id	sid	tid	token	lemma	pos
ejpam-5504	1	1	european	european	PROPN
ejpam-5504	1	2	journal	journal	PROPN
ejpam-5504	1	3	of	of	ADP
ejpam-5504	1	4	pure	pure	ADJ
ejpam-5504	1	5	and	and	CCONJ
ejpam-5504	1	6	applied	apply	VERB
ejpam-5504	1	7	mathematics	mathematic	NOUN
ejpam-5504	1	8	vol	vol	NOUN
ejpam-5504	1	9	.	.	PROPN
ejpam-5504	2	1	17	17	NUM
ejpam-5504	2	2	,	,	PUNCT
ejpam-5504	2	3	no	no	INTJ
ejpam-5504	2	4	.	.	NOUN
ejpam-5504	2	5	4	4	NUM
ejpam-5504	2	6	,	,	PUNCT
ejpam-5504	2	7	2024	2024	NUM
ejpam-5504	2	8	,	,	PUNCT
ejpam-5504	2	9	3660	3660	NUM
ejpam-5504	2	10	-	-	SYM
ejpam-5504	2	11	3676	3676	NUM
ejpam-5504	2	12	issn	issn	PROPN
ejpam-5504	2	13	1307	1307	NUM
ejpam-5504	2	14	-	-	SYM
ejpam-5504	2	15	5543	5543	NUM
ejpam-5504	2	16	–	–	PUNCT
ejpam-5504	2	17	ejpam.com	ejpam.com	X
ejpam-5504	2	18	published	publish	VERB
ejpam-5504	2	19	by	by	ADP
ejpam-5504	2	20	new	new	PROPN
ejpam-5504	2	21	york	york	PROPN
ejpam-5504	2	22	business	business	PROPN
ejpam-5504	2	23	global	global	ADJ
ejpam-5504	2	24	additional	additional	ADJ
ejpam-5504	2	25	studies	study	NOUN
ejpam-5504	2	26	on	on	ADP
ejpam-5504	2	27	displacement	displacement	ADJ
ejpam-5504	2	28	mapping	mapping	NOUN
ejpam-5504	2	29	with	with	ADP
ejpam-5504	2	30	restrictions	restriction	NOUN
ejpam-5504	2	31	salihah	salihah	PROPN
ejpam-5504	2	32	thabet	thabet	ADJ
ejpam-5504	2	33	alwadani	alwadani	ADJ
ejpam-5504	2	34	mathematics	mathematics	PROPN
ejpam-5504	2	35	,	,	PUNCT
ejpam-5504	2	36	yanbu	yanbu	PROPN
ejpam-5504	2	37	industrial	industrial	PROPN
ejpam-5504	2	38	college	college	PROPN
ejpam-5504	2	39	,	,	PUNCT
ejpam-5504	2	40	the	the	DET
ejpam-5504	2	41	royal	royal	ADJ
ejpam-5504	2	42	comission	comission	NOUN
ejpam-5504	2	43	for	for	ADP
ejpam-5504	2	44	jubail	jubail	PROPN
ejpam-5504	2	45	and	and	CCONJ
ejpam-5504	2	46	yanbu	yanbu	ADJ
ejpam-5504	2	47	,	,	PUNCT
ejpam-5504	2	48	yanbu	yanbu	ADJ
ejpam-5504	2	49	,	,	PUNCT
ejpam-5504	2	50	saudi	saudi	PROPN
ejpam-5504	2	51	arabia	arabia	PROPN
ejpam-5504	2	52	abstract	abstract	NOUN
ejpam-5504	2	53	.	.	PUNCT
ejpam-5504	3	1	the	the	DET
ejpam-5504	3	2	theory	theory	NOUN
ejpam-5504	3	3	of	of	ADP
ejpam-5504	3	4	monotone	monotone	ADJ
ejpam-5504	3	5	operators	operator	NOUN
ejpam-5504	3	6	is	be	AUX
ejpam-5504	3	7	fundamental	fundamental	ADJ
ejpam-5504	3	8	in	in	ADP
ejpam-5504	3	9	modern	modern	ADJ
ejpam-5504	3	10	optimization	optimization	NOUN
ejpam-5504	3	11	and	and	CCONJ
ejpam-5504	3	12	various	various	ADJ
ejpam-5504	3	13	areas	area	NOUN
ejpam-5504	3	14	of	of	ADP
ejpam-5504	3	15	nonlinear	nonlinear	ADJ
ejpam-5504	3	16	analysis	analysis	NOUN
ejpam-5504	3	17	.	.	PUNCT
ejpam-5504	4	1	key	key	ADJ
ejpam-5504	4	2	classes	class	NOUN
ejpam-5504	4	3	of	of	ADP
ejpam-5504	4	4	monotone	monotone	ADJ
ejpam-5504	4	5	operators	operator	NOUN
ejpam-5504	4	6	include	include	VERB
ejpam-5504	4	7	matrices	matrix	NOUN
ejpam-5504	4	8	with	with	ADP
ejpam-5504	4	9	a	a	DET
ejpam-5504	4	10	positive	positive	ADJ
ejpam-5504	4	11	semidefinite	semidefinite	NOUN
ejpam-5504	4	12	symmetric	symmetric	ADJ
ejpam-5504	4	13	component	component	NOUN
ejpam-5504	4	14	and	and	CCONJ
ejpam-5504	4	15	subdifferential	subdifferential	ADJ
ejpam-5504	4	16	operators	operator	NOUN
ejpam-5504	4	17	.	.	PUNCT
ejpam-5504	5	1	in	in	ADP
ejpam-5504	5	2	this	this	DET
ejpam-5504	5	3	paper	paper	NOUN
ejpam-5504	5	4	,	,	PUNCT
ejpam-5504	5	5	we	we	PRON
ejpam-5504	5	6	extend	extend	VERB
ejpam-5504	5	7	our	our	PRON
ejpam-5504	5	8	investigation	investigation	NOUN
ejpam-5504	5	9	to	to	ADP
ejpam-5504	5	10	displacement	displacement	ADJ
ejpam-5504	5	11	mappings	mapping	NOUN
ejpam-5504	5	12	.	.	PUNCT
ejpam-5504	6	1	we	we	PRON
ejpam-5504	6	2	derive	derive	VERB
ejpam-5504	6	3	formulas	formula	NOUN
ejpam-5504	6	4	for	for	ADP
ejpam-5504	6	5	set	set	NOUN
ejpam-5504	6	6	-	-	PUNCT
ejpam-5504	6	7	valued	value	VERB
ejpam-5504	6	8	and	and	CCONJ
ejpam-5504	6	9	moore	moore	PROPN
ejpam-5504	6	10	-	-	PUNCT
ejpam-5504	6	11	penrose	penrose	PROPN
ejpam-5504	6	12	inverses	inverse	VERB
ejpam-5504	6	13	.	.	PUNCT
ejpam-5504	7	1	additionally	additionally	ADV
ejpam-5504	7	2	,	,	PUNCT
ejpam-5504	7	3	we	we	PRON
ejpam-5504	7	4	conduct	conduct	VERB
ejpam-5504	7	5	a	a	DET
ejpam-5504	7	6	thorough	thorough	ADJ
ejpam-5504	7	7	examination	examination	NOUN
ejpam-5504	7	8	of	of	ADP
ejpam-5504	7	9	the	the	DET
ejpam-5504	7	10	operators	operator	NOUN
ejpam-5504	7	11	(	(	PUNCT
ejpam-5504	7	12	one	one	NUM
ejpam-5504	7	13	-	-	PUNCT
ejpam-5504	7	14	half	half	NOUN
ejpam-5504	7	15	times	time	NOUN
ejpam-5504	7	16	the	the	DET
ejpam-5504	7	17	identity	identity	NOUN
ejpam-5504	7	18	plus	plus	CCONJ
ejpam-5504	7	19	t	t	PROPN
ejpam-5504	7	20	)	)	PUNCT
ejpam-5504	7	21	and	and	CCONJ
ejpam-5504	7	22	its	its	PRON
ejpam-5504	7	23	inverse	inverse	NOUN
ejpam-5504	7	24	,	,	PUNCT
ejpam-5504	7	25	providing	provide	VERB
ejpam-5504	7	26	a	a	DET
ejpam-5504	7	27	formula	formula	NOUN
ejpam-5504	7	28	for	for	ADP
ejpam-5504	7	29	the	the	DET
ejpam-5504	7	30	inverse	inverse	NOUN
ejpam-5504	7	31	of	of	ADP
ejpam-5504	7	32	the	the	DET
ejpam-5504	7	33	operator	operator	NOUN
ejpam-5504	7	34	.	.	PUNCT
ejpam-5504	8	1	our	our	PRON
ejpam-5504	8	2	results	result	NOUN
ejpam-5504	8	3	are	be	AUX
ejpam-5504	8	4	illustrated	illustrate	VERB
ejpam-5504	8	5	through	through	ADP
ejpam-5504	8	6	an	an	DET
ejpam-5504	8	7	analysis	analysis	NOUN
ejpam-5504	8	8	of	of	ADP
ejpam-5504	8	9	reflected	reflect	VERB
ejpam-5504	8	10	and	and	CCONJ
ejpam-5504	8	11	projection	projection	NOUN
ejpam-5504	8	12	operators	operator	NOUN
ejpam-5504	8	13	onto	onto	ADP
ejpam-5504	8	14	closed	closed	ADJ
ejpam-5504	8	15	linear	linear	ADJ
ejpam-5504	8	16	subspaces	subspace	NOUN
ejpam-5504	8	17	.	.	PUNCT
ejpam-5504	9	1	2020	2020	NUM
ejpam-5504	9	2	mathematics	mathematic	NOUN
ejpam-5504	9	3	subject	subject	NOUN
ejpam-5504	9	4	classifications	classification	NOUN
ejpam-5504	9	5	:	:	PUNCT
ejpam-5504	9	6	47h09	47h09	NUM
ejpam-5504	9	7	,	,	PUNCT
ejpam-5504	9	8	47h05	47h05	NUM
ejpam-5504	9	9	,	,	PUNCT
ejpam-5504	9	10	47a06	47a06	NUM
ejpam-5504	9	11	,	,	PUNCT
ejpam-5504	9	12	90c25	90c25	NUM
ejpam-5504	9	13	key	key	ADJ
ejpam-5504	9	14	words	word	NOUN
ejpam-5504	9	15	and	and	CCONJ
ejpam-5504	9	16	phrases	phrase	NOUN
ejpam-5504	9	17	:	:	PUNCT
ejpam-5504	9	18	displacement	displacement	ADJ
ejpam-5504	9	19	mapping	mapping	NOUN
ejpam-5504	9	20	,	,	PUNCT
ejpam-5504	9	21	maximally	maximally	ADV
ejpam-5504	9	22	monotone	monotone	ADJ
ejpam-5504	9	23	operator	operator	NOUN
ejpam-5504	9	24	,	,	PUNCT
ejpam-5504	9	25	nonexpansive	nonexpansive	ADJ
ejpam-5504	9	26	mapping	mapping	NOUN
ejpam-5504	9	27	,	,	PUNCT
ejpam-5504	9	28	,	,	PUNCT
ejpam-5504	9	29	moore	moore	PROPN
ejpam-5504	9	30	-	-	PUNCT
ejpam-5504	9	31	penrose	penrose	PROPN
ejpam-5504	9	32	inverse	inverse	NOUN
ejpam-5504	9	33	set	set	NOUN
ejpam-5504	9	34	-	-	PUNCT
ejpam-5504	9	35	valued	value	VERB
ejpam-5504	9	36	inverse	inverse	NOUN
ejpam-5504	9	37	,	,	PUNCT
ejpam-5504	9	38	inverse	inverse	NOUN
ejpam-5504	9	39	,	,	PUNCT
ejpam-5504	9	40	yosida	yosida	PROPN
ejpam-5504	9	41	approximation	approximation	NOUN
ejpam-5504	9	42	1	1	NUM
ejpam-5504	9	43	.	.	PUNCT
ejpam-5504	10	1	introduction	introduction	NOUN
ejpam-5504	10	2	it	it	PRON
ejpam-5504	10	3	is	be	AUX
ejpam-5504	10	4	well	well	ADV
ejpam-5504	10	5	known	know	VERB
ejpam-5504	10	6	that	that	SCONJ
ejpam-5504	10	7	one	one	NUM
ejpam-5504	10	8	of	of	ADP
ejpam-5504	10	9	important	important	ADJ
ejpam-5504	10	10	classes	class	NOUN
ejpam-5504	10	11	of	of	ADP
ejpam-5504	10	12	monotone	monotone	ADJ
ejpam-5504	10	13	operators	operator	NOUN
ejpam-5504	10	14	are	be	AUX
ejpam-5504	10	15	displacement	displacement	ADJ
ejpam-5504	10	16	mappings	mapping	NOUN
ejpam-5504	10	17	of	of	ADP
ejpam-5504	10	18	nonexpansive	nonexpansive	ADJ
ejpam-5504	10	19	mappings	mapping	NOUN
ejpam-5504	10	20	.	.	PUNCT
ejpam-5504	11	1	there	there	PRON
ejpam-5504	11	2	are	be	VERB
ejpam-5504	11	3	many	many	ADJ
ejpam-5504	11	4	key	key	ADJ
ejpam-5504	11	5	examples	example	NOUN
ejpam-5504	11	6	that	that	PRON
ejpam-5504	11	7	have	have	AUX
ejpam-5504	11	8	proven	prove	VERB
ejpam-5504	11	9	how	how	SCONJ
ejpam-5504	11	10	these	these	DET
ejpam-5504	11	11	mappings	mapping	NOUN
ejpam-5504	11	12	are	be	AUX
ejpam-5504	11	13	highly	highly	ADV
ejpam-5504	11	14	useful	useful	ADJ
ejpam-5504	11	15	in	in	ADP
ejpam-5504	11	16	optimization	optimization	NOUN
ejpam-5504	11	17	problems	problem	NOUN
ejpam-5504	11	18	.	.	PUNCT
ejpam-5504	12	1	for	for	ADP
ejpam-5504	12	2	example	example	NOUN
ejpam-5504	12	3	,	,	PUNCT
ejpam-5504	12	4	in	in	ADP
ejpam-5504	12	5	2016	2016	NUM
ejpam-5504	12	6	heinz	heinz	PROPN
ejpam-5504	12	7	h.	h.	PROPN
ejpam-5504	12	8	bauschke	bauschke	PROPN
ejpam-5504	12	9	,	,	PUNCT
ejpam-5504	12	10	warren	warren	PROPN
ejpam-5504	12	11	hare	hare	PROPN
ejpam-5504	12	12	,	,	PUNCT
ejpam-5504	12	13	and	and	CCONJ
ejpam-5504	12	14	walaa	walaa	PROPN
ejpam-5504	12	15	moursi	moursi	PROPN
ejpam-5504	12	16	used	use	VERB
ejpam-5504	12	17	displacement	displacement	ADJ
ejpam-5504	12	18	mappings	mapping	NOUN
ejpam-5504	12	19	in	in	ADP
ejpam-5504	12	20	analyzing	analyze	VERB
ejpam-5504	12	21	the	the	DET
ejpam-5504	12	22	range	range	NOUN
ejpam-5504	12	23	of	of	ADP
ejpam-5504	12	24	the	the	DET
ejpam-5504	12	25	douglas	douglas	PROPN
ejpam-5504	12	26	–	–	PUNCT
ejpam-5504	12	27	rachford	rachford	ADJ
ejpam-5504	12	28	operator	operator	NOUN
ejpam-5504	12	29	to	to	PART
ejpam-5504	12	30	derive	derive	VERB
ejpam-5504	12	31	valuable	valuable	ADJ
ejpam-5504	12	32	duality	duality	NOUN
ejpam-5504	12	33	results	result	NOUN
ejpam-5504	12	34	,	,	PUNCT
ejpam-5504	12	35	see	see	VERB
ejpam-5504	12	36	[	[	X
ejpam-5504	12	37	5	5	NUM
ejpam-5504	12	38	]	]	PUNCT
ejpam-5504	12	39	.	.	PUNCT
ejpam-5504	13	1	additionally	additionally	ADV
ejpam-5504	13	2	,	,	PUNCT
ejpam-5504	13	3	the	the	DET
ejpam-5504	13	4	asymptotic	asymptotic	ADJ
ejpam-5504	13	5	regularity	regularity	NOUN
ejpam-5504	13	6	results	result	NOUN
ejpam-5504	13	7	for	for	ADP
ejpam-5504	13	8	nonexpansive	nonexpansive	ADJ
ejpam-5504	13	9	mappings	mapping	NOUN
ejpam-5504	13	10	were	be	AUX
ejpam-5504	13	11	generalized	generalize	VERB
ejpam-5504	13	12	in	in	ADP
ejpam-5504	13	13	[	[	X
ejpam-5504	13	14	8	8	NUM
ejpam-5504	13	15	]	]	PUNCT
ejpam-5504	13	16	to	to	ADP
ejpam-5504	13	17	the	the	DET
ejpam-5504	13	18	broader	broad	ADJ
ejpam-5504	13	19	context	context	NOUN
ejpam-5504	13	20	of	of	ADP
ejpam-5504	13	21	displacement	displacement	ADJ
ejpam-5504	13	22	mappings	mapping	NOUN
ejpam-5504	13	23	.	.	PUNCT
ejpam-5504	14	1	overall	overall	ADV
ejpam-5504	14	2	,	,	PUNCT
ejpam-5504	14	3	the	the	DET
ejpam-5504	14	4	displacement	displacement	ADJ
ejpam-5504	14	5	mapping	mapping	NOUN
ejpam-5504	14	6	framework	framework	NOUN
ejpam-5504	14	7	has	have	AUX
ejpam-5504	14	8	emerged	emerge	VERB
ejpam-5504	14	9	as	as	ADP
ejpam-5504	14	10	a	a	DET
ejpam-5504	14	11	powerful	powerful	ADJ
ejpam-5504	14	12	tool	tool	NOUN
ejpam-5504	14	13	for	for	ADP
ejpam-5504	14	14	analyzing	analyze	VERB
ejpam-5504	14	15	the	the	DET
ejpam-5504	14	16	behavior	behavior	NOUN
ejpam-5504	14	17	of	of	ADP
ejpam-5504	14	18	nonexpansive	nonexpansive	ADJ
ejpam-5504	14	19	mappings	mapping	NOUN
ejpam-5504	14	20	,	,	PUNCT
ejpam-5504	14	21	with	with	ADP
ejpam-5504	14	22	a	a	DET
ejpam-5504	14	23	range	range	NOUN
ejpam-5504	14	24	of	of	ADP
ejpam-5504	14	25	important	important	ADJ
ejpam-5504	14	26	applications	application	NOUN
ejpam-5504	14	27	in	in	ADP
ejpam-5504	14	28	optimization	optimization	NOUN
ejpam-5504	14	29	and	and	CCONJ
ejpam-5504	14	30	related	related	ADJ
ejpam-5504	14	31	areas	area	NOUN
ejpam-5504	14	32	.	.	PUNCT
ejpam-5504	15	1	throughout	throughout	ADP
ejpam-5504	15	2	,	,	PUNCT
ejpam-5504	15	3	we	we	PRON
ejpam-5504	15	4	assume	assume	VERB
ejpam-5504	15	5	that	that	SCONJ
ejpam-5504	15	6	x	x	PRON
ejpam-5504	15	7	is	be	AUX
ejpam-5504	15	8	a	a	DET
ejpam-5504	15	9	real	real	ADJ
ejpam-5504	15	10	hilbert	hilbert	NOUN
ejpam-5504	15	11	space	space	NOUN
ejpam-5504	15	12	with	with	ADP
ejpam-5504	15	13	inner	inner	ADJ
ejpam-5504	15	14	product	product	NOUN
ejpam-5504	15	15	⟨	⟨	VERB
ejpam-5504	15	16	·	·	PUNCT
ejpam-5504	15	17	,	,	PUNCT
ejpam-5504	15	18	·	·	PUNCT
ejpam-5504	15	19	⟩	⟩	NOUN
ejpam-5504	15	20	:	:	PUNCT
ejpam-5504	15	21	x	x	PUNCT
ejpam-5504	15	22	×	×	NOUN
ejpam-5504	15	23	x	x	INTJ
ejpam-5504	15	24	→	→	SYM
ejpam-5504	15	25	r	r	NOUN
ejpam-5504	15	26	,	,	PUNCT
ejpam-5504	15	27	(	(	PUNCT
ejpam-5504	15	28	1	1	X
ejpam-5504	15	29	)	)	PUNCT
ejpam-5504	15	30	doi	doi	NOUN
ejpam-5504	15	31	:	:	PUNCT
ejpam-5504	15	32	https://doi.org/10.29020/nybg.ejpam.v17i4.5504	https://doi.org/10.29020/nybg.ejpam.v17i4.5504	VERB
ejpam-5504	15	33	email	email	NOUN
ejpam-5504	15	34	address	address	NOUN
ejpam-5504	15	35	:	:	PUNCT
ejpam-5504	15	36	salihah.s.alwadani@gmail.com	salihah.s.alwadani@gmail.com	PROPN
ejpam-5504	15	37	(	(	PUNCT
ejpam-5504	15	38	s.	s.	PROPN
ejpam-5504	15	39	t.	t.	PROPN
ejpam-5504	15	40	alwadani	alwadani	PROPN
ejpam-5504	15	41	)	)	PUNCT
ejpam-5504	15	42	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5504	15	43	3660	3660	NUM
ejpam-5504	15	44	copyright	copyright	NOUN
ejpam-5504	15	45	:	:	PUNCT
ejpam-5504	15	46	©	©	PROPN
ejpam-5504	15	47	2024	2024	NUM
ejpam-5504	15	48	the	the	DET
ejpam-5504	15	49	author(s	author(s	NOUN
ejpam-5504	15	50	)	)	PUNCT
ejpam-5504	15	51	.	.	PUNCT
ejpam-5504	16	1	(	(	PUNCT
ejpam-5504	16	2	cc	cc	NOUN
ejpam-5504	16	3	by	by	ADP
ejpam-5504	16	4	-	-	PUNCT
ejpam-5504	16	5	nc	nc	PROPN
ejpam-5504	16	6	4.0	4.0	NUM
ejpam-5504	16	7	)	)	PUNCT
ejpam-5504	16	8	s.t	s.t	PROPN
ejpam-5504	16	9	.	.	PROPN
ejpam-5504	16	10	alwadani	alwadani	PROPN
ejpam-5504	16	11	/	/	SYM
ejpam-5504	16	12	eur	eur	PROPN
ejpam-5504	16	13	.	.	PUNCT
ejpam-5504	17	1	j.	j.	PROPN
ejpam-5504	17	2	pure	pure	PROPN
ejpam-5504	17	3	appl	appl	PROPN
ejpam-5504	17	4	.	.	PROPN
ejpam-5504	17	5	math	math	PROPN
ejpam-5504	17	6	,	,	PUNCT
ejpam-5504	17	7	17	17	NUM
ejpam-5504	17	8	(	(	PUNCT
ejpam-5504	17	9	4	4	NUM
ejpam-5504	17	10	)	)	PUNCT
ejpam-5504	17	11	(	(	PUNCT
ejpam-5504	17	12	2024	2024	NUM
ejpam-5504	17	13	)	)	PUNCT
ejpam-5504	17	14	,	,	PUNCT
ejpam-5504	17	15	3660	3660	NUM
ejpam-5504	17	16	-	-	SYM
ejpam-5504	17	17	3676	3676	NUM
ejpam-5504	17	18	3661	3661	NUM
ejpam-5504	17	19	and	and	CCONJ
ejpam-5504	17	20	induced	induce	VERB
ejpam-5504	17	21	norm	norm	NOUN
ejpam-5504	17	22	∥	∥	X
ejpam-5504	17	23	·	·	PUNCT
ejpam-5504	17	24	∥	∥	X
ejpam-5504	17	25	:	:	PUNCT
ejpam-5504	18	1	x	x	X
ejpam-5504	18	2	→	→	PUNCT
ejpam-5504	18	3	r	r	NOUN
ejpam-5504	18	4	:	:	PUNCT
ejpam-5504	18	5	x	x	SYM
ejpam-5504	18	6	7→	7→	NUM
ejpam-5504	18	7	√	√	NUM
ejpam-5504	18	8	⟨x	⟨x	NUM
ejpam-5504	18	9	,	,	PUNCT
ejpam-5504	18	10	x⟩.	x⟩.	PROPN
ejpam-5504	18	11	we	we	PRON
ejpam-5504	18	12	also	also	ADV
ejpam-5504	18	13	assume	assume	VERB
ejpam-5504	18	14	that	that	SCONJ
ejpam-5504	18	15	a	a	DET
ejpam-5504	18	16	:	:	PUNCT
ejpam-5504	18	17	x	x	SYM
ejpam-5504	18	18	⇒	⇒	NOUN
ejpam-5504	18	19	x	x	X
ejpam-5504	18	20	and	and	CCONJ
ejpam-5504	18	21	b	b	NOUN
ejpam-5504	18	22	:	:	PUNCT
ejpam-5504	18	23	x	x	SYM
ejpam-5504	18	24	⇒	⇒	NOUN
ejpam-5504	18	25	x	x	PUNCT
ejpam-5504	18	26	are	be	AUX
ejpam-5504	18	27	maximally	maximally	ADV
ejpam-5504	18	28	monotone	monotone	ADJ
ejpam-5504	18	29	operators	operator	NOUN
ejpam-5504	18	30	.	.	PUNCT
ejpam-5504	19	1	the	the	DET
ejpam-5504	19	2	resolvent	resolvent	NOUN
ejpam-5504	19	3	and	and	CCONJ
ejpam-5504	19	4	the	the	DET
ejpam-5504	19	5	reflected	reflect	VERB
ejpam-5504	19	6	resolvent	resolvent	NOUN
ejpam-5504	19	7	associated	associate	VERB
ejpam-5504	19	8	with	with	ADP
ejpam-5504	19	9	a	a	PRON
ejpam-5504	19	10	are	be	AUX
ejpam-5504	19	11	ja	ja	PROPN
ejpam-5504	19	12	=	=	PUNCT
ejpam-5504	19	13	(	(	PUNCT
ejpam-5504	19	14	id+a)−1	id+a)−1	NOUN
ejpam-5504	19	15	and	and	CCONJ
ejpam-5504	19	16	ra	ra	NOUN
ejpam-5504	19	17	=	=	SYM
ejpam-5504	20	1	2ja	2ja	NOUN
ejpam-5504	20	2	−	−	PROPN
ejpam-5504	21	1	i	i	PROPN
ejpam-5504	21	2	d	d	PROPN
ejpam-5504	21	3	,	,	PUNCT
ejpam-5504	21	4	(	(	PUNCT
ejpam-5504	21	5	2	2	X
ejpam-5504	21	6	)	)	PUNCT
ejpam-5504	21	7	respectively	respectively	ADV
ejpam-5504	21	8	.	.	PUNCT
ejpam-5504	22	1	an	an	DET
ejpam-5504	22	2	operator	operator	NOUN
ejpam-5504	22	3	t	t	NOUN
ejpam-5504	22	4	:	:	PUNCT
ejpam-5504	22	5	x	x	SYM
ejpam-5504	22	6	⇒	⇒	PROPN
ejpam-5504	22	7	x	x	VERB
ejpam-5504	22	8	is	be	AUX
ejpam-5504	22	9	nonexpansive	nonexpansive	ADJ
ejpam-5504	22	10	if	if	SCONJ
ejpam-5504	22	11	it	it	PRON
ejpam-5504	22	12	is	be	AUX
ejpam-5504	22	13	lipschitz	lipschitz	NOUN
ejpam-5504	22	14	continuous	continuous	ADJ
ejpam-5504	22	15	with	with	ADP
ejpam-5504	22	16	constant	constant	ADJ
ejpam-5504	22	17	1	1	NUM
ejpam-5504	22	18	,	,	PUNCT
ejpam-5504	22	19	i.e.	i.e.	X
ejpam-5504	22	20	,	,	PUNCT
ejpam-5504	22	21	(	(	PUNCT
ejpam-5504	22	22	∀x	∀x	X
ejpam-5504	22	23	∈	∈	PROPN
ejpam-5504	22	24	x	x	X
ejpam-5504	22	25	)	)	PUNCT
ejpam-5504	22	26	(	(	PUNCT
ejpam-5504	22	27	∀y	∀y	PROPN
ejpam-5504	22	28	∈	∈	PROPN
ejpam-5504	22	29	x	x	X
ejpam-5504	22	30	)	)	PUNCT
ejpam-5504	23	1	∥tx	∥tx	CCONJ
ejpam-5504	24	1	−	−	PROPN
ejpam-5504	24	2	ty∥	ty∥	NOUN
ejpam-5504	24	3	≤	≤	ADV
ejpam-5504	25	1	∥x	∥x	AUX
ejpam-5504	25	2	−	−	PROPN
ejpam-5504	25	3	y∥.	y∥.	NOUN
ejpam-5504	25	4	(	(	PUNCT
ejpam-5504	25	5	3	3	NUM
ejpam-5504	25	6	)	)	PUNCT
ejpam-5504	25	7	moreover	moreover	ADV
ejpam-5504	25	8	,	,	PUNCT
ejpam-5504	25	9	t	t	X
ejpam-5504	25	10	:	:	PUNCT
ejpam-5504	25	11	d	d	X
ejpam-5504	25	12	⇒	⇒	NOUN
ejpam-5504	25	13	x	x	PUNCT
ejpam-5504	25	14	is	be	AUX
ejpam-5504	25	15	firmly	firmly	ADV
ejpam-5504	25	16	nonexpansive	nonexpansive	ADJ
ejpam-5504	25	17	if	if	SCONJ
ejpam-5504	25	18	(	(	PUNCT
ejpam-5504	25	19	∀x	∀x	X
ejpam-5504	25	20	∈	∈	PROPN
ejpam-5504	25	21	d	d	NOUN
ejpam-5504	25	22	)	)	PUNCT
ejpam-5504	25	23	(	(	PUNCT
ejpam-5504	25	24	∀y	∀y	PROPN
ejpam-5504	25	25	∈	∈	PROPN
ejpam-5504	25	26	d	d	NOUN
ejpam-5504	25	27	)	)	PUNCT
ejpam-5504	26	1	∥tx	∥tx	PRON
ejpam-5504	26	2	−	−	PROPN
ejpam-5504	26	3	ty∥2	ty∥2	NOUN
ejpam-5504	26	4	+	+	CCONJ
ejpam-5504	26	5	∥(id−t)x	∥(id−t)x	PROPN
ejpam-5504	26	6	−	−	PROPN
ejpam-5504	26	7	(	(	PUNCT
ejpam-5504	26	8	id−t)y∥2	id−t)y∥2	PROPN
ejpam-5504	26	9	≤	≤	PUNCT
ejpam-5504	27	1	∥x	∥x	PROPN
ejpam-5504	27	2	−	−	PROPN
ejpam-5504	27	3	y∥2	y∥2	NOUN
ejpam-5504	27	4	.	.	PUNCT
ejpam-5504	28	1	(	(	PUNCT
ejpam-5504	28	2	4	4	X
ejpam-5504	28	3	)	)	PUNCT
ejpam-5504	28	4	fact	fact	NOUN
ejpam-5504	28	5	1	1	NUM
ejpam-5504	28	6	.	.	PUNCT
ejpam-5504	29	1	[	[	X
ejpam-5504	29	2	4	4	NUM
ejpam-5504	29	3	,	,	PUNCT
ejpam-5504	29	4	definition	definition	NOUN
ejpam-5504	29	5	4.10	4.10	NUM
ejpam-5504	29	6	]	]	PUNCT
ejpam-5504	29	7	let	let	VERB
ejpam-5504	29	8	d	d	PRON
ejpam-5504	29	9	be	be	AUX
ejpam-5504	29	10	a	a	DET
ejpam-5504	29	11	nonempty	nonempty	ADJ
ejpam-5504	29	12	subset	subset	NOUN
ejpam-5504	29	13	of	of	ADP
ejpam-5504	29	14	x	x	PRON
ejpam-5504	29	15	,	,	PUNCT
ejpam-5504	29	16	let	let	VERB
ejpam-5504	29	17	t	t	NOUN
ejpam-5504	29	18	:	:	PUNCT
ejpam-5504	29	19	d	d	X
ejpam-5504	29	20	→	→	SYM
ejpam-5504	29	21	x	x	PART
ejpam-5504	29	22	,	,	PUNCT
ejpam-5504	29	23	and	and	CCONJ
ejpam-5504	29	24	let	let	VERB
ejpam-5504	29	25	β	β	PRON
ejpam-5504	29	26	∈	∈	PROPN
ejpam-5504	29	27	r++	r++	NOUN
ejpam-5504	29	28	,	,	PUNCT
ejpam-5504	29	29	where	where	SCONJ
ejpam-5504	29	30	r++	r++	NOUN
ejpam-5504	29	31	is	be	AUX
ejpam-5504	29	32	the	the	DET
ejpam-5504	29	33	set	set	NOUN
ejpam-5504	29	34	of	of	ADP
ejpam-5504	29	35	strictly	strictly	ADV
ejpam-5504	29	36	positive	positive	ADJ
ejpam-5504	29	37	real	real	ADJ
ejpam-5504	29	38	numbers	number	NOUN
ejpam-5504	29	39	]	]	PUNCT
ejpam-5504	29	40	0,+∞	0,+∞	NUM
ejpam-5504	30	1	[	[	X
ejpam-5504	30	2	.	.	PUNCT
ejpam-5504	31	1	then	then	ADV
ejpam-5504	31	2	t	t	PROPN
ejpam-5504	31	3	is	be	AUX
ejpam-5504	31	4	β	β	NOUN
ejpam-5504	31	5	-	-	ADJ
ejpam-5504	31	6	cocoercive	cocoercive	ADJ
ejpam-5504	31	7	(	(	PUNCT
ejpam-5504	31	8	or	or	CCONJ
ejpam-5504	31	9	βinverse	βinverse	VERB
ejpam-5504	31	10	strongly	strongly	ADV
ejpam-5504	31	11	monotone	monotone	ADJ
ejpam-5504	31	12	)	)	PUNCT
ejpam-5504	31	13	if	if	SCONJ
ejpam-5504	31	14	βt	βt	NOUN
ejpam-5504	31	15	is	be	AUX
ejpam-5504	31	16	firmly	firmly	ADV
ejpam-5504	31	17	nonexpansive	nonexpansive	ADJ
ejpam-5504	31	18	,	,	PUNCT
ejpam-5504	31	19	i.e.	i.e.	X
ejpam-5504	31	20	,	,	PUNCT
ejpam-5504	31	21	(	(	PUNCT
ejpam-5504	31	22	∀x	∀x	X
ejpam-5504	31	23	∈	∈	PROPN
ejpam-5504	31	24	d	d	NOUN
ejpam-5504	31	25	)	)	PUNCT
ejpam-5504	31	26	(	(	PUNCT
ejpam-5504	31	27	∀y	∀y	PROPN
ejpam-5504	31	28	∈	∈	PROPN
ejpam-5504	31	29	d	d	NOUN
ejpam-5504	31	30	)	)	PUNCT
ejpam-5504	31	31	⟨x	⟨x	VERB
ejpam-5504	31	32	−	−	PROPN
ejpam-5504	31	33	y	y	PROPN
ejpam-5504	31	34	,	,	PUNCT
ejpam-5504	31	35	tx	tx	PROPN
ejpam-5504	31	36	−	−	PROPN
ejpam-5504	31	37	ty⟩	ty⟩	PRON
ejpam-5504	31	38	≥	≥	NOUN
ejpam-5504	32	1	β∥tx	β∥tx	INTJ
ejpam-5504	32	2	−	−	PROPN
ejpam-5504	32	3	ty∥2	ty∥2	PROPN
ejpam-5504	32	4	.	.	PUNCT
ejpam-5504	33	1	in	in	ADP
ejpam-5504	33	2	optimization	optimization	NOUN
ejpam-5504	33	3	,	,	PUNCT
ejpam-5504	33	4	we	we	PRON
ejpam-5504	33	5	have	have	AUX
ejpam-5504	33	6	seen	see	VERB
ejpam-5504	33	7	the	the	DET
ejpam-5504	33	8	importance	importance	NOUN
ejpam-5504	33	9	the	the	DET
ejpam-5504	33	10	displacement	displacement	ADJ
ejpam-5504	33	11	mappings	mapping	NOUN
ejpam-5504	33	12	of	of	ADP
ejpam-5504	33	13	nonexpansive	nonexpansive	ADJ
ejpam-5504	33	14	mappings	mapping	NOUN
ejpam-5504	33	15	:	:	PUNCT
ejpam-5504	33	16	id−r	id−r	NOUN
ejpam-5504	33	17	(	(	PUNCT
ejpam-5504	33	18	5	5	NUM
ejpam-5504	33	19	)	)	PUNCT
ejpam-5504	33	20	because	because	SCONJ
ejpam-5504	33	21	of	of	ADP
ejpam-5504	33	22	the	the	DET
ejpam-5504	33	23	nice	nice	ADJ
ejpam-5504	33	24	properities	properitie	NOUN
ejpam-5504	33	25	that	that	PRON
ejpam-5504	33	26	have	have	VERB
ejpam-5504	33	27	such	such	ADJ
ejpam-5504	33	28	as	as	ADP
ejpam-5504	33	29	monotonicity	monotonicity	NOUN
ejpam-5504	33	30	which	which	PRON
ejpam-5504	33	31	plays	play	VERB
ejpam-5504	33	32	a	a	DET
ejpam-5504	33	33	central	central	ADJ
ejpam-5504	33	34	role	role	NOUN
ejpam-5504	33	35	in	in	ADP
ejpam-5504	33	36	modern	modern	ADJ
ejpam-5504	33	37	optimization	optimization	NOUN
ejpam-5504	33	38	(	(	PUNCT
ejpam-5504	33	39	see	see	VERB
ejpam-5504	33	40	[	[	X
ejpam-5504	33	41	4	4	NUM
ejpam-5504	33	42	,	,	PUNCT
ejpam-5504	33	43	11	11	NUM
ejpam-5504	33	44	,	,	PUNCT
ejpam-5504	33	45	18	18	NUM
ejpam-5504	33	46	,	,	PUNCT
ejpam-5504	33	47	20–23	20–23	NOUN
ejpam-5504	33	48	]	]	PUNCT
ejpam-5504	33	49	for	for	ADP
ejpam-5504	33	50	more	more	ADJ
ejpam-5504	33	51	details	detail	NOUN
ejpam-5504	33	52	)	)	PUNCT
ejpam-5504	33	53	.	.	PUNCT
ejpam-5504	34	1	a	a	DET
ejpam-5504	34	2	comprehensive	comprehensive	ADJ
ejpam-5504	34	3	analysis	analysis	NOUN
ejpam-5504	34	4	of	of	ADP
ejpam-5504	34	5	the	the	DET
ejpam-5504	34	6	displacement	displacement	ADJ
ejpam-5504	34	7	mappings	mapping	NOUN
ejpam-5504	34	8	of	of	ADP
ejpam-5504	34	9	nonexpansive	nonexpansive	ADJ
ejpam-5504	34	10	mappings	mapping	NOUN
ejpam-5504	34	11	from	from	ADP
ejpam-5504	34	12	the	the	DET
ejpam-5504	34	13	point	point	NOUN
ejpam-5504	34	14	of	of	ADP
ejpam-5504	34	15	view	view	NOUN
ejpam-5504	34	16	of	of	ADP
ejpam-5504	34	17	monotone	monotone	ADJ
ejpam-5504	34	18	operator	operator	NOUN
ejpam-5504	34	19	theory	theory	NOUN
ejpam-5504	34	20	under	under	ADP
ejpam-5504	34	21	the	the	DET
ejpam-5504	34	22	condition	condition	NOUN
ejpam-5504	34	23	of	of	ADP
ejpam-5504	34	24	isometry	isometry	NOUN
ejpam-5504	34	25	of	of	ADP
ejpam-5504	34	26	finite	finite	ADJ
ejpam-5504	34	27	order	order	NOUN
ejpam-5504	34	28	of	of	ADP
ejpam-5504	34	29	r	r	NOUN
ejpam-5504	34	30	are	be	AUX
ejpam-5504	34	31	given	give	VERB
ejpam-5504	34	32	in	in	ADP
ejpam-5504	34	33	[	[	PUNCT
ejpam-5504	34	34	2	2	NUM
ejpam-5504	34	35	,	,	PUNCT
ejpam-5504	34	36	lemma	lemma	PROPN
ejpam-5504	34	37	]	]	PUNCT
ejpam-5504	34	38	and	and	CCONJ
ejpam-5504	34	39	[	[	X
ejpam-5504	34	40	1	1	NUM
ejpam-5504	34	41	,	,	PUNCT
ejpam-5504	34	42	section	section	NOUN
ejpam-5504	34	43	3	3	NUM
ejpam-5504	34	44	]	]	PUNCT
ejpam-5504	34	45	.	.	PUNCT
ejpam-5504	35	1	we	we	PRON
ejpam-5504	35	2	refer	refer	VERB
ejpam-5504	35	3	the	the	DET
ejpam-5504	35	4	reder	reder	NOUN
ejpam-5504	35	5	to	to	ADP
ejpam-5504	35	6	[	[	X
ejpam-5504	35	7	18	18	NUM
ejpam-5504	35	8	,	,	PUNCT
ejpam-5504	35	9	exercise	exercise	VERB
ejpam-5504	35	10	12.16	12.16	NUM
ejpam-5504	35	11	]	]	PUNCT
ejpam-5504	35	12	,	,	PUNCT
ejpam-5504	35	13	and	and	CCONJ
ejpam-5504	35	14	[	[	X
ejpam-5504	35	15	4	4	NUM
ejpam-5504	35	16	,	,	PUNCT
ejpam-5504	35	17	example	example	NOUN
ejpam-5504	35	18	20.29	20.29	NUM
ejpam-5504	35	19	]	]	PUNCT
ejpam-5504	35	20	,	,	PUNCT
ejpam-5504	35	21	[	[	X
ejpam-5504	35	22	7	7	NUM
ejpam-5504	35	23	]	]	PUNCT
ejpam-5504	35	24	.	.	PUNCT
ejpam-5504	36	1	more	more	ADJ
ejpam-5504	36	2	information	information	NOUN
ejpam-5504	36	3	is	be	AUX
ejpam-5504	36	4	in	in	ADP
ejpam-5504	36	5	[	[	X
ejpam-5504	36	6	10	10	NUM
ejpam-5504	36	7	,	,	PUNCT
ejpam-5504	36	8	15	15	NUM
ejpam-5504	36	9	,	,	PUNCT
ejpam-5504	36	10	17	17	NUM
ejpam-5504	36	11	,	,	PUNCT
ejpam-5504	36	12	19	19	NUM
ejpam-5504	36	13	]	]	PUNCT
ejpam-5504	36	14	.	.	PUNCT
ejpam-5504	37	1	throughout	throughout	ADP
ejpam-5504	37	2	this	this	DET
ejpam-5504	37	3	paper	paper	NOUN
ejpam-5504	37	4	,	,	PUNCT
ejpam-5504	37	5	we	we	PRON
ejpam-5504	37	6	assume	assume	VERB
ejpam-5504	37	7	that	that	SCONJ
ejpam-5504	37	8	r	r	NOUN
ejpam-5504	37	9	:	:	PUNCT
ejpam-5504	37	10	x	x	X
ejpam-5504	37	11	→	→	PUNCT
ejpam-5504	37	12	x	x	X
ejpam-5504	37	13	is	be	AUX
ejpam-5504	37	14	linear	linear	ADJ
ejpam-5504	37	15	and	and	CCONJ
ejpam-5504	37	16	nonexpansive	nonexpansive	ADJ
ejpam-5504	37	17	,	,	PUNCT
ejpam-5504	37	18	with	with	ADP
ejpam-5504	37	19	d	d	NOUN
ejpam-5504	37	20	:	:	PUNCT
ejpam-5504	37	21	=	=	PUNCT
ejpam-5504	37	22	fix	fix	NOUN
ejpam-5504	37	23	r	r	NOUN
ejpam-5504	37	24	=	=	SYM
ejpam-5504	37	25	ker	ker	X
ejpam-5504	37	26	(	(	PUNCT
ejpam-5504	37	27	id−r	id−r	NOUN
ejpam-5504	37	28	)	)	PUNCT
ejpam-5504	37	29	.	.	PUNCT
ejpam-5504	38	1	(	(	PUNCT
ejpam-5504	38	2	6	6	NUM
ejpam-5504	38	3	)	)	PUNCT
ejpam-5504	38	4	in	in	ADP
ejpam-5504	38	5	this	this	DET
ejpam-5504	38	6	paper	paper	NOUN
ejpam-5504	38	7	,	,	PUNCT
ejpam-5504	38	8	we	we	PRON
ejpam-5504	38	9	study	study	VERB
ejpam-5504	38	10	the	the	DET
ejpam-5504	38	11	displacement	displacement	NOUN
ejpam-5504	38	12	mapping	mapping	NOUN
ejpam-5504	38	13	using	use	VERB
ejpam-5504	38	14	the	the	DET
ejpam-5504	38	15	assumption	assumption	NOUN
ejpam-5504	38	16	in	in	ADP
ejpam-5504	38	17	(	(	PUNCT
ejpam-5504	38	18	6	6	NUM
ejpam-5504	38	19	)	)	PUNCT
ejpam-5504	38	20	.	.	PUNCT
ejpam-5504	39	1	our	our	PRON
ejpam-5504	39	2	results	result	NOUN
ejpam-5504	39	3	can	can	AUX
ejpam-5504	39	4	be	be	AUX
ejpam-5504	39	5	summarized	summarize	VERB
ejpam-5504	39	6	as	as	SCONJ
ejpam-5504	39	7	follows	follow	VERB
ejpam-5504	39	8	•	•	NUM
ejpam-5504	39	9	proposition	proposition	NOUN
ejpam-5504	39	10	1	1	NUM
ejpam-5504	39	11	,	,	PUNCT
ejpam-5504	39	12	lemma	lemma	PROPN
ejpam-5504	39	13	1	1	NUM
ejpam-5504	39	14	,	,	PUNCT
ejpam-5504	39	15	and	and	CCONJ
ejpam-5504	39	16	remark	remark	VERB
ejpam-5504	39	17	1	1	NUM
ejpam-5504	39	18	collect	collect	VERB
ejpam-5504	39	19	some	some	DET
ejpam-5504	39	20	useful	useful	ADJ
ejpam-5504	39	21	properities	properitie	NOUN
ejpam-5504	39	22	of	of	ADP
ejpam-5504	39	23	the	the	DET
ejpam-5504	39	24	dispdisplacment	dispdisplacment	NOUN
ejpam-5504	39	25	mapping	mapping	NOUN
ejpam-5504	39	26	and	and	CCONJ
ejpam-5504	39	27	its	its	PRON
ejpam-5504	39	28	inverse	inverse	NOUN
ejpam-5504	39	29	,	,	PUNCT
ejpam-5504	39	30	which	which	PRON
ejpam-5504	39	31	will	will	AUX
ejpam-5504	39	32	be	be	AUX
ejpam-5504	39	33	useful	useful	ADJ
ejpam-5504	39	34	in	in	ADP
ejpam-5504	39	35	our	our	PRON
ejpam-5504	39	36	study	study	NOUN
ejpam-5504	39	37	.	.	PUNCT
ejpam-5504	40	1	•	•	NUM
ejpam-5504	40	2	lemma	lemma	PROPN
ejpam-5504	40	3	2	2	NUM
ejpam-5504	40	4	provides	provide	VERB
ejpam-5504	40	5	a	a	DET
ejpam-5504	40	6	formula	formula	NOUN
ejpam-5504	40	7	and	and	CCONJ
ejpam-5504	40	8	gives	give	VERB
ejpam-5504	40	9	nice	nice	ADJ
ejpam-5504	40	10	properties	property	NOUN
ejpam-5504	40	11	of	of	ADP
ejpam-5504	40	12	the	the	DET
ejpam-5504	40	13	operator	operator	NOUN
ejpam-5504	40	14	t.	t.	NOUN
ejpam-5504	40	15	•	•	NOUN
ejpam-5504	40	16	we	we	PRON
ejpam-5504	40	17	derive	derive	VERB
ejpam-5504	40	18	a	a	DET
ejpam-5504	40	19	formula	formula	NOUN
ejpam-5504	40	20	for	for	ADP
ejpam-5504	40	21	the	the	DET
ejpam-5504	40	22	inverse	inverse	NOUN
ejpam-5504	40	23	of	of	ADP
ejpam-5504	40	24	the	the	DET
ejpam-5504	40	25	displacment	displacment	ADJ
ejpam-5504	40	26	mapping	mapping	NOUN
ejpam-5504	40	27	(	(	PUNCT
ejpam-5504	40	28	see	see	VERB
ejpam-5504	40	29	theorem	theorem	NOUN
ejpam-5504	40	30	2	2	NUM
ejpam-5504	40	31	(	(	PUNCT
ejpam-5504	40	32	i	i	NOUN
ejpam-5504	40	33	)	)	PUNCT
ejpam-5504	40	34	)	)	PUNCT
ejpam-5504	40	35	.	.	PUNCT
ejpam-5504	41	1	a	a	DET
ejpam-5504	41	2	formula	formula	NOUN
ejpam-5504	41	3	for	for	ADP
ejpam-5504	41	4	the	the	DET
ejpam-5504	41	5	moore	moore	PROPN
ejpam-5504	41	6	-	-	PUNCT
ejpam-5504	41	7	penrose	penrose	PROPN
ejpam-5504	41	8	inverse	inverse	NOUN
ejpam-5504	41	9	of	of	ADP
ejpam-5504	41	10	the	the	DET
ejpam-5504	41	11	displacement	displacement	NOUN
ejpam-5504	41	12	mapping	mapping	NOUN
ejpam-5504	41	13	is	be	AUX
ejpam-5504	41	14	given	give	VERB
ejpam-5504	41	15	in	in	ADP
ejpam-5504	41	16	theorem	theorem	ADJ
ejpam-5504	41	17	2(ii	2(ii	NUM
ejpam-5504	41	18	)	)	PUNCT
ejpam-5504	41	19	.	.	PUNCT
ejpam-5504	42	1	s.t	s.t	PROPN
ejpam-5504	42	2	.	.	PROPN
ejpam-5504	42	3	alwadani	alwadani	PROPN
ejpam-5504	42	4	/	/	SYM
ejpam-5504	42	5	eur	eur	PROPN
ejpam-5504	42	6	.	.	PUNCT
ejpam-5504	43	1	j.	j.	PROPN
ejpam-5504	43	2	pure	pure	PROPN
ejpam-5504	43	3	appl	appl	PROPN
ejpam-5504	43	4	.	.	PROPN
ejpam-5504	43	5	math	math	PROPN
ejpam-5504	43	6	,	,	PUNCT
ejpam-5504	43	7	17	17	NUM
ejpam-5504	43	8	(	(	PUNCT
ejpam-5504	43	9	4	4	NUM
ejpam-5504	43	10	)	)	PUNCT
ejpam-5504	43	11	(	(	PUNCT
ejpam-5504	43	12	2024	2024	NUM
ejpam-5504	43	13	)	)	PUNCT
ejpam-5504	43	14	,	,	PUNCT
ejpam-5504	43	15	3660	3660	NUM
ejpam-5504	43	16	-	-	SYM
ejpam-5504	43	17	3676	3676	NUM
ejpam-5504	43	18	3662	3662	NUM
ejpam-5504	43	19	•	•	NOUN
ejpam-5504	43	20	theorem	theorem	NOUN
ejpam-5504	43	21	3	3	NUM
ejpam-5504	43	22	gives	give	VERB
ejpam-5504	43	23	a	a	DET
ejpam-5504	43	24	comprehensive	comprehensive	ADJ
ejpam-5504	43	25	study	study	NOUN
ejpam-5504	43	26	of	of	ADP
ejpam-5504	43	27	the	the	DET
ejpam-5504	43	28	the	the	DET
ejpam-5504	43	29	operators	operator	NOUN
ejpam-5504	43	30	(	(	PUNCT
ejpam-5504	43	31	1/2	1/2	NUM
ejpam-5504	43	32	)	)	PUNCT
ejpam-5504	44	1	id+t	id+t	ADJ
ejpam-5504	44	2	and	and	CCONJ
ejpam-5504	44	3	its	its	PRON
ejpam-5504	44	4	inverse	inverse	NOUN
ejpam-5504	44	5	.	.	PUNCT
ejpam-5504	45	1	additionaly	additionaly	PROPN
ejpam-5504	45	2	,	,	PUNCT
ejpam-5504	45	3	we	we	PRON
ejpam-5504	45	4	derive	derive	VERB
ejpam-5504	45	5	a	a	DET
ejpam-5504	45	6	formula	formula	NOUN
ejpam-5504	45	7	of	of	ADP
ejpam-5504	45	8	(	(	PUNCT
ejpam-5504	45	9	(	(	PUNCT
ejpam-5504	45	10	1/2	1/2	NUM
ejpam-5504	45	11	)	)	PUNCT
ejpam-5504	46	1	id+t	id+t	ADV
ejpam-5504	46	2	)	)	PUNCT
ejpam-5504	46	3	−1	−1	NOUN
ejpam-5504	46	4	and	and	CCONJ
ejpam-5504	46	5	prove	prove	VERB
ejpam-5504	46	6	that	that	PRON
ejpam-5504	46	7	is	be	AUX
ejpam-5504	46	8	equal	equal	ADJ
ejpam-5504	46	9	to	to	ADP
ejpam-5504	46	10	the	the	DET
ejpam-5504	46	11	resolvant	resolvant	NOUN
ejpam-5504	46	12	of	of	ADP
ejpam-5504	46	13	the	the	DET
ejpam-5504	46	14	operator	operator	NOUN
ejpam-5504	46	15	2	2	NUM
ejpam-5504	46	16	t.	t.	NOUN
ejpam-5504	46	17	•	•	NOUN
ejpam-5504	46	18	we	we	PRON
ejpam-5504	46	19	illustrates	illustrate	VERB
ejpam-5504	46	20	the	the	DET
ejpam-5504	46	21	reults	reult	NOUN
ejpam-5504	46	22	by	by	ADP
ejpam-5504	46	23	giving	give	VERB
ejpam-5504	46	24	four	four	NUM
ejpam-5504	46	25	examples	example	NOUN
ejpam-5504	46	26	.	.	PUNCT
ejpam-5504	47	1	the	the	DET
ejpam-5504	47	2	first	first	ADJ
ejpam-5504	47	3	two	two	NUM
ejpam-5504	47	4	examples	example	NOUN
ejpam-5504	47	5	are	be	AUX
ejpam-5504	47	6	related	relate	VERB
ejpam-5504	47	7	to	to	ADP
ejpam-5504	47	8	the	the	DET
ejpam-5504	47	9	projection	projection	NOUN
ejpam-5504	47	10	operator	operator	NOUN
ejpam-5504	47	11	to	to	ADP
ejpam-5504	47	12	a	a	DET
ejpam-5504	47	13	closed	closed	ADJ
ejpam-5504	47	14	linear	linear	NOUN
ejpam-5504	47	15	subspace	subspace	NOUN
ejpam-5504	47	16	(	(	PUNCT
ejpam-5504	47	17	see	see	VERB
ejpam-5504	47	18	example	example	NOUN
ejpam-5504	47	19	2	2	NUM
ejpam-5504	47	20	and	and	CCONJ
ejpam-5504	47	21	example	example	NOUN
ejpam-5504	47	22	3	3	NUM
ejpam-5504	47	23	)	)	PUNCT
ejpam-5504	47	24	,	,	PUNCT
ejpam-5504	47	25	while	while	SCONJ
ejpam-5504	47	26	the	the	DET
ejpam-5504	47	27	other	other	ADJ
ejpam-5504	47	28	two	two	NUM
ejpam-5504	47	29	are	be	AUX
ejpam-5504	47	30	related	relate	VERB
ejpam-5504	47	31	to	to	ADP
ejpam-5504	47	32	the	the	DET
ejpam-5504	47	33	reflected	reflect	VERB
ejpam-5504	47	34	operator	operator	NOUN
ejpam-5504	47	35	to	to	PART
ejpam-5504	47	36	closed	close	VERB
ejpam-5504	47	37	linear	linear	ADJ
ejpam-5504	47	38	subspace	subspace	NOUN
ejpam-5504	47	39	(	(	PUNCT
ejpam-5504	47	40	see	see	VERB
ejpam-5504	47	41	example	example	NOUN
ejpam-5504	47	42	4	4	NUM
ejpam-5504	47	43	and	and	CCONJ
ejpam-5504	47	44	example	example	NOUN
ejpam-5504	47	45	5	5	NUM
ejpam-5504	47	46	)	)	PUNCT
ejpam-5504	47	47	.	.	PUNCT
ejpam-5504	48	1	2	2	X
ejpam-5504	48	2	.	.	NOUN
ejpam-5504	48	3	results	result	VERB
ejpam-5504	48	4	important	important	ADJ
ejpam-5504	48	5	properties	property	NOUN
ejpam-5504	48	6	of	of	ADP
ejpam-5504	48	7	the	the	DET
ejpam-5504	48	8	displacement	displacement	ADJ
ejpam-5504	48	9	mapping	mapping	NOUN
ejpam-5504	48	10	(	(	PUNCT
ejpam-5504	48	11	id−r	id−r	PROPN
ejpam-5504	48	12	)	)	PUNCT
ejpam-5504	48	13	and	and	CCONJ
ejpam-5504	48	14	its	its	PRON
ejpam-5504	48	15	inverse	inverse	NOUN
ejpam-5504	48	16	are	be	AUX
ejpam-5504	48	17	given	give	VERB
ejpam-5504	48	18	in	in	ADP
ejpam-5504	48	19	the	the	DET
ejpam-5504	48	20	next	next	ADJ
ejpam-5504	48	21	proposition	proposition	NOUN
ejpam-5504	48	22	.	.	PUNCT
ejpam-5504	49	1	proposition	proposition	NOUN
ejpam-5504	49	2	1	1	NUM
ejpam-5504	49	3	.	.	PUNCT
ejpam-5504	50	1	let	let	VERB
ejpam-5504	50	2	r	r	NOUN
ejpam-5504	50	3	be	be	AUX
ejpam-5504	50	4	nonexpansive	nonexpansive	ADJ
ejpam-5504	50	5	operator	operator	NOUN
ejpam-5504	50	6	,	,	PUNCT
ejpam-5504	50	7	then	then	ADV
ejpam-5504	50	8	the	the	DET
ejpam-5504	50	9	following	follow	VERB
ejpam-5504	50	10	holds	hold	VERB
ejpam-5504	50	11	:	:	PUNCT
ejpam-5504	50	12	(	(	PUNCT
ejpam-5504	50	13	i	i	NOUN
ejpam-5504	50	14	)	)	PUNCT
ejpam-5504	50	15	1	1	NUM
ejpam-5504	50	16	2	2	NUM
ejpam-5504	50	17	(	(	PUNCT
ejpam-5504	50	18	id−r	id−r	NOUN
ejpam-5504	50	19	)	)	PUNCT
ejpam-5504	50	20	is	be	AUX
ejpam-5504	50	21	firmly	firmly	ADV
ejpam-5504	50	22	nonexpansive	nonexpansive	ADJ
ejpam-5504	50	23	.	.	PUNCT
ejpam-5504	51	1	(	(	PUNCT
ejpam-5504	51	2	ii	ii	NOUN
ejpam-5504	51	3	)	)	PUNCT
ejpam-5504	51	4	id−r	id−r	NOUN
ejpam-5504	51	5	is	be	AUX
ejpam-5504	51	6	nonexpansive	nonexpansive	ADJ
ejpam-5504	51	7	.	.	PUNCT
ejpam-5504	52	1	(	(	PUNCT
ejpam-5504	52	2	iii	iii	NOUN
ejpam-5504	52	3	)	)	PUNCT
ejpam-5504	52	4	id−r	id−r	NOUN
ejpam-5504	52	5	and	and	CCONJ
ejpam-5504	52	6	(	(	PUNCT
ejpam-5504	52	7	id−r)−1	id−r)−1	PRON
ejpam-5504	52	8	are	be	AUX
ejpam-5504	52	9	maximally	maximally	ADV
ejpam-5504	52	10	monotone	monotone	ADJ
ejpam-5504	52	11	.	.	PUNCT
ejpam-5504	53	1	(	(	PUNCT
ejpam-5504	53	2	iv	iv	X
ejpam-5504	53	3	)	)	PUNCT
ejpam-5504	53	4	id−r	id−r	NOUN
ejpam-5504	53	5	is	be	AUX
ejpam-5504	53	6	1	1	NUM
ejpam-5504	53	7	2	2	NUM
ejpam-5504	53	8	-cocoercive	-cocoercive	NOUN
ejpam-5504	53	9	.	.	PUNCT
ejpam-5504	54	1	(	(	PUNCT
ejpam-5504	54	2	v	v	NOUN
ejpam-5504	54	3	)	)	PUNCT
ejpam-5504	54	4	(	(	PUNCT
ejpam-5504	54	5	id−r)−1	id−r)−1	PRON
ejpam-5504	54	6	is	be	AUX
ejpam-5504	54	7	strongly	strongly	ADV
ejpam-5504	54	8	monotone*with	monotone*with	ADJ
ejpam-5504	54	9	constant	constant	ADJ
ejpam-5504	54	10	1	1	NUM
ejpam-5504	54	11	2	2	NUM
ejpam-5504	54	12	.	.	PUNCT
ejpam-5504	55	1	(	(	PUNCT
ejpam-5504	55	2	vi	vi	NOUN
ejpam-5504	55	3	)	)	PUNCT
ejpam-5504	55	4	id−r	id−r	NOUN
ejpam-5504	55	5	is	be	AUX
ejpam-5504	55	6	3∗	3∗	NUM
ejpam-5504	55	7	monotone	monotone	NOUN
ejpam-5504	55	8	.	.	PUNCT
ejpam-5504	56	1	(	(	PUNCT
ejpam-5504	56	2	vii	vii	PROPN
ejpam-5504	56	3	)	)	PUNCT
ejpam-5504	56	4	(	(	PUNCT
ejpam-5504	56	5	id−r)−1	id−r)−1	PROPN
ejpam-5504	56	6	is	be	AUX
ejpam-5504	56	7	3∗	3∗	NUM
ejpam-5504	56	8	monotone	monotone	ADJ
ejpam-5504	56	9	(	(	PUNCT
ejpam-5504	56	10	viii	viii	NOUN
ejpam-5504	56	11	)	)	PUNCT
ejpam-5504	56	12	id−r	id−r	NOUN
ejpam-5504	56	13	is	be	AUX
ejpam-5504	56	14	paramonotone	paramonotone	NOUN
ejpam-5504	56	15	.	.	PUNCT
ejpam-5504	57	1	(	(	PUNCT
ejpam-5504	57	2	ix	ix	PROPN
ejpam-5504	57	3	)	)	PUNCT
ejpam-5504	57	4	(	(	PUNCT
ejpam-5504	57	5	id−r	id−r	NOUN
ejpam-5504	57	6	)	)	PUNCT
ejpam-5504	57	7	−1	−1	NOUN
ejpam-5504	57	8	−	−	NOUN
ejpam-5504	57	9	1	1	NUM
ejpam-5504	57	10	2	2	NUM
ejpam-5504	57	11	i	i	NOUN
ejpam-5504	57	12	d	d	PROPN
ejpam-5504	57	13	is	be	AUX
ejpam-5504	57	14	maximally	maximally	ADV
ejpam-5504	57	15	monotone	monotone	ADJ
ejpam-5504	57	16	.	.	PUNCT
ejpam-5504	58	1	proof	proof	NOUN
ejpam-5504	58	2	.	.	PUNCT
ejpam-5504	59	1	(	(	PUNCT
ejpam-5504	59	2	i	i	NOUN
ejpam-5504	59	3	):	):	PUNCT
ejpam-5504	59	4	we	we	PRON
ejpam-5504	59	5	have	have	VERB
ejpam-5504	59	6	r	r	NOUN
ejpam-5504	59	7	is	be	AUX
ejpam-5504	59	8	nonexpansive	nonexpansive	ADJ
ejpam-5504	59	9	⇔	⇔	PROPN
ejpam-5504	59	10	−r	−r	PROPN
ejpam-5504	59	11	=	=	SYM
ejpam-5504	59	12	2	2	NUM
ejpam-5504	59	13	(	(	PUNCT
ejpam-5504	59	14	(	(	PUNCT
ejpam-5504	59	15	id−r	id−r	NOUN
ejpam-5504	59	16	)	)	PUNCT
ejpam-5504	59	17	/2	/2	PUNCT
ejpam-5504	59	18	)	)	PUNCT
ejpam-5504	60	1	is	be	AUX
ejpam-5504	60	2	nonexpansive	nonexpansive	ADJ
ejpam-5504	60	3	⇔	⇔	X
ejpam-5504	60	4	(	(	PUNCT
ejpam-5504	60	5	id−r	id−r	PROPN
ejpam-5504	60	6	)	)	PUNCT
ejpam-5504	60	7	/2	/2	PUNCT
ejpam-5504	60	8	is	be	AUX
ejpam-5504	60	9	firmly	firmly	ADV
ejpam-5504	60	10	nonexpansive	nonexpansive	ADJ
ejpam-5504	60	11	,	,	PUNCT
ejpam-5504	60	12	by	by	ADP
ejpam-5504	60	13	[	[	X
ejpam-5504	60	14	4	4	NUM
ejpam-5504	60	15	,	,	PUNCT
ejpam-5504	60	16	proposition	proposition	NOUN
ejpam-5504	60	17	4.4	4.4	NUM
ejpam-5504	60	18	]	]	PUNCT
ejpam-5504	60	19	.	.	PUNCT
ejpam-5504	61	1	(	(	PUNCT
ejpam-5504	61	2	ii	ii	NUM
ejpam-5504	61	3	):	):	PUNCT
ejpam-5504	61	4	it	it	PRON
ejpam-5504	61	5	follows	follow	VERB
ejpam-5504	61	6	from	from	ADP
ejpam-5504	61	7	(	(	PUNCT
ejpam-5504	61	8	i	i	NOUN
ejpam-5504	61	9	)	)	PUNCT
ejpam-5504	61	10	and	and	CCONJ
ejpam-5504	61	11	[	[	X
ejpam-5504	61	12	4	4	NUM
ejpam-5504	61	13	,	,	PUNCT
ejpam-5504	61	14	proposition	proposition	NOUN
ejpam-5504	61	15	4.2	4.2	NUM
ejpam-5504	61	16	]	]	PUNCT
ejpam-5504	61	17	.	.	PUNCT
ejpam-5504	62	1	(	(	PUNCT
ejpam-5504	62	2	iii	iii	NOUN
ejpam-5504	62	3	):	):	PUNCT
ejpam-5504	62	4	see	see	VERB
ejpam-5504	62	5	[	[	X
ejpam-5504	62	6	4	4	NUM
ejpam-5504	62	7	,	,	PUNCT
ejpam-5504	62	8	example	example	NOUN
ejpam-5504	62	9	25.20(v	25.20(v	NUM
ejpam-5504	62	10	)	)	PUNCT
ejpam-5504	62	11	]	]	PUNCT
ejpam-5504	62	12	or	or	CCONJ
ejpam-5504	62	13	[	[	X
ejpam-5504	62	14	2	2	NUM
ejpam-5504	62	15	,	,	PUNCT
ejpam-5504	62	16	theorem	theorem	VERB
ejpam-5504	62	17	7.1	7.1	NUM
ejpam-5504	62	18	]	]	PUNCT
ejpam-5504	62	19	.	.	PUNCT
ejpam-5504	63	1	(	(	PUNCT
ejpam-5504	63	2	iv	iv	X
ejpam-5504	63	3	):	):	PUNCT
ejpam-5504	63	4	combine	combine	PROPN
ejpam-5504	63	5	(	(	PUNCT
ejpam-5504	63	6	i	i	NOUN
ejpam-5504	63	7	)	)	PUNCT
ejpam-5504	63	8	and	and	CCONJ
ejpam-5504	63	9	fact	fact	NOUN
ejpam-5504	63	10	1	1	NUM
ejpam-5504	63	11	.	.	PUNCT
ejpam-5504	64	1	(	(	PUNCT
ejpam-5504	64	2	v	v	NOUN
ejpam-5504	64	3	):	):	PUNCT
ejpam-5504	64	4	take	take	NOUN
ejpam-5504	64	5	(	(	PUNCT
ejpam-5504	64	6	x	x	NOUN
ejpam-5504	64	7	,	,	PUNCT
ejpam-5504	64	8	u	u	NOUN
ejpam-5504	64	9	)	)	PUNCT
ejpam-5504	64	10	∈	∈	NOUN
ejpam-5504	64	11	gra(id−r)−1	gra(id−r)−1	NOUN
ejpam-5504	64	12	and	and	CCONJ
ejpam-5504	64	13	(	(	PUNCT
ejpam-5504	64	14	y	y	PROPN
ejpam-5504	64	15	,	,	PUNCT
ejpam-5504	64	16	v	v	NOUN
ejpam-5504	64	17	)	)	PUNCT
ejpam-5504	64	18	∈	∈	NOUN
ejpam-5504	64	19	gra(id−r)−1	gra(id−r)−1	NOUN
ejpam-5504	64	20	.	.	PUNCT
ejpam-5504	65	1	then	then	ADV
ejpam-5504	65	2	u	u	PROPN
ejpam-5504	65	3	∈	∈	PROPN
ejpam-5504	65	4	(	(	PUNCT
ejpam-5504	65	5	id−r)−1x	id−r)−1x	NOUN
ejpam-5504	65	6	⇒	⇒	NOUN
ejpam-5504	65	7	x	x	PUNCT
ejpam-5504	66	1	=	=	PUNCT
ejpam-5504	66	2	u	u	NOUN
ejpam-5504	66	3	−	−	PROPN
ejpam-5504	66	4	ru	ru	NOUN
ejpam-5504	66	5	and	and	CCONJ
ejpam-5504	66	6	v	v	ADP
ejpam-5504	66	7	∈	∈	PROPN
ejpam-5504	66	8	(	(	PUNCT
ejpam-5504	66	9	id−r)−1y	id−r)−1y	ADJ
ejpam-5504	66	10	⇒	⇒	PROPN
ejpam-5504	67	1	y	y	PROPN
ejpam-5504	68	1	=	=	PROPN
ejpam-5504	69	1	v	v	ADP
ejpam-5504	69	2	−	−	PROPN
ejpam-5504	69	3	rv	rv	PROPN
ejpam-5504	69	4	.	.	PROPN
ejpam-5504	69	5	⟨u	⟨u	NOUN
ejpam-5504	70	1	−	−	NOUN
ejpam-5504	70	2	v	v	NOUN
ejpam-5504	70	3	,	,	PUNCT
ejpam-5504	70	4	x	x	PROPN
ejpam-5504	70	5	−	−	PROPN
ejpam-5504	70	6	y⟩	y⟩	NOUN
ejpam-5504	70	7	≥	≥	NOUN
ejpam-5504	70	8	1	1	NUM
ejpam-5504	70	9	2	2	NUM
ejpam-5504	70	10	∥x	∥x	PROPN
ejpam-5504	70	11	−	−	PROPN
ejpam-5504	70	12	y∥2	y∥2	ADJ
ejpam-5504	70	13	⇔	⇔	X
ejpam-5504	70	14	⟨u	⟨u	NOUN
ejpam-5504	70	15	−	−	NOUN
ejpam-5504	70	16	v	v	NOUN
ejpam-5504	70	17	,	,	PUNCT
ejpam-5504	70	18	(	(	PUNCT
ejpam-5504	70	19	u	u	NOUN
ejpam-5504	70	20	−	−	PROPN
ejpam-5504	70	21	ru)−	ru)−	PROPN
ejpam-5504	70	22	(	(	PUNCT
ejpam-5504	70	23	v	v	NOUN
ejpam-5504	70	24	−	−	PROPN
ejpam-5504	70	25	rv)⟩	rv)⟩	NOUN
ejpam-5504	70	26	≥	≥	NUM
ejpam-5504	70	27	1	1	NUM
ejpam-5504	70	28	2	2	NUM
ejpam-5504	70	29	∥(u	∥(u	NOUN
ejpam-5504	70	30	−	−	PROPN
ejpam-5504	70	31	ru)−	ru)−	NOUN
ejpam-5504	70	32	(	(	PUNCT
ejpam-5504	70	33	v	v	ADP
ejpam-5504	70	34	−	−	PROPN
ejpam-5504	70	35	rv)∥2	rv)∥2	PROPN
ejpam-5504	70	36	,	,	PUNCT
ejpam-5504	70	37	∗an	∗an	PUNCT
ejpam-5504	70	38	operator	operator	NOUN
ejpam-5504	70	39	a	a	DET
ejpam-5504	70	40	:	:	PUNCT
ejpam-5504	70	41	x	x	SYM
ejpam-5504	70	42	⇒	⇒	NOUN
ejpam-5504	70	43	x	x	VERB
ejpam-5504	70	44	is	be	AUX
ejpam-5504	70	45	strongly	strongly	ADV
ejpam-5504	70	46	monotone	monotone	ADJ
ejpam-5504	70	47	with	with	ADP
ejpam-5504	70	48	constant	constant	ADJ
ejpam-5504	70	49	β	β	X
ejpam-5504	70	50	∈	∈	NOUN
ejpam-5504	70	51	r++	r++	NOUN
ejpam-5504	70	52	if	if	SCONJ
ejpam-5504	70	53	a	a	DET
ejpam-5504	70	54	−	−	PROPN
ejpam-5504	70	55	β	β	X
ejpam-5504	70	56	i	i	PROPN
ejpam-5504	70	57	d	d	PROPN
ejpam-5504	70	58	is	be	AUX
ejpam-5504	70	59	montone	montone	NOUN
ejpam-5504	70	60	,	,	PUNCT
ejpam-5504	70	61	i.e.	i.e.	X
ejpam-5504	70	62	,	,	PUNCT
ejpam-5504	70	63	(	(	PUNCT
ejpam-5504	70	64	∀(x	∀(x	X
ejpam-5504	70	65	,	,	PUNCT
ejpam-5504	70	66	u	u	NOUN
ejpam-5504	70	67	)	)	PUNCT
ejpam-5504	70	68	∈	∈	PROPN
ejpam-5504	70	69	gra	gra	PROPN
ejpam-5504	70	70	a	a	PRON
ejpam-5504	70	71	)	)	PUNCT
ejpam-5504	70	72	(	(	PUNCT
ejpam-5504	70	73	∀(y	∀(y	NUM
ejpam-5504	70	74	,	,	PUNCT
ejpam-5504	70	75	v	v	NOUN
ejpam-5504	70	76	)	)	PUNCT
ejpam-5504	70	77	∈	∈	PROPN
ejpam-5504	70	78	gra	gra	PROPN
ejpam-5504	70	79	a	a	PRON
ejpam-5504	70	80	)	)	PUNCT
ejpam-5504	70	81	⟨x	⟨x	VERB
ejpam-5504	70	82	−	−	PROPN
ejpam-5504	70	83	y	y	PROPN
ejpam-5504	70	84	,	,	PUNCT
ejpam-5504	70	85	u	u	PROPN
ejpam-5504	70	86	−	−	PROPN
ejpam-5504	70	87	v⟩	v⟩	PUNCT
ejpam-5504	70	88	≥	≥	NOUN
ejpam-5504	70	89	β∥x	β∥x	PUNCT
ejpam-5504	70	90	−	−	PROPN
ejpam-5504	70	91	y∥2	y∥2	NOUN
ejpam-5504	70	92	.	.	PUNCT
ejpam-5504	71	1	s.t	s.t	PROPN
ejpam-5504	71	2	.	.	PROPN
ejpam-5504	71	3	alwadani	alwadani	PROPN
ejpam-5504	71	4	/	/	SYM
ejpam-5504	71	5	eur	eur	PROPN
ejpam-5504	71	6	.	.	PUNCT
ejpam-5504	72	1	j.	j.	PROPN
ejpam-5504	72	2	pure	pure	PROPN
ejpam-5504	72	3	appl	appl	PROPN
ejpam-5504	72	4	.	.	PROPN
ejpam-5504	72	5	math	math	PROPN
ejpam-5504	72	6	,	,	PUNCT
ejpam-5504	72	7	17	17	NUM
ejpam-5504	72	8	(	(	PUNCT
ejpam-5504	72	9	4	4	NUM
ejpam-5504	72	10	)	)	PUNCT
ejpam-5504	72	11	(	(	PUNCT
ejpam-5504	72	12	2024	2024	NUM
ejpam-5504	72	13	)	)	PUNCT
ejpam-5504	72	14	,	,	PUNCT
ejpam-5504	72	15	3660	3660	NUM
ejpam-5504	72	16	-	-	SYM
ejpam-5504	72	17	3676	3676	NUM
ejpam-5504	72	18	3663	3663	NUM
ejpam-5504	72	19	which	which	PRON
ejpam-5504	72	20	deduce	deduce	VERB
ejpam-5504	72	21	from	from	ADP
ejpam-5504	72	22	(	(	PUNCT
ejpam-5504	72	23	iv	iv	X
ejpam-5504	72	24	)	)	PUNCT
ejpam-5504	72	25	and	and	CCONJ
ejpam-5504	72	26	footnote	footnote	VERB
ejpam-5504	72	27	*	*	PUNCT
ejpam-5504	72	28	that	that	PRON
ejpam-5504	72	29	(	(	PUNCT
ejpam-5504	72	30	id−r)−1	id−r)−1	PRON
ejpam-5504	72	31	is	be	AUX
ejpam-5504	72	32	strongly	strongly	ADV
ejpam-5504	72	33	monotone	monotone	ADJ
ejpam-5504	72	34	with	with	ADP
ejpam-5504	72	35	constant	constant	ADJ
ejpam-5504	72	36	(	(	PUNCT
ejpam-5504	72	37	1/2	1/2	NUM
ejpam-5504	72	38	)	)	PUNCT
ejpam-5504	72	39	.	.	PUNCT
ejpam-5504	73	1	(	(	PUNCT
ejpam-5504	73	2	vi	vi	NOUN
ejpam-5504	73	3	)	)	PUNCT
ejpam-5504	73	4	and	and	CCONJ
ejpam-5504	73	5	(	(	PUNCT
ejpam-5504	73	6	vii	vii	PROPN
ejpam-5504	73	7	):	):	PUNCT
ejpam-5504	73	8	it	it	PRON
ejpam-5504	73	9	follows	follow	VERB
ejpam-5504	73	10	from	from	ADP
ejpam-5504	73	11	(	(	PUNCT
ejpam-5504	73	12	iv	iv	X
ejpam-5504	73	13	)	)	PUNCT
ejpam-5504	73	14	that	that	SCONJ
ejpam-5504	73	15	id−r	id−r	NOUN
ejpam-5504	73	16	is	be	AUX
ejpam-5504	73	17	bounded	bound	VERB
ejpam-5504	73	18	by	by	ADP
ejpam-5504	73	19	(	(	PUNCT
ejpam-5504	73	20	1/2	1/2	NUM
ejpam-5504	73	21	)	)	PUNCT
ejpam-5504	73	22	and	and	CCONJ
ejpam-5504	73	23	its	its	PRON
ejpam-5504	73	24	monotone	monotone	NOUN
ejpam-5504	73	25	by	by	ADP
ejpam-5504	73	26	(	(	PUNCT
ejpam-5504	73	27	iii	iii	NOUN
ejpam-5504	73	28	)	)	PUNCT
ejpam-5504	73	29	.	.	PUNCT
ejpam-5504	74	1	hence	hence	ADV
ejpam-5504	74	2	,	,	PUNCT
ejpam-5504	74	3	id−r	id−r	NOUN
ejpam-5504	74	4	and	and	CCONJ
ejpam-5504	74	5	(	(	PUNCT
ejpam-5504	74	6	id−r)−1	id−r)−1	PRON
ejpam-5504	74	7	are	be	AUX
ejpam-5504	74	8	3∗	3∗	NUM
ejpam-5504	74	9	monotone	monotone	NOUN
ejpam-5504	74	10	by	by	ADP
ejpam-5504	74	11	[	[	X
ejpam-5504	74	12	4	4	NUM
ejpam-5504	74	13	,	,	PUNCT
ejpam-5504	74	14	proposition	proposition	NOUN
ejpam-5504	74	15	25.16(i	25.16(i	NUM
ejpam-5504	74	16	)	)	PUNCT
ejpam-5504	74	17	&	&	CCONJ
ejpam-5504	74	18	(	(	PUNCT
ejpam-5504	74	19	iv	iv	X
ejpam-5504	74	20	)	)	PUNCT
ejpam-5504	74	21	]	]	PUNCT
ejpam-5504	74	22	.	.	PUNCT
ejpam-5504	75	1	(	(	PUNCT
ejpam-5504	75	2	viii	viii	ADJ
ejpam-5504	75	3	):	):	PUNCT
ejpam-5504	75	4	see	see	VERB
ejpam-5504	75	5	[	[	X
ejpam-5504	75	6	4	4	NUM
ejpam-5504	75	7	,	,	PUNCT
ejpam-5504	75	8	example	example	NOUN
ejpam-5504	75	9	22.9	22.9	NUM
ejpam-5504	75	10	]	]	PUNCT
ejpam-5504	75	11	.	.	PUNCT
ejpam-5504	76	1	(	(	PUNCT
ejpam-5504	76	2	ix	ix	ADV
ejpam-5504	76	3	):	):	PUNCT
ejpam-5504	76	4	by	by	ADP
ejpam-5504	76	5	(	(	PUNCT
ejpam-5504	76	6	iv	iv	X
ejpam-5504	76	7	)	)	PUNCT
ejpam-5504	76	8	and	and	CCONJ
ejpam-5504	76	9	[	[	X
ejpam-5504	76	10	4	4	NUM
ejpam-5504	76	11	,	,	PUNCT
ejpam-5504	76	12	example	example	NOUN
ejpam-5504	76	13	22.7	22.7	NUM
ejpam-5504	76	14	]	]	PUNCT
ejpam-5504	76	15	,	,	PUNCT
ejpam-5504	76	16	(	(	PUNCT
ejpam-5504	76	17	id−r)−1	id−r)−1	X
ejpam-5504	76	18	is	be	AUX
ejpam-5504	76	19	(	(	PUNCT
ejpam-5504	76	20	1/2)strongly	1/2)strongly	ADV
ejpam-5504	76	21	monotone	monotone	ADJ
ejpam-5504	76	22	,	,	PUNCT
ejpam-5504	76	23	i.e.	i.e.	X
ejpam-5504	76	24	,	,	PUNCT
ejpam-5504	76	25	b	b	X
ejpam-5504	76	26	:	:	PUNCT
ejpam-5504	76	27	=	=	SYM
ejpam-5504	76	28	(	(	PUNCT
ejpam-5504	76	29	id−r)−1	id−r)−1	NUM
ejpam-5504	76	30	−	−	NUM
ejpam-5504	76	31	1	1	NUM
ejpam-5504	76	32	2	2	NUM
ejpam-5504	76	33	i	i	NOUN
ejpam-5504	76	34	d	d	PROPN
ejpam-5504	76	35	is	be	AUX
ejpam-5504	76	36	still	still	ADV
ejpam-5504	76	37	monotone	monotone	ADJ
ejpam-5504	76	38	.	.	PUNCT
ejpam-5504	77	1	if	if	SCONJ
ejpam-5504	77	2	b	b	PROPN
ejpam-5504	77	3	was	be	AUX
ejpam-5504	77	4	not	not	PART
ejpam-5504	77	5	maximally	maximally	ADV
ejpam-5504	77	6	monotone	monotone	ADJ
ejpam-5504	77	7	,	,	PUNCT
ejpam-5504	77	8	then	then	ADV
ejpam-5504	77	9	neither	neither	PRON
ejpam-5504	77	10	would	would	AUX
ejpam-5504	77	11	be	be	AUX
ejpam-5504	77	12	b	b	PROPN
ejpam-5504	77	13	+	+	CCONJ
ejpam-5504	77	14	1	1	NUM
ejpam-5504	77	15	2	2	NUM
ejpam-5504	77	16	i	i	NOUN
ejpam-5504	77	17	d	d	NOUN
ejpam-5504	77	18	=	=	SYM
ejpam-5504	77	19	(	(	PUNCT
ejpam-5504	77	20	id−r)−1	id−r)−1	NUM
ejpam-5504	77	21	which	which	PRON
ejpam-5504	77	22	would	would	AUX
ejpam-5504	77	23	contradict	contradict	VERB
ejpam-5504	77	24	(	(	PUNCT
ejpam-5504	77	25	iii	iii	NOUN
ejpam-5504	77	26	)	)	PUNCT
ejpam-5504	77	27	.	.	PUNCT
ejpam-5504	78	1	■	■	PUNCT
ejpam-5504	78	2	lemma	lemma	PROPN
ejpam-5504	78	3	1	1	X
ejpam-5504	78	4	.	.	PUNCT
ejpam-5504	78	5	set	set	VERB
ejpam-5504	79	1	d	d	NOUN
ejpam-5504	79	2	:	:	PUNCT
ejpam-5504	79	3	=	=	NUM
ejpam-5504	79	4	ker	ker	X
ejpam-5504	79	5	(	(	PUNCT
ejpam-5504	79	6	id−r	id−r	NOUN
ejpam-5504	79	7	)	)	PUNCT
ejpam-5504	79	8	=	=	SYM
ejpam-5504	80	1	fix	fix	NOUN
ejpam-5504	80	2	r.	r.	PROPN
ejpam-5504	80	3	then	then	ADV
ejpam-5504	80	4	the	the	DET
ejpam-5504	80	5	following	follow	VERB
ejpam-5504	80	6	holds	hold	VERB
ejpam-5504	80	7	:	:	PUNCT
ejpam-5504	80	8	(	(	PUNCT
ejpam-5504	80	9	i	i	NOUN
ejpam-5504	80	10	)	)	PUNCT
ejpam-5504	81	1	d	d	NOUN
ejpam-5504	81	2	is	be	AUX
ejpam-5504	81	3	a	a	DET
ejpam-5504	81	4	closed	closed	ADJ
ejpam-5504	81	5	linear	linear	ADJ
ejpam-5504	81	6	subspace	subspace	NOUN
ejpam-5504	81	7	.	.	PUNCT
ejpam-5504	82	1	(	(	PUNCT
ejpam-5504	82	2	ii	ii	NOUN
ejpam-5504	82	3	)	)	PUNCT
ejpam-5504	82	4	fix	fix	VERB
ejpam-5504	82	5	r∗	r∗	NOUN
ejpam-5504	82	6	=	=	PUNCT
ejpam-5504	82	7	d.	d.	PROPN
ejpam-5504	82	8	(	(	PUNCT
ejpam-5504	82	9	iii	iii	NOUN
ejpam-5504	82	10	)	)	PUNCT
ejpam-5504	82	11	ran	run	VERB
ejpam-5504	82	12	(	(	PUNCT
ejpam-5504	82	13	id−r	id−r	NOUN
ejpam-5504	82	14	)	)	PUNCT
ejpam-5504	83	1	=	=	PRON
ejpam-5504	83	2	ran	run	VERB
ejpam-5504	83	3	(	(	PUNCT
ejpam-5504	83	4	id−r∗	id−r∗	PROPN
ejpam-5504	83	5	)	)	PUNCT
ejpam-5504	83	6	=	=	SYM
ejpam-5504	83	7	d⊥.	d⊥.	NOUN
ejpam-5504	83	8	proof	proof	NOUN
ejpam-5504	83	9	.	.	PUNCT
ejpam-5504	84	1	(	(	PUNCT
ejpam-5504	84	2	i	i	NOUN
ejpam-5504	84	3	):	):	PUNCT
ejpam-5504	84	4	let	let	VERB
ejpam-5504	84	5	x	x	PRON
ejpam-5504	84	6	,	,	PUNCT
ejpam-5504	84	7	y	y	PROPN
ejpam-5504	84	8	∈	∈	PROPN
ejpam-5504	85	1	d	d	ADP
ejpam-5504	85	2	such	such	ADJ
ejpam-5504	85	3	that	that	SCONJ
ejpam-5504	85	4	x	x	PUNCT
ejpam-5504	86	1	−	−	NOUN
ejpam-5504	86	2	rx	rx	VERB
ejpam-5504	86	3	=	=	SYM
ejpam-5504	86	4	0	0	PROPN
ejpam-5504	86	5	and	and	CCONJ
ejpam-5504	86	6	y	y	PROPN
ejpam-5504	86	7	−	−	PROPN
ejpam-5504	87	1	ry	ry	PROPN
ejpam-5504	87	2	=	=	NOUN
ejpam-5504	87	3	0	0	X
ejpam-5504	87	4	.	.	PUNCT
ejpam-5504	88	1	let	let	VERB
ejpam-5504	88	2	α	α	PRON
ejpam-5504	88	3	,	,	PUNCT
ejpam-5504	88	4	β	β	PROPN
ejpam-5504	88	5	∈	∈	PROPN
ejpam-5504	88	6	r.	r.	PROPN
ejpam-5504	88	7	then	then	ADV
ejpam-5504	88	8	(	(	PUNCT
ejpam-5504	88	9	id−r	id−r	NOUN
ejpam-5504	88	10	)	)	PUNCT
ejpam-5504	88	11	(	(	PUNCT
ejpam-5504	88	12	αx	αx	ADV
ejpam-5504	89	1	+	+	CCONJ
ejpam-5504	89	2	βy	βy	ADJ
ejpam-5504	89	3	)	)	PUNCT
ejpam-5504	89	4	=	=	SYM
ejpam-5504	89	5	(	(	PUNCT
ejpam-5504	89	6	id−r	id−r	NOUN
ejpam-5504	89	7	)	)	PUNCT
ejpam-5504	89	8	(	(	PUNCT
ejpam-5504	89	9	αx	αx	X
ejpam-5504	89	10	)	)	PUNCT
ejpam-5504	90	1	+	+	CCONJ
ejpam-5504	90	2	(	(	PUNCT
ejpam-5504	90	3	id−r	id−r	NOUN
ejpam-5504	90	4	)	)	PUNCT
ejpam-5504	90	5	(	(	PUNCT
ejpam-5504	90	6	βy	βy	ADJ
ejpam-5504	90	7	)	)	PUNCT
ejpam-5504	90	8	=	=	SYM
ejpam-5504	90	9	α(x	α(x	PROPN
ejpam-5504	90	10	−	−	NUM
ejpam-5504	90	11	rx	rx	NOUN
ejpam-5504	90	12	)	)	PUNCT
ejpam-5504	91	1	+	+	CCONJ
ejpam-5504	91	2	β(y	β(y	PROPN
ejpam-5504	91	3	−	−	PROPN
ejpam-5504	91	4	ry	ry	NOUN
ejpam-5504	91	5	)	)	PUNCT
ejpam-5504	91	6	=	=	SYM
ejpam-5504	91	7	0	0	PUNCT
ejpam-5504	92	1	+	+	CCONJ
ejpam-5504	92	2	0	0	NUM
ejpam-5504	92	3	=	=	SYM
ejpam-5504	92	4	0	0	X
ejpam-5504	92	5	.	.	PUNCT
ejpam-5504	93	1	therefore	therefore	ADV
ejpam-5504	93	2	,	,	PUNCT
ejpam-5504	93	3	αx	αx	ADV
ejpam-5504	93	4	+	+	CCONJ
ejpam-5504	93	5	βy	βy	DET
ejpam-5504	93	6	∈	∈	PROPN
ejpam-5504	93	7	d	d	NOUN
ejpam-5504	93	8	and	and	CCONJ
ejpam-5504	93	9	hence	hence	ADV
ejpam-5504	93	10	d	d	PRON
ejpam-5504	93	11	is	be	AUX
ejpam-5504	93	12	a	a	DET
ejpam-5504	93	13	linear	linear	ADJ
ejpam-5504	93	14	subspace	subspace	NOUN
ejpam-5504	93	15	.	.	PUNCT
ejpam-5504	94	1	to	to	PART
ejpam-5504	94	2	show	show	VERB
ejpam-5504	94	3	that	that	SCONJ
ejpam-5504	94	4	d	d	NOUN
ejpam-5504	94	5	is	be	AUX
ejpam-5504	94	6	closed	closed	ADJ
ejpam-5504	94	7	,	,	PUNCT
ejpam-5504	94	8	let	let	VERB
ejpam-5504	94	9	(	(	PUNCT
ejpam-5504	94	10	xn	xn	X
ejpam-5504	94	11	)	)	PUNCT
ejpam-5504	94	12	be	be	VERB
ejpam-5504	94	13	a	a	DET
ejpam-5504	94	14	sequence	sequence	NOUN
ejpam-5504	94	15	in	in	ADP
ejpam-5504	94	16	d	d	PROPN
ejpam-5504	94	17	such	such	ADJ
ejpam-5504	94	18	that	that	PRON
ejpam-5504	94	19	(	(	PUNCT
ejpam-5504	94	20	xn	xn	X
ejpam-5504	94	21	)	)	PUNCT
ejpam-5504	94	22	converges	converge	VERB
ejpam-5504	94	23	to	to	PART
ejpam-5504	94	24	x.	x.	PROPN
ejpam-5504	94	25	then	then	ADV
ejpam-5504	94	26	lim	lim	PROPN
ejpam-5504	94	27	n→∞	n→∞	PROPN
ejpam-5504	94	28	(	(	PUNCT
ejpam-5504	94	29	id−r)(x	id−r)(x	NOUN
ejpam-5504	94	30	−	−	PROPN
ejpam-5504	94	31	xn	xn	NUM
ejpam-5504	94	32	)	)	PUNCT
ejpam-5504	95	1	=	=	SYM
ejpam-5504	95	2	lim	lim	PROPN
ejpam-5504	95	3	n→∞	n→∞	X
ejpam-5504	95	4	(	(	PUNCT
ejpam-5504	95	5	id−r)x	id−r)x	PROPN
ejpam-5504	95	6	−	−	PROPN
ejpam-5504	95	7	lim	lim	PROPN
ejpam-5504	95	8	n→∞	n→∞	X
ejpam-5504	96	1	(	(	PUNCT
ejpam-5504	96	2	id−r)xn	id−r)xn	NOUN
ejpam-5504	96	3	=	=	SYM
ejpam-5504	96	4	(	(	PUNCT
ejpam-5504	96	5	id−r)x	id−r)x	PROPN
ejpam-5504	96	6	−	−	PROPN
ejpam-5504	96	7	(	(	PUNCT
ejpam-5504	96	8	id−r)x	id−r)x	PROPN
ejpam-5504	96	9	=	=	SYM
ejpam-5504	96	10	0	0	NUM
ejpam-5504	96	11	.	.	PUNCT
ejpam-5504	97	1	therefore	therefore	ADV
ejpam-5504	97	2	,	,	PUNCT
ejpam-5504	97	3	x	x	PUNCT
ejpam-5504	97	4	∈	∈	PROPN
ejpam-5504	97	5	d	d	NOUN
ejpam-5504	97	6	and	and	CCONJ
ejpam-5504	97	7	hence	hence	ADV
ejpam-5504	97	8	d	d	PRON
ejpam-5504	97	9	is	be	AUX
ejpam-5504	97	10	closed	closed	ADJ
ejpam-5504	97	11	.	.	PUNCT
ejpam-5504	98	1	(	(	PUNCT
ejpam-5504	98	2	ii	ii	NOUN
ejpam-5504	98	3	)	)	PUNCT
ejpam-5504	98	4	and	and	CCONJ
ejpam-5504	98	5	(	(	PUNCT
ejpam-5504	98	6	iii	iii	X
ejpam-5504	98	7	):	):	PUNCT
ejpam-5504	98	8	it	it	PRON
ejpam-5504	98	9	follows	follow	VERB
ejpam-5504	98	10	from	from	ADP
ejpam-5504	98	11	proposition	proposition	NOUN
ejpam-5504	98	12	1(iii	1(iii	NUM
ejpam-5504	98	13	)	)	PUNCT
ejpam-5504	98	14	&	&	CCONJ
ejpam-5504	98	15	(	(	PUNCT
ejpam-5504	98	16	iv	iv	X
ejpam-5504	98	17	)	)	PUNCT
ejpam-5504	98	18	that	that	SCONJ
ejpam-5504	98	19	id−r	id−r	NOUN
ejpam-5504	98	20	is	be	AUX
ejpam-5504	98	21	monotone	monotone	ADJ
ejpam-5504	98	22	and	and	CCONJ
ejpam-5504	98	23	bounded	bound	VERB
ejpam-5504	98	24	.	.	PUNCT
ejpam-5504	99	1	hence	hence	ADV
ejpam-5504	99	2	,	,	PUNCT
ejpam-5504	99	3	fix	fix	VERB
ejpam-5504	99	4	r∗	r∗	NOUN
ejpam-5504	99	5	=	=	PUNCT
ejpam-5504	99	6	fix	fix	NOUN
ejpam-5504	99	7	r	r	NOUN
ejpam-5504	99	8	=	=	SYM
ejpam-5504	99	9	d	d	PROPN
ejpam-5504	99	10	and	and	CCONJ
ejpam-5504	99	11	ran	run	VERB
ejpam-5504	99	12	(	(	PUNCT
ejpam-5504	99	13	id−r	id−r	NOUN
ejpam-5504	99	14	)	)	PUNCT
ejpam-5504	100	1	=	=	PRON
ejpam-5504	100	2	ran	run	VERB
ejpam-5504	100	3	(	(	PUNCT
ejpam-5504	100	4	id−r∗	id−r∗	PROPN
ejpam-5504	100	5	)	)	PUNCT
ejpam-5504	100	6	=	=	PUNCT
ejpam-5504	100	7	d⊥	d⊥	NOUN
ejpam-5504	100	8	by	by	ADP
ejpam-5504	100	9	[	[	X
ejpam-5504	100	10	4	4	NUM
ejpam-5504	100	11	,	,	PUNCT
ejpam-5504	100	12	proposition	proposition	NOUN
ejpam-5504	100	13	20.17	20.17	NUM
ejpam-5504	100	14	]	]	PUNCT
ejpam-5504	100	15	.	.	PUNCT
ejpam-5504	101	1	■	■	PUNCT
ejpam-5504	101	2	remark	remark	NOUN
ejpam-5504	101	3	1	1	NUM
ejpam-5504	101	4	.	.	PUNCT
ejpam-5504	101	5	suppose	suppose	VERB
ejpam-5504	101	6	that	that	SCONJ
ejpam-5504	101	7	x	x	X
ejpam-5504	101	8	=	=	SYM
ejpam-5504	101	9	ℓ2(n	ℓ2(n	PROPN
ejpam-5504	101	10	)	)	PUNCT
ejpam-5504	101	11	and	and	CCONJ
ejpam-5504	101	12	that	that	SCONJ
ejpam-5504	101	13	r	r	NOUN
ejpam-5504	101	14	:	:	PUNCT
ejpam-5504	101	15	x	x	X
ejpam-5504	101	16	→	→	PUNCT
ejpam-5504	101	17	x	x	SYM
ejpam-5504	101	18	:	:	PUNCT
ejpam-5504	101	19	(	(	PUNCT
ejpam-5504	101	20	xn)n∈n	xn)n∈n	PROPN
ejpam-5504	101	21	7→	7→	PROPN
ejpam-5504	101	22	(	(	PUNCT
ejpam-5504	101	23	(	(	PUNCT
ejpam-5504	101	24	(	(	PUNCT
ejpam-5504	101	25	1	1	NUM
ejpam-5504	101	26	−	−	NOUN
ejpam-5504	101	27	εn)xn	εn)xn	NOUN
ejpam-5504	101	28	)	)	PUNCT
ejpam-5504	101	29	)	)	PUNCT
ejpam-5504	102	1	n∈n	n∈n	NOUN
ejpam-5504	102	2	,	,	PUNCT
ejpam-5504	102	3	(	(	PUNCT
ejpam-5504	102	4	7	7	X
ejpam-5504	102	5	)	)	PUNCT
ejpam-5504	102	6	where	where	SCONJ
ejpam-5504	102	7	(	(	PUNCT
ejpam-5504	102	8	εn)n∈n	εn)n∈n	NOUN
ejpam-5504	102	9	lies	lie	VERB
ejpam-5504	102	10	in	in	ADP
ejpam-5504	102	11	]	]	X
ejpam-5504	102	12	0	0	NUM
ejpam-5504	102	13	,	,	PUNCT
ejpam-5504	102	14	1	1	NUM
ejpam-5504	102	15	[	[	PUNCT
ejpam-5504	102	16	with	with	ADP
ejpam-5504	102	17	εn	εn	ADJ
ejpam-5504	102	18	→	→	SYM
ejpam-5504	102	19	0	0	NUM
ejpam-5504	102	20	.	.	PUNCT
ejpam-5504	103	1	then	then	ADV
ejpam-5504	103	2	the	the	DET
ejpam-5504	103	3	following	follow	VERB
ejpam-5504	103	4	holds	hold	VERB
ejpam-5504	103	5	:	:	PUNCT
ejpam-5504	103	6	(	(	PUNCT
ejpam-5504	103	7	i	i	NOUN
ejpam-5504	103	8	)	)	PUNCT
ejpam-5504	103	9	id−r	id−r	NOUN
ejpam-5504	103	10	:	:	PUNCT
ejpam-5504	103	11	(	(	PUNCT
ejpam-5504	103	12	xn)n∈n	xn)n∈n	PROPN
ejpam-5504	103	13	7→	7→	PROPN
ejpam-5504	103	14	(	(	PUNCT
ejpam-5504	103	15	εnxn	εnxn	NOUN
ejpam-5504	103	16	)	)	PUNCT
ejpam-5504	103	17	n∈n	n∈n	NOUN
ejpam-5504	103	18	is	be	AUX
ejpam-5504	103	19	a	a	DET
ejpam-5504	103	20	compact	compact	ADJ
ejpam-5504	103	21	operator	operator	NOUN
ejpam-5504	103	22	.	.	PUNCT
ejpam-5504	104	1	(	(	PUNCT
ejpam-5504	104	2	ii	ii	NOUN
ejpam-5504	104	3	)	)	PUNCT
ejpam-5504	104	4	d	d	NOUN
ejpam-5504	104	5	=	=	PUNCT
ejpam-5504	104	6	fix	fix	NOUN
ejpam-5504	104	7	r	r	NOUN
ejpam-5504	104	8	=	=	PUNCT
ejpam-5504	104	9	{	{	PUNCT
ejpam-5504	104	10	0	0	NUM
ejpam-5504	104	11	}	}	PUNCT
ejpam-5504	104	12	.	.	PUNCT
ejpam-5504	105	1	(	(	PUNCT
ejpam-5504	105	2	iii	iii	NOUN
ejpam-5504	105	3	)	)	PUNCT
ejpam-5504	105	4	ran	run	VERB
ejpam-5504	105	5	(	(	PUNCT
ejpam-5504	105	6	id−r	id−r	NOUN
ejpam-5504	105	7	)	)	PUNCT
ejpam-5504	105	8	is	be	AUX
ejpam-5504	105	9	not	not	PART
ejpam-5504	105	10	closed	closed	ADJ
ejpam-5504	105	11	.	.	PUNCT
ejpam-5504	106	1	(	(	PUNCT
ejpam-5504	106	2	iv	iv	X
ejpam-5504	106	3	)	)	PUNCT
ejpam-5504	106	4	ran	run	VERB
ejpam-5504	106	5	r	r	NOUN
ejpam-5504	106	6	is	be	AUX
ejpam-5504	106	7	a	a	DET
ejpam-5504	106	8	closed	closed	ADJ
ejpam-5504	106	9	subspace	subspace	NOUN
ejpam-5504	106	10	.	.	PUNCT
ejpam-5504	107	1	proof	proof	NOUN
ejpam-5504	107	2	.	.	PUNCT
ejpam-5504	108	1	(	(	PUNCT
ejpam-5504	108	2	i	i	NOUN
ejpam-5504	108	3	)	)	PUNCT
ejpam-5504	108	4	and	and	CCONJ
ejpam-5504	108	5	(	(	PUNCT
ejpam-5504	108	6	ii	ii	NOUN
ejpam-5504	108	7	):	):	PUNCT
ejpam-5504	108	8	see	see	VERB
ejpam-5504	108	9	[	[	X
ejpam-5504	108	10	12	12	NUM
ejpam-5504	108	11	,	,	PUNCT
ejpam-5504	108	12	propositionii.4.6	propositionii.4.6	PROPN
ejpam-5504	108	13	]	]	X
ejpam-5504	108	14	.	.	PUNCT
ejpam-5504	109	1	(	(	PUNCT
ejpam-5504	109	2	iii	iii	X
ejpam-5504	109	3	):	):	PUNCT
ejpam-5504	109	4	it	it	PRON
ejpam-5504	109	5	follows	follow	VERB
ejpam-5504	109	6	from	from	ADP
ejpam-5504	109	7	[	[	X
ejpam-5504	109	8	16	16	NUM
ejpam-5504	109	9	,	,	PUNCT
ejpam-5504	109	10	proposition	proposition	NOUN
ejpam-5504	109	11	3.4.6	3.4.6	NUM
ejpam-5504	109	12	]	]	PUNCT
ejpam-5504	109	13	that	that	PRON
ejpam-5504	109	14	ran	run	VERB
ejpam-5504	109	15	(	(	PUNCT
ejpam-5504	109	16	id−r	id−r	PROPN
ejpam-5504	109	17	)	)	PUNCT
ejpam-5504	109	18	is	be	AUX
ejpam-5504	109	19	closed	close	VERB
ejpam-5504	109	20	if	if	SCONJ
ejpam-5504	109	21	and	and	CCONJ
ejpam-5504	109	22	only	only	ADV
ejpam-5504	109	23	if	if	SCONJ
ejpam-5504	109	24	ran	run	VERB
ejpam-5504	109	25	(	(	PUNCT
ejpam-5504	109	26	id−r	id−r	PROPN
ejpam-5504	109	27	)	)	PUNCT
ejpam-5504	109	28	is	be	AUX
ejpam-5504	109	29	finite	finite	ADJ
ejpam-5504	109	30	-	-	ADJ
ejpam-5504	109	31	dimensional	dimensional	ADJ
ejpam-5504	109	32	.	.	PUNCT
ejpam-5504	110	1	on	on	ADP
ejpam-5504	110	2	the	the	DET
ejpam-5504	110	3	other	other	ADJ
ejpam-5504	110	4	hand	hand	NOUN
ejpam-5504	110	5	,	,	PUNCT
ejpam-5504	110	6	x	x	X
ejpam-5504	110	7	=	=	PUNCT
ejpam-5504	110	8	d⊥	d⊥	NOUN
ejpam-5504	110	9	=	=	NOUN
ejpam-5504	110	10	ran	run	VERB
ejpam-5504	110	11	(	(	PUNCT
ejpam-5504	110	12	id−r	id−r	NOUN
ejpam-5504	110	13	)	)	PUNCT
ejpam-5504	110	14	,	,	PUNCT
ejpam-5504	110	15	i.e.	i.e.	X
ejpam-5504	110	16	,	,	PUNCT
ejpam-5504	110	17	the	the	DET
ejpam-5504	110	18	range	range	NOUN
ejpam-5504	110	19	of	of	ADP
ejpam-5504	110	20	id−r	id−r	NOUN
ejpam-5504	110	21	is	be	AUX
ejpam-5504	110	22	dense	dense	ADJ
ejpam-5504	110	23	in	in	ADP
ejpam-5504	110	24	the	the	DET
ejpam-5504	110	25	infinite	infinite	ADJ
ejpam-5504	110	26	-	-	PUNCT
ejpam-5504	110	27	dimensional	dimensional	ADJ
ejpam-5504	110	28	space	space	NOUN
ejpam-5504	110	29	x.	x.	NOUN
ejpam-5504	110	30	altogether	altogether	ADV
ejpam-5504	110	31	,	,	PUNCT
ejpam-5504	110	32	ran	run	VERB
ejpam-5504	110	33	(	(	PUNCT
ejpam-5504	110	34	id−r	id−r	NOUN
ejpam-5504	110	35	)	)	PUNCT
ejpam-5504	110	36	is	be	AUX
ejpam-5504	110	37	not	not	PART
ejpam-5504	110	38	closed	closed	ADJ
ejpam-5504	110	39	.	.	PUNCT
ejpam-5504	111	1	(	(	PUNCT
ejpam-5504	111	2	iv	iv	NUM
ejpam-5504	111	3	):	):	PUNCT
ejpam-5504	111	4	see	see	VERB
ejpam-5504	111	5	[	[	X
ejpam-5504	111	6	16	16	NUM
ejpam-5504	111	7	,	,	PUNCT
ejpam-5504	111	8	lemma	lemma	PROPN
ejpam-5504	111	9	3.4.20	3.4.20	NUM
ejpam-5504	111	10	]	]	PUNCT
ejpam-5504	111	11	.	.	PUNCT
ejpam-5504	112	1	■	■	PUNCT
ejpam-5504	112	2	s.t	s.t	PROPN
ejpam-5504	112	3	.	.	PROPN
ejpam-5504	112	4	alwadani	alwadani	PROPN
ejpam-5504	112	5	/	/	SYM
ejpam-5504	112	6	eur	eur	PROPN
ejpam-5504	112	7	.	.	PUNCT
ejpam-5504	113	1	j.	j.	PROPN
ejpam-5504	113	2	pure	pure	PROPN
ejpam-5504	113	3	appl	appl	PROPN
ejpam-5504	113	4	.	.	PROPN
ejpam-5504	113	5	math	math	PROPN
ejpam-5504	113	6	,	,	PUNCT
ejpam-5504	113	7	17	17	NUM
ejpam-5504	113	8	(	(	PUNCT
ejpam-5504	113	9	4	4	NUM
ejpam-5504	113	10	)	)	PUNCT
ejpam-5504	113	11	(	(	PUNCT
ejpam-5504	113	12	2024	2024	NUM
ejpam-5504	113	13	)	)	PUNCT
ejpam-5504	113	14	,	,	PUNCT
ejpam-5504	113	15	3660	3660	NUM
ejpam-5504	113	16	-	-	SYM
ejpam-5504	113	17	3676	3676	NUM
ejpam-5504	113	18	3664	3664	NUM
ejpam-5504	113	19	lemma	lemma	PROPN
ejpam-5504	113	20	2	2	NUM
ejpam-5504	113	21	.	.	PUNCT
ejpam-5504	113	22	suppose	suppose	VERB
ejpam-5504	113	23	that	that	PRON
ejpam-5504	113	24	ran	run	VERB
ejpam-5504	113	25	(	(	PUNCT
ejpam-5504	113	26	id−r	id−r	PROPN
ejpam-5504	113	27	)	)	PUNCT
ejpam-5504	113	28	is	be	AUX
ejpam-5504	113	29	closed	close	VERB
ejpam-5504	113	30	;	;	PUNCT
ejpam-5504	113	31	equivalently	equivalently	ADV
ejpam-5504	113	32	,	,	PUNCT
ejpam-5504	113	33	ran	run	VERB
ejpam-5504	113	34	(	(	PUNCT
ejpam-5504	113	35	id−r	id−r	NOUN
ejpam-5504	113	36	)	)	PUNCT
ejpam-5504	113	37	=	=	SYM
ejpam-5504	113	38	d⊥.	d⊥.	NOUN
ejpam-5504	113	39	set	set	VERB
ejpam-5504	113	40	t	t	NOUN
ejpam-5504	113	41	:	:	PUNCT
ejpam-5504	114	1	=	=	SYM
ejpam-5504	114	2	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	114	3	pd⊥	pd⊥	NOUN
ejpam-5504	114	4	−	−	NUM
ejpam-5504	114	5	1	1	NUM
ejpam-5504	114	6	2	2	NUM
ejpam-5504	114	7	pd⊥	pd⊥	PROPN
ejpam-5504	114	8	.	.	PUNCT
ejpam-5504	115	1	(	(	PUNCT
ejpam-5504	115	2	8)	8)	NUM
ejpam-5504	115	3	then	then	ADV
ejpam-5504	115	4	,	,	PUNCT
ejpam-5504	115	5	(	(	PUNCT
ejpam-5504	115	6	i	i	NOUN
ejpam-5504	115	7	)	)	PUNCT
ejpam-5504	115	8	ran	run	VERB
ejpam-5504	115	9	(	(	PUNCT
ejpam-5504	115	10	id−r)∗	id−r)∗	PROPN
ejpam-5504	115	11	=	=	PROPN
ejpam-5504	115	12	d⊥.	d⊥.	PROPN
ejpam-5504	115	13	(	(	PUNCT
ejpam-5504	115	14	ii	ii	NOUN
ejpam-5504	115	15	)	)	PUNCT
ejpam-5504	115	16	t	t	PROPN
ejpam-5504	115	17	is	be	AUX
ejpam-5504	115	18	a	a	DET
ejpam-5504	115	19	linear	linear	ADJ
ejpam-5504	115	20	and	and	CCONJ
ejpam-5504	115	21	continuous	continuous	ADJ
ejpam-5504	115	22	.	.	PUNCT
ejpam-5504	116	1	(	(	PUNCT
ejpam-5504	116	2	iii	iii	X
ejpam-5504	116	3	)	)	PUNCT
ejpam-5504	116	4	t	t	PROPN
ejpam-5504	116	5	is	be	AUX
ejpam-5504	116	6	monotone	monotone	ADJ
ejpam-5504	116	7	.	.	PUNCT
ejpam-5504	117	1	(	(	PUNCT
ejpam-5504	117	2	iv	iv	X
ejpam-5504	117	3	)	)	PUNCT
ejpam-5504	117	4	t	t	PROPN
ejpam-5504	117	5	is	be	AUX
ejpam-5504	117	6	maximally	maximally	ADV
ejpam-5504	117	7	monotone	monotone	ADJ
ejpam-5504	117	8	.	.	PUNCT
ejpam-5504	118	1	(	(	PUNCT
ejpam-5504	118	2	v	v	NOUN
ejpam-5504	118	3	)	)	PUNCT
ejpam-5504	118	4	ran	run	VERB
ejpam-5504	118	5	t	t	PROPN
ejpam-5504	118	6	⊆	⊆	NUM
ejpam-5504	118	7	d⊥	d⊥	NOUN
ejpam-5504	118	8	,	,	PUNCT
ejpam-5504	118	9	where	where	SCONJ
ejpam-5504	118	10	d	d	PROPN
ejpam-5504	118	11	=	=	SYM
ejpam-5504	118	12	ker(id−r	ker(id−r	PROPN
ejpam-5504	118	13	)	)	PUNCT
ejpam-5504	118	14	.	.	PUNCT
ejpam-5504	119	1	(	(	PUNCT
ejpam-5504	119	2	vi	vi	X
ejpam-5504	119	3	)	)	PUNCT
ejpam-5504	119	4	pd⊥	pd⊥	PROPN
ejpam-5504	119	5	t	t	PROPN
ejpam-5504	119	6	=	=	PUNCT
ejpam-5504	119	7	t	t	PROPN
ejpam-5504	119	8	pd⊥	pd⊥	PROPN
ejpam-5504	119	9	=	=	PUNCT
ejpam-5504	120	1	t.	t.	NOUN
ejpam-5504	120	2	proof	proof	NOUN
ejpam-5504	120	3	.	.	PUNCT
ejpam-5504	121	1	(	(	PUNCT
ejpam-5504	121	2	i	i	NOUN
ejpam-5504	121	3	):	):	PUNCT
ejpam-5504	121	4	by	by	ADP
ejpam-5504	121	5	using	use	VERB
ejpam-5504	121	6	the	the	DET
ejpam-5504	121	7	closeness	closeness	NOUN
ejpam-5504	121	8	of	of	ADP
ejpam-5504	121	9	ran	ran	NOUN
ejpam-5504	121	10	(	(	PUNCT
ejpam-5504	121	11	id−r	id−r	NOUN
ejpam-5504	121	12	)	)	PUNCT
ejpam-5504	121	13	and	and	CCONJ
ejpam-5504	121	14	...	...	PUNCT
ejpam-5504	121	15	ran	run	VERB
ejpam-5504	121	16	(	(	PUNCT
ejpam-5504	121	17	id−r)∗	id−r)∗	PROPN
ejpam-5504	121	18	=	=	NUM
ejpam-5504	121	19	ran	run	VERB
ejpam-5504	121	20	(	(	PUNCT
ejpam-5504	121	21	id−r∗	id−r∗	NOUN
ejpam-5504	121	22	)	)	PUNCT
ejpam-5504	122	1	=	=	PRON
ejpam-5504	122	2	ran	run	VERB
ejpam-5504	122	3	(	(	PUNCT
ejpam-5504	122	4	id−r	id−r	NOUN
ejpam-5504	122	5	)	)	PUNCT
ejpam-5504	122	6	=	=	SYM
ejpam-5504	122	7	d⊥.	d⊥.	NOUN
ejpam-5504	122	8	(	(	PUNCT
ejpam-5504	122	9	ii	ii	PROPN
ejpam-5504	122	10	):	):	PUNCT
ejpam-5504	122	11	this	this	PRON
ejpam-5504	122	12	is	be	AUX
ejpam-5504	122	13	clear	clear	ADJ
ejpam-5504	122	14	because	because	SCONJ
ejpam-5504	122	15	t	t	PROPN
ejpam-5504	122	16	is	be	AUX
ejpam-5504	122	17	defined	define	VERB
ejpam-5504	122	18	using	use	VERB
ejpam-5504	122	19	pd⊥	pd⊥	PROPN
ejpam-5504	122	20	,	,	PUNCT
ejpam-5504	122	21	which	which	PRON
ejpam-5504	122	22	is	be	AUX
ejpam-5504	122	23	a	a	DET
ejpam-5504	122	24	linear	linear	ADJ
ejpam-5504	122	25	and	and	CCONJ
ejpam-5504	122	26	continuous	continuous	ADJ
ejpam-5504	122	27	operator	operator	NOUN
ejpam-5504	122	28	.	.	PUNCT
ejpam-5504	123	1	(	(	PUNCT
ejpam-5504	123	2	iii	iii	NOUN
ejpam-5504	123	3	):	):	PUNCT
ejpam-5504	123	4	see	see	VERB
ejpam-5504	123	5	[	[	X
ejpam-5504	123	6	4	4	NUM
ejpam-5504	123	7	,	,	PUNCT
ejpam-5504	123	8	example	example	NOUN
ejpam-5504	123	9	20.12	20.12	NUM
ejpam-5504	123	10	]	]	PUNCT
ejpam-5504	123	11	.	.	PUNCT
ejpam-5504	124	1	(	(	PUNCT
ejpam-5504	124	2	iv	iv	X
ejpam-5504	124	3	):	):	PUNCT
ejpam-5504	124	4	combine	combine	PROPN
ejpam-5504	124	5	(	(	PUNCT
ejpam-5504	124	6	ii	ii	NOUN
ejpam-5504	124	7	)	)	PUNCT
ejpam-5504	124	8	,	,	PUNCT
ejpam-5504	124	9	(	(	PUNCT
ejpam-5504	124	10	iii	iii	NOUN
ejpam-5504	124	11	)	)	PUNCT
ejpam-5504	124	12	and	and	CCONJ
ejpam-5504	124	13	[	[	X
ejpam-5504	124	14	4	4	NUM
ejpam-5504	124	15	,	,	PUNCT
ejpam-5504	124	16	corollary	corollary	NOUN
ejpam-5504	124	17	20.28	20.28	NUM
ejpam-5504	124	18	]	]	PUNCT
ejpam-5504	124	19	.	.	PUNCT
ejpam-5504	125	1	(	(	PUNCT
ejpam-5504	125	2	v	v	NOUN
ejpam-5504	125	3	):	):	PUNCT
ejpam-5504	125	4	it	it	PRON
ejpam-5504	125	5	follows	follow	VERB
ejpam-5504	125	6	directly	directly	ADV
ejpam-5504	125	7	from	from	ADP
ejpam-5504	125	8	(	(	PUNCT
ejpam-5504	125	9	8)	8)	NUM
ejpam-5504	125	10	.	.	PUNCT
ejpam-5504	126	1	(	(	PUNCT
ejpam-5504	126	2	vi	vi	ADJ
ejpam-5504	126	3	):	):	PUNCT
ejpam-5504	126	4	since	since	SCONJ
ejpam-5504	126	5	ran	run	VERB
ejpam-5504	126	6	t	t	PROPN
ejpam-5504	126	7	⊆	⊆	NUM
ejpam-5504	126	8	d⊥	d⊥	NOUN
ejpam-5504	126	9	by	by	ADP
ejpam-5504	126	10	using	use	VERB
ejpam-5504	126	11	(	(	PUNCT
ejpam-5504	126	12	v	v	NOUN
ejpam-5504	126	13	)	)	PUNCT
ejpam-5504	126	14	,	,	PUNCT
ejpam-5504	126	15	we	we	PRON
ejpam-5504	126	16	obtain	obtain	VERB
ejpam-5504	126	17	pd⊥	pd⊥	PROPN
ejpam-5504	126	18	t	t	NOUN
ejpam-5504	127	1	=	=	PUNCT
ejpam-5504	127	2	t.	t.	NOUN
ejpam-5504	127	3	moreover	moreover	ADV
ejpam-5504	127	4	,	,	PUNCT
ejpam-5504	127	5	both	both	DET
ejpam-5504	127	6	t	t	PROPN
ejpam-5504	127	7	and	and	CCONJ
ejpam-5504	127	8	pd⊥	pd⊥	PROPN
ejpam-5504	127	9	commute	commute	NOUN
ejpam-5504	127	10	and	and	CCONJ
ejpam-5504	127	11	so	so	ADV
ejpam-5504	127	12	t	t	PROPN
ejpam-5504	128	1	pd⊥	pd⊥	PROPN
ejpam-5504	128	2	=	=	PUNCT
ejpam-5504	129	1	pd⊥	pd⊥	PROPN
ejpam-5504	129	2	t	t	NOUN
ejpam-5504	130	1	=	=	PUNCT
ejpam-5504	130	2	t.	t.	PROPN
ejpam-5504	130	3	■	■	PUNCT
ejpam-5504	130	4	remark	remark	NOUN
ejpam-5504	130	5	2	2	NUM
ejpam-5504	130	6	.	.	PUNCT
ejpam-5504	131	1	it	it	PRON
ejpam-5504	131	2	is	be	AUX
ejpam-5504	131	3	well	well	ADV
ejpam-5504	131	4	known	know	VERB
ejpam-5504	131	5	that	that	PRON
ejpam-5504	131	6	ran	run	VERB
ejpam-5504	131	7	(	(	PUNCT
ejpam-5504	131	8	id−r	id−r	PROPN
ejpam-5504	131	9	)	)	PUNCT
ejpam-5504	131	10	is	be	AUX
ejpam-5504	131	11	closed	close	VERB
ejpam-5504	131	12	if	if	SCONJ
ejpam-5504	131	13	and	and	CCONJ
ejpam-5504	131	14	only	only	ADV
ejpam-5504	131	15	if	if	SCONJ
ejpam-5504	131	16	there	there	PRON
ejpam-5504	131	17	exists	exist	VERB
ejpam-5504	131	18	α	α	PROPN
ejpam-5504	131	19	>	>	X
ejpam-5504	131	20	0	0	NUM
ejpam-5504	131	21	such	such	ADJ
ejpam-5504	131	22	that	that	SCONJ
ejpam-5504	131	23	(	(	PUNCT
ejpam-5504	131	24	∀y	∀y	PROPN
ejpam-5504	131	25	∈	∈	PROPN
ejpam-5504	131	26	(	(	PUNCT
ejpam-5504	131	27	ker(id−r))⊥	ker(id−r))⊥	NOUN
ejpam-5504	131	28	=	=	SYM
ejpam-5504	131	29	d⊥	d⊥	NOUN
ejpam-5504	131	30	)	)	PUNCT
ejpam-5504	131	31	∥y	∥y	PROPN
ejpam-5504	131	32	−	−	PROPN
ejpam-5504	131	33	ry∥	ry∥	PROPN
ejpam-5504	131	34	≥	≥	PROPN
ejpam-5504	131	35	α∥y∥	α∥y∥	PROPN
ejpam-5504	131	36	;	;	PUNCT
ejpam-5504	131	37	(	(	PUNCT
ejpam-5504	131	38	9	9	X
ejpam-5504	131	39	)	)	PUNCT
ejpam-5504	131	40	proof	proof	NOUN
ejpam-5504	131	41	.	.	PUNCT
ejpam-5504	132	1	see	see	VERB
ejpam-5504	132	2	[	[	X
ejpam-5504	132	3	13	13	NUM
ejpam-5504	132	4	,	,	PUNCT
ejpam-5504	132	5	theorem	theorem	VERB
ejpam-5504	132	6	8.18	8.18	NUM
ejpam-5504	132	7	]	]	PUNCT
ejpam-5504	132	8	.	.	PUNCT
ejpam-5504	133	1	■	■	PUNCT
ejpam-5504	133	2	proposition	proposition	NOUN
ejpam-5504	133	3	2	2	NUM
ejpam-5504	133	4	.	.	PUNCT
ejpam-5504	133	5	suppose	suppose	VERB
ejpam-5504	133	6	that	that	SCONJ
ejpam-5504	133	7	(	(	PUNCT
ejpam-5504	133	8	9	9	X
ejpam-5504	133	9	)	)	PUNCT
ejpam-5504	133	10	holds	hold	VERB
ejpam-5504	133	11	,	,	PUNCT
ejpam-5504	133	12	then	then	ADV
ejpam-5504	133	13	the	the	DET
ejpam-5504	133	14	operator	operator	NOUN
ejpam-5504	133	15	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	133	16	:	:	PUNCT
ejpam-5504	133	17	d⊥	d⊥	NOUN
ejpam-5504	133	18	→	→	SYM
ejpam-5504	133	19	d⊥	d⊥	NOUN
ejpam-5504	133	20	,	,	PUNCT
ejpam-5504	133	21	(	(	PUNCT
ejpam-5504	133	22	10	10	NUM
ejpam-5504	133	23	)	)	PUNCT
ejpam-5504	133	24	(	(	PUNCT
ejpam-5504	133	25	i	i	NOUN
ejpam-5504	133	26	)	)	PUNCT
ejpam-5504	133	27	is	be	AUX
ejpam-5504	133	28	a	a	DET
ejpam-5504	133	29	linear	linear	ADJ
ejpam-5504	133	30	selection	selection	NOUN
ejpam-5504	133	31	of	of	ADP
ejpam-5504	133	32	t−1	t−1	PROPN
ejpam-5504	133	33	.	.	PUNCT
ejpam-5504	134	1	(	(	PUNCT
ejpam-5504	134	2	ii	ii	NOUN
ejpam-5504	134	3	)	)	PUNCT
ejpam-5504	134	4	is	be	AUX
ejpam-5504	134	5	continuous	continuous	ADJ
ejpam-5504	134	6	and	and	CCONJ
ejpam-5504	134	7	its	its	PRON
ejpam-5504	134	8	norm	norm	NOUN
ejpam-5504	134	9	is	be	AUX
ejpam-5504	134	10	bounded	bound	VERB
ejpam-5504	134	11	above	above	ADV
ejpam-5504	134	12	by	by	ADP
ejpam-5504	134	13	1	1	NUM
ejpam-5504	134	14	/	/	SYM
ejpam-5504	134	15	α	α	NOUN
ejpam-5504	134	16	.	.	PUNCT
ejpam-5504	135	1	s.t	s.t	PROPN
ejpam-5504	135	2	.	.	PROPN
ejpam-5504	135	3	alwadani	alwadani	PROPN
ejpam-5504	135	4	/	/	SYM
ejpam-5504	135	5	eur	eur	PROPN
ejpam-5504	135	6	.	.	PUNCT
ejpam-5504	136	1	j.	j.	PROPN
ejpam-5504	136	2	pure	pure	PROPN
ejpam-5504	136	3	appl	appl	PROPN
ejpam-5504	136	4	.	.	PROPN
ejpam-5504	136	5	math	math	PROPN
ejpam-5504	136	6	,	,	PUNCT
ejpam-5504	136	7	17	17	NUM
ejpam-5504	136	8	(	(	PUNCT
ejpam-5504	136	9	4	4	NUM
ejpam-5504	136	10	)	)	PUNCT
ejpam-5504	136	11	(	(	PUNCT
ejpam-5504	136	12	2024	2024	NUM
ejpam-5504	136	13	)	)	PUNCT
ejpam-5504	136	14	,	,	PUNCT
ejpam-5504	136	15	3660	3660	NUM
ejpam-5504	136	16	-	-	SYM
ejpam-5504	136	17	3676	3676	NUM
ejpam-5504	136	18	3665	3665	NUM
ejpam-5504	136	19	proof	proof	NOUN
ejpam-5504	136	20	.	.	PUNCT
ejpam-5504	137	1	(	(	PUNCT
ejpam-5504	137	2	i	i	NOUN
ejpam-5504	137	3	):	):	PUNCT
ejpam-5504	137	4	it	it	PRON
ejpam-5504	137	5	follows	follow	VERB
ejpam-5504	137	6	from	from	ADP
ejpam-5504	137	7	(	(	PUNCT
ejpam-5504	137	8	8)	8)	NUM
ejpam-5504	137	9	and	and	CCONJ
ejpam-5504	137	10	lemma	lemma	PROPN
ejpam-5504	137	11	2	2	NUM
ejpam-5504	137	12	.	.	PUNCT
ejpam-5504	137	13	(	(	PUNCT
ejpam-5504	137	14	ii	ii	NOUN
ejpam-5504	137	15	):	):	PUNCT
ejpam-5504	137	16	clear	clear	ADJ
ejpam-5504	137	17	from	from	ADP
ejpam-5504	137	18	(	(	PUNCT
ejpam-5504	137	19	9	9	NUM
ejpam-5504	137	20	)	)	PUNCT
ejpam-5504	137	21	.	.	PUNCT
ejpam-5504	138	1	■	■	PUNCT
ejpam-5504	138	2	theorem	theorem	ADJ
ejpam-5504	138	3	1	1	NUM
ejpam-5504	138	4	.	.	PUNCT
ejpam-5504	138	5	suppose	suppose	VERB
ejpam-5504	138	6	that	that	PRON
ejpam-5504	138	7	ran	run	VERB
ejpam-5504	138	8	(	(	PUNCT
ejpam-5504	138	9	id−r	id−r	PROPN
ejpam-5504	138	10	)	)	PUNCT
ejpam-5504	138	11	is	be	AUX
ejpam-5504	138	12	closed	close	VERB
ejpam-5504	138	13	.	.	PUNCT
ejpam-5504	139	1	set	set	VERB
ejpam-5504	139	2	a	a	PRON
ejpam-5504	139	3	:	:	PUNCT
ejpam-5504	139	4	=	=	SYM
ejpam-5504	139	5	(	(	PUNCT
ejpam-5504	139	6	id−r)−1	id−r)−1	NUM
ejpam-5504	139	7	−	−	NUM
ejpam-5504	139	8	1	1	NUM
ejpam-5504	139	9	2	2	NUM
ejpam-5504	139	10	i	i	PROPN
ejpam-5504	139	11	d	d	PROPN
ejpam-5504	139	12	,	,	PUNCT
ejpam-5504	139	13	(	(	PUNCT
ejpam-5504	139	14	11	11	NUM
ejpam-5504	139	15	)	)	PUNCT
ejpam-5504	139	16	and	and	CCONJ
ejpam-5504	139	17	defined	define	VERB
ejpam-5504	139	18	qa	qa	NOUN
ejpam-5504	139	19	:	:	PUNCT
ejpam-5504	139	20	dom	dom	NOUN
ejpam-5504	139	21	a	a	X
ejpam-5504	139	22	→	→	X
ejpam-5504	139	23	x	x	SYM
ejpam-5504	139	24	:	:	PUNCT
ejpam-5504	139	25	y	y	PROPN
ejpam-5504	139	26	7→	7→	PROPN
ejpam-5504	139	27	pay	pay	VERB
ejpam-5504	139	28	y.	y.	NOUN
ejpam-5504	139	29	(	(	PUNCT
ejpam-5504	139	30	12	12	NUM
ejpam-5504	139	31	)	)	PUNCT
ejpam-5504	139	32	set	set	NOUN
ejpam-5504	140	1	b	b	NOUN
ejpam-5504	140	2	:	:	PUNCT
ejpam-5504	140	3	=	=	X
ejpam-5504	140	4	pdom	pdom	NOUN
ejpam-5504	140	5	a	a	DET
ejpam-5504	140	6	qa	qa	PROPN
ejpam-5504	140	7	pdom	pdom	NOUN
ejpam-5504	140	8	a	a	PRON
ejpam-5504	140	9	.	.	PUNCT
ejpam-5504	141	1	(	(	PUNCT
ejpam-5504	141	2	13	13	NUM
ejpam-5504	141	3	)	)	PUNCT
ejpam-5504	141	4	then	then	ADV
ejpam-5504	141	5	the	the	DET
ejpam-5504	141	6	following	follow	VERB
ejpam-5504	141	7	holds	hold	VERB
ejpam-5504	141	8	;	;	PUNCT
ejpam-5504	141	9	(	(	PUNCT
ejpam-5504	141	10	i	i	NOUN
ejpam-5504	141	11	)	)	PUNCT
ejpam-5504	141	12	dom	dom	NOUN
ejpam-5504	141	13	a	a	DET
ejpam-5504	141	14	=	=	X
ejpam-5504	141	15	d⊥	d⊥	NOUN
ejpam-5504	141	16	and	and	CCONJ
ejpam-5504	141	17	is	be	AUX
ejpam-5504	141	18	closed	closed	ADJ
ejpam-5504	141	19	.	.	PUNCT
ejpam-5504	142	1	(	(	PUNCT
ejpam-5504	142	2	ii	ii	NOUN
ejpam-5504	142	3	)	)	PUNCT
ejpam-5504	142	4	a	a	PRON
ejpam-5504	142	5	is	be	AUX
ejpam-5504	142	6	linear	linear	PROPN
ejpam-5504	142	7	relation	relation	NOUN
ejpam-5504	142	8	.	.	PUNCT
ejpam-5504	143	1	(	(	PUNCT
ejpam-5504	143	2	iii	iii	X
ejpam-5504	143	3	)	)	PUNCT
ejpam-5504	143	4	a	a	PRON
ejpam-5504	143	5	is	be	AUX
ejpam-5504	143	6	maximally	maximally	ADV
ejpam-5504	143	7	monotone	monotone	ADJ
ejpam-5504	143	8	.	.	PUNCT
ejpam-5504	144	1	(	(	PUNCT
ejpam-5504	144	2	iv	iv	X
ejpam-5504	144	3	)	)	PUNCT
ejpam-5504	144	4	we	we	PRON
ejpam-5504	144	5	have	have	VERB
ejpam-5504	144	6	(	(	PUNCT
ejpam-5504	144	7	∀y	∀y	PROPN
ejpam-5504	144	8	∈	∈	PROPN
ejpam-5504	144	9	dom	dom	NOUN
ejpam-5504	144	10	a	a	NOUN
ejpam-5504	144	11	)	)	PUNCT
ejpam-5504	144	12	qay	qay	NOUN
ejpam-5504	145	1	=	=	PUNCT
ejpam-5504	145	2	pd⊥(id−r)−1y	pd⊥(id−r)−1y	PROPN
ejpam-5504	145	3	−	−	NOUN
ejpam-5504	145	4	1	1	NUM
ejpam-5504	145	5	2	2	NUM
ejpam-5504	145	6	pd⊥	pd⊥	PROPN
ejpam-5504	145	7	y.	y.	NOUN
ejpam-5504	145	8	(	(	PUNCT
ejpam-5504	145	9	v	v	NOUN
ejpam-5504	145	10	)	)	PUNCT
ejpam-5504	145	11	b	b	NOUN
ejpam-5504	145	12	is	be	AUX
ejpam-5504	145	13	maximally	maximally	ADV
ejpam-5504	145	14	monotone	monotone	ADJ
ejpam-5504	145	15	,	,	PUNCT
ejpam-5504	145	16	linear	linear	ADJ
ejpam-5504	145	17	and	and	CCONJ
ejpam-5504	145	18	continuous	continuous	ADJ
ejpam-5504	145	19	.	.	PUNCT
ejpam-5504	146	1	(	(	PUNCT
ejpam-5504	146	2	vi	vi	NOUN
ejpam-5504	146	3	)	)	PUNCT
ejpam-5504	146	4	a	a	DET
ejpam-5504	146	5	=	=	PUNCT
ejpam-5504	146	6	nd⊥	nd⊥	PROPN
ejpam-5504	146	7	+	+	PROPN
ejpam-5504	146	8	b.	b.	PROPN
ejpam-5504	146	9	(	(	PUNCT
ejpam-5504	146	10	vii	vii	PROPN
ejpam-5504	146	11	)	)	PUNCT
ejpam-5504	146	12	b	b	PROPN
ejpam-5504	146	13	=	=	SYM
ejpam-5504	146	14	t.	t.	PROPN
ejpam-5504	146	15	(	(	PUNCT
ejpam-5504	146	16	viii	viii	NOUN
ejpam-5504	146	17	)	)	PUNCT
ejpam-5504	146	18	b|dom	b|dom	NOUN
ejpam-5504	146	19	a	a	PRON
ejpam-5504	146	20	is	be	AUX
ejpam-5504	146	21	a	a	DET
ejpam-5504	146	22	selection	selection	NOUN
ejpam-5504	146	23	of	of	ADP
ejpam-5504	146	24	a|dom	a|dom	ADJ
ejpam-5504	146	25	a.	a.	NOUN
ejpam-5504	146	26	proof	proof	NOUN
ejpam-5504	146	27	.	.	PUNCT
ejpam-5504	147	1	(	(	PUNCT
ejpam-5504	147	2	i	i	NOUN
ejpam-5504	147	3	):	):	PUNCT
ejpam-5504	147	4	from	from	ADP
ejpam-5504	147	5	(	(	PUNCT
ejpam-5504	147	6	11	11	NUM
ejpam-5504	147	7	)	)	PUNCT
ejpam-5504	147	8	dom	dom	NOUN
ejpam-5504	147	9	a	a	PRON
ejpam-5504	147	10	=	=	PUNCT
ejpam-5504	147	11	ran	run	VERB
ejpam-5504	147	12	(	(	PUNCT
ejpam-5504	147	13	id−r	id−r	NOUN
ejpam-5504	147	14	)	)	PUNCT
ejpam-5504	147	15	=	=	SYM
ejpam-5504	147	16	d⊥	d⊥	NOUN
ejpam-5504	147	17	,	,	PUNCT
ejpam-5504	147	18	which	which	PRON
ejpam-5504	147	19	is	be	AUX
ejpam-5504	147	20	closed	close	VERB
ejpam-5504	147	21	by	by	ADP
ejpam-5504	147	22	the	the	DET
ejpam-5504	147	23	assumption	assumption	NOUN
ejpam-5504	147	24	.	.	PUNCT
ejpam-5504	148	1	(	(	PUNCT
ejpam-5504	148	2	ii	ii	NUM
ejpam-5504	148	3	):	):	PUNCT
ejpam-5504	148	4	it	it	PRON
ejpam-5504	148	5	is	be	AUX
ejpam-5504	148	6	clear	clear	ADJ
ejpam-5504	148	7	that	that	SCONJ
ejpam-5504	148	8	a	a	PRON
ejpam-5504	148	9	is	be	AUX
ejpam-5504	148	10	a	a	DET
ejpam-5504	148	11	linear	linear	ADJ
ejpam-5504	148	12	relation	relation	NOUN
ejpam-5504	148	13	,	,	PUNCT
ejpam-5504	148	14	i.e.	i.e.	X
ejpam-5504	148	15	,	,	PUNCT
ejpam-5504	148	16	gra	gra	PROPN
ejpam-5504	148	17	a	a	PRON
ejpam-5504	148	18	is	be	AUX
ejpam-5504	148	19	a	a	DET
ejpam-5504	148	20	linear	linear	ADJ
ejpam-5504	148	21	subspace	subspace	NOUN
ejpam-5504	148	22	,	,	PUNCT
ejpam-5504	149	1	that	that	SCONJ
ejpam-5504	149	2	a0	a0	NOUN
ejpam-5504	149	3	=	=	SYM
ejpam-5504	149	4	d	d	PROPN
ejpam-5504	149	5	,	,	PUNCT
ejpam-5504	149	6	and	and	CCONJ
ejpam-5504	149	7	by	by	ADP
ejpam-5504	149	8	(	(	PUNCT
ejpam-5504	149	9	i	i	NOUN
ejpam-5504	149	10	)	)	PUNCT
ejpam-5504	149	11	the	the	DET
ejpam-5504	149	12	dom	dom	NOUN
ejpam-5504	149	13	a	a	DET
ejpam-5504	149	14	=	=	NOUN
ejpam-5504	149	15	d⊥	d⊥	NOUN
ejpam-5504	149	16	is	be	AUX
ejpam-5504	149	17	closed	closed	ADJ
ejpam-5504	149	18	.	.	PUNCT
ejpam-5504	150	1	(	(	PUNCT
ejpam-5504	150	2	iii	iii	X
ejpam-5504	150	3	):	):	PUNCT
ejpam-5504	150	4	it	it	PRON
ejpam-5504	150	5	follows	follow	VERB
ejpam-5504	150	6	directly	directly	ADV
ejpam-5504	150	7	from	from	ADP
ejpam-5504	150	8	proposition	proposition	NOUN
ejpam-5504	150	9	1(ix	1(ix	NUM
ejpam-5504	150	10	)	)	PUNCT
ejpam-5504	150	11	.	.	PUNCT
ejpam-5504	151	1	(	(	PUNCT
ejpam-5504	151	2	iv	iv	X
ejpam-5504	151	3	):	):	PUNCT
ejpam-5504	151	4	by	by	ADP
ejpam-5504	151	5	[	[	X
ejpam-5504	151	6	9	9	NUM
ejpam-5504	151	7	,	,	PUNCT
ejpam-5504	151	8	proposition	proposition	NOUN
ejpam-5504	151	9	6.2	6.2	NUM
ejpam-5504	151	10	]	]	PUNCT
ejpam-5504	151	11	,	,	PUNCT
ejpam-5504	151	12	we	we	PRON
ejpam-5504	151	13	have	have	VERB
ejpam-5504	151	14	(	(	PUNCT
ejpam-5504	151	15	∀y	∀y	PROPN
ejpam-5504	151	16	∈	∈	PROPN
ejpam-5504	151	17	dom	dom	NOUN
ejpam-5504	151	18	a	a	PRON
ejpam-5504	151	19	)	)	PUNCT
ejpam-5504	151	20	qay	qay	PROPN
ejpam-5504	151	21	=	=	SYM
ejpam-5504	151	22	p(a0)⊥(ay	p(a0)⊥(ay	PROPN
ejpam-5504	151	23	)	)	PUNCT
ejpam-5504	151	24	∈	∈	PROPN
ejpam-5504	151	25	ay	ay	NOUN
ejpam-5504	151	26	.	.	PUNCT
ejpam-5504	152	1	hence	hence	ADV
ejpam-5504	152	2	,	,	PUNCT
ejpam-5504	152	3	(	(	PUNCT
ejpam-5504	152	4	∀y	∀y	NUM
ejpam-5504	152	5	∈	∈	PROPN
ejpam-5504	152	6	d⊥	d⊥	NOUN
ejpam-5504	152	7	)	)	PUNCT
ejpam-5504	152	8	qay	qay	NOUN
ejpam-5504	152	9	=	=	PUNCT
ejpam-5504	152	10	pd⊥(ay	pd⊥(ay	NOUN
ejpam-5504	152	11	)	)	PUNCT
ejpam-5504	153	1	=	=	SYM
ejpam-5504	153	2	pd⊥	pd⊥	PROPN
ejpam-5504	153	3	(	(	PUNCT
ejpam-5504	153	4	(	(	PUNCT
ejpam-5504	153	5	id−r)−1y	id−r)−1y	INTJ
ejpam-5504	153	6	−	−	NOUN
ejpam-5504	153	7	1	1	NUM
ejpam-5504	153	8	2	2	NUM
ejpam-5504	153	9	y	y	NOUN
ejpam-5504	153	10	)	)	PUNCT
ejpam-5504	154	1	=	=	PUNCT
ejpam-5504	155	1	pd⊥(id−r)−1y	pd⊥(id−r)−1y	NOUN
ejpam-5504	155	2	−	−	NOUN
ejpam-5504	155	3	1	1	NUM
ejpam-5504	155	4	2	2	NUM
ejpam-5504	155	5	pd⊥	pd⊥	PROPN
ejpam-5504	155	6	y.	y.	NOUN
ejpam-5504	155	7	(	(	PUNCT
ejpam-5504	155	8	v	v	NOUN
ejpam-5504	155	9	):	):	PUNCT
ejpam-5504	155	10	see	see	VERB
ejpam-5504	155	11	[	[	X
ejpam-5504	155	12	9	9	NUM
ejpam-5504	155	13	,	,	PUNCT
ejpam-5504	155	14	example	example	NOUN
ejpam-5504	155	15	6.4(i	6.4(i	NUM
ejpam-5504	155	16	)	)	PUNCT
ejpam-5504	155	17	]	]	PUNCT
ejpam-5504	155	18	.	.	PUNCT
ejpam-5504	156	1	(	(	PUNCT
ejpam-5504	156	2	vi	vi	ADJ
ejpam-5504	156	3	):	):	PUNCT
ejpam-5504	156	4	combining	combine	VERB
ejpam-5504	156	5	(	(	PUNCT
ejpam-5504	156	6	i	i	NOUN
ejpam-5504	156	7	)	)	PUNCT
ejpam-5504	156	8	and	and	CCONJ
ejpam-5504	156	9	[	[	X
ejpam-5504	156	10	9	9	NUM
ejpam-5504	156	11	,	,	PUNCT
ejpam-5504	156	12	example	example	NOUN
ejpam-5504	156	13	6.4(iii	6.4(iii	NUM
ejpam-5504	156	14	)	)	PUNCT
ejpam-5504	156	15	]	]	PUNCT
ejpam-5504	156	16	gives	give	VERB
ejpam-5504	156	17	a	a	DET
ejpam-5504	156	18	=	=	NOUN
ejpam-5504	156	19	ndom	ndom	NOUN
ejpam-5504	156	20	a	a	DET
ejpam-5504	156	21	+	+	X
ejpam-5504	156	22	b	b	NOUN
ejpam-5504	156	23	=	=	SYM
ejpam-5504	156	24	nd⊥	nd⊥	PROPN
ejpam-5504	156	25	+	+	PROPN
ejpam-5504	156	26	b.	b.	PROPN
ejpam-5504	156	27	(	(	PUNCT
ejpam-5504	156	28	vii	vii	PROPN
ejpam-5504	156	29	):	):	PUNCT
ejpam-5504	156	30	using	use	VERB
ejpam-5504	156	31	(	(	PUNCT
ejpam-5504	156	32	13	13	NUM
ejpam-5504	156	33	)	)	PUNCT
ejpam-5504	156	34	,	,	PUNCT
ejpam-5504	156	35	(	(	PUNCT
ejpam-5504	156	36	iv	iv	X
ejpam-5504	156	37	)	)	PUNCT
ejpam-5504	156	38	and	and	CCONJ
ejpam-5504	156	39	(	(	PUNCT
ejpam-5504	156	40	i	i	NOUN
ejpam-5504	156	41	)	)	PUNCT
ejpam-5504	156	42	gives	give	VERB
ejpam-5504	156	43	b	b	NOUN
ejpam-5504	156	44	=	=	SYM
ejpam-5504	156	45	pdom	pdom	NOUN
ejpam-5504	156	46	a	a	DET
ejpam-5504	156	47	qa	qa	PROPN
ejpam-5504	156	48	pdom	pdom	NOUN
ejpam-5504	156	49	a	a	DET
ejpam-5504	156	50	=	=	X
ejpam-5504	156	51	pd⊥	pd⊥	PROPN
ejpam-5504	156	52	(	(	PUNCT
ejpam-5504	156	53	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	156	54	−	−	NUM
ejpam-5504	156	55	1	1	NUM
ejpam-5504	156	56	2	2	NUM
ejpam-5504	156	57	pd⊥	pd⊥	PROPN
ejpam-5504	156	58	)	)	PUNCT
ejpam-5504	157	1	pd⊥	pd⊥	PROPN
ejpam-5504	157	2	=	=	PUNCT
ejpam-5504	157	3	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	157	4	pd⊥	pd⊥	NOUN
ejpam-5504	157	5	−	−	NUM
ejpam-5504	157	6	1	1	NUM
ejpam-5504	157	7	2	2	NUM
ejpam-5504	157	8	pd⊥	pd⊥	PROPN
ejpam-5504	157	9	s.t	s.t	PROPN
ejpam-5504	157	10	.	.	PROPN
ejpam-5504	157	11	alwadani	alwadani	PROPN
ejpam-5504	157	12	/	/	SYM
ejpam-5504	157	13	eur	eur	PROPN
ejpam-5504	157	14	.	.	PUNCT
ejpam-5504	158	1	j.	j.	PROPN
ejpam-5504	158	2	pure	pure	PROPN
ejpam-5504	158	3	appl	appl	PROPN
ejpam-5504	158	4	.	.	PROPN
ejpam-5504	158	5	math	math	PROPN
ejpam-5504	158	6	,	,	PUNCT
ejpam-5504	158	7	17	17	NUM
ejpam-5504	158	8	(	(	PUNCT
ejpam-5504	158	9	4	4	NUM
ejpam-5504	158	10	)	)	PUNCT
ejpam-5504	158	11	(	(	PUNCT
ejpam-5504	158	12	2024	2024	NUM
ejpam-5504	158	13	)	)	PUNCT
ejpam-5504	158	14	,	,	PUNCT
ejpam-5504	158	15	3660	3660	NUM
ejpam-5504	158	16	-	-	SYM
ejpam-5504	158	17	3676	3676	NUM
ejpam-5504	158	18	3666	3666	NUM
ejpam-5504	158	19	=	=	SYM
ejpam-5504	158	20	t	t	PROPN
ejpam-5504	158	21	(	(	PUNCT
ejpam-5504	158	22	from	from	ADP
ejpam-5504	158	23	(	(	PUNCT
ejpam-5504	158	24	8)	8)	NUM
ejpam-5504	158	25	)	)	PUNCT
ejpam-5504	158	26	.	.	PUNCT
ejpam-5504	159	1	(	(	PUNCT
ejpam-5504	159	2	viii	viii	ADJ
ejpam-5504	159	3	):	):	PUNCT
ejpam-5504	159	4	using	use	VERB
ejpam-5504	159	5	(	(	PUNCT
ejpam-5504	159	6	i	i	NOUN
ejpam-5504	159	7	)	)	PUNCT
ejpam-5504	159	8	gives	give	VERB
ejpam-5504	159	9	a|dom	a|dom	NOUN
ejpam-5504	159	10	a	a	DET
ejpam-5504	159	11	=	=	PUNCT
ejpam-5504	159	12	(	(	PUNCT
ejpam-5504	159	13	nd⊥	nd⊥	PROPN
ejpam-5504	159	14	+	+	CCONJ
ejpam-5504	159	15	b)|d⊥	b)|d⊥	PROPN
ejpam-5504	159	16	(	(	PUNCT
ejpam-5504	159	17	from	from	ADP
ejpam-5504	159	18	(	(	PUNCT
ejpam-5504	159	19	vi	vi	NOUN
ejpam-5504	159	20	)	)	PUNCT
ejpam-5504	159	21	)	)	PUNCT
ejpam-5504	160	1	=	=	SYM
ejpam-5504	160	2	(	(	PUNCT
ejpam-5504	160	3	nd⊥	nd⊥	PROPN
ejpam-5504	160	4	+	+	CCONJ
ejpam-5504	160	5	t)|d⊥	t)|d⊥	PROPN
ejpam-5504	160	6	(	(	PUNCT
ejpam-5504	160	7	from	from	ADP
ejpam-5504	160	8	(	(	PUNCT
ejpam-5504	160	9	vii	vii	PROPN
ejpam-5504	160	10	)	)	PUNCT
ejpam-5504	160	11	)	)	PUNCT
ejpam-5504	161	1	=	=	PRON
ejpam-5504	162	1	(	(	PUNCT
ejpam-5504	162	2	nd⊥	nd⊥	NOUN
ejpam-5504	162	3	+	+	CCONJ
ejpam-5504	162	4	pd⊥(id−r)−1	pd⊥(id−r)−1	VERB
ejpam-5504	162	5	pd⊥	pd⊥	PROPN
ejpam-5504	162	6	−	−	NOUN
ejpam-5504	162	7	1	1	NUM
ejpam-5504	162	8	2	2	NUM
ejpam-5504	162	9	pd⊥	pd⊥	PROPN
ejpam-5504	162	10	)	)	PUNCT
ejpam-5504	162	11	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5504	162	12	d⊥	d⊥	NOUN
ejpam-5504	162	13	(	(	PUNCT
ejpam-5504	162	14	from	from	ADP
ejpam-5504	162	15	(	(	PUNCT
ejpam-5504	162	16	8)	8)	NUM
ejpam-5504	162	17	)	)	PUNCT
ejpam-5504	162	18	≡	≡	PROPN
ejpam-5504	162	19	d	d	X
ejpam-5504	162	20	+	+	PUNCT
ejpam-5504	162	21	d⊥	d⊥	NOUN
ejpam-5504	162	22	(	(	PUNCT
ejpam-5504	162	23	because	because	SCONJ
ejpam-5504	162	24	nd⊥	nd⊥	PROPN
ejpam-5504	162	25	|d⊥	|d⊥	PROPN
ejpam-5504	162	26	≡	≡	PROPN
ejpam-5504	162	27	d	d	PROPN
ejpam-5504	162	28	)	)	PUNCT
ejpam-5504	162	29	,	,	PUNCT
ejpam-5504	162	30	and	and	CCONJ
ejpam-5504	162	31	b|dom	b|dom	NOUN
ejpam-5504	162	32	a	a	DET
ejpam-5504	162	33	=	=	X
ejpam-5504	162	34	t|d⊥	t|d⊥	ADJ
ejpam-5504	162	35	(	(	PUNCT
ejpam-5504	162	36	from	from	ADP
ejpam-5504	162	37	(	(	PUNCT
ejpam-5504	162	38	i	i	NOUN
ejpam-5504	162	39	)	)	PUNCT
ejpam-5504	162	40	and	and	CCONJ
ejpam-5504	162	41	(	(	PUNCT
ejpam-5504	162	42	vii	vii	PROPN
ejpam-5504	162	43	)	)	PUNCT
ejpam-5504	162	44	)	)	PUNCT
ejpam-5504	163	1	=	=	PUNCT
ejpam-5504	163	2	(	(	PUNCT
ejpam-5504	163	3	pd⊥(id−r)−1	pd⊥(id−r)−1	VERB
ejpam-5504	163	4	pd⊥	pd⊥	NOUN
ejpam-5504	163	5	−	−	NUM
ejpam-5504	163	6	1	1	NUM
ejpam-5504	163	7	2	2	NUM
ejpam-5504	163	8	pd⊥	pd⊥	PROPN
ejpam-5504	163	9	)	)	PUNCT
ejpam-5504	163	10	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5504	163	11	d⊥	d⊥	NOUN
ejpam-5504	163	12	(	(	PUNCT
ejpam-5504	163	13	from	from	ADP
ejpam-5504	163	14	(	(	PUNCT
ejpam-5504	163	15	8)	8)	NUM
ejpam-5504	163	16	)	)	PUNCT
ejpam-5504	163	17	=	=	X
ejpam-5504	163	18	d⊥.	d⊥.	NOUN
ejpam-5504	163	19	hence	hence	ADV
ejpam-5504	163	20	,	,	PUNCT
ejpam-5504	163	21	b|dom	b|dom	NOUN
ejpam-5504	163	22	a	a	PRON
ejpam-5504	163	23	is	be	AUX
ejpam-5504	163	24	a	a	DET
ejpam-5504	163	25	selection	selection	NOUN
ejpam-5504	163	26	of	of	ADP
ejpam-5504	163	27	a|dom	a|dom	NOUN
ejpam-5504	163	28	a.	a.	NOUN
ejpam-5504	163	29	■	■	PUNCT
ejpam-5504	163	30	in	in	ADP
ejpam-5504	163	31	the	the	DET
ejpam-5504	163	32	next	next	ADJ
ejpam-5504	163	33	theorem	theorem	NOUN
ejpam-5504	163	34	we	we	PRON
ejpam-5504	163	35	derive	derive	VERB
ejpam-5504	163	36	formulas	formula	NOUN
ejpam-5504	163	37	for	for	ADP
ejpam-5504	163	38	the	the	DET
ejpam-5504	163	39	inverse	inverse	NOUN
ejpam-5504	163	40	and	and	CCONJ
ejpam-5504	163	41	moore	moore	PROPN
ejpam-5504	163	42	-	-	PUNCT
ejpam-5504	163	43	penrose	penrose	PROPN
ejpam-5504	163	44	inverse	inverse	NOUN
ejpam-5504	163	45	of	of	ADP
ejpam-5504	163	46	the	the	DET
ejpam-5504	163	47	operator	operator	NOUN
ejpam-5504	163	48	(	(	PUNCT
ejpam-5504	163	49	id−r	id−r	PROPN
ejpam-5504	163	50	)	)	PUNCT
ejpam-5504	163	51	.	.	PUNCT
ejpam-5504	164	1	theorem	theorem	ADJ
ejpam-5504	164	2	2	2	NUM
ejpam-5504	164	3	.	.	NOUN
ejpam-5504	164	4	recall	recall	NOUN
ejpam-5504	164	5	from	from	ADP
ejpam-5504	164	6	(	(	PUNCT
ejpam-5504	164	7	8)	8)	NUM
ejpam-5504	164	8	and	and	CCONJ
ejpam-5504	164	9	(	(	PUNCT
ejpam-5504	164	10	11	11	NUM
ejpam-5504	164	11	)	)	PUNCT
ejpam-5504	164	12	that	that	PRON
ejpam-5504	164	13	t	t	X
ejpam-5504	164	14	:	:	PUNCT
ejpam-5504	165	1	=	=	SYM
ejpam-5504	165	2	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	165	3	pd⊥	pd⊥	NOUN
ejpam-5504	165	4	−	−	NUM
ejpam-5504	165	5	1	1	NUM
ejpam-5504	165	6	2	2	NUM
ejpam-5504	165	7	pd⊥	pd⊥	PROPN
ejpam-5504	165	8	,	,	PUNCT
ejpam-5504	165	9	and	and	CCONJ
ejpam-5504	165	10	a	a	DET
ejpam-5504	165	11	:	:	PUNCT
ejpam-5504	165	12	=	=	SYM
ejpam-5504	165	13	(	(	PUNCT
ejpam-5504	165	14	id−r)−1	id−r)−1	NUM
ejpam-5504	165	15	−	−	NUM
ejpam-5504	165	16	1	1	NUM
ejpam-5504	165	17	2	2	NUM
ejpam-5504	165	18	i	i	PROPN
ejpam-5504	165	19	d	d	PROPN
ejpam-5504	165	20	,	,	PUNCT
ejpam-5504	165	21	respectively.then	respectively.then	SCONJ
ejpam-5504	165	22	the	the	DET
ejpam-5504	165	23	following	follow	VERB
ejpam-5504	165	24	holds	hold	VERB
ejpam-5504	165	25	;	;	PUNCT
ejpam-5504	165	26	(	(	PUNCT
ejpam-5504	165	27	i	i	NOUN
ejpam-5504	165	28	)	)	PUNCT
ejpam-5504	165	29	the	the	DET
ejpam-5504	165	30	set	set	NOUN
ejpam-5504	165	31	-	-	PUNCT
ejpam-5504	165	32	valued	value	VERB
ejpam-5504	165	33	inverse	inverse	NOUN
ejpam-5504	165	34	of	of	ADP
ejpam-5504	165	35	id−r	id−r	NOUN
ejpam-5504	165	36	is	be	AUX
ejpam-5504	165	37	(	(	PUNCT
ejpam-5504	165	38	id−r)−1	id−r)−1	NOUN
ejpam-5504	165	39	=	=	SYM
ejpam-5504	165	40	1	1	NUM
ejpam-5504	165	41	2	2	NUM
ejpam-5504	165	42	id+t	id+t	NOUN
ejpam-5504	165	43	+	+	CCONJ
ejpam-5504	165	44	nd⊥	nd⊥	PROPN
ejpam-5504	165	45	.	.	PUNCT
ejpam-5504	166	1	(	(	PUNCT
ejpam-5504	166	2	14	14	NUM
ejpam-5504	166	3	)	)	PUNCT
ejpam-5504	166	4	(	(	PUNCT
ejpam-5504	166	5	ii	ii	NOUN
ejpam-5504	166	6	)	)	PUNCT
ejpam-5504	166	7	the	the	DET
ejpam-5504	166	8	moore	moore	PROPN
ejpam-5504	166	9	-	-	PUNCT
ejpam-5504	166	10	penrose	penrose	PROPN
ejpam-5504	166	11	inverse	inverse	NOUN
ejpam-5504	166	12	of	of	ADP
ejpam-5504	166	13	id−r	id−r	NOUN
ejpam-5504	166	14	is	be	AUX
ejpam-5504	166	15	(	(	PUNCT
ejpam-5504	166	16	id−r)†	id−r)†	PROPN
ejpam-5504	167	1	=	=	SYM
ejpam-5504	167	2	t	t	PROPN
ejpam-5504	167	3	+	+	CCONJ
ejpam-5504	167	4	1	1	NUM
ejpam-5504	167	5	2	2	NUM
ejpam-5504	167	6	pd⊥	pd⊥	PROPN
ejpam-5504	167	7	.	.	PUNCT
ejpam-5504	168	1	(	(	PUNCT
ejpam-5504	168	2	15	15	X
ejpam-5504	168	3	)	)	PUNCT
ejpam-5504	168	4	proof	proof	NOUN
ejpam-5504	168	5	.	.	PUNCT
ejpam-5504	169	1	(	(	PUNCT
ejpam-5504	169	2	i	i	NOUN
ejpam-5504	169	3	):	):	PUNCT
ejpam-5504	169	4	combining	combine	VERB
ejpam-5504	169	5	theorem	theorem	ADJ
ejpam-5504	169	6	1(vi	1(vi	NUM
ejpam-5504	169	7	)	)	PUNCT
ejpam-5504	169	8	&	&	CCONJ
ejpam-5504	169	9	(	(	PUNCT
ejpam-5504	169	10	vii	vii	PROPN
ejpam-5504	169	11	)	)	PUNCT
ejpam-5504	169	12	and	and	CCONJ
ejpam-5504	169	13	(	(	PUNCT
ejpam-5504	169	14	11	11	NUM
ejpam-5504	169	15	)	)	PUNCT
ejpam-5504	169	16	gives	give	VERB
ejpam-5504	169	17	(	(	PUNCT
ejpam-5504	169	18	id−r)−1	id−r)−1	NUM
ejpam-5504	169	19	−	−	PROPN
ejpam-5504	169	20	1	1	NUM
ejpam-5504	169	21	2	2	NUM
ejpam-5504	169	22	i	i	NOUN
ejpam-5504	169	23	d	d	NOUN
ejpam-5504	169	24	=	=	PUNCT
ejpam-5504	169	25	a	a	DET
ejpam-5504	169	26	=	=	PUNCT
ejpam-5504	169	27	nd⊥	nd⊥	PROPN
ejpam-5504	169	28	+	+	PROPN
ejpam-5504	169	29	t	t	PROPN
ejpam-5504	169	30	,	,	PUNCT
ejpam-5504	169	31	s.t	s.t	PROPN
ejpam-5504	169	32	.	.	PROPN
ejpam-5504	169	33	alwadani	alwadani	PROPN
ejpam-5504	169	34	/	/	SYM
ejpam-5504	169	35	eur	eur	PROPN
ejpam-5504	169	36	.	.	PUNCT
ejpam-5504	170	1	j.	j.	PROPN
ejpam-5504	170	2	pure	pure	PROPN
ejpam-5504	170	3	appl	appl	PROPN
ejpam-5504	170	4	.	.	PROPN
ejpam-5504	170	5	math	math	PROPN
ejpam-5504	170	6	,	,	PUNCT
ejpam-5504	170	7	17	17	NUM
ejpam-5504	170	8	(	(	PUNCT
ejpam-5504	170	9	4	4	NUM
ejpam-5504	170	10	)	)	PUNCT
ejpam-5504	170	11	(	(	PUNCT
ejpam-5504	170	12	2024	2024	NUM
ejpam-5504	170	13	)	)	PUNCT
ejpam-5504	170	14	,	,	PUNCT
ejpam-5504	170	15	3660	3660	NUM
ejpam-5504	170	16	-	-	SYM
ejpam-5504	170	17	3676	3676	NUM
ejpam-5504	170	18	3667	3667	NUM
ejpam-5504	170	19	hence	hence	ADV
ejpam-5504	170	20	,	,	PUNCT
ejpam-5504	170	21	(	(	PUNCT
ejpam-5504	170	22	id−r)−1	id−r)−1	X
ejpam-5504	170	23	=	=	PUNCT
ejpam-5504	170	24	nd⊥	nd⊥	PROPN
ejpam-5504	170	25	+	+	PROPN
ejpam-5504	171	1	t	t	NOUN
ejpam-5504	172	1	+	+	CCONJ
ejpam-5504	172	2	1	1	NUM
ejpam-5504	172	3	2	2	NUM
ejpam-5504	172	4	i	i	NOUN
ejpam-5504	172	5	d	d	PROPN
ejpam-5504	172	6	.	.	PUNCT
ejpam-5504	173	1	(	(	PUNCT
ejpam-5504	173	2	ii	ii	NUM
ejpam-5504	173	3	):	):	PUNCT
ejpam-5504	173	4	by	by	ADP
ejpam-5504	173	5	using	use	VERB
ejpam-5504	173	6	[	[	X
ejpam-5504	173	7	6	6	NUM
ejpam-5504	173	8	,	,	PUNCT
ejpam-5504	173	9	proposition	proposition	NOUN
ejpam-5504	173	10	2.1	2.1	NUM
ejpam-5504	173	11	]	]	PUNCT
ejpam-5504	173	12	and	and	CCONJ
ejpam-5504	173	13	we	we	PRON
ejpam-5504	173	14	obtain	obtain	VERB
ejpam-5504	173	15	(	(	PUNCT
ejpam-5504	173	16	id−r)†	id−r)†	NOUN
ejpam-5504	173	17	=	=	PROPN
ejpam-5504	173	18	p(id−r)∗	p(id−r)∗	PROPN
ejpam-5504	173	19	◦	◦	NOUN
ejpam-5504	173	20	(	(	PUNCT
ejpam-5504	173	21	id−r)−1	id−r)−1	PRON
ejpam-5504	173	22	◦	◦	NOUN
ejpam-5504	173	23	pran	pran	NOUN
ejpam-5504	173	24	(	(	PUNCT
ejpam-5504	173	25	id−r	id−r	PROPN
ejpam-5504	173	26	)	)	PUNCT
ejpam-5504	173	27	=	=	SYM
ejpam-5504	174	1	pd⊥	pd⊥	PROPN
ejpam-5504	174	2	◦	◦	NOUN
ejpam-5504	174	3	(	(	PUNCT
ejpam-5504	174	4	id−r)−1	id−r)−1	ADP
ejpam-5504	174	5	◦	◦	NOUN
ejpam-5504	174	6	pd⊥	pd⊥	PROPN
ejpam-5504	174	7	(	(	PUNCT
ejpam-5504	174	8	from	from	ADP
ejpam-5504	174	9	lemma	lemma	PROPN
ejpam-5504	174	10	2(i	2(i	NUM
ejpam-5504	174	11	)	)	PUNCT
ejpam-5504	174	12	)	)	PUNCT
ejpam-5504	175	1	=	=	PUNCT
ejpam-5504	175	2	pd⊥	pd⊥	PROPN
ejpam-5504	175	3	◦	◦	NOUN
ejpam-5504	175	4	(	(	PUNCT
ejpam-5504	175	5	1	1	NUM
ejpam-5504	175	6	2	2	NUM
ejpam-5504	175	7	id+t	id+t	NOUN
ejpam-5504	175	8	+	+	CCONJ
ejpam-5504	175	9	nd⊥	nd⊥	PROPN
ejpam-5504	175	10	)	)	PUNCT
ejpam-5504	175	11	◦	◦	NOUN
ejpam-5504	175	12	pd⊥	pd⊥	PROPN
ejpam-5504	175	13	(	(	PUNCT
ejpam-5504	175	14	from	from	ADP
ejpam-5504	175	15	(	(	PUNCT
ejpam-5504	175	16	i	i	NOUN
ejpam-5504	175	17	)	)	PUNCT
ejpam-5504	175	18	)	)	PUNCT
ejpam-5504	176	1	=	=	PUNCT
ejpam-5504	176	2	pd⊥	pd⊥	PROPN
ejpam-5504	176	3	◦	◦	NOUN
ejpam-5504	176	4	(	(	PUNCT
ejpam-5504	176	5	1	1	NUM
ejpam-5504	176	6	2	2	NUM
ejpam-5504	176	7	pd⊥	pd⊥	PROPN
ejpam-5504	176	8	+	+	NOUN
ejpam-5504	176	9	t	t	PROPN
ejpam-5504	176	10	pd⊥	pd⊥	PROPN
ejpam-5504	176	11	+	+	PROPN
ejpam-5504	176	12	d	d	NOUN
ejpam-5504	176	13	)	)	PUNCT
ejpam-5504	176	14	(	(	PUNCT
ejpam-5504	176	15	because	because	SCONJ
ejpam-5504	176	16	nd⊥	nd⊥	PROPN
ejpam-5504	176	17	|d⊥	|d⊥	PROPN
ejpam-5504	176	18	≡	≡	PROPN
ejpam-5504	176	19	d	d	PROPN
ejpam-5504	176	20	)	)	PUNCT
ejpam-5504	176	21	=	=	SYM
ejpam-5504	176	22	1	1	NUM
ejpam-5504	176	23	2	2	NUM
ejpam-5504	176	24	pd⊥	pd⊥	PROPN
ejpam-5504	176	25	+	+	PROPN
ejpam-5504	176	26	pd⊥	pd⊥	PROPN
ejpam-5504	176	27	t	t	X
ejpam-5504	176	28	pd⊥	pd⊥	PROPN
ejpam-5504	177	1	+0	+0	ADP
ejpam-5504	177	2	=	=	SYM
ejpam-5504	177	3	1	1	NUM
ejpam-5504	177	4	2	2	NUM
ejpam-5504	177	5	pd⊥	pd⊥	PROPN
ejpam-5504	177	6	+	+	PROPN
ejpam-5504	177	7	t	t	PROPN
ejpam-5504	177	8	(	(	PUNCT
ejpam-5504	177	9	from	from	ADP
ejpam-5504	177	10	lemma	lemma	PROPN
ejpam-5504	177	11	2(vi	2(vi	NUM
ejpam-5504	177	12	)	)	PUNCT
ejpam-5504	177	13	)	)	PUNCT
ejpam-5504	177	14	,	,	PUNCT
ejpam-5504	177	15	which	which	PRON
ejpam-5504	177	16	verified	verify	VERB
ejpam-5504	177	17	(	(	PUNCT
ejpam-5504	177	18	15	15	NUM
ejpam-5504	177	19	)	)	PUNCT
ejpam-5504	177	20	.	.	PUNCT
ejpam-5504	178	1	■	■	PUNCT
ejpam-5504	178	2	proposition	proposition	NOUN
ejpam-5504	178	3	3	3	NUM
ejpam-5504	178	4	(	(	PUNCT
ejpam-5504	178	5	uniqueness	uniqueness	NOUN
ejpam-5504	178	6	of	of	ADP
ejpam-5504	178	7	t	t	PROPN
ejpam-5504	178	8	)	)	PUNCT
ejpam-5504	178	9	.	.	PUNCT
ejpam-5504	179	1	let	let	VERB
ejpam-5504	179	2	t	t	PRON
ejpam-5504	179	3	◦	◦	VERB
ejpam-5504	179	4	:	:	PUNCT
ejpam-5504	179	5	x	x	X
ejpam-5504	179	6	→	→	PUNCT
ejpam-5504	179	7	x	x	AUX
ejpam-5504	179	8	be	be	AUX
ejpam-5504	179	9	such	such	ADJ
ejpam-5504	179	10	that	that	SCONJ
ejpam-5504	179	11	(	(	PUNCT
ejpam-5504	179	12	id−r)−1	id−r)−1	NOUN
ejpam-5504	179	13	=	=	SYM
ejpam-5504	179	14	1	1	NUM
ejpam-5504	179	15	2	2	NUM
ejpam-5504	179	16	id+t	id+t	NOUN
ejpam-5504	179	17	◦	◦	NOUN
ejpam-5504	179	18	+	+	CCONJ
ejpam-5504	179	19	nd⊥	nd⊥	PROPN
ejpam-5504	179	20	,	,	PUNCT
ejpam-5504	179	21	(	(	PUNCT
ejpam-5504	179	22	16	16	NUM
ejpam-5504	179	23	)	)	PUNCT
ejpam-5504	179	24	and	and	CCONJ
ejpam-5504	179	25	pd⊥	pd⊥	PROPN
ejpam-5504	179	26	t	t	PROPN
ejpam-5504	179	27	◦	◦	NOUN
ejpam-5504	179	28	pd⊥	pd⊥	PROPN
ejpam-5504	179	29	=	=	SYM
ejpam-5504	179	30	t	t	PROPN
ejpam-5504	179	31	◦	◦	NOUN
ejpam-5504	179	32	.	.	PUNCT
ejpam-5504	180	1	(	(	PUNCT
ejpam-5504	180	2	17	17	NUM
ejpam-5504	180	3	)	)	PUNCT
ejpam-5504	180	4	then	then	ADV
ejpam-5504	180	5	t	t	X
ejpam-5504	180	6	◦	◦	NOUN
ejpam-5504	180	7	=	=	SYM
ejpam-5504	180	8	t.	t.	NOUN
ejpam-5504	180	9	proof	proof	NOUN
ejpam-5504	180	10	.	.	PUNCT
ejpam-5504	181	1	by	by	ADP
ejpam-5504	181	2	using	use	VERB
ejpam-5504	181	3	(	(	PUNCT
ejpam-5504	181	4	8)	8)	NUM
ejpam-5504	181	5	,	,	PUNCT
ejpam-5504	181	6	we	we	PRON
ejpam-5504	181	7	have	have	VERB
ejpam-5504	181	8	t	t	NOUN
ejpam-5504	181	9	=	=	SYM
ejpam-5504	181	10	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	181	11	pd⊥	pd⊥	PROPN
ejpam-5504	181	12	−	−	NUM
ejpam-5504	182	1	1	1	NUM
ejpam-5504	182	2	2	2	NUM
ejpam-5504	182	3	pd⊥	pd⊥	PROPN
ejpam-5504	182	4	=	=	SYM
ejpam-5504	182	5	pd⊥	pd⊥	PROPN
ejpam-5504	182	6	(	(	PUNCT
ejpam-5504	182	7	1	1	NUM
ejpam-5504	182	8	2	2	NUM
ejpam-5504	182	9	id+t	id+t	NOUN
ejpam-5504	182	10	◦	◦	NOUN
ejpam-5504	182	11	+	+	CCONJ
ejpam-5504	182	12	nd⊥	nd⊥	PROPN
ejpam-5504	182	13	)	)	PUNCT
ejpam-5504	182	14	pd⊥	pd⊥	PROPN
ejpam-5504	182	15	−	−	NUM
ejpam-5504	182	16	1	1	NUM
ejpam-5504	182	17	2	2	NUM
ejpam-5504	182	18	pd⊥	pd⊥	PROPN
ejpam-5504	182	19	(	(	PUNCT
ejpam-5504	182	20	from	from	ADP
ejpam-5504	182	21	(	(	PUNCT
ejpam-5504	182	22	16	16	NUM
ejpam-5504	182	23	)	)	PUNCT
ejpam-5504	182	24	)	)	PUNCT
ejpam-5504	183	1	=	=	PUNCT
ejpam-5504	183	2	pd⊥	pd⊥	PROPN
ejpam-5504	183	3	t	t	PROPN
ejpam-5504	183	4	◦	◦	NOUN
ejpam-5504	183	5	pd⊥	pd⊥	PROPN
ejpam-5504	183	6	=	=	SYM
ejpam-5504	183	7	t	t	PROPN
ejpam-5504	183	8	◦	◦	NOUN
ejpam-5504	183	9	(	(	PUNCT
ejpam-5504	183	10	from	from	ADP
ejpam-5504	183	11	(	(	PUNCT
ejpam-5504	183	12	17	17	NUM
ejpam-5504	183	13	)	)	PUNCT
ejpam-5504	183	14	)	)	PUNCT
ejpam-5504	183	15	,	,	PUNCT
ejpam-5504	183	16	as	as	SCONJ
ejpam-5504	183	17	claimed	claim	VERB
ejpam-5504	183	18	.	.	PUNCT
ejpam-5504	184	1	■	■	PUNCT
ejpam-5504	184	2	theorem	theorem	ADJ
ejpam-5504	184	3	3	3	NUM
ejpam-5504	184	4	.	.	NOUN
ejpam-5504	184	5	recall	recall	NOUN
ejpam-5504	184	6	from	from	ADP
ejpam-5504	184	7	(	(	PUNCT
ejpam-5504	184	8	8)	8)	NUM
ejpam-5504	184	9	that	that	DET
ejpam-5504	184	10	t	t	NOUN
ejpam-5504	184	11	=	=	PUNCT
ejpam-5504	184	12	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	185	1	pd⊥	pd⊥	PROPN
ejpam-5504	185	2	−	−	NUM
ejpam-5504	185	3	1	1	NUM
ejpam-5504	185	4	2	2	NUM
ejpam-5504	185	5	pd⊥	pd⊥	PROPN
ejpam-5504	185	6	.	.	PUNCT
ejpam-5504	186	1	then	then	ADV
ejpam-5504	186	2	the	the	DET
ejpam-5504	186	3	following	follow	VERB
ejpam-5504	186	4	holds	hold	VERB
ejpam-5504	186	5	;	;	PUNCT
ejpam-5504	186	6	(	(	PUNCT
ejpam-5504	186	7	i	i	NOUN
ejpam-5504	186	8	)	)	PUNCT
ejpam-5504	186	9	(	(	PUNCT
ejpam-5504	186	10	1/2	1/2	NUM
ejpam-5504	186	11	)	)	PUNCT
ejpam-5504	186	12	id+t	id+t	PUNCT
ejpam-5504	186	13	is	be	AUX
ejpam-5504	186	14	1	1	NUM
ejpam-5504	186	15	2	2	NUM
ejpam-5504	186	16	-strongly	-strongly	ADV
ejpam-5504	186	17	monotone	monotone	ADJ
ejpam-5504	186	18	.	.	PUNCT
ejpam-5504	187	1	(	(	PUNCT
ejpam-5504	187	2	ii	ii	NOUN
ejpam-5504	187	3	)	)	PUNCT
ejpam-5504	187	4	(	(	PUNCT
ejpam-5504	187	5	(	(	PUNCT
ejpam-5504	187	6	1/2	1/2	NUM
ejpam-5504	187	7	)	)	PUNCT
ejpam-5504	188	1	id+t	id+t	ADV
ejpam-5504	188	2	)	)	PUNCT
ejpam-5504	188	3	−1	−1	NOUN
ejpam-5504	188	4	=	=	SYM
ejpam-5504	188	5	2j2	2j2	NUM
ejpam-5504	188	6	t.	t.	PROPN
ejpam-5504	188	7	s.t	s.t	PROPN
ejpam-5504	188	8	.	.	PROPN
ejpam-5504	188	9	alwadani	alwadani	PROPN
ejpam-5504	188	10	/	/	SYM
ejpam-5504	188	11	eur	eur	PROPN
ejpam-5504	188	12	.	.	PUNCT
ejpam-5504	189	1	j.	j.	PROPN
ejpam-5504	189	2	pure	pure	PROPN
ejpam-5504	189	3	appl	appl	PROPN
ejpam-5504	189	4	.	.	PROPN
ejpam-5504	189	5	math	math	PROPN
ejpam-5504	189	6	,	,	PUNCT
ejpam-5504	189	7	17	17	NUM
ejpam-5504	189	8	(	(	PUNCT
ejpam-5504	189	9	4	4	NUM
ejpam-5504	189	10	)	)	PUNCT
ejpam-5504	189	11	(	(	PUNCT
ejpam-5504	189	12	2024	2024	NUM
ejpam-5504	189	13	)	)	PUNCT
ejpam-5504	189	14	,	,	PUNCT
ejpam-5504	189	15	3660	3660	NUM
ejpam-5504	189	16	-	-	SYM
ejpam-5504	189	17	3676	3676	NUM
ejpam-5504	189	18	3668	3668	NUM
ejpam-5504	189	19	(	(	PUNCT
ejpam-5504	189	20	iii	iii	NOUN
ejpam-5504	189	21	)	)	PUNCT
ejpam-5504	189	22	2	2	NUM
ejpam-5504	189	23	t	t	NOUN
ejpam-5504	189	24	+	+	CCONJ
ejpam-5504	189	25	i	i	PROPN
ejpam-5504	189	26	d	d	NOUN
ejpam-5504	189	27	=	=	SYM
ejpam-5504	189	28	2	2	NUM
ejpam-5504	189	29	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	189	30	pd⊥	pd⊥	PROPN
ejpam-5504	189	31	+	+	PROPN
ejpam-5504	189	32	pd	pd	PROPN
ejpam-5504	189	33	.	.	PROPN
ejpam-5504	189	34	(	(	PUNCT
ejpam-5504	189	35	iv	iv	X
ejpam-5504	189	36	)	)	PUNCT
ejpam-5504	189	37	j2	j2	PROPN
ejpam-5504	189	38	t	t	PROPN
ejpam-5504	189	39	=	=	PROPN
ejpam-5504	189	40	pd	pd	PROPN
ejpam-5504	189	41	+	+	CCONJ
ejpam-5504	189	42	1	1	NUM
ejpam-5504	189	43	2	2	NUM
ejpam-5504	189	44	(	(	PUNCT
ejpam-5504	189	45	id−r)pd⊥	id−r)pd⊥	NOUN
ejpam-5504	189	46	.	.	PUNCT
ejpam-5504	190	1	(	(	PUNCT
ejpam-5504	190	2	v	v	NOUN
ejpam-5504	190	3	)	)	PUNCT
ejpam-5504	190	4	2j2	2j2	NUM
ejpam-5504	190	5	t	t	NOUN
ejpam-5504	191	1	=	=	SYM
ejpam-5504	191	2	(	(	PUNCT
ejpam-5504	191	3	id−r)pd⊥	id−r)pd⊥	NOUN
ejpam-5504	191	4	+2	+2	PROPN
ejpam-5504	191	5	pd	pd	PROPN
ejpam-5504	191	6	.	.	PUNCT
ejpam-5504	191	7	(	(	PUNCT
ejpam-5504	191	8	vi	vi	NOUN
ejpam-5504	191	9	)	)	PUNCT
ejpam-5504	191	10	(	(	PUNCT
ejpam-5504	191	11	id−r)pd⊥	id−r)pd⊥	NOUN
ejpam-5504	191	12	+2	+2	PROPN
ejpam-5504	191	13	pd	pd	NOUN
ejpam-5504	191	14	=	=	PUNCT
ejpam-5504	191	15	id−r	id−r	PROPN
ejpam-5504	191	16	+	+	CCONJ
ejpam-5504	191	17	2	2	NUM
ejpam-5504	191	18	pd	pd	NOUN
ejpam-5504	191	19	.	.	PUNCT
ejpam-5504	192	1	(	(	PUNCT
ejpam-5504	192	2	vii	vii	PROPN
ejpam-5504	192	3	)	)	PUNCT
ejpam-5504	192	4	we	we	PRON
ejpam-5504	192	5	have	have	VERB
ejpam-5504	192	6	(	(	PUNCT
ejpam-5504	192	7	1	1	NUM
ejpam-5504	192	8	2	2	NUM
ejpam-5504	192	9	id+t	id+t	NOUN
ejpam-5504	192	10	)	)	PUNCT
ejpam-5504	193	1	−1	−1	NOUN
ejpam-5504	193	2	=	=	SYM
ejpam-5504	193	3	2j2	2j2	NUM
ejpam-5504	193	4	t	t	NOUN
ejpam-5504	193	5	=	=	SYM
ejpam-5504	193	6	(	(	PUNCT
ejpam-5504	193	7	id−r)pd⊥	id−r)pd⊥	NOUN
ejpam-5504	193	8	+2	+2	PROPN
ejpam-5504	193	9	pd	pd	NOUN
ejpam-5504	193	10	=	=	PUNCT
ejpam-5504	193	11	id−r	id−r	PROPN
ejpam-5504	193	12	+	+	CCONJ
ejpam-5504	193	13	2	2	NUM
ejpam-5504	193	14	pd	pd	NOUN
ejpam-5504	193	15	.	.	PUNCT
ejpam-5504	194	1	(	(	PUNCT
ejpam-5504	194	2	18	18	NUM
ejpam-5504	194	3	)	)	PUNCT
ejpam-5504	194	4	(	(	PUNCT
ejpam-5504	194	5	viii	viii	NOUN
ejpam-5504	194	6	)	)	PUNCT
ejpam-5504	194	7	(	(	PUNCT
ejpam-5504	194	8	1	1	NUM
ejpam-5504	194	9	2	2	NUM
ejpam-5504	194	10	id+t	id+t	NOUN
ejpam-5504	194	11	)	)	PUNCT
ejpam-5504	195	1	−1	−1	NOUN
ejpam-5504	195	2	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5504	195	3	d⊥	d⊥	NOUN
ejpam-5504	195	4	=	=	SYM
ejpam-5504	195	5	id−r	id−r	NOUN
ejpam-5504	195	6	.	.	PUNCT
ejpam-5504	195	7	proof	proof	NOUN
ejpam-5504	195	8	.	.	PUNCT
ejpam-5504	196	1	(	(	PUNCT
ejpam-5504	196	2	i	i	NOUN
ejpam-5504	196	3	):	):	PUNCT
ejpam-5504	196	4	showing	show	VERB
ejpam-5504	196	5	that	that	SCONJ
ejpam-5504	196	6	1	1	NUM
ejpam-5504	196	7	2	2	NUM
ejpam-5504	196	8	id+t	id+t	ADV
ejpam-5504	196	9	is	be	AUX
ejpam-5504	196	10	(	(	PUNCT
ejpam-5504	196	11	1/2)-strongly	1/2)-strongly	NUM
ejpam-5504	196	12	monotone	monotone	ADJ
ejpam-5504	196	13	⇔	⇔	NOUN
ejpam-5504	196	14	1	1	NUM
ejpam-5504	196	15	2	2	NUM
ejpam-5504	196	16	id+t	id+t	NOUN
ejpam-5504	196	17	−	−	NOUN
ejpam-5504	197	1	1	1	NUM
ejpam-5504	197	2	2	2	NUM
ejpam-5504	197	3	i	i	NOUN
ejpam-5504	197	4	d	d	PROPN
ejpam-5504	197	5	=	=	SYM
ejpam-5504	197	6	t	t	PROPN
ejpam-5504	197	7	is	be	AUX
ejpam-5504	197	8	montone	montone	NOUN
ejpam-5504	197	9	,	,	PUNCT
ejpam-5504	197	10	which	which	PRON
ejpam-5504	197	11	is	be	AUX
ejpam-5504	197	12	verified	verify	VERB
ejpam-5504	197	13	by	by	ADP
ejpam-5504	197	14	lemma	lemma	PROPN
ejpam-5504	197	15	2(iii	2(iii	NUM
ejpam-5504	197	16	)	)	PUNCT
ejpam-5504	197	17	.	.	PUNCT
ejpam-5504	198	1	(	(	PUNCT
ejpam-5504	198	2	ii	ii	NOUN
ejpam-5504	198	3	):	):	PUNCT
ejpam-5504	198	4	from	from	ADP
ejpam-5504	198	5	lemma	lemma	PROPN
ejpam-5504	198	6	2(ii	2(ii	NUM
ejpam-5504	198	7	)	)	PUNCT
ejpam-5504	198	8	&	&	CCONJ
ejpam-5504	198	9	(	(	PUNCT
ejpam-5504	198	10	iv	iv	X
ejpam-5504	198	11	)	)	PUNCT
ejpam-5504	198	12	and	and	CCONJ
ejpam-5504	199	1	[	[	X
ejpam-5504	199	2	14	14	NUM
ejpam-5504	199	3	,	,	PUNCT
ejpam-5504	199	4	lemma	lemma	PROPN
ejpam-5504	199	5	2	2	NUM
ejpam-5504	199	6	]	]	PUNCT
ejpam-5504	199	7	,	,	PUNCT
ejpam-5504	199	8	we	we	PRON
ejpam-5504	199	9	have	have	VERB
ejpam-5504	199	10	(	(	PUNCT
ejpam-5504	199	11	1	1	NUM
ejpam-5504	199	12	2	2	NUM
ejpam-5504	199	13	id+t	id+t	NOUN
ejpam-5504	199	14	)	)	PUNCT
ejpam-5504	199	15	−1	−1	NOUN
ejpam-5504	199	16	=	=	SYM
ejpam-5504	199	17	(	(	PUNCT
ejpam-5504	199	18	1	1	NUM
ejpam-5504	199	19	2	2	NUM
ejpam-5504	199	20	(	(	PUNCT
ejpam-5504	199	21	id+2	id+2	NOUN
ejpam-5504	199	22	t	t	PROPN
ejpam-5504	199	23	)	)	PUNCT
ejpam-5504	199	24	)	)	PUNCT
ejpam-5504	199	25	−1	−1	NOUN
ejpam-5504	200	1	=	=	SYM
ejpam-5504	200	2	2	2	NUM
ejpam-5504	200	3	(	(	PUNCT
ejpam-5504	200	4	id+2t)−1	id+2t)−1	NOUN
ejpam-5504	200	5	=	=	SYM
ejpam-5504	200	6	2j2	2j2	NUM
ejpam-5504	200	7	t.	t.	PROPN
ejpam-5504	200	8	(	(	PUNCT
ejpam-5504	200	9	iii	iii	PROPN
ejpam-5504	200	10	):	):	PUNCT
ejpam-5504	200	11	by	by	ADP
ejpam-5504	200	12	using	use	VERB
ejpam-5504	200	13	(	(	PUNCT
ejpam-5504	200	14	8)	8)	NUM
ejpam-5504	200	15	and	and	CCONJ
ejpam-5504	200	16	lemma	lemma	PROPN
ejpam-5504	200	17	2(ii	2(ii	NUM
ejpam-5504	200	18	)	)	PUNCT
ejpam-5504	200	19	,	,	PUNCT
ejpam-5504	200	20	we	we	PRON
ejpam-5504	200	21	obtain	obtain	VERB
ejpam-5504	200	22	2	2	NUM
ejpam-5504	200	23	t	t	NOUN
ejpam-5504	200	24	=	=	SYM
ejpam-5504	200	25	2	2	NUM
ejpam-5504	200	26	(	(	PUNCT
ejpam-5504	200	27	pd⊥(id−r)−1	pd⊥(id−r)−1	VERB
ejpam-5504	200	28	pd⊥	pd⊥	PROPN
ejpam-5504	200	29	−	−	NUM
ejpam-5504	200	30	1	1	NUM
ejpam-5504	200	31	2	2	NUM
ejpam-5504	200	32	pd⊥	pd⊥	PROPN
ejpam-5504	200	33	)	)	PUNCT
ejpam-5504	201	1	=	=	SYM
ejpam-5504	201	2	2	2	NUM
ejpam-5504	201	3	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	201	4	pd⊥	pd⊥	PROPN
ejpam-5504	201	5	−pd⊥	−pd⊥	PROPN
ejpam-5504	201	6	,	,	PUNCT
ejpam-5504	201	7	hence	hence	ADV
ejpam-5504	201	8	2	2	NUM
ejpam-5504	201	9	t	t	NOUN
ejpam-5504	201	10	+	+	CCONJ
ejpam-5504	201	11	i	i	PROPN
ejpam-5504	201	12	d	d	NOUN
ejpam-5504	201	13	=	=	SYM
ejpam-5504	201	14	2	2	NUM
ejpam-5504	201	15	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	202	1	pd⊥	pd⊥	PROPN
ejpam-5504	202	2	−pd⊥	−pd⊥	PROPN
ejpam-5504	203	1	+	+	CCONJ
ejpam-5504	203	2	i	i	PROPN
ejpam-5504	203	3	d	d	NOUN
ejpam-5504	203	4	=	=	SYM
ejpam-5504	203	5	2	2	NUM
ejpam-5504	203	6	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	203	7	pd⊥	pd⊥	PROPN
ejpam-5504	203	8	+	+	PROPN
ejpam-5504	203	9	pd	pd	PROPN
ejpam-5504	203	10	.	.	PUNCT
ejpam-5504	204	1	(	(	PUNCT
ejpam-5504	204	2	iv	iv	NUM
ejpam-5504	204	3	):	):	PUNCT
ejpam-5504	204	4	from	from	ADP
ejpam-5504	204	5	(	(	PUNCT
ejpam-5504	204	6	iii	iii	NOUN
ejpam-5504	204	7	)	)	PUNCT
ejpam-5504	204	8	,	,	PUNCT
ejpam-5504	204	9	we	we	PRON
ejpam-5504	204	10	obtain	obtain	VERB
ejpam-5504	204	11	2	2	NUM
ejpam-5504	204	12	t	t	NOUN
ejpam-5504	204	13	+	+	CCONJ
ejpam-5504	204	14	i	i	PROPN
ejpam-5504	204	15	d	d	NOUN
ejpam-5504	204	16	=	=	SYM
ejpam-5504	204	17	2	2	NUM
ejpam-5504	204	18	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	204	19	pd⊥	pd⊥	PROPN
ejpam-5504	204	20	+	+	PROPN
ejpam-5504	204	21	pd	pd	PROPN
ejpam-5504	204	22	.	.	PROPN
ejpam-5504	204	23	put	put	VERB
ejpam-5504	204	24	differently	differently	ADV
ejpam-5504	204	25	,	,	PUNCT
ejpam-5504	204	26	2	2	NUM
ejpam-5504	204	27	t	t	NOUN
ejpam-5504	204	28	+	+	CCONJ
ejpam-5504	205	1	i	i	PROPN
ejpam-5504	205	2	d	d	NOUN
ejpam-5504	205	3	:	:	PUNCT
ejpam-5504	205	4	d	d	PROPN
ejpam-5504	205	5	⊕	⊕	PROPN
ejpam-5504	205	6	d⊥	d⊥	PROPN
ejpam-5504	205	7	→	→	PUNCT
ejpam-5504	205	8	d	d	PROPN
ejpam-5504	205	9	⊕	⊕	PROPN
ejpam-5504	205	10	d⊥	d⊥	NOUN
ejpam-5504	205	11	:	:	PUNCT
ejpam-5504	205	12	d	d	X
ejpam-5504	205	13	⊕	⊕	PROPN
ejpam-5504	205	14	d⊥	d⊥	NOUN
ejpam-5504	205	15	7→	7→	NUM
ejpam-5504	206	1	d	d	NOUN
ejpam-5504	206	2	+	+	CCONJ
ejpam-5504	206	3	2	2	NUM
ejpam-5504	206	4	pd⊥(id−r)−1d⊥.	pd⊥(id−r)−1d⊥.	NOUN
ejpam-5504	206	5	for	for	ADP
ejpam-5504	206	6	two	two	NUM
ejpam-5504	206	7	vectors	vector	NOUN
ejpam-5504	206	8	d⊥	d⊥	NOUN
ejpam-5504	206	9	,	,	PUNCT
ejpam-5504	206	10	e⊥	e⊥	ADJ
ejpam-5504	206	11	in	in	ADP
ejpam-5504	206	12	d⊥	d⊥	NOUN
ejpam-5504	206	13	,	,	PUNCT
ejpam-5504	206	14	we	we	PRON
ejpam-5504	206	15	have	have	VERB
ejpam-5504	206	16	the	the	DET
ejpam-5504	206	17	equivalences	equivalence	NOUN
ejpam-5504	206	18	,	,	PUNCT
ejpam-5504	206	19	e⊥	e⊥	ADJ
ejpam-5504	206	20	=	=	SYM
ejpam-5504	206	21	2	2	NUM
ejpam-5504	206	22	pd⊥(id−r)−1d⊥	pd⊥(id−r)−1d⊥	PROPN
ejpam-5504	206	23	⇔	⇔	X
ejpam-5504	206	24	d⊥	d⊥	NOUN
ejpam-5504	207	1	=	=	PUNCT
ejpam-5504	208	1	(	(	PUNCT
ejpam-5504	208	2	2	2	NUM
ejpam-5504	208	3	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	208	4	)	)	PUNCT
ejpam-5504	208	5	−1	−1	NOUN
ejpam-5504	208	6	e⊥	e⊥	ADJ
ejpam-5504	208	7	,	,	PUNCT
ejpam-5504	208	8	and	and	CCONJ
ejpam-5504	208	9	therefore	therefore	ADV
ejpam-5504	208	10	,	,	PUNCT
ejpam-5504	208	11	d⊥	d⊥	NOUN
ejpam-5504	208	12	=	=	SYM
ejpam-5504	208	13	(	(	PUNCT
ejpam-5504	208	14	2	2	NUM
ejpam-5504	208	15	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	208	16	)	)	PUNCT
ejpam-5504	208	17	−1	−1	NOUN
ejpam-5504	208	18	e⊥	e⊥	NOUN
ejpam-5504	208	19	=	=	PUNCT
ejpam-5504	208	20	(	(	PUNCT
ejpam-5504	208	21	2	2	NUM
ejpam-5504	208	22	(	(	PUNCT
ejpam-5504	208	23	pd⊥(id−r)−1))−1	pd⊥(id−r)−1))−1	X
ejpam-5504	208	24	e⊥	e⊥	PROPN
ejpam-5504	208	25	s.t	s.t	PROPN
ejpam-5504	208	26	.	.	PROPN
ejpam-5504	208	27	alwadani	alwadani	PROPN
ejpam-5504	208	28	/	/	SYM
ejpam-5504	208	29	eur	eur	PROPN
ejpam-5504	208	30	.	.	PUNCT
ejpam-5504	209	1	j.	j.	PROPN
ejpam-5504	209	2	pure	pure	PROPN
ejpam-5504	209	3	appl	appl	PROPN
ejpam-5504	209	4	.	.	PROPN
ejpam-5504	209	5	math	math	PROPN
ejpam-5504	209	6	,	,	PUNCT
ejpam-5504	209	7	17	17	NUM
ejpam-5504	209	8	(	(	PUNCT
ejpam-5504	209	9	4	4	NUM
ejpam-5504	209	10	)	)	PUNCT
ejpam-5504	209	11	(	(	PUNCT
ejpam-5504	209	12	2024	2024	NUM
ejpam-5504	209	13	)	)	PUNCT
ejpam-5504	209	14	,	,	PUNCT
ejpam-5504	209	15	3660	3660	NUM
ejpam-5504	209	16	-	-	SYM
ejpam-5504	209	17	3676	3676	NUM
ejpam-5504	209	18	3669	3669	NUM
ejpam-5504	209	19	=	=	SYM
ejpam-5504	209	20	1	1	NUM
ejpam-5504	209	21	2	2	NUM
ejpam-5504	209	22	(	(	PUNCT
ejpam-5504	209	23	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	209	24	)	)	PUNCT
ejpam-5504	209	25	−1	−1	NOUN
ejpam-5504	209	26	e⊥	e⊥	NOUN
ejpam-5504	209	27	=	=	SYM
ejpam-5504	209	28	1	1	NUM
ejpam-5504	209	29	2	2	NUM
ejpam-5504	209	30	(	(	PUNCT
ejpam-5504	209	31	id−r	id−r	NOUN
ejpam-5504	209	32	)	)	PUNCT
ejpam-5504	209	33	p−1	p−1	PROPN
ejpam-5504	209	34	d⊥	d⊥	NOUN
ejpam-5504	209	35	e⊥	e⊥	NOUN
ejpam-5504	209	36	=	=	SYM
ejpam-5504	209	37	1	1	NUM
ejpam-5504	209	38	2	2	NUM
ejpam-5504	209	39	(	(	PUNCT
ejpam-5504	209	40	id−r	id−r	NOUN
ejpam-5504	209	41	)	)	PUNCT
ejpam-5504	209	42	e⊥.	e⊥.	NOUN
ejpam-5504	209	43	hence	hence	ADV
ejpam-5504	209	44	,	,	PUNCT
ejpam-5504	209	45	(	(	PUNCT
ejpam-5504	209	46	2	2	NUM
ejpam-5504	209	47	t	t	NOUN
ejpam-5504	209	48	+	+	CCONJ
ejpam-5504	209	49	id)−1	id)−1	VERB
ejpam-5504	209	50	:	:	PUNCT
ejpam-5504	209	51	d	d	PROPN
ejpam-5504	209	52	⊕	⊕	PROPN
ejpam-5504	209	53	d⊥	d⊥	PROPN
ejpam-5504	209	54	→	→	PUNCT
ejpam-5504	209	55	d	d	PROPN
ejpam-5504	209	56	⊕	⊕	PROPN
ejpam-5504	209	57	d⊥	d⊥	NOUN
ejpam-5504	209	58	:	:	PUNCT
ejpam-5504	210	1	d	d	X
ejpam-5504	210	2	⊕	⊕	PROPN
ejpam-5504	210	3	d⊥	d⊥	NOUN
ejpam-5504	210	4	7→	7→	NUM
ejpam-5504	210	5	d	d	NOUN
ejpam-5504	210	6	+	+	NOUN
ejpam-5504	210	7	1	1	NUM
ejpam-5504	210	8	2	2	NUM
ejpam-5504	210	9	(	(	PUNCT
ejpam-5504	210	10	id−r)d⊥	id−r)d⊥	NOUN
ejpam-5504	210	11	;	;	PUNCT
ejpam-5504	210	12	equivalently	equivalently	ADV
ejpam-5504	210	13	,	,	PUNCT
ejpam-5504	210	14	j2	j2	PROPN
ejpam-5504	210	15	t	t	PROPN
ejpam-5504	210	16	=	=	PUNCT
ejpam-5504	210	17	(	(	PUNCT
ejpam-5504	210	18	2	2	NUM
ejpam-5504	210	19	t	t	NOUN
ejpam-5504	210	20	+	+	CCONJ
ejpam-5504	210	21	id)−1	id)−1	VERB
ejpam-5504	210	22	:	:	PUNCT
ejpam-5504	211	1	z	z	PROPN
ejpam-5504	211	2	7→	7→	NUM
ejpam-5504	211	3	pd	pd	NOUN
ejpam-5504	211	4	z	z	NOUN
ejpam-5504	211	5	+	+	CCONJ
ejpam-5504	211	6	1	1	NUM
ejpam-5504	211	7	2	2	NUM
ejpam-5504	211	8	(	(	PUNCT
ejpam-5504	211	9	id−r)pd⊥	id−r)pd⊥	PROPN
ejpam-5504	211	10	z.	z.	PROPN
ejpam-5504	211	11	(	(	PUNCT
ejpam-5504	211	12	v	v	NOUN
ejpam-5504	211	13	):	):	PUNCT
ejpam-5504	211	14	it	it	PRON
ejpam-5504	211	15	follows	follow	VERB
ejpam-5504	211	16	directly	directly	ADV
ejpam-5504	211	17	from	from	ADP
ejpam-5504	211	18	(	(	PUNCT
ejpam-5504	211	19	iv	iv	NOUN
ejpam-5504	211	20	)	)	PUNCT
ejpam-5504	211	21	.	.	PUNCT
ejpam-5504	212	1	(	(	PUNCT
ejpam-5504	212	2	vi	vi	ADJ
ejpam-5504	212	3	):	):	PUNCT
ejpam-5504	212	4	because	because	SCONJ
ejpam-5504	212	5	ker(id−r	ker(id−r	NOUN
ejpam-5504	212	6	)	)	PUNCT
ejpam-5504	212	7	=	=	SYM
ejpam-5504	213	1	d	d	NOUN
ejpam-5504	213	2	,	,	PUNCT
ejpam-5504	213	3	we	we	PRON
ejpam-5504	213	4	have	have	VERB
ejpam-5504	213	5	(	(	PUNCT
ejpam-5504	213	6	id−r)pd	id−r)pd	PROPN
ejpam-5504	213	7	≡	≡	PROPN
ejpam-5504	213	8	0	0	NUM
ejpam-5504	213	9	.	.	PUNCT
ejpam-5504	214	1	therefore	therefore	ADV
ejpam-5504	214	2	,	,	PUNCT
ejpam-5504	214	3	(	(	PUNCT
ejpam-5504	214	4	id−r)pd⊥	id−r)pd⊥	NOUN
ejpam-5504	214	5	+2	+2	PROPN
ejpam-5504	214	6	pd	pd	NOUN
ejpam-5504	214	7	=	=	PUNCT
ejpam-5504	214	8	id−r	id−r	PROPN
ejpam-5504	214	9	+	+	CCONJ
ejpam-5504	214	10	2	2	NUM
ejpam-5504	214	11	pd	pd	NOUN
ejpam-5504	214	12	.	.	PUNCT
ejpam-5504	215	1	(	(	PUNCT
ejpam-5504	215	2	vii	vii	PROPN
ejpam-5504	215	3	):	):	PUNCT
ejpam-5504	215	4	combine	combine	PROPN
ejpam-5504	215	5	(	(	PUNCT
ejpam-5504	215	6	ii	ii	NOUN
ejpam-5504	215	7	)	)	PUNCT
ejpam-5504	215	8	,	,	PUNCT
ejpam-5504	215	9	(	(	PUNCT
ejpam-5504	215	10	v	v	NOUN
ejpam-5504	215	11	)	)	PUNCT
ejpam-5504	215	12	,	,	PUNCT
ejpam-5504	215	13	and	and	CCONJ
ejpam-5504	215	14	(	(	PUNCT
ejpam-5504	215	15	vi	vi	NOUN
ejpam-5504	215	16	)	)	PUNCT
ejpam-5504	215	17	.	.	PUNCT
ejpam-5504	216	1	(	(	PUNCT
ejpam-5504	216	2	viii	viii	ADJ
ejpam-5504	216	3	):	):	PUNCT
ejpam-5504	216	4	from	from	ADP
ejpam-5504	216	5	(	(	PUNCT
ejpam-5504	216	6	v	v	NOUN
ejpam-5504	216	7	)	)	PUNCT
ejpam-5504	216	8	,	,	PUNCT
ejpam-5504	216	9	we	we	PRON
ejpam-5504	216	10	obtain(1	obtain(1	VERB
ejpam-5504	216	11	2	2	NUM
ejpam-5504	216	12	id+t	id+t	NOUN
ejpam-5504	216	13	)	)	PUNCT
ejpam-5504	216	14	−1	−1	NOUN
ejpam-5504	216	15	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5504	216	16	d⊥	d⊥	NOUN
ejpam-5504	216	17	=	=	PUNCT
ejpam-5504	216	18	(	(	PUNCT
ejpam-5504	216	19	id−r	id−r	NOUN
ejpam-5504	216	20	+	+	CCONJ
ejpam-5504	216	21	2	2	NUM
ejpam-5504	216	22	pd	pd	NOUN
ejpam-5504	216	23	)	)	PUNCT
ejpam-5504	216	24	∣∣	∣∣	X
ejpam-5504	216	25	d⊥	d⊥	NOUN
ejpam-5504	216	26	=	=	SYM
ejpam-5504	216	27	id−r	id−r	NOUN
ejpam-5504	216	28	.	.	PUNCT
ejpam-5504	217	1	■	■	PUNCT
ejpam-5504	217	2	proposition	proposition	NOUN
ejpam-5504	217	3	4	4	NUM
ejpam-5504	217	4	.	.	PUNCT
ejpam-5504	218	1	let	let	VERB
ejpam-5504	218	2	m	m	PRON
ejpam-5504	218	3	∈	∈	VERB
ejpam-5504	218	4	{	{	PUNCT
ejpam-5504	218	5	2	2	NUM
ejpam-5504	218	6	,	,	PUNCT
ejpam-5504	218	7	3	3	NUM
ejpam-5504	218	8	,	,	PUNCT
ejpam-5504	218	9	.	.	PUNCT
ejpam-5504	218	10	.	.	PUNCT
ejpam-5504	218	11	.	.	PUNCT
ejpam-5504	219	1	}	}	PUNCT
ejpam-5504	220	1	and	and	CCONJ
ejpam-5504	220	2	assume	assume	VERB
ejpam-5504	220	3	that	that	SCONJ
ejpam-5504	220	4	rm	rm	NOUN
ejpam-5504	220	5	=	=	PUNCT
ejpam-5504	220	6	i	i	PROPN
ejpam-5504	220	7	d	d	PROPN
ejpam-5504	220	8	,	,	PUNCT
ejpam-5504	220	9	i.e.	i.e.	X
ejpam-5504	220	10	,	,	PUNCT
ejpam-5504	220	11	r	r	NOUN
ejpam-5504	220	12	is	be	AUX
ejpam-5504	220	13	an	an	DET
ejpam-5504	220	14	isometry	isometry	NOUN
ejpam-5504	220	15	of	of	ADP
ejpam-5504	220	16	finite	finite	PROPN
ejpam-5504	220	17	rank	rank	PROPN
ejpam-5504	220	18	m.	m.	NOUN
ejpam-5504	220	19	assume	assume	VERB
ejpam-5504	220	20	that	that	SCONJ
ejpam-5504	220	21	x	x	X
ejpam-5504	220	22	=	=	SYM
ejpam-5504	220	23	rm	rm	PROPN
ejpam-5504	220	24	and	and	CCONJ
ejpam-5504	220	25	recall	recall	VERB
ejpam-5504	220	26	from	from	ADP
ejpam-5504	220	27	[	[	X
ejpam-5504	220	28	2	2	NUM
ejpam-5504	220	29	,	,	PUNCT
ejpam-5504	220	30	lemma	lemma	PROPN
ejpam-5504	220	31	]	]	PUNCT
ejpam-5504	220	32	that	that	SCONJ
ejpam-5504	220	33	pd	pd	X
ejpam-5504	220	34	=	=	NOUN
ejpam-5504	220	35	1	1	NUM
ejpam-5504	220	36	m	m	NOUN
ejpam-5504	220	37	m−1	m−1	PROPN
ejpam-5504	220	38	∑	∑	PUNCT
ejpam-5504	220	39	k=0	k=0	PROPN
ejpam-5504	220	40	rk	rk	PROPN
ejpam-5504	220	41	and	and	CCONJ
ejpam-5504	220	42	pd⊥	pd⊥	PROPN
ejpam-5504	221	1	=	=	SYM
ejpam-5504	221	2	id−	id−	NUM
ejpam-5504	221	3	1	1	NUM
ejpam-5504	221	4	m	m	NOUN
ejpam-5504	221	5	m−1	m−1	PROPN
ejpam-5504	221	6	∑	∑	ADP
ejpam-5504	221	7	k=0	k=0	PROPN
ejpam-5504	221	8	rk	rk	VERB
ejpam-5504	221	9	,	,	PUNCT
ejpam-5504	221	10	(	(	PUNCT
ejpam-5504	221	11	19	19	NUM
ejpam-5504	221	12	)	)	PUNCT
ejpam-5504	221	13	where	where	SCONJ
ejpam-5504	221	14	d	d	NOUN
ejpam-5504	221	15	=	=	PRON
ejpam-5504	221	16	fix	fix	PROPN
ejpam-5504	221	17	r.	r.	PROPN
ejpam-5504	221	18	then	then	ADV
ejpam-5504	221	19	1	1	NUM
ejpam-5504	221	20	2	2	NUM
ejpam-5504	221	21	pd⊥	pd⊥	PROPN
ejpam-5504	221	22	(	(	PUNCT
ejpam-5504	221	23	r	r	NOUN
ejpam-5504	221	24	+	+	PROPN
ejpam-5504	221	25	r∗)pd⊥	r∗)pd⊥	PROPN
ejpam-5504	221	26	=	=	SYM
ejpam-5504	221	27	1	1	NUM
ejpam-5504	221	28	m	m	VERB
ejpam-5504	221	29	(	(	PUNCT
ejpam-5504	221	30	−	−	PROPN
ejpam-5504	221	31	id−	id−	PROPN
ejpam-5504	221	32	m−2	m−2	NOUN
ejpam-5504	221	33	∑	∑	ADP
ejpam-5504	221	34	k=2	k=2	PROPN
ejpam-5504	221	35	rk	rk	NOUN
ejpam-5504	221	36	+	+	CCONJ
ejpam-5504	221	37	max{1	max{1	PROPN
ejpam-5504	221	38	,	,	PUNCT
ejpam-5504	221	39	m	m	VERB
ejpam-5504	221	40	−	−	NOUN
ejpam-5504	221	41	2	2	NUM
ejpam-5504	221	42	}	}	SYM
ejpam-5504	221	43	2	2	NUM
ejpam-5504	221	44	(	(	PUNCT
ejpam-5504	221	45	r	r	NOUN
ejpam-5504	221	46	+	+	CCONJ
ejpam-5504	221	47	rm−1	rm−1	PROPN
ejpam-5504	221	48	)	)	PUNCT
ejpam-5504	221	49	)	)	PUNCT
ejpam-5504	221	50	.	.	PUNCT
ejpam-5504	222	1	(	(	PUNCT
ejpam-5504	222	2	20	20	X
ejpam-5504	222	3	)	)	PUNCT
ejpam-5504	222	4	proof	proof	NOUN
ejpam-5504	222	5	.	.	PUNCT
ejpam-5504	223	1	noted	note	VERB
ejpam-5504	223	2	that	that	SCONJ
ejpam-5504	223	3	r	r	NOUN
ejpam-5504	223	4	is	be	AUX
ejpam-5504	223	5	an	an	DET
ejpam-5504	223	6	isometry	isometry	ADJ
ejpam-5504	223	7	⇒	⇒	NOUN
ejpam-5504	223	8	r∗r	r∗r	ADJ
ejpam-5504	223	9	=	=	SYM
ejpam-5504	223	10	rr∗	rr∗	ADJ
ejpam-5504	223	11	=	=	PUNCT
ejpam-5504	223	12	i	i	PROPN
ejpam-5504	223	13	d	d	PROPN
ejpam-5504	223	14	,	,	PUNCT
ejpam-5504	223	15	so	so	ADV
ejpam-5504	223	16	r−1	r−1	PROPN
ejpam-5504	223	17	=	=	NOUN
ejpam-5504	223	18	r∗.	r∗.	NOUN
ejpam-5504	223	19	but	but	CCONJ
ejpam-5504	223	20	also	also	ADV
ejpam-5504	223	21	r	r	NOUN
ejpam-5504	223	22	has	have	AUX
ejpam-5504	223	23	rank	rank	PROPN
ejpam-5504	223	24	m	m	PRON
ejpam-5504	223	25	,	,	PUNCT
ejpam-5504	223	26	hence	hence	ADV
ejpam-5504	223	27	rm−1	rm−1	PROPN
ejpam-5504	223	28	=	=	PUNCT
ejpam-5504	224	1	r−1	r−1	PROPN
ejpam-5504	224	2	=	=	PUNCT
ejpam-5504	224	3	r∗.	r∗.	NOUN
ejpam-5504	224	4	by	by	ADP
ejpam-5504	224	5	using	use	VERB
ejpam-5504	224	6	these	these	DET
ejpam-5504	224	7	facts	fact	NOUN
ejpam-5504	224	8	,	,	PUNCT
ejpam-5504	224	9	we	we	PRON
ejpam-5504	224	10	obtain	obtain	VERB
ejpam-5504	224	11	pd⊥(r	pd⊥(r	NOUN
ejpam-5504	224	12	+	+	CCONJ
ejpam-5504	225	1	r∗)pd⊥	r∗)pd⊥	NOUN
ejpam-5504	225	2	=	=	SYM
ejpam-5504	225	3	pd⊥	pd⊥	PROPN
ejpam-5504	225	4	(	(	PUNCT
ejpam-5504	225	5	r	r	NOUN
ejpam-5504	225	6	+	+	NUM
ejpam-5504	225	7	r−1)pd⊥	r−1)pd⊥	X
ejpam-5504	225	8	=	=	SYM
ejpam-5504	225	9	pd⊥	pd⊥	PROPN
ejpam-5504	225	10	(	(	PUNCT
ejpam-5504	225	11	r	r	NOUN
ejpam-5504	225	12	+	+	PROPN
ejpam-5504	225	13	r−1	r−1	PROPN
ejpam-5504	225	14	)	)	PUNCT
ejpam-5504	225	15	(	(	PUNCT
ejpam-5504	225	16	id−	id−	NUM
ejpam-5504	225	17	1	1	NUM
ejpam-5504	225	18	m	m	NOUN
ejpam-5504	225	19	m−1	m−1	PROPN
ejpam-5504	225	20	∑	∑	PUNCT
ejpam-5504	225	21	k=0	k=0	PROPN
ejpam-5504	225	22	rk	rk	PROPN
ejpam-5504	225	23	)	)	PUNCT
ejpam-5504	225	24	(	(	PUNCT
ejpam-5504	225	25	from	from	ADP
ejpam-5504	225	26	(	(	PUNCT
ejpam-5504	225	27	19	19	NUM
ejpam-5504	225	28	)	)	PUNCT
ejpam-5504	225	29	)	)	PUNCT
ejpam-5504	226	1	=	=	SYM
ejpam-5504	226	2	pd⊥	pd⊥	PROPN
ejpam-5504	226	3	(	(	PUNCT
ejpam-5504	226	4	(	(	PUNCT
ejpam-5504	226	5	r	r	NOUN
ejpam-5504	226	6	+	+	NUM
ejpam-5504	226	7	r−1)−	r−1)−	NOUN
ejpam-5504	226	8	1	1	NUM
ejpam-5504	226	9	m	m	NOUN
ejpam-5504	226	10	m−1	m−1	PROPN
ejpam-5504	226	11	∑	∑	PUNCT
ejpam-5504	226	12	k=0	k=0	PROPN
ejpam-5504	226	13	(	(	PUNCT
ejpam-5504	226	14	r	r	NOUN
ejpam-5504	226	15	+	+	CCONJ
ejpam-5504	226	16	r−1)rk	r−1)rk	NOUN
ejpam-5504	226	17	)	)	PUNCT
ejpam-5504	227	1	=	=	SYM
ejpam-5504	227	2	pd⊥	pd⊥	PROPN
ejpam-5504	227	3	(	(	PUNCT
ejpam-5504	227	4	(	(	PUNCT
ejpam-5504	227	5	r	r	NOUN
ejpam-5504	227	6	+	+	NUM
ejpam-5504	227	7	r−1)−	r−1)−	NOUN
ejpam-5504	227	8	1	1	NUM
ejpam-5504	227	9	m	m	NOUN
ejpam-5504	227	10	m−1	m−1	PROPN
ejpam-5504	227	11	∑	∑	PUNCT
ejpam-5504	227	12	k=0	k=0	PROPN
ejpam-5504	227	13	(	(	PUNCT
ejpam-5504	227	14	rk+1	rk+1	ADP
ejpam-5504	227	15	+	+	X
ejpam-5504	227	16	rk−1	rk−1	NOUN
ejpam-5504	227	17	)	)	PUNCT
ejpam-5504	227	18	)	)	PUNCT
ejpam-5504	227	19	.	.	PUNCT
ejpam-5504	228	1	s.t	s.t	PROPN
ejpam-5504	228	2	.	.	PROPN
ejpam-5504	228	3	alwadani	alwadani	PROPN
ejpam-5504	228	4	/	/	SYM
ejpam-5504	228	5	eur	eur	PROPN
ejpam-5504	228	6	.	.	PUNCT
ejpam-5504	229	1	j.	j.	PROPN
ejpam-5504	229	2	pure	pure	PROPN
ejpam-5504	229	3	appl	appl	PROPN
ejpam-5504	229	4	.	.	PROPN
ejpam-5504	229	5	math	math	PROPN
ejpam-5504	229	6	,	,	PUNCT
ejpam-5504	229	7	17	17	NUM
ejpam-5504	229	8	(	(	PUNCT
ejpam-5504	229	9	4	4	NUM
ejpam-5504	229	10	)	)	PUNCT
ejpam-5504	229	11	(	(	PUNCT
ejpam-5504	229	12	2024	2024	NUM
ejpam-5504	229	13	)	)	PUNCT
ejpam-5504	229	14	,	,	PUNCT
ejpam-5504	229	15	3660	3660	NUM
ejpam-5504	229	16	-	-	SYM
ejpam-5504	229	17	3676	3676	NUM
ejpam-5504	229	18	3670	3670	NUM
ejpam-5504	229	19	since	since	SCONJ
ejpam-5504	229	20	r	r	NOUN
ejpam-5504	229	21	has	have	VERB
ejpam-5504	229	22	rank	rank	PROPN
ejpam-5504	229	23	m	m	PROPN
ejpam-5504	229	24	,	,	PUNCT
ejpam-5504	229	25	the	the	DET
ejpam-5504	229	26	following	follow	VERB
ejpam-5504	229	27	holds	hold	VERB
ejpam-5504	229	28	:	:	PUNCT
ejpam-5504	229	29	m−1	m−1	PROPN
ejpam-5504	229	30	∑	∑	PUNCT
ejpam-5504	229	31	k=0	k=0	PROPN
ejpam-5504	229	32	rk+1	rk+1	ADP
ejpam-5504	229	33	=	=	SYM
ejpam-5504	229	34	m−1	m−1	PROPN
ejpam-5504	229	35	∑	∑	PUNCT
ejpam-5504	229	36	k=0	k=0	PROPN
ejpam-5504	229	37	rk−1	rk−1	PROPN
ejpam-5504	229	38	=	=	SYM
ejpam-5504	229	39	m−1	m−1	PROPN
ejpam-5504	229	40	∑	∑	PUNCT
ejpam-5504	229	41	k=0	k=0	PROPN
ejpam-5504	229	42	rk	rk	PROPN
ejpam-5504	229	43	.	.	PUNCT
ejpam-5504	230	1	(	(	PUNCT
ejpam-5504	230	2	21	21	NUM
ejpam-5504	230	3	)	)	PUNCT
ejpam-5504	230	4	moreover	moreover	ADV
ejpam-5504	230	5	,	,	PUNCT
ejpam-5504	230	6	rl	rl	ADP
ejpam-5504	230	7	m−1	m−1	PROPN
ejpam-5504	230	8	∑	∑	PUNCT
ejpam-5504	230	9	k=0	k=0	PROPN
ejpam-5504	230	10	rk	rk	NOUN
ejpam-5504	230	11	=	=	SYM
ejpam-5504	230	12	m−1	m−1	PROPN
ejpam-5504	230	13	∑	∑	PUNCT
ejpam-5504	230	14	k=0	k=0	PROPN
ejpam-5504	230	15	rl+k	rl+k	PROPN
ejpam-5504	230	16	=	=	SYM
ejpam-5504	230	17	m−1	m−1	PROPN
ejpam-5504	230	18	∑	∑	PUNCT
ejpam-5504	230	19	k=0	k=0	PROPN
ejpam-5504	230	20	rk	rk	PROPN
ejpam-5504	230	21	(	(	PUNCT
ejpam-5504	230	22	22	22	NUM
ejpam-5504	230	23	)	)	PUNCT
ejpam-5504	230	24	thus	thus	ADV
ejpam-5504	230	25	,	,	PUNCT
ejpam-5504	230	26	(	(	PUNCT
ejpam-5504	230	27	r	r	NOUN
ejpam-5504	230	28	+	+	PROPN
ejpam-5504	230	29	r−1	r−1	PROPN
ejpam-5504	230	30	)	)	PUNCT
ejpam-5504	230	31	(	(	PUNCT
ejpam-5504	230	32	1	1	NUM
ejpam-5504	230	33	m	m	NOUN
ejpam-5504	230	34	m−1	m−1	PROPN
ejpam-5504	230	35	∑	∑	PUNCT
ejpam-5504	230	36	k=0	k=0	PROPN
ejpam-5504	230	37	rk	rk	NOUN
ejpam-5504	230	38	)	)	PUNCT
ejpam-5504	230	39	=	=	PUNCT
ejpam-5504	231	1	1	1	NUM
ejpam-5504	231	2	m	m	VERB
ejpam-5504	231	3	m−1	m−1	PROPN
ejpam-5504	231	4	∑	∑	PUNCT
ejpam-5504	231	5	k=0	k=0	PROPN
ejpam-5504	231	6	(	(	PUNCT
ejpam-5504	231	7	rk+1	rk+1	ADP
ejpam-5504	231	8	+	+	X
ejpam-5504	231	9	rk−1	rk−1	NOUN
ejpam-5504	231	10	)	)	PUNCT
ejpam-5504	231	11	=	=	SYM
ejpam-5504	231	12	2	2	NUM
ejpam-5504	231	13	m	m	NOUN
ejpam-5504	231	14	m−1	m−1	PROPN
ejpam-5504	231	15	∑	∑	PUNCT
ejpam-5504	231	16	k=0	k=0	PROPN
ejpam-5504	231	17	rk	rk	PROPN
ejpam-5504	231	18	.	.	PUNCT
ejpam-5504	232	1	(	(	PUNCT
ejpam-5504	232	2	23	23	NUM
ejpam-5504	232	3	)	)	PUNCT
ejpam-5504	232	4	therefore	therefore	ADV
ejpam-5504	232	5	,	,	PUNCT
ejpam-5504	232	6	pd⊥	pd⊥	PROPN
ejpam-5504	232	7	(	(	PUNCT
ejpam-5504	232	8	r	r	NOUN
ejpam-5504	232	9	+	+	NUM
ejpam-5504	232	10	r∗)pd⊥	r∗)pd⊥	PROPN
ejpam-5504	232	11	=	=	SYM
ejpam-5504	232	12	pd⊥	pd⊥	PROPN
ejpam-5504	232	13	(	(	PUNCT
ejpam-5504	232	14	(	(	PUNCT
ejpam-5504	232	15	r	r	NOUN
ejpam-5504	232	16	+	+	NUM
ejpam-5504	232	17	r−1)−	r−1)−	NOUN
ejpam-5504	232	18	1	1	NUM
ejpam-5504	232	19	m	m	NOUN
ejpam-5504	232	20	m−1	m−1	PROPN
ejpam-5504	232	21	∑	∑	PUNCT
ejpam-5504	232	22	k=0	k=0	PROPN
ejpam-5504	232	23	(	(	PUNCT
ejpam-5504	232	24	rk+1	rk+1	ADP
ejpam-5504	232	25	+	+	X
ejpam-5504	232	26	rk−1	rk−1	NOUN
ejpam-5504	232	27	)	)	PUNCT
ejpam-5504	232	28	)	)	PUNCT
ejpam-5504	233	1	=	=	SYM
ejpam-5504	233	2	pd⊥	pd⊥	PROPN
ejpam-5504	233	3	(	(	PUNCT
ejpam-5504	233	4	(	(	PUNCT
ejpam-5504	233	5	r	r	NOUN
ejpam-5504	233	6	+	+	X
ejpam-5504	233	7	r−1)−	r−1)−	ADJ
ejpam-5504	233	8	2	2	NUM
ejpam-5504	233	9	m	m	NOUN
ejpam-5504	233	10	m−1	m−1	PROPN
ejpam-5504	233	11	∑	∑	PUNCT
ejpam-5504	233	12	k=0	k=0	PROPN
ejpam-5504	233	13	rk	rk	PROPN
ejpam-5504	233	14	)	)	PUNCT
ejpam-5504	233	15	=	=	PUNCT
ejpam-5504	233	16	(	(	PUNCT
ejpam-5504	233	17	id−	id−	NUM
ejpam-5504	233	18	1	1	NUM
ejpam-5504	233	19	m	m	NOUN
ejpam-5504	233	20	m−1	m−1	PROPN
ejpam-5504	233	21	∑	∑	PUNCT
ejpam-5504	233	22	k=0	k=0	PROPN
ejpam-5504	233	23	rk	rk	PROPN
ejpam-5504	233	24	)	)	PUNCT
ejpam-5504	233	25	(	(	PUNCT
ejpam-5504	233	26	(	(	PUNCT
ejpam-5504	233	27	r	r	NOUN
ejpam-5504	233	28	+	+	X
ejpam-5504	233	29	r−1)−	r−1)−	ADJ
ejpam-5504	233	30	2	2	NUM
ejpam-5504	233	31	m	m	NOUN
ejpam-5504	233	32	m−1	m−1	PROPN
ejpam-5504	233	33	∑	∑	PUNCT
ejpam-5504	233	34	k=0	k=0	PROPN
ejpam-5504	233	35	rk	rk	PROPN
ejpam-5504	233	36	)	)	PUNCT
ejpam-5504	233	37	=	=	PUNCT
ejpam-5504	233	38	(	(	PUNCT
ejpam-5504	233	39	(	(	PUNCT
ejpam-5504	233	40	r	r	NOUN
ejpam-5504	233	41	+	+	X
ejpam-5504	233	42	r−1)−	r−1)−	ADJ
ejpam-5504	233	43	2	2	NUM
ejpam-5504	233	44	m	m	NOUN
ejpam-5504	233	45	m−1	m−1	PROPN
ejpam-5504	233	46	∑	∑	PUNCT
ejpam-5504	233	47	k=0	k=0	PROPN
ejpam-5504	233	48	rk	rk	PROPN
ejpam-5504	233	49	)	)	PUNCT
ejpam-5504	233	50	−	−	PROPN
ejpam-5504	234	1	(	(	PUNCT
ejpam-5504	234	2	1	1	NUM
ejpam-5504	234	3	m	m	NOUN
ejpam-5504	234	4	m−1	m−1	PROPN
ejpam-5504	234	5	∑	∑	PUNCT
ejpam-5504	234	6	k=0	k=0	PROPN
ejpam-5504	234	7	rk	rk	PROPN
ejpam-5504	234	8	)	)	PUNCT
ejpam-5504	234	9	(	(	PUNCT
ejpam-5504	234	10	(	(	PUNCT
ejpam-5504	234	11	r	r	NOUN
ejpam-5504	234	12	+	+	X
ejpam-5504	234	13	r−1)−	r−1)−	ADJ
ejpam-5504	234	14	2	2	NUM
ejpam-5504	234	15	m	m	NOUN
ejpam-5504	234	16	m−1	m−1	PROPN
ejpam-5504	234	17	∑	∑	PUNCT
ejpam-5504	234	18	k=0	k=0	PROPN
ejpam-5504	234	19	rk	rk	PROPN
ejpam-5504	234	20	)	)	PUNCT
ejpam-5504	234	21	=	=	PUNCT
ejpam-5504	235	1	(	(	PUNCT
ejpam-5504	235	2	(	(	PUNCT
ejpam-5504	235	3	r	r	NOUN
ejpam-5504	235	4	+	+	X
ejpam-5504	235	5	r−1)−	r−1)−	ADJ
ejpam-5504	235	6	2	2	NUM
ejpam-5504	235	7	m	m	NOUN
ejpam-5504	235	8	m−1	m−1	PROPN
ejpam-5504	235	9	∑	∑	PUNCT
ejpam-5504	235	10	k=0	k=0	PROPN
ejpam-5504	235	11	rk	rk	PROPN
ejpam-5504	235	12	)	)	PUNCT
ejpam-5504	236	1	−	−	PROPN
ejpam-5504	237	1	(	(	PUNCT
ejpam-5504	237	2	2	2	NUM
ejpam-5504	237	3	m	m	NOUN
ejpam-5504	237	4	m−1	m−1	PROPN
ejpam-5504	237	5	∑	∑	PUNCT
ejpam-5504	237	6	k=0	k=0	PROPN
ejpam-5504	237	7	rk	rk	VERB
ejpam-5504	237	8	−	−	NUM
ejpam-5504	237	9	2	2	NUM
ejpam-5504	237	10	m2	m2	PROPN
ejpam-5504	237	11	m−1	m−1	PROPN
ejpam-5504	237	12	∑	∑	PUNCT
ejpam-5504	237	13	l=0	l=0	PROPN
ejpam-5504	237	14	rl	rl	ADP
ejpam-5504	237	15	m−1	m−1	PROPN
ejpam-5504	237	16	∑	∑	PUNCT
ejpam-5504	237	17	k=0	k=0	PROPN
ejpam-5504	237	18	rk	rk	PROPN
ejpam-5504	237	19	)	)	PUNCT
ejpam-5504	237	20	=	=	PUNCT
ejpam-5504	238	1	(	(	PUNCT
ejpam-5504	238	2	(	(	PUNCT
ejpam-5504	238	3	r	r	NOUN
ejpam-5504	238	4	+	+	X
ejpam-5504	238	5	r−1)−	r−1)−	ADJ
ejpam-5504	238	6	2	2	NUM
ejpam-5504	238	7	m	m	NOUN
ejpam-5504	238	8	m−1	m−1	PROPN
ejpam-5504	238	9	∑	∑	PUNCT
ejpam-5504	238	10	k=0	k=0	PROPN
ejpam-5504	238	11	rk	rk	PROPN
ejpam-5504	238	12	)	)	PUNCT
ejpam-5504	239	1	−	−	PROPN
ejpam-5504	240	1	(	(	PUNCT
ejpam-5504	240	2	2	2	NUM
ejpam-5504	240	3	m	m	NOUN
ejpam-5504	240	4	m−1	m−1	PROPN
ejpam-5504	240	5	∑	∑	PUNCT
ejpam-5504	240	6	k=0	k=0	PROPN
ejpam-5504	240	7	rk	rk	VERB
ejpam-5504	240	8	−	−	NUM
ejpam-5504	240	9	2	2	NUM
ejpam-5504	240	10	m2	m2	PROPN
ejpam-5504	240	11	m−1	m−1	PROPN
ejpam-5504	240	12	∑	∑	PUNCT
ejpam-5504	240	13	l=0	l=0	PROPN
ejpam-5504	240	14	m−1	m−1	PROPN
ejpam-5504	240	15	∑	∑	PUNCT
ejpam-5504	240	16	k=0	k=0	PROPN
ejpam-5504	240	17	rk	rk	PROPN
ejpam-5504	240	18	)	)	PUNCT
ejpam-5504	240	19	=	=	PUNCT
ejpam-5504	241	1	(	(	PUNCT
ejpam-5504	241	2	(	(	PUNCT
ejpam-5504	241	3	r	r	NOUN
ejpam-5504	241	4	+	+	X
ejpam-5504	241	5	r−1)−	r−1)−	ADJ
ejpam-5504	241	6	2	2	NUM
ejpam-5504	241	7	m	m	NOUN
ejpam-5504	241	8	m−1	m−1	PROPN
ejpam-5504	241	9	∑	∑	PUNCT
ejpam-5504	241	10	k=0	k=0	PROPN
ejpam-5504	241	11	rk	rk	PROPN
ejpam-5504	241	12	)	)	PUNCT
ejpam-5504	242	1	−	−	PROPN
ejpam-5504	243	1	(	(	PUNCT
ejpam-5504	243	2	2	2	NUM
ejpam-5504	243	3	m	m	NOUN
ejpam-5504	243	4	m−1	m−1	PROPN
ejpam-5504	243	5	∑	∑	PUNCT
ejpam-5504	243	6	k=0	k=0	PROPN
ejpam-5504	243	7	rk	rk	VERB
ejpam-5504	243	8	−	−	NUM
ejpam-5504	243	9	2	2	NUM
ejpam-5504	243	10	m	m	NOUN
ejpam-5504	243	11	m2	m2	PROPN
ejpam-5504	243	12	m−1	m−1	PROPN
ejpam-5504	243	13	∑	∑	PUNCT
ejpam-5504	243	14	k=0	k=0	PROPN
ejpam-5504	243	15	rk	rk	PROPN
ejpam-5504	243	16	)	)	PUNCT
ejpam-5504	243	17	=	=	PUNCT
ejpam-5504	244	1	(	(	PUNCT
ejpam-5504	244	2	(	(	PUNCT
ejpam-5504	244	3	r	r	NOUN
ejpam-5504	244	4	+	+	X
ejpam-5504	244	5	r−1)−	r−1)−	ADJ
ejpam-5504	244	6	2	2	NUM
ejpam-5504	244	7	m	m	NOUN
ejpam-5504	244	8	m−1	m−1	PROPN
ejpam-5504	244	9	∑	∑	PUNCT
ejpam-5504	244	10	k=0	k=0	PROPN
ejpam-5504	244	11	rk	rk	PROPN
ejpam-5504	244	12	)	)	PUNCT
ejpam-5504	245	1	−	−	PROPN
ejpam-5504	246	1	(	(	PUNCT
ejpam-5504	246	2	2	2	NUM
ejpam-5504	246	3	m	m	NOUN
ejpam-5504	246	4	m−1	m−1	PROPN
ejpam-5504	246	5	∑	∑	PUNCT
ejpam-5504	246	6	k=0	k=0	PROPN
ejpam-5504	246	7	rk	rk	VERB
ejpam-5504	246	8	−	−	NUM
ejpam-5504	246	9	2	2	NUM
ejpam-5504	246	10	m	m	NOUN
ejpam-5504	246	11	m−1	m−1	PROPN
ejpam-5504	246	12	∑	∑	PUNCT
ejpam-5504	246	13	k=0	k=0	PROPN
ejpam-5504	246	14	rk	rk	PROPN
ejpam-5504	246	15	)	)	PUNCT
ejpam-5504	246	16	=	=	PUNCT
ejpam-5504	247	1	(	(	PUNCT
ejpam-5504	247	2	(	(	PUNCT
ejpam-5504	247	3	r	r	NOUN
ejpam-5504	247	4	+	+	X
ejpam-5504	247	5	r−1)−	r−1)−	ADJ
ejpam-5504	247	6	2	2	NUM
ejpam-5504	247	7	m	m	NOUN
ejpam-5504	247	8	m−1	m−1	PROPN
ejpam-5504	247	9	∑	∑	PUNCT
ejpam-5504	247	10	k=0	k=0	PROPN
ejpam-5504	247	11	rk	rk	PROPN
ejpam-5504	247	12	)	)	PUNCT
ejpam-5504	247	13	.	.	PUNCT
ejpam-5504	248	1	first	first	ADV
ejpam-5504	248	2	:	:	PUNCT
ejpam-5504	248	3	assume	assume	VERB
ejpam-5504	248	4	that	that	SCONJ
ejpam-5504	248	5	m	m	VERB
ejpam-5504	248	6	>	>	X
ejpam-5504	249	1	2	2	X
ejpam-5504	249	2	.	.	PUNCT
ejpam-5504	249	3	therefore	therefore	ADV
ejpam-5504	249	4	,	,	PUNCT
ejpam-5504	249	5	max{1	max{1	PROPN
ejpam-5504	249	6	,	,	PUNCT
ejpam-5504	249	7	m	m	VERB
ejpam-5504	249	8	−	−	NOUN
ejpam-5504	249	9	2	2	NUM
ejpam-5504	249	10	}	}	PUNCT
ejpam-5504	249	11	=	=	PUNCT
ejpam-5504	249	12	m	m	VERB
ejpam-5504	249	13	−	−	NOUN
ejpam-5504	249	14	2	2	NUM
ejpam-5504	249	15	.	.	PUNCT
ejpam-5504	250	1	then	then	ADV
ejpam-5504	250	2	pd⊥	pd⊥	PROPN
ejpam-5504	250	3	(	(	PUNCT
ejpam-5504	250	4	r	r	NOUN
ejpam-5504	250	5	+	+	PROPN
ejpam-5504	250	6	r∗)pd⊥	r∗)pd⊥	PROPN
ejpam-5504	250	7	=	=	PRON
ejpam-5504	250	8	(	(	PUNCT
ejpam-5504	250	9	r	r	NOUN
ejpam-5504	250	10	+	+	SYM
ejpam-5504	250	11	r−1)−	r−1)−	ADJ
ejpam-5504	250	12	2	2	NUM
ejpam-5504	250	13	m	m	NOUN
ejpam-5504	250	14	m−1	m−1	PROPN
ejpam-5504	250	15	∑	∑	PUNCT
ejpam-5504	250	16	k=0	k=0	PROPN
ejpam-5504	250	17	rk	rk	VERB
ejpam-5504	250	18	s.t	s.t	PROPN
ejpam-5504	250	19	.	.	PROPN
ejpam-5504	250	20	alwadani	alwadani	PROPN
ejpam-5504	250	21	/	/	SYM
ejpam-5504	250	22	eur	eur	PROPN
ejpam-5504	250	23	.	.	PUNCT
ejpam-5504	251	1	j.	j.	PROPN
ejpam-5504	251	2	pure	pure	PROPN
ejpam-5504	251	3	appl	appl	PROPN
ejpam-5504	251	4	.	.	PROPN
ejpam-5504	251	5	math	math	PROPN
ejpam-5504	251	6	,	,	PUNCT
ejpam-5504	251	7	17	17	NUM
ejpam-5504	251	8	(	(	PUNCT
ejpam-5504	251	9	4	4	NUM
ejpam-5504	251	10	)	)	PUNCT
ejpam-5504	251	11	(	(	PUNCT
ejpam-5504	251	12	2024	2024	NUM
ejpam-5504	251	13	)	)	PUNCT
ejpam-5504	251	14	,	,	PUNCT
ejpam-5504	251	15	3660	3660	NUM
ejpam-5504	251	16	-	-	SYM
ejpam-5504	251	17	3676	3676	NUM
ejpam-5504	251	18	3671	3671	NUM
ejpam-5504	251	19	=	=	SYM
ejpam-5504	251	20	2	2	NUM
ejpam-5504	251	21	m	m	NOUN
ejpam-5504	251	22	(	(	PUNCT
ejpam-5504	251	23	m	m	VERB
ejpam-5504	251	24	2	2	NUM
ejpam-5504	251	25	(	(	PUNCT
ejpam-5504	251	26	r	r	NOUN
ejpam-5504	251	27	+	+	PROPN
ejpam-5504	251	28	r−1)−	r−1)−	NOUN
ejpam-5504	251	29	m−1	m−1	PROPN
ejpam-5504	251	30	∑	∑	ADP
ejpam-5504	251	31	k=0	k=0	PROPN
ejpam-5504	251	32	rk	rk	PROPN
ejpam-5504	251	33	)	)	PUNCT
ejpam-5504	251	34	=	=	PUNCT
ejpam-5504	252	1	2	2	NUM
ejpam-5504	252	2	m	m	VERB
ejpam-5504	252	3	(	(	PUNCT
ejpam-5504	252	4	(	(	PUNCT
ejpam-5504	252	5	m	m	PROPN
ejpam-5504	252	6	2	2	NUM
ejpam-5504	252	7	−	−	NOUN
ejpam-5504	252	8	1	1	NUM
ejpam-5504	252	9	)	)	PUNCT
ejpam-5504	252	10	(	(	PUNCT
ejpam-5504	252	11	r	r	NOUN
ejpam-5504	252	12	+	+	NUM
ejpam-5504	252	13	r−1)−	r−1)−	ADJ
ejpam-5504	252	14	id−	id−	NOUN
ejpam-5504	252	15	m−2	m−2	PROPN
ejpam-5504	252	16	∑	∑	ADP
ejpam-5504	252	17	k=2	k=2	PROPN
ejpam-5504	252	18	rk	rk	PROPN
ejpam-5504	252	19	)	)	PUNCT
ejpam-5504	252	20	=	=	PUNCT
ejpam-5504	252	21	2	2	NUM
ejpam-5504	252	22	m	m	NOUN
ejpam-5504	252	23	(	(	PUNCT
ejpam-5504	252	24	−	−	PROPN
ejpam-5504	252	25	id+	id+	PROPN
ejpam-5504	252	26	m	m	PROPN
ejpam-5504	252	27	−	−	PROPN
ejpam-5504	252	28	2	2	NUM
ejpam-5504	252	29	2	2	NUM
ejpam-5504	252	30	(	(	PUNCT
ejpam-5504	252	31	r	r	NOUN
ejpam-5504	252	32	+	+	NOUN
ejpam-5504	252	33	rm−1)−	rm−1)−	PROPN
ejpam-5504	252	34	m−2	m−2	NUM
ejpam-5504	252	35	∑	∑	ADP
ejpam-5504	252	36	k=2	k=2	PROPN
ejpam-5504	252	37	rk	rk	PROPN
ejpam-5504	252	38	)	)	PUNCT
ejpam-5504	252	39	,	,	PUNCT
ejpam-5504	252	40	which	which	PRON
ejpam-5504	252	41	prove	prove	VERB
ejpam-5504	252	42	(	(	PUNCT
ejpam-5504	252	43	20	20	NUM
ejpam-5504	252	44	)	)	PUNCT
ejpam-5504	252	45	when	when	SCONJ
ejpam-5504	252	46	m	m	VERB
ejpam-5504	252	47	>	>	X
ejpam-5504	252	48	2	2	X
ejpam-5504	252	49	.	.	PUNCT
ejpam-5504	253	1	next	next	ADV
ejpam-5504	253	2	,	,	PUNCT
ejpam-5504	253	3	assume	assume	VERB
ejpam-5504	253	4	that	that	SCONJ
ejpam-5504	253	5	m	m	VERB
ejpam-5504	253	6	=	=	ADJ
ejpam-5504	254	1	2	2	X
ejpam-5504	254	2	.	.	PUNCT
ejpam-5504	254	3	then	then	ADV
ejpam-5504	254	4	max{1	max{1	NOUN
ejpam-5504	254	5	,	,	PUNCT
ejpam-5504	254	6	m	m	VERB
ejpam-5504	254	7	−	−	NOUN
ejpam-5504	254	8	1	1	NUM
ejpam-5504	254	9	}	}	PUNCT
ejpam-5504	254	10	=	=	SYM
ejpam-5504	254	11	1	1	NUM
ejpam-5504	254	12	and	and	CCONJ
ejpam-5504	254	13	r−1	r−1	PROPN
ejpam-5504	254	14	=	=	PUNCT
ejpam-5504	254	15	r2−1	r2−1	PROPN
ejpam-5504	254	16	=	=	SYM
ejpam-5504	254	17	r.	r.	PROPN
ejpam-5504	254	18	therefore	therefore	ADV
ejpam-5504	254	19	,	,	PUNCT
ejpam-5504	254	20	pd⊥	pd⊥	PROPN
ejpam-5504	254	21	(	(	PUNCT
ejpam-5504	254	22	r	r	NOUN
ejpam-5504	254	23	+	+	PROPN
ejpam-5504	254	24	r∗)pd⊥	r∗)pd⊥	PROPN
ejpam-5504	255	1	=	=	PRON
ejpam-5504	256	1	(	(	PUNCT
ejpam-5504	256	2	r	r	NOUN
ejpam-5504	256	3	+	+	SYM
ejpam-5504	256	4	r−1)−	r−1)−	ADJ
ejpam-5504	256	5	2	2	NUM
ejpam-5504	256	6	m	m	NOUN
ejpam-5504	256	7	m−1	m−1	PROPN
ejpam-5504	256	8	∑	∑	PUNCT
ejpam-5504	256	9	k=0	k=0	PROPN
ejpam-5504	256	10	rk	rk	NOUN
ejpam-5504	256	11	=	=	SYM
ejpam-5504	256	12	2r	2r	NUM
ejpam-5504	256	13	−	−	NOUN
ejpam-5504	256	14	2	2	NUM
ejpam-5504	256	15	2	2	NUM
ejpam-5504	256	16	(	(	PUNCT
ejpam-5504	256	17	id+r	id+r	ADV
ejpam-5504	256	18	)	)	PUNCT
ejpam-5504	256	19	=	=	SYM
ejpam-5504	257	1	2r	2r	NUM
ejpam-5504	257	2	−	−	NOUN
ejpam-5504	258	1	id−r	id−r	NOUN
ejpam-5504	258	2	=	=	NOUN
ejpam-5504	258	3	r	r	NOUN
ejpam-5504	258	4	−	−	PROPN
ejpam-5504	258	5	i	i	PROPN
ejpam-5504	258	6	d	d	PROPN
ejpam-5504	258	7	.	.	PUNCT
ejpam-5504	259	1	on	on	ADP
ejpam-5504	259	2	the	the	DET
ejpam-5504	259	3	other	other	ADJ
ejpam-5504	259	4	hand	hand	NOUN
ejpam-5504	259	5	,	,	PUNCT
ejpam-5504	259	6	2	2	NUM
ejpam-5504	259	7	m	m	VERB
ejpam-5504	259	8	(	(	PUNCT
ejpam-5504	259	9	−	−	PROPN
ejpam-5504	259	10	id+	id+	PROPN
ejpam-5504	259	11	max{1	max{1	PROPN
ejpam-5504	259	12	,	,	PUNCT
ejpam-5504	259	13	m	m	VERB
ejpam-5504	259	14	−	−	NOUN
ejpam-5504	259	15	2	2	NUM
ejpam-5504	259	16	}	}	SYM
ejpam-5504	259	17	2	2	NUM
ejpam-5504	259	18	(	(	PUNCT
ejpam-5504	259	19	r	r	NOUN
ejpam-5504	259	20	+	+	NOUN
ejpam-5504	259	21	rm−1)−	rm−1)−	PROPN
ejpam-5504	259	22	m−2	m−2	NUM
ejpam-5504	259	23	∑	∑	ADP
ejpam-5504	259	24	k=2	k=2	PROPN
ejpam-5504	259	25	rk	rk	PROPN
ejpam-5504	259	26	)	)	PUNCT
ejpam-5504	259	27	=	=	SYM
ejpam-5504	259	28	2	2	NUM
ejpam-5504	259	29	2	2	NUM
ejpam-5504	259	30	(	(	PUNCT
ejpam-5504	259	31	−	−	PROPN
ejpam-5504	259	32	id+	id+	PROPN
ejpam-5504	259	33	1	1	NUM
ejpam-5504	259	34	2	2	NUM
ejpam-5504	259	35	(	(	PUNCT
ejpam-5504	259	36	r	r	NOUN
ejpam-5504	259	37	+	+	NOUN
ejpam-5504	259	38	r	r	NOUN
ejpam-5504	259	39	)	)	PUNCT
ejpam-5504	260	1	−	−	NOUN
ejpam-5504	260	2	0	0	NUM
ejpam-5504	260	3	∑	∑	NOUN
ejpam-5504	260	4	k=2	k=2	PROPN
ejpam-5504	260	5	rk	rk	PROPN
ejpam-5504	260	6	)	)	PUNCT
ejpam-5504	261	1	=	=	PUNCT
ejpam-5504	262	1	−	−	PROPN
ejpam-5504	262	2	id+	id+	NOUN
ejpam-5504	262	3	1	1	NUM
ejpam-5504	262	4	2	2	NUM
ejpam-5504	262	5	(	(	PUNCT
ejpam-5504	262	6	2r)−	2r)−	NUM
ejpam-5504	262	7	0	0	NUM
ejpam-5504	263	1	=	=	SYM
ejpam-5504	264	1	−	−	ADP
ejpam-5504	264	2	id+r	id+r	NOUN
ejpam-5504	264	3	,	,	PUNCT
ejpam-5504	264	4	so	so	SCONJ
ejpam-5504	264	5	equality	equality	NOUN
ejpam-5504	264	6	holds	hold	VERB
ejpam-5504	264	7	when	when	SCONJ
ejpam-5504	264	8	m	m	VERB
ejpam-5504	264	9	=	=	SYM
ejpam-5504	264	10	2	2	X
ejpam-5504	264	11	.	.	X
ejpam-5504	264	12	■	■	NOUN
ejpam-5504	264	13	3	3	X
ejpam-5504	264	14	.	.	PUNCT
ejpam-5504	264	15	examples	example	NOUN
ejpam-5504	264	16	example	example	NOUN
ejpam-5504	264	17	1	1	NUM
ejpam-5504	264	18	(	(	PUNCT
ejpam-5504	264	19	isometry	isometry	NOUN
ejpam-5504	264	20	of	of	ADP
ejpam-5504	264	21	finite	finite	PROPN
ejpam-5504	264	22	rank	rank	PROPN
ejpam-5504	264	23	)	)	PUNCT
ejpam-5504	264	24	.	.	PUNCT
ejpam-5504	265	1	let	let	VERB
ejpam-5504	265	2	m	m	PRON
ejpam-5504	265	3	∈	∈	VERB
ejpam-5504	265	4	{	{	PUNCT
ejpam-5504	265	5	2	2	NUM
ejpam-5504	265	6	,	,	PUNCT
ejpam-5504	265	7	3	3	NUM
ejpam-5504	265	8	,	,	PUNCT
ejpam-5504	265	9	.	.	PUNCT
ejpam-5504	265	10	.	.	PUNCT
ejpam-5504	265	11	.	.	PUNCT
ejpam-5504	266	1	}	}	PUNCT
ejpam-5504	267	1	and	and	CCONJ
ejpam-5504	267	2	assume	assume	VERB
ejpam-5504	267	3	that	that	SCONJ
ejpam-5504	267	4	rm	rm	NOUN
ejpam-5504	267	5	=	=	PUNCT
ejpam-5504	267	6	i	i	PROPN
ejpam-5504	267	7	d	d	PROPN
ejpam-5504	267	8	.	.	PUNCT
ejpam-5504	268	1	(	(	PUNCT
ejpam-5504	268	2	24	24	NUM
ejpam-5504	268	3	)	)	PUNCT
ejpam-5504	268	4	then	then	ADV
ejpam-5504	268	5	the	the	DET
ejpam-5504	268	6	results	result	NOUN
ejpam-5504	268	7	in	in	ADP
ejpam-5504	268	8	section	section	NOUN
ejpam-5504	268	9	2	2	NUM
ejpam-5504	268	10	were	be	AUX
ejpam-5504	268	11	derived	derive	VERB
ejpam-5504	268	12	already	already	ADV
ejpam-5504	268	13	in	in	ADP
ejpam-5504	268	14	[	[	X
ejpam-5504	268	15	1	1	NUM
ejpam-5504	268	16	]	]	PUNCT
ejpam-5504	268	17	.	.	PUNCT
ejpam-5504	269	1	moreover	moreover	ADV
ejpam-5504	269	2	,	,	PUNCT
ejpam-5504	269	3	the	the	DET
ejpam-5504	269	4	work	work	NOUN
ejpam-5504	269	5	there	there	ADV
ejpam-5504	269	6	based	base	VERB
ejpam-5504	269	7	on	on	ADP
ejpam-5504	269	8	exploiting	exploit	VERB
ejpam-5504	269	9	(	(	PUNCT
ejpam-5504	269	10	24	24	NUM
ejpam-5504	269	11	)	)	PUNCT
ejpam-5504	269	12	yielded	yield	VERB
ejpam-5504	269	13	to	to	ADP
ejpam-5504	269	14	(	(	PUNCT
ejpam-5504	269	15	19	19	NUM
ejpam-5504	269	16	)	)	PUNCT
ejpam-5504	269	17	and	and	CCONJ
ejpam-5504	269	18	t	t	X
ejpam-5504	269	19	=	=	SYM
ejpam-5504	270	1	1	1	NUM
ejpam-5504	270	2	2	2	NUM
ejpam-5504	270	3	m	m	NOUN
ejpam-5504	270	4	m−1	m−1	PROPN
ejpam-5504	270	5	∑	∑	PUNCT
ejpam-5504	270	6	k=1	k=1	X
ejpam-5504	270	7	(	(	PUNCT
ejpam-5504	270	8	m	m	VERB
ejpam-5504	270	9	−	−	PROPN
ejpam-5504	270	10	2k	2k	NUM
ejpam-5504	270	11	)	)	PUNCT
ejpam-5504	270	12	rk	rk	NOUN
ejpam-5504	270	13	=	=	SYM
ejpam-5504	270	14	−t∗	−t∗	PROPN
ejpam-5504	270	15	,	,	PUNCT
ejpam-5504	270	16	(	(	PUNCT
ejpam-5504	270	17	25	25	NUM
ejpam-5504	270	18	)	)	PUNCT
ejpam-5504	270	19	which	which	PRON
ejpam-5504	270	20	is	be	AUX
ejpam-5504	270	21	always	always	ADV
ejpam-5504	270	22	skew	skew	ADJ
ejpam-5504	270	23	right	right	ADJ
ejpam-5504	270	24	-	-	PUNCT
ejpam-5504	270	25	shift	shift	NOUN
ejpam-5504	270	26	operator	operator	NOUN
ejpam-5504	270	27	,	,	PUNCT
ejpam-5504	270	28	t	t	PROPN
ejpam-5504	270	29	is	be	AUX
ejpam-5504	270	30	symmetric	symmetric	ADJ
ejpam-5504	270	31	only	only	ADV
ejpam-5504	270	32	when	when	SCONJ
ejpam-5504	270	33	m	m	VERB
ejpam-5504	270	34	=	=	SYM
ejpam-5504	270	35	2	2	X
ejpam-5504	270	36	.	.	X
ejpam-5504	270	37	s.t	s.t	PROPN
ejpam-5504	270	38	.	.	PROPN
ejpam-5504	270	39	alwadani	alwadani	PROPN
ejpam-5504	270	40	/	/	SYM
ejpam-5504	270	41	eur	eur	PROPN
ejpam-5504	270	42	.	.	PUNCT
ejpam-5504	271	1	j.	j.	PROPN
ejpam-5504	271	2	pure	pure	PROPN
ejpam-5504	271	3	appl	appl	PROPN
ejpam-5504	271	4	.	.	PROPN
ejpam-5504	271	5	math	math	PROPN
ejpam-5504	271	6	,	,	PUNCT
ejpam-5504	271	7	17	17	NUM
ejpam-5504	271	8	(	(	PUNCT
ejpam-5504	271	9	4	4	NUM
ejpam-5504	271	10	)	)	PUNCT
ejpam-5504	271	11	(	(	PUNCT
ejpam-5504	271	12	2024	2024	NUM
ejpam-5504	271	13	)	)	PUNCT
ejpam-5504	271	14	,	,	PUNCT
ejpam-5504	271	15	3660	3660	NUM
ejpam-5504	271	16	-	-	SYM
ejpam-5504	271	17	3676	3676	NUM
ejpam-5504	271	18	3672	3672	NUM
ejpam-5504	271	19	example	example	NOUN
ejpam-5504	271	20	2	2	NUM
ejpam-5504	271	21	.	.	PUNCT
ejpam-5504	272	1	let	let	VERB
ejpam-5504	272	2	u	u	PRON
ejpam-5504	272	3	be	be	AUX
ejpam-5504	272	4	a	a	DET
ejpam-5504	272	5	closed	closed	ADJ
ejpam-5504	272	6	subspace	subspace	NOUN
ejpam-5504	272	7	of	of	ADP
ejpam-5504	272	8	x	x	PUNCT
ejpam-5504	272	9	and	and	CCONJ
ejpam-5504	272	10	suppose	suppose	VERB
ejpam-5504	272	11	that	that	SCONJ
ejpam-5504	272	12	r	r	NOUN
ejpam-5504	272	13	=	=	SYM
ejpam-5504	272	14	pu	pu	PROPN
ejpam-5504	272	15	.	.	PUNCT
ejpam-5504	273	1	(	(	PUNCT
ejpam-5504	273	2	26	26	NUM
ejpam-5504	273	3	)	)	PUNCT
ejpam-5504	273	4	then	then	ADV
ejpam-5504	273	5	(	(	PUNCT
ejpam-5504	273	6	i	i	NOUN
ejpam-5504	273	7	)	)	PUNCT
ejpam-5504	274	1	d	d	PROPN
ejpam-5504	274	2	=	=	PUNCT
ejpam-5504	274	3	u.	u.	PROPN
ejpam-5504	274	4	(	(	PUNCT
ejpam-5504	274	5	ii	ii	NOUN
ejpam-5504	274	6	)	)	PUNCT
ejpam-5504	274	7	id−r	id−r	NOUN
ejpam-5504	274	8	=	=	SYM
ejpam-5504	274	9	pu⊥	pu⊥	PROPN
ejpam-5504	274	10	.	.	PUNCT
ejpam-5504	275	1	(	(	PUNCT
ejpam-5504	275	2	iii	iii	NOUN
ejpam-5504	275	3	)	)	PUNCT
ejpam-5504	275	4	ran	run	VERB
ejpam-5504	275	5	(	(	PUNCT
ejpam-5504	275	6	id−r	id−r	NOUN
ejpam-5504	275	7	)	)	PUNCT
ejpam-5504	275	8	=	=	SYM
ejpam-5504	276	1	d⊥	d⊥	NOUN
ejpam-5504	276	2	is	be	AUX
ejpam-5504	276	3	closed	closed	ADJ
ejpam-5504	276	4	.	.	PUNCT
ejpam-5504	277	1	(	(	PUNCT
ejpam-5504	277	2	iv	iv	X
ejpam-5504	277	3	)	)	PUNCT
ejpam-5504	277	4	(	(	PUNCT
ejpam-5504	277	5	id−r	id−r	NOUN
ejpam-5504	277	6	)	)	PUNCT
ejpam-5504	277	7	−1	−1	NOUN
ejpam-5504	277	8	=	=	NOUN
ejpam-5504	277	9	id+nu	id+nu	NOUN
ejpam-5504	277	10	.	.	PUNCT
ejpam-5504	278	1	(	(	PUNCT
ejpam-5504	278	2	v	v	NOUN
ejpam-5504	278	3	)	)	PUNCT
ejpam-5504	278	4	t	t	NOUN
ejpam-5504	278	5	=	=	SYM
ejpam-5504	278	6	1	1	NUM
ejpam-5504	278	7	2	2	NUM
ejpam-5504	278	8	pu⊥	pu⊥	PROPN
ejpam-5504	278	9	=	=	SYM
ejpam-5504	278	10	t∗.	t∗.	PROPN
ejpam-5504	278	11	(	(	PUNCT
ejpam-5504	278	12	vi	vi	NOUN
ejpam-5504	278	13	)	)	PUNCT
ejpam-5504	278	14	t	t	NOUN
ejpam-5504	278	15	is	be	AUX
ejpam-5504	278	16	always	always	ADV
ejpam-5504	278	17	symmetric	symmetric	ADJ
ejpam-5504	278	18	,	,	PUNCT
ejpam-5504	278	19	but	but	CCONJ
ejpam-5504	278	20	skew	skew	VERB
ejpam-5504	278	21	only	only	ADV
ejpam-5504	278	22	when	when	SCONJ
ejpam-5504	278	23	u	u	NOUN
ejpam-5504	278	24	=	=	NOUN
ejpam-5504	278	25	x.	x.	NOUN
ejpam-5504	278	26	proof	proof	NOUN
ejpam-5504	278	27	.	.	PUNCT
ejpam-5504	279	1	(	(	PUNCT
ejpam-5504	279	2	i	i	NOUN
ejpam-5504	279	3	):	):	PUNCT
ejpam-5504	279	4	d	d	NOUN
ejpam-5504	279	5	=	=	PUNCT
ejpam-5504	279	6	fix	fix	NOUN
ejpam-5504	279	7	r	r	NOUN
ejpam-5504	279	8	=	=	NOUN
ejpam-5504	279	9	fix	fix	NOUN
ejpam-5504	279	10	pu	pu	NOUN
ejpam-5504	279	11	=	=	PUNCT
ejpam-5504	279	12	{	{	PUNCT
ejpam-5504	279	13	x	x	PUNCT
ejpam-5504	279	14	∈	∈	NOUN
ejpam-5504	279	15	x	x	PUNCT
ejpam-5504	279	16	|	|	NOUN
ejpam-5504	279	17	x	x	X
ejpam-5504	279	18	=	=	NOUN
ejpam-5504	279	19	pu	pu	PROPN
ejpam-5504	279	20	x	x	PROPN
ejpam-5504	279	21	}	}	PUNCT
ejpam-5504	279	22	=	=	SYM
ejpam-5504	279	23	u.	u.	NOUN
ejpam-5504	279	24	(	(	PUNCT
ejpam-5504	279	25	ii	ii	NOUN
ejpam-5504	279	26	):	):	PUNCT
ejpam-5504	279	27	id−r	id−r	NOUN
ejpam-5504	279	28	=	=	SYM
ejpam-5504	279	29	id−pu	id−pu	NOUN
ejpam-5504	279	30	=	=	VERB
ejpam-5504	279	31	pu⊥	pu⊥	PROPN
ejpam-5504	279	32	.	.	PUNCT
ejpam-5504	280	1	(	(	PUNCT
ejpam-5504	280	2	iii	iii	X
ejpam-5504	280	3	):	):	PUNCT
ejpam-5504	280	4	by	by	ADP
ejpam-5504	280	5	using	use	VERB
ejpam-5504	280	6	(	(	PUNCT
ejpam-5504	280	7	ii	ii	NOUN
ejpam-5504	280	8	)	)	PUNCT
ejpam-5504	280	9	,	,	PUNCT
ejpam-5504	280	10	we	we	PRON
ejpam-5504	280	11	obtain	obtain	AUX
ejpam-5504	280	12	ran	ran	NOUN
ejpam-5504	280	13	(	(	PUNCT
ejpam-5504	280	14	id−r	id−r	NOUN
ejpam-5504	280	15	)	)	PUNCT
ejpam-5504	280	16	=	=	PRON
ejpam-5504	280	17	ran	run	VERB
ejpam-5504	280	18	(	(	PUNCT
ejpam-5504	280	19	id−pu	id−pu	ADV
ejpam-5504	280	20	)	)	PUNCT
ejpam-5504	281	1	=	=	SYM
ejpam-5504	281	2	u⊥	u⊥	PROPN
ejpam-5504	281	3	=	=	SYM
ejpam-5504	281	4	d⊥.	d⊥.	PROPN
ejpam-5504	281	5	(	(	PUNCT
ejpam-5504	281	6	iv	iv	NUM
ejpam-5504	281	7	):	):	PUNCT
ejpam-5504	281	8	from	from	ADP
ejpam-5504	281	9	[	[	X
ejpam-5504	281	10	4	4	NUM
ejpam-5504	281	11	,	,	PUNCT
ejpam-5504	281	12	example	example	NOUN
ejpam-5504	281	13	1	1	NUM
ejpam-5504	281	14	]	]	PUNCT
ejpam-5504	281	15	,	,	PUNCT
ejpam-5504	281	16	we	we	PRON
ejpam-5504	281	17	have	have	VERB
ejpam-5504	281	18	(	(	PUNCT
ejpam-5504	281	19	id−r	id−r	NOUN
ejpam-5504	281	20	)	)	PUNCT
ejpam-5504	281	21	−1	−1	NOUN
ejpam-5504	282	1	=	=	SYM
ejpam-5504	282	2	(	(	PUNCT
ejpam-5504	282	3	id−pu	id−pu	X
ejpam-5504	282	4	)	)	PUNCT
ejpam-5504	282	5	−1	−1	NOUN
ejpam-5504	283	1	=	=	SYM
ejpam-5504	283	2	p−1	p−1	PROPN
ejpam-5504	283	3	u⊥	u⊥	PROPN
ejpam-5504	283	4	=	=	PROPN
ejpam-5504	283	5	id+nu⊥	id+nu⊥	PROPN
ejpam-5504	283	6	.	.	PUNCT
ejpam-5504	284	1	(	(	PUNCT
ejpam-5504	284	2	v	v	NOUN
ejpam-5504	284	3	):	):	PUNCT
ejpam-5504	284	4	by	by	ADP
ejpam-5504	284	5	using	use	VERB
ejpam-5504	284	6	(	(	PUNCT
ejpam-5504	284	7	8)	8)	NUM
ejpam-5504	284	8	,	,	PUNCT
ejpam-5504	284	9	we	we	PRON
ejpam-5504	284	10	have	have	VERB
ejpam-5504	284	11	t	t	NOUN
ejpam-5504	284	12	=	=	SYM
ejpam-5504	284	13	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	284	14	pd⊥	pd⊥	PROPN
ejpam-5504	284	15	−	−	NUM
ejpam-5504	284	16	1	1	NUM
ejpam-5504	284	17	2	2	NUM
ejpam-5504	284	18	pd⊥	pd⊥	PROPN
ejpam-5504	284	19	=	=	SYM
ejpam-5504	284	20	pu⊥(id+nu⊥)pu⊥	pu⊥(id+nu⊥)pu⊥	PUNCT
ejpam-5504	285	1	−	−	NOUN
ejpam-5504	285	2	1	1	NUM
ejpam-5504	285	3	2	2	NUM
ejpam-5504	285	4	pu⊥	pu⊥	NOUN
ejpam-5504	285	5	=	=	NOUN
ejpam-5504	285	6	1	1	NUM
ejpam-5504	285	7	2	2	NUM
ejpam-5504	285	8	pu⊥	pu⊥	PROPN
ejpam-5504	285	9	=	=	SYM
ejpam-5504	285	10	t∗.	t∗.	PROPN
ejpam-5504	285	11	(	(	PUNCT
ejpam-5504	285	12	vi	vi	PROPN
ejpam-5504	285	13	):	):	PUNCT
ejpam-5504	285	14	follows	follow	VERB
ejpam-5504	285	15	from	from	ADP
ejpam-5504	285	16	(	(	PUNCT
ejpam-5504	285	17	v	v	NOUN
ejpam-5504	285	18	)	)	PUNCT
ejpam-5504	285	19	.	.	PUNCT
ejpam-5504	286	1	■	■	PUNCT
ejpam-5504	286	2	example	example	NOUN
ejpam-5504	286	3	3	3	X
ejpam-5504	286	4	.	.	PUNCT
ejpam-5504	287	1	let	let	VERB
ejpam-5504	287	2	u	u	PRON
ejpam-5504	287	3	be	be	AUX
ejpam-5504	287	4	a	a	DET
ejpam-5504	287	5	closed	closed	ADJ
ejpam-5504	287	6	subspace	subspace	NOUN
ejpam-5504	287	7	of	of	ADP
ejpam-5504	287	8	x	x	PUNCT
ejpam-5504	287	9	and	and	CCONJ
ejpam-5504	287	10	suppose	suppose	VERB
ejpam-5504	287	11	that	that	SCONJ
ejpam-5504	287	12	r	r	NOUN
ejpam-5504	287	13	=	=	SYM
ejpam-5504	287	14	−pu	−pu	VERB
ejpam-5504	287	15	.	.	PUNCT
ejpam-5504	288	1	(	(	PUNCT
ejpam-5504	288	2	27	27	NUM
ejpam-5504	288	3	)	)	PUNCT
ejpam-5504	288	4	then	then	ADV
ejpam-5504	288	5	(	(	PUNCT
ejpam-5504	288	6	i	i	NOUN
ejpam-5504	288	7	)	)	PUNCT
ejpam-5504	289	1	d	d	PROPN
ejpam-5504	289	2	=	=	PUNCT
ejpam-5504	289	3	{	{	PUNCT
ejpam-5504	289	4	0	0	NUM
ejpam-5504	289	5	}	}	PUNCT
ejpam-5504	289	6	.	.	PUNCT
ejpam-5504	290	1	(	(	PUNCT
ejpam-5504	290	2	ii	ii	NOUN
ejpam-5504	290	3	)	)	PUNCT
ejpam-5504	290	4	id−r	id−r	NOUN
ejpam-5504	290	5	=	=	SYM
ejpam-5504	290	6	id+pu	id+pu	NOUN
ejpam-5504	290	7	.	.	PUNCT
ejpam-5504	291	1	(	(	PUNCT
ejpam-5504	291	2	iii	iii	NOUN
ejpam-5504	291	3	)	)	PUNCT
ejpam-5504	291	4	ran	run	VERB
ejpam-5504	291	5	(	(	PUNCT
ejpam-5504	291	6	id−r	id−r	NOUN
ejpam-5504	291	7	)	)	PUNCT
ejpam-5504	291	8	=	=	SYM
ejpam-5504	292	1	x	x	X
ejpam-5504	292	2	.	.	PUNCT
ejpam-5504	292	3	(	(	PUNCT
ejpam-5504	292	4	iv	iv	X
ejpam-5504	292	5	)	)	PUNCT
ejpam-5504	292	6	(	(	PUNCT
ejpam-5504	292	7	id−r	id−r	NOUN
ejpam-5504	292	8	)	)	PUNCT
ejpam-5504	292	9	−1	−1	NOUN
ejpam-5504	292	10	=	=	SYM
ejpam-5504	292	11	1	1	NUM
ejpam-5504	292	12	2	2	NUM
ejpam-5504	292	13	id+	id+	NOUN
ejpam-5504	292	14	1	1	NUM
ejpam-5504	292	15	2	2	NUM
ejpam-5504	292	16	pu⊥	pu⊥	NOUN
ejpam-5504	292	17	.	.	PUNCT
ejpam-5504	293	1	(	(	PUNCT
ejpam-5504	293	2	v	v	NOUN
ejpam-5504	293	3	)	)	PUNCT
ejpam-5504	293	4	t	t	NOUN
ejpam-5504	293	5	=	=	SYM
ejpam-5504	293	6	1	1	NUM
ejpam-5504	293	7	2	2	NUM
ejpam-5504	293	8	pu	pu	NOUN
ejpam-5504	293	9	.	.	PUNCT
ejpam-5504	294	1	proof	proof	NOUN
ejpam-5504	294	2	.	.	PUNCT
ejpam-5504	295	1	(	(	PUNCT
ejpam-5504	295	2	i	i	NOUN
ejpam-5504	295	3	):	):	PUNCT
ejpam-5504	295	4	d	d	NOUN
ejpam-5504	295	5	=	=	PUNCT
ejpam-5504	295	6	fix	fix	NOUN
ejpam-5504	295	7	r	r	NOUN
ejpam-5504	295	8	=	=	PUNCT
ejpam-5504	295	9	fix(−pu	fix(−pu	PROPN
ejpam-5504	295	10	)	)	PUNCT
ejpam-5504	295	11	=	=	PRON
ejpam-5504	296	1	{	{	PUNCT
ejpam-5504	296	2	x	x	PUNCT
ejpam-5504	296	3	∈	∈	NOUN
ejpam-5504	296	4	x	x	PUNCT
ejpam-5504	296	5	|	|	NOUN
ejpam-5504	296	6	x	x	X
ejpam-5504	296	7	=	=	SYM
ejpam-5504	296	8	−pu	−pu	VERB
ejpam-5504	296	9	x	x	NOUN
ejpam-5504	296	10	}	}	PUNCT
ejpam-5504	296	11	=	=	SYM
ejpam-5504	296	12	{	{	PUNCT
ejpam-5504	296	13	0	0	NUM
ejpam-5504	296	14	}	}	PUNCT
ejpam-5504	296	15	.	.	PUNCT
ejpam-5504	297	1	(	(	PUNCT
ejpam-5504	297	2	ii	ii	NOUN
ejpam-5504	297	3	):	):	PUNCT
ejpam-5504	297	4	id−r	id−r	NOUN
ejpam-5504	297	5	=	=	SYM
ejpam-5504	297	6	id+pu	id+pu	NOUN
ejpam-5504	297	7	.	.	PUNCT
ejpam-5504	298	1	(	(	PUNCT
ejpam-5504	298	2	iii	iii	X
ejpam-5504	298	3	):	):	PUNCT
ejpam-5504	298	4	by	by	ADP
ejpam-5504	298	5	[	[	X
ejpam-5504	298	6	4	4	NUM
ejpam-5504	298	7	,	,	PUNCT
ejpam-5504	298	8	minty	minty	ADJ
ejpam-5504	298	9	theorem	theorem	NOUN
ejpam-5504	298	10	]	]	X
ejpam-5504	298	11	,	,	PUNCT
ejpam-5504	298	12	i	i	PROPN
ejpam-5504	298	13	d	d	PROPN
ejpam-5504	298	14	+	+	CCONJ
ejpam-5504	298	15	pu	pu	PROPN
ejpam-5504	298	16	has	have	VERB
ejpam-5504	298	17	full	full	ADJ
ejpam-5504	298	18	range	range	NOUN
ejpam-5504	298	19	d	d	NOUN
ejpam-5504	298	20	=	=	PUNCT
ejpam-5504	298	21	x.	x.	NOUN
ejpam-5504	298	22	(	(	PUNCT
ejpam-5504	298	23	iv	iv	NUM
ejpam-5504	298	24	):	):	PUNCT
ejpam-5504	298	25	(	(	PUNCT
ejpam-5504	298	26	id−r	id−r	NOUN
ejpam-5504	298	27	)	)	PUNCT
ejpam-5504	298	28	−1	−1	NOUN
ejpam-5504	299	1	=	=	NOUN
ejpam-5504	299	2	jpu	jpu	PROPN
ejpam-5504	299	3	=	=	SYM
ejpam-5504	299	4	1	1	NUM
ejpam-5504	299	5	2	2	NUM
ejpam-5504	299	6	pu	pu	NOUN
ejpam-5504	299	7	+	+	PROPN
ejpam-5504	299	8	pu⊥	pu⊥	NOUN
ejpam-5504	299	9	=	=	NOUN
ejpam-5504	299	10	1	1	NUM
ejpam-5504	299	11	2	2	NUM
ejpam-5504	299	12	id+	id+	NOUN
ejpam-5504	299	13	1	1	NUM
ejpam-5504	299	14	2	2	NUM
ejpam-5504	299	15	pu⊥	pu⊥	NOUN
ejpam-5504	299	16	.	.	PUNCT
ejpam-5504	300	1	(	(	PUNCT
ejpam-5504	300	2	v	v	NOUN
ejpam-5504	300	3	):	):	PUNCT
ejpam-5504	300	4	we	we	PRON
ejpam-5504	300	5	have	have	VERB
ejpam-5504	300	6	t	t	NOUN
ejpam-5504	300	7	=	=	SYM
ejpam-5504	300	8	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	300	9	pd⊥	pd⊥	PROPN
ejpam-5504	300	10	−	−	NUM
ejpam-5504	300	11	1	1	NUM
ejpam-5504	300	12	2	2	NUM
ejpam-5504	300	13	pd⊥	pd⊥	PROPN
ejpam-5504	300	14	=	=	NOUN
ejpam-5504	300	15	1	1	NUM
ejpam-5504	300	16	2	2	NUM
ejpam-5504	300	17	id+	id+	NOUN
ejpam-5504	300	18	1	1	NUM
ejpam-5504	300	19	2	2	NUM
ejpam-5504	300	20	id−1	id−1	PROPN
ejpam-5504	300	21	2	2	NUM
ejpam-5504	300	22	pu⊥	pu⊥	NOUN
ejpam-5504	300	23	−	−	NOUN
ejpam-5504	301	1	1	1	NUM
ejpam-5504	301	2	2	2	NUM
ejpam-5504	301	3	i	i	PROPN
ejpam-5504	301	4	d	d	PROPN
ejpam-5504	301	5	s.t	s.t	PROPN
ejpam-5504	301	6	.	.	PROPN
ejpam-5504	301	7	alwadani	alwadani	PROPN
ejpam-5504	301	8	/	/	SYM
ejpam-5504	301	9	eur	eur	PROPN
ejpam-5504	301	10	.	.	PUNCT
ejpam-5504	302	1	j.	j.	PROPN
ejpam-5504	302	2	pure	pure	PROPN
ejpam-5504	302	3	appl	appl	PROPN
ejpam-5504	302	4	.	.	PROPN
ejpam-5504	302	5	math	math	PROPN
ejpam-5504	302	6	,	,	PUNCT
ejpam-5504	302	7	17	17	NUM
ejpam-5504	302	8	(	(	PUNCT
ejpam-5504	302	9	4	4	NUM
ejpam-5504	302	10	)	)	PUNCT
ejpam-5504	302	11	(	(	PUNCT
ejpam-5504	302	12	2024	2024	NUM
ejpam-5504	302	13	)	)	PUNCT
ejpam-5504	302	14	,	,	PUNCT
ejpam-5504	302	15	3660	3660	NUM
ejpam-5504	302	16	-	-	SYM
ejpam-5504	302	17	3676	3676	NUM
ejpam-5504	302	18	3673	3673	NUM
ejpam-5504	302	19	=	=	SYM
ejpam-5504	302	20	1	1	NUM
ejpam-5504	302	21	2	2	NUM
ejpam-5504	302	22	pu	pu	NOUN
ejpam-5504	302	23	.	.	PUNCT
ejpam-5504	303	1	■	■	PUNCT
ejpam-5504	303	2	example	example	NOUN
ejpam-5504	303	3	4	4	X
ejpam-5504	303	4	.	.	PUNCT
ejpam-5504	304	1	let	let	VERB
ejpam-5504	304	2	u	u	PRON
ejpam-5504	304	3	be	be	AUX
ejpam-5504	304	4	a	a	DET
ejpam-5504	304	5	closed	closed	ADJ
ejpam-5504	304	6	subspace	subspace	NOUN
ejpam-5504	304	7	of	of	ADP
ejpam-5504	304	8	x	x	PUNCT
ejpam-5504	304	9	and	and	CCONJ
ejpam-5504	304	10	suppose	suppose	VERB
ejpam-5504	304	11	that	that	SCONJ
ejpam-5504	304	12	r	r	NOUN
ejpam-5504	304	13	=	=	SYM
ejpam-5504	304	14	ru	ru	NOUN
ejpam-5504	304	15	.	.	PUNCT
ejpam-5504	305	1	(	(	PUNCT
ejpam-5504	305	2	28	28	NUM
ejpam-5504	305	3	)	)	PUNCT
ejpam-5504	305	4	then	then	ADV
ejpam-5504	305	5	(	(	PUNCT
ejpam-5504	305	6	i	i	NOUN
ejpam-5504	305	7	)	)	PUNCT
ejpam-5504	306	1	d	d	PROPN
ejpam-5504	306	2	=	=	PUNCT
ejpam-5504	306	3	u.	u.	PROPN
ejpam-5504	306	4	(	(	PUNCT
ejpam-5504	306	5	ii	ii	NOUN
ejpam-5504	306	6	)	)	PUNCT
ejpam-5504	306	7	id−r	id−r	NOUN
ejpam-5504	306	8	=	=	SYM
ejpam-5504	306	9	2	2	NUM
ejpam-5504	306	10	pu⊥	pu⊥	NOUN
ejpam-5504	306	11	.	.	PUNCT
ejpam-5504	307	1	(	(	PUNCT
ejpam-5504	307	2	iii	iii	NOUN
ejpam-5504	307	3	)	)	PUNCT
ejpam-5504	307	4	ran	run	VERB
ejpam-5504	307	5	(	(	PUNCT
ejpam-5504	307	6	id−r	id−r	NOUN
ejpam-5504	307	7	)	)	PUNCT
ejpam-5504	307	8	=	=	SYM
ejpam-5504	308	1	d⊥	d⊥	NOUN
ejpam-5504	308	2	is	be	AUX
ejpam-5504	308	3	closed	closed	ADJ
ejpam-5504	308	4	.	.	PUNCT
ejpam-5504	309	1	(	(	PUNCT
ejpam-5504	309	2	iv	iv	X
ejpam-5504	309	3	)	)	PUNCT
ejpam-5504	309	4	(	(	PUNCT
ejpam-5504	309	5	id−r	id−r	NOUN
ejpam-5504	309	6	)	)	PUNCT
ejpam-5504	309	7	−1	−1	NOUN
ejpam-5504	310	1	=	=	SYM
ejpam-5504	310	2	1	1	NUM
ejpam-5504	310	3	2	2	NUM
ejpam-5504	310	4	id+nu	id+nu	NOUN
ejpam-5504	310	5	.	.	PUNCT
ejpam-5504	311	1	(	(	PUNCT
ejpam-5504	311	2	v	v	NOUN
ejpam-5504	311	3	)	)	PUNCT
ejpam-5504	311	4	t	t	NOUN
ejpam-5504	311	5	=	=	SYM
ejpam-5504	312	1	0	0	X
ejpam-5504	312	2	.	.	PUNCT
ejpam-5504	313	1	proof	proof	NOUN
ejpam-5504	313	2	.	.	PUNCT
ejpam-5504	314	1	(	(	PUNCT
ejpam-5504	314	2	i	i	NOUN
ejpam-5504	314	3	):	):	PUNCT
ejpam-5504	314	4	d	d	NOUN
ejpam-5504	314	5	=	=	PUNCT
ejpam-5504	314	6	fix	fix	NOUN
ejpam-5504	314	7	r	r	NOUN
ejpam-5504	314	8	=	=	SYM
ejpam-5504	314	9	fix(ru	fix(ru	NOUN
ejpam-5504	314	10	)	)	PUNCT
ejpam-5504	314	11	=	=	PRON
ejpam-5504	315	1	{	{	PUNCT
ejpam-5504	315	2	x	x	PUNCT
ejpam-5504	315	3	∈	∈	NOUN
ejpam-5504	315	4	x	x	PUNCT
ejpam-5504	315	5	|	|	NOUN
ejpam-5504	315	6	x	x	X
ejpam-5504	315	7	=	=	PUNCT
ejpam-5504	315	8	rux	rux	PROPN
ejpam-5504	315	9	}	}	PUNCT
ejpam-5504	315	10	=	=	SYM
ejpam-5504	315	11	{	{	PUNCT
ejpam-5504	315	12	x	x	PUNCT
ejpam-5504	315	13	∈	∈	NOUN
ejpam-5504	315	14	x	x	PUNCT
ejpam-5504	315	15	|	|	NOUN
ejpam-5504	315	16	2x	2x	NUM
ejpam-5504	315	17	=	=	SYM
ejpam-5504	315	18	2	2	NUM
ejpam-5504	315	19	pu	pu	PROPN
ejpam-5504	315	20	}	}	PUNCT
ejpam-5504	315	21	=	=	SYM
ejpam-5504	315	22	u.	u.	NOUN
ejpam-5504	315	23	(	(	PUNCT
ejpam-5504	315	24	ii	ii	NOUN
ejpam-5504	315	25	):	):	PUNCT
ejpam-5504	315	26	id−r	id−r	NOUN
ejpam-5504	315	27	=	=	SYM
ejpam-5504	315	28	id−ru	id−ru	CCONJ
ejpam-5504	315	29	=	=	SYM
ejpam-5504	315	30	(	(	PUNCT
ejpam-5504	315	31	pu	pu	PROPN
ejpam-5504	315	32	+	+	PROPN
ejpam-5504	315	33	pu⊥	pu⊥	PROPN
ejpam-5504	315	34	)	)	PUNCT
ejpam-5504	315	35	−	−	PROPN
ejpam-5504	316	1	(	(	PUNCT
ejpam-5504	316	2	pu	pu	PROPN
ejpam-5504	316	3	−pu⊥	−pu⊥	PROPN
ejpam-5504	316	4	)	)	PUNCT
ejpam-5504	317	1	=	=	SYM
ejpam-5504	317	2	2	2	NUM
ejpam-5504	317	3	pu⊥	pu⊥	NOUN
ejpam-5504	317	4	.	.	PUNCT
ejpam-5504	318	1	(	(	PUNCT
ejpam-5504	318	2	iii	iii	NOUN
ejpam-5504	318	3	):	):	PUNCT
ejpam-5504	318	4	ran	ran	NOUN
ejpam-5504	318	5	(	(	PUNCT
ejpam-5504	318	6	id−r	id−r	NOUN
ejpam-5504	318	7	)	)	PUNCT
ejpam-5504	318	8	=	=	PRON
ejpam-5504	318	9	ran	run	VERB
ejpam-5504	318	10	(	(	PUNCT
ejpam-5504	318	11	2	2	NUM
ejpam-5504	318	12	pu⊥	pu⊥	PROPN
ejpam-5504	318	13	)	)	PUNCT
ejpam-5504	318	14	=	=	PUNCT
ejpam-5504	318	15	d⊥	d⊥	NOUN
ejpam-5504	318	16	is	be	AUX
ejpam-5504	318	17	closed	closed	ADJ
ejpam-5504	318	18	.	.	PUNCT
ejpam-5504	319	1	(	(	PUNCT
ejpam-5504	319	2	iv	iv	X
ejpam-5504	319	3	):	):	PUNCT
ejpam-5504	319	4	(	(	PUNCT
ejpam-5504	319	5	id−r	id−r	NOUN
ejpam-5504	319	6	)	)	PUNCT
ejpam-5504	319	7	−1	−1	NOUN
ejpam-5504	319	8	=	=	SYM
ejpam-5504	319	9	(	(	PUNCT
ejpam-5504	319	10	2(id−pu	2(id−pu	NUM
ejpam-5504	319	11	)	)	PUNCT
ejpam-5504	319	12	)	)	PUNCT
ejpam-5504	319	13	−1	−1	NOUN
ejpam-5504	320	1	=	=	SYM
ejpam-5504	320	2	1	1	NUM
ejpam-5504	320	3	2	2	NUM
ejpam-5504	320	4	id+nu⊥	id+nu⊥	NOUN
ejpam-5504	320	5	.	.	PUNCT
ejpam-5504	321	1	(	(	PUNCT
ejpam-5504	321	2	v	v	NOUN
ejpam-5504	321	3	):	):	PUNCT
ejpam-5504	321	4	we	we	PRON
ejpam-5504	321	5	have	have	VERB
ejpam-5504	321	6	t	t	NOUN
ejpam-5504	321	7	=	=	SYM
ejpam-5504	321	8	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	321	9	pd⊥	pd⊥	PROPN
ejpam-5504	321	10	−	−	NUM
ejpam-5504	322	1	1	1	NUM
ejpam-5504	322	2	2	2	NUM
ejpam-5504	322	3	pd⊥	pd⊥	PROPN
ejpam-5504	322	4	=	=	SYM
ejpam-5504	322	5	pd⊥	pd⊥	PROPN
ejpam-5504	322	6	(	(	PUNCT
ejpam-5504	322	7	1	1	NUM
ejpam-5504	322	8	2	2	NUM
ejpam-5504	322	9	id+nu⊥	id+nu⊥	NOUN
ejpam-5504	322	10	)	)	PUNCT
ejpam-5504	322	11	pu⊥	pu⊥	NOUN
ejpam-5504	322	12	−	−	NOUN
ejpam-5504	322	13	1	1	NUM
ejpam-5504	322	14	2	2	NUM
ejpam-5504	322	15	pu⊥	pu⊥	NOUN
ejpam-5504	322	16	=	=	NOUN
ejpam-5504	322	17	1	1	NUM
ejpam-5504	322	18	2	2	NUM
ejpam-5504	322	19	pu⊥	pu⊥	NOUN
ejpam-5504	322	20	−	−	NOUN
ejpam-5504	322	21	1	1	NUM
ejpam-5504	322	22	2	2	NUM
ejpam-5504	322	23	pu⊥	pu⊥	NOUN
ejpam-5504	322	24	=	=	NOUN
ejpam-5504	322	25	0	0	NUM
ejpam-5504	322	26	.	.	PUNCT
ejpam-5504	323	1	■	■	PUNCT
ejpam-5504	323	2	example	example	NOUN
ejpam-5504	323	3	5	5	NUM
ejpam-5504	323	4	.	.	PUNCT
ejpam-5504	324	1	let	let	VERB
ejpam-5504	324	2	u	u	PRON
ejpam-5504	324	3	be	be	AUX
ejpam-5504	324	4	a	a	DET
ejpam-5504	324	5	closed	closed	ADJ
ejpam-5504	324	6	subspace	subspace	NOUN
ejpam-5504	324	7	of	of	ADP
ejpam-5504	324	8	x	x	PUNCT
ejpam-5504	324	9	and	and	CCONJ
ejpam-5504	324	10	suppose	suppose	VERB
ejpam-5504	324	11	that	that	SCONJ
ejpam-5504	324	12	r	r	NOUN
ejpam-5504	324	13	=	=	PUNCT
ejpam-5504	324	14	−ru	−ru	ADV
ejpam-5504	324	15	.	.	PUNCT
ejpam-5504	325	1	(	(	PUNCT
ejpam-5504	325	2	29	29	NUM
ejpam-5504	325	3	)	)	PUNCT
ejpam-5504	325	4	then	then	ADV
ejpam-5504	325	5	(	(	PUNCT
ejpam-5504	325	6	i	i	NOUN
ejpam-5504	325	7	)	)	PUNCT
ejpam-5504	326	1	d	d	NOUN
ejpam-5504	326	2	=	=	PRON
ejpam-5504	326	3	fix	fix	NOUN
ejpam-5504	326	4	(	(	PUNCT
ejpam-5504	326	5	−	−	PROPN
ejpam-5504	326	6	ru	ru	NOUN
ejpam-5504	326	7	)	)	PUNCT
ejpam-5504	327	1	=	=	SYM
ejpam-5504	327	2	u⊥.	u⊥.	PROPN
ejpam-5504	327	3	(	(	PUNCT
ejpam-5504	327	4	ii	ii	NOUN
ejpam-5504	327	5	)	)	PUNCT
ejpam-5504	327	6	id−r	id−r	NOUN
ejpam-5504	327	7	=	=	SYM
ejpam-5504	327	8	2	2	NUM
ejpam-5504	327	9	pu	pu	NOUN
ejpam-5504	327	10	.	.	PUNCT
ejpam-5504	328	1	(	(	PUNCT
ejpam-5504	328	2	iii	iii	NOUN
ejpam-5504	328	3	)	)	PUNCT
ejpam-5504	328	4	ran	run	VERB
ejpam-5504	328	5	(	(	PUNCT
ejpam-5504	328	6	id−r	id−r	PROPN
ejpam-5504	328	7	)	)	PUNCT
ejpam-5504	329	1	=	=	SYM
ejpam-5504	329	2	u	u	NOUN
ejpam-5504	329	3	is	be	AUX
ejpam-5504	329	4	closed	closed	ADJ
ejpam-5504	329	5	.	.	PUNCT
ejpam-5504	330	1	(	(	PUNCT
ejpam-5504	330	2	iv	iv	X
ejpam-5504	330	3	)	)	PUNCT
ejpam-5504	330	4	(	(	PUNCT
ejpam-5504	330	5	id−r	id−r	NOUN
ejpam-5504	330	6	)	)	PUNCT
ejpam-5504	330	7	−1	−1	NOUN
ejpam-5504	331	1	=	=	SYM
ejpam-5504	331	2	1	1	NUM
ejpam-5504	331	3	2	2	NUM
ejpam-5504	331	4	id+nu	id+nu	NOUN
ejpam-5504	331	5	.	.	PUNCT
ejpam-5504	332	1	(	(	PUNCT
ejpam-5504	332	2	v	v	NOUN
ejpam-5504	332	3	)	)	PUNCT
ejpam-5504	332	4	t	t	NOUN
ejpam-5504	332	5	=	=	SYM
ejpam-5504	333	1	0	0	X
ejpam-5504	333	2	.	.	PUNCT
ejpam-5504	334	1	proof	proof	NOUN
ejpam-5504	334	2	.	.	PUNCT
ejpam-5504	335	1	(	(	PUNCT
ejpam-5504	335	2	i	i	NOUN
ejpam-5504	335	3	):	):	PUNCT
ejpam-5504	335	4	note	note	VERB
ejpam-5504	335	5	that	that	SCONJ
ejpam-5504	335	6	−ru	−ru	ADV
ejpam-5504	335	7	=	=	SYM
ejpam-5504	335	8	ru⊥	ru⊥	PROPN
ejpam-5504	335	9	and	and	CCONJ
ejpam-5504	335	10	we	we	PRON
ejpam-5504	335	11	learn	learn	VERB
ejpam-5504	335	12	from	from	ADP
ejpam-5504	335	13	example	example	NOUN
ejpam-5504	335	14	4	4	NUM
ejpam-5504	335	15	that	that	PRON
ejpam-5504	335	16	d	d	NOUN
ejpam-5504	335	17	=	=	PUNCT
ejpam-5504	335	18	fix	fix	NOUN
ejpam-5504	335	19	r	r	NOUN
ejpam-5504	335	20	=	=	SYM
ejpam-5504	335	21	u⊥.	u⊥.	PROPN
ejpam-5504	335	22	(	(	PUNCT
ejpam-5504	335	23	ii	ii	NOUN
ejpam-5504	335	24	):	):	PUNCT
ejpam-5504	335	25	id−r	id−r	NOUN
ejpam-5504	335	26	=	=	SYM
ejpam-5504	335	27	id−ru⊥	id−ru⊥	PROPN
ejpam-5504	336	1	=	=	SYM
ejpam-5504	337	1	(	(	PUNCT
ejpam-5504	337	2	pu	pu	PROPN
ejpam-5504	337	3	+	+	PROPN
ejpam-5504	337	4	pu⊥	pu⊥	PROPN
ejpam-5504	337	5	)	)	PUNCT
ejpam-5504	337	6	−	−	PROPN
ejpam-5504	338	1	(	(	PUNCT
ejpam-5504	338	2	2	2	NUM
ejpam-5504	338	3	pu⊥	pu⊥	NOUN
ejpam-5504	338	4	−	−	PROPN
ejpam-5504	338	5	i	i	NOUN
ejpam-5504	338	6	d	d	PROPN
ejpam-5504	338	7	)	)	PUNCT
ejpam-5504	339	1	=	=	PRON
ejpam-5504	339	2	(	(	PUNCT
ejpam-5504	339	3	pu	pu	PROPN
ejpam-5504	339	4	+	+	PROPN
ejpam-5504	339	5	pu⊥	pu⊥	PROPN
ejpam-5504	339	6	)	)	PUNCT
ejpam-5504	339	7	−	−	PROPN
ejpam-5504	340	1	(	(	PUNCT
ejpam-5504	340	2	pu⊥	pu⊥	PROPN
ejpam-5504	340	3	−pu	−pu	PROPN
ejpam-5504	340	4	)	)	PUNCT
ejpam-5504	340	5	=	=	SYM
ejpam-5504	340	6	2	2	NUM
ejpam-5504	340	7	pu	pu	NOUN
ejpam-5504	340	8	.	.	PUNCT
ejpam-5504	341	1	(	(	PUNCT
ejpam-5504	341	2	iii	iii	X
ejpam-5504	341	3	):	):	PUNCT
ejpam-5504	341	4	by	by	ADP
ejpam-5504	341	5	using	use	VERB
ejpam-5504	341	6	(	(	PUNCT
ejpam-5504	341	7	ii	ii	NOUN
ejpam-5504	341	8	)	)	PUNCT
ejpam-5504	341	9	,	,	PUNCT
ejpam-5504	341	10	we	we	PRON
ejpam-5504	341	11	have	have	AUX
ejpam-5504	341	12	ran	run	VERB
ejpam-5504	341	13	(	(	PUNCT
ejpam-5504	341	14	id−r	id−r	NOUN
ejpam-5504	341	15	)	)	PUNCT
ejpam-5504	341	16	=	=	PRON
ejpam-5504	342	1	ran	run	VERB
ejpam-5504	342	2	(	(	PUNCT
ejpam-5504	342	3	2	2	NUM
ejpam-5504	342	4	pu	pu	NOUN
ejpam-5504	342	5	)	)	PUNCT
ejpam-5504	343	1	=	=	PUNCT
ejpam-5504	344	1	d	d	X
ejpam-5504	344	2	=	=	PUNCT
ejpam-5504	344	3	u.	u.	PROPN
ejpam-5504	344	4	(	(	PUNCT
ejpam-5504	344	5	iv	iv	NUM
ejpam-5504	344	6	):	):	PUNCT
ejpam-5504	344	7	(	(	PUNCT
ejpam-5504	344	8	id−r	id−r	NOUN
ejpam-5504	344	9	)	)	PUNCT
ejpam-5504	344	10	−1	−1	NOUN
ejpam-5504	344	11	=	=	SYM
ejpam-5504	344	12	references	reference	NOUN
ejpam-5504	344	13	3674	3674	NUM
ejpam-5504	344	14	(	(	PUNCT
ejpam-5504	344	15	id−(ru⊥	id−(ru⊥	NOUN
ejpam-5504	344	16	)	)	PUNCT
ejpam-5504	344	17	)	)	PUNCT
ejpam-5504	344	18	−1	−1	NOUN
ejpam-5504	344	19	=	=	SYM
ejpam-5504	344	20	(	(	PUNCT
ejpam-5504	344	21	id−(2	id−(2	NOUN
ejpam-5504	344	22	pu⊥	pu⊥	PROPN
ejpam-5504	344	23	−	−	PROPN
ejpam-5504	344	24	i	i	PROPN
ejpam-5504	344	25	d	d	PROPN
ejpam-5504	344	26	)	)	PUNCT
ejpam-5504	344	27	)	)	PUNCT
ejpam-5504	344	28	−1	−1	NOUN
ejpam-5504	344	29	=	=	SYM
ejpam-5504	344	30	(	(	PUNCT
ejpam-5504	344	31	2(id−pu⊥	2(id−pu⊥	NUM
ejpam-5504	344	32	)	)	PUNCT
ejpam-5504	344	33	)	)	PUNCT
ejpam-5504	344	34	−1	−1	NOUN
ejpam-5504	345	1	=	=	SYM
ejpam-5504	345	2	1	1	NUM
ejpam-5504	345	3	2	2	NUM
ejpam-5504	345	4	id+nu	id+nu	VERB
ejpam-5504	345	5	by	by	ADP
ejpam-5504	345	6	[	[	X
ejpam-5504	345	7	4	4	NUM
ejpam-5504	345	8	,	,	PUNCT
ejpam-5504	345	9	example	example	NOUN
ejpam-5504	345	10	]	]	PUNCT
ejpam-5504	345	11	.	.	PUNCT
ejpam-5504	346	1	(	(	PUNCT
ejpam-5504	346	2	v	v	NOUN
ejpam-5504	346	3	):	):	PUNCT
ejpam-5504	346	4	by	by	ADP
ejpam-5504	346	5	using	use	VERB
ejpam-5504	346	6	(	(	PUNCT
ejpam-5504	346	7	8)	8)	NUM
ejpam-5504	346	8	,	,	PUNCT
ejpam-5504	346	9	we	we	PRON
ejpam-5504	346	10	have	have	VERB
ejpam-5504	346	11	t	t	NOUN
ejpam-5504	346	12	=	=	SYM
ejpam-5504	346	13	pd⊥(id−r)−1	pd⊥(id−r)−1	NOUN
ejpam-5504	346	14	pd⊥	pd⊥	PROPN
ejpam-5504	346	15	−	−	NUM
ejpam-5504	347	1	1	1	NUM
ejpam-5504	347	2	2	2	NUM
ejpam-5504	347	3	pd⊥	pd⊥	PROPN
ejpam-5504	347	4	=	=	SYM
ejpam-5504	347	5	pd⊥	pd⊥	PROPN
ejpam-5504	347	6	(	(	PUNCT
ejpam-5504	347	7	1	1	NUM
ejpam-5504	347	8	2	2	NUM
ejpam-5504	347	9	id+nu	id+nu	NOUN
ejpam-5504	347	10	)	)	PUNCT
ejpam-5504	347	11	pu⊥	pu⊥	NOUN
ejpam-5504	347	12	−	−	NOUN
ejpam-5504	347	13	1	1	NUM
ejpam-5504	347	14	2	2	NUM
ejpam-5504	347	15	pu⊥	pu⊥	NOUN
ejpam-5504	347	16	=	=	NOUN
ejpam-5504	347	17	1	1	NUM
ejpam-5504	347	18	2	2	NUM
ejpam-5504	347	19	pu⊥	pu⊥	NOUN
ejpam-5504	347	20	−	−	NOUN
ejpam-5504	347	21	1	1	NUM
ejpam-5504	347	22	2	2	NUM
ejpam-5504	347	23	pu⊥	pu⊥	NOUN
ejpam-5504	347	24	=	=	NOUN
ejpam-5504	347	25	0	0	NUM
ejpam-5504	347	26	.	.	PUNCT
ejpam-5504	348	1	■	■	ADJ
ejpam-5504	348	2	acknowledgements	acknowledgement	VERB
ejpam-5504	348	3	the	the	DET
ejpam-5504	348	4	author	author	NOUN
ejpam-5504	348	5	expresses	express	VERB
ejpam-5504	348	6	gratitude	gratitude	NOUN
ejpam-5504	348	7	to	to	ADP
ejpam-5504	348	8	the	the	DET
ejpam-5504	348	9	reviewers	reviewer	NOUN
ejpam-5504	348	10	for	for	ADP
ejpam-5504	348	11	their	their	PRON
ejpam-5504	348	12	insightful	insightful	ADJ
ejpam-5504	348	13	comments	comment	NOUN
ejpam-5504	348	14	and	and	CCONJ
ejpam-5504	348	15	constructive	constructive	ADJ
ejpam-5504	348	16	feedback	feedback	NOUN
ejpam-5504	348	17	,	,	PUNCT
ejpam-5504	348	18	which	which	PRON
ejpam-5504	348	19	greatly	greatly	ADV
ejpam-5504	348	20	contributed	contribute	VERB
ejpam-5504	348	21	to	to	ADP
ejpam-5504	348	22	enhancing	enhance	VERB
ejpam-5504	348	23	the	the	DET
ejpam-5504	348	24	quality	quality	NOUN
ejpam-5504	348	25	of	of	ADP
ejpam-5504	348	26	the	the	DET
ejpam-5504	348	27	work	work	NOUN
ejpam-5504	348	28	.	.	PUNCT
ejpam-5504	349	1	clarification	clarification	NOUN
ejpam-5504	349	2	please	please	INTJ
ejpam-5504	349	3	note	note	VERB
ejpam-5504	349	4	that	that	SCONJ
ejpam-5504	349	5	a	a	DET
ejpam-5504	349	6	preprint	preprint	NOUN
ejpam-5504	349	7	has	have	AUX
ejpam-5504	349	8	previously	previously	ADV
ejpam-5504	349	9	been	be	AUX
ejpam-5504	349	10	published	publish	VERB
ejpam-5504	349	11	in	in	ADP
ejpam-5504	349	12	arxiv	arxiv	PROPN
ejpam-5504	349	13	and	and	CCONJ
ejpam-5504	349	14	available	available	ADJ
ejpam-5504	349	15	in	in	ADP
ejpam-5504	349	16	[	[	X
ejpam-5504	349	17	3	3	NUM
ejpam-5504	349	18	]	]	PUNCT
ejpam-5504	349	19	.	.	PUNCT
ejpam-5504	350	1	there	there	PRON
ejpam-5504	350	2	is	be	VERB
ejpam-5504	350	3	no	no	DET
ejpam-5504	350	4	conflict	conflict	NOUN
ejpam-5504	350	5	of	of	ADP
ejpam-5504	350	6	interest	interest	NOUN
ejpam-5504	350	7	and	and	CCONJ
ejpam-5504	350	8	there	there	PRON
ejpam-5504	350	9	is	be	VERB
ejpam-5504	350	10	no	no	DET
ejpam-5504	350	11	data	datum	NOUN
ejpam-5504	350	12	were	be	AUX
ejpam-5504	350	13	used	use	VERB
ejpam-5504	350	14	to	to	PART
ejpam-5504	350	15	support	support	VERB
ejpam-5504	350	16	this	this	DET
ejpam-5504	350	17	study	study	NOUN
ejpam-5504	350	18	.	.	PUNCT
ejpam-5504	351	1	references	reference	NOUN
ejpam-5504	351	2	[	[	X
ejpam-5504	351	3	1	1	X
ejpam-5504	351	4	]	]	PUNCT
ejpam-5504	351	5	salihah	salihah	ADJ
ejpam-5504	351	6	alwadani	alwadani	ADJ
ejpam-5504	351	7	,	,	PUNCT
ejpam-5504	351	8	heinz	heinz	PROPN
ejpam-5504	351	9	h	h	PROPN
ejpam-5504	351	10	bauschke	bauschke	PROPN
ejpam-5504	351	11	,	,	PUNCT
ejpam-5504	351	12	julian	julian	PROPN
ejpam-5504	351	13	p	p	PROPN
ejpam-5504	351	14	revalski	revalski	PROPN
ejpam-5504	351	15	,	,	PUNCT
ejpam-5504	351	16	and	and	CCONJ
ejpam-5504	351	17	xianfu	xianfu	PROPN
ejpam-5504	351	18	wang	wang	PROPN
ejpam-5504	351	19	.	.	PUNCT
ejpam-5504	352	1	resolvents	resolvent	NOUN
ejpam-5504	352	2	and	and	CCONJ
ejpam-5504	352	3	yosida	yosida	PROPN
ejpam-5504	352	4	approximations	approximation	NOUN
ejpam-5504	352	5	of	of	ADP
ejpam-5504	352	6	displacement	displacement	ADJ
ejpam-5504	352	7	mappings	mapping	NOUN
ejpam-5504	352	8	of	of	ADP
ejpam-5504	352	9	isometries	isometry	NOUN
ejpam-5504	352	10	.	.	PUNCT
ejpam-5504	353	1	setvalued	setvalued	ADJ
ejpam-5504	353	2	and	and	CCONJ
ejpam-5504	353	3	variational	variational	ADJ
ejpam-5504	353	4	analysis	analysis	NOUN
ejpam-5504	353	5	,	,	PUNCT
ejpam-5504	353	6	29:721–733	29:721–733	NUM
ejpam-5504	353	7	,	,	PUNCT
ejpam-5504	353	8	2021	2021	NUM
ejpam-5504	353	9	.	.	PUNCT
ejpam-5504	354	1	[	[	X
ejpam-5504	354	2	2	2	X
ejpam-5504	354	3	]	]	PUNCT
ejpam-5504	354	4	salihah	salihah	ADJ
ejpam-5504	354	5	thabet	thabet	ADJ
ejpam-5504	354	6	alwadani	alwadani	ADJ
ejpam-5504	354	7	.	.	PUNCT
ejpam-5504	355	1	on	on	ADP
ejpam-5504	355	2	the	the	DET
ejpam-5504	355	3	behaviour	behaviour	NOUN
ejpam-5504	355	4	of	of	ADP
ejpam-5504	355	5	algorithms	algorithm	NOUN
ejpam-5504	355	6	featuring	feature	VERB
ejpam-5504	355	7	compositions	composition	NOUN
ejpam-5504	355	8	of	of	ADP
ejpam-5504	355	9	projectors	projector	NOUN
ejpam-5504	355	10	and	and	CCONJ
ejpam-5504	355	11	proximal	proximal	ADJ
ejpam-5504	355	12	mappings	mapping	NOUN
ejpam-5504	355	13	with	with	ADP
ejpam-5504	355	14	no	no	DET
ejpam-5504	355	15	solutions	solution	NOUN
ejpam-5504	355	16	.	.	PUNCT
ejpam-5504	356	1	phd	phd	NOUN
ejpam-5504	356	2	thesis	thesis	PROPN
ejpam-5504	356	3	,	,	PUNCT
ejpam-5504	356	4	university	university	PROPN
ejpam-5504	356	5	of	of	ADP
ejpam-5504	356	6	british	british	PROPN
ejpam-5504	356	7	columbia	columbia	PROPN
ejpam-5504	356	8	,	,	PUNCT
ejpam-5504	356	9	2021	2021	NUM
ejpam-5504	356	10	.	.	PUNCT
ejpam-5504	357	1	[	[	X
ejpam-5504	357	2	3	3	X
ejpam-5504	357	3	]	]	PUNCT
ejpam-5504	357	4	salihah	salihah	ADJ
ejpam-5504	357	5	thabet	thabet	ADJ
ejpam-5504	357	6	alwadani	alwadani	ADJ
ejpam-5504	357	7	.	.	PUNCT
ejpam-5504	358	1	additional	additional	ADJ
ejpam-5504	358	2	studies	study	NOUN
ejpam-5504	358	3	on	on	ADP
ejpam-5504	358	4	displacement	displacement	ADJ
ejpam-5504	358	5	mapping	mapping	NOUN
ejpam-5504	358	6	with	with	ADP
ejpam-5504	358	7	restrictions	restriction	NOUN
ejpam-5504	358	8	.	.	PUNCT
ejpam-5504	359	1	arxiv	arxiv	PROPN
ejpam-5504	359	2	preprint	preprint	NOUN
ejpam-5504	359	3	arxiv:2405.13510	arxiv:2405.13510	NOUN
ejpam-5504	359	4	,	,	PUNCT
ejpam-5504	359	5	2024	2024	NUM
ejpam-5504	359	6	.	.	PUNCT
ejpam-5504	360	1	[	[	X
ejpam-5504	360	2	4	4	X
ejpam-5504	360	3	]	]	PUNCT
ejpam-5504	360	4	heinz	heinz	ADJ
ejpam-5504	360	5	h	h	PROPN
ejpam-5504	360	6	bauschke	bauschke	PROPN
ejpam-5504	360	7	,	,	PUNCT
ejpam-5504	360	8	patrick	patrick	PROPN
ejpam-5504	360	9	l	l	PROPN
ejpam-5504	360	10	combettes	combettes	PROPN
ejpam-5504	360	11	,	,	PUNCT
ejpam-5504	360	12	heinz	heinz	ADJ
ejpam-5504	360	13	h	h	NOUN
ejpam-5504	360	14	bauschke	bauschke	NOUN
ejpam-5504	360	15	,	,	PUNCT
ejpam-5504	360	16	and	and	CCONJ
ejpam-5504	360	17	patrick	patrick	PROPN
ejpam-5504	360	18	l	l	PROPN
ejpam-5504	360	19	combettes	combettes	PROPN
ejpam-5504	360	20	.	.	PUNCT
ejpam-5504	360	21	correction	correction	NOUN
ejpam-5504	360	22	to	to	PART
ejpam-5504	360	23	:	:	PUNCT
ejpam-5504	360	24	convex	convex	VERB
ejpam-5504	360	25	analysis	analysis	NOUN
ejpam-5504	360	26	and	and	CCONJ
ejpam-5504	360	27	monotone	monotone	ADJ
ejpam-5504	360	28	operator	operator	NOUN
ejpam-5504	360	29	theory	theory	NOUN
ejpam-5504	360	30	in	in	ADP
ejpam-5504	360	31	hilbert	hilbert	PROPN
ejpam-5504	360	32	spaces	space	NOUN
ejpam-5504	360	33	.	.	PUNCT
ejpam-5504	361	1	springer	springer	NOUN
ejpam-5504	361	2	,	,	PUNCT
ejpam-5504	361	3	2017	2017	NUM
ejpam-5504	361	4	.	.	PUNCT
ejpam-5504	362	1	[	[	X
ejpam-5504	362	2	5	5	NUM
ejpam-5504	362	3	]	]	PUNCT
ejpam-5504	362	4	heinz	heinz	ADJ
ejpam-5504	362	5	h	h	PROPN
ejpam-5504	362	6	bauschke	bauschke	PROPN
ejpam-5504	362	7	,	,	PUNCT
ejpam-5504	362	8	warren	warren	PROPN
ejpam-5504	362	9	l	l	PROPN
ejpam-5504	362	10	hare	hare	NOUN
ejpam-5504	362	11	,	,	PUNCT
ejpam-5504	362	12	and	and	CCONJ
ejpam-5504	362	13	walaa	walaa	PROPN
ejpam-5504	362	14	m	m	PROPN
ejpam-5504	362	15	moursi	moursi	ADJ
ejpam-5504	362	16	.	.	PUNCT
ejpam-5504	363	1	on	on	ADP
ejpam-5504	363	2	the	the	DET
ejpam-5504	363	3	range	range	NOUN
ejpam-5504	363	4	of	of	ADP
ejpam-5504	363	5	the	the	DET
ejpam-5504	363	6	douglas	douglas	PROPN
ejpam-5504	363	7	–	–	PUNCT
ejpam-5504	363	8	rachford	rachford	ADJ
ejpam-5504	363	9	operator	operator	NOUN
ejpam-5504	363	10	.	.	PUNCT
ejpam-5504	364	1	mathematics	mathematic	NOUN
ejpam-5504	364	2	of	of	ADP
ejpam-5504	364	3	operations	operation	NOUN
ejpam-5504	364	4	research	research	NOUN
ejpam-5504	364	5	,	,	PUNCT
ejpam-5504	364	6	41(3):884–897	41(3):884–897	PROPN
ejpam-5504	364	7	,	,	PUNCT
ejpam-5504	364	8	2016	2016	NUM
ejpam-5504	364	9	.	.	PUNCT
ejpam-5504	365	1	references	reference	NOUN
ejpam-5504	365	2	3675	3675	NUM
ejpam-5504	365	3	[	[	X
ejpam-5504	365	4	6	6	NUM
ejpam-5504	365	5	]	]	PUNCT
ejpam-5504	365	6	heinz	heinz	PROPN
ejpam-5504	365	7	h	h	PROPN
ejpam-5504	365	8	bauschke	bauschke	PROPN
ejpam-5504	365	9	,	,	PUNCT
ejpam-5504	365	10	victoria	victoria	PROPN
ejpam-5504	365	11	martı́n	martı́n	PROPN
ejpam-5504	365	12	-	-	PROPN
ejpam-5504	365	13	márquez	márquez	PROPN
ejpam-5504	365	14	,	,	PUNCT
ejpam-5504	365	15	sarah	sarah	PROPN
ejpam-5504	365	16	m	m	PROPN
ejpam-5504	365	17	moffat	moffat	PROPN
ejpam-5504	365	18	,	,	PUNCT
ejpam-5504	365	19	and	and	CCONJ
ejpam-5504	365	20	xianfu	xianfu	PROPN
ejpam-5504	365	21	wang	wang	PROPN
ejpam-5504	365	22	.	.	PUNCT
ejpam-5504	366	1	compositions	composition	NOUN
ejpam-5504	366	2	and	and	CCONJ
ejpam-5504	366	3	convex	convex	NOUN
ejpam-5504	366	4	combinations	combination	NOUN
ejpam-5504	366	5	of	of	ADP
ejpam-5504	366	6	asymptotically	asymptotically	ADV
ejpam-5504	366	7	regular	regular	ADJ
ejpam-5504	366	8	firmly	firmly	ADV
ejpam-5504	366	9	nonexpansive	nonexpansive	ADJ
ejpam-5504	366	10	mappings	mapping	NOUN
ejpam-5504	366	11	are	be	AUX
ejpam-5504	366	12	also	also	ADV
ejpam-5504	366	13	asymptotically	asymptotically	ADV
ejpam-5504	366	14	regular	regular	ADJ
ejpam-5504	366	15	.	.	PUNCT
ejpam-5504	367	1	fixed	fix	VERB
ejpam-5504	367	2	point	point	NOUN
ejpam-5504	367	3	theory	theory	NOUN
ejpam-5504	367	4	and	and	CCONJ
ejpam-5504	367	5	applications	application	NOUN
ejpam-5504	367	6	,	,	PUNCT
ejpam-5504	367	7	2012:1–11	2012:1–11	NUM
ejpam-5504	367	8	,	,	PUNCT
ejpam-5504	367	9	2012	2012	NUM
ejpam-5504	367	10	.	.	PUNCT
ejpam-5504	368	1	[	[	X
ejpam-5504	368	2	7	7	X
ejpam-5504	368	3	]	]	X
ejpam-5504	368	4	heinz	heinz	ADJ
ejpam-5504	368	5	h	h	NOUN
ejpam-5504	368	6	bauschke	bauschke	NOUN
ejpam-5504	368	7	and	and	CCONJ
ejpam-5504	368	8	walaa	walaa	PROPN
ejpam-5504	368	9	m	m	PROPN
ejpam-5504	368	10	moursi	moursi	ADJ
ejpam-5504	368	11	.	.	PUNCT
ejpam-5504	369	1	on	on	ADP
ejpam-5504	369	2	the	the	DET
ejpam-5504	369	3	order	order	NOUN
ejpam-5504	369	4	of	of	ADP
ejpam-5504	369	5	the	the	DET
ejpam-5504	369	6	operators	operator	NOUN
ejpam-5504	369	7	in	in	ADP
ejpam-5504	369	8	the	the	DET
ejpam-5504	369	9	douglas	douglas	PROPN
ejpam-5504	369	10	–	–	PUNCT
ejpam-5504	369	11	rachford	rachford	ADJ
ejpam-5504	369	12	algorithm	algorithm	NOUN
ejpam-5504	369	13	.	.	PUNCT
ejpam-5504	370	1	optimization	optimization	NOUN
ejpam-5504	370	2	letters	letter	NOUN
ejpam-5504	370	3	,	,	PUNCT
ejpam-5504	370	4	10:447–455	10:447–455	NUM
ejpam-5504	370	5	,	,	PUNCT
ejpam-5504	370	6	2016	2016	NUM
ejpam-5504	370	7	.	.	PUNCT
ejpam-5504	371	1	[	[	X
ejpam-5504	371	2	8	8	NUM
ejpam-5504	371	3	]	]	X
ejpam-5504	371	4	heinz	heinz	ADJ
ejpam-5504	371	5	h	h	PROPN
ejpam-5504	371	6	bauschke	bauschke	NOUN
ejpam-5504	371	7	and	and	CCONJ
ejpam-5504	371	8	walaa	walaa	PROPN
ejpam-5504	371	9	m	m	PROPN
ejpam-5504	371	10	moursi	moursi	ADJ
ejpam-5504	371	11	.	.	PUNCT
ejpam-5504	372	1	the	the	DET
ejpam-5504	372	2	magnitude	magnitude	NOUN
ejpam-5504	372	3	of	of	ADP
ejpam-5504	372	4	the	the	DET
ejpam-5504	372	5	minimal	minimal	ADJ
ejpam-5504	372	6	displacement	displacement	ADJ
ejpam-5504	372	7	vector	vector	NOUN
ejpam-5504	372	8	for	for	ADP
ejpam-5504	372	9	compositions	composition	NOUN
ejpam-5504	372	10	and	and	CCONJ
ejpam-5504	372	11	convex	convex	NOUN
ejpam-5504	372	12	combinations	combination	NOUN
ejpam-5504	372	13	of	of	ADP
ejpam-5504	372	14	firmly	firmly	ADV
ejpam-5504	372	15	nonexpansive	nonexpansive	ADJ
ejpam-5504	372	16	mappings	mapping	NOUN
ejpam-5504	372	17	.	.	PUNCT
ejpam-5504	373	1	optimization	optimization	NOUN
ejpam-5504	373	2	letters	letter	NOUN
ejpam-5504	373	3	,	,	PUNCT
ejpam-5504	373	4	12:1465–1474	12:1465–1474	NUM
ejpam-5504	373	5	,	,	PUNCT
ejpam-5504	373	6	2018	2018	NUM
ejpam-5504	373	7	.	.	PUNCT
ejpam-5504	374	1	[	[	X
ejpam-5504	374	2	9	9	NUM
ejpam-5504	374	3	]	]	PUNCT
ejpam-5504	374	4	heinz	heinz	ADJ
ejpam-5504	374	5	h	h	PROPN
ejpam-5504	374	6	bauschke	bauschke	PROPN
ejpam-5504	374	7	,	,	PUNCT
ejpam-5504	374	8	xianfu	xianfu	PROPN
ejpam-5504	374	9	wang	wang	PROPN
ejpam-5504	374	10	,	,	PUNCT
ejpam-5504	374	11	and	and	CCONJ
ejpam-5504	374	12	liangjin	liangjin	ADJ
ejpam-5504	374	13	yao	yao	NOUN
ejpam-5504	374	14	.	.	PUNCT
ejpam-5504	375	1	on	on	ADP
ejpam-5504	375	2	borwein	borwein	ADJ
ejpam-5504	375	3	–	–	PUNCT
ejpam-5504	375	4	wiersma	wiersma	NOUN
ejpam-5504	375	5	decompositions	decomposition	NOUN
ejpam-5504	375	6	of	of	ADP
ejpam-5504	375	7	monotone	monotone	ADJ
ejpam-5504	375	8	linear	linear	ADJ
ejpam-5504	375	9	relations	relation	NOUN
ejpam-5504	375	10	.	.	PUNCT
ejpam-5504	376	1	siam	siam	PROPN
ejpam-5504	376	2	journal	journal	PROPN
ejpam-5504	376	3	on	on	ADP
ejpam-5504	376	4	optimization	optimization	NOUN
ejpam-5504	376	5	,	,	PUNCT
ejpam-5504	376	6	20(5):2636–2652	20(5):2636–2652	NUM
ejpam-5504	376	7	,	,	PUNCT
ejpam-5504	376	8	2010	2010	NUM
ejpam-5504	376	9	.	.	PUNCT
ejpam-5504	377	1	[	[	X
ejpam-5504	377	2	10	10	NUM
ejpam-5504	377	3	]	]	X
ejpam-5504	377	4	imtiyaz	imtiyaz	PROPN
ejpam-5504	377	5	ahmad	ahmad	PROPN
ejpam-5504	377	6	bhat	bhat	PROPN
ejpam-5504	377	7	,	,	PUNCT
ejpam-5504	377	8	lakshmi	lakshmi	PROPN
ejpam-5504	377	9	narayan	narayan	PROPN
ejpam-5504	377	10	mishra	mishra	PROPN
ejpam-5504	377	11	,	,	PUNCT
ejpam-5504	377	12	vishnu	vishnu	PROPN
ejpam-5504	377	13	narayan	narayan	PROPN
ejpam-5504	377	14	mishra	mishra	PROPN
ejpam-5504	377	15	,	,	PUNCT
ejpam-5504	377	16	and	and	CCONJ
ejpam-5504	377	17	cemil	cemil	NOUN
ejpam-5504	377	18	tunç.	tunç.	NOUN
ejpam-5504	377	19	analysis	analysis	NOUN
ejpam-5504	377	20	of	of	ADP
ejpam-5504	377	21	efficient	efficient	ADJ
ejpam-5504	377	22	discretization	discretization	NOUN
ejpam-5504	377	23	technique	technique	NOUN
ejpam-5504	377	24	for	for	ADP
ejpam-5504	377	25	nonlinear	nonlinear	ADJ
ejpam-5504	377	26	integral	integral	ADJ
ejpam-5504	377	27	equations	equation	NOUN
ejpam-5504	377	28	of	of	ADP
ejpam-5504	377	29	hammerstein	hammerstein	PROPN
ejpam-5504	377	30	type	type	PROPN
ejpam-5504	377	31	.	.	PUNCT
ejpam-5504	378	1	international	international	ADJ
ejpam-5504	378	2	journal	journal	PROPN
ejpam-5504	378	3	of	of	ADP
ejpam-5504	378	4	numerical	numerical	ADJ
ejpam-5504	378	5	methods	method	NOUN
ejpam-5504	378	6	for	for	ADP
ejpam-5504	378	7	heat	heat	NOUN
ejpam-5504	378	8	&	&	CCONJ
ejpam-5504	378	9	fluid	fluid	ADJ
ejpam-5504	378	10	flow	flow	NOUN
ejpam-5504	378	11	,	,	PUNCT
ejpam-5504	378	12	2024	2024	NUM
ejpam-5504	378	13	.	.	PUNCT
ejpam-5504	379	1	[	[	X
ejpam-5504	379	2	11	11	NUM
ejpam-5504	379	3	]	]	X
ejpam-5504	379	4	regina	regina	PROPN
ejpam-5504	379	5	s	s	PROPN
ejpam-5504	379	6	burachik	burachik	PROPN
ejpam-5504	379	7	,	,	PUNCT
ejpam-5504	379	8	alfredo	alfredo	NOUN
ejpam-5504	379	9	n	n	CCONJ
ejpam-5504	379	10	iusem	iusem	NOUN
ejpam-5504	379	11	,	,	PUNCT
ejpam-5504	379	12	regina	regina	PROPN
ejpam-5504	379	13	s	s	PROPN
ejpam-5504	379	14	burachik	burachik	PROPN
ejpam-5504	379	15	,	,	PUNCT
ejpam-5504	379	16	and	and	CCONJ
ejpam-5504	379	17	alfredo	alfredo	NOUN
ejpam-5504	379	18	n	n	CCONJ
ejpam-5504	379	19	iusem	iusem	ADJ
ejpam-5504	379	20	.	.	PUNCT
ejpam-5504	380	1	enlargements	enlargement	NOUN
ejpam-5504	380	2	of	of	ADP
ejpam-5504	380	3	monotone	monotone	ADJ
ejpam-5504	380	4	operators	operator	NOUN
ejpam-5504	380	5	.	.	PUNCT
ejpam-5504	381	1	springer	springer	NOUN
ejpam-5504	381	2	,	,	PUNCT
ejpam-5504	381	3	2008	2008	NUM
ejpam-5504	381	4	.	.	PUNCT
ejpam-5504	382	1	[	[	X
ejpam-5504	382	2	12	12	NUM
ejpam-5504	382	3	]	]	X
ejpam-5504	382	4	john	john	PROPN
ejpam-5504	382	5	b	b	PROPN
ejpam-5504	382	6	conway	conway	PROPN
ejpam-5504	382	7	.	.	PUNCT
ejpam-5504	383	1	a	a	DET
ejpam-5504	383	2	course	course	NOUN
ejpam-5504	383	3	in	in	ADP
ejpam-5504	383	4	functional	functional	ADJ
ejpam-5504	383	5	analysis	analysis	NOUN
ejpam-5504	383	6	,	,	PUNCT
ejpam-5504	383	7	volume	volume	NOUN
ejpam-5504	383	8	96	96	NUM
ejpam-5504	383	9	.	.	PUNCT
ejpam-5504	383	10	springer	springer	NOUN
ejpam-5504	383	11	,	,	PUNCT
ejpam-5504	383	12	2019	2019	NUM
ejpam-5504	383	13	.	.	PUNCT
ejpam-5504	384	1	[	[	X
ejpam-5504	384	2	13	13	NUM
ejpam-5504	384	3	]	]	X
ejpam-5504	384	4	frank	frank	ADJ
ejpam-5504	384	5	deutsch	deutsch	PROPN
ejpam-5504	384	6	and	and	CCONJ
ejpam-5504	384	7	f	f	PROPN
ejpam-5504	384	8	deutsch	deutsch	PROPN
ejpam-5504	384	9	.	.	PUNCT
ejpam-5504	385	1	best	good	ADJ
ejpam-5504	385	2	approximation	approximation	NOUN
ejpam-5504	385	3	in	in	ADP
ejpam-5504	385	4	inner	inner	ADJ
ejpam-5504	385	5	product	product	NOUN
ejpam-5504	385	6	spaces	space	NOUN
ejpam-5504	385	7	,	,	PUNCT
ejpam-5504	385	8	volume	volume	NOUN
ejpam-5504	385	9	7	7	NUM
ejpam-5504	385	10	.	.	PUNCT
ejpam-5504	385	11	springer	springer	NOUN
ejpam-5504	385	12	,	,	PUNCT
ejpam-5504	385	13	2001	2001	NUM
ejpam-5504	385	14	.	.	PUNCT
ejpam-5504	386	1	[	[	X
ejpam-5504	386	2	14	14	NUM
ejpam-5504	386	3	]	]	X
ejpam-5504	386	4	jonathan	jonathan	PROPN
ejpam-5504	386	5	eckstein	eckstein	PROPN
ejpam-5504	386	6	and	and	CCONJ
ejpam-5504	386	7	dimitri	dimitri	PROPN
ejpam-5504	386	8	p	p	PROPN
ejpam-5504	386	9	bertsekas	bertsekas	PROPN
ejpam-5504	386	10	.	.	PUNCT
ejpam-5504	387	1	on	on	ADP
ejpam-5504	387	2	the	the	DET
ejpam-5504	387	3	douglas	douglas	PROPN
ejpam-5504	387	4	—	—	PUNCT
ejpam-5504	387	5	rachford	rachford	ADJ
ejpam-5504	387	6	splitting	splitting	NOUN
ejpam-5504	387	7	method	method	NOUN
ejpam-5504	387	8	and	and	CCONJ
ejpam-5504	387	9	the	the	DET
ejpam-5504	387	10	proximal	proximal	ADJ
ejpam-5504	387	11	point	point	NOUN
ejpam-5504	387	12	algorithm	algorithm	NOUN
ejpam-5504	387	13	for	for	ADP
ejpam-5504	387	14	maximal	maximal	ADJ
ejpam-5504	387	15	monotone	monotone	ADJ
ejpam-5504	387	16	operators	operator	NOUN
ejpam-5504	387	17	.	.	PUNCT
ejpam-5504	388	1	mathematical	mathematical	ADJ
ejpam-5504	388	2	programming	programming	NOUN
ejpam-5504	388	3	,	,	PUNCT
ejpam-5504	388	4	55:293–318	55:293–318	NUM
ejpam-5504	388	5	,	,	PUNCT
ejpam-5504	388	6	1992	1992	NUM
ejpam-5504	388	7	.	.	PUNCT
ejpam-5504	389	1	[	[	X
ejpam-5504	389	2	15	15	NUM
ejpam-5504	389	3	]	]	X
ejpam-5504	389	4	mohammed	mohammed	PROPN
ejpam-5504	389	5	sumebo	sumebo	PROPN
ejpam-5504	389	6	hogeme	hogeme	NOUN
ejpam-5504	389	7	,	,	PUNCT
ejpam-5504	389	8	mesfin	mesfin	ADJ
ejpam-5504	389	9	mekuria	mekuria	PROPN
ejpam-5504	389	10	woldaregay	woldaregay	NOUN
ejpam-5504	389	11	,	,	PUNCT
ejpam-5504	389	12	laxmi	laxmi	NOUN
ejpam-5504	389	13	rathour	rathour	NOUN
ejpam-5504	389	14	,	,	PUNCT
ejpam-5504	389	15	and	and	CCONJ
ejpam-5504	389	16	vishnu	vishnu	PROPN
ejpam-5504	389	17	narayan	narayan	PROPN
ejpam-5504	389	18	mishra	mishra	PROPN
ejpam-5504	389	19	.	.	PUNCT
ejpam-5504	390	1	a	a	DET
ejpam-5504	390	2	stable	stable	ADJ
ejpam-5504	390	3	numerical	numerical	ADJ
ejpam-5504	390	4	method	method	NOUN
ejpam-5504	390	5	for	for	ADP
ejpam-5504	390	6	singularly	singularly	ADV
ejpam-5504	390	7	perturbed	perturb	VERB
ejpam-5504	390	8	fredholm	fredholm	NOUN
ejpam-5504	390	9	integro	integro	PROPN
ejpam-5504	390	10	differential	differential	ADJ
ejpam-5504	390	11	equation	equation	NOUN
ejpam-5504	390	12	using	use	VERB
ejpam-5504	390	13	exponentially	exponentially	ADV
ejpam-5504	390	14	fitted	fit	VERB
ejpam-5504	390	15	difference	difference	NOUN
ejpam-5504	390	16	method	method	NOUN
ejpam-5504	390	17	.	.	PUNCT
ejpam-5504	391	1	journal	journal	NOUN
ejpam-5504	391	2	of	of	ADP
ejpam-5504	391	3	computational	computational	ADJ
ejpam-5504	391	4	and	and	CCONJ
ejpam-5504	391	5	applied	applied	ADJ
ejpam-5504	391	6	mathematics	mathematic	NOUN
ejpam-5504	391	7	,	,	PUNCT
ejpam-5504	391	8	441:115709	441:115709	NUM
ejpam-5504	391	9	,	,	PUNCT
ejpam-5504	391	10	2024	2024	NUM
ejpam-5504	391	11	.	.	PUNCT
ejpam-5504	392	1	[	[	X
ejpam-5504	392	2	16	16	NUM
ejpam-5504	392	3	]	]	X
ejpam-5504	392	4	robert	robert	PROPN
ejpam-5504	392	5	e	e	PROPN
ejpam-5504	392	6	megginson	megginson	PROPN
ejpam-5504	392	7	.	.	PUNCT
ejpam-5504	393	1	a	a	DET
ejpam-5504	393	2	course	course	NOUN
ejpam-5504	393	3	in	in	ADP
ejpam-5504	393	4	functional	functional	ADJ
ejpam-5504	393	5	analysis	analysis	NOUN
ejpam-5504	393	6	.	.	PUNCT
ejpam-5504	394	1	[	[	X
ejpam-5504	394	2	17	17	NUM
ejpam-5504	394	3	]	]	X
ejpam-5504	394	4	naol	naol	NOUN
ejpam-5504	394	5	tufa	tufa	PROPN
ejpam-5504	394	6	negero	negero	NOUN
ejpam-5504	394	7	,	,	PUNCT
ejpam-5504	394	8	gemechis	gemechis	NOUN
ejpam-5504	394	9	file	file	NOUN
ejpam-5504	394	10	duressa	duressa	NOUN
ejpam-5504	394	11	,	,	PUNCT
ejpam-5504	394	12	laxmi	laxmi	NOUN
ejpam-5504	394	13	rathour	rathour	NOUN
ejpam-5504	394	14	,	,	PUNCT
ejpam-5504	394	15	and	and	CCONJ
ejpam-5504	394	16	vishnu	vishnu	PROPN
ejpam-5504	394	17	narayan	narayan	PROPN
ejpam-5504	394	18	mishra	mishra	PROPN
ejpam-5504	394	19	.	.	PUNCT
ejpam-5504	395	1	a	a	DET
ejpam-5504	395	2	novel	novel	NOUN
ejpam-5504	395	3	fitted	fit	VERB
ejpam-5504	395	4	numerical	numerical	ADJ
ejpam-5504	395	5	scheme	scheme	NOUN
ejpam-5504	395	6	for	for	ADP
ejpam-5504	395	7	singularly	singularly	ADV
ejpam-5504	395	8	perturbed	perturb	VERB
ejpam-5504	395	9	delay	delay	NOUN
ejpam-5504	395	10	parabolic	parabolic	ADJ
ejpam-5504	395	11	problems	problem	NOUN
ejpam-5504	395	12	with	with	ADP
ejpam-5504	395	13	two	two	NUM
ejpam-5504	395	14	small	small	ADJ
ejpam-5504	395	15	parameters	parameter	NOUN
ejpam-5504	395	16	.	.	PUNCT
ejpam-5504	396	1	partial	partial	ADJ
ejpam-5504	396	2	differential	differential	ADJ
ejpam-5504	396	3	equations	equation	NOUN
ejpam-5504	396	4	in	in	ADP
ejpam-5504	396	5	applied	applied	ADJ
ejpam-5504	396	6	mathematics	mathematic	NOUN
ejpam-5504	396	7	,	,	PUNCT
ejpam-5504	396	8	8:100546	8:100546	NUM
ejpam-5504	396	9	,	,	PUNCT
ejpam-5504	396	10	2023	2023	NUM
ejpam-5504	396	11	.	.	PUNCT
ejpam-5504	397	1	[	[	X
ejpam-5504	397	2	18	18	NUM
ejpam-5504	397	3	]	]	X
ejpam-5504	397	4	r	r	NOUN
ejpam-5504	397	5	tyrrell	tyrrell	NOUN
ejpam-5504	397	6	rockafellar	rockafellar	ADJ
ejpam-5504	397	7	and	and	CCONJ
ejpam-5504	397	8	roger	roger	PROPN
ejpam-5504	397	9	j	j	PROPN
ejpam-5504	397	10	-	-	PUNCT
ejpam-5504	397	11	b	b	NOUN
ejpam-5504	397	12	wets	wet	VERB
ejpam-5504	397	13	.	.	PUNCT
ejpam-5504	398	1	springer	springer	NOUN
ejpam-5504	398	2	-	-	PUNCT
ejpam-5504	398	3	verlag	verlag	PROPN
ejpam-5504	398	4	,	,	PUNCT
ejpam-5504	398	5	corrected	correct	VERB
ejpam-5504	398	6	3rd	3rd	ADJ
ejpam-5504	398	7	printing	printing	NOUN
ejpam-5504	398	8	,	,	PUNCT
ejpam-5504	398	9	2009	2009	NUM
ejpam-5504	398	10	.	.	PUNCT
ejpam-5504	399	1	references	reference	NOUN
ejpam-5504	399	2	3676	3676	NUM
ejpam-5504	399	3	[	[	X
ejpam-5504	399	4	19	19	NUM
ejpam-5504	399	5	]	]	PUNCT
ejpam-5504	399	6	mk	mk	PROPN
ejpam-5504	399	7	sharma	sharma	PROPN
ejpam-5504	399	8	,	,	PUNCT
ejpam-5504	399	9	nitesh	nitesh	ADJ
ejpam-5504	399	10	dhiman	dhiman	NOUN
ejpam-5504	399	11	,	,	PUNCT
ejpam-5504	399	12	shubham	shubham	PROPN
ejpam-5504	399	13	kumar	kumar	PROPN
ejpam-5504	399	14	,	,	PUNCT
ejpam-5504	399	15	laxmi	laxmi	NOUN
ejpam-5504	399	16	rathour	rathour	NOUN
ejpam-5504	399	17	,	,	PUNCT
ejpam-5504	399	18	vishnu	vishnu	PROPN
ejpam-5504	399	19	narayan	narayan	PROPN
ejpam-5504	399	20	mishra	mishra	PROPN
ejpam-5504	399	21	,	,	PUNCT
ejpam-5504	399	22	et	et	PROPN
ejpam-5504	399	23	al	al	PROPN
ejpam-5504	399	24	.	.	PROPN
ejpam-5504	399	25	neutrosophic	neutrosophic	PROPN
ejpam-5504	399	26	monte	monte	PROPN
ejpam-5504	399	27	carlo	carlo	PROPN
ejpam-5504	399	28	simulation	simulation	PROPN
ejpam-5504	399	29	approach	approach	NOUN
ejpam-5504	399	30	for	for	ADP
ejpam-5504	399	31	decision	decision	NOUN
ejpam-5504	399	32	making	making	NOUN
ejpam-5504	399	33	in	in	ADP
ejpam-5504	399	34	medical	medical	ADJ
ejpam-5504	399	35	diagnostic	diagnostic	ADJ
ejpam-5504	399	36	process	process	NOUN
ejpam-5504	399	37	under	under	ADP
ejpam-5504	399	38	uncertain	uncertain	ADJ
ejpam-5504	399	39	environment	environment	NOUN
ejpam-5504	399	40	.	.	PUNCT
ejpam-5504	400	1	int	int	PROPN
ejpam-5504	400	2	j	j	PROPN
ejpam-5504	400	3	neutrosophic	neutrosophic	PROPN
ejpam-5504	400	4	sci	sci	PROPN
ejpam-5504	400	5	,	,	PUNCT
ejpam-5504	400	6	22(1):08–16	22(1):08–16	NUM
ejpam-5504	400	7	,	,	PUNCT
ejpam-5504	400	8	2023	2023	NUM
ejpam-5504	400	9	.	.	PUNCT
ejpam-5504	401	1	[	[	X
ejpam-5504	401	2	20	20	NUM
ejpam-5504	401	3	]	]	X
ejpam-5504	401	4	stephen	stephen	PROPN
ejpam-5504	401	5	simons	simons	PROPN
ejpam-5504	401	6	.	.	PUNCT
ejpam-5504	402	1	minimax	minimax	NOUN
ejpam-5504	402	2	and	and	CCONJ
ejpam-5504	402	3	monotonicity	monotonicity	NOUN
ejpam-5504	402	4	.	.	PUNCT
ejpam-5504	402	5	springer	springer	PROPN
ejpam-5504	402	6	,	,	PUNCT
ejpam-5504	402	7	2006	2006	NUM
ejpam-5504	402	8	.	.	PUNCT
ejpam-5504	403	1	[	[	X
ejpam-5504	403	2	21	21	NUM
ejpam-5504	403	3	]	]	X
ejpam-5504	403	4	stephen	stephen	PROPN
ejpam-5504	403	5	simons	simons	PROPN
ejpam-5504	403	6	and	and	CCONJ
ejpam-5504	403	7	f	f	PROPN
ejpam-5504	403	8	takens	taken	NOUN
ejpam-5504	403	9	.	.	PUNCT
ejpam-5504	403	10	from	from	ADP
ejpam-5504	403	11	hahn	hahn	NOUN
ejpam-5504	403	12	-	-	PUNCT
ejpam-5504	403	13	banach	banach	NOUN
ejpam-5504	403	14	to	to	ADP
ejpam-5504	403	15	monotonicity	monotonicity	NOUN
ejpam-5504	403	16	,	,	PUNCT
ejpam-5504	403	17	volume	volume	NOUN
ejpam-5504	403	18	1693	1693	NUM
ejpam-5504	403	19	.	.	PUNCT
ejpam-5504	403	20	springer	springer	NOUN
ejpam-5504	403	21	,	,	PUNCT
ejpam-5504	403	22	2008	2008	NUM
ejpam-5504	403	23	.	.	PUNCT
ejpam-5504	404	1	[	[	X
ejpam-5504	404	2	22	22	NUM
ejpam-5504	404	3	]	]	PUNCT
ejpam-5504	404	4	eberhard	eberhard	NOUN
ejpam-5504	404	5	zeidler	zeidler	NOUN
ejpam-5504	404	6	.	.	PUNCT
ejpam-5504	405	1	nonlinear	nonlinear	ADJ
ejpam-5504	405	2	functional	functional	ADJ
ejpam-5504	405	3	analysis	analysis	NOUN
ejpam-5504	405	4	and	and	CCONJ
ejpam-5504	405	5	its	its	PRON
ejpam-5504	405	6	applications	application	NOUN
ejpam-5504	405	7	:	:	PUNCT
ejpam-5504	405	8	ii	ii	PROPN
ejpam-5504	405	9	/	/	SYM
ejpam-5504	405	10	b	b	PROPN
ejpam-5504	405	11	:	:	PUNCT
ejpam-5504	405	12	nonlinear	nonlinear	ADJ
ejpam-5504	405	13	monotone	monotone	ADJ
ejpam-5504	405	14	operators	operator	NOUN
ejpam-5504	405	15	.	.	PUNCT
ejpam-5504	406	1	springer	springer	NOUN
ejpam-5504	406	2	science	science	PROPN
ejpam-5504	406	3	&	&	CCONJ
ejpam-5504	406	4	business	business	NOUN
ejpam-5504	406	5	media	medium	NOUN
ejpam-5504	406	6	,	,	PUNCT
ejpam-5504	406	7	2013	2013	NUM
ejpam-5504	406	8	.	.	PUNCT
ejpam-5504	407	1	[	[	X
ejpam-5504	407	2	23	23	NUM
ejpam-5504	407	3	]	]	PUNCT
ejpam-5504	407	4	eberhard	eberhard	NOUN
ejpam-5504	407	5	zeidler	zeidler	NOUN
ejpam-5504	407	6	.	.	PUNCT
ejpam-5504	408	1	nonlinear	nonlinear	ADJ
ejpam-5504	408	2	functional	functional	ADJ
ejpam-5504	408	3	analysis	analysis	NOUN
ejpam-5504	408	4	and	and	CCONJ
ejpam-5504	408	5	its	its	PRON
ejpam-5504	408	6	applications	application	NOUN
ejpam-5504	408	7	:	:	PUNCT
ejpam-5504	408	8	iii	iii	NUM
ejpam-5504	408	9	:	:	PUNCT
ejpam-5504	408	10	variational	variational	ADJ
ejpam-5504	408	11	methods	method	NOUN
ejpam-5504	408	12	and	and	CCONJ
ejpam-5504	408	13	optimization	optimization	NOUN
ejpam-5504	408	14	.	.	PUNCT
ejpam-5504	409	1	springer	springer	NOUN
ejpam-5504	409	2	science	science	PROPN
ejpam-5504	409	3	&	&	CCONJ
ejpam-5504	409	4	business	business	NOUN
ejpam-5504	409	5	media	medium	NOUN
ejpam-5504	409	6	,	,	PUNCT
ejpam-5504	409	7	2013	2013	NUM
ejpam-5504	409	8	.	.	PUNCT