id	sid	tid	token	lemma	pos
ejpam-6029	1	1	european	european	PROPN
ejpam-6029	1	2	journal	journal	PROPN
ejpam-6029	1	3	of	of	ADP
ejpam-6029	1	4	pure	pure	ADJ
ejpam-6029	1	5	and	and	CCONJ
ejpam-6029	1	6	applied	applied	ADJ
ejpam-6029	1	7	mathematics	mathematic	NOUN
ejpam-6029	1	8	2025	2025	NUM
ejpam-6029	1	9	,	,	PUNCT
ejpam-6029	1	10	vol	vol	NOUN
ejpam-6029	1	11	.	.	PROPN
ejpam-6029	1	12	18	18	NUM
ejpam-6029	1	13	,	,	PUNCT
ejpam-6029	1	14	issue	issue	NOUN
ejpam-6029	1	15	2	2	NUM
ejpam-6029	1	16	,	,	PUNCT
ejpam-6029	1	17	article	article	NOUN
ejpam-6029	1	18	number	number	NOUN
ejpam-6029	1	19	6029	6029	NUM
ejpam-6029	1	20	issn	issn	PROPN
ejpam-6029	1	21	1307	1307	NUM
ejpam-6029	1	22	-	-	SYM
ejpam-6029	1	23	5543	5543	NUM
ejpam-6029	1	24	–	–	PUNCT
ejpam-6029	1	25	ejpam.com	ejpam.com	X
ejpam-6029	1	26	published	publish	VERB
ejpam-6029	1	27	by	by	ADP
ejpam-6029	1	28	new	new	PROPN
ejpam-6029	1	29	york	york	PROPN
ejpam-6029	1	30	business	business	PROPN
ejpam-6029	1	31	global	global	ADJ
ejpam-6029	1	32	common	common	ADJ
ejpam-6029	1	33	fixed	fix	VERB
ejpam-6029	1	34	point	point	NOUN
ejpam-6029	1	35	results	result	NOUN
ejpam-6029	1	36	on	on	ADP
ejpam-6029	1	37	double	double	ADJ
ejpam-6029	1	38	-	-	PUNCT
ejpam-6029	1	39	composed	compose	VERB
ejpam-6029	1	40	cone	cone	NOUN
ejpam-6029	1	41	-	-	PUNCT
ejpam-6029	1	42	metric	metric	ADJ
ejpam-6029	1	43	-	-	PUNCT
ejpam-6029	1	44	like	like	ADJ
ejpam-6029	1	45	spaces	space	NOUN
ejpam-6029	1	46	for	for	ADP
ejpam-6029	1	47	generalized	generalized	ADJ
ejpam-6029	1	48	rational	rational	ADJ
ejpam-6029	1	49	contractions	contraction	NOUN
ejpam-6029	1	50	with	with	ADP
ejpam-6029	1	51	applications	application	NOUN
ejpam-6029	1	52	anas	anas	PROPN
ejpam-6029	1	53	a.	a.	PROPN
ejpam-6029	1	54	hijab1,2	hijab1,2	PROPN
ejpam-6029	1	55	,	,	PUNCT
ejpam-6029	1	56	laith	laith	PROPN
ejpam-6029	1	57	k.	k.	PROPN
ejpam-6029	1	58	shaakir1	shaakir1	PROPN
ejpam-6029	1	59	,	,	PUNCT
ejpam-6029	1	60	sarah	sarah	PROPN
ejpam-6029	1	61	aljohani3,∗	aljohani3,∗	NOUN
ejpam-6029	1	62	,	,	PUNCT
ejpam-6029	1	63	nabil	nabil	PROPN
ejpam-6029	1	64	mlaiki3	mlaiki3	PROPN
ejpam-6029	1	65	1	1	NUM
ejpam-6029	1	66	department	department	NOUN
ejpam-6029	1	67	of	of	ADP
ejpam-6029	1	68	mathematics	mathematic	NOUN
ejpam-6029	1	69	,	,	PUNCT
ejpam-6029	1	70	college	college	NOUN
ejpam-6029	1	71	of	of	ADP
ejpam-6029	1	72	computer	computer	NOUN
ejpam-6029	1	73	sciences	sciences	PROPN
ejpam-6029	1	74	and	and	CCONJ
ejpam-6029	1	75	mathematics	mathematic	NOUN
ejpam-6029	1	76	,	,	PUNCT
ejpam-6029	1	77	tikrit	tikrit	NOUN
ejpam-6029	1	78	university	university	NOUN
ejpam-6029	1	79	,	,	PUNCT
ejpam-6029	1	80	tikrit	tikrit	NOUN
ejpam-6029	1	81	,	,	PUNCT
ejpam-6029	1	82	iraq	iraq	PROPN
ejpam-6029	1	83	2	2	NUM
ejpam-6029	1	84	department	department	NOUN
ejpam-6029	1	85	of	of	ADP
ejpam-6029	1	86	mathematics	mathematic	NOUN
ejpam-6029	1	87	,	,	PUNCT
ejpam-6029	1	88	education	education	NOUN
ejpam-6029	1	89	for	for	ADP
ejpam-6029	1	90	pure	pure	ADJ
ejpam-6029	1	91	sciences	science	NOUN
ejpam-6029	1	92	college	college	PROPN
ejpam-6029	1	93	,	,	PUNCT
ejpam-6029	1	94	tikrit	tikrit	NOUN
ejpam-6029	1	95	university	university	NOUN
ejpam-6029	1	96	,	,	PUNCT
ejpam-6029	1	97	tikrit	tikrit	NOUN
ejpam-6029	1	98	,	,	PUNCT
ejpam-6029	1	99	iraq	iraq	PROPN
ejpam-6029	1	100	3	3	NUM
ejpam-6029	1	101	department	department	NOUN
ejpam-6029	1	102	of	of	ADP
ejpam-6029	1	103	mathematics	mathematic	NOUN
ejpam-6029	1	104	and	and	CCONJ
ejpam-6029	1	105	sciences	science	NOUN
ejpam-6029	1	106	,	,	PUNCT
ejpam-6029	1	107	prince	prince	PROPN
ejpam-6029	1	108	sultan	sultan	PROPN
ejpam-6029	1	109	university	university	PROPN
ejpam-6029	1	110	,	,	PUNCT
ejpam-6029	1	111	11586	11586	NUM
ejpam-6029	1	112	riyadh	riyadh	NOUN
ejpam-6029	1	113	,	,	PUNCT
ejpam-6029	1	114	saudi	saudi	PROPN
ejpam-6029	1	115	arabia	arabia	PROPN
ejpam-6029	1	116	abstract	abstract	NOUN
ejpam-6029	1	117	.	.	PUNCT
ejpam-6029	2	1	this	this	DET
ejpam-6029	2	2	paper	paper	NOUN
ejpam-6029	2	3	presents	present	VERB
ejpam-6029	2	4	a	a	DET
ejpam-6029	2	5	novel	novel	ADJ
ejpam-6029	2	6	concept	concept	NOUN
ejpam-6029	2	7	,	,	PUNCT
ejpam-6029	2	8	known	know	VERB
ejpam-6029	2	9	as	as	ADP
ejpam-6029	2	10	a	a	DET
ejpam-6029	2	11	double	double	ADV
ejpam-6029	2	12	-	-	PUNCT
ejpam-6029	2	13	composed	compose	VERB
ejpam-6029	2	14	cone	cone	NOUN
ejpam-6029	2	15	-	-	PUNCT
ejpam-6029	2	16	metric	metric	ADJ
ejpam-6029	2	17	-	-	PUNCT
ejpam-6029	2	18	like	like	ADJ
ejpam-6029	2	19	space	space	NOUN
ejpam-6029	2	20	,	,	PUNCT
ejpam-6029	2	21	which	which	PRON
ejpam-6029	2	22	extends	extend	VERB
ejpam-6029	2	23	the	the	DET
ejpam-6029	2	24	idea	idea	NOUN
ejpam-6029	2	25	of	of	ADP
ejpam-6029	2	26	a	a	DET
ejpam-6029	2	27	double	double	ADV
ejpam-6029	2	28	-	-	PUNCT
ejpam-6029	2	29	composed	compose	VERB
ejpam-6029	2	30	cone	cone	NOUN
ejpam-6029	2	31	-	-	PUNCT
ejpam-6029	2	32	metric	metric	ADJ
ejpam-6029	2	33	space	space	NOUN
ejpam-6029	2	34	.	.	PUNCT
ejpam-6029	3	1	in	in	ADP
ejpam-6029	3	2	this	this	DET
ejpam-6029	3	3	new	new	ADJ
ejpam-6029	3	4	space	space	NOUN
ejpam-6029	3	5	,	,	PUNCT
ejpam-6029	3	6	the	the	DET
ejpam-6029	3	7	selfdistance	selfdistance	NOUN
ejpam-6029	3	8	may	may	AUX
ejpam-6029	3	9	not	not	PART
ejpam-6029	3	10	necessarily	necessarily	ADV
ejpam-6029	3	11	be	be	AUX
ejpam-6029	3	12	zero	zero	NUM
ejpam-6029	3	13	;	;	PUNCT
ejpam-6029	3	14	however	however	ADV
ejpam-6029	3	15	,	,	PUNCT
ejpam-6029	3	16	if	if	SCONJ
ejpam-6029	3	17	the	the	DET
ejpam-6029	3	18	distance	distance	NOUN
ejpam-6029	3	19	metric	metric	NOUN
ejpam-6029	3	20	is	be	AUX
ejpam-6029	3	21	zero	zero	NUM
ejpam-6029	3	22	,	,	PUNCT
ejpam-6029	3	23	it	it	PRON
ejpam-6029	3	24	must	must	AUX
ejpam-6029	3	25	be	be	AUX
ejpam-6029	3	26	for	for	ADP
ejpam-6029	3	27	identical	identical	ADJ
ejpam-6029	3	28	points	point	NOUN
ejpam-6029	3	29	.	.	PUNCT
ejpam-6029	4	1	additionally	additionally	ADV
ejpam-6029	4	2	,	,	PUNCT
ejpam-6029	4	3	this	this	DET
ejpam-6029	4	4	text	text	NOUN
ejpam-6029	4	5	introduces	introduce	VERB
ejpam-6029	4	6	several	several	ADJ
ejpam-6029	4	7	results	result	NOUN
ejpam-6029	4	8	pertaining	pertain	VERB
ejpam-6029	4	9	to	to	ADP
ejpam-6029	4	10	this	this	DET
ejpam-6029	4	11	innovative	innovative	ADJ
ejpam-6029	4	12	concept	concept	NOUN
ejpam-6029	4	13	,	,	PUNCT
ejpam-6029	4	14	including	include	VERB
ejpam-6029	4	15	theorems	theorem	NOUN
ejpam-6029	4	16	that	that	PRON
ejpam-6029	4	17	demonstrate	demonstrate	VERB
ejpam-6029	4	18	the	the	DET
ejpam-6029	4	19	existence	existence	NOUN
ejpam-6029	4	20	of	of	ADP
ejpam-6029	4	21	common	common	ADJ
ejpam-6029	4	22	fixed	fix	VERB
ejpam-6029	4	23	points	point	NOUN
ejpam-6029	4	24	for	for	ADP
ejpam-6029	4	25	two	two	NUM
ejpam-6029	4	26	mappings	mapping	NOUN
ejpam-6029	4	27	that	that	PRON
ejpam-6029	4	28	satisfy	satisfy	VERB
ejpam-6029	4	29	generalized	generalize	VERB
ejpam-6029	4	30	non	non	ADJ
ejpam-6029	4	31	-	-	ADJ
ejpam-6029	4	32	linear	linear	ADJ
ejpam-6029	4	33	rational	rational	ADJ
ejpam-6029	4	34	contractions	contraction	NOUN
ejpam-6029	4	35	within	within	ADP
ejpam-6029	4	36	our	our	PRON
ejpam-6029	4	37	new	new	ADJ
ejpam-6029	4	38	space	space	NOUN
ejpam-6029	4	39	.	.	PUNCT
ejpam-6029	5	1	various	various	ADJ
ejpam-6029	5	2	examples	example	NOUN
ejpam-6029	5	3	are	be	AUX
ejpam-6029	5	4	provided	provide	VERB
ejpam-6029	5	5	to	to	PART
ejpam-6029	5	6	illustrate	illustrate	VERB
ejpam-6029	5	7	the	the	DET
ejpam-6029	5	8	main	main	ADJ
ejpam-6029	5	9	results	result	NOUN
ejpam-6029	5	10	and	and	CCONJ
ejpam-6029	5	11	their	their	PRON
ejpam-6029	5	12	relationship	relationship	NOUN
ejpam-6029	5	13	with	with	ADP
ejpam-6029	5	14	other	other	ADJ
ejpam-6029	5	15	cone	cone	NOUN
ejpam-6029	5	16	metric	metric	ADJ
ejpam-6029	5	17	spaces	space	NOUN
ejpam-6029	5	18	.	.	PUNCT
ejpam-6029	6	1	finally	finally	ADV
ejpam-6029	6	2	,	,	PUNCT
ejpam-6029	6	3	we	we	PRON
ejpam-6029	6	4	demonstrate	demonstrate	VERB
ejpam-6029	6	5	applications	application	NOUN
ejpam-6029	6	6	to	to	PART
ejpam-6029	6	7	nonlinear	nonlinear	VERB
ejpam-6029	6	8	integral	integral	ADJ
ejpam-6029	6	9	equations	equation	NOUN
ejpam-6029	6	10	and	and	CCONJ
ejpam-6029	6	11	boundary	boundary	ADJ
ejpam-6029	6	12	value	value	NOUN
ejpam-6029	6	13	problems	problem	NOUN
ejpam-6029	6	14	(	(	PUNCT
ejpam-6029	6	15	bvps	bvps	NOUN
ejpam-6029	6	16	)	)	PUNCT
ejpam-6029	6	17	to	to	PART
ejpam-6029	6	18	validate	validate	VERB
ejpam-6029	6	19	our	our	PRON
ejpam-6029	6	20	findings	finding	NOUN
ejpam-6029	6	21	.	.	PUNCT
ejpam-6029	7	1	2020	2020	NUM
ejpam-6029	7	2	mathematics	mathematic	NOUN
ejpam-6029	7	3	subject	subject	NOUN
ejpam-6029	7	4	classifications	classification	NOUN
ejpam-6029	7	5	:	:	PUNCT
ejpam-6029	7	6	47h10	47h10	NUM
ejpam-6029	7	7	,	,	PUNCT
ejpam-6029	7	8	54e50	54e50	NUM
ejpam-6029	7	9	,	,	PUNCT
ejpam-6029	7	10	54h25	54h25	NUM
ejpam-6029	7	11	key	key	ADJ
ejpam-6029	7	12	words	word	NOUN
ejpam-6029	7	13	and	and	CCONJ
ejpam-6029	7	14	phrases	phrase	NOUN
ejpam-6029	7	15	:	:	PUNCT
ejpam-6029	7	16	fixed	fix	VERB
ejpam-6029	7	17	point	point	NOUN
ejpam-6029	7	18	,	,	PUNCT
ejpam-6029	7	19	cone	cone	NOUN
ejpam-6029	7	20	metric	metric	ADJ
ejpam-6029	7	21	space	space	NOUN
ejpam-6029	7	22	,	,	PUNCT
ejpam-6029	7	23	double	double	ADJ
ejpam-6029	7	24	-	-	PUNCT
ejpam-6029	7	25	controlled	control	VERB
ejpam-6029	7	26	metric	metric	ADJ
ejpam-6029	7	27	-	-	PUNCT
ejpam-6029	7	28	like	like	ADJ
ejpam-6029	7	29	spaces	space	NOUN
ejpam-6029	7	30	,	,	PUNCT
ejpam-6029	7	31	double	double	ADJ
ejpam-6029	7	32	-	-	PUNCT
ejpam-6029	7	33	composed	compose	VERB
ejpam-6029	7	34	cone	cone	NOUN
ejpam-6029	7	35	metric	metric	ADJ
ejpam-6029	7	36	spaces	space	NOUN
ejpam-6029	7	37	,	,	PUNCT
ejpam-6029	7	38	double	double	ADJ
ejpam-6029	7	39	-	-	PUNCT
ejpam-6029	7	40	composed	compose	VERB
ejpam-6029	7	41	cone	cone	NOUN
ejpam-6029	7	42	-	-	PUNCT
ejpam-6029	7	43	metric	metric	ADJ
ejpam-6029	7	44	-	-	PUNCT
ejpam-6029	7	45	like	like	ADJ
ejpam-6029	7	46	spaces	space	NOUN
ejpam-6029	7	47	.	.	PUNCT
ejpam-6029	8	1	1	1	X
ejpam-6029	8	2	.	.	X
ejpam-6029	8	3	introduction	introduction	NOUN
ejpam-6029	8	4	fixed	fix	VERB
ejpam-6029	8	5	-	-	PUNCT
ejpam-6029	8	6	point	point	NOUN
ejpam-6029	8	7	theory	theory	NOUN
ejpam-6029	8	8	is	be	AUX
ejpam-6029	8	9	a	a	DET
ejpam-6029	8	10	fundamental	fundamental	ADJ
ejpam-6029	8	11	branch	branch	NOUN
ejpam-6029	8	12	of	of	ADP
ejpam-6029	8	13	functional	functional	ADJ
ejpam-6029	8	14	and	and	CCONJ
ejpam-6029	8	15	mathematical	mathematical	ADJ
ejpam-6029	8	16	analysis	analysis	NOUN
ejpam-6029	8	17	that	that	PRON
ejpam-6029	8	18	addresses	address	VERB
ejpam-6029	8	19	the	the	DET
ejpam-6029	8	20	existence	existence	NOUN
ejpam-6029	8	21	and	and	CCONJ
ejpam-6029	8	22	uniqueness	uniqueness	NOUN
ejpam-6029	8	23	of	of	ADP
ejpam-6029	8	24	solutions	solution	NOUN
ejpam-6029	8	25	to	to	ADP
ejpam-6029	8	26	integral	integral	ADJ
ejpam-6029	8	27	-	-	PUNCT
ejpam-6029	8	28	differential	differential	NOUN
ejpam-6029	8	29	equations	equation	NOUN
ejpam-6029	8	30	.	.	PUNCT
ejpam-6029	9	1	building	build	VERB
ejpam-6029	9	2	upon	upon	SCONJ
ejpam-6029	9	3	the	the	DET
ejpam-6029	9	4	renowned	renowned	ADJ
ejpam-6029	9	5	banach	banach	NOUN
ejpam-6029	9	6	contraction	contraction	NOUN
ejpam-6029	9	7	principle	principle	NOUN
ejpam-6029	9	8	[	[	X
ejpam-6029	9	9	1	1	NUM
ejpam-6029	9	10	]	]	PUNCT
ejpam-6029	9	11	,	,	PUNCT
ejpam-6029	9	12	numerous	numerous	ADJ
ejpam-6029	9	13	scholars	scholar	NOUN
ejpam-6029	9	14	have	have	AUX
ejpam-6029	9	15	made	make	VERB
ejpam-6029	9	16	significant	significant	ADJ
ejpam-6029	9	17	contributions	contribution	NOUN
ejpam-6029	9	18	to	to	ADP
ejpam-6029	9	19	this	this	DET
ejpam-6029	9	20	field	field	NOUN
ejpam-6029	9	21	.	.	PUNCT
ejpam-6029	10	1	various	various	ADJ
ejpam-6029	10	2	results	result	NOUN
ejpam-6029	10	3	have	have	AUX
ejpam-6029	10	4	emerged	emerge	VERB
ejpam-6029	10	5	concerning	concern	VERB
ejpam-6029	10	6	mappings	mapping	NOUN
ejpam-6029	10	7	that	that	PRON
ejpam-6029	10	8	satisfy	satisfy	VERB
ejpam-6029	10	9	different	different	ADJ
ejpam-6029	10	10	contractive	contractive	ADJ
ejpam-6029	10	11	conditions	condition	NOUN
ejpam-6029	10	12	across	across	ADP
ejpam-6029	10	13	diverse	diverse	ADJ
ejpam-6029	10	14	types	type	NOUN
ejpam-6029	10	15	of	of	ADP
ejpam-6029	10	16	metric	metric	ADJ
ejpam-6029	10	17	spaces	space	NOUN
ejpam-6029	10	18	.	.	PUNCT
ejpam-6029	11	1	∗corresponding	∗corresponde	VERB
ejpam-6029	11	2	author	author	NOUN
ejpam-6029	11	3	.	.	PUNCT
ejpam-6029	12	1	doi	doi	NOUN
ejpam-6029	12	2	:	:	PUNCT
ejpam-6029	12	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6029	https://doi.org/10.29020/nybg.ejpam.v18i2.6029	NOUN
ejpam-6029	12	4	email	email	NOUN
ejpam-6029	12	5	addresses	address	NOUN
ejpam-6029	12	6	:	:	PUNCT
ejpam-6029	13	1	anas	anas	PROPN
ejpam-6029	13	2	abass@tu.edu.iq	abass@tu.edu.iq	PROPN
ejpam-6029	13	3	(	(	PUNCT
ejpam-6029	13	4	a.	a.	NOUN
ejpam-6029	13	5	a.	a.	PROPN
ejpam-6029	13	6	hijab	hijab	PROPN
ejpam-6029	13	7	)	)	PUNCT
ejpam-6029	13	8	,	,	PUNCT
ejpam-6029	13	9	dr.laithkhaleel@tu.edu.iq	dr.laithkhaleel@tu.edu.iq	PROPN
ejpam-6029	13	10	(	(	PUNCT
ejpam-6029	13	11	l.	l.	PROPN
ejpam-6029	13	12	k.	k.	PROPN
ejpam-6029	13	13	shaakir	shaakir	PROPN
ejpam-6029	13	14	)	)	PUNCT
ejpam-6029	13	15	,	,	PUNCT
ejpam-6029	13	16	sjohani@psu.edu.sa	sjohani@psu.edu.sa	PROPN
ejpam-6029	13	17	(	(	PUNCT
ejpam-6029	13	18	s.	s.	PROPN
ejpam-6029	13	19	aljohani	aljohani	PROPN
ejpam-6029	13	20	)	)	PUNCT
ejpam-6029	13	21	,	,	PUNCT
ejpam-6029	13	22	nmlaiki@psu.edu.sa	nmlaiki@psu.edu.sa	NOUN
ejpam-6029	13	23	(	(	PUNCT
ejpam-6029	13	24	n.	n.	PROPN
ejpam-6029	13	25	mlaiki	mlaiki	PROPN
ejpam-6029	13	26	)	)	PUNCT
ejpam-6029	13	27	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6029	13	28	1	1	NUM
ejpam-6029	13	29	copyright	copyright	NOUN
ejpam-6029	13	30	:	:	PUNCT
ejpam-6029	13	31	©	©	PROPN
ejpam-6029	13	32	2025	2025	NUM
ejpam-6029	13	33	the	the	DET
ejpam-6029	13	34	author(s	author(s	NOUN
ejpam-6029	13	35	)	)	PUNCT
ejpam-6029	13	36	.	.	PUNCT
ejpam-6029	14	1	(	(	PUNCT
ejpam-6029	14	2	cc	cc	NOUN
ejpam-6029	14	3	by	by	ADP
ejpam-6029	14	4	-	-	PUNCT
ejpam-6029	14	5	nc	nc	PROPN
ejpam-6029	14	6	4.0	4.0	NUM
ejpam-6029	14	7	)	)	PUNCT
ejpam-6029	14	8	a.	a.	NOUN
ejpam-6029	14	9	a.	a.	PROPN
ejpam-6029	14	10	hijab	hijab	PROPN
ejpam-6029	14	11	et	et	PROPN
ejpam-6029	14	12	al	al	PROPN
ejpam-6029	14	13	.	.	PUNCT
ejpam-6029	14	14	/	/	SYM
ejpam-6029	14	15	eur	eur	PROPN
ejpam-6029	14	16	.	.	PUNCT
ejpam-6029	15	1	j.	j.	PROPN
ejpam-6029	15	2	pure	pure	PROPN
ejpam-6029	15	3	appl	appl	PROPN
ejpam-6029	15	4	.	.	PROPN
ejpam-6029	15	5	math	math	PROPN
ejpam-6029	15	6	,	,	PUNCT
ejpam-6029	15	7	18	18	NUM
ejpam-6029	15	8	(	(	PUNCT
ejpam-6029	15	9	2	2	NUM
ejpam-6029	15	10	)	)	PUNCT
ejpam-6029	15	11	(	(	PUNCT
ejpam-6029	15	12	2025	2025	NUM
ejpam-6029	15	13	)	)	PUNCT
ejpam-6029	15	14	,	,	PUNCT
ejpam-6029	15	15	6029	6029	NUM
ejpam-6029	15	16	2	2	NUM
ejpam-6029	15	17	of	of	ADP
ejpam-6029	15	18	23	23	NUM
ejpam-6029	15	19	one	one	NUM
ejpam-6029	15	20	such	such	ADJ
ejpam-6029	15	21	extension	extension	NOUN
ejpam-6029	15	22	is	be	AUX
ejpam-6029	15	23	b	b	NOUN
ejpam-6029	15	24	-	-	PUNCT
ejpam-6029	15	25	metric	metric	ADJ
ejpam-6029	15	26	spaces	space	NOUN
ejpam-6029	15	27	,	,	PUNCT
ejpam-6029	15	28	which	which	PRON
ejpam-6029	15	29	were	be	AUX
ejpam-6029	15	30	introduced	introduce	VERB
ejpam-6029	15	31	independently	independently	ADV
ejpam-6029	15	32	by	by	ADP
ejpam-6029	15	33	czerwik	czerwik	PROPN
ejpam-6029	16	1	[	[	X
ejpam-6029	16	2	2	2	NUM
ejpam-6029	16	3	]	]	PUNCT
ejpam-6029	16	4	and	and	CCONJ
ejpam-6029	16	5	bakhtin	bakhtin	NOUN
ejpam-6029	16	6	[	[	X
ejpam-6029	16	7	3	3	NUM
ejpam-6029	16	8	]	]	PUNCT
ejpam-6029	16	9	.	.	PUNCT
ejpam-6029	17	1	in	in	ADP
ejpam-6029	17	2	recent	recent	ADJ
ejpam-6029	17	3	years	year	NOUN
ejpam-6029	17	4	,	,	PUNCT
ejpam-6029	17	5	there	there	PRON
ejpam-6029	17	6	have	have	AUX
ejpam-6029	17	7	been	be	AUX
ejpam-6029	17	8	several	several	ADJ
ejpam-6029	17	9	generalizations	generalization	NOUN
ejpam-6029	17	10	of	of	ADP
ejpam-6029	17	11	b	b	NOUN
ejpam-6029	17	12	-	-	PUNCT
ejpam-6029	17	13	metric	metric	ADJ
ejpam-6029	17	14	spaces	space	NOUN
ejpam-6029	17	15	,	,	PUNCT
ejpam-6029	17	16	such	such	ADJ
ejpam-6029	17	17	as	as	ADP
ejpam-6029	17	18	bv(s)-metric	bv(s)-metric	ADJ
ejpam-6029	17	19	spaces	space	NOUN
ejpam-6029	17	20	proposed	propose	VERB
ejpam-6029	17	21	by	by	ADP
ejpam-6029	17	22	mitrović	mitrović	NOUN
ejpam-6029	17	23	et	et	PROPN
ejpam-6029	17	24	al	al	PROPN
ejpam-6029	17	25	.	.	PUNCT
ejpam-6029	18	1	[	[	X
ejpam-6029	18	2	4	4	NUM
ejpam-6029	18	3	]	]	PUNCT
ejpam-6029	18	4	.	.	PUNCT
ejpam-6029	19	1	kamran	kamran	PROPN
ejpam-6029	19	2	et	et	PROPN
ejpam-6029	19	3	al	al	PROPN
ejpam-6029	19	4	.	.	PUNCT
ejpam-6029	20	1	[	[	X
ejpam-6029	20	2	5	5	NUM
ejpam-6029	20	3	]	]	PUNCT
ejpam-6029	20	4	extended	extended	ADJ
ejpam-6029	20	5	b	b	X
ejpam-6029	20	6	-	-	ADJ
ejpam-6029	20	7	metric	metric	ADJ
ejpam-6029	20	8	spaces	space	NOUN
ejpam-6029	20	9	,	,	PUNCT
ejpam-6029	20	10	while	while	SCONJ
ejpam-6029	20	11	in	in	ADP
ejpam-6029	20	12	2018	2018	NUM
ejpam-6029	20	13	,	,	PUNCT
ejpam-6029	20	14	mlaiki	mlaiki	PROPN
ejpam-6029	21	1	[	[	X
ejpam-6029	21	2	6	6	NUM
ejpam-6029	21	3	]	]	PUNCT
ejpam-6029	21	4	,	,	PUNCT
ejpam-6029	21	5	and	and	CCONJ
ejpam-6029	21	6	abdeljawad	abdeljawad	NOUN
ejpam-6029	21	7	et	et	PROPN
ejpam-6029	21	8	al	al	PROPN
ejpam-6029	21	9	.	.	PUNCT
ejpam-6029	22	1	[	[	X
ejpam-6029	22	2	7	7	X
ejpam-6029	22	3	]	]	PUNCT
ejpam-6029	22	4	introduced	introduce	VERB
ejpam-6029	22	5	the	the	DET
ejpam-6029	22	6	concept	concept	NOUN
ejpam-6029	22	7	of	of	ADP
ejpam-6029	22	8	controlled	control	VERB
ejpam-6029	22	9	metric	metric	ADJ
ejpam-6029	22	10	-	-	PUNCT
ejpam-6029	22	11	type	type	NOUN
ejpam-6029	22	12	spaces	space	NOUN
ejpam-6029	22	13	and	and	CCONJ
ejpam-6029	22	14	double	double	ADJ
ejpam-6029	22	15	-	-	PUNCT
ejpam-6029	22	16	controlled	control	VERB
ejpam-6029	22	17	metric	metric	ADJ
ejpam-6029	22	18	spaces	space	NOUN
ejpam-6029	22	19	,	,	PUNCT
ejpam-6029	22	20	respectively	respectively	ADV
ejpam-6029	22	21	.	.	PUNCT
ejpam-6029	23	1	amini	amini	PROPN
ejpam-6029	23	2	-	-	ADJ
ejpam-6029	23	3	harandi	harandi	X
ejpam-6029	24	1	[	[	X
ejpam-6029	24	2	8	8	NUM
ejpam-6029	24	3	]	]	PUNCT
ejpam-6029	24	4	(	(	PUNCT
ejpam-6029	24	5	and	and	CCONJ
ejpam-6029	24	6	independence	independence	NOUN
ejpam-6029	24	7	hitzler	hitzler	ADV
ejpam-6029	24	8	et	et	PROPN
ejpam-6029	24	9	al	al	PROPN
ejpam-6029	24	10	.	.	PUNCT
ejpam-6029	25	1	[	[	X
ejpam-6029	25	2	9	9	NUM
ejpam-6029	25	3	]	]	PUNCT
ejpam-6029	25	4	)	)	PUNCT
ejpam-6029	25	5	have	have	AUX
ejpam-6029	25	6	expanded	expand	VERB
ejpam-6029	25	7	the	the	DET
ejpam-6029	25	8	concept	concept	NOUN
ejpam-6029	25	9	of	of	ADP
ejpam-6029	25	10	partial	partial	ADJ
ejpam-6029	25	11	metric	metric	ADJ
ejpam-6029	25	12	spaces	space	NOUN
ejpam-6029	25	13	by	by	ADP
ejpam-6029	25	14	defining	define	VERB
ejpam-6029	25	15	metric	metric	ADJ
ejpam-6029	25	16	-	-	PUNCT
ejpam-6029	25	17	like	like	ADJ
ejpam-6029	25	18	spaces	space	NOUN
ejpam-6029	25	19	,	,	PUNCT
ejpam-6029	25	20	also	also	ADV
ejpam-6029	25	21	known	know	VERB
ejpam-6029	25	22	as	as	ADP
ejpam-6029	25	23	(	(	PUNCT
ejpam-6029	25	24	dislocated	dislocate	VERB
ejpam-6029	25	25	metric	metric	ADJ
ejpam-6029	25	26	spaces	space	NOUN
ejpam-6029	25	27	)	)	PUNCT
ejpam-6029	25	28	.	.	PUNCT
ejpam-6029	26	1	the	the	DET
ejpam-6029	26	2	most	most	ADV
ejpam-6029	26	3	comprehensive	comprehensive	ADJ
ejpam-6029	26	4	generalization	generalization	NOUN
ejpam-6029	26	5	,	,	PUNCT
ejpam-6029	26	6	the	the	DET
ejpam-6029	26	7	b	b	NOUN
ejpam-6029	26	8	-	-	PUNCT
ejpam-6029	26	9	metric	metric	ADJ
ejpam-6029	26	10	-	-	PUNCT
ejpam-6029	26	11	like	like	ADJ
ejpam-6029	26	12	space	space	NOUN
ejpam-6029	26	13	,	,	PUNCT
ejpam-6029	26	14	was	be	AUX
ejpam-6029	26	15	introduced	introduce	VERB
ejpam-6029	26	16	by	by	ADP
ejpam-6029	26	17	alghamdi	alghamdi	PROPN
ejpam-6029	26	18	et	et	PROPN
ejpam-6029	26	19	al	al	PROPN
ejpam-6029	26	20	.	.	PUNCT
ejpam-6029	27	1	[	[	X
ejpam-6029	27	2	10	10	NUM
ejpam-6029	27	3	]	]	PUNCT
ejpam-6029	27	4	.	.	PUNCT
ejpam-6029	28	1	several	several	ADJ
ejpam-6029	28	2	fixed	fix	VERB
ejpam-6029	28	3	-	-	PUNCT
ejpam-6029	28	4	point	point	NOUN
ejpam-6029	28	5	results	result	NOUN
ejpam-6029	28	6	have	have	AUX
ejpam-6029	28	7	been	be	AUX
ejpam-6029	28	8	explored	explore	VERB
ejpam-6029	28	9	in	in	ADP
ejpam-6029	28	10	b	b	NOUN
ejpam-6029	28	11	-	-	ADJ
ejpam-6029	28	12	metric	metric	ADJ
ejpam-6029	28	13	and	and	CCONJ
ejpam-6029	28	14	their	their	PRON
ejpam-6029	28	15	predecessors	predecessor	NOUN
ejpam-6029	28	16	(	(	PUNCT
ejpam-6029	28	17	see	see	VERB
ejpam-6029	28	18	[	[	X
ejpam-6029	28	19	11	11	NUM
ejpam-6029	28	20	,	,	PUNCT
ejpam-6029	28	21	12	12	NUM
ejpam-6029	28	22	]	]	PUNCT
ejpam-6029	28	23	)	)	PUNCT
ejpam-6029	28	24	.	.	PUNCT
ejpam-6029	29	1	in	in	ADP
ejpam-6029	29	2	addition	addition	NOUN
ejpam-6029	29	3	,	,	PUNCT
ejpam-6029	29	4	in	in	ADP
ejpam-6029	29	5	2020	2020	NUM
ejpam-6029	29	6	,	,	PUNCT
ejpam-6029	29	7	mlaiki	mlaiki	PROPN
ejpam-6029	30	1	[	[	X
ejpam-6029	30	2	13	13	NUM
ejpam-6029	30	3	]	]	PUNCT
ejpam-6029	30	4	and	and	CCONJ
ejpam-6029	30	5	ayoob	ayoob	PROPN
ejpam-6029	30	6	et	et	PROPN
ejpam-6029	30	7	al	al	PROPN
ejpam-6029	30	8	.	.	PUNCT
ejpam-6029	31	1	[	[	X
ejpam-6029	31	2	14	14	NUM
ejpam-6029	31	3	]	]	PUNCT
ejpam-6029	31	4	introduced	introduce	VERB
ejpam-6029	31	5	double	double	ADJ
ejpam-6029	31	6	-	-	PUNCT
ejpam-6029	31	7	controlled	control	VERB
ejpam-6029	31	8	metric	metric	ADJ
ejpam-6029	31	9	-	-	PUNCT
ejpam-6029	31	10	like	like	ADJ
ejpam-6029	31	11	spaces	space	NOUN
ejpam-6029	31	12	as	as	ADP
ejpam-6029	31	13	a	a	DET
ejpam-6029	31	14	further	further	ADJ
ejpam-6029	31	15	extension	extension	NOUN
ejpam-6029	31	16	of	of	ADP
ejpam-6029	31	17	double	double	ADJ
ejpam-6029	31	18	-	-	PUNCT
ejpam-6029	31	19	controlled	control	VERB
ejpam-6029	31	20	metric	metric	ADJ
ejpam-6029	31	21	-	-	PUNCT
ejpam-6029	31	22	type	type	NOUN
ejpam-6029	31	23	spaces	space	NOUN
ejpam-6029	31	24	.	.	PUNCT
ejpam-6029	32	1	in	in	ADP
ejpam-6029	32	2	2023	2023	NUM
ejpam-6029	32	3	,	,	PUNCT
ejpam-6029	32	4	ayoob	ayoob	PROPN
ejpam-6029	32	5	et	et	PROPN
ejpam-6029	32	6	al	al	PROPN
ejpam-6029	32	7	.	.	PUNCT
ejpam-6029	33	1	[	[	X
ejpam-6029	33	2	15	15	NUM
ejpam-6029	33	3	]	]	PUNCT
ejpam-6029	33	4	proposed	propose	VERB
ejpam-6029	33	5	an	an	DET
ejpam-6029	33	6	extension	extension	NOUN
ejpam-6029	33	7	of	of	ADP
ejpam-6029	33	8	metric	metric	ADJ
ejpam-6029	33	9	spaces	space	NOUN
ejpam-6029	33	10	known	know	VERB
ejpam-6029	33	11	as	as	ADP
ejpam-6029	33	12	double	double	ADV
ejpam-6029	33	13	-	-	PUNCT
ejpam-6029	33	14	composed	compose	VERB
ejpam-6029	33	15	metric	metric	ADJ
ejpam-6029	33	16	spaces	space	NOUN
ejpam-6029	33	17	,	,	PUNCT
ejpam-6029	33	18	which	which	PRON
ejpam-6029	33	19	involve	involve	VERB
ejpam-6029	33	20	two	two	NUM
ejpam-6029	33	21	composed	compose	VERB
ejpam-6029	33	22	functions	function	NOUN
ejpam-6029	33	23	in	in	ADP
ejpam-6029	33	24	the	the	DET
ejpam-6029	33	25	triangular	triangular	NOUN
ejpam-6029	33	26	inequality	inequality	NOUN
ejpam-6029	33	27	.	.	PUNCT
ejpam-6029	34	1	huang	huang	PROPN
ejpam-6029	34	2	et	et	PROPN
ejpam-6029	34	3	al	al	PROPN
ejpam-6029	34	4	.	.	PUNCT
ejpam-6029	35	1	[	[	X
ejpam-6029	35	2	16	16	NUM
ejpam-6029	35	3	]	]	PUNCT
ejpam-6029	35	4	introduced	introduce	VERB
ejpam-6029	35	5	the	the	DET
ejpam-6029	35	6	concept	concept	NOUN
ejpam-6029	35	7	of	of	ADP
ejpam-6029	35	8	cone	cone	NOUN
ejpam-6029	35	9	metric	metric	ADJ
ejpam-6029	35	10	spaces	space	NOUN
ejpam-6029	35	11	as	as	ADP
ejpam-6029	35	12	an	an	DET
ejpam-6029	35	13	extension	extension	NOUN
ejpam-6029	35	14	of	of	ADP
ejpam-6029	35	15	traditional	traditional	ADJ
ejpam-6029	35	16	metric	metric	ADJ
ejpam-6029	35	17	spaces	space	NOUN
ejpam-6029	35	18	.	.	PUNCT
ejpam-6029	36	1	following	follow	VERB
ejpam-6029	36	2	this	this	PRON
ejpam-6029	36	3	,	,	PUNCT
ejpam-6029	36	4	hussain	hussain	PROPN
ejpam-6029	36	5	et	et	PROPN
ejpam-6029	36	6	al	al	PROPN
ejpam-6029	36	7	.	.	PUNCT
ejpam-6029	37	1	[	[	X
ejpam-6029	37	2	17	17	NUM
ejpam-6029	37	3	]	]	PUNCT
ejpam-6029	37	4	introduced	introduce	VERB
ejpam-6029	37	5	cone	cone	PROPN
ejpam-6029	37	6	b	b	X
ejpam-6029	37	7	-	-	PUNCT
ejpam-6029	37	8	metric	metric	ADJ
ejpam-6029	37	9	spaces	space	NOUN
ejpam-6029	37	10	and	and	CCONJ
ejpam-6029	37	11	shateri	shateri	VERB
ejpam-6029	37	12	[	[	X
ejpam-6029	37	13	18	18	NUM
ejpam-6029	37	14	]	]	PUNCT
ejpam-6029	37	15	presented	present	VERB
ejpam-6029	37	16	fixed	fix	VERB
ejpam-6029	37	17	-	-	PUNCT
ejpam-6029	37	18	point	point	NOUN
ejpam-6029	37	19	theorems	theorem	NOUN
ejpam-6029	37	20	on	on	ADP
ejpam-6029	37	21	double	double	ADJ
ejpam-6029	37	22	-	-	PUNCT
ejpam-6029	37	23	controlled	control	VERB
ejpam-6029	37	24	cone	cone	NOUN
ejpam-6029	37	25	metric	metric	ADJ
ejpam-6029	37	26	spaces	space	NOUN
ejpam-6029	37	27	.	.	PUNCT
ejpam-6029	38	1	subsequently	subsequently	ADV
ejpam-6029	38	2	,	,	PUNCT
ejpam-6029	38	3	anas	anas	PROPN
ejpam-6029	38	4	et	et	PROPN
ejpam-6029	38	5	al	al	PROPN
ejpam-6029	38	6	.	.	PUNCT
ejpam-6029	39	1	[	[	X
ejpam-6029	39	2	19	19	NUM
ejpam-6029	39	3	]	]	PUNCT
ejpam-6029	39	4	introduced	introduce	VERB
ejpam-6029	39	5	type	type	NOUN
ejpam-6029	39	6	i	i	PROPN
ejpam-6029	39	7	and	and	CCONJ
ejpam-6029	39	8	ii	ii	PROPN
ejpam-6029	39	9	composed	compose	VERB
ejpam-6029	39	10	cone	cone	NOUN
ejpam-6029	39	11	metric	metric	ADJ
ejpam-6029	39	12	spaces	space	NOUN
ejpam-6029	39	13	and	and	CCONJ
ejpam-6029	39	14	[	[	X
ejpam-6029	39	15	20	20	NUM
ejpam-6029	39	16	]	]	PUNCT
ejpam-6029	39	17	extended	extend	VERB
ejpam-6029	39	18	double	double	ADV
ejpam-6029	39	19	-	-	PUNCT
ejpam-6029	39	20	composed	compose	VERB
ejpam-6029	39	21	metric	metric	ADJ
ejpam-6029	39	22	spaces	space	NOUN
ejpam-6029	39	23	to	to	PART
ejpam-6029	39	24	double	double	ADV
ejpam-6029	39	25	-	-	PUNCT
ejpam-6029	39	26	composed	compose	VERB
ejpam-6029	39	27	metric	metric	ADJ
ejpam-6029	39	28	-	-	PUNCT
ejpam-6029	39	29	like	like	ADJ
ejpam-6029	39	30	spaces	space	NOUN
ejpam-6029	39	31	(	(	PUNCT
ejpam-6029	39	32	see	see	VERB
ejpam-6029	39	33	[	[	X
ejpam-6029	39	34	21–27	21–27	NOUN
ejpam-6029	39	35	]	]	PUNCT
ejpam-6029	39	36	)	)	PUNCT
ejpam-6029	39	37	.	.	PUNCT
ejpam-6029	40	1	in	in	ADP
ejpam-6029	40	2	2020	2020	NUM
ejpam-6029	40	3	,	,	PUNCT
ejpam-6029	40	4	lateef	lateef	PROPN
ejpam-6029	40	5	[	[	X
ejpam-6029	40	6	28	28	NUM
ejpam-6029	40	7	]	]	PUNCT
ejpam-6029	40	8	proved	prove	VERB
ejpam-6029	40	9	fisher	fisher	NOUN
ejpam-6029	40	10	-	-	PUNCT
ejpam-6029	40	11	type	type	NOUN
ejpam-6029	40	12	fixed	fix	VERB
ejpam-6029	40	13	point	point	NOUN
ejpam-6029	40	14	results	result	NOUN
ejpam-6029	40	15	in	in	ADP
ejpam-6029	40	16	controlled	control	VERB
ejpam-6029	40	17	metric	metric	ADJ
ejpam-6029	40	18	spaces	space	NOUN
ejpam-6029	40	19	,	,	PUNCT
ejpam-6029	40	20	with	with	ADP
ejpam-6029	40	21	subsequent	subsequent	ADJ
ejpam-6029	40	22	discussion	discussion	NOUN
ejpam-6029	40	23	by	by	ADP
ejpam-6029	40	24	authors	author	NOUN
ejpam-6029	40	25	including	include	VERB
ejpam-6029	40	26	dass	dass	PROPN
ejpam-6029	40	27	and	and	CCONJ
ejpam-6029	40	28	gupta	gupta	NOUN
ejpam-6029	40	29	[	[	X
ejpam-6029	40	30	29	29	NUM
ejpam-6029	40	31	]	]	PUNCT
ejpam-6029	40	32	and	and	CCONJ
ejpam-6029	40	33	jaggi	jaggi	NOUN
ejpam-6029	41	1	[	[	X
ejpam-6029	41	2	30	30	NUM
ejpam-6029	41	3	]	]	PUNCT
ejpam-6029	41	4	utilizing	utilize	VERB
ejpam-6029	41	5	a	a	DET
ejpam-6029	41	6	contraction	contraction	NOUN
ejpam-6029	41	7	condition	condition	NOUN
ejpam-6029	41	8	of	of	ADP
ejpam-6029	41	9	the	the	DET
ejpam-6029	41	10	rational	rational	ADJ
ejpam-6029	41	11	-	-	PUNCT
ejpam-6029	41	12	types	type	NOUN
ejpam-6029	41	13	.	.	PUNCT
ejpam-6029	42	1	additionally	additionally	ADV
ejpam-6029	42	2	,	,	PUNCT
ejpam-6029	42	3	ahmad	ahmad	PROPN
ejpam-6029	42	4	et	et	PROPN
ejpam-6029	42	5	al	al	PROPN
ejpam-6029	42	6	.	.	PUNCT
ejpam-6029	43	1	[	[	X
ejpam-6029	43	2	31	31	NUM
ejpam-6029	43	3	]	]	PUNCT
ejpam-6029	43	4	provided	provide	VERB
ejpam-6029	43	5	a	a	DET
ejpam-6029	43	6	generalization	generalization	NOUN
ejpam-6029	43	7	of	of	ADP
ejpam-6029	43	8	rational	rational	ADJ
ejpam-6029	43	9	contractions	contraction	NOUN
ejpam-6029	43	10	in	in	ADP
ejpam-6029	43	11	double	double	ADJ
ejpam-6029	43	12	-	-	PUNCT
ejpam-6029	43	13	controlled	control	VERB
ejpam-6029	43	14	metric	metric	ADJ
ejpam-6029	43	15	spaces	space	NOUN
ejpam-6029	43	16	for	for	ADP
ejpam-6029	43	17	common	common	ADJ
ejpam-6029	43	18	fixed	fix	VERB
ejpam-6029	43	19	point	point	NOUN
ejpam-6029	43	20	theorems	theorem	NOUN
ejpam-6029	43	21	.	.	PUNCT
ejpam-6029	44	1	for	for	ADP
ejpam-6029	44	2	further	further	ADJ
ejpam-6029	44	3	details	detail	NOUN
ejpam-6029	44	4	,	,	PUNCT
ejpam-6029	44	5	see	see	VERB
ejpam-6029	44	6	[	[	X
ejpam-6029	44	7	25	25	NUM
ejpam-6029	44	8	,	,	PUNCT
ejpam-6029	44	9	32–34	32–34	NUM
ejpam-6029	44	10	]	]	PUNCT
ejpam-6029	44	11	.	.	PUNCT
ejpam-6029	45	1	the	the	DET
ejpam-6029	45	2	objective	objective	NOUN
ejpam-6029	45	3	of	of	ADP
ejpam-6029	45	4	the	the	DET
ejpam-6029	45	5	current	current	ADJ
ejpam-6029	45	6	study	study	NOUN
ejpam-6029	45	7	is	be	AUX
ejpam-6029	45	8	to	to	PART
ejpam-6029	45	9	establish	establish	VERB
ejpam-6029	45	10	common	common	ADJ
ejpam-6029	45	11	fixed	fix	VERB
ejpam-6029	45	12	point	point	NOUN
ejpam-6029	45	13	results	result	NOUN
ejpam-6029	45	14	for	for	ADP
ejpam-6029	45	15	new	new	ADJ
ejpam-6029	45	16	generalized	generalized	ADJ
ejpam-6029	45	17	rational	rational	ADJ
ejpam-6029	45	18	contractions	contraction	NOUN
ejpam-6029	45	19	,	,	PUNCT
ejpam-6029	45	20	serving	serve	VERB
ejpam-6029	45	21	as	as	ADP
ejpam-6029	45	22	a	a	DET
ejpam-6029	45	23	generalization	generalization	NOUN
ejpam-6029	45	24	of	of	ADP
ejpam-6029	45	25	various	various	ADJ
ejpam-6029	45	26	types	type	NOUN
ejpam-6029	45	27	of	of	ADP
ejpam-6029	45	28	metric	metric	ADJ
ejpam-6029	45	29	spaces	space	NOUN
ejpam-6029	45	30	mentioned	mention	VERB
ejpam-6029	45	31	previously	previously	ADV
ejpam-6029	45	32	.	.	PUNCT
ejpam-6029	46	1	this	this	DET
ejpam-6029	46	2	study	study	NOUN
ejpam-6029	46	3	introduces	introduce	VERB
ejpam-6029	46	4	a	a	DET
ejpam-6029	46	5	new	new	ADJ
ejpam-6029	46	6	class	class	NOUN
ejpam-6029	46	7	known	know	VERB
ejpam-6029	46	8	as	as	ADP
ejpam-6029	46	9	double	double	ADV
ejpam-6029	46	10	-	-	PUNCT
ejpam-6029	46	11	composed	compose	VERB
ejpam-6029	46	12	cone	cone	NOUN
ejpam-6029	46	13	metric	metric	ADJ
ejpam-6029	46	14	-	-	PUNCT
ejpam-6029	46	15	like	like	ADJ
ejpam-6029	46	16	spaces	space	NOUN
ejpam-6029	46	17	(	(	PUNCT
ejpam-6029	46	18	for	for	ADP
ejpam-6029	46	19	short	short	ADJ
ejpam-6029	46	20	,	,	PUNCT
ejpam-6029	46	21	dccml	dccml	NOUN
ejpam-6029	46	22	-	-	PUNCT
ejpam-6029	46	23	space	space	NOUN
ejpam-6029	46	24	)	)	PUNCT
ejpam-6029	46	25	.	.	PUNCT
ejpam-6029	47	1	the	the	DET
ejpam-6029	47	2	goal	goal	NOUN
ejpam-6029	47	3	is	be	AUX
ejpam-6029	47	4	to	to	PART
ejpam-6029	47	5	present	present	VERB
ejpam-6029	47	6	common	common	ADJ
ejpam-6029	47	7	fixed	fix	VERB
ejpam-6029	47	8	point	point	NOUN
ejpam-6029	47	9	results	result	NOUN
ejpam-6029	47	10	involving	involve	VERB
ejpam-6029	47	11	various	various	ADJ
ejpam-6029	47	12	types	type	NOUN
ejpam-6029	47	13	of	of	ADP
ejpam-6029	47	14	generalized	generalized	ADJ
ejpam-6029	47	15	rational	rational	ADJ
ejpam-6029	47	16	contractions	contraction	NOUN
ejpam-6029	47	17	,	,	PUNCT
ejpam-6029	47	18	accompanied	accompany	VERB
ejpam-6029	47	19	by	by	ADP
ejpam-6029	47	20	examples	example	NOUN
ejpam-6029	47	21	.	.	PUNCT
ejpam-6029	48	1	finally	finally	ADV
ejpam-6029	48	2	,	,	PUNCT
ejpam-6029	48	3	the	the	DET
ejpam-6029	48	4	manuscript	manuscript	NOUN
ejpam-6029	48	5	introduces	introduce	VERB
ejpam-6029	48	6	applications	application	NOUN
ejpam-6029	48	7	of	of	ADP
ejpam-6029	48	8	nonlinear	nonlinear	ADJ
ejpam-6029	48	9	integral	integral	ADJ
ejpam-6029	48	10	equations	equation	NOUN
ejpam-6029	48	11	and	and	CCONJ
ejpam-6029	48	12	boundary	boundary	ADJ
ejpam-6029	48	13	value	value	NOUN
ejpam-6029	48	14	problems	problem	NOUN
ejpam-6029	48	15	(	(	PUNCT
ejpam-6029	48	16	bvps	bvps	NOUN
ejpam-6029	48	17	)	)	PUNCT
ejpam-6029	48	18	that	that	PRON
ejpam-6029	48	19	support	support	VERB
ejpam-6029	48	20	our	our	PRON
ejpam-6029	48	21	fixed	fix	VERB
ejpam-6029	48	22	-	-	PUNCT
ejpam-6029	48	23	point	point	NOUN
ejpam-6029	48	24	theorems	theorem	NOUN
ejpam-6029	48	25	within	within	ADP
ejpam-6029	48	26	these	these	DET
ejpam-6029	48	27	new	new	ADJ
ejpam-6029	48	28	spaces	space	NOUN
ejpam-6029	48	29	.	.	PUNCT
ejpam-6029	49	1	2	2	X
ejpam-6029	49	2	.	.	X
ejpam-6029	49	3	preliminaries	preliminary	NOUN
ejpam-6029	49	4	this	this	DET
ejpam-6029	49	5	section	section	NOUN
ejpam-6029	49	6	revisits	revisit	VERB
ejpam-6029	49	7	some	some	DET
ejpam-6029	49	8	notations	notation	NOUN
ejpam-6029	49	9	basic	basic	ADJ
ejpam-6029	49	10	concepts	concept	NOUN
ejpam-6029	49	11	,	,	PUNCT
ejpam-6029	49	12	definitions	definition	NOUN
ejpam-6029	49	13	,	,	PUNCT
ejpam-6029	49	14	and	and	CCONJ
ejpam-6029	49	15	lemmas	lemma	VERB
ejpam-6029	49	16	from	from	ADP
ejpam-6029	49	17	prior	prior	ADJ
ejpam-6029	49	18	research	research	NOUN
ejpam-6029	49	19	that	that	PRON
ejpam-6029	49	20	will	will	AUX
ejpam-6029	49	21	be	be	AUX
ejpam-6029	49	22	utilized	utilize	VERB
ejpam-6029	49	23	throughout	throughout	ADP
ejpam-6029	49	24	the	the	DET
ejpam-6029	49	25	remainder	remainder	NOUN
ejpam-6029	49	26	of	of	ADP
ejpam-6029	49	27	this	this	DET
ejpam-6029	49	28	manuscript	manuscript	NOUN
ejpam-6029	49	29	.	.	PUNCT
ejpam-6029	50	1	definition	definition	NOUN
ejpam-6029	50	2	1	1	NUM
ejpam-6029	50	3	.	.	PUNCT
ejpam-6029	51	1	[	[	X
ejpam-6029	51	2	16	16	NUM
ejpam-6029	51	3	]	]	PUNCT
ejpam-6029	51	4	let	let	VERB
ejpam-6029	51	5	e	e	PRON
ejpam-6029	51	6	be	be	AUX
ejpam-6029	51	7	a	a	DET
ejpam-6029	51	8	real	real	ADJ
ejpam-6029	51	9	banach	banach	NOUN
ejpam-6029	51	10	space	space	NOUN
ejpam-6029	51	11	and	and	CCONJ
ejpam-6029	52	1	p	p	PROPN
ejpam-6029	52	2	⊂	⊂	PROPN
ejpam-6029	52	3	e.	e.	PROPN
ejpam-6029	52	4	p	p	PROPN
ejpam-6029	52	5	is	be	AUX
ejpam-6029	52	6	called	call	VERB
ejpam-6029	52	7	a	a	DET
ejpam-6029	52	8	cone	cone	NOUN
ejpam-6029	52	9	if	if	SCONJ
ejpam-6029	52	10	it	it	PRON
ejpam-6029	52	11	satisfies	satisfy	VERB
ejpam-6029	52	12	the	the	DET
ejpam-6029	52	13	following	follow	VERB
ejpam-6029	52	14	conditions	condition	NOUN
ejpam-6029	52	15	:	:	PUNCT
ejpam-6029	52	16	(	(	PUNCT
ejpam-6029	52	17	p1	p1	NOUN
ejpam-6029	52	18	)	)	PUNCT
ejpam-6029	52	19	{	{	PUNCT
ejpam-6029	52	20	0e	0e	X
ejpam-6029	52	21	}	}	PUNCT
ejpam-6029	52	22	=	=	NOUN
ejpam-6029	52	23	̸	̸	NUM
ejpam-6029	52	24	p	p	NOUN
ejpam-6029	52	25	is	be	AUX
ejpam-6029	52	26	nonempty	nonempty	ADJ
ejpam-6029	52	27	and	and	CCONJ
ejpam-6029	52	28	closed	close	VERB
ejpam-6029	52	29	,	,	PUNCT
ejpam-6029	52	30	(	(	PUNCT
ejpam-6029	52	31	p2	p2	X
ejpam-6029	52	32	)	)	PUNCT
ejpam-6029	52	33	α1a+	α1a+	NOUN
ejpam-6029	52	34	α2b	α2b	NUM
ejpam-6029	52	35	∈	∈	PROPN
ejpam-6029	52	36	p	p	NOUN
ejpam-6029	52	37	for	for	ADP
ejpam-6029	52	38	all	all	DET
ejpam-6029	52	39	a	a	PRON
ejpam-6029	52	40	,	,	PUNCT
ejpam-6029	52	41	b	b	PROPN
ejpam-6029	52	42	∈	∈	PROPN
ejpam-6029	52	43	p	p	X
ejpam-6029	52	44	,	,	PUNCT
ejpam-6029	52	45	where	where	SCONJ
ejpam-6029	52	46	α1	α1	PROPN
ejpam-6029	52	47	,	,	PUNCT
ejpam-6029	52	48	α2	α2	PROPN
ejpam-6029	52	49	≥	≥	NOUN
ejpam-6029	52	50	0	0	NUM
ejpam-6029	52	51	,	,	PUNCT
ejpam-6029	53	1	a.	a.	NOUN
ejpam-6029	53	2	a.	a.	PROPN
ejpam-6029	53	3	hijab	hijab	PROPN
ejpam-6029	53	4	et	et	PROPN
ejpam-6029	53	5	al	al	PROPN
ejpam-6029	53	6	.	.	PUNCT
ejpam-6029	53	7	/	/	SYM
ejpam-6029	53	8	eur	eur	PROPN
ejpam-6029	53	9	.	.	PUNCT
ejpam-6029	54	1	j.	j.	PROPN
ejpam-6029	54	2	pure	pure	PROPN
ejpam-6029	54	3	appl	appl	PROPN
ejpam-6029	54	4	.	.	PROPN
ejpam-6029	54	5	math	math	PROPN
ejpam-6029	54	6	,	,	PUNCT
ejpam-6029	54	7	18	18	NUM
ejpam-6029	54	8	(	(	PUNCT
ejpam-6029	54	9	2	2	NUM
ejpam-6029	54	10	)	)	PUNCT
ejpam-6029	54	11	(	(	PUNCT
ejpam-6029	54	12	2025	2025	NUM
ejpam-6029	54	13	)	)	PUNCT
ejpam-6029	54	14	,	,	PUNCT
ejpam-6029	54	15	6029	6029	NUM
ejpam-6029	54	16	3	3	NUM
ejpam-6029	54	17	of	of	ADP
ejpam-6029	54	18	23	23	NUM
ejpam-6029	54	19	(	(	PUNCT
ejpam-6029	54	20	p3	p3	NOUN
ejpam-6029	54	21	)	)	PUNCT
ejpam-6029	54	22	p	p	NOUN
ejpam-6029	54	23	∩	∩	NOUN
ejpam-6029	54	24	(	(	PUNCT
ejpam-6029	54	25	−p	−p	NOUN
ejpam-6029	54	26	)	)	PUNCT
ejpam-6029	54	27	=	=	PUNCT
ejpam-6029	54	28	{	{	PUNCT
ejpam-6029	54	29	0e	0e	NOUN
ejpam-6029	54	30	}	}	PUNCT
ejpam-6029	54	31	,	,	PUNCT
ejpam-6029	54	32	where	where	SCONJ
ejpam-6029	54	33	0e	0e	PROPN
ejpam-6029	54	34	is	be	AUX
ejpam-6029	54	35	the	the	DET
ejpam-6029	54	36	zero	zero	NUM
ejpam-6029	54	37	element	element	NOUN
ejpam-6029	54	38	of	of	ADP
ejpam-6029	54	39	e.	e.	PROPN
ejpam-6029	54	40	consider	consider	VERB
ejpam-6029	54	41	a	a	DET
ejpam-6029	54	42	cone	cone	NOUN
ejpam-6029	54	43	p	p	NOUN
ejpam-6029	54	44	,	,	PUNCT
ejpam-6029	54	45	we	we	PRON
ejpam-6029	54	46	can	can	AUX
ejpam-6029	54	47	define	define	VERB
ejpam-6029	54	48	a	a	DET
ejpam-6029	54	49	partial	partial	ADJ
ejpam-6029	54	50	ordering	ordering	NOUN
ejpam-6029	54	51	⪯	⪯	NOUN
ejpam-6029	54	52	on	on	ADP
ejpam-6029	54	53	e	e	NOUN
ejpam-6029	54	54	with	with	ADP
ejpam-6029	54	55	respect	respect	NOUN
ejpam-6029	54	56	to	to	ADP
ejpam-6029	54	57	p	p	NOUN
ejpam-6029	54	58	by	by	ADP
ejpam-6029	54	59	a	a	DET
ejpam-6029	54	60	⪯	⪯	NOUN
ejpam-6029	54	61	b	b	NOUN
ejpam-6029	54	62	if	if	SCONJ
ejpam-6029	55	1	and	and	CCONJ
ejpam-6029	55	2	only	only	ADV
ejpam-6029	55	3	if	if	SCONJ
ejpam-6029	55	4	b	b	X
ejpam-6029	55	5	−	−	NOUN
ejpam-6029	55	6	a	a	DET
ejpam-6029	55	7	∈	∈	PROPN
ejpam-6029	55	8	p	p	NOUN
ejpam-6029	55	9	.	.	PUNCT
ejpam-6029	56	1	here	here	ADV
ejpam-6029	56	2	,	,	PUNCT
ejpam-6029	56	3	a	a	DET
ejpam-6029	56	4	≺	≺	NOUN
ejpam-6029	56	5	b	b	NOUN
ejpam-6029	56	6	indicates	indicate	VERB
ejpam-6029	56	7	that	that	SCONJ
ejpam-6029	56	8	a	a	DET
ejpam-6029	56	9	⪯	⪯	NOUN
ejpam-6029	56	10	b	b	NOUN
ejpam-6029	56	11	and	and	CCONJ
ejpam-6029	56	12	a	a	DET
ejpam-6029	56	13	̸=	̸=	PROPN
ejpam-6029	56	14	b	b	NUM
ejpam-6029	56	15	,	,	PUNCT
ejpam-6029	56	16	but	but	CCONJ
ejpam-6029	56	17	a	a	DET
ejpam-6029	56	18	≪	≪	PUNCT
ejpam-6029	56	19	b	b	NOUN
ejpam-6029	56	20	stands	stand	VERB
ejpam-6029	56	21	for	for	ADP
ejpam-6029	56	22	b−	b−	PROPN
ejpam-6029	56	23	a	a	DET
ejpam-6029	56	24	∈	∈	PROPN
ejpam-6029	56	25	intp	intp	NOUN
ejpam-6029	56	26	,	,	PUNCT
ejpam-6029	56	27	such	such	ADJ
ejpam-6029	56	28	that	that	SCONJ
ejpam-6029	56	29	intp	intp	PROPN
ejpam-6029	56	30	denotes	denote	VERB
ejpam-6029	56	31	the	the	DET
ejpam-6029	56	32	interior	interior	NOUN
ejpam-6029	56	33	of	of	ADP
ejpam-6029	56	34	p	p	PROPN
ejpam-6029	56	35	.	.	PUNCT
ejpam-6029	57	1	let	let	VERB
ejpam-6029	57	2	e	e	PRON
ejpam-6029	57	3	be	be	AUX
ejpam-6029	57	4	a	a	DET
ejpam-6029	57	5	banach	banach	NOUN
ejpam-6029	57	6	space	space	NOUN
ejpam-6029	57	7	,	,	PUNCT
ejpam-6029	57	8	p	p	PROPN
ejpam-6029	57	9	be	be	AUX
ejpam-6029	57	10	a	a	DET
ejpam-6029	57	11	cone	cone	NOUN
ejpam-6029	57	12	in	in	ADP
ejpam-6029	57	13	e	e	NOUN
ejpam-6029	57	14	such	such	ADJ
ejpam-6029	57	15	as	as	ADP
ejpam-6029	57	16	intp	intp	PROPN
ejpam-6029	57	17	̸=	̸=	PROPN
ejpam-6029	57	18	ϕ	ϕ	PROPN
ejpam-6029	57	19	and	and	CCONJ
ejpam-6029	57	20	⪯	⪯	NOUN
ejpam-6029	57	21	is	be	AUX
ejpam-6029	57	22	the	the	DET
ejpam-6029	57	23	partial	partial	ADJ
ejpam-6029	57	24	ordering	ordering	NOUN
ejpam-6029	57	25	of	of	ADP
ejpam-6029	57	26	p	p	NOUN
ejpam-6029	57	27	.	.	PUNCT
ejpam-6029	58	1	the	the	DET
ejpam-6029	58	2	cone	cone	NOUN
ejpam-6029	58	3	p	p	NOUN
ejpam-6029	58	4	is	be	AUX
ejpam-6029	58	5	called	call	VERB
ejpam-6029	58	6	normal	normal	ADJ
ejpam-6029	58	7	if	if	SCONJ
ejpam-6029	58	8	there	there	PRON
ejpam-6029	58	9	exists	exist	VERB
ejpam-6029	58	10	a	a	DET
ejpam-6029	58	11	constant	constant	ADJ
ejpam-6029	58	12	number	number	NOUN
ejpam-6029	58	13	m	m	VERB
ejpam-6029	58	14	>	>	X
ejpam-6029	58	15	0	0	NUM
ejpam-6029	58	16	such	such	ADJ
ejpam-6029	58	17	that	that	PRON
ejpam-6029	58	18	for	for	SCONJ
ejpam-6029	58	19	all	all	DET
ejpam-6029	58	20	a	a	PRON
ejpam-6029	58	21	,	,	PUNCT
ejpam-6029	58	22	b	b	X
ejpam-6029	58	23	∈	∈	PROPN
ejpam-6029	58	24	e	e	NOUN
ejpam-6029	58	25	and	and	CCONJ
ejpam-6029	58	26	0e	0e	PROPN
ejpam-6029	58	27	⪯	⪯	VERB
ejpam-6029	58	28	a	a	DET
ejpam-6029	58	29	⪯	⪯	NOUN
ejpam-6029	58	30	b⇒	b⇒	PROPN
ejpam-6029	58	31	∥a∥	∥a∥	PROPN
ejpam-6029	58	32	≤m∥b∥	≤m∥b∥	PUNCT
ejpam-6029	58	33	it	it	PRON
ejpam-6029	58	34	holds	hold	VERB
ejpam-6029	58	35	or	or	CCONJ
ejpam-6029	58	36	equivalently	equivalently	ADV
ejpam-6029	58	37	,	,	PUNCT
ejpam-6029	58	38	if	if	SCONJ
ejpam-6029	58	39	inf{∥a+	inf{∥a+	ADJ
ejpam-6029	58	40	b∥	b∥	NOUN
ejpam-6029	58	41	:	:	PUNCT
ejpam-6029	58	42	a	a	X
ejpam-6029	58	43	,	,	PUNCT
ejpam-6029	58	44	b	b	PROPN
ejpam-6029	58	45	∈	∈	PROPN
ejpam-6029	58	46	p	p	NOUN
ejpam-6029	58	47	,	,	PUNCT
ejpam-6029	58	48	∥a∥	∥a∥	ADJ
ejpam-6029	58	49	=	=	SYM
ejpam-6029	58	50	∥b∥	∥b∥	VERB
ejpam-6029	58	51	=	=	SYM
ejpam-6029	58	52	1	1	X
ejpam-6029	58	53	}	}	PUNCT
ejpam-6029	58	54	>	>	X
ejpam-6029	58	55	0	0	X
ejpam-6029	58	56	.	.	PUNCT
ejpam-6029	59	1	for	for	ADP
ejpam-6029	59	2	a	a	DET
ejpam-6029	59	3	non	non	ADJ
ejpam-6029	59	4	-	-	ADJ
ejpam-6029	59	5	normal	normal	ADJ
ejpam-6029	59	6	cone	cone	NOUN
ejpam-6029	59	7	(	(	PUNCT
ejpam-6029	59	8	see	see	VERB
ejpam-6029	59	9	[	[	X
ejpam-6029	59	10	18	18	NUM
ejpam-6029	59	11	]	]	NUM
ejpam-6029	59	12	)	)	PUNCT
ejpam-6029	59	13	.	.	PUNCT
ejpam-6029	60	1	moreover	moreover	ADV
ejpam-6029	60	2	,	,	PUNCT
ejpam-6029	60	3	p	p	NOUN
ejpam-6029	60	4	is	be	AUX
ejpam-6029	60	5	called	call	VERB
ejpam-6029	60	6	a	a	DET
ejpam-6029	60	7	solid	solid	ADJ
ejpam-6029	60	8	if	if	SCONJ
ejpam-6029	60	9	intp	intp	PROPN
ejpam-6029	60	10	̸=	̸=	PROPN
ejpam-6029	60	11	ϕ.	ϕ.	VERB
ejpam-6029	60	12	now	now	ADV
ejpam-6029	60	13	,	,	PUNCT
ejpam-6029	60	14	we	we	PRON
ejpam-6029	60	15	present	present	VERB
ejpam-6029	60	16	some	some	DET
ejpam-6029	60	17	basic	basic	ADJ
ejpam-6029	60	18	notations	notation	NOUN
ejpam-6029	60	19	of	of	ADP
ejpam-6029	60	20	cone	cone	NOUN
ejpam-6029	60	21	b	b	X
ejpam-6029	60	22	-	-	PUNCT
ejpam-6029	60	23	metric	metric	ADJ
ejpam-6029	60	24	spaces	space	NOUN
ejpam-6029	60	25	and	and	CCONJ
ejpam-6029	60	26	their	their	PRON
ejpam-6029	60	27	properties	property	NOUN
ejpam-6029	60	28	.	.	PUNCT
ejpam-6029	61	1	definition	definition	NOUN
ejpam-6029	61	2	2	2	NUM
ejpam-6029	61	3	.	.	PUNCT
ejpam-6029	62	1	[	[	X
ejpam-6029	62	2	17	17	NUM
ejpam-6029	62	3	]	]	PUNCT
ejpam-6029	62	4	let	let	VERB
ejpam-6029	62	5	γ	γ	X
ejpam-6029	62	6	be	be	AUX
ejpam-6029	62	7	a	a	DET
ejpam-6029	62	8	non	non	ADJ
ejpam-6029	62	9	-	-	ADJ
ejpam-6029	62	10	empty	empty	ADJ
ejpam-6029	62	11	set	set	NOUN
ejpam-6029	62	12	and	and	CCONJ
ejpam-6029	62	13	s	s	NOUN
ejpam-6029	62	14	≥	≥	NOUN
ejpam-6029	62	15	1	1	NUM
ejpam-6029	62	16	.	.	PUNCT
ejpam-6029	62	17	assume	assume	VERB
ejpam-6029	62	18	that	that	SCONJ
ejpam-6029	62	19	a	a	DET
ejpam-6029	62	20	mapping	mapping	NOUN
ejpam-6029	62	21	db	db	X
ejpam-6029	62	22	:	:	PUNCT
ejpam-6029	62	23	γ×	γ×	PROPN
ejpam-6029	62	24	γ	γ	X
ejpam-6029	62	25	→	→	SYM
ejpam-6029	62	26	e	e	NOUN
ejpam-6029	62	27	satisfies	satisfy	VERB
ejpam-6029	62	28	the	the	DET
ejpam-6029	62	29	following	follow	VERB
ejpam-6029	62	30	conditions	condition	NOUN
ejpam-6029	62	31	:	:	PUNCT
ejpam-6029	62	32	for	for	ADP
ejpam-6029	62	33	all	all	DET
ejpam-6029	62	34	a	a	DET
ejpam-6029	62	35	,	,	PUNCT
ejpam-6029	62	36	b	b	NOUN
ejpam-6029	62	37	,	,	PUNCT
ejpam-6029	62	38	c	c	PROPN
ejpam-6029	62	39	∈	∈	PROPN
ejpam-6029	62	40	γ	γ	X
ejpam-6029	62	41	,	,	PUNCT
ejpam-6029	62	42	(	(	PUNCT
ejpam-6029	62	43	cb1	cb1	PROPN
ejpam-6029	62	44	)	)	PUNCT
ejpam-6029	62	45	db(a	db(a	PROPN
ejpam-6029	62	46	,	,	PUNCT
ejpam-6029	62	47	b	b	NOUN
ejpam-6029	62	48	)	)	PUNCT
ejpam-6029	63	1	=	=	SYM
ejpam-6029	63	2	0e	0e	NOUN
ejpam-6029	63	3	if	if	SCONJ
ejpam-6029	63	4	and	and	CCONJ
ejpam-6029	63	5	only	only	ADV
ejpam-6029	63	6	if	if	SCONJ
ejpam-6029	63	7	a	a	DET
ejpam-6029	63	8	=	=	SYM
ejpam-6029	63	9	b	b	NOUN
ejpam-6029	63	10	,	,	PUNCT
ejpam-6029	63	11	(	(	PUNCT
ejpam-6029	63	12	cb2	cb2	NOUN
ejpam-6029	63	13	)	)	PUNCT
ejpam-6029	63	14	db(a	db(a	PROPN
ejpam-6029	63	15	,	,	PUNCT
ejpam-6029	63	16	b	b	NOUN
ejpam-6029	63	17	)	)	PUNCT
ejpam-6029	63	18	=	=	NOUN
ejpam-6029	63	19	db(b	db(b	NOUN
ejpam-6029	63	20	,	,	PUNCT
ejpam-6029	63	21	a	a	PRON
ejpam-6029	63	22	)	)	PUNCT
ejpam-6029	63	23	,	,	PUNCT
ejpam-6029	63	24	(	(	PUNCT
ejpam-6029	63	25	cb3	cb3	NOUN
ejpam-6029	63	26	)	)	PUNCT
ejpam-6029	63	27	db(a	db(a	NOUN
ejpam-6029	63	28	,	,	PUNCT
ejpam-6029	63	29	b	b	X
ejpam-6029	63	30	)	)	PUNCT
ejpam-6029	63	31	⪯	⪯	NOUN
ejpam-6029	63	32	s	s	PART
ejpam-6029	63	33	(	(	PUNCT
ejpam-6029	63	34	db(a	db(a	NOUN
ejpam-6029	63	35	,	,	PUNCT
ejpam-6029	63	36	c	c	NOUN
ejpam-6029	63	37	)	)	PUNCT
ejpam-6029	64	1	+	+	CCONJ
ejpam-6029	64	2	db(c	db(c	NOUN
ejpam-6029	64	3	,	,	PUNCT
ejpam-6029	64	4	a	a	PRON
ejpam-6029	64	5	)	)	PUNCT
ejpam-6029	64	6	)	)	PUNCT
ejpam-6029	64	7	.	.	PUNCT
ejpam-6029	65	1	the	the	DET
ejpam-6029	65	2	pair	pair	NOUN
ejpam-6029	65	3	(	(	PUNCT
ejpam-6029	65	4	γ	γ	X
ejpam-6029	65	5	,	,	PUNCT
ejpam-6029	65	6	db	db	PROPN
ejpam-6029	65	7	)	)	PUNCT
ejpam-6029	65	8	is	be	AUX
ejpam-6029	65	9	called	call	VERB
ejpam-6029	65	10	a	a	DET
ejpam-6029	65	11	cone	cone	NOUN
ejpam-6029	65	12	b	b	NOUN
ejpam-6029	65	13	-	-	PUNCT
ejpam-6029	65	14	metric	metric	ADJ
ejpam-6029	65	15	space	space	NOUN
ejpam-6029	65	16	.	.	PUNCT
ejpam-6029	66	1	if	if	SCONJ
ejpam-6029	66	2	changing	change	VERB
ejpam-6029	66	3	condition	condition	NOUN
ejpam-6029	66	4	(	(	PUNCT
ejpam-6029	66	5	cb1	cb1	PROPN
ejpam-6029	66	6	)	)	PUNCT
ejpam-6029	66	7	in	in	ADP
ejpam-6029	66	8	definition	definition	NOUN
ejpam-6029	66	9	2	2	NUM
ejpam-6029	66	10	to	to	ADP
ejpam-6029	66	11	db(a	db(a	NOUN
ejpam-6029	66	12	,	,	PUNCT
ejpam-6029	66	13	b	b	NOUN
ejpam-6029	66	14	)	)	PUNCT
ejpam-6029	66	15	=	=	SYM
ejpam-6029	66	16	0e	0e	NOUN
ejpam-6029	66	17	,	,	PUNCT
ejpam-6029	66	18	implies	imply	VERB
ejpam-6029	66	19	a	a	DET
ejpam-6029	66	20	=	=	SYM
ejpam-6029	66	21	b	b	NOUN
ejpam-6029	66	22	,	,	PUNCT
ejpam-6029	66	23	then	then	ADV
ejpam-6029	66	24	(	(	PUNCT
ejpam-6029	66	25	γ	γ	X
ejpam-6029	66	26	,	,	PUNCT
ejpam-6029	66	27	db	db	PROPN
ejpam-6029	66	28	)	)	PUNCT
ejpam-6029	66	29	is	be	AUX
ejpam-6029	66	30	called	call	VERB
ejpam-6029	66	31	a	a	DET
ejpam-6029	66	32	cone	cone	NOUN
ejpam-6029	66	33	b	b	X
ejpam-6029	66	34	-	-	PUNCT
ejpam-6029	66	35	metric	metric	ADJ
ejpam-6029	66	36	-	-	PUNCT
ejpam-6029	66	37	like	like	ADJ
ejpam-6029	66	38	space	space	NOUN
ejpam-6029	66	39	.	.	PUNCT
ejpam-6029	67	1	obviously	obviously	ADV
ejpam-6029	67	2	,	,	PUNCT
ejpam-6029	67	3	cone	cone	NOUN
ejpam-6029	67	4	b	b	X
ejpam-6029	67	5	-	-	PUNCT
ejpam-6029	67	6	metric	metric	ADJ
ejpam-6029	67	7	-	-	PUNCT
ejpam-6029	67	8	like	like	ADJ
ejpam-6029	67	9	spaces	space	NOUN
ejpam-6029	67	10	are	be	AUX
ejpam-6029	67	11	generalized	generalize	VERB
ejpam-6029	67	12	to	to	ADP
ejpam-6029	67	13	cone	cone	NOUN
ejpam-6029	67	14	b	b	X
ejpam-6029	67	15	-	-	PUNCT
ejpam-6029	67	16	metric	metric	ADJ
ejpam-6029	67	17	spaces	space	NOUN
ejpam-6029	67	18	,	,	PUNCT
ejpam-6029	67	19	cone	cone	NOUN
ejpam-6029	67	20	metric	metric	ADJ
ejpam-6029	67	21	-	-	PUNCT
ejpam-6029	67	22	like	like	ADJ
ejpam-6029	67	23	spaces	space	NOUN
ejpam-6029	67	24	,	,	PUNCT
ejpam-6029	67	25	cone	cone	NOUN
ejpam-6029	67	26	metric	metric	ADJ
ejpam-6029	67	27	spaces	space	NOUN
ejpam-6029	67	28	and	and	CCONJ
ejpam-6029	67	29	metric	metric	ADJ
ejpam-6029	67	30	spaces	space	NOUN
ejpam-6029	67	31	,	,	PUNCT
ejpam-6029	67	32	respectively	respectively	ADV
ejpam-6029	67	33	,	,	PUNCT
ejpam-6029	67	34	but	but	CCONJ
ejpam-6029	67	35	the	the	DET
ejpam-6029	67	36	same	same	ADJ
ejpam-6029	67	37	is	be	AUX
ejpam-6029	67	38	not	not	PART
ejpam-6029	67	39	true	true	ADJ
ejpam-6029	67	40	vice	vice	NOUN
ejpam-6029	67	41	versa	versa	ADV
ejpam-6029	67	42	(	(	PUNCT
ejpam-6029	67	43	see	see	VERB
ejpam-6029	67	44	[	[	X
ejpam-6029	67	45	17	17	NUM
ejpam-6029	67	46	,	,	PUNCT
ejpam-6029	67	47	19	19	NUM
ejpam-6029	67	48	,	,	PUNCT
ejpam-6029	67	49	21–25	21–25	NUM
ejpam-6029	67	50	,	,	PUNCT
ejpam-6029	67	51	27	27	NUM
ejpam-6029	67	52	]	]	NUM
ejpam-6029	67	53	)	)	PUNCT
ejpam-6029	67	54	.	.	PUNCT
ejpam-6029	68	1	abdeljawad	abdeljawad	NOUN
ejpam-6029	68	2	et	et	PROPN
ejpam-6029	68	3	al	al	PROPN
ejpam-6029	68	4	.	.	PUNCT
ejpam-6029	69	1	[	[	X
ejpam-6029	69	2	7	7	X
ejpam-6029	69	3	]	]	PUNCT
ejpam-6029	69	4	introduced	introduce	VERB
ejpam-6029	69	5	double	double	ADJ
ejpam-6029	69	6	-	-	PUNCT
ejpam-6029	69	7	controlled	control	VERB
ejpam-6029	69	8	type	type	NOUN
ejpam-6029	69	9	-	-	PUNCT
ejpam-6029	69	10	metric	metric	ADJ
ejpam-6029	69	11	spaces	space	NOUN
ejpam-6029	69	12	.	.	PUNCT
ejpam-6029	70	1	mlaiki	mlaiki	PROPN
ejpam-6029	70	2	et	et	PROPN
ejpam-6029	70	3	al	al	PROPN
ejpam-6029	70	4	.	.	PUNCT
ejpam-6029	71	1	[	[	X
ejpam-6029	71	2	13	13	NUM
ejpam-6029	71	3	]	]	X
ejpam-6029	71	4	generalized	generalized	ADJ
ejpam-6029	71	5	double	double	ADJ
ejpam-6029	71	6	-	-	PUNCT
ejpam-6029	71	7	controlled	control	VERB
ejpam-6029	71	8	metric	metric	ADJ
ejpam-6029	71	9	-	-	PUNCT
ejpam-6029	71	10	type	type	NOUN
ejpam-6029	71	11	spaces	space	NOUN
ejpam-6029	71	12	(	(	PUNCT
ejpam-6029	71	13	dcmts	dcmts	PROPN
ejpam-6029	71	14	)	)	PUNCT
ejpam-6029	71	15	to	to	ADP
ejpam-6029	71	16	double	double	ADV
ejpam-6029	71	17	-	-	PUNCT
ejpam-6029	71	18	controlled	control	VERB
ejpam-6029	71	19	metric	metric	ADJ
ejpam-6029	71	20	-	-	PUNCT
ejpam-6029	71	21	like	like	ADJ
ejpam-6029	71	22	spaces	space	NOUN
ejpam-6029	71	23	(	(	PUNCT
ejpam-6029	71	24	dcmls	dcmls	NOUN
ejpam-6029	71	25	)	)	PUNCT
ejpam-6029	71	26	.	.	PUNCT
ejpam-6029	72	1	moreover	moreover	ADV
ejpam-6029	72	2	,	,	PUNCT
ejpam-6029	72	3	we	we	PRON
ejpam-6029	72	4	expand	expand	VERB
ejpam-6029	72	5	on	on	ADP
ejpam-6029	72	6	the	the	DET
ejpam-6029	72	7	expanded	expand	VERB
ejpam-6029	72	8	on	on	ADP
ejpam-6029	72	9	cone	cone	NOUN
ejpam-6029	72	10	metric	metric	ADJ
ejpam-6029	72	11	space	space	NOUN
ejpam-6029	72	12	as	as	SCONJ
ejpam-6029	72	13	follows	follow	VERB
ejpam-6029	72	14	:	:	PUNCT
ejpam-6029	72	15	definition	definition	NOUN
ejpam-6029	72	16	3	3	NUM
ejpam-6029	72	17	.	.	PUNCT
ejpam-6029	73	1	[	[	X
ejpam-6029	73	2	18	18	NUM
ejpam-6029	73	3	]	]	PUNCT
ejpam-6029	73	4	consider	consider	VERB
ejpam-6029	73	5	a	a	DET
ejpam-6029	73	6	set	set	NOUN
ejpam-6029	73	7	γ	γ	PROPN
ejpam-6029	73	8	̸=	̸=	PROPN
ejpam-6029	73	9	ϕ	ϕ	PROPN
ejpam-6029	73	10	and	and	CCONJ
ejpam-6029	73	11	non	non	ADJ
ejpam-6029	73	12	-	-	ADJ
ejpam-6029	73	13	comparable	comparable	ADJ
ejpam-6029	73	14	functions	function	NOUN
ejpam-6029	73	15	ω1	ω1	PROPN
ejpam-6029	73	16	,	,	PUNCT
ejpam-6029	73	17	ω2	ω2	ADJ
ejpam-6029	73	18	:	:	PUNCT
ejpam-6029	73	19	γ×	γ×	PROPN
ejpam-6029	73	20	γ	γ	X
ejpam-6029	73	21	→	→	SYM
ejpam-6029	73	22	[	[	X
ejpam-6029	73	23	1,∞	1,∞	NUM
ejpam-6029	73	24	)	)	PUNCT
ejpam-6029	73	25	.	.	PUNCT
ejpam-6029	74	1	assume	assume	VERB
ejpam-6029	74	2	that	that	SCONJ
ejpam-6029	74	3	a	a	DET
ejpam-6029	74	4	mapping	mapping	NOUN
ejpam-6029	74	5	σ	σ	NOUN
ejpam-6029	74	6	:	:	PUNCT
ejpam-6029	74	7	γ	γ	X
ejpam-6029	74	8	×	×	NOUN
ejpam-6029	74	9	γ	γ	X
ejpam-6029	74	10	→	→	SYM
ejpam-6029	74	11	e	e	NOUN
ejpam-6029	74	12	satisfies	satisfy	VERB
ejpam-6029	74	13	the	the	DET
ejpam-6029	74	14	conditions	condition	NOUN
ejpam-6029	74	15	below	below	ADV
ejpam-6029	74	16	:	:	PUNCT
ejpam-6029	74	17	for	for	ADP
ejpam-6029	74	18	all	all	DET
ejpam-6029	74	19	a	a	DET
ejpam-6029	74	20	,	,	PUNCT
ejpam-6029	74	21	b	b	NOUN
ejpam-6029	74	22	,	,	PUNCT
ejpam-6029	74	23	c	c	PROPN
ejpam-6029	74	24	∈	∈	PROPN
ejpam-6029	74	25	γ	γ	X
ejpam-6029	74	26	,	,	PUNCT
ejpam-6029	74	27	(	(	PUNCT
ejpam-6029	74	28	c1	c1	NOUN
ejpam-6029	74	29	)	)	PUNCT
ejpam-6029	74	30	σ(a	σ(a	PROPN
ejpam-6029	74	31	,	,	PUNCT
ejpam-6029	74	32	b	b	NOUN
ejpam-6029	74	33	)	)	PUNCT
ejpam-6029	75	1	=	=	NOUN
ejpam-6029	75	2	0e	0e	NOUN
ejpam-6029	75	3	implies	imply	VERB
ejpam-6029	75	4	a	a	DET
ejpam-6029	75	5	=	=	SYM
ejpam-6029	75	6	b	b	PROPN
ejpam-6029	75	7	,	,	PUNCT
ejpam-6029	75	8	(	(	PUNCT
ejpam-6029	75	9	c2	c2	PROPN
ejpam-6029	75	10	)	)	PUNCT
ejpam-6029	75	11	σ(a	σ(a	PROPN
ejpam-6029	75	12	,	,	PUNCT
ejpam-6029	75	13	b	b	NOUN
ejpam-6029	75	14	)	)	PUNCT
ejpam-6029	75	15	=	=	SYM
ejpam-6029	75	16	σ(b	σ(b	PROPN
ejpam-6029	75	17	,	,	PUNCT
ejpam-6029	75	18	a	a	PRON
ejpam-6029	75	19	)	)	PUNCT
ejpam-6029	75	20	,	,	PUNCT
ejpam-6029	75	21	(	(	PUNCT
ejpam-6029	75	22	c3	c3	PROPN
ejpam-6029	75	23	)	)	PUNCT
ejpam-6029	75	24	σ(a	σ(a	PROPN
ejpam-6029	75	25	,	,	PUNCT
ejpam-6029	75	26	b	b	NOUN
ejpam-6029	75	27	)	)	PUNCT
ejpam-6029	75	28	⪯	⪯	NOUN
ejpam-6029	75	29	ω1(a	ω1(a	PRON
ejpam-6029	75	30	,	,	PUNCT
ejpam-6029	75	31	c)σ(a	c)σ(a	NOUN
ejpam-6029	75	32	,	,	PUNCT
ejpam-6029	75	33	c	c	NOUN
ejpam-6029	75	34	)	)	PUNCT
ejpam-6029	76	1	+	+	CCONJ
ejpam-6029	76	2	ω2(c	ω2(c	NUM
ejpam-6029	76	3	,	,	PUNCT
ejpam-6029	76	4	b)σ(c	b)σ(c	ADJ
ejpam-6029	76	5	,	,	PUNCT
ejpam-6029	76	6	b	b	NOUN
ejpam-6029	76	7	)	)	PUNCT
ejpam-6029	76	8	.	.	PUNCT
ejpam-6029	77	1	the	the	DET
ejpam-6029	77	2	pair	pair	NOUN
ejpam-6029	77	3	(	(	PUNCT
ejpam-6029	77	4	γ	γ	X
ejpam-6029	77	5	,	,	PUNCT
ejpam-6029	77	6	σ	σ	PROPN
ejpam-6029	77	7	)	)	PUNCT
ejpam-6029	77	8	is	be	AUX
ejpam-6029	77	9	referred	refer	VERB
ejpam-6029	77	10	to	to	ADP
ejpam-6029	77	11	as	as	ADP
ejpam-6029	77	12	a	a	DET
ejpam-6029	77	13	double	double	ADJ
ejpam-6029	77	14	controlled	control	VERB
ejpam-6029	77	15	cone	cone	NOUN
ejpam-6029	77	16	-	-	PUNCT
ejpam-6029	77	17	metric	metric	ADJ
ejpam-6029	77	18	-	-	PUNCT
ejpam-6029	77	19	like	like	ADJ
ejpam-6029	77	20	space	space	NOUN
ejpam-6029	77	21	(	(	PUNCT
ejpam-6029	77	22	dccmls	dccmls	PROPN
ejpam-6029	77	23	)	)	PUNCT
ejpam-6029	77	24	(	(	PUNCT
ejpam-6029	77	25	see	see	VERB
ejpam-6029	77	26	[	[	X
ejpam-6029	77	27	18	18	NUM
ejpam-6029	77	28	,	,	PUNCT
ejpam-6029	77	29	26	26	NUM
ejpam-6029	77	30	,	,	PUNCT
ejpam-6029	77	31	28	28	NUM
ejpam-6029	77	32	,	,	PUNCT
ejpam-6029	77	33	35	35	NUM
ejpam-6029	77	34	]	]	PUNCT
ejpam-6029	77	35	)	)	PUNCT
ejpam-6029	77	36	.	.	PUNCT
ejpam-6029	78	1	a.	a.	PROPN
ejpam-6029	78	2	a.	a.	PROPN
ejpam-6029	78	3	hijab	hijab	PROPN
ejpam-6029	78	4	et	et	PROPN
ejpam-6029	78	5	al	al	PROPN
ejpam-6029	78	6	.	.	PUNCT
ejpam-6029	78	7	/	/	SYM
ejpam-6029	78	8	eur	eur	PROPN
ejpam-6029	78	9	.	.	PUNCT
ejpam-6029	79	1	j.	j.	PROPN
ejpam-6029	79	2	pure	pure	PROPN
ejpam-6029	79	3	appl	appl	PROPN
ejpam-6029	79	4	.	.	PROPN
ejpam-6029	79	5	math	math	PROPN
ejpam-6029	79	6	,	,	PUNCT
ejpam-6029	79	7	18	18	NUM
ejpam-6029	79	8	(	(	PUNCT
ejpam-6029	79	9	2	2	NUM
ejpam-6029	79	10	)	)	PUNCT
ejpam-6029	79	11	(	(	PUNCT
ejpam-6029	79	12	2025	2025	NUM
ejpam-6029	79	13	)	)	PUNCT
ejpam-6029	79	14	,	,	PUNCT
ejpam-6029	79	15	6029	6029	NUM
ejpam-6029	79	16	4	4	NUM
ejpam-6029	79	17	of	of	ADP
ejpam-6029	79	18	23	23	NUM
ejpam-6029	79	19	ayoob	ayoob	NOUN
ejpam-6029	79	20	et	et	PROPN
ejpam-6029	79	21	al	al	PROPN
ejpam-6029	79	22	.	.	PUNCT
ejpam-6029	80	1	[	[	X
ejpam-6029	80	2	15	15	NUM
ejpam-6029	80	3	]	]	PUNCT
ejpam-6029	80	4	introduced	introduce	VERB
ejpam-6029	80	5	generalizations	generalization	NOUN
ejpam-6029	80	6	of	of	ADP
ejpam-6029	80	7	dcmts	dcmts	NOUN
ejpam-6029	80	8	and	and	CCONJ
ejpam-6029	80	9	named	name	VERB
ejpam-6029	80	10	it	it	PRON
ejpam-6029	80	11	a	a	DET
ejpam-6029	80	12	doublecomposed	doublecompose	VERB
ejpam-6029	80	13	metric	metric	ADJ
ejpam-6029	80	14	space	space	NOUN
ejpam-6029	80	15	(	(	PUNCT
ejpam-6029	80	16	abbreviated	abbreviate	VERB
ejpam-6029	80	17	as	as	ADP
ejpam-6029	80	18	dcms	dcms	NOUN
ejpam-6029	80	19	)	)	PUNCT
ejpam-6029	80	20	.	.	PUNCT
ejpam-6029	81	1	in	in	ADP
ejpam-6029	81	2	the	the	DET
ejpam-6029	81	3	same	same	ADJ
ejpam-6029	81	4	vein	vein	NOUN
ejpam-6029	81	5	,	,	PUNCT
ejpam-6029	81	6	anas	anas	PROPN
ejpam-6029	81	7	et	et	PROPN
ejpam-6029	81	8	al	al	PROPN
ejpam-6029	81	9	.	.	PUNCT
ejpam-6029	82	1	[	[	X
ejpam-6029	82	2	19	19	NUM
ejpam-6029	82	3	]	]	PUNCT
ejpam-6029	82	4	extended	extended	ADJ
ejpam-6029	82	5	dcms	dcms	NOUN
ejpam-6029	82	6	to	to	ADP
ejpam-6029	82	7	a	a	DET
ejpam-6029	82	8	type	type	NOUN
ejpam-6029	82	9	ii	ii	NOUN
ejpam-6029	82	10	composed	compose	VERB
ejpam-6029	82	11	cone	cone	NOUN
ejpam-6029	82	12	-	-	PUNCT
ejpam-6029	82	13	metric	metric	ADJ
ejpam-6029	82	14	space	space	NOUN
ejpam-6029	82	15	(	(	PUNCT
ejpam-6029	82	16	c2cms	c2cms	NUM
ejpam-6029	82	17	)	)	PUNCT
ejpam-6029	82	18	and	and	CCONJ
ejpam-6029	82	19	[	[	X
ejpam-6029	82	20	20	20	NUM
ejpam-6029	82	21	]	]	PUNCT
ejpam-6029	82	22	further	far	ADV
ejpam-6029	82	23	generalized	generalize	VERB
ejpam-6029	82	24	dcms	dcms	NOUN
ejpam-6029	82	25	to	to	ADP
ejpam-6029	82	26	a	a	DET
ejpam-6029	82	27	double	double	ADJ
ejpam-6029	82	28	composed	compose	VERB
ejpam-6029	82	29	metric	metric	ADJ
ejpam-6029	82	30	-	-	PUNCT
ejpam-6029	82	31	like	like	ADJ
ejpam-6029	82	32	space	space	NOUN
ejpam-6029	82	33	known	know	VERB
ejpam-6029	82	34	as	as	ADP
ejpam-6029	82	35	dcml	dcml	NOUN
ejpam-6029	82	36	-	-	PUNCT
ejpam-6029	82	37	space	space	NOUN
ejpam-6029	82	38	.	.	PUNCT
ejpam-6029	83	1	in	in	ADP
ejpam-6029	83	2	this	this	DET
ejpam-6029	83	3	context	context	NOUN
ejpam-6029	83	4	,	,	PUNCT
ejpam-6029	83	5	we	we	PRON
ejpam-6029	83	6	present	present	VERB
ejpam-6029	83	7	the	the	DET
ejpam-6029	83	8	double	double	ADJ
ejpam-6029	83	9	composed	compose	VERB
ejpam-6029	83	10	cone	cone	NOUN
ejpam-6029	83	11	-	-	PUNCT
ejpam-6029	83	12	metric	metric	ADJ
ejpam-6029	83	13	-	-	PUNCT
ejpam-6029	83	14	like	like	ADJ
ejpam-6029	83	15	space	space	NOUN
ejpam-6029	83	16	,	,	PUNCT
ejpam-6029	83	17	dccml	dccml	NOUN
ejpam-6029	83	18	-	-	PUNCT
ejpam-6029	83	19	space	space	NOUN
ejpam-6029	83	20	,	,	PUNCT
ejpam-6029	83	21	as	as	SCONJ
ejpam-6029	83	22	outlined	outline	VERB
ejpam-6029	83	23	below	below	ADV
ejpam-6029	83	24	:	:	PUNCT
ejpam-6029	83	25	definition	definition	NOUN
ejpam-6029	83	26	4	4	NUM
ejpam-6029	83	27	.	.	PUNCT
ejpam-6029	84	1	[	[	X
ejpam-6029	84	2	19	19	NUM
ejpam-6029	84	3	]	]	PUNCT
ejpam-6029	84	4	let	let	VERB
ejpam-6029	84	5	γ	γ	X
ejpam-6029	84	6	be	be	AUX
ejpam-6029	84	7	a	a	DET
ejpam-6029	84	8	non	non	ADJ
ejpam-6029	84	9	-	-	ADJ
ejpam-6029	84	10	empty	empty	ADJ
ejpam-6029	84	11	set	set	NOUN
ejpam-6029	84	12	and	and	CCONJ
ejpam-6029	84	13	f	f	NOUN
ejpam-6029	84	14	,	,	PUNCT
ejpam-6029	84	15	g	g	NOUN
ejpam-6029	84	16	:	:	PUNCT
ejpam-6029	84	17	p	p	X
ejpam-6029	84	18	→	→	PUNCT
ejpam-6029	84	19	p	p	X
ejpam-6029	84	20	be	be	AUX
ejpam-6029	84	21	nonconstant	nonconstant	ADJ
ejpam-6029	84	22	functions	function	NOUN
ejpam-6029	84	23	.	.	PUNCT
ejpam-6029	85	1	consider	consider	VERB
ejpam-6029	85	2	the	the	DET
ejpam-6029	85	3	mapping	mapping	NOUN
ejpam-6029	85	4	dc	dc	PROPN
ejpam-6029	85	5	:	:	PUNCT
ejpam-6029	85	6	γ	γ	X
ejpam-6029	85	7	×	×	PROPN
ejpam-6029	85	8	γ	γ	X
ejpam-6029	85	9	→	→	SYM
ejpam-6029	85	10	e	e	NOUN
ejpam-6029	85	11	that	that	PRON
ejpam-6029	85	12	adheres	adhere	VERB
ejpam-6029	85	13	to	to	ADP
ejpam-6029	85	14	the	the	DET
ejpam-6029	85	15	following	following	ADJ
ejpam-6029	85	16	conditions	condition	NOUN
ejpam-6029	85	17	:	:	PUNCT
ejpam-6029	85	18	for	for	ADP
ejpam-6029	85	19	all	all	DET
ejpam-6029	85	20	a	a	DET
ejpam-6029	85	21	,	,	PUNCT
ejpam-6029	85	22	b	b	NOUN
ejpam-6029	85	23	,	,	PUNCT
ejpam-6029	85	24	c	c	PROPN
ejpam-6029	85	25	∈	∈	PROPN
ejpam-6029	85	26	γ	γ	X
ejpam-6029	85	27	,	,	PUNCT
ejpam-6029	85	28	(	(	PUNCT
ejpam-6029	85	29	d1	d1	NOUN
ejpam-6029	85	30	)	)	PUNCT
ejpam-6029	85	31	dc(a	dc(a	NOUN
ejpam-6029	85	32	,	,	PUNCT
ejpam-6029	85	33	b	b	NOUN
ejpam-6029	85	34	)	)	PUNCT
ejpam-6029	85	35	=	=	SYM
ejpam-6029	85	36	0e	0e	NOUN
ejpam-6029	86	1	if	if	SCONJ
ejpam-6029	86	2	and	and	CCONJ
ejpam-6029	86	3	only	only	ADV
ejpam-6029	86	4	if	if	SCONJ
ejpam-6029	86	5	a	a	DET
ejpam-6029	86	6	=	=	SYM
ejpam-6029	86	7	b	b	NOUN
ejpam-6029	86	8	,	,	PUNCT
ejpam-6029	86	9	(	(	PUNCT
ejpam-6029	86	10	d2	d2	PROPN
ejpam-6029	86	11	)	)	PUNCT
ejpam-6029	86	12	dc(a	dc(a	PROPN
ejpam-6029	86	13	,	,	PUNCT
ejpam-6029	86	14	b	b	NOUN
ejpam-6029	86	15	)	)	PUNCT
ejpam-6029	86	16	=	=	PUNCT
ejpam-6029	86	17	dc(b	dc(b	PROPN
ejpam-6029	86	18	,	,	PUNCT
ejpam-6029	86	19	a	a	PRON
ejpam-6029	86	20	)	)	PUNCT
ejpam-6029	86	21	,	,	PUNCT
ejpam-6029	86	22	(	(	PUNCT
ejpam-6029	86	23	d3	d3	PROPN
ejpam-6029	86	24	)	)	PUNCT
ejpam-6029	86	25	dc(a	dc(a	PROPN
ejpam-6029	86	26	,	,	PUNCT
ejpam-6029	86	27	b	b	X
ejpam-6029	86	28	)	)	PUNCT
ejpam-6029	86	29	⪯	⪯	NOUN
ejpam-6029	86	30	f	f	PROPN
ejpam-6029	86	31	(	(	PUNCT
ejpam-6029	86	32	dc(a	dc(a	X
ejpam-6029	86	33	,	,	PUNCT
ejpam-6029	86	34	c	c	NOUN
ejpam-6029	86	35	)	)	PUNCT
ejpam-6029	86	36	)	)	PUNCT
ejpam-6029	87	1	+	+	CCONJ
ejpam-6029	87	2	g	g	PROPN
ejpam-6029	87	3	(	(	PUNCT
ejpam-6029	87	4	dc(c	dc(c	PROPN
ejpam-6029	87	5	,	,	PUNCT
ejpam-6029	87	6	b	b	NOUN
ejpam-6029	87	7	)	)	PUNCT
ejpam-6029	87	8	)	)	PUNCT
ejpam-6029	87	9	.	.	PUNCT
ejpam-6029	88	1	then	then	ADV
ejpam-6029	88	2	the	the	DET
ejpam-6029	88	3	pair	pair	NOUN
ejpam-6029	88	4	(	(	PUNCT
ejpam-6029	88	5	γ	γ	X
ejpam-6029	88	6	,	,	PUNCT
ejpam-6029	88	7	dc	dc	PROPN
ejpam-6029	88	8	)	)	PUNCT
ejpam-6029	88	9	is	be	AUX
ejpam-6029	88	10	referred	refer	VERB
ejpam-6029	88	11	to	to	ADP
ejpam-6029	88	12	as	as	ADP
ejpam-6029	88	13	a	a	DET
ejpam-6029	88	14	c2cms	c2cms	PROPN
ejpam-6029	88	15	.	.	PUNCT
ejpam-6029	89	1	example	example	NOUN
ejpam-6029	90	1	1	1	NUM
ejpam-6029	90	2	.	.	PUNCT
ejpam-6029	91	1	let	let	AUX
ejpam-6029	91	2	e	e	NOUN
ejpam-6029	91	3	=	=	NOUN
ejpam-6029	91	4	r2	r2	PROPN
ejpam-6029	91	5	,	,	PUNCT
ejpam-6029	91	6	p	p	NOUN
ejpam-6029	91	7	=	=	X
ejpam-6029	91	8	{	{	PUNCT
ejpam-6029	91	9	u	u	NOUN
ejpam-6029	91	10	=	=	SYM
ejpam-6029	91	11	(	(	PUNCT
ejpam-6029	91	12	r	r	NOUN
ejpam-6029	91	13	,	,	PUNCT
ejpam-6029	91	14	s	s	NOUN
ejpam-6029	91	15	)	)	PUNCT
ejpam-6029	91	16	∈	∈	PROPN
ejpam-6029	91	17	e	e	NOUN
ejpam-6029	91	18	:	:	PUNCT
ejpam-6029	91	19	r	r	X
ejpam-6029	91	20	,	,	PUNCT
ejpam-6029	91	21	s	s	PART
ejpam-6029	91	22	≥	≥	NOUN
ejpam-6029	91	23	0	0	NUM
ejpam-6029	91	24	}	}	PUNCT
ejpam-6029	91	25	,	,	PUNCT
ejpam-6029	91	26	and	and	CCONJ
ejpam-6029	91	27	γ	γ	X
ejpam-6029	91	28	=	=	SYM
ejpam-6029	91	29	r.	r.	PROPN
ejpam-6029	91	30	let	let	VERB
ejpam-6029	91	31	dc	dc	PROPN
ejpam-6029	91	32	:	:	PUNCT
ejpam-6029	91	33	γ×	γ×	PROPN
ejpam-6029	91	34	γ	γ	X
ejpam-6029	91	35	→	→	SYM
ejpam-6029	91	36	e	e	X
ejpam-6029	91	37	be	be	AUX
ejpam-6029	91	38	defined	define	VERB
ejpam-6029	91	39	by	by	ADP
ejpam-6029	91	40	dc(a	dc(a	NOUN
ejpam-6029	91	41	,	,	PUNCT
ejpam-6029	91	42	b	b	NOUN
ejpam-6029	91	43	)	)	PUNCT
ejpam-6029	91	44	=	=	SYM
ejpam-6029	91	45	(	(	PUNCT
ejpam-6029	91	46	e1(a−	e1(a−	NUM
ejpam-6029	91	47	b)3	b)3	PROPN
ejpam-6029	91	48	,	,	PUNCT
ejpam-6029	91	49	e2(a−	e2(a−	CCONJ
ejpam-6029	91	50	b)2	b)2	ADJ
ejpam-6029	91	51	)	)	PUNCT
ejpam-6029	91	52	,	,	PUNCT
ejpam-6029	91	53	where	where	SCONJ
ejpam-6029	91	54	e1	e1	PROPN
ejpam-6029	91	55	,	,	PUNCT
ejpam-6029	91	56	e2	e2	X
ejpam-6029	91	57	≥	≥	NUM
ejpam-6029	91	58	0	0	NUM
ejpam-6029	91	59	.	.	PUNCT
ejpam-6029	92	1	define	define	VERB
ejpam-6029	92	2	f	f	NOUN
ejpam-6029	92	3	,	,	PUNCT
ejpam-6029	92	4	g	g	NOUN
ejpam-6029	92	5	:	:	PUNCT
ejpam-6029	92	6	p	p	X
ejpam-6029	92	7	→	→	PUNCT
ejpam-6029	92	8	p	p	NOUN
ejpam-6029	92	9	by	by	ADP
ejpam-6029	92	10	f(u	f(u	PROPN
ejpam-6029	92	11	)	)	PUNCT
ejpam-6029	92	12	=	=	PUNCT
ejpam-6029	93	1	(	(	PUNCT
ejpam-6029	93	2	e4r	e4r	NOUN
ejpam-6029	93	3	−	−	PROPN
ejpam-6029	93	4	1	1	NUM
ejpam-6029	93	5	,	,	PUNCT
ejpam-6029	93	6	e2s	e2s	ADJ
ejpam-6029	93	7	−	−	PROPN
ejpam-6029	93	8	1	1	NUM
ejpam-6029	93	9	)	)	PUNCT
ejpam-6029	93	10	and	and	CCONJ
ejpam-6029	93	11	g(u	g(u	PROPN
ejpam-6029	93	12	)	)	PUNCT
ejpam-6029	93	13	=	=	SYM
ejpam-6029	93	14	(	(	PUNCT
ejpam-6029	93	15	4r	4r	NOUN
ejpam-6029	93	16	,	,	PUNCT
ejpam-6029	93	17	2s	2s	NUM
ejpam-6029	93	18	)	)	PUNCT
ejpam-6029	93	19	,	,	PUNCT
ejpam-6029	93	20	u	u	PROPN
ejpam-6029	93	21	∈	∈	PROPN
ejpam-6029	93	22	p	p	NOUN
ejpam-6029	93	23	.	.	PUNCT
ejpam-6029	94	1	it	it	PRON
ejpam-6029	94	2	is	be	AUX
ejpam-6029	94	3	not	not	PART
ejpam-6029	94	4	difficult	difficult	ADJ
ejpam-6029	94	5	to	to	PART
ejpam-6029	94	6	see	see	VERB
ejpam-6029	94	7	that	that	SCONJ
ejpam-6029	94	8	(	(	PUNCT
ejpam-6029	94	9	a	a	DET
ejpam-6029	94	10	−	−	PROPN
ejpam-6029	94	11	b)3	b)3	PROPN
ejpam-6029	94	12	≤	≤	NOUN
ejpam-6029	94	13	4a3	4a3	NUM
ejpam-6029	95	1	+	+	CCONJ
ejpam-6029	95	2	4b3	4b3	NUM
ejpam-6029	95	3	≤	≤	NOUN
ejpam-6029	95	4	(	(	PUNCT
ejpam-6029	95	5	e4a	e4a	PROPN
ejpam-6029	95	6	3	3	NUM
ejpam-6029	95	7	−	−	NOUN
ejpam-6029	95	8	1	1	NUM
ejpam-6029	95	9	)	)	PUNCT
ejpam-6029	95	10	+	+	NUM
ejpam-6029	95	11	4b3	4b3	NUM
ejpam-6029	95	12	.	.	PUNCT
ejpam-6029	96	1	also	also	ADV
ejpam-6029	96	2	,	,	PUNCT
ejpam-6029	96	3	(	(	PUNCT
ejpam-6029	96	4	a	a	DET
ejpam-6029	96	5	−	−	PROPN
ejpam-6029	96	6	b)2	b)2	ADJ
ejpam-6029	96	7	≤	≤	NUM
ejpam-6029	96	8	2a2	2a2	NUM
ejpam-6029	96	9	+	+	CCONJ
ejpam-6029	96	10	2b2	2b2	NUM
ejpam-6029	96	11	≤	≤	NUM
ejpam-6029	96	12	(	(	PUNCT
ejpam-6029	96	13	e4a	e4a	PROPN
ejpam-6029	96	14	2	2	NUM
ejpam-6029	96	15	−	−	NOUN
ejpam-6029	96	16	1	1	NUM
ejpam-6029	96	17	)	)	PUNCT
ejpam-6029	96	18	+	+	CCONJ
ejpam-6029	96	19	2b2	2b2	NUM
ejpam-6029	96	20	.	.	PUNCT
ejpam-6029	97	1	therefore	therefore	ADV
ejpam-6029	97	2	,	,	PUNCT
ejpam-6029	97	3	(	(	PUNCT
ejpam-6029	97	4	γ	γ	X
ejpam-6029	97	5	,	,	PUNCT
ejpam-6029	97	6	dc	dc	PROPN
ejpam-6029	97	7	)	)	PUNCT
ejpam-6029	97	8	is	be	AUX
ejpam-6029	97	9	a	a	DET
ejpam-6029	97	10	c2cms	c2cms	PROPN
ejpam-6029	97	11	.	.	PUNCT
ejpam-6029	98	1	now	now	ADV
ejpam-6029	98	2	we	we	PRON
ejpam-6029	98	3	introduce	introduce	VERB
ejpam-6029	98	4	our	our	PRON
ejpam-6029	98	5	generalization	generalization	NOUN
ejpam-6029	98	6	of	of	ADP
ejpam-6029	98	7	the	the	DET
ejpam-6029	98	8	dcml	dcml	NOUN
ejpam-6029	98	9	-	-	PUNCT
ejpam-6029	98	10	spaces	space	NOUN
ejpam-6029	98	11	.	.	PUNCT
ejpam-6029	99	1	definition	definition	NOUN
ejpam-6029	99	2	5	5	NUM
ejpam-6029	99	3	.	.	PUNCT
ejpam-6029	99	4	let	let	VERB
ejpam-6029	99	5	γ	γ	NOUN
ejpam-6029	99	6	be	be	AUX
ejpam-6029	99	7	a	a	DET
ejpam-6029	99	8	non	non	ADJ
ejpam-6029	99	9	-	-	ADJ
ejpam-6029	99	10	empty	empty	ADJ
ejpam-6029	99	11	set	set	NOUN
ejpam-6029	99	12	and	and	CCONJ
ejpam-6029	99	13	f	f	NOUN
ejpam-6029	99	14	,	,	PUNCT
ejpam-6029	99	15	g	g	NOUN
ejpam-6029	99	16	:	:	PUNCT
ejpam-6029	99	17	p	p	X
ejpam-6029	99	18	→	→	PUNCT
ejpam-6029	99	19	p	p	X
ejpam-6029	99	20	be	be	AUX
ejpam-6029	99	21	nonconstant	nonconstant	ADJ
ejpam-6029	99	22	functions	function	NOUN
ejpam-6029	99	23	.	.	PUNCT
ejpam-6029	100	1	consider	consider	VERB
ejpam-6029	100	2	the	the	DET
ejpam-6029	100	3	mapping	mapping	NOUN
ejpam-6029	100	4	lc	lc	NOUN
ejpam-6029	100	5	:	:	PUNCT
ejpam-6029	100	6	γ	γ	X
ejpam-6029	100	7	×	×	NOUN
ejpam-6029	100	8	γ	γ	X
ejpam-6029	100	9	→	→	SYM
ejpam-6029	100	10	e	e	NOUN
ejpam-6029	100	11	that	that	PRON
ejpam-6029	100	12	adheres	adhere	VERB
ejpam-6029	100	13	to	to	ADP
ejpam-6029	100	14	the	the	DET
ejpam-6029	100	15	following	following	ADJ
ejpam-6029	100	16	conditions	condition	NOUN
ejpam-6029	100	17	:	:	PUNCT
ejpam-6029	100	18	for	for	ADP
ejpam-6029	100	19	all	all	DET
ejpam-6029	100	20	a	a	DET
ejpam-6029	100	21	,	,	PUNCT
ejpam-6029	100	22	b	b	NOUN
ejpam-6029	100	23	,	,	PUNCT
ejpam-6029	100	24	c	c	PROPN
ejpam-6029	100	25	∈	∈	PROPN
ejpam-6029	100	26	γ	γ	X
ejpam-6029	100	27	,	,	PUNCT
ejpam-6029	100	28	(	(	PUNCT
ejpam-6029	100	29	l1	l1	PROPN
ejpam-6029	100	30	)	)	PUNCT
ejpam-6029	100	31	lc(a	lc(a	PROPN
ejpam-6029	100	32	,	,	PUNCT
ejpam-6029	100	33	b	b	X
ejpam-6029	100	34	)	)	PUNCT
ejpam-6029	100	35	=	=	SYM
ejpam-6029	100	36	0e	0e	NOUN
ejpam-6029	100	37	⇒	⇒	VERB
ejpam-6029	100	38	a	a	DET
ejpam-6029	100	39	=	=	SYM
ejpam-6029	100	40	b	b	PROPN
ejpam-6029	100	41	,	,	PUNCT
ejpam-6029	100	42	(	(	PUNCT
ejpam-6029	100	43	l2	l2	NOUN
ejpam-6029	100	44	)	)	PUNCT
ejpam-6029	100	45	lc(a	lc(a	PROPN
ejpam-6029	100	46	,	,	PUNCT
ejpam-6029	100	47	b	b	NOUN
ejpam-6029	100	48	)	)	PUNCT
ejpam-6029	100	49	=	=	VERB
ejpam-6029	101	1	lc(b	lc(b	X
ejpam-6029	101	2	,	,	PUNCT
ejpam-6029	101	3	a	a	PRON
ejpam-6029	101	4	)	)	PUNCT
ejpam-6029	101	5	,	,	PUNCT
ejpam-6029	101	6	(	(	PUNCT
ejpam-6029	101	7	l3	l3	NOUN
ejpam-6029	101	8	)	)	PUNCT
ejpam-6029	101	9	lc(a	lc(a	PROPN
ejpam-6029	101	10	,	,	PUNCT
ejpam-6029	101	11	b	b	X
ejpam-6029	101	12	)	)	PUNCT
ejpam-6029	101	13	⪯	⪯	NOUN
ejpam-6029	101	14	f	f	PROPN
ejpam-6029	101	15	(	(	PUNCT
ejpam-6029	101	16	lc(a	lc(a	PROPN
ejpam-6029	101	17	,	,	PUNCT
ejpam-6029	101	18	c	c	NOUN
ejpam-6029	101	19	)	)	PUNCT
ejpam-6029	101	20	)	)	PUNCT
ejpam-6029	102	1	+	+	CCONJ
ejpam-6029	102	2	g	g	PROPN
ejpam-6029	102	3	(	(	PUNCT
ejpam-6029	102	4	lc(c	lc(c	PROPN
ejpam-6029	102	5	,	,	PUNCT
ejpam-6029	102	6	b	b	NOUN
ejpam-6029	102	7	)	)	PUNCT
ejpam-6029	102	8	)	)	PUNCT
ejpam-6029	102	9	.	.	PUNCT
ejpam-6029	103	1	the	the	DET
ejpam-6029	103	2	pair	pair	NOUN
ejpam-6029	103	3	(	(	PUNCT
ejpam-6029	103	4	γ	γ	X
ejpam-6029	103	5	,	,	PUNCT
ejpam-6029	103	6	lc	lc	PROPN
ejpam-6029	103	7	)	)	PUNCT
ejpam-6029	103	8	is	be	AUX
ejpam-6029	103	9	known	know	VERB
ejpam-6029	103	10	as	as	ADP
ejpam-6029	103	11	a	a	DET
ejpam-6029	103	12	double	double	ADV
ejpam-6029	103	13	-	-	PUNCT
ejpam-6029	103	14	composed	compose	VERB
ejpam-6029	103	15	cone	cone	NOUN
ejpam-6029	103	16	metric	metric	ADJ
ejpam-6029	103	17	-	-	PUNCT
ejpam-6029	103	18	like	like	ADJ
ejpam-6029	103	19	space	space	NOUN
ejpam-6029	103	20	(	(	PUNCT
ejpam-6029	103	21	dccml	dccml	NOUN
ejpam-6029	103	22	-	-	PUNCT
ejpam-6029	103	23	space	space	NOUN
ejpam-6029	103	24	)	)	PUNCT
ejpam-6029	103	25	.	.	PUNCT
ejpam-6029	104	1	the	the	DET
ejpam-6029	104	2	following	follow	VERB
ejpam-6029	104	3	examples	example	NOUN
ejpam-6029	104	4	demonstrate	demonstrate	VERB
ejpam-6029	104	5	that	that	SCONJ
ejpam-6029	104	6	every	every	DET
ejpam-6029	104	7	c2cms	c2cms	PROPN
ejpam-6029	104	8	is	be	AUX
ejpam-6029	104	9	a	a	DET
ejpam-6029	104	10	dccml	dccml	NOUN
ejpam-6029	104	11	-	-	PUNCT
ejpam-6029	104	12	space	space	NOUN
ejpam-6029	104	13	;	;	PUNCT
ejpam-6029	104	14	however	however	ADV
ejpam-6029	104	15	,	,	PUNCT
ejpam-6029	104	16	the	the	DET
ejpam-6029	104	17	converse	converse	NOUN
ejpam-6029	104	18	is	be	AUX
ejpam-6029	104	19	not	not	PART
ejpam-6029	104	20	always	always	ADV
ejpam-6029	104	21	true	true	ADJ
ejpam-6029	104	22	.	.	PUNCT
ejpam-6029	105	1	example	example	NOUN
ejpam-6029	106	1	2	2	NUM
ejpam-6029	106	2	.	.	PUNCT
ejpam-6029	106	3	let	let	VERB
ejpam-6029	106	4	e	e	NOUN
ejpam-6029	106	5	=	=	NOUN
ejpam-6029	106	6	r2	r2	PROPN
ejpam-6029	106	7	,	,	PUNCT
ejpam-6029	106	8	p	p	NOUN
ejpam-6029	106	9	=	=	X
ejpam-6029	106	10	{	{	PUNCT
ejpam-6029	106	11	u	u	NOUN
ejpam-6029	106	12	=	=	SYM
ejpam-6029	106	13	(	(	PUNCT
ejpam-6029	106	14	r	r	NOUN
ejpam-6029	106	15	,	,	PUNCT
ejpam-6029	106	16	s	s	NOUN
ejpam-6029	106	17	)	)	PUNCT
ejpam-6029	106	18	∈	∈	PROPN
ejpam-6029	106	19	e	e	NOUN
ejpam-6029	106	20	:	:	PUNCT
ejpam-6029	106	21	r	r	X
ejpam-6029	106	22	,	,	PUNCT
ejpam-6029	106	23	s	s	PART
ejpam-6029	106	24	≥	≥	NOUN
ejpam-6029	106	25	0	0	NUM
ejpam-6029	106	26	}	}	PUNCT
ejpam-6029	106	27	,	,	PUNCT
ejpam-6029	106	28	and	and	CCONJ
ejpam-6029	106	29	γ	γ	X
ejpam-6029	106	30	=	=	SYM
ejpam-6029	106	31	r.	r.	PROPN
ejpam-6029	106	32	then	then	ADV
ejpam-6029	106	33	lc	lc	PROPN
ejpam-6029	106	34	:	:	PUNCT
ejpam-6029	107	1	γ×γ	γ×γ	PROPN
ejpam-6029	107	2	→	→	PUNCT
ejpam-6029	107	3	e	e	NOUN
ejpam-6029	107	4	is	be	AUX
ejpam-6029	107	5	defined	define	VERB
ejpam-6029	107	6	as	as	ADP
ejpam-6029	107	7	lc(a	lc(a	NUM
ejpam-6029	107	8	,	,	PUNCT
ejpam-6029	107	9	b	b	NOUN
ejpam-6029	107	10	)	)	PUNCT
ejpam-6029	107	11	=	=	SYM
ejpam-6029	107	12	(	(	PUNCT
ejpam-6029	107	13	e1(a+	e1(a+	PROPN
ejpam-6029	107	14	b)p	b)p	NOUN
ejpam-6029	107	15	,	,	PUNCT
ejpam-6029	107	16	e2(a+	e2(a+	PROPN
ejpam-6029	107	17	b)q	b)q	X
ejpam-6029	107	18	)	)	PUNCT
ejpam-6029	107	19	,	,	PUNCT
ejpam-6029	107	20	where	where	SCONJ
ejpam-6029	107	21	e1	e1	PROPN
ejpam-6029	107	22	,	,	PUNCT
ejpam-6029	107	23	e2	e2	X
ejpam-6029	107	24	≥	≥	NUM
ejpam-6029	107	25	0	0	NUM
ejpam-6029	107	26	and	and	CCONJ
ejpam-6029	107	27	p	p	X
ejpam-6029	107	28	,	,	PUNCT
ejpam-6029	107	29	q	q	ADJ
ejpam-6029	107	30	>	>	X
ejpam-6029	107	31	1	1	NUM
ejpam-6029	107	32	and	and	CCONJ
ejpam-6029	107	33	p	p	PROPN
ejpam-6029	107	34	̸=	̸=	PROPN
ejpam-6029	107	35	q.	q.	NOUN
ejpam-6029	107	36	define	define	VERB
ejpam-6029	107	37	f	f	PROPN
ejpam-6029	107	38	,	,	PUNCT
ejpam-6029	107	39	g	g	NOUN
ejpam-6029	107	40	:	:	PUNCT
ejpam-6029	107	41	p	p	X
ejpam-6029	107	42	→	→	PUNCT
ejpam-6029	107	43	p	p	NOUN
ejpam-6029	107	44	by	by	ADP
ejpam-6029	107	45	f(u	f(u	PROPN
ejpam-6029	107	46	)	)	PUNCT
ejpam-6029	108	1	=	=	PRON
ejpam-6029	108	2	(	(	PUNCT
ejpam-6029	108	3	(	(	PUNCT
ejpam-6029	108	4	1	1	NUM
ejpam-6029	108	5	+	+	NOUN
ejpam-6029	108	6	2p−1rp)n−1	2p−1rp)n−1	PROPN
ejpam-6029	108	7	n	n	NOUN
ejpam-6029	108	8	,	,	PUNCT
ejpam-6029	108	9	(	(	PUNCT
ejpam-6029	108	10	1	1	NUM
ejpam-6029	108	11	+	+	NOUN
ejpam-6029	108	12	2q−1rq)n−1	2q−1rq)n−1	NUM
ejpam-6029	108	13	n	n	NOUN
ejpam-6029	108	14	)	)	PUNCT
ejpam-6029	108	15	and	and	CCONJ
ejpam-6029	108	16	g(u	g(u	PROPN
ejpam-6029	108	17	)	)	PUNCT
ejpam-6029	109	1	=	=	PRON
ejpam-6029	109	2	(	(	PUNCT
ejpam-6029	109	3	(	(	PUNCT
ejpam-6029	109	4	1	1	NUM
ejpam-6029	109	5	+	+	NOUN
ejpam-6029	109	6	2p−1rp)m−1	2p−1rp)m−1	PROPN
ejpam-6029	109	7	m	m	PRON
ejpam-6029	109	8	,	,	PUNCT
ejpam-6029	109	9	(	(	PUNCT
ejpam-6029	109	10	1	1	NUM
ejpam-6029	109	11	+	+	NOUN
ejpam-6029	109	12	2q−1rq)m−1	2q−1rq)m−1	PROPN
ejpam-6029	109	13	m	m	NOUN
ejpam-6029	109	14	)	)	PUNCT
ejpam-6029	109	15	,	,	PUNCT
ejpam-6029	109	16	u	u	PROPN
ejpam-6029	109	17	∈	∈	PROPN
ejpam-6029	109	18	p	p	X
ejpam-6029	109	19	,	,	PUNCT
ejpam-6029	109	20	n	n	PRON
ejpam-6029	109	21	≥	≥	NOUN
ejpam-6029	109	22	a.	a.	NOUN
ejpam-6029	109	23	a.	a.	PROPN
ejpam-6029	110	1	hijab	hijab	PROPN
ejpam-6029	110	2	et	et	PROPN
ejpam-6029	110	3	al	al	PROPN
ejpam-6029	110	4	.	.	PUNCT
ejpam-6029	110	5	/	/	SYM
ejpam-6029	110	6	eur	eur	PROPN
ejpam-6029	110	7	.	.	PUNCT
ejpam-6029	111	1	j.	j.	PROPN
ejpam-6029	111	2	pure	pure	PROPN
ejpam-6029	111	3	appl	appl	PROPN
ejpam-6029	111	4	.	.	PROPN
ejpam-6029	111	5	math	math	PROPN
ejpam-6029	111	6	,	,	PUNCT
ejpam-6029	111	7	18	18	NUM
ejpam-6029	111	8	(	(	PUNCT
ejpam-6029	111	9	2	2	NUM
ejpam-6029	111	10	)	)	PUNCT
ejpam-6029	111	11	(	(	PUNCT
ejpam-6029	111	12	2025	2025	NUM
ejpam-6029	111	13	)	)	PUNCT
ejpam-6029	111	14	,	,	PUNCT
ejpam-6029	111	15	6029	6029	NUM
ejpam-6029	111	16	5	5	NUM
ejpam-6029	111	17	of	of	ADP
ejpam-6029	111	18	23	23	NUM
ejpam-6029	111	19	m	m	NOUN
ejpam-6029	111	20	≥	≥	NOUN
ejpam-6029	111	21	1	1	NUM
ejpam-6029	111	22	.	.	PUNCT
ejpam-6029	112	1	obviously	obviously	ADV
ejpam-6029	112	2	,	,	PUNCT
ejpam-6029	112	3	conditions	condition	NOUN
ejpam-6029	112	4	(	(	PUNCT
ejpam-6029	112	5	l1	l1	PROPN
ejpam-6029	112	6	)	)	PUNCT
ejpam-6029	112	7	and	and	CCONJ
ejpam-6029	112	8	(	(	PUNCT
ejpam-6029	112	9	l2	l2	NOUN
ejpam-6029	112	10	)	)	PUNCT
ejpam-6029	112	11	of	of	ADP
ejpam-6029	112	12	definition	definition	NOUN
ejpam-6029	112	13	5	5	NUM
ejpam-6029	112	14	are	be	AUX
ejpam-6029	112	15	satisfied	satisfied	ADJ
ejpam-6029	112	16	.	.	PUNCT
ejpam-6029	113	1	note	note	VERB
ejpam-6029	113	2	that	that	SCONJ
ejpam-6029	113	3	if	if	SCONJ
ejpam-6029	113	4	a	a	PRON
ejpam-6029	113	5	,	,	PUNCT
ejpam-6029	113	6	b	b	NOUN
ejpam-6029	113	7	are	be	AUX
ejpam-6029	113	8	two	two	NUM
ejpam-6029	113	9	nonnegative	nonnegative	ADJ
ejpam-6029	113	10	real	real	ADJ
ejpam-6029	113	11	numbers	number	NOUN
ejpam-6029	113	12	,	,	PUNCT
ejpam-6029	113	13	then	then	ADV
ejpam-6029	113	14	(	(	PUNCT
ejpam-6029	113	15	a	a	DET
ejpam-6029	113	16	+	+	X
ejpam-6029	113	17	b)q	b)q	NOUN
ejpam-6029	113	18	≤	≤	NUM
ejpam-6029	113	19	2q−1aq	2q−1aq	PROPN
ejpam-6029	113	20	+	+	CCONJ
ejpam-6029	113	21	2q−1bq	2q−1bq	NUM
ejpam-6029	113	22	,	,	PUNCT
ejpam-6029	113	23	q	q	X
ejpam-6029	113	24	>	>	X
ejpam-6029	113	25	1	1	NUM
ejpam-6029	113	26	,	,	PUNCT
ejpam-6029	113	27	and	and	CCONJ
ejpam-6029	113	28	1	1	NUM
ejpam-6029	113	29	+	+	CCONJ
ejpam-6029	113	30	na	na	ADP
ejpam-6029	113	31	≤	≤	NUM
ejpam-6029	113	32	(	(	PUNCT
ejpam-6029	113	33	1	1	NUM
ejpam-6029	113	34	+	+	CCONJ
ejpam-6029	113	35	a)n	a)n	NOUN
ejpam-6029	113	36	is	be	AUX
ejpam-6029	113	37	bernoulli	bernoulli	PROPN
ejpam-6029	113	38	’s	’s	PART
ejpam-6029	113	39	inequality	inequality	NOUN
ejpam-6029	113	40	.	.	PUNCT
ejpam-6029	114	1	hence	hence	ADV
ejpam-6029	114	2	,	,	PUNCT
ejpam-6029	114	3	a	a	DET
ejpam-6029	114	4	≤	≤	NOUN
ejpam-6029	114	5	(	(	PUNCT
ejpam-6029	114	6	1+a)n−1	1+a)n−1	NUM
ejpam-6029	114	7	n	n	NOUN
ejpam-6029	114	8	for	for	ADP
ejpam-6029	114	9	any	any	DET
ejpam-6029	114	10	n	n	PRON
ejpam-6029	114	11	≥	≥	NOUN
ejpam-6029	114	12	1	1	NUM
ejpam-6029	114	13	,	,	PUNCT
ejpam-6029	114	14	by	by	ADP
ejpam-6029	114	15	the	the	DET
ejpam-6029	114	16	same	same	ADJ
ejpam-6029	114	17	way	way	NOUN
ejpam-6029	114	18	for	for	ADP
ejpam-6029	114	19	p	p	PROPN
ejpam-6029	114	20	>	>	X
ejpam-6029	114	21	1,m	1,m	X
ejpam-6029	114	22	>	>	X
ejpam-6029	115	1	1	1	X
ejpam-6029	115	2	.	.	X
ejpam-6029	115	3	we	we	PRON
ejpam-6029	115	4	can	can	AUX
ejpam-6029	115	5	easily	easily	ADV
ejpam-6029	115	6	deduce	deduce	VERB
ejpam-6029	115	7	that	that	SCONJ
ejpam-6029	115	8	the	the	DET
ejpam-6029	115	9	condition	condition	NOUN
ejpam-6029	115	10	(	(	PUNCT
ejpam-6029	115	11	l3	l3	NOUN
ejpam-6029	115	12	)	)	PUNCT
ejpam-6029	115	13	is	be	AUX
ejpam-6029	115	14	satisfied	satisfied	ADJ
ejpam-6029	115	15	.	.	PUNCT
ejpam-6029	116	1	therefore	therefore	ADV
ejpam-6029	116	2	,	,	PUNCT
ejpam-6029	116	3	(	(	PUNCT
ejpam-6029	116	4	γ	γ	X
ejpam-6029	116	5	,	,	PUNCT
ejpam-6029	116	6	lc	lc	PROPN
ejpam-6029	116	7	)	)	PUNCT
ejpam-6029	116	8	is	be	AUX
ejpam-6029	116	9	a	a	DET
ejpam-6029	116	10	dccml	dccml	NOUN
ejpam-6029	116	11	-	-	PUNCT
ejpam-6029	116	12	space	space	NOUN
ejpam-6029	116	13	.	.	PUNCT
ejpam-6029	117	1	obviously	obviously	ADV
ejpam-6029	117	2	,	,	PUNCT
ejpam-6029	117	3	(	(	PUNCT
ejpam-6029	117	4	γ	γ	X
ejpam-6029	117	5	,	,	PUNCT
ejpam-6029	117	6	lc	lc	NOUN
ejpam-6029	117	7	)	)	PUNCT
ejpam-6029	117	8	is	be	AUX
ejpam-6029	117	9	not	not	PART
ejpam-6029	117	10	a	a	DET
ejpam-6029	117	11	c2cms	c2cms	NOUN
ejpam-6029	117	12	because	because	SCONJ
ejpam-6029	117	13	it	it	PRON
ejpam-6029	117	14	does	do	AUX
ejpam-6029	117	15	not	not	PART
ejpam-6029	117	16	satisfy	satisfy	VERB
ejpam-6029	117	17	(	(	PUNCT
ejpam-6029	117	18	d1	d1	PROPN
ejpam-6029	117	19	)	)	PUNCT
ejpam-6029	117	20	.	.	PUNCT
ejpam-6029	118	1	example	example	NOUN
ejpam-6029	119	1	3	3	X
ejpam-6029	119	2	.	.	X
ejpam-6029	119	3	consider	consider	VERB
ejpam-6029	119	4	e	e	NOUN
ejpam-6029	119	5	=	=	NOUN
ejpam-6029	119	6	r2	r2	PROPN
ejpam-6029	119	7	,	,	PUNCT
ejpam-6029	119	8	p	p	NOUN
ejpam-6029	119	9	=	=	X
ejpam-6029	119	10	{	{	PUNCT
ejpam-6029	119	11	u	u	NOUN
ejpam-6029	119	12	=	=	SYM
ejpam-6029	119	13	(	(	PUNCT
ejpam-6029	119	14	r	r	NOUN
ejpam-6029	119	15	,	,	PUNCT
ejpam-6029	119	16	s	s	NOUN
ejpam-6029	119	17	)	)	PUNCT
ejpam-6029	119	18	∈	∈	PROPN
ejpam-6029	119	19	e	e	NOUN
ejpam-6029	119	20	:	:	PUNCT
ejpam-6029	119	21	r	r	X
ejpam-6029	119	22	,	,	PUNCT
ejpam-6029	119	23	s	s	PART
ejpam-6029	119	24	≥	≥	NOUN
ejpam-6029	119	25	0	0	NUM
ejpam-6029	119	26	}	}	PUNCT
ejpam-6029	119	27	and	and	CCONJ
ejpam-6029	119	28	γ	γ	X
ejpam-6029	119	29	=	=	SYM
ejpam-6029	119	30	r.	r.	PROPN
ejpam-6029	119	31	define	define	VERB
ejpam-6029	119	32	lc	lc	PROPN
ejpam-6029	119	33	:	:	PUNCT
ejpam-6029	119	34	γ×	γ×	PROPN
ejpam-6029	119	35	γ	γ	X
ejpam-6029	119	36	→	→	SYM
ejpam-6029	119	37	e	e	NOUN
ejpam-6029	119	38	by	by	ADP
ejpam-6029	119	39	lc(a	lc(a	PROPN
ejpam-6029	119	40	,	,	PUNCT
ejpam-6029	119	41	b	b	X
ejpam-6029	119	42	)	)	PUNCT
ejpam-6029	119	43	=	=	SYM
ejpam-6029	119	44	(	(	PUNCT
ejpam-6029	119	45	sinh(eσ(a	sinh(eσ(a	ADJ
ejpam-6029	119	46	,	,	PUNCT
ejpam-6029	119	47	b	b	NOUN
ejpam-6029	119	48	)	)	PUNCT
ejpam-6029	119	49	)	)	PUNCT
ejpam-6029	119	50	,	,	PUNCT
ejpam-6029	119	51	e(a+b	e(a+b	NOUN
ejpam-6029	119	52	)	)	PUNCT
ejpam-6029	120	1	−	−	PROPN
ejpam-6029	120	2	1	1	NUM
ejpam-6029	120	3	)	)	PUNCT
ejpam-6029	120	4	,	,	PUNCT
ejpam-6029	120	5	where	where	SCONJ
ejpam-6029	120	6	e	e	X
ejpam-6029	120	7	≥	≥	X
ejpam-6029	120	8	0	0	NUM
ejpam-6029	120	9	,	,	PUNCT
ejpam-6029	120	10	and	and	CCONJ
ejpam-6029	120	11	σ(a	σ(a	PROPN
ejpam-6029	120	12	,	,	PUNCT
ejpam-6029	120	13	b	b	NOUN
ejpam-6029	120	14	)	)	PUNCT
ejpam-6029	120	15	is	be	AUX
ejpam-6029	120	16	a	a	DET
ejpam-6029	120	17	dcmls	dcmls	NOUN
ejpam-6029	120	18	with	with	ADP
ejpam-6029	120	19	two	two	NUM
ejpam-6029	120	20	controlled	control	VERB
ejpam-6029	120	21	functions	function	NOUN
ejpam-6029	120	22	ω1	ω1	PROPN
ejpam-6029	120	23	,	,	PUNCT
ejpam-6029	120	24	ω2	ω2	ADJ
ejpam-6029	120	25	:	:	PUNCT
ejpam-6029	120	26	γ×	γ×	PROPN
ejpam-6029	120	27	γ	γ	X
ejpam-6029	120	28	→	→	SYM
ejpam-6029	120	29	[	[	X
ejpam-6029	120	30	1,∞	1,∞	NUM
ejpam-6029	120	31	)	)	PUNCT
ejpam-6029	120	32	.	.	PUNCT
ejpam-6029	121	1	take	take	VERB
ejpam-6029	121	2	f	f	NOUN
ejpam-6029	121	3	,	,	PUNCT
ejpam-6029	121	4	g	g	NOUN
ejpam-6029	121	5	:	:	PUNCT
ejpam-6029	121	6	p	p	X
ejpam-6029	121	7	→	→	PUNCT
ejpam-6029	121	8	p	p	NOUN
ejpam-6029	121	9	defined	define	VERB
ejpam-6029	121	10	by	by	ADP
ejpam-6029	121	11	f(u	f(u	PROPN
ejpam-6029	121	12	)	)	PUNCT
ejpam-6029	121	13	=	=	PRON
ejpam-6029	122	1	(	(	PUNCT
ejpam-6029	122	2	sinh(2ω1(a	sinh(2ω1(a	PROPN
ejpam-6029	122	3	,	,	PUNCT
ejpam-6029	122	4	c)r	c)r	ADV
ejpam-6029	122	5	)	)	PUNCT
ejpam-6029	122	6	,	,	PUNCT
ejpam-6029	122	7	s2	s2	PROPN
ejpam-6029	122	8	+	+	PROPN
ejpam-6029	122	9	2u	2u	PROPN
ejpam-6029	122	10	2	2	NUM
ejpam-6029	122	11	)	)	PUNCT
ejpam-6029	122	12	and	and	CCONJ
ejpam-6029	122	13	g(u	g(u	PROPN
ejpam-6029	122	14	)	)	PUNCT
ejpam-6029	122	15	=	=	PRON
ejpam-6029	122	16	(	(	PUNCT
ejpam-6029	122	17	sinh(2ω2(c	sinh(2ω2(c	NOUN
ejpam-6029	122	18	,	,	PUNCT
ejpam-6029	122	19	b)r	b)r	NOUN
ejpam-6029	122	20	)	)	PUNCT
ejpam-6029	122	21	,	,	PUNCT
ejpam-6029	122	22	s2	s2	VERB
ejpam-6029	122	23	+	+	PROPN
ejpam-6029	122	24	2s	2s	PROPN
ejpam-6029	122	25	2	2	NUM
ejpam-6029	122	26	)	)	PUNCT
ejpam-6029	122	27	,	,	PUNCT
ejpam-6029	122	28	where	where	SCONJ
ejpam-6029	122	29	u	u	PROPN
ejpam-6029	122	30	∈	∈	PROPN
ejpam-6029	122	31	p	p	X
ejpam-6029	122	32	.	.	PUNCT
ejpam-6029	123	1	evidently	evidently	ADV
ejpam-6029	123	2	,	,	PUNCT
ejpam-6029	123	3	(	(	PUNCT
ejpam-6029	123	4	l1	l1	PROPN
ejpam-6029	123	5	)	)	PUNCT
ejpam-6029	123	6	and	and	CCONJ
ejpam-6029	123	7	(	(	PUNCT
ejpam-6029	123	8	l2	l2	NOUN
ejpam-6029	123	9	)	)	PUNCT
ejpam-6029	123	10	are	be	AUX
ejpam-6029	123	11	satisfied	satisfied	ADJ
ejpam-6029	123	12	.	.	PUNCT
ejpam-6029	124	1	since	since	SCONJ
ejpam-6029	124	2	sinh(r	sinh(r	PROPN
ejpam-6029	124	3	)	)	PUNCT
ejpam-6029	124	4	is	be	AUX
ejpam-6029	124	5	an	an	DET
ejpam-6029	124	6	increasing	increase	VERB
ejpam-6029	124	7	function	function	NOUN
ejpam-6029	124	8	,	,	PUNCT
ejpam-6029	124	9	for	for	ADP
ejpam-6029	124	10	all	all	DET
ejpam-6029	124	11	a	a	PRON
ejpam-6029	124	12	,	,	PUNCT
ejpam-6029	124	13	b	b	PROPN
ejpam-6029	124	14	≥	≥	NOUN
ejpam-6029	124	15	0	0	NUM
ejpam-6029	124	16	,	,	PUNCT
ejpam-6029	124	17	sinh(a+	sinh(a+	NOUN
ejpam-6029	124	18	b	b	X
ejpam-6029	124	19	)	)	PUNCT
ejpam-6029	124	20	≤	≤	NUM
ejpam-6029	124	21	sinh(2max{a	sinh(2max{a	NOUN
ejpam-6029	124	22	,	,	PUNCT
ejpam-6029	124	23	b	b	NOUN
ejpam-6029	124	24	}	}	PUNCT
ejpam-6029	124	25	)	)	PUNCT
ejpam-6029	124	26	≤	≤	PROPN
ejpam-6029	125	1	sinh(2a	sinh(2a	ADJ
ejpam-6029	125	2	)	)	PUNCT
ejpam-6029	125	3	+	+	PROPN
ejpam-6029	125	4	sinh(2b	sinh(2b	PROPN
ejpam-6029	125	5	)	)	PUNCT
ejpam-6029	125	6	.	.	PUNCT
ejpam-6029	126	1	therefore	therefore	ADV
ejpam-6029	126	2	,	,	PUNCT
ejpam-6029	126	3	for	for	ADP
ejpam-6029	126	4	each	each	DET
ejpam-6029	126	5	a	a	DET
ejpam-6029	126	6	,	,	PUNCT
ejpam-6029	126	7	b	b	NOUN
ejpam-6029	126	8	,	,	PUNCT
ejpam-6029	126	9	c	c	PROPN
ejpam-6029	126	10	∈	∈	PROPN
ejpam-6029	126	11	γ	γ	X
ejpam-6029	126	12	,	,	PUNCT
ejpam-6029	126	13	sinh	sinh	NOUN
ejpam-6029	126	14	(	(	PUNCT
ejpam-6029	126	15	eσ(a	eσ(a	PROPN
ejpam-6029	126	16	,	,	PUNCT
ejpam-6029	126	17	b	b	NOUN
ejpam-6029	126	18	)	)	PUNCT
ejpam-6029	126	19	)	)	PUNCT
ejpam-6029	126	20	≤	≤	NUM
ejpam-6029	126	21	sinh	sinh	NOUN
ejpam-6029	126	22	(	(	PUNCT
ejpam-6029	126	23	eω1(a	eω1(a	PROPN
ejpam-6029	126	24	,	,	PUNCT
ejpam-6029	126	25	c)σ(a	c)σ(a	NOUN
ejpam-6029	126	26	,	,	PUNCT
ejpam-6029	126	27	c	c	NOUN
ejpam-6029	126	28	)	)	PUNCT
ejpam-6029	127	1	+	+	CCONJ
ejpam-6029	127	2	eω2(c	eω2(c	PROPN
ejpam-6029	127	3	,	,	PUNCT
ejpam-6029	127	4	b)σ(c	b)σ(c	ADJ
ejpam-6029	127	5	,	,	PUNCT
ejpam-6029	127	6	b	b	NOUN
ejpam-6029	127	7	)	)	PUNCT
ejpam-6029	127	8	)	)	PUNCT
ejpam-6029	127	9	≤	≤	NUM
ejpam-6029	127	10	sinh	sinh	NOUN
ejpam-6029	127	11	(	(	PUNCT
ejpam-6029	127	12	ω1(a	ω1(a	PROPN
ejpam-6029	127	13	,	,	PUNCT
ejpam-6029	127	14	c	c	NOUN
ejpam-6029	127	15	)	)	PUNCT
ejpam-6029	127	16	sinh(eσ(a	sinh(eσ(a	ADJ
ejpam-6029	127	17	,	,	PUNCT
ejpam-6029	127	18	c	c	NOUN
ejpam-6029	127	19	)	)	PUNCT
ejpam-6029	127	20	)	)	PUNCT
ejpam-6029	128	1	+	+	PUNCT
ejpam-6029	128	2	ω2(c	ω2(c	NUM
ejpam-6029	128	3	,	,	PUNCT
ejpam-6029	128	4	b	b	NOUN
ejpam-6029	128	5	)	)	PUNCT
ejpam-6029	128	6	sinh(eσ(c	sinh(eσ(c	ADJ
ejpam-6029	128	7	,	,	PUNCT
ejpam-6029	128	8	b	b	NOUN
ejpam-6029	128	9	)	)	PUNCT
ejpam-6029	128	10	)	)	PUNCT
ejpam-6029	128	11	)	)	PUNCT
ejpam-6029	128	12	≤	≤	NUM
ejpam-6029	128	13	sinh	sinh	NOUN
ejpam-6029	128	14	(	(	PUNCT
ejpam-6029	128	15	2ω1(a	2ω1(a	NUM
ejpam-6029	128	16	,	,	PUNCT
ejpam-6029	128	17	c)lc(a	c)lc(a	NOUN
ejpam-6029	128	18	,	,	PUNCT
ejpam-6029	128	19	c	c	NOUN
ejpam-6029	128	20	)	)	PUNCT
ejpam-6029	128	21	)	)	PUNCT
ejpam-6029	129	1	+	+	CCONJ
ejpam-6029	129	2	sinh	sinh	NOUN
ejpam-6029	129	3	(	(	PUNCT
ejpam-6029	129	4	2ω2(c	2ω2(c	NUM
ejpam-6029	129	5	,	,	PUNCT
ejpam-6029	129	6	b)lc(c	b)lc(c	PROPN
ejpam-6029	129	7	,	,	PUNCT
ejpam-6029	129	8	b	b	NOUN
ejpam-6029	129	9	)	)	PUNCT
ejpam-6029	129	10	)	)	PUNCT
ejpam-6029	129	11	,	,	PUNCT
ejpam-6029	129	12	(	(	PUNCT
ejpam-6029	129	13	1	1	X
ejpam-6029	129	14	)	)	PUNCT
ejpam-6029	129	15	and	and	CCONJ
ejpam-6029	129	16	e(a+b	e(a+b	NOUN
ejpam-6029	129	17	)	)	PUNCT
ejpam-6029	130	1	−	−	ADP
ejpam-6029	130	2	1	1	NUM
ejpam-6029	130	3	≤	≤	NUM
ejpam-6029	130	4	ea+2c+b	ea+2c+b	CCONJ
ejpam-6029	130	5	−	−	PROPN
ejpam-6029	130	6	1	1	NUM
ejpam-6029	130	7	=	=	SYM
ejpam-6029	130	8	ea+ceb+c	ea+ceb+c	ADV
ejpam-6029	130	9	−	−	NUM
ejpam-6029	130	10	1	1	NUM
ejpam-6029	130	11	≤	≤	NUM
ejpam-6029	130	12	e2(a+c	e2(a+c	NOUN
ejpam-6029	130	13	)	)	PUNCT
ejpam-6029	131	1	+	+	SYM
ejpam-6029	131	2	e2(c+b	e2(c+b	X
ejpam-6029	131	3	)	)	PUNCT
ejpam-6029	131	4	2	2	NUM
ejpam-6029	131	5	−	−	PROPN
ejpam-6029	131	6	1	1	NUM
ejpam-6029	131	7	=	=	SYM
ejpam-6029	131	8	e2(a+c	e2(a+c	NOUN
ejpam-6029	131	9	)	)	PUNCT
ejpam-6029	131	10	−	−	NOUN
ejpam-6029	132	1	1	1	NUM
ejpam-6029	132	2	2	2	NUM
ejpam-6029	132	3	+	+	NUM
ejpam-6029	132	4	e2(c+b	e2(c+b	PROPN
ejpam-6029	132	5	)	)	PUNCT
ejpam-6029	132	6	−	−	PROPN
ejpam-6029	132	7	1	1	NUM
ejpam-6029	132	8	2	2	NUM
ejpam-6029	132	9	.	.	PUNCT
ejpam-6029	133	1	(	(	PUNCT
ejpam-6029	133	2	2	2	NUM
ejpam-6029	133	3	)	)	PUNCT
ejpam-6029	133	4	thus	thus	ADV
ejpam-6029	133	5	,	,	PUNCT
ejpam-6029	133	6	from	from	ADP
ejpam-6029	133	7	(	(	PUNCT
ejpam-6029	133	8	1	1	NUM
ejpam-6029	133	9	)	)	PUNCT
ejpam-6029	133	10	,	,	PUNCT
ejpam-6029	133	11	(	(	PUNCT
ejpam-6029	133	12	2	2	NUM
ejpam-6029	133	13	)	)	PUNCT
ejpam-6029	133	14	,	,	PUNCT
ejpam-6029	133	15	we	we	PRON
ejpam-6029	133	16	get	get	VERB
ejpam-6029	133	17	lc(a	lc(a	NOUN
ejpam-6029	133	18	,	,	PUNCT
ejpam-6029	133	19	b	b	X
ejpam-6029	133	20	)	)	PUNCT
ejpam-6029	133	21	⪯	⪯	NOUN
ejpam-6029	133	22	f(lc(a	f(lc(a	PROPN
ejpam-6029	133	23	,	,	PUNCT
ejpam-6029	133	24	c	c	NOUN
ejpam-6029	133	25	)	)	PUNCT
ejpam-6029	133	26	)	)	PUNCT
ejpam-6029	134	1	+	+	CCONJ
ejpam-6029	134	2	g(lc(c	g(lc(c	NOUN
ejpam-6029	134	3	,	,	PUNCT
ejpam-6029	134	4	b	b	NOUN
ejpam-6029	134	5	)	)	PUNCT
ejpam-6029	134	6	)	)	PUNCT
ejpam-6029	134	7	.	.	PUNCT
ejpam-6029	135	1	then	then	ADV
ejpam-6029	135	2	,	,	PUNCT
ejpam-6029	135	3	(	(	PUNCT
ejpam-6029	135	4	γ	γ	X
ejpam-6029	135	5	,	,	PUNCT
ejpam-6029	135	6	lc	lc	PROPN
ejpam-6029	135	7	)	)	PUNCT
ejpam-6029	135	8	is	be	AUX
ejpam-6029	135	9	a	a	DET
ejpam-6029	135	10	dccml	dccml	NOUN
ejpam-6029	135	11	-	-	PUNCT
ejpam-6029	135	12	space	space	NOUN
ejpam-6029	135	13	.	.	PUNCT
ejpam-6029	136	1	clearly	clearly	ADV
ejpam-6029	136	2	,	,	PUNCT
ejpam-6029	136	3	it	it	PRON
ejpam-6029	136	4	is	be	AUX
ejpam-6029	136	5	not	not	PART
ejpam-6029	136	6	c2cms	c2cms	PROPN
ejpam-6029	136	7	or	or	CCONJ
ejpam-6029	136	8	dcml	dcml	NOUN
ejpam-6029	136	9	-	-	PUNCT
ejpam-6029	136	10	space	space	NOUN
ejpam-6029	136	11	.	.	PUNCT
ejpam-6029	137	1	afterwards	afterwards	ADV
ejpam-6029	137	2	,	,	PUNCT
ejpam-6029	137	3	we	we	PRON
ejpam-6029	137	4	define	define	VERB
ejpam-6029	137	5	the	the	DET
ejpam-6029	137	6	topology	topology	NOUN
ejpam-6029	137	7	of	of	ADP
ejpam-6029	137	8	the	the	DET
ejpam-6029	137	9	dccml	dccml	NOUN
ejpam-6029	137	10	-	-	PUNCT
ejpam-6029	137	11	space	space	NOUN
ejpam-6029	137	12	on	on	ADP
ejpam-6029	137	13	γ	γ	PROPN
ejpam-6029	137	14	.	.	PROPN
ejpam-6029	137	15	definition	definition	NOUN
ejpam-6029	137	16	6	6	NUM
ejpam-6029	137	17	.	.	PUNCT
ejpam-6029	138	1	let	let	AUX
ejpam-6029	138	2	(	(	PUNCT
ejpam-6029	138	3	γ	γ	X
ejpam-6029	138	4	,	,	PUNCT
ejpam-6029	138	5	lc	lc	PROPN
ejpam-6029	138	6	)	)	PUNCT
ejpam-6029	138	7	be	be	AUX
ejpam-6029	138	8	a	a	DET
ejpam-6029	138	9	dccml	dccml	NOUN
ejpam-6029	138	10	-	-	PUNCT
ejpam-6029	138	11	space	space	NOUN
ejpam-6029	138	12	,	,	PUNCT
ejpam-6029	138	13	where	where	SCONJ
ejpam-6029	138	14	p	p	NOUN
ejpam-6029	138	15	is	be	AUX
ejpam-6029	138	16	a	a	DET
ejpam-6029	138	17	normal	normal	ADJ
ejpam-6029	138	18	cone	cone	NOUN
ejpam-6029	138	19	with	with	ADP
ejpam-6029	138	20	normal	normal	ADJ
ejpam-6029	138	21	constant	constant	ADJ
ejpam-6029	138	22	m	m	NOUN
ejpam-6029	138	23	,	,	PUNCT
ejpam-6029	138	24	and	and	CCONJ
ejpam-6029	138	25	{	{	PUNCT
ejpam-6029	138	26	an	an	PRON
ejpam-6029	138	27	}	}	PUNCT
ejpam-6029	138	28	be	be	AUX
ejpam-6029	138	29	a	a	DET
ejpam-6029	138	30	sequence	sequence	NOUN
ejpam-6029	138	31	in	in	ADP
ejpam-6029	138	32	γ	γ	PROPN
ejpam-6029	138	33	.	.	PUNCT
ejpam-6029	139	1	(	(	PUNCT
ejpam-6029	139	2	i	i	NOUN
ejpam-6029	139	3	)	)	PUNCT
ejpam-6029	139	4	the	the	DET
ejpam-6029	139	5	sequence	sequence	NOUN
ejpam-6029	139	6	{	{	PUNCT
ejpam-6029	139	7	an	an	PRON
ejpam-6029	139	8	}	}	PUNCT
ejpam-6029	139	9	is	be	AUX
ejpam-6029	139	10	called	call	VERB
ejpam-6029	139	11	convergent	convergent	NOUN
ejpam-6029	139	12	to	to	ADP
ejpam-6029	139	13	a0	a0	PROPN
ejpam-6029	139	14	∈	∈	PROPN
ejpam-6029	139	15	γ	γ	PROPN
ejpam-6029	139	16	if	if	SCONJ
ejpam-6029	139	17	lim	lim	PROPN
ejpam-6029	139	18	n→∞	n→∞	NUM
ejpam-6029	139	19	lc(an	lc(an	PROPN
ejpam-6029	139	20	,	,	PUNCT
ejpam-6029	139	21	a0	a0	PROPN
ejpam-6029	139	22	)	)	PUNCT
ejpam-6029	139	23	=	=	SYM
ejpam-6029	139	24	lc(a0	lc(a0	X
ejpam-6029	139	25	,	,	PUNCT
ejpam-6029	139	26	a0	a0	NOUN
ejpam-6029	139	27	)	)	PUNCT
ejpam-6029	139	28	,	,	PUNCT
ejpam-6029	140	1	i.e.	i.e.	X
ejpam-6029	140	2	,	,	PUNCT
ejpam-6029	140	3	lim	lim	PROPN
ejpam-6029	140	4	n→∞	n→∞	NUM
ejpam-6029	140	5	an	an	DET
ejpam-6029	140	6	=	=	PROPN
ejpam-6029	140	7	a0	a0	PROPN
ejpam-6029	140	8	.	.	PUNCT
ejpam-6029	140	9	(	(	PUNCT
ejpam-6029	140	10	ii	ii	NOUN
ejpam-6029	140	11	)	)	PUNCT
ejpam-6029	140	12	{	{	PUNCT
ejpam-6029	140	13	an	an	X
ejpam-6029	140	14	}	}	PUNCT
ejpam-6029	140	15	in	in	ADP
ejpam-6029	140	16	γ	γ	PROPN
ejpam-6029	140	17	is	be	AUX
ejpam-6029	140	18	called	call	VERB
ejpam-6029	140	19	lc	lc	NOUN
ejpam-6029	140	20	-	-	PUNCT
ejpam-6029	140	21	cauchy	cauchy	NOUN
ejpam-6029	140	22	if	if	SCONJ
ejpam-6029	140	23	lim	lim	PROPN
ejpam-6029	140	24	n	n	CCONJ
ejpam-6029	140	25	,	,	PUNCT
ejpam-6029	140	26	m→∞	m→∞	NOUN
ejpam-6029	140	27	lc(an	lc(an	PROPN
ejpam-6029	140	28	,	,	PUNCT
ejpam-6029	140	29	am	be	AUX
ejpam-6029	140	30	)	)	PUNCT
ejpam-6029	140	31	is	be	AUX
ejpam-6029	140	32	a	a	DET
ejpam-6029	140	33	converges	converge	NOUN
ejpam-6029	140	34	in	in	ADP
ejpam-6029	140	35	γ	γ	NOUN
ejpam-6029	140	36	,	,	PUNCT
ejpam-6029	140	37	i.e.	i.e.	X
ejpam-6029	140	38	,	,	PUNCT
ejpam-6029	140	39	for	for	ADP
ejpam-6029	140	40	every	every	DET
ejpam-6029	140	41	c	c	PROPN
ejpam-6029	140	42	∈	∈	PROPN
ejpam-6029	140	43	e	e	NOUN
ejpam-6029	140	44	with	with	ADP
ejpam-6029	140	45	0e	0e	NOUN
ejpam-6029	140	46	≪	≪	VERB
ejpam-6029	140	47	c	c	X
ejpam-6029	140	48	,	,	PUNCT
ejpam-6029	140	49	there	there	PRON
ejpam-6029	140	50	is	be	VERB
ejpam-6029	140	51	a	a	DET
ejpam-6029	140	52	positive	positive	ADJ
ejpam-6029	140	53	integer	integer	NOUN
ejpam-6029	140	54	n0	n0	NOUN
ejpam-6029	140	55	∈	∈	PROPN
ejpam-6029	140	56	n	n	PRON
ejpam-6029	140	57	such	such	ADJ
ejpam-6029	140	58	that	that	SCONJ
ejpam-6029	140	59	lc(an	lc(an	PROPN
ejpam-6029	140	60	,	,	PUNCT
ejpam-6029	140	61	am	be	AUX
ejpam-6029	140	62	)	)	PUNCT
ejpam-6029	140	63	≪	≪	PUNCT
ejpam-6029	140	64	c	c	NOUN
ejpam-6029	140	65	for	for	ADP
ejpam-6029	140	66	all	all	DET
ejpam-6029	140	67	n	n	CCONJ
ejpam-6029	140	68	,	,	PUNCT
ejpam-6029	140	69	m	m	VERB
ejpam-6029	140	70	>	>	X
ejpam-6029	140	71	n0	n0	PROPN
ejpam-6029	140	72	.	.	PUNCT
ejpam-6029	140	73	a.	a.	PROPN
ejpam-6029	140	74	a.	a.	PROPN
ejpam-6029	140	75	hijab	hijab	PROPN
ejpam-6029	140	76	et	et	PROPN
ejpam-6029	140	77	al	al	PROPN
ejpam-6029	140	78	.	.	PUNCT
ejpam-6029	140	79	/	/	SYM
ejpam-6029	140	80	eur	eur	PROPN
ejpam-6029	140	81	.	.	PUNCT
ejpam-6029	141	1	j.	j.	PROPN
ejpam-6029	141	2	pure	pure	PROPN
ejpam-6029	141	3	appl	appl	PROPN
ejpam-6029	141	4	.	.	PROPN
ejpam-6029	141	5	math	math	PROPN
ejpam-6029	141	6	,	,	PUNCT
ejpam-6029	141	7	18	18	NUM
ejpam-6029	141	8	(	(	PUNCT
ejpam-6029	141	9	2	2	NUM
ejpam-6029	141	10	)	)	PUNCT
ejpam-6029	141	11	(	(	PUNCT
ejpam-6029	141	12	2025	2025	NUM
ejpam-6029	141	13	)	)	PUNCT
ejpam-6029	141	14	,	,	PUNCT
ejpam-6029	141	15	6029	6029	NUM
ejpam-6029	141	16	6	6	NUM
ejpam-6029	141	17	of	of	ADP
ejpam-6029	141	18	23	23	NUM
ejpam-6029	141	19	(	(	PUNCT
ejpam-6029	141	20	iii	iii	NOUN
ejpam-6029	141	21	)	)	PUNCT
ejpam-6029	141	22	the	the	DET
ejpam-6029	141	23	space	space	NOUN
ejpam-6029	141	24	(	(	PUNCT
ejpam-6029	141	25	γ	γ	X
ejpam-6029	141	26	,	,	PUNCT
ejpam-6029	141	27	lc	lc	PROPN
ejpam-6029	141	28	)	)	PUNCT
ejpam-6029	141	29	is	be	AUX
ejpam-6029	141	30	said	say	VERB
ejpam-6029	141	31	to	to	PART
ejpam-6029	141	32	be	be	AUX
ejpam-6029	141	33	lc	lc	NOUN
ejpam-6029	141	34	-	-	PUNCT
ejpam-6029	141	35	complete	complete	ADJ
ejpam-6029	141	36	if	if	SCONJ
ejpam-6029	141	37	every	every	DET
ejpam-6029	141	38	lc	lc	NOUN
ejpam-6029	141	39	-	-	PUNCT
ejpam-6029	141	40	cauchy	cauchy	NOUN
ejpam-6029	141	41	sequence	sequence	NOUN
ejpam-6029	141	42	in	in	ADP
ejpam-6029	141	43	γ	γ	PROPN
ejpam-6029	141	44	converges	converge	NOUN
ejpam-6029	141	45	to	to	ADP
ejpam-6029	141	46	a	a	DET
ejpam-6029	141	47	point	point	NOUN
ejpam-6029	141	48	in	in	ADP
ejpam-6029	141	49	γ	γ	PROPN
ejpam-6029	141	50	,	,	PUNCT
ejpam-6029	141	51	i.e.	i.e.	X
ejpam-6029	141	52	,	,	PUNCT
ejpam-6029	141	53	lim	lim	PROPN
ejpam-6029	141	54	n→∞	n→∞	NUM
ejpam-6029	141	55	lc(an	lc(an	PROPN
ejpam-6029	141	56	,	,	PUNCT
ejpam-6029	141	57	a0	a0	PROPN
ejpam-6029	141	58	)	)	PUNCT
ejpam-6029	141	59	=	=	SYM
ejpam-6029	141	60	lc(a0	lc(a0	X
ejpam-6029	141	61	,	,	PUNCT
ejpam-6029	141	62	a0	a0	NOUN
ejpam-6029	141	63	)	)	PUNCT
ejpam-6029	141	64	=	=	PROPN
ejpam-6029	141	65	lim	lim	PROPN
ejpam-6029	141	66	n	n	CCONJ
ejpam-6029	141	67	,	,	PUNCT
ejpam-6029	141	68	m→∞	m→∞	NOUN
ejpam-6029	141	69	lc(an	lc(an	PROPN
ejpam-6029	141	70	,	,	PUNCT
ejpam-6029	141	71	am	be	AUX
ejpam-6029	141	72	)	)	PUNCT
ejpam-6029	141	73	.	.	PUNCT
ejpam-6029	142	1	definition	definition	NOUN
ejpam-6029	142	2	7	7	NUM
ejpam-6029	142	3	.	.	PUNCT
ejpam-6029	143	1	let	let	AUX
ejpam-6029	143	2	(	(	PUNCT
ejpam-6029	143	3	γ	γ	X
ejpam-6029	143	4	,	,	PUNCT
ejpam-6029	143	5	lc	lc	PROPN
ejpam-6029	143	6	)	)	PUNCT
ejpam-6029	143	7	be	be	AUX
ejpam-6029	143	8	a	a	DET
ejpam-6029	143	9	dccml	dccml	NOUN
ejpam-6029	143	10	-	-	PUNCT
ejpam-6029	143	11	space	space	NOUN
ejpam-6029	143	12	via	via	ADP
ejpam-6029	143	13	f	f	PROPN
ejpam-6029	143	14	and	and	CCONJ
ejpam-6029	143	15	g	g	NOUN
ejpam-6029	143	16	,	,	PUNCT
ejpam-6029	143	17	where	where	SCONJ
ejpam-6029	143	18	p	p	NOUN
ejpam-6029	143	19	is	be	AUX
ejpam-6029	143	20	a	a	DET
ejpam-6029	143	21	normal	normal	ADJ
ejpam-6029	143	22	cone	cone	NOUN
ejpam-6029	143	23	with	with	ADP
ejpam-6029	143	24	normal	normal	ADJ
ejpam-6029	143	25	constant	constant	ADJ
ejpam-6029	143	26	m	m	NOUN
ejpam-6029	143	27	.	.	PUNCT
ejpam-6029	144	1	suppose	suppose	VERB
ejpam-6029	144	2	a0	a0	PROPN
ejpam-6029	144	3	∈	∈	PROPN
ejpam-6029	144	4	γ	γ	NOUN
ejpam-6029	144	5	and	and	CCONJ
ejpam-6029	144	6	0e	0e	PROPN
ejpam-6029	144	7	≺	≺	NOUN
ejpam-6029	144	8	c.	c.	PROPN
ejpam-6029	144	9	then	then	ADV
ejpam-6029	144	10	lc	lc	PROPN
ejpam-6029	144	11	-	-	PUNCT
ejpam-6029	144	12	ball	ball	NOUN
ejpam-6029	144	13	with	with	ADP
ejpam-6029	144	14	center	center	NOUN
ejpam-6029	144	15	a0	a0	NOUN
ejpam-6029	144	16	and	and	CCONJ
ejpam-6029	144	17	radius	radius	PROPN
ejpam-6029	144	18	c	c	PROPN
ejpam-6029	144	19	is	be	AUX
ejpam-6029	144	20	b(a0	b(a0	ADJ
ejpam-6029	144	21	,	,	PUNCT
ejpam-6029	144	22	c	c	X
ejpam-6029	144	23	)	)	PUNCT
ejpam-6029	144	24	=	=	PRON
ejpam-6029	144	25	{	{	PUNCT
ejpam-6029	144	26	b	b	X
ejpam-6029	144	27	∈	∈	PROPN
ejpam-6029	144	28	γ	γ	X
ejpam-6029	144	29	:	:	PUNCT
ejpam-6029	144	30	|lc(a0	|lc(a0	NUM
ejpam-6029	144	31	,	,	PUNCT
ejpam-6029	144	32	b	b	X
ejpam-6029	144	33	)	)	PUNCT
ejpam-6029	145	1	−	−	NOUN
ejpam-6029	145	2	lc(a0	lc(a0	NOUN
ejpam-6029	145	3	,	,	PUNCT
ejpam-6029	145	4	a0)|	a0)|	NOUN
ejpam-6029	145	5	≺	≺	NOUN
ejpam-6029	145	6	c	c	NOUN
ejpam-6029	145	7	}	}	PUNCT
ejpam-6029	145	8	,	,	PUNCT
ejpam-6029	145	9	and	and	CCONJ
ejpam-6029	145	10	put	put	VERB
ejpam-6029	145	11	b	b	NOUN
ejpam-6029	145	12	=	=	SYM
ejpam-6029	145	13	{	{	PUNCT
ejpam-6029	145	14	b(a0	b(a0	NOUN
ejpam-6029	145	15	,	,	PUNCT
ejpam-6029	145	16	c	c	NOUN
ejpam-6029	145	17	)	)	PUNCT
ejpam-6029	145	18	:	:	PUNCT
ejpam-6029	145	19	a0	a0	PROPN
ejpam-6029	145	20	∈	∈	PROPN
ejpam-6029	145	21	γ	γ	NOUN
ejpam-6029	145	22	and	and	CCONJ
ejpam-6029	145	23	0e	0e	NOUN
ejpam-6029	145	24	≪	≪	ADJ
ejpam-6029	145	25	c	c	X
ejpam-6029	145	26	}	}	PUNCT
ejpam-6029	145	27	.	.	PUNCT
ejpam-6029	146	1	lemma	lemma	PROPN
ejpam-6029	146	2	1	1	NUM
ejpam-6029	146	3	.	.	PUNCT
ejpam-6029	147	1	the	the	DET
ejpam-6029	147	2	collection	collection	NOUN
ejpam-6029	147	3	b	b	PROPN
ejpam-6029	147	4	=	=	SYM
ejpam-6029	147	5	{	{	PUNCT
ejpam-6029	147	6	b(a0	b(a0	NOUN
ejpam-6029	147	7	,	,	PUNCT
ejpam-6029	147	8	c	c	NOUN
ejpam-6029	147	9	)	)	PUNCT
ejpam-6029	147	10	:	:	PUNCT
ejpam-6029	147	11	a0	a0	PROPN
ejpam-6029	147	12	∈	∈	PROPN
ejpam-6029	147	13	γ	γ	NOUN
ejpam-6029	147	14	and	and	CCONJ
ejpam-6029	147	15	0e	0e	NOUN
ejpam-6029	147	16	≪	≪	PUNCT
ejpam-6029	147	17	c	c	X
ejpam-6029	147	18	}	}	PUNCT
ejpam-6029	147	19	of	of	ADP
ejpam-6029	147	20	all	all	DET
ejpam-6029	147	21	open	open	ADJ
ejpam-6029	147	22	balls	ball	NOUN
ejpam-6029	147	23	forms	form	VERB
ejpam-6029	147	24	a	a	DET
ejpam-6029	147	25	basis	basis	NOUN
ejpam-6029	147	26	for	for	ADP
ejpam-6029	147	27	a	a	DET
ejpam-6029	147	28	topology	topology	NOUN
ejpam-6029	147	29	τlc	τlc	NOUN
ejpam-6029	147	30	on	on	ADP
ejpam-6029	147	31	γ	γ	PROPN
ejpam-6029	147	32	.	.	PUNCT
ejpam-6029	147	33	proof	proof	NOUN
ejpam-6029	147	34	.	.	PUNCT
ejpam-6029	148	1	let	let	VERB
ejpam-6029	148	2	a0	a0	PROPN
ejpam-6029	148	3	∈	∈	PROPN
ejpam-6029	148	4	γ	γ	PROPN
ejpam-6029	148	5	.	.	PUNCT
ejpam-6029	149	1	so	so	ADV
ejpam-6029	149	2	,	,	PUNCT
ejpam-6029	149	3	a0	a0	PROPN
ejpam-6029	149	4	∈	∈	PROPN
ejpam-6029	149	5	b(a0	b(a0	NOUN
ejpam-6029	149	6	,	,	PUNCT
ejpam-6029	149	7	c	c	NOUN
ejpam-6029	149	8	)	)	PUNCT
ejpam-6029	149	9	for	for	ADP
ejpam-6029	149	10	0e	0e	NOUN
ejpam-6029	149	11	≺	≺	NOUN
ejpam-6029	149	12	c	c	X
ejpam-6029	149	13	,	,	PUNCT
ejpam-6029	149	14	which	which	PRON
ejpam-6029	149	15	implies	imply	VERB
ejpam-6029	149	16	that	that	SCONJ
ejpam-6029	149	17	a0	a0	PROPN
ejpam-6029	149	18	∈	∈	PROPN
ejpam-6029	149	19	b(a0	b(a0	X
ejpam-6029	149	20	,	,	PUNCT
ejpam-6029	149	21	c	c	X
ejpam-6029	149	22	)	)	PUNCT
ejpam-6029	149	23	⊆⋃	⊆⋃	PROPN
ejpam-6029	149	24	a0∈γ	a0∈γ	PROPN
ejpam-6029	149	25	0e≺c	0e≺c	NOUN
ejpam-6029	149	26	b(a0	b(a0	X
ejpam-6029	149	27	,	,	PUNCT
ejpam-6029	149	28	c	c	NOUN
ejpam-6029	149	29	)	)	PUNCT
ejpam-6029	149	30	.	.	PUNCT
ejpam-6029	150	1	now	now	ADV
ejpam-6029	150	2	,	,	PUNCT
ejpam-6029	150	3	assume	assume	VERB
ejpam-6029	150	4	that	that	SCONJ
ejpam-6029	150	5	b	b	PROPN
ejpam-6029	150	6	∈	∈	PROPN
ejpam-6029	150	7	b(a0	b(a0	NOUN
ejpam-6029	150	8	,	,	PUNCT
ejpam-6029	150	9	c1	c1	PROPN
ejpam-6029	150	10	)	)	PUNCT
ejpam-6029	150	11	∩	∩	PROPN
ejpam-6029	150	12	b(a0	b(a0	X
ejpam-6029	150	13	,	,	PUNCT
ejpam-6029	150	14	c2	c2	PROPN
ejpam-6029	150	15	)	)	PUNCT
ejpam-6029	150	16	.	.	PUNCT
ejpam-6029	151	1	then	then	ADV
ejpam-6029	151	2	there	there	PRON
ejpam-6029	151	3	exists	exist	VERB
ejpam-6029	151	4	0e	0e	NOUN
ejpam-6029	151	5	≺	≺	NOUN
ejpam-6029	151	6	c	c	NOUN
ejpam-6029	151	7	such	such	ADJ
ejpam-6029	151	8	that	that	DET
ejpam-6029	151	9	b(a0	b(a0	NOUN
ejpam-6029	151	10	,	,	PUNCT
ejpam-6029	151	11	c	c	X
ejpam-6029	151	12	)	)	PUNCT
ejpam-6029	151	13	⊆	⊆	NUM
ejpam-6029	151	14	b(a0	b(a0	X
ejpam-6029	151	15	,	,	PUNCT
ejpam-6029	151	16	c1	c1	PROPN
ejpam-6029	151	17	)	)	PUNCT
ejpam-6029	151	18	and	and	CCONJ
ejpam-6029	151	19	b(a0	b(a0	X
ejpam-6029	151	20	,	,	PUNCT
ejpam-6029	151	21	c	c	X
ejpam-6029	151	22	)	)	PUNCT
ejpam-6029	151	23	⊆	⊆	NUM
ejpam-6029	151	24	b(a0	b(a0	X
ejpam-6029	151	25	,	,	PUNCT
ejpam-6029	151	26	c2	c2	PROPN
ejpam-6029	151	27	)	)	PUNCT
ejpam-6029	151	28	.	.	PUNCT
ejpam-6029	152	1	let	let	VERB
ejpam-6029	152	2	d	d	X
ejpam-6029	152	3	∈	∈	PROPN
ejpam-6029	152	4	b(b	b(b	PROPN
ejpam-6029	152	5	,	,	PUNCT
ejpam-6029	152	6	c	c	NOUN
ejpam-6029	152	7	)	)	PUNCT
ejpam-6029	152	8	,	,	PUNCT
ejpam-6029	152	9	then	then	ADV
ejpam-6029	152	10	lc(b	lc(b	NOUN
ejpam-6029	152	11	,	,	PUNCT
ejpam-6029	152	12	d	d	NOUN
ejpam-6029	152	13	)	)	PUNCT
ejpam-6029	152	14	−	−	NOUN
ejpam-6029	152	15	lc(b	lc(b	NOUN
ejpam-6029	152	16	,	,	PUNCT
ejpam-6029	152	17	b	b	NOUN
ejpam-6029	152	18	)	)	PUNCT
ejpam-6029	152	19	≪	≪	PUNCT
ejpam-6029	152	20	c.	c.	PROPN
ejpam-6029	152	21	thus	thus	ADV
ejpam-6029	152	22	,	,	PUNCT
ejpam-6029	152	23	b(b	b(b	PROPN
ejpam-6029	152	24	,	,	PUNCT
ejpam-6029	152	25	c	c	X
ejpam-6029	152	26	)	)	PUNCT
ejpam-6029	152	27	⊆	⊆	NUM
ejpam-6029	152	28	b(a0	b(a0	X
ejpam-6029	152	29	,	,	PUNCT
ejpam-6029	152	30	c1	c1	PROPN
ejpam-6029	152	31	)	)	PUNCT
ejpam-6029	152	32	∩b(a0	∩b(a0	PROPN
ejpam-6029	152	33	,	,	PUNCT
ejpam-6029	152	34	c2	c2	PROPN
ejpam-6029	152	35	)	)	PUNCT
ejpam-6029	152	36	.	.	PUNCT
ejpam-6029	153	1	definition	definition	NOUN
ejpam-6029	153	2	8	8	NUM
ejpam-6029	153	3	.	.	PUNCT
ejpam-6029	154	1	[	[	X
ejpam-6029	154	2	36	36	NUM
ejpam-6029	154	3	]	]	PUNCT
ejpam-6029	154	4	presume	presume	VERB
ejpam-6029	154	5	p	p	NOUN
ejpam-6029	154	6	is	be	AUX
ejpam-6029	154	7	a	a	DET
ejpam-6029	154	8	solid	solid	ADJ
ejpam-6029	154	9	cone	cone	NOUN
ejpam-6029	154	10	in	in	ADP
ejpam-6029	154	11	a	a	DET
ejpam-6029	154	12	banach	banach	NOUN
ejpam-6029	154	13	space	space	NOUN
ejpam-6029	154	14	e.	e.	PROPN
ejpam-6029	155	1	a	a	DET
ejpam-6029	155	2	sequence	sequence	NOUN
ejpam-6029	155	3	{	{	PUNCT
ejpam-6029	155	4	an	an	PROPN
ejpam-6029	155	5	}	}	PUNCT
ejpam-6029	155	6	⊂	⊂	PROPN
ejpam-6029	155	7	p	p	X
ejpam-6029	155	8	is	be	AUX
ejpam-6029	155	9	said	say	VERB
ejpam-6029	155	10	to	to	PART
ejpam-6029	155	11	converge	converge	VERB
ejpam-6029	155	12	if	if	SCONJ
ejpam-6029	155	13	for	for	ADP
ejpam-6029	155	14	each	each	DET
ejpam-6029	155	15	0e	0e	NOUN
ejpam-6029	155	16	≪	≪	PUNCT
ejpam-6029	155	17	c	c	X
ejpam-6029	155	18	there	there	PRON
ejpam-6029	155	19	exists	exist	VERB
ejpam-6029	155	20	n	n	PRON
ejpam-6029	155	21	such	such	ADJ
ejpam-6029	155	22	that	that	SCONJ
ejpam-6029	155	23	an	an	DET
ejpam-6029	155	24	≪	≪	ADJ
ejpam-6029	155	25	c	c	NOUN
ejpam-6029	155	26	for	for	ADP
ejpam-6029	155	27	all	all	DET
ejpam-6029	155	28	n	n	CCONJ
ejpam-6029	155	29	>	>	X
ejpam-6029	155	30	n	n	X
ejpam-6029	155	31	.	.	PUNCT
ejpam-6029	156	1	lemma	lemma	PROPN
ejpam-6029	156	2	2	2	NUM
ejpam-6029	156	3	.	.	PUNCT
ejpam-6029	157	1	[	[	X
ejpam-6029	157	2	32	32	NUM
ejpam-6029	157	3	]	]	PUNCT
ejpam-6029	157	4	if	if	SCONJ
ejpam-6029	157	5	e	e	NOUN
ejpam-6029	157	6	is	be	AUX
ejpam-6029	157	7	a	a	DET
ejpam-6029	157	8	real	real	ADJ
ejpam-6029	157	9	banach	banach	NOUN
ejpam-6029	157	10	space	space	NOUN
ejpam-6029	157	11	with	with	ADP
ejpam-6029	157	12	a	a	DET
ejpam-6029	157	13	solid	solid	ADJ
ejpam-6029	157	14	cone	cone	NOUN
ejpam-6029	157	15	p	p	NOUN
ejpam-6029	157	16	and	and	CCONJ
ejpam-6029	157	17	{	{	PUNCT
ejpam-6029	157	18	an	an	PROPN
ejpam-6029	157	19	}	}	PUNCT
ejpam-6029	157	20	⊂	⊂	PROPN
ejpam-6029	157	21	p	p	X
ejpam-6029	157	22	is	be	AUX
ejpam-6029	157	23	a	a	DET
ejpam-6029	157	24	sequence	sequence	NOUN
ejpam-6029	157	25	with	with	ADP
ejpam-6029	157	26	∥an∥	∥an∥	ADP
ejpam-6029	157	27	→	→	SYM
ejpam-6029	157	28	0	0	NUM
ejpam-6029	157	29	,	,	PUNCT
ejpam-6029	157	30	as	as	ADP
ejpam-6029	157	31	n→	n→	ADV
ejpam-6029	157	32	+	+	PROPN
ejpam-6029	157	33	∞	∞	PROPN
ejpam-6029	157	34	,	,	PUNCT
ejpam-6029	157	35	then	then	ADV
ejpam-6029	157	36	{	{	PUNCT
ejpam-6029	157	37	an	an	PRON
ejpam-6029	157	38	}	}	PUNCT
ejpam-6029	157	39	is	be	AUX
ejpam-6029	157	40	a	a	DET
ejpam-6029	157	41	convergent	convergent	NOUN
ejpam-6029	157	42	sequence	sequence	NOUN
ejpam-6029	157	43	.	.	PUNCT
ejpam-6029	158	1	lemma	lemma	PROPN
ejpam-6029	158	2	3	3	NUM
ejpam-6029	158	3	.	.	PUNCT
ejpam-6029	159	1	[	[	X
ejpam-6029	159	2	32	32	NUM
ejpam-6029	159	3	]	]	PUNCT
ejpam-6029	159	4	let	let	VERB
ejpam-6029	159	5	e	e	PRON
ejpam-6029	159	6	be	be	AUX
ejpam-6029	159	7	a	a	DET
ejpam-6029	159	8	real	real	ADJ
ejpam-6029	159	9	banach	banach	NOUN
ejpam-6029	159	10	space	space	NOUN
ejpam-6029	159	11	with	with	ADP
ejpam-6029	159	12	a	a	DET
ejpam-6029	159	13	solid	solid	ADJ
ejpam-6029	159	14	cone	cone	NOUN
ejpam-6029	159	15	p	p	NOUN
ejpam-6029	159	16	.	.	PUNCT
ejpam-6029	160	1	(	(	PUNCT
ejpam-6029	160	2	i	i	NOUN
ejpam-6029	160	3	)	)	PUNCT
ejpam-6029	160	4	if	if	SCONJ
ejpam-6029	160	5	r	r	NOUN
ejpam-6029	160	6	,	,	PUNCT
ejpam-6029	160	7	s	s	PROPN
ejpam-6029	160	8	,	,	PUNCT
ejpam-6029	160	9	t	t	PROPN
ejpam-6029	160	10	∈	∈	PROPN
ejpam-6029	160	11	e	e	NOUN
ejpam-6029	160	12	and	and	CCONJ
ejpam-6029	160	13	r	r	NOUN
ejpam-6029	160	14	⪯	⪯	NOUN
ejpam-6029	160	15	s	s	PART
ejpam-6029	160	16	≪	≪	PROPN
ejpam-6029	160	17	t	t	PROPN
ejpam-6029	160	18	,	,	PUNCT
ejpam-6029	160	19	then	then	ADV
ejpam-6029	160	20	r	r	NOUN
ejpam-6029	160	21	≪	≪	VERB
ejpam-6029	160	22	t.	t.	PROPN
ejpam-6029	160	23	(	(	PUNCT
ejpam-6029	160	24	ii	ii	PROPN
ejpam-6029	160	25	)	)	PUNCT
ejpam-6029	160	26	if	if	SCONJ
ejpam-6029	160	27	r	r	NOUN
ejpam-6029	160	28	∈	∈	PROPN
ejpam-6029	160	29	p	p	NOUN
ejpam-6029	160	30	and	and	CCONJ
ejpam-6029	160	31	r	r	NOUN
ejpam-6029	160	32	≪	≪	NOUN
ejpam-6029	160	33	t	t	NOUN
ejpam-6029	160	34	for	for	ADP
ejpam-6029	160	35	each	each	DET
ejpam-6029	160	36	t	t	NOUN
ejpam-6029	160	37	≫	≫	PROPN
ejpam-6029	160	38	0e	0e	NOUN
ejpam-6029	160	39	,	,	PUNCT
ejpam-6029	160	40	then	then	ADV
ejpam-6029	160	41	r	r	NOUN
ejpam-6029	160	42	=	=	SYM
ejpam-6029	160	43	0e	0e	NOUN
ejpam-6029	160	44	.	.	PUNCT
ejpam-6029	161	1	in	in	ADP
ejpam-6029	161	2	general	general	ADJ
ejpam-6029	161	3	,	,	PUNCT
ejpam-6029	161	4	the	the	DET
ejpam-6029	161	5	limit	limit	NOUN
ejpam-6029	161	6	of	of	ADP
ejpam-6029	161	7	a	a	DET
ejpam-6029	161	8	convergent	convergent	NOUN
ejpam-6029	161	9	sequence	sequence	NOUN
ejpam-6029	161	10	in	in	ADP
ejpam-6029	161	11	dccml	dccml	NOUN
ejpam-6029	161	12	-	-	PUNCT
ejpam-6029	161	13	space	space	NOUN
ejpam-6029	161	14	may	may	AUX
ejpam-6029	161	15	not	not	PART
ejpam-6029	161	16	be	be	AUX
ejpam-6029	161	17	unique	unique	ADJ
ejpam-6029	161	18	.	.	PUNCT
ejpam-6029	162	1	proposition	proposition	NOUN
ejpam-6029	162	2	1	1	NUM
ejpam-6029	162	3	.	.	PUNCT
ejpam-6029	163	1	let	let	VERB
ejpam-6029	163	2	e	e	PRON
ejpam-6029	163	3	be	be	AUX
ejpam-6029	163	4	a	a	DET
ejpam-6029	163	5	real	real	ADJ
ejpam-6029	163	6	banach	banach	NOUN
ejpam-6029	163	7	space	space	NOUN
ejpam-6029	163	8	with	with	ADP
ejpam-6029	163	9	a	a	DET
ejpam-6029	163	10	solid	solid	ADJ
ejpam-6029	163	11	cone	cone	NOUN
ejpam-6029	163	12	p	p	NOUN
ejpam-6029	163	13	and	and	CCONJ
ejpam-6029	163	14	{	{	PUNCT
ejpam-6029	163	15	an	an	PROPN
ejpam-6029	163	16	}	}	PUNCT
ejpam-6029	163	17	⊂	⊂	PROPN
ejpam-6029	163	18	p	p	X
ejpam-6029	163	19	.	.	PUNCT
ejpam-6029	164	1	let	let	VERB
ejpam-6029	164	2	(	(	PUNCT
ejpam-6029	164	3	γ	γ	X
ejpam-6029	164	4	,	,	PUNCT
ejpam-6029	164	5	lc	lc	PROPN
ejpam-6029	164	6	)	)	PUNCT
ejpam-6029	164	7	be	be	AUX
ejpam-6029	164	8	a	a	DET
ejpam-6029	164	9	dccml	dccml	NOUN
ejpam-6029	164	10	-	-	PUNCT
ejpam-6029	164	11	space	space	NOUN
ejpam-6029	164	12	via	via	ADP
ejpam-6029	164	13	f	f	PROPN
ejpam-6029	164	14	and	and	CCONJ
ejpam-6029	164	15	g.	g.	PROPN
ejpam-6029	164	16	assume	assume	AUX
ejpam-6029	164	17	lim	lim	PROPN
ejpam-6029	164	18	n→∞	n→∞	NUM
ejpam-6029	164	19	lc(an	lc(an	PROPN
ejpam-6029	164	20	,	,	PUNCT
ejpam-6029	164	21	a0	a0	PROPN
ejpam-6029	164	22	)	)	PUNCT
ejpam-6029	164	23	=	=	SYM
ejpam-6029	165	1	0e	0e	NOUN
ejpam-6029	165	2	.	.	PUNCT
ejpam-6029	166	1	then	then	ADV
ejpam-6029	166	2	,	,	PUNCT
ejpam-6029	166	3	every	every	DET
ejpam-6029	166	4	convergent	convergent	NOUN
ejpam-6029	166	5	sequence	sequence	NOUN
ejpam-6029	166	6	has	have	VERB
ejpam-6029	166	7	a	a	DET
ejpam-6029	166	8	unique	unique	ADJ
ejpam-6029	166	9	limit	limit	NOUN
ejpam-6029	166	10	,	,	PUNCT
ejpam-6029	166	11	i.e.	i.e.	X
ejpam-6029	166	12	,	,	PUNCT
ejpam-6029	166	13	∥lc(an	∥lc(an	PROPN
ejpam-6029	166	14	,	,	PUNCT
ejpam-6029	166	15	a0)∥	a0)∥	PUNCT
ejpam-6029	166	16	→	→	SYM
ejpam-6029	166	17	0	0	NUM
ejpam-6029	166	18	implies	imply	VERB
ejpam-6029	166	19	that	that	SCONJ
ejpam-6029	166	20	lim	lim	PROPN
ejpam-6029	166	21	n→∞	n→∞	PRON
ejpam-6029	166	22	an	an	DET
ejpam-6029	166	23	=	=	PROPN
ejpam-6029	166	24	a0	a0	NOUN
ejpam-6029	166	25	is	be	AUX
ejpam-6029	166	26	unique	unique	ADJ
ejpam-6029	166	27	.	.	PUNCT
ejpam-6029	167	1	proof	proof	NOUN
ejpam-6029	167	2	.	.	PUNCT
ejpam-6029	168	1	the	the	DET
ejpam-6029	168	2	proof	proof	NOUN
ejpam-6029	168	3	is	be	AUX
ejpam-6029	168	4	omitted	omit	VERB
ejpam-6029	168	5	.	.	PUNCT
ejpam-6029	169	1	let	let	VERB
ejpam-6029	169	2	(	(	PUNCT
ejpam-6029	169	3	γ	γ	X
ejpam-6029	169	4	,	,	PUNCT
ejpam-6029	169	5	lc	lc	PROPN
ejpam-6029	169	6	)	)	PUNCT
ejpam-6029	169	7	be	be	AUX
ejpam-6029	169	8	a	a	DET
ejpam-6029	169	9	dccml	dccml	NOUN
ejpam-6029	169	10	-	-	PUNCT
ejpam-6029	169	11	space	space	NOUN
ejpam-6029	169	12	.	.	PUNCT
ejpam-6029	170	1	define	define	VERB
ejpam-6029	170	2	l̂c	l̂c	NOUN
ejpam-6029	170	3	:	:	PUNCT
ejpam-6029	170	4	γ	γ	X
ejpam-6029	170	5	2	2	NUM
ejpam-6029	170	6	→	→	SYM
ejpam-6029	170	7	e	e	X
ejpam-6029	170	8	by	by	ADP
ejpam-6029	170	9	l̂c(a	l̂c(a	PROPN
ejpam-6029	170	10	,	,	PUNCT
ejpam-6029	170	11	b	b	NOUN
ejpam-6029	170	12	)	)	PUNCT
ejpam-6029	170	13	=	=	SYM
ejpam-6029	170	14	|2lc(a	|2lc(a	PROPN
ejpam-6029	170	15	,	,	PUNCT
ejpam-6029	170	16	b)−	b)−	PROPN
ejpam-6029	170	17	lc(a	lc(a	NOUN
ejpam-6029	170	18	,	,	PUNCT
ejpam-6029	170	19	a)−	a)−	PROPN
ejpam-6029	170	20	lc(b	lc(b	PUNCT
ejpam-6029	170	21	,	,	PUNCT
ejpam-6029	170	22	b)|	b)|	NOUN
ejpam-6029	170	23	,	,	PUNCT
ejpam-6029	170	24	∀a	∀a	X
ejpam-6029	170	25	,	,	PUNCT
ejpam-6029	170	26	b	b	PROPN
ejpam-6029	170	27	∈	∈	PROPN
ejpam-6029	170	28	γ	γ	X
ejpam-6029	170	29	.	.	PUNCT
ejpam-6029	171	1	obviously	obviously	ADV
ejpam-6029	171	2	,	,	PUNCT
ejpam-6029	171	3	l̂c(a	l̂c(a	PROPN
ejpam-6029	171	4	,	,	PUNCT
ejpam-6029	171	5	a	a	PRON
ejpam-6029	171	6	)	)	PUNCT
ejpam-6029	171	7	=	=	SYM
ejpam-6029	171	8	0e	0e	NOUN
ejpam-6029	171	9	,	,	PUNCT
ejpam-6029	171	10	∀a	∀a	NOUN
ejpam-6029	171	11	∈	∈	PROPN
ejpam-6029	171	12	γ	γ	X
ejpam-6029	171	13	.	.	PUNCT
ejpam-6029	171	14	let	let	VERB
ejpam-6029	171	15	ψ	ψ	PART
ejpam-6029	171	16	be	be	AUX
ejpam-6029	171	17	the	the	DET
ejpam-6029	171	18	family	family	NOUN
ejpam-6029	171	19	of	of	ADP
ejpam-6029	171	20	all	all	PRON
ejpam-6029	171	21	onto	onto	ADP
ejpam-6029	171	22	mappings	mapping	NOUN
ejpam-6029	171	23	ψ	ψ	X
ejpam-6029	171	24	:	:	PUNCT
ejpam-6029	171	25	[	[	X
ejpam-6029	171	26	0,∞	0,∞	NOUN
ejpam-6029	171	27	)	)	PUNCT
ejpam-6029	171	28	→	→	PUNCT
ejpam-6029	172	1	[	[	X
ejpam-6029	172	2	0,∞	0,∞	NOUN
ejpam-6029	172	3	)	)	PUNCT
ejpam-6029	172	4	under	under	ADP
ejpam-6029	172	5	the	the	DET
ejpam-6029	172	6	following	follow	VERB
ejpam-6029	172	7	necessities	necessity	NOUN
ejpam-6029	172	8	:	:	PUNCT
ejpam-6029	172	9	r	r	NOUN
ejpam-6029	172	10	≤	≤	NUM
ejpam-6029	172	11	ψ(r	ψ(r	NOUN
ejpam-6029	172	12	)	)	PUNCT
ejpam-6029	172	13	for	for	ADP
ejpam-6029	172	14	each	each	DET
ejpam-6029	172	15	r	r	NOUN
ejpam-6029	172	16	∈	∈	PROPN
ejpam-6029	173	1	[	[	X
ejpam-6029	173	2	0,∞	0,∞	NOUN
ejpam-6029	173	3	)	)	PUNCT
ejpam-6029	173	4	,	,	PUNCT
ejpam-6029	173	5	and	and	CCONJ
ejpam-6029	173	6	ψ	ψ	AUX
ejpam-6029	173	7	′	′	NUM
ejpam-6029	173	8	(	(	PUNCT
ejpam-6029	173	9	the	the	DET
ejpam-6029	173	10	derivative	derivative	NOUN
ejpam-6029	173	11	of	of	ADP
ejpam-6029	173	12	ψ	ψ	NOUN
ejpam-6029	173	13	)	)	PUNCT
ejpam-6029	173	14	increases	increase	VERB
ejpam-6029	173	15	[	[	X
ejpam-6029	173	16	37	37	NUM
ejpam-6029	173	17	]	]	PUNCT
ejpam-6029	173	18	.	.	PUNCT
ejpam-6029	174	1	next	next	ADV
ejpam-6029	174	2	,	,	PUNCT
ejpam-6029	174	3	we	we	PRON
ejpam-6029	174	4	present	present	VERB
ejpam-6029	174	5	the	the	DET
ejpam-6029	174	6	following	follow	VERB
ejpam-6029	174	7	lemma	lemma	PROPN
ejpam-6029	174	8	,	,	PUNCT
ejpam-6029	174	9	utilizing	utilize	VERB
ejpam-6029	174	10	results	result	NOUN
ejpam-6029	174	11	from	from	ADP
ejpam-6029	174	12	the	the	DET
ejpam-6029	174	13	literature	literature	NOUN
ejpam-6029	174	14	.	.	PUNCT
ejpam-6029	175	1	lemma	lemma	PROPN
ejpam-6029	175	2	4	4	NUM
ejpam-6029	175	3	.	.	PUNCT
ejpam-6029	176	1	[	[	X
ejpam-6029	176	2	20	20	NUM
ejpam-6029	176	3	]	]	PUNCT
ejpam-6029	176	4	let	let	VERB
ejpam-6029	176	5	ψ	ψ	ADP
ejpam-6029	176	6	∈	∈	PROPN
ejpam-6029	176	7	ψ	ψ	NOUN
ejpam-6029	176	8	,	,	PUNCT
ejpam-6029	176	9	then	then	ADV
ejpam-6029	176	10	for	for	ADP
ejpam-6029	176	11	all	all	DET
ejpam-6029	176	12	x	x	SYM
ejpam-6029	176	13	∈	∈	PROPN
ejpam-6029	177	1	[	[	X
ejpam-6029	177	2	0	0	NUM
ejpam-6029	177	3	,	,	PUNCT
ejpam-6029	177	4	1	1	NUM
ejpam-6029	177	5	]	]	PUNCT
ejpam-6029	177	6	and	and	CCONJ
ejpam-6029	177	7	0	0	NUM
ejpam-6029	177	8	<	<	X
ejpam-6029	177	9	q	q	X
ejpam-6029	177	10	≤	≤	NUM
ejpam-6029	177	11	1	1	NUM
ejpam-6029	177	12	≤	≤	NOUN
ejpam-6029	177	13	p	p	X
ejpam-6029	177	14	,	,	PUNCT
ejpam-6029	177	15	we	we	PRON
ejpam-6029	177	16	have	have	VERB
ejpam-6029	177	17	(	(	PUNCT
ejpam-6029	177	18	i	i	NOUN
ejpam-6029	177	19	)	)	PUNCT
ejpam-6029	177	20	(	(	PUNCT
ejpam-6029	177	21	ψ(x	ψ(x	NOUN
ejpam-6029	177	22	p	p	NOUN
ejpam-6029	177	23	)	)	PUNCT
ejpam-6029	177	24	)	)	PUNCT
ejpam-6029	177	25	1	1	NUM
ejpam-6029	177	26	p	p	NOUN
ejpam-6029	177	27	≤	≤	NUM
ejpam-6029	177	28	ψ(x	ψ(x	NOUN
ejpam-6029	177	29	)	)	PUNCT
ejpam-6029	177	30	≤	≤	NUM
ejpam-6029	177	31	(	(	PUNCT
ejpam-6029	177	32	ψ(x	ψ(x	NOUN
ejpam-6029	177	33	q	q	NOUN
ejpam-6029	177	34	)	)	PUNCT
ejpam-6029	177	35	)	)	PUNCT
ejpam-6029	177	36	1	1	NUM
ejpam-6029	177	37	q	q	NOUN
ejpam-6029	177	38	;	;	PUNCT
ejpam-6029	177	39	(	(	PUNCT
ejpam-6029	177	40	ii	ii	NOUN
ejpam-6029	177	41	)	)	PUNCT
ejpam-6029	177	42	(	(	PUNCT
ejpam-6029	177	43	ψ−1(x	ψ−1(x	PROPN
ejpam-6029	177	44	q	q	NOUN
ejpam-6029	177	45	)	)	PUNCT
ejpam-6029	177	46	)	)	PUNCT
ejpam-6029	178	1	1	1	NUM
ejpam-6029	178	2	q	q	PROPN
ejpam-6029	178	3	≤	≤	PROPN
ejpam-6029	178	4	ψ−1(x	ψ−1(x	PROPN
ejpam-6029	178	5	)	)	PUNCT
ejpam-6029	178	6	≤	≤	NOUN
ejpam-6029	178	7	(	(	PUNCT
ejpam-6029	178	8	ψ−1(x	ψ−1(x	PROPN
ejpam-6029	178	9	p	p	NOUN
ejpam-6029	178	10	)	)	PUNCT
ejpam-6029	178	11	)	)	PUNCT
ejpam-6029	178	12	1	1	NUM
ejpam-6029	178	13	p	p	NOUN
ejpam-6029	178	14	.	.	PUNCT
ejpam-6029	179	1	a.	a.	PROPN
ejpam-6029	179	2	a.	a.	PROPN
ejpam-6029	179	3	hijab	hijab	PROPN
ejpam-6029	179	4	et	et	PROPN
ejpam-6029	179	5	al	al	PROPN
ejpam-6029	179	6	.	.	PUNCT
ejpam-6029	179	7	/	/	SYM
ejpam-6029	179	8	eur	eur	PROPN
ejpam-6029	179	9	.	.	PUNCT
ejpam-6029	180	1	j.	j.	PROPN
ejpam-6029	180	2	pure	pure	PROPN
ejpam-6029	180	3	appl	appl	PROPN
ejpam-6029	180	4	.	.	PROPN
ejpam-6029	180	5	math	math	PROPN
ejpam-6029	180	6	,	,	PUNCT
ejpam-6029	180	7	18	18	NUM
ejpam-6029	180	8	(	(	PUNCT
ejpam-6029	180	9	2	2	NUM
ejpam-6029	180	10	)	)	PUNCT
ejpam-6029	180	11	(	(	PUNCT
ejpam-6029	180	12	2025	2025	NUM
ejpam-6029	180	13	)	)	PUNCT
ejpam-6029	180	14	,	,	PUNCT
ejpam-6029	180	15	6029	6029	NUM
ejpam-6029	180	16	7	7	NUM
ejpam-6029	180	17	of	of	ADP
ejpam-6029	180	18	23	23	NUM
ejpam-6029	180	19	3	3	NUM
ejpam-6029	180	20	.	.	PUNCT
ejpam-6029	180	21	main	main	ADJ
ejpam-6029	180	22	results	result	NOUN
ejpam-6029	180	23	this	this	DET
ejpam-6029	180	24	section	section	NOUN
ejpam-6029	180	25	presents	present	VERB
ejpam-6029	180	26	some	some	DET
ejpam-6029	180	27	fixed	fix	VERB
ejpam-6029	180	28	-	-	PUNCT
ejpam-6029	180	29	point	point	NOUN
ejpam-6029	180	30	results	result	NOUN
ejpam-6029	180	31	within	within	ADP
ejpam-6029	180	32	the	the	DET
ejpam-6029	180	33	framework	framework	NOUN
ejpam-6029	180	34	of	of	ADP
ejpam-6029	180	35	dccml	dccml	NOUN
ejpam-6029	180	36	-	-	PUNCT
ejpam-6029	180	37	space	space	NOUN
ejpam-6029	180	38	.	.	PUNCT
ejpam-6029	181	1	in	in	ADP
ejpam-6029	181	2	this	this	DET
ejpam-6029	181	3	work	work	NOUN
ejpam-6029	181	4	,	,	PUNCT
ejpam-6029	181	5	the	the	DET
ejpam-6029	181	6	first	first	ADJ
ejpam-6029	181	7	theorem	theorem	NOUN
ejpam-6029	181	8	for	for	ADP
ejpam-6029	181	9	common	common	ADJ
ejpam-6029	181	10	fixed	fix	VERB
ejpam-6029	181	11	points	point	NOUN
ejpam-6029	181	12	is	be	AUX
ejpam-6029	181	13	analogous	analogous	ADJ
ejpam-6029	181	14	to	to	ADP
ejpam-6029	181	15	the	the	DET
ejpam-6029	181	16	non	non	ADJ
ejpam-6029	181	17	-	-	ADJ
ejpam-6029	181	18	linear	linear	ADJ
ejpam-6029	181	19	generalization	generalization	NOUN
ejpam-6029	181	20	rational	rational	ADJ
ejpam-6029	181	21	contraction	contraction	NOUN
ejpam-6029	181	22	,	,	PUNCT
ejpam-6029	181	23	with	with	ADP
ejpam-6029	181	24	the	the	DET
ejpam-6029	181	25	self	self	NOUN
ejpam-6029	181	26	-	-	PUNCT
ejpam-6029	181	27	mapping	mapping	NOUN
ejpam-6029	181	28	of	of	ADP
ejpam-6029	181	29	dccml	dccml	NOUN
ejpam-6029	181	30	-	-	PUNCT
ejpam-6029	181	31	space	space	NOUN
ejpam-6029	181	32	,	,	PUNCT
ejpam-6029	181	33	see	see	VERB
ejpam-6029	181	34	[	[	X
ejpam-6029	181	35	31	31	NUM
ejpam-6029	181	36	,	,	PUNCT
ejpam-6029	181	37	38	38	NUM
ejpam-6029	181	38	]	]	PUNCT
ejpam-6029	181	39	.	.	PUNCT
ejpam-6029	182	1	motivated	motivate	VERB
ejpam-6029	182	2	by	by	ADP
ejpam-6029	182	3	ahmad	ahmad	PROPN
ejpam-6029	182	4	et	et	PROPN
ejpam-6029	182	5	al	al	PROPN
ejpam-6029	182	6	.	.	PUNCT
ejpam-6029	183	1	[	[	X
ejpam-6029	183	2	31	31	NUM
ejpam-6029	183	3	]	]	PUNCT
ejpam-6029	183	4	,	,	PUNCT
ejpam-6029	183	5	we	we	PRON
ejpam-6029	183	6	denote	denote	VERB
ejpam-6029	183	7	by	by	ADP
ejpam-6029	183	8	∆	∆	PROPN
ejpam-6029	183	9	the	the	DET
ejpam-6029	183	10	family	family	NOUN
ejpam-6029	183	11	of	of	ADP
ejpam-6029	183	12	all	all	DET
ejpam-6029	183	13	mappings	mapping	NOUN
ejpam-6029	184	1	λ	λ	X
ejpam-6029	184	2	:	:	PUNCT
ejpam-6029	184	3	γ2	γ2	PROPN
ejpam-6029	184	4	→	→	SYM
ejpam-6029	185	1	[	[	X
ejpam-6029	185	2	0	0	NUM
ejpam-6029	185	3	,	,	PUNCT
ejpam-6029	185	4	1	1	NUM
ejpam-6029	185	5	)	)	PUNCT
ejpam-6029	185	6	with	with	ADP
ejpam-6029	185	7	any	any	DET
ejpam-6029	185	8	mapping	mapping	NOUN
ejpam-6029	185	9	(	(	PUNCT
ejpam-6029	185	10	say	say	INTJ
ejpam-6029	185	11	)	)	PUNCT
ejpam-6029	185	12	t	t	NOUN
ejpam-6029	185	13	:	:	PUNCT
ejpam-6029	185	14	γ	γ	X
ejpam-6029	185	15	→	→	SYM
ejpam-6029	185	16	γ	γ	X
ejpam-6029	185	17	satisfying	satisfy	VERB
ejpam-6029	185	18	the	the	DET
ejpam-6029	185	19	following	following	ADJ
ejpam-6029	185	20	conditions	condition	NOUN
ejpam-6029	185	21	:	:	PUNCT
ejpam-6029	185	22	(	(	PUNCT
ejpam-6029	185	23	i	i	NOUN
ejpam-6029	185	24	)	)	PUNCT
ejpam-6029	186	1	λ(ta	λ(ta	PROPN
ejpam-6029	186	2	,	,	PUNCT
ejpam-6029	186	3	b	b	NOUN
ejpam-6029	186	4	)	)	PUNCT
ejpam-6029	186	5	≤	≤	NOUN
ejpam-6029	186	6	λ(a	λ(a	NOUN
ejpam-6029	186	7	,	,	PUNCT
ejpam-6029	186	8	b	b	NOUN
ejpam-6029	186	9	)	)	PUNCT
ejpam-6029	186	10	for	for	ADP
ejpam-6029	186	11	each	each	PRON
ejpam-6029	186	12	a	a	NOUN
ejpam-6029	186	13	,	,	PUNCT
ejpam-6029	186	14	b	b	PROPN
ejpam-6029	186	15	∈	∈	PROPN
ejpam-6029	186	16	γ	γ	X
ejpam-6029	186	17	.	.	PROPN
ejpam-6029	186	18	(	(	PUNCT
ejpam-6029	186	19	ii	ii	NOUN
ejpam-6029	186	20	)	)	PUNCT
ejpam-6029	186	21	λ(a	λ(a	NOUN
ejpam-6029	186	22	,	,	PUNCT
ejpam-6029	186	23	tb	tb	NOUN
ejpam-6029	186	24	)	)	PUNCT
ejpam-6029	186	25	≤	≤	NUM
ejpam-6029	186	26	λ(a	λ(a	NOUN
ejpam-6029	186	27	,	,	PUNCT
ejpam-6029	186	28	b	b	NOUN
ejpam-6029	186	29	)	)	PUNCT
ejpam-6029	186	30	for	for	ADP
ejpam-6029	186	31	each	each	DET
ejpam-6029	186	32	a	a	NOUN
ejpam-6029	186	33	,	,	PUNCT
ejpam-6029	186	34	b	b	X
ejpam-6029	186	35	∈	∈	PROPN
ejpam-6029	186	36	γ	γ	X
ejpam-6029	186	37	.	.	PUNCT
ejpam-6029	186	38	clearly	clearly	ADV
ejpam-6029	186	39	,	,	PUNCT
ejpam-6029	186	40	since	since	SCONJ
ejpam-6029	186	41	λ	λ	PROPN
ejpam-6029	186	42	∈	∈	PROPN
ejpam-6029	186	43	∆	∆	X
ejpam-6029	186	44	the	the	DET
ejpam-6029	186	45	iterative	iterative	NOUN
ejpam-6029	186	46	λj(a	λj(a	NOUN
ejpam-6029	186	47	,	,	PUNCT
ejpam-6029	186	48	b	b	NOUN
ejpam-6029	186	49	)	)	PUNCT
ejpam-6029	186	50	→	→	SYM
ejpam-6029	186	51	0	0	PUNCT
ejpam-6029	187	1	as	as	SCONJ
ejpam-6029	187	2	j	j	PROPN
ejpam-6029	187	3	→	→	PUNCT
ejpam-6029	187	4	+	+	PROPN
ejpam-6029	187	5	∞.	∞.	PROPN
ejpam-6029	187	6	now	now	ADV
ejpam-6029	187	7	,	,	PUNCT
ejpam-6029	187	8	we	we	PRON
ejpam-6029	187	9	state	state	VERB
ejpam-6029	187	10	and	and	CCONJ
ejpam-6029	187	11	prove	prove	VERB
ejpam-6029	187	12	the	the	DET
ejpam-6029	187	13	common	common	ADJ
ejpam-6029	187	14	fixed	fix	VERB
ejpam-6029	187	15	point	point	NOUN
ejpam-6029	187	16	results	result	NOUN
ejpam-6029	187	17	in	in	ADP
ejpam-6029	187	18	dccml	dccml	NOUN
ejpam-6029	187	19	-	-	PUNCT
ejpam-6029	187	20	space	space	NOUN
ejpam-6029	187	21	.	.	PUNCT
ejpam-6029	188	1	theorem	theorem	NOUN
ejpam-6029	188	2	1	1	NUM
ejpam-6029	188	3	.	.	X
ejpam-6029	189	1	assume	assume	VERB
ejpam-6029	189	2	(	(	PUNCT
ejpam-6029	189	3	γ	γ	X
ejpam-6029	189	4	,	,	PUNCT
ejpam-6029	189	5	lc	lc	PROPN
ejpam-6029	189	6	)	)	PUNCT
ejpam-6029	189	7	is	be	AUX
ejpam-6029	189	8	an	an	DET
ejpam-6029	189	9	lc	lc	NOUN
ejpam-6029	189	10	-	-	PUNCT
ejpam-6029	189	11	complete	complete	ADJ
ejpam-6029	189	12	dccml	dccml	NOUN
ejpam-6029	189	13	-	-	PUNCT
ejpam-6029	189	14	space	space	NOUN
ejpam-6029	189	15	with	with	ADP
ejpam-6029	189	16	two	two	NUM
ejpam-6029	189	17	non	non	ADJ
ejpam-6029	189	18	-	-	ADJ
ejpam-6029	189	19	constant	constant	ADJ
ejpam-6029	189	20	functions	function	NOUN
ejpam-6029	189	21	f	f	NOUN
ejpam-6029	189	22	,	,	PUNCT
ejpam-6029	189	23	g	g	NOUN
ejpam-6029	189	24	:	:	PUNCT
ejpam-6029	189	25	p	p	X
ejpam-6029	189	26	→	→	SYM
ejpam-6029	189	27	p	p	X
ejpam-6029	189	28	,	,	PUNCT
ejpam-6029	189	29	where	where	SCONJ
ejpam-6029	189	30	p	p	NOUN
ejpam-6029	189	31	is	be	AUX
ejpam-6029	189	32	a	a	DET
ejpam-6029	189	33	normal	normal	ADJ
ejpam-6029	189	34	cone	cone	NOUN
ejpam-6029	189	35	via	via	ADP
ejpam-6029	189	36	normal	normal	ADJ
ejpam-6029	189	37	constant	constant	ADJ
ejpam-6029	189	38	m	m	NOUN
ejpam-6029	189	39	.	.	PUNCT
ejpam-6029	190	1	let	let	VERB
ejpam-6029	190	2	t1	t1	NOUN
ejpam-6029	190	3	,	,	PUNCT
ejpam-6029	190	4	t2	t2	NOUN
ejpam-6029	190	5	:	:	PUNCT
ejpam-6029	190	6	γ	γ	X
ejpam-6029	190	7	→	→	SYM
ejpam-6029	190	8	γ	γ	X
ejpam-6029	190	9	be	be	AUX
ejpam-6029	190	10	a	a	DET
ejpam-6029	190	11	mappings	mapping	NOUN
ejpam-6029	190	12	and	and	CCONJ
ejpam-6029	190	13	there	there	PRON
ejpam-6029	190	14	exists	exist	VERB
ejpam-6029	190	15	λ	λ	PROPN
ejpam-6029	190	16	∈	∈	PROPN
ejpam-6029	190	17	∆	∆	PROPN
ejpam-6029	191	1	such	such	ADJ
ejpam-6029	191	2	that	that	SCONJ
ejpam-6029	191	3	lc(t1a	lc(t1a	PROPN
ejpam-6029	191	4	,	,	PUNCT
ejpam-6029	191	5	t2b	t2b	PROPN
ejpam-6029	191	6	)	)	PUNCT
ejpam-6029	191	7	⪯	⪯	PROPN
ejpam-6029	191	8	λ(a	λ(a	PROPN
ejpam-6029	191	9	,	,	PUNCT
ejpam-6029	191	10	b)m̃(a	b)m̃(a	PROPN
ejpam-6029	191	11	,	,	PUNCT
ejpam-6029	191	12	b	b	NOUN
ejpam-6029	191	13	)	)	PUNCT
ejpam-6029	191	14	,	,	PUNCT
ejpam-6029	191	15	for	for	ADP
ejpam-6029	191	16	all	all	DET
ejpam-6029	191	17	a	a	PRON
ejpam-6029	191	18	,	,	PUNCT
ejpam-6029	191	19	b	b	PROPN
ejpam-6029	191	20	∈	∈	PROPN
ejpam-6029	191	21	γ	γ	X
ejpam-6029	191	22	,	,	PUNCT
ejpam-6029	191	23	(	(	PUNCT
ejpam-6029	191	24	3	3	X
ejpam-6029	191	25	)	)	PUNCT
ejpam-6029	191	26	where	where	SCONJ
ejpam-6029	191	27	m̃(a	m̃(a	NOUN
ejpam-6029	191	28	,	,	PUNCT
ejpam-6029	191	29	b	b	NOUN
ejpam-6029	191	30	)	)	PUNCT
ejpam-6029	191	31	=	=	SYM
ejpam-6029	191	32	max	max	PROPN
ejpam-6029	191	33	{	{	PUNCT
ejpam-6029	191	34	lc(a	lc(a	PROPN
ejpam-6029	191	35	,	,	PUNCT
ejpam-6029	191	36	b),lc(a	b),lc(a	PROPN
ejpam-6029	191	37	,	,	PUNCT
ejpam-6029	191	38	t1a),lc(b	t1a),lc(b	NOUN
ejpam-6029	191	39	,	,	PUNCT
ejpam-6029	191	40	t2b	t2b	PROPN
ejpam-6029	191	41	)	)	PUNCT
ejpam-6029	191	42	,	,	PUNCT
ejpam-6029	191	43	lc(a	lc(a	PROPN
ejpam-6029	191	44	,	,	PUNCT
ejpam-6029	191	45	t1a)lc(b	t1a)lc(b	NOUN
ejpam-6029	191	46	,	,	PUNCT
ejpam-6029	191	47	t2b	t2b	PROPN
ejpam-6029	191	48	)	)	PUNCT
ejpam-6029	191	49	1	1	NUM
ejpam-6029	191	50	+	+	CCONJ
ejpam-6029	191	51	lc(a	lc(a	NUM
ejpam-6029	191	52	,	,	PUNCT
ejpam-6029	191	53	b	b	NOUN
ejpam-6029	191	54	)	)	PUNCT
ejpam-6029	191	55	,	,	PUNCT
ejpam-6029	191	56	lc(b	lc(b	PROPN
ejpam-6029	191	57	,	,	PUNCT
ejpam-6029	191	58	t2b	t2b	PROPN
ejpam-6029	191	59	)	)	PUNCT
ejpam-6029	191	60	[	[	PUNCT
ejpam-6029	191	61	1	1	NUM
ejpam-6029	191	62	+	+	NUM
ejpam-6029	191	63	lc(a	lc(a	NUM
ejpam-6029	191	64	,	,	PUNCT
ejpam-6029	191	65	t1a	t1a	NOUN
ejpam-6029	191	66	)	)	PUNCT
ejpam-6029	191	67	]	]	PUNCT
ejpam-6029	191	68	1	1	NUM
ejpam-6029	191	69	+	+	CCONJ
ejpam-6029	191	70	lc(a	lc(a	NUM
ejpam-6029	191	71	,	,	PUNCT
ejpam-6029	191	72	b	b	NOUN
ejpam-6029	191	73	)	)	PUNCT
ejpam-6029	191	74	,	,	PUNCT
ejpam-6029	191	75	[	[	PUNCT
ejpam-6029	191	76	lc(a	lc(a	X
ejpam-6029	191	77	,	,	PUNCT
ejpam-6029	191	78	t1a	t1a	NUM
ejpam-6029	191	79	)	)	PUNCT
ejpam-6029	192	1	+	+	CCONJ
ejpam-6029	192	2	lc(b	lc(b	PROPN
ejpam-6029	192	3	,	,	PUNCT
ejpam-6029	192	4	t2b	t2b	PROPN
ejpam-6029	192	5	)	)	PUNCT
ejpam-6029	192	6	]	]	PUNCT
ejpam-6029	193	1	lc(t1a	lc(t1a	PROPN
ejpam-6029	193	2	,	,	PUNCT
ejpam-6029	193	3	t2b	t2b	PROPN
ejpam-6029	193	4	)	)	PUNCT
ejpam-6029	193	5	1	1	NUM
ejpam-6029	193	6	+	+	CCONJ
ejpam-6029	193	7	lc(a	lc(a	NUM
ejpam-6029	193	8	,	,	PUNCT
ejpam-6029	193	9	b	b	NOUN
ejpam-6029	193	10	)	)	PUNCT
ejpam-6029	193	11	+	+	CCONJ
ejpam-6029	193	12	lc(t1a	lc(t1a	PROPN
ejpam-6029	193	13	,	,	PUNCT
ejpam-6029	193	14	t2b	t2b	PROPN
ejpam-6029	193	15	)	)	PUNCT
ejpam-6029	193	16	}	}	PUNCT
ejpam-6029	193	17	.	.	PUNCT
ejpam-6029	194	1	for	for	ADP
ejpam-6029	194	2	a0	a0	PROPN
ejpam-6029	194	3	∈	∈	PROPN
ejpam-6029	194	4	γ	γ	PROPN
ejpam-6029	194	5	,	,	PUNCT
ejpam-6029	194	6	we	we	PRON
ejpam-6029	194	7	set	set	VERB
ejpam-6029	194	8	a	a	DET
ejpam-6029	194	9	sequence	sequence	NOUN
ejpam-6029	194	10	{	{	PUNCT
ejpam-6029	194	11	an	an	PRON
ejpam-6029	194	12	}	}	PUNCT
ejpam-6029	194	13	defined	define	VERB
ejpam-6029	194	14	as	as	ADP
ejpam-6029	194	15	a2n+1	a2n+1	NOUN
ejpam-6029	194	16	=	=	SYM
ejpam-6029	194	17	t1a2n	t1a2n	PUNCT
ejpam-6029	194	18	and	and	CCONJ
ejpam-6029	194	19	a2n+2	a2n+2	PRON
ejpam-6029	195	1	=	=	SYM
ejpam-6029	195	2	t2a2n+1	t2a2n+1	NUM
ejpam-6029	195	3	for	for	ADP
ejpam-6029	195	4	every	every	DET
ejpam-6029	195	5	n	n	PRON
ejpam-6029	195	6	≥	≥	NOUN
ejpam-6029	195	7	0	0	NUM
ejpam-6029	195	8	.	.	PUNCT
ejpam-6029	196	1	suppose	suppose	VERB
ejpam-6029	196	2	(	(	PUNCT
ejpam-6029	196	3	i	i	NOUN
ejpam-6029	196	4	)	)	PUNCT
ejpam-6029	196	5	f	f	PROPN
ejpam-6029	196	6	and	and	CCONJ
ejpam-6029	196	7	g	g	PROPN
ejpam-6029	196	8	are	be	AUX
ejpam-6029	196	9	bounded	bound	VERB
ejpam-6029	196	10	and	and	CCONJ
ejpam-6029	196	11	non	non	ADJ
ejpam-6029	196	12	-	-	ADJ
ejpam-6029	196	13	decreasing	decrease	VERB
ejpam-6029	196	14	,	,	PUNCT
ejpam-6029	196	15	g	g	PROPN
ejpam-6029	196	16	is	be	AUX
ejpam-6029	196	17	sub	sub	ADJ
ejpam-6029	196	18	-	-	ADJ
ejpam-6029	196	19	additive	additive	ADJ
ejpam-6029	196	20	and	and	CCONJ
ejpam-6029	196	21	g(λa	g(λa	NOUN
ejpam-6029	196	22	)	)	PUNCT
ejpam-6029	196	23	≺	≺	NOUN
ejpam-6029	196	24	a	a	PRON
ejpam-6029	196	25	,	,	PUNCT
ejpam-6029	196	26	λ	λ	PROPN
ejpam-6029	196	27	∈	∈	PROPN
ejpam-6029	196	28	(	(	PUNCT
ejpam-6029	196	29	0	0	NUM
ejpam-6029	196	30	,	,	PUNCT
ejpam-6029	196	31	1	1	NUM
ejpam-6029	196	32	)	)	PUNCT
ejpam-6029	196	33	;	;	PUNCT
ejpam-6029	196	34	(	(	PUNCT
ejpam-6029	196	35	ii	ii	X
ejpam-6029	196	36	)	)	PUNCT
ejpam-6029	196	37	lim	lim	PROPN
ejpam-6029	196	38	n	n	CCONJ
ejpam-6029	196	39	,	,	PUNCT
ejpam-6029	196	40	m→∞	m→∞	NUM
ejpam-6029	196	41	∑n−2	∑n−2	NOUN
ejpam-6029	197	1	i	i	PRON
ejpam-6029	197	2	=	=	VERB
ejpam-6029	197	3	m	m	VERB
ejpam-6029	197	4	∥gi−mf	∥gi−mf	NOUN
ejpam-6029	197	5	(	(	PUNCT
ejpam-6029	197	6	ξilc(a0	ξilc(a0	NOUN
ejpam-6029	197	7	,	,	PUNCT
ejpam-6029	197	8	a1	a1	NOUN
ejpam-6029	197	9	)	)	PUNCT
ejpam-6029	197	10	)	)	PUNCT
ejpam-6029	197	11	∥+	∥+	PROPN
ejpam-6029	198	1	∥gn−m−1	∥gn−m−1	PROPN
ejpam-6029	198	2	(	(	PUNCT
ejpam-6029	198	3	ξn−1lc(a0	ξn−1lc(a0	PROPN
ejpam-6029	198	4	,	,	PUNCT
ejpam-6029	198	5	a1	a1	NOUN
ejpam-6029	198	6	)	)	PUNCT
ejpam-6029	198	7	)	)	PUNCT
ejpam-6029	198	8	∥	∥	X
ejpam-6029	198	9	=	=	SYM
ejpam-6029	198	10	0	0	NUM
ejpam-6029	198	11	,	,	PUNCT
ejpam-6029	198	12	where	where	SCONJ
ejpam-6029	198	13	ξ	ξ	X
ejpam-6029	198	14	=	=	SYM
ejpam-6029	198	15	λ(a0	λ(a0	X
ejpam-6029	198	16	,	,	PUNCT
ejpam-6029	198	17	a1	a1	PROPN
ejpam-6029	198	18	)	)	PUNCT
ejpam-6029	198	19	<	<	X
ejpam-6029	198	20	1	1	X
ejpam-6029	198	21	.	.	PUNCT
ejpam-6029	199	1	if	if	SCONJ
ejpam-6029	199	2	for	for	ADP
ejpam-6029	199	3	every	every	DET
ejpam-6029	199	4	fixed	fix	VERB
ejpam-6029	199	5	point	point	NOUN
ejpam-6029	199	6	a	a	ADV
ejpam-6029	199	7	,	,	PUNCT
ejpam-6029	199	8	we	we	PRON
ejpam-6029	199	9	conclude	conclude	VERB
ejpam-6029	199	10	that	that	PRON
ejpam-6029	199	11	lc(a	lc(a	NOUN
ejpam-6029	199	12	,	,	PUNCT
ejpam-6029	199	13	a	a	PRON
ejpam-6029	199	14	)	)	PUNCT
ejpam-6029	199	15	=	=	SYM
ejpam-6029	199	16	0e	0e	NOUN
ejpam-6029	199	17	,	,	PUNCT
ejpam-6029	199	18	then	then	ADV
ejpam-6029	199	19	t1	t1	NOUN
ejpam-6029	199	20	and	and	CCONJ
ejpam-6029	199	21	t2	t2	PROPN
ejpam-6029	199	22	have	have	VERB
ejpam-6029	199	23	a	a	DET
ejpam-6029	199	24	unique	unique	ADJ
ejpam-6029	199	25	common	common	ADJ
ejpam-6029	199	26	fixed	fix	VERB
ejpam-6029	199	27	point	point	NOUN
ejpam-6029	199	28	.	.	PUNCT
ejpam-6029	200	1	proof	proof	NOUN
ejpam-6029	200	2	.	.	PUNCT
ejpam-6029	201	1	let	let	VERB
ejpam-6029	201	2	a0	a0	PROPN
ejpam-6029	201	3	∈	∈	PROPN
ejpam-6029	201	4	γ	γ	PROPN
ejpam-6029	201	5	.	.	PROPN
ejpam-6029	202	1	then	then	ADV
ejpam-6029	202	2	,	,	PUNCT
ejpam-6029	202	3	{	{	PUNCT
ejpam-6029	202	4	an	an	PRON
ejpam-6029	202	5	}	}	PUNCT
ejpam-6029	202	6	is	be	AUX
ejpam-6029	202	7	constructed	construct	VERB
ejpam-6029	202	8	in	in	ADP
ejpam-6029	202	9	γ	γ	NOUN
ejpam-6029	202	10	by	by	ADP
ejpam-6029	202	11	a2n+1	a2n+1	PROPN
ejpam-6029	202	12	=	=	SYM
ejpam-6029	202	13	t1a2n	t1a2n	PUNCT
ejpam-6029	202	14	and	and	CCONJ
ejpam-6029	202	15	a2n+2	a2n+2	PRON
ejpam-6029	203	1	=	=	SYM
ejpam-6029	203	2	t2a2n+1	t2a2n+1	PROPN
ejpam-6029	203	3	,	,	PUNCT
ejpam-6029	203	4	for	for	ADP
ejpam-6029	203	5	all	all	DET
ejpam-6029	203	6	n	n	PRON
ejpam-6029	203	7	∈	∈	PROPN
ejpam-6029	203	8	n.	n.	NOUN
ejpam-6029	203	9	if	if	SCONJ
ejpam-6029	203	10	there	there	PRON
ejpam-6029	203	11	exists	exist	VERB
ejpam-6029	203	12	n0	n0	PROPN
ejpam-6029	203	13	∈	∈	PROPN
ejpam-6029	203	14	n	n	X
ejpam-6029	203	15	for	for	ADP
ejpam-6029	203	16	which	which	PRON
ejpam-6029	203	17	an0	an0	PROPN
ejpam-6029	203	18	+	+	PROPN
ejpam-6029	203	19	1	1	PROPN
ejpam-6029	203	20	=	=	SYM
ejpam-6029	203	21	an0	an0	PROPN
ejpam-6029	203	22	,	,	PUNCT
ejpam-6029	203	23	then	then	ADV
ejpam-6029	203	24	t1an0	t1an0	VERB
ejpam-6029	203	25	=	=	PROPN
ejpam-6029	203	26	an0	an0	PROPN
ejpam-6029	203	27	.	.	PUNCT
ejpam-6029	204	1	therefore	therefore	ADV
ejpam-6029	204	2	,	,	PUNCT
ejpam-6029	204	3	there	there	PRON
ejpam-6029	204	4	is	be	VERB
ejpam-6029	204	5	nothing	nothing	PRON
ejpam-6029	204	6	to	to	PART
ejpam-6029	204	7	prove	prove	VERB
ejpam-6029	204	8	.	.	PUNCT
ejpam-6029	205	1	thus	thus	ADV
ejpam-6029	205	2	,	,	PUNCT
ejpam-6029	205	3	we	we	PRON
ejpam-6029	205	4	assume	assume	VERB
ejpam-6029	205	5	that	that	SCONJ
ejpam-6029	205	6	an+1	an+1	AUX
ejpam-6029	205	7	̸=	̸=	PROPN
ejpam-6029	205	8	an	an	PRON
ejpam-6029	205	9	for	for	ADP
ejpam-6029	205	10	all	all	PRON
ejpam-6029	205	11	n	n	DET
ejpam-6029	205	12	∈	∈	PROPN
ejpam-6029	205	13	n.	n.	NOUN
ejpam-6029	205	14	from	from	ADP
ejpam-6029	205	15	inequality	inequality	NOUN
ejpam-6029	205	16	(	(	PUNCT
ejpam-6029	205	17	3	3	NUM
ejpam-6029	205	18	)	)	PUNCT
ejpam-6029	205	19	,	,	PUNCT
ejpam-6029	205	20	we	we	PRON
ejpam-6029	205	21	obtain	obtain	VERB
ejpam-6029	205	22	lc(a2n+1	lc(a2n+1	NOUN
ejpam-6029	205	23	,	,	PUNCT
ejpam-6029	205	24	a2n+2	a2n+2	PUNCT
ejpam-6029	205	25	)	)	PUNCT
ejpam-6029	205	26	=	=	SYM
ejpam-6029	206	1	lc(t1a2n	lc(t1a2n	PROPN
ejpam-6029	206	2	,	,	PUNCT
ejpam-6029	206	3	t2a2n+1	t2a2n+1	NUM
ejpam-6029	206	4	)	)	PUNCT
ejpam-6029	206	5	⪯	⪯	NOUN
ejpam-6029	206	6	λ(a2n	λ(a2n	NOUN
ejpam-6029	206	7	,	,	PUNCT
ejpam-6029	206	8	a2n+1))m̃(a2n	a2n+1))m̃(a2n	PUNCT
ejpam-6029	206	9	,	,	PUNCT
ejpam-6029	206	10	a2n+1	a2n+1	NOUN
ejpam-6029	206	11	)	)	PUNCT
ejpam-6029	206	12	,	,	PUNCT
ejpam-6029	206	13	a.	a.	NOUN
ejpam-6029	206	14	a.	a.	PROPN
ejpam-6029	207	1	hijab	hijab	PROPN
ejpam-6029	207	2	et	et	PROPN
ejpam-6029	207	3	al	al	PROPN
ejpam-6029	207	4	.	.	PUNCT
ejpam-6029	207	5	/	/	SYM
ejpam-6029	207	6	eur	eur	PROPN
ejpam-6029	207	7	.	.	PUNCT
ejpam-6029	208	1	j.	j.	PROPN
ejpam-6029	208	2	pure	pure	PROPN
ejpam-6029	208	3	appl	appl	PROPN
ejpam-6029	208	4	.	.	PROPN
ejpam-6029	208	5	math	math	PROPN
ejpam-6029	208	6	,	,	PUNCT
ejpam-6029	208	7	18	18	NUM
ejpam-6029	208	8	(	(	PUNCT
ejpam-6029	208	9	2	2	NUM
ejpam-6029	208	10	)	)	PUNCT
ejpam-6029	208	11	(	(	PUNCT
ejpam-6029	208	12	2025	2025	NUM
ejpam-6029	208	13	)	)	PUNCT
ejpam-6029	208	14	,	,	PUNCT
ejpam-6029	208	15	6029	6029	NUM
ejpam-6029	208	16	8	8	NUM
ejpam-6029	208	17	of	of	ADP
ejpam-6029	208	18	23	23	NUM
ejpam-6029	208	19	where	where	SCONJ
ejpam-6029	208	20	m̃(a2n	m̃(a2n	PROPN
ejpam-6029	208	21	,	,	PUNCT
ejpam-6029	208	22	a2n+1	a2n+1	PROPN
ejpam-6029	208	23	)	)	PUNCT
ejpam-6029	208	24	=	=	SYM
ejpam-6029	208	25	max	max	PROPN
ejpam-6029	208	26	{	{	PUNCT
ejpam-6029	208	27	lc(a2n	lc(a2n	PROPN
ejpam-6029	208	28	,	,	PUNCT
ejpam-6029	208	29	a2n+1),lc(a2n	a2n+1),lc(a2n	PRON
ejpam-6029	208	30	,	,	PUNCT
ejpam-6029	208	31	t1a2n),lc(a2n+1	t1a2n),lc(a2n+1	NOUN
ejpam-6029	208	32	,	,	PUNCT
ejpam-6029	208	33	t2a2n+1	t2a2n+1	NUM
ejpam-6029	208	34	)	)	PUNCT
ejpam-6029	208	35	,	,	PUNCT
ejpam-6029	208	36	lc(a2n	lc(a2n	PROPN
ejpam-6029	208	37	,	,	PUNCT
ejpam-6029	208	38	t1a2n)lc(a2n+1	t1a2n)lc(a2n+1	NOUN
ejpam-6029	208	39	,	,	PUNCT
ejpam-6029	208	40	t2a2n+1	t2a2n+1	NUM
ejpam-6029	208	41	)	)	PUNCT
ejpam-6029	208	42	1	1	NUM
ejpam-6029	209	1	+	+	PUNCT
ejpam-6029	209	2	lc(a2n	lc(a2n	PROPN
ejpam-6029	209	3	,	,	PUNCT
ejpam-6029	209	4	a2n+1	a2n+1	NOUN
ejpam-6029	209	5	)	)	PUNCT
ejpam-6029	209	6	,	,	PUNCT
ejpam-6029	209	7	lc(a2n+1	lc(a2n+1	PROPN
ejpam-6029	209	8	,	,	PUNCT
ejpam-6029	209	9	t2a2n+1)[1	t2a2n+1)[1	PROPN
ejpam-6029	209	10	+	+	ADJ
ejpam-6029	209	11	lc(a2n	lc(a2n	PROPN
ejpam-6029	209	12	,	,	PUNCT
ejpam-6029	209	13	t1a2n	t1a2n	NUM
ejpam-6029	209	14	)	)	PUNCT
ejpam-6029	209	15	]	]	PUNCT
ejpam-6029	209	16	1	1	NUM
ejpam-6029	209	17	+	+	PUNCT
ejpam-6029	209	18	lc(a2n	lc(a2n	PROPN
ejpam-6029	209	19	,	,	PUNCT
ejpam-6029	209	20	a2n+1	a2n+1	NOUN
ejpam-6029	209	21	)	)	PUNCT
ejpam-6029	209	22	,	,	PUNCT
ejpam-6029	209	23	[	[	PUNCT
ejpam-6029	209	24	lc(a2n	lc(a2n	PROPN
ejpam-6029	209	25	,	,	PUNCT
ejpam-6029	209	26	t1a2n	t1a2n	NUM
ejpam-6029	209	27	)	)	PUNCT
ejpam-6029	209	28	+	+	SYM
ejpam-6029	209	29	lc(a2n+1	lc(a2n+1	NOUN
ejpam-6029	209	30	,	,	PUNCT
ejpam-6029	209	31	t2a2n+1	t2a2n+1	NUM
ejpam-6029	209	32	)	)	PUNCT
ejpam-6029	209	33	]	]	PUNCT
ejpam-6029	210	1	lc(t1a2n	lc(t1a2n	VERB
ejpam-6029	210	2	,	,	PUNCT
ejpam-6029	210	3	t2a2n+1	t2a2n+1	NUM
ejpam-6029	210	4	)	)	PUNCT
ejpam-6029	210	5	1	1	NUM
ejpam-6029	210	6	+	+	PUNCT
ejpam-6029	210	7	lc(a2n	lc(a2n	PROPN
ejpam-6029	210	8	,	,	PUNCT
ejpam-6029	210	9	a2n+1	a2n+1	NOUN
ejpam-6029	210	10	)	)	PUNCT
ejpam-6029	210	11	+	+	CCONJ
ejpam-6029	210	12	lc(t1a2n	lc(t1a2n	NUM
ejpam-6029	210	13	,	,	PUNCT
ejpam-6029	210	14	t2a2n+1	t2a2n+1	NUM
ejpam-6029	210	15	)	)	PUNCT
ejpam-6029	210	16	}	}	PUNCT
ejpam-6029	210	17	=	=	SYM
ejpam-6029	210	18	max	max	X
ejpam-6029	210	19	{	{	PUNCT
ejpam-6029	210	20	lc(a2n	lc(a2n	PROPN
ejpam-6029	210	21	,	,	PUNCT
ejpam-6029	210	22	a2n+1),lc(a2n	a2n+1),lc(a2n	PRON
ejpam-6029	210	23	,	,	PUNCT
ejpam-6029	210	24	a2n+1),lc(a2n+1	a2n+1),lc(a2n+1	PROPN
ejpam-6029	210	25	,	,	PUNCT
ejpam-6029	210	26	a2n+2	a2n+2	PRON
ejpam-6029	210	27	)	)	PUNCT
ejpam-6029	210	28	,	,	PUNCT
ejpam-6029	210	29	lc(a2n	lc(a2n	PROPN
ejpam-6029	210	30	,	,	PUNCT
ejpam-6029	210	31	a2n+1)lc(a2n+1	a2n+1)lc(a2n+1	PROPN
ejpam-6029	210	32	,	,	PUNCT
ejpam-6029	210	33	a2n+2	a2n+2	PRON
ejpam-6029	210	34	)	)	PUNCT
ejpam-6029	210	35	1	1	NUM
ejpam-6029	210	36	+	+	NUM
ejpam-6029	210	37	lc(a2n	lc(a2n	PROPN
ejpam-6029	210	38	,	,	PUNCT
ejpam-6029	210	39	a2n+1	a2n+1	NOUN
ejpam-6029	210	40	)	)	PUNCT
ejpam-6029	210	41	,	,	PUNCT
ejpam-6029	210	42	lc(a2n+1	lc(a2n+1	PROPN
ejpam-6029	210	43	,	,	PUNCT
ejpam-6029	210	44	a2n+2)[1	a2n+2)[1	PROPN
ejpam-6029	210	45	+	+	PROPN
ejpam-6029	210	46	lc(a2n	lc(a2n	PROPN
ejpam-6029	210	47	,	,	PUNCT
ejpam-6029	210	48	a2n+1	a2n+1	NOUN
ejpam-6029	210	49	)	)	PUNCT
ejpam-6029	210	50	]	]	PUNCT
ejpam-6029	211	1	1	1	NUM
ejpam-6029	211	2	+	+	PUNCT
ejpam-6029	211	3	lc(a2n	lc(a2n	PROPN
ejpam-6029	211	4	,	,	PUNCT
ejpam-6029	211	5	a2n+1	a2n+1	NOUN
ejpam-6029	211	6	)	)	PUNCT
ejpam-6029	211	7	,	,	PUNCT
ejpam-6029	211	8	[	[	PUNCT
ejpam-6029	211	9	lc(a2n	lc(a2n	PROPN
ejpam-6029	211	10	,	,	PUNCT
ejpam-6029	211	11	a2n+1	a2n+1	NOUN
ejpam-6029	211	12	)	)	PUNCT
ejpam-6029	211	13	+	+	SYM
ejpam-6029	211	14	lc(a2n+1	lc(a2n+1	NOUN
ejpam-6029	211	15	,	,	PUNCT
ejpam-6029	211	16	a2n+2	a2n+2	PRON
ejpam-6029	211	17	)	)	PUNCT
ejpam-6029	211	18	]	]	PUNCT
ejpam-6029	212	1	lc(a2n+1	lc(a2n+1	NOUN
ejpam-6029	212	2	,	,	PUNCT
ejpam-6029	212	3	a2n+2	a2n+2	PUNCT
ejpam-6029	212	4	)	)	PUNCT
ejpam-6029	212	5	1	1	NUM
ejpam-6029	213	1	+	+	NUM
ejpam-6029	213	2	lc(a2n	lc(a2n	PROPN
ejpam-6029	213	3	,	,	PUNCT
ejpam-6029	213	4	a2n+1	a2n+1	NOUN
ejpam-6029	213	5	)	)	PUNCT
ejpam-6029	213	6	+	+	SYM
ejpam-6029	213	7	lc(a2n+1	lc(a2n+1	NOUN
ejpam-6029	213	8	,	,	PUNCT
ejpam-6029	213	9	a2n+2	a2n+2	PRON
ejpam-6029	213	10	)	)	PUNCT
ejpam-6029	213	11	}	}	PUNCT
ejpam-6029	213	12	⪯	⪯	VERB
ejpam-6029	213	13	max	max	PROPN
ejpam-6029	213	14	{	{	PUNCT
ejpam-6029	213	15	lc(a2n	lc(a2n	PROPN
ejpam-6029	213	16	,	,	PUNCT
ejpam-6029	213	17	a2n+1),lc(a2n+1	a2n+1),lc(a2n+1	PROPN
ejpam-6029	213	18	,	,	PUNCT
ejpam-6029	213	19	a2n+2	a2n+2	PRON
ejpam-6029	213	20	)	)	PUNCT
ejpam-6029	213	21	}	}	PUNCT
ejpam-6029	213	22	.	.	PUNCT
ejpam-6029	214	1	hence	hence	ADV
ejpam-6029	214	2	,	,	PUNCT
ejpam-6029	214	3	lc(a2n+1	lc(a2n+1	PROPN
ejpam-6029	214	4	,	,	PUNCT
ejpam-6029	214	5	a2n+2	a2n+2	PRON
ejpam-6029	214	6	)	)	PUNCT
ejpam-6029	214	7	⪯	⪯	PROPN
ejpam-6029	214	8	λ(a2n	λ(a2n	NOUN
ejpam-6029	214	9	,	,	PUNCT
ejpam-6029	214	10	a2n+1)m̃(a2n	a2n+1)m̃(a2n	NOUN
ejpam-6029	214	11	,	,	PUNCT
ejpam-6029	214	12	a2n+1	a2n+1	PROPN
ejpam-6029	214	13	)	)	PUNCT
ejpam-6029	214	14	,	,	PUNCT
ejpam-6029	214	15	where	where	SCONJ
ejpam-6029	214	16	m̃(a2n	m̃(a2n	PROPN
ejpam-6029	214	17	,	,	PUNCT
ejpam-6029	214	18	a2n+1	a2n+1	PROPN
ejpam-6029	214	19	)	)	PUNCT
ejpam-6029	214	20	=	=	SYM
ejpam-6029	214	21	max{lc(a2n	max{lc(a2n	NOUN
ejpam-6029	214	22	,	,	PUNCT
ejpam-6029	214	23	a2n+1),lc(a2n+1	a2n+1),lc(a2n+1	PROPN
ejpam-6029	214	24	,	,	PUNCT
ejpam-6029	214	25	a2n+2	a2n+2	PRON
ejpam-6029	214	26	)	)	PUNCT
ejpam-6029	214	27	}	}	PUNCT
ejpam-6029	214	28	.	.	PUNCT
ejpam-6029	215	1	by	by	ADP
ejpam-6029	215	2	the	the	DET
ejpam-6029	215	3	properties	property	NOUN
ejpam-6029	215	4	of	of	ADP
ejpam-6029	215	5	the	the	DET
ejpam-6029	215	6	function	function	NOUN
ejpam-6029	215	7	λ	λ	X
ejpam-6029	215	8	we	we	PRON
ejpam-6029	215	9	deduce	deduce	VERB
ejpam-6029	215	10	that	that	DET
ejpam-6029	215	11	lc(a2n+1	lc(a2n+1	NOUN
ejpam-6029	215	12	,	,	PUNCT
ejpam-6029	215	13	a2n+2	a2n+2	PRON
ejpam-6029	215	14	)	)	PUNCT
ejpam-6029	215	15	⪯	⪯	PROPN
ejpam-6029	215	16	λ(a2n	λ(a2n	NOUN
ejpam-6029	215	17	,	,	PUNCT
ejpam-6029	215	18	a2n+1)m̃(a2n	a2n+1)m̃(a2n	NOUN
ejpam-6029	215	19	,	,	PUNCT
ejpam-6029	215	20	a2n+1	a2n+1	PROPN
ejpam-6029	215	21	)	)	PUNCT
ejpam-6029	215	22	=	=	SYM
ejpam-6029	215	23	λ(t2t1a2n−2	λ(t2t1a2n−2	PROPN
ejpam-6029	215	24	,	,	PUNCT
ejpam-6029	215	25	a2n+1)m̃(a2n	a2n+1)m̃(a2n	NOUN
ejpam-6029	215	26	,	,	PUNCT
ejpam-6029	215	27	a2n+1	a2n+1	NOUN
ejpam-6029	215	28	)	)	PUNCT
ejpam-6029	215	29	⪯	⪯	NOUN
ejpam-6029	215	30	λ(a2n−2	λ(a2n−2	PROPN
ejpam-6029	215	31	,	,	PUNCT
ejpam-6029	215	32	a2n+1)m̃(a2n	a2n+1)m̃(a2n	NOUN
ejpam-6029	215	33	,	,	PUNCT
ejpam-6029	215	34	a2n+1	a2n+1	NOUN
ejpam-6029	215	35	)	)	PUNCT
ejpam-6029	215	36	⪯	⪯	NOUN
ejpam-6029	215	37	·	·	PUNCT
ejpam-6029	215	38	·	·	PUNCT
ejpam-6029	215	39	·	·	PUNCT
ejpam-6029	216	1	⪯	⪯	NOUN
ejpam-6029	216	2	λ(a0	λ(a0	ADV
ejpam-6029	216	3	,	,	PUNCT
ejpam-6029	216	4	a2n+1)m̃(a2n	a2n+1)m̃(a2n	NOUN
ejpam-6029	216	5	,	,	PUNCT
ejpam-6029	216	6	a2n+1	a2n+1	PROPN
ejpam-6029	216	7	)	)	PUNCT
ejpam-6029	216	8	=	=	SYM
ejpam-6029	216	9	λ(a0	λ(a0	X
ejpam-6029	216	10	,	,	PUNCT
ejpam-6029	216	11	t1t2a2n−1)m̃(a2n	t1t2a2n−1)m̃(a2n	NOUN
ejpam-6029	216	12	,	,	PUNCT
ejpam-6029	216	13	a2n+1	a2n+1	NOUN
ejpam-6029	216	14	)	)	PUNCT
ejpam-6029	216	15	⪯	⪯	NOUN
ejpam-6029	216	16	λ(a0	λ(a0	X
ejpam-6029	216	17	,	,	PUNCT
ejpam-6029	216	18	a2n−1)(m̃(a2n	a2n−1)(m̃(a2n	PROPN
ejpam-6029	216	19	,	,	PUNCT
ejpam-6029	216	20	a2n+1	a2n+1	NOUN
ejpam-6029	216	21	)	)	PUNCT
ejpam-6029	216	22	⪯	⪯	NOUN
ejpam-6029	216	23	·	·	PUNCT
ejpam-6029	216	24	·	·	PUNCT
ejpam-6029	216	25	·	·	PUNCT
ejpam-6029	217	1	⪯	⪯	NOUN
ejpam-6029	217	2	λ(a0	λ(a0	NOUN
ejpam-6029	217	3	,	,	PUNCT
ejpam-6029	217	4	a1)m̃(a2n	a1)m̃(a2n	PROPN
ejpam-6029	217	5	,	,	PUNCT
ejpam-6029	217	6	a2n+1	a2n+1	PROPN
ejpam-6029	217	7	)	)	PUNCT
ejpam-6029	217	8	.	.	PUNCT
ejpam-6029	218	1	thus	thus	ADV
ejpam-6029	218	2	,	,	PUNCT
ejpam-6029	218	3	lc(a2n+1	lc(a2n+1	PROPN
ejpam-6029	218	4	,	,	PUNCT
ejpam-6029	218	5	a2n+2	a2n+2	PRON
ejpam-6029	218	6	)	)	PUNCT
ejpam-6029	218	7	⪯	⪯	NOUN
ejpam-6029	218	8	λ(a0	λ(a0	NOUN
ejpam-6029	218	9	,	,	PUNCT
ejpam-6029	218	10	a1)m̃(a2n	a1)m̃(a2n	PROPN
ejpam-6029	218	11	,	,	PUNCT
ejpam-6029	218	12	a2n+1	a2n+1	PROPN
ejpam-6029	218	13	)	)	PUNCT
ejpam-6029	218	14	.	.	PUNCT
ejpam-6029	219	1	(	(	PUNCT
ejpam-6029	219	2	4	4	X
ejpam-6029	219	3	)	)	PUNCT
ejpam-6029	219	4	if	if	SCONJ
ejpam-6029	219	5	m̃(a2n	m̃(a2n	PROPN
ejpam-6029	219	6	,	,	PUNCT
ejpam-6029	219	7	a2n+1	a2n+1	PROPN
ejpam-6029	219	8	)	)	PUNCT
ejpam-6029	219	9	=	=	SYM
ejpam-6029	219	10	lc(a2n+1	lc(a2n+1	NOUN
ejpam-6029	219	11	,	,	PUNCT
ejpam-6029	219	12	a2n+2	a2n+2	PRON
ejpam-6029	219	13	)	)	PUNCT
ejpam-6029	219	14	,	,	PUNCT
ejpam-6029	219	15	then	then	ADV
ejpam-6029	219	16	by	by	ADP
ejpam-6029	219	17	(	(	PUNCT
ejpam-6029	219	18	4	4	X
ejpam-6029	219	19	)	)	PUNCT
ejpam-6029	219	20	we	we	PRON
ejpam-6029	219	21	get	get	VERB
ejpam-6029	219	22	lc(a2n+1	lc(a2n+1	NOUN
ejpam-6029	219	23	,	,	PUNCT
ejpam-6029	219	24	a2n+2	a2n+2	PRON
ejpam-6029	219	25	)	)	PUNCT
ejpam-6029	219	26	⪯	⪯	NOUN
ejpam-6029	219	27	λ(a0	λ(a0	ADV
ejpam-6029	219	28	,	,	PUNCT
ejpam-6029	219	29	a1)lc(a2n+1	a1)lc(a2n+1	PROPN
ejpam-6029	219	30	,	,	PUNCT
ejpam-6029	219	31	a2n+2	a2n+2	PRON
ejpam-6029	219	32	)	)	PUNCT
ejpam-6029	219	33	≺	≺	NOUN
ejpam-6029	219	34	lc(a2n+1	lc(a2n+1	NOUN
ejpam-6029	219	35	,	,	PUNCT
ejpam-6029	219	36	a2n+2	a2n+2	PRON
ejpam-6029	219	37	)	)	PUNCT
ejpam-6029	219	38	,	,	PUNCT
ejpam-6029	219	39	which	which	PRON
ejpam-6029	219	40	is	be	AUX
ejpam-6029	219	41	a	a	DET
ejpam-6029	219	42	contradiction	contradiction	NOUN
ejpam-6029	219	43	.	.	PUNCT
ejpam-6029	220	1	on	on	ADP
ejpam-6029	220	2	the	the	DET
ejpam-6029	220	3	other	other	ADJ
ejpam-6029	220	4	hand	hand	NOUN
ejpam-6029	220	5	,	,	PUNCT
ejpam-6029	220	6	if	if	SCONJ
ejpam-6029	220	7	m̃(a2n	m̃(a2n	PROPN
ejpam-6029	220	8	,	,	PUNCT
ejpam-6029	220	9	a2n+1	a2n+1	PROPN
ejpam-6029	220	10	)	)	PUNCT
ejpam-6029	220	11	=	=	SYM
ejpam-6029	220	12	lc(a2n	lc(a2n	PROPN
ejpam-6029	220	13	,	,	PUNCT
ejpam-6029	220	14	a2n+1	a2n+1	NOUN
ejpam-6029	220	15	)	)	PUNCT
ejpam-6029	220	16	,	,	PUNCT
ejpam-6029	220	17	then	then	ADV
ejpam-6029	220	18	by	by	ADP
ejpam-6029	220	19	(	(	PUNCT
ejpam-6029	220	20	4	4	X
ejpam-6029	220	21	)	)	PUNCT
ejpam-6029	220	22	we	we	PRON
ejpam-6029	220	23	have	have	VERB
ejpam-6029	220	24	lc(a2n+1	lc(a2n+1	NOUN
ejpam-6029	220	25	,	,	PUNCT
ejpam-6029	220	26	a2n+2	a2n+2	PRON
ejpam-6029	220	27	)	)	PUNCT
ejpam-6029	220	28	⪯	⪯	NOUN
ejpam-6029	220	29	λ(a0	λ(a0	X
ejpam-6029	220	30	,	,	PUNCT
ejpam-6029	220	31	a1)lc(a2n	a1)lc(a2n	PROPN
ejpam-6029	220	32	,	,	PUNCT
ejpam-6029	220	33	a2n+1	a2n+1	NOUN
ejpam-6029	220	34	)	)	PUNCT
ejpam-6029	220	35	⪯	⪯	NOUN
ejpam-6029	220	36	(	(	PUNCT
ejpam-6029	220	37	λ(a0	λ(a0	X
ejpam-6029	220	38	,	,	PUNCT
ejpam-6029	220	39	a1	a1	NOUN
ejpam-6029	220	40	)	)	PUNCT
ejpam-6029	220	41	)	)	PUNCT
ejpam-6029	220	42	2lc(a2n−1	2lc(a2n−1	NUM
ejpam-6029	220	43	,	,	PUNCT
ejpam-6029	220	44	a2n	a2n	SYM
ejpam-6029	220	45	)	)	PUNCT
ejpam-6029	220	46	⪯	⪯	NOUN
ejpam-6029	220	47	·	·	PUNCT
ejpam-6029	220	48	·	·	PUNCT
ejpam-6029	220	49	·	·	PUNCT
ejpam-6029	221	1	⪯	⪯	NOUN
ejpam-6029	221	2	(	(	PUNCT
ejpam-6029	221	3	λ(a0	λ(a0	X
ejpam-6029	221	4	,	,	PUNCT
ejpam-6029	221	5	a1	a1	PROPN
ejpam-6029	221	6	)	)	PUNCT
ejpam-6029	221	7	)	)	PUNCT
ejpam-6029	222	1	nlc(a0	nlc(a0	NOUN
ejpam-6029	222	2	,	,	PUNCT
ejpam-6029	222	3	a1	a1	NOUN
ejpam-6029	222	4	)	)	PUNCT
ejpam-6029	222	5	.	.	PUNCT
ejpam-6029	223	1	applying	apply	VERB
ejpam-6029	223	2	it	it	PRON
ejpam-6029	223	3	recursively	recursively	ADV
ejpam-6029	223	4	,	,	PUNCT
ejpam-6029	223	5	we	we	PRON
ejpam-6029	223	6	have	have	VERB
ejpam-6029	223	7	lc(an	lc(an	PROPN
ejpam-6029	223	8	,	,	PUNCT
ejpam-6029	223	9	an+1	an+1	NOUN
ejpam-6029	223	10	)	)	PUNCT
ejpam-6029	223	11	⪯	⪯	PROPN
ejpam-6029	223	12	ξnlc(a0	ξnlc(a0	PROPN
ejpam-6029	223	13	,	,	PUNCT
ejpam-6029	223	14	a1	a1	PROPN
ejpam-6029	223	15	)	)	PUNCT
ejpam-6029	223	16	,	,	PUNCT
ejpam-6029	223	17	where	where	SCONJ
ejpam-6029	223	18	ξ	ξ	X
ejpam-6029	223	19	=	=	SYM
ejpam-6029	223	20	λ(a0	λ(a0	X
ejpam-6029	223	21	,	,	PUNCT
ejpam-6029	223	22	a1	a1	NOUN
ejpam-6029	223	23	)	)	PUNCT
ejpam-6029	223	24	.	.	PUNCT
ejpam-6029	224	1	(	(	PUNCT
ejpam-6029	224	2	5	5	X
ejpam-6029	224	3	)	)	PUNCT
ejpam-6029	224	4	a.	a.	NOUN
ejpam-6029	224	5	a.	a.	PROPN
ejpam-6029	225	1	hijab	hijab	PROPN
ejpam-6029	225	2	et	et	PROPN
ejpam-6029	225	3	al	al	PROPN
ejpam-6029	225	4	.	.	PUNCT
ejpam-6029	225	5	/	/	SYM
ejpam-6029	225	6	eur	eur	PROPN
ejpam-6029	225	7	.	.	PUNCT
ejpam-6029	226	1	j.	j.	PROPN
ejpam-6029	226	2	pure	pure	PROPN
ejpam-6029	226	3	appl	appl	PROPN
ejpam-6029	226	4	.	.	PROPN
ejpam-6029	226	5	math	math	PROPN
ejpam-6029	226	6	,	,	PUNCT
ejpam-6029	226	7	18	18	NUM
ejpam-6029	226	8	(	(	PUNCT
ejpam-6029	226	9	2	2	NUM
ejpam-6029	226	10	)	)	PUNCT
ejpam-6029	226	11	(	(	PUNCT
ejpam-6029	226	12	2025	2025	NUM
ejpam-6029	226	13	)	)	PUNCT
ejpam-6029	226	14	,	,	PUNCT
ejpam-6029	226	15	6029	6029	NUM
ejpam-6029	226	16	9	9	NUM
ejpam-6029	226	17	of	of	ADP
ejpam-6029	226	18	23	23	NUM
ejpam-6029	226	19	for	for	ADP
ejpam-6029	226	20	m	m	PROPN
ejpam-6029	226	21	<	<	X
ejpam-6029	226	22	n	n	CCONJ
ejpam-6029	226	23	,	,	PUNCT
ejpam-6029	226	24	and	and	CCONJ
ejpam-6029	226	25	n	n	CCONJ
ejpam-6029	226	26	,	,	PUNCT
ejpam-6029	226	27	m	m	VERB
ejpam-6029	226	28	∈	∈	ADJ
ejpam-6029	226	29	n	n	NOUN
ejpam-6029	226	30	and	and	CCONJ
ejpam-6029	226	31	condition	condition	NOUN
ejpam-6029	226	32	(	(	PUNCT
ejpam-6029	226	33	i	i	NOUN
ejpam-6029	226	34	)	)	PUNCT
ejpam-6029	226	35	,	,	PUNCT
ejpam-6029	226	36	we	we	PRON
ejpam-6029	226	37	deduce	deduce	VERB
ejpam-6029	226	38	that	that	SCONJ
ejpam-6029	226	39	lc(am	lc(am	PROPN
ejpam-6029	226	40	,	,	PUNCT
ejpam-6029	226	41	an	an	PRON
ejpam-6029	226	42	)	)	PUNCT
ejpam-6029	226	43	⪯	⪯	NOUN
ejpam-6029	226	44	f	f	PROPN
ejpam-6029	226	45	(	(	PUNCT
ejpam-6029	226	46	lc(am	lc(am	PROPN
ejpam-6029	226	47	,	,	PUNCT
ejpam-6029	226	48	am+1	am+1	PROPN
ejpam-6029	226	49	)	)	PUNCT
ejpam-6029	226	50	)	)	PUNCT
ejpam-6029	227	1	+	+	CCONJ
ejpam-6029	227	2	g	g	PROPN
ejpam-6029	227	3	(	(	PUNCT
ejpam-6029	227	4	lc(am+1	lc(am+1	PROPN
ejpam-6029	227	5	,	,	PUNCT
ejpam-6029	227	6	an	an	NOUN
ejpam-6029	227	7	)	)	PUNCT
ejpam-6029	227	8	)	)	PUNCT
ejpam-6029	227	9	⪯	⪯	PROPN
ejpam-6029	227	10	f	f	PROPN
ejpam-6029	227	11	(	(	PUNCT
ejpam-6029	227	12	lc(am	lc(am	PROPN
ejpam-6029	227	13	,	,	PUNCT
ejpam-6029	227	14	am+1	am+1	PROPN
ejpam-6029	227	15	)	)	PUNCT
ejpam-6029	227	16	)	)	PUNCT
ejpam-6029	228	1	+	+	CCONJ
ejpam-6029	228	2	gf	gf	X
ejpam-6029	228	3	(	(	PUNCT
ejpam-6029	228	4	lc(am+1	lc(am+1	PROPN
ejpam-6029	228	5	,	,	PUNCT
ejpam-6029	228	6	am+2	am+2	NOUN
ejpam-6029	228	7	)	)	PUNCT
ejpam-6029	228	8	)	)	PUNCT
ejpam-6029	229	1	+	+	CCONJ
ejpam-6029	229	2	g2	g2	PROPN
ejpam-6029	229	3	(	(	PUNCT
ejpam-6029	229	4	lc(am+2	lc(am+2	PROPN
ejpam-6029	229	5	,	,	PUNCT
ejpam-6029	229	6	an	an	PRON
ejpam-6029	229	7	)	)	PUNCT
ejpam-6029	229	8	)	)	PUNCT
ejpam-6029	229	9	...	...	PUNCT
ejpam-6029	230	1	⪯	⪯	VERB
ejpam-6029	230	2	n−2∑	n−2∑	PROPN
ejpam-6029	230	3	i	i	PRON
ejpam-6029	230	4	=	=	NOUN
ejpam-6029	230	5	m	m	VERB
ejpam-6029	230	6	gi−mf	gi−mf	NOUN
ejpam-6029	230	7	(	(	PUNCT
ejpam-6029	230	8	lc(ai	lc(ai	PROPN
ejpam-6029	230	9	,	,	PUNCT
ejpam-6029	230	10	ai+1	ai+1	NOUN
ejpam-6029	230	11	)	)	PUNCT
ejpam-6029	230	12	)	)	PUNCT
ejpam-6029	231	1	+	+	CCONJ
ejpam-6029	231	2	gn−m−1	gn−m−1	X
ejpam-6029	231	3	(	(	PUNCT
ejpam-6029	231	4	lc(an−1	lc(an−1	PROPN
ejpam-6029	231	5	,	,	PUNCT
ejpam-6029	231	6	an	an	NOUN
ejpam-6029	231	7	)	)	PUNCT
ejpam-6029	231	8	)	)	PUNCT
ejpam-6029	231	9	.	.	PUNCT
ejpam-6029	232	1	(	(	PUNCT
ejpam-6029	232	2	6	6	X
ejpam-6029	232	3	)	)	PUNCT
ejpam-6029	232	4	substituting	substitute	VERB
ejpam-6029	232	5	(	(	PUNCT
ejpam-6029	232	6	5	5	NUM
ejpam-6029	232	7	)	)	PUNCT
ejpam-6029	232	8	in	in	ADP
ejpam-6029	232	9	(	(	PUNCT
ejpam-6029	232	10	6	6	NUM
ejpam-6029	232	11	)	)	PUNCT
ejpam-6029	232	12	implies	imply	VERB
ejpam-6029	232	13	that	that	DET
ejpam-6029	232	14	∥lc(am	∥lc(am	PROPN
ejpam-6029	232	15	,	,	PUNCT
ejpam-6029	232	16	an)∥	an)∥	X
ejpam-6029	232	17	⪯m	⪯m	PROPN
ejpam-6029	232	18	[	[	PUNCT
ejpam-6029	232	19	∥	∥	X
ejpam-6029	232	20	n−2∑	n−2∑	NUM
ejpam-6029	232	21	i	i	PRON
ejpam-6029	232	22	=	=	NOUN
ejpam-6029	232	23	m	m	VERB
ejpam-6029	232	24	gi−mf	gi−mf	NOUN
ejpam-6029	232	25	(	(	PUNCT
ejpam-6029	232	26	ξilc(a0	ξilc(a0	NOUN
ejpam-6029	232	27	,	,	PUNCT
ejpam-6029	232	28	a1	a1	NOUN
ejpam-6029	232	29	)	)	PUNCT
ejpam-6029	232	30	)	)	PUNCT
ejpam-6029	233	1	∥+	∥+	PROPN
ejpam-6029	234	1	∥gn−m−1	∥gn−m−1	PROPN
ejpam-6029	234	2	(	(	PUNCT
ejpam-6029	234	3	ξn−1lc(a0	ξn−1lc(a0	PROPN
ejpam-6029	234	4	,	,	PUNCT
ejpam-6029	234	5	a1	a1	NOUN
ejpam-6029	234	6	)	)	PUNCT
ejpam-6029	234	7	)	)	PUNCT
ejpam-6029	234	8	∥	∥	PUNCT
ejpam-6029	234	9	]	]	PUNCT
ejpam-6029	234	10	.	.	PUNCT
ejpam-6029	235	1	thus	thus	ADV
ejpam-6029	235	2	,	,	PUNCT
ejpam-6029	235	3	as	as	ADP
ejpam-6029	235	4	n	n	CCONJ
ejpam-6029	235	5	,	,	PUNCT
ejpam-6029	235	6	m→	m→	NOUN
ejpam-6029	235	7	∞	∞	NUM
ejpam-6029	235	8	,	,	PUNCT
ejpam-6029	235	9	and	and	CCONJ
ejpam-6029	235	10	condition	condition	NOUN
ejpam-6029	235	11	(	(	PUNCT
ejpam-6029	235	12	ii	ii	NOUN
ejpam-6029	235	13	)	)	PUNCT
ejpam-6029	235	14	,	,	PUNCT
ejpam-6029	235	15	we	we	PRON
ejpam-6029	235	16	have	have	VERB
ejpam-6029	235	17	∥lc(am	∥lc(am	NUM
ejpam-6029	235	18	,	,	PUNCT
ejpam-6029	235	19	an)∥	an)∥	PUNCT
ejpam-6029	235	20	=	=	SYM
ejpam-6029	235	21	0	0	X
ejpam-6029	235	22	.	.	PUNCT
ejpam-6029	236	1	since	since	SCONJ
ejpam-6029	236	2	the	the	DET
ejpam-6029	236	3	sequence	sequence	NOUN
ejpam-6029	236	4	{	{	PUNCT
ejpam-6029	236	5	an	an	PRON
ejpam-6029	236	6	}	}	PUNCT
ejpam-6029	236	7	is	be	AUX
ejpam-6029	236	8	lc	lc	NOUN
ejpam-6029	236	9	-	-	PUNCT
ejpam-6029	236	10	cauchy	cauchy	NOUN
ejpam-6029	236	11	in	in	ADP
ejpam-6029	236	12	γ	γ	PROPN
ejpam-6029	236	13	,	,	PUNCT
ejpam-6029	236	14	which	which	PRON
ejpam-6029	236	15	is	be	AUX
ejpam-6029	236	16	lc	lc	NOUN
ejpam-6029	236	17	-	-	PUNCT
ejpam-6029	236	18	complete	complete	ADJ
ejpam-6029	236	19	dccml	dccml	NOUN
ejpam-6029	236	20	-	-	PUNCT
ejpam-6029	236	21	space	space	NOUN
ejpam-6029	236	22	,	,	PUNCT
ejpam-6029	236	23	there	there	PRON
ejpam-6029	236	24	exists	exist	VERB
ejpam-6029	236	25	an	an	DET
ejpam-6029	236	26	element	element	NOUN
ejpam-6029	236	27	a	a	DET
ejpam-6029	236	28	∈	∈	NOUN
ejpam-6029	236	29	γ	γ	NOUN
ejpam-6029	236	30	such	such	ADJ
ejpam-6029	236	31	that	that	SCONJ
ejpam-6029	236	32	{	{	PUNCT
ejpam-6029	236	33	an	an	NOUN
ejpam-6029	236	34	}	}	PUNCT
ejpam-6029	236	35	→	→	SYM
ejpam-6029	236	36	a.	a.	NOUN
ejpam-6029	236	37	hence	hence	ADV
ejpam-6029	236	38	lc(an	lc(an	PROPN
ejpam-6029	236	39	,	,	PUNCT
ejpam-6029	236	40	a	a	PRON
ejpam-6029	236	41	)	)	PUNCT
ejpam-6029	236	42	=	=	SYM
ejpam-6029	236	43	lc(a	lc(a	PROPN
ejpam-6029	236	44	,	,	PUNCT
ejpam-6029	236	45	a	a	PRON
ejpam-6029	236	46	)	)	PUNCT
ejpam-6029	236	47	=	=	SYM
ejpam-6029	236	48	lc(an	lc(an	PROPN
ejpam-6029	236	49	,	,	PUNCT
ejpam-6029	236	50	am	be	AUX
ejpam-6029	236	51	)	)	PUNCT
ejpam-6029	237	1	=	=	SYM
ejpam-6029	237	2	0e	0e	NOUN
ejpam-6029	237	3	.	.	PUNCT
ejpam-6029	238	1	(	(	PUNCT
ejpam-6029	238	2	7	7	X
ejpam-6029	238	3	)	)	PUNCT
ejpam-6029	238	4	now	now	ADV
ejpam-6029	238	5	,	,	PUNCT
ejpam-6029	238	6	we	we	PRON
ejpam-6029	238	7	prove	prove	VERB
ejpam-6029	238	8	that	that	SCONJ
ejpam-6029	238	9	t1a	t1a	NOUN
ejpam-6029	238	10	=	=	SYM
ejpam-6029	238	11	t2a	t2a	ADP
ejpam-6029	238	12	=	=	NOUN
ejpam-6029	238	13	a.	a.	NOUN
ejpam-6029	238	14	since	since	SCONJ
ejpam-6029	238	15	{	{	PUNCT
ejpam-6029	238	16	an	an	PROPN
ejpam-6029	238	17	}	}	PUNCT
ejpam-6029	238	18	→	→	SYM
ejpam-6029	238	19	a	a	PRON
ejpam-6029	238	20	,	,	PUNCT
ejpam-6029	238	21	as	as	ADP
ejpam-6029	238	22	n	n	PROPN
ejpam-6029	238	23	→	→	SYM
ejpam-6029	238	24	+	+	PROPN
ejpam-6029	238	25	∞	∞	PROPN
ejpam-6029	238	26	,	,	PUNCT
ejpam-6029	238	27	from	from	ADP
ejpam-6029	238	28	condition	condition	NOUN
ejpam-6029	238	29	(	(	PUNCT
ejpam-6029	238	30	i	i	NOUN
ejpam-6029	238	31	)	)	PUNCT
ejpam-6029	238	32	and	and	CCONJ
ejpam-6029	238	33	(	(	PUNCT
ejpam-6029	238	34	l3	l3	PROPN
ejpam-6029	238	35	)	)	PUNCT
ejpam-6029	238	36	,	,	PUNCT
ejpam-6029	238	37	we	we	PRON
ejpam-6029	238	38	deduce	deduce	VERB
ejpam-6029	238	39	that	that	PRON
ejpam-6029	238	40	lc(a	lc(a	NOUN
ejpam-6029	238	41	,	,	PUNCT
ejpam-6029	238	42	t1a	t1a	NUM
ejpam-6029	238	43	)	)	PUNCT
ejpam-6029	239	1	⪯	⪯	NOUN
ejpam-6029	239	2	f	f	PROPN
ejpam-6029	239	3	(	(	PUNCT
ejpam-6029	239	4	lc(a	lc(a	PROPN
ejpam-6029	239	5	,	,	PUNCT
ejpam-6029	239	6	a2n+2	a2n+2	PRON
ejpam-6029	239	7	)	)	PUNCT
ejpam-6029	239	8	)	)	PUNCT
ejpam-6029	240	1	+	+	CCONJ
ejpam-6029	240	2	g	g	PROPN
ejpam-6029	240	3	(	(	PUNCT
ejpam-6029	240	4	lc(a2n+2	lc(a2n+2	PROPN
ejpam-6029	240	5	,	,	PUNCT
ejpam-6029	240	6	t1a	t1a	NOUN
ejpam-6029	240	7	)	)	PUNCT
ejpam-6029	240	8	)	)	PUNCT
ejpam-6029	241	1	=	=	SYM
ejpam-6029	241	2	f	f	PROPN
ejpam-6029	241	3	(	(	PUNCT
ejpam-6029	241	4	lc(a	lc(a	PROPN
ejpam-6029	241	5	,	,	PUNCT
ejpam-6029	241	6	a2n+2	a2n+2	PRON
ejpam-6029	241	7	)	)	PUNCT
ejpam-6029	241	8	)	)	PUNCT
ejpam-6029	242	1	+	+	CCONJ
ejpam-6029	242	2	g	g	NOUN
ejpam-6029	242	3	(	(	PUNCT
ejpam-6029	242	4	lc(t1a	lc(t1a	PROPN
ejpam-6029	242	5	,	,	PUNCT
ejpam-6029	242	6	t2a2n+1	t2a2n+1	NUM
ejpam-6029	242	7	)	)	PUNCT
ejpam-6029	242	8	)	)	PUNCT
ejpam-6029	242	9	,	,	PUNCT
ejpam-6029	242	10	implying	imply	VERB
ejpam-6029	242	11	that	that	SCONJ
ejpam-6029	242	12	lc(t1a	lc(t1a	PROPN
ejpam-6029	242	13	,	,	PUNCT
ejpam-6029	242	14	t2a2n+1	t2a2n+1	NUM
ejpam-6029	242	15	)	)	PUNCT
ejpam-6029	242	16	⪯	⪯	NOUN
ejpam-6029	242	17	λ(a	λ(a	PROPN
ejpam-6029	242	18	,	,	PUNCT
ejpam-6029	242	19	a2n+1)m̃(a	a2n+1)m̃(a	PROPN
ejpam-6029	242	20	,	,	PUNCT
ejpam-6029	242	21	a2n+1	a2n+1	NOUN
ejpam-6029	242	22	)	)	PUNCT
ejpam-6029	242	23	,	,	PUNCT
ejpam-6029	242	24	and	and	CCONJ
ejpam-6029	242	25	m̃(a	m̃(a	PROPN
ejpam-6029	242	26	,	,	PUNCT
ejpam-6029	242	27	a2n+1	a2n+1	NOUN
ejpam-6029	242	28	)	)	PUNCT
ejpam-6029	242	29	=	=	SYM
ejpam-6029	242	30	max	max	X
ejpam-6029	242	31	{	{	PUNCT
ejpam-6029	242	32	lc(a	lc(a	PROPN
ejpam-6029	242	33	,	,	PUNCT
ejpam-6029	242	34	a2n+1),lc(a	a2n+1),lc(a	ADV
ejpam-6029	242	35	,	,	PUNCT
ejpam-6029	242	36	t1a),lc(a2n+1	t1a),lc(a2n+1	NOUN
ejpam-6029	242	37	,	,	PUNCT
ejpam-6029	242	38	t2a2n+1	t2a2n+1	NUM
ejpam-6029	242	39	)	)	PUNCT
ejpam-6029	242	40	,	,	PUNCT
ejpam-6029	242	41	lc(a	lc(a	PROPN
ejpam-6029	242	42	,	,	PUNCT
ejpam-6029	242	43	t1a)lc(a2n+1	t1a)lc(a2n+1	NUM
ejpam-6029	242	44	,	,	PUNCT
ejpam-6029	242	45	t2a2n+1	t2a2n+1	NUM
ejpam-6029	242	46	)	)	PUNCT
ejpam-6029	242	47	1	1	NUM
ejpam-6029	242	48	+	+	CCONJ
ejpam-6029	242	49	lc(a	lc(a	NUM
ejpam-6029	242	50	,	,	PUNCT
ejpam-6029	242	51	a2n+1	a2n+1	NOUN
ejpam-6029	242	52	)	)	PUNCT
ejpam-6029	242	53	,	,	PUNCT
ejpam-6029	242	54	lc(a2n+1	lc(a2n+1	PROPN
ejpam-6029	242	55	,	,	PUNCT
ejpam-6029	242	56	t2a2n+1)[1	t2a2n+1)[1	NOUN
ejpam-6029	242	57	+	+	CCONJ
ejpam-6029	242	58	lc(a	lc(a	NUM
ejpam-6029	242	59	,	,	PUNCT
ejpam-6029	242	60	t1a	t1a	NOUN
ejpam-6029	242	61	)	)	PUNCT
ejpam-6029	242	62	]	]	PUNCT
ejpam-6029	242	63	1	1	NUM
ejpam-6029	242	64	+	+	CCONJ
ejpam-6029	242	65	lc(a	lc(a	NUM
ejpam-6029	242	66	,	,	PUNCT
ejpam-6029	242	67	a2n+1	a2n+1	NOUN
ejpam-6029	242	68	)	)	PUNCT
ejpam-6029	242	69	,	,	PUNCT
ejpam-6029	242	70	[	[	PUNCT
ejpam-6029	242	71	lc(a	lc(a	X
ejpam-6029	242	72	,	,	PUNCT
ejpam-6029	242	73	t1a	t1a	NUM
ejpam-6029	242	74	)	)	PUNCT
ejpam-6029	242	75	+	+	SYM
ejpam-6029	242	76	lc(a2n+1	lc(a2n+1	NOUN
ejpam-6029	242	77	,	,	PUNCT
ejpam-6029	242	78	t2a2n+1	t2a2n+1	NUM
ejpam-6029	242	79	)	)	PUNCT
ejpam-6029	242	80	]	]	PUNCT
ejpam-6029	242	81	lc(t1a	lc(t1a	NUM
ejpam-6029	242	82	,	,	PUNCT
ejpam-6029	242	83	t2a2n+1	t2a2n+1	NUM
ejpam-6029	242	84	)	)	PUNCT
ejpam-6029	242	85	1	1	NUM
ejpam-6029	242	86	+	+	CCONJ
ejpam-6029	242	87	lc(a	lc(a	NUM
ejpam-6029	242	88	,	,	PUNCT
ejpam-6029	242	89	a2n+1	a2n+1	NOUN
ejpam-6029	242	90	)	)	PUNCT
ejpam-6029	243	1	+	+	CCONJ
ejpam-6029	243	2	lc(t1a	lc(t1a	PROPN
ejpam-6029	243	3	,	,	PUNCT
ejpam-6029	243	4	t2a2n+1	t2a2n+1	NUM
ejpam-6029	243	5	)	)	PUNCT
ejpam-6029	243	6	}	}	PUNCT
ejpam-6029	244	1	=	=	X
ejpam-6029	244	2	max	max	X
ejpam-6029	244	3	{	{	PUNCT
ejpam-6029	244	4	lc(a	lc(a	PROPN
ejpam-6029	244	5	,	,	PUNCT
ejpam-6029	244	6	a2n+1),lc(a	a2n+1),lc(a	ADV
ejpam-6029	244	7	,	,	PUNCT
ejpam-6029	244	8	t1a),lc(a2n+1	t1a),lc(a2n+1	ADJ
ejpam-6029	244	9	,	,	PUNCT
ejpam-6029	244	10	a2n+2	a2n+2	PRON
ejpam-6029	244	11	)	)	PUNCT
ejpam-6029	244	12	,	,	PUNCT
ejpam-6029	244	13	lc(a	lc(a	PROPN
ejpam-6029	244	14	,	,	PUNCT
ejpam-6029	244	15	t1a)lc(a2n+1	t1a)lc(a2n+1	ADJ
ejpam-6029	244	16	,	,	PUNCT
ejpam-6029	244	17	a2n+2	a2n+2	PRON
ejpam-6029	244	18	)	)	PUNCT
ejpam-6029	244	19	1	1	NUM
ejpam-6029	244	20	+	+	CCONJ
ejpam-6029	244	21	lc(a	lc(a	NUM
ejpam-6029	244	22	,	,	PUNCT
ejpam-6029	244	23	a2n+1	a2n+1	NOUN
ejpam-6029	244	24	)	)	PUNCT
ejpam-6029	244	25	,	,	PUNCT
ejpam-6029	244	26	lc(a2n+1	lc(a2n+1	PROPN
ejpam-6029	244	27	,	,	PUNCT
ejpam-6029	244	28	a2n+2)[1	a2n+2)[1	PROPN
ejpam-6029	244	29	+	+	X
ejpam-6029	244	30	lc(a	lc(a	NUM
ejpam-6029	244	31	,	,	PUNCT
ejpam-6029	244	32	t1a	t1a	NOUN
ejpam-6029	244	33	)	)	PUNCT
ejpam-6029	244	34	]	]	PUNCT
ejpam-6029	244	35	1	1	NUM
ejpam-6029	244	36	+	+	CCONJ
ejpam-6029	244	37	lc(a	lc(a	NUM
ejpam-6029	244	38	,	,	PUNCT
ejpam-6029	244	39	a2n+1	a2n+1	NOUN
ejpam-6029	244	40	)	)	PUNCT
ejpam-6029	244	41	,	,	PUNCT
ejpam-6029	244	42	[	[	PUNCT
ejpam-6029	244	43	lc(a	lc(a	X
ejpam-6029	244	44	,	,	PUNCT
ejpam-6029	244	45	t1a	t1a	NUM
ejpam-6029	244	46	)	)	PUNCT
ejpam-6029	244	47	+	+	SYM
ejpam-6029	244	48	lc(a2n+1	lc(a2n+1	NOUN
ejpam-6029	244	49	,	,	PUNCT
ejpam-6029	244	50	a2n+2	a2n+2	PRON
ejpam-6029	244	51	)	)	PUNCT
ejpam-6029	244	52	]	]	PUNCT
ejpam-6029	245	1	lc(t1a	lc(t1a	NUM
ejpam-6029	245	2	,	,	PUNCT
ejpam-6029	245	3	a2n+2	a2n+2	PRON
ejpam-6029	245	4	)	)	PUNCT
ejpam-6029	245	5	1	1	NUM
ejpam-6029	245	6	+	+	CCONJ
ejpam-6029	245	7	lc(a	lc(a	NUM
ejpam-6029	245	8	,	,	PUNCT
ejpam-6029	245	9	a2n+1	a2n+1	NOUN
ejpam-6029	245	10	)	)	PUNCT
ejpam-6029	245	11	+	+	CCONJ
ejpam-6029	245	12	lc(t1a	lc(t1a	PROPN
ejpam-6029	245	13	,	,	PUNCT
ejpam-6029	245	14	a2n+2	a2n+2	PRON
ejpam-6029	245	15	)	)	PUNCT
ejpam-6029	245	16	}	}	PUNCT
ejpam-6029	245	17	.	.	PUNCT
ejpam-6029	246	1	a.	a.	NOUN
ejpam-6029	246	2	a.	a.	PROPN
ejpam-6029	246	3	hijab	hijab	PROPN
ejpam-6029	246	4	et	et	PROPN
ejpam-6029	246	5	al	al	PROPN
ejpam-6029	246	6	.	.	PUNCT
ejpam-6029	246	7	/	/	SYM
ejpam-6029	246	8	eur	eur	PROPN
ejpam-6029	246	9	.	.	PUNCT
ejpam-6029	247	1	j.	j.	PROPN
ejpam-6029	247	2	pure	pure	PROPN
ejpam-6029	247	3	appl	appl	PROPN
ejpam-6029	247	4	.	.	PROPN
ejpam-6029	247	5	math	math	PROPN
ejpam-6029	247	6	,	,	PUNCT
ejpam-6029	247	7	18	18	NUM
ejpam-6029	247	8	(	(	PUNCT
ejpam-6029	247	9	2	2	NUM
ejpam-6029	247	10	)	)	PUNCT
ejpam-6029	247	11	(	(	PUNCT
ejpam-6029	247	12	2025	2025	NUM
ejpam-6029	247	13	)	)	PUNCT
ejpam-6029	247	14	,	,	PUNCT
ejpam-6029	247	15	6029	6029	NUM
ejpam-6029	247	16	10	10	NUM
ejpam-6029	247	17	of	of	ADP
ejpam-6029	247	18	23	23	NUM
ejpam-6029	247	19	by	by	ADP
ejpam-6029	247	20	assuming	assume	VERB
ejpam-6029	247	21	f	f	PROPN
ejpam-6029	247	22	and	and	CCONJ
ejpam-6029	247	23	g	g	PROPN
ejpam-6029	247	24	are	be	AUX
ejpam-6029	247	25	bounded	bound	VERB
ejpam-6029	247	26	and	and	CCONJ
ejpam-6029	247	27	taking	take	VERB
ejpam-6029	247	28	the	the	DET
ejpam-6029	247	29	limit	limit	NOUN
ejpam-6029	247	30	in	in	ADP
ejpam-6029	247	31	the	the	DET
ejpam-6029	247	32	above	above	ADJ
ejpam-6029	247	33	relationship	relationship	NOUN
ejpam-6029	247	34	and	and	CCONJ
ejpam-6029	247	35	(	(	PUNCT
ejpam-6029	247	36	7	7	NUM
ejpam-6029	247	37	)	)	PUNCT
ejpam-6029	247	38	,	,	PUNCT
ejpam-6029	247	39	we	we	PRON
ejpam-6029	247	40	obtain	obtain	VERB
ejpam-6029	247	41	that	that	SCONJ
ejpam-6029	247	42	0e	0e	ADJ
ejpam-6029	247	43	≺	≺	NOUN
ejpam-6029	247	44	lc(a	lc(a	NUM
ejpam-6029	247	45	,	,	PUNCT
ejpam-6029	247	46	t1a	t1a	NUM
ejpam-6029	247	47	)	)	PUNCT
ejpam-6029	247	48	⪯	⪯	NOUN
ejpam-6029	247	49	f(0	f(0	NOUN
ejpam-6029	247	50	)	)	PUNCT
ejpam-6029	248	1	+	+	CCONJ
ejpam-6029	248	2	g	g	PROPN
ejpam-6029	248	3	(	(	PUNCT
ejpam-6029	248	4	λ(a	λ(a	NOUN
ejpam-6029	248	5	,	,	PUNCT
ejpam-6029	248	6	a2n+1)lc(a	a2n+1)lc(a	NOUN
ejpam-6029	248	7	,	,	PUNCT
ejpam-6029	248	8	t1a	t1a	NOUN
ejpam-6029	248	9	)	)	PUNCT
ejpam-6029	248	10	)	)	PUNCT
ejpam-6029	248	11	.	.	PUNCT
ejpam-6029	249	1	we	we	PRON
ejpam-6029	249	2	use	use	VERB
ejpam-6029	249	3	the	the	DET
ejpam-6029	249	4	fact	fact	NOUN
ejpam-6029	249	5	that	that	SCONJ
ejpam-6029	249	6	λ(a	λ(a	NOUN
ejpam-6029	249	7	,	,	PUNCT
ejpam-6029	249	8	a2n+1	a2n+1	NOUN
ejpam-6029	249	9	)	)	PUNCT
ejpam-6029	249	10	∈	∈	NOUN
ejpam-6029	249	11	∆	∆	PROPN
ejpam-6029	249	12	and	and	CCONJ
ejpam-6029	249	13	condition	condition	NOUN
ejpam-6029	249	14	(	(	PUNCT
ejpam-6029	249	15	i	i	NOUN
ejpam-6029	249	16	)	)	PUNCT
ejpam-6029	249	17	,	,	PUNCT
ejpam-6029	249	18	we	we	PRON
ejpam-6029	249	19	can	can	AUX
ejpam-6029	249	20	take	take	VERB
ejpam-6029	249	21	g(λ(a	g(λ(a	NOUN
ejpam-6029	249	22	,	,	PUNCT
ejpam-6029	249	23	a2n+1)lc(a	a2n+1)lc(a	NOUN
ejpam-6029	249	24	,	,	PUNCT
ejpam-6029	249	25	t1a	t1a	NUM
ejpam-6029	249	26	)	)	PUNCT
ejpam-6029	249	27	)	)	PUNCT
ejpam-6029	249	28	≺	≺	NOUN
ejpam-6029	249	29	lc(a	lc(a	NUM
ejpam-6029	249	30	,	,	PUNCT
ejpam-6029	249	31	t1a	t1a	NUM
ejpam-6029	249	32	)	)	PUNCT
ejpam-6029	249	33	.	.	PUNCT
ejpam-6029	250	1	therefore	therefore	ADV
ejpam-6029	250	2	,	,	PUNCT
ejpam-6029	250	3	∥lc(a	∥lc(a	PROPN
ejpam-6029	250	4	,	,	PUNCT
ejpam-6029	250	5	t1a)∥	t1a)∥	PROPN
ejpam-6029	250	6	=	=	SYM
ejpam-6029	250	7	0	0	NUM
ejpam-6029	250	8	,	,	PUNCT
ejpam-6029	250	9	i.e.	i.e.	X
ejpam-6029	250	10	,	,	PUNCT
ejpam-6029	250	11	t1a	t1a	NOUN
ejpam-6029	250	12	=	=	SYM
ejpam-6029	250	13	a.	a.	NOUN
ejpam-6029	250	14	using	use	VERB
ejpam-6029	250	15	the	the	DET
ejpam-6029	250	16	same	same	ADJ
ejpam-6029	250	17	way	way	NOUN
ejpam-6029	250	18	as	as	ADP
ejpam-6029	250	19	for	for	ADP
ejpam-6029	250	20	the	the	DET
ejpam-6029	250	21	proof	proof	NOUN
ejpam-6029	250	22	of	of	ADP
ejpam-6029	250	23	t1	t1	PROPN
ejpam-6029	250	24	,	,	PUNCT
ejpam-6029	250	25	we	we	PRON
ejpam-6029	250	26	get	get	VERB
ejpam-6029	250	27	t2a	t2a	ADP
ejpam-6029	250	28	=	=	NOUN
ejpam-6029	250	29	a.	a.	NOUN
ejpam-6029	250	30	hence	hence	ADV
ejpam-6029	250	31	,	,	PUNCT
ejpam-6029	250	32	t1	t1	NOUN
ejpam-6029	250	33	and	and	CCONJ
ejpam-6029	250	34	t2	t2	PROPN
ejpam-6029	250	35	have	have	VERB
ejpam-6029	250	36	a	a	DET
ejpam-6029	250	37	common	common	ADJ
ejpam-6029	250	38	fixed	fix	VERB
ejpam-6029	250	39	point	point	NOUN
ejpam-6029	250	40	a.	a.	NOUN
ejpam-6029	250	41	let	let	VERB
ejpam-6029	250	42	a	a	PRON
ejpam-6029	250	43	and	and	CCONJ
ejpam-6029	250	44	a∗	a∗	PROPN
ejpam-6029	250	45	be	be	AUX
ejpam-6029	250	46	two	two	NUM
ejpam-6029	250	47	fixed	fix	VERB
ejpam-6029	250	48	points	point	NOUN
ejpam-6029	250	49	of	of	ADP
ejpam-6029	250	50	t1	t1	NOUN
ejpam-6029	250	51	and	and	CCONJ
ejpam-6029	250	52	t2	t2	NOUN
ejpam-6029	250	53	,	,	PUNCT
ejpam-6029	250	54	where	where	SCONJ
ejpam-6029	250	55	t1a	t1a	VERB
ejpam-6029	250	56	=	=	SYM
ejpam-6029	250	57	t2a	t2a	ADP
ejpam-6029	250	58	=	=	PUNCT
ejpam-6029	250	59	a	a	PRON
ejpam-6029	250	60	and	and	CCONJ
ejpam-6029	250	61	t1a	t1a	NOUN
ejpam-6029	250	62	∗	∗	NOUN
ejpam-6029	250	63	=	=	PUNCT
ejpam-6029	250	64	t2a	t2a	ADP
ejpam-6029	250	65	∗	∗	NOUN
ejpam-6029	250	66	=	=	PUNCT
ejpam-6029	250	67	a.	a.	NOUN
ejpam-6029	250	68	since	since	SCONJ
ejpam-6029	250	69	a	a	DET
ejpam-6029	250	70	̸=	̸=	PROPN
ejpam-6029	250	71	a∗	a∗	NOUN
ejpam-6029	250	72	,	,	PUNCT
ejpam-6029	250	73	it	it	PRON
ejpam-6029	250	74	implies	imply	VERB
ejpam-6029	250	75	tia	tia	PROPN
ejpam-6029	250	76	̸=	̸=	PROPN
ejpam-6029	250	77	tja	tja	PROPN
ejpam-6029	250	78	∗	∗	NOUN
ejpam-6029	250	79	,	,	PUNCT
ejpam-6029	250	80	i	i	PRON
ejpam-6029	250	81	,	,	PUNCT
ejpam-6029	250	82	j	j	PROPN
ejpam-6029	251	1	=	=	SYM
ejpam-6029	252	1	1	1	NUM
ejpam-6029	252	2	,	,	PUNCT
ejpam-6029	252	3	2	2	NUM
ejpam-6029	252	4	.	.	PUNCT
ejpam-6029	253	1	by	by	ADP
ejpam-6029	253	2	(	(	PUNCT
ejpam-6029	253	3	3	3	X
ejpam-6029	253	4	)	)	PUNCT
ejpam-6029	253	5	we	we	PRON
ejpam-6029	253	6	obtain	obtain	VERB
ejpam-6029	253	7	lc(a	lc(a	PUNCT
ejpam-6029	254	1	∗	∗	NOUN
ejpam-6029	254	2	,	,	PUNCT
ejpam-6029	254	3	a	a	PRON
ejpam-6029	254	4	)	)	PUNCT
ejpam-6029	254	5	=	=	SYM
ejpam-6029	254	6	lc(t1a	lc(t1a	ADJ
ejpam-6029	254	7	∗	∗	NOUN
ejpam-6029	254	8	,	,	PUNCT
ejpam-6029	254	9	t2a	t2a	PROPN
ejpam-6029	254	10	)	)	PUNCT
ejpam-6029	254	11	⪯	⪯	NOUN
ejpam-6029	254	12	λ(a∗	λ(a∗	PRON
ejpam-6029	254	13	,	,	PUNCT
ejpam-6029	254	14	a)m̃(a∗	a)m̃(a∗	PROPN
ejpam-6029	254	15	,	,	PUNCT
ejpam-6029	254	16	a	a	PRON
ejpam-6029	254	17	)	)	PUNCT
ejpam-6029	254	18	,	,	PUNCT
ejpam-6029	255	1	where	where	SCONJ
ejpam-6029	255	2	m̃(a∗	m̃(a∗	NOUN
ejpam-6029	255	3	,	,	PUNCT
ejpam-6029	255	4	a	a	PRON
ejpam-6029	255	5	)	)	PUNCT
ejpam-6029	255	6	=	=	SYM
ejpam-6029	255	7	max	max	PROPN
ejpam-6029	255	8	{	{	PUNCT
ejpam-6029	255	9	lc(a	lc(a	X
ejpam-6029	255	10	∗	∗	NOUN
ejpam-6029	255	11	,	,	PUNCT
ejpam-6029	255	12	a),lc(a	a),lc(a	PROPN
ejpam-6029	255	13	∗	∗	NOUN
ejpam-6029	255	14	,	,	PUNCT
ejpam-6029	255	15	t1a	t1a	PRON
ejpam-6029	255	16	∗),lc(a	∗),lc(a	NUM
ejpam-6029	255	17	,	,	PUNCT
ejpam-6029	255	18	t2a	t2a	PROPN
ejpam-6029	255	19	)	)	PUNCT
ejpam-6029	255	20	,	,	PUNCT
ejpam-6029	255	21	lc(a	lc(a	PUNCT
ejpam-6029	255	22	∗	∗	NOUN
ejpam-6029	255	23	,	,	PUNCT
ejpam-6029	255	24	t1a	t1a	PRON
ejpam-6029	255	25	∗)lc(a	∗)lc(a	PROPN
ejpam-6029	255	26	,	,	PUNCT
ejpam-6029	255	27	t2a	t2a	ADP
ejpam-6029	255	28	)	)	PUNCT
ejpam-6029	255	29	1	1	NUM
ejpam-6029	255	30	+	+	NUM
ejpam-6029	255	31	lc(a∗	lc(a∗	NOUN
ejpam-6029	255	32	,	,	PUNCT
ejpam-6029	255	33	a	a	PRON
ejpam-6029	255	34	)	)	PUNCT
ejpam-6029	255	35	,	,	PUNCT
ejpam-6029	255	36	lc(a	lc(a	PROPN
ejpam-6029	255	37	,	,	PUNCT
ejpam-6029	255	38	t2a)[1	t2a)[1	PRON
ejpam-6029	255	39	+	+	CCONJ
ejpam-6029	255	40	lc(a	lc(a	NUM
ejpam-6029	255	41	∗	∗	NOUN
ejpam-6029	255	42	,	,	PUNCT
ejpam-6029	255	43	t1a	t1a	CCONJ
ejpam-6029	255	44	∗	∗	NOUN
ejpam-6029	255	45	)	)	PUNCT
ejpam-6029	255	46	]	]	PUNCT
ejpam-6029	256	1	1	1	NUM
ejpam-6029	256	2	+	+	NUM
ejpam-6029	256	3	lc(a∗	lc(a∗	NOUN
ejpam-6029	256	4	,	,	PUNCT
ejpam-6029	256	5	a	a	PRON
ejpam-6029	256	6	)	)	PUNCT
ejpam-6029	256	7	,	,	PUNCT
ejpam-6029	256	8	[	[	PUNCT
ejpam-6029	256	9	lc(a	lc(a	X
ejpam-6029	256	10	∗	∗	NOUN
ejpam-6029	256	11	,	,	PUNCT
ejpam-6029	256	12	t1a	t1a	CCONJ
ejpam-6029	256	13	∗	∗	NOUN
ejpam-6029	256	14	)	)	PUNCT
ejpam-6029	256	15	+	+	NUM
ejpam-6029	256	16	lc(a	lc(a	NOUN
ejpam-6029	256	17	,	,	PUNCT
ejpam-6029	256	18	t2a	t2a	ADP
ejpam-6029	256	19	)	)	PUNCT
ejpam-6029	256	20	]	]	PUNCT
ejpam-6029	256	21	lc(t1a	lc(t1a	ADJ
ejpam-6029	256	22	∗	∗	NOUN
ejpam-6029	256	23	,	,	PUNCT
ejpam-6029	256	24	t2a	t2a	ADP
ejpam-6029	256	25	)	)	PUNCT
ejpam-6029	256	26	1	1	NUM
ejpam-6029	256	27	+	+	NUM
ejpam-6029	256	28	lc(a∗	lc(a∗	NOUN
ejpam-6029	256	29	,	,	PUNCT
ejpam-6029	256	30	a	a	PRON
ejpam-6029	256	31	)	)	PUNCT
ejpam-6029	256	32	+	+	NUM
ejpam-6029	256	33	lc(t1a∗	lc(t1a∗	NOUN
ejpam-6029	256	34	,	,	PUNCT
ejpam-6029	256	35	t2a	t2a	ADP
ejpam-6029	256	36	)	)	PUNCT
ejpam-6029	256	37	}	}	PUNCT
ejpam-6029	256	38	=	=	SYM
ejpam-6029	256	39	max	max	X
ejpam-6029	256	40	{	{	PUNCT
ejpam-6029	256	41	lc(a	lc(a	X
ejpam-6029	256	42	∗	∗	NOUN
ejpam-6029	256	43	,	,	PUNCT
ejpam-6029	256	44	a),lc(a	a),lc(a	PROPN
ejpam-6029	256	45	∗	∗	NOUN
ejpam-6029	256	46	,	,	PUNCT
ejpam-6029	256	47	a∗),lc(a	a∗),lc(a	NUM
ejpam-6029	256	48	,	,	PUNCT
ejpam-6029	256	49	a	a	PRON
ejpam-6029	256	50	)	)	PUNCT
ejpam-6029	256	51	,	,	PUNCT
ejpam-6029	256	52	lc(a	lc(a	PUNCT
ejpam-6029	256	53	∗	∗	NOUN
ejpam-6029	256	54	,	,	PUNCT
ejpam-6029	256	55	a∗)lc(a	a∗)lc(a	PROPN
ejpam-6029	256	56	,	,	PUNCT
ejpam-6029	256	57	a	a	PRON
ejpam-6029	256	58	)	)	PUNCT
ejpam-6029	256	59	1	1	NUM
ejpam-6029	256	60	+	+	NUM
ejpam-6029	256	61	lc(a∗	lc(a∗	NOUN
ejpam-6029	256	62	,	,	PUNCT
ejpam-6029	256	63	a	a	PRON
ejpam-6029	256	64	)	)	PUNCT
ejpam-6029	256	65	,	,	PUNCT
ejpam-6029	256	66	lc(a	lc(a	PROPN
ejpam-6029	256	67	,	,	PUNCT
ejpam-6029	256	68	a)[1	a)[1	PROPN
ejpam-6029	256	69	+	+	SYM
ejpam-6029	256	70	lc(a	lc(a	NUM
ejpam-6029	256	71	∗	∗	NOUN
ejpam-6029	256	72	,	,	PUNCT
ejpam-6029	256	73	a∗	a∗	NOUN
ejpam-6029	256	74	)	)	PUNCT
ejpam-6029	256	75	]	]	PUNCT
ejpam-6029	257	1	1	1	NUM
ejpam-6029	257	2	+	+	NUM
ejpam-6029	257	3	lc(a∗	lc(a∗	NOUN
ejpam-6029	257	4	,	,	PUNCT
ejpam-6029	257	5	a	a	PRON
ejpam-6029	257	6	)	)	PUNCT
ejpam-6029	257	7	,	,	PUNCT
ejpam-6029	257	8	[	[	PUNCT
ejpam-6029	257	9	lc(a	lc(a	X
ejpam-6029	257	10	∗	∗	NOUN
ejpam-6029	257	11	,	,	PUNCT
ejpam-6029	257	12	a∗	a∗	NOUN
ejpam-6029	257	13	)	)	PUNCT
ejpam-6029	257	14	+	+	PUNCT
ejpam-6029	257	15	lc(a	lc(a	NUM
ejpam-6029	257	16	,	,	PUNCT
ejpam-6029	257	17	a	a	PRON
ejpam-6029	257	18	)	)	PUNCT
ejpam-6029	257	19	]	]	PUNCT
ejpam-6029	257	20	lc(a	lc(a	PUNCT
ejpam-6029	257	21	∗	∗	NOUN
ejpam-6029	257	22	,	,	PUNCT
ejpam-6029	257	23	a	a	PRON
ejpam-6029	257	24	)	)	PUNCT
ejpam-6029	257	25	1	1	NUM
ejpam-6029	258	1	+	+	NUM
ejpam-6029	258	2	lc(a∗	lc(a∗	NOUN
ejpam-6029	258	3	,	,	PUNCT
ejpam-6029	258	4	a	a	PRON
ejpam-6029	258	5	)	)	PUNCT
ejpam-6029	258	6	+	+	NUM
ejpam-6029	258	7	lc(a∗	lc(a∗	NOUN
ejpam-6029	258	8	,	,	PUNCT
ejpam-6029	258	9	a	a	PRON
ejpam-6029	258	10	)	)	PUNCT
ejpam-6029	258	11	}	}	PUNCT
ejpam-6029	258	12	.	.	PUNCT
ejpam-6029	259	1	by	by	ADP
ejpam-6029	259	2	assuming	assume	VERB
ejpam-6029	259	3	any	any	DET
ejpam-6029	259	4	fixed	fixed	ADJ
ejpam-6029	259	5	point	point	NOUN
ejpam-6029	259	6	a	a	PRON
ejpam-6029	259	7	and	and	CCONJ
ejpam-6029	259	8	a∗	a∗	ADJ
ejpam-6029	259	9	,	,	PUNCT
ejpam-6029	259	10	lc(a	lc(a	PUNCT
ejpam-6029	259	11	∗	∗	NOUN
ejpam-6029	259	12	,	,	PUNCT
ejpam-6029	259	13	a∗	a∗	NOUN
ejpam-6029	259	14	)	)	PUNCT
ejpam-6029	259	15	=	=	SYM
ejpam-6029	259	16	lc(a	lc(a	PROPN
ejpam-6029	259	17	,	,	PUNCT
ejpam-6029	259	18	a	a	PRON
ejpam-6029	259	19	)	)	PUNCT
ejpam-6029	259	20	=	=	SYM
ejpam-6029	259	21	0e	0e	NOUN
ejpam-6029	259	22	and	and	CCONJ
ejpam-6029	259	23	the	the	DET
ejpam-6029	259	24	fact	fact	NOUN
ejpam-6029	259	25	that	that	SCONJ
ejpam-6029	259	26	λ(a∗	λ(a∗	X
ejpam-6029	259	27	,	,	PUNCT
ejpam-6029	259	28	a	a	DET
ejpam-6029	259	29	)	)	PUNCT
ejpam-6029	259	30	∈	∈	PROPN
ejpam-6029	260	1	[	[	X
ejpam-6029	260	2	0	0	NUM
ejpam-6029	260	3	,	,	PUNCT
ejpam-6029	260	4	1	1	NUM
ejpam-6029	260	5	)	)	PUNCT
ejpam-6029	260	6	,	,	PUNCT
ejpam-6029	260	7	the	the	DET
ejpam-6029	260	8	result	result	NOUN
ejpam-6029	260	9	is	be	AUX
ejpam-6029	260	10	lc(a	lc(a	PUNCT
ejpam-6029	260	11	∗	∗	NOUN
ejpam-6029	260	12	,	,	PUNCT
ejpam-6029	260	13	a	a	PRON
ejpam-6029	260	14	)	)	PUNCT
ejpam-6029	260	15	⪯	⪯	NOUN
ejpam-6029	260	16	λ(a∗	λ(a∗	NOUN
ejpam-6029	260	17	,	,	PUNCT
ejpam-6029	260	18	a)m̃(a∗	a)m̃(a∗	PROPN
ejpam-6029	260	19	,	,	PUNCT
ejpam-6029	260	20	a	a	PRON
ejpam-6029	260	21	)	)	PUNCT
ejpam-6029	260	22	≺	≺	NOUN
ejpam-6029	260	23	lc(a	lc(a	PUNCT
ejpam-6029	260	24	∗	∗	NOUN
ejpam-6029	260	25	,	,	PUNCT
ejpam-6029	260	26	a	a	PRON
ejpam-6029	260	27	)	)	PUNCT
ejpam-6029	260	28	.	.	PUNCT
ejpam-6029	261	1	thus	thus	ADV
ejpam-6029	261	2	,	,	PUNCT
ejpam-6029	261	3	∥lc(a	∥lc(a	NOUN
ejpam-6029	261	4	∗	∗	NOUN
ejpam-6029	261	5	,	,	PUNCT
ejpam-6029	261	6	a)∥	a)∥	PUNCT
ejpam-6029	262	1	=	=	SYM
ejpam-6029	262	2	0	0	PROPN
ejpam-6029	262	3	,	,	PUNCT
ejpam-6029	262	4	which	which	PRON
ejpam-6029	262	5	is	be	AUX
ejpam-6029	262	6	a	a	DET
ejpam-6029	262	7	contradiction	contradiction	NOUN
ejpam-6029	262	8	.	.	PUNCT
ejpam-6029	263	1	therefore	therefore	ADV
ejpam-6029	263	2	,	,	PUNCT
ejpam-6029	263	3	a∗	a∗	PROPN
ejpam-6029	263	4	=	=	SYM
ejpam-6029	263	5	a.	a.	NOUN
ejpam-6029	263	6	corollary	corollary	NOUN
ejpam-6029	263	7	1	1	PROPN
ejpam-6029	263	8	.	.	PUNCT
ejpam-6029	263	9	assume	assume	VERB
ejpam-6029	263	10	(	(	PUNCT
ejpam-6029	263	11	γ	γ	X
ejpam-6029	263	12	,	,	PUNCT
ejpam-6029	263	13	dc	dc	PROPN
ejpam-6029	263	14	)	)	PUNCT
ejpam-6029	263	15	is	be	AUX
ejpam-6029	263	16	a	a	DET
ejpam-6029	263	17	complete	complete	ADJ
ejpam-6029	263	18	c2cms	c2cms	NOUN
ejpam-6029	263	19	with	with	ADP
ejpam-6029	263	20	two	two	NUM
ejpam-6029	263	21	non	non	ADJ
ejpam-6029	263	22	-	-	ADJ
ejpam-6029	263	23	constant	constant	ADJ
ejpam-6029	263	24	functions	function	NOUN
ejpam-6029	263	25	f	f	NOUN
ejpam-6029	263	26	,	,	PUNCT
ejpam-6029	263	27	g	g	NOUN
ejpam-6029	263	28	:	:	PUNCT
ejpam-6029	263	29	p	p	X
ejpam-6029	263	30	→	→	SYM
ejpam-6029	263	31	p	p	X
ejpam-6029	263	32	,	,	PUNCT
ejpam-6029	263	33	where	where	SCONJ
ejpam-6029	263	34	p	p	NOUN
ejpam-6029	263	35	is	be	AUX
ejpam-6029	263	36	a	a	DET
ejpam-6029	263	37	normal	normal	ADJ
ejpam-6029	263	38	cone	cone	NOUN
ejpam-6029	263	39	via	via	ADP
ejpam-6029	263	40	normal	normal	ADJ
ejpam-6029	263	41	constant	constant	ADJ
ejpam-6029	263	42	m	m	NOUN
ejpam-6029	263	43	.	.	PUNCT
ejpam-6029	264	1	let	let	VERB
ejpam-6029	264	2	t1	t1	NOUN
ejpam-6029	264	3	,	,	PUNCT
ejpam-6029	264	4	t2	t2	NOUN
ejpam-6029	264	5	:	:	PUNCT
ejpam-6029	264	6	γ	γ	X
ejpam-6029	264	7	→	→	SYM
ejpam-6029	264	8	γ	γ	X
ejpam-6029	264	9	be	be	AUX
ejpam-6029	264	10	a	a	DET
ejpam-6029	264	11	mappings	mapping	NOUN
ejpam-6029	264	12	and	and	CCONJ
ejpam-6029	264	13	there	there	PRON
ejpam-6029	264	14	exists	exist	VERB
ejpam-6029	264	15	λ	λ	PROPN
ejpam-6029	264	16	∈	∈	PROPN
ejpam-6029	264	17	∆	∆	PROPN
ejpam-6029	264	18	such	such	ADJ
ejpam-6029	264	19	that	that	SCONJ
ejpam-6029	264	20	dc(t1a	dc(t1a	PROPN
ejpam-6029	264	21	,	,	PUNCT
ejpam-6029	264	22	t2b	t2b	PROPN
ejpam-6029	264	23	)	)	PUNCT
ejpam-6029	264	24	⪯	⪯	PROPN
ejpam-6029	264	25	λ(a	λ(a	PROPN
ejpam-6029	264	26	,	,	PUNCT
ejpam-6029	264	27	b)m̃(a	b)m̃(a	PROPN
ejpam-6029	264	28	,	,	PUNCT
ejpam-6029	264	29	b	b	NOUN
ejpam-6029	264	30	)	)	PUNCT
ejpam-6029	264	31	,	,	PUNCT
ejpam-6029	264	32	for	for	ADP
ejpam-6029	264	33	all	all	DET
ejpam-6029	264	34	a	a	PRON
ejpam-6029	264	35	,	,	PUNCT
ejpam-6029	264	36	b	b	PROPN
ejpam-6029	264	37	∈	∈	PROPN
ejpam-6029	264	38	γ	γ	X
ejpam-6029	264	39	,	,	PUNCT
ejpam-6029	264	40	(	(	PUNCT
ejpam-6029	264	41	8)	8)	NUM
ejpam-6029	264	42	where	where	SCONJ
ejpam-6029	264	43	m̃(a	m̃(a	PROPN
ejpam-6029	264	44	,	,	PUNCT
ejpam-6029	264	45	b	b	NOUN
ejpam-6029	264	46	)	)	PUNCT
ejpam-6029	264	47	=	=	SYM
ejpam-6029	264	48	max	max	PROPN
ejpam-6029	264	49	{	{	PUNCT
ejpam-6029	264	50	dc(a	dc(a	X
ejpam-6029	264	51	,	,	PUNCT
ejpam-6029	264	52	b),dc(a	b),dc(a	PROPN
ejpam-6029	264	53	,	,	PUNCT
ejpam-6029	264	54	t1a),dc(b	t1a),dc(b	NOUN
ejpam-6029	264	55	,	,	PUNCT
ejpam-6029	264	56	t2b	t2b	PROPN
ejpam-6029	264	57	)	)	PUNCT
ejpam-6029	264	58	,	,	PUNCT
ejpam-6029	264	59	dc(a	dc(a	NOUN
ejpam-6029	264	60	,	,	PUNCT
ejpam-6029	264	61	t1a)dc(b	t1a)dc(b	PROPN
ejpam-6029	264	62	,	,	PUNCT
ejpam-6029	264	63	t2b	t2b	PROPN
ejpam-6029	264	64	)	)	PUNCT
ejpam-6029	264	65	1	1	NUM
ejpam-6029	265	1	+	+	NOUN
ejpam-6029	265	2	dc(a	dc(a	NOUN
ejpam-6029	265	3	,	,	PUNCT
ejpam-6029	265	4	b	b	NOUN
ejpam-6029	265	5	)	)	PUNCT
ejpam-6029	265	6	,	,	PUNCT
ejpam-6029	265	7	dc(b	dc(b	PROPN
ejpam-6029	265	8	,	,	PUNCT
ejpam-6029	265	9	t2b	t2b	PROPN
ejpam-6029	265	10	)	)	PUNCT
ejpam-6029	266	1	[	[	PUNCT
ejpam-6029	266	2	1	1	NUM
ejpam-6029	266	3	+	+	NOUN
ejpam-6029	266	4	dc(a	dc(a	NOUN
ejpam-6029	266	5	,	,	PUNCT
ejpam-6029	266	6	t1a	t1a	NUM
ejpam-6029	266	7	)	)	PUNCT
ejpam-6029	266	8	]	]	PUNCT
ejpam-6029	267	1	1	1	NUM
ejpam-6029	267	2	+	+	NOUN
ejpam-6029	267	3	dc(a	dc(a	NOUN
ejpam-6029	267	4	,	,	PUNCT
ejpam-6029	267	5	b	b	NOUN
ejpam-6029	267	6	)	)	PUNCT
ejpam-6029	267	7	,	,	PUNCT
ejpam-6029	267	8	[	[	PUNCT
ejpam-6029	267	9	dc(a	dc(a	X
ejpam-6029	267	10	,	,	PUNCT
ejpam-6029	267	11	t1a	t1a	NUM
ejpam-6029	267	12	)	)	PUNCT
ejpam-6029	267	13	+	+	NOUN
ejpam-6029	267	14	dc(b	dc(b	ADJ
ejpam-6029	267	15	,	,	PUNCT
ejpam-6029	267	16	t2b	t2b	PROPN
ejpam-6029	267	17	)	)	PUNCT
ejpam-6029	267	18	]	]	PUNCT
ejpam-6029	268	1	dc(t1a	dc(t1a	PROPN
ejpam-6029	268	2	,	,	PUNCT
ejpam-6029	268	3	t2b	t2b	PROPN
ejpam-6029	268	4	)	)	PUNCT
ejpam-6029	268	5	1	1	NUM
ejpam-6029	269	1	+	+	NOUN
ejpam-6029	269	2	dc(a	dc(a	NOUN
ejpam-6029	269	3	,	,	PUNCT
ejpam-6029	269	4	b	b	NOUN
ejpam-6029	269	5	)	)	PUNCT
ejpam-6029	269	6	+	+	NOUN
ejpam-6029	269	7	dc(t1a	dc(t1a	PROPN
ejpam-6029	269	8	,	,	PUNCT
ejpam-6029	269	9	t2b	t2b	PROPN
ejpam-6029	269	10	)	)	PUNCT
ejpam-6029	269	11	}	}	PUNCT
ejpam-6029	269	12	.	.	PUNCT
ejpam-6029	270	1	for	for	ADP
ejpam-6029	270	2	a0	a0	PROPN
ejpam-6029	270	3	∈	∈	PROPN
ejpam-6029	270	4	γ	γ	PROPN
ejpam-6029	270	5	,	,	PUNCT
ejpam-6029	270	6	we	we	PRON
ejpam-6029	270	7	set	set	VERB
ejpam-6029	270	8	a	a	DET
ejpam-6029	270	9	sequence	sequence	NOUN
ejpam-6029	270	10	{	{	PUNCT
ejpam-6029	270	11	an	an	PRON
ejpam-6029	270	12	}	}	PUNCT
ejpam-6029	270	13	defined	define	VERB
ejpam-6029	270	14	as	as	ADP
ejpam-6029	270	15	a2n+1	a2n+1	NOUN
ejpam-6029	270	16	=	=	SYM
ejpam-6029	270	17	t1a2n	t1a2n	PUNCT
ejpam-6029	270	18	and	and	CCONJ
ejpam-6029	270	19	a2n+2	a2n+2	PRON
ejpam-6029	271	1	=	=	SYM
ejpam-6029	271	2	t2a2n+1	t2a2n+1	NUM
ejpam-6029	271	3	for	for	ADP
ejpam-6029	271	4	every	every	DET
ejpam-6029	271	5	n	n	PRON
ejpam-6029	271	6	≥	≥	NOUN
ejpam-6029	271	7	0	0	NUM
ejpam-6029	271	8	.	.	PUNCT
ejpam-6029	271	9	suppose	suppose	VERB
ejpam-6029	271	10	a.	a.	NOUN
ejpam-6029	271	11	a.	a.	PROPN
ejpam-6029	271	12	hijab	hijab	PROPN
ejpam-6029	271	13	et	et	PROPN
ejpam-6029	271	14	al	al	PROPN
ejpam-6029	271	15	.	.	PUNCT
ejpam-6029	271	16	/	/	SYM
ejpam-6029	271	17	eur	eur	PROPN
ejpam-6029	271	18	.	.	PUNCT
ejpam-6029	272	1	j.	j.	PROPN
ejpam-6029	272	2	pure	pure	PROPN
ejpam-6029	272	3	appl	appl	PROPN
ejpam-6029	272	4	.	.	PROPN
ejpam-6029	272	5	math	math	PROPN
ejpam-6029	272	6	,	,	PUNCT
ejpam-6029	272	7	18	18	NUM
ejpam-6029	272	8	(	(	PUNCT
ejpam-6029	272	9	2	2	NUM
ejpam-6029	272	10	)	)	PUNCT
ejpam-6029	272	11	(	(	PUNCT
ejpam-6029	272	12	2025	2025	NUM
ejpam-6029	272	13	)	)	PUNCT
ejpam-6029	272	14	,	,	PUNCT
ejpam-6029	272	15	6029	6029	NUM
ejpam-6029	272	16	11	11	NUM
ejpam-6029	272	17	of	of	ADP
ejpam-6029	272	18	23	23	NUM
ejpam-6029	272	19	(	(	PUNCT
ejpam-6029	272	20	i	i	NOUN
ejpam-6029	272	21	)	)	PUNCT
ejpam-6029	272	22	f	f	PROPN
ejpam-6029	272	23	and	and	CCONJ
ejpam-6029	272	24	g	g	PROPN
ejpam-6029	272	25	are	be	AUX
ejpam-6029	272	26	bounded	bound	VERB
ejpam-6029	272	27	and	and	CCONJ
ejpam-6029	272	28	non	non	ADJ
ejpam-6029	272	29	-	-	ADJ
ejpam-6029	272	30	decreasing	decrease	VERB
ejpam-6029	272	31	,	,	PUNCT
ejpam-6029	272	32	g	g	PROPN
ejpam-6029	272	33	is	be	AUX
ejpam-6029	272	34	sub	sub	ADJ
ejpam-6029	272	35	-	-	ADJ
ejpam-6029	272	36	additive	additive	ADJ
ejpam-6029	272	37	and	and	CCONJ
ejpam-6029	272	38	g(λa	g(λa	NOUN
ejpam-6029	272	39	)	)	PUNCT
ejpam-6029	272	40	≺	≺	NOUN
ejpam-6029	272	41	a	a	PRON
ejpam-6029	272	42	,	,	PUNCT
ejpam-6029	272	43	λ	λ	PROPN
ejpam-6029	272	44	∈	∈	PROPN
ejpam-6029	272	45	(	(	PUNCT
ejpam-6029	272	46	0	0	NUM
ejpam-6029	272	47	,	,	PUNCT
ejpam-6029	272	48	1	1	NUM
ejpam-6029	272	49	)	)	PUNCT
ejpam-6029	272	50	;	;	PUNCT
ejpam-6029	272	51	(	(	PUNCT
ejpam-6029	272	52	ii	ii	X
ejpam-6029	272	53	)	)	PUNCT
ejpam-6029	272	54	lim	lim	PROPN
ejpam-6029	272	55	n	n	CCONJ
ejpam-6029	272	56	,	,	PUNCT
ejpam-6029	272	57	m→∞	m→∞	NUM
ejpam-6029	272	58	∑n−2	∑n−2	NOUN
ejpam-6029	273	1	i	i	PRON
ejpam-6029	273	2	=	=	VERB
ejpam-6029	273	3	m	m	VERB
ejpam-6029	273	4	∥gi−mf	∥gi−mf	NOUN
ejpam-6029	273	5	(	(	PUNCT
ejpam-6029	273	6	ξidc(a0	ξidc(a0	X
ejpam-6029	273	7	,	,	PUNCT
ejpam-6029	273	8	a1	a1	NOUN
ejpam-6029	273	9	)	)	PUNCT
ejpam-6029	273	10	)	)	PUNCT
ejpam-6029	273	11	∥+	∥+	PROPN
ejpam-6029	274	1	∥gn−m−1	∥gn−m−1	PROPN
ejpam-6029	274	2	(	(	PUNCT
ejpam-6029	274	3	ξn−1dc(a0	ξn−1dc(a0	PROPN
ejpam-6029	274	4	,	,	PUNCT
ejpam-6029	274	5	a1	a1	NOUN
ejpam-6029	274	6	)	)	PUNCT
ejpam-6029	274	7	)	)	PUNCT
ejpam-6029	274	8	∥	∥	X
ejpam-6029	274	9	=	=	SYM
ejpam-6029	274	10	0	0	NUM
ejpam-6029	274	11	,	,	PUNCT
ejpam-6029	274	12	where	where	SCONJ
ejpam-6029	274	13	ξ	ξ	X
ejpam-6029	274	14	=	=	SYM
ejpam-6029	274	15	λ(a0	λ(a0	X
ejpam-6029	274	16	,	,	PUNCT
ejpam-6029	274	17	a1	a1	PROPN
ejpam-6029	274	18	)	)	PUNCT
ejpam-6029	274	19	<	<	X
ejpam-6029	274	20	1	1	X
ejpam-6029	274	21	.	.	PUNCT
ejpam-6029	275	1	then	then	ADV
ejpam-6029	275	2	t1	t1	PROPN
ejpam-6029	275	3	and	and	CCONJ
ejpam-6029	275	4	t2	t2	PROPN
ejpam-6029	275	5	have	have	VERB
ejpam-6029	275	6	a	a	DET
ejpam-6029	275	7	unique	unique	ADJ
ejpam-6029	275	8	common	common	ADJ
ejpam-6029	275	9	fixed	fix	VERB
ejpam-6029	275	10	point	point	NOUN
ejpam-6029	275	11	.	.	PUNCT
ejpam-6029	276	1	proof	proof	NOUN
ejpam-6029	276	2	.	.	PUNCT
ejpam-6029	277	1	the	the	DET
ejpam-6029	277	2	proof	proof	NOUN
ejpam-6029	277	3	follows	follow	VERB
ejpam-6029	277	4	from	from	ADP
ejpam-6029	277	5	theorem	theorem	NOUN
ejpam-6029	277	6	1	1	NUM
ejpam-6029	277	7	by	by	ADP
ejpam-6029	277	8	taking	take	VERB
ejpam-6029	277	9	(	(	PUNCT
ejpam-6029	277	10	γ	γ	X
ejpam-6029	277	11	,	,	PUNCT
ejpam-6029	277	12	lc	lc	PROPN
ejpam-6029	277	13	)	)	PUNCT
ejpam-6029	277	14	in	in	ADP
ejpam-6029	277	15	c2cms	c2cms	PROPN
ejpam-6029	277	16	.	.	PUNCT
ejpam-6029	278	1	then	then	ADV
ejpam-6029	278	2	,	,	PUNCT
ejpam-6029	278	3	some	some	DET
ejpam-6029	278	4	special	special	ADJ
ejpam-6029	278	5	cases	case	NOUN
ejpam-6029	278	6	of	of	ADP
ejpam-6029	278	7	theorem	theorem	NOUN
ejpam-6029	278	8	1	1	NUM
ejpam-6029	278	9	are	be	AUX
ejpam-6029	278	10	presented	present	VERB
ejpam-6029	278	11	,	,	PUNCT
ejpam-6029	278	12	and	and	CCONJ
ejpam-6029	278	13	since	since	SCONJ
ejpam-6029	278	14	every	every	DET
ejpam-6029	278	15	c2cms	c2cms	PROPN
ejpam-6029	278	16	is	be	AUX
ejpam-6029	278	17	a	a	DET
ejpam-6029	278	18	dccml	dccml	NOUN
ejpam-6029	278	19	-	-	PUNCT
ejpam-6029	278	20	space	space	NOUN
ejpam-6029	278	21	,	,	PUNCT
ejpam-6029	278	22	the	the	DET
ejpam-6029	278	23	last	last	ADJ
ejpam-6029	278	24	cases	case	NOUN
ejpam-6029	278	25	of	of	ADP
ejpam-6029	278	26	corollary	corollary	ADJ
ejpam-6029	278	27	1	1	NUM
ejpam-6029	278	28	are	be	AUX
ejpam-6029	278	29	investigated	investigate	VERB
ejpam-6029	278	30	,	,	PUNCT
ejpam-6029	278	31	while	while	SCONJ
ejpam-6029	278	32	the	the	DET
ejpam-6029	278	33	early	early	ADJ
ejpam-6029	278	34	cases	case	NOUN
ejpam-6029	278	35	of	of	ADP
ejpam-6029	278	36	corollary	corollary	ADJ
ejpam-6029	278	37	1	1	NUM
ejpam-6029	278	38	are	be	AUX
ejpam-6029	278	39	omitted	omit	VERB
ejpam-6029	278	40	.	.	PUNCT
ejpam-6029	279	1	corollary	corollary	ADJ
ejpam-6029	279	2	2	2	NUM
ejpam-6029	279	3	.	.	PUNCT
ejpam-6029	280	1	let	let	VERB
ejpam-6029	280	2	(	(	PUNCT
ejpam-6029	280	3	γ	γ	X
ejpam-6029	280	4	,	,	PUNCT
ejpam-6029	280	5	lc	lc	PROPN
ejpam-6029	280	6	)	)	PUNCT
ejpam-6029	280	7	be	be	VERB
ejpam-6029	280	8	a	a	DET
ejpam-6029	280	9	lc	lc	NOUN
ejpam-6029	280	10	-	-	PUNCT
ejpam-6029	280	11	complete	complete	ADJ
ejpam-6029	280	12	dccml	dccml	NOUN
ejpam-6029	280	13	-	-	PUNCT
ejpam-6029	280	14	space	space	NOUN
ejpam-6029	280	15	with	with	ADP
ejpam-6029	280	16	two	two	NUM
ejpam-6029	280	17	non	non	ADJ
ejpam-6029	280	18	-	-	ADJ
ejpam-6029	280	19	constant	constant	ADJ
ejpam-6029	280	20	functions	function	NOUN
ejpam-6029	280	21	f	f	NOUN
ejpam-6029	280	22	,	,	PUNCT
ejpam-6029	280	23	g	g	NOUN
ejpam-6029	280	24	:	:	PUNCT
ejpam-6029	280	25	p	p	X
ejpam-6029	280	26	→	→	SYM
ejpam-6029	280	27	p	p	X
ejpam-6029	280	28	,	,	PUNCT
ejpam-6029	280	29	where	where	SCONJ
ejpam-6029	280	30	p	p	NOUN
ejpam-6029	280	31	is	be	AUX
ejpam-6029	280	32	a	a	DET
ejpam-6029	280	33	normal	normal	ADJ
ejpam-6029	280	34	cone	cone	NOUN
ejpam-6029	280	35	via	via	ADP
ejpam-6029	280	36	the	the	DET
ejpam-6029	280	37	normal	normal	ADJ
ejpam-6029	280	38	constant	constant	ADJ
ejpam-6029	280	39	m	m	NOUN
ejpam-6029	280	40	.	.	PUNCT
ejpam-6029	281	1	suppose	suppose	VERB
ejpam-6029	281	2	that	that	SCONJ
ejpam-6029	281	3	t1	t1	NOUN
ejpam-6029	281	4	,	,	PUNCT
ejpam-6029	281	5	t2	t2	NOUN
ejpam-6029	281	6	:	:	PUNCT
ejpam-6029	281	7	γ	γ	X
ejpam-6029	281	8	→	→	SYM
ejpam-6029	281	9	γ	γ	X
ejpam-6029	281	10	is	be	AUX
ejpam-6029	281	11	a	a	DET
ejpam-6029	281	12	mappings	mapping	NOUN
ejpam-6029	281	13	and	and	CCONJ
ejpam-6029	281	14	λj	λj	PROPN
ejpam-6029	281	15	∈	∈	PROPN
ejpam-6029	281	16	∆	∆	PROPN
ejpam-6029	281	17	,	,	PUNCT
ejpam-6029	281	18	j	j	PROPN
ejpam-6029	281	19	=	=	SYM
ejpam-6029	281	20	1	1	NUM
ejpam-6029	281	21	,	,	PUNCT
ejpam-6029	281	22	·	·	PUNCT
ejpam-6029	281	23	·	·	PUNCT
ejpam-6029	281	24	·	·	PUNCT
ejpam-6029	281	25	,	,	PUNCT
ejpam-6029	281	26	6	6	NUM
ejpam-6029	281	27	,	,	PUNCT
ejpam-6029	281	28	such	such	ADJ
ejpam-6029	281	29	that	that	SCONJ
ejpam-6029	281	30	lc(t1a	lc(t1a	PROPN
ejpam-6029	281	31	,	,	PUNCT
ejpam-6029	281	32	t2b	t2b	PROPN
ejpam-6029	281	33	)	)	PUNCT
ejpam-6029	281	34	⪯λ1(a	⪯λ1(a	PROPN
ejpam-6029	281	35	,	,	PUNCT
ejpam-6029	281	36	b)lc(a	b)lc(a	PROPN
ejpam-6029	281	37	,	,	PUNCT
ejpam-6029	281	38	b	b	NOUN
ejpam-6029	281	39	)	)	PUNCT
ejpam-6029	281	40	+	+	SYM
ejpam-6029	281	41	λ2(a	λ2(a	NOUN
ejpam-6029	281	42	,	,	PUNCT
ejpam-6029	281	43	b)lc(a	b)lc(a	NUM
ejpam-6029	281	44	,	,	PUNCT
ejpam-6029	281	45	t1a	t1a	NUM
ejpam-6029	281	46	)	)	PUNCT
ejpam-6029	281	47	+	+	CCONJ
ejpam-6029	282	1	λ3(a	λ3(a	NOUN
ejpam-6029	282	2	,	,	PUNCT
ejpam-6029	282	3	b)lc(b	b)lc(b	NOUN
ejpam-6029	282	4	,	,	PUNCT
ejpam-6029	282	5	t2b	t2b	PROPN
ejpam-6029	282	6	)	)	PUNCT
ejpam-6029	282	7	+	+	CCONJ
ejpam-6029	282	8	λ4(a	λ4(a	PROPN
ejpam-6029	282	9	,	,	PUNCT
ejpam-6029	282	10	b	b	NOUN
ejpam-6029	282	11	)	)	PUNCT
ejpam-6029	282	12	lc(a	lc(a	NUM
ejpam-6029	282	13	,	,	PUNCT
ejpam-6029	282	14	t1a)lc(b	t1a)lc(b	NOUN
ejpam-6029	282	15	,	,	PUNCT
ejpam-6029	282	16	t2b	t2b	PROPN
ejpam-6029	282	17	)	)	PUNCT
ejpam-6029	282	18	1	1	NUM
ejpam-6029	282	19	+	+	CCONJ
ejpam-6029	282	20	lc(a	lc(a	NUM
ejpam-6029	282	21	,	,	PUNCT
ejpam-6029	282	22	b	b	NOUN
ejpam-6029	282	23	)	)	PUNCT
ejpam-6029	282	24	+	+	CCONJ
ejpam-6029	282	25	λ5(a	λ5(a	NUM
ejpam-6029	282	26	,	,	PUNCT
ejpam-6029	282	27	b	b	NOUN
ejpam-6029	282	28	)	)	PUNCT
ejpam-6029	282	29	lc(b	lc(b	PROPN
ejpam-6029	282	30	,	,	PUNCT
ejpam-6029	282	31	t2b	t2b	PROPN
ejpam-6029	282	32	)	)	PUNCT
ejpam-6029	282	33	[	[	PUNCT
ejpam-6029	282	34	1	1	NUM
ejpam-6029	282	35	+	+	NUM
ejpam-6029	282	36	lc(a	lc(a	NUM
ejpam-6029	282	37	,	,	PUNCT
ejpam-6029	282	38	t1a	t1a	NOUN
ejpam-6029	282	39	)	)	PUNCT
ejpam-6029	282	40	]	]	PUNCT
ejpam-6029	282	41	1	1	NUM
ejpam-6029	282	42	+	+	CCONJ
ejpam-6029	282	43	lc(a	lc(a	NUM
ejpam-6029	282	44	,	,	PUNCT
ejpam-6029	282	45	b	b	NOUN
ejpam-6029	282	46	)	)	PUNCT
ejpam-6029	282	47	+	+	PROPN
ejpam-6029	282	48	λ6(a	λ6(a	NUM
ejpam-6029	282	49	,	,	PUNCT
ejpam-6029	282	50	b	b	NOUN
ejpam-6029	282	51	)	)	PUNCT
ejpam-6029	282	52	[	[	PUNCT
ejpam-6029	282	53	lc(a	lc(a	X
ejpam-6029	282	54	,	,	PUNCT
ejpam-6029	282	55	t1a	t1a	NUM
ejpam-6029	282	56	)	)	PUNCT
ejpam-6029	282	57	+	+	CCONJ
ejpam-6029	282	58	lc(b	lc(b	PROPN
ejpam-6029	282	59	,	,	PUNCT
ejpam-6029	282	60	t2b	t2b	PROPN
ejpam-6029	282	61	)	)	PUNCT
ejpam-6029	282	62	]	]	PUNCT
ejpam-6029	283	1	lc(t1a	lc(t1a	PROPN
ejpam-6029	283	2	,	,	PUNCT
ejpam-6029	283	3	t2b	t2b	PROPN
ejpam-6029	283	4	)	)	PUNCT
ejpam-6029	283	5	1	1	NUM
ejpam-6029	283	6	+	+	CCONJ
ejpam-6029	283	7	lc(a	lc(a	NUM
ejpam-6029	283	8	,	,	PUNCT
ejpam-6029	283	9	b	b	NOUN
ejpam-6029	283	10	)	)	PUNCT
ejpam-6029	283	11	+	+	CCONJ
ejpam-6029	283	12	lc(t1a	lc(t1a	PROPN
ejpam-6029	283	13	,	,	PUNCT
ejpam-6029	283	14	t2b	t2b	PROPN
ejpam-6029	283	15	)	)	PUNCT
ejpam-6029	283	16	,	,	PUNCT
ejpam-6029	283	17	(	(	PUNCT
ejpam-6029	283	18	9	9	X
ejpam-6029	283	19	)	)	PUNCT
ejpam-6029	283	20	for	for	ADP
ejpam-6029	283	21	all	all	DET
ejpam-6029	283	22	a	a	PRON
ejpam-6029	283	23	,	,	PUNCT
ejpam-6029	283	24	b	b	PROPN
ejpam-6029	283	25	∈	∈	PROPN
ejpam-6029	283	26	γ	γ	X
ejpam-6029	283	27	,	,	PUNCT
ejpam-6029	283	28	where	where	SCONJ
ejpam-6029	283	29	∑6	∑6	PROPN
ejpam-6029	283	30	j=1	j=1	PROPN
ejpam-6029	283	31	λj(a	λj(a	X
ejpam-6029	283	32	,	,	PUNCT
ejpam-6029	283	33	b	b	X
ejpam-6029	283	34	)	)	PUNCT
ejpam-6029	283	35	<	<	X
ejpam-6029	283	36	1	1	X
ejpam-6029	283	37	.	.	X
ejpam-6029	283	38	for	for	ADP
ejpam-6029	283	39	a0	a0	PROPN
ejpam-6029	283	40	∈	∈	PROPN
ejpam-6029	283	41	γ	γ	PROPN
ejpam-6029	283	42	,	,	PUNCT
ejpam-6029	283	43	take	take	VERB
ejpam-6029	283	44	the	the	DET
ejpam-6029	283	45	sequence	sequence	NOUN
ejpam-6029	283	46	{	{	PUNCT
ejpam-6029	283	47	an	an	NOUN
ejpam-6029	283	48	}	}	PUNCT
ejpam-6029	283	49	as	as	ADP
ejpam-6029	283	50	a2n+1	a2n+1	NOUN
ejpam-6029	283	51	=	=	SYM
ejpam-6029	283	52	t1a2n	t1a2n	PUNCT
ejpam-6029	283	53	and	and	CCONJ
ejpam-6029	283	54	a2n+2	a2n+2	PRON
ejpam-6029	283	55	=	=	SYM
ejpam-6029	283	56	t2a2n+1	t2a2n+1	NUM
ejpam-6029	283	57	for	for	ADP
ejpam-6029	283	58	every	every	DET
ejpam-6029	283	59	n	n	PRON
ejpam-6029	283	60	≥	≥	NOUN
ejpam-6029	283	61	0	0	NUM
ejpam-6029	283	62	.	.	PUNCT
ejpam-6029	284	1	let	let	VERB
ejpam-6029	284	2	ξ	ξ	X
ejpam-6029	284	3	=	=	SYM
ejpam-6029	284	4	λ1(a0,a1)+λ2(a0,a1	λ1(a0,a1)+λ2(a0,a1	X
ejpam-6029	284	5	)	)	PUNCT
ejpam-6029	285	1	1−	1−	NUM
ejpam-6029	285	2	∑6	∑6	PROPN
ejpam-6029	285	3	j=3	j=3	CCONJ
ejpam-6029	285	4	λj(a0,a1	λj(a0,a1	NUM
ejpam-6029	285	5	)	)	PUNCT
ejpam-6029	285	6	<	<	X
ejpam-6029	285	7	1	1	X
ejpam-6029	285	8	.	.	PUNCT
ejpam-6029	285	9	suppose	suppose	VERB
ejpam-6029	285	10	(	(	PUNCT
ejpam-6029	285	11	i	i	NOUN
ejpam-6029	285	12	)	)	PUNCT
ejpam-6029	285	13	f	f	PROPN
ejpam-6029	285	14	and	and	CCONJ
ejpam-6029	285	15	g	g	PROPN
ejpam-6029	285	16	are	be	AUX
ejpam-6029	285	17	bounded	bound	VERB
ejpam-6029	285	18	and	and	CCONJ
ejpam-6029	285	19	non	non	ADJ
ejpam-6029	285	20	-	-	ADJ
ejpam-6029	285	21	decreasing	decrease	VERB
ejpam-6029	285	22	,	,	PUNCT
ejpam-6029	285	23	g	g	PROPN
ejpam-6029	285	24	is	be	AUX
ejpam-6029	285	25	sub	sub	ADJ
ejpam-6029	285	26	-	-	ADJ
ejpam-6029	285	27	additive	additive	ADJ
ejpam-6029	285	28	,	,	PUNCT
ejpam-6029	285	29	and	and	CCONJ
ejpam-6029	285	30	g(λa	g(λa	NOUN
ejpam-6029	285	31	)	)	PUNCT
ejpam-6029	285	32	≺	≺	NOUN
ejpam-6029	285	33	a	a	PRON
ejpam-6029	285	34	,	,	PUNCT
ejpam-6029	285	35	λ	λ	PROPN
ejpam-6029	285	36	∈	∈	PROPN
ejpam-6029	285	37	(	(	PUNCT
ejpam-6029	285	38	0	0	NUM
ejpam-6029	285	39	,	,	PUNCT
ejpam-6029	285	40	1	1	NUM
ejpam-6029	285	41	)	)	PUNCT
ejpam-6029	285	42	;	;	PUNCT
ejpam-6029	285	43	(	(	PUNCT
ejpam-6029	285	44	ii	ii	X
ejpam-6029	285	45	)	)	PUNCT
ejpam-6029	285	46	lim	lim	PROPN
ejpam-6029	285	47	n	n	CCONJ
ejpam-6029	285	48	,	,	PUNCT
ejpam-6029	285	49	m→∞	m→∞	NUM
ejpam-6029	285	50	∑n−2	∑n−2	NOUN
ejpam-6029	286	1	i	i	PRON
ejpam-6029	286	2	=	=	VERB
ejpam-6029	286	3	m	m	VERB
ejpam-6029	286	4	∥gi−mf	∥gi−mf	NOUN
ejpam-6029	286	5	(	(	PUNCT
ejpam-6029	286	6	ξilc(a0	ξilc(a0	NOUN
ejpam-6029	286	7	,	,	PUNCT
ejpam-6029	286	8	a1	a1	NOUN
ejpam-6029	286	9	)	)	PUNCT
ejpam-6029	286	10	)	)	PUNCT
ejpam-6029	286	11	∥+	∥+	PROPN
ejpam-6029	287	1	∥gn−m−1	∥gn−m−1	PROPN
ejpam-6029	287	2	(	(	PUNCT
ejpam-6029	287	3	ξn−1lc(a0	ξn−1lc(a0	PROPN
ejpam-6029	287	4	,	,	PUNCT
ejpam-6029	287	5	a1	a1	NOUN
ejpam-6029	287	6	)	)	PUNCT
ejpam-6029	287	7	)	)	PUNCT
ejpam-6029	287	8	∥	∥	X
ejpam-6029	287	9	=	=	PUNCT
ejpam-6029	288	1	0	0	X
ejpam-6029	288	2	.	.	PUNCT
ejpam-6029	289	1	if	if	SCONJ
ejpam-6029	289	2	for	for	ADP
ejpam-6029	289	3	every	every	DET
ejpam-6029	289	4	fixed	fix	VERB
ejpam-6029	289	5	point	point	NOUN
ejpam-6029	289	6	a	a	ADV
ejpam-6029	289	7	,	,	PUNCT
ejpam-6029	289	8	we	we	PRON
ejpam-6029	289	9	conclude	conclude	VERB
ejpam-6029	289	10	that	that	PRON
ejpam-6029	289	11	lc(a	lc(a	NOUN
ejpam-6029	289	12	,	,	PUNCT
ejpam-6029	289	13	a	a	PRON
ejpam-6029	289	14	)	)	PUNCT
ejpam-6029	289	15	=	=	SYM
ejpam-6029	289	16	0e	0e	NOUN
ejpam-6029	289	17	,	,	PUNCT
ejpam-6029	289	18	then	then	ADV
ejpam-6029	289	19	t1	t1	NOUN
ejpam-6029	289	20	and	and	CCONJ
ejpam-6029	289	21	t2	t2	PROPN
ejpam-6029	289	22	have	have	VERB
ejpam-6029	289	23	a	a	DET
ejpam-6029	289	24	unique	unique	ADJ
ejpam-6029	289	25	common	common	ADJ
ejpam-6029	289	26	fixed	fix	VERB
ejpam-6029	289	27	point	point	NOUN
ejpam-6029	289	28	.	.	PUNCT
ejpam-6029	290	1	proof	proof	NOUN
ejpam-6029	290	2	.	.	PUNCT
ejpam-6029	291	1	it	it	PRON
ejpam-6029	291	2	is	be	AUX
ejpam-6029	291	3	observed	observe	VERB
ejpam-6029	291	4	that	that	SCONJ
ejpam-6029	291	5	for	for	ADP
ejpam-6029	291	6	each	each	DET
ejpam-6029	291	7	a	a	NOUN
ejpam-6029	291	8	,	,	PUNCT
ejpam-6029	291	9	b	b	X
ejpam-6029	291	10	∈	∈	PROPN
ejpam-6029	291	11	γ	γ	X
ejpam-6029	291	12	,	,	PUNCT
ejpam-6029	291	13	there	there	PRON
ejpam-6029	291	14	exist	exist	VERB
ejpam-6029	291	15	λj	λj	PROPN
ejpam-6029	291	16	∈	∈	PROPN
ejpam-6029	291	17	∆	∆	PROPN
ejpam-6029	291	18	,	,	PUNCT
ejpam-6029	291	19	j	j	PROPN
ejpam-6029	291	20	=	=	SYM
ejpam-6029	291	21	1	1	NUM
ejpam-6029	291	22	,	,	PUNCT
ejpam-6029	291	23	·	·	PUNCT
ejpam-6029	291	24	·	·	PUNCT
ejpam-6029	291	25	·	·	PUNCT
ejpam-6029	291	26	,	,	PUNCT
ejpam-6029	291	27	6	6	NUM
ejpam-6029	291	28	,	,	PUNCT
ejpam-6029	291	29	such	such	ADJ
ejpam-6029	291	30	that	that	SCONJ
ejpam-6029	291	31	λ(a	λ(a	NOUN
ejpam-6029	291	32	,	,	PUNCT
ejpam-6029	291	33	b	b	NOUN
ejpam-6029	291	34	)	)	PUNCT
ejpam-6029	291	35	=	=	SYM
ejpam-6029	291	36	∑6	∑6	PROPN
ejpam-6029	291	37	j=1	j=1	PROPN
ejpam-6029	291	38	λj(a	λj(a	NOUN
ejpam-6029	291	39	,	,	PUNCT
ejpam-6029	291	40	b	b	X
ejpam-6029	291	41	)	)	PUNCT
ejpam-6029	291	42	<	<	X
ejpam-6029	291	43	1	1	NUM
ejpam-6029	291	44	,	,	PUNCT
ejpam-6029	291	45	resulting	result	VERB
ejpam-6029	291	46	in	in	ADP
ejpam-6029	291	47	lc(t1a	lc(t1a	PROPN
ejpam-6029	291	48	,	,	PUNCT
ejpam-6029	291	49	t2b	t2b	PROPN
ejpam-6029	291	50	)	)	PUNCT
ejpam-6029	291	51	⪯λ1(a	⪯λ1(a	PROPN
ejpam-6029	291	52	,	,	PUNCT
ejpam-6029	291	53	b)lc(a	b)lc(a	PROPN
ejpam-6029	291	54	,	,	PUNCT
ejpam-6029	291	55	b	b	NOUN
ejpam-6029	291	56	)	)	PUNCT
ejpam-6029	291	57	+	+	SYM
ejpam-6029	291	58	λ2(a	λ2(a	NOUN
ejpam-6029	291	59	,	,	PUNCT
ejpam-6029	291	60	b)lc(a	b)lc(a	NUM
ejpam-6029	291	61	,	,	PUNCT
ejpam-6029	291	62	t1a	t1a	NUM
ejpam-6029	291	63	)	)	PUNCT
ejpam-6029	292	1	+	+	CCONJ
ejpam-6029	293	1	λ3(a	λ3(a	NOUN
ejpam-6029	293	2	,	,	PUNCT
ejpam-6029	293	3	b)lc(b	b)lc(b	NOUN
ejpam-6029	293	4	,	,	PUNCT
ejpam-6029	293	5	t2b	t2b	PROPN
ejpam-6029	293	6	)	)	PUNCT
ejpam-6029	293	7	+	+	CCONJ
ejpam-6029	293	8	λ4(a	λ4(a	PROPN
ejpam-6029	293	9	,	,	PUNCT
ejpam-6029	293	10	b	b	NOUN
ejpam-6029	293	11	)	)	PUNCT
ejpam-6029	293	12	lc(a	lc(a	NUM
ejpam-6029	293	13	,	,	PUNCT
ejpam-6029	293	14	t1a)lc(b	t1a)lc(b	NOUN
ejpam-6029	293	15	,	,	PUNCT
ejpam-6029	293	16	t2b	t2b	PROPN
ejpam-6029	293	17	)	)	PUNCT
ejpam-6029	293	18	1	1	NUM
ejpam-6029	293	19	+	+	CCONJ
ejpam-6029	293	20	lc(a	lc(a	NUM
ejpam-6029	293	21	,	,	PUNCT
ejpam-6029	293	22	b	b	NOUN
ejpam-6029	293	23	)	)	PUNCT
ejpam-6029	293	24	+	+	CCONJ
ejpam-6029	293	25	λ5(a	λ5(a	NUM
ejpam-6029	293	26	,	,	PUNCT
ejpam-6029	293	27	b	b	NOUN
ejpam-6029	293	28	)	)	PUNCT
ejpam-6029	293	29	lc(b	lc(b	PROPN
ejpam-6029	293	30	,	,	PUNCT
ejpam-6029	293	31	t2b	t2b	PROPN
ejpam-6029	293	32	)	)	PUNCT
ejpam-6029	293	33	[	[	PUNCT
ejpam-6029	293	34	1	1	NUM
ejpam-6029	293	35	+	+	NUM
ejpam-6029	293	36	lc(a	lc(a	NUM
ejpam-6029	293	37	,	,	PUNCT
ejpam-6029	293	38	t1a	t1a	NOUN
ejpam-6029	293	39	)	)	PUNCT
ejpam-6029	293	40	]	]	PUNCT
ejpam-6029	293	41	1	1	NUM
ejpam-6029	293	42	+	+	CCONJ
ejpam-6029	293	43	lc(a	lc(a	NUM
ejpam-6029	293	44	,	,	PUNCT
ejpam-6029	293	45	b	b	NOUN
ejpam-6029	293	46	)	)	PUNCT
ejpam-6029	293	47	+	+	PROPN
ejpam-6029	293	48	λ6(a	λ6(a	NUM
ejpam-6029	293	49	,	,	PUNCT
ejpam-6029	293	50	b	b	NOUN
ejpam-6029	293	51	)	)	PUNCT
ejpam-6029	293	52	[	[	PUNCT
ejpam-6029	293	53	lc(a	lc(a	X
ejpam-6029	293	54	,	,	PUNCT
ejpam-6029	293	55	t1a	t1a	NUM
ejpam-6029	293	56	)	)	PUNCT
ejpam-6029	293	57	+	+	CCONJ
ejpam-6029	293	58	lc(b	lc(b	PROPN
ejpam-6029	293	59	,	,	PUNCT
ejpam-6029	293	60	t2b	t2b	PROPN
ejpam-6029	293	61	)	)	PUNCT
ejpam-6029	293	62	]	]	PUNCT
ejpam-6029	294	1	lc(t1a	lc(t1a	PROPN
ejpam-6029	294	2	,	,	PUNCT
ejpam-6029	294	3	t2b	t2b	PROPN
ejpam-6029	294	4	)	)	PUNCT
ejpam-6029	294	5	1	1	NUM
ejpam-6029	294	6	+	+	CCONJ
ejpam-6029	294	7	lc(a	lc(a	NUM
ejpam-6029	294	8	,	,	PUNCT
ejpam-6029	294	9	b	b	NOUN
ejpam-6029	294	10	)	)	PUNCT
ejpam-6029	294	11	+	+	CCONJ
ejpam-6029	294	12	lc(t1a	lc(t1a	PROPN
ejpam-6029	294	13	,	,	PUNCT
ejpam-6029	294	14	t2b	t2b	PROPN
ejpam-6029	294	15	)	)	PUNCT
ejpam-6029	294	16	⪯	⪯	NOUN
ejpam-6029	294	17	[	[	PUNCT
ejpam-6029	294	18	6∑	6∑	NUM
ejpam-6029	294	19	j=1	j=1	NOUN
ejpam-6029	294	20	λj(a	λj(a	NOUN
ejpam-6029	294	21	,	,	PUNCT
ejpam-6029	294	22	b	b	NOUN
ejpam-6029	294	23	)	)	PUNCT
ejpam-6029	294	24	]	]	PUNCT
ejpam-6029	294	25	max	max	PROPN
ejpam-6029	294	26	{	{	PUNCT
ejpam-6029	294	27	lc(a	lc(a	PROPN
ejpam-6029	294	28	,	,	PUNCT
ejpam-6029	294	29	b),lc(a	b),lc(a	PROPN
ejpam-6029	294	30	,	,	PUNCT
ejpam-6029	294	31	t1a),lc(b	t1a),lc(b	NOUN
ejpam-6029	294	32	,	,	PUNCT
ejpam-6029	294	33	t2b	t2b	PROPN
ejpam-6029	294	34	)	)	PUNCT
ejpam-6029	294	35	,	,	PUNCT
ejpam-6029	294	36	lc(a	lc(a	PROPN
ejpam-6029	294	37	,	,	PUNCT
ejpam-6029	294	38	t1a)lc(b	t1a)lc(b	NOUN
ejpam-6029	294	39	,	,	PUNCT
ejpam-6029	294	40	t2b	t2b	PROPN
ejpam-6029	294	41	)	)	PUNCT
ejpam-6029	294	42	1	1	NUM
ejpam-6029	294	43	+	+	CCONJ
ejpam-6029	294	44	lc(a	lc(a	NUM
ejpam-6029	294	45	,	,	PUNCT
ejpam-6029	294	46	b	b	NOUN
ejpam-6029	294	47	)	)	PUNCT
ejpam-6029	294	48	,	,	PUNCT
ejpam-6029	294	49	lc(b	lc(b	PROPN
ejpam-6029	294	50	,	,	PUNCT
ejpam-6029	294	51	t2b	t2b	PROPN
ejpam-6029	294	52	)	)	PUNCT
ejpam-6029	294	53	[	[	PUNCT
ejpam-6029	294	54	1	1	NUM
ejpam-6029	294	55	+	+	NUM
ejpam-6029	294	56	lc(a	lc(a	NUM
ejpam-6029	294	57	,	,	PUNCT
ejpam-6029	294	58	t1a	t1a	NOUN
ejpam-6029	294	59	)	)	PUNCT
ejpam-6029	294	60	]	]	PUNCT
ejpam-6029	294	61	1	1	NUM
ejpam-6029	294	62	+	+	CCONJ
ejpam-6029	294	63	lc(a	lc(a	NUM
ejpam-6029	294	64	,	,	PUNCT
ejpam-6029	294	65	b	b	NOUN
ejpam-6029	294	66	)	)	PUNCT
ejpam-6029	294	67	,	,	PUNCT
ejpam-6029	294	68	[	[	PUNCT
ejpam-6029	294	69	lc(a	lc(a	X
ejpam-6029	294	70	,	,	PUNCT
ejpam-6029	294	71	t1a	t1a	NUM
ejpam-6029	294	72	)	)	PUNCT
ejpam-6029	295	1	+	+	CCONJ
ejpam-6029	295	2	lc(b	lc(b	PROPN
ejpam-6029	295	3	,	,	PUNCT
ejpam-6029	295	4	t2b	t2b	PROPN
ejpam-6029	295	5	)	)	PUNCT
ejpam-6029	295	6	]	]	PUNCT
ejpam-6029	296	1	lc(t1a	lc(t1a	PROPN
ejpam-6029	296	2	,	,	PUNCT
ejpam-6029	296	3	t2b	t2b	PROPN
ejpam-6029	296	4	)	)	PUNCT
ejpam-6029	296	5	1	1	NUM
ejpam-6029	296	6	+	+	CCONJ
ejpam-6029	296	7	lc(a	lc(a	NUM
ejpam-6029	296	8	,	,	PUNCT
ejpam-6029	296	9	b	b	NOUN
ejpam-6029	296	10	)	)	PUNCT
ejpam-6029	296	11	+	+	CCONJ
ejpam-6029	296	12	lc(t1a	lc(t1a	PROPN
ejpam-6029	296	13	,	,	PUNCT
ejpam-6029	296	14	t2b	t2b	PROPN
ejpam-6029	296	15	)	)	PUNCT
ejpam-6029	296	16	}	}	PUNCT
ejpam-6029	296	17	=	=	SYM
ejpam-6029	296	18	λ(a	λ(a	NOUN
ejpam-6029	296	19	,	,	PUNCT
ejpam-6029	296	20	b)m̃(a	b)m̃(a	PROPN
ejpam-6029	296	21	,	,	PUNCT
ejpam-6029	296	22	b	b	NOUN
ejpam-6029	296	23	)	)	PUNCT
ejpam-6029	296	24	.	.	PUNCT
ejpam-6029	297	1	a.	a.	PROPN
ejpam-6029	297	2	a.	a.	PROPN
ejpam-6029	297	3	hijab	hijab	PROPN
ejpam-6029	297	4	et	et	PROPN
ejpam-6029	297	5	al	al	PROPN
ejpam-6029	297	6	.	.	PUNCT
ejpam-6029	297	7	/	/	SYM
ejpam-6029	297	8	eur	eur	PROPN
ejpam-6029	297	9	.	.	PUNCT
ejpam-6029	298	1	j.	j.	PROPN
ejpam-6029	298	2	pure	pure	PROPN
ejpam-6029	298	3	appl	appl	PROPN
ejpam-6029	298	4	.	.	PROPN
ejpam-6029	298	5	math	math	PROPN
ejpam-6029	298	6	,	,	PUNCT
ejpam-6029	298	7	18	18	NUM
ejpam-6029	298	8	(	(	PUNCT
ejpam-6029	298	9	2	2	NUM
ejpam-6029	298	10	)	)	PUNCT
ejpam-6029	298	11	(	(	PUNCT
ejpam-6029	298	12	2025	2025	NUM
ejpam-6029	298	13	)	)	PUNCT
ejpam-6029	298	14	,	,	PUNCT
ejpam-6029	298	15	6029	6029	NUM
ejpam-6029	298	16	12	12	NUM
ejpam-6029	298	17	of	of	ADP
ejpam-6029	298	18	23	23	NUM
ejpam-6029	298	19	therefore	therefore	ADV
ejpam-6029	298	20	,	,	PUNCT
ejpam-6029	298	21	through	through	ADP
ejpam-6029	298	22	theorem	theorem	NOUN
ejpam-6029	298	23	1	1	NUM
ejpam-6029	298	24	we	we	PRON
ejpam-6029	298	25	obtain	obtain	VERB
ejpam-6029	298	26	the	the	DET
ejpam-6029	298	27	desired	desire	VERB
ejpam-6029	298	28	result	result	NOUN
ejpam-6029	298	29	.	.	PUNCT
ejpam-6029	299	1	moreover	moreover	ADV
ejpam-6029	299	2	,	,	PUNCT
ejpam-6029	299	3	let	let	VERB
ejpam-6029	299	4	a0	a0	PROPN
ejpam-6029	299	5	∈	∈	PROPN
ejpam-6029	299	6	γ	γ	PROPN
ejpam-6029	299	7	.	.	PROPN
ejpam-6029	299	8	a	a	DET
ejpam-6029	299	9	sequence	sequence	NOUN
ejpam-6029	299	10	{	{	PUNCT
ejpam-6029	299	11	an	an	NOUN
ejpam-6029	299	12	}	}	PUNCT
ejpam-6029	299	13	in	in	ADP
ejpam-6029	299	14	γ	γ	PROPN
ejpam-6029	299	15	defined	define	VERB
ejpam-6029	299	16	as	as	ADP
ejpam-6029	299	17	a2n+1	a2n+1	NOUN
ejpam-6029	299	18	=	=	SYM
ejpam-6029	299	19	t1a2n	t1a2n	PUNCT
ejpam-6029	299	20	and	and	CCONJ
ejpam-6029	299	21	a2n+2	a2n+2	PRON
ejpam-6029	299	22	=	=	PUNCT
ejpam-6029	300	1	t2a2n+1,∀n	t2a2n+1,∀n	PROPN
ejpam-6029	300	2	∈	∈	PROPN
ejpam-6029	300	3	n.	n.	NOUN
ejpam-6029	300	4	then	then	ADV
ejpam-6029	300	5	,	,	PUNCT
ejpam-6029	300	6	lc(a2n+1	lc(a2n+1	PROPN
ejpam-6029	300	7	,	,	PUNCT
ejpam-6029	300	8	a2n+2	a2n+2	PRON
ejpam-6029	300	9	)	)	PUNCT
ejpam-6029	300	10	=	=	SYM
ejpam-6029	300	11	lc(t1a2n	lc(t1a2n	PROPN
ejpam-6029	300	12	,	,	PUNCT
ejpam-6029	300	13	t2a2n+1	t2a2n+1	NUM
ejpam-6029	300	14	)	)	PUNCT
ejpam-6029	300	15	⪯	⪯	NOUN
ejpam-6029	300	16	[	[	PUNCT
ejpam-6029	300	17	λ1(a0	λ1(a0	X
ejpam-6029	300	18	,	,	PUNCT
ejpam-6029	300	19	a1	a1	NOUN
ejpam-6029	300	20	)	)	PUNCT
ejpam-6029	300	21	+	+	CCONJ
ejpam-6029	300	22	λ2(a0	λ2(a0	ADJ
ejpam-6029	300	23	,	,	PUNCT
ejpam-6029	300	24	a1	a1	NOUN
ejpam-6029	300	25	)	)	PUNCT
ejpam-6029	300	26	1−	1−	NUM
ejpam-6029	301	1	∑6	∑6	PROPN
ejpam-6029	301	2	j=3	j=3	X
ejpam-6029	301	3	λj(a0	λj(a0	PROPN
ejpam-6029	301	4	,	,	PUNCT
ejpam-6029	301	5	a1	a1	NOUN
ejpam-6029	301	6	)	)	PUNCT
ejpam-6029	301	7	]	]	PUNCT
ejpam-6029	302	1	lc(a2n	lc(a2n	PROPN
ejpam-6029	302	2	,	,	PUNCT
ejpam-6029	302	3	a2n+1	a2n+1	NOUN
ejpam-6029	302	4	)	)	PUNCT
ejpam-6029	302	5	.	.	PUNCT
ejpam-6029	303	1	remark	remark	PROPN
ejpam-6029	303	2	1	1	NUM
ejpam-6029	303	3	.	.	PUNCT
ejpam-6029	304	1	in	in	ADP
ejpam-6029	304	2	theorem	theorem	ADJ
ejpam-6029	304	3	1	1	NUM
ejpam-6029	304	4	and	and	CCONJ
ejpam-6029	304	5	corollaries	corollary	NOUN
ejpam-6029	304	6	1	1	NUM
ejpam-6029	304	7	and	and	CCONJ
ejpam-6029	304	8	2	2	NUM
ejpam-6029	304	9	,	,	PUNCT
ejpam-6029	304	10	if	if	SCONJ
ejpam-6029	304	11	p	p	NOUN
ejpam-6029	304	12	=	=	PUNCT
ejpam-6029	304	13	r+	r+	NOUN
ejpam-6029	304	14	is	be	AUX
ejpam-6029	304	15	taken	take	VERB
ejpam-6029	304	16	,	,	PUNCT
ejpam-6029	304	17	the	the	DET
ejpam-6029	304	18	condition	condition	NOUN
ejpam-6029	304	19	(	(	PUNCT
ejpam-6029	304	20	i	i	NOUN
ejpam-6029	304	21	)	)	PUNCT
ejpam-6029	304	22	is	be	AUX
ejpam-6029	304	23	interchanged	interchange	VERB
ejpam-6029	304	24	to	to	ADP
ejpam-6029	304	25	f	f	PROPN
ejpam-6029	304	26	and	and	CCONJ
ejpam-6029	304	27	g	g	PROPN
ejpam-6029	304	28	are	be	AUX
ejpam-6029	304	29	continuous	continuous	ADJ
ejpam-6029	304	30	and	and	CCONJ
ejpam-6029	304	31	non	non	ADJ
ejpam-6029	304	32	-	-	ADJ
ejpam-6029	304	33	decreasing	decrease	VERB
ejpam-6029	304	34	,	,	PUNCT
ejpam-6029	304	35	g	g	PROPN
ejpam-6029	304	36	is	be	AUX
ejpam-6029	304	37	sub	sub	ADJ
ejpam-6029	304	38	-	-	ADJ
ejpam-6029	304	39	additive	additive	ADJ
ejpam-6029	304	40	,	,	PUNCT
ejpam-6029	304	41	and	and	CCONJ
ejpam-6029	304	42	g(λa	g(λa	NOUN
ejpam-6029	304	43	)	)	PUNCT
ejpam-6029	304	44	<	<	X
ejpam-6029	304	45	a	a	X
ejpam-6029	304	46	,	,	PUNCT
ejpam-6029	304	47	λ	λ	PROPN
ejpam-6029	304	48	∈	∈	PROPN
ejpam-6029	304	49	(	(	PUNCT
ejpam-6029	304	50	0	0	NUM
ejpam-6029	304	51	,	,	PUNCT
ejpam-6029	304	52	1	1	NUM
ejpam-6029	304	53	)	)	PUNCT
ejpam-6029	304	54	;	;	PUNCT
ejpam-6029	304	55	and	and	CCONJ
ejpam-6029	304	56	condition	condition	NOUN
ejpam-6029	304	57	(	(	PUNCT
ejpam-6029	304	58	ii	ii	NOUN
ejpam-6029	304	59	)	)	PUNCT
ejpam-6029	304	60	to	to	ADP
ejpam-6029	304	61	n−2∑	n−2∑	PROPN
ejpam-6029	304	62	i	i	PRON
ejpam-6029	304	63	=	=	NOUN
ejpam-6029	304	64	m	m	VERB
ejpam-6029	304	65	gi−mf	gi−mf	NOUN
ejpam-6029	304	66	(	(	PUNCT
ejpam-6029	304	67	ξilc(a0	ξilc(a0	NOUN
ejpam-6029	304	68	,	,	PUNCT
ejpam-6029	304	69	a1	a1	NOUN
ejpam-6029	304	70	)	)	PUNCT
ejpam-6029	304	71	)	)	PUNCT
ejpam-6029	305	1	+	+	CCONJ
ejpam-6029	305	2	gn−m−1	gn−m−1	X
ejpam-6029	305	3	(	(	PUNCT
ejpam-6029	305	4	ξn−1lc(a0	ξn−1lc(a0	PROPN
ejpam-6029	305	5	,	,	PUNCT
ejpam-6029	305	6	a1	a1	NOUN
ejpam-6029	305	7	)	)	PUNCT
ejpam-6029	305	8	)	)	PUNCT
ejpam-6029	305	9	→	→	SYM
ejpam-6029	305	10	0	0	NUM
ejpam-6029	305	11	,	,	PUNCT
ejpam-6029	305	12	as	as	ADP
ejpam-6029	305	13	n	n	CCONJ
ejpam-6029	305	14	,	,	PUNCT
ejpam-6029	305	15	m	m	PROPN
ejpam-6029	305	16	→	→	SYM
ejpam-6029	305	17	∞.	∞.	PROPN
ejpam-6029	305	18	then	then	ADV
ejpam-6029	305	19	,	,	PUNCT
ejpam-6029	305	20	the	the	DET
ejpam-6029	305	21	study	study	NOUN
ejpam-6029	305	22	reveals	reveal	VERB
ejpam-6029	305	23	the	the	DET
ejpam-6029	305	24	same	same	ADJ
ejpam-6029	305	25	special	special	ADJ
ejpam-6029	305	26	results	result	NOUN
ejpam-6029	305	27	in	in	ADP
ejpam-6029	305	28	the	the	DET
ejpam-6029	305	29	spaces	space	NOUN
ejpam-6029	305	30	dcms	dcms	NOUN
ejpam-6029	305	31	and	and	CCONJ
ejpam-6029	305	32	dcml	dcml	NOUN
ejpam-6029	305	33	-	-	PUNCT
ejpam-6029	305	34	spaces	space	NOUN
ejpam-6029	305	35	,	,	PUNCT
ejpam-6029	305	36	respectively	respectively	ADV
ejpam-6029	305	37	.	.	PUNCT
ejpam-6029	306	1	by	by	ADP
ejpam-6029	306	2	providing	provide	VERB
ejpam-6029	306	3	t1	t1	NOUN
ejpam-6029	306	4	=	=	SYM
ejpam-6029	306	5	t2	t2	PROPN
ejpam-6029	306	6	=	=	SYM
ejpam-6029	306	7	t	t	PROPN
ejpam-6029	306	8	in	in	ADP
ejpam-6029	306	9	theorem	theorem	PROPN
ejpam-6029	306	10	1	1	NUM
ejpam-6029	306	11	,	,	PUNCT
ejpam-6029	306	12	and	and	CCONJ
ejpam-6029	306	13	corollaries	corollary	NOUN
ejpam-6029	306	14	1	1	NUM
ejpam-6029	306	15	and	and	CCONJ
ejpam-6029	306	16	2	2	NUM
ejpam-6029	306	17	,	,	PUNCT
ejpam-6029	306	18	respectively	respectively	ADV
ejpam-6029	306	19	,	,	PUNCT
ejpam-6029	306	20	we	we	PRON
ejpam-6029	306	21	derive	derive	VERB
ejpam-6029	306	22	the	the	DET
ejpam-6029	306	23	following	follow	VERB
ejpam-6029	306	24	corollaries	corollary	NOUN
ejpam-6029	306	25	:	:	PUNCT
ejpam-6029	306	26	corollary	corollary	ADJ
ejpam-6029	306	27	3	3	X
ejpam-6029	306	28	.	.	PUNCT
ejpam-6029	307	1	assume	assume	VERB
ejpam-6029	307	2	(	(	PUNCT
ejpam-6029	307	3	γ	γ	X
ejpam-6029	307	4	,	,	PUNCT
ejpam-6029	307	5	lc	lc	PROPN
ejpam-6029	307	6	)	)	PUNCT
ejpam-6029	307	7	is	be	AUX
ejpam-6029	307	8	an	an	DET
ejpam-6029	307	9	lc	lc	NOUN
ejpam-6029	307	10	-	-	PUNCT
ejpam-6029	307	11	complete	complete	ADJ
ejpam-6029	307	12	dccml	dccml	NOUN
ejpam-6029	307	13	-	-	PUNCT
ejpam-6029	307	14	space	space	NOUN
ejpam-6029	307	15	,	,	PUNCT
ejpam-6029	307	16	where	where	SCONJ
ejpam-6029	307	17	p	p	NOUN
ejpam-6029	307	18	is	be	AUX
ejpam-6029	307	19	a	a	DET
ejpam-6029	307	20	normal	normal	ADJ
ejpam-6029	307	21	cone	cone	NOUN
ejpam-6029	307	22	via	via	ADP
ejpam-6029	307	23	normal	normal	ADJ
ejpam-6029	307	24	constant	constant	ADJ
ejpam-6029	307	25	m	m	NOUN
ejpam-6029	307	26	.	.	PUNCT
ejpam-6029	308	1	let	let	VERB
ejpam-6029	308	2	t	t	NOUN
ejpam-6029	308	3	:	:	PUNCT
ejpam-6029	308	4	γ	γ	X
ejpam-6029	308	5	→	→	SYM
ejpam-6029	308	6	γ	γ	X
ejpam-6029	308	7	be	be	AUX
ejpam-6029	308	8	a	a	DET
ejpam-6029	308	9	mapping	mapping	NOUN
ejpam-6029	308	10	and	and	CCONJ
ejpam-6029	308	11	there	there	PRON
ejpam-6029	308	12	exists	exist	VERB
ejpam-6029	308	13	λ	λ	PROPN
ejpam-6029	308	14	∈	∈	PROPN
ejpam-6029	308	15	∆	∆	PROPN
ejpam-6029	308	16	such	such	ADJ
ejpam-6029	308	17	that	that	SCONJ
ejpam-6029	308	18	lc(ta	lc(ta	PROPN
ejpam-6029	308	19	,	,	PUNCT
ejpam-6029	308	20	tb	tb	NOUN
ejpam-6029	308	21	)	)	PUNCT
ejpam-6029	308	22	⪯	⪯	NOUN
ejpam-6029	308	23	λ(a	λ(a	PROPN
ejpam-6029	308	24	,	,	PUNCT
ejpam-6029	308	25	b)m̃(a	b)m̃(a	PROPN
ejpam-6029	308	26	,	,	PUNCT
ejpam-6029	308	27	b	b	NOUN
ejpam-6029	308	28	)	)	PUNCT
ejpam-6029	308	29	,	,	PUNCT
ejpam-6029	308	30	for	for	ADP
ejpam-6029	308	31	all	all	DET
ejpam-6029	308	32	a	a	PRON
ejpam-6029	308	33	,	,	PUNCT
ejpam-6029	308	34	b	b	PROPN
ejpam-6029	308	35	∈	∈	PROPN
ejpam-6029	308	36	γ	γ	X
ejpam-6029	308	37	,	,	PUNCT
ejpam-6029	308	38	(	(	PUNCT
ejpam-6029	308	39	10	10	NUM
ejpam-6029	308	40	)	)	PUNCT
ejpam-6029	308	41	where	where	SCONJ
ejpam-6029	308	42	m̃(a	m̃(a	NOUN
ejpam-6029	308	43	,	,	PUNCT
ejpam-6029	308	44	b	b	NOUN
ejpam-6029	308	45	)	)	PUNCT
ejpam-6029	308	46	=	=	SYM
ejpam-6029	308	47	max	max	PROPN
ejpam-6029	308	48	{	{	PUNCT
ejpam-6029	308	49	lc(a	lc(a	PROPN
ejpam-6029	308	50	,	,	PUNCT
ejpam-6029	308	51	b),lc(a	b),lc(a	PROPN
ejpam-6029	308	52	,	,	PUNCT
ejpam-6029	308	53	ta),lc(b	ta),lc(b	PROPN
ejpam-6029	308	54	,	,	PUNCT
ejpam-6029	308	55	t	t	PROPN
ejpam-6029	308	56	b	b	PROPN
ejpam-6029	308	57	)	)	PUNCT
ejpam-6029	308	58	,	,	PUNCT
ejpam-6029	308	59	lc(a	lc(a	PROPN
ejpam-6029	308	60	,	,	PUNCT
ejpam-6029	308	61	ta)lc(b	ta)lc(b	PROPN
ejpam-6029	308	62	,	,	PUNCT
ejpam-6029	308	63	t	t	PROPN
ejpam-6029	308	64	b	b	NUM
ejpam-6029	308	65	)	)	PUNCT
ejpam-6029	308	66	1	1	NUM
ejpam-6029	308	67	+	+	CCONJ
ejpam-6029	308	68	lc(a	lc(a	NUM
ejpam-6029	308	69	,	,	PUNCT
ejpam-6029	308	70	b	b	NOUN
ejpam-6029	308	71	)	)	PUNCT
ejpam-6029	308	72	,	,	PUNCT
ejpam-6029	308	73	lc(b	lc(b	PROPN
ejpam-6029	308	74	,	,	PUNCT
ejpam-6029	308	75	t	t	PROPN
ejpam-6029	308	76	b	b	NUM
ejpam-6029	308	77	)	)	PUNCT
ejpam-6029	308	78	[	[	PUNCT
ejpam-6029	308	79	1	1	NUM
ejpam-6029	308	80	+	+	CCONJ
ejpam-6029	308	81	lc(a	lc(a	NOUN
ejpam-6029	308	82	,	,	PUNCT
ejpam-6029	308	83	ta	ta	NOUN
ejpam-6029	308	84	)	)	PUNCT
ejpam-6029	308	85	]	]	PUNCT
ejpam-6029	309	1	1	1	NUM
ejpam-6029	309	2	+	+	CCONJ
ejpam-6029	309	3	lc(a	lc(a	NUM
ejpam-6029	309	4	,	,	PUNCT
ejpam-6029	309	5	b	b	NOUN
ejpam-6029	309	6	)	)	PUNCT
ejpam-6029	309	7	,	,	PUNCT
ejpam-6029	309	8	[	[	PUNCT
ejpam-6029	309	9	lc(a	lc(a	X
ejpam-6029	309	10	,	,	PUNCT
ejpam-6029	309	11	ta	ta	NOUN
ejpam-6029	309	12	)	)	PUNCT
ejpam-6029	309	13	+	+	CCONJ
ejpam-6029	309	14	lc(b	lc(b	PROPN
ejpam-6029	309	15	,	,	PUNCT
ejpam-6029	309	16	t	t	PROPN
ejpam-6029	309	17	b	b	PROPN
ejpam-6029	309	18	)	)	PUNCT
ejpam-6029	309	19	]	]	PUNCT
ejpam-6029	310	1	lc(ta	lc(ta	ADV
ejpam-6029	310	2	,	,	PUNCT
ejpam-6029	310	3	tb	tb	NOUN
ejpam-6029	310	4	)	)	PUNCT
ejpam-6029	310	5	1	1	NUM
ejpam-6029	311	1	+	+	CCONJ
ejpam-6029	311	2	lc(a	lc(a	NUM
ejpam-6029	311	3	,	,	PUNCT
ejpam-6029	311	4	b	b	NOUN
ejpam-6029	311	5	)	)	PUNCT
ejpam-6029	311	6	+	+	CCONJ
ejpam-6029	311	7	lc(ta	lc(ta	ADJ
ejpam-6029	311	8	,	,	PUNCT
ejpam-6029	311	9	tb	tb	NOUN
ejpam-6029	311	10	)	)	PUNCT
ejpam-6029	311	11	}	}	PUNCT
ejpam-6029	311	12	.	.	PUNCT
ejpam-6029	312	1	for	for	ADP
ejpam-6029	312	2	a0	a0	PROPN
ejpam-6029	312	3	∈	∈	PROPN
ejpam-6029	312	4	γ	γ	PROPN
ejpam-6029	312	5	,	,	PUNCT
ejpam-6029	312	6	we	we	PRON
ejpam-6029	312	7	take	take	VERB
ejpam-6029	312	8	the	the	DET
ejpam-6029	312	9	sequence	sequence	NOUN
ejpam-6029	312	10	{	{	PUNCT
ejpam-6029	312	11	an	an	PRON
ejpam-6029	312	12	}	}	PUNCT
ejpam-6029	312	13	defined	define	VERB
ejpam-6029	312	14	as	as	ADP
ejpam-6029	312	15	an+1	an+1	NOUN
ejpam-6029	312	16	=	=	SYM
ejpam-6029	312	17	tna0	tna0	PROPN
ejpam-6029	312	18	for	for	ADP
ejpam-6029	312	19	every	every	DET
ejpam-6029	312	20	n	n	PRON
ejpam-6029	312	21	≥	≥	NOUN
ejpam-6029	312	22	0	0	NUM
ejpam-6029	312	23	.	.	PUNCT
ejpam-6029	313	1	suppose	suppose	VERB
ejpam-6029	313	2	(	(	PUNCT
ejpam-6029	313	3	i	i	NOUN
ejpam-6029	313	4	)	)	PUNCT
ejpam-6029	313	5	f	f	PROPN
ejpam-6029	313	6	and	and	CCONJ
ejpam-6029	313	7	g	g	PROPN
ejpam-6029	313	8	are	be	AUX
ejpam-6029	313	9	bounded	bound	VERB
ejpam-6029	313	10	and	and	CCONJ
ejpam-6029	313	11	non	non	ADJ
ejpam-6029	313	12	-	-	ADJ
ejpam-6029	313	13	decreasing	decrease	VERB
ejpam-6029	313	14	,	,	PUNCT
ejpam-6029	313	15	g	g	PROPN
ejpam-6029	313	16	is	be	AUX
ejpam-6029	313	17	sub	sub	ADJ
ejpam-6029	313	18	-	-	ADJ
ejpam-6029	313	19	additive	additive	ADJ
ejpam-6029	313	20	,	,	PUNCT
ejpam-6029	313	21	and	and	CCONJ
ejpam-6029	313	22	g(λa	g(λa	NOUN
ejpam-6029	313	23	)	)	PUNCT
ejpam-6029	313	24	≺	≺	NOUN
ejpam-6029	313	25	a	a	PRON
ejpam-6029	313	26	,	,	PUNCT
ejpam-6029	313	27	λ	λ	PROPN
ejpam-6029	313	28	∈	∈	PROPN
ejpam-6029	313	29	(	(	PUNCT
ejpam-6029	313	30	0	0	NUM
ejpam-6029	313	31	,	,	PUNCT
ejpam-6029	313	32	1	1	NUM
ejpam-6029	313	33	)	)	PUNCT
ejpam-6029	313	34	;	;	PUNCT
ejpam-6029	313	35	(	(	PUNCT
ejpam-6029	313	36	ii	ii	X
ejpam-6029	313	37	)	)	PUNCT
ejpam-6029	313	38	lim	lim	PROPN
ejpam-6029	313	39	n	n	CCONJ
ejpam-6029	313	40	,	,	PUNCT
ejpam-6029	313	41	m→∞	m→∞	NUM
ejpam-6029	313	42	∑n−2	∑n−2	NOUN
ejpam-6029	314	1	i	i	PRON
ejpam-6029	314	2	=	=	VERB
ejpam-6029	314	3	m	m	VERB
ejpam-6029	314	4	∥gi−mf	∥gi−mf	NOUN
ejpam-6029	314	5	(	(	PUNCT
ejpam-6029	314	6	ξilc(a0	ξilc(a0	NOUN
ejpam-6029	314	7	,	,	PUNCT
ejpam-6029	314	8	a1	a1	NOUN
ejpam-6029	314	9	)	)	PUNCT
ejpam-6029	314	10	)	)	PUNCT
ejpam-6029	314	11	∥+	∥+	PROPN
ejpam-6029	315	1	∥gn−m−1	∥gn−m−1	PROPN
ejpam-6029	315	2	(	(	PUNCT
ejpam-6029	315	3	ξn−1lc(a0	ξn−1lc(a0	PROPN
ejpam-6029	315	4	,	,	PUNCT
ejpam-6029	315	5	a1	a1	NOUN
ejpam-6029	315	6	)	)	PUNCT
ejpam-6029	315	7	)	)	PUNCT
ejpam-6029	315	8	∥	∥	X
ejpam-6029	315	9	=	=	SYM
ejpam-6029	315	10	0	0	NUM
ejpam-6029	315	11	,	,	PUNCT
ejpam-6029	315	12	where	where	SCONJ
ejpam-6029	315	13	ξ	ξ	X
ejpam-6029	315	14	=	=	SYM
ejpam-6029	315	15	λ(a0	λ(a0	X
ejpam-6029	315	16	,	,	PUNCT
ejpam-6029	315	17	a1	a1	PROPN
ejpam-6029	315	18	)	)	PUNCT
ejpam-6029	315	19	<	<	X
ejpam-6029	315	20	1	1	X
ejpam-6029	315	21	.	.	PUNCT
ejpam-6029	316	1	if	if	SCONJ
ejpam-6029	316	2	for	for	ADP
ejpam-6029	316	3	every	every	DET
ejpam-6029	316	4	fixed	fix	VERB
ejpam-6029	316	5	point	point	NOUN
ejpam-6029	316	6	a	a	ADV
ejpam-6029	316	7	,	,	PUNCT
ejpam-6029	316	8	we	we	PRON
ejpam-6029	316	9	conclude	conclude	VERB
ejpam-6029	316	10	that	that	PRON
ejpam-6029	316	11	lc(a	lc(a	NOUN
ejpam-6029	316	12	,	,	PUNCT
ejpam-6029	316	13	a	a	PRON
ejpam-6029	316	14	)	)	PUNCT
ejpam-6029	316	15	=	=	SYM
ejpam-6029	316	16	0e	0e	NOUN
ejpam-6029	316	17	,	,	PUNCT
ejpam-6029	316	18	then	then	ADV
ejpam-6029	316	19	t	t	PROPN
ejpam-6029	316	20	has	have	VERB
ejpam-6029	316	21	a	a	DET
ejpam-6029	316	22	unique	unique	ADJ
ejpam-6029	316	23	fixed	fix	VERB
ejpam-6029	316	24	point	point	NOUN
ejpam-6029	316	25	.	.	PUNCT
ejpam-6029	317	1	proof	proof	NOUN
ejpam-6029	317	2	.	.	PUNCT
ejpam-6029	318	1	the	the	DET
ejpam-6029	318	2	proof	proof	NOUN
ejpam-6029	318	3	follows	follow	VERB
ejpam-6029	318	4	from	from	ADP
ejpam-6029	318	5	theorem	theorem	NOUN
ejpam-6029	318	6	1	1	NUM
ejpam-6029	318	7	by	by	ADP
ejpam-6029	318	8	taking	take	VERB
ejpam-6029	318	9	the	the	DET
ejpam-6029	318	10	self	self	NOUN
ejpam-6029	318	11	-	-	PUNCT
ejpam-6029	318	12	map	map	NOUN
ejpam-6029	318	13	t	t	NOUN
ejpam-6029	318	14	:	:	PUNCT
ejpam-6029	318	15	γ	γ	X
ejpam-6029	318	16	→	→	SYM
ejpam-6029	318	17	γ	γ	PROPN
ejpam-6029	318	18	as	as	ADP
ejpam-6029	318	19	t1	t1	NOUN
ejpam-6029	318	20	=	=	SYM
ejpam-6029	318	21	t2	t2	PROPN
ejpam-6029	318	22	=	=	SYM
ejpam-6029	318	23	t	t	PROPN
ejpam-6029	318	24	.	.	PUNCT
ejpam-6029	319	1	a.	a.	PROPN
ejpam-6029	319	2	a.	a.	PROPN
ejpam-6029	319	3	hijab	hijab	PROPN
ejpam-6029	319	4	et	et	PROPN
ejpam-6029	319	5	al	al	PROPN
ejpam-6029	319	6	.	.	PUNCT
ejpam-6029	319	7	/	/	SYM
ejpam-6029	319	8	eur	eur	PROPN
ejpam-6029	319	9	.	.	PUNCT
ejpam-6029	320	1	j.	j.	PROPN
ejpam-6029	320	2	pure	pure	PROPN
ejpam-6029	320	3	appl	appl	PROPN
ejpam-6029	320	4	.	.	PROPN
ejpam-6029	320	5	math	math	PROPN
ejpam-6029	320	6	,	,	PUNCT
ejpam-6029	320	7	18	18	NUM
ejpam-6029	320	8	(	(	PUNCT
ejpam-6029	320	9	2	2	NUM
ejpam-6029	320	10	)	)	PUNCT
ejpam-6029	320	11	(	(	PUNCT
ejpam-6029	320	12	2025	2025	NUM
ejpam-6029	320	13	)	)	PUNCT
ejpam-6029	320	14	,	,	PUNCT
ejpam-6029	320	15	6029	6029	NUM
ejpam-6029	320	16	13	13	NUM
ejpam-6029	320	17	of	of	ADP
ejpam-6029	320	18	23	23	NUM
ejpam-6029	320	19	corollary	corollary	ADJ
ejpam-6029	320	20	4	4	NUM
ejpam-6029	320	21	.	.	PUNCT
ejpam-6029	320	22	suppose	suppose	VERB
ejpam-6029	320	23	that	that	SCONJ
ejpam-6029	320	24	(	(	PUNCT
ejpam-6029	320	25	γ	γ	X
ejpam-6029	320	26	,	,	PUNCT
ejpam-6029	320	27	lc	lc	PROPN
ejpam-6029	320	28	)	)	PUNCT
ejpam-6029	320	29	is	be	AUX
ejpam-6029	320	30	a	a	DET
ejpam-6029	320	31	complete	complete	ADJ
ejpam-6029	320	32	c2cms	c2cms	PROPN
ejpam-6029	320	33	,	,	PUNCT
ejpam-6029	320	34	where	where	SCONJ
ejpam-6029	320	35	p	p	NOUN
ejpam-6029	320	36	is	be	AUX
ejpam-6029	320	37	a	a	DET
ejpam-6029	320	38	normal	normal	ADJ
ejpam-6029	320	39	cone	cone	NOUN
ejpam-6029	320	40	via	via	ADP
ejpam-6029	320	41	normal	normal	ADJ
ejpam-6029	320	42	constant	constant	ADJ
ejpam-6029	320	43	m	m	NOUN
ejpam-6029	320	44	.	.	PUNCT
ejpam-6029	321	1	let	let	VERB
ejpam-6029	321	2	t	t	NOUN
ejpam-6029	321	3	:	:	PUNCT
ejpam-6029	321	4	γ	γ	X
ejpam-6029	321	5	→	→	SYM
ejpam-6029	321	6	γ	γ	X
ejpam-6029	321	7	be	be	AUX
ejpam-6029	321	8	a	a	DET
ejpam-6029	321	9	mapping	mapping	NOUN
ejpam-6029	321	10	and	and	CCONJ
ejpam-6029	321	11	there	there	PRON
ejpam-6029	321	12	exists	exist	VERB
ejpam-6029	321	13	λ	λ	PROPN
ejpam-6029	321	14	∈	∈	PROPN
ejpam-6029	321	15	∆	∆	PROPN
ejpam-6029	321	16	such	such	ADJ
ejpam-6029	321	17	that	that	SCONJ
ejpam-6029	321	18	dc(ta	dc(ta	PROPN
ejpam-6029	321	19	,	,	PUNCT
ejpam-6029	321	20	tb	tb	NOUN
ejpam-6029	321	21	)	)	PUNCT
ejpam-6029	321	22	⪯	⪯	NOUN
ejpam-6029	321	23	λ(a	λ(a	PROPN
ejpam-6029	321	24	,	,	PUNCT
ejpam-6029	321	25	b)m̃(a	b)m̃(a	PROPN
ejpam-6029	321	26	,	,	PUNCT
ejpam-6029	321	27	b	b	NOUN
ejpam-6029	321	28	)	)	PUNCT
ejpam-6029	321	29	,	,	PUNCT
ejpam-6029	321	30	for	for	ADP
ejpam-6029	321	31	all	all	DET
ejpam-6029	321	32	a	a	DET
ejpam-6029	321	33	,	,	PUNCT
ejpam-6029	321	34	b	b	PROPN
ejpam-6029	321	35	∈	∈	PROPN
ejpam-6029	321	36	γ	γ	X
ejpam-6029	321	37	,	,	PUNCT
ejpam-6029	321	38	(	(	PUNCT
ejpam-6029	321	39	11	11	NUM
ejpam-6029	321	40	)	)	PUNCT
ejpam-6029	321	41	where	where	SCONJ
ejpam-6029	321	42	m̃(a	m̃(a	NOUN
ejpam-6029	321	43	,	,	PUNCT
ejpam-6029	321	44	b	b	NOUN
ejpam-6029	321	45	)	)	PUNCT
ejpam-6029	321	46	=	=	SYM
ejpam-6029	321	47	max	max	PROPN
ejpam-6029	321	48	{	{	PUNCT
ejpam-6029	321	49	dc(a	dc(a	X
ejpam-6029	321	50	,	,	PUNCT
ejpam-6029	321	51	b),dc(a	b),dc(a	PROPN
ejpam-6029	321	52	,	,	PUNCT
ejpam-6029	321	53	ta),dc(b	ta),dc(b	NOUN
ejpam-6029	321	54	,	,	PUNCT
ejpam-6029	321	55	t	t	PROPN
ejpam-6029	321	56	b	b	PROPN
ejpam-6029	321	57	)	)	PUNCT
ejpam-6029	321	58	,	,	PUNCT
ejpam-6029	321	59	dc(a	dc(a	NOUN
ejpam-6029	321	60	,	,	PUNCT
ejpam-6029	321	61	ta)dc(b	ta)dc(b	PROPN
ejpam-6029	321	62	,	,	PUNCT
ejpam-6029	321	63	t	t	PROPN
ejpam-6029	321	64	b	b	PROPN
ejpam-6029	321	65	)	)	PUNCT
ejpam-6029	321	66	1	1	NUM
ejpam-6029	322	1	+	+	NOUN
ejpam-6029	322	2	dc(a	dc(a	NOUN
ejpam-6029	322	3	,	,	PUNCT
ejpam-6029	322	4	b	b	NOUN
ejpam-6029	322	5	)	)	PUNCT
ejpam-6029	322	6	,	,	PUNCT
ejpam-6029	322	7	dc(b	dc(b	PROPN
ejpam-6029	322	8	,	,	PUNCT
ejpam-6029	322	9	t	t	PROPN
ejpam-6029	322	10	b	b	X
ejpam-6029	322	11	)	)	PUNCT
ejpam-6029	322	12	[	[	PUNCT
ejpam-6029	322	13	1	1	NUM
ejpam-6029	322	14	+	+	NOUN
ejpam-6029	322	15	dc(a	dc(a	NOUN
ejpam-6029	322	16	,	,	PUNCT
ejpam-6029	322	17	ta	ta	NOUN
ejpam-6029	322	18	)	)	PUNCT
ejpam-6029	322	19	]	]	PUNCT
ejpam-6029	323	1	1	1	NUM
ejpam-6029	323	2	+	+	NOUN
ejpam-6029	323	3	dc(a	dc(a	NOUN
ejpam-6029	323	4	,	,	PUNCT
ejpam-6029	323	5	b	b	NOUN
ejpam-6029	323	6	)	)	PUNCT
ejpam-6029	323	7	,	,	PUNCT
ejpam-6029	323	8	[	[	PUNCT
ejpam-6029	323	9	dc(a	dc(a	X
ejpam-6029	323	10	,	,	PUNCT
ejpam-6029	323	11	ta	ta	NOUN
ejpam-6029	323	12	)	)	PUNCT
ejpam-6029	323	13	+	+	NOUN
ejpam-6029	323	14	dc(b	dc(b	ADJ
ejpam-6029	323	15	,	,	PUNCT
ejpam-6029	323	16	t	t	PROPN
ejpam-6029	323	17	b	b	PROPN
ejpam-6029	323	18	)	)	PUNCT
ejpam-6029	323	19	]	]	PUNCT
ejpam-6029	324	1	dc(ta	dc(ta	PROPN
ejpam-6029	324	2	,	,	PUNCT
ejpam-6029	324	3	tb	tb	NOUN
ejpam-6029	324	4	)	)	PUNCT
ejpam-6029	324	5	1	1	NUM
ejpam-6029	325	1	+	+	NOUN
ejpam-6029	325	2	dc(a	dc(a	NOUN
ejpam-6029	325	3	,	,	PUNCT
ejpam-6029	325	4	b	b	NOUN
ejpam-6029	325	5	)	)	PUNCT
ejpam-6029	325	6	+	+	NOUN
ejpam-6029	325	7	dc(ta	dc(ta	PROPN
ejpam-6029	325	8	,	,	PUNCT
ejpam-6029	325	9	tb	tb	NOUN
ejpam-6029	325	10	)	)	PUNCT
ejpam-6029	325	11	}	}	PUNCT
ejpam-6029	325	12	.	.	PUNCT
ejpam-6029	326	1	for	for	ADP
ejpam-6029	326	2	a0	a0	PROPN
ejpam-6029	326	3	∈	∈	PROPN
ejpam-6029	326	4	γ	γ	PROPN
ejpam-6029	326	5	,	,	PUNCT
ejpam-6029	326	6	we	we	PRON
ejpam-6029	326	7	take	take	VERB
ejpam-6029	326	8	the	the	DET
ejpam-6029	326	9	sequence	sequence	NOUN
ejpam-6029	326	10	{	{	PUNCT
ejpam-6029	326	11	an	an	PRON
ejpam-6029	326	12	}	}	PUNCT
ejpam-6029	326	13	defined	define	VERB
ejpam-6029	326	14	as	as	ADP
ejpam-6029	326	15	an+1	an+1	NOUN
ejpam-6029	326	16	=	=	SYM
ejpam-6029	326	17	tna0	tna0	PROPN
ejpam-6029	326	18	for	for	ADP
ejpam-6029	326	19	every	every	DET
ejpam-6029	326	20	n	n	PRON
ejpam-6029	326	21	≥	≥	NOUN
ejpam-6029	326	22	0	0	NUM
ejpam-6029	326	23	.	.	PUNCT
ejpam-6029	327	1	assume	assume	VERB
ejpam-6029	327	2	that	that	SCONJ
ejpam-6029	327	3	(	(	PUNCT
ejpam-6029	327	4	i	i	NOUN
ejpam-6029	327	5	)	)	PUNCT
ejpam-6029	327	6	f	f	PROPN
ejpam-6029	327	7	and	and	CCONJ
ejpam-6029	327	8	g	g	PROPN
ejpam-6029	327	9	are	be	AUX
ejpam-6029	327	10	bounded	bound	VERB
ejpam-6029	327	11	and	and	CCONJ
ejpam-6029	327	12	non	non	ADJ
ejpam-6029	327	13	-	-	ADJ
ejpam-6029	327	14	decreasing	decrease	VERB
ejpam-6029	327	15	,	,	PUNCT
ejpam-6029	327	16	g	g	PROPN
ejpam-6029	327	17	is	be	AUX
ejpam-6029	327	18	sub	sub	ADJ
ejpam-6029	327	19	-	-	ADJ
ejpam-6029	327	20	additive	additive	ADJ
ejpam-6029	327	21	,	,	PUNCT
ejpam-6029	327	22	and	and	CCONJ
ejpam-6029	327	23	g(λa	g(λa	NOUN
ejpam-6029	327	24	)	)	PUNCT
ejpam-6029	327	25	≺	≺	NOUN
ejpam-6029	327	26	a	a	PRON
ejpam-6029	327	27	,	,	PUNCT
ejpam-6029	327	28	λ	λ	PROPN
ejpam-6029	327	29	∈	∈	PROPN
ejpam-6029	327	30	(	(	PUNCT
ejpam-6029	327	31	0	0	NUM
ejpam-6029	327	32	,	,	PUNCT
ejpam-6029	327	33	1	1	NUM
ejpam-6029	327	34	)	)	PUNCT
ejpam-6029	327	35	;	;	PUNCT
ejpam-6029	327	36	(	(	PUNCT
ejpam-6029	327	37	ii	ii	X
ejpam-6029	327	38	)	)	PUNCT
ejpam-6029	327	39	lim	lim	PROPN
ejpam-6029	327	40	n	n	CCONJ
ejpam-6029	327	41	,	,	PUNCT
ejpam-6029	327	42	m→∞	m→∞	NUM
ejpam-6029	327	43	∑n−2	∑n−2	NOUN
ejpam-6029	328	1	i	i	PRON
ejpam-6029	328	2	=	=	VERB
ejpam-6029	328	3	m	m	VERB
ejpam-6029	328	4	∥gi−mf	∥gi−mf	NOUN
ejpam-6029	328	5	(	(	PUNCT
ejpam-6029	328	6	ξidc(a0	ξidc(a0	X
ejpam-6029	328	7	,	,	PUNCT
ejpam-6029	328	8	a1	a1	NOUN
ejpam-6029	328	9	)	)	PUNCT
ejpam-6029	328	10	)	)	PUNCT
ejpam-6029	328	11	∥+	∥+	PROPN
ejpam-6029	329	1	∥gn−m−1	∥gn−m−1	PROPN
ejpam-6029	329	2	(	(	PUNCT
ejpam-6029	329	3	ξn−1dc(a0	ξn−1dc(a0	PROPN
ejpam-6029	329	4	,	,	PUNCT
ejpam-6029	329	5	a1	a1	NOUN
ejpam-6029	329	6	)	)	PUNCT
ejpam-6029	329	7	)	)	PUNCT
ejpam-6029	329	8	∥	∥	X
ejpam-6029	329	9	=	=	SYM
ejpam-6029	329	10	0	0	NUM
ejpam-6029	329	11	,	,	PUNCT
ejpam-6029	329	12	where	where	SCONJ
ejpam-6029	329	13	ξ	ξ	X
ejpam-6029	329	14	=	=	SYM
ejpam-6029	329	15	λ(a0	λ(a0	X
ejpam-6029	329	16	,	,	PUNCT
ejpam-6029	329	17	a1	a1	PROPN
ejpam-6029	329	18	)	)	PUNCT
ejpam-6029	329	19	<	<	X
ejpam-6029	329	20	1	1	X
ejpam-6029	329	21	.	.	PUNCT
ejpam-6029	329	22	then	then	ADV
ejpam-6029	329	23	t	t	PROPN
ejpam-6029	329	24	ensures	ensure	VERB
ejpam-6029	329	25	a	a	DET
ejpam-6029	329	26	unique	unique	ADJ
ejpam-6029	329	27	fixed	fix	VERB
ejpam-6029	329	28	point	point	NOUN
ejpam-6029	329	29	.	.	PUNCT
ejpam-6029	330	1	proof	proof	NOUN
ejpam-6029	330	2	.	.	PUNCT
ejpam-6029	331	1	the	the	DET
ejpam-6029	331	2	proof	proof	NOUN
ejpam-6029	331	3	follows	follow	VERB
ejpam-6029	331	4	from	from	ADP
ejpam-6029	331	5	corollary	corollary	ADJ
ejpam-6029	331	6	1	1	NUM
ejpam-6029	331	7	by	by	ADP
ejpam-6029	331	8	taking	take	VERB
ejpam-6029	331	9	the	the	DET
ejpam-6029	331	10	self	self	NOUN
ejpam-6029	331	11	-	-	PUNCT
ejpam-6029	331	12	map	map	NOUN
ejpam-6029	331	13	t	t	NOUN
ejpam-6029	331	14	:	:	PUNCT
ejpam-6029	331	15	γ	γ	X
ejpam-6029	331	16	→	→	SYM
ejpam-6029	331	17	γ	γ	PROPN
ejpam-6029	331	18	as	as	ADP
ejpam-6029	331	19	t1	t1	NOUN
ejpam-6029	331	20	=	=	SYM
ejpam-6029	331	21	t2	t2	PROPN
ejpam-6029	331	22	=	=	SYM
ejpam-6029	331	23	t	t	PROPN
ejpam-6029	331	24	.	.	PUNCT
ejpam-6029	332	1	corollary	corollary	ADJ
ejpam-6029	332	2	5	5	NUM
ejpam-6029	332	3	.	.	PUNCT
ejpam-6029	332	4	suppose	suppose	VERB
ejpam-6029	332	5	that	that	SCONJ
ejpam-6029	332	6	(	(	PUNCT
ejpam-6029	332	7	γ	γ	X
ejpam-6029	332	8	,	,	PUNCT
ejpam-6029	332	9	lc	lc	PROPN
ejpam-6029	332	10	)	)	PUNCT
ejpam-6029	332	11	is	be	AUX
ejpam-6029	332	12	an	an	DET
ejpam-6029	332	13	lc	lc	NOUN
ejpam-6029	332	14	-	-	PUNCT
ejpam-6029	332	15	complete	complete	ADJ
ejpam-6029	332	16	dccml	dccml	NOUN
ejpam-6029	332	17	-	-	PUNCT
ejpam-6029	332	18	space	space	NOUN
ejpam-6029	332	19	,	,	PUNCT
ejpam-6029	332	20	where	where	SCONJ
ejpam-6029	332	21	p	p	NOUN
ejpam-6029	332	22	is	be	AUX
ejpam-6029	332	23	a	a	DET
ejpam-6029	332	24	normal	normal	ADJ
ejpam-6029	332	25	cone	cone	NOUN
ejpam-6029	332	26	via	via	ADP
ejpam-6029	332	27	normal	normal	ADJ
ejpam-6029	332	28	constant	constant	ADJ
ejpam-6029	332	29	m	m	NOUN
ejpam-6029	332	30	.	.	PUNCT
ejpam-6029	333	1	let	let	VERB
ejpam-6029	333	2	t	t	NOUN
ejpam-6029	333	3	:	:	PUNCT
ejpam-6029	333	4	γ	γ	X
ejpam-6029	333	5	→	→	SYM
ejpam-6029	333	6	γ	γ	X
ejpam-6029	333	7	be	be	AUX
ejpam-6029	333	8	a	a	DET
ejpam-6029	333	9	mapping	mapping	NOUN
ejpam-6029	333	10	and	and	CCONJ
ejpam-6029	333	11	there	there	PRON
ejpam-6029	333	12	exists	exist	VERB
ejpam-6029	333	13	λj	λj	PROPN
ejpam-6029	333	14	∈	∈	PROPN
ejpam-6029	333	15	∆	∆	PROPN
ejpam-6029	333	16	,	,	PUNCT
ejpam-6029	333	17	j	j	PROPN
ejpam-6029	333	18	=	=	SYM
ejpam-6029	333	19	1	1	NUM
ejpam-6029	333	20	,	,	PUNCT
ejpam-6029	333	21	·	·	PUNCT
ejpam-6029	333	22	·	·	PUNCT
ejpam-6029	334	1	·	·	PUNCT
ejpam-6029	334	2	,	,	PUNCT
ejpam-6029	334	3	5	5	NUM
ejpam-6029	334	4	,	,	PUNCT
ejpam-6029	334	5	such	such	ADJ
ejpam-6029	334	6	that	that	SCONJ
ejpam-6029	334	7	lc(ta	lc(ta	PROPN
ejpam-6029	334	8	,	,	PUNCT
ejpam-6029	334	9	tb	tb	NOUN
ejpam-6029	334	10	)	)	PUNCT
ejpam-6029	334	11	⪯λ1(a	⪯λ1(a	NOUN
ejpam-6029	334	12	,	,	PUNCT
ejpam-6029	334	13	b)lc(a	b)lc(a	NUM
ejpam-6029	334	14	,	,	PUNCT
ejpam-6029	334	15	b	b	NOUN
ejpam-6029	334	16	)	)	PUNCT
ejpam-6029	334	17	+	+	SYM
ejpam-6029	335	1	λ2(a	λ2(a	NOUN
ejpam-6029	335	2	,	,	PUNCT
ejpam-6029	335	3	b)lc(a	b)lc(a	PROPN
ejpam-6029	335	4	,	,	PUNCT
ejpam-6029	335	5	ta	ta	NOUN
ejpam-6029	335	6	)	)	PUNCT
ejpam-6029	336	1	+	+	PUNCT
ejpam-6029	337	1	λ3(a	λ3(a	NOUN
ejpam-6029	337	2	,	,	PUNCT
ejpam-6029	337	3	b)lc(b	b)lc(b	NOUN
ejpam-6029	337	4	,	,	PUNCT
ejpam-6029	337	5	t	t	PROPN
ejpam-6029	337	6	b	b	X
ejpam-6029	337	7	)	)	PUNCT
ejpam-6029	337	8	+	+	CCONJ
ejpam-6029	337	9	λ4(a	λ4(a	PROPN
ejpam-6029	337	10	,	,	PUNCT
ejpam-6029	337	11	b	b	NOUN
ejpam-6029	337	12	)	)	PUNCT
ejpam-6029	337	13	lc(a	lc(a	NUM
ejpam-6029	337	14	,	,	PUNCT
ejpam-6029	337	15	ta)lc(b	ta)lc(b	PROPN
ejpam-6029	337	16	,	,	PUNCT
ejpam-6029	337	17	t	t	PROPN
ejpam-6029	337	18	b	b	NUM
ejpam-6029	337	19	)	)	PUNCT
ejpam-6029	337	20	1	1	NUM
ejpam-6029	337	21	+	+	CCONJ
ejpam-6029	337	22	lc(a	lc(a	NUM
ejpam-6029	337	23	,	,	PUNCT
ejpam-6029	337	24	b	b	NOUN
ejpam-6029	337	25	)	)	PUNCT
ejpam-6029	337	26	+	+	CCONJ
ejpam-6029	337	27	λ5(a	λ5(a	NUM
ejpam-6029	337	28	,	,	PUNCT
ejpam-6029	337	29	b	b	NOUN
ejpam-6029	337	30	)	)	PUNCT
ejpam-6029	337	31	lc(b	lc(b	NOUN
ejpam-6029	337	32	,	,	PUNCT
ejpam-6029	337	33	t	t	PROPN
ejpam-6029	337	34	b	b	NUM
ejpam-6029	337	35	)	)	PUNCT
ejpam-6029	337	36	[	[	PUNCT
ejpam-6029	337	37	1	1	NUM
ejpam-6029	337	38	+	+	CCONJ
ejpam-6029	337	39	lc(a	lc(a	NOUN
ejpam-6029	337	40	,	,	PUNCT
ejpam-6029	337	41	ta	ta	NOUN
ejpam-6029	337	42	)	)	PUNCT
ejpam-6029	337	43	]	]	PUNCT
ejpam-6029	337	44	1	1	NUM
ejpam-6029	337	45	+	+	CCONJ
ejpam-6029	337	46	lc(a	lc(a	NUM
ejpam-6029	337	47	,	,	PUNCT
ejpam-6029	337	48	b	b	NOUN
ejpam-6029	337	49	)	)	PUNCT
ejpam-6029	337	50	+	+	PROPN
ejpam-6029	338	1	λ6(a	λ6(a	NUM
ejpam-6029	338	2	,	,	PUNCT
ejpam-6029	338	3	b	b	NOUN
ejpam-6029	338	4	)	)	PUNCT
ejpam-6029	338	5	[	[	PUNCT
ejpam-6029	338	6	lc(a	lc(a	X
ejpam-6029	338	7	,	,	PUNCT
ejpam-6029	338	8	ta	ta	NOUN
ejpam-6029	338	9	)	)	PUNCT
ejpam-6029	339	1	+	+	CCONJ
ejpam-6029	339	2	lc(b	lc(b	PROPN
ejpam-6029	339	3	,	,	PUNCT
ejpam-6029	339	4	t	t	PROPN
ejpam-6029	339	5	b	b	PROPN
ejpam-6029	339	6	)	)	PUNCT
ejpam-6029	339	7	]	]	PUNCT
ejpam-6029	340	1	lc(ta	lc(ta	ADV
ejpam-6029	340	2	,	,	PUNCT
ejpam-6029	340	3	tb	tb	NOUN
ejpam-6029	340	4	)	)	PUNCT
ejpam-6029	340	5	1	1	NUM
ejpam-6029	341	1	+	+	CCONJ
ejpam-6029	341	2	lc(a	lc(a	NUM
ejpam-6029	341	3	,	,	PUNCT
ejpam-6029	341	4	b	b	NOUN
ejpam-6029	341	5	)	)	PUNCT
ejpam-6029	341	6	+	+	CCONJ
ejpam-6029	341	7	lc(ta	lc(ta	ADJ
ejpam-6029	341	8	,	,	PUNCT
ejpam-6029	341	9	tb	tb	NOUN
ejpam-6029	341	10	)	)	PUNCT
ejpam-6029	341	11	,	,	PUNCT
ejpam-6029	341	12	(	(	PUNCT
ejpam-6029	341	13	12	12	NUM
ejpam-6029	341	14	)	)	PUNCT
ejpam-6029	341	15	for	for	ADP
ejpam-6029	341	16	all	all	DET
ejpam-6029	341	17	a	a	PRON
ejpam-6029	341	18	,	,	PUNCT
ejpam-6029	341	19	b	b	X
ejpam-6029	341	20	∈	∈	PROPN
ejpam-6029	341	21	γ	γ	NOUN
ejpam-6029	341	22	with	with	ADP
ejpam-6029	341	23	∑6	∑6	PROPN
ejpam-6029	341	24	j=1	j=1	PROPN
ejpam-6029	341	25	λj(a	λj(a	NOUN
ejpam-6029	341	26	,	,	PUNCT
ejpam-6029	341	27	b	b	X
ejpam-6029	341	28	)	)	PUNCT
ejpam-6029	341	29	<	<	X
ejpam-6029	341	30	1	1	X
ejpam-6029	341	31	.	.	X
ejpam-6029	341	32	for	for	ADP
ejpam-6029	341	33	a0	a0	PROPN
ejpam-6029	341	34	∈	∈	PROPN
ejpam-6029	341	35	γ	γ	PROPN
ejpam-6029	341	36	,	,	PUNCT
ejpam-6029	341	37	we	we	PRON
ejpam-6029	341	38	take	take	VERB
ejpam-6029	341	39	the	the	DET
ejpam-6029	341	40	sequence	sequence	NOUN
ejpam-6029	341	41	{	{	PUNCT
ejpam-6029	341	42	an	an	PRON
ejpam-6029	341	43	}	}	PUNCT
ejpam-6029	341	44	as	as	ADP
ejpam-6029	341	45	an+1	an+1	NOUN
ejpam-6029	341	46	=	=	SYM
ejpam-6029	341	47	tna0	tna0	PROPN
ejpam-6029	341	48	for	for	ADP
ejpam-6029	341	49	every	every	DET
ejpam-6029	341	50	n	n	PRON
ejpam-6029	341	51	≥	≥	NOUN
ejpam-6029	341	52	0	0	NUM
ejpam-6029	341	53	.	.	PUNCT
ejpam-6029	342	1	let	let	VERB
ejpam-6029	342	2	ξ	ξ	X
ejpam-6029	342	3	=	=	SYM
ejpam-6029	342	4	λ1(a0,a1)+λ2(a0,a1	λ1(a0,a1)+λ2(a0,a1	X
ejpam-6029	342	5	)	)	PUNCT
ejpam-6029	343	1	1−	1−	NUM
ejpam-6029	343	2	∑6	∑6	PROPN
ejpam-6029	343	3	j=3	j=3	CCONJ
ejpam-6029	343	4	λj(a0,a1	λj(a0,a1	NUM
ejpam-6029	343	5	)	)	PUNCT
ejpam-6029	343	6	<	<	X
ejpam-6029	343	7	1	1	X
ejpam-6029	343	8	.	.	PUNCT
ejpam-6029	343	9	suppose	suppose	VERB
ejpam-6029	343	10	that	that	SCONJ
ejpam-6029	343	11	(	(	PUNCT
ejpam-6029	343	12	i	i	NOUN
ejpam-6029	343	13	)	)	PUNCT
ejpam-6029	343	14	f	f	PROPN
ejpam-6029	343	15	and	and	CCONJ
ejpam-6029	343	16	g	g	PROPN
ejpam-6029	343	17	are	be	AUX
ejpam-6029	343	18	bounded	bound	VERB
ejpam-6029	343	19	and	and	CCONJ
ejpam-6029	343	20	non	non	ADJ
ejpam-6029	343	21	-	-	ADJ
ejpam-6029	343	22	decreasing	decrease	VERB
ejpam-6029	343	23	,	,	PUNCT
ejpam-6029	343	24	g	g	PROPN
ejpam-6029	343	25	is	be	AUX
ejpam-6029	343	26	sub	sub	ADJ
ejpam-6029	343	27	-	-	ADJ
ejpam-6029	343	28	additive	additive	ADJ
ejpam-6029	343	29	,	,	PUNCT
ejpam-6029	343	30	and	and	CCONJ
ejpam-6029	343	31	g(λa	g(λa	NOUN
ejpam-6029	343	32	)	)	PUNCT
ejpam-6029	343	33	≺	≺	NOUN
ejpam-6029	343	34	a	a	PRON
ejpam-6029	343	35	,	,	PUNCT
ejpam-6029	343	36	λ	λ	PROPN
ejpam-6029	343	37	∈	∈	PROPN
ejpam-6029	343	38	(	(	PUNCT
ejpam-6029	343	39	0	0	NUM
ejpam-6029	343	40	,	,	PUNCT
ejpam-6029	343	41	1	1	NUM
ejpam-6029	343	42	)	)	PUNCT
ejpam-6029	343	43	;	;	PUNCT
ejpam-6029	343	44	(	(	PUNCT
ejpam-6029	343	45	ii	ii	X
ejpam-6029	343	46	)	)	PUNCT
ejpam-6029	343	47	lim	lim	PROPN
ejpam-6029	343	48	n	n	CCONJ
ejpam-6029	343	49	,	,	PUNCT
ejpam-6029	343	50	m→∞	m→∞	NUM
ejpam-6029	343	51	∑n−2	∑n−2	NOUN
ejpam-6029	344	1	i	i	PRON
ejpam-6029	344	2	=	=	VERB
ejpam-6029	344	3	m	m	VERB
ejpam-6029	344	4	∥gi−mf	∥gi−mf	NOUN
ejpam-6029	344	5	(	(	PUNCT
ejpam-6029	344	6	ξilc(a0	ξilc(a0	NOUN
ejpam-6029	344	7	,	,	PUNCT
ejpam-6029	344	8	a1	a1	NOUN
ejpam-6029	344	9	)	)	PUNCT
ejpam-6029	344	10	)	)	PUNCT
ejpam-6029	344	11	∥+	∥+	PROPN
ejpam-6029	345	1	∥gn−m−1	∥gn−m−1	PROPN
ejpam-6029	345	2	(	(	PUNCT
ejpam-6029	345	3	ξn−1lc(a0	ξn−1lc(a0	PROPN
ejpam-6029	345	4	,	,	PUNCT
ejpam-6029	345	5	a1	a1	NOUN
ejpam-6029	345	6	)	)	PUNCT
ejpam-6029	345	7	)	)	PUNCT
ejpam-6029	345	8	∥	∥	X
ejpam-6029	345	9	=	=	PUNCT
ejpam-6029	346	1	0	0	X
ejpam-6029	346	2	.	.	PUNCT
ejpam-6029	347	1	if	if	SCONJ
ejpam-6029	347	2	for	for	ADP
ejpam-6029	347	3	every	every	DET
ejpam-6029	347	4	fixed	fix	VERB
ejpam-6029	347	5	point	point	NOUN
ejpam-6029	347	6	a	a	ADV
ejpam-6029	347	7	,	,	PUNCT
ejpam-6029	347	8	we	we	PRON
ejpam-6029	347	9	conclude	conclude	VERB
ejpam-6029	347	10	that	that	PRON
ejpam-6029	347	11	lc(a	lc(a	NOUN
ejpam-6029	347	12	,	,	PUNCT
ejpam-6029	347	13	a	a	PRON
ejpam-6029	347	14	)	)	PUNCT
ejpam-6029	347	15	=	=	SYM
ejpam-6029	347	16	0e	0e	NOUN
ejpam-6029	347	17	,	,	PUNCT
ejpam-6029	347	18	then	then	ADV
ejpam-6029	347	19	t	t	PROPN
ejpam-6029	347	20	ensures	ensure	VERB
ejpam-6029	347	21	a	a	DET
ejpam-6029	347	22	unique	unique	ADJ
ejpam-6029	347	23	fixed	fix	VERB
ejpam-6029	347	24	point	point	NOUN
ejpam-6029	347	25	.	.	PUNCT
ejpam-6029	348	1	a.	a.	NOUN
ejpam-6029	348	2	a.	a.	PROPN
ejpam-6029	348	3	hijab	hijab	PROPN
ejpam-6029	348	4	et	et	PROPN
ejpam-6029	348	5	al	al	PROPN
ejpam-6029	348	6	.	.	PUNCT
ejpam-6029	348	7	/	/	SYM
ejpam-6029	348	8	eur	eur	PROPN
ejpam-6029	348	9	.	.	PUNCT
ejpam-6029	349	1	j.	j.	PROPN
ejpam-6029	349	2	pure	pure	PROPN
ejpam-6029	349	3	appl	appl	PROPN
ejpam-6029	349	4	.	.	PROPN
ejpam-6029	349	5	math	math	PROPN
ejpam-6029	349	6	,	,	PUNCT
ejpam-6029	349	7	18	18	NUM
ejpam-6029	349	8	(	(	PUNCT
ejpam-6029	349	9	2	2	NUM
ejpam-6029	349	10	)	)	PUNCT
ejpam-6029	349	11	(	(	PUNCT
ejpam-6029	349	12	2025	2025	NUM
ejpam-6029	349	13	)	)	PUNCT
ejpam-6029	349	14	,	,	PUNCT
ejpam-6029	349	15	6029	6029	NUM
ejpam-6029	349	16	14	14	NUM
ejpam-6029	349	17	of	of	ADP
ejpam-6029	349	18	23	23	NUM
ejpam-6029	349	19	proof	proof	NOUN
ejpam-6029	349	20	.	.	PUNCT
ejpam-6029	350	1	the	the	DET
ejpam-6029	350	2	proof	proof	NOUN
ejpam-6029	350	3	follows	follow	VERB
ejpam-6029	350	4	from	from	ADP
ejpam-6029	350	5	corollary	corollary	ADJ
ejpam-6029	350	6	2	2	NUM
ejpam-6029	350	7	by	by	ADP
ejpam-6029	350	8	setting	set	VERB
ejpam-6029	350	9	the	the	DET
ejpam-6029	350	10	self	self	NOUN
ejpam-6029	350	11	-	-	PUNCT
ejpam-6029	350	12	map	map	NOUN
ejpam-6029	350	13	t	t	NOUN
ejpam-6029	350	14	:	:	PUNCT
ejpam-6029	350	15	γ	γ	X
ejpam-6029	350	16	→	→	SYM
ejpam-6029	350	17	γ	γ	PROPN
ejpam-6029	350	18	as	as	ADP
ejpam-6029	350	19	t1	t1	NOUN
ejpam-6029	350	20	=	=	SYM
ejpam-6029	350	21	t2	t2	PROPN
ejpam-6029	350	22	=	=	SYM
ejpam-6029	350	23	t	t	PROPN
ejpam-6029	350	24	.	.	PUNCT
ejpam-6029	351	1	remark	remark	PROPN
ejpam-6029	351	2	2	2	NUM
ejpam-6029	351	3	.	.	PUNCT
ejpam-6029	352	1	it	it	PRON
ejpam-6029	352	2	is	be	AUX
ejpam-6029	352	3	worth	worth	ADJ
ejpam-6029	352	4	noting	note	VERB
ejpam-6029	352	5	that	that	SCONJ
ejpam-6029	352	6	the	the	DET
ejpam-6029	352	7	fourth	fourth	ADJ
ejpam-6029	352	8	member	member	NOUN
ejpam-6029	352	9	lc(a	lc(a	PUNCT
ejpam-6029	352	10	,	,	PUNCT
ejpam-6029	352	11	ta)lc(b	ta)lc(b	PROPN
ejpam-6029	352	12	,	,	PUNCT
ejpam-6029	352	13	t	t	PROPN
ejpam-6029	352	14	b	b	NUM
ejpam-6029	352	15	)	)	PUNCT
ejpam-6029	352	16	lc(a	lc(a	PROPN
ejpam-6029	352	17	,	,	PUNCT
ejpam-6029	352	18	b	b	NOUN
ejpam-6029	352	19	)	)	PUNCT
ejpam-6029	352	20	in	in	ADP
ejpam-6029	352	21	the	the	DET
ejpam-6029	352	22	sources	source	NOUN
ejpam-6029	352	23	[	[	X
ejpam-6029	352	24	35	35	NUM
ejpam-6029	352	25	,	,	PUNCT
ejpam-6029	352	26	39	39	NUM
ejpam-6029	352	27	]	]	PUNCT
ejpam-6029	352	28	raises	raise	VERB
ejpam-6029	352	29	some	some	DET
ejpam-6029	352	30	doubts	doubt	NOUN
ejpam-6029	352	31	.	.	PUNCT
ejpam-6029	353	1	indeed	indeed	ADV
ejpam-6029	353	2	,	,	PUNCT
ejpam-6029	353	3	it	it	PRON
ejpam-6029	353	4	follows	follow	VERB
ejpam-6029	353	5	from	from	ADP
ejpam-6029	353	6	the	the	DET
ejpam-6029	353	7	proof	proof	NOUN
ejpam-6029	353	8	of	of	ADP
ejpam-6029	353	9	the	the	DET
ejpam-6029	353	10	previous	previous	ADJ
ejpam-6029	353	11	references	reference	NOUN
ejpam-6029	353	12	and	and	CCONJ
ejpam-6029	353	13	others	other	NOUN
ejpam-6029	353	14	results	result	VERB
ejpam-6029	353	15	,	,	PUNCT
ejpam-6029	353	16	as	as	ADV
ejpam-6029	353	17	well	well	ADV
ejpam-6029	353	18	as	as	ADP
ejpam-6029	353	19	some	some	DET
ejpam-6029	353	20	examples	example	NOUN
ejpam-6029	353	21	in	in	ADP
ejpam-6029	353	22	these	these	DET
ejpam-6029	353	23	works	work	NOUN
ejpam-6029	353	24	,	,	PUNCT
ejpam-6029	353	25	from	from	ADP
ejpam-6029	353	26	which	which	PRON
ejpam-6029	353	27	we	we	PRON
ejpam-6029	353	28	obtain	obtain	VERB
ejpam-6029	353	29	the	the	DET
ejpam-6029	353	30	form	form	NOUN
ejpam-6029	353	31	0	0	NUM
ejpam-6029	353	32	0	0	NUM
ejpam-6029	353	33	,	,	PUNCT
ejpam-6029	353	34	a	a	DET
ejpam-6029	353	35	division	division	NOUN
ejpam-6029	353	36	by	by	ADP
ejpam-6029	353	37	zero	zero	NUM
ejpam-6029	353	38	.	.	PUNCT
ejpam-6029	354	1	this	this	PRON
ejpam-6029	354	2	is	be	AUX
ejpam-6029	354	3	incorrect	incorrect	ADJ
ejpam-6029	354	4	since	since	SCONJ
ejpam-6029	354	5	0	0	NUM
ejpam-6029	354	6	is	be	AUX
ejpam-6029	354	7	the	the	DET
ejpam-6029	354	8	unique	unique	ADJ
ejpam-6029	354	9	fixed	fix	VERB
ejpam-6029	354	10	point	point	NOUN
ejpam-6029	354	11	of	of	ADP
ejpam-6029	354	12	map	map	NOUN
ejpam-6029	354	13	t	t	NOUN
ejpam-6029	354	14	or	or	CCONJ
ejpam-6029	354	15	the	the	DET
ejpam-6029	354	16	distance	distance	NOUN
ejpam-6029	354	17	metric	metric	ADJ
ejpam-6029	354	18	approaches	approach	NOUN
ejpam-6029	354	19	zero	zero	NUM
ejpam-6029	354	20	.	.	PUNCT
ejpam-6029	355	1	the	the	DET
ejpam-6029	355	2	main	main	ADJ
ejpam-6029	355	3	motivation	motivation	NOUN
ejpam-6029	355	4	for	for	ADP
ejpam-6029	355	5	our	our	PRON
ejpam-6029	355	6	new	new	ADJ
ejpam-6029	355	7	results	result	NOUN
ejpam-6029	355	8	complements	complement	NOUN
ejpam-6029	355	9	and	and	CCONJ
ejpam-6029	355	10	provides	provide	VERB
ejpam-6029	355	11	entirely	entirely	ADV
ejpam-6029	355	12	new	new	ADJ
ejpam-6029	355	13	observations	observation	NOUN
ejpam-6029	355	14	.	.	PUNCT
ejpam-6029	356	1	remark	remark	PROPN
ejpam-6029	356	2	3	3	NUM
ejpam-6029	356	3	.	.	PUNCT
ejpam-6029	357	1	in	in	ADP
ejpam-6029	357	2	the	the	DET
ejpam-6029	357	3	following	following	NOUN
ejpam-6029	357	4	we	we	PRON
ejpam-6029	357	5	show	show	VERB
ejpam-6029	357	6	that	that	SCONJ
ejpam-6029	357	7	:	:	PUNCT
ejpam-6029	357	8	(	(	PUNCT
ejpam-6029	357	9	i	i	NOUN
ejpam-6029	357	10	)	)	PUNCT
ejpam-6029	357	11	our	our	PRON
ejpam-6029	357	12	results	result	NOUN
ejpam-6029	357	13	represent	represent	VERB
ejpam-6029	357	14	an	an	DET
ejpam-6029	357	15	improvement	improvement	NOUN
ejpam-6029	357	16	and	and	CCONJ
ejpam-6029	357	17	generalization	generalization	NOUN
ejpam-6029	357	18	of	of	ADP
ejpam-6029	357	19	the	the	DET
ejpam-6029	357	20	findings	finding	NOUN
ejpam-6029	357	21	of	of	ADP
ejpam-6029	357	22	lateef	lateef	PROPN
ejpam-6029	358	1	[	[	X
ejpam-6029	358	2	28	28	NUM
ejpam-6029	358	3	]	]	PUNCT
ejpam-6029	358	4	.	.	PUNCT
ejpam-6029	359	1	on	on	ADP
ejpam-6029	359	2	one	one	NUM
ejpam-6029	359	3	hand	hand	NOUN
ejpam-6029	359	4	,	,	PUNCT
ejpam-6029	359	5	if	if	SCONJ
ejpam-6029	359	6	λ2	λ2	NOUN
ejpam-6029	359	7	=	=	SYM
ejpam-6029	359	8	λ3	λ3	PROPN
ejpam-6029	359	9	=	=	NOUN
ejpam-6029	359	10	λ5	λ5	NOUN
ejpam-6029	359	11	=	=	SYM
ejpam-6029	359	12	λ6	λ6	NOUN
ejpam-6029	359	13	=	=	SYM
ejpam-6029	359	14	0	0	PROPN
ejpam-6029	359	15	,	,	PUNCT
ejpam-6029	359	16	the	the	DET
ejpam-6029	359	17	new	new	ADJ
ejpam-6029	359	18	generalized	generalized	ADJ
ejpam-6029	359	19	contraction	contraction	NOUN
ejpam-6029	359	20	becomes	become	VERB
ejpam-6029	359	21	a	a	DET
ejpam-6029	359	22	fisher	fisher	PROPN
ejpam-6029	359	23	contraction	contraction	NOUN
ejpam-6029	359	24	or	or	CCONJ
ejpam-6029	359	25	an	an	DET
ejpam-6029	359	26	improvement	improvement	NOUN
ejpam-6029	359	27	of	of	ADP
ejpam-6029	359	28	jaggi	jaggi	NOUN
ejpam-6029	359	29	work	work	NOUN
ejpam-6029	359	30	[	[	X
ejpam-6029	359	31	29	29	NUM
ejpam-6029	359	32	,	,	PUNCT
ejpam-6029	359	33	30	30	NUM
ejpam-6029	359	34	]	]	PUNCT
ejpam-6029	359	35	regarding	regard	VERB
ejpam-6029	359	36	common	common	ADJ
ejpam-6029	359	37	fixed	fix	VERB
ejpam-6029	359	38	points	point	NOUN
ejpam-6029	359	39	or	or	CCONJ
ejpam-6029	359	40	merely	merely	ADV
ejpam-6029	359	41	fixed	fix	VERB
ejpam-6029	359	42	points	point	NOUN
ejpam-6029	359	43	.	.	PUNCT
ejpam-6029	360	1	moreover	moreover	ADV
ejpam-6029	360	2	,	,	PUNCT
ejpam-6029	360	3	the	the	DET
ejpam-6029	360	4	conclusion	conclusion	NOUN
ejpam-6029	360	5	still	still	ADV
ejpam-6029	360	6	holds	hold	VERB
ejpam-6029	360	7	,	,	PUNCT
ejpam-6029	360	8	i.e.	i.e.	X
ejpam-6029	360	9	,	,	PUNCT
ejpam-6029	360	10	t	t	PROPN
ejpam-6029	360	11	has	have	VERB
ejpam-6029	360	12	a	a	DET
ejpam-6029	360	13	fixed	fix	VERB
ejpam-6029	360	14	point	point	NOUN
ejpam-6029	360	15	.	.	PUNCT
ejpam-6029	361	1	on	on	ADP
ejpam-6029	361	2	the	the	DET
ejpam-6029	361	3	other	other	ADJ
ejpam-6029	361	4	hand	hand	NOUN
ejpam-6029	361	5	,	,	PUNCT
ejpam-6029	361	6	we	we	PRON
ejpam-6029	361	7	extend	extend	VERB
ejpam-6029	361	8	the	the	DET
ejpam-6029	361	9	result	result	NOUN
ejpam-6029	361	10	in	in	ADP
ejpam-6029	361	11	dccml	dccml	NOUN
ejpam-6029	361	12	-	-	PUNCT
ejpam-6029	361	13	spaces	space	NOUN
ejpam-6029	361	14	and	and	CCONJ
ejpam-6029	361	15	c2cms	c2cms	NUM
ejpam-6029	361	16	,	,	PUNCT
ejpam-6029	361	17	instead	instead	ADV
ejpam-6029	361	18	of	of	ADP
ejpam-6029	361	19	dccmls	dccmls	NOUN
ejpam-6029	361	20	and	and	CCONJ
ejpam-6029	361	21	dccmts	dccmts	NOUN
ejpam-6029	361	22	.	.	PUNCT
ejpam-6029	362	1	in	in	ADP
ejpam-6029	362	2	other	other	ADJ
ejpam-6029	362	3	words	word	NOUN
ejpam-6029	362	4	,	,	PUNCT
ejpam-6029	362	5	we	we	PRON
ejpam-6029	362	6	broaden	broaden	VERB
ejpam-6029	362	7	the	the	DET
ejpam-6029	362	8	result	result	NOUN
ejpam-6029	362	9	to	to	ADP
ejpam-6029	362	10	dccml	dccml	NOUN
ejpam-6029	362	11	-	-	PUNCT
ejpam-6029	362	12	spaces	space	NOUN
ejpam-6029	362	13	.	.	PUNCT
ejpam-6029	363	1	(	(	PUNCT
ejpam-6029	363	2	ii	ii	NOUN
ejpam-6029	363	3	)	)	PUNCT
ejpam-6029	363	4	special	special	ADJ
ejpam-6029	363	5	cases	case	NOUN
ejpam-6029	363	6	for	for	ADP
ejpam-6029	363	7	corollaries	corollary	NOUN
ejpam-6029	363	8	2	2	NUM
ejpam-6029	363	9	and	and	CCONJ
ejpam-6029	363	10	5	5	NUM
ejpam-6029	363	11	:	:	PUNCT
ejpam-6029	363	12	case	case	NOUN
ejpam-6029	363	13	1	1	X
ejpam-6029	363	14	.	.	PUNCT
ejpam-6029	364	1	if	if	SCONJ
ejpam-6029	364	2	λ2	λ2	NOUN
ejpam-6029	364	3	=	=	SYM
ejpam-6029	364	4	λ3	λ3	PROPN
ejpam-6029	364	5	=	=	SYM
ejpam-6029	364	6	λ4	λ4	PROPN
ejpam-6029	364	7	=	=	SYM
ejpam-6029	364	8	λ6	λ6	PROPN
ejpam-6029	364	9	=	=	PUNCT
ejpam-6029	364	10	0	0	PROPN
ejpam-6029	364	11	,	,	PUNCT
ejpam-6029	364	12	then	then	ADV
ejpam-6029	364	13	we	we	PRON
ejpam-6029	364	14	obtain	obtain	VERB
ejpam-6029	364	15	the	the	DET
ejpam-6029	364	16	result	result	NOUN
ejpam-6029	364	17	of	of	ADP
ejpam-6029	364	18	the	the	DET
ejpam-6029	364	19	dass	dass	PROPN
ejpam-6029	364	20	and	and	CCONJ
ejpam-6029	364	21	gupta	gupta	PROPN
ejpam-6029	364	22	contraction	contraction	PROPN
ejpam-6029	364	23	,	,	PUNCT
ejpam-6029	364	24	where	where	SCONJ
ejpam-6029	364	25	λ1(a	λ1(a	NOUN
ejpam-6029	364	26	,	,	PUNCT
ejpam-6029	364	27	b	b	NOUN
ejpam-6029	364	28	)	)	PUNCT
ejpam-6029	364	29	=	=	SYM
ejpam-6029	364	30	k1	k1	NOUN
ejpam-6029	364	31	and	and	CCONJ
ejpam-6029	364	32	λ5(a	λ5(a	NOUN
ejpam-6029	364	33	,	,	PUNCT
ejpam-6029	364	34	b	b	NOUN
ejpam-6029	364	35	)	)	PUNCT
ejpam-6029	364	36	=	=	SYM
ejpam-6029	364	37	k2	k2	PROPN
ejpam-6029	364	38	,	,	PUNCT
ejpam-6029	364	39	k1	k1	PROPN
ejpam-6029	364	40	,	,	PUNCT
ejpam-6029	364	41	k2	k2	PROPN
ejpam-6029	364	42	∈	∈	PROPN
ejpam-6029	364	43	(	(	PUNCT
ejpam-6029	364	44	0	0	NUM
ejpam-6029	364	45	,	,	PUNCT
ejpam-6029	364	46	1	1	NUM
ejpam-6029	364	47	)	)	PUNCT
ejpam-6029	364	48	,	,	PUNCT
ejpam-6029	364	49	(	(	PUNCT
ejpam-6029	364	50	see	see	VERB
ejpam-6029	364	51	,	,	PUNCT
ejpam-6029	364	52	[	[	X
ejpam-6029	364	53	29	29	NUM
ejpam-6029	364	54	]	]	SYM
ejpam-6029	364	55	)	)	PUNCT
ejpam-6029	364	56	.	.	PUNCT
ejpam-6029	365	1	case	case	NOUN
ejpam-6029	365	2	2	2	X
ejpam-6029	365	3	.	.	PUNCT
ejpam-6029	366	1	if	if	SCONJ
ejpam-6029	366	2	λ2	λ2	NOUN
ejpam-6029	366	3	=	=	SYM
ejpam-6029	366	4	λ3	λ3	PROPN
ejpam-6029	366	5	=	=	SYM
ejpam-6029	366	6	λ4	λ4	ADJ
ejpam-6029	366	7	=	=	NOUN
ejpam-6029	367	1	λ5	λ5	NOUN
ejpam-6029	367	2	=	=	SYM
ejpam-6029	367	3	λ6	λ6	NOUN
ejpam-6029	367	4	=	=	SYM
ejpam-6029	367	5	0	0	PROPN
ejpam-6029	367	6	,	,	PUNCT
ejpam-6029	367	7	then	then	ADV
ejpam-6029	367	8	we	we	PRON
ejpam-6029	367	9	obtain	obtain	VERB
ejpam-6029	367	10	the	the	DET
ejpam-6029	367	11	result	result	NOUN
ejpam-6029	367	12	of	of	ADP
ejpam-6029	367	13	extending	extend	VERB
ejpam-6029	367	14	banach	banach	NOUN
ejpam-6029	367	15	contraction	contraction	NOUN
ejpam-6029	367	16	principle	principle	NOUN
ejpam-6029	367	17	.	.	PUNCT
ejpam-6029	368	1	case	case	NOUN
ejpam-6029	368	2	3	3	X
ejpam-6029	368	3	.	.	X
ejpam-6029	369	1	if	if	SCONJ
ejpam-6029	369	2	λ1	λ1	PROPN
ejpam-6029	369	3	=	=	SYM
ejpam-6029	369	4	λ4	λ4	NOUN
ejpam-6029	369	5	=	=	NOUN
ejpam-6029	370	1	λ5	λ5	NOUN
ejpam-6029	370	2	=	=	SYM
ejpam-6029	370	3	λ6	λ6	NOUN
ejpam-6029	370	4	=	=	SYM
ejpam-6029	370	5	0	0	PROPN
ejpam-6029	370	6	,	,	PUNCT
ejpam-6029	370	7	then	then	ADV
ejpam-6029	370	8	we	we	PRON
ejpam-6029	370	9	obtain	obtain	VERB
ejpam-6029	370	10	the	the	DET
ejpam-6029	370	11	result	result	NOUN
ejpam-6029	370	12	of	of	ADP
ejpam-6029	370	13	extending	extend	VERB
ejpam-6029	370	14	kannan	kannan	PROPN
ejpam-6029	370	15	’s	’s	PART
ejpam-6029	370	16	contraction	contraction	NOUN
ejpam-6029	370	17	.	.	PUNCT
ejpam-6029	371	1	case	case	NOUN
ejpam-6029	371	2	4	4	NUM
ejpam-6029	371	3	.	.	PUNCT
ejpam-6029	372	1	if	if	SCONJ
ejpam-6029	372	2	λ4	λ4	PROPN
ejpam-6029	372	3	=	=	SYM
ejpam-6029	372	4	λ5	λ5	NOUN
ejpam-6029	372	5	=	=	SYM
ejpam-6029	372	6	λ6	λ6	NOUN
ejpam-6029	372	7	=	=	SYM
ejpam-6029	372	8	0	0	PROPN
ejpam-6029	372	9	,	,	PUNCT
ejpam-6029	372	10	then	then	ADV
ejpam-6029	372	11	we	we	PRON
ejpam-6029	372	12	obtain	obtain	VERB
ejpam-6029	372	13	the	the	DET
ejpam-6029	372	14	result	result	NOUN
ejpam-6029	372	15	of	of	ADP
ejpam-6029	372	16	extending	extend	VERB
ejpam-6029	372	17	the	the	DET
ejpam-6029	372	18	riech	riech	NOUN
ejpam-6029	372	19	-	-	PUNCT
ejpam-6029	372	20	type	type	NOUN
ejpam-6029	372	21	contraction	contraction	NOUN
ejpam-6029	372	22	(	(	PUNCT
ejpam-6029	372	23	see	see	VERB
ejpam-6029	372	24	[	[	X
ejpam-6029	372	25	19	19	NUM
ejpam-6029	372	26	]	]	NUM
ejpam-6029	372	27	)	)	PUNCT
ejpam-6029	372	28	.	.	PUNCT
ejpam-6029	373	1	(	(	PUNCT
ejpam-6029	373	2	iii	iii	X
ejpam-6029	373	3	)	)	PUNCT
ejpam-6029	373	4	through	through	ADP
ejpam-6029	373	5	remark	remark	NOUN
ejpam-6029	373	6	1	1	NUM
ejpam-6029	373	7	,	,	PUNCT
ejpam-6029	373	8	we	we	PRON
ejpam-6029	373	9	know	know	VERB
ejpam-6029	373	10	that	that	SCONJ
ejpam-6029	373	11	every	every	DET
ejpam-6029	373	12	c2cms	c2cms	PROPN
ejpam-6029	373	13	is	be	AUX
ejpam-6029	373	14	a	a	DET
ejpam-6029	373	15	dccml	dccml	NOUN
ejpam-6029	373	16	-	-	PUNCT
ejpam-6029	373	17	space	space	NOUN
ejpam-6029	373	18	,	,	PUNCT
ejpam-6029	373	19	and	and	CCONJ
ejpam-6029	373	20	the	the	DET
ejpam-6029	373	21	selfdistance	selfdistance	NOUN
ejpam-6029	373	22	in	in	ADP
ejpam-6029	373	23	the	the	DET
ejpam-6029	373	24	latter	latter	NOUN
ejpam-6029	373	25	does	do	AUX
ejpam-6029	373	26	not	not	PART
ejpam-6029	373	27	need	need	VERB
ejpam-6029	373	28	to	to	PART
ejpam-6029	373	29	be	be	AUX
ejpam-6029	373	30	zero	zero	NUM
ejpam-6029	373	31	.	.	PUNCT
ejpam-6029	374	1	thus	thus	ADV
ejpam-6029	374	2	,	,	PUNCT
ejpam-6029	374	3	the	the	DET
ejpam-6029	374	4	new	new	ADJ
ejpam-6029	374	5	results	result	NOUN
ejpam-6029	374	6	are	be	AUX
ejpam-6029	374	7	still	still	ADV
ejpam-6029	374	8	valid	valid	ADJ
ejpam-6029	374	9	in	in	ADP
ejpam-6029	374	10	c2cms	c2cms	PROPN
ejpam-6029	374	11	.	.	PUNCT
ejpam-6029	375	1	(	(	PUNCT
ejpam-6029	375	2	iv	iv	X
ejpam-6029	375	3	)	)	PUNCT
ejpam-6029	375	4	towards	towards	ADP
ejpam-6029	375	5	the	the	DET
ejpam-6029	375	6	six	six	NUM
ejpam-6029	375	7	-	-	PUNCT
ejpam-6029	375	8	member	member	NOUN
ejpam-6029	375	9	in	in	ADP
ejpam-6029	375	10	corollary	corollary	ADJ
ejpam-6029	375	11	2	2	NUM
ejpam-6029	375	12	we	we	PRON
ejpam-6029	375	13	can	can	AUX
ejpam-6029	375	14	that	that	PRON
ejpam-6029	375	15	obtained	obtain	VERB
ejpam-6029	375	16	as	as	ADP
ejpam-6029	375	17	the	the	DET
ejpam-6029	375	18	form	form	NOUN
ejpam-6029	375	19	lc(a	lc(a	NOUN
ejpam-6029	375	20	,	,	PUNCT
ejpam-6029	375	21	t1a)lc(b	t1a)lc(b	NOUN
ejpam-6029	375	22	,	,	PUNCT
ejpam-6029	375	23	t1a)+lc(b	t1a)+lc(b	NOUN
ejpam-6029	375	24	,	,	PUNCT
ejpam-6029	375	25	t2b)lc(a	t2b)lc(a	PROPN
ejpam-6029	375	26	,	,	PUNCT
ejpam-6029	375	27	t2b	t2b	PROPN
ejpam-6029	375	28	)	)	PUNCT
ejpam-6029	375	29	1+lc(b	1+lc(b	NUM
ejpam-6029	375	30	,	,	PUNCT
ejpam-6029	375	31	t1a)+lc(a	t1a)+lc(a	PROPN
ejpam-6029	375	32	,	,	PUNCT
ejpam-6029	375	33	t2b	t2b	PROPN
ejpam-6029	375	34	)	)	PUNCT
ejpam-6029	375	35	,	,	PUNCT
ejpam-6029	375	36	which	which	PRON
ejpam-6029	375	37	implies	imply	VERB
ejpam-6029	375	38	that	that	SCONJ
ejpam-6029	375	39	it	it	PRON
ejpam-6029	375	40	is	be	AUX
ejpam-6029	375	41	less	less	ADJ
ejpam-6029	375	42	than	than	ADP
ejpam-6029	375	43	and	and	CCONJ
ejpam-6029	375	44	equal	equal	ADJ
ejpam-6029	375	45	to	to	ADP
ejpam-6029	375	46	lc(a	lc(a	NUM
ejpam-6029	375	47	,	,	PUNCT
ejpam-6029	375	48	t1a	t1a	NUM
ejpam-6029	375	49	)	)	PUNCT
ejpam-6029	376	1	+	+	NOUN
ejpam-6029	376	2	lc(b	lc(b	ADJ
ejpam-6029	376	3	,	,	PUNCT
ejpam-6029	376	4	t2b	t2b	PROPN
ejpam-6029	376	5	)	)	PUNCT
ejpam-6029	376	6	.	.	PUNCT
ejpam-6029	377	1	so	so	ADV
ejpam-6029	377	2	,	,	PUNCT
ejpam-6029	377	3	we	we	PRON
ejpam-6029	377	4	go	go	VERB
ejpam-6029	377	5	again	again	ADV
ejpam-6029	377	6	to	to	ADP
ejpam-6029	377	7	the	the	DET
ejpam-6029	377	8	second	second	ADJ
ejpam-6029	377	9	and	and	CCONJ
ejpam-6029	377	10	third	third	ADJ
ejpam-6029	377	11	members	member	NOUN
ejpam-6029	377	12	.	.	PUNCT
ejpam-6029	378	1	thus	thus	ADV
ejpam-6029	378	2	,	,	PUNCT
ejpam-6029	378	3	we	we	PRON
ejpam-6029	378	4	discuss	discuss	VERB
ejpam-6029	378	5	the	the	DET
ejpam-6029	378	6	result	result	NOUN
ejpam-6029	378	7	obtained	obtain	VERB
ejpam-6029	378	8	.	.	PUNCT
ejpam-6029	379	1	we	we	PRON
ejpam-6029	379	2	present	present	VERB
ejpam-6029	379	3	some	some	DET
ejpam-6029	379	4	examples	example	NOUN
ejpam-6029	379	5	below	below	ADV
ejpam-6029	379	6	to	to	PART
ejpam-6029	379	7	verify	verify	VERB
ejpam-6029	379	8	our	our	PRON
ejpam-6029	379	9	theorems	theorem	NOUN
ejpam-6029	379	10	.	.	PUNCT
ejpam-6029	379	11	example	example	NOUN
ejpam-6029	379	12	4	4	NUM
ejpam-6029	379	13	.	.	X
ejpam-6029	380	1	consider	consider	VERB
ejpam-6029	380	2	e	e	NOUN
ejpam-6029	380	3	=	=	NOUN
ejpam-6029	380	4	r2	r2	PROPN
ejpam-6029	380	5	,	,	PUNCT
ejpam-6029	380	6	p	p	NOUN
ejpam-6029	380	7	=	=	X
ejpam-6029	380	8	{	{	PUNCT
ejpam-6029	380	9	u	u	NOUN
ejpam-6029	380	10	=	=	SYM
ejpam-6029	380	11	(	(	PUNCT
ejpam-6029	380	12	r	r	NOUN
ejpam-6029	380	13	,	,	PUNCT
ejpam-6029	380	14	s	s	NOUN
ejpam-6029	380	15	)	)	PUNCT
ejpam-6029	380	16	∈	∈	PROPN
ejpam-6029	380	17	e	e	NOUN
ejpam-6029	380	18	:	:	PUNCT
ejpam-6029	380	19	r	r	X
ejpam-6029	380	20	,	,	PUNCT
ejpam-6029	380	21	s	s	PART
ejpam-6029	380	22	≥	≥	NOUN
ejpam-6029	380	23	0	0	NUM
ejpam-6029	380	24	}	}	PUNCT
ejpam-6029	380	25	,	,	PUNCT
ejpam-6029	380	26	and	and	CCONJ
ejpam-6029	380	27	γ	γ	X
ejpam-6029	380	28	=	=	SYM
ejpam-6029	381	1	[	[	X
ejpam-6029	381	2	0	0	NUM
ejpam-6029	381	3	,	,	PUNCT
ejpam-6029	381	4	1	1	NUM
ejpam-6029	381	5	]	]	PUNCT
ejpam-6029	381	6	.	.	PUNCT
ejpam-6029	382	1	now	now	ADV
ejpam-6029	382	2	,	,	PUNCT
ejpam-6029	382	3	lc	lc	PROPN
ejpam-6029	382	4	:	:	PUNCT
ejpam-6029	382	5	γ×	γ×	PROPN
ejpam-6029	382	6	γ	γ	X
ejpam-6029	382	7	→	→	SYM
ejpam-6029	382	8	e	e	X
ejpam-6029	382	9	is	be	AUX
ejpam-6029	382	10	defined	define	VERB
ejpam-6029	382	11	by	by	ADP
ejpam-6029	382	12	lc(a	lc(a	PROPN
ejpam-6029	382	13	,	,	PUNCT
ejpam-6029	382	14	b	b	X
ejpam-6029	382	15	)	)	PUNCT
ejpam-6029	382	16	=	=	SYM
ejpam-6029	382	17	(	(	PUNCT
ejpam-6029	382	18	sinh	sinh	PROPN
ejpam-6029	382	19	(	(	PUNCT
ejpam-6029	382	20	(	(	PUNCT
ejpam-6029	382	21	a+b)2	a+b)2	PROPN
ejpam-6029	382	22	2	2	NUM
ejpam-6029	382	23	)	)	PUNCT
ejpam-6029	382	24	,	,	PUNCT
ejpam-6029	382	25	0	0	NUM
ejpam-6029	382	26	)	)	PUNCT
ejpam-6029	382	27	.	.	PUNCT
ejpam-6029	383	1	then	then	ADV
ejpam-6029	383	2	lc	lc	PROPN
ejpam-6029	383	3	is	be	AUX
ejpam-6029	383	4	a	a	DET
ejpam-6029	383	5	dccml	dccml	NOUN
ejpam-6029	383	6	-	-	PUNCT
ejpam-6029	383	7	space	space	NOUN
ejpam-6029	383	8	with	with	ADP
ejpam-6029	383	9	two	two	NUM
ejpam-6029	383	10	functions	function	NOUN
ejpam-6029	383	11	,	,	PUNCT
ejpam-6029	383	12	f(u	f(u	PROPN
ejpam-6029	383	13	)	)	PUNCT
ejpam-6029	383	14	=(	=(	NOUN
ejpam-6029	383	15	sinh((a+b+2)r	sinh((a+b+2)r	PROPN
ejpam-6029	383	16	)	)	PUNCT
ejpam-6029	383	17	,	,	PUNCT
ejpam-6029	383	18	0	0	NUM
ejpam-6029	383	19	)	)	PUNCT
ejpam-6029	383	20	and	and	CCONJ
ejpam-6029	383	21	g(u	g(u	PROPN
ejpam-6029	383	22	)	)	PUNCT
ejpam-6029	383	23	=	=	PRON
ejpam-6029	383	24	(	(	PUNCT
ejpam-6029	383	25	sinh((a2+b2	sinh((a2+b2	PROPN
ejpam-6029	383	26	+	+	NOUN
ejpam-6029	383	27	1)r	1)r	NUM
ejpam-6029	383	28	)	)	PUNCT
ejpam-6029	383	29	,	,	PUNCT
ejpam-6029	383	30	0	0	NUM
ejpam-6029	383	31	)	)	PUNCT
ejpam-6029	383	32	,	,	PUNCT
ejpam-6029	384	1	where	where	SCONJ
ejpam-6029	384	2	u	u	PROPN
ejpam-6029	384	3	∈	∈	PROPN
ejpam-6029	384	4	p	p	X
ejpam-6029	384	5	,	,	PUNCT
ejpam-6029	384	6	by	by	ADP
ejpam-6029	384	7	the	the	DET
ejpam-6029	384	8	same	same	ADJ
ejpam-6029	384	9	process	process	NOUN
ejpam-6029	384	10	a.	a.	NOUN
ejpam-6029	384	11	a.	a.	PROPN
ejpam-6029	384	12	hijab	hijab	PROPN
ejpam-6029	384	13	et	et	PROPN
ejpam-6029	384	14	al	al	PROPN
ejpam-6029	384	15	.	.	PUNCT
ejpam-6029	384	16	/	/	SYM
ejpam-6029	384	17	eur	eur	PROPN
ejpam-6029	384	18	.	.	PUNCT
ejpam-6029	385	1	j.	j.	PROPN
ejpam-6029	385	2	pure	pure	PROPN
ejpam-6029	385	3	appl	appl	PROPN
ejpam-6029	385	4	.	.	PROPN
ejpam-6029	385	5	math	math	PROPN
ejpam-6029	385	6	,	,	PUNCT
ejpam-6029	385	7	18	18	NUM
ejpam-6029	385	8	(	(	PUNCT
ejpam-6029	385	9	2	2	NUM
ejpam-6029	385	10	)	)	PUNCT
ejpam-6029	385	11	(	(	PUNCT
ejpam-6029	385	12	2025	2025	NUM
ejpam-6029	385	13	)	)	PUNCT
ejpam-6029	385	14	,	,	PUNCT
ejpam-6029	385	15	6029	6029	NUM
ejpam-6029	385	16	15	15	NUM
ejpam-6029	385	17	of	of	ADP
ejpam-6029	385	18	23	23	NUM
ejpam-6029	385	19	as	as	ADP
ejpam-6029	385	20	for	for	ADP
ejpam-6029	385	21	example	example	NOUN
ejpam-6029	385	22	3	3	NUM
ejpam-6029	385	23	,	,	PUNCT
ejpam-6029	385	24	where	where	SCONJ
ejpam-6029	385	25	the	the	DET
ejpam-6029	385	26	function	function	NOUN
ejpam-6029	385	27	(	(	PUNCT
ejpam-6029	385	28	a+b)2	a+b)2	NOUN
ejpam-6029	385	29	2	2	NUM
ejpam-6029	385	30	is	be	AUX
ejpam-6029	385	31	a	a	DET
ejpam-6029	385	32	dcmls	dcmls	NOUN
ejpam-6029	385	33	.	.	PUNCT
ejpam-6029	386	1	moreover	moreover	ADV
ejpam-6029	386	2	,	,	PUNCT
ejpam-6029	386	3	(	(	PUNCT
ejpam-6029	386	4	a1	a1	PROPN
ejpam-6029	386	5	,	,	PUNCT
ejpam-6029	386	6	b1)(a2	b1)(a2	PROPN
ejpam-6029	386	7	,	,	PUNCT
ejpam-6029	386	8	b2	b2	NOUN
ejpam-6029	386	9	)	)	PUNCT
ejpam-6029	386	10	=	=	SYM
ejpam-6029	387	1	(	(	PUNCT
ejpam-6029	387	2	a1a2	a1a2	PROPN
ejpam-6029	387	3	,	,	PUNCT
ejpam-6029	387	4	b1b2	b1b2	NOUN
ejpam-6029	387	5	)	)	PUNCT
ejpam-6029	387	6	is	be	AUX
ejpam-6029	387	7	defined	define	VERB
ejpam-6029	387	8	in	in	ADP
ejpam-6029	387	9	[	[	X
ejpam-6029	387	10	40	40	NUM
ejpam-6029	387	11	]	]	PUNCT
ejpam-6029	387	12	.	.	PUNCT
ejpam-6029	388	1	define	define	VERB
ejpam-6029	388	2	t1	t1	NOUN
ejpam-6029	388	3	,	,	PUNCT
ejpam-6029	388	4	t2	t2	NOUN
ejpam-6029	388	5	:	:	PUNCT
ejpam-6029	388	6	γ	γ	X
ejpam-6029	388	7	→	→	SYM
ejpam-6029	388	8	γ	γ	X
ejpam-6029	388	9	by	by	ADP
ejpam-6029	388	10	t1a	t1a	NOUN
ejpam-6029	388	11	=	=	SYM
ejpam-6029	388	12	a	a	DET
ejpam-6029	388	13	2	2	NUM
ejpam-6029	388	14	and	and	CCONJ
ejpam-6029	388	15	t2a	t2a	ADP
ejpam-6029	388	16	=	=	PUNCT
ejpam-6029	388	17	a	a	DET
ejpam-6029	388	18	3	3	NUM
ejpam-6029	388	19	,	,	PUNCT
ejpam-6029	388	20	for	for	SCONJ
ejpam-6029	388	21	a	a	DET
ejpam-6029	388	22	∈	∈	PROPN
ejpam-6029	388	23	r.	r.	PROPN
ejpam-6029	388	24	choose	choose	VERB
ejpam-6029	388	25	λj	λj	PROPN
ejpam-6029	388	26	:	:	PUNCT
ejpam-6029	388	27	γ×	γ×	PROPN
ejpam-6029	388	28	γ	γ	X
ejpam-6029	388	29	→	→	SYM
ejpam-6029	389	1	[	[	X
ejpam-6029	389	2	0	0	NUM
ejpam-6029	389	3	,	,	PUNCT
ejpam-6029	389	4	1	1	NUM
ejpam-6029	389	5	)	)	PUNCT
ejpam-6029	389	6	,	,	PUNCT
ejpam-6029	389	7	for	for	ADP
ejpam-6029	389	8	j	j	PROPN
ejpam-6029	389	9	=	=	SYM
ejpam-6029	389	10	1	1	NUM
ejpam-6029	389	11	,	,	PUNCT
ejpam-6029	389	12	·	·	PUNCT
ejpam-6029	389	13	·	·	PUNCT
ejpam-6029	389	14	·	·	PUNCT
ejpam-6029	389	15	,	,	PUNCT
ejpam-6029	389	16	6	6	NUM
ejpam-6029	389	17	by	by	ADP
ejpam-6029	389	18	λ1(a	λ1(a	PROPN
ejpam-6029	389	19	,	,	PUNCT
ejpam-6029	389	20	b	b	NOUN
ejpam-6029	389	21	)	)	PUNCT
ejpam-6029	389	22	=	=	SYM
ejpam-6029	389	23	5+a+b	5+a+b	NUM
ejpam-6029	389	24	36	36	NUM
ejpam-6029	389	25	,	,	PUNCT
ejpam-6029	389	26	λ2(a	λ2(a	NOUN
ejpam-6029	389	27	,	,	PUNCT
ejpam-6029	389	28	b	b	NOUN
ejpam-6029	389	29	)	)	PUNCT
ejpam-6029	389	30	=	=	SYM
ejpam-6029	390	1	3+a+b	3+a+b	NUM
ejpam-6029	390	2	36	36	NUM
ejpam-6029	390	3	,	,	PUNCT
ejpam-6029	390	4	λ3(a	λ3(a	X
ejpam-6029	390	5	,	,	PUNCT
ejpam-6029	390	6	b	b	NOUN
ejpam-6029	390	7	)	)	PUNCT
ejpam-6029	390	8	=	=	PUNCT
ejpam-6029	391	1	2+a+b	2+a+b	NUM
ejpam-6029	391	2	36	36	NUM
ejpam-6029	391	3	,	,	PUNCT
ejpam-6029	391	4	λ4(a	λ4(a	PROPN
ejpam-6029	391	5	,	,	PUNCT
ejpam-6029	391	6	b	b	NOUN
ejpam-6029	391	7	)	)	PUNCT
ejpam-6029	391	8	=	=	SYM
ejpam-6029	391	9	4+a+b	4+a+b	NUM
ejpam-6029	391	10	36	36	NUM
ejpam-6029	391	11	,	,	PUNCT
ejpam-6029	391	12	λ5(a	λ5(a	X
ejpam-6029	391	13	,	,	PUNCT
ejpam-6029	391	14	b	b	NOUN
ejpam-6029	391	15	)	)	PUNCT
ejpam-6029	391	16	=	=	SYM
ejpam-6029	392	1	6+a+b	6+a+b	NUM
ejpam-6029	392	2	36	36	NUM
ejpam-6029	392	3	and	and	CCONJ
ejpam-6029	392	4	λ6(a	λ6(a	PROPN
ejpam-6029	392	5	,	,	PUNCT
ejpam-6029	392	6	b	b	NOUN
ejpam-6029	392	7	)	)	PUNCT
ejpam-6029	392	8	=	=	SYM
ejpam-6029	393	1	0	0	X
ejpam-6029	393	2	.	.	PUNCT
ejpam-6029	394	1	then	then	ADV
ejpam-6029	394	2	,	,	PUNCT
ejpam-6029	394	3	evidently	evidently	ADV
ejpam-6029	394	4	,	,	PUNCT
ejpam-6029	394	5	∑6	∑6	PROPN
ejpam-6029	394	6	j=1	j=1	PROPN
ejpam-6029	394	7	λj(a	λj(a	NOUN
ejpam-6029	394	8	,	,	PUNCT
ejpam-6029	394	9	b	b	X
ejpam-6029	394	10	)	)	PUNCT
ejpam-6029	394	11	=	=	SYM
ejpam-6029	394	12	20	20	NUM
ejpam-6029	394	13	+	+	SYM
ejpam-6029	394	14	5a+5b	5a+5b	NUM
ejpam-6029	394	15	36	36	NUM
ejpam-6029	394	16	<	<	X
ejpam-6029	394	17	1	1	NUM
ejpam-6029	394	18	.	.	PUNCT
ejpam-6029	394	19	also	also	ADV
ejpam-6029	394	20	,	,	PUNCT
ejpam-6029	394	21	λj(a	λj(a	PRON
ejpam-6029	394	22	,	,	PUNCT
ejpam-6029	394	23	b	b	X
ejpam-6029	394	24	)	)	PUNCT
ejpam-6029	394	25	∈	∈	PROPN
ejpam-6029	394	26	∆	∆	PROPN
ejpam-6029	394	27	with	with	ADP
ejpam-6029	394	28	two	two	NUM
ejpam-6029	394	29	maps	map	NOUN
ejpam-6029	394	30	t1	t1	NOUN
ejpam-6029	394	31	and	and	CCONJ
ejpam-6029	394	32	t2	t2	NOUN
ejpam-6029	394	33	for	for	ADP
ejpam-6029	394	34	all	all	DET
ejpam-6029	394	35	j	j	NOUN
ejpam-6029	395	1	=	=	SYM
ejpam-6029	395	2	1	1	NUM
ejpam-6029	395	3	,	,	PUNCT
ejpam-6029	395	4	·	·	PUNCT
ejpam-6029	395	5	·	·	PUNCT
ejpam-6029	395	6	·	·	PUNCT
ejpam-6029	395	7	,	,	PUNCT
ejpam-6029	395	8	6	6	X
ejpam-6029	395	9	.	.	PUNCT
ejpam-6029	396	1	now	now	ADV
ejpam-6029	396	2	,	,	PUNCT
ejpam-6029	396	3	consider	consider	VERB
ejpam-6029	396	4	a0	a0	NOUN
ejpam-6029	396	5	=	=	SYM
ejpam-6029	396	6	0	0	PROPN
ejpam-6029	396	7	and	and	CCONJ
ejpam-6029	396	8	a	a	DET
ejpam-6029	396	9	,	,	PUNCT
ejpam-6029	396	10	b	b	PROPN
ejpam-6029	396	11	∈	∈	PROPN
ejpam-6029	396	12	γ	γ	X
ejpam-6029	396	13	.	.	PROPN
ejpam-6029	397	1	then	then	ADV
ejpam-6029	397	2	,	,	PUNCT
ejpam-6029	397	3	lc(t1a	lc(t1a	PROPN
ejpam-6029	397	4	,	,	PUNCT
ejpam-6029	397	5	t2b	t2b	PROPN
ejpam-6029	397	6	)	)	PUNCT
ejpam-6029	397	7	=	=	PRON
ejpam-6029	397	8	(	(	PUNCT
ejpam-6029	397	9	sinh	sinh	PROPN
ejpam-6029	397	10	(	(	PUNCT
ejpam-6029	397	11	(	(	PUNCT
ejpam-6029	397	12	3a+	3a+	NUM
ejpam-6029	397	13	2b)2	2b)2	NUM
ejpam-6029	397	14	72	72	NUM
ejpam-6029	397	15	)	)	PUNCT
ejpam-6029	397	16	,	,	PUNCT
ejpam-6029	397	17	0	0	X
ejpam-6029	397	18	)	)	PUNCT
ejpam-6029	397	19	⪯	⪯	NOUN
ejpam-6029	397	20	5	5	NUM
ejpam-6029	398	1	+	+	CCONJ
ejpam-6029	398	2	a+	a+	PRON
ejpam-6029	398	3	b	b	X
ejpam-6029	398	4	36	36	NUM
ejpam-6029	398	5	(	(	PUNCT
ejpam-6029	398	6	sinh	sinh	PROPN
ejpam-6029	398	7	(	(	PUNCT
ejpam-6029	398	8	(	(	PUNCT
ejpam-6029	398	9	a+	a+	PRON
ejpam-6029	398	10	b)2	b)2	PROPN
ejpam-6029	398	11	2	2	NUM
ejpam-6029	398	12	)	)	PUNCT
ejpam-6029	398	13	,	,	PUNCT
ejpam-6029	398	14	0	0	NUM
ejpam-6029	398	15	)	)	PUNCT
ejpam-6029	399	1	+	+	CCONJ
ejpam-6029	399	2	3	3	NUM
ejpam-6029	399	3	+	+	NUM
ejpam-6029	399	4	a+	a+	PRON
ejpam-6029	399	5	b	b	X
ejpam-6029	399	6	36	36	NUM
ejpam-6029	399	7	(	(	PUNCT
ejpam-6029	399	8	sinh	sinh	PROPN
ejpam-6029	399	9	(	(	PUNCT
ejpam-6029	399	10	9a2	9a2	NUM
ejpam-6029	399	11	8	8	NUM
ejpam-6029	399	12	)	)	PUNCT
ejpam-6029	399	13	,	,	PUNCT
ejpam-6029	399	14	0	0	NUM
ejpam-6029	399	15	)	)	PUNCT
ejpam-6029	400	1	+	+	CCONJ
ejpam-6029	400	2	2	2	NUM
ejpam-6029	400	3	+	+	NUM
ejpam-6029	400	4	a+	a+	PRON
ejpam-6029	400	5	b	b	X
ejpam-6029	400	6	36	36	NUM
ejpam-6029	400	7	(	(	PUNCT
ejpam-6029	400	8	sinh	sinh	PROPN
ejpam-6029	400	9	(	(	PUNCT
ejpam-6029	400	10	16b2	16b2	NUM
ejpam-6029	400	11	18	18	NUM
ejpam-6029	400	12	)	)	PUNCT
ejpam-6029	400	13	,	,	PUNCT
ejpam-6029	400	14	0	0	NUM
ejpam-6029	400	15	)	)	PUNCT
ejpam-6029	401	1	+	+	CCONJ
ejpam-6029	401	2	4	4	NUM
ejpam-6029	401	3	+	+	NUM
ejpam-6029	401	4	a+	a+	PRON
ejpam-6029	401	5	b	b	X
ejpam-6029	401	6	36	36	NUM
ejpam-6029	401	7	(	(	PUNCT
ejpam-6029	401	8	sinh	sinh	PROPN
ejpam-6029	401	9	(	(	PUNCT
ejpam-6029	401	10	9a2	9a2	NUM
ejpam-6029	401	11	8	8	NUM
ejpam-6029	401	12	)	)	PUNCT
ejpam-6029	401	13	sinh	sinh	NOUN
ejpam-6029	401	14	(	(	PUNCT
ejpam-6029	401	15	16b2	16b2	NUM
ejpam-6029	401	16	18	18	NUM
ejpam-6029	401	17	)	)	PUNCT
ejpam-6029	401	18	,	,	PUNCT
ejpam-6029	401	19	0	0	NUM
ejpam-6029	401	20	)	)	PUNCT
ejpam-6029	401	21	1	1	NUM
ejpam-6029	402	1	+	+	CCONJ
ejpam-6029	402	2	(	(	PUNCT
ejpam-6029	402	3	sinh	sinh	PROPN
ejpam-6029	402	4	(	(	PUNCT
ejpam-6029	402	5	(	(	PUNCT
ejpam-6029	402	6	a+b)2	a+b)2	PROPN
ejpam-6029	402	7	2	2	NUM
ejpam-6029	402	8	)	)	PUNCT
ejpam-6029	402	9	,	,	PUNCT
ejpam-6029	402	10	0	0	NUM
ejpam-6029	402	11	)	)	PUNCT
ejpam-6029	403	1	+	+	CCONJ
ejpam-6029	403	2	6	6	NUM
ejpam-6029	403	3	+	+	CCONJ
ejpam-6029	403	4	a+	a+	PRON
ejpam-6029	403	5	b	b	X
ejpam-6029	403	6	36	36	NUM
ejpam-6029	403	7	(	(	PUNCT
ejpam-6029	403	8	sinh	sinh	PROPN
ejpam-6029	403	9	(	(	PUNCT
ejpam-6029	403	10	16b2	16b2	NUM
ejpam-6029	403	11	18	18	NUM
ejpam-6029	403	12	)	)	PUNCT
ejpam-6029	403	13	,	,	PUNCT
ejpam-6029	403	14	0	0	NUM
ejpam-6029	403	15	)	)	PUNCT
ejpam-6029	404	1	+	+	CCONJ
ejpam-6029	404	2	(	(	PUNCT
ejpam-6029	404	3	sinh	sinh	PROPN
ejpam-6029	404	4	(	(	PUNCT
ejpam-6029	404	5	9a2	9a2	NUM
ejpam-6029	404	6	8	8	NUM
ejpam-6029	404	7	)	)	PUNCT
ejpam-6029	404	8	sinh	sinh	NOUN
ejpam-6029	404	9	(	(	PUNCT
ejpam-6029	404	10	16b2	16b2	NUM
ejpam-6029	404	11	18	18	NUM
ejpam-6029	404	12	)	)	PUNCT
ejpam-6029	404	13	,	,	PUNCT
ejpam-6029	404	14	0	0	NUM
ejpam-6029	404	15	)	)	PUNCT
ejpam-6029	404	16	1	1	NUM
ejpam-6029	405	1	+	+	CCONJ
ejpam-6029	405	2	(	(	PUNCT
ejpam-6029	405	3	sinh	sinh	PROPN
ejpam-6029	405	4	(	(	PUNCT
ejpam-6029	405	5	(	(	PUNCT
ejpam-6029	405	6	a+b)2	a+b)2	PROPN
ejpam-6029	405	7	2	2	NUM
ejpam-6029	405	8	)	)	PUNCT
ejpam-6029	405	9	,	,	PUNCT
ejpam-6029	405	10	0	0	NUM
ejpam-6029	405	11	)	)	PUNCT
ejpam-6029	405	12	=	=	SYM
ejpam-6029	406	1	λ1(a	λ1(a	NOUN
ejpam-6029	406	2	,	,	PUNCT
ejpam-6029	406	3	b)lc(a	b)lc(a	PROPN
ejpam-6029	406	4	,	,	PUNCT
ejpam-6029	406	5	b	b	NOUN
ejpam-6029	406	6	)	)	PUNCT
ejpam-6029	406	7	+	+	SYM
ejpam-6029	406	8	λ2(a	λ2(a	NOUN
ejpam-6029	406	9	,	,	PUNCT
ejpam-6029	406	10	b)lc(a	b)lc(a	PROPN
ejpam-6029	406	11	,	,	PUNCT
ejpam-6029	406	12	ta	ta	NOUN
ejpam-6029	406	13	)	)	PUNCT
ejpam-6029	406	14	+	+	PUNCT
ejpam-6029	407	1	λ3(a	λ3(a	NOUN
ejpam-6029	407	2	,	,	PUNCT
ejpam-6029	407	3	b)lc(b	b)lc(b	NOUN
ejpam-6029	407	4	,	,	PUNCT
ejpam-6029	407	5	t	t	PROPN
ejpam-6029	407	6	b	b	X
ejpam-6029	407	7	)	)	PUNCT
ejpam-6029	407	8	+	+	CCONJ
ejpam-6029	407	9	λ4(a	λ4(a	PROPN
ejpam-6029	407	10	,	,	PUNCT
ejpam-6029	407	11	b	b	NOUN
ejpam-6029	407	12	)	)	PUNCT
ejpam-6029	407	13	lc(a	lc(a	NUM
ejpam-6029	407	14	,	,	PUNCT
ejpam-6029	407	15	ta)lc(b	ta)lc(b	PROPN
ejpam-6029	407	16	,	,	PUNCT
ejpam-6029	407	17	t	t	PROPN
ejpam-6029	407	18	b	b	NUM
ejpam-6029	407	19	)	)	PUNCT
ejpam-6029	407	20	1	1	NUM
ejpam-6029	407	21	+	+	CCONJ
ejpam-6029	407	22	lc(a	lc(a	NUM
ejpam-6029	407	23	,	,	PUNCT
ejpam-6029	407	24	b	b	NOUN
ejpam-6029	407	25	)	)	PUNCT
ejpam-6029	407	26	+	+	CCONJ
ejpam-6029	407	27	λ5(a	λ5(a	NUM
ejpam-6029	407	28	,	,	PUNCT
ejpam-6029	407	29	b	b	NOUN
ejpam-6029	407	30	)	)	PUNCT
ejpam-6029	407	31	lc(b	lc(b	NOUN
ejpam-6029	407	32	,	,	PUNCT
ejpam-6029	407	33	t	t	PROPN
ejpam-6029	407	34	b	b	NUM
ejpam-6029	407	35	)	)	PUNCT
ejpam-6029	407	36	[	[	PUNCT
ejpam-6029	407	37	1	1	NUM
ejpam-6029	407	38	+	+	CCONJ
ejpam-6029	407	39	lc(a	lc(a	NOUN
ejpam-6029	407	40	,	,	PUNCT
ejpam-6029	407	41	ta	ta	NOUN
ejpam-6029	407	42	)	)	PUNCT
ejpam-6029	407	43	]	]	PUNCT
ejpam-6029	407	44	1	1	NUM
ejpam-6029	407	45	+	+	CCONJ
ejpam-6029	407	46	lc(a	lc(a	NUM
ejpam-6029	407	47	,	,	PUNCT
ejpam-6029	407	48	b	b	NOUN
ejpam-6029	407	49	)	)	PUNCT
ejpam-6029	407	50	.	.	PUNCT
ejpam-6029	408	1	hence	hence	ADV
ejpam-6029	408	2	,	,	PUNCT
ejpam-6029	408	3	corollary	corollary	ADJ
ejpam-6029	408	4	2	2	NUM
ejpam-6029	408	5	is	be	AUX
ejpam-6029	408	6	fulfilled	fulfil	VERB
ejpam-6029	408	7	and	and	CCONJ
ejpam-6029	408	8	a	a	DET
ejpam-6029	408	9	=	=	SYM
ejpam-6029	408	10	0	0	NUM
ejpam-6029	408	11	∈	∈	PROPN
ejpam-6029	408	12	γ	γ	X
ejpam-6029	408	13	is	be	AUX
ejpam-6029	408	14	a	a	DET
ejpam-6029	408	15	common	common	ADJ
ejpam-6029	408	16	fixed	fix	VERB
ejpam-6029	408	17	point	point	NOUN
ejpam-6029	408	18	such	such	ADJ
ejpam-6029	408	19	that	that	SCONJ
ejpam-6029	408	20	t1a	t1a	NOUN
ejpam-6029	408	21	=	=	SYM
ejpam-6029	408	22	t2a	t2a	ADP
ejpam-6029	408	23	=	=	PUNCT
ejpam-6029	408	24	a.	a.	NOUN
ejpam-6029	408	25	example	example	NOUN
ejpam-6029	408	26	5	5	X
ejpam-6029	408	27	.	.	X
ejpam-6029	409	1	consider	consider	VERB
ejpam-6029	409	2	e	e	NOUN
ejpam-6029	409	3	=	=	SYM
ejpam-6029	409	4	r	r	NOUN
ejpam-6029	409	5	,	,	PUNCT
ejpam-6029	409	6	and	and	CCONJ
ejpam-6029	409	7	p	p	NOUN
ejpam-6029	409	8	=	=	PUNCT
ejpam-6029	409	9	r+	r+	X
ejpam-6029	409	10	.	.	PUNCT
ejpam-6029	410	1	let	let	VERB
ejpam-6029	410	2	γ	γ	X
ejpam-6029	410	3	=	=	SYM
ejpam-6029	410	4	{	{	PUNCT
ejpam-6029	410	5	1	1	NUM
ejpam-6029	410	6	,	,	PUNCT
ejpam-6029	410	7	2	2	NUM
ejpam-6029	410	8	,	,	PUNCT
ejpam-6029	410	9	3	3	NUM
ejpam-6029	410	10	}	}	PUNCT
ejpam-6029	410	11	.	.	PUNCT
ejpam-6029	411	1	define	define	VERB
ejpam-6029	411	2	a	a	DET
ejpam-6029	411	3	symmetric	symmetric	ADJ
ejpam-6029	411	4	map	map	NOUN
ejpam-6029	412	1	lc	lc	NOUN
ejpam-6029	412	2	:	:	PUNCT
ejpam-6029	412	3	γ×	γ×	PROPN
ejpam-6029	412	4	γ	γ	X
ejpam-6029	412	5	→	→	SYM
ejpam-6029	412	6	e	e	PROPN
ejpam-6029	412	7	by	by	ADP
ejpam-6029	412	8	lc(1	lc(1	PROPN
ejpam-6029	412	9	,	,	PUNCT
ejpam-6029	412	10	1	1	NUM
ejpam-6029	412	11	)	)	PUNCT
ejpam-6029	412	12	=	=	SYM
ejpam-6029	413	1	lc(2	lc(2	NOUN
ejpam-6029	413	2	,	,	PUNCT
ejpam-6029	413	3	2	2	NUM
ejpam-6029	413	4	)	)	PUNCT
ejpam-6029	413	5	=	=	SYM
ejpam-6029	413	6	0,lc(3	0,lc(3	PROPN
ejpam-6029	413	7	,	,	PUNCT
ejpam-6029	413	8	3	3	X
ejpam-6029	413	9	)	)	PUNCT
ejpam-6029	413	10	=	=	SYM
ejpam-6029	413	11	2	2	NUM
ejpam-6029	413	12	,	,	PUNCT
ejpam-6029	413	13	and	and	CCONJ
ejpam-6029	413	14	lc(1	lc(1	NOUN
ejpam-6029	413	15	,	,	PUNCT
ejpam-6029	413	16	2	2	NUM
ejpam-6029	413	17	)	)	PUNCT
ejpam-6029	413	18	=	=	SYM
ejpam-6029	413	19	11,lc(1	11,lc(1	NUM
ejpam-6029	413	20	,	,	PUNCT
ejpam-6029	413	21	3	3	NUM
ejpam-6029	413	22	)	)	PUNCT
ejpam-6029	413	23	=	=	SYM
ejpam-6029	413	24	6,lc(3	6,lc(3	NUM
ejpam-6029	413	25	,	,	PUNCT
ejpam-6029	413	26	2	2	NUM
ejpam-6029	413	27	)	)	PUNCT
ejpam-6029	413	28	=	=	SYM
ejpam-6029	413	29	3	3	X
ejpam-6029	413	30	.	.	X
ejpam-6029	413	31	take	take	VERB
ejpam-6029	413	32	f	f	NOUN
ejpam-6029	413	33	,	,	PUNCT
ejpam-6029	413	34	g	g	NOUN
ejpam-6029	413	35	:	:	PUNCT
ejpam-6029	413	36	p	p	X
ejpam-6029	413	37	→	→	SYM
ejpam-6029	413	38	p	p	X
ejpam-6029	413	39	;	;	PUNCT
ejpam-6029	413	40	it	it	PRON
ejpam-6029	413	41	is	be	AUX
ejpam-6029	413	42	defined	define	VERB
ejpam-6029	413	43	by	by	ADP
ejpam-6029	413	44	f(u	f(u	PROPN
ejpam-6029	413	45	)	)	PUNCT
ejpam-6029	414	1	=	=	PUNCT
ejpam-6029	414	2	sinh	sinh	NOUN
ejpam-6029	414	3	(	(	PUNCT
ejpam-6029	414	4	12	12	NUM
ejpam-6029	414	5	11u	11u	NUM
ejpam-6029	414	6	)	)	PUNCT
ejpam-6029	414	7	;	;	PUNCT
ejpam-6029	414	8	and	and	CCONJ
ejpam-6029	414	9	g(u	g(u	PROPN
ejpam-6029	414	10	)	)	PUNCT
ejpam-6029	414	11	=	=	PUNCT
ejpam-6029	414	12	(	(	PUNCT
ejpam-6029	414	13	3	3	NUM
ejpam-6029	414	14	11u	11u	NUM
ejpam-6029	414	15	)	)	PUNCT
ejpam-6029	414	16	,	,	PUNCT
ejpam-6029	414	17	where	where	SCONJ
ejpam-6029	414	18	u	u	PROPN
ejpam-6029	414	19	∈	∈	PROPN
ejpam-6029	414	20	p	p	X
ejpam-6029	414	21	.	.	PUNCT
ejpam-6029	415	1	evidently	evidently	ADV
ejpam-6029	415	2	,	,	PUNCT
ejpam-6029	415	3	valid	valid	ADJ
ejpam-6029	415	4	that	that	SCONJ
ejpam-6029	415	5	(	(	PUNCT
ejpam-6029	415	6	γ	γ	X
ejpam-6029	415	7	,	,	PUNCT
ejpam-6029	415	8	lc	lc	PROPN
ejpam-6029	415	9	)	)	PUNCT
ejpam-6029	415	10	is	be	AUX
ejpam-6029	415	11	a	a	DET
ejpam-6029	415	12	lc	lc	NOUN
ejpam-6029	415	13	-	-	PUNCT
ejpam-6029	415	14	complete	complete	ADJ
ejpam-6029	415	15	dccml	dccml	NOUN
ejpam-6029	415	16	-	-	PUNCT
ejpam-6029	415	17	space	space	NOUN
ejpam-6029	415	18	regarding	regard	VERB
ejpam-6029	415	19	f	f	PROPN
ejpam-6029	415	20	,	,	PUNCT
ejpam-6029	415	21	g	g	PROPN
ejpam-6029	415	22	,	,	PUNCT
ejpam-6029	415	23	and	and	CCONJ
ejpam-6029	415	24	lc(3	lc(3	NOUN
ejpam-6029	415	25	,	,	PUNCT
ejpam-6029	415	26	3	3	X
ejpam-6029	415	27	)	)	PUNCT
ejpam-6029	415	28	̸=	̸=	PROPN
ejpam-6029	415	29	0	0	NUM
ejpam-6029	415	30	.	.	PUNCT
ejpam-6029	416	1	therefore	therefore	ADV
ejpam-6029	416	2	,	,	PUNCT
ejpam-6029	416	3	(	(	PUNCT
ejpam-6029	416	4	γ	γ	X
ejpam-6029	416	5	,	,	PUNCT
ejpam-6029	416	6	lc	lc	NOUN
ejpam-6029	416	7	)	)	PUNCT
ejpam-6029	416	8	is	be	AUX
ejpam-6029	416	9	not	not	PART
ejpam-6029	416	10	a	a	DET
ejpam-6029	416	11	c2cms	c2cms	PROPN
ejpam-6029	416	12	,	,	PUNCT
ejpam-6029	416	13	see	see	VERB
ejpam-6029	416	14	[	[	X
ejpam-6029	416	15	20	20	NUM
ejpam-6029	416	16	]	]	PUNCT
ejpam-6029	416	17	.	.	PUNCT
ejpam-6029	417	1	further	far	ADV
ejpam-6029	417	2	,	,	PUNCT
ejpam-6029	417	3	let	let	VERB
ejpam-6029	417	4	us	we	PRON
ejpam-6029	417	5	define	define	VERB
ejpam-6029	417	6	a	a	DET
ejpam-6029	417	7	map	map	NOUN
ejpam-6029	417	8	t	t	NOUN
ejpam-6029	417	9	:	:	PUNCT
ejpam-6029	417	10	γ	γ	X
ejpam-6029	417	11	→	→	SYM
ejpam-6029	417	12	γ	γ	PROPN
ejpam-6029	417	13	as	as	ADP
ejpam-6029	417	14	t	t	PROPN
ejpam-6029	417	15	(	(	PUNCT
ejpam-6029	417	16	a	a	NOUN
ejpam-6029	417	17	)	)	PUNCT
ejpam-6029	417	18	=	=	SYM
ejpam-6029	417	19	{	{	PUNCT
ejpam-6029	417	20	2	2	NUM
ejpam-6029	417	21	if	if	SCONJ
ejpam-6029	417	22	a	a	DET
ejpam-6029	417	23	∈	∈	PROPN
ejpam-6029	417	24	{	{	PUNCT
ejpam-6029	417	25	2	2	NUM
ejpam-6029	417	26	,	,	PUNCT
ejpam-6029	417	27	3	3	NUM
ejpam-6029	417	28	}	}	SYM
ejpam-6029	417	29	3	3	NUM
ejpam-6029	417	30	if	if	SCONJ
ejpam-6029	417	31	a	a	DET
ejpam-6029	417	32	=	=	NOUN
ejpam-6029	417	33	1	1	NUM
ejpam-6029	417	34	.	.	PUNCT
ejpam-6029	417	35	then	then	ADV
ejpam-6029	417	36	,	,	PUNCT
ejpam-6029	417	37	t	t	PROPN
ejpam-6029	417	38	ensures	ensure	VERB
ejpam-6029	417	39	a	a	DET
ejpam-6029	417	40	unique	unique	ADJ
ejpam-6029	417	41	fixed	fix	VERB
ejpam-6029	417	42	point	point	NOUN
ejpam-6029	417	43	.	.	PUNCT
ejpam-6029	418	1	proof	proof	NOUN
ejpam-6029	418	2	.	.	PUNCT
ejpam-6029	419	1	let	let	VERB
ejpam-6029	419	2	us	we	PRON
ejpam-6029	419	3	take	take	VERB
ejpam-6029	419	4	λ(a	λ(a	NOUN
ejpam-6029	419	5	,	,	PUNCT
ejpam-6029	419	6	b	b	NOUN
ejpam-6029	419	7	)	)	PUNCT
ejpam-6029	419	8	=	=	SYM
ejpam-6029	419	9	3	3	NUM
ejpam-6029	419	10	2+a+b	2+a+b	NUM
ejpam-6029	419	11	∈	∈	PROPN
ejpam-6029	419	12	∆	∆	NOUN
ejpam-6029	419	13	,	,	PUNCT
ejpam-6029	419	14	for	for	ADP
ejpam-6029	419	15	all	all	DET
ejpam-6029	419	16	a	a	PRON
ejpam-6029	419	17	,	,	PUNCT
ejpam-6029	419	18	b	b	X
ejpam-6029	419	19	∈	∈	PROPN
ejpam-6029	419	20	γ	γ	PROPN
ejpam-6029	419	21	.	.	PUNCT
ejpam-6029	420	1	now	now	ADV
ejpam-6029	420	2	,	,	PUNCT
ejpam-6029	420	3	consider	consider	VERB
ejpam-6029	420	4	the	the	DET
ejpam-6029	420	5	following	follow	VERB
ejpam-6029	420	6	cases	case	NOUN
ejpam-6029	420	7	to	to	PART
ejpam-6029	420	8	show	show	VERB
ejpam-6029	420	9	that	that	DET
ejpam-6029	420	10	corollary	corollary	ADJ
ejpam-6029	420	11	3	3	NUM
ejpam-6029	420	12	satisfies	satisfie	NOUN
ejpam-6029	420	13	:	:	PUNCT
ejpam-6029	420	14	case	case	NOUN
ejpam-6029	420	15	1	1	NUM
ejpam-6029	420	16	.	.	PUNCT
ejpam-6029	421	1	a	a	DET
ejpam-6029	421	2	=	=	ADJ
ejpam-6029	421	3	1	1	NUM
ejpam-6029	421	4	,	,	PUNCT
ejpam-6029	421	5	b	b	NOUN
ejpam-6029	421	6	=	=	SYM
ejpam-6029	421	7	2	2	NUM
ejpam-6029	421	8	,	,	PUNCT
ejpam-6029	421	9	lc(t1	lc(t1	NOUN
ejpam-6029	421	10	,	,	PUNCT
ejpam-6029	421	11	t2	t2	NOUN
ejpam-6029	421	12	)	)	PUNCT
ejpam-6029	421	13	=	=	SYM
ejpam-6029	421	14	lc(3	lc(3	NOUN
ejpam-6029	421	15	,	,	PUNCT
ejpam-6029	421	16	2	2	NUM
ejpam-6029	421	17	)	)	PUNCT
ejpam-6029	421	18	=	=	SYM
ejpam-6029	422	1	3	3	NUM
ejpam-6029	422	2	⪯	⪯	NOUN
ejpam-6029	422	3	33	33	NUM
ejpam-6029	422	4	5	5	NUM
ejpam-6029	422	5	=	=	SYM
ejpam-6029	422	6	3	3	NUM
ejpam-6029	422	7	5	5	NUM
ejpam-6029	422	8	×	×	NOUN
ejpam-6029	422	9	11	11	NUM
ejpam-6029	422	10	=	=	SYM
ejpam-6029	422	11	λ(1	λ(1	PROPN
ejpam-6029	422	12	,	,	PUNCT
ejpam-6029	422	13	2)max{11	2)max{11	NUM
ejpam-6029	422	14	,	,	PUNCT
ejpam-6029	422	15	6	6	NUM
ejpam-6029	422	16	,	,	PUNCT
ejpam-6029	422	17	0	0	NUM
ejpam-6029	422	18	,	,	PUNCT
ejpam-6029	422	19	6×0	6×0	NOUN
ejpam-6029	422	20	1	1	NUM
ejpam-6029	422	21	+	+	SYM
ejpam-6029	422	22	11	11	NUM
ejpam-6029	422	23	,	,	PUNCT
ejpam-6029	422	24	0×[1	0×[1	PROPN
ejpam-6029	422	25	+	+	PROPN
ejpam-6029	422	26	6	6	NUM
ejpam-6029	422	27	]	]	SYM
ejpam-6029	422	28	1	1	NUM
ejpam-6029	422	29	+	+	SYM
ejpam-6029	422	30	11	11	NUM
ejpam-6029	422	31	,	,	PUNCT
ejpam-6029	422	32	[	[	X
ejpam-6029	422	33	6	6	NUM
ejpam-6029	422	34	+	+	NOUN
ejpam-6029	422	35	0]×3	0]×3	NOUN
ejpam-6029	422	36	1	1	NUM
ejpam-6029	422	37	+	+	NOUN
ejpam-6029	422	38	11	11	NUM
ejpam-6029	422	39	+	+	NOUN
ejpam-6029	422	40	3	3	NUM
ejpam-6029	422	41	}	}	PUNCT
ejpam-6029	422	42	;	;	PUNCT
ejpam-6029	423	1	a.	a.	NOUN
ejpam-6029	423	2	a.	a.	PROPN
ejpam-6029	423	3	hijab	hijab	PROPN
ejpam-6029	423	4	et	et	PROPN
ejpam-6029	423	5	al	al	PROPN
ejpam-6029	423	6	.	.	PUNCT
ejpam-6029	423	7	/	/	SYM
ejpam-6029	423	8	eur	eur	PROPN
ejpam-6029	423	9	.	.	PUNCT
ejpam-6029	424	1	j.	j.	PROPN
ejpam-6029	424	2	pure	pure	PROPN
ejpam-6029	424	3	appl	appl	PROPN
ejpam-6029	424	4	.	.	PROPN
ejpam-6029	424	5	math	math	PROPN
ejpam-6029	424	6	,	,	PUNCT
ejpam-6029	424	7	18	18	NUM
ejpam-6029	424	8	(	(	PUNCT
ejpam-6029	424	9	2	2	NUM
ejpam-6029	424	10	)	)	PUNCT
ejpam-6029	424	11	(	(	PUNCT
ejpam-6029	424	12	2025	2025	NUM
ejpam-6029	424	13	)	)	PUNCT
ejpam-6029	424	14	,	,	PUNCT
ejpam-6029	424	15	6029	6029	NUM
ejpam-6029	424	16	16	16	NUM
ejpam-6029	424	17	of	of	ADP
ejpam-6029	424	18	23	23	NUM
ejpam-6029	424	19	case	case	NOUN
ejpam-6029	424	20	2	2	NUM
ejpam-6029	424	21	.	.	PUNCT
ejpam-6029	425	1	a	a	DET
ejpam-6029	425	2	=	=	ADJ
ejpam-6029	425	3	1	1	NUM
ejpam-6029	425	4	,	,	PUNCT
ejpam-6029	425	5	b	b	NOUN
ejpam-6029	425	6	=	=	SYM
ejpam-6029	425	7	3	3	NUM
ejpam-6029	425	8	,	,	PUNCT
ejpam-6029	425	9	lc(t1	lc(t1	PROPN
ejpam-6029	425	10	,	,	PUNCT
ejpam-6029	425	11	t3	t3	PROPN
ejpam-6029	425	12	)	)	PUNCT
ejpam-6029	425	13	=	=	SYM
ejpam-6029	425	14	lc(3	lc(3	NOUN
ejpam-6029	425	15	,	,	PUNCT
ejpam-6029	425	16	2	2	NUM
ejpam-6029	425	17	)	)	PUNCT
ejpam-6029	425	18	=	=	SYM
ejpam-6029	425	19	3	3	NUM
ejpam-6029	425	20	⪯	⪯	NOUN
ejpam-6029	425	21	3	3	NUM
ejpam-6029	425	22	=	=	SYM
ejpam-6029	425	23	3	3	NUM
ejpam-6029	425	24	6	6	NUM
ejpam-6029	425	25	×	×	NOUN
ejpam-6029	425	26	6	6	NUM
ejpam-6029	425	27	=	=	SYM
ejpam-6029	425	28	λ(1	λ(1	PROPN
ejpam-6029	425	29	,	,	PUNCT
ejpam-6029	425	30	3)max{6	3)max{6	NUM
ejpam-6029	425	31	,	,	PUNCT
ejpam-6029	425	32	6	6	NUM
ejpam-6029	425	33	,	,	PUNCT
ejpam-6029	425	34	3	3	NUM
ejpam-6029	425	35	,	,	PUNCT
ejpam-6029	425	36	6×3	6×3	NUM
ejpam-6029	425	37	1	1	NUM
ejpam-6029	425	38	+	+	SYM
ejpam-6029	425	39	6	6	NUM
ejpam-6029	425	40	,	,	PUNCT
ejpam-6029	425	41	3×[1	3×[1	NUM
ejpam-6029	425	42	+	+	NOUN
ejpam-6029	425	43	6	6	NUM
ejpam-6029	425	44	]	]	SYM
ejpam-6029	425	45	1	1	NUM
ejpam-6029	425	46	+	+	SYM
ejpam-6029	425	47	6	6	NUM
ejpam-6029	425	48	,	,	PUNCT
ejpam-6029	425	49	[	[	X
ejpam-6029	425	50	6	6	NUM
ejpam-6029	425	51	+	+	NUM
ejpam-6029	425	52	3]×3	3]×3	NUM
ejpam-6029	425	53	1	1	NUM
ejpam-6029	425	54	+	+	NOUN
ejpam-6029	425	55	6	6	NUM
ejpam-6029	425	56	+	+	NOUN
ejpam-6029	425	57	3	3	NUM
ejpam-6029	425	58	}	}	PUNCT
ejpam-6029	425	59	;	;	PUNCT
ejpam-6029	425	60	case	case	NOUN
ejpam-6029	425	61	3	3	NUM
ejpam-6029	425	62	.	.	PUNCT
ejpam-6029	426	1	a	a	DET
ejpam-6029	426	2	=	=	ADJ
ejpam-6029	426	3	2	2	NUM
ejpam-6029	426	4	,	,	PUNCT
ejpam-6029	426	5	b	b	NOUN
ejpam-6029	426	6	=	=	SYM
ejpam-6029	426	7	3	3	NUM
ejpam-6029	426	8	,	,	PUNCT
ejpam-6029	426	9	lc(t2	lc(t2	NOUN
ejpam-6029	426	10	,	,	PUNCT
ejpam-6029	426	11	t3	t3	PROPN
ejpam-6029	426	12	)	)	PUNCT
ejpam-6029	426	13	=	=	PUNCT
ejpam-6029	426	14	lc(2	lc(2	NOUN
ejpam-6029	426	15	,	,	PUNCT
ejpam-6029	426	16	2	2	NUM
ejpam-6029	426	17	)	)	PUNCT
ejpam-6029	426	18	=	=	SYM
ejpam-6029	426	19	0	0	NUM
ejpam-6029	426	20	⪯	⪯	NOUN
ejpam-6029	426	21	9	9	NUM
ejpam-6029	426	22	7	7	NUM
ejpam-6029	426	23	=	=	SYM
ejpam-6029	426	24	3	3	NUM
ejpam-6029	426	25	7	7	NUM
ejpam-6029	426	26	×	×	NOUN
ejpam-6029	426	27	3	3	NUM
ejpam-6029	426	28	=	=	SYM
ejpam-6029	426	29	λ(2	λ(2	PROPN
ejpam-6029	426	30	,	,	PUNCT
ejpam-6029	426	31	3)max{3	3)max{3	NUM
ejpam-6029	426	32	,	,	PUNCT
ejpam-6029	426	33	0	0	NUM
ejpam-6029	426	34	,	,	PUNCT
ejpam-6029	426	35	3	3	NUM
ejpam-6029	426	36	,	,	PUNCT
ejpam-6029	426	37	0×3	0×3	X
ejpam-6029	426	38	1	1	NUM
ejpam-6029	426	39	+	+	SYM
ejpam-6029	426	40	3	3	NUM
ejpam-6029	426	41	,	,	PUNCT
ejpam-6029	426	42	3×[1	3×[1	NUM
ejpam-6029	426	43	+	+	NOUN
ejpam-6029	426	44	0	0	NUM
ejpam-6029	426	45	]	]	X
ejpam-6029	426	46	1	1	NUM
ejpam-6029	426	47	+	+	SYM
ejpam-6029	426	48	3	3	NUM
ejpam-6029	426	49	,	,	PUNCT
ejpam-6029	426	50	[	[	X
ejpam-6029	426	51	0	0	NUM
ejpam-6029	426	52	+	+	NOUN
ejpam-6029	426	53	3]×0	3]×0	NUM
ejpam-6029	426	54	1	1	NUM
ejpam-6029	426	55	+	+	NOUN
ejpam-6029	426	56	3	3	NUM
ejpam-6029	426	57	+	+	NOUN
ejpam-6029	426	58	0	0	NUM
ejpam-6029	426	59	}	}	PUNCT
ejpam-6029	426	60	.	.	PUNCT
ejpam-6029	427	1	since	since	SCONJ
ejpam-6029	427	2	lc(3	lc(3	PROPN
ejpam-6029	427	3	,	,	PUNCT
ejpam-6029	427	4	3	3	X
ejpam-6029	427	5	)	)	PUNCT
ejpam-6029	427	6	̸=	̸=	PROPN
ejpam-6029	427	7	0	0	NUM
ejpam-6029	427	8	,	,	PUNCT
ejpam-6029	427	9	we	we	PRON
ejpam-6029	427	10	further	far	ADV
ejpam-6029	427	11	take	take	VERB
ejpam-6029	427	12	case	case	NOUN
ejpam-6029	427	13	4	4	NUM
ejpam-6029	427	14	.	.	PUNCT
ejpam-6029	428	1	a	a	PRON
ejpam-6029	428	2	=	=	ADJ
ejpam-6029	428	3	1	1	NUM
ejpam-6029	428	4	,	,	PUNCT
ejpam-6029	428	5	b	b	NOUN
ejpam-6029	428	6	=	=	SYM
ejpam-6029	428	7	1	1	NUM
ejpam-6029	428	8	,	,	PUNCT
ejpam-6029	428	9	lc(t1	lc(t1	NOUN
ejpam-6029	428	10	,	,	PUNCT
ejpam-6029	428	11	t1	t1	NOUN
ejpam-6029	428	12	)	)	PUNCT
ejpam-6029	429	1	=	=	SYM
ejpam-6029	429	2	lc(3	lc(3	PROPN
ejpam-6029	429	3	,	,	PUNCT
ejpam-6029	429	4	3	3	NUM
ejpam-6029	429	5	)	)	PUNCT
ejpam-6029	429	6	=	=	SYM
ejpam-6029	429	7	2	2	NUM
ejpam-6029	429	8	⪯	⪯	NOUN
ejpam-6029	429	9	126	126	NUM
ejpam-6029	429	10	4	4	NUM
ejpam-6029	429	11	=	=	SYM
ejpam-6029	429	12	3	3	NUM
ejpam-6029	429	13	4	4	NUM
ejpam-6029	429	14	×	×	NOUN
ejpam-6029	429	15	42	42	NUM
ejpam-6029	429	16	=	=	SYM
ejpam-6029	429	17	λ(1	λ(1	PROPN
ejpam-6029	429	18	,	,	PUNCT
ejpam-6029	429	19	2)max{0	2)max{0	NUM
ejpam-6029	429	20	,	,	PUNCT
ejpam-6029	429	21	6	6	NUM
ejpam-6029	429	22	,	,	PUNCT
ejpam-6029	429	23	6	6	NUM
ejpam-6029	429	24	,	,	PUNCT
ejpam-6029	429	25	6×6	6×6	NUM
ejpam-6029	429	26	1	1	NUM
ejpam-6029	429	27	+	+	SYM
ejpam-6029	429	28	0	0	NUM
ejpam-6029	429	29	,	,	PUNCT
ejpam-6029	429	30	6×[1	6×[1	NUM
ejpam-6029	429	31	+	+	NOUN
ejpam-6029	429	32	6	6	NUM
ejpam-6029	429	33	]	]	SYM
ejpam-6029	429	34	1	1	NUM
ejpam-6029	429	35	+	+	NOUN
ejpam-6029	429	36	0	0	NUM
ejpam-6029	429	37	,	,	PUNCT
ejpam-6029	430	1	[	[	X
ejpam-6029	430	2	6	6	NUM
ejpam-6029	430	3	+	+	NOUN
ejpam-6029	430	4	6]×2	6]×2	PROPN
ejpam-6029	430	5	1	1	NUM
ejpam-6029	430	6	+	+	NOUN
ejpam-6029	430	7	0	0	NUM
ejpam-6029	430	8	+	+	NOUN
ejpam-6029	430	9	2	2	NUM
ejpam-6029	430	10	}	}	PUNCT
ejpam-6029	430	11	.	.	PUNCT
ejpam-6029	431	1	consider	consider	VERB
ejpam-6029	431	2	a0	a0	NOUN
ejpam-6029	431	3	=	=	SYM
ejpam-6029	431	4	2	2	NUM
ejpam-6029	431	5	∈	∈	PROPN
ejpam-6029	431	6	γ	γ	NOUN
ejpam-6029	431	7	.	.	PUNCT
ejpam-6029	432	1	thus	thus	ADV
ejpam-6029	432	2	,	,	PUNCT
ejpam-6029	432	3	an	an	DET
ejpam-6029	432	4	=	=	X
ejpam-6029	432	5	tna0	tna0	NOUN
ejpam-6029	432	6	=	=	SYM
ejpam-6029	432	7	2	2	NUM
ejpam-6029	432	8	for	for	ADP
ejpam-6029	432	9	each	each	DET
ejpam-6029	432	10	n	n	PRON
ejpam-6029	432	11	≥	≥	NOUN
ejpam-6029	432	12	1	1	NUM
ejpam-6029	432	13	.	.	X
ejpam-6029	433	1	for	for	ADP
ejpam-6029	433	2	condition	condition	NOUN
ejpam-6029	433	3	(	(	PUNCT
ejpam-6029	433	4	i	i	NOUN
ejpam-6029	433	5	)	)	PUNCT
ejpam-6029	433	6	in	in	ADP
ejpam-6029	433	7	corollary	corollary	ADJ
ejpam-6029	433	8	3	3	NUM
ejpam-6029	433	9	,	,	PUNCT
ejpam-6029	433	10	we	we	PRON
ejpam-6029	433	11	reach	reach	VERB
ejpam-6029	433	12	that	that	SCONJ
ejpam-6029	433	13	u	u	PROPN
ejpam-6029	433	14	≺	≺	NOUN
ejpam-6029	433	15	f(u	f(u	PROPN
ejpam-6029	433	16	)	)	PUNCT
ejpam-6029	433	17	=	=	PUNCT
ejpam-6029	433	18	sinh	sinh	NOUN
ejpam-6029	433	19	(	(	PUNCT
ejpam-6029	433	20	12	12	NUM
ejpam-6029	433	21	11u	11u	NUM
ejpam-6029	433	22	)	)	PUNCT
ejpam-6029	433	23	,	,	PUNCT
ejpam-6029	433	24	(	(	PUNCT
ejpam-6029	433	25	3	3	NUM
ejpam-6029	433	26	11u	11u	NUM
ejpam-6029	433	27	)	)	PUNCT
ejpam-6029	434	1	=	=	SYM
ejpam-6029	434	2	g(u	g(u	PROPN
ejpam-6029	434	3	)	)	PUNCT
ejpam-6029	434	4	≺	≺	NOUN
ejpam-6029	434	5	u	u	NOUN
ejpam-6029	434	6	,	,	PUNCT
ejpam-6029	434	7	0e	0e	NOUN
ejpam-6029	434	8	≺	≺	NOUN
ejpam-6029	434	9	u	u	PROPN
ejpam-6029	434	10	,	,	PUNCT
ejpam-6029	434	11	and	and	CCONJ
ejpam-6029	434	12	g(λ(a	g(λ(a	NOUN
ejpam-6029	434	13	,	,	PUNCT
ejpam-6029	434	14	b)u	b)u	NOUN
ejpam-6029	434	15	)	)	PUNCT
ejpam-6029	434	16	≺	≺	NOUN
ejpam-6029	434	17	u	u	NOUN
ejpam-6029	434	18	,	,	PUNCT
ejpam-6029	434	19	u	u	PROPN
ejpam-6029	434	20	∈	∈	PROPN
ejpam-6029	434	21	p	p	NOUN
ejpam-6029	434	22	.	.	PUNCT
ejpam-6029	435	1	moreover	moreover	ADV
ejpam-6029	435	2	,	,	PUNCT
ejpam-6029	435	3	we	we	PRON
ejpam-6029	435	4	see	see	VERB
ejpam-6029	435	5	that	that	SCONJ
ejpam-6029	435	6	lim	lim	PROPN
ejpam-6029	435	7	n→∞	n→∞	X
ejpam-6029	435	8	a	a	DET
ejpam-6029	435	9	,	,	PUNCT
ejpam-6029	435	10	b∈γ	b∈γ	ADJ
ejpam-6029	435	11	(	(	PUNCT
ejpam-6029	435	12	λ(a	λ(a	PROPN
ejpam-6029	435	13	,	,	PUNCT
ejpam-6029	435	14	b	b	NOUN
ejpam-6029	435	15	)	)	PUNCT
ejpam-6029	435	16	)	)	PUNCT
ejpam-6029	436	1	n	n	NOUN
ejpam-6029	436	2	=	=	SYM
ejpam-6029	436	3	0	0	X
ejpam-6029	436	4	.	.	PUNCT
ejpam-6029	437	1	therefore	therefore	ADV
ejpam-6029	437	2	,	,	PUNCT
ejpam-6029	437	3	all	all	DET
ejpam-6029	437	4	the	the	DET
ejpam-6029	437	5	conditions	condition	NOUN
ejpam-6029	437	6	of	of	ADP
ejpam-6029	437	7	corollary	corollary	ADJ
ejpam-6029	437	8	3	3	NUM
ejpam-6029	437	9	are	be	AUX
ejpam-6029	437	10	satisfied	satisfied	ADJ
ejpam-6029	437	11	and	and	CCONJ
ejpam-6029	437	12	a	a	DET
ejpam-6029	437	13	fixed	fix	VERB
ejpam-6029	437	14	point	point	NOUN
ejpam-6029	437	15	is	be	AUX
ejpam-6029	437	16	given	give	VERB
ejpam-6029	437	17	as	as	ADP
ejpam-6029	437	18	a	a	DET
ejpam-6029	437	19	=	=	SYM
ejpam-6029	437	20	2	2	NUM
ejpam-6029	437	21	.	.	NOUN
ejpam-6029	438	1	afterwards	afterwards	ADV
ejpam-6029	438	2	,	,	PUNCT
ejpam-6029	438	3	we	we	PRON
ejpam-6029	438	4	present	present	VERB
ejpam-6029	438	5	the	the	DET
ejpam-6029	438	6	iterative	iterative	NOUN
ejpam-6029	438	7	fixed	fix	VERB
ejpam-6029	438	8	point	point	NOUN
ejpam-6029	438	9	t	t	PROPN
ejpam-6029	439	1	k	k	NOUN
ejpam-6029	439	2	,	,	PUNCT
ejpam-6029	439	3	k	k	PROPN
ejpam-6029	439	4	>	>	X
ejpam-6029	439	5	1	1	NUM
ejpam-6029	439	6	as	as	SCONJ
ejpam-6029	439	7	follows	follow	VERB
ejpam-6029	439	8	.	.	PUNCT
ejpam-6029	440	1	theorem	theorem	NOUN
ejpam-6029	440	2	2	2	NUM
ejpam-6029	440	3	.	.	PUNCT
ejpam-6029	440	4	suppose	suppose	VERB
ejpam-6029	440	5	(	(	PUNCT
ejpam-6029	440	6	γ	γ	X
ejpam-6029	440	7	,	,	PUNCT
ejpam-6029	440	8	lc	lc	PROPN
ejpam-6029	440	9	)	)	PUNCT
ejpam-6029	440	10	is	be	AUX
ejpam-6029	440	11	an	an	DET
ejpam-6029	440	12	lc	lc	NOUN
ejpam-6029	440	13	-	-	PUNCT
ejpam-6029	440	14	complete	complete	ADJ
ejpam-6029	440	15	dccml	dccml	NOUN
ejpam-6029	440	16	-	-	PUNCT
ejpam-6029	440	17	space	space	NOUN
ejpam-6029	440	18	with	with	ADP
ejpam-6029	440	19	two	two	NUM
ejpam-6029	440	20	non	non	ADJ
ejpam-6029	440	21	-	-	ADJ
ejpam-6029	440	22	constant	constant	ADJ
ejpam-6029	440	23	functions	function	NOUN
ejpam-6029	440	24	f	f	NOUN
ejpam-6029	440	25	,	,	PUNCT
ejpam-6029	440	26	g	g	NOUN
ejpam-6029	440	27	:	:	PUNCT
ejpam-6029	440	28	p	p	X
ejpam-6029	440	29	→	→	SYM
ejpam-6029	440	30	p	p	X
ejpam-6029	440	31	,	,	PUNCT
ejpam-6029	440	32	where	where	SCONJ
ejpam-6029	440	33	p	p	NOUN
ejpam-6029	440	34	is	be	AUX
ejpam-6029	440	35	a	a	DET
ejpam-6029	440	36	normal	normal	ADJ
ejpam-6029	440	37	cone	cone	NOUN
ejpam-6029	440	38	via	via	ADP
ejpam-6029	440	39	normal	normal	ADJ
ejpam-6029	440	40	constant	constant	ADJ
ejpam-6029	440	41	m	m	NOUN
ejpam-6029	440	42	.	.	PUNCT
ejpam-6029	441	1	let	let	VERB
ejpam-6029	441	2	t	t	NOUN
ejpam-6029	441	3	:	:	PUNCT
ejpam-6029	441	4	γ	γ	X
ejpam-6029	441	5	→	→	SYM
ejpam-6029	441	6	γ	γ	X
ejpam-6029	441	7	be	be	AUX
ejpam-6029	441	8	a	a	DET
ejpam-6029	441	9	mapping	mapping	NOUN
ejpam-6029	441	10	and	and	CCONJ
ejpam-6029	441	11	there	there	PRON
ejpam-6029	441	12	exists	exist	VERB
ejpam-6029	441	13	λ	λ	PROPN
ejpam-6029	441	14	∈	∈	PROPN
ejpam-6029	441	15	∆	∆	PROPN
ejpam-6029	441	16	such	such	ADJ
ejpam-6029	441	17	that	that	SCONJ
ejpam-6029	441	18	lc(t	lc(t	PROPN
ejpam-6029	441	19	ka	ka	PROPN
ejpam-6029	441	20	,	,	PUNCT
ejpam-6029	441	21	t	t	PROPN
ejpam-6029	441	22	kb	kb	PROPN
ejpam-6029	441	23	)	)	PUNCT
ejpam-6029	441	24	⪯	⪯	PROPN
ejpam-6029	441	25	λ(a	λ(a	PROPN
ejpam-6029	441	26	,	,	PUNCT
ejpam-6029	441	27	b)m̃(a	b)m̃(a	PROPN
ejpam-6029	441	28	,	,	PUNCT
ejpam-6029	441	29	b	b	NOUN
ejpam-6029	441	30	)	)	PUNCT
ejpam-6029	441	31	,	,	PUNCT
ejpam-6029	441	32	for	for	ADP
ejpam-6029	441	33	all	all	DET
ejpam-6029	441	34	a	a	PRON
ejpam-6029	441	35	,	,	PUNCT
ejpam-6029	441	36	b	b	PROPN
ejpam-6029	441	37	∈	∈	PROPN
ejpam-6029	441	38	γ	γ	X
ejpam-6029	441	39	,	,	PUNCT
ejpam-6029	441	40	(	(	PUNCT
ejpam-6029	441	41	13	13	NUM
ejpam-6029	441	42	)	)	PUNCT
ejpam-6029	441	43	where	where	SCONJ
ejpam-6029	441	44	m̃(a	m̃(a	NOUN
ejpam-6029	441	45	,	,	PUNCT
ejpam-6029	441	46	b	b	NOUN
ejpam-6029	441	47	)	)	PUNCT
ejpam-6029	441	48	=	=	SYM
ejpam-6029	441	49	max	max	PROPN
ejpam-6029	441	50	{	{	PUNCT
ejpam-6029	441	51	lc(a	lc(a	PROPN
ejpam-6029	441	52	,	,	PUNCT
ejpam-6029	441	53	b),lc(a	b),lc(a	PROPN
ejpam-6029	441	54	,	,	PUNCT
ejpam-6029	441	55	t	t	PROPN
ejpam-6029	441	56	ka),lc(b	ka),lc(b	PROPN
ejpam-6029	441	57	,	,	PUNCT
ejpam-6029	441	58	t	t	PROPN
ejpam-6029	441	59	kb	kb	PROPN
ejpam-6029	441	60	)	)	PUNCT
ejpam-6029	441	61	,	,	PUNCT
ejpam-6029	441	62	lc(a	lc(a	PROPN
ejpam-6029	441	63	,	,	PUNCT
ejpam-6029	441	64	t	t	PROPN
ejpam-6029	441	65	ka)lc(b	ka)lc(b	PROPN
ejpam-6029	441	66	,	,	PUNCT
ejpam-6029	441	67	t	t	PROPN
ejpam-6029	441	68	kb	kb	PROPN
ejpam-6029	441	69	)	)	PUNCT
ejpam-6029	441	70	1	1	NUM
ejpam-6029	442	1	+	+	CCONJ
ejpam-6029	442	2	lc(a	lc(a	NUM
ejpam-6029	442	3	,	,	PUNCT
ejpam-6029	442	4	b	b	NOUN
ejpam-6029	442	5	)	)	PUNCT
ejpam-6029	442	6	,	,	PUNCT
ejpam-6029	442	7	lc(b	lc(b	PROPN
ejpam-6029	442	8	,	,	PUNCT
ejpam-6029	442	9	t	t	PROPN
ejpam-6029	442	10	kb	kb	PROPN
ejpam-6029	442	11	)	)	PUNCT
ejpam-6029	443	1	[	[	PUNCT
ejpam-6029	443	2	1	1	NUM
ejpam-6029	443	3	+	+	CCONJ
ejpam-6029	443	4	lc(a	lc(a	NUM
ejpam-6029	443	5	,	,	PUNCT
ejpam-6029	443	6	t	t	PROPN
ejpam-6029	443	7	ka	ka	PROPN
ejpam-6029	443	8	)	)	PUNCT
ejpam-6029	443	9	]	]	PUNCT
ejpam-6029	444	1	1	1	NUM
ejpam-6029	444	2	+	+	CCONJ
ejpam-6029	444	3	lc(a	lc(a	NUM
ejpam-6029	444	4	,	,	PUNCT
ejpam-6029	444	5	b	b	NOUN
ejpam-6029	444	6	)	)	PUNCT
ejpam-6029	444	7	,	,	PUNCT
ejpam-6029	444	8	[	[	PUNCT
ejpam-6029	444	9	lc(a	lc(a	X
ejpam-6029	444	10	,	,	PUNCT
ejpam-6029	444	11	t	t	PROPN
ejpam-6029	444	12	ka	ka	PROPN
ejpam-6029	444	13	)	)	PUNCT
ejpam-6029	444	14	+	+	CCONJ
ejpam-6029	444	15	lc(b	lc(b	PROPN
ejpam-6029	444	16	,	,	PUNCT
ejpam-6029	444	17	t	t	PROPN
ejpam-6029	444	18	kb	kb	PROPN
ejpam-6029	444	19	)	)	PUNCT
ejpam-6029	444	20	]	]	PUNCT
ejpam-6029	445	1	lc(t	lc(t	PROPN
ejpam-6029	445	2	ka	ka	PROPN
ejpam-6029	445	3	,	,	PUNCT
ejpam-6029	445	4	t	t	PROPN
ejpam-6029	445	5	kb	kb	PROPN
ejpam-6029	445	6	)	)	PUNCT
ejpam-6029	445	7	1	1	NUM
ejpam-6029	446	1	+	+	CCONJ
ejpam-6029	446	2	lc(a	lc(a	NUM
ejpam-6029	446	3	,	,	PUNCT
ejpam-6029	446	4	b	b	NOUN
ejpam-6029	446	5	)	)	PUNCT
ejpam-6029	446	6	+	+	CCONJ
ejpam-6029	446	7	lc(t	lc(t	X
ejpam-6029	446	8	ka	ka	PROPN
ejpam-6029	446	9	,	,	PUNCT
ejpam-6029	446	10	t	t	PROPN
ejpam-6029	446	11	kb	kb	PROPN
ejpam-6029	446	12	)	)	PUNCT
ejpam-6029	446	13	}	}	PUNCT
ejpam-6029	446	14	.	.	PUNCT
ejpam-6029	447	1	for	for	ADP
ejpam-6029	447	2	a0	a0	PROPN
ejpam-6029	447	3	∈	∈	PROPN
ejpam-6029	447	4	γ	γ	PROPN
ejpam-6029	447	5	,	,	PUNCT
ejpam-6029	447	6	we	we	PRON
ejpam-6029	447	7	set	set	VERB
ejpam-6029	447	8	a	a	DET
ejpam-6029	447	9	sequence	sequence	NOUN
ejpam-6029	447	10	{	{	PUNCT
ejpam-6029	447	11	an	an	PRON
ejpam-6029	447	12	}	}	PUNCT
ejpam-6029	447	13	defined	define	VERB
ejpam-6029	447	14	as	as	ADP
ejpam-6029	447	15	an+1	an+1	NOUN
ejpam-6029	447	16	=	=	SYM
ejpam-6029	447	17	tna0	tna0	PROPN
ejpam-6029	447	18	for	for	ADP
ejpam-6029	447	19	every	every	DET
ejpam-6029	447	20	n	n	PRON
ejpam-6029	447	21	≥	≥	NOUN
ejpam-6029	447	22	0	0	NUM
ejpam-6029	447	23	.	.	PUNCT
ejpam-6029	448	1	suppose	suppose	VERB
ejpam-6029	448	2	that	that	SCONJ
ejpam-6029	448	3	(	(	PUNCT
ejpam-6029	448	4	i	i	NOUN
ejpam-6029	448	5	)	)	PUNCT
ejpam-6029	448	6	f	f	PROPN
ejpam-6029	448	7	and	and	CCONJ
ejpam-6029	448	8	g	g	PROPN
ejpam-6029	448	9	are	be	AUX
ejpam-6029	448	10	bounded	bound	VERB
ejpam-6029	448	11	and	and	CCONJ
ejpam-6029	448	12	non	non	ADJ
ejpam-6029	448	13	-	-	ADJ
ejpam-6029	448	14	decreasing	decrease	VERB
ejpam-6029	448	15	,	,	PUNCT
ejpam-6029	448	16	g	g	PROPN
ejpam-6029	448	17	is	be	AUX
ejpam-6029	448	18	sub	sub	ADJ
ejpam-6029	448	19	-	-	ADJ
ejpam-6029	448	20	additive	additive	ADJ
ejpam-6029	448	21	,	,	PUNCT
ejpam-6029	448	22	and	and	CCONJ
ejpam-6029	448	23	g(λa	g(λa	NOUN
ejpam-6029	448	24	)	)	PUNCT
ejpam-6029	448	25	≺	≺	NOUN
ejpam-6029	448	26	a	a	PRON
ejpam-6029	448	27	,	,	PUNCT
ejpam-6029	448	28	λ	λ	PROPN
ejpam-6029	448	29	∈	∈	PROPN
ejpam-6029	448	30	(	(	PUNCT
ejpam-6029	448	31	0	0	NUM
ejpam-6029	448	32	,	,	PUNCT
ejpam-6029	448	33	1	1	NUM
ejpam-6029	448	34	)	)	PUNCT
ejpam-6029	448	35	;	;	PUNCT
ejpam-6029	448	36	(	(	PUNCT
ejpam-6029	448	37	ii	ii	X
ejpam-6029	448	38	)	)	PUNCT
ejpam-6029	448	39	lim	lim	PROPN
ejpam-6029	448	40	n	n	CCONJ
ejpam-6029	448	41	,	,	PUNCT
ejpam-6029	448	42	m→∞	m→∞	NUM
ejpam-6029	448	43	∑n−2	∑n−2	NOUN
ejpam-6029	449	1	i	i	PRON
ejpam-6029	449	2	=	=	VERB
ejpam-6029	449	3	m	m	VERB
ejpam-6029	449	4	∥gi−mf	∥gi−mf	NOUN
ejpam-6029	449	5	(	(	PUNCT
ejpam-6029	449	6	ξilc(a0	ξilc(a0	NOUN
ejpam-6029	449	7	,	,	PUNCT
ejpam-6029	449	8	a1	a1	NOUN
ejpam-6029	449	9	)	)	PUNCT
ejpam-6029	449	10	)	)	PUNCT
ejpam-6029	449	11	∥+	∥+	PROPN
ejpam-6029	450	1	∥gn−m−1	∥gn−m−1	PROPN
ejpam-6029	450	2	(	(	PUNCT
ejpam-6029	450	3	ξn−1lc(a0	ξn−1lc(a0	PROPN
ejpam-6029	450	4	,	,	PUNCT
ejpam-6029	450	5	a1	a1	NOUN
ejpam-6029	450	6	)	)	PUNCT
ejpam-6029	450	7	)	)	PUNCT
ejpam-6029	450	8	∥	∥	X
ejpam-6029	450	9	=	=	SYM
ejpam-6029	450	10	0	0	NUM
ejpam-6029	450	11	,	,	PUNCT
ejpam-6029	450	12	where	where	SCONJ
ejpam-6029	450	13	ξ	ξ	X
ejpam-6029	450	14	=	=	SYM
ejpam-6029	450	15	λ(a0	λ(a0	X
ejpam-6029	450	16	,	,	PUNCT
ejpam-6029	450	17	a1	a1	PROPN
ejpam-6029	450	18	)	)	PUNCT
ejpam-6029	450	19	<	<	X
ejpam-6029	450	20	1	1	X
ejpam-6029	450	21	.	.	PUNCT
ejpam-6029	451	1	if	if	SCONJ
ejpam-6029	451	2	for	for	ADP
ejpam-6029	451	3	every	every	DET
ejpam-6029	451	4	fixed	fix	VERB
ejpam-6029	451	5	point	point	NOUN
ejpam-6029	451	6	a	a	ADV
ejpam-6029	451	7	,	,	PUNCT
ejpam-6029	451	8	we	we	PRON
ejpam-6029	451	9	conclude	conclude	VERB
ejpam-6029	451	10	that	that	PRON
ejpam-6029	451	11	lc(a	lc(a	NOUN
ejpam-6029	451	12	,	,	PUNCT
ejpam-6029	451	13	a	a	PRON
ejpam-6029	451	14	)	)	PUNCT
ejpam-6029	451	15	=	=	SYM
ejpam-6029	451	16	0e	0e	NOUN
ejpam-6029	451	17	,	,	PUNCT
ejpam-6029	451	18	then	then	ADV
ejpam-6029	451	19	t	t	PROPN
ejpam-6029	451	20	k	k	PROPN
ejpam-6029	451	21	has	have	VERB
ejpam-6029	451	22	a	a	DET
ejpam-6029	451	23	unique	unique	ADJ
ejpam-6029	451	24	fixed	fix	VERB
ejpam-6029	451	25	point	point	NOUN
ejpam-6029	451	26	.	.	PUNCT
ejpam-6029	452	1	proof	proof	NOUN
ejpam-6029	452	2	.	.	PUNCT
ejpam-6029	453	1	the	the	DET
ejpam-6029	453	2	proof	proof	NOUN
ejpam-6029	453	3	follows	follow	VERB
ejpam-6029	453	4	from	from	ADP
ejpam-6029	453	5	corollary	corollary	ADJ
ejpam-6029	453	6	3	3	NUM
ejpam-6029	453	7	by	by	ADP
ejpam-6029	453	8	taking	take	VERB
ejpam-6029	453	9	t	t	PROPN
ejpam-6029	453	10	ka	ka	PROPN
ejpam-6029	454	1	=	=	PUNCT
ejpam-6029	454	2	a.	a.	PROPN
ejpam-6029	454	3	subsequently	subsequently	ADV
ejpam-6029	454	4	,	,	PUNCT
ejpam-6029	454	5	we	we	PRON
ejpam-6029	454	6	observe	observe	VERB
ejpam-6029	454	7	t	t	PROPN
ejpam-6029	454	8	k(ta	k(ta	PROPN
ejpam-6029	454	9	)	)	PUNCT
ejpam-6029	454	10	=	=	SYM
ejpam-6029	454	11	t	t	PROPN
ejpam-6029	454	12	(	(	PUNCT
ejpam-6029	454	13	t	t	PROPN
ejpam-6029	454	14	ka	ka	PROPN
ejpam-6029	454	15	)	)	PUNCT
ejpam-6029	454	16	=	=	SYM
ejpam-6029	454	17	ta	ta	PROPN
ejpam-6029	454	18	.	.	PUNCT
ejpam-6029	455	1	hence	hence	ADV
ejpam-6029	455	2	,	,	PUNCT
ejpam-6029	455	3	t	t	PROPN
ejpam-6029	455	4	k	k	PROPN
ejpam-6029	455	5	has	have	VERB
ejpam-6029	455	6	a	a	DET
ejpam-6029	455	7	fixed	fix	VERB
ejpam-6029	455	8	point	point	NOUN
ejpam-6029	455	9	ta	ta	PROPN
ejpam-6029	455	10	and	and	CCONJ
ejpam-6029	455	11	ta	ta	X
ejpam-6029	455	12	=	=	PUNCT
ejpam-6029	455	13	a	a	PROPN
ejpam-6029	455	14	,	,	PUNCT
ejpam-6029	455	15	which	which	PRON
ejpam-6029	455	16	means	mean	VERB
ejpam-6029	455	17	that	that	SCONJ
ejpam-6029	455	18	t	t	PROPN
ejpam-6029	455	19	k	k	PROPN
ejpam-6029	455	20	has	have	VERB
ejpam-6029	455	21	a	a	DET
ejpam-6029	455	22	unique	unique	ADJ
ejpam-6029	455	23	fixed	fix	VERB
ejpam-6029	455	24	point	point	NOUN
ejpam-6029	455	25	,	,	PUNCT
ejpam-6029	455	26	where	where	SCONJ
ejpam-6029	455	27	t	t	PROPN
ejpam-6029	455	28	has	have	VERB
ejpam-6029	455	29	a	a	DET
ejpam-6029	455	30	fixed	fix	VERB
ejpam-6029	455	31	point	point	NOUN
ejpam-6029	456	1	a.	a.	NOUN
ejpam-6029	456	2	a.	a.	PROPN
ejpam-6029	456	3	a.	a.	PROPN
ejpam-6029	457	1	hijab	hijab	PROPN
ejpam-6029	457	2	et	et	PROPN
ejpam-6029	457	3	al	al	PROPN
ejpam-6029	457	4	.	.	PUNCT
ejpam-6029	457	5	/	/	SYM
ejpam-6029	457	6	eur	eur	PROPN
ejpam-6029	457	7	.	.	PUNCT
ejpam-6029	458	1	j.	j.	PROPN
ejpam-6029	458	2	pure	pure	PROPN
ejpam-6029	458	3	appl	appl	PROPN
ejpam-6029	458	4	.	.	PROPN
ejpam-6029	458	5	math	math	PROPN
ejpam-6029	458	6	,	,	PUNCT
ejpam-6029	458	7	18	18	NUM
ejpam-6029	458	8	(	(	PUNCT
ejpam-6029	458	9	2	2	NUM
ejpam-6029	458	10	)	)	PUNCT
ejpam-6029	458	11	(	(	PUNCT
ejpam-6029	458	12	2025	2025	NUM
ejpam-6029	458	13	)	)	PUNCT
ejpam-6029	458	14	,	,	PUNCT
ejpam-6029	458	15	6029	6029	NUM
ejpam-6029	458	16	17	17	NUM
ejpam-6029	458	17	of	of	ADP
ejpam-6029	458	18	23	23	NUM
ejpam-6029	458	19	corollary	corollary	ADJ
ejpam-6029	458	20	6	6	NUM
ejpam-6029	458	21	.	.	PUNCT
ejpam-6029	459	1	suppose	suppose	VERB
ejpam-6029	459	2	(	(	PUNCT
ejpam-6029	459	3	γ	γ	X
ejpam-6029	459	4	,	,	PUNCT
ejpam-6029	459	5	lc	lc	PROPN
ejpam-6029	459	6	)	)	PUNCT
ejpam-6029	459	7	is	be	AUX
ejpam-6029	459	8	a	a	DET
ejpam-6029	459	9	complete	complete	ADJ
ejpam-6029	459	10	c2cms	c2cms	NOUN
ejpam-6029	459	11	with	with	ADP
ejpam-6029	459	12	two	two	NUM
ejpam-6029	459	13	non	non	ADJ
ejpam-6029	459	14	-	-	ADJ
ejpam-6029	459	15	constant	constant	ADJ
ejpam-6029	459	16	functions	function	NOUN
ejpam-6029	459	17	f	f	NOUN
ejpam-6029	459	18	,	,	PUNCT
ejpam-6029	459	19	g	g	NOUN
ejpam-6029	459	20	:	:	PUNCT
ejpam-6029	459	21	p	p	X
ejpam-6029	459	22	→	→	SYM
ejpam-6029	459	23	p	p	X
ejpam-6029	459	24	,	,	PUNCT
ejpam-6029	459	25	where	where	SCONJ
ejpam-6029	459	26	p	p	NOUN
ejpam-6029	459	27	is	be	AUX
ejpam-6029	459	28	a	a	DET
ejpam-6029	459	29	normal	normal	ADJ
ejpam-6029	459	30	cone	cone	NOUN
ejpam-6029	459	31	via	via	ADP
ejpam-6029	459	32	normal	normal	ADJ
ejpam-6029	459	33	constant	constant	ADJ
ejpam-6029	459	34	m	m	NOUN
ejpam-6029	459	35	.	.	PUNCT
ejpam-6029	460	1	let	let	VERB
ejpam-6029	460	2	t	t	NOUN
ejpam-6029	460	3	:	:	PUNCT
ejpam-6029	460	4	γ	γ	X
ejpam-6029	460	5	→	→	SYM
ejpam-6029	460	6	γ	γ	X
ejpam-6029	460	7	be	be	AUX
ejpam-6029	460	8	a	a	DET
ejpam-6029	460	9	mapping	mapping	NOUN
ejpam-6029	460	10	and	and	CCONJ
ejpam-6029	460	11	there	there	PRON
ejpam-6029	460	12	exists	exist	VERB
ejpam-6029	460	13	λ	λ	PROPN
ejpam-6029	460	14	∈	∈	PROPN
ejpam-6029	460	15	∆	∆	PROPN
ejpam-6029	460	16	such	such	ADJ
ejpam-6029	460	17	that	that	PRON
ejpam-6029	460	18	dc(t	dc(t	PROPN
ejpam-6029	460	19	ka	ka	PROPN
ejpam-6029	460	20	,	,	PUNCT
ejpam-6029	460	21	t	t	PROPN
ejpam-6029	460	22	kb	kb	PROPN
ejpam-6029	460	23	)	)	PUNCT
ejpam-6029	460	24	⪯	⪯	PROPN
ejpam-6029	460	25	λ(a	λ(a	PROPN
ejpam-6029	460	26	,	,	PUNCT
ejpam-6029	460	27	b)m̃(a	b)m̃(a	PROPN
ejpam-6029	460	28	,	,	PUNCT
ejpam-6029	460	29	b	b	NOUN
ejpam-6029	460	30	)	)	PUNCT
ejpam-6029	460	31	,	,	PUNCT
ejpam-6029	460	32	for	for	ADP
ejpam-6029	460	33	all	all	DET
ejpam-6029	460	34	a	a	PRON
ejpam-6029	460	35	,	,	PUNCT
ejpam-6029	460	36	b	b	PROPN
ejpam-6029	460	37	∈	∈	PROPN
ejpam-6029	460	38	γ	γ	X
ejpam-6029	460	39	,	,	PUNCT
ejpam-6029	460	40	(	(	PUNCT
ejpam-6029	460	41	14	14	NUM
ejpam-6029	460	42	)	)	PUNCT
ejpam-6029	460	43	where	where	SCONJ
ejpam-6029	460	44	m̃(a	m̃(a	NOUN
ejpam-6029	460	45	,	,	PUNCT
ejpam-6029	460	46	b	b	NOUN
ejpam-6029	460	47	)	)	PUNCT
ejpam-6029	460	48	=	=	SYM
ejpam-6029	460	49	max	max	PROPN
ejpam-6029	460	50	{	{	PUNCT
ejpam-6029	460	51	dc(a	dc(a	X
ejpam-6029	460	52	,	,	PUNCT
ejpam-6029	460	53	b),dc(a	b),dc(a	PROPN
ejpam-6029	460	54	,	,	PUNCT
ejpam-6029	460	55	t	t	PROPN
ejpam-6029	460	56	ka),dc(b	ka),dc(b	PROPN
ejpam-6029	460	57	,	,	PUNCT
ejpam-6029	460	58	t	t	PROPN
ejpam-6029	460	59	kb	kb	PROPN
ejpam-6029	460	60	)	)	PUNCT
ejpam-6029	460	61	,	,	PUNCT
ejpam-6029	460	62	dc(a	dc(a	PROPN
ejpam-6029	460	63	,	,	PUNCT
ejpam-6029	460	64	t	t	PROPN
ejpam-6029	460	65	ka)dc(b	ka)dc(b	PROPN
ejpam-6029	460	66	,	,	PUNCT
ejpam-6029	460	67	t	t	PROPN
ejpam-6029	460	68	kb	kb	PROPN
ejpam-6029	460	69	)	)	PUNCT
ejpam-6029	460	70	1	1	NUM
ejpam-6029	461	1	+	+	NOUN
ejpam-6029	461	2	dc(a	dc(a	NOUN
ejpam-6029	461	3	,	,	PUNCT
ejpam-6029	461	4	b	b	NOUN
ejpam-6029	461	5	)	)	PUNCT
ejpam-6029	461	6	,	,	PUNCT
ejpam-6029	461	7	dc(b	dc(b	PROPN
ejpam-6029	461	8	,	,	PUNCT
ejpam-6029	461	9	t	t	PROPN
ejpam-6029	461	10	kb	kb	PROPN
ejpam-6029	461	11	)	)	PUNCT
ejpam-6029	461	12	[	[	PUNCT
ejpam-6029	461	13	1	1	NUM
ejpam-6029	461	14	+	+	NOUN
ejpam-6029	461	15	dc(a	dc(a	NOUN
ejpam-6029	461	16	,	,	PUNCT
ejpam-6029	461	17	t	t	PROPN
ejpam-6029	461	18	ka	ka	PROPN
ejpam-6029	461	19	)	)	PUNCT
ejpam-6029	461	20	]	]	PUNCT
ejpam-6029	462	1	1	1	NUM
ejpam-6029	462	2	+	+	NOUN
ejpam-6029	462	3	dc(a	dc(a	NOUN
ejpam-6029	462	4	,	,	PUNCT
ejpam-6029	462	5	b	b	NOUN
ejpam-6029	462	6	)	)	PUNCT
ejpam-6029	462	7	,	,	PUNCT
ejpam-6029	462	8	[	[	PUNCT
ejpam-6029	462	9	dc(a	dc(a	X
ejpam-6029	462	10	,	,	PUNCT
ejpam-6029	462	11	t	t	PROPN
ejpam-6029	462	12	ka	ka	PROPN
ejpam-6029	462	13	)	)	PUNCT
ejpam-6029	462	14	+	+	NOUN
ejpam-6029	462	15	dc(b	dc(b	ADJ
ejpam-6029	462	16	,	,	PUNCT
ejpam-6029	462	17	t	t	PROPN
ejpam-6029	462	18	kb	kb	PROPN
ejpam-6029	462	19	)	)	PUNCT
ejpam-6029	462	20	]	]	PUNCT
ejpam-6029	462	21	dc(t	dc(t	X
ejpam-6029	463	1	ka	ka	PROPN
ejpam-6029	463	2	,	,	PUNCT
ejpam-6029	463	3	t	t	PROPN
ejpam-6029	463	4	kb	kb	PROPN
ejpam-6029	463	5	)	)	PUNCT
ejpam-6029	463	6	1	1	NUM
ejpam-6029	464	1	+	+	NOUN
ejpam-6029	464	2	dc(a	dc(a	NOUN
ejpam-6029	464	3	,	,	PUNCT
ejpam-6029	464	4	b	b	NOUN
ejpam-6029	464	5	)	)	PUNCT
ejpam-6029	464	6	+	+	PROPN
ejpam-6029	464	7	dc(t	dc(t	X
ejpam-6029	464	8	ka	ka	PROPN
ejpam-6029	464	9	,	,	PUNCT
ejpam-6029	464	10	t	t	PROPN
ejpam-6029	464	11	kb	kb	PROPN
ejpam-6029	464	12	)	)	PUNCT
ejpam-6029	464	13	}	}	PUNCT
ejpam-6029	464	14	.	.	PUNCT
ejpam-6029	465	1	for	for	ADP
ejpam-6029	465	2	a0	a0	PROPN
ejpam-6029	465	3	∈	∈	PROPN
ejpam-6029	465	4	γ	γ	PROPN
ejpam-6029	465	5	,	,	PUNCT
ejpam-6029	465	6	take	take	VERB
ejpam-6029	465	7	the	the	DET
ejpam-6029	465	8	sequence	sequence	NOUN
ejpam-6029	465	9	{	{	PUNCT
ejpam-6029	465	10	an	an	PRON
ejpam-6029	465	11	}	}	PUNCT
ejpam-6029	465	12	defined	define	VERB
ejpam-6029	465	13	as	as	ADP
ejpam-6029	465	14	an+1	an+1	NOUN
ejpam-6029	465	15	=	=	SYM
ejpam-6029	465	16	tna0	tna0	PROPN
ejpam-6029	465	17	for	for	ADP
ejpam-6029	465	18	every	every	DET
ejpam-6029	465	19	n	n	PRON
ejpam-6029	465	20	≥	≥	NOUN
ejpam-6029	465	21	0	0	NUM
ejpam-6029	465	22	.	.	PUNCT
ejpam-6029	466	1	suppose	suppose	VERB
ejpam-6029	466	2	(	(	PUNCT
ejpam-6029	466	3	i	i	NOUN
ejpam-6029	466	4	)	)	PUNCT
ejpam-6029	466	5	f	f	PROPN
ejpam-6029	466	6	and	and	CCONJ
ejpam-6029	466	7	g	g	PROPN
ejpam-6029	466	8	are	be	AUX
ejpam-6029	466	9	bounded	bound	VERB
ejpam-6029	466	10	and	and	CCONJ
ejpam-6029	466	11	non	non	ADJ
ejpam-6029	466	12	-	-	ADJ
ejpam-6029	466	13	decreasing	decrease	VERB
ejpam-6029	466	14	,	,	PUNCT
ejpam-6029	466	15	g	g	PROPN
ejpam-6029	466	16	is	be	AUX
ejpam-6029	466	17	sub	sub	ADJ
ejpam-6029	466	18	-	-	ADJ
ejpam-6029	466	19	additive	additive	ADJ
ejpam-6029	466	20	,	,	PUNCT
ejpam-6029	466	21	and	and	CCONJ
ejpam-6029	466	22	g(λa	g(λa	NOUN
ejpam-6029	466	23	)	)	PUNCT
ejpam-6029	466	24	≺	≺	NOUN
ejpam-6029	466	25	a	a	PRON
ejpam-6029	466	26	,	,	PUNCT
ejpam-6029	466	27	λ	λ	PROPN
ejpam-6029	466	28	∈	∈	PROPN
ejpam-6029	466	29	(	(	PUNCT
ejpam-6029	466	30	0	0	NUM
ejpam-6029	466	31	,	,	PUNCT
ejpam-6029	466	32	1	1	NUM
ejpam-6029	466	33	)	)	PUNCT
ejpam-6029	466	34	;	;	PUNCT
ejpam-6029	466	35	(	(	PUNCT
ejpam-6029	466	36	ii	ii	X
ejpam-6029	466	37	)	)	PUNCT
ejpam-6029	466	38	lim	lim	PROPN
ejpam-6029	466	39	n	n	CCONJ
ejpam-6029	466	40	,	,	PUNCT
ejpam-6029	466	41	m→∞	m→∞	NUM
ejpam-6029	466	42	∑n−2	∑n−2	NOUN
ejpam-6029	467	1	i	i	PRON
ejpam-6029	467	2	=	=	VERB
ejpam-6029	467	3	m	m	VERB
ejpam-6029	467	4	∥gi−mf	∥gi−mf	NOUN
ejpam-6029	467	5	(	(	PUNCT
ejpam-6029	467	6	ξidc(a0	ξidc(a0	X
ejpam-6029	467	7	,	,	PUNCT
ejpam-6029	467	8	a1	a1	NOUN
ejpam-6029	467	9	)	)	PUNCT
ejpam-6029	467	10	)	)	PUNCT
ejpam-6029	467	11	∥+	∥+	PROPN
ejpam-6029	468	1	∥gn−m−1	∥gn−m−1	PROPN
ejpam-6029	468	2	(	(	PUNCT
ejpam-6029	468	3	ξn−1dc(a0	ξn−1dc(a0	PROPN
ejpam-6029	468	4	,	,	PUNCT
ejpam-6029	468	5	a1	a1	NOUN
ejpam-6029	468	6	)	)	PUNCT
ejpam-6029	468	7	)	)	PUNCT
ejpam-6029	468	8	∥	∥	X
ejpam-6029	468	9	=	=	SYM
ejpam-6029	468	10	0	0	NUM
ejpam-6029	468	11	,	,	PUNCT
ejpam-6029	468	12	where	where	SCONJ
ejpam-6029	468	13	ξ	ξ	X
ejpam-6029	468	14	=	=	SYM
ejpam-6029	468	15	λ(a0	λ(a0	X
ejpam-6029	468	16	,	,	PUNCT
ejpam-6029	468	17	a1	a1	PROPN
ejpam-6029	468	18	)	)	PUNCT
ejpam-6029	468	19	<	<	X
ejpam-6029	468	20	1	1	X
ejpam-6029	468	21	.	.	PUNCT
ejpam-6029	469	1	then	then	ADV
ejpam-6029	469	2	t	t	PROPN
ejpam-6029	469	3	k	k	PROPN
ejpam-6029	469	4	ensures	ensure	VERB
ejpam-6029	469	5	a	a	DET
ejpam-6029	469	6	unique	unique	ADJ
ejpam-6029	469	7	fixed	fix	VERB
ejpam-6029	469	8	point	point	NOUN
ejpam-6029	469	9	.	.	PUNCT
ejpam-6029	470	1	corollary	corollary	ADJ
ejpam-6029	470	2	7	7	PROPN
ejpam-6029	470	3	.	.	PUNCT
ejpam-6029	471	1	assume	assume	VERB
ejpam-6029	471	2	(	(	PUNCT
ejpam-6029	471	3	γ	γ	X
ejpam-6029	471	4	,	,	PUNCT
ejpam-6029	471	5	lc	lc	PROPN
ejpam-6029	471	6	)	)	PUNCT
ejpam-6029	471	7	is	be	AUX
ejpam-6029	471	8	an	an	DET
ejpam-6029	471	9	lc	lc	NOUN
ejpam-6029	471	10	-	-	PUNCT
ejpam-6029	471	11	complete	complete	ADJ
ejpam-6029	471	12	dccml	dccml	NOUN
ejpam-6029	471	13	-	-	PUNCT
ejpam-6029	471	14	space	space	NOUN
ejpam-6029	471	15	with	with	ADP
ejpam-6029	471	16	two	two	NUM
ejpam-6029	471	17	non	non	ADJ
ejpam-6029	471	18	-	-	ADJ
ejpam-6029	471	19	constant	constant	ADJ
ejpam-6029	471	20	functions	function	NOUN
ejpam-6029	471	21	f	f	NOUN
ejpam-6029	471	22	,	,	PUNCT
ejpam-6029	471	23	g	g	NOUN
ejpam-6029	471	24	:	:	PUNCT
ejpam-6029	471	25	p	p	X
ejpam-6029	471	26	→	→	SYM
ejpam-6029	471	27	p	p	X
ejpam-6029	471	28	,	,	PUNCT
ejpam-6029	471	29	where	where	SCONJ
ejpam-6029	471	30	p	p	NOUN
ejpam-6029	471	31	is	be	AUX
ejpam-6029	471	32	a	a	DET
ejpam-6029	471	33	normal	normal	ADJ
ejpam-6029	471	34	cone	cone	NOUN
ejpam-6029	471	35	via	via	ADP
ejpam-6029	471	36	normal	normal	ADJ
ejpam-6029	471	37	constant	constant	ADJ
ejpam-6029	471	38	m	m	NOUN
ejpam-6029	471	39	.	.	PUNCT
ejpam-6029	472	1	let	let	VERB
ejpam-6029	472	2	t	t	NOUN
ejpam-6029	472	3	:	:	PUNCT
ejpam-6029	472	4	γ	γ	X
ejpam-6029	472	5	→	→	SYM
ejpam-6029	472	6	γ	γ	X
ejpam-6029	472	7	be	be	AUX
ejpam-6029	472	8	a	a	DET
ejpam-6029	472	9	mapping	mapping	NOUN
ejpam-6029	472	10	and	and	CCONJ
ejpam-6029	472	11	there	there	PRON
ejpam-6029	472	12	exists	exist	VERB
ejpam-6029	472	13	λj	λj	PROPN
ejpam-6029	472	14	∈	∈	PROPN
ejpam-6029	472	15	∆	∆	PROPN
ejpam-6029	472	16	,	,	PUNCT
ejpam-6029	472	17	j	j	PROPN
ejpam-6029	472	18	=	=	SYM
ejpam-6029	472	19	1	1	NUM
ejpam-6029	472	20	,	,	PUNCT
ejpam-6029	472	21	·	·	PUNCT
ejpam-6029	472	22	·	·	PUNCT
ejpam-6029	472	23	·	·	PUNCT
ejpam-6029	472	24	,	,	PUNCT
ejpam-6029	472	25	6	6	NUM
ejpam-6029	472	26	,	,	PUNCT
ejpam-6029	472	27	such	such	ADJ
ejpam-6029	472	28	that	that	SCONJ
ejpam-6029	472	29	lc(t	lc(t	PROPN
ejpam-6029	472	30	ka	ka	PROPN
ejpam-6029	472	31	,	,	PUNCT
ejpam-6029	472	32	t	t	PROPN
ejpam-6029	472	33	kb	kb	PROPN
ejpam-6029	472	34	)	)	PUNCT
ejpam-6029	472	35	⪯λ1(a	⪯λ1(a	PROPN
ejpam-6029	472	36	,	,	PUNCT
ejpam-6029	472	37	b)lc(a	b)lc(a	NUM
ejpam-6029	472	38	,	,	PUNCT
ejpam-6029	472	39	b	b	NOUN
ejpam-6029	472	40	)	)	PUNCT
ejpam-6029	472	41	+	+	SYM
ejpam-6029	472	42	λ2(a	λ2(a	NOUN
ejpam-6029	472	43	,	,	PUNCT
ejpam-6029	472	44	b)lc(a	b)lc(a	PROPN
ejpam-6029	472	45	,	,	PUNCT
ejpam-6029	472	46	t	t	PROPN
ejpam-6029	472	47	ka	ka	PROPN
ejpam-6029	472	48	)	)	PUNCT
ejpam-6029	473	1	+	+	PUNCT
ejpam-6029	474	1	λ3(a	λ3(a	NOUN
ejpam-6029	474	2	,	,	PUNCT
ejpam-6029	474	3	b)lc(b	b)lc(b	NOUN
ejpam-6029	474	4	,	,	PUNCT
ejpam-6029	474	5	t	t	PROPN
ejpam-6029	474	6	kb	kb	PROPN
ejpam-6029	474	7	)	)	PUNCT
ejpam-6029	475	1	+	+	CCONJ
ejpam-6029	475	2	λ4(a	λ4(a	PROPN
ejpam-6029	475	3	,	,	PUNCT
ejpam-6029	475	4	b	b	NOUN
ejpam-6029	475	5	)	)	PUNCT
ejpam-6029	475	6	lc(a	lc(a	PROPN
ejpam-6029	475	7	,	,	PUNCT
ejpam-6029	475	8	t	t	PROPN
ejpam-6029	475	9	ka)lc(b	ka)lc(b	PROPN
ejpam-6029	475	10	,	,	PUNCT
ejpam-6029	475	11	t	t	PROPN
ejpam-6029	475	12	kb	kb	PROPN
ejpam-6029	475	13	)	)	PUNCT
ejpam-6029	475	14	1	1	NUM
ejpam-6029	476	1	+	+	CCONJ
ejpam-6029	476	2	lc(a	lc(a	NUM
ejpam-6029	476	3	,	,	PUNCT
ejpam-6029	476	4	b	b	NOUN
ejpam-6029	476	5	)	)	PUNCT
ejpam-6029	477	1	+	+	CCONJ
ejpam-6029	477	2	λ5(a	λ5(a	NUM
ejpam-6029	477	3	,	,	PUNCT
ejpam-6029	477	4	b	b	NOUN
ejpam-6029	477	5	)	)	PUNCT
ejpam-6029	477	6	lc(b	lc(b	NOUN
ejpam-6029	477	7	,	,	PUNCT
ejpam-6029	477	8	t	t	PROPN
ejpam-6029	477	9	kb	kb	PROPN
ejpam-6029	477	10	)	)	PUNCT
ejpam-6029	478	1	[	[	PUNCT
ejpam-6029	478	2	1	1	NUM
ejpam-6029	478	3	+	+	CCONJ
ejpam-6029	478	4	lc(a	lc(a	NUM
ejpam-6029	478	5	,	,	PUNCT
ejpam-6029	478	6	t	t	PROPN
ejpam-6029	478	7	ka	ka	PROPN
ejpam-6029	478	8	)	)	PUNCT
ejpam-6029	478	9	]	]	PUNCT
ejpam-6029	479	1	1	1	NUM
ejpam-6029	479	2	+	+	CCONJ
ejpam-6029	479	3	lc(a	lc(a	NUM
ejpam-6029	479	4	,	,	PUNCT
ejpam-6029	479	5	b	b	NOUN
ejpam-6029	479	6	)	)	PUNCT
ejpam-6029	479	7	+	+	PROPN
ejpam-6029	480	1	λ6(a	λ6(a	NUM
ejpam-6029	480	2	,	,	PUNCT
ejpam-6029	480	3	b	b	NOUN
ejpam-6029	480	4	)	)	PUNCT
ejpam-6029	480	5	[	[	PUNCT
ejpam-6029	480	6	lc(a	lc(a	X
ejpam-6029	480	7	,	,	PUNCT
ejpam-6029	480	8	t	t	PROPN
ejpam-6029	480	9	ka	ka	PROPN
ejpam-6029	480	10	)	)	PUNCT
ejpam-6029	481	1	+	+	CCONJ
ejpam-6029	481	2	lc(b	lc(b	PROPN
ejpam-6029	481	3	,	,	PUNCT
ejpam-6029	481	4	t	t	PROPN
ejpam-6029	481	5	kb	kb	PROPN
ejpam-6029	481	6	)	)	PUNCT
ejpam-6029	481	7	]	]	PUNCT
ejpam-6029	482	1	lc(t	lc(t	PROPN
ejpam-6029	482	2	ka	ka	PROPN
ejpam-6029	482	3	,	,	PUNCT
ejpam-6029	482	4	t	t	PROPN
ejpam-6029	482	5	kb	kb	PROPN
ejpam-6029	482	6	)	)	PUNCT
ejpam-6029	482	7	1	1	NUM
ejpam-6029	483	1	+	+	CCONJ
ejpam-6029	483	2	lc(a	lc(a	NUM
ejpam-6029	483	3	,	,	PUNCT
ejpam-6029	483	4	b	b	NOUN
ejpam-6029	483	5	)	)	PUNCT
ejpam-6029	483	6	+	+	CCONJ
ejpam-6029	483	7	lc(t	lc(t	X
ejpam-6029	483	8	ka	ka	PROPN
ejpam-6029	483	9	,	,	PUNCT
ejpam-6029	483	10	t	t	PROPN
ejpam-6029	483	11	kb	kb	PROPN
ejpam-6029	483	12	)	)	PUNCT
ejpam-6029	483	13	,	,	PUNCT
ejpam-6029	483	14	(	(	PUNCT
ejpam-6029	483	15	15	15	NUM
ejpam-6029	483	16	)	)	PUNCT
ejpam-6029	483	17	for	for	ADP
ejpam-6029	483	18	all	all	DET
ejpam-6029	483	19	a	a	PRON
ejpam-6029	483	20	,	,	PUNCT
ejpam-6029	483	21	b	b	PROPN
ejpam-6029	483	22	∈	∈	PROPN
ejpam-6029	483	23	γ	γ	X
ejpam-6029	483	24	,	,	PUNCT
ejpam-6029	483	25	where	where	SCONJ
ejpam-6029	483	26	∑6	∑6	PROPN
ejpam-6029	483	27	j=1	j=1	PROPN
ejpam-6029	483	28	λj(a	λj(a	X
ejpam-6029	483	29	,	,	PUNCT
ejpam-6029	483	30	b	b	X
ejpam-6029	483	31	)	)	PUNCT
ejpam-6029	483	32	<	<	X
ejpam-6029	484	1	1	1	X
ejpam-6029	484	2	.	.	X
ejpam-6029	484	3	for	for	ADP
ejpam-6029	484	4	a0	a0	PROPN
ejpam-6029	484	5	∈	∈	PROPN
ejpam-6029	484	6	γ	γ	PROPN
ejpam-6029	484	7	,	,	PUNCT
ejpam-6029	484	8	take	take	VERB
ejpam-6029	484	9	the	the	DET
ejpam-6029	484	10	sequence	sequence	NOUN
ejpam-6029	484	11	{	{	PUNCT
ejpam-6029	484	12	an	an	PRON
ejpam-6029	484	13	}	}	PUNCT
ejpam-6029	484	14	as	as	ADP
ejpam-6029	484	15	an+1	an+1	NOUN
ejpam-6029	484	16	=	=	SYM
ejpam-6029	484	17	tna0	tna0	PROPN
ejpam-6029	484	18	for	for	ADP
ejpam-6029	484	19	every	every	DET
ejpam-6029	484	20	n	n	PRON
ejpam-6029	484	21	≥	≥	NOUN
ejpam-6029	484	22	0	0	NUM
ejpam-6029	484	23	.	.	PUNCT
ejpam-6029	485	1	let	let	VERB
ejpam-6029	485	2	ξ	ξ	X
ejpam-6029	485	3	=	=	SYM
ejpam-6029	485	4	λ1(a0,a1)+λ2(a0,a1	λ1(a0,a1)+λ2(a0,a1	X
ejpam-6029	485	5	)	)	PUNCT
ejpam-6029	486	1	1−	1−	NUM
ejpam-6029	486	2	∑6	∑6	PROPN
ejpam-6029	486	3	j=3	j=3	CCONJ
ejpam-6029	486	4	λj(a0,a1	λj(a0,a1	NUM
ejpam-6029	486	5	)	)	PUNCT
ejpam-6029	486	6	<	<	X
ejpam-6029	486	7	1	1	X
ejpam-6029	486	8	.	.	PUNCT
ejpam-6029	486	9	suppose	suppose	VERB
ejpam-6029	486	10	that	that	SCONJ
ejpam-6029	486	11	(	(	PUNCT
ejpam-6029	486	12	i	i	NOUN
ejpam-6029	486	13	)	)	PUNCT
ejpam-6029	486	14	f	f	PROPN
ejpam-6029	486	15	and	and	CCONJ
ejpam-6029	486	16	g	g	PROPN
ejpam-6029	486	17	are	be	AUX
ejpam-6029	486	18	bounded	bound	VERB
ejpam-6029	486	19	and	and	CCONJ
ejpam-6029	486	20	non	non	ADJ
ejpam-6029	486	21	-	-	ADJ
ejpam-6029	486	22	decreasing	decrease	VERB
ejpam-6029	486	23	,	,	PUNCT
ejpam-6029	486	24	g	g	PROPN
ejpam-6029	486	25	is	be	AUX
ejpam-6029	486	26	sub	sub	ADJ
ejpam-6029	486	27	-	-	ADJ
ejpam-6029	486	28	additive	additive	ADJ
ejpam-6029	486	29	,	,	PUNCT
ejpam-6029	486	30	and	and	CCONJ
ejpam-6029	486	31	g(λa	g(λa	NOUN
ejpam-6029	486	32	)	)	PUNCT
ejpam-6029	486	33	≺	≺	NOUN
ejpam-6029	486	34	a	a	PRON
ejpam-6029	486	35	,	,	PUNCT
ejpam-6029	486	36	λ	λ	PROPN
ejpam-6029	486	37	∈	∈	PROPN
ejpam-6029	486	38	(	(	PUNCT
ejpam-6029	486	39	0	0	NUM
ejpam-6029	486	40	,	,	PUNCT
ejpam-6029	486	41	1	1	NUM
ejpam-6029	486	42	)	)	PUNCT
ejpam-6029	486	43	;	;	PUNCT
ejpam-6029	486	44	(	(	PUNCT
ejpam-6029	486	45	ii	ii	X
ejpam-6029	486	46	)	)	PUNCT
ejpam-6029	486	47	lim	lim	PROPN
ejpam-6029	486	48	n	n	CCONJ
ejpam-6029	486	49	,	,	PUNCT
ejpam-6029	486	50	m→∞	m→∞	NUM
ejpam-6029	486	51	∑n−2	∑n−2	NOUN
ejpam-6029	487	1	i	i	PRON
ejpam-6029	487	2	=	=	VERB
ejpam-6029	487	3	m	m	VERB
ejpam-6029	487	4	∥gi−mf	∥gi−mf	NOUN
ejpam-6029	487	5	(	(	PUNCT
ejpam-6029	487	6	ξilc(a0	ξilc(a0	NOUN
ejpam-6029	487	7	,	,	PUNCT
ejpam-6029	487	8	a1	a1	NOUN
ejpam-6029	487	9	)	)	PUNCT
ejpam-6029	487	10	)	)	PUNCT
ejpam-6029	487	11	∥+	∥+	PROPN
ejpam-6029	488	1	∥gn−m−1	∥gn−m−1	PROPN
ejpam-6029	488	2	(	(	PUNCT
ejpam-6029	488	3	ξn−1lc(a0	ξn−1lc(a0	PROPN
ejpam-6029	488	4	,	,	PUNCT
ejpam-6029	488	5	a1	a1	NOUN
ejpam-6029	488	6	)	)	PUNCT
ejpam-6029	488	7	)	)	PUNCT
ejpam-6029	488	8	∥	∥	X
ejpam-6029	488	9	=	=	PUNCT
ejpam-6029	489	1	0	0	X
ejpam-6029	489	2	.	.	PUNCT
ejpam-6029	490	1	if	if	SCONJ
ejpam-6029	490	2	for	for	ADP
ejpam-6029	490	3	every	every	DET
ejpam-6029	490	4	fixed	fix	VERB
ejpam-6029	490	5	point	point	NOUN
ejpam-6029	490	6	a	a	ADV
ejpam-6029	490	7	,	,	PUNCT
ejpam-6029	490	8	we	we	PRON
ejpam-6029	490	9	conclude	conclude	VERB
ejpam-6029	490	10	that	that	PRON
ejpam-6029	490	11	lc(a	lc(a	NOUN
ejpam-6029	490	12	,	,	PUNCT
ejpam-6029	490	13	a	a	PRON
ejpam-6029	490	14	)	)	PUNCT
ejpam-6029	490	15	=	=	SYM
ejpam-6029	490	16	0e	0e	NOUN
ejpam-6029	490	17	,	,	PUNCT
ejpam-6029	490	18	then	then	ADV
ejpam-6029	490	19	t	t	PROPN
ejpam-6029	490	20	k	k	PROPN
ejpam-6029	490	21	possesses	possess	VERB
ejpam-6029	490	22	a	a	DET
ejpam-6029	490	23	unique	unique	ADJ
ejpam-6029	490	24	fixed	fix	VERB
ejpam-6029	490	25	point	point	NOUN
ejpam-6029	490	26	.	.	PUNCT
ejpam-6029	491	1	4	4	X
ejpam-6029	491	2	.	.	X
ejpam-6029	491	3	applications	application	NOUN
ejpam-6029	491	4	the	the	DET
ejpam-6029	491	5	fixed	fix	VERB
ejpam-6029	491	6	-	-	PUNCT
ejpam-6029	491	7	point	point	NOUN
ejpam-6029	491	8	results	result	NOUN
ejpam-6029	491	9	play	play	VERB
ejpam-6029	491	10	a	a	DET
ejpam-6029	491	11	vital	vital	ADJ
ejpam-6029	491	12	role	role	NOUN
ejpam-6029	491	13	in	in	ADP
ejpam-6029	491	14	the	the	DET
ejpam-6029	491	15	existence	existence	NOUN
ejpam-6029	491	16	of	of	ADP
ejpam-6029	491	17	theory	theory	NOUN
ejpam-6029	491	18	of	of	ADP
ejpam-6029	491	19	various	various	ADJ
ejpam-6029	491	20	classes	class	NOUN
ejpam-6029	491	21	of	of	ADP
ejpam-6029	491	22	equations	equation	NOUN
ejpam-6029	491	23	,	,	PUNCT
ejpam-6029	491	24	particularly	particularly	ADV
ejpam-6029	491	25	,	,	PUNCT
ejpam-6029	491	26	for	for	ADP
ejpam-6029	491	27	solving	solve	VERB
ejpam-6029	491	28	differential	differential	ADJ
ejpam-6029	491	29	equations	equation	NOUN
ejpam-6029	491	30	,	,	PUNCT
ejpam-6029	491	31	integral	integral	ADJ
ejpam-6029	491	32	equations	equation	NOUN
ejpam-6029	491	33	,	,	PUNCT
ejpam-6029	491	34	and	and	CCONJ
ejpam-6029	491	35	fractional	fractional	ADJ
ejpam-6029	491	36	differential	differential	ADJ
ejpam-6029	491	37	equations	equation	NOUN
ejpam-6029	491	38	.	.	PUNCT
ejpam-6029	492	1	this	this	PRON
ejpam-6029	492	2	has	have	AUX
ejpam-6029	492	3	led	lead	VERB
ejpam-6029	492	4	to	to	ADP
ejpam-6029	492	5	significant	significant	ADJ
ejpam-6029	492	6	improvements	improvement	NOUN
ejpam-6029	492	7	in	in	ADP
ejpam-6029	492	8	the	the	DET
ejpam-6029	492	9	applications	application	NOUN
ejpam-6029	492	10	of	of	ADP
ejpam-6029	492	11	fixedpoint	fixedpoint	NOUN
ejpam-6029	492	12	techniques	technique	NOUN
ejpam-6029	492	13	.	.	PUNCT
ejpam-6029	493	1	a.	a.	NOUN
ejpam-6029	493	2	a.	a.	PROPN
ejpam-6029	493	3	hijab	hijab	PROPN
ejpam-6029	493	4	et	et	PROPN
ejpam-6029	493	5	al	al	PROPN
ejpam-6029	493	6	.	.	PUNCT
ejpam-6029	493	7	/	/	SYM
ejpam-6029	493	8	eur	eur	PROPN
ejpam-6029	493	9	.	.	PUNCT
ejpam-6029	494	1	j.	j.	PROPN
ejpam-6029	494	2	pure	pure	PROPN
ejpam-6029	494	3	appl	appl	PROPN
ejpam-6029	494	4	.	.	PROPN
ejpam-6029	494	5	math	math	PROPN
ejpam-6029	494	6	,	,	PUNCT
ejpam-6029	494	7	18	18	NUM
ejpam-6029	494	8	(	(	PUNCT
ejpam-6029	494	9	2	2	NUM
ejpam-6029	494	10	)	)	PUNCT
ejpam-6029	494	11	(	(	PUNCT
ejpam-6029	494	12	2025	2025	NUM
ejpam-6029	494	13	)	)	PUNCT
ejpam-6029	494	14	,	,	PUNCT
ejpam-6029	494	15	6029	6029	NUM
ejpam-6029	494	16	18	18	NUM
ejpam-6029	494	17	of	of	ADP
ejpam-6029	494	18	23	23	NUM
ejpam-6029	494	19	4.1	4.1	NUM
ejpam-6029	494	20	.	.	PUNCT
ejpam-6029	495	1	non	non	ADJ
ejpam-6029	495	2	-	-	ADJ
ejpam-6029	495	3	linear	linear	ADJ
ejpam-6029	495	4	integral	integral	ADJ
ejpam-6029	495	5	equations	equation	NOUN
ejpam-6029	495	6	consider	consider	VERB
ejpam-6029	495	7	γ	γ	NOUN
ejpam-6029	495	8	=	=	SYM
ejpam-6029	495	9	c[0	c[0	PROPN
ejpam-6029	495	10	,	,	PUNCT
ejpam-6029	495	11	1	1	NUM
ejpam-6029	495	12	]	]	PUNCT
ejpam-6029	495	13	,	,	PUNCT
ejpam-6029	495	14	the	the	DET
ejpam-6029	495	15	class	class	NOUN
ejpam-6029	495	16	of	of	ADP
ejpam-6029	495	17	all	all	DET
ejpam-6029	495	18	continuous	continuous	ADJ
ejpam-6029	495	19	functions	function	NOUN
ejpam-6029	495	20	on	on	ADP
ejpam-6029	495	21	[	[	X
ejpam-6029	495	22	0	0	NUM
ejpam-6029	495	23	,	,	PUNCT
ejpam-6029	495	24	1	1	NUM
ejpam-6029	495	25	]	]	PUNCT
ejpam-6029	495	26	.	.	PUNCT
ejpam-6029	496	1	let	let	VERB
ejpam-6029	496	2	e	e	NOUN
ejpam-6029	496	3	=	=	SYM
ejpam-6029	496	4	c[0	c[0	PROPN
ejpam-6029	496	5	,	,	PUNCT
ejpam-6029	496	6	1	1	NUM
ejpam-6029	496	7	]	]	PUNCT
ejpam-6029	497	1	so	so	SCONJ
ejpam-6029	497	2	that	that	SCONJ
ejpam-6029	497	3	p	p	X
ejpam-6029	497	4	=	=	X
ejpam-6029	497	5	{	{	PUNCT
ejpam-6029	497	6	h(t	h(t	PROPN
ejpam-6029	497	7	)	)	PUNCT
ejpam-6029	497	8	∈	∈	PROPN
ejpam-6029	497	9	e	e	NOUN
ejpam-6029	497	10	:	:	PUNCT
ejpam-6029	497	11	h(t	h(t	PROPN
ejpam-6029	497	12	)	)	PUNCT
ejpam-6029	497	13	≥	≥	NOUN
ejpam-6029	497	14	0	0	NUM
ejpam-6029	497	15	,	,	PUNCT
ejpam-6029	497	16	t	t	PROPN
ejpam-6029	497	17	∈	∈	PROPN
ejpam-6029	498	1	[	[	X
ejpam-6029	498	2	0	0	NUM
ejpam-6029	498	3	,	,	PUNCT
ejpam-6029	498	4	1	1	NUM
ejpam-6029	498	5	]	]	PUNCT
ejpam-6029	498	6	}	}	PUNCT
ejpam-6029	498	7	is	be	AUX
ejpam-6029	498	8	equipped	equip	VERB
ejpam-6029	498	9	via	via	ADP
ejpam-6029	498	10	the	the	DET
ejpam-6029	498	11	norm	norm	NOUN
ejpam-6029	498	12	∥η∥	∥η∥	PROPN
ejpam-6029	498	13	=	=	PUNCT
ejpam-6029	498	14	∥η∥∞	∥η∥∞	PUNCT
ejpam-6029	498	15	+	+	CCONJ
ejpam-6029	498	16	∥η′∥∞.	∥η′∥∞.	NOUN
ejpam-6029	498	17	we	we	PRON
ejpam-6029	498	18	endow	endow	VERB
ejpam-6029	498	19	γ	γ	PROPN
ejpam-6029	498	20	with	with	ADP
ejpam-6029	498	21	dccml	dccml	NOUN
ejpam-6029	498	22	-	-	PUNCT
ejpam-6029	498	23	space	space	NOUN
ejpam-6029	498	24	as	as	SCONJ
ejpam-6029	498	25	follows	follow	VERB
ejpam-6029	498	26	,	,	PUNCT
ejpam-6029	498	27	lc(η1	lc(η1	NOUN
ejpam-6029	498	28	,	,	PUNCT
ejpam-6029	498	29	η2)(t	η2)(t	PROPN
ejpam-6029	498	30	)	)	PUNCT
ejpam-6029	499	1	=	=	PRON
ejpam-6029	499	2	(	(	PUNCT
ejpam-6029	499	3	sup	sup	NOUN
ejpam-6029	499	4	t∈[0,1	t∈[0,1	NOUN
ejpam-6029	499	5	]	]	X
ejpam-6029	499	6	sinh	sinh	NOUN
ejpam-6029	499	7	(	(	PUNCT
ejpam-6029	499	8	|η1(t)|+	|η1(t)|+	PROPN
ejpam-6029	499	9	|η2(t)|)p	|η2(t)|)p	SYM
ejpam-6029	499	10	)	)	PUNCT
ejpam-6029	499	11	1	1	NUM
ejpam-6029	499	12	p	p	NOUN
ejpam-6029	499	13	et	et	NOUN
ejpam-6029	499	14	,	,	PUNCT
ejpam-6029	499	15	for	for	ADP
ejpam-6029	499	16	each	each	DET
ejpam-6029	499	17	η1	η1	NOUN
ejpam-6029	499	18	,	,	PUNCT
ejpam-6029	499	19	η2	η2	PROPN
ejpam-6029	499	20	∈	∈	PROPN
ejpam-6029	499	21	γ	γ	X
ejpam-6029	499	22	,	,	PUNCT
ejpam-6029	499	23	and	and	CCONJ
ejpam-6029	499	24	p	p	PRON
ejpam-6029	499	25	≥	≥	NUM
ejpam-6029	499	26	1	1	NUM
ejpam-6029	499	27	.	.	PUNCT
ejpam-6029	500	1	(	(	PUNCT
ejpam-6029	500	2	16	16	NUM
ejpam-6029	500	3	)	)	PUNCT
ejpam-6029	500	4	evidently	evidently	ADV
ejpam-6029	500	5	,	,	PUNCT
ejpam-6029	500	6	(	(	PUNCT
ejpam-6029	500	7	γ	γ	X
ejpam-6029	500	8	,	,	PUNCT
ejpam-6029	500	9	lc	lc	PROPN
ejpam-6029	500	10	)	)	PUNCT
ejpam-6029	500	11	is	be	AUX
ejpam-6029	500	12	an	an	DET
ejpam-6029	500	13	lc	lc	NOUN
ejpam-6029	500	14	-	-	PUNCT
ejpam-6029	500	15	completedccml	completedccml	NOUN
ejpam-6029	500	16	-	-	NOUN
ejpam-6029	500	17	space	space	NOUN
ejpam-6029	500	18	,	,	PUNCT
ejpam-6029	500	19	where	where	SCONJ
ejpam-6029	500	20	f(u	f(u	NOUN
ejpam-6029	500	21	)	)	PUNCT
ejpam-6029	500	22	=	=	PUNCT
ejpam-6029	501	1	[	[	X
ejpam-6029	501	2	sinh((1+η1+η2)(2u	sinh((1+η1+η2)(2u	PROPN
ejpam-6029	501	3	)	)	PUNCT
ejpam-6029	501	4	p	p	NOUN
ejpam-6029	501	5	)	)	PUNCT
ejpam-6029	501	6	]	]	PUNCT
ejpam-6029	501	7	1	1	NUM
ejpam-6029	501	8	p	p	NOUN
ejpam-6029	501	9	,	,	PUNCT
ejpam-6029	501	10	and	and	CCONJ
ejpam-6029	501	11	g(u	g(u	PROPN
ejpam-6029	501	12	)	)	PUNCT
ejpam-6029	501	13	=	=	SYM
ejpam-6029	502	1	[	[	X
ejpam-6029	502	2	sinh((2	sinh((2	X
ejpam-6029	502	3	+	+	CCONJ
ejpam-6029	502	4	η21	η21	PROPN
ejpam-6029	502	5	+	+	CCONJ
ejpam-6029	502	6	η22)(2u	η22)(2u	PROPN
ejpam-6029	502	7	)	)	PUNCT
ejpam-6029	502	8	p	p	NOUN
ejpam-6029	502	9	)	)	PUNCT
ejpam-6029	502	10	]	]	PUNCT
ejpam-6029	502	11	1	1	NUM
ejpam-6029	502	12	p	p	NOUN
ejpam-6029	502	13	,	,	PUNCT
ejpam-6029	502	14	u	u	PROPN
ejpam-6029	502	15	∈	∈	PROPN
ejpam-6029	502	16	p	p	PROPN
ejpam-6029	502	17	.	.	PUNCT
ejpam-6029	503	1	theorem	theorem	NOUN
ejpam-6029	503	2	3	3	X
ejpam-6029	504	1	.	.	PUNCT
ejpam-6029	504	2	assume	assume	VERB
ejpam-6029	504	3	that	that	SCONJ
ejpam-6029	504	4	for	for	ADP
ejpam-6029	504	5	each	each	DET
ejpam-6029	504	6	η1	η1	NOUN
ejpam-6029	504	7	,	,	PUNCT
ejpam-6029	504	8	η1	η1	NOUN
ejpam-6029	504	9	∈	∈	PROPN
ejpam-6029	504	10	γ	γ	X
ejpam-6029	504	11	=	=	SYM
ejpam-6029	504	12	c[0	c[0	PROPN
ejpam-6029	504	13	,	,	PUNCT
ejpam-6029	504	14	1	1	NUM
ejpam-6029	504	15	]	]	PUNCT
ejpam-6029	504	16	,	,	PUNCT
ejpam-6029	504	17	(	(	PUNCT
ejpam-6029	504	18	i	i	NOUN
ejpam-6029	504	19	)	)	PUNCT
ejpam-6029	504	20	there	there	PRON
ejpam-6029	504	21	exist	exist	VERB
ejpam-6029	504	22	a	a	DET
ejpam-6029	504	23	function	function	NOUN
ejpam-6029	504	24	λ	λ	X
ejpam-6029	504	25	∈	∈	NOUN
ejpam-6029	504	26	∆	∆	PROPN
ejpam-6029	504	27	,	,	PUNCT
ejpam-6029	504	28	and	and	CCONJ
ejpam-6029	504	29	0	0	NUM
ejpam-6029	504	30	<	<	X
ejpam-6029	504	31	β	β	X
ejpam-6029	504	32	<	<	X
ejpam-6029	504	33	1	1	NUM
ejpam-6029	504	34	,	,	PUNCT
ejpam-6029	504	35	such	such	ADJ
ejpam-6029	504	36	that	that	SCONJ
ejpam-6029	504	37	,	,	PUNCT
ejpam-6029	504	38	|ξ(t	|ξ(t	PROPN
ejpam-6029	504	39	,	,	PUNCT
ejpam-6029	504	40	ν	ν	PROPN
ejpam-6029	504	41	,	,	PUNCT
ejpam-6029	504	42	η1(ν))|+	η1(ν))|+	PROPN
ejpam-6029	504	43	|ξ(t	|ξ(t	PROPN
ejpam-6029	504	44	,	,	PUNCT
ejpam-6029	504	45	ν	ν	NOUN
ejpam-6029	504	46	,	,	PUNCT
ejpam-6029	504	47	η2(ν))|	η2(ν))|	PROPN
ejpam-6029	504	48	<	<	X
ejpam-6029	504	49	β	β	X
ejpam-6029	504	50	2	2	NUM
ejpam-6029	504	51	λ(η1(ν	λ(η1(ν	PROPN
ejpam-6029	504	52	)	)	PUNCT
ejpam-6029	504	53	,	,	PUNCT
ejpam-6029	504	54	η2(ν))(|η1(ν)|+	η2(ν))(|η1(ν)|+	PROPN
ejpam-6029	504	55	|η2(ν)|	|η2(ν)|	PROPN
ejpam-6029	504	56	)	)	PUNCT
ejpam-6029	504	57	;	;	PUNCT
ejpam-6029	504	58	(	(	PUNCT
ejpam-6029	504	59	17	17	NUM
ejpam-6029	504	60	)	)	PUNCT
ejpam-6029	504	61	(	(	PUNCT
ejpam-6029	504	62	ii	ii	NOUN
ejpam-6029	504	63	)	)	PUNCT
ejpam-6029	504	64	ξ	ξ	PROPN
ejpam-6029	504	65	(	(	PUNCT
ejpam-6029	504	66	t	t	PROPN
ejpam-6029	504	67	,	,	PUNCT
ejpam-6029	504	68	ν	ν	PROPN
ejpam-6029	504	69	,	,	PUNCT
ejpam-6029	504	70	∫	∫	PROPN
ejpam-6029	504	71	1	1	NUM
ejpam-6029	504	72	0	0	NUM
ejpam-6029	504	73	ξ(t	ξ(t	NOUN
ejpam-6029	504	74	,	,	PUNCT
ejpam-6029	504	75	ν	ν	NOUN
ejpam-6029	504	76	,	,	PUNCT
ejpam-6029	504	77	η(ν))dν	η(ν))dν	NOUN
ejpam-6029	504	78	)	)	PUNCT
ejpam-6029	504	79	<	<	X
ejpam-6029	504	80	ξ(t	ξ(t	NOUN
ejpam-6029	504	81	,	,	PUNCT
ejpam-6029	504	82	ν	ν	NOUN
ejpam-6029	504	83	,	,	PUNCT
ejpam-6029	504	84	η(ν	η(ν	PROPN
ejpam-6029	504	85	)	)	PUNCT
ejpam-6029	504	86	)	)	PUNCT
ejpam-6029	504	87	for	for	ADP
ejpam-6029	504	88	some	some	DET
ejpam-6029	504	89	t	t	PROPN
ejpam-6029	504	90	,	,	PUNCT
ejpam-6029	504	91	ν	ν	PROPN
ejpam-6029	504	92	∈	∈	PROPN
ejpam-6029	505	1	[	[	X
ejpam-6029	505	2	0	0	NUM
ejpam-6029	505	3	,	,	PUNCT
ejpam-6029	505	4	1	1	NUM
ejpam-6029	505	5	]	]	PUNCT
ejpam-6029	505	6	.	.	PUNCT
ejpam-6029	506	1	then	then	ADV
ejpam-6029	506	2	,	,	PUNCT
ejpam-6029	506	3	this	this	DET
ejpam-6029	506	4	integral	integral	ADJ
ejpam-6029	506	5	equation	equation	NOUN
ejpam-6029	506	6	η(ν	η(ν	PROPN
ejpam-6029	506	7	)	)	PUNCT
ejpam-6029	506	8	=	=	SYM
ejpam-6029	507	1	∫	∫	PROPN
ejpam-6029	507	2	1	1	NUM
ejpam-6029	507	3	0	0	NUM
ejpam-6029	507	4	ξ(t	ξ(t	NOUN
ejpam-6029	507	5	,	,	PUNCT
ejpam-6029	507	6	ν	ν	NOUN
ejpam-6029	507	7	,	,	PUNCT
ejpam-6029	507	8	η(ν))dν	η(ν))dν	PROPN
ejpam-6029	507	9	,	,	PUNCT
ejpam-6029	507	10	admits	admit	VERB
ejpam-6029	507	11	a	a	DET
ejpam-6029	507	12	unique	unique	ADJ
ejpam-6029	507	13	solution	solution	NOUN
ejpam-6029	507	14	in	in	ADP
ejpam-6029	507	15	c[0	c[0	PROPN
ejpam-6029	507	16	,	,	PUNCT
ejpam-6029	507	17	1	1	NUM
ejpam-6029	507	18	]	]	PUNCT
ejpam-6029	507	19	.	.	PUNCT
ejpam-6029	508	1	proof	proof	NOUN
ejpam-6029	508	2	.	.	PUNCT
ejpam-6029	509	1	let	let	VERB
ejpam-6029	509	2	t	t	NOUN
ejpam-6029	509	3	:	:	PUNCT
ejpam-6029	509	4	γ	γ	X
ejpam-6029	509	5	→	→	SYM
ejpam-6029	509	6	γ	γ	X
ejpam-6029	509	7	be	be	AUX
ejpam-6029	509	8	continuous	continuous	ADJ
ejpam-6029	509	9	defined	define	VERB
ejpam-6029	509	10	by	by	ADP
ejpam-6029	509	11	tη(ν	tη(ν	X
ejpam-6029	509	12	)	)	PUNCT
ejpam-6029	509	13	=	=	SYM
ejpam-6029	510	1	∫	∫	PROPN
ejpam-6029	510	2	1	1	NUM
ejpam-6029	510	3	0	0	NUM
ejpam-6029	510	4	ξ(t	ξ(t	NOUN
ejpam-6029	510	5	,	,	PUNCT
ejpam-6029	510	6	ν	ν	NOUN
ejpam-6029	510	7	,	,	PUNCT
ejpam-6029	510	8	η(ν))dν	η(ν))dν	NOUN
ejpam-6029	510	9	.	.	PUNCT
ejpam-6029	511	1	then	then	ADV
ejpam-6029	511	2	lc(tη1	lc(tη1	VERB
ejpam-6029	511	3	,	,	PUNCT
ejpam-6029	511	4	tη2)(t	tη2)(t	PROPN
ejpam-6029	511	5	)	)	PUNCT
ejpam-6029	511	6	=	=	PUNCT
ejpam-6029	511	7	(	(	PUNCT
ejpam-6029	511	8	sup	sup	NOUN
ejpam-6029	511	9	t∈[0,1	t∈[0,1	NOUN
ejpam-6029	511	10	]	]	X
ejpam-6029	511	11	sinh	sinh	NOUN
ejpam-6029	511	12	(	(	PUNCT
ejpam-6029	511	13	|tη1(t)|+	|tη1(t)|+	NOUN
ejpam-6029	511	14	|tη2(t)|	|tη2(t)|	NOUN
ejpam-6029	511	15	)	)	PUNCT
ejpam-6029	512	1	p	p	X
ejpam-6029	512	2	)	)	PUNCT
ejpam-6029	512	3	1	1	NUM
ejpam-6029	512	4	p	p	NOUN
ejpam-6029	512	5	et	et	NOUN
ejpam-6029	512	6	,	,	PUNCT
ejpam-6029	512	7	from	from	ADP
ejpam-6029	512	8	lemma	lemma	PROPN
ejpam-6029	512	9	4	4	NUM
ejpam-6029	512	10	,	,	PUNCT
ejpam-6029	512	11	we	we	PRON
ejpam-6029	512	12	have	have	AUX
ejpam-6029	512	13	(	(	PUNCT
ejpam-6029	512	14	sinh	sinh	VERB
ejpam-6029	512	15	(	(	PUNCT
ejpam-6029	512	16	|tη1(t)|+	|tη1(t)|+	NOUN
ejpam-6029	512	17	|tη2(t)|	|tη2(t)|	NOUN
ejpam-6029	512	18	)	)	PUNCT
ejpam-6029	512	19	p	p	X
ejpam-6029	512	20	)	)	PUNCT
ejpam-6029	512	21	1	1	NUM
ejpam-6029	512	22	p	p	NOUN
ejpam-6029	512	23	⪯	⪯	NOUN
ejpam-6029	512	24	sinh	sinh	PROPN
ejpam-6029	512	25	|tη1(t)|+	|tη1(t)|+	NOUN
ejpam-6029	512	26	|tη2(t)|	|tη2(t)|	ADJ
ejpam-6029	512	27	⪯	⪯	NOUN
ejpam-6029	513	1	2|tη1(t)|+	2|tη1(t)|+	NUM
ejpam-6029	513	2	|tη2(t)|	|tη2(t)|	ADJ
ejpam-6029	513	3	=	=	SYM
ejpam-6029	513	4	2	2	NUM
ejpam-6029	513	5	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-6029	513	6	1	1	NUM
ejpam-6029	513	7	0	0	NUM
ejpam-6029	513	8	ξ(t	ξ(t	NOUN
ejpam-6029	513	9	,	,	PUNCT
ejpam-6029	513	10	ν	ν	NOUN
ejpam-6029	513	11	,	,	PUNCT
ejpam-6029	513	12	η1(ν))dν	η1(ν))dν	VERB
ejpam-6029	513	13	∣∣∣∣+	∣∣∣∣+	PROPN
ejpam-6029	513	14	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-6029	513	15	1	1	NUM
ejpam-6029	513	16	0	0	NUM
ejpam-6029	513	17	ξ(t	ξ(t	NOUN
ejpam-6029	513	18	,	,	PUNCT
ejpam-6029	513	19	ν	ν	X
ejpam-6029	513	20	,	,	PUNCT
ejpam-6029	513	21	η2(ν))dν	η2(ν))dν	NOUN
ejpam-6029	513	22	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6029	513	23	⪯	⪯	NOUN
ejpam-6029	513	24	2	2	NUM
ejpam-6029	513	25	∫	∫	NOUN
ejpam-6029	513	26	1	1	NUM
ejpam-6029	513	27	0	0	X
ejpam-6029	513	28	|ξ(t	|ξ(t	PROPN
ejpam-6029	513	29	,	,	PUNCT
ejpam-6029	513	30	ν	ν	NOUN
ejpam-6029	513	31	,	,	PUNCT
ejpam-6029	513	32	η1(ν))|	η1(ν))|	NOUN
ejpam-6029	513	33	dν	dν	VERB
ejpam-6029	513	34	+	+	CCONJ
ejpam-6029	513	35	∫	∫	PROPN
ejpam-6029	513	36	1	1	NUM
ejpam-6029	513	37	0	0	X
ejpam-6029	513	38	|ξ(t	|ξ(t	PROPN
ejpam-6029	513	39	,	,	PUNCT
ejpam-6029	513	40	ν	ν	PROPN
ejpam-6029	513	41	,	,	PUNCT
ejpam-6029	513	42	η2(ν))|	η2(ν))|	PROPN
ejpam-6029	513	43	dν	dν	VERB
ejpam-6029	513	44	=	=	SYM
ejpam-6029	513	45	2	2	NUM
ejpam-6029	513	46	∫	∫	NOUN
ejpam-6029	513	47	1	1	NUM
ejpam-6029	513	48	0	0	X
ejpam-6029	513	49	|ξ(t	|ξ(t	PROPN
ejpam-6029	513	50	,	,	PUNCT
ejpam-6029	513	51	ν	ν	NOUN
ejpam-6029	513	52	,	,	PUNCT
ejpam-6029	513	53	η1(ν))|+	η1(ν))|+	PROPN
ejpam-6029	513	54	|ξ(t	|ξ(t	PROPN
ejpam-6029	513	55	,	,	PUNCT
ejpam-6029	513	56	ν	ν	PROPN
ejpam-6029	513	57	,	,	PUNCT
ejpam-6029	513	58	η2(ν))|	η2(ν))|	PROPN
ejpam-6029	513	59	dν	dν	VERB
ejpam-6029	513	60	⪯	⪯	PROPN
ejpam-6029	513	61	2	2	NUM
ejpam-6029	513	62	∫	∫	NOUN
ejpam-6029	513	63	1	1	NUM
ejpam-6029	513	64	0	0	NUM
ejpam-6029	513	65	β	β	X
ejpam-6029	513	66	2	2	NUM
ejpam-6029	513	67	λ(η1(ν	λ(η1(ν	PROPN
ejpam-6029	513	68	)	)	PUNCT
ejpam-6029	513	69	,	,	PUNCT
ejpam-6029	513	70	η2(ν))(|η1(ν)|+	η2(ν))(|η1(ν)|+	PROPN
ejpam-6029	513	71	|η2(ν)|)dν	|η2(ν)|)dν	PROPN
ejpam-6029	513	72	a.	a.	NOUN
ejpam-6029	513	73	a.	a.	PROPN
ejpam-6029	514	1	hijab	hijab	PROPN
ejpam-6029	514	2	et	et	PROPN
ejpam-6029	514	3	al	al	PROPN
ejpam-6029	514	4	.	.	PUNCT
ejpam-6029	514	5	/	/	SYM
ejpam-6029	514	6	eur	eur	PROPN
ejpam-6029	514	7	.	.	PUNCT
ejpam-6029	515	1	j.	j.	PROPN
ejpam-6029	515	2	pure	pure	PROPN
ejpam-6029	515	3	appl	appl	PROPN
ejpam-6029	515	4	.	.	PROPN
ejpam-6029	515	5	math	math	PROPN
ejpam-6029	515	6	,	,	PUNCT
ejpam-6029	515	7	18	18	NUM
ejpam-6029	515	8	(	(	PUNCT
ejpam-6029	515	9	2	2	NUM
ejpam-6029	515	10	)	)	PUNCT
ejpam-6029	515	11	(	(	PUNCT
ejpam-6029	515	12	2025	2025	NUM
ejpam-6029	515	13	)	)	PUNCT
ejpam-6029	515	14	,	,	PUNCT
ejpam-6029	515	15	6029	6029	NUM
ejpam-6029	515	16	19	19	NUM
ejpam-6029	515	17	of	of	ADP
ejpam-6029	515	18	23	23	NUM
ejpam-6029	515	19	=	=	SYM
ejpam-6029	515	20	β	β	X
ejpam-6029	515	21	∫	∫	PROPN
ejpam-6029	515	22	1	1	NUM
ejpam-6029	515	23	0	0	NUM
ejpam-6029	515	24	λ(η1(ν	λ(η1(ν	PROPN
ejpam-6029	515	25	)	)	PUNCT
ejpam-6029	515	26	,	,	PUNCT
ejpam-6029	515	27	η2(ν	η2(ν	NOUN
ejpam-6029	515	28	)	)	PUNCT
ejpam-6029	515	29	)	)	PUNCT
ejpam-6029	516	1	[	[	X
ejpam-6029	516	2	(	(	PUNCT
ejpam-6029	516	3	|η1(ν)|+	|η1(ν)|+	PROPN
ejpam-6029	516	4	|η2(ν)|)p	|η2(ν)|)p	NUM
ejpam-6029	516	5	]	]	SYM
ejpam-6029	516	6	1	1	NUM
ejpam-6029	516	7	p	p	NOUN
ejpam-6029	516	8	dν	dν	PROPN
ejpam-6029	516	9	⪯	⪯	PROPN
ejpam-6029	516	10	β	β	X
ejpam-6029	516	11	∫	∫	PROPN
ejpam-6029	517	1	1	1	NUM
ejpam-6029	517	2	0	0	NUM
ejpam-6029	517	3	λ(η1(ν	λ(η1(ν	PROPN
ejpam-6029	517	4	)	)	PUNCT
ejpam-6029	517	5	,	,	PUNCT
ejpam-6029	517	6	η2(ν	η2(ν	NOUN
ejpam-6029	517	7	)	)	PUNCT
ejpam-6029	517	8	)	)	PUNCT
ejpam-6029	518	1	[	[	X
ejpam-6029	518	2	sinh(|η1(ν)|+	sinh(|η1(ν)|+	VERB
ejpam-6029	518	3	|η2(ν)|)p	|η2(ν)|)p	NOUN
ejpam-6029	518	4	]	]	SYM
ejpam-6029	518	5	1	1	NUM
ejpam-6029	518	6	p	p	NOUN
ejpam-6029	518	7	dν	dν	PROPN
ejpam-6029	518	8	⪯	⪯	NOUN
ejpam-6029	518	9	βlc(η1	βlc(η1	PROPN
ejpam-6029	518	10	,	,	PUNCT
ejpam-6029	518	11	η2)(t	η2)(t	PROPN
ejpam-6029	518	12	)	)	PUNCT
ejpam-6029	518	13	∫	∫	PROPN
ejpam-6029	519	1	1	1	NUM
ejpam-6029	519	2	0	0	X
ejpam-6029	519	3	λ(η1(ν	λ(η1(ν	PROPN
ejpam-6029	519	4	)	)	PUNCT
ejpam-6029	519	5	,	,	PUNCT
ejpam-6029	519	6	η2(ν))dν	η2(ν))dν	NOUN
ejpam-6029	519	7	⪯	⪯	VERB
ejpam-6029	519	8	βλ(η1(ν	βλ(η1(ν	PROPN
ejpam-6029	519	9	)	)	PUNCT
ejpam-6029	519	10	,	,	PUNCT
ejpam-6029	519	11	η2(ν))lc(η1	η2(ν))lc(η1	PROPN
ejpam-6029	519	12	,	,	PUNCT
ejpam-6029	519	13	η2)(t	η2)(t	PROPN
ejpam-6029	519	14	)	)	PUNCT
ejpam-6029	519	15	.	.	PUNCT
ejpam-6029	520	1	we	we	PRON
ejpam-6029	520	2	observe	observe	VERB
ejpam-6029	520	3	that	that	SCONJ
ejpam-6029	520	4	lc(tη1	lc(tη1	PROPN
ejpam-6029	520	5	,	,	PUNCT
ejpam-6029	520	6	tη2)(t	tη2)(t	PROPN
ejpam-6029	520	7	)	)	PUNCT
ejpam-6029	520	8	⪯	⪯	NOUN
ejpam-6029	520	9	βλ(η1(ν	βλ(η1(ν	PROPN
ejpam-6029	520	10	)	)	PUNCT
ejpam-6029	520	11	,	,	PUNCT
ejpam-6029	520	12	η2(ν))lc(η1	η2(ν))lc(η1	PROPN
ejpam-6029	520	13	,	,	PUNCT
ejpam-6029	520	14	η2)(t	η2)(t	PROPN
ejpam-6029	520	15	)	)	PUNCT
ejpam-6029	520	16	,	,	PUNCT
ejpam-6029	520	17	where	where	SCONJ
ejpam-6029	520	18	0	0	PUNCT
ejpam-6029	520	19	<	<	X
ejpam-6029	520	20	β	β	X
ejpam-6029	520	21	<	<	X
ejpam-6029	520	22	1	1	NUM
ejpam-6029	520	23	and	and	CCONJ
ejpam-6029	520	24	λ	λ	X
ejpam-6029	520	25	∈	∈	PROPN
ejpam-6029	521	1	∆.	∆.	X
ejpam-6029	521	2	hence	hence	ADV
ejpam-6029	521	3	,	,	PUNCT
ejpam-6029	521	4	all	all	PRON
ejpam-6029	521	5	of	of	ADP
ejpam-6029	521	6	the	the	DET
ejpam-6029	521	7	requirements	requirement	NOUN
ejpam-6029	521	8	for	for	ADP
ejpam-6029	521	9	corollary	corollary	ADJ
ejpam-6029	521	10	5	5	NUM
ejpam-6029	521	11	have	have	AUX
ejpam-6029	521	12	been	be	AUX
ejpam-6029	521	13	met	meet	VERB
ejpam-6029	521	14	.	.	PUNCT
ejpam-6029	522	1	we	we	PRON
ejpam-6029	522	2	obtain	obtain	VERB
ejpam-6029	522	3	the	the	DET
ejpam-6029	522	4	desired	desire	VERB
ejpam-6029	522	5	results	result	NOUN
ejpam-6029	522	6	.	.	PUNCT
ejpam-6029	523	1	4.2	4.2	NUM
ejpam-6029	523	2	.	.	PUNCT
ejpam-6029	523	3	boundary	boundary	ADJ
ejpam-6029	523	4	value	value	NOUN
ejpam-6029	523	5	problems	problem	NOUN
ejpam-6029	523	6	the	the	DET
ejpam-6029	523	7	current	current	ADJ
ejpam-6029	523	8	study	study	NOUN
ejpam-6029	523	9	results	result	NOUN
ejpam-6029	523	10	will	will	AUX
ejpam-6029	523	11	be	be	AUX
ejpam-6029	523	12	applied	apply	VERB
ejpam-6029	523	13	to	to	PART
ejpam-6029	523	14	solve	solve	VERB
ejpam-6029	523	15	the	the	DET
ejpam-6029	523	16	first	first	ADJ
ejpam-6029	523	17	-	-	PUNCT
ejpam-6029	523	18	order	order	NOUN
ejpam-6029	523	19	periodic	periodic	ADJ
ejpam-6029	523	20	bvps	bvps	NOUN
ejpam-6029	523	21	:	:	PUNCT
ejpam-6029	523	22	ϖ	ϖ	NOUN
ejpam-6029	523	23	′	′	NUM
ejpam-6029	523	24	(	(	PUNCT
ejpam-6029	523	25	t	t	NOUN
ejpam-6029	523	26	)	)	PUNCT
ejpam-6029	524	1	=	=	SYM
ejpam-6029	524	2	h(t	h(t	PROPN
ejpam-6029	524	3	,	,	PUNCT
ejpam-6029	524	4	ϖ(t	ϖ(t	PROPN
ejpam-6029	524	5	)	)	PUNCT
ejpam-6029	524	6	)	)	PUNCT
ejpam-6029	525	1	,	,	PUNCT
ejpam-6029	525	2	t	t	PROPN
ejpam-6029	525	3	∈	∈	PROPN
ejpam-6029	526	1	[	[	X
ejpam-6029	526	2	0	0	NUM
ejpam-6029	526	3	,	,	PUNCT
ejpam-6029	526	4	1	1	NUM
ejpam-6029	526	5	]	]	PUNCT
ejpam-6029	526	6	(	(	PUNCT
ejpam-6029	526	7	18	18	NUM
ejpam-6029	526	8	)	)	PUNCT
ejpam-6029	526	9	ϖ(0	ϖ(0	PROPN
ejpam-6029	526	10	)	)	PUNCT
ejpam-6029	526	11	=	=	SYM
ejpam-6029	526	12	ϖ(1	ϖ(1	NOUN
ejpam-6029	526	13	)	)	PUNCT
ejpam-6029	526	14	,	,	PUNCT
ejpam-6029	526	15	where	where	SCONJ
ejpam-6029	526	16	h	h	NOUN
ejpam-6029	526	17	:	:	PUNCT
ejpam-6029	526	18	[	[	X
ejpam-6029	526	19	0	0	NUM
ejpam-6029	526	20	,	,	PUNCT
ejpam-6029	526	21	1	1	NUM
ejpam-6029	526	22	]	]	SYM
ejpam-6029	526	23	×	×	NOUN
ejpam-6029	526	24	r	r	NOUN
ejpam-6029	526	25	→	→	SYM
ejpam-6029	526	26	r	r	NOUN
ejpam-6029	526	27	is	be	AUX
ejpam-6029	526	28	a	a	DET
ejpam-6029	526	29	continuous	continuous	ADJ
ejpam-6029	526	30	function	function	NOUN
ejpam-6029	526	31	on	on	ADP
ejpam-6029	526	32	[	[	X
ejpam-6029	526	33	0	0	NUM
ejpam-6029	526	34	,	,	PUNCT
ejpam-6029	526	35	1	1	NUM
ejpam-6029	526	36	]	]	PUNCT
ejpam-6029	526	37	.	.	PUNCT
ejpam-6029	527	1	the	the	DET
ejpam-6029	527	2	problem	problem	NOUN
ejpam-6029	527	3	above	above	ADV
ejpam-6029	527	4	can	can	AUX
ejpam-6029	527	5	be	be	AUX
ejpam-6029	527	6	formulated	formulate	VERB
ejpam-6029	527	7	as	as	ADP
ejpam-6029	527	8	:	:	PUNCT
ejpam-6029	527	9	ϖ	ϖ	NOUN
ejpam-6029	527	10	′	′	NUM
ejpam-6029	527	11	(	(	PUNCT
ejpam-6029	527	12	t	t	PROPN
ejpam-6029	527	13	)	)	PUNCT
ejpam-6029	527	14	+	+	CCONJ
ejpam-6029	527	15	δϖ(t	δϖ(t	NUM
ejpam-6029	527	16	)	)	PUNCT
ejpam-6029	528	1	=	=	SYM
ejpam-6029	528	2	h(t	h(t	PROPN
ejpam-6029	528	3	,	,	PUNCT
ejpam-6029	528	4	ϖ(t	ϖ(t	PROPN
ejpam-6029	528	5	)	)	PUNCT
ejpam-6029	528	6	)	)	PUNCT
ejpam-6029	529	1	+	+	CCONJ
ejpam-6029	529	2	δϖ(t	δϖ(t	NUM
ejpam-6029	529	3	)	)	PUNCT
ejpam-6029	529	4	,	,	PUNCT
ejpam-6029	529	5	t	t	PROPN
ejpam-6029	529	6	∈	∈	PROPN
ejpam-6029	530	1	[	[	X
ejpam-6029	530	2	0	0	NUM
ejpam-6029	530	3	,	,	PUNCT
ejpam-6029	530	4	1	1	NUM
ejpam-6029	530	5	]	]	PUNCT
ejpam-6029	530	6	(	(	PUNCT
ejpam-6029	530	7	19	19	NUM
ejpam-6029	530	8	)	)	PUNCT
ejpam-6029	530	9	ϖ(0	ϖ(0	NOUN
ejpam-6029	530	10	)	)	PUNCT
ejpam-6029	530	11	=	=	SYM
ejpam-6029	530	12	ϖ(1	ϖ(1	NOUN
ejpam-6029	530	13	)	)	PUNCT
ejpam-6029	530	14	.	.	PUNCT
ejpam-6029	531	1	the	the	DET
ejpam-6029	531	2	problem	problem	NOUN
ejpam-6029	531	3	(	(	PUNCT
ejpam-6029	531	4	19	19	NUM
ejpam-6029	531	5	)	)	PUNCT
ejpam-6029	531	6	is	be	AUX
ejpam-6029	531	7	equivalent	equivalent	ADJ
ejpam-6029	531	8	to	to	ADP
ejpam-6029	531	9	the	the	DET
ejpam-6029	531	10	following	follow	VERB
ejpam-6029	531	11	integral	integral	ADJ
ejpam-6029	531	12	equation	equation	NOUN
ejpam-6029	531	13	:	:	PUNCT
ejpam-6029	531	14	ϖ(t	ϖ(t	X
ejpam-6029	531	15	)	)	PUNCT
ejpam-6029	532	1	=	=	SYM
ejpam-6029	532	2	∫	∫	PROPN
ejpam-6029	532	3	1	1	NUM
ejpam-6029	532	4	0	0	NUM
ejpam-6029	532	5	g(t	g(t	PROPN
ejpam-6029	532	6	,	,	PUNCT
ejpam-6029	532	7	u	u	NOUN
ejpam-6029	532	8	)	)	PUNCT
ejpam-6029	532	9	(	(	PUNCT
ejpam-6029	532	10	h(u	h(u	PROPN
ejpam-6029	532	11	,	,	PUNCT
ejpam-6029	532	12	ϖ(u	ϖ(u	PROPN
ejpam-6029	532	13	)	)	PUNCT
ejpam-6029	532	14	)	)	PUNCT
ejpam-6029	533	1	+	+	CCONJ
ejpam-6029	533	2	δϖ(u	δϖ(u	NOUN
ejpam-6029	533	3	)	)	PUNCT
ejpam-6029	533	4	)	)	PUNCT
ejpam-6029	533	5	du	du	PROPN
ejpam-6029	533	6	,	,	PUNCT
ejpam-6029	533	7	(	(	PUNCT
ejpam-6029	533	8	20	20	NUM
ejpam-6029	533	9	)	)	PUNCT
ejpam-6029	533	10	where	where	SCONJ
ejpam-6029	533	11	g	g	PROPN
ejpam-6029	533	12	is	be	AUX
ejpam-6029	533	13	a	a	DET
ejpam-6029	533	14	green	green	ADJ
ejpam-6029	533	15	function	function	NOUN
ejpam-6029	533	16	defined	define	VERB
ejpam-6029	533	17	by	by	ADP
ejpam-6029	533	18	g(t	g(t	PROPN
ejpam-6029	533	19	,	,	PUNCT
ejpam-6029	533	20	u	u	NOUN
ejpam-6029	533	21	)	)	PUNCT
ejpam-6029	533	22	=	=	SYM
ejpam-6029	533	23	{	{	PUNCT
ejpam-6029	533	24	eδ(u−t+1	eδ(u−t+1	NOUN
ejpam-6029	533	25	)	)	PUNCT
ejpam-6029	533	26	eδ−1	eδ−1	NOUN
ejpam-6029	533	27	0	0	NUM
ejpam-6029	533	28	≤	≤	NUM
ejpam-6029	533	29	u	u	NOUN
ejpam-6029	533	30	≤	≤	X
ejpam-6029	533	31	t	t	PROPN
ejpam-6029	533	32	eδ(u−t	eδ(u−t	PROPN
ejpam-6029	533	33	)	)	PUNCT
ejpam-6029	533	34	eδ−1	eδ−1	PROPN
ejpam-6029	533	35	t	t	PROPN
ejpam-6029	533	36	≤	≤	NUM
ejpam-6029	533	37	u	u	NOUN
ejpam-6029	533	38	≤	≤	ADJ
ejpam-6029	533	39	1	1	NUM
ejpam-6029	533	40	.	.	PUNCT
ejpam-6029	534	1	thus	thus	ADV
ejpam-6029	534	2	,	,	PUNCT
ejpam-6029	534	3	it	it	PRON
ejpam-6029	534	4	is	be	AUX
ejpam-6029	534	5	noticed	notice	VERB
ejpam-6029	534	6	that	that	SCONJ
ejpam-6029	534	7	∫	∫	PROPN
ejpam-6029	534	8	1	1	NUM
ejpam-6029	534	9	0	0	NUM
ejpam-6029	534	10	g(t	g(t	PROPN
ejpam-6029	534	11	,	,	PUNCT
ejpam-6029	534	12	u)du	u)du	PROPN
ejpam-6029	534	13	=	=	SYM
ejpam-6029	534	14	1	1	NUM
ejpam-6029	534	15	δ	δ	NOUN
ejpam-6029	534	16	.	.	PUNCT
ejpam-6029	535	1	let	let	VERB
ejpam-6029	535	2	γ	γ	X
ejpam-6029	535	3	=	=	SYM
ejpam-6029	535	4	c[0	c[0	PROPN
ejpam-6029	535	5	,	,	PUNCT
ejpam-6029	535	6	1	1	NUM
ejpam-6029	535	7	]	]	PUNCT
ejpam-6029	535	8	.	.	PUNCT
ejpam-6029	536	1	define	define	VERB
ejpam-6029	536	2	lc	lc	PROPN
ejpam-6029	536	3	:	:	PUNCT
ejpam-6029	536	4	γ×	γ×	PROPN
ejpam-6029	536	5	γ	γ	X
ejpam-6029	536	6	→	→	SYM
ejpam-6029	536	7	e	e	PROPN
ejpam-6029	536	8	,	,	PUNCT
ejpam-6029	536	9	where	where	SCONJ
ejpam-6029	536	10	e	e	NOUN
ejpam-6029	536	11	=	=	SYM
ejpam-6029	536	12	c[0	c[0	PROPN
ejpam-6029	536	13	,	,	PUNCT
ejpam-6029	536	14	1	1	NUM
ejpam-6029	536	15	]	]	PUNCT
ejpam-6029	536	16	,	,	PUNCT
ejpam-6029	536	17	p	p	NOUN
ejpam-6029	536	18	=	=	SYM
ejpam-6029	536	19	{	{	PUNCT
ejpam-6029	536	20	φ(t	φ(t	PROPN
ejpam-6029	536	21	)	)	PUNCT
ejpam-6029	536	22	∈	∈	PROPN
ejpam-6029	536	23	e	e	NOUN
ejpam-6029	536	24	:	:	PUNCT
ejpam-6029	536	25	φ(t	φ(t	PROPN
ejpam-6029	536	26	)	)	PUNCT
ejpam-6029	536	27	≥	≥	NOUN
ejpam-6029	536	28	0	0	NUM
ejpam-6029	536	29	,	,	PUNCT
ejpam-6029	536	30	t	t	PROPN
ejpam-6029	536	31	∈	∈	PROPN
ejpam-6029	537	1	[	[	X
ejpam-6029	537	2	0	0	NUM
ejpam-6029	537	3	,	,	PUNCT
ejpam-6029	537	4	1	1	NUM
ejpam-6029	537	5	]	]	PUNCT
ejpam-6029	537	6	}	}	PUNCT
ejpam-6029	537	7	is	be	AUX
ejpam-6029	537	8	a	a	DET
ejpam-6029	537	9	dccml	dccml	NOUN
ejpam-6029	537	10	-	-	PUNCT
ejpam-6029	537	11	space	space	NOUN
ejpam-6029	537	12	,	,	PUNCT
ejpam-6029	537	13	by	by	ADP
ejpam-6029	537	14	lc(ϖ1	lc(ϖ1	PROPN
ejpam-6029	537	15	,	,	PUNCT
ejpam-6029	537	16	ϖ2)(t	ϖ2)(t	PROPN
ejpam-6029	537	17	)	)	PUNCT
ejpam-6029	538	1	=	=	PRON
ejpam-6029	538	2	(	(	PUNCT
ejpam-6029	538	3	e|ϖ1(t)|+|ϖ2(t)|	e|ϖ1(t)|+|ϖ2(t)|	ADV
ejpam-6029	538	4	−	−	PROPN
ejpam-6029	538	5	1	1	NUM
ejpam-6029	538	6	)	)	PUNCT
ejpam-6029	538	7	φ(t	φ(t	PROPN
ejpam-6029	538	8	)	)	PUNCT
ejpam-6029	538	9	,	,	PUNCT
ejpam-6029	538	10	(	(	PUNCT
ejpam-6029	538	11	21	21	NUM
ejpam-6029	538	12	)	)	PUNCT
ejpam-6029	538	13	where	where	SCONJ
ejpam-6029	538	14	φ(t	φ(t	NOUN
ejpam-6029	538	15	)	)	PUNCT
ejpam-6029	538	16	=	=	SYM
ejpam-6029	538	17	et	et	X
ejpam-6029	538	18	>	>	X
ejpam-6029	538	19	0	0	NUM
ejpam-6029	538	20	,	,	PUNCT
ejpam-6029	538	21	and	and	CCONJ
ejpam-6029	538	22	(	(	PUNCT
ejpam-6029	538	23	γ	γ	X
ejpam-6029	538	24	,	,	PUNCT
ejpam-6029	538	25	lc	lc	PROPN
ejpam-6029	538	26	)	)	PUNCT
ejpam-6029	538	27	is	be	AUX
ejpam-6029	538	28	an	an	DET
ejpam-6029	538	29	lc	lc	NOUN
ejpam-6029	538	30	-	-	PUNCT
ejpam-6029	538	31	complete	complete	ADJ
ejpam-6029	538	32	dccml	dccml	NOUN
ejpam-6029	538	33	-	-	PUNCT
ejpam-6029	538	34	space	space	NOUN
ejpam-6029	538	35	via	via	ADP
ejpam-6029	538	36	f(u	f(u	PROPN
ejpam-6029	538	37	)	)	PUNCT
ejpam-6029	538	38	=	=	SYM
ejpam-6029	538	39	g(u	g(u	ADJ
ejpam-6029	538	40	)	)	PUNCT
ejpam-6029	538	41	=(	=(	NOUN
ejpam-6029	538	42	u2	u2	PROPN
ejpam-6029	538	43	+	+	PROPN
ejpam-6029	538	44	2u	2u	PROPN
ejpam-6029	538	45	2	2	NUM
ejpam-6029	538	46	)	)	PUNCT
ejpam-6029	538	47	et	et	NOUN
ejpam-6029	538	48	.	.	PUNCT
ejpam-6029	539	1	moreover	moreover	ADV
ejpam-6029	539	2	,	,	PUNCT
ejpam-6029	539	3	let	let	VERB
ejpam-6029	539	4	t	t	NOUN
ejpam-6029	539	5	:	:	PUNCT
ejpam-6029	539	6	γ	γ	X
ejpam-6029	539	7	→	→	SYM
ejpam-6029	539	8	γ	γ	X
ejpam-6029	539	9	be	be	AUX
ejpam-6029	539	10	a	a	DET
ejpam-6029	539	11	mapping	mapping	NOUN
ejpam-6029	539	12	defined	define	VERB
ejpam-6029	539	13	by	by	ADP
ejpam-6029	539	14	tϖ(t	tϖ(t	PUNCT
ejpam-6029	539	15	)	)	PUNCT
ejpam-6029	539	16	=	=	SYM
ejpam-6029	540	1	∫	∫	PROPN
ejpam-6029	540	2	1	1	NUM
ejpam-6029	540	3	0	0	NUM
ejpam-6029	540	4	g(t	g(t	PROPN
ejpam-6029	540	5	,	,	PUNCT
ejpam-6029	540	6	u	u	NOUN
ejpam-6029	540	7	)	)	PUNCT
ejpam-6029	540	8	(	(	PUNCT
ejpam-6029	540	9	h(u	h(u	PROPN
ejpam-6029	540	10	,	,	PUNCT
ejpam-6029	540	11	ϖ(u	ϖ(u	PROPN
ejpam-6029	540	12	)	)	PUNCT
ejpam-6029	540	13	)	)	PUNCT
ejpam-6029	541	1	+	+	CCONJ
ejpam-6029	541	2	δϖ(u	δϖ(u	NOUN
ejpam-6029	541	3	)	)	PUNCT
ejpam-6029	541	4	)	)	PUNCT
ejpam-6029	541	5	du	du	PROPN
ejpam-6029	541	6	,	,	PUNCT
ejpam-6029	541	7	(	(	PUNCT
ejpam-6029	541	8	22	22	NUM
ejpam-6029	541	9	)	)	PUNCT
ejpam-6029	541	10	a.	a.	NOUN
ejpam-6029	541	11	a.	a.	PROPN
ejpam-6029	542	1	hijab	hijab	PROPN
ejpam-6029	542	2	et	et	PROPN
ejpam-6029	542	3	al	al	PROPN
ejpam-6029	542	4	.	.	PUNCT
ejpam-6029	542	5	/	/	SYM
ejpam-6029	542	6	eur	eur	PROPN
ejpam-6029	542	7	.	.	PUNCT
ejpam-6029	543	1	j.	j.	PROPN
ejpam-6029	543	2	pure	pure	PROPN
ejpam-6029	543	3	appl	appl	PROPN
ejpam-6029	543	4	.	.	PROPN
ejpam-6029	543	5	math	math	PROPN
ejpam-6029	543	6	,	,	PUNCT
ejpam-6029	543	7	18	18	NUM
ejpam-6029	543	8	(	(	PUNCT
ejpam-6029	543	9	2	2	NUM
ejpam-6029	543	10	)	)	PUNCT
ejpam-6029	543	11	(	(	PUNCT
ejpam-6029	543	12	2025	2025	NUM
ejpam-6029	543	13	)	)	PUNCT
ejpam-6029	543	14	,	,	PUNCT
ejpam-6029	543	15	6029	6029	NUM
ejpam-6029	543	16	20	20	NUM
ejpam-6029	543	17	of	of	ADP
ejpam-6029	543	18	23	23	NUM
ejpam-6029	543	19	corollary	corollary	ADJ
ejpam-6029	543	20	3	3	NUM
ejpam-6029	543	21	is	be	AUX
ejpam-6029	543	22	utilized	utilize	VERB
ejpam-6029	543	23	to	to	PART
ejpam-6029	543	24	show	show	VERB
ejpam-6029	543	25	that	that	SCONJ
ejpam-6029	543	26	t	t	PROPN
ejpam-6029	543	27	has	have	VERB
ejpam-6029	543	28	a	a	DET
ejpam-6029	543	29	unique	unique	ADJ
ejpam-6029	543	30	fixed	fix	VERB
ejpam-6029	543	31	point	point	NOUN
ejpam-6029	543	32	,	,	PUNCT
ejpam-6029	543	33	which	which	PRON
ejpam-6029	543	34	is	be	AUX
ejpam-6029	543	35	the	the	DET
ejpam-6029	543	36	solution	solution	NOUN
ejpam-6029	543	37	for	for	ADP
ejpam-6029	543	38	the	the	DET
ejpam-6029	543	39	bvp	bvp	NOUN
ejpam-6029	543	40	(	(	PUNCT
ejpam-6029	543	41	18	18	NUM
ejpam-6029	543	42	)	)	PUNCT
ejpam-6029	543	43	.	.	PUNCT
ejpam-6029	544	1	theorem	theorem	ADJ
ejpam-6029	544	2	4	4	NUM
ejpam-6029	544	3	.	.	PUNCT
ejpam-6029	544	4	assume	assume	VERB
ejpam-6029	544	5	that	that	SCONJ
ejpam-6029	544	6	there	there	PRON
ejpam-6029	544	7	exists	exist	VERB
ejpam-6029	544	8	δ	δ	PROPN
ejpam-6029	544	9	>	>	X
ejpam-6029	544	10	0	0	NUM
ejpam-6029	544	11	such	such	ADJ
ejpam-6029	544	12	that	that	SCONJ
ejpam-6029	544	13	,	,	PUNCT
ejpam-6029	544	14	for	for	ADP
ejpam-6029	544	15	each	each	DET
ejpam-6029	544	16	ϖ1	ϖ1	NOUN
ejpam-6029	544	17	,	,	PUNCT
ejpam-6029	544	18	ϖ2	ϖ2	NOUN
ejpam-6029	544	19	∈	∈	PROPN
ejpam-6029	544	20	γ	γ	X
ejpam-6029	544	21	,	,	PUNCT
ejpam-6029	544	22	|h(t	|h(t	PROPN
ejpam-6029	544	23	,	,	PUNCT
ejpam-6029	544	24	ϖ1(t	ϖ1(t	NUM
ejpam-6029	544	25	)	)	PUNCT
ejpam-6029	544	26	)	)	PUNCT
ejpam-6029	545	1	+	+	CCONJ
ejpam-6029	545	2	δϖ1(t)|+	δϖ1(t)|+	PROPN
ejpam-6029	545	3	|h(t	|h(t	PROPN
ejpam-6029	545	4	,	,	PUNCT
ejpam-6029	545	5	ϖ2(t	ϖ2(t	PROPN
ejpam-6029	545	6	)	)	PUNCT
ejpam-6029	545	7	)	)	PUNCT
ejpam-6029	546	1	+	+	CCONJ
ejpam-6029	546	2	δϖ2(t)|	δϖ2(t)|	ADV
ejpam-6029	546	3	≤	≤	ADJ
ejpam-6029	546	4	δ	δ	NOUN
ejpam-6029	546	5	3	3	NUM
ejpam-6029	546	6	(	(	PUNCT
ejpam-6029	546	7	|ϖ1(t)|+	|ϖ1(t)|+	PROPN
ejpam-6029	546	8	|ϖ2(t)|	|ϖ2(t)|	NOUN
ejpam-6029	546	9	)	)	PUNCT
ejpam-6029	546	10	.	.	PUNCT
ejpam-6029	547	1	then	then	ADV
ejpam-6029	547	2	,	,	PUNCT
ejpam-6029	547	3	bvp	bvp	PROPN
ejpam-6029	547	4	(	(	PUNCT
ejpam-6029	547	5	18	18	NUM
ejpam-6029	547	6	)	)	PUNCT
ejpam-6029	547	7	possesses	possess	VERB
ejpam-6029	547	8	a	a	DET
ejpam-6029	547	9	unique	unique	ADJ
ejpam-6029	547	10	solution	solution	NOUN
ejpam-6029	547	11	in	in	ADP
ejpam-6029	547	12	γ	γ	PROPN
ejpam-6029	547	13	.	.	PUNCT
ejpam-6029	547	14	proof	proof	NOUN
ejpam-6029	547	15	.	.	PUNCT
ejpam-6029	548	1	let	let	VERB
ejpam-6029	548	2	lc	lc	NOUN
ejpam-6029	548	3	be	be	AUX
ejpam-6029	548	4	a	a	DET
ejpam-6029	548	5	mapping	mapping	NOUN
ejpam-6029	548	6	given	give	VERB
ejpam-6029	548	7	in	in	ADP
ejpam-6029	548	8	(	(	PUNCT
ejpam-6029	548	9	21	21	NUM
ejpam-6029	548	10	)	)	PUNCT
ejpam-6029	548	11	,	,	PUNCT
ejpam-6029	548	12	t	t	PROPN
ejpam-6029	548	13	be	be	AUX
ejpam-6029	548	14	the	the	DET
ejpam-6029	548	15	operator	operator	NOUN
ejpam-6029	548	16	function	function	NOUN
ejpam-6029	548	17	in	in	ADP
ejpam-6029	548	18	(	(	PUNCT
ejpam-6029	548	19	22	22	NUM
ejpam-6029	548	20	)	)	PUNCT
ejpam-6029	548	21	.	.	PUNCT
ejpam-6029	549	1	then	then	ADV
ejpam-6029	549	2	lc(tϖ1	lc(tϖ1	NUM
ejpam-6029	549	3	,	,	PUNCT
ejpam-6029	549	4	tϖ2)(t	tϖ2)(t	PROPN
ejpam-6029	549	5	)	)	PUNCT
ejpam-6029	549	6	=	=	PRON
ejpam-6029	549	7	(	(	PUNCT
ejpam-6029	549	8	e|tϖ1(t)|+|tϖ2(t)|	e|tϖ1(t)|+|tϖ2(t)|	INTJ
ejpam-6029	549	9	−	−	PROPN
ejpam-6029	549	10	1	1	NUM
ejpam-6029	549	11	)	)	PUNCT
ejpam-6029	549	12	et	et	NOUN
ejpam-6029	549	13	=	=	PUNCT
ejpam-6029	550	1	(	(	PUNCT
ejpam-6029	550	2	e|	e|	PROPN
ejpam-6029	550	3	∫	∫	PROPN
ejpam-6029	550	4	1	1	NUM
ejpam-6029	550	5	0	0	NUM
ejpam-6029	550	6	g(t	g(t	PROPN
ejpam-6029	550	7	,	,	PUNCT
ejpam-6029	550	8	u)(h(u,ϖ1(u))+δϖ1(u))du|+|	u)(h(u,ϖ1(u))+δϖ1(u))du|+|	PROPN
ejpam-6029	550	9	∫	∫	NOUN
ejpam-6029	550	10	1	1	NUM
ejpam-6029	550	11	0	0	NUM
ejpam-6029	550	12	g(t	g(t	PROPN
ejpam-6029	550	13	,	,	PUNCT
ejpam-6029	550	14	u)(h(u,ϖ2(u))+δϖ2(u))du|	u)(h(u,ϖ2(u))+δϖ2(u))du|	PROPN
ejpam-6029	550	15	−	−	PROPN
ejpam-6029	550	16	1	1	NUM
ejpam-6029	550	17	)	)	PUNCT
ejpam-6029	550	18	et	et	NOUN
ejpam-6029	550	19	⪯	⪯	NOUN
ejpam-6029	550	20	(	(	PUNCT
ejpam-6029	550	21	e	e	NOUN
ejpam-6029	550	22	∫	∫	PROPN
ejpam-6029	550	23	1	1	NUM
ejpam-6029	550	24	0	0	NUM
ejpam-6029	550	25	g(t	g(t	PROPN
ejpam-6029	550	26	,	,	PUNCT
ejpam-6029	550	27	u)|h(u,ϖ1(u)+δϖ1(u))|+|h(u,ϖ2(u))+δϖ2(u)|du	u)|h(u,ϖ1(u)+δϖ1(u))|+|h(u,ϖ2(u))+δϖ2(u)|du	ADJ
ejpam-6029	550	28	−	−	NOUN
ejpam-6029	550	29	1	1	NUM
ejpam-6029	550	30	)	)	PUNCT
ejpam-6029	550	31	et	et	NOUN
ejpam-6029	550	32	⪯	⪯	NOUN
ejpam-6029	550	33	(	(	PUNCT
ejpam-6029	550	34	e	e	NOUN
ejpam-6029	550	35	∫	∫	PROPN
ejpam-6029	550	36	1	1	NUM
ejpam-6029	550	37	0	0	NUM
ejpam-6029	550	38	g(t	g(t	PROPN
ejpam-6029	550	39	,	,	PUNCT
ejpam-6029	550	40	u	u	NOUN
ejpam-6029	550	41	)	)	PUNCT
ejpam-6029	550	42	δ	δ	NOUN
ejpam-6029	550	43	3	3	NUM
ejpam-6029	550	44	(	(	PUNCT
ejpam-6029	550	45	|ϖ1(u)|+|ϖ2(u)|)du	|ϖ1(u)|+|ϖ2(u)|)du	PROPN
ejpam-6029	550	46	−	−	PROPN
ejpam-6029	550	47	1	1	X
ejpam-6029	550	48	)	)	PUNCT
ejpam-6029	550	49	et	et	NOUN
ejpam-6029	550	50	⪯	⪯	NOUN
ejpam-6029	550	51	(	(	PUNCT
ejpam-6029	550	52	e	e	NOUN
ejpam-6029	550	53	δ	δ	PROPN
ejpam-6029	550	54	3	3	NUM
ejpam-6029	550	55	(	(	PUNCT
ejpam-6029	550	56	|ϖ1(t)|+|ϖ2(t)|	|ϖ1(t)|+|ϖ2(t)|	NOUN
ejpam-6029	550	57	)	)	PUNCT
ejpam-6029	550	58	∫	∫	NOUN
ejpam-6029	550	59	1	1	NUM
ejpam-6029	550	60	0	0	NUM
ejpam-6029	550	61	g(t	g(t	PROPN
ejpam-6029	550	62	,	,	PUNCT
ejpam-6029	550	63	u)du	u)du	PROPN
ejpam-6029	550	64	−	−	PROPN
ejpam-6029	550	65	1	1	X
ejpam-6029	550	66	)	)	PUNCT
ejpam-6029	550	67	et	et	NOUN
ejpam-6029	550	68	⪯	⪯	NOUN
ejpam-6029	550	69	(	(	PUNCT
ejpam-6029	550	70	eδ(|ϖ1(t)|+|ϖ2(t)|	eδ(|ϖ1(t)|+|ϖ2(t)|	PROPN
ejpam-6029	550	71	)	)	PUNCT
ejpam-6029	550	72	1δ	1δ	NUM
ejpam-6029	550	73	−	−	PROPN
ejpam-6029	550	74	1	1	X
ejpam-6029	550	75	)	)	PUNCT
ejpam-6029	550	76	et	et	NOUN
ejpam-6029	550	77	3	3	NUM
ejpam-6029	550	78	,	,	PUNCT
ejpam-6029	550	79	(	(	PUNCT
ejpam-6029	550	80	since	since	SCONJ
ejpam-6029	550	81	ert	ert	NOUN
ejpam-6029	550	82	−	−	PROPN
ejpam-6029	550	83	1	1	NUM
ejpam-6029	550	84	≤	≤	NUM
ejpam-6029	550	85	r(et	r(et	NOUN
ejpam-6029	550	86	−	−	NOUN
ejpam-6029	550	87	1	1	NUM
ejpam-6029	550	88	)	)	PUNCT
ejpam-6029	550	89	,	,	PUNCT
ejpam-6029	550	90	r	r	NOUN
ejpam-6029	550	91	=	=	SYM
ejpam-6029	550	92	1	1	NUM
ejpam-6029	550	93	3	3	NUM
ejpam-6029	550	94	∈	∈	NOUN
ejpam-6029	550	95	(	(	PUNCT
ejpam-6029	550	96	0	0	NUM
ejpam-6029	550	97	,	,	PUNCT
ejpam-6029	550	98	1	1	NUM
ejpam-6029	550	99	)	)	PUNCT
ejpam-6029	550	100	)	)	PUNCT
ejpam-6029	550	101	.	.	PUNCT
ejpam-6029	551	1	⪯	⪯	PROPN
ejpam-6029	551	2	lc(ϖ1	lc(ϖ1	VERB
ejpam-6029	551	3	,	,	PUNCT
ejpam-6029	551	4	ϖ2	ϖ2	NOUN
ejpam-6029	551	5	)	)	PUNCT
ejpam-6029	551	6	sup	sup	NOUN
ejpam-6029	551	7	t∈[0,1	t∈[0,1	NOUN
ejpam-6029	551	8	]	]	PUNCT
ejpam-6029	551	9	et	et	NOUN
ejpam-6029	551	10	3	3	NUM
ejpam-6029	551	11	.	.	PUNCT
ejpam-6029	552	1	(	(	PUNCT
ejpam-6029	552	2	since	since	SCONJ
ejpam-6029	552	3	1	1	NUM
ejpam-6029	552	4	≤	≤	NUM
ejpam-6029	552	5	et	et	NOUN
ejpam-6029	552	6	,	,	PUNCT
ejpam-6029	552	7	t	t	PROPN
ejpam-6029	552	8	∈	∈	PROPN
ejpam-6029	553	1	[	[	X
ejpam-6029	553	2	0	0	NUM
ejpam-6029	553	3	,	,	PUNCT
ejpam-6029	553	4	1	1	NUM
ejpam-6029	553	5	]	]	NUM
ejpam-6029	553	6	)	)	PUNCT
ejpam-6029	553	7	.	.	PUNCT
ejpam-6029	554	1	we	we	PRON
ejpam-6029	554	2	deduce	deduce	VERB
ejpam-6029	554	3	that	that	DET
ejpam-6029	554	4	lc(tϖ1	lc(tϖ1	PROPN
ejpam-6029	554	5	,	,	PUNCT
ejpam-6029	554	6	tϖ2	tϖ2	PROPN
ejpam-6029	554	7	)	)	PUNCT
ejpam-6029	554	8	⪯	⪯	NOUN
ejpam-6029	554	9	λ(t)lc(ϖ1	λ(t)lc(ϖ1	NOUN
ejpam-6029	554	10	,	,	PUNCT
ejpam-6029	554	11	ϖ2	ϖ2	NOUN
ejpam-6029	554	12	)	)	PUNCT
ejpam-6029	554	13	⪯	⪯	NOUN
ejpam-6029	554	14	λ(t)m̃(ϖ1	λ(t)m̃(ϖ1	PROPN
ejpam-6029	554	15	,	,	PUNCT
ejpam-6029	554	16	ϖ2	ϖ2	NOUN
ejpam-6029	554	17	)	)	PUNCT
ejpam-6029	554	18	,	,	PUNCT
ejpam-6029	554	19	where	where	SCONJ
ejpam-6029	554	20	m̃(ϖ1	m̃(ϖ1	NOUN
ejpam-6029	554	21	,	,	PUNCT
ejpam-6029	554	22	ϖ2	ϖ2	NOUN
ejpam-6029	554	23	)	)	PUNCT
ejpam-6029	554	24	in	in	ADP
ejpam-6029	554	25	(	(	PUNCT
ejpam-6029	554	26	10	10	NUM
ejpam-6029	554	27	)	)	PUNCT
ejpam-6029	554	28	,	,	PUNCT
ejpam-6029	554	29	and	and	CCONJ
ejpam-6029	554	30	λ(t	λ(t	NOUN
ejpam-6029	554	31	)	)	PUNCT
ejpam-6029	554	32	=	=	SYM
ejpam-6029	554	33	sup	sup	NOUN
ejpam-6029	554	34	t∈[0,1	t∈[0,1	PROPN
ejpam-6029	554	35	]	]	PUNCT
ejpam-6029	554	36	et	et	NOUN
ejpam-6029	554	37	3	3	NUM
ejpam-6029	554	38	∈	∈	PROPN
ejpam-6029	554	39	(	(	PUNCT
ejpam-6029	554	40	0	0	NUM
ejpam-6029	554	41	,	,	PUNCT
ejpam-6029	554	42	1	1	NUM
ejpam-6029	554	43	)	)	PUNCT
ejpam-6029	554	44	.	.	PUNCT
ejpam-6029	555	1	therefore	therefore	ADV
ejpam-6029	555	2	,	,	PUNCT
ejpam-6029	555	3	t	t	PROPN
ejpam-6029	555	4	is	be	AUX
ejpam-6029	555	5	a	a	DET
ejpam-6029	555	6	generalized	generalized	ADJ
ejpam-6029	555	7	rational	rational	ADJ
ejpam-6029	555	8	contraction	contraction	NOUN
ejpam-6029	555	9	,	,	PUNCT
ejpam-6029	555	10	and	and	CCONJ
ejpam-6029	555	11	all	all	DET
ejpam-6029	555	12	the	the	DET
ejpam-6029	555	13	conditions	condition	NOUN
ejpam-6029	555	14	in	in	ADP
ejpam-6029	555	15	corollary	corollary	ADJ
ejpam-6029	555	16	3	3	NUM
ejpam-6029	555	17	hold	hold	NOUN
ejpam-6029	555	18	.	.	PUNCT
ejpam-6029	556	1	thus	thus	ADV
ejpam-6029	556	2	,	,	PUNCT
ejpam-6029	556	3	we	we	PRON
ejpam-6029	556	4	obtain	obtain	VERB
ejpam-6029	556	5	the	the	DET
ejpam-6029	556	6	desired	desire	VERB
ejpam-6029	556	7	result	result	NOUN
ejpam-6029	556	8	.	.	PUNCT
ejpam-6029	557	1	5	5	X
ejpam-6029	557	2	.	.	X
ejpam-6029	557	3	conclusions	conclusion	NOUN
ejpam-6029	557	4	this	this	DET
ejpam-6029	557	5	research	research	NOUN
ejpam-6029	557	6	introduces	introduce	VERB
ejpam-6029	557	7	a	a	DET
ejpam-6029	557	8	novel	novel	ADJ
ejpam-6029	557	9	concept	concept	NOUN
ejpam-6029	557	10	in	in	ADP
ejpam-6029	557	11	the	the	DET
ejpam-6029	557	12	realm	realm	NOUN
ejpam-6029	557	13	of	of	ADP
ejpam-6029	557	14	generalized	generalized	ADJ
ejpam-6029	557	15	metric	metric	ADJ
ejpam-6029	557	16	spaces	space	NOUN
ejpam-6029	557	17	,	,	PUNCT
ejpam-6029	557	18	called	call	VERB
ejpam-6029	557	19	double	double	ADV
ejpam-6029	557	20	-	-	PUNCT
ejpam-6029	557	21	composed	compose	VERB
ejpam-6029	557	22	cone	cone	NOUN
ejpam-6029	557	23	-	-	PUNCT
ejpam-6029	557	24	metric	metric	ADJ
ejpam-6029	557	25	-	-	PUNCT
ejpam-6029	557	26	like	like	ADJ
ejpam-6029	557	27	spaces	space	NOUN
ejpam-6029	557	28	,	,	PUNCT
ejpam-6029	557	29	which	which	PRON
ejpam-6029	557	30	is	be	AUX
ejpam-6029	557	31	illustrated	illustrate	VERB
ejpam-6029	557	32	through	through	ADP
ejpam-6029	557	33	a	a	DET
ejpam-6029	557	34	series	series	NOUN
ejpam-6029	557	35	of	of	ADP
ejpam-6029	557	36	examples	example	NOUN
ejpam-6029	557	37	.	.	PUNCT
ejpam-6029	558	1	we	we	PRON
ejpam-6029	558	2	derived	derive	VERB
ejpam-6029	558	3	generalization	generalization	NOUN
ejpam-6029	558	4	rational	rational	ADJ
ejpam-6029	558	5	-	-	PUNCT
ejpam-6029	558	6	type	type	NOUN
ejpam-6029	558	7	contraction	contraction	NOUN
ejpam-6029	558	8	theorems	theorem	VERB
ejpam-6029	558	9	for	for	ADP
ejpam-6029	558	10	a	a	DET
ejpam-6029	558	11	variety	variety	NOUN
ejpam-6029	558	12	of	of	ADP
ejpam-6029	558	13	mappings	mapping	NOUN
ejpam-6029	558	14	,	,	PUNCT
ejpam-6029	558	15	termed	term	VERB
ejpam-6029	558	16	common	common	ADJ
ejpam-6029	558	17	fixed	fix	VERB
ejpam-6029	558	18	points	point	NOUN
ejpam-6029	558	19	in	in	ADP
ejpam-6029	558	20	double	double	ADV
ejpam-6029	558	21	-	-	PUNCT
ejpam-6029	558	22	composed	compose	VERB
ejpam-6029	558	23	cone	cone	NOUN
ejpam-6029	558	24	-	-	PUNCT
ejpam-6029	558	25	metric	metric	ADJ
ejpam-6029	558	26	-	-	PUNCT
ejpam-6029	558	27	like	like	ADJ
ejpam-6029	558	28	spaces	space	NOUN
ejpam-6029	558	29	and	and	CCONJ
ejpam-6029	558	30	provided	provide	VERB
ejpam-6029	558	31	a	a	DET
ejpam-6029	558	32	number	number	NOUN
ejpam-6029	558	33	of	of	ADP
ejpam-6029	558	34	related	relate	VERB
ejpam-6029	558	35	results	result	NOUN
ejpam-6029	558	36	to	to	PART
ejpam-6029	558	37	support	support	VERB
ejpam-6029	558	38	our	our	PRON
ejpam-6029	558	39	theorems	theorem	NOUN
ejpam-6029	558	40	.	.	PUNCT
ejpam-6029	559	1	furthermore	furthermore	ADV
ejpam-6029	559	2	,	,	PUNCT
ejpam-6029	559	3	we	we	PRON
ejpam-6029	559	4	presented	present	VERB
ejpam-6029	559	5	numerous	numerous	ADJ
ejpam-6029	559	6	examples	example	NOUN
ejpam-6029	559	7	to	to	PART
ejpam-6029	559	8	substantiate	substantiate	VERB
ejpam-6029	559	9	the	the	DET
ejpam-6029	559	10	main	main	ADJ
ejpam-6029	559	11	results	result	NOUN
ejpam-6029	559	12	of	of	ADP
ejpam-6029	559	13	our	our	PRON
ejpam-6029	559	14	study	study	NOUN
ejpam-6029	559	15	.	.	PUNCT
ejpam-6029	560	1	the	the	DET
ejpam-6029	560	2	study	study	NOUN
ejpam-6029	560	3	demonstrates	demonstrate	VERB
ejpam-6029	560	4	applications	application	NOUN
ejpam-6029	560	5	of	of	ADP
ejpam-6029	560	6	nonlinear	nonlinear	ADJ
ejpam-6029	560	7	integral	integral	ADJ
ejpam-6029	560	8	equations	equation	NOUN
ejpam-6029	560	9	and	and	CCONJ
ejpam-6029	560	10	bvps	bvps	PROPN
ejpam-6029	560	11	,	,	PUNCT
ejpam-6029	560	12	proving	prove	VERB
ejpam-6029	560	13	the	the	DET
ejpam-6029	560	14	existence	existence	NOUN
ejpam-6029	560	15	of	of	ADP
ejpam-6029	560	16	solutions	solution	NOUN
ejpam-6029	560	17	.	.	PUNCT
ejpam-6029	561	1	this	this	DET
ejpam-6029	561	2	particular	particular	ADJ
ejpam-6029	561	3	new	new	ADJ
ejpam-6029	561	4	generalization	generalization	NOUN
ejpam-6029	561	5	provides	provide	VERB
ejpam-6029	561	6	valuable	valuable	ADJ
ejpam-6029	561	7	tools	tool	NOUN
ejpam-6029	561	8	for	for	ADP
ejpam-6029	561	9	studying	study	VERB
ejpam-6029	561	10	fixed	fix	VERB
ejpam-6029	561	11	point	point	NOUN
ejpam-6029	561	12	theorems	theorem	NOUN
ejpam-6029	561	13	.	.	PUNCT
ejpam-6029	562	1	the	the	DET
ejpam-6029	562	2	following	follow	VERB
ejpam-6029	562	3	points	point	NOUN
ejpam-6029	562	4	outline	outline	VERB
ejpam-6029	562	5	potential	potential	ADJ
ejpam-6029	562	6	open	open	ADJ
ejpam-6029	562	7	problems	problem	NOUN
ejpam-6029	562	8	and	and	CCONJ
ejpam-6029	562	9	avenues	avenue	NOUN
ejpam-6029	562	10	for	for	ADP
ejpam-6029	562	11	future	future	ADJ
ejpam-6029	562	12	research	research	NOUN
ejpam-6029	562	13	:	:	PUNCT
ejpam-6029	562	14	•	•	ADP
ejpam-6029	562	15	explore	explore	VERB
ejpam-6029	562	16	new	new	ADJ
ejpam-6029	562	17	generalizations	generalization	NOUN
ejpam-6029	562	18	of	of	ADP
ejpam-6029	562	19	double	double	ADV
ejpam-6029	562	20	-	-	PUNCT
ejpam-6029	562	21	composed	compose	VERB
ejpam-6029	562	22	cone	cone	NOUN
ejpam-6029	562	23	-	-	PUNCT
ejpam-6029	562	24	metric	metric	ADJ
ejpam-6029	562	25	-	-	PUNCT
ejpam-6029	562	26	like	like	ADJ
ejpam-6029	562	27	spaces	space	NOUN
ejpam-6029	562	28	,	,	PUNCT
ejpam-6029	562	29	such	such	ADJ
ejpam-6029	562	30	as	as	ADP
ejpam-6029	562	31	fuzzy	fuzzy	ADJ
ejpam-6029	562	32	double	double	ADV
ejpam-6029	562	33	-	-	PUNCT
ejpam-6029	562	34	composed	compose	VERB
ejpam-6029	562	35	metric	metric	ADJ
ejpam-6029	562	36	-	-	PUNCT
ejpam-6029	562	37	like	like	ADJ
ejpam-6029	562	38	spaces	space	NOUN
ejpam-6029	562	39	,	,	PUNCT
ejpam-6029	562	40	fuzzy	fuzzy	ADJ
ejpam-6029	562	41	double	double	ADV
ejpam-6029	562	42	-	-	PUNCT
ejpam-6029	562	43	composed	compose	VERB
ejpam-6029	562	44	cone	cone	NOUN
ejpam-6029	562	45	-	-	PUNCT
ejpam-6029	562	46	metric	metric	ADJ
ejpam-6029	562	47	-	-	PUNCT
ejpam-6029	562	48	like	like	ADJ
ejpam-6029	562	49	spaces	space	NOUN
ejpam-6029	562	50	,	,	PUNCT
ejpam-6029	562	51	and	and	CCONJ
ejpam-6029	562	52	neutrosophic	neutrosophic	ADJ
ejpam-6029	562	53	double	double	ADV
ejpam-6029	562	54	-	-	PUNCT
ejpam-6029	562	55	composed	compose	VERB
ejpam-6029	562	56	cone	cone	NOUN
ejpam-6029	562	57	-	-	PUNCT
ejpam-6029	562	58	metric	metric	ADJ
ejpam-6029	562	59	-	-	PUNCT
ejpam-6029	562	60	like	like	ADJ
ejpam-6029	562	61	spaces	space	NOUN
ejpam-6029	562	62	.	.	PUNCT
ejpam-6029	563	1	a.	a.	NOUN
ejpam-6029	563	2	a.	a.	PROPN
ejpam-6029	563	3	hijab	hijab	PROPN
ejpam-6029	563	4	et	et	PROPN
ejpam-6029	563	5	al	al	PROPN
ejpam-6029	563	6	.	.	PUNCT
ejpam-6029	563	7	/	/	SYM
ejpam-6029	563	8	eur	eur	PROPN
ejpam-6029	563	9	.	.	PUNCT
ejpam-6029	564	1	j.	j.	PROPN
ejpam-6029	564	2	pure	pure	PROPN
ejpam-6029	564	3	appl	appl	PROPN
ejpam-6029	564	4	.	.	PROPN
ejpam-6029	564	5	math	math	PROPN
ejpam-6029	564	6	,	,	PUNCT
ejpam-6029	564	7	18	18	NUM
ejpam-6029	564	8	(	(	PUNCT
ejpam-6029	564	9	2	2	NUM
ejpam-6029	564	10	)	)	PUNCT
ejpam-6029	564	11	(	(	PUNCT
ejpam-6029	564	12	2025	2025	NUM
ejpam-6029	564	13	)	)	PUNCT
ejpam-6029	564	14	,	,	PUNCT
ejpam-6029	564	15	6029	6029	NUM
ejpam-6029	564	16	21	21	NUM
ejpam-6029	564	17	of	of	ADP
ejpam-6029	564	18	23	23	NUM
ejpam-6029	564	19	•	•	NUM
ejpam-6029	564	20	establish	establish	VERB
ejpam-6029	564	21	new	new	ADJ
ejpam-6029	564	22	fixed	fix	VERB
ejpam-6029	564	23	point	point	NOUN
ejpam-6029	564	24	results	result	NOUN
ejpam-6029	564	25	in	in	ADP
ejpam-6029	564	26	various	various	ADJ
ejpam-6029	564	27	types	type	NOUN
ejpam-6029	564	28	of	of	ADP
ejpam-6029	564	29	contractions	contraction	NOUN
ejpam-6029	564	30	,	,	PUNCT
ejpam-6029	564	31	including	include	VERB
ejpam-6029	564	32	new	new	ADJ
ejpam-6029	564	33	nonlinear	nonlinear	ADJ
ejpam-6029	564	34	rational	rational	ADJ
ejpam-6029	564	35	contractions	contraction	NOUN
ejpam-6029	564	36	,	,	PUNCT
ejpam-6029	564	37	weak	weak	ADJ
ejpam-6029	564	38	contractions	contraction	NOUN
ejpam-6029	564	39	,	,	PUNCT
ejpam-6029	564	40	almost	almost	ADV
ejpam-6029	564	41	-	-	PUNCT
ejpam-6029	564	42	contraction	contraction	NOUN
ejpam-6029	564	43	,	,	PUNCT
ejpam-6029	564	44	and	and	CCONJ
ejpam-6029	564	45	(	(	PUNCT
ejpam-6029	564	46	ϕ	ϕ	PROPN
ejpam-6029	564	47	,	,	PUNCT
ejpam-6029	564	48	f	f	NOUN
ejpam-6029	564	49	)	)	PUNCT
ejpam-6029	564	50	contraction	contraction	NOUN
ejpam-6029	564	51	,	,	PUNCT
ejpam-6029	564	52	among	among	ADP
ejpam-6029	564	53	others	other	NOUN
ejpam-6029	564	54	.	.	PUNCT
ejpam-6029	565	1	•	•	NUM
ejpam-6029	565	2	develop	develop	VERB
ejpam-6029	565	3	deep	deep	ADJ
ejpam-6029	565	4	and	and	CCONJ
ejpam-6029	565	5	non	non	ADJ
ejpam-6029	565	6	-	-	ADJ
ejpam-6029	565	7	trivial	trivial	ADJ
ejpam-6029	565	8	applications	application	NOUN
ejpam-6029	565	9	of	of	ADP
ejpam-6029	565	10	our	our	PRON
ejpam-6029	565	11	main	main	ADJ
ejpam-6029	565	12	results	result	NOUN
ejpam-6029	565	13	to	to	PART
ejpam-6029	565	14	further	far	ADV
ejpam-6029	565	15	expand	expand	VERB
ejpam-6029	565	16	the	the	DET
ejpam-6029	565	17	scope	scope	NOUN
ejpam-6029	565	18	of	of	ADP
ejpam-6029	565	19	our	our	PRON
ejpam-6029	565	20	research	research	NOUN
ejpam-6029	565	21	.	.	PUNCT
ejpam-6029	566	1	acknowledgments	acknowledgment	NOUN
ejpam-6029	566	2	the	the	DET
ejpam-6029	566	3	authors	author	NOUN
ejpam-6029	566	4	s.	s.	PROPN
ejpam-6029	566	5	aljohani	aljohani	PROPN
ejpam-6029	566	6	and	and	CCONJ
ejpam-6029	566	7	n.	n.	PROPN
ejpam-6029	566	8	mlaiki	mlaiki	PROPN
ejpam-6029	566	9	would	would	AUX
ejpam-6029	566	10	like	like	VERB
ejpam-6029	566	11	to	to	PART
ejpam-6029	566	12	thank	thank	VERB
ejpam-6029	566	13	prince	prince	PROPN
ejpam-6029	566	14	sultan	sultan	PROPN
ejpam-6029	566	15	university	university	PROPN
ejpam-6029	566	16	for	for	ADP
ejpam-6029	566	17	paying	pay	VERB
ejpam-6029	566	18	the	the	DET
ejpam-6029	566	19	apc	apc	NOUN
ejpam-6029	566	20	and	and	CCONJ
ejpam-6029	566	21	for	for	ADP
ejpam-6029	566	22	the	the	DET
ejpam-6029	566	23	support	support	NOUN
ejpam-6029	566	24	through	through	ADP
ejpam-6029	566	25	the	the	DET
ejpam-6029	566	26	tas	tas	PROPN
ejpam-6029	566	27	research	research	NOUN
ejpam-6029	566	28	lab	lab	PROPN
ejpam-6029	566	29	.	.	PUNCT
ejpam-6029	567	1	author	author	NOUN
ejpam-6029	567	2	contributions	contribution	VERB
ejpam-6029	567	3	a.	a.	PROPN
ejpam-6029	567	4	a.	a.	PROPN
ejpam-6029	567	5	,	,	PUNCT
ejpam-6029	567	6	l.	l.	PROPN
ejpam-6029	567	7	kh	kh	PROPN
ejpam-6029	567	8	.	.	PROPN
ejpam-6029	567	9	,	,	PUNCT
ejpam-6029	567	10	s.	s.	PROPN
ejpam-6029	567	11	a.	a.	PROPN
ejpam-6029	567	12	and	and	CCONJ
ejpam-6029	567	13	n.	n.	PROPN
ejpam-6029	567	14	m.	m.	NOUN
ejpam-6029	567	15	wrote	write	VERB
ejpam-6029	567	16	the	the	DET
ejpam-6029	567	17	main	main	ADJ
ejpam-6029	567	18	manuscript	manuscript	NOUN
ejpam-6029	567	19	text	text	NOUN
ejpam-6029	567	20	.	.	PUNCT
ejpam-6029	568	1	all	all	DET
ejpam-6029	568	2	authors	author	NOUN
ejpam-6029	568	3	reviewed	review	VERB
ejpam-6029	568	4	the	the	DET
ejpam-6029	568	5	manuscript	manuscript	NOUN
ejpam-6029	568	6	.	.	PUNCT
ejpam-6029	569	1	conflicts	conflict	NOUN
ejpam-6029	569	2	of	of	ADP
ejpam-6029	569	3	interest	interest	NOUN
ejpam-6029	569	4	the	the	DET
ejpam-6029	569	5	authors	author	NOUN
ejpam-6029	569	6	declare	declare	VERB
ejpam-6029	569	7	no	no	DET
ejpam-6029	569	8	conflicts	conflict	NOUN
ejpam-6029	569	9	of	of	ADP
ejpam-6029	569	10	interest	interest	NOUN
ejpam-6029	569	11	.	.	PUNCT
ejpam-6029	570	1	references	reference	NOUN
ejpam-6029	570	2	[	[	X
ejpam-6029	570	3	1	1	NUM
ejpam-6029	570	4	]	]	PUNCT
ejpam-6029	570	5	s	s	VERB
ejpam-6029	570	6	banach	banach	NOUN
ejpam-6029	570	7	.	.	PUNCT
ejpam-6029	571	1	sur	sur	PROPN
ejpam-6029	571	2	les	les	PROPN
ejpam-6029	571	3	operations	operation	NOUN
ejpam-6029	571	4	dans	dan	NOUN
ejpam-6029	571	5	les	les	X
ejpam-6029	571	6	ensembles	ensemble	NOUN
ejpam-6029	571	7	et	et	PROPN
ejpam-6029	571	8	leur	leur	X
ejpam-6029	571	9	application	application	PROPN
ejpam-6029	571	10	aux	aux	PROPN
ejpam-6029	571	11	equation	equation	NOUN
ejpam-6029	571	12	sitegrales	sitegrale	NOUN
ejpam-6029	571	13	.	.	PUNCT
ejpam-6029	572	1	fundamenta	fundamenta	PROPN
ejpam-6029	572	2	mathematicae	mathematicae	PROPN
ejpam-6029	572	3	,	,	PUNCT
ejpam-6029	572	4	3:133–181	3:133–181	NUM
ejpam-6029	572	5	,	,	PUNCT
ejpam-6029	572	6	1922	1922	NUM
ejpam-6029	572	7	.	.	PUNCT
ejpam-6029	573	1	[	[	X
ejpam-6029	573	2	2	2	NUM
ejpam-6029	573	3	]	]	X
ejpam-6029	573	4	s	s	PART
ejpam-6029	573	5	czerwik	czerwik	PROPN
ejpam-6029	573	6	.	.	PUNCT
ejpam-6029	574	1	contraction	contraction	NOUN
ejpam-6029	574	2	mappings	mapping	NOUN
ejpam-6029	574	3	in	in	ADP
ejpam-6029	574	4	b	b	NOUN
ejpam-6029	574	5	-	-	ADJ
ejpam-6029	574	6	metric	metric	ADJ
ejpam-6029	574	7	spaces	space	NOUN
ejpam-6029	574	8	.	.	PUNCT
ejpam-6029	575	1	acta	acta	PROPN
ejpam-6029	575	2	mathematica	mathematica	PROPN
ejpam-6029	575	3	et	et	PROPN
ejpam-6029	575	4	informatica	informatica	PROPN
ejpam-6029	575	5	universitatis	universitatis	PROPN
ejpam-6029	575	6	ostraviensis	ostraviensis	PROPN
ejpam-6029	575	7	,	,	PUNCT
ejpam-6029	575	8	1:5–11	1:5–11	NUM
ejpam-6029	575	9	,	,	PUNCT
ejpam-6029	575	10	1993	1993	NUM
ejpam-6029	575	11	.	.	PUNCT
ejpam-6029	576	1	[	[	X
ejpam-6029	576	2	3	3	X
ejpam-6029	576	3	]	]	PUNCT
ejpam-6029	576	4	a	a	DET
ejpam-6029	576	5	bakhtin	bakhtin	NOUN
ejpam-6029	576	6	.	.	PUNCT
ejpam-6029	577	1	the	the	DET
ejpam-6029	577	2	contraction	contraction	NOUN
ejpam-6029	577	3	mapping	map	VERB
ejpam-6029	577	4	principle	principle	NOUN
ejpam-6029	577	5	in	in	ADP
ejpam-6029	577	6	almost	almost	ADV
ejpam-6029	577	7	metric	metric	ADJ
ejpam-6029	577	8	spaces	space	NOUN
ejpam-6029	577	9	.	.	PUNCT
ejpam-6029	578	1	functional	functional	ADJ
ejpam-6029	578	2	analysis	analysis	NOUN
ejpam-6029	578	3	,	,	PUNCT
ejpam-6029	578	4	30:26–37	30:26–37	PROPN
ejpam-6029	578	5	,	,	PUNCT
ejpam-6029	578	6	1989	1989	NUM
ejpam-6029	578	7	.	.	PUNCT
ejpam-6029	579	1	[	[	X
ejpam-6029	579	2	4	4	X
ejpam-6029	579	3	]	]	PUNCT
ejpam-6029	579	4	z	z	NOUN
ejpam-6029	579	5	d	d	NOUN
ejpam-6029	579	6	mitrović	mitrović	NOUN
ejpam-6029	579	7	and	and	CCONJ
ejpam-6029	579	8	s	s	VERB
ejpam-6029	579	9	radenović.	radenović.	NOUN
ejpam-6029	579	10	the	the	DET
ejpam-6029	579	11	banach	banach	NOUN
ejpam-6029	579	12	and	and	CCONJ
ejpam-6029	579	13	reich	reich	PROPN
ejpam-6029	579	14	contractions	contraction	NOUN
ejpam-6029	579	15	in	in	ADP
ejpam-6029	579	16	bv(s)-metric	bv(s)-metric	PROPN
ejpam-6029	579	17	spaces	space	NOUN
ejpam-6029	579	18	.	.	PUNCT
ejpam-6029	580	1	journal	journal	NOUN
ejpam-6029	580	2	of	of	ADP
ejpam-6029	580	3	fixed	fix	VERB
ejpam-6029	580	4	point	point	NOUN
ejpam-6029	580	5	theory	theory	NOUN
ejpam-6029	580	6	and	and	CCONJ
ejpam-6029	580	7	applications	application	NOUN
ejpam-6029	580	8	,	,	PUNCT
ejpam-6029	580	9	19:3087–3095	19:3087–3095	NUM
ejpam-6029	580	10	,	,	PUNCT
ejpam-6029	580	11	2017	2017	NUM
ejpam-6029	580	12	.	.	PUNCT
ejpam-6029	581	1	[	[	X
ejpam-6029	581	2	5	5	NUM
ejpam-6029	581	3	]	]	PUNCT
ejpam-6029	581	4	t	t	PROPN
ejpam-6029	581	5	kamran	kamran	PROPN
ejpam-6029	581	6	,	,	PUNCT
ejpam-6029	581	7	m	m	AUX
ejpam-6029	581	8	samreen	samreen	VERB
ejpam-6029	581	9	,	,	PUNCT
ejpam-6029	581	10	and	and	CCONJ
ejpam-6029	581	11	q	q	PROPN
ejpam-6029	581	12	ul	ul	INTJ
ejpam-6029	581	13	ain	ain	PROPN
ejpam-6029	581	14	.	.	PUNCT
ejpam-6029	582	1	a	a	DET
ejpam-6029	582	2	generalization	generalization	NOUN
ejpam-6029	582	3	of	of	ADP
ejpam-6029	582	4	b	b	NOUN
ejpam-6029	582	5	-	-	PUNCT
ejpam-6029	582	6	metric	metric	ADJ
ejpam-6029	582	7	space	space	NOUN
ejpam-6029	582	8	and	and	CCONJ
ejpam-6029	582	9	some	some	DET
ejpam-6029	582	10	fixed	fix	VERB
ejpam-6029	582	11	point	point	NOUN
ejpam-6029	582	12	theorems	theorem	NOUN
ejpam-6029	582	13	.	.	PUNCT
ejpam-6029	583	1	mathematics	mathematic	NOUN
ejpam-6029	583	2	,	,	PUNCT
ejpam-6029	583	3	5(2):19	5(2):19	NUM
ejpam-6029	583	4	,	,	PUNCT
ejpam-6029	583	5	2017	2017	NUM
ejpam-6029	583	6	.	.	PUNCT
ejpam-6029	584	1	[	[	X
ejpam-6029	584	2	6	6	NUM
ejpam-6029	584	3	]	]	PUNCT
ejpam-6029	584	4	n	n	PRON
ejpam-6029	584	5	mlaiki	mlaiki	NOUN
ejpam-6029	584	6	,	,	PUNCT
ejpam-6029	584	7	h	h	PROPN
ejpam-6029	584	8	aydi	aydi	ADJ
ejpam-6029	584	9	,	,	PUNCT
ejpam-6029	584	10	n	n	PRON
ejpam-6029	584	11	souayah	souayah	NOUN
ejpam-6029	584	12	,	,	PUNCT
ejpam-6029	584	13	and	and	CCONJ
ejpam-6029	584	14	t	t	PROPN
ejpam-6029	584	15	abdeljawad	abdeljawad	NOUN
ejpam-6029	584	16	.	.	PUNCT
ejpam-6029	585	1	controlled	control	VERB
ejpam-6029	585	2	metric	metric	ADJ
ejpam-6029	585	3	type	type	NOUN
ejpam-6029	585	4	spaces	space	NOUN
ejpam-6029	585	5	and	and	CCONJ
ejpam-6029	585	6	the	the	DET
ejpam-6029	585	7	related	related	ADJ
ejpam-6029	585	8	contraction	contraction	NOUN
ejpam-6029	585	9	principle	principle	NOUN
ejpam-6029	585	10	.	.	PUNCT
ejpam-6029	586	1	mathematics	mathematic	NOUN
ejpam-6029	586	2	,	,	PUNCT
ejpam-6029	586	3	6(12):194	6(12):194	PROPN
ejpam-6029	586	4	,	,	PUNCT
ejpam-6029	586	5	2018	2018	NUM
ejpam-6029	586	6	.	.	PUNCT
ejpam-6029	587	1	[	[	X
ejpam-6029	587	2	7	7	NUM
ejpam-6029	587	3	]	]	X
ejpam-6029	587	4	t	t	NOUN
ejpam-6029	587	5	abdeljawad	abdeljawad	NOUN
ejpam-6029	587	6	,	,	PUNCT
ejpam-6029	587	7	n	n	DET
ejpam-6029	587	8	mlaiki	mlaiki	NOUN
ejpam-6029	587	9	,	,	PUNCT
ejpam-6029	587	10	h	h	PROPN
ejpam-6029	587	11	aydi	aydi	ADJ
ejpam-6029	587	12	,	,	PUNCT
ejpam-6029	587	13	and	and	CCONJ
ejpam-6029	587	14	n	n	DET
ejpam-6029	587	15	souayah	souayah	NOUN
ejpam-6029	587	16	.	.	PUNCT
ejpam-6029	588	1	double	double	ADJ
ejpam-6029	588	2	controlled	control	VERB
ejpam-6029	588	3	metric	metric	ADJ
ejpam-6029	588	4	type	type	NOUN
ejpam-6029	588	5	spaces	space	NOUN
ejpam-6029	588	6	and	and	CCONJ
ejpam-6029	588	7	some	some	DET
ejpam-6029	588	8	fixed	fix	VERB
ejpam-6029	588	9	point	point	NOUN
ejpam-6029	588	10	results	result	NOUN
ejpam-6029	588	11	.	.	PUNCT
ejpam-6029	589	1	mathematics	mathematic	NOUN
ejpam-6029	589	2	,	,	PUNCT
ejpam-6029	589	3	6(12):320	6(12):320	PROPN
ejpam-6029	589	4	,	,	PUNCT
ejpam-6029	589	5	2018	2018	NUM
ejpam-6029	589	6	.	.	PUNCT
ejpam-6029	590	1	[	[	X
ejpam-6029	590	2	8	8	NUM
ejpam-6029	590	3	]	]	PUNCT
ejpam-6029	590	4	a	a	DET
ejpam-6029	590	5	amini	amini	NOUN
ejpam-6029	590	6	-	-	ADJ
ejpam-6029	590	7	harandi	harandi	X
ejpam-6029	590	8	.	.	PUNCT
ejpam-6029	591	1	metric	metric	ADJ
ejpam-6029	591	2	-	-	PUNCT
ejpam-6029	591	3	like	like	ADJ
ejpam-6029	591	4	spaces	space	NOUN
ejpam-6029	591	5	,	,	PUNCT
ejpam-6029	591	6	partial	partial	ADJ
ejpam-6029	591	7	metric	metric	ADJ
ejpam-6029	591	8	spaces	space	NOUN
ejpam-6029	591	9	and	and	CCONJ
ejpam-6029	591	10	fixed	fix	VERB
ejpam-6029	591	11	points	point	NOUN
ejpam-6029	591	12	.	.	PUNCT
ejpam-6029	592	1	fixed	fix	VERB
ejpam-6029	592	2	point	point	NOUN
ejpam-6029	592	3	theory	theory	NOUN
ejpam-6029	592	4	application	application	NOUN
ejpam-6029	592	5	,	,	PUNCT
ejpam-6029	592	6	204(2012	204(2012	NUM
ejpam-6029	592	7	)	)	PUNCT
ejpam-6029	592	8	,	,	PUNCT
ejpam-6029	592	9	2012	2012	NUM
ejpam-6029	592	10	.	.	PUNCT
ejpam-6029	593	1	[	[	X
ejpam-6029	593	2	9	9	X
ejpam-6029	593	3	]	]	X
ejpam-6029	593	4	p	p	X
ejpam-6029	593	5	hitzler	hitzler	NOUN
ejpam-6029	593	6	and	and	CCONJ
ejpam-6029	593	7	a	a	DET
ejpam-6029	593	8	k	k	PROPN
ejpam-6029	593	9	seda	seda	NOUN
ejpam-6029	593	10	.	.	PUNCT
ejpam-6029	594	1	dislocated	dislocated	ADJ
ejpam-6029	594	2	topologies	topology	NOUN
ejpam-6029	594	3	.	.	PUNCT
ejpam-6029	595	1	journal	journal	NOUN
ejpam-6029	595	2	of	of	ADP
ejpam-6029	595	3	electrical	electrical	ADJ
ejpam-6029	595	4	engineering	engineering	NOUN
ejpam-6029	595	5	,	,	PUNCT
ejpam-6029	595	6	51(12):3–7	51(12):3–7	NUM
ejpam-6029	595	7	,	,	PUNCT
ejpam-6029	595	8	2000	2000	NUM
ejpam-6029	595	9	.	.	PUNCT
ejpam-6029	596	1	[	[	X
ejpam-6029	596	2	10	10	NUM
ejpam-6029	596	3	]	]	X
ejpam-6029	596	4	m	m	NOUN
ejpam-6029	596	5	alghamdi	alghamdi	NOUN
ejpam-6029	596	6	,	,	PUNCT
ejpam-6029	596	7	n	n	CCONJ
ejpam-6029	596	8	hussain	hussain	NOUN
ejpam-6029	596	9	,	,	PUNCT
ejpam-6029	596	10	and	and	CCONJ
ejpam-6029	596	11	p	p	PRON
ejpam-6029	596	12	salimi	salimi	PROPN
ejpam-6029	596	13	.	.	PUNCT
ejpam-6029	597	1	fixed	fix	VERB
ejpam-6029	597	2	point	point	NOUN
ejpam-6029	597	3	and	and	CCONJ
ejpam-6029	597	4	coupled	couple	VERB
ejpam-6029	597	5	fixed	fix	VERB
ejpam-6029	597	6	point	point	NOUN
ejpam-6029	597	7	theorems	theorem	NOUN
ejpam-6029	597	8	on	on	ADP
ejpam-6029	597	9	b	b	X
ejpam-6029	597	10	-	-	PUNCT
ejpam-6029	597	11	metric	metric	ADJ
ejpam-6029	597	12	-	-	PUNCT
ejpam-6029	597	13	like	like	ADJ
ejpam-6029	597	14	spaces	space	NOUN
ejpam-6029	597	15	.	.	PUNCT
ejpam-6029	598	1	journal	journal	PROPN
ejpam-6029	598	2	of	of	ADP
ejpam-6029	598	3	inequalities	inequality	NOUN
ejpam-6029	598	4	and	and	CCONJ
ejpam-6029	598	5	applications	application	NOUN
ejpam-6029	598	6	,	,	PUNCT
ejpam-6029	598	7	402(2013	402(2013	NUM
ejpam-6029	598	8	)	)	PUNCT
ejpam-6029	598	9	,	,	PUNCT
ejpam-6029	598	10	2013	2013	NUM
ejpam-6029	598	11	.	.	PUNCT
ejpam-6029	599	1	a.	a.	NOUN
ejpam-6029	599	2	a.	a.	PROPN
ejpam-6029	599	3	hijab	hijab	PROPN
ejpam-6029	599	4	et	et	PROPN
ejpam-6029	599	5	al	al	PROPN
ejpam-6029	599	6	.	.	PUNCT
ejpam-6029	599	7	/	/	SYM
ejpam-6029	599	8	eur	eur	PROPN
ejpam-6029	599	9	.	.	PUNCT
ejpam-6029	600	1	j.	j.	PROPN
ejpam-6029	600	2	pure	pure	PROPN
ejpam-6029	600	3	appl	appl	PROPN
ejpam-6029	600	4	.	.	PROPN
ejpam-6029	600	5	math	math	PROPN
ejpam-6029	600	6	,	,	PUNCT
ejpam-6029	600	7	18	18	NUM
ejpam-6029	600	8	(	(	PUNCT
ejpam-6029	600	9	2	2	NUM
ejpam-6029	600	10	)	)	PUNCT
ejpam-6029	600	11	(	(	PUNCT
ejpam-6029	600	12	2025	2025	NUM
ejpam-6029	600	13	)	)	PUNCT
ejpam-6029	600	14	,	,	PUNCT
ejpam-6029	600	15	6029	6029	NUM
ejpam-6029	600	16	22	22	NUM
ejpam-6029	600	17	of	of	ADP
ejpam-6029	600	18	23	23	NUM
ejpam-6029	601	1	[	[	SYM
ejpam-6029	601	2	11	11	NUM
ejpam-6029	601	3	]	]	X
ejpam-6029	601	4	z	z	NOUN
ejpam-6029	601	5	mitrovic	mitrovic	PROPN
ejpam-6029	601	6	,	,	PUNCT
ejpam-6029	601	7	h	h	PROPN
ejpam-6029	601	8	işık	işık	PROPN
ejpam-6029	601	9	,	,	PUNCT
ejpam-6029	601	10	and	and	CCONJ
ejpam-6029	601	11	s	s	VERB
ejpam-6029	601	12	radenovic	radenovic	ADJ
ejpam-6029	601	13	.	.	PUNCT
ejpam-6029	602	1	the	the	DET
ejpam-6029	602	2	new	new	ADJ
ejpam-6029	602	3	results	result	NOUN
ejpam-6029	602	4	in	in	ADP
ejpam-6029	602	5	extended	extended	ADJ
ejpam-6029	602	6	b	b	X
ejpam-6029	602	7	-	-	ADJ
ejpam-6029	602	8	metric	metric	ADJ
ejpam-6029	602	9	spaces	space	NOUN
ejpam-6029	602	10	and	and	CCONJ
ejpam-6029	602	11	applications	application	NOUN
ejpam-6029	602	12	.	.	PUNCT
ejpam-6029	603	1	international	international	ADJ
ejpam-6029	603	2	journal	journal	PROPN
ejpam-6029	603	3	of	of	ADP
ejpam-6029	603	4	nonlinear	nonlinear	ADJ
ejpam-6029	603	5	analysis	analysis	NOUN
ejpam-6029	603	6	and	and	CCONJ
ejpam-6029	603	7	applications	application	NOUN
ejpam-6029	603	8	,	,	PUNCT
ejpam-6029	603	9	11(1):473–482	11(1):473–482	PROPN
ejpam-6029	603	10	,	,	PUNCT
ejpam-6029	603	11	2020	2020	NUM
ejpam-6029	603	12	.	.	PUNCT
ejpam-6029	604	1	[	[	X
ejpam-6029	604	2	12	12	NUM
ejpam-6029	604	3	]	]	X
ejpam-6029	604	4	j	j	PROPN
ejpam-6029	604	5	r	r	NOUN
ejpam-6029	604	6	roshan	roshan	PROPN
ejpam-6029	604	7	,	,	PUNCT
ejpam-6029	604	8	v	v	NOUN
ejpam-6029	604	9	parvaneh	parvaneh	NOUN
ejpam-6029	604	10	,	,	PUNCT
ejpam-6029	604	11	and	and	CCONJ
ejpam-6029	604	12	z	z	PROPN
ejpam-6029	604	13	kadelburg	kadelburg	NOUN
ejpam-6029	604	14	.	.	PUNCT
ejpam-6029	605	1	new	new	ADJ
ejpam-6029	605	2	fixed	fix	VERB
ejpam-6029	605	3	point	point	NOUN
ejpam-6029	605	4	results	result	NOUN
ejpam-6029	605	5	in	in	ADP
ejpam-6029	605	6	b	b	NOUN
ejpam-6029	605	7	-	-	ADJ
ejpam-6029	605	8	rectangular	rectangular	ADJ
ejpam-6029	605	9	metric	metric	ADJ
ejpam-6029	605	10	spaces	space	NOUN
ejpam-6029	605	11	.	.	PUNCT
ejpam-6029	606	1	nonlinear	nonlinear	ADJ
ejpam-6029	606	2	analysis	analysis	NOUN
ejpam-6029	606	3	:	:	PUNCT
ejpam-6029	606	4	modelling	modelling	NOUN
ejpam-6029	606	5	and	and	CCONJ
ejpam-6029	606	6	control	control	NOUN
ejpam-6029	606	7	,	,	PUNCT
ejpam-6029	606	8	21(5):614–634	21(5):614–634	PROPN
ejpam-6029	606	9	,	,	PUNCT
ejpam-6029	606	10	2016	2016	NUM
ejpam-6029	606	11	.	.	PUNCT
ejpam-6029	607	1	[	[	X
ejpam-6029	607	2	13	13	NUM
ejpam-6029	607	3	]	]	PUNCT
ejpam-6029	607	4	n	n	PRON
ejpam-6029	607	5	mlaiki	mlaiki	PROPN
ejpam-6029	607	6	.	.	PUNCT
ejpam-6029	607	7	double	double	PROPN
ejpam-6029	607	8	controlled	control	VERB
ejpam-6029	607	9	metric	metric	ADJ
ejpam-6029	607	10	-	-	PUNCT
ejpam-6029	607	11	like	like	ADJ
ejpam-6029	607	12	spaces	space	NOUN
ejpam-6029	607	13	.	.	PUNCT
ejpam-6029	608	1	journal	journal	PROPN
ejpam-6029	608	2	of	of	ADP
ejpam-6029	608	3	inequalities	inequality	NOUN
ejpam-6029	608	4	and	and	CCONJ
ejpam-6029	608	5	applications	application	NOUN
ejpam-6029	608	6	,	,	PUNCT
ejpam-6029	608	7	189(2020	189(2020	NUM
ejpam-6029	608	8	)	)	PUNCT
ejpam-6029	608	9	,	,	PUNCT
ejpam-6029	608	10	2020	2020	NUM
ejpam-6029	608	11	.	.	PUNCT
ejpam-6029	609	1	[	[	X
ejpam-6029	609	2	14	14	NUM
ejpam-6029	609	3	]	]	X
ejpam-6029	609	4	i	i	PRON
ejpam-6029	609	5	ayoob	ayoob	VERB
ejpam-6029	609	6	,	,	PUNCT
ejpam-6029	609	7	n	n	PROPN
ejpam-6029	609	8	z	z	PROPN
ejpam-6029	609	9	chuan	chuan	PROPN
ejpam-6029	609	10	,	,	PUNCT
ejpam-6029	609	11	and	and	CCONJ
ejpam-6029	609	12	nmlaiki	nmlaiki	ADJ
ejpam-6029	609	13	.	.	PUNCT
ejpam-6029	610	1	hardy	hardy	ADJ
ejpam-6029	610	2	-	-	PUNCT
ejpam-6029	610	3	rogers	rogers	NOUN
ejpam-6029	610	4	type	type	NOUN
ejpam-6029	610	5	contraction	contraction	NOUN
ejpam-6029	610	6	in	in	ADP
ejpam-6029	610	7	double	double	ADJ
ejpam-6029	610	8	controlled	control	VERB
ejpam-6029	610	9	metric	metric	ADJ
ejpam-6029	610	10	-	-	PUNCT
ejpam-6029	610	11	like	like	ADJ
ejpam-6029	610	12	spaces	space	NOUN
ejpam-6029	610	13	.	.	PUNCT
ejpam-6029	611	1	aims	aim	VERB
ejpam-6029	611	2	mathematics	mathematic	NOUN
ejpam-6029	611	3	,	,	PUNCT
ejpam-6029	611	4	8(6):13623–13636	8(6):13623–13636	PROPN
ejpam-6029	611	5	,	,	PUNCT
ejpam-6029	611	6	2023	2023	NUM
ejpam-6029	611	7	.	.	PUNCT
ejpam-6029	612	1	[	[	X
ejpam-6029	612	2	15	15	NUM
ejpam-6029	612	3	]	]	X
ejpam-6029	612	4	i	i	PRON
ejpam-6029	612	5	ayoob	ayoob	VERB
ejpam-6029	612	6	,	,	PUNCT
ejpam-6029	612	7	n	n	PROPN
ejpam-6029	612	8	z	z	PROPN
ejpam-6029	612	9	chuan	chuan	PROPN
ejpam-6029	612	10	,	,	PUNCT
ejpam-6029	612	11	and	and	CCONJ
ejpam-6029	612	12	n	n	PRON
ejpam-6029	612	13	mlaiki	mlaiki	PROPN
ejpam-6029	612	14	.	.	PUNCT
ejpam-6029	613	1	double	double	ADJ
ejpam-6029	613	2	-	-	PUNCT
ejpam-6029	613	3	composed	compose	VERB
ejpam-6029	613	4	metric	metric	ADJ
ejpam-6029	613	5	spaces	space	NOUN
ejpam-6029	613	6	.	.	PUNCT
ejpam-6029	614	1	mathematics	mathematic	NOUN
ejpam-6029	614	2	,	,	PUNCT
ejpam-6029	614	3	11(8):1866	11(8):1866	NUM
ejpam-6029	614	4	,	,	PUNCT
ejpam-6029	614	5	2023	2023	NUM
ejpam-6029	614	6	.	.	PUNCT
ejpam-6029	615	1	[	[	X
ejpam-6029	615	2	16	16	NUM
ejpam-6029	615	3	]	]	X
ejpam-6029	615	4	h	h	NOUN
ejpam-6029	615	5	long	long	ADJ
ejpam-6029	615	6	-	-	PUNCT
ejpam-6029	615	7	guang	guang	PROPN
ejpam-6029	615	8	and	and	CCONJ
ejpam-6029	615	9	z	z	PROPN
ejpam-6029	615	10	xian	xian	PROPN
ejpam-6029	615	11	.	.	PUNCT
ejpam-6029	616	1	cone	cone	PROPN
ejpam-6029	616	2	metric	metric	ADJ
ejpam-6029	616	3	spaces	space	NOUN
ejpam-6029	616	4	and	and	CCONJ
ejpam-6029	616	5	fixed	fix	VERB
ejpam-6029	616	6	point	point	NOUN
ejpam-6029	616	7	theorems	theorem	NOUN
ejpam-6029	616	8	of	of	ADP
ejpam-6029	616	9	contractive	contractive	ADJ
ejpam-6029	616	10	mappins	mappin	NOUN
ejpam-6029	616	11	.	.	PUNCT
ejpam-6029	617	1	journal	journal	NOUN
ejpam-6029	617	2	of	of	ADP
ejpam-6029	617	3	mathematical	mathematical	ADJ
ejpam-6029	617	4	analysis	analysis	NOUN
ejpam-6029	617	5	and	and	CCONJ
ejpam-6029	617	6	applications	application	NOUN
ejpam-6029	617	7	,	,	PUNCT
ejpam-6029	617	8	332(2):1468–1476	332(2):1468–1476	PROPN
ejpam-6029	617	9	,	,	PUNCT
ejpam-6029	617	10	2007	2007	NUM
ejpam-6029	617	11	.	.	PUNCT
ejpam-6029	618	1	[	[	X
ejpam-6029	618	2	17	17	NUM
ejpam-6029	618	3	]	]	PUNCT
ejpam-6029	618	4	n	n	X
ejpam-6029	618	5	hussain	hussain	NOUN
ejpam-6029	618	6	and	and	CCONJ
ejpam-6029	618	7	m	m	PROPN
ejpam-6029	618	8	h	h	NOUN
ejpam-6029	618	9	shah	shah	NOUN
ejpam-6029	618	10	.	.	PUNCT
ejpam-6029	619	1	kkm	kkm	PROPN
ejpam-6029	619	2	mappings	mapping	VERB
ejpam-6029	619	3	in	in	ADP
ejpam-6029	619	4	cone	cone	PROPN
ejpam-6029	619	5	b	b	X
ejpam-6029	619	6	-	-	PUNCT
ejpam-6029	619	7	metric	metric	ADJ
ejpam-6029	619	8	spaces	space	NOUN
ejpam-6029	619	9	.	.	PUNCT
ejpam-6029	620	1	computers	computer	NOUN
ejpam-6029	620	2	and	and	CCONJ
ejpam-6029	620	3	mathematics	mathematic	NOUN
ejpam-6029	620	4	with	with	ADP
ejpam-6029	620	5	applications	application	NOUN
ejpam-6029	620	6	,	,	PUNCT
ejpam-6029	620	7	62(4):1677–1684	62(4):1677–1684	NUM
ejpam-6029	620	8	,	,	PUNCT
ejpam-6029	620	9	2011	2011	NUM
ejpam-6029	620	10	.	.	PUNCT
ejpam-6029	621	1	[	[	X
ejpam-6029	621	2	18	18	NUM
ejpam-6029	621	3	]	]	PUNCT
ejpam-6029	621	4	t	t	PROPN
ejpam-6029	621	5	l	l	PROPN
ejpam-6029	621	6	shateri	shateri	PROPN
ejpam-6029	621	7	.	.	PUNCT
ejpam-6029	622	1	double	double	PROPN
ejpam-6029	622	2	controlled	control	VERB
ejpam-6029	622	3	cone	cone	NOUN
ejpam-6029	622	4	metric	metric	ADJ
ejpam-6029	622	5	spaces	space	NOUN
ejpam-6029	622	6	and	and	CCONJ
ejpam-6029	622	7	the	the	DET
ejpam-6029	622	8	related	related	ADJ
ejpam-6029	622	9	fixed	fix	VERB
ejpam-6029	622	10	point	point	NOUN
ejpam-6029	622	11	theorems	theorem	NOUN
ejpam-6029	622	12	.	.	PUNCT
ejpam-6029	623	1	arxiv	arxiv	PROPN
ejpam-6029	623	2	preprint	preprint	VERB
ejpam-6029	623	3	arxiv:2208.06812	arxiv:2208.06812	PROPN
ejpam-6029	623	4	.	.	PUNCT
ejpam-6029	623	5	,	,	PUNCT
ejpam-6029	623	6	2022	2022	NUM
ejpam-6029	623	7	.	.	PUNCT
ejpam-6029	624	1	[	[	X
ejpam-6029	624	2	19	19	NUM
ejpam-6029	624	3	]	]	X
ejpam-6029	624	4	a	a	DET
ejpam-6029	624	5	a	a	DET
ejpam-6029	624	6	hijab	hijab	NOUN
ejpam-6029	624	7	,	,	PUNCT
ejpam-6029	624	8	l	l	PROPN
ejpam-6029	624	9	k	k	X
ejpam-6029	624	10	shaakir	shaakir	PROPN
ejpam-6029	624	11	,	,	PUNCT
ejpam-6029	624	12	s	s	NOUN
ejpam-6029	624	13	aljohani	aljohani	NOUN
ejpam-6029	624	14	,	,	PUNCT
ejpam-6029	624	15	and	and	CCONJ
ejpam-6029	624	16	n	n	PRON
ejpam-6029	624	17	mlaiki	mlaiki	PROPN
ejpam-6029	624	18	.	.	PUNCT
ejpam-6029	625	1	fredholm	fredholm	ADJ
ejpam-6029	625	2	integral	integral	ADJ
ejpam-6029	625	3	equation	equation	NOUN
ejpam-6029	625	4	in	in	ADP
ejpam-6029	625	5	composed	compose	VERB
ejpam-6029	625	6	-	-	PUNCT
ejpam-6029	625	7	cone	cone	NOUN
ejpam-6029	625	8	metric	metric	ADJ
ejpam-6029	625	9	spaces	space	NOUN
ejpam-6029	625	10	.	.	PUNCT
ejpam-6029	626	1	boundary	boundary	ADJ
ejpam-6029	626	2	value	value	NOUN
ejpam-6029	626	3	problems	problem	NOUN
ejpam-6029	626	4	,	,	PUNCT
ejpam-6029	626	5	64(2024	64(2024	NOUN
ejpam-6029	626	6	)	)	PUNCT
ejpam-6029	626	7	,	,	PUNCT
ejpam-6029	626	8	2024	2024	NUM
ejpam-6029	626	9	.	.	PUNCT
ejpam-6029	627	1	[	[	X
ejpam-6029	627	2	20	20	NUM
ejpam-6029	627	3	]	]	PUNCT
ejpam-6029	627	4	a	a	DET
ejpam-6029	627	5	a	a	DET
ejpam-6029	627	6	hijab	hijab	NOUN
ejpam-6029	627	7	,	,	PUNCT
ejpam-6029	627	8	l	l	PROPN
ejpam-6029	627	9	k	k	X
ejpam-6029	627	10	shaakir	shaakir	PROPN
ejpam-6029	627	11	,	,	PUNCT
ejpam-6029	627	12	s	s	NOUN
ejpam-6029	627	13	aljohani	aljohani	NOUN
ejpam-6029	627	14	,	,	PUNCT
ejpam-6029	627	15	and	and	CCONJ
ejpam-6029	627	16	n	n	PRON
ejpam-6029	627	17	mlaiki	mlaiki	PROPN
ejpam-6029	627	18	.	.	PUNCT
ejpam-6029	628	1	double	double	ADJ
ejpam-6029	628	2	composed	compose	VERB
ejpam-6029	628	3	metric	metric	ADJ
ejpam-6029	628	4	-	-	PUNCT
ejpam-6029	628	5	like	like	ADJ
ejpam-6029	628	6	spaces	space	NOUN
ejpam-6029	628	7	via	via	ADP
ejpam-6029	628	8	some	some	DET
ejpam-6029	628	9	fixed	fix	VERB
ejpam-6029	628	10	point	point	NOUN
ejpam-6029	628	11	theorems[j	theorems[j	PROPN
ejpam-6029	628	12	]	]	PUNCT
ejpam-6029	628	13	.	.	PUNCT
ejpam-6029	629	1	aims	aim	VERB
ejpam-6029	629	2	mathematics	mathematic	NOUN
ejpam-6029	629	3	,	,	PUNCT
ejpam-6029	629	4	9(10):27205–27219	9(10):27205–27219	NUM
ejpam-6029	629	5	,	,	PUNCT
ejpam-6029	629	6	2024	2024	NUM
ejpam-6029	629	7	.	.	PUNCT
ejpam-6029	630	1	[	[	X
ejpam-6029	630	2	21	21	NUM
ejpam-6029	630	3	]	]	PUNCT
ejpam-6029	630	4	a	a	DET
ejpam-6029	630	5	n	n	ADV
ejpam-6029	630	6	branga	branga	ADV
ejpam-6029	630	7	and	and	CCONJ
ejpam-6029	630	8	i	i	PRON
ejpam-6029	630	9	m	m	VERB
ejpam-6029	630	10	olaru	olaru	NOUN
ejpam-6029	630	11	.	.	PUNCT
ejpam-6029	631	1	cone	cone	PROPN
ejpam-6029	631	2	metric	metric	ADJ
ejpam-6029	631	3	spaces	space	NOUN
ejpam-6029	631	4	over	over	ADP
ejpam-6029	631	5	topological	topological	ADJ
ejpam-6029	631	6	modules	module	NOUN
ejpam-6029	631	7	and	and	CCONJ
ejpam-6029	631	8	fixed	fix	VERB
ejpam-6029	631	9	point	point	NOUN
ejpam-6029	631	10	theorems	theorem	NOUN
ejpam-6029	631	11	for	for	ADP
ejpam-6029	631	12	lipschitz	lipschitz	NOUN
ejpam-6029	631	13	mappings	mapping	NOUN
ejpam-6029	631	14	.	.	PUNCT
ejpam-6029	632	1	mathematics	mathematic	NOUN
ejpam-6029	632	2	,	,	PUNCT
ejpam-6029	632	3	8(5):724	8(5):724	NUM
ejpam-6029	632	4	,	,	PUNCT
ejpam-6029	632	5	2020	2020	NUM
ejpam-6029	632	6	.	.	PUNCT
ejpam-6029	633	1	[	[	X
ejpam-6029	633	2	22	22	NUM
ejpam-6029	633	3	]	]	X
ejpam-6029	633	4	w	w	NOUN
ejpam-6029	633	5	shatanawi	shatanawi	ADJ
ejpam-6029	633	6	,	,	PUNCT
ejpam-6029	633	7	z	z	NOUN
ejpam-6029	633	8	dmitrović	dmitrović	NOUN
ejpam-6029	633	9	,	,	PUNCT
ejpam-6029	633	10	and	and	CCONJ
ejpam-6029	633	11	n	n	CCONJ
ejpam-6029	633	12	hussain	hussain	NOUN
ejpam-6029	633	13	s	s	PRON
ejpam-6029	633	14	radenović.	radenović.	PROPN
ejpam-6029	633	15	on	on	ADP
ejpam-6029	633	16	generalized	generalized	ADJ
ejpam-6029	633	17	hardy	hardy	ADJ
ejpam-6029	633	18	–	–	PUNCT
ejpam-6029	633	19	rogers	roger	NOUN
ejpam-6029	633	20	type	type	NOUN
ejpam-6029	633	21	α	α	NOUN
ejpam-6029	633	22	-	-	ADJ
ejpam-6029	633	23	admissible	admissible	ADJ
ejpam-6029	633	24	mappings	mapping	NOUN
ejpam-6029	633	25	in	in	ADP
ejpam-6029	633	26	cone	cone	NOUN
ejpam-6029	633	27	b	b	X
ejpam-6029	633	28	-	-	ADJ
ejpam-6029	633	29	metric	metric	ADJ
ejpam-6029	633	30	spaces	space	NOUN
ejpam-6029	633	31	over	over	ADP
ejpam-6029	633	32	banach	banach	NOUN
ejpam-6029	633	33	algebras	algebra	NOUN
ejpam-6029	633	34	.	.	PUNCT
ejpam-6029	633	35	symmetry	symmetry	PROPN
ejpam-6029	633	36	,	,	PUNCT
ejpam-6029	633	37	12(1):81	12(1):81	NUM
ejpam-6029	633	38	,	,	PUNCT
ejpam-6029	633	39	2020	2020	NUM
ejpam-6029	633	40	.	.	PUNCT
ejpam-6029	634	1	[	[	X
ejpam-6029	634	2	23	23	NUM
ejpam-6029	634	3	]	]	X
ejpam-6029	634	4	m	m	VERB
ejpam-6029	634	5	nazam	nazam	ADJ
ejpam-6029	634	6	,	,	PUNCT
ejpam-6029	634	7	a	a	DET
ejpam-6029	634	8	arif	arif	PROPN
ejpam-6029	634	9	,	,	PUNCT
ejpam-6029	634	10	h	h	PROPN
ejpam-6029	634	11	mahmood	mahmood	PROPN
ejpam-6029	634	12	,	,	PUNCT
ejpam-6029	634	13	and	and	CCONJ
ejpam-6029	634	14	c	c	PROPN
ejpam-6029	634	15	park	park	NOUN
ejpam-6029	634	16	.	.	PUNCT
ejpam-6029	635	1	some	some	DET
ejpam-6029	635	2	results	result	NOUN
ejpam-6029	635	3	in	in	ADP
ejpam-6029	635	4	cone	cone	NOUN
ejpam-6029	635	5	metric	metric	ADJ
ejpam-6029	635	6	spaces	space	NOUN
ejpam-6029	635	7	with	with	ADP
ejpam-6029	635	8	applications	application	NOUN
ejpam-6029	635	9	in	in	ADP
ejpam-6029	635	10	homotopy	homotopy	NOUN
ejpam-6029	635	11	theory	theory	NOUN
ejpam-6029	635	12	.	.	PUNCT
ejpam-6029	636	1	open	open	ADJ
ejpam-6029	636	2	mathematics	mathematic	NOUN
ejpam-6029	636	3	,	,	PUNCT
ejpam-6029	636	4	18(1):295–306	18(1):295–306	NOUN
ejpam-6029	636	5	,	,	PUNCT
ejpam-6029	636	6	2020	2020	NUM
ejpam-6029	636	7	.	.	PUNCT
ejpam-6029	637	1	[	[	X
ejpam-6029	637	2	24	24	NUM
ejpam-6029	637	3	]	]	X
ejpam-6029	637	4	q	q	PROPN
ejpam-6029	637	5	meng	meng	PROPN
ejpam-6029	637	6	.	.	PUNCT
ejpam-6029	638	1	on	on	ADP
ejpam-6029	638	2	generalized	generalized	ADJ
ejpam-6029	638	3	algebraic	algebraic	ADJ
ejpam-6029	638	4	cone	cone	NOUN
ejpam-6029	638	5	metric	metric	ADJ
ejpam-6029	638	6	spaces	space	NOUN
ejpam-6029	638	7	and	and	CCONJ
ejpam-6029	638	8	fixed	fix	VERB
ejpam-6029	638	9	point	point	NOUN
ejpam-6029	638	10	theorems	theorem	NOUN
ejpam-6029	638	11	.	.	PUNCT
ejpam-6029	639	1	chinese	chinese	ADJ
ejpam-6029	639	2	annals	annal	NOUN
ejpam-6029	639	3	of	of	ADP
ejpam-6029	639	4	mathematics	mathematic	NOUN
ejpam-6029	639	5	,	,	PUNCT
ejpam-6029	639	6	series	series	NOUN
ejpam-6029	639	7	b	b	PROPN
ejpam-6029	639	8	,	,	PUNCT
ejpam-6029	639	9	40(3):429–438	40(3):429–438	NOUN
ejpam-6029	639	10	,	,	PUNCT
ejpam-6029	639	11	2019	2019	NUM
ejpam-6029	639	12	.	.	PUNCT
ejpam-6029	640	1	[	[	X
ejpam-6029	640	2	25	25	NUM
ejpam-6029	640	3	]	]	X
ejpam-6029	640	4	s	s	VERB
ejpam-6029	640	5	m	m	VERB
ejpam-6029	640	6	a	a	DET
ejpam-6029	640	7	abou	abou	PROPN
ejpam-6029	640	8	-	-	PUNCT
ejpam-6029	640	9	bakr	bakr	PROPN
ejpam-6029	640	10	.	.	PUNCT
ejpam-6029	641	1	coupled	couple	VERB
ejpam-6029	641	2	fixed	fix	VERB
ejpam-6029	641	3	point	point	NOUN
ejpam-6029	641	4	theorems	theorem	NOUN
ejpam-6029	641	5	for	for	ADP
ejpam-6029	641	6	some	some	DET
ejpam-6029	641	7	type	type	NOUN
ejpam-6029	641	8	of	of	ADP
ejpam-6029	641	9	contraction	contraction	NOUN
ejpam-6029	641	10	mappings	mapping	NOUN
ejpam-6029	641	11	in	in	ADP
ejpam-6029	641	12	b	b	NOUN
ejpam-6029	641	13	-	-	PUNCT
ejpam-6029	641	14	cone	cone	NOUN
ejpam-6029	641	15	and	and	CCONJ
ejpam-6029	641	16	b	b	NOUN
ejpam-6029	641	17	-	-	PUNCT
ejpam-6029	641	18	theta	theta	ADJ
ejpam-6029	641	19	cone	cone	NOUN
ejpam-6029	641	20	metric	metric	ADJ
ejpam-6029	641	21	spaces	space	NOUN
ejpam-6029	641	22	.	.	PUNCT
ejpam-6029	642	1	journal	journal	NOUN
ejpam-6029	642	2	of	of	ADP
ejpam-6029	642	3	mathematics	mathematic	NOUN
ejpam-6029	642	4	,	,	PUNCT
ejpam-6029	642	5	2021(1):5569674	2021(1):5569674	NOUN
ejpam-6029	642	6	,	,	PUNCT
ejpam-6029	642	7	2021	2021	NUM
ejpam-6029	642	8	.	.	PUNCT
ejpam-6029	643	1	[	[	X
ejpam-6029	643	2	26	26	NUM
ejpam-6029	643	3	]	]	X
ejpam-6029	643	4	j	j	PROPN
ejpam-6029	643	5	fernandez	fernandez	PROPN
ejpam-6029	643	6	,	,	PUNCT
ejpam-6029	643	7	n	n	PROPN
ejpam-6029	643	8	malviya	malviya	PROPN
ejpam-6029	643	9	,	,	PUNCT
ejpam-6029	643	10	a	a	DET
ejpam-6029	643	11	savić	savić	NOUN
ejpam-6029	643	12	,	,	PUNCT
ejpam-6029	643	13	m	m	VERB
ejpam-6029	643	14	paunović	paunović	ADJ
ejpam-6029	643	15	,	,	PUNCT
ejpam-6029	643	16	and	and	CCONJ
ejpam-6029	643	17	z	z	NOUN
ejpam-6029	643	18	d	d	PROPN
ejpam-6029	643	19	mitrović.	mitrović.	PROPN
ejpam-6029	643	20	the	the	DET
ejpam-6029	643	21	extended	extended	ADJ
ejpam-6029	643	22	cone	cone	NOUN
ejpam-6029	643	23	b	b	X
ejpam-6029	643	24	-	-	PUNCT
ejpam-6029	643	25	metric	metric	ADJ
ejpam-6029	643	26	-	-	PUNCT
ejpam-6029	643	27	like	like	ADJ
ejpam-6029	643	28	spaces	space	NOUN
ejpam-6029	643	29	over	over	ADP
ejpam-6029	643	30	banach	banach	NOUN
ejpam-6029	643	31	algebra	algebra	NOUN
ejpam-6029	643	32	and	and	CCONJ
ejpam-6029	643	33	some	some	DET
ejpam-6029	643	34	applications	application	NOUN
ejpam-6029	643	35	.	.	PUNCT
ejpam-6029	644	1	mathematics	mathematic	NOUN
ejpam-6029	644	2	,	,	PUNCT
ejpam-6029	644	3	10(1):149	10(1):149	NUM
ejpam-6029	644	4	,	,	PUNCT
ejpam-6029	644	5	2022	2022	NUM
ejpam-6029	644	6	.	.	PUNCT
ejpam-6029	645	1	[	[	X
ejpam-6029	645	2	27	27	NUM
ejpam-6029	645	3	]	]	X
ejpam-6029	645	4	s	s	VERB
ejpam-6029	645	5	m	m	VERB
ejpam-6029	645	6	a	a	DET
ejpam-6029	645	7	abou	abou	PROPN
ejpam-6029	645	8	-	-	PUNCT
ejpam-6029	645	9	bakr	bakr	PROPN
ejpam-6029	645	10	.	.	PUNCT
ejpam-6029	646	1	theta	theta	PROPN
ejpam-6029	646	2	cone	cone	NOUN
ejpam-6029	646	3	metric	metric	ADJ
ejpam-6029	646	4	spaces	space	NOUN
ejpam-6029	646	5	and	and	CCONJ
ejpam-6029	646	6	some	some	DET
ejpam-6029	646	7	fixed	fix	VERB
ejpam-6029	646	8	point	point	NOUN
ejpam-6029	646	9	theorems	theorem	NOUN
ejpam-6029	646	10	.	.	PUNCT
ejpam-6029	646	11	journal	journal	PROPN
ejpam-6029	646	12	of	of	ADP
ejpam-6029	646	13	mathematics	mathematic	NOUN
ejpam-6029	646	14	,	,	PUNCT
ejpam-6029	646	15	2020(1):8895568	2020(1):8895568	NUM
ejpam-6029	646	16	,	,	PUNCT
ejpam-6029	646	17	2020	2020	NUM
ejpam-6029	646	18	.	.	PUNCT
ejpam-6029	647	1	[	[	X
ejpam-6029	647	2	28	28	NUM
ejpam-6029	647	3	]	]	X
ejpam-6029	647	4	d	d	X
ejpam-6029	647	5	lateef	lateef	PROPN
ejpam-6029	647	6	.	.	PUNCT
ejpam-6029	648	1	fisher	fisher	PROPN
ejpam-6029	648	2	type	type	NOUN
ejpam-6029	648	3	fixed	fix	VERB
ejpam-6029	648	4	point	point	NOUN
ejpam-6029	648	5	results	result	NOUN
ejpam-6029	648	6	in	in	ADP
ejpam-6029	648	7	controlled	control	VERB
ejpam-6029	648	8	metric	metric	ADJ
ejpam-6029	648	9	spaces	space	NOUN
ejpam-6029	648	10	.	.	PUNCT
ejpam-6029	649	1	journal	journal	NOUN
ejpam-6029	649	2	of	of	ADP
ejpam-6029	649	3	mathematics	mathematic	NOUN
ejpam-6029	649	4	and	and	CCONJ
ejpam-6029	649	5	computer	computer	NOUN
ejpam-6029	649	6	science	science	NOUN
ejpam-6029	649	7	,	,	PUNCT
ejpam-6029	649	8	20(3):234–240	20(3):234–240	PROPN
ejpam-6029	649	9	,	,	PUNCT
ejpam-6029	649	10	2020	2020	NUM
ejpam-6029	649	11	.	.	PUNCT
ejpam-6029	650	1	[	[	X
ejpam-6029	650	2	29	29	NUM
ejpam-6029	650	3	]	]	SYM
ejpam-6029	650	4	b	b	X
ejpam-6029	650	5	k	k	X
ejpam-6029	650	6	dass	dass	PROPN
ejpam-6029	650	7	and	and	CCONJ
ejpam-6029	650	8	s	s	NOUN
ejpam-6029	650	9	gupta	gupta	PROPN
ejpam-6029	650	10	.	.	PUNCT
ejpam-6029	651	1	an	an	DET
ejpam-6029	651	2	extension	extension	NOUN
ejpam-6029	651	3	of	of	ADP
ejpam-6029	651	4	banach	banach	NOUN
ejpam-6029	651	5	contraction	contraction	NOUN
ejpam-6029	651	6	principle	principle	NOUN
ejpam-6029	651	7	through	through	ADP
ejpam-6029	651	8	rational	rational	ADJ
ejpam-6029	651	9	expression	expression	NOUN
ejpam-6029	651	10	.	.	PUNCT
ejpam-6029	652	1	indian	indian	ADJ
ejpam-6029	652	2	journal	journal	PROPN
ejpam-6029	652	3	of	of	ADP
ejpam-6029	652	4	pure	pure	ADJ
ejpam-6029	652	5	and	and	CCONJ
ejpam-6029	652	6	applied	applied	ADJ
ejpam-6029	652	7	mathematics	mathematic	NOUN
ejpam-6029	652	8	,	,	PUNCT
ejpam-6029	652	9	6(12):1455–1458	6(12):1455–1458	NOUN
ejpam-6029	652	10	,	,	PUNCT
ejpam-6029	652	11	1975	1975	NUM
ejpam-6029	652	12	.	.	PUNCT
ejpam-6029	653	1	a.	a.	NOUN
ejpam-6029	653	2	a.	a.	PROPN
ejpam-6029	653	3	hijab	hijab	PROPN
ejpam-6029	653	4	et	et	PROPN
ejpam-6029	653	5	al	al	PROPN
ejpam-6029	653	6	.	.	PUNCT
ejpam-6029	653	7	/	/	SYM
ejpam-6029	653	8	eur	eur	PROPN
ejpam-6029	653	9	.	.	PUNCT
ejpam-6029	654	1	j.	j.	PROPN
ejpam-6029	654	2	pure	pure	PROPN
ejpam-6029	654	3	appl	appl	PROPN
ejpam-6029	654	4	.	.	PROPN
ejpam-6029	654	5	math	math	PROPN
ejpam-6029	654	6	,	,	PUNCT
ejpam-6029	654	7	18	18	NUM
ejpam-6029	654	8	(	(	PUNCT
ejpam-6029	654	9	2	2	NUM
ejpam-6029	654	10	)	)	PUNCT
ejpam-6029	654	11	(	(	PUNCT
ejpam-6029	654	12	2025	2025	NUM
ejpam-6029	654	13	)	)	PUNCT
ejpam-6029	654	14	,	,	PUNCT
ejpam-6029	654	15	6029	6029	NUM
ejpam-6029	654	16	23	23	NUM
ejpam-6029	654	17	of	of	ADP
ejpam-6029	654	18	23	23	NUM
ejpam-6029	655	1	[	[	SYM
ejpam-6029	655	2	30	30	NUM
ejpam-6029	655	3	]	]	X
ejpam-6029	655	4	d	d	X
ejpam-6029	655	5	s	s	X
ejpam-6029	655	6	jaggi	jaggi	NOUN
ejpam-6029	655	7	.	.	PUNCT
ejpam-6029	656	1	some	some	DET
ejpam-6029	656	2	unique	unique	ADJ
ejpam-6029	656	3	fixed	fix	VERB
ejpam-6029	656	4	point	point	NOUN
ejpam-6029	656	5	theorems	theorem	NOUN
ejpam-6029	656	6	.	.	PUNCT
ejpam-6029	656	7	indian	indian	PROPN
ejpam-6029	656	8	journal	journal	PROPN
ejpam-6029	656	9	of	of	ADP
ejpam-6029	656	10	pure	pure	ADJ
ejpam-6029	656	11	and	and	CCONJ
ejpam-6029	656	12	applied	applied	ADJ
ejpam-6029	656	13	mathematics	mathematic	NOUN
ejpam-6029	656	14	,	,	PUNCT
ejpam-6029	656	15	8(2):223–230	8(2):223–230	NUM
ejpam-6029	656	16	,	,	PUNCT
ejpam-6029	656	17	1977	1977	NUM
ejpam-6029	656	18	.	.	PUNCT
ejpam-6029	657	1	[	[	X
ejpam-6029	657	2	31	31	NUM
ejpam-6029	657	3	]	]	X
ejpam-6029	657	4	k	k	PROPN
ejpam-6029	657	5	ahmad	ahmad	PROPN
ejpam-6029	657	6	,	,	PUNCT
ejpam-6029	657	7	g	g	PROPN
ejpam-6029	657	8	murtaza	murtaza	PROPN
ejpam-6029	657	9	,	,	PUNCT
ejpam-6029	657	10	s	s	PART
ejpam-6029	657	11	alshaikey	alshaikey	NOUN
ejpam-6029	657	12	,	,	PUNCT
ejpam-6029	657	13	u	u	NOUN
ejpam-6029	657	14	ishtiaq	ishtiaq	NOUN
ejpam-6029	657	15	,	,	PUNCT
ejpam-6029	657	16	and	and	CCONJ
ejpam-6029	657	17	i	i	PRON
ejpam-6029	657	18	k	k	PROPN
ejpam-6029	657	19	argyros	argyros	PROPN
ejpam-6029	657	20	.	.	PUNCT
ejpam-6029	658	1	common	common	ADJ
ejpam-6029	658	2	fixed	fix	VERB
ejpam-6029	658	3	point	point	NOUN
ejpam-6029	658	4	results	result	NOUN
ejpam-6029	658	5	on	on	ADP
ejpam-6029	658	6	a	a	DET
ejpam-6029	658	7	double	double	ADJ
ejpam-6029	658	8	-	-	PUNCT
ejpam-6029	658	9	controlled	control	VERB
ejpam-6029	658	10	metric	metric	ADJ
ejpam-6029	658	11	space	space	NOUN
ejpam-6029	658	12	for	for	ADP
ejpam-6029	658	13	generalized	generalized	ADJ
ejpam-6029	658	14	rational	rational	ADJ
ejpam-6029	658	15	-	-	PUNCT
ejpam-6029	658	16	type	type	NOUN
ejpam-6029	658	17	contractions	contraction	NOUN
ejpam-6029	658	18	with	with	ADP
ejpam-6029	658	19	application	application	NOUN
ejpam-6029	658	20	.	.	PUNCT
ejpam-6029	659	1	axioms	axiom	NOUN
ejpam-6029	659	2	,	,	PUNCT
ejpam-6029	659	3	12(10):941	12(10):941	NUM
ejpam-6029	659	4	,	,	PUNCT
ejpam-6029	659	5	2023	2023	NUM
ejpam-6029	659	6	.	.	PUNCT
ejpam-6029	660	1	[	[	X
ejpam-6029	660	2	32	32	NUM
ejpam-6029	660	3	]	]	X
ejpam-6029	660	4	h	h	PROPN
ejpam-6029	660	5	huang	huang	PROPN
ejpam-6029	660	6	and	and	CCONJ
ejpam-6029	660	7	s	s	VERB
ejpam-6029	660	8	radenovic	radenovic	ADJ
ejpam-6029	660	9	.	.	PUNCT
ejpam-6029	661	1	common	common	ADJ
ejpam-6029	661	2	fixed	fix	VERB
ejpam-6029	661	3	point	point	NOUN
ejpam-6029	661	4	theorems	theorem	NOUN
ejpam-6029	661	5	of	of	ADP
ejpam-6029	661	6	generalized	generalized	ADJ
ejpam-6029	661	7	lipschitz	lipschitz	NOUN
ejpam-6029	661	8	mappings	mapping	NOUN
ejpam-6029	661	9	in	in	ADP
ejpam-6029	661	10	cone	cone	NOUN
ejpam-6029	661	11	metric	metric	ADJ
ejpam-6029	661	12	spaces	space	NOUN
ejpam-6029	661	13	over	over	ADP
ejpam-6029	661	14	banach	banach	NOUN
ejpam-6029	661	15	algebras	algebra	NOUN
ejpam-6029	661	16	.	.	PUNCT
ejpam-6029	662	1	applied	apply	VERB
ejpam-6029	662	2	mathematics	mathematic	NOUN
ejpam-6029	662	3	and	and	CCONJ
ejpam-6029	662	4	information	information	NOUN
ejpam-6029	662	5	sciences	science	NOUN
ejpam-6029	662	6	,	,	PUNCT
ejpam-6029	662	7	9(6):2983	9(6):2983	PRON
ejpam-6029	662	8	,	,	PUNCT
ejpam-6029	662	9	2015	2015	NUM
ejpam-6029	662	10	.	.	PUNCT
ejpam-6029	663	1	[	[	X
ejpam-6029	663	2	33	33	NUM
ejpam-6029	663	3	]	]	PUNCT
ejpam-6029	663	4	a	a	DET
ejpam-6029	663	5	a	a	DET
ejpam-6029	663	6	hijab	hijab	NOUN
ejpam-6029	663	7	and	and	CCONJ
ejpam-6029	663	8	l	l	NOUN
ejpam-6029	663	9	k	k	PROPN
ejpam-6029	663	10	shaakir	shaakir	NOUN
ejpam-6029	663	11	.	.	PUNCT
ejpam-6029	664	1	new	new	ADJ
ejpam-6029	664	2	generalization	generalization	NOUN
ejpam-6029	664	3	of	of	ADP
ejpam-6029	664	4	strong	strong	ADV
ejpam-6029	664	5	-	-	PUNCT
ejpam-6029	664	6	composed	compose	VERB
ejpam-6029	664	7	metric	metric	ADJ
ejpam-6029	664	8	type	type	NOUN
ejpam-6029	664	9	spaces	space	NOUN
ejpam-6029	664	10	with	with	ADP
ejpam-6029	664	11	special	special	ADJ
ejpam-6029	664	12	(	(	PUNCT
ejpam-6029	664	13	ψ	ψ	NOUN
ejpam-6029	664	14	,	,	PUNCT
ejpam-6029	664	15	ϕ)-contraction	ϕ)-contraction	NOUN
ejpam-6029	664	16	.	.	PUNCT
ejpam-6029	665	1	advances	advance	NOUN
ejpam-6029	665	2	in	in	ADP
ejpam-6029	665	3	fixed	fix	VERB
ejpam-6029	665	4	point	point	NOUN
ejpam-6029	665	5	theory	theory	NOUN
ejpam-6029	665	6	,	,	PUNCT
ejpam-6029	665	7	15(5	15(5	NUM
ejpam-6029	665	8	)	)	PUNCT
ejpam-6029	665	9	,	,	PUNCT
ejpam-6029	665	10	2025	2025	NUM
ejpam-6029	665	11	.	.	PUNCT
ejpam-6029	666	1	[	[	X
ejpam-6029	666	2	34	34	NUM
ejpam-6029	666	3	]	]	X
ejpam-6029	666	4	a	a	DET
ejpam-6029	666	5	a	a	DET
ejpam-6029	666	6	hijab	hijab	NOUN
ejpam-6029	666	7	,	,	PUNCT
ejpam-6029	666	8	l	l	PROPN
ejpam-6029	666	9	k	k	X
ejpam-6029	666	10	shaakir	shaakir	PROPN
ejpam-6029	666	11	,	,	PUNCT
ejpam-6029	666	12	s	s	NOUN
ejpam-6029	666	13	aljohani	aljohani	NOUN
ejpam-6029	666	14	,	,	PUNCT
ejpam-6029	666	15	and	and	CCONJ
ejpam-6029	666	16	n	n	PRON
ejpam-6029	666	17	mlaiki	mlaiki	PROPN
ejpam-6029	666	18	.	.	PUNCT
ejpam-6029	667	1	results	result	NOUN
ejpam-6029	667	2	on	on	ADP
ejpam-6029	667	3	common	common	ADJ
ejpam-6029	667	4	fixed	fix	VERB
ejpam-6029	667	5	points	point	NOUN
ejpam-6029	667	6	in	in	ADP
ejpam-6029	667	7	strong	strong	ADV
ejpam-6029	667	8	-	-	PUNCT
ejpam-6029	667	9	composed	compose	VERB
ejpam-6029	667	10	-	-	PUNCT
ejpam-6029	667	11	cone	cone	NOUN
ejpam-6029	667	12	metric	metric	ADJ
ejpam-6029	667	13	spaces	space	NOUN
ejpam-6029	667	14	.	.	PUNCT
ejpam-6029	668	1	international	international	ADJ
ejpam-6029	668	2	journal	journal	NOUN
ejpam-6029	668	3	of	of	ADP
ejpam-6029	668	4	analysis	analysis	NOUN
ejpam-6029	668	5	and	and	CCONJ
ejpam-6029	668	6	applications	application	NOUN
ejpam-6029	668	7	,	,	PUNCT
ejpam-6029	668	8	23(75	23(75	NUM
ejpam-6029	668	9	)	)	PUNCT
ejpam-6029	668	10	,	,	PUNCT
ejpam-6029	668	11	2025	2025	NUM
ejpam-6029	668	12	.	.	PUNCT
ejpam-6029	669	1	[	[	X
ejpam-6029	669	2	35	35	NUM
ejpam-6029	669	3	]	]	PUNCT
ejpam-6029	669	4	a	a	DET
ejpam-6029	669	5	h	h	NOUN
ejpam-6029	669	6	jothy	jothy	ADJ
ejpam-6029	669	7	,	,	PUNCT
ejpam-6029	669	8	p	p	PROPN
ejpam-6029	669	9	s	s	PROPN
ejpam-6029	669	10	srinivasan	srinivasan	NOUN
ejpam-6029	669	11	,	,	PUNCT
ejpam-6029	669	12	l	l	NOUN
ejpam-6029	669	13	rathour	rathour	NOUN
ejpam-6029	669	14	,	,	PUNCT
ejpam-6029	669	15	r	r	NOUN
ejpam-6029	669	16	theivaraman	theivaraman	NOUN
ejpam-6029	669	17	,	,	PUNCT
ejpam-6029	669	18	and	and	CCONJ
ejpam-6029	669	19	s	s	VERB
ejpam-6029	669	20	thenmozhi	thenmozhi	NOUN
ejpam-6029	669	21	.	.	PUNCT
ejpam-6029	670	1	some	some	DET
ejpam-6029	670	2	fixed	fix	VERB
ejpam-6029	670	3	point	point	NOUN
ejpam-6029	670	4	results	result	NOUN
ejpam-6029	670	5	on	on	ADP
ejpam-6029	670	6	double	double	ADJ
ejpam-6029	670	7	controlled	control	VERB
ejpam-6029	670	8	cone	cone	NOUN
ejpam-6029	670	9	metric	metric	ADJ
ejpam-6029	670	10	spaces	space	NOUN
ejpam-6029	670	11	.	.	PUNCT
ejpam-6029	671	1	korean	korean	ADJ
ejpam-6029	671	2	journal	journal	PROPN
ejpam-6029	671	3	of	of	ADP
ejpam-6029	671	4	mathematics	mathematic	NOUN
ejpam-6029	671	5	,	,	PUNCT
ejpam-6029	671	6	32(2):329–348	32(2):329–348	PROPN
ejpam-6029	671	7	,	,	PUNCT
ejpam-6029	671	8	2024	2024	NUM
ejpam-6029	671	9	.	.	PUNCT
ejpam-6029	672	1	[	[	X
ejpam-6029	672	2	36	36	NUM
ejpam-6029	672	3	]	]	X
ejpam-6029	672	4	z	z	NOUN
ejpam-6029	672	5	kadelburg	kadelburg	PROPN
ejpam-6029	672	6	and	and	CCONJ
ejpam-6029	672	7	s	s	VERB
ejpam-6029	672	8	radenovic	radenovic	ADJ
ejpam-6029	672	9	.	.	PUNCT
ejpam-6029	673	1	a	a	DET
ejpam-6029	673	2	note	note	NOUN
ejpam-6029	673	3	on	on	ADP
ejpam-6029	673	4	various	various	ADJ
ejpam-6029	673	5	types	type	NOUN
ejpam-6029	673	6	of	of	ADP
ejpam-6029	673	7	cones	cone	NOUN
ejpam-6029	673	8	and	and	CCONJ
ejpam-6029	673	9	fixed	fix	VERB
ejpam-6029	673	10	point	point	NOUN
ejpam-6029	673	11	results	result	NOUN
ejpam-6029	673	12	in	in	ADP
ejpam-6029	673	13	cone	cone	NOUN
ejpam-6029	673	14	metric	metric	ADJ
ejpam-6029	673	15	spaces	space	NOUN
ejpam-6029	673	16	.	.	PUNCT
ejpam-6029	674	1	asian	asian	ADJ
ejpam-6029	674	2	journal	journal	PROPN
ejpam-6029	674	3	of	of	ADP
ejpam-6029	674	4	mathematics	mathematic	NOUN
ejpam-6029	674	5	and	and	CCONJ
ejpam-6029	674	6	applications	application	NOUN
ejpam-6029	674	7	,	,	PUNCT
ejpam-6029	674	8	2013(104	2013(104	NUM
ejpam-6029	674	9	)	)	PUNCT
ejpam-6029	674	10	,	,	PUNCT
ejpam-6029	674	11	2013	2013	NUM
ejpam-6029	674	12	.	.	PUNCT
ejpam-6029	675	1	[	[	X
ejpam-6029	675	2	37	37	NUM
ejpam-6029	675	3	]	]	PUNCT
ejpam-6029	675	4	a	a	DET
ejpam-6029	675	5	karami	karami	NOUN
ejpam-6029	675	6	,	,	PUNCT
ejpam-6029	675	7	s	s	PART
ejpam-6029	675	8	sedghi	sedghi	X
ejpam-6029	675	9	,	,	PUNCT
ejpam-6029	675	10	and	and	CCONJ
ejpam-6029	676	1	z	z	NOUN
ejpam-6029	676	2	d	d	X
ejpam-6029	676	3	mitrović.	mitrović.	ADJ
ejpam-6029	676	4	solving	solve	VERB
ejpam-6029	676	5	existence	existence	NOUN
ejpam-6029	676	6	problems	problem	NOUN
ejpam-6029	676	7	via	via	ADP
ejpam-6029	676	8	contractions	contraction	NOUN
ejpam-6029	676	9	in	in	ADP
ejpam-6029	676	10	expanded	expand	VERB
ejpam-6029	676	11	b	b	X
ejpam-6029	676	12	-	-	PUNCT
ejpam-6029	676	13	metric	metric	ADJ
ejpam-6029	676	14	spaces	space	NOUN
ejpam-6029	676	15	.	.	PUNCT
ejpam-6029	677	1	the	the	DET
ejpam-6029	677	2	journal	journal	NOUN
ejpam-6029	677	3	of	of	ADP
ejpam-6029	677	4	analysis	analysis	NOUN
ejpam-6029	677	5	,	,	PUNCT
ejpam-6029	677	6	30(2):895–907	30(2):895–907	PROPN
ejpam-6029	677	7	,	,	PUNCT
ejpam-6029	677	8	2022	2022	NUM
ejpam-6029	677	9	.	.	PUNCT
ejpam-6029	678	1	[	[	X
ejpam-6029	678	2	38	38	NUM
ejpam-6029	678	3	]	]	X
ejpam-6029	678	4	c	c	PROPN
ejpam-6029	678	5	j	j	PROPN
ejpam-6029	678	6	kil	kil	PROPN
ejpam-6029	678	7	,	,	PUNCT
ejpam-6029	678	8	c	c	PROPN
ejpam-6029	678	9	s	s	PROPN
ejpam-6029	678	10	yu	yu	PROPN
ejpam-6029	678	11	,	,	PUNCT
ejpam-6029	678	12	and	and	CCONJ
ejpam-6029	678	13	u	u	PROPN
ejpam-6029	678	14	c	c	PROPN
ejpam-6029	678	15	han	han	PROPN
ejpam-6029	678	16	.	.	PUNCT
ejpam-6029	678	17	fixed	fix	VERB
ejpam-6029	678	18	point	point	NOUN
ejpam-6029	678	19	results	result	NOUN
ejpam-6029	678	20	for	for	ADP
ejpam-6029	678	21	some	some	DET
ejpam-6029	678	22	rational	rational	ADJ
ejpam-6029	678	23	type	type	NOUN
ejpam-6029	678	24	contractions	contraction	NOUN
ejpam-6029	678	25	in	in	ADP
ejpam-6029	678	26	double	double	ADV
ejpam-6029	678	27	-	-	PUNCT
ejpam-6029	678	28	composed	compose	VERB
ejpam-6029	678	29	metric	metric	ADJ
ejpam-6029	678	30	spaces	space	NOUN
ejpam-6029	678	31	and	and	CCONJ
ejpam-6029	678	32	applications	application	NOUN
ejpam-6029	678	33	.	.	PUNCT
ejpam-6029	679	1	informatica	informatica	PROPN
ejpam-6029	679	2	,	,	PUNCT
ejpam-6029	679	3	34(12):105–130	34(12):105–130	NUM
ejpam-6029	679	4	,	,	PUNCT
ejpam-6029	679	5	2023	2023	NUM
ejpam-6029	679	6	.	.	PUNCT
ejpam-6029	680	1	[	[	X
ejpam-6029	680	2	39	39	NUM
ejpam-6029	680	3	]	]	PUNCT
ejpam-6029	680	4	h	h	NOUN
ejpam-6029	680	5	a	a	DET
ejpam-6029	680	6	hammad	hammad	PROPN
ejpam-6029	680	7	and	and	CCONJ
ejpam-6029	680	8	m	m	PROPN
ejpam-6029	680	9	de	de	X
ejpam-6029	680	10	la	la	X
ejpam-6029	680	11	sen	sen	PROPN
ejpam-6029	680	12	.	.	PROPN
ejpam-6029	681	1	a	a	DET
ejpam-6029	681	2	solution	solution	NOUN
ejpam-6029	681	3	of	of	ADP
ejpam-6029	681	4	fredholm	fredholm	ADJ
ejpam-6029	681	5	integral	integral	ADJ
ejpam-6029	681	6	equation	equation	NOUN
ejpam-6029	681	7	by	by	ADP
ejpam-6029	681	8	using	use	VERB
ejpam-6029	681	9	the	the	DET
ejpam-6029	681	10	cyclic	cyclic	PROPN
ejpam-6029	681	11	η	η	PROPN
ejpam-6029	681	12	sq	sq	ADJ
ejpam-6029	681	13	-	-	ADJ
ejpam-6029	681	14	rational	rational	ADJ
ejpam-6029	681	15	contractive	contractive	ADJ
ejpam-6029	681	16	mappings	mapping	NOUN
ejpam-6029	681	17	technique	technique	NOUN
ejpam-6029	681	18	in	in	ADP
ejpam-6029	681	19	b	b	NOUN
ejpam-6029	681	20	-	-	PUNCT
ejpam-6029	681	21	metric	metric	ADJ
ejpam-6029	681	22	-	-	PUNCT
ejpam-6029	681	23	like	like	ADJ
ejpam-6029	681	24	spaces	space	NOUN
ejpam-6029	681	25	.	.	PUNCT
ejpam-6029	682	1	symmetry	symmetry	NOUN
ejpam-6029	682	2	,	,	PUNCT
ejpam-6029	682	3	11(9):1184	11(9):1184	NUM
ejpam-6029	682	4	,	,	PUNCT
ejpam-6029	682	5	2019	2019	NUM
ejpam-6029	682	6	.	.	PUNCT
ejpam-6029	683	1	[	[	X
ejpam-6029	683	2	40	40	NUM
ejpam-6029	683	3	]	]	PUNCT
ejpam-6029	683	4	n	n	CCONJ
ejpam-6029	683	5	faried	farie	VERB
ejpam-6029	683	6	,	,	PUNCT
ejpam-6029	683	7	s	s	VERB
ejpam-6029	683	8	m	m	VERB
ejpam-6029	683	9	a	a	DET
ejpam-6029	683	10	abou	abou	PROPN
ejpam-6029	683	11	-	-	PUNCT
ejpam-6029	683	12	bakr	bakr	PROPN
ejpam-6029	683	13	,	,	PUNCT
ejpam-6029	683	14	h	h	PROPN
ejpam-6029	683	15	abd	abd	PROPN
ejpam-6029	683	16	el	el	PROPN
ejpam-6029	683	17	-	-	PROPN
ejpam-6029	683	18	ghaffar	ghaffar	NOUN
ejpam-6029	683	19	,	,	PUNCT
ejpam-6029	683	20	and	and	CCONJ
ejpam-6029	683	21	s	s	AUX
ejpam-6029	683	22	s	s	VERB
ejpam-6029	683	23	almassri	almassri	PROPN
ejpam-6029	683	24	.	.	PUNCT
ejpam-6029	684	1	fixed	fix	VERB
ejpam-6029	684	2	-	-	PUNCT
ejpam-6029	684	3	point	point	NOUN
ejpam-6029	684	4	theorems	theorem	NOUN
ejpam-6029	684	5	of	of	ADP
ejpam-6029	684	6	f∗-(ψ	f∗-(ψ	NOUN
ejpam-6029	684	7	,	,	PUNCT
ejpam-6029	684	8	ϕ	ϕ	NOUN
ejpam-6029	684	9	)	)	PUNCT
ejpam-6029	684	10	integral	integral	ADJ
ejpam-6029	684	11	-	-	PUNCT
ejpam-6029	684	12	type	type	NOUN
ejpam-6029	684	13	contractive	contractive	ADJ
ejpam-6029	684	14	conditions	condition	NOUN
ejpam-6029	684	15	on	on	ADP
ejpam-6029	684	16	1e	1e	NOUN
ejpam-6029	684	17	-	-	PUNCT
ejpam-6029	684	18	complete	complete	ADJ
ejpam-6029	684	19	multiplicative	multiplicative	ADJ
ejpam-6029	684	20	partial	partial	ADJ
ejpam-6029	684	21	cone	cone	NOUN
ejpam-6029	684	22	metric	metric	ADJ
ejpam-6029	684	23	spaces	space	NOUN
ejpam-6029	684	24	over	over	ADP
ejpam-6029	684	25	banach	banach	NOUN
ejpam-6029	684	26	algebras	algebra	NOUN
ejpam-6029	684	27	and	and	CCONJ
ejpam-6029	684	28	applications	application	NOUN
ejpam-6029	684	29	.	.	PUNCT
ejpam-6029	685	1	journal	journal	PROPN
ejpam-6029	685	2	of	of	ADP
ejpam-6029	685	3	inequalities	inequality	NOUN
ejpam-6029	685	4	and	and	CCONJ
ejpam-6029	685	5	applications	application	NOUN
ejpam-6029	685	6	,	,	PUNCT
ejpam-6029	685	7	144(2023	144(2023	NUM
ejpam-6029	685	8	)	)	PUNCT
ejpam-6029	685	9	,	,	PUNCT
ejpam-6029	685	10	2023	2023	NUM
ejpam-6029	685	11	.	.	PUNCT