VERB
ejpam-3096	105	10	,	,	PUNCT
ejpam-3096	105	11	e	e	X
ejpam-3096	105	12	=	=	PROPN
ejpam-3096	105	13	c1	c1	PROPN
ejpam-3096	105	14	r[0	r[0	PROPN
ejpam-3096	105	15	,	,	PUNCT
ejpam-3096	105	16	1	1	NUM
ejpam-3096	105	17	]	]	PUNCT
ejpam-3096	105	18	,	,	PUNCT
ejpam-3096	105	19	p	p	NOUN
ejpam-3096	105	20	=	=	PUNCT
ejpam-3096	105	21	{	{	PUNCT
ejpam-3096	105	22	x	x	SYM
ejpam-3096	105	23	∈	∈	PROPN
ejpam-3096	105	24	e	e	NOUN
ejpam-3096	105	25	:	:	PUNCT
ejpam-3096	105	26	x(t	x(t	PROPN
ejpam-3096	105	27	)	)	PUNCT
ejpam-3096	105	28	≥	≥	NOUN
ejpam-3096	105	29	0	0	NUM
ejpam-3096	105	30	on	on	ADP
ejpam-3096	105	31	[	[	X
ejpam-3096	105	32	0	0	NUM
ejpam-3096	105	33	,	,	PUNCT
ejpam-3096	105	34	1	1	NUM
ejpam-3096	105	35	]	]	PUNCT
ejpam-3096	105	36	}	}	PUNCT
ejpam-3096	105	37	as	as	ADV
ejpam-3096	105	38	well	well	ADV
ejpam-3096	105	39	ψ(δ	ψ(δ	ADV
ejpam-3096	105	40	)	)	PUNCT
ejpam-3096	106	1	=	=	SYM
ejpam-3096	106	2	δ	δ	NOUN
ejpam-3096	106	3	1	1	NUM
ejpam-3096	106	4	+	+	NUM
ejpam-3096	106	5	δ	δ	PROPN
ejpam-3096	106	6	;	;	PUNCT
ejpam-3096	106	7	δ	δ	PROPN
ejpam-3096	106	8	∈	∈	PROPN
ejpam-3096	106	9	(	(	PUNCT
ejpam-3096	106	10	0	0	NUM
ejpam-3096	106	11	,	,	PUNCT
ejpam-3096	106	12	1	1	NUM
ejpam-3096	106	13	)	)	PUNCT
ejpam-3096	106	14	.	.	PUNCT
ejpam-3096	107	1	the	the	DET
ejpam-3096	107	2	following	follow	VERB
ejpam-3096	107	3	theorem	theorem	NOUN
ejpam-3096	107	4	is	be	AUX
ejpam-3096	107	5	our	our	PRON
ejpam-3096	107	6	first	first	ADJ
ejpam-3096	107	7	main	main	ADJ
ejpam-3096	107	8	results	result	NOUN
ejpam-3096	107	9	.	.	PUNCT
ejpam-3096	108	1	theorem	theorem	NOUN
ejpam-3096	108	2	1	1	NUM
ejpam-3096	108	3	.	.	PUNCT
ejpam-3096	109	1	suppose	suppose	VERB
ejpam-3096	109	2	(	(	PUNCT
ejpam-3096	109	3	x,4	x,4	NUM
ejpam-3096	109	4	)	)	PUNCT
ejpam-3096	109	5	is	be	AUX
ejpam-3096	109	6	(	(	PUNCT
ejpam-3096	109	7	p.o.s	p.o.s	NOUN
ejpam-3096	109	8	)	)	PUNCT
ejpam-3096	109	9	with	with	ADP
ejpam-3096	109	10	assume	assume	PROPN
ejpam-3096	109	11	(	(	PUNCT
ejpam-3096	109	12	x	x	X
ejpam-3096	109	13	,	,	PUNCT
ejpam-3096	109	14	d∗	d∗	PROPN
ejpam-3096	109	15	)	)	PUNCT
ejpam-3096	109	16	is	be	AUX
ejpam-3096	109	17	a	a	DET
ejpam-3096	109	18	generalized	generalized	ADJ
ejpam-3096	109	19	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	109	20	and	and	CCONJ
ejpam-3096	109	21	p	p	NOUN
ejpam-3096	109	22	is	be	AUX
ejpam-3096	109	23	(	(	PUNCT
ejpam-3096	109	24	o.c	o.c	PROPN
ejpam-3096	109	25	)	)	PUNCT
ejpam-3096	109	26	with	with	ADP
ejpam-3096	109	27	normal	normal	ADJ
ejpam-3096	109	28	cone	cone	NOUN
ejpam-3096	109	29	k.	k.	PROPN
ejpam-3096	109	30	let	let	VERB
ejpam-3096	109	31	£	£	SYM
ejpam-3096	109	32	,	,	PUNCT
ejpam-3096	109	33	t	t	X
ejpam-3096	109	34	:	:	PUNCT
ejpam-3096	109	35	x	x	X
ejpam-3096	109	36	→	→	PUNCT
ejpam-3096	109	37	x	x	PUNCT
ejpam-3096	109	38	be	be	AUX
ejpam-3096	109	39	two	two	NUM
ejpam-3096	109	40	maps	map	NOUN
ejpam-3096	109	41	(	(	PUNCT
ejpam-3096	109	42	s.t	s.t	PROPN
ejpam-3096	109	43	)	)	PUNCT
ejpam-3096	109	44	,	,	PUNCT
ejpam-3096	109	45	d∗(tx	d∗(tx	PROPN
ejpam-3096	109	46	,	,	PUNCT
ejpam-3096	109	47	ty	ty	INTJ
ejpam-3096	109	48	,	,	PUNCT
ejpam-3096	109	49	tz	tz	NOUN
ejpam-3096	109	50	)	)	PUNCT
ejpam-3096	109	51	≤	≤	NOUN
ejpam-3096	109	52	φ(d∗(£x,£y,£z	φ(d∗(£x,£y,£z	NUM
ejpam-3096	109	53	)	)	PUNCT
ejpam-3096	109	54	)	)	PUNCT
ejpam-3096	109	55	...........................................................	...........................................................	PUNCT
ejpam-3096	110	1	(	(	PUNCT
ejpam-3096	110	2	3.1	3.1	NUM
ejpam-3096	110	3	)	)	PUNCT
ejpam-3096	110	4	and	and	CCONJ
ejpam-3096	110	5	assume	assume	VERB
ejpam-3096	110	6	the	the	DET
ejpam-3096	110	7	following	following	NOUN
ejpam-3096	110	8	:	:	PUNCT
ejpam-3096	110	9	a	a	X
ejpam-3096	110	10	)	)	PUNCT
ejpam-3096	110	11	t	t	NOUN
ejpam-3096	110	12	is	be	AUX
ejpam-3096	110	13	weakly	weakly	ADV
ejpam-3096	110	14	increasing	increase	VERB
ejpam-3096	110	15	with	with	ADP
ejpam-3096	110	16	respect	respect	NOUN
ejpam-3096	110	17	to	to	ADP
ejpam-3096	110	18	£	£	SYM
ejpam-3096	110	19	,	,	PUNCT
ejpam-3096	110	20	b	b	NOUN
ejpam-3096	110	21	)	)	PUNCT
ejpam-3096	110	22	£	£	NOUN
ejpam-3096	110	23	x	x	PUNCT
ejpam-3096	110	24	is	be	AUX
ejpam-3096	110	25	a	a	DET
ejpam-3096	110	26	complete	complete	ADJ
ejpam-3096	110	27	sub	sub	NOUN
ejpam-3096	110	28	-	-	NOUN
ejpam-3096	110	29	space	space	NOUN
ejpam-3096	110	30	of	of	ADP
ejpam-3096	110	31	x	x	X
ejpam-3096	110	32	,	,	PUNCT
ejpam-3096	110	33	c	c	NOUN
ejpam-3096	110	34	)	)	PUNCT
ejpam-3096	110	35	x	x	X
ejpam-3096	110	36	is	be	AUX
ejpam-3096	110	37	regular	regular	ADJ
ejpam-3096	110	38	.	.	PUNCT
ejpam-3096	111	1	for	for	ADP
ejpam-3096	111	2	each	each	DET
ejpam-3096	111	3	x	x	PROPN
ejpam-3096	111	4	,	,	PUNCT
ejpam-3096	111	5	y	y	PROPN
ejpam-3096	111	6	,	,	PUNCT
ejpam-3096	111	7	z	z	NOUN
ejpam-3096	111	8	∈	∈	PROPN
ejpam-3096	111	9	x	x	PUNCT
ejpam-3096	111	10	with	with	ADP
ejpam-3096	111	11	£	£	SYM
ejpam-3096	111	12	z	z	NOUN
ejpam-3096	111	13	4	4	NUM
ejpam-3096	111	14	£	£	SYM
ejpam-3096	111	15	y	y	PROPN
ejpam-3096	111	16	4	4	NUM
ejpam-3096	111	17	£	£	NOUN
ejpam-3096	111	18	x	x	PUNCT
ejpam-3096	111	19	where	where	SCONJ
ejpam-3096	111	20	φ	φ	PROPN
ejpam-3096	111	21	is	be	AUX
ejpam-3096	111	22	a	a	DET
ejpam-3096	111	23	φ	φ	NOUN
ejpam-3096	111	24	-	-	PUNCT
ejpam-3096	111	25	map	map	NOUN
ejpam-3096	111	26	.	.	PUNCT
ejpam-3096	112	1	in	in	ADP
ejpam-3096	112	2	that	that	DET
ejpam-3096	112	3	case	case	NOUN
ejpam-3096	112	4	£	£	PROPN
ejpam-3096	112	5	and	and	CCONJ
ejpam-3096	112	6	t	t	PROPN
ejpam-3096	112	7	have	have	VERB
ejpam-3096	112	8	a	a	DET
ejpam-3096	112	9	coincidence	coincidence	NOUN
ejpam-3096	112	10	point	point	NOUN
ejpam-3096	112	11	.	.	PUNCT
ejpam-3096	113	1	proof	proof	NOUN
ejpam-3096	113	2	.	.	PUNCT
ejpam-3096	114	1	assume	assume	VERB
ejpam-3096	114	2	that	that	SCONJ
ejpam-3096	114	3	a	a	DET
ejpam-3096	114	4	point	point	NOUN
ejpam-3096	114	5	x0	x0	PROPN
ejpam-3096	114	6	∈	∈	PROPN
ejpam-3096	114	7	x	x	PUNCT
ejpam-3096	114	8	is	be	AUX
ejpam-3096	114	9	arbitrary	arbitrary	ADJ
ejpam-3096	114	10	.	.	PUNCT
ejpam-3096	115	1	by	by	ADP
ejpam-3096	115	2	definition	definition	NOUN
ejpam-3096	115	3	(	(	PUNCT
ejpam-3096	115	4	4	4	X
ejpam-3096	115	5	)	)	PUNCT
ejpam-3096	115	6	we	we	PRON
ejpam-3096	115	7	have	have	AUX
ejpam-3096	115	8	tx	tx	ADP
ejpam-3096	115	9	⊆	⊆	NUM
ejpam-3096	115	10	£	£	SYM
ejpam-3096	115	11	x	x	NOUN
ejpam-3096	115	12	,	,	PUNCT
ejpam-3096	115	13	thus	thus	ADV
ejpam-3096	115	14	we	we	PRON
ejpam-3096	115	15	can	can	AUX
ejpam-3096	115	16	construct	construct	VERB
ejpam-3096	115	17	a	a	DET
ejpam-3096	115	18	sequence	sequence	NOUN
ejpam-3096	115	19	{	{	PUNCT
ejpam-3096	115	20	xs	xs	NOUN
ejpam-3096	115	21	}	}	PUNCT
ejpam-3096	115	22	in	in	ADP
ejpam-3096	115	23	x	x	PUNCT
ejpam-3096	115	24	via	via	ADP
ejpam-3096	115	25	:	:	PUNCT
ejpam-3096	115	26	£	£	SYM
ejpam-3096	115	27	xs+1	xs+1	NOUN
ejpam-3096	115	28	=	=	SYM
ejpam-3096	115	29	txs	txs	PROPN
ejpam-3096	115	30	,	,	PUNCT
ejpam-3096	115	31	∀s	∀s	PROPN
ejpam-3096	115	32	∈	∈	PROPN
ejpam-3096	115	33	n0	n0	PROPN
ejpam-3096	115	34	.	.	PUNCT
ejpam-3096	116	1	since	since	SCONJ
ejpam-3096	116	2	t	t	PROPN
ejpam-3096	116	3	is	be	AUX
ejpam-3096	116	4	weakly	weakly	ADV
ejpam-3096	116	5	increasing	increase	VERB
ejpam-3096	116	6	with	with	ADP
ejpam-3096	116	7	respect	respect	NOUN
ejpam-3096	116	8	to	to	ADP
ejpam-3096	116	9	£	£	PROPN
ejpam-3096	116	10	and	and	CCONJ
ejpam-3096	116	11	x1	x1	PROPN
ejpam-3096	116	12	∈	∈	PROPN
ejpam-3096	116	13	£	£	SYM
ejpam-3096	116	14	−1(tx0	−1(tx0	NOUN
ejpam-3096	116	15	)	)	PUNCT
ejpam-3096	116	16	and	and	CCONJ
ejpam-3096	116	17	x2	x2	PROPN
ejpam-3096	116	18	∈	∈	PROPN
ejpam-3096	116	19	£	£	SYM
ejpam-3096	116	20	−1(tx1	−1(tx1	NOUN
ejpam-3096	116	21	)	)	PUNCT
ejpam-3096	116	22	,	,	PUNCT
ejpam-3096	116	23	in	in	ADP
ejpam-3096	116	24	that	that	DET
ejpam-3096	116	25	case	case	NOUN
ejpam-3096	116	26	we	we	PRON
ejpam-3096	116	27	get	get	VERB
ejpam-3096	116	28	:	:	PUNCT
ejpam-3096	116	29	£	£	SYM
ejpam-3096	116	30	x1	x1	NUM
ejpam-3096	116	31	4	4	NUM
ejpam-3096	116	32	£	£	SYM
ejpam-3096	116	33	x2	x2	PROPN
ejpam-3096	116	34	4	4	NUM
ejpam-3096	116	35	£	£	SYM
ejpam-3096	116	36	x3	x3	ADJ
ejpam-3096	116	37	4	4	NUM
ejpam-3096	116	38	.........	.........	SYM
ejpam-3096	116	39	4	4	NUM
ejpam-3096	116	40	£	£	SYM
ejpam-3096	116	41	xs	xs	NOUN
ejpam-3096	116	42	4	4	NUM
ejpam-3096	116	43	£	£	SYM
ejpam-3096	116	44	xs+1	xs+1	PROPN
ejpam-3096	116	45	4	4	NUM
ejpam-3096	116	46	.........	.........	PUNCT
ejpam-3096	116	47	now	now	ADV
ejpam-3096	116	48	establish	establish	VERB
ejpam-3096	116	49	that	that	SCONJ
ejpam-3096	116	50	{	{	PUNCT
ejpam-3096	116	51	£	£	SYM
ejpam-3096	116	52	xs	xs	NOUN
ejpam-3096	116	53	}	}	PUNCT
ejpam-3096	116	54	is	be	AUX
ejpam-3096	116	55	a	a	DET
ejpam-3096	116	56	cauchy	cauchy	ADJ
ejpam-3096	116	57	sequence	sequence	NOUN
ejpam-3096	116	58	in	in	ADP
ejpam-3096	116	59	(	(	PUNCT
ejpam-3096	116	60	£	£	PROPN
ejpam-3096	116	61	(	(	PUNCT
ejpam-3096	116	62	x	x	NOUN
ejpam-3096	116	63	)	)	PUNCT
ejpam-3096	116	64	,	,	PUNCT
ejpam-3096	116	65	d∗	d∗	PROPN
ejpam-3096	116	66	)	)	PUNCT
ejpam-3096	116	67	.	.	PUNCT
ejpam-3096	117	1	we	we	PRON
ejpam-3096	117	2	will	will	AUX
ejpam-3096	117	3	discuss	discuss	VERB
ejpam-3096	117	4	two	two	NUM
ejpam-3096	117	5	cases	case	NOUN
ejpam-3096	117	6	:	:	PUNCT
ejpam-3096	117	7	(	(	PUNCT
ejpam-3096	117	8	a)there	a)there	PROPN
ejpam-3096	117	9	exists	exist	VERB
ejpam-3096	117	10	s	s	PART
ejpam-3096	117	11	∈	∈	PROPN
ejpam-3096	117	12	n	n	CCONJ
ejpam-3096	117	13	(	(	PUNCT
ejpam-3096	117	14	s.t	s.t	PROPN
ejpam-3096	117	15	)	)	PUNCT
ejpam-3096	117	16	£	£	PROPN
ejpam-3096	117	17	xs	xs	NOUN
ejpam-3096	117	18	=	=	PUNCT
ejpam-3096	117	19	£	£	SYM
ejpam-3096	117	20	xs+1	xs+1	NOUN
ejpam-3096	117	21	.	.	PUNCT
ejpam-3096	117	22	using	use	VERB
ejpam-3096	117	23	the	the	DET
ejpam-3096	117	24	considered	consider	VERB
ejpam-3096	117	25	contractive	contractive	ADJ
ejpam-3096	117	26	condition	condition	NOUN
ejpam-3096	117	27	,	,	PUNCT
ejpam-3096	117	28	get	get	VERB
ejpam-3096	117	29	:	:	PUNCT
ejpam-3096	117	30	txs	txs	NOUN
ejpam-3096	117	31	=	=	SYM
ejpam-3096	117	32	txs+1	txs+1	NOUN
ejpam-3096	117	33	,	,	PUNCT
ejpam-3096	117	34	that	that	ADV
ejpam-3096	117	35	is	is	ADV
ejpam-3096	117	36	,	,	PUNCT
ejpam-3096	118	1	£	£	PROPN
ejpam-3096	118	2	xs+1	xs+1	NOUN
ejpam-3096	118	3	=	=	PUNCT
ejpam-3096	118	4	£	£	SYM
ejpam-3096	118	5	xs+2	xs+2	NUM
ejpam-3096	118	6	.	.	PUNCT
ejpam-3096	119	1	therefore	therefore	ADV
ejpam-3096	119	2	we	we	PRON
ejpam-3096	119	3	have	have	VERB
ejpam-3096	119	4	£	£	SYM
ejpam-3096	119	5	xr	xr	NOUN
ejpam-3096	119	6	=	=	SYM
ejpam-3096	119	7	£	£	SYM
ejpam-3096	119	8	xs	xs	NOUN
ejpam-3096	119	9	,	,	PUNCT
ejpam-3096	119	10	∀	∀	X
ejpam-3096	119	11	r	r	NOUN
ejpam-3096	119	12	≥	≥	NOUN
ejpam-3096	119	13	s	s	PART
ejpam-3096	119	14	⇒	⇒	NOUN
ejpam-3096	119	15	{	{	PUNCT
ejpam-3096	119	16	£	£	SYM
ejpam-3096	119	17	xs	xs	NOUN
ejpam-3096	119	18	}	}	PUNCT
ejpam-3096	119	19	is	be	AUX
ejpam-3096	119	20	a	a	DET
ejpam-3096	119	21	cauchy	cauchy	ADJ
ejpam-3096	119	22	sequence	sequence	NOUN
ejpam-3096	119	23	in	in	ADP
ejpam-3096	119	24	(	(	PUNCT
ejpam-3096	119	25	£	£	PROPN
ejpam-3096	119	26	(	(	PUNCT
ejpam-3096	119	27	x	x	NOUN
ejpam-3096	119	28	)	)	PUNCT
ejpam-3096	119	29	,	,	PUNCT
ejpam-3096	119	30	d∗	d∗	PROPN
ejpam-3096	119	31	)	)	PUNCT
ejpam-3096	119	32	.	.	PUNCT
ejpam-3096	120	1	(	(	PUNCT
ejpam-3096	120	2	b	b	X
ejpam-3096	120	3	)	)	PUNCT
ejpam-3096	120	4	the	the	DET
ejpam-3096	120	5	successive	successive	ADJ
ejpam-3096	120	6	conditions	condition	NOUN
ejpam-3096	120	7	of	of	ADP
ejpam-3096	120	8	a	a	DET
ejpam-3096	120	9	sequence	sequence	NOUN
ejpam-3096	120	10	{	{	PUNCT
ejpam-3096	120	11	£	£	SYM
ejpam-3096	120	12	xs	xs	NOUN
ejpam-3096	120	13	}	}	PUNCT
ejpam-3096	120	14	are	be	AUX
ejpam-3096	120	15	different	different	ADJ
ejpam-3096	120	16	.	.	PUNCT
ejpam-3096	121	1	from	from	ADP
ejpam-3096	121	2	the	the	DET
ejpam-3096	121	3	above	above	ADJ
ejpam-3096	121	4	inequality	inequality	NOUN
ejpam-3096	121	5	(	(	PUNCT
ejpam-3096	121	6	3.1	3.1	NUM
ejpam-3096	121	7	)	)	PUNCT
ejpam-3096	121	8	,	,	PUNCT
ejpam-3096	121	9	we	we	PRON
ejpam-3096	121	10	obtain	obtain	VERB
ejpam-3096	121	11	:	:	PUNCT
ejpam-3096	122	1	d∗(£xs,£xs,£xs+1	d∗(£xs,£xs,£xs+1	ADJ
ejpam-3096	122	2	)	)	PUNCT
ejpam-3096	122	3	≤	≤	ADJ
ejpam-3096	122	4	d∗(txs−1	d∗(txs−1	NOUN
ejpam-3096	122	5	,	,	PUNCT
ejpam-3096	122	6	txs−1	txs−1	PROPN
ejpam-3096	122	7	,	,	PUNCT
ejpam-3096	122	8	txs	txs	NOUN
ejpam-3096	122	9	)	)	PUNCT
ejpam-3096	122	10	≤	≤	NOUN
ejpam-3096	122	11	φ(d∗(£xs−1,£xs−1,£xs	φ(d∗(£xs−1,£xs−1,£xs	PROPN
ejpam-3096	122	12	)	)	PUNCT
ejpam-3096	122	13	)	)	PUNCT
ejpam-3096	122	14	≤	≤	NUM
ejpam-3096	122	15	φ2(d∗(£xs−2,£xs−2,£xs−1	φ2(d∗(£xs−2,£xs−2,£xs−1	PROPN
ejpam-3096	122	16	)	)	PUNCT
ejpam-3096	122	17	)	)	PUNCT
ejpam-3096	122	18	..........	..........	PUNCT
ejpam-3096	123	1	≤	≤	NUM
ejpam-3096	123	2	φs(d∗(£x0,£x0,£x1	φs(d∗(£x0,£x0,£x1	NUM
ejpam-3096	123	3	)	)	PUNCT
ejpam-3096	123	4	)	)	PUNCT
ejpam-3096	123	5	.	.	PUNCT
ejpam-3096	124	1	fix	fix	NOUN
ejpam-3096	124	2	d	d	NOUN
ejpam-3096	124	3	,	,	PUNCT
ejpam-3096	124	4	0	0	NUM
ejpam-3096	124	5	�	�	PROPN
ejpam-3096	124	6	d.	d.	PROPN
ejpam-3096	124	7	by	by	ADP
ejpam-3096	124	8	means	mean	NOUN
ejpam-3096	124	9	of	of	ADP
ejpam-3096	124	10	the	the	DET
ejpam-3096	124	11	characteristic	characteristic	ADJ
ejpam-3096	124	12	(	(	PUNCT
ejpam-3096	124	13	c	c	NOUN
ejpam-3096	124	14	)	)	PUNCT
ejpam-3096	124	15	of	of	ADP
ejpam-3096	124	16	definition	definition	NOUN
ejpam-3096	124	17	(	(	PUNCT
ejpam-3096	124	18	6	6	NUM
ejpam-3096	124	19	)	)	PUNCT
ejpam-3096	124	20	,	,	PUNCT
ejpam-3096	124	21	∃	∃	PROPN
ejpam-3096	124	22	s0	s0	PROPN
ejpam-3096	124	23	∈	∈	PROPN
ejpam-3096	124	24	n	n	PROPN
ejpam-3096	124	25	(	(	PUNCT
ejpam-3096	124	26	s.t	s.t	PROPN
ejpam-3096	124	27	)	)	PUNCT
ejpam-3096	124	28	,	,	PUNCT
ejpam-3096	124	29	φs(d∗(£x0,£x0,£x1	φs(d∗(£x0,£x0,£x1	PROPN
ejpam-3096	124	30	)	)	PUNCT
ejpam-3096	124	31	)	)	PUNCT
ejpam-3096	124	32	�	�	PROPN
ejpam-3096	125	1	d	d	ADP
ejpam-3096	125	2	∀	∀	X
ejpam-3096	125	3	s	s	PART
ejpam-3096	125	4	≥	≥	NOUN
ejpam-3096	125	5	s0	s0	PROPN
ejpam-3096	125	6	.	.	PUNCT
ejpam-3096	126	1	according	accord	VERB
ejpam-3096	126	2	the	the	DET
ejpam-3096	126	3	remark	remark	NOUN
ejpam-3096	126	4	(	(	PUNCT
ejpam-3096	126	5	2−r1	2−r1	NUM
ejpam-3096	126	6	)	)	PUNCT
ejpam-3096	126	7	,	,	PUNCT
ejpam-3096	126	8	we	we	PRON
ejpam-3096	126	9	get	get	VERB
ejpam-3096	126	10	:	:	PUNCT
ejpam-3096	126	11	d∗(£xs,£xs,£xs+1	d∗(£xs,£xs,£xs+1	ADJ
ejpam-3096	126	12	)	)	PUNCT
ejpam-3096	126	13	�	�	PROPN
ejpam-3096	126	14	d	d	ADP
ejpam-3096	126	15	∀	∀	X
ejpam-3096	126	16	s	s	PART
ejpam-3096	126	17	≥	≥	NOUN
ejpam-3096	126	18	s0	s0	PROPN
ejpam-3096	126	19	.	.	PUNCT
ejpam-3096	127	1	in	in	ADP
ejpam-3096	127	2	the	the	DET
ejpam-3096	127	3	same	same	ADJ
ejpam-3096	127	4	method	method	NOUN
ejpam-3096	127	5	choose	choose	VERB
ejpam-3096	127	6	a	a	DET
ejpam-3096	127	7	natural	natural	ADJ
ejpam-3096	127	8	number	number	NOUN
ejpam-3096	127	9	s1	s1	NOUN
ejpam-3096	127	10	∈	∈	PROPN
ejpam-3096	127	11	n	n	CCONJ
ejpam-3096	127	12	(	(	PUNCT
ejpam-3096	127	13	s.t	s.t	PROPN
ejpam-3096	127	14	):	):	PUNCT
ejpam-3096	127	15	d∗(£xr,£xr,£xr+1	d∗(£xr,£xr,£xr+1	NOUN
ejpam-3096	127	16	)	)	PUNCT
ejpam-3096	127	17	<	<	X
ejpam-3096	127	18	d−	d−	PROPN
ejpam-3096	127	19	φ(d	φ(d	NUM
ejpam-3096	127	20	)	)	PUNCT
ejpam-3096	127	21	∀	∀	X
ejpam-3096	128	1	r	r	NOUN
ejpam-3096	128	2	≥	≥	NOUN
ejpam-3096	128	3	s1	s1	NOUN
ejpam-3096	128	4	............................................	............................................	PUNCT
ejpam-3096	128	5	(	(	PUNCT
ejpam-3096	128	6	3.2	3.2	NUM
ejpam-3096	128	7	)	)	PUNCT
ejpam-3096	128	8	a.	a.	NOUN
ejpam-3096	128	9	m.	m.	PROPN
ejpam-3096	128	10	al	al	PROPN
ejpam-3096	128	11	.	.	PROPN
ejpam-3096	128	12	jumaili	jumaili	PROPN
ejpam-3096	128	13	/	/	SYM
ejpam-3096	128	14	eur	eur	PROPN
ejpam-3096	128	15	.	.	PUNCT
ejpam-3096	129	1	j.	j.	PROPN
ejpam-3096	129	2	pure	pure	PROPN
ejpam-3096	129	3	appl	appl	PROPN
ejpam-3096	129	4	.	.	PROPN
ejpam-3096	129	5	math	math	PROPN
ejpam-3096	129	6	,	,	PUNCT
ejpam-3096	129	7	10	10	NUM
ejpam-3096	129	8	(	(	PUNCT
ejpam-3096	129	9	5	5	NUM
ejpam-3096	129	10	)	)	PUNCT
ejpam-3096	129	11	(	(	PUNCT
ejpam-3096	129	12	2017	2017	NUM
ejpam-3096	129	13	)	)	PUNCT
ejpam-3096	129	14	,	,	PUNCT
ejpam-3096	129	15	1023	1023	NUM
ejpam-3096	129	16	-	-	SYM
ejpam-3096	129	17	1034	1034	NUM
ejpam-3096	129	18	1028	1028	NUM
ejpam-3096	129	19	now	now	ADV
ejpam-3096	129	20	via	via	ADP
ejpam-3096	129	21	induction	induction	NOUN
ejpam-3096	129	22	on	on	ADP
ejpam-3096	129	23	r	r	NOUN
ejpam-3096	129	24	we	we	PRON
ejpam-3096	129	25	will	will	AUX
ejpam-3096	129	26	prove	prove	VERB
ejpam-3096	129	27	the	the	DET
ejpam-3096	129	28	following	follow	VERB
ejpam-3096	129	29	claim	claim	NOUN
ejpam-3096	129	30	:	:	PUNCT
ejpam-3096	129	31	d∗(£xs,£xs,£xr	d∗(£xs,£xs,£xr	NOUN
ejpam-3096	129	32	)	)	PUNCT
ejpam-3096	129	33	�	�	PROPN
ejpam-3096	129	34	d	d	NOUN
ejpam-3096	129	35	∀	∀	X
ejpam-3096	129	36	r	r	NOUN
ejpam-3096	129	37	>	>	X
ejpam-3096	129	38	s	s	PART
ejpam-3096	129	39	≥	≥	NOUN
ejpam-3096	129	40	s1	s1	NOUN
ejpam-3096	129	41	.............................................................	.............................................................	PUNCT
ejpam-3096	129	42	(	(	PUNCT
ejpam-3096	129	43	3.3	3.3	NUM
ejpam-3096	129	44	)	)	PUNCT
ejpam-3096	129	45	by	by	ADP
ejpam-3096	129	46	using	use	VERB
ejpam-3096	129	47	the	the	DET
ejpam-3096	129	48	inequality	inequality	NOUN
ejpam-3096	129	49	(	(	PUNCT
ejpam-3096	129	50	3.2	3.2	NUM
ejpam-3096	129	51	)	)	PUNCT
ejpam-3096	129	52	and	and	CCONJ
ejpam-3096	129	53	the	the	DET
ejpam-3096	129	54	truth	truth	NOUN
ejpam-3096	129	55	that	that	PRON
ejpam-3096	129	56	d−	d−	PROPN
ejpam-3096	129	57	φ(d	φ(d	NUM
ejpam-3096	129	58	)	)	PUNCT
ejpam-3096	129	59	<	<	X
ejpam-3096	130	1	d	d	X
ejpam-3096	130	2	,	,	PUNCT
ejpam-3096	130	3	we	we	PRON
ejpam-3096	130	4	have	have	VERB
ejpam-3096	130	5	the	the	DET
ejpam-3096	130	6	inequality	inequality	NOUN
ejpam-3096	130	7	(	(	PUNCT
ejpam-3096	130	8	3.3	3.3	NUM
ejpam-3096	130	9	)	)	PUNCT
ejpam-3096	130	10	holds	hold	VERB
ejpam-3096	130	11	for	for	ADP
ejpam-3096	130	12	r	r	NOUN
ejpam-3096	130	13	=	=	PUNCT
ejpam-3096	130	14	s+	s+	PUNCT
ejpam-3096	130	15	1	1	X
ejpam-3096	130	16	.	.	X
ejpam-3096	130	17	assume	assume	VERB
ejpam-3096	130	18	that	that	SCONJ
ejpam-3096	130	19	the	the	DET
ejpam-3096	130	20	inequality	inequality	NOUN
ejpam-3096	130	21	(	(	PUNCT
ejpam-3096	130	22	3.3	3.3	NUM
ejpam-3096	130	23	)	)	PUNCT
ejpam-3096	130	24	holds	hold	VERB
ejpam-3096	130	25	for	for	ADP
ejpam-3096	130	26	r	r	NOUN
ejpam-3096	130	27	=	=	SYM
ejpam-3096	130	28	h.	h.	NOUN
ejpam-3096	130	29	for	for	ADP
ejpam-3096	130	30	r	r	NOUN
ejpam-3096	130	31	=	=	SYM
ejpam-3096	130	32	h+	h+	X
ejpam-3096	130	33	1	1	NUM
ejpam-3096	130	34	and	and	CCONJ
ejpam-3096	130	35	by	by	ADP
ejpam-3096	130	36	using	use	VERB
ejpam-3096	130	37	remark	remark	NOUN
ejpam-3096	130	38	(	(	PUNCT
ejpam-3096	130	39	2	2	X
ejpam-3096	130	40	)	)	PUNCT
ejpam-3096	130	41	we	we	PRON
ejpam-3096	130	42	obtain	obtain	VERB
ejpam-3096	130	43	:	:	PUNCT
ejpam-3096	130	44	d∗(£xs,£xs,£xh+1	d∗(£xs,£xs,£xh+1	X
ejpam-3096	130	45	)	)	PUNCT
ejpam-3096	130	46	≤	≤	NUM
ejpam-3096	131	1	d∗(£xs,£xs,£xs+1	d∗(£xs,£xs,£xs+1	NOUN
ejpam-3096	131	2	)	)	PUNCT
ejpam-3096	131	3	+	+	NOUN
ejpam-3096	131	4	d∗(£xs+1,£xs+1,£xh+1	d∗(£xs+1,£xs+1,£xh+1	NOUN
ejpam-3096	131	5	)	)	PUNCT
ejpam-3096	131	6	�	�	PROPN
ejpam-3096	131	7	d−	d−	PROPN
ejpam-3096	131	8	φ(d	φ(d	NUM
ejpam-3096	131	9	)	)	PUNCT
ejpam-3096	132	1	+	+	CCONJ
ejpam-3096	132	2	φ(d∗(£xs,£xs,£xh	φ(d∗(£xs,£xs,£xh	PROPN
ejpam-3096	132	3	)	)	PUNCT
ejpam-3096	132	4	)	)	PUNCT
ejpam-3096	132	5	�	�	PROPN
ejpam-3096	132	6	d−	d−	PROPN
ejpam-3096	132	7	φ(d	φ(d	NUM
ejpam-3096	132	8	)	)	PUNCT
ejpam-3096	133	1	+	+	CCONJ
ejpam-3096	133	2	φ(d	φ(d	NUM
ejpam-3096	133	3	)	)	PUNCT
ejpam-3096	134	1	=	=	SYM
ejpam-3096	134	2	d.	d.	NOUN
ejpam-3096	134	3	by	by	ADP
ejpam-3096	134	4	induction	induction	NOUN
ejpam-3096	134	5	on	on	ADP
ejpam-3096	134	6	r	r	NOUN
ejpam-3096	134	7	,	,	PUNCT
ejpam-3096	134	8	we	we	PRON
ejpam-3096	134	9	conclude	conclude	VERB
ejpam-3096	134	10	that	that	SCONJ
ejpam-3096	134	11	the	the	DET
ejpam-3096	134	12	inequality	inequality	NOUN
ejpam-3096	134	13	(	(	PUNCT
ejpam-3096	134	14	3.3	3.3	NUM
ejpam-3096	134	15	)	)	PUNCT
ejpam-3096	134	16	holds	hold	VERB
ejpam-3096	134	17	∀	∀	X
ejpam-3096	134	18	r	r	NOUN
ejpam-3096	134	19	>	>	X
ejpam-3096	134	20	s	s	PART
ejpam-3096	134	21	≥	≥	NOUN
ejpam-3096	134	22	s1	s1	NOUN
ejpam-3096	134	23	.	.	PUNCT
ejpam-3096	135	1	now	now	ADV
ejpam-3096	135	2	the	the	DET
ejpam-3096	135	3	part	part	NOUN
ejpam-3096	135	4	(	(	PUNCT
ejpam-3096	135	5	d	d	NOUN
ejpam-3096	135	6	)	)	PUNCT
ejpam-3096	135	7	of	of	ADP
ejpam-3096	135	8	definition	definition	NOUN
ejpam-3096	135	9	(	(	PUNCT
ejpam-3096	135	10	1	1	NUM
ejpam-3096	135	11	)	)	PUNCT
ejpam-3096	135	12	implies	imply	VERB
ejpam-3096	135	13	that	that	SCONJ
ejpam-3096	135	14	,	,	PUNCT
ejpam-3096	135	15	d∗(xr	d∗(xr	PROPN
ejpam-3096	135	16	,	,	PUNCT
ejpam-3096	135	17	xs	xs	PROPN
ejpam-3096	135	18	,	,	PUNCT
ejpam-3096	135	19	xl	xl	PROPN
ejpam-3096	135	20	)	)	PUNCT
ejpam-3096	135	21	≤	≤	ADJ
ejpam-3096	135	22	d∗(xr	d∗(xr	NOUN
ejpam-3096	135	23	,	,	PUNCT
ejpam-3096	135	24	xr	xr	PROPN
ejpam-3096	135	25	,	,	PUNCT
ejpam-3096	135	26	xs	xs	PROPN
ejpam-3096	135	27	)	)	PUNCT
ejpam-3096	136	1	+	+	X
ejpam-3096	136	2	d∗(xs	d∗(xs	PROPN
ejpam-3096	136	3	,	,	PUNCT
ejpam-3096	136	4	xl	xl	PROPN
ejpam-3096	136	5	,	,	PUNCT
ejpam-3096	136	6	xl	xl	PROPN
ejpam-3096	136	7	)	)	PUNCT
ejpam-3096	136	8	�	�	PROPN
ejpam-3096	136	9	2d	2d	PROPN
ejpam-3096	136	10	holds	hold	VERB
ejpam-3096	136	11	for	for	ADP
ejpam-3096	136	12	r	r	NOUN
ejpam-3096	136	13	,	,	PUNCT
ejpam-3096	136	14	s	s	PART
ejpam-3096	136	15	,	,	PUNCT
ejpam-3096	136	16	l	l	NOUN
ejpam-3096	136	17	≥	≥	NOUN
ejpam-3096	136	18	s1	s1	NOUN
ejpam-3096	136	19	.	.	PUNCT
ejpam-3096	137	1	therefore	therefore	ADV
ejpam-3096	137	2	,	,	PUNCT
ejpam-3096	137	3	{	{	PUNCT
ejpam-3096	137	4	£	£	SYM
ejpam-3096	137	5	xs	xs	NOUN
ejpam-3096	137	6	}	}	PUNCT
ejpam-3096	137	7	is	be	AUX
ejpam-3096	137	8	(	(	PUNCT
ejpam-3096	137	9	d∗−cauchysequence	d∗−cauchysequence	NOUN
ejpam-3096	137	10	)	)	PUNCT
ejpam-3096	137	11	in	in	ADP
ejpam-3096	137	12	(	(	PUNCT
ejpam-3096	137	13	£	£	NOUN
ejpam-3096	137	14	(	(	PUNCT
ejpam-3096	137	15	x	x	NOUN
ejpam-3096	137	16	)	)	PUNCT
ejpam-3096	137	17	,	,	PUNCT
ejpam-3096	137	18	d∗	d∗	PROPN
ejpam-3096	137	19	)	)	PUNCT
ejpam-3096	137	20	which	which	PRON
ejpam-3096	137	21	is	be	AUX
ejpam-3096	137	22	complete	complete	ADJ
ejpam-3096	137	23	by	by	ADP
ejpam-3096	137	24	assumption	assumption	NOUN
ejpam-3096	137	25	.	.	PUNCT
ejpam-3096	138	1	thus	thus	ADV
ejpam-3096	138	2	,	,	PUNCT
ejpam-3096	138	3	∃	∃	PROPN
ejpam-3096	138	4	u	u	NOUN
ejpam-3096	138	5	=	=	PUNCT
ejpam-3096	138	6	£	£	SYM
ejpam-3096	138	7	v	v	NOUN
ejpam-3096	138	8	and	and	CCONJ
ejpam-3096	138	9	z	z	NOUN
ejpam-3096	138	10	∈	∈	PROPN
ejpam-3096	138	11	x	x	X
ejpam-3096	138	12	(	(	PUNCT
ejpam-3096	138	13	s.t	s.t	PROPN
ejpam-3096	138	14	)	)	PUNCT
ejpam-3096	138	15	,	,	PUNCT
ejpam-3096	138	16	lims→∞£xs	lims→∞£xs	ADJ
ejpam-3096	138	17	=	=	SYM
ejpam-3096	138	18	u	u	NOUN
ejpam-3096	138	19	=	=	PROPN
ejpam-3096	138	20	£	£	SYM
ejpam-3096	138	21	z	z	NOUN
ejpam-3096	138	22	......................................................................	......................................................................	PUNCT
ejpam-3096	138	23	(3.4	(3.4	VERB
ejpam-3096	138	24	)	)	PUNCT
ejpam-3096	138	25	since	since	SCONJ
ejpam-3096	138	26	x	x	PRON
ejpam-3096	138	27	is	be	AUX
ejpam-3096	138	28	regular	regular	ADJ
ejpam-3096	138	29	and	and	CCONJ
ejpam-3096	138	30	{	{	PUNCT
ejpam-3096	138	31	£	£	SYM
ejpam-3096	138	32	xs	xs	NOUN
ejpam-3096	138	33	}	}	PUNCT
ejpam-3096	138	34	is	be	AUX
ejpam-3096	138	35	a	a	DET
ejpam-3096	138	36	non	non	ADJ
ejpam-3096	138	37	-	-	ADJ
ejpam-3096	138	38	decreasing	decrease	VERB
ejpam-3096	138	39	sequence	sequence	NOUN
ejpam-3096	138	40	,	,	PUNCT
ejpam-3096	138	41	we	we	PRON
ejpam-3096	138	42	get	get	VERB
ejpam-3096	138	43	from	from	ADP
ejpam-3096	138	44	(	(	PUNCT
ejpam-3096	138	45	3.4	3.4	NUM
ejpam-3096	138	46	)	)	PUNCT
ejpam-3096	138	47	that	that	SCONJ
ejpam-3096	138	48	£	£	SYM
ejpam-3096	138	49	xs	xs	PROPN
ejpam-3096	138	50	4	4	NUM
ejpam-3096	138	51	£	£	SYM
ejpam-3096	138	52	z	z	NOUN
ejpam-3096	138	53	∀	∀	NOUN
ejpam-3096	138	54	s	s	NOUN
ejpam-3096	138	55	∈	∈	PROPN
ejpam-3096	138	56	n.	n.	NOUN
ejpam-3096	138	57	assume	assume	VERB
ejpam-3096	138	58	that	that	SCONJ
ejpam-3096	138	59	£	£	AUX
ejpam-3096	138	60	xs	xs	PROPN
ejpam-3096	138	61	6=	6=	ADP
ejpam-3096	138	62	£	£	PROPN
ejpam-3096	138	63	z.	z.	NOUN
ejpam-3096	138	64	fix	fix	NOUN
ejpam-3096	138	65	d	d	PROPN
ejpam-3096	138	66	,	,	PUNCT
ejpam-3096	138	67	0	0	NUM
ejpam-3096	138	68	�	�	PROPN
ejpam-3096	138	69	d	d	PROPN
ejpam-3096	138	70	,	,	PUNCT
ejpam-3096	138	71	choose	choose	VERB
ejpam-3096	138	72	,	,	PUNCT
ejpam-3096	138	73	s	s	VERB
ejpam-3096	138	74	∈	∈	PROPN
ejpam-3096	138	75	n	n	CCONJ
ejpam-3096	138	76	(	(	PUNCT
ejpam-3096	138	77	s.t	s.t	PROPN
ejpam-3096	138	78	)	)	PUNCT
ejpam-3096	138	79	,	,	PUNCT
ejpam-3096	138	80	d∗(£xs,£z,£z	d∗(£xs,£z,£z	NOUN
ejpam-3096	138	81	)	)	PUNCT
ejpam-3096	138	82	�	�	PROPN
ejpam-3096	139	1	d	d	ADP
ejpam-3096	139	2	2	2	NUM
ejpam-3096	139	3	and	and	CCONJ
ejpam-3096	139	4	d∗(£xs+1,£z,£z	d∗(£xs+1,£z,£z	ADJ
ejpam-3096	139	5	)	)	PUNCT
ejpam-3096	139	6	�	�	PROPN
ejpam-3096	139	7	d	d	ADP
ejpam-3096	139	8	2	2	NUM
ejpam-3096	139	9	.	.	PUNCT
ejpam-3096	140	1	therefore	therefore	ADV
ejpam-3096	140	2	,	,	PUNCT
ejpam-3096	140	3	we	we	PRON
ejpam-3096	140	4	can	can	AUX
ejpam-3096	140	5	apply	apply	VERB
ejpam-3096	140	6	the	the	DET
ejpam-3096	140	7	considered	consider	VERB
ejpam-3096	140	8	contractive	contractive	ADJ
ejpam-3096	140	9	condition	condition	NOUN
ejpam-3096	140	10	to	to	PART
ejpam-3096	140	11	obtain	obtain	VERB
ejpam-3096	140	12	:	:	PUNCT
ejpam-3096	140	13	d∗(tz	d∗(tz	NOUN
ejpam-3096	140	14	,	,	PUNCT
ejpam-3096	140	15	tz,£z	tz,£z	NOUN
ejpam-3096	140	16	)	)	PUNCT
ejpam-3096	140	17	≤	≤	NOUN
ejpam-3096	141	1	d∗(tz	d∗(tz	PROPN
ejpam-3096	141	2	,	,	PUNCT
ejpam-3096	141	3	tz	tz	NOUN
ejpam-3096	141	4	,	,	PUNCT
ejpam-3096	141	5	txs	txs	PROPN
ejpam-3096	141	6	)	)	PUNCT
ejpam-3096	141	7	+	+	ADJ
ejpam-3096	141	8	d∗(txs,£z,£z	d∗(txs,£z,£z	VERB
ejpam-3096	141	9	)	)	PUNCT
ejpam-3096	141	10	≤	≤	NOUN
ejpam-3096	141	11	φ(d∗(£xs,£z,£z	φ(d∗(£xs,£z,£z	NUM
ejpam-3096	141	12	)	)	PUNCT
ejpam-3096	141	13	)	)	PUNCT
ejpam-3096	142	1	+	+	PUNCT
ejpam-3096	142	2	d∗(£xs+1,£z,£z	d∗(£xs+1,£z,£z	NOUN
ejpam-3096	142	3	)	)	PUNCT
ejpam-3096	142	4	(	(	PUNCT
ejpam-3096	142	5	using	use	VERB
ejpam-3096	142	6	(	(	PUNCT
ejpam-3096	142	7	3.1	3.1	NUM
ejpam-3096	142	8	)	)	PUNCT
ejpam-3096	142	9	)	)	PUNCT
ejpam-3096	142	10	<	<	X
ejpam-3096	142	11	d∗(£xs,£z,£z	d∗(£xs,£z,£z	NOUN
ejpam-3096	142	12	)	)	PUNCT
ejpam-3096	143	1	+	+	X
ejpam-3096	143	2	d∗(£xs+1,£z,£z	d∗(£xs+1,£z,£z	ADJ
ejpam-3096	143	3	)	)	PUNCT
ejpam-3096	143	4	�	�	PROPN
ejpam-3096	144	1	d	d	ADP
ejpam-3096	144	2	2	2	NUM
ejpam-3096	145	1	+	+	CCONJ
ejpam-3096	145	2	d	d	PROPN
ejpam-3096	145	3	d	d	X
ejpam-3096	145	4	=	=	SYM
ejpam-3096	145	5	d.	d.	PROPN
ejpam-3096	145	6	since	since	SCONJ
ejpam-3096	145	7	d	d	PROPN
ejpam-3096	145	8	∈	∈	PROPN
ejpam-3096	145	9	intp	intp	NOUN
ejpam-3096	145	10	,	,	PUNCT
ejpam-3096	145	11	via	via	ADP
ejpam-3096	145	12	remark	remark	NOUN
ejpam-3096	145	13	(	(	PUNCT
ejpam-3096	145	14	2−r1	2−r1	NUM
ejpam-3096	145	15	)	)	PUNCT
ejpam-3096	145	16	it	it	PRON
ejpam-3096	145	17	follows	follow	VERB
ejpam-3096	145	18	that	that	SCONJ
ejpam-3096	146	1	d∗(tz	d∗(tz	PROPN
ejpam-3096	146	2	,	,	PUNCT
ejpam-3096	146	3	tz,£z	tz,£z	PROPN
ejpam-3096	146	4	)	)	PUNCT
ejpam-3096	146	5	=	=	SYM
ejpam-3096	146	6	0	0	NUM
ejpam-3096	146	7	such	such	ADJ
ejpam-3096	146	8	that	that	SCONJ
ejpam-3096	146	9	tz	tz	NOUN
ejpam-3096	146	10	=	=	SYM
ejpam-3096	146	11	£	£	PROPN
ejpam-3096	146	12	z.	z.	NOUN
ejpam-3096	146	13	thus	thus	ADV
ejpam-3096	146	14	z	z	PROPN
ejpam-3096	146	15	is	be	AUX
ejpam-3096	146	16	a	a	DET
ejpam-3096	146	17	coincidence	coincidence	NOUN
ejpam-3096	146	18	point	point	NOUN
ejpam-3096	146	19	for	for	ADP
ejpam-3096	146	20	£	£	NOUN
ejpam-3096	146	21	and	and	CCONJ
ejpam-3096	146	22	t.	t.	NOUN
ejpam-3096	146	23	next	next	ADV
ejpam-3096	146	24	,	,	PUNCT
ejpam-3096	146	25	remember	remember	VERB
ejpam-3096	146	26	the	the	DET
ejpam-3096	146	27	following	follow	VERB
ejpam-3096	146	28	case	case	NOUN
ejpam-3096	146	29	see	see	VERB
ejpam-3096	146	30	[	[	X
ejpam-3096	146	31	19	19	NUM
ejpam-3096	146	32	]	]	PUNCT
ejpam-3096	146	33	to	to	PART
ejpam-3096	146	34	explain	explain	VERB
ejpam-3096	146	35	the	the	DET
ejpam-3096	146	36	validity	validity	NOUN
ejpam-3096	146	37	of	of	ADP
ejpam-3096	146	38	theorem	theorem	NOUN
ejpam-3096	146	39	(	(	PUNCT
ejpam-3096	146	40	1	1	NUM
ejpam-3096	146	41	)	)	PUNCT
ejpam-3096	146	42	.	.	PUNCT
ejpam-3096	147	1	example	example	NOUN
ejpam-3096	148	1	4	4	X
ejpam-3096	148	2	.	.	X
ejpam-3096	148	3	assume	assume	VERB
ejpam-3096	148	4	that	that	SCONJ
ejpam-3096	148	5	(	(	PUNCT
ejpam-3096	148	6	x	x	NOUN
ejpam-3096	148	7	,	,	PUNCT
ejpam-3096	148	8	d∗	d∗	PROPN
ejpam-3096	148	9	)	)	PUNCT
ejpam-3096	148	10	is	be	AUX
ejpam-3096	148	11	a	a	DET
ejpam-3096	148	12	generalized	generalized	ADJ
ejpam-3096	148	13	d∗-m.sp	d∗-m.sp	X
ejpam-3096	148	14	.	.	X
ejpam-3096	149	1	consider	consider	VERB
ejpam-3096	149	2	example	example	NOUN
ejpam-3096	149	3	(	(	PUNCT
ejpam-3096	149	4	2	2	NUM
ejpam-3096	149	5	)	)	PUNCT
ejpam-3096	149	6	,	,	PUNCT
ejpam-3096	149	7	with	with	ADP
ejpam-3096	149	8	the	the	DET
ejpam-3096	149	9	reverse	reverse	ADJ
ejpam-3096	149	10	order	order	NOUN
ejpam-3096	149	11	:	:	PUNCT
ejpam-3096	149	12	x	x	SYM
ejpam-3096	149	13	4	4	NUM
ejpam-3096	149	14	y	y	PROPN
ejpam-3096	149	15	⇔	⇔	X
ejpam-3096	149	16	x	x	SYM
ejpam-3096	149	17	≥	≥	PROPN
ejpam-3096	149	18	y.	y.	NOUN
ejpam-3096	149	19	define	define	VERB
ejpam-3096	149	20	a	a	DET
ejpam-3096	149	21	maps	map	NOUN
ejpam-3096	149	22	t	t	NOUN
ejpam-3096	149	23	:	:	PUNCT
ejpam-3096	150	1	x	x	PROPN
ejpam-3096	150	2	×x	×x	ADP
ejpam-3096	150	3	→	→	SYM
ejpam-3096	150	4	x	x	X
ejpam-3096	150	5	and	and	CCONJ
ejpam-3096	150	6	£	£	PROPN
ejpam-3096	150	7	:	:	PUNCT
ejpam-3096	150	8	x	x	X
ejpam-3096	150	9	×x	×x	PROPN
ejpam-3096	150	10	→	→	SYM
ejpam-3096	150	11	x	x	PUNCT
ejpam-3096	150	12	as	as	SCONJ
ejpam-3096	150	13	follows	follow	VERB
ejpam-3096	150	14	:	:	PUNCT
ejpam-3096	150	15	tx	tx	PROPN
ejpam-3096	150	16	=	=	PUNCT
ejpam-3096	150	17	2x	2x	NOUN
ejpam-3096	150	18	and	and	CCONJ
ejpam-3096	150	19	£	£	SYM
ejpam-3096	150	20	x	x	X
ejpam-3096	150	21	=	=	SYM
ejpam-3096	150	22	3x	3x	PROPN
ejpam-3096	150	23	and	and	CCONJ
ejpam-3096	150	24	a	a	DET
ejpam-3096	150	25	φ	φ	VERB
ejpam-3096	150	26	-	-	PUNCT
ejpam-3096	150	27	map	map	NOUN
ejpam-3096	150	28	define	define	NOUN
ejpam-3096	150	29	by	by	ADP
ejpam-3096	150	30	φ(w	φ(w	PROPN
ejpam-3096	150	31	)	)	PUNCT
ejpam-3096	150	32	=	=	SYM
ejpam-3096	150	33	w	w	PROPN
ejpam-3096	150	34	2	2	NUM
ejpam-3096	150	35	,	,	PUNCT
ejpam-3096	150	36	w	w	PROPN
ejpam-3096	150	37	∈	∈	PROPN
ejpam-3096	150	38	p.	p.	NOUN
ejpam-3096	150	39	hence	hence	ADV
ejpam-3096	150	40	all	all	DET
ejpam-3096	150	41	the	the	DET
ejpam-3096	150	42	conditions	condition	NOUN
ejpam-3096	150	43	of	of	ADP
ejpam-3096	150	44	theorem	theorem	NOUN
ejpam-3096	150	45	(	(	PUNCT
ejpam-3096	150	46	1	1	NUM
ejpam-3096	150	47	)	)	PUNCT
ejpam-3096	150	48	are	be	AUX
ejpam-3096	150	49	satisfied	satisfied	ADJ
ejpam-3096	150	50	;	;	PUNCT
ejpam-3096	150	51	particularly	particularly	ADV
ejpam-3096	150	52	one	one	PRON
ejpam-3096	150	53	can	can	AUX
ejpam-3096	150	54	be	be	AUX
ejpam-3096	150	55	able	able	ADJ
ejpam-3096	150	56	to	to	PART
ejpam-3096	150	57	reduce	reduce	VERB
ejpam-3096	150	58	condition	condition	NOUN
ejpam-3096	150	59	(	(	PUNCT
ejpam-3096	150	60	3.1	3.1	NUM
ejpam-3096	150	61	)	)	PUNCT
ejpam-3096	150	62	to	to	PART
ejpam-3096	150	63	:	:	PUNCT
ejpam-3096	150	64	2(|x	2(|x	NUM
ejpam-3096	151	1	−	−	NOUN
ejpam-3096	151	2	y|	y|	NOUN
ejpam-3096	151	3	+	+	CCONJ
ejpam-3096	151	4	|y	|y	VERB
ejpam-3096	151	5	−	−	PROPN
ejpam-3096	151	6	z|	z|	PROPN
ejpam-3096	151	7	+	+	PROPN
ejpam-3096	151	8	|z	|z	PROPN
ejpam-3096	151	9	−	−	PROPN
ejpam-3096	151	10	x|)u	x|)u	PROPN
ejpam-3096	151	11	≥	≥	NUM
ejpam-3096	151	12	3	3	NUM
ejpam-3096	151	13	2(|x	2(|x	NUM
ejpam-3096	151	14	−	−	ADP
ejpam-3096	151	15	y|	y|	NOUN
ejpam-3096	151	16	+	+	CCONJ
ejpam-3096	151	17	|y	|y	VERB
ejpam-3096	151	18	−	−	PROPN
ejpam-3096	151	19	z|	z|	PROPN
ejpam-3096	151	20	+	+	PROPN
ejpam-3096	151	21	|z	|z	PROPN
ejpam-3096	151	22	−	−	PROPN
ejpam-3096	151	23	x|)u	x|)u	PROPN
ejpam-3096	151	24	,	,	PUNCT
ejpam-3096	151	25	and	and	CCONJ
ejpam-3096	151	26	holds	hold	VERB
ejpam-3096	151	27	∀	∀	NOUN
ejpam-3096	151	28	x	x	NOUN
ejpam-3096	151	29	,	,	PUNCT
ejpam-3096	151	30	y	y	PROPN
ejpam-3096	151	31	,	,	PUNCT
ejpam-3096	151	32	z	z	NOUN
ejpam-3096	151	33	∈	∈	PROPN
ejpam-3096	152	1	[	[	X
ejpam-3096	152	2	0,+∞	0,+∞	NUM
ejpam-3096	152	3	)	)	PUNCT
ejpam-3096	152	4	.	.	PUNCT
ejpam-3096	153	1	as	as	ADV
ejpam-3096	153	2	well	well	ADV
ejpam-3096	153	3	,	,	PUNCT
ejpam-3096	153	4	t	t	PROPN
ejpam-3096	153	5	is	be	AUX
ejpam-3096	153	6	weakly	weakly	ADV
ejpam-3096	153	7	increasing	increase	VERB
ejpam-3096	153	8	with	with	ADP
ejpam-3096	153	9	respect	respect	NOUN
ejpam-3096	153	10	to	to	ADP
ejpam-3096	153	11	£	£	SYM
ejpam-3096	153	12	,	,	PUNCT
ejpam-3096	153	13	since	since	SCONJ
ejpam-3096	153	14	£	£	SYM
ejpam-3096	153	15	y	y	NOUN
ejpam-3096	153	16	=	=	PUNCT
ejpam-3096	153	17	tx	tx	PROPN
ejpam-3096	153	18	⇒	⇒	NOUN
ejpam-3096	153	19	3y	3y	NUM
ejpam-3096	153	20	=	=	SYM
ejpam-3096	153	21	2x	2x	NUM
ejpam-3096	153	22	⇒	⇒	X
ejpam-3096	153	23	y	y	PROPN
ejpam-3096	153	24	=	=	PUNCT
ejpam-3096	153	25	2x	2x	NUM
ejpam-3096	153	26	3	3	NUM
ejpam-3096	153	27	,	,	PUNCT
ejpam-3096	153	28	which	which	PRON
ejpam-3096	153	29	mean	mean	VERB
ejpam-3096	153	30	implies	imply	VERB
ejpam-3096	153	31	tx	tx	PROPN
ejpam-3096	153	32	=	=	SYM
ejpam-3096	153	33	2x	2x	NUM
ejpam-3096	153	34	≥	≥	NUM
ejpam-3096	153	35	2y	2y	NUM
ejpam-3096	154	1	=	=	SYM
ejpam-3096	154	2	ty	ty	INTJ
ejpam-3096	154	3	,	,	PUNCT
ejpam-3096	154	4	it	it	PRON
ejpam-3096	154	5	mean	mean	VERB
ejpam-3096	154	6	tx	tx	VERB
ejpam-3096	154	7	4	4	NUM
ejpam-3096	154	8	ty	ty	NUM
ejpam-3096	154	9	.	.	PUNCT
ejpam-3096	155	1	clear	clear	ADJ
ejpam-3096	155	2	that	that	SCONJ
ejpam-3096	155	3	,	,	PUNCT
ejpam-3096	155	4	0	0	PUNCT
ejpam-3096	155	5	a	a	DET
ejpam-3096	155	6	coincidence	coincidence	NOUN
ejpam-3096	155	7	point	point	NOUN
ejpam-3096	155	8	of	of	ADP
ejpam-3096	155	9	£	£	NOUN
ejpam-3096	155	10	and	and	CCONJ
ejpam-3096	155	11	t.	t.	NOUN
ejpam-3096	155	12	corollary	corollary	ADJ
ejpam-3096	155	13	1	1	PROPN
ejpam-3096	155	14	.	.	PUNCT
ejpam-3096	156	1	assume	assume	VERB
ejpam-3096	156	2	(	(	PUNCT
ejpam-3096	156	3	x,4	x,4	X
ejpam-3096	156	4	)	)	PUNCT
ejpam-3096	156	5	is	be	AUX
ejpam-3096	156	6	(	(	PUNCT
ejpam-3096	156	7	p.o.s	p.o.s	NOUN
ejpam-3096	156	8	)	)	PUNCT
ejpam-3096	156	9	with	with	AUX
ejpam-3096	156	10	suppose	suppose	VERB
ejpam-3096	156	11	that	that	SCONJ
ejpam-3096	156	12	(	(	PUNCT
ejpam-3096	156	13	x	x	NOUN
ejpam-3096	156	14	,	,	PUNCT
ejpam-3096	156	15	d∗	d∗	PROPN
ejpam-3096	156	16	)	)	PUNCT
ejpam-3096	156	17	is	be	AUX
ejpam-3096	156	18	a	a	DET
ejpam-3096	156	19	generalized	generalized	ADJ
ejpam-3096	156	20	d∗m.sp	d∗m.sp	NOUN
ejpam-3096	156	21	and	and	CCONJ
ejpam-3096	156	22	p	p	NOUN
ejpam-3096	156	23	is	be	AUX
ejpam-3096	156	24	(	(	PUNCT
ejpam-3096	156	25	o.c	o.c	PROPN
ejpam-3096	156	26	)	)	PUNCT
ejpam-3096	156	27	.	.	PUNCT
ejpam-3096	157	1	let	let	VERB
ejpam-3096	157	2	£	£	SYM
ejpam-3096	157	3	,	,	PUNCT
ejpam-3096	157	4	t	t	X
ejpam-3096	157	5	:	:	PUNCT
ejpam-3096	157	6	x	x	X
ejpam-3096	157	7	→	→	PUNCT
ejpam-3096	157	8	x	x	PUNCT
ejpam-3096	157	9	be	be	AUX
ejpam-3096	157	10	two	two	NUM
ejpam-3096	157	11	non	non	ADJ
ejpam-3096	157	12	-	-	ADJ
ejpam-3096	157	13	decreasing	decrease	VERB
ejpam-3096	157	14	maps	map	NOUN
ejpam-3096	157	15	.	.	PUNCT
ejpam-3096	158	1	assume	assume	VERB
ejpam-3096	158	2	that	that	SCONJ
ejpam-3096	158	3	∀	∀	NOUN
ejpam-3096	158	4	x	x	NOUN
ejpam-3096	158	5	,	,	PUNCT
ejpam-3096	158	6	y	y	PROPN
ejpam-3096	158	7	,	,	PUNCT
ejpam-3096	158	8	z	z	NOUN
ejpam-3096	158	9	∈	∈	PROPN
ejpam-3096	158	10	x	x	PUNCT
ejpam-3096	158	11	with	with	ADP
ejpam-3096	158	12	z	z	PROPN
ejpam-3096	158	13	4	4	NUM
ejpam-3096	158	14	y	y	PROPN
ejpam-3096	158	15	4	4	NUM
ejpam-3096	158	16	x	x	SYM
ejpam-3096	158	17	∃	∃	PROPN
ejpam-3096	158	18	some	some	DET
ejpam-3096	158	19	h	h	NOUN
ejpam-3096	158	20	∈	∈	PROPN
ejpam-3096	159	1	[	[	X
ejpam-3096	159	2	0	0	NUM
ejpam-3096	159	3	,	,	PUNCT
ejpam-3096	159	4	1	1	NUM
ejpam-3096	159	5	)	)	PUNCT
ejpam-3096	159	6	(	(	PUNCT
ejpam-3096	159	7	s.t	s.t	PROPN
ejpam-3096	159	8	):	):	PUNCT
ejpam-3096	159	9	d∗(tx	d∗(tx	PROPN
ejpam-3096	159	10	,	,	PUNCT
ejpam-3096	159	11	ty	ty	INTJ
ejpam-3096	159	12	,	,	PUNCT
ejpam-3096	159	13	tz	tz	PROPN
ejpam-3096	159	14	)	)	PUNCT
ejpam-3096	159	15	≤	≤	NOUN
ejpam-3096	159	16	hd∗(£x,£y,£z	hd∗(£x,£y,£z	NOUN
ejpam-3096	159	17	)	)	PUNCT
ejpam-3096	159	18	holds	hold	VERB
ejpam-3096	159	19	.	.	PUNCT
ejpam-3096	160	1	assume	assume	VERB
ejpam-3096	160	2	the	the	DET
ejpam-3096	160	3	following	following	NOUN
ejpam-3096	160	4	:	:	PUNCT
ejpam-3096	160	5	a.	a.	PROPN
ejpam-3096	160	6	m.	m.	PROPN
ejpam-3096	160	7	al	al	PROPN
ejpam-3096	160	8	.	.	PROPN
ejpam-3096	160	9	jumaili	jumaili	PROPN
ejpam-3096	160	10	/	/	SYM
ejpam-3096	160	11	eur	eur	PROPN
ejpam-3096	160	12	.	.	PUNCT
ejpam-3096	161	1	j.	j.	PROPN
ejpam-3096	161	2	pure	pure	PROPN
ejpam-3096	161	3	appl	appl	PROPN
ejpam-3096	161	4	.	.	PROPN
ejpam-3096	161	5	math	math	PROPN
ejpam-3096	161	6	,	,	PUNCT
ejpam-3096	161	7	10	10	NUM
ejpam-3096	161	8	(	(	PUNCT
ejpam-3096	161	9	5	5	NUM
ejpam-3096	161	10	)	)	PUNCT
ejpam-3096	161	11	(	(	PUNCT
ejpam-3096	161	12	2017	2017	NUM
ejpam-3096	161	13	)	)	PUNCT
ejpam-3096	161	14	,	,	PUNCT
ejpam-3096	161	15	1023	1023	NUM
ejpam-3096	161	16	-	-	SYM
ejpam-3096	161	17	1034	1034	NUM
ejpam-3096	161	18	1029	1029	NUM
ejpam-3096	161	19	a	a	PRON
ejpam-3096	161	20	)	)	PUNCT
ejpam-3096	161	21	t	t	PROPN
ejpam-3096	161	22	is	be	AUX
ejpam-3096	161	23	weakly	weakly	ADV
ejpam-3096	161	24	increasing	increase	VERB
ejpam-3096	161	25	with	with	ADP
ejpam-3096	161	26	respect	respect	NOUN
ejpam-3096	161	27	to	to	ADP
ejpam-3096	161	28	£	£	SYM
ejpam-3096	161	29	,	,	PUNCT
ejpam-3096	161	30	b	b	NOUN
ejpam-3096	161	31	)	)	PUNCT
ejpam-3096	161	32	£	£	NOUN
ejpam-3096	161	33	x	x	PUNCT
ejpam-3096	161	34	is	be	AUX
ejpam-3096	161	35	a	a	DET
ejpam-3096	161	36	complete	complete	ADJ
ejpam-3096	161	37	sub	sub	NOUN
ejpam-3096	161	38	-	-	NOUN
ejpam-3096	161	39	space	space	NOUN
ejpam-3096	161	40	of	of	ADP
ejpam-3096	161	41	x	x	X
ejpam-3096	161	42	,	,	PUNCT
ejpam-3096	161	43	c	c	NOUN
ejpam-3096	161	44	)	)	PUNCT
ejpam-3096	161	45	x	x	X
ejpam-3096	161	46	is	be	AUX
ejpam-3096	161	47	regular	regular	ADJ
ejpam-3096	161	48	.	.	PUNCT
ejpam-3096	162	1	in	in	ADP
ejpam-3096	162	2	that	that	DET
ejpam-3096	162	3	case	case	NOUN
ejpam-3096	162	4	£	£	PROPN
ejpam-3096	162	5	and	and	CCONJ
ejpam-3096	162	6	t	t	PROPN
ejpam-3096	162	7	have	have	VERB
ejpam-3096	162	8	a	a	DET
ejpam-3096	162	9	coincidence	coincidence	NOUN
ejpam-3096	162	10	point	point	NOUN
ejpam-3096	162	11	.	.	PUNCT
ejpam-3096	163	1	proof	proof	NOUN
ejpam-3096	163	2	.	.	PUNCT
ejpam-3096	164	1	the	the	DET
ejpam-3096	164	2	proof	proof	NOUN
ejpam-3096	164	3	is	be	AUX
ejpam-3096	164	4	directly	directly	ADV
ejpam-3096	164	5	consequence	consequence	NOUN
ejpam-3096	164	6	from	from	ADP
ejpam-3096	164	7	theorem	theorem	ADJ
ejpam-3096	164	8	(	(	PUNCT
ejpam-3096	164	9	1	1	NUM
ejpam-3096	164	10	)	)	PUNCT
ejpam-3096	164	11	when	when	SCONJ
ejpam-3096	164	12	taking	take	VERB
ejpam-3096	164	13	φ(w	φ(w	PROPN
ejpam-3096	164	14	)	)	PUNCT
ejpam-3096	164	15	=	=	SYM
ejpam-3096	165	1	hw	hw	PROPN
ejpam-3096	165	2	.	.	PUNCT
ejpam-3096	165	3	remark	remark	PROPN
ejpam-3096	165	4	4	4	NUM
ejpam-3096	165	5	.	.	PUNCT
ejpam-3096	166	1	if	if	SCONJ
ejpam-3096	166	2	the	the	DET
ejpam-3096	166	3	mapping	mapping	NOUN
ejpam-3096	166	4	£	£	PROPN
ejpam-3096	166	5	:	:	PUNCT
ejpam-3096	166	6	x	x	SYM
ejpam-3096	166	7	→	→	PUNCT
ejpam-3096	166	8	x	x	SYM
ejpam-3096	166	9	is	be	AUX
ejpam-3096	166	10	identity	identity	NOUN
ejpam-3096	166	11	,	,	PUNCT
ejpam-3096	166	12	we	we	PRON
ejpam-3096	166	13	get	get	VERB
ejpam-3096	166	14	the	the	DET
ejpam-3096	166	15	following	follow	VERB
ejpam-3096	166	16	(	(	PUNCT
ejpam-3096	166	17	f.p	f.p	NOUN
ejpam-3096	166	18	)	)	PUNCT
ejpam-3096	166	19	result	result	NOUN
ejpam-3096	166	20	.	.	PUNCT
ejpam-3096	167	1	corollary	corollary	ADJ
ejpam-3096	167	2	2	2	NUM
ejpam-3096	167	3	.	.	PUNCT
ejpam-3096	167	4	assume	assume	VERB
ejpam-3096	167	5	(	(	PUNCT
ejpam-3096	167	6	x,4	x,4	X
ejpam-3096	167	7	)	)	PUNCT
ejpam-3096	167	8	is	be	AUX
ejpam-3096	167	9	(	(	PUNCT
ejpam-3096	167	10	p.o.s	p.o.s	NOUN
ejpam-3096	167	11	)	)	PUNCT
ejpam-3096	167	12	and	and	CCONJ
ejpam-3096	167	13	suppose	suppose	VERB
ejpam-3096	167	14	that	that	SCONJ
ejpam-3096	167	15	(	(	PUNCT
ejpam-3096	167	16	x	x	NOUN
ejpam-3096	167	17	,	,	PUNCT
ejpam-3096	167	18	d∗	d∗	PROPN
ejpam-3096	167	19	)	)	PUNCT
ejpam-3096	167	20	is	be	AUX
ejpam-3096	167	21	a	a	DET
ejpam-3096	167	22	complete	complete	ADJ
ejpam-3096	167	23	generalized	generalize	VERB
ejpam-3096	167	24	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	167	25	and	and	CCONJ
ejpam-3096	167	26	p	p	NOUN
ejpam-3096	167	27	is	be	AUX
ejpam-3096	167	28	(	(	PUNCT
ejpam-3096	167	29	o.c	o.c	PROPN
ejpam-3096	167	30	)	)	PUNCT
ejpam-3096	167	31	.	.	PUNCT
ejpam-3096	168	1	let	let	VERB
ejpam-3096	168	2	t	t	NOUN
ejpam-3096	168	3	:	:	PUNCT
ejpam-3096	168	4	x	x	X
ejpam-3096	168	5	→	→	PUNCT
ejpam-3096	168	6	x	x	PUNCT
ejpam-3096	168	7	be	be	AUX
ejpam-3096	168	8	a	a	DET
ejpam-3096	168	9	mapping	mapping	NOUN
ejpam-3096	168	10	(	(	PUNCT
ejpam-3096	168	11	s.t	s.t	PROPN
ejpam-3096	168	12	)	)	PUNCT
ejpam-3096	168	13	d∗(tx	d∗(tx	PROPN
ejpam-3096	168	14	,	,	PUNCT
ejpam-3096	168	15	ty	ty	INTJ
ejpam-3096	168	16	,	,	PUNCT
ejpam-3096	168	17	tz	tz	NOUN
ejpam-3096	168	18	)	)	PUNCT
ejpam-3096	168	19	≤	≤	NOUN
ejpam-3096	168	20	φ(d∗(x	φ(d∗(x	NOUN
ejpam-3096	168	21	,	,	PUNCT
ejpam-3096	168	22	y	y	PROPN
ejpam-3096	168	23	,	,	PUNCT
ejpam-3096	168	24	z	z	NOUN
ejpam-3096	168	25	)	)	PUNCT
ejpam-3096	168	26	)	)	PUNCT
ejpam-3096	168	27	holds	hold	VERB
ejpam-3096	168	28	∀	∀	NOUN
ejpam-3096	168	29	x	x	NOUN
ejpam-3096	168	30	,	,	PUNCT
ejpam-3096	168	31	y	y	PROPN
ejpam-3096	168	32	,	,	PUNCT
ejpam-3096	168	33	z	z	NOUN
ejpam-3096	168	34	∈	∈	PROPN
ejpam-3096	168	35	x	x	PUNCT
ejpam-3096	168	36	with	with	ADP
ejpam-3096	168	37	z	z	PROPN
ejpam-3096	168	38	4	4	NUM
ejpam-3096	168	39	y	y	PROPN
ejpam-3096	168	40	4	4	NUM
ejpam-3096	168	41	x	x	X
ejpam-3096	168	42	where	where	SCONJ
ejpam-3096	168	43	φ	φ	PROPN
ejpam-3096	168	44	is	be	AUX
ejpam-3096	168	45	a	a	DET
ejpam-3096	168	46	φ	φ	NOUN
ejpam-3096	168	47	-	-	PUNCT
ejpam-3096	168	48	map	map	NOUN
ejpam-3096	168	49	.	.	PUNCT
ejpam-3096	169	1	assume	assume	VERB
ejpam-3096	169	2	the	the	DET
ejpam-3096	169	3	following	following	NOUN
ejpam-3096	169	4	:	:	PUNCT
ejpam-3096	169	5	a	a	X
ejpam-3096	169	6	)	)	PUNCT
ejpam-3096	169	7	tx	tx	ADP
ejpam-3096	169	8	4	4	NUM
ejpam-3096	169	9	t	t	NOUN
ejpam-3096	169	10	(	(	PUNCT
ejpam-3096	169	11	tx	tx	PROPN
ejpam-3096	169	12	)	)	PUNCT
ejpam-3096	169	13	∀	∀	X
ejpam-3096	170	1	x	x	X
ejpam-3096	170	2	∈	∈	NOUN
ejpam-3096	170	3	x	x	X
ejpam-3096	170	4	,	,	PUNCT
ejpam-3096	170	5	b	b	NOUN
ejpam-3096	170	6	)	)	PUNCT
ejpam-3096	170	7	x	x	PUNCT
ejpam-3096	170	8	is	be	AUX
ejpam-3096	170	9	regular	regular	ADJ
ejpam-3096	170	10	.	.	PUNCT
ejpam-3096	171	1	in	in	ADP
ejpam-3096	171	2	that	that	DET
ejpam-3096	171	3	case	case	NOUN
ejpam-3096	171	4	t	t	NOUN
ejpam-3096	171	5	has	have	VERB
ejpam-3096	171	6	a	a	DET
ejpam-3096	171	7	(	(	PUNCT
ejpam-3096	171	8	f.p	f.p	NOUN
ejpam-3096	171	9	)	)	PUNCT
ejpam-3096	171	10	.	.	PUNCT
ejpam-3096	172	1	next	next	ADV
ejpam-3096	172	2	,	,	PUNCT
ejpam-3096	172	3	our	our	PRON
ejpam-3096	172	4	result	result	NOUN
ejpam-3096	172	5	is	be	AUX
ejpam-3096	172	6	the	the	DET
ejpam-3096	172	7	following	follow	VERB
ejpam-3096	172	8	generalization	generalization	NOUN
ejpam-3096	172	9	of	of	ADP
ejpam-3096	172	10	theorem	theorem	NOUN
ejpam-3096	172	11	(	(	PUNCT
ejpam-3096	172	12	1	1	NUM
ejpam-3096	172	13	)	)	PUNCT
ejpam-3096	172	14	.	.	PUNCT
ejpam-3096	173	1	theorem	theorem	NOUN
ejpam-3096	173	2	2	2	NUM
ejpam-3096	173	3	.	.	X
ejpam-3096	173	4	assume	assume	VERB
ejpam-3096	173	5	(	(	PUNCT
ejpam-3096	173	6	x,4	x,4	X
ejpam-3096	173	7	)	)	PUNCT
ejpam-3096	173	8	is	be	AUX
ejpam-3096	173	9	(	(	PUNCT
ejpam-3096	173	10	p.o.s	p.o.s	NOUN
ejpam-3096	173	11	)	)	PUNCT
ejpam-3096	173	12	and	and	CCONJ
ejpam-3096	173	13	suppose	suppose	VERB
ejpam-3096	173	14	that	that	SCONJ
ejpam-3096	173	15	(	(	PUNCT
ejpam-3096	173	16	x	x	NOUN
ejpam-3096	173	17	,	,	PUNCT
ejpam-3096	173	18	d∗	d∗	PROPN
ejpam-3096	173	19	)	)	PUNCT
ejpam-3096	173	20	is	be	AUX
ejpam-3096	173	21	a	a	DET
ejpam-3096	173	22	complete	complete	ADJ
ejpam-3096	173	23	generalized	generalize	VERB
ejpam-3096	173	24	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	173	25	and	and	CCONJ
ejpam-3096	173	26	p	p	NOUN
ejpam-3096	173	27	is	be	AUX
ejpam-3096	173	28	(	(	PUNCT
ejpam-3096	173	29	o.c	o.c	PROPN
ejpam-3096	173	30	)	)	PUNCT
ejpam-3096	173	31	,	,	PUNCT
ejpam-3096	173	32	and	and	CCONJ
ejpam-3096	173	33	let	let	VERB
ejpam-3096	173	34	£	£	SYM
ejpam-3096	173	35	,	,	PUNCT
ejpam-3096	173	36	t	t	X
ejpam-3096	173	37	:	:	PUNCT
ejpam-3096	173	38	x	x	X
ejpam-3096	173	39	→	→	PUNCT
ejpam-3096	173	40	x	x	PUNCT
ejpam-3096	173	41	be	be	AUX
ejpam-3096	173	42	a	a	DET
ejpam-3096	173	43	non	non	ADJ
ejpam-3096	173	44	-	-	ADJ
ejpam-3096	173	45	decreasing	decrease	VERB
ejpam-3096	173	46	maps	map	NOUN
ejpam-3096	173	47	.	.	PUNCT
ejpam-3096	174	1	assume	assume	VERB
ejpam-3096	174	2	that	that	SCONJ
ejpam-3096	174	3	∀	∀	NOUN
ejpam-3096	174	4	x	x	NOUN
ejpam-3096	174	5	,	,	PUNCT
ejpam-3096	174	6	y	y	PROPN
ejpam-3096	174	7	,	,	PUNCT
ejpam-3096	174	8	z	z	NOUN
ejpam-3096	174	9	∈	∈	PROPN
ejpam-3096	174	10	x	x	PUNCT
ejpam-3096	174	11	with	with	ADP
ejpam-3096	174	12	£	£	SYM
ejpam-3096	174	13	z	z	NOUN
ejpam-3096	174	14	4	4	NUM
ejpam-3096	174	15	£	£	SYM
ejpam-3096	174	16	y	y	PROPN
ejpam-3096	174	17	4	4	NUM
ejpam-3096	174	18	£	£	NOUN
ejpam-3096	174	19	x	x	PRON
ejpam-3096	174	20	there	there	PRON
ejpam-3096	174	21	exists	exist	VERB
ejpam-3096	174	22	,	,	PUNCT
ejpam-3096	174	23	φ(x	φ(x	PROPN
ejpam-3096	174	24	,	,	PUNCT
ejpam-3096	174	25	y	y	PROPN
ejpam-3096	174	26	,	,	PUNCT
ejpam-3096	174	27	z	z	NOUN
ejpam-3096	174	28	)	)	PUNCT
ejpam-3096	174	29	∈	∈	PROPN
ejpam-3096	174	30	{	{	PUNCT
ejpam-3096	174	31	d∗(£x,£y,£z	d∗(£x,£y,£z	PROPN
ejpam-3096	174	32	)	)	PUNCT
ejpam-3096	174	33	,	,	PUNCT
ejpam-3096	174	34	d∗(£x,£x	d∗(£x,£x	NOUN
ejpam-3096	174	35	,	,	PUNCT
ejpam-3096	174	36	tx	tx	PROPN
ejpam-3096	174	37	)	)	PUNCT
ejpam-3096	174	38	,	,	PUNCT
ejpam-3096	174	39	d∗(£y,£y	d∗(£y,£y	PROPN
ejpam-3096	174	40	,	,	PUNCT
ejpam-3096	174	41	ty	ty	NOUN
ejpam-3096	174	42	)	)	PUNCT
ejpam-3096	174	43	,	,	PUNCT
ejpam-3096	174	44	d∗(tx,£y,£z	d∗(tx,£y,£z	NOUN
ejpam-3096	174	45	)	)	PUNCT
ejpam-3096	174	46	}	}	PUNCT
ejpam-3096	174	47	(	(	PUNCT
ejpam-3096	174	48	s.t	s.t	PROPN
ejpam-3096	174	49	):	):	PUNCT
ejpam-3096	174	50	d∗(tx	d∗(tx	PROPN
ejpam-3096	174	51	,	,	PUNCT
ejpam-3096	174	52	ty	ty	INTJ
ejpam-3096	174	53	,	,	PUNCT
ejpam-3096	174	54	tz	tz	NOUN
ejpam-3096	174	55	)	)	PUNCT
ejpam-3096	174	56	≤	≤	NOUN
ejpam-3096	174	57	φ(φ(x	φ(φ(x	NOUN
ejpam-3096	174	58	,	,	PUNCT
ejpam-3096	174	59	y	y	PROPN
ejpam-3096	174	60	,	,	PUNCT
ejpam-3096	174	61	z	z	NOUN
ejpam-3096	174	62	)	)	PUNCT
ejpam-3096	174	63	)	)	PUNCT
ejpam-3096	174	64	where	where	SCONJ
ejpam-3096	174	65	φ	φ	PROPN
ejpam-3096	174	66	is	be	AUX
ejpam-3096	174	67	a	a	DET
ejpam-3096	174	68	φ	φ	NOUN
ejpam-3096	174	69	-	-	PUNCT
ejpam-3096	174	70	map	map	NOUN
ejpam-3096	174	71	.	.	PUNCT
ejpam-3096	175	1	assume	assume	VERB
ejpam-3096	175	2	the	the	DET
ejpam-3096	175	3	following	following	NOUN
ejpam-3096	175	4	:	:	PUNCT
ejpam-3096	175	5	a	a	X
ejpam-3096	175	6	)	)	PUNCT
ejpam-3096	175	7	t	t	NOUN
ejpam-3096	175	8	is	be	AUX
ejpam-3096	175	9	weakly	weakly	ADV
ejpam-3096	175	10	increasing	increase	VERB
ejpam-3096	175	11	with	with	ADP
ejpam-3096	175	12	respect	respect	NOUN
ejpam-3096	175	13	to	to	ADP
ejpam-3096	175	14	£	£	SYM
ejpam-3096	175	15	,	,	PUNCT
ejpam-3096	175	16	b	b	NOUN
ejpam-3096	175	17	)	)	PUNCT
ejpam-3096	175	18	x	x	PUNCT
ejpam-3096	175	19	is	be	AUX
ejpam-3096	175	20	regular	regular	ADJ
ejpam-3096	175	21	.	.	PUNCT
ejpam-3096	176	1	in	in	ADP
ejpam-3096	176	2	that	that	DET
ejpam-3096	176	3	case	case	NOUN
ejpam-3096	176	4	£	£	PROPN
ejpam-3096	176	5	and	and	CCONJ
ejpam-3096	176	6	t	t	PROPN
ejpam-3096	176	7	have	have	VERB
ejpam-3096	176	8	a	a	DET
ejpam-3096	176	9	coincidence	coincidence	NOUN
ejpam-3096	176	10	point	point	NOUN
ejpam-3096	176	11	.	.	PUNCT
ejpam-3096	177	1	proof	proof	NOUN
ejpam-3096	177	2	.	.	PUNCT
ejpam-3096	178	1	assume	assume	VERB
ejpam-3096	178	2	that	that	SCONJ
ejpam-3096	178	3	a	a	DET
ejpam-3096	178	4	point	point	NOUN
ejpam-3096	178	5	x0	x0	PROPN
ejpam-3096	178	6	∈	∈	PROPN
ejpam-3096	178	7	x	x	PUNCT
ejpam-3096	178	8	is	be	AUX
ejpam-3096	178	9	arbitrary	arbitrary	ADJ
ejpam-3096	178	10	.	.	PUNCT
ejpam-3096	179	1	by	by	ADP
ejpam-3096	179	2	definition	definition	NOUN
ejpam-3096	179	3	(	(	PUNCT
ejpam-3096	179	4	4	4	X
ejpam-3096	179	5	)	)	PUNCT
ejpam-3096	179	6	we	we	PRON
ejpam-3096	179	7	have	have	AUX
ejpam-3096	179	8	,	,	PUNCT
ejpam-3096	179	9	tx	tx	VERB
ejpam-3096	179	10	⊆	⊆	NUM
ejpam-3096	179	11	£	£	SYM
ejpam-3096	179	12	x	x	NUM
ejpam-3096	179	13	,	,	PUNCT
ejpam-3096	179	14	thus	thus	ADV
ejpam-3096	179	15	construct	construct	VERB
ejpam-3096	179	16	a	a	DET
ejpam-3096	179	17	sequence	sequence	NOUN
ejpam-3096	179	18	{	{	PUNCT
ejpam-3096	179	19	xs	xs	NOUN
ejpam-3096	179	20	}	}	PUNCT
ejpam-3096	179	21	in	in	ADP
ejpam-3096	179	22	x	x	PUNCT
ejpam-3096	179	23	defined	define	VERB
ejpam-3096	179	24	via	via	ADP
ejpam-3096	179	25	:	:	PUNCT
ejpam-3096	179	26	£	£	SYM
ejpam-3096	179	27	xs+1	xs+1	NOUN
ejpam-3096	179	28	=	=	SYM
ejpam-3096	179	29	txs	txs	PROPN
ejpam-3096	179	30	,	,	PUNCT
ejpam-3096	179	31	for	for	ADP
ejpam-3096	179	32	each	each	DET
ejpam-3096	179	33	s	s	X
ejpam-3096	179	34	∈	∈	PROPN
ejpam-3096	179	35	n	n	NOUN
ejpam-3096	179	36	.	.	PUNCT
ejpam-3096	180	1	since	since	SCONJ
ejpam-3096	180	2	x1	x1	PROPN
ejpam-3096	180	3	∈	∈	PROPN
ejpam-3096	180	4	£	£	SYM
ejpam-3096	180	5	−1(tx0	−1(tx0	NOUN
ejpam-3096	180	6	)	)	PUNCT
ejpam-3096	180	7	and	and	CCONJ
ejpam-3096	180	8	x2	x2	PROPN
ejpam-3096	180	9	∈	∈	PROPN
ejpam-3096	180	10	£	£	SYM
ejpam-3096	180	11	−1(tx1	−1(tx1	NOUN
ejpam-3096	180	12	)	)	PUNCT
ejpam-3096	180	13	,	,	PUNCT
ejpam-3096	180	14	and	and	CCONJ
ejpam-3096	180	15	via	via	ADP
ejpam-3096	180	16	t	t	PROPN
ejpam-3096	180	17	is	be	AUX
ejpam-3096	180	18	weakly	weakly	ADV
ejpam-3096	180	19	increasing	increase	VERB
ejpam-3096	180	20	with	with	ADP
ejpam-3096	180	21	respect	respect	NOUN
ejpam-3096	180	22	to	to	ADP
ejpam-3096	180	23	£	£	SYM
ejpam-3096	180	24	,	,	PUNCT
ejpam-3096	180	25	we	we	PRON
ejpam-3096	180	26	get	get	VERB
ejpam-3096	180	27	that	that	PRON
ejpam-3096	180	28	:	:	PUNCT
ejpam-3096	180	29	£	£	SYM
ejpam-3096	180	30	x1	x1	NUM
ejpam-3096	180	31	=	=	SYM
ejpam-3096	180	32	tx0	tx0	PROPN
ejpam-3096	180	33	4	4	NUM
ejpam-3096	180	34	tx1	tx1	NOUN
ejpam-3096	180	35	=	=	SYM
ejpam-3096	180	36	£	£	SYM
ejpam-3096	180	37	x2	x2	NOUN
ejpam-3096	180	38	4	4	NUM
ejpam-3096	180	39	tx2	tx2	NOUN
ejpam-3096	180	40	=	=	SYM
ejpam-3096	180	41	£	£	SYM
ejpam-3096	180	42	x3	x3	ADJ
ejpam-3096	180	43	.	.	PUNCT
ejpam-3096	181	1	continuing	continue	VERB
ejpam-3096	181	2	this	this	DET
ejpam-3096	181	3	process	process	NOUN
ejpam-3096	181	4	,	,	PUNCT
ejpam-3096	181	5	we	we	PRON
ejpam-3096	181	6	obtain	obtain	VERB
ejpam-3096	181	7	that	that	PRON
ejpam-3096	181	8	:	:	PUNCT
ejpam-3096	181	9	£	£	SYM
ejpam-3096	181	10	x1	x1	NUM
ejpam-3096	181	11	4	4	NUM
ejpam-3096	181	12	£	£	SYM
ejpam-3096	181	13	x2	x2	PROPN
ejpam-3096	181	14	4	4	NUM
ejpam-3096	181	15	£	£	SYM
ejpam-3096	181	16	x3	x3	ADJ
ejpam-3096	181	17	4	4	NUM
ejpam-3096	181	18	.........	.........	SYM
ejpam-3096	181	19	4	4	NUM
ejpam-3096	181	20	£	£	SYM
ejpam-3096	181	21	xs	xs	NOUN
ejpam-3096	181	22	4	4	NUM
ejpam-3096	181	23	£	£	SYM
ejpam-3096	181	24	xs+1	xs+1	PROPN
ejpam-3096	181	25	4	4	NUM
ejpam-3096	181	26	.........	.........	PUNCT
ejpam-3096	181	27	assume	assume	VERB
ejpam-3096	181	28	that	that	SCONJ
ejpam-3096	181	29	∃	∃	PROPN
ejpam-3096	181	30	s0	s0	PROPN
ejpam-3096	181	31	∈	∈	PROPN
ejpam-3096	181	32	{	{	PUNCT
ejpam-3096	181	33	1	1	NUM
ejpam-3096	181	34	,	,	PUNCT
ejpam-3096	181	35	2	2	NUM
ejpam-3096	181	36	,	,	PUNCT
ejpam-3096	181	37	3	3	NUM
ejpam-3096	181	38	,	,	PUNCT
ejpam-3096	181	39	.....	.....	PUNCT
ejpam-3096	181	40	}	}	PUNCT
ejpam-3096	181	41	(	(	PUNCT
ejpam-3096	181	42	s.t	s.t	PROPN
ejpam-3096	181	43	)	)	PUNCT
ejpam-3096	181	44	φ(xs0	φ(xs0	PROPN
ejpam-3096	181	45	,	,	PUNCT
ejpam-3096	181	46	xs0	xs0	PROPN
ejpam-3096	181	47	,	,	PUNCT
ejpam-3096	181	48	xs0−1	xs0−1	PROPN
ejpam-3096	181	49	)	)	PUNCT
ejpam-3096	182	1	=	=	PUNCT
ejpam-3096	182	2	0	0	PUNCT
ejpam-3096	183	1	thus	thus	ADV
ejpam-3096	183	2	it	it	PRON
ejpam-3096	183	3	is	be	AUX
ejpam-3096	183	4	clear	clear	ADJ
ejpam-3096	183	5	that	that	SCONJ
ejpam-3096	183	6	£	£	SYM
ejpam-3096	183	7	xs0−1	xs0−1	NOUN
ejpam-3096	183	8	=	=	PUNCT
ejpam-3096	183	9	£	£	SYM
ejpam-3096	183	10	xs0	xs0	NOUN
ejpam-3096	183	11	=	=	PRON
ejpam-3096	183	12	txs0−1	txs0−1	PROPN
ejpam-3096	183	13	therefore	therefore	ADV
ejpam-3096	183	14	we	we	PRON
ejpam-3096	183	15	are	be	AUX
ejpam-3096	183	16	completed	complete	VERB
ejpam-3096	183	17	.	.	PUNCT
ejpam-3096	184	1	next	next	ADV
ejpam-3096	184	2	we	we	PRON
ejpam-3096	184	3	can	can	AUX
ejpam-3096	184	4	assume	assume	VERB
ejpam-3096	184	5	φ(xs	φ(x	NOUN
ejpam-3096	184	6	,	,	PUNCT
ejpam-3096	184	7	xs	xs	PROPN
ejpam-3096	184	8	,	,	PUNCT
ejpam-3096	184	9	xs−1	xs−1	PROPN
ejpam-3096	184	10	)	)	PUNCT
ejpam-3096	184	11	>	>	SYM
ejpam-3096	185	1	0	0	NUM
ejpam-3096	185	2	∀	∀	X
ejpam-3096	185	3	s	s	NOUN
ejpam-3096	185	4	≥	≥	NOUN
ejpam-3096	185	5	1	1	NUM
ejpam-3096	185	6	.	.	PUNCT
ejpam-3096	186	1	assume	assume	VERB
ejpam-3096	186	2	£	£	SYM
ejpam-3096	186	3	xs−1	xs−1	PROPN
ejpam-3096	186	4	6=	6=	ADP
ejpam-3096	186	5	£	£	SYM
ejpam-3096	186	6	xs	xs	NOUN
ejpam-3096	186	7	∀	∀	NOUN
ejpam-3096	186	8	s	s	PART
ejpam-3096	186	9	∈	∈	PROPN
ejpam-3096	186	10	n	n	CCONJ
ejpam-3096	186	11	therefore	therefore	ADV
ejpam-3096	186	12	for	for	ADP
ejpam-3096	186	13	s	s	PROPN
ejpam-3096	186	14	∈	∈	PROPN
ejpam-3096	187	1	n	n	CCONJ
ejpam-3096	187	2	we	we	PRON
ejpam-3096	187	3	obtain	obtain	VERB
ejpam-3096	187	4	:	:	PUNCT
ejpam-3096	187	5	d∗(£xs,£xs,£xs+1	d∗(£xs,£xs,£xs+1	ADJ
ejpam-3096	187	6	)	)	PUNCT
ejpam-3096	187	7	=	=	SYM
ejpam-3096	187	8	d∗(txs−1	d∗(txs−1	NOUN
ejpam-3096	187	9	,	,	PUNCT
ejpam-3096	187	10	txs−1	txs−1	PROPN
ejpam-3096	187	11	,	,	PUNCT
ejpam-3096	187	12	txs	txs	NOUN
ejpam-3096	187	13	)	)	PUNCT
ejpam-3096	187	14	≤	≤	NOUN
ejpam-3096	187	15	φ(φ(xs−1	φ(φ(xs−1	NOUN
ejpam-3096	187	16	,	,	PUNCT
ejpam-3096	187	17	xs−1	xs−1	PROPN
ejpam-3096	187	18	,	,	PUNCT
ejpam-3096	187	19	xs	xs	PROPN
ejpam-3096	187	20	)	)	PUNCT
ejpam-3096	187	21	)	)	PUNCT
ejpam-3096	187	22	where	where	SCONJ
ejpam-3096	187	23	,	,	PUNCT
ejpam-3096	187	24	φ(xs−1	φ(xs−1	NOUN
ejpam-3096	187	25	,	,	PUNCT
ejpam-3096	187	26	xs−1	xs−1	PROPN
ejpam-3096	187	27	,	,	PUNCT
ejpam-3096	187	28	xs	xs	PROPN
ejpam-3096	187	29	)	)	PUNCT
ejpam-3096	187	30	∈	∈	PROPN
ejpam-3096	187	31	{	{	PUNCT
ejpam-3096	187	32	d∗(£xs−1,£xs−1,£xs	d∗(£xs−1,£xs−1,£xs	ADJ
ejpam-3096	187	33	)	)	PUNCT
ejpam-3096	187	34	,	,	PUNCT
ejpam-3096	187	35	d∗(£xs−1,£xs−1	d∗(£xs−1,£xs−1	PROPN
ejpam-3096	187	36	,	,	PUNCT
ejpam-3096	187	37	txs−1	txs−1	PROPN
ejpam-3096	187	38	)	)	PUNCT
ejpam-3096	187	39	,	,	PUNCT
ejpam-3096	187	40	d∗(£xs,£xs	d∗(£xs,£xs	PROPN
ejpam-3096	187	41	,	,	PUNCT
ejpam-3096	187	42	txs	txs	NOUN
ejpam-3096	187	43	)	)	PUNCT
ejpam-3096	187	44	,	,	PUNCT
ejpam-3096	187	45	d	d	PROPN
ejpam-3096	187	46	∗(txs−1	∗(txs−1	PROPN
ejpam-3096	187	47	,	,	PUNCT
ejpam-3096	187	48	txs−1,£xs	txs−1,£xs	PROPN
ejpam-3096	187	49	)	)	PUNCT
ejpam-3096	187	50	}	}	PUNCT
ejpam-3096	188	1	=	=	SYM
ejpam-3096	188	2	{	{	PUNCT
ejpam-3096	188	3	d∗(£xs−1,£xs−1,£xs	d∗(£xs−1,£xs−1,£xs	ADJ
ejpam-3096	188	4	)	)	PUNCT
ejpam-3096	188	5	,	,	PUNCT
ejpam-3096	188	6	d∗(£xs−1,£xs−1,£xs	d∗(£xs−1,£xs−1,£xs	ADJ
ejpam-3096	188	7	)	)	PUNCT
ejpam-3096	188	8	,	,	PUNCT
ejpam-3096	188	9	d	d	PROPN
ejpam-3096	188	10	∗(£xs,£xs,£xs+1	∗(£xs,£xs,£xs+1	PROPN
ejpam-3096	188	11	)	)	PUNCT
ejpam-3096	188	12	,	,	PUNCT
ejpam-3096	188	13	d	d	NOUN
ejpam-3096	188	14	∗(£xs,£xs,£xs	∗(£xs,£xs,£xs	X
ejpam-3096	188	15	)	)	PUNCT
ejpam-3096	188	16	}	}	PUNCT
ejpam-3096	188	17	=	=	SYM
ejpam-3096	188	18	{	{	PUNCT
ejpam-3096	188	19	d∗(£xs−1,£xs−1,£xs	d∗(£xs−1,£xs−1,£xs	ADJ
ejpam-3096	188	20	)	)	PUNCT
ejpam-3096	188	21	,	,	PUNCT
ejpam-3096	188	22	d∗(£xs,£xs,£xs+1	d∗(£xs,£xs,£xs+1	NOUN
ejpam-3096	188	23	)	)	PUNCT
ejpam-3096	188	24	,	,	PUNCT
ejpam-3096	188	25	0	0	NUM
ejpam-3096	188	26	}	}	PUNCT
ejpam-3096	188	27	.	.	PUNCT
ejpam-3096	189	1	a.	a.	PROPN
ejpam-3096	189	2	m.	m.	PROPN
ejpam-3096	189	3	al	al	PROPN
ejpam-3096	189	4	.	.	PROPN
ejpam-3096	189	5	jumaili	jumaili	PROPN
ejpam-3096	189	6	/	/	SYM
ejpam-3096	189	7	eur	eur	PROPN
ejpam-3096	189	8	.	.	PUNCT
ejpam-3096	190	1	j.	j.	PROPN
ejpam-3096	190	2	pure	pure	PROPN
ejpam-3096	190	3	appl	appl	PROPN
ejpam-3096	190	4	.	.	PROPN
ejpam-3096	190	5	math	math	PROPN
ejpam-3096	190	6	,	,	PUNCT
ejpam-3096	190	7	10	10	NUM
ejpam-3096	190	8	(	(	PUNCT
ejpam-3096	190	9	5	5	NUM
ejpam-3096	190	10	)	)	PUNCT
ejpam-3096	190	11	(	(	PUNCT
ejpam-3096	190	12	2017	2017	NUM
ejpam-3096	190	13	)	)	PUNCT
ejpam-3096	190	14	,	,	PUNCT
ejpam-3096	190	15	1023	1023	NUM
ejpam-3096	190	16	-	-	SYM
ejpam-3096	190	17	1034	1034	NUM
ejpam-3096	190	18	1030	1030	NUM
ejpam-3096	190	19	i.	i.	NOUN
ejpam-3096	190	20	if	if	SCONJ
ejpam-3096	190	21	φ(xs−1	φ(xs−1	NOUN
ejpam-3096	190	22	,	,	PUNCT
ejpam-3096	190	23	xs−1	xs−1	PROPN
ejpam-3096	190	24	,	,	PUNCT
ejpam-3096	190	25	xs	xs	PROPN
ejpam-3096	190	26	)	)	PUNCT
ejpam-3096	190	27	=	=	PUNCT
ejpam-3096	191	1	d∗(£xs,£xs,£xs+1	d∗(£xs,£xs,£xs+1	X
ejpam-3096	191	2	)	)	PUNCT
ejpam-3096	191	3	therefore	therefore	ADV
ejpam-3096	191	4	,	,	PUNCT
ejpam-3096	191	5	d∗(£xs,£xs,£xs+1	d∗(£xs,£xs,£xs+1	NOUN
ejpam-3096	191	6	)	)	PUNCT
ejpam-3096	191	7	≤	≤	NOUN
ejpam-3096	191	8	φ(d∗(£xs,£xs,£xs+1	φ(d∗(£xs,£xs,£xs+1	NOUN
ejpam-3096	191	9	)	)	PUNCT
ejpam-3096	191	10	)	)	PUNCT
ejpam-3096	191	11	,	,	PUNCT
ejpam-3096	191	12	and	and	CCONJ
ejpam-3096	191	13	via	via	ADP
ejpam-3096	191	14	the	the	DET
ejpam-3096	191	15	characteristic	characteristic	NOUN
ejpam-3096	191	16	of	of	ADP
ejpam-3096	191	17	φ	φ	PROPN
ejpam-3096	191	18	-	-	PUNCT
ejpam-3096	191	19	map	map	NOUN
ejpam-3096	191	20	we	we	PRON
ejpam-3096	191	21	get	get	VERB
ejpam-3096	191	22	:	:	PUNCT
ejpam-3096	191	23	d∗(£xs,£xs,£xs+1	d∗(£xs,£xs,£xs+1	ADJ
ejpam-3096	191	24	)	)	PUNCT
ejpam-3096	191	25	<	<	X
ejpam-3096	191	26	d∗(£xs,£xs,£xs+1	d∗(£xs,£xs,£xs+1	X
ejpam-3096	191	27	)	)	PUNCT
ejpam-3096	191	28	which	which	PRON
ejpam-3096	191	29	is	be	AUX
ejpam-3096	191	30	impossible	impossible	ADJ
ejpam-3096	191	31	.	.	PUNCT
ejpam-3096	192	1	ii	ii	PROPN
ejpam-3096	192	2	.	.	PUNCT
ejpam-3096	193	1	if	if	SCONJ
ejpam-3096	193	2	φ(xs−1	φ(xs−1	NOUN
ejpam-3096	193	3	,	,	PUNCT
ejpam-3096	193	4	xs−1	xs−1	PROPN
ejpam-3096	193	5	,	,	PUNCT
ejpam-3096	193	6	xs	xs	PROPN
ejpam-3096	193	7	)	)	PUNCT
ejpam-3096	193	8	=	=	SYM
ejpam-3096	193	9	0	0	NUM
ejpam-3096	193	10	,	,	PUNCT
ejpam-3096	193	11	hence	hence	ADV
ejpam-3096	193	12	d∗(£xs,£xs,£xs+1	d∗(£xs,£xs,£xs+1	NOUN
ejpam-3096	193	13	)	)	PUNCT
ejpam-3096	193	14	≤	≤	NOUN
ejpam-3096	193	15	φ(0	φ(0	ADJ
ejpam-3096	193	16	)	)	PUNCT
ejpam-3096	193	17	<	<	X
ejpam-3096	193	18	0	0	NUM
ejpam-3096	193	19	which	which	PRON
ejpam-3096	193	20	is	be	AUX
ejpam-3096	193	21	a	a	DET
ejpam-3096	193	22	contradiction	contradiction	NOUN
ejpam-3096	193	23	.	.	PUNCT
ejpam-3096	194	1	so	so	ADV
ejpam-3096	194	2	,	,	PUNCT
ejpam-3096	194	3	φ(xs−1	φ(xs−1	NOUN
ejpam-3096	194	4	,	,	PUNCT
ejpam-3096	194	5	xs−1	xs−1	PROPN
ejpam-3096	194	6	,	,	PUNCT
ejpam-3096	194	7	xs	xs	PROPN
ejpam-3096	194	8	)	)	PUNCT
ejpam-3096	194	9	=	=	SYM
ejpam-3096	194	10	d∗(£xs−1,£xs−1,£xs	d∗(£xs−1,£xs−1,£xs	ADJ
ejpam-3096	194	11	)	)	PUNCT
ejpam-3096	194	12	,	,	PUNCT
ejpam-3096	194	13	thus	thus	ADV
ejpam-3096	194	14	d∗(£xs,£xs,£xs+1	d∗(£xs,£xs,£xs+1	ADJ
ejpam-3096	194	15	)	)	PUNCT
ejpam-3096	194	16	≤	≤	NOUN
ejpam-3096	194	17	φ(d∗(£xs−1,£xs−1,£xs	φ(d∗(£xs−1,£xs−1,£xs	PROPN
ejpam-3096	194	18	)	)	PUNCT
ejpam-3096	194	19	)	)	PUNCT
ejpam-3096	195	1	after	after	ADP
ejpam-3096	195	2	that	that	PRON
ejpam-3096	195	3	for	for	ADP
ejpam-3096	195	4	s	s	PROPN
ejpam-3096	195	5	∈	∈	PROPN
ejpam-3096	195	6	n	n	X
ejpam-3096	195	7	,	,	PUNCT
ejpam-3096	195	8	we	we	PRON
ejpam-3096	195	9	obtain	obtain	VERB
ejpam-3096	195	10	:	:	PUNCT
ejpam-3096	195	11	d∗(£xs,£xs,£xs+1	d∗(£xs,£xs,£xs+1	ADJ
ejpam-3096	195	12	)	)	PUNCT
ejpam-3096	195	13	=	=	SYM
ejpam-3096	195	14	d∗(txs−1	d∗(txs−1	NOUN
ejpam-3096	195	15	,	,	PUNCT
ejpam-3096	195	16	txs−1	txs−1	PROPN
ejpam-3096	195	17	,	,	PUNCT
ejpam-3096	195	18	txs	txs	NOUN
ejpam-3096	195	19	)	)	PUNCT
ejpam-3096	195	20	≤	≤	NOUN
ejpam-3096	195	21	φ(d∗(£xs−1,£xs−1,£xs	φ(d∗(£xs−1,£xs−1,£xs	PROPN
ejpam-3096	195	22	)	)	PUNCT
ejpam-3096	195	23	)	)	PUNCT
ejpam-3096	195	24	≤	≤	NUM
ejpam-3096	196	1	φ2(d∗(£xs−2,£xs−2,£xs−1	φ2(d∗(£xs−2,£xs−2,£xs−1	PROPN
ejpam-3096	196	2	)	)	PUNCT
ejpam-3096	196	3	)	)	PUNCT
ejpam-3096	196	4	..........	..........	PUNCT
ejpam-3096	197	1	≤	≤	NUM
ejpam-3096	197	2	φs(d∗(£x0,£x0,£x1	φs(d∗(£x0,£x0,£x1	NUM
ejpam-3096	197	3	)	)	PUNCT
ejpam-3096	197	4	)	)	PUNCT
ejpam-3096	198	1	we	we	PRON
ejpam-3096	198	2	can	can	AUX
ejpam-3096	198	3	show	show	VERB
ejpam-3096	198	4	that	that	SCONJ
ejpam-3096	198	5	{	{	PUNCT
ejpam-3096	198	6	£	£	SYM
ejpam-3096	198	7	xs	xs	NOUN
ejpam-3096	198	8	}	}	PUNCT
ejpam-3096	198	9	is	be	AUX
ejpam-3096	198	10	a	a	DET
ejpam-3096	198	11	cauchy	cauchy	ADJ
ejpam-3096	198	12	sequence	sequence	NOUN
ejpam-3096	198	13	by	by	ADP
ejpam-3096	198	14	similar	similar	ADJ
ejpam-3096	198	15	method	method	NOUN
ejpam-3096	198	16	to	to	ADP
ejpam-3096	198	17	that	that	PRON
ejpam-3096	198	18	in	in	ADP
ejpam-3096	198	19	the	the	DET
ejpam-3096	198	20	evidence	evidence	NOUN
ejpam-3096	198	21	of	of	ADP
ejpam-3096	198	22	theorem	theorem	NOUN
ejpam-3096	198	23	(	(	PUNCT
ejpam-3096	198	24	1	1	NUM
ejpam-3096	198	25	)	)	PUNCT
ejpam-3096	198	26	.	.	PUNCT
ejpam-3096	199	1	since	since	SCONJ
ejpam-3096	199	2	x	x	PROPN
ejpam-3096	199	3	is	be	AUX
ejpam-3096	199	4	d∗-complete	d∗-complete	NOUN
ejpam-3096	199	5	,	,	PUNCT
ejpam-3096	199	6	so	so	CCONJ
ejpam-3096	199	7	{	{	PUNCT
ejpam-3096	199	8	£	£	SYM
ejpam-3096	199	9	xs	xs	NOUN
ejpam-3096	199	10	}	}	PUNCT
ejpam-3096	199	11	is	be	AUX
ejpam-3096	199	12	convergent	convergent	ADJ
ejpam-3096	199	13	to	to	ADP
ejpam-3096	199	14	a	a	DET
ejpam-3096	199	15	point	point	NOUN
ejpam-3096	199	16	u	u	NOUN
ejpam-3096	199	17	in	in	ADP
ejpam-3096	199	18	x.	x.	NOUN
ejpam-3096	199	19	now	now	ADV
ejpam-3096	199	20	we	we	PRON
ejpam-3096	199	21	explain	explain	VERB
ejpam-3096	199	22	that	that	SCONJ
ejpam-3096	199	23	£	£	SYM
ejpam-3096	199	24	u	u	NOUN
ejpam-3096	199	25	=	=	PROPN
ejpam-3096	199	26	tu	tu	PROPN
ejpam-3096	199	27	.	.	PUNCT
ejpam-3096	200	1	since	since	SCONJ
ejpam-3096	200	2	{	{	PUNCT
ejpam-3096	200	3	£	£	SYM
ejpam-3096	200	4	xs	xs	NOUN
ejpam-3096	200	5	}	}	PUNCT
ejpam-3096	200	6	non	non	ADJ
ejpam-3096	200	7	-	-	ADJ
ejpam-3096	200	8	decreasing	decrease	VERB
ejpam-3096	200	9	sequence	sequence	NOUN
ejpam-3096	200	10	and	and	CCONJ
ejpam-3096	200	11	£	£	SYM
ejpam-3096	200	12	xs	xs	PROPN
ejpam-3096	200	13	→	→	SYM
ejpam-3096	200	14	u	u	PROPN
ejpam-3096	200	15	,	,	PUNCT
ejpam-3096	200	16	therefore	therefore	ADV
ejpam-3096	200	17	by	by	ADP
ejpam-3096	200	18	regularity	regularity	NOUN
ejpam-3096	200	19	of	of	ADP
ejpam-3096	200	20	x	x	PRON
ejpam-3096	200	21	we	we	PRON
ejpam-3096	200	22	have	have	VERB
ejpam-3096	200	23	£	£	SYM
ejpam-3096	200	24	xs	xs	PROPN
ejpam-3096	200	25	4	4	NUM
ejpam-3096	200	26	u	u	NOUN
ejpam-3096	200	27	∀	∀	X
ejpam-3096	200	28	s.	s.	PROPN
ejpam-3096	200	29	if	if	SCONJ
ejpam-3096	200	30	£	£	SYM
ejpam-3096	200	31	xs	xs	PROPN
ejpam-3096	200	32	=	=	SYM
ejpam-3096	200	33	u	u	PROPN
ejpam-3096	200	34	for	for	ADP
ejpam-3096	200	35	some	some	DET
ejpam-3096	200	36	u	u	NOUN
ejpam-3096	200	37	,	,	PUNCT
ejpam-3096	200	38	hence	hence	ADV
ejpam-3096	200	39	,	,	PUNCT
ejpam-3096	200	40	by	by	ADP
ejpam-3096	200	41	construction	construction	NOUN
ejpam-3096	200	42	we	we	PRON
ejpam-3096	200	43	obtain	obtain	VERB
ejpam-3096	200	44	,	,	PUNCT
ejpam-3096	200	45	£	£	NOUN
ejpam-3096	200	46	xs+1	xs+1	NOUN
ejpam-3096	200	47	=	=	SYM
ejpam-3096	200	48	u	u	PROPN
ejpam-3096	200	49	and	and	CCONJ
ejpam-3096	200	50	u	u	NOUN
ejpam-3096	200	51	is	be	AUX
ejpam-3096	200	52	(	(	PUNCT
ejpam-3096	200	53	f.p	f.p	NOUN
ejpam-3096	200	54	)	)	PUNCT
ejpam-3096	200	55	.	.	PUNCT
ejpam-3096	201	1	so	so	ADV
ejpam-3096	201	2	we	we	PRON
ejpam-3096	201	3	presume	presume	VERB
ejpam-3096	201	4	that	that	SCONJ
ejpam-3096	201	5	£	£	SYM
ejpam-3096	201	6	xs	xs	PROPN
ejpam-3096	201	7	6=	6=	SYM
ejpam-3096	201	8	u	u	PROPN
ejpam-3096	201	9	,	,	PUNCT
ejpam-3096	201	10	thus	thus	ADV
ejpam-3096	201	11	for	for	ADP
ejpam-3096	201	12	s	s	PROPN
ejpam-3096	201	13	∈	∈	PROPN
ejpam-3096	201	14	n	n	INTJ
ejpam-3096	201	15	we	we	PRON
ejpam-3096	201	16	obtain	obtain	VERB
ejpam-3096	201	17	:	:	PUNCT
ejpam-3096	201	18	d∗(£u	d∗(£u	PROPN
ejpam-3096	201	19	,	,	PUNCT
ejpam-3096	201	20	tu	tu	PROPN
ejpam-3096	201	21	,	,	PUNCT
ejpam-3096	201	22	tu	tu	PROPN
ejpam-3096	201	23	)	)	PUNCT
ejpam-3096	201	24	≤	≤	ADV
ejpam-3096	202	1	d∗(£u,£xs,£xs	d∗(£u,£xs,£xs	PROPN
ejpam-3096	202	2	)	)	PUNCT
ejpam-3096	203	1	+	+	PROPN
ejpam-3096	203	2	d∗(£xs	d∗(£xs	PROPN
ejpam-3096	203	3	,	,	PUNCT
ejpam-3096	203	4	tu	tu	PROPN
ejpam-3096	203	5	,	,	PUNCT
ejpam-3096	203	6	tu	tu	PROPN
ejpam-3096	203	7	)	)	PUNCT
ejpam-3096	203	8	=	=	SYM
ejpam-3096	203	9	d∗(£u,£xs,£xs	d∗(£u,£xs,£xs	ADJ
ejpam-3096	203	10	)	)	PUNCT
ejpam-3096	204	1	+	+	X
ejpam-3096	204	2	d∗(txs−1	d∗(txs−1	PROPN
ejpam-3096	204	3	,	,	PUNCT
ejpam-3096	204	4	tu	tu	PROPN
ejpam-3096	204	5	,	,	PUNCT
ejpam-3096	204	6	tu	tu	PROPN
ejpam-3096	204	7	)	)	PUNCT
ejpam-3096	204	8	≤	≤	ADV
ejpam-3096	204	9	d∗(£u,£xs,£xs	d∗(£u,£xs,£xs	ADJ
ejpam-3096	204	10	)	)	PUNCT
ejpam-3096	204	11	+	+	SYM
ejpam-3096	204	12	φ(φ(xs−1	φ(φ(xs−1	NOUN
ejpam-3096	204	13	,	,	PUNCT
ejpam-3096	204	14	u	u	NOUN
ejpam-3096	204	15	,	,	PUNCT
ejpam-3096	204	16	u	u	NOUN
ejpam-3096	204	17	)	)	PUNCT
ejpam-3096	204	18	)	)	PUNCT
ejpam-3096	204	19	where	where	SCONJ
ejpam-3096	204	20	,	,	PUNCT
ejpam-3096	204	21	φ(xs−1	φ(xs−1	NUM
ejpam-3096	204	22	,	,	PUNCT
ejpam-3096	204	23	u	u	NOUN
ejpam-3096	204	24	,	,	PUNCT
ejpam-3096	204	25	u	u	NOUN
ejpam-3096	204	26	)	)	PUNCT
ejpam-3096	204	27	∈	∈	PROPN
ejpam-3096	204	28	{	{	PUNCT
ejpam-3096	204	29	d∗(£xs−1,£u,£u	d∗(£xs−1,£u,£u	PROPN
ejpam-3096	204	30	)	)	PUNCT
ejpam-3096	204	31	,	,	PUNCT
ejpam-3096	204	32	d∗(£xs−1,£xs−1	d∗(£xs−1,£xs−1	PROPN
ejpam-3096	204	33	,	,	PUNCT
ejpam-3096	204	34	txs−1	txs−1	PROPN
ejpam-3096	204	35	)	)	PUNCT
ejpam-3096	204	36	,	,	PUNCT
ejpam-3096	204	37	d∗(£xs−1,£xs−1	d∗(£xs−1,£xs−1	PROPN
ejpam-3096	204	38	,	,	PUNCT
ejpam-3096	204	39	txs−1	txs−1	PROPN
ejpam-3096	204	40	)	)	PUNCT
ejpam-3096	204	41	,	,	PUNCT
ejpam-3096	204	42	d	d	PROPN
ejpam-3096	204	43	∗(txs−1,£xs−1,£u	∗(txs−1,£xs−1,£u	PROPN
ejpam-3096	204	44	)	)	PUNCT
ejpam-3096	204	45	}	}	PUNCT
ejpam-3096	204	46	=	=	SYM
ejpam-3096	204	47	{	{	PUNCT
ejpam-3096	204	48	d∗(£xs−1,£u,£u	d∗(£xs−1,£u,£u	PROPN
ejpam-3096	204	49	)	)	PUNCT
ejpam-3096	204	50	,	,	PUNCT
ejpam-3096	204	51	d∗(£xs−1,£xs−1,£xs	d∗(£xs−1,£xs−1,£xs	ADJ
ejpam-3096	204	52	)	)	PUNCT
ejpam-3096	204	53	,	,	PUNCT
ejpam-3096	204	54	d	d	PROPN
ejpam-3096	204	55	∗(£xs,£xs−1,£u	∗(£xs,£xs−1,£u	PROPN
ejpam-3096	204	56	)	)	PUNCT
ejpam-3096	204	57	}	}	PUNCT
ejpam-3096	204	58	fix	fix	VERB
ejpam-3096	204	59	d	d	NOUN
ejpam-3096	204	60	,	,	PUNCT
ejpam-3096	204	61	0	0	NUM
ejpam-3096	204	62	�	�	PROPN
ejpam-3096	204	63	d	d	PROPN
ejpam-3096	204	64	,	,	PUNCT
ejpam-3096	204	65	and	and	CCONJ
ejpam-3096	204	66	choose	choose	VERB
ejpam-3096	204	67	n1	n1	PROPN
ejpam-3096	204	68	∈	∈	PROPN
ejpam-3096	204	69	n	n	CCONJ
ejpam-3096	204	70	(	(	PUNCT
ejpam-3096	204	71	s.t	s.t	PROPN
ejpam-3096	204	72	)	)	PUNCT
ejpam-3096	204	73	,	,	PUNCT
ejpam-3096	204	74	d∗(£u,£xs,£xs	d∗(£u,£xs,£xs	PROPN
ejpam-3096	204	75	)	)	PUNCT
ejpam-3096	204	76	�	�	PROPN
ejpam-3096	205	1	d	d	ADP
ejpam-3096	205	2	2	2	NUM
ejpam-3096	205	3	and	and	CCONJ
ejpam-3096	205	4	d∗(£xs−1,£u,£u	d∗(£xs−1,£u,£u	PROPN
ejpam-3096	205	5	)	)	PUNCT
ejpam-3096	205	6	�	�	PROPN
ejpam-3096	205	7	d	d	ADP
ejpam-3096	205	8	2	2	NUM
ejpam-3096	205	9	,	,	PUNCT
ejpam-3096	205	10	∀	∀	NOUN
ejpam-3096	205	11	s	s	PART
ejpam-3096	205	12	≥	≥	NOUN
ejpam-3096	205	13	n1	n1	NOUN
ejpam-3096	205	14	.	.	PUNCT
ejpam-3096	206	1	we	we	PRON
ejpam-3096	206	2	can	can	AUX
ejpam-3096	206	3	discuss	discuss	VERB
ejpam-3096	206	4	three	three	NUM
ejpam-3096	206	5	cases	case	NOUN
ejpam-3096	206	6	as	as	ADP
ejpam-3096	206	7	following	follow	VERB
ejpam-3096	206	8	:	:	PUNCT
ejpam-3096	206	9	a.	a.	NOUN
ejpam-3096	206	10	if	if	SCONJ
ejpam-3096	206	11	φ(xs−1	φ(xs−1	NOUN
ejpam-3096	206	12	,	,	PUNCT
ejpam-3096	206	13	u	u	NOUN
ejpam-3096	206	14	,	,	PUNCT
ejpam-3096	206	15	u	u	NOUN
ejpam-3096	206	16	)	)	PUNCT
ejpam-3096	206	17	=	=	SYM
ejpam-3096	206	18	d∗(£xs−1,£u,£u	d∗(£xs−1,£u,£u	PROPN
ejpam-3096	206	19	)	)	PUNCT
ejpam-3096	206	20	,	,	PUNCT
ejpam-3096	206	21	therefore	therefore	ADV
ejpam-3096	206	22	we	we	PRON
ejpam-3096	206	23	have	have	VERB
ejpam-3096	206	24	:	:	PUNCT
ejpam-3096	206	25	d∗(£u	d∗(£u	PROPN
ejpam-3096	206	26	,	,	PUNCT
ejpam-3096	206	27	tu	tu	PROPN
ejpam-3096	206	28	,	,	PUNCT
ejpam-3096	206	29	tu	tu	PROPN
ejpam-3096	206	30	)	)	PUNCT
ejpam-3096	206	31	≤	≤	ADV
ejpam-3096	207	1	d∗(£u,£xs,£xs	d∗(£u,£xs,£xs	ADV
ejpam-3096	207	2	)	)	PUNCT
ejpam-3096	207	3	+	+	SYM
ejpam-3096	207	4	φ(d∗(£xs−1,£u,£u	φ(d∗(£xs−1,£u,£u	ADJ
ejpam-3096	207	5	)	)	PUNCT
ejpam-3096	207	6	)	)	PUNCT
ejpam-3096	208	1	<	<	X
ejpam-3096	208	2	d∗(£u,£xs,£xs	d∗(£u,£xs,£xs	X
ejpam-3096	208	3	)	)	PUNCT
ejpam-3096	208	4	+	+	ADJ
ejpam-3096	208	5	d∗(£xs−1,£u,£u	d∗(£xs−1,£u,£u	PROPN
ejpam-3096	208	6	)	)	PUNCT
ejpam-3096	208	7	�	�	PROPN
ejpam-3096	209	1	d	d	ADP
ejpam-3096	209	2	2	2	NUM
ejpam-3096	210	1	+	+	CCONJ
ejpam-3096	210	2	d	d	PROPN
ejpam-3096	210	3	2	2	X
ejpam-3096	210	4	=	=	SYM
ejpam-3096	210	5	d.	d.	PROPN
ejpam-3096	210	6	b.	b.	PROPN
ejpam-3096	211	1	if	if	SCONJ
ejpam-3096	211	2	φ(xs−1	φ(xs−1	NOUN
ejpam-3096	211	3	,	,	PUNCT
ejpam-3096	211	4	u	u	NOUN
ejpam-3096	211	5	,	,	PUNCT
ejpam-3096	211	6	u	u	NOUN
ejpam-3096	211	7	)	)	PUNCT
ejpam-3096	211	8	=	=	SYM
ejpam-3096	211	9	d∗(£xs−1,£xs−1,£xs	d∗(£xs−1,£xs−1,£xs	ADJ
ejpam-3096	211	10	)	)	PUNCT
ejpam-3096	211	11	,	,	PUNCT
ejpam-3096	211	12	after	after	SCONJ
ejpam-3096	211	13	that	that	PRON
ejpam-3096	211	14	we	we	PRON
ejpam-3096	211	15	obtain	obtain	VERB
ejpam-3096	211	16	:	:	PUNCT
ejpam-3096	211	17	d∗(£u	d∗(£u	PROPN
ejpam-3096	211	18	,	,	PUNCT
ejpam-3096	211	19	tu	tu	PROPN
ejpam-3096	211	20	,	,	PUNCT
ejpam-3096	211	21	tu	tu	PROPN
ejpam-3096	211	22	)	)	PUNCT
ejpam-3096	211	23	≤	≤	ADV
ejpam-3096	211	24	d∗(£u,£xs,£xs	d∗(£u,£xs,£xs	ADJ
ejpam-3096	211	25	)	)	PUNCT
ejpam-3096	211	26	+	+	NUM
ejpam-3096	211	27	φ(d∗(£xs−1,£xs−1,£xs	φ(d∗(£xs−1,£xs−1,£xs	PROPN
ejpam-3096	211	28	)	)	PUNCT
ejpam-3096	211	29	)	)	PUNCT
ejpam-3096	212	1	<	<	X
ejpam-3096	212	2	d∗(£u,£xs,£xs	d∗(£u,£xs,£xs	X
ejpam-3096	212	3	)	)	PUNCT
ejpam-3096	212	4	+	+	NOUN
ejpam-3096	212	5	d∗(£xs−1,£xs−1,£u	d∗(£xs−1,£xs−1,£u	ADJ
ejpam-3096	212	6	)	)	PUNCT
ejpam-3096	212	7	�	�	PROPN
ejpam-3096	213	1	d	d	ADP
ejpam-3096	213	2	2	2	NUM
ejpam-3096	214	1	+	+	CCONJ
ejpam-3096	214	2	d	d	PROPN
ejpam-3096	214	3	2	2	X
ejpam-3096	214	4	=	=	SYM
ejpam-3096	214	5	d.	d.	PROPN
ejpam-3096	214	6	a.	a.	PROPN
ejpam-3096	214	7	m.	m.	PROPN
ejpam-3096	215	1	al	al	PROPN
ejpam-3096	215	2	.	.	PROPN
ejpam-3096	215	3	jumaili	jumaili	PROPN
ejpam-3096	215	4	/	/	SYM
ejpam-3096	215	5	eur	eur	PROPN
ejpam-3096	215	6	.	.	PUNCT
ejpam-3096	216	1	j.	j.	PROPN
ejpam-3096	216	2	pure	pure	PROPN
ejpam-3096	216	3	appl	appl	PROPN
ejpam-3096	216	4	.	.	PROPN
ejpam-3096	216	5	math	math	PROPN
ejpam-3096	216	6	,	,	PUNCT
ejpam-3096	216	7	10	10	NUM
ejpam-3096	216	8	(	(	PUNCT
ejpam-3096	216	9	5	5	NUM
ejpam-3096	216	10	)	)	PUNCT
ejpam-3096	216	11	(	(	PUNCT
ejpam-3096	216	12	2017	2017	NUM
ejpam-3096	216	13	)	)	PUNCT
ejpam-3096	216	14	,	,	PUNCT
ejpam-3096	216	15	1023	1023	NUM
ejpam-3096	216	16	-	-	SYM
ejpam-3096	216	17	1034	1034	NUM
ejpam-3096	216	18	1031	1031	NUM
ejpam-3096	216	19	c.	c.	NOUN
ejpam-3096	216	20	if	if	SCONJ
ejpam-3096	216	21	φ(xs−1	φ(xs−1	NOUN
ejpam-3096	216	22	,	,	PUNCT
ejpam-3096	216	23	u	u	NOUN
ejpam-3096	216	24	,	,	PUNCT
ejpam-3096	216	25	u	u	NOUN
ejpam-3096	216	26	)	)	PUNCT
ejpam-3096	216	27	=	=	PUNCT
ejpam-3096	216	28	d∗(£xs,£xs−1,£u	d∗(£xs,£xs−1,£u	X
ejpam-3096	216	29	)	)	PUNCT
ejpam-3096	216	30	,	,	PUNCT
ejpam-3096	216	31	thus	thus	ADV
ejpam-3096	216	32	we	we	PRON
ejpam-3096	216	33	get	get	VERB
ejpam-3096	216	34	:	:	PUNCT
ejpam-3096	216	35	d∗(£u	d∗(£u	PROPN
ejpam-3096	216	36	,	,	PUNCT
ejpam-3096	216	37	tu	tu	PROPN
ejpam-3096	216	38	,	,	PUNCT
ejpam-3096	216	39	tu	tu	PROPN
ejpam-3096	216	40	)	)	PUNCT
ejpam-3096	216	41	≤	≤	ADV
ejpam-3096	217	1	d∗(£u,£xs,£xs	d∗(£u,£xs,£xs	ADV
ejpam-3096	217	2	)	)	PUNCT
ejpam-3096	218	1	+	+	CCONJ
ejpam-3096	218	2	φ(d∗(£xs,£xs−1,£u	φ(d∗(£xs,£xs−1,£u	ADJ
ejpam-3096	218	3	)	)	PUNCT
ejpam-3096	218	4	)	)	PUNCT
ejpam-3096	219	1	<	<	X
ejpam-3096	219	2	d∗(£u,£xs,£xs	d∗(£u,£xs,£xs	X
ejpam-3096	219	3	)	)	PUNCT
ejpam-3096	219	4	+	+	NOUN
ejpam-3096	219	5	d∗(£xs,£xs−1,£u	d∗(£xs,£xs−1,£u	ADJ
ejpam-3096	219	6	)	)	PUNCT
ejpam-3096	219	7	≤	≤	PUNCT
ejpam-3096	219	8	d∗(£u,£xs,£xs	d∗(£u,£xs,£xs	ADJ
ejpam-3096	219	9	)	)	PUNCT
ejpam-3096	220	1	+	+	NUM
ejpam-3096	220	2	d∗(£xs,£xs,£xs−1	d∗(£xs,£xs,£xs−1	NUM
ejpam-3096	220	3	)	)	PUNCT
ejpam-3096	221	1	+	+	VERB
ejpam-3096	221	2	d∗(£xs−1,£u,£u	d∗(£xs−1,£u,£u	NOUN
ejpam-3096	221	3	)	)	PUNCT
ejpam-3096	221	4	�	�	PROPN
ejpam-3096	221	5	d.	d.	PROPN
ejpam-3096	221	6	whenever	whenever	SCONJ
ejpam-3096	221	7	s	s	VERB
ejpam-3096	221	8	∈	∈	PROPN
ejpam-3096	221	9	n	n	CCONJ
ejpam-3096	221	10	,	,	PUNCT
ejpam-3096	221	11	therefore	therefore	ADV
ejpam-3096	221	12	in	in	ADP
ejpam-3096	221	13	all	all	DET
ejpam-3096	221	14	above	above	ADP
ejpam-3096	221	15	cases	case	NOUN
ejpam-3096	221	16	we	we	PRON
ejpam-3096	221	17	have	have	VERB
ejpam-3096	221	18	:	:	PUNCT
ejpam-3096	221	19	d∗(£u	d∗(£u	PROPN
ejpam-3096	221	20	,	,	PUNCT
ejpam-3096	221	21	tu	tu	PROPN
ejpam-3096	221	22	,	,	PUNCT
ejpam-3096	221	23	tu	tu	PROPN
ejpam-3096	221	24	)	)	PUNCT
ejpam-3096	221	25	�	�	PROPN
ejpam-3096	221	26	d	d	PROPN
ejpam-3096	221	27	for	for	ADP
ejpam-3096	221	28	arbitrary	arbitrary	ADJ
ejpam-3096	221	29	d	d	PROPN
ejpam-3096	221	30	∈	∈	PROPN
ejpam-3096	221	31	intp	intp	NOUN
ejpam-3096	221	32	.	.	PUNCT
ejpam-3096	222	1	according	accord	VERB
ejpam-3096	222	2	the	the	DET
ejpam-3096	222	3	remark	remark	NOUN
ejpam-3096	222	4	(	(	PUNCT
ejpam-3096	222	5	2−r3	2−r3	NUM
ejpam-3096	222	6	)	)	PUNCT
ejpam-3096	222	7	,	,	PUNCT
ejpam-3096	222	8	it	it	PRON
ejpam-3096	222	9	follows	follow	VERB
ejpam-3096	222	10	that	that	SCONJ
ejpam-3096	222	11	d∗(£u	d∗(£u	PROPN
ejpam-3096	222	12	,	,	PUNCT
ejpam-3096	222	13	tu	tu	PROPN
ejpam-3096	222	14	,	,	PUNCT
ejpam-3096	222	15	tu	tu	PROPN
ejpam-3096	222	16	)	)	PUNCT
ejpam-3096	222	17	=	=	SYM
ejpam-3096	222	18	0	0	NUM
ejpam-3096	222	19	,	,	PUNCT
ejpam-3096	222	20	which	which	PRON
ejpam-3096	222	21	implies	imply	VERB
ejpam-3096	222	22	that	that	SCONJ
ejpam-3096	222	23	£	£	SYM
ejpam-3096	222	24	u	u	NOUN
ejpam-3096	222	25	=	=	PROPN
ejpam-3096	222	26	tu	tu	PROPN
ejpam-3096	222	27	.	.	PUNCT
ejpam-3096	223	1	thus	thus	ADV
ejpam-3096	223	2	we	we	PRON
ejpam-3096	223	3	conclude	conclude	VERB
ejpam-3096	223	4	that	that	SCONJ
ejpam-3096	223	5	u	u	PROPN
ejpam-3096	223	6	is	be	AUX
ejpam-3096	223	7	a	a	DET
ejpam-3096	223	8	coincidence	coincidence	NOUN
ejpam-3096	223	9	point	point	NOUN
ejpam-3096	223	10	for	for	ADP
ejpam-3096	223	11	£	£	NOUN
ejpam-3096	223	12	and	and	CCONJ
ejpam-3096	223	13	t.	t.	NOUN
ejpam-3096	223	14	corollary	corollary	ADJ
ejpam-3096	223	15	3	3	PROPN
ejpam-3096	223	16	.	.	PUNCT
ejpam-3096	224	1	assume	assume	VERB
ejpam-3096	224	2	(	(	PUNCT
ejpam-3096	224	3	x,4	x,4	X
ejpam-3096	224	4	)	)	PUNCT
ejpam-3096	224	5	is	be	AUX
ejpam-3096	224	6	(	(	PUNCT
ejpam-3096	224	7	p.o.s	p.o.s	NOUN
ejpam-3096	224	8	)	)	PUNCT
ejpam-3096	224	9	and	and	CCONJ
ejpam-3096	224	10	suppose	suppose	VERB
ejpam-3096	224	11	that	that	SCONJ
ejpam-3096	224	12	(	(	PUNCT
ejpam-3096	224	13	x	x	NOUN
ejpam-3096	224	14	,	,	PUNCT
ejpam-3096	224	15	d∗	d∗	PROPN
ejpam-3096	224	16	)	)	PUNCT
ejpam-3096	224	17	is	be	AUX
ejpam-3096	224	18	a	a	DET
ejpam-3096	224	19	complete	complete	ADJ
ejpam-3096	224	20	generalized	generalize	VERB
ejpam-3096	224	21	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	224	22	and	and	CCONJ
ejpam-3096	224	23	p	p	NOUN
ejpam-3096	224	24	is	be	AUX
ejpam-3096	224	25	(	(	PUNCT
ejpam-3096	224	26	o.c	o.c	PROPN
ejpam-3096	224	27	)	)	PUNCT
ejpam-3096	224	28	.	.	PUNCT
ejpam-3096	225	1	let	let	VERB
ejpam-3096	225	2	£	£	SYM
ejpam-3096	225	3	,	,	PUNCT
ejpam-3096	225	4	t	t	X
ejpam-3096	225	5	:	:	PUNCT
ejpam-3096	225	6	x	x	X
ejpam-3096	225	7	→	→	PUNCT
ejpam-3096	225	8	x	x	PART
ejpam-3096	225	9	be	be	AUX
ejpam-3096	225	10	non	non	ADJ
ejpam-3096	225	11	-	-	ADJ
ejpam-3096	225	12	decreasing	decrease	VERB
ejpam-3096	225	13	mappings	mapping	NOUN
ejpam-3096	225	14	.	.	PUNCT
ejpam-3096	226	1	assume	assume	VERB
ejpam-3096	226	2	that	that	SCONJ
ejpam-3096	226	3	for	for	ADP
ejpam-3096	226	4	some	some	DET
ejpam-3096	226	5	h	h	NOUN
ejpam-3096	226	6	∈	∈	PROPN
ejpam-3096	227	1	[	[	X
ejpam-3096	227	2	0	0	NUM
ejpam-3096	227	3	,	,	PUNCT
ejpam-3096	227	4	1	1	NUM
ejpam-3096	227	5	)	)	PUNCT
ejpam-3096	227	6	,	,	PUNCT
ejpam-3096	227	7	and	and	CCONJ
ejpam-3096	227	8	∀	∀	X
ejpam-3096	227	9	x	x	NOUN
ejpam-3096	227	10	,	,	PUNCT
ejpam-3096	227	11	y	y	PROPN
ejpam-3096	227	12	,	,	PUNCT
ejpam-3096	227	13	z	z	NOUN
ejpam-3096	227	14	∈	∈	PROPN
ejpam-3096	227	15	x	x	PUNCT
ejpam-3096	227	16	with	with	ADP
ejpam-3096	227	17	fz	fz	ADP
ejpam-3096	227	18	4	4	NUM
ejpam-3096	227	19	£	£	SYM
ejpam-3096	227	20	y	y	PROPN
ejpam-3096	227	21	4	4	NUM
ejpam-3096	227	22	£	£	NOUN
ejpam-3096	227	23	x	x	NOUN
ejpam-3096	227	24	,	,	PUNCT
ejpam-3096	227	25	∃	∃	PROPN
ejpam-3096	227	26	φ(x	φ(x	PROPN
ejpam-3096	227	27	,	,	PUNCT
ejpam-3096	227	28	y	y	PROPN
ejpam-3096	227	29	,	,	PUNCT
ejpam-3096	227	30	z	z	NOUN
ejpam-3096	227	31	)	)	PUNCT
ejpam-3096	227	32	∈	∈	PROPN
ejpam-3096	227	33	{	{	PUNCT
ejpam-3096	227	34	d∗(£x,£y,£z	d∗(£x,£y,£z	PROPN
ejpam-3096	227	35	)	)	PUNCT
ejpam-3096	227	36	,	,	PUNCT
ejpam-3096	227	37	d∗(£x,£x	d∗(£x,£x	NOUN
ejpam-3096	227	38	,	,	PUNCT
ejpam-3096	227	39	tx	tx	PROPN
ejpam-3096	227	40	)	)	PUNCT
ejpam-3096	227	41	,	,	PUNCT
ejpam-3096	227	42	d∗(£y,£y	d∗(£y,£y	PROPN
ejpam-3096	227	43	,	,	PUNCT
ejpam-3096	227	44	ty	ty	NOUN
ejpam-3096	227	45	)	)	PUNCT
ejpam-3096	227	46	,	,	PUNCT
ejpam-3096	227	47	d∗(tx,£y,£z	d∗(tx,£y,£z	NOUN
ejpam-3096	227	48	)	)	PUNCT
ejpam-3096	227	49	}	}	PUNCT
ejpam-3096	227	50	(	(	PUNCT
ejpam-3096	227	51	s.t	s.t	PROPN
ejpam-3096	227	52	):	):	PUNCT
ejpam-3096	227	53	d∗(tx	d∗(tx	PROPN
ejpam-3096	227	54	,	,	PUNCT
ejpam-3096	227	55	ty	ty	INTJ
ejpam-3096	227	56	,	,	PUNCT
ejpam-3096	227	57	tz	tz	NOUN
ejpam-3096	227	58	)	)	PUNCT
ejpam-3096	227	59	≤	≤	NOUN
ejpam-3096	227	60	hφ(x	hφ(x	PROPN
ejpam-3096	227	61	,	,	PUNCT
ejpam-3096	227	62	y	y	PROPN
ejpam-3096	227	63	,	,	PUNCT
ejpam-3096	227	64	z	z	NOUN
ejpam-3096	227	65	)	)	PUNCT
ejpam-3096	227	66	.	.	PUNCT
ejpam-3096	228	1	we	we	PRON
ejpam-3096	228	2	assume	assume	VERB
ejpam-3096	228	3	the	the	DET
ejpam-3096	228	4	following	following	NOUN
ejpam-3096	228	5	:	:	PUNCT
ejpam-3096	228	6	a	a	X
ejpam-3096	228	7	)	)	PUNCT
ejpam-3096	228	8	t	t	NOUN
ejpam-3096	228	9	is	be	AUX
ejpam-3096	228	10	weakly	weakly	ADV
ejpam-3096	228	11	increasing	increase	VERB
ejpam-3096	228	12	with	with	ADP
ejpam-3096	228	13	respect	respect	NOUN
ejpam-3096	228	14	to	to	ADP
ejpam-3096	228	15	£	£	SYM
ejpam-3096	228	16	,	,	PUNCT
ejpam-3096	228	17	b	b	NOUN
ejpam-3096	228	18	)	)	PUNCT
ejpam-3096	228	19	x	x	PUNCT
ejpam-3096	228	20	is	be	AUX
ejpam-3096	228	21	regular	regular	ADJ
ejpam-3096	228	22	.	.	PUNCT
ejpam-3096	229	1	in	in	ADP
ejpam-3096	229	2	that	that	DET
ejpam-3096	229	3	case	case	NOUN
ejpam-3096	229	4	£	£	PROPN
ejpam-3096	229	5	and	and	CCONJ
ejpam-3096	229	6	t	t	PROPN
ejpam-3096	229	7	have	have	VERB
ejpam-3096	229	8	a	a	DET
ejpam-3096	229	9	coincidence	coincidence	NOUN
ejpam-3096	229	10	point	point	NOUN
ejpam-3096	229	11	.	.	PUNCT
ejpam-3096	230	1	proof	proof	NOUN
ejpam-3096	230	2	.	.	PUNCT
ejpam-3096	231	1	the	the	DET
ejpam-3096	231	2	proof	proof	NOUN
ejpam-3096	231	3	is	be	AUX
ejpam-3096	231	4	direct	direct	ADJ
ejpam-3096	231	5	result	result	NOUN
ejpam-3096	231	6	from	from	ADP
ejpam-3096	231	7	theorem	theorem	ADJ
ejpam-3096	231	8	(	(	PUNCT
ejpam-3096	231	9	2	2	NUM
ejpam-3096	231	10	)	)	PUNCT
ejpam-3096	231	11	.	.	PUNCT
ejpam-3096	232	1	remark	remark	NOUN
ejpam-3096	232	2	5	5	NUM
ejpam-3096	232	3	.	.	PUNCT
ejpam-3096	233	1	if	if	SCONJ
ejpam-3096	233	2	the	the	DET
ejpam-3096	233	3	mapping	mapping	NOUN
ejpam-3096	233	4	£	£	PROPN
ejpam-3096	233	5	:	:	PUNCT
ejpam-3096	233	6	x	x	SYM
ejpam-3096	233	7	→	→	PUNCT
ejpam-3096	233	8	x	x	SYM
ejpam-3096	233	9	is	be	AUX
ejpam-3096	233	10	identity	identity	NOUN
ejpam-3096	233	11	,	,	PUNCT
ejpam-3096	233	12	so	so	ADV
ejpam-3096	233	13	from	from	ADP
ejpam-3096	233	14	theorem	theorem	NOUN
ejpam-3096	233	15	(	(	PUNCT
ejpam-3096	233	16	2	2	NUM
ejpam-3096	233	17	)	)	PUNCT
ejpam-3096	233	18	we	we	PRON
ejpam-3096	233	19	get	get	VERB
ejpam-3096	233	20	easily	easily	ADV
ejpam-3096	233	21	the	the	DET
ejpam-3096	233	22	following	follow	VERB
ejpam-3096	233	23	(	(	PUNCT
ejpam-3096	233	24	f.p	f.p	NOUN
ejpam-3096	233	25	)	)	PUNCT
ejpam-3096	233	26	result	result	NOUN
ejpam-3096	233	27	.	.	PUNCT
ejpam-3096	234	1	corollary	corollary	ADJ
ejpam-3096	234	2	4	4	NUM
ejpam-3096	234	3	.	.	PUNCT
ejpam-3096	235	1	assume	assume	VERB
ejpam-3096	235	2	(	(	PUNCT
ejpam-3096	235	3	x,4	x,4	X
ejpam-3096	235	4	)	)	PUNCT
ejpam-3096	235	5	is	be	AUX
ejpam-3096	235	6	(	(	PUNCT
ejpam-3096	235	7	p.o.s	p.o.s	NOUN
ejpam-3096	235	8	)	)	PUNCT
ejpam-3096	235	9	and	and	CCONJ
ejpam-3096	235	10	suppose	suppose	VERB
ejpam-3096	235	11	that	that	SCONJ
ejpam-3096	235	12	(	(	PUNCT
ejpam-3096	235	13	x	x	NOUN
ejpam-3096	235	14	,	,	PUNCT
ejpam-3096	235	15	d∗	d∗	PROPN
ejpam-3096	235	16	)	)	PUNCT
ejpam-3096	235	17	is	be	AUX
ejpam-3096	235	18	a	a	DET
ejpam-3096	235	19	complete	complete	ADJ
ejpam-3096	235	20	generalized	generalize	VERB
ejpam-3096	235	21	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	235	22	and	and	CCONJ
ejpam-3096	235	23	p	p	NOUN
ejpam-3096	235	24	is	be	AUX
ejpam-3096	235	25	(	(	PUNCT
ejpam-3096	235	26	o.c	o.c	PROPN
ejpam-3096	235	27	)	)	PUNCT
ejpam-3096	235	28	.	.	PUNCT
ejpam-3096	236	1	let	let	VERB
ejpam-3096	236	2	£	£	SYM
ejpam-3096	236	3	,	,	PUNCT
ejpam-3096	236	4	t	t	X
ejpam-3096	236	5	:	:	PUNCT
ejpam-3096	236	6	x	x	X
ejpam-3096	236	7	→	→	PUNCT
ejpam-3096	236	8	x	x	PART
ejpam-3096	236	9	be	be	AUX
ejpam-3096	236	10	non	non	ADJ
ejpam-3096	236	11	-	-	ADJ
ejpam-3096	236	12	decreasing	decrease	VERB
ejpam-3096	236	13	mappings	mapping	NOUN
ejpam-3096	236	14	,	,	PUNCT
ejpam-3096	236	15	(	(	PUNCT
ejpam-3096	236	16	s.t	s.t	PROPN
ejpam-3096	236	17	):	):	PUNCT
ejpam-3096	236	18	d∗(tx	d∗(tx	PROPN
ejpam-3096	236	19	,	,	PUNCT
ejpam-3096	236	20	ty	ty	INTJ
ejpam-3096	236	21	,	,	PUNCT
ejpam-3096	236	22	tz	tz	NOUN
ejpam-3096	236	23	)	)	PUNCT
ejpam-3096	236	24	≤	≤	NOUN
ejpam-3096	236	25	φ(φ(x	φ(φ(x	NOUN
ejpam-3096	236	26	,	,	PUNCT
ejpam-3096	236	27	y	y	PROPN
ejpam-3096	236	28	,	,	PUNCT
ejpam-3096	236	29	z	z	NOUN
ejpam-3096	236	30	)	)	PUNCT
ejpam-3096	236	31	)	)	PUNCT
ejpam-3096	236	32	where	where	SCONJ
ejpam-3096	236	33	φ(x	φ(x	PROPN
ejpam-3096	236	34	,	,	PUNCT
ejpam-3096	236	35	y	y	PROPN
ejpam-3096	236	36	,	,	PUNCT
ejpam-3096	236	37	z	z	NOUN
ejpam-3096	236	38	)	)	PUNCT
ejpam-3096	236	39	∈	∈	PROPN
ejpam-3096	236	40	{	{	PUNCT
ejpam-3096	236	41	d∗(x	d∗(x	PROPN
ejpam-3096	236	42	,	,	PUNCT
ejpam-3096	236	43	y	y	PROPN
ejpam-3096	236	44	,	,	PUNCT
ejpam-3096	236	45	z	z	NOUN
ejpam-3096	236	46	)	)	PUNCT
ejpam-3096	236	47	,	,	PUNCT
ejpam-3096	236	48	d∗(x	d∗(x	PROPN
ejpam-3096	236	49	,	,	PUNCT
ejpam-3096	236	50	x	x	PRON
ejpam-3096	236	51	,	,	PUNCT
ejpam-3096	236	52	tx	tx	PROPN
ejpam-3096	236	53	)	)	PUNCT
ejpam-3096	236	54	,	,	PUNCT
ejpam-3096	236	55	d∗(y	d∗(y	PROPN
ejpam-3096	236	56	,	,	PUNCT
ejpam-3096	236	57	y	y	PROPN
ejpam-3096	236	58	,	,	PUNCT
ejpam-3096	236	59	ty	ty	NOUN
ejpam-3096	236	60	)	)	PUNCT
ejpam-3096	236	61	,	,	PUNCT
ejpam-3096	236	62	d∗(tx	d∗(tx	PROPN
ejpam-3096	236	63	,	,	PUNCT
ejpam-3096	236	64	y	y	PROPN
ejpam-3096	236	65	,	,	PUNCT
ejpam-3096	236	66	z	z	NOUN
ejpam-3096	236	67	)	)	PUNCT
ejpam-3096	236	68	}	}	PUNCT
ejpam-3096	236	69	and	and	CCONJ
ejpam-3096	236	70	∀	∀	X
ejpam-3096	236	71	x	x	NOUN
ejpam-3096	236	72	,	,	PUNCT
ejpam-3096	236	73	y	y	PROPN
ejpam-3096	236	74	,	,	PUNCT
ejpam-3096	236	75	z	z	NOUN
ejpam-3096	236	76	∈	∈	PROPN
ejpam-3096	236	77	x	x	PUNCT
ejpam-3096	236	78	with	with	ADP
ejpam-3096	236	79	z	z	PROPN
ejpam-3096	236	80	4	4	NUM
ejpam-3096	236	81	y	y	PROPN
ejpam-3096	236	82	4	4	NUM
ejpam-3096	236	83	x	x	NOUN
ejpam-3096	236	84	,	,	PUNCT
ejpam-3096	236	85	where	where	SCONJ
ejpam-3096	236	86	φ	φ	PROPN
ejpam-3096	236	87	is	be	AUX
ejpam-3096	236	88	a	a	DET
ejpam-3096	236	89	φ	φ	NOUN
ejpam-3096	236	90	-	-	PUNCT
ejpam-3096	236	91	map	map	NOUN
ejpam-3096	236	92	.	.	PUNCT
ejpam-3096	237	1	assume	assume	VERB
ejpam-3096	237	2	the	the	DET
ejpam-3096	237	3	following	following	NOUN
ejpam-3096	237	4	:	:	PUNCT
ejpam-3096	237	5	a	a	X
ejpam-3096	237	6	)	)	PUNCT
ejpam-3096	237	7	tx	tx	ADP
ejpam-3096	237	8	4	4	NUM
ejpam-3096	237	9	t	t	NOUN
ejpam-3096	237	10	(	(	PUNCT
ejpam-3096	237	11	tx	tx	PROPN
ejpam-3096	237	12	)	)	PUNCT
ejpam-3096	237	13	∀	∀	X
ejpam-3096	238	1	x	x	X
ejpam-3096	238	2	∈	∈	NOUN
ejpam-3096	238	3	x	x	X
ejpam-3096	238	4	,	,	PUNCT
ejpam-3096	238	5	b	b	NOUN
ejpam-3096	238	6	)	)	PUNCT
ejpam-3096	238	7	x	x	PUNCT
ejpam-3096	238	8	is	be	AUX
ejpam-3096	238	9	regular	regular	ADJ
ejpam-3096	238	10	.	.	PUNCT
ejpam-3096	239	1	in	in	ADP
ejpam-3096	239	2	that	that	DET
ejpam-3096	239	3	case	case	NOUN
ejpam-3096	239	4	t	t	NOUN
ejpam-3096	239	5	has	have	VERB
ejpam-3096	239	6	(	(	PUNCT
ejpam-3096	239	7	f.p	f.p	PROPN
ejpam-3096	239	8	)	)	PUNCT
ejpam-3096	239	9	.	.	PUNCT
ejpam-3096	240	1	next	next	ADV
ejpam-3096	240	2	,	,	PUNCT
ejpam-3096	240	3	we	we	PRON
ejpam-3096	240	4	present	present	VERB
ejpam-3096	240	5	a	a	DET
ejpam-3096	240	6	sufficient	sufficient	ADJ
ejpam-3096	240	7	condition	condition	NOUN
ejpam-3096	240	8	for	for	ADP
ejpam-3096	240	9	the	the	DET
ejpam-3096	240	10	unique	unique	ADJ
ejpam-3096	240	11	-	-	PUNCT
ejpam-3096	240	12	ness	ness	NOUN
ejpam-3096	240	13	of	of	ADP
ejpam-3096	240	14	the	the	DET
ejpam-3096	240	15	point	point	NOUN
ejpam-3096	240	16	of	of	ADP
ejpam-3096	240	17	coincidence	coincidence	NOUN
ejpam-3096	240	18	in	in	ADP
ejpam-3096	240	19	the	the	DET
ejpam-3096	240	20	following	follow	VERB
ejpam-3096	240	21	result	result	NOUN
ejpam-3096	240	22	.	.	PUNCT
ejpam-3096	241	1	theorem	theorem	NOUN
ejpam-3096	241	2	3	3	X
ejpam-3096	242	1	.	.	PUNCT
ejpam-3096	242	2	assume	assume	VERB
ejpam-3096	242	3	that	that	SCONJ
ejpam-3096	242	4	(	(	PUNCT
ejpam-3096	242	5	x,4	x,4	X
ejpam-3096	242	6	)	)	PUNCT
ejpam-3096	242	7	is	be	AUX
ejpam-3096	242	8	a	a	DET
ejpam-3096	242	9	totally	totally	ADV
ejpam-3096	242	10	ordered	order	VERB
ejpam-3096	242	11	set	set	NOUN
ejpam-3096	242	12	and	and	CCONJ
ejpam-3096	242	13	(	(	PUNCT
ejpam-3096	242	14	x	x	NOUN
ejpam-3096	242	15	,	,	PUNCT
ejpam-3096	242	16	d∗	d∗	PROPN
ejpam-3096	242	17	)	)	PUNCT
ejpam-3096	242	18	is	be	AUX
ejpam-3096	242	19	a	a	DET
ejpam-3096	242	20	complete	complete	ADJ
ejpam-3096	242	21	generalized	generalized	ADJ
ejpam-3096	242	22	d∗-m.sp	d∗-m.sp	NOUN
ejpam-3096	242	23	,	,	PUNCT
ejpam-3096	242	24	p	p	NOUN
ejpam-3096	242	25	is	be	AUX
ejpam-3096	242	26	(	(	PUNCT
ejpam-3096	242	27	o.c	o.c	PROPN
ejpam-3096	242	28	)	)	PUNCT
ejpam-3096	242	29	.	.	PUNCT
ejpam-3096	243	1	let	let	VERB
ejpam-3096	243	2	£	£	SYM
ejpam-3096	243	3	,	,	PUNCT
ejpam-3096	243	4	t	t	X
ejpam-3096	243	5	:	:	PUNCT
ejpam-3096	243	6	x	x	X
ejpam-3096	243	7	→	→	PUNCT
ejpam-3096	243	8	x	x	PART
ejpam-3096	243	9	be	be	AUX
ejpam-3096	243	10	non	non	ADJ
ejpam-3096	243	11	-	-	ADJ
ejpam-3096	243	12	decreasing	decrease	VERB
ejpam-3096	243	13	mappings	mapping	NOUN
ejpam-3096	243	14	.	.	PUNCT
ejpam-3096	244	1	assume	assume	VERB
ejpam-3096	244	2	that	that	SCONJ
ejpam-3096	244	3	∀	∀	NOUN
ejpam-3096	244	4	x	x	NOUN
ejpam-3096	244	5	,	,	PUNCT
ejpam-3096	244	6	y	y	PROPN
ejpam-3096	244	7	,	,	PUNCT
ejpam-3096	244	8	z	z	NOUN
ejpam-3096	244	9	∈	∈	PROPN
ejpam-3096	244	10	x	x	PUNCT
ejpam-3096	244	11	with	with	ADP
ejpam-3096	244	12	£	£	SYM
ejpam-3096	244	13	z	z	NOUN
ejpam-3096	244	14	4	4	NUM
ejpam-3096	244	15	£	£	SYM
ejpam-3096	244	16	y	y	PROPN
ejpam-3096	244	17	4	4	NUM
ejpam-3096	244	18	£	£	PROPN
ejpam-3096	244	19	x	x	SYM
ejpam-3096	244	20	∃	∃	PROPN
ejpam-3096	244	21	,	,	PUNCT
ejpam-3096	244	22	φ(x	φ(x	PROPN
ejpam-3096	244	23	,	,	PUNCT
ejpam-3096	244	24	y	y	PROPN
ejpam-3096	244	25	,	,	PUNCT
ejpam-3096	244	26	z	z	NOUN
ejpam-3096	244	27	)	)	PUNCT
ejpam-3096	244	28	∈	∈	PROPN
ejpam-3096	244	29	{	{	PUNCT
ejpam-3096	244	30	d∗(£x,£y,£z	d∗(£x,£y,£z	PROPN
ejpam-3096	244	31	)	)	PUNCT
ejpam-3096	244	32	,	,	PUNCT
ejpam-3096	244	33	d∗(£x,£x	d∗(£x,£x	NOUN
ejpam-3096	244	34	,	,	PUNCT
ejpam-3096	244	35	tx	tx	PROPN
ejpam-3096	244	36	)	)	PUNCT
ejpam-3096	244	37	,	,	PUNCT
ejpam-3096	244	38	d∗(£y,£y	d∗(£y,£y	PROPN
ejpam-3096	244	39	,	,	PUNCT
ejpam-3096	244	40	ty	ty	NOUN
ejpam-3096	244	41	)	)	PUNCT
ejpam-3096	244	42	,	,	PUNCT
ejpam-3096	244	43	d∗(tx,£y,£z	d∗(tx,£y,£z	NOUN
ejpam-3096	244	44	)	)	PUNCT
ejpam-3096	244	45	}	}	PUNCT
ejpam-3096	244	46	(	(	PUNCT
ejpam-3096	244	47	s.t	s.t	PROPN
ejpam-3096	244	48	):	):	PUNCT
ejpam-3096	244	49	d∗(tx	d∗(tx	PROPN
ejpam-3096	244	50	,	,	PUNCT
ejpam-3096	244	51	ty	ty	INTJ
ejpam-3096	244	52	,	,	PUNCT
ejpam-3096	244	53	tz	tz	NOUN
ejpam-3096	244	54	)	)	PUNCT
ejpam-3096	244	55	≤	≤	NOUN
ejpam-3096	244	56	φ(φ(x	φ(φ(x	NOUN
ejpam-3096	244	57	,	,	PUNCT
ejpam-3096	244	58	y	y	PROPN
ejpam-3096	244	59	,	,	PUNCT
ejpam-3096	244	60	z	z	NOUN
ejpam-3096	244	61	)	)	PUNCT
ejpam-3096	244	62	)	)	PUNCT
ejpam-3096	244	63	where	where	SCONJ
ejpam-3096	244	64	φ	φ	PROPN
ejpam-3096	244	65	is	be	AUX
ejpam-3096	244	66	a	a	DET
ejpam-3096	244	67	φ	φ	NOUN
ejpam-3096	244	68	-	-	PUNCT
ejpam-3096	244	69	map	map	NOUN
ejpam-3096	244	70	.	.	PUNCT
ejpam-3096	245	1	assume	assume	VERB
ejpam-3096	245	2	the	the	DET
ejpam-3096	245	3	following	following	NOUN
ejpam-3096	245	4	:	:	PUNCT
ejpam-3096	245	5	a	a	X
ejpam-3096	245	6	)	)	PUNCT
ejpam-3096	245	7	t	t	NOUN
ejpam-3096	245	8	is	be	AUX
ejpam-3096	245	9	weakly	weakly	ADV
ejpam-3096	245	10	increasing	increase	VERB
ejpam-3096	245	11	with	with	ADP
ejpam-3096	245	12	respect	respect	NOUN
ejpam-3096	245	13	to	to	ADP
ejpam-3096	245	14	£	£	SYM
ejpam-3096	245	15	,	,	PUNCT
ejpam-3096	245	16	b	b	NOUN
ejpam-3096	245	17	)	)	PUNCT
ejpam-3096	245	18	x	x	PUNCT
ejpam-3096	245	19	is	be	AUX
ejpam-3096	245	20	regular	regular	ADJ
ejpam-3096	245	21	.	.	PUNCT
ejpam-3096	246	1	in	in	ADP
ejpam-3096	246	2	that	that	DET
ejpam-3096	246	3	case	case	NOUN
ejpam-3096	246	4	£	£	PROPN
ejpam-3096	246	5	and	and	CCONJ
ejpam-3096	246	6	t	t	PROPN
ejpam-3096	246	7	have	have	VERB
ejpam-3096	246	8	a	a	DET
ejpam-3096	246	9	unique	unique	ADJ
ejpam-3096	246	10	coincidence	coincidence	NOUN
ejpam-3096	246	11	point	point	NOUN
ejpam-3096	246	12	.	.	PUNCT
ejpam-3096	247	1	references	reference	NOUN
ejpam-3096	247	2	1032	1032	NUM
ejpam-3096	247	3	proof	proof	NOUN
ejpam-3096	247	4	.	.	PUNCT
ejpam-3096	248	1	assume	assume	VERB
ejpam-3096	248	2	that	that	SCONJ
ejpam-3096	248	3	£	£	PROPN
ejpam-3096	248	4	and	and	CCONJ
ejpam-3096	248	5	t	t	PROPN
ejpam-3096	248	6	have	have	VERB
ejpam-3096	248	7	two	two	NUM
ejpam-3096	248	8	points	point	NOUN
ejpam-3096	248	9	of	of	ADP
ejpam-3096	248	10	coincidence	coincidence	NOUN
ejpam-3096	248	11	,	,	PUNCT
ejpam-3096	248	12	u	u	NOUN
ejpam-3096	248	13	and	and	CCONJ
ejpam-3096	248	14	w	w	PROPN
ejpam-3096	248	15	,	,	PUNCT
ejpam-3096	248	16	(	(	PUNCT
ejpam-3096	248	17	s.t	s.t	PROPN
ejpam-3096	248	18	)	)	PUNCT
ejpam-3096	248	19	£	£	PROPN
ejpam-3096	248	20	u	u	NOUN
ejpam-3096	248	21	=	=	PROPN
ejpam-3096	248	22	tu	tu	PROPN
ejpam-3096	248	23	and	and	CCONJ
ejpam-3096	248	24	£	£	SYM
ejpam-3096	248	25	w	w	NOUN
ejpam-3096	248	26	=	=	SYM
ejpam-3096	248	27	tw,£u	tw,£u	PROPN
ejpam-3096	248	28	6=	6=	PROPN
ejpam-3096	248	29	£	£	SYM
ejpam-3096	248	30	w.	w.	NOUN
ejpam-3096	248	31	as	as	ADP
ejpam-3096	248	32	(	(	PUNCT
ejpam-3096	248	33	x,4	x,4	X
ejpam-3096	248	34	)	)	PUNCT
ejpam-3096	248	35	is	be	AUX
ejpam-3096	248	36	a	a	DET
ejpam-3096	248	37	totally	totally	ADV
ejpam-3096	248	38	ordered	order	VERB
ejpam-3096	248	39	set	set	NOUN
ejpam-3096	248	40	and	and	CCONJ
ejpam-3096	248	41	u	u	NOUN
ejpam-3096	248	42	,	,	PUNCT
ejpam-3096	248	43	w	w	PROPN
ejpam-3096	248	44	∈	∈	PROPN
ejpam-3096	248	45	x	x	X
ejpam-3096	248	46	,	,	PUNCT
ejpam-3096	248	47	assume	assume	VERB
ejpam-3096	248	48	that	that	SCONJ
ejpam-3096	248	49	u	u	PROPN
ejpam-3096	248	50	≺	≺	VERB
ejpam-3096	248	51	w.	w.	NOUN
ejpam-3096	248	52	by	by	ADP
ejpam-3096	248	53	means	mean	NOUN
ejpam-3096	248	54	of	of	ADP
ejpam-3096	248	55	the	the	DET
ejpam-3096	248	56	contractive	contractive	ADJ
ejpam-3096	248	57	condition	condition	NOUN
ejpam-3096	248	58	we	we	PRON
ejpam-3096	248	59	have	have	VERB
ejpam-3096	248	60	that	that	PRON
ejpam-3096	248	61	:	:	PUNCT
ejpam-3096	248	62	d∗(£u,£w,£w	d∗(£u,£w,£w	PROPN
ejpam-3096	248	63	)	)	PUNCT
ejpam-3096	248	64	=	=	SYM
ejpam-3096	249	1	d∗(tu,£w,£w	d∗(tu,£w,£w	PROPN
ejpam-3096	249	2	)	)	PUNCT
ejpam-3096	249	3	≤	≤	NOUN
ejpam-3096	250	1	φ(φ(u	φ(φ(u	PROPN
ejpam-3096	250	2	,	,	PUNCT
ejpam-3096	250	3	w	w	NOUN
ejpam-3096	250	4	,	,	PUNCT
ejpam-3096	250	5	w	w	NOUN
ejpam-3096	250	6	)	)	PUNCT
ejpam-3096	250	7	)	)	PUNCT
ejpam-3096	250	8	holds	hold	VERB
ejpam-3096	250	9	for	for	ADP
ejpam-3096	250	10	some	some	PRON
ejpam-3096	250	11	,	,	PUNCT
ejpam-3096	250	12	φ(u	φ(u	PROPN
ejpam-3096	250	13	,	,	PUNCT
ejpam-3096	250	14	w	w	PROPN
ejpam-3096	250	15	,	,	PUNCT
ejpam-3096	250	16	w	w	NOUN
ejpam-3096	250	17	)	)	PUNCT
ejpam-3096	250	18	∈	∈	PROPN
ejpam-3096	250	19	{	{	PUNCT
ejpam-3096	250	20	d∗(£u,£w,£w	d∗(£u,£w,£w	PROPN
ejpam-3096	250	21	)	)	PUNCT
ejpam-3096	250	22	,	,	PUNCT
ejpam-3096	250	23	d∗(£u,£u	d∗(£u,£u	PROPN
ejpam-3096	250	24	,	,	PUNCT
ejpam-3096	250	25	tu	tu	PROPN
ejpam-3096	250	26	)	)	PUNCT
ejpam-3096	250	27	,	,	PUNCT
ejpam-3096	250	28	d∗(£u,£u	d∗(£u,£u	PROPN
ejpam-3096	250	29	,	,	PUNCT
ejpam-3096	250	30	tu	tu	PROPN
ejpam-3096	250	31	)	)	PUNCT
ejpam-3096	250	32	,	,	PUNCT
ejpam-3096	250	33	d∗(tu,£u,£w	d∗(tu,£u,£w	PROPN
ejpam-3096	250	34	)	)	PUNCT
ejpam-3096	250	35	}	}	PUNCT
ejpam-3096	250	36	=	=	SYM
ejpam-3096	250	37	{	{	PUNCT
ejpam-3096	250	38	0	0	NUM
ejpam-3096	250	39	,	,	PUNCT
ejpam-3096	250	40	d∗(£u,£w,£w	d∗(£u,£w,£w	PROPN
ejpam-3096	250	41	)	)	PUNCT
ejpam-3096	250	42	}	}	PUNCT
ejpam-3096	250	43	by	by	ADP
ejpam-3096	250	44	means	mean	NOUN
ejpam-3096	250	45	of	of	ADP
ejpam-3096	250	46	characteristic	characteristic	NOUN
ejpam-3096	250	47	of	of	ADP
ejpam-3096	250	48	φ	φ	PROPN
ejpam-3096	250	49	-	-	NOUN
ejpam-3096	250	50	mapping	mapping	NOUN
ejpam-3096	250	51	we	we	PRON
ejpam-3096	250	52	get	get	VERB
ejpam-3096	250	53	a	a	DET
ejpam-3096	250	54	contradiction	contradiction	NOUN
ejpam-3096	250	55	.	.	PUNCT
ejpam-3096	251	1	therefore	therefore	ADV
ejpam-3096	251	2	£	£	SYM
ejpam-3096	251	3	u	u	NOUN
ejpam-3096	251	4	=	=	PUNCT
ejpam-3096	251	5	£	£	SYM
ejpam-3096	251	6	w.	w.	NOUN
ejpam-3096	251	7	thus	thus	ADV
ejpam-3096	251	8	£	£	PROPN
ejpam-3096	251	9	and	and	CCONJ
ejpam-3096	251	10	t	t	PROPN
ejpam-3096	251	11	have	have	VERB
ejpam-3096	251	12	a	a	DET
ejpam-3096	251	13	unique	unique	ADJ
ejpam-3096	251	14	point	point	NOUN
ejpam-3096	251	15	of	of	ADP
ejpam-3096	251	16	coincidence	coincidence	NOUN
ejpam-3096	251	17	£	£	NOUN
ejpam-3096	251	18	u	u	NOUN
ejpam-3096	251	19	=	=	PROPN
ejpam-3096	251	20	tu	tu	PROPN
ejpam-3096	251	21	.	.	PUNCT
ejpam-3096	251	22	acknowledgements	acknowledgement	NOUN
ejpam-3096	251	23	i	i	PRON
ejpam-3096	251	24	would	would	AUX
ejpam-3096	251	25	like	like	VERB
ejpam-3096	251	26	to	to	PART
ejpam-3096	251	27	express	express	VERB
ejpam-3096	251	28	my	my	PRON
ejpam-3096	251	29	sincere	sincere	ADJ
ejpam-3096	251	30	gratitude	gratitude	NOUN
ejpam-3096	251	31	to	to	ADP
ejpam-3096	251	32	the	the	DET
ejpam-3096	251	33	referees	referee	NOUN
ejpam-3096	251	34	for	for	ADP
ejpam-3096	251	35	their	their	PRON
ejpam-3096	251	36	valuable	valuable	ADJ
ejpam-3096	251	37	suggestions	suggestion	NOUN
ejpam-3096	251	38	and	and	CCONJ
ejpam-3096	251	39	comments	comment	NOUN
ejpam-3096	251	40	which	which	PRON
ejpam-3096	251	41	improved	improve	VERB
ejpam-3096	251	42	the	the	DET
ejpam-3096	251	43	paper	paper	NOUN
ejpam-3096	251	44	.	.	PUNCT
ejpam-3096	252	1	references	reference	NOUN
ejpam-3096	252	2	[	[	X
ejpam-3096	252	3	1	1	NUM
ejpam-3096	252	4	]	]	PUNCT
ejpam-3096	252	5	r.	r.	PROPN
ejpam-3096	252	6	p.	p.	PROPN
ejpam-3096	252	7	agarwal	agarwal	PROPN
ejpam-3096	252	8	,	,	PUNCT
ejpam-3096	252	9	m.	m.	NOUN
ejpam-3096	252	10	a.	a.	PROPN
ejpam-3096	252	11	el	el	PROPN
ejpam-3096	252	12	-	-	PROPN
ejpam-3096	252	13	gebeily	gebeily	PROPN
ejpam-3096	252	14	,	,	PUNCT
ejpam-3096	252	15	d.	d.	PROPN
ejpam-3096	252	16	o’regan	o’regan	PROPN
ejpam-3096	252	17	.	.	PUNCT
ejpam-3096	253	1	generalized	generalized	ADJ
ejpam-3096	253	2	contractions	contraction	NOUN
ejpam-3096	253	3	in	in	ADP
ejpam-3096	253	4	partially	partially	ADV
ejpam-3096	253	5	ordered	order	VERB
ejpam-3096	253	6	metric	metric	ADJ
ejpam-3096	253	7	spaces	space	NOUN
ejpam-3096	253	8	,	,	PUNCT
ejpam-3096	253	9	appl.anal	appl.anal	NUM
ejpam-3096	253	10	,	,	PUNCT
ejpam-3096	253	11	(	(	PUNCT
ejpam-3096	253	12	87	87	NUM
ejpam-3096	253	13	)	)	PUNCT
ejpam-3096	253	14	,	,	PUNCT
ejpam-3096	253	15	1	1	NUM
ejpam-3096	253	16	-	-	SYM
ejpam-3096	253	17	8	8	NUM
ejpam-3096	253	18	,	,	PUNCT
ejpam-3096	253	19	2008	2008	NUM
ejpam-3096	253	20	.	.	PUNCT
ejpam-3096	254	1	[	[	X
ejpam-3096	254	2	2	2	NUM
ejpam-3096	254	3	]	]	PUNCT
ejpam-3096	254	4	c.	c.	PROPN
ejpam-3096	254	5	t.	t.	PROPN
ejpam-3096	254	6	aage	aage	PROPN
ejpam-3096	254	7	and	and	CCONJ
ejpam-3096	254	8	j.	j.	PROPN
ejpam-3096	254	9	n.	n.	PROPN
ejpam-3096	254	10	salunke	salunke	PROPN
ejpam-3096	254	11	.	.	PUNCT
ejpam-3096	255	1	some	some	DET
ejpam-3096	255	2	fixed	fix	VERB
ejpam-3096	255	3	points	point	NOUN
ejpam-3096	255	4	theorems	theorem	NOUN
ejpam-3096	255	5	in	in	ADP
ejpam-3096	255	6	generalized	generalized	ADJ
ejpam-3096	255	7	d∗-metric	d∗-metric	ADJ
ejpam-3096	255	8	spaces	space	NOUN
ejpam-3096	255	9	,	,	PUNCT
ejpam-3096	255	10	appl.sci	appl.sci	X
ejpam-3096	255	11	,	,	PUNCT
ejpam-3096	255	12	(	(	PUNCT
ejpam-3096	255	13	12	12	NUM
ejpam-3096	255	14	)	)	PUNCT
ejpam-3096	255	15	,	,	PUNCT
ejpam-3096	255	16	1	1	NUM
ejpam-3096	255	17	-	-	SYM
ejpam-3096	255	18	13	13	NUM
ejpam-3096	255	19	,	,	PUNCT
ejpam-3096	255	20	2010	2010	NUM
ejpam-3096	255	21	.	.	PUNCT
ejpam-3096	256	1	[	[	X
ejpam-3096	256	2	3	3	NUM
ejpam-3096	256	3	]	]	X
ejpam-3096	256	4	i.	i.	NOUN
ejpam-3096	256	5	arandelović	arandelović	PROPN
ejpam-3096	256	6	,	,	PUNCT
ejpam-3096	256	7	z.	z.	PROPN
ejpam-3096	256	8	kadelburg	kadelburg	PROPN
ejpam-3096	256	9	,	,	PUNCT
ejpam-3096	256	10	s.	s.	PROPN
ejpam-3096	257	1	radenović.	radenović.	PROPN
ejpam-3096	257	2	boyd	boyd	PROPN
ejpam-3096	257	3	-	-	PUNCT
ejpam-3096	257	4	wong	wong	PROPN
ejpam-3096	257	5	-	-	PUNCT
ejpam-3096	257	6	type	type	NOUN
ejpam-3096	257	7	common	common	ADJ
ejpam-3096	257	8	fixed	fix	VERB
ejpam-3096	257	9	point	point	NOUN
ejpam-3096	257	10	results	result	NOUN
ejpam-3096	257	11	in	in	ADP
ejpam-3096	257	12	cone	cone	NOUN
ejpam-3096	257	13	metric	metric	ADJ
ejpam-3096	257	14	spaces	space	NOUN
ejpam-3096	257	15	,	,	PUNCT
ejpam-3096	257	16	appl.math.comput	appl.math.comput	PROPN
ejpam-3096	257	17	,	,	PUNCT
ejpam-3096	257	18	(	(	PUNCT
ejpam-3096	257	19	217	217	NUM
ejpam-3096	257	20	)	)	PUNCT
ejpam-3096	257	21	,	,	PUNCT
ejpam-3096	257	22	7167	7167	NUM
ejpam-3096	257	23	-	-	SYM
ejpam-3096	257	24	7171	7171	NUM
ejpam-3096	257	25	,	,	PUNCT
ejpam-3096	257	26	2011	2011	NUM
ejpam-3096	257	27	.	.	PUNCT
ejpam-3096	258	1	[	[	X
ejpam-3096	258	2	4	4	NUM
ejpam-3096	258	3	]	]	PUNCT
ejpam-3096	258	4	a.	a.	NOUN
ejpam-3096	258	5	m.	m.	PROPN
ejpam-3096	258	6	al	al	PROPN
ejpam-3096	258	7	.	.	PROPN
ejpam-3096	258	8	jumaili	jumaili	PROPN
ejpam-3096	258	9	and	and	CCONJ
ejpam-3096	258	10	x.	x.	PROPN
ejpam-3096	258	11	s.	s.	PROPN
ejpam-3096	258	12	yang	yang	PROPN
ejpam-3096	258	13	.	.	PUNCT
ejpam-3096	259	1	fixed	fix	VERB
ejpam-3096	259	2	point	point	NOUN
ejpam-3096	259	3	theorems	theorem	NOUN
ejpam-3096	259	4	and	and	CCONJ
ejpam-3096	259	5	∇∗-distance	∇∗-distance	NOUN
ejpam-3096	259	6	in	in	ADP
ejpam-3096	259	7	partially	partially	ADV
ejpam-3096	259	8	ordered	order	VERB
ejpam-3096	259	9	d∗-metric	d∗-metric	ADJ
ejpam-3096	259	10	spaces	space	NOUN
ejpam-3096	259	11	,	,	PUNCT
ejpam-3096	259	12	int.journalofmath	int.journalofmath	NUM
ejpam-3096	259	13	,	,	PUNCT
ejpam-3096	259	14	analysis	analysis	NOUN
ejpam-3096	259	15	.	.	PUNCT
ejpam-3096	260	1	6(59	6(59	NUM
ejpam-3096	260	2	)	)	PUNCT
ejpam-3096	260	3	,	,	PUNCT
ejpam-3096	260	4	2949	2949	NUM
ejpam-3096	260	5	-	-	SYM
ejpam-3096	260	6	2955	2955	NUM
ejpam-3096	260	7	,	,	PUNCT
ejpam-3096	260	8	2012	2012	NUM
ejpam-3096	260	9	.	.	PUNCT
ejpam-3096	261	1	[	[	X
ejpam-3096	261	2	5	5	X
ejpam-3096	261	3	]	]	PUNCT
ejpam-3096	261	4	s.	s.	PROPN
ejpam-3096	261	5	banach	banach	PROPN
ejpam-3096	261	6	.	.	PUNCT
ejpam-3096	262	1	sur	sur	PROPN
ejpam-3096	262	2	les	les	X
ejpam-3096	262	3	opérations	opération	NOUN
ejpam-3096	262	4	dans	dan	NOUN
ejpam-3096	262	5	les	les	X
ejpam-3096	262	6	ensembles	ensemble	NOUN
ejpam-3096	262	7	abstraits	abstrait	NOUN
ejpam-3096	262	8	et	et	PROPN
ejpam-3096	262	9	leur	leur	X
ejpam-3096	262	10	application	application	PROPN
ejpam-3096	262	11	aux	aux	PROPN
ejpam-3096	262	12	équations	équations	PROPN
ejpam-3096	262	13	intégrales	intégrale	NOUN
ejpam-3096	262	14	,	,	PUNCT
ejpam-3096	262	15	fund.math	fund.math	NOUN
ejpam-3096	262	16	,	,	PUNCT
ejpam-3096	262	17	(	(	PUNCT
ejpam-3096	262	18	3	3	NUM
ejpam-3096	262	19	)	)	PUNCT
ejpam-3096	262	20	,	,	PUNCT
ejpam-3096	262	21	133	133	NUM
ejpam-3096	262	22	-	-	SYM
ejpam-3096	262	23	181	181	NUM
ejpam-3096	262	24	,	,	PUNCT
ejpam-3096	262	25	1922	1922	NUM
ejpam-3096	262	26	.	.	PUNCT
ejpam-3096	263	1	[	[	X
ejpam-3096	263	2	6	6	NUM
ejpam-3096	263	3	]	]	PUNCT
ejpam-3096	263	4	l.	l.	PROPN
ejpam-3096	263	5	b.	b.	PROPN
ejpam-3096	263	6	ćirić.	ćirić.	PROPN
ejpam-3096	263	7	a	a	DET
ejpam-3096	263	8	generalization	generalization	NOUN
ejpam-3096	263	9	of	of	ADP
ejpam-3096	263	10	banach	banach	NOUN
ejpam-3096	263	11	’s	’s	PART
ejpam-3096	263	12	contraction	contraction	NOUN
ejpam-3096	263	13	principle	principle	NOUN
ejpam-3096	263	14	,	,	PUNCT
ejpam-3096	263	15	proc.amer.math.soc	proc.amer.math.soc	PROPN
ejpam-3096	263	16	,	,	PUNCT
ejpam-3096	263	17	(	(	PUNCT
ejpam-3096	263	18	45	45	NUM
ejpam-3096	263	19	)	)	PUNCT
ejpam-3096	263	20	,	,	PUNCT
ejpam-3096	263	21	267	267	NUM
ejpam-3096	263	22	-	-	SYM
ejpam-3096	263	23	273	273	NUM
ejpam-3096	263	24	,	,	PUNCT
ejpam-3096	263	25	1974	1974	NUM
ejpam-3096	263	26	.	.	PUNCT
ejpam-3096	264	1	[	[	X
ejpam-3096	264	2	7	7	X
ejpam-3096	264	3	]	]	X
ejpam-3096	264	4	l.	l.	PROPN
ejpam-3096	264	5	b.	b.	PROPN
ejpam-3096	264	6	ćirić	ćirić	PROPN
ejpam-3096	264	7	,	,	PUNCT
ejpam-3096	264	8	s.	s.	PROPN
ejpam-3096	264	9	n.	n.	PROPN
ejpam-3096	264	10	ješić	ješić	PROPN
ejpam-3096	264	11	,	,	PUNCT
ejpam-3096	264	12	m.	m.	NOUN
ejpam-3096	264	13	m.	m.	PROPN
ejpam-3096	264	14	milovanović	milovanović	PROPN
ejpam-3096	264	15	,	,	PUNCT
ejpam-3096	264	16	j.s	j.s	PROPN
ejpam-3096	264	17	.	.	PROPN
ejpam-3096	264	18	ume	ume	PROPN
ejpam-3096	264	19	,	,	PUNCT
ejpam-3096	264	20	on	on	ADP
ejpam-3096	264	21	the	the	DET
ejpam-3096	264	22	steepest	steep	ADJ
ejpam-3096	264	23	descent	descent	NOUN
ejpam-3096	264	24	approximation	approximation	NOUN
ejpam-3096	264	25	method	method	NOUN
ejpam-3096	264	26	for	for	ADP
ejpam-3096	264	27	the	the	DET
ejpam-3096	264	28	zeros	zero	NOUN
ejpam-3096	264	29	of	of	ADP
ejpam-3096	264	30	generalized	generalized	ADJ
ejpam-3096	264	31	accretive	accretive	ADJ
ejpam-3096	264	32	operators	operator	NOUN
ejpam-3096	264	33	,	,	PUNCT
ejpam-3096	264	34	nonlinearanal.−	nonlinearanal.−	PROPN
ejpam-3096	264	35	tma	tma	PROPN
ejpam-3096	264	36	,	,	PUNCT
ejpam-3096	264	37	(	(	PUNCT
ejpam-3096	264	38	69	69	NUM
ejpam-3096	264	39	)	)	PUNCT
ejpam-3096	264	40	,	,	PUNCT
ejpam-3096	264	41	763	763	NUM
ejpam-3096	264	42	-	-	SYM
ejpam-3096	264	43	769	769	NUM
ejpam-3096	264	44	,	,	PUNCT
ejpam-3096	264	45	2008	2008	NUM
ejpam-3096	264	46	.	.	PUNCT
ejpam-3096	265	1	[	[	X
ejpam-3096	265	2	8	8	NUM
ejpam-3096	265	3	]	]	PUNCT
ejpam-3096	265	4	l.	l.	PROPN
ejpam-3096	265	5	b.	b.	PROPN
ejpam-3096	265	6	ćirić.	ćirić.	PROPN
ejpam-3096	265	7	coincidence	coincidence	NOUN
ejpam-3096	265	8	and	and	CCONJ
ejpam-3096	265	9	fixed	fix	VERB
ejpam-3096	265	10	points	point	NOUN
ejpam-3096	265	11	for	for	ADP
ejpam-3096	265	12	maps	map	NOUN
ejpam-3096	265	13	on	on	ADP
ejpam-3096	265	14	topological	topological	ADJ
ejpam-3096	265	15	spaces	space	NOUN
ejpam-3096	265	16	,	,	PUNCT
ejpam-3096	265	17	topologyappl	topologyappl	ADJ
ejpam-3096	265	18	,	,	PUNCT
ejpam-3096	265	19	(	(	PUNCT
ejpam-3096	265	20	154	154	NUM
ejpam-3096	265	21	)	)	PUNCT
ejpam-3096	265	22	,	,	PUNCT
ejpam-3096	265	23	3100	3100	NUM
ejpam-3096	265	24	-	-	SYM
ejpam-3096	265	25	3106	3106	NUM
ejpam-3096	265	26	,	,	PUNCT
ejpam-3096	265	27	2007	2007	NUM
ejpam-3096	265	28	.	.	PUNCT
ejpam-3096	266	1	[	[	X
ejpam-3096	266	2	9	9	NUM
ejpam-3096	266	3	]	]	X
ejpam-3096	266	4	b.	b.	PROPN
ejpam-3096	266	5	c.	c.	PROPN
ejpam-3096	266	6	dhage	dhage	PROPN
ejpam-3096	266	7	.	.	PUNCT
ejpam-3096	267	1	generalized	generalize	VERB
ejpam-3096	267	2	metric	metric	ADJ
ejpam-3096	267	3	spaces	space	NOUN
ejpam-3096	267	4	and	and	CCONJ
ejpam-3096	267	5	mappings	mapping	NOUN
ejpam-3096	267	6	with	with	ADP
ejpam-3096	267	7	fixed	fix	VERB
ejpam-3096	267	8	point	point	NOUN
ejpam-3096	267	9	,	,	PUNCT
ejpam-3096	267	10	bull.calcuttamath	bull.calcuttamath	NOUN
ejpam-3096	267	11	,	,	PUNCT
ejpam-3096	267	12	soc	soc	NOUN
ejpam-3096	267	13	,	,	PUNCT
ejpam-3096	267	14	(	(	PUNCT
ejpam-3096	267	15	84	84	NUM
ejpam-3096	267	16	)	)	PUNCT
ejpam-3096	267	17	,	,	PUNCT
ejpam-3096	267	18	329	329	NUM
ejpam-3096	267	19	-	-	SYM
ejpam-3096	267	20	336	336	NUM
ejpam-3096	267	21	,	,	PUNCT
ejpam-3096	267	22	1992	1992	NUM
ejpam-3096	267	23	.	.	PUNCT
ejpam-3096	268	1	[	[	X
ejpam-3096	268	2	10	10	NUM
ejpam-3096	268	3	]	]	X
ejpam-3096	268	4	c.	c.	PROPN
ejpam-3096	268	5	di	di	NOUN
ejpam-3096	268	6	bari	bari	NOUN
ejpam-3096	268	7	and	and	CCONJ
ejpam-3096	268	8	p.	p.	PROPN
ejpam-3096	268	9	vetro	vetro	PROPN
ejpam-3096	268	10	.	.	PUNCT
ejpam-3096	269	1	φ	φ	VERB
ejpam-3096	269	2	-	-	PUNCT
ejpam-3096	269	3	pairs	pair	NOUN
ejpam-3096	269	4	and	and	CCONJ
ejpam-3096	269	5	common	common	ADJ
ejpam-3096	269	6	fixed	fix	VERB
ejpam-3096	269	7	points	point	NOUN
ejpam-3096	269	8	in	in	ADP
ejpam-3096	269	9	cone	cone	NOUN
ejpam-3096	269	10	metric	metric	ADJ
ejpam-3096	269	11	spaces	space	NOUN
ejpam-3096	269	12	,	,	PUNCT
ejpam-3096	269	13	rend.circolomat.palermo	rend.circolomat.palermo	PROPN
ejpam-3096	269	14	,	,	PUNCT
ejpam-3096	269	15	(	(	PUNCT
ejpam-3096	269	16	57	57	NUM
ejpam-3096	269	17	)	)	PUNCT
ejpam-3096	269	18	,	,	PUNCT
ejpam-3096	269	19	279	279	NUM
ejpam-3096	269	20	-	-	SYM
ejpam-3096	269	21	285	285	NUM
ejpam-3096	269	22	,	,	PUNCT
ejpam-3096	269	23	2008	2008	NUM
ejpam-3096	269	24	.	.	PUNCT
ejpam-3096	270	1	references	reference	NOUN
ejpam-3096	270	2	1033	1033	NUM
ejpam-3096	270	3	[	[	X
ejpam-3096	270	4	11	11	NUM
ejpam-3096	270	5	]	]	PUNCT
ejpam-3096	270	6	j.	j.	PROPN
ejpam-3096	270	7	x.	x.	PROPN
ejpam-3096	270	8	fang	fang	PROPN
ejpam-3096	270	9	,	,	PUNCT
ejpam-3096	270	10	y.	y.	PROPN
ejpam-3096	270	11	gao	gao	PROPN
ejpam-3096	270	12	.	.	PUNCT
ejpam-3096	271	1	common	common	ADJ
ejpam-3096	271	2	fixed	fix	VERB
ejpam-3096	271	3	point	point	NOUN
ejpam-3096	271	4	theorems	theorem	NOUN
ejpam-3096	271	5	under	under	ADP
ejpam-3096	271	6	strict	strict	ADJ
ejpam-3096	271	7	contractive	contractive	ADJ
ejpam-3096	271	8	conditions	condition	NOUN
ejpam-3096	271	9	in	in	ADP
ejpam-3096	271	10	menger	menger	PROPN
ejpam-3096	271	11	spaces	space	NOUN
ejpam-3096	271	12	,	,	PUNCT
ejpam-3096	271	13	nonlinearanal.−	nonlinearanal.−	PROPN
ejpam-3096	271	14	tma	tma	PROPN
ejpam-3096	271	15	,	,	PUNCT
ejpam-3096	271	16	(	(	PUNCT
ejpam-3096	271	17	70	70	NUM
ejpam-3096	271	18	)	)	PUNCT
ejpam-3096	271	19	,	,	PUNCT
ejpam-3096	271	20	184	184	NUM
ejpam-3096	271	21	-	-	SYM
ejpam-3096	271	22	193	193	NUM
ejpam-3096	271	23	,	,	PUNCT
ejpam-3096	271	24	2009	2009	NUM
ejpam-3096	271	25	.	.	PUNCT
ejpam-3096	272	1	[	[	X
ejpam-3096	272	2	12	12	NUM
ejpam-3096	272	3	]	]	PUNCT
ejpam-3096	272	4	t.	t.	PROPN
ejpam-3096	272	5	gnana	gnana	PROPN
ejpam-3096	272	6	bhaskar	bhaskar	PROPN
ejpam-3096	272	7	,	,	PUNCT
ejpam-3096	272	8	v.	v.	ADP
ejpam-3096	272	9	lakshmikantham	lakshmikantham	NOUN
ejpam-3096	272	10	.	.	PUNCT
ejpam-3096	273	1	fixed	fix	VERB
ejpam-3096	273	2	point	point	NOUN
ejpam-3096	273	3	theorems	theorem	NOUN
ejpam-3096	273	4	in	in	ADP
ejpam-3096	273	5	partially	partially	ADV
ejpam-3096	273	6	ordered	order	VERB
ejpam-3096	273	7	metric	metric	ADJ
ejpam-3096	273	8	spaces	space	NOUN
ejpam-3096	273	9	and	and	CCONJ
ejpam-3096	273	10	applications	application	NOUN
ejpam-3096	273	11	,	,	PUNCT
ejpam-3096	273	12	nonlinearanal.−	nonlinearanal.−	PROPN
ejpam-3096	273	13	tma	tma	PROPN
ejpam-3096	273	14	,	,	PUNCT
ejpam-3096	273	15	(	(	PUNCT
ejpam-3096	273	16	65	65	NUM
ejpam-3096	273	17	)	)	PUNCT
ejpam-3096	273	18	,	,	PUNCT
ejpam-3096	273	19	1379	1379	NUM
ejpam-3096	273	20	-	-	SYM
ejpam-3096	273	21	1393	1393	NUM
ejpam-3096	273	22	,	,	PUNCT
ejpam-3096	273	23	2006	2006	NUM
ejpam-3096	273	24	.	.	PUNCT
ejpam-3096	274	1	[	[	X
ejpam-3096	274	2	13	13	NUM
ejpam-3096	274	3	]	]	PUNCT
ejpam-3096	274	4	t.	t.	PROPN
ejpam-3096	274	5	gnana	gnana	PROPN
ejpam-3096	274	6	bhaskar	bhaskar	PROPN
ejpam-3096	274	7	,	,	PUNCT
ejpam-3096	274	8	v.	v.	ADP
ejpam-3096	274	9	lakshmikantham	lakshmikantham	PROPN
ejpam-3096	274	10	,	,	PUNCT
ejpam-3096	274	11	j.	j.	PROPN
ejpam-3096	274	12	vasundhara	vasundhara	PROPN
ejpam-3096	274	13	devi	devi	PROPN
ejpam-3096	274	14	.	.	PUNCT
ejpam-3096	275	1	monotone	monotone	ADJ
ejpam-3096	275	2	iterative	iterative	NOUN
ejpam-3096	275	3	technique	technique	NOUN
ejpam-3096	275	4	for	for	ADP
ejpam-3096	275	5	functional	functional	ADJ
ejpam-3096	275	6	differential	differential	ADJ
ejpam-3096	275	7	equations	equation	NOUN
ejpam-3096	275	8	with	with	ADP
ejpam-3096	275	9	retardation	retardation	NOUN
ejpam-3096	275	10	and	and	CCONJ
ejpam-3096	275	11	anticipation	anticipation	NOUN
ejpam-3096	275	12	,	,	PUNCT
ejpam-3096	275	13	nonlinearanal.−	nonlinearanal.−	PROPN
ejpam-3096	275	14	tma	tma	PROPN
ejpam-3096	275	15	,	,	PUNCT
ejpam-3096	275	16	66(10	66(10	PROPN
ejpam-3096	275	17	)	)	PUNCT
ejpam-3096	275	18	,	,	PUNCT
ejpam-3096	275	19	2237	2237	NUM
ejpam-3096	275	20	-	-	SYM
ejpam-3096	275	21	2242	2242	NUM
ejpam-3096	275	22	,	,	PUNCT
ejpam-3096	275	23	2007	2007	NUM
ejpam-3096	275	24	.	.	PUNCT
ejpam-3096	276	1	[	[	X
ejpam-3096	276	2	14	14	NUM
ejpam-3096	276	3	]	]	X
ejpam-3096	276	4	n.	n.	PROPN
ejpam-3096	276	5	hussain	hussain	PROPN
ejpam-3096	276	6	.	.	PUNCT
ejpam-3096	277	1	common	common	ADJ
ejpam-3096	277	2	fixed	fix	VERB
ejpam-3096	277	3	points	point	NOUN
ejpam-3096	277	4	in	in	ADP
ejpam-3096	277	5	best	good	ADJ
ejpam-3096	277	6	approximation	approximation	NOUN
ejpam-3096	277	7	for	for	ADP
ejpam-3096	277	8	banach	banach	NOUN
ejpam-3096	277	9	operator	operator	NOUN
ejpam-3096	277	10	pairs	pair	NOUN
ejpam-3096	277	11	with	with	ADP
ejpam-3096	277	12	.	.	PUNCT
ejpam-3096	278	1	ćirić	ćirić	NOUN
ejpam-3096	278	2	type	type	NOUN
ejpam-3096	278	3	i	i	PROPN
ejpam-3096	278	4	-	-	PUNCT
ejpam-3096	278	5	contractions	contraction	NOUN
ejpam-3096	278	6	,	,	PUNCT
ejpam-3096	278	7	j.math.anal.appl	j.math.anal.appl	NOUN
ejpam-3096	278	8	,	,	PUNCT
ejpam-3096	278	9	(	(	PUNCT
ejpam-3096	278	10	338	338	NUM
ejpam-3096	278	11	)	)	PUNCT
ejpam-3096	278	12	,	,	PUNCT
ejpam-3096	278	13	1351	1351	NUM
ejpam-3096	278	14	-	-	SYM
ejpam-3096	278	15	1363	1363	NUM
ejpam-3096	278	16	,	,	PUNCT
ejpam-3096	278	17	2008	2008	NUM
ejpam-3096	278	18	.	.	PUNCT
ejpam-3096	279	1	[	[	X
ejpam-3096	279	2	15	15	NUM
ejpam-3096	279	3	]	]	X
ejpam-3096	279	4	h.	h.	PROPN
ejpam-3096	279	5	long	long	PROPN
ejpam-3096	279	6	-	-	PUNCT
ejpam-3096	279	7	guang	guang	PROPN
ejpam-3096	279	8	,	,	PUNCT
ejpam-3096	279	9	z.	z.	PROPN
ejpam-3096	279	10	xian	xian	PROPN
ejpam-3096	279	11	.	.	PUNCT
ejpam-3096	280	1	cone	cone	PROPN
ejpam-3096	280	2	metric	metric	ADJ
ejpam-3096	280	3	spaces	space	NOUN
ejpam-3096	280	4	and	and	CCONJ
ejpam-3096	280	5	fixed	fix	VERB
ejpam-3096	280	6	point	point	NOUN
ejpam-3096	280	7	theorems	theorem	NOUN
ejpam-3096	280	8	of	of	ADP
ejpam-3096	280	9	contractive	contractive	ADJ
ejpam-3096	280	10	mappings	mapping	NOUN
ejpam-3096	280	11	,	,	PUNCT
ejpam-3096	280	12	j.math.anal.appl	j.math.anal.appl	NOUN
ejpam-3096	280	13	,	,	PUNCT
ejpam-3096	280	14	(	(	PUNCT
ejpam-3096	280	15	332	332	NUM
ejpam-3096	280	16	)	)	PUNCT
ejpam-3096	280	17	,	,	PUNCT
ejpam-3096	280	18	1468	1468	NUM
ejpam-3096	280	19	-	-	SYM
ejpam-3096	280	20	1476	1476	NUM
ejpam-3096	280	21	,	,	PUNCT
ejpam-3096	280	22	2007	2007	NUM
ejpam-3096	280	23	.	.	PUNCT
ejpam-3096	281	1	[	[	X
ejpam-3096	281	2	16	16	NUM
ejpam-3096	281	3	]	]	X
ejpam-3096	281	4	n.	n.	PROPN
ejpam-3096	281	5	v.	v.	CCONJ
ejpam-3096	281	6	luong	luong	PROPN
ejpam-3096	281	7	and	and	CCONJ
ejpam-3096	281	8	n.	n.	PROPN
ejpam-3096	281	9	x.	x.	PROPN
ejpam-3096	281	10	thuan	thuan	PROPN
ejpam-3096	281	11	.	.	PUNCT
ejpam-3096	282	1	common	common	ADJ
ejpam-3096	282	2	fixed	fix	VERB
ejpam-3096	282	3	point	point	NOUN
ejpam-3096	282	4	theorem	theorem	VERB
ejpam-3096	282	5	in	in	ADP
ejpam-3096	282	6	compact	compact	ADJ
ejpam-3096	282	7	d∗-metric	d∗-metric	ADJ
ejpam-3096	282	8	spaces	space	NOUN
ejpam-3096	282	9	,	,	PUNCT
ejpam-3096	282	10	internationalmathematicalforum	internationalmathematicalforum	NOUN
ejpam-3096	282	11	,	,	PUNCT
ejpam-3096	282	12	6(13	6(13	NUM
ejpam-3096	282	13	)	)	PUNCT
ejpam-3096	282	14	,	,	PUNCT
ejpam-3096	282	15	605	605	NUM
ejpam-3096	282	16	-	-	SYM
ejpam-3096	282	17	612	612	NUM
ejpam-3096	282	18	,	,	PUNCT
ejpam-3096	282	19	2011	2011	NUM
ejpam-3096	282	20	.	.	PUNCT
ejpam-3096	283	1	[	[	X
ejpam-3096	283	2	17	17	NUM
ejpam-3096	283	3	]	]	PUNCT
ejpam-3096	283	4	j.	j.	PROPN
ejpam-3096	283	5	j.	j.	PROPN
ejpam-3096	283	6	nieto	nieto	PROPN
ejpam-3096	283	7	,	,	PUNCT
ejpam-3096	283	8	r.	r.	PROPN
ejpam-3096	283	9	r.	r.	PROPN
ejpam-3096	283	10	lopez	lopez	PROPN
ejpam-3096	283	11	,	,	PUNCT
ejpam-3096	283	12	contractive	contractive	ADJ
ejpam-3096	283	13	mapping	mapping	NOUN
ejpam-3096	283	14	theorems	theorem	NOUN
ejpam-3096	283	15	in	in	ADP
ejpam-3096	283	16	partially	partially	ADV
ejpam-3096	283	17	ordered	order	VERB
ejpam-3096	283	18	sets	set	NOUN
ejpam-3096	283	19	and	and	CCONJ
ejpam-3096	283	20	applications	application	NOUN
ejpam-3096	283	21	to	to	ADP
ejpam-3096	283	22	ordinary	ordinary	ADJ
ejpam-3096	283	23	differential	differential	ADJ
ejpam-3096	283	24	equations	equation	NOUN
ejpam-3096	283	25	,	,	PUNCT
ejpam-3096	283	26	order	order	NOUN
ejpam-3096	283	27	,	,	PUNCT
ejpam-3096	283	28	(	(	PUNCT
ejpam-3096	283	29	22	22	NUM
ejpam-3096	283	30	)	)	PUNCT
ejpam-3096	283	31	,	,	PUNCT
ejpam-3096	283	32	223	223	NUM
ejpam-3096	283	33	-	-	SYM
ejpam-3096	283	34	239	239	NUM
ejpam-3096	283	35	,	,	PUNCT
ejpam-3096	283	36	2005	2005	NUM
ejpam-3096	283	37	.	.	PUNCT
ejpam-3096	284	1	[	[	X
ejpam-3096	284	2	18	18	NUM
ejpam-3096	284	3	]	]	PUNCT
ejpam-3096	284	4	j.	j.	PROPN
ejpam-3096	284	5	j.	j.	PROPN
ejpam-3096	284	6	nieto	nieto	PROPN
ejpam-3096	284	7	,	,	PUNCT
ejpam-3096	284	8	r.	r.	PROPN
ejpam-3096	284	9	r.	r.	PROPN
ejpam-3096	284	10	lopez	lopez	PROPN
ejpam-3096	284	11	.	.	PUNCT
ejpam-3096	285	1	existence	existence	NOUN
ejpam-3096	285	2	and	and	CCONJ
ejpam-3096	285	3	uniqueness	uniqueness	NOUN
ejpam-3096	285	4	of	of	ADP
ejpam-3096	285	5	fixed	fix	VERB
ejpam-3096	285	6	point	point	NOUN
ejpam-3096	285	7	in	in	ADP
ejpam-3096	285	8	partially	partially	ADV
ejpam-3096	285	9	ordered	order	VERB
ejpam-3096	285	10	sets	set	NOUN
ejpam-3096	285	11	and	and	CCONJ
ejpam-3096	285	12	applications	application	NOUN
ejpam-3096	285	13	to	to	ADP
ejpam-3096	285	14	ordinary	ordinary	ADJ
ejpam-3096	285	15	differential	differential	ADJ
ejpam-3096	285	16	equations	equation	NOUN
ejpam-3096	285	17	,	,	PUNCT
ejpam-3096	285	18	actamath.sin.eng.ser	actamath.sin.eng.ser	PROPN
ejpam-3096	285	19	,	,	PUNCT
ejpam-3096	285	20	(	(	PUNCT
ejpam-3096	285	21	23	23	NUM
ejpam-3096	285	22	)	)	PUNCT
ejpam-3096	285	23	,	,	PUNCT
ejpam-3096	285	24	2205	2205	NUM
ejpam-3096	285	25	-	-	SYM
ejpam-3096	285	26	2212	2212	NUM
ejpam-3096	285	27	,	,	PUNCT
ejpam-3096	285	28	2007	2007	NUM
ejpam-3096	285	29	.	.	PUNCT
ejpam-3096	286	1	[	[	X
ejpam-3096	286	2	19	19	NUM
ejpam-3096	286	3	]	]	X
ejpam-3096	286	4	h.	h.	PROPN
ejpam-3096	286	5	k.	k.	PROPN
ejpam-3096	286	6	nashine	nashine	PROPN
ejpam-3096	286	7	,	,	PUNCT
ejpam-3096	286	8	z.	z.	PROPN
ejpam-3096	286	9	kadelburg	kadelburg	PROPN
ejpam-3096	286	10	,	,	PUNCT
ejpam-3096	286	11	r.	r.	PROPN
ejpam-3096	286	12	p.	p.	PROPN
ejpam-3096	286	13	pathak	pathak	PROPN
ejpam-3096	286	14	,	,	PUNCT
ejpam-3096	286	15	s.	s.	PROPN
ejpam-3096	286	16	radenović.	radenović.	PROPN
ejpam-3096	286	17	coincidence	coincidence	NOUN
ejpam-3096	286	18	and	and	CCONJ
ejpam-3096	286	19	fixed	fix	VERB
ejpam-3096	286	20	point	point	NOUN
ejpam-3096	286	21	results	result	NOUN
ejpam-3096	286	22	in	in	ADP
ejpam-3096	286	23	ordered	order	VERB
ejpam-3096	286	24	g	g	NOUN
ejpam-3096	286	25	-	-	PUNCT
ejpam-3096	286	26	cone	cone	NOUN
ejpam-3096	286	27	metric	metric	ADJ
ejpam-3096	286	28	spaces	space	NOUN
ejpam-3096	286	29	,	,	PUNCT
ejpam-3096	286	30	math.comput.modelling	math.comput.modelle	VERB
ejpam-3096	286	31	,	,	PUNCT
ejpam-3096	286	32	(	(	PUNCT
ejpam-3096	286	33	57	57	NUM
ejpam-3096	286	34	)	)	PUNCT
ejpam-3096	286	35	,	,	PUNCT
ejpam-3096	286	36	701709	701709	NUM
ejpam-3096	286	37	,	,	PUNCT
ejpam-3096	286	38	2013	2013	NUM
ejpam-3096	286	39	.	.	PUNCT
ejpam-3096	287	1	[	[	X
ejpam-3096	287	2	20	20	NUM
ejpam-3096	287	3	]	]	PUNCT
ejpam-3096	287	4	h.	h.	PROPN
ejpam-3096	287	5	k.	k.	PROPN
ejpam-3096	287	6	nashine	nashine	PROPN
ejpam-3096	287	7	,	,	PUNCT
ejpam-3096	287	8	b.	b.	PROPN
ejpam-3096	287	9	samet	samet	PROPN
ejpam-3096	287	10	.	.	PUNCT
ejpam-3096	288	1	fixed	fix	VERB
ejpam-3096	288	2	point	point	NOUN
ejpam-3096	288	3	results	result	NOUN
ejpam-3096	288	4	for	for	ADP
ejpam-3096	288	5	mappings	mapping	NOUN
ejpam-3096	288	6	satisfying	satisfy	VERB
ejpam-3096	288	7	(	(	PUNCT
ejpam-3096	288	8	ψ	ψ	NOUN
ejpam-3096	288	9	,	,	PUNCT
ejpam-3096	288	10	φ)-weakly	φ)-weakly	VERB
ejpam-3096	288	11	contractive	contractive	ADJ
ejpam-3096	288	12	condition	condition	NOUN
ejpam-3096	288	13	in	in	ADP
ejpam-3096	288	14	partially	partially	ADV
ejpam-3096	288	15	ordered	order	VERB
ejpam-3096	288	16	metric	metric	ADJ
ejpam-3096	288	17	spaces	space	NOUN
ejpam-3096	288	18	,	,	PUNCT
ejpam-3096	288	19	nonlinearanal	nonlinearanal	ADJ
ejpam-3096	288	20	,	,	PUNCT
ejpam-3096	288	21	(	(	PUNCT
ejpam-3096	288	22	74	74	NUM
ejpam-3096	288	23	)	)	PUNCT
ejpam-3096	288	24	,	,	PUNCT
ejpam-3096	288	25	22012209	22012209	NUM
ejpam-3096	288	26	,	,	PUNCT
ejpam-3096	288	27	2011	2011	NUM
ejpam-3096	288	28	.	.	PUNCT
ejpam-3096	289	1	[	[	X
ejpam-3096	289	2	21	21	NUM
ejpam-3096	289	3	]	]	X
ejpam-3096	289	4	d.	d.	PROPN
ejpam-3096	289	5	o’regan	o’regan	PROPN
ejpam-3096	289	6	,	,	PUNCT
ejpam-3096	289	7	r.	r.	PROPN
ejpam-3096	289	8	saadati	saadati	PROPN
ejpam-3096	289	9	.	.	PUNCT
ejpam-3096	290	1	nonlinear	nonlinear	ADJ
ejpam-3096	290	2	contraction	contraction	NOUN
ejpam-3096	290	3	theorems	theorem	VERB
ejpam-3096	290	4	in	in	ADP
ejpam-3096	290	5	probabilistic	probabilistic	ADJ
ejpam-3096	290	6	spaces	space	NOUN
ejpam-3096	290	7	,	,	PUNCT
ejpam-3096	290	8	appl.math.comput	appl.math.comput	PROPN
ejpam-3096	290	9	,	,	PUNCT
ejpam-3096	290	10	(	(	PUNCT
ejpam-3096	290	11	195	195	NUM
ejpam-3096	290	12	)	)	PUNCT
ejpam-3096	290	13	,	,	PUNCT
ejpam-3096	290	14	86	86	NUM
ejpam-3096	290	15	-	-	SYM
ejpam-3096	290	16	93	93	NUM
ejpam-3096	290	17	,	,	PUNCT
ejpam-3096	290	18	2008	2008	NUM
ejpam-3096	290	19	.	.	PUNCT
ejpam-3096	291	1	[	[	X
ejpam-3096	291	2	22	22	NUM
ejpam-3096	291	3	]	]	PUNCT
ejpam-3096	291	4	a.	a.	NOUN
ejpam-3096	291	5	petru̧sel	petru̧sel	PROPN
ejpam-3096	291	6	,	,	PUNCT
ejpam-3096	291	7	i.	i.	PROPN
ejpam-3096	291	8	a.	a.	PROPN
ejpam-3096	291	9	rus	rus	PROPN
ejpam-3096	291	10	.	.	PUNCT
ejpam-3096	291	11	fixed	fix	VERB
ejpam-3096	291	12	point	point	NOUN
ejpam-3096	291	13	theorems	theorem	NOUN
ejpam-3096	291	14	in	in	ADP
ejpam-3096	291	15	ordered	order	VERB
ejpam-3096	291	16	l	l	NOUN
ejpam-3096	291	17	-	-	NOUN
ejpam-3096	291	18	spaces	space	NOUN
ejpam-3096	291	19	,	,	PUNCT
ejpam-3096	291	20	proc.amer.math.soc	proc.amer.math.soc	PROPN
ejpam-3096	291	21	,	,	PUNCT
ejpam-3096	291	22	(	(	PUNCT
ejpam-3096	291	23	134	134	NUM
ejpam-3096	291	24	)	)	PUNCT
ejpam-3096	291	25	,	,	PUNCT
ejpam-3096	291	26	411	411	NUM
ejpam-3096	291	27	-	-	SYM
ejpam-3096	291	28	418	418	NUM
ejpam-3096	291	29	,	,	PUNCT
ejpam-3096	291	30	2006	2006	NUM
ejpam-3096	291	31	.	.	PUNCT
ejpam-3096	292	1	[	[	X
ejpam-3096	292	2	23	23	NUM
ejpam-3096	292	3	]	]	PUNCT
ejpam-3096	292	4	a.	a.	NOUN
ejpam-3096	292	5	c.	c.	PROPN
ejpam-3096	292	6	m.	m.	PROPN
ejpam-3096	292	7	ran	run	VERB
ejpam-3096	292	8	,	,	PUNCT
ejpam-3096	292	9	m.	m.	PROPN
ejpam-3096	292	10	c.	c.	PROPN
ejpam-3096	292	11	b.	b.	PROPN
ejpam-3096	292	12	reurings	reurings	PROPN
ejpam-3096	292	13	.	.	PUNCT
ejpam-3096	293	1	a	a	DET
ejpam-3096	293	2	fixed	fix	VERB
ejpam-3096	293	3	point	point	NOUN
ejpam-3096	293	4	theorem	theorem	VERB
ejpam-3096	293	5	in	in	ADP
ejpam-3096	293	6	partially	partially	ADV
ejpam-3096	293	7	ordered	order	VERB
ejpam-3096	293	8	sets	set	NOUN
ejpam-3096	293	9	and	and	CCONJ
ejpam-3096	293	10	some	some	DET
ejpam-3096	293	11	applications	application	NOUN
ejpam-3096	293	12	to	to	PART
ejpam-3096	293	13	matrix	matrix	VERB
ejpam-3096	293	14	equations	equation	NOUN
ejpam-3096	293	15	,	,	PUNCT
ejpam-3096	293	16	proc.amer.math.soc	proc.amer.math.soc	PROPN
ejpam-3096	293	17	,	,	PUNCT
ejpam-3096	293	18	(	(	PUNCT
ejpam-3096	293	19	132	132	NUM
ejpam-3096	293	20	)	)	PUNCT
ejpam-3096	293	21	,	,	PUNCT
ejpam-3096	293	22	1435	1435	NUM
ejpam-3096	293	23	-	-	SYM
ejpam-3096	293	24	1443	1443	NUM
ejpam-3096	293	25	,	,	PUNCT
ejpam-3096	293	26	2004	2004	NUM
ejpam-3096	293	27	.	.	PUNCT
ejpam-3096	294	1	[	[	X
ejpam-3096	294	2	24	24	NUM
ejpam-3096	294	3	]	]	PUNCT
ejpam-3096	294	4	s.	s.	PROPN
ejpam-3096	294	5	shaban	shaban	PROPN
ejpam-3096	294	6	,	,	PUNCT
ejpam-3096	294	7	s.	s.	PROPN
ejpam-3096	294	8	nabi	nabi	PROPN
ejpam-3096	294	9	,	,	PUNCT
ejpam-3096	294	10	z.	z.	PROPN
ejpam-3096	294	11	haiyun	haiyun	PROPN
ejpam-3096	294	12	.	.	PUNCT
ejpam-3096	295	1	a	a	DET
ejpam-3096	295	2	common	common	ADJ
ejpam-3096	295	3	fixed	fix	VERB
ejpam-3096	295	4	point	point	NOUN
ejpam-3096	295	5	theorem	theorem	VERB
ejpam-3096	295	6	in	in	ADP
ejpam-3096	295	7	d∗-metric	d∗-metric	ADJ
ejpam-3096	295	8	spaces	space	NOUN
ejpam-3096	295	9	.	.	PUNCT
ejpam-3096	296	1	hindawi	hindawi	ADJ
ejpam-3096	296	2	publishing	publishing	NOUN
ejpam-3096	296	3	corporation	corporation	NOUN
ejpam-3096	296	4	.	.	PUNCT
ejpam-3096	297	1	fixedpointtheoryandapplications	fixedpointtheoryandapplication	NOUN
ejpam-3096	297	2	,	,	PUNCT
ejpam-3096	297	3	article	article	NOUN
ejpam-3096	297	4	i	i	PROPN
ejpam-3096	297	5	d	d	PROPN
ejpam-3096	297	6	27906	27906	NUM
ejpam-3096	297	7	,	,	PUNCT
ejpam-3096	297	8	p.13	p.13	NOUN
ejpam-3096	297	9	,	,	PUNCT
ejpam-3096	297	10	doi:10.1155	doi:10.1155	NOUN
ejpam-3096	297	11	,	,	PUNCT
ejpam-3096	297	12	2007	2007	NUM
ejpam-3096	297	13	.	.	PUNCT
ejpam-3096	298	1	references	reference	NOUN
ejpam-3096	298	2	1034	1034	NUM
ejpam-3096	298	3	[	[	X
ejpam-3096	298	4	25	25	NUM
ejpam-3096	298	5	]	]	PUNCT
ejpam-3096	298	6	t.	t.	NOUN
ejpam-3096	298	7	veerapandi	veerapandi	PROPN
ejpam-3096	298	8	and	and	CCONJ
ejpam-3096	298	9	aji	aji	PROPN
ejpam-3096	298	10	m.	m.	PROPN
ejpam-3096	298	11	pillai	pillai	PROPN
ejpam-3096	298	12	.	.	PUNCT
ejpam-3096	299	1	some	some	DET
ejpam-3096	299	2	common	common	ADJ
ejpam-3096	299	3	fixed	fix	VERB
ejpam-3096	299	4	point	point	NOUN
ejpam-3096	299	5	theorems	theorem	NOUN
ejpam-3096	299	6	in	in	ADP
ejpam-3096	299	7	d∗metric	d∗metric	ADJ
ejpam-3096	299	8	spaces	space	NOUN
ejpam-3096	299	9	,	,	PUNCT
ejpam-3096	299	10	africanjournalofmathematicsandcomputerscienceresearch	africanjournalofmathematicsandcomputerscienceresearch	ADV
ejpam-3096	299	11	,	,	PUNCT
ejpam-3096	299	12	4(12	4(12	NUM
ejpam-3096	299	13	)	)	PUNCT
ejpam-3096	299	14	,	,	PUNCT
ejpam-3096	299	15	357367	357367	NUM
ejpam-3096	299	16	,	,	PUNCT
ejpam-3096	299	17	2011	2011	NUM
ejpam-3096	299	18	.	.	PUNCT
ejpam-3096	300	1	[	[	X
ejpam-3096	300	2	26	26	NUM
ejpam-3096	300	3	]	]	PUNCT
ejpam-3096	300	4	t.	t.	NOUN
ejpam-3096	300	5	veerapandi	veerapandi	PROPN
ejpam-3096	300	6	and	and	CCONJ
ejpam-3096	300	7	aji	aji	PROPN
ejpam-3096	300	8	m.	m.	PROPN
ejpam-3096	300	9	pillai	pillai	PROPN
ejpam-3096	300	10	.	.	PUNCT
ejpam-3096	301	1	a	a	DET
ejpam-3096	301	2	common	common	ADJ
ejpam-3096	301	3	fixed	fix	VERB
ejpam-3096	301	4	point	point	NOUN
ejpam-3096	301	5	theorems	theorem	NOUN
ejpam-3096	301	6	in	in	ADP
ejpam-3096	301	7	d∗-metric	d∗-metric	ADJ
ejpam-3096	301	8	spaces	space	NOUN
ejpam-3096	301	9	,	,	PUNCT
ejpam-3096	301	10	africanjournalofmathematicsandcomputerscienceresearch	africanjournalofmathematicsandcomputerscienceresearch	ADJ
ejpam-3096	301	11	,	,	PUNCT
ejpam-3096	301	12	4(8	4(8	NUM
ejpam-3096	301	13	)	)	PUNCT
ejpam-3096	301	14	,	,	PUNCT
ejpam-3096	301	15	273280	273280	NUM
ejpam-3096	301	16	,	,	PUNCT
ejpam-3096	301	17	2011	2011	NUM
ejpam-3096	301	18	.	.	PUNCT
ejpam-3096	302	1	[	[	X
ejpam-3096	302	2	27	27	NUM
ejpam-3096	302	3	]	]	PUNCT
ejpam-3096	302	4	j.	j.	PROPN
ejpam-3096	302	5	s.	s.	PROPN
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ejpam-3096	302	7	.	.	PUNCT
ejpam-3096	303	1	newton	newton	PROPN
ejpam-3096	303	2	method	method	PROPN
ejpam-3096	303	3	for	for	ADP
ejpam-3096	303	4	convex	convex	NOUN
ejpam-3096	303	5	operators	operator	NOUN
ejpam-3096	303	6	in	in	ADP
ejpam-3096	303	7	partially	partially	ADV
ejpam-3096	303	8	ordered	order	VERB
ejpam-3096	303	9	spaces	space	NOUN
ejpam-3096	303	10	,	,	PUNCT
ejpam-3096	303	11	siamj.numer.anal	siamj.numer.anal	PROPN
ejpam-3096	303	12	,	,	PUNCT
ejpam-3096	303	13	(	(	PUNCT
ejpam-3096	303	14	4	4	NUM
ejpam-3096	303	15	)	)	PUNCT
ejpam-3096	303	16	,	,	PUNCT
ejpam-3096	303	17	406	406	NUM
ejpam-3096	303	18	-	-	SYM
ejpam-3096	303	19	432	432	NUM
ejpam-3096	303	20	,	,	PUNCT
ejpam-3096	303	21	1967	1967	NUM
ejpam-3096	303	22	.	.	PUNCT