id	sid	tid	token	lemma	pos
ejpam-5505	1	1	european	european	PROPN
ejpam-5505	1	2	journal	journal	PROPN
ejpam-5505	1	3	of	of	ADP
ejpam-5505	1	4	pure	pure	ADJ
ejpam-5505	1	5	and	and	CCONJ
ejpam-5505	1	6	applied	apply	VERB
ejpam-5505	1	7	mathematics	mathematic	NOUN
ejpam-5505	1	8	vol	vol	NOUN
ejpam-5505	1	9	.	.	PROPN
ejpam-5505	2	1	17	17	NUM
ejpam-5505	2	2	,	,	PUNCT
ejpam-5505	2	3	no	no	INTJ
ejpam-5505	2	4	.	.	NOUN
ejpam-5505	2	5	4	4	NUM
ejpam-5505	2	6	,	,	PUNCT
ejpam-5505	2	7	2024	2024	NUM
ejpam-5505	2	8	,	,	PUNCT
ejpam-5505	2	9	3642	3642	NUM
ejpam-5505	2	10	-	-	SYM
ejpam-5505	2	11	3659	3659	NUM
ejpam-5505	2	12	issn	issn	PROPN
ejpam-5505	2	13	1307	1307	NUM
ejpam-5505	2	14	-	-	SYM
ejpam-5505	2	15	5543	5543	NUM
ejpam-5505	2	16	–	–	PUNCT
ejpam-5505	2	17	ejpam.com	ejpam.com	X
ejpam-5505	2	18	published	publish	VERB
ejpam-5505	2	19	by	by	ADP
ejpam-5505	2	20	new	new	PROPN
ejpam-5505	2	21	york	york	PROPN
ejpam-5505	2	22	business	business	NOUN
ejpam-5505	2	23	global	global	ADJ
ejpam-5505	2	24	compositions	composition	NOUN
ejpam-5505	2	25	of	of	ADP
ejpam-5505	2	26	resolvents	resolvent	NOUN
ejpam-5505	2	27	:	:	PUNCT
ejpam-5505	2	28	fixed	fix	VERB
ejpam-5505	2	29	points	point	NOUN
ejpam-5505	2	30	sets	set	NOUN
ejpam-5505	2	31	and	and	CCONJ
ejpam-5505	2	32	set	set	NOUN
ejpam-5505	2	33	of	of	ADP
ejpam-5505	2	34	cycles	cycle	NOUN
ejpam-5505	2	35	salihah	salihah	ADJ
ejpam-5505	2	36	thabet	thabet	ADJ
ejpam-5505	2	37	alwadani	alwadani	ADJ
ejpam-5505	2	38	mathematics	mathematics	PROPN
ejpam-5505	2	39	,	,	PUNCT
ejpam-5505	2	40	royal	royal	PROPN
ejpam-5505	2	41	commission	commission	PROPN
ejpam-5505	2	42	yanbu	yanbu	ADJ
ejpam-5505	2	43	colleges	college	NOUN
ejpam-5505	2	44	and	and	CCONJ
ejpam-5505	2	45	institutes	institute	NOUN
ejpam-5505	2	46	,	,	PUNCT
ejpam-5505	2	47	yanbu	yanbu	PROPN
ejpam-5505	2	48	,	,	PUNCT
ejpam-5505	2	49	saudi	saudi	PROPN
ejpam-5505	2	50	arabia	arabia	PROPN
ejpam-5505	2	51	abstract	abstract	NOUN
ejpam-5505	2	52	.	.	PUNCT
ejpam-5505	3	1	in	in	ADP
ejpam-5505	3	2	this	this	DET
ejpam-5505	3	3	paper	paper	NOUN
ejpam-5505	3	4	,	,	PUNCT
ejpam-5505	3	5	we	we	PRON
ejpam-5505	3	6	investigate	investigate	VERB
ejpam-5505	3	7	the	the	DET
ejpam-5505	3	8	cycles	cycle	NOUN
ejpam-5505	3	9	and	and	CCONJ
ejpam-5505	3	10	fixed	fix	VERB
ejpam-5505	3	11	point	point	NOUN
ejpam-5505	3	12	sets	set	NOUN
ejpam-5505	3	13	of	of	ADP
ejpam-5505	3	14	compositions	composition	NOUN
ejpam-5505	3	15	of	of	ADP
ejpam-5505	3	16	resolvents	resolvent	NOUN
ejpam-5505	3	17	using	use	VERB
ejpam-5505	3	18	attouch	attouch	ADJ
ejpam-5505	3	19	–	–	PUNCT
ejpam-5505	3	20	théra	théra	NUM
ejpam-5505	3	21	duality	duality	NOUN
ejpam-5505	3	22	.	.	PUNCT
ejpam-5505	4	1	we	we	PRON
ejpam-5505	4	2	demonstrate	demonstrate	VERB
ejpam-5505	4	3	that	that	SCONJ
ejpam-5505	4	4	the	the	DET
ejpam-5505	4	5	cycles	cycle	NOUN
ejpam-5505	4	6	defined	define	VERB
ejpam-5505	4	7	by	by	ADP
ejpam-5505	4	8	the	the	DET
ejpam-5505	4	9	resolvent	resolvent	ADJ
ejpam-5505	4	10	operators	operator	NOUN
ejpam-5505	4	11	can	can	AUX
ejpam-5505	4	12	be	be	AUX
ejpam-5505	4	13	formulated	formulate	VERB
ejpam-5505	4	14	in	in	ADP
ejpam-5505	4	15	hilbert	hilbert	NOUN
ejpam-5505	4	16	space	space	NOUN
ejpam-5505	4	17	as	as	ADP
ejpam-5505	4	18	solutions	solution	NOUN
ejpam-5505	4	19	to	to	ADP
ejpam-5505	4	20	a	a	DET
ejpam-5505	4	21	fixed	fix	VERB
ejpam-5505	4	22	point	point	NOUN
ejpam-5505	4	23	equation	equation	NOUN
ejpam-5505	4	24	.	.	PUNCT
ejpam-5505	5	1	furthermore	furthermore	ADV
ejpam-5505	5	2	,	,	PUNCT
ejpam-5505	5	3	we	we	PRON
ejpam-5505	5	4	introduce	introduce	VERB
ejpam-5505	5	5	the	the	DET
ejpam-5505	5	6	relationship	relationship	NOUN
ejpam-5505	5	7	between	between	ADP
ejpam-5505	5	8	these	these	DET
ejpam-5505	5	9	cycles	cycle	NOUN
ejpam-5505	5	10	and	and	CCONJ
ejpam-5505	5	11	the	the	DET
ejpam-5505	5	12	fixed	fix	VERB
ejpam-5505	5	13	point	point	NOUN
ejpam-5505	5	14	sets	set	NOUN
ejpam-5505	5	15	of	of	ADP
ejpam-5505	5	16	the	the	DET
ejpam-5505	5	17	compositions	composition	NOUN
ejpam-5505	5	18	of	of	ADP
ejpam-5505	5	19	resolvents	resolvent	NOUN
ejpam-5505	5	20	.	.	PUNCT
ejpam-5505	6	1	2020	2020	NUM
ejpam-5505	6	2	mathematics	mathematic	NOUN
ejpam-5505	6	3	subject	subject	NOUN
ejpam-5505	6	4	classifications	classification	NOUN
ejpam-5505	6	5	:	:	PUNCT
ejpam-5505	6	6	47h09	47h09	NUM
ejpam-5505	6	7	,	,	PUNCT
ejpam-5505	6	8	47h05	47h05	NUM
ejpam-5505	6	9	,	,	PUNCT
ejpam-5505	6	10	47a06	47a06	NUM
ejpam-5505	6	11	,	,	PUNCT
ejpam-5505	6	12	90c25	90c25	NUM
ejpam-5505	6	13	key	key	ADJ
ejpam-5505	6	14	words	word	NOUN
ejpam-5505	6	15	and	and	CCONJ
ejpam-5505	6	16	phrases	phrase	NOUN
ejpam-5505	6	17	:	:	PUNCT
ejpam-5505	6	18	displacement	displacement	ADJ
ejpam-5505	6	19	mapping	mapping	NOUN
ejpam-5505	6	20	,	,	PUNCT
ejpam-5505	6	21	attouch	attouch	ADJ
ejpam-5505	6	22	–	–	PUNCT
ejpam-5505	6	23	théra	théra	NUM
ejpam-5505	6	24	duality	duality	NOUN
ejpam-5505	6	25	,	,	PUNCT
ejpam-5505	6	26	maximally	maximally	ADV
ejpam-5505	6	27	monotone	monotone	ADJ
ejpam-5505	6	28	operator	operator	NOUN
ejpam-5505	6	29	,	,	PUNCT
ejpam-5505	6	30	nonexpansive	nonexpansive	ADJ
ejpam-5505	6	31	mapping	mapping	NOUN
ejpam-5505	6	32	,	,	PUNCT
ejpam-5505	6	33	,	,	PUNCT
ejpam-5505	6	34	fixed	fix	VERB
ejpam-5505	6	35	point	point	NOUN
ejpam-5505	6	36	set	set	NOUN
ejpam-5505	6	37	,	,	PUNCT
ejpam-5505	6	38	resolvent	resolvent	ADJ
ejpam-5505	6	39	operator	operator	NOUN
ejpam-5505	6	40	,	,	PUNCT
ejpam-5505	6	41	set	set	NOUN
ejpam-5505	6	42	-	-	PUNCT
ejpam-5505	6	43	valued	value	VERB
ejpam-5505	6	44	inverse	inverse	NOUN
ejpam-5505	6	45	1	1	NUM
ejpam-5505	6	46	.	.	PUNCT
ejpam-5505	7	1	introduction	introduction	NOUN
ejpam-5505	7	2	throughout	throughout	ADV
ejpam-5505	7	3	,	,	PUNCT
ejpam-5505	7	4	we	we	PRON
ejpam-5505	7	5	assume	assume	VERB
ejpam-5505	7	6	that	that	SCONJ
ejpam-5505	7	7	x	x	PRON
ejpam-5505	7	8	is	be	AUX
ejpam-5505	7	9	a	a	DET
ejpam-5505	7	10	real	real	ADJ
ejpam-5505	7	11	hilbert	hilbert	NOUN
ejpam-5505	7	12	space	space	NOUN
ejpam-5505	7	13	with	with	ADP
ejpam-5505	7	14	inner	inner	ADJ
ejpam-5505	7	15	product	product	NOUN
ejpam-5505	7	16	⟨	⟨	VERB
ejpam-5505	7	17	·	·	PUNCT
ejpam-5505	7	18	,	,	PUNCT
ejpam-5505	7	19	·	·	PUNCT
ejpam-5505	7	20	⟩	⟩	NOUN
ejpam-5505	7	21	:	:	PUNCT
ejpam-5505	8	1	x	x	PUNCT
ejpam-5505	8	2	×	×	NOUN
ejpam-5505	8	3	x	x	INTJ
ejpam-5505	8	4	→	→	SYM
ejpam-5505	8	5	r	r	NOUN
ejpam-5505	8	6	,	,	PUNCT
ejpam-5505	8	7	and	and	CCONJ
ejpam-5505	8	8	induced	induce	VERB
ejpam-5505	8	9	norm	norm	NOUN
ejpam-5505	8	10	∥	∥	X
ejpam-5505	8	11	·	·	PUNCT
ejpam-5505	8	12	∥	∥	X
ejpam-5505	8	13	:	:	PUNCT
ejpam-5505	9	1	x	x	X
ejpam-5505	9	2	→	→	PUNCT
ejpam-5505	9	3	r	r	NOUN
ejpam-5505	9	4	:	:	PUNCT
ejpam-5505	9	5	x	x	SYM
ejpam-5505	9	6	7→	7→	NUM
ejpam-5505	9	7	√	√	NUM
ejpam-5505	9	8	⟨x	⟨x	NUM
ejpam-5505	9	9	,	,	PUNCT
ejpam-5505	9	10	x⟩.	x⟩.	PROPN
ejpam-5505	9	11	for	for	ADP
ejpam-5505	9	12	more	more	ADJ
ejpam-5505	9	13	details	detail	NOUN
ejpam-5505	9	14	about	about	ADP
ejpam-5505	9	15	hilbert	hilbert	NOUN
ejpam-5505	9	16	space	space	NOUN
ejpam-5505	9	17	,	,	PUNCT
ejpam-5505	9	18	we	we	PRON
ejpam-5505	9	19	refere	refere	VERB
ejpam-5505	9	20	the	the	DET
ejpam-5505	9	21	redear	redear	NOUN
ejpam-5505	9	22	to	to	ADP
ejpam-5505	9	23	[	[	X
ejpam-5505	9	24	10	10	NUM
ejpam-5505	9	25	]	]	PUNCT
ejpam-5505	9	26	and	and	CCONJ
ejpam-5505	9	27	[	[	X
ejpam-5505	9	28	13	13	NUM
ejpam-5505	9	29	]	]	PUNCT
ejpam-5505	9	30	.	.	PUNCT
ejpam-5505	10	1	an	an	DET
ejpam-5505	10	2	operator	operator	NOUN
ejpam-5505	10	3	t	t	NOUN
ejpam-5505	10	4	:	:	PUNCT
ejpam-5505	10	5	x	x	X
ejpam-5505	10	6	→	→	PUNCT
ejpam-5505	10	7	x	x	X
ejpam-5505	10	8	is	be	AUX
ejpam-5505	10	9	nonexpansive	nonexpansive	ADJ
ejpam-5505	10	10	if	if	SCONJ
ejpam-5505	10	11	it	it	PRON
ejpam-5505	10	12	is	be	AUX
ejpam-5505	10	13	lipschitz	lipschitz	NOUN
ejpam-5505	10	14	continuous	continuous	ADJ
ejpam-5505	10	15	with	with	ADP
ejpam-5505	10	16	constant	constant	ADJ
ejpam-5505	10	17	1	1	NUM
ejpam-5505	10	18	,	,	PUNCT
ejpam-5505	10	19	i.e.	i.e.	X
ejpam-5505	10	20	,	,	PUNCT
ejpam-5505	10	21	(	(	PUNCT
ejpam-5505	10	22	∀x	∀x	X
ejpam-5505	10	23	∈	∈	PROPN
ejpam-5505	10	24	x	x	X
ejpam-5505	10	25	)	)	PUNCT
ejpam-5505	10	26	(	(	PUNCT
ejpam-5505	10	27	∀y	∀y	PROPN
ejpam-5505	10	28	∈	∈	PROPN
ejpam-5505	10	29	x	x	X
ejpam-5505	10	30	)	)	PUNCT
ejpam-5505	11	1	∥tx	∥tx	CCONJ
ejpam-5505	12	1	−	−	PROPN
ejpam-5505	12	2	ty∥	ty∥	NOUN
ejpam-5505	12	3	≤	≤	ADV
ejpam-5505	13	1	∥x	∥x	AUX
ejpam-5505	13	2	−	−	PROPN
ejpam-5505	13	3	y∥.	y∥.	NOUN
ejpam-5505	13	4	(	(	PUNCT
ejpam-5505	13	5	1	1	NUM
ejpam-5505	13	6	)	)	PUNCT
ejpam-5505	13	7	nonexpansive	nonexpansive	ADJ
ejpam-5505	13	8	operators	operator	NOUN
ejpam-5505	13	9	play	play	VERB
ejpam-5505	13	10	a	a	DET
ejpam-5505	13	11	major	major	ADJ
ejpam-5505	13	12	role	role	NOUN
ejpam-5505	13	13	in	in	ADP
ejpam-5505	13	14	optimization	optimization	NOUN
ejpam-5505	13	15	because	because	SCONJ
ejpam-5505	13	16	the	the	DET
ejpam-5505	13	17	set	set	NOUN
ejpam-5505	13	18	of	of	ADP
ejpam-5505	13	19	fixed	fix	VERB
ejpam-5505	13	20	points	point	NOUN
ejpam-5505	13	21	fix	fix	NOUN
ejpam-5505	13	22	r	r	NOUN
ejpam-5505	13	23	:	:	PUNCT
ejpam-5505	13	24	=	=	SYM
ejpam-5505	13	25	{	{	PUNCT
ejpam-5505	13	26	x	x	SYM
ejpam-5505	13	27	∈	∈	NOUN
ejpam-5505	13	28	x	x	PUNCT
ejpam-5505	13	29	|	|	NOUN
ejpam-5505	13	30	x	x	X
ejpam-5505	13	31	=	=	SYM
ejpam-5505	13	32	rx	rx	ADJ
ejpam-5505	13	33	}	}	PUNCT
ejpam-5505	13	34	usually	usually	ADV
ejpam-5505	13	35	represents	represent	VERB
ejpam-5505	13	36	solutions	solution	NOUN
ejpam-5505	13	37	to	to	ADP
ejpam-5505	13	38	inclusion	inclusion	NOUN
ejpam-5505	13	39	problems	problem	NOUN
ejpam-5505	13	40	and	and	CCONJ
ejpam-5505	13	41	optimization	optimization	NOUN
ejpam-5505	13	42	tasks	task	NOUN
ejpam-5505	13	43	.	.	PUNCT
ejpam-5505	14	1	for	for	ADP
ejpam-5505	14	2	more	more	ADJ
ejpam-5505	14	3	details	detail	NOUN
ejpam-5505	14	4	about	about	ADP
ejpam-5505	14	5	nonexpansive	nonexpansive	ADJ
ejpam-5505	14	6	operators	operator	NOUN
ejpam-5505	14	7	and	and	CCONJ
ejpam-5505	14	8	the	the	DET
ejpam-5505	14	9	fixed	fix	VERB
ejpam-5505	14	10	point	point	NOUN
ejpam-5505	14	11	set	set	NOUN
ejpam-5505	14	12	,	,	PUNCT
ejpam-5505	14	13	we	we	PRON
ejpam-5505	14	14	refer	refer	VERB
ejpam-5505	14	15	the	the	DET
ejpam-5505	14	16	reader	reader	NOUN
ejpam-5505	14	17	to	to	ADP
ejpam-5505	14	18	[	[	X
ejpam-5505	14	19	1]-[6	1]-[6	X
ejpam-5505	14	20	]	]	X
ejpam-5505	14	21	,	,	PUNCT
ejpam-5505	15	1	[	[	X
ejpam-5505	15	2	7]-[8	7]-[8	X
ejpam-5505	15	3	]	]	X
ejpam-5505	15	4	,	,	PUNCT
ejpam-5505	15	5	[	[	X
ejpam-5505	15	6	11	11	NUM
ejpam-5505	15	7	]	]	PUNCT
ejpam-5505	15	8	,	,	PUNCT
ejpam-5505	15	9	[	[	X
ejpam-5505	15	10	16	16	NUM
ejpam-5505	15	11	]	]	PUNCT
ejpam-5505	15	12	,	,	PUNCT
ejpam-5505	15	13	[	[	X
ejpam-5505	15	14	17	17	NUM
ejpam-5505	15	15	]	]	PUNCT
ejpam-5505	15	16	,	,	PUNCT
ejpam-5505	15	17	and	and	CCONJ
ejpam-5505	15	18	[	[	X
ejpam-5505	15	19	2	2	NUM
ejpam-5505	15	20	,	,	PUNCT
ejpam-5505	15	21	chapters	chapter	NOUN
ejpam-5505	15	22	3	3	NUM
ejpam-5505	15	23	and	and	CCONJ
ejpam-5505	15	24	6	6	NUM
ejpam-5505	15	25	]	]	PUNCT
ejpam-5505	15	26	.	.	PUNCT
ejpam-5505	16	1	moreover	moreover	ADV
ejpam-5505	16	2	,	,	PUNCT
ejpam-5505	16	3	t	t	X
ejpam-5505	16	4	:	:	PUNCT
ejpam-5505	16	5	d	d	X
ejpam-5505	16	6	→	→	PUNCT
ejpam-5505	16	7	x	x	X
ejpam-5505	16	8	is	be	AUX
ejpam-5505	16	9	firmly	firmly	ADV
ejpam-5505	16	10	nonexpansive	nonexpansive	ADJ
ejpam-5505	16	11	if	if	SCONJ
ejpam-5505	16	12	(	(	PUNCT
ejpam-5505	16	13	∀x	∀x	X
ejpam-5505	16	14	∈	∈	PROPN
ejpam-5505	16	15	d	d	NOUN
ejpam-5505	16	16	)	)	PUNCT
ejpam-5505	16	17	(	(	PUNCT
ejpam-5505	16	18	∀y	∀y	PROPN
ejpam-5505	16	19	∈	∈	PROPN
ejpam-5505	16	20	d	d	NOUN
ejpam-5505	16	21	)	)	PUNCT
ejpam-5505	17	1	∥tx	∥tx	PRON
ejpam-5505	17	2	−	−	PROPN
ejpam-5505	17	3	ty∥2	ty∥2	NOUN
ejpam-5505	17	4	+	+	CCONJ
ejpam-5505	17	5	∥(id−t)x	∥(id−t)x	PROPN
ejpam-5505	17	6	−	−	PROPN
ejpam-5505	17	7	(	(	PUNCT
ejpam-5505	17	8	id−t)y∥2	id−t)y∥2	PROPN
ejpam-5505	17	9	≤	≤	PUNCT
ejpam-5505	18	1	∥x	∥x	PROPN
ejpam-5505	18	2	−	−	PROPN
ejpam-5505	18	3	y∥2	y∥2	NOUN
ejpam-5505	18	4	.	.	PUNCT
ejpam-5505	19	1	(	(	PUNCT
ejpam-5505	19	2	2	2	X
ejpam-5505	19	3	)	)	PUNCT
ejpam-5505	19	4	doi	doi	NOUN
ejpam-5505	19	5	:	:	PUNCT
ejpam-5505	19	6	https://doi.org/10.29020/nybg.ejpam.v17i4.5505	https://doi.org/10.29020/nybg.ejpam.v17i4.5505	ADJ
ejpam-5505	19	7	email	email	NOUN
ejpam-5505	19	8	address	address	NOUN
ejpam-5505	19	9	:	:	PUNCT
ejpam-5505	19	10	salihah.s.alwadani@gmail.com	salihah.s.alwadani@gmail.com	PROPN
ejpam-5505	19	11	(	(	PUNCT
ejpam-5505	19	12	s.	s.	PROPN
ejpam-5505	19	13	t.	t.	PROPN
ejpam-5505	19	14	alwadani	alwadani	PROPN
ejpam-5505	19	15	)	)	PUNCT
ejpam-5505	19	16	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5505	19	17	3642	3642	NUM
ejpam-5505	19	18	copyright	copyright	NOUN
ejpam-5505	19	19	:	:	PUNCT
ejpam-5505	19	20	©	©	PROPN
ejpam-5505	19	21	2024	2024	NUM
ejpam-5505	19	22	the	the	DET
ejpam-5505	19	23	author(s	author(s	NOUN
ejpam-5505	19	24	)	)	PUNCT
ejpam-5505	19	25	.	.	PUNCT
ejpam-5505	20	1	(	(	PUNCT
ejpam-5505	20	2	cc	cc	NOUN
ejpam-5505	20	3	by	by	ADP
ejpam-5505	20	4	-	-	PUNCT
ejpam-5505	20	5	nc	nc	PROPN
ejpam-5505	20	6	4.0	4.0	NUM
ejpam-5505	20	7	)	)	PUNCT
ejpam-5505	20	8	s.th.alwadani	s.th.alwadani	NOUN
ejpam-5505	20	9	/	/	SYM
ejpam-5505	20	10	eur	eur	NOUN
ejpam-5505	20	11	.	.	PUNCT
ejpam-5505	21	1	j.	j.	PROPN
ejpam-5505	21	2	pure	pure	PROPN
ejpam-5505	21	3	appl	appl	PROPN
ejpam-5505	21	4	.	.	PROPN
ejpam-5505	21	5	math	math	PROPN
ejpam-5505	21	6	,	,	PUNCT
ejpam-5505	21	7	17	17	NUM
ejpam-5505	21	8	(	(	PUNCT
ejpam-5505	21	9	4	4	NUM
ejpam-5505	21	10	)	)	PUNCT
ejpam-5505	21	11	(	(	PUNCT
ejpam-5505	21	12	2024	2024	NUM
ejpam-5505	21	13	)	)	PUNCT
ejpam-5505	21	14	,	,	PUNCT
ejpam-5505	21	15	3642	3642	NUM
ejpam-5505	21	16	-	-	SYM
ejpam-5505	21	17	3659	3659	NUM
ejpam-5505	21	18	3643	3643	NUM
ejpam-5505	21	19	firmly	firmly	ADV
ejpam-5505	21	20	nonexpansive	nonexpansive	ADJ
ejpam-5505	21	21	operators	operator	NOUN
ejpam-5505	21	22	are	be	AUX
ejpam-5505	21	23	also	also	ADV
ejpam-5505	21	24	central	central	ADJ
ejpam-5505	21	25	due	due	ADP
ejpam-5505	21	26	to	to	ADP
ejpam-5505	21	27	their	their	PRON
ejpam-5505	21	28	favorable	favorable	ADJ
ejpam-5505	21	29	convergence	convergence	NOUN
ejpam-5505	21	30	properties	property	NOUN
ejpam-5505	21	31	for	for	ADP
ejpam-5505	21	32	iterates	iterate	NOUN
ejpam-5505	21	33	and	and	CCONJ
ejpam-5505	21	34	their	their	PRON
ejpam-5505	21	35	correspondence	correspondence	NOUN
ejpam-5505	21	36	with	with	ADP
ejpam-5505	21	37	maximal	maximal	ADJ
ejpam-5505	21	38	monotone	monotone	ADJ
ejpam-5505	21	39	operators	operator	NOUN
ejpam-5505	21	40	.	.	PUNCT
ejpam-5505	22	1	recall	recall	VERB
ejpam-5505	22	2	that	that	SCONJ
ejpam-5505	22	3	a	a	DET
ejpam-5505	22	4	set	set	NOUN
ejpam-5505	22	5	-	-	PUNCT
ejpam-5505	22	6	valued	value	VERB
ejpam-5505	22	7	operator	operator	NOUN
ejpam-5505	22	8	a	a	DET
ejpam-5505	22	9	:	:	PUNCT
ejpam-5505	22	10	x	x	SYM
ejpam-5505	22	11	⇒	⇒	NOUN
ejpam-5505	22	12	x	x	PUNCT
ejpam-5505	22	13	with	with	ADP
ejpam-5505	22	14	graph	graph	NOUN
ejpam-5505	22	15	gra	gra	PROPN
ejpam-5505	22	16	a	a	PRON
ejpam-5505	22	17	is	be	AUX
ejpam-5505	22	18	monotone	monotone	ADJ
ejpam-5505	22	19	if	if	SCONJ
ejpam-5505	22	20	(	(	PUNCT
ejpam-5505	22	21	∀	∀	X
ejpam-5505	22	22	(	(	PUNCT
ejpam-5505	22	23	x	x	X
ejpam-5505	22	24	,	,	PUNCT
ejpam-5505	22	25	u	u	NOUN
ejpam-5505	22	26	)	)	PUNCT
ejpam-5505	22	27	∈	∈	PROPN
ejpam-5505	22	28	gra	gra	PROPN
ejpam-5505	22	29	a	a	PRON
ejpam-5505	22	30	)	)	PUNCT
ejpam-5505	22	31	(	(	PUNCT
ejpam-5505	22	32	∀	∀	X
ejpam-5505	22	33	(	(	PUNCT
ejpam-5505	22	34	y	y	NOUN
ejpam-5505	22	35	,	,	PUNCT
ejpam-5505	22	36	v	v	NOUN
ejpam-5505	22	37	)	)	PUNCT
ejpam-5505	22	38	∈	∈	PROPN
ejpam-5505	22	39	gra	gra	PROPN
ejpam-5505	22	40	a	a	PRON
ejpam-5505	22	41	)	)	PUNCT
ejpam-5505	22	42	⟨x	⟨x	VERB
ejpam-5505	22	43	−	−	PROPN
ejpam-5505	22	44	y	y	PROPN
ejpam-5505	22	45	,	,	PUNCT
ejpam-5505	22	46	u	u	NOUN
ejpam-5505	22	47	−	−	PROPN
ejpam-5505	22	48	v⟩	v⟩	VERB
ejpam-5505	22	49	≥	≥	NOUN
ejpam-5505	22	50	0	0	NUM
ejpam-5505	22	51	.	.	PUNCT
ejpam-5505	23	1	furthermore	furthermore	ADV
ejpam-5505	23	2	,	,	PUNCT
ejpam-5505	23	3	a	a	PRON
ejpam-5505	23	4	is	be	AUX
ejpam-5505	23	5	maximally	maximally	ADV
ejpam-5505	23	6	monotone	monotone	ADJ
ejpam-5505	23	7	if	if	SCONJ
ejpam-5505	23	8	there	there	PRON
ejpam-5505	23	9	does	do	AUX
ejpam-5505	23	10	not	not	PART
ejpam-5505	23	11	exist	exist	VERB
ejpam-5505	23	12	a	a	DET
ejpam-5505	23	13	monotone	monotone	ADJ
ejpam-5505	23	14	operator	operator	NOUN
ejpam-5505	23	15	b	b	NOUN
ejpam-5505	23	16	:	:	PUNCT
ejpam-5505	23	17	x	x	SYM
ejpam-5505	23	18	⇒	⇒	NOUN
ejpam-5505	23	19	x	x	PUNCT
ejpam-5505	23	20	such	such	ADJ
ejpam-5505	23	21	that	that	SCONJ
ejpam-5505	23	22	gra	gra	PROPN
ejpam-5505	23	23	b	b	PROPN
ejpam-5505	23	24	properly	properly	ADV
ejpam-5505	23	25	contains	contain	VERB
ejpam-5505	23	26	gra	gra	PROPN
ejpam-5505	23	27	a	a	PRON
ejpam-5505	23	28	,	,	PUNCT
ejpam-5505	23	29	i.e.	i.e.	X
ejpam-5505	23	30	,	,	PUNCT
ejpam-5505	23	31	for	for	SCONJ
ejpam-5505	23	32	every	every	DET
ejpam-5505	23	33	(	(	PUNCT
ejpam-5505	23	34	x	x	NOUN
ejpam-5505	23	35	,	,	PUNCT
ejpam-5505	23	36	u	u	NOUN
ejpam-5505	23	37	)	)	PUNCT
ejpam-5505	23	38	∈	∈	PROPN
ejpam-5505	23	39	x	x	SYM
ejpam-5505	23	40	×	×	NOUN
ejpam-5505	23	41	x	x	SYM
ejpam-5505	23	42	,	,	PUNCT
ejpam-5505	23	43	(	(	PUNCT
ejpam-5505	23	44	x	x	NOUN
ejpam-5505	23	45	,	,	PUNCT
ejpam-5505	23	46	u	u	NOUN
ejpam-5505	23	47	)	)	PUNCT
ejpam-5505	23	48	∈	∈	PROPN
ejpam-5505	23	49	gra	gra	PROPN
ejpam-5505	23	50	a	a	DET
ejpam-5505	23	51	⇔	⇔	X
ejpam-5505	23	52	(	(	PUNCT
ejpam-5505	23	53	∀	∀	X
ejpam-5505	23	54	(	(	PUNCT
ejpam-5505	23	55	y	y	NOUN
ejpam-5505	23	56	,	,	PUNCT
ejpam-5505	23	57	v	v	NOUN
ejpam-5505	23	58	)	)	PUNCT
ejpam-5505	23	59	∈	∈	PROPN
ejpam-5505	23	60	gra	gra	PROPN
ejpam-5505	23	61	a	a	PRON
ejpam-5505	23	62	)	)	PUNCT
ejpam-5505	23	63	⟨x	⟨x	VERB
ejpam-5505	23	64	−	−	PROPN
ejpam-5505	23	65	y	y	PROPN
ejpam-5505	23	66	,	,	PUNCT
ejpam-5505	23	67	u	u	NOUN
ejpam-5505	23	68	−	−	PROPN
ejpam-5505	23	69	v⟩	v⟩	VERB
ejpam-5505	23	70	≥	≥	NOUN
ejpam-5505	23	71	0	0	NUM
ejpam-5505	23	72	.	.	PUNCT
ejpam-5505	24	1	it	it	PRON
ejpam-5505	24	2	is	be	AUX
ejpam-5505	24	3	well	well	ADV
ejpam-5505	24	4	known	know	VERB
ejpam-5505	24	5	that	that	SCONJ
ejpam-5505	24	6	monotone	monotone	ADJ
ejpam-5505	24	7	and	and	CCONJ
ejpam-5505	24	8	maximally	maximally	ADV
ejpam-5505	24	9	monotone	monotone	ADJ
ejpam-5505	24	10	operators	operator	NOUN
ejpam-5505	24	11	play	play	VERB
ejpam-5505	24	12	central	central	ADJ
ejpam-5505	24	13	roles	role	NOUN
ejpam-5505	24	14	in	in	ADP
ejpam-5505	24	15	various	various	ADJ
ejpam-5505	24	16	areas	area	NOUN
ejpam-5505	24	17	of	of	ADP
ejpam-5505	24	18	modern	modern	ADJ
ejpam-5505	24	19	nonlinear	nonlinear	ADJ
ejpam-5505	24	20	analysis	analysis	NOUN
ejpam-5505	24	21	.	.	PUNCT
ejpam-5505	25	1	see	see	VERB
ejpam-5505	25	2	[	[	X
ejpam-5505	25	3	10	10	NUM
ejpam-5505	25	4	]	]	PUNCT
ejpam-5505	25	5	,	,	PUNCT
ejpam-5505	25	6	[	[	X
ejpam-5505	25	7	14	14	NUM
ejpam-5505	25	8	]	]	PUNCT
ejpam-5505	25	9	,	,	PUNCT
ejpam-5505	26	1	[	[	X
ejpam-5505	26	2	15]-[22	15]-[22	NOUN
ejpam-5505	26	3	]	]	PUNCT
ejpam-5505	26	4	,	,	PUNCT
ejpam-5505	26	5	and	and	CCONJ
ejpam-5505	26	6	[	[	X
ejpam-5505	26	7	20	20	NUM
ejpam-5505	26	8	]	]	PUNCT
ejpam-5505	26	9	for	for	ADP
ejpam-5505	26	10	background	background	NOUN
ejpam-5505	26	11	material	material	NOUN
ejpam-5505	26	12	.	.	PUNCT
ejpam-5505	27	1	let	let	VERB
ejpam-5505	27	2	a	a	DET
ejpam-5505	27	3	:	:	PUNCT
ejpam-5505	27	4	x	x	SYM
ejpam-5505	27	5	⇒	⇒	NOUN
ejpam-5505	27	6	x	x	PUNCT
ejpam-5505	27	7	be	be	AUX
ejpam-5505	27	8	a	a	DET
ejpam-5505	27	9	maximally	maximally	ADV
ejpam-5505	27	10	monotone	monotone	ADJ
ejpam-5505	27	11	operator	operator	NOUN
ejpam-5505	27	12	and	and	CCONJ
ejpam-5505	27	13	denote	denote	VERB
ejpam-5505	27	14	the	the	DET
ejpam-5505	27	15	associated	associated	ADJ
ejpam-5505	27	16	resolvent	resolvent	NOUN
ejpam-5505	27	17	by	by	ADP
ejpam-5505	27	18	ja	ja	PROPN
ejpam-5505	27	19	:	:	PUNCT
ejpam-5505	27	20	=	=	SYM
ejpam-5505	27	21	(	(	PUNCT
ejpam-5505	27	22	id+a)−1	id+a)−1	NOUN
ejpam-5505	27	23	.	.	PUNCT
ejpam-5505	28	1	(	(	PUNCT
ejpam-5505	28	2	3	3	X
ejpam-5505	28	3	)	)	PUNCT
ejpam-5505	28	4	in	in	ADP
ejpam-5505	28	5	[	[	X
ejpam-5505	28	6	21	21	NUM
ejpam-5505	28	7	]	]	PUNCT
ejpam-5505	28	8	,	,	PUNCT
ejpam-5505	28	9	minty	minty	ADJ
ejpam-5505	28	10	observed	observe	VERB
ejpam-5505	28	11	that	that	SCONJ
ejpam-5505	28	12	ja	ja	PROPN
ejpam-5505	28	13	is	be	AUX
ejpam-5505	28	14	a	a	DET
ejpam-5505	28	15	firmly	firmly	ADV
ejpam-5505	28	16	nonexpansive	nonexpansive	ADJ
ejpam-5505	28	17	operator	operator	NOUN
ejpam-5505	28	18	from	from	ADP
ejpam-5505	28	19	x	x	PRON
ejpam-5505	28	20	to	to	PART
ejpam-5505	28	21	x.	x.	NOUN
ejpam-5505	28	22	for	for	ADP
ejpam-5505	28	23	more	more	ADJ
ejpam-5505	28	24	information	information	NOUN
ejpam-5505	28	25	about	about	ADP
ejpam-5505	28	26	the	the	DET
ejpam-5505	28	27	relationship	relationship	NOUN
ejpam-5505	28	28	between	between	ADP
ejpam-5505	28	29	firmly	firmly	ADV
ejpam-5505	28	30	nonexpansive	nonexpansive	ADJ
ejpam-5505	28	31	mappings	mapping	NOUN
ejpam-5505	28	32	and	and	CCONJ
ejpam-5505	28	33	maximally	maximally	ADV
ejpam-5505	28	34	monotone	monotone	ADJ
ejpam-5505	28	35	operators	operator	NOUN
ejpam-5505	28	36	,	,	PUNCT
ejpam-5505	28	37	see	see	VERB
ejpam-5505	28	38	[	[	X
ejpam-5505	28	39	12	12	NUM
ejpam-5505	28	40	]	]	PUNCT
ejpam-5505	28	41	.	.	PUNCT
ejpam-5505	29	1	the	the	DET
ejpam-5505	29	2	hilber	hilber	PROPN
ejpam-5505	29	3	product	product	NOUN
ejpam-5505	29	4	space	space	NOUN
ejpam-5505	29	5	,	,	PUNCT
ejpam-5505	29	6	x	x	PUNCT
ejpam-5505	29	7	=	=	PRON
ejpam-5505	29	8	{	{	PUNCT
ejpam-5505	29	9	x	x	SYM
ejpam-5505	29	10	=	=	SYM
ejpam-5505	29	11	(	(	PUNCT
ejpam-5505	29	12	xi)i∈i	xi)i∈i	X
ejpam-5505	29	13	∣∣∣	∣∣∣	NOUN
ejpam-5505	29	14	(	(	PUNCT
ejpam-5505	29	15	∀i	∀i	X
ejpam-5505	29	16	∈	∈	PROPN
ejpam-5505	29	17	i	i	NOUN
ejpam-5505	29	18	)	)	PUNCT
ejpam-5505	29	19	xi	xi	X
ejpam-5505	29	20	∈	∈	PROPN
ejpam-5505	29	21	x	x	PUNCT
ejpam-5505	29	22	}	}	PUNCT
ejpam-5505	29	23	,	,	PUNCT
ejpam-5505	29	24	where	where	SCONJ
ejpam-5505	29	25	m	m	VERB
ejpam-5505	29	26	∈	∈	NOUN
ejpam-5505	29	27	{	{	PUNCT
ejpam-5505	29	28	2	2	NUM
ejpam-5505	29	29	,	,	PUNCT
ejpam-5505	29	30	3	3	NUM
ejpam-5505	29	31	,	,	PUNCT
ejpam-5505	29	32	.	.	PUNCT
ejpam-5505	29	33	.	.	PUNCT
ejpam-5505	29	34	.	.	PUNCT
ejpam-5505	30	1	}	}	PUNCT
ejpam-5505	31	1	and	and	CCONJ
ejpam-5505	31	2	i	i	PRON
ejpam-5505	31	3	=	=	PUNCT
ejpam-5505	31	4	{	{	PUNCT
ejpam-5505	31	5	1	1	NUM
ejpam-5505	31	6	,	,	PUNCT
ejpam-5505	31	7	2	2	NUM
ejpam-5505	31	8	,	,	PUNCT
ejpam-5505	31	9	.	.	PUNCT
ejpam-5505	31	10	.	.	PUNCT
ejpam-5505	31	11	.	.	PUNCT
ejpam-5505	32	1	,	,	PUNCT
ejpam-5505	32	2	m	m	VERB
ejpam-5505	32	3	}	}	PUNCT
ejpam-5505	32	4	.	.	PUNCT
ejpam-5505	33	1	let	let	VERB
ejpam-5505	33	2	ai	ai	VERB
ejpam-5505	33	3	:	:	PUNCT
ejpam-5505	33	4	x	x	SYM
ejpam-5505	33	5	⇒	⇒	NOUN
ejpam-5505	33	6	x	x	PUNCT
ejpam-5505	33	7	be	be	VERB
ejpam-5505	33	8	maximally	maximally	ADV
ejpam-5505	33	9	monotone	monotone	ADJ
ejpam-5505	33	10	operators	operator	NOUN
ejpam-5505	33	11	,	,	PUNCT
ejpam-5505	33	12	(	(	PUNCT
ejpam-5505	33	13	4	4	NUM
ejpam-5505	33	14	)	)	PUNCT
ejpam-5505	33	15	with	with	ADP
ejpam-5505	33	16	resolvents	resolvent	NOUN
ejpam-5505	33	17	ja1	ja1	ADV
ejpam-5505	33	18	,	,	PUNCT
ejpam-5505	33	19	ja2	ja2	PROPN
ejpam-5505	33	20	,	,	PUNCT
ejpam-5505	33	21	.	.	PUNCT
ejpam-5505	33	22	.	.	PUNCT
ejpam-5505	34	1	.	.	PUNCT
ejpam-5505	35	1	,	,	PUNCT
ejpam-5505	35	2	jam	jam	NOUN
ejpam-5505	35	3	which	which	PRON
ejpam-5505	35	4	we	we	PRON
ejpam-5505	35	5	also	also	ADV
ejpam-5505	35	6	write	write	VERB
ejpam-5505	35	7	more	more	ADV
ejpam-5505	35	8	simply	simply	ADV
ejpam-5505	35	9	as	as	ADP
ejpam-5505	35	10	j1	j1	PROPN
ejpam-5505	35	11	,	,	PUNCT
ejpam-5505	35	12	j2	j2	PROPN
ejpam-5505	35	13	,	,	PUNCT
ejpam-5505	35	14	.	.	PUNCT
ejpam-5505	35	15	.	.	PUNCT
ejpam-5505	36	1	.	.	PUNCT
ejpam-5505	37	1	,	,	PUNCT
ejpam-5505	37	2	jm	jm	PROPN
ejpam-5505	37	3	.	.	PROPN
ejpam-5505	37	4	set	set	VERB
ejpam-5505	37	5	a	a	DET
ejpam-5505	37	6	=	=	NOUN
ejpam-5505	37	7	a1	a1	NOUN
ejpam-5505	37	8	×	×	PROPN
ejpam-5505	37	9	a2	a2	PROPN
ejpam-5505	37	10	×	×	PROPN
ejpam-5505	37	11	·	·	PUNCT
ejpam-5505	37	12	·	·	PUNCT
ejpam-5505	37	13	·	·	PUNCT
ejpam-5505	38	1	×	×	NOUN
ejpam-5505	38	2	am	am	NOUN
ejpam-5505	38	3	.	.	PUNCT
ejpam-5505	39	1	(	(	PUNCT
ejpam-5505	39	2	5	5	NUM
ejpam-5505	39	3	)	)	PUNCT
ejpam-5505	39	4	then	then	ADV
ejpam-5505	39	5	ja	ja	INTJ
ejpam-5505	39	6	:	:	PUNCT
ejpam-5505	39	7	x	x	X
ejpam-5505	39	8	→	→	PUNCT
ejpam-5505	39	9	x	x	SYM
ejpam-5505	39	10	:	:	PUNCT
ejpam-5505	39	11	(	(	PUNCT
ejpam-5505	39	12	x1	x1	PROPN
ejpam-5505	39	13	,	,	PUNCT
ejpam-5505	39	14	x2	x2	PROPN
ejpam-5505	39	15	,	,	PUNCT
ejpam-5505	39	16	.	.	PUNCT
ejpam-5505	39	17	.	.	PUNCT
ejpam-5505	39	18	.	.	PUNCT
ejpam-5505	40	1	,	,	PUNCT
ejpam-5505	40	2	xm	xm	PROPN
ejpam-5505	40	3	)	)	PUNCT
ejpam-5505	41	1	7→	7→	PROPN
ejpam-5505	41	2	(	(	PUNCT
ejpam-5505	41	3	j1x1	j1x1	NOUN
ejpam-5505	41	4	,	,	PUNCT
ejpam-5505	41	5	j2x2	j2x2	NOUN
ejpam-5505	41	6	,	,	PUNCT
ejpam-5505	41	7	.	.	PUNCT
ejpam-5505	41	8	.	.	PUNCT
ejpam-5505	42	1	.	.	PUNCT
ejpam-5505	43	1	,	,	PUNCT
ejpam-5505	43	2	jmxm	jmxm	ADJ
ejpam-5505	43	3	)	)	PUNCT
ejpam-5505	43	4	.	.	PUNCT
ejpam-5505	44	1	(	(	PUNCT
ejpam-5505	44	2	6	6	X
ejpam-5505	44	3	)	)	PUNCT
ejpam-5505	44	4	define	define	VERB
ejpam-5505	44	5	the	the	DET
ejpam-5505	44	6	circular	circular	ADJ
ejpam-5505	44	7	right	right	ADJ
ejpam-5505	44	8	-	-	PUNCT
ejpam-5505	44	9	shift	shift	NOUN
ejpam-5505	44	10	operator	operator	NOUN
ejpam-5505	44	11	r	r	NOUN
ejpam-5505	44	12	:	:	PUNCT
ejpam-5505	44	13	(	(	PUNCT
ejpam-5505	44	14	x1	x1	PROPN
ejpam-5505	44	15	,	,	PUNCT
ejpam-5505	44	16	x2	x2	PROPN
ejpam-5505	44	17	,	,	PUNCT
ejpam-5505	44	18	.	.	PUNCT
ejpam-5505	44	19	.	.	PUNCT
ejpam-5505	45	1	.	.	PUNCT
ejpam-5505	46	1	,	,	PUNCT
ejpam-5505	46	2	xm	xm	PROPN
ejpam-5505	46	3	)	)	PUNCT
ejpam-5505	47	1	7→	7→	PROPN
ejpam-5505	47	2	(	(	PUNCT
ejpam-5505	47	3	xm	xm	PROPN
ejpam-5505	47	4	,	,	PUNCT
ejpam-5505	47	5	x1	x1	PROPN
ejpam-5505	47	6	,	,	PUNCT
ejpam-5505	47	7	x2	x2	PROPN
ejpam-5505	47	8	,	,	PUNCT
ejpam-5505	47	9	.	.	PUNCT
ejpam-5505	47	10	.	.	PUNCT
ejpam-5505	48	1	.	.	PUNCT
ejpam-5505	49	1	,	,	PUNCT
ejpam-5505	49	2	xm−1	xm−1	PROPN
ejpam-5505	49	3	)	)	PUNCT
ejpam-5505	49	4	.	.	PUNCT
ejpam-5505	50	1	(	(	PUNCT
ejpam-5505	50	2	7	7	X
ejpam-5505	50	3	)	)	PUNCT
ejpam-5505	50	4	define	define	VERB
ejpam-5505	50	5	the	the	DET
ejpam-5505	50	6	fixed	fix	VERB
ejpam-5505	50	7	point	point	NOUN
ejpam-5505	50	8	sets	set	NOUN
ejpam-5505	50	9	of	of	ADP
ejpam-5505	50	10	the	the	DET
ejpam-5505	50	11	cyclic	cyclic	ADJ
ejpam-5505	50	12	compositions	composition	NOUN
ejpam-5505	50	13	of	of	ADP
ejpam-5505	50	14	resolvants	resolvant	NOUN
ejpam-5505	50	15	:	:	PUNCT
ejpam-5505	50	16	f1	f1	NOUN
ejpam-5505	50	17	:	:	PUNCT
ejpam-5505	50	18	=	=	SYM
ejpam-5505	50	19	fix(j1jm	fix(j1jm	PROPN
ejpam-5505	50	20	.	.	PUNCT
ejpam-5505	50	21	.	.	PUNCT
ejpam-5505	50	22	.	.	PUNCT
ejpam-5505	51	1	j2	j2	PROPN
ejpam-5505	51	2	)	)	PUNCT
ejpam-5505	51	3	,	,	PUNCT
ejpam-5505	51	4	(	(	PUNCT
ejpam-5505	51	5	8)	8)	NUM
ejpam-5505	51	6	f2	f2	PRON
ejpam-5505	51	7	:	:	PUNCT
ejpam-5505	51	8	=	=	SYM
ejpam-5505	51	9	fix(j2j1jm	fix(j2j1jm	INTJ
ejpam-5505	51	10	.	.	PUNCT
ejpam-5505	51	11	.	.	PUNCT
ejpam-5505	51	12	.	.	PUNCT
ejpam-5505	52	1	j3	j3	PROPN
ejpam-5505	52	2	)	)	PUNCT
ejpam-5505	52	3	,	,	PUNCT
ejpam-5505	52	4	(	(	PUNCT
ejpam-5505	52	5	9	9	NUM
ejpam-5505	52	6	)	)	PUNCT
ejpam-5505	52	7	...	...	PUNCT
ejpam-5505	53	1	(	(	PUNCT
ejpam-5505	53	2	10	10	NUM
ejpam-5505	53	3	)	)	PUNCT
ejpam-5505	53	4	fm	fm	NOUN
ejpam-5505	53	5	:	:	PUNCT
ejpam-5505	53	6	=	=	SYM
ejpam-5505	53	7	fix(jmjm−1	fix(jmjm−1	NOUN
ejpam-5505	53	8	.	.	PUNCT
ejpam-5505	53	9	.	.	PUNCT
ejpam-5505	53	10	.	.	PUNCT
ejpam-5505	54	1	j1	j1	PROPN
ejpam-5505	54	2	)	)	PUNCT
ejpam-5505	54	3	.	.	PUNCT
ejpam-5505	55	1	(	(	PUNCT
ejpam-5505	55	2	11	11	NUM
ejpam-5505	55	3	)	)	PUNCT
ejpam-5505	55	4	the	the	DET
ejpam-5505	55	5	prospects	prospect	NOUN
ejpam-5505	55	6	of	of	ADP
ejpam-5505	55	7	applying	apply	VERB
ejpam-5505	55	8	the	the	DET
ejpam-5505	55	9	compositions	composition	NOUN
ejpam-5505	55	10	of	of	ADP
ejpam-5505	55	11	resolvents	resolvent	NOUN
ejpam-5505	55	12	in	in	ADP
ejpam-5505	55	13	practical	practical	ADJ
ejpam-5505	55	14	applications	application	NOUN
ejpam-5505	55	15	are	be	AUX
ejpam-5505	55	16	broad	broad	ADJ
ejpam-5505	55	17	and	and	CCONJ
ejpam-5505	55	18	significant	significant	ADJ
ejpam-5505	55	19	,	,	PUNCT
ejpam-5505	55	20	particularly	particularly	ADV
ejpam-5505	55	21	in	in	ADP
ejpam-5505	55	22	fields	field	NOUN
ejpam-5505	55	23	such	such	ADJ
ejpam-5505	55	24	as	as	ADP
ejpam-5505	55	25	optimization	optimization	NOUN
ejpam-5505	55	26	,	,	PUNCT
ejpam-5505	55	27	control	control	NOUN
ejpam-5505	55	28	theory	theory	NOUN
ejpam-5505	55	29	,	,	PUNCT
ejpam-5505	55	30	and	and	CCONJ
ejpam-5505	55	31	mathematical	mathematical	ADJ
ejpam-5505	55	32	analysis	analysis	NOUN
ejpam-5505	55	33	.	.	PUNCT
ejpam-5505	56	1	here	here	ADV
ejpam-5505	56	2	are	be	AUX
ejpam-5505	56	3	some	some	DET
ejpam-5505	56	4	key	key	ADJ
ejpam-5505	56	5	areas	area	NOUN
ejpam-5505	56	6	where	where	SCONJ
ejpam-5505	56	7	these	these	DET
ejpam-5505	56	8	applications	application	NOUN
ejpam-5505	56	9	are	be	AUX
ejpam-5505	56	10	emerging	emerge	VERB
ejpam-5505	56	11	:	:	PUNCT
ejpam-5505	56	12	s.th.alwadani	s.th.alwadani	ADJ
ejpam-5505	56	13	/	/	SYM
ejpam-5505	56	14	eur	eur	PROPN
ejpam-5505	56	15	.	.	PUNCT
ejpam-5505	57	1	j.	j.	PROPN
ejpam-5505	57	2	pure	pure	PROPN
ejpam-5505	57	3	appl	appl	PROPN
ejpam-5505	57	4	.	.	PROPN
ejpam-5505	57	5	math	math	PROPN
ejpam-5505	57	6	,	,	PUNCT
ejpam-5505	57	7	17	17	NUM
ejpam-5505	57	8	(	(	PUNCT
ejpam-5505	57	9	4	4	NUM
ejpam-5505	57	10	)	)	PUNCT
ejpam-5505	57	11	(	(	PUNCT
ejpam-5505	57	12	2024	2024	NUM
ejpam-5505	57	13	)	)	PUNCT
ejpam-5505	57	14	,	,	PUNCT
ejpam-5505	57	15	3642	3642	NUM
ejpam-5505	57	16	-	-	SYM
ejpam-5505	57	17	3659	3659	NUM
ejpam-5505	57	18	3644	3644	NUM
ejpam-5505	57	19	1	1	NUM
ejpam-5505	57	20	.	.	PUNCT
ejpam-5505	58	1	in	in	ADP
ejpam-5505	58	2	the	the	DET
ejpam-5505	58	3	area	area	NOUN
ejpam-5505	58	4	of	of	ADP
ejpam-5505	58	5	optimization	optimization	NOUN
ejpam-5505	58	6	and	and	CCONJ
ejpam-5505	58	7	control	control	NOUN
ejpam-5505	58	8	:	:	PUNCT
ejpam-5505	58	9	compositions	composition	NOUN
ejpam-5505	58	10	of	of	ADP
ejpam-5505	58	11	resolvents	resolvent	NOUN
ejpam-5505	58	12	are	be	AUX
ejpam-5505	58	13	crucial	crucial	ADJ
ejpam-5505	58	14	in	in	ADP
ejpam-5505	58	15	optimization	optimization	NOUN
ejpam-5505	58	16	problems	problem	NOUN
ejpam-5505	58	17	,	,	PUNCT
ejpam-5505	58	18	particularly	particularly	ADV
ejpam-5505	58	19	in	in	ADP
ejpam-5505	58	20	convex	convex	ADJ
ejpam-5505	58	21	optimization	optimization	NOUN
ejpam-5505	58	22	and	and	CCONJ
ejpam-5505	58	23	monotone	monotone	ADJ
ejpam-5505	58	24	inclusion	inclusion	NOUN
ejpam-5505	58	25	problems	problem	NOUN
ejpam-5505	58	26	.	.	PUNCT
ejpam-5505	59	1	they	they	PRON
ejpam-5505	59	2	provide	provide	VERB
ejpam-5505	59	3	a	a	DET
ejpam-5505	59	4	framework	framework	NOUN
ejpam-5505	59	5	for	for	ADP
ejpam-5505	59	6	developing	develop	VERB
ejpam-5505	59	7	algorithms	algorithm	NOUN
ejpam-5505	59	8	that	that	PRON
ejpam-5505	59	9	can	can	AUX
ejpam-5505	59	10	efficiently	efficiently	ADV
ejpam-5505	59	11	find	find	VERB
ejpam-5505	59	12	solutions	solution	NOUN
ejpam-5505	59	13	to	to	ADP
ejpam-5505	59	14	complex	complex	ADJ
ejpam-5505	59	15	optimization	optimization	NOUN
ejpam-5505	59	16	tasks	task	NOUN
ejpam-5505	59	17	.	.	PUNCT
ejpam-5505	60	1	for	for	ADP
ejpam-5505	60	2	instance	instance	NOUN
ejpam-5505	60	3	,	,	PUNCT
ejpam-5505	60	4	the	the	DET
ejpam-5505	60	5	resolvent	resolvent	ADJ
ejpam-5505	60	6	composition	composition	NOUN
ejpam-5505	60	7	is	be	AUX
ejpam-5505	60	8	a	a	DET
ejpam-5505	60	9	monotonicity	monotonicity	NOUN
ejpam-5505	60	10	-	-	PUNCT
ejpam-5505	60	11	preserving	preserve	VERB
ejpam-5505	60	12	operation	operation	NOUN
ejpam-5505	60	13	that	that	PRON
ejpam-5505	60	14	can	can	AUX
ejpam-5505	60	15	be	be	AUX
ejpam-5505	60	16	linked	link	VERB
ejpam-5505	60	17	to	to	ADP
ejpam-5505	60	18	proximal	proximal	ADJ
ejpam-5505	60	19	compositions	composition	NOUN
ejpam-5505	60	20	,	,	PUNCT
ejpam-5505	60	21	which	which	PRON
ejpam-5505	60	22	are	be	AUX
ejpam-5505	60	23	essential	essential	ADJ
ejpam-5505	60	24	in	in	ADP
ejpam-5505	60	25	convex	convex	ADJ
ejpam-5505	60	26	analysis	analysis	NOUN
ejpam-5505	60	27	.	.	PUNCT
ejpam-5505	61	1	this	this	DET
ejpam-5505	61	2	relationship	relationship	NOUN
ejpam-5505	61	3	allows	allow	VERB
ejpam-5505	61	4	for	for	ADP
ejpam-5505	61	5	the	the	DET
ejpam-5505	61	6	relaxation	relaxation	NOUN
ejpam-5505	61	7	of	of	ADP
ejpam-5505	61	8	monotone	monotone	ADJ
ejpam-5505	61	9	inclusion	inclusion	NOUN
ejpam-5505	61	10	problems	problem	NOUN
ejpam-5505	61	11	,	,	PUNCT
ejpam-5505	61	12	making	make	VERB
ejpam-5505	61	13	it	it	PRON
ejpam-5505	61	14	easier	easy	ADJ
ejpam-5505	61	15	to	to	PART
ejpam-5505	61	16	solve	solve	VERB
ejpam-5505	61	17	them	they	PRON
ejpam-5505	61	18	in	in	ADP
ejpam-5505	61	19	practical	practical	ADJ
ejpam-5505	61	20	scenarios	scenario	NOUN
ejpam-5505	61	21	.	.	PUNCT
ejpam-5505	62	1	see	see	VERB
ejpam-5505	62	2	[	[	X
ejpam-5505	62	3	18	18	NUM
ejpam-5505	62	4	]	]	SYM
ejpam-5505	62	5	.	.	PUNCT
ejpam-5505	63	1	2	2	X
ejpam-5505	63	2	.	.	X
ejpam-5505	63	3	in	in	ADP
ejpam-5505	63	4	the	the	DET
ejpam-5505	63	5	area	area	NOUN
ejpam-5505	63	6	of	of	ADP
ejpam-5505	63	7	equilibrium	equilibrium	NOUN
ejpam-5505	63	8	problems	problem	NOUN
ejpam-5505	63	9	:	:	PUNCT
ejpam-5505	63	10	the	the	DET
ejpam-5505	63	11	compositions	composition	NOUN
ejpam-5505	63	12	of	of	ADP
ejpam-5505	63	13	resolvents	resolvent	NOUN
ejpam-5505	63	14	encapsulate	encapsulate	VERB
ejpam-5505	63	15	known	known	ADJ
ejpam-5505	63	16	concepts	concept	NOUN
ejpam-5505	63	17	and	and	CCONJ
ejpam-5505	63	18	introduce	introduce	VERB
ejpam-5505	63	19	new	new	ADJ
ejpam-5505	63	20	operations	operation	NOUN
ejpam-5505	63	21	that	that	PRON
ejpam-5505	63	22	are	be	AUX
ejpam-5505	63	23	pertinent	pertinent	ADJ
ejpam-5505	63	24	to	to	ADP
ejpam-5505	63	25	equilibrium	equilibrium	NOUN
ejpam-5505	63	26	problems	problem	NOUN
ejpam-5505	63	27	.	.	PUNCT
ejpam-5505	64	1	this	this	PRON
ejpam-5505	64	2	is	be	AUX
ejpam-5505	64	3	particularly	particularly	ADV
ejpam-5505	64	4	relevant	relevant	ADJ
ejpam-5505	64	5	in	in	ADP
ejpam-5505	64	6	economic	economic	ADJ
ejpam-5505	64	7	models	model	NOUN
ejpam-5505	64	8	and	and	CCONJ
ejpam-5505	64	9	game	game	NOUN
ejpam-5505	64	10	theory	theory	NOUN
ejpam-5505	64	11	,	,	PUNCT
ejpam-5505	64	12	where	where	SCONJ
ejpam-5505	64	13	finding	find	VERB
ejpam-5505	64	14	equilibria	equilibrium	NOUN
ejpam-5505	64	15	is	be	AUX
ejpam-5505	64	16	essential	essential	ADJ
ejpam-5505	64	17	.	.	PUNCT
ejpam-5505	65	1	the	the	DET
ejpam-5505	65	2	properties	property	NOUN
ejpam-5505	65	3	established	establish	VERB
ejpam-5505	65	4	in	in	ADP
ejpam-5505	65	5	the	the	DET
ejpam-5505	65	6	study	study	NOUN
ejpam-5505	65	7	of	of	ADP
ejpam-5505	65	8	resolvent	resolvent	ADJ
ejpam-5505	65	9	compositions	composition	NOUN
ejpam-5505	65	10	can	can	AUX
ejpam-5505	65	11	lead	lead	VERB
ejpam-5505	65	12	to	to	ADP
ejpam-5505	65	13	new	new	ADJ
ejpam-5505	65	14	insights	insight	NOUN
ejpam-5505	65	15	and	and	CCONJ
ejpam-5505	65	16	methods	method	NOUN
ejpam-5505	65	17	for	for	ADP
ejpam-5505	65	18	analyzing	analyze	VERB
ejpam-5505	65	19	these	these	DET
ejpam-5505	65	20	problems	problem	NOUN
ejpam-5505	65	21	[	[	X
ejpam-5505	65	22	18	18	NUM
ejpam-5505	65	23	]	]	PUNCT
ejpam-5505	65	24	.	.	PUNCT
ejpam-5505	66	1	3	3	X
ejpam-5505	66	2	.	.	X
ejpam-5505	66	3	applications	application	NOUN
ejpam-5505	66	4	in	in	ADP
ejpam-5505	66	5	fluid	fluid	ADJ
ejpam-5505	66	6	dynamics	dynamic	NOUN
ejpam-5505	66	7	:	:	PUNCT
ejpam-5505	66	8	in	in	ADP
ejpam-5505	66	9	fluid	fluid	ADJ
ejpam-5505	66	10	dynamics	dynamic	NOUN
ejpam-5505	66	11	,	,	PUNCT
ejpam-5505	66	12	the	the	DET
ejpam-5505	66	13	mean	mean	ADJ
ejpam-5505	66	14	resolvent	resolvent	ADJ
ejpam-5505	66	15	operator	operator	NOUN
ejpam-5505	66	16	has	have	AUX
ejpam-5505	66	17	been	be	AUX
ejpam-5505	66	18	used	use	VERB
ejpam-5505	66	19	to	to	PART
ejpam-5505	66	20	analyze	analyze	VERB
ejpam-5505	66	21	the	the	DET
ejpam-5505	66	22	stability	stability	NOUN
ejpam-5505	66	23	of	of	ADP
ejpam-5505	66	24	flows	flow	NOUN
ejpam-5505	66	25	and	and	CCONJ
ejpam-5505	66	26	predict	predict	VERB
ejpam-5505	66	27	the	the	DET
ejpam-5505	66	28	behavior	behavior	NOUN
ejpam-5505	66	29	of	of	ADP
ejpam-5505	66	30	turbulent	turbulent	ADJ
ejpam-5505	66	31	systems	system	NOUN
ejpam-5505	66	32	.	.	PUNCT
ejpam-5505	67	1	the	the	DET
ejpam-5505	67	2	application	application	NOUN
ejpam-5505	67	3	of	of	ADP
ejpam-5505	67	4	resolvent	resolvent	ADJ
ejpam-5505	67	5	compositions	composition	NOUN
ejpam-5505	67	6	in	in	ADP
ejpam-5505	67	7	this	this	DET
ejpam-5505	67	8	context	context	NOUN
ejpam-5505	67	9	can	can	AUX
ejpam-5505	67	10	enhance	enhance	VERB
ejpam-5505	67	11	our	our	PRON
ejpam-5505	67	12	understanding	understanding	NOUN
ejpam-5505	67	13	of	of	ADP
ejpam-5505	67	14	flow	flow	NOUN
ejpam-5505	67	15	dynamics	dynamic	NOUN
ejpam-5505	67	16	and	and	CCONJ
ejpam-5505	67	17	improve	improve	VERB
ejpam-5505	67	18	control	control	NOUN
ejpam-5505	67	19	strategies	strategy	NOUN
ejpam-5505	67	20	for	for	ADP
ejpam-5505	67	21	various	various	ADJ
ejpam-5505	67	22	engineering	engineering	NOUN
ejpam-5505	67	23	applications	application	NOUN
ejpam-5505	67	24	[	[	X
ejpam-5505	67	25	19	19	NUM
ejpam-5505	67	26	]	]	PUNCT
ejpam-5505	67	27	.	.	PUNCT
ejpam-5505	68	1	4	4	X
ejpam-5505	68	2	.	.	X
ejpam-5505	68	3	in	in	ADP
ejpam-5505	68	4	the	the	DET
ejpam-5505	68	5	area	area	NOUN
ejpam-5505	68	6	of	of	ADP
ejpam-5505	68	7	signal	signal	NOUN
ejpam-5505	68	8	processing	processing	NOUN
ejpam-5505	68	9	and	and	CCONJ
ejpam-5505	68	10	data	datum	NOUN
ejpam-5505	68	11	analysis	analysis	NOUN
ejpam-5505	68	12	:	:	PUNCT
ejpam-5505	68	13	resolvent	resolvent	ADJ
ejpam-5505	68	14	compositions	composition	NOUN
ejpam-5505	68	15	can	can	AUX
ejpam-5505	68	16	also	also	ADV
ejpam-5505	68	17	be	be	AUX
ejpam-5505	68	18	applied	apply	VERB
ejpam-5505	68	19	in	in	ADP
ejpam-5505	68	20	signal	signal	ADJ
ejpam-5505	68	21	processing	processing	NOUN
ejpam-5505	68	22	,	,	PUNCT
ejpam-5505	68	23	particularly	particularly	ADV
ejpam-5505	68	24	in	in	ADP
ejpam-5505	68	25	filtering	filter	VERB
ejpam-5505	68	26	and	and	CCONJ
ejpam-5505	68	27	data	datum	NOUN
ejpam-5505	68	28	reconstruction	reconstruction	NOUN
ejpam-5505	68	29	techniques	technique	NOUN
ejpam-5505	68	30	.	.	PUNCT
ejpam-5505	69	1	by	by	ADP
ejpam-5505	69	2	leveraging	leverage	VERB
ejpam-5505	69	3	the	the	DET
ejpam-5505	69	4	mathematical	mathematical	ADJ
ejpam-5505	69	5	properties	property	NOUN
ejpam-5505	69	6	of	of	ADP
ejpam-5505	69	7	resolvents	resolvent	NOUN
ejpam-5505	69	8	,	,	PUNCT
ejpam-5505	69	9	engineers	engineer	NOUN
ejpam-5505	69	10	can	can	AUX
ejpam-5505	69	11	develop	develop	VERB
ejpam-5505	69	12	more	more	ADV
ejpam-5505	69	13	effective	effective	ADJ
ejpam-5505	69	14	algorithms	algorithm	NOUN
ejpam-5505	69	15	for	for	ADP
ejpam-5505	69	16	noise	noise	NOUN
ejpam-5505	69	17	reduction	reduction	NOUN
ejpam-5505	69	18	and	and	CCONJ
ejpam-5505	69	19	signal	signal	NOUN
ejpam-5505	69	20	enhancement	enhancement	NOUN
ejpam-5505	69	21	,	,	PUNCT
ejpam-5505	69	22	which	which	PRON
ejpam-5505	69	23	are	be	AUX
ejpam-5505	69	24	critical	critical	ADJ
ejpam-5505	69	25	in	in	ADP
ejpam-5505	69	26	communications	communication	NOUN
ejpam-5505	69	27	and	and	CCONJ
ejpam-5505	69	28	multimedia	multimedia	NOUN
ejpam-5505	69	29	applications	application	NOUN
ejpam-5505	69	30	[	[	X
ejpam-5505	69	31	18	18	NUM
ejpam-5505	69	32	]	]	PUNCT
ejpam-5505	69	33	.	.	PUNCT
ejpam-5505	70	1	the	the	DET
ejpam-5505	70	2	compositions	composition	NOUN
ejpam-5505	70	3	of	of	ADP
ejpam-5505	70	4	resolvents	resolvent	NOUN
ejpam-5505	70	5	hold	hold	VERB
ejpam-5505	70	6	significant	significant	ADJ
ejpam-5505	70	7	promise	promise	NOUN
ejpam-5505	70	8	for	for	ADP
ejpam-5505	70	9	practical	practical	ADJ
ejpam-5505	70	10	applications	application	NOUN
ejpam-5505	70	11	across	across	ADP
ejpam-5505	70	12	various	various	ADJ
ejpam-5505	70	13	fields	field	NOUN
ejpam-5505	70	14	,	,	PUNCT
ejpam-5505	70	15	including	include	VERB
ejpam-5505	70	16	optimization	optimization	NOUN
ejpam-5505	70	17	,	,	PUNCT
ejpam-5505	70	18	control	control	NOUN
ejpam-5505	70	19	theory	theory	NOUN
ejpam-5505	70	20	,	,	PUNCT
ejpam-5505	70	21	fluid	fluid	ADJ
ejpam-5505	70	22	dynamics	dynamic	NOUN
ejpam-5505	70	23	,	,	PUNCT
ejpam-5505	70	24	and	and	CCONJ
ejpam-5505	70	25	signal	signal	ADJ
ejpam-5505	70	26	processing	processing	NOUN
ejpam-5505	70	27	.	.	PUNCT
ejpam-5505	71	1	as	as	SCONJ
ejpam-5505	71	2	research	research	NOUN
ejpam-5505	71	3	continues	continue	VERB
ejpam-5505	71	4	to	to	PART
ejpam-5505	71	5	explore	explore	VERB
ejpam-5505	71	6	these	these	DET
ejpam-5505	71	7	compositions	composition	NOUN
ejpam-5505	71	8	,	,	PUNCT
ejpam-5505	71	9	we	we	PRON
ejpam-5505	71	10	can	can	AUX
ejpam-5505	71	11	expect	expect	VERB
ejpam-5505	71	12	to	to	PART
ejpam-5505	71	13	see	see	VERB
ejpam-5505	71	14	innovative	innovative	ADJ
ejpam-5505	71	15	solutions	solution	NOUN
ejpam-5505	71	16	and	and	CCONJ
ejpam-5505	71	17	methodologies	methodology	NOUN
ejpam-5505	71	18	that	that	PRON
ejpam-5505	71	19	leverage	leverage	VERB
ejpam-5505	71	20	their	their	PRON
ejpam-5505	71	21	mathematical	mathematical	ADJ
ejpam-5505	71	22	properties	property	NOUN
ejpam-5505	71	23	to	to	PART
ejpam-5505	71	24	address	address	VERB
ejpam-5505	71	25	complex	complex	ADJ
ejpam-5505	71	26	real	real	ADJ
ejpam-5505	71	27	-	-	PUNCT
ejpam-5505	71	28	world	world	NOUN
ejpam-5505	71	29	problems	problem	NOUN
ejpam-5505	71	30	.	.	PUNCT
ejpam-5505	72	1	definition	definition	NOUN
ejpam-5505	72	2	1	1	NUM
ejpam-5505	72	3	.	.	PUNCT
ejpam-5505	73	1	[	[	X
ejpam-5505	73	2	2	2	NUM
ejpam-5505	73	3	,	,	PUNCT
ejpam-5505	73	4	definition	definition	NOUN
ejpam-5505	73	5	5.1	5.1	NUM
ejpam-5505	73	6	]	]	PUNCT
ejpam-5505	73	7	let	let	VERB
ejpam-5505	73	8	z1	z1	NUM
ejpam-5505	73	9	∈	∈	PROPN
ejpam-5505	73	10	f1	f1	NOUN
ejpam-5505	73	11	.	.	PUNCT
ejpam-5505	74	1	set	set	PROPN
ejpam-5505	74	2	z2	z2	PROPN
ejpam-5505	74	3	:	:	PUNCT
ejpam-5505	74	4	=	=	SYM
ejpam-5505	74	5	j2z1	j2z1	PROPN
ejpam-5505	74	6	,	,	PUNCT
ejpam-5505	74	7	z3	z3	PROPN
ejpam-5505	74	8	:	:	PUNCT
ejpam-5505	74	9	=	=	SYM
ejpam-5505	74	10	j3z2	j3z2	NOUN
ejpam-5505	74	11	,	,	PUNCT
ejpam-5505	74	12	·	·	PUNCT
ejpam-5505	74	13	·	·	PUNCT
ejpam-5505	74	14	·	·	PUNCT
ejpam-5505	74	15	,	,	PUNCT
ejpam-5505	74	16	zm−1	zm−1	NOUN
ejpam-5505	74	17	:	:	PUNCT
ejpam-5505	74	18	=	=	SYM
ejpam-5505	74	19	jm−1zm−2	jm−1zm−2	NUM
ejpam-5505	74	20	,	,	PUNCT
ejpam-5505	74	21	and	and	CCONJ
ejpam-5505	74	22	zm	zm	PROPN
ejpam-5505	74	23	:	:	PUNCT
ejpam-5505	74	24	=	=	SYM
ejpam-5505	74	25	jmzm−1	jmzm−1	PROPN
ejpam-5505	74	26	.	.	PUNCT
ejpam-5505	75	1	the	the	DET
ejpam-5505	75	2	truple	truple	PROPN
ejpam-5505	75	3	z	z	PROPN
ejpam-5505	76	1	=	=	SYM
ejpam-5505	77	1	(	(	PUNCT
ejpam-5505	77	2	z1	z1	PROPN
ejpam-5505	77	3	,	,	PUNCT
ejpam-5505	77	4	z2	z2	PROPN
ejpam-5505	77	5	,	,	PUNCT
ejpam-5505	77	6	.	.	PUNCT
ejpam-5505	77	7	.	.	PUNCT
ejpam-5505	77	8	.	.	PUNCT
ejpam-5505	78	1	,	,	PUNCT
ejpam-5505	78	2	zm	zm	PROPN
ejpam-5505	78	3	)	)	PUNCT
ejpam-5505	78	4	∈	∈	PROPN
ejpam-5505	78	5	x	x	PUNCT
ejpam-5505	78	6	is	be	AUX
ejpam-5505	78	7	called	call	VERB
ejpam-5505	78	8	a	a	DET
ejpam-5505	78	9	cycle	cycle	NOUN
ejpam-5505	78	10	.	.	PUNCT
ejpam-5505	79	1	the	the	DET
ejpam-5505	79	2	notation	notation	NOUN
ejpam-5505	79	3	used	use	VERB
ejpam-5505	79	4	in	in	ADP
ejpam-5505	79	5	the	the	DET
ejpam-5505	79	6	paper	paper	NOUN
ejpam-5505	79	7	is	be	AUX
ejpam-5505	79	8	standard	standard	ADJ
ejpam-5505	79	9	and	and	CCONJ
ejpam-5505	79	10	follows	follow	VERB
ejpam-5505	79	11	largely	largely	ADV
ejpam-5505	79	12	,	,	PUNCT
ejpam-5505	79	13	e.g.	e.g.	ADV
ejpam-5505	79	14	,	,	PUNCT
ejpam-5505	79	15	[	[	X
ejpam-5505	79	16	2	2	NUM
ejpam-5505	79	17	]	]	PUNCT
ejpam-5505	79	18	and	and	CCONJ
ejpam-5505	79	19	[	[	X
ejpam-5505	79	20	10	10	NUM
ejpam-5505	79	21	]	]	PUNCT
ejpam-5505	79	22	.	.	PUNCT
ejpam-5505	80	1	2	2	X
ejpam-5505	80	2	.	.	X
ejpam-5505	80	3	aim	aim	NOUN
ejpam-5505	80	4	and	and	CCONJ
ejpam-5505	80	5	outline	outline	NOUN
ejpam-5505	80	6	of	of	ADP
ejpam-5505	80	7	this	this	DET
ejpam-5505	80	8	paper	paper	NOUN
ejpam-5505	80	9	our	our	PRON
ejpam-5505	80	10	main	main	ADJ
ejpam-5505	80	11	results	result	NOUN
ejpam-5505	80	12	can	can	AUX
ejpam-5505	80	13	be	be	AUX
ejpam-5505	80	14	summarized	summarize	VERB
ejpam-5505	80	15	as	as	SCONJ
ejpam-5505	80	16	follows	follow	VERB
ejpam-5505	80	17	:	:	PUNCT
ejpam-5505	80	18	•	•	NOUN
ejpam-5505	80	19	theorem	theorem	ADJ
ejpam-5505	80	20	1	1	NUM
ejpam-5505	80	21	and	and	CCONJ
ejpam-5505	80	22	theorem	theorem	VERB
ejpam-5505	80	23	2	2	NUM
ejpam-5505	80	24	sketche	sketche	NOUN
ejpam-5505	80	25	the	the	DET
ejpam-5505	80	26	relationship	relationship	NOUN
ejpam-5505	80	27	between	between	ADP
ejpam-5505	80	28	the	the	DET
ejpam-5505	80	29	cycles	cycle	NOUN
ejpam-5505	80	30	and	and	CCONJ
ejpam-5505	80	31	the	the	DET
ejpam-5505	80	32	fixed	fix	VERB
ejpam-5505	80	33	point	point	NOUN
ejpam-5505	80	34	sets	set	NOUN
ejpam-5505	80	35	of	of	ADP
ejpam-5505	80	36	the	the	DET
ejpam-5505	80	37	composition	composition	NOUN
ejpam-5505	80	38	of	of	ADP
ejpam-5505	80	39	resolvants	resolvant	NOUN
ejpam-5505	80	40	.	.	PUNCT
ejpam-5505	81	1	•	•	NUM
ejpam-5505	81	2	the	the	DET
ejpam-5505	81	3	cycles	cycle	NOUN
ejpam-5505	81	4	that	that	PRON
ejpam-5505	81	5	are	be	AUX
ejpam-5505	81	6	defined	define	VERB
ejpam-5505	81	7	by	by	ADP
ejpam-5505	81	8	the	the	DET
ejpam-5505	81	9	resolvant	resolvant	ADJ
ejpam-5505	81	10	operators	operator	NOUN
ejpam-5505	81	11	can	can	AUX
ejpam-5505	81	12	be	be	AUX
ejpam-5505	81	13	formulated	formulate	VERB
ejpam-5505	81	14	in	in	ADP
ejpam-5505	81	15	hilbert	hilbert	NOUN
ejpam-5505	81	16	product	product	NOUN
ejpam-5505	81	17	space	space	NOUN
ejpam-5505	81	18	as	as	ADP
ejpam-5505	81	19	a	a	DET
ejpam-5505	81	20	solution	solution	NOUN
ejpam-5505	81	21	to	to	ADP
ejpam-5505	81	22	a	a	DET
ejpam-5505	81	23	fixed	fix	VERB
ejpam-5505	81	24	point	point	NOUN
ejpam-5505	81	25	equation	equation	NOUN
ejpam-5505	81	26	(	(	PUNCT
ejpam-5505	81	27	see	see	VERB
ejpam-5505	81	28	lemma	lemma	PROPN
ejpam-5505	81	29	2	2	PROPN
ejpam-5505	81	30	and	and	CCONJ
ejpam-5505	81	31	lemma	lemma	PROPN
ejpam-5505	81	32	4	4	NUM
ejpam-5505	81	33	)	)	PUNCT
ejpam-5505	81	34	.	.	PUNCT
ejpam-5505	82	1	s.th.alwadani	s.th.alwadani	ADJ
ejpam-5505	82	2	/	/	SYM
ejpam-5505	82	3	eur	eur	PROPN
ejpam-5505	82	4	.	.	PUNCT
ejpam-5505	83	1	j.	j.	PROPN
ejpam-5505	83	2	pure	pure	PROPN
ejpam-5505	83	3	appl	appl	PROPN
ejpam-5505	83	4	.	.	PROPN
ejpam-5505	83	5	math	math	PROPN
ejpam-5505	83	6	,	,	PUNCT
ejpam-5505	83	7	17	17	NUM
ejpam-5505	83	8	(	(	PUNCT
ejpam-5505	83	9	4	4	NUM
ejpam-5505	83	10	)	)	PUNCT
ejpam-5505	83	11	(	(	PUNCT
ejpam-5505	83	12	2024	2024	NUM
ejpam-5505	83	13	)	)	PUNCT
ejpam-5505	83	14	,	,	PUNCT
ejpam-5505	83	15	3642	3642	NUM
ejpam-5505	83	16	-	-	SYM
ejpam-5505	83	17	3659	3659	NUM
ejpam-5505	83	18	3645	3645	NUM
ejpam-5505	83	19	•	•	NOUN
ejpam-5505	83	20	we	we	PRON
ejpam-5505	83	21	study	study	VERB
ejpam-5505	83	22	the	the	DET
ejpam-5505	83	23	set	set	NOUN
ejpam-5505	83	24	of	of	ADP
ejpam-5505	83	25	classical	classical	ADJ
ejpam-5505	83	26	cycles	cycle	NOUN
ejpam-5505	83	27	that	that	PRON
ejpam-5505	83	28	are	be	AUX
ejpam-5505	83	29	defined	define	VERB
ejpam-5505	83	30	by	by	ADP
ejpam-5505	83	31	using	use	VERB
ejpam-5505	83	32	resolvant	resolvant	ADJ
ejpam-5505	83	33	operators	operator	NOUN
ejpam-5505	83	34	and	and	CCONJ
ejpam-5505	83	35	the	the	DET
ejpam-5505	83	36	set	set	NOUN
ejpam-5505	83	37	of	of	ADP
ejpam-5505	83	38	classical	classical	ADJ
ejpam-5505	83	39	gap	gap	NOUN
ejpam-5505	83	40	vectors	vector	NOUN
ejpam-5505	83	41	see	see	VERB
ejpam-5505	83	42	theorem	theorem	VERB
ejpam-5505	83	43	4	4	NUM
ejpam-5505	83	44	.	.	NOUN
ejpam-5505	83	45	•	•	NOUN
ejpam-5505	83	46	if	if	SCONJ
ejpam-5505	83	47	one	one	NUM
ejpam-5505	83	48	of	of	ADP
ejpam-5505	83	49	the	the	DET
ejpam-5505	83	50	fixed	fix	VERB
ejpam-5505	83	51	point	point	NOUN
ejpam-5505	83	52	sets	set	NOUN
ejpam-5505	83	53	of	of	ADP
ejpam-5505	83	54	composition	composition	NOUN
ejpam-5505	83	55	of	of	ADP
ejpam-5505	83	56	resolvents	resolvent	NOUN
ejpam-5505	83	57	is	be	AUX
ejpam-5505	83	58	not	not	PART
ejpam-5505	83	59	empty	empty	ADJ
ejpam-5505	83	60	,	,	PUNCT
ejpam-5505	83	61	then	then	ADV
ejpam-5505	83	62	the	the	DET
ejpam-5505	83	63	individuals	individual	NOUN
ejpam-5505	83	64	fixed	fix	VERB
ejpam-5505	83	65	point	point	NOUN
ejpam-5505	83	66	sets	set	NOUN
ejpam-5505	83	67	are	be	AUX
ejpam-5505	83	68	equal	equal	ADJ
ejpam-5505	83	69	and	and	CCONJ
ejpam-5505	83	70	their	their	PRON
ejpam-5505	83	71	intersection	intersection	NOUN
ejpam-5505	83	72	is	be	AUX
ejpam-5505	83	73	not	not	PART
ejpam-5505	83	74	empty	empty	ADJ
ejpam-5505	83	75	(	(	PUNCT
ejpam-5505	83	76	see	see	VERB
ejpam-5505	83	77	lemma	lemma	PROPN
ejpam-5505	83	78	5	5	NUM
ejpam-5505	83	79	)	)	PUNCT
ejpam-5505	83	80	.	.	PUNCT
ejpam-5505	84	1	•	•	NUM
ejpam-5505	84	2	in	in	ADP
ejpam-5505	84	3	section	section	NOUN
ejpam-5505	84	4	5	5	NUM
ejpam-5505	84	5	,	,	PUNCT
ejpam-5505	84	6	we	we	PRON
ejpam-5505	84	7	use	use	VERB
ejpam-5505	84	8	attouch	attouch	ADJ
ejpam-5505	84	9	–	–	PUNCT
ejpam-5505	84	10	théra	théra	NUM
ejpam-5505	84	11	duality	duality	NOUN
ejpam-5505	84	12	to	to	PART
ejpam-5505	84	13	study	study	VERB
ejpam-5505	84	14	the	the	DET
ejpam-5505	84	15	cycles	cycle	NOUN
ejpam-5505	84	16	and	and	CCONJ
ejpam-5505	84	17	the	the	DET
ejpam-5505	84	18	fixed	fix	VERB
ejpam-5505	84	19	point	point	NOUN
ejpam-5505	84	20	sets	set	NOUN
ejpam-5505	84	21	of	of	ADP
ejpam-5505	84	22	compositions	composition	NOUN
ejpam-5505	84	23	of	of	ADP
ejpam-5505	84	24	resolvents	resolvent	NOUN
ejpam-5505	84	25	operators	operator	NOUN
ejpam-5505	84	26	.	.	PUNCT
ejpam-5505	85	1	approach	approach	NOUN
ejpam-5505	85	2	of	of	ADP
ejpam-5505	85	3	this	this	DET
ejpam-5505	85	4	paper	paper	NOUN
ejpam-5505	85	5	is	be	AUX
ejpam-5505	85	6	novel	novel	ADJ
ejpam-5505	85	7	as	as	SCONJ
ejpam-5505	85	8	it	it	PRON
ejpam-5505	85	9	utilizes	utilize	VERB
ejpam-5505	85	10	attouch	attouch	ADJ
ejpam-5505	85	11	–	–	PUNCT
ejpam-5505	85	12	théra	théra	NUM
ejpam-5505	85	13	duality	duality	NOUN
ejpam-5505	85	14	to	to	PART
ejpam-5505	85	15	conduct	conduct	VERB
ejpam-5505	85	16	an	an	DET
ejpam-5505	85	17	indepth	indepth	ADJ
ejpam-5505	85	18	investigation	investigation	NOUN
ejpam-5505	85	19	of	of	ADP
ejpam-5505	85	20	the	the	DET
ejpam-5505	85	21	cycles	cycle	NOUN
ejpam-5505	85	22	and	and	CCONJ
ejpam-5505	85	23	fixed	fix	VERB
ejpam-5505	85	24	point	point	NOUN
ejpam-5505	85	25	sets	set	NOUN
ejpam-5505	85	26	related	relate	VERB
ejpam-5505	85	27	to	to	ADP
ejpam-5505	85	28	compositions	composition	NOUN
ejpam-5505	85	29	of	of	ADP
ejpam-5505	85	30	resolvents	resolvent	NOUN
ejpam-5505	85	31	.	.	PUNCT
ejpam-5505	86	1	this	this	DET
ejpam-5505	86	2	duality	duality	NOUN
ejpam-5505	86	3	offers	offer	VERB
ejpam-5505	86	4	a	a	DET
ejpam-5505	86	5	powerful	powerful	ADJ
ejpam-5505	86	6	framework	framework	NOUN
ejpam-5505	86	7	for	for	ADP
ejpam-5505	86	8	uncovering	uncover	VERB
ejpam-5505	86	9	the	the	DET
ejpam-5505	86	10	intricate	intricate	ADJ
ejpam-5505	86	11	structures	structure	NOUN
ejpam-5505	86	12	and	and	CCONJ
ejpam-5505	86	13	dynamics	dynamic	NOUN
ejpam-5505	86	14	inherent	inherent	ADJ
ejpam-5505	86	15	in	in	ADP
ejpam-5505	86	16	these	these	DET
ejpam-5505	86	17	mathematical	mathematical	ADJ
ejpam-5505	86	18	constructs	construct	NOUN
ejpam-5505	86	19	.	.	PUNCT
ejpam-5505	87	1	in	in	ADP
ejpam-5505	87	2	summary	summary	NOUN
ejpam-5505	87	3	,	,	PUNCT
ejpam-5505	87	4	applying	apply	VERB
ejpam-5505	87	5	attouch	attouch	ADJ
ejpam-5505	87	6	–	–	PUNCT
ejpam-5505	87	7	théra	théra	NUM
ejpam-5505	87	8	duality	duality	NOUN
ejpam-5505	87	9	to	to	PART
ejpam-5505	87	10	analyze	analyze	VERB
ejpam-5505	87	11	cycles	cycle	NOUN
ejpam-5505	87	12	and	and	CCONJ
ejpam-5505	87	13	fixed	fix	VERB
ejpam-5505	87	14	point	point	NOUN
ejpam-5505	87	15	sets	set	NOUN
ejpam-5505	87	16	in	in	ADP
ejpam-5505	87	17	resolvent	resolvent	ADJ
ejpam-5505	87	18	compositions	composition	NOUN
ejpam-5505	87	19	represents	represent	VERB
ejpam-5505	87	20	a	a	DET
ejpam-5505	87	21	significant	significant	ADJ
ejpam-5505	87	22	advancement	advancement	NOUN
ejpam-5505	87	23	in	in	ADP
ejpam-5505	87	24	the	the	DET
ejpam-5505	87	25	field	field	NOUN
ejpam-5505	87	26	.	.	PUNCT
ejpam-5505	88	1	more	more	ADJ
ejpam-5505	88	2	information	information	NOUN
ejpam-5505	88	3	about	about	ADP
ejpam-5505	88	4	attouch	attouch	ADJ
ejpam-5505	88	5	–	–	PUNCT
ejpam-5505	88	6	théra	théra	NUM
ejpam-5505	88	7	duality	duality	NOUN
ejpam-5505	88	8	is	be	AUX
ejpam-5505	88	9	in	in	ADP
ejpam-5505	88	10	the	the	DET
ejpam-5505	88	11	next	next	ADJ
ejpam-5505	88	12	section	section	NOUN
ejpam-5505	88	13	.	.	PUNCT
ejpam-5505	89	1	3	3	X
ejpam-5505	89	2	.	.	X
ejpam-5505	89	3	attouch	attouch	ADJ
ejpam-5505	89	4	–	–	PUNCT
ejpam-5505	89	5	théra	théra	NUM
ejpam-5505	89	6	duality	duality	NOUN
ejpam-5505	89	7	let	let	VERB
ejpam-5505	89	8	a	a	PRON
ejpam-5505	89	9	and	and	CCONJ
ejpam-5505	89	10	b	b	NOUN
ejpam-5505	89	11	be	be	AUX
ejpam-5505	89	12	two	two	NUM
ejpam-5505	89	13	maximally	maximally	ADV
ejpam-5505	89	14	monotone	monotone	ADJ
ejpam-5505	89	15	operators	operator	NOUN
ejpam-5505	89	16	on	on	ADP
ejpam-5505	89	17	x.	x.	NOUN
ejpam-5505	89	18	the	the	DET
ejpam-5505	89	19	primal	primal	ADJ
ejpam-5505	89	20	problem	problem	NOUN
ejpam-5505	89	21	associated	associate	VERB
ejpam-5505	89	22	with	with	ADP
ejpam-5505	89	23	(	(	PUNCT
ejpam-5505	89	24	a	a	DET
ejpam-5505	89	25	,	,	PUNCT
ejpam-5505	89	26	b	b	NOUN
ejpam-5505	89	27	)	)	PUNCT
ejpam-5505	89	28	is	be	AUX
ejpam-5505	89	29	to	to	PART
ejpam-5505	89	30	find	find	VERB
ejpam-5505	89	31	x	x	X
ejpam-5505	89	32	∈	∈	PROPN
ejpam-5505	89	33	x	x	X
ejpam-5505	89	34	such	such	ADJ
ejpam-5505	89	35	that	that	DET
ejpam-5505	89	36	0	0	NUM
ejpam-5505	89	37	∈	∈	NOUN
ejpam-5505	89	38	ax	ax	NOUN
ejpam-5505	89	39	+	+	CCONJ
ejpam-5505	89	40	bx	bx	NOUN
ejpam-5505	89	41	.	.	PUNCT
ejpam-5505	90	1	(	(	PUNCT
ejpam-5505	90	2	12	12	NUM
ejpam-5505	90	3	)	)	PUNCT
ejpam-5505	90	4	the	the	DET
ejpam-5505	90	5	set	set	NOUN
ejpam-5505	90	6	of	of	ADP
ejpam-5505	90	7	primal	primal	ADJ
ejpam-5505	90	8	solutions	solution	NOUN
ejpam-5505	90	9	associated	associate	VERB
ejpam-5505	90	10	with	with	ADP
ejpam-5505	90	11	(	(	PUNCT
ejpam-5505	90	12	a	a	DET
ejpam-5505	90	13	,	,	PUNCT
ejpam-5505	90	14	b	b	NOUN
ejpam-5505	90	15	)	)	PUNCT
ejpam-5505	90	16	are	be	AUX
ejpam-5505	90	17	the	the	DET
ejpam-5505	90	18	solutions	solution	NOUN
ejpam-5505	90	19	to	to	ADP
ejpam-5505	90	20	the	the	DET
ejpam-5505	90	21	corresponding	corresponding	ADJ
ejpam-5505	90	22	sum	sum	NOUN
ejpam-5505	90	23	problem	problem	NOUN
ejpam-5505	90	24	(	(	PUNCT
ejpam-5505	90	25	12	12	NUM
ejpam-5505	90	26	)	)	PUNCT
ejpam-5505	90	27	are	be	AUX
ejpam-5505	90	28	defined	define	VERB
ejpam-5505	90	29	as	as	ADP
ejpam-5505	90	30	psol(a	psol(a	NUM
ejpam-5505	90	31	,	,	PUNCT
ejpam-5505	90	32	b	b	NOUN
ejpam-5505	90	33	)	)	PUNCT
ejpam-5505	90	34	:	:	PUNCT
ejpam-5505	91	1	=	=	SYM
ejpam-5505	91	2	zer(a	zer(a	NUM
ejpam-5505	91	3	,	,	PUNCT
ejpam-5505	91	4	b	b	NOUN
ejpam-5505	91	5	)	)	PUNCT
ejpam-5505	91	6	=	=	SYM
ejpam-5505	91	7	(	(	PUNCT
ejpam-5505	91	8	a	a	DET
ejpam-5505	91	9	,	,	PUNCT
ejpam-5505	91	10	b)−1(0	b)−1(0	NOUN
ejpam-5505	91	11	)	)	PUNCT
ejpam-5505	91	12	=	=	PRON
ejpam-5505	91	13	{	{	PUNCT
ejpam-5505	91	14	x	x	PUNCT
ejpam-5505	91	15	∈	∈	PROPN
ejpam-5505	91	16	x	x	INTJ
ejpam-5505	91	17	∣∣∣	∣∣∣	NOUN
ejpam-5505	91	18	0	0	NUM
ejpam-5505	91	19	∈	∈	NOUN
ejpam-5505	91	20	(	(	PUNCT
ejpam-5505	91	21	a	a	DET
ejpam-5505	91	22	+	+	X
ejpam-5505	91	23	b)x	b)x	X
ejpam-5505	91	24	}	}	PUNCT
ejpam-5505	91	25	.	.	PUNCT
ejpam-5505	92	1	(	(	PUNCT
ejpam-5505	92	2	13	13	NUM
ejpam-5505	92	3	)	)	PUNCT
ejpam-5505	92	4	now	now	ADV
ejpam-5505	92	5	define	define	VERB
ejpam-5505	92	6	b	b	X
ejpam-5505	92	7	>	>	X
ejpam-5505	92	8	:	:	PUNCT
ejpam-5505	92	9	=	=	SYM
ejpam-5505	92	10	(	(	PUNCT
ejpam-5505	92	11	−	−	PROPN
ejpam-5505	92	12	i	i	NOUN
ejpam-5505	92	13	d	d	PROPN
ejpam-5505	92	14	)	)	PUNCT
ejpam-5505	92	15	◦	◦	NOUN
ejpam-5505	92	16	b	b	SYM
ejpam-5505	92	17	◦	◦	NOUN
ejpam-5505	92	18	(	(	PUNCT
ejpam-5505	92	19	−	−	PROPN
ejpam-5505	92	20	i	i	PROPN
ejpam-5505	92	21	d	d	PROPN
ejpam-5505	92	22	)	)	PUNCT
ejpam-5505	92	23	and	and	CCONJ
ejpam-5505	92	24	b−	b−	NOUN
ejpam-5505	92	25	>	>	X
ejpam-5505	92	26	:	:	PUNCT
ejpam-5505	93	1	=	=	SYM
ejpam-5505	93	2	(	(	PUNCT
ejpam-5505	93	3	b−1	b−1	PROPN
ejpam-5505	93	4	)	)	PUNCT
ejpam-5505	93	5	>	>	X
ejpam-5505	93	6	=	=	PUNCT
ejpam-5505	93	7	(	(	PUNCT
ejpam-5505	93	8	b>)−1	b>)−1	NOUN
ejpam-5505	93	9	.	.	PUNCT
ejpam-5505	94	1	this	this	PRON
ejpam-5505	94	2	allows	allow	VERB
ejpam-5505	94	3	us	we	PRON
ejpam-5505	94	4	to	to	PART
ejpam-5505	94	5	define	define	VERB
ejpam-5505	94	6	the	the	DET
ejpam-5505	94	7	dual	dual	ADJ
ejpam-5505	94	8	pair	pair	NOUN
ejpam-5505	94	9	of	of	ADP
ejpam-5505	94	10	(	(	PUNCT
ejpam-5505	94	11	a	a	DET
ejpam-5505	94	12	,	,	PUNCT
ejpam-5505	94	13	b	b	NOUN
ejpam-5505	94	14	):	):	PUNCT
ejpam-5505	94	15	(	(	PUNCT
ejpam-5505	94	16	a	a	NOUN
ejpam-5505	94	17	,	,	PUNCT
ejpam-5505	94	18	b)∗	b)∗	PROPN
ejpam-5505	94	19	:	:	PUNCT
ejpam-5505	95	1	=	=	SYM
ejpam-5505	95	2	(	(	PUNCT
ejpam-5505	95	3	a−1	a−1	PROPN
ejpam-5505	95	4	,	,	PUNCT
ejpam-5505	95	5	b−	b−	NOUN
ejpam-5505	95	6	>	>	PUNCT
ejpam-5505	95	7	)	)	PUNCT
ejpam-5505	95	8	.	.	PUNCT
ejpam-5505	96	1	(	(	PUNCT
ejpam-5505	96	2	14	14	NUM
ejpam-5505	96	3	)	)	PUNCT
ejpam-5505	96	4	then	then	ADV
ejpam-5505	96	5	the	the	DET
ejpam-5505	96	6	dual	dual	ADJ
ejpam-5505	96	7	problem	problem	NOUN
ejpam-5505	96	8	associated	associate	VERB
ejpam-5505	96	9	with	with	ADP
ejpam-5505	96	10	(	(	PUNCT
ejpam-5505	96	11	a	a	DET
ejpam-5505	96	12	,	,	PUNCT
ejpam-5505	96	13	b	b	NOUN
ejpam-5505	96	14	)	)	PUNCT
ejpam-5505	96	15	is	be	AUX
ejpam-5505	96	16	defined	define	VERB
ejpam-5505	96	17	to	to	PART
ejpam-5505	96	18	be	be	AUX
ejpam-5505	96	19	the	the	DET
ejpam-5505	96	20	primal	primal	ADJ
ejpam-5505	96	21	problem	problem	NOUN
ejpam-5505	96	22	associated	associate	VERB
ejpam-5505	96	23	with	with	ADP
ejpam-5505	96	24	the	the	DET
ejpam-5505	96	25	dual	dual	ADJ
ejpam-5505	96	26	pair	pair	NOUN
ejpam-5505	96	27	(	(	PUNCT
ejpam-5505	96	28	a−1	a−1	PROPN
ejpam-5505	96	29	,	,	PUNCT
ejpam-5505	96	30	b−	b−	NOUN
ejpam-5505	96	31	>	>	PUNCT
ejpam-5505	96	32	):	):	PUNCT
ejpam-5505	96	33	find	find	VERB
ejpam-5505	96	34	y	y	PROPN
ejpam-5505	96	35	∈	∈	PROPN
ejpam-5505	96	36	x	x	PUNCT
ejpam-5505	96	37	such	such	ADJ
ejpam-5505	96	38	that	that	DET
ejpam-5505	96	39	0	0	NUM
ejpam-5505	96	40	∈	∈	NOUN
ejpam-5505	96	41	a−1y	a−1y	NOUN
ejpam-5505	96	42	+	+	X
ejpam-5505	96	43	b−>y	b−>y	ADJ
ejpam-5505	96	44	=	=	SYM
ejpam-5505	96	45	a−1y	a−1y	ADJ
ejpam-5505	96	46	−	−	PROPN
ejpam-5505	96	47	b−1(−y	b−1(−y	NOUN
ejpam-5505	96	48	)	)	PUNCT
ejpam-5505	96	49	.	.	PUNCT
ejpam-5505	97	1	(	(	PUNCT
ejpam-5505	97	2	15	15	X
ejpam-5505	97	3	)	)	PUNCT
ejpam-5505	97	4	the	the	DET
ejpam-5505	97	5	set	set	NOUN
ejpam-5505	97	6	of	of	ADP
ejpam-5505	97	7	of	of	ADP
ejpam-5505	97	8	dual	dual	ADJ
ejpam-5505	97	9	solutions	solution	NOUN
ejpam-5505	97	10	associated	associate	VERB
ejpam-5505	97	11	with	with	ADP
ejpam-5505	97	12	(	(	PUNCT
ejpam-5505	97	13	a	a	DET
ejpam-5505	97	14	,	,	PUNCT
ejpam-5505	97	15	b	b	NOUN
ejpam-5505	97	16	)	)	PUNCT
ejpam-5505	97	17	are	be	AUX
ejpam-5505	97	18	the	the	DET
ejpam-5505	97	19	solutions	solution	NOUN
ejpam-5505	97	20	to	to	ADP
ejpam-5505	97	21	the	the	DET
ejpam-5505	97	22	corresponding	corresponding	ADJ
ejpam-5505	97	23	sum	sum	NOUN
ejpam-5505	97	24	problem	problem	NOUN
ejpam-5505	97	25	(	(	PUNCT
ejpam-5505	97	26	15	15	NUM
ejpam-5505	97	27	):	):	PUNCT
ejpam-5505	97	28	dsol(a	dsol(a	PROPN
ejpam-5505	97	29	,	,	PUNCT
ejpam-5505	97	30	b	b	NOUN
ejpam-5505	97	31	)	)	PUNCT
ejpam-5505	97	32	:	:	PUNCT
ejpam-5505	98	1	=	=	SYM
ejpam-5505	98	2	psol(a	psol(a	NUM
ejpam-5505	98	3	,	,	PUNCT
ejpam-5505	98	4	b)∗	b)∗	PROPN
ejpam-5505	98	5	=	=	SYM
ejpam-5505	98	6	zer	zer	PROPN
ejpam-5505	98	7	(	(	PUNCT
ejpam-5505	98	8	a−1	a−1	PROPN
ejpam-5505	98	9	+	+	PROPN
ejpam-5505	98	10	b−	b−	PROPN
ejpam-5505	98	11	>	>	PUNCT
ejpam-5505	98	12	)	)	PUNCT
ejpam-5505	98	13	=	=	PRON
ejpam-5505	98	14	{	{	PUNCT
ejpam-5505	98	15	y	y	PROPN
ejpam-5505	98	16	∈	∈	PROPN
ejpam-5505	98	17	x	x	PUNCT
ejpam-5505	98	18	∣∣∣	∣∣∣	NOUN
ejpam-5505	98	19	0	0	NUM
ejpam-5505	98	20	∈	∈	NOUN
ejpam-5505	98	21	(	(	PUNCT
ejpam-5505	98	22	a−1	a−1	PROPN
ejpam-5505	98	23	+	+	CCONJ
ejpam-5505	98	24	b−>)y	b−>)y	NOUN
ejpam-5505	98	25	}	}	PUNCT
ejpam-5505	98	26	.	.	PUNCT
ejpam-5505	99	1	(	(	PUNCT
ejpam-5505	99	2	16	16	NUM
ejpam-5505	99	3	)	)	PUNCT
ejpam-5505	99	4	because	because	SCONJ
ejpam-5505	99	5	(	(	PUNCT
ejpam-5505	99	6	a−1)−1	a−1)−1	NOUN
ejpam-5505	99	7	=	=	SYM
ejpam-5505	99	8	a	a	NOUN
ejpam-5505	99	9	,	,	PUNCT
ejpam-5505	99	10	(	(	PUNCT
ejpam-5505	99	11	a	a	PRON
ejpam-5505	99	12	>	>	PUNCT
ejpam-5505	99	13	)	)	PUNCT
ejpam-5505	99	14	>	>	X
ejpam-5505	100	1	=	=	PUNCT
ejpam-5505	100	2	a	a	PRON
ejpam-5505	100	3	,	,	PUNCT
ejpam-5505	100	4	and	and	CCONJ
ejpam-5505	100	5	(	(	PUNCT
ejpam-5505	100	6	a−>)−	a−>)−	PROPN
ejpam-5505	100	7	>	>	X
ejpam-5505	100	8	=	=	PUNCT
ejpam-5505	100	9	a	a	PROPN
ejpam-5505	100	10	,	,	PUNCT
ejpam-5505	100	11	we	we	PRON
ejpam-5505	100	12	have	have	AUX
ejpam-5505	100	13	(	(	PUNCT
ejpam-5505	100	14	a	a	DET
ejpam-5505	100	15	,	,	PUNCT
ejpam-5505	100	16	b)∗∗	b)∗∗	NOUN
ejpam-5505	100	17	=	=	SYM
ejpam-5505	100	18	(	(	PUNCT
ejpam-5505	100	19	a	a	DET
ejpam-5505	100	20	,	,	PUNCT
ejpam-5505	100	21	b	b	NOUN
ejpam-5505	100	22	)	)	PUNCT
ejpam-5505	100	23	.	.	PUNCT
ejpam-5505	101	1	(	(	PUNCT
ejpam-5505	101	2	17	17	NUM
ejpam-5505	101	3	)	)	PUNCT
ejpam-5505	101	4	s.th.alwadani	s.th.alwadani	X
ejpam-5505	101	5	/	/	SYM
ejpam-5505	101	6	eur	eur	NOUN
ejpam-5505	101	7	.	.	PUNCT
ejpam-5505	102	1	j.	j.	PROPN
ejpam-5505	102	2	pure	pure	PROPN
ejpam-5505	102	3	appl	appl	PROPN
ejpam-5505	102	4	.	.	PROPN
ejpam-5505	102	5	math	math	PROPN
ejpam-5505	102	6	,	,	PUNCT
ejpam-5505	102	7	17	17	NUM
ejpam-5505	102	8	(	(	PUNCT
ejpam-5505	102	9	4	4	NUM
ejpam-5505	102	10	)	)	PUNCT
ejpam-5505	102	11	(	(	PUNCT
ejpam-5505	102	12	2024	2024	NUM
ejpam-5505	102	13	)	)	PUNCT
ejpam-5505	102	14	,	,	PUNCT
ejpam-5505	102	15	3642	3642	NUM
ejpam-5505	102	16	-	-	SYM
ejpam-5505	102	17	3659	3659	NUM
ejpam-5505	102	18	3646	3646	NUM
ejpam-5505	102	19	lemma	lemma	PROPN
ejpam-5505	102	20	1	1	X
ejpam-5505	102	21	.	.	PUNCT
ejpam-5505	103	1	let	let	VERB
ejpam-5505	103	2	a	a	PRON
ejpam-5505	103	3	and	and	CCONJ
ejpam-5505	103	4	b	b	NOUN
ejpam-5505	103	5	be	be	VERB
ejpam-5505	103	6	maximally	maximally	ADV
ejpam-5505	103	7	monotone	monotone	ADJ
ejpam-5505	103	8	on	on	ADP
ejpam-5505	103	9	x.	x.	NOUN
ejpam-5505	103	10	let	let	VERB
ejpam-5505	103	11	x	x	PRON
ejpam-5505	103	12	and	and	CCONJ
ejpam-5505	103	13	y	y	PROPN
ejpam-5505	103	14	in	in	ADP
ejpam-5505	103	15	x.	x.	PROPN
ejpam-5505	103	16	then	then	ADV
ejpam-5505	103	17	the	the	DET
ejpam-5505	103	18	following	follow	VERB
ejpam-5505	103	19	holds	hold	VERB
ejpam-5505	103	20	:	:	PUNCT
ejpam-5505	103	21	(	(	PUNCT
ejpam-5505	103	22	i	i	NOUN
ejpam-5505	103	23	)	)	PUNCT
ejpam-5505	103	24	if	if	SCONJ
ejpam-5505	103	25	psol(a	psol(a	NUM
ejpam-5505	103	26	,	,	PUNCT
ejpam-5505	103	27	b	b	NOUN
ejpam-5505	103	28	)	)	PUNCT
ejpam-5505	103	29	=	=	SYM
ejpam-5505	103	30	{	{	PUNCT
ejpam-5505	103	31	x	x	NOUN
ejpam-5505	103	32	}	}	PUNCT
ejpam-5505	103	33	,	,	PUNCT
ejpam-5505	103	34	then	then	ADV
ejpam-5505	103	35	dsol(a	dsol(a	PROPN
ejpam-5505	103	36	,	,	PUNCT
ejpam-5505	103	37	b	b	NOUN
ejpam-5505	103	38	)	)	PUNCT
ejpam-5505	104	1	=	=	NOUN
ejpam-5505	104	2	ax	ax	NOUN
ejpam-5505	104	3	∩	∩	NOUN
ejpam-5505	104	4	(	(	PUNCT
ejpam-5505	104	5	−bx	−bx	NOUN
ejpam-5505	104	6	)	)	PUNCT
ejpam-5505	104	7	and	and	CCONJ
ejpam-5505	104	8	dsol(a	dsol(a	PROPN
ejpam-5505	104	9	,	,	PUNCT
ejpam-5505	104	10	b	b	NOUN
ejpam-5505	104	11	)	)	PUNCT
ejpam-5505	104	12	=	=	NOUN
ejpam-5505	104	13	ax	ax	NOUN
ejpam-5505	104	14	∩	∩	NOUN
ejpam-5505	104	15	b>(−x	b>(−x	NOUN
ejpam-5505	104	16	)	)	PUNCT
ejpam-5505	104	17	.	.	PUNCT
ejpam-5505	105	1	(	(	PUNCT
ejpam-5505	105	2	ii	ii	NOUN
ejpam-5505	105	3	)	)	PUNCT
ejpam-5505	105	4	if	if	SCONJ
ejpam-5505	105	5	dsol(a	dsol(a	PROPN
ejpam-5505	105	6	,	,	PUNCT
ejpam-5505	105	7	b	b	NOUN
ejpam-5505	105	8	)	)	PUNCT
ejpam-5505	105	9	=	=	SYM
ejpam-5505	105	10	{	{	PUNCT
ejpam-5505	105	11	y	y	NOUN
ejpam-5505	105	12	}	}	PUNCT
ejpam-5505	105	13	,	,	PUNCT
ejpam-5505	105	14	then	then	ADV
ejpam-5505	105	15	psol(a	psol(a	NUM
ejpam-5505	105	16	,	,	PUNCT
ejpam-5505	105	17	b	b	NOUN
ejpam-5505	105	18	)	)	PUNCT
ejpam-5505	105	19	=	=	SYM
ejpam-5505	105	20	(	(	PUNCT
ejpam-5505	105	21	a−1y	a−1y	ADJ
ejpam-5505	105	22	)	)	PUNCT
ejpam-5505	105	23	∩	∩	ADJ
ejpam-5505	105	24	b−1(−y	b−1(−y	NOUN
ejpam-5505	105	25	)	)	PUNCT
ejpam-5505	105	26	and	and	CCONJ
ejpam-5505	105	27	psol(a	psol(a	NUM
ejpam-5505	105	28	,	,	PUNCT
ejpam-5505	105	29	b	b	NOUN
ejpam-5505	105	30	)	)	PUNCT
ejpam-5505	105	31	=	=	SYM
ejpam-5505	105	32	(	(	PUNCT
ejpam-5505	105	33	a−1y	a−1y	ADJ
ejpam-5505	105	34	)	)	PUNCT
ejpam-5505	105	35	∩	∩	NOUN
ejpam-5505	105	36	(	(	PUNCT
ejpam-5505	105	37	−b−>(y	−b−>(y	X
ejpam-5505	105	38	)	)	PUNCT
ejpam-5505	105	39	)	)	PUNCT
ejpam-5505	105	40	.	.	PUNCT
ejpam-5505	106	1	(	(	PUNCT
ejpam-5505	106	2	iii	iii	X
ejpam-5505	106	3	)	)	PUNCT
ejpam-5505	106	4	if	if	SCONJ
ejpam-5505	106	5	psol(a	psol(a	NUM
ejpam-5505	106	6	,	,	PUNCT
ejpam-5505	106	7	b	b	NOUN
ejpam-5505	106	8	)	)	PUNCT
ejpam-5505	106	9	=	=	SYM
ejpam-5505	106	10	{	{	PUNCT
ejpam-5505	106	11	x	x	NOUN
ejpam-5505	106	12	}	}	PUNCT
ejpam-5505	106	13	and	and	CCONJ
ejpam-5505	106	14	ax	ax	NOUN
ejpam-5505	106	15	is	be	AUX
ejpam-5505	106	16	a	a	DET
ejpam-5505	106	17	singelton	singelton	NOUN
ejpam-5505	106	18	,	,	PUNCT
ejpam-5505	106	19	then	then	ADV
ejpam-5505	106	20	dsol(a	dsol(a	PROPN
ejpam-5505	106	21	,	,	PUNCT
ejpam-5505	106	22	b	b	NOUN
ejpam-5505	106	23	)	)	PUNCT
ejpam-5505	106	24	=	=	NOUN
ejpam-5505	106	25	ax	ax	NOUN
ejpam-5505	106	26	.	.	PUNCT
ejpam-5505	107	1	(	(	PUNCT
ejpam-5505	107	2	iv	iv	X
ejpam-5505	107	3	)	)	PUNCT
ejpam-5505	107	4	if	if	SCONJ
ejpam-5505	107	5	psol(a	psol(a	NUM
ejpam-5505	107	6	,	,	PUNCT
ejpam-5505	107	7	b	b	NOUN
ejpam-5505	107	8	)	)	PUNCT
ejpam-5505	107	9	=	=	SYM
ejpam-5505	107	10	{	{	PUNCT
ejpam-5505	107	11	x	x	NOUN
ejpam-5505	107	12	}	}	PUNCT
ejpam-5505	107	13	and	and	CCONJ
ejpam-5505	107	14	bx	bx	PROPN
ejpam-5505	107	15	and	and	CCONJ
ejpam-5505	107	16	b>(−x	b>(−x	NOUN
ejpam-5505	107	17	)	)	PUNCT
ejpam-5505	107	18	are	be	AUX
ejpam-5505	107	19	singelton	singelton	ADJ
ejpam-5505	107	20	,	,	PUNCT
ejpam-5505	107	21	then	then	ADV
ejpam-5505	107	22	dsol(a	dsol(a	PROPN
ejpam-5505	107	23	,	,	PUNCT
ejpam-5505	107	24	b	b	NOUN
ejpam-5505	107	25	)	)	PUNCT
ejpam-5505	107	26	=	=	SYM
ejpam-5505	107	27	−bx	−bx	PROPN
ejpam-5505	107	28	and	and	CCONJ
ejpam-5505	107	29	dsol(a	dsol(a	PROPN
ejpam-5505	107	30	,	,	PUNCT
ejpam-5505	107	31	b	b	NOUN
ejpam-5505	107	32	)	)	PUNCT
ejpam-5505	107	33	=	=	SYM
ejpam-5505	107	34	b>(−x	b>(−x	NOUN
ejpam-5505	107	35	)	)	PUNCT
ejpam-5505	107	36	.	.	PUNCT
ejpam-5505	108	1	(	(	PUNCT
ejpam-5505	108	2	v	v	NOUN
ejpam-5505	108	3	)	)	PUNCT
ejpam-5505	108	4	if	if	SCONJ
ejpam-5505	108	5	dsol(a	dsol(a	PROPN
ejpam-5505	108	6	,	,	PUNCT
ejpam-5505	108	7	b	b	NOUN
ejpam-5505	108	8	)	)	PUNCT
ejpam-5505	108	9	=	=	SYM
ejpam-5505	108	10	{	{	PUNCT
ejpam-5505	108	11	y	y	NOUN
ejpam-5505	108	12	}	}	PUNCT
ejpam-5505	108	13	and	and	CCONJ
ejpam-5505	108	14	a−1y	a−1y	NOUN
ejpam-5505	108	15	is	be	AUX
ejpam-5505	108	16	a	a	DET
ejpam-5505	108	17	singelton	singelton	NOUN
ejpam-5505	108	18	,	,	PUNCT
ejpam-5505	108	19	then	then	ADV
ejpam-5505	108	20	psol(a	psol(a	NUM
ejpam-5505	108	21	,	,	PUNCT
ejpam-5505	108	22	b	b	NOUN
ejpam-5505	108	23	)	)	PUNCT
ejpam-5505	108	24	=	=	SYM
ejpam-5505	108	25	a−1y	a−1y	PROPN
ejpam-5505	108	26	.	.	PUNCT
ejpam-5505	109	1	(	(	PUNCT
ejpam-5505	109	2	vi	vi	NOUN
ejpam-5505	109	3	)	)	PUNCT
ejpam-5505	109	4	if	if	SCONJ
ejpam-5505	109	5	dsol(a	dsol(a	PROPN
ejpam-5505	109	6	,	,	PUNCT
ejpam-5505	109	7	b	b	NOUN
ejpam-5505	109	8	)	)	PUNCT
ejpam-5505	109	9	=	=	SYM
ejpam-5505	109	10	{	{	PUNCT
ejpam-5505	109	11	y	y	NOUN
ejpam-5505	109	12	}	}	PUNCT
ejpam-5505	109	13	and	and	CCONJ
ejpam-5505	109	14	b−1(−y	b−1(−y	NOUN
ejpam-5505	109	15	)	)	PUNCT
ejpam-5505	109	16	and	and	CCONJ
ejpam-5505	109	17	(	(	PUNCT
ejpam-5505	109	18	−b−>(y	−b−>(y	NOUN
ejpam-5505	109	19	)	)	PUNCT
ejpam-5505	109	20	)	)	PUNCT
ejpam-5505	109	21	are	be	AUX
ejpam-5505	109	22	a	a	DET
ejpam-5505	109	23	singelton	singelton	NOUN
ejpam-5505	109	24	,	,	PUNCT
ejpam-5505	109	25	then	then	ADV
ejpam-5505	109	26	psol(a	psol(a	NUM
ejpam-5505	109	27	,	,	PUNCT
ejpam-5505	109	28	b	b	NOUN
ejpam-5505	109	29	)	)	PUNCT
ejpam-5505	109	30	=	=	SYM
ejpam-5505	109	31	b−1(−y	b−1(−y	NOUN
ejpam-5505	109	32	)	)	PUNCT
ejpam-5505	109	33	and	and	CCONJ
ejpam-5505	109	34	psol(a	psol(a	NUM
ejpam-5505	109	35	,	,	PUNCT
ejpam-5505	109	36	b	b	NOUN
ejpam-5505	109	37	)	)	PUNCT
ejpam-5505	109	38	=	=	SYM
ejpam-5505	109	39	(	(	PUNCT
ejpam-5505	109	40	−b−>(y	−b−>(y	PROPN
ejpam-5505	109	41	)	)	PUNCT
ejpam-5505	109	42	)	)	PUNCT
ejpam-5505	109	43	.	.	PUNCT
ejpam-5505	110	1	proof	proof	NOUN
ejpam-5505	110	2	.	.	PUNCT
ejpam-5505	111	1	(	(	PUNCT
ejpam-5505	111	2	i	i	NOUN
ejpam-5505	111	3	):	):	PUNCT
ejpam-5505	111	4	from	from	ADP
ejpam-5505	111	5	(	(	PUNCT
ejpam-5505	111	6	13	13	NUM
ejpam-5505	111	7	)	)	PUNCT
ejpam-5505	111	8	,	,	PUNCT
ejpam-5505	111	9	it	it	PRON
ejpam-5505	111	10	follows	follow	VERB
ejpam-5505	111	11	that	that	SCONJ
ejpam-5505	111	12	x	x	SYM
ejpam-5505	111	13	∈	∈	PROPN
ejpam-5505	111	14	psol(a	psol(a	NUM
ejpam-5505	111	15	,	,	PUNCT
ejpam-5505	111	16	b	b	NOUN
ejpam-5505	111	17	)	)	PUNCT
ejpam-5505	111	18	⇔	⇔	NOUN
ejpam-5505	111	19	(	(	PUNCT
ejpam-5505	111	20	a	a	PRON
ejpam-5505	111	21	+	+	PROPN
ejpam-5505	111	22	b)−1(0	b)−1(0	NOUN
ejpam-5505	111	23	)	)	PUNCT
ejpam-5505	111	24	̸=	̸=	PROPN
ejpam-5505	111	25	∅	∅	NOUN
ejpam-5505	111	26	⇔	⇔	NOUN
ejpam-5505	111	27	∅	∅	NOUN
ejpam-5505	111	28	̸=	̸=	PROPN
ejpam-5505	111	29	ax	ax	NOUN
ejpam-5505	111	30	∩	∩	NOUN
ejpam-5505	111	31	(	(	PUNCT
ejpam-5505	111	32	−bx	−bx	NOUN
ejpam-5505	111	33	)	)	PUNCT
ejpam-5505	111	34	⇔	⇔	NOUN
ejpam-5505	111	35	∅	∅	NOUN
ejpam-5505	111	36	̸=	̸=	PROPN
ejpam-5505	111	37	ax	ax	NOUN
ejpam-5505	111	38	∩	∩	NOUN
ejpam-5505	111	39	(	(	PUNCT
ejpam-5505	111	40	(	(	PUNCT
ejpam-5505	111	41	−	−	PROPN
ejpam-5505	111	42	i	i	NOUN
ejpam-5505	111	43	d	d	PROPN
ejpam-5505	111	44	)	)	PUNCT
ejpam-5505	112	1	◦	◦	NOUN
ejpam-5505	112	2	b	b	SYM
ejpam-5505	112	3	◦	◦	NOUN
ejpam-5505	112	4	(	(	PUNCT
ejpam-5505	112	5	−	−	PROPN
ejpam-5505	112	6	id)(−x	id)(−x	NUM
ejpam-5505	112	7	)	)	PUNCT
ejpam-5505	112	8	)	)	PUNCT
ejpam-5505	113	1	⇔	⇔	NOUN
ejpam-5505	113	2	∅	∅	NOUN
ejpam-5505	113	3	̸=	̸=	PROPN
ejpam-5505	113	4	ax	ax	NOUN
ejpam-5505	113	5	∩	∩	NOUN
ejpam-5505	113	6	b>(−x	b>(−x	NOUN
ejpam-5505	113	7	)	)	PUNCT
ejpam-5505	113	8	⇔	⇔	NOUN
ejpam-5505	113	9	∅	∅	NOUN
ejpam-5505	113	10	̸=	̸=	PROPN
ejpam-5505	113	11	ax	ax	NOUN
ejpam-5505	113	12	∩	∩	NOUN
ejpam-5505	113	13	b>(−x	b>(−x	NOUN
ejpam-5505	113	14	)	)	PUNCT
ejpam-5505	113	15	⊆	⊆	NUM
ejpam-5505	113	16	dsol(a	dsol(a	PROPN
ejpam-5505	113	17	,	,	PUNCT
ejpam-5505	113	18	b	b	NOUN
ejpam-5505	113	19	)	)	PUNCT
ejpam-5505	113	20	⇔	⇔	NOUN
ejpam-5505	113	21	∅	∅	NOUN
ejpam-5505	113	22	̸=	̸=	PROPN
ejpam-5505	113	23	ax	ax	NOUN
ejpam-5505	113	24	∩	∩	NOUN
ejpam-5505	113	25	(	(	PUNCT
ejpam-5505	113	26	−bx	−bx	NOUN
ejpam-5505	113	27	)	)	PUNCT
ejpam-5505	113	28	⊆	⊆	NUM
ejpam-5505	113	29	dsol(a	dsol(a	PROPN
ejpam-5505	113	30	,	,	PUNCT
ejpam-5505	113	31	b	b	NOUN
ejpam-5505	113	32	)	)	PUNCT
ejpam-5505	113	33	.	.	PUNCT
ejpam-5505	114	1	since	since	SCONJ
ejpam-5505	114	2	psol(a	psol(a	NUM
ejpam-5505	114	3	,	,	PUNCT
ejpam-5505	114	4	b	b	NOUN
ejpam-5505	114	5	)	)	PUNCT
ejpam-5505	114	6	=	=	SYM
ejpam-5505	114	7	{	{	PUNCT
ejpam-5505	114	8	x	x	NOUN
ejpam-5505	114	9	}	}	PUNCT
ejpam-5505	114	10	and	and	CCONJ
ejpam-5505	114	11	by	by	ADP
ejpam-5505	114	12	using	use	VERB
ejpam-5505	114	13	(	(	PUNCT
ejpam-5505	114	14	13	13	NUM
ejpam-5505	114	15	)	)	PUNCT
ejpam-5505	114	16	,	,	PUNCT
ejpam-5505	114	17	it	it	PRON
ejpam-5505	114	18	follows	follow	VERB
ejpam-5505	114	19	that	that	SCONJ
ejpam-5505	114	20	ax	ax	NOUN
ejpam-5505	114	21	∩	∩	NOUN
ejpam-5505	114	22	(	(	PUNCT
ejpam-5505	114	23	−bx	−bx	NOUN
ejpam-5505	114	24	)	)	PUNCT
ejpam-5505	114	25	=	=	SYM
ejpam-5505	114	26	dsol(a	dsol(a	PROPN
ejpam-5505	114	27	,	,	PUNCT
ejpam-5505	114	28	b	b	NOUN
ejpam-5505	114	29	)	)	PUNCT
ejpam-5505	114	30	and	and	CCONJ
ejpam-5505	114	31	ax	ax	NOUN
ejpam-5505	114	32	∩	∩	NOUN
ejpam-5505	114	33	b>(−x	b>(−x	NOUN
ejpam-5505	114	34	)	)	PUNCT
ejpam-5505	114	35	=	=	SYM
ejpam-5505	114	36	dsol(a	dsol(a	PROPN
ejpam-5505	114	37	,	,	PUNCT
ejpam-5505	114	38	b	b	NOUN
ejpam-5505	114	39	)	)	PUNCT
ejpam-5505	114	40	.	.	PUNCT
ejpam-5505	115	1	(	(	PUNCT
ejpam-5505	115	2	ii	ii	NOUN
ejpam-5505	115	3	):	):	PUNCT
ejpam-5505	115	4	from	from	ADP
ejpam-5505	115	5	(	(	PUNCT
ejpam-5505	115	6	16	16	NUM
ejpam-5505	115	7	)	)	PUNCT
ejpam-5505	115	8	,	,	PUNCT
ejpam-5505	115	9	it	it	PRON
ejpam-5505	115	10	follows	follow	VERB
ejpam-5505	115	11	that	that	SCONJ
ejpam-5505	115	12	y	y	PROPN
ejpam-5505	115	13	∈	∈	PROPN
ejpam-5505	115	14	dsol(a	dsol(a	PROPN
ejpam-5505	115	15	,	,	PUNCT
ejpam-5505	115	16	b	b	NOUN
ejpam-5505	115	17	)	)	PUNCT
ejpam-5505	115	18	⇔	⇔	NOUN
ejpam-5505	115	19	(	(	PUNCT
ejpam-5505	115	20	a−1	a−1	PROPN
ejpam-5505	115	21	+	+	CCONJ
ejpam-5505	115	22	b−>)−1(0	b−>)−1(0	PROPN
ejpam-5505	115	23	)	)	PUNCT
ejpam-5505	115	24	̸=	̸=	PROPN
ejpam-5505	115	25	∅	∅	NOUN
ejpam-5505	115	26	s.th.alwadani	s.th.alwadani	NOUN
ejpam-5505	115	27	/	/	SYM
ejpam-5505	115	28	eur	eur	NOUN
ejpam-5505	115	29	.	.	PUNCT
ejpam-5505	116	1	j.	j.	PROPN
ejpam-5505	116	2	pure	pure	PROPN
ejpam-5505	116	3	appl	appl	PROPN
ejpam-5505	116	4	.	.	PROPN
ejpam-5505	116	5	math	math	PROPN
ejpam-5505	116	6	,	,	PUNCT
ejpam-5505	116	7	17	17	NUM
ejpam-5505	116	8	(	(	PUNCT
ejpam-5505	116	9	4	4	NUM
ejpam-5505	116	10	)	)	PUNCT
ejpam-5505	116	11	(	(	PUNCT
ejpam-5505	116	12	2024	2024	NUM
ejpam-5505	116	13	)	)	PUNCT
ejpam-5505	116	14	,	,	PUNCT
ejpam-5505	116	15	3642	3642	NUM
ejpam-5505	116	16	-	-	SYM
ejpam-5505	116	17	3659	3659	NUM
ejpam-5505	116	18	3647	3647	NUM
ejpam-5505	116	19	⇔	⇔	PROPN
ejpam-5505	116	20	a−1(y	a−1(y	PROPN
ejpam-5505	116	21	)	)	PUNCT
ejpam-5505	116	22	∩	∩	NOUN
ejpam-5505	116	23	(	(	PUNCT
ejpam-5505	116	24	−b−>(y	−b−>(y	X
ejpam-5505	116	25	)	)	PUNCT
ejpam-5505	116	26	)	)	PUNCT
ejpam-5505	117	1	̸=	̸=	PROPN
ejpam-5505	117	2	∅	∅	VERB
ejpam-5505	117	3	⇔	⇔	PROPN
ejpam-5505	117	4	a−1(y	a−1(y	PROPN
ejpam-5505	117	5	)	)	PUNCT
ejpam-5505	117	6	∩	∩	ADJ
ejpam-5505	117	7	b−1(−y	b−1(−y	NOUN
ejpam-5505	117	8	)	)	PUNCT
ejpam-5505	117	9	̸=	̸=	PROPN
ejpam-5505	117	10	∅	∅	NOUN
ejpam-5505	117	11	⇔	⇔	NOUN
ejpam-5505	117	12	∅	∅	NOUN
ejpam-5505	117	13	̸=	̸=	PROPN
ejpam-5505	117	14	a−1(y	a−1(y	PROPN
ejpam-5505	117	15	)	)	PUNCT
ejpam-5505	117	16	∩	∩	ADJ
ejpam-5505	117	17	b−1(−y	b−1(−y	NOUN
ejpam-5505	117	18	)	)	PUNCT
ejpam-5505	117	19	⊆	⊆	NUM
ejpam-5505	117	20	psol(a	psol(a	NUM
ejpam-5505	117	21	,	,	PUNCT
ejpam-5505	117	22	b	b	NOUN
ejpam-5505	117	23	)	)	PUNCT
ejpam-5505	117	24	.	.	PUNCT
ejpam-5505	118	1	since	since	SCONJ
ejpam-5505	118	2	dsol(a	dsol(a	PROPN
ejpam-5505	118	3	,	,	PUNCT
ejpam-5505	118	4	b	b	NOUN
ejpam-5505	118	5	)	)	PUNCT
ejpam-5505	118	6	=	=	SYM
ejpam-5505	118	7	{	{	PUNCT
ejpam-5505	118	8	y	y	NOUN
ejpam-5505	118	9	}	}	PUNCT
ejpam-5505	118	10	and	and	CCONJ
ejpam-5505	118	11	by	by	ADP
ejpam-5505	118	12	using	use	VERB
ejpam-5505	118	13	(	(	PUNCT
ejpam-5505	118	14	16	16	NUM
ejpam-5505	118	15	)	)	PUNCT
ejpam-5505	118	16	,	,	PUNCT
ejpam-5505	118	17	it	it	PRON
ejpam-5505	118	18	follows	follow	VERB
ejpam-5505	118	19	that	that	SCONJ
ejpam-5505	118	20	a−1(y	a−1(y	PROPN
ejpam-5505	118	21	)	)	PUNCT
ejpam-5505	118	22	∩	∩	ADJ
ejpam-5505	118	23	b−1(−y	b−1(−y	NOUN
ejpam-5505	118	24	)	)	PUNCT
ejpam-5505	118	25	=	=	SYM
ejpam-5505	118	26	psol(a	psol(a	NUM
ejpam-5505	118	27	,	,	PUNCT
ejpam-5505	118	28	b	b	NOUN
ejpam-5505	118	29	)	)	PUNCT
ejpam-5505	118	30	.	.	PUNCT
ejpam-5505	119	1	(	(	PUNCT
ejpam-5505	119	2	iii	iii	NOUN
ejpam-5505	119	3	):	):	PUNCT
ejpam-5505	119	4	from	from	ADP
ejpam-5505	119	5	(	(	PUNCT
ejpam-5505	119	6	i	i	NOUN
ejpam-5505	119	7	)	)	PUNCT
ejpam-5505	119	8	,	,	PUNCT
ejpam-5505	119	9	we	we	PRON
ejpam-5505	119	10	have	have	VERB
ejpam-5505	119	11	ax	ax	NOUN
ejpam-5505	119	12	∩	∩	NOUN
ejpam-5505	119	13	(	(	PUNCT
ejpam-5505	119	14	−bx	−bx	NOUN
ejpam-5505	119	15	)	)	PUNCT
ejpam-5505	119	16	=	=	SYM
ejpam-5505	119	17	dsol(a	dsol(a	PROPN
ejpam-5505	119	18	,	,	PUNCT
ejpam-5505	119	19	b	b	NOUN
ejpam-5505	119	20	)	)	PUNCT
ejpam-5505	119	21	,	,	PUNCT
ejpam-5505	119	22	and	and	CCONJ
ejpam-5505	119	23	ax	ax	NOUN
ejpam-5505	119	24	∩	∩	NOUN
ejpam-5505	119	25	b>(−x	b>(−x	NOUN
ejpam-5505	119	26	)	)	PUNCT
ejpam-5505	119	27	=	=	SYM
ejpam-5505	119	28	dsol(a	dsol(a	PROPN
ejpam-5505	119	29	,	,	PUNCT
ejpam-5505	119	30	b	b	NOUN
ejpam-5505	119	31	)	)	PUNCT
ejpam-5505	119	32	.	.	PUNCT
ejpam-5505	120	1	since	since	SCONJ
ejpam-5505	120	2	ax	ax	NOUN
ejpam-5505	120	3	is	be	AUX
ejpam-5505	120	4	a	a	DET
ejpam-5505	120	5	singelton	singelton	NOUN
ejpam-5505	120	6	then	then	ADV
ejpam-5505	120	7	we	we	PRON
ejpam-5505	120	8	obtain	obtain	VERB
ejpam-5505	120	9	dsol(a	dsol(a	PROPN
ejpam-5505	120	10	,	,	PUNCT
ejpam-5505	120	11	b	b	NOUN
ejpam-5505	120	12	)	)	PUNCT
ejpam-5505	120	13	=	=	NOUN
ejpam-5505	120	14	ax	ax	NOUN
ejpam-5505	120	15	∩	∩	NOUN
ejpam-5505	120	16	(	(	PUNCT
ejpam-5505	120	17	−bx	−bx	NOUN
ejpam-5505	120	18	)	)	PUNCT
ejpam-5505	120	19	=	=	NOUN
ejpam-5505	120	20	ax	ax	NOUN
ejpam-5505	120	21	,	,	PUNCT
ejpam-5505	120	22	and	and	CCONJ
ejpam-5505	120	23	dsol(a	dsol(a	PROPN
ejpam-5505	120	24	,	,	PUNCT
ejpam-5505	120	25	b	b	NOUN
ejpam-5505	120	26	)	)	PUNCT
ejpam-5505	120	27	=	=	NOUN
ejpam-5505	120	28	ax	ax	NOUN
ejpam-5505	120	29	∩	∩	NOUN
ejpam-5505	120	30	b>(−x	b>(−x	NOUN
ejpam-5505	120	31	)	)	PUNCT
ejpam-5505	120	32	=	=	SYM
ejpam-5505	120	33	ax	ax	NOUN
ejpam-5505	120	34	.	.	PUNCT
ejpam-5505	121	1	(	(	PUNCT
ejpam-5505	121	2	iv	iv	NUM
ejpam-5505	121	3	):	):	PUNCT
ejpam-5505	121	4	from	from	ADP
ejpam-5505	121	5	(	(	PUNCT
ejpam-5505	121	6	i	i	NOUN
ejpam-5505	121	7	)	)	PUNCT
ejpam-5505	121	8	,	,	PUNCT
ejpam-5505	121	9	we	we	PRON
ejpam-5505	121	10	have	have	VERB
ejpam-5505	121	11	ax	ax	NOUN
ejpam-5505	121	12	∩	∩	NOUN
ejpam-5505	121	13	(	(	PUNCT
ejpam-5505	121	14	−bx	−bx	NOUN
ejpam-5505	121	15	)	)	PUNCT
ejpam-5505	121	16	=	=	SYM
ejpam-5505	121	17	dsol(a	dsol(a	PROPN
ejpam-5505	121	18	,	,	PUNCT
ejpam-5505	121	19	b	b	NOUN
ejpam-5505	121	20	)	)	PUNCT
ejpam-5505	121	21	and	and	CCONJ
ejpam-5505	121	22	ax	ax	NOUN
ejpam-5505	121	23	∩	∩	NOUN
ejpam-5505	121	24	b>(−x	b>(−x	NOUN
ejpam-5505	121	25	)	)	PUNCT
ejpam-5505	122	1	=	=	SYM
ejpam-5505	122	2	dsol(a	dsol(a	PROPN
ejpam-5505	122	3	,	,	PUNCT
ejpam-5505	122	4	b	b	NOUN
ejpam-5505	122	5	)	)	PUNCT
ejpam-5505	122	6	.	.	PUNCT
ejpam-5505	123	1	since	since	SCONJ
ejpam-5505	123	2	bx	bx	PROPN
ejpam-5505	123	3	and	and	CCONJ
ejpam-5505	123	4	b>(−x	b>(−x	NOUN
ejpam-5505	123	5	)	)	PUNCT
ejpam-5505	123	6	are	be	AUX
ejpam-5505	123	7	singelton	singelton	ADJ
ejpam-5505	123	8	,	,	PUNCT
ejpam-5505	123	9	it	it	PRON
ejpam-5505	123	10	follows	follow	VERB
ejpam-5505	123	11	that	that	SCONJ
ejpam-5505	123	12	dsol(a	dsol(a	PROPN
ejpam-5505	123	13	,	,	PUNCT
ejpam-5505	123	14	b	b	NOUN
ejpam-5505	123	15	)	)	PUNCT
ejpam-5505	123	16	=	=	NOUN
ejpam-5505	123	17	ax	ax	NOUN
ejpam-5505	123	18	∩	∩	NOUN
ejpam-5505	123	19	(	(	PUNCT
ejpam-5505	123	20	−bx	−bx	NOUN
ejpam-5505	123	21	)	)	PUNCT
ejpam-5505	123	22	=	=	SYM
ejpam-5505	123	23	−bx	−bx	PROPN
ejpam-5505	123	24	and	and	CCONJ
ejpam-5505	123	25	dsol(a	dsol(a	PROPN
ejpam-5505	123	26	,	,	PUNCT
ejpam-5505	123	27	b	b	NOUN
ejpam-5505	123	28	)	)	PUNCT
ejpam-5505	123	29	=	=	NOUN
ejpam-5505	123	30	ax	ax	NOUN
ejpam-5505	123	31	∩	∩	NOUN
ejpam-5505	123	32	b>(−x	b>(−x	NOUN
ejpam-5505	123	33	)	)	PUNCT
ejpam-5505	123	34	=	=	PUNCT
ejpam-5505	123	35	b>(−x	b>(−x	NOUN
ejpam-5505	123	36	)	)	PUNCT
ejpam-5505	123	37	.	.	PUNCT
ejpam-5505	124	1	(	(	PUNCT
ejpam-5505	124	2	v	v	NOUN
ejpam-5505	124	3	):	):	PUNCT
ejpam-5505	124	4	from	from	ADP
ejpam-5505	124	5	(	(	PUNCT
ejpam-5505	124	6	ii	ii	NOUN
ejpam-5505	124	7	)	)	PUNCT
ejpam-5505	124	8	,	,	PUNCT
ejpam-5505	124	9	we	we	PRON
ejpam-5505	124	10	have	have	VERB
ejpam-5505	124	11	(	(	PUNCT
ejpam-5505	124	12	a−1y	a−1y	ADJ
ejpam-5505	124	13	)	)	PUNCT
ejpam-5505	124	14	∩	∩	ADJ
ejpam-5505	124	15	b−1(−y	b−1(−y	NOUN
ejpam-5505	124	16	)	)	PUNCT
ejpam-5505	125	1	=	=	SYM
ejpam-5505	125	2	psol(a	psol(a	NUM
ejpam-5505	125	3	,	,	PUNCT
ejpam-5505	125	4	b	b	NOUN
ejpam-5505	125	5	)	)	PUNCT
ejpam-5505	125	6	and	and	CCONJ
ejpam-5505	125	7	(	(	PUNCT
ejpam-5505	125	8	a−1y	a−1y	ADJ
ejpam-5505	125	9	)	)	PUNCT
ejpam-5505	125	10	∩	∩	NOUN
ejpam-5505	125	11	(	(	PUNCT
ejpam-5505	125	12	−b−>(y	−b−>(y	X
ejpam-5505	125	13	)	)	PUNCT
ejpam-5505	125	14	)	)	PUNCT
ejpam-5505	126	1	=	=	SYM
ejpam-5505	126	2	dsol(a	dsol(a	PROPN
ejpam-5505	126	3	,	,	PUNCT
ejpam-5505	126	4	b	b	NOUN
ejpam-5505	126	5	)	)	PUNCT
ejpam-5505	126	6	.	.	PUNCT
ejpam-5505	127	1	since	since	SCONJ
ejpam-5505	127	2	a−1y	a−1y	NOUN
ejpam-5505	127	3	is	be	AUX
ejpam-5505	127	4	a	a	DET
ejpam-5505	127	5	singelton	singelton	NOUN
ejpam-5505	127	6	,	,	PUNCT
ejpam-5505	127	7	we	we	PRON
ejpam-5505	127	8	obtain	obtain	VERB
ejpam-5505	127	9	psol(a	psol(a	NUM
ejpam-5505	127	10	,	,	PUNCT
ejpam-5505	127	11	b	b	NOUN
ejpam-5505	127	12	)	)	PUNCT
ejpam-5505	127	13	=	=	SYM
ejpam-5505	127	14	(	(	PUNCT
ejpam-5505	127	15	a−1y	a−1y	ADJ
ejpam-5505	127	16	)	)	PUNCT
ejpam-5505	127	17	∩	∩	ADJ
ejpam-5505	127	18	b−1(−y	b−1(−y	NOUN
ejpam-5505	127	19	)	)	PUNCT
ejpam-5505	127	20	=	=	SYM
ejpam-5505	128	1	a−1y	a−1y	NOUN
ejpam-5505	128	2	and	and	CCONJ
ejpam-5505	128	3	psol(a	psol(a	NUM
ejpam-5505	128	4	,	,	PUNCT
ejpam-5505	128	5	b	b	NOUN
ejpam-5505	128	6	)	)	PUNCT
ejpam-5505	128	7	=	=	SYM
ejpam-5505	128	8	(	(	PUNCT
ejpam-5505	128	9	a−1y	a−1y	ADJ
ejpam-5505	128	10	)	)	PUNCT
ejpam-5505	128	11	∩	∩	NOUN
ejpam-5505	128	12	(	(	PUNCT
ejpam-5505	128	13	−b−>(y	−b−>(y	X
ejpam-5505	128	14	)	)	PUNCT
ejpam-5505	128	15	)	)	PUNCT
ejpam-5505	129	1	=	=	SYM
ejpam-5505	129	2	a−1y	a−1y	ADJ
ejpam-5505	129	3	.	.	PUNCT
ejpam-5505	130	1	(	(	PUNCT
ejpam-5505	130	2	vi	vi	NOUN
ejpam-5505	130	3	):	):	PUNCT
ejpam-5505	130	4	from	from	ADP
ejpam-5505	130	5	(	(	PUNCT
ejpam-5505	130	6	ii	ii	NOUN
ejpam-5505	130	7	)	)	PUNCT
ejpam-5505	130	8	,	,	PUNCT
ejpam-5505	130	9	we	we	PRON
ejpam-5505	130	10	have	have	VERB
ejpam-5505	130	11	(	(	PUNCT
ejpam-5505	130	12	a−1y	a−1y	ADJ
ejpam-5505	130	13	)	)	PUNCT
ejpam-5505	130	14	∩	∩	ADJ
ejpam-5505	130	15	b−1(−y	b−1(−y	NOUN
ejpam-5505	130	16	)	)	PUNCT
ejpam-5505	131	1	=	=	SYM
ejpam-5505	131	2	psol(a	psol(a	NUM
ejpam-5505	131	3	,	,	PUNCT
ejpam-5505	131	4	b	b	NOUN
ejpam-5505	131	5	)	)	PUNCT
ejpam-5505	131	6	and	and	CCONJ
ejpam-5505	131	7	(	(	PUNCT
ejpam-5505	131	8	a−1y	a−1y	ADJ
ejpam-5505	131	9	)	)	PUNCT
ejpam-5505	131	10	∩	∩	NOUN
ejpam-5505	131	11	(	(	PUNCT
ejpam-5505	131	12	−b−>(y	−b−>(y	X
ejpam-5505	131	13	)	)	PUNCT
ejpam-5505	131	14	)	)	PUNCT
ejpam-5505	132	1	=	=	SYM
ejpam-5505	132	2	dsol(a	dsol(a	PROPN
ejpam-5505	132	3	,	,	PUNCT
ejpam-5505	132	4	b	b	NOUN
ejpam-5505	132	5	)	)	PUNCT
ejpam-5505	132	6	.	.	PUNCT
ejpam-5505	133	1	since	since	SCONJ
ejpam-5505	133	2	b−1(−y	b−1(−y	PROPN
ejpam-5505	133	3	)	)	PUNCT
ejpam-5505	133	4	and	and	CCONJ
ejpam-5505	133	5	(	(	PUNCT
ejpam-5505	133	6	−b−>(y	−b−>(y	NOUN
ejpam-5505	133	7	)	)	PUNCT
ejpam-5505	133	8	)	)	PUNCT
ejpam-5505	133	9	are	be	AUX
ejpam-5505	133	10	singelton	singelton	ADJ
ejpam-5505	133	11	,	,	PUNCT
ejpam-5505	133	12	we	we	PRON
ejpam-5505	133	13	obtain	obtain	VERB
ejpam-5505	133	14	psol(a	psol(a	NUM
ejpam-5505	133	15	,	,	PUNCT
ejpam-5505	133	16	b	b	NOUN
ejpam-5505	133	17	)	)	PUNCT
ejpam-5505	133	18	=	=	SYM
ejpam-5505	133	19	(	(	PUNCT
ejpam-5505	133	20	a−1y	a−1y	ADJ
ejpam-5505	133	21	)	)	PUNCT
ejpam-5505	133	22	∩	∩	ADJ
ejpam-5505	133	23	b−1(−y	b−1(−y	NOUN
ejpam-5505	133	24	)	)	PUNCT
ejpam-5505	133	25	=	=	SYM
ejpam-5505	133	26	b−1(−y	b−1(−y	NOUN
ejpam-5505	133	27	)	)	PUNCT
ejpam-5505	133	28	and	and	CCONJ
ejpam-5505	133	29	psol(a	psol(a	NUM
ejpam-5505	133	30	,	,	PUNCT
ejpam-5505	133	31	b	b	NOUN
ejpam-5505	133	32	)	)	PUNCT
ejpam-5505	133	33	=	=	SYM
ejpam-5505	133	34	(	(	PUNCT
ejpam-5505	133	35	a−1y	a−1y	ADJ
ejpam-5505	133	36	)	)	PUNCT
ejpam-5505	133	37	∩	∩	NOUN
ejpam-5505	133	38	(	(	PUNCT
ejpam-5505	133	39	−b−>(y	−b−>(y	X
ejpam-5505	133	40	)	)	PUNCT
ejpam-5505	133	41	)	)	PUNCT
ejpam-5505	134	1	=	=	PUNCT
ejpam-5505	134	2	−b−>(y	−b−>(y	PROPN
ejpam-5505	134	3	)	)	PUNCT
ejpam-5505	134	4	.	.	PUNCT
ejpam-5505	135	1	■	■	PUNCT
ejpam-5505	135	2	for	for	ADP
ejpam-5505	135	3	more	more	ADJ
ejpam-5505	135	4	information	information	NOUN
ejpam-5505	135	5	about	about	ADP
ejpam-5505	135	6	the	the	DET
ejpam-5505	135	7	attouch	attouch	ADJ
ejpam-5505	135	8	–	–	PUNCT
ejpam-5505	135	9	théra	théra	NUM
ejpam-5505	135	10	duality	duality	NOUN
ejpam-5505	135	11	,	,	PUNCT
ejpam-5505	135	12	we	we	PRON
ejpam-5505	135	13	refer	refer	VERB
ejpam-5505	135	14	the	the	DET
ejpam-5505	135	15	reader	reader	NOUN
ejpam-5505	135	16	to	to	ADP
ejpam-5505	135	17	[	[	X
ejpam-5505	135	18	5	5	NUM
ejpam-5505	135	19	]	]	PUNCT
ejpam-5505	135	20	.	.	PUNCT
ejpam-5505	136	1	s.th.alwadani	s.th.alwadani	ADJ
ejpam-5505	136	2	/	/	SYM
ejpam-5505	136	3	eur	eur	PROPN
ejpam-5505	136	4	.	.	PUNCT
ejpam-5505	137	1	j.	j.	PROPN
ejpam-5505	137	2	pure	pure	PROPN
ejpam-5505	137	3	appl	appl	PROPN
ejpam-5505	137	4	.	.	PROPN
ejpam-5505	137	5	math	math	PROPN
ejpam-5505	137	6	,	,	PUNCT
ejpam-5505	137	7	17	17	NUM
ejpam-5505	137	8	(	(	PUNCT
ejpam-5505	137	9	4	4	NUM
ejpam-5505	137	10	)	)	PUNCT
ejpam-5505	137	11	(	(	PUNCT
ejpam-5505	137	12	2024	2024	NUM
ejpam-5505	137	13	)	)	PUNCT
ejpam-5505	137	14	,	,	PUNCT
ejpam-5505	137	15	3642	3642	NUM
ejpam-5505	137	16	-	-	SYM
ejpam-5505	137	17	3659	3659	NUM
ejpam-5505	137	18	3648	3648	NUM
ejpam-5505	137	19	4	4	NUM
ejpam-5505	137	20	.	.	PUNCT
ejpam-5505	138	1	correspondence	correspondence	NOUN
ejpam-5505	138	2	of	of	ADP
ejpam-5505	138	3	properties	property	NOUN
ejpam-5505	138	4	and	and	CCONJ
ejpam-5505	138	5	results	result	VERB
ejpam-5505	138	6	this	this	DET
ejpam-5505	138	7	section	section	NOUN
ejpam-5505	138	8	presents	present	VERB
ejpam-5505	138	9	some	some	PRON
ejpam-5505	138	10	of	of	ADP
ejpam-5505	138	11	our	our	PRON
ejpam-5505	138	12	key	key	ADJ
ejpam-5505	138	13	findings	finding	NOUN
ejpam-5505	138	14	regarding	regard	VERB
ejpam-5505	138	15	the	the	DET
ejpam-5505	138	16	cycles	cycle	NOUN
ejpam-5505	138	17	and	and	CCONJ
ejpam-5505	138	18	fixed	fix	VERB
ejpam-5505	138	19	point	point	NOUN
ejpam-5505	138	20	sets	set	NOUN
ejpam-5505	138	21	of	of	ADP
ejpam-5505	138	22	resolvent	resolvent	ADJ
ejpam-5505	138	23	compositions	composition	NOUN
ejpam-5505	138	24	,	,	PUNCT
ejpam-5505	138	25	beginning	begin	VERB
ejpam-5505	138	26	with	with	ADP
ejpam-5505	138	27	an	an	DET
ejpam-5505	138	28	exploration	exploration	NOUN
ejpam-5505	138	29	of	of	ADP
ejpam-5505	138	30	their	their	PRON
ejpam-5505	138	31	interrelationship	interrelationship	NOUN
ejpam-5505	138	32	,	,	PUNCT
ejpam-5505	138	33	as	as	SCONJ
ejpam-5505	138	34	demonstrated	demonstrate	VERB
ejpam-5505	138	35	in	in	ADP
ejpam-5505	138	36	theorem	theorem	ADJ
ejpam-5505	138	37	1	1	NUM
ejpam-5505	138	38	and	and	CCONJ
ejpam-5505	138	39	theorem	theorem	VERB
ejpam-5505	138	40	2	2	NUM
ejpam-5505	138	41	.	.	PUNCT
ejpam-5505	138	42	theorem	theorem	NOUN
ejpam-5505	138	43	1	1	NUM
ejpam-5505	138	44	.	.	PUNCT
ejpam-5505	139	1	the	the	DET
ejpam-5505	139	2	following	follow	VERB
ejpam-5505	139	3	are	be	AUX
ejpam-5505	139	4	equivalent	equivalent	ADJ
ejpam-5505	139	5	(	(	PUNCT
ejpam-5505	139	6	i	i	NOUN
ejpam-5505	139	7	)	)	PUNCT
ejpam-5505	139	8	cycle	cycle	NOUN
ejpam-5505	139	9	exists	exist	VERB
ejpam-5505	139	10	.	.	PUNCT
ejpam-5505	140	1	(	(	PUNCT
ejpam-5505	140	2	ii	ii	NOUN
ejpam-5505	140	3	)	)	PUNCT
ejpam-5505	140	4	for	for	ADP
ejpam-5505	140	5	all	all	DET
ejpam-5505	140	6	1	1	NUM
ejpam-5505	140	7	≤	≤	NUM
ejpam-5505	140	8	i	i	PRON
ejpam-5505	140	9	≤	≤	NOUN
ejpam-5505	140	10	m	m	ADP
ejpam-5505	140	11	,	,	PUNCT
ejpam-5505	140	12	the	the	DET
ejpam-5505	140	13	fixed	fix	VERB
ejpam-5505	140	14	point	point	NOUN
ejpam-5505	140	15	sets	set	NOUN
ejpam-5505	140	16	of	of	ADP
ejpam-5505	140	17	cyclic	cyclic	ADJ
ejpam-5505	140	18	compositions	composition	NOUN
ejpam-5505	140	19	of	of	ADP
ejpam-5505	140	20	resolvants	resolvant	NOUN
ejpam-5505	140	21	fi	fi	NOUN
ejpam-5505	140	22	̸=	̸=	PROPN
ejpam-5505	140	23	∅.	∅.	ADP
ejpam-5505	140	24	proof	proof	NOUN
ejpam-5505	140	25	.	.	PUNCT
ejpam-5505	140	26	”	"	PUNCT
ejpam-5505	141	1	(	(	PUNCT
ejpam-5505	141	2	i)⇒(ii	i)⇒(ii	ADV
ejpam-5505	141	3	)	)	PUNCT
ejpam-5505	141	4	”	"	PUNCT
ejpam-5505	141	5	:	:	PUNCT
ejpam-5505	141	6	let	let	VERB
ejpam-5505	141	7	z	z	NOUN
ejpam-5505	141	8	=	=	SYM
ejpam-5505	141	9	(	(	PUNCT
ejpam-5505	141	10	z1	z1	PROPN
ejpam-5505	141	11	,	,	PUNCT
ejpam-5505	141	12	z2	z2	PROPN
ejpam-5505	141	13	,	,	PUNCT
ejpam-5505	141	14	.	.	PUNCT
ejpam-5505	141	15	.	.	PUNCT
ejpam-5505	142	1	.	.	PUNCT
ejpam-5505	143	1	,	,	PUNCT
ejpam-5505	143	2	zm−1	zm−1	PROPN
ejpam-5505	143	3	,	,	PUNCT
ejpam-5505	143	4	zm	zm	PROPN
ejpam-5505	143	5	)	)	PUNCT
ejpam-5505	143	6	be	be	AUX
ejpam-5505	143	7	a	a	DET
ejpam-5505	143	8	cycle	cycle	NOUN
ejpam-5505	143	9	.	.	PUNCT
ejpam-5505	144	1	then	then	ADV
ejpam-5505	144	2	by	by	ADP
ejpam-5505	144	3	definition	definition	NOUN
ejpam-5505	144	4	1	1	NUM
ejpam-5505	144	5	,	,	PUNCT
ejpam-5505	144	6	we	we	PRON
ejpam-5505	144	7	have	have	VERB
ejpam-5505	144	8	z1	z1	NOUN
ejpam-5505	144	9	=	=	SYM
ejpam-5505	144	10	j1zm	j1zm	PROPN
ejpam-5505	144	11	,	,	PUNCT
ejpam-5505	144	12	z2	z2	PROPN
ejpam-5505	144	13	=	=	SYM
ejpam-5505	144	14	j2z1	j2z1	PROPN
ejpam-5505	144	15	,	,	PUNCT
ejpam-5505	144	16	z3	z3	PROPN
ejpam-5505	144	17	=	=	SYM
ejpam-5505	144	18	j3z2	j3z2	NOUN
ejpam-5505	144	19	,	,	PUNCT
ejpam-5505	144	20	·	·	PUNCT
ejpam-5505	144	21	·	·	PUNCT
ejpam-5505	144	22	·	·	PUNCT
ejpam-5505	144	23	,	,	PUNCT
ejpam-5505	144	24	zm−1	zm−1	PROPN
ejpam-5505	144	25	=	=	PUNCT
ejpam-5505	144	26	jm−1zm−2	jm−1zm−2	PROPN
ejpam-5505	144	27	,	,	PUNCT
ejpam-5505	144	28	and	and	CCONJ
ejpam-5505	144	29	zm	zm	PROPN
ejpam-5505	144	30	=	=	SYM
ejpam-5505	144	31	jmzm−1	jmzm−1	PROPN
ejpam-5505	144	32	.	.	PUNCT
ejpam-5505	145	1	this	this	PRON
ejpam-5505	145	2	gives	give	VERB
ejpam-5505	145	3	that	that	DET
ejpam-5505	145	4	z1	z1	NOUN
ejpam-5505	145	5	=	=	X
ejpam-5505	145	6	j1jm	j1jm	X
ejpam-5505	145	7	.	.	PUNCT
ejpam-5505	145	8	.	.	PUNCT
ejpam-5505	145	9	.	.	PUNCT
ejpam-5505	146	1	j3j2z1	j3j2z1	PROPN
ejpam-5505	146	2	z2	z2	NOUN
ejpam-5505	146	3	=	=	PUNCT
ejpam-5505	146	4	j2j1	j2j1	PROPN
ejpam-5505	146	5	.	.	PUNCT
ejpam-5505	146	6	.	.	PUNCT
ejpam-5505	146	7	.	.	PUNCT
ejpam-5505	147	1	j4j3z2	j4j3z2	NOUN
ejpam-5505	147	2	...	...	PUNCT
ejpam-5505	148	1	zi	zi	X
ejpam-5505	148	2	=	=	PUNCT
ejpam-5505	149	1	jiji−1	jiji−1	PROPN
ejpam-5505	149	2	.	.	PUNCT
ejpam-5505	149	3	.	.	PUNCT
ejpam-5505	149	4	.	.	PUNCT
ejpam-5505	150	1	j1jm	j1jm	PROPN
ejpam-5505	150	2	.	.	PUNCT
ejpam-5505	150	3	.	.	PUNCT
ejpam-5505	150	4	.	.	PUNCT
ejpam-5505	151	1	ji+1zi	ji+1zi	PROPN
ejpam-5505	151	2	...	...	PUNCT
ejpam-5505	152	1	zm	zm	PROPN
ejpam-5505	152	2	=	=	SYM
ejpam-5505	152	3	jmjm−1	jmjm−1	PROPN
ejpam-5505	152	4	.	.	PUNCT
ejpam-5505	152	5	.	.	PUNCT
ejpam-5505	152	6	.	.	PUNCT
ejpam-5505	153	1	j2j1zm	j2j1zm	PROPN
ejpam-5505	153	2	.	.	PUNCT
ejpam-5505	154	1	therefore	therefore	ADV
ejpam-5505	154	2	,	,	PUNCT
ejpam-5505	154	3	z1	z1	PROPN
ejpam-5505	154	4	∈	∈	PROPN
ejpam-5505	154	5	f1	f1	NOUN
ejpam-5505	154	6	,	,	PUNCT
ejpam-5505	154	7	z2	z2	PROPN
ejpam-5505	154	8	∈	∈	PROPN
ejpam-5505	154	9	f2	f2	PROPN
ejpam-5505	154	10	,	,	PUNCT
ejpam-5505	154	11	.	.	PUNCT
ejpam-5505	154	12	.	.	PUNCT
ejpam-5505	154	13	.	.	PUNCT
ejpam-5505	155	1	,	,	PUNCT
ejpam-5505	155	2	zi	zi	PROPN
ejpam-5505	155	3	∈	∈	PROPN
ejpam-5505	155	4	fi	fi	NOUN
ejpam-5505	155	5	,	,	PUNCT
ejpam-5505	155	6	.	.	PUNCT
ejpam-5505	155	7	.	.	PUNCT
ejpam-5505	156	1	.	.	PUNCT
ejpam-5505	157	1	,	,	PUNCT
ejpam-5505	157	2	zm	zm	PROPN
ejpam-5505	157	3	∈	∈	PROPN
ejpam-5505	157	4	fm	fm	PROPN
ejpam-5505	157	5	by	by	ADP
ejpam-5505	157	6	(	(	PUNCT
ejpam-5505	157	7	8)-(11	8)-(11	NUM
ejpam-5505	157	8	)	)	PUNCT
ejpam-5505	157	9	.	.	PUNCT
ejpam-5505	158	1	this	this	PRON
ejpam-5505	158	2	implies	imply	VERB
ejpam-5505	158	3	that	that	SCONJ
ejpam-5505	158	4	f1	f1	PROPN
ejpam-5505	158	5	̸=	̸=	PROPN
ejpam-5505	158	6	∅	∅	NOUN
ejpam-5505	158	7	,	,	PUNCT
ejpam-5505	158	8	f2	f2	PROPN
ejpam-5505	158	9	̸=	̸=	PROPN
ejpam-5505	158	10	∅	∅	NOUN
ejpam-5505	158	11	,	,	PUNCT
ejpam-5505	158	12	.	.	PUNCT
ejpam-5505	158	13	.	.	PUNCT
ejpam-5505	158	14	.	.	PUNCT
ejpam-5505	159	1	,	,	PUNCT
ejpam-5505	159	2	fi	fi	NOUN
ejpam-5505	159	3	̸=	̸=	NOUN
ejpam-5505	159	4	∅	∅	NOUN
ejpam-5505	159	5	,	,	PUNCT
ejpam-5505	159	6	.	.	PUNCT
ejpam-5505	159	7	.	.	PUNCT
ejpam-5505	159	8	.	.	PUNCT
ejpam-5505	160	1	,	,	PUNCT
ejpam-5505	160	2	fm	fm	PROPN
ejpam-5505	160	3	̸=	̸=	PROPN
ejpam-5505	160	4	∅.	∅.	ADV
ejpam-5505	160	5	”	"	PUNCT
ejpam-5505	160	6	(	(	PUNCT
ejpam-5505	160	7	ii)⇒(i	ii)⇒(i	NOUN
ejpam-5505	160	8	)	)	PUNCT
ejpam-5505	160	9	”	"	PUNCT
ejpam-5505	160	10	:	:	PUNCT
ejpam-5505	160	11	let	let	VERB
ejpam-5505	160	12	fm	fm	PROPN
ejpam-5505	160	13	̸=	̸=	PROPN
ejpam-5505	160	14	∅	∅	NOUN
ejpam-5505	160	15	and	and	CCONJ
ejpam-5505	160	16	zm	zm	PROPN
ejpam-5505	160	17	∈	∈	PROPN
ejpam-5505	160	18	fm	fm	PROPN
ejpam-5505	160	19	.	.	PROPN
ejpam-5505	161	1	then	then	ADV
ejpam-5505	161	2	zm	zm	PROPN
ejpam-5505	161	3	∈	∈	PROPN
ejpam-5505	161	4	fix	fix	NOUN
ejpam-5505	161	5	(	(	PUNCT
ejpam-5505	161	6	jmjm−1	jmjm−1	NOUN
ejpam-5505	161	7	.	.	PUNCT
ejpam-5505	161	8	.	.	PUNCT
ejpam-5505	161	9	.	.	PUNCT
ejpam-5505	162	1	j2j1	j2j1	PROPN
ejpam-5505	162	2	)	)	PUNCT
ejpam-5505	162	3	zm	zm	PROPN
ejpam-5505	162	4	,	,	PUNCT
ejpam-5505	162	5	by	by	ADP
ejpam-5505	162	6	(	(	PUNCT
ejpam-5505	162	7	11	11	NUM
ejpam-5505	162	8	)	)	PUNCT
ejpam-5505	162	9	.	.	PUNCT
ejpam-5505	163	1	therefore	therefore	ADV
ejpam-5505	163	2	,	,	PUNCT
ejpam-5505	163	3	zm	zm	PROPN
ejpam-5505	163	4	=	=	SYM
ejpam-5505	163	5	jmjm−1	jmjm−1	PROPN
ejpam-5505	163	6	.	.	PUNCT
ejpam-5505	163	7	.	.	PUNCT
ejpam-5505	163	8	.	.	PUNCT
ejpam-5505	164	1	j2j1zm	j2j1zm	NOUN
ejpam-5505	164	2	.	.	PUNCT
ejpam-5505	165	1	next	next	ADV
ejpam-5505	165	2	,	,	PUNCT
ejpam-5505	165	3	applying	apply	VERB
ejpam-5505	165	4	j1	j1	PROPN
ejpam-5505	165	5	gives	give	VERB
ejpam-5505	165	6	j1zm	j1zm	PUNCT
ejpam-5505	166	1	=	=	SYM
ejpam-5505	166	2	j1	j1	PROPN
ejpam-5505	166	3	(	(	PUNCT
ejpam-5505	166	4	jmjm−1	jmjm−1	PROPN
ejpam-5505	166	5	.	.	PUNCT
ejpam-5505	166	6	.	.	PUNCT
ejpam-5505	166	7	.	.	PUNCT
ejpam-5505	167	1	j2	j2	PROPN
ejpam-5505	167	2	)	)	PUNCT
ejpam-5505	167	3	(	(	PUNCT
ejpam-5505	167	4	j1zm	j1zm	X
ejpam-5505	167	5	)	)	PUNCT
ejpam-5505	167	6	,	,	PUNCT
ejpam-5505	167	7	which	which	PRON
ejpam-5505	167	8	is	be	AUX
ejpam-5505	167	9	equivalent	equivalent	ADJ
ejpam-5505	167	10	to	to	ADP
ejpam-5505	167	11	j1zm	j1zm	PUNCT
ejpam-5505	167	12	∈	∈	PROPN
ejpam-5505	167	13	fix	fix	NOUN
ejpam-5505	167	14	(	(	PUNCT
ejpam-5505	167	15	j1jmjm−1	j1jmjm−1	PROPN
ejpam-5505	167	16	.	.	PUNCT
ejpam-5505	167	17	.	.	PUNCT
ejpam-5505	167	18	.	.	PUNCT
ejpam-5505	168	1	j3j2	j3j2	X
ejpam-5505	168	2	)	)	PUNCT
ejpam-5505	168	3	⇔	⇔	PROPN
ejpam-5505	168	4	j1zm	j1zm	PUNCT
ejpam-5505	168	5	∈	∈	PROPN
ejpam-5505	168	6	f1	f1	NOUN
ejpam-5505	168	7	̸=	̸=	PROPN
ejpam-5505	168	8	∅.	∅.	ADP
ejpam-5505	168	9	additionaly	additionaly	PROPN
ejpam-5505	168	10	,	,	PUNCT
ejpam-5505	168	11	let	let	VERB
ejpam-5505	168	12	z2	z2	PROPN
ejpam-5505	168	13	∈	∈	PROPN
ejpam-5505	168	14	f2	f2	PROPN
ejpam-5505	168	15	such	such	ADJ
ejpam-5505	168	16	taht	taht	ADJ
ejpam-5505	168	17	z2	z2	NOUN
ejpam-5505	168	18	=	=	SYM
ejpam-5505	169	1	j2z1	j2z1	PROPN
ejpam-5505	169	2	.	.	PUNCT
ejpam-5505	170	1	keep	keep	VERB
ejpam-5505	170	2	doing	do	VERB
ejpam-5505	170	3	this	this	PRON
ejpam-5505	170	4	gives	give	VERB
ejpam-5505	170	5	,	,	PUNCT
ejpam-5505	170	6	zm−2	zm−2	PROPN
ejpam-5505	170	7	=	=	PUNCT
ejpam-5505	170	8	jm−2jm−3	jm−2jm−3	PROPN
ejpam-5505	170	9	.	.	PUNCT
ejpam-5505	170	10	.	.	PUNCT
ejpam-5505	170	11	.	.	PUNCT
ejpam-5505	171	1	j1jmjm−1zm−2	j1jmjm−1zm−2	PROPN
ejpam-5505	171	2	.	.	PUNCT
ejpam-5505	172	1	then	then	ADV
ejpam-5505	172	2	,	,	PUNCT
ejpam-5505	172	3	jm−1zm−2	jm−1zm−2	PROPN
ejpam-5505	172	4	=	=	PUNCT
ejpam-5505	172	5	jm−1	jm−1	PROPN
ejpam-5505	172	6	(	(	PUNCT
ejpam-5505	172	7	jm−2jm−3	jm−2jm−3	PROPN
ejpam-5505	172	8	.	.	PUNCT
ejpam-5505	172	9	.	.	PUNCT
ejpam-5505	172	10	.	.	PUNCT
ejpam-5505	173	1	j1jm	j1jm	PUNCT
ejpam-5505	173	2	)	)	PUNCT
ejpam-5505	173	3	(	(	PUNCT
ejpam-5505	173	4	jm−1zm−2	jm−1zm−2	NUM
ejpam-5505	173	5	)	)	PUNCT
ejpam-5505	173	6	,	,	PUNCT
ejpam-5505	173	7	and	and	CCONJ
ejpam-5505	173	8	jm−1zm−2	jm−1zm−2	NUM
ejpam-5505	173	9	∈	∈	NOUN
ejpam-5505	173	10	fix	fix	NOUN
ejpam-5505	173	11	(	(	PUNCT
ejpam-5505	173	12	jm−1jm−2jm−3	jm−1jm−2jm−3	PROPN
ejpam-5505	173	13	.	.	PUNCT
ejpam-5505	173	14	.	.	PUNCT
ejpam-5505	173	15	.	.	PUNCT
ejpam-5505	174	1	j1jm	j1jm	PUNCT
ejpam-5505	174	2	)	)	PUNCT
ejpam-5505	174	3	,	,	PUNCT
ejpam-5505	174	4	which	which	PRON
ejpam-5505	174	5	is	be	AUX
ejpam-5505	174	6	equivalent	equivalent	ADJ
ejpam-5505	174	7	to	to	ADP
ejpam-5505	174	8	jm−1jm−2	jm−1jm−2	PROPN
ejpam-5505	174	9	∈	∈	PROPN
ejpam-5505	174	10	fm−1	fm−1	PROPN
ejpam-5505	174	11	̸=	̸=	PROPN
ejpam-5505	174	12	∅.	∅.	ADP
ejpam-5505	174	13	moreover	moreover	ADV
ejpam-5505	174	14	,	,	PUNCT
ejpam-5505	174	15	let	let	VERB
ejpam-5505	174	16	zm−1	zm−1	PROPN
ejpam-5505	174	17	∈	∈	PROPN
ejpam-5505	174	18	fm−1	fm−1	PROPN
ejpam-5505	174	19	such	such	ADJ
ejpam-5505	174	20	that	that	DET
ejpam-5505	174	21	zm−1	zm−1	PROPN
ejpam-5505	174	22	=	=	PUNCT
ejpam-5505	174	23	jm−1zm−2	jm−1zm−2	SYM
ejpam-5505	174	24	.	.	PUNCT
ejpam-5505	175	1	it	it	PRON
ejpam-5505	175	2	follows	follow	VERB
ejpam-5505	175	3	that	that	SCONJ
ejpam-5505	175	4	zm−1	zm−1	PROPN
ejpam-5505	175	5	=	=	PUNCT
ejpam-5505	175	6	jm−1jm−2jm−3	jm−1jm−2jm−3	PROPN
ejpam-5505	175	7	.	.	PUNCT
ejpam-5505	175	8	.	.	PUNCT
ejpam-5505	175	9	.	.	PUNCT
ejpam-5505	176	1	j1jmzm−1	j1jmzm−1	NOUN
ejpam-5505	176	2	,	,	PUNCT
ejpam-5505	176	3	s.th.alwadani	s.th.alwadani	X
ejpam-5505	176	4	/	/	SYM
ejpam-5505	176	5	eur	eur	PROPN
ejpam-5505	176	6	.	.	PUNCT
ejpam-5505	177	1	j.	j.	PROPN
ejpam-5505	177	2	pure	pure	PROPN
ejpam-5505	177	3	appl	appl	PROPN
ejpam-5505	177	4	.	.	PROPN
ejpam-5505	177	5	math	math	PROPN
ejpam-5505	177	6	,	,	PUNCT
ejpam-5505	177	7	17	17	NUM
ejpam-5505	177	8	(	(	PUNCT
ejpam-5505	177	9	4	4	NUM
ejpam-5505	177	10	)	)	PUNCT
ejpam-5505	177	11	(	(	PUNCT
ejpam-5505	177	12	2024	2024	NUM
ejpam-5505	177	13	)	)	PUNCT
ejpam-5505	177	14	,	,	PUNCT
ejpam-5505	177	15	3642	3642	NUM
ejpam-5505	177	16	-	-	SYM
ejpam-5505	177	17	3659	3659	NUM
ejpam-5505	177	18	3649	3649	NUM
ejpam-5505	177	19	and	and	CCONJ
ejpam-5505	177	20	jmzm−1	jmzm−1	PROPN
ejpam-5505	177	21	=	=	SYM
ejpam-5505	177	22	jm	jm	PROPN
ejpam-5505	177	23	(	(	PUNCT
ejpam-5505	177	24	jm−1jm−2jm−3	jm−1jm−2jm−3	PROPN
ejpam-5505	177	25	.	.	PUNCT
ejpam-5505	177	26	.	.	PUNCT
ejpam-5505	177	27	.	.	PUNCT
ejpam-5505	178	1	j1	j1	PROPN
ejpam-5505	178	2	)	)	PUNCT
ejpam-5505	179	1	jmzm−1	jmzm−1	PROPN
ejpam-5505	179	2	.	.	PUNCT
ejpam-5505	180	1	therefore	therefore	ADV
ejpam-5505	180	2	,	,	PUNCT
ejpam-5505	180	3	jmzm−1	jmzm−1	PROPN
ejpam-5505	180	4	∈	∈	PROPN
ejpam-5505	180	5	fix	fix	NOUN
ejpam-5505	180	6	(	(	PUNCT
ejpam-5505	180	7	jmjm−1jm−2jm−3	jmjm−1jm−2jm−3	PROPN
ejpam-5505	180	8	.	.	PUNCT
ejpam-5505	180	9	.	.	PUNCT
ejpam-5505	180	10	.	.	PUNCT
ejpam-5505	181	1	j1	j1	PROPN
ejpam-5505	181	2	)	)	PUNCT
ejpam-5505	181	3	.	.	PUNCT
ejpam-5505	182	1	this	this	PRON
ejpam-5505	182	2	is	be	AUX
ejpam-5505	182	3	equivalent	equivalent	ADJ
ejpam-5505	182	4	to	to	ADP
ejpam-5505	182	5	jmzm−1	jmzm−1	PROPN
ejpam-5505	182	6	∈	∈	PROPN
ejpam-5505	182	7	fix	fix	NOUN
ejpam-5505	182	8	fm	fm	NOUN
ejpam-5505	182	9	̸=	̸=	PROPN
ejpam-5505	182	10	∅.	∅.	ADP
ejpam-5505	182	11	all	all	DET
ejpam-5505	182	12	these	these	PRON
ejpam-5505	182	13	together	together	ADV
ejpam-5505	182	14	give	give	VERB
ejpam-5505	182	15	(	(	PUNCT
ejpam-5505	182	16	z1	z1	PROPN
ejpam-5505	182	17	,	,	PUNCT
ejpam-5505	182	18	z2	z2	PROPN
ejpam-5505	182	19	,	,	PUNCT
ejpam-5505	182	20	.	.	PUNCT
ejpam-5505	182	21	.	.	PUNCT
ejpam-5505	183	1	.	.	PUNCT
ejpam-5505	184	1	,	,	PUNCT
ejpam-5505	184	2	zm−1	zm−1	PROPN
ejpam-5505	184	3	,	,	PUNCT
ejpam-5505	184	4	zm	zm	PROPN
ejpam-5505	184	5	)	)	PUNCT
ejpam-5505	184	6	∈	∈	PROPN
ejpam-5505	185	1	x	x	PUNCT
ejpam-5505	185	2	satisfying	satisfy	VERB
ejpam-5505	185	3	that	that	SCONJ
ejpam-5505	185	4	(	(	PUNCT
ejpam-5505	185	5	z1	z1	PROPN
ejpam-5505	185	6	,	,	PUNCT
ejpam-5505	185	7	z2	z2	PROPN
ejpam-5505	185	8	,	,	PUNCT
ejpam-5505	185	9	.	.	PUNCT
ejpam-5505	185	10	.	.	PUNCT
ejpam-5505	185	11	.	.	PUNCT
ejpam-5505	186	1	,	,	PUNCT
ejpam-5505	186	2	zm−1	zm−1	PROPN
ejpam-5505	186	3	,	,	PUNCT
ejpam-5505	186	4	zm	zm	PROPN
ejpam-5505	186	5	)	)	PUNCT
ejpam-5505	187	1	=	=	PRON
ejpam-5505	187	2	(	(	PUNCT
ejpam-5505	187	3	j1zm	j1zm	PUNCT
ejpam-5505	187	4	,	,	PUNCT
ejpam-5505	187	5	j2z1	j2z1	ADP
ejpam-5505	187	6	,	,	PUNCT
ejpam-5505	187	7	.	.	PUNCT
ejpam-5505	187	8	.	.	PUNCT
ejpam-5505	188	1	.	.	PUNCT
ejpam-5505	189	1	,	,	PUNCT
ejpam-5505	189	2	jm−1zm−2	jm−1zm−2	X
ejpam-5505	189	3	,	,	PUNCT
ejpam-5505	189	4	jmzm−1	jmzm−1	PROPN
ejpam-5505	189	5	)	)	PUNCT
ejpam-5505	189	6	.	.	PUNCT
ejpam-5505	190	1	■	■	PUNCT
ejpam-5505	190	2	lemma	lemma	PROPN
ejpam-5505	190	3	2	2	X
ejpam-5505	190	4	.	.	PUNCT
ejpam-5505	191	1	let	let	VERB
ejpam-5505	191	2	z	z	NOUN
ejpam-5505	191	3	∈	∈	PROPN
ejpam-5505	191	4	x	x	X
ejpam-5505	191	5	is	be	AUX
ejpam-5505	191	6	a	a	DET
ejpam-5505	191	7	cycle	cycle	NOUN
ejpam-5505	191	8	.	.	PUNCT
ejpam-5505	192	1	then	then	ADV
ejpam-5505	192	2	z	z	X
ejpam-5505	192	3	=	=	SYM
ejpam-5505	192	4	ja	ja	PROPN
ejpam-5505	192	5	(	(	PUNCT
ejpam-5505	192	6	rz	rz	PROPN
ejpam-5505	192	7	)	)	PUNCT
ejpam-5505	192	8	.	.	PUNCT
ejpam-5505	193	1	(	(	PUNCT
ejpam-5505	193	2	18	18	NUM
ejpam-5505	193	3	)	)	PUNCT
ejpam-5505	193	4	moreover	moreover	ADV
ejpam-5505	193	5	,	,	PUNCT
ejpam-5505	193	6	solving	solve	VERB
ejpam-5505	193	7	(	(	PUNCT
ejpam-5505	193	8	18	18	NUM
ejpam-5505	193	9	)	)	PUNCT
ejpam-5505	193	10	is	be	AUX
ejpam-5505	193	11	equivalent	equivalent	ADJ
ejpam-5505	193	12	to	to	PART
ejpam-5505	193	13	solve	solve	VERB
ejpam-5505	193	14	0	0	NUM
ejpam-5505	193	15	∈	∈	PROPN
ejpam-5505	193	16	a(z	a(z	PROPN
ejpam-5505	193	17	)	)	PUNCT
ejpam-5505	194	1	+	+	CCONJ
ejpam-5505	194	2	(	(	PUNCT
ejpam-5505	194	3	i	i	NOUN
ejpam-5505	194	4	d	d	NOUN
ejpam-5505	195	1	−	−	PROPN
ejpam-5505	196	1	r	r	NOUN
ejpam-5505	196	2	)	)	PUNCT
ejpam-5505	196	3	(	(	PUNCT
ejpam-5505	196	4	z	z	NOUN
ejpam-5505	196	5	)	)	PUNCT
ejpam-5505	196	6	.	.	PUNCT
ejpam-5505	197	1	(	(	PUNCT
ejpam-5505	197	2	19	19	NUM
ejpam-5505	197	3	)	)	PUNCT
ejpam-5505	197	4	proof	proof	NOUN
ejpam-5505	197	5	.	.	PUNCT
ejpam-5505	198	1	given	give	VERB
ejpam-5505	198	2	that	that	DET
ejpam-5505	198	3	z	z	NOUN
ejpam-5505	198	4	=	=	SYM
ejpam-5505	198	5	(	(	PUNCT
ejpam-5505	198	6	z1	z1	PROPN
ejpam-5505	198	7	,	,	PUNCT
ejpam-5505	198	8	z2	z2	PROPN
ejpam-5505	198	9	,	,	PUNCT
ejpam-5505	198	10	.	.	PUNCT
ejpam-5505	198	11	.	.	PUNCT
ejpam-5505	198	12	.	.	PUNCT
ejpam-5505	199	1	,	,	PUNCT
ejpam-5505	199	2	zm	zm	PROPN
ejpam-5505	199	3	)	)	PUNCT
ejpam-5505	199	4	∈	∈	PROPN
ejpam-5505	199	5	x	x	X
ejpam-5505	199	6	is	be	AUX
ejpam-5505	199	7	a	a	DET
ejpam-5505	199	8	cycle	cycle	NOUN
ejpam-5505	199	9	.	.	PUNCT
ejpam-5505	200	1	then	then	ADV
ejpam-5505	200	2	definition	definition	NOUN
ejpam-5505	200	3	1	1	NUM
ejpam-5505	200	4	gives	give	VERB
ejpam-5505	200	5	that	that	DET
ejpam-5505	200	6	z1	z1	NOUN
ejpam-5505	200	7	=	=	SYM
ejpam-5505	200	8	j1zm	j1zm	PROPN
ejpam-5505	200	9	,	,	PUNCT
ejpam-5505	200	10	z2	z2	PROPN
ejpam-5505	200	11	=	=	SYM
ejpam-5505	200	12	j2z1	j2z1	PROPN
ejpam-5505	200	13	,	,	PUNCT
ejpam-5505	200	14	z3	z3	PROPN
ejpam-5505	200	15	=	=	SYM
ejpam-5505	200	16	j3z2	j3z2	NOUN
ejpam-5505	200	17	,	,	PUNCT
ejpam-5505	200	18	·	·	PUNCT
ejpam-5505	200	19	·	·	PUNCT
ejpam-5505	200	20	·	·	PUNCT
ejpam-5505	200	21	,	,	PUNCT
ejpam-5505	200	22	zm−1	zm−1	PROPN
ejpam-5505	200	23	=	=	PUNCT
ejpam-5505	200	24	jm−1zm−2	jm−1zm−2	PROPN
ejpam-5505	200	25	,	,	PUNCT
ejpam-5505	200	26	and	and	CCONJ
ejpam-5505	200	27	zm	zm	PROPN
ejpam-5505	200	28	=	=	SYM
ejpam-5505	200	29	jmzm−1	jmzm−1	PROPN
ejpam-5505	200	30	.	.	PUNCT
ejpam-5505	201	1	hence	hence	ADV
ejpam-5505	201	2	,	,	PUNCT
ejpam-5505	201	3	z	z	NOUN
ejpam-5505	201	4	=	=	SYM
ejpam-5505	201	5	(	(	PUNCT
ejpam-5505	201	6	z1	z1	PROPN
ejpam-5505	201	7	,	,	PUNCT
ejpam-5505	201	8	z2	z2	PROPN
ejpam-5505	201	9	,	,	PUNCT
ejpam-5505	201	10	.	.	PUNCT
ejpam-5505	201	11	.	.	PUNCT
ejpam-5505	201	12	.	.	PUNCT
ejpam-5505	202	1	,	,	PUNCT
ejpam-5505	202	2	zm−1	zm−1	PROPN
ejpam-5505	202	3	,	,	PUNCT
ejpam-5505	202	4	zm	zm	PROPN
ejpam-5505	202	5	)	)	PUNCT
ejpam-5505	203	1	=	=	PRON
ejpam-5505	203	2	(	(	PUNCT
ejpam-5505	203	3	j1zm	j1zm	PUNCT
ejpam-5505	203	4	,	,	PUNCT
ejpam-5505	203	5	j2z1	j2z1	ADP
ejpam-5505	203	6	,	,	PUNCT
ejpam-5505	203	7	.	.	PUNCT
ejpam-5505	203	8	.	.	PUNCT
ejpam-5505	204	1	.	.	PUNCT
ejpam-5505	205	1	,	,	PUNCT
ejpam-5505	205	2	jm−1zm−2	jm−1zm−2	X
ejpam-5505	205	3	,	,	PUNCT
ejpam-5505	205	4	jmzm−1	jmzm−1	PROPN
ejpam-5505	205	5	)	)	PUNCT
ejpam-5505	206	1	=	=	PRON
ejpam-5505	206	2	(	(	PUNCT
ejpam-5505	206	3	j1	j1	PROPN
ejpam-5505	206	4	,	,	PUNCT
ejpam-5505	206	5	j2	j2	PROPN
ejpam-5505	206	6	,	,	PUNCT
ejpam-5505	206	7	.	.	PUNCT
ejpam-5505	206	8	.	.	PUNCT
ejpam-5505	206	9	.	.	PUNCT
ejpam-5505	207	1	,	,	PUNCT
ejpam-5505	207	2	jm−1	jm−1	PROPN
ejpam-5505	207	3	,	,	PUNCT
ejpam-5505	207	4	jm	jm	PROPN
ejpam-5505	207	5	)	)	PUNCT
ejpam-5505	207	6	(	(	PUNCT
ejpam-5505	207	7	zm	zm	PROPN
ejpam-5505	207	8	,	,	PUNCT
ejpam-5505	207	9	z1	z1	PROPN
ejpam-5505	207	10	,	,	PUNCT
ejpam-5505	207	11	.	.	PUNCT
ejpam-5505	207	12	.	.	PUNCT
ejpam-5505	208	1	.	.	PUNCT
ejpam-5505	209	1	,	,	PUNCT
ejpam-5505	209	2	zm−2	zm−2	PROPN
ejpam-5505	209	3	,	,	PUNCT
ejpam-5505	209	4	zm−1	zm−1	PROPN
ejpam-5505	209	5	)	)	PUNCT
ejpam-5505	210	1	=	=	PUNCT
ejpam-5505	210	2	ja	ja	INTJ
ejpam-5505	210	3	(	(	PUNCT
ejpam-5505	210	4	r	r	NOUN
ejpam-5505	210	5	(	(	PUNCT
ejpam-5505	210	6	z1	z1	PROPN
ejpam-5505	210	7	,	,	PUNCT
ejpam-5505	210	8	z2	z2	PROPN
ejpam-5505	210	9	,	,	PUNCT
ejpam-5505	210	10	.	.	PUNCT
ejpam-5505	210	11	.	.	PUNCT
ejpam-5505	210	12	.	.	PUNCT
ejpam-5505	211	1	,	,	PUNCT
ejpam-5505	211	2	zm−1	zm−1	PROPN
ejpam-5505	211	3	,	,	PUNCT
ejpam-5505	211	4	zm	zm	PROPN
ejpam-5505	211	5	)	)	PUNCT
ejpam-5505	211	6	)	)	PUNCT
ejpam-5505	212	1	=	=	SYM
ejpam-5505	212	2	ja	ja	PROPN
ejpam-5505	212	3	(	(	PUNCT
ejpam-5505	212	4	rz	rz	PROPN
ejpam-5505	212	5	)	)	PUNCT
ejpam-5505	212	6	.	.	PUNCT
ejpam-5505	213	1	note	note	VERB
ejpam-5505	213	2	that	that	SCONJ
ejpam-5505	213	3	z	z	NOUN
ejpam-5505	213	4	=	=	SYM
ejpam-5505	213	5	ja(rz	ja(rz	PROPN
ejpam-5505	213	6	)	)	PUNCT
ejpam-5505	213	7	⇔	⇔	PROPN
ejpam-5505	213	8	z	z	PROPN
ejpam-5505	214	1	=	=	PUNCT
ejpam-5505	215	1	(	(	PUNCT
ejpam-5505	215	2	i	i	NOUN
ejpam-5505	215	3	d	d	PROPN
ejpam-5505	215	4	+	+	CCONJ
ejpam-5505	215	5	a	a	X
ejpam-5505	215	6	)	)	PUNCT
ejpam-5505	215	7	−1	−1	NOUN
ejpam-5505	215	8	(	(	PUNCT
ejpam-5505	215	9	rz	rz	NOUN
ejpam-5505	215	10	)	)	PUNCT
ejpam-5505	215	11	by	by	ADP
ejpam-5505	215	12	(	(	PUNCT
ejpam-5505	215	13	3	3	NUM
ejpam-5505	215	14	)	)	PUNCT
ejpam-5505	215	15	.	.	PUNCT
ejpam-5505	216	1	therefore	therefore	ADV
ejpam-5505	216	2	,	,	PUNCT
ejpam-5505	216	3	we	we	PRON
ejpam-5505	216	4	obtain	obtain	VERB
ejpam-5505	216	5	rz	rz	NOUN
ejpam-5505	216	6	∈	∈	PROPN
ejpam-5505	216	7	z	z	PROPN
ejpam-5505	216	8	+	+	CCONJ
ejpam-5505	216	9	a(z	a(z	PROPN
ejpam-5505	216	10	)	)	PUNCT
ejpam-5505	216	11	⇔	⇔	NOUN
ejpam-5505	216	12	0	0	NUM
ejpam-5505	216	13	∈	∈	PROPN
ejpam-5505	216	14	a(z	a(z	PROPN
ejpam-5505	216	15	)	)	PUNCT
ejpam-5505	217	1	+	+	CCONJ
ejpam-5505	217	2	(	(	PUNCT
ejpam-5505	217	3	i	i	NOUN
ejpam-5505	217	4	d	d	NOUN
ejpam-5505	218	1	−	−	PROPN
ejpam-5505	219	1	r	r	NOUN
ejpam-5505	219	2	)	)	PUNCT
ejpam-5505	219	3	(	(	PUNCT
ejpam-5505	219	4	z	z	NOUN
ejpam-5505	219	5	)	)	PUNCT
ejpam-5505	219	6	.	.	PUNCT
ejpam-5505	220	1	■	■	PUNCT
ejpam-5505	220	2	define	define	VERB
ejpam-5505	220	3	the	the	DET
ejpam-5505	220	4	set	set	NOUN
ejpam-5505	220	5	of	of	ADP
ejpam-5505	220	6	all	all	DET
ejpam-5505	220	7	cycles	cycle	NOUN
ejpam-5505	220	8	by	by	ADP
ejpam-5505	220	9	z	z	NOUN
ejpam-5505	220	10	:	:	PUNCT
ejpam-5505	220	11	=	=	PUNCT
ejpam-5505	220	12	fix(jar	fix(jar	ADJ
ejpam-5505	220	13	)	)	PUNCT
ejpam-5505	220	14	.	.	PUNCT
ejpam-5505	221	1	(	(	PUNCT
ejpam-5505	221	2	20	20	NUM
ejpam-5505	221	3	)	)	PUNCT
ejpam-5505	221	4	define	define	VERB
ejpam-5505	221	5	fi	fi	NOUN
ejpam-5505	221	6	:	:	PUNCT
ejpam-5505	221	7	=	=	SYM
ejpam-5505	221	8	{	{	PUNCT
ejpam-5505	221	9	z	z	NOUN
ejpam-5505	221	10	∈	∈	PROPN
ejpam-5505	222	1	x	x	X
ejpam-5505	222	2	|	|	ADV
ejpam-5505	222	3	z	z	NOUN
ejpam-5505	222	4	=	=	SYM
ejpam-5505	222	5	ji	ji	PROPN
ejpam-5505	222	6	.	.	PUNCT
ejpam-5505	222	7	.	.	PUNCT
ejpam-5505	222	8	.	.	PUNCT
ejpam-5505	223	1	j1jm	j1jm	PROPN
ejpam-5505	223	2	.	.	PUNCT
ejpam-5505	223	3	.	.	PUNCT
ejpam-5505	223	4	.	.	PUNCT
ejpam-5505	224	1	ji+1z	ji+1z	PROPN
ejpam-5505	224	2	}	}	PUNCT
ejpam-5505	224	3	.	.	PUNCT
ejpam-5505	225	1	(	(	PUNCT
ejpam-5505	225	2	21	21	NUM
ejpam-5505	225	3	)	)	PUNCT
ejpam-5505	225	4	moreover	moreover	ADV
ejpam-5505	225	5	,	,	PUNCT
ejpam-5505	225	6	qi	qi	PROPN
ejpam-5505	225	7	:	:	PUNCT
ejpam-5505	225	8	x	x	X
ejpam-5505	225	9	→	→	PUNCT
ejpam-5505	225	10	x	x	SYM
ejpam-5505	225	11	:	:	PUNCT
ejpam-5505	225	12	z	z	NOUN
ejpam-5505	225	13	7→	7→	NUM
ejpam-5505	225	14	zi	zi	NOUN
ejpam-5505	225	15	.	.	PUNCT
ejpam-5505	226	1	(	(	PUNCT
ejpam-5505	226	2	22	22	NUM
ejpam-5505	226	3	)	)	PUNCT
ejpam-5505	226	4	the	the	DET
ejpam-5505	226	5	relationship	relationship	NOUN
ejpam-5505	226	6	between	between	ADP
ejpam-5505	226	7	the	the	DET
ejpam-5505	226	8	fixed	fix	VERB
ejpam-5505	226	9	point	point	NOUN
ejpam-5505	226	10	set	set	NOUN
ejpam-5505	226	11	of	of	ADP
ejpam-5505	226	12	composition	composition	NOUN
ejpam-5505	226	13	of	of	ADP
ejpam-5505	226	14	m	m	PROPN
ejpam-5505	226	15	resolvants	resolvant	NOUN
ejpam-5505	226	16	fi	fi	NOUN
ejpam-5505	226	17	’s	’s	NOUN
ejpam-5505	226	18	and	and	CCONJ
ejpam-5505	226	19	the	the	DET
ejpam-5505	226	20	set	set	NOUN
ejpam-5505	226	21	of	of	ADP
ejpam-5505	226	22	all	all	DET
ejpam-5505	226	23	cycles	cycle	NOUN
ejpam-5505	226	24	z	z	NOUN
ejpam-5505	226	25	are	be	AUX
ejpam-5505	226	26	given	give	VERB
ejpam-5505	226	27	in	in	ADP
ejpam-5505	226	28	the	the	DET
ejpam-5505	226	29	following	follow	VERB
ejpam-5505	226	30	theorem	theorem	VERB
ejpam-5505	226	31	.	.	PUNCT
ejpam-5505	227	1	s.th.alwadani	s.th.alwadani	ADJ
ejpam-5505	227	2	/	/	SYM
ejpam-5505	227	3	eur	eur	PROPN
ejpam-5505	227	4	.	.	PUNCT
ejpam-5505	228	1	j.	j.	PROPN
ejpam-5505	228	2	pure	pure	PROPN
ejpam-5505	228	3	appl	appl	PROPN
ejpam-5505	228	4	.	.	PROPN
ejpam-5505	228	5	math	math	PROPN
ejpam-5505	228	6	,	,	PUNCT
ejpam-5505	228	7	17	17	NUM
ejpam-5505	228	8	(	(	PUNCT
ejpam-5505	228	9	4	4	NUM
ejpam-5505	228	10	)	)	PUNCT
ejpam-5505	228	11	(	(	PUNCT
ejpam-5505	228	12	2024	2024	NUM
ejpam-5505	228	13	)	)	PUNCT
ejpam-5505	228	14	,	,	PUNCT
ejpam-5505	228	15	3642	3642	NUM
ejpam-5505	228	16	-	-	SYM
ejpam-5505	228	17	3659	3659	NUM
ejpam-5505	228	18	3650	3650	NUM
ejpam-5505	228	19	theorem	theorem	NOUN
ejpam-5505	228	20	2	2	NUM
ejpam-5505	228	21	.	.	PUNCT
ejpam-5505	228	22	for	for	ADP
ejpam-5505	228	23	every	every	DET
ejpam-5505	228	24	1	1	NUM
ejpam-5505	228	25	≤	≤	NUM
ejpam-5505	228	26	i	i	PRON
ejpam-5505	228	27	,	,	PUNCT
ejpam-5505	228	28	j	j	PROPN
ejpam-5505	228	29	≤	≤	PROPN
ejpam-5505	228	30	m	m	PROPN
ejpam-5505	228	31	,	,	PUNCT
ejpam-5505	228	32	the	the	DET
ejpam-5505	228	33	following	follow	VERB
ejpam-5505	228	34	hold	hold	NOUN
ejpam-5505	228	35	:	:	PUNCT
ejpam-5505	228	36	(	(	PUNCT
ejpam-5505	228	37	i	i	NOUN
ejpam-5505	228	38	)	)	PUNCT
ejpam-5505	228	39	fi	fi	NOUN
ejpam-5505	228	40	are	be	AUX
ejpam-5505	228	41	closed	close	VERB
ejpam-5505	228	42	and	and	CCONJ
ejpam-5505	228	43	convex	convex	NOUN
ejpam-5505	228	44	.	.	PUNCT
ejpam-5505	229	1	moreover	moreover	ADV
ejpam-5505	229	2	,	,	PUNCT
ejpam-5505	229	3	fm	fm	PROPN
ejpam-5505	229	4	=	=	PUNCT
ejpam-5505	229	5	(	(	PUNCT
ejpam-5505	229	6	jmjm−1	jmjm−1	NOUN
ejpam-5505	229	7	.	.	PUNCT
ejpam-5505	229	8	.	.	PUNCT
ejpam-5505	229	9	.	.	PUNCT
ejpam-5505	230	1	j3j2	j3j2	X
ejpam-5505	230	2	)	)	PUNCT
ejpam-5505	230	3	(	(	PUNCT
ejpam-5505	230	4	f1	f1	NOUN
ejpam-5505	230	5	)	)	PUNCT
ejpam-5505	230	6	=	=	PUNCT
ejpam-5505	231	1	(	(	PUNCT
ejpam-5505	231	2	jmjm−1	jmjm−1	NOUN
ejpam-5505	231	3	.	.	PUNCT
ejpam-5505	231	4	.	.	PUNCT
ejpam-5505	231	5	.	.	PUNCT
ejpam-5505	232	1	j3	j3	PROPN
ejpam-5505	232	2	)	)	PUNCT
ejpam-5505	232	3	(	(	PUNCT
ejpam-5505	232	4	f2	f2	ADV
ejpam-5505	232	5	)	)	PUNCT
ejpam-5505	232	6	=	=	SYM
ejpam-5505	232	7	·	·	PUNCT
ejpam-5505	232	8	·	·	PUNCT
ejpam-5505	232	9	·	·	PUNCT
ejpam-5505	233	1	=	=	SYM
ejpam-5505	233	2	jmjm−1	jmjm−1	NOUN
ejpam-5505	233	3	(	(	PUNCT
ejpam-5505	233	4	fm−2	fm−2	PROPN
ejpam-5505	233	5	)	)	PUNCT
ejpam-5505	233	6	=	=	SYM
ejpam-5505	233	7	jm	jm	PROPN
ejpam-5505	233	8	(	(	PUNCT
ejpam-5505	233	9	fm−1	fm−1	PROPN
ejpam-5505	233	10	)	)	PUNCT
ejpam-5505	233	11	.	.	PUNCT
ejpam-5505	234	1	(	(	PUNCT
ejpam-5505	234	2	23	23	NUM
ejpam-5505	234	3	)	)	PUNCT
ejpam-5505	234	4	fm−1	fm−1	NOUN
ejpam-5505	234	5	=	=	SYM
ejpam-5505	234	6	(	(	PUNCT
ejpam-5505	234	7	jm−1	jm−1	PROPN
ejpam-5505	234	8	.	.	PUNCT
ejpam-5505	234	9	.	.	PUNCT
ejpam-5505	234	10	.	.	PUNCT
ejpam-5505	235	1	j3j2j1	j3j2j1	PROPN
ejpam-5505	235	2	)	)	PUNCT
ejpam-5505	235	3	(	(	PUNCT
ejpam-5505	235	4	fm	fm	PROPN
ejpam-5505	235	5	)	)	PUNCT
ejpam-5505	235	6	=	=	SYM
ejpam-5505	236	1	(	(	PUNCT
ejpam-5505	236	2	jm−1	jm−1	PROPN
ejpam-5505	236	3	.	.	PUNCT
ejpam-5505	236	4	.	.	PUNCT
ejpam-5505	236	5	.	.	PUNCT
ejpam-5505	237	1	j3j2	j3j2	X
ejpam-5505	237	2	)	)	PUNCT
ejpam-5505	237	3	(	(	PUNCT
ejpam-5505	237	4	f1	f1	NOUN
ejpam-5505	237	5	)	)	PUNCT
ejpam-5505	237	6	=	=	SYM
ejpam-5505	237	7	·	·	PUNCT
ejpam-5505	237	8	·	·	PUNCT
ejpam-5505	237	9	·	·	PUNCT
ejpam-5505	238	1	=	=	SYM
ejpam-5505	238	2	jm−1	jm−1	PROPN
ejpam-5505	238	3	(	(	PUNCT
ejpam-5505	238	4	fm−2	fm−2	PROPN
ejpam-5505	238	5	)	)	PUNCT
ejpam-5505	238	6	.	.	PUNCT
ejpam-5505	239	1	(	(	PUNCT
ejpam-5505	239	2	24	24	NUM
ejpam-5505	239	3	)	)	PUNCT
ejpam-5505	239	4	...	...	PUNCT
ejpam-5505	240	1	(	(	PUNCT
ejpam-5505	240	2	25	25	NUM
ejpam-5505	240	3	)	)	PUNCT
ejpam-5505	240	4	f2	f2	PROPN
ejpam-5505	240	5	=	=	SYM
ejpam-5505	240	6	(	(	PUNCT
ejpam-5505	240	7	j2j1jm	j2j1jm	PROPN
ejpam-5505	240	8	.	.	PUNCT
ejpam-5505	240	9	.	.	PUNCT
ejpam-5505	240	10	.	.	PUNCT
ejpam-5505	241	1	j4	j4	PROPN
ejpam-5505	241	2	)	)	PUNCT
ejpam-5505	241	3	(	(	PUNCT
ejpam-5505	241	4	f3	f3	PROPN
ejpam-5505	241	5	)	)	PUNCT
ejpam-5505	241	6	=	=	SYM
ejpam-5505	241	7	(	(	PUNCT
ejpam-5505	241	8	j2j1jm	j2j1jm	PROPN
ejpam-5505	241	9	.	.	PUNCT
ejpam-5505	241	10	.	.	PUNCT
ejpam-5505	241	11	.	.	PUNCT
ejpam-5505	242	1	j5	j5	PROPN
ejpam-5505	242	2	)	)	PUNCT
ejpam-5505	242	3	(	(	PUNCT
ejpam-5505	242	4	f4	f4	PROPN
ejpam-5505	242	5	)	)	PUNCT
ejpam-5505	242	6	=	=	SYM
ejpam-5505	242	7	·	·	PUNCT
ejpam-5505	242	8	·	·	PUNCT
ejpam-5505	242	9	·	·	PUNCT
ejpam-5505	243	1	=	=	SYM
ejpam-5505	243	2	j2j1	j2j1	PROPN
ejpam-5505	243	3	(	(	PUNCT
ejpam-5505	243	4	fm	fm	PROPN
ejpam-5505	243	5	)	)	PUNCT
ejpam-5505	244	1	=	=	SYM
ejpam-5505	244	2	j2	j2	PROPN
ejpam-5505	244	3	(	(	PUNCT
ejpam-5505	244	4	f1	f1	PROPN
ejpam-5505	244	5	)	)	PUNCT
ejpam-5505	244	6	.	.	PUNCT
ejpam-5505	245	1	(	(	PUNCT
ejpam-5505	245	2	26	26	NUM
ejpam-5505	245	3	)	)	PUNCT
ejpam-5505	245	4	f1	f1	NOUN
ejpam-5505	245	5	=	=	SYM
ejpam-5505	245	6	(	(	PUNCT
ejpam-5505	245	7	j1jm	j1jm	PROPN
ejpam-5505	245	8	.	.	PUNCT
ejpam-5505	245	9	.	.	PUNCT
ejpam-5505	245	10	.	.	PUNCT
ejpam-5505	246	1	j4j3	j4j3	PROPN
ejpam-5505	246	2	)	)	PUNCT
ejpam-5505	246	3	(	(	PUNCT
ejpam-5505	246	4	f2	f2	ADV
ejpam-5505	246	5	)	)	PUNCT
ejpam-5505	246	6	=	=	PUNCT
ejpam-5505	246	7	(	(	PUNCT
ejpam-5505	246	8	j1jm	j1jm	PROPN
ejpam-5505	246	9	.	.	PUNCT
ejpam-5505	246	10	.	.	PUNCT
ejpam-5505	246	11	.	.	PUNCT
ejpam-5505	247	1	j4	j4	PROPN
ejpam-5505	247	2	)	)	PUNCT
ejpam-5505	247	3	(	(	PUNCT
ejpam-5505	247	4	f3	f3	ADJ
ejpam-5505	247	5	)	)	PUNCT
ejpam-5505	247	6	=	=	SYM
ejpam-5505	247	7	·	·	PUNCT
ejpam-5505	247	8	·	·	PUNCT
ejpam-5505	247	9	·	·	PUNCT
ejpam-5505	248	1	=	=	PUNCT
ejpam-5505	248	2	(	(	PUNCT
ejpam-5505	248	3	j1jm	j1jm	PUNCT
ejpam-5505	248	4	)	)	PUNCT
ejpam-5505	248	5	(	(	PUNCT
ejpam-5505	248	6	fm−1	fm−1	NOUN
ejpam-5505	248	7	)	)	PUNCT
ejpam-5505	248	8	=	=	SYM
ejpam-5505	248	9	j1	j1	PROPN
ejpam-5505	248	10	(	(	PUNCT
ejpam-5505	248	11	fm	fm	PROPN
ejpam-5505	248	12	)	)	PUNCT
ejpam-5505	248	13	.	.	PUNCT
ejpam-5505	249	1	(	(	PUNCT
ejpam-5505	249	2	27	27	NUM
ejpam-5505	249	3	)	)	PUNCT
ejpam-5505	249	4	(	(	PUNCT
ejpam-5505	249	5	ii	ii	NOUN
ejpam-5505	249	6	)	)	PUNCT
ejpam-5505	249	7	∩m	∩m	PROPN
ejpam-5505	250	1	i=1	i=1	PROPN
ejpam-5505	250	2	fix	fix	VERB
ejpam-5505	250	3	ji	ji	PROPN
ejpam-5505	250	4	⊆	⊆	NUM
ejpam-5505	250	5	∩m	∩m	PROPN
ejpam-5505	250	6	i=1fi	i=1fi	NOUN
ejpam-5505	250	7	.	.	PUNCT
ejpam-5505	251	1	if	if	SCONJ
ejpam-5505	251	2	fi	fi	NOUN
ejpam-5505	251	3	=	=	NOUN
ejpam-5505	251	4	∅	∅	NOUN
ejpam-5505	251	5	,	,	PUNCT
ejpam-5505	251	6	then	then	ADV
ejpam-5505	251	7	∩m	∩m	PROPN
ejpam-5505	251	8	i=1	i=1	PROPN
ejpam-5505	252	1	fix	fix	VERB
ejpam-5505	252	2	ji	ji	NOUN
ejpam-5505	252	3	=	=	PROPN
ejpam-5505	252	4	∅.	∅.	X
ejpam-5505	252	5	(	(	PUNCT
ejpam-5505	252	6	iii	iii	NOUN
ejpam-5505	252	7	)	)	PUNCT
ejpam-5505	252	8	for	for	ADP
ejpam-5505	252	9	1	1	NUM
ejpam-5505	252	10	≤	≤	NUM
ejpam-5505	252	11	i	i	PRON
ejpam-5505	252	12	≤	≤	NOUN
ejpam-5505	252	13	m	m	VERB
ejpam-5505	252	14	−	−	PROPN
ejpam-5505	252	15	1	1	NUM
ejpam-5505	252	16	,	,	PUNCT
ejpam-5505	252	17	ji+1	ji+1	NOUN
ejpam-5505	252	18	(	(	PUNCT
ejpam-5505	252	19	fi	fi	NOUN
ejpam-5505	252	20	)	)	PUNCT
ejpam-5505	252	21	=	=	SYM
ejpam-5505	252	22	fi+1	fi+1	NOUN
ejpam-5505	252	23	and	and	CCONJ
ejpam-5505	252	24	j1	j1	PROPN
ejpam-5505	252	25	(	(	PUNCT
ejpam-5505	252	26	fm	fm	PROPN
ejpam-5505	252	27	)	)	PUNCT
ejpam-5505	253	1	=	=	SYM
ejpam-5505	253	2	f1	f1	NOUN
ejpam-5505	253	3	.	.	PUNCT
ejpam-5505	254	1	this	this	PRON
ejpam-5505	254	2	implies	imply	VERB
ejpam-5505	254	3	that	that	DET
ejpam-5505	254	4	jar	jar	NOUN
ejpam-5505	254	5	(	(	PUNCT
ejpam-5505	254	6	f1	f1	PROPN
ejpam-5505	254	7	×	×	NOUN
ejpam-5505	254	8	f2	f2	PROPN
ejpam-5505	254	9	×	×	NOUN
ejpam-5505	254	10	·	·	PUNCT
ejpam-5505	254	11	·	·	PUNCT
ejpam-5505	254	12	·	·	PUNCT
ejpam-5505	254	13	×	×	NOUN
ejpam-5505	254	14	fm	fm	NOUN
ejpam-5505	254	15	)	)	PUNCT
ejpam-5505	255	1	=	=	SYM
ejpam-5505	255	2	f1	f1	PROPN
ejpam-5505	255	3	×	×	NOUN
ejpam-5505	255	4	f2	f2	PROPN
ejpam-5505	255	5	×	×	NOUN
ejpam-5505	255	6	·	·	PUNCT
ejpam-5505	255	7	·	·	PUNCT
ejpam-5505	255	8	·	·	PUNCT
ejpam-5505	255	9	×	×	PROPN
ejpam-5505	255	10	fm	fm	PROPN
ejpam-5505	255	11	.	.	PUNCT
ejpam-5505	256	1	(	(	PUNCT
ejpam-5505	256	2	28	28	NUM
ejpam-5505	256	3	)	)	PUNCT
ejpam-5505	256	4	(	(	PUNCT
ejpam-5505	256	5	iv	iv	X
ejpam-5505	256	6	)	)	PUNCT
ejpam-5505	256	7	fi	fi	NOUN
ejpam-5505	256	8	̸=	̸=	PROPN
ejpam-5505	256	9	∅	∅	NOUN
ejpam-5505	256	10	if	if	SCONJ
ejpam-5505	256	11	and	and	CCONJ
ejpam-5505	256	12	only	only	ADV
ejpam-5505	256	13	if	if	SCONJ
ejpam-5505	256	14	fj	fj	PROPN
ejpam-5505	256	15	̸=	̸=	PROPN
ejpam-5505	256	16	∅	∅	NOUN
ejpam-5505	256	17	if	if	SCONJ
ejpam-5505	256	18	and	and	CCONJ
ejpam-5505	256	19	only	only	ADV
ejpam-5505	256	20	if	if	SCONJ
ejpam-5505	256	21	z	z	NOUN
ejpam-5505	256	22	=	=	SYM
ejpam-5505	256	23	∅.	∅.	X
ejpam-5505	256	24	(	(	PUNCT
ejpam-5505	256	25	v	v	NOUN
ejpam-5505	256	26	)	)	PUNCT
ejpam-5505	256	27	z	z	NOUN
ejpam-5505	256	28	is	be	AUX
ejpam-5505	256	29	closed	close	VERB
ejpam-5505	256	30	and	and	CCONJ
ejpam-5505	256	31	convex	convex	ADJ
ejpam-5505	256	32	,	,	PUNCT
ejpam-5505	256	33	and	and	CCONJ
ejpam-5505	256	34	z	z	NOUN
ejpam-5505	256	35	⊆	⊆	NUM
ejpam-5505	256	36	f1	f1	NOUN
ejpam-5505	256	37	×	×	NOUN
ejpam-5505	256	38	f2	f2	PROPN
ejpam-5505	256	39	×	×	NOUN
ejpam-5505	256	40	·	·	PUNCT
ejpam-5505	256	41	·	·	PUNCT
ejpam-5505	256	42	·	·	PUNCT
ejpam-5505	257	1	×	×	PROPN
ejpam-5505	257	2	fm	fm	PROPN
ejpam-5505	257	3	.	.	PROPN
ejpam-5505	257	4	(	(	PUNCT
ejpam-5505	257	5	vi	vi	X
ejpam-5505	257	6	)	)	PUNCT
ejpam-5505	257	7	the	the	DET
ejpam-5505	257	8	mapping	mapping	NOUN
ejpam-5505	257	9	qi|z	qi|z	VERB
ejpam-5505	257	10	:	:	PUNCT
ejpam-5505	257	11	z	z	X
ejpam-5505	257	12	→	→	SYM
ejpam-5505	257	13	fi	fi	NOUN
ejpam-5505	257	14	is	be	AUX
ejpam-5505	257	15	bijective	bijective	ADJ
ejpam-5505	257	16	and	and	CCONJ
ejpam-5505	257	17	qi	qi	PROPN
ejpam-5505	257	18	(	(	PUNCT
ejpam-5505	257	19	z	z	NOUN
ejpam-5505	257	20	)	)	PUNCT
ejpam-5505	257	21	=	=	PUNCT
ejpam-5505	258	1	fi	fi	NOUN
ejpam-5505	258	2	.	.	NOUN
ejpam-5505	258	3	proof	proof	NOUN
ejpam-5505	258	4	.	.	PUNCT
ejpam-5505	259	1	(	(	PUNCT
ejpam-5505	259	2	i	i	NOUN
ejpam-5505	259	3	):	):	PUNCT
ejpam-5505	259	4	since	since	SCONJ
ejpam-5505	259	5	each	each	DET
ejpam-5505	259	6	ji	ji	PROPN
ejpam-5505	259	7	is	be	AUX
ejpam-5505	259	8	firmly	firmly	ADV
ejpam-5505	259	9	nonexpansive	nonexpansive	ADJ
ejpam-5505	259	10	,	,	PUNCT
ejpam-5505	259	11	it	it	PRON
ejpam-5505	259	12	follows	follow	VERB
ejpam-5505	259	13	that	that	SCONJ
ejpam-5505	259	14	ji	ji	PROPN
ejpam-5505	259	15	is	be	AUX
ejpam-5505	259	16	nonexpansive	nonexpansive	ADJ
ejpam-5505	259	17	.	.	PUNCT
ejpam-5505	260	1	therefore	therefore	ADV
ejpam-5505	260	2	,	,	PUNCT
ejpam-5505	260	3	by	by	ADP
ejpam-5505	260	4	[	[	X
ejpam-5505	260	5	16	16	NUM
ejpam-5505	260	6	,	,	PUNCT
ejpam-5505	260	7	lemma	lemma	PROPN
ejpam-5505	260	8	2.1.12	2.1.12	NUM
ejpam-5505	260	9	(	(	PUNCT
ejpam-5505	260	10	ii	ii	NOUN
ejpam-5505	260	11	)	)	PUNCT
ejpam-5505	260	12	]	]	PUNCT
ejpam-5505	260	13	,	,	PUNCT
ejpam-5505	260	14	the	the	DET
ejpam-5505	260	15	composition	composition	NOUN
ejpam-5505	260	16	ji	ji	PROPN
ejpam-5505	260	17	.	.	PUNCT
ejpam-5505	260	18	.	.	PUNCT
ejpam-5505	260	19	.	.	PUNCT
ejpam-5505	261	1	j1jm	j1jm	PROPN
ejpam-5505	261	2	.	.	PUNCT
ejpam-5505	261	3	.	.	PUNCT
ejpam-5505	261	4	.	.	PUNCT
ejpam-5505	262	1	ji+1	ji+1	PROPN
ejpam-5505	262	2	is	be	AUX
ejpam-5505	262	3	also	also	ADV
ejpam-5505	262	4	nonexpansive	nonexpansive	ADJ
ejpam-5505	262	5	.	.	PUNCT
ejpam-5505	263	1	as	as	ADP
ejpam-5505	263	2	a	a	DET
ejpam-5505	263	3	result	result	NOUN
ejpam-5505	263	4	,	,	PUNCT
ejpam-5505	263	5	fi	fi	NOUN
ejpam-5505	263	6	is	be	AUX
ejpam-5505	263	7	closed	close	VERB
ejpam-5505	263	8	and	and	CCONJ
ejpam-5505	263	9	convex	convex	VERB
ejpam-5505	263	10	by	by	ADP
ejpam-5505	263	11	[	[	X
ejpam-5505	263	12	16	16	NUM
ejpam-5505	263	13	,	,	PUNCT
ejpam-5505	263	14	proposition	proposition	NOUN
ejpam-5505	263	15	2.1.11	2.1.11	NUM
ejpam-5505	263	16	]	]	PUNCT
ejpam-5505	263	17	.	.	PUNCT
ejpam-5505	264	1	let	let	VERB
ejpam-5505	264	2	x	x	SYM
ejpam-5505	264	3	∈	∈	PROPN
ejpam-5505	264	4	fm	fm	PROPN
ejpam-5505	264	5	⇔	⇔	PROPN
ejpam-5505	264	6	x	x	SYM
ejpam-5505	264	7	∈	∈	PROPN
ejpam-5505	264	8	fix	fix	NOUN
ejpam-5505	264	9	(	(	PUNCT
ejpam-5505	264	10	jmjm−1	jmjm−1	NOUN
ejpam-5505	264	11	.	.	PUNCT
ejpam-5505	264	12	.	.	PUNCT
ejpam-5505	264	13	.	.	PUNCT
ejpam-5505	265	1	j3j2j1	j3j2j1	PROPN
ejpam-5505	265	2	)	)	PUNCT
ejpam-5505	265	3	⇔	⇔	NOUN
ejpam-5505	265	4	x	x	PUNCT
ejpam-5505	265	5	=	=	SYM
ejpam-5505	265	6	jmjm−1	jmjm−1	PROPN
ejpam-5505	265	7	.	.	PUNCT
ejpam-5505	265	8	.	.	PUNCT
ejpam-5505	265	9	.	.	PUNCT
ejpam-5505	266	1	j3j2j1x	j3j2j1x	PROPN
ejpam-5505	266	2	.	.	PUNCT
ejpam-5505	267	1	then	then	ADV
ejpam-5505	267	2	,	,	PUNCT
ejpam-5505	267	3	j1x	j1x	PROPN
ejpam-5505	267	4	=	=	SYM
ejpam-5505	267	5	j1	j1	PROPN
ejpam-5505	267	6	(	(	PUNCT
ejpam-5505	267	7	jmjm−1	jmjm−1	PROPN
ejpam-5505	267	8	.	.	PUNCT
ejpam-5505	267	9	.	.	PUNCT
ejpam-5505	267	10	.	.	PUNCT
ejpam-5505	268	1	j3j2j1	j3j2j1	NOUN
ejpam-5505	268	2	)	)	PUNCT
ejpam-5505	268	3	x	x	PUNCT
ejpam-5505	269	1	=	=	PUNCT
ejpam-5505	269	2	(	(	PUNCT
ejpam-5505	269	3	j1jmjm−1	j1jmjm−1	PROPN
ejpam-5505	269	4	.	.	PUNCT
ejpam-5505	269	5	.	.	PUNCT
ejpam-5505	269	6	.	.	PUNCT
ejpam-5505	270	1	j3j2	j3j2	X
ejpam-5505	270	2	)	)	PUNCT
ejpam-5505	270	3	(	(	PUNCT
ejpam-5505	270	4	j1x	j1x	PROPN
ejpam-5505	270	5	)	)	PUNCT
ejpam-5505	270	6	.	.	PUNCT
ejpam-5505	271	1	therefore	therefore	ADV
ejpam-5505	271	2	,	,	PUNCT
ejpam-5505	271	3	j1x	j1x	PROPN
ejpam-5505	271	4	∈	∈	PROPN
ejpam-5505	271	5	fix	fix	NOUN
ejpam-5505	271	6	(	(	PUNCT
ejpam-5505	271	7	j1jmjm−1	j1jmjm−1	PROPN
ejpam-5505	271	8	.	.	PUNCT
ejpam-5505	271	9	.	.	PUNCT
ejpam-5505	271	10	.	.	PUNCT
ejpam-5505	272	1	j3j2	j3j2	X
ejpam-5505	272	2	)	)	PUNCT
ejpam-5505	272	3	⇔	⇔	PROPN
ejpam-5505	272	4	j1x	j1x	PROPN
ejpam-5505	272	5	∈	∈	PROPN
ejpam-5505	272	6	f1	f1	NOUN
ejpam-5505	272	7	.	.	PUNCT
ejpam-5505	273	1	it	it	PRON
ejpam-5505	273	2	follows	follow	VERB
ejpam-5505	273	3	that	that	SCONJ
ejpam-5505	273	4	j1	j1	PROPN
ejpam-5505	273	5	(	(	PUNCT
ejpam-5505	273	6	fm	fm	PROPN
ejpam-5505	273	7	)	)	PUNCT
ejpam-5505	273	8	⊆	⊆	NUM
ejpam-5505	273	9	f1	f1	NOUN
ejpam-5505	273	10	.	.	PUNCT
ejpam-5505	274	1	(	(	PUNCT
ejpam-5505	274	2	29	29	NUM
ejpam-5505	274	3	)	)	PUNCT
ejpam-5505	274	4	moreover	moreover	ADV
ejpam-5505	274	5	,	,	PUNCT
ejpam-5505	274	6	(	(	PUNCT
ejpam-5505	274	7	j2j1	j2j1	PROPN
ejpam-5505	274	8	)	)	PUNCT
ejpam-5505	274	9	(	(	PUNCT
ejpam-5505	274	10	fm	fm	PROPN
ejpam-5505	274	11	)	)	PUNCT
ejpam-5505	274	12	=	=	PRON
ejpam-5505	275	1	(	(	PUNCT
ejpam-5505	275	2	j2j1	j2j1	PROPN
ejpam-5505	275	3	)	)	PUNCT
ejpam-5505	275	4	(	(	PUNCT
ejpam-5505	275	5	fix	fix	NOUN
ejpam-5505	275	6	(	(	PUNCT
ejpam-5505	275	7	jmjm−1	jmjm−1	PROPN
ejpam-5505	275	8	.	.	PUNCT
ejpam-5505	275	9	.	.	PUNCT
ejpam-5505	275	10	.	.	PUNCT
ejpam-5505	276	1	j2j1	j2j1	PROPN
ejpam-5505	276	2	)	)	PUNCT
ejpam-5505	276	3	)	)	PUNCT
ejpam-5505	277	1	⊆	⊆	NUM
ejpam-5505	277	2	j2	j2	NOUN
ejpam-5505	277	3	(	(	PUNCT
ejpam-5505	277	4	fix	fix	NOUN
ejpam-5505	277	5	(	(	PUNCT
ejpam-5505	277	6	j1jmjm−1	j1jmjm−1	PROPN
ejpam-5505	277	7	.	.	PUNCT
ejpam-5505	277	8	.	.	PUNCT
ejpam-5505	277	9	.	.	PUNCT
ejpam-5505	278	1	j3j2	j3j2	X
ejpam-5505	278	2	)	)	PUNCT
ejpam-5505	278	3	)	)	PUNCT
ejpam-5505	278	4	(	(	PUNCT
ejpam-5505	278	5	30	30	NUM
ejpam-5505	278	6	)	)	PUNCT
ejpam-5505	278	7	⊆	⊆	NUM
ejpam-5505	278	8	fix	fix	NOUN
ejpam-5505	278	9	(	(	PUNCT
ejpam-5505	278	10	j2j1jmjm−1	j2j1jmjm−1	PROPN
ejpam-5505	278	11	.	.	PUNCT
ejpam-5505	278	12	.	.	PUNCT
ejpam-5505	278	13	.	.	PUNCT
ejpam-5505	279	1	j4j3	j4j3	PROPN
ejpam-5505	279	2	)	)	PUNCT
ejpam-5505	280	1	=	=	SYM
ejpam-5505	280	2	f2	f2	PROPN
ejpam-5505	280	3	,	,	PUNCT
ejpam-5505	280	4	(	(	PUNCT
ejpam-5505	280	5	31	31	NUM
ejpam-5505	280	6	)	)	PUNCT
ejpam-5505	280	7	hence	hence	ADV
ejpam-5505	280	8	(	(	PUNCT
ejpam-5505	280	9	j3j2j1	j3j2j1	PROPN
ejpam-5505	280	10	)	)	PUNCT
ejpam-5505	280	11	(	(	PUNCT
ejpam-5505	280	12	fm	fm	PROPN
ejpam-5505	280	13	)	)	PUNCT
ejpam-5505	280	14	=	=	SYM
ejpam-5505	280	15	(	(	PUNCT
ejpam-5505	280	16	j3j2j1	j3j2j1	PROPN
ejpam-5505	280	17	)	)	PUNCT
ejpam-5505	280	18	(	(	PUNCT
ejpam-5505	280	19	fix	fix	NOUN
ejpam-5505	280	20	(	(	PUNCT
ejpam-5505	280	21	jmjm−1	jmjm−1	PROPN
ejpam-5505	280	22	.	.	PUNCT
ejpam-5505	280	23	.	.	PUNCT
ejpam-5505	280	24	.	.	PUNCT
ejpam-5505	281	1	j2j1	j2j1	PROPN
ejpam-5505	281	2	)	)	PUNCT
ejpam-5505	281	3	)	)	PUNCT
ejpam-5505	282	1	⊆	⊆	NUM
ejpam-5505	282	2	(	(	PUNCT
ejpam-5505	282	3	j3j2	j3j2	X
ejpam-5505	282	4	)	)	PUNCT
ejpam-5505	282	5	(	(	PUNCT
ejpam-5505	282	6	fix	fix	NOUN
ejpam-5505	282	7	(	(	PUNCT
ejpam-5505	282	8	j1jmjm−1	j1jmjm−1	PROPN
ejpam-5505	282	9	.	.	PUNCT
ejpam-5505	282	10	.	.	PUNCT
ejpam-5505	282	11	.	.	PUNCT
ejpam-5505	283	1	j3j2	j3j2	X
ejpam-5505	283	2	)	)	PUNCT
ejpam-5505	283	3	)	)	PUNCT
ejpam-5505	284	1	(	(	PUNCT
ejpam-5505	284	2	32	32	NUM
ejpam-5505	284	3	)	)	PUNCT
ejpam-5505	284	4	⊆	⊆	NUM
ejpam-5505	284	5	j3	j3	PROPN
ejpam-5505	284	6	(	(	PUNCT
ejpam-5505	284	7	fix	fix	PROPN
ejpam-5505	284	8	(	(	PUNCT
ejpam-5505	284	9	j2j1jmjm−1	j2j1jmjm−1	PROPN
ejpam-5505	284	10	.	.	PUNCT
ejpam-5505	284	11	.	.	PUNCT
ejpam-5505	284	12	.	.	PUNCT
ejpam-5505	285	1	j4j3	j4j3	PROPN
ejpam-5505	285	2	)	)	PUNCT
ejpam-5505	285	3	)	)	PUNCT
ejpam-5505	286	1	(	(	PUNCT
ejpam-5505	286	2	33	33	NUM
ejpam-5505	286	3	)	)	PUNCT
ejpam-5505	286	4	⊆	⊆	NUM
ejpam-5505	286	5	fix	fix	NOUN
ejpam-5505	286	6	(	(	PUNCT
ejpam-5505	286	7	j3j2j1jmjm−1	j3j2j1jmjm−1	PROPN
ejpam-5505	286	8	.	.	PUNCT
ejpam-5505	286	9	.	.	PUNCT
ejpam-5505	286	10	.	.	PUNCT
ejpam-5505	287	1	j5j4	j5j4	ADV
ejpam-5505	287	2	)	)	PUNCT
ejpam-5505	287	3	=	=	SYM
ejpam-5505	287	4	f3	f3	PROPN
ejpam-5505	287	5	,	,	PUNCT
ejpam-5505	287	6	(	(	PUNCT
ejpam-5505	287	7	34	34	NUM
ejpam-5505	287	8	)	)	PUNCT
ejpam-5505	287	9	until	until	ADP
ejpam-5505	287	10	finally	finally	ADV
ejpam-5505	287	11	fm	fm	PROPN
ejpam-5505	287	12	=	=	PRON
ejpam-5505	287	13	fix	fix	NOUN
ejpam-5505	287	14	(	(	PUNCT
ejpam-5505	287	15	jmjm−1	jmjm−1	NOUN
ejpam-5505	287	16	.	.	PUNCT
ejpam-5505	287	17	.	.	PUNCT
ejpam-5505	287	18	.	.	PUNCT
ejpam-5505	288	1	j2j1	j2j1	X
ejpam-5505	289	1	=	=	PUNCT
ejpam-5505	289	2	(	(	PUNCT
ejpam-5505	289	3	jmjm−1	jmjm−1	PROPN
ejpam-5505	289	4	.	.	PUNCT
ejpam-5505	289	5	.	.	PUNCT
ejpam-5505	289	6	.	.	PUNCT
ejpam-5505	290	1	j2j1	j2j1	PROPN
ejpam-5505	291	1	)	)	PUNCT
ejpam-5505	291	2	(	(	PUNCT
ejpam-5505	291	3	fix	fix	NOUN
ejpam-5505	291	4	(	(	PUNCT
ejpam-5505	291	5	jmjm−1	jmjm−1	PROPN
ejpam-5505	291	6	.	.	PUNCT
ejpam-5505	291	7	.	.	PUNCT
ejpam-5505	291	8	.	.	PUNCT
ejpam-5505	292	1	j2j1	j2j1	PROPN
ejpam-5505	292	2	)	)	PUNCT
ejpam-5505	292	3	)	)	PUNCT
ejpam-5505	293	1	(	(	PUNCT
ejpam-5505	293	2	35	35	NUM
ejpam-5505	293	3	)	)	PUNCT
ejpam-5505	293	4	s.th.alwadani	s.th.alwadani	X
ejpam-5505	293	5	/	/	SYM
ejpam-5505	293	6	eur	eur	NOUN
ejpam-5505	293	7	.	.	PUNCT
ejpam-5505	294	1	j.	j.	PROPN
ejpam-5505	294	2	pure	pure	PROPN
ejpam-5505	294	3	appl	appl	PROPN
ejpam-5505	294	4	.	.	PROPN
ejpam-5505	294	5	math	math	PROPN
ejpam-5505	294	6	,	,	PUNCT
ejpam-5505	294	7	17	17	NUM
ejpam-5505	294	8	(	(	PUNCT
ejpam-5505	294	9	4	4	NUM
ejpam-5505	294	10	)	)	PUNCT
ejpam-5505	294	11	(	(	PUNCT
ejpam-5505	294	12	2024	2024	NUM
ejpam-5505	294	13	)	)	PUNCT
ejpam-5505	294	14	,	,	PUNCT
ejpam-5505	294	15	3642	3642	NUM
ejpam-5505	294	16	-	-	SYM
ejpam-5505	294	17	3659	3659	NUM
ejpam-5505	294	18	3651	3651	NUM
ejpam-5505	294	19	⊆	⊆	NUM
ejpam-5505	294	20	(	(	PUNCT
ejpam-5505	294	21	jmjm−1	jmjm−1	NOUN
ejpam-5505	294	22	.	.	PUNCT
ejpam-5505	294	23	.	.	PUNCT
ejpam-5505	294	24	.	.	PUNCT
ejpam-5505	295	1	j2	j2	PROPN
ejpam-5505	295	2	)	)	PUNCT
ejpam-5505	295	3	(	(	PUNCT
ejpam-5505	295	4	fix	fix	NOUN
ejpam-5505	295	5	(	(	PUNCT
ejpam-5505	295	6	j1jm	j1jm	PROPN
ejpam-5505	295	7	.	.	PUNCT
ejpam-5505	295	8	.	.	PUNCT
ejpam-5505	295	9	.	.	PUNCT
ejpam-5505	296	1	j3j2	j3j2	X
ejpam-5505	296	2	)	)	PUNCT
ejpam-5505	296	3	)	)	PUNCT
ejpam-5505	297	1	(	(	PUNCT
ejpam-5505	297	2	36	36	NUM
ejpam-5505	297	3	)	)	PUNCT
ejpam-5505	297	4	...	...	PUNCT
ejpam-5505	298	1	(	(	PUNCT
ejpam-5505	298	2	37	37	NUM
ejpam-5505	298	3	)	)	PUNCT
ejpam-5505	298	4	⊆	⊆	NUM
ejpam-5505	298	5	jm	jm	NOUN
ejpam-5505	298	6	(	(	PUNCT
ejpam-5505	298	7	fix	fix	NOUN
ejpam-5505	298	8	(	(	PUNCT
ejpam-5505	298	9	jm−1jm−2	jm−1jm−2	X
ejpam-5505	298	10	.	.	PUNCT
ejpam-5505	298	11	.	.	PUNCT
ejpam-5505	298	12	.	.	PUNCT
ejpam-5505	298	13	j2j1jm	j2j1jm	PROPN
ejpam-5505	298	14	)	)	PUNCT
ejpam-5505	298	15	)	)	PUNCT
ejpam-5505	299	1	=	=	SYM
ejpam-5505	299	2	jm	jm	PROPN
ejpam-5505	299	3	(	(	PUNCT
ejpam-5505	299	4	fm−1	fm−1	PROPN
ejpam-5505	299	5	)	)	PUNCT
ejpam-5505	299	6	(	(	PUNCT
ejpam-5505	299	7	38	38	NUM
ejpam-5505	299	8	)	)	PUNCT
ejpam-5505	299	9	⊆	⊆	NUM
ejpam-5505	299	10	fix	fix	NOUN
ejpam-5505	299	11	(	(	PUNCT
ejpam-5505	299	12	jmjm−1	jmjm−1	NOUN
ejpam-5505	299	13	.	.	PUNCT
ejpam-5505	299	14	.	.	PUNCT
ejpam-5505	299	15	.	.	PUNCT
ejpam-5505	300	1	j2j1	j2j1	X
ejpam-5505	300	2	)	)	PUNCT
ejpam-5505	300	3	=	=	SYM
ejpam-5505	300	4	fm	fm	PROPN
ejpam-5505	300	5	.	.	PROPN
ejpam-5505	301	1	(	(	PUNCT
ejpam-5505	301	2	39	39	NUM
ejpam-5505	301	3	)	)	PUNCT
ejpam-5505	301	4	hence	hence	ADV
ejpam-5505	301	5	,	,	PUNCT
ejpam-5505	301	6	equality	equality	NOUN
ejpam-5505	301	7	holds	hold	VERB
ejpam-5505	301	8	throughout	throughout	ADP
ejpam-5505	301	9	(	(	PUNCT
ejpam-5505	301	10	35	35	NUM
ejpam-5505	301	11	)	)	PUNCT
ejpam-5505	301	12	to	to	ADP
ejpam-5505	301	13	(	(	PUNCT
ejpam-5505	301	14	39	39	NUM
ejpam-5505	301	15	)	)	PUNCT
ejpam-5505	301	16	,	,	PUNCT
ejpam-5505	301	17	and	and	CCONJ
ejpam-5505	301	18	we	we	PRON
ejpam-5505	301	19	are	be	AUX
ejpam-5505	301	20	done	do	VERB
ejpam-5505	301	21	.	.	PUNCT
ejpam-5505	302	1	the	the	DET
ejpam-5505	302	2	same	same	ADJ
ejpam-5505	302	3	approach	approach	NOUN
ejpam-5505	302	4	will	will	AUX
ejpam-5505	302	5	verify	verify	VERB
ejpam-5505	302	6	(	(	PUNCT
ejpam-5505	302	7	24)-(27	24)-(27	NUM
ejpam-5505	302	8	)	)	PUNCT
ejpam-5505	302	9	.	.	PUNCT
ejpam-5505	303	1	(	(	PUNCT
ejpam-5505	303	2	ii	ii	NUM
ejpam-5505	303	3	):	):	PUNCT
ejpam-5505	303	4	it	it	PRON
ejpam-5505	303	5	is	be	AUX
ejpam-5505	303	6	well	well	ADV
ejpam-5505	303	7	known	know	VERB
ejpam-5505	303	8	that	that	SCONJ
ejpam-5505	303	9	∩m	∩m	PROPN
ejpam-5505	304	1	i=1	i=1	PROPN
ejpam-5505	304	2	fix	fix	VERB
ejpam-5505	304	3	ji	ji	PROPN
ejpam-5505	304	4	⊆	⊆	NUM
ejpam-5505	304	5	f1	f1	NOUN
ejpam-5505	304	6	,	,	PUNCT
ejpam-5505	304	7	∩m	∩m	PROPN
ejpam-5505	305	1	i=1	i=1	PROPN
ejpam-5505	305	2	fix	fix	VERB
ejpam-5505	305	3	ji	ji	PROPN
ejpam-5505	305	4	⊆	⊆	NUM
ejpam-5505	305	5	f2	f2	NOUN
ejpam-5505	305	6	,	,	PUNCT
ejpam-5505	305	7	·	·	PUNCT
ejpam-5505	305	8	·	·	PUNCT
ejpam-5505	305	9	·	·	PUNCT
ejpam-5505	305	10	,	,	PUNCT
ejpam-5505	306	1	∩m	∩m	PROPN
ejpam-5505	306	2	i=1	i=1	PROPN
ejpam-5505	307	1	fix	fix	VERB
ejpam-5505	307	2	ji	ji	PROPN
ejpam-5505	307	3	⊆	⊆	NUM
ejpam-5505	307	4	fm	fm	NOUN
ejpam-5505	307	5	.	.	PUNCT
ejpam-5505	308	1	hence	hence	ADV
ejpam-5505	308	2	m⋂	m⋂	ADV
ejpam-5505	308	3	i=1	i=1	PRON
ejpam-5505	308	4	fix	fix	VERB
ejpam-5505	308	5	ji	ji	PROPN
ejpam-5505	308	6	⊆	⊆	NUM
ejpam-5505	308	7	m⋂	m⋂	NOUN
ejpam-5505	308	8	i=1	i=1	PROPN
ejpam-5505	308	9	fi	fi	PROPN
ejpam-5505	308	10	.	.	PUNCT
ejpam-5505	309	1	this	this	PRON
ejpam-5505	309	2	also	also	ADV
ejpam-5505	309	3	implies	imply	VERB
ejpam-5505	309	4	that	that	SCONJ
ejpam-5505	309	5	∩m	∩m	PROPN
ejpam-5505	309	6	i=1	i=1	PROPN
ejpam-5505	310	1	fix	fix	VERB
ejpam-5505	310	2	ji	ji	NOUN
ejpam-5505	310	3	=	=	NOUN
ejpam-5505	310	4	∅	∅	NOUN
ejpam-5505	310	5	if	if	SCONJ
ejpam-5505	310	6	fi	fi	NOUN
ejpam-5505	310	7	=	=	NOUN
ejpam-5505	310	8	∅.	∅.	X
ejpam-5505	310	9	(	(	PUNCT
ejpam-5505	310	10	iii	iii	NOUN
ejpam-5505	310	11	):	):	PUNCT
ejpam-5505	310	12	from	from	ADP
ejpam-5505	310	13	(	(	PUNCT
ejpam-5505	310	14	i	i	NOUN
ejpam-5505	310	15	)	)	PUNCT
ejpam-5505	310	16	,	,	PUNCT
ejpam-5505	310	17	we	we	PRON
ejpam-5505	310	18	have	have	VERB
ejpam-5505	310	19	j1	j1	PROPN
ejpam-5505	310	20	(	(	PUNCT
ejpam-5505	310	21	fm	fm	PROPN
ejpam-5505	310	22	)	)	PUNCT
ejpam-5505	310	23	=	=	SYM
ejpam-5505	310	24	f1	f1	PROPN
ejpam-5505	310	25	,	,	PUNCT
ejpam-5505	310	26	j2	j2	PROPN
ejpam-5505	310	27	(	(	PUNCT
ejpam-5505	310	28	f1	f1	PROPN
ejpam-5505	310	29	)	)	PUNCT
ejpam-5505	311	1	=	=	PUNCT
ejpam-5505	311	2	f2	f2	PROPN
ejpam-5505	311	3	,	,	PUNCT
ejpam-5505	311	4	.	.	PUNCT
ejpam-5505	311	5	.	.	PUNCT
ejpam-5505	311	6	.	.	PUNCT
ejpam-5505	312	1	,	,	PUNCT
ejpam-5505	312	2	jm	jm	PROPN
ejpam-5505	312	3	(	(	PUNCT
ejpam-5505	312	4	fm−1	fm−1	PROPN
ejpam-5505	312	5	)	)	PUNCT
ejpam-5505	312	6	=	=	SYM
ejpam-5505	312	7	fm	fm	PROPN
ejpam-5505	312	8	.	.	PROPN
ejpam-5505	313	1	(	(	PUNCT
ejpam-5505	313	2	40	40	NUM
ejpam-5505	313	3	)	)	PUNCT
ejpam-5505	313	4	using	use	VERB
ejpam-5505	313	5	(	(	PUNCT
ejpam-5505	313	6	6	6	NUM
ejpam-5505	313	7	)	)	PUNCT
ejpam-5505	313	8	,	,	PUNCT
ejpam-5505	313	9	(	(	PUNCT
ejpam-5505	313	10	7	7	X
ejpam-5505	313	11	)	)	PUNCT
ejpam-5505	313	12	and	and	CCONJ
ejpam-5505	313	13	(	(	PUNCT
ejpam-5505	313	14	40	40	NUM
ejpam-5505	313	15	)	)	PUNCT
ejpam-5505	313	16	,	,	PUNCT
ejpam-5505	313	17	we	we	PRON
ejpam-5505	313	18	obtain	obtain	VERB
ejpam-5505	313	19	jar	jar	NOUN
ejpam-5505	313	20	(	(	PUNCT
ejpam-5505	313	21	f1	f1	PROPN
ejpam-5505	313	22	×	×	NOUN
ejpam-5505	313	23	f2	f2	PROPN
ejpam-5505	313	24	×	×	NOUN
ejpam-5505	313	25	·	·	PUNCT
ejpam-5505	313	26	·	·	PUNCT
ejpam-5505	313	27	·	·	PUNCT
ejpam-5505	314	1	×	×	NOUN
ejpam-5505	314	2	fm−1	fm−1	PROPN
ejpam-5505	314	3	×	×	NOUN
ejpam-5505	314	4	fm	fm	NOUN
ejpam-5505	314	5	)	)	PUNCT
ejpam-5505	315	1	=	=	SYM
ejpam-5505	315	2	ja	ja	INTJ
ejpam-5505	315	3	(	(	PUNCT
ejpam-5505	315	4	fm	fm	PROPN
ejpam-5505	315	5	×	×	PROPN
ejpam-5505	315	6	f1	f1	PROPN
ejpam-5505	315	7	×	×	NOUN
ejpam-5505	315	8	f2	f2	PROPN
ejpam-5505	315	9	×	×	NOUN
ejpam-5505	315	10	·	·	PUNCT
ejpam-5505	315	11	·	·	PUNCT
ejpam-5505	315	12	·	·	PUNCT
ejpam-5505	316	1	×	×	PROPN
ejpam-5505	316	2	fm−1	fm−1	NOUN
ejpam-5505	316	3	)	)	PUNCT
ejpam-5505	317	1	=	=	PUNCT
ejpam-5505	317	2	(	(	PUNCT
ejpam-5505	317	3	j1	j1	PROPN
ejpam-5505	317	4	,	,	PUNCT
ejpam-5505	317	5	j2	j2	PROPN
ejpam-5505	317	6	,	,	PUNCT
ejpam-5505	317	7	·	·	PUNCT
ejpam-5505	317	8	·	·	PUNCT
ejpam-5505	317	9	·	·	PUNCT
ejpam-5505	317	10	,	,	PUNCT
ejpam-5505	317	11	jm	jm	PROPN
ejpam-5505	317	12	)	)	PUNCT
ejpam-5505	317	13	(	(	PUNCT
ejpam-5505	317	14	fm	fm	NOUN
ejpam-5505	317	15	×	×	PROPN
ejpam-5505	317	16	f1	f1	PROPN
ejpam-5505	317	17	×	×	NOUN
ejpam-5505	317	18	f2	f2	PROPN
ejpam-5505	317	19	×	×	NOUN
ejpam-5505	317	20	·	·	PUNCT
ejpam-5505	317	21	·	·	PUNCT
ejpam-5505	317	22	·	·	PUNCT
ejpam-5505	318	1	×	×	PROPN
ejpam-5505	318	2	fm−1	fm−1	NOUN
ejpam-5505	318	3	)	)	PUNCT
ejpam-5505	319	1	=	=	PUNCT
ejpam-5505	319	2	f1	f1	PROPN
ejpam-5505	319	3	×	×	NOUN
ejpam-5505	319	4	f2	f2	PROPN
ejpam-5505	319	5	×	×	NOUN
ejpam-5505	319	6	·	·	PUNCT
ejpam-5505	319	7	·	·	PUNCT
ejpam-5505	319	8	·	·	PUNCT
ejpam-5505	320	1	×	×	NOUN
ejpam-5505	320	2	fm−1	fm−1	PROPN
ejpam-5505	320	3	×	×	PROPN
ejpam-5505	320	4	fm	fm	PROPN
ejpam-5505	320	5	.	.	PUNCT
ejpam-5505	321	1	(	(	PUNCT
ejpam-5505	321	2	iv	iv	X
ejpam-5505	321	3	):	):	PUNCT
ejpam-5505	321	4	it	it	PRON
ejpam-5505	321	5	is	be	AUX
ejpam-5505	321	6	clear	clear	ADJ
ejpam-5505	321	7	from	from	ADP
ejpam-5505	321	8	the	the	DET
ejpam-5505	321	9	definitions	definition	NOUN
ejpam-5505	321	10	of	of	ADP
ejpam-5505	321	11	fi	fi	NOUN
ejpam-5505	321	12	,	,	PUNCT
ejpam-5505	321	13	fj	fj	PROPN
ejpam-5505	321	14	and	and	CCONJ
ejpam-5505	321	15	z.	z.	PROPN
ejpam-5505	321	16	(	(	PUNCT
ejpam-5505	321	17	v	v	NOUN
ejpam-5505	321	18	):	):	PUNCT
ejpam-5505	321	19	since	since	SCONJ
ejpam-5505	321	20	jar	jar	NOUN
ejpam-5505	321	21	is	be	AUX
ejpam-5505	321	22	nonexpansive	nonexpansive	ADJ
ejpam-5505	321	23	and	and	CCONJ
ejpam-5505	321	24	z	z	NOUN
ejpam-5505	321	25	=	=	NOUN
ejpam-5505	321	26	fix	fix	NOUN
ejpam-5505	321	27	jar	jar	NOUN
ejpam-5505	321	28	,	,	PUNCT
ejpam-5505	321	29	it	it	PRON
ejpam-5505	321	30	follows	follow	VERB
ejpam-5505	321	31	that	that	SCONJ
ejpam-5505	321	32	z	z	NOUN
ejpam-5505	321	33	is	be	AUX
ejpam-5505	321	34	closed	close	VERB
ejpam-5505	321	35	and	and	CCONJ
ejpam-5505	321	36	convex	convex	VERB
ejpam-5505	321	37	by	by	ADP
ejpam-5505	321	38	[	[	X
ejpam-5505	321	39	16	16	NUM
ejpam-5505	321	40	,	,	PUNCT
ejpam-5505	321	41	proposition	proposition	NOUN
ejpam-5505	321	42	2.1.11	2.1.11	NUM
ejpam-5505	321	43	]	]	PUNCT
ejpam-5505	321	44	.	.	PUNCT
ejpam-5505	322	1	moreover	moreover	ADV
ejpam-5505	322	2	,	,	PUNCT
ejpam-5505	322	3	let	let	VERB
ejpam-5505	322	4	z	z	NOUN
ejpam-5505	322	5	=	=	SYM
ejpam-5505	322	6	(	(	PUNCT
ejpam-5505	322	7	z1	z1	PROPN
ejpam-5505	322	8	,	,	PUNCT
ejpam-5505	322	9	z2	z2	PROPN
ejpam-5505	322	10	,	,	PUNCT
ejpam-5505	322	11	.	.	PUNCT
ejpam-5505	322	12	.	.	PUNCT
ejpam-5505	323	1	.	.	PUNCT
ejpam-5505	324	1	,	,	PUNCT
ejpam-5505	324	2	zm	zm	PROPN
ejpam-5505	324	3	)	)	PUNCT
ejpam-5505	324	4	∈	∈	PROPN
ejpam-5505	324	5	fix	fix	NOUN
ejpam-5505	324	6	jar	jar	NOUN
ejpam-5505	324	7	⇔	⇔	PROPN
ejpam-5505	324	8	z	z	PROPN
ejpam-5505	324	9	=	=	SYM
ejpam-5505	324	10	jarz	jarz	PROPN
ejpam-5505	324	11	.	.	PUNCT
ejpam-5505	325	1	this	this	PRON
ejpam-5505	325	2	implies	imply	VERB
ejpam-5505	325	3	z1	z1	NOUN
ejpam-5505	325	4	=	=	SYM
ejpam-5505	325	5	j1jm	j1jm	X
ejpam-5505	325	6	.	.	PUNCT
ejpam-5505	325	7	.	.	PUNCT
ejpam-5505	325	8	.	.	PUNCT
ejpam-5505	326	1	j2z1	j2z1	ADP
ejpam-5505	326	2	,	,	PUNCT
ejpam-5505	326	3	...	...	PUNCT
ejpam-5505	327	1	zi	zi	X
ejpam-5505	327	2	=	=	PUNCT
ejpam-5505	328	1	jiji−1	jiji−1	PROPN
ejpam-5505	328	2	.	.	PUNCT
ejpam-5505	328	3	.	.	PUNCT
ejpam-5505	328	4	.	.	PUNCT
ejpam-5505	329	1	j1jm	j1jm	PROPN
ejpam-5505	329	2	.	.	PUNCT
ejpam-5505	329	3	.	.	PUNCT
ejpam-5505	329	4	.	.	PUNCT
ejpam-5505	330	1	ji+1zi	ji+1zi	PROPN
ejpam-5505	330	2	,	,	PUNCT
ejpam-5505	330	3	...	...	PUNCT
ejpam-5505	331	1	zm	zm	PROPN
ejpam-5505	331	2	=	=	SYM
ejpam-5505	331	3	jmjm−1	jmjm−1	PROPN
ejpam-5505	331	4	.	.	PUNCT
ejpam-5505	331	5	.	.	PUNCT
ejpam-5505	331	6	.	.	PUNCT
ejpam-5505	332	1	j1zm	j1zm	PUNCT
ejpam-5505	332	2	.	.	PUNCT
ejpam-5505	333	1	hence	hence	ADV
ejpam-5505	333	2	,	,	PUNCT
ejpam-5505	333	3	z	z	NOUN
ejpam-5505	333	4	=	=	SYM
ejpam-5505	333	5	(	(	PUNCT
ejpam-5505	333	6	z1	z1	PROPN
ejpam-5505	333	7	,	,	PUNCT
ejpam-5505	333	8	z2	z2	PROPN
ejpam-5505	333	9	,	,	PUNCT
ejpam-5505	333	10	.	.	PUNCT
ejpam-5505	333	11	.	.	PUNCT
ejpam-5505	333	12	.	.	PUNCT
ejpam-5505	334	1	,	,	PUNCT
ejpam-5505	334	2	zm	zm	PROPN
ejpam-5505	334	3	)	)	PUNCT
ejpam-5505	334	4	∈	∈	PROPN
ejpam-5505	334	5	f1	f1	NOUN
ejpam-5505	334	6	×	×	NOUN
ejpam-5505	334	7	f2	f2	PROPN
ejpam-5505	334	8	×	×	NOUN
ejpam-5505	334	9	·	·	PUNCT
ejpam-5505	334	10	·	·	PUNCT
ejpam-5505	334	11	·	·	PUNCT
ejpam-5505	335	1	×	×	NOUN
ejpam-5505	335	2	fm−1	fm−1	PROPN
ejpam-5505	335	3	×	×	PROPN
ejpam-5505	335	4	fm	fm	PROPN
ejpam-5505	335	5	.	.	PROPN
ejpam-5505	336	1	since	since	SCONJ
ejpam-5505	336	2	this	this	PRON
ejpam-5505	336	3	is	be	AUX
ejpam-5505	336	4	true	true	ADJ
ejpam-5505	336	5	for	for	ADP
ejpam-5505	336	6	all	all	DET
ejpam-5505	336	7	z	z	NOUN
ejpam-5505	336	8	∈	∈	PROPN
ejpam-5505	336	9	z	z	NOUN
ejpam-5505	336	10	,	,	PUNCT
ejpam-5505	336	11	it	it	PRON
ejpam-5505	336	12	follows	follow	VERB
ejpam-5505	336	13	that	that	SCONJ
ejpam-5505	336	14	z	z	NOUN
ejpam-5505	336	15	⊆	⊆	NUM
ejpam-5505	336	16	f1	f1	NOUN
ejpam-5505	336	17	×	×	NOUN
ejpam-5505	336	18	f2	f2	PROPN
ejpam-5505	336	19	×	×	NOUN
ejpam-5505	336	20	·	·	PUNCT
ejpam-5505	336	21	·	·	PUNCT
ejpam-5505	336	22	·	·	PUNCT
ejpam-5505	337	1	×	×	NOUN
ejpam-5505	337	2	fm−1	fm−1	PROPN
ejpam-5505	337	3	×	×	PROPN
ejpam-5505	337	4	fm	fm	PROPN
ejpam-5505	337	5	.	.	PROPN
ejpam-5505	338	1	(	(	PUNCT
ejpam-5505	338	2	vi	vi	X
ejpam-5505	338	3	):	):	PUNCT
ejpam-5505	338	4	it	it	PRON
ejpam-5505	338	5	is	be	AUX
ejpam-5505	338	6	clear	clear	ADJ
ejpam-5505	338	7	from	from	ADP
ejpam-5505	338	8	(	(	PUNCT
ejpam-5505	338	9	i	i	NOUN
ejpam-5505	338	10	)	)	PUNCT
ejpam-5505	338	11	that	that	SCONJ
ejpam-5505	338	12	qi	qi	PRON
ejpam-5505	338	13	:	:	PUNCT
ejpam-5505	338	14	z	z	PROPN
ejpam-5505	338	15	→	→	SYM
ejpam-5505	338	16	fi	fi	NOUN
ejpam-5505	338	17	is	be	AUX
ejpam-5505	338	18	surjective	surjective	ADJ
ejpam-5505	338	19	.	.	PUNCT
ejpam-5505	339	1	to	to	PART
ejpam-5505	339	2	show	show	VERB
ejpam-5505	339	3	qi	qi	PROPN
ejpam-5505	339	4	is	be	AUX
ejpam-5505	339	5	injective	injective	ADJ
ejpam-5505	339	6	,	,	PUNCT
ejpam-5505	339	7	suppose	suppose	VERB
ejpam-5505	339	8	z	z	NOUN
ejpam-5505	339	9	=	=	SYM
ejpam-5505	339	10	(	(	PUNCT
ejpam-5505	339	11	z1	z1	PROPN
ejpam-5505	339	12	,	,	PUNCT
ejpam-5505	339	13	z2	z2	PROPN
ejpam-5505	339	14	,	,	PUNCT
ejpam-5505	339	15	.	.	PUNCT
ejpam-5505	339	16	.	.	PUNCT
ejpam-5505	340	1	.	.	PUNCT
ejpam-5505	341	1	,	,	PUNCT
ejpam-5505	341	2	zm	zm	PROPN
ejpam-5505	341	3	)	)	PUNCT
ejpam-5505	341	4	,	,	PUNCT
ejpam-5505	341	5	z̃	z̃	PROPN
ejpam-5505	341	6	=	=	SYM
ejpam-5505	341	7	(	(	PUNCT
ejpam-5505	341	8	z̃1	z̃1	PROPN
ejpam-5505	341	9	,	,	PUNCT
ejpam-5505	341	10	z̃2	z̃2	PROPN
ejpam-5505	341	11	,	,	PUNCT
ejpam-5505	341	12	.	.	PUNCT
ejpam-5505	341	13	.	.	PUNCT
ejpam-5505	341	14	.	.	PUNCT
ejpam-5505	342	1	,	,	PUNCT
ejpam-5505	342	2	z̃m	z̃m	X
ejpam-5505	342	3	)	)	PUNCT
ejpam-5505	342	4	∈	∈	PROPN
ejpam-5505	342	5	z	z	PROPN
ejpam-5505	342	6	and	and	CCONJ
ejpam-5505	342	7	qi	qi	PROPN
ejpam-5505	342	8	(	(	PUNCT
ejpam-5505	342	9	z	z	NOUN
ejpam-5505	342	10	)	)	PUNCT
ejpam-5505	343	1	=	=	SYM
ejpam-5505	343	2	qi	qi	PROPN
ejpam-5505	343	3	(	(	PUNCT
ejpam-5505	343	4	z̃	z̃	PROPN
ejpam-5505	343	5	)	)	PUNCT
ejpam-5505	343	6	.	.	PUNCT
ejpam-5505	344	1	this	this	PRON
ejpam-5505	344	2	implies	imply	VERB
ejpam-5505	344	3	that	that	SCONJ
ejpam-5505	344	4	zi	zi	NOUN
ejpam-5505	344	5	=	=	SYM
ejpam-5505	344	6	z̃i	z̃i	PROPN
ejpam-5505	344	7	.	.	PUNCT
ejpam-5505	345	1	because	because	SCONJ
ejpam-5505	345	2	z	z	PROPN
ejpam-5505	345	3	and	and	CCONJ
ejpam-5505	345	4	z̃	z̃	PROPN
ejpam-5505	345	5	are	be	AUX
ejpam-5505	345	6	cycles	cycle	NOUN
ejpam-5505	345	7	,	,	PUNCT
ejpam-5505	345	8	it	it	PRON
ejpam-5505	345	9	follows	follow	VERB
ejpam-5505	345	10	that	that	PRON
ejpam-5505	345	11	zi+1	zi+1	NOUN
ejpam-5505	345	12	=	=	NOUN
ejpam-5505	345	13	ji+1zi	ji+1zi	X
ejpam-5505	345	14	=	=	SYM
ejpam-5505	345	15	ji+1z̃i	ji+1z̃i	X
ejpam-5505	346	1	=	=	SYM
ejpam-5505	346	2	z̃i+1	z̃i+1	NOUN
ejpam-5505	346	3	(	(	PUNCT
ejpam-5505	346	4	41	41	NUM
ejpam-5505	346	5	)	)	PUNCT
ejpam-5505	346	6	s.th.alwadani	s.th.alwadani	X
ejpam-5505	346	7	/	/	SYM
ejpam-5505	346	8	eur	eur	NOUN
ejpam-5505	346	9	.	.	PUNCT
ejpam-5505	347	1	j.	j.	PROPN
ejpam-5505	347	2	pure	pure	PROPN
ejpam-5505	347	3	appl	appl	PROPN
ejpam-5505	347	4	.	.	PROPN
ejpam-5505	347	5	math	math	PROPN
ejpam-5505	347	6	,	,	PUNCT
ejpam-5505	347	7	17	17	NUM
ejpam-5505	347	8	(	(	PUNCT
ejpam-5505	347	9	4	4	NUM
ejpam-5505	347	10	)	)	PUNCT
ejpam-5505	347	11	(	(	PUNCT
ejpam-5505	347	12	2024	2024	NUM
ejpam-5505	347	13	)	)	PUNCT
ejpam-5505	347	14	,	,	PUNCT
ejpam-5505	347	15	3642	3642	NUM
ejpam-5505	347	16	-	-	SYM
ejpam-5505	347	17	3659	3659	NUM
ejpam-5505	347	18	3652	3652	NUM
ejpam-5505	347	19	...	...	PUNCT
ejpam-5505	347	20	(	(	PUNCT
ejpam-5505	347	21	42	42	NUM
ejpam-5505	347	22	)	)	PUNCT
ejpam-5505	347	23	zm	zm	PROPN
ejpam-5505	348	1	=	=	PUNCT
ejpam-5505	348	2	jmzm−1	jmzm−1	PROPN
ejpam-5505	348	3	=	=	SYM
ejpam-5505	348	4	jm	jm	PROPN
ejpam-5505	348	5	z̃m−1	z̃m−1	PROPN
ejpam-5505	348	6	=	=	SYM
ejpam-5505	348	7	z̃m	z̃m	PROPN
ejpam-5505	348	8	(	(	PUNCT
ejpam-5505	348	9	43	43	NUM
ejpam-5505	348	10	)	)	PUNCT
ejpam-5505	348	11	z1	z1	NOUN
ejpam-5505	348	12	=	=	PUNCT
ejpam-5505	348	13	j1zm	j1zm	PUNCT
ejpam-5505	348	14	=	=	PUNCT
ejpam-5505	348	15	j1z̃m	j1z̃m	PROPN
ejpam-5505	348	16	=	=	SYM
ejpam-5505	348	17	z̃1	z̃1	PROPN
ejpam-5505	348	18	(	(	PUNCT
ejpam-5505	348	19	44	44	NUM
ejpam-5505	348	20	)	)	PUNCT
ejpam-5505	348	21	z2	z2	NOUN
ejpam-5505	348	22	=	=	PUNCT
ejpam-5505	348	23	j2z1	j2z1	PROPN
ejpam-5505	348	24	=	=	SYM
ejpam-5505	348	25	j2z̃1	j2z̃1	NOUN
ejpam-5505	349	1	=	=	PUNCT
ejpam-5505	349	2	z̃2	z̃2	PROPN
ejpam-5505	349	3	(	(	PUNCT
ejpam-5505	349	4	45	45	NUM
ejpam-5505	349	5	)	)	PUNCT
ejpam-5505	349	6	...	...	PUNCT
ejpam-5505	350	1	(	(	PUNCT
ejpam-5505	350	2	46	46	X
ejpam-5505	350	3	)	)	PUNCT
ejpam-5505	350	4	zi−1	zi−1	NOUN
ejpam-5505	350	5	=	=	PUNCT
ejpam-5505	350	6	ji−1zi−2	ji−1zi−2	NUM
ejpam-5505	350	7	=	=	SYM
ejpam-5505	350	8	ji−1z̃i−2	ji−1z̃i−2	NOUN
ejpam-5505	350	9	=	=	SYM
ejpam-5505	350	10	z̃i−1	z̃i−1	PROPN
ejpam-5505	350	11	.	.	PUNCT
ejpam-5505	351	1	(	(	PUNCT
ejpam-5505	351	2	47	47	NUM
ejpam-5505	351	3	)	)	PUNCT
ejpam-5505	351	4	from	from	ADP
ejpam-5505	351	5	(	(	PUNCT
ejpam-5505	351	6	41)-(47	41)-(47	NOUN
ejpam-5505	351	7	)	)	PUNCT
ejpam-5505	351	8	,	,	PUNCT
ejpam-5505	351	9	we	we	PRON
ejpam-5505	351	10	have	have	VERB
ejpam-5505	351	11	z	z	NOUN
ejpam-5505	351	12	=	=	SYM
ejpam-5505	351	13	z̃.	z̃.	PROPN
ejpam-5505	351	14	■	■	PUNCT
ejpam-5505	351	15	lemma	lemma	PROPN
ejpam-5505	351	16	3	3	X
ejpam-5505	351	17	.	.	PUNCT
ejpam-5505	352	1	let	let	VERB
ejpam-5505	352	2	∩m	∩m	PROPN
ejpam-5505	353	1	i=1	i=1	PROPN
ejpam-5505	353	2	fix	fix	VERB
ejpam-5505	353	3	ji	ji	PROPN
ejpam-5505	353	4	̸=	̸=	PROPN
ejpam-5505	353	5	∅	∅	NOUN
ejpam-5505	353	6	:	:	PUNCT
ejpam-5505	353	7	=	=	SYM
ejpam-5505	353	8	d.	d.	PROPN
ejpam-5505	353	9	then	then	ADV
ejpam-5505	353	10	the	the	DET
ejpam-5505	353	11	following	follow	VERB
ejpam-5505	353	12	holds	hold	VERB
ejpam-5505	353	13	:	:	PUNCT
ejpam-5505	353	14	(	(	PUNCT
ejpam-5505	353	15	i	i	NOUN
ejpam-5505	353	16	)	)	PUNCT
ejpam-5505	353	17	for	for	ADP
ejpam-5505	353	18	all	all	PRON
ejpam-5505	353	19	i	i	PRON
ejpam-5505	353	20	such	such	ADJ
ejpam-5505	353	21	that	that	SCONJ
ejpam-5505	353	22	1	1	NUM
ejpam-5505	353	23	≤	≤	NUM
ejpam-5505	353	24	i	i	PRON
ejpam-5505	353	25	≤	≤	NOUN
ejpam-5505	353	26	m	m	ADP
ejpam-5505	353	27	,	,	PUNCT
ejpam-5505	353	28	it	it	PRON
ejpam-5505	353	29	holds	hold	VERB
ejpam-5505	353	30	that	that	DET
ejpam-5505	353	31	fi	fi	NOUN
ejpam-5505	354	1	=	=	X
ejpam-5505	354	2	d.	d.	PROPN
ejpam-5505	354	3	(	(	PUNCT
ejpam-5505	354	4	ii	ii	PROPN
ejpam-5505	354	5	)	)	PUNCT
ejpam-5505	354	6	z	z	NOUN
ejpam-5505	354	7	=	=	PRON
ejpam-5505	354	8	{	{	PUNCT
ejpam-5505	354	9	(	(	PUNCT
ejpam-5505	354	10	z	z	NOUN
ejpam-5505	354	11	,	,	PUNCT
ejpam-5505	354	12	z	z	PROPN
ejpam-5505	354	13	,	,	PUNCT
ejpam-5505	354	14	·	·	PUNCT
ejpam-5505	354	15	·	·	PUNCT
ejpam-5505	354	16	·	·	PUNCT
ejpam-5505	354	17	,	,	PUNCT
ejpam-5505	354	18	z	z	X
ejpam-5505	354	19	)	)	PUNCT
ejpam-5505	355	1	|	|	ADV
ejpam-5505	355	2	z	z	X
ejpam-5505	355	3	∈	∈	PROPN
ejpam-5505	355	4	d	d	X
ejpam-5505	355	5	}	}	PUNCT
ejpam-5505	355	6	=	=	SYM
ejpam-5505	355	7	dm	dm	NUM
ejpam-5505	355	8	∩	∩	NOUN
ejpam-5505	355	9	∆.	∆.	NOUN
ejpam-5505	355	10	proof	proof	NOUN
ejpam-5505	355	11	.	.	PUNCT
ejpam-5505	356	1	(	(	PUNCT
ejpam-5505	356	2	i	i	NOUN
ejpam-5505	356	3	):	):	PUNCT
ejpam-5505	356	4	since	since	SCONJ
ejpam-5505	356	5	ji	ji	PROPN
ejpam-5505	356	6	is	be	AUX
ejpam-5505	356	7	firmly	firmly	ADV
ejpam-5505	356	8	nonexpansive	nonexpansive	ADJ
ejpam-5505	356	9	for	for	ADP
ejpam-5505	356	10	every	every	DET
ejpam-5505	356	11	1	1	NUM
ejpam-5505	356	12	≤	≤	NUM
ejpam-5505	356	13	i	i	NOUN
ejpam-5505	356	14	≤	≤	NOUN
ejpam-5505	356	15	m	m	ADP
ejpam-5505	356	16	,	,	PUNCT
ejpam-5505	356	17	then	then	ADV
ejpam-5505	356	18	by	by	ADP
ejpam-5505	356	19	[	[	X
ejpam-5505	356	20	10	10	NUM
ejpam-5505	356	21	,	,	PUNCT
ejpam-5505	356	22	corollary	corollary	NOUN
ejpam-5505	356	23	4.51	4.51	NUM
ejpam-5505	356	24	]	]	PUNCT
ejpam-5505	356	25	,	,	PUNCT
ejpam-5505	356	26	we	we	PRON
ejpam-5505	356	27	have	have	VERB
ejpam-5505	356	28	(	(	PUNCT
ejpam-5505	356	29	∀(1	∀(1	PROPN
ejpam-5505	356	30	≤	≤	PUNCT
ejpam-5505	356	31	i	i	PRON
ejpam-5505	356	32	≤	≤	NOUN
ejpam-5505	356	33	m	m	PROPN
ejpam-5505	356	34	)	)	PUNCT
ejpam-5505	356	35	)	)	PUNCT
ejpam-5505	356	36	,	,	PUNCT
ejpam-5505	356	37	fix	fix	NOUN
ejpam-5505	356	38	(	(	PUNCT
ejpam-5505	356	39	jiji−1	jiji−1	PROPN
ejpam-5505	356	40	·	·	PUNCT
ejpam-5505	356	41	·	·	PUNCT
ejpam-5505	356	42	·	·	PUNCT
ejpam-5505	356	43	j1jm	j1jm	PUNCT
ejpam-5505	356	44	·	·	PUNCT
ejpam-5505	356	45	·	·	PUNCT
ejpam-5505	356	46	·	·	PUNCT
ejpam-5505	356	47	ji+1	ji+1	X
ejpam-5505	356	48	)	)	PUNCT
ejpam-5505	357	1	=	=	SYM
ejpam-5505	357	2	d.	d.	PROPN
ejpam-5505	357	3	(	(	PUNCT
ejpam-5505	357	4	ii	ii	PROPN
ejpam-5505	357	5	):	):	PUNCT
ejpam-5505	357	6	let	let	VERB
ejpam-5505	357	7	z	z	NOUN
ejpam-5505	357	8	=	=	SYM
ejpam-5505	357	9	(	(	PUNCT
ejpam-5505	357	10	z1	z1	PROPN
ejpam-5505	357	11	,	,	PUNCT
ejpam-5505	357	12	z2	z2	PROPN
ejpam-5505	357	13	,	,	PUNCT
ejpam-5505	357	14	·	·	PUNCT
ejpam-5505	357	15	·	·	PUNCT
ejpam-5505	357	16	·	·	PUNCT
ejpam-5505	357	17	,	,	PUNCT
ejpam-5505	358	1	zm	zm	PROPN
ejpam-5505	358	2	)	)	PUNCT
ejpam-5505	358	3	∈	∈	PROPN
ejpam-5505	358	4	z.	z.	PROPN
ejpam-5505	358	5	then	then	ADV
ejpam-5505	358	6	,	,	PUNCT
ejpam-5505	358	7	z1	z1	PROPN
ejpam-5505	358	8	=	=	PUNCT
ejpam-5505	358	9	j1jmjm−1	j1jmjm−1	PROPN
ejpam-5505	358	10	·	·	PUNCT
ejpam-5505	358	11	·	·	PUNCT
ejpam-5505	358	12	·	·	PUNCT
ejpam-5505	358	13	j2z1	j2z1	ADP
ejpam-5505	358	14	⇔	⇔	PROPN
ejpam-5505	358	15	z1	z1	PROPN
ejpam-5505	358	16	∈	∈	PROPN
ejpam-5505	358	17	f1	f1	NOUN
ejpam-5505	358	18	=	=	SYM
ejpam-5505	358	19	d	d	PROPN
ejpam-5505	358	20	z2	z2	PROPN
ejpam-5505	358	21	=	=	SYM
ejpam-5505	358	22	j2j1jm	j2j1jm	X
ejpam-5505	358	23	·	·	PUNCT
ejpam-5505	358	24	·	·	PUNCT
ejpam-5505	358	25	·	·	PUNCT
ejpam-5505	359	1	j3z2	j3z2	ADP
ejpam-5505	359	2	⇔	⇔	PROPN
ejpam-5505	359	3	z2	z2	PROPN
ejpam-5505	359	4	∈	∈	PROPN
ejpam-5505	359	5	f2	f2	PROPN
ejpam-5505	360	1	=	=	SYM
ejpam-5505	360	2	d	d	PROPN
ejpam-5505	360	3	...	...	PUNCT
ejpam-5505	361	1	zm	zm	PROPN
ejpam-5505	361	2	=	=	PUNCT
ejpam-5505	362	1	jmjm−1jm−2	jmjm−1jm−2	PROPN
ejpam-5505	362	2	·	·	PUNCT
ejpam-5505	362	3	·	·	PUNCT
ejpam-5505	362	4	·	·	PUNCT
ejpam-5505	362	5	j1zm	j1zm	PUNCT
ejpam-5505	362	6	⇔	⇔	PROPN
ejpam-5505	362	7	zm	zm	PROPN
ejpam-5505	362	8	∈	∈	PROPN
ejpam-5505	362	9	fm	fm	PROPN
ejpam-5505	362	10	=	=	PROPN
ejpam-5505	362	11	d.	d.	PROPN
ejpam-5505	362	12	therefore	therefore	ADV
ejpam-5505	362	13	,	,	PUNCT
ejpam-5505	362	14	z	z	NOUN
ejpam-5505	362	15	=	=	SYM
ejpam-5505	362	16	(	(	PUNCT
ejpam-5505	362	17	z1	z1	PROPN
ejpam-5505	362	18	,	,	PUNCT
ejpam-5505	362	19	z2	z2	PROPN
ejpam-5505	362	20	,	,	PUNCT
ejpam-5505	362	21	·	·	PUNCT
ejpam-5505	362	22	·	·	PUNCT
ejpam-5505	362	23	·	·	PUNCT
ejpam-5505	362	24	,	,	PUNCT
ejpam-5505	362	25	zm	zm	PROPN
ejpam-5505	362	26	)	)	PUNCT
ejpam-5505	362	27	∈	∈	PROPN
ejpam-5505	362	28	f1	f1	NOUN
ejpam-5505	362	29	×	×	NOUN
ejpam-5505	362	30	f2	f2	PROPN
ejpam-5505	362	31	×	×	NOUN
ejpam-5505	362	32	·	·	PUNCT
ejpam-5505	362	33	·	·	PUNCT
ejpam-5505	362	34	·	·	PUNCT
ejpam-5505	363	1	×	×	NOUN
ejpam-5505	363	2	fm	fm	NOUN
ejpam-5505	363	3	=	=	PUNCT
ejpam-5505	364	1	d	d	X
ejpam-5505	364	2	×	×	NUM
ejpam-5505	364	3	u	u	NOUN
ejpam-5505	364	4	×	×	NOUN
ejpam-5505	364	5	d	d	X
ejpam-5505	364	6	×	×	PROPN
ejpam-5505	364	7	·	·	PUNCT
ejpam-5505	364	8	·	·	PUNCT
ejpam-5505	364	9	·	·	PUNCT
ejpam-5505	365	1	×	×	NOUN
ejpam-5505	365	2	d	d	NOUN
ejpam-5505	365	3	=	=	PUNCT
ejpam-5505	365	4	dm	dm	PROPN
ejpam-5505	365	5	and	and	CCONJ
ejpam-5505	365	6	z	z	NOUN
ejpam-5505	365	7	=	=	SYM
ejpam-5505	365	8	(	(	PUNCT
ejpam-5505	365	9	z1	z1	PROPN
ejpam-5505	365	10	,	,	PUNCT
ejpam-5505	365	11	z2	z2	PROPN
ejpam-5505	365	12	,	,	PUNCT
ejpam-5505	365	13	·	·	PUNCT
ejpam-5505	365	14	·	·	PUNCT
ejpam-5505	365	15	·	·	PUNCT
ejpam-5505	365	16	,	,	PUNCT
ejpam-5505	365	17	zm	zm	PROPN
ejpam-5505	365	18	)	)	PUNCT
ejpam-5505	365	19	=	=	PRON
ejpam-5505	366	1	(	(	PUNCT
ejpam-5505	366	2	z	z	NOUN
ejpam-5505	366	3	,	,	PUNCT
ejpam-5505	366	4	z	z	PROPN
ejpam-5505	366	5	,	,	PUNCT
ejpam-5505	366	6	·	·	PUNCT
ejpam-5505	366	7	·	·	PUNCT
ejpam-5505	366	8	·	·	PUNCT
ejpam-5505	366	9	,	,	PUNCT
ejpam-5505	366	10	z	z	X
ejpam-5505	366	11	)	)	PUNCT
ejpam-5505	366	12	∈	∈	PROPN
ejpam-5505	366	13	d.	d.	PROPN
ejpam-5505	366	14	therefore	therefore	ADV
ejpam-5505	366	15	,	,	PUNCT
ejpam-5505	366	16	z	z	PROPN
ejpam-5505	366	17	∈	∈	PROPN
ejpam-5505	366	18	dm	dm	PROPN
ejpam-5505	366	19	∩	∩	PROPN
ejpam-5505	366	20	d.	d.	PROPN
ejpam-5505	366	21	■	■	PUNCT
ejpam-5505	366	22	remark	remark	VERB
ejpam-5505	366	23	1	1	NUM
ejpam-5505	366	24	.	.	PUNCT
ejpam-5505	367	1	when	when	SCONJ
ejpam-5505	367	2	m	m	VERB
ejpam-5505	367	3	=	=	SYM
ejpam-5505	367	4	2	2	NUM
ejpam-5505	367	5	,	,	PUNCT
ejpam-5505	367	6	we	we	PRON
ejpam-5505	367	7	have	have	VERB
ejpam-5505	367	8	j1	j1	PROPN
ejpam-5505	367	9	(	(	PUNCT
ejpam-5505	367	10	f2	f2	PROPN
ejpam-5505	367	11	)	)	PUNCT
ejpam-5505	367	12	=	=	SYM
ejpam-5505	367	13	f1	f1	NOUN
ejpam-5505	367	14	and	and	CCONJ
ejpam-5505	367	15	j2	j2	PROPN
ejpam-5505	367	16	(	(	PUNCT
ejpam-5505	367	17	f1	f1	PROPN
ejpam-5505	367	18	)	)	PUNCT
ejpam-5505	367	19	=	=	SYM
ejpam-5505	367	20	f2	f2	PROPN
ejpam-5505	367	21	.	.	PUNCT
ejpam-5505	368	1	proof	proof	NOUN
ejpam-5505	368	2	.	.	PUNCT
ejpam-5505	369	1	let	let	VERB
ejpam-5505	369	2	z	z	NOUN
ejpam-5505	369	3	∈	∈	PROPN
ejpam-5505	369	4	f1	f1	NOUN
ejpam-5505	369	5	.	.	PUNCT
ejpam-5505	370	1	this	this	PRON
ejpam-5505	370	2	implies	imply	VERB
ejpam-5505	370	3	that	that	SCONJ
ejpam-5505	370	4	z	z	NOUN
ejpam-5505	370	5	=	=	PUNCT
ejpam-5505	370	6	j1j2z	j1j2z	PUNCT
ejpam-5505	370	7	and	and	CCONJ
ejpam-5505	370	8	j2z	j2z	PROPN
ejpam-5505	370	9	=	=	SYM
ejpam-5505	370	10	j2j1(j2z	j2j1(j2z	PROPN
ejpam-5505	370	11	)	)	PUNCT
ejpam-5505	370	12	.	.	PUNCT
ejpam-5505	371	1	therefore	therefore	ADV
ejpam-5505	371	2	,	,	PUNCT
ejpam-5505	371	3	j2	j2	PROPN
ejpam-5505	371	4	(	(	PUNCT
ejpam-5505	371	5	f1	f1	PROPN
ejpam-5505	371	6	)	)	PUNCT
ejpam-5505	371	7	⊆	⊆	NUM
ejpam-5505	371	8	f2	f2	PROPN
ejpam-5505	371	9	.	.	PUNCT
ejpam-5505	372	1	(	(	PUNCT
ejpam-5505	372	2	48	48	NUM
ejpam-5505	372	3	)	)	PUNCT
ejpam-5505	372	4	s.th.alwadani	s.th.alwadani	NOUN
ejpam-5505	372	5	/	/	SYM
ejpam-5505	372	6	eur	eur	NOUN
ejpam-5505	372	7	.	.	PUNCT
ejpam-5505	373	1	j.	j.	PROPN
ejpam-5505	373	2	pure	pure	PROPN
ejpam-5505	373	3	appl	appl	PROPN
ejpam-5505	373	4	.	.	PROPN
ejpam-5505	373	5	math	math	PROPN
ejpam-5505	373	6	,	,	PUNCT
ejpam-5505	373	7	17	17	NUM
ejpam-5505	373	8	(	(	PUNCT
ejpam-5505	373	9	4	4	NUM
ejpam-5505	373	10	)	)	PUNCT
ejpam-5505	373	11	(	(	PUNCT
ejpam-5505	373	12	2024	2024	NUM
ejpam-5505	373	13	)	)	PUNCT
ejpam-5505	373	14	,	,	PUNCT
ejpam-5505	373	15	3642	3642	NUM
ejpam-5505	373	16	-	-	SYM
ejpam-5505	373	17	3659	3659	NUM
ejpam-5505	373	18	3653	3653	NUM
ejpam-5505	373	19	let	let	VERB
ejpam-5505	373	20	z̃	z̃	PROPN
ejpam-5505	373	21	∈	∈	PROPN
ejpam-5505	373	22	f2	f2	PROPN
ejpam-5505	373	23	.	.	PUNCT
ejpam-5505	374	1	it	it	PRON
ejpam-5505	374	2	follows	follow	VERB
ejpam-5505	374	3	that	that	SCONJ
ejpam-5505	374	4	z̃	z̃	PROPN
ejpam-5505	374	5	=	=	SYM
ejpam-5505	374	6	j2j1z̃	j2j1z̃	PROPN
ejpam-5505	374	7	and	and	CCONJ
ejpam-5505	374	8	j1z̃	j1z̃	ADJ
ejpam-5505	374	9	=	=	SYM
ejpam-5505	374	10	j1j2(j1z̃	j1j2(j1z̃	PROPN
ejpam-5505	374	11	)	)	PUNCT
ejpam-5505	374	12	.	.	PUNCT
ejpam-5505	375	1	thus	thus	ADV
ejpam-5505	375	2	,	,	PUNCT
ejpam-5505	375	3	j1	j1	PROPN
ejpam-5505	375	4	(	(	PUNCT
ejpam-5505	375	5	f2	f2	PROPN
ejpam-5505	375	6	)	)	PUNCT
ejpam-5505	375	7	⊆	⊆	NUM
ejpam-5505	375	8	f1	f1	NOUN
ejpam-5505	375	9	(	(	PUNCT
ejpam-5505	375	10	49	49	NUM
ejpam-5505	375	11	)	)	PUNCT
ejpam-5505	375	12	now	now	ADV
ejpam-5505	375	13	,	,	PUNCT
ejpam-5505	375	14	applying	apply	VERB
ejpam-5505	375	15	j1	j1	PROPN
ejpam-5505	375	16	and	and	CCONJ
ejpam-5505	375	17	j2	j2	PROPN
ejpam-5505	375	18	to	to	ADP
ejpam-5505	375	19	(	(	PUNCT
ejpam-5505	375	20	48	48	NUM
ejpam-5505	375	21	)	)	PUNCT
ejpam-5505	375	22	and	and	CCONJ
ejpam-5505	375	23	(	(	PUNCT
ejpam-5505	375	24	49	49	NUM
ejpam-5505	375	25	)	)	PUNCT
ejpam-5505	375	26	,	,	PUNCT
ejpam-5505	375	27	respectively	respectively	ADV
ejpam-5505	375	28	,	,	PUNCT
ejpam-5505	375	29	we	we	PRON
ejpam-5505	375	30	obtain	obtain	VERB
ejpam-5505	375	31	f1	f1	NOUN
ejpam-5505	375	32	⊆	⊆	NUM
ejpam-5505	375	33	j1	j1	PROPN
ejpam-5505	375	34	(	(	PUNCT
ejpam-5505	375	35	f2	f2	PROPN
ejpam-5505	375	36	)	)	PUNCT
ejpam-5505	375	37	and	and	CCONJ
ejpam-5505	375	38	f2	f2	PROPN
ejpam-5505	375	39	⊆	⊆	NUM
ejpam-5505	375	40	j2	j2	PROPN
ejpam-5505	375	41	(	(	PUNCT
ejpam-5505	375	42	f1	f1	PROPN
ejpam-5505	375	43	)	)	PUNCT
ejpam-5505	375	44	.	.	PUNCT
ejpam-5505	376	1	hence	hence	ADV
ejpam-5505	376	2	,	,	PUNCT
ejpam-5505	376	3	f1	f1	PROPN
ejpam-5505	376	4	=	=	PROPN
ejpam-5505	376	5	j1	j1	PROPN
ejpam-5505	376	6	(	(	PUNCT
ejpam-5505	376	7	f2	f2	PROPN
ejpam-5505	376	8	)	)	PUNCT
ejpam-5505	376	9	and	and	CCONJ
ejpam-5505	376	10	f2	f2	PROPN
ejpam-5505	376	11	=	=	SYM
ejpam-5505	376	12	j2	j2	PROPN
ejpam-5505	376	13	(	(	PUNCT
ejpam-5505	376	14	f1	f1	PROPN
ejpam-5505	376	15	)	)	PUNCT
ejpam-5505	376	16	.	.	PUNCT
ejpam-5505	377	1	■	■	PUNCT
ejpam-5505	377	2	lemma	lemma	PROPN
ejpam-5505	377	3	4	4	X
ejpam-5505	377	4	.	.	PUNCT
ejpam-5505	377	5	recall	recall	NOUN
ejpam-5505	377	6	from	from	ADP
ejpam-5505	377	7	(	(	PUNCT
ejpam-5505	377	8	20	20	NUM
ejpam-5505	377	9	)	)	PUNCT
ejpam-5505	377	10	that	that	SCONJ
ejpam-5505	377	11	z	z	NOUN
ejpam-5505	377	12	=	=	PUNCT
ejpam-5505	377	13	fix	fix	NOUN
ejpam-5505	377	14	jar	jar	NOUN
ejpam-5505	377	15	.	.	PUNCT
ejpam-5505	378	1	then	then	ADV
ejpam-5505	378	2	it	it	PRON
ejpam-5505	378	3	follows	follow	VERB
ejpam-5505	378	4	that	that	SCONJ
ejpam-5505	378	5	z	z	NOUN
ejpam-5505	378	6	=	=	PUNCT
ejpam-5505	378	7	fix	fix	NOUN
ejpam-5505	378	8	jar	jar	NOUN
ejpam-5505	378	9	=	=	PRON
ejpam-5505	378	10	fix	fix	VERB
ejpam-5505	378	11	j	j	NOUN
ejpam-5505	378	12	1	1	NUM
ejpam-5505	378	13	2	2	NUM
ejpam-5505	378	14	a	a	PRON
ejpam-5505	378	15	(	(	PUNCT
ejpam-5505	378	16	i	i	NOUN
ejpam-5505	378	17	d	d	PROPN
ejpam-5505	378	18	+	+	CCONJ
ejpam-5505	378	19	r	r	NOUN
ejpam-5505	378	20	2	2	NUM
ejpam-5505	378	21	)	)	PUNCT
ejpam-5505	378	22	.	.	PUNCT
ejpam-5505	379	1	proof	proof	NOUN
ejpam-5505	379	2	.	.	PUNCT
ejpam-5505	380	1	let	let	VERB
ejpam-5505	380	2	x	x	PUNCT
ejpam-5505	380	3	∈	∈	PROPN
ejpam-5505	380	4	fix	fix	NOUN
ejpam-5505	380	5	(	(	PUNCT
ejpam-5505	380	6	jar	jar	NOUN
ejpam-5505	380	7	)	)	PUNCT
ejpam-5505	380	8	.	.	PUNCT
ejpam-5505	381	1	then	then	ADV
ejpam-5505	381	2	x	x	X
ejpam-5505	381	3	=	=	SYM
ejpam-5505	381	4	jarx	jarx	NOUN
ejpam-5505	381	5	⇔	⇔	X
ejpam-5505	381	6	rx	rx	X
ejpam-5505	381	7	∈	∈	PROPN
ejpam-5505	381	8	x	x	PUNCT
ejpam-5505	382	1	+	+	CCONJ
ejpam-5505	382	2	ax	ax	ADJ
ejpam-5505	382	3	⇔	⇔	X
ejpam-5505	382	4	0	0	NUM
ejpam-5505	382	5	∈	∈	PROPN
ejpam-5505	382	6	(	(	PUNCT
ejpam-5505	382	7	x	x	SYM
ejpam-5505	382	8	−	−	NOUN
ejpam-5505	382	9	rx	rx	ADJ
ejpam-5505	382	10	)	)	PUNCT
ejpam-5505	382	11	+	+	CCONJ
ejpam-5505	382	12	a(x	a(x	PROPN
ejpam-5505	382	13	)	)	PUNCT
ejpam-5505	382	14	⇔	⇔	NOUN
ejpam-5505	382	15	0	0	SYM
ejpam-5505	382	16	∈	∈	PROPN
ejpam-5505	382	17	(	(	PUNCT
ejpam-5505	382	18	x	x	SYM
ejpam-5505	382	19	−	−	NOUN
ejpam-5505	382	20	rx	rx	ADJ
ejpam-5505	382	21	)	)	PUNCT
ejpam-5505	382	22	2	2	NUM
ejpam-5505	382	23	+	+	SYM
ejpam-5505	382	24	a(x	a(x	NOUN
ejpam-5505	382	25	)	)	PUNCT
ejpam-5505	382	26	2	2	NUM
ejpam-5505	382	27	⇔	⇔	X
ejpam-5505	382	28	0	0	NUM
ejpam-5505	382	29	∈	∈	PROPN
ejpam-5505	382	30	x	x	X
ejpam-5505	382	31	−	−	PROPN
ejpam-5505	382	32	(	(	PUNCT
ejpam-5505	382	33	i	i	NOUN
ejpam-5505	382	34	d	d	PROPN
ejpam-5505	382	35	+	+	CCONJ
ejpam-5505	382	36	r	r	NOUN
ejpam-5505	382	37	2	2	NUM
ejpam-5505	382	38	)	)	PUNCT
ejpam-5505	382	39	x	x	PUNCT
ejpam-5505	383	1	+	+	PUNCT
ejpam-5505	383	2	a(x	a(x	NOUN
ejpam-5505	383	3	)	)	PUNCT
ejpam-5505	383	4	2	2	NUM
ejpam-5505	383	5	adding	add	VERB
ejpam-5505	383	6	and	and	CCONJ
ejpam-5505	383	7	subtracting	subtract	VERB
ejpam-5505	383	8	x	x	SYM
ejpam-5505	383	9	2	2	NUM
ejpam-5505	383	10	⇔	⇔	X
ejpam-5505	383	11	(	(	PUNCT
ejpam-5505	383	12	i	i	NOUN
ejpam-5505	383	13	d	d	PROPN
ejpam-5505	383	14	+	+	CCONJ
ejpam-5505	383	15	r	r	NOUN
ejpam-5505	383	16	2	2	NUM
ejpam-5505	383	17	)	)	PUNCT
ejpam-5505	383	18	x	x	SYM
ejpam-5505	383	19	∈	∈	PROPN
ejpam-5505	383	20	(	(	PUNCT
ejpam-5505	383	21	i	i	NOUN
ejpam-5505	383	22	d	d	PROPN
ejpam-5505	383	23	+	+	CCONJ
ejpam-5505	383	24	1	1	NUM
ejpam-5505	383	25	2	2	NUM
ejpam-5505	383	26	a	a	NOUN
ejpam-5505	383	27	)	)	PUNCT
ejpam-5505	383	28	(	(	PUNCT
ejpam-5505	383	29	x	x	X
ejpam-5505	383	30	)	)	PUNCT
ejpam-5505	383	31	⇔	⇔	NOUN
ejpam-5505	383	32	x	x	PUNCT
ejpam-5505	383	33	=	=	SYM
ejpam-5505	383	34	j	j	PROPN
ejpam-5505	383	35	1	1	NUM
ejpam-5505	383	36	2	2	NUM
ejpam-5505	383	37	a	a	PRON
ejpam-5505	383	38	(	(	PUNCT
ejpam-5505	383	39	i	i	NOUN
ejpam-5505	383	40	d	d	PROPN
ejpam-5505	383	41	+	+	CCONJ
ejpam-5505	383	42	r	r	NOUN
ejpam-5505	383	43	2	2	NUM
ejpam-5505	383	44	)	)	PUNCT
ejpam-5505	383	45	(	(	PUNCT
ejpam-5505	383	46	x	x	X
ejpam-5505	383	47	)	)	PUNCT
ejpam-5505	383	48	⇔	⇔	NOUN
ejpam-5505	383	49	x	x	SYM
ejpam-5505	383	50	∈	∈	PROPN
ejpam-5505	383	51	fix	fix	NOUN
ejpam-5505	383	52	j	j	PROPN
ejpam-5505	383	53	1	1	NUM
ejpam-5505	383	54	2	2	NUM
ejpam-5505	383	55	a	a	PRON
ejpam-5505	383	56	(	(	PUNCT
ejpam-5505	383	57	i	i	NOUN
ejpam-5505	383	58	d	d	PROPN
ejpam-5505	383	59	+	+	CCONJ
ejpam-5505	383	60	r	r	NOUN
ejpam-5505	383	61	2	2	NUM
ejpam-5505	383	62	)	)	PUNCT
ejpam-5505	383	63	.	.	PUNCT
ejpam-5505	384	1	■	■	PUNCT
ejpam-5505	384	2	lemma	lemma	PROPN
ejpam-5505	384	3	5	5	NUM
ejpam-5505	384	4	.	.	PUNCT
ejpam-5505	384	5	suppose	suppose	VERB
ejpam-5505	384	6	that	that	SCONJ
ejpam-5505	384	7	fix	fix	NOUN
ejpam-5505	384	8	ji	ji	PROPN
ejpam-5505	384	9	̸=	̸=	PROPN
ejpam-5505	384	10	∅	∅	NOUN
ejpam-5505	384	11	for	for	ADP
ejpam-5505	384	12	each	each	DET
ejpam-5505	384	13	1	1	NUM
ejpam-5505	384	14	≤	≤	NUM
ejpam-5505	384	15	i	i	PRON
ejpam-5505	384	16	≤	≤	ADJ
ejpam-5505	384	17	m.	m.	NOUN
ejpam-5505	384	18	then	then	ADV
ejpam-5505	384	19	the	the	DET
ejpam-5505	384	20	following	follow	VERB
ejpam-5505	384	21	are	be	AUX
ejpam-5505	384	22	equivalent	equivalent	ADJ
ejpam-5505	384	23	:	:	PUNCT
ejpam-5505	384	24	(	(	PUNCT
ejpam-5505	384	25	i	i	NOUN
ejpam-5505	384	26	)	)	PUNCT
ejpam-5505	385	1	∩m	∩m	PROPN
ejpam-5505	386	1	i=1	i=1	PROPN
ejpam-5505	386	2	fix	fix	VERB
ejpam-5505	386	3	ji	ji	PROPN
ejpam-5505	386	4	̸=	̸=	PROPN
ejpam-5505	386	5	∅.	∅.	PROPN
ejpam-5505	386	6	(	(	PUNCT
ejpam-5505	386	7	ii	ii	NOUN
ejpam-5505	386	8	)	)	PUNCT
ejpam-5505	386	9	f1	f1	NOUN
ejpam-5505	386	10	=	=	SYM
ejpam-5505	386	11	f2	f2	PROPN
ejpam-5505	386	12	=	=	SYM
ejpam-5505	386	13	·	·	PUNCT
ejpam-5505	386	14	·	·	PUNCT
ejpam-5505	386	15	·	·	PUNCT
ejpam-5505	387	1	=	=	SYM
ejpam-5505	387	2	fm	fm	X
ejpam-5505	387	3	̸=	̸=	PROPN
ejpam-5505	387	4	∅.	∅.	PRON
ejpam-5505	387	5	proof	proof	NOUN
ejpam-5505	387	6	.	.	PUNCT
ejpam-5505	388	1	(	(	PUNCT
ejpam-5505	388	2	i	i	NOUN
ejpam-5505	388	3	):	):	PUNCT
ejpam-5505	388	4	let	let	VERB
ejpam-5505	388	5	∩m	∩m	PROPN
ejpam-5505	388	6	i=1	i=1	PROPN
ejpam-5505	389	1	fix	fix	VERB
ejpam-5505	389	2	ji	ji	PROPN
ejpam-5505	389	3	̸=	̸=	PROPN
ejpam-5505	389	4	∅	∅	NOUN
ejpam-5505	389	5	⇒	⇒	NOUN
ejpam-5505	389	6	f1	f1	PROPN
ejpam-5505	389	7	̸=	̸=	PROPN
ejpam-5505	389	8	∅	∅	NOUN
ejpam-5505	389	9	,	,	PUNCT
ejpam-5505	389	10	f2	f2	PROPN
ejpam-5505	389	11	̸=	̸=	PROPN
ejpam-5505	389	12	∅	∅	NOUN
ejpam-5505	389	13	,	,	PUNCT
ejpam-5505	389	14	·	·	PUNCT
ejpam-5505	389	15	·	·	PUNCT
ejpam-5505	390	1	·	·	PUNCT
ejpam-5505	390	2	,	,	PUNCT
ejpam-5505	390	3	fm	fm	PROPN
ejpam-5505	390	4	̸=	̸=	PROPN
ejpam-5505	390	5	∅	∅	NOUN
ejpam-5505	390	6	and	and	CCONJ
ejpam-5505	390	7	from	from	ADP
ejpam-5505	390	8	lemma	lemma	PROPN
ejpam-5505	390	9	3(i	3(i	NUM
ejpam-5505	390	10	)	)	PUNCT
ejpam-5505	390	11	,	,	PUNCT
ejpam-5505	390	12	it	it	PRON
ejpam-5505	390	13	follows	follow	VERB
ejpam-5505	390	14	that	that	DET
ejpam-5505	390	15	f1	f1	NOUN
ejpam-5505	390	16	=	=	SYM
ejpam-5505	390	17	f2	f2	PROPN
ejpam-5505	390	18	=	=	SYM
ejpam-5505	390	19	·	·	PUNCT
ejpam-5505	390	20	·	·	PUNCT
ejpam-5505	390	21	·	·	PUNCT
ejpam-5505	391	1	=	=	PUNCT
ejpam-5505	391	2	fm	fm	NOUN
ejpam-5505	392	1	=	=	PUNCT
ejpam-5505	393	1	∩m	∩m	PROPN
ejpam-5505	394	1	i=1	i=1	PRON
ejpam-5505	394	2	fix	fix	VERB
ejpam-5505	394	3	ji	ji	PROPN
ejpam-5505	394	4	.	.	PUNCT
ejpam-5505	395	1	(	(	PUNCT
ejpam-5505	395	2	ii	ii	NOUN
ejpam-5505	395	3	):	):	PUNCT
ejpam-5505	395	4	let	let	VERB
ejpam-5505	395	5	f1	f1	NOUN
ejpam-5505	395	6	=	=	SYM
ejpam-5505	395	7	f2	f2	PROPN
ejpam-5505	395	8	=	=	SYM
ejpam-5505	395	9	·	·	PUNCT
ejpam-5505	395	10	·	·	PUNCT
ejpam-5505	395	11	·	·	PUNCT
ejpam-5505	396	1	=	=	SYM
ejpam-5505	396	2	fm	fm	PROPN
ejpam-5505	396	3	̸=	̸=	PROPN
ejpam-5505	396	4	∅.	∅.	AUX
ejpam-5505	396	5	applying	apply	VERB
ejpam-5505	396	6	theorem	theorem	ADJ
ejpam-5505	396	7	2	2	NUM
ejpam-5505	396	8	(	(	PUNCT
ejpam-5505	396	9	iv	iv	X
ejpam-5505	396	10	)	)	PUNCT
ejpam-5505	396	11	gives	give	VERB
ejpam-5505	396	12	z	z	NOUN
ejpam-5505	396	13	̸=	̸=	PROPN
ejpam-5505	396	14	∅.	∅.	ADP
ejpam-5505	396	15	■	■	X
ejpam-5505	396	16	5	5	NUM
ejpam-5505	396	17	.	.	PUNCT
ejpam-5505	396	18	consequences	consequence	NOUN
ejpam-5505	396	19	of	of	ADP
ejpam-5505	396	20	attouch	attouch	ADJ
ejpam-5505	396	21	-	-	PUNCT
ejpam-5505	396	22	théra	théra	NUM
ejpam-5505	396	23	duality	duality	NOUN
ejpam-5505	396	24	recall	recall	NOUN
ejpam-5505	396	25	(	(	PUNCT
ejpam-5505	396	26	5	5	NUM
ejpam-5505	396	27	)	)	PUNCT
ejpam-5505	396	28	that	that	PRON
ejpam-5505	396	29	a	a	DET
ejpam-5505	396	30	=	=	NOUN
ejpam-5505	396	31	a1	a1	NOUN
ejpam-5505	396	32	×	×	PROPN
ejpam-5505	396	33	a2	a2	PROPN
ejpam-5505	396	34	×	×	PROPN
ejpam-5505	396	35	·	·	PUNCT
ejpam-5505	396	36	·	·	PUNCT
ejpam-5505	396	37	·	·	PUNCT
ejpam-5505	396	38	×	×	NOUN
ejpam-5505	396	39	am	am	NOUN
ejpam-5505	396	40	.	.	PUNCT
ejpam-5505	397	1	s.th.alwadani	s.th.alwadani	ADJ
ejpam-5505	397	2	/	/	SYM
ejpam-5505	397	3	eur	eur	PROPN
ejpam-5505	397	4	.	.	PUNCT
ejpam-5505	398	1	j.	j.	PROPN
ejpam-5505	398	2	pure	pure	PROPN
ejpam-5505	398	3	appl	appl	PROPN
ejpam-5505	398	4	.	.	PROPN
ejpam-5505	398	5	math	math	PROPN
ejpam-5505	398	6	,	,	PUNCT
ejpam-5505	398	7	17	17	NUM
ejpam-5505	398	8	(	(	PUNCT
ejpam-5505	398	9	4	4	NUM
ejpam-5505	398	10	)	)	PUNCT
ejpam-5505	398	11	(	(	PUNCT
ejpam-5505	398	12	2024	2024	NUM
ejpam-5505	398	13	)	)	PUNCT
ejpam-5505	398	14	,	,	PUNCT
ejpam-5505	398	15	3642	3642	NUM
ejpam-5505	398	16	-	-	SYM
ejpam-5505	398	17	3659	3659	NUM
ejpam-5505	398	18	3654	3654	NUM
ejpam-5505	398	19	from	from	ADP
ejpam-5505	398	20	now	now	ADV
ejpam-5505	398	21	on	on	ADV
ejpam-5505	398	22	,	,	PUNCT
ejpam-5505	398	23	suppose	suppose	VERB
ejpam-5505	398	24	that	that	SCONJ
ejpam-5505	398	25	a	a	PRON
ejpam-5505	398	26	is	be	AUX
ejpam-5505	398	27	maximally	maximally	ADV
ejpam-5505	398	28	monotone	monotone	ADJ
ejpam-5505	398	29	on	on	ADP
ejpam-5505	398	30	x	x	SYM
ejpam-5505	398	31	,	,	PUNCT
ejpam-5505	398	32	(	(	PUNCT
ejpam-5505	398	33	50	50	NUM
ejpam-5505	398	34	)	)	PUNCT
ejpam-5505	398	35	and	and	CCONJ
ejpam-5505	398	36	c	c	NOUN
ejpam-5505	398	37	:	:	PUNCT
ejpam-5505	398	38	=	=	PUNCT
ejpam-5505	398	39	zer	zer	X
ejpam-5505	398	40	a	a	PRON
ejpam-5505	398	41	is	be	AUX
ejpam-5505	398	42	not	not	PART
ejpam-5505	398	43	empty	empty	ADJ
ejpam-5505	398	44	.	.	PUNCT
ejpam-5505	399	1	(	(	PUNCT
ejpam-5505	399	2	51	51	NUM
ejpam-5505	399	3	)	)	PUNCT
ejpam-5505	399	4	recall	recall	NOUN
ejpam-5505	399	5	(	(	PUNCT
ejpam-5505	399	6	20	20	NUM
ejpam-5505	399	7	)	)	PUNCT
ejpam-5505	399	8	,	,	PUNCT
ejpam-5505	399	9	which	which	PRON
ejpam-5505	399	10	states	state	VERB
ejpam-5505	399	11	that	that	SCONJ
ejpam-5505	399	12	z	z	NOUN
ejpam-5505	399	13	:	:	PUNCT
ejpam-5505	399	14	=	=	PUNCT
ejpam-5505	399	15	fix(jar	fix(jar	ADJ
ejpam-5505	399	16	)	)	PUNCT
ejpam-5505	399	17	.	.	PUNCT
ejpam-5505	400	1	proposition	proposition	NOUN
ejpam-5505	400	2	1	1	NUM
ejpam-5505	400	3	.	.	PUNCT
ejpam-5505	401	1	the	the	DET
ejpam-5505	401	2	following	follow	VERB
ejpam-5505	401	3	holds	hold	VERB
ejpam-5505	401	4	:	:	PUNCT
ejpam-5505	401	5	(	(	PUNCT
ejpam-5505	401	6	i	i	NOUN
ejpam-5505	401	7	)	)	PUNCT
ejpam-5505	401	8	z	z	NOUN
ejpam-5505	402	1	=	=	NOUN
ejpam-5505	402	2	psol	psol	NOUN
ejpam-5505	402	3	(	(	PUNCT
ejpam-5505	402	4	i	i	NOUN
ejpam-5505	402	5	d	d	NOUN
ejpam-5505	402	6	−	−	PROPN
ejpam-5505	402	7	r	r	NOUN
ejpam-5505	402	8	)	)	PUNCT
ejpam-5505	402	9	.	.	PUNCT
ejpam-5505	403	1	(	(	PUNCT
ejpam-5505	403	2	ii	ii	X
ejpam-5505	403	3	)	)	PUNCT
ejpam-5505	403	4	a	a	PRON
ejpam-5505	404	1	+	+	X
ejpam-5505	404	2	i	i	NOUN
ejpam-5505	404	3	d	d	NOUN
ejpam-5505	404	4	−	−	PROPN
ejpam-5505	405	1	r	r	NOUN
ejpam-5505	405	2	is	be	AUX
ejpam-5505	405	3	maximally	maximally	ADV
ejpam-5505	405	4	monotone	monotone	ADJ
ejpam-5505	405	5	.	.	PUNCT
ejpam-5505	406	1	(	(	PUNCT
ejpam-5505	406	2	iii	iii	X
ejpam-5505	406	3	)	)	PUNCT
ejpam-5505	406	4	z	z	NOUN
ejpam-5505	406	5	is	be	AUX
ejpam-5505	406	6	closed	close	VERB
ejpam-5505	406	7	and	and	CCONJ
ejpam-5505	406	8	convex	convex	NOUN
ejpam-5505	406	9	.	.	PUNCT
ejpam-5505	407	1	proof	proof	NOUN
ejpam-5505	407	2	.	.	PUNCT
ejpam-5505	408	1	(	(	PUNCT
ejpam-5505	408	2	i	i	NOUN
ejpam-5505	408	3	):	):	PUNCT
ejpam-5505	408	4	combine	combine	VERB
ejpam-5505	408	5	lemma	lemma	PROPN
ejpam-5505	408	6	2	2	NUM
ejpam-5505	408	7	and	and	CCONJ
ejpam-5505	408	8	(	(	PUNCT
ejpam-5505	408	9	13	13	NUM
ejpam-5505	408	10	)	)	PUNCT
ejpam-5505	408	11	.	.	PUNCT
ejpam-5505	409	1	(	(	PUNCT
ejpam-5505	409	2	ii	ii	NOUN
ejpam-5505	409	3	):	):	PUNCT
ejpam-5505	409	4	note	note	VERB
ejpam-5505	409	5	that	that	SCONJ
ejpam-5505	410	1	i	i	PRON
ejpam-5505	410	2	d	d	NOUN
ejpam-5505	410	3	−	−	PROPN
ejpam-5505	411	1	r	r	NOUN
ejpam-5505	411	2	is	be	AUX
ejpam-5505	411	3	linear	linear	ADJ
ejpam-5505	411	4	,	,	PUNCT
ejpam-5505	411	5	full	full	ADJ
ejpam-5505	411	6	domain	domain	NOUN
ejpam-5505	411	7	,	,	PUNCT
ejpam-5505	411	8	and	and	CCONJ
ejpam-5505	411	9	maximally	maximally	ADV
ejpam-5505	411	10	monotone	monotone	ADJ
ejpam-5505	411	11	by	by	ADP
ejpam-5505	411	12	[	[	X
ejpam-5505	411	13	2	2	NUM
ejpam-5505	411	14	,	,	PUNCT
ejpam-5505	411	15	theorem	theorem	VERB
ejpam-5505	411	16	7.1	7.1	NUM
ejpam-5505	411	17	]	]	PUNCT
ejpam-5505	411	18	.	.	PUNCT
ejpam-5505	412	1	moreover	moreover	ADV
ejpam-5505	412	2	,	,	PUNCT
ejpam-5505	412	3	a	a	PRON
ejpam-5505	412	4	is	be	AUX
ejpam-5505	412	5	maximally	maximally	ADV
ejpam-5505	412	6	monotone	monotone	ADJ
ejpam-5505	412	7	by	by	ADP
ejpam-5505	412	8	assumption	assumption	NOUN
ejpam-5505	412	9	.	.	PUNCT
ejpam-5505	413	1	therefore	therefore	ADV
ejpam-5505	413	2	,	,	PUNCT
ejpam-5505	413	3	the	the	DET
ejpam-5505	413	4	sum	sum	NOUN
ejpam-5505	413	5	is	be	AUX
ejpam-5505	413	6	maximally	maximally	ADV
ejpam-5505	413	7	monotone	monotone	ADJ
ejpam-5505	413	8	by	by	ADP
ejpam-5505	413	9	[	[	X
ejpam-5505	413	10	10	10	NUM
ejpam-5505	413	11	,	,	PUNCT
ejpam-5505	413	12	corollary	corollary	ADJ
ejpam-5505	413	13	25.5	25.5	NUM
ejpam-5505	413	14	(	(	PUNCT
ejpam-5505	413	15	i	i	NOUN
ejpam-5505	413	16	)	)	PUNCT
ejpam-5505	413	17	]	]	PUNCT
ejpam-5505	414	1	(	(	PUNCT
ejpam-5505	414	2	iii	iii	X
ejpam-5505	414	3	):	):	PUNCT
ejpam-5505	414	4	it	it	PRON
ejpam-5505	414	5	follows	follow	VERB
ejpam-5505	414	6	directly	directly	ADV
ejpam-5505	414	7	from	from	ADP
ejpam-5505	414	8	(	(	PUNCT
ejpam-5505	414	9	i	i	NOUN
ejpam-5505	414	10	)	)	PUNCT
ejpam-5505	414	11	and	and	CCONJ
ejpam-5505	414	12	theorem	theorem	VERB
ejpam-5505	414	13	2	2	NUM
ejpam-5505	414	14	(	(	PUNCT
ejpam-5505	414	15	v	v	NOUN
ejpam-5505	414	16	)	)	PUNCT
ejpam-5505	414	17	.	.	PUNCT
ejpam-5505	415	1	■	■	PUNCT
ejpam-5505	415	2	theorem	theorem	ADJ
ejpam-5505	415	3	3	3	NUM
ejpam-5505	415	4	.	.	NOUN
ejpam-5505	415	5	recall	recall	NOUN
ejpam-5505	415	6	from	from	ADP
ejpam-5505	415	7	lemma	lemma	PROPN
ejpam-5505	415	8	2	2	NUM
ejpam-5505	415	9	,	,	PUNCT
ejpam-5505	415	10	the	the	DET
ejpam-5505	415	11	primal	primal	ADJ
ejpam-5505	415	12	(	(	PUNCT
ejpam-5505	415	13	attouch	attouch	NOUN
ejpam-5505	415	14	-	-	PUNCT
ejpam-5505	415	15	théra	théra	NUM
ejpam-5505	415	16	)	)	PUNCT
ejpam-5505	415	17	problem	problem	NOUN
ejpam-5505	415	18	:	:	PUNCT
ejpam-5505	415	19	0	0	NUM
ejpam-5505	415	20	∈	∈	PROPN
ejpam-5505	415	21	a(z	a(z	PROPN
ejpam-5505	415	22	)	)	PUNCT
ejpam-5505	416	1	+	+	CCONJ
ejpam-5505	416	2	(	(	PUNCT
ejpam-5505	416	3	i	i	NOUN
ejpam-5505	416	4	d	d	PROPN
ejpam-5505	416	5	−	−	PROPN
ejpam-5505	416	6	r)(z	r)(z	NOUN
ejpam-5505	416	7	)	)	PUNCT
ejpam-5505	416	8	,	,	PUNCT
ejpam-5505	416	9	for	for	ADP
ejpam-5505	416	10	the	the	DET
ejpam-5505	416	11	pair	pair	NOUN
ejpam-5505	416	12	(	(	PUNCT
ejpam-5505	416	13	a	a	X
ejpam-5505	416	14	,	,	PUNCT
ejpam-5505	416	15	i	i	PROPN
ejpam-5505	416	16	d	d	NOUN
ejpam-5505	416	17	−	−	NOUN
ejpam-5505	416	18	r	r	NOUN
ejpam-5505	416	19	)	)	PUNCT
ejpam-5505	416	20	.	.	PUNCT
ejpam-5505	417	1	the	the	DET
ejpam-5505	417	2	attouch	attouch	ADJ
ejpam-5505	417	3	-	-	PUNCT
ejpam-5505	417	4	théra	théra	NUM
ejpam-5505	417	5	dual	dual	ADJ
ejpam-5505	417	6	problem	problem	NOUN
ejpam-5505	417	7	is	be	AUX
ejpam-5505	417	8	0	0	NUM
ejpam-5505	417	9	∈	∈	PROPN
ejpam-5505	417	10	a−1(y	a−1(y	PROPN
ejpam-5505	417	11	)	)	PUNCT
ejpam-5505	418	1	+	+	CCONJ
ejpam-5505	418	2	(	(	PUNCT
ejpam-5505	418	3	i	i	NOUN
ejpam-5505	418	4	d	d	PROPN
ejpam-5505	418	5	−	−	PROPN
ejpam-5505	418	6	r)−1(y	r)−1(y	PROPN
ejpam-5505	418	7	)	)	PUNCT
ejpam-5505	418	8	(	(	PUNCT
ejpam-5505	418	9	52	52	NUM
ejpam-5505	418	10	)	)	PUNCT
ejpam-5505	418	11	or	or	CCONJ
ejpam-5505	418	12	0	0	NUM
ejpam-5505	418	13	∈	∈	NOUN
ejpam-5505	418	14	(	(	PUNCT
ejpam-5505	418	15	a−1	a−1	PROPN
ejpam-5505	418	16	+	+	PROPN
ejpam-5505	418	17	nd⊥	nd⊥	PROPN
ejpam-5505	418	18	)	)	PUNCT
ejpam-5505	418	19	(	(	PUNCT
ejpam-5505	418	20	y	y	NOUN
ejpam-5505	418	21	)	)	PUNCT
ejpam-5505	418	22	+	+	CCONJ
ejpam-5505	418	23	(	(	PUNCT
ejpam-5505	418	24	1	1	NUM
ejpam-5505	418	25	2	2	NUM
ejpam-5505	418	26	i	i	NOUN
ejpam-5505	418	27	d	d	PROPN
ejpam-5505	418	28	+	+	PROPN
ejpam-5505	418	29	t	t	PROPN
ejpam-5505	418	30	)	)	PUNCT
ejpam-5505	418	31	(	(	PUNCT
ejpam-5505	418	32	y	y	NOUN
ejpam-5505	418	33	)	)	PUNCT
ejpam-5505	418	34	.	.	PUNCT
ejpam-5505	419	1	(	(	PUNCT
ejpam-5505	419	2	53	53	NUM
ejpam-5505	419	3	)	)	PUNCT
ejpam-5505	419	4	moreover	moreover	ADV
ejpam-5505	419	5	,	,	PUNCT
ejpam-5505	419	6	dsol(a	dsol(a	PROPN
ejpam-5505	419	7	,	,	PUNCT
ejpam-5505	419	8	i	i	PROPN
ejpam-5505	419	9	d	d	NOUN
ejpam-5505	419	10	−	−	NOUN
ejpam-5505	419	11	r	r	NOUN
ejpam-5505	419	12	)	)	PUNCT
ejpam-5505	419	13	=	=	SYM
ejpam-5505	419	14	zer	zer	X
ejpam-5505	419	15	(	(	PUNCT
ejpam-5505	419	16	a−1	a−1	PROPN
ejpam-5505	419	17	+	+	PROPN
ejpam-5505	419	18	nd⊥	nd⊥	PROPN
ejpam-5505	419	19	+	+	CCONJ
ejpam-5505	419	20	1	1	NUM
ejpam-5505	419	21	2	2	NUM
ejpam-5505	419	22	i	i	NOUN
ejpam-5505	419	23	d	d	PROPN
ejpam-5505	419	24	+	+	PROPN
ejpam-5505	419	25	t	t	PROPN
ejpam-5505	419	26	)	)	PUNCT
ejpam-5505	419	27	.	.	PUNCT
ejpam-5505	420	1	(	(	PUNCT
ejpam-5505	420	2	54	54	NUM
ejpam-5505	420	3	)	)	PUNCT
ejpam-5505	420	4	proof	proof	NOUN
ejpam-5505	420	5	.	.	PUNCT
ejpam-5505	421	1	the	the	DET
ejpam-5505	421	2	dual	dual	ADJ
ejpam-5505	421	3	pair	pair	NOUN
ejpam-5505	421	4	of	of	ADP
ejpam-5505	421	5	(	(	PUNCT
ejpam-5505	421	6	a	a	X
ejpam-5505	421	7	,	,	PUNCT
ejpam-5505	421	8	(	(	PUNCT
ejpam-5505	421	9	i	i	NOUN
ejpam-5505	421	10	d	d	NOUN
ejpam-5505	421	11	−	−	PROPN
ejpam-5505	421	12	r	r	NOUN
ejpam-5505	421	13	)	)	PUNCT
ejpam-5505	421	14	)	)	PUNCT
ejpam-5505	421	15	is	be	AUX
ejpam-5505	421	16	(	(	PUNCT
ejpam-5505	421	17	a	a	PRON
ejpam-5505	421	18	,	,	PUNCT
ejpam-5505	421	19	(	(	PUNCT
ejpam-5505	421	20	i	i	NOUN
ejpam-5505	421	21	d	d	NOUN
ejpam-5505	421	22	−	−	PROPN
ejpam-5505	422	1	r	r	NOUN
ejpam-5505	422	2	)	)	PUNCT
ejpam-5505	422	3	)	)	PUNCT
ejpam-5505	422	4	∗	∗	NOUN
ejpam-5505	422	5	=	=	PUNCT
ejpam-5505	422	6	(	(	PUNCT
ejpam-5505	422	7	a−1	a−1	PROPN
ejpam-5505	422	8	,	,	PUNCT
ejpam-5505	422	9	(	(	PUNCT
ejpam-5505	422	10	i	i	NOUN
ejpam-5505	422	11	d	d	NOUN
ejpam-5505	422	12	−	−	PROPN
ejpam-5505	423	1	r	r	NOUN
ejpam-5505	423	2	)	)	PUNCT
ejpam-5505	423	3	−	−	NOUN
ejpam-5505	423	4	>	>	PUNCT
ejpam-5505	423	5	)	)	PUNCT
ejpam-5505	423	6	.	.	PUNCT
ejpam-5505	424	1	because	because	SCONJ
ejpam-5505	424	2	of	of	ADP
ejpam-5505	424	3	the	the	DET
ejpam-5505	424	4	linearity	linearity	NOUN
ejpam-5505	424	5	of	of	ADP
ejpam-5505	424	6	r	r	NOUN
ejpam-5505	424	7	,	,	PUNCT
ejpam-5505	424	8	it	it	PRON
ejpam-5505	424	9	follows	follow	VERB
ejpam-5505	424	10	that	that	SCONJ
ejpam-5505	424	11	(	(	PUNCT
ejpam-5505	424	12	i	i	NOUN
ejpam-5505	424	13	d	d	NOUN
ejpam-5505	424	14	−	−	PROPN
ejpam-5505	424	15	r	r	NOUN
ejpam-5505	424	16	)	)	PUNCT
ejpam-5505	425	1	−	−	NOUN
ejpam-5505	425	2	>	>	X
ejpam-5505	425	3	=	=	PUNCT
ejpam-5505	426	1	(	(	PUNCT
ejpam-5505	426	2	−	−	PROPN
ejpam-5505	426	3	i	i	NOUN
ejpam-5505	426	4	d	d	PROPN
ejpam-5505	426	5	)	)	PUNCT
ejpam-5505	426	6	◦	◦	NOUN
ejpam-5505	426	7	(	(	PUNCT
ejpam-5505	426	8	i	i	NOUN
ejpam-5505	426	9	d	d	NOUN
ejpam-5505	426	10	−	−	PROPN
ejpam-5505	426	11	r	r	NOUN
ejpam-5505	426	12	)	)	PUNCT
ejpam-5505	426	13	−1	−1	NOUN
ejpam-5505	426	14	◦	◦	NOUN
ejpam-5505	426	15	(	(	PUNCT
ejpam-5505	426	16	−id	−id	PROPN
ejpam-5505	426	17	)	)	PUNCT
ejpam-5505	426	18	=	=	SYM
ejpam-5505	426	19	(	(	PUNCT
ejpam-5505	426	20	i	i	NOUN
ejpam-5505	426	21	d	d	NOUN
ejpam-5505	426	22	−	−	PROPN
ejpam-5505	427	1	r	r	NOUN
ejpam-5505	427	2	)	)	PUNCT
ejpam-5505	427	3	−1	−1	NOUN
ejpam-5505	427	4	.	.	PUNCT
ejpam-5505	428	1	hence	hence	ADV
ejpam-5505	428	2	,	,	PUNCT
ejpam-5505	428	3	attouch	attouch	ADJ
ejpam-5505	428	4	-	-	PUNCT
ejpam-5505	428	5	théra	théra	NUM
ejpam-5505	428	6	dual	dual	ADJ
ejpam-5505	428	7	problem	problem	NOUN
ejpam-5505	428	8	simplifies	simplifie	NOUN
ejpam-5505	428	9	to	to	ADP
ejpam-5505	428	10	0	0	NUM
ejpam-5505	428	11	∈	∈	NOUN
ejpam-5505	428	12	a−1(y	a−1(y	PROPN
ejpam-5505	428	13	)	)	PUNCT
ejpam-5505	429	1	+	+	CCONJ
ejpam-5505	429	2	(	(	PUNCT
ejpam-5505	429	3	i	i	NOUN
ejpam-5505	429	4	d	d	NOUN
ejpam-5505	429	5	−	−	PROPN
ejpam-5505	429	6	r	r	NOUN
ejpam-5505	429	7	)	)	PUNCT
ejpam-5505	429	8	−1(y	−1(y	PUNCT
ejpam-5505	429	9	)	)	PUNCT
ejpam-5505	429	10	.	.	PUNCT
ejpam-5505	430	1	s.th.alwadani	s.th.alwadani	ADJ
ejpam-5505	430	2	/	/	SYM
ejpam-5505	430	3	eur	eur	PROPN
ejpam-5505	430	4	.	.	PUNCT
ejpam-5505	431	1	j.	j.	PROPN
ejpam-5505	431	2	pure	pure	PROPN
ejpam-5505	431	3	appl	appl	PROPN
ejpam-5505	431	4	.	.	PROPN
ejpam-5505	431	5	math	math	PROPN
ejpam-5505	431	6	,	,	PUNCT
ejpam-5505	431	7	17	17	NUM
ejpam-5505	431	8	(	(	PUNCT
ejpam-5505	431	9	4	4	NUM
ejpam-5505	431	10	)	)	PUNCT
ejpam-5505	431	11	(	(	PUNCT
ejpam-5505	431	12	2024	2024	NUM
ejpam-5505	431	13	)	)	PUNCT
ejpam-5505	431	14	,	,	PUNCT
ejpam-5505	431	15	3642	3642	NUM
ejpam-5505	431	16	-	-	SYM
ejpam-5505	431	17	3659	3659	NUM
ejpam-5505	431	18	3655	3655	NUM
ejpam-5505	431	19	from	from	ADP
ejpam-5505	431	20	[	[	X
ejpam-5505	431	21	3	3	NUM
ejpam-5505	431	22	,	,	PUNCT
ejpam-5505	431	23	theorem	theorem	VERB
ejpam-5505	431	24	2.8	2.8	NUM
ejpam-5505	431	25	(	(	PUNCT
ejpam-5505	431	26	i	i	NOUN
ejpam-5505	431	27	)	)	PUNCT
ejpam-5505	431	28	]	]	PUNCT
ejpam-5505	431	29	,	,	PUNCT
ejpam-5505	431	30	we	we	PRON
ejpam-5505	431	31	obtain	obtain	VERB
ejpam-5505	431	32	0	0	NUM
ejpam-5505	431	33	∈	∈	NOUN
ejpam-5505	431	34	a−1(y	a−1(y	PROPN
ejpam-5505	431	35	)	)	PUNCT
ejpam-5505	432	1	+	+	CCONJ
ejpam-5505	432	2	(	(	PUNCT
ejpam-5505	432	3	i	i	NOUN
ejpam-5505	432	4	d	d	NOUN
ejpam-5505	432	5	−	−	PROPN
ejpam-5505	432	6	r	r	NOUN
ejpam-5505	432	7	)	)	PUNCT
ejpam-5505	432	8	−1(y	−1(y	PROPN
ejpam-5505	432	9	)	)	PUNCT
ejpam-5505	432	10	⇔	⇔	X
ejpam-5505	432	11	0	0	NUM
ejpam-5505	432	12	∈	∈	PROPN
ejpam-5505	432	13	a−1(y	a−1(y	PROPN
ejpam-5505	432	14	)	)	PUNCT
ejpam-5505	433	1	+	+	CCONJ
ejpam-5505	433	2	(	(	PUNCT
ejpam-5505	433	3	nd⊥	nd⊥	NOUN
ejpam-5505	433	4	+	+	NOUN
ejpam-5505	433	5	1	1	NUM
ejpam-5505	433	6	2	2	NUM
ejpam-5505	433	7	i	i	NOUN
ejpam-5505	433	8	d	d	PROPN
ejpam-5505	433	9	+	+	PROPN
ejpam-5505	433	10	t	t	PROPN
ejpam-5505	433	11	)	)	PUNCT
ejpam-5505	433	12	(	(	PUNCT
ejpam-5505	433	13	y	y	PROPN
ejpam-5505	433	14	)	)	PUNCT
ejpam-5505	433	15	⇔	⇔	PROPN
ejpam-5505	433	16	0	0	NUM
ejpam-5505	433	17	∈	∈	PROPN
ejpam-5505	433	18	(	(	PUNCT
ejpam-5505	433	19	a−1	a−1	PROPN
ejpam-5505	433	20	+	+	PROPN
ejpam-5505	433	21	nd⊥	nd⊥	PROPN
ejpam-5505	433	22	)	)	PUNCT
ejpam-5505	433	23	(	(	PUNCT
ejpam-5505	433	24	y	y	NOUN
ejpam-5505	433	25	)	)	PUNCT
ejpam-5505	434	1	+	+	CCONJ
ejpam-5505	434	2	(	(	PUNCT
ejpam-5505	434	3	1	1	NUM
ejpam-5505	434	4	2	2	NUM
ejpam-5505	434	5	i	i	NOUN
ejpam-5505	434	6	d	d	PROPN
ejpam-5505	434	7	+	+	PROPN
ejpam-5505	434	8	t	t	PROPN
ejpam-5505	434	9	)	)	PUNCT
ejpam-5505	434	10	(	(	PUNCT
ejpam-5505	434	11	y	y	NOUN
ejpam-5505	434	12	)	)	PUNCT
ejpam-5505	434	13	,	,	PUNCT
ejpam-5505	434	14	which	which	DET
ejpam-5505	434	15	verifies	verifie	NOUN
ejpam-5505	434	16	(	(	PUNCT
ejpam-5505	434	17	53	53	NUM
ejpam-5505	434	18	)	)	PUNCT
ejpam-5505	434	19	.	.	PUNCT
ejpam-5505	435	1	next	next	ADV
ejpam-5505	435	2	,	,	PUNCT
ejpam-5505	435	3	applying	apply	VERB
ejpam-5505	435	4	(	(	PUNCT
ejpam-5505	435	5	16	16	NUM
ejpam-5505	435	6	)	)	PUNCT
ejpam-5505	435	7	,	,	PUNCT
ejpam-5505	435	8	(	(	PUNCT
ejpam-5505	435	9	52	52	NUM
ejpam-5505	435	10	)	)	PUNCT
ejpam-5505	435	11	,	,	PUNCT
ejpam-5505	435	12	and	and	CCONJ
ejpam-5505	435	13	(	(	PUNCT
ejpam-5505	435	14	53	53	NUM
ejpam-5505	435	15	)	)	PUNCT
ejpam-5505	435	16	yields	yield	NOUN
ejpam-5505	435	17	dsol(a	dsol(a	PROPN
ejpam-5505	435	18	,	,	PUNCT
ejpam-5505	435	19	i	i	PROPN
ejpam-5505	435	20	d	d	NOUN
ejpam-5505	435	21	−	−	NOUN
ejpam-5505	435	22	r	r	NOUN
ejpam-5505	435	23	)	)	PUNCT
ejpam-5505	435	24	=	=	SYM
ejpam-5505	435	25	zer	zer	X
ejpam-5505	435	26	(	(	PUNCT
ejpam-5505	435	27	a−1	a−1	PROPN
ejpam-5505	435	28	+	+	CCONJ
ejpam-5505	435	29	(	(	PUNCT
ejpam-5505	435	30	i	i	NOUN
ejpam-5505	435	31	d	d	NOUN
ejpam-5505	435	32	−	−	PROPN
ejpam-5505	435	33	r	r	NOUN
ejpam-5505	435	34	)	)	PUNCT
ejpam-5505	435	35	−1	−1	NOUN
ejpam-5505	435	36	)	)	PUNCT
ejpam-5505	436	1	=	=	PUNCT
ejpam-5505	436	2	zer	zer	PROPN
ejpam-5505	436	3	(	(	PUNCT
ejpam-5505	436	4	a−1	a−1	PROPN
ejpam-5505	436	5	+	+	PROPN
ejpam-5505	436	6	nd⊥	nd⊥	PROPN
ejpam-5505	436	7	+	+	CCONJ
ejpam-5505	436	8	1	1	NUM
ejpam-5505	436	9	2	2	NUM
ejpam-5505	436	10	i	i	NOUN
ejpam-5505	436	11	d	d	PROPN
ejpam-5505	436	12	+	+	PROPN
ejpam-5505	436	13	t	t	PROPN
ejpam-5505	436	14	)	)	PUNCT
ejpam-5505	436	15	.	.	PUNCT
ejpam-5505	437	1	■	■	PUNCT
ejpam-5505	437	2	proposition	proposition	NOUN
ejpam-5505	437	3	2	2	NUM
ejpam-5505	437	4	.	.	PUNCT
ejpam-5505	438	1	the	the	DET
ejpam-5505	438	2	solution	solution	NOUN
ejpam-5505	438	3	set	set	VERB
ejpam-5505	438	4	of	of	ADP
ejpam-5505	438	5	(	(	PUNCT
ejpam-5505	438	6	52	52	NUM
ejpam-5505	438	7	)	)	PUNCT
ejpam-5505	438	8	is	be	AUX
ejpam-5505	438	9	at	at	ADP
ejpam-5505	438	10	most	most	ADJ
ejpam-5505	438	11	a	a	DET
ejpam-5505	438	12	sigleton	sigleton	NOUN
ejpam-5505	438	13	and	and	CCONJ
ejpam-5505	438	14	possibly	possibly	ADV
ejpam-5505	438	15	empty	empty	ADJ
ejpam-5505	438	16	.	.	PUNCT
ejpam-5505	439	1	proof	proof	NOUN
ejpam-5505	439	2	.	.	PUNCT
ejpam-5505	440	1	[	[	X
ejpam-5505	440	2	3	3	NUM
ejpam-5505	440	3	,	,	PUNCT
ejpam-5505	440	4	theorem	theorem	VERB
ejpam-5505	440	5	2.8	2.8	NUM
ejpam-5505	440	6	(	(	PUNCT
ejpam-5505	440	7	i	i	NOUN
ejpam-5505	440	8	)	)	PUNCT
ejpam-5505	440	9	]	]	PUNCT
ejpam-5505	441	1	gives	give	VERB
ejpam-5505	441	2	(	(	PUNCT
ejpam-5505	441	3	i	i	NOUN
ejpam-5505	441	4	d	d	NOUN
ejpam-5505	441	5	−	−	PROPN
ejpam-5505	441	6	r	r	NOUN
ejpam-5505	441	7	)	)	PUNCT
ejpam-5505	441	8	−1	−1	NOUN
ejpam-5505	441	9	=	=	VERB
ejpam-5505	442	1	nd⊥	nd⊥	NOUN
ejpam-5505	442	2	+	+	NOUN
ejpam-5505	442	3	1	1	NUM
ejpam-5505	442	4	2	2	NUM
ejpam-5505	442	5	i	i	NOUN
ejpam-5505	442	6	d	d	PROPN
ejpam-5505	443	1	+	+	PROPN
ejpam-5505	443	2	t.	t.	PROPN
ejpam-5505	443	3	i	i	PROPN
ejpam-5505	443	4	d	d	PROPN
ejpam-5505	443	5	−	−	PROPN
ejpam-5505	443	6	r	r	NOUN
ejpam-5505	443	7	is	be	AUX
ejpam-5505	443	8	(	(	PUNCT
ejpam-5505	443	9	1/2)-cocoercive	1/2)-cocoercive	NUM
ejpam-5505	443	10	because	because	SCONJ
ejpam-5505	443	11	r	r	NOUN
ejpam-5505	443	12	is	be	AUX
ejpam-5505	443	13	nonexpansive	nonexpansive	ADJ
ejpam-5505	443	14	by	by	ADP
ejpam-5505	443	15	[	[	X
ejpam-5505	443	16	10	10	NUM
ejpam-5505	443	17	,	,	PUNCT
ejpam-5505	443	18	proposition	proposition	NOUN
ejpam-5505	443	19	4.11	4.11	NUM
ejpam-5505	443	20	]	]	PUNCT
ejpam-5505	443	21	.	.	PUNCT
ejpam-5505	444	1	hence	hence	ADV
ejpam-5505	444	2	,	,	PUNCT
ejpam-5505	444	3	(	(	PUNCT
ejpam-5505	444	4	i	i	NOUN
ejpam-5505	444	5	d	d	NOUN
ejpam-5505	444	6	−	−	PROPN
ejpam-5505	444	7	r	r	NOUN
ejpam-5505	444	8	)	)	PUNCT
ejpam-5505	444	9	−1	−1	NOUN
ejpam-5505	444	10	=	=	VERB
ejpam-5505	445	1	nd⊥	nd⊥	NOUN
ejpam-5505	445	2	+	+	NOUN
ejpam-5505	445	3	1	1	NUM
ejpam-5505	445	4	2	2	NUM
ejpam-5505	445	5	i	i	NOUN
ejpam-5505	445	6	d	d	PROPN
ejpam-5505	446	1	+	+	PROPN
ejpam-5505	446	2	t	t	PROPN
ejpam-5505	446	3	is	be	AUX
ejpam-5505	446	4	(	(	PUNCT
ejpam-5505	446	5	1/2)-strongly	1/2)-strongly	ADV
ejpam-5505	446	6	monotone	monotone	ADJ
ejpam-5505	446	7	by	by	ADP
ejpam-5505	446	8	[	[	X
ejpam-5505	446	9	2	2	NUM
ejpam-5505	446	10	,	,	PUNCT
ejpam-5505	446	11	lemma	lemma	PROPN
ejpam-5505	446	12	7.8(iv	7.8(iv	NUM
ejpam-5505	446	13	)	)	PUNCT
ejpam-5505	446	14	]	]	PUNCT
ejpam-5505	446	15	.	.	PUNCT
ejpam-5505	447	1	then	then	ADV
ejpam-5505	447	2	a−1	a−1	PROPN
ejpam-5505	447	3	+	+	CCONJ
ejpam-5505	447	4	(	(	PUNCT
ejpam-5505	447	5	i	i	NOUN
ejpam-5505	447	6	d	d	NOUN
ejpam-5505	447	7	−	−	PROPN
ejpam-5505	447	8	r	r	NOUN
ejpam-5505	447	9	)	)	PUNCT
ejpam-5505	447	10	−1	−1	NOUN
ejpam-5505	447	11	=	=	NOUN
ejpam-5505	447	12	1	1	NUM
ejpam-5505	447	13	2	2	NUM
ejpam-5505	447	14	i	i	NOUN
ejpam-5505	447	15	d	d	PROPN
ejpam-5505	447	16	+	+	CCONJ
ejpam-5505	447	17	(	(	PUNCT
ejpam-5505	447	18	nd⊥	nd⊥	PROPN
ejpam-5505	447	19	+	+	PROPN
ejpam-5505	447	20	t	t	NOUN
ejpam-5505	447	21	+	+	CCONJ
ejpam-5505	447	22	a−1	a−1	PROPN
ejpam-5505	447	23	)	)	PUNCT
ejpam-5505	447	24	is	be	AUX
ejpam-5505	447	25	strongly	strongly	ADV
ejpam-5505	447	26	monotone	monotone	ADJ
ejpam-5505	447	27	.	.	PUNCT
ejpam-5505	448	1	hence	hence	ADV
ejpam-5505	448	2	,	,	PUNCT
ejpam-5505	448	3	it	it	PRON
ejpam-5505	448	4	follows	follow	VERB
ejpam-5505	448	5	that	that	SCONJ
ejpam-5505	448	6	zer	zer	PROPN
ejpam-5505	448	7	(	(	PUNCT
ejpam-5505	448	8	a−1	a−1	PROPN
ejpam-5505	448	9	+	+	CCONJ
ejpam-5505	448	10	(	(	PUNCT
ejpam-5505	448	11	i	i	NOUN
ejpam-5505	448	12	d	d	NOUN
ejpam-5505	448	13	−	−	PROPN
ejpam-5505	448	14	r	r	NOUN
ejpam-5505	448	15	)	)	PUNCT
ejpam-5505	448	16	−1	−1	NOUN
ejpam-5505	448	17	)	)	PUNCT
ejpam-5505	448	18	=	=	PRON
ejpam-5505	449	1	(	(	PUNCT
ejpam-5505	449	2	a−1	a−1	PROPN
ejpam-5505	449	3	+	+	CCONJ
ejpam-5505	449	4	(	(	PUNCT
ejpam-5505	449	5	i	i	NOUN
ejpam-5505	449	6	d	d	NOUN
ejpam-5505	449	7	−	−	PROPN
ejpam-5505	449	8	r	r	NOUN
ejpam-5505	449	9	)	)	PUNCT
ejpam-5505	449	10	−1	−1	NOUN
ejpam-5505	449	11	)	)	PUNCT
ejpam-5505	449	12	−1	−1	NOUN
ejpam-5505	449	13	(	(	PUNCT
ejpam-5505	449	14	0	0	NUM
ejpam-5505	449	15	)	)	PUNCT
ejpam-5505	449	16	is	be	AUX
ejpam-5505	449	17	at	at	ADP
ejpam-5505	449	18	most	most	ADJ
ejpam-5505	449	19	a	a	DET
ejpam-5505	449	20	singleton	singleton	NOUN
ejpam-5505	449	21	by	by	ADP
ejpam-5505	449	22	[	[	X
ejpam-5505	449	23	10	10	NUM
ejpam-5505	449	24	,	,	PUNCT
ejpam-5505	449	25	proposition	proposition	NOUN
ejpam-5505	449	26	23.35	23.35	NUM
ejpam-5505	449	27	]	]	PUNCT
ejpam-5505	449	28	.	.	PUNCT
ejpam-5505	450	1	■	■	PUNCT
ejpam-5505	450	2	theorem	theorem	ADJ
ejpam-5505	450	3	4	4	NUM
ejpam-5505	450	4	.	.	PUNCT
ejpam-5505	450	5	let	let	VERB
ejpam-5505	450	6	psol(a	psol(a	NUM
ejpam-5505	450	7	,	,	PUNCT
ejpam-5505	450	8	i	i	PROPN
ejpam-5505	450	9	d	d	NOUN
ejpam-5505	450	10	−	−	NOUN
ejpam-5505	450	11	r	r	NOUN
ejpam-5505	450	12	)	)	PUNCT
ejpam-5505	450	13	=	=	SYM
ejpam-5505	450	14	z	z	NOUN
ejpam-5505	450	15	and	and	CCONJ
ejpam-5505	450	16	recall	recall	PROPN
ejpam-5505	450	17	(	(	PUNCT
ejpam-5505	450	18	54	54	NUM
ejpam-5505	450	19	)	)	PUNCT
ejpam-5505	450	20	,	,	PUNCT
ejpam-5505	450	21	which	which	PRON
ejpam-5505	450	22	states	state	VERB
ejpam-5505	450	23	that	that	SCONJ
ejpam-5505	450	24	dsol(a	dsol(a	PROPN
ejpam-5505	450	25	,	,	PUNCT
ejpam-5505	450	26	i	i	PROPN
ejpam-5505	450	27	d	d	NOUN
ejpam-5505	450	28	−	−	NOUN
ejpam-5505	450	29	r	r	NOUN
ejpam-5505	450	30	)	)	PUNCT
ejpam-5505	450	31	=	=	SYM
ejpam-5505	450	32	zer	zer	X
ejpam-5505	450	33	(	(	PUNCT
ejpam-5505	450	34	a−1	a−1	PROPN
ejpam-5505	450	35	+	+	PROPN
ejpam-5505	450	36	nd⊥	nd⊥	PROPN
ejpam-5505	450	37	+	+	CCONJ
ejpam-5505	450	38	1	1	NUM
ejpam-5505	450	39	2	2	NUM
ejpam-5505	450	40	i	i	NOUN
ejpam-5505	450	41	d	d	PROPN
ejpam-5505	450	42	+	+	PROPN
ejpam-5505	450	43	t	t	PROPN
ejpam-5505	450	44	)	)	PUNCT
ejpam-5505	450	45	.	.	PUNCT
ejpam-5505	451	1	then	then	ADV
ejpam-5505	451	2	dsol	dsol	VERB
ejpam-5505	451	3	(	(	PUNCT
ejpam-5505	451	4	i	i	NOUN
ejpam-5505	451	5	d	d	NOUN
ejpam-5505	451	6	−	−	PROPN
ejpam-5505	451	7	r	r	NOUN
ejpam-5505	451	8	)	)	PUNCT
ejpam-5505	451	9	=	=	PUNCT
ejpam-5505	452	1	(	(	PUNCT
ejpam-5505	452	2	r	r	NOUN
ejpam-5505	452	3	−	−	PROPN
ejpam-5505	452	4	i	i	PROPN
ejpam-5505	452	5	d	d	PROPN
ejpam-5505	452	6	)	)	PUNCT
ejpam-5505	452	7	z	z	NOUN
ejpam-5505	453	1	=	=	PUNCT
ejpam-5505	453	2			PUNCT
ejpam-5505	453	3	{	{	PUNCT
ejpam-5505	453	4	j2(a−1+nd⊥+t)(0	j2(a−1+nd⊥+t)(0	PROPN
ejpam-5505	453	5	)	)	PUNCT
ejpam-5505	453	6	}	}	PUNCT
ejpam-5505	453	7	,	,	PUNCT
ejpam-5505	453	8	i	i	PRON
ejpam-5505	453	9	f	f	PROPN
ejpam-5505	453	10	z	z	PROPN
ejpam-5505	453	11	̸=	̸=	PROPN
ejpam-5505	453	12	∅	∅	NOUN
ejpam-5505	453	13	∅	∅	NOUN
ejpam-5505	453	14	,	,	PUNCT
ejpam-5505	453	15	i	i	PRON
ejpam-5505	453	16	f	f	NOUN
ejpam-5505	453	17	z	z	NOUN
ejpam-5505	453	18	=	=	PUNCT
ejpam-5505	453	19	∅.	∅.	X
ejpam-5505	453	20	(	(	PUNCT
ejpam-5505	453	21	55	55	NUM
ejpam-5505	453	22	)	)	PUNCT
ejpam-5505	453	23	moreover	moreover	ADV
ejpam-5505	453	24	,	,	PUNCT
ejpam-5505	453	25	if	if	SCONJ
ejpam-5505	453	26	y∗	y∗	ADV
ejpam-5505	453	27	:	:	PUNCT
ejpam-5505	453	28	=	=	SYM
ejpam-5505	453	29	j2(a−1+nd⊥+t)(0	j2(a−1+nd⊥+t)(0	PROPN
ejpam-5505	453	30	)	)	PUNCT
ejpam-5505	453	31	exists	exist	VERB
ejpam-5505	453	32	,	,	PUNCT
ejpam-5505	453	33	then	then	ADV
ejpam-5505	453	34	the	the	DET
ejpam-5505	453	35	following	follow	VERB
ejpam-5505	453	36	holds	hold	VERB
ejpam-5505	453	37	:	:	PUNCT
ejpam-5505	453	38	(	(	PUNCT
ejpam-5505	453	39	i	i	NOUN
ejpam-5505	453	40	)	)	PUNCT
ejpam-5505	453	41	y∗	y∗	PROPN
ejpam-5505	453	42	∈	∈	PROPN
ejpam-5505	453	43	d⊥.	d⊥.	NOUN
ejpam-5505	453	44	(	(	PUNCT
ejpam-5505	453	45	ii	ii	NOUN
ejpam-5505	453	46	)	)	PUNCT
ejpam-5505	453	47	y∗	y∗	ADV
ejpam-5505	453	48	is	be	AUX
ejpam-5505	453	49	the	the	DET
ejpam-5505	453	50	only	only	ADJ
ejpam-5505	453	51	vector	vector	NOUN
ejpam-5505	453	52	that	that	PRON
ejpam-5505	453	53	makes	make	VERB
ejpam-5505	453	54	a−1y	a−1y	NOUN
ejpam-5505	453	55	∩−(nd⊥y	∩−(nd⊥y	ADV
ejpam-5505	453	56	+	+	CCONJ
ejpam-5505	453	57	1	1	NUM
ejpam-5505	453	58	2	2	NUM
ejpam-5505	453	59	y	y	NOUN
ejpam-5505	453	60	+	+	CCONJ
ejpam-5505	453	61	ty	ty	NOUN
ejpam-5505	453	62	)	)	PUNCT
ejpam-5505	453	63	non	non	ADJ
ejpam-5505	453	64	-	-	ADJ
ejpam-5505	453	65	empty	empty	ADJ
ejpam-5505	453	66	.	.	PUNCT
ejpam-5505	454	1	(	(	PUNCT
ejpam-5505	454	2	iii	iii	X
ejpam-5505	454	3	)	)	PUNCT
ejpam-5505	454	4	z	z	NOUN
ejpam-5505	454	5	=	=	SYM
ejpam-5505	454	6	a−1y∗	a−1y∗	PROPN
ejpam-5505	454	7	∩	∩	NOUN
ejpam-5505	454	8	(	(	PUNCT
ejpam-5505	454	9	−	−	PROPN
ejpam-5505	454	10	1	1	NUM
ejpam-5505	454	11	2	2	NUM
ejpam-5505	454	12	y∗	y∗	ADV
ejpam-5505	454	13	−	−	PROPN
ejpam-5505	454	14	ty∗	ty∗	NOUN
ejpam-5505	454	15	−	−	PROPN
ejpam-5505	454	16	d	d	NOUN
ejpam-5505	454	17	)	)	PUNCT
ejpam-5505	454	18	.	.	PUNCT
ejpam-5505	455	1	s.th.alwadani	s.th.alwadani	ADJ
ejpam-5505	455	2	/	/	SYM
ejpam-5505	455	3	eur	eur	PROPN
ejpam-5505	455	4	.	.	PUNCT
ejpam-5505	456	1	j.	j.	PROPN
ejpam-5505	456	2	pure	pure	PROPN
ejpam-5505	456	3	appl	appl	PROPN
ejpam-5505	456	4	.	.	PROPN
ejpam-5505	456	5	math	math	PROPN
ejpam-5505	456	6	,	,	PUNCT
ejpam-5505	456	7	17	17	NUM
ejpam-5505	456	8	(	(	PUNCT
ejpam-5505	456	9	4	4	NUM
ejpam-5505	456	10	)	)	PUNCT
ejpam-5505	456	11	(	(	PUNCT
ejpam-5505	456	12	2024	2024	NUM
ejpam-5505	456	13	)	)	PUNCT
ejpam-5505	456	14	,	,	PUNCT
ejpam-5505	456	15	3642	3642	NUM
ejpam-5505	456	16	-	-	SYM
ejpam-5505	456	17	3659	3659	NUM
ejpam-5505	456	18	3656	3656	NUM
ejpam-5505	456	19	proof	proof	NOUN
ejpam-5505	456	20	.	.	PUNCT
ejpam-5505	457	1	by	by	ADP
ejpam-5505	457	2	using	use	VERB
ejpam-5505	457	3	(	(	PUNCT
ejpam-5505	457	4	16	16	NUM
ejpam-5505	457	5	)	)	PUNCT
ejpam-5505	457	6	,	,	PUNCT
ejpam-5505	457	7	we	we	PRON
ejpam-5505	457	8	have	have	VERB
ejpam-5505	457	9	y	y	PROPN
ejpam-5505	457	10	∈	∈	PROPN
ejpam-5505	457	11	dsol	dsol	NOUN
ejpam-5505	457	12	(	(	PUNCT
ejpam-5505	457	13	a	a	X
ejpam-5505	457	14	,	,	PUNCT
ejpam-5505	457	15	i	i	PROPN
ejpam-5505	457	16	d	d	NOUN
ejpam-5505	457	17	−	−	PROPN
ejpam-5505	457	18	r	r	NOUN
ejpam-5505	457	19	)	)	PUNCT
ejpam-5505	457	20	.	.	PUNCT
ejpam-5505	458	1	this	this	PRON
ejpam-5505	458	2	implies	imply	VERB
ejpam-5505	458	3	that	that	SCONJ
ejpam-5505	458	4	0	0	NUM
ejpam-5505	458	5	∈	∈	PROPN
ejpam-5505	458	6	a−1(y	a−1(y	PROPN
ejpam-5505	458	7	)	)	PUNCT
ejpam-5505	459	1	+	+	CCONJ
ejpam-5505	459	2	(	(	PUNCT
ejpam-5505	459	3	i	i	NOUN
ejpam-5505	459	4	d	d	PROPN
ejpam-5505	459	5	−	−	PROPN
ejpam-5505	459	6	r)−1(y	r)−1(y	PROPN
ejpam-5505	459	7	)	)	PUNCT
ejpam-5505	459	8	(	(	PUNCT
ejpam-5505	459	9	∀z	∀z	NOUN
ejpam-5505	459	10	∈	∈	PROPN
ejpam-5505	459	11	z	z	PROPN
ejpam-5505	459	12	)	)	PUNCT
ejpam-5505	459	13	⇔	⇔	PROPN
ejpam-5505	459	14	z	z	PROPN
ejpam-5505	459	15	∈	∈	PROPN
ejpam-5505	459	16	a−1(y	a−1(y	PROPN
ejpam-5505	459	17	)	)	PUNCT
ejpam-5505	459	18	and	and	CCONJ
ejpam-5505	459	19	−	−	PROPN
ejpam-5505	459	20	z	z	NOUN
ejpam-5505	459	21	∈	∈	PROPN
ejpam-5505	459	22	(	(	PUNCT
ejpam-5505	459	23	i	i	NOUN
ejpam-5505	459	24	d	d	PROPN
ejpam-5505	459	25	−	−	PROPN
ejpam-5505	459	26	r)−1(y	r)−1(y	PROPN
ejpam-5505	459	27	)	)	PUNCT
ejpam-5505	459	28	(	(	PUNCT
ejpam-5505	459	29	∀z	∀z	NOUN
ejpam-5505	459	30	∈	∈	PROPN
ejpam-5505	459	31	z	z	PROPN
ejpam-5505	459	32	)	)	PUNCT
ejpam-5505	459	33	⇔	⇔	PROPN
ejpam-5505	459	34	y	y	PROPN
ejpam-5505	459	35	∈	∈	PROPN
ejpam-5505	459	36	a(z	a(z	PROPN
ejpam-5505	459	37	)	)	PUNCT
ejpam-5505	459	38	and	and	CCONJ
ejpam-5505	459	39	y	y	NOUN
ejpam-5505	459	40	=	=	PUNCT
ejpam-5505	459	41	(	(	PUNCT
ejpam-5505	459	42	i	i	NOUN
ejpam-5505	459	43	d	d	PROPN
ejpam-5505	459	44	−	−	PROPN
ejpam-5505	459	45	r)(−z	r)(−z	NUM
ejpam-5505	459	46	)	)	PUNCT
ejpam-5505	459	47	(	(	PUNCT
ejpam-5505	459	48	∀z	∀z	NOUN
ejpam-5505	459	49	∈	∈	PROPN
ejpam-5505	459	50	z	z	PROPN
ejpam-5505	459	51	)	)	PUNCT
ejpam-5505	459	52	.	.	PUNCT
ejpam-5505	460	1	hence	hence	ADV
ejpam-5505	460	2	,	,	PUNCT
ejpam-5505	460	3	for	for	ADP
ejpam-5505	460	4	all	all	DET
ejpam-5505	460	5	z	z	NOUN
ejpam-5505	460	6	∈	∈	PROPN
ejpam-5505	460	7	z	z	NOUN
ejpam-5505	460	8	,	,	PUNCT
ejpam-5505	460	9	it	it	PRON
ejpam-5505	460	10	follows	follow	VERB
ejpam-5505	460	11	that	that	SCONJ
ejpam-5505	460	12	y	y	PROPN
ejpam-5505	460	13	=	=	SYM
ejpam-5505	460	14	rz	rz	NOUN
ejpam-5505	460	15	−	−	PROPN
ejpam-5505	460	16	z	z	PROPN
ejpam-5505	460	17	and	and	CCONJ
ejpam-5505	460	18	dsol	dsol	VERB
ejpam-5505	460	19	(	(	PUNCT
ejpam-5505	460	20	i	i	NOUN
ejpam-5505	460	21	d	d	NOUN
ejpam-5505	460	22	−	−	PROPN
ejpam-5505	461	1	r	r	NOUN
ejpam-5505	461	2	)	)	PUNCT
ejpam-5505	462	1	=	=	SYM
ejpam-5505	462	2	∪z∈z{rz	∪z∈z{rz	NUM
ejpam-5505	462	3	−	−	PROPN
ejpam-5505	463	1	z	z	NOUN
ejpam-5505	464	1	|	|	ADV
ejpam-5505	464	2	z	z	PROPN
ejpam-5505	464	3	∈	∈	PROPN
ejpam-5505	465	1	z	z	X
ejpam-5505	465	2	}	}	PUNCT
ejpam-5505	465	3	=	=	SYM
ejpam-5505	465	4	(	(	PUNCT
ejpam-5505	465	5	r	r	NOUN
ejpam-5505	465	6	−	−	PROPN
ejpam-5505	465	7	i	i	PROPN
ejpam-5505	465	8	d	d	PROPN
ejpam-5505	465	9	)	)	PUNCT
ejpam-5505	465	10	z.	z.	PROPN
ejpam-5505	466	1	additionally	additionally	ADV
ejpam-5505	466	2	,	,	PUNCT
ejpam-5505	466	3	if	if	SCONJ
ejpam-5505	466	4	z	z	PROPN
ejpam-5505	466	5	̸=	̸=	PROPN
ejpam-5505	466	6	∅	∅	NOUN
ejpam-5505	466	7	,	,	PUNCT
ejpam-5505	466	8	then	then	ADV
ejpam-5505	466	9	using	use	VERB
ejpam-5505	466	10	[	[	X
ejpam-5505	466	11	3	3	NUM
ejpam-5505	466	12	,	,	PUNCT
ejpam-5505	466	13	theorem	theorem	VERB
ejpam-5505	466	14	2.4	2.4	NUM
ejpam-5505	466	15	]	]	PUNCT
ejpam-5505	466	16	and	and	CCONJ
ejpam-5505	466	17	(	(	PUNCT
ejpam-5505	466	18	3	3	X
ejpam-5505	466	19	)	)	PUNCT
ejpam-5505	466	20	gives	give	VERB
ejpam-5505	466	21	0	0	NUM
ejpam-5505	466	22	∈	∈	PROPN
ejpam-5505	466	23	a−1(y	a−1(y	PROPN
ejpam-5505	466	24	)	)	PUNCT
ejpam-5505	467	1	+	+	CCONJ
ejpam-5505	467	2	(	(	PUNCT
ejpam-5505	467	3	i	i	NOUN
ejpam-5505	467	4	d	d	PROPN
ejpam-5505	467	5	−	−	PROPN
ejpam-5505	467	6	r)−1(y	r)−1(y	PROPN
ejpam-5505	467	7	)	)	PUNCT
ejpam-5505	467	8	⇔	⇔	X
ejpam-5505	467	9	0	0	NUM
ejpam-5505	467	10	∈	∈	PROPN
ejpam-5505	467	11	a−1(y	a−1(y	PROPN
ejpam-5505	467	12	)	)	PUNCT
ejpam-5505	468	1	+	+	CCONJ
ejpam-5505	468	2	(	(	PUNCT
ejpam-5505	468	3	1	1	NUM
ejpam-5505	468	4	2	2	NUM
ejpam-5505	468	5	i	i	NOUN
ejpam-5505	468	6	d	d	PROPN
ejpam-5505	468	7	+	+	PROPN
ejpam-5505	468	8	t	t	PROPN
ejpam-5505	468	9	+	+	CCONJ
ejpam-5505	468	10	nd⊥	nd⊥	PROPN
ejpam-5505	468	11	)	)	PUNCT
ejpam-5505	468	12	(	(	PUNCT
ejpam-5505	468	13	y	y	X
ejpam-5505	468	14	)	)	PUNCT
ejpam-5505	468	15	⇔	⇔	NOUN
ejpam-5505	468	16	0	0	SYM
ejpam-5505	468	17	∈	∈	PROPN
ejpam-5505	468	18	(	(	PUNCT
ejpam-5505	468	19	i	i	NOUN
ejpam-5505	468	20	d	d	PROPN
ejpam-5505	468	21	+	+	PROPN
ejpam-5505	468	22	2	2	NUM
ejpam-5505	468	23	(	(	PUNCT
ejpam-5505	468	24	a−1	a−1	PROPN
ejpam-5505	468	25	+	+	PROPN
ejpam-5505	468	26	t	t	PROPN
ejpam-5505	468	27	+	+	CCONJ
ejpam-5505	468	28	nd⊥	nd⊥	PROPN
ejpam-5505	468	29	)	)	PUNCT
ejpam-5505	468	30	)	)	PUNCT
ejpam-5505	468	31	(	(	PUNCT
ejpam-5505	468	32	y	y	X
ejpam-5505	468	33	)	)	PUNCT
ejpam-5505	468	34	⇔	⇔	PROPN
ejpam-5505	468	35	y	y	PROPN
ejpam-5505	469	1	=	=	PRON
ejpam-5505	470	1	(	(	PUNCT
ejpam-5505	470	2	i	i	PROPN
ejpam-5505	470	3	d	d	PROPN
ejpam-5505	470	4	+	+	PROPN
ejpam-5505	470	5	2	2	NUM
ejpam-5505	470	6	(	(	PUNCT
ejpam-5505	470	7	a−1	a−1	PROPN
ejpam-5505	470	8	+	+	PROPN
ejpam-5505	470	9	t	t	PROPN
ejpam-5505	470	10	+	+	CCONJ
ejpam-5505	470	11	nd⊥	nd⊥	PROPN
ejpam-5505	470	12	)	)	PUNCT
ejpam-5505	470	13	)	)	PUNCT
ejpam-5505	470	14	−1	−1	NOUN
ejpam-5505	470	15	(	(	PUNCT
ejpam-5505	470	16	0	0	NUM
ejpam-5505	470	17	)	)	PUNCT
ejpam-5505	471	1	⇔	⇔	PROPN
ejpam-5505	471	2	y	y	PROPN
ejpam-5505	471	3	=	=	PUNCT
ejpam-5505	471	4	j2(a−1+t+nd⊥	j2(a−1+t+nd⊥	PROPN
ejpam-5505	471	5	)	)	PUNCT
ejpam-5505	471	6	(	(	PUNCT
ejpam-5505	471	7	0	0	NUM
ejpam-5505	471	8	)	)	PUNCT
ejpam-5505	471	9	.	.	PUNCT
ejpam-5505	472	1	however	however	ADV
ejpam-5505	472	2	,	,	PUNCT
ejpam-5505	472	3	if	if	SCONJ
ejpam-5505	472	4	z	z	NOUN
ejpam-5505	472	5	=	=	SYM
ejpam-5505	472	6	∅	∅	NOUN
ejpam-5505	472	7	,	,	PUNCT
ejpam-5505	472	8	then	then	ADV
ejpam-5505	472	9	using	use	VERB
ejpam-5505	472	10	[	[	X
ejpam-5505	472	11	9	9	NUM
ejpam-5505	472	12	,	,	PUNCT
ejpam-5505	472	13	proposition	proposition	NOUN
ejpam-5505	472	14	2.4	2.4	NUM
ejpam-5505	472	15	(	(	PUNCT
ejpam-5505	472	16	v	v	NOUN
ejpam-5505	472	17	)	)	PUNCT
ejpam-5505	472	18	]	]	PUNCT
ejpam-5505	472	19	∅	∅	NOUN
ejpam-5505	472	20	=	=	PUNCT
ejpam-5505	472	21	dsol	dsol	NOUN
ejpam-5505	472	22	(	(	PUNCT
ejpam-5505	472	23	a	a	X
ejpam-5505	472	24	,	,	PUNCT
ejpam-5505	472	25	i	i	PROPN
ejpam-5505	472	26	d	d	NOUN
ejpam-5505	472	27	−	−	PROPN
ejpam-5505	472	28	r	r	NOUN
ejpam-5505	472	29	)	)	PUNCT
ejpam-5505	472	30	=	=	PUNCT
ejpam-5505	472	31	dsol	dsol	NOUN
ejpam-5505	472	32	(	(	PUNCT
ejpam-5505	472	33	i	i	NOUN
ejpam-5505	472	34	d	d	NOUN
ejpam-5505	472	35	−	−	PROPN
ejpam-5505	472	36	r	r	NOUN
ejpam-5505	472	37	)	)	PUNCT
ejpam-5505	472	38	.	.	PUNCT
ejpam-5505	473	1	(	(	PUNCT
ejpam-5505	473	2	i	i	NOUN
ejpam-5505	473	3	):	):	PUNCT
ejpam-5505	473	4	by	by	ADP
ejpam-5505	473	5	[	[	X
ejpam-5505	473	6	3	3	NUM
ejpam-5505	473	7	,	,	PUNCT
ejpam-5505	473	8	theorem	theorem	VERB
ejpam-5505	473	9	2.7	2.7	NUM
ejpam-5505	473	10	]	]	PUNCT
ejpam-5505	473	11	,	,	PUNCT
ejpam-5505	473	12	we	we	PRON
ejpam-5505	473	13	have	have	VERB
ejpam-5505	473	14	dom(id	dom(id	NOUN
ejpam-5505	473	15	−	−	PROPN
ejpam-5505	473	16	r)−1	r)−1	NOUN
ejpam-5505	473	17	=	=	NOUN
ejpam-5505	473	18	d⊥.	d⊥.	NOUN
ejpam-5505	473	19	this	this	PRON
ejpam-5505	473	20	implies	imply	VERB
ejpam-5505	473	21	that	that	SCONJ
ejpam-5505	473	22	y	y	PROPN
ejpam-5505	473	23	∈	∈	PROPN
ejpam-5505	473	24	d⊥.	d⊥.	NOUN
ejpam-5505	473	25	(	(	PUNCT
ejpam-5505	473	26	ii	ii	PROPN
ejpam-5505	473	27	):	):	PUNCT
ejpam-5505	473	28	combine	combine	VERB
ejpam-5505	473	29	proposition	proposition	NOUN
ejpam-5505	473	30	2	2	NUM
ejpam-5505	473	31	and	and	CCONJ
ejpam-5505	473	32	[	[	X
ejpam-5505	473	33	9	9	NUM
ejpam-5505	473	34	,	,	PUNCT
ejpam-5505	473	35	proposition	proposition	NOUN
ejpam-5505	473	36	2.4	2.4	NUM
ejpam-5505	473	37	]	]	PUNCT
ejpam-5505	473	38	.	.	PUNCT
ejpam-5505	474	1	(	(	PUNCT
ejpam-5505	474	2	iii	iii	X
ejpam-5505	474	3	):	):	PUNCT
ejpam-5505	474	4	combine	combine	PROPN
ejpam-5505	474	5	(	(	PUNCT
ejpam-5505	474	6	i	i	NOUN
ejpam-5505	474	7	)	)	PUNCT
ejpam-5505	474	8	,	,	PUNCT
ejpam-5505	474	9	(	(	PUNCT
ejpam-5505	474	10	ii	ii	NOUN
ejpam-5505	474	11	)	)	PUNCT
ejpam-5505	474	12	,	,	PUNCT
ejpam-5505	474	13	and	and	CCONJ
ejpam-5505	474	14	[	[	X
ejpam-5505	474	15	2	2	NUM
ejpam-5505	474	16	,	,	PUNCT
ejpam-5505	474	17	proposition	proposition	NOUN
ejpam-5505	474	18	9.3	9.3	NUM
ejpam-5505	474	19	(	(	PUNCT
ejpam-5505	474	20	i	i	NOUN
ejpam-5505	474	21	)	)	PUNCT
ejpam-5505	474	22	]	]	PUNCT
ejpam-5505	474	23	where	where	SCONJ
ejpam-5505	474	24	n−1	n−1	PROPN
ejpam-5505	474	25	c	c	PROPN
ejpam-5505	474	26	is	be	AUX
ejpam-5505	474	27	replaced	replace	VERB
ejpam-5505	474	28	by	by	ADP
ejpam-5505	474	29	a−1	a−1	PROPN
ejpam-5505	474	30	.	.	PUNCT
ejpam-5505	475	1	■	■	PUNCT
ejpam-5505	475	2	lemma	lemma	PROPN
ejpam-5505	475	3	6	6	NUM
ejpam-5505	475	4	.	.	PUNCT
ejpam-5505	475	5	denote	denote	VERB
ejpam-5505	475	6	by	by	ADP
ejpam-5505	475	7	y∗	y∗	PROPN
ejpam-5505	475	8	=	=	SYM
ejpam-5505	475	9	(	(	PUNCT
ejpam-5505	475	10	y1	y1	INTJ
ejpam-5505	475	11	,	,	PUNCT
ejpam-5505	475	12	y2	y2	PROPN
ejpam-5505	475	13	,	,	PUNCT
ejpam-5505	475	14	·	·	PUNCT
ejpam-5505	475	15	·	·	PUNCT
ejpam-5505	475	16	·	·	PUNCT
ejpam-5505	475	17	,	,	PUNCT
ejpam-5505	475	18	ym	ym	INTJ
ejpam-5505	475	19	)	)	PUNCT
ejpam-5505	475	20	the	the	DET
ejpam-5505	475	21	unique	unique	ADJ
ejpam-5505	475	22	solution	solution	NOUN
ejpam-5505	475	23	of	of	ADP
ejpam-5505	475	24	(	(	PUNCT
ejpam-5505	475	25	53	53	NUM
ejpam-5505	475	26	)	)	PUNCT
ejpam-5505	475	27	.	.	PUNCT
ejpam-5505	476	1	then	then	ADV
ejpam-5505	476	2	the	the	DET
ejpam-5505	476	3	following	follow	VERB
ejpam-5505	476	4	holds	hold	VERB
ejpam-5505	476	5	:	:	PUNCT
ejpam-5505	476	6	(	(	PUNCT
ejpam-5505	476	7	i	i	NOUN
ejpam-5505	476	8	)	)	PUNCT
ejpam-5505	476	9	the	the	DET
ejpam-5505	476	10	mapping	mapping	NOUN
ejpam-5505	476	11	j1	j1	NOUN
ejpam-5505	476	12	:	:	PUNCT
ejpam-5505	476	13	fm	fm	PROPN
ejpam-5505	476	14	→	→	SYM
ejpam-5505	476	15	f1	f1	PROPN
ejpam-5505	476	16	is	be	AUX
ejpam-5505	476	17	bijective	bijective	ADJ
ejpam-5505	476	18	on	on	ADP
ejpam-5505	476	19	fm	fm	PROPN
ejpam-5505	476	20	and	and	CCONJ
ejpam-5505	476	21	it	it	PRON
ejpam-5505	476	22	is	be	AUX
ejpam-5505	476	23	given	give	VERB
ejpam-5505	476	24	by	by	ADP
ejpam-5505	476	25	j1	j1	PROPN
ejpam-5505	476	26	(	(	PUNCT
ejpam-5505	476	27	z	z	NOUN
ejpam-5505	476	28	)	)	PUNCT
ejpam-5505	477	1	=	=	PUNCT
ejpam-5505	477	2	z	z	NOUN
ejpam-5505	478	1	−	−	PROPN
ejpam-5505	478	2	y1	y1	NOUN
ejpam-5505	478	3	.	.	PUNCT
ejpam-5505	479	1	moreover	moreover	ADV
ejpam-5505	479	2	,	,	PUNCT
ejpam-5505	479	3	for	for	ADP
ejpam-5505	479	4	1	1	NUM
ejpam-5505	479	5	≤	≤	NUM
ejpam-5505	479	6	i	i	PRON
ejpam-5505	479	7	≤	≤	NOUN
ejpam-5505	479	8	m	m	VERB
ejpam-5505	479	9	−	−	PROPN
ejpam-5505	479	10	1	1	NUM
ejpam-5505	479	11	the	the	DET
ejpam-5505	479	12	mapping	mapping	NOUN
ejpam-5505	479	13	ji+1	ji+1	NOUN
ejpam-5505	479	14	:	:	PUNCT
ejpam-5505	479	15	fi	fi	NOUN
ejpam-5505	479	16	→	→	PUNCT
ejpam-5505	479	17	fi+1	fi+1	PROPN
ejpam-5505	479	18	is	be	AUX
ejpam-5505	479	19	bijective	bijective	ADJ
ejpam-5505	479	20	and	and	CCONJ
ejpam-5505	479	21	is	be	AUX
ejpam-5505	479	22	given	give	VERB
ejpam-5505	479	23	by	by	ADP
ejpam-5505	479	24	ji+1	ji+1	PROPN
ejpam-5505	479	25	(	(	PUNCT
ejpam-5505	479	26	z	z	NOUN
ejpam-5505	479	27	)	)	PUNCT
ejpam-5505	480	1	=	=	PUNCT
ejpam-5505	480	2	z	z	NOUN
ejpam-5505	481	1	−	−	NOUN
ejpam-5505	481	2	yi+1	yi+1	X
ejpam-5505	481	3	.	.	PUNCT
ejpam-5505	482	1	(	(	PUNCT
ejpam-5505	482	2	ii	ii	NOUN
ejpam-5505	482	3	)	)	PUNCT
ejpam-5505	482	4	the	the	DET
ejpam-5505	482	5	fixed	fix	VERB
ejpam-5505	482	6	point	point	NOUN
ejpam-5505	482	7	sets	set	VERB
ejpam-5505	482	8	f1	f1	NOUN
ejpam-5505	482	9	=	=	SYM
ejpam-5505	482	10	fm	fm	PROPN
ejpam-5505	483	1	−	−	PROPN
ejpam-5505	483	2	y1	y1	INTJ
ejpam-5505	483	3	and	and	CCONJ
ejpam-5505	483	4	fi+1	fi+1	NOUN
ejpam-5505	483	5	=	=	NOUN
ejpam-5505	483	6	fi	fi	NOUN
ejpam-5505	484	1	−	−	PROPN
ejpam-5505	484	2	yi+1	yi+1	PROPN
ejpam-5505	484	3	.	.	PUNCT
ejpam-5505	485	1	references	reference	NOUN
ejpam-5505	485	2	3657	3657	NUM
ejpam-5505	485	3	proof	proof	NOUN
ejpam-5505	485	4	.	.	PUNCT
ejpam-5505	486	1	(	(	PUNCT
ejpam-5505	486	2	i	i	NOUN
ejpam-5505	486	3	):	):	PUNCT
ejpam-5505	486	4	let	let	VERB
ejpam-5505	486	5	z	z	NOUN
ejpam-5505	486	6	and	and	CCONJ
ejpam-5505	486	7	z̃	z̃	PROPN
ejpam-5505	486	8	be	be	VERB
ejpam-5505	486	9	in	in	ADP
ejpam-5505	486	10	fm	fm	NOUN
ejpam-5505	486	11	satisfying	satisfy	VERB
ejpam-5505	486	12	that	that	SCONJ
ejpam-5505	486	13	j1z	j1z	NOUN
ejpam-5505	486	14	=	=	PUNCT
ejpam-5505	487	1	j1z̃.	j1z̃.	ADV
ejpam-5505	487	2	our	our	PRON
ejpam-5505	487	3	goal	goal	NOUN
ejpam-5505	487	4	is	be	AUX
ejpam-5505	487	5	to	to	PART
ejpam-5505	487	6	show	show	VERB
ejpam-5505	487	7	that	that	SCONJ
ejpam-5505	487	8	j1	j1	PROPN
ejpam-5505	487	9	is	be	AUX
ejpam-5505	487	10	injective	injective	ADJ
ejpam-5505	487	11	on	on	ADP
ejpam-5505	487	12	fm	fm	PROPN
ejpam-5505	487	13	.	.	PUNCT
ejpam-5505	488	1	then	then	ADV
ejpam-5505	488	2	,	,	PUNCT
ejpam-5505	488	3	we	we	PRON
ejpam-5505	488	4	have	have	VERB
ejpam-5505	488	5	z	z	NOUN
ejpam-5505	488	6	=	=	SYM
ejpam-5505	488	7	jmjm−1	jmjm−1	NOUN
ejpam-5505	488	8	·	·	PUNCT
ejpam-5505	488	9	·	·	PUNCT
ejpam-5505	488	10	·	·	PUNCT
ejpam-5505	489	1	jiji−1	jiji−1	PROPN
ejpam-5505	489	2	·	·	PUNCT
ejpam-5505	489	3	·	·	PUNCT
ejpam-5505	489	4	·	·	PUNCT
ejpam-5505	489	5	j1z	j1z	NOUN
ejpam-5505	489	6	and	and	CCONJ
ejpam-5505	489	7	z̃	z̃	PROPN
ejpam-5505	489	8	=	=	SYM
ejpam-5505	489	9	jmjm−1	jmjm−1	PROPN
ejpam-5505	489	10	·	·	PUNCT
ejpam-5505	489	11	·	·	PUNCT
ejpam-5505	489	12	·	·	PUNCT
ejpam-5505	490	1	jiji−1	jiji−1	PROPN
ejpam-5505	490	2	·	·	PUNCT
ejpam-5505	490	3	·	·	PUNCT
ejpam-5505	490	4	·	·	PUNCT
ejpam-5505	490	5	j1z̃.	j1z̃.	ADV
ejpam-5505	490	6	since	since	SCONJ
ejpam-5505	490	7	j1z	j1z	PROPN
ejpam-5505	490	8	=	=	PUNCT
ejpam-5505	490	9	j1z̃	j1z̃	PROPN
ejpam-5505	490	10	,	,	PUNCT
ejpam-5505	490	11	then	then	ADV
ejpam-5505	490	12	we	we	PRON
ejpam-5505	490	13	obtain	obtain	VERB
ejpam-5505	490	14	z	z	NOUN
ejpam-5505	490	15	=	=	SYM
ejpam-5505	490	16	z̃.	z̃.	PROPN
ejpam-5505	490	17	thus	thus	ADV
ejpam-5505	490	18	,	,	PUNCT
ejpam-5505	490	19	j1	j1	PROPN
ejpam-5505	490	20	is	be	AUX
ejpam-5505	490	21	an	an	DET
ejpam-5505	490	22	injective	injective	ADJ
ejpam-5505	490	23	mapping	mapping	NOUN
ejpam-5505	490	24	on	on	ADP
ejpam-5505	490	25	fm	fm	PROPN
ejpam-5505	490	26	.	.	PUNCT
ejpam-5505	491	1	moreover	moreover	ADV
ejpam-5505	491	2	,	,	PUNCT
ejpam-5505	491	3	remark	remark	NOUN
ejpam-5505	491	4	1	1	NUM
ejpam-5505	491	5	shows	show	VERB
ejpam-5505	491	6	that	that	SCONJ
ejpam-5505	491	7	j1	j1	PROPN
ejpam-5505	491	8	is	be	AUX
ejpam-5505	491	9	a	a	DET
ejpam-5505	491	10	surjective	surjective	ADJ
ejpam-5505	491	11	mapping	mapping	NOUN
ejpam-5505	491	12	on	on	ADP
ejpam-5505	491	13	fm	fm	PROPN
ejpam-5505	491	14	.	.	PROPN
ejpam-5505	492	1	therefore	therefore	ADV
ejpam-5505	492	2	,	,	PUNCT
ejpam-5505	492	3	j1	j1	PROPN
ejpam-5505	492	4	is	be	AUX
ejpam-5505	492	5	a	a	DET
ejpam-5505	492	6	bijective	bijective	ADJ
ejpam-5505	492	7	mapping	mapping	NOUN
ejpam-5505	492	8	on	on	ADP
ejpam-5505	492	9	fm	fm	PROPN
ejpam-5505	492	10	.	.	PROPN
ejpam-5505	493	1	for	for	ADP
ejpam-5505	493	2	every	every	DET
ejpam-5505	493	3	z	z	PROPN
ejpam-5505	493	4	∈	∈	PROPN
ejpam-5505	493	5	fm	fm	PROPN
ejpam-5505	493	6	,	,	PUNCT
ejpam-5505	493	7	we	we	PRON
ejpam-5505	493	8	have	have	VERB
ejpam-5505	493	9	z	z	NOUN
ejpam-5505	493	10	=	=	SYM
ejpam-5505	493	11	jmjm−1	jmjm−1	NOUN
ejpam-5505	493	12	·	·	PUNCT
ejpam-5505	493	13	·	·	PUNCT
ejpam-5505	493	14	·	·	PUNCT
ejpam-5505	494	1	jiji−1	jiji−1	PROPN
ejpam-5505	494	2	·	·	PUNCT
ejpam-5505	494	3	·	·	PUNCT
ejpam-5505	494	4	·	·	PUNCT
ejpam-5505	494	5	j1z	j1z	X
ejpam-5505	494	6	.	.	PUNCT
ejpam-5505	495	1	(	(	PUNCT
ejpam-5505	495	2	56	56	NUM
ejpam-5505	495	3	)	)	PUNCT
ejpam-5505	495	4	set	set	VERB
ejpam-5505	495	5	z1	z1	PROPN
ejpam-5505	495	6	=	=	SYM
ejpam-5505	495	7	j1z	j1z	PROPN
ejpam-5505	495	8	,	,	PUNCT
ejpam-5505	495	9	z2	z2	PROPN
ejpam-5505	495	10	=	=	SYM
ejpam-5505	495	11	j2z1	j2z1	PROPN
ejpam-5505	495	12	,	,	PUNCT
ejpam-5505	495	13	·	·	PUNCT
ejpam-5505	495	14	·	·	PUNCT
ejpam-5505	495	15	·	·	PUNCT
ejpam-5505	495	16	,	,	PUNCT
ejpam-5505	495	17	zm−1	zm−1	PROPN
ejpam-5505	495	18	=	=	PUNCT
ejpam-5505	495	19	jm−1zm−2	jm−1zm−2	PROPN
ejpam-5505	495	20	,	,	PUNCT
ejpam-5505	495	21	zm	zm	PROPN
ejpam-5505	495	22	=	=	SYM
ejpam-5505	495	23	jmzm−1	jmzm−1	PROPN
ejpam-5505	495	24	.	.	PUNCT
ejpam-5505	496	1	therefore	therefore	ADV
ejpam-5505	496	2	,	,	PUNCT
ejpam-5505	496	3	using	use	VERB
ejpam-5505	496	4	(	(	PUNCT
ejpam-5505	496	5	56	56	NUM
ejpam-5505	496	6	)	)	PUNCT
ejpam-5505	496	7	,	,	PUNCT
ejpam-5505	496	8	we	we	PRON
ejpam-5505	496	9	have	have	VERB
ejpam-5505	496	10	z	z	NOUN
ejpam-5505	496	11	=	=	SYM
ejpam-5505	496	12	jmzm−1	jmzm−1	PROPN
ejpam-5505	496	13	and	and	CCONJ
ejpam-5505	496	14	z	z	NOUN
ejpam-5505	496	15	=	=	SYM
ejpam-5505	496	16	(	(	PUNCT
ejpam-5505	496	17	z1	z1	PROPN
ejpam-5505	496	18	,	,	PUNCT
ejpam-5505	496	19	z2	z2	PROPN
ejpam-5505	496	20	,	,	PUNCT
ejpam-5505	496	21	·	·	PUNCT
ejpam-5505	496	22	·	·	PUNCT
ejpam-5505	496	23	·	·	PUNCT
ejpam-5505	496	24	,	,	PUNCT
ejpam-5505	496	25	zm−1	zm−1	NOUN
ejpam-5505	496	26	,	,	PUNCT
ejpam-5505	496	27	z	z	NOUN
ejpam-5505	496	28	)	)	PUNCT
ejpam-5505	496	29	.	.	PUNCT
ejpam-5505	497	1	therefore	therefore	ADV
ejpam-5505	497	2	,	,	PUNCT
ejpam-5505	497	3	theorem	theorem	VERB
ejpam-5505	497	4	4	4	NUM
ejpam-5505	497	5	gives	give	NOUN
ejpam-5505	497	6	(	(	PUNCT
ejpam-5505	497	7	y1	y1	PROPN
ejpam-5505	497	8	,	,	PUNCT
ejpam-5505	497	9	y2	y2	PROPN
ejpam-5505	497	10	,	,	PUNCT
ejpam-5505	497	11	·	·	PUNCT
ejpam-5505	497	12	·	·	PUNCT
ejpam-5505	497	13	·	·	PUNCT
ejpam-5505	497	14	,	,	PUNCT
ejpam-5505	497	15	ym	ym	INTJ
ejpam-5505	497	16	)	)	PUNCT
ejpam-5505	498	1	=	=	PUNCT
ejpam-5505	498	2	(	(	PUNCT
ejpam-5505	498	3	z	z	PROPN
ejpam-5505	498	4	,	,	PUNCT
ejpam-5505	498	5	z1	z1	VERB
ejpam-5505	498	6	,	,	PUNCT
ejpam-5505	498	7	z2	z2	PROPN
ejpam-5505	498	8	,	,	PUNCT
ejpam-5505	498	9	·	·	PUNCT
ejpam-5505	498	10	·	·	PUNCT
ejpam-5505	498	11	·	·	PUNCT
ejpam-5505	498	12	,	,	PUNCT
ejpam-5505	498	13	zm−1	zm−1	PROPN
ejpam-5505	498	14	)	)	PUNCT
ejpam-5505	499	1	−	−	PROPN
ejpam-5505	499	2	(	(	PUNCT
ejpam-5505	499	3	z1	z1	PROPN
ejpam-5505	499	4	,	,	PUNCT
ejpam-5505	499	5	z2	z2	PROPN
ejpam-5505	499	6	,	,	PUNCT
ejpam-5505	499	7	·	·	PUNCT
ejpam-5505	499	8	·	·	PUNCT
ejpam-5505	499	9	·	·	PUNCT
ejpam-5505	499	10	,	,	PUNCT
ejpam-5505	499	11	zm−1	zm−1	PROPN
ejpam-5505	499	12	,	,	PUNCT
ejpam-5505	499	13	zm	zm	PROPN
ejpam-5505	499	14	)	)	PUNCT
ejpam-5505	499	15	and	and	CCONJ
ejpam-5505	499	16	therefore	therefore	ADV
ejpam-5505	499	17	,	,	PUNCT
ejpam-5505	499	18	y1	y1	NOUN
ejpam-5505	499	19	=	=	PUNCT
ejpam-5505	499	20	z	z	NOUN
ejpam-5505	499	21	−	−	NOUN
ejpam-5505	499	22	z1	z1	ADJ
ejpam-5505	499	23	⇒	⇒	NOUN
ejpam-5505	499	24	z1	z1	NOUN
ejpam-5505	499	25	=	=	SYM
ejpam-5505	499	26	z	z	NOUN
ejpam-5505	499	27	−	−	NOUN
ejpam-5505	499	28	y1	y1	ADJ
ejpam-5505	499	29	⇒	⇒	NOUN
ejpam-5505	499	30	j1z	j1z	NOUN
ejpam-5505	500	1	=	=	PUNCT
ejpam-5505	500	2	z	z	PROPN
ejpam-5505	500	3	−	−	PROPN
ejpam-5505	500	4	y1	y1	PROPN
ejpam-5505	500	5	.	.	PUNCT
ejpam-5505	501	1	the	the	DET
ejpam-5505	501	2	proof	proof	NOUN
ejpam-5505	501	3	of	of	ADP
ejpam-5505	501	4	ji	ji	PROPN
ejpam-5505	501	5	is	be	AUX
ejpam-5505	501	6	the	the	DET
ejpam-5505	501	7	same	same	ADJ
ejpam-5505	501	8	as	as	ADP
ejpam-5505	501	9	j1	j1	PROPN
ejpam-5505	501	10	.	.	PUNCT
ejpam-5505	502	1	(	(	PUNCT
ejpam-5505	502	2	ii	ii	NUM
ejpam-5505	502	3	):	):	PUNCT
ejpam-5505	502	4	it	it	PRON
ejpam-5505	502	5	follows	follow	VERB
ejpam-5505	502	6	from	from	ADP
ejpam-5505	502	7	(	(	PUNCT
ejpam-5505	502	8	i	i	NOUN
ejpam-5505	502	9	)	)	PUNCT
ejpam-5505	502	10	that	that	SCONJ
ejpam-5505	502	11	for	for	ADP
ejpam-5505	502	12	every	every	DET
ejpam-5505	502	13	z	z	PROPN
ejpam-5505	502	14	∈	∈	PROPN
ejpam-5505	502	15	fm	fm	PROPN
ejpam-5505	502	16	,	,	PUNCT
ejpam-5505	502	17	we	we	PRON
ejpam-5505	502	18	obtain	obtain	VERB
ejpam-5505	502	19	j1z	j1z	NOUN
ejpam-5505	502	20	=	=	PUNCT
ejpam-5505	503	1	z	z	NOUN
ejpam-5505	503	2	−	−	PROPN
ejpam-5505	503	3	y1	y1	PROPN
ejpam-5505	503	4	.	.	PUNCT
ejpam-5505	504	1	then	then	ADV
ejpam-5505	504	2	by	by	ADP
ejpam-5505	504	3	theorem	theorem	ADJ
ejpam-5505	504	4	2(iii	2(iii	NOUN
ejpam-5505	504	5	)	)	PUNCT
ejpam-5505	504	6	we	we	PRON
ejpam-5505	504	7	have	have	VERB
ejpam-5505	504	8	f1	f1	NOUN
ejpam-5505	504	9	=	=	SYM
ejpam-5505	504	10	fm	fm	PROPN
ejpam-5505	504	11	−	−	PROPN
ejpam-5505	504	12	y1	y1	PROPN
ejpam-5505	504	13	.	.	PUNCT
ejpam-5505	505	1	the	the	DET
ejpam-5505	505	2	proof	proof	NOUN
ejpam-5505	505	3	for	for	ADP
ejpam-5505	505	4	fi+1	fi+1	NOUN
ejpam-5505	505	5	=	=	PROPN
ejpam-5505	505	6	fi	fi	NOUN
ejpam-5505	505	7	−	−	NOUN
ejpam-5505	505	8	yi+1	yi+1	PROPN
ejpam-5505	505	9	is	be	AUX
ejpam-5505	505	10	the	the	DET
ejpam-5505	505	11	same	same	ADJ
ejpam-5505	505	12	as	as	ADP
ejpam-5505	505	13	f1	f1	NOUN
ejpam-5505	505	14	.	.	PUNCT
ejpam-5505	506	1	■	■	PUNCT
ejpam-5505	506	2	acknowledgements	acknowledgement	VERB
ejpam-5505	506	3	the	the	DET
ejpam-5505	506	4	author	author	NOUN
ejpam-5505	506	5	expresses	express	VERB
ejpam-5505	506	6	gratitude	gratitude	NOUN
ejpam-5505	506	7	to	to	ADP
ejpam-5505	506	8	the	the	DET
ejpam-5505	506	9	reviewers	reviewer	NOUN
ejpam-5505	506	10	for	for	ADP
ejpam-5505	506	11	their	their	PRON
ejpam-5505	506	12	insightful	insightful	ADJ
ejpam-5505	506	13	comments	comment	NOUN
ejpam-5505	506	14	and	and	CCONJ
ejpam-5505	506	15	constructive	constructive	ADJ
ejpam-5505	506	16	feedback	feedback	NOUN
ejpam-5505	506	17	,	,	PUNCT
ejpam-5505	506	18	which	which	PRON
ejpam-5505	506	19	greatly	greatly	ADV
ejpam-5505	506	20	contributed	contribute	VERB
ejpam-5505	506	21	to	to	ADP
ejpam-5505	506	22	enhancing	enhance	VERB
ejpam-5505	506	23	the	the	DET
ejpam-5505	506	24	quality	quality	NOUN
ejpam-5505	506	25	of	of	ADP
ejpam-5505	506	26	the	the	DET
ejpam-5505	506	27	work	work	NOUN
ejpam-5505	506	28	.	.	PUNCT
ejpam-5505	507	1	6	6	X
ejpam-5505	507	2	.	.	X
ejpam-5505	507	3	clarification	clarification	NOUN
ejpam-5505	507	4	please	please	INTJ
ejpam-5505	507	5	note	note	VERB
ejpam-5505	507	6	that	that	SCONJ
ejpam-5505	507	7	a	a	DET
ejpam-5505	507	8	preprint	preprint	NOUN
ejpam-5505	507	9	has	have	AUX
ejpam-5505	507	10	been	be	AUX
ejpam-5505	507	11	published	publish	VERB
ejpam-5505	507	12	on	on	ADP
ejpam-5505	507	13	arxiv	arxiv	PROPN
ejpam-5505	507	14	and	and	CCONJ
ejpam-5505	507	15	is	be	AUX
ejpam-5505	507	16	referenced	reference	VERB
ejpam-5505	507	17	in	in	ADP
ejpam-5505	507	18	[	[	X
ejpam-5505	507	19	4	4	NUM
ejpam-5505	507	20	]	]	PUNCT
ejpam-5505	507	21	.	.	PUNCT
ejpam-5505	508	1	there	there	PRON
ejpam-5505	508	2	is	be	VERB
ejpam-5505	508	3	no	no	DET
ejpam-5505	508	4	conflict	conflict	NOUN
ejpam-5505	508	5	of	of	ADP
ejpam-5505	508	6	interest	interest	NOUN
ejpam-5505	508	7	,	,	PUNCT
ejpam-5505	508	8	and	and	CCONJ
ejpam-5505	508	9	no	no	DET
ejpam-5505	508	10	data	datum	NOUN
ejpam-5505	508	11	were	be	AUX
ejpam-5505	508	12	used	use	VERB
ejpam-5505	508	13	to	to	PART
ejpam-5505	508	14	support	support	VERB
ejpam-5505	508	15	this	this	DET
ejpam-5505	508	16	study	study	NOUN
ejpam-5505	508	17	.	.	PUNCT
ejpam-5505	509	1	references	reference	NOUN
ejpam-5505	509	2	[	[	X
ejpam-5505	509	3	1	1	X
ejpam-5505	509	4	]	]	PUNCT
ejpam-5505	509	5	salihah	salihah	ADJ
ejpam-5505	509	6	alwadani	alwadani	ADJ
ejpam-5505	509	7	,	,	PUNCT
ejpam-5505	509	8	heinz	heinz	PROPN
ejpam-5505	509	9	h	h	NOUN
ejpam-5505	509	10	bauschke	bauschke	NOUN
ejpam-5505	509	11	,	,	PUNCT
ejpam-5505	509	12	and	and	CCONJ
ejpam-5505	509	13	xianfu	xianfu	PROPN
ejpam-5505	509	14	wang	wang	PROPN
ejpam-5505	509	15	.	.	PUNCT
ejpam-5505	510	1	fixed	fix	VERB
ejpam-5505	510	2	points	point	NOUN
ejpam-5505	510	3	of	of	ADP
ejpam-5505	510	4	compositions	composition	NOUN
ejpam-5505	510	5	of	of	ADP
ejpam-5505	510	6	nonexpansive	nonexpansive	ADJ
ejpam-5505	510	7	mappings	mapping	NOUN
ejpam-5505	510	8	:	:	PUNCT
ejpam-5505	510	9	finitely	finitely	ADV
ejpam-5505	510	10	many	many	ADJ
ejpam-5505	510	11	linear	linear	ADJ
ejpam-5505	510	12	reflectors	reflector	NOUN
ejpam-5505	510	13	.	.	PUNCT
ejpam-5505	511	1	arxiv	arxiv	PROPN
ejpam-5505	511	2	preprint	preprint	PROPN
ejpam-5505	511	3	arxiv:2004.12582	arxiv:2004.12582	PROPN
ejpam-5505	511	4	,	,	PUNCT
ejpam-5505	511	5	2020	2020	NUM
ejpam-5505	511	6	.	.	PUNCT
ejpam-5505	512	1	[	[	X
ejpam-5505	512	2	2	2	X
ejpam-5505	512	3	]	]	PUNCT
ejpam-5505	512	4	salihah	salihah	ADJ
ejpam-5505	512	5	thabet	thabet	ADJ
ejpam-5505	512	6	alwadani	alwadani	ADJ
ejpam-5505	512	7	.	.	PUNCT
ejpam-5505	513	1	on	on	ADP
ejpam-5505	513	2	the	the	DET
ejpam-5505	513	3	behaviour	behaviour	NOUN
ejpam-5505	513	4	of	of	ADP
ejpam-5505	513	5	algorithms	algorithm	NOUN
ejpam-5505	513	6	featuring	feature	VERB
ejpam-5505	513	7	compositions	composition	NOUN
ejpam-5505	513	8	of	of	ADP
ejpam-5505	513	9	projectors	projector	NOUN
ejpam-5505	513	10	and	and	CCONJ
ejpam-5505	513	11	proximal	proximal	ADJ
ejpam-5505	513	12	mappings	mapping	NOUN
ejpam-5505	513	13	with	with	ADP
ejpam-5505	513	14	no	no	DET
ejpam-5505	513	15	solutions	solution	NOUN
ejpam-5505	513	16	.	.	PUNCT
ejpam-5505	514	1	phd	phd	NOUN
ejpam-5505	514	2	thesis	thesis	PROPN
ejpam-5505	514	3	,	,	PUNCT
ejpam-5505	514	4	university	university	PROPN
ejpam-5505	514	5	of	of	ADP
ejpam-5505	514	6	british	british	PROPN
ejpam-5505	514	7	columbia	columbia	PROPN
ejpam-5505	514	8	,	,	PUNCT
ejpam-5505	514	9	2021	2021	NUM
ejpam-5505	514	10	.	.	PUNCT
ejpam-5505	515	1	[	[	X
ejpam-5505	515	2	3	3	X
ejpam-5505	515	3	]	]	PUNCT
ejpam-5505	515	4	salihah	salihah	ADJ
ejpam-5505	515	5	thabet	thabet	ADJ
ejpam-5505	515	6	alwadani	alwadani	ADJ
ejpam-5505	515	7	.	.	PUNCT
ejpam-5505	516	1	additional	additional	ADJ
ejpam-5505	516	2	studies	study	NOUN
ejpam-5505	516	3	on	on	ADP
ejpam-5505	516	4	displacement	displacement	ADJ
ejpam-5505	516	5	mapping	mapping	NOUN
ejpam-5505	516	6	with	with	ADP
ejpam-5505	516	7	restrictions	restriction	NOUN
ejpam-5505	516	8	.	.	PUNCT
ejpam-5505	517	1	arxiv	arxiv	PROPN
ejpam-5505	517	2	preprint	preprint	NOUN
ejpam-5505	517	3	arxiv:2405.13510	arxiv:2405.13510	NOUN
ejpam-5505	517	4	,	,	PUNCT
ejpam-5505	517	5	2024	2024	NUM
ejpam-5505	517	6	.	.	PUNCT
ejpam-5505	518	1	references	reference	NOUN
ejpam-5505	518	2	3658	3658	NUM
ejpam-5505	518	3	[	[	X
ejpam-5505	518	4	4	4	NUM
ejpam-5505	518	5	]	]	PUNCT
ejpam-5505	518	6	salihah	salihah	ADJ
ejpam-5505	518	7	thabet	thabet	ADJ
ejpam-5505	518	8	alwadani	alwadani	ADJ
ejpam-5505	518	9	.	.	PUNCT
ejpam-5505	519	1	compositions	composition	NOUN
ejpam-5505	519	2	of	of	ADP
ejpam-5505	519	3	resolvents	resolvent	NOUN
ejpam-5505	519	4	:	:	PUNCT
ejpam-5505	519	5	fixed	fix	VERB
ejpam-5505	519	6	points	point	NOUN
ejpam-5505	519	7	sets	set	NOUN
ejpam-5505	519	8	and	and	CCONJ
ejpam-5505	519	9	set	set	NOUN
ejpam-5505	519	10	of	of	ADP
ejpam-5505	519	11	cycles	cycle	NOUN
ejpam-5505	519	12	.	.	PUNCT
ejpam-5505	520	1	arxiv	arxiv	PROPN
ejpam-5505	520	2	preprint	preprint	PROPN
ejpam-5505	520	3	arxiv:2406.01041	arxiv:2406.01041	PROPN
ejpam-5505	520	4	,	,	PUNCT
ejpam-5505	520	5	2024	2024	NUM
ejpam-5505	520	6	.	.	PUNCT
ejpam-5505	521	1	[	[	X
ejpam-5505	521	2	5	5	NUM
ejpam-5505	521	3	]	]	SYM
ejpam-5505	521	4	hédy	hédy	NOUN
ejpam-5505	521	5	attouch	attouch	ADJ
ejpam-5505	521	6	and	and	CCONJ
ejpam-5505	521	7	michel	michel	PROPN
ejpam-5505	521	8	théra	théra	PROPN
ejpam-5505	521	9	.	.	PUNCT
ejpam-5505	522	1	a	a	DET
ejpam-5505	522	2	general	general	ADJ
ejpam-5505	522	3	duality	duality	NOUN
ejpam-5505	522	4	principle	principle	NOUN
ejpam-5505	522	5	for	for	ADP
ejpam-5505	522	6	the	the	DET
ejpam-5505	522	7	sum	sum	NOUN
ejpam-5505	522	8	of	of	ADP
ejpam-5505	522	9	two	two	NUM
ejpam-5505	522	10	operators	operator	NOUN
ejpam-5505	522	11	.	.	PUNCT
ejpam-5505	523	1	journal	journal	NOUN
ejpam-5505	523	2	of	of	ADP
ejpam-5505	523	3	convex	convex	PROPN
ejpam-5505	523	4	analysis	analysis	NOUN
ejpam-5505	523	5	,	,	PUNCT
ejpam-5505	523	6	3:1–24	3:1–24	NUM
ejpam-5505	523	7	,	,	PUNCT
ejpam-5505	523	8	1996	1996	NUM
ejpam-5505	523	9	.	.	PUNCT
ejpam-5505	524	1	[	[	X
ejpam-5505	524	2	6	6	NUM
ejpam-5505	524	3	]	]	PUNCT
ejpam-5505	524	4	heinz	heinz	PROPN
ejpam-5505	524	5	h	h	PROPN
ejpam-5505	524	6	bauschke	bauschke	PROPN
ejpam-5505	524	7	.	.	PUNCT
ejpam-5505	525	1	the	the	DET
ejpam-5505	525	2	approximation	approximation	NOUN
ejpam-5505	525	3	of	of	ADP
ejpam-5505	525	4	fixed	fix	VERB
ejpam-5505	525	5	points	point	NOUN
ejpam-5505	525	6	of	of	ADP
ejpam-5505	525	7	compositions	composition	NOUN
ejpam-5505	525	8	of	of	ADP
ejpam-5505	525	9	nonexpansive	nonexpansive	ADJ
ejpam-5505	525	10	mappings	mapping	NOUN
ejpam-5505	525	11	in	in	ADP
ejpam-5505	525	12	hilbert	hilbert	NOUN
ejpam-5505	525	13	space	space	NOUN
ejpam-5505	525	14	.	.	PUNCT
ejpam-5505	526	1	journal	journal	PROPN
ejpam-5505	526	2	of	of	ADP
ejpam-5505	526	3	mathematical	mathematical	ADJ
ejpam-5505	526	4	analysis	analysis	NOUN
ejpam-5505	526	5	and	and	CCONJ
ejpam-5505	526	6	applications	application	NOUN
ejpam-5505	526	7	,	,	PUNCT
ejpam-5505	526	8	202(1):150–159	202(1):150–159	NUM
ejpam-5505	526	9	,	,	PUNCT
ejpam-5505	526	10	1996	1996	NUM
ejpam-5505	526	11	.	.	PUNCT
ejpam-5505	527	1	[	[	X
ejpam-5505	527	2	7	7	X
ejpam-5505	527	3	]	]	X
ejpam-5505	527	4	heinz	heinz	ADJ
ejpam-5505	527	5	h	h	PROPN
ejpam-5505	527	6	bauschke	bauschke	PROPN
ejpam-5505	527	7	and	and	CCONJ
ejpam-5505	527	8	jonathan	jonathan	PROPN
ejpam-5505	527	9	m	m	PROPN
ejpam-5505	527	10	borwein	borwein	PROPN
ejpam-5505	527	11	.	.	PUNCT
ejpam-5505	528	1	on	on	ADP
ejpam-5505	528	2	the	the	DET
ejpam-5505	528	3	convergence	convergence	NOUN
ejpam-5505	528	4	of	of	ADP
ejpam-5505	528	5	von	von	PROPN
ejpam-5505	528	6	neumann	neumann	PROPN
ejpam-5505	528	7	’s	’s	PART
ejpam-5505	528	8	alternating	alternate	VERB
ejpam-5505	528	9	projection	projection	NOUN
ejpam-5505	528	10	algorithm	algorithm	NOUN
ejpam-5505	528	11	for	for	ADP
ejpam-5505	528	12	two	two	NUM
ejpam-5505	528	13	sets	set	NOUN
ejpam-5505	528	14	.	.	PUNCT
ejpam-5505	529	1	springer	springer	NOUN
ejpam-5505	529	2	j.	j.	PROPN
ejpam-5505	529	3	set	set	PROPN
ejpam-5505	529	4	-	-	PUNCT
ejpam-5505	529	5	valued	value	VERB
ejpam-5505	529	6	analysis	analysis	NOUN
ejpam-5505	529	7	,	,	PUNCT
ejpam-5505	529	8	968:185	968:185	NOUN
ejpam-5505	529	9	–	–	PUNCT
ejpam-5505	529	10	212	212	NUM
ejpam-5505	529	11	,	,	PUNCT
ejpam-5505	529	12	1993	1993	NUM
ejpam-5505	529	13	.	.	PUNCT
ejpam-5505	530	1	[	[	X
ejpam-5505	530	2	8	8	NUM
ejpam-5505	530	3	]	]	X
ejpam-5505	530	4	heinz	heinz	ADJ
ejpam-5505	530	5	h	h	PROPN
ejpam-5505	530	6	bauschke	bauschke	PROPN
ejpam-5505	530	7	,	,	PUNCT
ejpam-5505	530	8	jonathan	jonathan	PROPN
ejpam-5505	530	9	m	m	PROPN
ejpam-5505	530	10	borwein	borwein	PROPN
ejpam-5505	530	11	,	,	PUNCT
ejpam-5505	530	12	and	and	CCONJ
ejpam-5505	530	13	adrian	adrian	PROPN
ejpam-5505	530	14	s	s	PROPN
ejpam-5505	530	15	lewis	lewis	PROPN
ejpam-5505	530	16	.	.	PUNCT
ejpam-5505	531	1	the	the	DET
ejpam-5505	531	2	method	method	NOUN
ejpam-5505	531	3	of	of	ADP
ejpam-5505	531	4	cyclic	cyclic	ADJ
ejpam-5505	531	5	projections	projection	NOUN
ejpam-5505	531	6	for	for	ADP
ejpam-5505	531	7	closed	closed	ADJ
ejpam-5505	531	8	convex	convex	NOUN
ejpam-5505	531	9	sets	set	NOUN
ejpam-5505	531	10	in	in	ADP
ejpam-5505	531	11	hilbert	hilbert	NOUN
ejpam-5505	531	12	space	space	NOUN
ejpam-5505	531	13	.	.	PUNCT
ejpam-5505	532	1	contemporary	contemporary	ADJ
ejpam-5505	532	2	mathematics	mathematic	NOUN
ejpam-5505	532	3	,	,	PUNCT
ejpam-5505	532	4	204:1	204:1	NUM
ejpam-5505	532	5	–	–	PUNCT
ejpam-5505	532	6	38	38	NUM
ejpam-5505	532	7	,	,	PUNCT
ejpam-5505	532	8	1997	1997	NUM
ejpam-5505	532	9	.	.	PUNCT
ejpam-5505	533	1	[	[	X
ejpam-5505	533	2	9	9	NUM
ejpam-5505	533	3	]	]	PUNCT
ejpam-5505	533	4	heinz	heinz	ADJ
ejpam-5505	533	5	h	h	PROPN
ejpam-5505	533	6	bauschke	bauschke	PROPN
ejpam-5505	533	7	,	,	PUNCT
ejpam-5505	533	8	radu	radu	VERB
ejpam-5505	533	9	i	i	PRON
ejpam-5505	533	10	boţ	boţ	NOUN
ejpam-5505	533	11	,	,	PUNCT
ejpam-5505	533	12	warren	warren	PROPN
ejpam-5505	533	13	l	l	PROPN
ejpam-5505	533	14	hare	hare	NOUN
ejpam-5505	533	15	,	,	PUNCT
ejpam-5505	533	16	and	and	CCONJ
ejpam-5505	533	17	walaa	walaa	PROPN
ejpam-5505	533	18	m	m	PROPN
ejpam-5505	533	19	moursi	moursi	ADJ
ejpam-5505	533	20	.	.	PUNCT
ejpam-5505	534	1	attouch	attouch	ADJ
ejpam-5505	534	2	–	–	PUNCT
ejpam-5505	534	3	théra	théra	NUM
ejpam-5505	534	4	duality	duality	NOUN
ejpam-5505	534	5	revisited	revisit	VERB
ejpam-5505	534	6	:	:	PUNCT
ejpam-5505	534	7	paramonotonicity	paramonotonicity	NOUN
ejpam-5505	534	8	and	and	CCONJ
ejpam-5505	534	9	operator	operator	NOUN
ejpam-5505	534	10	splitting	splitting	NOUN
ejpam-5505	534	11	.	.	PUNCT
ejpam-5505	535	1	journal	journal	PROPN
ejpam-5505	535	2	of	of	ADP
ejpam-5505	535	3	approximation	approximation	NOUN
ejpam-5505	535	4	theory	theory	NOUN
ejpam-5505	535	5	,	,	PUNCT
ejpam-5505	535	6	164(8):1065–1084	164(8):1065–1084	PROPN
ejpam-5505	535	7	,	,	PUNCT
ejpam-5505	535	8	2012	2012	NUM
ejpam-5505	535	9	.	.	PUNCT
ejpam-5505	536	1	[	[	X
ejpam-5505	536	2	10	10	NUM
ejpam-5505	536	3	]	]	X
ejpam-5505	536	4	heinz	heinz	PROPN
ejpam-5505	536	5	h	h	PROPN
ejpam-5505	536	6	bauschke	bauschke	PROPN
ejpam-5505	536	7	,	,	PUNCT
ejpam-5505	536	8	patrick	patrick	PROPN
ejpam-5505	536	9	l	l	PROPN
ejpam-5505	536	10	combettes	combettes	PROPN
ejpam-5505	536	11	,	,	PUNCT
ejpam-5505	536	12	heinz	heinz	ADJ
ejpam-5505	536	13	h	h	NOUN
ejpam-5505	536	14	bauschke	bauschke	NOUN
ejpam-5505	536	15	,	,	PUNCT
ejpam-5505	536	16	and	and	CCONJ
ejpam-5505	536	17	patrick	patrick	PROPN
ejpam-5505	536	18	l	l	PROPN
ejpam-5505	536	19	combettes	combettes	PROPN
ejpam-5505	536	20	.	.	PUNCT
ejpam-5505	537	1	convex	convex	VERB
ejpam-5505	537	2	analysis	analysis	NOUN
ejpam-5505	537	3	and	and	CCONJ
ejpam-5505	537	4	monotone	monotone	ADJ
ejpam-5505	537	5	operator	operator	NOUN
ejpam-5505	537	6	theory	theory	NOUN
ejpam-5505	537	7	in	in	ADP
ejpam-5505	537	8	hilbert	hilbert	PROPN
ejpam-5505	537	9	spaces	space	NOUN
ejpam-5505	537	10	.	.	PUNCT
ejpam-5505	538	1	springer	springer	NOUN
ejpam-5505	538	2	,	,	PUNCT
ejpam-5505	538	3	2017	2017	NUM
ejpam-5505	538	4	.	.	PUNCT
ejpam-5505	539	1	[	[	X
ejpam-5505	539	2	11	11	NUM
ejpam-5505	539	3	]	]	X
ejpam-5505	539	4	heinz	heinz	PROPN
ejpam-5505	539	5	h	h	PROPN
ejpam-5505	539	6	bauschke	bauschke	PROPN
ejpam-5505	539	7	,	,	PUNCT
ejpam-5505	539	8	patrick	patrick	PROPN
ejpam-5505	539	9	l	l	PROPN
ejpam-5505	539	10	combettes	combette	NOUN
ejpam-5505	539	11	,	,	PUNCT
ejpam-5505	539	12	and	and	CCONJ
ejpam-5505	539	13	d	d	PROPN
ejpam-5505	539	14	russell	russell	PROPN
ejpam-5505	539	15	luke	luke	PROPN
ejpam-5505	539	16	.	.	PUNCT
ejpam-5505	540	1	finding	find	VERB
ejpam-5505	540	2	best	good	ADJ
ejpam-5505	540	3	approximation	approximation	NOUN
ejpam-5505	540	4	pairs	pair	NOUN
ejpam-5505	540	5	relative	relative	ADJ
ejpam-5505	540	6	to	to	ADP
ejpam-5505	540	7	two	two	NUM
ejpam-5505	540	8	closed	closed	ADJ
ejpam-5505	540	9	convex	convex	NOUN
ejpam-5505	540	10	sets	set	NOUN
ejpam-5505	540	11	in	in	ADP
ejpam-5505	540	12	hilbert	hilbert	PROPN
ejpam-5505	540	13	spaces	space	NOUN
ejpam-5505	540	14	.	.	PUNCT
ejpam-5505	541	1	journal	journal	NOUN
ejpam-5505	541	2	of	of	ADP
ejpam-5505	541	3	approximation	approximation	NOUN
ejpam-5505	541	4	theory	theory	NOUN
ejpam-5505	541	5	,	,	PUNCT
ejpam-5505	541	6	127(2):178–192	127(2):178–192	NUM
ejpam-5505	541	7	,	,	PUNCT
ejpam-5505	541	8	2004	2004	NUM
ejpam-5505	541	9	.	.	PUNCT
ejpam-5505	542	1	[	[	X
ejpam-5505	542	2	12	12	NUM
ejpam-5505	542	3	]	]	X
ejpam-5505	542	4	heinz	heinz	PROPN
ejpam-5505	542	5	h	h	PROPN
ejpam-5505	542	6	bauschke	bauschke	PROPN
ejpam-5505	542	7	,	,	PUNCT
ejpam-5505	542	8	sarah	sarah	PROPN
ejpam-5505	542	9	m	m	PROPN
ejpam-5505	542	10	moffat	moffat	PROPN
ejpam-5505	542	11	,	,	PUNCT
ejpam-5505	542	12	and	and	CCONJ
ejpam-5505	542	13	xianfu	xianfu	PROPN
ejpam-5505	542	14	wang	wang	PROPN
ejpam-5505	542	15	.	.	PUNCT
ejpam-5505	543	1	firmly	firmly	ADV
ejpam-5505	543	2	nonexpansive	nonexpansive	ADJ
ejpam-5505	543	3	mappings	mapping	NOUN
ejpam-5505	543	4	and	and	CCONJ
ejpam-5505	543	5	maximally	maximally	ADV
ejpam-5505	543	6	monotone	monotone	ADJ
ejpam-5505	543	7	operators	operator	NOUN
ejpam-5505	543	8	:	:	PUNCT
ejpam-5505	543	9	correspondence	correspondence	NOUN
ejpam-5505	543	10	and	and	CCONJ
ejpam-5505	543	11	duality	duality	NOUN
ejpam-5505	543	12	.	.	PUNCT
ejpam-5505	544	1	set	set	NOUN
ejpam-5505	544	2	-	-	PUNCT
ejpam-5505	544	3	valued	value	VERB
ejpam-5505	544	4	and	and	CCONJ
ejpam-5505	544	5	variational	variational	ADJ
ejpam-5505	544	6	analysis	analysis	NOUN
ejpam-5505	544	7	,	,	PUNCT
ejpam-5505	544	8	20:131–153	20:131–153	NOUN
ejpam-5505	544	9	,	,	PUNCT
ejpam-5505	544	10	2012	2012	NUM
ejpam-5505	544	11	.	.	PUNCT
ejpam-5505	545	1	[	[	X
ejpam-5505	545	2	13	13	NUM
ejpam-5505	545	3	]	]	X
ejpam-5505	545	4	sterling	sterling	NOUN
ejpam-5505	545	5	k	k	PROPN
ejpam-5505	545	6	berberian	berberian	PROPN
ejpam-5505	545	7	.	.	PUNCT
ejpam-5505	546	1	introduction	introduction	NOUN
ejpam-5505	546	2	to	to	ADP
ejpam-5505	546	3	hilbert	hilbert	PROPN
ejpam-5505	546	4	space	space	NOUN
ejpam-5505	546	5	,	,	PUNCT
ejpam-5505	546	6	volume	volume	NOUN
ejpam-5505	546	7	287	287	NUM
ejpam-5505	546	8	.	.	PUNCT
ejpam-5505	547	1	oxford	oxford	PROPN
ejpam-5505	547	2	university	university	PROPN
ejpam-5505	547	3	press	press	NOUN
ejpam-5505	547	4	,	,	PUNCT
ejpam-5505	547	5	1961	1961	NUM
ejpam-5505	547	6	.	.	PUNCT
ejpam-5505	548	1	[	[	X
ejpam-5505	548	2	14	14	NUM
ejpam-5505	548	3	]	]	X
ejpam-5505	548	4	jonathan	jonathan	PROPN
ejpam-5505	548	5	m	m	PROPN
ejpam-5505	548	6	borwein	borwein	PROPN
ejpam-5505	548	7	,	,	PUNCT
ejpam-5505	548	8	jon	jon	PROPN
ejpam-5505	548	9	d	d	PROPN
ejpam-5505	548	10	vanderwerff	vanderwerff	PROPN
ejpam-5505	548	11	,	,	PUNCT
ejpam-5505	548	12	et	et	PROPN
ejpam-5505	548	13	al	al	PROPN
ejpam-5505	548	14	.	.	PROPN
ejpam-5505	548	15	convex	convex	PROPN
ejpam-5505	548	16	functions	function	NOUN
ejpam-5505	548	17	:	:	PUNCT
ejpam-5505	548	18	constructions	construction	NOUN
ejpam-5505	548	19	,	,	PUNCT
ejpam-5505	548	20	characterizations	characterization	NOUN
ejpam-5505	548	21	and	and	CCONJ
ejpam-5505	548	22	counterexamples	counterexample	NOUN
ejpam-5505	548	23	,	,	PUNCT
ejpam-5505	548	24	volume	volume	NOUN
ejpam-5505	548	25	109	109	NUM
ejpam-5505	548	26	.	.	PUNCT
ejpam-5505	549	1	cambridge	cambridge	PROPN
ejpam-5505	549	2	university	university	PROPN
ejpam-5505	549	3	press	press	PROPN
ejpam-5505	549	4	cambridge	cambridge	PROPN
ejpam-5505	549	5	,	,	PUNCT
ejpam-5505	549	6	2010	2010	NUM
ejpam-5505	549	7	.	.	PUNCT
ejpam-5505	550	1	[	[	X
ejpam-5505	550	2	15	15	NUM
ejpam-5505	550	3	]	]	X
ejpam-5505	550	4	regina	regina	PROPN
ejpam-5505	550	5	s	s	PROPN
ejpam-5505	550	6	burachik	burachik	PROPN
ejpam-5505	550	7	,	,	PUNCT
ejpam-5505	550	8	alfredo	alfredo	NOUN
ejpam-5505	550	9	n	n	CCONJ
ejpam-5505	550	10	iusem	iusem	NOUN
ejpam-5505	550	11	,	,	PUNCT
ejpam-5505	550	12	regina	regina	PROPN
ejpam-5505	550	13	s	s	PROPN
ejpam-5505	550	14	burachik	burachik	PROPN
ejpam-5505	550	15	,	,	PUNCT
ejpam-5505	550	16	and	and	CCONJ
ejpam-5505	550	17	alfredo	alfredo	NOUN
ejpam-5505	550	18	n	n	CCONJ
ejpam-5505	550	19	iusem	iusem	ADJ
ejpam-5505	550	20	.	.	PUNCT
ejpam-5505	551	1	enlargements	enlargement	NOUN
ejpam-5505	551	2	of	of	ADP
ejpam-5505	551	3	monotone	monotone	ADJ
ejpam-5505	551	4	operators	operator	NOUN
ejpam-5505	551	5	.	.	PUNCT
ejpam-5505	552	1	springer	springer	NOUN
ejpam-5505	552	2	,	,	PUNCT
ejpam-5505	552	3	2008	2008	NUM
ejpam-5505	552	4	.	.	PUNCT
ejpam-5505	553	1	[	[	X
ejpam-5505	553	2	16	16	NUM
ejpam-5505	553	3	]	]	X
ejpam-5505	553	4	andrzej	andrzej	PROPN
ejpam-5505	553	5	cegielski	cegielski	PROPN
ejpam-5505	553	6	.	.	PUNCT
ejpam-5505	554	1	iterative	iterative	NOUN
ejpam-5505	554	2	methods	method	NOUN
ejpam-5505	554	3	for	for	ADP
ejpam-5505	554	4	fixed	fix	VERB
ejpam-5505	554	5	point	point	NOUN
ejpam-5505	554	6	problems	problem	NOUN
ejpam-5505	554	7	in	in	ADP
ejpam-5505	554	8	hilbert	hilbert	PROPN
ejpam-5505	554	9	spaces	space	NOUN
ejpam-5505	554	10	,	,	PUNCT
ejpam-5505	554	11	volume	volume	NOUN
ejpam-5505	554	12	2057	2057	NUM
ejpam-5505	554	13	.	.	PUNCT
ejpam-5505	555	1	springer	springer	NOUN
ejpam-5505	555	2	,	,	PUNCT
ejpam-5505	555	3	2012	2012	NUM
ejpam-5505	555	4	.	.	PUNCT
ejpam-5505	556	1	[	[	X
ejpam-5505	556	2	17	17	NUM
ejpam-5505	556	3	]	]	PUNCT
ejpam-5505	556	4	ward	ward	NOUN
ejpam-5505	556	5	cheney	cheney	NOUN
ejpam-5505	556	6	and	and	CCONJ
ejpam-5505	556	7	allen	allen	VERB
ejpam-5505	556	8	a	a	DET
ejpam-5505	556	9	goldstein	goldstein	PROPN
ejpam-5505	556	10	.	.	PUNCT
ejpam-5505	557	1	proximity	proximity	NOUN
ejpam-5505	557	2	maps	map	NOUN
ejpam-5505	557	3	for	for	ADP
ejpam-5505	557	4	convex	convex	NOUN
ejpam-5505	557	5	sets	set	NOUN
ejpam-5505	557	6	.	.	PUNCT
ejpam-5505	558	1	proceedings	proceeding	NOUN
ejpam-5505	558	2	of	of	ADP
ejpam-5505	558	3	the	the	DET
ejpam-5505	558	4	american	american	PROPN
ejpam-5505	558	5	mathematical	mathematical	PROPN
ejpam-5505	558	6	society	society	NOUN
ejpam-5505	558	7	,	,	PUNCT
ejpam-5505	558	8	10(3):448–450	10(3):448–450	NUM
ejpam-5505	558	9	,	,	PUNCT
ejpam-5505	558	10	1959	1959	NUM
ejpam-5505	558	11	.	.	PUNCT
ejpam-5505	559	1	references	reference	NOUN
ejpam-5505	559	2	3659	3659	NUM
ejpam-5505	559	3	[	[	X
ejpam-5505	559	4	18	18	NUM
ejpam-5505	559	5	]	]	X
ejpam-5505	559	6	patrick	patrick	PROPN
ejpam-5505	559	7	l	l	PROPN
ejpam-5505	559	8	combettes	combettes	PROPN
ejpam-5505	559	9	.	.	PUNCT
ejpam-5505	560	1	resolvent	resolvent	ADJ
ejpam-5505	560	2	and	and	CCONJ
ejpam-5505	560	3	proximal	proximal	ADJ
ejpam-5505	560	4	compositions	composition	NOUN
ejpam-5505	560	5	.	.	PUNCT
ejpam-5505	561	1	set	set	NOUN
ejpam-5505	561	2	-	-	PUNCT
ejpam-5505	561	3	valued	value	VERB
ejpam-5505	561	4	and	and	CCONJ
ejpam-5505	561	5	variational	variational	ADJ
ejpam-5505	561	6	analysis	analysis	NOUN
ejpam-5505	561	7	,	,	PUNCT
ejpam-5505	561	8	31(3):22	31(3):22	NUM
ejpam-5505	561	9	,	,	PUNCT
ejpam-5505	561	10	2023	2023	NUM
ejpam-5505	561	11	.	.	PUNCT
ejpam-5505	562	1	[	[	X
ejpam-5505	562	2	19	19	NUM
ejpam-5505	562	3	]	]	X
ejpam-5505	562	4	colin	colin	PROPN
ejpam-5505	562	5	leclercq	leclercq	PROPN
ejpam-5505	562	6	and	and	CCONJ
ejpam-5505	562	7	denis	denis	PROPN
ejpam-5505	562	8	sipp	sipp	PROPN
ejpam-5505	562	9	.	.	PUNCT
ejpam-5505	563	1	mean	mean	VERB
ejpam-5505	563	2	resolvent	resolvent	ADJ
ejpam-5505	563	3	operator	operator	NOUN
ejpam-5505	563	4	of	of	ADP
ejpam-5505	563	5	a	a	DET
ejpam-5505	563	6	statistically	statistically	ADV
ejpam-5505	563	7	steady	steady	ADJ
ejpam-5505	563	8	flow	flow	NOUN
ejpam-5505	563	9	.	.	PUNCT
ejpam-5505	564	1	journal	journal	NOUN
ejpam-5505	564	2	of	of	ADP
ejpam-5505	564	3	fluid	fluid	ADJ
ejpam-5505	564	4	mechanics	mechanic	NOUN
ejpam-5505	564	5	,	,	PUNCT
ejpam-5505	564	6	968	968	NUM
ejpam-5505	564	7	:	:	PUNCT
ejpam-5505	564	8	a13	a13	NOUN
ejpam-5505	564	9	,	,	PUNCT
ejpam-5505	564	10	2023	2023	NUM
ejpam-5505	564	11	.	.	PUNCT
ejpam-5505	565	1	[	[	X
ejpam-5505	565	2	20	20	NUM
ejpam-5505	565	3	]	]	X
ejpam-5505	565	4	martinez	martinez	PROPN
ejpam-5505	565	5	-	-	PUNCT
ejpam-5505	565	6	legaz	legaz	PROPN
ejpam-5505	565	7	and	and	CCONJ
ejpam-5505	565	8	benar	benar	PROPN
ejpam-5505	565	9	fux	fux	PROPN
ejpam-5505	565	10	svaiter	svaiter	NOUN
ejpam-5505	565	11	.	.	PUNCT
ejpam-5505	566	1	monotone	monotone	ADJ
ejpam-5505	566	2	operators	operator	NOUN
ejpam-5505	566	3	representable	representable	VERB
ejpam-5505	566	4	by	by	ADP
ejpam-5505	566	5	lsc	lsc	PROPN
ejpam-5505	566	6	convex	convex	PROPN
ejpam-5505	566	7	functions	function	NOUN
ejpam-5505	566	8	.	.	PUNCT
ejpam-5505	567	1	set	set	NOUN
ejpam-5505	567	2	-	-	PUNCT
ejpam-5505	567	3	valued	value	VERB
ejpam-5505	567	4	analysis	analysis	NOUN
ejpam-5505	567	5	,	,	PUNCT
ejpam-5505	567	6	10(3):21–46	10(3):21–46	NUM
ejpam-5505	567	7	,	,	PUNCT
ejpam-5505	567	8	2005	2005	NUM
ejpam-5505	567	9	.	.	PUNCT
ejpam-5505	568	1	[	[	X
ejpam-5505	568	2	21	21	NUM
ejpam-5505	568	3	]	]	X
ejpam-5505	568	4	george	george	PROPN
ejpam-5505	568	5	j	j	PROPN
ejpam-5505	568	6	minty	minty	PROPN
ejpam-5505	568	7	.	.	PUNCT
ejpam-5505	569	1	monotone	monotone	ADJ
ejpam-5505	569	2	(	(	PUNCT
ejpam-5505	569	3	nonlinear	nonlinear	ADJ
ejpam-5505	569	4	)	)	PUNCT
ejpam-5505	569	5	operators	operator	NOUN
ejpam-5505	569	6	in	in	ADP
ejpam-5505	569	7	hilbert	hilbert	PROPN
ejpam-5505	569	8	space	space	NOUN
ejpam-5505	569	9	.	.	PUNCT
ejpam-5505	570	1	1962	1962	NUM
ejpam-5505	570	2	.	.	PUNCT
ejpam-5505	571	1	[	[	X
ejpam-5505	571	2	22	22	NUM
ejpam-5505	571	3	]	]	PUNCT
ejpam-5505	571	4	eberhard	eberhard	NOUN
ejpam-5505	571	5	zeidler	zeidler	NOUN
ejpam-5505	571	6	.	.	PUNCT
ejpam-5505	572	1	nonlinear	nonlinear	ADJ
ejpam-5505	572	2	functional	functional	ADJ
ejpam-5505	572	3	analysis	analysis	NOUN
ejpam-5505	572	4	and	and	CCONJ
ejpam-5505	572	5	its	its	PRON
ejpam-5505	572	6	applications	application	NOUN
ejpam-5505	572	7	i	i	PRON
ejpam-5505	572	8	:	:	PUNCT
ejpam-5505	572	9	fixed	fix	VERB
ejpam-5505	572	10	point	point	NOUN
ejpam-5505	572	11	theorems	theorem	NOUN
ejpam-5505	572	12	.	.	PUNCT
ejpam-5505	573	1	springer	springer	NOUN
ejpam-5505	573	2	-	-	PUNCT
ejpam-5505	573	3	verlag	verlag	PROPN
ejpam-5505	573	4	,	,	PUNCT
ejpam-5505	573	5	1993	1993	NUM
ejpam-5505	573	6	.	.	PUNCT