id	sid	tid	token	lemma	pos
ejpam-3831	1	1	european	european	PROPN
ejpam-3831	1	2	journal	journal	PROPN
ejpam-3831	1	3	of	of	ADP
ejpam-3831	1	4	pure	pure	ADJ
ejpam-3831	1	5	and	and	CCONJ
ejpam-3831	1	6	applied	apply	VERB
ejpam-3831	1	7	mathematics	mathematic	NOUN
ejpam-3831	1	8	vol	vol	NOUN
ejpam-3831	1	9	.	.	PROPN
ejpam-3831	2	1	13	13	NUM
ejpam-3831	2	2	,	,	PUNCT
ejpam-3831	2	3	no	no	INTJ
ejpam-3831	2	4	.	.	NOUN
ejpam-3831	2	5	4	4	NUM
ejpam-3831	2	6	,	,	PUNCT
ejpam-3831	2	7	2020	2020	NUM
ejpam-3831	2	8	,	,	PUNCT
ejpam-3831	2	9	995	995	NUM
ejpam-3831	2	10	-	-	SYM
ejpam-3831	2	11	1015	1015	NUM
ejpam-3831	2	12	issn	issn	PROPN
ejpam-3831	2	13	1307	1307	NUM
ejpam-3831	2	14	-	-	SYM
ejpam-3831	2	15	5543	5543	NUM
ejpam-3831	2	16	–	–	PUNCT
ejpam-3831	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3831	2	18	published	publish	VERB
ejpam-3831	2	19	by	by	ADP
ejpam-3831	2	20	new	new	PROPN
ejpam-3831	2	21	york	york	PROPN
ejpam-3831	2	22	business	business	PROPN
ejpam-3831	2	23	global	global	ADJ
ejpam-3831	2	24	solving	solve	VERB
ejpam-3831	2	25	a	a	DET
ejpam-3831	2	26	class	class	NOUN
ejpam-3831	2	27	of	of	ADP
ejpam-3831	2	28	integral	integral	ADJ
ejpam-3831	2	29	equations	equation	NOUN
ejpam-3831	2	30	via	via	ADP
ejpam-3831	2	31	contractive	contractive	ADJ
ejpam-3831	2	32	mapping	mapping	NOUN
ejpam-3831	2	33	with	with	ADP
ejpam-3831	2	34	rational	rational	ADJ
ejpam-3831	2	35	type	type	NOUN
ejpam-3831	2	36	abdullah1	abdullah1	NOUN
ejpam-3831	2	37	,	,	PUNCT
ejpam-3831	2	38	m.	m.	NOUN
ejpam-3831	2	39	sarwar1	sarwar1	PROPN
ejpam-3831	2	40	,	,	PUNCT
ejpam-3831	2	41	z.	z.	PROPN
ejpam-3831	2	42	mustafa2	mustafa2	PROPN
ejpam-3831	2	43	,	,	PUNCT
ejpam-3831	3	1	m.m.m	m.m.m	X
ejpam-3831	3	2	.	.	PUNCT
ejpam-3831	4	1	jaradat2,∗	jaradat2,∗	PROPN
ejpam-3831	4	2	1	1	NUM
ejpam-3831	4	3	department	department	NOUN
ejpam-3831	4	4	of	of	ADP
ejpam-3831	4	5	mathematics	mathematics	PROPN
ejpam-3831	4	6	,	,	PUNCT
ejpam-3831	4	7	university	university	NOUN
ejpam-3831	4	8	of	of	ADP
ejpam-3831	4	9	malakand	malakand	PROPN
ejpam-3831	4	10	,	,	PUNCT
ejpam-3831	4	11	chakdara	chakdara	NOUN
ejpam-3831	4	12	dir(l	dir(l	PROPN
ejpam-3831	4	13	)	)	PUNCT
ejpam-3831	4	14	,	,	PUNCT
ejpam-3831	4	15	pakistan	pakistan	PROPN
ejpam-3831	4	16	.	.	PUNCT
ejpam-3831	5	1	2	2	NUM
ejpam-3831	5	2	department	department	NOUN
ejpam-3831	5	3	of	of	ADP
ejpam-3831	5	4	mathematics	mathematic	NOUN
ejpam-3831	5	5	,	,	PUNCT
ejpam-3831	5	6	statistics	statistic	NOUN
ejpam-3831	5	7	and	and	CCONJ
ejpam-3831	5	8	physics	physics	PROPN
ejpam-3831	5	9	,	,	PUNCT
ejpam-3831	5	10	qatar	qatar	PROPN
ejpam-3831	5	11	university	university	PROPN
ejpam-3831	5	12	,	,	PUNCT
ejpam-3831	5	13	doha	doha	PROPN
ejpam-3831	5	14	-	-	PUNCT
ejpam-3831	5	15	qatar	qatar	NOUN
ejpam-3831	5	16	.	.	PUNCT
ejpam-3831	6	1	abstract	abstract	ADJ
ejpam-3831	6	2	.	.	PUNCT
ejpam-3831	7	1	in	in	ADP
ejpam-3831	7	2	this	this	DET
ejpam-3831	7	3	paper	paper	NOUN
ejpam-3831	7	4	,	,	PUNCT
ejpam-3831	7	5	using	use	VERB
ejpam-3831	7	6	rational	rational	ADJ
ejpam-3831	7	7	type	type	NOUN
ejpam-3831	7	8	contractive	contractive	ADJ
ejpam-3831	7	9	conditions	condition	NOUN
ejpam-3831	7	10	,	,	PUNCT
ejpam-3831	7	11	the	the	DET
ejpam-3831	7	12	existence	existence	NOUN
ejpam-3831	7	13	and	and	CCONJ
ejpam-3831	7	14	uniqueness	uniqueness	NOUN
ejpam-3831	7	15	of	of	ADP
ejpam-3831	7	16	common	common	ADJ
ejpam-3831	7	17	coupled	couple	VERB
ejpam-3831	7	18	fixed	fix	VERB
ejpam-3831	7	19	point	point	NOUN
ejpam-3831	7	20	theorem	theorem	VERB
ejpam-3831	7	21	in	in	ADP
ejpam-3831	7	22	the	the	DET
ejpam-3831	7	23	set	set	NOUN
ejpam-3831	7	24	up	up	ADP
ejpam-3831	7	25	of	of	ADP
ejpam-3831	7	26	gb	gb	ADV
ejpam-3831	7	27	-	-	PUNCT
ejpam-3831	7	28	metric	metric	ADJ
ejpam-3831	7	29	spaces	space	NOUN
ejpam-3831	7	30	is	be	AUX
ejpam-3831	7	31	studied	study	VERB
ejpam-3831	7	32	.	.	PUNCT
ejpam-3831	8	1	the	the	DET
ejpam-3831	8	2	derived	derive	VERB
ejpam-3831	8	3	result	result	NOUN
ejpam-3831	8	4	cover	cover	NOUN
ejpam-3831	8	5	and	and	CCONJ
ejpam-3831	8	6	generalize	generalize	VERB
ejpam-3831	8	7	some	some	DET
ejpam-3831	8	8	well	well	ADV
ejpam-3831	8	9	-	-	PUNCT
ejpam-3831	8	10	known	know	VERB
ejpam-3831	8	11	comparable	comparable	ADJ
ejpam-3831	8	12	results	result	NOUN
ejpam-3831	8	13	in	in	ADP
ejpam-3831	8	14	the	the	DET
ejpam-3831	8	15	existing	exist	VERB
ejpam-3831	8	16	literature	literature	NOUN
ejpam-3831	8	17	.	.	PUNCT
ejpam-3831	9	1	then	then	ADV
ejpam-3831	9	2	we	we	PRON
ejpam-3831	9	3	use	use	VERB
ejpam-3831	9	4	the	the	DET
ejpam-3831	9	5	derived	derive	VERB
ejpam-3831	9	6	results	result	NOUN
ejpam-3831	9	7	to	to	PART
ejpam-3831	9	8	prove	prove	VERB
ejpam-3831	9	9	the	the	DET
ejpam-3831	9	10	existence	existence	NOUN
ejpam-3831	9	11	and	and	CCONJ
ejpam-3831	9	12	uniqueness	uniqueness	ADJ
ejpam-3831	9	13	solution	solution	NOUN
ejpam-3831	9	14	for	for	ADP
ejpam-3831	9	15	some	some	DET
ejpam-3831	9	16	classes	class	NOUN
ejpam-3831	9	17	of	of	ADP
ejpam-3831	9	18	integral	integral	ADJ
ejpam-3831	9	19	equations	equation	NOUN
ejpam-3831	9	20	.	.	PUNCT
ejpam-3831	10	1	further	far	ADV
ejpam-3831	10	2	more	more	ADV
ejpam-3831	10	3	,	,	PUNCT
ejpam-3831	10	4	an	an	DET
ejpam-3831	10	5	example	example	NOUN
ejpam-3831	10	6	of	of	ADP
ejpam-3831	10	7	such	such	ADJ
ejpam-3831	10	8	type	type	NOUN
ejpam-3831	10	9	of	of	ADP
ejpam-3831	10	10	integral	integral	ADJ
ejpam-3831	10	11	equation	equation	NOUN
ejpam-3831	10	12	is	be	AUX
ejpam-3831	10	13	presented	present	VERB
ejpam-3831	10	14	.	.	PUNCT
ejpam-3831	11	1	2020	2020	NUM
ejpam-3831	11	2	mathematics	mathematics	PROPN
ejpam-3831	11	3	subject	subject	NOUN
ejpam-3831	11	4	classifications	classification	NOUN
ejpam-3831	11	5	:	:	PUNCT
ejpam-3831	11	6	47h10	47h10	NUM
ejpam-3831	11	7	,	,	PUNCT
ejpam-3831	11	8	54h25	54h25	NUM
ejpam-3831	11	9	key	key	ADJ
ejpam-3831	11	10	words	word	NOUN
ejpam-3831	11	11	and	and	CCONJ
ejpam-3831	11	12	phrases	phrase	NOUN
ejpam-3831	11	13	:	:	PUNCT
ejpam-3831	11	14	integral	integral	ADJ
ejpam-3831	11	15	equations	equation	NOUN
ejpam-3831	11	16	,	,	PUNCT
ejpam-3831	11	17	complete	complete	VERB
ejpam-3831	11	18	gb	gb	ADV
ejpam-3831	11	19	-	-	PUNCT
ejpam-3831	11	20	metric	metric	ADJ
ejpam-3831	11	21	space	space	NOUN
ejpam-3831	11	22	,	,	PUNCT
ejpam-3831	11	23	cauchy	cauchy	ADJ
ejpam-3831	11	24	sequence	sequence	NOUN
ejpam-3831	11	25	,	,	PUNCT
ejpam-3831	11	26	common	common	ADJ
ejpam-3831	11	27	coupled	couple	VERB
ejpam-3831	11	28	fixed	fix	VERB
ejpam-3831	11	29	point	point	NOUN
ejpam-3831	11	30	.	.	PUNCT
ejpam-3831	12	1	1	1	X
ejpam-3831	12	2	.	.	X
ejpam-3831	12	3	introduction	introduction	NOUN
ejpam-3831	12	4	and	and	CCONJ
ejpam-3831	12	5	preliminaries	preliminary	NOUN
ejpam-3831	12	6	the	the	DET
ejpam-3831	12	7	notion	notion	NOUN
ejpam-3831	12	8	of	of	ADP
ejpam-3831	12	9	metric	metric	ADJ
ejpam-3831	12	10	space	space	NOUN
ejpam-3831	12	11	has	have	AUX
ejpam-3831	12	12	been	be	AUX
ejpam-3831	12	13	generalized	generalize	VERB
ejpam-3831	12	14	in	in	ADP
ejpam-3831	12	15	different	different	ADJ
ejpam-3831	12	16	directions	direction	NOUN
ejpam-3831	12	17	.	.	PUNCT
ejpam-3831	13	1	in	in	ADP
ejpam-3831	13	2	particular	particular	ADJ
ejpam-3831	13	3	,	,	PUNCT
ejpam-3831	13	4	mustafa	mustafa	NOUN
ejpam-3831	13	5	and	and	CCONJ
ejpam-3831	13	6	sims	sim	NOUN
ejpam-3831	14	1	[	[	X
ejpam-3831	14	2	18	18	NUM
ejpam-3831	14	3	]	]	PUNCT
ejpam-3831	14	4	introduced	introduce	VERB
ejpam-3831	14	5	a	a	DET
ejpam-3831	14	6	new	new	ADJ
ejpam-3831	14	7	generalization	generalization	NOUN
ejpam-3831	14	8	of	of	ADP
ejpam-3831	14	9	metric	metric	ADJ
ejpam-3831	14	10	space	space	NOUN
ejpam-3831	14	11	known	know	VERB
ejpam-3831	14	12	as	as	ADP
ejpam-3831	14	13	g	g	NOUN
ejpam-3831	14	14	-	-	PUNCT
ejpam-3831	14	15	metric	metric	ADJ
ejpam-3831	14	16	space	space	NOUN
ejpam-3831	14	17	.	.	PUNCT
ejpam-3831	15	1	in	in	ADP
ejpam-3831	15	2	fact	fact	NOUN
ejpam-3831	15	3	,	,	PUNCT
ejpam-3831	15	4	they	they	PRON
ejpam-3831	15	5	assigned	assign	VERB
ejpam-3831	15	6	a	a	DET
ejpam-3831	15	7	non	non	ADJ
ejpam-3831	15	8	-	-	ADJ
ejpam-3831	15	9	negative	negative	ADJ
ejpam-3831	15	10	real	real	ADJ
ejpam-3831	15	11	number	number	NOUN
ejpam-3831	15	12	to	to	ADP
ejpam-3831	15	13	every	every	DET
ejpam-3831	15	14	triplet	triplet	NOUN
ejpam-3831	15	15	of	of	ADP
ejpam-3831	15	16	elements	element	NOUN
ejpam-3831	15	17	of	of	ADP
ejpam-3831	15	18	a	a	DET
ejpam-3831	15	19	metric	metric	ADJ
ejpam-3831	15	20	space	space	NOUN
ejpam-3831	15	21	m	m	PROPN
ejpam-3831	15	22	and	and	CCONJ
ejpam-3831	15	23	studied	study	VERB
ejpam-3831	15	24	fixed	fix	VERB
ejpam-3831	15	25	point	point	NOUN
ejpam-3831	15	26	results	result	NOUN
ejpam-3831	15	27	.	.	PUNCT
ejpam-3831	16	1	further	far	ADV
ejpam-3831	16	2	,	,	PUNCT
ejpam-3831	16	3	in	in	ADP
ejpam-3831	16	4	the	the	DET
ejpam-3831	16	5	setting	setting	NOUN
ejpam-3831	16	6	of	of	ADP
ejpam-3831	16	7	g	g	NOUN
ejpam-3831	16	8	-	-	PUNCT
ejpam-3831	16	9	metric	metric	ADJ
ejpam-3831	16	10	space	space	NOUN
ejpam-3831	16	11	,	,	PUNCT
ejpam-3831	16	12	mustafa	mustafa	PROPN
ejpam-3831	16	13	et	et	PROPN
ejpam-3831	16	14	al	al	PROPN
ejpam-3831	16	15	.	.	PUNCT
ejpam-3831	17	1	[	[	X
ejpam-3831	17	2	20	20	NUM
ejpam-3831	17	3	]	]	PUNCT
ejpam-3831	17	4	investigated	investigate	VERB
ejpam-3831	17	5	some	some	DET
ejpam-3831	17	6	fixed	fix	VERB
ejpam-3831	17	7	point	point	NOUN
ejpam-3831	17	8	results	result	NOUN
ejpam-3831	17	9	for	for	ADP
ejpam-3831	17	10	mappings	mapping	NOUN
ejpam-3831	17	11	via	via	ADP
ejpam-3831	17	12	rational	rational	ADJ
ejpam-3831	17	13	type	type	NOUN
ejpam-3831	17	14	contractions	contraction	NOUN
ejpam-3831	17	15	.	.	PUNCT
ejpam-3831	18	1	abbas	abbas	PROPN
ejpam-3831	18	2	and	and	CCONJ
ejpam-3831	18	3	rhoades	rhoade	NOUN
ejpam-3831	18	4	[	[	X
ejpam-3831	18	5	2	2	X
ejpam-3831	18	6	]	]	PUNCT
ejpam-3831	18	7	opened	open	VERB
ejpam-3831	18	8	the	the	DET
ejpam-3831	18	9	study	study	NOUN
ejpam-3831	18	10	of	of	ADP
ejpam-3831	18	11	finding	find	VERB
ejpam-3831	18	12	common	common	ADJ
ejpam-3831	18	13	fixed	fix	VERB
ejpam-3831	18	14	points	point	NOUN
ejpam-3831	18	15	in	in	ADP
ejpam-3831	18	16	g	g	NOUN
ejpam-3831	18	17	-	-	PUNCT
ejpam-3831	18	18	metric	metric	ADJ
ejpam-3831	18	19	spaces	space	NOUN
ejpam-3831	18	20	.	.	PUNCT
ejpam-3831	19	1	shatanawi	shatanawi	ADJ
ejpam-3831	20	1	[	[	X
ejpam-3831	20	2	15	15	NUM
ejpam-3831	20	3	]	]	SYM
ejpam-3831	20	4	studied	study	VERB
ejpam-3831	20	5	applications	application	NOUN
ejpam-3831	20	6	to	to	ADP
ejpam-3831	20	7	integral	integral	ADJ
ejpam-3831	20	8	equations	equation	NOUN
ejpam-3831	20	9	via	via	ADP
ejpam-3831	20	10	fixed	fix	VERB
ejpam-3831	20	11	point	point	NOUN
ejpam-3831	20	12	results	result	NOUN
ejpam-3831	20	13	for	for	ADP
ejpam-3831	20	14	two	two	NUM
ejpam-3831	20	15	weakly	weakly	ADJ
ejpam-3831	20	16	increasing	increase	VERB
ejpam-3831	20	17	mappings	mapping	NOUN
ejpam-3831	20	18	f	f	NOUN
ejpam-3831	20	19	and	and	CCONJ
ejpam-3831	20	20	g	g	NOUN
ejpam-3831	20	21	with	with	ADP
ejpam-3831	20	22	respect	respect	NOUN
ejpam-3831	20	23	to	to	ADP
ejpam-3831	20	24	partial	partial	ADJ
ejpam-3831	20	25	ordering	ordering	NOUN
ejpam-3831	20	26	relation	relation	NOUN
ejpam-3831	20	27	�	�	PROPN
ejpam-3831	20	28	in	in	ADP
ejpam-3831	20	29	gmetric	gmetric	PROPN
ejpam-3831	20	30	spaces	space	NOUN
ejpam-3831	20	31	.	.	PUNCT
ejpam-3831	21	1	after	after	SCONJ
ejpam-3831	21	2	that	that	PRON
ejpam-3831	21	3	several	several	ADJ
ejpam-3831	21	4	fixed	fix	VERB
ejpam-3831	21	5	point	point	NOUN
ejpam-3831	21	6	results	result	NOUN
ejpam-3831	21	7	were	be	AUX
ejpam-3831	21	8	proved	prove	VERB
ejpam-3831	21	9	in	in	ADP
ejpam-3831	21	10	these	these	DET
ejpam-3831	21	11	spaces	space	NOUN
ejpam-3831	21	12	.	.	PUNCT
ejpam-3831	22	1	some	some	PRON
ejpam-3831	22	2	of	of	ADP
ejpam-3831	22	3	these	these	DET
ejpam-3831	22	4	works	work	NOUN
ejpam-3831	22	5	are	be	AUX
ejpam-3831	22	6	noted	note	VERB
ejpam-3831	22	7	in	in	ADP
ejpam-3831	22	8	[	[	PUNCT
ejpam-3831	22	9	[	[	X
ejpam-3831	22	10	8],[3],[19],[22],[23	8],[3],[19],[22],[23	NOUN
ejpam-3831	22	11	]	]	X
ejpam-3831	22	12	]	]	PUNCT
ejpam-3831	22	13	.	.	PUNCT
ejpam-3831	23	1	recently	recently	ADV
ejpam-3831	23	2	aghajani	aghajani	VERB
ejpam-3831	23	3	et	et	PROPN
ejpam-3831	23	4	al	al	PROPN
ejpam-3831	23	5	.	.	PUNCT
ejpam-3831	24	1	[	[	X
ejpam-3831	24	2	1	1	X
ejpam-3831	24	3	]	]	PUNCT
ejpam-3831	24	4	introduced	introduce	VERB
ejpam-3831	24	5	the	the	DET
ejpam-3831	24	6	concept	concept	NOUN
ejpam-3831	24	7	of	of	ADP
ejpam-3831	24	8	gb	gb	ADV
ejpam-3831	24	9	-	-	PUNCT
ejpam-3831	24	10	metric	metric	ADJ
ejpam-3831	24	11	spaces	space	NOUN
ejpam-3831	24	12	by	by	ADP
ejpam-3831	24	13	combining	combine	VERB
ejpam-3831	24	14	the	the	DET
ejpam-3831	24	15	definition	definition	NOUN
ejpam-3831	24	16	of	of	ADP
ejpam-3831	24	17	g	g	NOUN
ejpam-3831	24	18	-	-	PUNCT
ejpam-3831	24	19	metric	metric	ADJ
ejpam-3831	24	20	and	and	CCONJ
ejpam-3831	24	21	b	b	NOUN
ejpam-3831	24	22	-	-	PUNCT
ejpam-3831	24	23	metric	metric	ADJ
ejpam-3831	24	24	spaces	space	NOUN
ejpam-3831	24	25	and	and	CCONJ
ejpam-3831	24	26	studied	study	VERB
ejpam-3831	24	27	a	a	DET
ejpam-3831	24	28	common	common	ADJ
ejpam-3831	24	29	fixed	fix	VERB
ejpam-3831	24	30	result	result	NOUN
ejpam-3831	24	31	for	for	ADP
ejpam-3831	24	32	six	six	NUM
ejpam-3831	24	33	mappings	mapping	NOUN
ejpam-3831	24	34	.	.	PUNCT
ejpam-3831	25	1	jamal	jamal	PROPN
ejpam-3831	25	2	rezaei	rezaei	PROPN
ejpam-3831	25	3	et	et	PROPN
ejpam-3831	25	4	al	al	PROPN
ejpam-3831	25	5	.	.	PUNCT
ejpam-3831	26	1	[	[	X
ejpam-3831	26	2	13	13	NUM
ejpam-3831	26	3	]	]	PUNCT
ejpam-3831	26	4	obtained	obtain	VERB
ejpam-3831	26	5	common	common	ADJ
ejpam-3831	26	6	fixed	fix	VERB
ejpam-3831	26	7	point	point	NOUN
ejpam-3831	26	8	results	result	NOUN
ejpam-3831	26	9	for	for	ADP
ejpam-3831	26	10	three	three	NUM
ejpam-3831	26	11	maps	map	NOUN
ejpam-3831	26	12	in	in	ADP
ejpam-3831	26	13	discontinuous	discontinuous	ADJ
ejpam-3831	26	14	gb	gb	ADV
ejpam-3831	26	15	-	-	PUNCT
ejpam-3831	26	16	metric	metric	ADJ
ejpam-3831	26	17	spaces	space	NOUN
ejpam-3831	26	18	.	.	PUNCT
ejpam-3831	27	1	sedghi	sedghi	PROPN
ejpam-3831	27	2	et	et	PROPN
ejpam-3831	27	3	al	al	PROPN
ejpam-3831	27	4	.	.	PUNCT
ejpam-3831	28	1	[	[	X
ejpam-3831	28	2	14	14	NUM
ejpam-3831	28	3	]	]	PUNCT
ejpam-3831	28	4	derived	derive	VERB
ejpam-3831	28	5	coupled	couple	VERB
ejpam-3831	28	6	fixed	fix	VERB
ejpam-3831	28	7	point	point	NOUN
ejpam-3831	28	8	theorems	theorem	NOUN
ejpam-3831	28	9	∗corresponding	∗corresponde	VERB
ejpam-3831	28	10	author	author	NOUN
ejpam-3831	28	11	.	.	PUNCT
ejpam-3831	29	1	doi	doi	NOUN
ejpam-3831	29	2	:	:	PUNCT
ejpam-3831	29	3	https://doi.org/10.29020/nybg.ejpam.v13i4.3831	https://doi.org/10.29020/nybg.ejpam.v13i4.3831	PROPN
ejpam-3831	29	4	email	email	NOUN
ejpam-3831	29	5	addresses	address	VERB
ejpam-3831	29	6	:	:	PUNCT
ejpam-3831	29	7	abdullahibad474@gmail.com	abdullahibad474@gmail.com	X
ejpam-3831	29	8	(	(	PUNCT
ejpam-3831	29	9	abdullah	abdullah	PROPN
ejpam-3831	29	10	)	)	PUNCT
ejpam-3831	29	11	,	,	PUNCT
ejpam-3831	29	12	sarwarswati@gmail.com	sarwarswati@gmail.com	X
ejpam-3831	29	13	(	(	PUNCT
ejpam-3831	29	14	m.	m.	NOUN
ejpam-3831	29	15	sarwar	sarwar	PROPN
ejpam-3831	29	16	)	)	PUNCT
ejpam-3831	29	17	,	,	PUNCT
ejpam-3831	29	18	zead@qu.edu.qa	zead@qu.edu.qa	PROPN
ejpam-3831	29	19	(	(	PUNCT
ejpam-3831	29	20	z.	z.	PROPN
ejpam-3831	29	21	mustafa	mustafa	PROPN
ejpam-3831	29	22	)	)	PUNCT
ejpam-3831	29	23	,	,	PUNCT
ejpam-3831	29	24	mmjst4@qu.edu.qa	mmjst4@qu.edu.qa	PROPN
ejpam-3831	29	25	(	(	PUNCT
ejpam-3831	29	26	m.m.m	m.m.m	NOUN
ejpam-3831	29	27	.	.	PUNCT
ejpam-3831	29	28	jaradat	jaradat	PROPN
ejpam-3831	29	29	)	)	PUNCT
ejpam-3831	29	30	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3831	30	1	995	995	NUM
ejpam-3831	30	2	c	c	X
ejpam-3831	30	3	©	©	NOUN
ejpam-3831	30	4	2020	2020	NUM
ejpam-3831	30	5	ejpam	ejpam	VERB
ejpam-3831	30	6	all	all	DET
ejpam-3831	30	7	rights	right	NOUN
ejpam-3831	30	8	reserved	reserve	VERB
ejpam-3831	30	9	.	.	PUNCT
ejpam-3831	31	1	m.m.m	m.m.m	AUX
ejpam-3831	31	2	.	.	PUNCT
ejpam-3831	32	1	jaradat	jaradat	PROPN
ejpam-3831	32	2	et	et	PROPN
ejpam-3831	32	3	al	al	PROPN
ejpam-3831	32	4	.	.	PUNCT
ejpam-3831	32	5	/	/	SYM
ejpam-3831	32	6	eur	eur	PROPN
ejpam-3831	32	7	.	.	PUNCT
ejpam-3831	33	1	j.	j.	PROPN
ejpam-3831	33	2	pure	pure	PROPN
ejpam-3831	33	3	appl	appl	PROPN
ejpam-3831	33	4	.	.	PROPN
ejpam-3831	33	5	math	math	PROPN
ejpam-3831	33	6	,	,	PUNCT
ejpam-3831	33	7	13	13	NUM
ejpam-3831	33	8	(	(	PUNCT
ejpam-3831	33	9	4	4	NUM
ejpam-3831	33	10	)	)	PUNCT
ejpam-3831	33	11	(	(	PUNCT
ejpam-3831	33	12	2020	2020	NUM
ejpam-3831	33	13	)	)	PUNCT
ejpam-3831	33	14	,	,	PUNCT
ejpam-3831	33	15	995	995	NUM
ejpam-3831	33	16	-	-	SYM
ejpam-3831	33	17	1015	1015	NUM
ejpam-3831	33	18	996	996	NUM
ejpam-3831	33	19	in	in	ADP
ejpam-3831	33	20	gb	gb	ADV
ejpam-3831	33	21	-	-	PUNCT
ejpam-3831	33	22	metric	metric	ADJ
ejpam-3831	33	23	spaces	space	NOUN
ejpam-3831	33	24	.	.	PUNCT
ejpam-3831	34	1	khomdram	khomdram	NOUN
ejpam-3831	34	2	et	et	PROPN
ejpam-3831	34	3	al	al	PROPN
ejpam-3831	34	4	.	.	PUNCT
ejpam-3831	35	1	[	[	X
ejpam-3831	35	2	4	4	NUM
ejpam-3831	35	3	]	]	PUNCT
ejpam-3831	35	4	obtained	obtain	VERB
ejpam-3831	35	5	a	a	DET
ejpam-3831	35	6	coupled	couple	VERB
ejpam-3831	35	7	fixed	fix	VERB
ejpam-3831	35	8	point	point	NOUN
ejpam-3831	35	9	theorem	theorem	VERB
ejpam-3831	35	10	in	in	ADP
ejpam-3831	35	11	gb	gb	ADV
ejpam-3831	35	12	-	-	PUNCT
ejpam-3831	35	13	metric	metric	ADJ
ejpam-3831	35	14	space	space	NOUN
ejpam-3831	35	15	using	use	VERB
ejpam-3831	35	16	rational	rational	ADJ
ejpam-3831	35	17	type	type	NOUN
ejpam-3831	35	18	contractive	contractive	ADJ
ejpam-3831	35	19	conditions	condition	NOUN
ejpam-3831	35	20	.	.	PUNCT
ejpam-3831	36	1	in	in	ADP
ejpam-3831	36	2	addition	addition	NOUN
ejpam-3831	36	3	mustafa	mustafa	PROPN
ejpam-3831	36	4	et	et	PROPN
ejpam-3831	36	5	al	al	PROPN
ejpam-3831	36	6	.	.	PUNCT
ejpam-3831	37	1	[	[	X
ejpam-3831	37	2	21	21	NUM
ejpam-3831	37	3	]	]	PUNCT
ejpam-3831	37	4	worked	work	VERB
ejpam-3831	37	5	on	on	ADP
ejpam-3831	37	6	applications	application	NOUN
ejpam-3831	37	7	to	to	ADP
ejpam-3831	37	8	a	a	DET
ejpam-3831	37	9	system	system	NOUN
ejpam-3831	37	10	of	of	ADP
ejpam-3831	37	11	integral	integral	ADJ
ejpam-3831	37	12	equations	equation	NOUN
ejpam-3831	37	13	with	with	ADP
ejpam-3831	37	14	the	the	DET
ejpam-3831	37	15	help	help	NOUN
ejpam-3831	37	16	of	of	ADP
ejpam-3831	37	17	tripled	triple	VERB
ejpam-3831	37	18	coincidence	coincidence	NOUN
ejpam-3831	37	19	point	point	NOUN
ejpam-3831	37	20	in	in	ADP
ejpam-3831	37	21	ordered	order	VERB
ejpam-3831	37	22	gb	gb	ADV
ejpam-3831	37	23	-	-	PUNCT
ejpam-3831	37	24	metric	metric	ADJ
ejpam-3831	37	25	spaces	space	NOUN
ejpam-3831	37	26	.	.	PUNCT
ejpam-3831	38	1	guo	guo	PROPN
ejpam-3831	38	2	and	and	CCONJ
ejpam-3831	38	3	lakshmikantham	lakshmikantham	ADJ
ejpam-3831	38	4	[	[	X
ejpam-3831	38	5	5	5	NUM
ejpam-3831	38	6	]	]	PUNCT
ejpam-3831	38	7	gave	give	VERB
ejpam-3831	38	8	the	the	DET
ejpam-3831	38	9	concept	concept	NOUN
ejpam-3831	38	10	of	of	ADP
ejpam-3831	38	11	coupled	couple	VERB
ejpam-3831	38	12	fixed	fix	VERB
ejpam-3831	38	13	point	point	NOUN
ejpam-3831	38	14	of	of	ADP
ejpam-3831	38	15	non	non	ADJ
ejpam-3831	38	16	-	-	ADJ
ejpam-3831	38	17	linear	linear	ADJ
ejpam-3831	38	18	operator	operator	NOUN
ejpam-3831	38	19	with	with	ADP
ejpam-3831	38	20	applications	application	NOUN
ejpam-3831	38	21	.	.	PUNCT
ejpam-3831	39	1	lakshmikantham	lakshmikantham	VERB
ejpam-3831	39	2	et	et	PROPN
ejpam-3831	39	3	al	al	PROPN
ejpam-3831	39	4	.	.	PUNCT
ejpam-3831	40	1	[	[	X
ejpam-3831	40	2	16	16	NUM
ejpam-3831	40	3	]	]	PUNCT
ejpam-3831	40	4	introduced	introduce	VERB
ejpam-3831	40	5	ćirić	ćirić	NOUN
ejpam-3831	40	6	type	type	NOUN
ejpam-3831	40	7	mappings	mapping	NOUN
ejpam-3831	40	8	in	in	ADP
ejpam-3831	40	9	the	the	DET
ejpam-3831	40	10	framework	framework	NOUN
ejpam-3831	40	11	of	of	ADP
ejpam-3831	40	12	gb−metric	gb−metric	PROPN
ejpam-3831	40	13	spaces	space	NOUN
ejpam-3831	40	14	.	.	PUNCT
ejpam-3831	41	1	sintunavarat	sintunavarat	VERB
ejpam-3831	41	2	et	et	PROPN
ejpam-3831	41	3	al	al	PROPN
ejpam-3831	41	4	.	.	PUNCT
ejpam-3831	42	1	[	[	X
ejpam-3831	42	2	17	17	NUM
ejpam-3831	42	3	]	]	PUNCT
ejpam-3831	42	4	used	use	VERB
ejpam-3831	42	5	the	the	DET
ejpam-3831	42	6	nonlinear	nonlinear	ADJ
ejpam-3831	42	7	contraction	contraction	NOUN
ejpam-3831	42	8	to	to	PART
ejpam-3831	42	9	established	establish	VERB
ejpam-3831	42	10	a	a	DET
ejpam-3831	42	11	coupled	couple	VERB
ejpam-3831	42	12	fixed	fix	VERB
ejpam-3831	42	13	point	point	NOUN
ejpam-3831	42	14	results	result	NOUN
ejpam-3831	42	15	in	in	ADP
ejpam-3831	42	16	complete	complete	ADJ
ejpam-3831	42	17	metric	metric	ADJ
ejpam-3831	42	18	spaces	space	NOUN
ejpam-3831	42	19	without	without	ADP
ejpam-3831	42	20	the	the	DET
ejpam-3831	42	21	mixed	mixed	ADJ
ejpam-3831	42	22	monotone	monotone	ADJ
ejpam-3831	42	23	property	property	NOUN
ejpam-3831	42	24	.	.	PUNCT
ejpam-3831	43	1	using	use	VERB
ejpam-3831	43	2	generalized	generalized	ADJ
ejpam-3831	43	3	contractive	contractive	ADJ
ejpam-3831	43	4	condition	condition	NOUN
ejpam-3831	43	5	,	,	PUNCT
ejpam-3831	43	6	nashie	nashie	NOUN
ejpam-3831	43	7	et	et	PROPN
ejpam-3831	43	8	al	al	PROPN
ejpam-3831	43	9	.	.	PUNCT
ejpam-3831	44	1	[	[	X
ejpam-3831	44	2	6	6	NUM
ejpam-3831	44	3	]	]	PUNCT
ejpam-3831	44	4	proved	prove	VERB
ejpam-3831	44	5	the	the	DET
ejpam-3831	44	6	existence	existence	NOUN
ejpam-3831	44	7	and	and	CCONJ
ejpam-3831	44	8	uniqueness	uniqueness	NOUN
ejpam-3831	44	9	of	of	ADP
ejpam-3831	44	10	a	a	DET
ejpam-3831	44	11	common	common	ADJ
ejpam-3831	44	12	coupled	couple	VERB
ejpam-3831	44	13	fixed	fix	VERB
ejpam-3831	44	14	point	point	NOUN
ejpam-3831	44	15	theorem	theorem	NOUN
ejpam-3831	44	16	for	for	ADP
ejpam-3831	44	17	a	a	DET
ejpam-3831	44	18	pair	pair	NOUN
ejpam-3831	44	19	of	of	ADP
ejpam-3831	44	20	mappings	mapping	NOUN
ejpam-3831	44	21	in	in	ADP
ejpam-3831	44	22	complete	complete	ADJ
ejpam-3831	44	23	cone	cone	NOUN
ejpam-3831	44	24	metric	metric	ADJ
ejpam-3831	44	25	space	space	NOUN
ejpam-3831	44	26	.	.	PUNCT
ejpam-3831	45	1	radenović	radenović	VERB
ejpam-3831	46	1	[	[	X
ejpam-3831	46	2	10	10	NUM
ejpam-3831	46	3	]	]	PUNCT
ejpam-3831	46	4	presented	present	VERB
ejpam-3831	46	5	some	some	DET
ejpam-3831	46	6	remarks	remark	NOUN
ejpam-3831	46	7	on	on	ADP
ejpam-3831	46	8	some	some	DET
ejpam-3831	46	9	recent	recent	ADJ
ejpam-3831	46	10	coupled	couple	VERB
ejpam-3831	46	11	coincidence	coincidence	NOUN
ejpam-3831	46	12	point	point	NOUN
ejpam-3831	46	13	results	result	NOUN
ejpam-3831	46	14	in	in	ADP
ejpam-3831	46	15	symmetric	symmetric	ADJ
ejpam-3831	46	16	g	g	NOUN
ejpam-3831	46	17	-	-	PUNCT
ejpam-3831	46	18	metric	metric	ADJ
ejpam-3831	46	19	spaces	space	NOUN
ejpam-3831	46	20	and	and	CCONJ
ejpam-3831	46	21	reduce	reduce	VERB
ejpam-3831	46	22	some	some	DET
ejpam-3831	46	23	coupled	couple	VERB
ejpam-3831	46	24	coincidence	coincidence	NOUN
ejpam-3831	46	25	point	point	NOUN
ejpam-3831	46	26	results	result	NOUN
ejpam-3831	46	27	to	to	ADP
ejpam-3831	46	28	more	more	ADJ
ejpam-3831	46	29	general	general	ADJ
ejpam-3831	46	30	forms	form	NOUN
ejpam-3831	46	31	.	.	PUNCT
ejpam-3831	47	1	for	for	ADP
ejpam-3831	47	2	more	more	ADJ
ejpam-3831	47	3	details	detail	NOUN
ejpam-3831	47	4	on	on	ADP
ejpam-3831	47	5	coupled	couple	VERB
ejpam-3831	47	6	fixed	fix	VERB
ejpam-3831	47	7	point	point	NOUN
ejpam-3831	47	8	results	result	NOUN
ejpam-3831	47	9	we	we	PRON
ejpam-3831	47	10	refer	refer	VERB
ejpam-3831	47	11	the	the	DET
ejpam-3831	47	12	reader	reader	NOUN
ejpam-3831	47	13	to	to	ADP
ejpam-3831	47	14	[	[	X
ejpam-3831	47	15	[	[	X
ejpam-3831	47	16	12	12	NUM
ejpam-3831	47	17	]	]	PUNCT
ejpam-3831	47	18	,	,	PUNCT
ejpam-3831	47	19	[	[	X
ejpam-3831	47	20	9],[10	9],[10	X
ejpam-3831	47	21	]	]	X
ejpam-3831	47	22	,	,	PUNCT
ejpam-3831	47	23	[	[	X
ejpam-3831	47	24	11	11	NUM
ejpam-3831	47	25	]	]	PUNCT
ejpam-3831	47	26	,	,	PUNCT
ejpam-3831	47	27	[	[	X
ejpam-3831	47	28	7	7	NUM
ejpam-3831	47	29	]	]	X
ejpam-3831	47	30	]	]	PUNCT
ejpam-3831	47	31	.	.	PUNCT
ejpam-3831	48	1	in	in	ADP
ejpam-3831	48	2	the	the	DET
ejpam-3831	48	3	current	current	ADJ
ejpam-3831	48	4	work	work	NOUN
ejpam-3831	48	5	we	we	PRON
ejpam-3831	48	6	will	will	AUX
ejpam-3831	48	7	obtain	obtain	VERB
ejpam-3831	48	8	a	a	DET
ejpam-3831	48	9	common	common	ADJ
ejpam-3831	48	10	triple	triple	ADJ
ejpam-3831	48	11	fixed	fix	VERB
ejpam-3831	48	12	point	point	NOUN
ejpam-3831	48	13	in	in	ADP
ejpam-3831	48	14	gb	gb	ADV
ejpam-3831	48	15	-	-	PUNCT
ejpam-3831	48	16	metric	metric	ADJ
ejpam-3831	48	17	space	space	NOUN
ejpam-3831	48	18	using	use	VERB
ejpam-3831	48	19	contraction	contraction	NOUN
ejpam-3831	48	20	with	with	ADP
ejpam-3831	48	21	rational	rational	ADJ
ejpam-3831	48	22	type	type	NOUN
ejpam-3831	48	23	.	.	PUNCT
ejpam-3831	49	1	definition	definition	NOUN
ejpam-3831	49	2	1	1	NUM
ejpam-3831	49	3	.	.	PUNCT
ejpam-3831	50	1	[	[	X
ejpam-3831	50	2	18	18	NUM
ejpam-3831	50	3	]	]	PUNCT
ejpam-3831	50	4	let	let	VERB
ejpam-3831	50	5	s	s	PRON
ejpam-3831	50	6	6=	6=	NOUN
ejpam-3831	50	7	∅	∅	NOUN
ejpam-3831	50	8	and	and	CCONJ
ejpam-3831	50	9	g	g	NOUN
ejpam-3831	50	10	:	:	PUNCT
ejpam-3831	50	11	s3	s3	PROPN
ejpam-3831	50	12	→	→	SYM
ejpam-3831	50	13	r+	r+	PART
ejpam-3831	50	14	satisfies	satisfie	NOUN
ejpam-3831	50	15	:	:	PUNCT
ejpam-3831	50	16	g1	g1	X
ejpam-3831	50	17	)	)	PUNCT
ejpam-3831	50	18	g(p	g(p	PROPN
ejpam-3831	50	19	,	,	PUNCT
ejpam-3831	50	20	q	q	NOUN
ejpam-3831	50	21	,	,	PUNCT
ejpam-3831	50	22	r	r	NOUN
ejpam-3831	50	23	)	)	PUNCT
ejpam-3831	50	24	=	=	SYM
ejpam-3831	50	25	0	0	PUNCT
ejpam-3831	51	1	if	if	SCONJ
ejpam-3831	51	2	p	p	NOUN
ejpam-3831	51	3	=	=	X
ejpam-3831	51	4	q	q	NOUN
ejpam-3831	51	5	=	=	SYM
ejpam-3831	51	6	r	r	NOUN
ejpam-3831	51	7	;	;	PUNCT
ejpam-3831	51	8	g2	g2	PROPN
ejpam-3831	51	9	)	)	PUNCT
ejpam-3831	52	1	g(p	g(p	PROPN
ejpam-3831	52	2	,	,	PUNCT
ejpam-3831	52	3	p	p	X
ejpam-3831	52	4	,	,	PUNCT
ejpam-3831	52	5	q	q	PROPN
ejpam-3831	52	6	)	)	PUNCT
ejpam-3831	52	7	>	>	X
ejpam-3831	52	8	0	0	PUNCT
ejpam-3831	53	1	for	for	ADP
ejpam-3831	53	2	all	all	DET
ejpam-3831	53	3	p	p	NOUN
ejpam-3831	53	4	,	,	PUNCT
ejpam-3831	53	5	q	q	PROPN
ejpam-3831	53	6	∈	∈	PROPN
ejpam-3831	53	7	s	s	VERB
ejpam-3831	53	8	with	with	ADP
ejpam-3831	53	9	p	p	PROPN
ejpam-3831	53	10	6=	6=	PROPN
ejpam-3831	53	11	q	q	PROPN
ejpam-3831	53	12	;	;	PUNCT
ejpam-3831	53	13	g3	g3	NOUN
ejpam-3831	53	14	)	)	PUNCT
ejpam-3831	53	15	g(p	g(p	PROPN
ejpam-3831	53	16	,	,	PUNCT
ejpam-3831	53	17	q	q	NOUN
ejpam-3831	53	18	,	,	PUNCT
ejpam-3831	53	19	q	q	NOUN
ejpam-3831	53	20	)	)	PUNCT
ejpam-3831	53	21	≤	≤	NOUN
ejpam-3831	53	22	g(p	g(p	NOUN
ejpam-3831	53	23	,	,	PUNCT
ejpam-3831	53	24	q	q	NOUN
ejpam-3831	53	25	,	,	PUNCT
ejpam-3831	53	26	r	r	NOUN
ejpam-3831	53	27	)	)	PUNCT
ejpam-3831	53	28	for	for	ADP
ejpam-3831	53	29	all	all	DET
ejpam-3831	53	30	p	p	NOUN
ejpam-3831	53	31	,	,	PUNCT
ejpam-3831	53	32	q	q	ADJ
ejpam-3831	53	33	,	,	PUNCT
ejpam-3831	53	34	r	r	NOUN
ejpam-3831	53	35	∈	∈	NOUN
ejpam-3831	53	36	s	s	NOUN
ejpam-3831	53	37	with	with	ADP
ejpam-3831	53	38	q	q	PROPN
ejpam-3831	53	39	6=	6=	ADP
ejpam-3831	53	40	r	r	NOUN
ejpam-3831	53	41	;	;	PUNCT
ejpam-3831	53	42	g4	g4	NOUN
ejpam-3831	53	43	)	)	PUNCT
ejpam-3831	53	44	g(p	g(p	PROPN
ejpam-3831	53	45	,	,	PUNCT
ejpam-3831	53	46	q	q	NOUN
ejpam-3831	53	47	,	,	PUNCT
ejpam-3831	53	48	r	r	NOUN
ejpam-3831	53	49	)	)	PUNCT
ejpam-3831	53	50	=	=	NOUN
ejpam-3831	54	1	g(q	g(q	NOUN
ejpam-3831	54	2	,	,	PUNCT
ejpam-3831	54	3	r	r	NOUN
ejpam-3831	54	4	,	,	PUNCT
ejpam-3831	54	5	p	p	NOUN
ejpam-3831	54	6	)	)	PUNCT
ejpam-3831	54	7	=	=	SYM
ejpam-3831	54	8	g(r	g(r	PROPN
ejpam-3831	54	9	,	,	PUNCT
ejpam-3831	54	10	p	p	X
ejpam-3831	54	11	,	,	PUNCT
ejpam-3831	54	12	q	q	NOUN
ejpam-3831	54	13	)	)	PUNCT
ejpam-3831	54	14	=	=	SYM
ejpam-3831	54	15	·	·	PUNCT
ejpam-3831	54	16	·	·	PUNCT
ejpam-3831	54	17	·	·	PUNCT
ejpam-3831	54	18	(	(	PUNCT
ejpam-3831	54	19	symmetry	symmetry	NOUN
ejpam-3831	54	20	in	in	ADP
ejpam-3831	54	21	all	all	DET
ejpam-3831	54	22	three	three	NUM
ejpam-3831	54	23	variables	variable	NOUN
ejpam-3831	54	24	)	)	PUNCT
ejpam-3831	54	25	;	;	PUNCT
ejpam-3831	54	26	g5	g5	NOUN
ejpam-3831	54	27	)	)	PUNCT
ejpam-3831	54	28	g(p	g(p	PROPN
ejpam-3831	54	29	,	,	PUNCT
ejpam-3831	54	30	q	q	NOUN
ejpam-3831	54	31	,	,	PUNCT
ejpam-3831	54	32	r	r	NOUN
ejpam-3831	54	33	)	)	PUNCT
ejpam-3831	54	34	≤	≤	NOUN
ejpam-3831	54	35	g(p	g(p	PROPN
ejpam-3831	54	36	,	,	PUNCT
ejpam-3831	54	37	t	t	PROPN
ejpam-3831	54	38	,	,	PUNCT
ejpam-3831	54	39	t	t	PROPN
ejpam-3831	54	40	)	)	PUNCT
ejpam-3831	55	1	+	+	PROPN
ejpam-3831	55	2	g(t	g(t	PROPN
ejpam-3831	55	3	,	,	PUNCT
ejpam-3831	55	4	q	q	NOUN
ejpam-3831	55	5	,	,	PUNCT
ejpam-3831	55	6	r	r	NOUN
ejpam-3831	55	7	)	)	PUNCT
ejpam-3831	55	8	for	for	ADP
ejpam-3831	55	9	all	all	DET
ejpam-3831	55	10	p	p	NOUN
ejpam-3831	55	11	,	,	PUNCT
ejpam-3831	55	12	q	q	ADJ
ejpam-3831	55	13	,	,	PUNCT
ejpam-3831	55	14	r	r	NOUN
ejpam-3831	55	15	,	,	PUNCT
ejpam-3831	55	16	t	t	PROPN
ejpam-3831	55	17	∈	∈	PROPN
ejpam-3831	55	18	s.	s.	PROPN
ejpam-3831	55	19	then	then	ADV
ejpam-3831	55	20	g	g	PROPN
ejpam-3831	55	21	is	be	AUX
ejpam-3831	55	22	called	call	VERB
ejpam-3831	55	23	generalized	generalized	ADJ
ejpam-3831	55	24	metric	metric	ADJ
ejpam-3831	55	25	on	on	ADP
ejpam-3831	55	26	s	s	NOUN
ejpam-3831	55	27	,	,	PUNCT
ejpam-3831	55	28	and	and	CCONJ
ejpam-3831	55	29	the	the	DET
ejpam-3831	55	30	pair	pair	NOUN
ejpam-3831	55	31	(	(	PUNCT
ejpam-3831	55	32	s	s	X
ejpam-3831	55	33	,	,	PUNCT
ejpam-3831	55	34	g	g	NOUN
ejpam-3831	55	35	)	)	PUNCT
ejpam-3831	55	36	is	be	AUX
ejpam-3831	55	37	called	call	VERB
ejpam-3831	55	38	g	g	NOUN
ejpam-3831	55	39	-	-	PUNCT
ejpam-3831	55	40	metric	metric	ADJ
ejpam-3831	55	41	space	space	NOUN
ejpam-3831	55	42	.	.	PUNCT
ejpam-3831	56	1	definition	definition	NOUN
ejpam-3831	56	2	2	2	NUM
ejpam-3831	56	3	.	.	PUNCT
ejpam-3831	57	1	[	[	X
ejpam-3831	57	2	1	1	X
ejpam-3831	57	3	]	]	PUNCT
ejpam-3831	57	4	let	let	VERB
ejpam-3831	57	5	y	y	PROPN
ejpam-3831	57	6	6=	6=	PROPN
ejpam-3831	57	7	∅	∅	NOUN
ejpam-3831	57	8	and	and	CCONJ
ejpam-3831	57	9	s	s	PRON
ejpam-3831	57	10	≥	≥	NUM
ejpam-3831	57	11	1	1	NUM
ejpam-3831	57	12	be	be	AUX
ejpam-3831	57	13	a	a	DET
ejpam-3831	57	14	given	give	VERB
ejpam-3831	57	15	real	real	ADJ
ejpam-3831	57	16	number	number	NOUN
ejpam-3831	57	17	.	.	PUNCT
ejpam-3831	58	1	suppose	suppose	VERB
ejpam-3831	58	2	that	that	SCONJ
ejpam-3831	58	3	a	a	DET
ejpam-3831	58	4	mapping	mapping	NOUN
ejpam-3831	58	5	gb	gb	NOUN
ejpam-3831	58	6	:	:	PUNCT
ejpam-3831	58	7	y	y	PROPN
ejpam-3831	58	8	×	×	NOUN
ejpam-3831	58	9	y	y	PROPN
ejpam-3831	58	10	×	×	PROPN
ejpam-3831	58	11	y	y	PROPN
ejpam-3831	58	12	→	→	PUNCT
ejpam-3831	58	13	r+	r+	NOUN
ejpam-3831	58	14	satisfies	satisfie	NOUN
ejpam-3831	58	15	:	:	PUNCT
ejpam-3831	58	16	(	(	PUNCT
ejpam-3831	58	17	gb1	gb1	NOUN
ejpam-3831	58	18	)	)	PUNCT
ejpam-3831	58	19	gb(a	gb(a	PUNCT
ejpam-3831	58	20	,	,	PUNCT
ejpam-3831	58	21	b	b	NOUN
ejpam-3831	58	22	,	,	PUNCT
ejpam-3831	58	23	c	c	NOUN
ejpam-3831	58	24	)	)	PUNCT
ejpam-3831	58	25	=	=	SYM
ejpam-3831	58	26	0	0	PUNCT
ejpam-3831	59	1	if	if	SCONJ
ejpam-3831	59	2	a	a	DET
ejpam-3831	59	3	=	=	SYM
ejpam-3831	59	4	b	b	NOUN
ejpam-3831	59	5	=	=	SYM
ejpam-3831	59	6	c	c	PROPN
ejpam-3831	59	7	,	,	PUNCT
ejpam-3831	59	8	(	(	PUNCT
ejpam-3831	59	9	gb2	gb2	PROPN
ejpam-3831	59	10	)	)	PUNCT
ejpam-3831	59	11	gb(a	gb(a	PROPN
ejpam-3831	59	12	,	,	PUNCT
ejpam-3831	59	13	a	a	DET
ejpam-3831	59	14	,	,	PUNCT
ejpam-3831	59	15	b	b	NOUN
ejpam-3831	59	16	)	)	PUNCT
ejpam-3831	59	17	>	>	X
ejpam-3831	59	18	0	0	PUNCT
ejpam-3831	60	1	for	for	ADP
ejpam-3831	60	2	all	all	DET
ejpam-3831	60	3	a	a	PRON
ejpam-3831	60	4	,	,	PUNCT
ejpam-3831	60	5	b	b	X
ejpam-3831	60	6	∈	∈	PROPN
ejpam-3831	60	7	y	y	PROPN
ejpam-3831	60	8	with	with	ADP
ejpam-3831	60	9	a	a	DET
ejpam-3831	60	10	6=	6=	PROPN
ejpam-3831	60	11	b	b	PROPN
ejpam-3831	60	12	,	,	PUNCT
ejpam-3831	60	13	(	(	PUNCT
ejpam-3831	60	14	gb3	gb3	NOUN
ejpam-3831	60	15	)	)	PUNCT
ejpam-3831	60	16	gb(a	gb(a	NOUN
ejpam-3831	60	17	,	,	PUNCT
ejpam-3831	60	18	b	b	NOUN
ejpam-3831	60	19	,	,	PUNCT
ejpam-3831	60	20	b	b	NOUN
ejpam-3831	60	21	)	)	PUNCT
ejpam-3831	60	22	≤	≤	NOUN
ejpam-3831	60	23	gb(a	gb(a	NOUN
ejpam-3831	60	24	,	,	PUNCT
ejpam-3831	60	25	b	b	NOUN
ejpam-3831	60	26	,	,	PUNCT
ejpam-3831	60	27	c	c	NOUN
ejpam-3831	60	28	)	)	PUNCT
ejpam-3831	60	29	for	for	ADP
ejpam-3831	60	30	all	all	DET
ejpam-3831	60	31	a	a	DET
ejpam-3831	60	32	,	,	PUNCT
ejpam-3831	60	33	b	b	NOUN
ejpam-3831	60	34	,	,	PUNCT
ejpam-3831	60	35	c	c	PROPN
ejpam-3831	60	36	∈	∈	PROPN
ejpam-3831	60	37	y	y	PROPN
ejpam-3831	60	38	with	with	ADP
ejpam-3831	60	39	b	b	PROPN
ejpam-3831	60	40	6=	6=	ADP
ejpam-3831	60	41	c	c	PROPN
ejpam-3831	60	42	,	,	PUNCT
ejpam-3831	60	43	(	(	PUNCT
ejpam-3831	60	44	gb4	gb4	NOUN
ejpam-3831	60	45	)	)	PUNCT
ejpam-3831	60	46	gb(a	gb(a	NOUN
ejpam-3831	60	47	,	,	PUNCT
ejpam-3831	60	48	b	b	NOUN
ejpam-3831	60	49	,	,	PUNCT
ejpam-3831	60	50	c	c	NOUN
ejpam-3831	60	51	)	)	PUNCT
ejpam-3831	60	52	=	=	VERB
ejpam-3831	61	1	gb(p{a	gb(p{a	VERB
ejpam-3831	61	2	,	,	PUNCT
ejpam-3831	61	3	b	b	NOUN
ejpam-3831	61	4	,	,	PUNCT
ejpam-3831	61	5	c	c	NOUN
ejpam-3831	61	6	}	}	PUNCT
ejpam-3831	61	7	)	)	PUNCT
ejpam-3831	61	8	where	where	SCONJ
ejpam-3831	61	9	p	p	NOUN
ejpam-3831	61	10	is	be	AUX
ejpam-3831	61	11	a	a	DET
ejpam-3831	61	12	permutation	permutation	NOUN
ejpam-3831	61	13	of	of	ADP
ejpam-3831	61	14	a	a	DET
ejpam-3831	61	15	,	,	PUNCT
ejpam-3831	61	16	b	b	NOUN
ejpam-3831	61	17	,	,	PUNCT
ejpam-3831	61	18	c	c	PROPN
ejpam-3831	61	19	(	(	PUNCT
ejpam-3831	61	20	symmetry	symmetry	PROPN
ejpam-3831	61	21	)	)	PUNCT
ejpam-3831	61	22	(	(	PUNCT
ejpam-3831	61	23	gb5	gb5	NOUN
ejpam-3831	61	24	)	)	PUNCT
ejpam-3831	61	25	gb(a	gb(a	PROPN
ejpam-3831	61	26	,	,	PUNCT
ejpam-3831	61	27	b	b	NOUN
ejpam-3831	61	28	,	,	PUNCT
ejpam-3831	61	29	c	c	NOUN
ejpam-3831	61	30	)	)	PUNCT
ejpam-3831	61	31	≤	≤	NOUN
ejpam-3831	61	32	s(gb(a	s(gb(a	NOUN
ejpam-3831	61	33	,	,	PUNCT
ejpam-3831	61	34	u	u	NOUN
ejpam-3831	61	35	,	,	PUNCT
ejpam-3831	61	36	u	u	NOUN
ejpam-3831	61	37	)	)	PUNCT
ejpam-3831	61	38	+	+	ADV
ejpam-3831	61	39	gb(u	gb(u	NUM
ejpam-3831	61	40	,	,	PUNCT
ejpam-3831	61	41	b	b	NOUN
ejpam-3831	61	42	,	,	PUNCT
ejpam-3831	61	43	c	c	NOUN
ejpam-3831	61	44	)	)	PUNCT
ejpam-3831	61	45	)	)	PUNCT
ejpam-3831	61	46	for	for	ADP
ejpam-3831	61	47	all	all	DET
ejpam-3831	61	48	a	a	DET
ejpam-3831	61	49	,	,	PUNCT
ejpam-3831	61	50	b	b	NOUN
ejpam-3831	61	51	,	,	PUNCT
ejpam-3831	61	52	c	c	X
ejpam-3831	61	53	,	,	PUNCT
ejpam-3831	61	54	u	u	PROPN
ejpam-3831	61	55	∈	∈	PROPN
ejpam-3831	61	56	y	y	PROPN
ejpam-3831	61	57	.	.	PUNCT
ejpam-3831	62	1	then	then	ADV
ejpam-3831	62	2	gb	gb	PRON
ejpam-3831	62	3	is	be	AUX
ejpam-3831	62	4	called	call	VERB
ejpam-3831	62	5	gb	gb	ADV
ejpam-3831	62	6	-	-	PUNCT
ejpam-3831	62	7	metric	metric	ADJ
ejpam-3831	62	8	on	on	ADP
ejpam-3831	62	9	y	y	PROPN
ejpam-3831	62	10	,	,	PUNCT
ejpam-3831	62	11	and	and	CCONJ
ejpam-3831	62	12	the	the	DET
ejpam-3831	62	13	pair	pair	NOUN
ejpam-3831	62	14	(	(	PUNCT
ejpam-3831	62	15	y	y	NOUN
ejpam-3831	62	16	,	,	PUNCT
ejpam-3831	62	17	gb	gb	PROPN
ejpam-3831	62	18	)	)	PUNCT
ejpam-3831	62	19	is	be	AUX
ejpam-3831	62	20	called	call	VERB
ejpam-3831	62	21	gb	gb	ADV
ejpam-3831	62	22	-	-	PUNCT
ejpam-3831	62	23	metric	metric	ADJ
ejpam-3831	62	24	space	space	NOUN
ejpam-3831	62	25	.	.	PUNCT
ejpam-3831	63	1	if	if	SCONJ
ejpam-3831	63	2	s	s	NOUN
ejpam-3831	63	3	=	=	NOUN
ejpam-3831	63	4	1	1	NUM
ejpam-3831	63	5	,	,	PUNCT
ejpam-3831	63	6	then	then	ADV
ejpam-3831	63	7	gb	gb	PRON
ejpam-3831	63	8	reduce	reduce	VERB
ejpam-3831	63	9	to	to	ADP
ejpam-3831	63	10	g	g	NOUN
ejpam-3831	63	11	-	-	PUNCT
ejpam-3831	63	12	metric	metric	ADJ
ejpam-3831	63	13	space	space	NOUN
ejpam-3831	63	14	.	.	PUNCT
ejpam-3831	64	1	gb	gb	PRON
ejpam-3831	64	2	is	be	AUX
ejpam-3831	64	3	the	the	DET
ejpam-3831	64	4	generalization	generalization	NOUN
ejpam-3831	64	5	of	of	ADP
ejpam-3831	64	6	g	g	NOUN
ejpam-3831	64	7	-	-	PUNCT
ejpam-3831	64	8	metric	metric	ADJ
ejpam-3831	64	9	,	,	PUNCT
ejpam-3831	64	10	evidently	evidently	ADV
ejpam-3831	64	11	every	every	DET
ejpam-3831	64	12	g	g	NOUN
ejpam-3831	64	13	-	-	PUNCT
ejpam-3831	64	14	metric	metric	ADJ
ejpam-3831	64	15	is	be	AUX
ejpam-3831	64	16	a	a	DET
ejpam-3831	64	17	gb	gb	ADV
ejpam-3831	64	18	-	-	PUNCT
ejpam-3831	64	19	metric	metric	ADJ
ejpam-3831	64	20	.	.	PUNCT
ejpam-3831	65	1	remark	remark	NOUN
ejpam-3831	65	2	1	1	NUM
ejpam-3831	65	3	.	.	PUNCT
ejpam-3831	66	1	every	every	DET
ejpam-3831	66	2	g	g	NOUN
ejpam-3831	66	3	-	-	PUNCT
ejpam-3831	66	4	metric	metric	ADJ
ejpam-3831	66	5	space	space	NOUN
ejpam-3831	66	6	(	(	PUNCT
ejpam-3831	66	7	x	x	NOUN
ejpam-3831	66	8	,	,	PUNCT
ejpam-3831	66	9	g	g	NOUN
ejpam-3831	66	10	)	)	PUNCT
ejpam-3831	66	11	defines	define	VERB
ejpam-3831	66	12	a	a	DET
ejpam-3831	66	13	gb	gb	ADV
ejpam-3831	66	14	-	-	PUNCT
ejpam-3831	66	15	metric	metric	ADJ
ejpam-3831	66	16	space	space	NOUN
ejpam-3831	66	17	with	with	ADP
ejpam-3831	66	18	s	s	NOUN
ejpam-3831	66	19	=	=	SYM
ejpam-3831	66	20	2p−1	2p−1	NUM
ejpam-3831	66	21	by	by	ADP
ejpam-3831	66	22	gb(x	gb(x	PROPN
ejpam-3831	66	23	,	,	PUNCT
ejpam-3831	66	24	y	y	PROPN
ejpam-3831	66	25	,	,	PUNCT
ejpam-3831	66	26	z	z	NOUN
ejpam-3831	66	27	)	)	PUNCT
ejpam-3831	66	28	=	=	SYM
ejpam-3831	67	1	(	(	PUNCT
ejpam-3831	67	2	g(x	g(x	PROPN
ejpam-3831	67	3	,	,	PUNCT
ejpam-3831	67	4	y	y	PROPN
ejpam-3831	67	5	,	,	PUNCT
ejpam-3831	67	6	z))p	z))p	NOUN
ejpam-3831	67	7	,	,	PUNCT
ejpam-3831	67	8	where	where	SCONJ
ejpam-3831	67	9	p	p	NOUN
ejpam-3831	67	10	>	>	X
ejpam-3831	67	11	1	1	NUM
ejpam-3831	67	12	is	be	AUX
ejpam-3831	67	13	a	a	DET
ejpam-3831	67	14	real	real	ADJ
ejpam-3831	67	15	number	number	NOUN
ejpam-3831	67	16	.	.	PUNCT
ejpam-3831	68	1	further	far	ADV
ejpam-3831	68	2	every	every	DET
ejpam-3831	68	3	gb	gb	ADV
ejpam-3831	68	4	-	-	PUNCT
ejpam-3831	68	5	metric	metric	NOUN
ejpam-3831	68	6	is	be	AUX
ejpam-3831	68	7	a	a	DET
ejpam-3831	68	8	g	g	NOUN
ejpam-3831	68	9	-	-	PUNCT
ejpam-3831	68	10	metric	metric	ADJ
ejpam-3831	68	11	when	when	SCONJ
ejpam-3831	68	12	s	s	VERB
ejpam-3831	68	13	=	=	NOUN
ejpam-3831	68	14	1	1	NUM
ejpam-3831	68	15	,	,	PUNCT
ejpam-3831	68	16	but	but	CCONJ
ejpam-3831	68	17	,	,	PUNCT
ejpam-3831	68	18	in	in	ADP
ejpam-3831	68	19	general	general	ADJ
ejpam-3831	68	20	,	,	PUNCT
ejpam-3831	68	21	not	not	PART
ejpam-3831	68	22	every	every	DET
ejpam-3831	68	23	gb	gb	NOUN
ejpam-3831	68	24	-	-	PUNCT
ejpam-3831	68	25	metric	metric	NOUN
ejpam-3831	68	26	is	be	AUX
ejpam-3831	68	27	a	a	DET
ejpam-3831	68	28	g	g	NOUN
ejpam-3831	68	29	-	-	PUNCT
ejpam-3831	68	30	metric	metric	ADJ
ejpam-3831	68	31	,	,	PUNCT
ejpam-3831	68	32	for	for	ADP
ejpam-3831	68	33	example	example	NOUN
ejpam-3831	68	34	,	,	PUNCT
ejpam-3831	68	35	let	let	VERB
ejpam-3831	68	36	x	x	PUNCT
ejpam-3831	68	37	=	=	SYM
ejpam-3831	68	38	r	r	NOUN
ejpam-3831	68	39	and	and	CCONJ
ejpam-3831	68	40	the	the	DET
ejpam-3831	68	41	metric	metric	NOUN
ejpam-3831	68	42	gb	gb	NOUN
ejpam-3831	68	43	is	be	AUX
ejpam-3831	68	44	defined	define	VERB
ejpam-3831	68	45	by	by	ADP
ejpam-3831	68	46	gb(x	gb(x	PROPN
ejpam-3831	68	47	,	,	PUNCT
ejpam-3831	68	48	y	y	PROPN
ejpam-3831	68	49	,	,	PUNCT
ejpam-3831	68	50	z	z	NOUN
ejpam-3831	69	1	)	)	PUNCT
ejpam-3831	69	2	=	=	SYM
ejpam-3831	69	3	max	max	PROPN
ejpam-3831	69	4	{	{	PUNCT
ejpam-3831	69	5	|x−	|x−	PROPN
ejpam-3831	69	6	y|2	y|2	PROPN
ejpam-3831	69	7	,	,	PUNCT
ejpam-3831	69	8	|y	|y	ADJ
ejpam-3831	69	9	−	−	PROPN
ejpam-3831	69	10	z|2	z|2	PROPN
ejpam-3831	69	11	,	,	PUNCT
ejpam-3831	69	12	|z	|z	PROPN
ejpam-3831	69	13	−	−	PROPN
ejpam-3831	69	14	x|2	x|2	PROPN
ejpam-3831	69	15	}	}	PUNCT
ejpam-3831	69	16	,	,	PUNCT
ejpam-3831	69	17	for	for	ADP
ejpam-3831	69	18	all	all	DET
ejpam-3831	69	19	x	x	NOUN
ejpam-3831	69	20	,	,	PUNCT
ejpam-3831	69	21	y	y	PROPN
ejpam-3831	69	22	,	,	PUNCT
ejpam-3831	69	23	z	z	PROPN
ejpam-3831	69	24	∈	∈	PROPN
ejpam-3831	69	25	r.	r.	PROPN
ejpam-3831	69	26	then	then	ADV
ejpam-3831	69	27	gb	gb	PROPN
ejpam-3831	69	28	is	be	AUX
ejpam-3831	69	29	a	a	DET
ejpam-3831	69	30	gb	gb	NOUN
ejpam-3831	69	31	-	-	PUNCT
ejpam-3831	69	32	metric	metric	ADJ
ejpam-3831	69	33	on	on	ADP
ejpam-3831	69	34	r	r	NOUN
ejpam-3831	69	35	with	with	ADP
ejpam-3831	69	36	s	s	NOUN
ejpam-3831	69	37	=	=	SYM
ejpam-3831	69	38	22−1	22−1	NUM
ejpam-3831	69	39	=	=	SYM
ejpam-3831	69	40	2	2	NUM
ejpam-3831	69	41	,	,	PUNCT
ejpam-3831	69	42	but	but	CCONJ
ejpam-3831	69	43	it	it	PRON
ejpam-3831	69	44	is	be	AUX
ejpam-3831	69	45	not	not	PART
ejpam-3831	69	46	a	a	DET
ejpam-3831	69	47	g	g	NOUN
ejpam-3831	69	48	-	-	PUNCT
ejpam-3831	69	49	metric	metric	ADJ
ejpam-3831	69	50	on	on	ADP
ejpam-3831	69	51	r.	r.	PROPN
ejpam-3831	69	52	m.m.m	m.m.m	PROPN
ejpam-3831	69	53	.	.	PUNCT
ejpam-3831	70	1	jaradat	jaradat	PROPN
ejpam-3831	70	2	et	et	PROPN
ejpam-3831	70	3	al	al	PROPN
ejpam-3831	70	4	.	.	PUNCT
ejpam-3831	70	5	/	/	SYM
ejpam-3831	70	6	eur	eur	PROPN
ejpam-3831	70	7	.	.	PUNCT
ejpam-3831	71	1	j.	j.	PROPN
ejpam-3831	71	2	pure	pure	PROPN
ejpam-3831	71	3	appl	appl	PROPN
ejpam-3831	71	4	.	.	PROPN
ejpam-3831	71	5	math	math	PROPN
ejpam-3831	71	6	,	,	PUNCT
ejpam-3831	71	7	13	13	NUM
ejpam-3831	71	8	(	(	PUNCT
ejpam-3831	71	9	4	4	NUM
ejpam-3831	71	10	)	)	PUNCT
ejpam-3831	71	11	(	(	PUNCT
ejpam-3831	71	12	2020	2020	NUM
ejpam-3831	71	13	)	)	PUNCT
ejpam-3831	71	14	,	,	PUNCT
ejpam-3831	71	15	995	995	NUM
ejpam-3831	71	16	-	-	SYM
ejpam-3831	71	17	1015	1015	NUM
ejpam-3831	71	18	997	997	NUM
ejpam-3831	71	19	proposition	proposition	NOUN
ejpam-3831	71	20	1	1	NUM
ejpam-3831	71	21	.	.	PUNCT
ejpam-3831	72	1	[	[	X
ejpam-3831	72	2	1	1	X
ejpam-3831	72	3	]	]	AUX
ejpam-3831	72	4	let	let	VERB
ejpam-3831	72	5	x	x	PRON
ejpam-3831	72	6	be	be	AUX
ejpam-3831	72	7	a	a	DET
ejpam-3831	72	8	gb	gb	ADV
ejpam-3831	72	9	-	-	PUNCT
ejpam-3831	72	10	metric	metric	ADJ
ejpam-3831	72	11	space	space	NOUN
ejpam-3831	72	12	,	,	PUNCT
ejpam-3831	72	13	then	then	ADV
ejpam-3831	72	14	for	for	ADP
ejpam-3831	72	15	each	each	DET
ejpam-3831	72	16	x	x	PROPN
ejpam-3831	72	17	,	,	PUNCT
ejpam-3831	72	18	y	y	PROPN
ejpam-3831	72	19	,	,	PUNCT
ejpam-3831	72	20	z	z	PROPN
ejpam-3831	72	21	,	,	PUNCT
ejpam-3831	72	22	a	a	DET
ejpam-3831	72	23	∈	∈	NOUN
ejpam-3831	72	24	x	x	PUNCT
ejpam-3831	72	25	the	the	DET
ejpam-3831	72	26	following	follow	VERB
ejpam-3831	72	27	holds	hold	VERB
ejpam-3831	72	28	:	:	PUNCT
ejpam-3831	72	29	(	(	PUNCT
ejpam-3831	72	30	1	1	X
ejpam-3831	72	31	)	)	PUNCT
ejpam-3831	72	32	if	if	SCONJ
ejpam-3831	72	33	gb(x	gb(x	ADJ
ejpam-3831	72	34	,	,	PUNCT
ejpam-3831	72	35	y	y	PROPN
ejpam-3831	72	36	,	,	PUNCT
ejpam-3831	72	37	z	z	NOUN
ejpam-3831	72	38	)	)	PUNCT
ejpam-3831	72	39	=	=	SYM
ejpam-3831	73	1	0	0	PUNCT
ejpam-3831	74	1	then	then	ADV
ejpam-3831	74	2	x	x	X
ejpam-3831	74	3	=	=	SYM
ejpam-3831	74	4	y	y	PROPN
ejpam-3831	74	5	=	=	SYM
ejpam-3831	74	6	z.	z.	PROPN
ejpam-3831	74	7	(	(	PUNCT
ejpam-3831	74	8	2	2	NUM
ejpam-3831	74	9	)	)	PUNCT
ejpam-3831	74	10	g(x	g(x	NOUN
ejpam-3831	74	11	,	,	PUNCT
ejpam-3831	74	12	y	y	PROPN
ejpam-3831	74	13	,	,	PUNCT
ejpam-3831	74	14	z	z	NOUN
ejpam-3831	74	15	)	)	PUNCT
ejpam-3831	74	16	≤	≤	NOUN
ejpam-3831	74	17	s(gb(x	s(gb(x	PROPN
ejpam-3831	74	18	,	,	PUNCT
ejpam-3831	74	19	x	x	NOUN
ejpam-3831	74	20	,	,	PUNCT
ejpam-3831	74	21	y	y	PROPN
ejpam-3831	74	22	)	)	PUNCT
ejpam-3831	75	1	+	+	ADV
ejpam-3831	75	2	gb(x	gb(x	ADJ
ejpam-3831	75	3	,	,	PUNCT
ejpam-3831	75	4	x	x	NOUN
ejpam-3831	75	5	,	,	PUNCT
ejpam-3831	75	6	z	z	NOUN
ejpam-3831	75	7	)	)	PUNCT
ejpam-3831	75	8	)	)	PUNCT
ejpam-3831	75	9	.	.	PUNCT
ejpam-3831	76	1	(	(	PUNCT
ejpam-3831	76	2	3	3	X
ejpam-3831	76	3	)	)	PUNCT
ejpam-3831	76	4	gb(x	gb(x	PROPN
ejpam-3831	76	5	,	,	PUNCT
ejpam-3831	76	6	y	y	PROPN
ejpam-3831	76	7	,	,	PUNCT
ejpam-3831	76	8	y	y	NOUN
ejpam-3831	76	9	)	)	PUNCT
ejpam-3831	76	10	≤	≤	NOUN
ejpam-3831	77	1	2sgb(y	2sgb(y	NUM
ejpam-3831	77	2	,	,	PUNCT
ejpam-3831	77	3	x	x	X
ejpam-3831	77	4	,	,	PUNCT
ejpam-3831	77	5	x	x	NOUN
ejpam-3831	77	6	)	)	PUNCT
ejpam-3831	77	7	.	.	PUNCT
ejpam-3831	78	1	(	(	PUNCT
ejpam-3831	78	2	4	4	X
ejpam-3831	78	3	)	)	PUNCT
ejpam-3831	78	4	gb(x	gb(x	PROPN
ejpam-3831	78	5	,	,	PUNCT
ejpam-3831	78	6	y	y	PROPN
ejpam-3831	78	7	,	,	PUNCT
ejpam-3831	78	8	z	z	NOUN
ejpam-3831	78	9	)	)	PUNCT
ejpam-3831	78	10	≤	≤	PUNCT
ejpam-3831	79	1	s(g(x	s(g(x	PROPN
ejpam-3831	79	2	,	,	PUNCT
ejpam-3831	79	3	a	a	DET
ejpam-3831	79	4	,	,	PUNCT
ejpam-3831	79	5	z	z	NOUN
ejpam-3831	79	6	)	)	PUNCT
ejpam-3831	79	7	+	+	PROPN
ejpam-3831	79	8	g(a	g(a	PROPN
ejpam-3831	79	9	,	,	PUNCT
ejpam-3831	79	10	y	y	PROPN
ejpam-3831	79	11	,	,	PUNCT
ejpam-3831	79	12	z	z	NOUN
ejpam-3831	79	13	)	)	PUNCT
ejpam-3831	79	14	)	)	PUNCT
ejpam-3831	79	15	.	.	PUNCT
ejpam-3831	80	1	definition	definition	NOUN
ejpam-3831	80	2	3	3	NUM
ejpam-3831	80	3	.	.	PUNCT
ejpam-3831	81	1	[	[	X
ejpam-3831	81	2	1	1	X
ejpam-3831	81	3	]	]	PUNCT
ejpam-3831	81	4	let	let	VERB
ejpam-3831	81	5	x	x	SYM
ejpam-3831	81	6	′	′	PRON
ejpam-3831	81	7	be	be	AUX
ejpam-3831	81	8	a	a	DET
ejpam-3831	81	9	gb	gb	ADV
ejpam-3831	81	10	-	-	PUNCT
ejpam-3831	81	11	metric	metric	ADJ
ejpam-3831	81	12	space	space	NOUN
ejpam-3831	81	13	.	.	PUNCT
ejpam-3831	82	1	a	a	DET
ejpam-3831	82	2	sequence	sequence	NOUN
ejpam-3831	82	3	{	{	PUNCT
ejpam-3831	82	4	x′n	x′n	NOUN
ejpam-3831	82	5	}	}	PUNCT
ejpam-3831	82	6	in	in	ADP
ejpam-3831	82	7	x	x	VERB
ejpam-3831	82	8	is	be	AUX
ejpam-3831	82	9	said	say	VERB
ejpam-3831	82	10	to	to	PART
ejpam-3831	82	11	be	be	AUX
ejpam-3831	82	12	:	:	PUNCT
ejpam-3831	82	13	(	(	PUNCT
ejpam-3831	82	14	1	1	X
ejpam-3831	82	15	)	)	PUNCT
ejpam-3831	82	16	gb	gb	NOUN
ejpam-3831	82	17	-	-	PUNCT
ejpam-3831	82	18	cauchy	cauchy	ADJ
ejpam-3831	82	19	sequence	sequence	NOUN
ejpam-3831	82	20	if	if	SCONJ
ejpam-3831	82	21	,	,	PUNCT
ejpam-3831	82	22	for	for	ADP
ejpam-3831	82	23	each	each	DET
ejpam-3831	82	24	ε	ε	PROPN
ejpam-3831	82	25	>	>	X
ejpam-3831	82	26	0	0	PUNCT
ejpam-3831	83	1	there	there	PRON
ejpam-3831	83	2	exists	exist	VERB
ejpam-3831	83	3	n0	n0	PROPN
ejpam-3831	83	4	∈	∈	PROPN
ejpam-3831	83	5	z+	z+	NUM
ejpam-3831	83	6	such	such	ADJ
ejpam-3831	83	7	that	that	PRON
ejpam-3831	83	8	for	for	ADP
ejpam-3831	83	9	all	all	DET
ejpam-3831	83	10	m	m	PROPN
ejpam-3831	83	11	,	,	PUNCT
ejpam-3831	83	12	n	n	CCONJ
ejpam-3831	83	13	,	,	PUNCT
ejpam-3831	83	14	l	l	PROPN
ejpam-3831	83	15	≥	≥	NUM
ejpam-3831	83	16	n0	n0	NUM
ejpam-3831	83	17	,	,	PUNCT
ejpam-3831	83	18	gb(xn	gb(xn	PROPN
ejpam-3831	83	19	,	,	PUNCT
ejpam-3831	83	20	xm	xm	PROPN
ejpam-3831	83	21	,	,	PUNCT
ejpam-3831	83	22	xl	xl	PROPN
ejpam-3831	83	23	)	)	PUNCT
ejpam-3831	83	24	<	<	X
ejpam-3831	83	25	ε	ε	PROPN
ejpam-3831	83	26	.	.	PUNCT
ejpam-3831	84	1	(	(	PUNCT
ejpam-3831	84	2	2	2	X
ejpam-3831	84	3	)	)	PUNCT
ejpam-3831	84	4	gb	gb	NOUN
ejpam-3831	84	5	-	-	PUNCT
ejpam-3831	84	6	convergent	convergent	NOUN
ejpam-3831	84	7	to	to	ADP
ejpam-3831	84	8	a	a	DET
ejpam-3831	84	9	point	point	NOUN
ejpam-3831	84	10	x	x	SYM
ejpam-3831	84	11	∈	∈	NOUN
ejpam-3831	84	12	x	x	INTJ
ejpam-3831	84	13	if	if	SCONJ
ejpam-3831	84	14	for	for	ADP
ejpam-3831	84	15	each	each	DET
ejpam-3831	84	16	ε	ε	PROPN
ejpam-3831	84	17	>	>	X
ejpam-3831	84	18	0	0	PROPN
ejpam-3831	84	19	,	,	PUNCT
ejpam-3831	84	20	there	there	PRON
ejpam-3831	84	21	exists	exist	VERB
ejpam-3831	84	22	n0	n0	PROPN
ejpam-3831	84	23	∈	∈	PROPN
ejpam-3831	84	24	z+	z+	NUM
ejpam-3831	84	25	such	such	ADJ
ejpam-3831	84	26	that	that	SCONJ
ejpam-3831	84	27	,	,	PUNCT
ejpam-3831	84	28	for	for	ADP
ejpam-3831	84	29	all	all	DET
ejpam-3831	84	30	m	m	PROPN
ejpam-3831	84	31	,	,	PUNCT
ejpam-3831	84	32	n	n	PRON
ejpam-3831	84	33	≥	≥	NOUN
ejpam-3831	84	34	n0	n0	NUM
ejpam-3831	84	35	,	,	PUNCT
ejpam-3831	84	36	gb(xn	gb(xn	PROPN
ejpam-3831	84	37	,	,	PUNCT
ejpam-3831	84	38	xm	xm	PROPN
ejpam-3831	84	39	,	,	PUNCT
ejpam-3831	84	40	x	x	X
ejpam-3831	84	41	)	)	PUNCT
ejpam-3831	84	42	<	<	X
ejpam-3831	84	43	ε	ε	PROPN
ejpam-3831	84	44	.	.	PUNCT
ejpam-3831	84	45	proposition	proposition	NOUN
ejpam-3831	84	46	2	2	NUM
ejpam-3831	84	47	.	.	PUNCT
ejpam-3831	85	1	[	[	X
ejpam-3831	85	2	1	1	X
ejpam-3831	85	3	]	]	AUX
ejpam-3831	85	4	let	let	VERB
ejpam-3831	85	5	x	x	PRON
ejpam-3831	85	6	be	be	AUX
ejpam-3831	85	7	a	a	DET
ejpam-3831	85	8	gb	gb	ADV
ejpam-3831	85	9	-	-	PUNCT
ejpam-3831	85	10	metric	metric	ADJ
ejpam-3831	85	11	space	space	NOUN
ejpam-3831	85	12	,	,	PUNCT
ejpam-3831	85	13	then	then	ADV
ejpam-3831	85	14	the	the	DET
ejpam-3831	85	15	following	following	NOUN
ejpam-3831	85	16	are	be	AUX
ejpam-3831	85	17	equivalent	equivalent	ADJ
ejpam-3831	85	18	:	:	PUNCT
ejpam-3831	85	19	(	(	PUNCT
ejpam-3831	85	20	1	1	X
ejpam-3831	85	21	)	)	PUNCT
ejpam-3831	85	22	the	the	DET
ejpam-3831	85	23	sequence	sequence	NOUN
ejpam-3831	85	24	xn	xn	PROPN
ejpam-3831	85	25	is	be	AUX
ejpam-3831	85	26	gb	gb	NOUN
ejpam-3831	85	27	-	-	PUNCT
ejpam-3831	85	28	cauchy	cauchy	NOUN
ejpam-3831	85	29	.	.	PUNCT
ejpam-3831	86	1	(	(	PUNCT
ejpam-3831	86	2	2	2	X
ejpam-3831	86	3	)	)	PUNCT
ejpam-3831	86	4	for	for	ADP
ejpam-3831	86	5	any	any	DET
ejpam-3831	86	6	ε	ε	PROPN
ejpam-3831	86	7	>	>	X
ejpam-3831	86	8	0	0	PROPN
ejpam-3831	86	9	,	,	PUNCT
ejpam-3831	86	10	there	there	PRON
ejpam-3831	86	11	exists	exist	VERB
ejpam-3831	86	12	n0	n0	PROPN
ejpam-3831	86	13	∈	∈	PROPN
ejpam-3831	86	14	n	n	PRON
ejpam-3831	87	1	such	such	ADJ
ejpam-3831	87	2	that	that	SCONJ
ejpam-3831	87	3	g(xn	g(xn	NOUN
ejpam-3831	87	4	,	,	PUNCT
ejpam-3831	87	5	xm	xm	PROPN
ejpam-3831	87	6	,	,	PUNCT
ejpam-3831	87	7	xm	xm	PROPN
ejpam-3831	87	8	)	)	PUNCT
ejpam-3831	87	9	<	<	X
ejpam-3831	87	10	ε	ε	PROPN
ejpam-3831	87	11	,	,	PUNCT
ejpam-3831	87	12	for	for	ADP
ejpam-3831	87	13	all	all	DET
ejpam-3831	87	14	m	m	PROPN
ejpam-3831	87	15	,	,	PUNCT
ejpam-3831	87	16	n	n	PRON
ejpam-3831	87	17	≥	≥	NOUN
ejpam-3831	87	18	n0	n0	NUM
ejpam-3831	87	19	.	.	PUNCT
ejpam-3831	87	20	proposition	proposition	NOUN
ejpam-3831	87	21	3	3	NUM
ejpam-3831	87	22	.	.	PUNCT
ejpam-3831	88	1	[	[	X
ejpam-3831	88	2	1	1	X
ejpam-3831	88	3	]	]	X
ejpam-3831	88	4	the	the	DET
ejpam-3831	88	5	following	follow	VERB
ejpam-3831	88	6	are	be	AUX
ejpam-3831	88	7	equivalent	equivalent	ADJ
ejpam-3831	88	8	in	in	ADP
ejpam-3831	88	9	(	(	PUNCT
ejpam-3831	88	10	x	x	NOUN
ejpam-3831	88	11	,	,	PUNCT
ejpam-3831	88	12	gb	gb	NOUN
ejpam-3831	88	13	)	)	PUNCT
ejpam-3831	88	14	metric	metric	ADJ
ejpam-3831	88	15	spaces	space	NOUN
ejpam-3831	88	16	:	:	PUNCT
ejpam-3831	88	17	(	(	PUNCT
ejpam-3831	88	18	a1	a1	NOUN
ejpam-3831	88	19	)	)	PUNCT
ejpam-3831	88	20	{	{	PUNCT
ejpam-3831	88	21	xn	xn	X
ejpam-3831	88	22	}	}	PUNCT
ejpam-3831	88	23	is	be	AUX
ejpam-3831	88	24	gb	gb	NOUN
ejpam-3831	88	25	-	-	PUNCT
ejpam-3831	88	26	convergent	convergent	NOUN
ejpam-3831	88	27	to	to	PART
ejpam-3831	88	28	x.	x.	PROPN
ejpam-3831	88	29	(	(	PUNCT
ejpam-3831	88	30	a2	a2	PROPN
ejpam-3831	88	31	)	)	PUNCT
ejpam-3831	88	32	gb(xn	gb(xn	PROPN
ejpam-3831	88	33	,	,	PUNCT
ejpam-3831	88	34	xn	xn	PROPN
ejpam-3831	88	35	,	,	PUNCT
ejpam-3831	88	36	x)→	x)→	PROPN
ejpam-3831	88	37	0	0	PUNCT
ejpam-3831	88	38	as	as	ADP
ejpam-3831	88	39	n→	n→	ADV
ejpam-3831	88	40	+	+	PROPN
ejpam-3831	88	41	∞.	∞.	PROPN
ejpam-3831	88	42	(	(	PUNCT
ejpam-3831	88	43	a3	a3	NOUN
ejpam-3831	88	44	)	)	PUNCT
ejpam-3831	88	45	gb(xnx	gb(xnx	NOUN
ejpam-3831	88	46	,	,	PUNCT
ejpam-3831	88	47	x)→	x)→	PROPN
ejpam-3831	88	48	0	0	PUNCT
ejpam-3831	88	49	as	as	ADP
ejpam-3831	88	50	n→	n→	ADV
ejpam-3831	89	1	+	+	ADJ
ejpam-3831	89	2	∞.	∞.	PROPN
ejpam-3831	89	3	definition	definition	NOUN
ejpam-3831	89	4	4	4	NUM
ejpam-3831	89	5	.	.	PUNCT
ejpam-3831	90	1	[	[	X
ejpam-3831	90	2	1	1	X
ejpam-3831	90	3	]	]	PUNCT
ejpam-3831	90	4	a	a	DET
ejpam-3831	90	5	gb	gb	ADV
ejpam-3831	90	6	-	-	PUNCT
ejpam-3831	90	7	metric	metric	ADJ
ejpam-3831	90	8	space	space	NOUN
ejpam-3831	90	9	x	x	PUNCT
ejpam-3831	90	10	is	be	AUX
ejpam-3831	90	11	called	call	VERB
ejpam-3831	90	12	gb	gb	ADV
ejpam-3831	90	13	-	-	PUNCT
ejpam-3831	90	14	complete	complete	ADJ
ejpam-3831	90	15	if	if	SCONJ
ejpam-3831	90	16	every	every	DET
ejpam-3831	90	17	gb	gb	NOUN
ejpam-3831	90	18	-	-	PUNCT
ejpam-3831	90	19	cauchy	cauchy	ADJ
ejpam-3831	90	20	sequence	sequence	NOUN
ejpam-3831	90	21	is	be	AUX
ejpam-3831	90	22	gb	gb	NOUN
ejpam-3831	90	23	-	-	PUNCT
ejpam-3831	90	24	convergent	convergent	NOUN
ejpam-3831	90	25	in	in	ADP
ejpam-3831	90	26	x.	x.	NOUN
ejpam-3831	90	27	definition	definition	NOUN
ejpam-3831	90	28	5	5	NUM
ejpam-3831	90	29	.	.	PUNCT
ejpam-3831	91	1	[	[	X
ejpam-3831	91	2	5	5	NUM
ejpam-3831	91	3	]	]	PUNCT
ejpam-3831	91	4	let	let	VERB
ejpam-3831	91	5	m	m	PRON
ejpam-3831	91	6	′	′	AUX
ejpam-3831	91	7	be	be	AUX
ejpam-3831	91	8	a	a	DET
ejpam-3831	91	9	metric	metric	ADJ
ejpam-3831	91	10	space	space	NOUN
ejpam-3831	91	11	and	and	CCONJ
ejpam-3831	91	12	let	let	VERB
ejpam-3831	91	13	f	f	PRON
ejpam-3831	91	14	:	:	PUNCT
ejpam-3831	91	15	m	m	VERB
ejpam-3831	91	16	×	×	NOUN
ejpam-3831	91	17	m	m	INTJ
ejpam-3831	91	18	→	→	VERB
ejpam-3831	91	19	m	m	AUX
ejpam-3831	91	20	be	be	AUX
ejpam-3831	91	21	a	a	DET
ejpam-3831	91	22	function	function	NOUN
ejpam-3831	91	23	.	.	PUNCT
ejpam-3831	92	1	an	an	DET
ejpam-3831	92	2	element	element	NOUN
ejpam-3831	92	3	(	(	PUNCT
ejpam-3831	92	4	m	m	PROPN
ejpam-3831	92	5	,	,	PUNCT
ejpam-3831	92	6	n	n	CCONJ
ejpam-3831	92	7	)	)	PUNCT
ejpam-3831	92	8	∈	∈	PROPN
ejpam-3831	92	9	m	m	VERB
ejpam-3831	92	10	×	×	NOUN
ejpam-3831	92	11	m	m	VERB
ejpam-3831	92	12	is	be	AUX
ejpam-3831	92	13	said	say	VERB
ejpam-3831	92	14	to	to	PART
ejpam-3831	92	15	be	be	AUX
ejpam-3831	92	16	a	a	DET
ejpam-3831	92	17	coupled	couple	VERB
ejpam-3831	92	18	fixed	fix	VERB
ejpam-3831	92	19	point	point	NOUN
ejpam-3831	92	20	of	of	ADP
ejpam-3831	92	21	the	the	DET
ejpam-3831	92	22	mapping	mapping	NOUN
ejpam-3831	92	23	f	f	NOUN
ejpam-3831	93	1	if	if	SCONJ
ejpam-3831	93	2	f	f	PROPN
ejpam-3831	93	3	(	(	PUNCT
ejpam-3831	93	4	m	m	PROPN
ejpam-3831	93	5	,	,	PUNCT
ejpam-3831	93	6	n	n	CCONJ
ejpam-3831	93	7	)	)	PUNCT
ejpam-3831	93	8	=	=	SYM
ejpam-3831	93	9	m	m	PROPN
ejpam-3831	93	10	,	,	PUNCT
ejpam-3831	93	11	f	f	PROPN
ejpam-3831	93	12	(	(	PUNCT
ejpam-3831	93	13	n	n	CCONJ
ejpam-3831	93	14	,	,	PUNCT
ejpam-3831	93	15	m	m	NOUN
ejpam-3831	93	16	)	)	PUNCT
ejpam-3831	93	17	=	=	SYM
ejpam-3831	93	18	n.	n.	NOUN
ejpam-3831	93	19	2	2	NUM
ejpam-3831	93	20	.	.	PUNCT
ejpam-3831	93	21	main	main	ADJ
ejpam-3831	93	22	result	result	NOUN
ejpam-3831	93	23	throughout	throughout	ADP
ejpam-3831	93	24	the	the	DET
ejpam-3831	93	25	paper	paper	NOUN
ejpam-3831	93	26	we	we	PRON
ejpam-3831	93	27	will	will	AUX
ejpam-3831	93	28	use	use	VERB
ejpam-3831	93	29	the	the	DET
ejpam-3831	93	30	following	following	ADJ
ejpam-3831	93	31	generalized	generalized	ADJ
ejpam-3831	93	32	contraction	contraction	NOUN
ejpam-3831	93	33	.	.	PUNCT
ejpam-3831	94	1	assume	assume	VERB
ejpam-3831	94	2	that	that	SCONJ
ejpam-3831	94	3	(	(	PUNCT
ejpam-3831	94	4	x	x	NOUN
ejpam-3831	94	5	,	,	PUNCT
ejpam-3831	94	6	gb	gb	PRON
ejpam-3831	94	7	)	)	PUNCT
ejpam-3831	94	8	is	be	AUX
ejpam-3831	94	9	generalized	generalize	VERB
ejpam-3831	94	10	gb	gb	ADV
ejpam-3831	94	11	-	-	PUNCT
ejpam-3831	94	12	metric	metric	ADJ
ejpam-3831	94	13	space	space	NOUN
ejpam-3831	94	14	.	.	PUNCT
ejpam-3831	95	1	the	the	DET
ejpam-3831	95	2	mappings	mapping	NOUN
ejpam-3831	95	3	f	f	X
ejpam-3831	95	4	,	,	PUNCT
ejpam-3831	95	5	h	h	NOUN
ejpam-3831	95	6	,	,	PUNCT
ejpam-3831	95	7	t	t	NOUN
ejpam-3831	95	8	:	:	PUNCT
ejpam-3831	95	9	x	x	PROPN
ejpam-3831	95	10	×x	×x	X
ejpam-3831	95	11	→	→	SYM
ejpam-3831	95	12	x	x	X
ejpam-3831	95	13	are	be	AUX
ejpam-3831	95	14	said	say	VERB
ejpam-3831	95	15	to	to	PART
ejpam-3831	95	16	satisfy	satisfy	VERB
ejpam-3831	95	17	the	the	DET
ejpam-3831	95	18	generalized	generalized	ADJ
ejpam-3831	95	19	contraction	contraction	NOUN
ejpam-3831	95	20	if	if	SCONJ
ejpam-3831	95	21	for	for	ADP
ejpam-3831	95	22	a	a	DET
ejpam-3831	95	23	,	,	PUNCT
ejpam-3831	95	24	b	b	PROPN
ejpam-3831	95	25	,	,	PUNCT
ejpam-3831	95	26	u	u	NOUN
ejpam-3831	95	27	,	,	PUNCT
ejpam-3831	95	28	v	v	NOUN
ejpam-3831	95	29	,	,	PUNCT
ejpam-3831	95	30	x	x	PRON
ejpam-3831	95	31	,	,	PUNCT
ejpam-3831	95	32	y	y	PROPN
ejpam-3831	95	33	∈	∈	PROPN
ejpam-3831	95	34	x	x	X
ejpam-3831	95	35	gb	gb	PROPN
ejpam-3831	95	36	(	(	PUNCT
ejpam-3831	95	37	f	f	X
ejpam-3831	95	38	(	(	PUNCT
ejpam-3831	95	39	a	a	DET
ejpam-3831	95	40	,	,	PUNCT
ejpam-3831	95	41	b	b	NOUN
ejpam-3831	95	42	)	)	PUNCT
ejpam-3831	95	43	,	,	PUNCT
ejpam-3831	95	44	h(u	h(u	PROPN
ejpam-3831	95	45	,	,	PUNCT
ejpam-3831	95	46	v	v	NOUN
ejpam-3831	95	47	)	)	PUNCT
ejpam-3831	95	48	,	,	PUNCT
ejpam-3831	95	49	t	t	PROPN
ejpam-3831	95	50	(	(	PUNCT
ejpam-3831	95	51	x	x	PROPN
ejpam-3831	95	52	,	,	PUNCT
ejpam-3831	95	53	y	y	PROPN
ejpam-3831	95	54	)	)	PUNCT
ejpam-3831	95	55	)	)	PUNCT
ejpam-3831	96	1	≤	≤	PUNCT
ejpam-3831	96	2	n	n	CCONJ
ejpam-3831	96	3	(	(	PUNCT
ejpam-3831	96	4	a	a	PRON
ejpam-3831	96	5	,	,	PUNCT
ejpam-3831	96	6	b	b	PROPN
ejpam-3831	96	7	,	,	PUNCT
ejpam-3831	96	8	u	u	NOUN
ejpam-3831	96	9	,	,	PUNCT
ejpam-3831	96	10	v	v	NOUN
ejpam-3831	96	11	,	,	PUNCT
ejpam-3831	96	12	x	x	NOUN
ejpam-3831	96	13	,	,	PUNCT
ejpam-3831	96	14	y	y	PROPN
ejpam-3831	96	15	)	)	PUNCT
ejpam-3831	96	16	,	,	PUNCT
ejpam-3831	96	17	where	where	SCONJ
ejpam-3831	96	18	n	n	X
ejpam-3831	96	19	(	(	PUNCT
ejpam-3831	96	20	a	a	PRON
ejpam-3831	96	21	,	,	PUNCT
ejpam-3831	96	22	b	b	PROPN
ejpam-3831	96	23	,	,	PUNCT
ejpam-3831	96	24	u	u	NOUN
ejpam-3831	96	25	,	,	PUNCT
ejpam-3831	96	26	v	v	NOUN
ejpam-3831	96	27	,	,	PUNCT
ejpam-3831	96	28	x	x	NOUN
ejpam-3831	96	29	,	,	PUNCT
ejpam-3831	96	30	y	y	NOUN
ejpam-3831	96	31	)	)	PUNCT
ejpam-3831	96	32	=	=	SYM
ejpam-3831	97	1	α1(a	α1(a	NUM
ejpam-3831	97	2	,	,	PUNCT
ejpam-3831	97	3	u	u	NOUN
ejpam-3831	97	4	)	)	PUNCT
ejpam-3831	97	5	·	·	PUNCT
ejpam-3831	98	1	gb(a	gb(a	X
ejpam-3831	98	2	,	,	PUNCT
ejpam-3831	98	3	u	u	NOUN
ejpam-3831	98	4	,	,	PUNCT
ejpam-3831	98	5	x	x	X
ejpam-3831	98	6	)	)	PUNCT
ejpam-3831	98	7	+	+	ADJ
ejpam-3831	98	8	gb(b	gb(b	NOUN
ejpam-3831	98	9	,	,	PUNCT
ejpam-3831	98	10	v	v	NOUN
ejpam-3831	98	11	,	,	PUNCT
ejpam-3831	98	12	y	y	NOUN
ejpam-3831	98	13	)	)	PUNCT
ejpam-3831	98	14	2	2	NUM
ejpam-3831	99	1	+	+	PROPN
ejpam-3831	99	2	α2(a	α2(a	PROPN
ejpam-3831	99	3	,	,	PUNCT
ejpam-3831	99	4	u	u	NOUN
ejpam-3831	99	5	)	)	PUNCT
ejpam-3831	99	6	gb	gb	ADP
ejpam-3831	99	7	(	(	PUNCT
ejpam-3831	99	8	f	f	X
ejpam-3831	99	9	(	(	PUNCT
ejpam-3831	99	10	a	a	DET
ejpam-3831	99	11	,	,	PUNCT
ejpam-3831	99	12	b	b	NOUN
ejpam-3831	99	13	)	)	PUNCT
ejpam-3831	99	14	,	,	PUNCT
ejpam-3831	99	15	h(u	h(u	PROPN
ejpam-3831	99	16	,	,	PUNCT
ejpam-3831	99	17	v	v	NOUN
ejpam-3831	99	18	)	)	PUNCT
ejpam-3831	99	19	,	,	PUNCT
ejpam-3831	99	20	t	t	PROPN
ejpam-3831	99	21	(	(	PUNCT
ejpam-3831	99	22	x	x	PROPN
ejpam-3831	99	23	,	,	PUNCT
ejpam-3831	99	24	y	y	NOUN
ejpam-3831	99	25	)	)	PUNCT
ejpam-3831	99	26	)	)	PUNCT
ejpam-3831	99	27	gb(a	gb(a	X
ejpam-3831	99	28	,	,	PUNCT
ejpam-3831	99	29	u	u	NOUN
ejpam-3831	99	30	,	,	PUNCT
ejpam-3831	99	31	x	x	NOUN
ejpam-3831	99	32	)	)	PUNCT
ejpam-3831	99	33	ωs(a	ωs(a	NUM
ejpam-3831	99	34	,	,	PUNCT
ejpam-3831	99	35	u	u	NOUN
ejpam-3831	99	36	,	,	PUNCT
ejpam-3831	99	37	x	x	X
ejpam-3831	99	38	,	,	PUNCT
ejpam-3831	99	39	b	b	PROPN
ejpam-3831	99	40	,	,	PUNCT
ejpam-3831	99	41	v	v	NOUN
ejpam-3831	99	42	,	,	PUNCT
ejpam-3831	99	43	y	y	NOUN
ejpam-3831	99	44	)	)	PUNCT
ejpam-3831	99	45	+	+	NOUN
ejpam-3831	99	46	α3(a	α3(a	NUM
ejpam-3831	99	47	,	,	PUNCT
ejpam-3831	99	48	u	u	NOUN
ejpam-3831	99	49	)	)	PUNCT
ejpam-3831	99	50	gb	gb	ADP
ejpam-3831	99	51	(	(	PUNCT
ejpam-3831	99	52	f	f	X
ejpam-3831	99	53	(	(	PUNCT
ejpam-3831	99	54	a	a	DET
ejpam-3831	99	55	,	,	PUNCT
ejpam-3831	99	56	b	b	NOUN
ejpam-3831	99	57	)	)	PUNCT
ejpam-3831	99	58	,	,	PUNCT
ejpam-3831	99	59	h(u	h(u	PROPN
ejpam-3831	99	60	,	,	PUNCT
ejpam-3831	99	61	v	v	NOUN
ejpam-3831	99	62	)	)	PUNCT
ejpam-3831	99	63	,	,	PUNCT
ejpam-3831	99	64	t	t	PROPN
ejpam-3831	99	65	(	(	PUNCT
ejpam-3831	99	66	x	x	PROPN
ejpam-3831	99	67	,	,	PUNCT
ejpam-3831	99	68	y	y	NOUN
ejpam-3831	99	69	)	)	PUNCT
ejpam-3831	99	70	)	)	PUNCT
ejpam-3831	100	1	gb(b	gb(b	X
ejpam-3831	100	2	,	,	PUNCT
ejpam-3831	100	3	v	v	NOUN
ejpam-3831	100	4	,	,	PUNCT
ejpam-3831	100	5	y	y	NOUN
ejpam-3831	100	6	)	)	PUNCT
ejpam-3831	100	7	ωs(a	ωs(a	NUM
ejpam-3831	100	8	,	,	PUNCT
ejpam-3831	100	9	u	u	NOUN
ejpam-3831	100	10	,	,	PUNCT
ejpam-3831	100	11	x	x	X
ejpam-3831	100	12	,	,	PUNCT
ejpam-3831	100	13	b	b	PROPN
ejpam-3831	100	14	,	,	PUNCT
ejpam-3831	100	15	v	v	NOUN
ejpam-3831	100	16	,	,	PUNCT
ejpam-3831	100	17	y	y	NOUN
ejpam-3831	100	18	)	)	PUNCT
ejpam-3831	100	19	m.m.m	m.m.m	NOUN
ejpam-3831	100	20	.	.	PUNCT
ejpam-3831	101	1	jaradat	jaradat	PROPN
ejpam-3831	101	2	et	et	PROPN
ejpam-3831	101	3	al	al	PROPN
ejpam-3831	101	4	.	.	PUNCT
ejpam-3831	101	5	/	/	SYM
ejpam-3831	101	6	eur	eur	PROPN
ejpam-3831	101	7	.	.	PUNCT
ejpam-3831	102	1	j.	j.	PROPN
ejpam-3831	102	2	pure	pure	PROPN
ejpam-3831	102	3	appl	appl	PROPN
ejpam-3831	102	4	.	.	PROPN
ejpam-3831	102	5	math	math	PROPN
ejpam-3831	102	6	,	,	PUNCT
ejpam-3831	102	7	13	13	NUM
ejpam-3831	102	8	(	(	PUNCT
ejpam-3831	102	9	4	4	NUM
ejpam-3831	102	10	)	)	PUNCT
ejpam-3831	102	11	(	(	PUNCT
ejpam-3831	102	12	2020	2020	NUM
ejpam-3831	102	13	)	)	PUNCT
ejpam-3831	102	14	,	,	PUNCT
ejpam-3831	102	15	995	995	NUM
ejpam-3831	102	16	-	-	SYM
ejpam-3831	102	17	1015	1015	NUM
ejpam-3831	102	18	998	998	NUM
ejpam-3831	102	19	+	+	SYM
ejpam-3831	102	20	α4(a	α4(a	NUM
ejpam-3831	102	21	,	,	PUNCT
ejpam-3831	102	22	u	u	NOUN
ejpam-3831	102	23	)	)	PUNCT
ejpam-3831	102	24	gb	gb	ADP
ejpam-3831	102	25	(	(	PUNCT
ejpam-3831	102	26	a	a	PRON
ejpam-3831	102	27	,	,	PUNCT
ejpam-3831	102	28	a	a	X
ejpam-3831	102	29	,	,	PUNCT
ejpam-3831	102	30	f	f	PROPN
ejpam-3831	102	31	(	(	PUNCT
ejpam-3831	102	32	a	a	DET
ejpam-3831	102	33	,	,	PUNCT
ejpam-3831	102	34	b	b	NOUN
ejpam-3831	102	35	)	)	PUNCT
ejpam-3831	102	36	)	)	PUNCT
ejpam-3831	103	1	gb(a	gb(a	X
ejpam-3831	103	2	,	,	PUNCT
ejpam-3831	103	3	u	u	NOUN
ejpam-3831	103	4	,	,	PUNCT
ejpam-3831	103	5	x	x	NOUN
ejpam-3831	103	6	)	)	PUNCT
ejpam-3831	103	7	ωs(a	ωs(a	NUM
ejpam-3831	103	8	,	,	PUNCT
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ejpam-3831	103	12	,	,	PUNCT
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ejpam-3831	103	14	,	,	PUNCT
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ejpam-3831	103	16	,	,	PUNCT
ejpam-3831	103	17	y	y	NOUN
ejpam-3831	103	18	)	)	PUNCT
ejpam-3831	103	19	+	+	PUNCT
ejpam-3831	104	1	α5(u	α5(u	NUM
ejpam-3831	104	2	,	,	PUNCT
ejpam-3831	104	3	x	x	X
ejpam-3831	104	4	)	)	PUNCT
ejpam-3831	104	5	gb	gb	ADP
ejpam-3831	104	6	(	(	PUNCT
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ejpam-3831	104	8	,	,	PUNCT
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ejpam-3831	104	10	,	,	PUNCT
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ejpam-3831	104	12	(	(	PUNCT
ejpam-3831	104	13	a	a	DET
ejpam-3831	104	14	,	,	PUNCT
ejpam-3831	104	15	b	b	NOUN
ejpam-3831	104	16	)	)	PUNCT
ejpam-3831	104	17	)	)	PUNCT
ejpam-3831	105	1	gb(b	gb(b	X
ejpam-3831	105	2	,	,	PUNCT
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ejpam-3831	105	4	,	,	PUNCT
ejpam-3831	105	5	y	y	NOUN
ejpam-3831	105	6	)	)	PUNCT
ejpam-3831	105	7	ωs(a	ωs(a	NUM
ejpam-3831	105	8	,	,	PUNCT
ejpam-3831	105	9	u	u	NOUN
ejpam-3831	105	10	,	,	PUNCT
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ejpam-3831	105	12	,	,	PUNCT
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ejpam-3831	105	14	,	,	PUNCT
ejpam-3831	105	15	v	v	NOUN
ejpam-3831	105	16	,	,	PUNCT
ejpam-3831	105	17	y	y	NOUN
ejpam-3831	105	18	)	)	PUNCT
ejpam-3831	106	1	+	+	NOUN
ejpam-3831	106	2	α6(u	α6(u	PROPN
ejpam-3831	106	3	,	,	PUNCT
ejpam-3831	106	4	x	x	NOUN
ejpam-3831	106	5	)	)	PUNCT
ejpam-3831	106	6	gb	gb	ADP
ejpam-3831	106	7	(	(	PUNCT
ejpam-3831	106	8	u	u	NOUN
ejpam-3831	106	9	,	,	PUNCT
ejpam-3831	106	10	u	u	PROPN
ejpam-3831	106	11	,	,	PUNCT
ejpam-3831	106	12	h(u	h(u	PROPN
ejpam-3831	106	13	,	,	PUNCT
ejpam-3831	106	14	v	v	NOUN
ejpam-3831	106	15	)	)	PUNCT
ejpam-3831	106	16	)	)	PUNCT
ejpam-3831	106	17	gb(a	gb(a	X
ejpam-3831	106	18	,	,	PUNCT
ejpam-3831	106	19	u	u	NOUN
ejpam-3831	106	20	,	,	PUNCT
ejpam-3831	106	21	x	x	NOUN
ejpam-3831	106	22	)	)	PUNCT
ejpam-3831	106	23	ωs(a	ωs(a	NUM
ejpam-3831	106	24	,	,	PUNCT
ejpam-3831	106	25	u	u	NOUN
ejpam-3831	106	26	,	,	PUNCT
ejpam-3831	106	27	x	x	X
ejpam-3831	106	28	,	,	PUNCT
ejpam-3831	106	29	b	b	PROPN
ejpam-3831	106	30	,	,	PUNCT
ejpam-3831	106	31	v	v	NOUN
ejpam-3831	106	32	,	,	PUNCT
ejpam-3831	106	33	y	y	PROPN
ejpam-3831	106	34	)	)	PUNCT
ejpam-3831	106	35	+	+	CCONJ
ejpam-3831	106	36	α7(u	α7(u	ADJ
ejpam-3831	106	37	,	,	PUNCT
ejpam-3831	106	38	x	x	X
ejpam-3831	106	39	)	)	PUNCT
ejpam-3831	106	40	gb	gb	ADP
ejpam-3831	106	41	(	(	PUNCT
ejpam-3831	106	42	u	u	NOUN
ejpam-3831	106	43	,	,	PUNCT
ejpam-3831	106	44	u	u	PROPN
ejpam-3831	106	45	,	,	PUNCT
ejpam-3831	106	46	h(u	h(u	PROPN
ejpam-3831	106	47	,	,	PUNCT
ejpam-3831	106	48	v	v	NOUN
ejpam-3831	106	49	)	)	PUNCT
ejpam-3831	106	50	)	)	PUNCT
ejpam-3831	107	1	gb(b	gb(b	X
ejpam-3831	107	2	,	,	PUNCT
ejpam-3831	107	3	v	v	NOUN
ejpam-3831	107	4	,	,	PUNCT
ejpam-3831	107	5	y	y	NOUN
ejpam-3831	107	6	)	)	PUNCT
ejpam-3831	107	7	ωs(a	ωs(a	NUM
ejpam-3831	107	8	,	,	PUNCT
ejpam-3831	107	9	u	u	NOUN
ejpam-3831	107	10	,	,	PUNCT
ejpam-3831	107	11	x	x	X
ejpam-3831	107	12	,	,	PUNCT
ejpam-3831	107	13	b	b	PROPN
ejpam-3831	107	14	,	,	PUNCT
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ejpam-3831	107	16	,	,	PUNCT
ejpam-3831	107	17	y	y	NOUN
ejpam-3831	107	18	)	)	PUNCT
ejpam-3831	108	1	+	+	NOUN
ejpam-3831	108	2	α8(u	α8(u	NUM
ejpam-3831	108	3	,	,	PUNCT
ejpam-3831	108	4	x	x	NOUN
ejpam-3831	108	5	)	)	PUNCT
ejpam-3831	108	6	gb	gb	ADP
ejpam-3831	108	7	(	(	PUNCT
ejpam-3831	108	8	x	x	NOUN
ejpam-3831	108	9	,	,	PUNCT
ejpam-3831	108	10	x	x	PROPN
ejpam-3831	108	11	,	,	PUNCT
ejpam-3831	108	12	t	t	PROPN
ejpam-3831	108	13	(	(	PUNCT
ejpam-3831	108	14	x	x	PROPN
ejpam-3831	108	15	,	,	PUNCT
ejpam-3831	108	16	y	y	NOUN
ejpam-3831	108	17	)	)	PUNCT
ejpam-3831	108	18	)	)	PUNCT
ejpam-3831	108	19	gb(a	gb(a	X
ejpam-3831	108	20	,	,	PUNCT
ejpam-3831	108	21	u	u	NOUN
ejpam-3831	108	22	,	,	PUNCT
ejpam-3831	108	23	x	x	NOUN
ejpam-3831	108	24	)	)	PUNCT
ejpam-3831	108	25	ωs(a	ωs(a	NUM
ejpam-3831	108	26	,	,	PUNCT
ejpam-3831	108	27	u	u	NOUN
ejpam-3831	108	28	,	,	PUNCT
ejpam-3831	108	29	x	x	X
ejpam-3831	108	30	,	,	PUNCT
ejpam-3831	108	31	b	b	PROPN
ejpam-3831	108	32	,	,	PUNCT
ejpam-3831	108	33	v	v	NOUN
ejpam-3831	108	34	,	,	PUNCT
ejpam-3831	108	35	y	y	PROPN
ejpam-3831	108	36	)	)	PUNCT
ejpam-3831	108	37	+	+	CCONJ
ejpam-3831	109	1	α9(x	α9(x	NUM
ejpam-3831	109	2	,	,	PUNCT
ejpam-3831	109	3	a	a	PRON
ejpam-3831	109	4	)	)	PUNCT
ejpam-3831	109	5	gb	gb	PROPN
ejpam-3831	109	6	(	(	PUNCT
ejpam-3831	109	7	x	x	NOUN
ejpam-3831	109	8	,	,	PUNCT
ejpam-3831	109	9	x	x	PROPN
ejpam-3831	109	10	,	,	PUNCT
ejpam-3831	109	11	t	t	PROPN
ejpam-3831	109	12	(	(	PUNCT
ejpam-3831	109	13	x	x	PROPN
ejpam-3831	109	14	,	,	PUNCT
ejpam-3831	109	15	y	y	NOUN
ejpam-3831	109	16	)	)	PUNCT
ejpam-3831	109	17	)	)	PUNCT
ejpam-3831	110	1	gb(b	gb(b	X
ejpam-3831	110	2	,	,	PUNCT
ejpam-3831	110	3	v	v	NOUN
ejpam-3831	110	4	,	,	PUNCT
ejpam-3831	110	5	y	y	NOUN
ejpam-3831	110	6	)	)	PUNCT
ejpam-3831	110	7	ωs(a	ωs(a	NUM
ejpam-3831	110	8	,	,	PUNCT
ejpam-3831	110	9	u	u	NOUN
ejpam-3831	110	10	,	,	PUNCT
ejpam-3831	110	11	x	x	X
ejpam-3831	110	12	,	,	PUNCT
ejpam-3831	110	13	b	b	PROPN
ejpam-3831	110	14	,	,	PUNCT
ejpam-3831	110	15	v	v	NOUN
ejpam-3831	110	16	,	,	PUNCT
ejpam-3831	110	17	y	y	NOUN
ejpam-3831	110	18	)	)	PUNCT
ejpam-3831	111	1	+	+	NOUN
ejpam-3831	111	2	α10(x	α10(x	NOUN
ejpam-3831	111	3	,	,	PUNCT
ejpam-3831	111	4	a	a	PRON
ejpam-3831	111	5	)	)	PUNCT
ejpam-3831	111	6	gb	gb	PROPN
ejpam-3831	111	7	(	(	PUNCT
ejpam-3831	111	8	a	a	PRON
ejpam-3831	111	9	,	,	PUNCT
ejpam-3831	111	10	u	u	NOUN
ejpam-3831	111	11	,	,	PUNCT
ejpam-3831	111	12	t	t	PROPN
ejpam-3831	111	13	(	(	PUNCT
ejpam-3831	111	14	x	x	PROPN
ejpam-3831	111	15	,	,	PUNCT
ejpam-3831	111	16	y	y	NOUN
ejpam-3831	111	17	)	)	PUNCT
ejpam-3831	111	18	)	)	PUNCT
ejpam-3831	111	19	gb(a	gb(a	X
ejpam-3831	111	20	,	,	PUNCT
ejpam-3831	111	21	u	u	NOUN
ejpam-3831	111	22	,	,	PUNCT
ejpam-3831	111	23	x	x	NOUN
ejpam-3831	111	24	)	)	PUNCT
ejpam-3831	111	25	ωs(a	ωs(a	NUM
ejpam-3831	111	26	,	,	PUNCT
ejpam-3831	111	27	u	u	NOUN
ejpam-3831	111	28	,	,	PUNCT
ejpam-3831	111	29	x	x	X
ejpam-3831	111	30	,	,	PUNCT
ejpam-3831	111	31	b	b	PROPN
ejpam-3831	111	32	,	,	PUNCT
ejpam-3831	111	33	v	v	NOUN
ejpam-3831	111	34	,	,	PUNCT
ejpam-3831	111	35	y	y	NOUN
ejpam-3831	111	36	)	)	PUNCT
ejpam-3831	111	37	+	+	CCONJ
ejpam-3831	111	38	α11(x	α11(x	NOUN
ejpam-3831	111	39	,	,	PUNCT
ejpam-3831	111	40	a	a	PRON
ejpam-3831	111	41	)	)	PUNCT
ejpam-3831	111	42	gb	gb	PROPN
ejpam-3831	111	43	(	(	PUNCT
ejpam-3831	111	44	u	u	NOUN
ejpam-3831	111	45	,	,	PUNCT
ejpam-3831	111	46	x	x	PROPN
ejpam-3831	111	47	,	,	PUNCT
ejpam-3831	111	48	f	f	PROPN
ejpam-3831	111	49	(	(	PUNCT
ejpam-3831	111	50	a	a	DET
ejpam-3831	111	51	,	,	PUNCT
ejpam-3831	111	52	b	b	NOUN
ejpam-3831	111	53	)	)	PUNCT
ejpam-3831	111	54	)	)	PUNCT
ejpam-3831	111	55	gb(b	gb(b	X
ejpam-3831	111	56	,	,	PUNCT
ejpam-3831	111	57	v	v	NOUN
ejpam-3831	111	58	,	,	PUNCT
ejpam-3831	111	59	y	y	NOUN
ejpam-3831	111	60	)	)	PUNCT
ejpam-3831	111	61	ωs(a	ωs(a	NUM
ejpam-3831	111	62	,	,	PUNCT
ejpam-3831	111	63	u	u	NOUN
ejpam-3831	111	64	,	,	PUNCT
ejpam-3831	111	65	x	x	X
ejpam-3831	111	66	,	,	PUNCT
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ejpam-3831	111	68	,	,	PUNCT
ejpam-3831	111	69	v	v	NOUN
ejpam-3831	111	70	,	,	PUNCT
ejpam-3831	111	71	y	y	NOUN
ejpam-3831	111	72	)	)	PUNCT
ejpam-3831	112	1	+	+	NOUN
ejpam-3831	112	2	α12(x	α12(x	NOUN
ejpam-3831	112	3	,	,	PUNCT
ejpam-3831	112	4	a	a	PRON
ejpam-3831	112	5	)	)	PUNCT
ejpam-3831	112	6	gb	gb	PROPN
ejpam-3831	112	7	(	(	PUNCT
ejpam-3831	112	8	x	x	NOUN
ejpam-3831	112	9	,	,	PUNCT
ejpam-3831	112	10	a	a	PRON
ejpam-3831	112	11	,	,	PUNCT
ejpam-3831	112	12	h(u	h(u	PROPN
ejpam-3831	112	13	,	,	PUNCT
ejpam-3831	112	14	v	v	NOUN
ejpam-3831	112	15	)	)	PUNCT
ejpam-3831	112	16	)	)	PUNCT
ejpam-3831	112	17	gb(a	gb(a	X
ejpam-3831	112	18	,	,	PUNCT
ejpam-3831	112	19	u	u	NOUN
ejpam-3831	112	20	,	,	PUNCT
ejpam-3831	112	21	x	x	NOUN
ejpam-3831	112	22	)	)	PUNCT
ejpam-3831	112	23	ωs(a	ωs(a	NUM
ejpam-3831	112	24	,	,	PUNCT
ejpam-3831	112	25	u	u	NOUN
ejpam-3831	112	26	,	,	PUNCT
ejpam-3831	112	27	x	x	X
ejpam-3831	112	28	,	,	PUNCT
ejpam-3831	112	29	b	b	PROPN
ejpam-3831	112	30	,	,	PUNCT
ejpam-3831	112	31	v	v	NOUN
ejpam-3831	112	32	,	,	PUNCT
ejpam-3831	112	33	y	y	PROPN
ejpam-3831	112	34	)	)	PUNCT
ejpam-3831	112	35	,	,	PUNCT
ejpam-3831	112	36	(	(	PUNCT
ejpam-3831	112	37	1	1	X
ejpam-3831	112	38	)	)	PUNCT
ejpam-3831	112	39	ω1(a	ω1(a	NUM
ejpam-3831	112	40	,	,	PUNCT
ejpam-3831	112	41	u	u	NOUN
ejpam-3831	112	42	,	,	PUNCT
ejpam-3831	112	43	x	x	X
ejpam-3831	112	44	,	,	PUNCT
ejpam-3831	112	45	b	b	PROPN
ejpam-3831	112	46	,	,	PUNCT
ejpam-3831	112	47	v	v	NOUN
ejpam-3831	112	48	,	,	PUNCT
ejpam-3831	112	49	y	y	NOUN
ejpam-3831	112	50	)	)	PUNCT
ejpam-3831	113	1	=	=	PUNCT
ejpam-3831	114	1	[	[	X
ejpam-3831	114	2	1	1	NUM
ejpam-3831	114	3	+	+	CCONJ
ejpam-3831	114	4	gb(a	gb(a	NOUN
ejpam-3831	114	5	,	,	PUNCT
ejpam-3831	114	6	u	u	NOUN
ejpam-3831	114	7	,	,	PUNCT
ejpam-3831	114	8	x	x	X
ejpam-3831	114	9	)	)	PUNCT
ejpam-3831	114	10	+	+	CCONJ
ejpam-3831	114	11	gb(b	gb(b	NOUN
ejpam-3831	114	12	,	,	PUNCT
ejpam-3831	114	13	v	v	NOUN
ejpam-3831	114	14	,	,	PUNCT
ejpam-3831	114	15	y	y	PROPN
ejpam-3831	114	16	)	)	PUNCT
ejpam-3831	114	17	]	]	X
ejpam-3831	114	18	,	,	PUNCT
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ejpam-3831	114	20	,	,	PUNCT
ejpam-3831	114	21	u	u	NOUN
ejpam-3831	114	22	,	,	PUNCT
ejpam-3831	114	23	x	x	X
ejpam-3831	114	24	,	,	PUNCT
ejpam-3831	114	25	b	b	PROPN
ejpam-3831	114	26	,	,	PUNCT
ejpam-3831	114	27	v	v	NOUN
ejpam-3831	114	28	,	,	PUNCT
ejpam-3831	114	29	y	y	NOUN
ejpam-3831	114	30	)	)	PUNCT
ejpam-3831	114	31	=	=	SYM
ejpam-3831	114	32	sω1(a	sω1(a	PROPN
ejpam-3831	114	33	,	,	PUNCT
ejpam-3831	114	34	u	u	NOUN
ejpam-3831	114	35	,	,	PUNCT
ejpam-3831	114	36	x	x	X
ejpam-3831	114	37	,	,	PUNCT
ejpam-3831	114	38	b	b	PROPN
ejpam-3831	114	39	,	,	PUNCT
ejpam-3831	114	40	v	v	NOUN
ejpam-3831	114	41	,	,	PUNCT
ejpam-3831	114	42	y	y	PROPN
ejpam-3831	114	43	)	)	PUNCT
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ejpam-3831	114	45	αi	αi	VERB
ejpam-3831	114	46	:	:	PUNCT
ejpam-3831	114	47	x	x	X
ejpam-3831	114	48	×x	×x	ADP
ejpam-3831	114	49	→	→	SYM
ejpam-3831	114	50	[	[	X
ejpam-3831	114	51	0	0	NUM
ejpam-3831	114	52	,	,	PUNCT
ejpam-3831	114	53	1	1	NUM
ejpam-3831	114	54	)	)	PUNCT
ejpam-3831	114	55	,	,	PUNCT
ejpam-3831	114	56	i	i	PRON
ejpam-3831	114	57	=	=	NOUN
ejpam-3831	114	58	1	1	NUM
ejpam-3831	114	59	,	,	PUNCT
ejpam-3831	114	60	2	2	NUM
ejpam-3831	114	61	,	,	PUNCT
ejpam-3831	114	62	3	3	NUM
ejpam-3831	114	63	,	,	PUNCT
ejpam-3831	114	64	·	·	PUNCT
ejpam-3831	114	65	·	·	PUNCT
ejpam-3831	114	66	·	·	PUNCT
ejpam-3831	114	67	,	,	PUNCT
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ejpam-3831	114	69	.	.	PUNCT
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ejpam-3831	115	2	that	that	DET
ejpam-3831	115	3	0	0	NUM
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ejpam-3831	115	5	s[α1(x	s[α1(x	NOUN
ejpam-3831	115	6	,	,	PUNCT
ejpam-3831	115	7	y)+α4(x	y)+α4(x	PROPN
ejpam-3831	115	8	,	,	PUNCT
ejpam-3831	115	9	y)+α5(x	y)+α5(x	NOUN
ejpam-3831	115	10	,	,	PUNCT
ejpam-3831	115	11	y)+α10(x	y)+α10(x	NOUN
ejpam-3831	115	12	,	,	PUNCT
ejpam-3831	115	13	y)+α12(x	y)+α12(x	PROPN
ejpam-3831	115	14	,	,	PUNCT
ejpam-3831	115	15	y)]+[α2(x	y)]+[α2(x	NOUN
ejpam-3831	115	16	,	,	PUNCT
ejpam-3831	115	17	y)+α3(x	y)+α3(x	PROPN
ejpam-3831	115	18	,	,	PUNCT
ejpam-3831	115	19	y)+	y)+	NOUN
ejpam-3831	115	20	11∑	11∑	NOUN
ejpam-3831	115	21	i=6	i=6	PROPN
ejpam-3831	115	22	αi(x	αi(x	NUM
ejpam-3831	115	23	,	,	PUNCT
ejpam-3831	115	24	y	y	PROPN
ejpam-3831	115	25	)	)	PUNCT
ejpam-3831	115	26	]	]	PUNCT
ejpam-3831	116	1	<	<	X
ejpam-3831	116	2	1	1	X
ejpam-3831	116	3	.	.	PUNCT
ejpam-3831	116	4	(	(	PUNCT
ejpam-3831	116	5	2	2	X
ejpam-3831	116	6	)	)	PUNCT
ejpam-3831	116	7	theorem	theorem	NOUN
ejpam-3831	116	8	1	1	NUM
ejpam-3831	116	9	.	.	PUNCT
ejpam-3831	117	1	let	let	AUX
ejpam-3831	117	2	(	(	PUNCT
ejpam-3831	117	3	x	x	NOUN
ejpam-3831	117	4	,	,	PUNCT
ejpam-3831	117	5	gb	gb	PRON
ejpam-3831	117	6	)	)	PUNCT
ejpam-3831	117	7	be	be	AUX
ejpam-3831	117	8	a	a	DET
ejpam-3831	117	9	complete	complete	ADJ
ejpam-3831	117	10	gb	gb	ADV
ejpam-3831	117	11	-	-	PUNCT
ejpam-3831	117	12	metric	metric	ADJ
ejpam-3831	117	13	space	space	NOUN
ejpam-3831	117	14	and	and	CCONJ
ejpam-3831	117	15	let	let	VERB
ejpam-3831	117	16	f	f	X
ejpam-3831	117	17	,	,	PUNCT
ejpam-3831	117	18	h	h	PROPN
ejpam-3831	117	19	,	,	PUNCT
ejpam-3831	117	20	t	t	NOUN
ejpam-3831	117	21	:	:	PUNCT
ejpam-3831	117	22	x	x	PUNCT
ejpam-3831	117	23	×	×	NOUN
ejpam-3831	117	24	x	x	INTJ
ejpam-3831	117	25	→	→	PUNCT
ejpam-3831	117	26	x	x	PUNCT
ejpam-3831	117	27	be	be	AUX
ejpam-3831	117	28	mappings	mapping	NOUN
ejpam-3831	117	29	satisfying	satisfy	VERB
ejpam-3831	117	30	the	the	DET
ejpam-3831	117	31	above	above	ADJ
ejpam-3831	117	32	generalized	generalized	ADJ
ejpam-3831	117	33	contraction(1	contraction(1	NOUN
ejpam-3831	117	34	)	)	PUNCT
ejpam-3831	117	35	and	and	CCONJ
ejpam-3831	117	36	the	the	DET
ejpam-3831	117	37	following	follow	VERB
ejpam-3831	117	38	conditions	condition	NOUN
ejpam-3831	117	39	satisfied	satisfy	VERB
ejpam-3831	117	40	∀i	∀i	NOUN
ejpam-3831	117	41	,	,	PUNCT
ejpam-3831	117	42	i	i	PRON
ejpam-3831	117	43	=	=	NOUN
ejpam-3831	117	44	1	1	NUM
ejpam-3831	117	45	,	,	PUNCT
ejpam-3831	117	46	·	·	PUNCT
ejpam-3831	117	47	·	·	PUNCT
ejpam-3831	117	48	·	·	PUNCT
ejpam-3831	117	49	,	,	PUNCT
ejpam-3831	117	50	12	12	NUM
ejpam-3831	117	51	:	:	PUNCT
ejpam-3831	117	52	(	(	PUNCT
ejpam-3831	117	53	i	i	NOUN
ejpam-3831	117	54	)	)	PUNCT
ejpam-3831	117	55	αi(f	αi(f	NOUN
ejpam-3831	117	56	(	(	PUNCT
ejpam-3831	117	57	x1	x1	PROPN
ejpam-3831	117	58	,	,	PUNCT
ejpam-3831	117	59	y1	y1	PROPN
ejpam-3831	117	60	)	)	PUNCT
ejpam-3831	117	61	,	,	PUNCT
ejpam-3831	117	62	y	y	NOUN
ejpam-3831	117	63	)	)	PUNCT
ejpam-3831	117	64	≤	≤	NOUN
ejpam-3831	117	65	αi(x1	αi(x1	NOUN
ejpam-3831	117	66	,	,	PUNCT
ejpam-3831	117	67	y	y	NOUN
ejpam-3831	117	68	)	)	PUNCT
ejpam-3831	117	69	and	and	CCONJ
ejpam-3831	117	70	αi(x	αi(x	NUM
ejpam-3831	117	71	,	,	PUNCT
ejpam-3831	117	72	f	f	PROPN
ejpam-3831	117	73	(	(	PUNCT
ejpam-3831	117	74	x1	x1	PROPN
ejpam-3831	117	75	,	,	PUNCT
ejpam-3831	117	76	y1	y1	NOUN
ejpam-3831	117	77	)	)	PUNCT
ejpam-3831	117	78	)	)	PUNCT
ejpam-3831	117	79	≤	≤	NOUN
ejpam-3831	117	80	αi(x	αi(x	NUM
ejpam-3831	117	81	,	,	PUNCT
ejpam-3831	117	82	x1	x1	NUM
ejpam-3831	117	83	)	)	PUNCT
ejpam-3831	117	84	)	)	PUNCT
ejpam-3831	117	85	;	;	PUNCT
ejpam-3831	117	86	(	(	PUNCT
ejpam-3831	117	87	ii	ii	NOUN
ejpam-3831	117	88	)	)	PUNCT
ejpam-3831	117	89	αi(h(x1	αi(h(x1	PROPN
ejpam-3831	117	90	,	,	PUNCT
ejpam-3831	117	91	y1	y1	NOUN
ejpam-3831	117	92	)	)	PUNCT
ejpam-3831	117	93	,	,	PUNCT
ejpam-3831	117	94	y	y	NOUN
ejpam-3831	117	95	)	)	PUNCT
ejpam-3831	117	96	≤	≤	NOUN
ejpam-3831	117	97	αi(x1	αi(x1	NOUN
ejpam-3831	117	98	,	,	PUNCT
ejpam-3831	117	99	y	y	NOUN
ejpam-3831	117	100	)	)	PUNCT
ejpam-3831	117	101	and	and	CCONJ
ejpam-3831	117	102	αi(x	αi(x	NUM
ejpam-3831	117	103	,	,	PUNCT
ejpam-3831	117	104	h(x1	h(x1	NOUN
ejpam-3831	117	105	,	,	PUNCT
ejpam-3831	117	106	y1	y1	NOUN
ejpam-3831	117	107	)	)	PUNCT
ejpam-3831	117	108	)	)	PUNCT
ejpam-3831	117	109	≤	≤	NOUN
ejpam-3831	117	110	αi(x	αi(x	NUM
ejpam-3831	117	111	,	,	PUNCT
ejpam-3831	117	112	x1	x1	NUM
ejpam-3831	117	113	)	)	PUNCT
ejpam-3831	117	114	)	)	PUNCT
ejpam-3831	117	115	;	;	PUNCT
ejpam-3831	117	116	(	(	PUNCT
ejpam-3831	117	117	iii	iii	NOUN
ejpam-3831	117	118	)	)	PUNCT
ejpam-3831	117	119	αi(t	αi(t	X
ejpam-3831	117	120	(	(	PUNCT
ejpam-3831	117	121	x1	x1	PROPN
ejpam-3831	117	122	,	,	PUNCT
ejpam-3831	117	123	y1	y1	PROPN
ejpam-3831	117	124	)	)	PUNCT
ejpam-3831	117	125	,	,	PUNCT
ejpam-3831	117	126	y	y	NOUN
ejpam-3831	117	127	)	)	PUNCT
ejpam-3831	117	128	≤	≤	NOUN
ejpam-3831	117	129	αi(x1	αi(x1	NOUN
ejpam-3831	117	130	,	,	PUNCT
ejpam-3831	117	131	y	y	NOUN
ejpam-3831	117	132	)	)	PUNCT
ejpam-3831	117	133	and	and	CCONJ
ejpam-3831	117	134	αi(x	αi(x	NUM
ejpam-3831	117	135	,	,	PUNCT
ejpam-3831	117	136	t	t	PROPN
ejpam-3831	117	137	(	(	PUNCT
ejpam-3831	117	138	x1	x1	PROPN
ejpam-3831	117	139	,	,	PUNCT
ejpam-3831	117	140	y1	y1	NOUN
ejpam-3831	117	141	)	)	PUNCT
ejpam-3831	117	142	)	)	PUNCT
ejpam-3831	117	143	≤	≤	NOUN
ejpam-3831	117	144	αi(x	αi(x	NUM
ejpam-3831	117	145	,	,	PUNCT
ejpam-3831	117	146	x1	x1	NUM
ejpam-3831	117	147	)	)	PUNCT
ejpam-3831	117	148	)	)	PUNCT
ejpam-3831	117	149	.	.	PUNCT
ejpam-3831	118	1	then	then	ADV
ejpam-3831	118	2	f	f	X
ejpam-3831	118	3	,	,	PUNCT
ejpam-3831	118	4	h	h	PROPN
ejpam-3831	118	5	,	,	PUNCT
ejpam-3831	118	6	t	t	PROPN
ejpam-3831	118	7	have	have	VERB
ejpam-3831	118	8	a	a	DET
ejpam-3831	118	9	unique	unique	ADJ
ejpam-3831	118	10	common	common	ADJ
ejpam-3831	118	11	coupled	couple	VERB
ejpam-3831	118	12	fixed	fix	VERB
ejpam-3831	118	13	point	point	NOUN
ejpam-3831	118	14	in	in	ADP
ejpam-3831	118	15	x.	x.	NOUN
ejpam-3831	118	16	proof	proof	NOUN
ejpam-3831	118	17	.	.	PUNCT
ejpam-3831	119	1	define	define	VERB
ejpam-3831	119	2	the	the	DET
ejpam-3831	119	3	sequences	sequence	NOUN
ejpam-3831	119	4	{	{	PUNCT
ejpam-3831	119	5	xn	xn	NUM
ejpam-3831	119	6	}	}	PUNCT
ejpam-3831	119	7	and	and	CCONJ
ejpam-3831	119	8	{	{	PUNCT
ejpam-3831	119	9	yn	yn	NOUN
ejpam-3831	119	10	}	}	PUNCT
ejpam-3831	119	11	in	in	ADP
ejpam-3831	119	12	x	x	PUNCT
ejpam-3831	119	13	by	by	ADP
ejpam-3831	119	14	the	the	DET
ejpam-3831	119	15	rule	rule	NOUN
ejpam-3831	119	16	:	:	PUNCT
ejpam-3831	119	17	x3k+1	x3k+1	SCONJ
ejpam-3831	120	1	=	=	SYM
ejpam-3831	120	2	f	f	PROPN
ejpam-3831	120	3	(	(	PUNCT
ejpam-3831	120	4	x3k	x3k	NOUN
ejpam-3831	120	5	,	,	PUNCT
ejpam-3831	120	6	y3k	y3k	NOUN
ejpam-3831	120	7	)	)	PUNCT
ejpam-3831	120	8	,	,	PUNCT
ejpam-3831	120	9	(	(	PUNCT
ejpam-3831	120	10	3	3	X
ejpam-3831	120	11	)	)	PUNCT
ejpam-3831	120	12	y3k+1	y3k+1	NOUN
ejpam-3831	120	13	=	=	SYM
ejpam-3831	120	14	f	f	PROPN
ejpam-3831	120	15	(	(	PUNCT
ejpam-3831	120	16	y3k	y3k	NOUN
ejpam-3831	120	17	,	,	PUNCT
ejpam-3831	120	18	x3k	x3k	NOUN
ejpam-3831	120	19	)	)	PUNCT
ejpam-3831	120	20	,	,	PUNCT
ejpam-3831	120	21	.	.	PUNCT
ejpam-3831	120	22	x3k+2	x3k+2	PUNCT
ejpam-3831	121	1	=	=	NOUN
ejpam-3831	121	2	h(x3k+1	h(x3k+1	X
ejpam-3831	121	3	,	,	PUNCT
ejpam-3831	121	4	y3k+1	y3k+1	NOUN
ejpam-3831	121	5	)	)	PUNCT
ejpam-3831	121	6	,	,	PUNCT
ejpam-3831	121	7	(	(	PUNCT
ejpam-3831	121	8	4	4	X
ejpam-3831	121	9	)	)	PUNCT
ejpam-3831	121	10	y3k+2	y3k+2	PROPN
ejpam-3831	121	11	=	=	SYM
ejpam-3831	121	12	h(yk+1	h(yk+1	PROPN
ejpam-3831	121	13	,	,	PUNCT
ejpam-3831	121	14	x3k+1	x3k+1	ADJ
ejpam-3831	121	15	)	)	PUNCT
ejpam-3831	121	16	,	,	PUNCT
ejpam-3831	121	17	x3k+3	x3k+3	PUNCT
ejpam-3831	122	1	=	=	SYM
ejpam-3831	122	2	t	t	PROPN
ejpam-3831	122	3	(	(	PUNCT
ejpam-3831	122	4	x3k+2	x3k+2	PROPN
ejpam-3831	122	5	,	,	PUNCT
ejpam-3831	122	6	y3k+2	y3k+2	NOUN
ejpam-3831	122	7	)	)	PUNCT
ejpam-3831	122	8	(	(	PUNCT
ejpam-3831	122	9	5	5	NUM
ejpam-3831	122	10	)	)	PUNCT
ejpam-3831	122	11	y3k+3	y3k+3	NOUN
ejpam-3831	123	1	=	=	SYM
ejpam-3831	123	2	t	t	PROPN
ejpam-3831	123	3	(	(	PUNCT
ejpam-3831	123	4	yk+2	yk+2	NOUN
ejpam-3831	123	5	,	,	PUNCT
ejpam-3831	123	6	x3k+2	x3k+2	X
ejpam-3831	123	7	)	)	PUNCT
ejpam-3831	123	8	,	,	PUNCT
ejpam-3831	123	9	where	where	SCONJ
ejpam-3831	123	10	k	k	PROPN
ejpam-3831	123	11	=	=	SYM
ejpam-3831	123	12	0	0	NUM
ejpam-3831	123	13	,	,	PUNCT
ejpam-3831	123	14	1	1	NUM
ejpam-3831	123	15	,	,	PUNCT
ejpam-3831	123	16	2	2	NUM
ejpam-3831	123	17	,	,	PUNCT
ejpam-3831	123	18	3	3	NUM
ejpam-3831	123	19	,	,	PUNCT
ejpam-3831	123	20	·	·	PUNCT
ejpam-3831	123	21	·	·	PUNCT
ejpam-3831	123	22	·	·	PUNCT
ejpam-3831	123	23	and	and	CCONJ
ejpam-3831	123	24	x0	x0	NUM
ejpam-3831	123	25	,	,	PUNCT
ejpam-3831	123	26	y0	y0	PROPN
ejpam-3831	123	27	to	to	PART
ejpam-3831	123	28	be	be	AUX
ejpam-3831	123	29	arbitrary	arbitrary	ADJ
ejpam-3831	123	30	in	in	ADP
ejpam-3831	123	31	x.	x.	NOUN
ejpam-3831	123	32	now	now	ADV
ejpam-3831	123	33	,	,	PUNCT
ejpam-3831	123	34	consider	consider	VERB
ejpam-3831	123	35	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	123	36	,	,	PUNCT
ejpam-3831	123	37	x3k+2	x3k+2	PRON
ejpam-3831	123	38	,	,	PUNCT
ejpam-3831	123	39	x3k+3	x3k+3	NOUN
ejpam-3831	123	40	)	)	PUNCT
ejpam-3831	123	41	=	=	SYM
ejpam-3831	123	42	gb(f	gb(f	X
ejpam-3831	123	43	(	(	PUNCT
ejpam-3831	123	44	x3k	x3k	NOUN
ejpam-3831	123	45	,	,	PUNCT
ejpam-3831	123	46	y3k	y3k	NOUN
ejpam-3831	123	47	)	)	PUNCT
ejpam-3831	123	48	,	,	PUNCT
ejpam-3831	123	49	h(x3k+1	h(x3k+1	X
ejpam-3831	123	50	,	,	PUNCT
ejpam-3831	123	51	y3k+1	y3k+1	NOUN
ejpam-3831	123	52	)	)	PUNCT
ejpam-3831	123	53	,	,	PUNCT
ejpam-3831	123	54	t	t	PROPN
ejpam-3831	123	55	(	(	PUNCT
ejpam-3831	123	56	x3k+2	x3k+2	PROPN
ejpam-3831	123	57	,	,	PUNCT
ejpam-3831	123	58	y3k+2	y3k+2	NOUN
ejpam-3831	123	59	)	)	PUNCT
ejpam-3831	123	60	)	)	PUNCT
ejpam-3831	124	1	m.m.m	m.m.m	NOUN
ejpam-3831	124	2	.	.	PUNCT
ejpam-3831	125	1	jaradat	jaradat	PROPN
ejpam-3831	125	2	et	et	PROPN
ejpam-3831	125	3	al	al	PROPN
ejpam-3831	125	4	.	.	PUNCT
ejpam-3831	125	5	/	/	SYM
ejpam-3831	125	6	eur	eur	PROPN
ejpam-3831	125	7	.	.	PUNCT
ejpam-3831	126	1	j.	j.	PROPN
ejpam-3831	126	2	pure	pure	PROPN
ejpam-3831	126	3	appl	appl	PROPN
ejpam-3831	126	4	.	.	PROPN
ejpam-3831	126	5	math	math	PROPN
ejpam-3831	126	6	,	,	PUNCT
ejpam-3831	126	7	13	13	NUM
ejpam-3831	126	8	(	(	PUNCT
ejpam-3831	126	9	4	4	NUM
ejpam-3831	126	10	)	)	PUNCT
ejpam-3831	126	11	(	(	PUNCT
ejpam-3831	126	12	2020	2020	NUM
ejpam-3831	126	13	)	)	PUNCT
ejpam-3831	126	14	,	,	PUNCT
ejpam-3831	126	15	995	995	NUM
ejpam-3831	126	16	-	-	SYM
ejpam-3831	126	17	1015	1015	NUM
ejpam-3831	126	18	999	999	NUM
ejpam-3831	126	19	≤	≤	NUM
ejpam-3831	126	20	α1(x3k	α1(x3k	NOUN
ejpam-3831	126	21	,	,	PUNCT
ejpam-3831	126	22	x3k+1	x3k+1	ADJ
ejpam-3831	126	23	)	)	PUNCT
ejpam-3831	126	24	.	.	PUNCT
ejpam-3831	127	1	gb(x3k	gb(x3k	NOUN
ejpam-3831	127	2	,	,	PUNCT
ejpam-3831	127	3	x3k+1	x3k+1	ADV
ejpam-3831	127	4	,	,	PUNCT
ejpam-3831	127	5	x3k+2	x3k+2	PUNCT
ejpam-3831	127	6	)	)	PUNCT
ejpam-3831	128	1	+	+	ADJ
ejpam-3831	128	2	gb(y3k	gb(y3k	PROPN
ejpam-3831	128	3	,	,	PUNCT
ejpam-3831	128	4	y3k+1	y3k+1	NOUN
ejpam-3831	128	5	,	,	PUNCT
ejpam-3831	128	6	y3k+2	y3k+2	NOUN
ejpam-3831	128	7	)	)	PUNCT
ejpam-3831	128	8	2	2	NUM
ejpam-3831	128	9	+	+	NOUN
ejpam-3831	128	10	α2(x3k	α2(x3k	NUM
ejpam-3831	128	11	,	,	PUNCT
ejpam-3831	128	12	x3k+1	x3k+1	PUNCT
ejpam-3831	128	13	)	)	PUNCT
ejpam-3831	128	14	·	·	PUNCT
ejpam-3831	128	15	gb	gb	PRON
ejpam-3831	128	16	(	(	PUNCT
ejpam-3831	128	17	f	f	X
ejpam-3831	128	18	(	(	PUNCT
ejpam-3831	128	19	x3k	x3k	NOUN
ejpam-3831	128	20	,	,	PUNCT
ejpam-3831	128	21	y3k	y3k	NOUN
ejpam-3831	128	22	)	)	PUNCT
ejpam-3831	128	23	,	,	PUNCT
ejpam-3831	128	24	h(x3k+1	h(x3k+1	X
ejpam-3831	128	25	,	,	PUNCT
ejpam-3831	128	26	y3k+1	y3k+1	NOUN
ejpam-3831	128	27	)	)	PUNCT
ejpam-3831	128	28	,	,	PUNCT
ejpam-3831	128	29	t	t	PROPN
ejpam-3831	128	30	(	(	PUNCT
ejpam-3831	128	31	x3k+2	x3k+2	PROPN
ejpam-3831	128	32	,	,	PUNCT
ejpam-3831	128	33	y3k+2	y3k+2	NOUN
ejpam-3831	128	34	)	)	PUNCT
ejpam-3831	128	35	)	)	PUNCT
ejpam-3831	128	36	gb(x3k	gb(x3k	NOUN
ejpam-3831	128	37	,	,	PUNCT
ejpam-3831	128	38	x3k+1	x3k+1	ADV
ejpam-3831	128	39	,	,	PUNCT
ejpam-3831	128	40	x3k+2	x3k+2	X
ejpam-3831	128	41	)	)	PUNCT
ejpam-3831	128	42	ωs(x3k	ωs(x3k	NUM
ejpam-3831	128	43	,	,	PUNCT
ejpam-3831	128	44	x3k+1	x3k+1	ADV
ejpam-3831	128	45	,	,	PUNCT
ejpam-3831	128	46	x3k+2	x3k+2	NOUN
ejpam-3831	128	47	,	,	PUNCT
ejpam-3831	128	48	y3k	y3k	NOUN
ejpam-3831	128	49	,	,	PUNCT
ejpam-3831	128	50	y3k+1	y3k+1	NOUN
ejpam-3831	128	51	,	,	PUNCT
ejpam-3831	128	52	y3k+2	y3k+2	NOUN
ejpam-3831	128	53	)	)	PUNCT
ejpam-3831	128	54	+	+	NOUN
ejpam-3831	128	55	α3(x3k	α3(x3k	NUM
ejpam-3831	128	56	,	,	PUNCT
ejpam-3831	128	57	x3k+1	x3k+1	PUNCT
ejpam-3831	128	58	)	)	PUNCT
ejpam-3831	128	59	·	·	PUNCT
ejpam-3831	128	60	gb	gb	PRON
ejpam-3831	128	61	(	(	PUNCT
ejpam-3831	128	62	f	f	X
ejpam-3831	128	63	(	(	PUNCT
ejpam-3831	128	64	x3k	x3k	NOUN
ejpam-3831	128	65	,	,	PUNCT
ejpam-3831	128	66	y3k	y3k	NOUN
ejpam-3831	128	67	)	)	PUNCT
ejpam-3831	128	68	,	,	PUNCT
ejpam-3831	128	69	h(x3k+1	h(x3k+1	X
ejpam-3831	128	70	,	,	PUNCT
ejpam-3831	128	71	y3k+1	y3k+1	NOUN
ejpam-3831	128	72	)	)	PUNCT
ejpam-3831	128	73	,	,	PUNCT
ejpam-3831	128	74	t	t	PROPN
ejpam-3831	128	75	(	(	PUNCT
ejpam-3831	128	76	x3k+2	x3k+2	PROPN
ejpam-3831	128	77	,	,	PUNCT
ejpam-3831	128	78	y3k+2	y3k+2	PROPN
ejpam-3831	128	79	)	)	PUNCT
ejpam-3831	128	80	)	)	PUNCT
ejpam-3831	129	1	gb(y3k	gb(y3k	PROPN
ejpam-3831	129	2	,	,	PUNCT
ejpam-3831	129	3	y3k+1	y3k+1	NOUN
ejpam-3831	129	4	,	,	PUNCT
ejpam-3831	129	5	y3k+2	y3k+2	NOUN
ejpam-3831	129	6	)	)	PUNCT
ejpam-3831	129	7	ωs(x3k	ωs(x3k	NUM
ejpam-3831	129	8	,	,	PUNCT
ejpam-3831	129	9	x3k+1	x3k+1	ADV
ejpam-3831	129	10	,	,	PUNCT
ejpam-3831	129	11	x3k+2	x3k+2	NOUN
ejpam-3831	129	12	,	,	PUNCT
ejpam-3831	129	13	y3k	y3k	NOUN
ejpam-3831	129	14	,	,	PUNCT
ejpam-3831	129	15	y3k+1	y3k+1	NOUN
ejpam-3831	129	16	,	,	PUNCT
ejpam-3831	129	17	y3k+2	y3k+2	NOUN
ejpam-3831	129	18	)	)	PUNCT
ejpam-3831	129	19	+	+	NOUN
ejpam-3831	129	20	α4(x3k	α4(x3k	NOUN
ejpam-3831	129	21	,	,	PUNCT
ejpam-3831	129	22	x3k+1	x3k+1	ADJ
ejpam-3831	129	23	)	)	PUNCT
ejpam-3831	129	24	·	·	PUNCT
ejpam-3831	129	25	gb(x3k	gb(x3k	NOUN
ejpam-3831	129	26	,	,	PUNCT
ejpam-3831	129	27	x3k	x3k	PROPN
ejpam-3831	129	28	,	,	PUNCT
ejpam-3831	129	29	f	f	PROPN
ejpam-3831	129	30	(	(	PUNCT
ejpam-3831	129	31	x3k	x3k	PROPN
ejpam-3831	129	32	,	,	PUNCT
ejpam-3831	129	33	y3k))gb(x3k	y3k))gb(x3k	PROPN
ejpam-3831	129	34	,	,	PUNCT
ejpam-3831	129	35	x3k+1	x3k+1	ADJ
ejpam-3831	129	36	,	,	PUNCT
ejpam-3831	129	37	x3k+2	x3k+2	X
ejpam-3831	129	38	)	)	PUNCT
ejpam-3831	129	39	ωs(x3k	ωs(x3k	NUM
ejpam-3831	129	40	,	,	PUNCT
ejpam-3831	129	41	x3k+1	x3k+1	ADV
ejpam-3831	129	42	,	,	PUNCT
ejpam-3831	129	43	x3k+2	x3k+2	NOUN
ejpam-3831	129	44	,	,	PUNCT
ejpam-3831	129	45	y3k	y3k	NOUN
ejpam-3831	129	46	,	,	PUNCT
ejpam-3831	129	47	y3k+1	y3k+1	NOUN
ejpam-3831	129	48	,	,	PUNCT
ejpam-3831	129	49	y3k+2	y3k+2	NOUN
ejpam-3831	129	50	)	)	PUNCT
ejpam-3831	129	51	+	+	NOUN
ejpam-3831	129	52	α5(x3k+1	α5(x3k+1	NOUN
ejpam-3831	129	53	,	,	PUNCT
ejpam-3831	129	54	x3k+2	x3k+2	X
ejpam-3831	129	55	)	)	PUNCT
ejpam-3831	129	56	·	·	PUNCT
ejpam-3831	129	57	gb(x3k	gb(x3k	NOUN
ejpam-3831	129	58	,	,	PUNCT
ejpam-3831	129	59	x3k	x3k	PROPN
ejpam-3831	129	60	,	,	PUNCT
ejpam-3831	129	61	f	f	PROPN
ejpam-3831	129	62	(	(	PUNCT
ejpam-3831	129	63	x3k	x3k	PROPN
ejpam-3831	129	64	,	,	PUNCT
ejpam-3831	129	65	y3k))gb(y3k	y3k))gb(y3k	NOUN
ejpam-3831	129	66	,	,	PUNCT
ejpam-3831	129	67	y3k+1	y3k+1	NOUN
ejpam-3831	129	68	,	,	PUNCT
ejpam-3831	129	69	y3k+2	y3k+2	NOUN
ejpam-3831	129	70	)	)	PUNCT
ejpam-3831	129	71	ωs(x3k	ωs(x3k	NUM
ejpam-3831	129	72	,	,	PUNCT
ejpam-3831	129	73	x3k+1	x3k+1	ADV
ejpam-3831	129	74	,	,	PUNCT
ejpam-3831	129	75	x3k+2	x3k+2	NOUN
ejpam-3831	129	76	,	,	PUNCT
ejpam-3831	129	77	y3k	y3k	NOUN
ejpam-3831	129	78	,	,	PUNCT
ejpam-3831	129	79	y3k+1	y3k+1	NOUN
ejpam-3831	129	80	,	,	PUNCT
ejpam-3831	129	81	y3k+2	y3k+2	NOUN
ejpam-3831	129	82	)	)	PUNCT
ejpam-3831	129	83	+	+	NOUN
ejpam-3831	129	84	α6(x3k+1	α6(x3k+1	ADJ
ejpam-3831	129	85	,	,	PUNCT
ejpam-3831	129	86	x3k+2	x3k+2	X
ejpam-3831	129	87	)	)	PUNCT
ejpam-3831	129	88	·	·	PUNCT
ejpam-3831	130	1	gb(x3k+1	gb(x3k+1	VERB
ejpam-3831	130	2	,	,	PUNCT
ejpam-3831	130	3	x3k+1	x3k+1	ADJ
ejpam-3831	130	4	,	,	PUNCT
ejpam-3831	130	5	h(x3k+1	h(x3k+1	NOUN
ejpam-3831	130	6	,	,	PUNCT
ejpam-3831	130	7	y3k+1))gb(x3k	y3k+1))gb(x3k	NOUN
ejpam-3831	130	8	,	,	PUNCT
ejpam-3831	130	9	x3k+1	x3k+1	ADV
ejpam-3831	130	10	,	,	PUNCT
ejpam-3831	130	11	x3k+2	x3k+2	X
ejpam-3831	130	12	)	)	PUNCT
ejpam-3831	130	13	ωs(x3k	ωs(x3k	NUM
ejpam-3831	130	14	,	,	PUNCT
ejpam-3831	130	15	x3k+1	x3k+1	ADV
ejpam-3831	130	16	,	,	PUNCT
ejpam-3831	130	17	x3k+2	x3k+2	NOUN
ejpam-3831	130	18	,	,	PUNCT
ejpam-3831	130	19	y3k	y3k	NOUN
ejpam-3831	130	20	,	,	PUNCT
ejpam-3831	130	21	y3k+1	y3k+1	NOUN
ejpam-3831	130	22	,	,	PUNCT
ejpam-3831	130	23	y3k+2	y3k+2	NOUN
ejpam-3831	130	24	)	)	PUNCT
ejpam-3831	130	25	+	+	ADV
ejpam-3831	130	26	α7(x3k+1	α7(x3k+1	NOUN
ejpam-3831	130	27	,	,	PUNCT
ejpam-3831	130	28	x3k+2	x3k+2	X
ejpam-3831	130	29	)	)	PUNCT
ejpam-3831	130	30	·	·	PUNCT
ejpam-3831	131	1	gb(x3k+1	gb(x3k+1	VERB
ejpam-3831	131	2	,	,	PUNCT
ejpam-3831	131	3	x3k+1	x3k+1	ADJ
ejpam-3831	131	4	,	,	PUNCT
ejpam-3831	131	5	h(x3k+1	h(x3k+1	NOUN
ejpam-3831	131	6	,	,	PUNCT
ejpam-3831	131	7	y3k+1))gb(y3k	y3k+1))gb(y3k	NOUN
ejpam-3831	131	8	,	,	PUNCT
ejpam-3831	131	9	y3k+1	y3k+1	NOUN
ejpam-3831	131	10	,	,	PUNCT
ejpam-3831	131	11	y3k+2	y3k+2	NOUN
ejpam-3831	131	12	)	)	PUNCT
ejpam-3831	131	13	ωs(x3k	ωs(x3k	NUM
ejpam-3831	131	14	,	,	PUNCT
ejpam-3831	131	15	x3k+1	x3k+1	ADV
ejpam-3831	131	16	,	,	PUNCT
ejpam-3831	131	17	x3k+2	x3k+2	NOUN
ejpam-3831	131	18	,	,	PUNCT
ejpam-3831	131	19	y3k	y3k	NOUN
ejpam-3831	131	20	,	,	PUNCT
ejpam-3831	131	21	y3k+1	y3k+1	NOUN
ejpam-3831	131	22	,	,	PUNCT
ejpam-3831	131	23	y3k+2	y3k+2	NOUN
ejpam-3831	131	24	)	)	PUNCT
ejpam-3831	131	25	+	+	NOUN
ejpam-3831	131	26	α8(x3k+1	α8(x3k+1	NOUN
ejpam-3831	131	27	,	,	PUNCT
ejpam-3831	131	28	x3k+2	x3k+2	X
ejpam-3831	131	29	)	)	PUNCT
ejpam-3831	131	30	·	·	PUNCT
ejpam-3831	132	1	gb(x3k+2	gb(x3k+2	NOUN
ejpam-3831	132	2	,	,	PUNCT
ejpam-3831	132	3	x3k+2	x3k+2	PROPN
ejpam-3831	132	4	,	,	PUNCT
ejpam-3831	132	5	t	t	PROPN
ejpam-3831	132	6	(	(	PUNCT
ejpam-3831	132	7	x3k+2	x3k+2	NOUN
ejpam-3831	132	8	,	,	PUNCT
ejpam-3831	132	9	y3k+2))gb(x3k	y3k+2))gb(x3k	NOUN
ejpam-3831	132	10	,	,	PUNCT
ejpam-3831	132	11	x3k+1	x3k+1	ADV
ejpam-3831	132	12	,	,	PUNCT
ejpam-3831	132	13	x3k+2	x3k+2	X
ejpam-3831	132	14	)	)	PUNCT
ejpam-3831	132	15	ωs(x3k	ωs(x3k	NUM
ejpam-3831	132	16	,	,	PUNCT
ejpam-3831	132	17	x3k+1	x3k+1	ADV
ejpam-3831	132	18	,	,	PUNCT
ejpam-3831	132	19	x3k+2	x3k+2	NOUN
ejpam-3831	132	20	,	,	PUNCT
ejpam-3831	132	21	y3k	y3k	NOUN
ejpam-3831	132	22	,	,	PUNCT
ejpam-3831	132	23	y3k+1	y3k+1	NOUN
ejpam-3831	132	24	,	,	PUNCT
ejpam-3831	132	25	y3k+2	y3k+2	NOUN
ejpam-3831	132	26	)	)	PUNCT
ejpam-3831	132	27	+	+	PROPN
ejpam-3831	132	28	α9(x3k+2	α9(x3k+2	PROPN
ejpam-3831	132	29	,	,	PUNCT
ejpam-3831	132	30	x3k	x3k	NOUN
ejpam-3831	132	31	)	)	PUNCT
ejpam-3831	132	32	·	·	PUNCT
ejpam-3831	133	1	gb(x3k+2	gb(x3k+2	NOUN
ejpam-3831	133	2	,	,	PUNCT
ejpam-3831	133	3	x3k+2	x3k+2	PROPN
ejpam-3831	133	4	,	,	PUNCT
ejpam-3831	133	5	t	t	PROPN
ejpam-3831	133	6	(	(	PUNCT
ejpam-3831	133	7	x3k+2	x3k+2	PROPN
ejpam-3831	133	8	,	,	PUNCT
ejpam-3831	133	9	y3k+2))gb(y3k	y3k+2))gb(y3k	PROPN
ejpam-3831	133	10	,	,	PUNCT
ejpam-3831	133	11	y3k+1	y3k+1	NOUN
ejpam-3831	133	12	,	,	PUNCT
ejpam-3831	133	13	y3k+2	y3k+2	NOUN
ejpam-3831	133	14	)	)	PUNCT
ejpam-3831	133	15	ωs(x3k	ωs(x3k	NUM
ejpam-3831	133	16	,	,	PUNCT
ejpam-3831	133	17	x3k+1	x3k+1	ADV
ejpam-3831	133	18	,	,	PUNCT
ejpam-3831	133	19	x3k+2	x3k+2	NOUN
ejpam-3831	133	20	,	,	PUNCT
ejpam-3831	133	21	y3k	y3k	NOUN
ejpam-3831	133	22	,	,	PUNCT
ejpam-3831	133	23	y3k+1	y3k+1	NOUN
ejpam-3831	133	24	,	,	PUNCT
ejpam-3831	133	25	y3k+2	y3k+2	NOUN
ejpam-3831	133	26	)	)	PUNCT
ejpam-3831	133	27	+	+	NOUN
ejpam-3831	133	28	α10(x3k+2	α10(x3k+2	NUM
ejpam-3831	133	29	,	,	PUNCT
ejpam-3831	133	30	x3k	x3k	NOUN
ejpam-3831	133	31	)	)	PUNCT
ejpam-3831	133	32	·	·	PUNCT
ejpam-3831	133	33	gb(x3k	gb(x3k	NOUN
ejpam-3831	133	34	,	,	PUNCT
ejpam-3831	133	35	x3k+1	x3k+1	PROPN
ejpam-3831	133	36	,	,	PUNCT
ejpam-3831	133	37	t	t	PROPN
ejpam-3831	133	38	(	(	PUNCT
ejpam-3831	133	39	x3k+2	x3k+2	NOUN
ejpam-3831	133	40	,	,	PUNCT
ejpam-3831	133	41	y3k+2))gb(x3k	y3k+2))gb(x3k	NOUN
ejpam-3831	133	42	,	,	PUNCT
ejpam-3831	133	43	x3k+1	x3k+1	ADV
ejpam-3831	133	44	,	,	PUNCT
ejpam-3831	133	45	x3k+2	x3k+2	X
ejpam-3831	133	46	)	)	PUNCT
ejpam-3831	133	47	ωs(x3k	ωs(x3k	NUM
ejpam-3831	133	48	,	,	PUNCT
ejpam-3831	133	49	x3k+1	x3k+1	ADV
ejpam-3831	133	50	,	,	PUNCT
ejpam-3831	133	51	x3k+2	x3k+2	NOUN
ejpam-3831	133	52	,	,	PUNCT
ejpam-3831	133	53	y3k	y3k	NOUN
ejpam-3831	133	54	,	,	PUNCT
ejpam-3831	133	55	y3k+1	y3k+1	NOUN
ejpam-3831	133	56	,	,	PUNCT
ejpam-3831	133	57	y3k+2	y3k+2	NOUN
ejpam-3831	133	58	)	)	PUNCT
ejpam-3831	133	59	+	+	NOUN
ejpam-3831	133	60	α11(x3k+2	α11(x3k+2	NOUN
ejpam-3831	133	61	,	,	PUNCT
ejpam-3831	133	62	x3k	x3k	NOUN
ejpam-3831	133	63	)	)	PUNCT
ejpam-3831	133	64	·	·	PUNCT
ejpam-3831	134	1	gb(x3k+1	gb(x3k+1	VERB
ejpam-3831	134	2	,	,	PUNCT
ejpam-3831	134	3	x3k+2	x3k+2	PROPN
ejpam-3831	134	4	,	,	PUNCT
ejpam-3831	134	5	f	f	PROPN
ejpam-3831	134	6	(	(	PUNCT
ejpam-3831	134	7	x3k	x3k	PROPN
ejpam-3831	134	8	,	,	PUNCT
ejpam-3831	134	9	y3k))gb(y3k	y3k))gb(y3k	NOUN
ejpam-3831	134	10	,	,	PUNCT
ejpam-3831	134	11	y3k+1	y3k+1	NOUN
ejpam-3831	134	12	,	,	PUNCT
ejpam-3831	134	13	y3k+2	y3k+2	NOUN
ejpam-3831	134	14	)	)	PUNCT
ejpam-3831	134	15	ωs(x3k	ωs(x3k	NUM
ejpam-3831	134	16	,	,	PUNCT
ejpam-3831	134	17	x3k+1	x3k+1	ADV
ejpam-3831	134	18	,	,	PUNCT
ejpam-3831	134	19	x3k+2	x3k+2	NOUN
ejpam-3831	134	20	,	,	PUNCT
ejpam-3831	134	21	y3k	y3k	NOUN
ejpam-3831	134	22	,	,	PUNCT
ejpam-3831	134	23	y3k+1	y3k+1	NOUN
ejpam-3831	134	24	,	,	PUNCT
ejpam-3831	134	25	y3k+2	y3k+2	NOUN
ejpam-3831	134	26	)	)	PUNCT
ejpam-3831	134	27	+	+	NOUN
ejpam-3831	134	28	α12(x3k+2	α12(x3k+2	NOUN
ejpam-3831	134	29	,	,	PUNCT
ejpam-3831	134	30	x3k	x3k	NOUN
ejpam-3831	134	31	)	)	PUNCT
ejpam-3831	134	32	·	·	PUNCT
ejpam-3831	135	1	gb(x3k+2	gb(x3k+2	NOUN
ejpam-3831	135	2	,	,	PUNCT
ejpam-3831	135	3	x3k	x3k	NOUN
ejpam-3831	135	4	,	,	PUNCT
ejpam-3831	135	5	h(x3k+1	h(x3k+1	NOUN
ejpam-3831	135	6	,	,	PUNCT
ejpam-3831	135	7	y3k+1))gb(x3k	y3k+1))gb(x3k	NOUN
ejpam-3831	135	8	,	,	PUNCT
ejpam-3831	135	9	x3k+1	x3k+1	ADV
ejpam-3831	135	10	,	,	PUNCT
ejpam-3831	135	11	x3k+2	x3k+2	X
ejpam-3831	135	12	)	)	PUNCT
ejpam-3831	135	13	ωs(x3k	ωs(x3k	NUM
ejpam-3831	135	14	,	,	PUNCT
ejpam-3831	135	15	x3k+1	x3k+1	ADV
ejpam-3831	135	16	,	,	PUNCT
ejpam-3831	135	17	x3k+2	x3k+2	NOUN
ejpam-3831	135	18	,	,	PUNCT
ejpam-3831	135	19	y3k	y3k	NOUN
ejpam-3831	135	20	,	,	PUNCT
ejpam-3831	135	21	y3k+1	y3k+1	NOUN
ejpam-3831	135	22	,	,	PUNCT
ejpam-3831	135	23	y3k+2	y3k+2	NOUN
ejpam-3831	135	24	)	)	PUNCT
ejpam-3831	135	25	now	now	ADV
ejpam-3831	135	26	,	,	PUNCT
ejpam-3831	135	27	with	with	ADP
ejpam-3831	135	28	the	the	DET
ejpam-3831	135	29	help	help	NOUN
ejpam-3831	135	30	of	of	ADP
ejpam-3831	135	31	condition	condition	NOUN
ejpam-3831	135	32	(	(	PUNCT
ejpam-3831	135	33	i	i	NOUN
ejpam-3831	135	34	)	)	PUNCT
ejpam-3831	135	35	,	,	PUNCT
ejpam-3831	135	36	we	we	PRON
ejpam-3831	135	37	have	have	VERB
ejpam-3831	135	38	αi(x3k	αi(x3k	NUM
ejpam-3831	135	39	,	,	PUNCT
ejpam-3831	135	40	x3k+1	x3k+1	PUNCT
ejpam-3831	135	41	)	)	PUNCT
ejpam-3831	135	42	=	=	SYM
ejpam-3831	136	1	αi(x3k	αi(x3k	PROPN
ejpam-3831	136	2	,	,	PUNCT
ejpam-3831	136	3	f	f	PROPN
ejpam-3831	136	4	(	(	PUNCT
ejpam-3831	136	5	x3k	x3k	NOUN
ejpam-3831	136	6	,	,	PUNCT
ejpam-3831	136	7	y3k	y3k	NOUN
ejpam-3831	136	8	)	)	PUNCT
ejpam-3831	136	9	)	)	PUNCT
ejpam-3831	136	10	≤	≤	NUM
ejpam-3831	137	1	αi(x3k	αi(x3k	NUM
ejpam-3831	137	2	,	,	PUNCT
ejpam-3831	137	3	x3k	x3k	NUM
ejpam-3831	137	4	)	)	PUNCT
ejpam-3831	137	5	=	=	SYM
ejpam-3831	138	1	αi(x3k	αi(x3k	NUM
ejpam-3831	138	2	,	,	PUNCT
ejpam-3831	138	3	f	f	PROPN
ejpam-3831	138	4	(	(	PUNCT
ejpam-3831	138	5	x3k−1	x3k−1	PROPN
ejpam-3831	138	6	,	,	PUNCT
ejpam-3831	138	7	y3k−1	y3k−1	PROPN
ejpam-3831	138	8	)	)	PUNCT
ejpam-3831	138	9	)	)	PUNCT
ejpam-3831	139	1	≤	≤	NUM
ejpam-3831	139	2	αi(x3k	αi(x3k	NUM
ejpam-3831	139	3	,	,	PUNCT
ejpam-3831	139	4	x3k−1	x3k−1	PROPN
ejpam-3831	139	5	)	)	PUNCT
ejpam-3831	139	6	=	=	SYM
ejpam-3831	139	7	αi(f	αi(f	NOUN
ejpam-3831	139	8	(	(	PUNCT
ejpam-3831	139	9	x3k−1	x3k−1	PROPN
ejpam-3831	139	10	,	,	PUNCT
ejpam-3831	139	11	y3k−1	y3k−1	PROPN
ejpam-3831	139	12	)	)	PUNCT
ejpam-3831	139	13	,	,	PUNCT
ejpam-3831	139	14	x3k−1	x3k−1	PROPN
ejpam-3831	139	15	)	)	PUNCT
ejpam-3831	139	16	≤	≤	NOUN
ejpam-3831	139	17	αi(x3k−1	αi(x3k−1	NOUN
ejpam-3831	139	18	,	,	PUNCT
ejpam-3831	139	19	x3k−1	x3k−1	PROPN
ejpam-3831	139	20	)	)	PUNCT
ejpam-3831	139	21	≤	≤	NOUN
ejpam-3831	139	22	·	·	PUNCT
ejpam-3831	139	23	·	·	PUNCT
ejpam-3831	139	24	·	·	PUNCT
ejpam-3831	140	1	≤	≤	NUM
ejpam-3831	140	2	αi(x0	αi(x0	PROPN
ejpam-3831	140	3	,	,	PUNCT
ejpam-3831	140	4	x0	x0	PROPN
ejpam-3831	140	5	)	)	PUNCT
ejpam-3831	140	6	for	for	ADP
ejpam-3831	140	7	all	all	DET
ejpam-3831	140	8	i	i	PRON
ejpam-3831	140	9	=	=	NOUN
ejpam-3831	140	10	1	1	NUM
ejpam-3831	140	11	,	,	PUNCT
ejpam-3831	140	12	2	2	NUM
ejpam-3831	140	13	,	,	PUNCT
ejpam-3831	140	14	3	3	NUM
ejpam-3831	140	15	,	,	PUNCT
ejpam-3831	140	16	4	4	NUM
ejpam-3831	140	17	.	.	PUNCT
ejpam-3831	140	18	similarly	similarly	ADV
ejpam-3831	140	19	by	by	ADP
ejpam-3831	140	20	using	use	VERB
ejpam-3831	140	21	(	(	PUNCT
ejpam-3831	140	22	ii	ii	NOUN
ejpam-3831	140	23	)	)	PUNCT
ejpam-3831	140	24	and	and	CCONJ
ejpam-3831	140	25	(	(	PUNCT
ejpam-3831	140	26	iii	iii	X
ejpam-3831	140	27	)	)	PUNCT
ejpam-3831	140	28	one	one	NOUN
ejpam-3831	140	29	can	can	AUX
ejpam-3831	140	30	show	show	VERB
ejpam-3831	140	31	that	that	SCONJ
ejpam-3831	140	32	αi(x3k+1	αi(x3k+1	NOUN
ejpam-3831	140	33	,	,	PUNCT
ejpam-3831	140	34	x3k+2	x3k+2	SYM
ejpam-3831	140	35	)	)	PUNCT
ejpam-3831	140	36	≤	≤	NUM
ejpam-3831	140	37	αi(x0	αi(x0	PROPN
ejpam-3831	140	38	,	,	PUNCT
ejpam-3831	140	39	x0	x0	PROPN
ejpam-3831	140	40	)	)	PUNCT
ejpam-3831	140	41	for	for	ADP
ejpam-3831	140	42	all	all	DET
ejpam-3831	140	43	i	i	PRON
ejpam-3831	140	44	=	=	NOUN
ejpam-3831	140	45	5	5	NUM
ejpam-3831	140	46	,	,	PUNCT
ejpam-3831	140	47	6	6	NUM
ejpam-3831	140	48	,	,	PUNCT
ejpam-3831	140	49	7	7	NUM
ejpam-3831	140	50	,	,	PUNCT
ejpam-3831	140	51	8	8	NUM
ejpam-3831	140	52	.	.	PUNCT
ejpam-3831	140	53	αi(x3k+2	αi(x3k+2	NUM
ejpam-3831	140	54	,	,	PUNCT
ejpam-3831	140	55	x3k	x3k	NOUN
ejpam-3831	140	56	)	)	PUNCT
ejpam-3831	140	57	≤	≤	NUM
ejpam-3831	140	58	αi(x0	αi(x0	PROPN
ejpam-3831	140	59	,	,	PUNCT
ejpam-3831	140	60	x0	x0	PROPN
ejpam-3831	140	61	)	)	PUNCT
ejpam-3831	140	62	for	for	ADP
ejpam-3831	140	63	all	all	DET
ejpam-3831	140	64	i	i	PRON
ejpam-3831	140	65	=	=	NOUN
ejpam-3831	140	66	9	9	NUM
ejpam-3831	140	67	,	,	PUNCT
ejpam-3831	140	68	10	10	NUM
ejpam-3831	140	69	,	,	PUNCT
ejpam-3831	140	70	11	11	NUM
ejpam-3831	140	71	,	,	PUNCT
ejpam-3831	140	72	12	12	NUM
ejpam-3831	140	73	.	.	PUNCT
ejpam-3831	141	1	so	so	ADV
ejpam-3831	141	2	by	by	ADP
ejpam-3831	141	3	using	use	VERB
ejpam-3831	141	4	the	the	DET
ejpam-3831	141	5	above	above	ADJ
ejpam-3831	141	6	and	and	CCONJ
ejpam-3831	141	7	(	(	PUNCT
ejpam-3831	141	8	3	3	NUM
ejpam-3831	141	9	)	)	PUNCT
ejpam-3831	141	10	and	and	CCONJ
ejpam-3831	141	11	(	(	PUNCT
ejpam-3831	141	12	4	4	X
ejpam-3831	141	13	)	)	PUNCT
ejpam-3831	141	14	one	one	NOUN
ejpam-3831	141	15	has	have	AUX
ejpam-3831	141	16	gb(x3k+1	gb(x3k+1	VERB
ejpam-3831	141	17	,	,	PUNCT
ejpam-3831	141	18	x3k+2	x3k+2	PRON
ejpam-3831	141	19	,	,	PUNCT
ejpam-3831	141	20	x3k+3	x3k+3	NOUN
ejpam-3831	141	21	)	)	PUNCT
ejpam-3831	141	22	≤	≤	NUM
ejpam-3831	141	23	α1(x0	α1(x0	NUM
ejpam-3831	141	24	,	,	PUNCT
ejpam-3831	141	25	x0	x0	PROPN
ejpam-3831	141	26	)	)	PUNCT
ejpam-3831	141	27	.	.	PUNCT
ejpam-3831	142	1	gb(x3k	gb(x3k	NOUN
ejpam-3831	142	2	,	,	PUNCT
ejpam-3831	142	3	x3k+1	x3k+1	ADV
ejpam-3831	142	4	,	,	PUNCT
ejpam-3831	142	5	x3k+2	x3k+2	PUNCT
ejpam-3831	142	6	)	)	PUNCT
ejpam-3831	143	1	+	+	ADJ
ejpam-3831	143	2	gb(y3k	gb(y3k	PROPN
ejpam-3831	143	3	,	,	PUNCT
ejpam-3831	143	4	y3k+1	y3k+1	NOUN
ejpam-3831	143	5	,	,	PUNCT
ejpam-3831	143	6	y3k+2	y3k+2	NOUN
ejpam-3831	143	7	)	)	PUNCT
ejpam-3831	143	8	2	2	NUM
ejpam-3831	143	9	m.m.m	m.m.m	NOUN
ejpam-3831	143	10	.	.	PUNCT
ejpam-3831	144	1	jaradat	jaradat	PROPN
ejpam-3831	144	2	et	et	PROPN
ejpam-3831	144	3	al	al	PROPN
ejpam-3831	144	4	.	.	PUNCT
ejpam-3831	144	5	/	/	SYM
ejpam-3831	144	6	eur	eur	PROPN
ejpam-3831	144	7	.	.	PUNCT
ejpam-3831	145	1	j.	j.	PROPN
ejpam-3831	145	2	pure	pure	PROPN
ejpam-3831	145	3	appl	appl	PROPN
ejpam-3831	145	4	.	.	PROPN
ejpam-3831	145	5	math	math	PROPN
ejpam-3831	145	6	,	,	PUNCT
ejpam-3831	145	7	13	13	NUM
ejpam-3831	145	8	(	(	PUNCT
ejpam-3831	145	9	4	4	NUM
ejpam-3831	145	10	)	)	PUNCT
ejpam-3831	145	11	(	(	PUNCT
ejpam-3831	145	12	2020	2020	NUM
ejpam-3831	145	13	)	)	PUNCT
ejpam-3831	145	14	,	,	PUNCT
ejpam-3831	145	15	995	995	NUM
ejpam-3831	145	16	-	-	SYM
ejpam-3831	145	17	1015	1015	NUM
ejpam-3831	145	18	1000	1000	NUM
ejpam-3831	146	1	+	+	ADV
ejpam-3831	146	2	α2(x0	α2(x0	PRON
ejpam-3831	146	3	,	,	PUNCT
ejpam-3831	146	4	x0	x0	PROPN
ejpam-3831	146	5	)	)	PUNCT
ejpam-3831	147	1	·	·	PUNCT
ejpam-3831	147	2	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	147	3	,	,	PUNCT
ejpam-3831	147	4	x3k+2	x3k+2	PROPN
ejpam-3831	147	5	,	,	PUNCT
ejpam-3831	147	6	x3k+3)gb(x3k	x3k+3)gb(x3k	PROPN
ejpam-3831	147	7	,	,	PUNCT
ejpam-3831	147	8	x3k+1	x3k+1	ADV
ejpam-3831	147	9	,	,	PUNCT
ejpam-3831	147	10	x3k+2	x3k+2	X
ejpam-3831	147	11	)	)	PUNCT
ejpam-3831	147	12	ωs(x3k	ωs(x3k	NUM
ejpam-3831	147	13	,	,	PUNCT
ejpam-3831	147	14	x3k+1	x3k+1	ADV
ejpam-3831	147	15	,	,	PUNCT
ejpam-3831	147	16	x3k+2	x3k+2	NOUN
ejpam-3831	147	17	,	,	PUNCT
ejpam-3831	147	18	y3k	y3k	NOUN
ejpam-3831	147	19	,	,	PUNCT
ejpam-3831	147	20	y3k+1	y3k+1	NOUN
ejpam-3831	147	21	,	,	PUNCT
ejpam-3831	147	22	y3k+2	y3k+2	NOUN
ejpam-3831	147	23	)	)	PUNCT
ejpam-3831	147	24	+	+	NOUN
ejpam-3831	147	25	α3(x0	α3(x0	NUM
ejpam-3831	147	26	,	,	PUNCT
ejpam-3831	147	27	x0	x0	PROPN
ejpam-3831	147	28	)	)	PUNCT
ejpam-3831	147	29	·	·	PUNCT
ejpam-3831	148	1	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	148	2	,	,	PUNCT
ejpam-3831	148	3	x3k+2	x3k+2	PROPN
ejpam-3831	148	4	,	,	PUNCT
ejpam-3831	148	5	x3k+3)gb(y3k	x3k+3)gb(y3k	PROPN
ejpam-3831	148	6	,	,	PUNCT
ejpam-3831	148	7	y3k+1	y3k+1	NOUN
ejpam-3831	148	8	,	,	PUNCT
ejpam-3831	148	9	y3k+2	y3k+2	NOUN
ejpam-3831	148	10	)	)	PUNCT
ejpam-3831	148	11	ωs(x3k	ωs(x3k	NUM
ejpam-3831	148	12	,	,	PUNCT
ejpam-3831	148	13	x3k+1	x3k+1	ADV
ejpam-3831	148	14	,	,	PUNCT
ejpam-3831	148	15	x3k+2	x3k+2	NOUN
ejpam-3831	148	16	,	,	PUNCT
ejpam-3831	148	17	y3k	y3k	NOUN
ejpam-3831	148	18	,	,	PUNCT
ejpam-3831	148	19	y3k+1	y3k+1	NOUN
ejpam-3831	148	20	,	,	PUNCT
ejpam-3831	148	21	y3k+2	y3k+2	NOUN
ejpam-3831	148	22	)	)	PUNCT
ejpam-3831	148	23	+	+	NOUN
ejpam-3831	148	24	α4(x0	α4(x0	ADV
ejpam-3831	148	25	,	,	PUNCT
ejpam-3831	148	26	x0	x0	PROPN
ejpam-3831	148	27	)	)	PUNCT
ejpam-3831	148	28	·	·	PUNCT
ejpam-3831	149	1	gb(x3k	gb(x3k	NOUN
ejpam-3831	149	2	,	,	PUNCT
ejpam-3831	149	3	x3k	x3k	NOUN
ejpam-3831	149	4	,	,	PUNCT
ejpam-3831	149	5	x3k+1)gb(x3k	x3k+1)gb(x3k	PROPN
ejpam-3831	149	6	,	,	PUNCT
ejpam-3831	149	7	x3k+1	x3k+1	ADV
ejpam-3831	149	8	,	,	PUNCT
ejpam-3831	149	9	x3k+2	x3k+2	X
ejpam-3831	149	10	)	)	PUNCT
ejpam-3831	149	11	ωs(x3k	ωs(x3k	NUM
ejpam-3831	149	12	,	,	PUNCT
ejpam-3831	149	13	x3k+1	x3k+1	ADV
ejpam-3831	149	14	,	,	PUNCT
ejpam-3831	149	15	x3k+2	x3k+2	NOUN
ejpam-3831	149	16	,	,	PUNCT
ejpam-3831	149	17	y3k	y3k	NOUN
ejpam-3831	149	18	,	,	PUNCT
ejpam-3831	149	19	y3k+1	y3k+1	NOUN
ejpam-3831	149	20	,	,	PUNCT
ejpam-3831	149	21	y3k+2	y3k+2	NOUN
ejpam-3831	149	22	)	)	PUNCT
ejpam-3831	149	23	+	+	NOUN
ejpam-3831	149	24	α5(x0	α5(x0	NOUN
ejpam-3831	149	25	,	,	PUNCT
ejpam-3831	149	26	x0	x0	PROPN
ejpam-3831	149	27	)	)	PUNCT
ejpam-3831	149	28	·	·	PUNCT
ejpam-3831	150	1	gb(x3k	gb(x3k	NOUN
ejpam-3831	150	2	,	,	PUNCT
ejpam-3831	150	3	x3k	x3k	PROPN
ejpam-3831	150	4	,	,	PUNCT
ejpam-3831	150	5	x3k+1)gb(y3k+1	x3k+1)gb(y3k+1	PROPN
ejpam-3831	150	6	,	,	PUNCT
ejpam-3831	150	7	y3k+1	y3k+1	NOUN
ejpam-3831	150	8	,	,	PUNCT
ejpam-3831	150	9	y3k+2	y3k+2	NOUN
ejpam-3831	150	10	)	)	PUNCT
ejpam-3831	150	11	ωs(x3k	ωs(x3k	NUM
ejpam-3831	150	12	,	,	PUNCT
ejpam-3831	150	13	x3k+1	x3k+1	ADV
ejpam-3831	150	14	,	,	PUNCT
ejpam-3831	150	15	x3k+2	x3k+2	NOUN
ejpam-3831	150	16	,	,	PUNCT
ejpam-3831	150	17	y3k	y3k	NOUN
ejpam-3831	150	18	,	,	PUNCT
ejpam-3831	150	19	y3k+1	y3k+1	NOUN
ejpam-3831	150	20	,	,	PUNCT
ejpam-3831	150	21	y3k+2	y3k+2	NOUN
ejpam-3831	150	22	)	)	PUNCT
ejpam-3831	150	23	+	+	NOUN
ejpam-3831	150	24	α6(x0	α6(x0	NOUN
ejpam-3831	150	25	,	,	PUNCT
ejpam-3831	150	26	x0	x0	PROPN
ejpam-3831	150	27	)	)	PUNCT
ejpam-3831	150	28	·	·	PUNCT
ejpam-3831	151	1	gb(x3k+1	gb(x3k+1	VERB
ejpam-3831	151	2	,	,	PUNCT
ejpam-3831	151	3	x3k+1	x3k+1	ADJ
ejpam-3831	151	4	,	,	PUNCT
ejpam-3831	151	5	x3k+2)gb(x3k	x3k+2)gb(x3k	PROPN
ejpam-3831	151	6	,	,	PUNCT
ejpam-3831	151	7	x3k+1	x3k+1	ADJ
ejpam-3831	151	8	,	,	PUNCT
ejpam-3831	151	9	x3k+2	x3k+2	X
ejpam-3831	151	10	)	)	PUNCT
ejpam-3831	151	11	ωs(x3k	ωs(x3k	NUM
ejpam-3831	151	12	,	,	PUNCT
ejpam-3831	151	13	x3k+1	x3k+1	ADV
ejpam-3831	151	14	,	,	PUNCT
ejpam-3831	151	15	x3k+2	x3k+2	NOUN
ejpam-3831	151	16	,	,	PUNCT
ejpam-3831	151	17	y3k	y3k	NOUN
ejpam-3831	151	18	,	,	PUNCT
ejpam-3831	151	19	y3k+1	y3k+1	NOUN
ejpam-3831	151	20	,	,	PUNCT
ejpam-3831	151	21	y3k+2	y3k+2	NOUN
ejpam-3831	151	22	)	)	PUNCT
ejpam-3831	151	23	+	+	NOUN
ejpam-3831	151	24	α7(x0	α7(x0	NUM
ejpam-3831	151	25	,	,	PUNCT
ejpam-3831	151	26	x0	x0	PROPN
ejpam-3831	151	27	)	)	PUNCT
ejpam-3831	151	28	·	·	PUNCT
ejpam-3831	152	1	gb(x3k+1	gb(x3k+1	VERB
ejpam-3831	152	2	,	,	PUNCT
ejpam-3831	152	3	x3k+1	x3k+1	ADJ
ejpam-3831	152	4	,	,	PUNCT
ejpam-3831	152	5	x3k+2)gb(y3k	x3k+2)gb(y3k	PROPN
ejpam-3831	152	6	,	,	PUNCT
ejpam-3831	152	7	y3k+1	y3k+1	NOUN
ejpam-3831	152	8	,	,	PUNCT
ejpam-3831	152	9	y3k+2	y3k+2	NOUN
ejpam-3831	152	10	)	)	PUNCT
ejpam-3831	152	11	ωs(x3k	ωs(x3k	NUM
ejpam-3831	152	12	,	,	PUNCT
ejpam-3831	152	13	x3k+1	x3k+1	ADV
ejpam-3831	152	14	,	,	PUNCT
ejpam-3831	152	15	x3k+2	x3k+2	NOUN
ejpam-3831	152	16	,	,	PUNCT
ejpam-3831	152	17	y3k	y3k	NOUN
ejpam-3831	152	18	,	,	PUNCT
ejpam-3831	152	19	y3k+1	y3k+1	NOUN
ejpam-3831	152	20	,	,	PUNCT
ejpam-3831	152	21	y3k+2	y3k+2	NOUN
ejpam-3831	152	22	)	)	PUNCT
ejpam-3831	153	1	+	+	NOUN
ejpam-3831	153	2	α8(x0	α8(x0	NOUN
ejpam-3831	153	3	,	,	PUNCT
ejpam-3831	153	4	x0	x0	PROPN
ejpam-3831	153	5	)	)	PUNCT
ejpam-3831	153	6	·	·	PUNCT
ejpam-3831	153	7	gb(x3k+2	gb(x3k+2	ADJ
ejpam-3831	153	8	,	,	PUNCT
ejpam-3831	153	9	x3k+2	x3k+2	PROPN
ejpam-3831	153	10	,	,	PUNCT
ejpam-3831	153	11	x3k+3)gb(x3k	x3k+3)gb(x3k	PROPN
ejpam-3831	153	12	,	,	PUNCT
ejpam-3831	153	13	x3k+1	x3k+1	ADV
ejpam-3831	153	14	,	,	PUNCT
ejpam-3831	153	15	x3k+2	x3k+2	X
ejpam-3831	153	16	)	)	PUNCT
ejpam-3831	153	17	ωs(x3k	ωs(x3k	NUM
ejpam-3831	153	18	,	,	PUNCT
ejpam-3831	153	19	x3k+1	x3k+1	ADV
ejpam-3831	153	20	,	,	PUNCT
ejpam-3831	153	21	x3k+2	x3k+2	NOUN
ejpam-3831	153	22	,	,	PUNCT
ejpam-3831	153	23	y3k	y3k	NOUN
ejpam-3831	153	24	,	,	PUNCT
ejpam-3831	153	25	y3k+1	y3k+1	NOUN
ejpam-3831	153	26	,	,	PUNCT
ejpam-3831	153	27	y3k+2	y3k+2	NOUN
ejpam-3831	153	28	)	)	PUNCT
ejpam-3831	153	29	+	+	NOUN
ejpam-3831	153	30	α9(x0	α9(x0	ADJ
ejpam-3831	153	31	,	,	PUNCT
ejpam-3831	153	32	x0	x0	PROPN
ejpam-3831	153	33	)	)	PUNCT
ejpam-3831	153	34	·	·	PUNCT
ejpam-3831	153	35	gb(x3k+2	gb(x3k+2	ADJ
ejpam-3831	153	36	,	,	PUNCT
ejpam-3831	153	37	x3k+2	x3k+2	PROPN
ejpam-3831	153	38	,	,	PUNCT
ejpam-3831	153	39	x3k+3)gb(y3k	x3k+3)gb(y3k	PROPN
ejpam-3831	153	40	,	,	PUNCT
ejpam-3831	153	41	y3k+1	y3k+1	NOUN
ejpam-3831	153	42	,	,	PUNCT
ejpam-3831	153	43	y3k+2	y3k+2	NOUN
ejpam-3831	153	44	)	)	PUNCT
ejpam-3831	153	45	ωs(x3k	ωs(x3k	NUM
ejpam-3831	153	46	,	,	PUNCT
ejpam-3831	153	47	x3k+1	x3k+1	ADV
ejpam-3831	153	48	,	,	PUNCT
ejpam-3831	153	49	x3k+2	x3k+2	NOUN
ejpam-3831	153	50	,	,	PUNCT
ejpam-3831	153	51	y3k	y3k	NOUN
ejpam-3831	153	52	,	,	PUNCT
ejpam-3831	153	53	y3k+1	y3k+1	NOUN
ejpam-3831	153	54	,	,	PUNCT
ejpam-3831	153	55	y3k+2	y3k+2	NOUN
ejpam-3831	153	56	)	)	PUNCT
ejpam-3831	153	57	+	+	ADV
ejpam-3831	153	58	α10(x0	α10(x0	PROPN
ejpam-3831	153	59	,	,	PUNCT
ejpam-3831	153	60	x0	x0	PROPN
ejpam-3831	153	61	)	)	PUNCT
ejpam-3831	153	62	·	·	PUNCT
ejpam-3831	153	63	gb(x3k	gb(x3k	NOUN
ejpam-3831	153	64	,	,	PUNCT
ejpam-3831	153	65	x3k+1	x3k+1	PROPN
ejpam-3831	153	66	,	,	PUNCT
ejpam-3831	153	67	x3k+3)gb(x3k	x3k+3)gb(x3k	PROPN
ejpam-3831	153	68	,	,	PUNCT
ejpam-3831	153	69	x3k+1	x3k+1	ADV
ejpam-3831	153	70	,	,	PUNCT
ejpam-3831	153	71	x3k+2	x3k+2	X
ejpam-3831	153	72	)	)	PUNCT
ejpam-3831	153	73	ωs(x3k	ωs(x3k	NUM
ejpam-3831	153	74	,	,	PUNCT
ejpam-3831	153	75	x3k+1	x3k+1	ADV
ejpam-3831	153	76	,	,	PUNCT
ejpam-3831	153	77	x3k+2	x3k+2	NOUN
ejpam-3831	153	78	,	,	PUNCT
ejpam-3831	153	79	y3k	y3k	NOUN
ejpam-3831	153	80	,	,	PUNCT
ejpam-3831	153	81	y3k+1	y3k+1	NOUN
ejpam-3831	153	82	,	,	PUNCT
ejpam-3831	153	83	y3k+2	y3k+2	NOUN
ejpam-3831	153	84	)	)	PUNCT
ejpam-3831	153	85	+	+	ADJ
ejpam-3831	153	86	α11(x0	α11(x0	PROPN
ejpam-3831	153	87	,	,	PUNCT
ejpam-3831	153	88	x0	x0	PROPN
ejpam-3831	153	89	)	)	PUNCT
ejpam-3831	153	90	·	·	PUNCT
ejpam-3831	154	1	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	154	2	,	,	PUNCT
ejpam-3831	154	3	x3k+2	x3k+2	PROPN
ejpam-3831	154	4	,	,	PUNCT
ejpam-3831	154	5	x3k+1)gb(y3k	x3k+1)gb(y3k	PROPN
ejpam-3831	154	6	,	,	PUNCT
ejpam-3831	154	7	y3k+1	y3k+1	NOUN
ejpam-3831	154	8	,	,	PUNCT
ejpam-3831	154	9	y3k+2	y3k+2	NOUN
ejpam-3831	154	10	)	)	PUNCT
ejpam-3831	154	11	ωs(x3k	ωs(x3k	NUM
ejpam-3831	154	12	,	,	PUNCT
ejpam-3831	154	13	x3k+1	x3k+1	ADV
ejpam-3831	154	14	,	,	PUNCT
ejpam-3831	154	15	x3k+2	x3k+2	NOUN
ejpam-3831	154	16	,	,	PUNCT
ejpam-3831	154	17	y3k	y3k	NOUN
ejpam-3831	154	18	,	,	PUNCT
ejpam-3831	154	19	y3k+1	y3k+1	NOUN
ejpam-3831	154	20	,	,	PUNCT
ejpam-3831	154	21	y3k+2	y3k+2	NOUN
ejpam-3831	154	22	)	)	PUNCT
ejpam-3831	154	23	+	+	NOUN
ejpam-3831	154	24	α12(x0	α12(x0	NUM
ejpam-3831	154	25	,	,	PUNCT
ejpam-3831	154	26	x0	x0	PROPN
ejpam-3831	154	27	)	)	PUNCT
ejpam-3831	154	28	·	·	PUNCT
ejpam-3831	155	1	gb(x3k+2	gb(x3k+2	NOUN
ejpam-3831	155	2	,	,	PUNCT
ejpam-3831	155	3	x3k	x3k	NOUN
ejpam-3831	155	4	,	,	PUNCT
ejpam-3831	155	5	x3k+2)gb(x3k	x3k+2)gb(x3k	PROPN
ejpam-3831	155	6	,	,	PUNCT
ejpam-3831	155	7	x3k+1	x3k+1	ADJ
ejpam-3831	155	8	,	,	PUNCT
ejpam-3831	155	9	x3k+2	x3k+2	X
ejpam-3831	155	10	)	)	PUNCT
ejpam-3831	155	11	ωs(x3k	ωs(x3k	NUM
ejpam-3831	155	12	,	,	PUNCT
ejpam-3831	155	13	x3k+1	x3k+1	ADV
ejpam-3831	155	14	,	,	PUNCT
ejpam-3831	155	15	x3k+2	x3k+2	NOUN
ejpam-3831	155	16	,	,	PUNCT
ejpam-3831	155	17	y3k	y3k	NOUN
ejpam-3831	155	18	,	,	PUNCT
ejpam-3831	155	19	y3k+1	y3k+1	NOUN
ejpam-3831	155	20	,	,	PUNCT
ejpam-3831	155	21	y3k+2	y3k+2	NOUN
ejpam-3831	155	22	)	)	PUNCT
ejpam-3831	155	23	now	now	ADV
ejpam-3831	155	24	using	use	VERB
ejpam-3831	155	25	(	(	PUNCT
ejpam-3831	155	26	gb3	gb3	NOUN
ejpam-3831	155	27	)	)	PUNCT
ejpam-3831	155	28	,	,	PUNCT
ejpam-3831	155	29	(	(	PUNCT
ejpam-3831	155	30	gb4	gb4	NOUN
ejpam-3831	155	31	)	)	PUNCT
ejpam-3831	155	32	and	and	CCONJ
ejpam-3831	155	33	(	(	PUNCT
ejpam-3831	155	34	gb5	gb5	NOUN
ejpam-3831	155	35	)	)	PUNCT
ejpam-3831	155	36	of	of	ADP
ejpam-3831	155	37	definition	definition	NOUN
ejpam-3831	155	38	2	2	NUM
ejpam-3831	155	39	we	we	PRON
ejpam-3831	155	40	have	have	AUX
ejpam-3831	155	41	gb(x3k+1	gb(x3k+1	VERB
ejpam-3831	155	42	,	,	PUNCT
ejpam-3831	155	43	x3k+2	x3k+2	PRON
ejpam-3831	155	44	,	,	PUNCT
ejpam-3831	155	45	x3k+3	x3k+3	ADJ
ejpam-3831	155	46	≤	≤	NUM
ejpam-3831	155	47	α1(x0	α1(x0	NUM
ejpam-3831	155	48	,	,	PUNCT
ejpam-3831	155	49	x0	x0	PROPN
ejpam-3831	155	50	)	)	PUNCT
ejpam-3831	155	51	.	.	PUNCT
ejpam-3831	156	1	gb(x3k	gb(x3k	NOUN
ejpam-3831	156	2	,	,	PUNCT
ejpam-3831	156	3	x3k+1	x3k+1	ADV
ejpam-3831	156	4	,	,	PUNCT
ejpam-3831	156	5	x3k+2	x3k+2	PUNCT
ejpam-3831	156	6	)	)	PUNCT
ejpam-3831	157	1	+	+	ADJ
ejpam-3831	157	2	gb(y3k	gb(y3k	PROPN
ejpam-3831	157	3	,	,	PUNCT
ejpam-3831	157	4	y3k+1	y3k+1	NOUN
ejpam-3831	157	5	,	,	PUNCT
ejpam-3831	157	6	y3k+2	y3k+2	NOUN
ejpam-3831	157	7	)	)	PUNCT
ejpam-3831	157	8	2	2	NUM
ejpam-3831	158	1	+	+	NOUN
ejpam-3831	158	2	α2(x0	α2(x0	PRON
ejpam-3831	158	3	,	,	PUNCT
ejpam-3831	158	4	x0	x0	PROPN
ejpam-3831	158	5	)	)	PUNCT
ejpam-3831	158	6	·	·	PUNCT
ejpam-3831	158	7	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	158	8	,	,	PUNCT
ejpam-3831	158	9	x3k+2	x3k+2	PROPN
ejpam-3831	158	10	,	,	PUNCT
ejpam-3831	158	11	x3k+3)gb(x3k	x3k+3)gb(x3k	PROPN
ejpam-3831	158	12	,	,	PUNCT
ejpam-3831	158	13	x3k+1	x3k+1	ADV
ejpam-3831	158	14	,	,	PUNCT
ejpam-3831	158	15	x3k+2	x3k+2	X
ejpam-3831	158	16	)	)	PUNCT
ejpam-3831	158	17	ωs(x3k	ωs(x3k	NUM
ejpam-3831	158	18	,	,	PUNCT
ejpam-3831	158	19	x3k+1	x3k+1	ADV
ejpam-3831	158	20	,	,	PUNCT
ejpam-3831	158	21	x3k+2	x3k+2	NOUN
ejpam-3831	158	22	,	,	PUNCT
ejpam-3831	158	23	y3k	y3k	NOUN
ejpam-3831	158	24	,	,	PUNCT
ejpam-3831	158	25	y3k+1	y3k+1	NOUN
ejpam-3831	158	26	,	,	PUNCT
ejpam-3831	158	27	y3k+2	y3k+2	NOUN
ejpam-3831	158	28	)	)	PUNCT
ejpam-3831	158	29	+	+	NOUN
ejpam-3831	158	30	α3(x0	α3(x0	NUM
ejpam-3831	158	31	,	,	PUNCT
ejpam-3831	158	32	x0	x0	PROPN
ejpam-3831	158	33	)	)	PUNCT
ejpam-3831	158	34	·	·	PUNCT
ejpam-3831	159	1	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	159	2	,	,	PUNCT
ejpam-3831	159	3	x3k+2	x3k+2	PROPN
ejpam-3831	159	4	,	,	PUNCT
ejpam-3831	159	5	x3k+3)gb(y3k	x3k+3)gb(y3k	PROPN
ejpam-3831	159	6	,	,	PUNCT
ejpam-3831	159	7	y3k+1	y3k+1	NOUN
ejpam-3831	159	8	,	,	PUNCT
ejpam-3831	159	9	y3k+2	y3k+2	NOUN
ejpam-3831	159	10	)	)	PUNCT
ejpam-3831	159	11	ωs(x3k	ωs(x3k	NUM
ejpam-3831	159	12	,	,	PUNCT
ejpam-3831	159	13	x3k+1	x3k+1	ADV
ejpam-3831	159	14	,	,	PUNCT
ejpam-3831	159	15	x3k+2	x3k+2	NOUN
ejpam-3831	159	16	,	,	PUNCT
ejpam-3831	159	17	y3k	y3k	NOUN
ejpam-3831	159	18	,	,	PUNCT
ejpam-3831	159	19	y3k+1	y3k+1	NOUN
ejpam-3831	159	20	,	,	PUNCT
ejpam-3831	159	21	y3k+2	y3k+2	NOUN
ejpam-3831	159	22	)	)	PUNCT
ejpam-3831	159	23	+	+	NOUN
ejpam-3831	159	24	α4(x0	α4(x0	ADV
ejpam-3831	159	25	,	,	PUNCT
ejpam-3831	159	26	x0	x0	PROPN
ejpam-3831	159	27	)	)	PUNCT
ejpam-3831	159	28	·	·	PUNCT
ejpam-3831	160	1	gb(x3k	gb(x3k	NOUN
ejpam-3831	160	2	,	,	PUNCT
ejpam-3831	160	3	x3k+1	x3k+1	ADJ
ejpam-3831	160	4	,	,	PUNCT
ejpam-3831	160	5	x3k+2)gb(x3k	x3k+2)gb(x3k	PROPN
ejpam-3831	160	6	,	,	PUNCT
ejpam-3831	160	7	x3k+1	x3k+1	ADJ
ejpam-3831	160	8	,	,	PUNCT
ejpam-3831	160	9	x3k+2	x3k+2	X
ejpam-3831	160	10	)	)	PUNCT
ejpam-3831	160	11	ωs(x3k	ωs(x3k	NUM
ejpam-3831	160	12	,	,	PUNCT
ejpam-3831	160	13	x3k+1	x3k+1	ADV
ejpam-3831	160	14	,	,	PUNCT
ejpam-3831	160	15	x3k+2	x3k+2	NOUN
ejpam-3831	160	16	,	,	PUNCT
ejpam-3831	160	17	y3k	y3k	NOUN
ejpam-3831	160	18	,	,	PUNCT
ejpam-3831	160	19	y3k+1	y3k+1	NOUN
ejpam-3831	160	20	,	,	PUNCT
ejpam-3831	160	21	y3k+2	y3k+2	NOUN
ejpam-3831	160	22	)	)	PUNCT
ejpam-3831	160	23	+	+	NOUN
ejpam-3831	160	24	α5(x0	α5(x0	NOUN
ejpam-3831	160	25	,	,	PUNCT
ejpam-3831	160	26	x0	x0	PROPN
ejpam-3831	160	27	)	)	PUNCT
ejpam-3831	160	28	·	·	PUNCT
ejpam-3831	160	29	gb(x3k	gb(x3k	NOUN
ejpam-3831	160	30	,	,	PUNCT
ejpam-3831	160	31	x3k+1	x3k+1	ADJ
ejpam-3831	160	32	,	,	PUNCT
ejpam-3831	160	33	x3k+2)gb(y3k+1	x3k+2)gb(y3k+1	PROPN
ejpam-3831	160	34	,	,	PUNCT
ejpam-3831	160	35	y3k+1	y3k+1	NOUN
ejpam-3831	160	36	,	,	PUNCT
ejpam-3831	160	37	y3k+2	y3k+2	NOUN
ejpam-3831	160	38	)	)	PUNCT
ejpam-3831	160	39	ωs(x3k	ωs(x3k	NUM
ejpam-3831	160	40	,	,	PUNCT
ejpam-3831	160	41	x3k+1	x3k+1	ADV
ejpam-3831	160	42	,	,	PUNCT
ejpam-3831	160	43	x3k+2	x3k+2	NOUN
ejpam-3831	160	44	,	,	PUNCT
ejpam-3831	160	45	y3k	y3k	NOUN
ejpam-3831	160	46	,	,	PUNCT
ejpam-3831	160	47	y3k+1	y3k+1	NOUN
ejpam-3831	160	48	,	,	PUNCT
ejpam-3831	160	49	y3k+2	y3k+2	NOUN
ejpam-3831	160	50	)	)	PUNCT
ejpam-3831	160	51	+	+	NOUN
ejpam-3831	160	52	α6(x0	α6(x0	NOUN
ejpam-3831	160	53	,	,	PUNCT
ejpam-3831	160	54	x0	x0	PROPN
ejpam-3831	160	55	)	)	PUNCT
ejpam-3831	160	56	·	·	PUNCT
ejpam-3831	161	1	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	161	2	,	,	PUNCT
ejpam-3831	161	3	x3k+2	x3k+2	PROPN
ejpam-3831	161	4	,	,	PUNCT
ejpam-3831	161	5	x3k+3)gb(x3k	x3k+3)gb(x3k	PROPN
ejpam-3831	161	6	,	,	PUNCT
ejpam-3831	161	7	x3k+1	x3k+1	ADV
ejpam-3831	161	8	,	,	PUNCT
ejpam-3831	161	9	x3k+2	x3k+2	X
ejpam-3831	161	10	)	)	PUNCT
ejpam-3831	161	11	ωs(x3k	ωs(x3k	NUM
ejpam-3831	161	12	,	,	PUNCT
ejpam-3831	161	13	x3k+1	x3k+1	ADV
ejpam-3831	161	14	,	,	PUNCT
ejpam-3831	161	15	x3k+2	x3k+2	NOUN
ejpam-3831	161	16	,	,	PUNCT
ejpam-3831	161	17	y3k	y3k	NOUN
ejpam-3831	161	18	,	,	PUNCT
ejpam-3831	161	19	y3k+1	y3k+1	NOUN
ejpam-3831	161	20	,	,	PUNCT
ejpam-3831	161	21	y3k+2	y3k+2	NOUN
ejpam-3831	161	22	)	)	PUNCT
ejpam-3831	161	23	+	+	NOUN
ejpam-3831	161	24	α7(x0	α7(x0	NUM
ejpam-3831	161	25	,	,	PUNCT
ejpam-3831	161	26	x0	x0	PROPN
ejpam-3831	161	27	)	)	PUNCT
ejpam-3831	161	28	·	·	PUNCT
ejpam-3831	162	1	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	162	2	,	,	PUNCT
ejpam-3831	162	3	x3k+2	x3k+2	PROPN
ejpam-3831	162	4	,	,	PUNCT
ejpam-3831	162	5	x3k+3)gb(y3k	x3k+3)gb(y3k	PROPN
ejpam-3831	162	6	,	,	PUNCT
ejpam-3831	162	7	y3k+1	y3k+1	NOUN
ejpam-3831	162	8	,	,	PUNCT
ejpam-3831	162	9	y3k+2	y3k+2	NOUN
ejpam-3831	162	10	)	)	PUNCT
ejpam-3831	162	11	ωs(x3k	ωs(x3k	NUM
ejpam-3831	162	12	,	,	PUNCT
ejpam-3831	162	13	x3k+1	x3k+1	ADV
ejpam-3831	162	14	,	,	PUNCT
ejpam-3831	162	15	x3k+2	x3k+2	NOUN
ejpam-3831	162	16	,	,	PUNCT
ejpam-3831	162	17	y3k	y3k	NOUN
ejpam-3831	162	18	,	,	PUNCT
ejpam-3831	162	19	y3k+1	y3k+1	NOUN
ejpam-3831	162	20	,	,	PUNCT
ejpam-3831	162	21	y3k+2	y3k+2	NOUN
ejpam-3831	162	22	)	)	PUNCT
ejpam-3831	162	23	m.m.m	m.m.m	NOUN
ejpam-3831	162	24	.	.	PUNCT
ejpam-3831	163	1	jaradat	jaradat	PROPN
ejpam-3831	163	2	et	et	PROPN
ejpam-3831	163	3	al	al	PROPN
ejpam-3831	163	4	.	.	PUNCT
ejpam-3831	163	5	/	/	SYM
ejpam-3831	163	6	eur	eur	PROPN
ejpam-3831	163	7	.	.	PUNCT
ejpam-3831	164	1	j.	j.	PROPN
ejpam-3831	164	2	pure	pure	PROPN
ejpam-3831	164	3	appl	appl	PROPN
ejpam-3831	164	4	.	.	PROPN
ejpam-3831	164	5	math	math	PROPN
ejpam-3831	164	6	,	,	PUNCT
ejpam-3831	164	7	13	13	NUM
ejpam-3831	164	8	(	(	PUNCT
ejpam-3831	164	9	4	4	NUM
ejpam-3831	164	10	)	)	PUNCT
ejpam-3831	164	11	(	(	PUNCT
ejpam-3831	164	12	2020	2020	NUM
ejpam-3831	164	13	)	)	PUNCT
ejpam-3831	164	14	,	,	PUNCT
ejpam-3831	164	15	995	995	NUM
ejpam-3831	164	16	-	-	SYM
ejpam-3831	164	17	1015	1015	NUM
ejpam-3831	164	18	1001	1001	NUM
ejpam-3831	165	1	+	+	ADV
ejpam-3831	165	2	α8(x0	α8(x0	NOUN
ejpam-3831	165	3	,	,	PUNCT
ejpam-3831	165	4	x0	x0	PROPN
ejpam-3831	165	5	)	)	PUNCT
ejpam-3831	165	6	·	·	PUNCT
ejpam-3831	165	7	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	165	8	,	,	PUNCT
ejpam-3831	165	9	x3k+2	x3k+2	PROPN
ejpam-3831	165	10	,	,	PUNCT
ejpam-3831	165	11	x3k+3)gb(x3k	x3k+3)gb(x3k	PROPN
ejpam-3831	165	12	,	,	PUNCT
ejpam-3831	165	13	x3k+1	x3k+1	ADV
ejpam-3831	165	14	,	,	PUNCT
ejpam-3831	165	15	x3k+2	x3k+2	X
ejpam-3831	165	16	)	)	PUNCT
ejpam-3831	165	17	ωs(x3k	ωs(x3k	NUM
ejpam-3831	165	18	,	,	PUNCT
ejpam-3831	165	19	x3k+1	x3k+1	ADV
ejpam-3831	165	20	,	,	PUNCT
ejpam-3831	165	21	x3k+2	x3k+2	NOUN
ejpam-3831	165	22	,	,	PUNCT
ejpam-3831	165	23	y3k	y3k	NOUN
ejpam-3831	165	24	,	,	PUNCT
ejpam-3831	165	25	y3k+1	y3k+1	NOUN
ejpam-3831	165	26	,	,	PUNCT
ejpam-3831	165	27	y3k+2	y3k+2	NOUN
ejpam-3831	165	28	)	)	PUNCT
ejpam-3831	165	29	+	+	NOUN
ejpam-3831	165	30	α9(x0	α9(x0	ADJ
ejpam-3831	165	31	,	,	PUNCT
ejpam-3831	165	32	x0	x0	PROPN
ejpam-3831	165	33	)	)	PUNCT
ejpam-3831	165	34	·	·	PUNCT
ejpam-3831	165	35	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	165	36	,	,	PUNCT
ejpam-3831	165	37	x3k+2	x3k+2	PROPN
ejpam-3831	165	38	,	,	PUNCT
ejpam-3831	165	39	x3k+3)gb(y3k	x3k+3)gb(y3k	PROPN
ejpam-3831	165	40	,	,	PUNCT
ejpam-3831	165	41	y3k+1	y3k+1	NOUN
ejpam-3831	165	42	,	,	PUNCT
ejpam-3831	165	43	y3k+2	y3k+2	NOUN
ejpam-3831	165	44	)	)	PUNCT
ejpam-3831	165	45	ωs(x3k	ωs(x3k	NUM
ejpam-3831	165	46	,	,	PUNCT
ejpam-3831	165	47	x3k+1	x3k+1	ADV
ejpam-3831	165	48	,	,	PUNCT
ejpam-3831	165	49	x3k+2	x3k+2	NOUN
ejpam-3831	165	50	,	,	PUNCT
ejpam-3831	165	51	y3k	y3k	NOUN
ejpam-3831	165	52	,	,	PUNCT
ejpam-3831	165	53	y3k+1	y3k+1	NOUN
ejpam-3831	165	54	,	,	PUNCT
ejpam-3831	165	55	y3k+2	y3k+2	NOUN
ejpam-3831	165	56	)	)	PUNCT
ejpam-3831	165	57	+	+	ADV
ejpam-3831	165	58	α10(x0	α10(x0	PROPN
ejpam-3831	165	59	,	,	PUNCT
ejpam-3831	165	60	x0	x0	PROPN
ejpam-3831	165	61	)	)	PUNCT
ejpam-3831	165	62	·	·	PUNCT
ejpam-3831	165	63	gb(x3k	gb(x3k	NOUN
ejpam-3831	165	64	,	,	PUNCT
ejpam-3831	165	65	x3k+1	x3k+1	ADJ
ejpam-3831	165	66	,	,	PUNCT
ejpam-3831	165	67	x3k+2)gb(x3k	x3k+2)gb(x3k	PROPN
ejpam-3831	165	68	,	,	PUNCT
ejpam-3831	165	69	x3k+1	x3k+1	ADJ
ejpam-3831	165	70	,	,	PUNCT
ejpam-3831	165	71	x3k+2	x3k+2	PUNCT
ejpam-3831	165	72	)	)	PUNCT
ejpam-3831	165	73	ω1(x3k	ω1(x3k	PROPN
ejpam-3831	165	74	,	,	PUNCT
ejpam-3831	165	75	x3k+1	x3k+1	ADV
ejpam-3831	165	76	,	,	PUNCT
ejpam-3831	165	77	x3k+2	x3k+2	NOUN
ejpam-3831	165	78	,	,	PUNCT
ejpam-3831	165	79	y3k	y3k	NOUN
ejpam-3831	165	80	,	,	PUNCT
ejpam-3831	165	81	y3k+1	y3k+1	NOUN
ejpam-3831	165	82	,	,	PUNCT
ejpam-3831	165	83	y3k+2	y3k+2	NOUN
ejpam-3831	165	84	)	)	PUNCT
ejpam-3831	165	85	+	+	ADV
ejpam-3831	165	86	α10(x0	α10(x0	PROPN
ejpam-3831	165	87	,	,	PUNCT
ejpam-3831	165	88	x0	x0	PROPN
ejpam-3831	165	89	)	)	PUNCT
ejpam-3831	165	90	·	·	PUNCT
ejpam-3831	165	91	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	165	92	,	,	PUNCT
ejpam-3831	165	93	x3k+2	x3k+2	PROPN
ejpam-3831	165	94	,	,	PUNCT
ejpam-3831	165	95	x3k+3)gb(x3k	x3k+3)gb(x3k	PROPN
ejpam-3831	165	96	,	,	PUNCT
ejpam-3831	165	97	x3k+1	x3k+1	ADV
ejpam-3831	165	98	,	,	PUNCT
ejpam-3831	165	99	x3k+2	x3k+2	PUNCT
ejpam-3831	165	100	)	)	PUNCT
ejpam-3831	165	101	ω1(x3k	ω1(x3k	PROPN
ejpam-3831	165	102	,	,	PUNCT
ejpam-3831	165	103	x3k+1	x3k+1	ADV
ejpam-3831	165	104	,	,	PUNCT
ejpam-3831	165	105	x3k+2	x3k+2	NOUN
ejpam-3831	165	106	,	,	PUNCT
ejpam-3831	165	107	y3k	y3k	NOUN
ejpam-3831	165	108	,	,	PUNCT
ejpam-3831	165	109	y3k+1	y3k+1	NOUN
ejpam-3831	165	110	,	,	PUNCT
ejpam-3831	165	111	y3k+2	y3k+2	NOUN
ejpam-3831	165	112	)	)	PUNCT
ejpam-3831	166	1	+	+	ADJ
ejpam-3831	166	2	α11(x0	α11(x0	PROPN
ejpam-3831	166	3	,	,	PUNCT
ejpam-3831	166	4	x0	x0	PROPN
ejpam-3831	166	5	)	)	PUNCT
ejpam-3831	166	6	·	·	PUNCT
ejpam-3831	166	7	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	166	8	,	,	PUNCT
ejpam-3831	166	9	x3k+2	x3k+2	PROPN
ejpam-3831	166	10	,	,	PUNCT
ejpam-3831	166	11	x3k+3)gb(y3k	x3k+3)gb(y3k	PROPN
ejpam-3831	166	12	,	,	PUNCT
ejpam-3831	166	13	y3k+1	y3k+1	NOUN
ejpam-3831	166	14	,	,	PUNCT
ejpam-3831	166	15	y3k+2	y3k+2	NOUN
ejpam-3831	166	16	)	)	PUNCT
ejpam-3831	166	17	ωs(x3k	ωs(x3k	NUM
ejpam-3831	166	18	,	,	PUNCT
ejpam-3831	166	19	x3k+1	x3k+1	ADV
ejpam-3831	166	20	,	,	PUNCT
ejpam-3831	166	21	x3k+2	x3k+2	NOUN
ejpam-3831	166	22	,	,	PUNCT
ejpam-3831	166	23	y3k	y3k	NOUN
ejpam-3831	166	24	,	,	PUNCT
ejpam-3831	166	25	y3k+1	y3k+1	NOUN
ejpam-3831	166	26	,	,	PUNCT
ejpam-3831	166	27	y3k+2	y3k+2	NOUN
ejpam-3831	166	28	)	)	PUNCT
ejpam-3831	166	29	+	+	NOUN
ejpam-3831	166	30	α12(x0	α12(x0	NUM
ejpam-3831	166	31	,	,	PUNCT
ejpam-3831	166	32	x0	x0	PROPN
ejpam-3831	166	33	)	)	PUNCT
ejpam-3831	166	34	·	·	PUNCT
ejpam-3831	166	35	gb(x3k	gb(x3k	NOUN
ejpam-3831	166	36	,	,	PUNCT
ejpam-3831	166	37	x3k+1	x3k+1	ADJ
ejpam-3831	166	38	,	,	PUNCT
ejpam-3831	166	39	x3k+2)gb(x3k	x3k+2)gb(x3k	PROPN
ejpam-3831	166	40	,	,	PUNCT
ejpam-3831	166	41	x3k+1	x3k+1	ADJ
ejpam-3831	166	42	,	,	PUNCT
ejpam-3831	166	43	x3k+2	x3k+2	X
ejpam-3831	166	44	)	)	PUNCT
ejpam-3831	166	45	ωs(x3k	ωs(x3k	NUM
ejpam-3831	166	46	,	,	PUNCT
ejpam-3831	166	47	x3k+1	x3k+1	ADV
ejpam-3831	166	48	,	,	PUNCT
ejpam-3831	166	49	x3k+2	x3k+2	NOUN
ejpam-3831	166	50	,	,	PUNCT
ejpam-3831	166	51	y3k	y3k	NOUN
ejpam-3831	166	52	,	,	PUNCT
ejpam-3831	166	53	y3k+1	y3k+1	NOUN
ejpam-3831	166	54	,	,	PUNCT
ejpam-3831	166	55	y3k+2	y3k+2	NOUN
ejpam-3831	166	56	)	)	PUNCT
ejpam-3831	167	1	which	which	PRON
ejpam-3831	167	2	implies	imply	VERB
ejpam-3831	167	3	that	that	SCONJ
ejpam-3831	167	4	gb(x3k+1	gb(x3k+1	VERB
ejpam-3831	167	5	,	,	PUNCT
ejpam-3831	167	6	x3k+2	x3k+2	PRON
ejpam-3831	167	7	,	,	PUNCT
ejpam-3831	167	8	x3k+3	x3k+3	NOUN
ejpam-3831	167	9	)	)	PUNCT
ejpam-3831	167	10	≤	≤	NUM
ejpam-3831	167	11	α1(x0	α1(x0	NUM
ejpam-3831	167	12	,	,	PUNCT
ejpam-3831	167	13	x0	x0	PROPN
ejpam-3831	167	14	)	)	PUNCT
ejpam-3831	168	1	.	.	PUNCT
ejpam-3831	169	1	gb(x3k	gb(x3k	NOUN
ejpam-3831	169	2	,	,	PUNCT
ejpam-3831	169	3	x3k+1	x3k+1	ADV
ejpam-3831	169	4	,	,	PUNCT
ejpam-3831	169	5	x3k+2	x3k+2	PUNCT
ejpam-3831	169	6	)	)	PUNCT
ejpam-3831	170	1	+	+	ADJ
ejpam-3831	170	2	gb(y3k	gb(y3k	PROPN
ejpam-3831	170	3	,	,	PUNCT
ejpam-3831	170	4	y3k+1	y3k+1	NOUN
ejpam-3831	170	5	,	,	PUNCT
ejpam-3831	170	6	y3k+2	y3k+2	NOUN
ejpam-3831	170	7	)	)	PUNCT
ejpam-3831	170	8	2	2	NUM
ejpam-3831	171	1	+	+	NOUN
ejpam-3831	171	2	α2(x0	α2(x0	PRON
ejpam-3831	171	3	,	,	PUNCT
ejpam-3831	171	4	x0	x0	PROPN
ejpam-3831	171	5	)	)	PUNCT
ejpam-3831	171	6	·	·	PUNCT
ejpam-3831	171	7	gb(x3k+1	gb(x3k+1	PROPN
ejpam-3831	171	8	,	,	PUNCT
ejpam-3831	171	9	x3k+2	x3k+2	PRON
ejpam-3831	171	10	,	,	PUNCT
ejpam-3831	171	11	x3k+3	x3k+3	PROPN
ejpam-3831	171	12	)	)	PUNCT
ejpam-3831	171	13	+	+	CCONJ
ejpam-3831	171	14	α3(x0	α3(x0	NUM
ejpam-3831	171	15	,	,	PUNCT
ejpam-3831	171	16	x0	x0	PROPN
ejpam-3831	171	17	)	)	PUNCT
ejpam-3831	171	18	·	·	PUNCT
ejpam-3831	171	19	gb(x3k+1	gb(x3k+1	PROPN
ejpam-3831	171	20	,	,	PUNCT
ejpam-3831	171	21	x3k+2	x3k+2	PRON
ejpam-3831	171	22	,	,	PUNCT
ejpam-3831	171	23	x3k+3	x3k+3	NOUN
ejpam-3831	171	24	)	)	PUNCT
ejpam-3831	172	1	+	+	ADV
ejpam-3831	172	2	α4(x0	α4(x0	ADV
ejpam-3831	172	3	,	,	PUNCT
ejpam-3831	172	4	x0	x0	PROPN
ejpam-3831	172	5	)	)	PUNCT
ejpam-3831	172	6	·	·	PUNCT
ejpam-3831	172	7	gb(x3k	gb(x3k	NOUN
ejpam-3831	172	8	,	,	PUNCT
ejpam-3831	172	9	x3k+1	x3k+1	ADV
ejpam-3831	172	10	,	,	PUNCT
ejpam-3831	172	11	x3k+2	x3k+2	PUNCT
ejpam-3831	172	12	)	)	PUNCT
ejpam-3831	172	13	+	+	CCONJ
ejpam-3831	172	14	α5(x0	α5(x0	ADV
ejpam-3831	172	15	,	,	PUNCT
ejpam-3831	172	16	x0	x0	PROPN
ejpam-3831	172	17	)	)	PUNCT
ejpam-3831	172	18	·	·	PUNCT
ejpam-3831	172	19	gb(x3k	gb(x3k	NOUN
ejpam-3831	172	20	,	,	PUNCT
ejpam-3831	172	21	x3k+1	x3k+1	ADV
ejpam-3831	172	22	,	,	PUNCT
ejpam-3831	172	23	x3k+2	x3k+2	PUNCT
ejpam-3831	172	24	)	)	PUNCT
ejpam-3831	173	1	+	+	ADV
ejpam-3831	173	2	α6(x0	α6(x0	NOUN
ejpam-3831	173	3	,	,	PUNCT
ejpam-3831	173	4	x0	x0	PROPN
ejpam-3831	173	5	)	)	PUNCT
ejpam-3831	173	6	·	·	PUNCT
ejpam-3831	173	7	gb(x3k+1	gb(x3k+1	PROPN
ejpam-3831	173	8	,	,	PUNCT
ejpam-3831	173	9	x3k+2	x3k+2	PRON
ejpam-3831	173	10	,	,	PUNCT
ejpam-3831	173	11	x3k+3	x3k+3	PROPN
ejpam-3831	173	12	)	)	PUNCT
ejpam-3831	173	13	+	+	CCONJ
ejpam-3831	173	14	α7(x0	α7(x0	NUM
ejpam-3831	173	15	,	,	PUNCT
ejpam-3831	173	16	x0	x0	PROPN
ejpam-3831	173	17	)	)	PUNCT
ejpam-3831	173	18	·	·	PUNCT
ejpam-3831	173	19	gb(x3k+1	gb(x3k+1	PROPN
ejpam-3831	173	20	,	,	PUNCT
ejpam-3831	173	21	x3k+2	x3k+2	PRON
ejpam-3831	173	22	,	,	PUNCT
ejpam-3831	173	23	x3k+3	x3k+3	NOUN
ejpam-3831	173	24	)	)	PUNCT
ejpam-3831	174	1	+	+	NOUN
ejpam-3831	174	2	α8(x0	α8(x0	NOUN
ejpam-3831	174	3	,	,	PUNCT
ejpam-3831	174	4	x0	x0	PROPN
ejpam-3831	174	5	)	)	PUNCT
ejpam-3831	174	6	·	·	PUNCT
ejpam-3831	174	7	gb(x3k+1	gb(x3k+1	PROPN
ejpam-3831	174	8	,	,	PUNCT
ejpam-3831	174	9	x3k+2	x3k+2	PRON
ejpam-3831	174	10	,	,	PUNCT
ejpam-3831	174	11	x3k+3	x3k+3	NOUN
ejpam-3831	174	12	)	)	PUNCT
ejpam-3831	174	13	+	+	CCONJ
ejpam-3831	174	14	α9(x0	α9(x0	ADJ
ejpam-3831	174	15	,	,	PUNCT
ejpam-3831	174	16	x0	x0	PROPN
ejpam-3831	174	17	)	)	PUNCT
ejpam-3831	174	18	·	·	PUNCT
ejpam-3831	174	19	gb(x3k+1	gb(x3k+1	PROPN
ejpam-3831	174	20	,	,	PUNCT
ejpam-3831	174	21	x3k+2	x3k+2	PRON
ejpam-3831	174	22	,	,	PUNCT
ejpam-3831	174	23	x3k+3	x3k+3	NOUN
ejpam-3831	174	24	)	)	PUNCT
ejpam-3831	175	1	+	+	ADV
ejpam-3831	175	2	α10(x0	α10(x0	PROPN
ejpam-3831	175	3	,	,	PUNCT
ejpam-3831	175	4	x0	x0	PROPN
ejpam-3831	175	5	)	)	PUNCT
ejpam-3831	175	6	·	·	PUNCT
ejpam-3831	175	7	gb(x3k	gb(x3k	NOUN
ejpam-3831	175	8	,	,	PUNCT
ejpam-3831	175	9	x3k+1	x3k+1	ADV
ejpam-3831	175	10	,	,	PUNCT
ejpam-3831	175	11	x3k+2	x3k+2	PUNCT
ejpam-3831	175	12	)	)	PUNCT
ejpam-3831	176	1	+	+	CCONJ
ejpam-3831	176	2	α10(x0	α10(x0	ADV
ejpam-3831	176	3	,	,	PUNCT
ejpam-3831	176	4	x0	x0	PROPN
ejpam-3831	176	5	)	)	PUNCT
ejpam-3831	176	6	·	·	PUNCT
ejpam-3831	177	1	gb(x3k+1	gb(x3k+1	PROPN
ejpam-3831	177	2	,	,	PUNCT
ejpam-3831	177	3	x3k+2	x3k+2	PRON
ejpam-3831	177	4	,	,	PUNCT
ejpam-3831	177	5	x3k+3	x3k+3	NOUN
ejpam-3831	177	6	)	)	PUNCT
ejpam-3831	178	1	+	+	ADJ
ejpam-3831	178	2	α11(x0	α11(x0	PROPN
ejpam-3831	178	3	,	,	PUNCT
ejpam-3831	178	4	x0	x0	PROPN
ejpam-3831	178	5	)	)	PUNCT
ejpam-3831	178	6	·	·	PUNCT
ejpam-3831	178	7	gb(x3k+1	gb(x3k+1	PROPN
ejpam-3831	178	8	,	,	PUNCT
ejpam-3831	178	9	x3k+2	x3k+2	PRON
ejpam-3831	178	10	,	,	PUNCT
ejpam-3831	178	11	x3k+3	x3k+3	NOUN
ejpam-3831	178	12	)	)	PUNCT
ejpam-3831	179	1	+	+	NUM
ejpam-3831	179	2	α12(x0	α12(x0	NUM
ejpam-3831	179	3	,	,	PUNCT
ejpam-3831	179	4	x0	x0	PROPN
ejpam-3831	179	5	)	)	PUNCT
ejpam-3831	179	6	·	·	PUNCT
ejpam-3831	179	7	gb(x3k	gb(x3k	NOUN
ejpam-3831	179	8	,	,	PUNCT
ejpam-3831	179	9	x3k+1	x3k+1	ADV
ejpam-3831	179	10	,	,	PUNCT
ejpam-3831	179	11	x3k+2	x3k+2	PUNCT
ejpam-3831	179	12	)	)	PUNCT
ejpam-3831	179	13	.	.	PUNCT
ejpam-3831	180	1	which	which	PRON
ejpam-3831	180	2	further	far	ADV
ejpam-3831	180	3	implies	imply	VERB
ejpam-3831	180	4	that	that	SCONJ
ejpam-3831	180	5	(	(	PUNCT
ejpam-3831	180	6	1−	1−	NUM
ejpam-3831	180	7	α2(x0	α2(x0	NUM
ejpam-3831	180	8	,	,	PUNCT
ejpam-3831	180	9	x0)−	x0)−	PROPN
ejpam-3831	180	10	α3(x0	α3(x0	PROPN
ejpam-3831	180	11	,	,	PUNCT
ejpam-3831	180	12	x0)−	x0)−	PROPN
ejpam-3831	180	13	11∑	11∑	PROPN
ejpam-3831	180	14	i=6	i=6	PROPN
ejpam-3831	180	15	αi(x0	αi(x0	PROPN
ejpam-3831	180	16	,	,	PUNCT
ejpam-3831	180	17	x0	x0	PROPN
ejpam-3831	180	18	)	)	PUNCT
ejpam-3831	180	19	)	)	PUNCT
ejpam-3831	180	20	·	·	PUNCT
ejpam-3831	180	21	gb(x3k+1	gb(x3k+1	PROPN
ejpam-3831	180	22	,	,	PUNCT
ejpam-3831	180	23	x3k+2	x3k+2	PRON
ejpam-3831	180	24	,	,	PUNCT
ejpam-3831	180	25	x3k+3	x3k+3	NOUN
ejpam-3831	180	26	)	)	PUNCT
ejpam-3831	180	27	≤	≤	NOUN
ejpam-3831	180	28	(	(	PUNCT
ejpam-3831	180	29	α1(x0	α1(x0	NUM
ejpam-3831	180	30	,	,	PUNCT
ejpam-3831	180	31	x0	x0	PROPN
ejpam-3831	180	32	)	)	PUNCT
ejpam-3831	180	33	2	2	NUM
ejpam-3831	180	34	+	+	CCONJ
ejpam-3831	180	35	α4(x0	α4(x0	ADV
ejpam-3831	180	36	,	,	PUNCT
ejpam-3831	180	37	x0	x0	PROPN
ejpam-3831	180	38	)	)	PUNCT
ejpam-3831	181	1	+	+	CCONJ
ejpam-3831	181	2	α5(x0	α5(x0	ADV
ejpam-3831	181	3	,	,	PUNCT
ejpam-3831	181	4	x0	x0	PROPN
ejpam-3831	181	5	)	)	PUNCT
ejpam-3831	182	1	+	+	CCONJ
ejpam-3831	182	2	α10(x0	α10(x0	ADV
ejpam-3831	182	3	,	,	PUNCT
ejpam-3831	182	4	x0	x0	PROPN
ejpam-3831	182	5	)	)	PUNCT
ejpam-3831	183	1	+	+	NUM
ejpam-3831	183	2	α12(x0	α12(x0	NUM
ejpam-3831	183	3	,	,	PUNCT
ejpam-3831	183	4	x0	x0	PROPN
ejpam-3831	183	5	)	)	PUNCT
ejpam-3831	183	6	)	)	PUNCT
ejpam-3831	184	1	·	·	PUNCT
ejpam-3831	184	2	gb(x3k	gb(x3k	NOUN
ejpam-3831	184	3	,	,	PUNCT
ejpam-3831	184	4	x3k+1	x3k+1	ADV
ejpam-3831	184	5	,	,	PUNCT
ejpam-3831	184	6	x3k+2	x3k+2	PUNCT
ejpam-3831	184	7	)	)	PUNCT
ejpam-3831	185	1	+	+	CCONJ
ejpam-3831	185	2	α1(x0	α1(x0	NUM
ejpam-3831	185	3	,	,	PUNCT
ejpam-3831	185	4	x0	x0	PROPN
ejpam-3831	185	5	)	)	PUNCT
ejpam-3831	185	6	2	2	NUM
ejpam-3831	185	7	·	·	PUNCT
ejpam-3831	185	8	gb(y3k	gb(y3k	PROPN
ejpam-3831	185	9	,	,	PUNCT
ejpam-3831	185	10	y3k+1	y3k+1	NOUN
ejpam-3831	185	11	,	,	PUNCT
ejpam-3831	185	12	y3k+2	y3k+2	PROPN
ejpam-3831	185	13	)	)	PUNCT
ejpam-3831	185	14	.	.	PUNCT
ejpam-3831	186	1	which	which	PRON
ejpam-3831	186	2	gives	give	VERB
ejpam-3831	186	3	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	186	4	,	,	PUNCT
ejpam-3831	186	5	x3k+2	x3k+2	PRON
ejpam-3831	186	6	,	,	PUNCT
ejpam-3831	186	7	x3k+3	x3k+3	PROPN
ejpam-3831	186	8	)	)	PUNCT
ejpam-3831	186	9	(	(	PUNCT
ejpam-3831	186	10	6	6	NUM
ejpam-3831	186	11	)	)	PUNCT
ejpam-3831	186	12	≤	≤	NOUN
ejpam-3831	186	13	(	(	PUNCT
ejpam-3831	186	14	α1(x0,x0	α1(x0,x0	PROPN
ejpam-3831	186	15	)	)	PUNCT
ejpam-3831	186	16	2	2	NUM
ejpam-3831	187	1	+	+	CCONJ
ejpam-3831	187	2	α4(x0	α4(x0	ADV
ejpam-3831	187	3	,	,	PUNCT
ejpam-3831	187	4	x0	x0	PROPN
ejpam-3831	187	5	)	)	PUNCT
ejpam-3831	188	1	+	+	CCONJ
ejpam-3831	188	2	α5(x0	α5(x0	ADV
ejpam-3831	188	3	,	,	PUNCT
ejpam-3831	188	4	x0	x0	PROPN
ejpam-3831	188	5	)	)	PUNCT
ejpam-3831	189	1	+	+	CCONJ
ejpam-3831	189	2	α10(x0	α10(x0	ADV
ejpam-3831	189	3	,	,	PUNCT
ejpam-3831	189	4	x0	x0	PROPN
ejpam-3831	189	5	)	)	PUNCT
ejpam-3831	190	1	+	+	NUM
ejpam-3831	190	2	α12(x0	α12(x0	NUM
ejpam-3831	190	3	,	,	PUNCT
ejpam-3831	190	4	x0	x0	PROPN
ejpam-3831	190	5	)	)	PUNCT
ejpam-3831	190	6	)	)	PUNCT
ejpam-3831	191	1	(	(	PUNCT
ejpam-3831	191	2	1−	1−	NUM
ejpam-3831	191	3	α2(x0	α2(x0	NUM
ejpam-3831	191	4	,	,	PUNCT
ejpam-3831	191	5	x0)−	x0)−	PROPN
ejpam-3831	191	6	α3(x0	α3(x0	PROPN
ejpam-3831	191	7	,	,	PUNCT
ejpam-3831	191	8	x0)−	x0)−	PROPN
ejpam-3831	191	9	11∑	11∑	PROPN
ejpam-3831	191	10	i=6	i=6	PROPN
ejpam-3831	191	11	αi(x0	αi(x0	PROPN
ejpam-3831	191	12	,	,	PUNCT
ejpam-3831	191	13	x0	x0	PROPN
ejpam-3831	191	14	)	)	PUNCT
ejpam-3831	191	15	)	)	PUNCT
ejpam-3831	192	1	.gb(x3k	.gb(x3k	PUNCT
ejpam-3831	192	2	,	,	PUNCT
ejpam-3831	192	3	x3k+1	x3k+1	ADV
ejpam-3831	192	4	,	,	PUNCT
ejpam-3831	192	5	x3k+2	x3k+2	CCONJ
ejpam-3831	192	6	)	)	PUNCT
ejpam-3831	192	7	m.m.m	m.m.m	NOUN
ejpam-3831	192	8	.	.	PUNCT
ejpam-3831	192	9	jaradat	jaradat	PROPN
ejpam-3831	192	10	et	et	PROPN
ejpam-3831	192	11	al	al	PROPN
ejpam-3831	192	12	.	.	PUNCT
ejpam-3831	192	13	/	/	SYM
ejpam-3831	192	14	eur	eur	PROPN
ejpam-3831	192	15	.	.	PUNCT
ejpam-3831	193	1	j.	j.	PROPN
ejpam-3831	193	2	pure	pure	PROPN
ejpam-3831	193	3	appl	appl	PROPN
ejpam-3831	193	4	.	.	PROPN
ejpam-3831	193	5	math	math	PROPN
ejpam-3831	193	6	,	,	PUNCT
ejpam-3831	193	7	13	13	NUM
ejpam-3831	193	8	(	(	PUNCT
ejpam-3831	193	9	4	4	NUM
ejpam-3831	193	10	)	)	PUNCT
ejpam-3831	193	11	(	(	PUNCT
ejpam-3831	193	12	2020	2020	NUM
ejpam-3831	193	13	)	)	PUNCT
ejpam-3831	193	14	,	,	PUNCT
ejpam-3831	193	15	995	995	NUM
ejpam-3831	193	16	-	-	SYM
ejpam-3831	193	17	1015	1015	NUM
ejpam-3831	193	18	1002	1002	NUM
ejpam-3831	193	19	+	+	CCONJ
ejpam-3831	193	20	α1(x0	α1(x0	NUM
ejpam-3831	193	21	,	,	PUNCT
ejpam-3831	193	22	x0	x0	PROPN
ejpam-3831	193	23	)	)	PUNCT
ejpam-3831	193	24	2	2	NUM
ejpam-3831	193	25	(	(	PUNCT
ejpam-3831	193	26	1−	1−	NUM
ejpam-3831	193	27	α2(x0	α2(x0	NUM
ejpam-3831	193	28	,	,	PUNCT
ejpam-3831	193	29	x0)−	x0)−	PROPN
ejpam-3831	193	30	α3(x0	α3(x0	PROPN
ejpam-3831	193	31	,	,	PUNCT
ejpam-3831	193	32	x0)−	x0)−	PROPN
ejpam-3831	193	33	11∑	11∑	PROPN
ejpam-3831	193	34	i=6	i=6	PROPN
ejpam-3831	193	35	αi(x0	αi(x0	PROPN
ejpam-3831	193	36	,	,	PUNCT
ejpam-3831	193	37	x0	x0	PROPN
ejpam-3831	193	38	)	)	PUNCT
ejpam-3831	193	39	)	)	PUNCT
ejpam-3831	194	1	·	·	PUNCT
ejpam-3831	194	2	gb(y3k	gb(y3k	PROPN
ejpam-3831	194	3	,	,	PUNCT
ejpam-3831	194	4	y3k+1	y3k+1	NOUN
ejpam-3831	194	5	,	,	PUNCT
ejpam-3831	194	6	y3k+2	y3k+2	NOUN
ejpam-3831	194	7	)	)	PUNCT
ejpam-3831	194	8	.	.	PUNCT
ejpam-3831	195	1	similarly	similarly	ADV
ejpam-3831	195	2	for	for	ADP
ejpam-3831	195	3	the	the	DET
ejpam-3831	195	4	sequence	sequence	NOUN
ejpam-3831	195	5	{	{	PUNCT
ejpam-3831	195	6	yn	yn	PROPN
ejpam-3831	195	7	}	}	PUNCT
ejpam-3831	195	8	,	,	PUNCT
ejpam-3831	195	9	we	we	PRON
ejpam-3831	195	10	have	have	VERB
ejpam-3831	195	11	gb(y3k+1	gb(y3k+1	NOUN
ejpam-3831	195	12	,	,	PUNCT
ejpam-3831	195	13	y3k+2	y3k+2	PROPN
ejpam-3831	195	14	,	,	PUNCT
ejpam-3831	195	15	y3k+3	y3k+3	NUM
ejpam-3831	195	16	)	)	PUNCT
ejpam-3831	195	17	(	(	PUNCT
ejpam-3831	195	18	7	7	X
ejpam-3831	195	19	)	)	PUNCT
ejpam-3831	195	20	≤	≤	NOUN
ejpam-3831	195	21	(	(	PUNCT
ejpam-3831	195	22	α1(x0,x0	α1(x0,x0	PROPN
ejpam-3831	195	23	)	)	PUNCT
ejpam-3831	195	24	2	2	NUM
ejpam-3831	196	1	+	+	CCONJ
ejpam-3831	196	2	α4(x0	α4(x0	ADV
ejpam-3831	196	3	,	,	PUNCT
ejpam-3831	196	4	x0	x0	PROPN
ejpam-3831	196	5	)	)	PUNCT
ejpam-3831	197	1	+	+	CCONJ
ejpam-3831	197	2	α5(x0	α5(x0	ADV
ejpam-3831	197	3	,	,	PUNCT
ejpam-3831	197	4	x0	x0	PROPN
ejpam-3831	197	5	)	)	PUNCT
ejpam-3831	198	1	+	+	CCONJ
ejpam-3831	198	2	α10(x0	α10(x0	ADV
ejpam-3831	198	3	,	,	PUNCT
ejpam-3831	198	4	x0	x0	PROPN
ejpam-3831	198	5	)	)	PUNCT
ejpam-3831	199	1	+	+	NUM
ejpam-3831	199	2	α12(x0	α12(x0	NUM
ejpam-3831	199	3	,	,	PUNCT
ejpam-3831	199	4	x0	x0	PROPN
ejpam-3831	199	5	)	)	PUNCT
ejpam-3831	199	6	)	)	PUNCT
ejpam-3831	200	1	(	(	PUNCT
ejpam-3831	200	2	1−	1−	NUM
ejpam-3831	200	3	α2(x0	α2(x0	NUM
ejpam-3831	200	4	,	,	PUNCT
ejpam-3831	200	5	x0)−	x0)−	PROPN
ejpam-3831	200	6	α3(x0	α3(x0	PROPN
ejpam-3831	200	7	,	,	PUNCT
ejpam-3831	200	8	x0)−	x0)−	PROPN
ejpam-3831	200	9	11∑	11∑	PROPN
ejpam-3831	200	10	i=6	i=6	PROPN
ejpam-3831	200	11	αi(x0	αi(x0	PROPN
ejpam-3831	200	12	,	,	PUNCT
ejpam-3831	200	13	x0	x0	PROPN
ejpam-3831	200	14	)	)	PUNCT
ejpam-3831	200	15	)	)	PUNCT
ejpam-3831	201	1	.gb(y3k	.gb(y3k	NUM
ejpam-3831	201	2	,	,	PUNCT
ejpam-3831	201	3	y3k+1	y3k+1	NOUN
ejpam-3831	201	4	,	,	PUNCT
ejpam-3831	201	5	y3k+2	y3k+2	NOUN
ejpam-3831	201	6	)	)	PUNCT
ejpam-3831	201	7	+	+	NUM
ejpam-3831	201	8	α1(x0	α1(x0	NUM
ejpam-3831	201	9	,	,	PUNCT
ejpam-3831	201	10	x0	x0	PROPN
ejpam-3831	201	11	)	)	PUNCT
ejpam-3831	201	12	2	2	NUM
ejpam-3831	201	13	(	(	PUNCT
ejpam-3831	201	14	1−	1−	NUM
ejpam-3831	201	15	α2(x0	α2(x0	NUM
ejpam-3831	201	16	,	,	PUNCT
ejpam-3831	201	17	x0)−	x0)−	PROPN
ejpam-3831	201	18	α3(x0	α3(x0	PROPN
ejpam-3831	201	19	,	,	PUNCT
ejpam-3831	201	20	x0)−	x0)−	PROPN
ejpam-3831	201	21	11∑	11∑	PROPN
ejpam-3831	201	22	i=6	i=6	PROPN
ejpam-3831	201	23	αi(x0	αi(x0	PROPN
ejpam-3831	201	24	,	,	PUNCT
ejpam-3831	201	25	x0	x0	PROPN
ejpam-3831	201	26	)	)	PUNCT
ejpam-3831	201	27	)	)	PUNCT
ejpam-3831	202	1	·	·	PUNCT
ejpam-3831	202	2	gb(x3k	gb(x3k	NOUN
ejpam-3831	202	3	,	,	PUNCT
ejpam-3831	202	4	x3k+1	x3k+1	ADV
ejpam-3831	202	5	,	,	PUNCT
ejpam-3831	202	6	x3k+2	x3k+2	PUNCT
ejpam-3831	202	7	)	)	PUNCT
ejpam-3831	202	8	.	.	PUNCT
ejpam-3831	203	1	adding	add	VERB
ejpam-3831	203	2	inequalities	inequality	NOUN
ejpam-3831	203	3	(	(	PUNCT
ejpam-3831	203	4	6	6	NUM
ejpam-3831	203	5	)	)	PUNCT
ejpam-3831	203	6	,	,	PUNCT
ejpam-3831	203	7	and	and	CCONJ
ejpam-3831	203	8	(	(	PUNCT
ejpam-3831	203	9	7	7	X
ejpam-3831	203	10	)	)	PUNCT
ejpam-3831	203	11	we	we	PRON
ejpam-3831	203	12	get	get	VERB
ejpam-3831	203	13	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	203	14	,	,	PUNCT
ejpam-3831	203	15	x3k+2	x3k+2	PRON
ejpam-3831	203	16	,	,	PUNCT
ejpam-3831	203	17	x3k+3	x3k+3	NOUN
ejpam-3831	203	18	)	)	PUNCT
ejpam-3831	204	1	+	+	ADJ
ejpam-3831	204	2	gb(y3k+1	gb(y3k+1	NOUN
ejpam-3831	204	3	,	,	PUNCT
ejpam-3831	204	4	y3k+2	y3k+2	PROPN
ejpam-3831	204	5	,	,	PUNCT
ejpam-3831	204	6	y3k+3	y3k+3	ADJ
ejpam-3831	204	7	)	)	PUNCT
ejpam-3831	204	8	≤	≤	NOUN
ejpam-3831	204	9	h.	h.	NOUN
ejpam-3831	204	10	(	(	PUNCT
ejpam-3831	204	11	gb(x3k	gb(x3k	PROPN
ejpam-3831	204	12	,	,	PUNCT
ejpam-3831	204	13	x3k+1	x3k+1	ADV
ejpam-3831	204	14	,	,	PUNCT
ejpam-3831	204	15	x3k+2	x3k+2	PUNCT
ejpam-3831	204	16	)	)	PUNCT
ejpam-3831	205	1	+	+	ADJ
ejpam-3831	205	2	gb(y3k	gb(y3k	PROPN
ejpam-3831	205	3	,	,	PUNCT
ejpam-3831	205	4	y3k+1	y3k+1	NOUN
ejpam-3831	205	5	,	,	PUNCT
ejpam-3831	205	6	y3k+2	y3k+2	NOUN
ejpam-3831	205	7	)	)	PUNCT
ejpam-3831	205	8	)	)	PUNCT
ejpam-3831	205	9	,	,	PUNCT
ejpam-3831	205	10	where	where	SCONJ
ejpam-3831	205	11	0	0	NUM
ejpam-3831	205	12	≤	≤	NUM
ejpam-3831	205	13	h	h	NOUN
ejpam-3831	205	14	=	=	PRON
ejpam-3831	205	15	(	(	PUNCT
ejpam-3831	205	16	α1(x0	α1(x0	NUM
ejpam-3831	205	17	,	,	PUNCT
ejpam-3831	205	18	x0	x0	PROPN
ejpam-3831	205	19	)	)	PUNCT
ejpam-3831	206	1	+	+	CCONJ
ejpam-3831	206	2	α4(x0	α4(x0	ADV
ejpam-3831	206	3	,	,	PUNCT
ejpam-3831	206	4	x0	x0	PROPN
ejpam-3831	206	5	)	)	PUNCT
ejpam-3831	207	1	+	+	CCONJ
ejpam-3831	207	2	α5(x0	α5(x0	ADV
ejpam-3831	207	3	,	,	PUNCT
ejpam-3831	207	4	x0	x0	PROPN
ejpam-3831	207	5	)	)	PUNCT
ejpam-3831	208	1	+	+	CCONJ
ejpam-3831	208	2	α10(x0	α10(x0	ADV
ejpam-3831	208	3	,	,	PUNCT
ejpam-3831	208	4	x0	x0	PROPN
ejpam-3831	208	5	)	)	PUNCT
ejpam-3831	209	1	+	+	NUM
ejpam-3831	209	2	α12(x0	α12(x0	NUM
ejpam-3831	209	3	,	,	PUNCT
ejpam-3831	209	4	x0	x0	PROPN
ejpam-3831	209	5	)	)	PUNCT
ejpam-3831	209	6	)	)	PUNCT
ejpam-3831	210	1	(	(	PUNCT
ejpam-3831	210	2	1−	1−	NUM
ejpam-3831	210	3	α2(x0	α2(x0	NUM
ejpam-3831	210	4	,	,	PUNCT
ejpam-3831	210	5	x0)−	x0)−	PROPN
ejpam-3831	210	6	α3(x0	α3(x0	PROPN
ejpam-3831	210	7	,	,	PUNCT
ejpam-3831	210	8	x0)−	x0)−	PROPN
ejpam-3831	210	9	11∑	11∑	PROPN
ejpam-3831	210	10	i=6	i=6	PROPN
ejpam-3831	210	11	αi(x0	αi(x0	PROPN
ejpam-3831	210	12	,	,	PUNCT
ejpam-3831	210	13	x0	x0	PROPN
ejpam-3831	210	14	)	)	PUNCT
ejpam-3831	210	15	)	)	PUNCT
ejpam-3831	210	16	.	.	PUNCT
ejpam-3831	211	1	by	by	ADP
ejpam-3831	211	2	(	(	PUNCT
ejpam-3831	211	3	2	2	X
ejpam-3831	211	4	)	)	PUNCT
ejpam-3831	211	5	we	we	PRON
ejpam-3831	211	6	have	have	VERB
ejpam-3831	211	7	0	0	NUM
ejpam-3831	211	8	<	<	X
ejpam-3831	211	9	h	h	X
ejpam-3831	211	10	<	<	X
ejpam-3831	211	11	1	1	NUM
ejpam-3831	211	12	s	s	NOUN
ejpam-3831	211	13	.	.	PUNCT
ejpam-3831	212	1	(	(	PUNCT
ejpam-3831	212	2	8)	8)	NUM
ejpam-3831	212	3	similarly	similarly	ADV
ejpam-3831	212	4	,	,	PUNCT
ejpam-3831	212	5	gb(x3k+2	gb(x3k+2	PROPN
ejpam-3831	212	6	,	,	PUNCT
ejpam-3831	212	7	x3k+3	x3k+3	NOUN
ejpam-3831	212	8	,	,	PUNCT
ejpam-3831	212	9	x3k+4	x3k+4	ADJ
ejpam-3831	212	10	)	)	PUNCT
ejpam-3831	213	1	+	+	NOUN
ejpam-3831	213	2	gb(y3k+2	gb(y3k+2	ADJ
ejpam-3831	213	3	,	,	PUNCT
ejpam-3831	213	4	y3k+3	y3k+3	PROPN
ejpam-3831	213	5	,	,	PUNCT
ejpam-3831	213	6	y3k+4	y3k+4	PROPN
ejpam-3831	213	7	)	)	PUNCT
ejpam-3831	213	8	≤	≤	NUM
ejpam-3831	213	9	h	h	NOUN
ejpam-3831	213	10	·	·	PUNCT
ejpam-3831	213	11	(	(	PUNCT
ejpam-3831	213	12	gb(x3k+1	gb(x3k+1	PROPN
ejpam-3831	213	13	,	,	PUNCT
ejpam-3831	213	14	x3k+2	x3k+2	PRON
ejpam-3831	213	15	,	,	PUNCT
ejpam-3831	213	16	x3k+3	x3k+3	NOUN
ejpam-3831	213	17	)	)	PUNCT
ejpam-3831	214	1	+	+	ADJ
ejpam-3831	214	2	gb(y3k+1	gb(y3k+1	NOUN
ejpam-3831	214	3	,	,	PUNCT
ejpam-3831	214	4	y3k+2	y3k+2	PROPN
ejpam-3831	214	5	,	,	PUNCT
ejpam-3831	214	6	y3k+3	y3k+3	PROPN
ejpam-3831	214	7	)	)	PUNCT
ejpam-3831	214	8	)	)	PUNCT
ejpam-3831	214	9	.	.	PUNCT
ejpam-3831	215	1	continuing	continue	VERB
ejpam-3831	215	2	this	this	DET
ejpam-3831	215	3	way	way	NOUN
ejpam-3831	215	4	,	,	PUNCT
ejpam-3831	215	5	we	we	PRON
ejpam-3831	215	6	have	have	VERB
ejpam-3831	215	7	gb(xn	gb(xn	PROPN
ejpam-3831	215	8	,	,	PUNCT
ejpam-3831	215	9	xn+1	xn+1	PROPN
ejpam-3831	215	10	,	,	PUNCT
ejpam-3831	215	11	xn+2	xn+2	NUM
ejpam-3831	215	12	)	)	PUNCT
ejpam-3831	216	1	+	+	ADJ
ejpam-3831	216	2	gb(yn	gb(yn	NOUN
ejpam-3831	216	3	,	,	PUNCT
ejpam-3831	216	4	yn+1	yn+1	PROPN
ejpam-3831	216	5	,	,	PUNCT
ejpam-3831	216	6	yn+2	yn+2	NUM
ejpam-3831	216	7	)	)	PUNCT
ejpam-3831	216	8	≤	≤	NUM
ejpam-3831	216	9	h	h	NOUN
ejpam-3831	216	10	·	·	PUNCT
ejpam-3831	216	11	(	(	PUNCT
ejpam-3831	216	12	gb(xn−1	gb(xn−1	PROPN
ejpam-3831	216	13	,	,	PUNCT
ejpam-3831	216	14	xn	xn	PROPN
ejpam-3831	216	15	,	,	PUNCT
ejpam-3831	216	16	xn+1	xn+1	NUM
ejpam-3831	216	17	)	)	PUNCT
ejpam-3831	217	1	+	+	ADV
ejpam-3831	217	2	gb(yn−1	gb(yn−1	PROPN
ejpam-3831	217	3	,	,	PUNCT
ejpam-3831	217	4	yn	yn	PROPN
ejpam-3831	217	5	,	,	PUNCT
ejpam-3831	217	6	yn+1	yn+1	NUM
ejpam-3831	217	7	)	)	PUNCT
ejpam-3831	217	8	)	)	PUNCT
ejpam-3831	217	9	≤	≤	NUM
ejpam-3831	217	10	h2	h2	NOUN
ejpam-3831	217	11	·	·	PUNCT
ejpam-3831	217	12	(	(	PUNCT
ejpam-3831	217	13	gb(xn−2	gb(xn−2	X
ejpam-3831	217	14	,	,	PUNCT
ejpam-3831	217	15	xn−1	xn−1	PROPN
ejpam-3831	217	16	,	,	PUNCT
ejpam-3831	217	17	xn	xn	PUNCT
ejpam-3831	217	18	)	)	PUNCT
ejpam-3831	218	1	+	+	ADV
ejpam-3831	218	2	gb(yn−2	gb(yn−2	PROPN
ejpam-3831	218	3	,	,	PUNCT
ejpam-3831	218	4	yn−1	yn−1	PROPN
ejpam-3831	218	5	,	,	PUNCT
ejpam-3831	218	6	yn	yn	PROPN
ejpam-3831	218	7	)	)	PUNCT
ejpam-3831	218	8	)	)	PUNCT
ejpam-3831	218	9	≤	≤	NUM
ejpam-3831	218	10	h3	h3	NOUN
ejpam-3831	218	11	·	·	PUNCT
ejpam-3831	218	12	(	(	PUNCT
ejpam-3831	218	13	gb(xn−3	gb(xn−3	X
ejpam-3831	218	14	,	,	PUNCT
ejpam-3831	218	15	xn−2	xn−2	PROPN
ejpam-3831	218	16	,	,	PUNCT
ejpam-3831	218	17	xn−1	xn−1	PROPN
ejpam-3831	218	18	)	)	PUNCT
ejpam-3831	218	19	+	+	NOUN
ejpam-3831	218	20	gb(yn−3	gb(yn−3	NOUN
ejpam-3831	218	21	,	,	PUNCT
ejpam-3831	218	22	yn−2	yn−2	PROPN
ejpam-3831	218	23	,	,	PUNCT
ejpam-3831	218	24	yn−1	yn−1	NOUN
ejpam-3831	218	25	)	)	PUNCT
ejpam-3831	218	26	)	)	PUNCT
ejpam-3831	218	27	≤	≤	NOUN
ejpam-3831	218	28	·	·	PUNCT
ejpam-3831	218	29	·	·	PUNCT
ejpam-3831	218	30	·	·	PUNCT
ejpam-3831	219	1	≤	≤	NUM
ejpam-3831	219	2	hn+1	hn+1	X
ejpam-3831	219	3	·	·	PUNCT
ejpam-3831	219	4	(	(	PUNCT
ejpam-3831	219	5	gb(x0	gb(x0	PROPN
ejpam-3831	219	6	,	,	PUNCT
ejpam-3831	219	7	x1	x1	PROPN
ejpam-3831	219	8	,	,	PUNCT
ejpam-3831	219	9	x2	x2	PROPN
ejpam-3831	219	10	)	)	PUNCT
ejpam-3831	219	11	+	+	ADP
ejpam-3831	219	12	gb(y0	gb(y0	NOUN
ejpam-3831	219	13	,	,	PUNCT
ejpam-3831	219	14	y1	y1	NOUN
ejpam-3831	219	15	,	,	PUNCT
ejpam-3831	219	16	y2	y2	PROPN
ejpam-3831	219	17	)	)	PUNCT
ejpam-3831	219	18	)	)	PUNCT
ejpam-3831	219	19	.	.	PUNCT
ejpam-3831	220	1	(	(	PUNCT
ejpam-3831	220	2	9	9	X
ejpam-3831	220	3	)	)	PUNCT
ejpam-3831	220	4	let	let	VERB
ejpam-3831	220	5	gb(xn	gb(xn	PROPN
ejpam-3831	220	6	,	,	PUNCT
ejpam-3831	220	7	xn+1	xn+1	PROPN
ejpam-3831	220	8	,	,	PUNCT
ejpam-3831	220	9	xn+2	xn+2	NUM
ejpam-3831	220	10	)	)	PUNCT
ejpam-3831	221	1	+	+	ADJ
ejpam-3831	221	2	gb(yn	gb(yn	NOUN
ejpam-3831	221	3	,	,	PUNCT
ejpam-3831	221	4	yn+1	yn+1	PROPN
ejpam-3831	221	5	,	,	PUNCT
ejpam-3831	221	6	yn+2	yn+2	NUM
ejpam-3831	221	7	)	)	PUNCT
ejpam-3831	221	8	=	=	PRON
ejpam-3831	221	9	ψn	ψn	PROPN
ejpam-3831	221	10	.	.	PUNCT
ejpam-3831	222	1	m.m.m	m.m.m	AUX
ejpam-3831	222	2	.	.	PUNCT
ejpam-3831	223	1	jaradat	jaradat	PROPN
ejpam-3831	223	2	et	et	PROPN
ejpam-3831	223	3	al	al	PROPN
ejpam-3831	223	4	.	.	PUNCT
ejpam-3831	223	5	/	/	SYM
ejpam-3831	223	6	eur	eur	PROPN
ejpam-3831	223	7	.	.	PUNCT
ejpam-3831	224	1	j.	j.	PROPN
ejpam-3831	224	2	pure	pure	PROPN
ejpam-3831	224	3	appl	appl	PROPN
ejpam-3831	224	4	.	.	PROPN
ejpam-3831	224	5	math	math	PROPN
ejpam-3831	224	6	,	,	PUNCT
ejpam-3831	224	7	13	13	NUM
ejpam-3831	224	8	(	(	PUNCT
ejpam-3831	224	9	4	4	NUM
ejpam-3831	224	10	)	)	PUNCT
ejpam-3831	224	11	(	(	PUNCT
ejpam-3831	224	12	2020	2020	NUM
ejpam-3831	224	13	)	)	PUNCT
ejpam-3831	224	14	,	,	PUNCT
ejpam-3831	224	15	995	995	NUM
ejpam-3831	224	16	-	-	SYM
ejpam-3831	224	17	1015	1015	NUM
ejpam-3831	224	18	1003	1003	NUM
ejpam-3831	224	19	then	then	ADV
ejpam-3831	224	20	the	the	DET
ejpam-3831	224	21	pattern	pattern	NOUN
ejpam-3831	224	22	(	(	PUNCT
ejpam-3831	224	23	9	9	NUM
ejpam-3831	224	24	)	)	PUNCT
ejpam-3831	224	25	can	can	AUX
ejpam-3831	224	26	be	be	AUX
ejpam-3831	224	27	written	write	VERB
ejpam-3831	224	28	as	as	ADP
ejpam-3831	224	29	ψn	ψn	VERB
ejpam-3831	224	30	≤	≤	NUM
ejpam-3831	224	31	h.ψn−1	h.ψn−1	VERB
ejpam-3831	224	32	≤	≤	NUM
ejpam-3831	224	33	h2.ψn−2	h2.ψn−2	PROPN
ejpam-3831	224	34	≤	≤	NOUN
ejpam-3831	224	35	·	·	PUNCT
ejpam-3831	224	36	·	·	PUNCT
ejpam-3831	224	37	·	·	PUNCT
ejpam-3831	225	1	≤	≤	ADV
ejpam-3831	225	2	hn	hn	PRON
ejpam-3831	225	3	·	·	PUNCT
ejpam-3831	225	4	ψ0	ψ0	PROPN
ejpam-3831	225	5	.	.	PUNCT
ejpam-3831	226	1	(	(	PUNCT
ejpam-3831	226	2	10	10	NUM
ejpam-3831	226	3	)	)	PUNCT
ejpam-3831	226	4	now	now	ADV
ejpam-3831	226	5	,	,	PUNCT
ejpam-3831	226	6	we	we	PRON
ejpam-3831	226	7	prove	prove	VERB
ejpam-3831	226	8	that	that	SCONJ
ejpam-3831	226	9	sequences	sequence	NOUN
ejpam-3831	226	10	{	{	PUNCT
ejpam-3831	226	11	xn	xn	NUM
ejpam-3831	226	12	}	}	PUNCT
ejpam-3831	226	13	and	and	CCONJ
ejpam-3831	226	14	{	{	PUNCT
ejpam-3831	226	15	yn	yn	NOUN
ejpam-3831	226	16	}	}	PUNCT
ejpam-3831	226	17	are	be	AUX
ejpam-3831	226	18	gb−cauchy	gb−cauchy	NOUN
ejpam-3831	226	19	.	.	PUNCT
ejpam-3831	227	1	by	by	ADP
ejpam-3831	227	2	(	(	PUNCT
ejpam-3831	227	3	8)	8)	NUM
ejpam-3831	227	4	we	we	PRON
ejpam-3831	227	5	have	have	AUX
ejpam-3831	227	6	0	0	NUM
ejpam-3831	227	7	≤	≤	NUM
ejpam-3831	228	1	sh	sh	INTJ
ejpam-3831	228	2	<	<	X
ejpam-3831	229	1	1	1	X
ejpam-3831	229	2	.	.	PUNCT
ejpam-3831	229	3	let	let	VERB
ejpam-3831	229	4	j	j	PROPN
ejpam-3831	229	5	>	>	X
ejpam-3831	229	6	k.	k.	PROPN
ejpam-3831	229	7	then	then	ADV
ejpam-3831	229	8	gb(xk	gb(xk	PROPN
ejpam-3831	229	9	,	,	PUNCT
ejpam-3831	229	10	xj	xj	PROPN
ejpam-3831	229	11	,	,	PUNCT
ejpam-3831	229	12	xj	xj	PROPN
ejpam-3831	229	13	)	)	PUNCT
ejpam-3831	230	1	+	+	NOUN
ejpam-3831	230	2	gb(yk	gb(yk	PROPN
ejpam-3831	230	3	,	,	PUNCT
ejpam-3831	230	4	yj	yj	PROPN
ejpam-3831	230	5	,	,	PUNCT
ejpam-3831	230	6	yj	yj	PROPN
ejpam-3831	230	7	)	)	PUNCT
ejpam-3831	230	8	≤	≤	NOUN
ejpam-3831	230	9	s[gb(xk	s[gb(xk	NUM
ejpam-3831	230	10	,	,	PUNCT
ejpam-3831	230	11	xk+1	xk+1	X
ejpam-3831	230	12	,	,	PUNCT
ejpam-3831	230	13	xk+1	xk+1	PUNCT
ejpam-3831	230	14	)	)	PUNCT
ejpam-3831	231	1	+	+	NOUN
ejpam-3831	231	2	gb(xk+1	gb(xk+1	NOUN
ejpam-3831	231	3	,	,	PUNCT
ejpam-3831	231	4	xj	xj	PROPN
ejpam-3831	231	5	,	,	PUNCT
ejpam-3831	231	6	xj	xj	PROPN
ejpam-3831	231	7	)	)	PUNCT
ejpam-3831	232	1	+	+	NOUN
ejpam-3831	232	2	gb(yk	gb(yk	PROPN
ejpam-3831	232	3	,	,	PUNCT
ejpam-3831	232	4	yk+1	yk+1	NOUN
ejpam-3831	232	5	,	,	PUNCT
ejpam-3831	232	6	yk+1	yk+1	NOUN
ejpam-3831	232	7	)	)	PUNCT
ejpam-3831	233	1	+	+	NOUN
ejpam-3831	233	2	gb(yk+1	gb(yk+1	NOUN
ejpam-3831	233	3	,	,	PUNCT
ejpam-3831	233	4	yj	yj	PROPN
ejpam-3831	233	5	,	,	PUNCT
ejpam-3831	233	6	yj	yj	PROPN
ejpam-3831	233	7	)	)	PUNCT
ejpam-3831	233	8	]	]	PUNCT
ejpam-3831	233	9	≤	≤	NUM
ejpam-3831	233	10	s[gb(xk	s[gb(xk	NUM
ejpam-3831	233	11	,	,	PUNCT
ejpam-3831	233	12	xk+1	xk+1	X
ejpam-3831	233	13	,	,	PUNCT
ejpam-3831	233	14	xk+1	xk+1	PUNCT
ejpam-3831	233	15	)	)	PUNCT
ejpam-3831	234	1	+	+	NOUN
ejpam-3831	234	2	gb(yk	gb(yk	ADJ
ejpam-3831	234	3	,	,	PUNCT
ejpam-3831	234	4	yk+1	yk+1	NOUN
ejpam-3831	234	5	,	,	PUNCT
ejpam-3831	234	6	yk+1	yk+1	NOUN
ejpam-3831	234	7	)	)	PUNCT
ejpam-3831	234	8	]	]	PUNCT
ejpam-3831	235	1	+	+	CCONJ
ejpam-3831	235	2	s2[gb(xk+1	s2[gb(xk+1	ADJ
ejpam-3831	235	3	,	,	PUNCT
ejpam-3831	235	4	xk+2	xk+2	NUM
ejpam-3831	235	5	,	,	PUNCT
ejpam-3831	235	6	xk+2	xk+2	NUM
ejpam-3831	235	7	)	)	PUNCT
ejpam-3831	235	8	+	+	NOUN
ejpam-3831	235	9	gb(yk+1	gb(yk+1	NOUN
ejpam-3831	235	10	,	,	PUNCT
ejpam-3831	235	11	yk+2	yk+2	NOUN
ejpam-3831	235	12	,	,	PUNCT
ejpam-3831	235	13	yk+2	yk+2	NOUN
ejpam-3831	235	14	)	)	PUNCT
ejpam-3831	235	15	]	]	PUNCT
ejpam-3831	236	1	+	+	X
ejpam-3831	236	2	s3[gb(xk+2	s3[gb(xk+2	NUM
ejpam-3831	236	3	,	,	PUNCT
ejpam-3831	236	4	xk+3	xk+3	NOUN
ejpam-3831	236	5	,	,	PUNCT
ejpam-3831	236	6	xk+3	xk+3	PROPN
ejpam-3831	236	7	)	)	PUNCT
ejpam-3831	237	1	+	+	PROPN
ejpam-3831	237	2	gb(yk+2	gb(yk+2	PROPN
ejpam-3831	237	3	,	,	PUNCT
ejpam-3831	237	4	yk+3	yk+3	NOUN
ejpam-3831	237	5	,	,	PUNCT
ejpam-3831	237	6	yk+3	yk+3	ADP
ejpam-3831	237	7	]	]	X
ejpam-3831	237	8	+	+	X
ejpam-3831	237	9	·	·	PUNCT
ejpam-3831	237	10	·	·	PUNCT
ejpam-3831	237	11	·	·	PUNCT
ejpam-3831	238	1	+	+	X
ejpam-3831	238	2	sj−k[gb(xj−1	sj−k[gb(xj−1	PROPN
ejpam-3831	238	3	,	,	PUNCT
ejpam-3831	238	4	xj	xj	PROPN
ejpam-3831	238	5	,	,	PUNCT
ejpam-3831	238	6	xj	xj	PROPN
ejpam-3831	238	7	)	)	PUNCT
ejpam-3831	239	1	+	+	ADV
ejpam-3831	239	2	gb(yj−1	gb(yj−1	NOUN
ejpam-3831	239	3	,	,	PUNCT
ejpam-3831	239	4	yj	yj	PROPN
ejpam-3831	239	5	,	,	PUNCT
ejpam-3831	239	6	yj	yj	PROPN
ejpam-3831	239	7	]	]	PUNCT
ejpam-3831	239	8	≤	≤	NUM
ejpam-3831	239	9	shkψ0	shkψ0	NOUN
ejpam-3831	240	1	+	+	CCONJ
ejpam-3831	240	2	s2hk+1ψ0	s2hk+1ψ0	PROPN
ejpam-3831	240	3	+	+	PROPN
ejpam-3831	240	4	s3hk+2ψ0	s3hk+2ψ0	PROPN
ejpam-3831	240	5	+	+	CCONJ
ejpam-3831	240	6	·	·	PUNCT
ejpam-3831	240	7	·	·	PUNCT
ejpam-3831	240	8	·	·	PUNCT
ejpam-3831	240	9	+	+	NUM
ejpam-3831	240	10	sj−khj−1ψ0	sj−khj−1ψ0	PROPN
ejpam-3831	240	11	≤	≤	NOUN
ejpam-3831	240	12	shk[1	shk[1	X
ejpam-3831	240	13	+	+	X
ejpam-3831	240	14	sh+	sh+	ADJ
ejpam-3831	240	15	(	(	PUNCT
ejpam-3831	240	16	sh)2	sh)2	NOUN
ejpam-3831	240	17	+	+	CCONJ
ejpam-3831	240	18	(	(	PUNCT
ejpam-3831	240	19	sh)3	sh)3	PROPN
ejpam-3831	240	20	+	+	PROPN
ejpam-3831	240	21	·	·	PUNCT
ejpam-3831	240	22	·	·	PUNCT
ejpam-3831	240	23	·	·	PUNCT
ejpam-3831	241	1	]	]	PUNCT
ejpam-3831	241	2	ψ0	ψ0	NOUN
ejpam-3831	241	3	=	=	X
ejpam-3831	241	4	shk	shk	PROPN
ejpam-3831	241	5	1−	1−	NUM
ejpam-3831	241	6	sh	sh	INTJ
ejpam-3831	241	7	ψ0.→	ψ0.→	VERB
ejpam-3831	241	8	0	0	PROPN
ejpam-3831	241	9	as	as	ADP
ejpam-3831	241	10	k	k	PROPN
ejpam-3831	241	11	→	→	PROPN
ejpam-3831	241	12	+	+	PROPN
ejpam-3831	241	13	∞.	∞.	PROPN
ejpam-3831	241	14	hence	hence	ADV
ejpam-3831	241	15	gb(xk	gb(xk	PROPN
ejpam-3831	241	16	,	,	PUNCT
ejpam-3831	241	17	xj	xj	PROPN
ejpam-3831	241	18	,	,	PUNCT
ejpam-3831	241	19	xj)+gb(yk	xj)+gb(yk	PROPN
ejpam-3831	241	20	,	,	PUNCT
ejpam-3831	241	21	yj	yj	PROPN
ejpam-3831	241	22	,	,	PUNCT
ejpam-3831	241	23	yj)→	yj)→	NOUN
ejpam-3831	241	24	0	0	NUM
ejpam-3831	241	25	as	as	ADP
ejpam-3831	241	26	k	k	PROPN
ejpam-3831	241	27	→	→	SYM
ejpam-3831	241	28	+	+	PROPN
ejpam-3831	241	29	∞	∞	PROPN
ejpam-3831	241	30	,	,	PUNCT
ejpam-3831	241	31	which	which	PRON
ejpam-3831	241	32	shows	show	VERB
ejpam-3831	241	33	that	that	SCONJ
ejpam-3831	241	34	{	{	PUNCT
ejpam-3831	241	35	xn	xn	X
ejpam-3831	241	36	}	}	PUNCT
ejpam-3831	241	37	and	and	CCONJ
ejpam-3831	241	38	{	{	PUNCT
ejpam-3831	241	39	yn	yn	NOUN
ejpam-3831	241	40	}	}	PUNCT
ejpam-3831	241	41	are	be	AUX
ejpam-3831	241	42	gb−cauchy	gb−cauchy	NOUN
ejpam-3831	241	43	sequences	sequence	NOUN
ejpam-3831	241	44	in	in	ADP
ejpam-3831	241	45	x	x	PUNCT
ejpam-3831	241	46	by	by	ADP
ejpam-3831	241	47	proposition	proposition	NOUN
ejpam-3831	241	48	2	2	NUM
ejpam-3831	241	49	.	.	PUNCT
ejpam-3831	242	1	but	but	CCONJ
ejpam-3831	242	2	due	due	ADP
ejpam-3831	242	3	to	to	ADP
ejpam-3831	242	4	the	the	DET
ejpam-3831	242	5	completeness	completeness	NOUN
ejpam-3831	242	6	of	of	ADP
ejpam-3831	242	7	gb	gb	ADV
ejpam-3831	242	8	-	-	PUNCT
ejpam-3831	242	9	metric	metric	ADJ
ejpam-3831	242	10	spaces	space	NOUN
ejpam-3831	242	11	,	,	PUNCT
ejpam-3831	242	12	we	we	PRON
ejpam-3831	242	13	have	have	VERB
ejpam-3831	242	14	xn	xn	X
ejpam-3831	243	1	→	→	SYM
ejpam-3831	243	2	x	x	X
ejpam-3831	243	3	and	and	CCONJ
ejpam-3831	243	4	yn	yn	PROPN
ejpam-3831	243	5	→	→	SYM
ejpam-3831	243	6	y	y	PROPN
ejpam-3831	243	7	as	as	ADP
ejpam-3831	243	8	n→	n→	ADV
ejpam-3831	243	9	+	+	PROPN
ejpam-3831	243	10	∞	∞	PROPN
ejpam-3831	243	11	,	,	PUNCT
ejpam-3831	243	12	for	for	ADP
ejpam-3831	243	13	x	x	X
ejpam-3831	243	14	,	,	PUNCT
ejpam-3831	243	15	y	y	PROPN
ejpam-3831	243	16	∈	∈	PROPN
ejpam-3831	243	17	x.	x.	NOUN
ejpam-3831	244	1	now	now	ADV
ejpam-3831	244	2	,	,	PUNCT
ejpam-3831	244	3	we	we	PRON
ejpam-3831	244	4	show	show	VERB
ejpam-3831	244	5	that	that	SCONJ
ejpam-3831	244	6	(	(	PUNCT
ejpam-3831	244	7	x	x	X
ejpam-3831	244	8	,	,	PUNCT
ejpam-3831	244	9	y	y	NOUN
ejpam-3831	244	10	)	)	PUNCT
ejpam-3831	244	11	is	be	AUX
ejpam-3831	244	12	common	common	ADJ
ejpam-3831	244	13	coupled	couple	VERB
ejpam-3831	244	14	fixed	fix	VERB
ejpam-3831	244	15	points	point	NOUN
ejpam-3831	244	16	of	of	ADP
ejpam-3831	244	17	f	f	PROPN
ejpam-3831	244	18	,	,	PUNCT
ejpam-3831	244	19	h	h	PROPN
ejpam-3831	244	20	and	and	CCONJ
ejpam-3831	244	21	t.	t.	PROPN
ejpam-3831	244	22	suppose	suppose	VERB
ejpam-3831	244	23	that	that	SCONJ
ejpam-3831	244	24	x	x	PROPN
ejpam-3831	244	25	6=	6=	NUM
ejpam-3831	244	26	f	f	X
ejpam-3831	244	27	(	(	PUNCT
ejpam-3831	244	28	x	x	PROPN
ejpam-3831	244	29	,	,	PUNCT
ejpam-3831	244	30	y	y	PROPN
ejpam-3831	244	31	)	)	PUNCT
ejpam-3831	244	32	and	and	CCONJ
ejpam-3831	244	33	gb(x	gb(x	PROPN
ejpam-3831	244	34	,	,	PUNCT
ejpam-3831	244	35	f	f	PROPN
ejpam-3831	244	36	(	(	PUNCT
ejpam-3831	244	37	x	x	PROPN
ejpam-3831	244	38	,	,	PUNCT
ejpam-3831	244	39	y	y	PROPN
ejpam-3831	244	40	)	)	PUNCT
ejpam-3831	244	41	,	,	PUNCT
ejpam-3831	244	42	f	f	PROPN
ejpam-3831	244	43	(	(	PUNCT
ejpam-3831	244	44	x	x	PROPN
ejpam-3831	244	45	,	,	PUNCT
ejpam-3831	244	46	y	y	NOUN
ejpam-3831	244	47	)	)	PUNCT
ejpam-3831	244	48	)	)	PUNCT
ejpam-3831	244	49	>	>	X
ejpam-3831	245	1	0	0	X
ejpam-3831	245	2	.	.	PUNCT
ejpam-3831	245	3	thus	thus	ADV
ejpam-3831	245	4	from	from	ADP
ejpam-3831	245	5	definition	definition	NOUN
ejpam-3831	245	6	of	of	ADP
ejpam-3831	245	7	gb	gb	ADV
ejpam-3831	245	8	-	-	PUNCT
ejpam-3831	245	9	metric	metric	ADJ
ejpam-3831	245	10	we	we	PRON
ejpam-3831	245	11	have	have	VERB
ejpam-3831	245	12	gb(x	gb(x	NUM
ejpam-3831	245	13	,	,	PUNCT
ejpam-3831	245	14	f	f	PROPN
ejpam-3831	245	15	(	(	PUNCT
ejpam-3831	245	16	x	x	PROPN
ejpam-3831	245	17	,	,	PUNCT
ejpam-3831	245	18	y	y	PROPN
ejpam-3831	245	19	)	)	PUNCT
ejpam-3831	245	20	,	,	PUNCT
ejpam-3831	245	21	f	f	PROPN
ejpam-3831	245	22	(	(	PUNCT
ejpam-3831	245	23	x	x	PROPN
ejpam-3831	245	24	,	,	PUNCT
ejpam-3831	245	25	y	y	NOUN
ejpam-3831	245	26	)	)	PUNCT
ejpam-3831	245	27	)	)	PUNCT
ejpam-3831	245	28	≤	≤	NOUN
ejpam-3831	245	29	gb(x	gb(x	PUNCT
ejpam-3831	245	30	,	,	PUNCT
ejpam-3831	245	31	x3k+2	x3k+2	PROPN
ejpam-3831	245	32	,	,	PUNCT
ejpam-3831	245	33	f	f	PROPN
ejpam-3831	245	34	(	(	PUNCT
ejpam-3831	245	35	x	x	PROPN
ejpam-3831	245	36	,	,	PUNCT
ejpam-3831	245	37	y	y	NOUN
ejpam-3831	245	38	)	)	PUNCT
ejpam-3831	245	39	)	)	PUNCT
ejpam-3831	246	1	≤	≤	NUM
ejpam-3831	246	2	s	s	PART
ejpam-3831	246	3	·	·	PUNCT
ejpam-3831	246	4	[	[	PUNCT
ejpam-3831	246	5	gb(x	gb(x	X
ejpam-3831	246	6	,	,	PUNCT
ejpam-3831	246	7	x3k+3	x3k+3	NOUN
ejpam-3831	246	8	,	,	PUNCT
ejpam-3831	246	9	x3k+3	x3k+3	PROPN
ejpam-3831	246	10	)	)	PUNCT
ejpam-3831	247	1	+	+	ADJ
ejpam-3831	247	2	gb(x3k+3	gb(x3k+3	ADJ
ejpam-3831	247	3	,	,	PUNCT
ejpam-3831	247	4	x3k+2	x3k+2	PROPN
ejpam-3831	247	5	,	,	PUNCT
ejpam-3831	247	6	f	f	PROPN
ejpam-3831	247	7	(	(	PUNCT
ejpam-3831	247	8	x	x	PROPN
ejpam-3831	247	9	,	,	PUNCT
ejpam-3831	247	10	y	y	NOUN
ejpam-3831	247	11	)	)	PUNCT
ejpam-3831	247	12	)	)	PUNCT
ejpam-3831	247	13	]	]	PUNCT
ejpam-3831	248	1	=	=	SYM
ejpam-3831	248	2	s	s	X
ejpam-3831	248	3	·	·	PUNCT
ejpam-3831	248	4	gb(x	gb(x	ADJ
ejpam-3831	248	5	,	,	PUNCT
ejpam-3831	248	6	x3k+3	x3k+3	PROPN
ejpam-3831	248	7	,	,	PUNCT
ejpam-3831	248	8	x3k+3	x3k+3	PROPN
ejpam-3831	248	9	)	)	PUNCT
ejpam-3831	249	1	+	+	PRON
ejpam-3831	249	2	s	s	X
ejpam-3831	249	3	·	·	PUNCT
ejpam-3831	249	4	gb	gb	ADP
ejpam-3831	249	5	(	(	PUNCT
ejpam-3831	249	6	t	t	PROPN
ejpam-3831	249	7	(	(	PUNCT
ejpam-3831	249	8	x3k+2	x3k+2	PROPN
ejpam-3831	249	9	,	,	PUNCT
ejpam-3831	249	10	y3k+2	y3k+2	PROPN
ejpam-3831	249	11	)	)	PUNCT
ejpam-3831	249	12	,	,	PUNCT
ejpam-3831	249	13	h(x3k+1	h(x3k+1	X
ejpam-3831	249	14	,	,	PUNCT
ejpam-3831	249	15	y3k+1	y3k+1	NOUN
ejpam-3831	249	16	)	)	PUNCT
ejpam-3831	249	17	,	,	PUNCT
ejpam-3831	249	18	f	f	PROPN
ejpam-3831	249	19	(	(	PUNCT
ejpam-3831	249	20	x	x	PROPN
ejpam-3831	249	21	,	,	PUNCT
ejpam-3831	249	22	y	y	PROPN
ejpam-3831	249	23	)	)	PUNCT
ejpam-3831	249	24	)	)	PUNCT
ejpam-3831	250	1	≤	≤	PROPN
ejpam-3831	250	2	s	s	PART
ejpam-3831	250	3	·	·	PUNCT
ejpam-3831	250	4	gb(x	gb(x	ADJ
ejpam-3831	250	5	,	,	PUNCT
ejpam-3831	250	6	x3k+3	x3k+3	PROPN
ejpam-3831	250	7	,	,	PUNCT
ejpam-3831	250	8	x3k+3	x3k+3	PROPN
ejpam-3831	250	9	)	)	PUNCT
ejpam-3831	250	10	+	+	CCONJ
ejpam-3831	250	11	sα1(x3k+2	sα1(x3k+2	NOUN
ejpam-3831	250	12	,	,	PUNCT
ejpam-3831	250	13	x3k+1	x3k+1	ADJ
ejpam-3831	250	14	)	)	PUNCT
ejpam-3831	250	15	.	.	PUNCT
ejpam-3831	251	1	gb(x3k+2	gb(x3k+2	PROPN
ejpam-3831	251	2	,	,	PUNCT
ejpam-3831	251	3	x3k+1	x3k+1	ADV
ejpam-3831	251	4	,	,	PUNCT
ejpam-3831	251	5	x	x	X
ejpam-3831	251	6	)	)	PUNCT
ejpam-3831	251	7	+	+	ADV
ejpam-3831	251	8	gb(y3k+2	gb(y3k+2	NOUN
ejpam-3831	251	9	,	,	PUNCT
ejpam-3831	251	10	y3k+1	y3k+1	NOUN
ejpam-3831	251	11	,	,	PUNCT
ejpam-3831	251	12	y	y	NOUN
ejpam-3831	251	13	)	)	PUNCT
ejpam-3831	251	14	2	2	NUM
ejpam-3831	251	15	+	+	NOUN
ejpam-3831	251	16	s.α2(x3k+2	s.α2(x3k+2	NOUN
ejpam-3831	251	17	,	,	PUNCT
ejpam-3831	251	18	x3k+1	x3k+1	ADJ
ejpam-3831	251	19	)	)	PUNCT
ejpam-3831	251	20	·	·	PUNCT
ejpam-3831	251	21	gb	gb	PRON
ejpam-3831	251	22	(	(	PUNCT
ejpam-3831	251	23	t	t	PROPN
ejpam-3831	251	24	(	(	PUNCT
ejpam-3831	251	25	x3k+2	x3k+2	PROPN
ejpam-3831	251	26	,	,	PUNCT
ejpam-3831	251	27	y3k+2	y3k+2	PROPN
ejpam-3831	251	28	)	)	PUNCT
ejpam-3831	251	29	,	,	PUNCT
ejpam-3831	251	30	h(x3k+1	h(x3k+1	X
ejpam-3831	251	31	,	,	PUNCT
ejpam-3831	251	32	y3k+1	y3k+1	NOUN
ejpam-3831	251	33	)	)	PUNCT
ejpam-3831	251	34	,	,	PUNCT
ejpam-3831	251	35	f	f	PROPN
ejpam-3831	251	36	(	(	PUNCT
ejpam-3831	251	37	x	x	PROPN
ejpam-3831	251	38	,	,	PUNCT
ejpam-3831	251	39	y	y	PROPN
ejpam-3831	251	40	)	)	PUNCT
ejpam-3831	251	41	)	)	PUNCT
ejpam-3831	251	42	)	)	PUNCT
ejpam-3831	252	1	gb(x3k+2	gb(x3k+2	PROPN
ejpam-3831	252	2	,	,	PUNCT
ejpam-3831	252	3	x3k+1	x3k+1	ADJ
ejpam-3831	252	4	,	,	PUNCT
ejpam-3831	252	5	x	x	X
ejpam-3831	252	6	)	)	PUNCT
ejpam-3831	252	7	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	252	8	,	,	PUNCT
ejpam-3831	252	9	x3k+1	x3k+1	ADV
ejpam-3831	252	10	,	,	PUNCT
ejpam-3831	252	11	x	x	NOUN
ejpam-3831	252	12	,	,	PUNCT
ejpam-3831	252	13	y3k+2	y3k+2	PROPN
ejpam-3831	252	14	,	,	PUNCT
ejpam-3831	252	15	y3k+1	y3k+1	NOUN
ejpam-3831	252	16	,	,	PUNCT
ejpam-3831	252	17	y	y	NOUN
ejpam-3831	252	18	)	)	PUNCT
ejpam-3831	253	1	+	+	ADV
ejpam-3831	253	2	s.α3(x3k+2	s.α3(x3k+2	PROPN
ejpam-3831	253	3	,	,	PUNCT
ejpam-3831	253	4	x3k+1	x3k+1	PUNCT
ejpam-3831	253	5	)	)	PUNCT
ejpam-3831	253	6	·	·	PUNCT
ejpam-3831	254	1	gb	gb	PRON
ejpam-3831	254	2	(	(	PUNCT
ejpam-3831	254	3	t	t	PROPN
ejpam-3831	254	4	(	(	PUNCT
ejpam-3831	254	5	x3k+2	x3k+2	PROPN
ejpam-3831	254	6	,	,	PUNCT
ejpam-3831	254	7	y3k+2	y3k+2	PROPN
ejpam-3831	254	8	)	)	PUNCT
ejpam-3831	254	9	,	,	PUNCT
ejpam-3831	254	10	h(x3k+1	h(x3k+1	X
ejpam-3831	254	11	,	,	PUNCT
ejpam-3831	254	12	y3k+1	y3k+1	NOUN
ejpam-3831	254	13	)	)	PUNCT
ejpam-3831	254	14	,	,	PUNCT
ejpam-3831	254	15	f	f	PROPN
ejpam-3831	254	16	(	(	PUNCT
ejpam-3831	254	17	x	x	PROPN
ejpam-3831	254	18	,	,	PUNCT
ejpam-3831	254	19	y	y	PROPN
ejpam-3831	254	20	)	)	PUNCT
ejpam-3831	254	21	)	)	PUNCT
ejpam-3831	254	22	)	)	PUNCT
ejpam-3831	255	1	gb(y3k+2	gb(y3k+2	NOUN
ejpam-3831	255	2	,	,	PUNCT
ejpam-3831	255	3	y3k+1	y3k+1	NOUN
ejpam-3831	255	4	,	,	PUNCT
ejpam-3831	255	5	y	y	NOUN
ejpam-3831	255	6	)	)	PUNCT
ejpam-3831	255	7	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	255	8	,	,	PUNCT
ejpam-3831	255	9	x3k+1	x3k+1	ADV
ejpam-3831	255	10	,	,	PUNCT
ejpam-3831	255	11	x	x	NOUN
ejpam-3831	255	12	,	,	PUNCT
ejpam-3831	255	13	y3k+2	y3k+2	PROPN
ejpam-3831	255	14	,	,	PUNCT
ejpam-3831	255	15	y3k+1	y3k+1	NOUN
ejpam-3831	255	16	,	,	PUNCT
ejpam-3831	255	17	y	y	NOUN
ejpam-3831	255	18	)	)	PUNCT
ejpam-3831	256	1	+	+	NOUN
ejpam-3831	256	2	s.α4(x3k+2	s.α4(x3k+2	NOUN
ejpam-3831	256	3	,	,	PUNCT
ejpam-3831	256	4	x3k+1	x3k+1	ADJ
ejpam-3831	256	5	)	)	PUNCT
ejpam-3831	256	6	·	·	PUNCT
ejpam-3831	256	7	gb(x3k+2	gb(x3k+2	ADJ
ejpam-3831	256	8	,	,	PUNCT
ejpam-3831	256	9	x3k+2	x3k+2	PROPN
ejpam-3831	256	10	,	,	PUNCT
ejpam-3831	256	11	t	t	PROPN
ejpam-3831	256	12	(	(	PUNCT
ejpam-3831	256	13	x3k+2	x3k+2	PROPN
ejpam-3831	256	14	,	,	PUNCT
ejpam-3831	256	15	y3k+2))gb(x3k+2	y3k+2))gb(x3k+2	PROPN
ejpam-3831	256	16	,	,	PUNCT
ejpam-3831	256	17	x3k+1	x3k+1	ADJ
ejpam-3831	256	18	,	,	PUNCT
ejpam-3831	256	19	x	x	X
ejpam-3831	256	20	)	)	PUNCT
ejpam-3831	256	21	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	256	22	,	,	PUNCT
ejpam-3831	256	23	x3k+1	x3k+1	ADV
ejpam-3831	256	24	,	,	PUNCT
ejpam-3831	256	25	x	x	NOUN
ejpam-3831	256	26	,	,	PUNCT
ejpam-3831	256	27	y3k+2	y3k+2	PROPN
ejpam-3831	256	28	,	,	PUNCT
ejpam-3831	256	29	y3k+1	y3k+1	NOUN
ejpam-3831	256	30	,	,	PUNCT
ejpam-3831	256	31	y	y	NOUN
ejpam-3831	256	32	)	)	PUNCT
ejpam-3831	257	1	+	+	NOUN
ejpam-3831	257	2	s.α5(x3k+1	s.α5(x3k+1	NOUN
ejpam-3831	257	3	,	,	PUNCT
ejpam-3831	257	4	x	x	X
ejpam-3831	257	5	)	)	PUNCT
ejpam-3831	257	6	·	·	PUNCT
ejpam-3831	257	7	gb(x3k+2	gb(x3k+2	NOUN
ejpam-3831	257	8	,	,	PUNCT
ejpam-3831	257	9	x3k+2	x3k+2	PROPN
ejpam-3831	257	10	,	,	PUNCT
ejpam-3831	257	11	t	t	PROPN
ejpam-3831	257	12	(	(	PUNCT
ejpam-3831	257	13	x3k+2	x3k+2	X
ejpam-3831	257	14	,	,	PUNCT
ejpam-3831	257	15	y3k+2))gb(y3k+2	y3k+2))gb(y3k+2	NOUN
ejpam-3831	257	16	,	,	PUNCT
ejpam-3831	257	17	y3k+1	y3k+1	NOUN
ejpam-3831	257	18	,	,	PUNCT
ejpam-3831	257	19	y	y	NOUN
ejpam-3831	257	20	)	)	PUNCT
ejpam-3831	257	21	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	257	22	,	,	PUNCT
ejpam-3831	257	23	x3k+1	x3k+1	ADV
ejpam-3831	257	24	,	,	PUNCT
ejpam-3831	257	25	x	x	NOUN
ejpam-3831	257	26	,	,	PUNCT
ejpam-3831	257	27	y3k+2	y3k+2	PROPN
ejpam-3831	257	28	,	,	PUNCT
ejpam-3831	257	29	y3k+1	y3k+1	NOUN
ejpam-3831	257	30	,	,	PUNCT
ejpam-3831	257	31	y	y	NOUN
ejpam-3831	257	32	)	)	PUNCT
ejpam-3831	257	33	+	+	NOUN
ejpam-3831	257	34	s.α6(x3k+1	s.α6(x3k+1	NOUN
ejpam-3831	257	35	,	,	PUNCT
ejpam-3831	257	36	x	x	NOUN
ejpam-3831	257	37	)	)	PUNCT
ejpam-3831	257	38	·	·	PUNCT
ejpam-3831	257	39	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	257	40	,	,	PUNCT
ejpam-3831	257	41	x3k+1	x3k+1	ADJ
ejpam-3831	257	42	,	,	PUNCT
ejpam-3831	257	43	h(x3k+1	h(x3k+1	NOUN
ejpam-3831	257	44	,	,	PUNCT
ejpam-3831	257	45	y3k+1))gb(x3k+2	y3k+1))gb(x3k+2	NOUN
ejpam-3831	257	46	,	,	PUNCT
ejpam-3831	257	47	x3k+1	x3k+1	ADV
ejpam-3831	257	48	,	,	PUNCT
ejpam-3831	257	49	x	x	X
ejpam-3831	257	50	)	)	PUNCT
ejpam-3831	257	51	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	257	52	,	,	PUNCT
ejpam-3831	257	53	x3k+1	x3k+1	ADV
ejpam-3831	257	54	,	,	PUNCT
ejpam-3831	257	55	x	x	NOUN
ejpam-3831	257	56	,	,	PUNCT
ejpam-3831	257	57	y3k+2	y3k+2	PROPN
ejpam-3831	257	58	,	,	PUNCT
ejpam-3831	257	59	y3k+1	y3k+1	NOUN
ejpam-3831	257	60	,	,	PUNCT
ejpam-3831	257	61	y	y	NOUN
ejpam-3831	257	62	)	)	PUNCT
ejpam-3831	258	1	+	+	NOUN
ejpam-3831	258	2	s.α7(x3k+1	s.α7(x3k+1	NOUN
ejpam-3831	258	3	,	,	PUNCT
ejpam-3831	258	4	x	x	NOUN
ejpam-3831	258	5	)	)	PUNCT
ejpam-3831	258	6	·	·	PUNCT
ejpam-3831	258	7	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	258	8	,	,	PUNCT
ejpam-3831	258	9	x3k+1	x3k+1	ADJ
ejpam-3831	258	10	,	,	PUNCT
ejpam-3831	258	11	h(x3k+1	h(x3k+1	NOUN
ejpam-3831	258	12	,	,	PUNCT
ejpam-3831	258	13	y3k+1))gb(y3k+2	y3k+1))gb(y3k+2	NOUN
ejpam-3831	258	14	,	,	PUNCT
ejpam-3831	258	15	y3k+1	y3k+1	NOUN
ejpam-3831	258	16	,	,	PUNCT
ejpam-3831	258	17	y	y	NOUN
ejpam-3831	258	18	)	)	PUNCT
ejpam-3831	258	19	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	258	20	,	,	PUNCT
ejpam-3831	258	21	x3k+1	x3k+1	ADV
ejpam-3831	258	22	,	,	PUNCT
ejpam-3831	258	23	x	x	NOUN
ejpam-3831	258	24	,	,	PUNCT
ejpam-3831	258	25	y3k+2	y3k+2	PROPN
ejpam-3831	258	26	,	,	PUNCT
ejpam-3831	258	27	y3k+1	y3k+1	NOUN
ejpam-3831	258	28	,	,	PUNCT
ejpam-3831	258	29	y	y	NOUN
ejpam-3831	258	30	)	)	PUNCT
ejpam-3831	258	31	m.m.m	m.m.m	NOUN
ejpam-3831	258	32	.	.	PUNCT
ejpam-3831	259	1	jaradat	jaradat	PROPN
ejpam-3831	259	2	et	et	PROPN
ejpam-3831	259	3	al	al	PROPN
ejpam-3831	259	4	.	.	PUNCT
ejpam-3831	259	5	/	/	SYM
ejpam-3831	259	6	eur	eur	PROPN
ejpam-3831	259	7	.	.	PUNCT
ejpam-3831	260	1	j.	j.	PROPN
ejpam-3831	260	2	pure	pure	PROPN
ejpam-3831	260	3	appl	appl	PROPN
ejpam-3831	260	4	.	.	PROPN
ejpam-3831	260	5	math	math	PROPN
ejpam-3831	260	6	,	,	PUNCT
ejpam-3831	260	7	13	13	NUM
ejpam-3831	260	8	(	(	PUNCT
ejpam-3831	260	9	4	4	NUM
ejpam-3831	260	10	)	)	PUNCT
ejpam-3831	260	11	(	(	PUNCT
ejpam-3831	260	12	2020	2020	NUM
ejpam-3831	260	13	)	)	PUNCT
ejpam-3831	260	14	,	,	PUNCT
ejpam-3831	260	15	995	995	NUM
ejpam-3831	260	16	-	-	SYM
ejpam-3831	260	17	1015	1015	NUM
ejpam-3831	260	18	1004	1004	NUM
ejpam-3831	261	1	+	+	SYM
ejpam-3831	261	2	s.α8(x3k+1	s.α8(x3k+1	NOUN
ejpam-3831	261	3	,	,	PUNCT
ejpam-3831	261	4	x	x	NOUN
ejpam-3831	261	5	)	)	PUNCT
ejpam-3831	261	6	·	·	PUNCT
ejpam-3831	262	1	gb(x	gb(x	NUM
ejpam-3831	262	2	,	,	PUNCT
ejpam-3831	262	3	x	x	X
ejpam-3831	262	4	,	,	PUNCT
ejpam-3831	262	5	f	f	PROPN
ejpam-3831	262	6	(	(	PUNCT
ejpam-3831	262	7	x	x	PROPN
ejpam-3831	262	8	,	,	PUNCT
ejpam-3831	262	9	y))gb(x3k+2	y))gb(x3k+2	PROPN
ejpam-3831	262	10	,	,	PUNCT
ejpam-3831	262	11	x3k+1	x3k+1	ADV
ejpam-3831	262	12	,	,	PUNCT
ejpam-3831	262	13	x	x	X
ejpam-3831	262	14	)	)	PUNCT
ejpam-3831	262	15	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	262	16	,	,	PUNCT
ejpam-3831	262	17	x3k+1	x3k+1	ADV
ejpam-3831	262	18	,	,	PUNCT
ejpam-3831	262	19	x	x	NOUN
ejpam-3831	262	20	,	,	PUNCT
ejpam-3831	262	21	y3k+2	y3k+2	PROPN
ejpam-3831	262	22	,	,	PUNCT
ejpam-3831	262	23	y3k+1	y3k+1	NOUN
ejpam-3831	262	24	,	,	PUNCT
ejpam-3831	262	25	y	y	NOUN
ejpam-3831	262	26	)	)	PUNCT
ejpam-3831	263	1	+	+	PROPN
ejpam-3831	263	2	s.α9(x	s.α9(x	PROPN
ejpam-3831	263	3	,	,	PUNCT
ejpam-3831	263	4	x3k+2	x3k+2	X
ejpam-3831	263	5	)	)	PUNCT
ejpam-3831	263	6	·	·	PUNCT
ejpam-3831	264	1	gb(x	gb(x	NUM
ejpam-3831	264	2	,	,	PUNCT
ejpam-3831	264	3	x	x	X
ejpam-3831	264	4	,	,	PUNCT
ejpam-3831	264	5	f	f	PROPN
ejpam-3831	264	6	(	(	PUNCT
ejpam-3831	264	7	x	x	X
ejpam-3831	264	8	,	,	PUNCT
ejpam-3831	264	9	y))gb(y3k+2	y))gb(y3k+2	PROPN
ejpam-3831	264	10	,	,	PUNCT
ejpam-3831	264	11	y3k+1	y3k+1	NOUN
ejpam-3831	264	12	,	,	PUNCT
ejpam-3831	264	13	y	y	NOUN
ejpam-3831	264	14	)	)	PUNCT
ejpam-3831	264	15	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	264	16	,	,	PUNCT
ejpam-3831	264	17	x3k+1	x3k+1	ADV
ejpam-3831	264	18	,	,	PUNCT
ejpam-3831	264	19	x	x	NOUN
ejpam-3831	264	20	,	,	PUNCT
ejpam-3831	264	21	y3k+2	y3k+2	PROPN
ejpam-3831	264	22	,	,	PUNCT
ejpam-3831	264	23	y3k+1	y3k+1	NOUN
ejpam-3831	264	24	,	,	PUNCT
ejpam-3831	264	25	y	y	NOUN
ejpam-3831	264	26	)	)	PUNCT
ejpam-3831	264	27	+	+	NOUN
ejpam-3831	264	28	s.α10(x	s.α10(x	PROPN
ejpam-3831	264	29	,	,	PUNCT
ejpam-3831	264	30	x3k+2	x3k+2	X
ejpam-3831	264	31	)	)	PUNCT
ejpam-3831	264	32	·	·	PUNCT
ejpam-3831	264	33	gb(x3k+2	gb(x3k+2	PROPN
ejpam-3831	264	34	,	,	PUNCT
ejpam-3831	264	35	x3k+1	x3k+1	ADV
ejpam-3831	264	36	,	,	PUNCT
ejpam-3831	264	37	f	f	PROPN
ejpam-3831	264	38	(	(	PUNCT
ejpam-3831	264	39	x	x	PROPN
ejpam-3831	264	40	,	,	PUNCT
ejpam-3831	264	41	y))gb(x3k+2	y))gb(x3k+2	PROPN
ejpam-3831	264	42	,	,	PUNCT
ejpam-3831	264	43	x3k+1	x3k+1	ADV
ejpam-3831	264	44	,	,	PUNCT
ejpam-3831	264	45	x	x	X
ejpam-3831	264	46	)	)	PUNCT
ejpam-3831	264	47	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	264	48	,	,	PUNCT
ejpam-3831	264	49	x3k+1	x3k+1	ADV
ejpam-3831	264	50	,	,	PUNCT
ejpam-3831	264	51	x	x	NOUN
ejpam-3831	264	52	,	,	PUNCT
ejpam-3831	264	53	y3k+2	y3k+2	PROPN
ejpam-3831	264	54	,	,	PUNCT
ejpam-3831	264	55	y3k+1	y3k+1	NOUN
ejpam-3831	264	56	,	,	PUNCT
ejpam-3831	264	57	y	y	NOUN
ejpam-3831	264	58	)	)	PUNCT
ejpam-3831	265	1	+	+	NOUN
ejpam-3831	265	2	s.α11(x	s.α11(x	NOUN
ejpam-3831	265	3	,	,	PUNCT
ejpam-3831	265	4	x3k+2	x3k+2	X
ejpam-3831	265	5	)	)	PUNCT
ejpam-3831	266	1	·	·	PUNCT
ejpam-3831	266	2	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	266	3	,	,	PUNCT
ejpam-3831	266	4	x	x	X
ejpam-3831	266	5	,	,	PUNCT
ejpam-3831	266	6	t	t	PROPN
ejpam-3831	266	7	(	(	PUNCT
ejpam-3831	266	8	x3k+2	x3k+2	X
ejpam-3831	266	9	,	,	PUNCT
ejpam-3831	266	10	y3k+2))gb(y3k+2	y3k+2))gb(y3k+2	NOUN
ejpam-3831	266	11	,	,	PUNCT
ejpam-3831	266	12	y3k+1	y3k+1	NOUN
ejpam-3831	266	13	,	,	PUNCT
ejpam-3831	266	14	y	y	NOUN
ejpam-3831	266	15	)	)	PUNCT
ejpam-3831	266	16	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	266	17	,	,	PUNCT
ejpam-3831	266	18	x3k+1	x3k+1	ADV
ejpam-3831	266	19	,	,	PUNCT
ejpam-3831	266	20	x	x	NOUN
ejpam-3831	266	21	,	,	PUNCT
ejpam-3831	266	22	y3k+2	y3k+2	PROPN
ejpam-3831	266	23	,	,	PUNCT
ejpam-3831	266	24	y3k+1	y3k+1	NOUN
ejpam-3831	266	25	,	,	PUNCT
ejpam-3831	266	26	y	y	NOUN
ejpam-3831	266	27	)	)	PUNCT
ejpam-3831	267	1	+	+	PROPN
ejpam-3831	267	2	s.α12(x	s.α12(x	PROPN
ejpam-3831	267	3	,	,	PUNCT
ejpam-3831	267	4	x3k+2	x3k+2	X
ejpam-3831	267	5	)	)	PUNCT
ejpam-3831	267	6	·	·	PUNCT
ejpam-3831	268	1	gb(x	gb(x	NUM
ejpam-3831	268	2	,	,	PUNCT
ejpam-3831	268	3	x3k+2	x3k+2	NOUN
ejpam-3831	268	4	,	,	PUNCT
ejpam-3831	268	5	h(x3k+1	h(x3k+1	NOUN
ejpam-3831	268	6	,	,	PUNCT
ejpam-3831	268	7	y3k+1))gb(x3k+2	y3k+1))gb(x3k+2	NOUN
ejpam-3831	268	8	,	,	PUNCT
ejpam-3831	268	9	x3k+1	x3k+1	ADV
ejpam-3831	268	10	,	,	PUNCT
ejpam-3831	268	11	x	x	X
ejpam-3831	268	12	)	)	PUNCT
ejpam-3831	268	13	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	268	14	,	,	PUNCT
ejpam-3831	268	15	x3k+1	x3k+1	ADV
ejpam-3831	268	16	,	,	PUNCT
ejpam-3831	268	17	x	x	NOUN
ejpam-3831	268	18	,	,	PUNCT
ejpam-3831	268	19	y3k+2	y3k+2	PROPN
ejpam-3831	268	20	,	,	PUNCT
ejpam-3831	268	21	y3k+1	y3k+1	NOUN
ejpam-3831	268	22	,	,	PUNCT
ejpam-3831	268	23	y	y	NOUN
ejpam-3831	268	24	)	)	PUNCT
ejpam-3831	268	25	.	.	PUNCT
ejpam-3831	269	1	using	use	VERB
ejpam-3831	269	2	(	(	PUNCT
ejpam-3831	269	3	3	3	NUM
ejpam-3831	269	4	)	)	PUNCT
ejpam-3831	269	5	and	and	CCONJ
ejpam-3831	269	6	(	(	PUNCT
ejpam-3831	269	7	4	4	NUM
ejpam-3831	269	8	)	)	PUNCT
ejpam-3831	269	9	,	,	PUNCT
ejpam-3831	269	10	we	we	PRON
ejpam-3831	269	11	have	have	VERB
ejpam-3831	269	12	gb(x	gb(x	ADJ
ejpam-3831	269	13	,	,	PUNCT
ejpam-3831	269	14	f	f	PROPN
ejpam-3831	269	15	(	(	PUNCT
ejpam-3831	269	16	x	x	PROPN
ejpam-3831	269	17	,	,	PUNCT
ejpam-3831	269	18	y	y	PROPN
ejpam-3831	269	19	)	)	PUNCT
ejpam-3831	269	20	,	,	PUNCT
ejpam-3831	269	21	f	f	PROPN
ejpam-3831	269	22	(	(	PUNCT
ejpam-3831	269	23	x	x	PROPN
ejpam-3831	269	24	,	,	PUNCT
ejpam-3831	269	25	y	y	NOUN
ejpam-3831	269	26	)	)	PUNCT
ejpam-3831	269	27	)	)	PUNCT
ejpam-3831	269	28	≤	≤	NOUN
ejpam-3831	269	29	gb(x	gb(x	PUNCT
ejpam-3831	269	30	,	,	PUNCT
ejpam-3831	269	31	x3k+2	x3k+2	PROPN
ejpam-3831	269	32	,	,	PUNCT
ejpam-3831	269	33	f	f	PROPN
ejpam-3831	269	34	(	(	PUNCT
ejpam-3831	269	35	x	x	PROPN
ejpam-3831	269	36	,	,	PUNCT
ejpam-3831	269	37	y	y	NOUN
ejpam-3831	269	38	)	)	PUNCT
ejpam-3831	269	39	)	)	PUNCT
ejpam-3831	270	1	≤	≤	PROPN
ejpam-3831	270	2	s	s	PART
ejpam-3831	270	3	·	·	PUNCT
ejpam-3831	270	4	gb(x	gb(x	ADJ
ejpam-3831	270	5	,	,	PUNCT
ejpam-3831	270	6	x3k+3	x3k+3	PROPN
ejpam-3831	270	7	,	,	PUNCT
ejpam-3831	270	8	x3k+3	x3k+3	PROPN
ejpam-3831	270	9	)	)	PUNCT
ejpam-3831	270	10	+	+	CCONJ
ejpam-3831	270	11	sα1(x3k+2	sα1(x3k+2	NOUN
ejpam-3831	270	12	,	,	PUNCT
ejpam-3831	270	13	x3k+1	x3k+1	ADJ
ejpam-3831	270	14	)	)	PUNCT
ejpam-3831	270	15	.	.	PUNCT
ejpam-3831	271	1	gb(x3k+2	gb(x3k+2	PROPN
ejpam-3831	271	2	,	,	PUNCT
ejpam-3831	271	3	x3k+1	x3k+1	ADV
ejpam-3831	271	4	,	,	PUNCT
ejpam-3831	271	5	x	x	X
ejpam-3831	271	6	)	)	PUNCT
ejpam-3831	271	7	+	+	ADV
ejpam-3831	271	8	gb(y3k+2	gb(y3k+2	NOUN
ejpam-3831	271	9	,	,	PUNCT
ejpam-3831	271	10	y3k+1	y3k+1	NOUN
ejpam-3831	271	11	,	,	PUNCT
ejpam-3831	271	12	y	y	NOUN
ejpam-3831	271	13	)	)	PUNCT
ejpam-3831	271	14	2	2	NUM
ejpam-3831	271	15	+	+	NOUN
ejpam-3831	271	16	s.α2(x3k+2	s.α2(x3k+2	NOUN
ejpam-3831	271	17	,	,	PUNCT
ejpam-3831	271	18	x3k+1	x3k+1	ADJ
ejpam-3831	271	19	)	)	PUNCT
ejpam-3831	271	20	·	·	PUNCT
ejpam-3831	271	21	gb	gb	PRON
ejpam-3831	271	22	(	(	PUNCT
ejpam-3831	271	23	x3k+3	x3k+3	PROPN
ejpam-3831	271	24	,	,	PUNCT
ejpam-3831	271	25	x3k+2	x3k+2	PROPN
ejpam-3831	271	26	,	,	PUNCT
ejpam-3831	271	27	f	f	PROPN
ejpam-3831	271	28	(	(	PUNCT
ejpam-3831	271	29	x	x	PROPN
ejpam-3831	271	30	,	,	PUNCT
ejpam-3831	271	31	y	y	NOUN
ejpam-3831	271	32	)	)	PUNCT
ejpam-3831	271	33	)	)	PUNCT
ejpam-3831	272	1	gb(x3k+2	gb(x3k+2	PROPN
ejpam-3831	272	2	,	,	PUNCT
ejpam-3831	272	3	x3k+1	x3k+1	ADJ
ejpam-3831	272	4	,	,	PUNCT
ejpam-3831	272	5	x	x	X
ejpam-3831	272	6	)	)	PUNCT
ejpam-3831	272	7	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	272	8	,	,	PUNCT
ejpam-3831	272	9	x3k+1	x3k+1	ADV
ejpam-3831	272	10	,	,	PUNCT
ejpam-3831	272	11	x	x	NOUN
ejpam-3831	272	12	,	,	PUNCT
ejpam-3831	272	13	y3k+2	y3k+2	PROPN
ejpam-3831	272	14	,	,	PUNCT
ejpam-3831	272	15	y3k+1	y3k+1	NOUN
ejpam-3831	272	16	,	,	PUNCT
ejpam-3831	272	17	y	y	NOUN
ejpam-3831	272	18	)	)	PUNCT
ejpam-3831	273	1	+	+	ADV
ejpam-3831	273	2	s.α3(x3k+2	s.α3(x3k+2	PROPN
ejpam-3831	273	3	,	,	PUNCT
ejpam-3831	273	4	x3k+1	x3k+1	PUNCT
ejpam-3831	273	5	)	)	PUNCT
ejpam-3831	273	6	·	·	PUNCT
ejpam-3831	274	1	gb	gb	PRON
ejpam-3831	274	2	(	(	PUNCT
ejpam-3831	274	3	x3k+3	x3k+3	PROPN
ejpam-3831	274	4	,	,	PUNCT
ejpam-3831	274	5	x3k+2	x3k+2	PROPN
ejpam-3831	274	6	,	,	PUNCT
ejpam-3831	274	7	f	f	PROPN
ejpam-3831	274	8	(	(	PUNCT
ejpam-3831	274	9	x	x	PROPN
ejpam-3831	274	10	,	,	PUNCT
ejpam-3831	274	11	y	y	NOUN
ejpam-3831	274	12	)	)	PUNCT
ejpam-3831	274	13	)	)	PUNCT
ejpam-3831	274	14	gb(y3k+2	gb(y3k+2	NOUN
ejpam-3831	274	15	,	,	PUNCT
ejpam-3831	274	16	y3k+1	y3k+1	NOUN
ejpam-3831	274	17	,	,	PUNCT
ejpam-3831	274	18	y	y	NOUN
ejpam-3831	274	19	)	)	PUNCT
ejpam-3831	274	20	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	274	21	,	,	PUNCT
ejpam-3831	274	22	x3k+1	x3k+1	ADV
ejpam-3831	274	23	,	,	PUNCT
ejpam-3831	274	24	x	x	NOUN
ejpam-3831	274	25	,	,	PUNCT
ejpam-3831	274	26	y3k+2	y3k+2	PROPN
ejpam-3831	274	27	,	,	PUNCT
ejpam-3831	274	28	y3k+1	y3k+1	NOUN
ejpam-3831	274	29	,	,	PUNCT
ejpam-3831	274	30	y	y	NOUN
ejpam-3831	274	31	)	)	PUNCT
ejpam-3831	274	32	+	+	NOUN
ejpam-3831	274	33	s.α4(x3k+2	s.α4(x3k+2	NOUN
ejpam-3831	274	34	,	,	PUNCT
ejpam-3831	274	35	x3k+1	x3k+1	ADJ
ejpam-3831	274	36	)	)	PUNCT
ejpam-3831	274	37	·	·	PUNCT
ejpam-3831	275	1	gb(x3k+2	gb(x3k+2	ADJ
ejpam-3831	275	2	,	,	PUNCT
ejpam-3831	275	3	x3k+2	x3k+2	PROPN
ejpam-3831	275	4	,	,	PUNCT
ejpam-3831	275	5	x3k+3)gb(x3k+2	x3k+3)gb(x3k+2	PROPN
ejpam-3831	275	6	,	,	PUNCT
ejpam-3831	275	7	x3k+1	x3k+1	ADV
ejpam-3831	275	8	,	,	PUNCT
ejpam-3831	275	9	x	x	X
ejpam-3831	275	10	)	)	PUNCT
ejpam-3831	275	11	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	275	12	,	,	PUNCT
ejpam-3831	275	13	x3k+1	x3k+1	ADV
ejpam-3831	275	14	,	,	PUNCT
ejpam-3831	275	15	x	x	NOUN
ejpam-3831	275	16	,	,	PUNCT
ejpam-3831	275	17	y3k+2	y3k+2	PROPN
ejpam-3831	275	18	,	,	PUNCT
ejpam-3831	275	19	y3k+1	y3k+1	NOUN
ejpam-3831	275	20	,	,	PUNCT
ejpam-3831	275	21	y	y	NOUN
ejpam-3831	275	22	)	)	PUNCT
ejpam-3831	276	1	+	+	NOUN
ejpam-3831	276	2	s.α5(x3k+1	s.α5(x3k+1	NOUN
ejpam-3831	276	3	,	,	PUNCT
ejpam-3831	276	4	x	x	X
ejpam-3831	276	5	)	)	PUNCT
ejpam-3831	276	6	·	·	PUNCT
ejpam-3831	276	7	gb(x3k+2	gb(x3k+2	NOUN
ejpam-3831	276	8	,	,	PUNCT
ejpam-3831	276	9	x3k+2	x3k+2	PROPN
ejpam-3831	276	10	,	,	PUNCT
ejpam-3831	276	11	x3k+3)gb(y3k+2	x3k+3)gb(y3k+2	PROPN
ejpam-3831	276	12	,	,	PUNCT
ejpam-3831	276	13	y3k+1	y3k+1	NOUN
ejpam-3831	276	14	,	,	PUNCT
ejpam-3831	276	15	y	y	NOUN
ejpam-3831	276	16	)	)	PUNCT
ejpam-3831	276	17	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	276	18	,	,	PUNCT
ejpam-3831	276	19	x3k+1	x3k+1	ADV
ejpam-3831	276	20	,	,	PUNCT
ejpam-3831	276	21	x	x	NOUN
ejpam-3831	276	22	,	,	PUNCT
ejpam-3831	276	23	y3k+2	y3k+2	PROPN
ejpam-3831	276	24	,	,	PUNCT
ejpam-3831	276	25	y3k+1	y3k+1	NOUN
ejpam-3831	276	26	,	,	PUNCT
ejpam-3831	276	27	y	y	NOUN
ejpam-3831	276	28	)	)	PUNCT
ejpam-3831	276	29	+	+	NOUN
ejpam-3831	276	30	s.α6(x3k+1	s.α6(x3k+1	NOUN
ejpam-3831	276	31	,	,	PUNCT
ejpam-3831	276	32	x	x	NOUN
ejpam-3831	276	33	)	)	PUNCT
ejpam-3831	276	34	·	·	PUNCT
ejpam-3831	276	35	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	276	36	,	,	PUNCT
ejpam-3831	276	37	x3k+1	x3k+1	ADJ
ejpam-3831	276	38	,	,	PUNCT
ejpam-3831	276	39	x3k+2)gb(x3k+2	x3k+2)gb(x3k+2	PROPN
ejpam-3831	276	40	,	,	PUNCT
ejpam-3831	276	41	x3k+1	x3k+1	ADV
ejpam-3831	276	42	,	,	PUNCT
ejpam-3831	276	43	x	x	X
ejpam-3831	276	44	)	)	PUNCT
ejpam-3831	276	45	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	276	46	,	,	PUNCT
ejpam-3831	276	47	x3k+1	x3k+1	ADV
ejpam-3831	276	48	,	,	PUNCT
ejpam-3831	276	49	x	x	NOUN
ejpam-3831	276	50	,	,	PUNCT
ejpam-3831	276	51	y3k+2	y3k+2	PROPN
ejpam-3831	276	52	,	,	PUNCT
ejpam-3831	276	53	y3k+1	y3k+1	NOUN
ejpam-3831	276	54	,	,	PUNCT
ejpam-3831	276	55	y	y	NOUN
ejpam-3831	276	56	)	)	PUNCT
ejpam-3831	277	1	+	+	NOUN
ejpam-3831	277	2	s.α7(x3k+1	s.α7(x3k+1	NOUN
ejpam-3831	277	3	,	,	PUNCT
ejpam-3831	277	4	x	x	NOUN
ejpam-3831	277	5	)	)	PUNCT
ejpam-3831	277	6	·	·	PUNCT
ejpam-3831	277	7	gb(x3k+1	gb(x3k+1	NOUN
ejpam-3831	277	8	,	,	PUNCT
ejpam-3831	277	9	x3k+1	x3k+1	ADJ
ejpam-3831	277	10	,	,	PUNCT
ejpam-3831	277	11	x3k+2)gb(y3k+2	x3k+2)gb(y3k+2	PROPN
ejpam-3831	277	12	,	,	PUNCT
ejpam-3831	277	13	y3k+1	y3k+1	NOUN
ejpam-3831	277	14	,	,	PUNCT
ejpam-3831	277	15	y	y	NOUN
ejpam-3831	277	16	)	)	PUNCT
ejpam-3831	277	17	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	277	18	,	,	PUNCT
ejpam-3831	277	19	x3k+1	x3k+1	ADV
ejpam-3831	277	20	,	,	PUNCT
ejpam-3831	277	21	x	x	NOUN
ejpam-3831	277	22	,	,	PUNCT
ejpam-3831	277	23	y3k+2	y3k+2	PROPN
ejpam-3831	277	24	,	,	PUNCT
ejpam-3831	277	25	y3k+1	y3k+1	NOUN
ejpam-3831	277	26	,	,	PUNCT
ejpam-3831	277	27	y	y	NOUN
ejpam-3831	277	28	)	)	PUNCT
ejpam-3831	278	1	+	+	NOUN
ejpam-3831	278	2	s.α8(x3k+1	s.α8(x3k+1	NOUN
ejpam-3831	278	3	,	,	PUNCT
ejpam-3831	278	4	x	x	NOUN
ejpam-3831	278	5	)	)	PUNCT
ejpam-3831	278	6	·	·	PUNCT
ejpam-3831	278	7	gb(x	gb(x	NUM
ejpam-3831	278	8	,	,	PUNCT
ejpam-3831	278	9	x	x	X
ejpam-3831	278	10	,	,	PUNCT
ejpam-3831	278	11	f	f	PROPN
ejpam-3831	278	12	(	(	PUNCT
ejpam-3831	278	13	x	x	PROPN
ejpam-3831	278	14	,	,	PUNCT
ejpam-3831	278	15	y))gb(x3k+2	y))gb(x3k+2	PROPN
ejpam-3831	278	16	,	,	PUNCT
ejpam-3831	278	17	x3k+1	x3k+1	ADV
ejpam-3831	278	18	,	,	PUNCT
ejpam-3831	278	19	x	x	X
ejpam-3831	278	20	)	)	PUNCT
ejpam-3831	278	21	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	278	22	,	,	PUNCT
ejpam-3831	278	23	x3k+1	x3k+1	ADV
ejpam-3831	278	24	,	,	PUNCT
ejpam-3831	278	25	x	x	NOUN
ejpam-3831	278	26	,	,	PUNCT
ejpam-3831	278	27	y3k+2	y3k+2	PROPN
ejpam-3831	278	28	,	,	PUNCT
ejpam-3831	278	29	y3k+1	y3k+1	NOUN
ejpam-3831	278	30	,	,	PUNCT
ejpam-3831	278	31	y	y	NOUN
ejpam-3831	278	32	)	)	PUNCT
ejpam-3831	279	1	+	+	PROPN
ejpam-3831	279	2	s.α9(x	s.α9(x	PROPN
ejpam-3831	279	3	,	,	PUNCT
ejpam-3831	279	4	x3k+2	x3k+2	X
ejpam-3831	279	5	)	)	PUNCT
ejpam-3831	279	6	·	·	PUNCT
ejpam-3831	280	1	gb(x	gb(x	NUM
ejpam-3831	280	2	,	,	PUNCT
ejpam-3831	280	3	x	x	X
ejpam-3831	280	4	,	,	PUNCT
ejpam-3831	280	5	f	f	PROPN
ejpam-3831	280	6	(	(	PUNCT
ejpam-3831	280	7	x	x	X
ejpam-3831	280	8	,	,	PUNCT
ejpam-3831	280	9	y))gb(y3k+2	y))gb(y3k+2	PROPN
ejpam-3831	280	10	,	,	PUNCT
ejpam-3831	280	11	y3k+1	y3k+1	NOUN
ejpam-3831	280	12	,	,	PUNCT
ejpam-3831	280	13	y	y	NOUN
ejpam-3831	280	14	)	)	PUNCT
ejpam-3831	280	15	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	280	16	,	,	PUNCT
ejpam-3831	280	17	x3k+1	x3k+1	ADV
ejpam-3831	280	18	,	,	PUNCT
ejpam-3831	280	19	x	x	NOUN
ejpam-3831	280	20	,	,	PUNCT
ejpam-3831	280	21	y3k+2	y3k+2	PROPN
ejpam-3831	280	22	,	,	PUNCT
ejpam-3831	280	23	y3k+1	y3k+1	NOUN
ejpam-3831	280	24	,	,	PUNCT
ejpam-3831	280	25	y	y	NOUN
ejpam-3831	280	26	)	)	PUNCT
ejpam-3831	280	27	+	+	NOUN
ejpam-3831	280	28	s.α10(x	s.α10(x	PROPN
ejpam-3831	280	29	,	,	PUNCT
ejpam-3831	280	30	x3k+2	x3k+2	X
ejpam-3831	280	31	)	)	PUNCT
ejpam-3831	280	32	·	·	PUNCT
ejpam-3831	280	33	gb(x3k+2	gb(x3k+2	PROPN
ejpam-3831	280	34	,	,	PUNCT
ejpam-3831	280	35	x3k+1	x3k+1	ADV
ejpam-3831	280	36	,	,	PUNCT
ejpam-3831	280	37	f	f	PROPN
ejpam-3831	280	38	(	(	PUNCT
ejpam-3831	280	39	x	x	PROPN
ejpam-3831	280	40	,	,	PUNCT
ejpam-3831	280	41	y))gb(x3k+2	y))gb(x3k+2	PROPN
ejpam-3831	280	42	,	,	PUNCT
ejpam-3831	280	43	x3k+1	x3k+1	ADV
ejpam-3831	280	44	,	,	PUNCT
ejpam-3831	280	45	x	x	X
ejpam-3831	280	46	)	)	PUNCT
ejpam-3831	280	47	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	280	48	,	,	PUNCT
ejpam-3831	280	49	x3k+1	x3k+1	ADV
ejpam-3831	280	50	,	,	PUNCT
ejpam-3831	280	51	x	x	NOUN
ejpam-3831	280	52	,	,	PUNCT
ejpam-3831	280	53	y3k+2	y3k+2	PROPN
ejpam-3831	280	54	,	,	PUNCT
ejpam-3831	280	55	y3k+1	y3k+1	NOUN
ejpam-3831	280	56	,	,	PUNCT
ejpam-3831	280	57	y	y	NOUN
ejpam-3831	280	58	)	)	PUNCT
ejpam-3831	281	1	+	+	NOUN
ejpam-3831	281	2	s.α11(x	s.α11(x	NOUN
ejpam-3831	281	3	,	,	PUNCT
ejpam-3831	281	4	x3k+2	x3k+2	X
ejpam-3831	281	5	)	)	PUNCT
ejpam-3831	282	1	·	·	PUNCT
ejpam-3831	282	2	gb(x3k+1	gb(x3k+1	VERB
ejpam-3831	282	3	,	,	PUNCT
ejpam-3831	282	4	x	x	X
ejpam-3831	282	5	,	,	PUNCT
ejpam-3831	282	6	x3k+3)gb(y3k+2	x3k+3)gb(y3k+2	PROPN
ejpam-3831	282	7	,	,	PUNCT
ejpam-3831	282	8	y3k+1	y3k+1	NOUN
ejpam-3831	282	9	,	,	PUNCT
ejpam-3831	282	10	y	y	NOUN
ejpam-3831	282	11	)	)	PUNCT
ejpam-3831	282	12	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	282	13	,	,	PUNCT
ejpam-3831	282	14	x3k+1	x3k+1	ADV
ejpam-3831	282	15	,	,	PUNCT
ejpam-3831	282	16	x	x	NOUN
ejpam-3831	282	17	,	,	PUNCT
ejpam-3831	282	18	y3k+2	y3k+2	PROPN
ejpam-3831	282	19	,	,	PUNCT
ejpam-3831	282	20	y3k+1	y3k+1	NOUN
ejpam-3831	282	21	,	,	PUNCT
ejpam-3831	282	22	y	y	NOUN
ejpam-3831	282	23	)	)	PUNCT
ejpam-3831	283	1	+	+	PROPN
ejpam-3831	283	2	s.α12(x	s.α12(x	PROPN
ejpam-3831	283	3	,	,	PUNCT
ejpam-3831	283	4	x3k+2	x3k+2	X
ejpam-3831	283	5	)	)	PUNCT
ejpam-3831	283	6	·	·	PUNCT
ejpam-3831	284	1	gb(x	gb(x	NUM
ejpam-3831	284	2	,	,	PUNCT
ejpam-3831	284	3	x3k+2	x3k+2	CCONJ
ejpam-3831	284	4	,	,	PUNCT
ejpam-3831	284	5	x3k+2)gb(x3k+2	x3k+2)gb(x3k+2	PROPN
ejpam-3831	284	6	,	,	PUNCT
ejpam-3831	284	7	x3k+1	x3k+1	ADV
ejpam-3831	284	8	,	,	PUNCT
ejpam-3831	284	9	x	x	X
ejpam-3831	284	10	)	)	PUNCT
ejpam-3831	284	11	ωs(x3k+2	ωs(x3k+2	NUM
ejpam-3831	284	12	,	,	PUNCT
ejpam-3831	284	13	x3k+1	x3k+1	ADV
ejpam-3831	284	14	,	,	PUNCT
ejpam-3831	284	15	x	x	NOUN
ejpam-3831	284	16	,	,	PUNCT
ejpam-3831	284	17	y3k+2	y3k+2	PROPN
ejpam-3831	284	18	,	,	PUNCT
ejpam-3831	284	19	y3k+1	y3k+1	NOUN
ejpam-3831	284	20	,	,	PUNCT
ejpam-3831	284	21	y	y	NOUN
ejpam-3831	284	22	)	)	PUNCT
ejpam-3831	284	23	.	.	PUNCT
ejpam-3831	285	1	since	since	SCONJ
ejpam-3831	285	2	{	{	PUNCT
ejpam-3831	285	3	xn	xn	X
ejpam-3831	285	4	}	}	PUNCT
ejpam-3831	285	5	and	and	CCONJ
ejpam-3831	285	6	{	{	PUNCT
ejpam-3831	285	7	yn	yn	NOUN
ejpam-3831	285	8	}	}	PUNCT
ejpam-3831	285	9	are	be	AUX
ejpam-3831	285	10	gb−convergent	gb−convergent	NOUN
ejpam-3831	285	11	sequences	sequence	NOUN
ejpam-3831	285	12	converges	converge	NOUN
ejpam-3831	285	13	to	to	ADP
ejpam-3831	285	14	x	x	PUNCT
ejpam-3831	285	15	and	and	CCONJ
ejpam-3831	285	16	y	y	PROPN
ejpam-3831	285	17	respectively	respectively	ADV
ejpam-3831	285	18	.	.	PUNCT
ejpam-3831	286	1	m.m.m	m.m.m	AUX
ejpam-3831	286	2	.	.	PUNCT
ejpam-3831	287	1	jaradat	jaradat	PROPN
ejpam-3831	287	2	et	et	PROPN
ejpam-3831	287	3	al	al	PROPN
ejpam-3831	287	4	.	.	PUNCT
ejpam-3831	287	5	/	/	SYM
ejpam-3831	287	6	eur	eur	PROPN
ejpam-3831	287	7	.	.	PUNCT
ejpam-3831	288	1	j.	j.	PROPN
ejpam-3831	288	2	pure	pure	PROPN
ejpam-3831	288	3	appl	appl	PROPN
ejpam-3831	288	4	.	.	PROPN
ejpam-3831	288	5	math	math	PROPN
ejpam-3831	288	6	,	,	PUNCT
ejpam-3831	288	7	13	13	NUM
ejpam-3831	288	8	(	(	PUNCT
ejpam-3831	288	9	4	4	NUM
ejpam-3831	288	10	)	)	PUNCT
ejpam-3831	288	11	(	(	PUNCT
ejpam-3831	288	12	2020	2020	NUM
ejpam-3831	288	13	)	)	PUNCT
ejpam-3831	288	14	,	,	PUNCT
ejpam-3831	288	15	995	995	NUM
ejpam-3831	288	16	-	-	SYM
ejpam-3831	288	17	1015	1015	NUM
ejpam-3831	288	18	1005	1005	NUM
ejpam-3831	288	19	therefore	therefore	ADV
ejpam-3831	288	20	,	,	PUNCT
ejpam-3831	288	21	by	by	ADP
ejpam-3831	288	22	taking	take	VERB
ejpam-3831	288	23	lim	lim	PROPN
ejpam-3831	288	24	sup	sup	PROPN
ejpam-3831	288	25	as	as	ADP
ejpam-3831	288	26	k	k	PROPN
ejpam-3831	288	27	→	→	PROPN
ejpam-3831	289	1	+	+	PROPN
ejpam-3831	289	2	∞	∞	NUM
ejpam-3831	289	3	of	of	ADP
ejpam-3831	289	4	the	the	DET
ejpam-3831	289	5	above	above	ADJ
ejpam-3831	289	6	and	and	CCONJ
ejpam-3831	289	7	using	use	VERB
ejpam-3831	289	8	condition	condition	NOUN
ejpam-3831	289	9	(	(	PUNCT
ejpam-3831	289	10	i	i	NOUN
ejpam-3831	289	11	)	)	PUNCT
ejpam-3831	289	12	,	,	PUNCT
ejpam-3831	289	13	we	we	PRON
ejpam-3831	289	14	have	have	VERB
ejpam-3831	289	15	gb(x	gb(x	ADJ
ejpam-3831	289	16	,	,	PUNCT
ejpam-3831	289	17	f	f	PROPN
ejpam-3831	289	18	(	(	PUNCT
ejpam-3831	289	19	x	x	PROPN
ejpam-3831	289	20	,	,	PUNCT
ejpam-3831	289	21	y	y	PROPN
ejpam-3831	289	22	)	)	PUNCT
ejpam-3831	289	23	,	,	PUNCT
ejpam-3831	289	24	f	f	PROPN
ejpam-3831	289	25	(	(	PUNCT
ejpam-3831	289	26	x	x	PROPN
ejpam-3831	289	27	,	,	PUNCT
ejpam-3831	289	28	y	y	NOUN
ejpam-3831	289	29	)	)	PUNCT
ejpam-3831	289	30	)	)	PUNCT
ejpam-3831	289	31	≤	≤	PROPN
ejpam-3831	289	32	s	s	PART
ejpam-3831	289	33	·	·	PUNCT
ejpam-3831	289	34	gb(x	gb(x	ADJ
ejpam-3831	289	35	,	,	PUNCT
ejpam-3831	289	36	x	x	X
ejpam-3831	289	37	,	,	PUNCT
ejpam-3831	289	38	x	x	X
ejpam-3831	289	39	)	)	PUNCT
ejpam-3831	289	40	+	+	NUM
ejpam-3831	289	41	sα1(x0	sα1(x0	NOUN
ejpam-3831	289	42	,	,	PUNCT
ejpam-3831	289	43	x0	x0	PROPN
ejpam-3831	289	44	)	)	PUNCT
ejpam-3831	289	45	.	.	PUNCT
ejpam-3831	290	1	gb(x	gb(x	PUNCT
ejpam-3831	290	2	,	,	PUNCT
ejpam-3831	290	3	x	x	X
ejpam-3831	290	4	,	,	PUNCT
ejpam-3831	290	5	x	x	X
ejpam-3831	290	6	)	)	PUNCT
ejpam-3831	290	7	+	+	ADJ
ejpam-3831	290	8	gb(y	gb(y	X
ejpam-3831	290	9	,	,	PUNCT
ejpam-3831	290	10	y	y	PROPN
ejpam-3831	290	11	,	,	PUNCT
ejpam-3831	290	12	y	y	NOUN
ejpam-3831	290	13	)	)	PUNCT
ejpam-3831	290	14	2	2	NUM
ejpam-3831	290	15	+	+	CCONJ
ejpam-3831	290	16	s.α2(x0	s.α2(x0	X
ejpam-3831	290	17	,	,	PUNCT
ejpam-3831	290	18	x0	x0	PROPN
ejpam-3831	290	19	)	)	PUNCT
ejpam-3831	290	20	·	·	PUNCT
ejpam-3831	291	1	lim	lim	PROPN
ejpam-3831	291	2	supk→∞gb	supk→∞gb	PROPN
ejpam-3831	291	3	(	(	PUNCT
ejpam-3831	291	4	x3k+3	x3k+3	PROPN
ejpam-3831	291	5	,	,	PUNCT
ejpam-3831	291	6	x3k+2	x3k+2	PROPN
ejpam-3831	291	7	,	,	PUNCT
ejpam-3831	291	8	f	f	PROPN
ejpam-3831	291	9	(	(	PUNCT
ejpam-3831	291	10	x	x	PROPN
ejpam-3831	291	11	,	,	PUNCT
ejpam-3831	291	12	y	y	PROPN
ejpam-3831	291	13	)	)	PUNCT
ejpam-3831	291	14	)	)	PUNCT
ejpam-3831	292	1	gb(x	gb(x	PUNCT
ejpam-3831	292	2	,	,	PUNCT
ejpam-3831	292	3	x	x	X
ejpam-3831	292	4	,	,	PUNCT
ejpam-3831	292	5	x	x	X
ejpam-3831	292	6	)	)	PUNCT
ejpam-3831	292	7	ωs(x	ωs(x	PUNCT
ejpam-3831	292	8	,	,	PUNCT
ejpam-3831	292	9	x	x	X
ejpam-3831	292	10	,	,	PUNCT
ejpam-3831	292	11	x	x	X
ejpam-3831	292	12	,	,	PUNCT
ejpam-3831	292	13	y	y	PROPN
ejpam-3831	292	14	,	,	PUNCT
ejpam-3831	292	15	y	y	PROPN
ejpam-3831	292	16	,	,	PUNCT
ejpam-3831	292	17	y	y	PROPN
ejpam-3831	292	18	)	)	PUNCT
ejpam-3831	292	19	+	+	CCONJ
ejpam-3831	292	20	s.α3(x0	s.α3(x0	PROPN
ejpam-3831	292	21	,	,	PUNCT
ejpam-3831	292	22	x0	x0	PROPN
ejpam-3831	292	23	)	)	PUNCT
ejpam-3831	292	24	·	·	PUNCT
ejpam-3831	293	1	lim	lim	PROPN
ejpam-3831	293	2	supk→∞gb	supk→∞gb	PROPN
ejpam-3831	293	3	(	(	PUNCT
ejpam-3831	293	4	x3k+3	x3k+3	PROPN
ejpam-3831	293	5	,	,	PUNCT
ejpam-3831	293	6	x3k+2	x3k+2	PROPN
ejpam-3831	293	7	,	,	PUNCT
ejpam-3831	293	8	f	f	PROPN
ejpam-3831	293	9	(	(	PUNCT
ejpam-3831	293	10	x	x	NOUN
ejpam-3831	293	11	,	,	PUNCT
ejpam-3831	293	12	y)gb(y	y)gb(y	PROPN
ejpam-3831	293	13	,	,	PUNCT
ejpam-3831	293	14	y	y	PROPN
ejpam-3831	293	15	,	,	PUNCT
ejpam-3831	293	16	y	y	NOUN
ejpam-3831	293	17	)	)	PUNCT
ejpam-3831	293	18	ωs(x	ωs(x	NUM
ejpam-3831	293	19	,	,	PUNCT
ejpam-3831	293	20	x	x	X
ejpam-3831	293	21	,	,	PUNCT
ejpam-3831	293	22	x	x	X
ejpam-3831	293	23	,	,	PUNCT
ejpam-3831	293	24	y	y	PROPN
ejpam-3831	293	25	,	,	PUNCT
ejpam-3831	293	26	y	y	PROPN
ejpam-3831	293	27	,	,	PUNCT
ejpam-3831	293	28	y	y	PROPN
ejpam-3831	293	29	)	)	PUNCT
ejpam-3831	293	30	+	+	CCONJ
ejpam-3831	293	31	s.α4(x0	s.α4(x0	PROPN
ejpam-3831	293	32	,	,	PUNCT
ejpam-3831	293	33	x0	x0	PROPN
ejpam-3831	293	34	)	)	PUNCT
ejpam-3831	293	35	·	·	PUNCT
ejpam-3831	294	1	gb(x	gb(x	NUM
ejpam-3831	294	2	,	,	PUNCT
ejpam-3831	294	3	x	x	X
ejpam-3831	294	4	,	,	PUNCT
ejpam-3831	294	5	x)gb(x	x)gb(x	PRON
ejpam-3831	294	6	,	,	PUNCT
ejpam-3831	294	7	x	x	NOUN
ejpam-3831	294	8	,	,	PUNCT
ejpam-3831	294	9	x	x	X
ejpam-3831	294	10	)	)	PUNCT
ejpam-3831	294	11	ωs(x	ωs(x	PUNCT
ejpam-3831	294	12	,	,	PUNCT
ejpam-3831	294	13	x	x	X
ejpam-3831	294	14	,	,	PUNCT
ejpam-3831	294	15	x	x	X
ejpam-3831	294	16	,	,	PUNCT
ejpam-3831	294	17	y	y	PROPN
ejpam-3831	294	18	,	,	PUNCT
ejpam-3831	294	19	y	y	PROPN
ejpam-3831	294	20	,	,	PUNCT
ejpam-3831	294	21	y	y	PROPN
ejpam-3831	294	22	)	)	PUNCT
ejpam-3831	294	23	+	+	CCONJ
ejpam-3831	294	24	s.α5(x0	s.α5(x0	PROPN
ejpam-3831	294	25	,	,	PUNCT
ejpam-3831	294	26	x	x	NOUN
ejpam-3831	294	27	)	)	PUNCT
ejpam-3831	294	28	·	·	PUNCT
ejpam-3831	294	29	gb(x	gb(x	NUM
ejpam-3831	294	30	,	,	PUNCT
ejpam-3831	294	31	x	x	X
ejpam-3831	294	32	,	,	PUNCT
ejpam-3831	294	33	x)gb(y	x)gb(y	PROPN
ejpam-3831	294	34	,	,	PUNCT
ejpam-3831	294	35	y	y	PROPN
ejpam-3831	294	36	,	,	PUNCT
ejpam-3831	294	37	y	y	NOUN
ejpam-3831	294	38	)	)	PUNCT
ejpam-3831	294	39	ωs(x	ωs(x	NUM
ejpam-3831	294	40	,	,	PUNCT
ejpam-3831	294	41	x	x	X
ejpam-3831	294	42	,	,	PUNCT
ejpam-3831	294	43	x	x	X
ejpam-3831	294	44	,	,	PUNCT
ejpam-3831	294	45	y	y	PROPN
ejpam-3831	294	46	,	,	PUNCT
ejpam-3831	294	47	y	y	PROPN
ejpam-3831	294	48	,	,	PUNCT
ejpam-3831	294	49	y	y	PROPN
ejpam-3831	294	50	)	)	PUNCT
ejpam-3831	295	1	+	+	CCONJ
ejpam-3831	295	2	s.α6(x0	s.α6(x0	PROPN
ejpam-3831	295	3	,	,	PUNCT
ejpam-3831	295	4	x	x	NOUN
ejpam-3831	295	5	)	)	PUNCT
ejpam-3831	295	6	·	·	PUNCT
ejpam-3831	296	1	gb(x	gb(x	NUM
ejpam-3831	296	2	,	,	PUNCT
ejpam-3831	296	3	x	x	X
ejpam-3831	296	4	,	,	PUNCT
ejpam-3831	296	5	x)gb(x	x)gb(x	PRON
ejpam-3831	296	6	,	,	PUNCT
ejpam-3831	296	7	x	x	NOUN
ejpam-3831	296	8	,	,	PUNCT
ejpam-3831	296	9	x	x	X
ejpam-3831	296	10	)	)	PUNCT
ejpam-3831	296	11	ωs(x	ωs(x	PUNCT
ejpam-3831	296	12	,	,	PUNCT
ejpam-3831	296	13	x	x	X
ejpam-3831	296	14	,	,	PUNCT
ejpam-3831	296	15	x	x	X
ejpam-3831	296	16	,	,	PUNCT
ejpam-3831	296	17	y	y	PROPN
ejpam-3831	296	18	,	,	PUNCT
ejpam-3831	296	19	y	y	PROPN
ejpam-3831	296	20	,	,	PUNCT
ejpam-3831	296	21	y	y	PROPN
ejpam-3831	296	22	)	)	PUNCT
ejpam-3831	296	23	+	+	CCONJ
ejpam-3831	296	24	s.α7(x0	s.α7(x0	PROPN
ejpam-3831	296	25	,	,	PUNCT
ejpam-3831	296	26	x	x	NOUN
ejpam-3831	296	27	)	)	PUNCT
ejpam-3831	296	28	·	·	PUNCT
ejpam-3831	296	29	gb(x	gb(x	NUM
ejpam-3831	296	30	,	,	PUNCT
ejpam-3831	296	31	x	x	X
ejpam-3831	296	32	,	,	PUNCT
ejpam-3831	296	33	x)gb(y	x)gb(y	PROPN
ejpam-3831	296	34	,	,	PUNCT
ejpam-3831	296	35	y	y	PROPN
ejpam-3831	296	36	,	,	PUNCT
ejpam-3831	296	37	y	y	NOUN
ejpam-3831	296	38	)	)	PUNCT
ejpam-3831	296	39	ωs(x	ωs(x	NUM
ejpam-3831	296	40	,	,	PUNCT
ejpam-3831	296	41	x	x	X
ejpam-3831	296	42	,	,	PUNCT
ejpam-3831	296	43	x	x	X
ejpam-3831	296	44	,	,	PUNCT
ejpam-3831	296	45	y	y	PROPN
ejpam-3831	296	46	,	,	PUNCT
ejpam-3831	296	47	y	y	PROPN
ejpam-3831	296	48	,	,	PUNCT
ejpam-3831	296	49	y	y	PROPN
ejpam-3831	296	50	)	)	PUNCT
ejpam-3831	296	51	+	+	CCONJ
ejpam-3831	297	1	s.α8(x0	s.α8(x0	ADP
ejpam-3831	297	2	,	,	PUNCT
ejpam-3831	297	3	x	x	X
ejpam-3831	297	4	)	)	PUNCT
ejpam-3831	297	5	·	·	PUNCT
ejpam-3831	298	1	gb(x	gb(x	NUM
ejpam-3831	298	2	,	,	PUNCT
ejpam-3831	298	3	x	x	X
ejpam-3831	298	4	,	,	PUNCT
ejpam-3831	298	5	f	f	PROPN
ejpam-3831	298	6	(	(	PUNCT
ejpam-3831	298	7	x	x	X
ejpam-3831	298	8	,	,	PUNCT
ejpam-3831	298	9	y))gb(x	y))gb(x	ADJ
ejpam-3831	298	10	,	,	PUNCT
ejpam-3831	298	11	x	x	X
ejpam-3831	298	12	,	,	PUNCT
ejpam-3831	298	13	x	x	X
ejpam-3831	298	14	)	)	PUNCT
ejpam-3831	298	15	ωs(x	ωs(x	PUNCT
ejpam-3831	298	16	,	,	PUNCT
ejpam-3831	298	17	x	x	X
ejpam-3831	298	18	,	,	PUNCT
ejpam-3831	298	19	x	x	X
ejpam-3831	298	20	,	,	PUNCT
ejpam-3831	298	21	y	y	PROPN
ejpam-3831	298	22	,	,	PUNCT
ejpam-3831	298	23	y	y	PROPN
ejpam-3831	298	24	,	,	PUNCT
ejpam-3831	298	25	y	y	PROPN
ejpam-3831	298	26	)	)	PUNCT
ejpam-3831	298	27	+	+	CCONJ
ejpam-3831	299	1	s.α9(x	s.α9(x	PROPN
ejpam-3831	299	2	,	,	PUNCT
ejpam-3831	299	3	x0	x0	PROPN
ejpam-3831	299	4	)	)	PUNCT
ejpam-3831	299	5	·	·	PUNCT
ejpam-3831	300	1	gb(x	gb(x	NUM
ejpam-3831	300	2	,	,	PUNCT
ejpam-3831	300	3	x	x	X
ejpam-3831	300	4	,	,	PUNCT
ejpam-3831	300	5	f	f	PROPN
ejpam-3831	300	6	(	(	PUNCT
ejpam-3831	300	7	x	x	X
ejpam-3831	300	8	,	,	PUNCT
ejpam-3831	300	9	y))gb(y	y))gb(y	PRON
ejpam-3831	300	10	,	,	PUNCT
ejpam-3831	300	11	y	y	PROPN
ejpam-3831	300	12	,	,	PUNCT
ejpam-3831	300	13	y	y	PROPN
ejpam-3831	300	14	)	)	PUNCT
ejpam-3831	300	15	ωs(x	ωs(x	NUM
ejpam-3831	300	16	,	,	PUNCT
ejpam-3831	300	17	x	x	X
ejpam-3831	300	18	,	,	PUNCT
ejpam-3831	300	19	x	x	X
ejpam-3831	300	20	,	,	PUNCT
ejpam-3831	300	21	y	y	PROPN
ejpam-3831	300	22	,	,	PUNCT
ejpam-3831	300	23	y	y	PROPN
ejpam-3831	300	24	,	,	PUNCT
ejpam-3831	300	25	y	y	PROPN
ejpam-3831	300	26	)	)	PUNCT
ejpam-3831	301	1	+	+	CCONJ
ejpam-3831	301	2	s.α10(x	s.α10(x	PROPN
ejpam-3831	301	3	,	,	PUNCT
ejpam-3831	301	4	x0	x0	PROPN
ejpam-3831	301	5	)	)	PUNCT
ejpam-3831	301	6	·	·	PUNCT
ejpam-3831	302	1	lim	lim	PROPN
ejpam-3831	302	2	supk→∞gb	supk→∞gb	PROPN
ejpam-3831	302	3	(	(	PUNCT
ejpam-3831	302	4	x3k+2	x3k+2	PROPN
ejpam-3831	302	5	,	,	PUNCT
ejpam-3831	302	6	x3k+1	x3k+1	PROPN
ejpam-3831	302	7	,	,	PUNCT
ejpam-3831	302	8	f	f	PROPN
ejpam-3831	302	9	(	(	PUNCT
ejpam-3831	302	10	x	x	PROPN
ejpam-3831	302	11	,	,	PUNCT
ejpam-3831	302	12	y)gb(x	y)gb(x	ADJ
ejpam-3831	302	13	,	,	PUNCT
ejpam-3831	302	14	x	x	NOUN
ejpam-3831	302	15	,	,	PUNCT
ejpam-3831	302	16	x	x	X
ejpam-3831	302	17	)	)	PUNCT
ejpam-3831	302	18	ωs(x	ωs(x	PUNCT
ejpam-3831	302	19	,	,	PUNCT
ejpam-3831	302	20	x	x	X
ejpam-3831	302	21	,	,	PUNCT
ejpam-3831	302	22	x	x	X
ejpam-3831	302	23	,	,	PUNCT
ejpam-3831	302	24	y	y	PROPN
ejpam-3831	302	25	,	,	PUNCT
ejpam-3831	302	26	y	y	PROPN
ejpam-3831	302	27	,	,	PUNCT
ejpam-3831	302	28	y	y	PROPN
ejpam-3831	302	29	)	)	PUNCT
ejpam-3831	302	30	+	+	CCONJ
ejpam-3831	302	31	s.α11(x	s.α11(x	NOUN
ejpam-3831	302	32	,	,	PUNCT
ejpam-3831	302	33	x0	x0	PROPN
ejpam-3831	302	34	)	)	PUNCT
ejpam-3831	302	35	·	·	PUNCT
ejpam-3831	303	1	gb(x	gb(x	NUM
ejpam-3831	303	2	,	,	PUNCT
ejpam-3831	303	3	x	x	X
ejpam-3831	303	4	,	,	PUNCT
ejpam-3831	303	5	x)gb(y	x)gb(y	PROPN
ejpam-3831	303	6	,	,	PUNCT
ejpam-3831	303	7	y	y	PROPN
ejpam-3831	303	8	,	,	PUNCT
ejpam-3831	303	9	y	y	NOUN
ejpam-3831	303	10	)	)	PUNCT
ejpam-3831	303	11	ωs(x	ωs(x	NUM
ejpam-3831	303	12	,	,	PUNCT
ejpam-3831	303	13	x	x	X
ejpam-3831	303	14	,	,	PUNCT
ejpam-3831	303	15	x	x	X
ejpam-3831	303	16	,	,	PUNCT
ejpam-3831	303	17	y	y	PROPN
ejpam-3831	303	18	,	,	PUNCT
ejpam-3831	303	19	y	y	PROPN
ejpam-3831	303	20	,	,	PUNCT
ejpam-3831	303	21	y	y	PROPN
ejpam-3831	303	22	)	)	PUNCT
ejpam-3831	304	1	+	+	CCONJ
ejpam-3831	304	2	s.α12(x	s.α12(x	PROPN
ejpam-3831	304	3	,	,	PUNCT
ejpam-3831	304	4	x0	x0	PROPN
ejpam-3831	304	5	)	)	PUNCT
ejpam-3831	304	6	·	·	PUNCT
ejpam-3831	305	1	gb(x	gb(x	NUM
ejpam-3831	305	2	,	,	PUNCT
ejpam-3831	305	3	x	x	X
ejpam-3831	305	4	,	,	PUNCT
ejpam-3831	305	5	x)gb(x	x)gb(x	PRON
ejpam-3831	305	6	,	,	PUNCT
ejpam-3831	305	7	x	x	NOUN
ejpam-3831	305	8	,	,	PUNCT
ejpam-3831	305	9	x	x	X
ejpam-3831	305	10	)	)	PUNCT
ejpam-3831	305	11	ωs(x	ωs(x	PUNCT
ejpam-3831	305	12	,	,	PUNCT
ejpam-3831	305	13	x	x	X
ejpam-3831	305	14	,	,	PUNCT
ejpam-3831	305	15	x	x	X
ejpam-3831	305	16	,	,	PUNCT
ejpam-3831	305	17	y	y	PROPN
ejpam-3831	305	18	,	,	PUNCT
ejpam-3831	305	19	y	y	PROPN
ejpam-3831	305	20	,	,	PUNCT
ejpam-3831	305	21	y	y	PROPN
ejpam-3831	305	22	)	)	PUNCT
ejpam-3831	305	23	.	.	PUNCT
ejpam-3831	306	1	sincegb(x	sincegb(x	ADJ
ejpam-3831	306	2	,	,	PUNCT
ejpam-3831	306	3	x	x	X
ejpam-3831	306	4	,	,	PUNCT
ejpam-3831	306	5	x	x	X
ejpam-3831	306	6	)	)	PUNCT
ejpam-3831	306	7	=	=	PUNCT
ejpam-3831	306	8	gb(y	gb(y	ADJ
ejpam-3831	306	9	,	,	PUNCT
ejpam-3831	306	10	y	y	PROPN
ejpam-3831	306	11	,	,	PUNCT
ejpam-3831	306	12	y	y	NOUN
ejpam-3831	306	13	)	)	PUNCT
ejpam-3831	306	14	=	=	SYM
ejpam-3831	307	1	gb(z	gb(z	NOUN
ejpam-3831	307	2	,	,	PUNCT
ejpam-3831	307	3	z	z	NOUN
ejpam-3831	307	4	,	,	PUNCT
ejpam-3831	307	5	z	z	NOUN
ejpam-3831	307	6	)	)	PUNCT
ejpam-3831	307	7	=	=	SYM
ejpam-3831	307	8	0	0	NUM
ejpam-3831	307	9	for	for	ADP
ejpam-3831	307	10	all	all	DET
ejpam-3831	307	11	x	x	NOUN
ejpam-3831	307	12	,	,	PUNCT
ejpam-3831	307	13	y	y	PROPN
ejpam-3831	307	14	,	,	PUNCT
ejpam-3831	307	15	z	z	PROPN
ejpam-3831	307	16	∈	∈	PROPN
ejpam-3831	307	17	x.	x.	NOUN
ejpam-3831	307	18	therefore	therefore	ADV
ejpam-3831	307	19	,	,	PUNCT
ejpam-3831	307	20	gb(x	gb(x	PROPN
ejpam-3831	307	21	,	,	PUNCT
ejpam-3831	307	22	f	f	PROPN
ejpam-3831	307	23	(	(	PUNCT
ejpam-3831	307	24	x	x	PROPN
ejpam-3831	307	25	,	,	PUNCT
ejpam-3831	307	26	y	y	PROPN
ejpam-3831	307	27	)	)	PUNCT
ejpam-3831	307	28	,	,	PUNCT
ejpam-3831	307	29	f	f	PROPN
ejpam-3831	307	30	(	(	PUNCT
ejpam-3831	307	31	x	x	PROPN
ejpam-3831	307	32	,	,	PUNCT
ejpam-3831	307	33	y	y	NOUN
ejpam-3831	307	34	)	)	PUNCT
ejpam-3831	307	35	)	)	PUNCT
ejpam-3831	307	36	≤	≤	ADV
ejpam-3831	307	37	0	0	NUM
ejpam-3831	307	38	.	.	PUNCT
ejpam-3831	308	1	which	which	PRON
ejpam-3831	308	2	is	be	AUX
ejpam-3831	308	3	contradiction	contradiction	NOUN
ejpam-3831	308	4	to	to	ADP
ejpam-3831	308	5	our	our	PRON
ejpam-3831	308	6	assumption	assumption	NOUN
ejpam-3831	308	7	that	that	SCONJ
ejpam-3831	308	8	gb(x	gb(x	PROPN
ejpam-3831	308	9	,	,	PUNCT
ejpam-3831	308	10	f	f	PROPN
ejpam-3831	308	11	(	(	PUNCT
ejpam-3831	308	12	x	x	PROPN
ejpam-3831	308	13	,	,	PUNCT
ejpam-3831	308	14	y	y	PROPN
ejpam-3831	308	15	)	)	PUNCT
ejpam-3831	308	16	,	,	PUNCT
ejpam-3831	308	17	f	f	PROPN
ejpam-3831	308	18	(	(	PUNCT
ejpam-3831	308	19	x	x	PROPN
ejpam-3831	308	20	,	,	PUNCT
ejpam-3831	308	21	y	y	NOUN
ejpam-3831	308	22	)	)	PUNCT
ejpam-3831	308	23	)	)	PUNCT
ejpam-3831	309	1	>	>	X
ejpam-3831	310	1	0	0	X
ejpam-3831	310	2	.	.	PUNCT
ejpam-3831	310	3	hence	hence	ADV
ejpam-3831	310	4	gb(x	gb(x	PROPN
ejpam-3831	310	5	,	,	PUNCT
ejpam-3831	310	6	f	f	PROPN
ejpam-3831	310	7	(	(	PUNCT
ejpam-3831	310	8	x	x	PROPN
ejpam-3831	310	9	,	,	PUNCT
ejpam-3831	310	10	y	y	PROPN
ejpam-3831	310	11	)	)	PUNCT
ejpam-3831	310	12	,	,	PUNCT
ejpam-3831	310	13	f	f	PROPN
ejpam-3831	310	14	(	(	PUNCT
ejpam-3831	310	15	x	x	PROPN
ejpam-3831	310	16	,	,	PUNCT
ejpam-3831	310	17	y	y	NOUN
ejpam-3831	310	18	)	)	PUNCT
ejpam-3831	310	19	)	)	PUNCT
ejpam-3831	311	1	=	=	PUNCT
ejpam-3831	311	2	0	0	X
ejpam-3831	311	3	.	.	NOUN
ejpam-3831	311	4	which	which	PRON
ejpam-3831	311	5	implies	imply	VERB
ejpam-3831	311	6	that	that	SCONJ
ejpam-3831	311	7	x	x	X
ejpam-3831	311	8	=	=	SYM
ejpam-3831	311	9	f	f	X
ejpam-3831	311	10	(	(	PUNCT
ejpam-3831	311	11	x	x	PROPN
ejpam-3831	311	12	,	,	PUNCT
ejpam-3831	311	13	y	y	PROPN
ejpam-3831	311	14	)	)	PUNCT
ejpam-3831	311	15	and	and	CCONJ
ejpam-3831	311	16	similarly	similarly	ADV
ejpam-3831	311	17	y	y	PROPN
ejpam-3831	311	18	=	=	SYM
ejpam-3831	311	19	f	f	PROPN
ejpam-3831	311	20	(	(	PUNCT
ejpam-3831	311	21	y	y	PROPN
ejpam-3831	311	22	,	,	PUNCT
ejpam-3831	311	23	x	x	NOUN
ejpam-3831	311	24	)	)	PUNCT
ejpam-3831	311	25	.	.	PUNCT
ejpam-3831	312	1	thus	thus	ADV
ejpam-3831	312	2	(	(	PUNCT
ejpam-3831	312	3	x	x	X
ejpam-3831	312	4	,	,	PUNCT
ejpam-3831	312	5	y	y	NOUN
ejpam-3831	312	6	)	)	PUNCT
ejpam-3831	312	7	is	be	AUX
ejpam-3831	312	8	a	a	DET
ejpam-3831	312	9	coupled	couple	VERB
ejpam-3831	312	10	fixed	fix	VERB
ejpam-3831	312	11	point	point	NOUN
ejpam-3831	312	12	of	of	ADP
ejpam-3831	312	13	f.	f.	PROPN
ejpam-3831	312	14	similarly	similarly	ADV
ejpam-3831	312	15	we	we	PRON
ejpam-3831	312	16	can	can	AUX
ejpam-3831	312	17	show	show	VERB
ejpam-3831	312	18	that	that	SCONJ
ejpam-3831	312	19	(	(	PUNCT
ejpam-3831	312	20	x	x	X
ejpam-3831	312	21	,	,	PUNCT
ejpam-3831	312	22	y	y	NOUN
ejpam-3831	312	23	)	)	PUNCT
ejpam-3831	312	24	is	be	AUX
ejpam-3831	312	25	a	a	DET
ejpam-3831	312	26	coupled	couple	VERB
ejpam-3831	312	27	fixed	fix	VERB
ejpam-3831	312	28	point	point	NOUN
ejpam-3831	312	29	of	of	ADP
ejpam-3831	312	30	h	h	NOUN
ejpam-3831	312	31	and	and	CCONJ
ejpam-3831	312	32	t.	t.	NOUN
ejpam-3831	312	33	hence	hence	ADV
ejpam-3831	312	34	(	(	PUNCT
ejpam-3831	312	35	x	x	X
ejpam-3831	312	36	,	,	PUNCT
ejpam-3831	312	37	y	y	NOUN
ejpam-3831	312	38	)	)	PUNCT
ejpam-3831	312	39	is	be	AUX
ejpam-3831	312	40	a	a	DET
ejpam-3831	312	41	common	common	ADJ
ejpam-3831	312	42	coupled	couple	VERB
ejpam-3831	312	43	fixed	fix	VERB
ejpam-3831	312	44	point	point	NOUN
ejpam-3831	312	45	of	of	ADP
ejpam-3831	312	46	f	f	PROPN
ejpam-3831	312	47	,	,	PUNCT
ejpam-3831	312	48	h	h	NOUN
ejpam-3831	312	49	and	and	CCONJ
ejpam-3831	312	50	t.	t.	PROPN
ejpam-3831	312	51	to	to	PART
ejpam-3831	312	52	show	show	VERB
ejpam-3831	312	53	the	the	DET
ejpam-3831	312	54	uniqueness	uniqueness	NOUN
ejpam-3831	312	55	,	,	PUNCT
ejpam-3831	312	56	suppose	suppose	VERB
ejpam-3831	312	57	that	that	SCONJ
ejpam-3831	312	58	f	f	X
ejpam-3831	312	59	,	,	PUNCT
ejpam-3831	312	60	h	h	PROPN
ejpam-3831	312	61	and	and	CCONJ
ejpam-3831	312	62	t	t	PROPN
ejpam-3831	312	63	have	have	VERB
ejpam-3831	312	64	two	two	NUM
ejpam-3831	312	65	common	common	ADJ
ejpam-3831	312	66	coupled	couple	VERB
ejpam-3831	312	67	fixed	fix	VERB
ejpam-3831	312	68	points	point	NOUN
ejpam-3831	312	69	(	(	PUNCT
ejpam-3831	312	70	x	x	X
ejpam-3831	312	71	,	,	PUNCT
ejpam-3831	312	72	y	y	PROPN
ejpam-3831	312	73	)	)	PUNCT
ejpam-3831	312	74	and	and	CCONJ
ejpam-3831	312	75	(	(	PUNCT
ejpam-3831	312	76	u	u	NOUN
ejpam-3831	312	77	,	,	PUNCT
ejpam-3831	312	78	v	v	NOUN
ejpam-3831	312	79	)	)	PUNCT
ejpam-3831	312	80	.	.	PUNCT
ejpam-3831	313	1	then	then	ADV
ejpam-3831	313	2	from	from	ADP
ejpam-3831	313	3	given	give	VERB
ejpam-3831	313	4	condition	condition	NOUN
ejpam-3831	313	5	one	one	NUM
ejpam-3831	313	6	has	have	VERB
ejpam-3831	313	7	gb(x	gb(x	ADJ
ejpam-3831	313	8	,	,	PUNCT
ejpam-3831	313	9	u	u	NOUN
ejpam-3831	313	10	,	,	PUNCT
ejpam-3831	313	11	u	u	NOUN
ejpam-3831	313	12	)	)	PUNCT
ejpam-3831	313	13	=	=	SYM
ejpam-3831	313	14	gb(f	gb(f	X
ejpam-3831	313	15	(	(	PUNCT
ejpam-3831	313	16	x	x	NOUN
ejpam-3831	313	17	,	,	PUNCT
ejpam-3831	313	18	y	y	PROPN
ejpam-3831	313	19	)	)	PUNCT
ejpam-3831	313	20	,	,	PUNCT
ejpam-3831	313	21	h(u	h(u	PROPN
ejpam-3831	313	22	,	,	PUNCT
ejpam-3831	313	23	v	v	NOUN
ejpam-3831	313	24	)	)	PUNCT
ejpam-3831	313	25	,	,	PUNCT
ejpam-3831	313	26	t	t	PROPN
ejpam-3831	313	27	(	(	PUNCT
ejpam-3831	313	28	u	u	NOUN
ejpam-3831	313	29	,	,	PUNCT
ejpam-3831	313	30	v	v	NOUN
ejpam-3831	313	31	)	)	PUNCT
ejpam-3831	313	32	)	)	PUNCT
ejpam-3831	313	33	≤	≤	NOUN
ejpam-3831	313	34	α1(x	α1(x	PROPN
ejpam-3831	313	35	,	,	PUNCT
ejpam-3831	313	36	u	u	NOUN
ejpam-3831	313	37	)	)	PUNCT
ejpam-3831	313	38	·	·	PUNCT
ejpam-3831	314	1	gb(x	gb(x	NUM
ejpam-3831	314	2	,	,	PUNCT
ejpam-3831	314	3	u	u	NOUN
ejpam-3831	314	4	,	,	PUNCT
ejpam-3831	314	5	u	u	NOUN
ejpam-3831	314	6	)	)	PUNCT
ejpam-3831	314	7	+	+	ADP
ejpam-3831	314	8	gb(y	gb(y	ADJ
ejpam-3831	314	9	,	,	PUNCT
ejpam-3831	314	10	v	v	NOUN
ejpam-3831	314	11	,	,	PUNCT
ejpam-3831	314	12	v	v	NOUN
ejpam-3831	314	13	)	)	PUNCT
ejpam-3831	314	14	2	2	NUM
ejpam-3831	314	15	+	+	CCONJ
ejpam-3831	314	16	s.α2(x	s.α2(x	PROPN
ejpam-3831	314	17	,	,	PUNCT
ejpam-3831	314	18	u	u	NOUN
ejpam-3831	314	19	)	)	PUNCT
ejpam-3831	314	20	·	·	PUNCT
ejpam-3831	314	21	gb	gb	PRON
ejpam-3831	314	22	(	(	PUNCT
ejpam-3831	314	23	f	f	X
ejpam-3831	314	24	(	(	PUNCT
ejpam-3831	314	25	x	x	PROPN
ejpam-3831	314	26	,	,	PUNCT
ejpam-3831	314	27	y	y	PROPN
ejpam-3831	314	28	)	)	PUNCT
ejpam-3831	314	29	,	,	PUNCT
ejpam-3831	314	30	h(u	h(u	PROPN
ejpam-3831	314	31	,	,	PUNCT
ejpam-3831	314	32	v	v	NOUN
ejpam-3831	314	33	)	)	PUNCT
ejpam-3831	314	34	,	,	PUNCT
ejpam-3831	314	35	t	t	PROPN
ejpam-3831	314	36	(	(	PUNCT
ejpam-3831	314	37	u	u	NOUN
ejpam-3831	314	38	,	,	PUNCT
ejpam-3831	314	39	v	v	NOUN
ejpam-3831	314	40	)	)	PUNCT
ejpam-3831	314	41	)	)	PUNCT
ejpam-3831	314	42	)	)	PUNCT
ejpam-3831	315	1	gb(x	gb(x	PUNCT
ejpam-3831	315	2	,	,	PUNCT
ejpam-3831	315	3	u	u	NOUN
ejpam-3831	315	4	,	,	PUNCT
ejpam-3831	315	5	u	u	NOUN
ejpam-3831	315	6	)	)	PUNCT
ejpam-3831	315	7	ωs(x	ωs(x	NUM
ejpam-3831	315	8	,	,	PUNCT
ejpam-3831	315	9	u	u	NOUN
ejpam-3831	315	10	,	,	PUNCT
ejpam-3831	315	11	u	u	NOUN
ejpam-3831	315	12	,	,	PUNCT
ejpam-3831	315	13	y	y	PROPN
ejpam-3831	315	14	,	,	PUNCT
ejpam-3831	315	15	v	v	NOUN
ejpam-3831	315	16	,	,	PUNCT
ejpam-3831	315	17	v	v	NOUN
ejpam-3831	315	18	)	)	PUNCT
ejpam-3831	315	19	m.m.m	m.m.m	NOUN
ejpam-3831	315	20	.	.	PUNCT
ejpam-3831	316	1	jaradat	jaradat	PROPN
ejpam-3831	316	2	et	et	PROPN
ejpam-3831	316	3	al	al	PROPN
ejpam-3831	316	4	.	.	PUNCT
ejpam-3831	316	5	/	/	SYM
ejpam-3831	316	6	eur	eur	PROPN
ejpam-3831	316	7	.	.	PUNCT
ejpam-3831	317	1	j.	j.	PROPN
ejpam-3831	317	2	pure	pure	PROPN
ejpam-3831	317	3	appl	appl	PROPN
ejpam-3831	317	4	.	.	PROPN
ejpam-3831	317	5	math	math	PROPN
ejpam-3831	317	6	,	,	PUNCT
ejpam-3831	317	7	13	13	NUM
ejpam-3831	317	8	(	(	PUNCT
ejpam-3831	317	9	4	4	NUM
ejpam-3831	317	10	)	)	PUNCT
ejpam-3831	317	11	(	(	PUNCT
ejpam-3831	317	12	2020	2020	NUM
ejpam-3831	317	13	)	)	PUNCT
ejpam-3831	317	14	,	,	PUNCT
ejpam-3831	317	15	995	995	NUM
ejpam-3831	317	16	-	-	SYM
ejpam-3831	317	17	1015	1015	NUM
ejpam-3831	317	18	1006	1006	NUM
ejpam-3831	317	19	+	+	CCONJ
ejpam-3831	317	20	s.α3(x	s.α3(x	PROPN
ejpam-3831	317	21	,	,	PUNCT
ejpam-3831	317	22	u	u	NOUN
ejpam-3831	317	23	)	)	PUNCT
ejpam-3831	317	24	·	·	PUNCT
ejpam-3831	318	1	gb	gb	PRON
ejpam-3831	318	2	(	(	PUNCT
ejpam-3831	318	3	f	f	X
ejpam-3831	318	4	(	(	PUNCT
ejpam-3831	318	5	x	x	PROPN
ejpam-3831	318	6	,	,	PUNCT
ejpam-3831	318	7	y	y	PROPN
ejpam-3831	318	8	)	)	PUNCT
ejpam-3831	318	9	,	,	PUNCT
ejpam-3831	318	10	h(u	h(u	PROPN
ejpam-3831	318	11	,	,	PUNCT
ejpam-3831	318	12	v	v	NOUN
ejpam-3831	318	13	)	)	PUNCT
ejpam-3831	318	14	,	,	PUNCT
ejpam-3831	318	15	t	t	PROPN
ejpam-3831	318	16	(	(	PUNCT
ejpam-3831	318	17	u	u	NOUN
ejpam-3831	318	18	,	,	PUNCT
ejpam-3831	318	19	v	v	NOUN
ejpam-3831	318	20	)	)	PUNCT
ejpam-3831	318	21	)	)	PUNCT
ejpam-3831	318	22	gb(y	gb(y	ADV
ejpam-3831	318	23	,	,	PUNCT
ejpam-3831	318	24	v	v	NOUN
ejpam-3831	318	25	,	,	PUNCT
ejpam-3831	318	26	v	v	NOUN
ejpam-3831	318	27	)	)	PUNCT
ejpam-3831	318	28	ωs(x	ωs(x	NUM
ejpam-3831	318	29	,	,	PUNCT
ejpam-3831	318	30	u	u	NOUN
ejpam-3831	318	31	,	,	PUNCT
ejpam-3831	318	32	u	u	NOUN
ejpam-3831	318	33	,	,	PUNCT
ejpam-3831	318	34	y	y	PROPN
ejpam-3831	318	35	,	,	PUNCT
ejpam-3831	318	36	v	v	NOUN
ejpam-3831	318	37	,	,	PUNCT
ejpam-3831	318	38	v	v	NOUN
ejpam-3831	318	39	)	)	PUNCT
ejpam-3831	318	40	+	+	CCONJ
ejpam-3831	319	1	s.α4(x	s.α4(x	PROPN
ejpam-3831	319	2	,	,	PUNCT
ejpam-3831	319	3	u	u	NOUN
ejpam-3831	319	4	)	)	PUNCT
ejpam-3831	319	5	·	·	PUNCT
ejpam-3831	320	1	gb(x	gb(x	NUM
ejpam-3831	320	2	,	,	PUNCT
ejpam-3831	320	3	x	x	X
ejpam-3831	320	4	,	,	PUNCT
ejpam-3831	320	5	f	f	PROPN
ejpam-3831	320	6	(	(	PUNCT
ejpam-3831	320	7	x	x	X
ejpam-3831	320	8	,	,	PUNCT
ejpam-3831	320	9	y))gb(x	y))gb(x	NUM
ejpam-3831	320	10	,	,	PUNCT
ejpam-3831	320	11	u	u	NOUN
ejpam-3831	320	12	,	,	PUNCT
ejpam-3831	320	13	u	u	NOUN
ejpam-3831	320	14	)	)	PUNCT
ejpam-3831	320	15	ωs(x	ωs(x	NUM
ejpam-3831	320	16	,	,	PUNCT
ejpam-3831	320	17	u	u	NOUN
ejpam-3831	320	18	,	,	PUNCT
ejpam-3831	320	19	u	u	NOUN
ejpam-3831	320	20	,	,	PUNCT
ejpam-3831	320	21	y	y	PROPN
ejpam-3831	320	22	,	,	PUNCT
ejpam-3831	320	23	v	v	NOUN
ejpam-3831	320	24	,	,	PUNCT
ejpam-3831	320	25	v	v	NOUN
ejpam-3831	320	26	)	)	PUNCT
ejpam-3831	320	27	+	+	CCONJ
ejpam-3831	321	1	s.α5(u	s.α5(u	ADJ
ejpam-3831	321	2	,	,	PUNCT
ejpam-3831	321	3	u	u	NOUN
ejpam-3831	321	4	)	)	PUNCT
ejpam-3831	321	5	·	·	PUNCT
ejpam-3831	322	1	gb(x	gb(x	NUM
ejpam-3831	322	2	,	,	PUNCT
ejpam-3831	322	3	x	x	X
ejpam-3831	322	4	,	,	PUNCT
ejpam-3831	322	5	f	f	PROPN
ejpam-3831	322	6	(	(	PUNCT
ejpam-3831	322	7	x	x	X
ejpam-3831	322	8	,	,	PUNCT
ejpam-3831	322	9	y))gb(y	y))gb(y	PRON
ejpam-3831	322	10	,	,	PUNCT
ejpam-3831	322	11	v	v	NOUN
ejpam-3831	322	12	,	,	PUNCT
ejpam-3831	322	13	v	v	NOUN
ejpam-3831	322	14	)	)	PUNCT
ejpam-3831	322	15	ωs(x	ωs(x	NUM
ejpam-3831	322	16	,	,	PUNCT
ejpam-3831	322	17	u	u	NOUN
ejpam-3831	322	18	,	,	PUNCT
ejpam-3831	322	19	u	u	NOUN
ejpam-3831	322	20	,	,	PUNCT
ejpam-3831	322	21	y	y	PROPN
ejpam-3831	322	22	,	,	PUNCT
ejpam-3831	322	23	v	v	NOUN
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ejpam-3831	322	68	,	,	PUNCT
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ejpam-3831	323	21	,	,	PUNCT
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ejpam-3831	327	21	,	,	PUNCT
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ejpam-3831	327	25	,	,	PUNCT
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ejpam-3831	330	12	,	,	PUNCT
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ejpam-3831	331	5	u	u	NOUN
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ejpam-3831	331	17	,	,	PUNCT
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ejpam-3831	331	22	,	,	PUNCT
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ejpam-3831	331	50	,	,	PUNCT
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ejpam-3831	331	85	u	u	NOUN
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ejpam-3831	331	104	·	·	PUNCT
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ejpam-3831	333	21	v	v	NOUN
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ejpam-3831	333	28	·	·	PUNCT
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ejpam-3831	334	3	u	u	NOUN
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ejpam-3831	334	5	u)gb(y	u)gb(y	ADJ
ejpam-3831	334	6	,	,	PUNCT
ejpam-3831	334	7	v	v	NOUN
ejpam-3831	334	8	,	,	PUNCT
ejpam-3831	334	9	v	v	NOUN
ejpam-3831	334	10	)	)	PUNCT
ejpam-3831	334	11	ωs(x	ωs(x	NUM
ejpam-3831	334	12	,	,	PUNCT
ejpam-3831	334	13	u	u	NOUN
ejpam-3831	334	14	,	,	PUNCT
ejpam-3831	334	15	u	u	NOUN
ejpam-3831	334	16	,	,	PUNCT
ejpam-3831	334	17	y	y	PROPN
ejpam-3831	334	18	,	,	PUNCT
ejpam-3831	334	19	v	v	NOUN
ejpam-3831	334	20	,	,	PUNCT
ejpam-3831	334	21	v	v	NOUN
ejpam-3831	334	22	)	)	PUNCT
ejpam-3831	334	23	+	+	SYM
ejpam-3831	334	24	α8(u	α8(u	NUM
ejpam-3831	334	25	,	,	PUNCT
ejpam-3831	334	26	u	u	NOUN
ejpam-3831	334	27	)	)	PUNCT
ejpam-3831	334	28	·	·	PUNCT
ejpam-3831	335	1	gb(u	gb(u	NUM
ejpam-3831	335	2	,	,	PUNCT
ejpam-3831	335	3	u	u	NOUN
ejpam-3831	335	4	,	,	PUNCT
ejpam-3831	335	5	u)gb(x	u)gb(x	PROPN
ejpam-3831	335	6	,	,	PUNCT
ejpam-3831	335	7	u	u	NOUN
ejpam-3831	335	8	,	,	PUNCT
ejpam-3831	335	9	u	u	NOUN
ejpam-3831	335	10	)	)	PUNCT
ejpam-3831	335	11	ωs(x	ωs(x	NUM
ejpam-3831	335	12	,	,	PUNCT
ejpam-3831	335	13	u	u	NOUN
ejpam-3831	335	14	,	,	PUNCT
ejpam-3831	335	15	u	u	NOUN
ejpam-3831	335	16	,	,	PUNCT
ejpam-3831	335	17	y	y	PROPN
ejpam-3831	335	18	,	,	PUNCT
ejpam-3831	335	19	v	v	NOUN
ejpam-3831	335	20	,	,	PUNCT
ejpam-3831	335	21	v	v	NOUN
ejpam-3831	335	22	)	)	PUNCT
ejpam-3831	335	23	m.m.m	m.m.m	NOUN
ejpam-3831	335	24	.	.	PUNCT
ejpam-3831	336	1	jaradat	jaradat	PROPN
ejpam-3831	336	2	et	et	PROPN
ejpam-3831	336	3	al	al	PROPN
ejpam-3831	336	4	.	.	PUNCT
ejpam-3831	336	5	/	/	SYM
ejpam-3831	336	6	eur	eur	PROPN
ejpam-3831	336	7	.	.	PUNCT
ejpam-3831	337	1	j.	j.	PROPN
ejpam-3831	337	2	pure	pure	PROPN
ejpam-3831	337	3	appl	appl	PROPN
ejpam-3831	337	4	.	.	PROPN
ejpam-3831	337	5	math	math	PROPN
ejpam-3831	337	6	,	,	PUNCT
ejpam-3831	337	7	13	13	NUM
ejpam-3831	337	8	(	(	PUNCT
ejpam-3831	337	9	4	4	NUM
ejpam-3831	337	10	)	)	PUNCT
ejpam-3831	337	11	(	(	PUNCT
ejpam-3831	337	12	2020	2020	NUM
ejpam-3831	337	13	)	)	PUNCT
ejpam-3831	337	14	,	,	PUNCT
ejpam-3831	337	15	995	995	NUM
ejpam-3831	337	16	-	-	SYM
ejpam-3831	337	17	1015	1015	NUM
ejpam-3831	337	18	1007	1007	NUM
ejpam-3831	337	19	+	+	CCONJ
ejpam-3831	337	20	α9(u	α9(u	NUM
ejpam-3831	337	21	,	,	PUNCT
ejpam-3831	337	22	x	x	X
ejpam-3831	337	23	)	)	PUNCT
ejpam-3831	337	24	·	·	PUNCT
ejpam-3831	338	1	gb(u	gb(u	NUM
ejpam-3831	338	2	,	,	PUNCT
ejpam-3831	338	3	u	u	NOUN
ejpam-3831	338	4	,	,	PUNCT
ejpam-3831	338	5	u)gb(y	u)gb(y	ADJ
ejpam-3831	338	6	,	,	PUNCT
ejpam-3831	338	7	v	v	NOUN
ejpam-3831	338	8	,	,	PUNCT
ejpam-3831	338	9	v	v	NOUN
ejpam-3831	338	10	)	)	PUNCT
ejpam-3831	338	11	ωs(x	ωs(x	NUM
ejpam-3831	338	12	,	,	PUNCT
ejpam-3831	338	13	u	u	NOUN
ejpam-3831	338	14	,	,	PUNCT
ejpam-3831	338	15	u	u	NOUN
ejpam-3831	338	16	,	,	PUNCT
ejpam-3831	338	17	y	y	PROPN
ejpam-3831	338	18	,	,	PUNCT
ejpam-3831	338	19	v	v	NOUN
ejpam-3831	338	20	,	,	PUNCT
ejpam-3831	338	21	v	v	NOUN
ejpam-3831	338	22	)	)	PUNCT
ejpam-3831	338	23	+	+	X
ejpam-3831	338	24	α10(u	α10(u	ADV
ejpam-3831	338	25	,	,	PUNCT
ejpam-3831	338	26	x	x	X
ejpam-3831	338	27	)	)	PUNCT
ejpam-3831	338	28	·	·	PUNCT
ejpam-3831	338	29	gb(x	gb(x	NUM
ejpam-3831	338	30	,	,	PUNCT
ejpam-3831	338	31	u	u	NOUN
ejpam-3831	338	32	,	,	PUNCT
ejpam-3831	338	33	u)gb(x	u)gb(x	PROPN
ejpam-3831	338	34	,	,	PUNCT
ejpam-3831	338	35	u	u	NOUN
ejpam-3831	338	36	,	,	PUNCT
ejpam-3831	338	37	u	u	NOUN
ejpam-3831	338	38	)	)	PUNCT
ejpam-3831	338	39	ωs(x	ωs(x	NUM
ejpam-3831	338	40	,	,	PUNCT
ejpam-3831	338	41	u	u	NOUN
ejpam-3831	338	42	,	,	PUNCT
ejpam-3831	338	43	u	u	NOUN
ejpam-3831	338	44	,	,	PUNCT
ejpam-3831	338	45	y	y	PROPN
ejpam-3831	338	46	,	,	PUNCT
ejpam-3831	338	47	v	v	NOUN
ejpam-3831	338	48	,	,	PUNCT
ejpam-3831	338	49	v	v	NOUN
ejpam-3831	338	50	)	)	PUNCT
ejpam-3831	338	51	+	+	NUM
ejpam-3831	338	52	α11(u	α11(u	NOUN
ejpam-3831	338	53	,	,	PUNCT
ejpam-3831	338	54	x	x	NOUN
ejpam-3831	338	55	)	)	PUNCT
ejpam-3831	338	56	·	·	PUNCT
ejpam-3831	338	57	gb(u	gb(u	NUM
ejpam-3831	338	58	,	,	PUNCT
ejpam-3831	338	59	u	u	NOUN
ejpam-3831	338	60	,	,	PUNCT
ejpam-3831	338	61	x)gb(y	x)gb(y	PROPN
ejpam-3831	338	62	,	,	PUNCT
ejpam-3831	338	63	v	v	NOUN
ejpam-3831	338	64	,	,	PUNCT
ejpam-3831	338	65	v	v	NOUN
ejpam-3831	338	66	)	)	PUNCT
ejpam-3831	338	67	ωs(x	ωs(x	NUM
ejpam-3831	338	68	,	,	PUNCT
ejpam-3831	338	69	u	u	NOUN
ejpam-3831	338	70	,	,	PUNCT
ejpam-3831	338	71	u	u	NOUN
ejpam-3831	338	72	,	,	PUNCT
ejpam-3831	338	73	y	y	PROPN
ejpam-3831	338	74	,	,	PUNCT
ejpam-3831	338	75	v	v	NOUN
ejpam-3831	338	76	,	,	PUNCT
ejpam-3831	338	77	v	v	NOUN
ejpam-3831	338	78	)	)	PUNCT
ejpam-3831	338	79	+	+	CCONJ
ejpam-3831	338	80	α12(u	α12(u	NUM
ejpam-3831	338	81	,	,	PUNCT
ejpam-3831	338	82	x	x	NOUN
ejpam-3831	338	83	)	)	PUNCT
ejpam-3831	338	84	·	·	PUNCT
ejpam-3831	339	1	gb(u	gb(u	NUM
ejpam-3831	339	2	,	,	PUNCT
ejpam-3831	339	3	x	x	PRON
ejpam-3831	339	4	,	,	PUNCT
ejpam-3831	339	5	u)gb(x	u)gb(x	PROPN
ejpam-3831	339	6	,	,	PUNCT
ejpam-3831	339	7	u	u	NOUN
ejpam-3831	339	8	,	,	PUNCT
ejpam-3831	339	9	u	u	NOUN
ejpam-3831	339	10	)	)	PUNCT
ejpam-3831	339	11	ωs(x	ωs(x	NUM
ejpam-3831	339	12	,	,	PUNCT
ejpam-3831	339	13	u	u	NOUN
ejpam-3831	339	14	,	,	PUNCT
ejpam-3831	339	15	u	u	NOUN
ejpam-3831	339	16	,	,	PUNCT
ejpam-3831	339	17	y	y	PROPN
ejpam-3831	339	18	,	,	PUNCT
ejpam-3831	339	19	v	v	NOUN
ejpam-3831	339	20	,	,	PUNCT
ejpam-3831	339	21	v	v	NOUN
ejpam-3831	339	22	)	)	PUNCT
ejpam-3831	339	23	.	.	PUNCT
ejpam-3831	340	1	thus	thus	ADV
ejpam-3831	340	2	we	we	PRON
ejpam-3831	340	3	have	have	VERB
ejpam-3831	340	4	gb(x	gb(x	ADJ
ejpam-3831	340	5	,	,	PUNCT
ejpam-3831	340	6	u	u	NOUN
ejpam-3831	340	7	,	,	PUNCT
ejpam-3831	340	8	u	u	NOUN
ejpam-3831	340	9	)	)	PUNCT
ejpam-3831	340	10	≤	≤	NOUN
ejpam-3831	340	11	α1(x	α1(x	PROPN
ejpam-3831	340	12	,	,	PUNCT
ejpam-3831	340	13	u	u	NOUN
ejpam-3831	340	14	)	)	PUNCT
ejpam-3831	340	15	·	·	PUNCT
ejpam-3831	341	1	gb(x	gb(x	NUM
ejpam-3831	341	2	,	,	PUNCT
ejpam-3831	341	3	u	u	NOUN
ejpam-3831	341	4	,	,	PUNCT
ejpam-3831	341	5	u	u	NOUN
ejpam-3831	341	6	)	)	PUNCT
ejpam-3831	341	7	+	+	ADP
ejpam-3831	341	8	gb(y	gb(y	ADJ
ejpam-3831	341	9	,	,	PUNCT
ejpam-3831	341	10	v	v	NOUN
ejpam-3831	341	11	,	,	PUNCT
ejpam-3831	341	12	v	v	NOUN
ejpam-3831	341	13	)	)	PUNCT
ejpam-3831	341	14	2	2	NUM
ejpam-3831	341	15	+	+	CCONJ
ejpam-3831	341	16	α2(x	α2(x	PROPN
ejpam-3831	341	17	,	,	PUNCT
ejpam-3831	341	18	u	u	NOUN
ejpam-3831	341	19	)	)	PUNCT
ejpam-3831	341	20	·	·	PUNCT
ejpam-3831	341	21	gb(x	gb(x	NUM
ejpam-3831	341	22	,	,	PUNCT
ejpam-3831	341	23	u	u	NOUN
ejpam-3831	341	24	,	,	PUNCT
ejpam-3831	341	25	u	u	NOUN
ejpam-3831	341	26	)	)	PUNCT
ejpam-3831	341	27	+	+	CCONJ
ejpam-3831	341	28	α3(x	α3(x	PROPN
ejpam-3831	341	29	,	,	PUNCT
ejpam-3831	341	30	u	u	NOUN
ejpam-3831	341	31	)	)	PUNCT
ejpam-3831	341	32	·	·	PUNCT
ejpam-3831	341	33	gb(x	gb(x	NUM
ejpam-3831	341	34	,	,	PUNCT
ejpam-3831	341	35	u	u	NOUN
ejpam-3831	341	36	,	,	PUNCT
ejpam-3831	341	37	u	u	NOUN
ejpam-3831	341	38	)	)	PUNCT
ejpam-3831	341	39	+	+	CCONJ
ejpam-3831	341	40	α10(u	α10(u	ADV
ejpam-3831	341	41	,	,	PUNCT
ejpam-3831	341	42	x	x	X
ejpam-3831	341	43	)	)	PUNCT
ejpam-3831	341	44	·	·	PUNCT
ejpam-3831	341	45	gb(x	gb(x	NUM
ejpam-3831	341	46	,	,	PUNCT
ejpam-3831	341	47	u	u	NOUN
ejpam-3831	341	48	,	,	PUNCT
ejpam-3831	341	49	u	u	NOUN
ejpam-3831	341	50	)	)	PUNCT
ejpam-3831	341	51	+	+	NUM
ejpam-3831	341	52	α11(u	α11(u	NOUN
ejpam-3831	341	53	,	,	PUNCT
ejpam-3831	341	54	x	x	NOUN
ejpam-3831	341	55	)	)	PUNCT
ejpam-3831	341	56	·	·	PUNCT
ejpam-3831	341	57	gb(x	gb(x	NUM
ejpam-3831	341	58	,	,	PUNCT
ejpam-3831	341	59	u	u	NOUN
ejpam-3831	341	60	,	,	PUNCT
ejpam-3831	341	61	u	u	NOUN
ejpam-3831	341	62	)	)	PUNCT
ejpam-3831	341	63	+	+	CCONJ
ejpam-3831	341	64	α12(u	α12(u	NUM
ejpam-3831	341	65	,	,	PUNCT
ejpam-3831	341	66	x	x	X
ejpam-3831	341	67	)	)	PUNCT
ejpam-3831	341	68	·	·	PUNCT
ejpam-3831	341	69	gb(x	gb(x	NUM
ejpam-3831	341	70	,	,	PUNCT
ejpam-3831	341	71	u	u	NOUN
ejpam-3831	341	72	,	,	PUNCT
ejpam-3831	341	73	u	u	NOUN
ejpam-3831	341	74	)	)	PUNCT
ejpam-3831	341	75	further	further	ADJ
ejpam-3831	341	76	simplification	simplification	NOUN
ejpam-3831	341	77	gives	give	VERB
ejpam-3831	341	78	(	(	PUNCT
ejpam-3831	341	79	1−	1−	NUM
ejpam-3831	341	80	α1(x	α1(x	PROPN
ejpam-3831	341	81	,	,	PUNCT
ejpam-3831	341	82	u	u	NOUN
ejpam-3831	341	83	)	)	PUNCT
ejpam-3831	341	84	2	2	NUM
ejpam-3831	341	85	−	−	NOUN
ejpam-3831	342	1	α2(x	α2(x	PROPN
ejpam-3831	342	2	,	,	PUNCT
ejpam-3831	342	3	u)−	u)−	PROPN
ejpam-3831	342	4	α3(x	α3(x	PROPN
ejpam-3831	342	5	,	,	PUNCT
ejpam-3831	342	6	u)−	u)−	PROPN
ejpam-3831	342	7	12∑	12∑	NUM
ejpam-3831	342	8	i=10	i=10	NOUN
ejpam-3831	342	9	αi(u	αi(u	NOUN
ejpam-3831	342	10	,	,	PUNCT
ejpam-3831	342	11	x	x	NOUN
ejpam-3831	342	12	)	)	PUNCT
ejpam-3831	342	13	)	)	PUNCT
ejpam-3831	343	1	gb(x	gb(x	PUNCT
ejpam-3831	343	2	,	,	PUNCT
ejpam-3831	343	3	u	u	NOUN
ejpam-3831	343	4	,	,	PUNCT
ejpam-3831	343	5	u	u	NOUN
ejpam-3831	343	6	)	)	PUNCT
ejpam-3831	343	7	≤	≤	NOUN
ejpam-3831	343	8	α1(x	α1(x	PROPN
ejpam-3831	343	9	,	,	PUNCT
ejpam-3831	343	10	u	u	NOUN
ejpam-3831	343	11	)	)	PUNCT
ejpam-3831	343	12	2	2	NUM
ejpam-3831	343	13	·	·	PUNCT
ejpam-3831	343	14	gb(y	gb(y	NUM
ejpam-3831	343	15	,	,	PUNCT
ejpam-3831	343	16	v	v	NOUN
ejpam-3831	343	17	,	,	PUNCT
ejpam-3831	343	18	v	v	NOUN
ejpam-3831	343	19	)	)	PUNCT
ejpam-3831	343	20	.	.	PUNCT
ejpam-3831	344	1	(	(	PUNCT
ejpam-3831	344	2	11	11	NUM
ejpam-3831	344	3	)	)	PUNCT
ejpam-3831	344	4	similarly	similarly	ADV
ejpam-3831	344	5	(	(	PUNCT
ejpam-3831	344	6	1−	1−	NUM
ejpam-3831	344	7	α1(x	α1(x	PROPN
ejpam-3831	344	8	,	,	PUNCT
ejpam-3831	344	9	u	u	NOUN
ejpam-3831	344	10	)	)	PUNCT
ejpam-3831	344	11	2	2	NUM
ejpam-3831	344	12	−	−	NOUN
ejpam-3831	345	1	α2(x	α2(x	PROPN
ejpam-3831	345	2	,	,	PUNCT
ejpam-3831	345	3	u)−	u)−	PROPN
ejpam-3831	345	4	α3(x	α3(x	PROPN
ejpam-3831	345	5	,	,	PUNCT
ejpam-3831	345	6	u)−	u)−	PROPN
ejpam-3831	345	7	12∑	12∑	NUM
ejpam-3831	345	8	i=10	i=10	NOUN
ejpam-3831	345	9	αi(u	αi(u	NOUN
ejpam-3831	345	10	,	,	PUNCT
ejpam-3831	345	11	x	x	NOUN
ejpam-3831	345	12	)	)	PUNCT
ejpam-3831	345	13	)	)	PUNCT
ejpam-3831	346	1	·	·	PUNCT
ejpam-3831	346	2	gb(y	gb(y	ADV
ejpam-3831	346	3	,	,	PUNCT
ejpam-3831	346	4	v	v	NOUN
ejpam-3831	346	5	,	,	PUNCT
ejpam-3831	346	6	v	v	NOUN
ejpam-3831	346	7	)	)	PUNCT
ejpam-3831	346	8	≤	≤	NOUN
ejpam-3831	346	9	α1(x	α1(x	PROPN
ejpam-3831	346	10	,	,	PUNCT
ejpam-3831	346	11	u	u	NOUN
ejpam-3831	346	12	)	)	PUNCT
ejpam-3831	346	13	2	2	NUM
ejpam-3831	346	14	·	·	PUNCT
ejpam-3831	346	15	gb(x	gb(x	NUM
ejpam-3831	346	16	,	,	PUNCT
ejpam-3831	346	17	u	u	NOUN
ejpam-3831	346	18	,	,	PUNCT
ejpam-3831	346	19	u	u	NOUN
ejpam-3831	346	20	)	)	PUNCT
ejpam-3831	346	21	.	.	PUNCT
ejpam-3831	347	1	(	(	PUNCT
ejpam-3831	347	2	12	12	X
ejpam-3831	347	3	)	)	PUNCT
ejpam-3831	347	4	adding	add	VERB
ejpam-3831	347	5	inequalities	inequality	NOUN
ejpam-3831	347	6	(	(	PUNCT
ejpam-3831	347	7	11	11	NUM
ejpam-3831	347	8	)	)	PUNCT
ejpam-3831	347	9	and	and	CCONJ
ejpam-3831	347	10	(	(	PUNCT
ejpam-3831	347	11	12	12	NUM
ejpam-3831	347	12	)	)	PUNCT
ejpam-3831	347	13	,	,	PUNCT
ejpam-3831	347	14	we	we	PRON
ejpam-3831	347	15	get	get	VERB
ejpam-3831	347	16	(	(	PUNCT
ejpam-3831	347	17	1−	1−	NUM
ejpam-3831	347	18	α1(x	α1(x	PROPN
ejpam-3831	347	19	,	,	PUNCT
ejpam-3831	347	20	u	u	NOUN
ejpam-3831	347	21	)	)	PUNCT
ejpam-3831	347	22	2	2	NUM
ejpam-3831	347	23	−	−	NOUN
ejpam-3831	348	1	α2(x	α2(x	PROPN
ejpam-3831	348	2	,	,	PUNCT
ejpam-3831	348	3	u)−	u)−	PROPN
ejpam-3831	348	4	α3(x	α3(x	PROPN
ejpam-3831	348	5	,	,	PUNCT
ejpam-3831	348	6	u)−	u)−	PROPN
ejpam-3831	348	7	12∑	12∑	NUM
ejpam-3831	348	8	i=10	i=10	NOUN
ejpam-3831	348	9	αi(u	αi(u	NOUN
ejpam-3831	348	10	,	,	PUNCT
ejpam-3831	348	11	x	x	NOUN
ejpam-3831	348	12	)	)	PUNCT
ejpam-3831	348	13	)	)	PUNCT
ejpam-3831	348	14	·	·	PUNCT
ejpam-3831	349	1	[	[	PUNCT
ejpam-3831	349	2	gb(x	gb(x	PUNCT
ejpam-3831	349	3	,	,	PUNCT
ejpam-3831	349	4	u	u	NOUN
ejpam-3831	349	5	,	,	PUNCT
ejpam-3831	349	6	u	u	NOUN
ejpam-3831	349	7	)	)	PUNCT
ejpam-3831	349	8	+	+	ADP
ejpam-3831	349	9	gb(y	gb(y	ADJ
ejpam-3831	349	10	,	,	PUNCT
ejpam-3831	349	11	v	v	NOUN
ejpam-3831	349	12	,	,	PUNCT
ejpam-3831	349	13	v	v	NOUN
ejpam-3831	349	14	)	)	PUNCT
ejpam-3831	349	15	]	]	PUNCT
ejpam-3831	349	16	≤	≤	PROPN
ejpam-3831	349	17	α1(x	α1(x	PROPN
ejpam-3831	349	18	,	,	PUNCT
ejpam-3831	349	19	u	u	NOUN
ejpam-3831	349	20	)	)	PUNCT
ejpam-3831	349	21	2	2	NUM
ejpam-3831	349	22	·	·	PUNCT
ejpam-3831	349	23	[	[	PUNCT
ejpam-3831	349	24	gb(x	gb(x	ADJ
ejpam-3831	349	25	,	,	PUNCT
ejpam-3831	349	26	u	u	NOUN
ejpam-3831	349	27	,	,	PUNCT
ejpam-3831	349	28	u	u	NOUN
ejpam-3831	349	29	)	)	PUNCT
ejpam-3831	350	1	+	+	ADP
ejpam-3831	350	2	gb(y	gb(y	ADJ
ejpam-3831	350	3	,	,	PUNCT
ejpam-3831	350	4	v	v	NOUN
ejpam-3831	350	5	,	,	PUNCT
ejpam-3831	350	6	v	v	NOUN
ejpam-3831	350	7	)	)	PUNCT
ejpam-3831	350	8	]	]	PUNCT
ejpam-3831	350	9	.	.	PUNCT
ejpam-3831	351	1	which	which	PRON
ejpam-3831	351	2	implies	imply	VERB
ejpam-3831	351	3	that	that	SCONJ
ejpam-3831	351	4	(	(	PUNCT
ejpam-3831	351	5	1−	1−	NUM
ejpam-3831	351	6	3∑	3∑	NUM
ejpam-3831	351	7	i=1	i=1	PROPN
ejpam-3831	351	8	αi(u	αi(u	NOUN
ejpam-3831	351	9	,	,	PUNCT
ejpam-3831	351	10	x)−	x)−	PROPN
ejpam-3831	351	11	12∑	12∑	NUM
ejpam-3831	351	12	i=10	i=10	PRON
ejpam-3831	351	13	αi(u	αi(u	NOUN
ejpam-3831	351	14	,	,	PUNCT
ejpam-3831	351	15	x	x	NOUN
ejpam-3831	351	16	)	)	PUNCT
ejpam-3831	351	17	)	)	PUNCT
ejpam-3831	351	18	·	·	PUNCT
ejpam-3831	352	1	[	[	PUNCT
ejpam-3831	352	2	gb(x	gb(x	PUNCT
ejpam-3831	352	3	,	,	PUNCT
ejpam-3831	352	4	u	u	NOUN
ejpam-3831	352	5	,	,	PUNCT
ejpam-3831	352	6	u	u	NOUN
ejpam-3831	352	7	)	)	PUNCT
ejpam-3831	352	8	+	+	ADP
ejpam-3831	352	9	gb(y	gb(y	ADJ
ejpam-3831	352	10	,	,	PUNCT
ejpam-3831	352	11	v	v	NOUN
ejpam-3831	352	12	,	,	PUNCT
ejpam-3831	352	13	v	v	NOUN
ejpam-3831	352	14	)	)	PUNCT
ejpam-3831	352	15	]	]	PUNCT
ejpam-3831	352	16	≤	≤	NUM
ejpam-3831	352	17	0	0	NUM
ejpam-3831	352	18	,	,	PUNCT
ejpam-3831	352	19	but	but	CCONJ
ejpam-3831	352	20	1−	1−	NUM
ejpam-3831	352	21	3∑	3∑	NUM
ejpam-3831	352	22	i=1	i=1	PROPN
ejpam-3831	352	23	αi(u	αi(u	NOUN
ejpam-3831	352	24	,	,	PUNCT
ejpam-3831	352	25	x)−	x)−	PROPN
ejpam-3831	352	26	12∑	12∑	NUM
ejpam-3831	352	27	i=10	i=10	PRON
ejpam-3831	352	28	αi(u	αi(u	NOUN
ejpam-3831	352	29	,	,	PUNCT
ejpam-3831	352	30	x	x	X
ejpam-3831	352	31	)	)	PUNCT
ejpam-3831	352	32	>	>	X
ejpam-3831	352	33	0	0	X
ejpam-3831	352	34	.	.	PUNCT
ejpam-3831	353	1	therefore	therefore	ADV
ejpam-3831	353	2	,	,	PUNCT
ejpam-3831	353	3	gb(x	gb(x	ADJ
ejpam-3831	353	4	,	,	PUNCT
ejpam-3831	353	5	u	u	NOUN
ejpam-3831	353	6	,	,	PUNCT
ejpam-3831	353	7	u	u	NOUN
ejpam-3831	353	8	)	)	PUNCT
ejpam-3831	353	9	+	+	ADP
ejpam-3831	353	10	gb(y	gb(y	ADJ
ejpam-3831	353	11	,	,	PUNCT
ejpam-3831	353	12	v	v	NOUN
ejpam-3831	353	13	,	,	PUNCT
ejpam-3831	353	14	v	v	NOUN
ejpam-3831	353	15	)	)	PUNCT
ejpam-3831	353	16	=	=	SYM
ejpam-3831	353	17	0	0	X
ejpam-3831	353	18	.	.	PUNCT
ejpam-3831	353	19	m.m.m	m.m.m	NOUN
ejpam-3831	353	20	.	.	PUNCT
ejpam-3831	354	1	jaradat	jaradat	PROPN
ejpam-3831	354	2	et	et	PROPN
ejpam-3831	354	3	al	al	PROPN
ejpam-3831	354	4	.	.	PUNCT
ejpam-3831	354	5	/	/	SYM
ejpam-3831	354	6	eur	eur	PROPN
ejpam-3831	354	7	.	.	PUNCT
ejpam-3831	355	1	j.	j.	PROPN
ejpam-3831	355	2	pure	pure	PROPN
ejpam-3831	355	3	appl	appl	PROPN
ejpam-3831	355	4	.	.	PROPN
ejpam-3831	355	5	math	math	PROPN
ejpam-3831	355	6	,	,	PUNCT
ejpam-3831	355	7	13	13	NUM
ejpam-3831	355	8	(	(	PUNCT
ejpam-3831	355	9	4	4	NUM
ejpam-3831	355	10	)	)	PUNCT
ejpam-3831	355	11	(	(	PUNCT
ejpam-3831	355	12	2020	2020	NUM
ejpam-3831	355	13	)	)	PUNCT
ejpam-3831	355	14	,	,	PUNCT
ejpam-3831	355	15	995	995	NUM
ejpam-3831	355	16	-	-	SYM
ejpam-3831	355	17	1015	1015	NUM
ejpam-3831	355	18	1008	1008	NUM
ejpam-3831	355	19	thus	thus	ADV
ejpam-3831	355	20	we	we	PRON
ejpam-3831	355	21	have	have	VERB
ejpam-3831	355	22	gb(x	gb(x	ADJ
ejpam-3831	355	23	,	,	PUNCT
ejpam-3831	355	24	u	u	NOUN
ejpam-3831	355	25	,	,	PUNCT
ejpam-3831	355	26	u	u	NOUN
ejpam-3831	355	27	)	)	PUNCT
ejpam-3831	355	28	=	=	PUNCT
ejpam-3831	356	1	gb(y	gb(y	ADJ
ejpam-3831	356	2	,	,	PUNCT
ejpam-3831	356	3	v	v	NOUN
ejpam-3831	356	4	,	,	PUNCT
ejpam-3831	356	5	v	v	NOUN
ejpam-3831	356	6	)	)	PUNCT
ejpam-3831	356	7	=	=	SYM
ejpam-3831	356	8	0	0	NUM
ejpam-3831	356	9	which	which	PRON
ejpam-3831	356	10	implies	imply	VERB
ejpam-3831	356	11	x	x	NOUN
ejpam-3831	356	12	=	=	SYM
ejpam-3831	356	13	u	u	PROPN
ejpam-3831	356	14	and	and	CCONJ
ejpam-3831	356	15	y	y	NOUN
ejpam-3831	356	16	=	=	PROPN
ejpam-3831	357	1	v.	v.	CCONJ
ejpam-3831	357	2	hence	hence	ADV
ejpam-3831	357	3	(	(	PUNCT
ejpam-3831	357	4	x	x	X
ejpam-3831	357	5	,	,	PUNCT
ejpam-3831	357	6	y	y	NOUN
ejpam-3831	357	7	)	)	PUNCT
ejpam-3831	357	8	is	be	AUX
ejpam-3831	357	9	the	the	DET
ejpam-3831	357	10	unique	unique	ADJ
ejpam-3831	357	11	common	common	ADJ
ejpam-3831	357	12	coupled	couple	VERB
ejpam-3831	357	13	fixed	fix	VERB
ejpam-3831	357	14	point	point	NOUN
ejpam-3831	357	15	of	of	ADP
ejpam-3831	357	16	f	f	PROPN
ejpam-3831	357	17	,	,	PUNCT
ejpam-3831	357	18	h	h	NOUN
ejpam-3831	357	19	and	and	CCONJ
ejpam-3831	357	20	t.	t.	PROPN
ejpam-3831	357	21	now	now	ADV
ejpam-3831	357	22	,	,	PUNCT
ejpam-3831	357	23	we	we	PRON
ejpam-3831	357	24	present	present	VERB
ejpam-3831	357	25	some	some	DET
ejpam-3831	357	26	corollaries	corollary	NOUN
ejpam-3831	357	27	.	.	PUNCT
ejpam-3831	358	1	corollary	corollary	ADJ
ejpam-3831	358	2	1	1	NUM
ejpam-3831	358	3	.	.	PUNCT
ejpam-3831	359	1	let	let	AUX
ejpam-3831	359	2	(	(	PUNCT
ejpam-3831	359	3	x	x	NOUN
ejpam-3831	359	4	,	,	PUNCT
ejpam-3831	359	5	gb	gb	PRON
ejpam-3831	359	6	)	)	PUNCT
ejpam-3831	359	7	be	be	AUX
ejpam-3831	359	8	a	a	DET
ejpam-3831	359	9	complete	complete	ADJ
ejpam-3831	359	10	gb	gb	ADV
ejpam-3831	359	11	-	-	PUNCT
ejpam-3831	359	12	metric	metric	ADJ
ejpam-3831	359	13	space	space	NOUN
ejpam-3831	359	14	and	and	CCONJ
ejpam-3831	359	15	let	let	VERB
ejpam-3831	359	16	h	h	NOUN
ejpam-3831	359	17	,	,	PUNCT
ejpam-3831	359	18	t	t	NOUN
ejpam-3831	359	19	:	:	PUNCT
ejpam-3831	359	20	x	x	PUNCT
ejpam-3831	360	1	×	×	NOUN
ejpam-3831	360	2	x	x	INTJ
ejpam-3831	360	3	→	→	PUNCT
ejpam-3831	360	4	x	x	PUNCT
ejpam-3831	360	5	be	be	AUX
ejpam-3831	360	6	mappings	mapping	NOUN
ejpam-3831	360	7	satisfying	satisfy	VERB
ejpam-3831	360	8	the	the	DET
ejpam-3831	360	9	following	follow	VERB
ejpam-3831	360	10	condition	condition	NOUN
ejpam-3831	360	11	,	,	PUNCT
ejpam-3831	360	12	(	(	PUNCT
ejpam-3831	360	13	i	i	NOUN
ejpam-3831	360	14	)	)	PUNCT
ejpam-3831	360	15	αi(h(x1	αi(h(x1	PROPN
ejpam-3831	360	16	,	,	PUNCT
ejpam-3831	360	17	y1	y1	NOUN
ejpam-3831	360	18	)	)	PUNCT
ejpam-3831	360	19	,	,	PUNCT
ejpam-3831	360	20	y	y	NOUN
ejpam-3831	360	21	)	)	PUNCT
ejpam-3831	360	22	≤	≤	NOUN
ejpam-3831	360	23	αi(x1	αi(x1	NOUN
ejpam-3831	360	24	,	,	PUNCT
ejpam-3831	360	25	y	y	NOUN
ejpam-3831	360	26	)	)	PUNCT
ejpam-3831	360	27	,	,	PUNCT
ejpam-3831	360	28	αi(x	αi(x	NUM
ejpam-3831	360	29	,	,	PUNCT
ejpam-3831	360	30	h(x1	h(x1	NOUN
ejpam-3831	360	31	,	,	PUNCT
ejpam-3831	360	32	y1	y1	NOUN
ejpam-3831	360	33	)	)	PUNCT
ejpam-3831	360	34	)	)	PUNCT
ejpam-3831	360	35	≤	≤	NOUN
ejpam-3831	360	36	αi(x	αi(x	NUM
ejpam-3831	360	37	,	,	PUNCT
ejpam-3831	360	38	x1	x1	NUM
ejpam-3831	360	39	)	)	PUNCT
ejpam-3831	360	40	)	)	PUNCT
ejpam-3831	360	41	,	,	PUNCT
ejpam-3831	360	42	αi(t	αi(t	X
ejpam-3831	360	43	(	(	PUNCT
ejpam-3831	360	44	x1	x1	PROPN
ejpam-3831	360	45	,	,	PUNCT
ejpam-3831	360	46	y1	y1	PROPN
ejpam-3831	360	47	)	)	PUNCT
ejpam-3831	360	48	,	,	PUNCT
ejpam-3831	360	49	y	y	NOUN
ejpam-3831	360	50	)	)	PUNCT
ejpam-3831	360	51	≤	≤	NOUN
ejpam-3831	360	52	αi(x1	αi(x1	NOUN
ejpam-3831	360	53	,	,	PUNCT
ejpam-3831	360	54	y	y	NOUN
ejpam-3831	360	55	)	)	PUNCT
ejpam-3831	360	56	and	and	CCONJ
ejpam-3831	360	57	αi(x	αi(x	NUM
ejpam-3831	360	58	,	,	PUNCT
ejpam-3831	360	59	t	t	PROPN
ejpam-3831	360	60	(	(	PUNCT
ejpam-3831	360	61	x1	x1	PROPN
ejpam-3831	360	62	,	,	PUNCT
ejpam-3831	360	63	y1	y1	NOUN
ejpam-3831	360	64	)	)	PUNCT
ejpam-3831	360	65	)	)	PUNCT
ejpam-3831	360	66	≤	≤	NOUN
ejpam-3831	360	67	αi(x	αi(x	NUM
ejpam-3831	360	68	,	,	PUNCT
ejpam-3831	360	69	x1	x1	NUM
ejpam-3831	360	70	)	)	PUNCT
ejpam-3831	360	71	.	.	PUNCT
ejpam-3831	361	1	(	(	PUNCT
ejpam-3831	361	2	ii	ii	NOUN
ejpam-3831	361	3	)	)	PUNCT
ejpam-3831	361	4	gb	gb	PROPN
ejpam-3831	361	5	(	(	PUNCT
ejpam-3831	361	6	h(a	h(a	PROPN
ejpam-3831	361	7	,	,	PUNCT
ejpam-3831	361	8	b	b	NOUN
ejpam-3831	361	9	)	)	PUNCT
ejpam-3831	361	10	,	,	PUNCT
ejpam-3831	361	11	h(u	h(u	PROPN
ejpam-3831	361	12	,	,	PUNCT
ejpam-3831	361	13	v	v	NOUN
ejpam-3831	361	14	)	)	PUNCT
ejpam-3831	361	15	,	,	PUNCT
ejpam-3831	361	16	t	t	PROPN
ejpam-3831	361	17	(	(	PUNCT
ejpam-3831	361	18	x	x	PROPN
ejpam-3831	361	19	,	,	PUNCT
ejpam-3831	361	20	y	y	PROPN
ejpam-3831	361	21	)	)	PUNCT
ejpam-3831	361	22	)	)	PUNCT
ejpam-3831	361	23	≤	≤	PUNCT
ejpam-3831	361	24	α1(a	α1(a	NUM
ejpam-3831	361	25	,	,	PUNCT
ejpam-3831	361	26	u	u	NOUN
ejpam-3831	361	27	)	)	PUNCT
ejpam-3831	361	28	·	·	PUNCT
ejpam-3831	362	1	gb(a	gb(a	X
ejpam-3831	362	2	,	,	PUNCT
ejpam-3831	362	3	u	u	NOUN
ejpam-3831	362	4	,	,	PUNCT
ejpam-3831	362	5	x	x	X
ejpam-3831	362	6	)	)	PUNCT
ejpam-3831	362	7	+	+	ADJ
ejpam-3831	362	8	gb(b	gb(b	NOUN
ejpam-3831	362	9	,	,	PUNCT
ejpam-3831	362	10	v	v	NOUN
ejpam-3831	362	11	,	,	PUNCT
ejpam-3831	362	12	y	y	NOUN
ejpam-3831	362	13	)	)	PUNCT
ejpam-3831	362	14	2	2	NUM
ejpam-3831	363	1	+	+	PROPN
ejpam-3831	363	2	α2(a	α2(a	PROPN
ejpam-3831	363	3	,	,	PUNCT
ejpam-3831	363	4	u	u	NOUN
ejpam-3831	363	5	)	)	PUNCT
ejpam-3831	363	6	gb	gb	PROPN
ejpam-3831	363	7	(	(	PUNCT
ejpam-3831	363	8	h(a	h(a	PROPN
ejpam-3831	363	9	,	,	PUNCT
ejpam-3831	363	10	b	b	NOUN
ejpam-3831	363	11	)	)	PUNCT
ejpam-3831	363	12	,	,	PUNCT
ejpam-3831	363	13	h(u	h(u	PROPN
ejpam-3831	363	14	,	,	PUNCT
ejpam-3831	363	15	v	v	NOUN
ejpam-3831	363	16	)	)	PUNCT
ejpam-3831	363	17	,	,	PUNCT
ejpam-3831	363	18	t	t	PROPN
ejpam-3831	363	19	(	(	PUNCT
ejpam-3831	363	20	x	x	PROPN
ejpam-3831	363	21	,	,	PUNCT
ejpam-3831	363	22	y	y	NOUN
ejpam-3831	363	23	)	)	PUNCT
ejpam-3831	363	24	)	)	PUNCT
ejpam-3831	363	25	gb(a	gb(a	X
ejpam-3831	363	26	,	,	PUNCT
ejpam-3831	363	27	u	u	NOUN
ejpam-3831	363	28	,	,	PUNCT
ejpam-3831	363	29	x	x	NOUN
ejpam-3831	363	30	)	)	PUNCT
ejpam-3831	363	31	ωs(a	ωs(a	NUM
ejpam-3831	363	32	,	,	PUNCT
ejpam-3831	363	33	u	u	NOUN
ejpam-3831	363	34	,	,	PUNCT
ejpam-3831	363	35	x	x	X
ejpam-3831	363	36	,	,	PUNCT
ejpam-3831	363	37	b	b	PROPN
ejpam-3831	363	38	,	,	PUNCT
ejpam-3831	363	39	v	v	NOUN
ejpam-3831	363	40	,	,	PUNCT
ejpam-3831	363	41	y	y	NOUN
ejpam-3831	363	42	)	)	PUNCT
ejpam-3831	364	1	+	+	NOUN
ejpam-3831	364	2	α3(a	α3(a	NUM
ejpam-3831	364	3	,	,	PUNCT
ejpam-3831	364	4	u	u	NOUN
ejpam-3831	364	5	)	)	PUNCT
ejpam-3831	364	6	gb	gb	PROPN
ejpam-3831	364	7	(	(	PUNCT
ejpam-3831	364	8	h(a	h(a	PROPN
ejpam-3831	364	9	,	,	PUNCT
ejpam-3831	364	10	b	b	NOUN
ejpam-3831	364	11	)	)	PUNCT
ejpam-3831	364	12	,	,	PUNCT
ejpam-3831	364	13	h(u	h(u	PROPN
ejpam-3831	364	14	,	,	PUNCT
ejpam-3831	364	15	v	v	NOUN
ejpam-3831	364	16	)	)	PUNCT
ejpam-3831	364	17	,	,	PUNCT
ejpam-3831	364	18	t	t	PROPN
ejpam-3831	364	19	(	(	PUNCT
ejpam-3831	364	20	x	x	PROPN
ejpam-3831	364	21	,	,	PUNCT
ejpam-3831	364	22	y	y	NOUN
ejpam-3831	364	23	)	)	PUNCT
ejpam-3831	364	24	)	)	PUNCT
ejpam-3831	365	1	gb(b	gb(b	X
ejpam-3831	365	2	,	,	PUNCT
ejpam-3831	365	3	v	v	NOUN
ejpam-3831	365	4	,	,	PUNCT
ejpam-3831	365	5	y	y	NOUN
ejpam-3831	365	6	)	)	PUNCT
ejpam-3831	365	7	ωs(a	ωs(a	NUM
ejpam-3831	365	8	,	,	PUNCT
ejpam-3831	365	9	u	u	NOUN
ejpam-3831	365	10	,	,	PUNCT
ejpam-3831	365	11	x	x	X
ejpam-3831	365	12	,	,	PUNCT
ejpam-3831	365	13	b	b	PROPN
ejpam-3831	365	14	,	,	PUNCT
ejpam-3831	365	15	v	v	NOUN
ejpam-3831	365	16	,	,	PUNCT
ejpam-3831	365	17	y	y	NOUN
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ejpam-3831	366	3	,	,	PUNCT
ejpam-3831	366	4	u	u	NOUN
ejpam-3831	366	5	)	)	PUNCT
ejpam-3831	366	6	gb	gb	ADP
ejpam-3831	366	7	(	(	PUNCT
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ejpam-3831	366	9	,	,	PUNCT
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ejpam-3831	366	11	,	,	PUNCT
ejpam-3831	366	12	h(a	h(a	PROPN
ejpam-3831	366	13	,	,	PUNCT
ejpam-3831	366	14	b	b	NOUN
ejpam-3831	366	15	)	)	PUNCT
ejpam-3831	366	16	)	)	PUNCT
ejpam-3831	366	17	gb(a	gb(a	X
ejpam-3831	366	18	,	,	PUNCT
ejpam-3831	366	19	u	u	NOUN
ejpam-3831	366	20	,	,	PUNCT
ejpam-3831	366	21	x	x	NOUN
ejpam-3831	366	22	)	)	PUNCT
ejpam-3831	366	23	ωs(a	ωs(a	NUM
ejpam-3831	366	24	,	,	PUNCT
ejpam-3831	366	25	u	u	NOUN
ejpam-3831	366	26	,	,	PUNCT
ejpam-3831	366	27	x	x	X
ejpam-3831	366	28	,	,	PUNCT
ejpam-3831	366	29	b	b	PROPN
ejpam-3831	366	30	,	,	PUNCT
ejpam-3831	366	31	v	v	NOUN
ejpam-3831	366	32	,	,	PUNCT
ejpam-3831	366	33	y	y	NOUN
ejpam-3831	366	34	)	)	PUNCT
ejpam-3831	366	35	+	+	PUNCT
ejpam-3831	366	36	α5(u	α5(u	NUM
ejpam-3831	366	37	,	,	PUNCT
ejpam-3831	366	38	x	x	X
ejpam-3831	366	39	)	)	PUNCT
ejpam-3831	366	40	gb	gb	ADP
ejpam-3831	366	41	(	(	PUNCT
ejpam-3831	366	42	a	a	PRON
ejpam-3831	366	43	,	,	PUNCT
ejpam-3831	366	44	a	a	DET
ejpam-3831	366	45	,	,	PUNCT
ejpam-3831	366	46	h(a	h(a	PROPN
ejpam-3831	366	47	,	,	PUNCT
ejpam-3831	366	48	b	b	NOUN
ejpam-3831	366	49	)	)	PUNCT
ejpam-3831	366	50	)	)	PUNCT
ejpam-3831	367	1	gb(b	gb(b	X
ejpam-3831	367	2	,	,	PUNCT
ejpam-3831	367	3	v	v	NOUN
ejpam-3831	367	4	,	,	PUNCT
ejpam-3831	367	5	y	y	NOUN
ejpam-3831	367	6	)	)	PUNCT
ejpam-3831	367	7	ωs(a	ωs(a	NUM
ejpam-3831	367	8	,	,	PUNCT
ejpam-3831	367	9	u	u	NOUN
ejpam-3831	367	10	,	,	PUNCT
ejpam-3831	367	11	x	x	X
ejpam-3831	367	12	,	,	PUNCT
ejpam-3831	367	13	b	b	PROPN
ejpam-3831	367	14	,	,	PUNCT
ejpam-3831	367	15	v	v	NOUN
ejpam-3831	367	16	,	,	PUNCT
ejpam-3831	367	17	y	y	NOUN
ejpam-3831	367	18	)	)	PUNCT
ejpam-3831	368	1	+	+	NOUN
ejpam-3831	368	2	α6(u	α6(u	PROPN
ejpam-3831	368	3	,	,	PUNCT
ejpam-3831	368	4	x	x	NOUN
ejpam-3831	368	5	)	)	PUNCT
ejpam-3831	368	6	gb	gb	ADP
ejpam-3831	368	7	(	(	PUNCT
ejpam-3831	368	8	u	u	NOUN
ejpam-3831	368	9	,	,	PUNCT
ejpam-3831	368	10	u	u	PROPN
ejpam-3831	368	11	,	,	PUNCT
ejpam-3831	368	12	h(u	h(u	PROPN
ejpam-3831	368	13	,	,	PUNCT
ejpam-3831	368	14	v	v	NOUN
ejpam-3831	368	15	)	)	PUNCT
ejpam-3831	368	16	)	)	PUNCT
ejpam-3831	368	17	gb(a	gb(a	X
ejpam-3831	368	18	,	,	PUNCT
ejpam-3831	368	19	u	u	NOUN
ejpam-3831	368	20	,	,	PUNCT
ejpam-3831	368	21	x	x	NOUN
ejpam-3831	368	22	)	)	PUNCT
ejpam-3831	368	23	ωs(a	ωs(a	NUM
ejpam-3831	368	24	,	,	PUNCT
ejpam-3831	368	25	u	u	NOUN
ejpam-3831	368	26	,	,	PUNCT
ejpam-3831	368	27	x	x	X
ejpam-3831	368	28	,	,	PUNCT
ejpam-3831	368	29	b	b	PROPN
ejpam-3831	368	30	,	,	PUNCT
ejpam-3831	368	31	v	v	NOUN
ejpam-3831	368	32	,	,	PUNCT
ejpam-3831	368	33	y	y	PROPN
ejpam-3831	368	34	)	)	PUNCT
ejpam-3831	368	35	+	+	CCONJ
ejpam-3831	368	36	α7(u	α7(u	ADJ
ejpam-3831	368	37	,	,	PUNCT
ejpam-3831	368	38	x	x	X
ejpam-3831	368	39	)	)	PUNCT
ejpam-3831	368	40	gb	gb	ADP
ejpam-3831	368	41	(	(	PUNCT
ejpam-3831	368	42	u	u	NOUN
ejpam-3831	368	43	,	,	PUNCT
ejpam-3831	368	44	u	u	PROPN
ejpam-3831	368	45	,	,	PUNCT
ejpam-3831	368	46	h(u	h(u	PROPN
ejpam-3831	368	47	,	,	PUNCT
ejpam-3831	368	48	v	v	NOUN
ejpam-3831	368	49	)	)	PUNCT
ejpam-3831	368	50	)	)	PUNCT
ejpam-3831	369	1	gb(b	gb(b	X
ejpam-3831	369	2	,	,	PUNCT
ejpam-3831	369	3	v	v	NOUN
ejpam-3831	369	4	,	,	PUNCT
ejpam-3831	369	5	y	y	NOUN
ejpam-3831	369	6	)	)	PUNCT
ejpam-3831	369	7	ωs(a	ωs(a	NUM
ejpam-3831	369	8	,	,	PUNCT
ejpam-3831	369	9	u	u	NOUN
ejpam-3831	369	10	,	,	PUNCT
ejpam-3831	369	11	x	x	X
ejpam-3831	369	12	,	,	PUNCT
ejpam-3831	369	13	b	b	PROPN
ejpam-3831	369	14	,	,	PUNCT
ejpam-3831	369	15	v	v	NOUN
ejpam-3831	369	16	,	,	PUNCT
ejpam-3831	369	17	y	y	NOUN
ejpam-3831	369	18	)	)	PUNCT
ejpam-3831	370	1	+	+	NOUN
ejpam-3831	370	2	α8(u	α8(u	NUM
ejpam-3831	370	3	,	,	PUNCT
ejpam-3831	370	4	x	x	NOUN
ejpam-3831	370	5	)	)	PUNCT
ejpam-3831	370	6	gb	gb	ADP
ejpam-3831	370	7	(	(	PUNCT
ejpam-3831	370	8	x	x	NOUN
ejpam-3831	370	9	,	,	PUNCT
ejpam-3831	370	10	x	x	PROPN
ejpam-3831	370	11	,	,	PUNCT
ejpam-3831	370	12	t	t	PROPN
ejpam-3831	370	13	(	(	PUNCT
ejpam-3831	370	14	x	x	PROPN
ejpam-3831	370	15	,	,	PUNCT
ejpam-3831	370	16	y	y	NOUN
ejpam-3831	370	17	)	)	PUNCT
ejpam-3831	370	18	)	)	PUNCT
ejpam-3831	370	19	gb(a	gb(a	X
ejpam-3831	370	20	,	,	PUNCT
ejpam-3831	370	21	u	u	NOUN
ejpam-3831	370	22	,	,	PUNCT
ejpam-3831	370	23	x	x	NOUN
ejpam-3831	370	24	)	)	PUNCT
ejpam-3831	370	25	ωs(a	ωs(a	NUM
ejpam-3831	370	26	,	,	PUNCT
ejpam-3831	370	27	u	u	NOUN
ejpam-3831	370	28	,	,	PUNCT
ejpam-3831	370	29	x	x	X
ejpam-3831	370	30	,	,	PUNCT
ejpam-3831	370	31	b	b	PROPN
ejpam-3831	370	32	,	,	PUNCT
ejpam-3831	370	33	v	v	NOUN
ejpam-3831	370	34	,	,	PUNCT
ejpam-3831	370	35	y	y	PROPN
ejpam-3831	370	36	)	)	PUNCT
ejpam-3831	370	37	+	+	CCONJ
ejpam-3831	371	1	α9(x	α9(x	NUM
ejpam-3831	371	2	,	,	PUNCT
ejpam-3831	371	3	a	a	PRON
ejpam-3831	371	4	)	)	PUNCT
ejpam-3831	371	5	gb	gb	PROPN
ejpam-3831	371	6	(	(	PUNCT
ejpam-3831	371	7	x	x	NOUN
ejpam-3831	371	8	,	,	PUNCT
ejpam-3831	371	9	x	x	PROPN
ejpam-3831	371	10	,	,	PUNCT
ejpam-3831	371	11	t	t	PROPN
ejpam-3831	371	12	(	(	PUNCT
ejpam-3831	371	13	x	x	PROPN
ejpam-3831	371	14	,	,	PUNCT
ejpam-3831	371	15	y	y	NOUN
ejpam-3831	371	16	)	)	PUNCT
ejpam-3831	371	17	)	)	PUNCT
ejpam-3831	372	1	gb(b	gb(b	X
ejpam-3831	372	2	,	,	PUNCT
ejpam-3831	372	3	v	v	NOUN
ejpam-3831	372	4	,	,	PUNCT
ejpam-3831	372	5	y	y	NOUN
ejpam-3831	372	6	)	)	PUNCT
ejpam-3831	372	7	ωs(a	ωs(a	NUM
ejpam-3831	372	8	,	,	PUNCT
ejpam-3831	372	9	u	u	NOUN
ejpam-3831	372	10	,	,	PUNCT
ejpam-3831	372	11	x	x	X
ejpam-3831	372	12	,	,	PUNCT
ejpam-3831	372	13	b	b	PROPN
ejpam-3831	372	14	,	,	PUNCT
ejpam-3831	372	15	v	v	NOUN
ejpam-3831	372	16	,	,	PUNCT
ejpam-3831	372	17	y	y	NOUN
ejpam-3831	372	18	)	)	PUNCT
ejpam-3831	373	1	+	+	NOUN
ejpam-3831	373	2	α10(x	α10(x	NOUN
ejpam-3831	373	3	,	,	PUNCT
ejpam-3831	373	4	a	a	PRON
ejpam-3831	373	5	)	)	PUNCT
ejpam-3831	373	6	gb	gb	PROPN
ejpam-3831	373	7	(	(	PUNCT
ejpam-3831	373	8	a	a	PRON
ejpam-3831	373	9	,	,	PUNCT
ejpam-3831	373	10	u	u	NOUN
ejpam-3831	373	11	,	,	PUNCT
ejpam-3831	373	12	t	t	PROPN
ejpam-3831	373	13	(	(	PUNCT
ejpam-3831	373	14	x	x	PROPN
ejpam-3831	373	15	,	,	PUNCT
ejpam-3831	373	16	y	y	NOUN
ejpam-3831	373	17	)	)	PUNCT
ejpam-3831	373	18	)	)	PUNCT
ejpam-3831	373	19	gb(a	gb(a	X
ejpam-3831	373	20	,	,	PUNCT
ejpam-3831	373	21	u	u	NOUN
ejpam-3831	373	22	,	,	PUNCT
ejpam-3831	373	23	x	x	NOUN
ejpam-3831	373	24	)	)	PUNCT
ejpam-3831	373	25	ωs(a	ωs(a	NUM
ejpam-3831	373	26	,	,	PUNCT
ejpam-3831	373	27	u	u	NOUN
ejpam-3831	373	28	,	,	PUNCT
ejpam-3831	373	29	x	x	X
ejpam-3831	373	30	,	,	PUNCT
ejpam-3831	373	31	b	b	PROPN
ejpam-3831	373	32	,	,	PUNCT
ejpam-3831	373	33	v	v	NOUN
ejpam-3831	373	34	,	,	PUNCT
ejpam-3831	373	35	y	y	NOUN
ejpam-3831	373	36	)	)	PUNCT
ejpam-3831	373	37	+	+	CCONJ
ejpam-3831	373	38	α11(x	α11(x	NOUN
ejpam-3831	373	39	,	,	PUNCT
ejpam-3831	373	40	a	a	PRON
ejpam-3831	373	41	)	)	PUNCT
ejpam-3831	373	42	gb	gb	PROPN
ejpam-3831	373	43	(	(	PUNCT
ejpam-3831	373	44	u	u	NOUN
ejpam-3831	373	45	,	,	PUNCT
ejpam-3831	373	46	x	x	X
ejpam-3831	373	47	,	,	PUNCT
ejpam-3831	373	48	h(a	h(a	PROPN
ejpam-3831	373	49	,	,	PUNCT
ejpam-3831	373	50	b	b	NOUN
ejpam-3831	373	51	)	)	PUNCT
ejpam-3831	373	52	)	)	PUNCT
ejpam-3831	373	53	gb(b	gb(b	X
ejpam-3831	373	54	,	,	PUNCT
ejpam-3831	373	55	v	v	NOUN
ejpam-3831	373	56	,	,	PUNCT
ejpam-3831	373	57	y	y	NOUN
ejpam-3831	373	58	)	)	PUNCT
ejpam-3831	373	59	ωs(a	ωs(a	NUM
ejpam-3831	373	60	,	,	PUNCT
ejpam-3831	373	61	u	u	NOUN
ejpam-3831	373	62	,	,	PUNCT
ejpam-3831	373	63	x	x	X
ejpam-3831	373	64	,	,	PUNCT
ejpam-3831	373	65	b	b	PROPN
ejpam-3831	373	66	,	,	PUNCT
ejpam-3831	373	67	v	v	NOUN
ejpam-3831	373	68	,	,	PUNCT
ejpam-3831	373	69	y	y	NOUN
ejpam-3831	373	70	)	)	PUNCT
ejpam-3831	374	1	+	+	NOUN
ejpam-3831	374	2	α12(x	α12(x	NOUN
ejpam-3831	374	3	,	,	PUNCT
ejpam-3831	374	4	a	a	PRON
ejpam-3831	374	5	)	)	PUNCT
ejpam-3831	374	6	gb	gb	PROPN
ejpam-3831	374	7	(	(	PUNCT
ejpam-3831	374	8	x	x	NOUN
ejpam-3831	374	9	,	,	PUNCT
ejpam-3831	374	10	a	a	PRON
ejpam-3831	374	11	,	,	PUNCT
ejpam-3831	374	12	h(u	h(u	PROPN
ejpam-3831	374	13	,	,	PUNCT
ejpam-3831	374	14	v	v	NOUN
ejpam-3831	374	15	)	)	PUNCT
ejpam-3831	374	16	)	)	PUNCT
ejpam-3831	374	17	gb(a	gb(a	X
ejpam-3831	374	18	,	,	PUNCT
ejpam-3831	374	19	u	u	NOUN
ejpam-3831	374	20	,	,	PUNCT
ejpam-3831	374	21	x	x	NOUN
ejpam-3831	374	22	)	)	PUNCT
ejpam-3831	374	23	ωs(a	ωs(a	NUM
ejpam-3831	374	24	,	,	PUNCT
ejpam-3831	374	25	u	u	NOUN
ejpam-3831	374	26	,	,	PUNCT
ejpam-3831	374	27	x	x	X
ejpam-3831	374	28	,	,	PUNCT
ejpam-3831	374	29	b	b	PROPN
ejpam-3831	374	30	,	,	PUNCT
ejpam-3831	374	31	v	v	NOUN
ejpam-3831	374	32	,	,	PUNCT
ejpam-3831	374	33	y	y	PROPN
ejpam-3831	374	34	)	)	PUNCT
ejpam-3831	374	35	,	,	PUNCT
ejpam-3831	374	36	where	where	SCONJ
ejpam-3831	374	37	0	0	NUM
ejpam-3831	374	38	≤	≤	NUM
ejpam-3831	374	39	s[α1(x	s[α1(x	NOUN
ejpam-3831	374	40	,	,	PUNCT
ejpam-3831	374	41	y	y	NOUN
ejpam-3831	374	42	)	)	PUNCT
ejpam-3831	374	43	+	+	CCONJ
ejpam-3831	374	44	α4(x	α4(x	NUM
ejpam-3831	374	45	,	,	PUNCT
ejpam-3831	374	46	y	y	PROPN
ejpam-3831	374	47	)	)	PUNCT
ejpam-3831	374	48	+	+	CCONJ
ejpam-3831	374	49	α5(x	α5(x	PROPN
ejpam-3831	374	50	,	,	PUNCT
ejpam-3831	374	51	y	y	NOUN
ejpam-3831	374	52	)	)	PUNCT
ejpam-3831	374	53	+	+	SYM
ejpam-3831	374	54	α10(x	α10(x	NOUN
ejpam-3831	374	55	,	,	PUNCT
ejpam-3831	374	56	y	y	NOUN
ejpam-3831	374	57	)	)	PUNCT
ejpam-3831	374	58	+	+	SYM
ejpam-3831	374	59	α12(x	α12(x	PROPN
ejpam-3831	374	60	,	,	PUNCT
ejpam-3831	374	61	y	y	PROPN
ejpam-3831	374	62	)	)	PUNCT
ejpam-3831	374	63	]	]	PUNCT
ejpam-3831	375	1	+	+	CCONJ
ejpam-3831	376	1	[	[	X
ejpam-3831	376	2	α2(x	α2(x	PROPN
ejpam-3831	376	3	,	,	PUNCT
ejpam-3831	376	4	y	y	PROPN
ejpam-3831	376	5	)	)	PUNCT
ejpam-3831	376	6	+	+	CCONJ
ejpam-3831	376	7	α3(x	α3(x	PROPN
ejpam-3831	376	8	,	,	PUNCT
ejpam-3831	376	9	y	y	PROPN
ejpam-3831	376	10	)	)	PUNCT
ejpam-3831	376	11	+	+	CCONJ
ejpam-3831	376	12	11∑	11∑	NUM
ejpam-3831	376	13	i=6	i=6	NOUN
ejpam-3831	376	14	αi(x	αi(x	NUM
ejpam-3831	376	15	,	,	PUNCT
ejpam-3831	376	16	y	y	PROPN
ejpam-3831	376	17	)	)	PUNCT
ejpam-3831	376	18	]	]	PUNCT
ejpam-3831	376	19	<	<	X
ejpam-3831	376	20	1	1	X
ejpam-3831	376	21	.	.	PUNCT
ejpam-3831	376	22	then	then	ADV
ejpam-3831	376	23	h	h	NOUN
ejpam-3831	376	24	,	,	PUNCT
ejpam-3831	376	25	t	t	PROPN
ejpam-3831	376	26	have	have	VERB
ejpam-3831	376	27	a	a	DET
ejpam-3831	376	28	unique	unique	ADJ
ejpam-3831	376	29	common	common	ADJ
ejpam-3831	376	30	coupled	couple	VERB
ejpam-3831	376	31	fixed	fix	VERB
ejpam-3831	376	32	point	point	NOUN
ejpam-3831	376	33	in	in	ADP
ejpam-3831	376	34	x.	x.	NOUN
ejpam-3831	376	35	proof	proof	NOUN
ejpam-3831	376	36	.	.	PUNCT
ejpam-3831	377	1	taking	take	VERB
ejpam-3831	377	2	f	f	NOUN
ejpam-3831	377	3	=	=	NOUN
ejpam-3831	377	4	h	h	PROPN
ejpam-3831	377	5	in	in	ADP
ejpam-3831	377	6	theorem	theorem	NOUN
ejpam-3831	377	7	1	1	NUM
ejpam-3831	377	8	we	we	PRON
ejpam-3831	377	9	get	get	VERB
ejpam-3831	377	10	the	the	DET
ejpam-3831	377	11	required	required	ADJ
ejpam-3831	377	12	proof	proof	NOUN
ejpam-3831	377	13	.	.	PUNCT
ejpam-3831	378	1	corollary	corollary	ADJ
ejpam-3831	378	2	2	2	NUM
ejpam-3831	378	3	.	.	PUNCT
ejpam-3831	379	1	let	let	AUX
ejpam-3831	379	2	(	(	PUNCT
ejpam-3831	379	3	x	x	NOUN
ejpam-3831	379	4	,	,	PUNCT
ejpam-3831	379	5	gb	gb	PRON
ejpam-3831	379	6	)	)	PUNCT
ejpam-3831	379	7	be	be	AUX
ejpam-3831	379	8	a	a	DET
ejpam-3831	379	9	complete	complete	ADJ
ejpam-3831	379	10	gb	gb	ADV
ejpam-3831	379	11	-	-	PUNCT
ejpam-3831	379	12	metric	metric	ADJ
ejpam-3831	379	13	space	space	NOUN
ejpam-3831	379	14	and	and	CCONJ
ejpam-3831	379	15	let	let	VERB
ejpam-3831	379	16	t	t	NOUN
ejpam-3831	379	17	:	:	PUNCT
ejpam-3831	379	18	x2	x2	PROPN
ejpam-3831	379	19	→	→	PUNCT
ejpam-3831	379	20	x	x	X
ejpam-3831	379	21	be	be	AUX
ejpam-3831	379	22	a	a	DET
ejpam-3831	379	23	map	map	NOUN
ejpam-3831	379	24	satisfying	satisfy	VERB
ejpam-3831	379	25	the	the	DET
ejpam-3831	379	26	following	follow	VERB
ejpam-3831	379	27	condition	condition	NOUN
ejpam-3831	379	28	,	,	PUNCT
ejpam-3831	379	29	(	(	PUNCT
ejpam-3831	379	30	i	i	NOUN
ejpam-3831	379	31	)	)	PUNCT
ejpam-3831	379	32	αi(t	αi(t	X
ejpam-3831	379	33	(	(	PUNCT
ejpam-3831	379	34	x1	x1	PROPN
ejpam-3831	379	35	,	,	PUNCT
ejpam-3831	379	36	y1	y1	PROPN
ejpam-3831	379	37	)	)	PUNCT
ejpam-3831	379	38	,	,	PUNCT
ejpam-3831	379	39	y	y	NOUN
ejpam-3831	379	40	)	)	PUNCT
ejpam-3831	379	41	≤	≤	NOUN
ejpam-3831	379	42	αi(x1	αi(x1	NOUN
ejpam-3831	379	43	,	,	PUNCT
ejpam-3831	379	44	y	y	NOUN
ejpam-3831	379	45	)	)	PUNCT
ejpam-3831	379	46	and	and	CCONJ
ejpam-3831	379	47	αi(x	αi(x	NUM
ejpam-3831	379	48	,	,	PUNCT
ejpam-3831	379	49	t	t	PROPN
ejpam-3831	379	50	(	(	PUNCT
ejpam-3831	379	51	x1	x1	PROPN
ejpam-3831	379	52	,	,	PUNCT
ejpam-3831	379	53	y1	y1	NOUN
ejpam-3831	379	54	)	)	PUNCT
ejpam-3831	379	55	)	)	PUNCT
ejpam-3831	379	56	≤	≤	NOUN
ejpam-3831	379	57	αi(x	αi(x	NUM
ejpam-3831	379	58	,	,	PUNCT
ejpam-3831	379	59	x1	x1	NUM
ejpam-3831	379	60	)	)	PUNCT
ejpam-3831	379	61	)	)	PUNCT
ejpam-3831	380	1	(	(	PUNCT
ejpam-3831	380	2	ii	ii	NOUN
ejpam-3831	380	3	)	)	PUNCT
ejpam-3831	380	4	gb	gb	PROPN
ejpam-3831	380	5	(	(	PUNCT
ejpam-3831	380	6	t	t	PROPN
ejpam-3831	380	7	(	(	PUNCT
ejpam-3831	380	8	a	a	DET
ejpam-3831	380	9	,	,	PUNCT
ejpam-3831	380	10	b	b	NOUN
ejpam-3831	380	11	)	)	PUNCT
ejpam-3831	380	12	,	,	PUNCT
ejpam-3831	380	13	t	t	PROPN
ejpam-3831	380	14	(	(	PUNCT
ejpam-3831	380	15	u	u	NOUN
ejpam-3831	380	16	,	,	PUNCT
ejpam-3831	380	17	v	v	NOUN
ejpam-3831	380	18	)	)	PUNCT
ejpam-3831	380	19	,	,	PUNCT
ejpam-3831	380	20	t	t	PROPN
ejpam-3831	380	21	(	(	PUNCT
ejpam-3831	380	22	x	x	PROPN
ejpam-3831	380	23	,	,	PUNCT
ejpam-3831	380	24	y	y	PROPN
ejpam-3831	380	25	)	)	PUNCT
ejpam-3831	380	26	)	)	PUNCT
ejpam-3831	381	1	≤	≤	PUNCT
ejpam-3831	381	2	α1(a	α1(a	NUM
ejpam-3831	381	3	,	,	PUNCT
ejpam-3831	381	4	u	u	NOUN
ejpam-3831	381	5	)	)	PUNCT
ejpam-3831	381	6	·	·	PUNCT
ejpam-3831	381	7	gb(a	gb(a	X
ejpam-3831	381	8	,	,	PUNCT
ejpam-3831	381	9	u	u	NOUN
ejpam-3831	381	10	,	,	PUNCT
ejpam-3831	381	11	x	x	X
ejpam-3831	381	12	)	)	PUNCT
ejpam-3831	381	13	+	+	ADJ
ejpam-3831	381	14	gb(b	gb(b	NOUN
ejpam-3831	381	15	,	,	PUNCT
ejpam-3831	381	16	v	v	NOUN
ejpam-3831	381	17	,	,	PUNCT
ejpam-3831	381	18	y	y	NOUN
ejpam-3831	381	19	)	)	PUNCT
ejpam-3831	381	20	2	2	NUM
ejpam-3831	382	1	+	+	PROPN
ejpam-3831	382	2	α2(a	α2(a	PROPN
ejpam-3831	382	3	,	,	PUNCT
ejpam-3831	382	4	u	u	NOUN
ejpam-3831	382	5	)	)	PUNCT
ejpam-3831	382	6	gb	gb	ADP
ejpam-3831	382	7	(	(	PUNCT
ejpam-3831	382	8	t	t	PROPN
ejpam-3831	382	9	(	(	PUNCT
ejpam-3831	382	10	a	a	DET
ejpam-3831	382	11	,	,	PUNCT
ejpam-3831	382	12	b	b	NOUN
ejpam-3831	382	13	)	)	PUNCT
ejpam-3831	382	14	,	,	PUNCT
ejpam-3831	382	15	t	t	PROPN
ejpam-3831	382	16	(	(	PUNCT
ejpam-3831	382	17	u	u	NOUN
ejpam-3831	382	18	,	,	PUNCT
ejpam-3831	382	19	v	v	NOUN
ejpam-3831	382	20	)	)	PUNCT
ejpam-3831	382	21	,	,	PUNCT
ejpam-3831	382	22	t	t	PROPN
ejpam-3831	382	23	(	(	PUNCT
ejpam-3831	382	24	x	x	PROPN
ejpam-3831	382	25	,	,	PUNCT
ejpam-3831	382	26	y	y	NOUN
ejpam-3831	382	27	)	)	PUNCT
ejpam-3831	382	28	)	)	PUNCT
ejpam-3831	382	29	gb(a	gb(a	X
ejpam-3831	382	30	,	,	PUNCT
ejpam-3831	382	31	u	u	NOUN
ejpam-3831	382	32	,	,	PUNCT
ejpam-3831	382	33	x	x	NOUN
ejpam-3831	382	34	)	)	PUNCT
ejpam-3831	382	35	ωs(a	ωs(a	NUM
ejpam-3831	382	36	,	,	PUNCT
ejpam-3831	382	37	u	u	NOUN
ejpam-3831	382	38	,	,	PUNCT
ejpam-3831	382	39	x	x	X
ejpam-3831	382	40	,	,	PUNCT
ejpam-3831	382	41	b	b	PROPN
ejpam-3831	382	42	,	,	PUNCT
ejpam-3831	382	43	v	v	NOUN
ejpam-3831	382	44	,	,	PUNCT
ejpam-3831	382	45	y	y	NOUN
ejpam-3831	382	46	)	)	PUNCT
ejpam-3831	382	47	m.m.m	m.m.m	NOUN
ejpam-3831	382	48	.	.	PUNCT
ejpam-3831	383	1	jaradat	jaradat	PROPN
ejpam-3831	383	2	et	et	PROPN
ejpam-3831	383	3	al	al	PROPN
ejpam-3831	383	4	.	.	PUNCT
ejpam-3831	383	5	/	/	SYM
ejpam-3831	383	6	eur	eur	PROPN
ejpam-3831	383	7	.	.	PUNCT
ejpam-3831	384	1	j.	j.	PROPN
ejpam-3831	384	2	pure	pure	PROPN
ejpam-3831	384	3	appl	appl	PROPN
ejpam-3831	384	4	.	.	PROPN
ejpam-3831	384	5	math	math	PROPN
ejpam-3831	384	6	,	,	PUNCT
ejpam-3831	384	7	13	13	NUM
ejpam-3831	384	8	(	(	PUNCT
ejpam-3831	384	9	4	4	NUM
ejpam-3831	384	10	)	)	PUNCT
ejpam-3831	384	11	(	(	PUNCT
ejpam-3831	384	12	2020	2020	NUM
ejpam-3831	384	13	)	)	PUNCT
ejpam-3831	384	14	,	,	PUNCT
ejpam-3831	384	15	995	995	NUM
ejpam-3831	384	16	-	-	SYM
ejpam-3831	384	17	1015	1015	NUM
ejpam-3831	384	18	1009	1009	NUM
ejpam-3831	385	1	+	+	SYM
ejpam-3831	385	2	α3(a	α3(a	NUM
ejpam-3831	385	3	,	,	PUNCT
ejpam-3831	385	4	u	u	NOUN
ejpam-3831	385	5	)	)	PUNCT
ejpam-3831	385	6	gb	gb	ADP
ejpam-3831	385	7	(	(	PUNCT
ejpam-3831	385	8	t	t	PROPN
ejpam-3831	385	9	(	(	PUNCT
ejpam-3831	385	10	a	a	DET
ejpam-3831	385	11	,	,	PUNCT
ejpam-3831	385	12	b	b	NOUN
ejpam-3831	385	13	)	)	PUNCT
ejpam-3831	385	14	,	,	PUNCT
ejpam-3831	385	15	t	t	PROPN
ejpam-3831	385	16	(	(	PUNCT
ejpam-3831	385	17	u	u	NOUN
ejpam-3831	385	18	,	,	PUNCT
ejpam-3831	385	19	v	v	NOUN
ejpam-3831	385	20	)	)	PUNCT
ejpam-3831	385	21	,	,	PUNCT
ejpam-3831	385	22	t	t	PROPN
ejpam-3831	385	23	(	(	PUNCT
ejpam-3831	385	24	x	x	PROPN
ejpam-3831	385	25	,	,	PUNCT
ejpam-3831	385	26	y	y	NOUN
ejpam-3831	385	27	)	)	PUNCT
ejpam-3831	385	28	)	)	PUNCT
ejpam-3831	386	1	gb(b	gb(b	X
ejpam-3831	386	2	,	,	PUNCT
ejpam-3831	386	3	v	v	NOUN
ejpam-3831	386	4	,	,	PUNCT
ejpam-3831	386	5	y	y	NOUN
ejpam-3831	386	6	)	)	PUNCT
ejpam-3831	386	7	ωs(a	ωs(a	NUM
ejpam-3831	386	8	,	,	PUNCT
ejpam-3831	386	9	u	u	NOUN
ejpam-3831	386	10	,	,	PUNCT
ejpam-3831	386	11	x	x	X
ejpam-3831	386	12	,	,	PUNCT
ejpam-3831	386	13	b	b	PROPN
ejpam-3831	386	14	,	,	PUNCT
ejpam-3831	386	15	v	v	NOUN
ejpam-3831	386	16	,	,	PUNCT
ejpam-3831	386	17	y	y	NOUN
ejpam-3831	386	18	)	)	PUNCT
ejpam-3831	387	1	+	+	NOUN
ejpam-3831	387	2	α4(a	α4(a	NUM
ejpam-3831	387	3	,	,	PUNCT
ejpam-3831	387	4	u	u	NOUN
ejpam-3831	387	5	)	)	PUNCT
ejpam-3831	387	6	gb	gb	ADP
ejpam-3831	387	7	(	(	PUNCT
ejpam-3831	387	8	a	a	PRON
ejpam-3831	387	9	,	,	PUNCT
ejpam-3831	387	10	a	a	PRON
ejpam-3831	387	11	,	,	PUNCT
ejpam-3831	387	12	t	t	PROPN
ejpam-3831	387	13	(	(	PUNCT
ejpam-3831	387	14	a	a	DET
ejpam-3831	387	15	,	,	PUNCT
ejpam-3831	387	16	b	b	NOUN
ejpam-3831	387	17	)	)	PUNCT
ejpam-3831	387	18	)	)	PUNCT
ejpam-3831	387	19	gb(a	gb(a	X
ejpam-3831	387	20	,	,	PUNCT
ejpam-3831	387	21	u	u	NOUN
ejpam-3831	387	22	,	,	PUNCT
ejpam-3831	387	23	x	x	NOUN
ejpam-3831	387	24	)	)	PUNCT
ejpam-3831	387	25	ωs(a	ωs(a	NUM
ejpam-3831	387	26	,	,	PUNCT
ejpam-3831	387	27	u	u	NOUN
ejpam-3831	387	28	,	,	PUNCT
ejpam-3831	387	29	x	x	X
ejpam-3831	387	30	,	,	PUNCT
ejpam-3831	387	31	b	b	PROPN
ejpam-3831	387	32	,	,	PUNCT
ejpam-3831	387	33	v	v	NOUN
ejpam-3831	387	34	,	,	PUNCT
ejpam-3831	387	35	y	y	NOUN
ejpam-3831	387	36	)	)	PUNCT
ejpam-3831	387	37	+	+	PUNCT
ejpam-3831	387	38	α5(u	α5(u	NUM
ejpam-3831	387	39	,	,	PUNCT
ejpam-3831	387	40	x	x	X
ejpam-3831	387	41	)	)	PUNCT
ejpam-3831	387	42	gb	gb	ADP
ejpam-3831	387	43	(	(	PUNCT
ejpam-3831	387	44	a	a	PRON
ejpam-3831	387	45	,	,	PUNCT
ejpam-3831	387	46	a	a	PRON
ejpam-3831	387	47	,	,	PUNCT
ejpam-3831	387	48	t	t	PROPN
ejpam-3831	387	49	(	(	PUNCT
ejpam-3831	387	50	a	a	DET
ejpam-3831	387	51	,	,	PUNCT
ejpam-3831	387	52	b	b	NOUN
ejpam-3831	387	53	)	)	PUNCT
ejpam-3831	387	54	)	)	PUNCT
ejpam-3831	388	1	gb(b	gb(b	X
ejpam-3831	388	2	,	,	PUNCT
ejpam-3831	388	3	v	v	NOUN
ejpam-3831	388	4	,	,	PUNCT
ejpam-3831	388	5	y	y	NOUN
ejpam-3831	388	6	)	)	PUNCT
ejpam-3831	388	7	ωs(a	ωs(a	NUM
ejpam-3831	388	8	,	,	PUNCT
ejpam-3831	388	9	u	u	NOUN
ejpam-3831	388	10	,	,	PUNCT
ejpam-3831	388	11	x	x	X
ejpam-3831	388	12	,	,	PUNCT
ejpam-3831	388	13	b	b	PROPN
ejpam-3831	388	14	,	,	PUNCT
ejpam-3831	388	15	v	v	NOUN
ejpam-3831	388	16	,	,	PUNCT
ejpam-3831	388	17	y	y	NOUN
ejpam-3831	388	18	)	)	PUNCT
ejpam-3831	389	1	+	+	NOUN
ejpam-3831	389	2	α6(u	α6(u	PROPN
ejpam-3831	389	3	,	,	PUNCT
ejpam-3831	389	4	x	x	NOUN
ejpam-3831	389	5	)	)	PUNCT
ejpam-3831	389	6	gb	gb	ADP
ejpam-3831	389	7	(	(	PUNCT
ejpam-3831	389	8	u	u	NOUN
ejpam-3831	389	9	,	,	PUNCT
ejpam-3831	389	10	u	u	PROPN
ejpam-3831	389	11	,	,	PUNCT
ejpam-3831	389	12	t	t	PROPN
ejpam-3831	389	13	(	(	PUNCT
ejpam-3831	389	14	u	u	NOUN
ejpam-3831	389	15	,	,	PUNCT
ejpam-3831	389	16	v	v	NOUN
ejpam-3831	389	17	)	)	PUNCT
ejpam-3831	389	18	)	)	PUNCT
ejpam-3831	389	19	gb(a	gb(a	X
ejpam-3831	389	20	,	,	PUNCT
ejpam-3831	389	21	u	u	NOUN
ejpam-3831	389	22	,	,	PUNCT
ejpam-3831	389	23	x	x	NOUN
ejpam-3831	389	24	)	)	PUNCT
ejpam-3831	389	25	ωs(a	ωs(a	NUM
ejpam-3831	389	26	,	,	PUNCT
ejpam-3831	389	27	u	u	NOUN
ejpam-3831	389	28	,	,	PUNCT
ejpam-3831	389	29	x	x	X
ejpam-3831	389	30	,	,	PUNCT
ejpam-3831	389	31	b	b	PROPN
ejpam-3831	389	32	,	,	PUNCT
ejpam-3831	389	33	v	v	NOUN
ejpam-3831	389	34	,	,	PUNCT
ejpam-3831	389	35	y	y	PROPN
ejpam-3831	389	36	)	)	PUNCT
ejpam-3831	389	37	+	+	CCONJ
ejpam-3831	389	38	α7(u	α7(u	ADJ
ejpam-3831	389	39	,	,	PUNCT
ejpam-3831	389	40	x	x	X
ejpam-3831	389	41	)	)	PUNCT
ejpam-3831	389	42	gb	gb	ADP
ejpam-3831	389	43	(	(	PUNCT
ejpam-3831	389	44	u	u	NOUN
ejpam-3831	389	45	,	,	PUNCT
ejpam-3831	389	46	u	u	PROPN
ejpam-3831	389	47	,	,	PUNCT
ejpam-3831	389	48	t	t	PROPN
ejpam-3831	389	49	(	(	PUNCT
ejpam-3831	389	50	u	u	NOUN
ejpam-3831	389	51	,	,	PUNCT
ejpam-3831	389	52	v	v	NOUN
ejpam-3831	389	53	)	)	PUNCT
ejpam-3831	389	54	)	)	PUNCT
ejpam-3831	390	1	gb(b	gb(b	X
ejpam-3831	390	2	,	,	PUNCT
ejpam-3831	390	3	v	v	NOUN
ejpam-3831	390	4	,	,	PUNCT
ejpam-3831	390	5	y	y	NOUN
ejpam-3831	390	6	)	)	PUNCT
ejpam-3831	390	7	ωs(a	ωs(a	NUM
ejpam-3831	390	8	,	,	PUNCT
ejpam-3831	390	9	u	u	NOUN
ejpam-3831	390	10	,	,	PUNCT
ejpam-3831	390	11	x	x	X
ejpam-3831	390	12	,	,	PUNCT
ejpam-3831	390	13	b	b	PROPN
ejpam-3831	390	14	,	,	PUNCT
ejpam-3831	390	15	v	v	NOUN
ejpam-3831	390	16	,	,	PUNCT
ejpam-3831	390	17	y	y	NOUN
ejpam-3831	390	18	)	)	PUNCT
ejpam-3831	391	1	+	+	NOUN
ejpam-3831	391	2	α8(u	α8(u	NUM
ejpam-3831	391	3	,	,	PUNCT
ejpam-3831	391	4	x	x	NOUN
ejpam-3831	391	5	)	)	PUNCT
ejpam-3831	391	6	gb	gb	ADP
ejpam-3831	391	7	(	(	PUNCT
ejpam-3831	391	8	x	x	NOUN
ejpam-3831	391	9	,	,	PUNCT
ejpam-3831	391	10	x	x	PROPN
ejpam-3831	391	11	,	,	PUNCT
ejpam-3831	391	12	t	t	PROPN
ejpam-3831	391	13	(	(	PUNCT
ejpam-3831	391	14	x	x	PROPN
ejpam-3831	391	15	,	,	PUNCT
ejpam-3831	391	16	y	y	NOUN
ejpam-3831	391	17	)	)	PUNCT
ejpam-3831	391	18	)	)	PUNCT
ejpam-3831	391	19	gb(a	gb(a	X
ejpam-3831	391	20	,	,	PUNCT
ejpam-3831	391	21	u	u	NOUN
ejpam-3831	391	22	,	,	PUNCT
ejpam-3831	391	23	x	x	NOUN
ejpam-3831	391	24	)	)	PUNCT
ejpam-3831	391	25	ωs(a	ωs(a	NUM
ejpam-3831	391	26	,	,	PUNCT
ejpam-3831	391	27	u	u	NOUN
ejpam-3831	391	28	,	,	PUNCT
ejpam-3831	391	29	x	x	X
ejpam-3831	391	30	,	,	PUNCT
ejpam-3831	391	31	b	b	PROPN
ejpam-3831	391	32	,	,	PUNCT
ejpam-3831	391	33	v	v	NOUN
ejpam-3831	391	34	,	,	PUNCT
ejpam-3831	391	35	y	y	PROPN
ejpam-3831	391	36	)	)	PUNCT
ejpam-3831	391	37	+	+	CCONJ
ejpam-3831	392	1	α9(x	α9(x	NUM
ejpam-3831	392	2	,	,	PUNCT
ejpam-3831	392	3	a	a	PRON
ejpam-3831	392	4	)	)	PUNCT
ejpam-3831	392	5	gb	gb	PROPN
ejpam-3831	392	6	(	(	PUNCT
ejpam-3831	392	7	x	x	NOUN
ejpam-3831	392	8	,	,	PUNCT
ejpam-3831	392	9	x	x	PROPN
ejpam-3831	392	10	,	,	PUNCT
ejpam-3831	392	11	t	t	PROPN
ejpam-3831	392	12	(	(	PUNCT
ejpam-3831	392	13	x	x	PROPN
ejpam-3831	392	14	,	,	PUNCT
ejpam-3831	392	15	y	y	NOUN
ejpam-3831	392	16	)	)	PUNCT
ejpam-3831	392	17	)	)	PUNCT
ejpam-3831	393	1	gb(b	gb(b	X
ejpam-3831	393	2	,	,	PUNCT
ejpam-3831	393	3	v	v	NOUN
ejpam-3831	393	4	,	,	PUNCT
ejpam-3831	393	5	y	y	NOUN
ejpam-3831	393	6	)	)	PUNCT
ejpam-3831	393	7	ωs(a	ωs(a	NUM
ejpam-3831	393	8	,	,	PUNCT
ejpam-3831	393	9	u	u	NOUN
ejpam-3831	393	10	,	,	PUNCT
ejpam-3831	393	11	x	x	X
ejpam-3831	393	12	,	,	PUNCT
ejpam-3831	393	13	b	b	PROPN
ejpam-3831	393	14	,	,	PUNCT
ejpam-3831	393	15	v	v	NOUN
ejpam-3831	393	16	,	,	PUNCT
ejpam-3831	393	17	y	y	NOUN
ejpam-3831	393	18	)	)	PUNCT
ejpam-3831	394	1	+	+	NOUN
ejpam-3831	394	2	α10(x	α10(x	NOUN
ejpam-3831	394	3	,	,	PUNCT
ejpam-3831	394	4	a	a	PRON
ejpam-3831	394	5	)	)	PUNCT
ejpam-3831	394	6	gb	gb	PROPN
ejpam-3831	394	7	(	(	PUNCT
ejpam-3831	394	8	a	a	PRON
ejpam-3831	394	9	,	,	PUNCT
ejpam-3831	394	10	u	u	NOUN
ejpam-3831	394	11	,	,	PUNCT
ejpam-3831	394	12	t	t	PROPN
ejpam-3831	394	13	(	(	PUNCT
ejpam-3831	394	14	x	x	PROPN
ejpam-3831	394	15	,	,	PUNCT
ejpam-3831	394	16	y	y	NOUN
ejpam-3831	394	17	)	)	PUNCT
ejpam-3831	394	18	)	)	PUNCT
ejpam-3831	394	19	gb(a	gb(a	X
ejpam-3831	394	20	,	,	PUNCT
ejpam-3831	394	21	u	u	NOUN
ejpam-3831	394	22	,	,	PUNCT
ejpam-3831	394	23	x	x	NOUN
ejpam-3831	394	24	)	)	PUNCT
ejpam-3831	394	25	ωs(a	ωs(a	NUM
ejpam-3831	394	26	,	,	PUNCT
ejpam-3831	394	27	u	u	NOUN
ejpam-3831	394	28	,	,	PUNCT
ejpam-3831	394	29	x	x	X
ejpam-3831	394	30	,	,	PUNCT
ejpam-3831	394	31	b	b	PROPN
ejpam-3831	394	32	,	,	PUNCT
ejpam-3831	394	33	v	v	NOUN
ejpam-3831	394	34	,	,	PUNCT
ejpam-3831	394	35	y	y	NOUN
ejpam-3831	394	36	)	)	PUNCT
ejpam-3831	394	37	+	+	CCONJ
ejpam-3831	394	38	α11(x	α11(x	NOUN
ejpam-3831	394	39	,	,	PUNCT
ejpam-3831	394	40	a	a	PRON
ejpam-3831	394	41	)	)	PUNCT
ejpam-3831	394	42	gb	gb	PROPN
ejpam-3831	394	43	(	(	PUNCT
ejpam-3831	394	44	u	u	NOUN
ejpam-3831	394	45	,	,	PUNCT
ejpam-3831	394	46	x	x	PROPN
ejpam-3831	394	47	,	,	PUNCT
ejpam-3831	394	48	t	t	PROPN
ejpam-3831	394	49	(	(	PUNCT
ejpam-3831	394	50	a	a	DET
ejpam-3831	394	51	,	,	PUNCT
ejpam-3831	394	52	b	b	NOUN
ejpam-3831	394	53	)	)	PUNCT
ejpam-3831	394	54	)	)	PUNCT
ejpam-3831	394	55	gb(b	gb(b	X
ejpam-3831	394	56	,	,	PUNCT
ejpam-3831	394	57	v	v	NOUN
ejpam-3831	394	58	,	,	PUNCT
ejpam-3831	394	59	y	y	NOUN
ejpam-3831	394	60	)	)	PUNCT
ejpam-3831	394	61	ωs(a	ωs(a	NUM
ejpam-3831	394	62	,	,	PUNCT
ejpam-3831	394	63	u	u	NOUN
ejpam-3831	394	64	,	,	PUNCT
ejpam-3831	394	65	x	x	X
ejpam-3831	394	66	,	,	PUNCT
ejpam-3831	394	67	b	b	PROPN
ejpam-3831	394	68	,	,	PUNCT
ejpam-3831	394	69	v	v	NOUN
ejpam-3831	394	70	,	,	PUNCT
ejpam-3831	394	71	y	y	NOUN
ejpam-3831	394	72	)	)	PUNCT
ejpam-3831	395	1	+	+	NOUN
ejpam-3831	395	2	α12(x	α12(x	NOUN
ejpam-3831	395	3	,	,	PUNCT
ejpam-3831	395	4	a	a	PRON
ejpam-3831	395	5	)	)	PUNCT
ejpam-3831	395	6	gb	gb	PROPN
ejpam-3831	395	7	(	(	PUNCT
ejpam-3831	395	8	x	x	NOUN
ejpam-3831	395	9	,	,	PUNCT
ejpam-3831	395	10	a	a	PRON
ejpam-3831	395	11	,	,	PUNCT
ejpam-3831	395	12	t	t	PROPN
ejpam-3831	395	13	(	(	PUNCT
ejpam-3831	395	14	u	u	NOUN
ejpam-3831	395	15	,	,	PUNCT
ejpam-3831	395	16	v	v	NOUN
ejpam-3831	395	17	)	)	PUNCT
ejpam-3831	395	18	)	)	PUNCT
ejpam-3831	395	19	gb(a	gb(a	X
ejpam-3831	395	20	,	,	PUNCT
ejpam-3831	395	21	u	u	NOUN
ejpam-3831	395	22	,	,	PUNCT
ejpam-3831	395	23	x	x	NOUN
ejpam-3831	395	24	)	)	PUNCT
ejpam-3831	395	25	ωs(a	ωs(a	NUM
ejpam-3831	395	26	,	,	PUNCT
ejpam-3831	395	27	u	u	NOUN
ejpam-3831	395	28	,	,	PUNCT
ejpam-3831	395	29	x	x	X
ejpam-3831	395	30	,	,	PUNCT
ejpam-3831	395	31	b	b	PROPN
ejpam-3831	395	32	,	,	PUNCT
ejpam-3831	395	33	v	v	NOUN
ejpam-3831	395	34	,	,	PUNCT
ejpam-3831	395	35	y	y	PROPN
ejpam-3831	395	36	)	)	PUNCT
ejpam-3831	395	37	,	,	PUNCT
ejpam-3831	395	38	where	where	SCONJ
ejpam-3831	395	39	0	0	NUM
ejpam-3831	395	40	≤	≤	NUM
ejpam-3831	395	41	s[α1(x	s[α1(x	NOUN
ejpam-3831	395	42	,	,	PUNCT
ejpam-3831	395	43	y	y	NOUN
ejpam-3831	395	44	)	)	PUNCT
ejpam-3831	395	45	+	+	CCONJ
ejpam-3831	395	46	α4(x	α4(x	NUM
ejpam-3831	395	47	,	,	PUNCT
ejpam-3831	395	48	y	y	PROPN
ejpam-3831	395	49	)	)	PUNCT
ejpam-3831	395	50	+	+	CCONJ
ejpam-3831	395	51	α5(x	α5(x	PROPN
ejpam-3831	395	52	,	,	PUNCT
ejpam-3831	395	53	y	y	NOUN
ejpam-3831	395	54	)	)	PUNCT
ejpam-3831	395	55	+	+	SYM
ejpam-3831	395	56	α10(x	α10(x	NOUN
ejpam-3831	395	57	,	,	PUNCT
ejpam-3831	395	58	y	y	NOUN
ejpam-3831	395	59	)	)	PUNCT
ejpam-3831	395	60	+	+	SYM
ejpam-3831	395	61	α12(x	α12(x	PROPN
ejpam-3831	395	62	,	,	PUNCT
ejpam-3831	395	63	y	y	PROPN
ejpam-3831	395	64	)	)	PUNCT
ejpam-3831	395	65	]	]	PUNCT
ejpam-3831	396	1	+	+	CCONJ
ejpam-3831	397	1	[	[	X
ejpam-3831	397	2	α2(x	α2(x	PROPN
ejpam-3831	397	3	,	,	PUNCT
ejpam-3831	397	4	y	y	PROPN
ejpam-3831	397	5	)	)	PUNCT
ejpam-3831	397	6	+	+	CCONJ
ejpam-3831	397	7	α3(x	α3(x	PROPN
ejpam-3831	397	8	,	,	PUNCT
ejpam-3831	397	9	y	y	PROPN
ejpam-3831	397	10	)	)	PUNCT
ejpam-3831	397	11	+	+	CCONJ
ejpam-3831	397	12	11∑	11∑	NUM
ejpam-3831	397	13	i=6	i=6	NOUN
ejpam-3831	397	14	αi(x	αi(x	NUM
ejpam-3831	397	15	,	,	PUNCT
ejpam-3831	397	16	y	y	PROPN
ejpam-3831	397	17	)	)	PUNCT
ejpam-3831	397	18	]	]	PUNCT
ejpam-3831	397	19	<	<	X
ejpam-3831	397	20	1	1	X
ejpam-3831	397	21	.	.	PUNCT
ejpam-3831	397	22	then	then	ADV
ejpam-3831	397	23	t	t	PROPN
ejpam-3831	397	24	has	have	VERB
ejpam-3831	397	25	a	a	DET
ejpam-3831	397	26	unique	unique	ADJ
ejpam-3831	397	27	coupled	couple	VERB
ejpam-3831	397	28	fixed	fix	VERB
ejpam-3831	397	29	point	point	NOUN
ejpam-3831	397	30	in	in	ADP
ejpam-3831	397	31	x.	x.	NOUN
ejpam-3831	397	32	proof	proof	NOUN
ejpam-3831	397	33	.	.	PUNCT
ejpam-3831	398	1	taking	take	VERB
ejpam-3831	398	2	f	f	NOUN
ejpam-3831	398	3	=	=	PUNCT
ejpam-3831	398	4	h	h	PROPN
ejpam-3831	398	5	=	=	SYM
ejpam-3831	398	6	t	t	PROPN
ejpam-3831	398	7	in	in	ADP
ejpam-3831	398	8	theorem	theorem	NOUN
ejpam-3831	398	9	1	1	NUM
ejpam-3831	398	10	,	,	PUNCT
ejpam-3831	398	11	we	we	PRON
ejpam-3831	398	12	get	get	VERB
ejpam-3831	398	13	the	the	DET
ejpam-3831	398	14	required	required	ADJ
ejpam-3831	398	15	proof	proof	NOUN
ejpam-3831	398	16	.	.	PUNCT
ejpam-3831	399	1	the	the	DET
ejpam-3831	399	2	proof	proof	NOUN
ejpam-3831	399	3	of	of	ADP
ejpam-3831	399	4	the	the	DET
ejpam-3831	399	5	following	follow	VERB
ejpam-3831	399	6	corollary	corollary	NOUN
ejpam-3831	399	7	follows	follow	VERB
ejpam-3831	399	8	word	word	NOUN
ejpam-3831	399	9	by	by	ADP
ejpam-3831	399	10	word	word	NOUN
ejpam-3831	399	11	by	by	ADP
ejpam-3831	399	12	using	use	VERB
ejpam-3831	399	13	the	the	DET
ejpam-3831	399	14	same	same	ADJ
ejpam-3831	399	15	argument	argument	NOUN
ejpam-3831	399	16	as	as	ADP
ejpam-3831	399	17	in	in	ADP
ejpam-3831	399	18	the	the	DET
ejpam-3831	399	19	proof	proof	NOUN
ejpam-3831	399	20	of	of	ADP
ejpam-3831	399	21	theorem	theorem	ADJ
ejpam-3831	399	22	1	1	NUM
ejpam-3831	399	23	.	.	PUNCT
ejpam-3831	399	24	corollary	corollary	ADJ
ejpam-3831	399	25	3	3	X
ejpam-3831	399	26	.	.	PUNCT
ejpam-3831	400	1	let	let	AUX
ejpam-3831	400	2	(	(	PUNCT
ejpam-3831	400	3	x	x	NOUN
ejpam-3831	400	4	,	,	PUNCT
ejpam-3831	400	5	gb	gb	PRON
ejpam-3831	400	6	)	)	PUNCT
ejpam-3831	400	7	be	be	AUX
ejpam-3831	400	8	a	a	DET
ejpam-3831	400	9	complete	complete	ADJ
ejpam-3831	400	10	gb	gb	ADV
ejpam-3831	400	11	-	-	PUNCT
ejpam-3831	400	12	metric	metric	ADJ
ejpam-3831	400	13	space	space	NOUN
ejpam-3831	400	14	and	and	CCONJ
ejpam-3831	400	15	let	let	VERB
ejpam-3831	400	16	f	f	X
ejpam-3831	400	17	,	,	PUNCT
ejpam-3831	400	18	h	h	PROPN
ejpam-3831	400	19	,	,	PUNCT
ejpam-3831	400	20	t	t	NOUN
ejpam-3831	400	21	:	:	PUNCT
ejpam-3831	400	22	x	x	PROPN
ejpam-3831	400	23	×x	×x	ADP
ejpam-3831	400	24	→	→	SYM
ejpam-3831	400	25	x	x	PART
ejpam-3831	400	26	be	be	AUX
ejpam-3831	400	27	mappings	mapping	NOUN
ejpam-3831	400	28	satisfying	satisfy	VERB
ejpam-3831	400	29	the	the	DET
ejpam-3831	400	30	above	above	ADJ
ejpam-3831	400	31	generalized	generalized	ADJ
ejpam-3831	400	32	contraction(1	contraction(1	NOUN
ejpam-3831	400	33	)	)	PUNCT
ejpam-3831	400	34	and	and	CCONJ
ejpam-3831	400	35	the	the	DET
ejpam-3831	400	36	following	follow	VERB
ejpam-3831	400	37	conditions	condition	NOUN
ejpam-3831	400	38	.	.	PUNCT
ejpam-3831	401	1	(	(	PUNCT
ejpam-3831	401	2	i	i	NOUN
ejpam-3831	401	3	)	)	PUNCT
ejpam-3831	401	4	αi(f	αi(f	NOUN
ejpam-3831	402	1	(	(	PUNCT
ejpam-3831	402	2	x1	x1	PROPN
ejpam-3831	402	3	,	,	PUNCT
ejpam-3831	402	4	y1	y1	PROPN
ejpam-3831	402	5	)	)	PUNCT
ejpam-3831	402	6	,	,	PUNCT
ejpam-3831	402	7	y	y	NOUN
ejpam-3831	402	8	)	)	PUNCT
ejpam-3831	402	9	≤	≤	NOUN
ejpam-3831	402	10	αi(x1	αi(x1	NOUN
ejpam-3831	402	11	,	,	PUNCT
ejpam-3831	402	12	y	y	NOUN
ejpam-3831	402	13	)	)	PUNCT
ejpam-3831	402	14	and	and	CCONJ
ejpam-3831	402	15	αi(x	αi(x	NUM
ejpam-3831	402	16	,	,	PUNCT
ejpam-3831	402	17	f	f	PROPN
ejpam-3831	402	18	(	(	PUNCT
ejpam-3831	402	19	x1	x1	PROPN
ejpam-3831	402	20	,	,	PUNCT
ejpam-3831	402	21	y1	y1	NOUN
ejpam-3831	402	22	)	)	PUNCT
ejpam-3831	402	23	)	)	PUNCT
ejpam-3831	402	24	≤	≤	NOUN
ejpam-3831	402	25	αi(x	αi(x	NUM
ejpam-3831	402	26	,	,	PUNCT
ejpam-3831	402	27	x1	x1	NUM
ejpam-3831	402	28	)	)	PUNCT
ejpam-3831	402	29	)	)	PUNCT
ejpam-3831	402	30	;	;	PUNCT
ejpam-3831	402	31	(	(	PUNCT
ejpam-3831	402	32	ii	ii	NOUN
ejpam-3831	402	33	)	)	PUNCT
ejpam-3831	402	34	αi(h(x1	αi(h(x1	PROPN
ejpam-3831	402	35	,	,	PUNCT
ejpam-3831	402	36	y1	y1	NOUN
ejpam-3831	402	37	)	)	PUNCT
ejpam-3831	402	38	,	,	PUNCT
ejpam-3831	402	39	y	y	NOUN
ejpam-3831	402	40	)	)	PUNCT
ejpam-3831	402	41	≤	≤	NOUN
ejpam-3831	402	42	αi(x1	αi(x1	NOUN
ejpam-3831	402	43	,	,	PUNCT
ejpam-3831	402	44	y	y	NOUN
ejpam-3831	402	45	)	)	PUNCT
ejpam-3831	402	46	and	and	CCONJ
ejpam-3831	402	47	αi(x	αi(x	NUM
ejpam-3831	402	48	,	,	PUNCT
ejpam-3831	402	49	h(x1	h(x1	NOUN
ejpam-3831	402	50	,	,	PUNCT
ejpam-3831	402	51	y1	y1	NOUN
ejpam-3831	402	52	)	)	PUNCT
ejpam-3831	402	53	)	)	PUNCT
ejpam-3831	402	54	≤	≤	NOUN
ejpam-3831	402	55	αi(x	αi(x	NUM
ejpam-3831	402	56	,	,	PUNCT
ejpam-3831	402	57	x1	x1	NUM
ejpam-3831	402	58	)	)	PUNCT
ejpam-3831	402	59	)	)	PUNCT
ejpam-3831	402	60	;	;	PUNCT
ejpam-3831	402	61	(	(	PUNCT
ejpam-3831	402	62	iii	iii	NOUN
ejpam-3831	402	63	)	)	PUNCT
ejpam-3831	402	64	αi(t	αi(t	X
ejpam-3831	402	65	(	(	PUNCT
ejpam-3831	402	66	x1	x1	PROPN
ejpam-3831	402	67	,	,	PUNCT
ejpam-3831	402	68	y1	y1	PROPN
ejpam-3831	402	69	)	)	PUNCT
ejpam-3831	402	70	,	,	PUNCT
ejpam-3831	402	71	y	y	NOUN
ejpam-3831	402	72	)	)	PUNCT
ejpam-3831	402	73	≤	≤	NOUN
ejpam-3831	402	74	αi(x1	αi(x1	NOUN
ejpam-3831	402	75	,	,	PUNCT
ejpam-3831	402	76	y	y	NOUN
ejpam-3831	402	77	)	)	PUNCT
ejpam-3831	402	78	and	and	CCONJ
ejpam-3831	402	79	αi(x	αi(x	NUM
ejpam-3831	402	80	,	,	PUNCT
ejpam-3831	402	81	t	t	PROPN
ejpam-3831	402	82	(	(	PUNCT
ejpam-3831	402	83	x1	x1	PROPN
ejpam-3831	402	84	,	,	PUNCT
ejpam-3831	402	85	y1	y1	NOUN
ejpam-3831	402	86	)	)	PUNCT
ejpam-3831	402	87	)	)	PUNCT
ejpam-3831	402	88	≤	≤	NOUN
ejpam-3831	402	89	αi(x	αi(x	NUM
ejpam-3831	402	90	,	,	PUNCT
ejpam-3831	402	91	x1	x1	NUM
ejpam-3831	402	92	)	)	PUNCT
ejpam-3831	402	93	)	)	PUNCT
ejpam-3831	402	94	;	;	PUNCT
ejpam-3831	402	95	(	(	PUNCT
ejpam-3831	402	96	iv	iv	X
ejpam-3831	402	97	)	)	PUNCT
ejpam-3831	402	98	gb	gb	PROPN
ejpam-3831	402	99	(	(	PUNCT
ejpam-3831	402	100	f	f	X
ejpam-3831	402	101	(	(	PUNCT
ejpam-3831	402	102	a	a	DET
ejpam-3831	402	103	,	,	PUNCT
ejpam-3831	402	104	b	b	NOUN
ejpam-3831	402	105	)	)	PUNCT
ejpam-3831	402	106	,	,	PUNCT
ejpam-3831	402	107	h(u	h(u	PROPN
ejpam-3831	402	108	,	,	PUNCT
ejpam-3831	402	109	v	v	NOUN
ejpam-3831	402	110	)	)	PUNCT
ejpam-3831	402	111	,	,	PUNCT
ejpam-3831	402	112	t	t	PROPN
ejpam-3831	402	113	(	(	PUNCT
ejpam-3831	402	114	x	x	PROPN
ejpam-3831	402	115	,	,	PUNCT
ejpam-3831	402	116	y	y	PROPN
ejpam-3831	402	117	)	)	PUNCT
ejpam-3831	402	118	)	)	PUNCT
ejpam-3831	402	119	≤	≤	PUNCT
ejpam-3831	403	1	n	n	CCONJ
ejpam-3831	403	2	(	(	PUNCT
ejpam-3831	403	3	a	a	PRON
ejpam-3831	403	4	,	,	PUNCT
ejpam-3831	403	5	b	b	PROPN
ejpam-3831	403	6	,	,	PUNCT
ejpam-3831	403	7	u	u	NOUN
ejpam-3831	403	8	,	,	PUNCT
ejpam-3831	403	9	v	v	NOUN
ejpam-3831	403	10	,	,	PUNCT
ejpam-3831	403	11	x	x	NOUN
ejpam-3831	403	12	,	,	PUNCT
ejpam-3831	403	13	y	y	PROPN
ejpam-3831	403	14	)	)	PUNCT
ejpam-3831	403	15	.	.	PUNCT
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ejpam-3831	404	20	)	)	PUNCT
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ejpam-3831	406	5	)	)	PUNCT
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ejpam-3831	406	7	(	(	PUNCT
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ejpam-3831	408	5	)	)	PUNCT
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ejpam-3831	408	9	,	,	PUNCT
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ejpam-3831	408	17	)	)	PUNCT
ejpam-3831	408	18	)	)	PUNCT
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ejpam-3831	409	5	)	)	PUNCT
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ejpam-3831	409	9	,	,	PUNCT
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ejpam-3831	410	8	,	,	PUNCT
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ejpam-3831	415	7	ω1(a	ω1(a	PROPN
ejpam-3831	415	8	,	,	PUNCT
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ejpam-3831	415	12	,	,	PUNCT
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ejpam-3831	416	15	,	,	PUNCT
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ejpam-3831	417	14	,	,	PUNCT
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ejpam-3831	418	8	,	,	PUNCT
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ejpam-3831	418	12	,	,	PUNCT
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ejpam-3831	419	9	,	,	PUNCT
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ejpam-3831	419	15	,	,	PUNCT
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ejpam-3831	419	17	)	)	PUNCT
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ejpam-3831	419	19	gb(a	gb(a	X
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ejpam-3831	419	37	+	+	CCONJ
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ejpam-3831	419	47	,	,	PUNCT
ejpam-3831	419	48	f	f	PROPN
ejpam-3831	419	49	(	(	PUNCT
ejpam-3831	419	50	a	a	DET
ejpam-3831	419	51	,	,	PUNCT
ejpam-3831	419	52	b	b	NOUN
ejpam-3831	419	53	)	)	PUNCT
ejpam-3831	419	54	)	)	PUNCT
ejpam-3831	419	55	gb(b	gb(b	X
ejpam-3831	419	56	,	,	PUNCT
ejpam-3831	419	57	v	v	NOUN
ejpam-3831	419	58	,	,	PUNCT
ejpam-3831	419	59	y	y	NOUN
ejpam-3831	419	60	)	)	PUNCT
ejpam-3831	419	61	ω1(a	ω1(a	PROPN
ejpam-3831	419	62	,	,	PUNCT
ejpam-3831	419	63	u	u	NOUN
ejpam-3831	419	64	,	,	PUNCT
ejpam-3831	419	65	x	x	X
ejpam-3831	419	66	,	,	PUNCT
ejpam-3831	419	67	b	b	PROPN
ejpam-3831	419	68	,	,	PUNCT
ejpam-3831	419	69	v	v	NOUN
ejpam-3831	419	70	,	,	PUNCT
ejpam-3831	419	71	y	y	NOUN
ejpam-3831	419	72	)	)	PUNCT
ejpam-3831	420	1	+	+	NOUN
ejpam-3831	420	2	α12(x	α12(x	NOUN
ejpam-3831	420	3	,	,	PUNCT
ejpam-3831	420	4	a	a	PRON
ejpam-3831	420	5	)	)	PUNCT
ejpam-3831	420	6	gb	gb	PROPN
ejpam-3831	420	7	(	(	PUNCT
ejpam-3831	420	8	x	x	NOUN
ejpam-3831	420	9	,	,	PUNCT
ejpam-3831	420	10	a	a	PRON
ejpam-3831	420	11	,	,	PUNCT
ejpam-3831	420	12	h(u	h(u	PROPN
ejpam-3831	420	13	,	,	PUNCT
ejpam-3831	420	14	v	v	NOUN
ejpam-3831	420	15	)	)	PUNCT
ejpam-3831	420	16	)	)	PUNCT
ejpam-3831	420	17	gb(a	gb(a	X
ejpam-3831	420	18	,	,	PUNCT
ejpam-3831	420	19	u	u	NOUN
ejpam-3831	420	20	,	,	PUNCT
ejpam-3831	420	21	x	x	X
ejpam-3831	420	22	)	)	PUNCT
ejpam-3831	420	23	ω1(a	ω1(a	PROPN
ejpam-3831	420	24	,	,	PUNCT
ejpam-3831	420	25	u	u	NOUN
ejpam-3831	420	26	,	,	PUNCT
ejpam-3831	420	27	x	x	X
ejpam-3831	420	28	,	,	PUNCT
ejpam-3831	420	29	b	b	PROPN
ejpam-3831	420	30	,	,	PUNCT
ejpam-3831	420	31	v	v	NOUN
ejpam-3831	420	32	,	,	PUNCT
ejpam-3831	420	33	y	y	PROPN
ejpam-3831	420	34	)	)	PUNCT
ejpam-3831	420	35	,	,	PUNCT
ejpam-3831	420	36	(	(	PUNCT
ejpam-3831	420	37	13	13	NUM
ejpam-3831	420	38	)	)	PUNCT
ejpam-3831	420	39	and	and	CCONJ
ejpam-3831	420	40	αi	αi	VERB
ejpam-3831	420	41	:	:	PUNCT
ejpam-3831	421	1	x	x	PUNCT
ejpam-3831	421	2	×	×	NOUN
ejpam-3831	421	3	x	x	INTJ
ejpam-3831	421	4	→	→	SYM
ejpam-3831	422	1	[	[	X
ejpam-3831	422	2	0	0	NUM
ejpam-3831	422	3	,	,	PUNCT
ejpam-3831	422	4	1	1	NUM
ejpam-3831	422	5	)	)	PUNCT
ejpam-3831	423	1	,	,	PUNCT
ejpam-3831	423	2	i	i	PRON
ejpam-3831	423	3	=	=	NOUN
ejpam-3831	423	4	1	1	NUM
ejpam-3831	423	5	,	,	PUNCT
ejpam-3831	423	6	2	2	NUM
ejpam-3831	423	7	,	,	PUNCT
ejpam-3831	423	8	3	3	NUM
ejpam-3831	423	9	,	,	PUNCT
ejpam-3831	423	10	·	·	PUNCT
ejpam-3831	423	11	·	·	PUNCT
ejpam-3831	423	12	·	·	PUNCT
ejpam-3831	423	13	,	,	PUNCT
ejpam-3831	423	14	12	12	NUM
ejpam-3831	423	15	.	.	PUNCT
ejpam-3831	424	1	such	such	ADJ
ejpam-3831	424	2	that	that	DET
ejpam-3831	424	3	0	0	NUM
ejpam-3831	424	4	≤	≤	NUM
ejpam-3831	424	5	s[α1(x	s[α1(x	NOUN
ejpam-3831	424	6	,	,	PUNCT
ejpam-3831	424	7	y	y	NOUN
ejpam-3831	424	8	)	)	PUNCT
ejpam-3831	424	9	+	+	CCONJ
ejpam-3831	424	10	α4(x	α4(x	NUM
ejpam-3831	424	11	,	,	PUNCT
ejpam-3831	424	12	y	y	PROPN
ejpam-3831	424	13	)	)	PUNCT
ejpam-3831	425	1	+	+	CCONJ
ejpam-3831	425	2	α5(x	α5(x	PROPN
ejpam-3831	425	3	,	,	PUNCT
ejpam-3831	425	4	y	y	NOUN
ejpam-3831	425	5	)	)	PUNCT
ejpam-3831	426	1	+	+	NOUN
ejpam-3831	426	2	α10(x	α10(x	NOUN
ejpam-3831	426	3	,	,	PUNCT
ejpam-3831	426	4	y	y	NOUN
ejpam-3831	426	5	)	)	PUNCT
ejpam-3831	426	6	+	+	NOUN
ejpam-3831	426	7	α12(x	α12(x	PROPN
ejpam-3831	426	8	,	,	PUNCT
ejpam-3831	426	9	y	y	PROPN
ejpam-3831	426	10	)	)	PUNCT
ejpam-3831	426	11	]	]	PUNCT
ejpam-3831	427	1	+	+	CCONJ
ejpam-3831	428	1	[	[	X
ejpam-3831	428	2	α2(x	α2(x	PROPN
ejpam-3831	428	3	,	,	PUNCT
ejpam-3831	428	4	y	y	NOUN
ejpam-3831	428	5	)	)	PUNCT
ejpam-3831	428	6	+	+	PROPN
ejpam-3831	428	7	α3(x	α3(x	PROPN
ejpam-3831	428	8	,	,	PUNCT
ejpam-3831	428	9	y	y	PROPN
ejpam-3831	428	10	)	)	PUNCT
ejpam-3831	428	11	+	+	CCONJ
ejpam-3831	428	12	11∑	11∑	NUM
ejpam-3831	428	13	i=6	i=6	NOUN
ejpam-3831	428	14	αi(x	αi(x	NUM
ejpam-3831	428	15	,	,	PUNCT
ejpam-3831	428	16	y	y	PROPN
ejpam-3831	428	17	)	)	PUNCT
ejpam-3831	428	18	]	]	PUNCT
ejpam-3831	428	19	<	<	X
ejpam-3831	428	20	1	1	X
ejpam-3831	428	21	.	.	PUNCT
ejpam-3831	428	22	then	then	ADV
ejpam-3831	428	23	f	f	X
ejpam-3831	428	24	,	,	PUNCT
ejpam-3831	428	25	h	h	PROPN
ejpam-3831	428	26	,	,	PUNCT
ejpam-3831	428	27	t	t	PROPN
ejpam-3831	428	28	have	have	VERB
ejpam-3831	428	29	a	a	DET
ejpam-3831	428	30	unique	unique	ADJ
ejpam-3831	428	31	common	common	ADJ
ejpam-3831	428	32	coupled	couple	VERB
ejpam-3831	428	33	fixed	fix	VERB
ejpam-3831	428	34	point	point	NOUN
ejpam-3831	428	35	in	in	ADP
ejpam-3831	428	36	x.	x.	NOUN
ejpam-3831	428	37	remark	remark	PROPN
ejpam-3831	428	38	2	2	NUM
ejpam-3831	428	39	.	.	PUNCT
ejpam-3831	429	1	if	if	SCONJ
ejpam-3831	429	2	we	we	PRON
ejpam-3831	429	3	put	put	VERB
ejpam-3831	429	4	αi(x	αi(x	NUM
ejpam-3831	429	5	,	,	PUNCT
ejpam-3831	429	6	y	y	NOUN
ejpam-3831	429	7	)	)	PUNCT
ejpam-3831	429	8	=	=	SYM
ejpam-3831	429	9	αi	αi	VERB
ejpam-3831	429	10	for	for	ADP
ejpam-3831	429	11	i	i	PROPN
ejpam-3831	429	12	=	=	NOUN
ejpam-3831	429	13	1	1	NUM
ejpam-3831	429	14	,	,	PUNCT
ejpam-3831	429	15	2	2	NUM
ejpam-3831	429	16	,	,	PUNCT
ejpam-3831	429	17	3	3	NUM
ejpam-3831	429	18	,	,	PUNCT
ejpam-3831	429	19	·	·	PUNCT
ejpam-3831	429	20	·	·	PUNCT
ejpam-3831	429	21	·	·	PUNCT
ejpam-3831	429	22	,	,	PUNCT
ejpam-3831	429	23	9	9	NUM
ejpam-3831	429	24	and	and	CCONJ
ejpam-3831	429	25	αi(x	αi(x	NUM
ejpam-3831	429	26	,	,	PUNCT
ejpam-3831	429	27	y	y	NOUN
ejpam-3831	429	28	)	)	PUNCT
ejpam-3831	429	29	=	=	SYM
ejpam-3831	429	30	0	0	NUM
ejpam-3831	430	1	for	for	ADP
ejpam-3831	430	2	i	i	PRON
ejpam-3831	430	3	=	=	NOUN
ejpam-3831	430	4	10	10	NUM
ejpam-3831	430	5	,	,	PUNCT
ejpam-3831	430	6	11	11	NUM
ejpam-3831	430	7	,	,	PUNCT
ejpam-3831	430	8	12	12	NUM
ejpam-3831	430	9	in	in	ADP
ejpam-3831	430	10	condition	condition	NOUN
ejpam-3831	430	11	(	(	PUNCT
ejpam-3831	430	12	13	13	NUM
ejpam-3831	430	13	)	)	PUNCT
ejpam-3831	430	14	we	we	PRON
ejpam-3831	430	15	get	get	VERB
ejpam-3831	430	16	the	the	DET
ejpam-3831	430	17	theorem	theorem	NOUN
ejpam-3831	430	18	16	16	NUM
ejpam-3831	430	19	of	of	ADP
ejpam-3831	430	20	khomdram	khomdram	PROPN
ejpam-3831	430	21	et.al	et.al	PROPN
ejpam-3831	430	22	[	[	X
ejpam-3831	430	23	4	4	NUM
ejpam-3831	430	24	]	]	PUNCT
ejpam-3831	430	25	remark	remark	NOUN
ejpam-3831	430	26	3	3	NUM
ejpam-3831	430	27	.	.	PUNCT
ejpam-3831	431	1	if	if	SCONJ
ejpam-3831	431	2	we	we	PRON
ejpam-3831	431	3	put	put	VERB
ejpam-3831	431	4	αi(x	αi(x	NUM
ejpam-3831	431	5	,	,	PUNCT
ejpam-3831	431	6	y	y	NOUN
ejpam-3831	431	7	)	)	PUNCT
ejpam-3831	431	8	=	=	SYM
ejpam-3831	431	9	αi	αi	VERB
ejpam-3831	431	10	for	for	ADP
ejpam-3831	431	11	i	i	PROPN
ejpam-3831	431	12	=	=	NOUN
ejpam-3831	431	13	1	1	NUM
ejpam-3831	431	14	,	,	PUNCT
ejpam-3831	431	15	2	2	NUM
ejpam-3831	431	16	,	,	PUNCT
ejpam-3831	431	17	3	3	NUM
ejpam-3831	431	18	,	,	PUNCT
ejpam-3831	431	19	·	·	PUNCT
ejpam-3831	431	20	·	·	PUNCT
ejpam-3831	431	21	·	·	PUNCT
ejpam-3831	431	22	,	,	PUNCT
ejpam-3831	431	23	9	9	NUM
ejpam-3831	431	24	and	and	CCONJ
ejpam-3831	431	25	αi(x	αi(x	NUM
ejpam-3831	431	26	,	,	PUNCT
ejpam-3831	431	27	y	y	NOUN
ejpam-3831	431	28	)	)	PUNCT
ejpam-3831	431	29	=	=	SYM
ejpam-3831	431	30	0	0	NUM
ejpam-3831	432	1	for	for	ADP
ejpam-3831	432	2	i	i	PRON
ejpam-3831	432	3	=	=	NOUN
ejpam-3831	432	4	10	10	NUM
ejpam-3831	432	5	,	,	PUNCT
ejpam-3831	432	6	11	11	NUM
ejpam-3831	432	7	,	,	PUNCT
ejpam-3831	432	8	12	12	NUM
ejpam-3831	432	9	in	in	ADP
ejpam-3831	432	10	corollary	corollary	ADJ
ejpam-3831	432	11	1	1	NUM
ejpam-3831	432	12	we	we	PRON
ejpam-3831	432	13	get	get	VERB
ejpam-3831	432	14	the	the	DET
ejpam-3831	432	15	corollary	corollary	ADJ
ejpam-3831	432	16	17	17	NUM
ejpam-3831	432	17	of	of	ADP
ejpam-3831	432	18	khomdram	khomdram	PROPN
ejpam-3831	432	19	et.al	et.al	PROPN
ejpam-3831	433	1	[	[	X
ejpam-3831	433	2	4	4	NUM
ejpam-3831	433	3	]	]	PUNCT
ejpam-3831	433	4	example	example	NOUN
ejpam-3831	433	5	1	1	X
ejpam-3831	433	6	.	.	PUNCT
ejpam-3831	433	7	let	let	VERB
ejpam-3831	433	8	x	x	PUNCT
ejpam-3831	433	9	=	=	PUNCT
ejpam-3831	434	1	[	[	X
ejpam-3831	434	2	0,∞	0,∞	NOUN
ejpam-3831	434	3	)	)	PUNCT
ejpam-3831	434	4	with	with	ADP
ejpam-3831	434	5	complete	complete	ADJ
ejpam-3831	434	6	g	g	NOUN
ejpam-3831	434	7	-	-	PUNCT
ejpam-3831	434	8	metric	metric	NOUN
ejpam-3831	434	9	defined	define	VERB
ejpam-3831	434	10	by	by	ADP
ejpam-3831	434	11	g(x	g(x	PROPN
ejpam-3831	434	12	,	,	PUNCT
ejpam-3831	434	13	y	y	PROPN
ejpam-3831	434	14	,	,	PUNCT
ejpam-3831	434	15	z	z	NOUN
ejpam-3831	434	16	)	)	PUNCT
ejpam-3831	434	17	=	=	PRON
ejpam-3831	434	18	{	{	PUNCT
ejpam-3831	434	19	0	0	NUM
ejpam-3831	434	20	,	,	PUNCT
ejpam-3831	434	21	if	if	SCONJ
ejpam-3831	434	22	x	x	ADP
ejpam-3831	434	23	=	=	PUNCT
ejpam-3831	434	24	y	y	PROPN
ejpam-3831	434	25	=	=	SYM
ejpam-3831	434	26	z	z	PROPN
ejpam-3831	434	27	;	;	PUNCT
ejpam-3831	434	28	max{x	max{x	PROPN
ejpam-3831	434	29	,	,	PUNCT
ejpam-3831	434	30	y	y	PROPN
ejpam-3831	434	31	,	,	PUNCT
ejpam-3831	434	32	z	z	NOUN
ejpam-3831	434	33	}	}	PUNCT
ejpam-3831	434	34	,	,	PUNCT
ejpam-3831	434	35	otherwise	otherwise	ADV
ejpam-3831	434	36	,	,	PUNCT
ejpam-3831	434	37	and	and	CCONJ
ejpam-3831	434	38	define	define	VERB
ejpam-3831	434	39	the	the	DET
ejpam-3831	434	40	gb	gb	NOUN
ejpam-3831	434	41	metric	metric	ADJ
ejpam-3831	434	42	by	by	ADP
ejpam-3831	434	43	gb(x	gb(x	PROPN
ejpam-3831	434	44	,	,	PUNCT
ejpam-3831	434	45	y	y	PROPN
ejpam-3831	434	46	,	,	PUNCT
ejpam-3831	434	47	z	z	NOUN
ejpam-3831	434	48	)	)	PUNCT
ejpam-3831	434	49	=	=	SYM
ejpam-3831	434	50	(	(	PUNCT
ejpam-3831	434	51	g(x	g(x	PROPN
ejpam-3831	434	52	,	,	PUNCT
ejpam-3831	434	53	y	y	PROPN
ejpam-3831	434	54	,	,	PUNCT
ejpam-3831	434	55	z))3	z))3	PROPN
ejpam-3831	434	56	.	.	PUNCT
ejpam-3831	435	1	then	then	ADV
ejpam-3831	435	2	,	,	PUNCT
ejpam-3831	435	3	(	(	PUNCT
ejpam-3831	435	4	x	x	NOUN
ejpam-3831	435	5	,	,	PUNCT
ejpam-3831	435	6	gb	gb	PRON
ejpam-3831	435	7	)	)	PUNCT
ejpam-3831	435	8	is	be	AUX
ejpam-3831	435	9	a	a	DET
ejpam-3831	435	10	complete	complete	ADJ
ejpam-3831	435	11	gb	gb	ADV
ejpam-3831	435	12	-	-	PUNCT
ejpam-3831	435	13	metric	metric	ADJ
ejpam-3831	435	14	space	space	NOUN
ejpam-3831	435	15	with	with	ADP
ejpam-3831	435	16	s	s	NOUN
ejpam-3831	435	17	=	=	SYM
ejpam-3831	435	18	3	3	X
ejpam-3831	435	19	.	.	PUNCT
ejpam-3831	435	20	define	define	VERB
ejpam-3831	435	21	the	the	DET
ejpam-3831	435	22	mappings	mapping	NOUN
ejpam-3831	435	23	f	f	X
ejpam-3831	435	24	,	,	PUNCT
ejpam-3831	435	25	h	h	NOUN
ejpam-3831	435	26	and	and	CCONJ
ejpam-3831	435	27	t	t	PROPN
ejpam-3831	435	28	by	by	ADP
ejpam-3831	435	29	f	f	PROPN
ejpam-3831	435	30	(	(	PUNCT
ejpam-3831	435	31	x	x	PROPN
ejpam-3831	435	32	,	,	PUNCT
ejpam-3831	435	33	y	y	NOUN
ejpam-3831	435	34	)	)	PUNCT
ejpam-3831	435	35	=	=	SYM
ejpam-3831	436	1	2x+	2x+	NUM
ejpam-3831	436	2	y	y	PROPN
ejpam-3831	436	3	160	160	NUM
ejpam-3831	436	4	,	,	PUNCT
ejpam-3831	436	5	h(x	h(x	PROPN
ejpam-3831	436	6	,	,	PUNCT
ejpam-3831	436	7	y	y	PROPN
ejpam-3831	436	8	)	)	PUNCT
ejpam-3831	436	9	=	=	SYM
ejpam-3831	436	10	x+	x+	X
ejpam-3831	436	11	3y	3y	NUM
ejpam-3831	436	12	170	170	NUM
ejpam-3831	436	13	,	,	PUNCT
ejpam-3831	436	14	and	and	CCONJ
ejpam-3831	436	15	t	t	PROPN
ejpam-3831	436	16	(	(	PUNCT
ejpam-3831	436	17	x	x	NOUN
ejpam-3831	436	18	,	,	PUNCT
ejpam-3831	436	19	y	y	PROPN
ejpam-3831	436	20	)	)	PUNCT
ejpam-3831	436	21	=	=	PUNCT
ejpam-3831	437	1	4x+	4x+	NUM
ejpam-3831	437	2	5y	5y	NOUN
ejpam-3831	437	3	180	180	NUM
ejpam-3831	437	4	for	for	ADP
ejpam-3831	437	5	all	all	DET
ejpam-3831	437	6	x	x	NOUN
ejpam-3831	437	7	,	,	PUNCT
ejpam-3831	437	8	y	y	PROPN
ejpam-3831	437	9	,	,	PUNCT
ejpam-3831	437	10	z	z	NOUN
ejpam-3831	437	11	∈	∈	PROPN
ejpam-3831	437	12	x.	x.	NOUN
ejpam-3831	437	13	we	we	PRON
ejpam-3831	437	14	will	will	AUX
ejpam-3831	437	15	use	use	VERB
ejpam-3831	437	16	the	the	DET
ejpam-3831	437	17	following	follow	VERB
ejpam-3831	437	18	fact	fact	NOUN
ejpam-3831	437	19	:	:	PUNCT
ejpam-3831	437	20	for	for	ADP
ejpam-3831	437	21	δ	δ	PROPN
ejpam-3831	437	22	,	,	PUNCT
ejpam-3831	437	23	β,≥	β,≥	NUM
ejpam-3831	437	24	0	0	NUM
ejpam-3831	437	25	,	,	PUNCT
ejpam-3831	437	26	then	then	ADV
ejpam-3831	437	27	(	(	PUNCT
ejpam-3831	437	28	δ	δ	PROPN
ejpam-3831	437	29	+	+	X
ejpam-3831	437	30	β)p	β)p	ADJ
ejpam-3831	437	31	≤	≤	NOUN
ejpam-3831	437	32	22p−2(δp	22p−2(δp	NUM
ejpam-3831	437	33	+	+	NUM
ejpam-3831	437	34	βp	βp	NUM
ejpam-3831	437	35	)	)	PUNCT
ejpam-3831	437	36	(	(	PUNCT
ejpam-3831	437	37	14	14	NUM
ejpam-3831	437	38	)	)	PUNCT
ejpam-3831	437	39	now	now	ADV
ejpam-3831	437	40	for	for	ADP
ejpam-3831	437	41	a	a	DET
ejpam-3831	437	42	6=	6=	NUM
ejpam-3831	437	43	u	u	NOUN
ejpam-3831	437	44	6=	6=	PROPN
ejpam-3831	437	45	x	x	PROPN
ejpam-3831	437	46	and	and	CCONJ
ejpam-3831	437	47	b	b	PROPN
ejpam-3831	437	48	6=	6=	ADP
ejpam-3831	437	49	v	v	NOUN
ejpam-3831	437	50	6=	6=	ADP
ejpam-3831	438	1	y	y	PROPN
ejpam-3831	438	2	we	we	PRON
ejpam-3831	438	3	have	have	VERB
ejpam-3831	438	4	gb(f	gb(f	NOUN
ejpam-3831	438	5	(	(	PUNCT
ejpam-3831	438	6	a	a	DET
ejpam-3831	438	7	,	,	PUNCT
ejpam-3831	438	8	b	b	NOUN
ejpam-3831	438	9	)	)	PUNCT
ejpam-3831	438	10	,	,	PUNCT
ejpam-3831	438	11	h(u	h(u	PROPN
ejpam-3831	438	12	,	,	PUNCT
ejpam-3831	438	13	v	v	NOUN
ejpam-3831	438	14	)	)	PUNCT
ejpam-3831	438	15	,	,	PUNCT
ejpam-3831	438	16	t	t	PROPN
ejpam-3831	438	17	(	(	PUNCT
ejpam-3831	438	18	x	x	PROPN
ejpam-3831	438	19	,	,	PUNCT
ejpam-3831	438	20	y	y	NOUN
ejpam-3831	438	21	)	)	PUNCT
ejpam-3831	438	22	)	)	PUNCT
ejpam-3831	439	1	=	=	PUNCT
ejpam-3831	439	2	(	(	PUNCT
ejpam-3831	439	3	max{2a+	max{2a+	PROPN
ejpam-3831	439	4	b	b	PROPN
ejpam-3831	439	5	160	160	NUM
ejpam-3831	439	6	,	,	PUNCT
ejpam-3831	439	7	u+	u+	NOUN
ejpam-3831	439	8	3v	3v	NUM
ejpam-3831	439	9	170	170	NUM
ejpam-3831	439	10	,	,	PUNCT
ejpam-3831	439	11	4x+	4x+	NUM
ejpam-3831	439	12	5y	5y	NOUN
ejpam-3831	439	13	180	180	NUM
ejpam-3831	439	14	}	}	PUNCT
ejpam-3831	439	15	)	)	PUNCT
ejpam-3831	439	16	3	3	X
ejpam-3831	439	17	=	=	SYM
ejpam-3831	439	18	max{(2a+	max{(2a+	X
ejpam-3831	439	19	b	b	NOUN
ejpam-3831	439	20	160	160	NUM
ejpam-3831	439	21	)	)	PUNCT
ejpam-3831	439	22	3	3	NUM
ejpam-3831	439	23	,	,	PUNCT
ejpam-3831	439	24	(	(	PUNCT
ejpam-3831	439	25	u+	u+	NUM
ejpam-3831	439	26	3v	3v	NUM
ejpam-3831	439	27	170	170	NUM
ejpam-3831	439	28	)	)	PUNCT
ejpam-3831	439	29	3	3	NUM
ejpam-3831	439	30	,	,	PUNCT
ejpam-3831	439	31	(	(	PUNCT
ejpam-3831	439	32	4x+	4x+	NUM
ejpam-3831	439	33	5y	5y	NOUN
ejpam-3831	439	34	180	180	NUM
ejpam-3831	439	35	)	)	PUNCT
ejpam-3831	439	36	3	3	NUM
ejpam-3831	439	37	}	}	PUNCT
ejpam-3831	439	38	=	=	SYM
ejpam-3831	439	39	max{(2a+	max{(2a+	VERB
ejpam-3831	439	40	b)3	b)3	PROPN
ejpam-3831	439	41	(	(	PUNCT
ejpam-3831	439	42	160)3	160)3	NUM
ejpam-3831	439	43	,	,	PUNCT
ejpam-3831	439	44	(	(	PUNCT
ejpam-3831	439	45	u+	u+	NUM
ejpam-3831	439	46	3v)3	3v)3	NUM
ejpam-3831	439	47	(	(	PUNCT
ejpam-3831	439	48	170)3	170)3	NUM
ejpam-3831	439	49	,	,	PUNCT
ejpam-3831	439	50	(	(	PUNCT
ejpam-3831	439	51	4x+	4x+	NUM
ejpam-3831	439	52	5y)3	5y)3	NUM
ejpam-3831	439	53	(	(	PUNCT
ejpam-3831	439	54	180)3	180)3	NUM
ejpam-3831	439	55	}	}	PUNCT
ejpam-3831	439	56	m.m.m	m.m.m	NOUN
ejpam-3831	439	57	.	.	PUNCT
ejpam-3831	440	1	jaradat	jaradat	PROPN
ejpam-3831	440	2	et	et	PROPN
ejpam-3831	440	3	al	al	PROPN
ejpam-3831	440	4	.	.	PUNCT
ejpam-3831	440	5	/	/	SYM
ejpam-3831	440	6	eur	eur	PROPN
ejpam-3831	440	7	.	.	PUNCT
ejpam-3831	441	1	j.	j.	PROPN
ejpam-3831	441	2	pure	pure	PROPN
ejpam-3831	441	3	appl	appl	PROPN
ejpam-3831	441	4	.	.	PROPN
ejpam-3831	441	5	math	math	PROPN
ejpam-3831	441	6	,	,	PUNCT
ejpam-3831	441	7	13	13	NUM
ejpam-3831	441	8	(	(	PUNCT
ejpam-3831	441	9	4	4	NUM
ejpam-3831	441	10	)	)	PUNCT
ejpam-3831	441	11	(	(	PUNCT
ejpam-3831	441	12	2020	2020	NUM
ejpam-3831	441	13	)	)	PUNCT
ejpam-3831	441	14	,	,	PUNCT
ejpam-3831	441	15	995	995	NUM
ejpam-3831	441	16	-	-	SYM
ejpam-3831	441	17	1015	1015	NUM
ejpam-3831	441	18	1011	1011	NUM
ejpam-3831	441	19	(	(	PUNCT
ejpam-3831	441	20	by	by	ADP
ejpam-3831	441	21	using	use	VERB
ejpam-3831	441	22	(	(	PUNCT
ejpam-3831	441	23	14	14	NUM
ejpam-3831	441	24	)	)	PUNCT
ejpam-3831	441	25	for	for	ADP
ejpam-3831	441	26	p	p	NOUN
ejpam-3831	441	27	=	=	SYM
ejpam-3831	441	28	3	3	NUM
ejpam-3831	441	29	)	)	PUNCT
ejpam-3831	441	30	≤	≤	NOUN
ejpam-3831	441	31	16	16	NUM
ejpam-3831	441	32	max{8(a)3	max{8(a)3	ADJ
ejpam-3831	441	33	+	+	CCONJ
ejpam-3831	441	34	(	(	PUNCT
ejpam-3831	441	35	b)3	b)3	PROPN
ejpam-3831	441	36	(	(	PUNCT
ejpam-3831	441	37	160)3	160)3	NUM
ejpam-3831	441	38	,	,	PUNCT
ejpam-3831	441	39	(	(	PUNCT
ejpam-3831	441	40	u)3	u)3	ADJ
ejpam-3831	441	41	+	+	NUM
ejpam-3831	441	42	27(v)3	27(v)3	PROPN
ejpam-3831	441	43	(	(	PUNCT
ejpam-3831	441	44	170)3	170)3	NUM
ejpam-3831	441	45	,	,	PUNCT
ejpam-3831	441	46	64(x)3	64(x)3	VERB
ejpam-3831	441	47	+	+	X
ejpam-3831	441	48	125(y)3	125(y)3	NUM
ejpam-3831	441	49	(	(	PUNCT
ejpam-3831	441	50	180)3	180)3	PRON
ejpam-3831	441	51	}	}	PUNCT
ejpam-3831	441	52	≤	≤	NUM
ejpam-3831	441	53	16	16	NUM
ejpam-3831	441	54	(	(	PUNCT
ejpam-3831	441	55	160)3	160)3	NUM
ejpam-3831	441	56	max{8(a)3	max{8(a)3	ADJ
ejpam-3831	441	57	+	+	CCONJ
ejpam-3831	441	58	(	(	PUNCT
ejpam-3831	441	59	b)3	b)3	PROPN
ejpam-3831	441	60	,	,	PUNCT
ejpam-3831	441	61	(	(	PUNCT
ejpam-3831	441	62	u)3	u)3	PROPN
ejpam-3831	441	63	+	+	CCONJ
ejpam-3831	441	64	27(v)3	27(v)3	NUM
ejpam-3831	441	65	,	,	PUNCT
ejpam-3831	441	66	64(x)3	64(x)3	NOUN
ejpam-3831	441	67	+	+	CCONJ
ejpam-3831	441	68	125(y)3	125(y)3	NUM
ejpam-3831	441	69	}	}	PUNCT
ejpam-3831	441	70	≤	≤	NUM
ejpam-3831	441	71	16	16	NUM
ejpam-3831	441	72	(	(	PUNCT
ejpam-3831	441	73	160)3	160)3	NUM
ejpam-3831	441	74	max{125(a)3	max{125(a)3	PUNCT
ejpam-3831	442	1	+	+	SYM
ejpam-3831	443	1	125(b)3	125(b)3	NUM
ejpam-3831	443	2	,	,	PUNCT
ejpam-3831	443	3	125(u)3	125(u)3	NUM
ejpam-3831	443	4	+	+	SYM
ejpam-3831	443	5	125(v)3	125(v)3	NUM
ejpam-3831	443	6	,	,	PUNCT
ejpam-3831	443	7	125(x)3	125(x)3	NUM
ejpam-3831	443	8	+	+	CCONJ
ejpam-3831	443	9	125(y)3	125(y)3	NUM
ejpam-3831	443	10	}	}	PUNCT
ejpam-3831	443	11	≤	≤	NOUN
ejpam-3831	443	12	2000	2000	NUM
ejpam-3831	443	13	(	(	PUNCT
ejpam-3831	443	14	160)3	160)3	NUM
ejpam-3831	443	15	(	(	PUNCT
ejpam-3831	443	16	max{a3	max{a3	NOUN
ejpam-3831	443	17	,	,	PUNCT
ejpam-3831	443	18	u3	u3	NOUN
ejpam-3831	443	19	,	,	PUNCT
ejpam-3831	443	20	x3}+	x3}+	PROPN
ejpam-3831	443	21	max{b3	max{b3	NUM
ejpam-3831	443	22	,	,	PUNCT
ejpam-3831	443	23	v3	v3	PROPN
ejpam-3831	443	24	,	,	PUNCT
ejpam-3831	443	25	y3	y3	NOUN
ejpam-3831	443	26	}	}	PUNCT
ejpam-3831	443	27	)	)	PUNCT
ejpam-3831	444	1	=	=	SYM
ejpam-3831	444	2	4000	4000	NUM
ejpam-3831	444	3	(	(	PUNCT
ejpam-3831	444	4	160)3	160)3	NUM
ejpam-3831	444	5	max{a3	max{a3	NOUN
ejpam-3831	444	6	,	,	PUNCT
ejpam-3831	444	7	u3	u3	NOUN
ejpam-3831	444	8	,	,	PUNCT
ejpam-3831	444	9	x3}+	x3}+	PROPN
ejpam-3831	444	10	max{b3	max{b3	NUM
ejpam-3831	444	11	,	,	PUNCT
ejpam-3831	444	12	v3	v3	PROPN
ejpam-3831	444	13	,	,	PUNCT
ejpam-3831	444	14	y3	y3	NOUN
ejpam-3831	444	15	}	}	PUNCT
ejpam-3831	444	16	2	2	NUM
ejpam-3831	444	17	=	=	SYM
ejpam-3831	444	18	4000	4000	NUM
ejpam-3831	444	19	(	(	PUNCT
ejpam-3831	444	20	160)3	160)3	NUM
ejpam-3831	444	21	(	(	PUNCT
ejpam-3831	444	22	max{a	max{a	PROPN
ejpam-3831	444	23	,	,	PUNCT
ejpam-3831	444	24	u	u	NOUN
ejpam-3831	444	25	,	,	PUNCT
ejpam-3831	444	26	x})3	x})3	PUNCT
ejpam-3831	444	27	+	+	CCONJ
ejpam-3831	444	28	(	(	PUNCT
ejpam-3831	444	29	max{b	max{b	PROPN
ejpam-3831	444	30	,	,	PUNCT
ejpam-3831	444	31	v	v	NOUN
ejpam-3831	444	32	,	,	PUNCT
ejpam-3831	444	33	y})3	y})3	NOUN
ejpam-3831	444	34	2	2	NUM
ejpam-3831	444	35	=	=	SYM
ejpam-3831	444	36	1	1	NUM
ejpam-3831	444	37	1024	1024	NUM
ejpam-3831	444	38	gb(a	gb(a	NOUN
ejpam-3831	444	39	,	,	PUNCT
ejpam-3831	444	40	u	u	NOUN
ejpam-3831	444	41	,	,	PUNCT
ejpam-3831	444	42	x	x	X
ejpam-3831	444	43	)	)	PUNCT
ejpam-3831	444	44	+	+	ADJ
ejpam-3831	444	45	gb(b	gb(b	NOUN
ejpam-3831	444	46	,	,	PUNCT
ejpam-3831	444	47	v	v	NOUN
ejpam-3831	444	48	,	,	PUNCT
ejpam-3831	444	49	y	y	NOUN
ejpam-3831	444	50	)	)	PUNCT
ejpam-3831	444	51	2	2	NUM
ejpam-3831	444	52	≤	≤	NOUN
ejpam-3831	444	53	n	n	CCONJ
ejpam-3831	444	54	(	(	PUNCT
ejpam-3831	444	55	a	a	PRON
ejpam-3831	444	56	,	,	PUNCT
ejpam-3831	444	57	b	b	PROPN
ejpam-3831	444	58	,	,	PUNCT
ejpam-3831	444	59	u	u	NOUN
ejpam-3831	444	60	,	,	PUNCT
ejpam-3831	444	61	v	v	NOUN
ejpam-3831	444	62	,	,	PUNCT
ejpam-3831	444	63	x	x	NOUN
ejpam-3831	444	64	,	,	PUNCT
ejpam-3831	444	65	y	y	PROPN
ejpam-3831	444	66	)	)	PUNCT
ejpam-3831	444	67	,	,	PUNCT
ejpam-3831	444	68	where	where	SCONJ
ejpam-3831	444	69	α1(x	α1(x	PROPN
ejpam-3831	444	70	,	,	PUNCT
ejpam-3831	444	71	y	y	NOUN
ejpam-3831	444	72	)	)	PUNCT
ejpam-3831	444	73	=	=	SYM
ejpam-3831	444	74	1	1	NUM
ejpam-3831	444	75	1024	1024	NUM
ejpam-3831	444	76	and	and	CCONJ
ejpam-3831	444	77	αi(x	αi(x	NUM
ejpam-3831	444	78	,	,	PUNCT
ejpam-3831	444	79	y	y	NOUN
ejpam-3831	444	80	)	)	PUNCT
ejpam-3831	444	81	=	=	SYM
ejpam-3831	444	82	1	1	NUM
ejpam-3831	444	83	(	(	PUNCT
ejpam-3831	444	84	1024)2i−1	1024)2i−1	NUM
ejpam-3831	444	85	for	for	ADP
ejpam-3831	444	86	i	i	PRON
ejpam-3831	444	87	=	=	SYM
ejpam-3831	444	88	2	2	NUM
ejpam-3831	444	89	,	,	PUNCT
ejpam-3831	444	90	3	3	NUM
ejpam-3831	444	91	,	,	PUNCT
ejpam-3831	444	92	·	·	PUNCT
ejpam-3831	444	93	·	·	PUNCT
ejpam-3831	444	94	·	·	PUNCT
ejpam-3831	444	95	,	,	PUNCT
ejpam-3831	444	96	12	12	NUM
ejpam-3831	444	97	.	.	PUNCT
ejpam-3831	444	98	note	note	VERB
ejpam-3831	444	99	that	that	SCONJ
ejpam-3831	444	100	for	for	ADP
ejpam-3831	444	101	s	s	NOUN
ejpam-3831	444	102	=	=	SYM
ejpam-3831	444	103	3	3	NUM
ejpam-3831	444	104	we	we	PRON
ejpam-3831	444	105	have	have	VERB
ejpam-3831	444	106	s[α1(x	s[α1(x	NOUN
ejpam-3831	444	107	,	,	PUNCT
ejpam-3831	444	108	y)+α4(x	y)+α4(x	PROPN
ejpam-3831	444	109	,	,	PUNCT
ejpam-3831	444	110	y)+α5(x	y)+α5(x	NOUN
ejpam-3831	444	111	,	,	PUNCT
ejpam-3831	444	112	y)+α10(x	y)+α10(x	NOUN
ejpam-3831	444	113	,	,	PUNCT
ejpam-3831	444	114	y)+α12(x	y)+α12(x	PROPN
ejpam-3831	444	115	,	,	PUNCT
ejpam-3831	444	116	y)]+[α2(x	y)]+[α2(x	NOUN
ejpam-3831	444	117	,	,	PUNCT
ejpam-3831	444	118	y)+α3(x	y)+α3(x	PROPN
ejpam-3831	444	119	,	,	PUNCT
ejpam-3831	444	120	y)+	y)+	NOUN
ejpam-3831	444	121	11∑	11∑	NOUN
ejpam-3831	444	122	i=6	i=6	PROPN
ejpam-3831	444	123	αi(x	αi(x	NUM
ejpam-3831	444	124	,	,	PUNCT
ejpam-3831	444	125	y	y	PROPN
ejpam-3831	444	126	)	)	PUNCT
ejpam-3831	444	127	]	]	PUNCT
ejpam-3831	445	1	<	<	X
ejpam-3831	445	2	1	1	X
ejpam-3831	445	3	.	.	PUNCT
ejpam-3831	446	1	moreover	moreover	ADV
ejpam-3831	446	2	,	,	PUNCT
ejpam-3831	446	3	it	it	PRON
ejpam-3831	446	4	is	be	AUX
ejpam-3831	446	5	clear	clear	ADJ
ejpam-3831	446	6	that	that	SCONJ
ejpam-3831	446	7	the	the	DET
ejpam-3831	446	8	conditions	condition	NOUN
ejpam-3831	446	9	(	(	PUNCT
ejpam-3831	446	10	i	i	NOUN
ejpam-3831	446	11	)	)	PUNCT
ejpam-3831	446	12	,	,	PUNCT
ejpam-3831	446	13	(	(	PUNCT
ejpam-3831	446	14	ii	ii	NOUN
ejpam-3831	446	15	)	)	PUNCT
ejpam-3831	446	16	and	and	CCONJ
ejpam-3831	446	17	(	(	PUNCT
ejpam-3831	446	18	iii	iii	NOUN
ejpam-3831	446	19	)	)	PUNCT
ejpam-3831	446	20	of	of	ADP
ejpam-3831	446	21	theorem	theorem	ADJ
ejpam-3831	446	22	1	1	NUM
ejpam-3831	446	23	are	be	AUX
ejpam-3831	446	24	satisfied	satisfied	ADJ
ejpam-3831	446	25	.	.	PUNCT
ejpam-3831	447	1	hence	hence	ADV
ejpam-3831	447	2	,	,	PUNCT
ejpam-3831	447	3	f	f	X
ejpam-3831	447	4	,	,	PUNCT
ejpam-3831	447	5	h	h	PROPN
ejpam-3831	447	6	,	,	PUNCT
ejpam-3831	447	7	t	t	PROPN
ejpam-3831	447	8	satisfy	satisfy	VERB
ejpam-3831	447	9	all	all	DET
ejpam-3831	447	10	conditions	condition	NOUN
ejpam-3831	447	11	of	of	ADP
ejpam-3831	447	12	theorem	theorem	NOUN
ejpam-3831	447	13	1	1	NUM
ejpam-3831	447	14	,	,	PUNCT
ejpam-3831	447	15	and	and	CCONJ
ejpam-3831	447	16	(	(	PUNCT
ejpam-3831	447	17	x	x	X
ejpam-3831	447	18	,	,	PUNCT
ejpam-3831	447	19	y	y	NOUN
ejpam-3831	447	20	)	)	PUNCT
ejpam-3831	447	21	=	=	SYM
ejpam-3831	447	22	(	(	PUNCT
ejpam-3831	447	23	0	0	NUM
ejpam-3831	447	24	,	,	PUNCT
ejpam-3831	447	25	0	0	NUM
ejpam-3831	447	26	)	)	PUNCT
ejpam-3831	447	27	is	be	AUX
ejpam-3831	447	28	the	the	DET
ejpam-3831	447	29	unique	unique	ADJ
ejpam-3831	447	30	common	common	ADJ
ejpam-3831	447	31	coupled	couple	VERB
ejpam-3831	447	32	fixed	fix	VERB
ejpam-3831	447	33	point	point	NOUN
ejpam-3831	447	34	of	of	ADP
ejpam-3831	447	35	f	f	PROPN
ejpam-3831	447	36	,	,	PUNCT
ejpam-3831	447	37	h	h	NOUN
ejpam-3831	447	38	and	and	CCONJ
ejpam-3831	447	39	t	t	PROPN
ejpam-3831	447	40	.	.	PUNCT
ejpam-3831	448	1	3	3	X
ejpam-3831	448	2	.	.	X
ejpam-3831	448	3	application	application	NOUN
ejpam-3831	448	4	let	let	VERB
ejpam-3831	448	5	x	x	PUNCT
ejpam-3831	448	6	=	=	PRON
ejpam-3831	448	7	(	(	PUNCT
ejpam-3831	448	8	c[a	c[a	NUM
ejpam-3831	448	9	,	,	PUNCT
ejpam-3831	448	10	b],r	b],r	NOUN
ejpam-3831	448	11	)	)	PUNCT
ejpam-3831	448	12	denote	denote	VERB
ejpam-3831	448	13	the	the	DET
ejpam-3831	448	14	set	set	NOUN
ejpam-3831	448	15	of	of	ADP
ejpam-3831	448	16	all	all	DET
ejpam-3831	448	17	continuous	continuous	ADJ
ejpam-3831	448	18	functions	function	NOUN
ejpam-3831	448	19	from	from	ADP
ejpam-3831	448	20	[	[	X
ejpam-3831	448	21	a	a	PRON
ejpam-3831	448	22	,	,	PUNCT
ejpam-3831	448	23	b	b	NOUN
ejpam-3831	448	24	]	]	X
ejpam-3831	448	25	to	to	PART
ejpam-3831	448	26	r.	r.	VERB
ejpam-3831	448	27	in	in	ADP
ejpam-3831	448	28	this	this	DET
ejpam-3831	448	29	section	section	NOUN
ejpam-3831	448	30	,	,	PUNCT
ejpam-3831	448	31	we	we	PRON
ejpam-3831	448	32	will	will	AUX
ejpam-3831	448	33	use	use	VERB
ejpam-3831	448	34	corollary	corollary	ADJ
ejpam-3831	448	35	2	2	NUM
ejpam-3831	448	36	to	to	PART
ejpam-3831	448	37	show	show	VERB
ejpam-3831	448	38	that	that	SCONJ
ejpam-3831	448	39	there	there	PRON
ejpam-3831	448	40	is	be	VERB
ejpam-3831	448	41	a	a	DET
ejpam-3831	448	42	solution	solution	NOUN
ejpam-3831	448	43	to	to	ADP
ejpam-3831	448	44	the	the	DET
ejpam-3831	448	45	following	follow	VERB
ejpam-3831	448	46	integral	integral	ADJ
ejpam-3831	448	47	equation	equation	NOUN
ejpam-3831	448	48	:	:	PUNCT
ejpam-3831	448	49	u(t	u(t	NOUN
ejpam-3831	448	50	)	)	PUNCT
ejpam-3831	448	51	=	=	SYM
ejpam-3831	449	1	∫	∫	PROPN
ejpam-3831	449	2	b	b	PROPN
ejpam-3831	449	3	a	a	DET
ejpam-3831	449	4	h(t	h(t	PROPN
ejpam-3831	449	5	,	,	PUNCT
ejpam-3831	449	6	κ)f(κ	κ)f(κ	ADJ
ejpam-3831	449	7	,	,	PUNCT
ejpam-3831	449	8	u(κ))dκ	u(κ))dκ	PROPN
ejpam-3831	449	9	;	;	PUNCT
ejpam-3831	449	10	t	t	PROPN
ejpam-3831	449	11	∈	∈	PROPN
ejpam-3831	450	1	[	[	X
ejpam-3831	450	2	a	a	X
ejpam-3831	450	3	,	,	PUNCT
ejpam-3831	450	4	b	b	NOUN
ejpam-3831	450	5	]	]	X
ejpam-3831	450	6	,	,	PUNCT
ejpam-3831	450	7	(	(	PUNCT
ejpam-3831	450	8	15	15	NUM
ejpam-3831	450	9	)	)	PUNCT
ejpam-3831	450	10	where	where	SCONJ
ejpam-3831	450	11	u(κ	u(κ	NOUN
ejpam-3831	450	12	)	)	PUNCT
ejpam-3831	450	13	∈	∈	PROPN
ejpam-3831	450	14	x.	x.	NOUN
ejpam-3831	450	15	theorem	theorem	VERB
ejpam-3831	450	16	2	2	NUM
ejpam-3831	450	17	.	.	X
ejpam-3831	450	18	consider	consider	VERB
ejpam-3831	450	19	equation	equation	NOUN
ejpam-3831	450	20	(	(	PUNCT
ejpam-3831	450	21	15	15	NUM
ejpam-3831	450	22	)	)	PUNCT
ejpam-3831	450	23	and	and	CCONJ
ejpam-3831	450	24	suppose	suppose	VERB
ejpam-3831	450	25	:	:	PUNCT
ejpam-3831	450	26	(	(	PUNCT
ejpam-3831	450	27	i	i	NOUN
ejpam-3831	450	28	)	)	PUNCT
ejpam-3831	450	29	h	h	NOUN
ejpam-3831	450	30	:	:	PUNCT
ejpam-3831	451	1	[	[	X
ejpam-3831	451	2	a	a	X
ejpam-3831	451	3	,	,	PUNCT
ejpam-3831	451	4	b]×	b]×	NOUN
ejpam-3831	451	5	[	[	X
ejpam-3831	451	6	a	a	X
ejpam-3831	451	7	,	,	PUNCT
ejpam-3831	451	8	b]→	b]→	NOUN
ejpam-3831	452	1	[	[	X
ejpam-3831	452	2	0,∞	0,∞	NUM
ejpam-3831	452	3	)	)	PUNCT
ejpam-3831	452	4	is	be	AUX
ejpam-3831	452	5	a	a	DET
ejpam-3831	452	6	continuous	continuous	ADJ
ejpam-3831	452	7	function	function	NOUN
ejpam-3831	452	8	,	,	PUNCT
ejpam-3831	452	9	(	(	PUNCT
ejpam-3831	452	10	ii	ii	NOUN
ejpam-3831	452	11	)	)	PUNCT
ejpam-3831	452	12	f	f	NOUN
ejpam-3831	452	13	:	:	PUNCT
ejpam-3831	453	1	[	[	X
ejpam-3831	453	2	a	a	X
ejpam-3831	453	3	,	,	PUNCT
ejpam-3831	453	4	b]×r→	b]×r→	X
ejpam-3831	453	5	r	r	NOUN
ejpam-3831	453	6	,	,	PUNCT
ejpam-3831	453	7	is	be	AUX
ejpam-3831	453	8	continuous	continuous	ADJ
ejpam-3831	453	9	,	,	PUNCT
ejpam-3831	453	10	(	(	PUNCT
ejpam-3831	453	11	iii	iii	NOUN
ejpam-3831	453	12	)	)	PUNCT
ejpam-3831	453	13	maxt	maxt	NOUN
ejpam-3831	453	14	,	,	PUNCT
ejpam-3831	453	15	κ∈[a	κ∈[a	NOUN
ejpam-3831	453	16	,	,	PUNCT
ejpam-3831	453	17	b]h(t	b]h(t	ADJ
ejpam-3831	453	18	,	,	PUNCT
ejpam-3831	453	19	κ	κ	NOUN
ejpam-3831	453	20	)	)	PUNCT
ejpam-3831	453	21	<	<	X
ejpam-3831	453	22	α	α	PROPN
ejpam-3831	453	23	=	=	SYM
ejpam-3831	453	24	α1	α1	PROPN
ejpam-3831	453	25	4(b−a	4(b−a	NOUN
ejpam-3831	453	26	)	)	PUNCT
ejpam-3831	453	27	,	,	PUNCT
ejpam-3831	454	1	where	where	SCONJ
ejpam-3831	454	2	α1	α1	PROPN
ejpam-3831	454	3	=	=	SYM
ejpam-3831	454	4	1	1	NUM
ejpam-3831	454	5	30	30	NUM
ejpam-3831	454	6	,	,	PUNCT
ejpam-3831	454	7	m.m.m	m.m.m	NOUN
ejpam-3831	454	8	.	.	PUNCT
ejpam-3831	454	9	jaradat	jaradat	PROPN
ejpam-3831	454	10	et	et	PROPN
ejpam-3831	454	11	al	al	PROPN
ejpam-3831	454	12	.	.	PUNCT
ejpam-3831	454	13	/	/	SYM
ejpam-3831	454	14	eur	eur	PROPN
ejpam-3831	454	15	.	.	PUNCT
ejpam-3831	455	1	j.	j.	PROPN
ejpam-3831	455	2	pure	pure	PROPN
ejpam-3831	455	3	appl	appl	PROPN
ejpam-3831	455	4	.	.	PROPN
ejpam-3831	455	5	math	math	PROPN
ejpam-3831	455	6	,	,	PUNCT
ejpam-3831	455	7	13	13	NUM
ejpam-3831	455	8	(	(	PUNCT
ejpam-3831	455	9	4	4	NUM
ejpam-3831	455	10	)	)	PUNCT
ejpam-3831	455	11	(	(	PUNCT
ejpam-3831	455	12	2020	2020	NUM
ejpam-3831	455	13	)	)	PUNCT
ejpam-3831	455	14	,	,	PUNCT
ejpam-3831	455	15	995	995	NUM
ejpam-3831	455	16	-	-	SYM
ejpam-3831	455	17	1015	1015	NUM
ejpam-3831	455	18	1012	1012	NUM
ejpam-3831	455	19	(	(	PUNCT
ejpam-3831	455	20	iv	iv	X
ejpam-3831	455	21	)	)	PUNCT
ejpam-3831	455	22	for	for	ADP
ejpam-3831	455	23	all	all	DET
ejpam-3831	455	24	u(κ	u(κ	NOUN
ejpam-3831	455	25	)	)	PUNCT
ejpam-3831	455	26	∈	∈	PROPN
ejpam-3831	456	1	x	x	INTJ
ejpam-3831	456	2	we	we	PRON
ejpam-3831	456	3	have	have	VERB
ejpam-3831	456	4	|f(κ	|f(κ	PROPN
ejpam-3831	456	5	,	,	PUNCT
ejpam-3831	456	6	u(κ))|	u(κ))|	PROPN
ejpam-3831	456	7	≤	≤	NOUN
ejpam-3831	456	8	(	(	PUNCT
ejpam-3831	456	9	|u(κ)|)3	|u(κ)|)3	NOUN
ejpam-3831	456	10	.	.	PUNCT
ejpam-3831	457	1	then	then	ADV
ejpam-3831	457	2	equation	equation	NOUN
ejpam-3831	457	3	(	(	PUNCT
ejpam-3831	457	4	15	15	NUM
ejpam-3831	457	5	)	)	PUNCT
ejpam-3831	457	6	has	have	VERB
ejpam-3831	457	7	a	a	DET
ejpam-3831	457	8	solution	solution	NOUN
ejpam-3831	457	9	.	.	PUNCT
ejpam-3831	458	1	proof	proof	NOUN
ejpam-3831	458	2	.	.	PUNCT
ejpam-3831	459	1	let	let	VERB
ejpam-3831	459	2	x	x	PRON
ejpam-3831	459	3	be	be	AUX
ejpam-3831	459	4	as	as	ADV
ejpam-3831	459	5	defined	define	VERB
ejpam-3831	459	6	above	above	ADV
ejpam-3831	459	7	.	.	PUNCT
ejpam-3831	460	1	define	define	VERB
ejpam-3831	460	2	a	a	DET
ejpam-3831	460	3	mapping	mapping	NOUN
ejpam-3831	460	4	t	t	NOUN
ejpam-3831	460	5	:	:	PUNCT
ejpam-3831	460	6	x	x	X
ejpam-3831	460	7	×x	×x	ADP
ejpam-3831	460	8	→	→	SYM
ejpam-3831	460	9	x	x	PUNCT
ejpam-3831	460	10	by	by	ADP
ejpam-3831	460	11	t	t	PROPN
ejpam-3831	460	12	(	(	PUNCT
ejpam-3831	460	13	u(t	u(t	PROPN
ejpam-3831	460	14	)	)	PUNCT
ejpam-3831	460	15	,	,	PUNCT
ejpam-3831	460	16	v(t	v(t	NOUN
ejpam-3831	460	17	)	)	PUNCT
ejpam-3831	460	18	)	)	PUNCT
ejpam-3831	461	1	=	=	PUNCT
ejpam-3831	462	1	∫	∫	PROPN
ejpam-3831	462	2	b	b	PROPN
ejpam-3831	462	3	a	a	DET
ejpam-3831	462	4	h(t	h(t	PROPN
ejpam-3831	462	5	,	,	PUNCT
ejpam-3831	462	6	κ)f(κ	κ)f(κ	ADJ
ejpam-3831	462	7	,	,	PUNCT
ejpam-3831	462	8	u(κ	u(κ	NOUN
ejpam-3831	462	9	)	)	PUNCT
ejpam-3831	462	10	2	2	NUM
ejpam-3831	462	11	+	+	CCONJ
ejpam-3831	462	12	v(κ	v(κ	PROPN
ejpam-3831	462	13	)	)	PUNCT
ejpam-3831	462	14	2	2	NUM
ejpam-3831	462	15	)	)	PUNCT
ejpam-3831	462	16	dκ	dκ	PROPN
ejpam-3831	462	17	;	;	PUNCT
ejpam-3831	462	18	t	t	PROPN
ejpam-3831	462	19	∈	∈	PROPN
ejpam-3831	463	1	[	[	X
ejpam-3831	463	2	a	a	X
ejpam-3831	463	3	,	,	PUNCT
ejpam-3831	463	4	b	b	NOUN
ejpam-3831	463	5	]	]	X
ejpam-3831	463	6	.	.	PUNCT
ejpam-3831	464	1	(	(	PUNCT
ejpam-3831	464	2	16	16	NUM
ejpam-3831	464	3	)	)	PUNCT
ejpam-3831	464	4	for	for	ADP
ejpam-3831	464	5	all	all	DET
ejpam-3831	464	6	u	u	NOUN
ejpam-3831	464	7	,	,	PUNCT
ejpam-3831	464	8	v	v	NOUN
ejpam-3831	464	9	,	,	PUNCT
ejpam-3831	464	10	w	w	PROPN
ejpam-3831	464	11	∈	∈	PROPN
ejpam-3831	464	12	x	x	PUNCT
ejpam-3831	464	13	define	define	VERB
ejpam-3831	464	14	the	the	DET
ejpam-3831	464	15	gb	gb	NOUN
ejpam-3831	464	16	-	-	PUNCT
ejpam-3831	464	17	metric	metric	NOUN
ejpam-3831	464	18	on	on	ADP
ejpam-3831	464	19	x	x	PUNCT
ejpam-3831	464	20	by	by	ADP
ejpam-3831	464	21	gb(u	gb(u	NUM
ejpam-3831	464	22	,	,	PUNCT
ejpam-3831	464	23	v	v	NOUN
ejpam-3831	464	24	,	,	PUNCT
ejpam-3831	464	25	w	w	NOUN
ejpam-3831	464	26	)	)	PUNCT
ejpam-3831	464	27	=	=	SYM
ejpam-3831	464	28	(	(	PUNCT
ejpam-3831	464	29	{	{	PUNCT
ejpam-3831	464	30	0	0	NUM
ejpam-3831	464	31	,	,	PUNCT
ejpam-3831	464	32	if	if	SCONJ
ejpam-3831	464	33	u	u	PROPN
ejpam-3831	464	34	=	=	SYM
ejpam-3831	464	35	v	v	PROPN
ejpam-3831	464	36	=	=	SYM
ejpam-3831	464	37	w	w	NOUN
ejpam-3831	464	38	,	,	PUNCT
ejpam-3831	464	39	max{supκ∈[a	max{supκ∈[a	NOUN
ejpam-3831	464	40	,	,	PUNCT
ejpam-3831	464	41	b	b	NOUN
ejpam-3831	464	42	]	]	X
ejpam-3831	464	43	|u|	|u|	PROPN
ejpam-3831	464	44	,	,	PUNCT
ejpam-3831	464	45	supκ∈[a	supκ∈[a	NOUN
ejpam-3831	464	46	,	,	PUNCT
ejpam-3831	464	47	b	b	NOUN
ejpam-3831	464	48	]	]	X
ejpam-3831	464	49	|v|	|v|	NOUN
ejpam-3831	464	50	,	,	PUNCT
ejpam-3831	464	51	supκ∈[a	supκ∈[a	NOUN
ejpam-3831	464	52	,	,	PUNCT
ejpam-3831	464	53	b	b	NOUN
ejpam-3831	464	54	]	]	X
ejpam-3831	464	55	|w|	|w|	PROPN
ejpam-3831	464	56	}	}	PUNCT
ejpam-3831	464	57	,	,	PUNCT
ejpam-3831	464	58	otherwise	otherwise	ADV
ejpam-3831	464	59	.	.	PUNCT
ejpam-3831	465	1	}	}	PUNCT
ejpam-3831	465	2	)	)	PUNCT
ejpam-3831	465	3	3	3	NUM
ejpam-3831	465	4	(	(	PUNCT
ejpam-3831	465	5	17	17	NUM
ejpam-3831	465	6	)	)	PUNCT
ejpam-3831	465	7	clearly	clearly	ADV
ejpam-3831	465	8	that	that	SCONJ
ejpam-3831	465	9	(	(	PUNCT
ejpam-3831	465	10	x	x	NOUN
ejpam-3831	465	11	,	,	PUNCT
ejpam-3831	465	12	gb	gb	PRON
ejpam-3831	465	13	)	)	PUNCT
ejpam-3831	465	14	is	be	AUX
ejpam-3831	465	15	a	a	DET
ejpam-3831	465	16	complete	complete	ADJ
ejpam-3831	465	17	gb	gb	ADV
ejpam-3831	465	18	-	-	PUNCT
ejpam-3831	465	19	metric	metric	ADJ
ejpam-3831	465	20	space	space	NOUN
ejpam-3831	465	21	with	with	ADP
ejpam-3831	465	22	constant	constant	ADJ
ejpam-3831	465	23	(	(	PUNCT
ejpam-3831	465	24	s	s	NOUN
ejpam-3831	465	25	=	=	NOUN
ejpam-3831	465	26	4	4	NUM
ejpam-3831	465	27	)	)	PUNCT
ejpam-3831	465	28	.	.	PUNCT
ejpam-3831	466	1	now	now	ADV
ejpam-3831	466	2	,	,	PUNCT
ejpam-3831	466	3	for	for	ADP
ejpam-3831	466	4	li(κ	li(κ	NOUN
ejpam-3831	466	5	)	)	PUNCT
ejpam-3831	466	6	∈	∈	PROPN
ejpam-3831	467	1	x	x	NOUN
ejpam-3831	467	2	,	,	PUNCT
ejpam-3831	467	3	where	where	SCONJ
ejpam-3831	467	4	i	i	PRON
ejpam-3831	467	5	=	=	NOUN
ejpam-3831	467	6	1	1	NUM
ejpam-3831	467	7	,	,	PUNCT
ejpam-3831	467	8	2	2	NUM
ejpam-3831	467	9	,	,	PUNCT
ejpam-3831	467	10	3	3	NUM
ejpam-3831	467	11	,	,	PUNCT
ejpam-3831	467	12	4	4	NUM
ejpam-3831	467	13	,	,	PUNCT
ejpam-3831	467	14	5	5	NUM
ejpam-3831	467	15	,	,	PUNCT
ejpam-3831	467	16	6	6	NUM
ejpam-3831	467	17	we	we	PRON
ejpam-3831	467	18	have	have	VERB
ejpam-3831	467	19	gb(t	gb(t	NOUN
ejpam-3831	467	20	(	(	PUNCT
ejpam-3831	467	21	l1	l1	PROPN
ejpam-3831	467	22	,	,	PUNCT
ejpam-3831	467	23	l2	l2	NOUN
ejpam-3831	467	24	)	)	PUNCT
ejpam-3831	467	25	,	,	PUNCT
ejpam-3831	467	26	t	t	PROPN
ejpam-3831	467	27	(	(	PUNCT
ejpam-3831	467	28	l3	l3	PROPN
ejpam-3831	467	29	,	,	PUNCT
ejpam-3831	467	30	l4	l4	PROPN
ejpam-3831	467	31	)	)	PUNCT
ejpam-3831	467	32	,	,	PUNCT
ejpam-3831	467	33	t	t	PROPN
ejpam-3831	467	34	(	(	PUNCT
ejpam-3831	467	35	l5	l5	PROPN
ejpam-3831	467	36	,	,	PUNCT
ejpam-3831	467	37	l6	l6	NOUN
ejpam-3831	467	38	)	)	PUNCT
ejpam-3831	467	39	)	)	PUNCT
ejpam-3831	468	1	=	=	PUNCT
ejpam-3831	468	2	(	(	PUNCT
ejpam-3831	468	3	{	{	PUNCT
ejpam-3831	468	4	0	0	NUM
ejpam-3831	468	5	,	,	PUNCT
ejpam-3831	468	6	if	if	SCONJ
ejpam-3831	468	7	t	t	PROPN
ejpam-3831	468	8	(	(	PUNCT
ejpam-3831	468	9	l1	l1	PROPN
ejpam-3831	468	10	,	,	PUNCT
ejpam-3831	468	11	l2	l2	NOUN
ejpam-3831	468	12	)	)	PUNCT
ejpam-3831	469	1	=	=	SYM
ejpam-3831	469	2	t	t	PROPN
ejpam-3831	469	3	(	(	PUNCT
ejpam-3831	469	4	l3	l3	PROPN
ejpam-3831	469	5	,	,	PUNCT
ejpam-3831	469	6	l4	l4	PROPN
ejpam-3831	469	7	)	)	PUNCT
ejpam-3831	469	8	=	=	SYM
ejpam-3831	469	9	t	t	PROPN
ejpam-3831	469	10	(	(	PUNCT
ejpam-3831	469	11	l5	l5	PROPN
ejpam-3831	469	12	,	,	PUNCT
ejpam-3831	469	13	l6	l6	PROPN
ejpam-3831	469	14	)	)	PUNCT
ejpam-3831	469	15	,	,	PUNCT
ejpam-3831	469	16	max	max	PROPN
ejpam-3831	469	17	{	{	PUNCT
ejpam-3831	469	18	supκ∈[a	supκ∈[a	PROPN
ejpam-3831	469	19	,	,	PUNCT
ejpam-3831	469	20	b	b	NOUN
ejpam-3831	469	21	]	]	X
ejpam-3831	469	22	|t	|t	PROPN
ejpam-3831	469	23	(	(	PUNCT
ejpam-3831	469	24	l1	l1	PROPN
ejpam-3831	469	25	,	,	PUNCT
ejpam-3831	469	26	l2)|	l2)|	PROPN
ejpam-3831	469	27	,	,	PUNCT
ejpam-3831	469	28	supκ∈[a	supκ∈[a	NOUN
ejpam-3831	469	29	,	,	PUNCT
ejpam-3831	469	30	b	b	X
ejpam-3831	469	31	]	]	X
ejpam-3831	469	32	|t	|t	PROPN
ejpam-3831	469	33	(	(	PUNCT
ejpam-3831	469	34	l3	l3	PROPN
ejpam-3831	469	35	,	,	PUNCT
ejpam-3831	469	36	l4)|	l4)|	PROPN
ejpam-3831	469	37	,	,	PUNCT
ejpam-3831	469	38	supκ∈[a	supκ∈[a	NOUN
ejpam-3831	469	39	,	,	PUNCT
ejpam-3831	469	40	b	b	X
ejpam-3831	469	41	]	]	X
ejpam-3831	469	42	|t	|t	PROPN
ejpam-3831	469	43	(	(	PUNCT
ejpam-3831	469	44	l5	l5	PROPN
ejpam-3831	469	45	,	,	PUNCT
ejpam-3831	469	46	l6)|	l6)|	PROPN
ejpam-3831	469	47	}	}	PUNCT
ejpam-3831	469	48	,	,	PUNCT
ejpam-3831	469	49	otherwise	otherwise	ADV
ejpam-3831	469	50	.	.	PUNCT
ejpam-3831	469	51	}	}	PUNCT
ejpam-3831	469	52	)	)	PUNCT
ejpam-3831	469	53	3	3	NUM
ejpam-3831	469	54	(	(	PUNCT
ejpam-3831	469	55	18	18	NUM
ejpam-3831	469	56	)	)	PUNCT
ejpam-3831	469	57	now	now	ADV
ejpam-3831	469	58	,	,	PUNCT
ejpam-3831	469	59	sup	sup	NOUN
ejpam-3831	469	60	κ∈[a	κ∈[a	NOUN
ejpam-3831	469	61	,	,	PUNCT
ejpam-3831	469	62	b	b	NOUN
ejpam-3831	469	63	]	]	X
ejpam-3831	469	64	|t	|t	PROPN
ejpam-3831	469	65	(	(	PUNCT
ejpam-3831	469	66	l1	l1	PROPN
ejpam-3831	469	67	,	,	PUNCT
ejpam-3831	469	68	l2)|	l2)|	PROPN
ejpam-3831	469	69	=	=	SYM
ejpam-3831	469	70	sup	sup	NOUN
ejpam-3831	469	71	κ∈[a	κ∈[a	NOUN
ejpam-3831	469	72	,	,	PUNCT
ejpam-3831	469	73	b	b	NOUN
ejpam-3831	469	74	]	]	X
ejpam-3831	470	1	|	|	ADV
ejpam-3831	470	2	∫	∫	PROPN
ejpam-3831	470	3	b	b	PROPN
ejpam-3831	470	4	a	a	DET
ejpam-3831	470	5	h(t	h(t	PROPN
ejpam-3831	470	6	,	,	PUNCT
ejpam-3831	470	7	κ)f(κ	κ)f(κ	ADJ
ejpam-3831	470	8	,	,	PUNCT
ejpam-3831	470	9	l1(κ	l1(κ	NOUN
ejpam-3831	470	10	)	)	PUNCT
ejpam-3831	470	11	2	2	NUM
ejpam-3831	470	12	+	+	SYM
ejpam-3831	470	13	l2(κ	l2(κ	PROPN
ejpam-3831	470	14	)	)	PUNCT
ejpam-3831	470	15	2	2	NUM
ejpam-3831	470	16	)	)	PUNCT
ejpam-3831	471	1	dκ|	dκ|	NOUN
ejpam-3831	471	2	(	(	PUNCT
ejpam-3831	471	3	19	19	NUM
ejpam-3831	471	4	)	)	PUNCT
ejpam-3831	471	5	≤	≤	NUM
ejpam-3831	471	6	sup	sup	NOUN
ejpam-3831	471	7	κ∈[a	κ∈[a	NOUN
ejpam-3831	471	8	,	,	PUNCT
ejpam-3831	471	9	b	b	NOUN
ejpam-3831	471	10	]	]	X
ejpam-3831	471	11	∫	∫	PROPN
ejpam-3831	471	12	b	b	PROPN
ejpam-3831	471	13	a	a	DET
ejpam-3831	471	14	|h(t	|h(t	PROPN
ejpam-3831	471	15	,	,	PUNCT
ejpam-3831	471	16	κ)||f(κ	κ)||f(κ	NOUN
ejpam-3831	471	17	,	,	PUNCT
ejpam-3831	471	18	l1(κ	l1(κ	NOUN
ejpam-3831	471	19	)	)	PUNCT
ejpam-3831	471	20	2	2	NUM
ejpam-3831	471	21	+	+	SYM
ejpam-3831	471	22	l2(κ	l2(κ	PROPN
ejpam-3831	471	23	)	)	PUNCT
ejpam-3831	471	24	2	2	NUM
ejpam-3831	471	25	)	)	PUNCT
ejpam-3831	471	26	|dκ	|dκ	VERB
ejpam-3831	471	27	≤	≤	NUM
ejpam-3831	471	28	sup	sup	NOUN
ejpam-3831	471	29	κ∈[a	κ∈[a	NOUN
ejpam-3831	471	30	,	,	PUNCT
ejpam-3831	471	31	b	b	NOUN
ejpam-3831	471	32	]	]	X
ejpam-3831	471	33	∫	∫	PROPN
ejpam-3831	471	34	b	b	PROPN
ejpam-3831	471	35	a	a	DET
ejpam-3831	471	36	α|f(κ	α|f(κ	PROPN
ejpam-3831	471	37	,	,	PUNCT
ejpam-3831	471	38	l1(κ	l1(κ	NOUN
ejpam-3831	471	39	)	)	PUNCT
ejpam-3831	471	40	2	2	NUM
ejpam-3831	471	41	+	+	SYM
ejpam-3831	471	42	l2(κ	l2(κ	PROPN
ejpam-3831	471	43	)	)	PUNCT
ejpam-3831	471	44	2	2	NUM
ejpam-3831	471	45	)	)	PUNCT
ejpam-3831	471	46	|dκ	|dκ	VERB
ejpam-3831	471	47	≤	≤	NUM
ejpam-3831	471	48	sup	sup	NOUN
ejpam-3831	471	49	κ∈[a	κ∈[a	NOUN
ejpam-3831	471	50	,	,	PUNCT
ejpam-3831	471	51	b	b	NOUN
ejpam-3831	471	52	]	]	X
ejpam-3831	471	53	∫	∫	PROPN
ejpam-3831	471	54	b	b	PROPN
ejpam-3831	471	55	a	a	DET
ejpam-3831	471	56	α(|	α(|	PROPN
ejpam-3831	471	57	l1(κ	l1(κ	NOUN
ejpam-3831	471	58	)	)	PUNCT
ejpam-3831	471	59	2	2	NUM
ejpam-3831	471	60	|+	|+	NOUN
ejpam-3831	471	61	|	|	NOUN
ejpam-3831	471	62	l2(κ	l2(κ	PROPN
ejpam-3831	471	63	)	)	PUNCT
ejpam-3831	471	64	2	2	NUM
ejpam-3831	471	65	|)3dκ	|)3dκ	NOUN
ejpam-3831	471	66	(	(	PUNCT
ejpam-3831	471	67	by	by	ADP
ejpam-3831	471	68	using	use	VERB
ejpam-3831	471	69	(	(	PUNCT
ejpam-3831	471	70	14	14	NUM
ejpam-3831	471	71	)	)	PUNCT
ejpam-3831	471	72	for	for	ADP
ejpam-3831	471	73	p	p	NOUN
ejpam-3831	471	74	=	=	SYM
ejpam-3831	471	75	3	3	NUM
ejpam-3831	471	76	)	)	PUNCT
ejpam-3831	471	77	≤	≤	NUM
ejpam-3831	471	78	sup	sup	NOUN
ejpam-3831	471	79	κ∈[a	κ∈[a	NOUN
ejpam-3831	471	80	,	,	PUNCT
ejpam-3831	471	81	b	b	NOUN
ejpam-3831	471	82	]	]	X
ejpam-3831	471	83	∫	∫	PROPN
ejpam-3831	471	84	b	b	PROPN
ejpam-3831	471	85	a	a	DET
ejpam-3831	471	86	16α	16α	NUM
ejpam-3831	471	87	[	[	PUNCT
ejpam-3831	471	88	(	(	PUNCT
ejpam-3831	471	89	|	|	ADV
ejpam-3831	471	90	l1(κ	l1(κ	NOUN
ejpam-3831	471	91	)	)	PUNCT
ejpam-3831	471	92	2	2	NUM
ejpam-3831	472	1	|)3	|)3	PRON
ejpam-3831	472	2	+	+	CCONJ
ejpam-3831	472	3	(	(	PUNCT
ejpam-3831	472	4	|	|	NOUN
ejpam-3831	472	5	l2(κ	l2(κ	PROPN
ejpam-3831	472	6	)	)	PUNCT
ejpam-3831	472	7	2	2	NUM
ejpam-3831	473	1	|)3	|)3	X
ejpam-3831	473	2	]	]	PUNCT
ejpam-3831	473	3	dκ	dκ	ADP
ejpam-3831	473	4	≤	≤	NUM
ejpam-3831	473	5	sup	sup	NOUN
ejpam-3831	473	6	κ∈[a	κ∈[a	NOUN
ejpam-3831	473	7	,	,	PUNCT
ejpam-3831	473	8	b	b	NOUN
ejpam-3831	473	9	]	]	X
ejpam-3831	473	10	∫	∫	PROPN
ejpam-3831	473	11	b	b	PROPN
ejpam-3831	473	12	a	a	DET
ejpam-3831	473	13	2α	2α	NOUN
ejpam-3831	473	14	[	[	PUNCT
ejpam-3831	473	15	(	(	PUNCT
ejpam-3831	473	16	|l1(κ)|)3	|l1(κ)|)3	X
ejpam-3831	473	17	+	+	X
ejpam-3831	473	18	(	(	PUNCT
ejpam-3831	473	19	|l2(κ)|)3	|l2(κ)|)3	X
ejpam-3831	473	20	]	]	PUNCT
ejpam-3831	473	21	dκ	dκ	ADP
ejpam-3831	473	22	≤	≤	PROPN
ejpam-3831	473	23	∫	∫	PROPN
ejpam-3831	473	24	b	b	PROPN
ejpam-3831	473	25	a	a	DET
ejpam-3831	473	26	2α	2α	PROPN
ejpam-3831	473	27	[	[	PUNCT
ejpam-3831	473	28	gb(l1	gb(l1	PROPN
ejpam-3831	473	29	,	,	PUNCT
ejpam-3831	473	30	l3	l3	PROPN
ejpam-3831	473	31	,	,	PUNCT
ejpam-3831	473	32	l3	l3	X
ejpam-3831	473	33	)	)	PUNCT
ejpam-3831	474	1	+	+	NOUN
ejpam-3831	474	2	gb(l2	gb(l2	NOUN
ejpam-3831	474	3	,	,	PUNCT
ejpam-3831	474	4	l4	l4	PROPN
ejpam-3831	474	5	,	,	PUNCT
ejpam-3831	474	6	l6	l6	PROPN
ejpam-3831	474	7	)	)	PUNCT
ejpam-3831	474	8	]	]	PUNCT
ejpam-3831	474	9	dκ	dκ	ADP
ejpam-3831	474	10	≤	≤	ADJ
ejpam-3831	474	11	2α	2α	PROPN
ejpam-3831	474	12	[	[	PUNCT
ejpam-3831	474	13	gb(l1	gb(l1	PROPN
ejpam-3831	474	14	,	,	PUNCT
ejpam-3831	474	15	l3	l3	PROPN
ejpam-3831	474	16	,	,	PUNCT
ejpam-3831	474	17	l3	l3	X
ejpam-3831	474	18	)	)	PUNCT
ejpam-3831	475	1	+	+	NOUN
ejpam-3831	475	2	gb(l2	gb(l2	NOUN
ejpam-3831	475	3	,	,	PUNCT
ejpam-3831	475	4	l4	l4	PROPN
ejpam-3831	475	5	,	,	PUNCT
ejpam-3831	475	6	l6	l6	PROPN
ejpam-3831	475	7	)	)	PUNCT
ejpam-3831	475	8	]	]	PUNCT
ejpam-3831	476	1	∫	∫	PROPN
ejpam-3831	476	2	b	b	PROPN
ejpam-3831	476	3	a	a	PRON
ejpam-3831	476	4	dκ	dκ	PROPN
ejpam-3831	476	5	m.m.m	m.m.m	PROPN
ejpam-3831	476	6	.	.	PUNCT
ejpam-3831	477	1	jaradat	jaradat	PROPN
ejpam-3831	477	2	et	et	PROPN
ejpam-3831	477	3	al	al	PROPN
ejpam-3831	477	4	.	.	PUNCT
ejpam-3831	477	5	/	/	SYM
ejpam-3831	477	6	eur	eur	PROPN
ejpam-3831	477	7	.	.	PUNCT
ejpam-3831	478	1	j.	j.	PROPN
ejpam-3831	478	2	pure	pure	PROPN
ejpam-3831	478	3	appl	appl	PROPN
ejpam-3831	478	4	.	.	PROPN
ejpam-3831	478	5	math	math	PROPN
ejpam-3831	478	6	,	,	PUNCT
ejpam-3831	478	7	13	13	NUM
ejpam-3831	478	8	(	(	PUNCT
ejpam-3831	478	9	4	4	NUM
ejpam-3831	478	10	)	)	PUNCT
ejpam-3831	478	11	(	(	PUNCT
ejpam-3831	478	12	2020	2020	NUM
ejpam-3831	478	13	)	)	PUNCT
ejpam-3831	478	14	,	,	PUNCT
ejpam-3831	478	15	995	995	NUM
ejpam-3831	478	16	-	-	SYM
ejpam-3831	478	17	1015	1015	NUM
ejpam-3831	478	18	1013	1013	NUM
ejpam-3831	478	19	=	=	SYM
ejpam-3831	479	1	2α	2α	PROPN
ejpam-3831	479	2	[	[	PUNCT
ejpam-3831	479	3	gb(l1	gb(l1	PROPN
ejpam-3831	479	4	,	,	PUNCT
ejpam-3831	479	5	l3	l3	PROPN
ejpam-3831	479	6	,	,	PUNCT
ejpam-3831	479	7	l3	l3	X
ejpam-3831	479	8	)	)	PUNCT
ejpam-3831	480	1	+	+	NOUN
ejpam-3831	480	2	gb(l2	gb(l2	NOUN
ejpam-3831	480	3	,	,	PUNCT
ejpam-3831	480	4	l4	l4	PROPN
ejpam-3831	480	5	,	,	PUNCT
ejpam-3831	480	6	l6	l6	PROPN
ejpam-3831	480	7	)	)	PUNCT
ejpam-3831	480	8	]	]	PUNCT
ejpam-3831	480	9	|b−	|b−	PROPN
ejpam-3831	480	10	a|	a|	PROPN
ejpam-3831	480	11	=	=	SYM
ejpam-3831	480	12	α1	α1	PROPN
ejpam-3831	480	13	2	2	NUM
ejpam-3831	480	14	[	[	PUNCT
ejpam-3831	480	15	gb(l1	gb(l1	PROPN
ejpam-3831	480	16	,	,	PUNCT
ejpam-3831	480	17	l3	l3	PROPN
ejpam-3831	480	18	,	,	PUNCT
ejpam-3831	480	19	l3	l3	X
ejpam-3831	480	20	)	)	PUNCT
ejpam-3831	481	1	+	+	NOUN
ejpam-3831	481	2	gb(l2	gb(l2	NOUN
ejpam-3831	481	3	,	,	PUNCT
ejpam-3831	481	4	l4	l4	PROPN
ejpam-3831	481	5	,	,	PUNCT
ejpam-3831	481	6	l6	l6	PROPN
ejpam-3831	481	7	)	)	PUNCT
ejpam-3831	481	8	]	]	PUNCT
ejpam-3831	481	9	.	.	PUNCT
ejpam-3831	482	1	similarly	similarly	ADV
ejpam-3831	482	2	,	,	PUNCT
ejpam-3831	482	3	one	one	PRON
ejpam-3831	482	4	can	can	AUX
ejpam-3831	482	5	show	show	VERB
ejpam-3831	482	6	that	that	DET
ejpam-3831	482	7	sup	sup	NOUN
ejpam-3831	482	8	κ∈[a	κ∈[a	NOUN
ejpam-3831	482	9	,	,	PUNCT
ejpam-3831	482	10	b	b	NOUN
ejpam-3831	482	11	]	]	X
ejpam-3831	482	12	|t	|t	PROPN
ejpam-3831	482	13	(	(	PUNCT
ejpam-3831	482	14	l3	l3	PROPN
ejpam-3831	482	15	,	,	PUNCT
ejpam-3831	482	16	l4)|	l4)|	PROPN
ejpam-3831	482	17	≤	≤	PROPN
ejpam-3831	482	18	α1	α1	PROPN
ejpam-3831	482	19	2	2	NUM
ejpam-3831	482	20	[	[	PUNCT
ejpam-3831	482	21	gb(l1	gb(l1	PROPN
ejpam-3831	482	22	,	,	PUNCT
ejpam-3831	482	23	l3	l3	PROPN
ejpam-3831	482	24	,	,	PUNCT
ejpam-3831	482	25	l3	l3	X
ejpam-3831	482	26	)	)	PUNCT
ejpam-3831	483	1	+	+	NOUN
ejpam-3831	483	2	gb(l2	gb(l2	NOUN
ejpam-3831	483	3	,	,	PUNCT
ejpam-3831	483	4	l4	l4	PROPN
ejpam-3831	483	5	,	,	PUNCT
ejpam-3831	483	6	l6	l6	PROPN
ejpam-3831	483	7	)	)	PUNCT
ejpam-3831	483	8	]	]	PUNCT
ejpam-3831	483	9	.	.	PUNCT
ejpam-3831	484	1	(	(	PUNCT
ejpam-3831	484	2	20	20	NUM
ejpam-3831	484	3	)	)	PUNCT
ejpam-3831	484	4	and	and	CCONJ
ejpam-3831	484	5	sup	sup	NOUN
ejpam-3831	484	6	κ∈[a	κ∈[a	NOUN
ejpam-3831	484	7	,	,	PUNCT
ejpam-3831	484	8	b	b	NOUN
ejpam-3831	484	9	]	]	X
ejpam-3831	484	10	|t	|t	PROPN
ejpam-3831	484	11	(	(	PUNCT
ejpam-3831	484	12	l5	l5	PROPN
ejpam-3831	484	13	,	,	PUNCT
ejpam-3831	484	14	l6)|	l6)|	ADJ
ejpam-3831	484	15	≤	≤	NUM
ejpam-3831	484	16	α1	α1	PROPN
ejpam-3831	484	17	2	2	NUM
ejpam-3831	484	18	[	[	PUNCT
ejpam-3831	484	19	gb(l1	gb(l1	PROPN
ejpam-3831	484	20	,	,	PUNCT
ejpam-3831	484	21	l3	l3	PROPN
ejpam-3831	484	22	,	,	PUNCT
ejpam-3831	484	23	l3	l3	X
ejpam-3831	484	24	)	)	PUNCT
ejpam-3831	485	1	+	+	NOUN
ejpam-3831	485	2	gb(l2	gb(l2	NOUN
ejpam-3831	485	3	,	,	PUNCT
ejpam-3831	485	4	l4	l4	PROPN
ejpam-3831	485	5	,	,	PUNCT
ejpam-3831	485	6	l6	l6	PROPN
ejpam-3831	485	7	)	)	PUNCT
ejpam-3831	485	8	]	]	PUNCT
ejpam-3831	485	9	.	.	PUNCT
ejpam-3831	486	1	(	(	PUNCT
ejpam-3831	486	2	21	21	NUM
ejpam-3831	486	3	)	)	PUNCT
ejpam-3831	486	4	hence	hence	ADV
ejpam-3831	486	5	,	,	PUNCT
ejpam-3831	486	6	by	by	ADP
ejpam-3831	486	7	(	(	PUNCT
ejpam-3831	486	8	19	19	NUM
ejpam-3831	486	9	)	)	PUNCT
ejpam-3831	486	10	,	,	PUNCT
ejpam-3831	486	11	(	(	PUNCT
ejpam-3831	486	12	20	20	NUM
ejpam-3831	486	13	)	)	PUNCT
ejpam-3831	486	14	and	and	CCONJ
ejpam-3831	486	15	(	(	PUNCT
ejpam-3831	486	16	21	21	NUM
ejpam-3831	486	17	)	)	PUNCT
ejpam-3831	486	18	we	we	PRON
ejpam-3831	486	19	have	have	VERB
ejpam-3831	486	20	max	max	PROPN
ejpam-3831	486	21	{	{	PUNCT
ejpam-3831	486	22	supκ∈[a	supκ∈[a	PROPN
ejpam-3831	486	23	,	,	PUNCT
ejpam-3831	486	24	b	b	NOUN
ejpam-3831	486	25	]	]	X
ejpam-3831	486	26	|t	|t	PROPN
ejpam-3831	486	27	(	(	PUNCT
ejpam-3831	486	28	l1	l1	PROPN
ejpam-3831	486	29	,	,	PUNCT
ejpam-3831	486	30	l2)|	l2)|	PROPN
ejpam-3831	486	31	,	,	PUNCT
ejpam-3831	486	32	supκ∈[a	supκ∈[a	NOUN
ejpam-3831	486	33	,	,	PUNCT
ejpam-3831	486	34	b	b	X
ejpam-3831	486	35	]	]	X
ejpam-3831	486	36	|t	|t	PROPN
ejpam-3831	486	37	(	(	PUNCT
ejpam-3831	486	38	l3	l3	PROPN
ejpam-3831	486	39	,	,	PUNCT
ejpam-3831	486	40	l4)|	l4)|	PROPN
ejpam-3831	486	41	,	,	PUNCT
ejpam-3831	486	42	supκ∈[a	supκ∈[a	NOUN
ejpam-3831	486	43	,	,	PUNCT
ejpam-3831	486	44	b	b	X
ejpam-3831	486	45	]	]	X
ejpam-3831	486	46	|t	|t	PROPN
ejpam-3831	486	47	(	(	PUNCT
ejpam-3831	486	48	l5	l5	PROPN
ejpam-3831	486	49	,	,	PUNCT
ejpam-3831	486	50	l6)|	l6)|	ADJ
ejpam-3831	486	51	}	}	PUNCT
ejpam-3831	486	52	≤	≤	NUM
ejpam-3831	486	53	α1	α1	PROPN
ejpam-3831	486	54	2	2	NUM
ejpam-3831	486	55	[	[	PUNCT
ejpam-3831	486	56	gb(l1	gb(l1	PROPN
ejpam-3831	486	57	,	,	PUNCT
ejpam-3831	486	58	l3	l3	PROPN
ejpam-3831	486	59	,	,	PUNCT
ejpam-3831	486	60	l3	l3	X
ejpam-3831	486	61	)	)	PUNCT
ejpam-3831	487	1	+	+	NOUN
ejpam-3831	487	2	gb(l2	gb(l2	NOUN
ejpam-3831	487	3	,	,	PUNCT
ejpam-3831	487	4	l4	l4	PROPN
ejpam-3831	487	5	,	,	PUNCT
ejpam-3831	487	6	l6	l6	PROPN
ejpam-3831	487	7	)	)	PUNCT
ejpam-3831	487	8	]	]	PUNCT
ejpam-3831	487	9	(	(	PUNCT
ejpam-3831	487	10	22	22	NUM
ejpam-3831	487	11	)	)	PUNCT
ejpam-3831	487	12	thus	thus	ADV
ejpam-3831	487	13	,	,	PUNCT
ejpam-3831	487	14	gb(t	gb(t	X
ejpam-3831	487	15	(	(	PUNCT
ejpam-3831	487	16	l1	l1	PROPN
ejpam-3831	487	17	,	,	PUNCT
ejpam-3831	487	18	l2	l2	NOUN
ejpam-3831	487	19	)	)	PUNCT
ejpam-3831	487	20	,	,	PUNCT
ejpam-3831	487	21	t	t	PROPN
ejpam-3831	487	22	(	(	PUNCT
ejpam-3831	487	23	l3	l3	PROPN
ejpam-3831	487	24	,	,	PUNCT
ejpam-3831	487	25	l4	l4	PROPN
ejpam-3831	487	26	)	)	PUNCT
ejpam-3831	487	27	,	,	PUNCT
ejpam-3831	487	28	t	t	PROPN
ejpam-3831	487	29	(	(	PUNCT
ejpam-3831	487	30	l5	l5	PROPN
ejpam-3831	487	31	,	,	PUNCT
ejpam-3831	487	32	l6	l6	NOUN
ejpam-3831	487	33	)	)	PUNCT
ejpam-3831	487	34	)	)	PUNCT
ejpam-3831	487	35	≤	≤	NUM
ejpam-3831	487	36	α1	α1	PROPN
ejpam-3831	487	37	2	2	NUM
ejpam-3831	487	38	[	[	PUNCT
ejpam-3831	487	39	gb(l1	gb(l1	PROPN
ejpam-3831	487	40	,	,	PUNCT
ejpam-3831	487	41	l3	l3	PROPN
ejpam-3831	487	42	,	,	PUNCT
ejpam-3831	487	43	l3	l3	X
ejpam-3831	487	44	)	)	PUNCT
ejpam-3831	488	1	+	+	NOUN
ejpam-3831	488	2	gb(l2	gb(l2	NOUN
ejpam-3831	488	3	,	,	PUNCT
ejpam-3831	488	4	l4	l4	PROPN
ejpam-3831	488	5	,	,	PUNCT
ejpam-3831	488	6	l6	l6	PROPN
ejpam-3831	488	7	)	)	PUNCT
ejpam-3831	488	8	]	]	PUNCT
ejpam-3831	488	9	(	(	PUNCT
ejpam-3831	488	10	23	23	NUM
ejpam-3831	488	11	)	)	PUNCT
ejpam-3831	488	12	therefore	therefore	ADV
ejpam-3831	488	13	,	,	PUNCT
ejpam-3831	488	14	all	all	DET
ejpam-3831	488	15	conditions	condition	NOUN
ejpam-3831	488	16	of	of	ADP
ejpam-3831	488	17	corollary	corollary	ADJ
ejpam-3831	488	18	2	2	NUM
ejpam-3831	488	19	are	be	AUX
ejpam-3831	488	20	satisfied	satisfied	ADJ
ejpam-3831	488	21	for	for	ADP
ejpam-3831	488	22	αi	αi	NOUN
ejpam-3831	488	23	=	=	SYM
ejpam-3831	488	24	1	1	NUM
ejpam-3831	488	25	30	30	NUM
ejpam-3831	488	26	for	for	ADP
ejpam-3831	488	27	i	i	PRON
ejpam-3831	488	28	=	=	NOUN
ejpam-3831	488	29	1	1	NUM
ejpam-3831	488	30	,	,	PUNCT
ejpam-3831	488	31	2	2	NUM
ejpam-3831	488	32	,	,	PUNCT
ejpam-3831	488	33	·	·	PUNCT
ejpam-3831	488	34	·	·	PUNCT
ejpam-3831	488	35	·	·	PUNCT
ejpam-3831	488	36	,	,	PUNCT
ejpam-3831	488	37	12	12	NUM
ejpam-3831	488	38	.	.	PUNCT
ejpam-3831	489	1	as	as	ADP
ejpam-3831	489	2	a	a	DET
ejpam-3831	489	3	result	result	NOUN
ejpam-3831	489	4	of	of	ADP
ejpam-3831	489	5	corollary	corollary	ADJ
ejpam-3831	489	6	2	2	NUM
ejpam-3831	489	7	the	the	DET
ejpam-3831	489	8	mapping	mapping	NOUN
ejpam-3831	489	9	t	t	PROPN
ejpam-3831	489	10	has	have	VERB
ejpam-3831	489	11	a	a	DET
ejpam-3831	489	12	unique	unique	ADJ
ejpam-3831	489	13	coupled	couple	VERB
ejpam-3831	489	14	fixed	fix	VERB
ejpam-3831	489	15	point	point	NOUN
ejpam-3831	489	16	in	in	ADP
ejpam-3831	489	17	x	x	PUNCT
ejpam-3831	489	18	which	which	PRON
ejpam-3831	489	19	is	be	AUX
ejpam-3831	489	20	a	a	DET
ejpam-3831	489	21	solution	solution	NOUN
ejpam-3831	489	22	of	of	ADP
ejpam-3831	489	23	(	(	PUNCT
ejpam-3831	489	24	15	15	NUM
ejpam-3831	489	25	)	)	PUNCT
ejpam-3831	489	26	.	.	PUNCT
ejpam-3831	490	1	the	the	DET
ejpam-3831	490	2	following	following	ADJ
ejpam-3831	490	3	example	example	NOUN
ejpam-3831	490	4	illustrate	illustrate	VERB
ejpam-3831	490	5	the	the	DET
ejpam-3831	490	6	validity	validity	NOUN
ejpam-3831	490	7	of	of	ADP
ejpam-3831	490	8	theorem	theorem	ADJ
ejpam-3831	490	9	2	2	NUM
ejpam-3831	490	10	.	.	NOUN
ejpam-3831	490	11	example	example	NOUN
ejpam-3831	491	1	2	2	NUM
ejpam-3831	491	2	.	.	PUNCT
ejpam-3831	491	3	the	the	DET
ejpam-3831	491	4	following	follow	VERB
ejpam-3831	491	5	integral	integral	ADJ
ejpam-3831	491	6	equation	equation	NOUN
ejpam-3831	491	7	has	have	VERB
ejpam-3831	491	8	a	a	DET
ejpam-3831	491	9	solution	solution	NOUN
ejpam-3831	491	10	in	in	ADP
ejpam-3831	491	11	x	x	X
ejpam-3831	491	12	=	=	SYM
ejpam-3831	491	13	(	(	PUNCT
ejpam-3831	491	14	c[0	c[0	PROPN
ejpam-3831	491	15	,	,	PUNCT
ejpam-3831	491	16	1],r	1],r	NUM
ejpam-3831	491	17	)	)	PUNCT
ejpam-3831	491	18	.	.	PUNCT
ejpam-3831	492	1	u(t	u(t	NOUN
ejpam-3831	492	2	)	)	PUNCT
ejpam-3831	493	1	=	=	PUNCT
ejpam-3831	493	2	∫	∫	PROPN
ejpam-3831	494	1	1	1	NUM
ejpam-3831	494	2	0	0	NUM
ejpam-3831	494	3	tκ	tκ	ADP
ejpam-3831	494	4	130	130	NUM
ejpam-3831	494	5	(	(	PUNCT
ejpam-3831	494	6	e−κ)(u(κ))3dκ	e−κ)(u(κ))3dκ	NUM
ejpam-3831	494	7	;	;	PUNCT
ejpam-3831	494	8	t	t	PROPN
ejpam-3831	494	9	∈	∈	PROPN
ejpam-3831	495	1	[	[	X
ejpam-3831	495	2	0	0	NUM
ejpam-3831	495	3	,	,	PUNCT
ejpam-3831	495	4	1	1	NUM
ejpam-3831	495	5	]	]	PUNCT
ejpam-3831	495	6	.	.	PUNCT
ejpam-3831	496	1	(	(	PUNCT
ejpam-3831	496	2	24	24	NUM
ejpam-3831	496	3	)	)	PUNCT
ejpam-3831	496	4	proof	proof	NOUN
ejpam-3831	496	5	.	.	PUNCT
ejpam-3831	497	1	let	let	VERB
ejpam-3831	497	2	t	t	NOUN
ejpam-3831	497	3	:	:	PUNCT
ejpam-3831	497	4	x	x	PROPN
ejpam-3831	497	5	×x	×x	ADP
ejpam-3831	497	6	→	→	SYM
ejpam-3831	497	7	x	x	PART
ejpam-3831	497	8	be	be	AUX
ejpam-3831	497	9	defined	define	VERB
ejpam-3831	497	10	as	as	ADP
ejpam-3831	497	11	t	t	PROPN
ejpam-3831	497	12	(	(	PUNCT
ejpam-3831	497	13	u(t	u(t	PROPN
ejpam-3831	497	14	)	)	PUNCT
ejpam-3831	497	15	,	,	PUNCT
ejpam-3831	497	16	v(t	v(t	NOUN
ejpam-3831	497	17	)	)	PUNCT
ejpam-3831	497	18	)	)	PUNCT
ejpam-3831	498	1	=	=	PUNCT
ejpam-3831	498	2	∫	∫	PROPN
ejpam-3831	499	1	1	1	NUM
ejpam-3831	499	2	0	0	NUM
ejpam-3831	499	3	tκ	tκ	ADP
ejpam-3831	499	4	130	130	NUM
ejpam-3831	499	5	(	(	PUNCT
ejpam-3831	499	6	u(κ	u(κ	NOUN
ejpam-3831	499	7	)	)	PUNCT
ejpam-3831	499	8	2	2	NUM
ejpam-3831	499	9	+	+	CCONJ
ejpam-3831	499	10	v(κ	v(κ	PROPN
ejpam-3831	499	11	)	)	PUNCT
ejpam-3831	499	12	2	2	NUM
ejpam-3831	499	13	)	)	PUNCT
ejpam-3831	499	14	3	3	NUM
ejpam-3831	499	15	e−κdκ	e−κdκ	NOUN
ejpam-3831	499	16	;	;	PUNCT
ejpam-3831	499	17	t	t	PROPN
ejpam-3831	499	18	∈	∈	PROPN
ejpam-3831	500	1	[	[	X
ejpam-3831	500	2	0	0	NUM
ejpam-3831	500	3	,	,	PUNCT
ejpam-3831	500	4	1	1	NUM
ejpam-3831	500	5	]	]	PUNCT
ejpam-3831	500	6	.	.	PUNCT
ejpam-3831	501	1	by	by	ADP
ejpam-3831	501	2	specifying	specify	VERB
ejpam-3831	501	3	h(t	h(t	PROPN
ejpam-3831	501	4	,	,	PUNCT
ejpam-3831	501	5	κ	κ	NOUN
ejpam-3831	501	6	)	)	PUNCT
ejpam-3831	501	7	=	=	NOUN
ejpam-3831	501	8	tκ	tκ	ADP
ejpam-3831	501	9	130	130	NUM
ejpam-3831	501	10	,	,	PUNCT
ejpam-3831	501	11	f(κ	f(κ	PROPN
ejpam-3831	501	12	,	,	PUNCT
ejpam-3831	501	13	t	t	PROPN
ejpam-3831	501	14	)	)	PUNCT
ejpam-3831	501	15	=	=	SYM
ejpam-3831	501	16	t3e−κ	t3e−κ	NOUN
ejpam-3831	501	17	in	in	ADP
ejpam-3831	501	18	theorem	theorem	NOUN
ejpam-3831	501	19	2	2	NUM
ejpam-3831	501	20	we	we	PRON
ejpam-3831	501	21	get	get	VERB
ejpam-3831	501	22	that	that	PRON
ejpam-3831	501	23	:	:	PUNCT
ejpam-3831	501	24	(	(	PUNCT
ejpam-3831	501	25	i	i	NOUN
ejpam-3831	501	26	)	)	PUNCT
ejpam-3831	501	27	the	the	DET
ejpam-3831	501	28	function	function	NOUN
ejpam-3831	501	29	h(t	h(t	PROPN
ejpam-3831	501	30	,	,	PUNCT
ejpam-3831	501	31	κ	κ	NOUN
ejpam-3831	501	32	)	)	PUNCT
ejpam-3831	501	33	is	be	AUX
ejpam-3831	501	34	continuous	continuous	ADJ
ejpam-3831	501	35	on	on	ADP
ejpam-3831	501	36	[	[	X
ejpam-3831	501	37	0	0	NUM
ejpam-3831	501	38	,	,	PUNCT
ejpam-3831	501	39	1]×	1]×	NUM
ejpam-3831	501	40	[	[	X
ejpam-3831	501	41	0	0	NUM
ejpam-3831	501	42	,	,	PUNCT
ejpam-3831	501	43	1	1	NUM
ejpam-3831	501	44	]	]	NUM
ejpam-3831	501	45	,	,	PUNCT
ejpam-3831	501	46	(	(	PUNCT
ejpam-3831	501	47	ii	ii	NOUN
ejpam-3831	501	48	)	)	PUNCT
ejpam-3831	501	49	f(κ	f(κ	PROPN
ejpam-3831	501	50	,	,	PUNCT
ejpam-3831	501	51	t	t	PROPN
ejpam-3831	501	52	)	)	PUNCT
ejpam-3831	501	53	=	=	SYM
ejpam-3831	502	1	t3e−κ	t3e−κ	NOUN
ejpam-3831	502	2	is	be	AUX
ejpam-3831	502	3	continuous	continuous	ADJ
ejpam-3831	502	4	on	on	ADP
ejpam-3831	502	5	[	[	X
ejpam-3831	502	6	0	0	NUM
ejpam-3831	502	7	,	,	PUNCT
ejpam-3831	502	8	1]×r	1]×r	NUM
ejpam-3831	502	9	,	,	PUNCT
ejpam-3831	502	10	.	.	PUNCT
ejpam-3831	503	1	(	(	PUNCT
ejpam-3831	503	2	iii	iii	X
ejpam-3831	503	3	)	)	PUNCT
ejpam-3831	503	4	maxt	maxt	NOUN
ejpam-3831	503	5	,	,	PUNCT
ejpam-3831	503	6	κ∈[0,1]h(t	κ∈[0,1]h(t	NOUN
ejpam-3831	503	7	,	,	PUNCT
ejpam-3831	503	8	κ	κ	NOUN
ejpam-3831	503	9	)	)	PUNCT
ejpam-3831	503	10	=	=	SYM
ejpam-3831	503	11	maxt	maxt	NOUN
ejpam-3831	503	12	,	,	PUNCT
ejpam-3831	503	13	κ∈[0,1	κ∈[0,1	NOUN
ejpam-3831	503	14	]	]	PUNCT
ejpam-3831	503	15	tκ	tκ	ADP
ejpam-3831	503	16	130	130	NUM
ejpam-3831	503	17	=	=	SYM
ejpam-3831	503	18	1	1	NUM
ejpam-3831	503	19	130	130	NUM
ejpam-3831	503	20	<	<	SYM
ejpam-3831	503	21	1	1	NUM
ejpam-3831	503	22	120	120	NUM
ejpam-3831	503	23	=	=	SYM
ejpam-3831	503	24	α1	α1	PROPN
ejpam-3831	503	25	4(1−0	4(1−0	NUM
ejpam-3831	503	26	)	)	PUNCT
ejpam-3831	503	27	,	,	PUNCT
ejpam-3831	503	28	where	where	SCONJ
ejpam-3831	503	29	α1	α1	PROPN
ejpam-3831	503	30	=	=	SYM
ejpam-3831	503	31	1	1	NUM
ejpam-3831	503	32	30	30	NUM
ejpam-3831	503	33	.	.	PUNCT
ejpam-3831	504	1	(	(	PUNCT
ejpam-3831	504	2	iv	iv	X
ejpam-3831	504	3	)	)	PUNCT
ejpam-3831	504	4	also	also	ADV
ejpam-3831	504	5	|f(κ	|f(κ	PROPN
ejpam-3831	504	6	,	,	PUNCT
ejpam-3831	504	7	u(κ))|	u(κ))|	PROPN
ejpam-3831	504	8	=	=	SYM
ejpam-3831	504	9	|e−κ||(u(κ))3|	|e−κ||(u(κ))3|	PROPN
ejpam-3831	504	10	≤	≤	NOUN
ejpam-3831	504	11	(	(	PUNCT
ejpam-3831	504	12	|u(κ)|)3	|u(κ)|)3	NOUN
ejpam-3831	504	13	.	.	PUNCT
ejpam-3831	505	1	references	reference	NOUN
ejpam-3831	505	2	1014	1014	NUM
ejpam-3831	505	3	therefore	therefore	ADV
ejpam-3831	505	4	,	,	PUNCT
ejpam-3831	505	5	all	all	DET
ejpam-3831	505	6	conditions	condition	NOUN
ejpam-3831	505	7	of	of	ADP
ejpam-3831	505	8	theorem	theorem	ADJ
ejpam-3831	505	9	2	2	NUM
ejpam-3831	505	10	are	be	AUX
ejpam-3831	505	11	satisfied	satisfied	ADJ
ejpam-3831	505	12	,	,	PUNCT
ejpam-3831	505	13	hence	hence	ADV
ejpam-3831	505	14	the	the	DET
ejpam-3831	505	15	mapping	mapping	NOUN
ejpam-3831	505	16	t	t	PROPN
ejpam-3831	505	17	has	have	VERB
ejpam-3831	505	18	a	a	DET
ejpam-3831	505	19	fixed	fix	VERB
ejpam-3831	505	20	point	point	NOUN
ejpam-3831	505	21	in	in	ADP
ejpam-3831	505	22	x	x	NOUN
ejpam-3831	505	23	,	,	PUNCT
ejpam-3831	505	24	which	which	PRON
ejpam-3831	505	25	is	be	AUX
ejpam-3831	505	26	a	a	DET
ejpam-3831	505	27	solution	solution	NOUN
ejpam-3831	505	28	to	to	ADP
ejpam-3831	505	29	equation	equation	NOUN
ejpam-3831	505	30	(	(	PUNCT
ejpam-3831	505	31	24	24	NUM
ejpam-3831	505	32	)	)	PUNCT
ejpam-3831	505	33	,	,	PUNCT
ejpam-3831	505	34	that	that	PRON
ejpam-3831	505	35	is	is	ADV
ejpam-3831	505	36	t	t	PROPN
ejpam-3831	505	37	(	(	PUNCT
ejpam-3831	505	38	u(t	u(t	PROPN
ejpam-3831	505	39	)	)	PUNCT
ejpam-3831	505	40	,	,	PUNCT
ejpam-3831	505	41	u(t	u(t	NOUN
ejpam-3831	505	42	)	)	PUNCT
ejpam-3831	505	43	)	)	PUNCT
ejpam-3831	506	1	=	=	PUNCT
ejpam-3831	506	2	∫	∫	PROPN
ejpam-3831	507	1	1	1	NUM
ejpam-3831	507	2	0	0	NUM
ejpam-3831	507	3	tκ	tκ	ADP
ejpam-3831	507	4	130	130	NUM
ejpam-3831	507	5	(	(	PUNCT
ejpam-3831	507	6	u(κ	u(κ	NOUN
ejpam-3831	507	7	)	)	PUNCT
ejpam-3831	507	8	2	2	NUM
ejpam-3831	507	9	+	+	SYM
ejpam-3831	507	10	u(κ	u(κ	NOUN
ejpam-3831	507	11	)	)	PUNCT
ejpam-3831	507	12	2	2	NUM
ejpam-3831	507	13	)	)	PUNCT
ejpam-3831	507	14	3e−κdκ	3e−κdκ	NUM
ejpam-3831	508	1	=	=	SYM
ejpam-3831	508	2	∫	∫	PROPN
ejpam-3831	508	3	1	1	NUM
ejpam-3831	508	4	0	0	NUM
ejpam-3831	508	5	tκ	tκ	ADP
ejpam-3831	508	6	130	130	NUM
ejpam-3831	508	7	(	(	PUNCT
ejpam-3831	508	8	u(κ))3e−κdκ	u(κ))3e−κdκ	NOUN
ejpam-3831	508	9	;	;	PUNCT
ejpam-3831	508	10	t	t	PROPN
ejpam-3831	508	11	∈	∈	PROPN
ejpam-3831	509	1	[	[	X
ejpam-3831	509	2	0	0	NUM
ejpam-3831	509	3	,	,	PUNCT
ejpam-3831	509	4	1	1	NUM
ejpam-3831	509	5	]	]	PUNCT
ejpam-3831	509	6	=	=	SYM
ejpam-3831	509	7	u(t	u(t	NOUN
ejpam-3831	509	8	)	)	PUNCT
ejpam-3831	509	9	.	.	PUNCT
ejpam-3831	510	1	4	4	X
ejpam-3831	510	2	.	.	X
ejpam-3831	510	3	conclusions	conclusion	NOUN
ejpam-3831	510	4	we	we	PRON
ejpam-3831	510	5	have	have	AUX
ejpam-3831	510	6	introduced	introduce	VERB
ejpam-3831	510	7	rational	rational	ADJ
ejpam-3831	510	8	type	type	NOUN
ejpam-3831	510	9	contractive	contractive	ADJ
ejpam-3831	510	10	conditions	condition	NOUN
ejpam-3831	510	11	on	on	ADP
ejpam-3831	510	12	three	three	NUM
ejpam-3831	510	13	mappings	mapping	NOUN
ejpam-3831	510	14	to	to	PART
ejpam-3831	510	15	give	give	VERB
ejpam-3831	510	16	the	the	DET
ejpam-3831	510	17	existence	existence	NOUN
ejpam-3831	510	18	and	and	CCONJ
ejpam-3831	510	19	uniqueness	uniqueness	NOUN
ejpam-3831	510	20	of	of	ADP
ejpam-3831	510	21	common	common	ADJ
ejpam-3831	510	22	coupled	couple	VERB
ejpam-3831	510	23	fixed	fix	VERB
ejpam-3831	510	24	point	point	NOUN
ejpam-3831	510	25	theorem	theorem	VERB
ejpam-3831	510	26	in	in	ADP
ejpam-3831	510	27	the	the	DET
ejpam-3831	510	28	set	set	NOUN
ejpam-3831	510	29	up	up	ADP
ejpam-3831	510	30	of	of	ADP
ejpam-3831	510	31	gb	gb	ADV
ejpam-3831	510	32	-	-	PUNCT
ejpam-3831	510	33	metric	metric	ADJ
ejpam-3831	510	34	spaces	space	NOUN
ejpam-3831	510	35	.	.	PUNCT
ejpam-3831	511	1	the	the	DET
ejpam-3831	511	2	derived	derive	VERB
ejpam-3831	511	3	result	result	NOUN
ejpam-3831	511	4	cover	cover	NOUN
ejpam-3831	511	5	and	and	CCONJ
ejpam-3831	511	6	generalize	generalize	VERB
ejpam-3831	511	7	some	some	DET
ejpam-3831	511	8	well	well	ADV
ejpam-3831	511	9	-	-	PUNCT
ejpam-3831	511	10	known	know	VERB
ejpam-3831	511	11	comparable	comparable	ADJ
ejpam-3831	511	12	results	result	NOUN
ejpam-3831	511	13	in	in	ADP
ejpam-3831	511	14	the	the	DET
ejpam-3831	511	15	existing	exist	VERB
ejpam-3831	511	16	literature	literature	NOUN
ejpam-3831	511	17	.	.	PUNCT
ejpam-3831	512	1	also	also	ADV
ejpam-3831	512	2	we	we	PRON
ejpam-3831	512	3	presented	present	VERB
ejpam-3831	512	4	examples	example	NOUN
ejpam-3831	512	5	to	to	PART
ejpam-3831	512	6	illustrate	illustrate	VERB
ejpam-3831	512	7	the	the	DET
ejpam-3831	512	8	main	main	ADJ
ejpam-3831	512	9	results	result	NOUN
ejpam-3831	512	10	as	as	ADV
ejpam-3831	512	11	well	well	ADV
ejpam-3831	512	12	as	as	SCONJ
ejpam-3831	512	13	we	we	PRON
ejpam-3831	512	14	gave	give	VERB
ejpam-3831	512	15	an	an	DET
ejpam-3831	512	16	application	application	NOUN
ejpam-3831	512	17	to	to	PART
ejpam-3831	512	18	prove	prove	VERB
ejpam-3831	512	19	the	the	DET
ejpam-3831	512	20	existence	existence	NOUN
ejpam-3831	512	21	and	and	CCONJ
ejpam-3831	512	22	uniqueness	uniqueness	NOUN
ejpam-3831	512	23	of	of	ADP
ejpam-3831	512	24	a	a	DET
ejpam-3831	512	25	solution	solution	NOUN
ejpam-3831	512	26	for	for	ADP
ejpam-3831	512	27	a	a	DET
ejpam-3831	512	28	class	class	NOUN
ejpam-3831	512	29	of	of	ADP
ejpam-3831	512	30	integral	integral	ADJ
ejpam-3831	512	31	equations	equation	NOUN
ejpam-3831	512	32	.	.	PUNCT
ejpam-3831	513	1	references	reference	NOUN
ejpam-3831	513	2	[	[	X
ejpam-3831	513	3	1	1	X
ejpam-3831	513	4	]	]	PUNCT
ejpam-3831	513	5	j.	j.	PROPN
ejpam-3831	513	6	r.	r.	PROPN
ejpam-3831	513	7	roshan	roshan	PROPN
ejpam-3831	513	8	a.	a.	PROPN
ejpam-3831	513	9	aghajani	aghajani	PROPN
ejpam-3831	513	10	,	,	PUNCT
ejpam-3831	513	11	m.	m.	NOUN
ejpam-3831	513	12	abbas	abbas	PROPN
ejpam-3831	513	13	.	.	PUNCT
ejpam-3831	514	1	common	common	ADJ
ejpam-3831	514	2	fixed	fix	VERB
ejpam-3831	514	3	point	point	NOUN
ejpam-3831	514	4	of	of	ADP
ejpam-3831	514	5	generalized	generalized	ADJ
ejpam-3831	514	6	weak	weak	ADJ
ejpam-3831	514	7	contractive	contractive	ADJ
ejpam-3831	514	8	mappings	mapping	NOUN
ejpam-3831	514	9	in	in	ADP
ejpam-3831	514	10	partially	partially	ADV
ejpam-3831	514	11	ordered	order	VERB
ejpam-3831	514	12	gb	gb	ADV
ejpam-3831	514	13	-	-	PUNCT
ejpam-3831	514	14	metric	metric	ADJ
ejpam-3831	514	15	spaces	space	NOUN
ejpam-3831	514	16	.	.	PUNCT
ejpam-3831	515	1	filomat	filomat	PROPN
ejpam-3831	515	2	,	,	PUNCT
ejpam-3831	515	3	28(6):1087–1101	28(6):1087–1101	NUM
ejpam-3831	515	4	,	,	PUNCT
ejpam-3831	515	5	2014	2014	NUM
ejpam-3831	515	6	.	.	PUNCT
ejpam-3831	516	1	[	[	X
ejpam-3831	516	2	2	2	X
ejpam-3831	516	3	]	]	PUNCT
ejpam-3831	516	4	m.	m.	NOUN
ejpam-3831	516	5	abbas	abbas	PROPN
ejpam-3831	516	6	and	and	CCONJ
ejpam-3831	516	7	b.e	b.e	PROPN
ejpam-3831	516	8	.	.	PROPN
ejpam-3831	516	9	rhoades	rhoades	PROPN
ejpam-3831	516	10	.	.	PUNCT
ejpam-3831	517	1	common	common	ADJ
ejpam-3831	517	2	fixed	fix	VERB
ejpam-3831	517	3	point	point	NOUN
ejpam-3831	517	4	results	result	NOUN
ejpam-3831	517	5	for	for	ADP
ejpam-3831	517	6	noncommuting	noncommute	VERB
ejpam-3831	517	7	mappings	mapping	NOUN
ejpam-3831	517	8	without	without	ADP
ejpam-3831	517	9	continuity	continuity	NOUN
ejpam-3831	517	10	in	in	ADP
ejpam-3831	517	11	generalised	generalise	VERB
ejpam-3831	517	12	metric	metric	ADJ
ejpam-3831	517	13	spaces	space	NOUN
ejpam-3831	517	14	.	.	PUNCT
ejpam-3831	518	1	appl	appl	PROPN
ejpam-3831	518	2	.	.	PROPN
ejpam-3831	518	3	math	math	PROPN
ejpam-3831	518	4	.	.	PUNCT
ejpam-3831	519	1	comput	comput	NOUN
ejpam-3831	519	2	.	.	PUNCT
ejpam-3831	519	3	,	,	PUNCT
ejpam-3831	519	4	215:262	215:262	PROPN
ejpam-3831	519	5	–	–	PUNCT
ejpam-3831	519	6	269	269	NUM
ejpam-3831	519	7	,	,	PUNCT
ejpam-3831	519	8	2009	2009	NUM
ejpam-3831	519	9	.	.	PUNCT
ejpam-3831	520	1	[	[	X
ejpam-3831	520	2	3	3	X
ejpam-3831	520	3	]	]	X
ejpam-3831	520	4	ravi	ravi	PROPN
ejpam-3831	520	5	p.	p.	PROPN
ejpam-3831	520	6	agarwal	agarwal	PROPN
ejpam-3831	520	7	,	,	PUNCT
ejpam-3831	520	8	erdal	erdal	PROPN
ejpam-3831	520	9	karapinar	karapinar	PROPN
ejpam-3831	520	10	,	,	PUNCT
ejpam-3831	520	11	donal	donal	PROPN
ejpam-3831	520	12	oregan	oregan	PROPN
ejpam-3831	520	13	,	,	PUNCT
ejpam-3831	520	14	and	and	CCONJ
ejpam-3831	520	15	antonio	antonio	PROPN
ejpam-3831	520	16	francisco	francisco	PROPN
ejpam-3831	520	17	roldanlopez	roldanlopez	PROPN
ejpam-3831	520	18	de	de	PROPN
ejpam-3831	520	19	hierro	hierro	PROPN
ejpam-3831	520	20	.	.	PROPN
ejpam-3831	520	21	fixed	fix	VERB
ejpam-3831	520	22	point	point	NOUN
ejpam-3831	520	23	theory	theory	NOUN
ejpam-3831	520	24	in	in	ADP
ejpam-3831	520	25	metric	metric	ADJ
ejpam-3831	520	26	type	type	NOUN
ejpam-3831	520	27	spaces	space	NOUN
ejpam-3831	520	28	.	.	PUNCT
ejpam-3831	521	1	springer	springer	NOUN
ejpam-3831	521	2	,	,	PUNCT
ejpam-3831	521	3	international	international	PROPN
ejpam-3831	521	4	publishing	publishing	PROPN
ejpam-3831	521	5	switzerland	switzerland	PROPN
ejpam-3831	521	6	,	,	PUNCT
ejpam-3831	521	7	2015	2015	NUM
ejpam-3831	521	8	.	.	PUNCT
ejpam-3831	522	1	[	[	X
ejpam-3831	522	2	4	4	X
ejpam-3831	522	3	]	]	PUNCT
ejpam-3831	522	4	y.rohen	y.rohen	PROPN
ejpam-3831	522	5	b.	b.	PROPN
ejpam-3831	522	6	khomdram	khomdram	PROPN
ejpam-3831	522	7	and	and	CCONJ
ejpam-3831	522	8	t.singh	t.singh	NOUN
ejpam-3831	522	9	.	.	PUNCT
ejpam-3831	522	10	coupled	couple	VERB
ejpam-3831	522	11	fixed	fix	VERB
ejpam-3831	522	12	point	point	NOUN
ejpam-3831	522	13	theorems	theorem	NOUN
ejpam-3831	522	14	in	in	ADP
ejpam-3831	522	15	gb	gb	ADV
ejpam-3831	522	16	-	-	PUNCT
ejpam-3831	522	17	metric	metric	ADJ
ejpam-3831	522	18	space	space	NOUN
ejpam-3831	522	19	satisfying	satisfy	VERB
ejpam-3831	522	20	some	some	DET
ejpam-3831	522	21	rational	rational	ADJ
ejpam-3831	522	22	contractive	contractive	ADJ
ejpam-3831	522	23	conditions	condition	NOUN
ejpam-3831	522	24	.	.	PUNCT
ejpam-3831	523	1	springerplus	springerplus	PROPN
ejpam-3831	523	2	,	,	PUNCT
ejpam-3831	523	3	5(1261):1–16	5(1261):1–16	NUM
ejpam-3831	523	4	,	,	PUNCT
ejpam-3831	523	5	2016	2016	NUM
ejpam-3831	523	6	.	.	PUNCT
ejpam-3831	524	1	[	[	X
ejpam-3831	524	2	5	5	X
ejpam-3831	524	3	]	]	PUNCT
ejpam-3831	524	4	v.	v.	CCONJ
ejpam-3831	524	5	lakshmikantham	lakshmikantham	PROPN
ejpam-3831	524	6	d.	d.	PROPN
ejpam-3831	524	7	guo	guo	PROPN
ejpam-3831	524	8	.	.	PUNCT
ejpam-3831	524	9	coupled	couple	VERB
ejpam-3831	524	10	fixed	fix	VERB
ejpam-3831	524	11	points	point	NOUN
ejpam-3831	524	12	of	of	ADP
ejpam-3831	524	13	nonlinear	nonlinear	ADJ
ejpam-3831	524	14	operators	operator	NOUN
ejpam-3831	524	15	with	with	ADP
ejpam-3831	524	16	applications	application	NOUN
ejpam-3831	524	17	.	.	PUNCT
ejpam-3831	525	1	nonlinear	nonlinear	ADJ
ejpam-3831	525	2	anal	anal	PROPN
ejpam-3831	525	3	.	.	PUNCT
ejpam-3831	526	1	tma	tma	PROPN
ejpam-3831	526	2	,	,	PUNCT
ejpam-3831	526	3	11:623–632	11:623–632	NUM
ejpam-3831	526	4	,	,	PUNCT
ejpam-3831	526	5	1987	1987	NUM
ejpam-3831	526	6	.	.	PUNCT
ejpam-3831	527	1	[	[	X
ejpam-3831	527	2	6	6	NUM
ejpam-3831	527	3	]	]	PUNCT
ejpam-3831	527	4	c.thokchom	c.thokchom	PROPN
ejpam-3831	527	5	h.k	h.k	PROPN
ejpam-3831	527	6	.	.	PROPN
ejpam-3831	527	7	nashie	nashie	PROPN
ejpam-3831	527	8	,	,	PUNCT
ejpam-3831	527	9	y.	y.	PROPN
ejpam-3831	527	10	rohen	rohen	PROPN
ejpam-3831	527	11	.	.	PUNCT
ejpam-3831	528	1	cointegraion	cointegraion	NOUN
ejpam-3831	528	2	and	and	CCONJ
ejpam-3831	528	3	error	error	NOUN
ejpam-3831	528	4	-	-	PUNCT
ejpam-3831	528	5	correction	correction	NOUN
ejpam-3831	528	6	:	:	PUNCT
ejpam-3831	528	7	representation	representation	NOUN
ejpam-3831	528	8	,	,	PUNCT
ejpam-3831	528	9	estimation	estimation	NOUN
ejpam-3831	528	10	and	and	CCONJ
ejpam-3831	528	11	testing	testing	NOUN
ejpam-3831	528	12	.	.	PUNCT
ejpam-3831	529	1	international	international	ADJ
ejpam-3831	529	2	journal	journal	NOUN
ejpam-3831	529	3	of	of	ADP
ejpam-3831	529	4	pure	pure	ADJ
ejpam-3831	529	5	and	and	CCONJ
ejpam-3831	529	6	applied	applied	ADJ
ejpam-3831	529	7	mathematics	mathematic	NOUN
ejpam-3831	529	8	,	,	PUNCT
ejpam-3831	529	9	106(3):791–799	106(3):791–799	NUM
ejpam-3831	529	10	,	,	PUNCT
ejpam-3831	529	11	2016	2016	NUM
ejpam-3831	529	12	.	.	PUNCT
ejpam-3831	530	1	[	[	X
ejpam-3831	530	2	7	7	X
ejpam-3831	530	3	]	]	PUNCT
ejpam-3831	530	4	z.	z.	PROPN
ejpam-3831	530	5	kadelburg	kadelburg	PROPN
ejpam-3831	530	6	,	,	PUNCT
ejpam-3831	530	7	h.	h.	PROPN
ejpam-3831	530	8	kumar	kumar	PROPN
ejpam-3831	530	9	nashine	nashine	PROPN
ejpam-3831	530	10	,	,	PUNCT
ejpam-3831	530	11	and	and	CCONJ
ejpam-3831	530	12	s.	s.	PROPN
ejpam-3831	531	1	radenović.	radenović.	PROPN
ejpam-3831	531	2	common	common	ADJ
ejpam-3831	531	3	coupled	couple	VERB
ejpam-3831	531	4	fixed	fix	VERB
ejpam-3831	531	5	point	point	NOUN
ejpam-3831	531	6	results	result	NOUN
ejpam-3831	531	7	in	in	ADP
ejpam-3831	531	8	partially	partially	ADV
ejpam-3831	531	9	ordered	order	VERB
ejpam-3831	531	10	g	g	NOUN
ejpam-3831	531	11	-	-	PUNCT
ejpam-3831	531	12	metric	metric	ADJ
ejpam-3831	531	13	space	space	NOUN
ejpam-3831	531	14	.	.	PUNCT
ejpam-3831	532	1	bulletin	bulletin	NOUN
ejpam-3831	532	2	of	of	ADP
ejpam-3831	532	3	mathematical	mathematical	ADJ
ejpam-3831	532	4	analysis	analysis	NOUN
ejpam-3831	532	5	and	and	CCONJ
ejpam-3831	532	6	applications	application	NOUN
ejpam-3831	532	7	,	,	PUNCT
ejpam-3831	532	8	4(2):51–63	4(2):51–63	NUM
ejpam-3831	532	9	,	,	PUNCT
ejpam-3831	532	10	2012	2012	NUM
ejpam-3831	532	11	.	.	PUNCT
ejpam-3831	533	1	[	[	X
ejpam-3831	533	2	8	8	X
ejpam-3831	533	3	]	]	PUNCT
ejpam-3831	533	4	t.	t.	PROPN
ejpam-3831	533	5	nazir	nazir	PROPN
ejpam-3831	533	6	m.	m.	PROPN
ejpam-3831	533	7	abbas	abbas	PROPN
ejpam-3831	533	8	and	and	CCONJ
ejpam-3831	533	9	s.	s.	PROPN
ejpam-3831	534	1	radenović.	radenović.	INTJ
ejpam-3831	534	2	some	some	DET
ejpam-3831	534	3	periodic	periodic	ADJ
ejpam-3831	534	4	point	point	NOUN
ejpam-3831	534	5	results	result	NOUN
ejpam-3831	534	6	in	in	ADP
ejpam-3831	534	7	generalized	generalized	ADJ
ejpam-3831	534	8	metric	metric	ADJ
ejpam-3831	534	9	spaces	space	NOUN
ejpam-3831	534	10	.	.	PUNCT
ejpam-3831	535	1	appl	appl	PROPN
ejpam-3831	535	2	.	.	PROPN
ejpam-3831	535	3	math	math	PROPN
ejpam-3831	535	4	.	.	PUNCT
ejpam-3831	536	1	comput	comput	NOUN
ejpam-3831	536	2	,	,	PUNCT
ejpam-3831	536	3	217:4094–4099	217:4094–4099	NUM
ejpam-3831	536	4	,	,	PUNCT
ejpam-3831	536	5	2010	2010	NUM
ejpam-3831	536	6	.	.	PUNCT
ejpam-3831	537	1	references	reference	NOUN
ejpam-3831	537	2	1015	1015	NUM
ejpam-3831	538	1	[	[	X
ejpam-3831	538	2	9	9	NUM
ejpam-3831	538	3	]	]	PUNCT
ejpam-3831	538	4	s.	s.	PROPN
ejpam-3831	538	5	radenović	radenović	PROPN
ejpam-3831	538	6	r.	r.	PROPN
ejpam-3831	538	7	agarwal	agarwal	PROPN
ejpam-3831	538	8	,	,	PUNCT
ejpam-3831	538	9	z.	z.	PROPN
ejpam-3831	538	10	kadelburg	kadelburg	PROPN
ejpam-3831	538	11	.	.	PUNCT
ejpam-3831	539	1	on	on	ADP
ejpam-3831	539	2	coupled	couple	VERB
ejpam-3831	539	3	fixed	fix	VERB
ejpam-3831	539	4	point	point	NOUN
ejpam-3831	539	5	results	result	NOUN
ejpam-3831	539	6	in	in	ADP
ejpam-3831	539	7	asymmetric	asymmetric	ADJ
ejpam-3831	539	8	g−metric	g−metric	ADJ
ejpam-3831	539	9	spaces	space	NOUN
ejpam-3831	539	10	.	.	PUNCT
ejpam-3831	540	1	journal	journal	PROPN
ejpam-3831	540	2	of	of	ADP
ejpam-3831	540	3	inequalities	inequality	NOUN
ejpam-3831	540	4	and	and	CCONJ
ejpam-3831	540	5	applications	application	NOUN
ejpam-3831	540	6	,	,	PUNCT
ejpam-3831	540	7	2013:1–12	2013:1–12	NUM
ejpam-3831	540	8	,	,	PUNCT
ejpam-3831	540	9	2013	2013	NUM
ejpam-3831	540	10	.	.	PUNCT
ejpam-3831	541	1	[	[	X
ejpam-3831	541	2	10	10	NUM
ejpam-3831	541	3	]	]	PUNCT
ejpam-3831	541	4	s.	s.	PROPN
ejpam-3831	542	1	radenović.	radenović.	PROPN
ejpam-3831	542	2	remarks	remark	VERB
ejpam-3831	542	3	on	on	ADP
ejpam-3831	542	4	some	some	DET
ejpam-3831	542	5	recent	recent	ADJ
ejpam-3831	542	6	coupled	couple	VERB
ejpam-3831	542	7	coincidence	coincidence	NOUN
ejpam-3831	542	8	point	point	NOUN
ejpam-3831	542	9	results	result	NOUN
ejpam-3831	542	10	in	in	ADP
ejpam-3831	542	11	symmetric	symmetric	ADJ
ejpam-3831	542	12	g	g	NOUN
ejpam-3831	542	13	-	-	PUNCT
ejpam-3831	542	14	metric	metric	ADJ
ejpam-3831	542	15	spaces	space	NOUN
ejpam-3831	542	16	.	.	PUNCT
ejpam-3831	543	1	journal	journal	PROPN
ejpam-3831	543	2	of	of	ADP
ejpam-3831	543	3	operators	operator	NOUN
ejpam-3831	543	4	,	,	PUNCT
ejpam-3831	543	5	2013:8	2013:8	NUM
ejpam-3831	543	6	pages	page	NOUN
ejpam-3831	543	7	,	,	PUNCT
ejpam-3831	543	8	2013	2013	NUM
ejpam-3831	543	9	.	.	PUNCT
ejpam-3831	544	1	[	[	X
ejpam-3831	544	2	11	11	NUM
ejpam-3831	544	3	]	]	X
ejpam-3831	544	4	s.	s.	PROPN
ejpam-3831	544	5	radenović	radenović	PROPN
ejpam-3831	544	6	,	,	PUNCT
ejpam-3831	544	7	s.	s.	PROPN
ejpam-3831	544	8	pantelić	pantelić	PROPN
ejpam-3831	544	9	,	,	PUNCT
ejpam-3831	544	10	p.	p.	PROPN
ejpam-3831	544	11	salimi	salimi	PROPN
ejpam-3831	544	12	,	,	PUNCT
ejpam-3831	544	13	and	and	CCONJ
ejpam-3831	544	14	j.	j.	PROPN
ejpam-3831	544	15	vujaković.	vujaković.	PROPN
ejpam-3831	544	16	a	a	DET
ejpam-3831	544	17	note	note	NOUN
ejpam-3831	544	18	on	on	ADP
ejpam-3831	544	19	some	some	PRON
ejpam-3831	544	20	tripled	triple	VERB
ejpam-3831	544	21	coincidence	coincidence	NOUN
ejpam-3831	544	22	point	point	NOUN
ejpam-3831	544	23	results	result	NOUN
ejpam-3831	544	24	in	in	ADP
ejpam-3831	544	25	g−	g−	ADJ
ejpam-3831	544	26	metric	metric	ADJ
ejpam-3831	544	27	spaces	space	NOUN
ejpam-3831	544	28	.	.	PUNCT
ejpam-3831	545	1	international	international	ADJ
ejpam-3831	545	2	journal	journal	PROPN
ejpam-3831	545	3	of	of	ADP
ejpam-3831	545	4	mathematical	mathematical	ADJ
ejpam-3831	545	5	sciences	sciences	PROPN
ejpam-3831	545	6	and	and	CCONJ
ejpam-3831	545	7	engineering	engineering	NOUN
ejpam-3831	545	8	applications	application	NOUN
ejpam-3831	545	9	,	,	PUNCT
ejpam-3831	545	10	6(vi):23–38	6(vi):23–38	NUM
ejpam-3831	545	11	,	,	PUNCT
ejpam-3831	545	12	2012	2012	NUM
ejpam-3831	545	13	.	.	PUNCT
ejpam-3831	546	1	[	[	X
ejpam-3831	546	2	12	12	NUM
ejpam-3831	546	3	]	]	PUNCT
ejpam-3831	546	4	j.	j.	PROPN
ejpam-3831	546	5	r.	r.	PROPN
ejpam-3831	546	6	roshan	roshan	PROPN
ejpam-3831	546	7	,	,	PUNCT
ejpam-3831	546	8	n.	n.	PROPN
ejpam-3831	546	9	shobkolaei	shobkolaei	PROPN
ejpam-3831	546	10	,	,	PUNCT
ejpam-3831	546	11	s.	s.	PROPN
ejpam-3831	546	12	sedghi	sedghi	PROPN
ejpam-3831	546	13	,	,	PUNCT
ejpam-3831	546	14	v.	v.	CCONJ
ejpam-3831	546	15	parvaneh	parvaneh	NOUN
ejpam-3831	546	16	,	,	PUNCT
ejpam-3831	546	17	and	and	CCONJ
ejpam-3831	546	18	s.	s.	PROPN
ejpam-3831	546	19	radenović.	radenović.	PROPN
ejpam-3831	546	20	common	common	ADJ
ejpam-3831	546	21	fixed	fix	VERB
ejpam-3831	546	22	point	point	NOUN
ejpam-3831	546	23	theorem	theorem	NOUN
ejpam-3831	546	24	for	for	ADP
ejpam-3831	546	25	three	three	NUM
ejpam-3831	546	26	maps	map	NOUN
ejpam-3831	546	27	in	in	ADP
ejpam-3831	546	28	discontinuous	discontinuous	ADJ
ejpam-3831	546	29	gb	gb	ADV
ejpam-3831	546	30	-	-	PUNCT
ejpam-3831	546	31	metric	metric	ADJ
ejpam-3831	546	32	spaces	space	NOUN
ejpam-3831	546	33	.	.	PUNCT
ejpam-3831	547	1	acta	acta	PROPN
ejpam-3831	547	2	mathematica	mathematica	PROPN
ejpam-3831	547	3	scientia	scientia	PROPN
ejpam-3831	547	4	,	,	PUNCT
ejpam-3831	547	5	34	34	NUM
ejpam-3831	547	6	b(5):1–12	b(5):1–12	NOUN
ejpam-3831	547	7	,	,	PUNCT
ejpam-3831	547	8	2014	2014	NUM
ejpam-3831	547	9	.	.	PUNCT
ejpam-3831	548	1	[	[	X
ejpam-3831	548	2	13	13	NUM
ejpam-3831	548	3	]	]	X
ejpam-3831	548	4	j.r	j.r	PROPN
ejpam-3831	548	5	roshon	roshon	NOUN
ejpam-3831	548	6	.	.	PUNCT
ejpam-3831	549	1	common	common	ADJ
ejpam-3831	549	2	fixed	fix	VERB
ejpam-3831	549	3	point	point	NOUN
ejpam-3831	549	4	theorems	theorem	NOUN
ejpam-3831	549	5	for	for	ADP
ejpam-3831	549	6	three	three	NUM
ejpam-3831	549	7	maps	map	NOUN
ejpam-3831	549	8	in	in	ADP
ejpam-3831	549	9	discontinuous	discontinuous	ADJ
ejpam-3831	549	10	gb	gb	ADV
ejpam-3831	549	11	-	-	PUNCT
ejpam-3831	549	12	metric	metric	ADJ
ejpam-3831	549	13	spaces	space	NOUN
ejpam-3831	549	14	.	.	PUNCT
ejpam-3831	550	1	acta	acta	PROPN
ejpam-3831	550	2	mathematica	mathematica	PROPN
ejpam-3831	550	3	scientia	scientia	PROPN
ejpam-3831	550	4	,	,	PUNCT
ejpam-3831	550	5	34b(5):1643–1654	34b(5):1643–1654	NUM
ejpam-3831	550	6	,	,	PUNCT
ejpam-3831	550	7	2014	2014	NUM
ejpam-3831	550	8	.	.	PUNCT
ejpam-3831	551	1	[	[	X
ejpam-3831	551	2	14	14	NUM
ejpam-3831	551	3	]	]	X
ejpam-3831	551	4	j.r	j.r	PROPN
ejpam-3831	551	5	.	.	PROPN
ejpam-3831	551	6	roshan	roshan	PROPN
ejpam-3831	551	7	s.	s.	PROPN
ejpam-3831	551	8	sedghi	sedghi	PROPN
ejpam-3831	551	9	,	,	PUNCT
ejpam-3831	551	10	n.	n.	NOUN
ejpam-3831	551	11	shobkolaei	shobkolaei	NOUN
ejpam-3831	551	12	and	and	CCONJ
ejpam-3831	551	13	w.	w.	PROPN
ejpam-3831	551	14	shatanawi	shatanawi	PROPN
ejpam-3831	551	15	.	.	PUNCT
ejpam-3831	552	1	coupled	couple	VERB
ejpam-3831	552	2	fixed	fix	VERB
ejpam-3831	552	3	point	point	NOUN
ejpam-3831	552	4	theorems	theorem	NOUN
ejpam-3831	552	5	in	in	ADP
ejpam-3831	552	6	gb	gb	ADV
ejpam-3831	552	7	-	-	PUNCT
ejpam-3831	552	8	metric	metric	ADJ
ejpam-3831	552	9	spaces	space	NOUN
ejpam-3831	552	10	.	.	PUNCT
ejpam-3831	553	1	matematicki	matematicki	NOUN
ejpam-3831	553	2	vesnik	vesnik	NOUN
ejpam-3831	553	3	,	,	PUNCT
ejpam-3831	553	4	66(2):190–201	66(2):190–201	PROPN
ejpam-3831	553	5	,	,	PUNCT
ejpam-3831	553	6	2014	2014	NUM
ejpam-3831	553	7	.	.	PUNCT
ejpam-3831	554	1	[	[	X
ejpam-3831	554	2	15	15	NUM
ejpam-3831	554	3	]	]	X
ejpam-3831	554	4	w.	w.	PROPN
ejpam-3831	554	5	shatanawi	shatanawi	PROPN
ejpam-3831	554	6	.	.	PUNCT
ejpam-3831	555	1	some	some	DET
ejpam-3831	555	2	fixed	fix	VERB
ejpam-3831	555	3	point	point	NOUN
ejpam-3831	555	4	theorems	theorem	NOUN
ejpam-3831	555	5	in	in	ADP
ejpam-3831	555	6	ordered	order	VERB
ejpam-3831	555	7	g	g	NOUN
ejpam-3831	555	8	-	-	PUNCT
ejpam-3831	555	9	metric	metric	ADJ
ejpam-3831	555	10	spaces	space	NOUN
ejpam-3831	555	11	and	and	CCONJ
ejpam-3831	555	12	applications	application	NOUN
ejpam-3831	555	13	.	.	PUNCT
ejpam-3831	556	1	abstract	abstract	ADJ
ejpam-3831	556	2	and	and	CCONJ
ejpam-3831	556	3	applied	apply	VERB
ejpam-3831	556	4	analysis	analysis	NOUN
ejpam-3831	556	5	,	,	PUNCT
ejpam-3831	556	6	2011:11	2011:11	NUM
ejpam-3831	556	7	pages	page	NOUN
ejpam-3831	556	8	,	,	PUNCT
ejpam-3831	556	9	2011	2011	NUM
ejpam-3831	556	10	.	.	PUNCT
ejpam-3831	557	1	[	[	X
ejpam-3831	557	2	16	16	NUM
ejpam-3831	557	3	]	]	X
ejpam-3831	557	4	lj	lj	PROPN
ejpam-3831	557	5	.	.	PUNCT
ejpam-3831	558	1	ćirić	ćirić	PROPN
ejpam-3831	559	1	v.	v.	CCONJ
ejpam-3831	559	2	lakshmikantham	lakshmikantham	ADV
ejpam-3831	559	3	.	.	PUNCT
ejpam-3831	560	1	coupled	couple	VERB
ejpam-3831	560	2	fixed	fix	VERB
ejpam-3831	560	3	point	point	NOUN
ejpam-3831	560	4	theorems	theorem	NOUN
ejpam-3831	560	5	for	for	ADP
ejpam-3831	560	6	nonlinear	nonlinear	ADJ
ejpam-3831	560	7	contractions	contraction	NOUN
ejpam-3831	560	8	in	in	ADP
ejpam-3831	560	9	partially	partially	ADV
ejpam-3831	560	10	ordered	order	VERB
ejpam-3831	560	11	metric	metric	ADJ
ejpam-3831	560	12	spaces	space	NOUN
ejpam-3831	560	13	.	.	PUNCT
ejpam-3831	561	1	j.nonlinear	j.nonlinear	ADJ
ejpam-3831	561	2	analysis	analysis	NOUN
ejpam-3831	561	3	,	,	PUNCT
ejpam-3831	561	4	70:4341–4349	70:4341–4349	NUM
ejpam-3831	561	5	,	,	PUNCT
ejpam-3831	561	6	2009	2009	NUM
ejpam-3831	561	7	.	.	PUNCT
ejpam-3831	562	1	[	[	X
ejpam-3831	562	2	17	17	NUM
ejpam-3831	562	3	]	]	PUNCT
ejpam-3831	562	4	p.	p.	NOUN
ejpam-3831	562	5	kumam	kumam	PROPN
ejpam-3831	562	6	w.	w.	PROPN
ejpam-3831	562	7	sintunavarat	sintunavarat	PROPN
ejpam-3831	562	8	and	and	CCONJ
ejpam-3831	562	9	y.	y.	PROPN
ejpam-3831	562	10	je	je	PROPN
ejpam-3831	562	11	cho	cho	PROPN
ejpam-3831	562	12	.	.	PROPN
ejpam-3831	562	13	coupled	couple	VERB
ejpam-3831	562	14	fixed	fix	VERB
ejpam-3831	562	15	point	point	NOUN
ejpam-3831	562	16	theorems	theorem	NOUN
ejpam-3831	562	17	for	for	ADP
ejpam-3831	562	18	nonlinear	nonlinear	ADJ
ejpam-3831	562	19	contractions	contraction	NOUN
ejpam-3831	562	20	without	without	ADP
ejpam-3831	562	21	mixed	mixed	ADJ
ejpam-3831	562	22	monotone	monotone	ADJ
ejpam-3831	562	23	property	property	NOUN
ejpam-3831	562	24	.	.	PUNCT
ejpam-3831	563	1	fixed	fix	VERB
ejpam-3831	563	2	point	point	NOUN
ejpam-3831	563	3	theory	theory	NOUN
ejpam-3831	563	4	appl	appl	PROPN
ejpam-3831	563	5	.	.	PROPN
ejpam-3831	563	6	,	,	PUNCT
ejpam-3831	563	7	2012(170):1–16	2012(170):1–16	NUM
ejpam-3831	563	8	,	,	PUNCT
ejpam-3831	563	9	2012	2012	NUM
ejpam-3831	563	10	.	.	PUNCT
ejpam-3831	564	1	[	[	X
ejpam-3831	564	2	18	18	NUM
ejpam-3831	564	3	]	]	PUNCT
ejpam-3831	564	4	b.	b.	PROPN
ejpam-3831	564	5	sims	sims	PROPN
ejpam-3831	564	6	z.	z.	PROPN
ejpam-3831	564	7	mustafa	mustafa	PROPN
ejpam-3831	564	8	.	.	PUNCT
ejpam-3831	565	1	a	a	DET
ejpam-3831	565	2	new	new	ADJ
ejpam-3831	565	3	approach	approach	NOUN
ejpam-3831	565	4	to	to	ADP
ejpam-3831	565	5	generalized	generalize	VERB
ejpam-3831	565	6	metric	metric	ADJ
ejpam-3831	565	7	spaces	space	NOUN
ejpam-3831	565	8	.	.	PUNCT
ejpam-3831	566	1	j.	j.	PROPN
ejpam-3831	566	2	nonlinear	nonlinear	PROPN
ejpam-3831	566	3	and	and	CCONJ
ejpam-3831	566	4	convex	convex	ADJ
ejpam-3831	566	5	analsis	analsis	NOUN
ejpam-3831	566	6	,	,	PUNCT
ejpam-3831	566	7	7:289–297	7:289–297	NUM
ejpam-3831	566	8	,	,	PUNCT
ejpam-3831	566	9	2006	2006	NUM
ejpam-3831	566	10	.	.	PUNCT
ejpam-3831	567	1	[	[	X
ejpam-3831	567	2	19	19	NUM
ejpam-3831	567	3	]	]	PUNCT
ejpam-3831	567	4	b.	b.	NOUN
ejpam-3831	567	5	sims	sims	PROPN
ejpam-3831	567	6	z.	z.	PROPN
ejpam-3831	567	7	mustafa	mustafa	PROPN
ejpam-3831	567	8	.	.	PUNCT
ejpam-3831	568	1	fixed	fix	VERB
ejpam-3831	568	2	point	point	NOUN
ejpam-3831	568	3	theorems	theorem	NOUN
ejpam-3831	568	4	for	for	ADP
ejpam-3831	568	5	contractive	contractive	ADJ
ejpam-3831	568	6	mappings	mapping	NOUN
ejpam-3831	568	7	in	in	ADP
ejpam-3831	568	8	complete	complete	ADJ
ejpam-3831	568	9	g	g	NOUN
ejpam-3831	568	10	-	-	PUNCT
ejpam-3831	568	11	metric	metric	ADJ
ejpam-3831	568	12	space	space	NOUN
ejpam-3831	568	13	.	.	PUNCT
ejpam-3831	569	1	fixed	fix	VERB
ejpam-3831	569	2	point	point	NOUN
ejpam-3831	569	3	theory	theory	NOUN
ejpam-3831	569	4	appl	appl	PROPN
ejpam-3831	569	5	.	.	PROPN
ejpam-3831	569	6	,	,	PUNCT
ejpam-3831	569	7	2009:1–10	2009:1–10	NUM
ejpam-3831	569	8	,	,	PUNCT
ejpam-3831	569	9	2009	2009	NUM
ejpam-3831	569	10	.	.	PUNCT
ejpam-3831	570	1	[	[	X
ejpam-3831	570	2	20	20	NUM
ejpam-3831	570	3	]	]	PUNCT
ejpam-3831	570	4	f.	f.	PROPN
ejpam-3831	570	5	awawdeh	awawdeh	PROPN
ejpam-3831	570	6	z.	z.	PROPN
ejpam-3831	570	7	mustafa	mustafa	PROPN
ejpam-3831	570	8	,	,	PUNCT
ejpam-3831	570	9	h.	h.	PROPN
ejpam-3831	570	10	obiedat	obiedat	PROPN
ejpam-3831	570	11	.	.	PUNCT
ejpam-3831	571	1	some	some	DET
ejpam-3831	571	2	common	common	ADJ
ejpam-3831	571	3	fixed	fix	VERB
ejpam-3831	571	4	point	point	NOUN
ejpam-3831	571	5	theorems	theorem	NOUN
ejpam-3831	571	6	for	for	ADP
ejpam-3831	571	7	mapping	mapping	NOUN
ejpam-3831	571	8	on	on	ADP
ejpam-3831	571	9	complete	complete	ADJ
ejpam-3831	571	10	g	g	NOUN
ejpam-3831	571	11	-	-	PUNCT
ejpam-3831	571	12	metric	metric	ADJ
ejpam-3831	571	13	spaces	space	NOUN
ejpam-3831	571	14	.	.	PUNCT
ejpam-3831	572	1	fixed	fix	VERB
ejpam-3831	572	2	point	point	NOUN
ejpam-3831	572	3	theory	theory	NOUN
ejpam-3831	572	4	appl	appl	PROPN
ejpam-3831	572	5	.	.	PROPN
ejpam-3831	572	6	,	,	PUNCT
ejpam-3831	572	7	2008:1–12	2008:1–12	NOUN
ejpam-3831	572	8	,	,	PUNCT
ejpam-3831	572	9	2008	2008	NUM
ejpam-3831	572	10	.	.	PUNCT
ejpam-3831	573	1	[	[	X
ejpam-3831	573	2	21	21	NUM
ejpam-3831	573	3	]	]	X
ejpam-3831	573	4	j.r	j.r	PROPN
ejpam-3831	573	5	.	.	PROPN
ejpam-3831	573	6	roshan	roshan	PROPN
ejpam-3831	573	7	z.	z.	PROPN
ejpam-3831	573	8	mustafa	mustafa	PROPN
ejpam-3831	573	9	and	and	CCONJ
ejpam-3831	573	10	v.	v.	ADP
ejpam-3831	573	11	parvaneh	parvaneh	NOUN
ejpam-3831	573	12	.	.	PUNCT
ejpam-3831	574	1	existence	existence	NOUN
ejpam-3831	574	2	of	of	ADP
ejpam-3831	574	3	tripled	triple	VERB
ejpam-3831	574	4	coincidence	coincidence	NOUN
ejpam-3831	574	5	point	point	NOUN
ejpam-3831	574	6	in	in	ADP
ejpam-3831	574	7	ordered	order	VERB
ejpam-3831	574	8	gb	gb	ADV
ejpam-3831	574	9	-	-	PUNCT
ejpam-3831	574	10	metric	metric	ADJ
ejpam-3831	574	11	spaces	space	NOUN
ejpam-3831	574	12	and	and	CCONJ
ejpam-3831	574	13	applications	application	NOUN
ejpam-3831	574	14	to	to	ADP
ejpam-3831	574	15	a	a	DET
ejpam-3831	574	16	system	system	NOUN
ejpam-3831	574	17	of	of	ADP
ejpam-3831	574	18	integral	integral	ADJ
ejpam-3831	574	19	equations	equation	NOUN
ejpam-3831	574	20	.	.	PUNCT
ejpam-3831	575	1	j.	j.	PROPN
ejpam-3831	575	2	inequalities	inequalities	PROPN
ejpam-3831	575	3	appl	appl	PROPN
ejpam-3831	575	4	,	,	PUNCT
ejpam-3831	575	5	2013:1–27	2013:1–27	NUM
ejpam-3831	575	6	,	,	PUNCT
ejpam-3831	575	7	2013	2013	NUM
ejpam-3831	575	8	.	.	PUNCT
ejpam-3831	576	1	[	[	X
ejpam-3831	576	2	22	22	NUM
ejpam-3831	576	3	]	]	X
ejpam-3831	576	4	w.	w.	PROPN
ejpam-3831	576	5	shatanawi	shatanawi	PROPN
ejpam-3831	576	6	z.	z.	PROPN
ejpam-3831	576	7	mustafa	mustafa	PROPN
ejpam-3831	576	8	and	and	CCONJ
ejpam-3831	576	9	m.	m.	NOUN
ejpam-3831	576	10	bataineh	bataineh	PROPN
ejpam-3831	576	11	.	.	PUNCT
ejpam-3831	577	1	fixed	fix	VERB
ejpam-3831	577	2	point	point	NOUN
ejpam-3831	577	3	theorems	theorem	NOUN
ejpam-3831	577	4	on	on	ADP
ejpam-3831	577	5	uncomplete	uncomplete	ADJ
ejpam-3831	577	6	g	g	NOUN
ejpam-3831	577	7	-	-	PUNCT
ejpam-3831	577	8	metric	metric	ADJ
ejpam-3831	577	9	spaces	space	NOUN
ejpam-3831	577	10	.	.	PUNCT
ejpam-3831	578	1	j.	j.	PROPN
ejpam-3831	578	2	math.stat	math.stat	PROPN
ejpam-3831	578	3	.	.	PROPN
ejpam-3831	578	4	,	,	PUNCT
ejpam-3831	578	5	4(4):196–201	4(4):196–201	NOUN
ejpam-3831	578	6	,	,	PUNCT
ejpam-3831	578	7	2008	2008	NUM
ejpam-3831	578	8	.	.	PUNCT
ejpam-3831	579	1	[	[	X
ejpam-3831	579	2	23	23	NUM
ejpam-3831	579	3	]	]	X
ejpam-3831	579	4	w.	w.	PROPN
ejpam-3831	579	5	shatanawi	shatanawi	PROPN
ejpam-3831	579	6	z.	z.	PROPN
ejpam-3831	579	7	mustafa	mustafa	PROPN
ejpam-3831	579	8	and	and	CCONJ
ejpam-3831	579	9	m.	m.	NOUN
ejpam-3831	579	10	bataineh	bataineh	PROPN
ejpam-3831	579	11	.	.	PUNCT
ejpam-3831	580	1	existence	existence	NOUN
ejpam-3831	580	2	of	of	ADP
ejpam-3831	580	3	fixed	fix	VERB
ejpam-3831	580	4	point	point	NOUN
ejpam-3831	580	5	result	result	NOUN
ejpam-3831	580	6	in	in	ADP
ejpam-3831	580	7	g	g	NOUN
ejpam-3831	580	8	-	-	PUNCT
ejpam-3831	580	9	metric	metric	ADJ
ejpam-3831	580	10	spaces	space	NOUN
ejpam-3831	580	11	.	.	PUNCT
ejpam-3831	581	1	int	int	NOUN
ejpam-3831	581	2	.	.	PUNCT
ejpam-3831	582	1	j.	j.	PROPN
ejpam-3831	582	2	math	math	PROPN
ejpam-3831	582	3	.	.	PUNCT
ejpam-3831	583	1	math	math	NOUN
ejpam-3831	583	2	.	.	PUNCT
ejpam-3831	584	1	sci	sci	PROPN
ejpam-3831	584	2	.	.	PROPN
ejpam-3831	584	3	,	,	PUNCT
ejpam-3831	584	4	2009:1–10	2009:1–10	NUM
ejpam-3831	584	5	,	,	PUNCT
ejpam-3831	584	6	2009	2009	NUM
ejpam-3831	584	7	.	.	PUNCT