id	sid	tid	token	lemma	pos
ejpam-6583	1	1	european	european	PROPN
ejpam-6583	1	2	journal	journal	PROPN
ejpam-6583	1	3	of	of	ADP
ejpam-6583	1	4	pure	pure	ADJ
ejpam-6583	1	5	and	and	CCONJ
ejpam-6583	1	6	applied	applied	ADJ
ejpam-6583	1	7	mathematics	mathematic	NOUN
ejpam-6583	1	8	2025	2025	NUM
ejpam-6583	1	9	,	,	PUNCT
ejpam-6583	1	10	vol	vol	NOUN
ejpam-6583	1	11	.	.	PROPN
ejpam-6583	1	12	18	18	NUM
ejpam-6583	1	13	,	,	PUNCT
ejpam-6583	1	14	issue	issue	NOUN
ejpam-6583	1	15	3	3	NUM
ejpam-6583	1	16	,	,	PUNCT
ejpam-6583	1	17	article	article	NOUN
ejpam-6583	1	18	number	number	NOUN
ejpam-6583	1	19	6583	6583	NUM
ejpam-6583	1	20	issn	issn	VERB
ejpam-6583	1	21	1307	1307	NUM
ejpam-6583	1	22	-	-	SYM
ejpam-6583	1	23	5543	5543	NUM
ejpam-6583	1	24	–	–	PUNCT
ejpam-6583	1	25	ejpam.com	ejpam.com	X
ejpam-6583	1	26	published	publish	VERB
ejpam-6583	1	27	by	by	ADP
ejpam-6583	1	28	new	new	PROPN
ejpam-6583	1	29	york	york	PROPN
ejpam-6583	1	30	business	business	PROPN
ejpam-6583	1	31	global	global	PROPN
ejpam-6583	1	32	a	a	DET
ejpam-6583	1	33	natural	natural	ADJ
ejpam-6583	1	34	extension	extension	NOUN
ejpam-6583	1	35	of	of	ADP
ejpam-6583	1	36	the	the	DET
ejpam-6583	1	37	banach	banach	ADV
ejpam-6583	1	38	fixed	fix	VERB
ejpam-6583	1	39	-	-	PUNCT
ejpam-6583	1	40	point	point	NOUN
ejpam-6583	1	41	theorem	theorem	NOUN
ejpam-6583	1	42	in	in	ADP
ejpam-6583	1	43	a	a	DET
ejpam-6583	1	44	b	b	NOUN
ejpam-6583	1	45	-	-	PUNCT
ejpam-6583	1	46	metric	metric	ADJ
ejpam-6583	1	47	space	space	NOUN
ejpam-6583	1	48	with	with	ADP
ejpam-6583	1	49	an	an	DET
ejpam-6583	1	50	orthogonal	orthogonal	ADJ
ejpam-6583	1	51	direct	direct	ADJ
ejpam-6583	1	52	sum	sum	NOUN
ejpam-6583	1	53	structure	structure	NOUN
ejpam-6583	1	54	ghadah	ghadah	PROPN
ejpam-6583	1	55	albeladi1,∗	albeladi1,∗	NOUN
ejpam-6583	1	56	,	,	PUNCT
ejpam-6583	1	57	saleh	saleh	NOUN
ejpam-6583	1	58	omran2	omran2	NOUN
ejpam-6583	1	59	1	1	NUM
ejpam-6583	1	60	department	department	NOUN
ejpam-6583	1	61	of	of	ADP
ejpam-6583	1	62	mathematics	mathematic	NOUN
ejpam-6583	1	63	,	,	PUNCT
ejpam-6583	1	64	college	college	NOUN
ejpam-6583	1	65	of	of	ADP
ejpam-6583	1	66	sciences	sciences	PROPN
ejpam-6583	1	67	&	&	CCONJ
ejpam-6583	1	68	arts	art	NOUN
ejpam-6583	1	69	,	,	PUNCT
ejpam-6583	1	70	king	king	PROPN
ejpam-6583	1	71	abdulaziz	abdulaziz	PROPN
ejpam-6583	1	72	university	university	PROPN
ejpam-6583	1	73	,	,	PUNCT
ejpam-6583	1	74	rabigh	rabigh	NOUN
ejpam-6583	1	75	21911	21911	NUM
ejpam-6583	1	76	,	,	PUNCT
ejpam-6583	1	77	saudi	saudi	PROPN
ejpam-6583	1	78	arabia	arabia	PROPN
ejpam-6583	1	79	2	2	NUM
ejpam-6583	1	80	department	department	NOUN
ejpam-6583	1	81	of	of	ADP
ejpam-6583	1	82	mathematics	mathematic	NOUN
ejpam-6583	1	83	,	,	PUNCT
ejpam-6583	1	84	faculty	faculty	NOUN
ejpam-6583	1	85	of	of	ADP
ejpam-6583	1	86	science	science	NOUN
ejpam-6583	1	87	,	,	PUNCT
ejpam-6583	1	88	south	south	PROPN
ejpam-6583	1	89	valley	valley	PROPN
ejpam-6583	1	90	university	university	PROPN
ejpam-6583	1	91	,	,	PUNCT
ejpam-6583	1	92	qena	qena	NOUN
ejpam-6583	1	93	83523	83523	NUM
ejpam-6583	1	94	,	,	PUNCT
ejpam-6583	1	95	egypt	egypt	PROPN
ejpam-6583	1	96	abstract	abstract	PROPN
ejpam-6583	1	97	.	.	PUNCT
ejpam-6583	2	1	this	this	DET
ejpam-6583	2	2	study	study	NOUN
ejpam-6583	2	3	aims	aim	VERB
ejpam-6583	2	4	to	to	PART
ejpam-6583	2	5	develop	develop	VERB
ejpam-6583	2	6	new	new	ADJ
ejpam-6583	2	7	versions	version	NOUN
ejpam-6583	2	8	of	of	ADP
ejpam-6583	2	9	the	the	DET
ejpam-6583	2	10	banach	banach	ADV
ejpam-6583	2	11	fixed	fix	VERB
ejpam-6583	2	12	-	-	PUNCT
ejpam-6583	2	13	point	point	NOUN
ejpam-6583	2	14	theorem	theorem	NOUN
ejpam-6583	2	15	in	in	ADP
ejpam-6583	2	16	generalized	generalized	ADJ
ejpam-6583	2	17	metric	metric	ADJ
ejpam-6583	2	18	spaces	space	NOUN
ejpam-6583	2	19	endowed	endow	VERB
ejpam-6583	2	20	with	with	ADP
ejpam-6583	2	21	a	a	DET
ejpam-6583	2	22	direct	direct	ADJ
ejpam-6583	2	23	sum	sum	NOUN
ejpam-6583	2	24	structure	structure	NOUN
ejpam-6583	2	25	.	.	PUNCT
ejpam-6583	3	1	specifically	specifically	ADV
ejpam-6583	3	2	,	,	PUNCT
ejpam-6583	3	3	we	we	PRON
ejpam-6583	3	4	assume	assume	VERB
ejpam-6583	3	5	a	a	DET
ejpam-6583	3	6	diagonal	diagonal	ADJ
ejpam-6583	3	7	matrix	matrix	NOUN
ejpam-6583	3	8	a	a	PRON
ejpam-6583	3	9	in	in	ADP
ejpam-6583	3	10	rd×d	rd×d	PROPN
ejpam-6583	3	11	and	and	CCONJ
ejpam-6583	3	12	establish	establish	VERB
ejpam-6583	3	13	more	more	ADV
ejpam-6583	3	14	appropriate	appropriate	ADJ
ejpam-6583	3	15	contraction	contraction	NOUN
ejpam-6583	3	16	conditions	condition	NOUN
ejpam-6583	3	17	to	to	PART
ejpam-6583	3	18	improve	improve	VERB
ejpam-6583	3	19	the	the	DET
ejpam-6583	3	20	applicability	applicability	NOUN
ejpam-6583	3	21	of	of	ADP
ejpam-6583	3	22	fixed	fix	VERB
ejpam-6583	3	23	-	-	PUNCT
ejpam-6583	3	24	point	point	NOUN
ejpam-6583	3	25	results	result	NOUN
ejpam-6583	3	26	within	within	ADP
ejpam-6583	3	27	this	this	DET
ejpam-6583	3	28	framework	framework	NOUN
ejpam-6583	3	29	.	.	PUNCT
ejpam-6583	4	1	since	since	SCONJ
ejpam-6583	4	2	the	the	DET
ejpam-6583	4	3	condition	condition	NOUN
ejpam-6583	4	4	that	that	SCONJ
ejpam-6583	4	5	the	the	DET
ejpam-6583	4	6	matrix	matrix	NOUN
ejpam-6583	4	7	a	a	PRON
ejpam-6583	4	8	must	must	AUX
ejpam-6583	4	9	converge	converge	VERB
ejpam-6583	4	10	to	to	ADP
ejpam-6583	4	11	zero	zero	NUM
ejpam-6583	4	12	is	be	AUX
ejpam-6583	4	13	unnecessary	unnecessary	ADJ
ejpam-6583	4	14	,	,	PUNCT
ejpam-6583	4	15	our	our	PRON
ejpam-6583	4	16	approach	approach	NOUN
ejpam-6583	4	17	yields	yield	VERB
ejpam-6583	4	18	stronger	strong	ADJ
ejpam-6583	4	19	results	result	NOUN
ejpam-6583	4	20	than	than	ADP
ejpam-6583	4	21	the	the	DET
ejpam-6583	4	22	perov	perov	PROPN
ejpam-6583	4	23	one	one	NUM
ejpam-6583	4	24	.	.	PUNCT
ejpam-6583	5	1	as	as	ADP
ejpam-6583	5	2	an	an	DET
ejpam-6583	5	3	application	application	NOUN
ejpam-6583	5	4	of	of	ADP
ejpam-6583	5	5	our	our	PRON
ejpam-6583	5	6	findings	finding	NOUN
ejpam-6583	5	7	,	,	PUNCT
ejpam-6583	5	8	we	we	PRON
ejpam-6583	5	9	examine	examine	VERB
ejpam-6583	5	10	the	the	DET
ejpam-6583	5	11	existence	existence	NOUN
ejpam-6583	5	12	and	and	CCONJ
ejpam-6583	5	13	uniqueness	uniqueness	NOUN
ejpam-6583	5	14	of	of	ADP
ejpam-6583	5	15	solutions	solution	NOUN
ejpam-6583	5	16	for	for	ADP
ejpam-6583	5	17	a	a	DET
ejpam-6583	5	18	system	system	NOUN
ejpam-6583	5	19	of	of	ADP
ejpam-6583	5	20	matrix	matrix	NOUN
ejpam-6583	5	21	equations	equation	NOUN
ejpam-6583	5	22	.	.	PUNCT
ejpam-6583	6	1	this	this	DET
ejpam-6583	6	2	version	version	NOUN
ejpam-6583	6	3	is	be	AUX
ejpam-6583	6	4	more	more	ADV
ejpam-6583	6	5	powerful	powerful	ADJ
ejpam-6583	6	6	than	than	ADP
ejpam-6583	6	7	the	the	DET
ejpam-6583	6	8	perov	perov	PROPN
ejpam-6583	6	9	version	version	NOUN
ejpam-6583	6	10	.	.	PUNCT
ejpam-6583	7	1	we	we	PRON
ejpam-6583	7	2	introduced	introduce	VERB
ejpam-6583	7	3	some	some	DET
ejpam-6583	7	4	examples	example	NOUN
ejpam-6583	7	5	and	and	CCONJ
ejpam-6583	7	6	applications	application	NOUN
ejpam-6583	7	7	to	to	PART
ejpam-6583	7	8	illustrate	illustrate	VERB
ejpam-6583	7	9	our	our	PRON
ejpam-6583	7	10	result	result	NOUN
ejpam-6583	7	11	.	.	PUNCT
ejpam-6583	8	1	2020	2020	NUM
ejpam-6583	8	2	mathematics	mathematic	NOUN
ejpam-6583	8	3	subject	subject	NOUN
ejpam-6583	8	4	classifications	classification	NOUN
ejpam-6583	8	5	:	:	PUNCT
ejpam-6583	8	6	47h10	47h10	NUM
ejpam-6583	8	7	,	,	PUNCT
ejpam-6583	8	8	54h25	54h25	NUM
ejpam-6583	8	9	,	,	PUNCT
ejpam-6583	8	10	46a19	46a19	NUM
ejpam-6583	8	11	,	,	PUNCT
ejpam-6583	8	12	15a24	15a24	NUM
ejpam-6583	8	13	key	key	ADJ
ejpam-6583	8	14	words	word	NOUN
ejpam-6583	8	15	and	and	CCONJ
ejpam-6583	8	16	phrases	phrase	NOUN
ejpam-6583	8	17	:	:	PUNCT
ejpam-6583	8	18	fixed	fixed	ADJ
ejpam-6583	8	19	point	point	NOUN
ejpam-6583	8	20	,	,	PUNCT
ejpam-6583	8	21	banach	banach	NOUN
ejpam-6583	8	22	contraction	contraction	NOUN
ejpam-6583	8	23	principle	principle	NOUN
ejpam-6583	8	24	,	,	PUNCT
ejpam-6583	8	25	generalized	generalized	ADJ
ejpam-6583	8	26	b	b	X
ejpam-6583	8	27	-	-	ADJ
ejpam-6583	8	28	metric	metric	ADJ
ejpam-6583	8	29	space	space	NOUN
ejpam-6583	8	30	,	,	PUNCT
ejpam-6583	8	31	direct	direct	ADJ
ejpam-6583	8	32	sum	sum	NOUN
ejpam-6583	8	33	1	1	NUM
ejpam-6583	8	34	.	.	PUNCT
ejpam-6583	8	35	introduction	introduction	NOUN
ejpam-6583	8	36	a	a	DET
ejpam-6583	8	37	fixed	fix	VERB
ejpam-6583	8	38	-	-	PUNCT
ejpam-6583	8	39	point	point	NOUN
ejpam-6583	8	40	of	of	ADP
ejpam-6583	8	41	f	f	PROPN
ejpam-6583	8	42	on	on	ADP
ejpam-6583	8	43	x	x	X
ejpam-6583	8	44	is	be	AUX
ejpam-6583	8	45	an	an	DET
ejpam-6583	8	46	element	element	NOUN
ejpam-6583	8	47	q	q	NOUN
ejpam-6583	8	48	such	such	ADJ
ejpam-6583	8	49	that	that	SCONJ
ejpam-6583	8	50	f	f	PROPN
ejpam-6583	8	51	(	(	PUNCT
ejpam-6583	8	52	q	q	X
ejpam-6583	8	53	)	)	PUNCT
ejpam-6583	8	54	=	=	VERB
ejpam-6583	8	55	q.	q.	NOUN
ejpam-6583	8	56	under	under	ADP
ejpam-6583	8	57	certain	certain	ADJ
ejpam-6583	8	58	circumstances	circumstance	NOUN
ejpam-6583	8	59	on	on	ADP
ejpam-6583	8	60	the	the	DET
ejpam-6583	8	61	operator	operator	NOUN
ejpam-6583	8	62	f	f	PROPN
ejpam-6583	8	63	and	and	CCONJ
ejpam-6583	8	64	the	the	DET
ejpam-6583	8	65	space	space	NOUN
ejpam-6583	8	66	x	x	X
ejpam-6583	8	67	,	,	PUNCT
ejpam-6583	8	68	the	the	DET
ejpam-6583	8	69	operator	operator	NOUN
ejpam-6583	8	70	f	f	PROPN
ejpam-6583	8	71	admits	admit	VERB
ejpam-6583	8	72	one	one	NUM
ejpam-6583	8	73	or	or	CCONJ
ejpam-6583	8	74	more	more	ADJ
ejpam-6583	8	75	fixed	fix	VERB
ejpam-6583	8	76	points	point	NOUN
ejpam-6583	8	77	,	,	PUNCT
ejpam-6583	8	78	according	accord	VERB
ejpam-6583	8	79	to	to	ADP
ejpam-6583	8	80	the	the	DET
ejpam-6583	8	81	fixed	fix	VERB
ejpam-6583	8	82	-	-	PUNCT
ejpam-6583	8	83	point	point	NOUN
ejpam-6583	8	84	theorem	theorem	VERB
ejpam-6583	8	85	.	.	PUNCT
ejpam-6583	9	1	for	for	ADP
ejpam-6583	9	2	various	various	ADJ
ejpam-6583	9	3	applications	application	NOUN
ejpam-6583	9	4	of	of	ADP
ejpam-6583	9	5	the	the	DET
ejpam-6583	9	6	fixedpoint	fixedpoint	NOUN
ejpam-6583	9	7	theorem	theorem	NOUN
ejpam-6583	9	8	,	,	PUNCT
ejpam-6583	9	9	there	there	PRON
ejpam-6583	9	10	are	be	VERB
ejpam-6583	9	11	numerous	numerous	ADJ
ejpam-6583	9	12	outcomes	outcome	NOUN
ejpam-6583	9	13	brouwer	brouwer	X
ejpam-6583	9	14	’s	’s	PART
ejpam-6583	9	15	fixed	fix	VERB
ejpam-6583	9	16	-	-	PUNCT
ejpam-6583	9	17	point	point	NOUN
ejpam-6583	9	18	theorem	theorem	VERB
ejpam-6583	9	19	,	,	PUNCT
ejpam-6583	9	20	schauder	schauder	NOUN
ejpam-6583	9	21	’s	’s	PART
ejpam-6583	9	22	fixed	fix	VERB
ejpam-6583	9	23	-	-	PUNCT
ejpam-6583	9	24	point	point	NOUN
ejpam-6583	9	25	theorem	theorem	VERB
ejpam-6583	9	26	,	,	PUNCT
ejpam-6583	9	27	and	and	CCONJ
ejpam-6583	9	28	the	the	DET
ejpam-6583	9	29	banach	banach	NOUN
ejpam-6583	9	30	contraction	contraction	NOUN
ejpam-6583	9	31	principle	principle	NOUN
ejpam-6583	9	32	are	be	AUX
ejpam-6583	9	33	the	the	DET
ejpam-6583	9	34	foundational	foundational	ADJ
ejpam-6583	9	35	ideas	idea	NOUN
ejpam-6583	9	36	of	of	ADP
ejpam-6583	9	37	fixed	fix	VERB
ejpam-6583	9	38	-	-	PUNCT
ejpam-6583	9	39	point	point	NOUN
ejpam-6583	9	40	theory	theory	NOUN
ejpam-6583	9	41	.	.	PUNCT
ejpam-6583	10	1	perov	perov	PROPN
ejpam-6583	10	2	generalized	generalize	VERB
ejpam-6583	10	3	the	the	DET
ejpam-6583	10	4	notion	notion	NOUN
ejpam-6583	10	5	of	of	ADP
ejpam-6583	10	6	metric	metric	ADJ
ejpam-6583	10	7	spaces	space	NOUN
ejpam-6583	10	8	in	in	ADP
ejpam-6583	10	9	[	[	X
ejpam-6583	10	10	1	1	NUM
ejpam-6583	10	11	]	]	PUNCT
ejpam-6583	10	12	by	by	ADP
ejpam-6583	10	13	replacing	replace	VERB
ejpam-6583	10	14	the	the	DET
ejpam-6583	10	15	set	set	NOUN
ejpam-6583	10	16	of	of	ADP
ejpam-6583	10	17	real	real	ADJ
ejpam-6583	10	18	numbers	number	NOUN
ejpam-6583	10	19	with	with	ADP
ejpam-6583	10	20	vector	vector	NOUN
ejpam-6583	10	21	-	-	PUNCT
ejpam-6583	10	22	valued	value	VERB
ejpam-6583	10	23	space	space	NOUN
ejpam-6583	10	24	rd	rd	PROPN
ejpam-6583	10	25	.	.	PUNCT
ejpam-6583	11	1	thus	thus	ADV
ejpam-6583	11	2	,	,	PUNCT
ejpam-6583	11	3	the	the	DET
ejpam-6583	11	4	classical	classical	ADJ
ejpam-6583	11	5	contraction	contraction	NOUN
ejpam-6583	11	6	operator	operator	NOUN
ejpam-6583	11	7	principle	principle	NOUN
ejpam-6583	11	8	was	be	AUX
ejpam-6583	11	9	extended	extend	VERB
ejpam-6583	11	10	to	to	PART
ejpam-6583	11	11	contraction	contraction	VERB
ejpam-6583	11	12	operators	operator	NOUN
ejpam-6583	11	13	in	in	ADP
ejpam-6583	11	14	a	a	DET
ejpam-6583	11	15	vector	vector	NOUN
ejpam-6583	11	16	-	-	PUNCT
ejpam-6583	11	17	valued	value	VERB
ejpam-6583	11	18	metric	metric	ADJ
ejpam-6583	11	19	space	space	NOUN
ejpam-6583	11	20	,	,	PUNCT
ejpam-6583	11	21	known	know	VERB
ejpam-6583	11	22	as	as	ADP
ejpam-6583	11	23	a	a	DET
ejpam-6583	11	24	generalized	generalized	ADJ
ejpam-6583	11	25	∗corresponding	∗corresponde	VERB
ejpam-6583	11	26	author	author	NOUN
ejpam-6583	11	27	.	.	PUNCT
ejpam-6583	12	1	doi	doi	NOUN
ejpam-6583	12	2	:	:	PUNCT
ejpam-6583	12	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6583	https://doi.org/10.29020/nybg.ejpam.v18i3.6583	PROPN
ejpam-6583	12	4	email	email	NOUN
ejpam-6583	12	5	addresses	address	NOUN
ejpam-6583	12	6	:	:	PUNCT
ejpam-6583	12	7	galbeladi@kau.edu.sa	galbeladi@kau.edu.sa	PROPN
ejpam-6583	12	8	(	(	PUNCT
ejpam-6583	12	9	g.	g.	PROPN
ejpam-6583	12	10	albeladi	albeladi	PROPN
ejpam-6583	12	11	)	)	PUNCT
ejpam-6583	12	12	,	,	PUNCT
ejpam-6583	12	13	salehomran@yahoo.com	salehomran@yahoo.com	PROPN
ejpam-6583	12	14	(	(	PUNCT
ejpam-6583	12	15	s.	s.	PROPN
ejpam-6583	12	16	omran	omran	PROPN
ejpam-6583	12	17	)	)	PUNCT
ejpam-6583	12	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6583	13	1	1	1	NUM
ejpam-6583	13	2	copyright	copyright	NOUN
ejpam-6583	13	3	:	:	PUNCT
ejpam-6583	13	4	©	©	PROPN
ejpam-6583	13	5	2025	2025	NUM
ejpam-6583	13	6	the	the	DET
ejpam-6583	13	7	author(s	author(s	NOUN
ejpam-6583	13	8	)	)	PUNCT
ejpam-6583	13	9	.	.	PUNCT
ejpam-6583	14	1	(	(	PUNCT
ejpam-6583	14	2	cc	cc	NOUN
ejpam-6583	14	3	by	by	ADP
ejpam-6583	14	4	-	-	PUNCT
ejpam-6583	14	5	nc	nc	PROPN
ejpam-6583	14	6	4.0	4.0	NUM
ejpam-6583	14	7	)	)	PUNCT
ejpam-6583	14	8	g.	g.	NOUN
ejpam-6583	14	9	albeladi	albeladi	PROPN
ejpam-6583	14	10	,	,	PUNCT
ejpam-6583	14	11	s.	s.	PROPN
ejpam-6583	14	12	omran	omran	PROPN
ejpam-6583	14	13	/	/	SYM
ejpam-6583	14	14	eur	eur	PROPN
ejpam-6583	14	15	.	.	PUNCT
ejpam-6583	15	1	j.	j.	PROPN
ejpam-6583	15	2	pure	pure	PROPN
ejpam-6583	15	3	appl	appl	PROPN
ejpam-6583	15	4	.	.	PROPN
ejpam-6583	15	5	math	math	PROPN
ejpam-6583	15	6	,	,	PUNCT
ejpam-6583	15	7	18	18	NUM
ejpam-6583	15	8	(	(	PUNCT
ejpam-6583	15	9	3	3	NUM
ejpam-6583	15	10	)	)	PUNCT
ejpam-6583	15	11	(	(	PUNCT
ejpam-6583	15	12	2025	2025	NUM
ejpam-6583	15	13	)	)	PUNCT
ejpam-6583	15	14	,	,	PUNCT
ejpam-6583	15	15	6583	6583	NUM
ejpam-6583	15	16	2	2	NUM
ejpam-6583	15	17	of	of	ADP
ejpam-6583	15	18	27	27	NUM
ejpam-6583	15	19	metric	metric	ADJ
ejpam-6583	15	20	space	space	NOUN
ejpam-6583	15	21	.	.	PUNCT
ejpam-6583	16	1	in	in	ADP
ejpam-6583	16	2	this	this	DET
ejpam-6583	16	3	context	context	NOUN
ejpam-6583	16	4	,	,	PUNCT
ejpam-6583	16	5	several	several	ADJ
ejpam-6583	16	6	interesting	interesting	ADJ
ejpam-6583	16	7	results	result	NOUN
ejpam-6583	16	8	have	have	AUX
ejpam-6583	16	9	been	be	AUX
ejpam-6583	16	10	introduced	introduce	VERB
ejpam-6583	16	11	by	by	ADP
ejpam-6583	16	12	various	various	ADJ
ejpam-6583	16	13	authors	author	NOUN
ejpam-6583	16	14	(	(	PUNCT
ejpam-6583	16	15	see	see	VERB
ejpam-6583	16	16	[	[	X
ejpam-6583	16	17	2	2	NUM
ejpam-6583	16	18	,	,	PUNCT
ejpam-6583	16	19	3	3	NUM
ejpam-6583	16	20	]	]	NUM
ejpam-6583	16	21	)	)	PUNCT
ejpam-6583	16	22	.	.	PUNCT
ejpam-6583	17	1	omran	omran	PROPN
ejpam-6583	17	2	presented	present	VERB
ejpam-6583	17	3	versions	version	NOUN
ejpam-6583	17	4	of	of	ADP
ejpam-6583	17	5	banach	banach	ADV
ejpam-6583	17	6	fixed	fix	VERB
ejpam-6583	17	7	-	-	PUNCT
ejpam-6583	17	8	point	point	NOUN
ejpam-6583	17	9	theorems	theorem	NOUN
ejpam-6583	17	10	in	in	ADP
ejpam-6583	17	11	a	a	DET
ejpam-6583	17	12	generalized	generalize	VERB
ejpam-6583	17	13	metric	metric	ADJ
ejpam-6583	17	14	space	space	NOUN
ejpam-6583	17	15	endowed	endow	VERB
ejpam-6583	17	16	with	with	ADP
ejpam-6583	17	17	the	the	DET
ejpam-6583	17	18	hadamard	hadamard	ADJ
ejpam-6583	17	19	product	product	NOUN
ejpam-6583	17	20	.	.	PUNCT
ejpam-6583	18	1	omran	omran	PROPN
ejpam-6583	19	1	[	[	X
ejpam-6583	19	2	4	4	NUM
ejpam-6583	19	3	]	]	PUNCT
ejpam-6583	19	4	applied	apply	VERB
ejpam-6583	19	5	the	the	DET
ejpam-6583	19	6	hadamard	hadamard	ADJ
ejpam-6583	19	7	product	product	NOUN
ejpam-6583	19	8	to	to	PART
ejpam-6583	19	9	solve	solve	VERB
ejpam-6583	19	10	a	a	DET
ejpam-6583	19	11	system	system	NOUN
ejpam-6583	19	12	of	of	ADP
ejpam-6583	19	13	symmetric	symmetric	ADJ
ejpam-6583	19	14	positive	positive	ADJ
ejpam-6583	19	15	definite	definite	ADJ
ejpam-6583	19	16	matrix	matrix	NOUN
ejpam-6583	19	17	equations	equation	NOUN
ejpam-6583	19	18	,	,	PUNCT
ejpam-6583	19	19	demonstrating	demonstrate	VERB
ejpam-6583	19	20	that	that	PRON
ejpam-6583	19	21	results	result	NOUN
ejpam-6583	19	22	based	base	VERB
ejpam-6583	19	23	on	on	ADP
ejpam-6583	19	24	the	the	DET
ejpam-6583	19	25	hadamard	hadamard	ADJ
ejpam-6583	19	26	product	product	NOUN
ejpam-6583	19	27	of	of	ADP
ejpam-6583	19	28	a	a	DET
ejpam-6583	19	29	vector	vector	NOUN
ejpam-6583	19	30	-	-	PUNCT
ejpam-6583	19	31	valued	value	VERB
ejpam-6583	19	32	metric	metric	NOUN
ejpam-6583	19	33	are	be	AUX
ejpam-6583	19	34	stronger	strong	ADJ
ejpam-6583	19	35	than	than	ADP
ejpam-6583	19	36	those	those	PRON
ejpam-6583	19	37	using	use	VERB
ejpam-6583	19	38	perov	perov	NOUN
ejpam-6583	19	39	’s	’s	PART
ejpam-6583	19	40	condition	condition	NOUN
ejpam-6583	19	41	.	.	PUNCT
ejpam-6583	20	1	specifically	specifically	ADV
ejpam-6583	20	2	,	,	PUNCT
ejpam-6583	20	3	it	it	PRON
ejpam-6583	20	4	eliminates	eliminate	VERB
ejpam-6583	20	5	the	the	DET
ejpam-6583	20	6	need	need	NOUN
ejpam-6583	20	7	to	to	PART
ejpam-6583	20	8	assume	assume	VERB
ejpam-6583	20	9	that	that	SCONJ
ejpam-6583	20	10	a	a	PRON
ejpam-6583	20	11	is	be	AUX
ejpam-6583	20	12	a	a	DET
ejpam-6583	20	13	matrix	matrix	NOUN
ejpam-6583	20	14	converging	converge	VERB
ejpam-6583	20	15	to	to	ADP
ejpam-6583	20	16	zero	zero	NUM
ejpam-6583	20	17	.	.	PUNCT
ejpam-6583	21	1	in	in	ADP
ejpam-6583	21	2	banach	banach	NOUN
ejpam-6583	21	3	’s	’s	PART
ejpam-6583	21	4	1922	1922	NUM
ejpam-6583	21	5	thesis	thesis	NOUN
ejpam-6583	21	6	[	[	X
ejpam-6583	21	7	5	5	NUM
ejpam-6583	21	8	]	]	PUNCT
ejpam-6583	21	9	,	,	PUNCT
ejpam-6583	21	10	the	the	DET
ejpam-6583	21	11	fixed	fix	VERB
ejpam-6583	21	12	-	-	PUNCT
ejpam-6583	21	13	point	point	NOUN
ejpam-6583	21	14	theorem	theorem	VERB
ejpam-6583	21	15	—	—	PUNCT
ejpam-6583	21	16	also	also	ADV
ejpam-6583	21	17	known	know	VERB
ejpam-6583	21	18	as	as	ADP
ejpam-6583	21	19	the	the	DET
ejpam-6583	21	20	banach	banach	NOUN
ejpam-6583	21	21	contraction	contraction	NOUN
ejpam-6583	21	22	principle	principle	NOUN
ejpam-6583	21	23	—	—	PUNCT
ejpam-6583	21	24	was	be	AUX
ejpam-6583	21	25	first	first	ADV
ejpam-6583	21	26	used	use	VERB
ejpam-6583	21	27	in	in	ADP
ejpam-6583	21	28	its	its	PRON
ejpam-6583	21	29	final	final	ADJ
ejpam-6583	21	30	form	form	NOUN
ejpam-6583	21	31	in	in	ADP
ejpam-6583	21	32	1922	1922	NUM
ejpam-6583	21	33	to	to	PART
ejpam-6583	21	34	prove	prove	VERB
ejpam-6583	21	35	that	that	SCONJ
ejpam-6583	21	36	an	an	DET
ejpam-6583	21	37	integral	integral	ADJ
ejpam-6583	21	38	equation	equation	NOUN
ejpam-6583	21	39	had	have	VERB
ejpam-6583	21	40	a	a	DET
ejpam-6583	21	41	solution	solution	NOUN
ejpam-6583	21	42	.	.	PUNCT
ejpam-6583	22	1	since	since	SCONJ
ejpam-6583	22	2	then	then	ADV
ejpam-6583	22	3	,	,	PUNCT
ejpam-6583	22	4	it	it	PRON
ejpam-6583	22	5	has	have	AUX
ejpam-6583	22	6	been	be	AUX
ejpam-6583	22	7	found	find	VERB
ejpam-6583	22	8	to	to	PART
ejpam-6583	22	9	be	be	AUX
ejpam-6583	22	10	a	a	DET
ejpam-6583	22	11	useful	useful	ADJ
ejpam-6583	22	12	tool	tool	NOUN
ejpam-6583	22	13	for	for	ADP
ejpam-6583	22	14	solving	solve	VERB
ejpam-6583	22	15	many	many	ADJ
ejpam-6583	22	16	practical	practical	ADJ
ejpam-6583	22	17	problems	problem	NOUN
ejpam-6583	22	18	in	in	ADP
ejpam-6583	22	19	various	various	ADJ
ejpam-6583	22	20	branches	branch	NOUN
ejpam-6583	22	21	of	of	ADP
ejpam-6583	22	22	mathematical	mathematical	ADJ
ejpam-6583	22	23	analysis	analysis	NOUN
ejpam-6583	22	24	.	.	PUNCT
ejpam-6583	23	1	in	in	ADP
ejpam-6583	23	2	this	this	DET
ejpam-6583	23	3	principle	principle	NOUN
ejpam-6583	23	4	,	,	PUNCT
ejpam-6583	23	5	b	b	X
ejpam-6583	23	6	-	-	PUNCT
ejpam-6583	23	7	metric	metric	ADJ
ejpam-6583	23	8	space	space	NOUN
ejpam-6583	23	9	x	x	PUNCT
ejpam-6583	23	10	is	be	AUX
ejpam-6583	23	11	complete	complete	ADJ
ejpam-6583	23	12	if	if	SCONJ
ejpam-6583	23	13	f	f	X
ejpam-6583	23	14	:	:	PUNCT
ejpam-6583	23	15	x	x	X
ejpam-6583	23	16	→	→	PUNCT
ejpam-6583	23	17	x	x	X
ejpam-6583	23	18	is	be	AUX
ejpam-6583	23	19	a	a	DET
ejpam-6583	23	20	contraction	contraction	NOUN
ejpam-6583	23	21	operator	operator	NOUN
ejpam-6583	23	22	;	;	PUNCT
ejpam-6583	23	23	that	that	PRON
ejpam-6583	23	24	is	is	ADV
ejpam-6583	23	25	,	,	PUNCT
ejpam-6583	23	26	δr(fx	δr(fx	PROPN
ejpam-6583	23	27	,	,	PUNCT
ejpam-6583	23	28	fy	fy	PROPN
ejpam-6583	23	29	)	)	PUNCT
ejpam-6583	23	30	≤	≤	PUNCT
ejpam-6583	24	1	λδr(x	λδr(x	PROPN
ejpam-6583	24	2	,	,	PUNCT
ejpam-6583	24	3	y	y	NOUN
ejpam-6583	24	4	)	)	PUNCT
ejpam-6583	24	5	for	for	ADP
ejpam-6583	24	6	all	all	DET
ejpam-6583	24	7	x	x	NOUN
ejpam-6583	24	8	,	,	PUNCT
ejpam-6583	24	9	y	y	PROPN
ejpam-6583	24	10	∈	∈	PROPN
ejpam-6583	24	11	x	x	X
ejpam-6583	24	12	,	,	PUNCT
ejpam-6583	24	13	where	where	SCONJ
ejpam-6583	24	14	λ	λ	PROPN
ejpam-6583	24	15	∈	∈	PROPN
ejpam-6583	24	16	(	(	PUNCT
ejpam-6583	24	17	0	0	NUM
ejpam-6583	24	18	,	,	PUNCT
ejpam-6583	24	19	1s	1	NOUN
ejpam-6583	24	20	)	)	PUNCT
ejpam-6583	24	21	is	be	AUX
ejpam-6583	24	22	a	a	DET
ejpam-6583	24	23	constant	constant	ADJ
ejpam-6583	24	24	,	,	PUNCT
ejpam-6583	24	25	then	then	ADV
ejpam-6583	24	26	f	f	PROPN
ejpam-6583	24	27	has	have	VERB
ejpam-6583	24	28	a	a	DET
ejpam-6583	24	29	fixed	fix	VERB
ejpam-6583	24	30	point	point	NOUN
ejpam-6583	24	31	.	.	PUNCT
ejpam-6583	25	1	in	in	ADP
ejpam-6583	25	2	1989	1989	NUM
ejpam-6583	25	3	,	,	PUNCT
ejpam-6583	25	4	bakhtin	bakhtin	NOUN
ejpam-6583	25	5	[	[	X
ejpam-6583	25	6	6	6	NUM
ejpam-6583	25	7	]	]	PUNCT
ejpam-6583	25	8	introduced	introduce	VERB
ejpam-6583	25	9	the	the	DET
ejpam-6583	25	10	concept	concept	NOUN
ejpam-6583	25	11	of	of	ADP
ejpam-6583	25	12	b	b	NOUN
ejpam-6583	25	13	-	-	PUNCT
ejpam-6583	25	14	metric	metric	ADJ
ejpam-6583	25	15	spaces	space	NOUN
ejpam-6583	25	16	,	,	PUNCT
ejpam-6583	25	17	which	which	PRON
ejpam-6583	25	18	czerwik	czerwik	PROPN
ejpam-6583	25	19	further	far	ADV
ejpam-6583	25	20	developed	develop	VERB
ejpam-6583	25	21	in	in	ADP
ejpam-6583	25	22	1993	1993	NUM
ejpam-6583	25	23	[	[	X
ejpam-6583	25	24	7	7	NUM
ejpam-6583	25	25	]	]	PUNCT
ejpam-6583	25	26	.	.	PUNCT
ejpam-6583	26	1	this	this	DET
ejpam-6583	26	2	advancement	advancement	NOUN
ejpam-6583	26	3	sparked	spark	VERB
ejpam-6583	26	4	significant	significant	ADJ
ejpam-6583	26	5	research	research	NOUN
ejpam-6583	26	6	into	into	ADP
ejpam-6583	26	7	generalizing	generalize	VERB
ejpam-6583	26	8	the	the	DET
ejpam-6583	26	9	banach	banach	ADV
ejpam-6583	26	10	fixed	fix	VERB
ejpam-6583	26	11	-	-	PUNCT
ejpam-6583	26	12	point	point	NOUN
ejpam-6583	26	13	theorem	theorem	NOUN
ejpam-6583	26	14	for	for	ADP
ejpam-6583	26	15	b	b	NOUN
ejpam-6583	26	16	-	-	PUNCT
ejpam-6583	26	17	metric	metric	ADJ
ejpam-6583	26	18	spaces	space	NOUN
ejpam-6583	26	19	.	.	PUNCT
ejpam-6583	27	1	notable	notable	ADJ
ejpam-6583	27	2	contributions	contribution	NOUN
ejpam-6583	27	3	from	from	ADP
ejpam-6583	27	4	mehmet	mehmet	PROPN
ejpam-6583	27	5	kir	kir	PROPN
ejpam-6583	28	1	[	[	X
ejpam-6583	28	2	8	8	NUM
ejpam-6583	28	3	]	]	PUNCT
ejpam-6583	28	4	,	,	PUNCT
ejpam-6583	28	5	boriceanu	boriceanu	PROPN
ejpam-6583	29	1	[	[	X
ejpam-6583	29	2	9	9	NUM
ejpam-6583	29	3	]	]	PUNCT
ejpam-6583	29	4	,	,	PUNCT
ejpam-6583	29	5	bota	bota	NOUN
ejpam-6583	30	1	[	[	X
ejpam-6583	30	2	10	10	NUM
ejpam-6583	30	3	]	]	PUNCT
ejpam-6583	30	4	,	,	PUNCT
ejpam-6583	30	5	pacurar	pacurar	NOUN
ejpam-6583	30	6	[	[	X
ejpam-6583	30	7	11	11	NUM
ejpam-6583	30	8	]	]	PUNCT
ejpam-6583	30	9	,	,	PUNCT
ejpam-6583	30	10	and	and	CCONJ
ejpam-6583	30	11	czerwik	czerwik	PROPN
ejpam-6583	31	1	[	[	X
ejpam-6583	31	2	7	7	X
ejpam-6583	31	3	]	]	PUNCT
ejpam-6583	31	4	have	have	AUX
ejpam-6583	31	5	extended	extend	VERB
ejpam-6583	31	6	fixed	fix	VERB
ejpam-6583	31	7	-	-	PUNCT
ejpam-6583	31	8	point	point	NOUN
ejpam-6583	31	9	theorems	theorem	NOUN
ejpam-6583	31	10	in	in	ADP
ejpam-6583	31	11	this	this	DET
ejpam-6583	31	12	context	context	NOUN
ejpam-6583	31	13	.	.	PUNCT
ejpam-6583	32	1	additionally	additionally	ADV
ejpam-6583	32	2	,	,	PUNCT
ejpam-6583	32	3	czerwik	czerwik	PROPN
ejpam-6583	32	4	explored	explore	VERB
ejpam-6583	32	5	the	the	DET
ejpam-6583	32	6	convergence	convergence	NOUN
ejpam-6583	32	7	of	of	ADP
ejpam-6583	32	8	measurable	measurable	ADJ
ejpam-6583	32	9	functions	function	NOUN
ejpam-6583	32	10	with	with	ADP
ejpam-6583	32	11	respect	respect	NOUN
ejpam-6583	32	12	to	to	ADP
ejpam-6583	32	13	measure	measure	NOUN
ejpam-6583	32	14	and	and	CCONJ
ejpam-6583	32	15	generalized	generalize	VERB
ejpam-6583	32	16	the	the	DET
ejpam-6583	32	17	banach	banach	NOUN
ejpam-6583	32	18	contraction	contraction	NOUN
ejpam-6583	32	19	principle	principle	NOUN
ejpam-6583	32	20	.	.	PUNCT
ejpam-6583	33	1	in	in	ADP
ejpam-6583	33	2	the	the	DET
ejpam-6583	33	3	same	same	ADJ
ejpam-6583	33	4	year	year	NOUN
ejpam-6583	33	5	,	,	PUNCT
ejpam-6583	33	6	czerwik	czerwik	PROPN
ejpam-6583	33	7	[	[	X
ejpam-6583	33	8	7	7	X
ejpam-6583	33	9	]	]	PUNCT
ejpam-6583	33	10	proposed	propose	VERB
ejpam-6583	33	11	a	a	DET
ejpam-6583	33	12	new	new	ADJ
ejpam-6583	33	13	axiom	axiom	NOUN
ejpam-6583	33	14	for	for	ADP
ejpam-6583	33	15	semimetric	semimetric	ADJ
ejpam-6583	33	16	spaces	space	NOUN
ejpam-6583	33	17	,	,	PUNCT
ejpam-6583	33	18	relaxing	relax	VERB
ejpam-6583	33	19	the	the	DET
ejpam-6583	33	20	classical	classical	ADJ
ejpam-6583	33	21	triangle	triangle	NOUN
ejpam-6583	33	22	inequality	inequality	NOUN
ejpam-6583	33	23	to	to	PART
ejpam-6583	33	24	broaden	broaden	VERB
ejpam-6583	33	25	the	the	DET
ejpam-6583	33	26	scope	scope	NOUN
ejpam-6583	33	27	of	of	ADP
ejpam-6583	33	28	the	the	DET
ejpam-6583	33	29	banach	banach	NOUN
ejpam-6583	33	30	contraction	contraction	NOUN
ejpam-6583	33	31	principle	principle	NOUN
ejpam-6583	33	32	.	.	PUNCT
ejpam-6583	34	1	this	this	DET
ejpam-6583	34	2	idea	idea	NOUN
ejpam-6583	34	3	aligns	align	VERB
ejpam-6583	34	4	with	with	ADP
ejpam-6583	34	5	the	the	DET
ejpam-6583	34	6	nonlinear	nonlinear	ADJ
ejpam-6583	34	7	elastic	elastic	ADJ
ejpam-6583	34	8	matching	matching	NOUN
ejpam-6583	34	9	(	(	PUNCT
ejpam-6583	34	10	nem	nem	PROPN
ejpam-6583	34	11	)	)	PUNCT
ejpam-6583	34	12	distance	distance	NOUN
ejpam-6583	34	13	discussed	discuss	VERB
ejpam-6583	34	14	by	by	ADP
ejpam-6583	34	15	fagin	fagin	PROPN
ejpam-6583	34	16	et	et	PROPN
ejpam-6583	34	17	al	al	PROPN
ejpam-6583	34	18	.	.	PUNCT
ejpam-6583	35	1	[	[	X
ejpam-6583	35	2	12	12	NUM
ejpam-6583	35	3	]	]	PUNCT
ejpam-6583	35	4	,	,	PUNCT
ejpam-6583	35	5	which	which	PRON
ejpam-6583	35	6	has	have	AUX
ejpam-6583	35	7	found	find	VERB
ejpam-6583	35	8	applications	application	NOUN
ejpam-6583	35	9	in	in	ADP
ejpam-6583	35	10	diverse	diverse	ADJ
ejpam-6583	35	11	fields	field	NOUN
ejpam-6583	35	12	,	,	PUNCT
ejpam-6583	35	13	such	such	ADJ
ejpam-6583	35	14	as	as	ADP
ejpam-6583	35	15	trademark	trademark	NOUN
ejpam-6583	35	16	shape	shape	NOUN
ejpam-6583	35	17	analysis	analysis	NOUN
ejpam-6583	35	18	[	[	X
ejpam-6583	35	19	13	13	NUM
ejpam-6583	35	20	]	]	PUNCT
ejpam-6583	35	21	and	and	CCONJ
ejpam-6583	35	22	ice	ice	NOUN
ejpam-6583	35	23	floe	floe	NOUN
ejpam-6583	35	24	measurements	measurement	NOUN
ejpam-6583	35	25	[	[	X
ejpam-6583	35	26	14	14	NUM
ejpam-6583	35	27	]	]	PUNCT
ejpam-6583	35	28	.	.	PUNCT
ejpam-6583	36	1	building	build	VERB
ejpam-6583	36	2	on	on	ADP
ejpam-6583	36	3	this	this	DET
ejpam-6583	36	4	concept	concept	NOUN
ejpam-6583	36	5	,	,	PUNCT
ejpam-6583	36	6	q.	q.	PROPN
ejpam-6583	36	7	xia	xia	PROPN
ejpam-6583	37	1	[	[	X
ejpam-6583	37	2	15	15	NUM
ejpam-6583	37	3	]	]	PUNCT
ejpam-6583	37	4	applied	apply	VERB
ejpam-6583	37	5	semimetric	semimetric	ADJ
ejpam-6583	37	6	distances	distance	NOUN
ejpam-6583	37	7	to	to	PART
ejpam-6583	37	8	study	study	VERB
ejpam-6583	37	9	optimal	optimal	ADJ
ejpam-6583	37	10	transport	transport	NOUN
ejpam-6583	37	11	paths	path	NOUN
ejpam-6583	37	12	between	between	ADP
ejpam-6583	37	13	probability	probability	NOUN
ejpam-6583	37	14	measures	measure	NOUN
ejpam-6583	37	15	,	,	PUNCT
ejpam-6583	37	16	coining	coin	VERB
ejpam-6583	37	17	the	the	DET
ejpam-6583	37	18	term	term	NOUN
ejpam-6583	37	19	quasi	quasi	ADJ
ejpam-6583	37	20	-	-	ADJ
ejpam-6583	37	21	metric	metric	ADJ
ejpam-6583	37	22	spaces	space	NOUN
ejpam-6583	37	23	,	,	PUNCT
ejpam-6583	37	24	a	a	DET
ejpam-6583	37	25	designation	designation	NOUN
ejpam-6583	37	26	also	also	ADV
ejpam-6583	37	27	used	use	VERB
ejpam-6583	37	28	in	in	ADP
ejpam-6583	37	29	heinonen	heinonen	PROPN
ejpam-6583	37	30	’s	’s	PART
ejpam-6583	37	31	book	book	NOUN
ejpam-6583	38	1	[	[	X
ejpam-6583	38	2	16	16	NUM
ejpam-6583	38	3	]	]	PUNCT
ejpam-6583	38	4	.	.	PUNCT
ejpam-6583	39	1	our	our	PRON
ejpam-6583	39	2	goal	goal	NOUN
ejpam-6583	39	3	is	be	AUX
ejpam-6583	39	4	to	to	PART
ejpam-6583	39	5	further	far	ADV
ejpam-6583	39	6	extend	extend	VERB
ejpam-6583	39	7	well	well	ADV
ejpam-6583	39	8	-	-	PUNCT
ejpam-6583	39	9	known	know	VERB
ejpam-6583	39	10	fixed	fix	VERB
ejpam-6583	39	11	-	-	PUNCT
ejpam-6583	39	12	point	point	NOUN
ejpam-6583	39	13	theorems	theorem	NOUN
ejpam-6583	39	14	within	within	ADP
ejpam-6583	39	15	the	the	DET
ejpam-6583	39	16	framework	framework	NOUN
ejpam-6583	39	17	of	of	ADP
ejpam-6583	39	18	b	b	NOUN
ejpam-6583	39	19	-	-	PUNCT
ejpam-6583	39	20	metric	metric	ADJ
ejpam-6583	39	21	spaces	space	NOUN
ejpam-6583	39	22	.	.	PUNCT
ejpam-6583	40	1	some	some	DET
ejpam-6583	40	2	articles	article	NOUN
ejpam-6583	40	3	examine	examine	VERB
ejpam-6583	40	4	various	various	ADJ
ejpam-6583	40	5	generalizations	generalization	NOUN
ejpam-6583	40	6	of	of	ADP
ejpam-6583	40	7	classical	classical	ADJ
ejpam-6583	40	8	metric	metric	ADJ
ejpam-6583	40	9	spaces	space	NOUN
ejpam-6583	40	10	to	to	PART
ejpam-6583	40	11	establish	establish	VERB
ejpam-6583	40	12	new	new	ADJ
ejpam-6583	40	13	fixed	fix	VERB
ejpam-6583	40	14	-	-	PUNCT
ejpam-6583	40	15	point	point	NOUN
ejpam-6583	40	16	theorems	theorem	NOUN
ejpam-6583	40	17	.	.	PUNCT
ejpam-6583	41	1	building	build	VERB
ejpam-6583	41	2	on	on	ADP
ejpam-6583	41	3	the	the	DET
ejpam-6583	41	4	framework	framework	NOUN
ejpam-6583	41	5	of	of	ADP
ejpam-6583	41	6	b	b	NOUN
ejpam-6583	41	7	-	-	PUNCT
ejpam-6583	41	8	metric	metric	ADJ
ejpam-6583	41	9	spaces	space	NOUN
ejpam-6583	41	10	presented	present	VERB
ejpam-6583	41	11	by	by	ADP
ejpam-6583	41	12	jleli	jleli	ADJ
ejpam-6583	41	13	and	and	CCONJ
ejpam-6583	41	14	samet	samet	VERB
ejpam-6583	41	15	[	[	X
ejpam-6583	41	16	17	17	NUM
ejpam-6583	41	17	]	]	PUNCT
ejpam-6583	41	18	.	.	PUNCT
ejpam-6583	42	1	albargi	albargi	NOUN
ejpam-6583	42	2	and	and	CCONJ
ejpam-6583	42	3	ahmad	ahmad	PROPN
ejpam-6583	42	4	[	[	X
ejpam-6583	42	5	18	18	NUM
ejpam-6583	42	6	]	]	PUNCT
ejpam-6583	42	7	developed	develop	VERB
ejpam-6583	42	8	standard	standard	ADJ
ejpam-6583	42	9	f	f	X
ejpam-6583	42	10	-	-	PUNCT
ejpam-6583	42	11	fuzzy	fuzzy	ADJ
ejpam-6583	42	12	fixed	fix	VERB
ejpam-6583	42	13	-	-	PUNCT
ejpam-6583	42	14	point	point	NOUN
ejpam-6583	42	15	theorems	theorem	NOUN
ejpam-6583	42	16	under	under	ADP
ejpam-6583	42	17	rational	rational	ADJ
ejpam-6583	42	18	(	(	PUNCT
ejpam-6583	42	19	β-ϕ)-contractive	β-ϕ)-contractive	ADJ
ejpam-6583	42	20	conditions	condition	NOUN
ejpam-6583	42	21	,	,	PUNCT
ejpam-6583	42	22	with	with	ADP
ejpam-6583	42	23	applications	application	NOUN
ejpam-6583	42	24	to	to	ADP
ejpam-6583	42	25	fuzzy	fuzzy	ADJ
ejpam-6583	42	26	integrodifferential	integrodifferential	ADJ
ejpam-6583	42	27	equations	equation	NOUN
ejpam-6583	42	28	via	via	ADP
ejpam-6583	42	29	the	the	DET
ejpam-6583	42	30	generalized	generalize	VERB
ejpam-6583	42	31	hukuhara	hukuhara	ADJ
ejpam-6583	42	32	derivative	derivative	NOUN
ejpam-6583	42	33	.	.	PUNCT
ejpam-6583	43	1	furthermore	furthermore	ADV
ejpam-6583	43	2	,	,	PUNCT
ejpam-6583	43	3	huang	huang	PROPN
ejpam-6583	43	4	and	and	CCONJ
ejpam-6583	43	5	samet	samet	PROPN
ejpam-6583	44	1	[	[	X
ejpam-6583	44	2	19	19	NUM
ejpam-6583	44	3	]	]	PUNCT
ejpam-6583	44	4	introduced	introduce	VERB
ejpam-6583	44	5	two	two	NUM
ejpam-6583	44	6	novel	novel	ADJ
ejpam-6583	44	7	self	self	NOUN
ejpam-6583	44	8	-	-	PUNCT
ejpam-6583	44	9	mapping	mapping	NOUN
ejpam-6583	44	10	classes	class	NOUN
ejpam-6583	44	11	on	on	ADP
ejpam-6583	44	12	complete	complete	ADJ
ejpam-6583	44	13	metric	metric	ADJ
ejpam-6583	44	14	spaces	space	NOUN
ejpam-6583	44	15	:	:	PUNCT
ejpam-6583	44	16	p	p	X
ejpam-6583	44	17	-	-	PUNCT
ejpam-6583	44	18	contractions	contraction	NOUN
ejpam-6583	44	19	concerning	concern	VERB
ejpam-6583	44	20	families	family	NOUN
ejpam-6583	44	21	of	of	ADP
ejpam-6583	44	22	mappings	mapping	NOUN
ejpam-6583	44	23	,	,	PUNCT
ejpam-6583	44	24	and	and	CCONJ
ejpam-6583	44	25	(	(	PUNCT
ejpam-6583	44	26	ψ	ψ	X
ejpam-6583	44	27	,	,	PUNCT
ejpam-6583	44	28	γ	γ	X
ejpam-6583	44	29	,	,	PUNCT
ejpam-6583	44	30	α)-contractions	α)-contraction	NOUN
ejpam-6583	44	31	,	,	PUNCT
ejpam-6583	44	32	which	which	PRON
ejpam-6583	44	33	involve	involve	VERB
ejpam-6583	44	34	the	the	DET
ejpam-6583	44	35	euler	euler	NOUN
ejpam-6583	44	36	gamma	gamma	PROPN
ejpam-6583	44	37	function	function	PROPN
ejpam-6583	44	38	.	.	PUNCT
ejpam-6583	45	1	also	also	ADV
ejpam-6583	45	2	,	,	PUNCT
ejpam-6583	45	3	[	[	X
ejpam-6583	45	4	20	20	NUM
ejpam-6583	45	5	,	,	PUNCT
ejpam-6583	45	6	21	21	NUM
ejpam-6583	45	7	]	]	PUNCT
ejpam-6583	45	8	developed	develop	VERB
ejpam-6583	45	9	fixed	fix	VERB
ejpam-6583	45	10	-	-	PUNCT
ejpam-6583	45	11	point	point	NOUN
ejpam-6583	45	12	results	result	NOUN
ejpam-6583	45	13	to	to	PART
ejpam-6583	45	14	fuzzy	fuzzy	ADJ
ejpam-6583	45	15	normed	normed	ADJ
ejpam-6583	45	16	spaces	space	NOUN
ejpam-6583	45	17	using	use	VERB
ejpam-6583	45	18	a	a	DET
ejpam-6583	45	19	newly	newly	ADV
ejpam-6583	45	20	introduced	introduce	VERB
ejpam-6583	45	21	triangle	triangle	NOUN
ejpam-6583	45	22	property	property	NOUN
ejpam-6583	45	23	and	and	CCONJ
ejpam-6583	45	24	to	to	AUX
ejpam-6583	45	25	algebra	algebra	NOUN
ejpam-6583	45	26	fuzzy	fuzzy	ADJ
ejpam-6583	45	27	metric	metric	ADJ
ejpam-6583	45	28	spaces	space	NOUN
ejpam-6583	45	29	.	.	PUNCT
ejpam-6583	46	1	these	these	DET
ejpam-6583	46	2	results	result	NOUN
ejpam-6583	46	3	generalized	generalize	VERB
ejpam-6583	46	4	,	,	PUNCT
ejpam-6583	46	5	unified	unified	ADJ
ejpam-6583	46	6	,	,	PUNCT
ejpam-6583	46	7	and	and	CCONJ
ejpam-6583	46	8	improved	improve	VERB
ejpam-6583	46	9	many	many	ADJ
ejpam-6583	46	10	classical	classical	ADJ
ejpam-6583	46	11	theorems	theorem	NOUN
ejpam-6583	46	12	.	.	PUNCT
ejpam-6583	47	1	g.	g.	PROPN
ejpam-6583	47	2	albeladi	albeladi	PROPN
ejpam-6583	47	3	,	,	PUNCT
ejpam-6583	47	4	s.	s.	PROPN
ejpam-6583	47	5	omran	omran	PROPN
ejpam-6583	47	6	/	/	SYM
ejpam-6583	47	7	eur	eur	PROPN
ejpam-6583	47	8	.	.	PUNCT
ejpam-6583	48	1	j.	j.	PROPN
ejpam-6583	48	2	pure	pure	PROPN
ejpam-6583	48	3	appl	appl	PROPN
ejpam-6583	48	4	.	.	PROPN
ejpam-6583	48	5	math	math	PROPN
ejpam-6583	48	6	,	,	PUNCT
ejpam-6583	48	7	18	18	NUM
ejpam-6583	48	8	(	(	PUNCT
ejpam-6583	48	9	3	3	NUM
ejpam-6583	48	10	)	)	PUNCT
ejpam-6583	48	11	(	(	PUNCT
ejpam-6583	48	12	2025	2025	NUM
ejpam-6583	48	13	)	)	PUNCT
ejpam-6583	48	14	,	,	PUNCT
ejpam-6583	48	15	6583	6583	NUM
ejpam-6583	48	16	3	3	NUM
ejpam-6583	48	17	of	of	ADP
ejpam-6583	48	18	27	27	NUM
ejpam-6583	48	19	the	the	DET
ejpam-6583	48	20	aim	aim	NOUN
ejpam-6583	48	21	of	of	ADP
ejpam-6583	48	22	this	this	DET
ejpam-6583	48	23	work	work	NOUN
ejpam-6583	48	24	is	be	AUX
ejpam-6583	48	25	to	to	PART
ejpam-6583	48	26	present	present	VERB
ejpam-6583	48	27	new	new	ADJ
ejpam-6583	48	28	versions	version	NOUN
ejpam-6583	48	29	of	of	ADP
ejpam-6583	48	30	banach	banach	ADV
ejpam-6583	48	31	fixed	fix	VERB
ejpam-6583	48	32	-	-	PUNCT
ejpam-6583	48	33	point	point	NOUN
ejpam-6583	48	34	theorems	theorem	NOUN
ejpam-6583	48	35	in	in	ADP
ejpam-6583	48	36	a	a	DET
ejpam-6583	48	37	generalized	generalized	ADJ
ejpam-6583	48	38	b	b	X
ejpam-6583	48	39	-	-	ADJ
ejpam-6583	48	40	metric	metric	ADJ
ejpam-6583	48	41	space	space	NOUN
ejpam-6583	48	42	endowed	endow	VERB
ejpam-6583	48	43	with	with	ADP
ejpam-6583	48	44	the	the	DET
ejpam-6583	48	45	orthogonal	orthogonal	ADJ
ejpam-6583	48	46	direct	direct	ADJ
ejpam-6583	48	47	sum	sum	NOUN
ejpam-6583	48	48	,	,	PUNCT
ejpam-6583	48	49	where	where	SCONJ
ejpam-6583	48	50	a	a	PRON
ejpam-6583	48	51	is	be	AUX
ejpam-6583	48	52	a	a	DET
ejpam-6583	48	53	diagonal	diagonal	ADJ
ejpam-6583	48	54	matrix	matrix	NOUN
ejpam-6583	48	55	in	in	ADP
ejpam-6583	48	56	rd	rd	PROPN
ejpam-6583	48	57	.	.	PUNCT
ejpam-6583	49	1	this	this	DET
ejpam-6583	49	2	approach	approach	NOUN
ejpam-6583	49	3	,	,	PUNCT
ejpam-6583	49	4	constructed	construct	VERB
ejpam-6583	49	5	via	via	ADP
ejpam-6583	49	6	the	the	DET
ejpam-6583	49	7	direct	direct	ADJ
ejpam-6583	49	8	sum	sum	NOUN
ejpam-6583	49	9	,	,	PUNCT
ejpam-6583	49	10	ensures	ensure	VERB
ejpam-6583	49	11	more	more	ADV
ejpam-6583	49	12	suitable	suitable	ADJ
ejpam-6583	49	13	contraction	contraction	NOUN
ejpam-6583	49	14	conditions	condition	NOUN
ejpam-6583	49	15	.	.	PUNCT
ejpam-6583	50	1	now	now	ADV
ejpam-6583	50	2	,	,	PUNCT
ejpam-6583	50	3	we	we	PRON
ejpam-6583	50	4	can	can	AUX
ejpam-6583	50	5	summarize	summarize	VERB
ejpam-6583	50	6	the	the	DET
ejpam-6583	50	7	content	content	NOUN
ejpam-6583	50	8	of	of	ADP
ejpam-6583	50	9	this	this	DET
ejpam-6583	50	10	manuscript	manuscript	NOUN
ejpam-6583	50	11	as	as	SCONJ
ejpam-6583	50	12	follows	follow	VERB
ejpam-6583	50	13	:	:	PUNCT
ejpam-6583	50	14	section	section	NOUN
ejpam-6583	50	15	1	1	NUM
ejpam-6583	50	16	provides	provide	VERB
ejpam-6583	50	17	a	a	DET
ejpam-6583	50	18	brief	brief	ADJ
ejpam-6583	50	19	historical	historical	ADJ
ejpam-6583	50	20	overview	overview	NOUN
ejpam-6583	50	21	to	to	PART
ejpam-6583	50	22	put	put	VERB
ejpam-6583	50	23	the	the	DET
ejpam-6583	50	24	fixed	fix	VERB
ejpam-6583	50	25	-	-	PUNCT
ejpam-6583	50	26	point	point	NOUN
ejpam-6583	50	27	theorems	theorem	NOUN
ejpam-6583	50	28	established	establish	VERB
ejpam-6583	50	29	in	in	ADP
ejpam-6583	50	30	this	this	DET
ejpam-6583	50	31	paper	paper	NOUN
ejpam-6583	50	32	into	into	ADP
ejpam-6583	50	33	context	context	NOUN
ejpam-6583	50	34	.	.	PUNCT
ejpam-6583	51	1	section	section	NOUN
ejpam-6583	51	2	2	2	NUM
ejpam-6583	51	3	introduces	introduce	VERB
ejpam-6583	51	4	the	the	DET
ejpam-6583	51	5	definitions	definition	NOUN
ejpam-6583	51	6	and	and	CCONJ
ejpam-6583	51	7	basic	basic	ADJ
ejpam-6583	51	8	concepts	concept	NOUN
ejpam-6583	51	9	that	that	PRON
ejpam-6583	51	10	lay	lie	VERB
ejpam-6583	51	11	the	the	DET
ejpam-6583	51	12	foundation	foundation	NOUN
ejpam-6583	51	13	for	for	ADP
ejpam-6583	51	14	understanding	understand	VERB
ejpam-6583	51	15	generalized	generalize	VERB
ejpam-6583	51	16	b	b	X
ejpam-6583	51	17	-	-	ADJ
ejpam-6583	51	18	metric	metric	ADJ
ejpam-6583	51	19	spaces	space	NOUN
ejpam-6583	51	20	endowed	endow	VERB
ejpam-6583	51	21	with	with	ADP
ejpam-6583	51	22	the	the	DET
ejpam-6583	51	23	orthogonal	orthogonal	ADJ
ejpam-6583	51	24	direct	direct	ADJ
ejpam-6583	51	25	sum	sum	NOUN
ejpam-6583	51	26	.	.	PUNCT
ejpam-6583	52	1	section	section	NOUN
ejpam-6583	52	2	3	3	NUM
ejpam-6583	52	3	presents	present	VERB
ejpam-6583	52	4	several	several	ADJ
ejpam-6583	52	5	theorems	theorem	NOUN
ejpam-6583	52	6	that	that	PRON
ejpam-6583	52	7	generalize	generalize	VERB
ejpam-6583	52	8	the	the	DET
ejpam-6583	52	9	theorems	theorem	NOUN
ejpam-6583	52	10	given	give	VERB
ejpam-6583	52	11	in	in	ADP
ejpam-6583	52	12	[	[	X
ejpam-6583	52	13	1	1	NUM
ejpam-6583	52	14	,	,	PUNCT
ejpam-6583	52	15	4	4	NUM
ejpam-6583	52	16	]	]	PUNCT
ejpam-6583	52	17	,	,	PUNCT
ejpam-6583	52	18	which	which	PRON
ejpam-6583	52	19	prove	prove	VERB
ejpam-6583	52	20	the	the	DET
ejpam-6583	52	21	existence	existence	NOUN
ejpam-6583	52	22	and	and	CCONJ
ejpam-6583	52	23	uniqueness	uniqueness	NOUN
ejpam-6583	52	24	of	of	ADP
ejpam-6583	52	25	fixed	fix	VERB
ejpam-6583	52	26	points	point	NOUN
ejpam-6583	52	27	.	.	PUNCT
ejpam-6583	53	1	2	2	X
ejpam-6583	53	2	.	.	X
ejpam-6583	53	3	preliminaries	preliminary	NOUN
ejpam-6583	53	4	the	the	DET
ejpam-6583	53	5	real	real	ADJ
ejpam-6583	53	6	vector	vector	NOUN
ejpam-6583	53	7	space	space	NOUN
ejpam-6583	53	8	sum	sum	NOUN
ejpam-6583	53	9	of	of	ADP
ejpam-6583	53	10	the	the	DET
ejpam-6583	53	11	real	real	ADJ
ejpam-6583	53	12	vector	vector	NOUN
ejpam-6583	53	13	spaces	space	NOUN
ejpam-6583	53	14	r1	r1	NOUN
ejpam-6583	53	15	,	,	PUNCT
ejpam-6583	53	16	.	.	PUNCT
ejpam-6583	53	17	.	.	PUNCT
ejpam-6583	54	1	.	.	PUNCT
ejpam-6583	55	1	,	,	PUNCT
ejpam-6583	55	2	rd	rd	NOUN
ejpam-6583	55	3	in	in	ADP
ejpam-6583	55	4	a	a	DET
ejpam-6583	55	5	nonempty	nonempty	ADJ
ejpam-6583	55	6	finite	finite	ADJ
ejpam-6583	55	7	ordered	order	VERB
ejpam-6583	55	8	list	list	NOUN
ejpam-6583	55	9	is	be	AUX
ejpam-6583	55	10	the	the	DET
ejpam-6583	55	11	real	real	ADJ
ejpam-6583	55	12	vector	vector	NOUN
ejpam-6583	55	13	space	space	NOUN
ejpam-6583	55	14	whose	whose	DET
ejpam-6583	55	15	underlying	underlying	ADJ
ejpam-6583	55	16	set	set	NOUN
ejpam-6583	55	17	is	be	AUX
ejpam-6583	55	18	the	the	DET
ejpam-6583	55	19	cartesian	cartesian	ADJ
ejpam-6583	55	20	product	product	NOUN
ejpam-6583	55	21	r1	r1	NOUN
ejpam-6583	55	22	×	×	NOUN
ejpam-6583	55	23	·	·	PUNCT
ejpam-6583	55	24	·	·	PUNCT
ejpam-6583	55	25	·	·	PUNCT
ejpam-6583	56	1	×	×	NUM
ejpam-6583	56	2	rd	rd	NOUN
ejpam-6583	56	3	=	=	PUNCT
ejpam-6583	56	4	∏d	∏d	ADP
ejpam-6583	56	5	i=1ri	i=1ri	NUM
ejpam-6583	56	6	,	,	PUNCT
ejpam-6583	56	7	with	with	ADP
ejpam-6583	56	8	vector	vector	NOUN
ejpam-6583	56	9	space	space	NOUN
ejpam-6583	56	10	operations	operation	NOUN
ejpam-6583	56	11	defined	define	VERB
ejpam-6583	56	12	by	by	ADP
ejpam-6583	56	13	the	the	DET
ejpam-6583	56	14	following	follow	VERB
ejpam-6583	56	15	formulas	formula	NOUN
ejpam-6583	56	16	:	:	PUNCT
ejpam-6583	56	17	(	(	PUNCT
ejpam-6583	56	18	x1	x1	PROPN
ejpam-6583	56	19	,	,	PUNCT
ejpam-6583	56	20	x2	x2	PROPN
ejpam-6583	56	21	,	,	PUNCT
ejpam-6583	56	22	·	·	PUNCT
ejpam-6583	56	23	·	·	PUNCT
ejpam-6583	56	24	·	·	PUNCT
ejpam-6583	56	25	,	,	PUNCT
ejpam-6583	56	26	xd	xd	ADP
ejpam-6583	56	27	)	)	PUNCT
ejpam-6583	56	28	+	+	CCONJ
ejpam-6583	56	29	(	(	PUNCT
ejpam-6583	56	30	y1	y1	INTJ
ejpam-6583	56	31	,	,	PUNCT
ejpam-6583	56	32	y2	y2	PROPN
ejpam-6583	56	33	,	,	PUNCT
ejpam-6583	56	34	·	·	PUNCT
ejpam-6583	56	35	·	·	PUNCT
ejpam-6583	56	36	·	·	PUNCT
ejpam-6583	56	37	,	,	PUNCT
ejpam-6583	56	38	yd	yd	NOUN
ejpam-6583	56	39	)	)	PUNCT
ejpam-6583	56	40	=	=	SYM
ejpam-6583	56	41	(	(	PUNCT
ejpam-6583	56	42	x1	x1	PROPN
ejpam-6583	56	43	+	+	NUM
ejpam-6583	56	44	y1	y1	NOUN
ejpam-6583	56	45	,	,	PUNCT
ejpam-6583	56	46	x2	x2	PROPN
ejpam-6583	56	47	+	+	CCONJ
ejpam-6583	56	48	y2	y2	PROPN
ejpam-6583	56	49	,	,	PUNCT
ejpam-6583	56	50	·	·	PUNCT
ejpam-6583	56	51	·	·	PUNCT
ejpam-6583	56	52	·	·	PUNCT
ejpam-6583	56	53	,	,	PUNCT
ejpam-6583	56	54	xd	xd	INTJ
ejpam-6583	56	55	+	+	NUM
ejpam-6583	56	56	yd	yd	NOUN
ejpam-6583	56	57	)	)	PUNCT
ejpam-6583	56	58	.	.	PUNCT
ejpam-6583	57	1	α(x1	α(x1	ADJ
ejpam-6583	57	2	,	,	PUNCT
ejpam-6583	57	3	x2	x2	PROPN
ejpam-6583	57	4	,	,	PUNCT
ejpam-6583	57	5	·	·	PUNCT
ejpam-6583	57	6	·	·	PUNCT
ejpam-6583	57	7	·	·	PUNCT
ejpam-6583	57	8	,	,	PUNCT
ejpam-6583	57	9	xd	xd	ADP
ejpam-6583	57	10	)	)	PUNCT
ejpam-6583	57	11	=	=	SYM
ejpam-6583	57	12	(	(	PUNCT
ejpam-6583	57	13	αx1	αx1	PROPN
ejpam-6583	57	14	,	,	PUNCT
ejpam-6583	57	15	αx2	αx2	NOUN
ejpam-6583	57	16	,	,	PUNCT
ejpam-6583	57	17	·	·	PUNCT
ejpam-6583	57	18	·	·	PUNCT
ejpam-6583	57	19	·	·	PUNCT
ejpam-6583	57	20	,	,	PUNCT
ejpam-6583	57	21	αxd	αxd	NUM
ejpam-6583	57	22	)	)	PUNCT
ejpam-6583	57	23	.	.	PUNCT
ejpam-6583	58	1	definition	definition	NOUN
ejpam-6583	58	2	1	1	NUM
ejpam-6583	58	3	.	.	PUNCT
ejpam-6583	59	1	[	[	X
ejpam-6583	59	2	22	22	NUM
ejpam-6583	59	3	]	]	PUNCT
ejpam-6583	59	4	the	the	DET
ejpam-6583	59	5	direct	direct	ADJ
ejpam-6583	59	6	sum	sum	NOUN
ejpam-6583	59	7	,	,	PUNCT
ejpam-6583	59	8	or	or	CCONJ
ejpam-6583	59	9	external	external	ADJ
ejpam-6583	59	10	direct	direct	ADJ
ejpam-6583	59	11	sum	sum	NOUN
ejpam-6583	59	12	,	,	PUNCT
ejpam-6583	59	13	of	of	ADP
ejpam-6583	59	14	a	a	DET
ejpam-6583	59	15	family	family	NOUN
ejpam-6583	59	16	(	(	PUNCT
ejpam-6583	59	17	ri)i∈i	ri)i∈i	NUM
ejpam-6583	59	18	is	be	AUX
ejpam-6583	59	19	the	the	DET
ejpam-6583	59	20	following	follow	VERB
ejpam-6583	59	21	sub	sub	NOUN
ejpam-6583	59	22	-	-	NOUN
ejpam-6583	59	23	module	module	NOUN
ejpam-6583	59	24	of	of	ADP
ejpam-6583	59	25	∏	∏	PROPN
ejpam-6583	59	26	i∈i	i∈i	ADJ
ejpam-6583	59	27	ri	ri	NOUN
ejpam-6583	59	28	:	:	PUNCT
ejpam-6583	59	29	r⊕i	r⊕i	NOUN
ejpam-6583	59	30	=	=	SYM
ejpam-6583	59	31	⊕	⊕	PROPN
ejpam-6583	59	32	i∈i	i∈i	ADJ
ejpam-6583	59	33	ri	ri	PROPN
ejpam-6583	60	1	=	=	PUNCT
ejpam-6583	60	2	{	{	PUNCT
ejpam-6583	60	3	(	(	PUNCT
ejpam-6583	60	4	xi)i∈i	xi)i∈i	NUM
ejpam-6583	60	5	∈	∈	PROPN
ejpam-6583	60	6	∏	∏	PROPN
ejpam-6583	60	7	i∈i	i∈i	NOUN
ejpam-6583	60	8	ri	ri	PROPN
ejpam-6583	61	1	|	|	ADV
ejpam-6583	61	2	xi	xi	VERB
ejpam-6583	62	1	=	=	NOUN
ejpam-6583	62	2	0	0	NUM
ejpam-6583	63	1	for	for	ADP
ejpam-6583	63	2	almost	almost	ADV
ejpam-6583	63	3	all	all	PRON
ejpam-6583	63	4	i	i	PRON
ejpam-6583	63	5	∈	∈	VERB
ejpam-6583	63	6	i	i	PRON
ejpam-6583	63	7	}	}	PUNCT
ejpam-6583	63	8	.	.	PUNCT
ejpam-6583	64	1	immediately	immediately	ADV
ejpam-6583	64	2	,	,	PUNCT
ejpam-6583	64	3	this	this	PRON
ejpam-6583	64	4	defines	define	VERB
ejpam-6583	64	5	a	a	DET
ejpam-6583	64	6	sub	sub	NOUN
ejpam-6583	64	7	-	-	NOUN
ejpam-6583	64	8	module	module	NOUN
ejpam-6583	64	9	.	.	PUNCT
ejpam-6583	65	1	if	if	SCONJ
ejpam-6583	65	2	i	i	PRON
ejpam-6583	65	3	=	=	SYM
ejpam-6583	65	4	∅	∅	NOUN
ejpam-6583	65	5	,	,	PUNCT
ejpam-6583	65	6	then	then	ADV
ejpam-6583	65	7	⊕	⊕	PROPN
ejpam-6583	65	8	i∈i	i∈i	ADJ
ejpam-6583	65	9	ri	ri	PROPN
ejpam-6583	66	1	=	=	NOUN
ejpam-6583	66	2	0	0	PROPN
ejpam-6583	66	3	.	.	PUNCT
ejpam-6583	67	1	if	if	SCONJ
ejpam-6583	67	2	i	i	PRON
ejpam-6583	67	3	=	=	PUNCT
ejpam-6583	67	4	{	{	PUNCT
ejpam-6583	67	5	1	1	NUM
ejpam-6583	67	6	}	}	PUNCT
ejpam-6583	67	7	,	,	PUNCT
ejpam-6583	67	8	then	then	ADV
ejpam-6583	67	9	⊕	⊕	PROPN
ejpam-6583	67	10	i∈i	i∈i	ADJ
ejpam-6583	67	11	ri	ri	PROPN
ejpam-6583	68	1	=	=	PROPN
ejpam-6583	68	2	r1	r1	PROPN
ejpam-6583	68	3	.	.	PUNCT
ejpam-6583	69	1	if	if	SCONJ
ejpam-6583	69	2	i	i	PRON
ejpam-6583	69	3	=	=	PUNCT
ejpam-6583	69	4	{	{	PUNCT
ejpam-6583	69	5	1	1	NUM
ejpam-6583	69	6	,	,	PUNCT
ejpam-6583	69	7	2	2	NUM
ejpam-6583	69	8	,	,	PUNCT
ejpam-6583	69	9	·	·	PUNCT
ejpam-6583	69	10	·	·	PUNCT
ejpam-6583	69	11	·	·	PUNCT
ejpam-6583	69	12	,	,	PUNCT
ejpam-6583	69	13	d	d	X
ejpam-6583	69	14	}	}	PUNCT
ejpam-6583	69	15	,	,	PUNCT
ejpam-6583	69	16	then	then	ADV
ejpam-6583	69	17	⊕	⊕	PROPN
ejpam-6583	69	18	i∈i	i∈i	ADJ
ejpam-6583	69	19	ri	ri	PROPN
ejpam-6583	69	20	is	be	AUX
ejpam-6583	69	21	also	also	ADV
ejpam-6583	69	22	denoted	denote	VERB
ejpam-6583	69	23	by	by	ADP
ejpam-6583	69	24	r1	r1	PROPN
ejpam-6583	69	25	⊕	⊕	PROPN
ejpam-6583	69	26	r2	r2	PROPN
ejpam-6583	69	27	⊕	⊕	PROPN
ejpam-6583	69	28	r3	r3	PROPN
ejpam-6583	69	29	⊕	⊕	PROPN
ejpam-6583	69	30	·	·	PUNCT
ejpam-6583	69	31	·	·	PUNCT
ejpam-6583	70	1	·	·	PUNCT
ejpam-6583	70	2	⊕	⊕	PROPN
ejpam-6583	70	3	rd	rd	NOUN
ejpam-6583	71	1	=	=	PUNCT
ejpam-6583	71	2	⊕∑d	⊕∑d	NOUN
ejpam-6583	71	3	i=1ri	i=1ri	NUM
ejpam-6583	71	4	,	,	PUNCT
ejpam-6583	71	5	and	and	CCONJ
ejpam-6583	71	6	coincides	coincide	VERB
ejpam-6583	71	7	with	with	ADP
ejpam-6583	71	8	r1	r1	PROPN
ejpam-6583	71	9	×	×	PROPN
ejpam-6583	71	10	r2	r2	PROPN
ejpam-6583	71	11	×	×	PROPN
ejpam-6583	71	12	·	·	PUNCT
ejpam-6583	71	13	·	·	PUNCT
ejpam-6583	71	14	·	·	PUNCT
ejpam-6583	71	15	×	×	PROPN
ejpam-6583	71	16	rd	rd	PROPN
ejpam-6583	71	17	.	.	PUNCT
ejpam-6583	72	1	the	the	DET
ejpam-6583	72	2	direct	direct	ADJ
ejpam-6583	72	3	sum	sum	NOUN
ejpam-6583	72	4	⊕	⊕	PROPN
ejpam-6583	72	5	i∈i	i∈i	ADJ
ejpam-6583	72	6	ri	ri	PROPN
ejpam-6583	72	7	comes	come	VERB
ejpam-6583	72	8	with	with	ADP
ejpam-6583	72	9	an	an	DET
ejpam-6583	72	10	injection	injection	NOUN
ejpam-6583	72	11	ιj	ιj	ADP
ejpam-6583	72	12	:	:	PUNCT
ejpam-6583	72	13	rj	rj	PROPN
ejpam-6583	72	14	→	→	SYM
ejpam-6583	72	15	⊕	⊕	PROPN
ejpam-6583	72	16	i∈i	i∈i	ADJ
ejpam-6583	72	17	ri	ri	NOUN
ejpam-6583	72	18	for	for	ADP
ejpam-6583	72	19	every	every	DET
ejpam-6583	72	20	j	j	PROPN
ejpam-6583	72	21	∈	∈	PROPN
ejpam-6583	73	1	i	i	PRON
ejpam-6583	73	2	,	,	PUNCT
ejpam-6583	73	3	defined	define	VERB
ejpam-6583	73	4	by	by	ADP
ejpam-6583	73	5	its	its	PRON
ejpam-6583	73	6	components	component	NOUN
ejpam-6583	73	7	:	:	PUNCT
ejpam-6583	73	8	for	for	ADP
ejpam-6583	73	9	all	all	DET
ejpam-6583	73	10	xj	xj	PROPN
ejpam-6583	73	11	∈	∈	PROPN
ejpam-6583	73	12	rj	rj	PROPN
ejpam-6583	73	13	,	,	PUNCT
ejpam-6583	73	14	ιj(x)j	ιj(x)j	PUNCT
ejpam-6583	73	15	=	=	PUNCT
ejpam-6583	73	16	x	x	SYM
ejpam-6583	73	17	∈	∈	PROPN
ejpam-6583	73	18	rj	rj	PROPN
ejpam-6583	73	19	,	,	PUNCT
ejpam-6583	73	20	ιj(x)i	ιj(x)i	PUNCT
ejpam-6583	73	21	=	=	SYM
ejpam-6583	73	22	0	0	NUM
ejpam-6583	73	23	∈	∈	PROPN
ejpam-6583	73	24	ri	ri	NOUN
ejpam-6583	73	25	for	for	ADP
ejpam-6583	73	26	all	all	PRON
ejpam-6583	73	27	i	i	PRON
ejpam-6583	73	28	̸=	̸=	PROPN
ejpam-6583	73	29	j	j	PROPN
ejpam-6583	73	30	,	,	PUNCT
ejpam-6583	73	31	every	every	DET
ejpam-6583	73	32	ιj	ιj	NOUN
ejpam-6583	73	33	is	be	AUX
ejpam-6583	73	34	an	an	DET
ejpam-6583	73	35	injective	injective	ADJ
ejpam-6583	73	36	homomorphism	homomorphism	NOUN
ejpam-6583	73	37	.	.	PUNCT
ejpam-6583	74	1	if	if	SCONJ
ejpam-6583	74	2	r1	r1	PROPN
ejpam-6583	74	3	,	,	PUNCT
ejpam-6583	74	4	.	.	PUNCT
ejpam-6583	74	5	.	.	PUNCT
ejpam-6583	74	6	.	.	PUNCT
ejpam-6583	75	1	,	,	PUNCT
ejpam-6583	75	2	rd	rd	PROPN
ejpam-6583	75	3	are	be	AUX
ejpam-6583	75	4	normed	normed	ADJ
ejpam-6583	75	5	spaces	space	NOUN
ejpam-6583	75	6	,	,	PUNCT
ejpam-6583	75	7	their	their	PRON
ejpam-6583	75	8	vector	vector	NOUN
ejpam-6583	75	9	space	space	NOUN
ejpam-6583	75	10	sum	sum	NOUN
ejpam-6583	75	11	can	can	AUX
ejpam-6583	75	12	be	be	AUX
ejpam-6583	75	13	equipped	equip	VERB
ejpam-6583	75	14	with	with	ADP
ejpam-6583	75	15	a	a	DET
ejpam-6583	75	16	norm	norm	NOUN
ejpam-6583	75	17	inspired	inspire	VERB
ejpam-6583	75	18	by	by	ADP
ejpam-6583	75	19	the	the	DET
ejpam-6583	75	20	norm	norm	NOUN
ejpam-6583	75	21	of	of	ADP
ejpam-6583	75	22	the	the	DET
ejpam-6583	75	23	euclidean	euclidean	ADJ
ejpam-6583	75	24	n	n	PRON
ejpam-6583	75	25	space	space	NOUN
ejpam-6583	75	26	.	.	PUNCT
ejpam-6583	76	1	specifically	specifically	ADV
ejpam-6583	76	2	,	,	PUNCT
ejpam-6583	76	3	a	a	DET
ejpam-6583	76	4	norm	norm	NOUN
ejpam-6583	76	5	on	on	ADP
ejpam-6583	76	6	the	the	DET
ejpam-6583	76	7	vector	vector	NOUN
ejpam-6583	76	8	space	space	NOUN
ejpam-6583	76	9	sum	sum	NOUN
ejpam-6583	76	10	can	can	AUX
ejpam-6583	76	11	be	be	AUX
ejpam-6583	76	12	defined	define	VERB
ejpam-6583	76	13	in	in	ADP
ejpam-6583	76	14	a	a	DET
ejpam-6583	76	15	way	way	NOUN
ejpam-6583	76	16	that	that	PRON
ejpam-6583	76	17	resembles	resemble	VERB
ejpam-6583	76	18	the	the	DET
ejpam-6583	76	19	standard	standard	ADJ
ejpam-6583	76	20	euclidean	euclidean	ADJ
ejpam-6583	76	21	norm	norm	NOUN
ejpam-6583	76	22	.	.	PUNCT
ejpam-6583	77	1	definition	definition	NOUN
ejpam-6583	77	2	2	2	NUM
ejpam-6583	77	3	.	.	PUNCT
ejpam-6583	78	1	let	let	VERB
ejpam-6583	78	2	r1	r1	PROPN
ejpam-6583	78	3	,	,	PUNCT
ejpam-6583	78	4	·	·	PUNCT
ejpam-6583	78	5	·	·	PUNCT
ejpam-6583	78	6	·	·	PUNCT
ejpam-6583	78	7	,	,	PUNCT
ejpam-6583	78	8	rd	rd	NOUN
ejpam-6583	78	9	be	be	AUX
ejpam-6583	78	10	a	a	DET
ejpam-6583	78	11	normed	normed	ADJ
ejpam-6583	78	12	space	space	NOUN
ejpam-6583	78	13	with	with	ADP
ejpam-6583	78	14	respective	respective	ADJ
ejpam-6583	78	15	norms	norm	NOUN
ejpam-6583	79	1	|	|	ADV
ejpam-6583	79	2	·	·	PUNCT
ejpam-6583	79	3	|r1	|r1	NOUN
ejpam-6583	79	4	,	,	PUNCT
ejpam-6583	79	5	·	·	PUNCT
ejpam-6583	79	6	·	·	PUNCT
ejpam-6583	79	7	·	·	PUNCT
ejpam-6583	79	8	,	,	PUNCT
ejpam-6583	79	9	|	|	ADV
ejpam-6583	79	10	·	·	PUNCT
ejpam-6583	79	11	|rd	|rd	PRON
ejpam-6583	79	12	is	be	AUX
ejpam-6583	79	13	the	the	DET
ejpam-6583	79	14	normed	normed	ADJ
ejpam-6583	79	15	space	space	NOUN
ejpam-6583	79	16	whose	whose	DET
ejpam-6583	79	17	underlying	underlie	VERB
ejpam-6583	79	18	vector	vector	NOUN
ejpam-6583	79	19	space	space	NOUN
ejpam-6583	79	20	is	be	AUX
ejpam-6583	79	21	the	the	DET
ejpam-6583	79	22	vector	vector	NOUN
ejpam-6583	79	23	space	space	NOUN
ejpam-6583	79	24	sum	sum	NOUN
ejpam-6583	79	25	of	of	ADP
ejpam-6583	79	26	r1	r1	PROPN
ejpam-6583	79	27	,	,	PUNCT
ejpam-6583	79	28	·	·	PUNCT
ejpam-6583	79	29	·	·	PUNCT
ejpam-6583	79	30	·	·	PUNCT
ejpam-6583	79	31	,	,	PUNCT
ejpam-6583	79	32	rd	rd	PROPN
ejpam-6583	79	33	g.	g.	PROPN
ejpam-6583	79	34	albeladi	albeladi	PROPN
ejpam-6583	79	35	,	,	PUNCT
ejpam-6583	79	36	s.	s.	PROPN
ejpam-6583	79	37	omran	omran	PROPN
ejpam-6583	79	38	/	/	SYM
ejpam-6583	79	39	eur	eur	PROPN
ejpam-6583	79	40	.	.	PUNCT
ejpam-6583	80	1	j.	j.	PROPN
ejpam-6583	80	2	pure	pure	PROPN
ejpam-6583	80	3	appl	appl	PROPN
ejpam-6583	80	4	.	.	PROPN
ejpam-6583	80	5	math	math	PROPN
ejpam-6583	80	6	,	,	PUNCT
ejpam-6583	80	7	18	18	NUM
ejpam-6583	80	8	(	(	PUNCT
ejpam-6583	80	9	3	3	NUM
ejpam-6583	80	10	)	)	PUNCT
ejpam-6583	80	11	(	(	PUNCT
ejpam-6583	80	12	2025	2025	NUM
ejpam-6583	80	13	)	)	PUNCT
ejpam-6583	80	14	,	,	PUNCT
ejpam-6583	80	15	6583	6583	NUM
ejpam-6583	80	16	4	4	NUM
ejpam-6583	80	17	of	of	ADP
ejpam-6583	80	18	27	27	NUM
ejpam-6583	80	19	and	and	CCONJ
ejpam-6583	80	20	whose	whose	DET
ejpam-6583	80	21	norm	norm	NOUN
ejpam-6583	80	22	is	be	AUX
ejpam-6583	80	23	the	the	DET
ejpam-6583	80	24	direct	direct	ADJ
ejpam-6583	80	25	sum	sum	NOUN
ejpam-6583	80	26	norm	norm	NOUN
ejpam-6583	80	27	given	give	VERB
ejpam-6583	80	28	by	by	ADP
ejpam-6583	80	29	the	the	DET
ejpam-6583	80	30	formula	formula	NOUN
ejpam-6583	80	31	∥(x1	∥(x1	NOUN
ejpam-6583	80	32	,	,	PUNCT
ejpam-6583	80	33	·	·	PUNCT
ejpam-6583	80	34	·	·	PUNCT
ejpam-6583	80	35	·	·	PUNCT
ejpam-6583	80	36	,	,	PUNCT
ejpam-6583	80	37	xn)∥	xn)∥	PUNCT
ejpam-6583	81	1	=	=	SYM
ejpam-6583	81	2			PROPN
ejpam-6583	81	3	n∑	n∑	PROPN
ejpam-6583	81	4	j=1	j=1	NOUN
ejpam-6583	81	5	|	|	ADV
ejpam-6583	81	6	xj	xj	PROPN
ejpam-6583	81	7	|2rj	|2rj	VERB
ejpam-6583	81	8			PROPN
ejpam-6583	81	9	1	1	NUM
ejpam-6583	81	10	2	2	NUM
ejpam-6583	81	11	.	.	PUNCT
ejpam-6583	82	1	this	this	DET
ejpam-6583	82	2	normed	normed	PROPN
ejpam-6583	82	3	space	space	NOUN
ejpam-6583	82	4	is	be	AUX
ejpam-6583	82	5	dented	dent	VERB
ejpam-6583	82	6	by	by	ADP
ejpam-6583	82	7	r1	r1	PROPN
ejpam-6583	82	8	⊕	⊕	PROPN
ejpam-6583	82	9	·	·	PUNCT
ejpam-6583	82	10	·	·	PUNCT
ejpam-6583	82	11	·	·	PUNCT
ejpam-6583	82	12	⊕	⊕	PROPN
ejpam-6583	82	13	rd	rd	PROPN
ejpam-6583	82	14	.	.	PUNCT
ejpam-6583	83	1	corolary	corolary	ADJ
ejpam-6583	83	2	1	1	X
ejpam-6583	83	3	.	.	X
ejpam-6583	83	4	for	for	ADP
ejpam-6583	83	5	any	any	DET
ejpam-6583	83	6	two	two	NUM
ejpam-6583	83	7	spaces	space	NOUN
ejpam-6583	83	8	a	a	PRON
ejpam-6583	83	9	and	and	CCONJ
ejpam-6583	83	10	b	b	NOUN
ejpam-6583	83	11	,	,	PUNCT
ejpam-6583	83	12	the	the	DET
ejpam-6583	83	13	direct	direct	ADJ
ejpam-6583	83	14	sum	sum	NOUN
ejpam-6583	83	15	can	can	AUX
ejpam-6583	83	16	be	be	AUX
ejpam-6583	83	17	defined	define	VERB
ejpam-6583	83	18	as	as	ADP
ejpam-6583	83	19	a	a	DET
ejpam-6583	83	20	homomorphism	homomorphism	NOUN
ejpam-6583	83	21	f	f	X
ejpam-6583	83	22	:	:	PUNCT
ejpam-6583	83	23	a⊕b	a⊕b	PROPN
ejpam-6583	83	24	→ms	→ms	X
ejpam-6583	83	25	,	,	PUNCT
ejpam-6583	83	26	where	where	SCONJ
ejpam-6583	83	27	the	the	DET
ejpam-6583	83	28	matrix	matrix	NOUN
ejpam-6583	83	29	ms	ms	NOUN
ejpam-6583	83	30	of	of	ADP
ejpam-6583	83	31	size	size	NOUN
ejpam-6583	83	32	s	s	PROPN
ejpam-6583	83	33	,	,	PUNCT
ejpam-6583	83	34	given	give	VERB
ejpam-6583	83	35	by	by	ADP
ejpam-6583	83	36	:	:	PUNCT
ejpam-6583	83	37	f	f	PROPN
ejpam-6583	83	38	(	(	PUNCT
ejpam-6583	83	39	a	a	DET
ejpam-6583	83	40	,	,	PUNCT
ejpam-6583	83	41	b	b	NOUN
ejpam-6583	83	42	)	)	PUNCT
ejpam-6583	83	43	=	=	X
ejpam-6583	83	44	a⊕b	a⊕b	NOUN
ejpam-6583	83	45	=	=	SYM
ejpam-6583	83	46	(	(	PUNCT
ejpam-6583	83	47	a	a	DET
ejpam-6583	83	48	0	0	NUM
ejpam-6583	83	49	0	0	NUM
ejpam-6583	83	50	b	b	NOUN
ejpam-6583	83	51	)	)	PUNCT
ejpam-6583	83	52	,	,	PUNCT
ejpam-6583	83	53	where	where	SCONJ
ejpam-6583	83	54	a	a	PRON
ejpam-6583	83	55	and	and	CCONJ
ejpam-6583	83	56	b	b	NOUN
ejpam-6583	83	57	are	be	AUX
ejpam-6583	83	58	embedded	embed	VERB
ejpam-6583	83	59	as	as	ADP
ejpam-6583	83	60	diagonal	diagonal	ADJ
ejpam-6583	83	61	blocks	block	NOUN
ejpam-6583	83	62	in	in	ADP
ejpam-6583	83	63	the	the	DET
ejpam-6583	83	64	matrix	matrix	NOUN
ejpam-6583	83	65	form	form	NOUN
ejpam-6583	83	66	,	,	PUNCT
ejpam-6583	83	67	and	and	CCONJ
ejpam-6583	83	68	0	0	NUM
ejpam-6583	83	69	represents	represents	AUX
ejpam-6583	83	70	appropriately	appropriately	ADV
ejpam-6583	83	71	sized	size	VERB
ejpam-6583	83	72	zero	zero	NUM
ejpam-6583	83	73	matrices	matrix	NOUN
ejpam-6583	83	74	.	.	PUNCT
ejpam-6583	84	1	theorem	theorem	NOUN
ejpam-6583	84	2	1	1	NUM
ejpam-6583	84	3	.	.	PUNCT
ejpam-6583	85	1	[	[	X
ejpam-6583	85	2	23	23	NUM
ejpam-6583	85	3	]	]	PUNCT
ejpam-6583	85	4	let	let	VERB
ejpam-6583	85	5	r1,r2	r1,r2	PROPN
ejpam-6583	85	6	,	,	PUNCT
ejpam-6583	85	7	·	·	PUNCT
ejpam-6583	85	8	·	·	PUNCT
ejpam-6583	85	9	·	·	PUNCT
ejpam-6583	85	10	,	,	PUNCT
ejpam-6583	85	11	rd	rd	NOUN
ejpam-6583	85	12	be	be	AUX
ejpam-6583	85	13	a	a	DET
ejpam-6583	85	14	family	family	NOUN
ejpam-6583	85	15	of	of	ADP
ejpam-6583	85	16	sets	set	NOUN
ejpam-6583	85	17	of	of	ADP
ejpam-6583	85	18	all	all	DET
ejpam-6583	85	19	real	real	ADJ
ejpam-6583	85	20	numbers	number	NOUN
ejpam-6583	85	21	.	.	PUNCT
ejpam-6583	86	1	then	then	ADV
ejpam-6583	86	2	the	the	DET
ejpam-6583	86	3	following	follow	VERB
ejpam-6583	86	4	are	be	AUX
ejpam-6583	86	5	equivalent	equivalent	ADJ
ejpam-6583	86	6	:	:	PUNCT
ejpam-6583	86	7	1	1	X
ejpam-6583	86	8	.	.	PUNCT
ejpam-6583	86	9	r⊕d	r⊕d	NOUN
ejpam-6583	86	10	=	=	PUNCT
ejpam-6583	87	1	⊕∑d	⊕∑d	NOUN
ejpam-6583	87	2	i=1ri	i=1ri	PUNCT
ejpam-6583	87	3	is	be	AUX
ejpam-6583	87	4	a	a	DET
ejpam-6583	87	5	direct	direct	ADJ
ejpam-6583	87	6	sum	sum	NOUN
ejpam-6583	87	7	.	.	PUNCT
ejpam-6583	88	1	2	2	X
ejpam-6583	88	2	.	.	X
ejpam-6583	89	1	if	if	SCONJ
ejpam-6583	89	2	0	0	NUM
ejpam-6583	89	3	=	=	SYM
ejpam-6583	89	4	∑d	∑d	X
ejpam-6583	89	5	i=1	i=1	X
ejpam-6583	89	6	xi	xi	PROPN
ejpam-6583	89	7	,	,	PUNCT
ejpam-6583	89	8	xi	xi	PROPN
ejpam-6583	89	9	∈	∈	PROPN
ejpam-6583	89	10	ri	ri	PROPN
ejpam-6583	89	11	,	,	PUNCT
ejpam-6583	89	12	then	then	ADV
ejpam-6583	89	13	xi	xi	PROPN
ejpam-6583	89	14	=	=	SYM
ejpam-6583	89	15	0	0	PROPN
ejpam-6583	89	16	,	,	PUNCT
ejpam-6583	89	17	i	i	PRON
ejpam-6583	89	18	=	=	NOUN
ejpam-6583	89	19	1	1	NUM
ejpam-6583	89	20	,	,	PUNCT
ejpam-6583	89	21	2	2	NUM
ejpam-6583	89	22	,	,	PUNCT
ejpam-6583	89	23	·	·	PUNCT
ejpam-6583	89	24	·	·	PUNCT
ejpam-6583	89	25	·	·	PUNCT
ejpam-6583	89	26	,	,	PUNCT
ejpam-6583	89	27	d.	d.	PROPN
ejpam-6583	89	28	3	3	NUM
ejpam-6583	89	29	.	.	PUNCT
ejpam-6583	89	30	ri	ri	PROPN
ejpam-6583	89	31	∩	∩	NOUN
ejpam-6583	89	32	⊕∑d	⊕∑d	PART
ejpam-6583	89	33	j=1	j=1	PROPN
ejpam-6583	89	34	,	,	PUNCT
ejpam-6583	89	35	j	j	PROPN
ejpam-6583	89	36	̸=irj	̸=irj	NOUN
ejpam-6583	89	37	=	=	NOUN
ejpam-6583	89	38	0̃	0̃	NOUN
ejpam-6583	89	39	,	,	PUNCT
ejpam-6583	89	40	i	i	PRON
ejpam-6583	89	41	=	=	NOUN
ejpam-6583	89	42	1	1	NUM
ejpam-6583	89	43	,	,	PUNCT
ejpam-6583	89	44	2	2	NUM
ejpam-6583	89	45	,	,	PUNCT
ejpam-6583	89	46	·	·	PUNCT
ejpam-6583	89	47	·	·	PUNCT
ejpam-6583	89	48	·	·	PUNCT
ejpam-6583	89	49	,	,	PUNCT
ejpam-6583	89	50	d.	d.	PROPN
ejpam-6583	89	51	theorem	theorem	VERB
ejpam-6583	89	52	2	2	NUM
ejpam-6583	89	53	.	.	PUNCT
ejpam-6583	90	1	[	[	X
ejpam-6583	90	2	23	23	NUM
ejpam-6583	90	3	]	]	PUNCT
ejpam-6583	90	4	let	let	VERB
ejpam-6583	90	5	r1,r2	r1,r2	PROPN
ejpam-6583	90	6	,	,	PUNCT
ejpam-6583	90	7	·	·	PUNCT
ejpam-6583	90	8	·	·	PUNCT
ejpam-6583	90	9	·	·	PUNCT
ejpam-6583	90	10	,	,	PUNCT
ejpam-6583	90	11	rd	rd	NOUN
ejpam-6583	90	12	be	be	AUX
ejpam-6583	90	13	a	a	DET
ejpam-6583	90	14	family	family	NOUN
ejpam-6583	90	15	of	of	ADP
ejpam-6583	90	16	sets	set	NOUN
ejpam-6583	90	17	of	of	ADP
ejpam-6583	90	18	all	all	DET
ejpam-6583	90	19	real	real	ADJ
ejpam-6583	90	20	numbers	number	NOUN
ejpam-6583	90	21	,	,	PUNCT
ejpam-6583	90	22	and	and	CCONJ
ejpam-6583	90	23	let	let	VERB
ejpam-6583	90	24	r1×	r1×	VERB
ejpam-6583	90	25	·	·	PUNCT
ejpam-6583	90	26	·	·	PUNCT
ejpam-6583	90	27	·	·	PUNCT
ejpam-6583	90	28	×rd	×rd	ADJ
ejpam-6583	90	29	=	=	SYM
ejpam-6583	90	30	∏d	∏d	ADP
ejpam-6583	90	31	i=1ri	i=1ri	X
ejpam-6583	90	32	be	be	AUX
ejpam-6583	90	33	their	their	PRON
ejpam-6583	90	34	direct	direct	ADJ
ejpam-6583	90	35	product	product	NOUN
ejpam-6583	90	36	.	.	PUNCT
ejpam-6583	91	1	let	let	AUX
ejpam-6583	91	2	r∗	r∗	VERB
ejpam-6583	91	3	i	i	PRON
ejpam-6583	91	4	=	=	PUNCT
ejpam-6583	91	5	{	{	PUNCT
ejpam-6583	91	6	(	(	PUNCT
ejpam-6583	91	7	,	,	PUNCT
ejpam-6583	91	8	·	·	PUNCT
ejpam-6583	91	9	·	·	PUNCT
ejpam-6583	91	10	·	·	PUNCT
ejpam-6583	91	11	,	,	PUNCT
ejpam-6583	91	12	0	0	NUM
ejpam-6583	91	13	,	,	PUNCT
ejpam-6583	91	14	xi	xi	PROPN
ejpam-6583	91	15	,	,	PUNCT
ejpam-6583	91	16	0	0	NUM
ejpam-6583	91	17	,	,	PUNCT
ejpam-6583	91	18	·	·	PUNCT
ejpam-6583	91	19	·	·	PUNCT
ejpam-6583	91	20	·	·	PUNCT
ejpam-6583	91	21	,	,	PUNCT
ejpam-6583	91	22	0)|	0)|	NOUN
ejpam-6583	91	23	xi	xi	ADP
ejpam-6583	91	24	∈	∈	PROPN
ejpam-6583	91	25	ri	ri	PROPN
ejpam-6583	91	26	}	}	PUNCT
ejpam-6583	91	27	.	.	PUNCT
ejpam-6583	92	1	then	then	ADV
ejpam-6583	92	2	r⊕d	r⊕d	VERB
ejpam-6583	92	3	=	=	SYM
ejpam-6583	92	4	⊕∑d	⊕∑d	PROPN
ejpam-6583	92	5	i=1r∗	i=1r∗	PROPN
ejpam-6583	93	1	i	i	PRON
ejpam-6583	93	2	is	be	AUX
ejpam-6583	93	3	a	a	DET
ejpam-6583	93	4	direct	direct	ADJ
ejpam-6583	93	5	sum	sum	NOUN
ejpam-6583	93	6	of	of	ADP
ejpam-6583	93	7	r∗	r∗	PROPN
ejpam-6583	94	1	i	i	PRON
ejpam-6583	94	2	.	.	PUNCT
ejpam-6583	95	1	we	we	PRON
ejpam-6583	95	2	recall	recall	VERB
ejpam-6583	95	3	some	some	DET
ejpam-6583	95	4	reminders	reminder	NOUN
ejpam-6583	95	5	and	and	CCONJ
ejpam-6583	95	6	auxiliary	auxiliary	ADJ
ejpam-6583	95	7	results	result	NOUN
ejpam-6583	95	8	that	that	PRON
ejpam-6583	95	9	will	will	AUX
ejpam-6583	95	10	be	be	AUX
ejpam-6583	95	11	used	use	VERB
ejpam-6583	95	12	throughout	throughout	ADP
ejpam-6583	95	13	this	this	DET
ejpam-6583	95	14	paper	paper	NOUN
ejpam-6583	95	15	.	.	PUNCT
ejpam-6583	96	1	let	let	VERB
ejpam-6583	96	2	rd	rd	NOUN
ejpam-6583	96	3	denotes	denote	VERB
ejpam-6583	96	4	the	the	DET
ejpam-6583	96	5	orthogonal	orthogonal	ADJ
ejpam-6583	96	6	direct	direct	ADJ
ejpam-6583	96	7	sum	sum	NOUN
ejpam-6583	96	8	r	r	NOUN
ejpam-6583	96	9	⊕	⊕	PROPN
ejpam-6583	96	10	r	r	PROPN
ejpam-6583	96	11	⊕	⊕	PROPN
ejpam-6583	96	12	·	·	PUNCT
ejpam-6583	96	13	·	·	PUNCT
ejpam-6583	96	14	·	·	PUNCT
ejpam-6583	97	1	⊕	⊕	NOUN
ejpam-6583	97	2	r	r	NOUN
ejpam-6583	97	3	of	of	ADP
ejpam-6583	97	4	d	d	NOUN
ejpam-6583	97	5	-	-	PUNCT
ejpam-6583	97	6	copies	copy	NOUN
ejpam-6583	97	7	of	of	ADP
ejpam-6583	97	8	r.	r.	PROPN
ejpam-6583	97	9	let	let	VERB
ejpam-6583	97	10	r⊕d	r⊕d	NOUN
ejpam-6583	97	11	be	be	AUX
ejpam-6583	97	12	the	the	DET
ejpam-6583	97	13	direct	direct	ADJ
ejpam-6583	97	14	sum	sum	NOUN
ejpam-6583	97	15	set	set	NOUN
ejpam-6583	97	16	,	,	PUNCT
ejpam-6583	97	17	and	and	CCONJ
ejpam-6583	97	18	x	x	X
ejpam-6583	97	19	,	,	PUNCT
ejpam-6583	97	20	y	y	PROPN
ejpam-6583	97	21	∈	∈	PROPN
ejpam-6583	97	22	r⊕d	r⊕d	VERB
ejpam-6583	97	23	,	,	PUNCT
ejpam-6583	97	24	x	x	SYM
ejpam-6583	97	25	=	=	SYM
ejpam-6583	97	26	(	(	PUNCT
ejpam-6583	97	27	x1	x1	PROPN
ejpam-6583	97	28	,	,	PUNCT
ejpam-6583	97	29	x2	x2	PROPN
ejpam-6583	97	30	,	,	PUNCT
ejpam-6583	97	31	·	·	PUNCT
ejpam-6583	97	32	·	·	PUNCT
ejpam-6583	97	33	·	·	PUNCT
ejpam-6583	97	34	,	,	PUNCT
ejpam-6583	97	35	xd	xd	ADP
ejpam-6583	97	36	)	)	PUNCT
ejpam-6583	97	37	,	,	PUNCT
ejpam-6583	97	38	y	y	PROPN
ejpam-6583	97	39	=	=	SYM
ejpam-6583	97	40	(	(	PUNCT
ejpam-6583	97	41	y1	y1	PROPN
ejpam-6583	97	42	,	,	PUNCT
ejpam-6583	97	43	y2	y2	PROPN
ejpam-6583	97	44	,	,	PUNCT
ejpam-6583	97	45	·	·	PUNCT
ejpam-6583	97	46	·	·	PUNCT
ejpam-6583	97	47	·	·	PUNCT
ejpam-6583	97	48	,	,	PUNCT
ejpam-6583	97	49	yd	yd	PROPN
ejpam-6583	97	50	)	)	PUNCT
ejpam-6583	97	51	by	by	ADP
ejpam-6583	97	52	x	x	PROPN
ejpam-6583	97	53	≾	≾	PROPN
ejpam-6583	97	54	y	y	PROPN
ejpam-6583	97	55	(	(	PUNCT
ejpam-6583	97	56	respectively	respectively	ADV
ejpam-6583	97	57	,	,	PUNCT
ejpam-6583	97	58	xi	xi	ADP
ejpam-6583	97	59	<	<	X
ejpam-6583	97	60	yi	yi	PROPN
ejpam-6583	97	61	)	)	PUNCT
ejpam-6583	97	62	for	for	ADP
ejpam-6583	97	63	all	all	DET
ejpam-6583	97	64	i	i	PRON
ejpam-6583	97	65	=	=	NOUN
ejpam-6583	97	66	1	1	NUM
ejpam-6583	97	67	,	,	PUNCT
ejpam-6583	97	68	2	2	NUM
ejpam-6583	97	69	,	,	PUNCT
ejpam-6583	97	70	·	·	PUNCT
ejpam-6583	98	1	·	·	PUNCT
ejpam-6583	98	2	·	·	PUNCT
ejpam-6583	98	3	d.	d.	NOUN
ejpam-6583	98	4	in	in	ADP
ejpam-6583	98	5	addition	addition	NOUN
ejpam-6583	98	6	,	,	PUNCT
ejpam-6583	98	7	r⊕d	r⊕d	NOUN
ejpam-6583	98	8	+	+	X
ejpam-6583	99	1	=	=	SYM
ejpam-6583	99	2	{	{	PUNCT
ejpam-6583	99	3	x	x	PUNCT
ejpam-6583	99	4	∈	∈	PROPN
ejpam-6583	99	5	r⊕d	r⊕d	NOUN
ejpam-6583	99	6	:	:	PUNCT
ejpam-6583	99	7	xi	xi	NUM
ejpam-6583	99	8	≥	≥	NOUN
ejpam-6583	99	9	0	0	NUM
ejpam-6583	99	10	,	,	PUNCT
ejpam-6583	99	11	∀i	∀i	NOUN
ejpam-6583	99	12	=	=	SYM
ejpam-6583	99	13	1	1	NUM
ejpam-6583	99	14	,	,	PUNCT
ejpam-6583	99	15	2	2	NUM
ejpam-6583	99	16	,	,	PUNCT
ejpam-6583	99	17	·	·	PUNCT
ejpam-6583	99	18	·	·	PUNCT
ejpam-6583	99	19	·	·	PUNCT
ejpam-6583	99	20	,	,	PUNCT
ejpam-6583	99	21	d	d	X
ejpam-6583	99	22	}	}	PUNCT
ejpam-6583	99	23	is	be	AUX
ejpam-6583	99	24	the	the	DET
ejpam-6583	99	25	set	set	NOUN
ejpam-6583	99	26	of	of	ADP
ejpam-6583	99	27	positive	positive	ADJ
ejpam-6583	99	28	elements	element	NOUN
ejpam-6583	99	29	in	in	ADP
ejpam-6583	99	30	r⊕d	r⊕d	NOUN
ejpam-6583	99	31	,	,	PUNCT
ejpam-6583	99	32	and	and	CCONJ
ejpam-6583	99	33	we	we	PRON
ejpam-6583	99	34	denote	denote	VERB
ejpam-6583	99	35	x	x	PUNCT
ejpam-6583	99	36	≿	≿	ADP
ejpam-6583	99	37	0̃	0̃	NOUN
ejpam-6583	99	38	if	if	SCONJ
ejpam-6583	99	39	xi	xi	X
ejpam-6583	99	40	≥	≥	NOUN
ejpam-6583	99	41	0	0	NUM
ejpam-6583	99	42	for	for	ADP
ejpam-6583	99	43	all	all	DET
ejpam-6583	99	44	i	i	PRON
ejpam-6583	99	45	=	=	NOUN
ejpam-6583	99	46	1	1	NUM
ejpam-6583	99	47	,	,	PUNCT
ejpam-6583	99	48	2	2	NUM
ejpam-6583	99	49	,	,	PUNCT
ejpam-6583	99	50	·	·	PUNCT
ejpam-6583	99	51	·	·	PUNCT
ejpam-6583	99	52	·	·	PUNCT
ejpam-6583	99	53	,	,	PUNCT
ejpam-6583	99	54	d	d	X
ejpam-6583	99	55	,	,	PUNCT
ejpam-6583	99	56	where	where	SCONJ
ejpam-6583	99	57	0̃	0̃	NOUN
ejpam-6583	99	58	is	be	AUX
ejpam-6583	99	59	the	the	DET
ejpam-6583	99	60	d×	d×	NOUN
ejpam-6583	99	61	d	d	NOUN
ejpam-6583	99	62	zero	zero	NUM
ejpam-6583	99	63	matrix	matrix	NOUN
ejpam-6583	99	64	in	in	ADP
ejpam-6583	99	65	r⊕d	r⊕d	NOUN
ejpam-6583	99	66	.	.	PUNCT
ejpam-6583	100	1	by	by	ADP
ejpam-6583	100	2	taking	take	VERB
ejpam-6583	100	3	the	the	DET
ejpam-6583	100	4	product	product	NOUN
ejpam-6583	100	5	of	of	ADP
ejpam-6583	100	6	two	two	NUM
ejpam-6583	100	7	square	square	ADJ
ejpam-6583	100	8	diagonal	diagonal	ADJ
ejpam-6583	100	9	matrices	matrix	NOUN
ejpam-6583	100	10	,	,	PUNCT
ejpam-6583	100	11	we	we	PRON
ejpam-6583	100	12	can	can	AUX
ejpam-6583	100	13	define	define	VERB
ejpam-6583	100	14	x	x	X
ejpam-6583	100	15	·	·	PUNCT
ejpam-6583	100	16	y	y	NOUN
ejpam-6583	100	17	as	as	SCONJ
ejpam-6583	100	18	follows	follow	VERB
ejpam-6583	100	19	:	:	PUNCT
ejpam-6583	100	20	x	x	X
ejpam-6583	100	21	·	·	PUNCT
ejpam-6583	100	22	y	y	X
ejpam-6583	100	23	=	=	PUNCT
ejpam-6583	100	24			PROPN
ejpam-6583	100	25	x1y1	x1y1	X
ejpam-6583	100	26	0	0	NUM
ejpam-6583	100	27	·	·	PUNCT
ejpam-6583	100	28	·	·	PUNCT
ejpam-6583	100	29	·	·	PUNCT
ejpam-6583	101	1	0	0	NUM
ejpam-6583	101	2	0	0	NUM
ejpam-6583	102	1	x2y2	x2y2	NUM
ejpam-6583	102	2	·	·	PUNCT
ejpam-6583	102	3	·	·	PUNCT
ejpam-6583	102	4	·	·	PUNCT
ejpam-6583	102	5	0	0	NUM
ejpam-6583	102	6	...	...	PUNCT
ejpam-6583	102	7	...	...	PUNCT
ejpam-6583	102	8	.	.	PUNCT
ejpam-6583	102	9	.	.	PUNCT
ejpam-6583	102	10	.	.	PUNCT
ejpam-6583	103	1	...	...	PUNCT
ejpam-6583	104	1	0	0	NUM
ejpam-6583	104	2	0	0	NUM
ejpam-6583	104	3	·	·	PUNCT
ejpam-6583	104	4	·	·	PUNCT
ejpam-6583	104	5	·	·	PUNCT
ejpam-6583	105	1	xdyd	xdyd	NOUN
ejpam-6583	105	2			NOUN
ejpam-6583	105	3	=	=	SYM
ejpam-6583	105	4	diag	diag	PROPN
ejpam-6583	105	5	(	(	PUNCT
ejpam-6583	105	6	x1y1	x1y1	X
ejpam-6583	105	7	,	,	PUNCT
ejpam-6583	105	8	x2y2	x2y2	X
ejpam-6583	105	9	,	,	PUNCT
ejpam-6583	105	10	·	·	PUNCT
ejpam-6583	105	11	·	·	PUNCT
ejpam-6583	105	12	·	·	PUNCT
ejpam-6583	105	13	,	,	PUNCT
ejpam-6583	105	14	xdyd	xdyd	X
ejpam-6583	105	15	)	)	PUNCT
ejpam-6583	105	16	∈	∈	PROPN
ejpam-6583	105	17	r⊕d	r⊕d	NOUN
ejpam-6583	105	18	,	,	PUNCT
ejpam-6583	105	19	and	and	CCONJ
ejpam-6583	105	20	the	the	DET
ejpam-6583	105	21	direct	direct	ADJ
ejpam-6583	105	22	sum	sum	NOUN
ejpam-6583	105	23	unit	unit	NOUN
ejpam-6583	105	24	over	over	ADP
ejpam-6583	105	25	r⊕d	r⊕d	NOUN
ejpam-6583	105	26	will	will	AUX
ejpam-6583	105	27	be	be	AUX
ejpam-6583	105	28	denoted	denote	VERB
ejpam-6583	105	29	by	by	ADP
ejpam-6583	105	30	ir	ir	PROPN
ejpam-6583	105	31	⊕d	⊕d	NOUN
ejpam-6583	105	32	+	+	CCONJ
ejpam-6583	106	1	=	=	SYM
ejpam-6583	106	2			ADJ
ejpam-6583	106	3	1	1	NUM
ejpam-6583	106	4	0	0	NUM
ejpam-6583	106	5	·	·	PUNCT
ejpam-6583	106	6	·	·	PUNCT
ejpam-6583	106	7	·	·	PUNCT
ejpam-6583	106	8	0	0	NUM
ejpam-6583	106	9	0	0	NUM
ejpam-6583	106	10	1	1	NUM
ejpam-6583	106	11	·	·	PUNCT
ejpam-6583	106	12	·	·	PUNCT
ejpam-6583	106	13	·	·	PUNCT
ejpam-6583	106	14	0	0	NUM
ejpam-6583	106	15	...	...	PUNCT
ejpam-6583	106	16	...	...	PUNCT
ejpam-6583	106	17	.	.	PUNCT
ejpam-6583	106	18	.	.	PUNCT
ejpam-6583	106	19	.	.	PUNCT
ejpam-6583	107	1	...	...	PUNCT
ejpam-6583	108	1	0	0	NUM
ejpam-6583	108	2	0	0	NUM
ejpam-6583	108	3	·	·	PUNCT
ejpam-6583	108	4	·	·	PUNCT
ejpam-6583	108	5	·	·	PUNCT
ejpam-6583	108	6	1	1	NUM
ejpam-6583	108	7			NOUN
ejpam-6583	108	8	=	=	PUNCT
ejpam-6583	108	9	diag	diag	NOUN
ejpam-6583	108	10	(	(	PUNCT
ejpam-6583	108	11	1	1	NUM
ejpam-6583	108	12	,	,	PUNCT
ejpam-6583	108	13	1	1	NUM
ejpam-6583	108	14	,	,	PUNCT
ejpam-6583	108	15	·	·	PUNCT
ejpam-6583	108	16	·	·	PUNCT
ejpam-6583	108	17	·	·	PUNCT
ejpam-6583	108	18	,	,	PUNCT
ejpam-6583	108	19	1	1	X
ejpam-6583	108	20	)	)	PUNCT
ejpam-6583	108	21	.	.	PUNCT
ejpam-6583	109	1	g.	g.	PROPN
ejpam-6583	109	2	albeladi	albeladi	PROPN
ejpam-6583	109	3	,	,	PUNCT
ejpam-6583	109	4	s.	s.	PROPN
ejpam-6583	109	5	omran	omran	PROPN
ejpam-6583	109	6	/	/	SYM
ejpam-6583	109	7	eur	eur	PROPN
ejpam-6583	109	8	.	.	PUNCT
ejpam-6583	110	1	j.	j.	PROPN
ejpam-6583	110	2	pure	pure	PROPN
ejpam-6583	110	3	appl	appl	PROPN
ejpam-6583	110	4	.	.	PROPN
ejpam-6583	110	5	math	math	PROPN
ejpam-6583	110	6	,	,	PUNCT
ejpam-6583	110	7	18	18	NUM
ejpam-6583	110	8	(	(	PUNCT
ejpam-6583	110	9	3	3	NUM
ejpam-6583	110	10	)	)	PUNCT
ejpam-6583	110	11	(	(	PUNCT
ejpam-6583	110	12	2025	2025	NUM
ejpam-6583	110	13	)	)	PUNCT
ejpam-6583	110	14	,	,	PUNCT
ejpam-6583	110	15	6583	6583	NUM
ejpam-6583	110	16	5	5	NUM
ejpam-6583	110	17	of	of	ADP
ejpam-6583	110	18	27	27	NUM
ejpam-6583	110	19	an	an	DET
ejpam-6583	110	20	element	element	NOUN
ejpam-6583	110	21	x	x	X
ejpam-6583	110	22	=	=	SYM
ejpam-6583	110	23	(	(	PUNCT
ejpam-6583	110	24	x1	x1	PROPN
ejpam-6583	110	25	,	,	PUNCT
ejpam-6583	110	26	x2	x2	PROPN
ejpam-6583	110	27	,	,	PUNCT
ejpam-6583	110	28	·	·	PUNCT
ejpam-6583	110	29	·	·	PUNCT
ejpam-6583	110	30	·	·	PUNCT
ejpam-6583	110	31	,	,	PUNCT
ejpam-6583	110	32	xd	xd	X
ejpam-6583	110	33	)	)	PUNCT
ejpam-6583	110	34	∈	∈	PROPN
ejpam-6583	110	35	r⊕d	r⊕d	NOUN
ejpam-6583	110	36	has	have	VERB
ejpam-6583	110	37	an	an	DET
ejpam-6583	110	38	invers	inver	NOUN
ejpam-6583	110	39	if	if	SCONJ
ejpam-6583	110	40	xi	xi	PROPN
ejpam-6583	110	41	̸=	̸=	PROPN
ejpam-6583	110	42	0	0	NUM
ejpam-6583	110	43	,	,	PUNCT
ejpam-6583	110	44	for	for	ADP
ejpam-6583	110	45	all	all	DET
ejpam-6583	110	46	i	i	PRON
ejpam-6583	110	47	=	=	NOUN
ejpam-6583	110	48	1	1	NUM
ejpam-6583	110	49	,	,	PUNCT
ejpam-6583	110	50	2	2	NUM
ejpam-6583	110	51	,	,	PUNCT
ejpam-6583	110	52	·	·	PUNCT
ejpam-6583	110	53	·	·	PUNCT
ejpam-6583	110	54	·	·	PUNCT
ejpam-6583	110	55	,	,	PUNCT
ejpam-6583	111	1	d	d	NOUN
ejpam-6583	111	2	and	and	CCONJ
ejpam-6583	111	3	is	be	AUX
ejpam-6583	111	4	denoted	denote	VERB
ejpam-6583	111	5	by	by	ADP
ejpam-6583	111	6	x−1	x−1	PROPN
ejpam-6583	111	7	=	=	PROPN
ejpam-6583	111	8	diag	diag	NOUN
ejpam-6583	111	9	(	(	PUNCT
ejpam-6583	111	10	x−1	x−1	PROPN
ejpam-6583	111	11	1	1	NUM
ejpam-6583	111	12	,	,	PUNCT
ejpam-6583	111	13	x−1	x−1	PROPN
ejpam-6583	111	14	2	2	NUM
ejpam-6583	111	15	,	,	PUNCT
ejpam-6583	111	16	·	·	PUNCT
ejpam-6583	111	17	·	·	PUNCT
ejpam-6583	111	18	·	·	PUNCT
ejpam-6583	112	1	x−1	x−1	PUNCT
ejpam-6583	113	1	d	d	NOUN
ejpam-6583	113	2	)	)	PUNCT
ejpam-6583	114	1	=	=	SYM
ejpam-6583	114	2	diag	diag	NOUN
ejpam-6583	114	3	(	(	PUNCT
ejpam-6583	114	4	1	1	NUM
ejpam-6583	114	5	x1	x1	PROPN
ejpam-6583	114	6	,	,	PUNCT
ejpam-6583	114	7	1	1	NUM
ejpam-6583	114	8	x2	x2	PROPN
ejpam-6583	114	9	,	,	PUNCT
ejpam-6583	114	10	·	·	PUNCT
ejpam-6583	114	11	·	·	PUNCT
ejpam-6583	114	12	·	·	PUNCT
ejpam-6583	114	13	1	1	NUM
ejpam-6583	114	14	xd	xd	ADP
ejpam-6583	114	15	)	)	PUNCT
ejpam-6583	114	16	,	,	PUNCT
ejpam-6583	114	17	and	and	CCONJ
ejpam-6583	114	18	x	x	X
ejpam-6583	114	19	is	be	AUX
ejpam-6583	114	20	called	call	VERB
ejpam-6583	114	21	invertible	invertible	ADJ
ejpam-6583	114	22	if	if	SCONJ
ejpam-6583	114	23	it	it	PRON
ejpam-6583	114	24	has	have	VERB
ejpam-6583	114	25	an	an	DET
ejpam-6583	114	26	inverse	inverse	NOUN
ejpam-6583	114	27	.	.	PUNCT
ejpam-6583	115	1	definition	definition	NOUN
ejpam-6583	115	2	3	3	X
ejpam-6583	115	3	.	.	PUNCT
ejpam-6583	116	1	let	let	VERB
ejpam-6583	116	2	x	x	PRON
ejpam-6583	116	3	be	be	AUX
ejpam-6583	116	4	a	a	DET
ejpam-6583	116	5	nonempty	nonempty	ADJ
ejpam-6583	116	6	set	set	VERB
ejpam-6583	116	7	,	,	PUNCT
ejpam-6583	116	8	s	s	X
ejpam-6583	116	9	≥	≥	NUM
ejpam-6583	116	10	1	1	NUM
ejpam-6583	116	11	be	be	AUX
ejpam-6583	116	12	a	a	DET
ejpam-6583	116	13	constant	constant	ADJ
ejpam-6583	116	14	.	.	PUNCT
ejpam-6583	117	1	let	let	VERB
ejpam-6583	117	2	rd	rd	NOUN
ejpam-6583	117	3	denote	denote	VERB
ejpam-6583	117	4	the	the	DET
ejpam-6583	117	5	orthogonal	orthogonal	ADJ
ejpam-6583	117	6	direct	direct	ADJ
ejpam-6583	117	7	sum	sum	NOUN
ejpam-6583	117	8	r	r	NOUN
ejpam-6583	117	9	⊕	⊕	PROPN
ejpam-6583	117	10	r	r	PROPN
ejpam-6583	117	11	⊕	⊕	PROPN
ejpam-6583	117	12	·	·	PUNCT
ejpam-6583	117	13	·	·	PUNCT
ejpam-6583	117	14	·	·	PUNCT
ejpam-6583	118	1	⊕	⊕	NOUN
ejpam-6583	118	2	r	r	NOUN
ejpam-6583	118	3	of	of	ADP
ejpam-6583	118	4	d	d	NOUN
ejpam-6583	118	5	-	-	PUNCT
ejpam-6583	118	6	copies	copy	NOUN
ejpam-6583	118	7	of	of	ADP
ejpam-6583	118	8	r.	r.	PROPN
ejpam-6583	118	9	an	an	DET
ejpam-6583	118	10	operator	operator	NOUN
ejpam-6583	118	11	δb	δb	NOUN
ejpam-6583	118	12	r⊕d	r⊕d	NOUN
ejpam-6583	118	13	:	:	PUNCT
ejpam-6583	118	14	x	x	PUNCT
ejpam-6583	118	15	×	×	NOUN
ejpam-6583	118	16	x	x	PUNCT
ejpam-6583	118	17	→	→	SYM
ejpam-6583	118	18	r⊕d	r⊕d	NOUN
ejpam-6583	118	19	is	be	AUX
ejpam-6583	118	20	called	call	VERB
ejpam-6583	118	21	a	a	DET
ejpam-6583	118	22	generalized	generalized	ADJ
ejpam-6583	118	23	b	b	X
ejpam-6583	118	24	-	-	ADJ
ejpam-6583	118	25	metric	metric	ADJ
ejpam-6583	118	26	endowed	endow	VERB
ejpam-6583	118	27	with	with	ADP
ejpam-6583	118	28	the	the	DET
ejpam-6583	118	29	orthogonal	orthogonal	ADJ
ejpam-6583	118	30	direct	direct	ADJ
ejpam-6583	118	31	sum	sum	NOUN
ejpam-6583	118	32	if	if	SCONJ
ejpam-6583	118	33	the	the	DET
ejpam-6583	118	34	following	follow	VERB
ejpam-6583	118	35	properties	property	NOUN
ejpam-6583	118	36	are	be	AUX
ejpam-6583	118	37	satisfied	satisfied	ADJ
ejpam-6583	118	38	:	:	PUNCT
ejpam-6583	118	39	(	(	PUNCT
ejpam-6583	118	40	b1	b1	NOUN
ejpam-6583	118	41	)	)	PUNCT
ejpam-6583	118	42	δ	δ	PROPN
ejpam-6583	118	43	b	b	PROPN
ejpam-6583	118	44	r⊕d	r⊕d	NOUN
ejpam-6583	118	45	(	(	PUNCT
ejpam-6583	118	46	x	x	NOUN
ejpam-6583	118	47	,	,	PUNCT
ejpam-6583	118	48	y	y	NOUN
ejpam-6583	118	49	)	)	PUNCT
ejpam-6583	118	50	≿	≿	ADP
ejpam-6583	118	51	0̃	0̃	NOUN
ejpam-6583	118	52	,	,	PUNCT
ejpam-6583	118	53	for	for	ADP
ejpam-6583	118	54	all	all	DET
ejpam-6583	118	55	x	x	NOUN
ejpam-6583	118	56	,	,	PUNCT
ejpam-6583	118	57	y	y	PROPN
ejpam-6583	118	58	∈	∈	PROPN
ejpam-6583	118	59	x	x	X
ejpam-6583	118	60	and	and	CCONJ
ejpam-6583	118	61	δb	δb	NOUN
ejpam-6583	118	62	r⊕d	r⊕d	NOUN
ejpam-6583	118	63	(	(	PUNCT
ejpam-6583	118	64	x	x	X
ejpam-6583	118	65	,	,	PUNCT
ejpam-6583	118	66	y	y	NOUN
ejpam-6583	118	67	)	)	PUNCT
ejpam-6583	118	68	=	=	SYM
ejpam-6583	118	69	0̃	0̃	NOUN
ejpam-6583	119	1	if	if	SCONJ
ejpam-6583	119	2	and	and	CCONJ
ejpam-6583	119	3	only	only	ADV
ejpam-6583	119	4	if	if	SCONJ
ejpam-6583	119	5	x	x	X
ejpam-6583	119	6	=	=	SYM
ejpam-6583	119	7	y	y	PROPN
ejpam-6583	119	8	;	;	PUNCT
ejpam-6583	119	9	(	(	PUNCT
ejpam-6583	119	10	b2	b2	NOUN
ejpam-6583	119	11	)	)	PUNCT
ejpam-6583	119	12	δ	δ	PROPN
ejpam-6583	119	13	b	b	PROPN
ejpam-6583	119	14	r⊕d	r⊕d	NOUN
ejpam-6583	119	15	(	(	PUNCT
ejpam-6583	119	16	x	x	NOUN
ejpam-6583	119	17	,	,	PUNCT
ejpam-6583	119	18	y	y	NOUN
ejpam-6583	119	19	)	)	PUNCT
ejpam-6583	119	20	=	=	PUNCT
ejpam-6583	119	21	δb	δb	X
ejpam-6583	119	22	r⊕d	r⊕d	NOUN
ejpam-6583	119	23	(	(	PUNCT
ejpam-6583	119	24	y	y	NOUN
ejpam-6583	119	25	,	,	PUNCT
ejpam-6583	119	26	x	x	NOUN
ejpam-6583	119	27	)	)	PUNCT
ejpam-6583	119	28	,	,	PUNCT
ejpam-6583	119	29	for	for	ADP
ejpam-6583	119	30	all	all	DET
ejpam-6583	119	31	x	x	NOUN
ejpam-6583	119	32	,	,	PUNCT
ejpam-6583	119	33	y	y	PROPN
ejpam-6583	119	34	∈	∈	PROPN
ejpam-6583	119	35	x	x	X
ejpam-6583	119	36	;	;	PUNCT
ejpam-6583	119	37	(	(	PUNCT
ejpam-6583	119	38	b3	b3	PROPN
ejpam-6583	119	39	)	)	PUNCT
ejpam-6583	119	40	δ	δ	PROPN
ejpam-6583	119	41	b	b	PROPN
ejpam-6583	119	42	r⊕d	r⊕d	NOUN
ejpam-6583	119	43	(	(	PUNCT
ejpam-6583	119	44	x	x	X
ejpam-6583	119	45	,	,	PUNCT
ejpam-6583	119	46	z	z	NOUN
ejpam-6583	119	47	)	)	PUNCT
ejpam-6583	119	48	≾	≾	PROPN
ejpam-6583	119	49	s	s	PART
ejpam-6583	119	50	[	[	PUNCT
ejpam-6583	119	51	δb	δb	NOUN
ejpam-6583	119	52	r⊕d	r⊕d	NOUN
ejpam-6583	119	53	(	(	PUNCT
ejpam-6583	119	54	x	x	X
ejpam-6583	119	55	,	,	PUNCT
ejpam-6583	119	56	y	y	PROPN
ejpam-6583	119	57	)	)	PUNCT
ejpam-6583	119	58	+	+	CCONJ
ejpam-6583	119	59	δb	δb	NOUN
ejpam-6583	119	60	r⊕d	r⊕d	NOUN
ejpam-6583	119	61	(	(	PUNCT
ejpam-6583	119	62	y	y	NOUN
ejpam-6583	119	63	,	,	PUNCT
ejpam-6583	119	64	z	z	NOUN
ejpam-6583	119	65	)	)	PUNCT
ejpam-6583	119	66	]	]	PUNCT
ejpam-6583	119	67	,	,	PUNCT
ejpam-6583	119	68	for	for	ADP
ejpam-6583	119	69	all	all	DET
ejpam-6583	119	70	x	x	NOUN
ejpam-6583	119	71	,	,	PUNCT
ejpam-6583	119	72	y	y	PROPN
ejpam-6583	119	73	,	,	PUNCT
ejpam-6583	119	74	z	z	NOUN
ejpam-6583	119	75	∈	∈	PROPN
ejpam-6583	119	76	x	x	X
ejpam-6583	119	77	.	.	PUNCT
ejpam-6583	120	1	then	then	ADV
ejpam-6583	120	2	,	,	PUNCT
ejpam-6583	120	3	we	we	PRON
ejpam-6583	120	4	call	call	VERB
ejpam-6583	120	5	(	(	PUNCT
ejpam-6583	120	6	x	x	INTJ
ejpam-6583	120	7	,	,	PUNCT
ejpam-6583	120	8	r⊕d	r⊕d	NOUN
ejpam-6583	120	9	,	,	PUNCT
ejpam-6583	120	10	δb	δb	NOUN
ejpam-6583	120	11	r⊕d	r⊕d	NOUN
ejpam-6583	120	12	)	)	PUNCT
ejpam-6583	120	13	a	a	DET
ejpam-6583	120	14	generalized	generalized	ADJ
ejpam-6583	120	15	b	b	X
ejpam-6583	120	16	-	-	ADJ
ejpam-6583	120	17	metric	metric	ADJ
ejpam-6583	120	18	space	space	NOUN
ejpam-6583	120	19	on	on	ADP
ejpam-6583	120	20	x	x	X
ejpam-6583	120	21	.	.	PUNCT
ejpam-6583	120	22	example	example	NOUN
ejpam-6583	121	1	1	1	NUM
ejpam-6583	121	2	.	.	PUNCT
ejpam-6583	122	1	let	let	VERB
ejpam-6583	122	2	(	(	PUNCT
ejpam-6583	122	3	x	x	X
ejpam-6583	122	4	,	,	PUNCT
ejpam-6583	122	5	δr	δr	PROPN
ejpam-6583	122	6	)	)	PUNCT
ejpam-6583	122	7	be	be	VERB
ejpam-6583	122	8	a	a	DET
ejpam-6583	122	9	metric	metric	ADJ
ejpam-6583	122	10	space	space	NOUN
ejpam-6583	122	11	,	,	PUNCT
ejpam-6583	122	12	and	and	CCONJ
ejpam-6583	122	13	δb	δb	NOUN
ejpam-6583	122	14	r⊕d	r⊕d	NOUN
ejpam-6583	122	15	:	:	PUNCT
ejpam-6583	122	16	x	x	PUNCT
ejpam-6583	122	17	×	×	NOUN
ejpam-6583	122	18	x	x	PUNCT
ejpam-6583	122	19	→	→	PUNCT
ejpam-6583	122	20	r⊕d	r⊕d	NOUN
ejpam-6583	122	21	be	be	AUX
ejpam-6583	122	22	defined	define	VERB
ejpam-6583	122	23	by	by	ADP
ejpam-6583	122	24	δb	δb	NOUN
ejpam-6583	122	25	r⊕d	r⊕d	NOUN
ejpam-6583	122	26	(	(	PUNCT
ejpam-6583	122	27	x	x	X
ejpam-6583	122	28	,	,	PUNCT
ejpam-6583	122	29	y	y	NOUN
ejpam-6583	122	30	)	)	PUNCT
ejpam-6583	123	1	=	=	NOUN
ejpam-6583	123	2	diag	diag	NOUN
ejpam-6583	123	3	(	(	PUNCT
ejpam-6583	123	4	[	[	X
ejpam-6583	123	5	d(x	d(x	PROPN
ejpam-6583	123	6	,	,	PUNCT
ejpam-6583	123	7	y)]p	y)]p	NOUN
ejpam-6583	123	8	,	,	PUNCT
ejpam-6583	123	9	[	[	X
ejpam-6583	123	10	d(x	d(x	PROPN
ejpam-6583	123	11	,	,	PUNCT
ejpam-6583	123	12	y)]p	y)]p	PROPN
ejpam-6583	123	13	,	,	PUNCT
ejpam-6583	123	14	·	·	PUNCT
ejpam-6583	123	15	·	·	PUNCT
ejpam-6583	123	16	·	·	PUNCT
ejpam-6583	123	17	,	,	PUNCT
ejpam-6583	124	1	[	[	X
ejpam-6583	124	2	d(x	d(x	PROPN
ejpam-6583	124	3	,	,	PUNCT
ejpam-6583	124	4	y)]p	y)]p	PROPN
ejpam-6583	124	5	)	)	PUNCT
ejpam-6583	124	6	∈	∈	PROPN
ejpam-6583	124	7	r⊕d	r⊕d	NOUN
ejpam-6583	124	8	,	,	PUNCT
ejpam-6583	124	9	where	where	SCONJ
ejpam-6583	124	10	p	p	NOUN
ejpam-6583	124	11	>	>	X
ejpam-6583	124	12	1	1	NUM
ejpam-6583	124	13	is	be	AUX
ejpam-6583	124	14	a	a	DET
ejpam-6583	124	15	fixed	fixed	ADJ
ejpam-6583	124	16	real	real	ADJ
ejpam-6583	124	17	number	number	NOUN
ejpam-6583	124	18	.	.	PUNCT
ejpam-6583	125	1	then	then	ADV
ejpam-6583	125	2	δb	δb	NOUN
ejpam-6583	125	3	r⊕d	r⊕d	NOUN
ejpam-6583	125	4	is	be	AUX
ejpam-6583	125	5	the	the	DET
ejpam-6583	125	6	generalized	generalized	ADJ
ejpam-6583	125	7	b	b	X
ejpam-6583	125	8	-	-	ADJ
ejpam-6583	125	9	metric	metric	ADJ
ejpam-6583	125	10	space	space	NOUN
ejpam-6583	125	11	endowed	endow	VERB
ejpam-6583	125	12	with	with	ADP
ejpam-6583	125	13	the	the	DET
ejpam-6583	125	14	orthogonal	orthogonal	ADJ
ejpam-6583	125	15	direct	direct	ADJ
ejpam-6583	125	16	sum	sum	NOUN
ejpam-6583	125	17	,	,	PUNCT
ejpam-6583	125	18	where	where	SCONJ
ejpam-6583	125	19	s	s	VERB
ejpam-6583	125	20	=	=	NOUN
ejpam-6583	125	21	2p−1	2p−1	NUM
ejpam-6583	125	22	.	.	PUNCT
ejpam-6583	126	1	indeed	indeed	ADV
ejpam-6583	126	2	,	,	PUNCT
ejpam-6583	126	3	conditions	condition	NOUN
ejpam-6583	126	4	(	(	PUNCT
ejpam-6583	126	5	b1	b1	NOUN
ejpam-6583	126	6	)	)	PUNCT
ejpam-6583	126	7	and	and	CCONJ
ejpam-6583	126	8	(	(	PUNCT
ejpam-6583	126	9	b2	b2	NOUN
ejpam-6583	126	10	)	)	PUNCT
ejpam-6583	126	11	in	in	ADP
ejpam-6583	126	12	definition	definition	NOUN
ejpam-6583	126	13	3	3	NUM
ejpam-6583	126	14	are	be	AUX
ejpam-6583	126	15	satisfied	satisfied	ADJ
ejpam-6583	126	16	and	and	CCONJ
ejpam-6583	126	17	thus	thus	ADV
ejpam-6583	126	18	we	we	PRON
ejpam-6583	126	19	only	only	ADV
ejpam-6583	126	20	need	need	VERB
ejpam-6583	126	21	to	to	PART
ejpam-6583	126	22	show	show	VERB
ejpam-6583	126	23	that	that	PRON
ejpam-6583	126	24	condition	condition	NOUN
ejpam-6583	126	25	(	(	PUNCT
ejpam-6583	126	26	b3	b3	PROPN
ejpam-6583	126	27	)	)	PUNCT
ejpam-6583	126	28	holds	hold	VERB
ejpam-6583	126	29	for	for	ADP
ejpam-6583	126	30	δb	δb	NOUN
ejpam-6583	126	31	r⊕d	r⊕d	NOUN
ejpam-6583	126	32	.	.	PUNCT
ejpam-6583	127	1	it	it	PRON
ejpam-6583	127	2	is	be	AUX
ejpam-6583	127	3	easy	easy	ADJ
ejpam-6583	127	4	to	to	PART
ejpam-6583	127	5	see	see	VERB
ejpam-6583	127	6	that	that	SCONJ
ejpam-6583	127	7	if	if	SCONJ
ejpam-6583	127	8	1	1	NUM
ejpam-6583	127	9	<	<	X
ejpam-6583	127	10	p	p	X
ejpam-6583	127	11	<	<	X
ejpam-6583	127	12	+	+	PROPN
ejpam-6583	127	13	∞	∞	PROPN
ejpam-6583	127	14	,	,	PUNCT
ejpam-6583	127	15	then	then	ADV
ejpam-6583	127	16	the	the	DET
ejpam-6583	127	17	convexity	convexity	NOUN
ejpam-6583	127	18	of	of	ADP
ejpam-6583	127	19	the	the	DET
ejpam-6583	127	20	function	function	NOUN
ejpam-6583	127	21	f	f	PROPN
ejpam-6583	127	22	(	(	PUNCT
ejpam-6583	127	23	x	x	X
ejpam-6583	127	24	)	)	PUNCT
ejpam-6583	127	25	=	=	SYM
ejpam-6583	127	26	xp	xp	PROPN
ejpam-6583	127	27	,	,	PUNCT
ejpam-6583	127	28	where	where	SCONJ
ejpam-6583	127	29	x	x	X
ejpam-6583	127	30	≥	≥	X
ejpam-6583	127	31	0	0	NUM
ejpam-6583	127	32	,	,	PUNCT
ejpam-6583	127	33	implies	imply	VERB
ejpam-6583	127	34	(	(	PUNCT
ejpam-6583	127	35	a+	a+	PUNCT
ejpam-6583	127	36	c	c	NOUN
ejpam-6583	127	37	2	2	NUM
ejpam-6583	127	38	)	)	PUNCT
ejpam-6583	127	39	p	p	NOUN
ejpam-6583	127	40	≤	≤	NUM
ejpam-6583	127	41	1	1	NUM
ejpam-6583	127	42	2	2	NUM
ejpam-6583	127	43	(	(	PUNCT
ejpam-6583	127	44	ap	ap	PROPN
ejpam-6583	127	45	+	+	CCONJ
ejpam-6583	127	46	cp	cp	NOUN
ejpam-6583	127	47	)	)	PUNCT
ejpam-6583	127	48	,	,	PUNCT
ejpam-6583	127	49	and	and	CCONJ
ejpam-6583	127	50	hence	hence	ADV
ejpam-6583	127	51	(	(	PUNCT
ejpam-6583	127	52	a+	a+	X
ejpam-6583	127	53	c)p	c)p	X
ejpam-6583	127	54	≤	≤	NUM
ejpam-6583	127	55	2p−1(ap	2p−1(ap	NUM
ejpam-6583	127	56	+	+	SYM
ejpam-6583	127	57	cp	cp	NOUN
ejpam-6583	127	58	)	)	PUNCT
ejpam-6583	127	59	.	.	PUNCT
ejpam-6583	128	1	therefore	therefore	ADV
ejpam-6583	128	2	,	,	PUNCT
ejpam-6583	128	3	for	for	ADP
ejpam-6583	128	4	each	each	DET
ejpam-6583	128	5	x	x	PROPN
ejpam-6583	128	6	,	,	PUNCT
ejpam-6583	128	7	y	y	PROPN
ejpam-6583	128	8	,	,	PUNCT
ejpam-6583	128	9	z	z	PROPN
ejpam-6583	128	10	∈	∈	PROPN
ejpam-6583	128	11	x	x	X
ejpam-6583	128	12	,	,	PUNCT
ejpam-6583	128	13	we	we	PRON
ejpam-6583	128	14	get	get	VERB
ejpam-6583	128	15	δb	δb	ADP
ejpam-6583	128	16	r⊕d	r⊕d	NOUN
ejpam-6583	128	17	(	(	PUNCT
ejpam-6583	128	18	x	x	X
ejpam-6583	128	19	,	,	PUNCT
ejpam-6583	128	20	y	y	NOUN
ejpam-6583	128	21	)	)	PUNCT
ejpam-6583	128	22	=	=	NOUN
ejpam-6583	128	23	diag	diag	NOUN
ejpam-6583	128	24	(	(	PUNCT
ejpam-6583	128	25	[	[	X
ejpam-6583	128	26	d(x	d(x	PROPN
ejpam-6583	128	27	,	,	PUNCT
ejpam-6583	128	28	y)]p	y)]p	NOUN
ejpam-6583	128	29	,	,	PUNCT
ejpam-6583	128	30	[	[	X
ejpam-6583	128	31	d(x	d(x	PROPN
ejpam-6583	128	32	,	,	PUNCT
ejpam-6583	128	33	y)]p	y)]p	PROPN
ejpam-6583	128	34	,	,	PUNCT
ejpam-6583	128	35	·	·	PUNCT
ejpam-6583	128	36	·	·	PUNCT
ejpam-6583	128	37	·	·	PUNCT
ejpam-6583	128	38	,	,	PUNCT
ejpam-6583	129	1	[	[	X
ejpam-6583	129	2	d(x	d(x	PROPN
ejpam-6583	129	3	,	,	PUNCT
ejpam-6583	129	4	y)]p	y)]p	PROPN
ejpam-6583	129	5	)	)	PUNCT
ejpam-6583	129	6	≤	≤	NUM
ejpam-6583	129	7	diag	diag	NOUN
ejpam-6583	129	8	(	(	PUNCT
ejpam-6583	129	9	[	[	X
ejpam-6583	129	10	d(x	d(x	PROPN
ejpam-6583	129	11	,	,	PUNCT
ejpam-6583	129	12	z	z	NOUN
ejpam-6583	129	13	)	)	PUNCT
ejpam-6583	129	14	+	+	CCONJ
ejpam-6583	129	15	d(z	d(z	PROPN
ejpam-6583	129	16	,	,	PUNCT
ejpam-6583	129	17	y)]p	y)]p	PROPN
ejpam-6583	129	18	,	,	PUNCT
ejpam-6583	129	19	[	[	X
ejpam-6583	129	20	d(x	d(x	NOUN
ejpam-6583	129	21	,	,	PUNCT
ejpam-6583	129	22	z	z	NOUN
ejpam-6583	129	23	)	)	PUNCT
ejpam-6583	129	24	+	+	CCONJ
ejpam-6583	129	25	d(z	d(z	PROPN
ejpam-6583	129	26	,	,	PUNCT
ejpam-6583	129	27	y)]p	y)]p	PROPN
ejpam-6583	129	28	,	,	PUNCT
ejpam-6583	129	29	·	·	PUNCT
ejpam-6583	129	30	·	·	PUNCT
ejpam-6583	129	31	·	·	PUNCT
ejpam-6583	129	32	,	,	PUNCT
ejpam-6583	129	33	[	[	X
ejpam-6583	129	34	d(x	d(x	PROPN
ejpam-6583	129	35	,	,	PUNCT
ejpam-6583	129	36	z	z	NOUN
ejpam-6583	129	37	)	)	PUNCT
ejpam-6583	129	38	+	+	CCONJ
ejpam-6583	129	39	d(z	d(z	PROPN
ejpam-6583	129	40	,	,	PUNCT
ejpam-6583	129	41	y)]p	y)]p	PROPN
ejpam-6583	129	42	)	)	PUNCT
ejpam-6583	129	43	≤	≤	NUM
ejpam-6583	129	44	2p−1	2p−1	NUM
ejpam-6583	129	45	diag	diag	NOUN
ejpam-6583	129	46	(	(	PUNCT
ejpam-6583	129	47	d(x	d(x	PROPN
ejpam-6583	129	48	,	,	PUNCT
ejpam-6583	129	49	z)p	z)p	X
ejpam-6583	129	50	+	+	CCONJ
ejpam-6583	129	51	d(z	d(z	NOUN
ejpam-6583	129	52	,	,	PUNCT
ejpam-6583	129	53	y)p	y)p	ADJ
ejpam-6583	129	54	,	,	PUNCT
ejpam-6583	129	55	d(x	d(x	PROPN
ejpam-6583	129	56	,	,	PUNCT
ejpam-6583	129	57	z)p	z)p	X
ejpam-6583	129	58	+	+	CCONJ
ejpam-6583	129	59	d(z	d(z	NOUN
ejpam-6583	129	60	,	,	PUNCT
ejpam-6583	129	61	y)p	y)p	ADJ
ejpam-6583	129	62	,	,	PUNCT
ejpam-6583	129	63	·	·	PUNCT
ejpam-6583	129	64	·	·	PUNCT
ejpam-6583	129	65	·	·	PUNCT
ejpam-6583	129	66	,	,	PUNCT
ejpam-6583	129	67	d(x	d(x	PROPN
ejpam-6583	129	68	,	,	PUNCT
ejpam-6583	129	69	z)p	z)p	X
ejpam-6583	129	70	+	+	CCONJ
ejpam-6583	129	71	d(z	d(z	NOUN
ejpam-6583	129	72	,	,	PUNCT
ejpam-6583	129	73	y)p	y)p	ADJ
ejpam-6583	129	74	)	)	PUNCT
ejpam-6583	130	1	=	=	SYM
ejpam-6583	130	2	2p−1	2p−1	NUM
ejpam-6583	130	3	[	[	PUNCT
ejpam-6583	130	4	diag	diag	NOUN
ejpam-6583	130	5	(	(	PUNCT
ejpam-6583	130	6	d(x	d(x	PROPN
ejpam-6583	130	7	,	,	PUNCT
ejpam-6583	130	8	z)p	z)p	ADJ
ejpam-6583	130	9	,	,	PUNCT
ejpam-6583	130	10	d(x	d(x	PROPN
ejpam-6583	130	11	,	,	PUNCT
ejpam-6583	130	12	z)p	z)p	ADJ
ejpam-6583	130	13	,	,	PUNCT
ejpam-6583	130	14	·	·	PUNCT
ejpam-6583	130	15	·	·	PUNCT
ejpam-6583	130	16	·	·	PUNCT
ejpam-6583	130	17	,	,	PUNCT
ejpam-6583	130	18	d(x	d(x	PROPN
ejpam-6583	130	19	,	,	PUNCT
ejpam-6583	130	20	z)p	z)p	PUNCT
ejpam-6583	130	21	)	)	PUNCT
ejpam-6583	130	22	g.	g.	NOUN
ejpam-6583	130	23	albeladi	albeladi	PROPN
ejpam-6583	130	24	,	,	PUNCT
ejpam-6583	130	25	s.	s.	PROPN
ejpam-6583	130	26	omran	omran	PROPN
ejpam-6583	130	27	/	/	SYM
ejpam-6583	130	28	eur	eur	PROPN
ejpam-6583	130	29	.	.	PUNCT
ejpam-6583	131	1	j.	j.	PROPN
ejpam-6583	131	2	pure	pure	PROPN
ejpam-6583	131	3	appl	appl	PROPN
ejpam-6583	131	4	.	.	PROPN
ejpam-6583	131	5	math	math	PROPN
ejpam-6583	131	6	,	,	PUNCT
ejpam-6583	131	7	18	18	NUM
ejpam-6583	131	8	(	(	PUNCT
ejpam-6583	131	9	3	3	NUM
ejpam-6583	131	10	)	)	PUNCT
ejpam-6583	131	11	(	(	PUNCT
ejpam-6583	131	12	2025	2025	NUM
ejpam-6583	131	13	)	)	PUNCT
ejpam-6583	131	14	,	,	PUNCT
ejpam-6583	131	15	6583	6583	NUM
ejpam-6583	131	16	6	6	NUM
ejpam-6583	131	17	of	of	ADP
ejpam-6583	131	18	27	27	NUM
ejpam-6583	131	19	+	+	NUM
ejpam-6583	131	20	diag	diag	NOUN
ejpam-6583	131	21	(	(	PUNCT
ejpam-6583	131	22	d(z	d(z	PROPN
ejpam-6583	131	23	,	,	PUNCT
ejpam-6583	131	24	y)p	y)p	NOUN
ejpam-6583	131	25	,	,	PUNCT
ejpam-6583	131	26	d(z	d(z	NOUN
ejpam-6583	131	27	,	,	PUNCT
ejpam-6583	131	28	y)p	y)p	ADJ
ejpam-6583	131	29	,	,	PUNCT
ejpam-6583	131	30	·	·	PUNCT
ejpam-6583	131	31	·	·	PUNCT
ejpam-6583	131	32	·	·	PUNCT
ejpam-6583	131	33	,	,	PUNCT
ejpam-6583	131	34	d(z	d(z	PROPN
ejpam-6583	131	35	,	,	PUNCT
ejpam-6583	131	36	y)p	y)p	ADJ
ejpam-6583	131	37	)	)	PUNCT
ejpam-6583	131	38	]	]	PUNCT
ejpam-6583	132	1	=	=	PUNCT
ejpam-6583	132	2	2p−1	2p−1	NUM
ejpam-6583	132	3	[	[	PUNCT
ejpam-6583	132	4	δb	δb	NOUN
ejpam-6583	132	5	r⊕d	r⊕d	NOUN
ejpam-6583	132	6	(	(	PUNCT
ejpam-6583	132	7	x	x	X
ejpam-6583	132	8	,	,	PUNCT
ejpam-6583	132	9	z	z	NOUN
ejpam-6583	132	10	)	)	PUNCT
ejpam-6583	132	11	+	+	CCONJ
ejpam-6583	132	12	δb	δb	NOUN
ejpam-6583	132	13	r⊕d	r⊕d	NOUN
ejpam-6583	132	14	(	(	PUNCT
ejpam-6583	132	15	z	z	NOUN
ejpam-6583	132	16	,	,	PUNCT
ejpam-6583	132	17	y	y	PROPN
ejpam-6583	132	18	)	)	PUNCT
ejpam-6583	132	19	]	]	PUNCT
ejpam-6583	132	20	.	.	PUNCT
ejpam-6583	133	1	so	so	ADV
ejpam-6583	133	2	condition	condition	NOUN
ejpam-6583	133	3	(	(	PUNCT
ejpam-6583	133	4	b3	b3	PROPN
ejpam-6583	133	5	)	)	PUNCT
ejpam-6583	133	6	in	in	ADP
ejpam-6583	133	7	definition	definition	NOUN
ejpam-6583	133	8	3	3	NUM
ejpam-6583	133	9	holds	hold	VERB
ejpam-6583	133	10	and	and	CCONJ
ejpam-6583	133	11	then	then	ADV
ejpam-6583	133	12	δb	δb	NOUN
ejpam-6583	133	13	r⊕d	r⊕d	NOUN
ejpam-6583	133	14	is	be	AUX
ejpam-6583	133	15	a	a	DET
ejpam-6583	133	16	b	b	NOUN
ejpam-6583	133	17	-	-	ADJ
ejpam-6583	133	18	metric	metric	ADJ
ejpam-6583	133	19	coefficient	coefficient	NOUN
ejpam-6583	133	20	s	s	PART
ejpam-6583	133	21	=	=	NOUN
ejpam-6583	133	22	2p−1	2p−1	NUM
ejpam-6583	133	23	>	>	SYM
ejpam-6583	134	1	1	1	X
ejpam-6583	134	2	.	.	PUNCT
ejpam-6583	134	3	definition	definition	NOUN
ejpam-6583	134	4	4	4	NUM
ejpam-6583	134	5	.	.	PUNCT
ejpam-6583	134	6	suppose	suppose	VERB
ejpam-6583	134	7	that	that	SCONJ
ejpam-6583	134	8	(	(	PUNCT
ejpam-6583	134	9	x	x	X
ejpam-6583	134	10	,	,	PUNCT
ejpam-6583	134	11	r⊕d	r⊕d	NOUN
ejpam-6583	134	12	,	,	PUNCT
ejpam-6583	134	13	δb	δb	NOUN
ejpam-6583	134	14	r⊕d	r⊕d	NOUN
ejpam-6583	134	15	)	)	PUNCT
ejpam-6583	134	16	is	be	AUX
ejpam-6583	134	17	a	a	DET
ejpam-6583	134	18	generalized	generalized	ADJ
ejpam-6583	134	19	b	b	X
ejpam-6583	134	20	-	-	ADJ
ejpam-6583	134	21	metric	metric	ADJ
ejpam-6583	134	22	space	space	NOUN
ejpam-6583	134	23	endowed	endow	VERB
ejpam-6583	134	24	with	with	ADP
ejpam-6583	134	25	the	the	DET
ejpam-6583	134	26	orthogonal	orthogonal	ADJ
ejpam-6583	134	27	direct	direct	ADJ
ejpam-6583	134	28	sum	sum	NOUN
ejpam-6583	134	29	.	.	PUNCT
ejpam-6583	135	1	then	then	ADV
ejpam-6583	135	2	a	a	DET
ejpam-6583	135	3	sequence	sequence	NOUN
ejpam-6583	135	4	{	{	PUNCT
ejpam-6583	135	5	xn	xn	NOUN
ejpam-6583	135	6	}	}	PUNCT
ejpam-6583	135	7	in	in	ADP
ejpam-6583	135	8	x	x	PROPN
ejpam-6583	135	9	is	be	AUX
ejpam-6583	135	10	called	call	VERB
ejpam-6583	135	11	:	:	PUNCT
ejpam-6583	135	12	1	1	NUM
ejpam-6583	135	13	.	.	X
ejpam-6583	135	14	b	b	X
ejpam-6583	135	15	-	-	PUNCT
ejpam-6583	135	16	convergent	convergent	ADJ
ejpam-6583	135	17	sequence	sequence	NOUN
ejpam-6583	135	18	with	with	ADP
ejpam-6583	135	19	respect	respect	NOUN
ejpam-6583	135	20	to	to	ADP
ejpam-6583	135	21	r⊕d	r⊕d	NOUN
ejpam-6583	135	22	.	.	PUNCT
ejpam-6583	136	1	if	if	SCONJ
ejpam-6583	136	2	,	,	PUNCT
ejpam-6583	136	3	for	for	ADP
ejpam-6583	136	4	every	every	DET
ejpam-6583	136	5	ϵ̃	ϵ̃	PROPN
ejpam-6583	136	6	∈	∈	PROPN
ejpam-6583	136	7	r⊕d	r⊕d	NOUN
ejpam-6583	136	8	,	,	PUNCT
ejpam-6583	136	9	with	with	ADP
ejpam-6583	136	10	ϵ̃	ϵ̃	PROPN
ejpam-6583	136	11	≻	≻	PROPN
ejpam-6583	136	12	0̃	0̃	NOUN
ejpam-6583	136	13	,	,	PUNCT
ejpam-6583	136	14	if	if	SCONJ
ejpam-6583	136	15	there	there	PRON
ejpam-6583	136	16	exists	exist	VERB
ejpam-6583	136	17	x	x	X
ejpam-6583	136	18	∈	∈	PROPN
ejpam-6583	136	19	x	x	X
ejpam-6583	136	20	and	and	CCONJ
ejpam-6583	136	21	there	there	PRON
ejpam-6583	136	22	is	be	VERB
ejpam-6583	136	23	n	n	DET
ejpam-6583	136	24	∈	∈	PROPN
ejpam-6583	136	25	n	n	PRON
ejpam-6583	136	26	such	such	ADJ
ejpam-6583	136	27	that	that	PRON
ejpam-6583	136	28	for	for	ADP
ejpam-6583	136	29	all	all	DET
ejpam-6583	136	30	n	n	CCONJ
ejpam-6583	136	31	>	>	PUNCT
ejpam-6583	136	32	n	n	X
ejpam-6583	136	33	,	,	PUNCT
ejpam-6583	136	34	δb	δb	NOUN
ejpam-6583	136	35	r⊕d	r⊕d	NOUN
ejpam-6583	136	36	(	(	PUNCT
ejpam-6583	136	37	xn	xn	PROPN
ejpam-6583	136	38	,	,	PUNCT
ejpam-6583	136	39	x	x	NOUN
ejpam-6583	136	40	)	)	PUNCT
ejpam-6583	136	41	≺	≺	NOUN
ejpam-6583	136	42	ϵ̃.	ϵ̃.	NOUN
ejpam-6583	136	43	2	2	NUM
ejpam-6583	136	44	.	.	X
ejpam-6583	136	45	b	b	X
ejpam-6583	136	46	-	-	PUNCT
ejpam-6583	136	47	cauchy	cauchy	ADJ
ejpam-6583	136	48	sequence	sequence	NOUN
ejpam-6583	136	49	with	with	ADP
ejpam-6583	136	50	respect	respect	NOUN
ejpam-6583	136	51	to	to	ADP
ejpam-6583	136	52	r⊕d	r⊕d	NOUN
ejpam-6583	136	53	.	.	PUNCT
ejpam-6583	137	1	if	if	SCONJ
ejpam-6583	137	2	,	,	PUNCT
ejpam-6583	137	3	for	for	ADP
ejpam-6583	137	4	any	any	DET
ejpam-6583	137	5	ϵ̃	ϵ̃	PROPN
ejpam-6583	137	6	≻	≻	NOUN
ejpam-6583	137	7	0̃	0̃	NOUN
ejpam-6583	137	8	there	there	PRON
ejpam-6583	137	9	exists	exist	VERB
ejpam-6583	137	10	n	n	PRON
ejpam-6583	137	11	∈	∈	PROPN
ejpam-6583	137	12	n	n	PRON
ejpam-6583	137	13	such	such	ADJ
ejpam-6583	137	14	that	that	PRON
ejpam-6583	137	15	for	for	SCONJ
ejpam-6583	137	16	all	all	DET
ejpam-6583	137	17	n	n	CCONJ
ejpam-6583	137	18	,	,	PUNCT
ejpam-6583	137	19	m	m	VERB
ejpam-6583	137	20	>	>	X
ejpam-6583	137	21	n	n	X
ejpam-6583	137	22	,	,	PUNCT
ejpam-6583	137	23	δb	δb	NOUN
ejpam-6583	137	24	r⊕d	r⊕d	NOUN
ejpam-6583	137	25	(	(	PUNCT
ejpam-6583	137	26	xn	xn	PROPN
ejpam-6583	137	27	,	,	PUNCT
ejpam-6583	137	28	xm	xm	PROPN
ejpam-6583	137	29	)	)	PUNCT
ejpam-6583	137	30	≺	≺	NOUN
ejpam-6583	137	31	ϵ̃.	ϵ̃.	NUM
ejpam-6583	137	32	example	example	NOUN
ejpam-6583	138	1	2	2	NUM
ejpam-6583	138	2	.	.	X
ejpam-6583	138	3	assume	assume	VERB
ejpam-6583	138	4	that	that	SCONJ
ejpam-6583	138	5	x	x	X
ejpam-6583	138	6	=	=	PUNCT
ejpam-6583	138	7	lp(r	lp(r	X
ejpam-6583	138	8	)	)	PUNCT
ejpam-6583	138	9	with	with	ADP
ejpam-6583	138	10	p	p	PROPN
ejpam-6583	138	11	∈	∈	PROPN
ejpam-6583	138	12	(	(	PUNCT
ejpam-6583	138	13	0	0	NUM
ejpam-6583	138	14	,	,	PUNCT
ejpam-6583	138	15	1	1	NUM
ejpam-6583	138	16	)	)	PUNCT
ejpam-6583	138	17	,	,	PUNCT
ejpam-6583	138	18	where	where	SCONJ
ejpam-6583	138	19	lp(r	lp(r	PUNCT
ejpam-6583	138	20	)	)	PUNCT
ejpam-6583	138	21	:	:	PUNCT
ejpam-6583	139	1	=	=	SYM
ejpam-6583	139	2	{	{	PUNCT
ejpam-6583	139	3	{	{	PUNCT
ejpam-6583	139	4	xn	xn	NOUN
ejpam-6583	139	5	}	}	PUNCT
ejpam-6583	139	6	⊆	⊆	NUM
ejpam-6583	139	7	r	r	NOUN
ejpam-6583	139	8	|	|	NOUN
ejpam-6583	139	9	+	+	NOUN
ejpam-6583	139	10	∞∑	∞∑	NUM
ejpam-6583	139	11	n=1	n=1	PUNCT
ejpam-6583	139	12	|	|	ADV
ejpam-6583	139	13	xn	xn	PROPN
ejpam-6583	140	1	|p	|p	PROPN
ejpam-6583	140	2	<	<	X
ejpam-6583	140	3	+	+	NOUN
ejpam-6583	140	4	∞	∞	NUM
ejpam-6583	140	5	}	}	PUNCT
ejpam-6583	140	6	,	,	PUNCT
ejpam-6583	140	7	together	together	ADV
ejpam-6583	140	8	with	with	ADP
ejpam-6583	140	9	the	the	DET
ejpam-6583	140	10	operator	operator	NOUN
ejpam-6583	140	11	δb	δb	NOUN
ejpam-6583	140	12	r⊕d	r⊕d	NOUN
ejpam-6583	140	13	:	:	PUNCT
ejpam-6583	141	1	lp(r)×	lp(r)×	ADJ
ejpam-6583	141	2	lp(r	lp(r	X
ejpam-6583	141	3	)	)	PUNCT
ejpam-6583	141	4	→	→	PUNCT
ejpam-6583	141	5	r⊕d	r⊕d	NOUN
ejpam-6583	141	6	+	+	CCONJ
ejpam-6583	141	7	defined	define	VERB
ejpam-6583	141	8	by	by	ADP
ejpam-6583	141	9	δb	δb	NOUN
ejpam-6583	141	10	r⊕d	r⊕d	NOUN
ejpam-6583	141	11	(	(	PUNCT
ejpam-6583	141	12	x	x	X
ejpam-6583	141	13	,	,	PUNCT
ejpam-6583	141	14	y	y	NOUN
ejpam-6583	141	15	)	)	PUNCT
ejpam-6583	142	1	=	=	NOUN
ejpam-6583	142	2	diag	diag	NOUN
ejpam-6583	142	3	(	(	PUNCT
ejpam-6583	142	4	(	(	PUNCT
ejpam-6583	142	5	∑+∞	∑+∞	ADJ
ejpam-6583	142	6	n=1	n=1	PROPN
ejpam-6583	143	1	|	|	ADV
ejpam-6583	143	2	xn	xn	PROPN
ejpam-6583	144	1	−	−	PROPN
ejpam-6583	144	2	yn	yn	PROPN
ejpam-6583	144	3	|p	|p	PROPN
ejpam-6583	144	4	)	)	PUNCT
ejpam-6583	144	5	1	1	NUM
ejpam-6583	144	6	p	p	NOUN
ejpam-6583	144	7	,	,	PUNCT
ejpam-6583	144	8	·	·	PUNCT
ejpam-6583	144	9	·	·	PUNCT
ejpam-6583	144	10	·	·	PUNCT
ejpam-6583	144	11	,	,	PUNCT
ejpam-6583	144	12	(	(	PUNCT
ejpam-6583	144	13	∑+∞	∑+∞	ADJ
ejpam-6583	144	14	n=1	n=1	PROPN
ejpam-6583	145	1	|	|	ADV
ejpam-6583	145	2	xn	xn	PROPN
ejpam-6583	146	1	−	−	PROPN
ejpam-6583	146	2	yn	yn	PROPN
ejpam-6583	146	3	|p	|p	PROPN
ejpam-6583	146	4	)	)	PUNCT
ejpam-6583	146	5	1	1	NUM
ejpam-6583	146	6	p	p	NOUN
ejpam-6583	146	7	)	)	PUNCT
ejpam-6583	146	8	∈	∈	PROPN
ejpam-6583	146	9	r⊕d	r⊕d	NOUN
ejpam-6583	146	10	,	,	PUNCT
ejpam-6583	146	11	where	where	SCONJ
ejpam-6583	146	12	x	x	X
ejpam-6583	146	13	=	=	PRON
ejpam-6583	146	14	{	{	PUNCT
ejpam-6583	146	15	xn	xn	NUM
ejpam-6583	146	16	}	}	PUNCT
ejpam-6583	146	17	,	,	PUNCT
ejpam-6583	146	18	y	y	PROPN
ejpam-6583	146	19	=	=	PRON
ejpam-6583	146	20	{	{	PUNCT
ejpam-6583	146	21	yn	yn	PROPN
ejpam-6583	146	22	}	}	PUNCT
ejpam-6583	146	23	∈	∈	PROPN
ejpam-6583	146	24	lp(r	lp(r	X
ejpam-6583	146	25	)	)	PUNCT
ejpam-6583	146	26	,	,	PUNCT
ejpam-6583	146	27	is	be	AUX
ejpam-6583	146	28	a	a	DET
ejpam-6583	146	29	generalized	generalized	ADJ
ejpam-6583	146	30	b	b	X
ejpam-6583	146	31	-	-	ADJ
ejpam-6583	146	32	metric	metric	ADJ
ejpam-6583	146	33	space	space	NOUN
ejpam-6583	146	34	endowed	endow	VERB
ejpam-6583	146	35	with	with	ADP
ejpam-6583	146	36	the	the	DET
ejpam-6583	146	37	orthogonal	orthogonal	ADJ
ejpam-6583	146	38	direct	direct	ADJ
ejpam-6583	146	39	sum	sum	NOUN
ejpam-6583	146	40	,	,	PUNCT
ejpam-6583	146	41	where	where	SCONJ
ejpam-6583	146	42	coefficient	coefficient	NOUN
ejpam-6583	146	43	s	s	VERB
ejpam-6583	146	44	=	=	NOUN
ejpam-6583	146	45	2	2	NUM
ejpam-6583	146	46	1	1	NUM
ejpam-6583	146	47	p	p	NOUN
ejpam-6583	146	48	>	>	X
ejpam-6583	146	49	1	1	NUM
ejpam-6583	146	50	.	.	PUNCT
ejpam-6583	147	1	then	then	ADV
ejpam-6583	147	2	(	(	PUNCT
ejpam-6583	147	3	lp	lp	PROPN
ejpam-6583	147	4	,	,	PUNCT
ejpam-6583	147	5	rd	rd	PROPN
ejpam-6583	147	6	,	,	PUNCT
ejpam-6583	147	7	d	d	NOUN
ejpam-6583	147	8	)	)	PUNCT
ejpam-6583	147	9	is	be	AUX
ejpam-6583	147	10	a	a	DET
ejpam-6583	147	11	complete	complete	ADJ
ejpam-6583	147	12	generalized	generalized	ADJ
ejpam-6583	147	13	b	b	X
ejpam-6583	147	14	-	-	ADJ
ejpam-6583	147	15	metric	metric	ADJ
ejpam-6583	147	16	space	space	NOUN
ejpam-6583	147	17	endowed	endow	VERB
ejpam-6583	147	18	with	with	ADP
ejpam-6583	147	19	the	the	DET
ejpam-6583	147	20	orthogonal	orthogonal	ADJ
ejpam-6583	147	21	direct	direct	ADJ
ejpam-6583	147	22	sum	sum	NOUN
ejpam-6583	147	23	.	.	PUNCT
ejpam-6583	148	1	example	example	NOUN
ejpam-6583	149	1	3	3	X
ejpam-6583	149	2	.	.	X
ejpam-6583	149	3	assume	assume	VERB
ejpam-6583	149	4	that	that	SCONJ
ejpam-6583	149	5	x	x	X
ejpam-6583	149	6	=	=	PUNCT
ejpam-6583	149	7	lp(r	lp(r	X
ejpam-6583	149	8	)	)	PUNCT
ejpam-6583	149	9	with	with	ADP
ejpam-6583	149	10	p	p	PROPN
ejpam-6583	149	11	∈	∈	PROPN
ejpam-6583	149	12	(	(	PUNCT
ejpam-6583	149	13	0	0	NUM
ejpam-6583	149	14	,	,	PUNCT
ejpam-6583	149	15	1	1	NUM
ejpam-6583	149	16	)	)	PUNCT
ejpam-6583	149	17	,	,	PUNCT
ejpam-6583	149	18	where	where	SCONJ
ejpam-6583	149	19	lp(r	lp(r	PUNCT
ejpam-6583	149	20	)	)	PUNCT
ejpam-6583	149	21	:	:	PUNCT
ejpam-6583	149	22	=	=	SYM
ejpam-6583	149	23	x(t	x(t	NOUN
ejpam-6583	149	24	)	)	PUNCT
ejpam-6583	149	25	⊆	⊆	NUM
ejpam-6583	149	26	c([0	c([0	NOUN
ejpam-6583	149	27	,	,	PUNCT
ejpam-6583	149	28	1],r)|	1],r)|	ADJ
ejpam-6583	149	29	1∫	1∫	NUM
ejpam-6583	149	30	0	0	NUM
ejpam-6583	150	1	|	|	ADV
ejpam-6583	150	2	x(t	x(t	PROPN
ejpam-6583	150	3	)	)	PUNCT
ejpam-6583	150	4	|p	|p	PROPN
ejpam-6583	150	5	<	<	X
ejpam-6583	150	6	+	+	ADJ
ejpam-6583	150	7	∞	∞	PROPN
ejpam-6583	150	8			NOUN
ejpam-6583	150	9	,	,	PUNCT
ejpam-6583	150	10	together	together	ADV
ejpam-6583	150	11	with	with	ADP
ejpam-6583	150	12	the	the	DET
ejpam-6583	150	13	operator	operator	NOUN
ejpam-6583	151	1	d	d	NOUN
ejpam-6583	151	2	:	:	PUNCT
ejpam-6583	151	3	lp(r)×	lp(r)×	ADJ
ejpam-6583	151	4	lp(r	lp(r	X
ejpam-6583	151	5	)	)	PUNCT
ejpam-6583	151	6	→	→	PUNCT
ejpam-6583	151	7	r⊕d	r⊕d	NOUN
ejpam-6583	151	8	+	+	CCONJ
ejpam-6583	151	9	defined	define	VERB
ejpam-6583	151	10	by	by	ADP
ejpam-6583	151	11	δb	δb	NOUN
ejpam-6583	151	12	r⊕d	r⊕d	NOUN
ejpam-6583	151	13	(	(	PUNCT
ejpam-6583	151	14	x	x	X
ejpam-6583	151	15	,	,	PUNCT
ejpam-6583	151	16	y	y	NOUN
ejpam-6583	151	17	)	)	PUNCT
ejpam-6583	152	1	=	=	NOUN
ejpam-6583	152	2	diag	diag	NOUN
ejpam-6583	152	3	(	(	PUNCT
ejpam-6583	152	4	(	(	PUNCT
ejpam-6583	152	5	1∫	1∫	NUM
ejpam-6583	152	6	0	0	NUM
ejpam-6583	153	1	|	|	ADV
ejpam-6583	153	2	x(t)−	x(t)−	PROPN
ejpam-6583	153	3	y(t	y(t	PROPN
ejpam-6583	153	4	)	)	PUNCT
ejpam-6583	153	5	|p	|p	NOUN
ejpam-6583	153	6	dt	dt	NOUN
ejpam-6583	153	7	)	)	PUNCT
ejpam-6583	153	8	1	1	NUM
ejpam-6583	153	9	p	p	NOUN
ejpam-6583	153	10	,	,	PUNCT
ejpam-6583	153	11	·	·	PUNCT
ejpam-6583	153	12	·	·	PUNCT
ejpam-6583	153	13	·	·	PUNCT
ejpam-6583	154	1	,	,	PUNCT
ejpam-6583	154	2	(	(	PUNCT
ejpam-6583	154	3	1∫	1∫	NUM
ejpam-6583	154	4	0	0	NUM
ejpam-6583	154	5	|	|	ADV
ejpam-6583	154	6	x(t)−	x(t)−	PROPN
ejpam-6583	154	7	y(t	y(t	PROPN
ejpam-6583	154	8	)	)	PUNCT
ejpam-6583	154	9	|p	|p	NOUN
ejpam-6583	154	10	dt	dt	NOUN
ejpam-6583	154	11	)	)	PUNCT
ejpam-6583	154	12	1	1	NUM
ejpam-6583	154	13	p	p	NOUN
ejpam-6583	154	14	)	)	PUNCT
ejpam-6583	154	15	∈	∈	PROPN
ejpam-6583	154	16	r⊕d	r⊕d	NOUN
ejpam-6583	154	17	,	,	PUNCT
ejpam-6583	154	18	where	where	SCONJ
ejpam-6583	154	19	x	x	X
ejpam-6583	154	20	=	=	PRON
ejpam-6583	154	21	{	{	PUNCT
ejpam-6583	154	22	xn	xn	NUM
ejpam-6583	154	23	}	}	PUNCT
ejpam-6583	154	24	,	,	PUNCT
ejpam-6583	154	25	y	y	PROPN
ejpam-6583	154	26	=	=	PRON
ejpam-6583	154	27	{	{	PUNCT
ejpam-6583	154	28	yn	yn	PROPN
ejpam-6583	154	29	}	}	PUNCT
ejpam-6583	154	30	∈	∈	PROPN
ejpam-6583	154	31	lp(r	lp(r	X
ejpam-6583	154	32	)	)	PUNCT
ejpam-6583	154	33	,	,	PUNCT
ejpam-6583	154	34	is	be	AUX
ejpam-6583	154	35	a	a	DET
ejpam-6583	154	36	b	b	NOUN
ejpam-6583	154	37	-	-	PUNCT
ejpam-6583	154	38	metric	metric	ADJ
ejpam-6583	154	39	space	space	NOUN
ejpam-6583	154	40	with	with	ADP
ejpam-6583	154	41	coefficient	coefficient	NOUN
ejpam-6583	154	42	s	s	PART
ejpam-6583	154	43	=	=	NOUN
ejpam-6583	154	44	2	2	NUM
ejpam-6583	154	45	1	1	NUM
ejpam-6583	154	46	p	p	NOUN
ejpam-6583	154	47	>	>	X
ejpam-6583	154	48	1	1	NUM
ejpam-6583	154	49	.	.	PUNCT
ejpam-6583	155	1	then	then	ADV
ejpam-6583	155	2	(	(	PUNCT
ejpam-6583	155	3	lp	lp	NOUN
ejpam-6583	155	4	,	,	PUNCT
ejpam-6583	155	5	r⊕d	r⊕d	NOUN
ejpam-6583	155	6	,	,	PUNCT
ejpam-6583	155	7	δb	δb	NOUN
ejpam-6583	155	8	r⊕d	r⊕d	NOUN
ejpam-6583	155	9	)	)	PUNCT
ejpam-6583	155	10	is	be	AUX
ejpam-6583	155	11	a	a	DET
ejpam-6583	155	12	complete	complete	ADJ
ejpam-6583	155	13	generalized	generalized	ADJ
ejpam-6583	155	14	b	b	NOUN
ejpam-6583	155	15	-	-	ADJ
ejpam-6583	155	16	metric	metric	ADJ
ejpam-6583	155	17	endowed	endow	VERB
ejpam-6583	155	18	with	with	ADP
ejpam-6583	155	19	the	the	DET
ejpam-6583	155	20	orthogonal	orthogonal	ADJ
ejpam-6583	155	21	direct	direct	ADJ
ejpam-6583	155	22	sum	sum	NOUN
ejpam-6583	155	23	space	space	NOUN
ejpam-6583	155	24	.	.	PUNCT
ejpam-6583	156	1	g.	g.	PROPN
ejpam-6583	156	2	albeladi	albeladi	PROPN
ejpam-6583	156	3	,	,	PUNCT
ejpam-6583	156	4	s.	s.	PROPN
ejpam-6583	156	5	omran	omran	PROPN
ejpam-6583	156	6	/	/	SYM
ejpam-6583	156	7	eur	eur	PROPN
ejpam-6583	156	8	.	.	PUNCT
ejpam-6583	157	1	j.	j.	PROPN
ejpam-6583	157	2	pure	pure	PROPN
ejpam-6583	157	3	appl	appl	PROPN
ejpam-6583	157	4	.	.	PROPN
ejpam-6583	157	5	math	math	PROPN
ejpam-6583	157	6	,	,	PUNCT
ejpam-6583	157	7	18	18	NUM
ejpam-6583	157	8	(	(	PUNCT
ejpam-6583	157	9	3	3	NUM
ejpam-6583	157	10	)	)	PUNCT
ejpam-6583	157	11	(	(	PUNCT
ejpam-6583	157	12	2025	2025	NUM
ejpam-6583	157	13	)	)	PUNCT
ejpam-6583	157	14	,	,	PUNCT
ejpam-6583	157	15	6583	6583	NUM
ejpam-6583	157	16	7	7	NUM
ejpam-6583	157	17	of	of	ADP
ejpam-6583	157	18	27	27	NUM
ejpam-6583	157	19	example	example	NOUN
ejpam-6583	157	20	4	4	NUM
ejpam-6583	157	21	.	.	PUNCT
ejpam-6583	158	1	let	let	VERB
ejpam-6583	158	2	x	x	PUNCT
ejpam-6583	158	3	=	=	PUNCT
ejpam-6583	158	4	{	{	PUNCT
ejpam-6583	158	5	0	0	NUM
ejpam-6583	158	6	,	,	PUNCT
ejpam-6583	158	7	1	1	NUM
ejpam-6583	158	8	,	,	PUNCT
ejpam-6583	158	9	2	2	NUM
ejpam-6583	158	10	}	}	PUNCT
ejpam-6583	158	11	and	and	CCONJ
ejpam-6583	158	12	the	the	DET
ejpam-6583	158	13	operator	operator	NOUN
ejpam-6583	158	14	δb	δb	NOUN
ejpam-6583	158	15	:	:	PUNCT
ejpam-6583	158	16	x	x	PUNCT
ejpam-6583	158	17	×	×	NOUN
ejpam-6583	158	18	x	x	PUNCT
ejpam-6583	158	19	→	→	X
ejpam-6583	158	20	r+	r+	PRON
ejpam-6583	158	21	defined	define	VERB
ejpam-6583	158	22	by	by	ADP
ejpam-6583	158	23	δb(0	δb(0	NOUN
ejpam-6583	158	24	,	,	PUNCT
ejpam-6583	158	25	0	0	NUM
ejpam-6583	158	26	)	)	PUNCT
ejpam-6583	159	1	=	=	SYM
ejpam-6583	160	1	δb(1	δb(1	NOUN
ejpam-6583	160	2	,	,	PUNCT
ejpam-6583	160	3	1	1	NUM
ejpam-6583	160	4	)	)	PUNCT
ejpam-6583	160	5	=	=	SYM
ejpam-6583	161	1	δb(2	δb(2	NOUN
ejpam-6583	161	2	,	,	PUNCT
ejpam-6583	161	3	2	2	NUM
ejpam-6583	161	4	)	)	PUNCT
ejpam-6583	161	5	=	=	SYM
ejpam-6583	161	6	0	0	NUM
ejpam-6583	161	7	,	,	PUNCT
ejpam-6583	161	8	δb(0	δb(0	NOUN
ejpam-6583	161	9	,	,	PUNCT
ejpam-6583	161	10	1	1	NUM
ejpam-6583	161	11	)	)	PUNCT
ejpam-6583	161	12	=	=	SYM
ejpam-6583	162	1	δb(1	δb(1	PROPN
ejpam-6583	162	2	,	,	PUNCT
ejpam-6583	162	3	0	0	NUM
ejpam-6583	162	4	)	)	PUNCT
ejpam-6583	162	5	=	=	SYM
ejpam-6583	163	1	δb(1	δb(1	NOUN
ejpam-6583	163	2	,	,	PUNCT
ejpam-6583	163	3	2	2	NUM
ejpam-6583	163	4	)	)	PUNCT
ejpam-6583	163	5	=	=	SYM
ejpam-6583	164	1	δb(2	δb(2	NOUN
ejpam-6583	164	2	,	,	PUNCT
ejpam-6583	164	3	1	1	NUM
ejpam-6583	164	4	)	)	PUNCT
ejpam-6583	164	5	=	=	SYM
ejpam-6583	164	6	1	1	NUM
ejpam-6583	164	7	,	,	PUNCT
ejpam-6583	164	8	and	and	CCONJ
ejpam-6583	164	9	δb(2	δb(2	NOUN
ejpam-6583	164	10	,	,	PUNCT
ejpam-6583	164	11	0	0	NUM
ejpam-6583	164	12	)	)	PUNCT
ejpam-6583	164	13	=	=	PUNCT
ejpam-6583	165	1	δb(0	δb(0	NOUN
ejpam-6583	165	2	,	,	PUNCT
ejpam-6583	165	3	2	2	NUM
ejpam-6583	165	4	)	)	PUNCT
ejpam-6583	165	5	=	=	SYM
ejpam-6583	165	6	m	m	PROPN
ejpam-6583	165	7	,	,	PUNCT
ejpam-6583	165	8	where	where	SCONJ
ejpam-6583	165	9	m	m	VERB
ejpam-6583	165	10	is	be	AUX
ejpam-6583	165	11	given	give	VERB
ejpam-6583	165	12	real	real	ADJ
ejpam-6583	165	13	number	number	NOUN
ejpam-6583	165	14	such	such	ADJ
ejpam-6583	165	15	that	that	SCONJ
ejpam-6583	165	16	m	m	VERB
ejpam-6583	165	17	≥	≥	NOUN
ejpam-6583	165	18	2	2	NUM
ejpam-6583	165	19	.	.	PUNCT
ejpam-6583	166	1	δb	δb	NOUN
ejpam-6583	166	2	r⊕d	r⊕d	NOUN
ejpam-6583	166	3	(	(	PUNCT
ejpam-6583	166	4	x	x	X
ejpam-6583	166	5	,	,	PUNCT
ejpam-6583	166	6	y	y	NOUN
ejpam-6583	166	7	)	)	PUNCT
ejpam-6583	167	1	=	=	NOUN
ejpam-6583	167	2	diag	diag	NOUN
ejpam-6583	167	3	(	(	PUNCT
ejpam-6583	167	4	δb(x	δb(x	PROPN
ejpam-6583	167	5	,	,	PUNCT
ejpam-6583	167	6	y	y	NOUN
ejpam-6583	167	7	)	)	PUNCT
ejpam-6583	167	8	,	,	PUNCT
ejpam-6583	167	9	δb(x	δb(x	PROPN
ejpam-6583	167	10	,	,	PUNCT
ejpam-6583	167	11	y	y	NOUN
ejpam-6583	167	12	)	)	PUNCT
ejpam-6583	167	13	,	,	PUNCT
ejpam-6583	167	14	·	·	PUNCT
ejpam-6583	167	15	·	·	PUNCT
ejpam-6583	167	16	·	·	PUNCT
ejpam-6583	167	17	,	,	PUNCT
ejpam-6583	167	18	δb(x	δb(x	PROPN
ejpam-6583	167	19	,	,	PUNCT
ejpam-6583	167	20	y	y	NOUN
ejpam-6583	167	21	)	)	PUNCT
ejpam-6583	167	22	)	)	PUNCT
ejpam-6583	168	1	∈	∈	PROPN
ejpam-6583	168	2	r⊕d	r⊕d	NOUN
ejpam-6583	168	3	+	+	X
ejpam-6583	168	4	.	.	PUNCT
ejpam-6583	169	1	it	it	PRON
ejpam-6583	169	2	is	be	AUX
ejpam-6583	169	3	easy	easy	ADJ
ejpam-6583	169	4	to	to	PART
ejpam-6583	169	5	see	see	VERB
ejpam-6583	169	6	that	that	SCONJ
ejpam-6583	169	7	δb	δb	NOUN
ejpam-6583	169	8	r⊕d	r⊕d	NOUN
ejpam-6583	169	9	(	(	PUNCT
ejpam-6583	169	10	x	x	X
ejpam-6583	169	11	,	,	PUNCT
ejpam-6583	169	12	y	y	NOUN
ejpam-6583	169	13	)	)	PUNCT
ejpam-6583	169	14	≤	≤	NUM
ejpam-6583	169	15	m	m	VERB
ejpam-6583	169	16	2	2	NUM
ejpam-6583	169	17	[	[	PUNCT
ejpam-6583	169	18	δb	δb	NOUN
ejpam-6583	169	19	r⊕d	r⊕d	NOUN
ejpam-6583	169	20	(	(	PUNCT
ejpam-6583	169	21	x	x	X
ejpam-6583	169	22	,	,	PUNCT
ejpam-6583	169	23	z	z	NOUN
ejpam-6583	169	24	)	)	PUNCT
ejpam-6583	170	1	+	+	CCONJ
ejpam-6583	170	2	δb	δb	NOUN
ejpam-6583	170	3	r⊕d	r⊕d	NOUN
ejpam-6583	170	4	(	(	PUNCT
ejpam-6583	170	5	z	z	NOUN
ejpam-6583	170	6	,	,	PUNCT
ejpam-6583	170	7	y	y	PROPN
ejpam-6583	170	8	)	)	PUNCT
ejpam-6583	170	9	]	]	PUNCT
ejpam-6583	170	10	,	,	PUNCT
ejpam-6583	170	11	for	for	ADP
ejpam-6583	170	12	all	all	DET
ejpam-6583	170	13	x	x	NOUN
ejpam-6583	170	14	,	,	PUNCT
ejpam-6583	170	15	y	y	PROPN
ejpam-6583	170	16	,	,	PUNCT
ejpam-6583	170	17	z	z	NOUN
ejpam-6583	170	18	∈	∈	PROPN
ejpam-6583	170	19	x	x	X
ejpam-6583	170	20	.	.	PUNCT
ejpam-6583	171	1	therefore	therefore	ADV
ejpam-6583	171	2	,	,	PUNCT
ejpam-6583	171	3	(	(	PUNCT
ejpam-6583	171	4	x	x	X
ejpam-6583	171	5	,	,	PUNCT
ejpam-6583	171	6	r⊕d	r⊕d	NOUN
ejpam-6583	171	7	+	+	X
ejpam-6583	171	8	,	,	PUNCT
ejpam-6583	171	9	δb	δb	NOUN
ejpam-6583	171	10	r⊕d	r⊕d	NOUN
ejpam-6583	171	11	)	)	PUNCT
ejpam-6583	171	12	is	be	AUX
ejpam-6583	171	13	a	a	DET
ejpam-6583	171	14	generalized	generalized	ADJ
ejpam-6583	171	15	b	b	X
ejpam-6583	171	16	-	-	ADJ
ejpam-6583	171	17	metric	metric	ADJ
ejpam-6583	171	18	space	space	NOUN
ejpam-6583	171	19	with	with	ADP
ejpam-6583	171	20	coefficient	coefficient	NOUN
ejpam-6583	171	21	s	s	PART
ejpam-6583	171	22	=	=	NOUN
ejpam-6583	171	23	m	m	VERB
ejpam-6583	171	24	2	2	NUM
ejpam-6583	171	25	.	.	PUNCT
ejpam-6583	172	1	we	we	PRON
ejpam-6583	172	2	obtain	obtain	VERB
ejpam-6583	172	3	that	that	SCONJ
ejpam-6583	172	4	the	the	DET
ejpam-6583	172	5	ordinary	ordinary	ADJ
ejpam-6583	172	6	triangle	triangle	NOUN
ejpam-6583	172	7	inequality	inequality	NOUN
ejpam-6583	172	8	does	do	AUX
ejpam-6583	172	9	not	not	PART
ejpam-6583	172	10	hold	hold	VERB
ejpam-6583	172	11	if	if	SCONJ
ejpam-6583	172	12	m	m	VERB
ejpam-6583	172	13	>	>	X
ejpam-6583	172	14	2	2	NUM
ejpam-6583	172	15	,	,	PUNCT
ejpam-6583	172	16	and	and	CCONJ
ejpam-6583	172	17	then	then	ADV
ejpam-6583	172	18	(	(	PUNCT
ejpam-6583	172	19	x	x	X
ejpam-6583	172	20	,	,	PUNCT
ejpam-6583	172	21	d	d	X
ejpam-6583	172	22	)	)	PUNCT
ejpam-6583	172	23	is	be	AUX
ejpam-6583	172	24	not	not	PART
ejpam-6583	172	25	a	a	DET
ejpam-6583	172	26	metric	metric	ADJ
ejpam-6583	172	27	space	space	NOUN
ejpam-6583	172	28	.	.	PUNCT
ejpam-6583	173	1	corolary	corolary	ADJ
ejpam-6583	173	2	2	2	X
ejpam-6583	173	3	.	.	X
ejpam-6583	174	1	let	let	AUX
ejpam-6583	174	2	(	(	PUNCT
ejpam-6583	174	3	x	x	INTJ
ejpam-6583	174	4	,	,	PUNCT
ejpam-6583	174	5	r⊕d	r⊕d	NOUN
ejpam-6583	174	6	+	+	X
ejpam-6583	174	7	,	,	PUNCT
ejpam-6583	174	8	δb	δb	NOUN
ejpam-6583	174	9	r⊕d	r⊕d	NOUN
ejpam-6583	174	10	)	)	PUNCT
ejpam-6583	174	11	be	be	AUX
ejpam-6583	174	12	a	a	DET
ejpam-6583	174	13	generalized	generalized	ADJ
ejpam-6583	174	14	b	b	NOUN
ejpam-6583	174	15	-	-	ADJ
ejpam-6583	174	16	metric	metric	ADJ
ejpam-6583	174	17	space	space	NOUN
ejpam-6583	174	18	.	.	PUNCT
ejpam-6583	175	1	then	then	ADV
ejpam-6583	175	2	,	,	PUNCT
ejpam-6583	175	3	the	the	DET
ejpam-6583	175	4	following	follow	VERB
ejpam-6583	175	5	assertions	assertion	NOUN
ejpam-6583	175	6	hold	hold	VERB
ejpam-6583	175	7	:	:	PUNCT
ejpam-6583	176	1	1	1	X
ejpam-6583	176	2	.	.	X
ejpam-6583	176	3	a	a	DET
ejpam-6583	176	4	b	b	NOUN
ejpam-6583	176	5	-	-	PUNCT
ejpam-6583	176	6	convergent	convergent	ADJ
ejpam-6583	176	7	sequence	sequence	NOUN
ejpam-6583	176	8	with	with	ADP
ejpam-6583	176	9	respect	respect	NOUN
ejpam-6583	176	10	to	to	ADP
ejpam-6583	176	11	r⊕d	r⊕d	NOUN
ejpam-6583	176	12	has	have	VERB
ejpam-6583	176	13	a	a	DET
ejpam-6583	176	14	unique	unique	ADJ
ejpam-6583	176	15	limit	limit	NOUN
ejpam-6583	176	16	.	.	PUNCT
ejpam-6583	177	1	2	2	X
ejpam-6583	177	2	.	.	X
ejpam-6583	177	3	each	each	DET
ejpam-6583	177	4	b	b	NOUN
ejpam-6583	177	5	-	-	PUNCT
ejpam-6583	177	6	convergent	convergent	ADJ
ejpam-6583	177	7	sequence	sequence	NOUN
ejpam-6583	177	8	with	with	ADP
ejpam-6583	177	9	respect	respect	NOUN
ejpam-6583	177	10	to	to	ADP
ejpam-6583	177	11	r⊕d	r⊕d	NOUN
ejpam-6583	177	12	is	be	AUX
ejpam-6583	177	13	a	a	DET
ejpam-6583	177	14	b	b	PROPN
ejpam-6583	177	15	-	-	PUNCT
ejpam-6583	177	16	cauchy	cauchy	ADJ
ejpam-6583	177	17	sequence	sequence	NOUN
ejpam-6583	177	18	.	.	PUNCT
ejpam-6583	178	1	definition	definition	NOUN
ejpam-6583	178	2	5	5	NUM
ejpam-6583	178	3	.	.	PUNCT
ejpam-6583	178	4	suppose	suppose	VERB
ejpam-6583	178	5	that	that	SCONJ
ejpam-6583	178	6	(	(	PUNCT
ejpam-6583	178	7	x	x	X
ejpam-6583	178	8	,	,	PUNCT
ejpam-6583	178	9	r⊕d	r⊕d	NOUN
ejpam-6583	178	10	,	,	PUNCT
ejpam-6583	178	11	δb	δb	NOUN
ejpam-6583	178	12	r⊕d	r⊕d	NOUN
ejpam-6583	178	13	)	)	PUNCT
ejpam-6583	178	14	and	and	CCONJ
ejpam-6583	178	15	(	(	PUNCT
ejpam-6583	178	16	y	y	NOUN
ejpam-6583	178	17	,	,	PUNCT
ejpam-6583	178	18	r⊕d	r⊕d	NOUN
ejpam-6583	178	19	,	,	PUNCT
ejpam-6583	178	20	δb	δb	NOUN
ejpam-6583	178	21	r⊕d	r⊕d	NOUN
ejpam-6583	178	22	)	)	PUNCT
ejpam-6583	178	23	are	be	AUX
ejpam-6583	178	24	two	two	NUM
ejpam-6583	178	25	generalized	generalized	ADJ
ejpam-6583	178	26	b	b	X
ejpam-6583	178	27	-	-	ADJ
ejpam-6583	178	28	metric	metric	ADJ
ejpam-6583	178	29	spaces	space	NOUN
ejpam-6583	178	30	endowed	endow	VERB
ejpam-6583	178	31	with	with	ADP
ejpam-6583	178	32	the	the	DET
ejpam-6583	178	33	orthogonal	orthogonal	ADJ
ejpam-6583	178	34	direct	direct	ADJ
ejpam-6583	178	35	sum	sum	NOUN
ejpam-6583	178	36	.	.	PUNCT
ejpam-6583	179	1	1	1	X
ejpam-6583	179	2	.	.	X
ejpam-6583	179	3	the	the	DET
ejpam-6583	179	4	space	space	NOUN
ejpam-6583	179	5	(	(	PUNCT
ejpam-6583	179	6	x	x	INTJ
ejpam-6583	179	7	,	,	PUNCT
ejpam-6583	179	8	r⊕d	r⊕d	NOUN
ejpam-6583	179	9	,	,	PUNCT
ejpam-6583	179	10	δb	δb	NOUN
ejpam-6583	179	11	r⊕d	r⊕d	NOUN
ejpam-6583	179	12	)	)	PUNCT
ejpam-6583	179	13	is	be	AUX
ejpam-6583	179	14	a	a	DET
ejpam-6583	179	15	complete	complete	ADJ
ejpam-6583	179	16	if	if	SCONJ
ejpam-6583	179	17	every	every	DET
ejpam-6583	179	18	cauchy	cauchy	ADJ
ejpam-6583	179	19	sequence	sequence	NOUN
ejpam-6583	179	20	with	with	ADP
ejpam-6583	179	21	respect	respect	NOUN
ejpam-6583	179	22	to	to	ADP
ejpam-6583	179	23	rd	rd	PROPN
ejpam-6583	179	24	is	be	AUX
ejpam-6583	179	25	converges	converge	NOUN
ejpam-6583	179	26	.	.	PUNCT
ejpam-6583	180	1	2	2	X
ejpam-6583	180	2	.	.	X
ejpam-6583	180	3	a	a	DET
ejpam-6583	180	4	function	function	NOUN
ejpam-6583	180	5	f	f	NOUN
ejpam-6583	180	6	:	:	PUNCT
ejpam-6583	180	7	x	x	X
ejpam-6583	180	8	→	→	SYM
ejpam-6583	180	9	y	y	PROPN
ejpam-6583	180	10	is	be	AUX
ejpam-6583	180	11	said	say	VERB
ejpam-6583	180	12	to	to	PART
ejpam-6583	180	13	be	be	AUX
ejpam-6583	180	14	continuous	continuous	ADJ
ejpam-6583	180	15	at	at	ADP
ejpam-6583	180	16	a	a	DET
ejpam-6583	180	17	point	point	NOUN
ejpam-6583	180	18	x	x	SYM
ejpam-6583	180	19	∈	∈	NOUN
ejpam-6583	180	20	x	x	INTJ
ejpam-6583	180	21	if	if	SCONJ
ejpam-6583	180	22	,	,	PUNCT
ejpam-6583	180	23	for	for	ADP
ejpam-6583	180	24	every	every	DET
ejpam-6583	180	25	sequence	sequence	NOUN
ejpam-6583	180	26	{	{	PUNCT
ejpam-6583	180	27	xn	xn	NOUN
ejpam-6583	180	28	}	}	PUNCT
ejpam-6583	180	29	⊆	⊆	NUM
ejpam-6583	180	30	x	x	NOUN
ejpam-6583	180	31	that	that	PRON
ejpam-6583	180	32	converges	converge	VERB
ejpam-6583	180	33	to	to	ADP
ejpam-6583	180	34	x	x	PRON
ejpam-6583	180	35	,	,	PUNCT
ejpam-6583	180	36	the	the	DET
ejpam-6583	180	37	sequence	sequence	NOUN
ejpam-6583	180	38	f	f	PROPN
ejpam-6583	180	39	(	(	PUNCT
ejpam-6583	180	40	xn	xn	PROPN
ejpam-6583	180	41	)	)	PUNCT
ejpam-6583	180	42	converges	converge	NOUN
ejpam-6583	180	43	to	to	ADP
ejpam-6583	180	44	f	f	PROPN
ejpam-6583	180	45	(	(	PUNCT
ejpam-6583	180	46	x	x	NOUN
ejpam-6583	180	47	)	)	PUNCT
ejpam-6583	180	48	.	.	PUNCT
ejpam-6583	181	1	3	3	X
ejpam-6583	181	2	.	.	X
ejpam-6583	181	3	main	main	ADJ
ejpam-6583	181	4	results	result	NOUN
ejpam-6583	181	5	in	in	ADP
ejpam-6583	181	6	this	this	DET
ejpam-6583	181	7	section	section	NOUN
ejpam-6583	181	8	,	,	PUNCT
ejpam-6583	181	9	we	we	PRON
ejpam-6583	181	10	will	will	AUX
ejpam-6583	181	11	present	present	VERB
ejpam-6583	181	12	some	some	DET
ejpam-6583	181	13	banach	banach	ADV
ejpam-6583	181	14	fixed	fix	VERB
ejpam-6583	181	15	-	-	PUNCT
ejpam-6583	181	16	point	point	NOUN
ejpam-6583	181	17	theorems	theorem	NOUN
ejpam-6583	181	18	combining	combine	VERB
ejpam-6583	181	19	the	the	DET
ejpam-6583	181	20	direct	direct	ADJ
ejpam-6583	181	21	sum	sum	NOUN
ejpam-6583	181	22	.	.	PUNCT
ejpam-6583	182	1	definition	definition	NOUN
ejpam-6583	182	2	6	6	NUM
ejpam-6583	182	3	.	.	PUNCT
ejpam-6583	182	4	suppose	suppose	VERB
ejpam-6583	182	5	that	that	SCONJ
ejpam-6583	182	6	(	(	PUNCT
ejpam-6583	182	7	x	x	X
ejpam-6583	182	8	,	,	PUNCT
ejpam-6583	182	9	r⊕d	r⊕d	NOUN
ejpam-6583	182	10	,	,	PUNCT
ejpam-6583	182	11	δb	δb	NOUN
ejpam-6583	182	12	r⊕d	r⊕d	NOUN
ejpam-6583	182	13	)	)	PUNCT
ejpam-6583	182	14	is	be	AUX
ejpam-6583	182	15	a	a	DET
ejpam-6583	182	16	complete	complete	ADJ
ejpam-6583	182	17	generalized	generalized	ADJ
ejpam-6583	182	18	b	b	X
ejpam-6583	182	19	-	-	ADJ
ejpam-6583	182	20	metric	metric	ADJ
ejpam-6583	182	21	space	space	NOUN
ejpam-6583	182	22	endowed	endow	VERB
ejpam-6583	182	23	with	with	ADP
ejpam-6583	182	24	the	the	DET
ejpam-6583	182	25	orthogonal	orthogonal	ADJ
ejpam-6583	182	26	direct	direct	ADJ
ejpam-6583	182	27	sum	sum	NOUN
ejpam-6583	182	28	.	.	PUNCT
ejpam-6583	183	1	an	an	DET
ejpam-6583	183	2	operator	operator	NOUN
ejpam-6583	183	3	f	f	NOUN
ejpam-6583	183	4	:	:	PUNCT
ejpam-6583	183	5	x	x	X
ejpam-6583	183	6	→	→	PUNCT
ejpam-6583	183	7	x	x	X
ejpam-6583	183	8	is	be	AUX
ejpam-6583	183	9	said	say	VERB
ejpam-6583	183	10	to	to	PART
ejpam-6583	183	11	be	be	AUX
ejpam-6583	183	12	a	a	DET
ejpam-6583	183	13	contraction	contraction	NOUN
ejpam-6583	183	14	and	and	CCONJ
ejpam-6583	183	15	endowed	endow	VERB
ejpam-6583	183	16	with	with	ADP
ejpam-6583	183	17	the	the	DET
ejpam-6583	183	18	orthogonal	orthogonal	ADJ
ejpam-6583	183	19	direct	direct	ADJ
ejpam-6583	183	20	sum	sum	NOUN
ejpam-6583	183	21	if	if	SCONJ
ejpam-6583	183	22	there	there	PRON
ejpam-6583	183	23	exists	exist	VERB
ejpam-6583	183	24	a	a	DET
ejpam-6583	183	25	diagonal	diagonal	ADJ
ejpam-6583	183	26	matrix	matrix	NOUN
ejpam-6583	183	27	λ	λ	X
ejpam-6583	183	28	=	=	SYM
ejpam-6583	183	29	diag(λ1	diag(λ1	NOUN
ejpam-6583	183	30	,	,	PUNCT
ejpam-6583	183	31	λ2	λ2	NOUN
ejpam-6583	183	32	,	,	PUNCT
ejpam-6583	183	33	·	·	PUNCT
ejpam-6583	183	34	·	·	PUNCT
ejpam-6583	183	35	·	·	PUNCT
ejpam-6583	183	36	,	,	PUNCT
ejpam-6583	183	37	λd	λd	NOUN
ejpam-6583	183	38	)	)	PUNCT
ejpam-6583	183	39	∈	∈	PROPN
ejpam-6583	183	40	rd	rd	NOUN
ejpam-6583	184	1	+	+	CCONJ
ejpam-6583	184	2	with	with	ADP
ejpam-6583	184	3	0̃	0̃	PROPN
ejpam-6583	184	4	≾	≾	PROPN
ejpam-6583	184	5	λi	λi	NOUN
ejpam-6583	184	6	≺	≺	NOUN
ejpam-6583	184	7	1	1	NUM
ejpam-6583	184	8	s	s	VERB
ejpam-6583	184	9	such	such	ADJ
ejpam-6583	184	10	that	that	PRON
ejpam-6583	184	11	δb	δb	NOUN
ejpam-6583	184	12	r⊕d	r⊕d	NOUN
ejpam-6583	184	13	(	(	PUNCT
ejpam-6583	184	14	f	f	X
ejpam-6583	184	15	(	(	PUNCT
ejpam-6583	184	16	x	x	NOUN
ejpam-6583	184	17	)	)	PUNCT
ejpam-6583	184	18	,	,	PUNCT
ejpam-6583	184	19	f	f	PROPN
ejpam-6583	184	20	(	(	PUNCT
ejpam-6583	184	21	y	y	NOUN
ejpam-6583	184	22	)	)	PUNCT
ejpam-6583	184	23	)	)	PUNCT
ejpam-6583	185	1	≾	≾	PROPN
ejpam-6583	185	2	λ	λ	PROPN
ejpam-6583	185	3	δb	δb	NOUN
ejpam-6583	185	4	r⊕d	r⊕d	NOUN
ejpam-6583	185	5	(	(	PUNCT
ejpam-6583	185	6	x	x	X
ejpam-6583	185	7	,	,	PUNCT
ejpam-6583	185	8	y	y	PROPN
ejpam-6583	185	9	)	)	PUNCT
ejpam-6583	185	10	,	,	PUNCT
ejpam-6583	185	11	for	for	ADP
ejpam-6583	185	12	all	all	DET
ejpam-6583	185	13	x	x	NOUN
ejpam-6583	185	14	,	,	PUNCT
ejpam-6583	185	15	y	y	PROPN
ejpam-6583	185	16	∈	∈	PROPN
ejpam-6583	185	17	x	x	X
ejpam-6583	185	18	g.	g.	NOUN
ejpam-6583	185	19	albeladi	albeladi	PROPN
ejpam-6583	185	20	,	,	PUNCT
ejpam-6583	185	21	s.	s.	PROPN
ejpam-6583	185	22	omran	omran	PROPN
ejpam-6583	185	23	/	/	SYM
ejpam-6583	185	24	eur	eur	PROPN
ejpam-6583	185	25	.	.	PUNCT
ejpam-6583	186	1	j.	j.	PROPN
ejpam-6583	186	2	pure	pure	PROPN
ejpam-6583	186	3	appl	appl	PROPN
ejpam-6583	186	4	.	.	PROPN
ejpam-6583	186	5	math	math	PROPN
ejpam-6583	186	6	,	,	PUNCT
ejpam-6583	186	7	18	18	NUM
ejpam-6583	186	8	(	(	PUNCT
ejpam-6583	186	9	3	3	NUM
ejpam-6583	186	10	)	)	PUNCT
ejpam-6583	186	11	(	(	PUNCT
ejpam-6583	186	12	2025	2025	NUM
ejpam-6583	186	13	)	)	PUNCT
ejpam-6583	186	14	,	,	PUNCT
ejpam-6583	186	15	6583	6583	NUM
ejpam-6583	186	16	8	8	NUM
ejpam-6583	186	17	of	of	ADP
ejpam-6583	186	18	27	27	NUM
ejpam-6583	186	19	example	example	NOUN
ejpam-6583	186	20	5	5	NUM
ejpam-6583	186	21	.	.	PUNCT
ejpam-6583	187	1	let	let	VERB
ejpam-6583	187	2	x	x	PUNCT
ejpam-6583	187	3	=	=	SYM
ejpam-6583	187	4	r	r	NOUN
ejpam-6583	187	5	and	and	CCONJ
ejpam-6583	187	6	δb	δb	NOUN
ejpam-6583	187	7	r⊕d	r⊕d	NOUN
ejpam-6583	187	8	:	:	PUNCT
ejpam-6583	187	9	x	x	X
ejpam-6583	187	10	×x	×x	ADP
ejpam-6583	187	11	→	→	PUNCT
ejpam-6583	187	12	r⊕d	r⊕d	NOUN
ejpam-6583	187	13	be	be	VERB
ejpam-6583	187	14	a	a	DET
ejpam-6583	187	15	generalized	generalized	ADJ
ejpam-6583	187	16	b	b	X
ejpam-6583	187	17	-	-	ADJ
ejpam-6583	187	18	metric	metric	ADJ
ejpam-6583	187	19	space	space	NOUN
ejpam-6583	187	20	endowed	endow	VERB
ejpam-6583	187	21	with	with	ADP
ejpam-6583	187	22	the	the	DET
ejpam-6583	187	23	orthogonal	orthogonal	ADJ
ejpam-6583	187	24	direct	direct	ADJ
ejpam-6583	187	25	sum	sum	NOUN
ejpam-6583	187	26	defined	define	VERB
ejpam-6583	187	27	by	by	ADP
ejpam-6583	187	28	δb	δb	NOUN
ejpam-6583	187	29	r⊕d	r⊕d	NOUN
ejpam-6583	187	30	(	(	PUNCT
ejpam-6583	187	31	x	x	X
ejpam-6583	187	32	,	,	PUNCT
ejpam-6583	187	33	y	y	NOUN
ejpam-6583	187	34	)	)	PUNCT
ejpam-6583	188	1	=	=	NOUN
ejpam-6583	188	2	diag	diag	NOUN
ejpam-6583	188	3	(	(	PUNCT
ejpam-6583	188	4	|	|	ADV
ejpam-6583	188	5	x−	x−	PROPN
ejpam-6583	188	6	y	y	PROPN
ejpam-6583	188	7	|2	|2	NUM
ejpam-6583	188	8	,	,	PUNCT
ejpam-6583	188	9	|	|	ADV
ejpam-6583	188	10	x−	x−	PROPN
ejpam-6583	188	11	y	y	PROPN
ejpam-6583	188	12	|2	|2	NUM
ejpam-6583	188	13	,	,	PUNCT
ejpam-6583	188	14	·	·	PUNCT
ejpam-6583	188	15	·	·	PUNCT
ejpam-6583	188	16	·	·	PUNCT
ejpam-6583	188	17	,	,	PUNCT
ejpam-6583	188	18	|	|	ADV
ejpam-6583	188	19	x−	x−	PROPN
ejpam-6583	188	20	y	y	PROPN
ejpam-6583	188	21	|2	|2	NUM
ejpam-6583	188	22	)	)	PUNCT
ejpam-6583	188	23	∈	∈	PROPN
ejpam-6583	188	24	r⊕d	r⊕d	NOUN
ejpam-6583	188	25	,	,	PUNCT
ejpam-6583	188	26	and	and	CCONJ
ejpam-6583	188	27	let	let	VERB
ejpam-6583	188	28	λ	λ	X
ejpam-6583	188	29	=	=	PUNCT
ejpam-6583	188	30	diag	diag	X
ejpam-6583	188	31	(	(	PUNCT
ejpam-6583	188	32	1	1	NUM
ejpam-6583	188	33	4	4	NUM
ejpam-6583	188	34	,	,	PUNCT
ejpam-6583	188	35	1	1	NUM
ejpam-6583	188	36	4	4	NUM
ejpam-6583	188	37	,	,	PUNCT
ejpam-6583	188	38	·	·	PUNCT
ejpam-6583	188	39	·	·	PUNCT
ejpam-6583	188	40	·	·	PUNCT
ejpam-6583	188	41	,	,	PUNCT
ejpam-6583	188	42	1	1	NUM
ejpam-6583	188	43	4	4	NUM
ejpam-6583	188	44	)	)	PUNCT
ejpam-6583	188	45	and	and	CCONJ
ejpam-6583	188	46	f	f	X
ejpam-6583	188	47	:	:	PUNCT
ejpam-6583	188	48	x	x	X
ejpam-6583	188	49	→	→	PUNCT
ejpam-6583	188	50	x	x	X
ejpam-6583	188	51	such	such	ADJ
ejpam-6583	188	52	that	that	SCONJ
ejpam-6583	188	53	f	f	PROPN
ejpam-6583	188	54	(	(	PUNCT
ejpam-6583	188	55	x	x	X
ejpam-6583	188	56	)	)	PUNCT
ejpam-6583	188	57	=	=	SYM
ejpam-6583	188	58	x	x	SYM
ejpam-6583	188	59	2	2	X
ejpam-6583	188	60	.	.	PUNCT
ejpam-6583	189	1	then	then	ADV
ejpam-6583	189	2	,	,	PUNCT
ejpam-6583	189	3	δb	δb	NOUN
ejpam-6583	189	4	r⊕d	r⊕d	NOUN
ejpam-6583	189	5	(	(	PUNCT
ejpam-6583	189	6	f	f	PROPN
ejpam-6583	189	7	(	(	PUNCT
ejpam-6583	189	8	x),f	x),f	PROPN
ejpam-6583	189	9	(	(	PUNCT
ejpam-6583	189	10	y	y	NOUN
ejpam-6583	189	11	)	)	PUNCT
ejpam-6583	189	12	)	)	PUNCT
ejpam-6583	190	1	=	=	SYM
ejpam-6583	190	2	diag	diag	NOUN
ejpam-6583	190	3	(	(	PUNCT
ejpam-6583	190	4	1	1	NUM
ejpam-6583	190	5	4	4	NUM
ejpam-6583	190	6	·	·	PUNCT
ejpam-6583	190	7	|	|	ADV
ejpam-6583	190	8	x−	x−	PROPN
ejpam-6583	190	9	y	y	PROPN
ejpam-6583	190	10	|2	|2	NUM
ejpam-6583	190	11	,	,	PUNCT
ejpam-6583	190	12	1	1	NUM
ejpam-6583	190	13	4	4	NUM
ejpam-6583	190	14	·	·	PUNCT
ejpam-6583	190	15	|	|	ADV
ejpam-6583	190	16	x−	x−	PROPN
ejpam-6583	190	17	y	y	PROPN
ejpam-6583	190	18	|2	|2	NUM
ejpam-6583	190	19	,	,	PUNCT
ejpam-6583	190	20	·	·	PUNCT
ejpam-6583	190	21	·	·	PUNCT
ejpam-6583	190	22	·	·	PUNCT
ejpam-6583	190	23	,	,	PUNCT
ejpam-6583	190	24	1	1	NUM
ejpam-6583	190	25	4	4	NUM
ejpam-6583	190	26	·	·	PUNCT
ejpam-6583	190	27	|	|	ADV
ejpam-6583	190	28	x−	x−	PROPN
ejpam-6583	190	29	y	y	PROPN
ejpam-6583	190	30	|2	|2	NUM
ejpam-6583	190	31	)	)	PUNCT
ejpam-6583	190	32	∈	∈	PROPN
ejpam-6583	190	33	r⊕d	r⊕d	NOUN
ejpam-6583	190	34	.	.	PUNCT
ejpam-6583	191	1	it	it	PRON
ejpam-6583	191	2	is	be	AUX
ejpam-6583	191	3	clear	clear	ADJ
ejpam-6583	191	4	that	that	SCONJ
ejpam-6583	191	5	δb	δb	NOUN
ejpam-6583	191	6	r⊕d	r⊕d	NOUN
ejpam-6583	191	7	(	(	PUNCT
ejpam-6583	191	8	f	f	PROPN
ejpam-6583	191	9	(	(	PUNCT
ejpam-6583	191	10	x),f	x),f	PROPN
ejpam-6583	191	11	(	(	PUNCT
ejpam-6583	191	12	y	y	NOUN
ejpam-6583	191	13	)	)	PUNCT
ejpam-6583	191	14	)	)	PUNCT
ejpam-6583	192	1	≾	≾	PROPN
ejpam-6583	192	2	λ	λ	PROPN
ejpam-6583	192	3	·	·	PUNCT
ejpam-6583	192	4	δb	δb	NOUN
ejpam-6583	192	5	r⊕d	r⊕d	NOUN
ejpam-6583	192	6	(	(	PUNCT
ejpam-6583	192	7	x	x	X
ejpam-6583	192	8	,	,	PUNCT
ejpam-6583	192	9	y	y	PROPN
ejpam-6583	192	10	)	)	PUNCT
ejpam-6583	192	11	,	,	PUNCT
ejpam-6583	192	12	where	where	SCONJ
ejpam-6583	192	13	λ	λ	PROPN
ejpam-6583	192	14	≺	≺	VERB
ejpam-6583	192	15	ir	ir	PROPN
ejpam-6583	192	16	⊕d	⊕d	NOUN
ejpam-6583	192	17	+	+	X
ejpam-6583	192	18	.	.	PUNCT
ejpam-6583	193	1	therefore	therefore	ADV
ejpam-6583	193	2	,	,	PUNCT
ejpam-6583	193	3	f	f	PROPN
ejpam-6583	193	4	is	be	AUX
ejpam-6583	193	5	a	a	DET
ejpam-6583	193	6	contraction	contraction	NOUN
ejpam-6583	193	7	and	and	CCONJ
ejpam-6583	193	8	endowed	endow	VERB
ejpam-6583	193	9	with	with	ADP
ejpam-6583	193	10	the	the	DET
ejpam-6583	193	11	orthogonal	orthogonal	ADJ
ejpam-6583	193	12	direct	direct	ADJ
ejpam-6583	193	13	sum	sum	NOUN
ejpam-6583	193	14	on	on	ADP
ejpam-6583	193	15	a	a	DET
ejpam-6583	193	16	generalized	generalized	ADJ
ejpam-6583	193	17	b	b	X
ejpam-6583	193	18	-	-	ADJ
ejpam-6583	193	19	metric	metric	ADJ
ejpam-6583	193	20	space	space	NOUN
ejpam-6583	193	21	endowed	endow	VERB
ejpam-6583	193	22	with	with	ADP
ejpam-6583	193	23	direct	direct	ADJ
ejpam-6583	193	24	sum	sum	NOUN
ejpam-6583	193	25	(	(	PUNCT
ejpam-6583	193	26	x	x	INTJ
ejpam-6583	193	27	,	,	PUNCT
ejpam-6583	193	28	r⊕d	r⊕d	NOUN
ejpam-6583	193	29	,	,	PUNCT
ejpam-6583	193	30	δb	δb	NOUN
ejpam-6583	193	31	r⊕d	r⊕d	NOUN
ejpam-6583	193	32	)	)	PUNCT
ejpam-6583	193	33	.	.	PUNCT
ejpam-6583	194	1	example	example	NOUN
ejpam-6583	195	1	6	6	NUM
ejpam-6583	195	2	.	.	PUNCT
ejpam-6583	195	3	(	(	PUNCT
ejpam-6583	195	4	numerical	numerical	ADJ
ejpam-6583	195	5	example	example	NOUN
ejpam-6583	195	6	)	)	PUNCT
ejpam-6583	195	7	consider	consider	VERB
ejpam-6583	195	8	all	all	DET
ejpam-6583	195	9	hypotheses	hypothesis	NOUN
ejpam-6583	195	10	of	of	ADP
ejpam-6583	195	11	example	example	NOUN
ejpam-6583	195	12	4	4	NUM
ejpam-6583	195	13	are	be	AUX
ejpam-6583	195	14	true	true	ADJ
ejpam-6583	195	15	.	.	PUNCT
ejpam-6583	196	1	let	let	VERB
ejpam-6583	196	2	f	f	NOUN
ejpam-6583	196	3	:	:	PUNCT
ejpam-6583	196	4	x	x	X
ejpam-6583	196	5	→	→	PUNCT
ejpam-6583	196	6	x	x	X
ejpam-6583	196	7	such	such	ADJ
ejpam-6583	196	8	that	that	SCONJ
ejpam-6583	196	9	f	f	PROPN
ejpam-6583	196	10	(	(	PUNCT
ejpam-6583	196	11	x	x	X
ejpam-6583	196	12	)	)	PUNCT
ejpam-6583	196	13	=	=	PUNCT
ejpam-6583	196	14	x	x	SYM
ejpam-6583	196	15	4	4	X
ejpam-6583	196	16	.	.	PUNCT
ejpam-6583	197	1	then	then	ADV
ejpam-6583	197	2	,	,	PUNCT
ejpam-6583	197	3	δb	δb	NOUN
ejpam-6583	197	4	r⊕d	r⊕d	NOUN
ejpam-6583	197	5	(	(	PUNCT
ejpam-6583	197	6	f	f	PROPN
ejpam-6583	197	7	(	(	PUNCT
ejpam-6583	197	8	x),f	x),f	PROPN
ejpam-6583	197	9	(	(	PUNCT
ejpam-6583	197	10	y	y	NOUN
ejpam-6583	197	11	)	)	PUNCT
ejpam-6583	197	12	)	)	PUNCT
ejpam-6583	198	1	=	=	SYM
ejpam-6583	199	1	1	1	NUM
ejpam-6583	199	2	4	4	NUM
ejpam-6583	199	3	·	·	PUNCT
ejpam-6583	199	4	ir⊕d	ir⊕d	PROPN
ejpam-6583	199	5	+	+	CCONJ
ejpam-6583	199	6	diag	diag	PROPN
ejpam-6583	199	7	(	(	PUNCT
ejpam-6583	199	8	δb(x	δb(x	PROPN
ejpam-6583	199	9	,	,	PUNCT
ejpam-6583	199	10	y	y	NOUN
ejpam-6583	199	11	)	)	PUNCT
ejpam-6583	199	12	,	,	PUNCT
ejpam-6583	199	13	δb(x	δb(x	PROPN
ejpam-6583	199	14	,	,	PUNCT
ejpam-6583	199	15	y	y	NOUN
ejpam-6583	199	16	)	)	PUNCT
ejpam-6583	199	17	,	,	PUNCT
ejpam-6583	199	18	·	·	PUNCT
ejpam-6583	199	19	·	·	PUNCT
ejpam-6583	199	20	·	·	PUNCT
ejpam-6583	199	21	,	,	PUNCT
ejpam-6583	199	22	δb(x	δb(x	PROPN
ejpam-6583	199	23	,	,	PUNCT
ejpam-6583	199	24	y	y	NOUN
ejpam-6583	199	25	)	)	PUNCT
ejpam-6583	199	26	)	)	PUNCT
ejpam-6583	200	1	=	=	SYM
ejpam-6583	200	2	diag	diag	NOUN
ejpam-6583	200	3	(	(	PUNCT
ejpam-6583	200	4	1	1	NUM
ejpam-6583	200	5	4	4	NUM
ejpam-6583	200	6	,	,	PUNCT
ejpam-6583	200	7	1	1	NUM
ejpam-6583	200	8	4	4	NUM
ejpam-6583	200	9	,	,	PUNCT
ejpam-6583	200	10	·	·	PUNCT
ejpam-6583	200	11	·	·	PUNCT
ejpam-6583	200	12	·	·	PUNCT
ejpam-6583	200	13	,	,	PUNCT
ejpam-6583	200	14	1	1	NUM
ejpam-6583	200	15	4	4	NUM
ejpam-6583	200	16	)	)	PUNCT
ejpam-6583	200	17	·	·	PUNCT
ejpam-6583	200	18	diag	diag	NOUN
ejpam-6583	200	19	(	(	PUNCT
ejpam-6583	200	20	δb(x	δb(x	PROPN
ejpam-6583	200	21	,	,	PUNCT
ejpam-6583	200	22	y	y	NOUN
ejpam-6583	200	23	)	)	PUNCT
ejpam-6583	200	24	,	,	PUNCT
ejpam-6583	200	25	δb(x	δb(x	PROPN
ejpam-6583	200	26	,	,	PUNCT
ejpam-6583	200	27	y	y	NOUN
ejpam-6583	200	28	)	)	PUNCT
ejpam-6583	200	29	,	,	PUNCT
ejpam-6583	200	30	·	·	PUNCT
ejpam-6583	200	31	·	·	PUNCT
ejpam-6583	200	32	·	·	PUNCT
ejpam-6583	200	33	,	,	PUNCT
ejpam-6583	200	34	δb(x	δb(x	PROPN
ejpam-6583	200	35	,	,	PUNCT
ejpam-6583	200	36	y	y	NOUN
ejpam-6583	200	37	)	)	PUNCT
ejpam-6583	200	38	)	)	PUNCT
ejpam-6583	200	39	.	.	PUNCT
ejpam-6583	201	1	it	it	PRON
ejpam-6583	201	2	is	be	AUX
ejpam-6583	201	3	clear	clear	ADJ
ejpam-6583	201	4	that	that	SCONJ
ejpam-6583	201	5	δb	δb	NOUN
ejpam-6583	201	6	r⊕d	r⊕d	NOUN
ejpam-6583	201	7	(	(	PUNCT
ejpam-6583	201	8	f	f	PROPN
ejpam-6583	201	9	(	(	PUNCT
ejpam-6583	201	10	x),f	x),f	PROPN
ejpam-6583	201	11	(	(	PUNCT
ejpam-6583	201	12	y	y	NOUN
ejpam-6583	201	13	)	)	PUNCT
ejpam-6583	201	14	)	)	PUNCT
ejpam-6583	202	1	≾	≾	PROPN
ejpam-6583	202	2	λ	λ	PROPN
ejpam-6583	202	3	·	·	PUNCT
ejpam-6583	202	4	δb	δb	NOUN
ejpam-6583	202	5	r⊕d	r⊕d	NOUN
ejpam-6583	202	6	(	(	PUNCT
ejpam-6583	202	7	x	x	X
ejpam-6583	202	8	,	,	PUNCT
ejpam-6583	202	9	y	y	PROPN
ejpam-6583	202	10	)	)	PUNCT
ejpam-6583	202	11	,	,	PUNCT
ejpam-6583	202	12	where	where	SCONJ
ejpam-6583	202	13	λ	λ	PROPN
ejpam-6583	202	14	≺	≺	VERB
ejpam-6583	202	15	ir	ir	PROPN
ejpam-6583	202	16	⊕d	⊕d	NOUN
ejpam-6583	202	17	+	+	X
ejpam-6583	202	18	.	.	PUNCT
ejpam-6583	203	1	therefore	therefore	ADV
ejpam-6583	203	2	,	,	PUNCT
ejpam-6583	203	3	f	f	PROPN
ejpam-6583	203	4	is	be	AUX
ejpam-6583	203	5	a	a	DET
ejpam-6583	203	6	contraction	contraction	NOUN
ejpam-6583	203	7	endowed	endow	VERB
ejpam-6583	203	8	the	the	DET
ejpam-6583	203	9	direct	direct	ADJ
ejpam-6583	203	10	sum	sum	NOUN
ejpam-6583	203	11	for	for	ADP
ejpam-6583	203	12	the	the	DET
ejpam-6583	203	13	a	a	DET
ejpam-6583	203	14	generalized	generalized	ADJ
ejpam-6583	203	15	b	b	X
ejpam-6583	203	16	-	-	ADJ
ejpam-6583	203	17	metric	metric	ADJ
ejpam-6583	203	18	space	space	NOUN
ejpam-6583	203	19	endowed	endow	VERB
ejpam-6583	203	20	with	with	ADP
ejpam-6583	203	21	the	the	DET
ejpam-6583	203	22	orthogonal	orthogonal	ADJ
ejpam-6583	203	23	direct	direct	ADJ
ejpam-6583	203	24	sum	sum	NOUN
ejpam-6583	203	25	(	(	PUNCT
ejpam-6583	203	26	x	x	INTJ
ejpam-6583	203	27	,	,	PUNCT
ejpam-6583	203	28	r⊕d	r⊕d	NOUN
ejpam-6583	203	29	,	,	PUNCT
ejpam-6583	203	30	δb	δb	NOUN
ejpam-6583	203	31	r⊕d	r⊕d	NOUN
ejpam-6583	203	32	)	)	PUNCT
ejpam-6583	203	33	.	.	PUNCT
ejpam-6583	204	1	theorem	theorem	ADJ
ejpam-6583	204	2	3	3	NUM
ejpam-6583	204	3	(	(	PUNCT
ejpam-6583	204	4	banach	banach	NOUN
ejpam-6583	204	5	contraction	contraction	NOUN
ejpam-6583	204	6	type	type	NOUN
ejpam-6583	204	7	)	)	PUNCT
ejpam-6583	204	8	.	.	PUNCT
ejpam-6583	205	1	suppose	suppose	VERB
ejpam-6583	205	2	that	that	SCONJ
ejpam-6583	205	3	(	(	PUNCT
ejpam-6583	205	4	x	x	X
ejpam-6583	205	5	,	,	PUNCT
ejpam-6583	205	6	r⊕d	r⊕d	NOUN
ejpam-6583	205	7	,	,	PUNCT
ejpam-6583	205	8	δb	δb	NOUN
ejpam-6583	205	9	r⊕d	r⊕d	NOUN
ejpam-6583	205	10	)	)	PUNCT
ejpam-6583	205	11	is	be	AUX
ejpam-6583	205	12	a	a	DET
ejpam-6583	205	13	complete	complete	ADJ
ejpam-6583	205	14	generalized	generalized	ADJ
ejpam-6583	205	15	b	b	X
ejpam-6583	205	16	-	-	ADJ
ejpam-6583	205	17	metric	metric	ADJ
ejpam-6583	205	18	space	space	NOUN
ejpam-6583	205	19	endowed	endow	VERB
ejpam-6583	205	20	with	with	ADP
ejpam-6583	205	21	the	the	DET
ejpam-6583	205	22	orthogonal	orthogonal	ADJ
ejpam-6583	205	23	direct	direct	ADJ
ejpam-6583	205	24	sum	sum	NOUN
ejpam-6583	205	25	,	,	PUNCT
ejpam-6583	205	26	and	and	CCONJ
ejpam-6583	205	27	let	let	VERB
ejpam-6583	205	28	f	f	PRON
ejpam-6583	205	29	:	:	PUNCT
ejpam-6583	205	30	x	x	X
ejpam-6583	205	31	→	→	PUNCT
ejpam-6583	205	32	x	x	PUNCT
ejpam-6583	205	33	be	be	AUX
ejpam-6583	205	34	a	a	DET
ejpam-6583	205	35	contraction	contraction	NOUN
ejpam-6583	205	36	operator	operator	NOUN
ejpam-6583	205	37	endowed	endow	VERB
ejpam-6583	205	38	with	with	ADP
ejpam-6583	205	39	the	the	DET
ejpam-6583	205	40	direct	direct	ADJ
ejpam-6583	205	41	sum	sum	NOUN
ejpam-6583	205	42	.	.	PUNCT
ejpam-6583	206	1	that	that	PRON
ejpam-6583	206	2	is	is	ADV
ejpam-6583	206	3	,	,	PUNCT
ejpam-6583	206	4	δb	δb	NOUN
ejpam-6583	206	5	r⊕d	r⊕d	NOUN
ejpam-6583	206	6	(	(	PUNCT
ejpam-6583	206	7	f	f	PROPN
ejpam-6583	206	8	(	(	PUNCT
ejpam-6583	206	9	x),f	x),f	PROPN
ejpam-6583	206	10	(	(	PUNCT
ejpam-6583	206	11	y	y	NOUN
ejpam-6583	206	12	)	)	PUNCT
ejpam-6583	206	13	)	)	PUNCT
ejpam-6583	207	1	≾	≾	PROPN
ejpam-6583	207	2	diag(λ1	diag(λ1	NOUN
ejpam-6583	207	3	,	,	PUNCT
ejpam-6583	207	4	λ2	λ2	NOUN
ejpam-6583	207	5	,	,	PUNCT
ejpam-6583	207	6	.	.	PUNCT
ejpam-6583	207	7	.	.	PUNCT
ejpam-6583	207	8	.	.	PUNCT
ejpam-6583	208	1	,	,	PUNCT
ejpam-6583	208	2	λd	λd	NOUN
ejpam-6583	208	3	)	)	PUNCT
ejpam-6583	208	4	δ	δ	PROPN
ejpam-6583	208	5	b	b	PROPN
ejpam-6583	208	6	r⊕d	r⊕d	NOUN
ejpam-6583	208	7	(	(	PUNCT
ejpam-6583	208	8	x	x	NOUN
ejpam-6583	208	9	,	,	PUNCT
ejpam-6583	208	10	y	y	PROPN
ejpam-6583	208	11	)	)	PUNCT
ejpam-6583	208	12	,	,	PUNCT
ejpam-6583	208	13	for	for	ADP
ejpam-6583	208	14	all	all	DET
ejpam-6583	208	15	x	x	NOUN
ejpam-6583	208	16	,	,	PUNCT
ejpam-6583	208	17	y	y	PROPN
ejpam-6583	208	18	∈	∈	PROPN
ejpam-6583	208	19	x	x	X
ejpam-6583	208	20	,	,	PUNCT
ejpam-6583	208	21	where	where	SCONJ
ejpam-6583	208	22	λi	λi	ADP
ejpam-6583	208	23	∈	∈	PROPN
ejpam-6583	208	24	(	(	PUNCT
ejpam-6583	208	25	0	0	NUM
ejpam-6583	208	26	,	,	PUNCT
ejpam-6583	208	27	1	1	NUM
ejpam-6583	208	28	)	)	PUNCT
ejpam-6583	208	29	for	for	ADP
ejpam-6583	208	30	i	i	PRON
ejpam-6583	208	31	=	=	SYM
ejpam-6583	208	32	1	1	NUM
ejpam-6583	208	33	,	,	PUNCT
ejpam-6583	208	34	2	2	NUM
ejpam-6583	208	35	,	,	PUNCT
ejpam-6583	208	36	.	.	PUNCT
ejpam-6583	208	37	.	.	PUNCT
ejpam-6583	208	38	.	.	PUNCT
ejpam-6583	209	1	,	,	PUNCT
ejpam-6583	209	2	d.	d.	PROPN
ejpam-6583	209	3	then	then	ADV
ejpam-6583	209	4	f	f	PROPN
ejpam-6583	209	5	has	have	VERB
ejpam-6583	209	6	a	a	DET
ejpam-6583	209	7	unique	unique	ADJ
ejpam-6583	209	8	fixed	fix	VERB
ejpam-6583	209	9	-	-	PUNCT
ejpam-6583	209	10	point	point	NOUN
ejpam-6583	209	11	in	in	ADP
ejpam-6583	209	12	x	x	PROPN
ejpam-6583	209	13	.	.	PUNCT
ejpam-6583	210	1	g.	g.	PROPN
ejpam-6583	210	2	albeladi	albeladi	PROPN
ejpam-6583	210	3	,	,	PUNCT
ejpam-6583	210	4	s.	s.	PROPN
ejpam-6583	210	5	omran	omran	PROPN
ejpam-6583	210	6	/	/	SYM
ejpam-6583	210	7	eur	eur	PROPN
ejpam-6583	210	8	.	.	PUNCT
ejpam-6583	211	1	j.	j.	PROPN
ejpam-6583	211	2	pure	pure	PROPN
ejpam-6583	211	3	appl	appl	PROPN
ejpam-6583	211	4	.	.	PROPN
ejpam-6583	211	5	math	math	PROPN
ejpam-6583	211	6	,	,	PUNCT
ejpam-6583	211	7	18	18	NUM
ejpam-6583	211	8	(	(	PUNCT
ejpam-6583	211	9	3	3	NUM
ejpam-6583	211	10	)	)	PUNCT
ejpam-6583	211	11	(	(	PUNCT
ejpam-6583	211	12	2025	2025	NUM
ejpam-6583	211	13	)	)	PUNCT
ejpam-6583	211	14	,	,	PUNCT
ejpam-6583	211	15	6583	6583	NUM
ejpam-6583	211	16	9	9	NUM
ejpam-6583	211	17	of	of	ADP
ejpam-6583	211	18	27	27	NUM
ejpam-6583	211	19	proof	proof	NOUN
ejpam-6583	211	20	.	.	PUNCT
ejpam-6583	212	1	let	let	VERB
ejpam-6583	212	2	x0	x0	PROPN
ejpam-6583	212	3	be	be	AUX
ejpam-6583	212	4	any	any	DET
ejpam-6583	212	5	point	point	NOUN
ejpam-6583	212	6	in	in	ADP
ejpam-6583	212	7	x	x	SYM
ejpam-6583	212	8	,	,	PUNCT
ejpam-6583	212	9	that	that	ADV
ejpam-6583	212	10	is	is	ADV
ejpam-6583	212	11	x0	x0	PROPN
ejpam-6583	212	12	∈	∈	PROPN
ejpam-6583	213	1	x	x	X
ejpam-6583	213	2	.	.	PUNCT
ejpam-6583	214	1	let	let	VERB
ejpam-6583	214	2	us	we	PRON
ejpam-6583	214	3	define	define	VERB
ejpam-6583	214	4	a	a	DET
ejpam-6583	214	5	sequence	sequence	NOUN
ejpam-6583	214	6	{	{	PUNCT
ejpam-6583	214	7	xn	xn	NOUN
ejpam-6583	214	8	}	}	PUNCT
ejpam-6583	214	9	in	in	ADP
ejpam-6583	214	10	x	x	PUNCT
ejpam-6583	214	11	as	as	SCONJ
ejpam-6583	214	12	given	give	VERB
ejpam-6583	214	13	below	below	ADV
ejpam-6583	214	14	.	.	PUNCT
ejpam-6583	215	1	xn+1	xn+1	PUNCT
ejpam-6583	216	1	=	=	SYM
ejpam-6583	216	2	f	f	PROPN
ejpam-6583	216	3	(	(	PUNCT
ejpam-6583	216	4	xn	xn	PROPN
ejpam-6583	216	5	)	)	PUNCT
ejpam-6583	216	6	=	=	SYM
ejpam-6583	216	7	fn+1(x0	fn+1(x0	ADJ
ejpam-6583	216	8	)	)	PUNCT
ejpam-6583	216	9	∀	∀	X
ejpam-6583	216	10	n	n	PRON
ejpam-6583	216	11	≥	≥	NOUN
ejpam-6583	216	12	0	0	NUM
ejpam-6583	216	13	.	.	PUNCT
ejpam-6583	217	1	by	by	ADP
ejpam-6583	217	2	the	the	DET
ejpam-6583	217	3	contraction	contraction	NOUN
ejpam-6583	217	4	condition	condition	NOUN
ejpam-6583	217	5	,	,	PUNCT
ejpam-6583	217	6	we	we	PRON
ejpam-6583	217	7	get	get	VERB
ejpam-6583	217	8	δb	δb	ADP
ejpam-6583	217	9	r⊕d	r⊕d	NOUN
ejpam-6583	217	10	(	(	PUNCT
ejpam-6583	217	11	xn−1	xn−1	PROPN
ejpam-6583	217	12	,	,	PUNCT
ejpam-6583	217	13	xn	xn	PRON
ejpam-6583	217	14	)	)	PUNCT
ejpam-6583	218	1	=	=	PUNCT
ejpam-6583	218	2	δb	δb	X
ejpam-6583	218	3	r⊕d	r⊕d	NOUN
ejpam-6583	218	4	(	(	PUNCT
ejpam-6583	218	5	f	f	X
ejpam-6583	218	6	(	(	PUNCT
ejpam-6583	218	7	xn−2),f	xn−2),f	PROPN
ejpam-6583	218	8	(	(	PUNCT
ejpam-6583	218	9	xn−1	xn−1	PROPN
ejpam-6583	218	10	)	)	PUNCT
ejpam-6583	218	11	)	)	PUNCT
ejpam-6583	219	1	≾	≾	NOUN
ejpam-6583	219	2	diag	diag	NOUN
ejpam-6583	219	3	(	(	PUNCT
ejpam-6583	219	4	λ1	λ1	ADJ
ejpam-6583	219	5	,	,	PUNCT
ejpam-6583	219	6	λ2	λ2	NOUN
ejpam-6583	219	7	,	,	PUNCT
ejpam-6583	219	8	·	·	PUNCT
ejpam-6583	219	9	·	·	PUNCT
ejpam-6583	219	10	·	·	PUNCT
ejpam-6583	219	11	,	,	PUNCT
ejpam-6583	219	12	λd	λd	NOUN
ejpam-6583	219	13	)	)	PUNCT
ejpam-6583	220	1	[	[	X
ejpam-6583	220	2	δb	δb	X
ejpam-6583	220	3	r⊕d	r⊕d	NOUN
ejpam-6583	220	4	(	(	PUNCT
ejpam-6583	220	5	xn−2	xn−2	PROPN
ejpam-6583	220	6	,	,	PUNCT
ejpam-6583	220	7	xn−1	xn−1	PROPN
ejpam-6583	220	8	)	)	PUNCT
ejpam-6583	220	9	]	]	PUNCT
ejpam-6583	220	10	...	...	PUNCT
ejpam-6583	221	1	≾	≾	NOUN
ejpam-6583	221	2	diag	diag	NOUN
ejpam-6583	221	3	(	(	PUNCT
ejpam-6583	221	4	λn−1	λn−1	PROPN
ejpam-6583	221	5	1	1	NUM
ejpam-6583	221	6	,	,	PUNCT
ejpam-6583	221	7	λn−1	λn−1	PROPN
ejpam-6583	221	8	2	2	NUM
ejpam-6583	221	9	,	,	PUNCT
ejpam-6583	221	10	·	·	PUNCT
ejpam-6583	221	11	·	·	PUNCT
ejpam-6583	221	12	·	·	PUNCT
ejpam-6583	221	13	,	,	PUNCT
ejpam-6583	221	14	λn−1	λn−1	PROPN
ejpam-6583	221	15	d	d	PROPN
ejpam-6583	221	16	)	)	PUNCT
ejpam-6583	221	17	δb	δb	NOUN
ejpam-6583	221	18	r⊕d	r⊕d	NOUN
ejpam-6583	221	19	(	(	PUNCT
ejpam-6583	221	20	x0	x0	PROPN
ejpam-6583	221	21	,	,	PUNCT
ejpam-6583	221	22	x1	x1	PROPN
ejpam-6583	221	23	)	)	PUNCT
ejpam-6583	221	24	.	.	PUNCT
ejpam-6583	222	1	let	let	VERB
ejpam-6583	222	2	us	we	PRON
ejpam-6583	222	3	prove	prove	VERB
ejpam-6583	222	4	that	that	SCONJ
ejpam-6583	222	5	{	{	PUNCT
ejpam-6583	222	6	xn	xn	X
ejpam-6583	222	7	}	}	PUNCT
ejpam-6583	222	8	is	be	AUX
ejpam-6583	222	9	a	a	DET
ejpam-6583	222	10	cauchy	cauchy	ADJ
ejpam-6583	222	11	sequence	sequence	NOUN
ejpam-6583	222	12	.	.	PUNCT
ejpam-6583	223	1	suppose	suppose	VERB
ejpam-6583	223	2	that	that	SCONJ
ejpam-6583	223	3	n	n	PROPN
ejpam-6583	223	4	>	>	X
ejpam-6583	223	5	m	m	VERB
ejpam-6583	223	6	from	from	ADP
ejpam-6583	223	7	the	the	DET
ejpam-6583	223	8	contraction	contraction	NOUN
ejpam-6583	223	9	and	and	CCONJ
ejpam-6583	223	10	triangle	triangle	NOUN
ejpam-6583	223	11	inequality	inequality	NOUN
ejpam-6583	223	12	property	property	NOUN
ejpam-6583	223	13	,	,	PUNCT
ejpam-6583	223	14	we	we	PRON
ejpam-6583	223	15	can	can	AUX
ejpam-6583	223	16	write	write	VERB
ejpam-6583	223	17	as	as	ADP
ejpam-6583	223	18	:	:	PUNCT
ejpam-6583	223	19	δb	δb	NOUN
ejpam-6583	223	20	r⊕d	r⊕d	NOUN
ejpam-6583	223	21	(	(	PUNCT
ejpam-6583	223	22	xm	xm	PROPN
ejpam-6583	223	23	,	,	PUNCT
ejpam-6583	223	24	xn	xn	X
ejpam-6583	223	25	)	)	PUNCT
ejpam-6583	223	26	≾	≾	NOUN
ejpam-6583	223	27	sδb	sδb	VERB
ejpam-6583	223	28	r⊕d	r⊕d	NOUN
ejpam-6583	223	29	(	(	PUNCT
ejpam-6583	223	30	xm	xm	PROPN
ejpam-6583	223	31	,	,	PUNCT
ejpam-6583	223	32	xm+1	xm+1	PROPN
ejpam-6583	223	33	)	)	PUNCT
ejpam-6583	223	34	+	+	CCONJ
ejpam-6583	223	35	s2	s2	NOUN
ejpam-6583	223	36	δb	δb	NOUN
ejpam-6583	223	37	r⊕d	r⊕d	NOUN
ejpam-6583	223	38	(	(	PUNCT
ejpam-6583	223	39	xm+1	xm+1	PROPN
ejpam-6583	223	40	,	,	PUNCT
ejpam-6583	223	41	xm+2	xm+2	PROPN
ejpam-6583	223	42	)	)	PUNCT
ejpam-6583	223	43	+	+	CCONJ
ejpam-6583	223	44	s3	s3	PROPN
ejpam-6583	223	45	[	[	PUNCT
ejpam-6583	223	46	δb	δb	X
ejpam-6583	223	47	r⊕d	r⊕d	NOUN
ejpam-6583	223	48	(	(	PUNCT
ejpam-6583	223	49	xm+2	xm+2	PROPN
ejpam-6583	223	50	,	,	PUNCT
ejpam-6583	223	51	xm+3	xm+3	NUM
ejpam-6583	223	52	)	)	PUNCT
ejpam-6583	223	53	+	+	CCONJ
ejpam-6583	223	54	δb	δb	NOUN
ejpam-6583	223	55	r⊕d	r⊕d	NOUN
ejpam-6583	223	56	(	(	PUNCT
ejpam-6583	223	57	xm+3	xm+3	NUM
ejpam-6583	223	58	,	,	PUNCT
ejpam-6583	223	59	xn	xn	PROPN
ejpam-6583	223	60	)	)	PUNCT
ejpam-6583	223	61	]	]	PUNCT
ejpam-6583	223	62	...	...	PUNCT
ejpam-6583	224	1	≾	≾	PROPN
ejpam-6583	224	2	s	s	PART
ejpam-6583	224	3	δb	δb	NOUN
ejpam-6583	224	4	r⊕d	r⊕d	NOUN
ejpam-6583	224	5	(	(	PUNCT
ejpam-6583	224	6	xm	xm	PROPN
ejpam-6583	224	7	,	,	PUNCT
ejpam-6583	224	8	xm+1	xm+1	PROPN
ejpam-6583	224	9	)	)	PUNCT
ejpam-6583	224	10	+	+	CCONJ
ejpam-6583	224	11	s2	s2	NOUN
ejpam-6583	224	12	δb	δb	NOUN
ejpam-6583	224	13	r⊕d	r⊕d	NOUN
ejpam-6583	224	14	(	(	PUNCT
ejpam-6583	224	15	xm+1	xm+1	PROPN
ejpam-6583	224	16	,	,	PUNCT
ejpam-6583	224	17	xm+2	xm+2	PROPN
ejpam-6583	224	18	)	)	PUNCT
ejpam-6583	224	19	+	+	CCONJ
ejpam-6583	224	20	s3	s3	NOUN
ejpam-6583	224	21	δb	δb	NOUN
ejpam-6583	224	22	r⊕d	r⊕d	NOUN
ejpam-6583	224	23	(	(	PUNCT
ejpam-6583	224	24	xm+2	xm+2	PROPN
ejpam-6583	224	25	,	,	PUNCT
ejpam-6583	224	26	xm+3	xm+3	NUM
ejpam-6583	224	27	)	)	PUNCT
ejpam-6583	224	28	+	+	X
ejpam-6583	224	29	·	·	PUNCT
ejpam-6583	224	30	·	·	PUNCT
ejpam-6583	224	31	·	·	PUNCT
ejpam-6583	224	32	+	+	NUM
ejpam-6583	224	33	sn−m	sn−m	NOUN
ejpam-6583	224	34	δb	δb	NOUN
ejpam-6583	224	35	r⊕d	r⊕d	NOUN
ejpam-6583	224	36	(	(	PUNCT
ejpam-6583	224	37	xn−1	xn−1	PROPN
ejpam-6583	224	38	,	,	PUNCT
ejpam-6583	224	39	xn	xn	X
ejpam-6583	224	40	)	)	PUNCT
ejpam-6583	225	1	≾	≾	PROPN
ejpam-6583	225	2	s	s	VERB
ejpam-6583	225	3	diag(λm1	diag(λm1	ADJ
ejpam-6583	225	4	,	,	PUNCT
ejpam-6583	225	5	λ	λ	PROPN
ejpam-6583	225	6	m	m	VERB
ejpam-6583	225	7	2	2	NUM
ejpam-6583	225	8	,	,	PUNCT
ejpam-6583	225	9	·	·	PUNCT
ejpam-6583	225	10	·	·	PUNCT
ejpam-6583	225	11	·	·	PUNCT
ejpam-6583	225	12	,	,	PUNCT
ejpam-6583	225	13	λmd	λmd	NOUN
ejpam-6583	225	14	)	)	PUNCT
ejpam-6583	225	15	δb	δb	NOUN
ejpam-6583	225	16	r⊕d	r⊕d	NOUN
ejpam-6583	225	17	(	(	PUNCT
ejpam-6583	225	18	x0	x0	PROPN
ejpam-6583	225	19	,	,	PUNCT
ejpam-6583	225	20	x1	x1	PROPN
ejpam-6583	225	21	)	)	PUNCT
ejpam-6583	226	1	+	+	CCONJ
ejpam-6583	226	2	s2	s2	PROPN
ejpam-6583	226	3	diag(λm+1	diag(λm+1	PROPN
ejpam-6583	226	4	1	1	NUM
ejpam-6583	226	5	,	,	PUNCT
ejpam-6583	226	6	λm+1	λm+1	X
ejpam-6583	226	7	2	2	NUM
ejpam-6583	226	8	,	,	PUNCT
ejpam-6583	226	9	·	·	PUNCT
ejpam-6583	226	10	·	·	PUNCT
ejpam-6583	226	11	·	·	PUNCT
ejpam-6583	226	12	,	,	PUNCT
ejpam-6583	226	13	λm+1	λm+1	X
ejpam-6583	226	14	d	d	X
ejpam-6583	226	15	)	)	PUNCT
ejpam-6583	226	16	δb	δb	NOUN
ejpam-6583	226	17	r⊕d	r⊕d	NOUN
ejpam-6583	226	18	(	(	PUNCT
ejpam-6583	226	19	x0	x0	PROPN
ejpam-6583	226	20	,	,	PUNCT
ejpam-6583	226	21	x1	x1	PROPN
ejpam-6583	226	22	)	)	PUNCT
ejpam-6583	226	23	+	+	X
ejpam-6583	226	24	·	·	PUNCT
ejpam-6583	226	25	·	·	PUNCT
ejpam-6583	226	26	·	·	PUNCT
ejpam-6583	226	27	+	+	NUM
ejpam-6583	226	28	sn−m	sn−m	PROPN
ejpam-6583	226	29	diag(λn−1	diag(λn−1	ADJ
ejpam-6583	226	30	1	1	NUM
ejpam-6583	226	31	,	,	PUNCT
ejpam-6583	226	32	λn−1	λn−1	PROPN
ejpam-6583	226	33	2	2	NUM
ejpam-6583	226	34	,	,	PUNCT
ejpam-6583	226	35	·	·	PUNCT
ejpam-6583	226	36	·	·	PUNCT
ejpam-6583	226	37	·	·	PUNCT
ejpam-6583	226	38	,	,	PUNCT
ejpam-6583	226	39	λn−1	λn−1	PROPN
ejpam-6583	226	40	d	d	PROPN
ejpam-6583	226	41	)	)	PUNCT
ejpam-6583	226	42	δb	δb	NOUN
ejpam-6583	226	43	r⊕d	r⊕d	NOUN
ejpam-6583	226	44	(	(	PUNCT
ejpam-6583	226	45	x0	x0	PROPN
ejpam-6583	226	46	,	,	PUNCT
ejpam-6583	226	47	x1	x1	PROPN
ejpam-6583	226	48	)	)	PUNCT
ejpam-6583	226	49	=	=	SYM
ejpam-6583	227	1	(	(	PUNCT
ejpam-6583	227	2	(	(	PUNCT
ejpam-6583	227	3	s	s	VERB
ejpam-6583	227	4	λm1	λm1	PROPN
ejpam-6583	227	5	+	+	CCONJ
ejpam-6583	227	6	s2	s2	X
ejpam-6583	227	7	λm+1	λm+1	X
ejpam-6583	227	8	1	1	NUM
ejpam-6583	227	9	+	+	CCONJ
ejpam-6583	227	10	·	·	PUNCT
ejpam-6583	227	11	·	·	PUNCT
ejpam-6583	227	12	·	·	PUNCT
ejpam-6583	227	13	+	+	NUM
ejpam-6583	227	14	sn−m	sn−m	NOUN
ejpam-6583	227	15	λn−1	λn−1	PROPN
ejpam-6583	227	16	1	1	NUM
ejpam-6583	227	17	)	)	PUNCT
ejpam-6583	227	18	δb	δb	NOUN
ejpam-6583	227	19	r⊕d	r⊕d	NOUN
ejpam-6583	227	20	(	(	PUNCT
ejpam-6583	227	21	x0	x0	PROPN
ejpam-6583	227	22	,	,	PUNCT
ejpam-6583	227	23	x1	x1	PROPN
ejpam-6583	227	24	)	)	PUNCT
ejpam-6583	227	25	,	,	PUNCT
ejpam-6583	227	26	(	(	PUNCT
ejpam-6583	227	27	s	s	NOUN
ejpam-6583	227	28	λ	λ	X
ejpam-6583	227	29	m	m	VERB
ejpam-6583	227	30	2	2	NUM
ejpam-6583	227	31	+	+	CCONJ
ejpam-6583	227	32	s2	s2	X
ejpam-6583	227	33	λm+1	λm+1	X
ejpam-6583	227	34	2	2	NUM
ejpam-6583	227	35	+	+	CCONJ
ejpam-6583	227	36	·	·	PUNCT
ejpam-6583	227	37	·	·	PUNCT
ejpam-6583	227	38	·	·	PUNCT
ejpam-6583	228	1	+	+	X
ejpam-6583	228	2	sn−m	sn−m	ADJ
ejpam-6583	228	3	λn−1	λn−1	PROPN
ejpam-6583	228	4	2	2	NUM
ejpam-6583	228	5	)	)	PUNCT
ejpam-6583	228	6	δb	δb	NOUN
ejpam-6583	228	7	r⊕d	r⊕d	NOUN
ejpam-6583	228	8	(	(	PUNCT
ejpam-6583	228	9	x0	x0	PROPN
ejpam-6583	228	10	,	,	PUNCT
ejpam-6583	228	11	x1	x1	PROPN
ejpam-6583	228	12	)	)	PUNCT
ejpam-6583	228	13	,	,	PUNCT
ejpam-6583	228	14	·	·	PUNCT
ejpam-6583	228	15	·	·	PUNCT
ejpam-6583	228	16	·	·	PUNCT
ejpam-6583	228	17	,	,	PUNCT
ejpam-6583	228	18	(	(	PUNCT
ejpam-6583	228	19	sλmd	sλmd	NOUN
ejpam-6583	228	20	+	+	CCONJ
ejpam-6583	228	21	s2	s2	VERB
ejpam-6583	228	22	λm+1	λm+1	X
ejpam-6583	228	23	d	d	X
ejpam-6583	228	24	+	+	PROPN
ejpam-6583	228	25	·	·	PUNCT
ejpam-6583	228	26	·	·	PUNCT
ejpam-6583	228	27	·	·	PUNCT
ejpam-6583	228	28	+	+	NUM
ejpam-6583	228	29	sn−m	sn−m	NOUN
ejpam-6583	228	30	λn−1	λn−1	PROPN
ejpam-6583	228	31	d	d	PROPN
ejpam-6583	228	32	)	)	PUNCT
ejpam-6583	228	33	δb	δb	NOUN
ejpam-6583	228	34	r⊕d	r⊕d	NOUN
ejpam-6583	228	35	(	(	PUNCT
ejpam-6583	228	36	x0	x0	PROPN
ejpam-6583	228	37	,	,	PUNCT
ejpam-6583	228	38	x1	x1	PROPN
ejpam-6583	228	39	)	)	PUNCT
ejpam-6583	228	40	)	)	PUNCT
ejpam-6583	229	1	=	=	SYM
ejpam-6583	229	2	diag	diag	NOUN
ejpam-6583	229	3	(	(	PUNCT
ejpam-6583	229	4	n−m∑	n−m∑	INTJ
ejpam-6583	229	5	k=1	k=1	PROPN
ejpam-6583	229	6	n−1∑	n−1∑	NUM
ejpam-6583	229	7	j	j	PROPN
ejpam-6583	229	8	=	=	NOUN
ejpam-6583	229	9	m	m	PROPN
ejpam-6583	229	10	skλj1δ	skλj1δ	ADJ
ejpam-6583	229	11	b	b	PROPN
ejpam-6583	229	12	r⊕d	r⊕d	NOUN
ejpam-6583	229	13	(	(	PUNCT
ejpam-6583	229	14	x0	x0	PROPN
ejpam-6583	229	15	,	,	PUNCT
ejpam-6583	229	16	x1	x1	PROPN
ejpam-6583	229	17	)	)	PUNCT
ejpam-6583	229	18	,	,	PUNCT
ejpam-6583	229	19	n−m∑	n−m∑	INTJ
ejpam-6583	229	20	k=1	k=1	PROPN
ejpam-6583	229	21	n−1∑	n−1∑	NUM
ejpam-6583	229	22	j	j	X
ejpam-6583	229	23	=	=	NOUN
ejpam-6583	229	24	m	m	VERB
ejpam-6583	229	25	skλj2δ	skλj2δ	NOUN
ejpam-6583	229	26	b	b	PROPN
ejpam-6583	229	27	r⊕d	r⊕d	NOUN
ejpam-6583	229	28	(	(	PUNCT
ejpam-6583	229	29	x0	x0	PROPN
ejpam-6583	229	30	,	,	PUNCT
ejpam-6583	229	31	x1	x1	PROPN
ejpam-6583	229	32	)	)	PUNCT
ejpam-6583	229	33	,	,	PUNCT
ejpam-6583	229	34	·	·	PUNCT
ejpam-6583	229	35	·	·	PUNCT
ejpam-6583	229	36	·	·	PUNCT
ejpam-6583	229	37	,	,	PUNCT
ejpam-6583	229	38	n−m∑	n−m∑	INTJ
ejpam-6583	229	39	k=1	k=1	PROPN
ejpam-6583	229	40	n−1∑	n−1∑	NUM
ejpam-6583	229	41	j	j	X
ejpam-6583	230	1	=	=	NOUN
ejpam-6583	230	2	m	m	VERB
ejpam-6583	230	3	sk	sk	ADJ
ejpam-6583	230	4	λjdδ	λjdδ	NOUN
ejpam-6583	230	5	b	b	NUM
ejpam-6583	230	6	r⊕d	r⊕d	NOUN
ejpam-6583	230	7	(	(	PUNCT
ejpam-6583	230	8	x0	x0	PROPN
ejpam-6583	230	9	,	,	PUNCT
ejpam-6583	230	10	x1	x1	PROPN
ejpam-6583	230	11	)	)	PUNCT
ejpam-6583	230	12	)	)	PUNCT
ejpam-6583	231	1	=	=	SYM
ejpam-6583	231	2	diag	diag	NOUN
ejpam-6583	231	3	(	(	PUNCT
ejpam-6583	231	4	n−m∑	n−m∑	INTJ
ejpam-6583	231	5	k=1	k=1	PROPN
ejpam-6583	231	6	n−1∑	n−1∑	NUM
ejpam-6583	231	7	j	j	PROPN
ejpam-6583	231	8	=	=	PROPN
ejpam-6583	231	9	m	m	PROPN
ejpam-6583	231	10	skλj1	skλj1	PROPN
ejpam-6583	231	11	,	,	PUNCT
ejpam-6583	231	12	n−m∑	n−m∑	INTJ
ejpam-6583	231	13	k=1	k=1	PROPN
ejpam-6583	231	14	n−1∑	n−1∑	NUM
ejpam-6583	231	15	j	j	X
ejpam-6583	231	16	=	=	NOUN
ejpam-6583	231	17	m	m	PROPN
ejpam-6583	231	18	skλj2	skλj2	PROPN
ejpam-6583	231	19	,	,	PUNCT
ejpam-6583	231	20	·	·	PUNCT
ejpam-6583	231	21	·	·	PUNCT
ejpam-6583	231	22	·	·	PUNCT
ejpam-6583	231	23	,	,	PUNCT
ejpam-6583	231	24	n−m∑	n−m∑	INTJ
ejpam-6583	231	25	k=1	k=1	PROPN
ejpam-6583	231	26	n−1∑	n−1∑	NUM
ejpam-6583	231	27	j	j	X
ejpam-6583	231	28	=	=	NOUN
ejpam-6583	231	29	m	m	NOUN
ejpam-6583	231	30	skλjd	skλjd	NOUN
ejpam-6583	231	31	)	)	PUNCT
ejpam-6583	231	32	δb	δb	NOUN
ejpam-6583	231	33	r⊕d	r⊕d	NOUN
ejpam-6583	231	34	(	(	PUNCT
ejpam-6583	231	35	x0	x0	PROPN
ejpam-6583	231	36	,	,	PUNCT
ejpam-6583	231	37	x1	x1	PROPN
ejpam-6583	231	38	)	)	PUNCT
ejpam-6583	231	39	g.	g.	PROPN
ejpam-6583	231	40	albeladi	albeladi	PROPN
ejpam-6583	231	41	,	,	PUNCT
ejpam-6583	231	42	s.	s.	PROPN
ejpam-6583	231	43	omran	omran	PROPN
ejpam-6583	231	44	/	/	SYM
ejpam-6583	231	45	eur	eur	PROPN
ejpam-6583	231	46	.	.	PUNCT
ejpam-6583	232	1	j.	j.	PROPN
ejpam-6583	232	2	pure	pure	PROPN
ejpam-6583	232	3	appl	appl	PROPN
ejpam-6583	232	4	.	.	PROPN
ejpam-6583	232	5	math	math	PROPN
ejpam-6583	232	6	,	,	PUNCT
ejpam-6583	232	7	18	18	NUM
ejpam-6583	232	8	(	(	PUNCT
ejpam-6583	232	9	3	3	NUM
ejpam-6583	232	10	)	)	PUNCT
ejpam-6583	232	11	(	(	PUNCT
ejpam-6583	232	12	2025	2025	NUM
ejpam-6583	232	13	)	)	PUNCT
ejpam-6583	232	14	,	,	PUNCT
ejpam-6583	232	15	6583	6583	NUM
ejpam-6583	232	16	10	10	NUM
ejpam-6583	232	17	of	of	ADP
ejpam-6583	232	18	27	27	NUM
ejpam-6583	232	19	=	=	SYM
ejpam-6583	232	20	diag	diag	NOUN
ejpam-6583	232	21	(	(	PUNCT
ejpam-6583	232	22	sλm1	sλm1	PROPN
ejpam-6583	232	23	n−m−1∑	n−m−1∑	PROPN
ejpam-6583	232	24	j=0	j=0	PROPN
ejpam-6583	232	25	(	(	PUNCT
ejpam-6583	232	26	sλ1	sλ1	NOUN
ejpam-6583	232	27	)	)	PUNCT
ejpam-6583	232	28	j	j	PROPN
ejpam-6583	232	29	,	,	PUNCT
ejpam-6583	232	30	sλm2	sλm2	PROPN
ejpam-6583	232	31	n−m−1∑	n−m−1∑	PROPN
ejpam-6583	232	32	j=0	j=0	PROPN
ejpam-6583	232	33	(	(	PUNCT
ejpam-6583	232	34	sλ2	sλ2	NOUN
ejpam-6583	232	35	)	)	PUNCT
ejpam-6583	232	36	j	j	PROPN
ejpam-6583	232	37	,	,	PUNCT
ejpam-6583	232	38	·	·	PUNCT
ejpam-6583	232	39	·	·	PUNCT
ejpam-6583	232	40	·	·	PUNCT
ejpam-6583	232	41	,	,	PUNCT
ejpam-6583	232	42	sλmd	sλmd	PROPN
ejpam-6583	232	43	n−m−1∑	n−m−1∑	PROPN
ejpam-6583	232	44	j=0	j=0	PROPN
ejpam-6583	232	45	(	(	PUNCT
ejpam-6583	232	46	sλd	sλd	PROPN
ejpam-6583	232	47	)	)	PUNCT
ejpam-6583	232	48	j	j	PROPN
ejpam-6583	232	49	)	)	PUNCT
ejpam-6583	232	50	δb	δb	NOUN
ejpam-6583	232	51	r⊕d	r⊕d	NOUN
ejpam-6583	232	52	(	(	PUNCT
ejpam-6583	232	53	x0	x0	PROPN
ejpam-6583	232	54	,	,	PUNCT
ejpam-6583	232	55	x1	x1	PROPN
ejpam-6583	232	56	)	)	PUNCT
ejpam-6583	232	57	≾	≾	NOUN
ejpam-6583	232	58	diag	diag	NOUN
ejpam-6583	232	59	(	(	PUNCT
ejpam-6583	232	60	sλm1	sλm1	PROPN
ejpam-6583	232	61	+	+	PROPN
ejpam-6583	232	62	∞∑	∞∑	PROPN
ejpam-6583	232	63	j=0	j=0	PROPN
ejpam-6583	232	64	(	(	PUNCT
ejpam-6583	232	65	sλ1	sλ1	NOUN
ejpam-6583	232	66	)	)	PUNCT
ejpam-6583	232	67	j	j	PROPN
ejpam-6583	233	1	+	+	NUM
ejpam-6583	233	2	sλm2	sλm2	PROPN
ejpam-6583	233	3	+	+	VERB
ejpam-6583	233	4	∞∑	∞∑	NUM
ejpam-6583	233	5	j=0	j=0	PROPN
ejpam-6583	233	6	(	(	PUNCT
ejpam-6583	233	7	sλ2	sλ2	NOUN
ejpam-6583	233	8	)	)	PUNCT
ejpam-6583	233	9	j	j	PROPN
ejpam-6583	233	10	+	+	CCONJ
ejpam-6583	233	11	·	·	PUNCT
ejpam-6583	233	12	·	·	PUNCT
ejpam-6583	233	13	·	·	PUNCT
ejpam-6583	233	14	+	+	NUM
ejpam-6583	233	15	sλmd	sλmd	NOUN
ejpam-6583	233	16	+	+	PRON
ejpam-6583	233	17	∞∑	∞∑	NUM
ejpam-6583	233	18	j=0	j=0	PROPN
ejpam-6583	233	19	(	(	PUNCT
ejpam-6583	233	20	sλd	sλd	PROPN
ejpam-6583	233	21	)	)	PUNCT
ejpam-6583	233	22	j	j	PROPN
ejpam-6583	233	23	)	)	PUNCT
ejpam-6583	233	24	δb	δb	NOUN
ejpam-6583	233	25	r⊕d	r⊕d	NOUN
ejpam-6583	233	26	(	(	PUNCT
ejpam-6583	233	27	x0	x0	PROPN
ejpam-6583	233	28	,	,	PUNCT
ejpam-6583	233	29	x1	x1	PROPN
ejpam-6583	233	30	)	)	PUNCT
ejpam-6583	233	31	=	=	SYM
ejpam-6583	233	32	diag	diag	NOUN
ejpam-6583	233	33	(	(	PUNCT
ejpam-6583	233	34	sλm1	sλm1	PROPN
ejpam-6583	233	35	[	[	PUNCT
ejpam-6583	233	36	1	1	NUM
ejpam-6583	233	37	1−	1−	NUM
ejpam-6583	233	38	sλ1	sλ1	NOUN
ejpam-6583	233	39	]	]	PUNCT
ejpam-6583	233	40	,	,	PUNCT
ejpam-6583	233	41	sλm2	sλm2	PROPN
ejpam-6583	233	42	[	[	PUNCT
ejpam-6583	233	43	1	1	NUM
ejpam-6583	233	44	1−	1−	NUM
ejpam-6583	233	45	sλ2	sλ2	NOUN
ejpam-6583	233	46	]	]	PUNCT
ejpam-6583	233	47	,	,	PUNCT
ejpam-6583	233	48	·	·	PUNCT
ejpam-6583	233	49	·	·	PUNCT
ejpam-6583	233	50	·	·	PUNCT
ejpam-6583	233	51	,	,	PUNCT
ejpam-6583	233	52	sλmd	sλmd	PROPN
ejpam-6583	233	53	[	[	PUNCT
ejpam-6583	233	54	1	1	NUM
ejpam-6583	233	55	1−	1−	NUM
ejpam-6583	233	56	sλd	sλd	NOUN
ejpam-6583	233	57	]	]	PUNCT
ejpam-6583	233	58	)	)	PUNCT
ejpam-6583	233	59	δb	δb	NOUN
ejpam-6583	233	60	r⊕d	r⊕d	NOUN
ejpam-6583	233	61	(	(	PUNCT
ejpam-6583	233	62	x0	x0	PROPN
ejpam-6583	233	63	,	,	PUNCT
ejpam-6583	233	64	x1	x1	PROPN
ejpam-6583	233	65	)	)	PUNCT
ejpam-6583	233	66	≾	≾	NOUN
ejpam-6583	233	67	diag(sλm1	diag(sλm1	NOUN
ejpam-6583	233	68	,	,	PUNCT
ejpam-6583	233	69	·	·	PUNCT
ejpam-6583	233	70	·	·	PUNCT
ejpam-6583	233	71	·	·	PUNCT
ejpam-6583	233	72	,	,	PUNCT
ejpam-6583	233	73	sλmd	sλmd	NOUN
ejpam-6583	233	74	)	)	PUNCT
ejpam-6583	233	75	diag	diag	NOUN
ejpam-6583	233	76	(	(	PUNCT
ejpam-6583	233	77	[	[	PUNCT
ejpam-6583	233	78	1	1	NUM
ejpam-6583	233	79	1−	1−	NUM
ejpam-6583	233	80	sλ1	sλ1	NOUN
ejpam-6583	233	81	]	]	PUNCT
ejpam-6583	233	82	,	,	PUNCT
ejpam-6583	233	83	·	·	PUNCT
ejpam-6583	233	84	·	·	PUNCT
ejpam-6583	233	85	·	·	PUNCT
ejpam-6583	233	86	,	,	PUNCT
ejpam-6583	233	87	[	[	PUNCT
ejpam-6583	233	88	1	1	NUM
ejpam-6583	233	89	1−	1−	NUM
ejpam-6583	233	90	sλd	sλd	NOUN
ejpam-6583	233	91	]	]	PUNCT
ejpam-6583	233	92	)	)	PUNCT
ejpam-6583	233	93	δb	δb	NOUN
ejpam-6583	233	94	r⊕d	r⊕d	NOUN
ejpam-6583	233	95	(	(	PUNCT
ejpam-6583	233	96	x0	x0	PROPN
ejpam-6583	233	97	,	,	PUNCT
ejpam-6583	233	98	x1	x1	PROPN
ejpam-6583	233	99	)	)	PUNCT
ejpam-6583	233	100	→	→	SYM
ejpam-6583	233	101	0	0	NUM
ejpam-6583	233	102	,	,	PUNCT
ejpam-6583	233	103	as	as	ADP
ejpam-6583	233	104	n	n	CCONJ
ejpam-6583	233	105	,	,	PUNCT
ejpam-6583	233	106	m	m	PROPN
ejpam-6583	233	107	→	→	SYM
ejpam-6583	233	108	+	+	ADJ
ejpam-6583	233	109	∞.	∞.	PROPN
ejpam-6583	233	110	since	since	SCONJ
ejpam-6583	233	111	0̃	0̃	PROPN
ejpam-6583	233	112	≺	≺	NOUN
ejpam-6583	233	113	diag(sλj1	diag(sλj1	PROPN
ejpam-6583	233	114	,	,	PUNCT
ejpam-6583	233	115	sλ	sλ	ADP
ejpam-6583	233	116	j	j	PROPN
ejpam-6583	233	117	2	2	NUM
ejpam-6583	233	118	,	,	PUNCT
ejpam-6583	233	119	·	·	PUNCT
ejpam-6583	233	120	·	·	PUNCT
ejpam-6583	233	121	·	·	PUNCT
ejpam-6583	233	122	,	,	PUNCT
ejpam-6583	233	123	sλ	sλ	ADP
ejpam-6583	233	124	j	j	PROPN
ejpam-6583	233	125	d	d	PROPN
ejpam-6583	233	126	)	)	PUNCT
ejpam-6583	233	127	≺	≺	NOUN
ejpam-6583	233	128	ir	ir	PROPN
ejpam-6583	233	129	⊕d	⊕d	NOUN
ejpam-6583	233	130	+	+	CCONJ
ejpam-6583	233	131	and	and	CCONJ
ejpam-6583	233	132	δb	δb	NOUN
ejpam-6583	233	133	r⊕d	r⊕d	NOUN
ejpam-6583	233	134	(	(	PUNCT
ejpam-6583	233	135	x0	x0	PROPN
ejpam-6583	233	136	,	,	PUNCT
ejpam-6583	233	137	x1	x1	PROPN
ejpam-6583	233	138	)	)	PUNCT
ejpam-6583	233	139	are	be	AUX
ejpam-6583	233	140	fixed	fix	VERB
ejpam-6583	233	141	,	,	PUNCT
ejpam-6583	233	142	it	it	PRON
ejpam-6583	233	143	is	be	AUX
ejpam-6583	233	144	evident	evident	ADJ
ejpam-6583	233	145	that	that	SCONJ
ejpam-6583	233	146	by	by	ADP
ejpam-6583	233	147	selectingm	selectingm	ADJ
ejpam-6583	233	148	sufficiently	sufficiently	ADV
ejpam-6583	233	149	large	large	ADJ
ejpam-6583	233	150	(	(	PUNCT
ejpam-6583	233	151	with	with	ADP
ejpam-6583	233	152	n	n	NOUN
ejpam-6583	233	153	>	>	X
ejpam-6583	233	154	m	m	PROPN
ejpam-6583	233	155	)	)	PUNCT
ejpam-6583	233	156	,	,	PUNCT
ejpam-6583	233	157	we	we	PRON
ejpam-6583	233	158	can	can	AUX
ejpam-6583	233	159	make	make	VERB
ejpam-6583	233	160	δb	δb	NOUN
ejpam-6583	233	161	r⊕d	r⊕d	NOUN
ejpam-6583	233	162	(	(	PUNCT
ejpam-6583	233	163	xn	xn	PROPN
ejpam-6583	233	164	,	,	PUNCT
ejpam-6583	233	165	xm	xm	PROPN
ejpam-6583	233	166	)	)	PUNCT
ejpam-6583	233	167	arbitrarily	arbitrarily	ADV
ejpam-6583	233	168	small	small	ADJ
ejpam-6583	233	169	.	.	PUNCT
ejpam-6583	234	1	this	this	PRON
ejpam-6583	234	2	shows	show	VERB
ejpam-6583	234	3	that	that	SCONJ
ejpam-6583	234	4	{	{	PUNCT
ejpam-6583	234	5	xn	xn	X
ejpam-6583	234	6	}	}	PUNCT
ejpam-6583	234	7	is	be	AUX
ejpam-6583	234	8	a	a	DET
ejpam-6583	234	9	cauchy	cauchy	ADJ
ejpam-6583	234	10	sequence	sequence	NOUN
ejpam-6583	234	11	.	.	PUNCT
ejpam-6583	235	1	finally	finally	ADV
ejpam-6583	235	2	,	,	PUNCT
ejpam-6583	235	3	because	because	SCONJ
ejpam-6583	235	4	(	(	PUNCT
ejpam-6583	235	5	x	x	X
ejpam-6583	235	6	,	,	PUNCT
ejpam-6583	235	7	r⊕d	r⊕d	NOUN
ejpam-6583	235	8	,	,	PUNCT
ejpam-6583	235	9	δb	δb	NOUN
ejpam-6583	235	10	r⊕d	r⊕d	NOUN
ejpam-6583	235	11	)	)	PUNCT
ejpam-6583	235	12	is	be	AUX
ejpam-6583	235	13	complete	complete	ADJ
ejpam-6583	235	14	,	,	PUNCT
ejpam-6583	235	15	there	there	PRON
ejpam-6583	235	16	exists	exist	VERB
ejpam-6583	235	17	some	some	DET
ejpam-6583	235	18	z	z	NOUN
ejpam-6583	235	19	∈	∈	PROPN
ejpam-6583	235	20	x	x	PUNCT
ejpam-6583	235	21	such	such	ADJ
ejpam-6583	235	22	that	that	PRON
ejpam-6583	235	23	xn	xn	PROPN
ejpam-6583	236	1	→	→	SYM
ejpam-6583	236	2	z.	z.	PROPN
ejpam-6583	236	3	to	to	PART
ejpam-6583	236	4	show	show	VERB
ejpam-6583	236	5	that	that	SCONJ
ejpam-6583	236	6	x	x	PRON
ejpam-6583	236	7	has	have	VERB
ejpam-6583	236	8	a	a	DET
ejpam-6583	236	9	fixed	fix	VERB
ejpam-6583	236	10	point	point	NOUN
ejpam-6583	236	11	,	,	PUNCT
ejpam-6583	236	12	we	we	PRON
ejpam-6583	236	13	consider	consider	VERB
ejpam-6583	236	14	the	the	DET
ejpam-6583	236	15	distance	distance	NOUN
ejpam-6583	236	16	δb	δb	NOUN
ejpam-6583	236	17	r⊕d	r⊕d	NOUN
ejpam-6583	236	18	(	(	PUNCT
ejpam-6583	236	19	z	z	NOUN
ejpam-6583	236	20	,	,	PUNCT
ejpam-6583	236	21	f	f	PROPN
ejpam-6583	236	22	(	(	PUNCT
ejpam-6583	236	23	z	z	NOUN
ejpam-6583	236	24	)	)	PUNCT
ejpam-6583	236	25	)	)	PUNCT
ejpam-6583	236	26	.	.	PUNCT
ejpam-6583	237	1	from	from	ADP
ejpam-6583	237	2	the	the	DET
ejpam-6583	237	3	triangle	triangle	NOUN
ejpam-6583	237	4	inequality	inequality	NOUN
ejpam-6583	237	5	and	and	CCONJ
ejpam-6583	237	6	contraction	contraction	NOUN
ejpam-6583	237	7	condition	condition	NOUN
ejpam-6583	237	8	,	,	PUNCT
ejpam-6583	237	9	we	we	PRON
ejpam-6583	237	10	get	get	VERB
ejpam-6583	237	11	δb	δb	ADP
ejpam-6583	237	12	r⊕d	r⊕d	NOUN
ejpam-6583	237	13	(	(	PUNCT
ejpam-6583	237	14	z	z	NOUN
ejpam-6583	237	15	,	,	PUNCT
ejpam-6583	237	16	f	f	PROPN
ejpam-6583	237	17	(	(	PUNCT
ejpam-6583	237	18	z	z	NOUN
ejpam-6583	237	19	)	)	PUNCT
ejpam-6583	237	20	)	)	PUNCT
ejpam-6583	238	1	≾	≾	PROPN
ejpam-6583	238	2	s	s	PART
ejpam-6583	238	3	[	[	PUNCT
ejpam-6583	238	4	δb	δb	NOUN
ejpam-6583	238	5	r⊕d	r⊕d	NOUN
ejpam-6583	238	6	(	(	PUNCT
ejpam-6583	238	7	z	z	NOUN
ejpam-6583	238	8	,	,	PUNCT
ejpam-6583	238	9	xn	xn	PROPN
ejpam-6583	238	10	)	)	PUNCT
ejpam-6583	239	1	+	+	CCONJ
ejpam-6583	239	2	δb	δb	NOUN
ejpam-6583	239	3	r⊕d	r⊕d	NOUN
ejpam-6583	239	4	(	(	PUNCT
ejpam-6583	239	5	xn	xn	PROPN
ejpam-6583	239	6	,	,	PUNCT
ejpam-6583	239	7	f	f	PROPN
ejpam-6583	239	8	(	(	PUNCT
ejpam-6583	239	9	z	z	NOUN
ejpam-6583	239	10	)	)	PUNCT
ejpam-6583	239	11	)	)	PUNCT
ejpam-6583	239	12	]	]	PUNCT
ejpam-6583	240	1	=	=	PUNCT
ejpam-6583	240	2	s	s	X
ejpam-6583	240	3	[	[	PUNCT
ejpam-6583	240	4	δb	δb	NOUN
ejpam-6583	240	5	r⊕d	r⊕d	NOUN
ejpam-6583	240	6	(	(	PUNCT
ejpam-6583	240	7	z	z	NOUN
ejpam-6583	240	8	,	,	PUNCT
ejpam-6583	240	9	xn	xn	PROPN
ejpam-6583	240	10	)	)	PUNCT
ejpam-6583	241	1	+	+	CCONJ
ejpam-6583	241	2	δb	δb	NOUN
ejpam-6583	241	3	r⊕d	r⊕d	NOUN
ejpam-6583	241	4	(	(	PUNCT
ejpam-6583	241	5	f	f	PROPN
ejpam-6583	241	6	(	(	PUNCT
ejpam-6583	241	7	xn−1),f	xn−1),f	PROPN
ejpam-6583	241	8	(	(	PUNCT
ejpam-6583	241	9	z	z	NOUN
ejpam-6583	241	10	)	)	PUNCT
ejpam-6583	241	11	)	)	PUNCT
ejpam-6583	241	12	]	]	PUNCT
ejpam-6583	242	1	≾	≾	PROPN
ejpam-6583	242	2	s	s	X
ejpam-6583	242	3	[	[	PUNCT
ejpam-6583	242	4	δb	δb	NOUN
ejpam-6583	242	5	r⊕d	r⊕d	NOUN
ejpam-6583	242	6	(	(	PUNCT
ejpam-6583	242	7	z	z	NOUN
ejpam-6583	242	8	,	,	PUNCT
ejpam-6583	242	9	xn	xn	PUNCT
ejpam-6583	242	10	)	)	PUNCT
ejpam-6583	243	1	+	+	CCONJ
ejpam-6583	243	2	diag	diag	NOUN
ejpam-6583	243	3	(	(	PUNCT
ejpam-6583	243	4	λ1	λ1	ADJ
ejpam-6583	243	5	,	,	PUNCT
ejpam-6583	243	6	λ2	λ2	NOUN
ejpam-6583	243	7	,	,	PUNCT
ejpam-6583	243	8	·	·	PUNCT
ejpam-6583	243	9	·	·	PUNCT
ejpam-6583	243	10	·	·	PUNCT
ejpam-6583	243	11	,	,	PUNCT
ejpam-6583	243	12	λd	λd	NOUN
ejpam-6583	243	13	)	)	PUNCT
ejpam-6583	243	14	δb	δb	NOUN
ejpam-6583	243	15	r⊕d	r⊕d	NOUN
ejpam-6583	243	16	(	(	PUNCT
ejpam-6583	243	17	xn−1	xn−1	PROPN
ejpam-6583	243	18	,	,	PUNCT
ejpam-6583	243	19	z	z	NOUN
ejpam-6583	243	20	)	)	PUNCT
ejpam-6583	243	21	]	]	PUNCT
ejpam-6583	243	22	,	,	PUNCT
ejpam-6583	243	23	and	and	CCONJ
ejpam-6583	243	24	since	since	SCONJ
ejpam-6583	243	25	xn	xn	PROPN
ejpam-6583	243	26	→	→	SYM
ejpam-6583	243	27	z	z	X
ejpam-6583	243	28	,	,	PUNCT
ejpam-6583	243	29	it	it	PRON
ejpam-6583	243	30	is	be	AUX
ejpam-6583	243	31	clear	clear	ADJ
ejpam-6583	243	32	that	that	SCONJ
ejpam-6583	243	33	we	we	PRON
ejpam-6583	243	34	can	can	AUX
ejpam-6583	243	35	make	make	VERB
ejpam-6583	243	36	this	this	DET
ejpam-6583	243	37	distance	distance	NOUN
ejpam-6583	243	38	as	as	ADV
ejpam-6583	243	39	small	small	ADJ
ejpam-6583	243	40	as	as	SCONJ
ejpam-6583	243	41	we	we	PRON
ejpam-6583	243	42	please	please	VERB
ejpam-6583	243	43	by	by	ADP
ejpam-6583	243	44	choosing	choose	VERB
ejpam-6583	243	45	n	n	PRON
ejpam-6583	243	46	sufficiently	sufficiently	ADV
ejpam-6583	243	47	large	large	ADJ
ejpam-6583	243	48	.	.	PUNCT
ejpam-6583	244	1	we	we	PRON
ejpam-6583	244	2	conclude	conclude	VERB
ejpam-6583	244	3	that	that	SCONJ
ejpam-6583	244	4	δb	δb	NOUN
ejpam-6583	244	5	r⊕d	r⊕d	NOUN
ejpam-6583	244	6	(	(	PUNCT
ejpam-6583	244	7	z	z	NOUN
ejpam-6583	244	8	,	,	PUNCT
ejpam-6583	244	9	f	f	PROPN
ejpam-6583	244	10	(	(	PUNCT
ejpam-6583	244	11	z	z	NOUN
ejpam-6583	244	12	)	)	PUNCT
ejpam-6583	244	13	)	)	PUNCT
ejpam-6583	245	1	=	=	SYM
ejpam-6583	245	2	0	0	PUNCT
ejpam-6583	246	1	=	=	AUX
ejpam-6583	246	2	⇒	⇒	X
ejpam-6583	246	3	f	f	X
ejpam-6583	246	4	(	(	PUNCT
ejpam-6583	246	5	z	z	NOUN
ejpam-6583	246	6	)	)	PUNCT
ejpam-6583	247	1	=	=	SYM
ejpam-6583	247	2	z	z	NOUN
ejpam-6583	247	3	,	,	PUNCT
ejpam-6583	247	4	so	so	ADV
ejpam-6583	247	5	x	x	SYM
ejpam-6583	247	6	∈	∈	PROPN
ejpam-6583	247	7	x	x	X
ejpam-6583	247	8	is	be	AUX
ejpam-6583	247	9	a	a	DET
ejpam-6583	247	10	fixed	fix	VERB
ejpam-6583	247	11	-	-	PUNCT
ejpam-6583	247	12	point	point	NOUN
ejpam-6583	247	13	of	of	ADP
ejpam-6583	247	14	f	f	PROPN
ejpam-6583	247	15	.	.	PUNCT
ejpam-6583	248	1	to	to	PART
ejpam-6583	248	2	prove	prove	VERB
ejpam-6583	248	3	uniqueness	uniqueness	NOUN
ejpam-6583	248	4	,	,	PUNCT
ejpam-6583	248	5	suppose	suppose	VERB
ejpam-6583	248	6	there	there	PRON
ejpam-6583	248	7	are	be	VERB
ejpam-6583	248	8	two	two	NUM
ejpam-6583	248	9	fixed	fix	VERB
ejpam-6583	248	10	points	point	NOUN
ejpam-6583	249	1	x	x	X
ejpam-6583	249	2	=	=	SYM
ejpam-6583	249	3	f	f	X
ejpam-6583	249	4	(	(	PUNCT
ejpam-6583	249	5	x	x	NOUN
ejpam-6583	249	6	)	)	PUNCT
ejpam-6583	249	7	and	and	CCONJ
ejpam-6583	249	8	y	y	PROPN
ejpam-6583	249	9	=	=	SYM
ejpam-6583	249	10	f	f	PROPN
ejpam-6583	249	11	(	(	PUNCT
ejpam-6583	249	12	x	x	NOUN
ejpam-6583	249	13	)	)	PUNCT
ejpam-6583	249	14	.	.	PUNCT
ejpam-6583	250	1	then	then	ADV
ejpam-6583	250	2	,	,	PUNCT
ejpam-6583	250	3	from	from	ADP
ejpam-6583	250	4	the	the	DET
ejpam-6583	250	5	contraction	contraction	NOUN
ejpam-6583	250	6	condition	condition	NOUN
ejpam-6583	250	7	,	,	PUNCT
ejpam-6583	250	8	we	we	PRON
ejpam-6583	250	9	have	have	VERB
ejpam-6583	250	10	δb	δb	NOUN
ejpam-6583	250	11	r⊕d	r⊕d	NOUN
ejpam-6583	250	12	(	(	PUNCT
ejpam-6583	250	13	x	x	X
ejpam-6583	250	14	,	,	PUNCT
ejpam-6583	250	15	y	y	NOUN
ejpam-6583	250	16	)	)	PUNCT
ejpam-6583	250	17	=	=	PUNCT
ejpam-6583	250	18	δb	δb	X
ejpam-6583	250	19	r⊕d	r⊕d	NOUN
ejpam-6583	250	20	(	(	PUNCT
ejpam-6583	250	21	f	f	PROPN
ejpam-6583	250	22	(	(	PUNCT
ejpam-6583	250	23	x),f	x),f	PROPN
ejpam-6583	250	24	(	(	PUNCT
ejpam-6583	250	25	y	y	NOUN
ejpam-6583	250	26	)	)	PUNCT
ejpam-6583	250	27	)	)	PUNCT
ejpam-6583	251	1	≾	≾	NOUN
ejpam-6583	251	2	diag	diag	NOUN
ejpam-6583	251	3	(	(	PUNCT
ejpam-6583	251	4	λ1	λ1	ADJ
ejpam-6583	251	5	,	,	PUNCT
ejpam-6583	251	6	λ2	λ2	NOUN
ejpam-6583	251	7	,	,	PUNCT
ejpam-6583	251	8	·	·	PUNCT
ejpam-6583	251	9	·	·	PUNCT
ejpam-6583	251	10	·	·	PUNCT
ejpam-6583	251	11	,	,	PUNCT
ejpam-6583	251	12	λd	λd	NOUN
ejpam-6583	251	13	)	)	PUNCT
ejpam-6583	251	14	δb	δb	NOUN
ejpam-6583	251	15	r⊕d	r⊕d	NOUN
ejpam-6583	251	16	(	(	PUNCT
ejpam-6583	251	17	x	x	X
ejpam-6583	251	18	,	,	PUNCT
ejpam-6583	251	19	y	y	PROPN
ejpam-6583	251	20	)	)	PUNCT
ejpam-6583	251	21	this	this	PRON
ejpam-6583	251	22	implies	imply	VERB
ejpam-6583	251	23	δb	δb	NOUN
ejpam-6583	251	24	r⊕d	r⊕d	NOUN
ejpam-6583	251	25	(	(	PUNCT
ejpam-6583	251	26	x	x	X
ejpam-6583	251	27	,	,	PUNCT
ejpam-6583	251	28	y	y	NOUN
ejpam-6583	251	29	)	)	PUNCT
ejpam-6583	251	30	=	=	SYM
ejpam-6583	251	31	0	0	PUNCT
ejpam-6583	251	32	since	since	SCONJ
ejpam-6583	251	33	0̃	0̃	NOUN
ejpam-6583	251	34	≺	≺	NOUN
ejpam-6583	251	35	λ	λ	PROPN
ejpam-6583	251	36	≺	≺	NOUN
ejpam-6583	251	37	ir	ir	PROPN
ejpam-6583	251	38	⊕d	⊕d	NOUN
ejpam-6583	251	39	+	+	X
ejpam-6583	251	40	.	.	PUNCT
ejpam-6583	252	1	hence	hence	ADV
ejpam-6583	252	2	x	x	X
ejpam-6583	252	3	=	=	SYM
ejpam-6583	252	4	y	y	PROPN
ejpam-6583	252	5	,	,	PUNCT
ejpam-6583	252	6	and	and	CCONJ
ejpam-6583	252	7	the	the	DET
ejpam-6583	252	8	fixed	fix	VERB
ejpam-6583	252	9	-	-	PUNCT
ejpam-6583	252	10	point	point	NOUN
ejpam-6583	252	11	x	x	PUNCT
ejpam-6583	252	12	of	of	ADP
ejpam-6583	252	13	f	f	PROPN
ejpam-6583	252	14	is	be	AUX
ejpam-6583	252	15	unique	unique	ADJ
ejpam-6583	252	16	.	.	PUNCT
ejpam-6583	253	1	example	example	NOUN
ejpam-6583	253	2	7	7	NUM
ejpam-6583	253	3	(	(	PUNCT
ejpam-6583	253	4	a	a	DET
ejpam-6583	253	5	numerical	numerical	ADJ
ejpam-6583	253	6	iterative	iterative	NOUN
ejpam-6583	253	7	example	example	NOUN
ejpam-6583	253	8	)	)	PUNCT
ejpam-6583	253	9	.	.	PUNCT
ejpam-6583	254	1	let	let	VERB
ejpam-6583	254	2	x	x	PUNCT
ejpam-6583	254	3	=	=	PUNCT
ejpam-6583	254	4	r	r	NOUN
ejpam-6583	254	5	with	with	ADP
ejpam-6583	254	6	the	the	DET
ejpam-6583	254	7	generalized	generalize	VERB
ejpam-6583	254	8	metric	metric	NOUN
ejpam-6583	254	9	δb	δb	NOUN
ejpam-6583	254	10	r⊕d	r⊕d	NOUN
ejpam-6583	254	11	defined	define	VERB
ejpam-6583	254	12	as	as	ADP
ejpam-6583	254	13	:	:	PUNCT
ejpam-6583	254	14	δb	δb	NOUN
ejpam-6583	254	15	r⊕d	r⊕d	NOUN
ejpam-6583	254	16	(	(	PUNCT
ejpam-6583	254	17	x	x	X
ejpam-6583	254	18	,	,	PUNCT
ejpam-6583	254	19	y	y	NOUN
ejpam-6583	254	20	)	)	PUNCT
ejpam-6583	255	1	=	=	SYM
ejpam-6583	255	2	diag(|x−	diag(|x−	PROPN
ejpam-6583	255	3	y|2	y|2	PROPN
ejpam-6583	255	4	,	,	PUNCT
ejpam-6583	255	5	|x−	|x−	PROPN
ejpam-6583	255	6	y|2	y|2	PROPN
ejpam-6583	255	7	,	,	PUNCT
ejpam-6583	255	8	.	.	PUNCT
ejpam-6583	255	9	.	.	PUNCT
ejpam-6583	255	10	.	.	PUNCT
ejpam-6583	256	1	,	,	PUNCT
ejpam-6583	256	2	|x−	|x−	PROPN
ejpam-6583	256	3	y|2	y|2	PROPN
ejpam-6583	256	4	)	)	PUNCT
ejpam-6583	256	5	.	.	PUNCT
ejpam-6583	257	1	g.	g.	PROPN
ejpam-6583	257	2	albeladi	albeladi	PROPN
ejpam-6583	257	3	,	,	PUNCT
ejpam-6583	257	4	s.	s.	PROPN
ejpam-6583	257	5	omran	omran	PROPN
ejpam-6583	257	6	/	/	SYM
ejpam-6583	257	7	eur	eur	PROPN
ejpam-6583	257	8	.	.	PUNCT
ejpam-6583	258	1	j.	j.	PROPN
ejpam-6583	258	2	pure	pure	PROPN
ejpam-6583	258	3	appl	appl	PROPN
ejpam-6583	258	4	.	.	PROPN
ejpam-6583	258	5	math	math	PROPN
ejpam-6583	258	6	,	,	PUNCT
ejpam-6583	258	7	18	18	NUM
ejpam-6583	258	8	(	(	PUNCT
ejpam-6583	258	9	3	3	NUM
ejpam-6583	258	10	)	)	PUNCT
ejpam-6583	258	11	(	(	PUNCT
ejpam-6583	258	12	2025	2025	NUM
ejpam-6583	258	13	)	)	PUNCT
ejpam-6583	258	14	,	,	PUNCT
ejpam-6583	258	15	6583	6583	NUM
ejpam-6583	258	16	11	11	NUM
ejpam-6583	258	17	of	of	ADP
ejpam-6583	258	18	27	27	NUM
ejpam-6583	258	19	consider	consider	VERB
ejpam-6583	258	20	the	the	DET
ejpam-6583	258	21	function	function	NOUN
ejpam-6583	258	22	:	:	PUNCT
ejpam-6583	258	23	f	f	PROPN
ejpam-6583	258	24	(	(	PUNCT
ejpam-6583	258	25	x	x	X
ejpam-6583	258	26	)	)	PUNCT
ejpam-6583	258	27	=	=	SYM
ejpam-6583	258	28	x	x	SYM
ejpam-6583	258	29	3	3	X
ejpam-6583	258	30	.	.	PUNCT
ejpam-6583	259	1	we	we	PRON
ejpam-6583	259	2	choose	choose	VERB
ejpam-6583	259	3	the	the	DET
ejpam-6583	259	4	diagonal	diagonal	ADJ
ejpam-6583	259	5	contraction	contraction	NOUN
ejpam-6583	259	6	matrix	matrix	NOUN
ejpam-6583	259	7	:	:	PUNCT
ejpam-6583	259	8	λ	λ	X
ejpam-6583	259	9	=	=	PUNCT
ejpam-6583	259	10	diag	diag	PROPN
ejpam-6583	259	11	(	(	PUNCT
ejpam-6583	259	12	1	1	NUM
ejpam-6583	259	13	9	9	NUM
ejpam-6583	259	14	,	,	PUNCT
ejpam-6583	259	15	1	1	NUM
ejpam-6583	259	16	9	9	NUM
ejpam-6583	259	17	,	,	PUNCT
ejpam-6583	259	18	.	.	PUNCT
ejpam-6583	259	19	.	.	PUNCT
ejpam-6583	260	1	.	.	PUNCT
ejpam-6583	261	1	,	,	PUNCT
ejpam-6583	261	2	1	1	NUM
ejpam-6583	261	3	9	9	NUM
ejpam-6583	261	4	)	)	PUNCT
ejpam-6583	261	5	,	,	PUNCT
ejpam-6583	261	6	which	which	PRON
ejpam-6583	261	7	satisfies	satisfy	VERB
ejpam-6583	261	8	:	:	PUNCT
ejpam-6583	261	9	δb	δb	NOUN
ejpam-6583	261	10	r⊕d	r⊕d	NOUN
ejpam-6583	261	11	(	(	PUNCT
ejpam-6583	261	12	f	f	PROPN
ejpam-6583	261	13	(	(	PUNCT
ejpam-6583	261	14	x),f	x),f	PROPN
ejpam-6583	261	15	(	(	PUNCT
ejpam-6583	261	16	y	y	NOUN
ejpam-6583	261	17	)	)	PUNCT
ejpam-6583	261	18	)	)	PUNCT
ejpam-6583	262	1	=	=	PUNCT
ejpam-6583	262	2	1	1	NUM
ejpam-6583	262	3	9	9	NUM
ejpam-6583	262	4	·	·	PUNCT
ejpam-6583	262	5	δb	δb	NOUN
ejpam-6583	262	6	r⊕d	r⊕d	NOUN
ejpam-6583	262	7	(	(	PUNCT
ejpam-6583	262	8	x	x	X
ejpam-6583	262	9	,	,	PUNCT
ejpam-6583	262	10	y	y	PROPN
ejpam-6583	262	11	)	)	PUNCT
ejpam-6583	262	12	.	.	PUNCT
ejpam-6583	263	1	since	since	SCONJ
ejpam-6583	263	2	0	0	NUM
ejpam-6583	263	3	<	<	X
ejpam-6583	263	4	1	1	NUM
ejpam-6583	263	5	9	9	NUM
ejpam-6583	263	6	<	<	X
ejpam-6583	263	7	1	1	NUM
ejpam-6583	263	8	,	,	PUNCT
ejpam-6583	263	9	the	the	DET
ejpam-6583	263	10	operator	operator	NOUN
ejpam-6583	263	11	f	f	PROPN
ejpam-6583	263	12	satisfies	satisfy	VERB
ejpam-6583	263	13	the	the	DET
ejpam-6583	263	14	contraction	contraction	NOUN
ejpam-6583	263	15	condition	condition	NOUN
ejpam-6583	263	16	required	require	VERB
ejpam-6583	263	17	by	by	ADP
ejpam-6583	263	18	theorem	theorem	NOUN
ejpam-6583	263	19	3	3	NUM
ejpam-6583	263	20	,	,	PUNCT
ejpam-6583	263	21	we	we	PRON
ejpam-6583	263	22	can	can	AUX
ejpam-6583	263	23	find	find	VERB
ejpam-6583	263	24	the	the	DET
ejpam-6583	263	25	fixed	fix	VERB
ejpam-6583	263	26	-	-	PUNCT
ejpam-6583	263	27	point	point	NOUN
ejpam-6583	263	28	by	by	ADP
ejpam-6583	263	29	using	use	VERB
ejpam-6583	263	30	the	the	DET
ejpam-6583	263	31	iterative	iterative	ADJ
ejpam-6583	263	32	sequence	sequence	NOUN
ejpam-6583	263	33	:	:	PUNCT
ejpam-6583	263	34	xn+1	xn+1	X
ejpam-6583	264	1	=	=	SYM
ejpam-6583	264	2	f	f	PROPN
ejpam-6583	264	3	(	(	PUNCT
ejpam-6583	264	4	xn	xn	PROPN
ejpam-6583	264	5	)	)	PUNCT
ejpam-6583	264	6	,	,	PUNCT
ejpam-6583	264	7	starting	start	VERB
ejpam-6583	264	8	from	from	ADP
ejpam-6583	264	9	an	an	DET
ejpam-6583	264	10	arbitrary	arbitrary	ADJ
ejpam-6583	264	11	initial	initial	ADJ
ejpam-6583	264	12	point	point	NOUN
ejpam-6583	264	13	x0	x0	PROPN
ejpam-6583	264	14	=	=	SYM
ejpam-6583	264	15	6	6	NUM
ejpam-6583	264	16	,	,	PUNCT
ejpam-6583	264	17	we	we	PRON
ejpam-6583	264	18	get	get	VERB
ejpam-6583	264	19	:	:	PUNCT
ejpam-6583	265	1	x1	x1	PROPN
ejpam-6583	265	2	=	=	SYM
ejpam-6583	265	3	6	6	NUM
ejpam-6583	265	4	3	3	NUM
ejpam-6583	265	5	=	=	SYM
ejpam-6583	265	6	2	2	NUM
ejpam-6583	265	7	,	,	PUNCT
ejpam-6583	265	8	x2	x2	NOUN
ejpam-6583	265	9	=	=	NOUN
ejpam-6583	265	10	2	2	NUM
ejpam-6583	265	11	3	3	NUM
ejpam-6583	265	12	≈	≈	NUM
ejpam-6583	265	13	0.67	0.67	NUM
ejpam-6583	265	14	,	,	PUNCT
ejpam-6583	265	15	x3	x3	NOUN
ejpam-6583	265	16	=	=	NOUN
ejpam-6583	266	1	0.67	0.67	NUM
ejpam-6583	266	2	3	3	NUM
ejpam-6583	266	3	≈	≈	NUM
ejpam-6583	266	4	0.22	0.22	NUM
ejpam-6583	266	5	,	,	PUNCT
ejpam-6583	266	6	...	...	PUNCT
ejpam-6583	266	7	xn	xn	PUNCT
ejpam-6583	267	1	=	=	NOUN
ejpam-6583	267	2	6	6	NUM
ejpam-6583	267	3	3n	3n	NUM
ejpam-6583	267	4	,	,	PUNCT
ejpam-6583	267	5	...	...	PUNCT
ejpam-6583	268	1	taking	take	VERB
ejpam-6583	268	2	the	the	DET
ejpam-6583	268	3	limit	limit	NOUN
ejpam-6583	268	4	as	as	ADP
ejpam-6583	268	5	n→	n→	ADV
ejpam-6583	268	6	+	+	ADJ
ejpam-6583	268	7	∞	∞	PROPN
ejpam-6583	268	8	:	:	PUNCT
ejpam-6583	269	1	lim	lim	PROPN
ejpam-6583	269	2	n→+∞	n→+∞	VERB
ejpam-6583	269	3	xn	xn	PUNCT
ejpam-6583	270	1	=	=	SYM
ejpam-6583	270	2	lim	lim	PROPN
ejpam-6583	270	3	n→+∞	n→+∞	VERB
ejpam-6583	270	4	6	6	NUM
ejpam-6583	270	5	3n	3n	NOUN
ejpam-6583	270	6	=	=	SYM
ejpam-6583	270	7	0	0	NUM
ejpam-6583	270	8	.	.	PUNCT
ejpam-6583	271	1	thus	thus	ADV
ejpam-6583	271	2	,	,	PUNCT
ejpam-6583	271	3	the	the	DET
ejpam-6583	271	4	iterative	iterative	NOUN
ejpam-6583	271	5	process	process	NOUN
ejpam-6583	271	6	confirms	confirm	VERB
ejpam-6583	271	7	that	that	SCONJ
ejpam-6583	271	8	the	the	DET
ejpam-6583	271	9	fixed	fix	VERB
ejpam-6583	271	10	-	-	PUNCT
ejpam-6583	271	11	point	point	NOUN
ejpam-6583	271	12	of	of	ADP
ejpam-6583	271	13	f	f	PROPN
ejpam-6583	271	14	is	be	AUX
ejpam-6583	271	15	indeed	indeed	ADV
ejpam-6583	271	16	z	z	NOUN
ejpam-6583	271	17	=	=	SYM
ejpam-6583	271	18	0	0	PROPN
ejpam-6583	271	19	.	.	NOUN
ejpam-6583	271	20	example	example	NOUN
ejpam-6583	271	21	8	8	NUM
ejpam-6583	271	22	(	(	PUNCT
ejpam-6583	271	23	a	a	DET
ejpam-6583	271	24	fredholm	fredholm	ADJ
ejpam-6583	271	25	integral	integral	ADJ
ejpam-6583	271	26	equation	equation	NOUN
ejpam-6583	271	27	)	)	PUNCT
ejpam-6583	271	28	.	.	PUNCT
ejpam-6583	272	1	let	let	VERB
ejpam-6583	272	2	x	x	PRON
ejpam-6583	272	3	=	=	SYM
ejpam-6583	272	4	c([0	c([0	NOUN
ejpam-6583	272	5	,	,	PUNCT
ejpam-6583	272	6	1],r	1],r	NUM
ejpam-6583	272	7	)	)	PUNCT
ejpam-6583	272	8	,	,	PUNCT
ejpam-6583	272	9	the	the	DET
ejpam-6583	272	10	space	space	NOUN
ejpam-6583	272	11	of	of	ADP
ejpam-6583	272	12	continuous	continuous	ADJ
ejpam-6583	272	13	functions	function	NOUN
ejpam-6583	272	14	on	on	ADP
ejpam-6583	272	15	[	[	X
ejpam-6583	272	16	0	0	NUM
ejpam-6583	272	17	,	,	PUNCT
ejpam-6583	272	18	1	1	NUM
ejpam-6583	272	19	]	]	PUNCT
ejpam-6583	272	20	,	,	PUNCT
ejpam-6583	272	21	equipped	equip	VERB
ejpam-6583	272	22	with	with	ADP
ejpam-6583	272	23	the	the	DET
ejpam-6583	272	24	norm	norm	NOUN
ejpam-6583	272	25	:	:	PUNCT
ejpam-6583	272	26	∥f∥	∥f∥	ADJ
ejpam-6583	272	27	=	=	SYM
ejpam-6583	272	28	sup	sup	NOUN
ejpam-6583	272	29	x∈[0,1	x∈[0,1	NOUN
ejpam-6583	272	30	]	]	X
ejpam-6583	273	1	|f(x)|	|f(x)|	NOUN
ejpam-6583	273	2	.	.	PUNCT
ejpam-6583	273	3	define	define	VERB
ejpam-6583	273	4	the	the	DET
ejpam-6583	273	5	generalized	generalize	VERB
ejpam-6583	273	6	metric	metric	NOUN
ejpam-6583	273	7	:	:	PUNCT
ejpam-6583	273	8	δb	δb	NOUN
ejpam-6583	273	9	r⊕d	r⊕d	NOUN
ejpam-6583	273	10	(	(	PUNCT
ejpam-6583	273	11	f	f	X
ejpam-6583	273	12	,	,	PUNCT
ejpam-6583	273	13	g	g	NOUN
ejpam-6583	273	14	)	)	PUNCT
ejpam-6583	273	15	=	=	PUNCT
ejpam-6583	274	1	diag(∥f	diag(∥f	NOUN
ejpam-6583	274	2	−	−	NOUN
ejpam-6583	274	3	g∥2	g∥2	NOUN
ejpam-6583	274	4	,	,	PUNCT
ejpam-6583	274	5	∥f	∥f	PROPN
ejpam-6583	274	6	−	−	PROPN
ejpam-6583	274	7	g∥2	g∥2	NOUN
ejpam-6583	274	8	,	,	PUNCT
ejpam-6583	274	9	.	.	PUNCT
ejpam-6583	274	10	.	.	PUNCT
ejpam-6583	274	11	.	.	PUNCT
ejpam-6583	275	1	,	,	PUNCT
ejpam-6583	275	2	∥f	∥f	PROPN
ejpam-6583	275	3	−	−	PROPN
ejpam-6583	275	4	g∥2	g∥2	NOUN
ejpam-6583	275	5	)	)	PUNCT
ejpam-6583	275	6	.	.	PUNCT
ejpam-6583	276	1	g.	g.	PROPN
ejpam-6583	276	2	albeladi	albeladi	PROPN
ejpam-6583	276	3	,	,	PUNCT
ejpam-6583	276	4	s.	s.	PROPN
ejpam-6583	276	5	omran	omran	PROPN
ejpam-6583	276	6	/	/	SYM
ejpam-6583	276	7	eur	eur	PROPN
ejpam-6583	276	8	.	.	PUNCT
ejpam-6583	277	1	j.	j.	PROPN
ejpam-6583	277	2	pure	pure	PROPN
ejpam-6583	277	3	appl	appl	PROPN
ejpam-6583	277	4	.	.	PROPN
ejpam-6583	277	5	math	math	PROPN
ejpam-6583	277	6	,	,	PUNCT
ejpam-6583	277	7	18	18	NUM
ejpam-6583	277	8	(	(	PUNCT
ejpam-6583	277	9	3	3	NUM
ejpam-6583	277	10	)	)	PUNCT
ejpam-6583	277	11	(	(	PUNCT
ejpam-6583	277	12	2025	2025	NUM
ejpam-6583	277	13	)	)	PUNCT
ejpam-6583	277	14	,	,	PUNCT
ejpam-6583	277	15	6583	6583	NUM
ejpam-6583	277	16	12	12	NUM
ejpam-6583	277	17	of	of	ADP
ejpam-6583	277	18	27	27	NUM
ejpam-6583	277	19	consider	consider	VERB
ejpam-6583	277	20	the	the	DET
ejpam-6583	277	21	fredholm	fredholm	ADJ
ejpam-6583	277	22	integral	integral	ADJ
ejpam-6583	277	23	equation	equation	NOUN
ejpam-6583	277	24	:	:	PUNCT
ejpam-6583	277	25	f(x	f(x	PROPN
ejpam-6583	277	26	)	)	PUNCT
ejpam-6583	277	27	=	=	PUNCT
ejpam-6583	278	1	1∫	1∫	NUM
ejpam-6583	278	2	0	0	X
ejpam-6583	278	3	k(x	k(x	PROPN
ejpam-6583	278	4	,	,	PUNCT
ejpam-6583	278	5	t)f(t)dt	t)f(t)dt	NOUN
ejpam-6583	278	6	,	,	PUNCT
ejpam-6583	278	7	where	where	SCONJ
ejpam-6583	278	8	k(x	k(x	PROPN
ejpam-6583	278	9	,	,	PUNCT
ejpam-6583	278	10	t	t	PROPN
ejpam-6583	278	11	)	)	PUNCT
ejpam-6583	278	12	is	be	AUX
ejpam-6583	278	13	a	a	DET
ejpam-6583	278	14	continuous	continuous	ADJ
ejpam-6583	278	15	kernel	kernel	NOUN
ejpam-6583	278	16	.	.	PUNCT
ejpam-6583	278	17	define	define	VERB
ejpam-6583	278	18	the	the	DET
ejpam-6583	278	19	operator	operator	NOUN
ejpam-6583	278	20	f	f	PROPN
ejpam-6583	278	21	:	:	PUNCT
ejpam-6583	278	22	c([0	c([0	NOUN
ejpam-6583	278	23	,	,	PUNCT
ejpam-6583	278	24	1],r	1],r	NUM
ejpam-6583	278	25	)	)	PUNCT
ejpam-6583	278	26	→	→	SYM
ejpam-6583	278	27	c([0	c([0	NOUN
ejpam-6583	278	28	,	,	PUNCT
ejpam-6583	278	29	1],r	1],r	NUM
ejpam-6583	278	30	)	)	PUNCT
ejpam-6583	278	31	by	by	ADP
ejpam-6583	278	32	:	:	PUNCT
ejpam-6583	278	33	(	(	PUNCT
ejpam-6583	278	34	ff)(x	ff)(x	PROPN
ejpam-6583	278	35	)	)	PUNCT
ejpam-6583	278	36	=	=	PUNCT
ejpam-6583	279	1	1∫	1∫	NUM
ejpam-6583	279	2	0	0	X
ejpam-6583	279	3	k(x	k(x	PROPN
ejpam-6583	279	4	,	,	PUNCT
ejpam-6583	279	5	t)f(t)dt	t)f(t)dt	PROPN
ejpam-6583	279	6	.	.	PUNCT
ejpam-6583	279	7	suppose	suppose	VERB
ejpam-6583	279	8	there	there	PRON
ejpam-6583	279	9	exists	exist	VERB
ejpam-6583	279	10	λ	λ	PROPN
ejpam-6583	279	11	∈	∈	PROPN
ejpam-6583	279	12	(	(	PUNCT
ejpam-6583	279	13	0	0	NUM
ejpam-6583	279	14	,	,	PUNCT
ejpam-6583	279	15	1s	1s	NUM
ejpam-6583	279	16	)	)	PUNCT
ejpam-6583	279	17	such	such	ADJ
ejpam-6583	279	18	that	that	SCONJ
ejpam-6583	280	1	:	:	PUNCT
ejpam-6583	280	2	sup	sup	NOUN
ejpam-6583	280	3	x∈[0,1	x∈[0,1	X
ejpam-6583	280	4	]	]	X
ejpam-6583	281	1	1∫	1∫	NUM
ejpam-6583	281	2	0	0	NUM
ejpam-6583	281	3	|k(x	|k(x	NOUN
ejpam-6583	281	4	,	,	PUNCT
ejpam-6583	281	5	t)|dt	t)|dt	PROPN
ejpam-6583	281	6	≤	≤	PUNCT
ejpam-6583	281	7	λ	λ	PROPN
ejpam-6583	281	8	.	.	PROPN
ejpam-6583	281	9	for	for	ADP
ejpam-6583	281	10	any	any	DET
ejpam-6583	281	11	two	two	NUM
ejpam-6583	281	12	functions	function	NOUN
ejpam-6583	281	13	f	f	NOUN
ejpam-6583	281	14	,	,	PUNCT
ejpam-6583	281	15	g	g	PROPN
ejpam-6583	281	16	∈	∈	PROPN
ejpam-6583	281	17	c([0	c([0	NOUN
ejpam-6583	281	18	,	,	PUNCT
ejpam-6583	281	19	1],r	1],r	NUM
ejpam-6583	281	20	):	):	PUNCT
ejpam-6583	281	21	∥ff	∥ff	NUM
ejpam-6583	281	22	−	−	NOUN
ejpam-6583	281	23	fg∥2	fg∥2	ADJ
ejpam-6583	281	24	=	=	NOUN
ejpam-6583	281	25	sup	sup	NOUN
ejpam-6583	281	26	x∈[0,1	x∈[0,1	NOUN
ejpam-6583	281	27	]	]	PUNCT
ejpam-6583	281	28	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6583	281	29	1∫	1∫	NUM
ejpam-6583	281	30	0	0	NUM
ejpam-6583	281	31	k(x	k(x	PROPN
ejpam-6583	281	32	,	,	PUNCT
ejpam-6583	281	33	t)(f(t)−	t)(f(t)−	PRON
ejpam-6583	281	34	g(t))dt	g(t))dt	NOUN
ejpam-6583	281	35	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-6583	281	36	2	2	NUM
ejpam-6583	281	37	≤	≤	NUM
ejpam-6583	281	38	λ	λ	NOUN
ejpam-6583	281	39	sup	sup	NOUN
ejpam-6583	281	40	t∈[0,1	t∈[0,1	NUM
ejpam-6583	281	41	]	]	PUNCT
ejpam-6583	281	42	|f(t)−	|f(t)−	PROPN
ejpam-6583	281	43	g(t)|2	g(t)|2	PROPN
ejpam-6583	281	44	=	=	PRON
ejpam-6583	281	45	λ∥f	λ∥f	VERB
ejpam-6583	281	46	−	−	PROPN
ejpam-6583	281	47	g∥2	g∥2	NOUN
ejpam-6583	281	48	.	.	PUNCT
ejpam-6583	282	1	thus	thus	ADV
ejpam-6583	282	2	,	,	PUNCT
ejpam-6583	282	3	δb	δb	NOUN
ejpam-6583	282	4	r⊕d	r⊕d	NOUN
ejpam-6583	282	5	(	(	PUNCT
ejpam-6583	282	6	f	f	X
ejpam-6583	282	7	,	,	PUNCT
ejpam-6583	282	8	g	g	NOUN
ejpam-6583	282	9	)	)	PUNCT
ejpam-6583	282	10	is	be	AUX
ejpam-6583	282	11	a	a	DET
ejpam-6583	282	12	contraction	contraction	NOUN
ejpam-6583	282	13	with	with	ADP
ejpam-6583	282	14	λ	λ	PROPN
ejpam-6583	282	15	=	=	SYM
ejpam-6583	282	16	diag(λ	diag(λ	PROPN
ejpam-6583	282	17	,	,	PUNCT
ejpam-6583	282	18	λ	λ	PROPN
ejpam-6583	282	19	,	,	PUNCT
ejpam-6583	282	20	.	.	PUNCT
ejpam-6583	282	21	.	.	PUNCT
ejpam-6583	283	1	.	.	PUNCT
ejpam-6583	284	1	,	,	PUNCT
ejpam-6583	284	2	λ	λ	X
ejpam-6583	284	3	)	)	PUNCT
ejpam-6583	284	4	,	,	PUNCT
ejpam-6583	284	5	where	where	SCONJ
ejpam-6583	284	6	0	0	NUM
ejpam-6583	284	7	<	<	X
ejpam-6583	284	8	λ	λ	X
ejpam-6583	284	9	<	<	X
ejpam-6583	284	10	1	1	NUM
ejpam-6583	284	11	s	s	NOUN
ejpam-6583	284	12	and	and	CCONJ
ejpam-6583	284	13	δb	δb	NOUN
ejpam-6583	284	14	r⊕d	r⊕d	NOUN
ejpam-6583	284	15	(	(	PUNCT
ejpam-6583	284	16	ff	ff	NOUN
ejpam-6583	284	17	,	,	PUNCT
ejpam-6583	284	18	fg	fg	NOUN
ejpam-6583	284	19	)	)	PUNCT
ejpam-6583	284	20	≾	≾	NOUN
ejpam-6583	284	21	λδb	λδb	NOUN
ejpam-6583	284	22	r⊕d	r⊕d	NOUN
ejpam-6583	284	23	(	(	PUNCT
ejpam-6583	284	24	f	f	X
ejpam-6583	284	25	,	,	PUNCT
ejpam-6583	284	26	g	g	NOUN
ejpam-6583	284	27	)	)	PUNCT
ejpam-6583	284	28	.	.	PUNCT
ejpam-6583	285	1	by	by	ADP
ejpam-6583	285	2	theorem	theorem	NOUN
ejpam-6583	285	3	3	3	NUM
ejpam-6583	285	4	,	,	PUNCT
ejpam-6583	285	5	f	f	PROPN
ejpam-6583	285	6	has	have	VERB
ejpam-6583	285	7	a	a	DET
ejpam-6583	285	8	unique	unique	ADJ
ejpam-6583	285	9	fixed	fix	VERB
ejpam-6583	285	10	point	point	NOUN
ejpam-6583	285	11	,	,	PUNCT
ejpam-6583	285	12	meaning	mean	VERB
ejpam-6583	285	13	that	that	SCONJ
ejpam-6583	285	14	the	the	DET
ejpam-6583	285	15	integral	integral	ADJ
ejpam-6583	285	16	equation	equation	NOUN
ejpam-6583	285	17	has	have	VERB
ejpam-6583	285	18	a	a	DET
ejpam-6583	285	19	unique	unique	ADJ
ejpam-6583	285	20	solution	solution	NOUN
ejpam-6583	285	21	.	.	PUNCT
ejpam-6583	286	1	if	if	SCONJ
ejpam-6583	286	2	d	d	PROPN
ejpam-6583	286	3	=	=	SYM
ejpam-6583	286	4	1	1	NUM
ejpam-6583	286	5	and	and	CCONJ
ejpam-6583	286	6	s	s	X
ejpam-6583	286	7	=	=	SYM
ejpam-6583	286	8	1	1	NUM
ejpam-6583	286	9	,	,	PUNCT
ejpam-6583	286	10	then	then	ADV
ejpam-6583	286	11	the	the	DET
ejpam-6583	286	12	theorem	theorem	NOUN
ejpam-6583	286	13	3	3	NUM
ejpam-6583	286	14	can	can	AUX
ejpam-6583	286	15	be	be	AUX
ejpam-6583	286	16	reduced	reduce	VERB
ejpam-6583	286	17	to	to	ADP
ejpam-6583	286	18	the	the	DET
ejpam-6583	286	19	standard	standard	ADJ
ejpam-6583	286	20	banach	banach	NOUN
ejpam-6583	286	21	contraction	contraction	NOUN
ejpam-6583	286	22	principle	principle	NOUN
ejpam-6583	286	23	in	in	ADP
ejpam-6583	286	24	a	a	DET
ejpam-6583	286	25	metric	metric	ADJ
ejpam-6583	286	26	space	space	NOUN
ejpam-6583	286	27	.	.	PUNCT
ejpam-6583	287	1	corolary	corolary	ADJ
ejpam-6583	287	2	3	3	NUM
ejpam-6583	287	3	(	(	PUNCT
ejpam-6583	287	4	banach	banach	NOUN
ejpam-6583	287	5	contraction	contraction	NOUN
ejpam-6583	287	6	principle	principle	NOUN
ejpam-6583	287	7	,	,	PUNCT
ejpam-6583	287	8	[	[	X
ejpam-6583	287	9	5	5	NUM
ejpam-6583	287	10	]	]	PUNCT
ejpam-6583	287	11	)	)	PUNCT
ejpam-6583	287	12	.	.	PUNCT
ejpam-6583	287	13	suppose	suppose	VERB
ejpam-6583	287	14	that	that	SCONJ
ejpam-6583	287	15	(	(	PUNCT
ejpam-6583	287	16	x	x	X
ejpam-6583	287	17	,	,	PUNCT
ejpam-6583	287	18	d	d	X
ejpam-6583	287	19	)	)	PUNCT
ejpam-6583	287	20	is	be	AUX
ejpam-6583	287	21	a	a	DET
ejpam-6583	287	22	complete	complete	ADJ
ejpam-6583	287	23	metric	metric	ADJ
ejpam-6583	287	24	space	space	NOUN
ejpam-6583	287	25	and	and	CCONJ
ejpam-6583	287	26	f	f	NOUN
ejpam-6583	287	27	:	:	PUNCT
ejpam-6583	287	28	x	x	X
ejpam-6583	287	29	→	→	PUNCT
ejpam-6583	287	30	x	x	X
ejpam-6583	287	31	is	be	AUX
ejpam-6583	287	32	a	a	DET
ejpam-6583	287	33	contraction	contraction	NOUN
ejpam-6583	287	34	operator	operator	NOUN
ejpam-6583	287	35	with	with	ADP
ejpam-6583	287	36	lipschitz	lipschitz	NOUN
ejpam-6583	287	37	constant	constant	ADJ
ejpam-6583	287	38	λ	λ	NOUN
ejpam-6583	287	39	<	<	X
ejpam-6583	287	40	1	1	NUM
ejpam-6583	287	41	.	.	PUNCT
ejpam-6583	288	1	then	then	ADV
ejpam-6583	288	2	f	f	PROPN
ejpam-6583	288	3	has	have	VERB
ejpam-6583	288	4	a	a	DET
ejpam-6583	288	5	unique	unique	ADJ
ejpam-6583	288	6	fixed	fix	VERB
ejpam-6583	288	7	-	-	PUNCT
ejpam-6583	288	8	point	point	NOUN
ejpam-6583	288	9	z	z	NOUN
ejpam-6583	288	10	∈	∈	PROPN
ejpam-6583	288	11	x	x	X
ejpam-6583	288	12	.	.	PUNCT
ejpam-6583	289	1	theorem	theorem	ADJ
ejpam-6583	289	2	4	4	NUM
ejpam-6583	289	3	.	.	PUNCT
ejpam-6583	290	1	(	(	PUNCT
ejpam-6583	290	2	kannan	kannan	PROPN
ejpam-6583	290	3	type	type	NOUN
ejpam-6583	290	4	)	)	PUNCT
ejpam-6583	290	5	suppose	suppose	VERB
ejpam-6583	290	6	that	that	SCONJ
ejpam-6583	290	7	(	(	PUNCT
ejpam-6583	290	8	x	x	X
ejpam-6583	290	9	,	,	PUNCT
ejpam-6583	290	10	r⊕d	r⊕d	NOUN
ejpam-6583	290	11	,	,	PUNCT
ejpam-6583	290	12	δb	δb	NOUN
ejpam-6583	290	13	r⊕d	r⊕d	NOUN
ejpam-6583	290	14	)	)	PUNCT
ejpam-6583	290	15	is	be	AUX
ejpam-6583	290	16	a	a	DET
ejpam-6583	290	17	complete	complete	ADJ
ejpam-6583	290	18	generalized	generalized	ADJ
ejpam-6583	290	19	bmetric	bmetric	ADJ
ejpam-6583	290	20	space	space	NOUN
ejpam-6583	290	21	endowed	endow	VERB
ejpam-6583	290	22	with	with	ADP
ejpam-6583	290	23	the	the	DET
ejpam-6583	290	24	orthogonal	orthogonal	ADJ
ejpam-6583	290	25	direct	direct	ADJ
ejpam-6583	290	26	sum	sum	NOUN
ejpam-6583	290	27	and	and	CCONJ
ejpam-6583	290	28	f	f	NOUN
ejpam-6583	290	29	:	:	PUNCT
ejpam-6583	290	30	x	x	X
ejpam-6583	290	31	→	→	PUNCT
ejpam-6583	290	32	x	x	X
ejpam-6583	290	33	is	be	AUX
ejpam-6583	290	34	an	an	DET
ejpam-6583	290	35	operator	operator	NOUN
ejpam-6583	290	36	satisfying	satisfy	VERB
ejpam-6583	290	37	the	the	DET
ejpam-6583	290	38	following	follow	VERB
ejpam-6583	290	39	condition	condition	NOUN
ejpam-6583	290	40	δb	δb	ADP
ejpam-6583	290	41	r⊕d	r⊕d	NOUN
ejpam-6583	290	42	(	(	PUNCT
ejpam-6583	290	43	f	f	PROPN
ejpam-6583	290	44	(	(	PUNCT
ejpam-6583	290	45	x),f	x),f	PROPN
ejpam-6583	290	46	(	(	PUNCT
ejpam-6583	290	47	y	y	NOUN
ejpam-6583	290	48	)	)	PUNCT
ejpam-6583	290	49	)	)	PUNCT
ejpam-6583	291	1	≾	≾	NOUN
ejpam-6583	291	2	diag	diag	NOUN
ejpam-6583	291	3	(	(	PUNCT
ejpam-6583	291	4	α1	α1	PROPN
ejpam-6583	291	5	,	,	PUNCT
ejpam-6583	291	6	α2	α2	ADJ
ejpam-6583	291	7	,	,	PUNCT
ejpam-6583	291	8	·	·	PUNCT
ejpam-6583	291	9	·	·	PUNCT
ejpam-6583	291	10	·	·	PUNCT
ejpam-6583	291	11	,	,	PUNCT
ejpam-6583	291	12	αd	αd	PROPN
ejpam-6583	291	13	)	)	PUNCT
ejpam-6583	292	1	[	[	X
ejpam-6583	292	2	δb	δb	X
ejpam-6583	292	3	r⊕d	r⊕d	NOUN
ejpam-6583	292	4	(	(	PUNCT
ejpam-6583	292	5	x	x	X
ejpam-6583	292	6	,	,	PUNCT
ejpam-6583	292	7	f	f	PROPN
ejpam-6583	292	8	(	(	PUNCT
ejpam-6583	292	9	x	x	NOUN
ejpam-6583	292	10	)	)	PUNCT
ejpam-6583	292	11	)	)	PUNCT
ejpam-6583	293	1	+	+	CCONJ
ejpam-6583	293	2	δb	δb	NOUN
ejpam-6583	293	3	r⊕d	r⊕d	NOUN
ejpam-6583	293	4	(	(	PUNCT
ejpam-6583	293	5	y	y	PROPN
ejpam-6583	293	6	,	,	PUNCT
ejpam-6583	293	7	f	f	PROPN
ejpam-6583	293	8	(	(	PUNCT
ejpam-6583	293	9	y	y	NOUN
ejpam-6583	293	10	)	)	PUNCT
ejpam-6583	293	11	)	)	PUNCT
ejpam-6583	294	1	]	]	PUNCT
ejpam-6583	294	2	,	,	PUNCT
ejpam-6583	294	3	(	(	PUNCT
ejpam-6583	294	4	1	1	X
ejpam-6583	294	5	)	)	PUNCT
ejpam-6583	294	6	where	where	SCONJ
ejpam-6583	294	7	αi	αi	ADV
ejpam-6583	294	8	∈	∈	PROPN
ejpam-6583	294	9	(	(	PUNCT
ejpam-6583	294	10	0	0	NUM
ejpam-6583	294	11	,	,	PUNCT
ejpam-6583	294	12	12	12	NUM
ejpam-6583	294	13	)	)	PUNCT
ejpam-6583	294	14	for	for	ADP
ejpam-6583	294	15	all	all	DET
ejpam-6583	294	16	i	i	PRON
ejpam-6583	294	17	=	=	NOUN
ejpam-6583	294	18	1	1	NUM
ejpam-6583	294	19	,	,	PUNCT
ejpam-6583	294	20	2	2	NUM
ejpam-6583	294	21	,	,	PUNCT
ejpam-6583	294	22	·	·	PUNCT
ejpam-6583	294	23	·	·	PUNCT
ejpam-6583	294	24	·	·	PUNCT
ejpam-6583	294	25	,	,	PUNCT
ejpam-6583	294	26	d.	d.	PROPN
ejpam-6583	294	27	then	then	ADV
ejpam-6583	294	28	,	,	PUNCT
ejpam-6583	294	29	f	f	PROPN
ejpam-6583	294	30	has	have	VERB
ejpam-6583	294	31	a	a	DET
ejpam-6583	294	32	unique	unique	ADJ
ejpam-6583	294	33	fixed	fix	VERB
ejpam-6583	294	34	-	-	PUNCT
ejpam-6583	294	35	point	point	NOUN
ejpam-6583	294	36	in	in	ADP
ejpam-6583	294	37	x	x	PROPN
ejpam-6583	294	38	.	.	PUNCT
ejpam-6583	295	1	g.	g.	PROPN
ejpam-6583	295	2	albeladi	albeladi	PROPN
ejpam-6583	295	3	,	,	PUNCT
ejpam-6583	295	4	s.	s.	PROPN
ejpam-6583	295	5	omran	omran	PROPN
ejpam-6583	295	6	/	/	SYM
ejpam-6583	295	7	eur	eur	PROPN
ejpam-6583	295	8	.	.	PUNCT
ejpam-6583	296	1	j.	j.	PROPN
ejpam-6583	296	2	pure	pure	PROPN
ejpam-6583	296	3	appl	appl	PROPN
ejpam-6583	296	4	.	.	PROPN
ejpam-6583	296	5	math	math	PROPN
ejpam-6583	296	6	,	,	PUNCT
ejpam-6583	296	7	18	18	NUM
ejpam-6583	296	8	(	(	PUNCT
ejpam-6583	296	9	3	3	NUM
ejpam-6583	296	10	)	)	PUNCT
ejpam-6583	296	11	(	(	PUNCT
ejpam-6583	296	12	2025	2025	NUM
ejpam-6583	296	13	)	)	PUNCT
ejpam-6583	296	14	,	,	PUNCT
ejpam-6583	296	15	6583	6583	NUM
ejpam-6583	296	16	13	13	NUM
ejpam-6583	296	17	of	of	ADP
ejpam-6583	296	18	27	27	NUM
ejpam-6583	296	19	proof	proof	NOUN
ejpam-6583	296	20	.	.	PUNCT
ejpam-6583	297	1	let	let	VERB
ejpam-6583	297	2	x0	x0	PROPN
ejpam-6583	297	3	be	be	AUX
ejpam-6583	297	4	any	any	DET
ejpam-6583	297	5	point	point	NOUN
ejpam-6583	297	6	in	in	ADP
ejpam-6583	297	7	x	x	SYM
ejpam-6583	297	8	,	,	PUNCT
ejpam-6583	297	9	that	that	ADV
ejpam-6583	297	10	is	is	ADV
ejpam-6583	297	11	x0	x0	PROPN
ejpam-6583	297	12	∈	∈	PROPN
ejpam-6583	298	1	x	x	X
ejpam-6583	298	2	.	.	PUNCT
ejpam-6583	299	1	let	let	VERB
ejpam-6583	299	2	us	we	PRON
ejpam-6583	299	3	define	define	VERB
ejpam-6583	299	4	a	a	DET
ejpam-6583	299	5	sequence	sequence	NOUN
ejpam-6583	299	6	{	{	PUNCT
ejpam-6583	299	7	xn	xn	NOUN
ejpam-6583	299	8	}	}	PUNCT
ejpam-6583	299	9	in	in	ADP
ejpam-6583	299	10	x	x	PUNCT
ejpam-6583	299	11	as	as	SCONJ
ejpam-6583	299	12	given	give	VERB
ejpam-6583	299	13	below	below	ADV
ejpam-6583	299	14	.	.	PUNCT
ejpam-6583	300	1	xn+1	xn+1	PUNCT
ejpam-6583	301	1	=	=	SYM
ejpam-6583	301	2	f	f	PROPN
ejpam-6583	301	3	(	(	PUNCT
ejpam-6583	301	4	xn	xn	PROPN
ejpam-6583	301	5	)	)	PUNCT
ejpam-6583	301	6	=	=	SYM
ejpam-6583	301	7	fn+1(x0	fn+1(x0	ADJ
ejpam-6583	301	8	)	)	PUNCT
ejpam-6583	301	9	∀	∀	X
ejpam-6583	301	10	n	n	PRON
ejpam-6583	301	11	≥	≥	NOUN
ejpam-6583	301	12	0	0	NUM
ejpam-6583	301	13	.	.	PUNCT
ejpam-6583	302	1	we	we	PRON
ejpam-6583	302	2	have	have	VERB
ejpam-6583	302	3	δb	δb	NOUN
ejpam-6583	302	4	r⊕d	r⊕d	NOUN
ejpam-6583	302	5	(	(	PUNCT
ejpam-6583	302	6	xn	xn	PROPN
ejpam-6583	302	7	,	,	PUNCT
ejpam-6583	302	8	xn+1	xn+1	NUM
ejpam-6583	302	9	)	)	PUNCT
ejpam-6583	302	10	=	=	PUNCT
ejpam-6583	302	11	δb	δb	X
ejpam-6583	302	12	r⊕d	r⊕d	NOUN
ejpam-6583	302	13	(	(	PUNCT
ejpam-6583	302	14	f	f	PROPN
ejpam-6583	302	15	(	(	PUNCT
ejpam-6583	302	16	xn−1),f	xn−1),f	PROPN
ejpam-6583	302	17	(	(	PUNCT
ejpam-6583	302	18	xn	xn	NOUN
ejpam-6583	302	19	)	)	PUNCT
ejpam-6583	302	20	)	)	PUNCT
ejpam-6583	303	1	≾	≾	NOUN
ejpam-6583	303	2	diag	diag	NOUN
ejpam-6583	303	3	(	(	PUNCT
ejpam-6583	303	4	α1	α1	PROPN
ejpam-6583	303	5	,	,	PUNCT
ejpam-6583	303	6	α2	α2	ADJ
ejpam-6583	303	7	,	,	PUNCT
ejpam-6583	303	8	·	·	PUNCT
ejpam-6583	303	9	·	·	PUNCT
ejpam-6583	303	10	·	·	PUNCT
ejpam-6583	303	11	,	,	PUNCT
ejpam-6583	303	12	αd	αd	PROPN
ejpam-6583	303	13	)	)	PUNCT
ejpam-6583	303	14	[	[	PUNCT
ejpam-6583	303	15	δb	δb	NOUN
ejpam-6583	303	16	r⊕d	r⊕d	NOUN
ejpam-6583	303	17	(	(	PUNCT
ejpam-6583	303	18	xn−1,f	xn−1,f	X
ejpam-6583	303	19	(	(	PUNCT
ejpam-6583	303	20	xn−1	xn−1	PROPN
ejpam-6583	303	21	)	)	PUNCT
ejpam-6583	303	22	)	)	PUNCT
ejpam-6583	304	1	+	+	CCONJ
ejpam-6583	304	2	δb	δb	NOUN
ejpam-6583	304	3	r⊕d	r⊕d	NOUN
ejpam-6583	304	4	(	(	PUNCT
ejpam-6583	304	5	xn	xn	PROPN
ejpam-6583	304	6	,	,	PUNCT
ejpam-6583	304	7	f	f	PROPN
ejpam-6583	304	8	(	(	PUNCT
ejpam-6583	304	9	xn	xn	PROPN
ejpam-6583	304	10	)	)	PUNCT
ejpam-6583	304	11	)	)	PUNCT
ejpam-6583	304	12	]	]	PUNCT
ejpam-6583	305	1	=	=	PUNCT
ejpam-6583	305	2	diag	diag	PROPN
ejpam-6583	305	3	(	(	PUNCT
ejpam-6583	305	4	α1	α1	PROPN
ejpam-6583	305	5	,	,	PUNCT
ejpam-6583	305	6	α2	α2	ADJ
ejpam-6583	305	7	,	,	PUNCT
ejpam-6583	305	8	·	·	PUNCT
ejpam-6583	305	9	·	·	PUNCT
ejpam-6583	305	10	·	·	PUNCT
ejpam-6583	305	11	,	,	PUNCT
ejpam-6583	305	12	αd	αd	PROPN
ejpam-6583	305	13	)	)	PUNCT
ejpam-6583	305	14	δb	δb	NOUN
ejpam-6583	305	15	r⊕d	r⊕d	NOUN
ejpam-6583	305	16	(	(	PUNCT
ejpam-6583	305	17	xn−1	xn−1	PROPN
ejpam-6583	305	18	,	,	PUNCT
ejpam-6583	305	19	xn	xn	PUNCT
ejpam-6583	305	20	)	)	PUNCT
ejpam-6583	306	1	+	+	NOUN
ejpam-6583	306	2	diag	diag	NOUN
ejpam-6583	306	3	(	(	PUNCT
ejpam-6583	306	4	α1	α1	PROPN
ejpam-6583	306	5	,	,	PUNCT
ejpam-6583	306	6	α2	α2	ADJ
ejpam-6583	306	7	,	,	PUNCT
ejpam-6583	306	8	·	·	PUNCT
ejpam-6583	306	9	·	·	PUNCT
ejpam-6583	306	10	·	·	PUNCT
ejpam-6583	306	11	,	,	PUNCT
ejpam-6583	306	12	αd	αd	PROPN
ejpam-6583	306	13	)	)	PUNCT
ejpam-6583	306	14	δb	δb	NOUN
ejpam-6583	306	15	r⊕d	r⊕d	NOUN
ejpam-6583	306	16	(	(	PUNCT
ejpam-6583	306	17	xn	xn	PROPN
ejpam-6583	306	18	,	,	PUNCT
ejpam-6583	306	19	xn+1	xn+1	NUM
ejpam-6583	306	20	)	)	PUNCT
ejpam-6583	306	21	,	,	PUNCT
ejpam-6583	306	22	and	and	CCONJ
ejpam-6583	306	23	diag	diag	NOUN
ejpam-6583	306	24	(	(	PUNCT
ejpam-6583	306	25	(	(	PUNCT
ejpam-6583	306	26	1−	1−	NUM
ejpam-6583	306	27	α1	α1	PROPN
ejpam-6583	306	28	)	)	PUNCT
ejpam-6583	306	29	,	,	PUNCT
ejpam-6583	306	30	(	(	PUNCT
ejpam-6583	306	31	1−	1−	NUM
ejpam-6583	306	32	α2	α2	ADJ
ejpam-6583	306	33	)	)	PUNCT
ejpam-6583	306	34	,	,	PUNCT
ejpam-6583	306	35	·	·	PUNCT
ejpam-6583	306	36	·	·	PUNCT
ejpam-6583	306	37	·	·	PUNCT
ejpam-6583	306	38	,	,	PUNCT
ejpam-6583	306	39	(	(	PUNCT
ejpam-6583	306	40	1−	1−	NUM
ejpam-6583	306	41	αd	αd	PROPN
ejpam-6583	306	42	)	)	PUNCT
ejpam-6583	306	43	)	)	PUNCT
ejpam-6583	306	44	δb	δb	NOUN
ejpam-6583	306	45	r⊕d	r⊕d	NOUN
ejpam-6583	306	46	(	(	PUNCT
ejpam-6583	306	47	xn	xn	PROPN
ejpam-6583	306	48	,	,	PUNCT
ejpam-6583	306	49	xn+1	xn+1	X
ejpam-6583	306	50	)	)	PUNCT
ejpam-6583	306	51	≾	≾	NOUN
ejpam-6583	306	52	diag	diag	NOUN
ejpam-6583	306	53	(	(	PUNCT
ejpam-6583	306	54	α1	α1	PROPN
ejpam-6583	306	55	,	,	PUNCT
ejpam-6583	306	56	α2	α2	ADJ
ejpam-6583	306	57	,	,	PUNCT
ejpam-6583	306	58	·	·	PUNCT
ejpam-6583	306	59	·	·	PUNCT
ejpam-6583	306	60	·	·	PUNCT
ejpam-6583	306	61	,	,	PUNCT
ejpam-6583	306	62	·	·	PUNCT
ejpam-6583	306	63	·	·	PUNCT
ejpam-6583	306	64	·	·	PUNCT
ejpam-6583	306	65	αd	αd	X
ejpam-6583	306	66	)	)	PUNCT
ejpam-6583	306	67	δb	δb	NOUN
ejpam-6583	306	68	r⊕d	r⊕d	NOUN
ejpam-6583	306	69	(	(	PUNCT
ejpam-6583	306	70	xn−1	xn−1	PROPN
ejpam-6583	306	71	,	,	PUNCT
ejpam-6583	306	72	xn	xn	PROPN
ejpam-6583	306	73	)	)	PUNCT
ejpam-6583	306	74	,	,	PUNCT
ejpam-6583	306	75	since	since	SCONJ
ejpam-6583	306	76	the	the	DET
ejpam-6583	306	77	inverse	inverse	NOUN
ejpam-6583	306	78	of	of	ADP
ejpam-6583	306	79	the	the	DET
ejpam-6583	306	80	diagonal	diagonal	ADJ
ejpam-6583	306	81	matrix	matrix	NOUN
ejpam-6583	306	82	is	be	AUX
ejpam-6583	306	83	diag	diag	NOUN
ejpam-6583	306	84	(	(	PUNCT
ejpam-6583	306	85	(	(	PUNCT
ejpam-6583	306	86	1−	1−	NUM
ejpam-6583	306	87	α1	α1	PROPN
ejpam-6583	306	88	)	)	PUNCT
ejpam-6583	306	89	−1	−1	NOUN
ejpam-6583	306	90	,	,	PUNCT
ejpam-6583	306	91	(	(	PUNCT
ejpam-6583	306	92	1−	1−	NUM
ejpam-6583	306	93	α2	α2	ADJ
ejpam-6583	306	94	)	)	PUNCT
ejpam-6583	306	95	−1	−1	NOUN
ejpam-6583	306	96	,	,	PUNCT
ejpam-6583	306	97	·	·	PUNCT
ejpam-6583	306	98	·	·	PUNCT
ejpam-6583	306	99	·	·	PUNCT
ejpam-6583	306	100	,	,	PUNCT
ejpam-6583	306	101	(	(	PUNCT
ejpam-6583	306	102	1−	1−	NUM
ejpam-6583	306	103	αd	αd	PROPN
ejpam-6583	306	104	)	)	PUNCT
ejpam-6583	306	105	−1	−1	NOUN
ejpam-6583	306	106	)	)	PUNCT
ejpam-6583	306	107	.	.	PUNCT
ejpam-6583	307	1	thus	thus	ADV
ejpam-6583	307	2	,	,	PUNCT
ejpam-6583	307	3	δb	δb	NOUN
ejpam-6583	307	4	r⊕d	r⊕d	NOUN
ejpam-6583	307	5	(	(	PUNCT
ejpam-6583	307	6	xn	xn	PROPN
ejpam-6583	307	7	,	,	PUNCT
ejpam-6583	307	8	xn+1	xn+1	X
ejpam-6583	307	9	)	)	PUNCT
ejpam-6583	307	10	≾	≾	NOUN
ejpam-6583	307	11	diag	diag	NOUN
ejpam-6583	307	12	(	(	PUNCT
ejpam-6583	307	13	α1	α1	PROPN
ejpam-6583	307	14	(	(	PUNCT
ejpam-6583	307	15	1−	1−	NUM
ejpam-6583	307	16	α1	α1	PROPN
ejpam-6583	307	17	)	)	PUNCT
ejpam-6583	307	18	,	,	PUNCT
ejpam-6583	307	19	·	·	PUNCT
ejpam-6583	307	20	·	·	PUNCT
ejpam-6583	307	21	·	·	PUNCT
ejpam-6583	307	22	·	·	PUNCT
ejpam-6583	307	23	·	·	PUNCT
ejpam-6583	307	24	·	·	PUNCT
ejpam-6583	307	25	,	,	PUNCT
ejpam-6583	307	26	αd	αd	PROPN
ejpam-6583	307	27	(	(	PUNCT
ejpam-6583	307	28	1−	1−	NUM
ejpam-6583	307	29	αd	αd	PROPN
ejpam-6583	307	30	)	)	PUNCT
ejpam-6583	307	31	)	)	PUNCT
ejpam-6583	307	32	δb	δb	NOUN
ejpam-6583	307	33	r⊕d	r⊕d	NOUN
ejpam-6583	307	34	(	(	PUNCT
ejpam-6583	307	35	xn−1	xn−1	PROPN
ejpam-6583	307	36	,	,	PUNCT
ejpam-6583	307	37	xn	xn	X
ejpam-6583	307	38	)	)	PUNCT
ejpam-6583	308	1	≾	≾	NOUN
ejpam-6583	308	2	diag	diag	NOUN
ejpam-6583	308	3	(	(	PUNCT
ejpam-6583	308	4	(	(	PUNCT
ejpam-6583	308	5	α1	α1	PROPN
ejpam-6583	308	6	(	(	PUNCT
ejpam-6583	308	7	1−	1−	NUM
ejpam-6583	308	8	α1	α1	PROPN
ejpam-6583	308	9	)	)	PUNCT
ejpam-6583	308	10	)	)	PUNCT
ejpam-6583	308	11	2	2	NUM
ejpam-6583	308	12	,	,	PUNCT
ejpam-6583	308	13	·	·	PUNCT
ejpam-6583	308	14	·	·	PUNCT
ejpam-6583	308	15	·	·	PUNCT
ejpam-6583	308	16	·	·	PUNCT
ejpam-6583	308	17	·	·	PUNCT
ejpam-6583	308	18	·	·	PUNCT
ejpam-6583	308	19	,	,	PUNCT
ejpam-6583	308	20	(	(	PUNCT
ejpam-6583	308	21	αd	αd	PROPN
ejpam-6583	308	22	(	(	PUNCT
ejpam-6583	308	23	1−	1−	NUM
ejpam-6583	308	24	αd	αd	PROPN
ejpam-6583	308	25	)	)	PUNCT
ejpam-6583	308	26	)	)	PUNCT
ejpam-6583	308	27	2	2	X
ejpam-6583	308	28	)	)	PUNCT
ejpam-6583	308	29	δb	δb	NOUN
ejpam-6583	308	30	r⊕d	r⊕d	NOUN
ejpam-6583	308	31	(	(	PUNCT
ejpam-6583	308	32	xn−2	xn−2	PROPN
ejpam-6583	308	33	,	,	PUNCT
ejpam-6583	308	34	xn−1	xn−1	PROPN
ejpam-6583	308	35	)	)	PUNCT
ejpam-6583	308	36	≾	≾	NOUN
ejpam-6583	308	37	diag	diag	NOUN
ejpam-6583	308	38	(	(	PUNCT
ejpam-6583	308	39	(	(	PUNCT
ejpam-6583	308	40	α1	α1	PROPN
ejpam-6583	308	41	(	(	PUNCT
ejpam-6583	308	42	1−	1−	NUM
ejpam-6583	308	43	α1	α1	PROPN
ejpam-6583	308	44	)	)	PUNCT
ejpam-6583	308	45	)	)	PUNCT
ejpam-6583	308	46	3	3	NUM
ejpam-6583	308	47	,	,	PUNCT
ejpam-6583	308	48	·	·	PUNCT
ejpam-6583	308	49	·	·	PUNCT
ejpam-6583	308	50	·	·	PUNCT
ejpam-6583	308	51	,	,	PUNCT
ejpam-6583	308	52	(	(	PUNCT
ejpam-6583	308	53	αd	αd	PROPN
ejpam-6583	308	54	(	(	PUNCT
ejpam-6583	308	55	1−	1−	NUM
ejpam-6583	308	56	αd	αd	PROPN
ejpam-6583	308	57	)	)	PUNCT
ejpam-6583	308	58	)	)	PUNCT
ejpam-6583	308	59	3	3	X
ejpam-6583	308	60	)	)	PUNCT
ejpam-6583	308	61	δb	δb	NOUN
ejpam-6583	308	62	r⊕d	r⊕d	NOUN
ejpam-6583	308	63	(	(	PUNCT
ejpam-6583	308	64	xn−3	xn−3	PROPN
ejpam-6583	308	65	,	,	PUNCT
ejpam-6583	308	66	xn−2	xn−2	PROPN
ejpam-6583	308	67	)	)	PUNCT
ejpam-6583	308	68	...	...	PUNCT
ejpam-6583	309	1	≾	≾	NOUN
ejpam-6583	309	2	diag	diag	NOUN
ejpam-6583	309	3	(	(	PUNCT
ejpam-6583	309	4	(	(	PUNCT
ejpam-6583	309	5	α1	α1	PROPN
ejpam-6583	309	6	(	(	PUNCT
ejpam-6583	309	7	1−	1−	NUM
ejpam-6583	309	8	α1	α1	PROPN
ejpam-6583	309	9	)	)	PUNCT
ejpam-6583	309	10	)	)	PUNCT
ejpam-6583	309	11	n	n	X
ejpam-6583	309	12	,	,	PUNCT
ejpam-6583	309	13	·	·	PUNCT
ejpam-6583	309	14	·	·	PUNCT
ejpam-6583	309	15	·	·	PUNCT
ejpam-6583	309	16	·	·	PUNCT
ejpam-6583	309	17	·	·	PUNCT
ejpam-6583	309	18	·	·	PUNCT
ejpam-6583	309	19	,	,	PUNCT
ejpam-6583	309	20	(	(	PUNCT
ejpam-6583	309	21	αd	αd	PROPN
ejpam-6583	309	22	(	(	PUNCT
ejpam-6583	309	23	1−	1−	NUM
ejpam-6583	309	24	αd	αd	PROPN
ejpam-6583	309	25	)	)	PUNCT
ejpam-6583	309	26	)	)	PUNCT
ejpam-6583	309	27	n	n	CCONJ
ejpam-6583	309	28	)	)	PUNCT
ejpam-6583	309	29	δb	δb	NOUN
ejpam-6583	309	30	r⊕d	r⊕d	NOUN
ejpam-6583	309	31	(	(	PUNCT
ejpam-6583	309	32	x0	x0	PROPN
ejpam-6583	309	33	,	,	PUNCT
ejpam-6583	309	34	x1	x1	PROPN
ejpam-6583	309	35	)	)	PUNCT
ejpam-6583	309	36	,	,	PUNCT
ejpam-6583	309	37	if	if	SCONJ
ejpam-6583	309	38	we	we	PRON
ejpam-6583	309	39	let	let	VERB
ejpam-6583	309	40	βi	βi	NOUN
ejpam-6583	309	41	=	=	PUNCT
ejpam-6583	309	42	αi	αi	NOUN
ejpam-6583	309	43	1−	1−	NUM
ejpam-6583	309	44	αi	αi	ADV
ejpam-6583	309	45	,	,	PUNCT
ejpam-6583	309	46	then	then	ADV
ejpam-6583	309	47	δb	δb	NOUN
ejpam-6583	309	48	r⊕d	r⊕d	NOUN
ejpam-6583	309	49	(	(	PUNCT
ejpam-6583	309	50	xn	xn	PROPN
ejpam-6583	309	51	,	,	PUNCT
ejpam-6583	309	52	xn+1	xn+1	X
ejpam-6583	309	53	)	)	PUNCT
ejpam-6583	309	54	≾	≾	NOUN
ejpam-6583	309	55	diag	diag	NOUN
ejpam-6583	309	56	(	(	PUNCT
ejpam-6583	309	57	βn1	βn1	INTJ
ejpam-6583	309	58	,	,	PUNCT
ejpam-6583	309	59	βn2	βn2	PROPN
ejpam-6583	309	60	,	,	PUNCT
ejpam-6583	309	61	·	·	PUNCT
ejpam-6583	309	62	·	·	PUNCT
ejpam-6583	309	63	·	·	PUNCT
ejpam-6583	309	64	,	,	PUNCT
ejpam-6583	309	65	βnd	βnd	PROPN
ejpam-6583	309	66	)	)	PUNCT
ejpam-6583	309	67	δb	δb	NOUN
ejpam-6583	309	68	r⊕d	r⊕d	NOUN
ejpam-6583	309	69	(	(	PUNCT
ejpam-6583	309	70	x0	x0	PROPN
ejpam-6583	309	71	,	,	PUNCT
ejpam-6583	309	72	x1	x1	PROPN
ejpam-6583	309	73	)	)	PUNCT
ejpam-6583	309	74	.	.	PUNCT
ejpam-6583	310	1	let	let	VERB
ejpam-6583	310	2	us	we	PRON
ejpam-6583	310	3	prove	prove	VERB
ejpam-6583	310	4	that	that	SCONJ
ejpam-6583	310	5	{	{	PUNCT
ejpam-6583	310	6	xn	xn	X
ejpam-6583	310	7	}	}	PUNCT
ejpam-6583	310	8	is	be	AUX
ejpam-6583	310	9	a	a	DET
ejpam-6583	310	10	cauchy	cauchy	ADJ
ejpam-6583	310	11	sequence	sequence	NOUN
ejpam-6583	310	12	.	.	PUNCT
ejpam-6583	311	1	suppose	suppose	VERB
ejpam-6583	311	2	that	that	SCONJ
ejpam-6583	311	3	n	n	PROPN
ejpam-6583	311	4	>	>	X
ejpam-6583	311	5	m	m	PROPN
ejpam-6583	311	6	,	,	PUNCT
ejpam-6583	311	7	then	then	ADV
ejpam-6583	311	8	from	from	ADP
ejpam-6583	311	9	(	(	PUNCT
ejpam-6583	311	10	1	1	NUM
ejpam-6583	311	11	)	)	PUNCT
ejpam-6583	311	12	and	and	CCONJ
ejpam-6583	311	13	the	the	DET
ejpam-6583	311	14	triangle	triangle	NOUN
ejpam-6583	311	15	inequality	inequality	NOUN
ejpam-6583	311	16	property	property	NOUN
ejpam-6583	311	17	,	,	PUNCT
ejpam-6583	311	18	we	we	PRON
ejpam-6583	311	19	can	can	AUX
ejpam-6583	311	20	write	write	VERB
ejpam-6583	311	21	as	as	ADP
ejpam-6583	311	22	:	:	PUNCT
ejpam-6583	311	23	δb	δb	NOUN
ejpam-6583	311	24	r⊕d	r⊕d	NOUN
ejpam-6583	311	25	(	(	PUNCT
ejpam-6583	311	26	xm	xm	PROPN
ejpam-6583	311	27	,	,	PUNCT
ejpam-6583	311	28	xn	xn	PROPN
ejpam-6583	311	29	)	)	PUNCT
ejpam-6583	312	1	≾	≾	PROPN
ejpam-6583	312	2	s	s	PART
ejpam-6583	312	3	[	[	PUNCT
ejpam-6583	312	4	δb	δb	NOUN
ejpam-6583	312	5	r⊕d	r⊕d	NOUN
ejpam-6583	312	6	(	(	PUNCT
ejpam-6583	312	7	xm	xm	PROPN
ejpam-6583	312	8	,	,	PUNCT
ejpam-6583	312	9	xm+1	xm+1	PROPN
ejpam-6583	312	10	)	)	PUNCT
ejpam-6583	312	11	+	+	CCONJ
ejpam-6583	312	12	δb	δb	NOUN
ejpam-6583	312	13	r⊕d	r⊕d	NOUN
ejpam-6583	312	14	(	(	PUNCT
ejpam-6583	312	15	xm+1	xm+1	PROPN
ejpam-6583	312	16	,	,	PUNCT
ejpam-6583	312	17	xn	xn	PROPN
ejpam-6583	312	18	)	)	PUNCT
ejpam-6583	312	19	]	]	PUNCT
ejpam-6583	313	1	≾	≾	NOUN
ejpam-6583	313	2	sδb	sδb	VERB
ejpam-6583	313	3	r⊕d	r⊕d	NOUN
ejpam-6583	313	4	(	(	PUNCT
ejpam-6583	313	5	xm	xm	PROPN
ejpam-6583	313	6	,	,	PUNCT
ejpam-6583	313	7	xm+1	xm+1	PROPN
ejpam-6583	313	8	)	)	PUNCT
ejpam-6583	313	9	+	+	CCONJ
ejpam-6583	313	10	s2	s2	NOUN
ejpam-6583	313	11	[	[	PUNCT
ejpam-6583	313	12	δb	δb	NOUN
ejpam-6583	313	13	r⊕d	r⊕d	NOUN
ejpam-6583	313	14	(	(	PUNCT
ejpam-6583	313	15	xm+1	xm+1	PROPN
ejpam-6583	313	16	,	,	PUNCT
ejpam-6583	313	17	xm+2	xm+2	PROPN
ejpam-6583	313	18	)	)	PUNCT
ejpam-6583	313	19	+	+	CCONJ
ejpam-6583	313	20	δb	δb	NOUN
ejpam-6583	313	21	r⊕d	r⊕d	NOUN
ejpam-6583	313	22	(	(	PUNCT
ejpam-6583	313	23	xm+2	xm+2	PROPN
ejpam-6583	313	24	,	,	PUNCT
ejpam-6583	313	25	xn	xn	PROPN
ejpam-6583	313	26	)	)	PUNCT
ejpam-6583	313	27	]	]	PUNCT
ejpam-6583	313	28	g.	g.	PROPN
ejpam-6583	313	29	albeladi	albeladi	PROPN
ejpam-6583	313	30	,	,	PUNCT
ejpam-6583	313	31	s.	s.	PROPN
ejpam-6583	313	32	omran	omran	PROPN
ejpam-6583	313	33	/	/	SYM
ejpam-6583	313	34	eur	eur	PROPN
ejpam-6583	313	35	.	.	PUNCT
ejpam-6583	314	1	j.	j.	PROPN
ejpam-6583	314	2	pure	pure	PROPN
ejpam-6583	314	3	appl	appl	PROPN
ejpam-6583	314	4	.	.	PROPN
ejpam-6583	314	5	math	math	PROPN
ejpam-6583	314	6	,	,	PUNCT
ejpam-6583	314	7	18	18	NUM
ejpam-6583	314	8	(	(	PUNCT
ejpam-6583	314	9	3	3	NUM
ejpam-6583	314	10	)	)	PUNCT
ejpam-6583	314	11	(	(	PUNCT
ejpam-6583	314	12	2025	2025	NUM
ejpam-6583	314	13	)	)	PUNCT
ejpam-6583	314	14	,	,	PUNCT
ejpam-6583	314	15	6583	6583	NUM
ejpam-6583	314	16	14	14	NUM
ejpam-6583	314	17	of	of	ADP
ejpam-6583	314	18	27	27	NUM
ejpam-6583	314	19	≾	≾	PROPN
ejpam-6583	314	20	s	s	PART
ejpam-6583	314	21	δb	δb	NOUN
ejpam-6583	314	22	r⊕d	r⊕d	NOUN
ejpam-6583	314	23	(	(	PUNCT
ejpam-6583	314	24	xm	xm	PROPN
ejpam-6583	314	25	,	,	PUNCT
ejpam-6583	314	26	xm+1	xm+1	PROPN
ejpam-6583	314	27	)	)	PUNCT
ejpam-6583	314	28	+	+	CCONJ
ejpam-6583	314	29	s2	s2	NOUN
ejpam-6583	314	30	δb	δb	NOUN
ejpam-6583	314	31	r⊕d	r⊕d	NOUN
ejpam-6583	314	32	(	(	PUNCT
ejpam-6583	314	33	xm+1	xm+1	PROPN
ejpam-6583	314	34	,	,	PUNCT
ejpam-6583	314	35	xm+2	xm+2	PROPN
ejpam-6583	314	36	)	)	PUNCT
ejpam-6583	315	1	+	+	NUM
ejpam-6583	315	2	s3	s3	NOUN
ejpam-6583	315	3	[	[	PUNCT
ejpam-6583	315	4	δb	δb	X
ejpam-6583	315	5	r⊕d	r⊕d	NOUN
ejpam-6583	315	6	(	(	PUNCT
ejpam-6583	315	7	xm+2	xm+2	PROPN
ejpam-6583	315	8	,	,	PUNCT
ejpam-6583	315	9	xm+3	xm+3	NUM
ejpam-6583	315	10	)	)	PUNCT
ejpam-6583	315	11	+	+	CCONJ
ejpam-6583	315	12	δb	δb	NOUN
ejpam-6583	315	13	r⊕d	r⊕d	NOUN
ejpam-6583	315	14	(	(	PUNCT
ejpam-6583	315	15	xm+3	xm+3	NUM
ejpam-6583	315	16	,	,	PUNCT
ejpam-6583	315	17	xn	xn	PROPN
ejpam-6583	315	18	)	)	PUNCT
ejpam-6583	315	19	]	]	PUNCT
ejpam-6583	315	20	...	...	PUNCT
ejpam-6583	316	1	≾	≾	PROPN
ejpam-6583	316	2	s	s	PART
ejpam-6583	316	3	δb	δb	NOUN
ejpam-6583	316	4	r⊕d	r⊕d	NOUN
ejpam-6583	316	5	(	(	PUNCT
ejpam-6583	316	6	xm	xm	PROPN
ejpam-6583	316	7	,	,	PUNCT
ejpam-6583	316	8	xm+1	xm+1	PROPN
ejpam-6583	316	9	)	)	PUNCT
ejpam-6583	316	10	+	+	CCONJ
ejpam-6583	316	11	s2	s2	NOUN
ejpam-6583	316	12	δb	δb	NOUN
ejpam-6583	316	13	r⊕d	r⊕d	NOUN
ejpam-6583	316	14	(	(	PUNCT
ejpam-6583	316	15	xm+1	xm+1	PROPN
ejpam-6583	316	16	,	,	PUNCT
ejpam-6583	316	17	xm+2	xm+2	PROPN
ejpam-6583	316	18	)	)	PUNCT
ejpam-6583	317	1	+	+	NOUN
ejpam-6583	317	2	s3	s3	NOUN
ejpam-6583	317	3	δb	δb	NOUN
ejpam-6583	317	4	r⊕d	r⊕d	NOUN
ejpam-6583	317	5	(	(	PUNCT
ejpam-6583	317	6	xm+2	xm+2	PROPN
ejpam-6583	317	7	,	,	PUNCT
ejpam-6583	317	8	xm+3	xm+3	NUM
ejpam-6583	317	9	)	)	PUNCT
ejpam-6583	317	10	+	+	X
ejpam-6583	317	11	·	·	PUNCT
ejpam-6583	317	12	·	·	PUNCT
ejpam-6583	317	13	·	·	PUNCT
ejpam-6583	317	14	+	+	NUM
ejpam-6583	317	15	sn−mδb	sn−mδb	NOUN
ejpam-6583	317	16	r⊕d	r⊕d	NOUN
ejpam-6583	317	17	(	(	PUNCT
ejpam-6583	317	18	xn−1	xn−1	PROPN
ejpam-6583	317	19	,	,	PUNCT
ejpam-6583	317	20	xn	xn	PRON
ejpam-6583	317	21	)	)	PUNCT
ejpam-6583	318	1	=	=	SYM
ejpam-6583	318	2	diag	diag	NOUN
ejpam-6583	318	3	(	(	PUNCT
ejpam-6583	318	4	sβm1	sβm1	PROPN
ejpam-6583	318	5	,	,	PUNCT
ejpam-6583	318	6	·	·	PUNCT
ejpam-6583	318	7	·	·	PUNCT
ejpam-6583	318	8	·	·	PUNCT
ejpam-6583	318	9	,	,	PUNCT
ejpam-6583	318	10	sβmd	sβmd	NOUN
ejpam-6583	318	11	)	)	PUNCT
ejpam-6583	318	12	δb	δb	NOUN
ejpam-6583	318	13	r⊕d	r⊕d	NOUN
ejpam-6583	318	14	(	(	PUNCT
ejpam-6583	318	15	x0	x0	PROPN
ejpam-6583	318	16	,	,	PUNCT
ejpam-6583	318	17	x1	x1	PROPN
ejpam-6583	318	18	)	)	PUNCT
ejpam-6583	318	19	+	+	PUNCT
ejpam-6583	319	1	diag(s2βm+1	diag(s2βm+1	ADJ
ejpam-6583	319	2	1	1	NUM
ejpam-6583	319	3	,	,	PUNCT
ejpam-6583	319	4	·	·	PUNCT
ejpam-6583	319	5	·	·	PUNCT
ejpam-6583	319	6	·	·	PUNCT
ejpam-6583	319	7	,	,	PUNCT
ejpam-6583	319	8	s2βm+1	s2βm+1	PROPN
ejpam-6583	319	9	d	d	PROPN
ejpam-6583	319	10	)	)	PUNCT
ejpam-6583	319	11	δb	δb	NOUN
ejpam-6583	319	12	r⊕d	r⊕d	NOUN
ejpam-6583	319	13	(	(	PUNCT
ejpam-6583	319	14	x0	x0	PROPN
ejpam-6583	319	15	,	,	PUNCT
ejpam-6583	319	16	x1	x1	PROPN
ejpam-6583	319	17	)	)	PUNCT
ejpam-6583	319	18	+	+	X
ejpam-6583	319	19	·	·	PUNCT
ejpam-6583	319	20	·	·	PUNCT
ejpam-6583	319	21	·	·	PUNCT
ejpam-6583	319	22	+	+	NUM
ejpam-6583	319	23	diag	diag	NOUN
ejpam-6583	319	24	(	(	PUNCT
ejpam-6583	319	25	sn−mβn−1	sn−mβn−1	PROPN
ejpam-6583	319	26	1	1	NUM
ejpam-6583	319	27	,	,	PUNCT
ejpam-6583	319	28	·	·	PUNCT
ejpam-6583	319	29	·	·	PUNCT
ejpam-6583	319	30	·	·	PUNCT
ejpam-6583	319	31	,	,	PUNCT
ejpam-6583	319	32	sn−mβn−1	sn−mβn−1	PROPN
ejpam-6583	319	33	d	d	NOUN
ejpam-6583	319	34	)	)	PUNCT
ejpam-6583	319	35	δb	δb	NOUN
ejpam-6583	319	36	r⊕d	r⊕d	NOUN
ejpam-6583	319	37	(	(	PUNCT
ejpam-6583	319	38	x0	x0	PROPN
ejpam-6583	319	39	,	,	PUNCT
ejpam-6583	319	40	x1	x1	PROPN
ejpam-6583	319	41	)	)	PUNCT
ejpam-6583	320	1	=	=	SYM
ejpam-6583	320	2	diag	diag	NOUN
ejpam-6583	320	3	(	(	PUNCT
ejpam-6583	320	4	[	[	PUNCT
ejpam-6583	320	5	sβm1	sβm1	NOUN
ejpam-6583	320	6	+	+	CCONJ
ejpam-6583	320	7	s2βm+1	s2βm+1	ADJ
ejpam-6583	320	8	1	1	NUM
ejpam-6583	320	9	+	+	CCONJ
ejpam-6583	320	10	·	·	PUNCT
ejpam-6583	320	11	·	·	PUNCT
ejpam-6583	320	12	·	·	PUNCT
ejpam-6583	320	13	+	+	NUM
ejpam-6583	320	14	sn−mβn−1	sn−mβn−1	ADJ
ejpam-6583	320	15	1	1	NUM
ejpam-6583	320	16	]	]	PUNCT
ejpam-6583	320	17	,	,	PUNCT
ejpam-6583	320	18	·	·	PUNCT
ejpam-6583	320	19	·	·	PUNCT
ejpam-6583	320	20	·	·	PUNCT
ejpam-6583	320	21	,	,	PUNCT
ejpam-6583	320	22	[	[	PUNCT
ejpam-6583	320	23	sβmd	sβmd	NOUN
ejpam-6583	320	24	+	+	CCONJ
ejpam-6583	320	25	s2βm+1	s2βm+1	ADJ
ejpam-6583	320	26	d	d	X
ejpam-6583	320	27	+	+	PROPN
ejpam-6583	320	28	·	·	PUNCT
ejpam-6583	320	29	·	·	PUNCT
ejpam-6583	320	30	·	·	PUNCT
ejpam-6583	320	31	+	+	NUM
ejpam-6583	320	32	sn−mβn−1	sn−mβn−1	PROPN
ejpam-6583	320	33	d	d	X
ejpam-6583	320	34	]	]	X
ejpam-6583	320	35	)	)	PUNCT
ejpam-6583	320	36	δb	δb	NOUN
ejpam-6583	320	37	r⊕d	r⊕d	NOUN
ejpam-6583	320	38	(	(	PUNCT
ejpam-6583	320	39	x0	x0	PROPN
ejpam-6583	320	40	,	,	PUNCT
ejpam-6583	320	41	x1	x1	PROPN
ejpam-6583	320	42	)	)	PUNCT
ejpam-6583	321	1	=	=	SYM
ejpam-6583	321	2	diag	diag	NOUN
ejpam-6583	321	3	n−m∑	n−m∑	PROPN
ejpam-6583	321	4	i=1	i=1	PROPN
ejpam-6583	321	5	n−1∑	n−1∑	PROPN
ejpam-6583	321	6	j	j	X
ejpam-6583	322	1	=	=	NOUN
ejpam-6583	322	2	m	m	NOUN
ejpam-6583	322	3	siβj1	siβj1	NOUN
ejpam-6583	322	4	,	,	PUNCT
ejpam-6583	322	5	·	·	PUNCT
ejpam-6583	322	6	·	·	PUNCT
ejpam-6583	322	7	·	·	PUNCT
ejpam-6583	322	8	,	,	PUNCT
ejpam-6583	322	9	n−m∑	n−m∑	PROPN
ejpam-6583	322	10	i=1	i=1	PROPN
ejpam-6583	322	11	n−1∑	n−1∑	PROPN
ejpam-6583	322	12	j	j	PROPN
ejpam-6583	322	13	=	=	PROPN
ejpam-6583	322	14	m	m	PROPN
ejpam-6583	322	15	siβjd	siβjd	NOUN
ejpam-6583	322	16			PROPN
ejpam-6583	322	17	δb	δb	PROPN
ejpam-6583	322	18	r⊕d	r⊕d	NOUN
ejpam-6583	322	19	(	(	PUNCT
ejpam-6583	322	20	x0	x0	PROPN
ejpam-6583	322	21	,	,	PUNCT
ejpam-6583	322	22	x1	x1	PROPN
ejpam-6583	322	23	)	)	PUNCT
ejpam-6583	322	24	=	=	SYM
ejpam-6583	322	25	diag	diag	NOUN
ejpam-6583	322	26	(	(	PUNCT
ejpam-6583	322	27	sβm1	sβm1	PROPN
ejpam-6583	322	28	n−m−1∑	n−m−1∑	PROPN
ejpam-6583	322	29	j=0	j=0	PROPN
ejpam-6583	322	30	(	(	PUNCT
ejpam-6583	322	31	sβ1	sβ1	PROPN
ejpam-6583	322	32	)	)	PUNCT
ejpam-6583	322	33	j	j	PROPN
ejpam-6583	322	34	,	,	PUNCT
ejpam-6583	322	35	·	·	PUNCT
ejpam-6583	322	36	·	·	PUNCT
ejpam-6583	322	37	·	·	PUNCT
ejpam-6583	322	38	,	,	PUNCT
ejpam-6583	322	39	sβmd	sβmd	NOUN
ejpam-6583	322	40	n−m−1∑	n−m−1∑	PROPN
ejpam-6583	322	41	j=0	j=0	PROPN
ejpam-6583	322	42	(	(	PUNCT
ejpam-6583	322	43	sβd	sβd	PROPN
ejpam-6583	322	44	)	)	PUNCT
ejpam-6583	322	45	j	j	PROPN
ejpam-6583	322	46	)	)	PUNCT
ejpam-6583	322	47	δb	δb	NOUN
ejpam-6583	322	48	r⊕d	r⊕d	NOUN
ejpam-6583	322	49	(	(	PUNCT
ejpam-6583	322	50	x0	x0	PROPN
ejpam-6583	322	51	,	,	PUNCT
ejpam-6583	322	52	x1	x1	PROPN
ejpam-6583	322	53	)	)	PUNCT
ejpam-6583	322	54	≾	≾	NOUN
ejpam-6583	322	55	diag	diag	NOUN
ejpam-6583	322	56	(	(	PUNCT
ejpam-6583	322	57	sβm1	sβm1	NOUN
ejpam-6583	322	58	+	+	PROPN
ejpam-6583	322	59	∞∑	∞∑	PROPN
ejpam-6583	322	60	j=0	j=0	PROPN
ejpam-6583	322	61	(	(	PUNCT
ejpam-6583	322	62	sβ1	sβ1	PROPN
ejpam-6583	322	63	)	)	PUNCT
ejpam-6583	322	64	j	j	PROPN
ejpam-6583	322	65	,	,	PUNCT
ejpam-6583	322	66	·	·	PUNCT
ejpam-6583	322	67	·	·	PUNCT
ejpam-6583	322	68	·	·	PUNCT
ejpam-6583	322	69	,	,	PUNCT
ejpam-6583	322	70	sβmd	sβmd	NOUN
ejpam-6583	323	1	+	+	ADP
ejpam-6583	323	2	∞∑	∞∑	NUM
ejpam-6583	323	3	j=0	j=0	PROPN
ejpam-6583	323	4	(	(	PUNCT
ejpam-6583	323	5	sβd	sβd	PROPN
ejpam-6583	323	6	)	)	PUNCT
ejpam-6583	323	7	j	j	PROPN
ejpam-6583	323	8	)	)	PUNCT
ejpam-6583	323	9	δb	δb	NOUN
ejpam-6583	323	10	r⊕d	r⊕d	NOUN
ejpam-6583	323	11	(	(	PUNCT
ejpam-6583	323	12	x0	x0	PROPN
ejpam-6583	323	13	,	,	PUNCT
ejpam-6583	323	14	x1	x1	PROPN
ejpam-6583	323	15	)	)	PUNCT
ejpam-6583	324	1	=	=	SYM
ejpam-6583	324	2	diag	diag	NOUN
ejpam-6583	324	3	(	(	PUNCT
ejpam-6583	324	4	sβm1	sβm1	PROPN
ejpam-6583	324	5	,	,	PUNCT
ejpam-6583	324	6	·	·	PUNCT
ejpam-6583	324	7	·	·	PUNCT
ejpam-6583	324	8	·	·	PUNCT
ejpam-6583	324	9	,	,	PUNCT
ejpam-6583	324	10	sβmd	sβmd	NOUN
ejpam-6583	324	11	)	)	PUNCT
ejpam-6583	324	12	diag	diag	NOUN
ejpam-6583	324	13	(	(	PUNCT
ejpam-6583	324	14	+	+	ADJ
ejpam-6583	324	15	∞∑	∞∑	NUM
ejpam-6583	324	16	j=0	j=0	PROPN
ejpam-6583	324	17	(	(	PUNCT
ejpam-6583	324	18	sβ1	sβ1	PROPN
ejpam-6583	324	19	)	)	PUNCT
ejpam-6583	324	20	j	j	PROPN
ejpam-6583	324	21	,	,	PUNCT
ejpam-6583	324	22	·	·	PUNCT
ejpam-6583	324	23	·	·	PUNCT
ejpam-6583	324	24	·	·	PUNCT
ejpam-6583	325	1	+	+	ADP
ejpam-6583	325	2	∞∑	∞∑	NUM
ejpam-6583	325	3	j=0	j=0	PROPN
ejpam-6583	325	4	(	(	PUNCT
ejpam-6583	325	5	sβd	sβd	PROPN
ejpam-6583	325	6	)	)	PUNCT
ejpam-6583	325	7	j	j	PROPN
ejpam-6583	325	8	)	)	PUNCT
ejpam-6583	325	9	δb	δb	NOUN
ejpam-6583	325	10	r⊕d	r⊕d	NOUN
ejpam-6583	325	11	(	(	PUNCT
ejpam-6583	325	12	x0	x0	PROPN
ejpam-6583	325	13	,	,	PUNCT
ejpam-6583	325	14	x1	x1	PROPN
ejpam-6583	325	15	)	)	PUNCT
ejpam-6583	325	16	=	=	SYM
ejpam-6583	325	17	diag	diag	NOUN
ejpam-6583	325	18	(	(	PUNCT
ejpam-6583	325	19	sβm1	sβm1	PROPN
ejpam-6583	325	20	,	,	PUNCT
ejpam-6583	325	21	·	·	PUNCT
ejpam-6583	325	22	·	·	PUNCT
ejpam-6583	325	23	·	·	PUNCT
ejpam-6583	325	24	,	,	PUNCT
ejpam-6583	325	25	sβmd	sβmd	NOUN
ejpam-6583	325	26	)	)	PUNCT
ejpam-6583	325	27	diag	diag	NOUN
ejpam-6583	325	28	(	(	PUNCT
ejpam-6583	325	29	[	[	PUNCT
ejpam-6583	325	30	1	1	NUM
ejpam-6583	325	31	1−	1−	NUM
ejpam-6583	325	32	sβ1	sβ1	NOUN
ejpam-6583	325	33	]	]	PUNCT
ejpam-6583	325	34	,	,	PUNCT
ejpam-6583	325	35	·	·	PUNCT
ejpam-6583	325	36	·	·	PUNCT
ejpam-6583	325	37	·	·	PUNCT
ejpam-6583	325	38	,	,	PUNCT
ejpam-6583	325	39	[	[	PUNCT
ejpam-6583	325	40	1	1	NUM
ejpam-6583	325	41	1−	1−	NUM
ejpam-6583	325	42	sβd	sβd	NOUN
ejpam-6583	325	43	]	]	PUNCT
ejpam-6583	325	44	)	)	PUNCT
ejpam-6583	325	45	δb	δb	NOUN
ejpam-6583	325	46	r⊕d	r⊕d	NOUN
ejpam-6583	325	47	(	(	PUNCT
ejpam-6583	325	48	x0	x0	PROPN
ejpam-6583	325	49	,	,	PUNCT
ejpam-6583	325	50	x1	x1	PROPN
ejpam-6583	325	51	)	)	PUNCT
ejpam-6583	325	52	.	.	PUNCT
ejpam-6583	326	1	since	since	SCONJ
ejpam-6583	326	2	sβi	sβi	PROPN
ejpam-6583	326	3	∈	∈	PROPN
ejpam-6583	326	4	(	(	PUNCT
ejpam-6583	326	5	0	0	NUM
ejpam-6583	326	6	,	,	PUNCT
ejpam-6583	326	7	1	1	NUM
ejpam-6583	326	8	)	)	PUNCT
ejpam-6583	326	9	for	for	ADP
ejpam-6583	326	10	all	all	DET
ejpam-6583	326	11	i	i	PRON
ejpam-6583	326	12	=	=	NOUN
ejpam-6583	326	13	1	1	NUM
ejpam-6583	326	14	,	,	PUNCT
ejpam-6583	326	15	2	2	NUM
ejpam-6583	326	16	,	,	PUNCT
ejpam-6583	326	17	·	·	PUNCT
ejpam-6583	326	18	·	·	PUNCT
ejpam-6583	326	19	·	·	PUNCT
ejpam-6583	326	20	,	,	PUNCT
ejpam-6583	326	21	d	d	NOUN
ejpam-6583	326	22	and	and	CCONJ
ejpam-6583	326	23	δb	δb	NOUN
ejpam-6583	326	24	r⊕d	r⊕d	NOUN
ejpam-6583	326	25	(	(	PUNCT
ejpam-6583	326	26	x0	x0	PROPN
ejpam-6583	326	27	,	,	PUNCT
ejpam-6583	326	28	x1	x1	PROPN
ejpam-6583	326	29	)	)	PUNCT
ejpam-6583	326	30	are	be	AUX
ejpam-6583	326	31	fixed	fix	VERB
ejpam-6583	326	32	,	,	PUNCT
ejpam-6583	326	33	it	it	PRON
ejpam-6583	326	34	is	be	AUX
ejpam-6583	326	35	evident	evident	ADJ
ejpam-6583	326	36	that	that	SCONJ
ejpam-6583	326	37	by	by	ADP
ejpam-6583	326	38	selecting	select	VERB
ejpam-6583	326	39	m	m	PRON
ejpam-6583	326	40	sufficiently	sufficiently	ADV
ejpam-6583	326	41	large	large	ADJ
ejpam-6583	326	42	(	(	PUNCT
ejpam-6583	326	43	with	with	ADP
ejpam-6583	326	44	n	n	NOUN
ejpam-6583	326	45	>	>	X
ejpam-6583	326	46	m	m	PROPN
ejpam-6583	326	47	)	)	PUNCT
ejpam-6583	326	48	,	,	PUNCT
ejpam-6583	326	49	we	we	PRON
ejpam-6583	326	50	can	can	AUX
ejpam-6583	326	51	make	make	VERB
ejpam-6583	326	52	δb	δb	NOUN
ejpam-6583	326	53	r⊕d	r⊕d	NOUN
ejpam-6583	326	54	(	(	PUNCT
ejpam-6583	326	55	xn	xn	PROPN
ejpam-6583	326	56	,	,	PUNCT
ejpam-6583	326	57	xm	xm	PROPN
ejpam-6583	326	58	)	)	PUNCT
ejpam-6583	326	59	arbitrarily	arbitrarily	ADV
ejpam-6583	326	60	small	small	ADJ
ejpam-6583	326	61	.	.	PUNCT
ejpam-6583	327	1	this	this	PRON
ejpam-6583	327	2	shows	show	VERB
ejpam-6583	327	3	that	that	SCONJ
ejpam-6583	327	4	{	{	PUNCT
ejpam-6583	327	5	xn	xn	X
ejpam-6583	327	6	}	}	PUNCT
ejpam-6583	327	7	is	be	AUX
ejpam-6583	327	8	a	a	DET
ejpam-6583	327	9	cauchy	cauchy	ADJ
ejpam-6583	327	10	sequence	sequence	NOUN
ejpam-6583	327	11	.	.	PUNCT
ejpam-6583	328	1	finally	finally	ADV
ejpam-6583	328	2	,	,	PUNCT
ejpam-6583	328	3	because	because	SCONJ
ejpam-6583	328	4	(	(	PUNCT
ejpam-6583	328	5	x	x	X
ejpam-6583	328	6	,	,	PUNCT
ejpam-6583	328	7	r⊕d	r⊕d	NOUN
ejpam-6583	328	8	,	,	PUNCT
ejpam-6583	328	9	δb	δb	NOUN
ejpam-6583	328	10	r⊕d	r⊕d	NOUN
ejpam-6583	328	11	)	)	PUNCT
ejpam-6583	328	12	is	be	AUX
ejpam-6583	328	13	complete	complete	ADJ
ejpam-6583	328	14	,	,	PUNCT
ejpam-6583	328	15	there	there	PRON
ejpam-6583	328	16	exists	exist	VERB
ejpam-6583	328	17	some	some	DET
ejpam-6583	328	18	z	z	NOUN
ejpam-6583	328	19	∈	∈	PROPN
ejpam-6583	328	20	x	x	PUNCT
ejpam-6583	328	21	such	such	ADJ
ejpam-6583	328	22	that	that	PRON
ejpam-6583	328	23	xn	xn	PROPN
ejpam-6583	329	1	→	→	SYM
ejpam-6583	329	2	z.	z.	PROPN
ejpam-6583	329	3	to	to	PART
ejpam-6583	329	4	show	show	VERB
ejpam-6583	329	5	that	that	SCONJ
ejpam-6583	329	6	x	x	PRON
ejpam-6583	329	7	has	have	VERB
ejpam-6583	329	8	a	a	DET
ejpam-6583	329	9	fixed	fix	VERB
ejpam-6583	329	10	point	point	NOUN
ejpam-6583	329	11	,	,	PUNCT
ejpam-6583	329	12	we	we	PRON
ejpam-6583	329	13	consider	consider	VERB
ejpam-6583	329	14	the	the	DET
ejpam-6583	329	15	distance	distance	NOUN
ejpam-6583	329	16	δb	δb	NOUN
ejpam-6583	329	17	r⊕d	r⊕d	NOUN
ejpam-6583	329	18	(	(	PUNCT
ejpam-6583	329	19	z	z	NOUN
ejpam-6583	329	20	,	,	PUNCT
ejpam-6583	329	21	f	f	PROPN
ejpam-6583	329	22	(	(	PUNCT
ejpam-6583	329	23	z	z	NOUN
ejpam-6583	329	24	)	)	PUNCT
ejpam-6583	329	25	)	)	PUNCT
ejpam-6583	329	26	.	.	PUNCT
ejpam-6583	330	1	from	from	ADP
ejpam-6583	330	2	the	the	DET
ejpam-6583	330	3	triangle	triangle	NOUN
ejpam-6583	330	4	inequality	inequality	NOUN
ejpam-6583	330	5	and	and	CCONJ
ejpam-6583	330	6	contraction	contraction	NOUN
ejpam-6583	330	7	condition	condition	NOUN
ejpam-6583	330	8	,	,	PUNCT
ejpam-6583	330	9	we	we	PRON
ejpam-6583	330	10	get	get	VERB
ejpam-6583	330	11	δb	δb	ADP
ejpam-6583	330	12	r⊕d	r⊕d	NOUN
ejpam-6583	330	13	(	(	PUNCT
ejpam-6583	330	14	z	z	NOUN
ejpam-6583	330	15	,	,	PUNCT
ejpam-6583	330	16	f	f	PROPN
ejpam-6583	330	17	(	(	PUNCT
ejpam-6583	330	18	z	z	NOUN
ejpam-6583	330	19	)	)	PUNCT
ejpam-6583	330	20	)	)	PUNCT
ejpam-6583	331	1	≾	≾	PROPN
ejpam-6583	331	2	s	s	PART
ejpam-6583	331	3	[	[	PUNCT
ejpam-6583	331	4	δb	δb	NOUN
ejpam-6583	331	5	r⊕d	r⊕d	NOUN
ejpam-6583	331	6	(	(	PUNCT
ejpam-6583	331	7	z	z	NOUN
ejpam-6583	331	8	,	,	PUNCT
ejpam-6583	331	9	xn	xn	PROPN
ejpam-6583	331	10	)	)	PUNCT
ejpam-6583	332	1	+	+	CCONJ
ejpam-6583	332	2	δb	δb	NOUN
ejpam-6583	332	3	r⊕d	r⊕d	NOUN
ejpam-6583	332	4	(	(	PUNCT
ejpam-6583	332	5	xn	xn	PROPN
ejpam-6583	332	6	,	,	PUNCT
ejpam-6583	332	7	f	f	PROPN
ejpam-6583	332	8	(	(	PUNCT
ejpam-6583	332	9	z	z	NOUN
ejpam-6583	332	10	)	)	PUNCT
ejpam-6583	332	11	)	)	PUNCT
ejpam-6583	332	12	]	]	PUNCT
ejpam-6583	332	13	g.	g.	PROPN
ejpam-6583	332	14	albeladi	albeladi	PROPN
ejpam-6583	332	15	,	,	PUNCT
ejpam-6583	332	16	s.	s.	PROPN
ejpam-6583	332	17	omran	omran	PROPN
ejpam-6583	332	18	/	/	SYM
ejpam-6583	332	19	eur	eur	PROPN
ejpam-6583	332	20	.	.	PUNCT
ejpam-6583	333	1	j.	j.	PROPN
ejpam-6583	333	2	pure	pure	PROPN
ejpam-6583	333	3	appl	appl	PROPN
ejpam-6583	333	4	.	.	PROPN
ejpam-6583	333	5	math	math	PROPN
ejpam-6583	333	6	,	,	PUNCT
ejpam-6583	333	7	18	18	NUM
ejpam-6583	333	8	(	(	PUNCT
ejpam-6583	333	9	3	3	NUM
ejpam-6583	333	10	)	)	PUNCT
ejpam-6583	333	11	(	(	PUNCT
ejpam-6583	333	12	2025	2025	NUM
ejpam-6583	333	13	)	)	PUNCT
ejpam-6583	333	14	,	,	PUNCT
ejpam-6583	333	15	6583	6583	NUM
ejpam-6583	333	16	15	15	NUM
ejpam-6583	333	17	of	of	ADP
ejpam-6583	333	18	27	27	NUM
ejpam-6583	333	19	=	=	SYM
ejpam-6583	333	20	s	s	X
ejpam-6583	333	21	[	[	PUNCT
ejpam-6583	333	22	δb	δb	NOUN
ejpam-6583	333	23	r⊕d	r⊕d	NOUN
ejpam-6583	333	24	(	(	PUNCT
ejpam-6583	333	25	z	z	NOUN
ejpam-6583	333	26	,	,	PUNCT
ejpam-6583	333	27	xn	xn	PROPN
ejpam-6583	333	28	)	)	PUNCT
ejpam-6583	334	1	+	+	CCONJ
ejpam-6583	334	2	δb	δb	NOUN
ejpam-6583	334	3	r⊕d	r⊕d	NOUN
ejpam-6583	334	4	(	(	PUNCT
ejpam-6583	334	5	f	f	PROPN
ejpam-6583	334	6	(	(	PUNCT
ejpam-6583	334	7	xn−1),f	xn−1),f	PROPN
ejpam-6583	334	8	(	(	PUNCT
ejpam-6583	334	9	z	z	NOUN
ejpam-6583	334	10	)	)	PUNCT
ejpam-6583	334	11	)	)	PUNCT
ejpam-6583	334	12	]	]	PUNCT
ejpam-6583	335	1	≾	≾	PROPN
ejpam-6583	335	2	s	s	X
ejpam-6583	335	3	[	[	PUNCT
ejpam-6583	335	4	δb	δb	NOUN
ejpam-6583	335	5	r⊕d	r⊕d	NOUN
ejpam-6583	335	6	(	(	PUNCT
ejpam-6583	335	7	z	z	NOUN
ejpam-6583	335	8	,	,	PUNCT
ejpam-6583	335	9	xn	xn	PUNCT
ejpam-6583	335	10	)	)	PUNCT
ejpam-6583	336	1	+	+	CCONJ
ejpam-6583	336	2	diag	diag	PROPN
ejpam-6583	336	3	(	(	PUNCT
ejpam-6583	336	4	α1	α1	PROPN
ejpam-6583	336	5	,	,	PUNCT
ejpam-6583	336	6	·	·	PUNCT
ejpam-6583	336	7	·	·	PUNCT
ejpam-6583	336	8	·	·	PUNCT
ejpam-6583	336	9	,	,	PUNCT
ejpam-6583	336	10	αd	αd	PROPN
ejpam-6583	336	11	)	)	PUNCT
ejpam-6583	336	12	δb	δb	NOUN
ejpam-6583	336	13	r⊕d	r⊕d	NOUN
ejpam-6583	336	14	(	(	PUNCT
ejpam-6583	336	15	xn−1,f	xn−1,f	X
ejpam-6583	336	16	(	(	PUNCT
ejpam-6583	336	17	xn−1	xn−1	PROPN
ejpam-6583	336	18	)	)	PUNCT
ejpam-6583	336	19	)	)	PUNCT
ejpam-6583	337	1	+	+	CCONJ
ejpam-6583	337	2	δb	δb	NOUN
ejpam-6583	337	3	r⊕d	r⊕d	NOUN
ejpam-6583	337	4	(	(	PUNCT
ejpam-6583	337	5	z	z	NOUN
ejpam-6583	337	6	,	,	PUNCT
ejpam-6583	337	7	f	f	PROPN
ejpam-6583	337	8	(	(	PUNCT
ejpam-6583	337	9	z	z	NOUN
ejpam-6583	337	10	)	)	PUNCT
ejpam-6583	337	11	)	)	PUNCT
ejpam-6583	337	12	]	]	PUNCT
ejpam-6583	338	1	≾	≾	NOUN
ejpam-6583	338	2	diag	diag	NOUN
ejpam-6583	338	3	(	(	PUNCT
ejpam-6583	338	4	sα1	sα1	PROPN
ejpam-6583	338	5	,	,	PUNCT
ejpam-6583	338	6	·	·	PUNCT
ejpam-6583	338	7	·	·	PUNCT
ejpam-6583	338	8	·	·	PUNCT
ejpam-6583	338	9	,	,	PUNCT
ejpam-6583	338	10	sαd	sαd	NOUN
ejpam-6583	338	11	)	)	PUNCT
ejpam-6583	338	12	δb	δb	NOUN
ejpam-6583	338	13	r⊕d	r⊕d	NOUN
ejpam-6583	338	14	(	(	PUNCT
ejpam-6583	338	15	z	z	NOUN
ejpam-6583	338	16	,	,	PUNCT
ejpam-6583	338	17	f	f	PROPN
ejpam-6583	338	18	(	(	PUNCT
ejpam-6583	338	19	z	z	NOUN
ejpam-6583	338	20	)	)	PUNCT
ejpam-6583	338	21	)	)	PUNCT
ejpam-6583	338	22	,	,	PUNCT
ejpam-6583	338	23	since	since	SCONJ
ejpam-6583	338	24	xn	xn	PROPN
ejpam-6583	338	25	→	→	SYM
ejpam-6583	338	26	z	z	PROPN
ejpam-6583	338	27	and	and	CCONJ
ejpam-6583	338	28	sαi	sαi	PROPN
ejpam-6583	338	29	∈	∈	PROPN
ejpam-6583	338	30	(	(	PUNCT
ejpam-6583	338	31	0	0	NUM
ejpam-6583	338	32	,	,	PUNCT
ejpam-6583	338	33	1	1	NUM
ejpam-6583	338	34	)	)	PUNCT
ejpam-6583	338	35	,	,	PUNCT
ejpam-6583	338	36	∀i	∀i	NOUN
ejpam-6583	338	37	=	=	SYM
ejpam-6583	338	38	{	{	PUNCT
ejpam-6583	338	39	1	1	NUM
ejpam-6583	338	40	,	,	PUNCT
ejpam-6583	338	41	2	2	NUM
ejpam-6583	338	42	,	,	PUNCT
ejpam-6583	338	43	·	·	PUNCT
ejpam-6583	338	44	·	·	PUNCT
ejpam-6583	338	45	·	·	PUNCT
ejpam-6583	338	46	,	,	PUNCT
ejpam-6583	338	47	d	d	X
ejpam-6583	338	48	}	}	PUNCT
ejpam-6583	338	49	it	it	PRON
ejpam-6583	338	50	is	be	AUX
ejpam-6583	338	51	clear	clear	ADJ
ejpam-6583	338	52	that	that	SCONJ
ejpam-6583	338	53	we	we	PRON
ejpam-6583	338	54	can	can	AUX
ejpam-6583	338	55	make	make	VERB
ejpam-6583	338	56	this	this	DET
ejpam-6583	338	57	distance	distance	NOUN
ejpam-6583	338	58	as	as	ADV
ejpam-6583	338	59	small	small	ADJ
ejpam-6583	338	60	as	as	SCONJ
ejpam-6583	338	61	we	we	PRON
ejpam-6583	338	62	please	please	VERB
ejpam-6583	338	63	by	by	ADP
ejpam-6583	338	64	choosing	choose	VERB
ejpam-6583	338	65	n	n	PRON
ejpam-6583	338	66	sufficiently	sufficiently	ADV
ejpam-6583	338	67	large	large	ADJ
ejpam-6583	338	68	.	.	PUNCT
ejpam-6583	339	1	we	we	PRON
ejpam-6583	339	2	conclude	conclude	VERB
ejpam-6583	339	3	that	that	SCONJ
ejpam-6583	339	4	δb	δb	NOUN
ejpam-6583	339	5	r⊕d	r⊕d	NOUN
ejpam-6583	339	6	(	(	PUNCT
ejpam-6583	339	7	z	z	NOUN
ejpam-6583	339	8	,	,	PUNCT
ejpam-6583	339	9	f	f	PROPN
ejpam-6583	339	10	(	(	PUNCT
ejpam-6583	339	11	z	z	NOUN
ejpam-6583	339	12	)	)	PUNCT
ejpam-6583	339	13	)	)	PUNCT
ejpam-6583	340	1	=	=	SYM
ejpam-6583	340	2	0	0	PUNCT
ejpam-6583	341	1	=	=	AUX
ejpam-6583	341	2	⇒	⇒	X
ejpam-6583	341	3	f	f	X
ejpam-6583	341	4	(	(	PUNCT
ejpam-6583	341	5	z	z	NOUN
ejpam-6583	341	6	)	)	PUNCT
ejpam-6583	342	1	=	=	SYM
ejpam-6583	342	2	z	z	NOUN
ejpam-6583	342	3	,	,	PUNCT
ejpam-6583	342	4	so	so	ADV
ejpam-6583	342	5	z	z	NOUN
ejpam-6583	342	6	∈	∈	PROPN
ejpam-6583	342	7	x	x	X
ejpam-6583	342	8	is	be	AUX
ejpam-6583	342	9	a	a	DET
ejpam-6583	342	10	fixed	fix	VERB
ejpam-6583	342	11	-	-	PUNCT
ejpam-6583	342	12	point	point	NOUN
ejpam-6583	342	13	of	of	ADP
ejpam-6583	342	14	f	f	PROPN
ejpam-6583	342	15	.	.	PUNCT
ejpam-6583	343	1	to	to	PART
ejpam-6583	343	2	prove	prove	VERB
ejpam-6583	343	3	uniqueness	uniqueness	NOUN
ejpam-6583	343	4	,	,	PUNCT
ejpam-6583	343	5	suppose	suppose	VERB
ejpam-6583	343	6	there	there	PRON
ejpam-6583	343	7	are	be	VERB
ejpam-6583	343	8	two	two	NUM
ejpam-6583	343	9	fixed	fix	VERB
ejpam-6583	343	10	points	point	NOUN
ejpam-6583	344	1	x	x	X
ejpam-6583	344	2	=	=	SYM
ejpam-6583	344	3	f	f	X
ejpam-6583	344	4	(	(	PUNCT
ejpam-6583	344	5	x	x	NOUN
ejpam-6583	344	6	)	)	PUNCT
ejpam-6583	344	7	and	and	CCONJ
ejpam-6583	344	8	y	y	PROPN
ejpam-6583	344	9	=	=	SYM
ejpam-6583	344	10	f	f	PROPN
ejpam-6583	344	11	(	(	PUNCT
ejpam-6583	344	12	x	x	NOUN
ejpam-6583	344	13	)	)	PUNCT
ejpam-6583	344	14	.	.	PUNCT
ejpam-6583	345	1	then	then	ADV
ejpam-6583	345	2	,	,	PUNCT
ejpam-6583	345	3	from	from	ADP
ejpam-6583	345	4	the	the	DET
ejpam-6583	345	5	contraction	contraction	NOUN
ejpam-6583	345	6	condition	condition	NOUN
ejpam-6583	345	7	,	,	PUNCT
ejpam-6583	345	8	we	we	PRON
ejpam-6583	345	9	have	have	VERB
ejpam-6583	345	10	δb	δb	NOUN
ejpam-6583	345	11	r⊕d	r⊕d	NOUN
ejpam-6583	345	12	(	(	PUNCT
ejpam-6583	345	13	x	x	X
ejpam-6583	345	14	,	,	PUNCT
ejpam-6583	345	15	y	y	NOUN
ejpam-6583	345	16	)	)	PUNCT
ejpam-6583	345	17	=	=	PUNCT
ejpam-6583	345	18	δb	δb	X
ejpam-6583	345	19	r⊕d	r⊕d	NOUN
ejpam-6583	345	20	(	(	PUNCT
ejpam-6583	345	21	f	f	PROPN
ejpam-6583	345	22	(	(	PUNCT
ejpam-6583	345	23	x),f	x),f	PROPN
ejpam-6583	345	24	(	(	PUNCT
ejpam-6583	345	25	y	y	NOUN
ejpam-6583	345	26	)	)	PUNCT
ejpam-6583	345	27	)	)	PUNCT
ejpam-6583	346	1	≾	≾	NOUN
ejpam-6583	346	2	diag	diag	NOUN
ejpam-6583	346	3	(	(	PUNCT
ejpam-6583	346	4	sα1	sα1	PROPN
ejpam-6583	346	5	,	,	PUNCT
ejpam-6583	346	6	·	·	PUNCT
ejpam-6583	346	7	·	·	PUNCT
ejpam-6583	346	8	·	·	PUNCT
ejpam-6583	346	9	,	,	PUNCT
ejpam-6583	346	10	sαd	sαd	NOUN
ejpam-6583	346	11	)	)	PUNCT
ejpam-6583	347	1	[	[	X
ejpam-6583	347	2	δb	δb	X
ejpam-6583	347	3	r⊕d	r⊕d	NOUN
ejpam-6583	347	4	(	(	PUNCT
ejpam-6583	347	5	x	x	X
ejpam-6583	347	6	,	,	PUNCT
ejpam-6583	347	7	f	f	PROPN
ejpam-6583	347	8	(	(	PUNCT
ejpam-6583	347	9	x))+δb	x))+δb	PROPN
ejpam-6583	347	10	r⊕d	r⊕d	NOUN
ejpam-6583	347	11	(	(	PUNCT
ejpam-6583	347	12	y	y	PROPN
ejpam-6583	347	13	,	,	PUNCT
ejpam-6583	347	14	f	f	PROPN
ejpam-6583	347	15	(	(	PUNCT
ejpam-6583	347	16	y	y	NOUN
ejpam-6583	347	17	)	)	PUNCT
ejpam-6583	347	18	)	)	PUNCT
ejpam-6583	347	19	]	]	PUNCT
ejpam-6583	347	20	,	,	PUNCT
ejpam-6583	347	21	this	this	PRON
ejpam-6583	347	22	implies	imply	VERB
ejpam-6583	347	23	δb	δb	NOUN
ejpam-6583	347	24	r⊕d	r⊕d	NOUN
ejpam-6583	347	25	(	(	PUNCT
ejpam-6583	347	26	x	x	X
ejpam-6583	347	27	,	,	PUNCT
ejpam-6583	347	28	y	y	NOUN
ejpam-6583	347	29	)	)	PUNCT
ejpam-6583	347	30	=	=	SYM
ejpam-6583	348	1	0	0	X
ejpam-6583	348	2	.	.	PUNCT
ejpam-6583	349	1	hence	hence	ADV
ejpam-6583	349	2	x	x	X
ejpam-6583	349	3	=	=	SYM
ejpam-6583	349	4	y	y	PROPN
ejpam-6583	349	5	,	,	PUNCT
ejpam-6583	349	6	and	and	CCONJ
ejpam-6583	349	7	the	the	DET
ejpam-6583	349	8	fixed	fix	VERB
ejpam-6583	349	9	-	-	PUNCT
ejpam-6583	349	10	point	point	NOUN
ejpam-6583	349	11	x	x	PUNCT
ejpam-6583	349	12	of	of	ADP
ejpam-6583	349	13	f	f	PROPN
ejpam-6583	349	14	is	be	AUX
ejpam-6583	349	15	unique	unique	ADJ
ejpam-6583	349	16	.	.	PUNCT
ejpam-6583	350	1	if	if	SCONJ
ejpam-6583	350	2	d	d	PROPN
ejpam-6583	350	3	=	=	SYM
ejpam-6583	350	4	1	1	NUM
ejpam-6583	350	5	and	and	CCONJ
ejpam-6583	350	6	s	s	X
ejpam-6583	350	7	=	=	SYM
ejpam-6583	350	8	1	1	NUM
ejpam-6583	350	9	,	,	PUNCT
ejpam-6583	350	10	then	then	ADV
ejpam-6583	350	11	the	the	DET
ejpam-6583	350	12	theorem	theorem	NOUN
ejpam-6583	350	13	4	4	NUM
ejpam-6583	350	14	can	can	AUX
ejpam-6583	350	15	be	be	AUX
ejpam-6583	350	16	reduced	reduce	VERB
ejpam-6583	350	17	to	to	ADP
ejpam-6583	350	18	the	the	DET
ejpam-6583	350	19	standard	standard	ADJ
ejpam-6583	350	20	kannan	kannan	PROPN
ejpam-6583	350	21	in	in	ADP
ejpam-6583	350	22	the	the	DET
ejpam-6583	350	23	metric	metric	ADJ
ejpam-6583	350	24	space	space	NOUN
ejpam-6583	350	25	.	.	PUNCT
ejpam-6583	351	1	corolary	corolary	ADJ
ejpam-6583	351	2	4	4	NUM
ejpam-6583	351	3	(	(	PUNCT
ejpam-6583	351	4	kannan	kannan	PROPN
ejpam-6583	351	5	,	,	PUNCT
ejpam-6583	351	6	[	[	X
ejpam-6583	351	7	24	24	NUM
ejpam-6583	351	8	]	]	PUNCT
ejpam-6583	351	9	)	)	PUNCT
ejpam-6583	351	10	.	.	PUNCT
ejpam-6583	351	11	suppose	suppose	VERB
ejpam-6583	351	12	that	that	SCONJ
ejpam-6583	351	13	(	(	PUNCT
ejpam-6583	351	14	x	x	X
ejpam-6583	351	15	,	,	PUNCT
ejpam-6583	351	16	d	d	X
ejpam-6583	351	17	)	)	PUNCT
ejpam-6583	351	18	is	be	AUX
ejpam-6583	351	19	a	a	DET
ejpam-6583	351	20	complete	complete	ADJ
ejpam-6583	351	21	metric	metric	ADJ
ejpam-6583	351	22	space	space	NOUN
ejpam-6583	351	23	and	and	CCONJ
ejpam-6583	351	24	f	f	NOUN
ejpam-6583	351	25	:	:	PUNCT
ejpam-6583	351	26	x	x	X
ejpam-6583	351	27	→	→	PUNCT
ejpam-6583	351	28	x	x	X
ejpam-6583	351	29	is	be	AUX
ejpam-6583	351	30	an	an	DET
ejpam-6583	351	31	operator	operator	NOUN
ejpam-6583	351	32	such	such	ADJ
ejpam-6583	351	33	that	that	PRON
ejpam-6583	351	34	δ(fx	δ(fx	PROPN
ejpam-6583	351	35	,	,	PUNCT
ejpam-6583	351	36	fy	fy	PROPN
ejpam-6583	351	37	)	)	PUNCT
ejpam-6583	351	38	≤	≤	PUNCT
ejpam-6583	352	1	α	α	PROPN
ejpam-6583	353	1	[	[	X
ejpam-6583	353	2	δ(fx	δ(fx	PROPN
ejpam-6583	353	3	,	,	PUNCT
ejpam-6583	353	4	x	x	PRON
ejpam-6583	353	5	)	)	PUNCT
ejpam-6583	354	1	+	+	CCONJ
ejpam-6583	354	2	δ(fy	δ(fy	PROPN
ejpam-6583	354	3	,	,	PUNCT
ejpam-6583	354	4	y	y	NOUN
ejpam-6583	354	5	)	)	PUNCT
ejpam-6583	354	6	]	]	PUNCT
ejpam-6583	354	7	,	,	PUNCT
ejpam-6583	354	8	for	for	ADP
ejpam-6583	354	9	constant	constant	ADJ
ejpam-6583	354	10	α	α	PRON
ejpam-6583	354	11	∈	∈	PROPN
ejpam-6583	354	12	(	(	PUNCT
ejpam-6583	354	13	0	0	NUM
ejpam-6583	354	14	,	,	PUNCT
ejpam-6583	354	15	12	12	NUM
ejpam-6583	354	16	)	)	PUNCT
ejpam-6583	354	17	and	and	CCONJ
ejpam-6583	354	18	for	for	ADP
ejpam-6583	354	19	every	every	DET
ejpam-6583	354	20	x	x	NOUN
ejpam-6583	354	21	,	,	PUNCT
ejpam-6583	354	22	y	y	PROPN
ejpam-6583	354	23	∈	∈	PROPN
ejpam-6583	354	24	x	x	X
ejpam-6583	354	25	.	.	PUNCT
ejpam-6583	355	1	then	then	ADV
ejpam-6583	355	2	f	f	PROPN
ejpam-6583	355	3	has	have	VERB
ejpam-6583	355	4	a	a	DET
ejpam-6583	355	5	unique	unique	ADJ
ejpam-6583	355	6	fixed	fix	VERB
ejpam-6583	355	7	-	-	PUNCT
ejpam-6583	355	8	point	point	NOUN
ejpam-6583	355	9	z	z	NOUN
ejpam-6583	355	10	∈	∈	PROPN
ejpam-6583	355	11	x	x	X
ejpam-6583	355	12	.	.	PUNCT
ejpam-6583	356	1	theorem	theorem	NOUN
ejpam-6583	356	2	5	5	NUM
ejpam-6583	356	3	.	.	PUNCT
ejpam-6583	357	1	(	(	PUNCT
ejpam-6583	357	2	chatterjee	chatterjee	PROPN
ejpam-6583	357	3	type	type	NOUN
ejpam-6583	357	4	)	)	PUNCT
ejpam-6583	357	5	suppose	suppose	VERB
ejpam-6583	357	6	that	that	SCONJ
ejpam-6583	357	7	(	(	PUNCT
ejpam-6583	357	8	x	x	X
ejpam-6583	357	9	,	,	PUNCT
ejpam-6583	357	10	r⊕d	r⊕d	NOUN
ejpam-6583	357	11	,	,	PUNCT
ejpam-6583	357	12	δb	δb	NOUN
ejpam-6583	357	13	r⊕d	r⊕d	NOUN
ejpam-6583	357	14	)	)	PUNCT
ejpam-6583	357	15	is	be	AUX
ejpam-6583	357	16	a	a	DET
ejpam-6583	357	17	complete	complete	ADJ
ejpam-6583	357	18	generalized	generalized	ADJ
ejpam-6583	357	19	b	b	X
ejpam-6583	357	20	-	-	ADJ
ejpam-6583	357	21	metric	metric	ADJ
ejpam-6583	357	22	space	space	NOUN
ejpam-6583	357	23	endowed	endow	VERB
ejpam-6583	357	24	with	with	ADP
ejpam-6583	357	25	the	the	DET
ejpam-6583	357	26	orthogonal	orthogonal	ADJ
ejpam-6583	357	27	direct	direct	ADJ
ejpam-6583	357	28	sum	sum	NOUN
ejpam-6583	357	29	and	and	CCONJ
ejpam-6583	357	30	f	f	NOUN
ejpam-6583	357	31	:	:	PUNCT
ejpam-6583	357	32	x	x	X
ejpam-6583	357	33	→	→	PUNCT
ejpam-6583	357	34	x	x	X
ejpam-6583	357	35	is	be	AUX
ejpam-6583	357	36	an	an	DET
ejpam-6583	357	37	operator	operator	NOUN
ejpam-6583	357	38	satisfying	satisfy	VERB
ejpam-6583	357	39	the	the	DET
ejpam-6583	357	40	following	follow	VERB
ejpam-6583	357	41	condition	condition	NOUN
ejpam-6583	357	42	δb	δb	ADP
ejpam-6583	357	43	r⊕d	r⊕d	NOUN
ejpam-6583	357	44	(	(	PUNCT
ejpam-6583	357	45	f	f	PROPN
ejpam-6583	357	46	(	(	PUNCT
ejpam-6583	357	47	x),f	x),f	PROPN
ejpam-6583	357	48	(	(	PUNCT
ejpam-6583	357	49	y	y	NOUN
ejpam-6583	357	50	)	)	PUNCT
ejpam-6583	357	51	)	)	PUNCT
ejpam-6583	358	1	≾	≾	NOUN
ejpam-6583	358	2	diag	diag	NOUN
ejpam-6583	358	3	(	(	PUNCT
ejpam-6583	358	4	α1	α1	PROPN
ejpam-6583	358	5	,	,	PUNCT
ejpam-6583	358	6	·	·	PUNCT
ejpam-6583	358	7	·	·	PUNCT
ejpam-6583	358	8	·	·	PUNCT
ejpam-6583	358	9	,	,	PUNCT
ejpam-6583	358	10	αd	αd	PROPN
ejpam-6583	358	11	)	)	PUNCT
ejpam-6583	359	1	[	[	X
ejpam-6583	359	2	δb	δb	X
ejpam-6583	359	3	r⊕d	r⊕d	NOUN
ejpam-6583	359	4	(	(	PUNCT
ejpam-6583	359	5	f	f	X
ejpam-6583	359	6	(	(	PUNCT
ejpam-6583	359	7	x	x	NOUN
ejpam-6583	359	8	)	)	PUNCT
ejpam-6583	359	9	,	,	PUNCT
ejpam-6583	359	10	y	y	PROPN
ejpam-6583	359	11	)	)	PUNCT
ejpam-6583	359	12	+	+	CCONJ
ejpam-6583	359	13	δb	δb	NOUN
ejpam-6583	359	14	r⊕d	r⊕d	NOUN
ejpam-6583	359	15	(	(	PUNCT
ejpam-6583	359	16	f	f	PROPN
ejpam-6583	359	17	(	(	PUNCT
ejpam-6583	359	18	y	y	PROPN
ejpam-6583	359	19	)	)	PUNCT
ejpam-6583	359	20	,	,	PUNCT
ejpam-6583	359	21	x	x	X
ejpam-6583	359	22	)	)	PUNCT
ejpam-6583	359	23	]	]	PUNCT
ejpam-6583	359	24	,	,	PUNCT
ejpam-6583	359	25	(	(	PUNCT
ejpam-6583	359	26	2	2	X
ejpam-6583	359	27	)	)	PUNCT
ejpam-6583	359	28	for	for	ADP
ejpam-6583	359	29	sαi	sαi	NOUN
ejpam-6583	359	30	∈	∈	PROPN
ejpam-6583	359	31	(	(	PUNCT
ejpam-6583	359	32	0	0	NUM
ejpam-6583	359	33	,	,	PUNCT
ejpam-6583	359	34	12	12	NUM
ejpam-6583	359	35	)	)	PUNCT
ejpam-6583	359	36	for	for	ADP
ejpam-6583	359	37	all	all	DET
ejpam-6583	359	38	i	i	PRON
ejpam-6583	359	39	=	=	NOUN
ejpam-6583	359	40	1	1	NUM
ejpam-6583	359	41	,	,	PUNCT
ejpam-6583	359	42	2	2	NUM
ejpam-6583	359	43	,	,	PUNCT
ejpam-6583	359	44	·	·	PUNCT
ejpam-6583	359	45	·	·	PUNCT
ejpam-6583	359	46	·	·	PUNCT
ejpam-6583	359	47	,	,	PUNCT
ejpam-6583	359	48	d	d	X
ejpam-6583	359	49	,	,	PUNCT
ejpam-6583	359	50	and	and	CCONJ
ejpam-6583	359	51	for	for	ADP
ejpam-6583	359	52	each	each	DET
ejpam-6583	359	53	x	x	NOUN
ejpam-6583	359	54	,	,	PUNCT
ejpam-6583	359	55	y	y	PROPN
ejpam-6583	359	56	∈	∈	PROPN
ejpam-6583	359	57	x	x	X
ejpam-6583	359	58	.	.	PUNCT
ejpam-6583	360	1	then	then	ADV
ejpam-6583	360	2	,	,	PUNCT
ejpam-6583	360	3	f	f	PROPN
ejpam-6583	360	4	has	have	VERB
ejpam-6583	360	5	a	a	DET
ejpam-6583	360	6	unique	unique	ADJ
ejpam-6583	360	7	fixed	fix	VERB
ejpam-6583	360	8	-	-	PUNCT
ejpam-6583	360	9	point	point	NOUN
ejpam-6583	360	10	in	in	ADP
ejpam-6583	360	11	x	x	X
ejpam-6583	360	12	.	.	PUNCT
ejpam-6583	361	1	proof	proof	NOUN
ejpam-6583	361	2	.	.	PUNCT
ejpam-6583	362	1	let	let	VERB
ejpam-6583	362	2	x0	x0	PROPN
ejpam-6583	362	3	be	be	AUX
ejpam-6583	362	4	any	any	DET
ejpam-6583	362	5	point	point	NOUN
ejpam-6583	362	6	in	in	ADP
ejpam-6583	362	7	x	x	SYM
ejpam-6583	362	8	,	,	PUNCT
ejpam-6583	362	9	that	that	ADV
ejpam-6583	362	10	is	is	ADV
ejpam-6583	362	11	x0	x0	PROPN
ejpam-6583	362	12	∈	∈	PROPN
ejpam-6583	363	1	x	x	X
ejpam-6583	363	2	.	.	PUNCT
ejpam-6583	364	1	let	let	VERB
ejpam-6583	364	2	us	we	PRON
ejpam-6583	364	3	define	define	VERB
ejpam-6583	364	4	a	a	DET
ejpam-6583	364	5	sequence	sequence	NOUN
ejpam-6583	364	6	{	{	PUNCT
ejpam-6583	364	7	xn	xn	NOUN
ejpam-6583	364	8	}	}	PUNCT
ejpam-6583	364	9	in	in	ADP
ejpam-6583	364	10	x	x	PUNCT
ejpam-6583	364	11	as	as	SCONJ
ejpam-6583	364	12	given	give	VERB
ejpam-6583	364	13	below	below	ADV
ejpam-6583	364	14	.	.	PUNCT
ejpam-6583	365	1	xn+1	xn+1	PUNCT
ejpam-6583	366	1	=	=	SYM
ejpam-6583	366	2	f	f	PROPN
ejpam-6583	366	3	(	(	PUNCT
ejpam-6583	366	4	xn	xn	PROPN
ejpam-6583	366	5	)	)	PUNCT
ejpam-6583	366	6	=	=	SYM
ejpam-6583	366	7	fn+1(x0	fn+1(x0	ADJ
ejpam-6583	366	8	)	)	PUNCT
ejpam-6583	366	9	∀	∀	X
ejpam-6583	366	10	n	n	PRON
ejpam-6583	366	11	≥	≥	NOUN
ejpam-6583	366	12	0	0	NUM
ejpam-6583	366	13	.	.	PUNCT
ejpam-6583	367	1	we	we	PRON
ejpam-6583	367	2	have	have	VERB
ejpam-6583	367	3	δb	δb	NOUN
ejpam-6583	367	4	r⊕d	r⊕d	NOUN
ejpam-6583	367	5	(	(	PUNCT
ejpam-6583	367	6	xn	xn	PROPN
ejpam-6583	367	7	,	,	PUNCT
ejpam-6583	367	8	xn+1	xn+1	NUM
ejpam-6583	367	9	)	)	PUNCT
ejpam-6583	367	10	=	=	PUNCT
ejpam-6583	367	11	δb	δb	X
ejpam-6583	367	12	r⊕d	r⊕d	NOUN
ejpam-6583	367	13	(	(	PUNCT
ejpam-6583	367	14	f	f	PROPN
ejpam-6583	367	15	(	(	PUNCT
ejpam-6583	367	16	xn−1),f	xn−1),f	PROPN
ejpam-6583	367	17	(	(	PUNCT
ejpam-6583	367	18	xn	xn	PROPN
ejpam-6583	367	19	)	)	PUNCT
ejpam-6583	367	20	)	)	PUNCT
ejpam-6583	368	1	g.	g.	PROPN
ejpam-6583	368	2	albeladi	albeladi	PROPN
ejpam-6583	368	3	,	,	PUNCT
ejpam-6583	368	4	s.	s.	PROPN
ejpam-6583	368	5	omran	omran	PROPN
ejpam-6583	368	6	/	/	SYM
ejpam-6583	368	7	eur	eur	PROPN
ejpam-6583	368	8	.	.	PUNCT
ejpam-6583	369	1	j.	j.	PROPN
ejpam-6583	369	2	pure	pure	PROPN
ejpam-6583	369	3	appl	appl	PROPN
ejpam-6583	369	4	.	.	PROPN
ejpam-6583	369	5	math	math	PROPN
ejpam-6583	369	6	,	,	PUNCT
ejpam-6583	369	7	18	18	NUM
ejpam-6583	369	8	(	(	PUNCT
ejpam-6583	369	9	3	3	NUM
ejpam-6583	369	10	)	)	PUNCT
ejpam-6583	369	11	(	(	PUNCT
ejpam-6583	369	12	2025	2025	NUM
ejpam-6583	369	13	)	)	PUNCT
ejpam-6583	369	14	,	,	PUNCT
ejpam-6583	369	15	6583	6583	NUM
ejpam-6583	369	16	16	16	NUM
ejpam-6583	369	17	of	of	ADP
ejpam-6583	369	18	27	27	NUM
ejpam-6583	369	19	≾	≾	PROPN
ejpam-6583	369	20	diag	diag	NOUN
ejpam-6583	369	21	(	(	PUNCT
ejpam-6583	369	22	α1	α1	PROPN
ejpam-6583	369	23	,	,	PUNCT
ejpam-6583	369	24	·	·	PUNCT
ejpam-6583	369	25	·	·	PUNCT
ejpam-6583	369	26	·	·	PUNCT
ejpam-6583	369	27	,	,	PUNCT
ejpam-6583	369	28	αd	αd	PROPN
ejpam-6583	369	29	)	)	PUNCT
ejpam-6583	369	30	[	[	PUNCT
ejpam-6583	369	31	δb	δb	NOUN
ejpam-6583	369	32	r⊕d	r⊕d	NOUN
ejpam-6583	369	33	(	(	PUNCT
ejpam-6583	369	34	f	f	X
ejpam-6583	369	35	(	(	PUNCT
ejpam-6583	369	36	xn−1	xn−1	PROPN
ejpam-6583	369	37	)	)	PUNCT
ejpam-6583	369	38	,	,	PUNCT
ejpam-6583	369	39	xn	xn	PUNCT
ejpam-6583	369	40	)	)	PUNCT
ejpam-6583	370	1	+	+	CCONJ
ejpam-6583	370	2	δb	δb	NOUN
ejpam-6583	370	3	r⊕d	r⊕d	NOUN
ejpam-6583	370	4	(	(	PUNCT
ejpam-6583	370	5	f	f	X
ejpam-6583	370	6	(	(	PUNCT
ejpam-6583	370	7	xn	xn	PROPN
ejpam-6583	370	8	)	)	PUNCT
ejpam-6583	370	9	,	,	PUNCT
ejpam-6583	370	10	xn−1	xn−1	PROPN
ejpam-6583	370	11	)	)	PUNCT
ejpam-6583	370	12	]	]	PUNCT
ejpam-6583	371	1	=	=	PUNCT
ejpam-6583	371	2	diag	diag	PROPN
ejpam-6583	371	3	(	(	PUNCT
ejpam-6583	371	4	α1	α1	PROPN
ejpam-6583	371	5	,	,	PUNCT
ejpam-6583	371	6	·	·	PUNCT
ejpam-6583	371	7	·	·	PUNCT
ejpam-6583	371	8	·	·	PUNCT
ejpam-6583	371	9	,	,	PUNCT
ejpam-6583	371	10	αd	αd	PROPN
ejpam-6583	371	11	)	)	PUNCT
ejpam-6583	372	1	[	[	X
ejpam-6583	372	2	δb	δb	X
ejpam-6583	372	3	r⊕d	r⊕d	NOUN
ejpam-6583	372	4	(	(	PUNCT
ejpam-6583	372	5	xn	xn	PROPN
ejpam-6583	372	6	,	,	PUNCT
ejpam-6583	372	7	xn	xn	PUNCT
ejpam-6583	372	8	)	)	PUNCT
ejpam-6583	372	9	+	+	CCONJ
ejpam-6583	372	10	δb	δb	NOUN
ejpam-6583	372	11	r⊕d	r⊕d	NOUN
ejpam-6583	372	12	(	(	PUNCT
ejpam-6583	372	13	xn+1	xn+1	NUM
ejpam-6583	372	14	,	,	PUNCT
ejpam-6583	372	15	xn−1	xn−1	PROPN
ejpam-6583	372	16	)	)	PUNCT
ejpam-6583	372	17	]	]	PUNCT
ejpam-6583	373	1	=	=	PUNCT
ejpam-6583	373	2	diag	diag	X
ejpam-6583	373	3	(	(	PUNCT
ejpam-6583	373	4	α1	α1	PROPN
ejpam-6583	373	5	,	,	PUNCT
ejpam-6583	373	6	·	·	PUNCT
ejpam-6583	373	7	·	·	PUNCT
ejpam-6583	373	8	·	·	PUNCT
ejpam-6583	373	9	,	,	PUNCT
ejpam-6583	373	10	αd	αd	PROPN
ejpam-6583	373	11	)	)	PUNCT
ejpam-6583	373	12	δb	δb	NOUN
ejpam-6583	373	13	r⊕d	r⊕d	NOUN
ejpam-6583	373	14	(	(	PUNCT
ejpam-6583	373	15	f	f	PROPN
ejpam-6583	373	16	(	(	PUNCT
ejpam-6583	373	17	xn),f	xn),f	PROPN
ejpam-6583	373	18	(	(	PUNCT
ejpam-6583	373	19	xn−2	xn−2	PROPN
ejpam-6583	373	20	)	)	PUNCT
ejpam-6583	373	21	)	)	PUNCT
ejpam-6583	374	1	≾	≾	NOUN
ejpam-6583	374	2	diag	diag	NOUN
ejpam-6583	374	3	(	(	PUNCT
ejpam-6583	374	4	sα1	sα1	PROPN
ejpam-6583	374	5	,	,	PUNCT
ejpam-6583	374	6	·	·	PUNCT
ejpam-6583	374	7	·	·	PUNCT
ejpam-6583	374	8	·	·	PUNCT
ejpam-6583	374	9	,	,	PUNCT
ejpam-6583	374	10	sαd	sαd	NOUN
ejpam-6583	374	11	)	)	PUNCT
ejpam-6583	374	12	[	[	PUNCT
ejpam-6583	374	13	δb	δb	NOUN
ejpam-6583	374	14	r⊕d	r⊕d	NOUN
ejpam-6583	374	15	(	(	PUNCT
ejpam-6583	374	16	f	f	PROPN
ejpam-6583	374	17	(	(	PUNCT
ejpam-6583	374	18	xn),f	xn),f	PROPN
ejpam-6583	374	19	(	(	PUNCT
ejpam-6583	374	20	xn−1	xn−1	PROPN
ejpam-6583	374	21	)	)	PUNCT
ejpam-6583	374	22	)	)	PUNCT
ejpam-6583	375	1	+	+	CCONJ
ejpam-6583	375	2	δb	δb	NOUN
ejpam-6583	375	3	r⊕d	r⊕d	NOUN
ejpam-6583	375	4	(	(	PUNCT
ejpam-6583	375	5	f	f	PROPN
ejpam-6583	375	6	(	(	PUNCT
ejpam-6583	375	7	xn−1),f	xn−1),f	PROPN
ejpam-6583	375	8	(	(	PUNCT
ejpam-6583	375	9	xn−2	xn−2	PROPN
ejpam-6583	375	10	)	)	PUNCT
ejpam-6583	375	11	)	)	PUNCT
ejpam-6583	375	12	]	]	PUNCT
ejpam-6583	376	1	=	=	PUNCT
ejpam-6583	376	2	diag	diag	X
ejpam-6583	376	3	(	(	PUNCT
ejpam-6583	376	4	sα1	sα1	PROPN
ejpam-6583	376	5	,	,	PUNCT
ejpam-6583	376	6	·	·	PUNCT
ejpam-6583	376	7	·	·	PUNCT
ejpam-6583	376	8	·	·	PUNCT
ejpam-6583	376	9	,	,	PUNCT
ejpam-6583	376	10	sαd	sαd	NOUN
ejpam-6583	376	11	)	)	PUNCT
ejpam-6583	376	12	[	[	PUNCT
ejpam-6583	376	13	δb	δb	NOUN
ejpam-6583	376	14	r⊕d	r⊕d	NOUN
ejpam-6583	376	15	(	(	PUNCT
ejpam-6583	376	16	xn+1	xn+1	PROPN
ejpam-6583	376	17	,	,	PUNCT
ejpam-6583	376	18	xn	xn	PUNCT
ejpam-6583	376	19	)	)	PUNCT
ejpam-6583	377	1	+	+	CCONJ
ejpam-6583	377	2	δb	δb	NOUN
ejpam-6583	377	3	r⊕d	r⊕d	NOUN
ejpam-6583	377	4	(	(	PUNCT
ejpam-6583	377	5	xn	xn	PROPN
ejpam-6583	377	6	,	,	PUNCT
ejpam-6583	377	7	xn−1	xn−1	PROPN
ejpam-6583	377	8	)	)	PUNCT
ejpam-6583	377	9	]	]	PUNCT
ejpam-6583	377	10	.	.	PUNCT
ejpam-6583	378	1	thus	thus	ADV
ejpam-6583	378	2	,	,	PUNCT
ejpam-6583	378	3	δb	δb	NOUN
ejpam-6583	378	4	r⊕d	r⊕d	NOUN
ejpam-6583	378	5	(	(	PUNCT
ejpam-6583	378	6	xn	xn	PROPN
ejpam-6583	378	7	,	,	PUNCT
ejpam-6583	378	8	xn+1	xn+1	X
ejpam-6583	378	9	)	)	PUNCT
ejpam-6583	378	10	≾	≾	NOUN
ejpam-6583	378	11	diag	diag	NOUN
ejpam-6583	378	12	(	(	PUNCT
ejpam-6583	378	13	sα1	sα1	X
ejpam-6583	378	14	(	(	PUNCT
ejpam-6583	378	15	1−sα1	1−sα1	NUM
ejpam-6583	378	16	)	)	PUNCT
ejpam-6583	378	17	,	,	PUNCT
ejpam-6583	378	18	·	·	PUNCT
ejpam-6583	378	19	·	·	PUNCT
ejpam-6583	378	20	·	·	PUNCT
ejpam-6583	378	21	,	,	PUNCT
ejpam-6583	378	22	sαd	sαd	X
ejpam-6583	378	23	(	(	PUNCT
ejpam-6583	378	24	1−sαd	1−sαd	NOUN
ejpam-6583	378	25	)	)	PUNCT
ejpam-6583	378	26	)	)	PUNCT
ejpam-6583	378	27	δb	δb	NOUN
ejpam-6583	378	28	r⊕d	r⊕d	NOUN
ejpam-6583	378	29	(	(	PUNCT
ejpam-6583	378	30	xn−1	xn−1	PROPN
ejpam-6583	378	31	,	,	PUNCT
ejpam-6583	378	32	xn	xn	PROPN
ejpam-6583	378	33	)	)	PUNCT
ejpam-6583	378	34	,	,	PUNCT
ejpam-6583	378	35	put	put	VERB
ejpam-6583	378	36	(	(	PUNCT
ejpam-6583	378	37	sαi	sαi	PROPN
ejpam-6583	378	38	(	(	PUNCT
ejpam-6583	378	39	1−	1−	NUM
ejpam-6583	378	40	sαi	sαi	NOUN
ejpam-6583	378	41	)	)	PUNCT
ejpam-6583	378	42	=	=	PUNCT
ejpam-6583	378	43	λi	λi	X
ejpam-6583	378	44	)	)	PUNCT
ejpam-6583	378	45	=	=	SYM
ejpam-6583	378	46	diag(λ1	diag(λ1	NOUN
ejpam-6583	378	47	,	,	PUNCT
ejpam-6583	378	48	·	·	PUNCT
ejpam-6583	378	49	·	·	PUNCT
ejpam-6583	378	50	·	·	PUNCT
ejpam-6583	378	51	,	,	PUNCT
ejpam-6583	378	52	λd	λd	NOUN
ejpam-6583	378	53	)	)	PUNCT
ejpam-6583	378	54	δbr⊕d	δbr⊕d	NOUN
ejpam-6583	378	55	(	(	PUNCT
ejpam-6583	378	56	xn−1	xn−1	PROPN
ejpam-6583	378	57	,	,	PUNCT
ejpam-6583	378	58	xn	xn	PROPN
ejpam-6583	378	59	)	)	PUNCT
ejpam-6583	378	60	,	,	PUNCT
ejpam-6583	378	61	where	where	SCONJ
ejpam-6583	378	62	(	(	PUNCT
ejpam-6583	378	63	λ1	λ1	ADJ
ejpam-6583	378	64	,	,	PUNCT
ejpam-6583	378	65	,	,	PUNCT
ejpam-6583	378	66	·	·	PUNCT
ejpam-6583	378	67	·	·	PUNCT
ejpam-6583	378	68	·	·	PUNCT
ejpam-6583	378	69	,	,	PUNCT
ejpam-6583	378	70	λd	λd	NOUN
ejpam-6583	378	71	)	)	PUNCT
ejpam-6583	378	72	≺	≺	NOUN
ejpam-6583	378	73	ir	ir	PROPN
ejpam-6583	378	74	⊕d	⊕d	NOUN
ejpam-6583	378	75	+	+	CCONJ
ejpam-6583	378	76	≾	≾	PROPN
ejpam-6583	378	77	diag(λ21	diag(λ21	PROPN
ejpam-6583	378	78	,	,	PUNCT
ejpam-6583	378	79	·	·	PUNCT
ejpam-6583	378	80	·	·	PUNCT
ejpam-6583	378	81	·	·	PUNCT
ejpam-6583	378	82	,	,	PUNCT
ejpam-6583	378	83	λ2d	λ2d	NOUN
ejpam-6583	378	84	)	)	PUNCT
ejpam-6583	378	85	δbr⊕d	δbr⊕d	NOUN
ejpam-6583	378	86	(	(	PUNCT
ejpam-6583	378	87	xn−2	xn−2	PROPN
ejpam-6583	378	88	,	,	PUNCT
ejpam-6583	378	89	xn−1	xn−1	PROPN
ejpam-6583	378	90	)	)	PUNCT
ejpam-6583	378	91	≾	≾	PROPN
ejpam-6583	378	92	diag(λ31	diag(λ31	PROPN
ejpam-6583	378	93	,	,	PUNCT
ejpam-6583	378	94	·	·	PUNCT
ejpam-6583	378	95	·	·	PUNCT
ejpam-6583	378	96	·	·	PUNCT
ejpam-6583	378	97	,	,	PUNCT
ejpam-6583	378	98	λ3d	λ3d	X
ejpam-6583	378	99	)	)	PUNCT
ejpam-6583	378	100	δbr⊕d	δbr⊕d	NOUN
ejpam-6583	378	101	(	(	PUNCT
ejpam-6583	378	102	xn−3	xn−3	PROPN
ejpam-6583	378	103	,	,	PUNCT
ejpam-6583	378	104	xn−2	xn−2	PROPN
ejpam-6583	378	105	)	)	PUNCT
ejpam-6583	378	106	...	...	PUNCT
ejpam-6583	379	1	≾	≾	PROPN
ejpam-6583	379	2	diag(λn1	diag(λn1	PROPN
ejpam-6583	379	3	,	,	PUNCT
ejpam-6583	379	4	·	·	PUNCT
ejpam-6583	379	5	·	·	PUNCT
ejpam-6583	379	6	·	·	PUNCT
ejpam-6583	379	7	,	,	PUNCT
ejpam-6583	379	8	λnd	λnd	X
ejpam-6583	379	9	)	)	PUNCT
ejpam-6583	379	10	δbr⊕d	δbr⊕d	NOUN
ejpam-6583	379	11	(	(	PUNCT
ejpam-6583	379	12	x0	x0	PROPN
ejpam-6583	379	13	,	,	PUNCT
ejpam-6583	379	14	x1	x1	PROPN
ejpam-6583	379	15	)	)	PUNCT
ejpam-6583	379	16	.	.	PUNCT
ejpam-6583	379	17	let	let	VERB
ejpam-6583	379	18	us	we	PRON
ejpam-6583	379	19	prove	prove	VERB
ejpam-6583	379	20	that	that	SCONJ
ejpam-6583	379	21	{	{	PUNCT
ejpam-6583	379	22	xn	xn	X
ejpam-6583	379	23	}	}	PUNCT
ejpam-6583	379	24	is	be	AUX
ejpam-6583	379	25	a	a	DET
ejpam-6583	379	26	cauchy	cauchy	ADJ
ejpam-6583	379	27	sequence	sequence	NOUN
ejpam-6583	379	28	.	.	PUNCT
ejpam-6583	380	1	suppose	suppose	VERB
ejpam-6583	380	2	that	that	SCONJ
ejpam-6583	380	3	n	n	PROPN
ejpam-6583	380	4	>	>	X
ejpam-6583	380	5	m	m	PROPN
ejpam-6583	380	6	,	,	PUNCT
ejpam-6583	380	7	then	then	ADV
ejpam-6583	380	8	from	from	ADP
ejpam-6583	380	9	(	(	PUNCT
ejpam-6583	380	10	2	2	NUM
ejpam-6583	380	11	)	)	PUNCT
ejpam-6583	380	12	and	and	CCONJ
ejpam-6583	380	13	the	the	DET
ejpam-6583	380	14	triangle	triangle	NOUN
ejpam-6583	380	15	inequality	inequality	NOUN
ejpam-6583	380	16	property	property	NOUN
ejpam-6583	380	17	,	,	PUNCT
ejpam-6583	380	18	we	we	PRON
ejpam-6583	380	19	can	can	AUX
ejpam-6583	380	20	write	write	VERB
ejpam-6583	380	21	as	as	ADP
ejpam-6583	380	22	:	:	PUNCT
ejpam-6583	380	23	δb	δb	NOUN
ejpam-6583	380	24	r⊕d	r⊕d	NOUN
ejpam-6583	380	25	(	(	PUNCT
ejpam-6583	380	26	xm	xm	PROPN
ejpam-6583	380	27	,	,	PUNCT
ejpam-6583	380	28	xn	xn	PROPN
ejpam-6583	380	29	)	)	PUNCT
ejpam-6583	381	1	≾	≾	PROPN
ejpam-6583	381	2	s	s	PART
ejpam-6583	381	3	[	[	PUNCT
ejpam-6583	381	4	δb	δb	NOUN
ejpam-6583	381	5	r⊕d	r⊕d	NOUN
ejpam-6583	381	6	(	(	PUNCT
ejpam-6583	381	7	xm	xm	PROPN
ejpam-6583	381	8	,	,	PUNCT
ejpam-6583	381	9	xm+1	xm+1	PROPN
ejpam-6583	381	10	)	)	PUNCT
ejpam-6583	381	11	+	+	CCONJ
ejpam-6583	381	12	δb	δb	NOUN
ejpam-6583	381	13	r⊕d	r⊕d	NOUN
ejpam-6583	381	14	(	(	PUNCT
ejpam-6583	381	15	xm+1	xm+1	PROPN
ejpam-6583	381	16	,	,	PUNCT
ejpam-6583	381	17	xn	xn	PROPN
ejpam-6583	381	18	)	)	PUNCT
ejpam-6583	381	19	]	]	PUNCT
ejpam-6583	382	1	≾	≾	NOUN
ejpam-6583	382	2	sδb	sδb	VERB
ejpam-6583	382	3	r⊕d	r⊕d	NOUN
ejpam-6583	382	4	(	(	PUNCT
ejpam-6583	382	5	xm	xm	PROPN
ejpam-6583	382	6	,	,	PUNCT
ejpam-6583	382	7	xm+1	xm+1	PROPN
ejpam-6583	382	8	)	)	PUNCT
ejpam-6583	382	9	+	+	CCONJ
ejpam-6583	382	10	s2	s2	NOUN
ejpam-6583	382	11	[	[	PUNCT
ejpam-6583	382	12	δb	δb	NOUN
ejpam-6583	382	13	r⊕d	r⊕d	NOUN
ejpam-6583	382	14	(	(	PUNCT
ejpam-6583	382	15	xm+1	xm+1	PROPN
ejpam-6583	382	16	,	,	PUNCT
ejpam-6583	382	17	xm+2	xm+2	PROPN
ejpam-6583	382	18	)	)	PUNCT
ejpam-6583	382	19	+	+	CCONJ
ejpam-6583	382	20	δb	δb	NOUN
ejpam-6583	382	21	r⊕d	r⊕d	NOUN
ejpam-6583	382	22	(	(	PUNCT
ejpam-6583	382	23	xm+2	xm+2	PROPN
ejpam-6583	382	24	,	,	PUNCT
ejpam-6583	382	25	xn	xn	PROPN
ejpam-6583	382	26	)	)	PUNCT
ejpam-6583	382	27	]	]	PUNCT
ejpam-6583	383	1	≾	≾	NOUN
ejpam-6583	383	2	sδb	sδb	VERB
ejpam-6583	383	3	r⊕d	r⊕d	NOUN
ejpam-6583	383	4	(	(	PUNCT
ejpam-6583	383	5	xm	xm	PROPN
ejpam-6583	383	6	,	,	PUNCT
ejpam-6583	383	7	xm+1	xm+1	PROPN
ejpam-6583	383	8	)	)	PUNCT
ejpam-6583	383	9	+	+	CCONJ
ejpam-6583	383	10	s2δb	s2δb	SYM
ejpam-6583	383	11	r⊕d	r⊕d	NOUN
ejpam-6583	383	12	(	(	PUNCT
ejpam-6583	383	13	xm+1	xm+1	PROPN
ejpam-6583	383	14	,	,	PUNCT
ejpam-6583	383	15	xm+2	xm+2	PROPN
ejpam-6583	383	16	)	)	PUNCT
ejpam-6583	383	17	+	+	CCONJ
ejpam-6583	383	18	s3	s3	PROPN
ejpam-6583	383	19	[	[	PUNCT
ejpam-6583	383	20	δb	δb	X
ejpam-6583	383	21	r⊕d	r⊕d	NOUN
ejpam-6583	383	22	(	(	PUNCT
ejpam-6583	383	23	xm+2	xm+2	PROPN
ejpam-6583	383	24	,	,	PUNCT
ejpam-6583	383	25	xm+3	xm+3	NUM
ejpam-6583	383	26	)	)	PUNCT
ejpam-6583	383	27	+	+	CCONJ
ejpam-6583	383	28	δb	δb	NOUN
ejpam-6583	383	29	r⊕d	r⊕d	NOUN
ejpam-6583	383	30	(	(	PUNCT
ejpam-6583	383	31	xm+3	xm+3	NUM
ejpam-6583	383	32	,	,	PUNCT
ejpam-6583	383	33	xn	xn	PROPN
ejpam-6583	383	34	)	)	PUNCT
ejpam-6583	383	35	]	]	PUNCT
ejpam-6583	383	36	...	...	PUNCT
ejpam-6583	384	1	≾	≾	NOUN
ejpam-6583	384	2	sδb	sδb	VERB
ejpam-6583	384	3	r⊕d	r⊕d	NOUN
ejpam-6583	384	4	(	(	PUNCT
ejpam-6583	384	5	xm	xm	PROPN
ejpam-6583	384	6	,	,	PUNCT
ejpam-6583	384	7	xm+1	xm+1	PROPN
ejpam-6583	384	8	)	)	PUNCT
ejpam-6583	384	9	+	+	CCONJ
ejpam-6583	384	10	s2δb	s2δb	SYM
ejpam-6583	384	11	r⊕d	r⊕d	NOUN
ejpam-6583	384	12	(	(	PUNCT
ejpam-6583	384	13	xm+1	xm+1	PROPN
ejpam-6583	384	14	,	,	PUNCT
ejpam-6583	384	15	xm+2	xm+2	PROPN
ejpam-6583	384	16	)	)	PUNCT
ejpam-6583	384	17	+	+	CCONJ
ejpam-6583	384	18	·	·	PUNCT
ejpam-6583	384	19	·	·	PUNCT
ejpam-6583	384	20	·	·	PUNCT
ejpam-6583	384	21	+	+	NUM
ejpam-6583	384	22	sn−mδb	sn−mδb	NOUN
ejpam-6583	384	23	r⊕d	r⊕d	NOUN
ejpam-6583	384	24	(	(	PUNCT
ejpam-6583	384	25	xn−1	xn−1	PROPN
ejpam-6583	384	26	,	,	PUNCT
ejpam-6583	384	27	xn	xn	PUNCT
ejpam-6583	384	28	)	)	PUNCT
ejpam-6583	385	1	=	=	SYM
ejpam-6583	385	2	diag(sλm1	diag(sλm1	INTJ
ejpam-6583	385	3	,	,	PUNCT
ejpam-6583	385	4	sλ	sλ	NOUN
ejpam-6583	385	5	m	m	NOUN
ejpam-6583	385	6	2	2	NUM
ejpam-6583	385	7	,	,	PUNCT
ejpam-6583	385	8	·	·	PUNCT
ejpam-6583	385	9	·	·	PUNCT
ejpam-6583	385	10	·	·	PUNCT
ejpam-6583	385	11	,	,	PUNCT
ejpam-6583	385	12	sλmd	sλmd	NOUN
ejpam-6583	385	13	)	)	PUNCT
ejpam-6583	385	14	δb	δb	NOUN
ejpam-6583	385	15	r⊕d	r⊕d	NOUN
ejpam-6583	385	16	(	(	PUNCT
ejpam-6583	385	17	x0	x0	PROPN
ejpam-6583	385	18	,	,	PUNCT
ejpam-6583	385	19	x1	x1	PROPN
ejpam-6583	385	20	)	)	PUNCT
ejpam-6583	385	21	+	+	CCONJ
ejpam-6583	386	1	diag(s2λm+1	diag(s2λm+1	PROPN
ejpam-6583	386	2	1	1	NUM
ejpam-6583	386	3	,	,	PUNCT
ejpam-6583	386	4	s2λm+1	s2λm+1	VERB
ejpam-6583	386	5	2	2	NUM
ejpam-6583	386	6	,	,	PUNCT
ejpam-6583	386	7	·	·	PUNCT
ejpam-6583	386	8	·	·	PUNCT
ejpam-6583	386	9	·	·	PUNCT
ejpam-6583	386	10	,	,	PUNCT
ejpam-6583	386	11	s2λm+1	s2λm+1	PROPN
ejpam-6583	386	12	d	d	PROPN
ejpam-6583	386	13	)	)	PUNCT
ejpam-6583	386	14	δb	δb	NOUN
ejpam-6583	386	15	r⊕d	r⊕d	NOUN
ejpam-6583	386	16	(	(	PUNCT
ejpam-6583	386	17	x0	x0	PROPN
ejpam-6583	386	18	,	,	PUNCT
ejpam-6583	386	19	x1	x1	PROPN
ejpam-6583	386	20	)	)	PUNCT
ejpam-6583	386	21	+	+	X
ejpam-6583	386	22	·	·	PUNCT
ejpam-6583	386	23	·	·	PUNCT
ejpam-6583	386	24	·	·	PUNCT
ejpam-6583	386	25	+	+	NUM
ejpam-6583	386	26	diag(sn−mλn−1	diag(sn−mλn−1	ADJ
ejpam-6583	386	27	1	1	NUM
ejpam-6583	386	28	,	,	PUNCT
ejpam-6583	386	29	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	386	30	2	2	NUM
ejpam-6583	386	31	,	,	PUNCT
ejpam-6583	386	32	·	·	PUNCT
ejpam-6583	386	33	·	·	PUNCT
ejpam-6583	386	34	·	·	PUNCT
ejpam-6583	386	35	,	,	PUNCT
ejpam-6583	386	36	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	386	37	d	d	PROPN
ejpam-6583	386	38	)	)	PUNCT
ejpam-6583	386	39	δb	δb	NOUN
ejpam-6583	386	40	r⊕d	r⊕d	NOUN
ejpam-6583	386	41	(	(	PUNCT
ejpam-6583	386	42	x0	x0	PROPN
ejpam-6583	386	43	,	,	PUNCT
ejpam-6583	386	44	x1	x1	PROPN
ejpam-6583	386	45	)	)	PUNCT
ejpam-6583	387	1	=	=	SYM
ejpam-6583	387	2	(	(	PUNCT
ejpam-6583	387	3	(	(	PUNCT
ejpam-6583	387	4	sλm1	sλm1	PROPN
ejpam-6583	387	5	+	+	CCONJ
ejpam-6583	387	6	s2λm+1	s2λm+1	VERB
ejpam-6583	387	7	1	1	NUM
ejpam-6583	387	8	+	+	CCONJ
ejpam-6583	387	9	·	·	PUNCT
ejpam-6583	387	10	·	·	PUNCT
ejpam-6583	387	11	·	·	PUNCT
ejpam-6583	387	12	+	+	NUM
ejpam-6583	387	13	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	387	14	1	1	NUM
ejpam-6583	387	15	)	)	PUNCT
ejpam-6583	387	16	δb	δb	NOUN
ejpam-6583	387	17	r⊕d	r⊕d	NOUN
ejpam-6583	387	18	(	(	PUNCT
ejpam-6583	387	19	x0	x0	PROPN
ejpam-6583	387	20	,	,	PUNCT
ejpam-6583	387	21	x1	x1	PROPN
ejpam-6583	387	22	)	)	PUNCT
ejpam-6583	387	23	,	,	PUNCT
ejpam-6583	387	24	(	(	PUNCT
ejpam-6583	387	25	sλ	sλ	NOUN
ejpam-6583	387	26	m	m	VERB
ejpam-6583	387	27	2	2	NUM
ejpam-6583	387	28	+	+	CCONJ
ejpam-6583	387	29	s2λm+1	s2λm+1	VERB
ejpam-6583	387	30	2	2	NUM
ejpam-6583	387	31	+	+	CCONJ
ejpam-6583	387	32	·	·	PUNCT
ejpam-6583	387	33	·	·	PUNCT
ejpam-6583	387	34	·	·	PUNCT
ejpam-6583	387	35	+	+	NUM
ejpam-6583	387	36	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	387	37	2	2	NUM
ejpam-6583	387	38	)	)	PUNCT
ejpam-6583	387	39	δb	δb	NOUN
ejpam-6583	387	40	r⊕d	r⊕d	NOUN
ejpam-6583	387	41	(	(	PUNCT
ejpam-6583	387	42	x0	x0	PROPN
ejpam-6583	387	43	,	,	PUNCT
ejpam-6583	387	44	x1	x1	PROPN
ejpam-6583	387	45	)	)	PUNCT
ejpam-6583	387	46	,	,	PUNCT
ejpam-6583	387	47	·	·	PUNCT
ejpam-6583	387	48	·	·	PUNCT
ejpam-6583	387	49	·	·	PUNCT
ejpam-6583	387	50	,	,	PUNCT
ejpam-6583	387	51	(	(	PUNCT
ejpam-6583	387	52	sλmd	sλmd	NOUN
ejpam-6583	387	53	+	+	CCONJ
ejpam-6583	387	54	s2λm+1	s2λm+1	PROPN
ejpam-6583	387	55	d	d	PROPN
ejpam-6583	387	56	+	+	PROPN
ejpam-6583	387	57	·	·	PUNCT
ejpam-6583	387	58	·	·	PUNCT
ejpam-6583	387	59	·	·	PUNCT
ejpam-6583	387	60	+	+	NUM
ejpam-6583	387	61	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	387	62	d	d	NOUN
ejpam-6583	387	63	)	)	PUNCT
ejpam-6583	387	64	δb	δb	NOUN
ejpam-6583	387	65	r⊕d	r⊕d	NOUN
ejpam-6583	387	66	(	(	PUNCT
ejpam-6583	387	67	x0	x0	PROPN
ejpam-6583	387	68	,	,	PUNCT
ejpam-6583	387	69	x1	x1	PROPN
ejpam-6583	387	70	)	)	PUNCT
ejpam-6583	387	71	)	)	PUNCT
ejpam-6583	388	1	g.	g.	PROPN
ejpam-6583	388	2	albeladi	albeladi	PROPN
ejpam-6583	388	3	,	,	PUNCT
ejpam-6583	388	4	s.	s.	PROPN
ejpam-6583	388	5	omran	omran	PROPN
ejpam-6583	388	6	/	/	SYM
ejpam-6583	388	7	eur	eur	PROPN
ejpam-6583	388	8	.	.	PUNCT
ejpam-6583	389	1	j.	j.	PROPN
ejpam-6583	389	2	pure	pure	PROPN
ejpam-6583	389	3	appl	appl	PROPN
ejpam-6583	389	4	.	.	PROPN
ejpam-6583	389	5	math	math	PROPN
ejpam-6583	389	6	,	,	PUNCT
ejpam-6583	389	7	18	18	NUM
ejpam-6583	389	8	(	(	PUNCT
ejpam-6583	389	9	3	3	NUM
ejpam-6583	389	10	)	)	PUNCT
ejpam-6583	389	11	(	(	PUNCT
ejpam-6583	389	12	2025	2025	NUM
ejpam-6583	389	13	)	)	PUNCT
ejpam-6583	389	14	,	,	PUNCT
ejpam-6583	389	15	6583	6583	NUM
ejpam-6583	389	16	17	17	NUM
ejpam-6583	389	17	of	of	ADP
ejpam-6583	389	18	27	27	NUM
ejpam-6583	389	19	=	=	SYM
ejpam-6583	389	20	diag	diag	NOUN
ejpam-6583	389	21	(	(	PUNCT
ejpam-6583	389	22	n−m∑	n−m∑	INTJ
ejpam-6583	389	23	i=1	i=1	PROPN
ejpam-6583	389	24	n−1∑	n−1∑	PROPN
ejpam-6583	389	25	j	j	PROPN
ejpam-6583	389	26	=	=	NOUN
ejpam-6583	389	27	m	m	PROPN
ejpam-6583	389	28	siλj1δ	siλj1δ	ADJ
ejpam-6583	389	29	b	b	PROPN
ejpam-6583	389	30	r⊕d	r⊕d	NOUN
ejpam-6583	389	31	(	(	PUNCT
ejpam-6583	389	32	x0	x0	PROPN
ejpam-6583	389	33	,	,	PUNCT
ejpam-6583	389	34	x1	x1	PROPN
ejpam-6583	389	35	)	)	PUNCT
ejpam-6583	389	36	,	,	PUNCT
ejpam-6583	389	37	n−m∑	n−m∑	PROPN
ejpam-6583	389	38	i=1	i=1	PROPN
ejpam-6583	389	39	n−1∑	n−1∑	PROPN
ejpam-6583	389	40	j	j	X
ejpam-6583	390	1	=	=	PROPN
ejpam-6583	390	2	m	m	VERB
ejpam-6583	390	3	siλj2δ	siλj2δ	NOUN
ejpam-6583	390	4	b	b	PROPN
ejpam-6583	390	5	r⊕d	r⊕d	NOUN
ejpam-6583	390	6	(	(	PUNCT
ejpam-6583	390	7	x0	x0	PROPN
ejpam-6583	390	8	,	,	PUNCT
ejpam-6583	390	9	x1	x1	PROPN
ejpam-6583	390	10	)	)	PUNCT
ejpam-6583	390	11	,	,	PUNCT
ejpam-6583	390	12	·	·	PUNCT
ejpam-6583	390	13	·	·	PUNCT
ejpam-6583	390	14	·	·	PUNCT
ejpam-6583	390	15	,	,	PUNCT
ejpam-6583	390	16	n−m∑	n−m∑	PROPN
ejpam-6583	390	17	i=1	i=1	PROPN
ejpam-6583	390	18	n−1∑	n−1∑	PROPN
ejpam-6583	390	19	j	j	X
ejpam-6583	390	20	=	=	NOUN
ejpam-6583	390	21	m	m	VERB
ejpam-6583	390	22	siλjdδ	siλjdδ	ADJ
ejpam-6583	390	23	b	b	NUM
ejpam-6583	390	24	r⊕d	r⊕d	NOUN
ejpam-6583	390	25	(	(	PUNCT
ejpam-6583	390	26	x0	x0	PROPN
ejpam-6583	390	27	,	,	PUNCT
ejpam-6583	390	28	x1	x1	PROPN
ejpam-6583	390	29	)	)	PUNCT
ejpam-6583	390	30	)	)	PUNCT
ejpam-6583	391	1	=	=	SYM
ejpam-6583	391	2	diag	diag	NOUN
ejpam-6583	391	3	(	(	PUNCT
ejpam-6583	391	4	n−m∑	n−m∑	INTJ
ejpam-6583	391	5	i=1	i=1	PROPN
ejpam-6583	391	6	n−1∑	n−1∑	PROPN
ejpam-6583	391	7	j	j	X
ejpam-6583	391	8	=	=	PROPN
ejpam-6583	391	9	m	m	NOUN
ejpam-6583	391	10	siλj1	siλj1	NOUN
ejpam-6583	391	11	,	,	PUNCT
ejpam-6583	391	12	n−m∑	n−m∑	PROPN
ejpam-6583	391	13	i=1	i=1	PROPN
ejpam-6583	391	14	n−1∑	n−1∑	PROPN
ejpam-6583	391	15	j	j	PROPN
ejpam-6583	391	16	=	=	NOUN
ejpam-6583	391	17	m	m	PROPN
ejpam-6583	391	18	siλj2	siλj2	PROPN
ejpam-6583	391	19	,	,	PUNCT
ejpam-6583	391	20	·	·	PUNCT
ejpam-6583	391	21	·	·	PUNCT
ejpam-6583	391	22	·	·	PUNCT
ejpam-6583	391	23	,	,	PUNCT
ejpam-6583	391	24	n−m∑	n−m∑	PROPN
ejpam-6583	391	25	i=1	i=1	PROPN
ejpam-6583	391	26	n−1∑	n−1∑	PROPN
ejpam-6583	391	27	j	j	X
ejpam-6583	391	28	=	=	NOUN
ejpam-6583	391	29	m	m	NOUN
ejpam-6583	391	30	siλjd	siλjd	NOUN
ejpam-6583	391	31	)	)	PUNCT
ejpam-6583	391	32	δb	δb	NOUN
ejpam-6583	391	33	r⊕d	r⊕d	NOUN
ejpam-6583	391	34	(	(	PUNCT
ejpam-6583	391	35	x0	x0	PROPN
ejpam-6583	391	36	,	,	PUNCT
ejpam-6583	391	37	x1	x1	PROPN
ejpam-6583	391	38	)	)	PUNCT
ejpam-6583	392	1	=	=	SYM
ejpam-6583	392	2	diag	diag	NOUN
ejpam-6583	392	3	(	(	PUNCT
ejpam-6583	392	4	sλm1	sλm1	PROPN
ejpam-6583	392	5	n−m−1∑	n−m−1∑	PROPN
ejpam-6583	392	6	j=0	j=0	PROPN
ejpam-6583	392	7	(	(	PUNCT
ejpam-6583	392	8	sλ1	sλ1	NOUN
ejpam-6583	392	9	)	)	PUNCT
ejpam-6583	392	10	j	j	PROPN
ejpam-6583	392	11	,	,	PUNCT
ejpam-6583	392	12	sλm2	sλm2	PROPN
ejpam-6583	392	13	n−m−1∑	n−m−1∑	PROPN
ejpam-6583	392	14	j=0	j=0	PROPN
ejpam-6583	392	15	(	(	PUNCT
ejpam-6583	392	16	sλ2	sλ2	NOUN
ejpam-6583	392	17	)	)	PUNCT
ejpam-6583	392	18	j	j	PROPN
ejpam-6583	392	19	,	,	PUNCT
ejpam-6583	392	20	·	·	PUNCT
ejpam-6583	392	21	·	·	PUNCT
ejpam-6583	392	22	·	·	PUNCT
ejpam-6583	392	23	,	,	PUNCT
ejpam-6583	392	24	sλmd	sλmd	PROPN
ejpam-6583	392	25	n−m−1∑	n−m−1∑	PROPN
ejpam-6583	392	26	j=0	j=0	PROPN
ejpam-6583	392	27	(	(	PUNCT
ejpam-6583	392	28	sλd	sλd	PROPN
ejpam-6583	392	29	)	)	PUNCT
ejpam-6583	392	30	j	j	PROPN
ejpam-6583	392	31	)	)	PUNCT
ejpam-6583	392	32	δb	δb	NOUN
ejpam-6583	392	33	r⊕d	r⊕d	NOUN
ejpam-6583	392	34	(	(	PUNCT
ejpam-6583	392	35	x0	x0	PROPN
ejpam-6583	392	36	,	,	PUNCT
ejpam-6583	392	37	x1	x1	PROPN
ejpam-6583	392	38	)	)	PUNCT
ejpam-6583	392	39	≾	≾	NOUN
ejpam-6583	392	40	diag	diag	NOUN
ejpam-6583	392	41	(	(	PUNCT
ejpam-6583	392	42	sλm1	sλm1	PROPN
ejpam-6583	392	43	+	+	PROPN
ejpam-6583	392	44	∞∑	∞∑	PROPN
ejpam-6583	392	45	j=0	j=0	PROPN
ejpam-6583	392	46	(	(	PUNCT
ejpam-6583	392	47	sλ1	sλ1	NOUN
ejpam-6583	392	48	)	)	PUNCT
ejpam-6583	392	49	j	j	PROPN
ejpam-6583	392	50	,	,	PUNCT
ejpam-6583	392	51	sλm2	sλm2	PROPN
ejpam-6583	392	52	+	+	PRON
ejpam-6583	392	53	∞∑	∞∑	NUM
ejpam-6583	392	54	j=0	j=0	PROPN
ejpam-6583	392	55	(	(	PUNCT
ejpam-6583	392	56	sλ2	sλ2	NOUN
ejpam-6583	392	57	)	)	PUNCT
ejpam-6583	392	58	j	j	PROPN
ejpam-6583	392	59	,	,	PUNCT
ejpam-6583	392	60	·	·	PUNCT
ejpam-6583	392	61	·	·	PUNCT
ejpam-6583	392	62	·	·	PUNCT
ejpam-6583	392	63	,	,	PUNCT
ejpam-6583	392	64	sλm1	sλm1	PROPN
ejpam-6583	392	65	+	+	PROPN
ejpam-6583	392	66	∞∑	∞∑	PROPN
ejpam-6583	392	67	j=0	j=0	PROPN
ejpam-6583	392	68	(	(	PUNCT
ejpam-6583	392	69	sλd	sλd	PROPN
ejpam-6583	392	70	)	)	PUNCT
ejpam-6583	392	71	j	j	PROPN
ejpam-6583	392	72	)	)	PUNCT
ejpam-6583	392	73	δb	δb	NOUN
ejpam-6583	392	74	r⊕d	r⊕d	NOUN
ejpam-6583	392	75	(	(	PUNCT
ejpam-6583	392	76	x0	x0	PROPN
ejpam-6583	392	77	,	,	PUNCT
ejpam-6583	392	78	x1	x1	PROPN
ejpam-6583	392	79	)	)	PUNCT
ejpam-6583	393	1	=	=	SYM
ejpam-6583	393	2	diag	diag	NOUN
ejpam-6583	393	3	(	(	PUNCT
ejpam-6583	393	4	sλm1	sλm1	PROPN
ejpam-6583	393	5	[	[	PUNCT
ejpam-6583	393	6	1	1	NUM
ejpam-6583	393	7	1−	1−	NUM
ejpam-6583	393	8	sλ1	sλ1	NOUN
ejpam-6583	393	9	]	]	PUNCT
ejpam-6583	393	10	,	,	PUNCT
ejpam-6583	393	11	sλm2	sλm2	PROPN
ejpam-6583	393	12	[	[	PUNCT
ejpam-6583	393	13	1	1	NUM
ejpam-6583	393	14	1−	1−	NUM
ejpam-6583	393	15	sλ2	sλ2	NOUN
ejpam-6583	393	16	]	]	PUNCT
ejpam-6583	393	17	,	,	PUNCT
ejpam-6583	393	18	·	·	PUNCT
ejpam-6583	393	19	·	·	PUNCT
ejpam-6583	393	20	·	·	PUNCT
ejpam-6583	393	21	,	,	PUNCT
ejpam-6583	393	22	sλm1	sλm1	PROPN
ejpam-6583	393	23	[	[	PUNCT
ejpam-6583	393	24	1	1	NUM
ejpam-6583	393	25	1−	1−	NUM
ejpam-6583	393	26	sλd	sλd	NOUN
ejpam-6583	393	27	]	]	PUNCT
ejpam-6583	393	28	)	)	PUNCT
ejpam-6583	393	29	δb	δb	NOUN
ejpam-6583	393	30	r⊕d	r⊕d	NOUN
ejpam-6583	393	31	(	(	PUNCT
ejpam-6583	393	32	x0	x0	PROPN
ejpam-6583	393	33	,	,	PUNCT
ejpam-6583	393	34	x1	x1	PROPN
ejpam-6583	393	35	)	)	PUNCT
ejpam-6583	393	36	≾	≾	NOUN
ejpam-6583	393	37	diag(sλm1	diag(sλm1	NOUN
ejpam-6583	393	38	,	,	PUNCT
ejpam-6583	393	39	sλ	sλ	NOUN
ejpam-6583	393	40	m	m	NOUN
ejpam-6583	393	41	2	2	NUM
ejpam-6583	393	42	,	,	PUNCT
ejpam-6583	393	43	·	·	PUNCT
ejpam-6583	393	44	·	·	PUNCT
ejpam-6583	393	45	·	·	PUNCT
ejpam-6583	393	46	,	,	PUNCT
ejpam-6583	393	47	sλmd	sλmd	NOUN
ejpam-6583	393	48	)	)	PUNCT
ejpam-6583	393	49	diag	diag	NOUN
ejpam-6583	393	50	(	(	PUNCT
ejpam-6583	393	51	[	[	PUNCT
ejpam-6583	393	52	1	1	NUM
ejpam-6583	393	53	1−	1−	NUM
ejpam-6583	393	54	sλ1	sλ1	NOUN
ejpam-6583	393	55	]	]	PUNCT
ejpam-6583	393	56	,	,	PUNCT
ejpam-6583	393	57	[	[	PUNCT
ejpam-6583	393	58	1	1	NUM
ejpam-6583	393	59	1−	1−	NUM
ejpam-6583	393	60	sλ2	sλ2	NOUN
ejpam-6583	393	61	]	]	PUNCT
ejpam-6583	393	62	,	,	PUNCT
ejpam-6583	393	63	·	·	PUNCT
ejpam-6583	393	64	·	·	PUNCT
ejpam-6583	393	65	·	·	PUNCT
ejpam-6583	393	66	,	,	PUNCT
ejpam-6583	393	67	[	[	PUNCT
ejpam-6583	393	68	1	1	NUM
ejpam-6583	393	69	1−	1−	NUM
ejpam-6583	393	70	sλd	sλd	NOUN
ejpam-6583	393	71	]	]	PUNCT
ejpam-6583	393	72	)	)	PUNCT
ejpam-6583	393	73	δb	δb	NOUN
ejpam-6583	393	74	r⊕d	r⊕d	NOUN
ejpam-6583	393	75	(	(	PUNCT
ejpam-6583	393	76	x0	x0	PROPN
ejpam-6583	393	77	,	,	PUNCT
ejpam-6583	393	78	x1	x1	PROPN
ejpam-6583	393	79	)	)	PUNCT
ejpam-6583	393	80	→	→	SYM
ejpam-6583	393	81	0	0	NUM
ejpam-6583	393	82	,	,	PUNCT
ejpam-6583	393	83	as	as	ADP
ejpam-6583	393	84	n	n	CCONJ
ejpam-6583	393	85	,	,	PUNCT
ejpam-6583	393	86	m	m	PROPN
ejpam-6583	393	87	→	→	SYM
ejpam-6583	393	88	+	+	ADJ
ejpam-6583	393	89	∞.	∞.	PROPN
ejpam-6583	393	90	since	since	SCONJ
ejpam-6583	393	91	0̃	0̃	PROPN
ejpam-6583	393	92	≺	≺	NOUN
ejpam-6583	393	93	diag(sλj1	diag(sλj1	PROPN
ejpam-6583	393	94	,	,	PUNCT
ejpam-6583	393	95	sλ	sλ	ADP
ejpam-6583	393	96	j	j	PROPN
ejpam-6583	393	97	2	2	NUM
ejpam-6583	393	98	,	,	PUNCT
ejpam-6583	393	99	·	·	PUNCT
ejpam-6583	393	100	·	·	PUNCT
ejpam-6583	393	101	·	·	PUNCT
ejpam-6583	393	102	,	,	PUNCT
ejpam-6583	393	103	sλ	sλ	ADP
ejpam-6583	393	104	j	j	PROPN
ejpam-6583	393	105	d	d	PROPN
ejpam-6583	393	106	)	)	PUNCT
ejpam-6583	393	107	≺	≺	NOUN
ejpam-6583	393	108	ir	ir	PROPN
ejpam-6583	393	109	⊕d	⊕d	NOUN
ejpam-6583	393	110	+	+	CCONJ
ejpam-6583	393	111	and	and	CCONJ
ejpam-6583	393	112	δb	δb	NOUN
ejpam-6583	393	113	r⊕d	r⊕d	NOUN
ejpam-6583	393	114	(	(	PUNCT
ejpam-6583	393	115	x0	x0	PROPN
ejpam-6583	393	116	,	,	PUNCT
ejpam-6583	393	117	x1	x1	PROPN
ejpam-6583	393	118	)	)	PUNCT
ejpam-6583	393	119	are	be	AUX
ejpam-6583	393	120	fixed	fix	VERB
ejpam-6583	393	121	,	,	PUNCT
ejpam-6583	393	122	it	it	PRON
ejpam-6583	393	123	is	be	AUX
ejpam-6583	393	124	evident	evident	ADJ
ejpam-6583	393	125	that	that	SCONJ
ejpam-6583	393	126	by	by	ADP
ejpam-6583	393	127	selectingm	selectingm	ADJ
ejpam-6583	393	128	sufficiently	sufficiently	ADV
ejpam-6583	393	129	large	large	ADJ
ejpam-6583	393	130	(	(	PUNCT
ejpam-6583	393	131	with	with	ADP
ejpam-6583	393	132	n	n	NOUN
ejpam-6583	393	133	>	>	X
ejpam-6583	393	134	m	m	PROPN
ejpam-6583	393	135	)	)	PUNCT
ejpam-6583	393	136	,	,	PUNCT
ejpam-6583	393	137	we	we	PRON
ejpam-6583	393	138	can	can	AUX
ejpam-6583	393	139	make	make	VERB
ejpam-6583	393	140	δb	δb	NOUN
ejpam-6583	393	141	r⊕d	r⊕d	NOUN
ejpam-6583	393	142	(	(	PUNCT
ejpam-6583	393	143	xn	xn	PROPN
ejpam-6583	393	144	,	,	PUNCT
ejpam-6583	393	145	xm	xm	PROPN
ejpam-6583	393	146	)	)	PUNCT
ejpam-6583	393	147	arbitrarily	arbitrarily	ADV
ejpam-6583	393	148	small	small	ADJ
ejpam-6583	393	149	.	.	PUNCT
ejpam-6583	394	1	this	this	PRON
ejpam-6583	394	2	shows	show	VERB
ejpam-6583	394	3	that	that	SCONJ
ejpam-6583	394	4	{	{	PUNCT
ejpam-6583	394	5	xn	xn	X
ejpam-6583	394	6	}	}	PUNCT
ejpam-6583	394	7	is	be	AUX
ejpam-6583	394	8	a	a	DET
ejpam-6583	394	9	cauchy	cauchy	ADJ
ejpam-6583	394	10	sequence	sequence	NOUN
ejpam-6583	394	11	.	.	PUNCT
ejpam-6583	395	1	finally	finally	ADV
ejpam-6583	395	2	,	,	PUNCT
ejpam-6583	395	3	because	because	SCONJ
ejpam-6583	395	4	(	(	PUNCT
ejpam-6583	395	5	x	x	X
ejpam-6583	395	6	,	,	PUNCT
ejpam-6583	395	7	r⊕d	r⊕d	NOUN
ejpam-6583	395	8	,	,	PUNCT
ejpam-6583	395	9	δb	δb	NOUN
ejpam-6583	395	10	r⊕d	r⊕d	NOUN
ejpam-6583	395	11	)	)	PUNCT
ejpam-6583	395	12	is	be	AUX
ejpam-6583	395	13	complete	complete	ADJ
ejpam-6583	395	14	,	,	PUNCT
ejpam-6583	395	15	there	there	PRON
ejpam-6583	395	16	exists	exist	VERB
ejpam-6583	395	17	some	some	DET
ejpam-6583	395	18	z	z	NOUN
ejpam-6583	395	19	∈	∈	PROPN
ejpam-6583	395	20	x	x	PUNCT
ejpam-6583	395	21	such	such	ADJ
ejpam-6583	395	22	that	that	PRON
ejpam-6583	395	23	xn	xn	PROPN
ejpam-6583	396	1	→	→	SYM
ejpam-6583	396	2	z.	z.	PROPN
ejpam-6583	396	3	to	to	PART
ejpam-6583	396	4	show	show	VERB
ejpam-6583	396	5	that	that	SCONJ
ejpam-6583	396	6	x	x	PRON
ejpam-6583	396	7	has	have	VERB
ejpam-6583	396	8	a	a	DET
ejpam-6583	396	9	fixed	fix	VERB
ejpam-6583	396	10	point	point	NOUN
ejpam-6583	396	11	,	,	PUNCT
ejpam-6583	396	12	we	we	PRON
ejpam-6583	396	13	consider	consider	VERB
ejpam-6583	396	14	the	the	DET
ejpam-6583	396	15	distance	distance	NOUN
ejpam-6583	396	16	δb	δb	NOUN
ejpam-6583	396	17	r⊕d	r⊕d	NOUN
ejpam-6583	396	18	(	(	PUNCT
ejpam-6583	396	19	z	z	NOUN
ejpam-6583	396	20	,	,	PUNCT
ejpam-6583	396	21	f	f	PROPN
ejpam-6583	396	22	(	(	PUNCT
ejpam-6583	396	23	z	z	NOUN
ejpam-6583	396	24	)	)	PUNCT
ejpam-6583	396	25	)	)	PUNCT
ejpam-6583	396	26	.	.	PUNCT
ejpam-6583	397	1	from	from	ADP
ejpam-6583	397	2	the	the	DET
ejpam-6583	397	3	triangle	triangle	NOUN
ejpam-6583	397	4	inequality	inequality	NOUN
ejpam-6583	397	5	and	and	CCONJ
ejpam-6583	397	6	contraction	contraction	NOUN
ejpam-6583	397	7	condition	condition	NOUN
ejpam-6583	397	8	,	,	PUNCT
ejpam-6583	397	9	we	we	PRON
ejpam-6583	397	10	get	get	VERB
ejpam-6583	397	11	δb	δb	ADP
ejpam-6583	397	12	r⊕d	r⊕d	NOUN
ejpam-6583	397	13	(	(	PUNCT
ejpam-6583	397	14	z	z	NOUN
ejpam-6583	397	15	,	,	PUNCT
ejpam-6583	397	16	f	f	PROPN
ejpam-6583	397	17	(	(	PUNCT
ejpam-6583	397	18	z	z	NOUN
ejpam-6583	397	19	)	)	PUNCT
ejpam-6583	397	20	)	)	PUNCT
ejpam-6583	398	1	≾	≾	PROPN
ejpam-6583	398	2	s	s	PART
ejpam-6583	398	3	[	[	PUNCT
ejpam-6583	398	4	δb	δb	NOUN
ejpam-6583	398	5	r⊕d	r⊕d	NOUN
ejpam-6583	398	6	(	(	PUNCT
ejpam-6583	398	7	z	z	NOUN
ejpam-6583	398	8	,	,	PUNCT
ejpam-6583	398	9	xn	xn	PROPN
ejpam-6583	398	10	)	)	PUNCT
ejpam-6583	399	1	+	+	CCONJ
ejpam-6583	399	2	δb	δb	NOUN
ejpam-6583	399	3	r⊕d	r⊕d	NOUN
ejpam-6583	399	4	(	(	PUNCT
ejpam-6583	399	5	xn	xn	PROPN
ejpam-6583	399	6	,	,	PUNCT
ejpam-6583	399	7	f	f	PROPN
ejpam-6583	399	8	(	(	PUNCT
ejpam-6583	399	9	z	z	NOUN
ejpam-6583	399	10	)	)	PUNCT
ejpam-6583	399	11	)	)	PUNCT
ejpam-6583	399	12	]	]	PUNCT
ejpam-6583	400	1	=	=	PUNCT
ejpam-6583	400	2	s	s	X
ejpam-6583	400	3	[	[	PUNCT
ejpam-6583	400	4	δb	δb	NOUN
ejpam-6583	400	5	r⊕d	r⊕d	NOUN
ejpam-6583	400	6	(	(	PUNCT
ejpam-6583	400	7	z	z	NOUN
ejpam-6583	400	8	,	,	PUNCT
ejpam-6583	400	9	xn	xn	PROPN
ejpam-6583	400	10	)	)	PUNCT
ejpam-6583	401	1	+	+	CCONJ
ejpam-6583	401	2	δb	δb	NOUN
ejpam-6583	401	3	r⊕d	r⊕d	NOUN
ejpam-6583	401	4	(	(	PUNCT
ejpam-6583	401	5	f	f	PROPN
ejpam-6583	401	6	(	(	PUNCT
ejpam-6583	401	7	xn−1),f	xn−1),f	PROPN
ejpam-6583	401	8	(	(	PUNCT
ejpam-6583	401	9	z	z	NOUN
ejpam-6583	401	10	)	)	PUNCT
ejpam-6583	401	11	)	)	PUNCT
ejpam-6583	401	12	]	]	PUNCT
ejpam-6583	402	1	≾	≾	PROPN
ejpam-6583	402	2	s	s	X
ejpam-6583	402	3	[	[	PUNCT
ejpam-6583	402	4	δb	δb	NOUN
ejpam-6583	402	5	r⊕d	r⊕d	NOUN
ejpam-6583	402	6	(	(	PUNCT
ejpam-6583	402	7	z	z	NOUN
ejpam-6583	402	8	,	,	PUNCT
ejpam-6583	402	9	xn	xn	PUNCT
ejpam-6583	402	10	)	)	PUNCT
ejpam-6583	403	1	+	+	CCONJ
ejpam-6583	403	2	diag	diag	PROPN
ejpam-6583	403	3	(	(	PUNCT
ejpam-6583	403	4	α1	α1	PROPN
ejpam-6583	403	5	,	,	PUNCT
ejpam-6583	403	6	α2	α2	ADJ
ejpam-6583	403	7	,	,	PUNCT
ejpam-6583	403	8	·	·	PUNCT
ejpam-6583	403	9	·	·	PUNCT
ejpam-6583	403	10	·	·	PUNCT
ejpam-6583	403	11	,	,	PUNCT
ejpam-6583	403	12	αd	αd	PROPN
ejpam-6583	403	13	)	)	PUNCT
ejpam-6583	403	14	(	(	PUNCT
ejpam-6583	403	15	δb	δb	NOUN
ejpam-6583	403	16	r⊕d	r⊕d	NOUN
ejpam-6583	403	17	(	(	PUNCT
ejpam-6583	403	18	f	f	X
ejpam-6583	403	19	(	(	PUNCT
ejpam-6583	403	20	xn−1	xn−1	PROPN
ejpam-6583	403	21	)	)	PUNCT
ejpam-6583	403	22	,	,	PUNCT
ejpam-6583	403	23	z	z	NOUN
ejpam-6583	403	24	)	)	PUNCT
ejpam-6583	403	25	+	+	CCONJ
ejpam-6583	403	26	δb	δb	NOUN
ejpam-6583	403	27	r⊕d	r⊕d	NOUN
ejpam-6583	403	28	(	(	PUNCT
ejpam-6583	403	29	f	f	X
ejpam-6583	403	30	(	(	PUNCT
ejpam-6583	403	31	z	z	NOUN
ejpam-6583	403	32	)	)	PUNCT
ejpam-6583	403	33	,	,	PUNCT
ejpam-6583	403	34	xn−1	xn−1	PROPN
ejpam-6583	403	35	)	)	PUNCT
ejpam-6583	403	36	)	)	PUNCT
ejpam-6583	403	37	]	]	PUNCT
ejpam-6583	404	1	=	=	PUNCT
ejpam-6583	404	2	diag	diag	NOUN
ejpam-6583	404	3	(	(	PUNCT
ejpam-6583	404	4	s(1	s(1	PROPN
ejpam-6583	404	5	+	+	NUM
ejpam-6583	404	6	α1	α1	PROPN
ejpam-6583	404	7	)	)	PUNCT
ejpam-6583	404	8	,	,	PUNCT
ejpam-6583	404	9	s(1	s(1	PROPN
ejpam-6583	404	10	+	+	CCONJ
ejpam-6583	404	11	α2	α2	ADJ
ejpam-6583	404	12	)	)	PUNCT
ejpam-6583	404	13	,	,	PUNCT
ejpam-6583	404	14	·	·	PUNCT
ejpam-6583	404	15	·	·	PUNCT
ejpam-6583	404	16	·	·	PUNCT
ejpam-6583	404	17	,	,	PUNCT
ejpam-6583	404	18	s(1	s(1	PROPN
ejpam-6583	404	19	+	+	CCONJ
ejpam-6583	404	20	αd	αd	PROPN
ejpam-6583	404	21	)	)	PUNCT
ejpam-6583	404	22	)	)	PUNCT
ejpam-6583	404	23	δb	δb	NOUN
ejpam-6583	404	24	r⊕d	r⊕d	NOUN
ejpam-6583	404	25	(	(	PUNCT
ejpam-6583	404	26	xn	xn	PROPN
ejpam-6583	404	27	,	,	PUNCT
ejpam-6583	404	28	z	z	NOUN
ejpam-6583	404	29	)	)	PUNCT
ejpam-6583	405	1	+	+	NOUN
ejpam-6583	405	2	diag	diag	NOUN
ejpam-6583	405	3	(	(	PUNCT
ejpam-6583	405	4	sα1	sα1	PROPN
ejpam-6583	405	5	,	,	PUNCT
ejpam-6583	405	6	sα2	sα2	NOUN
ejpam-6583	405	7	,	,	PUNCT
ejpam-6583	405	8	·	·	PUNCT
ejpam-6583	405	9	·	·	PUNCT
ejpam-6583	405	10	·	·	PUNCT
ejpam-6583	405	11	,	,	PUNCT
ejpam-6583	405	12	sαd	sαd	NOUN
ejpam-6583	405	13	)	)	PUNCT
ejpam-6583	405	14	δb	δb	NOUN
ejpam-6583	405	15	r⊕d	r⊕d	NOUN
ejpam-6583	405	16	(	(	PUNCT
ejpam-6583	405	17	f	f	X
ejpam-6583	405	18	(	(	PUNCT
ejpam-6583	405	19	z	z	NOUN
ejpam-6583	405	20	)	)	PUNCT
ejpam-6583	405	21	,	,	PUNCT
ejpam-6583	405	22	xn−1	xn−1	PROPN
ejpam-6583	405	23	)	)	PUNCT
ejpam-6583	405	24	,	,	PUNCT
ejpam-6583	405	25	since	since	SCONJ
ejpam-6583	405	26	xn	xn	PROPN
ejpam-6583	405	27	→	→	SYM
ejpam-6583	405	28	z	z	NOUN
ejpam-6583	405	29	it	it	PRON
ejpam-6583	405	30	is	be	AUX
ejpam-6583	405	31	clear	clear	ADJ
ejpam-6583	405	32	that	that	SCONJ
ejpam-6583	405	33	δb	δb	NOUN
ejpam-6583	405	34	r⊕d	r⊕d	NOUN
ejpam-6583	405	35	(	(	PUNCT
ejpam-6583	405	36	z	z	NOUN
ejpam-6583	405	37	,	,	PUNCT
ejpam-6583	405	38	f	f	PROPN
ejpam-6583	405	39	(	(	PUNCT
ejpam-6583	405	40	z	z	NOUN
ejpam-6583	405	41	)	)	PUNCT
ejpam-6583	405	42	)	)	PUNCT
ejpam-6583	406	1	=	=	SYM
ejpam-6583	406	2	0	0	PUNCT
ejpam-6583	407	1	=	=	AUX
ejpam-6583	407	2	⇒	⇒	X
ejpam-6583	407	3	f	f	X
ejpam-6583	407	4	(	(	PUNCT
ejpam-6583	407	5	z	z	NOUN
ejpam-6583	407	6	)	)	PUNCT
ejpam-6583	408	1	=	=	SYM
ejpam-6583	408	2	z	z	NOUN
ejpam-6583	408	3	,	,	PUNCT
ejpam-6583	408	4	so	so	ADV
ejpam-6583	408	5	z	z	NOUN
ejpam-6583	408	6	∈	∈	PROPN
ejpam-6583	408	7	x	x	X
ejpam-6583	408	8	is	be	AUX
ejpam-6583	408	9	a	a	DET
ejpam-6583	408	10	fixed	fix	VERB
ejpam-6583	408	11	-	-	PUNCT
ejpam-6583	408	12	point	point	NOUN
ejpam-6583	408	13	of	of	ADP
ejpam-6583	408	14	f	f	PROPN
ejpam-6583	408	15	.	.	PUNCT
ejpam-6583	409	1	to	to	PART
ejpam-6583	409	2	prove	prove	VERB
ejpam-6583	409	3	uniqueness	uniqueness	NOUN
ejpam-6583	409	4	,	,	PUNCT
ejpam-6583	409	5	suppose	suppose	VERB
ejpam-6583	409	6	there	there	PRON
ejpam-6583	409	7	are	be	VERB
ejpam-6583	409	8	two	two	NUM
ejpam-6583	409	9	fixed	fix	VERB
ejpam-6583	409	10	points	point	NOUN
ejpam-6583	410	1	x	x	X
ejpam-6583	410	2	=	=	SYM
ejpam-6583	410	3	f	f	X
ejpam-6583	410	4	(	(	PUNCT
ejpam-6583	410	5	x	x	NOUN
ejpam-6583	410	6	)	)	PUNCT
ejpam-6583	410	7	and	and	CCONJ
ejpam-6583	410	8	y	y	PROPN
ejpam-6583	410	9	=	=	SYM
ejpam-6583	410	10	f	f	PROPN
ejpam-6583	410	11	(	(	PUNCT
ejpam-6583	410	12	y	y	NOUN
ejpam-6583	410	13	)	)	PUNCT
ejpam-6583	410	14	.	.	PUNCT
ejpam-6583	411	1	then	then	ADV
ejpam-6583	411	2	,	,	PUNCT
ejpam-6583	411	3	from	from	ADP
ejpam-6583	411	4	the	the	DET
ejpam-6583	411	5	contraction	contraction	NOUN
ejpam-6583	411	6	condition	condition	NOUN
ejpam-6583	411	7	,	,	PUNCT
ejpam-6583	411	8	we	we	PRON
ejpam-6583	411	9	have	have	VERB
ejpam-6583	411	10	δb	δb	NOUN
ejpam-6583	411	11	r⊕d	r⊕d	NOUN
ejpam-6583	411	12	(	(	PUNCT
ejpam-6583	411	13	x	x	X
ejpam-6583	411	14	,	,	PUNCT
ejpam-6583	411	15	y	y	NOUN
ejpam-6583	411	16	)	)	PUNCT
ejpam-6583	411	17	=	=	PUNCT
ejpam-6583	411	18	δb	δb	X
ejpam-6583	411	19	r⊕d	r⊕d	NOUN
ejpam-6583	411	20	(	(	PUNCT
ejpam-6583	411	21	f	f	PROPN
ejpam-6583	411	22	(	(	PUNCT
ejpam-6583	411	23	x),f	x),f	PROPN
ejpam-6583	411	24	(	(	PUNCT
ejpam-6583	411	25	y	y	NOUN
ejpam-6583	411	26	)	)	PUNCT
ejpam-6583	411	27	)	)	PUNCT
ejpam-6583	412	1	g.	g.	PROPN
ejpam-6583	412	2	albeladi	albeladi	PROPN
ejpam-6583	412	3	,	,	PUNCT
ejpam-6583	412	4	s.	s.	PROPN
ejpam-6583	412	5	omran	omran	PROPN
ejpam-6583	412	6	/	/	SYM
ejpam-6583	412	7	eur	eur	PROPN
ejpam-6583	412	8	.	.	PUNCT
ejpam-6583	413	1	j.	j.	PROPN
ejpam-6583	413	2	pure	pure	PROPN
ejpam-6583	413	3	appl	appl	PROPN
ejpam-6583	413	4	.	.	PROPN
ejpam-6583	413	5	math	math	PROPN
ejpam-6583	413	6	,	,	PUNCT
ejpam-6583	413	7	18	18	NUM
ejpam-6583	413	8	(	(	PUNCT
ejpam-6583	413	9	3	3	NUM
ejpam-6583	413	10	)	)	PUNCT
ejpam-6583	413	11	(	(	PUNCT
ejpam-6583	413	12	2025	2025	NUM
ejpam-6583	413	13	)	)	PUNCT
ejpam-6583	413	14	,	,	PUNCT
ejpam-6583	413	15	6583	6583	NUM
ejpam-6583	413	16	18	18	NUM
ejpam-6583	413	17	of	of	ADP
ejpam-6583	413	18	27	27	NUM
ejpam-6583	413	19	≾	≾	NOUN
ejpam-6583	413	20	diag	diag	NOUN
ejpam-6583	413	21	(	(	PUNCT
ejpam-6583	413	22	sα1	sα1	PROPN
ejpam-6583	413	23	,	,	PUNCT
ejpam-6583	413	24	·	·	PUNCT
ejpam-6583	413	25	·	·	PUNCT
ejpam-6583	413	26	·	·	PUNCT
ejpam-6583	413	27	,	,	PUNCT
ejpam-6583	413	28	sαd	sαd	NOUN
ejpam-6583	413	29	)	)	PUNCT
ejpam-6583	414	1	[	[	X
ejpam-6583	414	2	δb	δb	X
ejpam-6583	414	3	r⊕d	r⊕d	NOUN
ejpam-6583	414	4	(	(	PUNCT
ejpam-6583	414	5	f	f	X
ejpam-6583	414	6	(	(	PUNCT
ejpam-6583	414	7	x	x	NOUN
ejpam-6583	414	8	)	)	PUNCT
ejpam-6583	414	9	,	,	PUNCT
ejpam-6583	414	10	x	x	X
ejpam-6583	414	11	)	)	PUNCT
ejpam-6583	414	12	+	+	CCONJ
ejpam-6583	414	13	δb	δb	NOUN
ejpam-6583	414	14	r⊕d	r⊕d	NOUN
ejpam-6583	414	15	(	(	PUNCT
ejpam-6583	414	16	x	x	X
ejpam-6583	414	17	,	,	PUNCT
ejpam-6583	414	18	y	y	PROPN
ejpam-6583	414	19	)	)	PUNCT
ejpam-6583	414	20	+	+	CCONJ
ejpam-6583	414	21	δb	δb	NOUN
ejpam-6583	414	22	r⊕d	r⊕d	NOUN
ejpam-6583	414	23	(	(	PUNCT
ejpam-6583	414	24	f	f	PROPN
ejpam-6583	414	25	(	(	PUNCT
ejpam-6583	414	26	y	y	PROPN
ejpam-6583	414	27	)	)	PUNCT
ejpam-6583	414	28	,	,	PUNCT
ejpam-6583	414	29	y	y	PROPN
ejpam-6583	414	30	)	)	PUNCT
ejpam-6583	415	1	+	+	CCONJ
ejpam-6583	415	2	δb	δb	NOUN
ejpam-6583	415	3	r⊕d	r⊕d	NOUN
ejpam-6583	415	4	(	(	PUNCT
ejpam-6583	415	5	y	y	NOUN
ejpam-6583	415	6	,	,	PUNCT
ejpam-6583	415	7	x	x	NOUN
ejpam-6583	415	8	)	)	PUNCT
ejpam-6583	415	9	]	]	PUNCT
ejpam-6583	415	10	=	=	SYM
ejpam-6583	415	11	2	2	NUM
ejpam-6583	415	12	diag	diag	NOUN
ejpam-6583	415	13	(	(	PUNCT
ejpam-6583	415	14	sα1	sα1	PROPN
ejpam-6583	415	15	,	,	PUNCT
ejpam-6583	415	16	·	·	PUNCT
ejpam-6583	415	17	·	·	PUNCT
ejpam-6583	415	18	·	·	PUNCT
ejpam-6583	415	19	,	,	PUNCT
ejpam-6583	415	20	sαd	sαd	NOUN
ejpam-6583	415	21	)	)	PUNCT
ejpam-6583	415	22	δb	δb	NOUN
ejpam-6583	415	23	r⊕d	r⊕d	NOUN
ejpam-6583	415	24	(	(	PUNCT
ejpam-6583	415	25	x	x	NOUN
ejpam-6583	415	26	,	,	PUNCT
ejpam-6583	415	27	y	y	PROPN
ejpam-6583	415	28	)	)	PUNCT
ejpam-6583	415	29	≺	≺	NOUN
ejpam-6583	415	30	δb	δb	NOUN
ejpam-6583	415	31	r⊕d	r⊕d	NOUN
ejpam-6583	415	32	(	(	PUNCT
ejpam-6583	415	33	x	x	X
ejpam-6583	415	34	,	,	PUNCT
ejpam-6583	415	35	y	y	PROPN
ejpam-6583	415	36	)	)	PUNCT
ejpam-6583	415	37	,	,	PUNCT
ejpam-6583	415	38	this	this	PRON
ejpam-6583	415	39	implies	imply	VERB
ejpam-6583	415	40	δb	δb	NOUN
ejpam-6583	415	41	r⊕d	r⊕d	NOUN
ejpam-6583	415	42	(	(	PUNCT
ejpam-6583	415	43	x	x	X
ejpam-6583	415	44	,	,	PUNCT
ejpam-6583	415	45	y	y	NOUN
ejpam-6583	415	46	)	)	PUNCT
ejpam-6583	415	47	=	=	SYM
ejpam-6583	416	1	0	0	X
ejpam-6583	416	2	.	.	PUNCT
ejpam-6583	417	1	hence	hence	ADV
ejpam-6583	417	2	x	x	X
ejpam-6583	417	3	=	=	SYM
ejpam-6583	417	4	y	y	PROPN
ejpam-6583	417	5	,	,	PUNCT
ejpam-6583	417	6	and	and	CCONJ
ejpam-6583	417	7	the	the	DET
ejpam-6583	417	8	fixed	fix	VERB
ejpam-6583	417	9	-	-	PUNCT
ejpam-6583	417	10	point	point	NOUN
ejpam-6583	417	11	x	x	PUNCT
ejpam-6583	417	12	of	of	ADP
ejpam-6583	417	13	f	f	PROPN
ejpam-6583	417	14	is	be	AUX
ejpam-6583	417	15	unique	unique	ADJ
ejpam-6583	417	16	.	.	PUNCT
ejpam-6583	418	1	if	if	SCONJ
ejpam-6583	418	2	d	d	PROPN
ejpam-6583	418	3	=	=	SYM
ejpam-6583	418	4	1	1	NUM
ejpam-6583	418	5	and	and	CCONJ
ejpam-6583	418	6	s	s	X
ejpam-6583	418	7	=	=	SYM
ejpam-6583	418	8	1	1	NUM
ejpam-6583	418	9	,	,	PUNCT
ejpam-6583	418	10	then	then	ADV
ejpam-6583	418	11	the	the	DET
ejpam-6583	418	12	theorem	theorem	NOUN
ejpam-6583	418	13	5	5	NUM
ejpam-6583	418	14	can	can	AUX
ejpam-6583	418	15	be	be	AUX
ejpam-6583	418	16	reduced	reduce	VERB
ejpam-6583	418	17	to	to	ADP
ejpam-6583	418	18	the	the	DET
ejpam-6583	418	19	standard	standard	ADJ
ejpam-6583	418	20	chatterjee	chatterjee	NOUN
ejpam-6583	418	21	in	in	ADP
ejpam-6583	418	22	the	the	DET
ejpam-6583	418	23	metric	metric	ADJ
ejpam-6583	418	24	space	space	NOUN
ejpam-6583	418	25	.	.	PUNCT
ejpam-6583	419	1	corolary	corolary	ADJ
ejpam-6583	419	2	5	5	NUM
ejpam-6583	419	3	(	(	PUNCT
ejpam-6583	419	4	chatterjee	chatterjee	NOUN
ejpam-6583	419	5	,	,	PUNCT
ejpam-6583	419	6	[	[	X
ejpam-6583	419	7	25	25	NUM
ejpam-6583	419	8	]	]	PUNCT
ejpam-6583	419	9	)	)	PUNCT
ejpam-6583	419	10	.	.	PUNCT
ejpam-6583	420	1	suppose	suppose	VERB
ejpam-6583	420	2	that	that	SCONJ
ejpam-6583	420	3	(	(	PUNCT
ejpam-6583	420	4	x	x	X
ejpam-6583	420	5	,	,	PUNCT
ejpam-6583	420	6	d	d	X
ejpam-6583	420	7	)	)	PUNCT
ejpam-6583	420	8	is	be	AUX
ejpam-6583	420	9	a	a	DET
ejpam-6583	420	10	complete	complete	ADJ
ejpam-6583	420	11	metric	metric	ADJ
ejpam-6583	420	12	space	space	NOUN
ejpam-6583	420	13	and	and	CCONJ
ejpam-6583	420	14	f	f	NOUN
ejpam-6583	420	15	:	:	PUNCT
ejpam-6583	420	16	x	x	X
ejpam-6583	420	17	→	→	PUNCT
ejpam-6583	420	18	x	x	X
ejpam-6583	420	19	is	be	AUX
ejpam-6583	420	20	an	an	DET
ejpam-6583	420	21	operator	operator	NOUN
ejpam-6583	420	22	such	such	ADJ
ejpam-6583	420	23	that	that	PRON
ejpam-6583	420	24	δ(fx	δ(fx	PROPN
ejpam-6583	420	25	,	,	PUNCT
ejpam-6583	420	26	fy	fy	PROPN
ejpam-6583	420	27	)	)	PUNCT
ejpam-6583	420	28	≤	≤	PUNCT
ejpam-6583	421	1	α	α	PROPN
ejpam-6583	422	1	[	[	X
ejpam-6583	422	2	δ(fx	δ(fx	PROPN
ejpam-6583	422	3	,	,	PUNCT
ejpam-6583	422	4	y	y	NOUN
ejpam-6583	422	5	)	)	PUNCT
ejpam-6583	423	1	+	+	CCONJ
ejpam-6583	423	2	δ(fy	δ(fy	ADV
ejpam-6583	423	3	,	,	PUNCT
ejpam-6583	423	4	x	x	X
ejpam-6583	423	5	)	)	PUNCT
ejpam-6583	423	6	]	]	PUNCT
ejpam-6583	423	7	,	,	PUNCT
ejpam-6583	423	8	for	for	ADP
ejpam-6583	423	9	constant	constant	ADJ
ejpam-6583	423	10	α	α	PRON
ejpam-6583	423	11	∈	∈	PROPN
ejpam-6583	423	12	(	(	PUNCT
ejpam-6583	423	13	0	0	NUM
ejpam-6583	423	14	,	,	PUNCT
ejpam-6583	423	15	12	12	NUM
ejpam-6583	423	16	)	)	PUNCT
ejpam-6583	423	17	and	and	CCONJ
ejpam-6583	423	18	for	for	ADP
ejpam-6583	423	19	every	every	DET
ejpam-6583	423	20	x	x	NOUN
ejpam-6583	423	21	,	,	PUNCT
ejpam-6583	423	22	y	y	PROPN
ejpam-6583	423	23	∈	∈	PROPN
ejpam-6583	423	24	x	x	X
ejpam-6583	423	25	.	.	PUNCT
ejpam-6583	424	1	then	then	ADV
ejpam-6583	424	2	f	f	PROPN
ejpam-6583	424	3	has	have	VERB
ejpam-6583	424	4	a	a	DET
ejpam-6583	424	5	unique	unique	ADJ
ejpam-6583	424	6	fixed	fix	VERB
ejpam-6583	424	7	-	-	PUNCT
ejpam-6583	424	8	point	point	NOUN
ejpam-6583	424	9	z	z	NOUN
ejpam-6583	424	10	∈	∈	PROPN
ejpam-6583	424	11	x	x	X
ejpam-6583	424	12	.	.	PUNCT
ejpam-6583	425	1	theorem	theorem	NOUN
ejpam-6583	425	2	6	6	NUM
ejpam-6583	425	3	.	.	PUNCT
ejpam-6583	425	4	suppose	suppose	VERB
ejpam-6583	425	5	that	that	SCONJ
ejpam-6583	425	6	(	(	PUNCT
ejpam-6583	425	7	x	x	X
ejpam-6583	425	8	,	,	PUNCT
ejpam-6583	425	9	r⊕d	r⊕d	NOUN
ejpam-6583	425	10	,	,	PUNCT
ejpam-6583	425	11	δb	δb	NOUN
ejpam-6583	425	12	r⊕d	r⊕d	NOUN
ejpam-6583	425	13	)	)	PUNCT
ejpam-6583	425	14	is	be	AUX
ejpam-6583	425	15	a	a	DET
ejpam-6583	425	16	complete	complete	ADJ
ejpam-6583	425	17	generalized	generalized	ADJ
ejpam-6583	425	18	b	b	X
ejpam-6583	425	19	-	-	ADJ
ejpam-6583	425	20	metric	metric	ADJ
ejpam-6583	425	21	space	space	NOUN
ejpam-6583	425	22	endowed	endow	VERB
ejpam-6583	425	23	with	with	ADP
ejpam-6583	425	24	the	the	DET
ejpam-6583	425	25	orthogonal	orthogonal	ADJ
ejpam-6583	425	26	direct	direct	ADJ
ejpam-6583	425	27	sum	sum	NOUN
ejpam-6583	425	28	and	and	CCONJ
ejpam-6583	425	29	f	f	NOUN
ejpam-6583	425	30	:	:	PUNCT
ejpam-6583	425	31	x	x	X
ejpam-6583	425	32	→	→	PUNCT
ejpam-6583	425	33	x	x	X
ejpam-6583	425	34	is	be	AUX
ejpam-6583	425	35	an	an	DET
ejpam-6583	425	36	operator	operator	NOUN
ejpam-6583	425	37	satisfying	satisfy	VERB
ejpam-6583	425	38	the	the	DET
ejpam-6583	425	39	following	follow	VERB
ejpam-6583	425	40	condition	condition	NOUN
ejpam-6583	425	41	δb	δb	ADP
ejpam-6583	425	42	r⊕d	r⊕d	NOUN
ejpam-6583	425	43	(	(	PUNCT
ejpam-6583	425	44	fx	fx	PROPN
ejpam-6583	425	45	,	,	PUNCT
ejpam-6583	425	46	fy	fy	PROPN
ejpam-6583	425	47	)	)	PUNCT
ejpam-6583	425	48	≾	≾	PROPN
ejpam-6583	425	49	diag	diag	NOUN
ejpam-6583	425	50	(	(	PUNCT
ejpam-6583	425	51	α1	α1	PROPN
ejpam-6583	425	52	,	,	PUNCT
ejpam-6583	425	53	α2	α2	ADJ
ejpam-6583	425	54	,	,	PUNCT
ejpam-6583	425	55	·	·	PUNCT
ejpam-6583	425	56	·	·	PUNCT
ejpam-6583	425	57	·	·	PUNCT
ejpam-6583	425	58	,	,	PUNCT
ejpam-6583	425	59	αd	αd	PROPN
ejpam-6583	425	60	)	)	PUNCT
ejpam-6583	425	61	δb	δb	NOUN
ejpam-6583	425	62	r⊕d	r⊕d	NOUN
ejpam-6583	425	63	(	(	PUNCT
ejpam-6583	425	64	x	x	X
ejpam-6583	425	65	,	,	PUNCT
ejpam-6583	425	66	y	y	PROPN
ejpam-6583	425	67	)	)	PUNCT
ejpam-6583	426	1	+	+	NOUN
ejpam-6583	426	2	diag	diag	NOUN
ejpam-6583	426	3	(	(	PUNCT
ejpam-6583	426	4	β1	β1	PROPN
ejpam-6583	426	5	,	,	PUNCT
ejpam-6583	426	6	β2	β2	VERB
ejpam-6583	426	7	,	,	PUNCT
ejpam-6583	426	8	·	·	PUNCT
ejpam-6583	426	9	·	·	PUNCT
ejpam-6583	426	10	·	·	PUNCT
ejpam-6583	426	11	,	,	PUNCT
ejpam-6583	426	12	βd	βd	X
ejpam-6583	426	13	)	)	PUNCT
ejpam-6583	427	1	[	[	X
ejpam-6583	427	2	δb	δb	X
ejpam-6583	427	3	r⊕d	r⊕d	NOUN
ejpam-6583	427	4	(	(	PUNCT
ejpam-6583	427	5	x	x	X
ejpam-6583	427	6	,	,	PUNCT
ejpam-6583	427	7	f	f	PROPN
ejpam-6583	427	8	(	(	PUNCT
ejpam-6583	427	9	x	x	NOUN
ejpam-6583	427	10	)	)	PUNCT
ejpam-6583	427	11	)	)	PUNCT
ejpam-6583	428	1	+	+	CCONJ
ejpam-6583	428	2	δb	δb	NOUN
ejpam-6583	428	3	r⊕d	r⊕d	NOUN
ejpam-6583	428	4	(	(	PUNCT
ejpam-6583	428	5	y	y	PROPN
ejpam-6583	428	6	,	,	PUNCT
ejpam-6583	428	7	f	f	PROPN
ejpam-6583	428	8	(	(	PUNCT
ejpam-6583	428	9	y	y	NOUN
ejpam-6583	428	10	)	)	PUNCT
ejpam-6583	428	11	)	)	PUNCT
ejpam-6583	428	12	]	]	PUNCT
ejpam-6583	428	13	,	,	PUNCT
ejpam-6583	428	14	for	for	ADP
ejpam-6583	428	15	αi	αi	NOUN
ejpam-6583	428	16	,	,	PUNCT
ejpam-6583	428	17	βi	βi	PROPN
ejpam-6583	428	18	∈	∈	PROPN
ejpam-6583	428	19	rd	rd	NOUN
ejpam-6583	428	20	+	+	CCONJ
ejpam-6583	428	21	and	and	CCONJ
ejpam-6583	428	22	αi	αi	VERB
ejpam-6583	428	23	+	+	CCONJ
ejpam-6583	428	24	2βi	2βi	ADJ
ejpam-6583	428	25	∈	∈	PROPN
ejpam-6583	429	1	[	[	X
ejpam-6583	429	2	0	0	NUM
ejpam-6583	429	3	,	,	PUNCT
ejpam-6583	429	4	1	1	NUM
ejpam-6583	429	5	)	)	PUNCT
ejpam-6583	429	6	,	,	PUNCT
ejpam-6583	429	7	i	i	PRON
ejpam-6583	429	8	=	=	NOUN
ejpam-6583	429	9	1	1	NUM
ejpam-6583	429	10	,	,	PUNCT
ejpam-6583	429	11	2	2	NUM
ejpam-6583	429	12	,	,	PUNCT
ejpam-6583	429	13	·	·	PUNCT
ejpam-6583	429	14	·	·	PUNCT
ejpam-6583	429	15	·	·	PUNCT
ejpam-6583	429	16	,	,	PUNCT
ejpam-6583	429	17	d	d	X
ejpam-6583	429	18	for	for	ADP
ejpam-6583	429	19	each	each	DET
ejpam-6583	429	20	x	x	NOUN
ejpam-6583	429	21	,	,	PUNCT
ejpam-6583	429	22	y	y	PROPN
ejpam-6583	429	23	∈	∈	PROPN
ejpam-6583	429	24	x	x	X
ejpam-6583	429	25	.	.	PUNCT
ejpam-6583	430	1	then	then	ADV
ejpam-6583	430	2	,	,	PUNCT
ejpam-6583	430	3	f	f	PROPN
ejpam-6583	430	4	has	have	VERB
ejpam-6583	430	5	a	a	DET
ejpam-6583	430	6	unique	unique	ADJ
ejpam-6583	430	7	fixed	fix	VERB
ejpam-6583	430	8	-	-	PUNCT
ejpam-6583	430	9	point	point	NOUN
ejpam-6583	430	10	in	in	ADP
ejpam-6583	430	11	x	x	X
ejpam-6583	430	12	.	.	PUNCT
ejpam-6583	431	1	proof	proof	NOUN
ejpam-6583	431	2	.	.	PUNCT
ejpam-6583	432	1	let	let	VERB
ejpam-6583	432	2	x0	x0	PROPN
ejpam-6583	432	3	be	be	AUX
ejpam-6583	432	4	any	any	DET
ejpam-6583	432	5	point	point	NOUN
ejpam-6583	432	6	in	in	ADP
ejpam-6583	432	7	x	x	SYM
ejpam-6583	432	8	,	,	PUNCT
ejpam-6583	432	9	that	that	ADV
ejpam-6583	432	10	is	is	ADV
ejpam-6583	432	11	x0	x0	PROPN
ejpam-6583	432	12	∈	∈	PROPN
ejpam-6583	433	1	x	x	X
ejpam-6583	433	2	.	.	PUNCT
ejpam-6583	434	1	let	let	VERB
ejpam-6583	434	2	us	we	PRON
ejpam-6583	434	3	define	define	VERB
ejpam-6583	434	4	a	a	DET
ejpam-6583	434	5	sequence	sequence	NOUN
ejpam-6583	434	6	{	{	PUNCT
ejpam-6583	434	7	xn	xn	NOUN
ejpam-6583	434	8	}	}	PUNCT
ejpam-6583	434	9	in	in	ADP
ejpam-6583	434	10	x	x	PUNCT
ejpam-6583	434	11	as	as	SCONJ
ejpam-6583	434	12	given	give	VERB
ejpam-6583	434	13	below	below	ADV
ejpam-6583	434	14	.	.	PUNCT
ejpam-6583	435	1	xn+1	xn+1	PUNCT
ejpam-6583	436	1	=	=	SYM
ejpam-6583	436	2	f	f	PROPN
ejpam-6583	436	3	(	(	PUNCT
ejpam-6583	436	4	xn	xn	PROPN
ejpam-6583	436	5	)	)	PUNCT
ejpam-6583	436	6	=	=	SYM
ejpam-6583	436	7	fn+1(x0	fn+1(x0	ADJ
ejpam-6583	436	8	)	)	PUNCT
ejpam-6583	436	9	∀	∀	X
ejpam-6583	436	10	n	n	PRON
ejpam-6583	436	11	≥	≥	NOUN
ejpam-6583	436	12	0	0	NUM
ejpam-6583	436	13	.	.	PUNCT
ejpam-6583	437	1	we	we	PRON
ejpam-6583	437	2	have	have	VERB
ejpam-6583	437	3	δb	δb	NOUN
ejpam-6583	437	4	r⊕d	r⊕d	NOUN
ejpam-6583	437	5	(	(	PUNCT
ejpam-6583	437	6	xn	xn	PROPN
ejpam-6583	437	7	,	,	PUNCT
ejpam-6583	437	8	xn+1	xn+1	NUM
ejpam-6583	437	9	)	)	PUNCT
ejpam-6583	437	10	=	=	PUNCT
ejpam-6583	437	11	δb	δb	X
ejpam-6583	437	12	r⊕d	r⊕d	NOUN
ejpam-6583	437	13	(	(	PUNCT
ejpam-6583	437	14	f	f	PROPN
ejpam-6583	437	15	(	(	PUNCT
ejpam-6583	437	16	xn−1),f	xn−1),f	PROPN
ejpam-6583	437	17	(	(	PUNCT
ejpam-6583	437	18	xn	xn	NOUN
ejpam-6583	437	19	)	)	PUNCT
ejpam-6583	437	20	)	)	PUNCT
ejpam-6583	438	1	≾	≾	NOUN
ejpam-6583	438	2	diag	diag	NOUN
ejpam-6583	438	3	(	(	PUNCT
ejpam-6583	438	4	α1	α1	PROPN
ejpam-6583	438	5	,	,	PUNCT
ejpam-6583	438	6	α2	α2	ADJ
ejpam-6583	438	7	,	,	PUNCT
ejpam-6583	438	8	·	·	PUNCT
ejpam-6583	438	9	·	·	PUNCT
ejpam-6583	438	10	·	·	PUNCT
ejpam-6583	438	11	,	,	PUNCT
ejpam-6583	438	12	αd	αd	PROPN
ejpam-6583	438	13	)	)	PUNCT
ejpam-6583	438	14	δb	δb	NOUN
ejpam-6583	438	15	r⊕d	r⊕d	NOUN
ejpam-6583	438	16	(	(	PUNCT
ejpam-6583	438	17	xn−1	xn−1	PROPN
ejpam-6583	438	18	,	,	PUNCT
ejpam-6583	438	19	xn	xn	PUNCT
ejpam-6583	438	20	)	)	PUNCT
ejpam-6583	439	1	+	+	NOUN
ejpam-6583	439	2	diag	diag	NOUN
ejpam-6583	439	3	(	(	PUNCT
ejpam-6583	439	4	β1	β1	PROPN
ejpam-6583	439	5	,	,	PUNCT
ejpam-6583	439	6	β2	β2	VERB
ejpam-6583	439	7	,	,	PUNCT
ejpam-6583	439	8	·	·	PUNCT
ejpam-6583	439	9	·	·	PUNCT
ejpam-6583	439	10	·	·	PUNCT
ejpam-6583	439	11	,	,	PUNCT
ejpam-6583	439	12	βd	βd	X
ejpam-6583	439	13	)	)	PUNCT
ejpam-6583	440	1	[	[	X
ejpam-6583	440	2	δb	δb	X
ejpam-6583	440	3	r⊕d	r⊕d	NOUN
ejpam-6583	440	4	(	(	PUNCT
ejpam-6583	440	5	xn−1,f	xn−1,f	X
ejpam-6583	440	6	(	(	PUNCT
ejpam-6583	440	7	xn−1	xn−1	PROPN
ejpam-6583	440	8	)	)	PUNCT
ejpam-6583	440	9	)	)	PUNCT
ejpam-6583	441	1	+	+	CCONJ
ejpam-6583	441	2	δb	δb	NOUN
ejpam-6583	441	3	r⊕d	r⊕d	NOUN
ejpam-6583	441	4	(	(	PUNCT
ejpam-6583	441	5	xn	xn	PROPN
ejpam-6583	441	6	,	,	PUNCT
ejpam-6583	441	7	f	f	PROPN
ejpam-6583	441	8	(	(	PUNCT
ejpam-6583	441	9	xn	xn	PROPN
ejpam-6583	441	10	)	)	PUNCT
ejpam-6583	441	11	)	)	PUNCT
ejpam-6583	441	12	]	]	PUNCT
ejpam-6583	442	1	=	=	PUNCT
ejpam-6583	442	2	diag	diag	X
ejpam-6583	442	3	(	(	PUNCT
ejpam-6583	442	4	α1	α1	PROPN
ejpam-6583	442	5	,	,	PUNCT
ejpam-6583	442	6	α2	α2	ADJ
ejpam-6583	442	7	,	,	PUNCT
ejpam-6583	442	8	·	·	PUNCT
ejpam-6583	442	9	·	·	PUNCT
ejpam-6583	442	10	·	·	PUNCT
ejpam-6583	442	11	,	,	PUNCT
ejpam-6583	442	12	αd	αd	PROPN
ejpam-6583	442	13	)	)	PUNCT
ejpam-6583	442	14	δb	δb	NOUN
ejpam-6583	442	15	r⊕d	r⊕d	NOUN
ejpam-6583	442	16	(	(	PUNCT
ejpam-6583	442	17	xn−1	xn−1	PROPN
ejpam-6583	442	18	,	,	PUNCT
ejpam-6583	442	19	xn	xn	PUNCT
ejpam-6583	442	20	)	)	PUNCT
ejpam-6583	443	1	+	+	NOUN
ejpam-6583	443	2	diag	diag	NOUN
ejpam-6583	443	3	(	(	PUNCT
ejpam-6583	443	4	β1	β1	PROPN
ejpam-6583	443	5	,	,	PUNCT
ejpam-6583	443	6	β2	β2	VERB
ejpam-6583	443	7	,	,	PUNCT
ejpam-6583	443	8	·	·	PUNCT
ejpam-6583	443	9	·	·	PUNCT
ejpam-6583	443	10	·	·	PUNCT
ejpam-6583	443	11	,	,	PUNCT
ejpam-6583	443	12	βd	βd	X
ejpam-6583	443	13	)	)	PUNCT
ejpam-6583	444	1	[	[	X
ejpam-6583	444	2	δb	δb	X
ejpam-6583	444	3	r⊕d	r⊕d	NOUN
ejpam-6583	444	4	(	(	PUNCT
ejpam-6583	444	5	xn−1	xn−1	PROPN
ejpam-6583	444	6	,	,	PUNCT
ejpam-6583	444	7	xn	xn	PUNCT
ejpam-6583	444	8	)	)	PUNCT
ejpam-6583	445	1	+	+	CCONJ
ejpam-6583	445	2	δb	δb	NOUN
ejpam-6583	445	3	r⊕d	r⊕d	NOUN
ejpam-6583	445	4	(	(	PUNCT
ejpam-6583	445	5	xn	xn	PROPN
ejpam-6583	445	6	,	,	PUNCT
ejpam-6583	445	7	xn+1	xn+1	NUM
ejpam-6583	445	8	)	)	PUNCT
ejpam-6583	445	9	]	]	PUNCT
ejpam-6583	446	1	=	=	PUNCT
ejpam-6583	446	2	diag	diag	X
ejpam-6583	446	3	(	(	PUNCT
ejpam-6583	446	4	(	(	PUNCT
ejpam-6583	446	5	α1	α1	PROPN
ejpam-6583	446	6	+	+	CCONJ
ejpam-6583	446	7	β1	β1	PROPN
ejpam-6583	446	8	)	)	PUNCT
ejpam-6583	446	9	,	,	PUNCT
ejpam-6583	446	10	(	(	PUNCT
ejpam-6583	446	11	α2	α2	PROPN
ejpam-6583	446	12	+	+	CCONJ
ejpam-6583	446	13	β2	β2	NOUN
ejpam-6583	446	14	)	)	PUNCT
ejpam-6583	446	15	,	,	PUNCT
ejpam-6583	446	16	·	·	PUNCT
ejpam-6583	446	17	·	·	PUNCT
ejpam-6583	446	18	·	·	PUNCT
ejpam-6583	446	19	,	,	PUNCT
ejpam-6583	446	20	(	(	PUNCT
ejpam-6583	446	21	αd	αd	PROPN
ejpam-6583	446	22	+	+	CCONJ
ejpam-6583	446	23	βd	βd	NOUN
ejpam-6583	446	24	)	)	PUNCT
ejpam-6583	446	25	)	)	PUNCT
ejpam-6583	446	26	δb	δb	NOUN
ejpam-6583	446	27	r⊕d	r⊕d	NOUN
ejpam-6583	446	28	(	(	PUNCT
ejpam-6583	446	29	f	f	X
ejpam-6583	446	30	(	(	PUNCT
ejpam-6583	446	31	xn−2),f	xn−2),f	PROPN
ejpam-6583	446	32	(	(	PUNCT
ejpam-6583	446	33	xn−1	xn−1	PROPN
ejpam-6583	446	34	)	)	PUNCT
ejpam-6583	446	35	)	)	PUNCT
ejpam-6583	447	1	+	+	PUNCT
ejpam-6583	447	2	diag	diag	NOUN
ejpam-6583	447	3	(	(	PUNCT
ejpam-6583	447	4	β1	β1	PROPN
ejpam-6583	447	5	β2	β2	PROPN
ejpam-6583	447	6	,	,	PUNCT
ejpam-6583	447	7	·	·	PUNCT
ejpam-6583	447	8	·	·	PUNCT
ejpam-6583	447	9	·	·	PUNCT
ejpam-6583	447	10	,	,	PUNCT
ejpam-6583	447	11	βd	βd	X
ejpam-6583	447	12	)	)	PUNCT
ejpam-6583	447	13	δb	δb	NOUN
ejpam-6583	447	14	r⊕d	r⊕d	NOUN
ejpam-6583	447	15	(	(	PUNCT
ejpam-6583	447	16	xn	xn	PROPN
ejpam-6583	447	17	,	,	PUNCT
ejpam-6583	447	18	xn+1	xn+1	NUM
ejpam-6583	447	19	)	)	PUNCT
ejpam-6583	447	20	.	.	PUNCT
ejpam-6583	448	1	thus	thus	ADV
ejpam-6583	448	2	,	,	PUNCT
ejpam-6583	448	3	diag	diag	NOUN
ejpam-6583	448	4	(	(	PUNCT
ejpam-6583	448	5	(	(	PUNCT
ejpam-6583	448	6	1−	1−	NUM
ejpam-6583	448	7	β1	β1	NOUN
ejpam-6583	448	8	)	)	PUNCT
ejpam-6583	448	9	,	,	PUNCT
ejpam-6583	448	10	(	(	PUNCT
ejpam-6583	448	11	1−	1−	NUM
ejpam-6583	448	12	β2	β2	NOUN
ejpam-6583	448	13	)	)	PUNCT
ejpam-6583	448	14	,	,	PUNCT
ejpam-6583	448	15	·	·	PUNCT
ejpam-6583	448	16	·	·	PUNCT
ejpam-6583	448	17	·	·	PUNCT
ejpam-6583	448	18	,	,	PUNCT
ejpam-6583	448	19	(	(	PUNCT
ejpam-6583	448	20	1−	1−	NUM
ejpam-6583	448	21	βd	βd	NOUN
ejpam-6583	448	22	)	)	PUNCT
ejpam-6583	448	23	)	)	PUNCT
ejpam-6583	448	24	δb	δb	NOUN
ejpam-6583	448	25	r⊕d	r⊕d	NOUN
ejpam-6583	448	26	(	(	PUNCT
ejpam-6583	448	27	xn	xn	PROPN
ejpam-6583	448	28	,	,	PUNCT
ejpam-6583	448	29	xn+1	xn+1	NUM
ejpam-6583	448	30	)	)	PUNCT
ejpam-6583	448	31	g.	g.	NOUN
ejpam-6583	448	32	albeladi	albeladi	PROPN
ejpam-6583	448	33	,	,	PUNCT
ejpam-6583	448	34	s.	s.	PROPN
ejpam-6583	448	35	omran	omran	PROPN
ejpam-6583	448	36	/	/	SYM
ejpam-6583	448	37	eur	eur	PROPN
ejpam-6583	448	38	.	.	PUNCT
ejpam-6583	448	39	j.	j.	PROPN
ejpam-6583	448	40	pure	pure	PROPN
ejpam-6583	448	41	appl	appl	PROPN
ejpam-6583	448	42	.	.	PROPN
ejpam-6583	448	43	math	math	PROPN
ejpam-6583	448	44	,	,	PUNCT
ejpam-6583	448	45	18	18	NUM
ejpam-6583	448	46	(	(	PUNCT
ejpam-6583	448	47	3	3	NUM
ejpam-6583	448	48	)	)	PUNCT
ejpam-6583	448	49	(	(	PUNCT
ejpam-6583	448	50	2025	2025	NUM
ejpam-6583	448	51	)	)	PUNCT
ejpam-6583	448	52	,	,	PUNCT
ejpam-6583	448	53	6583	6583	NUM
ejpam-6583	448	54	19	19	NUM
ejpam-6583	448	55	of	of	ADP
ejpam-6583	448	56	27	27	NUM
ejpam-6583	448	57	≾	≾	NOUN
ejpam-6583	448	58	diag	diag	NOUN
ejpam-6583	448	59	(	(	PUNCT
ejpam-6583	448	60	(	(	PUNCT
ejpam-6583	448	61	α1	α1	PROPN
ejpam-6583	448	62	+	+	CCONJ
ejpam-6583	448	63	β1	β1	PROPN
ejpam-6583	448	64	)	)	PUNCT
ejpam-6583	448	65	,	,	PUNCT
ejpam-6583	448	66	(	(	PUNCT
ejpam-6583	448	67	α2	α2	PROPN
ejpam-6583	448	68	+	+	CCONJ
ejpam-6583	448	69	β2	β2	NOUN
ejpam-6583	448	70	)	)	PUNCT
ejpam-6583	448	71	,	,	PUNCT
ejpam-6583	448	72	·	·	PUNCT
ejpam-6583	448	73	·	·	PUNCT
ejpam-6583	448	74	·	·	PUNCT
ejpam-6583	448	75	,	,	PUNCT
ejpam-6583	448	76	(	(	PUNCT
ejpam-6583	448	77	αd	αd	PROPN
ejpam-6583	448	78	+	+	CCONJ
ejpam-6583	448	79	βd	βd	NOUN
ejpam-6583	448	80	)	)	PUNCT
ejpam-6583	448	81	)	)	PUNCT
ejpam-6583	448	82	δb	δb	NOUN
ejpam-6583	448	83	r⊕d	r⊕d	NOUN
ejpam-6583	448	84	(	(	PUNCT
ejpam-6583	448	85	f	f	X
ejpam-6583	448	86	(	(	PUNCT
ejpam-6583	448	87	xn−2),f	xn−2),f	PROPN
ejpam-6583	448	88	(	(	PUNCT
ejpam-6583	448	89	xn−1	xn−1	PROPN
ejpam-6583	448	90	)	)	PUNCT
ejpam-6583	448	91	)	)	PUNCT
ejpam-6583	448	92	.	.	PUNCT
ejpam-6583	449	1	this	this	PRON
ejpam-6583	449	2	implies	imply	VERB
ejpam-6583	449	3	that	that	SCONJ
ejpam-6583	449	4	δb	δb	NOUN
ejpam-6583	449	5	r⊕d	r⊕d	NOUN
ejpam-6583	449	6	(	(	PUNCT
ejpam-6583	449	7	xn	xn	PROPN
ejpam-6583	449	8	,	,	PUNCT
ejpam-6583	449	9	xn+1	xn+1	X
ejpam-6583	449	10	)	)	PUNCT
ejpam-6583	449	11	≾	≾	NOUN
ejpam-6583	449	12	diag	diag	NOUN
ejpam-6583	449	13	(	(	PUNCT
ejpam-6583	449	14	(	(	PUNCT
ejpam-6583	449	15	α1	α1	PROPN
ejpam-6583	449	16	+	+	CCONJ
ejpam-6583	449	17	β1	β1	PROPN
ejpam-6583	449	18	)	)	PUNCT
ejpam-6583	449	19	(	(	PUNCT
ejpam-6583	449	20	1−	1−	NUM
ejpam-6583	449	21	β1	β1	PROPN
ejpam-6583	449	22	)	)	PUNCT
ejpam-6583	449	23	,	,	PUNCT
ejpam-6583	449	24	·	·	PUNCT
ejpam-6583	449	25	·	·	PUNCT
ejpam-6583	449	26	·	·	PUNCT
ejpam-6583	449	27	,	,	PUNCT
ejpam-6583	449	28	(	(	PUNCT
ejpam-6583	449	29	αd	αd	PROPN
ejpam-6583	449	30	+	+	CCONJ
ejpam-6583	449	31	βd	βd	NOUN
ejpam-6583	449	32	)	)	PUNCT
ejpam-6583	449	33	(	(	PUNCT
ejpam-6583	449	34	1−	1−	NUM
ejpam-6583	449	35	βd	βd	NOUN
ejpam-6583	449	36	)	)	PUNCT
ejpam-6583	449	37	)	)	PUNCT
ejpam-6583	449	38	δb	δb	NOUN
ejpam-6583	449	39	r⊕d	r⊕d	NOUN
ejpam-6583	449	40	(	(	PUNCT
ejpam-6583	449	41	xn−1	xn−1	PROPN
ejpam-6583	449	42	,	,	PUNCT
ejpam-6583	449	43	xn	xn	PROPN
ejpam-6583	449	44	)	)	PUNCT
ejpam-6583	449	45	,	,	PUNCT
ejpam-6583	449	46	we	we	PRON
ejpam-6583	449	47	use	use	VERB
ejpam-6583	449	48	λi	λi	ADP
ejpam-6583	449	49	=	=	NOUN
ejpam-6583	449	50	αi	αi	NOUN
ejpam-6583	450	1	+	+	CCONJ
ejpam-6583	450	2	βi	βi	PROPN
ejpam-6583	450	3	1−	1−	NUM
ejpam-6583	450	4	βi	βi	NUM
ejpam-6583	450	5	∈	∈	PROPN
ejpam-6583	450	6	(	(	PUNCT
ejpam-6583	450	7	0	0	NUM
ejpam-6583	450	8	,	,	PUNCT
ejpam-6583	450	9	1	1	NUM
ejpam-6583	450	10	)	)	PUNCT
ejpam-6583	450	11	,	,	PUNCT
ejpam-6583	450	12	i	i	PRON
ejpam-6583	450	13	=	=	NOUN
ejpam-6583	450	14	1	1	NUM
ejpam-6583	450	15	,	,	PUNCT
ejpam-6583	450	16	2	2	NUM
ejpam-6583	450	17	,	,	PUNCT
ejpam-6583	450	18	·	·	PUNCT
ejpam-6583	450	19	·	·	PUNCT
ejpam-6583	450	20	·	·	PUNCT
ejpam-6583	450	21	,	,	PUNCT
ejpam-6583	451	1	d	d	X
ejpam-6583	451	2	we	we	PRON
ejpam-6583	451	3	obtain	obtain	VERB
ejpam-6583	451	4	δb	δb	NOUN
ejpam-6583	451	5	r⊕d	r⊕d	NOUN
ejpam-6583	451	6	(	(	PUNCT
ejpam-6583	451	7	xn	xn	PROPN
ejpam-6583	451	8	,	,	PUNCT
ejpam-6583	451	9	xn+1	xn+1	X
ejpam-6583	451	10	)	)	PUNCT
ejpam-6583	451	11	≾	≾	NOUN
ejpam-6583	451	12	diag	diag	NOUN
ejpam-6583	451	13	(	(	PUNCT
ejpam-6583	451	14	λ1	λ1	ADJ
ejpam-6583	451	15	,	,	PUNCT
ejpam-6583	451	16	λ2	λ2	NOUN
ejpam-6583	451	17	,	,	PUNCT
ejpam-6583	451	18	·	·	PUNCT
ejpam-6583	451	19	·	·	PUNCT
ejpam-6583	451	20	·	·	PUNCT
ejpam-6583	451	21	,	,	PUNCT
ejpam-6583	451	22	λd	λd	NOUN
ejpam-6583	451	23	)	)	PUNCT
ejpam-6583	451	24	δb	δb	NOUN
ejpam-6583	451	25	r⊕d	r⊕d	NOUN
ejpam-6583	451	26	(	(	PUNCT
ejpam-6583	451	27	xn	xn	PROPN
ejpam-6583	451	28	,	,	PUNCT
ejpam-6583	451	29	xn−1	xn−1	PROPN
ejpam-6583	451	30	)	)	PUNCT
ejpam-6583	451	31	.	.	PUNCT
ejpam-6583	452	1	so	so	ADV
ejpam-6583	452	2	δb	δb	NOUN
ejpam-6583	452	3	r⊕d	r⊕d	NOUN
ejpam-6583	452	4	(	(	PUNCT
ejpam-6583	452	5	xn	xn	PROPN
ejpam-6583	452	6	,	,	PUNCT
ejpam-6583	452	7	xn+1	xn+1	X
ejpam-6583	452	8	)	)	PUNCT
ejpam-6583	452	9	≾	≾	NOUN
ejpam-6583	452	10	diag	diag	NOUN
ejpam-6583	452	11	(	(	PUNCT
ejpam-6583	452	12	λ1	λ1	ADJ
ejpam-6583	452	13	,	,	PUNCT
ejpam-6583	452	14	λ2	λ2	NOUN
ejpam-6583	452	15	,	,	PUNCT
ejpam-6583	452	16	·	·	PUNCT
ejpam-6583	452	17	·	·	PUNCT
ejpam-6583	452	18	·	·	PUNCT
ejpam-6583	452	19	,	,	PUNCT
ejpam-6583	452	20	λd	λd	NOUN
ejpam-6583	452	21	)	)	PUNCT
ejpam-6583	452	22	δb	δb	NOUN
ejpam-6583	452	23	r⊕d	r⊕d	NOUN
ejpam-6583	452	24	(	(	PUNCT
ejpam-6583	452	25	xn−1	xn−1	PROPN
ejpam-6583	452	26	,	,	PUNCT
ejpam-6583	452	27	xn	xn	X
ejpam-6583	452	28	)	)	PUNCT
ejpam-6583	452	29	≾	≾	NOUN
ejpam-6583	452	30	diag	diag	NOUN
ejpam-6583	452	31	(	(	PUNCT
ejpam-6583	452	32	λ21	λ21	PROPN
ejpam-6583	452	33	,	,	PUNCT
ejpam-6583	452	34	λ22	λ22	PROPN
ejpam-6583	452	35	,	,	PUNCT
ejpam-6583	452	36	·	·	PUNCT
ejpam-6583	452	37	·	·	PUNCT
ejpam-6583	452	38	·	·	PUNCT
ejpam-6583	452	39	,	,	PUNCT
ejpam-6583	452	40	λ2d	λ2d	PUNCT
ejpam-6583	452	41	)	)	PUNCT
ejpam-6583	452	42	δb	δb	NOUN
ejpam-6583	452	43	r⊕d	r⊕d	NOUN
ejpam-6583	452	44	(	(	PUNCT
ejpam-6583	452	45	xn−2	xn−2	PROPN
ejpam-6583	452	46	,	,	PUNCT
ejpam-6583	452	47	xn−1	xn−1	PROPN
ejpam-6583	452	48	)	)	PUNCT
ejpam-6583	452	49	≾	≾	NOUN
ejpam-6583	452	50	diag	diag	NOUN
ejpam-6583	452	51	(	(	PUNCT
ejpam-6583	452	52	λ31	λ31	NOUN
ejpam-6583	452	53	,	,	PUNCT
ejpam-6583	452	54	λ32	λ32	VERB
ejpam-6583	452	55	,	,	PUNCT
ejpam-6583	452	56	·	·	PUNCT
ejpam-6583	452	57	·	·	PUNCT
ejpam-6583	452	58	·	·	PUNCT
ejpam-6583	452	59	,	,	PUNCT
ejpam-6583	452	60	λ3d	λ3d	PROPN
ejpam-6583	452	61	)	)	PUNCT
ejpam-6583	453	1	δb	δb	NOUN
ejpam-6583	453	2	r⊕d	r⊕d	NOUN
ejpam-6583	453	3	(	(	PUNCT
ejpam-6583	453	4	xn−3	xn−3	PROPN
ejpam-6583	453	5	,	,	PUNCT
ejpam-6583	453	6	xn−2	xn−2	PROPN
ejpam-6583	453	7	)	)	PUNCT
ejpam-6583	453	8	≾	≾	PROPN
ejpam-6583	453	9	...	...	PUNCT
ejpam-6583	454	1	≾	≾	NOUN
ejpam-6583	454	2	diag	diag	NOUN
ejpam-6583	454	3	(	(	PUNCT
ejpam-6583	454	4	λn1	λn1	NOUN
ejpam-6583	454	5	,	,	PUNCT
ejpam-6583	454	6	λn2	λn2	NOUN
ejpam-6583	454	7	,	,	PUNCT
ejpam-6583	454	8	·	·	PUNCT
ejpam-6583	454	9	·	·	PUNCT
ejpam-6583	454	10	·	·	PUNCT
ejpam-6583	454	11	,	,	PUNCT
ejpam-6583	454	12	λnd	λnd	X
ejpam-6583	454	13	)	)	PUNCT
ejpam-6583	454	14	δb	δb	NOUN
ejpam-6583	454	15	r⊕d	r⊕d	NOUN
ejpam-6583	454	16	(	(	PUNCT
ejpam-6583	454	17	x0	x0	PROPN
ejpam-6583	454	18	,	,	PUNCT
ejpam-6583	454	19	x1	x1	PROPN
ejpam-6583	454	20	)	)	PUNCT
ejpam-6583	454	21	.	.	PUNCT
ejpam-6583	455	1	let	let	VERB
ejpam-6583	455	2	us	we	PRON
ejpam-6583	455	3	prove	prove	VERB
ejpam-6583	455	4	that	that	SCONJ
ejpam-6583	455	5	{	{	PUNCT
ejpam-6583	455	6	xn	xn	X
ejpam-6583	455	7	}	}	PUNCT
ejpam-6583	455	8	is	be	AUX
ejpam-6583	455	9	a	a	DET
ejpam-6583	455	10	cauchy	cauchy	ADJ
ejpam-6583	455	11	sequence	sequence	NOUN
ejpam-6583	455	12	.	.	PUNCT
ejpam-6583	456	1	suppose	suppose	VERB
ejpam-6583	456	2	that	that	SCONJ
ejpam-6583	456	3	m	m	VERB
ejpam-6583	456	4	<	<	X
ejpam-6583	456	5	n	n	CCONJ
ejpam-6583	456	6	,	,	PUNCT
ejpam-6583	456	7	then	then	ADV
ejpam-6583	456	8	from	from	ADP
ejpam-6583	456	9	(	(	PUNCT
ejpam-6583	456	10	3	3	NUM
ejpam-6583	456	11	)	)	PUNCT
ejpam-6583	456	12	and	and	CCONJ
ejpam-6583	456	13	the	the	DET
ejpam-6583	456	14	triangle	triangle	NOUN
ejpam-6583	456	15	inequality	inequality	NOUN
ejpam-6583	456	16	property	property	NOUN
ejpam-6583	456	17	,	,	PUNCT
ejpam-6583	456	18	we	we	PRON
ejpam-6583	456	19	can	can	AUX
ejpam-6583	456	20	write	write	VERB
ejpam-6583	456	21	as	as	ADP
ejpam-6583	456	22	:	:	PUNCT
ejpam-6583	456	23	δb	δb	NOUN
ejpam-6583	456	24	r⊕d	r⊕d	NOUN
ejpam-6583	456	25	(	(	PUNCT
ejpam-6583	456	26	xm	xm	PROPN
ejpam-6583	456	27	,	,	PUNCT
ejpam-6583	456	28	xn	xn	X
ejpam-6583	456	29	)	)	PUNCT
ejpam-6583	456	30	≾	≾	NOUN
ejpam-6583	456	31	sδb	sδb	VERB
ejpam-6583	456	32	r⊕d	r⊕d	NOUN
ejpam-6583	456	33	(	(	PUNCT
ejpam-6583	456	34	xm	xm	PROPN
ejpam-6583	456	35	,	,	PUNCT
ejpam-6583	456	36	xm+1	xm+1	PROPN
ejpam-6583	456	37	)	)	PUNCT
ejpam-6583	456	38	+	+	NUM
ejpam-6583	456	39	sδb	sδb	NOUN
ejpam-6583	456	40	r⊕d	r⊕d	NOUN
ejpam-6583	456	41	(	(	PUNCT
ejpam-6583	456	42	xm+1	xm+1	PROPN
ejpam-6583	456	43	,	,	PUNCT
ejpam-6583	456	44	xn	xn	X
ejpam-6583	456	45	)	)	PUNCT
ejpam-6583	456	46	≾	≾	NOUN
ejpam-6583	456	47	sδb	sδb	VERB
ejpam-6583	456	48	r⊕d	r⊕d	NOUN
ejpam-6583	456	49	(	(	PUNCT
ejpam-6583	456	50	xm	xm	PROPN
ejpam-6583	456	51	,	,	PUNCT
ejpam-6583	456	52	xm+1	xm+1	PROPN
ejpam-6583	456	53	)	)	PUNCT
ejpam-6583	456	54	+	+	CCONJ
ejpam-6583	456	55	s2	s2	NOUN
ejpam-6583	456	56	[	[	PUNCT
ejpam-6583	456	57	δb	δb	NOUN
ejpam-6583	456	58	r⊕d	r⊕d	NOUN
ejpam-6583	456	59	(	(	PUNCT
ejpam-6583	456	60	xm+1	xm+1	PROPN
ejpam-6583	456	61	,	,	PUNCT
ejpam-6583	456	62	xm+2	xm+2	PROPN
ejpam-6583	456	63	)	)	PUNCT
ejpam-6583	456	64	+	+	CCONJ
ejpam-6583	456	65	δb	δb	NOUN
ejpam-6583	456	66	r⊕d	r⊕d	NOUN
ejpam-6583	456	67	(	(	PUNCT
ejpam-6583	456	68	xm+2	xm+2	PROPN
ejpam-6583	456	69	,	,	PUNCT
ejpam-6583	456	70	xn	xn	PROPN
ejpam-6583	456	71	)	)	PUNCT
ejpam-6583	456	72	]	]	PUNCT
ejpam-6583	457	1	≾	≾	NOUN
ejpam-6583	457	2	sδb	sδb	VERB
ejpam-6583	457	3	r⊕d	r⊕d	NOUN
ejpam-6583	457	4	(	(	PUNCT
ejpam-6583	457	5	xm	xm	PROPN
ejpam-6583	457	6	,	,	PUNCT
ejpam-6583	457	7	xm+1	xm+1	PROPN
ejpam-6583	457	8	)	)	PUNCT
ejpam-6583	457	9	+	+	CCONJ
ejpam-6583	457	10	s2δb	s2δb	SYM
ejpam-6583	457	11	r⊕d	r⊕d	NOUN
ejpam-6583	457	12	(	(	PUNCT
ejpam-6583	457	13	xm+1	xm+1	PROPN
ejpam-6583	457	14	,	,	PUNCT
ejpam-6583	457	15	xm+2	xm+2	PROPN
ejpam-6583	457	16	)	)	PUNCT
ejpam-6583	457	17	+	+	CCONJ
ejpam-6583	457	18	s3	s3	PROPN
ejpam-6583	457	19	[	[	PUNCT
ejpam-6583	457	20	δb	δb	X
ejpam-6583	457	21	r⊕d	r⊕d	NOUN
ejpam-6583	457	22	(	(	PUNCT
ejpam-6583	457	23	xm+2	xm+2	PROPN
ejpam-6583	457	24	,	,	PUNCT
ejpam-6583	457	25	xm+3	xm+3	NUM
ejpam-6583	457	26	)	)	PUNCT
ejpam-6583	457	27	+	+	CCONJ
ejpam-6583	457	28	δb	δb	NOUN
ejpam-6583	457	29	r⊕d	r⊕d	NOUN
ejpam-6583	457	30	(	(	PUNCT
ejpam-6583	457	31	xm+3	xm+3	NUM
ejpam-6583	457	32	,	,	PUNCT
ejpam-6583	457	33	xn	xn	PROPN
ejpam-6583	457	34	)	)	PUNCT
ejpam-6583	457	35	]	]	PUNCT
ejpam-6583	457	36	...	...	PUNCT
ejpam-6583	458	1	≾	≾	NOUN
ejpam-6583	458	2	sδb	sδb	VERB
ejpam-6583	458	3	r⊕d	r⊕d	NOUN
ejpam-6583	458	4	(	(	PUNCT
ejpam-6583	458	5	xm	xm	PROPN
ejpam-6583	458	6	,	,	PUNCT
ejpam-6583	458	7	xm+1	xm+1	PROPN
ejpam-6583	458	8	)	)	PUNCT
ejpam-6583	458	9	+	+	CCONJ
ejpam-6583	458	10	s2δb	s2δb	SYM
ejpam-6583	458	11	r⊕d	r⊕d	NOUN
ejpam-6583	458	12	(	(	PUNCT
ejpam-6583	458	13	xm+1	xm+1	PROPN
ejpam-6583	458	14	,	,	PUNCT
ejpam-6583	458	15	xm+2	xm+2	PROPN
ejpam-6583	458	16	)	)	PUNCT
ejpam-6583	458	17	+	+	CCONJ
ejpam-6583	458	18	·	·	PUNCT
ejpam-6583	458	19	·	·	PUNCT
ejpam-6583	458	20	·	·	PUNCT
ejpam-6583	458	21	+	+	NUM
ejpam-6583	458	22	sn−mδb	sn−mδb	NOUN
ejpam-6583	458	23	r⊕d	r⊕d	NOUN
ejpam-6583	458	24	(	(	PUNCT
ejpam-6583	458	25	xn−1	xn−1	PROPN
ejpam-6583	458	26	,	,	PUNCT
ejpam-6583	458	27	xn	xn	PRON
ejpam-6583	458	28	)	)	PUNCT
ejpam-6583	459	1	=	=	SYM
ejpam-6583	459	2	diag	diag	NOUN
ejpam-6583	459	3	(	(	PUNCT
ejpam-6583	459	4	sλm1	sλm1	PROPN
ejpam-6583	459	5	,	,	PUNCT
ejpam-6583	459	6	sλm2	sλm2	NOUN
ejpam-6583	459	7	,	,	PUNCT
ejpam-6583	459	8	·	·	PUNCT
ejpam-6583	459	9	·	·	PUNCT
ejpam-6583	459	10	·	·	PUNCT
ejpam-6583	459	11	,	,	PUNCT
ejpam-6583	459	12	sλmd	sλmd	NOUN
ejpam-6583	459	13	)	)	PUNCT
ejpam-6583	459	14	δb	δb	NOUN
ejpam-6583	459	15	r⊕d	r⊕d	NOUN
ejpam-6583	459	16	(	(	PUNCT
ejpam-6583	459	17	x0	x0	PROPN
ejpam-6583	459	18	,	,	PUNCT
ejpam-6583	459	19	x1	x1	PROPN
ejpam-6583	459	20	)	)	PUNCT
ejpam-6583	460	1	+	+	NUM
ejpam-6583	460	2	diag	diag	NOUN
ejpam-6583	460	3	(	(	PUNCT
ejpam-6583	460	4	s2λm+1	s2λm+1	PROPN
ejpam-6583	460	5	1	1	NUM
ejpam-6583	460	6	,	,	PUNCT
ejpam-6583	460	7	s2λm+1	s2λm+1	VERB
ejpam-6583	460	8	2	2	NUM
ejpam-6583	460	9	,	,	PUNCT
ejpam-6583	460	10	·	·	PUNCT
ejpam-6583	460	11	·	·	PUNCT
ejpam-6583	460	12	·	·	PUNCT
ejpam-6583	460	13	,	,	PUNCT
ejpam-6583	460	14	s2λm+1	s2λm+1	PROPN
ejpam-6583	460	15	d	d	PROPN
ejpam-6583	460	16	)	)	PUNCT
ejpam-6583	460	17	δb	δb	NOUN
ejpam-6583	460	18	r⊕d	r⊕d	NOUN
ejpam-6583	460	19	(	(	PUNCT
ejpam-6583	460	20	x0	x0	PROPN
ejpam-6583	460	21	,	,	PUNCT
ejpam-6583	460	22	x1	x1	PROPN
ejpam-6583	460	23	)	)	PUNCT
ejpam-6583	460	24	+	+	NOUN
ejpam-6583	460	25	diag	diag	NOUN
ejpam-6583	460	26	(	(	PUNCT
ejpam-6583	460	27	s3λm+2	s3λm+2	NOUN
ejpam-6583	460	28	1	1	NUM
ejpam-6583	460	29	,	,	PUNCT
ejpam-6583	460	30	s3λm+2	s3λm+2	NOUN
ejpam-6583	460	31	2	2	NUM
ejpam-6583	460	32	,	,	PUNCT
ejpam-6583	460	33	·	·	PUNCT
ejpam-6583	460	34	·	·	PUNCT
ejpam-6583	460	35	·	·	PUNCT
ejpam-6583	460	36	,	,	PUNCT
ejpam-6583	460	37	s3λm+2	s3λm+2	NOUN
ejpam-6583	460	38	d	d	NOUN
ejpam-6583	460	39	)	)	PUNCT
ejpam-6583	460	40	δb	δb	NOUN
ejpam-6583	460	41	r⊕d	r⊕d	NOUN
ejpam-6583	460	42	(	(	PUNCT
ejpam-6583	460	43	x0	x0	PROPN
ejpam-6583	460	44	,	,	PUNCT
ejpam-6583	460	45	x1	x1	PROPN
ejpam-6583	460	46	)	)	PUNCT
ejpam-6583	460	47	+	+	X
ejpam-6583	460	48	·	·	PUNCT
ejpam-6583	460	49	·	·	PUNCT
ejpam-6583	460	50	·	·	PUNCT
ejpam-6583	461	1	+	+	PUNCT
ejpam-6583	461	2	diag	diag	NOUN
ejpam-6583	461	3	(	(	PUNCT
ejpam-6583	461	4	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	461	5	1	1	NUM
ejpam-6583	461	6	,	,	PUNCT
ejpam-6583	461	7	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	461	8	2	2	NUM
ejpam-6583	461	9	,	,	PUNCT
ejpam-6583	461	10	·	·	PUNCT
ejpam-6583	461	11	·	·	PUNCT
ejpam-6583	461	12	·	·	PUNCT
ejpam-6583	461	13	,	,	PUNCT
ejpam-6583	461	14	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	461	15	d	d	X
ejpam-6583	461	16	)	)	PUNCT
ejpam-6583	461	17	δb	δb	NOUN
ejpam-6583	461	18	r⊕d	r⊕d	NOUN
ejpam-6583	461	19	(	(	PUNCT
ejpam-6583	461	20	x0	x0	PROPN
ejpam-6583	461	21	,	,	PUNCT
ejpam-6583	461	22	x1	x1	PROPN
ejpam-6583	461	23	)	)	PUNCT
ejpam-6583	461	24	=	=	SYM
ejpam-6583	461	25	(	(	PUNCT
ejpam-6583	461	26	(	(	PUNCT
ejpam-6583	461	27	sλm1	sλm1	PROPN
ejpam-6583	461	28	+	+	CCONJ
ejpam-6583	461	29	s2λm+1	s2λm+1	VERB
ejpam-6583	461	30	1	1	NUM
ejpam-6583	461	31	+	+	CCONJ
ejpam-6583	461	32	·	·	PUNCT
ejpam-6583	461	33	·	·	PUNCT
ejpam-6583	461	34	·	·	PUNCT
ejpam-6583	461	35	+	+	NUM
ejpam-6583	461	36	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	461	37	1	1	NUM
ejpam-6583	461	38	)	)	PUNCT
ejpam-6583	461	39	δb	δb	NOUN
ejpam-6583	461	40	r⊕d	r⊕d	NOUN
ejpam-6583	461	41	(	(	PUNCT
ejpam-6583	461	42	x0	x0	PROPN
ejpam-6583	461	43	,	,	PUNCT
ejpam-6583	461	44	x1	x1	PROPN
ejpam-6583	461	45	)	)	PUNCT
ejpam-6583	461	46	,	,	PUNCT
ejpam-6583	461	47	g.	g.	PROPN
ejpam-6583	461	48	albeladi	albeladi	PROPN
ejpam-6583	461	49	,	,	PUNCT
ejpam-6583	461	50	s.	s.	PROPN
ejpam-6583	461	51	omran	omran	PROPN
ejpam-6583	461	52	/	/	SYM
ejpam-6583	461	53	eur	eur	PROPN
ejpam-6583	461	54	.	.	PUNCT
ejpam-6583	462	1	j.	j.	PROPN
ejpam-6583	462	2	pure	pure	PROPN
ejpam-6583	462	3	appl	appl	PROPN
ejpam-6583	462	4	.	.	PROPN
ejpam-6583	462	5	math	math	PROPN
ejpam-6583	462	6	,	,	PUNCT
ejpam-6583	462	7	18	18	NUM
ejpam-6583	462	8	(	(	PUNCT
ejpam-6583	462	9	3	3	NUM
ejpam-6583	462	10	)	)	PUNCT
ejpam-6583	462	11	(	(	PUNCT
ejpam-6583	462	12	2025	2025	NUM
ejpam-6583	462	13	)	)	PUNCT
ejpam-6583	462	14	,	,	PUNCT
ejpam-6583	462	15	6583	6583	NUM
ejpam-6583	462	16	20	20	NUM
ejpam-6583	462	17	of	of	ADP
ejpam-6583	462	18	27	27	NUM
ejpam-6583	462	19	(	(	PUNCT
ejpam-6583	462	20	sλm2	sλm2	PROPN
ejpam-6583	462	21	+	+	CCONJ
ejpam-6583	462	22	s2λm+1	s2λm+1	VERB
ejpam-6583	462	23	2	2	NUM
ejpam-6583	462	24	+	+	CCONJ
ejpam-6583	462	25	·	·	PUNCT
ejpam-6583	462	26	·	·	PUNCT
ejpam-6583	462	27	·	·	PUNCT
ejpam-6583	463	1	+	+	NUM
ejpam-6583	463	2	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	463	3	2	2	NUM
ejpam-6583	463	4	)	)	PUNCT
ejpam-6583	463	5	δb	δb	NOUN
ejpam-6583	463	6	r⊕d	r⊕d	NOUN
ejpam-6583	463	7	(	(	PUNCT
ejpam-6583	463	8	x0	x0	PROPN
ejpam-6583	463	9	,	,	PUNCT
ejpam-6583	463	10	x1	x1	PROPN
ejpam-6583	463	11	)	)	PUNCT
ejpam-6583	463	12	,	,	PUNCT
ejpam-6583	463	13	·	·	PUNCT
ejpam-6583	463	14	·	·	PUNCT
ejpam-6583	463	15	·	·	PUNCT
ejpam-6583	463	16	,	,	PUNCT
ejpam-6583	463	17	(	(	PUNCT
ejpam-6583	463	18	sλmd	sλmd	NOUN
ejpam-6583	463	19	+	+	CCONJ
ejpam-6583	463	20	s2λm+1	s2λm+1	PROPN
ejpam-6583	463	21	d	d	PROPN
ejpam-6583	463	22	+	+	PROPN
ejpam-6583	463	23	·	·	PUNCT
ejpam-6583	463	24	·	·	PUNCT
ejpam-6583	463	25	·	·	PUNCT
ejpam-6583	463	26	+	+	NUM
ejpam-6583	463	27	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	463	28	d	d	NOUN
ejpam-6583	463	29	)	)	PUNCT
ejpam-6583	463	30	δb	δb	NOUN
ejpam-6583	463	31	r⊕d	r⊕d	NOUN
ejpam-6583	463	32	(	(	PUNCT
ejpam-6583	463	33	x0	x0	PROPN
ejpam-6583	463	34	,	,	PUNCT
ejpam-6583	463	35	x1	x1	PROPN
ejpam-6583	463	36	)	)	PUNCT
ejpam-6583	463	37	)	)	PUNCT
ejpam-6583	464	1	=	=	SYM
ejpam-6583	464	2	diag	diag	NOUN
ejpam-6583	464	3	(	(	PUNCT
ejpam-6583	464	4	∑n−m	∑n−m	INTJ
ejpam-6583	464	5	i=1	i=1	X
ejpam-6583	464	6	∑n−1	∑n−1	PROPN
ejpam-6583	464	7	j	j	X
ejpam-6583	464	8	=	=	PROPN
ejpam-6583	464	9	m	m	PROPN
ejpam-6583	464	10	s	s	PROPN
ejpam-6583	464	11	iλj1	iλj1	PROPN
ejpam-6583	464	12	,	,	PUNCT
ejpam-6583	464	13	·	·	PUNCT
ejpam-6583	464	14	·	·	PUNCT
ejpam-6583	464	15	·	·	PUNCT
ejpam-6583	464	16	,	,	PUNCT
ejpam-6583	464	17	∑n−m	∑n−m	X
ejpam-6583	464	18	i=1	i=1	X
ejpam-6583	464	19	∑n−1	∑n−1	PROPN
ejpam-6583	465	1	j	j	X
ejpam-6583	465	2	=	=	PROPN
ejpam-6583	465	3	m	m	PROPN
ejpam-6583	465	4	s	s	NOUN
ejpam-6583	465	5	iλjd	iλjd	NOUN
ejpam-6583	465	6	)	)	PUNCT
ejpam-6583	465	7	δb	δb	NOUN
ejpam-6583	465	8	r⊕d	r⊕d	NOUN
ejpam-6583	465	9	(	(	PUNCT
ejpam-6583	465	10	x0	x0	PROPN
ejpam-6583	465	11	,	,	PUNCT
ejpam-6583	465	12	x1	x1	PROPN
ejpam-6583	465	13	)	)	PUNCT
ejpam-6583	465	14	=	=	SYM
ejpam-6583	465	15	diag	diag	NOUN
ejpam-6583	465	16	(	(	PUNCT
ejpam-6583	465	17	sλm1	sλm1	PROPN
ejpam-6583	465	18	∑n−m−1	∑n−m−1	PROPN
ejpam-6583	465	19	j=0	j=0	PROPN
ejpam-6583	465	20	(	(	PUNCT
ejpam-6583	465	21	sλ1	sλ1	NOUN
ejpam-6583	465	22	)	)	PUNCT
ejpam-6583	465	23	j	j	PROPN
ejpam-6583	465	24	,	,	PUNCT
ejpam-6583	465	25	·	·	PUNCT
ejpam-6583	465	26	·	·	PUNCT
ejpam-6583	465	27	·	·	PUNCT
ejpam-6583	465	28	,	,	PUNCT
ejpam-6583	465	29	sλm1	sλm1	PROPN
ejpam-6583	465	30	∑n−m−1	∑n−m−1	PROPN
ejpam-6583	465	31	j=0	j=0	PROPN
ejpam-6583	465	32	(	(	PUNCT
ejpam-6583	465	33	sλd	sλd	PROPN
ejpam-6583	465	34	)	)	PUNCT
ejpam-6583	465	35	j	j	PROPN
ejpam-6583	465	36	)	)	PUNCT
ejpam-6583	465	37	δb	δb	NOUN
ejpam-6583	465	38	r⊕d	r⊕d	NOUN
ejpam-6583	465	39	(	(	PUNCT
ejpam-6583	465	40	x0	x0	PROPN
ejpam-6583	465	41	,	,	PUNCT
ejpam-6583	465	42	x1	x1	PROPN
ejpam-6583	465	43	)	)	PUNCT
ejpam-6583	465	44	≾	≾	NOUN
ejpam-6583	465	45	diag	diag	NOUN
ejpam-6583	465	46	(	(	PUNCT
ejpam-6583	465	47	sλm1	sλm1	PROPN
ejpam-6583	465	48	∑+∞	∑+∞	PUNCT
ejpam-6583	465	49	j=0	j=0	PROPN
ejpam-6583	465	50	(	(	PUNCT
ejpam-6583	465	51	sλ1	sλ1	NOUN
ejpam-6583	465	52	)	)	PUNCT
ejpam-6583	465	53	j	j	PROPN
ejpam-6583	465	54	,	,	PUNCT
ejpam-6583	465	55	·	·	PUNCT
ejpam-6583	465	56	·	·	PUNCT
ejpam-6583	465	57	·	·	PUNCT
ejpam-6583	465	58	,	,	PUNCT
ejpam-6583	465	59	sλm1	sλm1	PROPN
ejpam-6583	465	60	∑+∞	∑+∞	PUNCT
ejpam-6583	465	61	j=0	j=0	PROPN
ejpam-6583	465	62	(	(	PUNCT
ejpam-6583	465	63	sλd	sλd	PROPN
ejpam-6583	465	64	)	)	PUNCT
ejpam-6583	465	65	j	j	PROPN
ejpam-6583	465	66	)	)	PUNCT
ejpam-6583	465	67	δb	δb	NOUN
ejpam-6583	465	68	r⊕d	r⊕d	NOUN
ejpam-6583	465	69	(	(	PUNCT
ejpam-6583	465	70	x0	x0	PROPN
ejpam-6583	465	71	,	,	PUNCT
ejpam-6583	465	72	x1	x1	PROPN
ejpam-6583	465	73	)	)	PUNCT
ejpam-6583	466	1	=	=	SYM
ejpam-6583	466	2	diag	diag	NOUN
ejpam-6583	466	3	(	(	PUNCT
ejpam-6583	466	4	sλm1	sλm1	PROPN
ejpam-6583	466	5	[	[	PUNCT
ejpam-6583	466	6	1	1	NUM
ejpam-6583	466	7	1−	1−	NUM
ejpam-6583	466	8	sλ1	sλ1	NOUN
ejpam-6583	466	9	]	]	PUNCT
ejpam-6583	466	10	,	,	PUNCT
ejpam-6583	466	11	·	·	PUNCT
ejpam-6583	466	12	·	·	PUNCT
ejpam-6583	466	13	·	·	PUNCT
ejpam-6583	466	14	,	,	PUNCT
ejpam-6583	466	15	sλmd	sλmd	PROPN
ejpam-6583	466	16	[	[	PUNCT
ejpam-6583	466	17	1	1	NUM
ejpam-6583	466	18	1−	1−	NUM
ejpam-6583	466	19	sλd	sλd	NOUN
ejpam-6583	466	20	]	]	PUNCT
ejpam-6583	466	21	)	)	PUNCT
ejpam-6583	466	22	δb	δb	NOUN
ejpam-6583	466	23	r⊕d	r⊕d	NOUN
ejpam-6583	466	24	(	(	PUNCT
ejpam-6583	466	25	x0	x0	PROPN
ejpam-6583	466	26	,	,	PUNCT
ejpam-6583	466	27	x1	x1	PROPN
ejpam-6583	466	28	)	)	PUNCT
ejpam-6583	466	29	≾	≾	NOUN
ejpam-6583	466	30	diag	diag	NOUN
ejpam-6583	466	31	(	(	PUNCT
ejpam-6583	466	32	sλm1	sλm1	PROPN
ejpam-6583	466	33	,	,	PUNCT
ejpam-6583	466	34	·	·	PUNCT
ejpam-6583	466	35	·	·	PUNCT
ejpam-6583	466	36	·	·	PUNCT
ejpam-6583	466	37	,	,	PUNCT
ejpam-6583	466	38	sλmd	sλmd	NOUN
ejpam-6583	466	39	)	)	PUNCT
ejpam-6583	466	40	diag	diag	NOUN
ejpam-6583	466	41	(	(	PUNCT
ejpam-6583	466	42	[	[	PUNCT
ejpam-6583	466	43	1	1	NUM
ejpam-6583	466	44	1−	1−	NUM
ejpam-6583	466	45	sλ1	sλ1	NOUN
ejpam-6583	466	46	]	]	PUNCT
ejpam-6583	466	47	,	,	PUNCT
ejpam-6583	466	48	·	·	PUNCT
ejpam-6583	466	49	·	·	PUNCT
ejpam-6583	466	50	·	·	PUNCT
ejpam-6583	466	51	,	,	PUNCT
ejpam-6583	466	52	[	[	PUNCT
ejpam-6583	466	53	1	1	NUM
ejpam-6583	466	54	1−	1−	NUM
ejpam-6583	466	55	sλd	sλd	NOUN
ejpam-6583	466	56	]	]	PUNCT
ejpam-6583	466	57	)	)	PUNCT
ejpam-6583	466	58	δb	δb	NOUN
ejpam-6583	466	59	r⊕d	r⊕d	NOUN
ejpam-6583	466	60	(	(	PUNCT
ejpam-6583	466	61	x0	x0	PROPN
ejpam-6583	466	62	,	,	PUNCT
ejpam-6583	466	63	x1	x1	PROPN
ejpam-6583	466	64	)	)	PUNCT
ejpam-6583	466	65	→	→	SYM
ejpam-6583	466	66	0	0	NUM
ejpam-6583	466	67	,	,	PUNCT
ejpam-6583	466	68	as	as	ADP
ejpam-6583	466	69	n	n	CCONJ
ejpam-6583	466	70	,	,	PUNCT
ejpam-6583	466	71	m	m	PROPN
ejpam-6583	466	72	→	→	SYM
ejpam-6583	466	73	+	+	NOUN
ejpam-6583	466	74	∞.	∞.	PROPN
ejpam-6583	466	75	since	since	SCONJ
ejpam-6583	466	76	sλi	sλi	NOUN
ejpam-6583	466	77	∈	∈	PROPN
ejpam-6583	466	78	(	(	PUNCT
ejpam-6583	466	79	0	0	NUM
ejpam-6583	466	80	,	,	PUNCT
ejpam-6583	466	81	1	1	NUM
ejpam-6583	466	82	)	)	PUNCT
ejpam-6583	466	83	for	for	ADP
ejpam-6583	466	84	all	all	DET
ejpam-6583	466	85	i	i	PRON
ejpam-6583	466	86	=	=	NOUN
ejpam-6583	466	87	1	1	NUM
ejpam-6583	466	88	,	,	PUNCT
ejpam-6583	466	89	2	2	NUM
ejpam-6583	466	90	,	,	PUNCT
ejpam-6583	466	91	·	·	PUNCT
ejpam-6583	466	92	·	·	PUNCT
ejpam-6583	466	93	·	·	PUNCT
ejpam-6583	466	94	,	,	PUNCT
ejpam-6583	467	1	d	d	NOUN
ejpam-6583	467	2	and	and	CCONJ
ejpam-6583	467	3	δb	δb	NOUN
ejpam-6583	467	4	r⊕d	r⊕d	NOUN
ejpam-6583	467	5	(	(	PUNCT
ejpam-6583	467	6	x0	x0	PROPN
ejpam-6583	467	7	,	,	PUNCT
ejpam-6583	467	8	x1	x1	PROPN
ejpam-6583	467	9	)	)	PUNCT
ejpam-6583	467	10	are	be	AUX
ejpam-6583	467	11	fixed	fix	VERB
ejpam-6583	467	12	,	,	PUNCT
ejpam-6583	467	13	it	it	PRON
ejpam-6583	467	14	is	be	AUX
ejpam-6583	467	15	evident	evident	ADJ
ejpam-6583	467	16	that	that	SCONJ
ejpam-6583	467	17	by	by	ADP
ejpam-6583	467	18	selectingm	selectingm	ADJ
ejpam-6583	467	19	sufficiently	sufficiently	ADV
ejpam-6583	467	20	large	large	ADJ
ejpam-6583	467	21	(	(	PUNCT
ejpam-6583	467	22	with	with	ADP
ejpam-6583	467	23	n	n	NOUN
ejpam-6583	467	24	>	>	X
ejpam-6583	467	25	m	m	PROPN
ejpam-6583	467	26	)	)	PUNCT
ejpam-6583	467	27	,	,	PUNCT
ejpam-6583	467	28	we	we	PRON
ejpam-6583	467	29	can	can	AUX
ejpam-6583	467	30	make	make	VERB
ejpam-6583	467	31	δb	δb	NOUN
ejpam-6583	467	32	r⊕d	r⊕d	NOUN
ejpam-6583	467	33	(	(	PUNCT
ejpam-6583	467	34	xn	xn	PROPN
ejpam-6583	467	35	,	,	PUNCT
ejpam-6583	467	36	xm	xm	PROPN
ejpam-6583	467	37	)	)	PUNCT
ejpam-6583	467	38	arbitrarily	arbitrarily	ADV
ejpam-6583	467	39	small	small	ADJ
ejpam-6583	467	40	.	.	PUNCT
ejpam-6583	468	1	this	this	PRON
ejpam-6583	468	2	shows	show	VERB
ejpam-6583	468	3	that	that	SCONJ
ejpam-6583	468	4	{	{	PUNCT
ejpam-6583	468	5	xn	xn	X
ejpam-6583	468	6	}	}	PUNCT
ejpam-6583	468	7	is	be	AUX
ejpam-6583	468	8	a	a	DET
ejpam-6583	468	9	cauchy	cauchy	ADJ
ejpam-6583	468	10	sequence	sequence	NOUN
ejpam-6583	468	11	.	.	PUNCT
ejpam-6583	469	1	finally	finally	ADV
ejpam-6583	469	2	,	,	PUNCT
ejpam-6583	469	3	because	because	SCONJ
ejpam-6583	469	4	(	(	PUNCT
ejpam-6583	469	5	x	x	X
ejpam-6583	469	6	,	,	PUNCT
ejpam-6583	469	7	r⊕d	r⊕d	NOUN
ejpam-6583	469	8	,	,	PUNCT
ejpam-6583	469	9	δb	δb	NOUN
ejpam-6583	469	10	r⊕d	r⊕d	NOUN
ejpam-6583	469	11	)	)	PUNCT
ejpam-6583	469	12	is	be	AUX
ejpam-6583	469	13	complete	complete	ADJ
ejpam-6583	469	14	,	,	PUNCT
ejpam-6583	469	15	there	there	PRON
ejpam-6583	469	16	exists	exist	VERB
ejpam-6583	469	17	some	some	DET
ejpam-6583	469	18	z	z	NOUN
ejpam-6583	469	19	∈	∈	PROPN
ejpam-6583	469	20	x	x	PUNCT
ejpam-6583	469	21	such	such	ADJ
ejpam-6583	469	22	that	that	PRON
ejpam-6583	469	23	xn	xn	PROPN
ejpam-6583	470	1	→	→	SYM
ejpam-6583	470	2	z.	z.	PROPN
ejpam-6583	470	3	to	to	PART
ejpam-6583	470	4	show	show	VERB
ejpam-6583	470	5	that	that	SCONJ
ejpam-6583	470	6	z	z	NOUN
ejpam-6583	470	7	is	be	AUX
ejpam-6583	470	8	a	a	DET
ejpam-6583	470	9	fixed	fix	VERB
ejpam-6583	470	10	point	point	NOUN
ejpam-6583	470	11	,	,	PUNCT
ejpam-6583	470	12	we	we	PRON
ejpam-6583	470	13	consider	consider	VERB
ejpam-6583	470	14	the	the	DET
ejpam-6583	470	15	distance	distance	NOUN
ejpam-6583	470	16	δb	δb	NOUN
ejpam-6583	470	17	r⊕d	r⊕d	NOUN
ejpam-6583	470	18	(	(	PUNCT
ejpam-6583	470	19	z	z	NOUN
ejpam-6583	470	20	,	,	PUNCT
ejpam-6583	470	21	f	f	PROPN
ejpam-6583	470	22	(	(	PUNCT
ejpam-6583	470	23	z	z	NOUN
ejpam-6583	470	24	)	)	PUNCT
ejpam-6583	470	25	)	)	PUNCT
ejpam-6583	470	26	.	.	PUNCT
ejpam-6583	471	1	from	from	ADP
ejpam-6583	471	2	the	the	DET
ejpam-6583	471	3	triangle	triangle	NOUN
ejpam-6583	471	4	inequality	inequality	NOUN
ejpam-6583	471	5	and	and	CCONJ
ejpam-6583	471	6	contraction	contraction	NOUN
ejpam-6583	471	7	condition	condition	NOUN
ejpam-6583	471	8	,	,	PUNCT
ejpam-6583	471	9	we	we	PRON
ejpam-6583	471	10	get	get	VERB
ejpam-6583	471	11	δb	δb	ADP
ejpam-6583	471	12	r⊕d	r⊕d	NOUN
ejpam-6583	471	13	(	(	PUNCT
ejpam-6583	471	14	z	z	NOUN
ejpam-6583	471	15	,	,	PUNCT
ejpam-6583	471	16	f	f	PROPN
ejpam-6583	471	17	(	(	PUNCT
ejpam-6583	471	18	z	z	NOUN
ejpam-6583	471	19	)	)	PUNCT
ejpam-6583	471	20	)	)	PUNCT
ejpam-6583	472	1	≾	≾	PROPN
ejpam-6583	472	2	s[δb	s[δb	PROPN
ejpam-6583	472	3	r⊕d	r⊕d	NOUN
ejpam-6583	472	4	(	(	PUNCT
ejpam-6583	472	5	z	z	NOUN
ejpam-6583	472	6	,	,	PUNCT
ejpam-6583	472	7	xn	xn	PROPN
ejpam-6583	472	8	)	)	PUNCT
ejpam-6583	473	1	+	+	CCONJ
ejpam-6583	473	2	δb	δb	NOUN
ejpam-6583	473	3	r⊕d	r⊕d	NOUN
ejpam-6583	473	4	(	(	PUNCT
ejpam-6583	473	5	xn	xn	PROPN
ejpam-6583	473	6	,	,	PUNCT
ejpam-6583	473	7	f	f	PROPN
ejpam-6583	473	8	(	(	PUNCT
ejpam-6583	473	9	z	z	NOUN
ejpam-6583	473	10	)	)	PUNCT
ejpam-6583	473	11	)	)	PUNCT
ejpam-6583	473	12	]	]	PUNCT
ejpam-6583	474	1	=	=	PUNCT
ejpam-6583	474	2	s[δb	s[δb	NOUN
ejpam-6583	474	3	r⊕d	r⊕d	NOUN
ejpam-6583	474	4	(	(	PUNCT
ejpam-6583	474	5	z	z	NOUN
ejpam-6583	474	6	,	,	PUNCT
ejpam-6583	474	7	xn	xn	PROPN
ejpam-6583	474	8	)	)	PUNCT
ejpam-6583	475	1	+	+	CCONJ
ejpam-6583	475	2	δb	δb	NOUN
ejpam-6583	475	3	r⊕d	r⊕d	NOUN
ejpam-6583	475	4	(	(	PUNCT
ejpam-6583	475	5	f	f	PROPN
ejpam-6583	475	6	(	(	PUNCT
ejpam-6583	475	7	xn−1),f	xn−1),f	PROPN
ejpam-6583	475	8	(	(	PUNCT
ejpam-6583	475	9	z	z	NOUN
ejpam-6583	475	10	)	)	PUNCT
ejpam-6583	475	11	)	)	PUNCT
ejpam-6583	475	12	]	]	PUNCT
ejpam-6583	476	1	≾	≾	PROPN
ejpam-6583	476	2	s	s	X
ejpam-6583	476	3	[	[	PUNCT
ejpam-6583	476	4	δb	δb	NOUN
ejpam-6583	476	5	r⊕d	r⊕d	NOUN
ejpam-6583	476	6	(	(	PUNCT
ejpam-6583	476	7	z	z	NOUN
ejpam-6583	476	8	,	,	PUNCT
ejpam-6583	476	9	xn	xn	PUNCT
ejpam-6583	476	10	)	)	PUNCT
ejpam-6583	477	1	+	+	CCONJ
ejpam-6583	477	2	diag	diag	PROPN
ejpam-6583	477	3	(	(	PUNCT
ejpam-6583	477	4	α1	α1	PROPN
ejpam-6583	477	5	,	,	PUNCT
ejpam-6583	477	6	·	·	PUNCT
ejpam-6583	477	7	·	·	PUNCT
ejpam-6583	477	8	·	·	PUNCT
ejpam-6583	477	9	,	,	PUNCT
ejpam-6583	477	10	αd	αd	PROPN
ejpam-6583	477	11	)	)	PUNCT
ejpam-6583	477	12	δb	δb	NOUN
ejpam-6583	477	13	r⊕d	r⊕d	NOUN
ejpam-6583	477	14	(	(	PUNCT
ejpam-6583	477	15	xn−1	xn−1	PROPN
ejpam-6583	477	16	,	,	PUNCT
ejpam-6583	477	17	z	z	NOUN
ejpam-6583	477	18	)	)	PUNCT
ejpam-6583	477	19	+	+	CCONJ
ejpam-6583	477	20	diag	diag	NOUN
ejpam-6583	477	21	(	(	PUNCT
ejpam-6583	477	22	β1	β1	PROPN
ejpam-6583	477	23	,	,	PUNCT
ejpam-6583	477	24	·	·	PUNCT
ejpam-6583	477	25	·	·	PUNCT
ejpam-6583	477	26	·	·	PUNCT
ejpam-6583	477	27	,	,	PUNCT
ejpam-6583	477	28	βd	βd	X
ejpam-6583	477	29	)	)	PUNCT
ejpam-6583	477	30	[	[	PUNCT
ejpam-6583	477	31	δb	δb	NOUN
ejpam-6583	477	32	r⊕d	r⊕d	NOUN
ejpam-6583	477	33	(	(	PUNCT
ejpam-6583	477	34	xn−1,f	xn−1,f	X
ejpam-6583	477	35	(	(	PUNCT
ejpam-6583	477	36	xn−1	xn−1	PROPN
ejpam-6583	477	37	)	)	PUNCT
ejpam-6583	477	38	)	)	PUNCT
ejpam-6583	478	1	+	+	CCONJ
ejpam-6583	478	2	δb	δb	NOUN
ejpam-6583	478	3	r⊕d	r⊕d	NOUN
ejpam-6583	478	4	(	(	PUNCT
ejpam-6583	478	5	z	z	NOUN
ejpam-6583	478	6	,	,	PUNCT
ejpam-6583	478	7	f	f	PROPN
ejpam-6583	478	8	(	(	PUNCT
ejpam-6583	478	9	z	z	NOUN
ejpam-6583	478	10	)	)	PUNCT
ejpam-6583	478	11	)	)	PUNCT
ejpam-6583	479	1	]	]	PUNCT
ejpam-6583	479	2	]	]	PUNCT
ejpam-6583	479	3	,	,	PUNCT
ejpam-6583	479	4	therefore	therefore	ADV
ejpam-6583	479	5	(	(	PUNCT
ejpam-6583	479	6	1−	1−	NUM
ejpam-6583	479	7	sβ1	sβ1	NOUN
ejpam-6583	479	8	,	,	PUNCT
ejpam-6583	479	9	·	·	PUNCT
ejpam-6583	479	10	·	·	PUNCT
ejpam-6583	479	11	·	·	PUNCT
ejpam-6583	479	12	,	,	PUNCT
ejpam-6583	479	13	1−	1−	NUM
ejpam-6583	479	14	sβd	sβd	NOUN
ejpam-6583	479	15	)	)	PUNCT
ejpam-6583	479	16	δb	δb	NOUN
ejpam-6583	479	17	r⊕d	r⊕d	NOUN
ejpam-6583	479	18	(	(	PUNCT
ejpam-6583	479	19	z	z	NOUN
ejpam-6583	479	20	,	,	PUNCT
ejpam-6583	479	21	f	f	PROPN
ejpam-6583	479	22	(	(	PUNCT
ejpam-6583	479	23	z	z	NOUN
ejpam-6583	479	24	)	)	PUNCT
ejpam-6583	479	25	)	)	PUNCT
ejpam-6583	480	1	≾	≾	NOUN
ejpam-6583	480	2	sδb	sδb	VERB
ejpam-6583	480	3	r⊕d	r⊕d	NOUN
ejpam-6583	480	4	(	(	PUNCT
ejpam-6583	480	5	z	z	NOUN
ejpam-6583	480	6	,	,	PUNCT
ejpam-6583	480	7	xn	xn	PUNCT
ejpam-6583	480	8	)	)	PUNCT
ejpam-6583	481	1	+	+	CCONJ
ejpam-6583	481	2	diag	diag	PROPN
ejpam-6583	481	3	(	(	PUNCT
ejpam-6583	481	4	sα1	sα1	PROPN
ejpam-6583	481	5	,	,	PUNCT
ejpam-6583	481	6	·	·	PUNCT
ejpam-6583	481	7	·	·	PUNCT
ejpam-6583	481	8	·	·	PUNCT
ejpam-6583	481	9	,	,	PUNCT
ejpam-6583	481	10	sαd	sαd	NOUN
ejpam-6583	481	11	)	)	PUNCT
ejpam-6583	481	12	δb	δb	NOUN
ejpam-6583	481	13	r⊕d	r⊕d	NOUN
ejpam-6583	481	14	(	(	PUNCT
ejpam-6583	481	15	xn−1	xn−1	PROPN
ejpam-6583	481	16	,	,	PUNCT
ejpam-6583	481	17	z	z	NOUN
ejpam-6583	481	18	)	)	PUNCT
ejpam-6583	481	19	+	+	CCONJ
ejpam-6583	481	20	diag	diag	NOUN
ejpam-6583	481	21	(	(	PUNCT
ejpam-6583	481	22	sβ1	sβ1	PROPN
ejpam-6583	481	23	,	,	PUNCT
ejpam-6583	481	24	·	·	PUNCT
ejpam-6583	481	25	·	·	PUNCT
ejpam-6583	481	26	·	·	PUNCT
ejpam-6583	481	27	,	,	PUNCT
ejpam-6583	481	28	sβd	sβd	NOUN
ejpam-6583	481	29	)	)	PUNCT
ejpam-6583	482	1	[	[	PUNCT
ejpam-6583	482	2	δb	δb	NOUN
ejpam-6583	482	3	r⊕d	r⊕d	NOUN
ejpam-6583	482	4	(	(	PUNCT
ejpam-6583	482	5	xn−1,f	xn−1,f	X
ejpam-6583	482	6	(	(	PUNCT
ejpam-6583	482	7	xn−1	xn−1	PROPN
ejpam-6583	482	8	)	)	PUNCT
ejpam-6583	482	9	)	)	PUNCT
ejpam-6583	482	10	]	]	PUNCT
ejpam-6583	483	1	→	→	PUNCT
ejpam-6583	483	2	0	0	NUM
ejpam-6583	483	3	,	,	PUNCT
ejpam-6583	483	4	and	and	CCONJ
ejpam-6583	483	5	since	since	SCONJ
ejpam-6583	483	6	xn	xn	PROPN
ejpam-6583	483	7	→	→	SYM
ejpam-6583	483	8	z	z	NOUN
ejpam-6583	483	9	it	it	PRON
ejpam-6583	483	10	is	be	AUX
ejpam-6583	483	11	clear	clear	ADJ
ejpam-6583	483	12	that	that	SCONJ
ejpam-6583	483	13	we	we	PRON
ejpam-6583	483	14	can	can	AUX
ejpam-6583	483	15	make	make	VERB
ejpam-6583	483	16	this	this	DET
ejpam-6583	483	17	distance	distance	NOUN
ejpam-6583	483	18	as	as	ADV
ejpam-6583	483	19	small	small	ADJ
ejpam-6583	483	20	as	as	SCONJ
ejpam-6583	483	21	we	we	PRON
ejpam-6583	483	22	please	please	VERB
ejpam-6583	483	23	by	by	ADP
ejpam-6583	483	24	choosing	choose	VERB
ejpam-6583	483	25	n	n	PRON
ejpam-6583	483	26	sufficiently	sufficiently	ADV
ejpam-6583	483	27	large	large	ADJ
ejpam-6583	483	28	.	.	PUNCT
ejpam-6583	484	1	we	we	PRON
ejpam-6583	484	2	conclude	conclude	VERB
ejpam-6583	484	3	that	that	SCONJ
ejpam-6583	484	4	δb	δb	NOUN
ejpam-6583	484	5	r⊕d	r⊕d	NOUN
ejpam-6583	484	6	(	(	PUNCT
ejpam-6583	484	7	z	z	NOUN
ejpam-6583	484	8	,	,	PUNCT
ejpam-6583	484	9	f	f	PROPN
ejpam-6583	484	10	(	(	PUNCT
ejpam-6583	484	11	z	z	NOUN
ejpam-6583	484	12	)	)	PUNCT
ejpam-6583	484	13	)	)	PUNCT
ejpam-6583	485	1	=	=	SYM
ejpam-6583	485	2	0	0	PUNCT
ejpam-6583	486	1	=	=	AUX
ejpam-6583	486	2	⇒	⇒	X
ejpam-6583	486	3	f	f	X
ejpam-6583	486	4	(	(	PUNCT
ejpam-6583	486	5	z	z	NOUN
ejpam-6583	486	6	)	)	PUNCT
ejpam-6583	487	1	=	=	SYM
ejpam-6583	487	2	z	z	NOUN
ejpam-6583	487	3	,	,	PUNCT
ejpam-6583	487	4	so	so	ADV
ejpam-6583	487	5	z	z	NOUN
ejpam-6583	487	6	∈	∈	PROPN
ejpam-6583	487	7	x	x	X
ejpam-6583	487	8	is	be	AUX
ejpam-6583	487	9	a	a	DET
ejpam-6583	487	10	fixed	fix	VERB
ejpam-6583	487	11	-	-	PUNCT
ejpam-6583	487	12	point	point	NOUN
ejpam-6583	487	13	of	of	ADP
ejpam-6583	487	14	f	f	PROPN
ejpam-6583	487	15	.	.	PUNCT
ejpam-6583	488	1	to	to	PART
ejpam-6583	488	2	prove	prove	VERB
ejpam-6583	488	3	uniqueness	uniqueness	NOUN
ejpam-6583	488	4	,	,	PUNCT
ejpam-6583	488	5	suppose	suppose	VERB
ejpam-6583	488	6	there	there	PRON
ejpam-6583	488	7	are	be	VERB
ejpam-6583	488	8	two	two	NUM
ejpam-6583	488	9	fixed	fix	VERB
ejpam-6583	488	10	points	point	NOUN
ejpam-6583	489	1	x	x	X
ejpam-6583	489	2	=	=	SYM
ejpam-6583	489	3	f	f	X
ejpam-6583	489	4	(	(	PUNCT
ejpam-6583	489	5	x	x	NOUN
ejpam-6583	489	6	)	)	PUNCT
ejpam-6583	489	7	and	and	CCONJ
ejpam-6583	489	8	y	y	PROPN
ejpam-6583	489	9	=	=	SYM
ejpam-6583	489	10	f	f	PROPN
ejpam-6583	489	11	(	(	PUNCT
ejpam-6583	489	12	y	y	NOUN
ejpam-6583	489	13	)	)	PUNCT
ejpam-6583	489	14	.	.	PUNCT
ejpam-6583	490	1	then	then	ADV
ejpam-6583	490	2	,	,	PUNCT
ejpam-6583	490	3	from	from	ADP
ejpam-6583	490	4	the	the	DET
ejpam-6583	490	5	contraction	contraction	NOUN
ejpam-6583	490	6	condition	condition	NOUN
ejpam-6583	490	7	,	,	PUNCT
ejpam-6583	490	8	we	we	PRON
ejpam-6583	490	9	have	have	VERB
ejpam-6583	490	10	δb	δb	NOUN
ejpam-6583	490	11	r⊕d	r⊕d	NOUN
ejpam-6583	490	12	(	(	PUNCT
ejpam-6583	490	13	x	x	X
ejpam-6583	490	14	,	,	PUNCT
ejpam-6583	490	15	y	y	NOUN
ejpam-6583	490	16	)	)	PUNCT
ejpam-6583	490	17	=	=	PUNCT
ejpam-6583	490	18	δb	δb	X
ejpam-6583	490	19	r⊕d	r⊕d	NOUN
ejpam-6583	490	20	(	(	PUNCT
ejpam-6583	490	21	f	f	PROPN
ejpam-6583	490	22	(	(	PUNCT
ejpam-6583	490	23	x),f	x),f	PROPN
ejpam-6583	490	24	(	(	PUNCT
ejpam-6583	490	25	y	y	NOUN
ejpam-6583	490	26	)	)	PUNCT
ejpam-6583	490	27	)	)	PUNCT
ejpam-6583	491	1	g.	g.	PROPN
ejpam-6583	491	2	albeladi	albeladi	PROPN
ejpam-6583	491	3	,	,	PUNCT
ejpam-6583	491	4	s.	s.	PROPN
ejpam-6583	491	5	omran	omran	PROPN
ejpam-6583	491	6	/	/	SYM
ejpam-6583	491	7	eur	eur	PROPN
ejpam-6583	491	8	.	.	PUNCT
ejpam-6583	492	1	j.	j.	PROPN
ejpam-6583	492	2	pure	pure	PROPN
ejpam-6583	492	3	appl	appl	PROPN
ejpam-6583	492	4	.	.	PROPN
ejpam-6583	492	5	math	math	PROPN
ejpam-6583	492	6	,	,	PUNCT
ejpam-6583	492	7	18	18	NUM
ejpam-6583	492	8	(	(	PUNCT
ejpam-6583	492	9	3	3	NUM
ejpam-6583	492	10	)	)	PUNCT
ejpam-6583	492	11	(	(	PUNCT
ejpam-6583	492	12	2025	2025	NUM
ejpam-6583	492	13	)	)	PUNCT
ejpam-6583	492	14	,	,	PUNCT
ejpam-6583	492	15	6583	6583	NUM
ejpam-6583	492	16	21	21	NUM
ejpam-6583	492	17	of	of	ADP
ejpam-6583	492	18	27	27	NUM
ejpam-6583	492	19	≾	≾	PROPN
ejpam-6583	492	20	diag	diag	NOUN
ejpam-6583	492	21	(	(	PUNCT
ejpam-6583	492	22	α1	α1	PROPN
ejpam-6583	492	23	,	,	PUNCT
ejpam-6583	492	24	α2	α2	ADJ
ejpam-6583	492	25	,	,	PUNCT
ejpam-6583	492	26	·	·	PUNCT
ejpam-6583	492	27	·	·	PUNCT
ejpam-6583	492	28	·	·	PUNCT
ejpam-6583	492	29	,	,	PUNCT
ejpam-6583	492	30	αd	αd	PROPN
ejpam-6583	492	31	)	)	PUNCT
ejpam-6583	492	32	δb	δb	NOUN
ejpam-6583	492	33	r⊕d	r⊕d	NOUN
ejpam-6583	492	34	(	(	PUNCT
ejpam-6583	492	35	x	x	X
ejpam-6583	492	36	,	,	PUNCT
ejpam-6583	492	37	y	y	PROPN
ejpam-6583	492	38	)	)	PUNCT
ejpam-6583	493	1	+	+	NOUN
ejpam-6583	493	2	diag	diag	NOUN
ejpam-6583	493	3	(	(	PUNCT
ejpam-6583	493	4	β1	β1	PROPN
ejpam-6583	493	5	,	,	PUNCT
ejpam-6583	493	6	β2	β2	VERB
ejpam-6583	493	7	,	,	PUNCT
ejpam-6583	493	8	·	·	PUNCT
ejpam-6583	493	9	·	·	PUNCT
ejpam-6583	493	10	·	·	PUNCT
ejpam-6583	493	11	,	,	PUNCT
ejpam-6583	493	12	βd	βd	X
ejpam-6583	493	13	)	)	PUNCT
ejpam-6583	494	1	[	[	X
ejpam-6583	494	2	δb	δb	X
ejpam-6583	494	3	r⊕d	r⊕d	NOUN
ejpam-6583	494	4	(	(	PUNCT
ejpam-6583	494	5	x	x	X
ejpam-6583	494	6	,	,	PUNCT
ejpam-6583	494	7	f	f	PROPN
ejpam-6583	494	8	(	(	PUNCT
ejpam-6583	494	9	x	x	NOUN
ejpam-6583	494	10	)	)	PUNCT
ejpam-6583	494	11	)	)	PUNCT
ejpam-6583	495	1	+	+	CCONJ
ejpam-6583	495	2	δb	δb	NOUN
ejpam-6583	495	3	r⊕d	r⊕d	NOUN
ejpam-6583	495	4	(	(	PUNCT
ejpam-6583	495	5	y	y	PROPN
ejpam-6583	495	6	,	,	PUNCT
ejpam-6583	495	7	f	f	PROPN
ejpam-6583	495	8	(	(	PUNCT
ejpam-6583	495	9	y	y	NOUN
ejpam-6583	495	10	)	)	PUNCT
ejpam-6583	495	11	)	)	PUNCT
ejpam-6583	495	12	]	]	PUNCT
ejpam-6583	496	1	=	=	PUNCT
ejpam-6583	496	2	diag	diag	X
ejpam-6583	496	3	(	(	PUNCT
ejpam-6583	496	4	α1	α1	PROPN
ejpam-6583	496	5	,	,	PUNCT
ejpam-6583	496	6	α2	α2	ADJ
ejpam-6583	496	7	,	,	PUNCT
ejpam-6583	496	8	·	·	PUNCT
ejpam-6583	496	9	·	·	PUNCT
ejpam-6583	496	10	·	·	PUNCT
ejpam-6583	496	11	,	,	PUNCT
ejpam-6583	496	12	αd	αd	PROPN
ejpam-6583	496	13	)	)	PUNCT
ejpam-6583	496	14	δb	δb	NOUN
ejpam-6583	496	15	r⊕d	r⊕d	NOUN
ejpam-6583	496	16	(	(	PUNCT
ejpam-6583	496	17	x	x	NOUN
ejpam-6583	496	18	,	,	PUNCT
ejpam-6583	496	19	y	y	PROPN
ejpam-6583	496	20	)	)	PUNCT
ejpam-6583	496	21	≺	≺	NOUN
ejpam-6583	496	22	δb	δb	NOUN
ejpam-6583	496	23	r⊕d	r⊕d	NOUN
ejpam-6583	496	24	(	(	PUNCT
ejpam-6583	496	25	x	x	X
ejpam-6583	496	26	,	,	PUNCT
ejpam-6583	496	27	y	y	PROPN
ejpam-6583	496	28	)	)	PUNCT
ejpam-6583	496	29	,	,	PUNCT
ejpam-6583	496	30	this	this	PRON
ejpam-6583	496	31	implies	imply	VERB
ejpam-6583	496	32	δb	δb	NOUN
ejpam-6583	496	33	r⊕d	r⊕d	NOUN
ejpam-6583	496	34	(	(	PUNCT
ejpam-6583	496	35	x	x	X
ejpam-6583	496	36	,	,	PUNCT
ejpam-6583	496	37	y	y	NOUN
ejpam-6583	496	38	)	)	PUNCT
ejpam-6583	496	39	=	=	SYM
ejpam-6583	497	1	0	0	X
ejpam-6583	497	2	.	.	PUNCT
ejpam-6583	498	1	hence	hence	ADV
ejpam-6583	498	2	x	x	X
ejpam-6583	498	3	=	=	SYM
ejpam-6583	498	4	y	y	PROPN
ejpam-6583	498	5	,	,	PUNCT
ejpam-6583	498	6	and	and	CCONJ
ejpam-6583	498	7	the	the	DET
ejpam-6583	498	8	fixed	fix	VERB
ejpam-6583	498	9	-	-	PUNCT
ejpam-6583	498	10	point	point	NOUN
ejpam-6583	498	11	x	x	PUNCT
ejpam-6583	498	12	of	of	ADP
ejpam-6583	498	13	f	f	PROPN
ejpam-6583	498	14	is	be	AUX
ejpam-6583	498	15	unique	unique	ADJ
ejpam-6583	498	16	.	.	PUNCT
ejpam-6583	499	1	theorem	theorem	ADJ
ejpam-6583	499	2	7	7	NUM
ejpam-6583	499	3	.	.	PUNCT
ejpam-6583	499	4	suppose	suppose	VERB
ejpam-6583	499	5	that	that	SCONJ
ejpam-6583	499	6	(	(	PUNCT
ejpam-6583	499	7	x	x	X
ejpam-6583	499	8	,	,	PUNCT
ejpam-6583	499	9	r⊕d	r⊕d	NOUN
ejpam-6583	499	10	,	,	PUNCT
ejpam-6583	499	11	δb	δb	NOUN
ejpam-6583	499	12	r⊕d	r⊕d	NOUN
ejpam-6583	499	13	)	)	PUNCT
ejpam-6583	499	14	is	be	AUX
ejpam-6583	499	15	a	a	DET
ejpam-6583	499	16	complete	complete	ADJ
ejpam-6583	499	17	generalized	generalized	ADJ
ejpam-6583	499	18	b	b	X
ejpam-6583	499	19	-	-	ADJ
ejpam-6583	499	20	metric	metric	ADJ
ejpam-6583	499	21	space	space	NOUN
ejpam-6583	499	22	endowed	endow	VERB
ejpam-6583	499	23	with	with	ADP
ejpam-6583	499	24	the	the	DET
ejpam-6583	499	25	orthogonal	orthogonal	ADJ
ejpam-6583	499	26	direct	direct	ADJ
ejpam-6583	499	27	sum	sum	NOUN
ejpam-6583	499	28	and	and	CCONJ
ejpam-6583	499	29	f	f	NOUN
ejpam-6583	499	30	:	:	PUNCT
ejpam-6583	499	31	x	x	X
ejpam-6583	499	32	→	→	PUNCT
ejpam-6583	499	33	x	x	X
ejpam-6583	499	34	is	be	AUX
ejpam-6583	499	35	a	a	DET
ejpam-6583	499	36	continuous	continuous	ADJ
ejpam-6583	499	37	operator	operator	NOUN
ejpam-6583	499	38	satisfying	satisfy	VERB
ejpam-6583	499	39	the	the	DET
ejpam-6583	499	40	following	follow	VERB
ejpam-6583	499	41	condition	condition	NOUN
ejpam-6583	499	42	δb	δb	ADP
ejpam-6583	499	43	r⊕d	r⊕d	NOUN
ejpam-6583	499	44	(	(	PUNCT
ejpam-6583	499	45	fx	fx	PROPN
ejpam-6583	499	46	,	,	PUNCT
ejpam-6583	499	47	fy	fy	PROPN
ejpam-6583	499	48	)	)	PUNCT
ejpam-6583	499	49	≾	≾	PROPN
ejpam-6583	499	50	diag	diag	NOUN
ejpam-6583	499	51	(	(	PUNCT
ejpam-6583	499	52	α1	α1	PROPN
ejpam-6583	499	53	,	,	PUNCT
ejpam-6583	499	54	α2	α2	ADJ
ejpam-6583	499	55	,	,	PUNCT
ejpam-6583	499	56	·	·	PUNCT
ejpam-6583	499	57	·	·	PUNCT
ejpam-6583	499	58	·	·	PUNCT
ejpam-6583	499	59	,	,	PUNCT
ejpam-6583	499	60	αd	αd	PROPN
ejpam-6583	499	61	)	)	PUNCT
ejpam-6583	499	62	δb	δb	NOUN
ejpam-6583	499	63	r⊕d	r⊕d	NOUN
ejpam-6583	499	64	(	(	PUNCT
ejpam-6583	499	65	x	x	X
ejpam-6583	499	66	,	,	PUNCT
ejpam-6583	499	67	y	y	PROPN
ejpam-6583	499	68	)	)	PUNCT
ejpam-6583	499	69	(	(	PUNCT
ejpam-6583	500	1	3	3	X
ejpam-6583	500	2	)	)	PUNCT
ejpam-6583	500	3	+	+	NOUN
ejpam-6583	500	4	diag	diag	NOUN
ejpam-6583	500	5	(	(	PUNCT
ejpam-6583	500	6	β1	β1	PROPN
ejpam-6583	500	7	,	,	PUNCT
ejpam-6583	500	8	β2	β2	VERB
ejpam-6583	500	9	,	,	PUNCT
ejpam-6583	500	10	·	·	PUNCT
ejpam-6583	500	11	·	·	PUNCT
ejpam-6583	500	12	·	·	PUNCT
ejpam-6583	500	13	,	,	PUNCT
ejpam-6583	500	14	βd	βd	X
ejpam-6583	500	15	)	)	PUNCT
ejpam-6583	501	1	[	[	X
ejpam-6583	501	2	δb	δb	X
ejpam-6583	501	3	r⊕d	r⊕d	NOUN
ejpam-6583	501	4	(	(	PUNCT
ejpam-6583	501	5	x	x	X
ejpam-6583	501	6	,	,	PUNCT
ejpam-6583	501	7	f	f	PROPN
ejpam-6583	501	8	(	(	PUNCT
ejpam-6583	501	9	x	x	NOUN
ejpam-6583	501	10	)	)	PUNCT
ejpam-6583	501	11	)	)	PUNCT
ejpam-6583	502	1	+	+	CCONJ
ejpam-6583	502	2	δb	δb	NOUN
ejpam-6583	502	3	r⊕d	r⊕d	NOUN
ejpam-6583	502	4	(	(	PUNCT
ejpam-6583	502	5	y	y	PROPN
ejpam-6583	502	6	,	,	PUNCT
ejpam-6583	502	7	f	f	PROPN
ejpam-6583	502	8	(	(	PUNCT
ejpam-6583	502	9	y	y	NOUN
ejpam-6583	502	10	)	)	PUNCT
ejpam-6583	502	11	)	)	PUNCT
ejpam-6583	502	12	]	]	PUNCT
ejpam-6583	503	1	+	+	CCONJ
ejpam-6583	503	2	diag	diag	PROPN
ejpam-6583	503	3	(	(	PUNCT
ejpam-6583	503	4	γ1	γ1	PROPN
ejpam-6583	503	5	,	,	PUNCT
ejpam-6583	503	6	γ2	γ2	PROPN
ejpam-6583	503	7	,	,	PUNCT
ejpam-6583	503	8	·	·	PUNCT
ejpam-6583	503	9	·	·	PUNCT
ejpam-6583	503	10	·	·	PUNCT
ejpam-6583	503	11	,	,	PUNCT
ejpam-6583	503	12	γd	γd	ADP
ejpam-6583	503	13	)	)	PUNCT
ejpam-6583	504	1	[	[	X
ejpam-6583	504	2	δb	δb	X
ejpam-6583	504	3	r⊕d	r⊕d	NOUN
ejpam-6583	504	4	(	(	PUNCT
ejpam-6583	504	5	x	x	X
ejpam-6583	504	6	,	,	PUNCT
ejpam-6583	504	7	f	f	PROPN
ejpam-6583	504	8	(	(	PUNCT
ejpam-6583	504	9	y	y	NOUN
ejpam-6583	504	10	)	)	PUNCT
ejpam-6583	504	11	)	)	PUNCT
ejpam-6583	505	1	+	+	CCONJ
ejpam-6583	505	2	δb	δb	NOUN
ejpam-6583	505	3	r⊕d	r⊕d	NOUN
ejpam-6583	505	4	(	(	PUNCT
ejpam-6583	505	5	y	y	PROPN
ejpam-6583	505	6	,	,	PUNCT
ejpam-6583	505	7	f	f	PROPN
ejpam-6583	505	8	(	(	PUNCT
ejpam-6583	505	9	x))],(4	x))],(4	PROPN
ejpam-6583	505	10	)	)	PUNCT
ejpam-6583	505	11	for	for	ADP
ejpam-6583	505	12	αi	αi	NOUN
ejpam-6583	505	13	,	,	PUNCT
ejpam-6583	505	14	βi	βi	PRON
ejpam-6583	505	15	,	,	PUNCT
ejpam-6583	505	16	γi	γi	X
ejpam-6583	505	17	∈	∈	PROPN
ejpam-6583	505	18	r+	r+	PUNCT
ejpam-6583	505	19	∀	∀	PUNCT
ejpam-6583	506	1	i	i	NOUN
ejpam-6583	506	2	=	=	NOUN
ejpam-6583	506	3	1	1	NUM
ejpam-6583	506	4	,	,	PUNCT
ejpam-6583	506	5	2	2	NUM
ejpam-6583	506	6	,	,	PUNCT
ejpam-6583	506	7	3	3	NUM
ejpam-6583	506	8	,	,	PUNCT
ejpam-6583	506	9	·	·	PUNCT
ejpam-6583	506	10	·	·	PUNCT
ejpam-6583	506	11	·	·	PUNCT
ejpam-6583	506	12	,	,	PUNCT
ejpam-6583	507	1	d	d	NOUN
ejpam-6583	507	2	and	and	CCONJ
ejpam-6583	507	3	αi	αi	VERB
ejpam-6583	508	1	+	+	CCONJ
ejpam-6583	508	2	2(βi	2(βi	NUM
ejpam-6583	508	3	+	+	CCONJ
ejpam-6583	508	4	sγi	sγi	ADJ
ejpam-6583	508	5	)	)	PUNCT
ejpam-6583	508	6	∈	∈	NOUN
ejpam-6583	509	1	[	[	X
ejpam-6583	509	2	0	0	NUM
ejpam-6583	509	3	,	,	PUNCT
ejpam-6583	509	4	1	1	NUM
ejpam-6583	509	5	)	)	PUNCT
ejpam-6583	509	6	,	,	PUNCT
ejpam-6583	509	7	for	for	ADP
ejpam-6583	509	8	each	each	DET
ejpam-6583	509	9	x	x	NOUN
ejpam-6583	509	10	,	,	PUNCT
ejpam-6583	509	11	y	y	PROPN
ejpam-6583	509	12	∈	∈	PROPN
ejpam-6583	509	13	x	x	X
ejpam-6583	509	14	.	.	PUNCT
ejpam-6583	510	1	then	then	ADV
ejpam-6583	510	2	,	,	PUNCT
ejpam-6583	510	3	f	f	PROPN
ejpam-6583	510	4	has	have	VERB
ejpam-6583	510	5	a	a	DET
ejpam-6583	510	6	unique	unique	ADJ
ejpam-6583	510	7	fixed	fix	VERB
ejpam-6583	510	8	-	-	PUNCT
ejpam-6583	510	9	point	point	NOUN
ejpam-6583	510	10	in	in	ADP
ejpam-6583	510	11	x	x	X
ejpam-6583	510	12	.	.	PUNCT
ejpam-6583	511	1	proof	proof	NOUN
ejpam-6583	511	2	.	.	PUNCT
ejpam-6583	512	1	let	let	VERB
ejpam-6583	512	2	x0	x0	PROPN
ejpam-6583	512	3	be	be	AUX
ejpam-6583	512	4	any	any	DET
ejpam-6583	512	5	point	point	NOUN
ejpam-6583	512	6	in	in	ADP
ejpam-6583	512	7	x	x	SYM
ejpam-6583	512	8	,	,	PUNCT
ejpam-6583	512	9	that	that	ADV
ejpam-6583	512	10	is	is	ADV
ejpam-6583	512	11	x0	x0	PROPN
ejpam-6583	512	12	∈	∈	PROPN
ejpam-6583	513	1	x	x	X
ejpam-6583	513	2	.	.	PUNCT
ejpam-6583	514	1	let	let	VERB
ejpam-6583	514	2	us	we	PRON
ejpam-6583	514	3	define	define	VERB
ejpam-6583	514	4	a	a	DET
ejpam-6583	514	5	sequence	sequence	NOUN
ejpam-6583	514	6	{	{	PUNCT
ejpam-6583	514	7	xn	xn	NOUN
ejpam-6583	514	8	}	}	PUNCT
ejpam-6583	514	9	in	in	ADP
ejpam-6583	514	10	x	x	PUNCT
ejpam-6583	514	11	as	as	SCONJ
ejpam-6583	514	12	given	give	VERB
ejpam-6583	514	13	below	below	ADV
ejpam-6583	514	14	.	.	PUNCT
ejpam-6583	515	1	xn+1	xn+1	PUNCT
ejpam-6583	516	1	=	=	SYM
ejpam-6583	516	2	f	f	PROPN
ejpam-6583	516	3	(	(	PUNCT
ejpam-6583	516	4	xn	xn	PROPN
ejpam-6583	516	5	)	)	PUNCT
ejpam-6583	516	6	=	=	SYM
ejpam-6583	516	7	fn+1(x0	fn+1(x0	ADJ
ejpam-6583	516	8	)	)	PUNCT
ejpam-6583	516	9	∀	∀	X
ejpam-6583	516	10	n	n	PRON
ejpam-6583	516	11	≥	≥	NOUN
ejpam-6583	516	12	0	0	NUM
ejpam-6583	516	13	.	.	PUNCT
ejpam-6583	517	1	we	we	PRON
ejpam-6583	517	2	have	have	VERB
ejpam-6583	517	3	δb	δb	NOUN
ejpam-6583	517	4	r⊕d	r⊕d	NOUN
ejpam-6583	517	5	(	(	PUNCT
ejpam-6583	517	6	xn	xn	PROPN
ejpam-6583	517	7	,	,	PUNCT
ejpam-6583	517	8	xn+1	xn+1	NUM
ejpam-6583	517	9	)	)	PUNCT
ejpam-6583	517	10	=	=	PUNCT
ejpam-6583	517	11	δb	δb	X
ejpam-6583	517	12	r⊕d	r⊕d	NOUN
ejpam-6583	517	13	(	(	PUNCT
ejpam-6583	517	14	f	f	PROPN
ejpam-6583	517	15	(	(	PUNCT
ejpam-6583	517	16	xn−1),f	xn−1),f	PROPN
ejpam-6583	517	17	(	(	PUNCT
ejpam-6583	517	18	xn	xn	PROPN
ejpam-6583	517	19	)	)	PUNCT
ejpam-6583	517	20	)	)	PUNCT
ejpam-6583	518	1	≾	≾	PROPN
ejpam-6583	518	2	(	(	PUNCT
ejpam-6583	518	3	α1	α1	PROPN
ejpam-6583	518	4	,	,	PUNCT
ejpam-6583	518	5	α2	α2	ADJ
ejpam-6583	518	6	,	,	PUNCT
ejpam-6583	518	7	·	·	PUNCT
ejpam-6583	518	8	·	·	PUNCT
ejpam-6583	518	9	·	·	PUNCT
ejpam-6583	518	10	,	,	PUNCT
ejpam-6583	518	11	αd	αd	PROPN
ejpam-6583	518	12	)	)	PUNCT
ejpam-6583	518	13	δb	δb	NOUN
ejpam-6583	518	14	r⊕d	r⊕d	NOUN
ejpam-6583	518	15	(	(	PUNCT
ejpam-6583	518	16	xn−1	xn−1	PROPN
ejpam-6583	518	17	,	,	PUNCT
ejpam-6583	518	18	xn	xn	PUNCT
ejpam-6583	518	19	)	)	PUNCT
ejpam-6583	519	1	+	+	NOUN
ejpam-6583	519	2	diag	diag	NOUN
ejpam-6583	519	3	(	(	PUNCT
ejpam-6583	519	4	β1	β1	PROPN
ejpam-6583	519	5	,	,	PUNCT
ejpam-6583	519	6	β2	β2	VERB
ejpam-6583	519	7	,	,	PUNCT
ejpam-6583	519	8	·	·	PUNCT
ejpam-6583	519	9	·	·	PUNCT
ejpam-6583	519	10	·	·	PUNCT
ejpam-6583	519	11	,	,	PUNCT
ejpam-6583	519	12	βd	βd	X
ejpam-6583	519	13	)	)	PUNCT
ejpam-6583	520	1	[	[	X
ejpam-6583	520	2	δb	δb	X
ejpam-6583	520	3	r⊕d	r⊕d	NOUN
ejpam-6583	520	4	(	(	PUNCT
ejpam-6583	520	5	xn−1,f	xn−1,f	X
ejpam-6583	520	6	(	(	PUNCT
ejpam-6583	520	7	xn−1	xn−1	PROPN
ejpam-6583	520	8	)	)	PUNCT
ejpam-6583	520	9	)	)	PUNCT
ejpam-6583	521	1	+	+	CCONJ
ejpam-6583	521	2	δb	δb	NOUN
ejpam-6583	521	3	r⊕d	r⊕d	NOUN
ejpam-6583	521	4	(	(	PUNCT
ejpam-6583	521	5	xn	xn	PROPN
ejpam-6583	521	6	,	,	PUNCT
ejpam-6583	521	7	f	f	PROPN
ejpam-6583	521	8	(	(	PUNCT
ejpam-6583	521	9	xn	xn	PROPN
ejpam-6583	521	10	)	)	PUNCT
ejpam-6583	521	11	)	)	PUNCT
ejpam-6583	521	12	]	]	PUNCT
ejpam-6583	522	1	+	+	CCONJ
ejpam-6583	522	2	diag	diag	PROPN
ejpam-6583	522	3	(	(	PUNCT
ejpam-6583	522	4	γ1	γ1	PROPN
ejpam-6583	522	5	,	,	PUNCT
ejpam-6583	522	6	γ2	γ2	PROPN
ejpam-6583	522	7	,	,	PUNCT
ejpam-6583	522	8	·	·	PUNCT
ejpam-6583	522	9	·	·	PUNCT
ejpam-6583	522	10	·	·	PUNCT
ejpam-6583	522	11	,	,	PUNCT
ejpam-6583	522	12	γd	γd	ADP
ejpam-6583	522	13	)	)	PUNCT
ejpam-6583	523	1	[	[	X
ejpam-6583	523	2	δb	δb	X
ejpam-6583	523	3	r⊕d	r⊕d	NOUN
ejpam-6583	523	4	(	(	PUNCT
ejpam-6583	523	5	xn−1,f	xn−1,f	X
ejpam-6583	523	6	(	(	PUNCT
ejpam-6583	523	7	xn	xn	NOUN
ejpam-6583	523	8	)	)	PUNCT
ejpam-6583	523	9	)	)	PUNCT
ejpam-6583	524	1	+	+	CCONJ
ejpam-6583	524	2	δb	δb	NOUN
ejpam-6583	524	3	r⊕d	r⊕d	NOUN
ejpam-6583	524	4	(	(	PUNCT
ejpam-6583	524	5	xn	xn	PROPN
ejpam-6583	524	6	,	,	PUNCT
ejpam-6583	524	7	f	f	PROPN
ejpam-6583	524	8	(	(	PUNCT
ejpam-6583	524	9	xn−1	xn−1	PROPN
ejpam-6583	524	10	)	)	PUNCT
ejpam-6583	524	11	)	)	PUNCT
ejpam-6583	524	12	]	]	PUNCT
ejpam-6583	525	1	=	=	PUNCT
ejpam-6583	525	2	diag	diag	X
ejpam-6583	525	3	(	(	PUNCT
ejpam-6583	525	4	α1	α1	PROPN
ejpam-6583	525	5	,	,	PUNCT
ejpam-6583	525	6	α2	α2	ADJ
ejpam-6583	525	7	,	,	PUNCT
ejpam-6583	525	8	·	·	PUNCT
ejpam-6583	525	9	·	·	PUNCT
ejpam-6583	525	10	·	·	PUNCT
ejpam-6583	525	11	,	,	PUNCT
ejpam-6583	525	12	αd	αd	PROPN
ejpam-6583	525	13	)	)	PUNCT
ejpam-6583	525	14	δb	δb	NOUN
ejpam-6583	525	15	r⊕d	r⊕d	NOUN
ejpam-6583	525	16	(	(	PUNCT
ejpam-6583	525	17	xn−1	xn−1	PROPN
ejpam-6583	525	18	,	,	PUNCT
ejpam-6583	525	19	xn	xn	PUNCT
ejpam-6583	525	20	)	)	PUNCT
ejpam-6583	526	1	+	+	NOUN
ejpam-6583	526	2	diag	diag	NOUN
ejpam-6583	526	3	(	(	PUNCT
ejpam-6583	526	4	β1	β1	PROPN
ejpam-6583	526	5	,	,	PUNCT
ejpam-6583	526	6	β2	β2	VERB
ejpam-6583	526	7	,	,	PUNCT
ejpam-6583	526	8	·	·	PUNCT
ejpam-6583	526	9	·	·	PUNCT
ejpam-6583	526	10	·	·	PUNCT
ejpam-6583	526	11	,	,	PUNCT
ejpam-6583	526	12	βd	βd	X
ejpam-6583	526	13	)	)	PUNCT
ejpam-6583	527	1	[	[	X
ejpam-6583	527	2	δb	δb	X
ejpam-6583	527	3	r⊕d	r⊕d	NOUN
ejpam-6583	527	4	(	(	PUNCT
ejpam-6583	527	5	xn−1	xn−1	PROPN
ejpam-6583	527	6	,	,	PUNCT
ejpam-6583	527	7	xn	xn	PUNCT
ejpam-6583	527	8	)	)	PUNCT
ejpam-6583	528	1	+	+	CCONJ
ejpam-6583	528	2	δb	δb	NOUN
ejpam-6583	528	3	r⊕d	r⊕d	NOUN
ejpam-6583	528	4	(	(	PUNCT
ejpam-6583	528	5	xn	xn	PROPN
ejpam-6583	528	6	,	,	PUNCT
ejpam-6583	528	7	xn+1	xn+1	NUM
ejpam-6583	528	8	)	)	PUNCT
ejpam-6583	528	9	]	]	PUNCT
ejpam-6583	529	1	+	+	CCONJ
ejpam-6583	529	2	diag	diag	PROPN
ejpam-6583	529	3	(	(	PUNCT
ejpam-6583	529	4	γ1	γ1	PROPN
ejpam-6583	529	5	,	,	PUNCT
ejpam-6583	529	6	γ2	γ2	PROPN
ejpam-6583	529	7	,	,	PUNCT
ejpam-6583	529	8	·	·	PUNCT
ejpam-6583	529	9	·	·	PUNCT
ejpam-6583	529	10	·	·	PUNCT
ejpam-6583	529	11	,	,	PUNCT
ejpam-6583	529	12	γd	γd	ADP
ejpam-6583	529	13	)	)	PUNCT
ejpam-6583	530	1	[	[	X
ejpam-6583	530	2	δb	δb	X
ejpam-6583	530	3	r⊕d	r⊕d	NOUN
ejpam-6583	530	4	(	(	PUNCT
ejpam-6583	530	5	xn−1	xn−1	PROPN
ejpam-6583	530	6	,	,	PUNCT
ejpam-6583	530	7	xn+1	xn+1	NUM
ejpam-6583	530	8	)	)	PUNCT
ejpam-6583	530	9	)	)	PUNCT
ejpam-6583	530	10	]	]	PUNCT
ejpam-6583	530	11	≾	≾	PROPN
ejpam-6583	530	12	diag	diag	NOUN
ejpam-6583	530	13	(	(	PUNCT
ejpam-6583	530	14	α1	α1	PROPN
ejpam-6583	530	15	+	+	CCONJ
ejpam-6583	530	16	β1	β1	PROPN
ejpam-6583	530	17	,	,	PUNCT
ejpam-6583	530	18	α2	α2	PROPN
ejpam-6583	530	19	+	+	CCONJ
ejpam-6583	530	20	β2	β2	VERB
ejpam-6583	530	21	,	,	PUNCT
ejpam-6583	530	22	·	·	PUNCT
ejpam-6583	530	23	·	·	PUNCT
ejpam-6583	530	24	·	·	PUNCT
ejpam-6583	530	25	,	,	PUNCT
ejpam-6583	530	26	αd	αd	PROPN
ejpam-6583	530	27	+	+	CCONJ
ejpam-6583	530	28	βd	βd	ADV
ejpam-6583	530	29	)	)	PUNCT
ejpam-6583	530	30	δb	δb	NOUN
ejpam-6583	530	31	r⊕d	r⊕d	NOUN
ejpam-6583	530	32	(	(	PUNCT
ejpam-6583	530	33	xn−1	xn−1	PROPN
ejpam-6583	530	34	,	,	PUNCT
ejpam-6583	530	35	xn	xn	PUNCT
ejpam-6583	530	36	)	)	PUNCT
ejpam-6583	531	1	+	+	NOUN
ejpam-6583	531	2	diag	diag	NOUN
ejpam-6583	531	3	(	(	PUNCT
ejpam-6583	531	4	β1	β1	PROPN
ejpam-6583	531	5	,	,	PUNCT
ejpam-6583	531	6	β2	β2	VERB
ejpam-6583	531	7	,	,	PUNCT
ejpam-6583	531	8	·	·	PUNCT
ejpam-6583	531	9	·	·	PUNCT
ejpam-6583	531	10	·	·	PUNCT
ejpam-6583	531	11	,	,	PUNCT
ejpam-6583	531	12	βd	βd	X
ejpam-6583	531	13	)	)	PUNCT
ejpam-6583	531	14	δb	δb	NOUN
ejpam-6583	531	15	r⊕d	r⊕d	NOUN
ejpam-6583	531	16	(	(	PUNCT
ejpam-6583	531	17	xn	xn	PROPN
ejpam-6583	531	18	,	,	PUNCT
ejpam-6583	531	19	xn+1	xn+1	NUM
ejpam-6583	531	20	)	)	PUNCT
ejpam-6583	532	1	+	+	NUM
ejpam-6583	532	2	diag	diag	NOUN
ejpam-6583	532	3	(	(	PUNCT
ejpam-6583	532	4	sγ1	sγ1	PROPN
ejpam-6583	532	5	,	,	PUNCT
ejpam-6583	532	6	sγ2	sγ2	PROPN
ejpam-6583	532	7	,	,	PUNCT
ejpam-6583	532	8	·	·	PUNCT
ejpam-6583	532	9	·	·	PUNCT
ejpam-6583	532	10	·	·	PUNCT
ejpam-6583	532	11	,	,	PUNCT
ejpam-6583	532	12	sγd	sγd	PROPN
ejpam-6583	532	13	)	)	PUNCT
ejpam-6583	533	1	[	[	X
ejpam-6583	533	2	δb	δb	X
ejpam-6583	533	3	r⊕d	r⊕d	NOUN
ejpam-6583	533	4	(	(	PUNCT
ejpam-6583	533	5	xn−1	xn−1	PROPN
ejpam-6583	533	6	,	,	PUNCT
ejpam-6583	533	7	xn	xn	PUNCT
ejpam-6583	533	8	)	)	PUNCT
ejpam-6583	534	1	+	+	CCONJ
ejpam-6583	534	2	δb	δb	NOUN
ejpam-6583	534	3	r⊕d	r⊕d	NOUN
ejpam-6583	534	4	(	(	PUNCT
ejpam-6583	534	5	xn	xn	PROPN
ejpam-6583	534	6	,	,	PUNCT
ejpam-6583	534	7	xn+1	xn+1	NUM
ejpam-6583	534	8	)	)	PUNCT
ejpam-6583	534	9	)	)	PUNCT
ejpam-6583	534	10	]	]	PUNCT
ejpam-6583	535	1	=	=	PUNCT
ejpam-6583	535	2	diag	diag	NOUN
ejpam-6583	535	3	(	(	PUNCT
ejpam-6583	535	4	α1	α1	PROPN
ejpam-6583	535	5	+	+	CCONJ
ejpam-6583	535	6	β1	β1	PROPN
ejpam-6583	535	7	+	+	CCONJ
ejpam-6583	535	8	sγ1	sγ1	PROPN
ejpam-6583	535	9	,	,	PUNCT
ejpam-6583	535	10	α2	α2	PROPN
ejpam-6583	535	11	+	+	CCONJ
ejpam-6583	535	12	β2	β2	PROPN
ejpam-6583	535	13	+	+	CCONJ
ejpam-6583	535	14	sγ2	sγ2	NOUN
ejpam-6583	535	15	,	,	PUNCT
ejpam-6583	535	16	·	·	PUNCT
ejpam-6583	535	17	·	·	PUNCT
ejpam-6583	535	18	·	·	PUNCT
ejpam-6583	535	19	,	,	PUNCT
ejpam-6583	535	20	αd	αd	PROPN
ejpam-6583	535	21	+	+	CCONJ
ejpam-6583	535	22	βd	βd	ADJ
ejpam-6583	535	23	+	+	CCONJ
ejpam-6583	535	24	sγd	sγd	NOUN
ejpam-6583	535	25	)	)	PUNCT
ejpam-6583	535	26	δb	δb	NOUN
ejpam-6583	535	27	r⊕d	r⊕d	NOUN
ejpam-6583	535	28	(	(	PUNCT
ejpam-6583	535	29	xn−1	xn−1	PROPN
ejpam-6583	535	30	,	,	PUNCT
ejpam-6583	535	31	xn	xn	PROPN
ejpam-6583	535	32	)	)	PUNCT
ejpam-6583	535	33	g.	g.	PROPN
ejpam-6583	535	34	albeladi	albeladi	PROPN
ejpam-6583	535	35	,	,	PUNCT
ejpam-6583	535	36	s.	s.	PROPN
ejpam-6583	535	37	omran	omran	PROPN
ejpam-6583	535	38	/	/	SYM
ejpam-6583	535	39	eur	eur	PROPN
ejpam-6583	535	40	.	.	PUNCT
ejpam-6583	536	1	j.	j.	PROPN
ejpam-6583	536	2	pure	pure	PROPN
ejpam-6583	536	3	appl	appl	PROPN
ejpam-6583	536	4	.	.	PROPN
ejpam-6583	536	5	math	math	PROPN
ejpam-6583	536	6	,	,	PUNCT
ejpam-6583	536	7	18	18	NUM
ejpam-6583	536	8	(	(	PUNCT
ejpam-6583	536	9	3	3	NUM
ejpam-6583	536	10	)	)	PUNCT
ejpam-6583	536	11	(	(	PUNCT
ejpam-6583	536	12	2025	2025	NUM
ejpam-6583	536	13	)	)	PUNCT
ejpam-6583	536	14	,	,	PUNCT
ejpam-6583	536	15	6583	6583	NUM
ejpam-6583	536	16	22	22	NUM
ejpam-6583	536	17	of	of	ADP
ejpam-6583	536	18	27	27	NUM
ejpam-6583	537	1	+	+	NUM
ejpam-6583	537	2	diag	diag	NOUN
ejpam-6583	537	3	(	(	PUNCT
ejpam-6583	537	4	β1	β1	PROPN
ejpam-6583	537	5	+	+	CCONJ
ejpam-6583	537	6	sγ1	sγ1	PROPN
ejpam-6583	537	7	,	,	PUNCT
ejpam-6583	537	8	β2	β2	NOUN
ejpam-6583	537	9	+	+	CCONJ
ejpam-6583	537	10	sγ2	sγ2	NOUN
ejpam-6583	537	11	,	,	PUNCT
ejpam-6583	537	12	·	·	PUNCT
ejpam-6583	537	13	·	·	PUNCT
ejpam-6583	537	14	·	·	PUNCT
ejpam-6583	537	15	,	,	PUNCT
ejpam-6583	537	16	βd	βd	ADP
ejpam-6583	537	17	+	+	CCONJ
ejpam-6583	537	18	sγd	sγd	NOUN
ejpam-6583	537	19	)	)	PUNCT
ejpam-6583	537	20	δb	δb	NOUN
ejpam-6583	537	21	r⊕d	r⊕d	NOUN
ejpam-6583	537	22	(	(	PUNCT
ejpam-6583	537	23	xn	xn	PROPN
ejpam-6583	537	24	,	,	PUNCT
ejpam-6583	537	25	xn+1	xn+1	NUM
ejpam-6583	537	26	)	)	PUNCT
ejpam-6583	537	27	.	.	PUNCT
ejpam-6583	538	1	thus	thus	ADV
ejpam-6583	538	2	,	,	PUNCT
ejpam-6583	538	3	diag	diag	NOUN
ejpam-6583	538	4	(	(	PUNCT
ejpam-6583	538	5	(	(	PUNCT
ejpam-6583	538	6	1−	1−	NUM
ejpam-6583	538	7	(	(	PUNCT
ejpam-6583	538	8	β1	β1	PROPN
ejpam-6583	538	9	+	+	CCONJ
ejpam-6583	538	10	sγ1	sγ1	PROPN
ejpam-6583	538	11	)	)	PUNCT
ejpam-6583	538	12	)	)	PUNCT
ejpam-6583	538	13	,	,	PUNCT
ejpam-6583	538	14	(	(	PUNCT
ejpam-6583	538	15	1−	1−	NUM
ejpam-6583	538	16	(	(	PUNCT
ejpam-6583	538	17	β2	β2	NOUN
ejpam-6583	538	18	+	+	NOUN
ejpam-6583	538	19	sγ2	sγ2	NOUN
ejpam-6583	538	20	)	)	PUNCT
ejpam-6583	538	21	)	)	PUNCT
ejpam-6583	538	22	,	,	PUNCT
ejpam-6583	538	23	·	·	PUNCT
ejpam-6583	538	24	·	·	PUNCT
ejpam-6583	538	25	·	·	PUNCT
ejpam-6583	538	26	,	,	PUNCT
ejpam-6583	538	27	(	(	PUNCT
ejpam-6583	538	28	1−	1−	NUM
ejpam-6583	538	29	(	(	PUNCT
ejpam-6583	538	30	βd	βd	ADP
ejpam-6583	538	31	+	+	CCONJ
ejpam-6583	538	32	sγd	sγd	PROPN
ejpam-6583	538	33	)	)	PUNCT
ejpam-6583	538	34	)	)	PUNCT
ejpam-6583	538	35	)	)	PUNCT
ejpam-6583	538	36	δb	δb	NOUN
ejpam-6583	538	37	r⊕d	r⊕d	NOUN
ejpam-6583	538	38	(	(	PUNCT
ejpam-6583	538	39	xn	xn	PROPN
ejpam-6583	538	40	,	,	PUNCT
ejpam-6583	538	41	xn+1	xn+1	X
ejpam-6583	538	42	)	)	PUNCT
ejpam-6583	538	43	≾	≾	NOUN
ejpam-6583	538	44	diag	diag	NOUN
ejpam-6583	538	45	(	(	PUNCT
ejpam-6583	538	46	α1	α1	PROPN
ejpam-6583	538	47	+	+	CCONJ
ejpam-6583	538	48	β1	β1	PROPN
ejpam-6583	538	49	+	+	CCONJ
ejpam-6583	538	50	sγ1	sγ1	PROPN
ejpam-6583	538	51	,	,	PUNCT
ejpam-6583	538	52	α2	α2	PROPN
ejpam-6583	538	53	+	+	CCONJ
ejpam-6583	538	54	β2	β2	PROPN
ejpam-6583	538	55	+	+	CCONJ
ejpam-6583	538	56	sγ2	sγ2	NOUN
ejpam-6583	538	57	,	,	PUNCT
ejpam-6583	538	58	·	·	PUNCT
ejpam-6583	538	59	·	·	PUNCT
ejpam-6583	538	60	·	·	PUNCT
ejpam-6583	538	61	,	,	PUNCT
ejpam-6583	538	62	αd	αd	PROPN
ejpam-6583	538	63	+	+	CCONJ
ejpam-6583	538	64	βd	βd	ADJ
ejpam-6583	538	65	+	+	CCONJ
ejpam-6583	538	66	sγd	sγd	NOUN
ejpam-6583	538	67	)	)	PUNCT
ejpam-6583	538	68	δb	δb	NOUN
ejpam-6583	538	69	r⊕d	r⊕d	NOUN
ejpam-6583	538	70	(	(	PUNCT
ejpam-6583	538	71	xn−1	xn−1	PROPN
ejpam-6583	538	72	,	,	PUNCT
ejpam-6583	538	73	xn	xn	PROPN
ejpam-6583	538	74	)	)	PUNCT
ejpam-6583	538	75	.	.	PUNCT
ejpam-6583	539	1	this	this	PRON
ejpam-6583	539	2	implies	imply	VERB
ejpam-6583	539	3	that	that	SCONJ
ejpam-6583	539	4	δb	δb	NOUN
ejpam-6583	539	5	r⊕d	r⊕d	NOUN
ejpam-6583	539	6	(	(	PUNCT
ejpam-6583	539	7	xn	xn	PROPN
ejpam-6583	539	8	,	,	PUNCT
ejpam-6583	539	9	xn+1	xn+1	X
ejpam-6583	539	10	)	)	PUNCT
ejpam-6583	539	11	≾	≾	NOUN
ejpam-6583	539	12	diag	diag	NOUN
ejpam-6583	539	13	(	(	PUNCT
ejpam-6583	539	14	(	(	PUNCT
ejpam-6583	539	15	α1	α1	PROPN
ejpam-6583	539	16	+	+	CCONJ
ejpam-6583	539	17	β1	β1	PROPN
ejpam-6583	539	18	+	+	CCONJ
ejpam-6583	539	19	sγ1	sγ1	PROPN
ejpam-6583	539	20	)	)	PUNCT
ejpam-6583	539	21	(	(	PUNCT
ejpam-6583	539	22	1−	1−	NUM
ejpam-6583	539	23	(	(	PUNCT
ejpam-6583	539	24	β1	β1	PROPN
ejpam-6583	539	25	+	+	CCONJ
ejpam-6583	539	26	sγ1	sγ1	PROPN
ejpam-6583	539	27	)	)	PUNCT
ejpam-6583	539	28	)	)	PUNCT
ejpam-6583	539	29	,	,	PUNCT
ejpam-6583	539	30	(	(	PUNCT
ejpam-6583	539	31	α2	α2	ADJ
ejpam-6583	539	32	+	+	CCONJ
ejpam-6583	539	33	β2	β2	PROPN
ejpam-6583	539	34	+	+	CCONJ
ejpam-6583	539	35	sγ2	sγ2	NOUN
ejpam-6583	539	36	)	)	PUNCT
ejpam-6583	539	37	(	(	PUNCT
ejpam-6583	539	38	1−	1−	NUM
ejpam-6583	539	39	(	(	PUNCT
ejpam-6583	539	40	β2	β2	NOUN
ejpam-6583	539	41	+	+	NOUN
ejpam-6583	539	42	sγ2	sγ2	NOUN
ejpam-6583	539	43	)	)	PUNCT
ejpam-6583	539	44	)	)	PUNCT
ejpam-6583	539	45	,	,	PUNCT
ejpam-6583	539	46	·	·	PUNCT
ejpam-6583	539	47	·	·	PUNCT
ejpam-6583	539	48	·	·	PUNCT
ejpam-6583	539	49	,	,	PUNCT
ejpam-6583	539	50	(	(	PUNCT
ejpam-6583	539	51	αd	αd	PROPN
ejpam-6583	539	52	+	+	CCONJ
ejpam-6583	539	53	βd	βd	ADJ
ejpam-6583	539	54	+	+	CCONJ
ejpam-6583	539	55	sγd	sγd	PROPN
ejpam-6583	539	56	)	)	PUNCT
ejpam-6583	539	57	(	(	PUNCT
ejpam-6583	539	58	1−	1−	NUM
ejpam-6583	539	59	(	(	PUNCT
ejpam-6583	539	60	βd	βd	ADP
ejpam-6583	539	61	+	+	CCONJ
ejpam-6583	539	62	sγd	sγd	PROPN
ejpam-6583	539	63	)	)	PUNCT
ejpam-6583	539	64	)	)	PUNCT
ejpam-6583	539	65	)	)	PUNCT
ejpam-6583	539	66	δb	δb	NOUN
ejpam-6583	539	67	r⊕d	r⊕d	NOUN
ejpam-6583	539	68	(	(	PUNCT
ejpam-6583	539	69	xn−1	xn−1	PROPN
ejpam-6583	539	70	,	,	PUNCT
ejpam-6583	539	71	xn	xn	PROPN
ejpam-6583	539	72	)	)	PUNCT
ejpam-6583	539	73	.	.	PUNCT
ejpam-6583	540	1	we	we	PRON
ejpam-6583	540	2	use	use	VERB
ejpam-6583	540	3	λi	λi	ADP
ejpam-6583	540	4	=	=	NOUN
ejpam-6583	540	5	αi	αi	NOUN
ejpam-6583	541	1	+	+	CCONJ
ejpam-6583	541	2	βi	βi	PRON
ejpam-6583	541	3	+	+	NUM
ejpam-6583	541	4	sγi	sγi	VERB
ejpam-6583	541	5	1−	1−	NUM
ejpam-6583	541	6	(	(	PUNCT
ejpam-6583	541	7	βi	βi	PROPN
ejpam-6583	541	8	+	+	NUM
ejpam-6583	541	9	sγi	sγi	ADJ
ejpam-6583	541	10	)	)	PUNCT
ejpam-6583	541	11	∈	∈	PROPN
ejpam-6583	541	12	(	(	PUNCT
ejpam-6583	541	13	0	0	NUM
ejpam-6583	541	14	,	,	PUNCT
ejpam-6583	541	15	1	1	NUM
ejpam-6583	541	16	)	)	PUNCT
ejpam-6583	541	17	for	for	ADP
ejpam-6583	541	18	all	all	DET
ejpam-6583	541	19	i	i	PRON
ejpam-6583	541	20	=	=	NOUN
ejpam-6583	541	21	1	1	NUM
ejpam-6583	541	22	,	,	PUNCT
ejpam-6583	541	23	2	2	NUM
ejpam-6583	541	24	,	,	PUNCT
ejpam-6583	541	25	·	·	PUNCT
ejpam-6583	541	26	·	·	PUNCT
ejpam-6583	541	27	·	·	PUNCT
ejpam-6583	541	28	,	,	PUNCT
ejpam-6583	541	29	d	d	X
ejpam-6583	541	30	,	,	PUNCT
ejpam-6583	541	31	we	we	PRON
ejpam-6583	541	32	obtain	obtain	VERB
ejpam-6583	541	33	δb	δb	NOUN
ejpam-6583	541	34	r⊕d	r⊕d	NOUN
ejpam-6583	541	35	(	(	PUNCT
ejpam-6583	541	36	xn	xn	PROPN
ejpam-6583	541	37	,	,	PUNCT
ejpam-6583	541	38	xn+1	xn+1	X
ejpam-6583	541	39	)	)	PUNCT
ejpam-6583	541	40	≾	≾	NOUN
ejpam-6583	541	41	diag	diag	NOUN
ejpam-6583	541	42	(	(	PUNCT
ejpam-6583	541	43	λ1	λ1	ADJ
ejpam-6583	541	44	,	,	PUNCT
ejpam-6583	541	45	λ2	λ2	NOUN
ejpam-6583	541	46	,	,	PUNCT
ejpam-6583	541	47	·	·	PUNCT
ejpam-6583	541	48	·	·	PUNCT
ejpam-6583	541	49	·	·	PUNCT
ejpam-6583	541	50	,	,	PUNCT
ejpam-6583	541	51	λd	λd	NOUN
ejpam-6583	541	52	)	)	PUNCT
ejpam-6583	541	53	δb	δb	NOUN
ejpam-6583	541	54	r⊕d	r⊕d	NOUN
ejpam-6583	541	55	(	(	PUNCT
ejpam-6583	541	56	xn−1	xn−1	PROPN
ejpam-6583	541	57	,	,	PUNCT
ejpam-6583	541	58	xn	xn	PROPN
ejpam-6583	541	59	)	)	PUNCT
ejpam-6583	541	60	.	.	PUNCT
ejpam-6583	542	1	so	so	ADV
ejpam-6583	542	2	δb	δb	NOUN
ejpam-6583	542	3	r⊕d	r⊕d	NOUN
ejpam-6583	542	4	(	(	PUNCT
ejpam-6583	542	5	xn	xn	PROPN
ejpam-6583	542	6	,	,	PUNCT
ejpam-6583	542	7	xn+1	xn+1	X
ejpam-6583	542	8	)	)	PUNCT
ejpam-6583	542	9	≾	≾	NOUN
ejpam-6583	542	10	diag	diag	NOUN
ejpam-6583	542	11	(	(	PUNCT
ejpam-6583	542	12	λ1	λ1	ADJ
ejpam-6583	542	13	,	,	PUNCT
ejpam-6583	542	14	λ2	λ2	NOUN
ejpam-6583	542	15	,	,	PUNCT
ejpam-6583	542	16	·	·	PUNCT
ejpam-6583	542	17	·	·	PUNCT
ejpam-6583	542	18	·	·	PUNCT
ejpam-6583	542	19	,	,	PUNCT
ejpam-6583	542	20	λd	λd	NOUN
ejpam-6583	542	21	)	)	PUNCT
ejpam-6583	542	22	δb	δb	NOUN
ejpam-6583	542	23	r⊕d	r⊕d	NOUN
ejpam-6583	542	24	(	(	PUNCT
ejpam-6583	542	25	xn−1	xn−1	PROPN
ejpam-6583	542	26	,	,	PUNCT
ejpam-6583	542	27	xn	xn	X
ejpam-6583	542	28	)	)	PUNCT
ejpam-6583	542	29	≾	≾	NOUN
ejpam-6583	542	30	diag	diag	NOUN
ejpam-6583	542	31	(	(	PUNCT
ejpam-6583	542	32	λ21	λ21	PROPN
ejpam-6583	542	33	,	,	PUNCT
ejpam-6583	542	34	λ22	λ22	PROPN
ejpam-6583	542	35	,	,	PUNCT
ejpam-6583	542	36	·	·	PUNCT
ejpam-6583	542	37	·	·	PUNCT
ejpam-6583	542	38	·	·	PUNCT
ejpam-6583	542	39	,	,	PUNCT
ejpam-6583	542	40	λ2d	λ2d	PUNCT
ejpam-6583	542	41	)	)	PUNCT
ejpam-6583	542	42	δb	δb	NOUN
ejpam-6583	542	43	r⊕d	r⊕d	NOUN
ejpam-6583	542	44	(	(	PUNCT
ejpam-6583	542	45	xn−2	xn−2	PROPN
ejpam-6583	542	46	,	,	PUNCT
ejpam-6583	542	47	xn−1	xn−1	PROPN
ejpam-6583	542	48	)	)	PUNCT
ejpam-6583	542	49	≾	≾	NOUN
ejpam-6583	542	50	diag	diag	NOUN
ejpam-6583	542	51	(	(	PUNCT
ejpam-6583	542	52	λ31	λ31	NOUN
ejpam-6583	542	53	,	,	PUNCT
ejpam-6583	542	54	λ32	λ32	VERB
ejpam-6583	542	55	,	,	PUNCT
ejpam-6583	542	56	·	·	PUNCT
ejpam-6583	542	57	·	·	PUNCT
ejpam-6583	542	58	·	·	PUNCT
ejpam-6583	542	59	,	,	PUNCT
ejpam-6583	542	60	λ3d	λ3d	PROPN
ejpam-6583	542	61	)	)	PUNCT
ejpam-6583	543	1	δb	δb	NOUN
ejpam-6583	543	2	r⊕d	r⊕d	NOUN
ejpam-6583	543	3	(	(	PUNCT
ejpam-6583	543	4	xn−3	xn−3	PROPN
ejpam-6583	543	5	,	,	PUNCT
ejpam-6583	543	6	xn−2	xn−2	PROPN
ejpam-6583	543	7	)	)	PUNCT
ejpam-6583	543	8	≾	≾	PROPN
ejpam-6583	543	9	·	·	PUNCT
ejpam-6583	543	10	·	·	PUNCT
ejpam-6583	543	11	·	·	PUNCT
ejpam-6583	544	1	≾	≾	NOUN
ejpam-6583	544	2	diag	diag	NOUN
ejpam-6583	544	3	(	(	PUNCT
ejpam-6583	544	4	λn1	λn1	NOUN
ejpam-6583	544	5	,	,	PUNCT
ejpam-6583	544	6	λn2	λn2	NOUN
ejpam-6583	544	7	,	,	PUNCT
ejpam-6583	544	8	·	·	PUNCT
ejpam-6583	544	9	·	·	PUNCT
ejpam-6583	544	10	·	·	PUNCT
ejpam-6583	544	11	,	,	PUNCT
ejpam-6583	544	12	λnd	λnd	X
ejpam-6583	544	13	)	)	PUNCT
ejpam-6583	544	14	δb	δb	NOUN
ejpam-6583	544	15	r⊕d	r⊕d	NOUN
ejpam-6583	544	16	(	(	PUNCT
ejpam-6583	544	17	x0	x0	PROPN
ejpam-6583	544	18	,	,	PUNCT
ejpam-6583	544	19	x1	x1	PROPN
ejpam-6583	544	20	)	)	PUNCT
ejpam-6583	544	21	.	.	PUNCT
ejpam-6583	545	1	(	(	PUNCT
ejpam-6583	545	2	5	5	X
ejpam-6583	545	3	)	)	PUNCT
ejpam-6583	545	4	let	let	VERB
ejpam-6583	545	5	us	we	PRON
ejpam-6583	545	6	prove	prove	VERB
ejpam-6583	545	7	that	that	SCONJ
ejpam-6583	545	8	{	{	PUNCT
ejpam-6583	545	9	xn	xn	X
ejpam-6583	545	10	}	}	PUNCT
ejpam-6583	545	11	is	be	AUX
ejpam-6583	545	12	a	a	DET
ejpam-6583	545	13	cauchy	cauchy	ADJ
ejpam-6583	545	14	sequence	sequence	NOUN
ejpam-6583	545	15	.	.	PUNCT
ejpam-6583	546	1	suppose	suppose	VERB
ejpam-6583	546	2	that	that	SCONJ
ejpam-6583	546	3	m	m	VERB
ejpam-6583	546	4	<	<	X
ejpam-6583	546	5	n	n	CCONJ
ejpam-6583	546	6	,	,	PUNCT
ejpam-6583	546	7	then	then	ADV
ejpam-6583	546	8	from	from	ADP
ejpam-6583	546	9	(	(	PUNCT
ejpam-6583	546	10	5	5	NUM
ejpam-6583	546	11	)	)	PUNCT
ejpam-6583	546	12	and	and	CCONJ
ejpam-6583	546	13	the	the	DET
ejpam-6583	546	14	triangle	triangle	NOUN
ejpam-6583	546	15	inequality	inequality	NOUN
ejpam-6583	546	16	property	property	NOUN
ejpam-6583	546	17	,	,	PUNCT
ejpam-6583	546	18	we	we	PRON
ejpam-6583	546	19	can	can	AUX
ejpam-6583	546	20	write	write	VERB
ejpam-6583	546	21	as	as	ADP
ejpam-6583	546	22	:	:	PUNCT
ejpam-6583	546	23	δb	δb	NOUN
ejpam-6583	546	24	r⊕d	r⊕d	NOUN
ejpam-6583	546	25	(	(	PUNCT
ejpam-6583	546	26	xm	xm	PROPN
ejpam-6583	546	27	,	,	PUNCT
ejpam-6583	546	28	xn	xn	PROPN
ejpam-6583	546	29	)	)	PUNCT
ejpam-6583	547	1	≾	≾	PROPN
ejpam-6583	547	2	s	s	PART
ejpam-6583	547	3	[	[	PUNCT
ejpam-6583	547	4	δb	δb	NOUN
ejpam-6583	547	5	r⊕d	r⊕d	NOUN
ejpam-6583	547	6	(	(	PUNCT
ejpam-6583	547	7	xm	xm	PROPN
ejpam-6583	547	8	,	,	PUNCT
ejpam-6583	547	9	xm+1	xm+1	PROPN
ejpam-6583	547	10	)	)	PUNCT
ejpam-6583	547	11	+	+	CCONJ
ejpam-6583	547	12	δb	δb	NOUN
ejpam-6583	547	13	r⊕d	r⊕d	NOUN
ejpam-6583	547	14	(	(	PUNCT
ejpam-6583	547	15	xm+1	xm+1	PROPN
ejpam-6583	547	16	,	,	PUNCT
ejpam-6583	547	17	xn	xn	PROPN
ejpam-6583	547	18	)	)	PUNCT
ejpam-6583	547	19	]	]	PUNCT
ejpam-6583	548	1	≾	≾	NOUN
ejpam-6583	548	2	sδb	sδb	VERB
ejpam-6583	548	3	r⊕d	r⊕d	NOUN
ejpam-6583	548	4	(	(	PUNCT
ejpam-6583	548	5	xm	xm	PROPN
ejpam-6583	548	6	,	,	PUNCT
ejpam-6583	548	7	xm+1	xm+1	PROPN
ejpam-6583	548	8	)	)	PUNCT
ejpam-6583	548	9	+	+	CCONJ
ejpam-6583	548	10	s2	s2	NOUN
ejpam-6583	548	11	[	[	PUNCT
ejpam-6583	548	12	δb	δb	NOUN
ejpam-6583	548	13	r⊕d	r⊕d	NOUN
ejpam-6583	548	14	(	(	PUNCT
ejpam-6583	548	15	xm+1	xm+1	PROPN
ejpam-6583	548	16	,	,	PUNCT
ejpam-6583	548	17	xm+2	xm+2	PROPN
ejpam-6583	548	18	)	)	PUNCT
ejpam-6583	548	19	+	+	CCONJ
ejpam-6583	548	20	δb	δb	NOUN
ejpam-6583	548	21	r⊕d	r⊕d	NOUN
ejpam-6583	548	22	(	(	PUNCT
ejpam-6583	548	23	xm+2	xm+2	PROPN
ejpam-6583	548	24	,	,	PUNCT
ejpam-6583	548	25	xn	xn	PROPN
ejpam-6583	548	26	)	)	PUNCT
ejpam-6583	548	27	]	]	PUNCT
ejpam-6583	549	1	≾	≾	NOUN
ejpam-6583	549	2	sδb	sδb	VERB
ejpam-6583	549	3	r⊕d	r⊕d	NOUN
ejpam-6583	549	4	(	(	PUNCT
ejpam-6583	549	5	xm	xm	PROPN
ejpam-6583	549	6	,	,	PUNCT
ejpam-6583	549	7	xm+1	xm+1	PROPN
ejpam-6583	549	8	)	)	PUNCT
ejpam-6583	549	9	+	+	CCONJ
ejpam-6583	549	10	s2δb	s2δb	SYM
ejpam-6583	549	11	r⊕d	r⊕d	NOUN
ejpam-6583	549	12	(	(	PUNCT
ejpam-6583	549	13	xm+1	xm+1	PROPN
ejpam-6583	549	14	,	,	PUNCT
ejpam-6583	549	15	xm+2	xm+2	PROPN
ejpam-6583	549	16	)	)	PUNCT
ejpam-6583	549	17	+	+	CCONJ
ejpam-6583	549	18	s3	s3	PROPN
ejpam-6583	549	19	[	[	PUNCT
ejpam-6583	549	20	δb	δb	X
ejpam-6583	549	21	r⊕d	r⊕d	NOUN
ejpam-6583	549	22	(	(	PUNCT
ejpam-6583	549	23	xm+2	xm+2	PROPN
ejpam-6583	549	24	,	,	PUNCT
ejpam-6583	549	25	xm+3	xm+3	NUM
ejpam-6583	549	26	)	)	PUNCT
ejpam-6583	549	27	+	+	CCONJ
ejpam-6583	549	28	δb	δb	NOUN
ejpam-6583	549	29	r⊕d	r⊕d	NOUN
ejpam-6583	549	30	(	(	PUNCT
ejpam-6583	549	31	xm+3	xm+3	NUM
ejpam-6583	549	32	,	,	PUNCT
ejpam-6583	549	33	xn	xn	PROPN
ejpam-6583	549	34	)	)	PUNCT
ejpam-6583	549	35	]	]	PUNCT
ejpam-6583	549	36	...	...	PUNCT
ejpam-6583	550	1	≾	≾	NOUN
ejpam-6583	550	2	sδb	sδb	VERB
ejpam-6583	550	3	r⊕d	r⊕d	NOUN
ejpam-6583	550	4	(	(	PUNCT
ejpam-6583	550	5	xm	xm	PROPN
ejpam-6583	550	6	,	,	PUNCT
ejpam-6583	550	7	xm+1	xm+1	PROPN
ejpam-6583	550	8	)	)	PUNCT
ejpam-6583	550	9	+	+	CCONJ
ejpam-6583	550	10	s2δb	s2δb	SYM
ejpam-6583	550	11	r⊕d	r⊕d	NOUN
ejpam-6583	550	12	(	(	PUNCT
ejpam-6583	550	13	xm+1	xm+1	PROPN
ejpam-6583	550	14	,	,	PUNCT
ejpam-6583	550	15	xm+2	xm+2	PROPN
ejpam-6583	550	16	)	)	PUNCT
ejpam-6583	550	17	+	+	CCONJ
ejpam-6583	550	18	s3δb	s3δb	X
ejpam-6583	550	19	r⊕d	r⊕d	NOUN
ejpam-6583	550	20	(	(	PUNCT
ejpam-6583	550	21	xm+2	xm+2	PROPN
ejpam-6583	550	22	,	,	PUNCT
ejpam-6583	550	23	xm+3	xm+3	NUM
ejpam-6583	550	24	)	)	PUNCT
ejpam-6583	550	25	+	+	X
ejpam-6583	550	26	·	·	PUNCT
ejpam-6583	550	27	·	·	PUNCT
ejpam-6583	550	28	·	·	PUNCT
ejpam-6583	550	29	+	+	NUM
ejpam-6583	550	30	sn−mδb	sn−mδb	NOUN
ejpam-6583	550	31	r⊕d	r⊕d	NOUN
ejpam-6583	550	32	(	(	PUNCT
ejpam-6583	550	33	xn−1	xn−1	PROPN
ejpam-6583	550	34	,	,	PUNCT
ejpam-6583	550	35	xn	xn	PRON
ejpam-6583	550	36	)	)	PUNCT
ejpam-6583	551	1	=	=	SYM
ejpam-6583	551	2	diag	diag	NOUN
ejpam-6583	551	3	(	(	PUNCT
ejpam-6583	551	4	sλm1	sλm1	PROPN
ejpam-6583	551	5	,	,	PUNCT
ejpam-6583	551	6	sλm2	sλm2	NOUN
ejpam-6583	551	7	,	,	PUNCT
ejpam-6583	551	8	·	·	PUNCT
ejpam-6583	551	9	·	·	PUNCT
ejpam-6583	551	10	·	·	PUNCT
ejpam-6583	551	11	,	,	PUNCT
ejpam-6583	551	12	sλmd	sλmd	NOUN
ejpam-6583	551	13	)	)	PUNCT
ejpam-6583	551	14	δb	δb	NOUN
ejpam-6583	551	15	r⊕d	r⊕d	NOUN
ejpam-6583	551	16	(	(	PUNCT
ejpam-6583	551	17	x0	x0	PROPN
ejpam-6583	551	18	,	,	PUNCT
ejpam-6583	551	19	x1	x1	PROPN
ejpam-6583	551	20	)	)	PUNCT
ejpam-6583	552	1	+	+	NUM
ejpam-6583	552	2	diag	diag	NOUN
ejpam-6583	552	3	(	(	PUNCT
ejpam-6583	552	4	s2λm+1	s2λm+1	PROPN
ejpam-6583	552	5	1	1	NUM
ejpam-6583	552	6	,	,	PUNCT
ejpam-6583	552	7	s2λm+1	s2λm+1	VERB
ejpam-6583	552	8	2	2	NUM
ejpam-6583	552	9	,	,	PUNCT
ejpam-6583	552	10	·	·	PUNCT
ejpam-6583	552	11	·	·	PUNCT
ejpam-6583	552	12	·	·	PUNCT
ejpam-6583	552	13	,	,	PUNCT
ejpam-6583	552	14	s2λm+1	s2λm+1	PROPN
ejpam-6583	552	15	d	d	PROPN
ejpam-6583	552	16	)	)	PUNCT
ejpam-6583	552	17	δb	δb	NOUN
ejpam-6583	552	18	r⊕d	r⊕d	NOUN
ejpam-6583	552	19	(	(	PUNCT
ejpam-6583	552	20	x0	x0	PROPN
ejpam-6583	552	21	,	,	PUNCT
ejpam-6583	552	22	x1	x1	PROPN
ejpam-6583	552	23	)	)	PUNCT
ejpam-6583	552	24	g.	g.	PROPN
ejpam-6583	552	25	albeladi	albeladi	PROPN
ejpam-6583	552	26	,	,	PUNCT
ejpam-6583	552	27	s.	s.	PROPN
ejpam-6583	552	28	omran	omran	PROPN
ejpam-6583	552	29	/	/	SYM
ejpam-6583	552	30	eur	eur	PROPN
ejpam-6583	552	31	.	.	PUNCT
ejpam-6583	553	1	j.	j.	PROPN
ejpam-6583	553	2	pure	pure	PROPN
ejpam-6583	553	3	appl	appl	PROPN
ejpam-6583	553	4	.	.	PROPN
ejpam-6583	553	5	math	math	PROPN
ejpam-6583	553	6	,	,	PUNCT
ejpam-6583	553	7	18	18	NUM
ejpam-6583	553	8	(	(	PUNCT
ejpam-6583	553	9	3	3	NUM
ejpam-6583	553	10	)	)	PUNCT
ejpam-6583	553	11	(	(	PUNCT
ejpam-6583	553	12	2025	2025	NUM
ejpam-6583	553	13	)	)	PUNCT
ejpam-6583	553	14	,	,	PUNCT
ejpam-6583	553	15	6583	6583	NUM
ejpam-6583	553	16	23	23	NUM
ejpam-6583	553	17	of	of	ADP
ejpam-6583	553	18	27	27	NUM
ejpam-6583	554	1	+	+	NUM
ejpam-6583	554	2	diag	diag	NOUN
ejpam-6583	554	3	(	(	PUNCT
ejpam-6583	554	4	s3λm+2	s3λm+2	NOUN
ejpam-6583	554	5	1	1	NUM
ejpam-6583	554	6	,	,	PUNCT
ejpam-6583	554	7	s3λm+2	s3λm+2	NOUN
ejpam-6583	554	8	2	2	NUM
ejpam-6583	554	9	,	,	PUNCT
ejpam-6583	554	10	·	·	PUNCT
ejpam-6583	554	11	·	·	PUNCT
ejpam-6583	554	12	·	·	PUNCT
ejpam-6583	554	13	,	,	PUNCT
ejpam-6583	554	14	s3λm+2	s3λm+2	NOUN
ejpam-6583	554	15	d	d	NOUN
ejpam-6583	554	16	)	)	PUNCT
ejpam-6583	554	17	δb	δb	NOUN
ejpam-6583	554	18	r⊕d	r⊕d	NOUN
ejpam-6583	554	19	(	(	PUNCT
ejpam-6583	554	20	x0	x0	PROPN
ejpam-6583	554	21	,	,	PUNCT
ejpam-6583	554	22	x1	x1	PROPN
ejpam-6583	554	23	)	)	PUNCT
ejpam-6583	554	24	+	+	X
ejpam-6583	554	25	·	·	PUNCT
ejpam-6583	554	26	·	·	PUNCT
ejpam-6583	554	27	·	·	PUNCT
ejpam-6583	554	28	+	+	NUM
ejpam-6583	554	29	diag	diag	NOUN
ejpam-6583	554	30	(	(	PUNCT
ejpam-6583	554	31	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	554	32	1	1	NUM
ejpam-6583	554	33	,	,	PUNCT
ejpam-6583	554	34	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	554	35	2	2	NUM
ejpam-6583	554	36	,	,	PUNCT
ejpam-6583	554	37	·	·	PUNCT
ejpam-6583	554	38	·	·	PUNCT
ejpam-6583	554	39	·	·	PUNCT
ejpam-6583	554	40	,	,	PUNCT
ejpam-6583	554	41	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	554	42	d	d	X
ejpam-6583	554	43	)	)	PUNCT
ejpam-6583	554	44	δb	δb	NOUN
ejpam-6583	554	45	r⊕d	r⊕d	NOUN
ejpam-6583	554	46	(	(	PUNCT
ejpam-6583	554	47	x0	x0	PROPN
ejpam-6583	554	48	,	,	PUNCT
ejpam-6583	554	49	x1	x1	PROPN
ejpam-6583	554	50	)	)	PUNCT
ejpam-6583	555	1	=	=	SYM
ejpam-6583	555	2	diag	diag	NOUN
ejpam-6583	555	3	(	(	PUNCT
ejpam-6583	555	4	(	(	PUNCT
ejpam-6583	555	5	sλm1	sλm1	PROPN
ejpam-6583	555	6	+	+	CCONJ
ejpam-6583	555	7	s2λm+1	s2λm+1	VERB
ejpam-6583	555	8	1	1	NUM
ejpam-6583	555	9	+	+	CCONJ
ejpam-6583	555	10	·	·	PUNCT
ejpam-6583	555	11	·	·	PUNCT
ejpam-6583	555	12	·	·	PUNCT
ejpam-6583	555	13	+	+	NUM
ejpam-6583	555	14	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	555	15	1	1	NUM
ejpam-6583	555	16	)	)	PUNCT
ejpam-6583	555	17	,	,	PUNCT
ejpam-6583	555	18	(	(	PUNCT
ejpam-6583	555	19	sλm2	sλm2	PROPN
ejpam-6583	555	20	+	+	CCONJ
ejpam-6583	555	21	s2λm+1	s2λm+1	VERB
ejpam-6583	555	22	2	2	NUM
ejpam-6583	555	23	+	+	CCONJ
ejpam-6583	555	24	·	·	PUNCT
ejpam-6583	555	25	·	·	PUNCT
ejpam-6583	555	26	·	·	PUNCT
ejpam-6583	555	27	+	+	NUM
ejpam-6583	555	28	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	555	29	2	2	NUM
ejpam-6583	555	30	)	)	PUNCT
ejpam-6583	555	31	,	,	PUNCT
ejpam-6583	555	32	·	·	PUNCT
ejpam-6583	555	33	·	·	PUNCT
ejpam-6583	555	34	·	·	PUNCT
ejpam-6583	555	35	,	,	PUNCT
ejpam-6583	555	36	(	(	PUNCT
ejpam-6583	555	37	sλmd	sλmd	NOUN
ejpam-6583	555	38	+	+	CCONJ
ejpam-6583	555	39	s2λm+1	s2λm+1	PROPN
ejpam-6583	555	40	d	d	PROPN
ejpam-6583	555	41	+	+	PROPN
ejpam-6583	555	42	·	·	PUNCT
ejpam-6583	555	43	·	·	PUNCT
ejpam-6583	555	44	·	·	PUNCT
ejpam-6583	555	45	+	+	NUM
ejpam-6583	555	46	sn−mλn−1	sn−mλn−1	PROPN
ejpam-6583	555	47	d	d	NOUN
ejpam-6583	555	48	)	)	PUNCT
ejpam-6583	555	49	)	)	PUNCT
ejpam-6583	555	50	δb	δb	NOUN
ejpam-6583	555	51	r⊕d	r⊕d	NOUN
ejpam-6583	555	52	(	(	PUNCT
ejpam-6583	555	53	x0	x0	PROPN
ejpam-6583	555	54	,	,	PUNCT
ejpam-6583	555	55	x1	x1	PROPN
ejpam-6583	555	56	)	)	PUNCT
ejpam-6583	555	57	=	=	SYM
ejpam-6583	555	58	diag	diag	NOUN
ejpam-6583	555	59	(	(	PUNCT
ejpam-6583	555	60	n−m∑	n−m∑	INTJ
ejpam-6583	555	61	i=1	i=1	PROPN
ejpam-6583	555	62	n−1∑	n−1∑	PROPN
ejpam-6583	555	63	j	j	X
ejpam-6583	555	64	=	=	PROPN
ejpam-6583	555	65	m	m	NOUN
ejpam-6583	555	66	siλj1	siλj1	NOUN
ejpam-6583	555	67	,	,	PUNCT
ejpam-6583	555	68	n−m∑	n−m∑	PROPN
ejpam-6583	555	69	i=1	i=1	PROPN
ejpam-6583	555	70	n−1∑	n−1∑	PROPN
ejpam-6583	555	71	j	j	PROPN
ejpam-6583	555	72	=	=	NOUN
ejpam-6583	555	73	m	m	PROPN
ejpam-6583	555	74	siλj2	siλj2	PROPN
ejpam-6583	555	75	,	,	PUNCT
ejpam-6583	555	76	·	·	PUNCT
ejpam-6583	555	77	·	·	PUNCT
ejpam-6583	555	78	·	·	PUNCT
ejpam-6583	555	79	,	,	PUNCT
ejpam-6583	555	80	n−m∑	n−m∑	PROPN
ejpam-6583	555	81	i=1	i=1	PROPN
ejpam-6583	555	82	n−1∑	n−1∑	PROPN
ejpam-6583	555	83	j	j	X
ejpam-6583	556	1	=	=	NOUN
ejpam-6583	556	2	m	m	NOUN
ejpam-6583	556	3	siλjd	siλjd	NOUN
ejpam-6583	556	4	)	)	PUNCT
ejpam-6583	556	5	δb	δb	NOUN
ejpam-6583	556	6	r⊕d	r⊕d	NOUN
ejpam-6583	556	7	(	(	PUNCT
ejpam-6583	556	8	x0	x0	PROPN
ejpam-6583	556	9	,	,	PUNCT
ejpam-6583	556	10	x1	x1	PROPN
ejpam-6583	556	11	)	)	PUNCT
ejpam-6583	557	1	=	=	SYM
ejpam-6583	557	2	diag	diag	NOUN
ejpam-6583	557	3	(	(	PUNCT
ejpam-6583	557	4	sλm1	sλm1	PROPN
ejpam-6583	557	5	n−m−1∑	n−m−1∑	PROPN
ejpam-6583	557	6	j=0	j=0	PROPN
ejpam-6583	557	7	(	(	PUNCT
ejpam-6583	557	8	sλ1	sλ1	NOUN
ejpam-6583	557	9	)	)	PUNCT
ejpam-6583	557	10	j	j	PROPN
ejpam-6583	557	11	,	,	PUNCT
ejpam-6583	557	12	sλm2	sλm2	PROPN
ejpam-6583	557	13	n−m−1∑	n−m−1∑	PROPN
ejpam-6583	557	14	j=0	j=0	PROPN
ejpam-6583	557	15	(	(	PUNCT
ejpam-6583	557	16	sλ2	sλ2	NOUN
ejpam-6583	557	17	)	)	PUNCT
ejpam-6583	557	18	j	j	PROPN
ejpam-6583	557	19	,	,	PUNCT
ejpam-6583	557	20	·	·	PUNCT
ejpam-6583	557	21	·	·	PUNCT
ejpam-6583	557	22	·	·	PUNCT
ejpam-6583	557	23	,	,	PUNCT
ejpam-6583	557	24	sλm1	sλm1	PROPN
ejpam-6583	557	25	n−m−1∑	n−m−1∑	PROPN
ejpam-6583	557	26	j=0	j=0	PROPN
ejpam-6583	557	27	(	(	PUNCT
ejpam-6583	557	28	sλd	sλd	PROPN
ejpam-6583	557	29	)	)	PUNCT
ejpam-6583	557	30	j	j	PROPN
ejpam-6583	557	31	)	)	PUNCT
ejpam-6583	557	32	δb	δb	NOUN
ejpam-6583	557	33	r⊕d	r⊕d	NOUN
ejpam-6583	557	34	(	(	PUNCT
ejpam-6583	557	35	x0	x0	PROPN
ejpam-6583	557	36	,	,	PUNCT
ejpam-6583	557	37	x1	x1	PROPN
ejpam-6583	557	38	)	)	PUNCT
ejpam-6583	557	39	≾	≾	NOUN
ejpam-6583	557	40	diag	diag	NOUN
ejpam-6583	557	41	(	(	PUNCT
ejpam-6583	557	42	sλm1	sλm1	PROPN
ejpam-6583	557	43	+	+	PROPN
ejpam-6583	557	44	∞∑	∞∑	PROPN
ejpam-6583	557	45	j=0	j=0	PROPN
ejpam-6583	557	46	(	(	PUNCT
ejpam-6583	557	47	sλ1	sλ1	NOUN
ejpam-6583	557	48	)	)	PUNCT
ejpam-6583	557	49	j	j	PROPN
ejpam-6583	557	50	,	,	PUNCT
ejpam-6583	557	51	sλm2	sλm2	PROPN
ejpam-6583	557	52	+	+	PRON
ejpam-6583	557	53	∞∑	∞∑	NUM
ejpam-6583	557	54	j=0	j=0	PROPN
ejpam-6583	557	55	(	(	PUNCT
ejpam-6583	557	56	sλ2	sλ2	NOUN
ejpam-6583	557	57	)	)	PUNCT
ejpam-6583	557	58	j	j	PROPN
ejpam-6583	557	59	,	,	PUNCT
ejpam-6583	557	60	·	·	PUNCT
ejpam-6583	557	61	·	·	PUNCT
ejpam-6583	557	62	·	·	PUNCT
ejpam-6583	557	63	,	,	PUNCT
ejpam-6583	557	64	sλm1	sλm1	PROPN
ejpam-6583	557	65	+	+	PROPN
ejpam-6583	557	66	∞∑	∞∑	PROPN
ejpam-6583	557	67	j=0	j=0	PROPN
ejpam-6583	557	68	(	(	PUNCT
ejpam-6583	557	69	sλd	sλd	PROPN
ejpam-6583	557	70	)	)	PUNCT
ejpam-6583	557	71	j	j	PROPN
ejpam-6583	557	72	)	)	PUNCT
ejpam-6583	557	73	δb	δb	NOUN
ejpam-6583	557	74	r⊕d	r⊕d	NOUN
ejpam-6583	557	75	(	(	PUNCT
ejpam-6583	557	76	x0	x0	PROPN
ejpam-6583	557	77	,	,	PUNCT
ejpam-6583	557	78	x1	x1	PROPN
ejpam-6583	557	79	)	)	PUNCT
ejpam-6583	558	1	=	=	SYM
ejpam-6583	558	2	diag	diag	NOUN
ejpam-6583	558	3	(	(	PUNCT
ejpam-6583	558	4	sλm1	sλm1	PROPN
ejpam-6583	558	5	[	[	PUNCT
ejpam-6583	558	6	1	1	NUM
ejpam-6583	558	7	1−	1−	NUM
ejpam-6583	558	8	sλ1	sλ1	NOUN
ejpam-6583	558	9	]	]	PUNCT
ejpam-6583	558	10	,	,	PUNCT
ejpam-6583	558	11	sλm2	sλm2	PROPN
ejpam-6583	558	12	[	[	PUNCT
ejpam-6583	558	13	1	1	NUM
ejpam-6583	558	14	1−	1−	NUM
ejpam-6583	558	15	sλ2	sλ2	NOUN
ejpam-6583	558	16	]	]	PUNCT
ejpam-6583	558	17	,	,	PUNCT
ejpam-6583	558	18	·	·	PUNCT
ejpam-6583	558	19	·	·	PUNCT
ejpam-6583	558	20	·	·	PUNCT
ejpam-6583	558	21	,	,	PUNCT
ejpam-6583	558	22	sλmd	sλmd	PROPN
ejpam-6583	558	23	[	[	PUNCT
ejpam-6583	558	24	1	1	NUM
ejpam-6583	558	25	1−	1−	NUM
ejpam-6583	558	26	sλd	sλd	NOUN
ejpam-6583	558	27	]	]	PUNCT
ejpam-6583	558	28	)	)	PUNCT
ejpam-6583	558	29	δb	δb	NOUN
ejpam-6583	558	30	r⊕d	r⊕d	NOUN
ejpam-6583	558	31	(	(	PUNCT
ejpam-6583	558	32	x0	x0	PROPN
ejpam-6583	558	33	,	,	PUNCT
ejpam-6583	558	34	x1	x1	PROPN
ejpam-6583	558	35	)	)	PUNCT
ejpam-6583	558	36	≾	≾	NOUN
ejpam-6583	558	37	diag(sλm1	diag(sλm1	NOUN
ejpam-6583	558	38	,	,	PUNCT
ejpam-6583	558	39	·	·	PUNCT
ejpam-6583	558	40	·	·	PUNCT
ejpam-6583	558	41	·	·	PUNCT
ejpam-6583	558	42	,	,	PUNCT
ejpam-6583	558	43	sλmd	sλmd	NOUN
ejpam-6583	558	44	)	)	PUNCT
ejpam-6583	558	45	diag	diag	NOUN
ejpam-6583	558	46	(	(	PUNCT
ejpam-6583	558	47	[	[	PUNCT
ejpam-6583	558	48	1	1	NUM
ejpam-6583	558	49	1−	1−	NUM
ejpam-6583	558	50	sλ1	sλ1	NOUN
ejpam-6583	558	51	]	]	PUNCT
ejpam-6583	558	52	,	,	PUNCT
ejpam-6583	558	53	·	·	PUNCT
ejpam-6583	558	54	·	·	PUNCT
ejpam-6583	558	55	·	·	PUNCT
ejpam-6583	558	56	,	,	PUNCT
ejpam-6583	558	57	[	[	PUNCT
ejpam-6583	558	58	1	1	NUM
ejpam-6583	558	59	1−	1−	NUM
ejpam-6583	558	60	sλd	sλd	NOUN
ejpam-6583	558	61	]	]	PUNCT
ejpam-6583	558	62	)	)	PUNCT
ejpam-6583	558	63	δb	δb	NOUN
ejpam-6583	558	64	r⊕d	r⊕d	NOUN
ejpam-6583	558	65	(	(	PUNCT
ejpam-6583	558	66	x0	x0	PROPN
ejpam-6583	558	67	,	,	PUNCT
ejpam-6583	558	68	x1	x1	PROPN
ejpam-6583	558	69	)	)	PUNCT
ejpam-6583	558	70	→	→	SYM
ejpam-6583	558	71	0	0	NUM
ejpam-6583	558	72	,	,	PUNCT
ejpam-6583	558	73	as	as	ADP
ejpam-6583	558	74	n	n	CCONJ
ejpam-6583	558	75	,	,	PUNCT
ejpam-6583	558	76	m	m	PROPN
ejpam-6583	558	77	→	→	SYM
ejpam-6583	558	78	+	+	NOUN
ejpam-6583	558	79	∞.	∞.	PROPN
ejpam-6583	558	80	since	since	SCONJ
ejpam-6583	558	81	λi	λi	ADP
ejpam-6583	558	82	∈	∈	PROPN
ejpam-6583	558	83	(	(	PUNCT
ejpam-6583	558	84	0	0	NUM
ejpam-6583	558	85	,	,	PUNCT
ejpam-6583	558	86	1	1	NUM
ejpam-6583	558	87	)	)	PUNCT
ejpam-6583	558	88	∀i	∀i	NOUN
ejpam-6583	558	89	and	and	CCONJ
ejpam-6583	558	90	δb	δb	NOUN
ejpam-6583	558	91	r⊕d	r⊕d	NOUN
ejpam-6583	558	92	(	(	PUNCT
ejpam-6583	558	93	x0	x0	PROPN
ejpam-6583	558	94	,	,	PUNCT
ejpam-6583	558	95	x1	x1	PROPN
ejpam-6583	558	96	)	)	PUNCT
ejpam-6583	558	97	are	be	AUX
ejpam-6583	558	98	fixed	fix	VERB
ejpam-6583	558	99	,	,	PUNCT
ejpam-6583	558	100	it	it	PRON
ejpam-6583	558	101	is	be	AUX
ejpam-6583	558	102	evident	evident	ADJ
ejpam-6583	558	103	that	that	SCONJ
ejpam-6583	558	104	by	by	ADP
ejpam-6583	558	105	selecting	select	VERB
ejpam-6583	558	106	m	m	PRON
ejpam-6583	558	107	sufficiently	sufficiently	ADV
ejpam-6583	558	108	large	large	ADJ
ejpam-6583	558	109	(	(	PUNCT
ejpam-6583	558	110	with	with	ADP
ejpam-6583	558	111	n	n	NOUN
ejpam-6583	558	112	>	>	X
ejpam-6583	558	113	m	m	PROPN
ejpam-6583	558	114	)	)	PUNCT
ejpam-6583	558	115	,	,	PUNCT
ejpam-6583	558	116	we	we	PRON
ejpam-6583	558	117	can	can	AUX
ejpam-6583	558	118	make	make	VERB
ejpam-6583	558	119	δb	δb	NOUN
ejpam-6583	558	120	r⊕d	r⊕d	NOUN
ejpam-6583	558	121	(	(	PUNCT
ejpam-6583	558	122	xn	xn	PROPN
ejpam-6583	558	123	,	,	PUNCT
ejpam-6583	558	124	xm	xm	PROPN
ejpam-6583	558	125	)	)	PUNCT
ejpam-6583	558	126	arbitrarily	arbitrarily	ADV
ejpam-6583	558	127	small	small	ADJ
ejpam-6583	558	128	.	.	PUNCT
ejpam-6583	559	1	this	this	PRON
ejpam-6583	559	2	shows	show	VERB
ejpam-6583	559	3	that	that	SCONJ
ejpam-6583	559	4	{	{	PUNCT
ejpam-6583	559	5	xn	xn	X
ejpam-6583	559	6	}	}	PUNCT
ejpam-6583	559	7	is	be	AUX
ejpam-6583	559	8	a	a	DET
ejpam-6583	559	9	cauchy	cauchy	ADJ
ejpam-6583	559	10	sequence	sequence	NOUN
ejpam-6583	559	11	.	.	PUNCT
ejpam-6583	560	1	finally	finally	ADV
ejpam-6583	560	2	,	,	PUNCT
ejpam-6583	560	3	because	because	SCONJ
ejpam-6583	560	4	(	(	PUNCT
ejpam-6583	560	5	x	x	X
ejpam-6583	560	6	,	,	PUNCT
ejpam-6583	560	7	r⊕d	r⊕d	NOUN
ejpam-6583	560	8	,	,	PUNCT
ejpam-6583	560	9	δb	δb	NOUN
ejpam-6583	560	10	r⊕d	r⊕d	NOUN
ejpam-6583	560	11	)	)	PUNCT
ejpam-6583	560	12	is	be	AUX
ejpam-6583	560	13	complete	complete	ADJ
ejpam-6583	560	14	,	,	PUNCT
ejpam-6583	560	15	there	there	PRON
ejpam-6583	560	16	exists	exist	VERB
ejpam-6583	560	17	some	some	DET
ejpam-6583	560	18	z	z	NOUN
ejpam-6583	560	19	∈	∈	PROPN
ejpam-6583	560	20	x	x	PUNCT
ejpam-6583	560	21	such	such	ADJ
ejpam-6583	560	22	that	that	PRON
ejpam-6583	560	23	xn	xn	PROPN
ejpam-6583	561	1	→	→	SYM
ejpam-6583	561	2	z.	z.	PROPN
ejpam-6583	561	3	to	to	PART
ejpam-6583	561	4	show	show	VERB
ejpam-6583	561	5	that	that	SCONJ
ejpam-6583	561	6	x	x	PRON
ejpam-6583	561	7	is	be	AUX
ejpam-6583	561	8	a	a	DET
ejpam-6583	561	9	fixed	fix	VERB
ejpam-6583	561	10	point	point	NOUN
ejpam-6583	561	11	,	,	PUNCT
ejpam-6583	561	12	we	we	PRON
ejpam-6583	561	13	consider	consider	VERB
ejpam-6583	561	14	the	the	DET
ejpam-6583	561	15	distance	distance	NOUN
ejpam-6583	561	16	δb	δb	NOUN
ejpam-6583	561	17	r⊕d	r⊕d	NOUN
ejpam-6583	561	18	(	(	PUNCT
ejpam-6583	561	19	z	z	NOUN
ejpam-6583	561	20	,	,	PUNCT
ejpam-6583	561	21	f	f	PROPN
ejpam-6583	561	22	(	(	PUNCT
ejpam-6583	561	23	z	z	NOUN
ejpam-6583	561	24	)	)	PUNCT
ejpam-6583	561	25	)	)	PUNCT
ejpam-6583	561	26	.	.	PUNCT
ejpam-6583	562	1	from	from	ADP
ejpam-6583	562	2	the	the	DET
ejpam-6583	562	3	triangle	triangle	NOUN
ejpam-6583	562	4	g.	g.	NOUN
ejpam-6583	562	5	albeladi	albeladi	PROPN
ejpam-6583	562	6	,	,	PUNCT
ejpam-6583	562	7	s.	s.	PROPN
ejpam-6583	562	8	omran	omran	PROPN
ejpam-6583	562	9	/	/	SYM
ejpam-6583	562	10	eur	eur	PROPN
ejpam-6583	562	11	.	.	PUNCT
ejpam-6583	563	1	j.	j.	PROPN
ejpam-6583	563	2	pure	pure	PROPN
ejpam-6583	563	3	appl	appl	PROPN
ejpam-6583	563	4	.	.	PROPN
ejpam-6583	563	5	math	math	PROPN
ejpam-6583	563	6	,	,	PUNCT
ejpam-6583	563	7	18	18	NUM
ejpam-6583	563	8	(	(	PUNCT
ejpam-6583	563	9	3	3	NUM
ejpam-6583	563	10	)	)	PUNCT
ejpam-6583	563	11	(	(	PUNCT
ejpam-6583	563	12	2025	2025	NUM
ejpam-6583	563	13	)	)	PUNCT
ejpam-6583	563	14	,	,	PUNCT
ejpam-6583	563	15	6583	6583	NUM
ejpam-6583	563	16	24	24	NUM
ejpam-6583	563	17	of	of	ADP
ejpam-6583	563	18	27	27	NUM
ejpam-6583	563	19	inequality	inequality	NOUN
ejpam-6583	563	20	and	and	CCONJ
ejpam-6583	563	21	contraction	contraction	NOUN
ejpam-6583	563	22	condition	condition	NOUN
ejpam-6583	563	23	,	,	PUNCT
ejpam-6583	563	24	we	we	PRON
ejpam-6583	563	25	get	get	VERB
ejpam-6583	563	26	δb	δb	ADP
ejpam-6583	563	27	r⊕d	r⊕d	NOUN
ejpam-6583	563	28	(	(	PUNCT
ejpam-6583	563	29	z	z	NOUN
ejpam-6583	563	30	,	,	PUNCT
ejpam-6583	563	31	f	f	PROPN
ejpam-6583	563	32	(	(	PUNCT
ejpam-6583	563	33	z	z	NOUN
ejpam-6583	563	34	)	)	PUNCT
ejpam-6583	563	35	)	)	PUNCT
ejpam-6583	564	1	≾	≾	NOUN
ejpam-6583	564	2	sδb	sδb	VERB
ejpam-6583	564	3	r⊕d	r⊕d	NOUN
ejpam-6583	564	4	(	(	PUNCT
ejpam-6583	564	5	z	z	NOUN
ejpam-6583	564	6	,	,	PUNCT
ejpam-6583	564	7	xn	xn	PROPN
ejpam-6583	564	8	)	)	PUNCT
ejpam-6583	565	1	+	+	NUM
ejpam-6583	565	2	sδb	sδb	NOUN
ejpam-6583	565	3	r⊕d	r⊕d	NOUN
ejpam-6583	565	4	(	(	PUNCT
ejpam-6583	565	5	xn	xn	PROPN
ejpam-6583	565	6	,	,	PUNCT
ejpam-6583	565	7	f	f	PROPN
ejpam-6583	565	8	(	(	PUNCT
ejpam-6583	565	9	z	z	NOUN
ejpam-6583	565	10	)	)	PUNCT
ejpam-6583	565	11	)	)	PUNCT
ejpam-6583	566	1	=	=	SYM
ejpam-6583	566	2	sδb	sδb	PROPN
ejpam-6583	566	3	r⊕d	r⊕d	NOUN
ejpam-6583	566	4	(	(	PUNCT
ejpam-6583	566	5	z	z	NOUN
ejpam-6583	566	6	,	,	PUNCT
ejpam-6583	566	7	xn	xn	PROPN
ejpam-6583	566	8	)	)	PUNCT
ejpam-6583	567	1	+	+	NUM
ejpam-6583	567	2	sδb	sδb	NOUN
ejpam-6583	567	3	r⊕d	r⊕d	NOUN
ejpam-6583	567	4	(	(	PUNCT
ejpam-6583	567	5	f	f	PROPN
ejpam-6583	567	6	(	(	PUNCT
ejpam-6583	567	7	xn−1),f	xn−1),f	PROPN
ejpam-6583	567	8	(	(	PUNCT
ejpam-6583	567	9	z	z	NOUN
ejpam-6583	567	10	)	)	PUNCT
ejpam-6583	567	11	)	)	PUNCT
ejpam-6583	568	1	≾	≾	NOUN
ejpam-6583	568	2	sδb	sδb	VERB
ejpam-6583	568	3	r⊕d	r⊕d	NOUN
ejpam-6583	568	4	(	(	PUNCT
ejpam-6583	568	5	z	z	NOUN
ejpam-6583	568	6	,	,	PUNCT
ejpam-6583	568	7	xn	xn	PROPN
ejpam-6583	568	8	)	)	PUNCT
ejpam-6583	569	1	+	+	CCONJ
ejpam-6583	569	2	sdiag	sdiag	PROPN
ejpam-6583	569	3	(	(	PUNCT
ejpam-6583	569	4	α1	α1	PROPN
ejpam-6583	569	5	,	,	PUNCT
ejpam-6583	569	6	α2	α2	ADJ
ejpam-6583	569	7	,	,	PUNCT
ejpam-6583	569	8	·	·	PUNCT
ejpam-6583	569	9	·	·	PUNCT
ejpam-6583	569	10	·	·	PUNCT
ejpam-6583	569	11	,	,	PUNCT
ejpam-6583	569	12	αd	αd	PROPN
ejpam-6583	569	13	)	)	PUNCT
ejpam-6583	569	14	δb	δb	NOUN
ejpam-6583	569	15	r⊕d	r⊕d	NOUN
ejpam-6583	569	16	(	(	PUNCT
ejpam-6583	569	17	xn−1	xn−1	PROPN
ejpam-6583	569	18	,	,	PUNCT
ejpam-6583	569	19	z	z	NOUN
ejpam-6583	569	20	)	)	PUNCT
ejpam-6583	570	1	+	+	CCONJ
ejpam-6583	570	2	sdiag	sdiag	NOUN
ejpam-6583	570	3	(	(	PUNCT
ejpam-6583	570	4	β1	β1	PROPN
ejpam-6583	570	5	,	,	PUNCT
ejpam-6583	570	6	β2	β2	VERB
ejpam-6583	570	7	,	,	PUNCT
ejpam-6583	570	8	·	·	PUNCT
ejpam-6583	570	9	·	·	PUNCT
ejpam-6583	570	10	·	·	PUNCT
ejpam-6583	570	11	,	,	PUNCT
ejpam-6583	570	12	βd	βd	X
ejpam-6583	570	13	)	)	PUNCT
ejpam-6583	571	1	[	[	X
ejpam-6583	571	2	δb	δb	X
ejpam-6583	571	3	r⊕d	r⊕d	NOUN
ejpam-6583	571	4	(	(	PUNCT
ejpam-6583	571	5	xn−1,f	xn−1,f	X
ejpam-6583	571	6	(	(	PUNCT
ejpam-6583	571	7	xn−1	xn−1	PROPN
ejpam-6583	571	8	)	)	PUNCT
ejpam-6583	571	9	)	)	PUNCT
ejpam-6583	572	1	+	+	CCONJ
ejpam-6583	572	2	δb	δb	NOUN
ejpam-6583	572	3	r⊕d	r⊕d	NOUN
ejpam-6583	572	4	(	(	PUNCT
ejpam-6583	572	5	z	z	NOUN
ejpam-6583	572	6	,	,	PUNCT
ejpam-6583	572	7	f	f	PROPN
ejpam-6583	572	8	(	(	PUNCT
ejpam-6583	572	9	z	z	NOUN
ejpam-6583	572	10	)	)	PUNCT
ejpam-6583	572	11	)	)	PUNCT
ejpam-6583	572	12	]	]	PUNCT
ejpam-6583	573	1	+	+	CCONJ
ejpam-6583	573	2	sdiag	sdiag	NOUN
ejpam-6583	573	3	(	(	PUNCT
ejpam-6583	573	4	γ1	γ1	PROPN
ejpam-6583	573	5	,	,	PUNCT
ejpam-6583	573	6	γ2	γ2	PROPN
ejpam-6583	573	7	,	,	PUNCT
ejpam-6583	573	8	·	·	PUNCT
ejpam-6583	573	9	·	·	PUNCT
ejpam-6583	573	10	·	·	PUNCT
ejpam-6583	573	11	,	,	PUNCT
ejpam-6583	573	12	γd	γd	ADP
ejpam-6583	573	13	)	)	PUNCT
ejpam-6583	574	1	[	[	X
ejpam-6583	574	2	δb	δb	X
ejpam-6583	574	3	r⊕d	r⊕d	NOUN
ejpam-6583	574	4	(	(	PUNCT
ejpam-6583	574	5	xn−1,f	xn−1,f	X
ejpam-6583	574	6	(	(	PUNCT
ejpam-6583	574	7	z	z	NOUN
ejpam-6583	574	8	)	)	PUNCT
ejpam-6583	574	9	)	)	PUNCT
ejpam-6583	575	1	+	+	CCONJ
ejpam-6583	575	2	δb	δb	NOUN
ejpam-6583	575	3	r⊕d	r⊕d	NOUN
ejpam-6583	575	4	(	(	PUNCT
ejpam-6583	575	5	z	z	NOUN
ejpam-6583	575	6	,	,	PUNCT
ejpam-6583	575	7	f	f	PROPN
ejpam-6583	575	8	(	(	PUNCT
ejpam-6583	575	9	xn−1	xn−1	PROPN
ejpam-6583	575	10	)	)	PUNCT
ejpam-6583	575	11	)	)	PUNCT
ejpam-6583	575	12	]	]	PUNCT
ejpam-6583	576	1	=	=	PUNCT
ejpam-6583	576	2	sdiag	sdiag	NOUN
ejpam-6583	576	3	(	(	PUNCT
ejpam-6583	576	4	1	1	NUM
ejpam-6583	576	5	+	+	NUM
ejpam-6583	576	6	γ1	γ1	NOUN
ejpam-6583	576	7	,	,	PUNCT
ejpam-6583	576	8	1	1	NUM
ejpam-6583	576	9	+	+	CCONJ
ejpam-6583	576	10	γ2	γ2	ADJ
ejpam-6583	576	11	,	,	PUNCT
ejpam-6583	576	12	·	·	PUNCT
ejpam-6583	576	13	·	·	PUNCT
ejpam-6583	576	14	·	·	PUNCT
ejpam-6583	576	15	,	,	PUNCT
ejpam-6583	576	16	1	1	NUM
ejpam-6583	576	17	+	+	CCONJ
ejpam-6583	576	18	γd	γd	ADV
ejpam-6583	576	19	)	)	PUNCT
ejpam-6583	576	20	δb	δb	NOUN
ejpam-6583	576	21	r⊕d	r⊕d	NOUN
ejpam-6583	576	22	(	(	PUNCT
ejpam-6583	576	23	z	z	NOUN
ejpam-6583	576	24	,	,	PUNCT
ejpam-6583	576	25	xn	xn	PROPN
ejpam-6583	576	26	)	)	PUNCT
ejpam-6583	577	1	+	+	CCONJ
ejpam-6583	577	2	sdiag	sdiag	PROPN
ejpam-6583	577	3	(	(	PUNCT
ejpam-6583	577	4	α1	α1	PROPN
ejpam-6583	577	5	,	,	PUNCT
ejpam-6583	577	6	α2	α2	ADJ
ejpam-6583	577	7	,	,	PUNCT
ejpam-6583	577	8	·	·	PUNCT
ejpam-6583	577	9	·	·	PUNCT
ejpam-6583	577	10	·	·	PUNCT
ejpam-6583	577	11	,	,	PUNCT
ejpam-6583	577	12	αd	αd	PROPN
ejpam-6583	577	13	)	)	PUNCT
ejpam-6583	577	14	δb	δb	NOUN
ejpam-6583	577	15	r⊕d	r⊕d	NOUN
ejpam-6583	577	16	(	(	PUNCT
ejpam-6583	577	17	xn−1	xn−1	PROPN
ejpam-6583	577	18	,	,	PUNCT
ejpam-6583	577	19	z	z	NOUN
ejpam-6583	577	20	)	)	PUNCT
ejpam-6583	578	1	+	+	CCONJ
ejpam-6583	578	2	sdiag	sdiag	NOUN
ejpam-6583	578	3	(	(	PUNCT
ejpam-6583	578	4	β1	β1	PROPN
ejpam-6583	578	5	,	,	PUNCT
ejpam-6583	578	6	β2	β2	VERB
ejpam-6583	578	7	,	,	PUNCT
ejpam-6583	578	8	·	·	PUNCT
ejpam-6583	578	9	·	·	PUNCT
ejpam-6583	578	10	·	·	PUNCT
ejpam-6583	578	11	,	,	PUNCT
ejpam-6583	578	12	βd	βd	X
ejpam-6583	578	13	)	)	PUNCT
ejpam-6583	579	1	[	[	X
ejpam-6583	579	2	δb	δb	X
ejpam-6583	579	3	r⊕d	r⊕d	NOUN
ejpam-6583	579	4	(	(	PUNCT
ejpam-6583	579	5	xn−1	xn−1	PROPN
ejpam-6583	579	6	,	,	PUNCT
ejpam-6583	579	7	xn	xn	PUNCT
ejpam-6583	579	8	)	)	PUNCT
ejpam-6583	580	1	+	+	CCONJ
ejpam-6583	580	2	δb	δb	NOUN
ejpam-6583	580	3	r⊕d	r⊕d	NOUN
ejpam-6583	580	4	(	(	PUNCT
ejpam-6583	580	5	z	z	NOUN
ejpam-6583	580	6	,	,	PUNCT
ejpam-6583	580	7	f	f	PROPN
ejpam-6583	580	8	(	(	PUNCT
ejpam-6583	580	9	z	z	NOUN
ejpam-6583	580	10	)	)	PUNCT
ejpam-6583	580	11	)	)	PUNCT
ejpam-6583	580	12	]	]	PUNCT
ejpam-6583	581	1	+	+	CCONJ
ejpam-6583	581	2	sdiag	sdiag	NOUN
ejpam-6583	581	3	(	(	PUNCT
ejpam-6583	581	4	γ1	γ1	PROPN
ejpam-6583	581	5	,	,	PUNCT
ejpam-6583	581	6	γ2	γ2	PROPN
ejpam-6583	581	7	,	,	PUNCT
ejpam-6583	581	8	·	·	PUNCT
ejpam-6583	581	9	·	·	PUNCT
ejpam-6583	581	10	·	·	PUNCT
ejpam-6583	581	11	,	,	PUNCT
ejpam-6583	581	12	γd	γd	ADV
ejpam-6583	581	13	)	)	PUNCT
ejpam-6583	581	14	δb	δb	NOUN
ejpam-6583	581	15	r⊕d	r⊕d	NOUN
ejpam-6583	581	16	(	(	PUNCT
ejpam-6583	581	17	xn−1,f	xn−1,f	X
ejpam-6583	581	18	(	(	PUNCT
ejpam-6583	581	19	z	z	NOUN
ejpam-6583	581	20	)	)	PUNCT
ejpam-6583	581	21	)	)	PUNCT
ejpam-6583	581	22	,	,	PUNCT
ejpam-6583	581	23	hence	hence	ADV
ejpam-6583	581	24	diag	diag	X
ejpam-6583	581	25	(	(	PUNCT
ejpam-6583	581	26	1	1	NUM
ejpam-6583	581	27	+	+	CCONJ
ejpam-6583	581	28	sβ1	sβ1	NOUN
ejpam-6583	581	29	,	,	PUNCT
ejpam-6583	581	30	·	·	PUNCT
ejpam-6583	581	31	·	·	PUNCT
ejpam-6583	581	32	·	·	PUNCT
ejpam-6583	581	33	,	,	PUNCT
ejpam-6583	581	34	1	1	NUM
ejpam-6583	581	35	+	+	CCONJ
ejpam-6583	581	36	sβd	sβd	NOUN
ejpam-6583	581	37	)	)	PUNCT
ejpam-6583	581	38	δb	δb	NOUN
ejpam-6583	581	39	r⊕d	r⊕d	NOUN
ejpam-6583	581	40	(	(	PUNCT
ejpam-6583	581	41	z	z	NOUN
ejpam-6583	581	42	,	,	PUNCT
ejpam-6583	581	43	f	f	PROPN
ejpam-6583	581	44	(	(	PUNCT
ejpam-6583	581	45	z	z	NOUN
ejpam-6583	581	46	)	)	PUNCT
ejpam-6583	581	47	)	)	PUNCT
ejpam-6583	582	1	≾	≾	PROPN
ejpam-6583	582	2	sdiag	sdiag	NOUN
ejpam-6583	582	3	(	(	PUNCT
ejpam-6583	582	4	1	1	NUM
ejpam-6583	582	5	+	+	NUM
ejpam-6583	582	6	γ1	γ1	NOUN
ejpam-6583	582	7	,	,	PUNCT
ejpam-6583	582	8	·	·	PUNCT
ejpam-6583	582	9	·	·	PUNCT
ejpam-6583	582	10	·	·	PUNCT
ejpam-6583	582	11	,	,	PUNCT
ejpam-6583	582	12	1	1	NUM
ejpam-6583	582	13	+	+	CCONJ
ejpam-6583	582	14	γd	γd	ADV
ejpam-6583	582	15	)	)	PUNCT
ejpam-6583	582	16	δb	δb	NOUN
ejpam-6583	582	17	r⊕d	r⊕d	NOUN
ejpam-6583	582	18	(	(	PUNCT
ejpam-6583	582	19	z	z	NOUN
ejpam-6583	582	20	,	,	PUNCT
ejpam-6583	582	21	xn	xn	PROPN
ejpam-6583	582	22	)	)	PUNCT
ejpam-6583	583	1	+	+	CCONJ
ejpam-6583	583	2	sdiag	sdiag	PROPN
ejpam-6583	583	3	(	(	PUNCT
ejpam-6583	583	4	α1	α1	PROPN
ejpam-6583	583	5	,	,	PUNCT
ejpam-6583	583	6	·	·	PUNCT
ejpam-6583	583	7	·	·	PUNCT
ejpam-6583	583	8	·	·	PUNCT
ejpam-6583	583	9	,	,	PUNCT
ejpam-6583	583	10	αd	αd	PROPN
ejpam-6583	583	11	)	)	PUNCT
ejpam-6583	583	12	δb	δb	NOUN
ejpam-6583	583	13	r⊕d	r⊕d	NOUN
ejpam-6583	583	14	(	(	PUNCT
ejpam-6583	583	15	xn−1	xn−1	PROPN
ejpam-6583	583	16	,	,	PUNCT
ejpam-6583	583	17	z	z	NOUN
ejpam-6583	583	18	)	)	PUNCT
ejpam-6583	584	1	+	+	CCONJ
ejpam-6583	584	2	sdiag	sdiag	NOUN
ejpam-6583	584	3	(	(	PUNCT
ejpam-6583	584	4	β1	β1	PROPN
ejpam-6583	584	5	,	,	PUNCT
ejpam-6583	584	6	·	·	PUNCT
ejpam-6583	584	7	·	·	PUNCT
ejpam-6583	584	8	·	·	PUNCT
ejpam-6583	584	9	,	,	PUNCT
ejpam-6583	584	10	βd	βd	X
ejpam-6583	584	11	)	)	PUNCT
ejpam-6583	584	12	δb	δb	NOUN
ejpam-6583	584	13	r⊕d	r⊕d	NOUN
ejpam-6583	584	14	(	(	PUNCT
ejpam-6583	584	15	xn−1	xn−1	PROPN
ejpam-6583	584	16	,	,	PUNCT
ejpam-6583	584	17	xn	xn	PUNCT
ejpam-6583	584	18	)	)	PUNCT
ejpam-6583	585	1	+	+	CCONJ
ejpam-6583	585	2	sdiag	sdiag	NOUN
ejpam-6583	585	3	(	(	PUNCT
ejpam-6583	585	4	γ1	γ1	PROPN
ejpam-6583	585	5	,	,	PUNCT
ejpam-6583	585	6	·	·	PUNCT
ejpam-6583	585	7	·	·	PUNCT
ejpam-6583	585	8	·	·	PUNCT
ejpam-6583	585	9	,	,	PUNCT
ejpam-6583	585	10	γd	γd	ADV
ejpam-6583	585	11	)	)	PUNCT
ejpam-6583	585	12	δb	δb	NOUN
ejpam-6583	585	13	r⊕d	r⊕d	NOUN
ejpam-6583	585	14	(	(	PUNCT
ejpam-6583	585	15	f	f	X
ejpam-6583	585	16	(	(	PUNCT
ejpam-6583	585	17	xn−2),f	xn−2),f	PROPN
ejpam-6583	585	18	(	(	PUNCT
ejpam-6583	585	19	z	z	NOUN
ejpam-6583	585	20	)	)	PUNCT
ejpam-6583	585	21	)	)	PUNCT
ejpam-6583	585	22	,	,	PUNCT
ejpam-6583	585	23	and	and	CCONJ
ejpam-6583	585	24	since	since	SCONJ
ejpam-6583	585	25	xn	xn	PROPN
ejpam-6583	585	26	→	→	SYM
ejpam-6583	585	27	z	z	NOUN
ejpam-6583	585	28	it	it	PRON
ejpam-6583	585	29	is	be	AUX
ejpam-6583	585	30	clear	clear	ADJ
ejpam-6583	585	31	that	that	SCONJ
ejpam-6583	585	32	we	we	PRON
ejpam-6583	585	33	can	can	AUX
ejpam-6583	585	34	make	make	VERB
ejpam-6583	585	35	this	this	DET
ejpam-6583	585	36	distance	distance	NOUN
ejpam-6583	585	37	as	as	ADV
ejpam-6583	585	38	small	small	ADJ
ejpam-6583	585	39	as	as	SCONJ
ejpam-6583	585	40	we	we	PRON
ejpam-6583	585	41	please	please	VERB
ejpam-6583	585	42	by	by	ADP
ejpam-6583	585	43	choosing	choose	VERB
ejpam-6583	585	44	n	n	PRON
ejpam-6583	585	45	sufficiently	sufficiently	ADV
ejpam-6583	585	46	large	large	ADJ
ejpam-6583	585	47	.	.	PUNCT
ejpam-6583	586	1	we	we	PRON
ejpam-6583	586	2	conclude	conclude	VERB
ejpam-6583	586	3	that	that	SCONJ
ejpam-6583	586	4	δb	δb	NOUN
ejpam-6583	586	5	r⊕d	r⊕d	NOUN
ejpam-6583	586	6	(	(	PUNCT
ejpam-6583	586	7	z	z	NOUN
ejpam-6583	586	8	,	,	PUNCT
ejpam-6583	586	9	f	f	PROPN
ejpam-6583	586	10	(	(	PUNCT
ejpam-6583	586	11	z	z	NOUN
ejpam-6583	586	12	)	)	PUNCT
ejpam-6583	586	13	)	)	PUNCT
ejpam-6583	587	1	=	=	SYM
ejpam-6583	587	2	0	0	PUNCT
ejpam-6583	588	1	=	=	AUX
ejpam-6583	588	2	⇒	⇒	X
ejpam-6583	588	3	f	f	X
ejpam-6583	588	4	(	(	PUNCT
ejpam-6583	588	5	z	z	NOUN
ejpam-6583	588	6	)	)	PUNCT
ejpam-6583	589	1	=	=	SYM
ejpam-6583	589	2	z	z	NOUN
ejpam-6583	589	3	,	,	PUNCT
ejpam-6583	589	4	so	so	ADV
ejpam-6583	589	5	z	z	NOUN
ejpam-6583	589	6	∈	∈	PROPN
ejpam-6583	589	7	x	x	X
ejpam-6583	589	8	is	be	AUX
ejpam-6583	589	9	a	a	DET
ejpam-6583	589	10	fixed	fix	VERB
ejpam-6583	589	11	-	-	PUNCT
ejpam-6583	589	12	point	point	NOUN
ejpam-6583	589	13	of	of	ADP
ejpam-6583	589	14	f	f	PROPN
ejpam-6583	589	15	.	.	PUNCT
ejpam-6583	590	1	to	to	PART
ejpam-6583	590	2	prove	prove	VERB
ejpam-6583	590	3	uniqueness	uniqueness	NOUN
ejpam-6583	590	4	,	,	PUNCT
ejpam-6583	590	5	suppose	suppose	VERB
ejpam-6583	590	6	there	there	PRON
ejpam-6583	590	7	are	be	VERB
ejpam-6583	590	8	two	two	NUM
ejpam-6583	590	9	fixed	fix	VERB
ejpam-6583	590	10	points	point	NOUN
ejpam-6583	591	1	x	x	X
ejpam-6583	591	2	=	=	SYM
ejpam-6583	591	3	f	f	X
ejpam-6583	591	4	(	(	PUNCT
ejpam-6583	591	5	x	x	NOUN
ejpam-6583	591	6	)	)	PUNCT
ejpam-6583	591	7	and	and	CCONJ
ejpam-6583	591	8	y	y	PROPN
ejpam-6583	591	9	=	=	SYM
ejpam-6583	591	10	f	f	PROPN
ejpam-6583	591	11	(	(	PUNCT
ejpam-6583	591	12	y	y	NOUN
ejpam-6583	591	13	)	)	PUNCT
ejpam-6583	591	14	.	.	PUNCT
ejpam-6583	592	1	then	then	ADV
ejpam-6583	592	2	,	,	PUNCT
ejpam-6583	592	3	from	from	ADP
ejpam-6583	592	4	the	the	DET
ejpam-6583	592	5	contraction	contraction	NOUN
ejpam-6583	592	6	condition	condition	NOUN
ejpam-6583	592	7	,	,	PUNCT
ejpam-6583	592	8	we	we	PRON
ejpam-6583	592	9	have	have	VERB
ejpam-6583	592	10	δb	δb	NOUN
ejpam-6583	592	11	r⊕d	r⊕d	NOUN
ejpam-6583	592	12	(	(	PUNCT
ejpam-6583	592	13	x	x	X
ejpam-6583	592	14	,	,	PUNCT
ejpam-6583	592	15	y	y	NOUN
ejpam-6583	592	16	)	)	PUNCT
ejpam-6583	592	17	=	=	PUNCT
ejpam-6583	592	18	δb	δb	X
ejpam-6583	592	19	r⊕d	r⊕d	NOUN
ejpam-6583	592	20	(	(	PUNCT
ejpam-6583	592	21	f	f	PROPN
ejpam-6583	592	22	(	(	PUNCT
ejpam-6583	592	23	x),f	x),f	PROPN
ejpam-6583	592	24	(	(	PUNCT
ejpam-6583	592	25	y	y	NOUN
ejpam-6583	592	26	)	)	PUNCT
ejpam-6583	592	27	)	)	PUNCT
ejpam-6583	593	1	≾	≾	NOUN
ejpam-6583	593	2	diag	diag	NOUN
ejpam-6583	593	3	(	(	PUNCT
ejpam-6583	593	4	α1	α1	PROPN
ejpam-6583	593	5	,	,	PUNCT
ejpam-6583	593	6	α2	α2	ADJ
ejpam-6583	593	7	,	,	PUNCT
ejpam-6583	593	8	·	·	PUNCT
ejpam-6583	593	9	·	·	PUNCT
ejpam-6583	593	10	·	·	PUNCT
ejpam-6583	593	11	,	,	PUNCT
ejpam-6583	593	12	αd	αd	PROPN
ejpam-6583	593	13	)	)	PUNCT
ejpam-6583	593	14	δb	δb	NOUN
ejpam-6583	593	15	r⊕d	r⊕d	NOUN
ejpam-6583	593	16	(	(	PUNCT
ejpam-6583	593	17	x	x	X
ejpam-6583	593	18	,	,	PUNCT
ejpam-6583	593	19	y	y	PROPN
ejpam-6583	593	20	)	)	PUNCT
ejpam-6583	594	1	+	+	NOUN
ejpam-6583	594	2	diag	diag	NOUN
ejpam-6583	594	3	(	(	PUNCT
ejpam-6583	594	4	β1	β1	PROPN
ejpam-6583	594	5	,	,	PUNCT
ejpam-6583	594	6	β2	β2	VERB
ejpam-6583	594	7	,	,	PUNCT
ejpam-6583	594	8	·	·	PUNCT
ejpam-6583	594	9	·	·	PUNCT
ejpam-6583	594	10	·	·	PUNCT
ejpam-6583	594	11	,	,	PUNCT
ejpam-6583	594	12	βd	βd	X
ejpam-6583	594	13	)	)	PUNCT
ejpam-6583	595	1	[	[	X
ejpam-6583	595	2	δb	δb	X
ejpam-6583	595	3	r⊕d	r⊕d	NOUN
ejpam-6583	595	4	(	(	PUNCT
ejpam-6583	595	5	x	x	X
ejpam-6583	595	6	,	,	PUNCT
ejpam-6583	595	7	f	f	PROPN
ejpam-6583	595	8	(	(	PUNCT
ejpam-6583	595	9	x	x	NOUN
ejpam-6583	595	10	)	)	PUNCT
ejpam-6583	595	11	)	)	PUNCT
ejpam-6583	596	1	+	+	CCONJ
ejpam-6583	596	2	δb	δb	NOUN
ejpam-6583	596	3	r⊕d	r⊕d	NOUN
ejpam-6583	596	4	(	(	PUNCT
ejpam-6583	596	5	y	y	PROPN
ejpam-6583	596	6	,	,	PUNCT
ejpam-6583	596	7	f	f	PROPN
ejpam-6583	596	8	(	(	PUNCT
ejpam-6583	596	9	y	y	NOUN
ejpam-6583	596	10	)	)	PUNCT
ejpam-6583	596	11	)	)	PUNCT
ejpam-6583	596	12	]	]	PUNCT
ejpam-6583	597	1	+	+	CCONJ
ejpam-6583	597	2	diag	diag	PROPN
ejpam-6583	597	3	(	(	PUNCT
ejpam-6583	597	4	γ1	γ1	PROPN
ejpam-6583	597	5	,	,	PUNCT
ejpam-6583	597	6	γ2	γ2	PROPN
ejpam-6583	597	7	,	,	PUNCT
ejpam-6583	597	8	·	·	PUNCT
ejpam-6583	597	9	·	·	PUNCT
ejpam-6583	597	10	·	·	PUNCT
ejpam-6583	597	11	,	,	PUNCT
ejpam-6583	597	12	γd	γd	ADP
ejpam-6583	597	13	)	)	PUNCT
ejpam-6583	598	1	[	[	X
ejpam-6583	598	2	δb	δb	X
ejpam-6583	598	3	r⊕d	r⊕d	NOUN
ejpam-6583	598	4	(	(	PUNCT
ejpam-6583	598	5	x	x	X
ejpam-6583	598	6	,	,	PUNCT
ejpam-6583	598	7	f	f	PROPN
ejpam-6583	598	8	(	(	PUNCT
ejpam-6583	598	9	y	y	NOUN
ejpam-6583	598	10	)	)	PUNCT
ejpam-6583	598	11	)	)	PUNCT
ejpam-6583	599	1	+	+	CCONJ
ejpam-6583	599	2	δb	δb	NOUN
ejpam-6583	599	3	r⊕d	r⊕d	NOUN
ejpam-6583	599	4	(	(	PUNCT
ejpam-6583	599	5	y	y	PROPN
ejpam-6583	599	6	,	,	PUNCT
ejpam-6583	599	7	f	f	PROPN
ejpam-6583	599	8	(	(	PUNCT
ejpam-6583	599	9	x	x	NOUN
ejpam-6583	599	10	)	)	PUNCT
ejpam-6583	599	11	)	)	PUNCT
ejpam-6583	599	12	]	]	PUNCT
ejpam-6583	600	1	=	=	PUNCT
ejpam-6583	600	2	diag	diag	X
ejpam-6583	600	3	(	(	PUNCT
ejpam-6583	600	4	α1	α1	PROPN
ejpam-6583	600	5	,	,	PUNCT
ejpam-6583	600	6	α2	α2	ADJ
ejpam-6583	600	7	,	,	PUNCT
ejpam-6583	600	8	·	·	PUNCT
ejpam-6583	600	9	·	·	PUNCT
ejpam-6583	600	10	·	·	PUNCT
ejpam-6583	600	11	,	,	PUNCT
ejpam-6583	600	12	αd	αd	PROPN
ejpam-6583	600	13	)	)	PUNCT
ejpam-6583	600	14	δb	δb	NOUN
ejpam-6583	600	15	r⊕d	r⊕d	NOUN
ejpam-6583	600	16	(	(	PUNCT
ejpam-6583	600	17	x	x	X
ejpam-6583	600	18	,	,	PUNCT
ejpam-6583	600	19	y	y	PROPN
ejpam-6583	600	20	)	)	PUNCT
ejpam-6583	601	1	+	+	NOUN
ejpam-6583	601	2	diag	diag	NOUN
ejpam-6583	601	3	(	(	PUNCT
ejpam-6583	601	4	2γ1	2γ1	NUM
ejpam-6583	601	5	,	,	PUNCT
ejpam-6583	601	6	2γ2	2γ2	NUM
ejpam-6583	601	7	,	,	PUNCT
ejpam-6583	601	8	·	·	PUNCT
ejpam-6583	601	9	·	·	PUNCT
ejpam-6583	601	10	·	·	PUNCT
ejpam-6583	601	11	,	,	PUNCT
ejpam-6583	601	12	2γd	2γd	NOUN
ejpam-6583	601	13	)	)	PUNCT
ejpam-6583	601	14	δb	δb	NOUN
ejpam-6583	601	15	r⊕d	r⊕d	NOUN
ejpam-6583	601	16	(	(	PUNCT
ejpam-6583	601	17	x	x	X
ejpam-6583	601	18	,	,	PUNCT
ejpam-6583	601	19	y	y	NOUN
ejpam-6583	601	20	)	)	PUNCT
ejpam-6583	601	21	=	=	NOUN
ejpam-6583	601	22	diag	diag	NOUN
ejpam-6583	601	23	(	(	PUNCT
ejpam-6583	601	24	α1	α1	PROPN
ejpam-6583	601	25	+	+	CCONJ
ejpam-6583	601	26	2γ1	2γ1	NOUN
ejpam-6583	601	27	,	,	PUNCT
ejpam-6583	601	28	α2	α2	PROPN
ejpam-6583	601	29	+	+	CCONJ
ejpam-6583	601	30	2γ2	2γ2	NUM
ejpam-6583	601	31	,	,	PUNCT
ejpam-6583	601	32	·	·	PUNCT
ejpam-6583	601	33	·	·	PUNCT
ejpam-6583	601	34	·	·	PUNCT
ejpam-6583	601	35	,	,	PUNCT
ejpam-6583	601	36	αd	αd	PROPN
ejpam-6583	601	37	+	+	CCONJ
ejpam-6583	601	38	2γd	2γd	ADJ
ejpam-6583	601	39	)	)	PUNCT
ejpam-6583	601	40	δb	δb	NOUN
ejpam-6583	601	41	r⊕d	r⊕d	NOUN
ejpam-6583	601	42	(	(	PUNCT
ejpam-6583	601	43	x	x	X
ejpam-6583	601	44	,	,	PUNCT
ejpam-6583	601	45	y	y	PROPN
ejpam-6583	601	46	)	)	PUNCT
ejpam-6583	601	47	g.	g.	NOUN
ejpam-6583	601	48	albeladi	albeladi	PROPN
ejpam-6583	601	49	,	,	PUNCT
ejpam-6583	601	50	s.	s.	PROPN
ejpam-6583	601	51	omran	omran	PROPN
ejpam-6583	601	52	/	/	SYM
ejpam-6583	601	53	eur	eur	PROPN
ejpam-6583	601	54	.	.	PUNCT
ejpam-6583	602	1	j.	j.	PROPN
ejpam-6583	602	2	pure	pure	PROPN
ejpam-6583	602	3	appl	appl	PROPN
ejpam-6583	602	4	.	.	PROPN
ejpam-6583	602	5	math	math	PROPN
ejpam-6583	602	6	,	,	PUNCT
ejpam-6583	602	7	18	18	NUM
ejpam-6583	602	8	(	(	PUNCT
ejpam-6583	602	9	3	3	NUM
ejpam-6583	602	10	)	)	PUNCT
ejpam-6583	602	11	(	(	PUNCT
ejpam-6583	602	12	2025	2025	NUM
ejpam-6583	602	13	)	)	PUNCT
ejpam-6583	602	14	,	,	PUNCT
ejpam-6583	602	15	6583	6583	NUM
ejpam-6583	602	16	25	25	NUM
ejpam-6583	602	17	of	of	ADP
ejpam-6583	602	18	27	27	NUM
ejpam-6583	602	19	≺	≺	NOUN
ejpam-6583	602	20	δb	δb	NOUN
ejpam-6583	602	21	r⊕d	r⊕d	NOUN
ejpam-6583	602	22	(	(	PUNCT
ejpam-6583	602	23	x	x	X
ejpam-6583	602	24	,	,	PUNCT
ejpam-6583	602	25	y	y	PROPN
ejpam-6583	602	26	)	)	PUNCT
ejpam-6583	603	1	,	,	PUNCT
ejpam-6583	603	2	this	this	PRON
ejpam-6583	603	3	implies	imply	VERB
ejpam-6583	603	4	δb	δb	NOUN
ejpam-6583	603	5	r⊕d	r⊕d	NOUN
ejpam-6583	603	6	(	(	PUNCT
ejpam-6583	603	7	x	x	X
ejpam-6583	603	8	,	,	PUNCT
ejpam-6583	603	9	y	y	NOUN
ejpam-6583	603	10	)	)	PUNCT
ejpam-6583	603	11	=	=	SYM
ejpam-6583	604	1	0	0	X
ejpam-6583	604	2	.	.	PUNCT
ejpam-6583	605	1	hence	hence	ADV
ejpam-6583	605	2	x	x	X
ejpam-6583	605	3	=	=	SYM
ejpam-6583	605	4	y	y	PROPN
ejpam-6583	605	5	,	,	PUNCT
ejpam-6583	605	6	and	and	CCONJ
ejpam-6583	605	7	the	the	DET
ejpam-6583	605	8	fixed	fix	VERB
ejpam-6583	605	9	-	-	PUNCT
ejpam-6583	605	10	point	point	NOUN
ejpam-6583	605	11	x	x	PUNCT
ejpam-6583	605	12	of	of	ADP
ejpam-6583	605	13	f	f	PROPN
ejpam-6583	605	14	is	be	AUX
ejpam-6583	605	15	unique	unique	ADJ
ejpam-6583	605	16	.	.	PUNCT
ejpam-6583	606	1	4	4	X
ejpam-6583	606	2	.	.	X
ejpam-6583	606	3	conclusions	conclusion	NOUN
ejpam-6583	606	4	and	and	CCONJ
ejpam-6583	606	5	future	future	ADJ
ejpam-6583	606	6	work	work	NOUN
ejpam-6583	606	7	this	this	DET
ejpam-6583	606	8	research	research	NOUN
ejpam-6583	606	9	presents	present	VERB
ejpam-6583	606	10	novel	novel	ADJ
ejpam-6583	606	11	extensions	extension	NOUN
ejpam-6583	606	12	of	of	ADP
ejpam-6583	606	13	the	the	DET
ejpam-6583	606	14	banach	banach	ADV
ejpam-6583	606	15	fixed	fix	VERB
ejpam-6583	606	16	-	-	PUNCT
ejpam-6583	606	17	point	point	NOUN
ejpam-6583	606	18	theorem	theorem	NOUN
ejpam-6583	606	19	within	within	ADP
ejpam-6583	606	20	generalized	generalized	ADJ
ejpam-6583	606	21	metric	metric	ADJ
ejpam-6583	606	22	spaces	space	NOUN
ejpam-6583	606	23	that	that	PRON
ejpam-6583	606	24	include	include	VERB
ejpam-6583	606	25	a	a	DET
ejpam-6583	606	26	direct	direct	ADJ
ejpam-6583	606	27	sum	sum	NOUN
ejpam-6583	606	28	structure	structure	NOUN
ejpam-6583	606	29	.	.	PUNCT
ejpam-6583	607	1	by	by	ADP
ejpam-6583	607	2	introducing	introduce	VERB
ejpam-6583	607	3	a	a	DET
ejpam-6583	607	4	diagonal	diagonal	ADJ
ejpam-6583	607	5	matrix	matrix	NOUN
ejpam-6583	607	6	a	a	PRON
ejpam-6583	607	7	in	in	ADP
ejpam-6583	607	8	rd	rd	PROPN
ejpam-6583	607	9	,	,	PUNCT
ejpam-6583	607	10	we	we	PRON
ejpam-6583	607	11	establish	establish	VERB
ejpam-6583	607	12	evolved	evolved	ADJ
ejpam-6583	607	13	contraction	contraction	NOUN
ejpam-6583	607	14	conditions	condition	NOUN
ejpam-6583	607	15	that	that	PRON
ejpam-6583	607	16	enhance	enhance	VERB
ejpam-6583	607	17	the	the	DET
ejpam-6583	607	18	applicability	applicability	NOUN
ejpam-6583	607	19	of	of	ADP
ejpam-6583	607	20	fixed	fix	VERB
ejpam-6583	607	21	-	-	PUNCT
ejpam-6583	607	22	point	point	NOUN
ejpam-6583	607	23	results	result	NOUN
ejpam-6583	607	24	in	in	ADP
ejpam-6583	607	25	this	this	DET
ejpam-6583	607	26	framework	framework	NOUN
ejpam-6583	607	27	.	.	PUNCT
ejpam-6583	608	1	our	our	PRON
ejpam-6583	608	2	method	method	NOUN
ejpam-6583	608	3	provides	provide	VERB
ejpam-6583	608	4	a	a	DET
ejpam-6583	608	5	more	more	ADV
ejpam-6583	608	6	structured	structured	ADJ
ejpam-6583	608	7	and	and	CCONJ
ejpam-6583	608	8	flexible	flexible	ADJ
ejpam-6583	608	9	methodology	methodology	NOUN
ejpam-6583	608	10	for	for	ADP
ejpam-6583	608	11	analyzing	analyze	VERB
ejpam-6583	608	12	contraction	contraction	NOUN
ejpam-6583	608	13	operators	operator	NOUN
ejpam-6583	608	14	,	,	PUNCT
ejpam-6583	608	15	thereby	thereby	ADV
ejpam-6583	608	16	contributing	contribute	VERB
ejpam-6583	608	17	to	to	ADP
ejpam-6583	608	18	the	the	DET
ejpam-6583	608	19	promotion	promotion	NOUN
ejpam-6583	608	20	of	of	ADP
ejpam-6583	608	21	fixed	fix	VERB
ejpam-6583	608	22	-	-	PUNCT
ejpam-6583	608	23	point	point	NOUN
ejpam-6583	608	24	theory	theory	NOUN
ejpam-6583	608	25	in	in	ADP
ejpam-6583	608	26	vector	vector	NOUN
ejpam-6583	608	27	-	-	PUNCT
ejpam-6583	608	28	valued	value	VERB
ejpam-6583	608	29	metric	metric	ADJ
ejpam-6583	608	30	spaces	space	NOUN
ejpam-6583	608	31	.	.	PUNCT
ejpam-6583	609	1	the	the	DET
ejpam-6583	609	2	results	result	NOUN
ejpam-6583	609	3	obtained	obtain	VERB
ejpam-6583	609	4	extend	extend	VERB
ejpam-6583	609	5	classical	classical	ADJ
ejpam-6583	609	6	fixed	fix	VERB
ejpam-6583	609	7	-	-	PUNCT
ejpam-6583	609	8	point	point	NOUN
ejpam-6583	609	9	theorems	theorem	NOUN
ejpam-6583	609	10	and	and	CCONJ
ejpam-6583	609	11	offer	offer	VERB
ejpam-6583	609	12	new	new	ADJ
ejpam-6583	609	13	understandings	understanding	NOUN
ejpam-6583	609	14	of	of	ADP
ejpam-6583	609	15	the	the	DET
ejpam-6583	609	16	interplay	interplay	NOUN
ejpam-6583	609	17	between	between	ADP
ejpam-6583	609	18	metric	metric	ADJ
ejpam-6583	609	19	structures	structure	NOUN
ejpam-6583	609	20	and	and	CCONJ
ejpam-6583	609	21	direct	direct	ADJ
ejpam-6583	609	22	sum	sum	NOUN
ejpam-6583	609	23	operations	operation	NOUN
ejpam-6583	609	24	.	.	PUNCT
ejpam-6583	610	1	future	future	ADJ
ejpam-6583	610	2	studies	study	NOUN
ejpam-6583	610	3	may	may	AUX
ejpam-6583	610	4	expand	expand	VERB
ejpam-6583	610	5	these	these	DET
ejpam-6583	610	6	results	result	NOUN
ejpam-6583	610	7	to	to	ADP
ejpam-6583	610	8	more	more	ADV
ejpam-6583	610	9	comprehensive	comprehensive	ADJ
ejpam-6583	610	10	classes	class	NOUN
ejpam-6583	610	11	of	of	ADP
ejpam-6583	610	12	generalised	generalise	VERB
ejpam-6583	610	13	metric	metric	ADJ
ejpam-6583	610	14	spaces	space	NOUN
ejpam-6583	610	15	,	,	PUNCT
ejpam-6583	610	16	such	such	ADJ
ejpam-6583	610	17	as	as	ADP
ejpam-6583	610	18	g	g	NOUN
ejpam-6583	610	19	-	-	PUNCT
ejpam-6583	610	20	metric	metric	ADJ
ejpam-6583	610	21	or	or	CCONJ
ejpam-6583	610	22	partial	partial	ADJ
ejpam-6583	610	23	metric	metric	ADJ
ejpam-6583	610	24	spaces	space	NOUN
ejpam-6583	610	25	.	.	PUNCT
ejpam-6583	611	1	studying	study	VERB
ejpam-6583	611	2	non	non	ADJ
ejpam-6583	611	3	-	-	ADJ
ejpam-6583	611	4	diagonal	diagonal	ADJ
ejpam-6583	611	5	or	or	CCONJ
ejpam-6583	611	6	operator	operator	NOUN
ejpam-6583	611	7	-	-	PUNCT
ejpam-6583	611	8	valued	value	VERB
ejpam-6583	611	9	matrix	matrix	NOUN
ejpam-6583	611	10	systems	system	NOUN
ejpam-6583	611	11	within	within	ADP
ejpam-6583	611	12	the	the	DET
ejpam-6583	611	13	direct	direct	ADJ
ejpam-6583	611	14	sum	sum	NOUN
ejpam-6583	611	15	framework	framework	NOUN
ejpam-6583	611	16	could	could	AUX
ejpam-6583	611	17	yield	yield	VERB
ejpam-6583	611	18	more	more	ADJ
ejpam-6583	611	19	profound	profound	ADJ
ejpam-6583	611	20	insights	insight	NOUN
ejpam-6583	611	21	.	.	PUNCT
ejpam-6583	612	1	applications	application	NOUN
ejpam-6583	612	2	to	to	ADP
ejpam-6583	612	3	vector	vector	NOUN
ejpam-6583	612	4	-	-	PUNCT
ejpam-6583	612	5	valued	value	VERB
ejpam-6583	612	6	integral	integral	ADJ
ejpam-6583	612	7	and	and	CCONJ
ejpam-6583	612	8	differential	differential	ADJ
ejpam-6583	612	9	equations	equation	NOUN
ejpam-6583	612	10	,	,	PUNCT
ejpam-6583	612	11	as	as	ADV
ejpam-6583	612	12	well	well	ADV
ejpam-6583	612	13	as	as	ADP
ejpam-6583	612	14	iterative	iterative	ADJ
ejpam-6583	612	15	schemes	scheme	NOUN
ejpam-6583	612	16	for	for	ADP
ejpam-6583	612	17	approximating	approximate	VERB
ejpam-6583	612	18	fixed	fix	VERB
ejpam-6583	612	19	points	point	NOUN
ejpam-6583	612	20	under	under	ADP
ejpam-6583	612	21	the	the	DET
ejpam-6583	612	22	new	new	ADJ
ejpam-6583	612	23	conditions	condition	NOUN
ejpam-6583	612	24	,	,	PUNCT
ejpam-6583	612	25	also	also	ADV
ejpam-6583	612	26	certify	certify	VERB
ejpam-6583	612	27	further	further	ADJ
ejpam-6583	612	28	study	study	NOUN
ejpam-6583	612	29	.	.	PUNCT
ejpam-6583	613	1	acknowledgements	acknowledgement	NOUN
ejpam-6583	613	2	we	we	PRON
ejpam-6583	613	3	would	would	AUX
ejpam-6583	613	4	like	like	VERB
ejpam-6583	613	5	to	to	PART
ejpam-6583	613	6	extend	extend	VERB
ejpam-6583	613	7	my	my	PRON
ejpam-6583	613	8	sincere	sincere	ADJ
ejpam-6583	613	9	thanks	thank	NOUN
ejpam-6583	613	10	and	and	CCONJ
ejpam-6583	613	11	appreciation	appreciation	NOUN
ejpam-6583	613	12	to	to	ADP
ejpam-6583	613	13	dr	dr	PROPN
ejpam-6583	613	14	.	.	PROPN
ejpam-6583	613	15	mohamed	mohamed	PROPN
ejpam-6583	613	16	gamal	gamal	PROPN
ejpam-6583	613	17	for	for	ADP
ejpam-6583	613	18	reviewing	review	VERB
ejpam-6583	613	19	the	the	DET
ejpam-6583	613	20	paper	paper	NOUN
ejpam-6583	613	21	and	and	CCONJ
ejpam-6583	613	22	making	make	VERB
ejpam-6583	613	23	valuable	valuable	ADJ
ejpam-6583	613	24	modifications	modification	NOUN
ejpam-6583	613	25	.	.	PUNCT
ejpam-6583	614	1	declarations	declaration	NOUN
ejpam-6583	614	2	•	•	ADP
ejpam-6583	614	3	conflicts	conflict	NOUN
ejpam-6583	614	4	of	of	ADP
ejpam-6583	614	5	interest	interest	NOUN
ejpam-6583	614	6	the	the	DET
ejpam-6583	614	7	authors	author	NOUN
ejpam-6583	614	8	declare	declare	VERB
ejpam-6583	614	9	that	that	SCONJ
ejpam-6583	614	10	they	they	PRON
ejpam-6583	614	11	have	have	VERB
ejpam-6583	614	12	no	no	DET
ejpam-6583	614	13	conflicts	conflict	NOUN
ejpam-6583	614	14	of	of	ADP
ejpam-6583	614	15	interest	interest	NOUN
ejpam-6583	614	16	.	.	PUNCT
ejpam-6583	615	1	•	•	NUM
ejpam-6583	615	2	author	author	NOUN
ejpam-6583	615	3	’s	’s	PART
ejpam-6583	615	4	contributions	contribution	NOUN
ejpam-6583	615	5	conceptualization	conceptualization	NOUN
ejpam-6583	615	6	,	,	PUNCT
ejpam-6583	615	7	writing	write	VERB
ejpam-6583	615	8	original	original	ADJ
ejpam-6583	615	9	draft	draft	NOUN
ejpam-6583	615	10	(	(	PUNCT
ejpam-6583	615	11	g.	g.	NOUN
ejpam-6583	615	12	albeladi	albeladi	PROPN
ejpam-6583	615	13	)	)	PUNCT
ejpam-6583	615	14	;	;	PUNCT
ejpam-6583	615	15	methodology	methodology	NOUN
ejpam-6583	615	16	,	,	PUNCT
ejpam-6583	615	17	data	data	NOUN
ejpam-6583	615	18	curation	curation	NOUN
ejpam-6583	615	19	(	(	PUNCT
ejpam-6583	615	20	s.	s.	PROPN
ejpam-6583	615	21	omran	omran	PROPN
ejpam-6583	615	22	)	)	PUNCT
ejpam-6583	615	23	;	;	PUNCT
ejpam-6583	615	24	formal	formal	ADJ
ejpam-6583	615	25	analysis	analysis	NOUN
ejpam-6583	615	26	,	,	PUNCT
ejpam-6583	615	27	revisions	revision	NOUN
ejpam-6583	615	28	(	(	PUNCT
ejpam-6583	615	29	s.	s.	PROPN
ejpam-6583	615	30	omran	omran	PROPN
ejpam-6583	615	31	)	)	PUNCT
ejpam-6583	615	32	;	;	PUNCT
ejpam-6583	615	33	project	project	NOUN
ejpam-6583	615	34	administration	administration	NOUN
ejpam-6583	615	35	(	(	PUNCT
ejpam-6583	615	36	g.	g.	PROPN
ejpam-6583	615	37	albeladi	albeladi	PROPN
ejpam-6583	615	38	)	)	PUNCT
ejpam-6583	615	39	;	;	PUNCT
ejpam-6583	615	40	supervision	supervision	NOUN
ejpam-6583	615	41	(	(	PUNCT
ejpam-6583	615	42	s.	s.	PROPN
ejpam-6583	615	43	omran	omran	PROPN
ejpam-6583	615	44	)	)	PUNCT
ejpam-6583	615	45	.	.	PUNCT
ejpam-6583	616	1	references	reference	NOUN
ejpam-6583	616	2	[	[	X
ejpam-6583	616	3	1	1	X
ejpam-6583	616	4	]	]	PUNCT
ejpam-6583	616	5	ai	ai	AUX
ejpam-6583	616	6	perov	perov	NOUN
ejpam-6583	616	7	.	.	PUNCT
ejpam-6583	617	1	on	on	ADP
ejpam-6583	617	2	the	the	DET
ejpam-6583	617	3	cauchy	cauchy	ADJ
ejpam-6583	617	4	problem	problem	NOUN
ejpam-6583	617	5	for	for	ADP
ejpam-6583	617	6	a	a	DET
ejpam-6583	617	7	system	system	NOUN
ejpam-6583	617	8	of	of	ADP
ejpam-6583	617	9	ordinary	ordinary	ADJ
ejpam-6583	617	10	differential	differential	ADJ
ejpam-6583	617	11	equations	equation	NOUN
ejpam-6583	617	12	.	.	PUNCT
ejpam-6583	618	1	pviblizhen	pviblizhen	ADV
ejpam-6583	618	2	.	.	PUNCT
ejpam-6583	619	1	met	meet	VERB
ejpam-6583	619	2	.	.	PUNCT
ejpam-6583	620	1	reshen	reshen	NOUN
ejpam-6583	620	2	.	.	PUNCT
ejpam-6583	621	1	differ	differ	VERB
ejpam-6583	621	2	.	.	PUNCT
ejpam-6583	622	1	uvavn	uvavn	PROPN
ejpam-6583	622	2	,	,	PUNCT
ejpam-6583	622	3	2(1964):115–134	2(1964):115–134	NUM
ejpam-6583	622	4	,	,	PUNCT
ejpam-6583	622	5	1964	1964	NUM
ejpam-6583	622	6	.	.	PUNCT
ejpam-6583	623	1	[	[	X
ejpam-6583	623	2	2	2	X
ejpam-6583	623	3	]	]	X
ejpam-6583	623	4	muhammad	muhammad	PROPN
ejpam-6583	623	5	usman	usman	PROPN
ejpam-6583	623	6	ali	ali	PROPN
ejpam-6583	623	7	and	and	CCONJ
ejpam-6583	623	8	jong	jong	PROPN
ejpam-6583	623	9	kyu	kyu	PROPN
ejpam-6583	623	10	kim	kim	PROPN
ejpam-6583	623	11	.	.	PUNCT
ejpam-6583	624	1	an	an	DET
ejpam-6583	624	2	extension	extension	NOUN
ejpam-6583	624	3	of	of	ADP
ejpam-6583	624	4	vector	vector	NOUN
ejpam-6583	624	5	-	-	PUNCT
ejpam-6583	624	6	valued	value	VERB
ejpam-6583	624	7	metric	metric	ADJ
ejpam-6583	624	8	spaces	space	NOUN
ejpam-6583	624	9	and	and	CCONJ
ejpam-6583	624	10	perov	perov	PROPN
ejpam-6583	624	11	’s	’s	PART
ejpam-6583	624	12	fixed	fix	VERB
ejpam-6583	624	13	point	point	NOUN
ejpam-6583	624	14	theorem	theorem	NOUN
ejpam-6583	624	15	(	(	PUNCT
ejpam-6583	624	16	nonlinear	nonlinear	ADJ
ejpam-6583	624	17	analysis	analysis	NOUN
ejpam-6583	624	18	and	and	CCONJ
ejpam-6583	624	19	convex	convex	VERB
ejpam-6583	624	20	analysis	analysis	NOUN
ejpam-6583	624	21	)	)	PUNCT
ejpam-6583	624	22	.	.	PUNCT
ejpam-6583	625	1	research	research	PROPN
ejpam-6583	625	2	institute	institute	PROPN
ejpam-6583	625	3	for	for	ADP
ejpam-6583	625	4	mathematical	mathematical	ADJ
ejpam-6583	625	5	sciences	sciences	PROPN
ejpam-6583	625	6	kokyuroku	kokyuroku	PROPN
ejpam-6583	625	7	,	,	PUNCT
ejpam-6583	625	8	2114:12–20	2114:12–20	NUM
ejpam-6583	625	9	,	,	PUNCT
ejpam-6583	625	10	2019	2019	NUM
ejpam-6583	625	11	.	.	PUNCT
ejpam-6583	626	1	[	[	X
ejpam-6583	626	2	3	3	X
ejpam-6583	626	3	]	]	X
ejpam-6583	626	4	shaoyuan	shaoyuan	PROPN
ejpam-6583	626	5	xu	xu	PROPN
ejpam-6583	626	6	,	,	PUNCT
ejpam-6583	626	7	yan	yan	PROPN
ejpam-6583	626	8	han	han	PROPN
ejpam-6583	626	9	,	,	PUNCT
ejpam-6583	626	10	suzana	suzana	PROPN
ejpam-6583	626	11	aleksić	aleksić	PROPN
ejpam-6583	626	12	,	,	PUNCT
ejpam-6583	626	13	and	and	CCONJ
ejpam-6583	626	14	stojan	stojan	ADP
ejpam-6583	626	15	radenovic	radenovic	PROPN
ejpam-6583	626	16	.	.	PUNCT
ejpam-6583	627	1	fixed	fix	VERB
ejpam-6583	627	2	point	point	NOUN
ejpam-6583	627	3	results	result	NOUN
ejpam-6583	627	4	for	for	ADP
ejpam-6583	627	5	nonlinear	nonlinear	ADJ
ejpam-6583	627	6	contractions	contraction	NOUN
ejpam-6583	627	7	of	of	ADP
ejpam-6583	627	8	perov	perov	ADJ
ejpam-6583	627	9	type	type	NOUN
ejpam-6583	627	10	in	in	ADP
ejpam-6583	627	11	abstract	abstract	ADJ
ejpam-6583	627	12	metric	metric	ADJ
ejpam-6583	627	13	spaces	space	NOUN
ejpam-6583	627	14	with	with	ADP
ejpam-6583	627	15	applications	application	NOUN
ejpam-6583	627	16	.	.	PUNCT
ejpam-6583	628	1	2022	2022	NUM
ejpam-6583	628	2	.	.	PUNCT
ejpam-6583	629	1	g.	g.	PROPN
ejpam-6583	629	2	albeladi	albeladi	PROPN
ejpam-6583	629	3	,	,	PUNCT
ejpam-6583	629	4	s.	s.	PROPN
ejpam-6583	629	5	omran	omran	PROPN
ejpam-6583	629	6	/	/	SYM
ejpam-6583	629	7	eur	eur	PROPN
ejpam-6583	629	8	.	.	PUNCT
ejpam-6583	630	1	j.	j.	PROPN
ejpam-6583	630	2	pure	pure	PROPN
ejpam-6583	630	3	appl	appl	PROPN
ejpam-6583	630	4	.	.	PROPN
ejpam-6583	630	5	math	math	PROPN
ejpam-6583	630	6	,	,	PUNCT
ejpam-6583	630	7	18	18	NUM
ejpam-6583	630	8	(	(	PUNCT
ejpam-6583	630	9	3	3	NUM
ejpam-6583	630	10	)	)	PUNCT
ejpam-6583	630	11	(	(	PUNCT
ejpam-6583	630	12	2025	2025	NUM
ejpam-6583	630	13	)	)	PUNCT
ejpam-6583	630	14	,	,	PUNCT
ejpam-6583	630	15	6583	6583	NUM
ejpam-6583	630	16	26	26	NUM
ejpam-6583	630	17	of	of	ADP
ejpam-6583	630	18	27	27	NUM
ejpam-6583	630	19	[	[	SYM
ejpam-6583	630	20	4	4	NUM
ejpam-6583	630	21	]	]	X
ejpam-6583	630	22	saleh	saleh	NOUN
ejpam-6583	630	23	omran	omran	PROPN
ejpam-6583	630	24	,	,	PUNCT
ejpam-6583	630	25	ibtisammasmali	ibtisammasmali	VERB
ejpam-6583	630	26	,	,	PUNCT
ejpam-6583	630	27	and	and	CCONJ
ejpam-6583	630	28	ghaliah	ghaliah	PROPN
ejpam-6583	630	29	alhamzi	alhamzi	PROPN
ejpam-6583	630	30	.	.	PUNCT
ejpam-6583	631	1	banach	banach	ADV
ejpam-6583	631	2	fixed	fix	VERB
ejpam-6583	631	3	point	point	NOUN
ejpam-6583	631	4	theorems	theorem	NOUN
ejpam-6583	631	5	in	in	ADP
ejpam-6583	631	6	generalized	generalized	ADJ
ejpam-6583	631	7	metric	metric	ADJ
ejpam-6583	631	8	space	space	NOUN
ejpam-6583	631	9	endowed	endow	VERB
ejpam-6583	631	10	with	with	ADP
ejpam-6583	631	11	the	the	DET
ejpam-6583	631	12	hadamard	hadamard	ADJ
ejpam-6583	631	13	product	product	NOUN
ejpam-6583	631	14	.	.	PUNCT
ejpam-6583	632	1	symmetry	symmetry	NOUN
ejpam-6583	632	2	,	,	PUNCT
ejpam-6583	632	3	15(7):1325	15(7):1325	NUM
ejpam-6583	632	4	,	,	PUNCT
ejpam-6583	632	5	2023	2023	NUM
ejpam-6583	632	6	.	.	PUNCT
ejpam-6583	633	1	[	[	X
ejpam-6583	633	2	5	5	X
ejpam-6583	633	3	]	]	X
ejpam-6583	633	4	stefan	stefan	PROPN
ejpam-6583	633	5	banach	banach	PROPN
ejpam-6583	633	6	.	.	PUNCT
ejpam-6583	634	1	sur	sur	PROPN
ejpam-6583	634	2	les	les	X
ejpam-6583	634	3	opérations	opération	NOUN
ejpam-6583	634	4	dans	dan	NOUN
ejpam-6583	634	5	les	les	X
ejpam-6583	634	6	ensembles	ensemble	NOUN
ejpam-6583	634	7	abstraits	abstrait	NOUN
ejpam-6583	634	8	et	et	PROPN
ejpam-6583	634	9	leur	leur	X
ejpam-6583	634	10	application	application	PROPN
ejpam-6583	634	11	aux	aux	PROPN
ejpam-6583	634	12	équations	équations	PROPN
ejpam-6583	634	13	intégrales	intégrale	NOUN
ejpam-6583	634	14	.	.	PUNCT
ejpam-6583	635	1	fundamenta	fundamenta	PROPN
ejpam-6583	635	2	mathematicae	mathematicae	PROPN
ejpam-6583	635	3	,	,	PUNCT
ejpam-6583	635	4	3(1):133–181	3(1):133–181	NUM
ejpam-6583	635	5	,	,	PUNCT
ejpam-6583	635	6	1922	1922	NUM
ejpam-6583	635	7	.	.	PUNCT
ejpam-6583	636	1	[	[	X
ejpam-6583	636	2	6	6	NUM
ejpam-6583	636	3	]	]	PUNCT
ejpam-6583	636	4	a	a	DET
ejpam-6583	636	5	bakhtini	bakhtini	NOUN
ejpam-6583	636	6	.	.	PUNCT
ejpam-6583	637	1	the	the	DET
ejpam-6583	637	2	contraction	contraction	NOUN
ejpam-6583	637	3	mapping	mapping	NOUN
ejpam-6583	637	4	principle	principle	NOUN
ejpam-6583	637	5	in	in	ADP
ejpam-6583	637	6	almost	almost	ADV
ejpam-6583	637	7	metric	metric	ADJ
ejpam-6583	637	8	spaces	space	NOUN
ejpam-6583	637	9	.	.	PUNCT
ejpam-6583	638	1	funct	funct	ADJ
ejpam-6583	638	2	.	.	PUNCT
ejpam-6583	639	1	anal	anal	PROPN
ejpam-6583	639	2	.	.	PROPN
ejpam-6583	639	3	,	,	PUNCT
ejpam-6583	639	4	gos	gos	PROPN
ejpam-6583	639	5	.	.	PUNCT
ejpam-6583	639	6	ped	ped	PROPN
ejpam-6583	639	7	.	.	PROPN
ejpam-6583	639	8	inst	inst	PROPN
ejpam-6583	639	9	.	.	PUNCT
ejpam-6583	640	1	unianowsk	unianowsk	PROPN
ejpam-6583	640	2	,	,	PUNCT
ejpam-6583	640	3	30:26–37	30:26–37	PROPN
ejpam-6583	640	4	,	,	PUNCT
ejpam-6583	640	5	1989	1989	NUM
ejpam-6583	640	6	.	.	PUNCT
ejpam-6583	641	1	[	[	X
ejpam-6583	641	2	7	7	X
ejpam-6583	641	3	]	]	X
ejpam-6583	641	4	stefan	stefan	PROPN
ejpam-6583	641	5	czerwik	czerwik	PROPN
ejpam-6583	641	6	.	.	PUNCT
ejpam-6583	642	1	contraction	contraction	NOUN
ejpam-6583	642	2	mappings	mapping	NOUN
ejpam-6583	642	3	in	in	ADP
ejpam-6583	642	4	b	b	NOUN
ejpam-6583	642	5	-	-	ADJ
ejpam-6583	642	6	metric	metric	ADJ
ejpam-6583	642	7	spaces	space	NOUN
ejpam-6583	642	8	.	.	PUNCT
ejpam-6583	643	1	acta	acta	PROPN
ejpam-6583	643	2	mathematica	mathematica	PROPN
ejpam-6583	643	3	et	et	PROPN
ejpam-6583	643	4	informatica	informatica	PROPN
ejpam-6583	643	5	universitatis	universitatis	PROPN
ejpam-6583	643	6	ostraviensis	ostraviensis	PROPN
ejpam-6583	643	7	,	,	PUNCT
ejpam-6583	643	8	1(1):5–11	1(1):5–11	NUM
ejpam-6583	643	9	,	,	PUNCT
ejpam-6583	643	10	1993	1993	NUM
ejpam-6583	643	11	.	.	PUNCT
ejpam-6583	644	1	[	[	X
ejpam-6583	644	2	8	8	X
ejpam-6583	644	3	]	]	X
ejpam-6583	644	4	mehmet	mehmet	PROPN
ejpam-6583	644	5	kir	kir	PROPN
ejpam-6583	644	6	and	and	CCONJ
ejpam-6583	644	7	hukmi	hukmi	PROPN
ejpam-6583	644	8	kiziltunc	kiziltunc	NOUN
ejpam-6583	644	9	.	.	PUNCT
ejpam-6583	645	1	on	on	ADP
ejpam-6583	645	2	some	some	DET
ejpam-6583	645	3	well	well	ADV
ejpam-6583	645	4	known	know	VERB
ejpam-6583	645	5	fixed	fix	VERB
ejpam-6583	645	6	point	point	NOUN
ejpam-6583	645	7	theorems	theorem	NOUN
ejpam-6583	645	8	in	in	ADP
ejpam-6583	645	9	b	b	NOUN
ejpam-6583	645	10	-	-	ADJ
ejpam-6583	645	11	metric	metric	ADJ
ejpam-6583	645	12	spaces	space	NOUN
ejpam-6583	645	13	.	.	PUNCT
ejpam-6583	646	1	turkish	turkish	ADJ
ejpam-6583	646	2	journal	journal	NOUN
ejpam-6583	646	3	of	of	ADP
ejpam-6583	646	4	analysis	analysis	NOUN
ejpam-6583	646	5	and	and	CCONJ
ejpam-6583	646	6	number	number	NOUN
ejpam-6583	646	7	theory	theory	NOUN
ejpam-6583	646	8	,	,	PUNCT
ejpam-6583	646	9	1(1):13–16	1(1):13–16	NUM
ejpam-6583	646	10	,	,	PUNCT
ejpam-6583	646	11	2013	2013	NUM
ejpam-6583	646	12	.	.	PUNCT
ejpam-6583	647	1	[	[	X
ejpam-6583	647	2	9	9	NUM
ejpam-6583	647	3	]	]	X
ejpam-6583	647	4	monica	monica	PROPN
ejpam-6583	647	5	boriceanu	boriceanu	PROPN
ejpam-6583	647	6	.	.	PUNCT
ejpam-6583	648	1	fixed	fix	VERB
ejpam-6583	648	2	point	point	NOUN
ejpam-6583	648	3	theory	theory	NOUN
ejpam-6583	648	4	for	for	ADP
ejpam-6583	648	5	multivalued	multivalued	ADJ
ejpam-6583	648	6	generalized	generalized	ADJ
ejpam-6583	648	7	contraction	contraction	NOUN
ejpam-6583	648	8	on	on	ADP
ejpam-6583	648	9	a	a	DET
ejpam-6583	648	10	set	set	NOUN
ejpam-6583	648	11	with	with	ADP
ejpam-6583	648	12	two	two	NUM
ejpam-6583	648	13	b	b	NOUN
ejpam-6583	648	14	-	-	PUNCT
ejpam-6583	648	15	metrics	metric	NOUN
ejpam-6583	648	16	.	.	PUNCT
ejpam-6583	649	1	studia	studia	PROPN
ejpam-6583	649	2	universitatis	universitatis	PROPN
ejpam-6583	649	3	babes	babes	PROPN
ejpam-6583	649	4	-	-	PUNCT
ejpam-6583	649	5	bolyai	bolyai	PROPN
ejpam-6583	649	6	,	,	PUNCT
ejpam-6583	649	7	mathematica	mathematica	PROPN
ejpam-6583	649	8	,	,	PUNCT
ejpam-6583	649	9	(	(	PUNCT
ejpam-6583	649	10	3	3	NUM
ejpam-6583	649	11	)	)	PUNCT
ejpam-6583	649	12	,	,	PUNCT
ejpam-6583	649	13	2009	2009	NUM
ejpam-6583	649	14	.	.	PUNCT
ejpam-6583	650	1	[	[	X
ejpam-6583	650	2	10	10	NUM
ejpam-6583	650	3	]	]	X
ejpam-6583	650	4	monica	monica	PROPN
ejpam-6583	650	5	bota	bota	PROPN
ejpam-6583	650	6	,	,	PUNCT
ejpam-6583	650	7	andrea	andrea	PROPN
ejpam-6583	650	8	molnar	molnar	PROPN
ejpam-6583	650	9	,	,	PUNCT
ejpam-6583	650	10	and	and	CCONJ
ejpam-6583	650	11	csaba	csaba	PROPN
ejpam-6583	650	12	varga	varga	PROPN
ejpam-6583	650	13	.	.	PUNCT
ejpam-6583	651	1	on	on	ADP
ejpam-6583	651	2	ekeland	ekeland	PROPN
ejpam-6583	651	3	’s	’s	PART
ejpam-6583	651	4	variational	variational	ADJ
ejpam-6583	651	5	principle	principle	NOUN
ejpam-6583	651	6	in	in	ADP
ejpam-6583	651	7	b	b	NOUN
ejpam-6583	651	8	-	-	ADJ
ejpam-6583	651	9	metric	metric	ADJ
ejpam-6583	651	10	spaces	space	NOUN
ejpam-6583	651	11	.	.	PUNCT
ejpam-6583	652	1	fixed	fix	VERB
ejpam-6583	652	2	point	point	NOUN
ejpam-6583	652	3	theory	theory	NOUN
ejpam-6583	652	4	,	,	PUNCT
ejpam-6583	652	5	12(2):21–28	12(2):21–28	NUM
ejpam-6583	652	6	,	,	PUNCT
ejpam-6583	652	7	2011	2011	NUM
ejpam-6583	652	8	.	.	PUNCT
ejpam-6583	653	1	[	[	X
ejpam-6583	653	2	11	11	NUM
ejpam-6583	653	3	]	]	PUNCT
ejpam-6583	653	4	m	m	NOUN
ejpam-6583	653	5	pacurar	pacurar	NOUN
ejpam-6583	653	6	.	.	PUNCT
ejpam-6583	654	1	sequences	sequence	NOUN
ejpam-6583	654	2	of	of	ADP
ejpam-6583	654	3	almost	almost	ADV
ejpam-6583	654	4	contractions	contraction	NOUN
ejpam-6583	654	5	and	and	CCONJ
ejpam-6583	654	6	fixed	fix	VERB
ejpam-6583	654	7	points	point	NOUN
ejpam-6583	654	8	in	in	ADP
ejpam-6583	654	9	b	b	NOUN
ejpam-6583	654	10	-	-	ADJ
ejpam-6583	654	11	metric	metric	ADJ
ejpam-6583	654	12	spaces	space	NOUN
ejpam-6583	654	13	.	.	PUNCT
ejpam-6583	655	1	an	an	PRON
ejpam-6583	655	2	.	.	PROPN
ejpam-6583	655	3	univ	univ	PROPN
ejpam-6583	655	4	.	.	PUNCT
ejpam-6583	656	1	vest	vest	PROPN
ejpam-6583	656	2	.	.	PUNCT
ejpam-6583	657	1	timis	timis	NOUN
ejpam-6583	657	2	.	.	PUNCT
ejpam-6583	658	1	,	,	PUNCT
ejpam-6583	658	2	ser	ser	PROPN
ejpam-6583	658	3	.	.	PUNCT
ejpam-6583	658	4	mat.-inform	mat.-inform	PROPN
ejpam-6583	658	5	,	,	PUNCT
ejpam-6583	658	6	48(3):125–137	48(3):125–137	PROPN
ejpam-6583	658	7	,	,	PUNCT
ejpam-6583	658	8	2010	2010	NUM
ejpam-6583	658	9	.	.	PUNCT
ejpam-6583	659	1	[	[	X
ejpam-6583	659	2	12	12	NUM
ejpam-6583	659	3	]	]	X
ejpam-6583	659	4	ronald	ronald	PROPN
ejpam-6583	659	5	fagin	fagin	PROPN
ejpam-6583	659	6	and	and	CCONJ
ejpam-6583	659	7	larry	larry	PROPN
ejpam-6583	659	8	stockmeyer	stockmeyer	PROPN
ejpam-6583	659	9	.	.	PUNCT
ejpam-6583	660	1	relaxing	relax	VERB
ejpam-6583	660	2	the	the	DET
ejpam-6583	660	3	triangle	triangle	NOUN
ejpam-6583	660	4	inequality	inequality	NOUN
ejpam-6583	660	5	in	in	ADP
ejpam-6583	660	6	pattern	pattern	NOUN
ejpam-6583	660	7	matching	matching	NOUN
ejpam-6583	660	8	.	.	PUNCT
ejpam-6583	661	1	international	international	ADJ
ejpam-6583	661	2	journal	journal	PROPN
ejpam-6583	661	3	of	of	ADP
ejpam-6583	661	4	computer	computer	NOUN
ejpam-6583	661	5	vision	vision	NOUN
ejpam-6583	661	6	,	,	PUNCT
ejpam-6583	661	7	30:219–231	30:219–231	PROPN
ejpam-6583	661	8	,	,	PUNCT
ejpam-6583	661	9	1998	1998	NUM
ejpam-6583	661	10	.	.	PUNCT
ejpam-6583	662	1	[	[	X
ejpam-6583	662	2	13	13	NUM
ejpam-6583	662	3	]	]	X
ejpam-6583	662	4	g	g	PROPN
ejpam-6583	662	5	cortelazzo	cortelazzo	PROPN
ejpam-6583	662	6	,	,	PUNCT
ejpam-6583	662	7	gian	gian	PROPN
ejpam-6583	662	8	antonio	antonio	PROPN
ejpam-6583	662	9	mian	mian	PROPN
ejpam-6583	662	10	,	,	PUNCT
ejpam-6583	662	11	g	g	NOUN
ejpam-6583	662	12	vezzi	vezzi	NOUN
ejpam-6583	662	13	,	,	PUNCT
ejpam-6583	662	14	and	and	CCONJ
ejpam-6583	662	15	piero	piero	PROPN
ejpam-6583	662	16	zamperoni	zamperoni	PROPN
ejpam-6583	662	17	.	.	PUNCT
ejpam-6583	663	1	trademark	trademark	NOUN
ejpam-6583	663	2	shapes	shape	NOUN
ejpam-6583	663	3	description	description	NOUN
ejpam-6583	663	4	by	by	ADP
ejpam-6583	663	5	string	string	NOUN
ejpam-6583	663	6	-	-	PUNCT
ejpam-6583	663	7	matching	match	VERB
ejpam-6583	663	8	techniques	technique	NOUN
ejpam-6583	663	9	.	.	PUNCT
ejpam-6583	664	1	pattern	pattern	NOUN
ejpam-6583	664	2	recognition	recognition	NOUN
ejpam-6583	664	3	,	,	PUNCT
ejpam-6583	664	4	27(8):1005–1018	27(8):1005–1018	NUM
ejpam-6583	664	5	,	,	PUNCT
ejpam-6583	664	6	1994	1994	NUM
ejpam-6583	664	7	.	.	PUNCT
ejpam-6583	665	1	[	[	X
ejpam-6583	665	2	14	14	NUM
ejpam-6583	665	3	]	]	PUNCT
ejpam-6583	665	4	ross	ross	PROPN
ejpam-6583	665	5	mcconnell	mcconnell	PROPN
ejpam-6583	665	6	,	,	PUNCT
ejpam-6583	665	7	ronald	ronald	PROPN
ejpam-6583	665	8	kwok	kwok	PROPN
ejpam-6583	665	9	,	,	PUNCT
ejpam-6583	665	10	john	john	PROPN
ejpam-6583	665	11	c	c	PROPN
ejpam-6583	665	12	curlander	curlander	PROPN
ejpam-6583	665	13	,	,	PUNCT
ejpam-6583	665	14	wolfgang	wolfgang	PROPN
ejpam-6583	665	15	kober	kober	PROPN
ejpam-6583	665	16	,	,	PUNCT
ejpam-6583	665	17	and	and	CCONJ
ejpam-6583	665	18	shirley	shirley	PROPN
ejpam-6583	665	19	s	s	PROPN
ejpam-6583	665	20	pang	pang	NOUN
ejpam-6583	665	21	.	.	PUNCT
ejpam-6583	666	1	psi	psi	NOUN
ejpam-6583	666	2	-	-	PUNCT
ejpam-6583	666	3	s	s	NOUN
ejpam-6583	666	4	correlation	correlation	NOUN
ejpam-6583	666	5	and	and	CCONJ
ejpam-6583	666	6	dynamic	dynamic	ADJ
ejpam-6583	666	7	time	time	NOUN
ejpam-6583	666	8	warping	warp	VERB
ejpam-6583	666	9	:	:	PUNCT
ejpam-6583	666	10	two	two	NUM
ejpam-6583	666	11	methods	method	NOUN
ejpam-6583	666	12	for	for	ADP
ejpam-6583	666	13	tracking	track	VERB
ejpam-6583	666	14	ice	ice	NOUN
ejpam-6583	666	15	floes	floe	NOUN
ejpam-6583	666	16	in	in	ADP
ejpam-6583	666	17	sar	sar	PROPN
ejpam-6583	666	18	images	image	NOUN
ejpam-6583	666	19	.	.	PUNCT
ejpam-6583	667	1	ieee	ieee	NOUN
ejpam-6583	667	2	transactions	transaction	NOUN
ejpam-6583	667	3	on	on	ADP
ejpam-6583	667	4	geoscience	geoscience	NOUN
ejpam-6583	667	5	and	and	CCONJ
ejpam-6583	667	6	remote	remote	ADJ
ejpam-6583	667	7	sensing	sensing	NOUN
ejpam-6583	667	8	,	,	PUNCT
ejpam-6583	667	9	29(6):1004	29(6):1004	NUM
ejpam-6583	667	10	–	–	PUNCT
ejpam-6583	667	11	1012	1012	NUM
ejpam-6583	667	12	,	,	PUNCT
ejpam-6583	667	13	1991	1991	NUM
ejpam-6583	667	14	.	.	PUNCT
ejpam-6583	668	1	[	[	X
ejpam-6583	668	2	15	15	NUM
ejpam-6583	668	3	]	]	X
ejpam-6583	668	4	qinglan	qinglan	PROPN
ejpam-6583	668	5	xia	xia	PROPN
ejpam-6583	668	6	.	.	PUNCT
ejpam-6583	669	1	the	the	DET
ejpam-6583	669	2	geodesic	geodesic	ADJ
ejpam-6583	669	3	problem	problem	NOUN
ejpam-6583	669	4	in	in	ADP
ejpam-6583	669	5	quasimetric	quasimetric	ADJ
ejpam-6583	669	6	spaces	space	NOUN
ejpam-6583	669	7	.	.	PUNCT
ejpam-6583	670	1	journal	journal	NOUN
ejpam-6583	670	2	of	of	ADP
ejpam-6583	670	3	geometric	geometric	ADJ
ejpam-6583	670	4	analysis	analysis	NOUN
ejpam-6583	670	5	,	,	PUNCT
ejpam-6583	670	6	19:452–479	19:452–479	PROPN
ejpam-6583	670	7	,	,	PUNCT
ejpam-6583	670	8	2009	2009	NUM
ejpam-6583	670	9	.	.	PUNCT
ejpam-6583	671	1	[	[	X
ejpam-6583	671	2	16	16	NUM
ejpam-6583	671	3	]	]	X
ejpam-6583	671	4	juha	juha	PROPN
ejpam-6583	671	5	heinonen	heinonen	PROPN
ejpam-6583	671	6	.	.	PUNCT
ejpam-6583	672	1	lectures	lecture	NOUN
ejpam-6583	672	2	on	on	ADP
ejpam-6583	672	3	analysis	analysis	NOUN
ejpam-6583	672	4	on	on	ADP
ejpam-6583	672	5	metric	metric	ADJ
ejpam-6583	672	6	spaces	space	NOUN
ejpam-6583	672	7	.	.	PUNCT
ejpam-6583	673	1	springer	springer	NOUN
ejpam-6583	673	2	,	,	PUNCT
ejpam-6583	673	3	science	science	PROPN
ejpam-6583	673	4	&	&	CCONJ
ejpam-6583	673	5	business	business	NOUN
ejpam-6583	673	6	media	medium	NOUN
ejpam-6583	673	7	,	,	PUNCT
ejpam-6583	673	8	2001	2001	NUM
ejpam-6583	673	9	.	.	PUNCT
ejpam-6583	674	1	[	[	X
ejpam-6583	674	2	17	17	NUM
ejpam-6583	674	3	]	]	X
ejpam-6583	674	4	mohamed	mohamed	PROPN
ejpam-6583	674	5	jleli	jleli	PROPN
ejpam-6583	674	6	and	and	CCONJ
ejpam-6583	674	7	bessem	bessem	NOUN
ejpam-6583	674	8	samet	samet	NOUN
ejpam-6583	674	9	.	.	PUNCT
ejpam-6583	675	1	on	on	ADP
ejpam-6583	675	2	a	a	DET
ejpam-6583	675	3	new	new	ADJ
ejpam-6583	675	4	generalization	generalization	NOUN
ejpam-6583	675	5	of	of	ADP
ejpam-6583	675	6	metric	metric	ADJ
ejpam-6583	675	7	spaces	space	NOUN
ejpam-6583	675	8	.	.	PUNCT
ejpam-6583	676	1	journal	journal	NOUN
ejpam-6583	676	2	of	of	ADP
ejpam-6583	676	3	fixed	fix	VERB
ejpam-6583	676	4	point	point	NOUN
ejpam-6583	676	5	theory	theory	NOUN
ejpam-6583	676	6	and	and	CCONJ
ejpam-6583	676	7	applications	application	NOUN
ejpam-6583	676	8	,	,	PUNCT
ejpam-6583	676	9	2018	2018	NUM
ejpam-6583	676	10	.	.	PUNCT
ejpam-6583	677	1	[	[	X
ejpam-6583	677	2	18	18	NUM
ejpam-6583	677	3	]	]	X
ejpam-6583	677	4	amer	amer	PROPN
ejpam-6583	677	5	hassan	hassan	PROPN
ejpam-6583	677	6	albargi	albargi	PROPN
ejpam-6583	677	7	and	and	CCONJ
ejpam-6583	677	8	jamshaid	jamshaid	PROPN
ejpam-6583	677	9	ahmad	ahmad	PROPN
ejpam-6583	677	10	.	.	PUNCT
ejpam-6583	678	1	fixed	fix	VERB
ejpam-6583	678	2	point	point	NOUN
ejpam-6583	678	3	results	result	NOUN
ejpam-6583	678	4	of	of	ADP
ejpam-6583	678	5	fuzzy	fuzzy	ADJ
ejpam-6583	678	6	mappings	mapping	NOUN
ejpam-6583	678	7	with	with	ADP
ejpam-6583	678	8	applications	application	NOUN
ejpam-6583	678	9	.	.	PUNCT
ejpam-6583	679	1	aims	aim	VERB
ejpam-6583	679	2	mathematics	mathematic	NOUN
ejpam-6583	679	3	,	,	PUNCT
ejpam-6583	679	4	2023	2023	NUM
ejpam-6583	679	5	.	.	PUNCT
ejpam-6583	680	1	[	[	X
ejpam-6583	680	2	19	19	NUM
ejpam-6583	680	3	]	]	PUNCT
ejpam-6583	680	4	huaping	huape	VERB
ejpam-6583	680	5	huang	huang	PROPN
ejpam-6583	680	6	and	and	CCONJ
ejpam-6583	680	7	bessem	bessem	NOUN
ejpam-6583	680	8	samet	samet	PROPN
ejpam-6583	680	9	.	.	PUNCT
ejpam-6583	681	1	two	two	NUM
ejpam-6583	681	2	fixed	fix	VERB
ejpam-6583	681	3	point	point	NOUN
ejpam-6583	681	4	theorems	theorem	NOUN
ejpam-6583	681	5	in	in	ADP
ejpam-6583	681	6	complete	complete	ADJ
ejpam-6583	681	7	metric	metric	ADJ
ejpam-6583	681	8	spaces	space	NOUN
ejpam-6583	681	9	.	.	PUNCT
ejpam-6583	682	1	aims	aim	VERB
ejpam-6583	682	2	mathematics	mathematic	NOUN
ejpam-6583	682	3	,	,	PUNCT
ejpam-6583	682	4	2024	2024	NUM
ejpam-6583	682	5	.	.	PUNCT
ejpam-6583	683	1	[	[	X
ejpam-6583	683	2	20	20	NUM
ejpam-6583	683	3	]	]	PUNCT
ejpam-6583	683	4	raghad	raghad	VERB
ejpam-6583	683	5	i	i	PROPN
ejpam-6583	683	6	sabri	sabri	NOUN
ejpam-6583	683	7	and	and	CCONJ
ejpam-6583	683	8	buthainah	buthainah	PROPN
ejpam-6583	683	9	aa	aa	PROPN
ejpam-6583	683	10	ahmed	ahmed	PROPN
ejpam-6583	683	11	.	.	PUNCT
ejpam-6583	684	1	some	some	DET
ejpam-6583	684	2	results	result	NOUN
ejpam-6583	684	3	of	of	ADP
ejpam-6583	684	4	fixed	fix	VERB
ejpam-6583	684	5	point	point	NOUN
ejpam-6583	684	6	for	for	ADP
ejpam-6583	684	7	single	single	ADJ
ejpam-6583	684	8	value	value	NOUN
ejpam-6583	684	9	mapping	mapping	NOUN
ejpam-6583	684	10	in	in	ADP
ejpam-6583	684	11	fuzzy	fuzzy	ADJ
ejpam-6583	684	12	normed	normed	ADJ
ejpam-6583	684	13	space	space	NOUN
ejpam-6583	684	14	with	with	ADP
ejpam-6583	684	15	applications	application	NOUN
ejpam-6583	684	16	.	.	PUNCT
ejpam-6583	685	1	iraqi	iraqi	ADJ
ejpam-6583	685	2	journal	journal	PROPN
ejpam-6583	685	3	of	of	ADP
ejpam-6583	685	4	science	science	NOUN
ejpam-6583	685	5	,	,	PUNCT
ejpam-6583	685	6	pages	page	NOUN
ejpam-6583	685	7	2105–2113	2105–2113	NUM
ejpam-6583	685	8	,	,	PUNCT
ejpam-6583	685	9	2024	2024	NUM
ejpam-6583	685	10	.	.	PUNCT
ejpam-6583	686	1	[	[	X
ejpam-6583	686	2	21	21	NUM
ejpam-6583	686	3	]	]	X
ejpam-6583	686	4	raghad	raghad	VERB
ejpam-6583	686	5	i	i	PROPN
ejpam-6583	686	6	sabri	sabri	PROPN
ejpam-6583	686	7	,	,	PUNCT
ejpam-6583	686	8	jaafer	jaafer	NOUN
ejpam-6583	686	9	hmood	hmood	PROPN
ejpam-6583	686	10	eidi	eidi	PROPN
ejpam-6583	686	11	,	,	PUNCT
ejpam-6583	686	12	and	and	CCONJ
ejpam-6583	686	13	hussein	hussein	PROPN
ejpam-6583	686	14	s	s	PART
ejpam-6583	686	15	alallak	alallak	NOUN
ejpam-6583	686	16	.	.	PUNCT
ejpam-6583	687	1	fixed	fix	VERB
ejpam-6583	687	2	points	point	NOUN
ejpam-6583	687	3	results	result	NOUN
ejpam-6583	687	4	in	in	ADP
ejpam-6583	687	5	algebra	algebra	NOUN
ejpam-6583	687	6	fuzzy	fuzzy	ADJ
ejpam-6583	687	7	metric	metric	ADJ
ejpam-6583	687	8	space	space	NOUN
ejpam-6583	687	9	with	with	ADP
ejpam-6583	687	10	an	an	DET
ejpam-6583	687	11	application	application	NOUN
ejpam-6583	687	12	to	to	ADP
ejpam-6583	687	13	integral	integral	ADJ
ejpam-6583	687	14	equations	equation	NOUN
ejpam-6583	687	15	.	.	PUNCT
ejpam-6583	688	1	international	international	ADJ
ejpam-6583	688	2	journal	journal	PROPN
ejpam-6583	688	3	of	of	ADP
ejpam-6583	688	4	neutrosophic	neutrosophic	ADJ
ejpam-6583	688	5	science	science	NOUN
ejpam-6583	688	6	(	(	PUNCT
ejpam-6583	688	7	ijns	ijns	PROPN
ejpam-6583	688	8	)	)	PUNCT
ejpam-6583	688	9	,	,	PUNCT
ejpam-6583	688	10	25(4	25(4	NOUN
ejpam-6583	688	11	)	)	PUNCT
ejpam-6583	688	12	,	,	PUNCT
ejpam-6583	688	13	2025	2025	NUM
ejpam-6583	688	14	.	.	PUNCT
ejpam-6583	689	1	[	[	X
ejpam-6583	689	2	22	22	NUM
ejpam-6583	689	3	]	]	PUNCT
ejpam-6583	689	4	pierre	pierre	PROPN
ejpam-6583	689	5	antoine	antoine	PROPN
ejpam-6583	689	6	grillet	grillet	PROPN
ejpam-6583	689	7	.	.	PUNCT
ejpam-6583	690	1	abstract	abstract	ADJ
ejpam-6583	690	2	algebra	algebra	PROPN
ejpam-6583	690	3	,	,	PUNCT
ejpam-6583	690	4	volume	volume	NOUN
ejpam-6583	690	5	242	242	NUM
ejpam-6583	690	6	.	.	PUNCT
ejpam-6583	691	1	springer	springer	NOUN
ejpam-6583	691	2	,	,	PUNCT
ejpam-6583	691	3	science	science	PROPN
ejpam-6583	691	4	&	&	CCONJ
ejpam-6583	691	5	business	business	PROPN
ejpam-6583	691	6	g.	g.	PROPN
ejpam-6583	691	7	albeladi	albeladi	PROPN
ejpam-6583	691	8	,	,	PUNCT
ejpam-6583	691	9	s.	s.	PROPN
ejpam-6583	691	10	omran	omran	PROPN
ejpam-6583	691	11	/	/	SYM
ejpam-6583	691	12	eur	eur	PROPN
ejpam-6583	691	13	.	.	PUNCT
ejpam-6583	692	1	j.	j.	PROPN
ejpam-6583	692	2	pure	pure	PROPN
ejpam-6583	692	3	appl	appl	PROPN
ejpam-6583	692	4	.	.	PROPN
ejpam-6583	692	5	math	math	PROPN
ejpam-6583	692	6	,	,	PUNCT
ejpam-6583	692	7	18	18	NUM
ejpam-6583	692	8	(	(	PUNCT
ejpam-6583	692	9	3	3	NUM
ejpam-6583	692	10	)	)	PUNCT
ejpam-6583	692	11	(	(	PUNCT
ejpam-6583	692	12	2025	2025	NUM
ejpam-6583	692	13	)	)	PUNCT
ejpam-6583	692	14	,	,	PUNCT
ejpam-6583	692	15	6583	6583	NUM
ejpam-6583	692	16	27	27	NUM
ejpam-6583	692	17	of	of	ADP
ejpam-6583	692	18	27	27	NUM
ejpam-6583	692	19	media	medium	NOUN
ejpam-6583	692	20	,	,	PUNCT
ejpam-6583	692	21	2007	2007	NUM
ejpam-6583	692	22	.	.	PUNCT
ejpam-6583	693	1	[	[	X
ejpam-6583	693	2	23	23	NUM
ejpam-6583	693	3	]	]	X
ejpam-6583	693	4	phani	phani	PROPN
ejpam-6583	693	5	bhushan	bhushan	PROPN
ejpam-6583	693	6	bhattacharya	bhattacharya	PROPN
ejpam-6583	693	7	,	,	PUNCT
ejpam-6583	693	8	surender	surender	PROPN
ejpam-6583	693	9	kumar	kumar	PROPN
ejpam-6583	693	10	jain	jain	PROPN
ejpam-6583	693	11	,	,	PUNCT
ejpam-6583	693	12	and	and	CCONJ
ejpam-6583	693	13	sr	sr	PROPN
ejpam-6583	693	14	nagpaul	nagpaul	PROPN
ejpam-6583	693	15	.	.	PUNCT
ejpam-6583	694	1	basic	basic	ADJ
ejpam-6583	694	2	abstract	abstract	ADJ
ejpam-6583	694	3	algebra	algebra	NOUN
ejpam-6583	694	4	.	.	PUNCT
ejpam-6583	695	1	cambridge	cambridge	PROPN
ejpam-6583	695	2	,	,	PUNCT
ejpam-6583	695	3	university	university	NOUN
ejpam-6583	695	4	press	press	NOUN
ejpam-6583	695	5	,	,	PUNCT
ejpam-6583	695	6	1994	1994	NUM
ejpam-6583	695	7	.	.	PUNCT
ejpam-6583	696	1	[	[	X
ejpam-6583	696	2	24	24	NUM
ejpam-6583	696	3	]	]	PUNCT
ejpam-6583	696	4	rangachary	rangachary	PROPN
ejpam-6583	696	5	kannan	kannan	PROPN
ejpam-6583	696	6	.	.	PUNCT
ejpam-6583	697	1	some	some	DET
ejpam-6583	697	2	results	result	NOUN
ejpam-6583	697	3	on	on	ADP
ejpam-6583	697	4	fixed	fix	VERB
ejpam-6583	697	5	points	point	NOUN
ejpam-6583	697	6	.	.	PUNCT
ejpam-6583	698	1	bull	bull	NOUN
ejpam-6583	698	2	.	.	PUNCT
ejpam-6583	699	1	cal	cal	PROPN
ejpam-6583	699	2	.	.	PUNCT
ejpam-6583	700	1	math	math	NOUN
ejpam-6583	700	2	.	.	PUNCT
ejpam-6583	701	1	soc	soc	PROPN
ejpam-6583	701	2	.	.	PUNCT
ejpam-6583	701	3	,	,	PUNCT
ejpam-6583	701	4	60:71–76	60:71–76	NUM
ejpam-6583	701	5	,	,	PUNCT
ejpam-6583	701	6	1968	1968	NUM
ejpam-6583	701	7	.	.	PUNCT
ejpam-6583	702	1	[	[	X
ejpam-6583	702	2	25	25	NUM
ejpam-6583	702	3	]	]	X
ejpam-6583	702	4	mr	mr	PROPN
ejpam-6583	702	5	singh	singh	PROPN
ejpam-6583	702	6	and	and	CCONJ
ejpam-6583	702	7	ak	ak	PROPN
ejpam-6583	702	8	chatterjee	chatterjee	PROPN
ejpam-6583	702	9	.	.	PUNCT
ejpam-6583	703	1	fixed	fix	VERB
ejpam-6583	703	2	point	point	NOUN
ejpam-6583	703	3	theorems	theorem	NOUN
ejpam-6583	703	4	.	.	PUNCT
ejpam-6583	703	5	1974	1974	NUM
ejpam-6583	703	6	.	.	PUNCT