id	sid	tid	token	lemma	pos
ejpam-6031	1	1	european	european	PROPN
ejpam-6031	1	2	journal	journal	PROPN
ejpam-6031	1	3	of	of	ADP
ejpam-6031	1	4	pure	pure	ADJ
ejpam-6031	1	5	and	and	CCONJ
ejpam-6031	1	6	applied	applied	ADJ
ejpam-6031	1	7	mathematics	mathematic	NOUN
ejpam-6031	1	8	2025	2025	NUM
ejpam-6031	1	9	,	,	PUNCT
ejpam-6031	1	10	vol	vol	NOUN
ejpam-6031	1	11	.	.	PROPN
ejpam-6031	1	12	18	18	NUM
ejpam-6031	1	13	,	,	PUNCT
ejpam-6031	1	14	issue	issue	NOUN
ejpam-6031	1	15	2	2	NUM
ejpam-6031	1	16	,	,	PUNCT
ejpam-6031	1	17	article	article	NOUN
ejpam-6031	1	18	number	number	NOUN
ejpam-6031	1	19	6031	6031	NUM
ejpam-6031	1	20	issn	issn	VERB
ejpam-6031	1	21	1307	1307	NUM
ejpam-6031	1	22	-	-	SYM
ejpam-6031	1	23	5543	5543	NUM
ejpam-6031	1	24	–	–	PUNCT
ejpam-6031	1	25	ejpam.com	ejpam.com	X
ejpam-6031	1	26	published	publish	VERB
ejpam-6031	1	27	by	by	ADP
ejpam-6031	1	28	new	new	PROPN
ejpam-6031	1	29	york	york	PROPN
ejpam-6031	1	30	business	business	PROPN
ejpam-6031	1	31	global	global	PROPN
ejpam-6031	1	32	the	the	DET
ejpam-6031	1	33	composition	composition	NOUN
ejpam-6031	1	34	of	of	ADP
ejpam-6031	1	35	modified	modified	ADJ
ejpam-6031	1	36	reflection	reflection	NOUN
ejpam-6031	1	37	operators	operator	NOUN
ejpam-6031	1	38	and	and	CCONJ
ejpam-6031	1	39	their	their	PRON
ejpam-6031	1	40	fixed	fix	VERB
ejpam-6031	1	41	point	point	NOUN
ejpam-6031	1	42	sets	set	VERB
ejpam-6031	1	43	salihah	salihah	ADJ
ejpam-6031	1	44	thabet	thabet	ADJ
ejpam-6031	1	45	alwadani	alwadani	ADJ
ejpam-6031	1	46	mathematics	mathematics	PROPN
ejpam-6031	1	47	,	,	PUNCT
ejpam-6031	1	48	yanbu	yanbu	PROPN
ejpam-6031	1	49	industrial	industrial	PROPN
ejpam-6031	1	50	college	college	PROPN
ejpam-6031	1	51	,	,	PUNCT
ejpam-6031	1	52	the	the	DET
ejpam-6031	1	53	royal	royal	ADJ
ejpam-6031	1	54	comission	comission	NOUN
ejpam-6031	1	55	for	for	ADP
ejpam-6031	1	56	jubail	jubail	PROPN
ejpam-6031	1	57	and	and	CCONJ
ejpam-6031	1	58	yanbu	yanbu	ADJ
ejpam-6031	1	59	,	,	PUNCT
ejpam-6031	1	60	yanbu	yanbu	ADJ
ejpam-6031	1	61	,	,	PUNCT
ejpam-6031	1	62	saudi	saudi	PROPN
ejpam-6031	1	63	arabia	arabia	PROPN
ejpam-6031	1	64	abstract	abstract	NOUN
ejpam-6031	1	65	.	.	PUNCT
ejpam-6031	2	1	the	the	DET
ejpam-6031	2	2	modified	modify	VERB
ejpam-6031	2	3	reflection	reflection	NOUN
ejpam-6031	2	4	operator	operator	NOUN
ejpam-6031	2	5	plays	play	VERB
ejpam-6031	2	6	a	a	DET
ejpam-6031	2	7	crucial	crucial	ADJ
ejpam-6031	2	8	role	role	NOUN
ejpam-6031	2	9	in	in	ADP
ejpam-6031	2	10	optimization	optimization	NOUN
ejpam-6031	2	11	,	,	PUNCT
ejpam-6031	2	12	particularly	particularly	ADV
ejpam-6031	2	13	in	in	ADP
ejpam-6031	2	14	algorithms	algorithm	NOUN
ejpam-6031	2	15	designed	design	VERB
ejpam-6031	2	16	to	to	PART
ejpam-6031	2	17	solve	solve	VERB
ejpam-6031	2	18	constrained	constrained	ADJ
ejpam-6031	2	19	optimization	optimization	NOUN
ejpam-6031	2	20	problems	problem	NOUN
ejpam-6031	2	21	.	.	PUNCT
ejpam-6031	3	1	by	by	ADP
ejpam-6031	3	2	effectively	effectively	ADV
ejpam-6031	3	3	transforming	transform	VERB
ejpam-6031	3	4	feasible	feasible	ADJ
ejpam-6031	3	5	solutions	solution	NOUN
ejpam-6031	3	6	while	while	SCONJ
ejpam-6031	3	7	maintaining	maintain	VERB
ejpam-6031	3	8	their	their	PRON
ejpam-6031	3	9	viability	viability	NOUN
ejpam-6031	3	10	within	within	ADP
ejpam-6031	3	11	defined	define	VERB
ejpam-6031	3	12	constraints	constraint	NOUN
ejpam-6031	3	13	,	,	PUNCT
ejpam-6031	3	14	this	this	DET
ejpam-6031	3	15	operator	operator	NOUN
ejpam-6031	3	16	enables	enable	VERB
ejpam-6031	3	17	smoother	smooth	ADJ
ejpam-6031	3	18	navigation	navigation	NOUN
ejpam-6031	3	19	through	through	ADP
ejpam-6031	3	20	the	the	DET
ejpam-6031	3	21	solution	solution	NOUN
ejpam-6031	3	22	space	space	NOUN
ejpam-6031	3	23	.	.	PUNCT
ejpam-6031	4	1	it	it	PRON
ejpam-6031	4	2	enhances	enhance	VERB
ejpam-6031	4	3	convergence	convergence	NOUN
ejpam-6031	4	4	rates	rate	NOUN
ejpam-6031	4	5	and	and	CCONJ
ejpam-6031	4	6	stability	stability	NOUN
ejpam-6031	4	7	in	in	ADP
ejpam-6031	4	8	iterative	iterative	ADJ
ejpam-6031	4	9	methods	method	NOUN
ejpam-6031	4	10	,	,	PUNCT
ejpam-6031	4	11	such	such	ADJ
ejpam-6031	4	12	as	as	ADP
ejpam-6031	4	13	projected	project	VERB
ejpam-6031	4	14	gradient	gradient	ADJ
ejpam-6031	4	15	descent	descent	NOUN
ejpam-6031	4	16	and	and	CCONJ
ejpam-6031	4	17	proximal	proximal	ADJ
ejpam-6031	4	18	algorithms	algorithm	NOUN
ejpam-6031	4	19	.	.	PUNCT
ejpam-6031	5	1	in	in	ADP
ejpam-6031	5	2	this	this	DET
ejpam-6031	5	3	paper	paper	NOUN
ejpam-6031	5	4	,	,	PUNCT
ejpam-6031	5	5	we	we	PRON
ejpam-6031	5	6	investigate	investigate	VERB
ejpam-6031	5	7	the	the	DET
ejpam-6031	5	8	fixed	fix	VERB
ejpam-6031	5	9	point	point	NOUN
ejpam-6031	5	10	sets	set	NOUN
ejpam-6031	5	11	of	of	ADP
ejpam-6031	5	12	the	the	DET
ejpam-6031	5	13	compositions	composition	NOUN
ejpam-6031	5	14	of	of	ADP
ejpam-6031	5	15	three	three	NUM
ejpam-6031	5	16	modified	modify	VERB
ejpam-6031	5	17	reflection	reflection	NOUN
ejpam-6031	5	18	operators	operator	NOUN
ejpam-6031	5	19	onto	onto	ADP
ejpam-6031	5	20	linear	linear	ADJ
ejpam-6031	5	21	closed	close	VERB
ejpam-6031	5	22	subspaces	subspace	NOUN
ejpam-6031	5	23	.	.	PUNCT
ejpam-6031	6	1	we	we	PRON
ejpam-6031	6	2	also	also	ADV
ejpam-6031	6	3	derive	derive	VERB
ejpam-6031	6	4	formulas	formula	NOUN
ejpam-6031	6	5	for	for	ADP
ejpam-6031	6	6	the	the	DET
ejpam-6031	6	7	compositions	composition	NOUN
ejpam-6031	6	8	under	under	ADP
ejpam-6031	6	9	different	different	ADJ
ejpam-6031	6	10	parameters	parameter	NOUN
ejpam-6031	6	11	.	.	PUNCT
ejpam-6031	7	1	2020	2020	NUM
ejpam-6031	7	2	mathematics	mathematic	NOUN
ejpam-6031	7	3	subject	subject	NOUN
ejpam-6031	7	4	classifications	classification	NOUN
ejpam-6031	7	5	:	:	PUNCT
ejpam-6031	7	6	47h09	47h09	NUM
ejpam-6031	7	7	,	,	PUNCT
ejpam-6031	7	8	47h05	47h05	NUM
ejpam-6031	7	9	,	,	PUNCT
ejpam-6031	7	10	47a06	47a06	NUM
ejpam-6031	7	11	,	,	PUNCT
ejpam-6031	7	12	90c25	90c25	NUM
ejpam-6031	7	13	key	key	ADJ
ejpam-6031	7	14	words	word	NOUN
ejpam-6031	7	15	and	and	CCONJ
ejpam-6031	7	16	phrases	phrase	NOUN
ejpam-6031	7	17	:	:	PUNCT
ejpam-6031	7	18	composition	composition	NOUN
ejpam-6031	7	19	,	,	PUNCT
ejpam-6031	7	20	fixed	fix	VERB
ejpam-6031	7	21	point	point	NOUN
ejpam-6031	7	22	set	set	NOUN
ejpam-6031	7	23	,	,	PUNCT
ejpam-6031	7	24	linear	linear	ADJ
ejpam-6031	7	25	subspace	subspace	NOUN
ejpam-6031	7	26	,	,	PUNCT
ejpam-6031	7	27	orthogonal	orthogonal	ADJ
ejpam-6031	7	28	subspace	subspace	NOUN
ejpam-6031	7	29	,	,	PUNCT
ejpam-6031	7	30	projector	projector	NOUN
ejpam-6031	7	31	,	,	PUNCT
ejpam-6031	7	32	identity	identity	NOUN
ejpam-6031	7	33	operator	operator	NOUN
ejpam-6031	7	34	,	,	PUNCT
ejpam-6031	7	35	modified	modify	VERB
ejpam-6031	7	36	reflector	reflector	NOUN
ejpam-6031	7	37	opeartor	opeartor	NOUN
ejpam-6031	7	38	,	,	PUNCT
ejpam-6031	7	39	reflector	reflector	NOUN
ejpam-6031	7	40	operator	operator	NOUN
ejpam-6031	7	41	1	1	NUM
ejpam-6031	7	42	.	.	PUNCT
ejpam-6031	7	43	introduction	introduction	NOUN
ejpam-6031	7	44	the	the	DET
ejpam-6031	7	45	modified	modify	VERB
ejpam-6031	7	46	reflection	reflection	NOUN
ejpam-6031	7	47	operator	operator	NOUN
ejpam-6031	7	48	is	be	AUX
ejpam-6031	7	49	a	a	DET
ejpam-6031	7	50	vital	vital	ADJ
ejpam-6031	7	51	component	component	NOUN
ejpam-6031	7	52	in	in	ADP
ejpam-6031	7	53	optimization	optimization	NOUN
ejpam-6031	7	54	,	,	PUNCT
ejpam-6031	7	55	particularly	particularly	ADV
ejpam-6031	7	56	in	in	ADP
ejpam-6031	7	57	algorithms	algorithm	NOUN
ejpam-6031	7	58	that	that	PRON
ejpam-6031	7	59	address	address	VERB
ejpam-6031	7	60	constrained	constrain	VERB
ejpam-6031	7	61	optimization	optimization	NOUN
ejpam-6031	7	62	problems	problem	NOUN
ejpam-6031	7	63	.	.	PUNCT
ejpam-6031	8	1	this	this	DET
ejpam-6031	8	2	operator	operator	NOUN
ejpam-6031	8	3	facilitates	facilitate	VERB
ejpam-6031	8	4	the	the	DET
ejpam-6031	8	5	transformation	transformation	NOUN
ejpam-6031	8	6	of	of	ADP
ejpam-6031	8	7	feasible	feasible	ADJ
ejpam-6031	8	8	solutions	solution	NOUN
ejpam-6031	8	9	while	while	SCONJ
ejpam-6031	8	10	ensuring	ensure	VERB
ejpam-6031	8	11	they	they	PRON
ejpam-6031	8	12	remain	remain	VERB
ejpam-6031	8	13	within	within	ADP
ejpam-6031	8	14	the	the	DET
ejpam-6031	8	15	defined	define	VERB
ejpam-6031	8	16	constraints	constraint	NOUN
ejpam-6031	8	17	,	,	PUNCT
ejpam-6031	8	18	allowing	allow	VERB
ejpam-6031	8	19	for	for	ADP
ejpam-6031	8	20	a	a	DET
ejpam-6031	8	21	more	more	ADV
ejpam-6031	8	22	efficient	efficient	ADJ
ejpam-6031	8	23	exploration	exploration	NOUN
ejpam-6031	8	24	of	of	ADP
ejpam-6031	8	25	the	the	DET
ejpam-6031	8	26	solution	solution	NOUN
ejpam-6031	8	27	space	space	NOUN
ejpam-6031	8	28	.	.	PUNCT
ejpam-6031	9	1	by	by	ADP
ejpam-6031	9	2	enhancing	enhance	VERB
ejpam-6031	9	3	the	the	DET
ejpam-6031	9	4	convergence	convergence	NOUN
ejpam-6031	9	5	rates	rate	NOUN
ejpam-6031	9	6	and	and	CCONJ
ejpam-6031	9	7	stability	stability	NOUN
ejpam-6031	9	8	of	of	ADP
ejpam-6031	9	9	iterative	iterative	ADJ
ejpam-6031	9	10	methods	method	NOUN
ejpam-6031	9	11	,	,	PUNCT
ejpam-6031	9	12	such	such	ADJ
ejpam-6031	9	13	as	as	ADP
ejpam-6031	9	14	projected	project	VERB
ejpam-6031	9	15	gradient	gradient	ADJ
ejpam-6031	9	16	descent	descent	NOUN
ejpam-6031	9	17	and	and	CCONJ
ejpam-6031	9	18	proximal	proximal	ADJ
ejpam-6031	9	19	algorithms	algorithm	NOUN
ejpam-6031	9	20	,	,	PUNCT
ejpam-6031	9	21	the	the	DET
ejpam-6031	9	22	modified	modify	VERB
ejpam-6031	9	23	reflection	reflection	NOUN
ejpam-6031	9	24	operator	operator	NOUN
ejpam-6031	9	25	significantly	significantly	ADV
ejpam-6031	9	26	improves	improve	VERB
ejpam-6031	9	27	the	the	DET
ejpam-6031	9	28	performance	performance	NOUN
ejpam-6031	9	29	of	of	ADP
ejpam-6031	9	30	optimization	optimization	NOUN
ejpam-6031	9	31	algorithms	algorithm	NOUN
ejpam-6031	9	32	(	(	PUNCT
ejpam-6031	9	33	see	see	VERB
ejpam-6031	9	34	[	[	X
ejpam-6031	9	35	1	1	NUM
ejpam-6031	9	36	]	]	PUNCT
ejpam-6031	9	37	,	,	PUNCT
ejpam-6031	9	38	[	[	X
ejpam-6031	9	39	2	2	NUM
ejpam-6031	9	40	]	]	PUNCT
ejpam-6031	9	41	,	,	PUNCT
ejpam-6031	9	42	[	[	X
ejpam-6031	9	43	3	3	NUM
ejpam-6031	9	44	]	]	PUNCT
ejpam-6031	9	45	,	,	PUNCT
ejpam-6031	9	46	[	[	X
ejpam-6031	9	47	4	4	NUM
ejpam-6031	9	48	]	]	PUNCT
ejpam-6031	9	49	,	,	PUNCT
ejpam-6031	9	50	[	[	X
ejpam-6031	9	51	5	5	NUM
ejpam-6031	9	52	]	]	PUNCT
ejpam-6031	9	53	,	,	PUNCT
ejpam-6031	9	54	[	[	X
ejpam-6031	9	55	6	6	NUM
ejpam-6031	9	56	]	]	PUNCT
ejpam-6031	9	57	,	,	PUNCT
ejpam-6031	9	58	and	and	CCONJ
ejpam-6031	9	59	[	[	X
ejpam-6031	9	60	7	7	X
ejpam-6031	9	61	]	]	PUNCT
ejpam-6031	9	62	for	for	ADP
ejpam-6031	9	63	more	more	ADJ
ejpam-6031	9	64	information	information	NOUN
ejpam-6031	9	65	)	)	PUNCT
ejpam-6031	9	66	.	.	PUNCT
ejpam-6031	10	1	moreover	moreover	ADV
ejpam-6031	10	2	,	,	PUNCT
ejpam-6031	10	3	it	it	PRON
ejpam-6031	10	4	is	be	AUX
ejpam-6031	10	5	particularly	particularly	ADV
ejpam-6031	10	6	effective	effective	ADJ
ejpam-6031	10	7	in	in	ADP
ejpam-6031	10	8	navigating	navigate	VERB
ejpam-6031	10	9	non	non	ADJ
ejpam-6031	10	10	-	-	ADJ
ejpam-6031	10	11	convex	convex	ADJ
ejpam-6031	10	12	landscapes	landscape	NOUN
ejpam-6031	10	13	,	,	PUNCT
ejpam-6031	10	14	as	as	SCONJ
ejpam-6031	10	15	it	it	PRON
ejpam-6031	10	16	aids	aid	VERB
ejpam-6031	10	17	in	in	ADP
ejpam-6031	10	18	the	the	DET
ejpam-6031	10	19	exploration	exploration	NOUN
ejpam-6031	10	20	of	of	ADP
ejpam-6031	10	21	local	local	ADJ
ejpam-6031	10	22	minima	minima	NOUN
ejpam-6031	10	23	,	,	PUNCT
ejpam-6031	10	24	thereby	thereby	ADV
ejpam-6031	10	25	reducing	reduce	VERB
ejpam-6031	10	26	the	the	DET
ejpam-6031	10	27	risk	risk	NOUN
ejpam-6031	10	28	of	of	ADP
ejpam-6031	10	29	stagnation	stagnation	NOUN
ejpam-6031	10	30	in	in	ADP
ejpam-6031	10	31	suboptimal	suboptimal	ADJ
ejpam-6031	10	32	solutions	solution	NOUN
ejpam-6031	10	33	.	.	PUNCT
ejpam-6031	11	1	its	its	PRON
ejpam-6031	11	2	adaptability	adaptability	NOUN
ejpam-6031	11	3	to	to	ADP
ejpam-6031	11	4	various	various	ADJ
ejpam-6031	11	5	constraints	constraint	NOUN
ejpam-6031	11	6	further	far	ADV
ejpam-6031	11	7	underscores	underscore	VERB
ejpam-6031	11	8	its	its	PRON
ejpam-6031	11	9	versatility	versatility	NOUN
ejpam-6031	11	10	,	,	PUNCT
ejpam-6031	11	11	making	make	VERB
ejpam-6031	11	12	it	it	PRON
ejpam-6031	11	13	an	an	DET
ejpam-6031	11	14	essential	essential	ADJ
ejpam-6031	11	15	tool	tool	NOUN
ejpam-6031	11	16	in	in	ADP
ejpam-6031	11	17	a	a	DET
ejpam-6031	11	18	wide	wide	ADJ
ejpam-6031	11	19	range	range	NOUN
ejpam-6031	11	20	of	of	ADP
ejpam-6031	11	21	applications	application	NOUN
ejpam-6031	11	22	,	,	PUNCT
ejpam-6031	11	23	from	from	ADP
ejpam-6031	11	24	machine	machine	NOUN
ejpam-6031	11	25	learning	learn	VERB
ejpam-6031	11	26	doi	doi	NOUN
ejpam-6031	11	27	:	:	PUNCT
ejpam-6031	11	28	https://doi.org/10.29020/nybg.ejpam.v18i2.6031	https://doi.org/10.29020/nybg.ejpam.v18i2.6031	PROPN
ejpam-6031	11	29	email	email	NOUN
ejpam-6031	11	30	address	address	NOUN
ejpam-6031	11	31	:	:	PUNCT
ejpam-6031	11	32	salihah.s.alwadani@gmail.com	salihah.s.alwadani@gmail.com	PROPN
ejpam-6031	11	33	(	(	PUNCT
ejpam-6031	11	34	s.	s.	PROPN
ejpam-6031	11	35	th	th	PROPN
ejpam-6031	11	36	.	.	PUNCT
ejpam-6031	11	37	alwadani	alwadani	PROPN
ejpam-6031	11	38	)	)	PUNCT
ejpam-6031	11	39	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6031	12	1	1	1	NUM
ejpam-6031	12	2	copyright	copyright	NOUN
ejpam-6031	12	3	:	:	PUNCT
ejpam-6031	12	4	©	©	PROPN
ejpam-6031	12	5	2025	2025	NUM
ejpam-6031	12	6	the	the	DET
ejpam-6031	12	7	author(s	author(s	NOUN
ejpam-6031	12	8	)	)	PUNCT
ejpam-6031	12	9	.	.	PUNCT
ejpam-6031	13	1	(	(	PUNCT
ejpam-6031	13	2	cc	cc	NOUN
ejpam-6031	13	3	by	by	ADP
ejpam-6031	13	4	-	-	PUNCT
ejpam-6031	13	5	nc	nc	PROPN
ejpam-6031	13	6	4.0	4.0	NUM
ejpam-6031	13	7	)	)	PUNCT
ejpam-6031	13	8	s.th	s.th	PROPN
ejpam-6031	13	9	.	.	PUNCT
ejpam-6031	13	10	alwadani	alwadani	PROPN
ejpam-6031	13	11	/	/	SYM
ejpam-6031	13	12	eur	eur	PROPN
ejpam-6031	13	13	.	.	PUNCT
ejpam-6031	14	1	j.	j.	PROPN
ejpam-6031	14	2	pure	pure	PROPN
ejpam-6031	14	3	appl	appl	PROPN
ejpam-6031	14	4	.	.	PROPN
ejpam-6031	14	5	math	math	PROPN
ejpam-6031	14	6	,	,	PUNCT
ejpam-6031	14	7	18	18	NUM
ejpam-6031	14	8	(	(	PUNCT
ejpam-6031	14	9	2	2	NUM
ejpam-6031	14	10	)	)	PUNCT
ejpam-6031	14	11	(	(	PUNCT
ejpam-6031	14	12	2025	2025	NUM
ejpam-6031	14	13	)	)	PUNCT
ejpam-6031	14	14	,	,	PUNCT
ejpam-6031	14	15	6031	6031	NUM
ejpam-6031	14	16	2	2	NUM
ejpam-6031	14	17	of	of	ADP
ejpam-6031	14	18	13	13	NUM
ejpam-6031	14	19	to	to	ADP
ejpam-6031	14	20	engineering	engineering	NOUN
ejpam-6031	14	21	design	design	NOUN
ejpam-6031	14	22	.	.	PUNCT
ejpam-6031	15	1	overall	overall	ADV
ejpam-6031	15	2	,	,	PUNCT
ejpam-6031	15	3	the	the	DET
ejpam-6031	15	4	modified	modified	ADJ
ejpam-6031	15	5	reflection	reflection	NOUN
ejpam-6031	15	6	operator	operator	NOUN
ejpam-6031	15	7	contributes	contribute	VERB
ejpam-6031	15	8	to	to	ADP
ejpam-6031	15	9	more	more	ADV
ejpam-6031	15	10	robust	robust	ADJ
ejpam-6031	15	11	and	and	CCONJ
ejpam-6031	15	12	efficient	efficient	ADJ
ejpam-6031	15	13	optimization	optimization	NOUN
ejpam-6031	15	14	processes	process	NOUN
ejpam-6031	15	15	,	,	PUNCT
ejpam-6031	15	16	ensuring	ensure	VERB
ejpam-6031	15	17	that	that	SCONJ
ejpam-6031	15	18	algorithms	algorithm	NOUN
ejpam-6031	15	19	can	can	AUX
ejpam-6031	15	20	effectively	effectively	ADV
ejpam-6031	15	21	tackle	tackle	VERB
ejpam-6031	15	22	real	real	ADJ
ejpam-6031	15	23	-	-	PUNCT
ejpam-6031	15	24	world	world	NOUN
ejpam-6031	15	25	problems	problem	NOUN
ejpam-6031	15	26	(	(	PUNCT
ejpam-6031	15	27	see	see	VERB
ejpam-6031	15	28	[	[	X
ejpam-6031	15	29	8	8	NUM
ejpam-6031	15	30	]	]	PUNCT
ejpam-6031	15	31	for	for	ADP
ejpam-6031	15	32	more	more	ADJ
ejpam-6031	15	33	information	information	NOUN
ejpam-6031	15	34	)	)	PUNCT
ejpam-6031	15	35	.	.	PUNCT
ejpam-6031	16	1	throughout	throughout	ADV
ejpam-6031	16	2	,	,	PUNCT
ejpam-6031	16	3	we	we	PRON
ejpam-6031	16	4	assume	assume	VERB
ejpam-6031	16	5	that	that	SCONJ
ejpam-6031	16	6	h	h	NOUN
ejpam-6031	16	7	is	be	AUX
ejpam-6031	16	8	a	a	DET
ejpam-6031	16	9	real	real	ADJ
ejpam-6031	16	10	hilbert	hilbert	NOUN
ejpam-6031	16	11	space	space	NOUN
ejpam-6031	16	12	with	with	ADP
ejpam-6031	16	13	inner	inner	ADJ
ejpam-6031	16	14	product	product	NOUN
ejpam-6031	16	15	⟨	⟨	VERB
ejpam-6031	16	16	·	·	PUNCT
ejpam-6031	16	17	,	,	PUNCT
ejpam-6031	16	18	·	·	PUNCT
ejpam-6031	16	19	⟩	⟩	NOUN
ejpam-6031	16	20	:	:	PUNCT
ejpam-6031	16	21	h×h	h×h	NOUN
ejpam-6031	16	22	→	→	SYM
ejpam-6031	16	23	r	r	NOUN
ejpam-6031	16	24	,	,	PUNCT
ejpam-6031	16	25	(	(	PUNCT
ejpam-6031	16	26	1	1	NUM
ejpam-6031	16	27	)	)	PUNCT
ejpam-6031	16	28	and	and	CCONJ
ejpam-6031	16	29	induced	induce	VERB
ejpam-6031	16	30	norm	norm	NOUN
ejpam-6031	16	31	∥	∥	X
ejpam-6031	16	32	·	·	PUNCT
ejpam-6031	16	33	∥	∥	NUM
ejpam-6031	16	34	:	:	PUNCT
ejpam-6031	16	35	h	h	NOUN
ejpam-6031	16	36	→	→	SYM
ejpam-6031	16	37	r	r	NOUN
ejpam-6031	16	38	:	:	PUNCT
ejpam-6031	16	39	x	x	SYM
ejpam-6031	16	40	7→	7→	NUM
ejpam-6031	16	41	√	√	NUM
ejpam-6031	16	42	⟨x	⟨x	NUM
ejpam-6031	16	43	,	,	PUNCT
ejpam-6031	16	44	x⟩.	x⟩.	PROPN
ejpam-6031	16	45	let	let	VERB
ejpam-6031	16	46	a	a	DET
ejpam-6031	16	47	:	:	PUNCT
ejpam-6031	16	48	h	h	NOUN
ejpam-6031	16	49	⇒	⇒	NOUN
ejpam-6031	16	50	h	h	NOUN
ejpam-6031	16	51	be	be	AUX
ejpam-6031	16	52	an	an	DET
ejpam-6031	16	53	arbitrary	arbitrary	ADJ
ejpam-6031	16	54	set	set	VERB
ejpam-6031	16	55	valued	value	VERB
ejpam-6031	16	56	operator	operator	NOUN
ejpam-6031	16	57	,	,	PUNCT
ejpam-6031	16	58	i.e.	i.e.	X
ejpam-6031	16	59	,	,	PUNCT
ejpam-6031	16	60	ax	ax	NOUN
ejpam-6031	16	61	⊆	⊆	NUM
ejpam-6031	16	62	h	h	NOUN
ejpam-6031	16	63	(	(	PUNCT
ejpam-6031	16	64	∀x	∀x	X
ejpam-6031	16	65	∈	∈	PROPN
ejpam-6031	16	66	h	h	NOUN
ejpam-6031	16	67	)	)	PUNCT
ejpam-6031	16	68	.	.	PUNCT
ejpam-6031	17	1	the	the	DET
ejpam-6031	17	2	graph	graph	NOUN
ejpam-6031	17	3	of	of	ADP
ejpam-6031	17	4	a	a	PRON
ejpam-6031	17	5	,	,	PUNCT
ejpam-6031	17	6	donoted	donote	VERB
ejpam-6031	17	7	by	by	ADP
ejpam-6031	17	8	then	then	ADV
ejpam-6031	17	9	gra	gra	PROPN
ejpam-6031	17	10	a	a	PROPN
ejpam-6031	17	11	,	,	PUNCT
ejpam-6031	17	12	is	be	AUX
ejpam-6031	17	13	defined	define	VERB
ejpam-6031	17	14	as	as	ADP
ejpam-6031	17	15	gra	gra	PROPN
ejpam-6031	17	16	a	a	PROPN
ejpam-6031	17	17	=	=	X
ejpam-6031	17	18	{	{	PUNCT
ejpam-6031	17	19	(	(	PUNCT
ejpam-6031	17	20	x	x	NOUN
ejpam-6031	17	21	,	,	PUNCT
ejpam-6031	17	22	y	y	NOUN
ejpam-6031	17	23	)	)	PUNCT
ejpam-6031	17	24	∈	∈	PROPN
ejpam-6031	17	25	h×h	h×h	PROPN
ejpam-6031	17	26	|	|	NOUN
ejpam-6031	17	27	y	y	PROPN
ejpam-6031	17	28	∈	∈	NOUN
ejpam-6031	17	29	ax	ax	NOUN
ejpam-6031	17	30	}	}	PUNCT
ejpam-6031	17	31	.	.	PUNCT
ejpam-6031	18	1	a	a	DET
ejpam-6031	18	2	set	set	NOUN
ejpam-6031	18	3	-	-	PUNCT
ejpam-6031	18	4	valued	value	VERB
ejpam-6031	18	5	operator	operator	NOUN
ejpam-6031	18	6	a	a	PRON
ejpam-6031	18	7	:	:	PUNCT
ejpam-6031	18	8	h	h	NOUN
ejpam-6031	18	9	⇒	⇒	NOUN
ejpam-6031	18	10	h	h	NOUN
ejpam-6031	18	11	is	be	AUX
ejpam-6031	18	12	a	a	DET
ejpam-6031	18	13	monotone	monotone	NOUN
ejpam-6031	18	14	if	if	SCONJ
ejpam-6031	18	15	(	(	PUNCT
ejpam-6031	18	16	∀	∀	X
ejpam-6031	18	17	(	(	PUNCT
ejpam-6031	18	18	x	x	X
ejpam-6031	18	19	,	,	PUNCT
ejpam-6031	18	20	u	u	NOUN
ejpam-6031	18	21	)	)	PUNCT
ejpam-6031	18	22	∈	∈	PROPN
ejpam-6031	18	23	gra	gra	PROPN
ejpam-6031	18	24	a	a	NOUN
ejpam-6031	18	25	)	)	PUNCT
ejpam-6031	18	26	(	(	PUNCT
ejpam-6031	18	27	∀	∀	X
ejpam-6031	18	28	(	(	PUNCT
ejpam-6031	18	29	y	y	NOUN
ejpam-6031	18	30	,	,	PUNCT
ejpam-6031	18	31	v	v	NOUN
ejpam-6031	18	32	)	)	PUNCT
ejpam-6031	18	33	∈	∈	PROPN
ejpam-6031	18	34	gra	gra	PROPN
ejpam-6031	18	35	a	a	PRON
ejpam-6031	18	36	)	)	PUNCT
ejpam-6031	18	37	⟨x	⟨x	VERB
ejpam-6031	18	38	−	−	PROPN
ejpam-6031	18	39	y	y	PROPN
ejpam-6031	18	40	,	,	PUNCT
ejpam-6031	18	41	u	u	NOUN
ejpam-6031	18	42	−	−	PROPN
ejpam-6031	18	43	v⟩	v⟩	VERB
ejpam-6031	18	44	≥	≥	NOUN
ejpam-6031	18	45	0	0	NUM
ejpam-6031	18	46	.	.	PUNCT
ejpam-6031	19	1	a	a	DET
ejpam-6031	19	2	monotone	monotone	ADJ
ejpam-6031	19	3	operator	operator	NOUN
ejpam-6031	19	4	a	a	PRON
ejpam-6031	19	5	is	be	AUX
ejpam-6031	19	6	a	a	DET
ejpam-6031	19	7	maximally	maximally	ADV
ejpam-6031	19	8	monotone	monotone	ADJ
ejpam-6031	19	9	if	if	SCONJ
ejpam-6031	19	10	there	there	PRON
ejpam-6031	19	11	exists	exist	VERB
ejpam-6031	19	12	no	no	DET
ejpam-6031	19	13	monotone	monotone	ADJ
ejpam-6031	19	14	operator	operator	NOUN
ejpam-6031	19	15	b	b	NOUN
ejpam-6031	19	16	such	such	ADJ
ejpam-6031	19	17	that	that	PRON
ejpam-6031	19	18	gra	gra	PROPN
ejpam-6031	19	19	a	a	DET
ejpam-6031	19	20	⊂	⊂	PROPN
ejpam-6031	19	21	gra	gra	PROPN
ejpam-6031	19	22	b.	b.	PROPN
ejpam-6031	19	23	that	that	PRON
ejpam-6031	19	24	is	be	AUX
ejpam-6031	19	25	,	,	PUNCT
ejpam-6031	19	26	for	for	ADP
ejpam-6031	19	27	every	every	DET
ejpam-6031	19	28	(	(	PUNCT
ejpam-6031	19	29	x	x	NOUN
ejpam-6031	19	30	,	,	PUNCT
ejpam-6031	19	31	u	u	NOUN
ejpam-6031	19	32	)	)	PUNCT
ejpam-6031	19	33	∈	∈	PROPN
ejpam-6031	19	34	h×h	h×h	NOUN
ejpam-6031	19	35	,	,	PUNCT
ejpam-6031	19	36	(	(	PUNCT
ejpam-6031	19	37	(	(	PUNCT
ejpam-6031	19	38	x	x	X
ejpam-6031	19	39	,	,	PUNCT
ejpam-6031	19	40	u	u	NOUN
ejpam-6031	19	41	)	)	PUNCT
ejpam-6031	19	42	∈	∈	PROPN
ejpam-6031	19	43	gra	gra	PROPN
ejpam-6031	19	44	a	a	DET
ejpam-6031	19	45	)	)	PUNCT
ejpam-6031	19	46	⇔	⇔	X
ejpam-6031	19	47	(	(	PUNCT
ejpam-6031	19	48	∀	∀	X
ejpam-6031	19	49	(	(	PUNCT
ejpam-6031	19	50	y	y	NOUN
ejpam-6031	19	51	,	,	PUNCT
ejpam-6031	19	52	v	v	NOUN
ejpam-6031	19	53	)	)	PUNCT
ejpam-6031	19	54	∈	∈	PROPN
ejpam-6031	19	55	gra	gra	PROPN
ejpam-6031	19	56	a	a	PRON
ejpam-6031	19	57	)	)	PUNCT
ejpam-6031	19	58	⟨x	⟨x	VERB
ejpam-6031	19	59	−	−	PROPN
ejpam-6031	19	60	y	y	PROPN
ejpam-6031	19	61	,	,	PUNCT
ejpam-6031	19	62	u	u	NOUN
ejpam-6031	19	63	−	−	PROPN
ejpam-6031	19	64	v⟩	v⟩	VERB
ejpam-6031	19	65	≥	≥	NOUN
ejpam-6031	19	66	0	0	NUM
ejpam-6031	19	67	.	.	PUNCT
ejpam-6031	20	1	the	the	DET
ejpam-6031	20	2	i	i	PROPN
ejpam-6031	20	3	d	d	PROPN
ejpam-6031	20	4	is	be	AUX
ejpam-6031	20	5	the	the	DET
ejpam-6031	20	6	identity	identity	NOUN
ejpam-6031	20	7	operator	operator	NOUN
ejpam-6031	20	8	defines	define	NOUN
ejpam-6031	20	9	as	as	ADP
ejpam-6031	20	10	i	i	PROPN
ejpam-6031	20	11	d	d	PROPN
ejpam-6031	20	12	:	:	PUNCT
ejpam-6031	20	13	h	h	NOUN
ejpam-6031	20	14	→	→	SYM
ejpam-6031	20	15	h	h	NOUN
ejpam-6031	20	16	:	:	PUNCT
ejpam-6031	20	17	x	x	X
ejpam-6031	20	18	→	→	SYM
ejpam-6031	20	19	x	x	X
ejpam-6031	20	20	and	and	CCONJ
ejpam-6031	20	21	satisfies	satisfie	NOUN
ejpam-6031	20	22	(	(	PUNCT
ejpam-6031	20	23	8)	8)	NUM
ejpam-6031	20	24	.	.	PUNCT
ejpam-6031	21	1	definition	definition	NOUN
ejpam-6031	21	2	1	1	NUM
ejpam-6031	21	3	.	.	PUNCT
ejpam-6031	22	1	[	[	X
ejpam-6031	22	2	9	9	NUM
ejpam-6031	22	3	,	,	PUNCT
ejpam-6031	22	4	definition	definition	NOUN
ejpam-6031	22	5	3.28	3.28	NUM
ejpam-6031	22	6	]	]	PUNCT
ejpam-6031	22	7	let	let	VERB
ejpam-6031	22	8	a	a	PRON
ejpam-6031	22	9	be	be	AUX
ejpam-6031	22	10	a	a	DET
ejpam-6031	22	11	monotone	monotone	ADJ
ejpam-6031	22	12	operator	operator	NOUN
ejpam-6031	22	13	from	from	ADP
ejpam-6031	22	14	h	h	PROPN
ejpam-6031	22	15	⇒	⇒	PROPN
ejpam-6031	22	16	h	h	NOUN
ejpam-6031	22	17	and	and	CCONJ
ejpam-6031	22	18	denote	denote	VERB
ejpam-6031	22	19	the	the	DET
ejpam-6031	22	20	associated	associated	ADJ
ejpam-6031	22	21	resolvent	resolvent	NOUN
ejpam-6031	22	22	by	by	ADP
ejpam-6031	22	23	ja	ja	PROPN
ejpam-6031	22	24	=	=	SYM
ejpam-6031	22	25	(	(	PUNCT
ejpam-6031	22	26	id+a)−1	id+a)−1	NOUN
ejpam-6031	22	27	.	.	PUNCT
ejpam-6031	23	1	(	(	PUNCT
ejpam-6031	23	2	2	2	X
ejpam-6031	23	3	)	)	PUNCT
ejpam-6031	23	4	the	the	DET
ejpam-6031	23	5	reflected	reflect	VERB
ejpam-6031	23	6	resolvent	resolvent	NOUN
ejpam-6031	23	7	of	of	ADP
ejpam-6031	23	8	a	a	PRON
ejpam-6031	23	9	is	be	AUX
ejpam-6031	23	10	denoted	denote	VERB
ejpam-6031	23	11	by	by	ADP
ejpam-6031	23	12	ra	ra	PROPN
ejpam-6031	23	13	and	and	CCONJ
ejpam-6031	23	14	defined	define	VERB
ejpam-6031	23	15	by	by	ADP
ejpam-6031	23	16	ra	ra	PROPN
ejpam-6031	24	1	=	=	PROPN
ejpam-6031	24	2	2ja	2ja	PROPN
ejpam-6031	24	3	−	−	PROPN
ejpam-6031	25	1	i	i	PROPN
ejpam-6031	25	2	d	d	PROPN
ejpam-6031	25	3	.	.	PUNCT
ejpam-6031	26	1	(	(	PUNCT
ejpam-6031	26	2	3	3	X
ejpam-6031	26	3	)	)	PUNCT
ejpam-6031	26	4	example	example	NOUN
ejpam-6031	27	1	1	1	NUM
ejpam-6031	27	2	.	.	PUNCT
ejpam-6031	27	3	let	let	VERB
ejpam-6031	27	4	a	a	DET
ejpam-6031	27	5	=	=	X
ejpam-6031	27	6	i	i	PRON
ejpam-6031	27	7	d.	d.	PROPN
ejpam-6031	27	8	then	then	ADV
ejpam-6031	27	9	ja	ja	PROPN
ejpam-6031	27	10	=	=	NOUN
ejpam-6031	27	11	1	1	NUM
ejpam-6031	27	12	2	2	NUM
ejpam-6031	27	13	i	i	NOUN
ejpam-6031	27	14	d	d	PROPN
ejpam-6031	27	15	and	and	CCONJ
ejpam-6031	27	16	ra	ra	PROPN
ejpam-6031	28	1	=	=	NOUN
ejpam-6031	28	2	0	0	X
ejpam-6031	28	3	.	.	PUNCT
ejpam-6031	29	1	to	to	PART
ejpam-6031	29	2	show	show	VERB
ejpam-6031	29	3	that	that	PRON
ejpam-6031	29	4	let	let	VERB
ejpam-6031	29	5	y	y	PROPN
ejpam-6031	29	6	∈	∈	PROPN
ejpam-6031	29	7	h	h	NOUN
ejpam-6031	29	8	and	and	CCONJ
ejpam-6031	29	9	set	set	VERB
ejpam-6031	29	10	x	x	PUNCT
ejpam-6031	29	11	=	=	PUNCT
ejpam-6031	29	12	jay	jay	PROPN
ejpam-6031	29	13	.	.	PUNCT
ejpam-6031	30	1	then	then	ADV
ejpam-6031	30	2	y	y	PROPN
ejpam-6031	30	3	∈	∈	PROPN
ejpam-6031	30	4	(	(	PUNCT
ejpam-6031	30	5	id+a	id+a	PROPN
ejpam-6031	30	6	)	)	PUNCT
ejpam-6031	30	7	x.	x.	NOUN
ejpam-6031	31	1	this	this	PRON
ejpam-6031	31	2	implies	imply	VERB
ejpam-6031	31	3	that	that	SCONJ
ejpam-6031	31	4	y	y	PROPN
ejpam-6031	31	5	=	=	PUNCT
ejpam-6031	31	6	x	x	PROPN
ejpam-6031	32	1	+	+	NUM
ejpam-6031	32	2	x	x	SYM
ejpam-6031	32	3	⇔	⇔	PROPN
ejpam-6031	32	4	y	y	PROPN
ejpam-6031	32	5	=	=	PROPN
ejpam-6031	32	6	2x	2x	PROPN
ejpam-6031	32	7	⇔	⇔	X
ejpam-6031	32	8	x	x	PUNCT
ejpam-6031	32	9	=	=	SYM
ejpam-6031	32	10	1	1	NUM
ejpam-6031	32	11	2	2	NUM
ejpam-6031	32	12	y.	y.	NOUN
ejpam-6031	32	13	therefore	therefore	ADV
ejpam-6031	32	14	,	,	PUNCT
ejpam-6031	32	15	ja	ja	PROPN
ejpam-6031	32	16	=	=	NOUN
ejpam-6031	32	17	1	1	NUM
ejpam-6031	32	18	2	2	NUM
ejpam-6031	32	19	i	i	NOUN
ejpam-6031	32	20	d	d	PROPN
ejpam-6031	32	21	.	.	PUNCT
ejpam-6031	33	1	using	use	VERB
ejpam-6031	33	2	(	(	PUNCT
ejpam-6031	33	3	3	3	NUM
ejpam-6031	33	4	)	)	PUNCT
ejpam-6031	33	5	gives	give	VERB
ejpam-6031	33	6	ra	ra	NOUN
ejpam-6031	33	7	=	=	NOUN
ejpam-6031	33	8	2(1/2	2(1/2	NUM
ejpam-6031	33	9	)	)	PUNCT
ejpam-6031	33	10	id−	id−	X
ejpam-6031	34	1	i	i	NOUN
ejpam-6031	34	2	d	d	NOUN
ejpam-6031	34	3	=	=	SYM
ejpam-6031	34	4	0	0	X
ejpam-6031	34	5	.	.	PUNCT
ejpam-6031	35	1	definition	definition	NOUN
ejpam-6031	35	2	2	2	NUM
ejpam-6031	35	3	.	.	PUNCT
ejpam-6031	36	1	[	[	X
ejpam-6031	36	2	9	9	NUM
ejpam-6031	36	3	,	,	PUNCT
ejpam-6031	36	4	definition	definition	NOUN
ejpam-6031	36	5	4.1	4.1	NUM
ejpam-6031	36	6	]	]	PUNCT
ejpam-6031	36	7	let	let	VERB
ejpam-6031	36	8	u	u	PRON
ejpam-6031	36	9	be	be	AUX
ejpam-6031	36	10	a	a	DET
ejpam-6031	36	11	nonempty	nonempty	ADJ
ejpam-6031	36	12	subset	subset	NOUN
ejpam-6031	36	13	of	of	ADP
ejpam-6031	36	14	h.	h.	PROPN
ejpam-6031	36	15	a	a	DET
ejpam-6031	36	16	mapping	mapping	NOUN
ejpam-6031	36	17	t	t	NOUN
ejpam-6031	36	18	:	:	PUNCT
ejpam-6031	36	19	u	u	NOUN
ejpam-6031	36	20	→	→	X
ejpam-6031	36	21	h	h	NOUN
ejpam-6031	36	22	is	be	AUX
ejpam-6031	36	23	nonexpansive	nonexpansive	ADJ
ejpam-6031	36	24	or	or	CCONJ
ejpam-6031	36	25	lipschitz	lipschitz	VERB
ejpam-6031	36	26	continuous	continuous	ADJ
ejpam-6031	36	27	with	with	ADP
ejpam-6031	36	28	constant	constant	ADJ
ejpam-6031	36	29	1	1	NUM
ejpam-6031	36	30	,	,	PUNCT
ejpam-6031	36	31	i.e.	i.e.	X
ejpam-6031	36	32	,	,	PUNCT
ejpam-6031	36	33	(	(	PUNCT
ejpam-6031	36	34	∀x	∀x	X
ejpam-6031	36	35	∈	∈	PROPN
ejpam-6031	36	36	u	u	NOUN
ejpam-6031	36	37	)	)	PUNCT
ejpam-6031	36	38	(	(	PUNCT
ejpam-6031	36	39	∀y	∀y	NUM
ejpam-6031	36	40	∈	∈	PROPN
ejpam-6031	36	41	u	u	NOUN
ejpam-6031	36	42	)	)	PUNCT
ejpam-6031	37	1	∥tx	∥tx	ADP
ejpam-6031	37	2	−	−	PROPN
ejpam-6031	38	1	ty∥	ty∥	NOUN
ejpam-6031	38	2	≤	≤	ADV
ejpam-6031	39	1	∥x	∥x	AUX
ejpam-6031	39	2	−	−	PROPN
ejpam-6031	39	3	y∥.	y∥.	NOUN
ejpam-6031	39	4	(	(	PUNCT
ejpam-6031	39	5	4	4	NUM
ejpam-6031	39	6	)	)	PUNCT
ejpam-6031	39	7	moreover	moreover	ADV
ejpam-6031	39	8	,	,	PUNCT
ejpam-6031	39	9	t	t	X
ejpam-6031	39	10	:	:	PUNCT
ejpam-6031	39	11	u	u	NOUN
ejpam-6031	39	12	→	→	X
ejpam-6031	39	13	h	h	NOUN
ejpam-6031	39	14	is	be	AUX
ejpam-6031	39	15	firmly	firmly	ADV
ejpam-6031	39	16	nonexpansive	nonexpansive	ADJ
ejpam-6031	39	17	if	if	SCONJ
ejpam-6031	39	18	(	(	PUNCT
ejpam-6031	39	19	∀x	∀x	X
ejpam-6031	39	20	∈	∈	PROPN
ejpam-6031	39	21	u	u	NOUN
ejpam-6031	39	22	)	)	PUNCT
ejpam-6031	39	23	(	(	PUNCT
ejpam-6031	39	24	∀y	∀y	PROPN
ejpam-6031	39	25	∈	∈	PROPN
ejpam-6031	39	26	u	u	NOUN
ejpam-6031	39	27	)	)	PUNCT
ejpam-6031	39	28	∥tx	∥tx	ADP
ejpam-6031	40	1	−	−	PROPN
ejpam-6031	40	2	ty∥2	ty∥2	NOUN
ejpam-6031	40	3	+	+	CCONJ
ejpam-6031	40	4	∥(id−t)x	∥(id−t)x	PROPN
ejpam-6031	40	5	−	−	PROPN
ejpam-6031	40	6	(	(	PUNCT
ejpam-6031	40	7	id−t)y∥2	id−t)y∥2	PROPN
ejpam-6031	40	8	≤	≤	PUNCT
ejpam-6031	41	1	∥x	∥x	PROPN
ejpam-6031	41	2	−	−	PROPN
ejpam-6031	41	3	y∥2	y∥2	NOUN
ejpam-6031	41	4	.	.	PUNCT
ejpam-6031	42	1	(	(	PUNCT
ejpam-6031	42	2	5	5	X
ejpam-6031	42	3	)	)	PUNCT
ejpam-6031	42	4	the	the	DET
ejpam-6031	42	5	fix	fix	NOUN
ejpam-6031	42	6	t	t	NOUN
ejpam-6031	42	7	is	be	AUX
ejpam-6031	42	8	the	the	DET
ejpam-6031	42	9	set	set	NOUN
ejpam-6031	42	10	of	of	ADP
ejpam-6031	42	11	fixed	fix	VERB
ejpam-6031	42	12	points	point	NOUN
ejpam-6031	42	13	of	of	ADP
ejpam-6031	42	14	t	t	PROPN
ejpam-6031	42	15	defined	define	VERB
ejpam-6031	42	16	as	as	ADP
ejpam-6031	42	17	fix	fix	NOUN
ejpam-6031	42	18	t	t	NOUN
ejpam-6031	42	19	:	:	PUNCT
ejpam-6031	42	20	=	=	SYM
ejpam-6031	42	21	{	{	PUNCT
ejpam-6031	42	22	x	x	SYM
ejpam-6031	42	23	∈	∈	NOUN
ejpam-6031	42	24	h	h	NOUN
ejpam-6031	42	25	|	|	ADV
ejpam-6031	42	26	x	x	X
ejpam-6031	42	27	=	=	SYM
ejpam-6031	42	28	tx	tx	PROPN
ejpam-6031	42	29	}	}	PUNCT
ejpam-6031	42	30	.	.	PUNCT
ejpam-6031	43	1	(	(	PUNCT
ejpam-6031	43	2	6	6	X
ejpam-6031	43	3	)	)	PUNCT
ejpam-6031	43	4	s.th	s.th	PROPN
ejpam-6031	43	5	.	.	PUNCT
ejpam-6031	43	6	alwadani	alwadani	PROPN
ejpam-6031	43	7	/	/	SYM
ejpam-6031	43	8	eur	eur	PROPN
ejpam-6031	43	9	.	.	PUNCT
ejpam-6031	44	1	j.	j.	PROPN
ejpam-6031	44	2	pure	pure	PROPN
ejpam-6031	44	3	appl	appl	PROPN
ejpam-6031	44	4	.	.	PROPN
ejpam-6031	44	5	math	math	PROPN
ejpam-6031	44	6	,	,	PUNCT
ejpam-6031	44	7	18	18	NUM
ejpam-6031	44	8	(	(	PUNCT
ejpam-6031	44	9	2	2	NUM
ejpam-6031	44	10	)	)	PUNCT
ejpam-6031	44	11	(	(	PUNCT
ejpam-6031	44	12	2025	2025	NUM
ejpam-6031	44	13	)	)	PUNCT
ejpam-6031	44	14	,	,	PUNCT
ejpam-6031	44	15	6031	6031	NUM
ejpam-6031	44	16	3	3	NUM
ejpam-6031	44	17	of	of	ADP
ejpam-6031	44	18	13	13	NUM
ejpam-6031	44	19	definition	definition	NOUN
ejpam-6031	44	20	3	3	NUM
ejpam-6031	44	21	.	.	PUNCT
ejpam-6031	45	1	let	let	VERB
ejpam-6031	45	2	u	u	PRON
ejpam-6031	45	3	be	be	AUX
ejpam-6031	45	4	a	a	DET
ejpam-6031	45	5	nonempty	nonempty	ADV
ejpam-6031	45	6	closed	close	VERB
ejpam-6031	45	7	and	and	CCONJ
ejpam-6031	45	8	convex	convex	NOUN
ejpam-6031	45	9	subset	subset	NOUN
ejpam-6031	45	10	of	of	ADP
ejpam-6031	45	11	h	h	NOUN
ejpam-6031	45	12	and	and	CCONJ
ejpam-6031	45	13	let	let	VERB
ejpam-6031	45	14	z	z	PROPN
ejpam-6031	45	15	∈	∈	PROPN
ejpam-6031	45	16	h.	h.	NOUN
ejpam-6031	45	17	the	the	DET
ejpam-6031	45	18	projection	projection	NOUN
ejpam-6031	45	19	operator	operator	NOUN
ejpam-6031	45	20	(	(	PUNCT
ejpam-6031	45	21	this	this	PRON
ejpam-6031	45	22	is	be	AUX
ejpam-6031	45	23	also	also	ADV
ejpam-6031	45	24	known	know	VERB
ejpam-6031	45	25	as	as	ADP
ejpam-6031	45	26	the	the	DET
ejpam-6031	45	27	closet	closet	NOUN
ejpam-6031	45	28	point	point	NOUN
ejpam-6031	45	29	mapping	mapping	NOUN
ejpam-6031	45	30	)	)	PUNCT
ejpam-6031	45	31	of	of	ADP
ejpam-6031	45	32	z	z	PROPN
ejpam-6031	45	33	onto	onto	ADP
ejpam-6031	45	34	u	u	NOUN
ejpam-6031	45	35	is	be	AUX
ejpam-6031	45	36	the	the	DET
ejpam-6031	45	37	unique	unique	ADJ
ejpam-6031	45	38	point	point	NOUN
ejpam-6031	45	39	in	in	ADP
ejpam-6031	45	40	u	u	NOUN
ejpam-6031	45	41	denoted	denote	VERB
ejpam-6031	45	42	by	by	ADP
ejpam-6031	45	43	pu	pu	PROPN
ejpam-6031	45	44	z	z	PROPN
ejpam-6031	45	45	that	that	PRON
ejpam-6031	45	46	satisfies	satisfy	VERB
ejpam-6031	45	47	∥z	∥z	PROPN
ejpam-6031	45	48	−	−	PROPN
ejpam-6031	45	49	x∥	x∥	PUNCT
ejpam-6031	46	1	=	=	SYM
ejpam-6031	46	2	inf∥u	inf∥u	PROPN
ejpam-6031	47	1	−	−	PROPN
ejpam-6031	47	2	z∥	z∥	ADP
ejpam-6031	47	3	,	,	PUNCT
ejpam-6031	47	4	where	where	SCONJ
ejpam-6031	47	5	x	x	X
ejpam-6031	47	6	=	=	VERB
ejpam-6031	47	7	pu	pu	PROPN
ejpam-6031	47	8	z.	z.	PROPN
ejpam-6031	47	9	let	let	VERB
ejpam-6031	47	10	u	u	PRON
ejpam-6031	47	11	be	be	AUX
ejpam-6031	47	12	closed	close	VERB
ejpam-6031	47	13	linear	linear	ADJ
ejpam-6031	47	14	subspace	subspace	NOUN
ejpam-6031	47	15	.	.	PUNCT
ejpam-6031	48	1	then	then	ADV
ejpam-6031	48	2	,	,	PUNCT
ejpam-6031	48	3	ru	ru	X
ejpam-6031	48	4	:	:	PUNCT
ejpam-6031	48	5	=	=	SYM
ejpam-6031	48	6	2	2	NUM
ejpam-6031	48	7	pu	pu	NOUN
ejpam-6031	48	8	−	−	PROPN
ejpam-6031	49	1	i	i	PROPN
ejpam-6031	49	2	d	d	PROPN
ejpam-6031	49	3	.	.	PUNCT
ejpam-6031	50	1	(	(	PUNCT
ejpam-6031	50	2	7	7	NUM
ejpam-6031	50	3	)	)	PUNCT
ejpam-6031	50	4	and	and	CCONJ
ejpam-6031	50	5	i	i	NOUN
ejpam-6031	50	6	d	d	PROPN
ejpam-6031	50	7	:	:	PUNCT
ejpam-6031	50	8	=	=	SYM
ejpam-6031	50	9	pu	pu	PROPN
ejpam-6031	50	10	+	+	PROPN
ejpam-6031	50	11	pu⊥	pu⊥	PROPN
ejpam-6031	50	12	.	.	PUNCT
ejpam-6031	51	1	(	(	PUNCT
ejpam-6031	51	2	8)	8)	NUM
ejpam-6031	51	3	example	example	NOUN
ejpam-6031	51	4	2	2	X
ejpam-6031	51	5	.	.	PUNCT
ejpam-6031	52	1	let	let	VERB
ejpam-6031	52	2	u	u	PRON
ejpam-6031	52	3	be	be	AUX
ejpam-6031	52	4	a	a	DET
ejpam-6031	52	5	nonempty	nonempty	ADV
ejpam-6031	52	6	closed	close	VERB
ejpam-6031	52	7	convex	convex	NOUN
ejpam-6031	52	8	subset	subset	NOUN
ejpam-6031	52	9	of	of	ADP
ejpam-6031	52	10	h	h	NOUN
ejpam-6031	52	11	and	and	CCONJ
ejpam-6031	52	12	let	let	VERB
ejpam-6031	52	13	ru	ru	NOUN
ejpam-6031	52	14	=	=	SYM
ejpam-6031	52	15	2	2	NUM
ejpam-6031	52	16	pu	pu	NOUN
ejpam-6031	52	17	−	−	PROPN
ejpam-6031	53	1	i	i	PRON
ejpam-6031	53	2	d	d	PROPN
ejpam-6031	53	3	be	be	VERB
ejpam-6031	53	4	a	a	DET
ejpam-6031	53	5	nonexpansive	nonexpansive	ADJ
ejpam-6031	53	6	operator	operator	NOUN
ejpam-6031	53	7	on	on	ADP
ejpam-6031	53	8	u.	u.	NOUN
ejpam-6031	53	9	then	then	ADV
ejpam-6031	53	10	fix	fix	VERB
ejpam-6031	53	11	ru	ru	PROPN
ejpam-6031	53	12	=	=	PROPN
ejpam-6031	53	13	c.	c.	PROPN
ejpam-6031	53	14	to	to	PART
ejpam-6031	53	15	show	show	VERB
ejpam-6031	53	16	that	that	PRON
ejpam-6031	53	17	let	let	VERB
ejpam-6031	53	18	x	x	X
ejpam-6031	53	19	∈	∈	PROPN
ejpam-6031	53	20	h.	h.	NOUN
ejpam-6031	54	1	then	then	ADV
ejpam-6031	54	2	x	x	X
ejpam-6031	54	3	=	=	PUNCT
ejpam-6031	54	4	rux	rux	PROPN
ejpam-6031	54	5	.	.	PUNCT
ejpam-6031	55	1	using	use	VERB
ejpam-6031	55	2	(	(	PUNCT
ejpam-6031	55	3	3	3	X
ejpam-6031	55	4	)	)	PUNCT
ejpam-6031	55	5	gives	give	VERB
ejpam-6031	55	6	x	x	PUNCT
ejpam-6031	55	7	=	=	SYM
ejpam-6031	55	8	2	2	NUM
ejpam-6031	55	9	pu	pu	NOUN
ejpam-6031	55	10	x	x	PUNCT
ejpam-6031	56	1	−	−	PROPN
ejpam-6031	56	2	x.	x.	NOUN
ejpam-6031	56	3	this	this	PRON
ejpam-6031	56	4	implies	imply	VERB
ejpam-6031	56	5	that	that	SCONJ
ejpam-6031	56	6	pu	pu	PROPN
ejpam-6031	56	7	x	x	PUNCT
ejpam-6031	56	8	=	=	PUNCT
ejpam-6031	56	9	x	x	SYM
ejpam-6031	56	10	⇔	⇔	PROPN
ejpam-6031	56	11	x	x	X
ejpam-6031	56	12	∈	∈	PROPN
ejpam-6031	56	13	u.	u.	NOUN
ejpam-6031	56	14	example	example	NOUN
ejpam-6031	56	15	3	3	X
ejpam-6031	56	16	.	.	PUNCT
ejpam-6031	57	1	let	let	VERB
ejpam-6031	57	2	a	a	DET
ejpam-6031	57	3	=	=	PUNCT
ejpam-6031	57	4	a	a	DET
ejpam-6031	57	5	+	+	X
ejpam-6031	57	6	pu	pu	PROPN
ejpam-6031	57	7	,	,	PUNCT
ejpam-6031	57	8	where	where	SCONJ
ejpam-6031	57	9	u	u	NOUN
ejpam-6031	57	10	is	be	AUX
ejpam-6031	57	11	a	a	DET
ejpam-6031	57	12	closed	closed	ADJ
ejpam-6031	57	13	linear	linear	ADJ
ejpam-6031	57	14	subspace	subspace	NOUN
ejpam-6031	57	15	of	of	ADP
ejpam-6031	57	16	h	h	NOUN
ejpam-6031	57	17	and	and	CCONJ
ejpam-6031	57	18	a	a	DET
ejpam-6031	57	19	∈	∈	PROPN
ejpam-6031	57	20	h.	h.	NOUN
ejpam-6031	57	21	then	then	ADV
ejpam-6031	57	22	ja	ja	PROPN
ejpam-6031	57	23	=	=	PUNCT
ejpam-6031	57	24	(	(	PUNCT
ejpam-6031	57	25	id−	id−	NUM
ejpam-6031	57	26	1	1	NUM
ejpam-6031	57	27	2	2	NUM
ejpam-6031	57	28	pu	pu	NOUN
ejpam-6031	57	29	)	)	PUNCT
ejpam-6031	58	1	+	+	CCONJ
ejpam-6031	58	2	(	(	PUNCT
ejpam-6031	58	3	1	1	NUM
ejpam-6031	58	4	2	2	NUM
ejpam-6031	58	5	pu	pu	NOUN
ejpam-6031	58	6	−	−	PROPN
ejpam-6031	59	1	i	i	PROPN
ejpam-6031	59	2	d	d	PROPN
ejpam-6031	59	3	)	)	PUNCT
ejpam-6031	59	4	a	a	PRON
ejpam-6031	59	5	and	and	CCONJ
ejpam-6031	59	6	ra	ra	NOUN
ejpam-6031	60	1	=	=	PUNCT
ejpam-6031	60	2	(	(	PUNCT
ejpam-6031	60	3	id−pu	id−pu	X
ejpam-6031	60	4	)	)	PUNCT
ejpam-6031	61	1	+	+	CCONJ
ejpam-6031	61	2	(	(	PUNCT
ejpam-6031	61	3	pu	pu	PROPN
ejpam-6031	61	4	−2	−2	PROPN
ejpam-6031	61	5	i	i	PROPN
ejpam-6031	61	6	d	d	PROPN
ejpam-6031	61	7	)	)	PUNCT
ejpam-6031	61	8	a.	a.	NOUN
ejpam-6031	61	9	proof	proof	NOUN
ejpam-6031	61	10	.	.	PUNCT
ejpam-6031	62	1	see	see	VERB
ejpam-6031	62	2	[	[	X
ejpam-6031	62	3	9	9	NUM
ejpam-6031	62	4	,	,	PUNCT
ejpam-6031	62	5	lemma	lemma	PROPN
ejpam-6031	62	6	4.3	4.3	NUM
ejpam-6031	62	7	(	(	PUNCT
ejpam-6031	62	8	i	i	NOUN
ejpam-6031	62	9	)	)	PUNCT
ejpam-6031	62	10	and	and	CCONJ
ejpam-6031	62	11	(	(	PUNCT
ejpam-6031	62	12	ii	ii	NOUN
ejpam-6031	62	13	)	)	PUNCT
ejpam-6031	62	14	]	]	PUNCT
ejpam-6031	62	15	.	.	PUNCT
ejpam-6031	63	1	■	■	PUNCT
ejpam-6031	63	2	for	for	ADP
ejpam-6031	63	3	more	more	ADJ
ejpam-6031	63	4	details	detail	NOUN
ejpam-6031	63	5	about	about	ADP
ejpam-6031	63	6	the	the	DET
ejpam-6031	63	7	composition	composition	NOUN
ejpam-6031	63	8	of	of	ADP
ejpam-6031	63	9	reflectors	reflector	NOUN
ejpam-6031	63	10	,	,	PUNCT
ejpam-6031	63	11	see	see	VERB
ejpam-6031	63	12	[	[	X
ejpam-6031	63	13	10	10	NUM
ejpam-6031	63	14	]	]	PUNCT
ejpam-6031	63	15	,	,	PUNCT
ejpam-6031	63	16	[	[	X
ejpam-6031	63	17	9	9	NUM
ejpam-6031	63	18	]	]	PUNCT
ejpam-6031	63	19	,	,	PUNCT
ejpam-6031	63	20	[	[	X
ejpam-6031	63	21	11	11	NUM
ejpam-6031	63	22	]	]	PUNCT
ejpam-6031	63	23	,	,	PUNCT
ejpam-6031	63	24	[	[	X
ejpam-6031	63	25	2	2	NUM
ejpam-6031	63	26	]	]	PUNCT
ejpam-6031	63	27	,	,	PUNCT
ejpam-6031	63	28	[	[	X
ejpam-6031	63	29	12	12	NUM
ejpam-6031	63	30	]	]	PUNCT
ejpam-6031	63	31	,	,	PUNCT
ejpam-6031	63	32	and	and	CCONJ
ejpam-6031	63	33	[	[	X
ejpam-6031	63	34	13	13	NUM
ejpam-6031	63	35	]	]	PUNCT
ejpam-6031	63	36	.	.	PUNCT
ejpam-6031	64	1	a	a	DET
ejpam-6031	64	2	comprehensive	comprehensive	ADJ
ejpam-6031	64	3	analysis	analysis	NOUN
ejpam-6031	64	4	of	of	ADP
ejpam-6031	64	5	nonexpansive	nonexpansive	ADJ
ejpam-6031	64	6	mappings	mapping	NOUN
ejpam-6031	64	7	under	under	ADP
ejpam-6031	64	8	the	the	DET
ejpam-6031	64	9	condition	condition	NOUN
ejpam-6031	64	10	of	of	ADP
ejpam-6031	64	11	isometry	isometry	NOUN
ejpam-6031	64	12	of	of	ADP
ejpam-6031	64	13	finite	finite	ADJ
ejpam-6031	64	14	order	order	NOUN
ejpam-6031	64	15	of	of	ADP
ejpam-6031	64	16	r	r	NOUN
ejpam-6031	64	17	was	be	AUX
ejpam-6031	64	18	provided	provide	VERB
ejpam-6031	64	19	in	in	ADP
ejpam-6031	64	20	[	[	NOUN
ejpam-6031	64	21	9	9	NUM
ejpam-6031	64	22	,	,	PUNCT
ejpam-6031	64	23	lemma	lemma	PROPN
ejpam-6031	64	24	]	]	PUNCT
ejpam-6031	64	25	and	and	CCONJ
ejpam-6031	64	26	[	[	X
ejpam-6031	64	27	14	14	NUM
ejpam-6031	64	28	,	,	PUNCT
ejpam-6031	64	29	section	section	NOUN
ejpam-6031	64	30	3	3	NUM
ejpam-6031	64	31	]	]	PUNCT
ejpam-6031	64	32	.	.	PUNCT
ejpam-6031	65	1	we	we	PRON
ejpam-6031	65	2	refer	refer	VERB
ejpam-6031	65	3	the	the	DET
ejpam-6031	65	4	reader	reader	NOUN
ejpam-6031	65	5	to	to	ADP
ejpam-6031	65	6	[	[	X
ejpam-6031	65	7	15	15	NUM
ejpam-6031	65	8	,	,	PUNCT
ejpam-6031	65	9	exercise	exercise	VERB
ejpam-6031	65	10	12.16	12.16	NUM
ejpam-6031	65	11	]	]	PUNCT
ejpam-6031	65	12	,	,	PUNCT
ejpam-6031	65	13	[	[	X
ejpam-6031	65	14	2	2	NUM
ejpam-6031	65	15	,	,	PUNCT
ejpam-6031	65	16	example	example	NOUN
ejpam-6031	65	17	20.29	20.29	NUM
ejpam-6031	65	18	]	]	PUNCT
ejpam-6031	65	19	,	,	PUNCT
ejpam-6031	65	20	and	and	CCONJ
ejpam-6031	65	21	[	[	X
ejpam-6031	65	22	16	16	NUM
ejpam-6031	65	23	]	]	PUNCT
ejpam-6031	65	24	in	in	ADP
ejpam-6031	65	25	this	this	DET
ejpam-6031	65	26	paper	paper	NOUN
ejpam-6031	65	27	,	,	PUNCT
ejpam-6031	65	28	we	we	PRON
ejpam-6031	65	29	study	study	VERB
ejpam-6031	65	30	the	the	DET
ejpam-6031	65	31	composition	composition	NOUN
ejpam-6031	65	32	of	of	ADP
ejpam-6031	65	33	three	three	NUM
ejpam-6031	65	34	modified	modified	ADJ
ejpam-6031	65	35	reflection	reflection	NOUN
ejpam-6031	65	36	operators	operator	NOUN
ejpam-6031	65	37	and	and	CCONJ
ejpam-6031	65	38	their	their	PRON
ejpam-6031	65	39	fixed	fix	VERB
ejpam-6031	65	40	point	point	NOUN
ejpam-6031	65	41	sets	set	NOUN
ejpam-6031	65	42	..	..	PUNCT
ejpam-6031	66	1	our	our	PRON
ejpam-6031	66	2	results	result	NOUN
ejpam-6031	66	3	can	can	AUX
ejpam-6031	66	4	be	be	AUX
ejpam-6031	66	5	summarized	summarize	VERB
ejpam-6031	66	6	as	as	SCONJ
ejpam-6031	66	7	follows	follow	VERB
ejpam-6031	66	8	:	:	PUNCT
ejpam-6031	66	9	•	•	NUM
ejpam-6031	66	10	lemma	lemma	PROPN
ejpam-6031	66	11	1	1	NUM
ejpam-6031	66	12	and	and	CCONJ
ejpam-6031	66	13	lemma	lemma	PROPN
ejpam-6031	66	14	2	2	NUM
ejpam-6031	66	15	provide	provide	VERB
ejpam-6031	66	16	key	key	ADJ
ejpam-6031	66	17	properties	property	NOUN
ejpam-6031	66	18	concerning	concern	VERB
ejpam-6031	66	19	the	the	DET
ejpam-6031	66	20	fixed	fix	VERB
ejpam-6031	66	21	point	point	NOUN
ejpam-6031	66	22	set	set	NOUN
ejpam-6031	66	23	of	of	ADP
ejpam-6031	66	24	the	the	DET
ejpam-6031	66	25	composition	composition	NOUN
ejpam-6031	66	26	of	of	ADP
ejpam-6031	66	27	two	two	NUM
ejpam-6031	66	28	modified	modified	ADJ
ejpam-6031	66	29	reflection	reflection	NOUN
ejpam-6031	66	30	operators	operator	NOUN
ejpam-6031	66	31	.	.	PUNCT
ejpam-6031	67	1	•	•	NUM
ejpam-6031	67	2	theorem	theorem	ADJ
ejpam-6031	67	3	1	1	NUM
ejpam-6031	67	4	,	,	PUNCT
ejpam-6031	67	5	theorem	theorem	ADJ
ejpam-6031	67	6	2	2	NUM
ejpam-6031	67	7	,	,	PUNCT
ejpam-6031	67	8	and	and	CCONJ
ejpam-6031	67	9	theorem	theorem	VERB
ejpam-6031	67	10	3	3	NUM
ejpam-6031	67	11	show	show	VERB
ejpam-6031	67	12	that	that	SCONJ
ejpam-6031	67	13	the	the	DET
ejpam-6031	67	14	sequence	sequence	NOUN
ejpam-6031	67	15	in	in	ADP
ejpam-6031	67	16	which	which	PRON
ejpam-6031	67	17	three	three	NUM
ejpam-6031	67	18	modified	modified	ADJ
ejpam-6031	67	19	reflection	reflection	NOUN
ejpam-6031	67	20	operators	operator	NOUN
ejpam-6031	67	21	are	be	AUX
ejpam-6031	67	22	applied	apply	VERB
ejpam-6031	67	23	affects	affect	VERB
ejpam-6031	67	24	the	the	DET
ejpam-6031	67	25	fixed	fix	VERB
ejpam-6031	67	26	point	point	NOUN
ejpam-6031	67	27	set	set	NOUN
ejpam-6031	67	28	of	of	ADP
ejpam-6031	67	29	their	their	PRON
ejpam-6031	67	30	composition	composition	NOUN
ejpam-6031	67	31	.	.	PUNCT
ejpam-6031	68	1	these	these	DET
ejpam-6031	68	2	theorems	theorem	NOUN
ejpam-6031	68	3	offer	offer	VERB
ejpam-6031	68	4	valuable	valuable	ADJ
ejpam-6031	68	5	insights	insight	NOUN
ejpam-6031	68	6	into	into	ADP
ejpam-6031	68	7	the	the	DET
ejpam-6031	68	8	fixed	fix	VERB
ejpam-6031	68	9	point	point	NOUN
ejpam-6031	68	10	set	set	VERB
ejpam-6031	68	11	resulting	result	VERB
ejpam-6031	68	12	from	from	ADP
ejpam-6031	68	13	the	the	DET
ejpam-6031	68	14	composition	composition	NOUN
ejpam-6031	68	15	of	of	ADP
ejpam-6031	68	16	three	three	NUM
ejpam-6031	68	17	modified	modified	ADJ
ejpam-6031	68	18	reflection	reflection	NOUN
ejpam-6031	68	19	operators	operator	NOUN
ejpam-6031	68	20	.	.	PUNCT
ejpam-6031	69	1	•	•	NOUN
ejpam-6031	69	2	under	under	ADP
ejpam-6031	69	3	different	different	ADJ
ejpam-6031	69	4	parameters	parameter	NOUN
ejpam-6031	69	5	γ	γ	X
ejpam-6031	69	6	,	,	PUNCT
ejpam-6031	69	7	β	β	PROPN
ejpam-6031	69	8	,	,	PUNCT
ejpam-6031	69	9	α	α	PROPN
ejpam-6031	69	10	∈	∈	PROPN
ejpam-6031	69	11	(	(	PUNCT
ejpam-6031	69	12	0	0	NUM
ejpam-6031	69	13	,	,	PUNCT
ejpam-6031	69	14	1	1	NUM
ejpam-6031	69	15	]	]	PUNCT
ejpam-6031	69	16	,	,	PUNCT
ejpam-6031	69	17	we	we	PRON
ejpam-6031	69	18	derive	derive	VERB
ejpam-6031	69	19	formulas	formula	NOUN
ejpam-6031	69	20	for	for	ADP
ejpam-6031	69	21	the	the	DET
ejpam-6031	69	22	composition	composition	NOUN
ejpam-6031	69	23	of	of	ADP
ejpam-6031	69	24	two	two	NUM
ejpam-6031	69	25	modified	modify	VERB
ejpam-6031	69	26	reflection	reflection	NOUN
ejpam-6031	69	27	operators	operator	NOUN
ejpam-6031	69	28	(	(	PUNCT
ejpam-6031	69	29	see	see	VERB
ejpam-6031	69	30	lemma	lemma	PROPN
ejpam-6031	69	31	1	1	NUM
ejpam-6031	69	32	and	and	CCONJ
ejpam-6031	69	33	lemma	lemma	PROPN
ejpam-6031	69	34	2	2	NUM
ejpam-6031	69	35	)	)	PUNCT
ejpam-6031	69	36	.	.	PUNCT
ejpam-6031	70	1	additionally	additionally	ADV
ejpam-6031	70	2	,	,	PUNCT
ejpam-6031	70	3	formulas	formula	NOUN
ejpam-6031	70	4	for	for	ADP
ejpam-6031	70	5	the	the	DET
ejpam-6031	70	6	composition	composition	NOUN
ejpam-6031	70	7	of	of	ADP
ejpam-6031	70	8	three	three	NUM
ejpam-6031	70	9	modified	modify	VERB
ejpam-6031	70	10	reflection	reflection	NOUN
ejpam-6031	70	11	operators	operator	NOUN
ejpam-6031	70	12	are	be	AUX
ejpam-6031	70	13	given	give	VERB
ejpam-6031	70	14	in	in	ADP
ejpam-6031	70	15	theorem	theorem	ADJ
ejpam-6031	70	16	1	1	NUM
ejpam-6031	70	17	,	,	PUNCT
ejpam-6031	70	18	theorem	theorem	ADJ
ejpam-6031	70	19	2	2	NUM
ejpam-6031	70	20	,	,	PUNCT
ejpam-6031	70	21	and	and	CCONJ
ejpam-6031	70	22	theorem	theorem	VERB
ejpam-6031	70	23	3	3	NUM
ejpam-6031	70	24	.	.	PUNCT
ejpam-6031	71	1	the	the	DET
ejpam-6031	71	2	notation	notation	NOUN
ejpam-6031	71	3	employed	employ	VERB
ejpam-6031	71	4	in	in	ADP
ejpam-6031	71	5	this	this	DET
ejpam-6031	71	6	paper	paper	NOUN
ejpam-6031	71	7	is	be	AUX
ejpam-6031	71	8	standard	standard	ADJ
ejpam-6031	71	9	and	and	CCONJ
ejpam-6031	71	10	closely	closely	ADV
ejpam-6031	71	11	aligns	align	VERB
ejpam-6031	71	12	with	with	ADP
ejpam-6031	71	13	that	that	PRON
ejpam-6031	71	14	in	in	ADP
ejpam-6031	71	15	[	[	X
ejpam-6031	71	16	9	9	NUM
ejpam-6031	71	17	,	,	PUNCT
ejpam-6031	71	18	17	17	NUM
ejpam-6031	71	19	]	]	PUNCT
ejpam-6031	71	20	,	,	PUNCT
ejpam-6031	71	21	and	and	CCONJ
ejpam-6031	71	22	[	[	X
ejpam-6031	71	23	2	2	NUM
ejpam-6031	71	24	]	]	PUNCT
ejpam-6031	71	25	.	.	PUNCT
ejpam-6031	72	1	s.th	s.th	PROPN
ejpam-6031	72	2	.	.	PUNCT
ejpam-6031	72	3	alwadani	alwadani	PROPN
ejpam-6031	72	4	/	/	SYM
ejpam-6031	72	5	eur	eur	PROPN
ejpam-6031	72	6	.	.	PUNCT
ejpam-6031	73	1	j.	j.	PROPN
ejpam-6031	73	2	pure	pure	PROPN
ejpam-6031	73	3	appl	appl	PROPN
ejpam-6031	73	4	.	.	PROPN
ejpam-6031	73	5	math	math	PROPN
ejpam-6031	73	6	,	,	PUNCT
ejpam-6031	73	7	18	18	NUM
ejpam-6031	73	8	(	(	PUNCT
ejpam-6031	73	9	2	2	NUM
ejpam-6031	73	10	)	)	PUNCT
ejpam-6031	73	11	(	(	PUNCT
ejpam-6031	73	12	2025	2025	NUM
ejpam-6031	73	13	)	)	PUNCT
ejpam-6031	73	14	,	,	PUNCT
ejpam-6031	73	15	6031	6031	NUM
ejpam-6031	73	16	4	4	NUM
ejpam-6031	73	17	of	of	ADP
ejpam-6031	73	18	13	13	NUM
ejpam-6031	73	19	2	2	NUM
ejpam-6031	73	20	.	.	PUNCT
ejpam-6031	73	21	results	result	NOUN
ejpam-6031	73	22	in	in	ADP
ejpam-6031	73	23	this	this	DET
ejpam-6031	73	24	section	section	NOUN
ejpam-6031	73	25	,	,	PUNCT
ejpam-6031	73	26	we	we	PRON
ejpam-6031	73	27	will	will	AUX
ejpam-6031	73	28	present	present	VERB
ejpam-6031	73	29	significant	significant	ADJ
ejpam-6031	73	30	new	new	ADJ
ejpam-6031	73	31	results	result	NOUN
ejpam-6031	73	32	regarding	regard	VERB
ejpam-6031	73	33	the	the	DET
ejpam-6031	73	34	composition	composition	NOUN
ejpam-6031	73	35	of	of	ADP
ejpam-6031	73	36	two	two	NUM
ejpam-6031	73	37	and	and	CCONJ
ejpam-6031	73	38	three	three	NUM
ejpam-6031	73	39	modified	modified	ADJ
ejpam-6031	73	40	reflection	reflection	NOUN
ejpam-6031	73	41	operators	operator	NOUN
ejpam-6031	73	42	,	,	PUNCT
ejpam-6031	73	43	as	as	ADV
ejpam-6031	73	44	well	well	ADV
ejpam-6031	73	45	as	as	ADP
ejpam-6031	73	46	their	their	PRON
ejpam-6031	73	47	corresponding	corresponding	ADJ
ejpam-6031	73	48	fixed	fix	VERB
ejpam-6031	73	49	point	point	NOUN
ejpam-6031	73	50	sets	set	NOUN
ejpam-6031	73	51	.	.	PUNCT
ejpam-6031	74	1	we	we	PRON
ejpam-6031	74	2	will	will	AUX
ejpam-6031	74	3	explore	explore	VERB
ejpam-6031	74	4	the	the	DET
ejpam-6031	74	5	properties	property	NOUN
ejpam-6031	74	6	and	and	CCONJ
ejpam-6031	74	7	interactions	interaction	NOUN
ejpam-6031	74	8	of	of	ADP
ejpam-6031	74	9	these	these	DET
ejpam-6031	74	10	operators	operator	NOUN
ejpam-6031	74	11	,	,	PUNCT
ejpam-6031	74	12	highlighting	highlight	VERB
ejpam-6031	74	13	how	how	SCONJ
ejpam-6031	74	14	their	their	PRON
ejpam-6031	74	15	compositions	composition	NOUN
ejpam-6031	74	16	influence	influence	VERB
ejpam-6031	74	17	the	the	DET
ejpam-6031	74	18	structure	structure	NOUN
ejpam-6031	74	19	of	of	ADP
ejpam-6031	74	20	the	the	DET
ejpam-6031	74	21	fixed	fix	VERB
ejpam-6031	74	22	point	point	NOUN
ejpam-6031	74	23	sets	set	NOUN
ejpam-6031	74	24	.	.	PUNCT
ejpam-6031	75	1	lemma	lemma	PROPN
ejpam-6031	75	2	1	1	X
ejpam-6031	75	3	.	.	PUNCT
ejpam-6031	76	1	let	let	VERB
ejpam-6031	76	2	u	u	PRON
ejpam-6031	76	3	be	be	AUX
ejpam-6031	76	4	a	a	DET
ejpam-6031	76	5	closed	closed	ADJ
ejpam-6031	76	6	linear	linear	ADJ
ejpam-6031	76	7	subspace	subspace	NOUN
ejpam-6031	76	8	of	of	ADP
ejpam-6031	76	9	h	h	NOUN
ejpam-6031	76	10	,	,	PUNCT
ejpam-6031	76	11	and	and	CCONJ
ejpam-6031	76	12	let	let	VERB
ejpam-6031	76	13	u⊥	u⊥	PROPN
ejpam-6031	76	14	denote	denote	VERB
ejpam-6031	76	15	the	the	DET
ejpam-6031	76	16	orthogonal	orthogonal	ADJ
ejpam-6031	76	17	complement	complement	NOUN
ejpam-6031	76	18	of	of	ADP
ejpam-6031	76	19	u.	u.	NOUN
ejpam-6031	76	20	let	let	VERB
ejpam-6031	76	21	β	β	PRON
ejpam-6031	76	22	∈]0	∈]0	ADJ
ejpam-6031	76	23	,	,	PUNCT
ejpam-6031	76	24	1	1	NUM
ejpam-6031	76	25	]	]	PUNCT
ejpam-6031	76	26	.	.	PUNCT
ejpam-6031	77	1	recall	recall	PROPN
ejpam-6031	77	2	from	from	ADP
ejpam-6031	77	3	(	(	PUNCT
ejpam-6031	77	4	7	7	NUM
ejpam-6031	77	5	)	)	PUNCT
ejpam-6031	77	6	that	that	PRON
ejpam-6031	77	7	ru	ru	X
ejpam-6031	77	8	:	:	PUNCT
ejpam-6031	77	9	=	=	SYM
ejpam-6031	77	10	2	2	NUM
ejpam-6031	77	11	pu	pu	NOUN
ejpam-6031	77	12	−	−	PROPN
ejpam-6031	78	1	i	i	PROPN
ejpam-6031	78	2	d	d	PROPN
ejpam-6031	78	3	,	,	PUNCT
ejpam-6031	78	4	where	where	SCONJ
ejpam-6031	78	5	pu	pu	PROPN
ejpam-6031	78	6	is	be	AUX
ejpam-6031	78	7	defined	define	VERB
ejpam-6031	78	8	in	in	ADP
ejpam-6031	78	9	definition	definition	NOUN
ejpam-6031	78	10	3	3	NUM
ejpam-6031	78	11	.	.	PUNCT
ejpam-6031	79	1	the	the	DET
ejpam-6031	79	2	following	follow	VERB
ejpam-6031	79	3	results	result	NOUN
ejpam-6031	79	4	hold	hold	VERB
ejpam-6031	79	5	:	:	PUNCT
ejpam-6031	79	6	(	(	PUNCT
ejpam-6031	79	7	i	i	NOUN
ejpam-6031	79	8	)	)	PUNCT
ejpam-6031	79	9	ru⊥ru	ru⊥ru	NOUN
ejpam-6031	80	1	=	=	PUNCT
ejpam-6031	80	2	−	−	PROPN
ejpam-6031	81	1	i	i	NOUN
ejpam-6031	81	2	d	d	PROPN
ejpam-6031	81	3	=	=	PRON
ejpam-6031	81	4	ru	ru	PROPN
ejpam-6031	81	5	ru⊥	ru⊥	PROPN
ejpam-6031	81	6	.	.	PUNCT
ejpam-6031	82	1	(	(	PUNCT
ejpam-6031	82	2	ii	ii	NOUN
ejpam-6031	82	3	)	)	PUNCT
ejpam-6031	82	4	(	(	PUNCT
ejpam-6031	82	5	2β	2β	NUM
ejpam-6031	83	1	pu	pu	NOUN
ejpam-6031	83	2	−	−	PROPN
ejpam-6031	84	1	i	i	PROPN
ejpam-6031	84	2	d	d	PROPN
ejpam-6031	84	3	)	)	PUNCT
ejpam-6031	85	1	=	=	PUNCT
ejpam-6031	86	1	βru	βru	PROPN
ejpam-6031	86	2	+	+	CCONJ
ejpam-6031	86	3	(	(	PUNCT
ejpam-6031	86	4	1	1	NUM
ejpam-6031	86	5	−	−	NOUN
ejpam-6031	86	6	β)(−	β)(−	ADV
ejpam-6031	86	7	i	i	PROPN
ejpam-6031	86	8	d	d	PROPN
ejpam-6031	86	9	)	)	PUNCT
ejpam-6031	86	10	.	.	PUNCT
ejpam-6031	87	1	(	(	PUNCT
ejpam-6031	87	2	iii	iii	X
ejpam-6031	87	3	)	)	PUNCT
ejpam-6031	87	4	(	(	PUNCT
ejpam-6031	87	5	2β	2β	NUM
ejpam-6031	88	1	pu⊥	pu⊥	NOUN
ejpam-6031	88	2	−	−	PROPN
ejpam-6031	89	1	i	i	NOUN
ejpam-6031	89	2	d	d	PROPN
ejpam-6031	89	3	)	)	PUNCT
ejpam-6031	90	1	=	=	PUNCT
ejpam-6031	90	2	βru⊥	βru⊥	PROPN
ejpam-6031	91	1	+	+	CCONJ
ejpam-6031	91	2	(	(	PUNCT
ejpam-6031	91	3	1	1	NUM
ejpam-6031	91	4	−	−	NUM
ejpam-6031	91	5	β)(−	β)(−	ADV
ejpam-6031	91	6	i	i	PROPN
ejpam-6031	91	7	d	d	PROPN
ejpam-6031	91	8	)	)	PUNCT
ejpam-6031	91	9	.	.	PUNCT
ejpam-6031	92	1	(	(	PUNCT
ejpam-6031	92	2	iv	iv	X
ejpam-6031	92	3	)	)	PUNCT
ejpam-6031	92	4	−	−	PROPN
ejpam-6031	92	5	(	(	PUNCT
ejpam-6031	92	6	2β	2β	NUM
ejpam-6031	93	1	pu	pu	NOUN
ejpam-6031	93	2	−	−	PROPN
ejpam-6031	94	1	i	i	PROPN
ejpam-6031	94	2	d	d	PROPN
ejpam-6031	94	3	)	)	PUNCT
ejpam-6031	95	1	=	=	PUNCT
ejpam-6031	95	2	βru⊥	βru⊥	PROPN
ejpam-6031	96	1	+	+	CCONJ
ejpam-6031	96	2	(	(	PUNCT
ejpam-6031	96	3	1	1	NUM
ejpam-6031	96	4	−	−	NOUN
ejpam-6031	96	5	β	β	X
ejpam-6031	96	6	)	)	PUNCT
ejpam-6031	97	1	i	i	PRON
ejpam-6031	97	2	d.	d.	PROPN
ejpam-6031	97	3	(	(	PUNCT
ejpam-6031	97	4	v	v	NOUN
ejpam-6031	97	5	)	)	PUNCT
ejpam-6031	97	6	(	(	PUNCT
ejpam-6031	97	7	2β	2β	NUM
ejpam-6031	97	8	pu	pu	NOUN
ejpam-6031	97	9	−	−	PROPN
ejpam-6031	98	1	i	i	PROPN
ejpam-6031	98	2	d	d	PROPN
ejpam-6031	98	3	)	)	PUNCT
ejpam-6031	98	4	◦	◦	NOUN
ejpam-6031	98	5	(	(	PUNCT
ejpam-6031	98	6	−	−	PROPN
ejpam-6031	98	7	i	i	NOUN
ejpam-6031	98	8	d	d	PROPN
ejpam-6031	98	9	)	)	PUNCT
ejpam-6031	99	1	=	=	SYM
ejpam-6031	99	2	−	−	PROPN
ejpam-6031	99	3	(	(	PUNCT
ejpam-6031	99	4	2β	2β	NUM
ejpam-6031	99	5	pu	pu	NOUN
ejpam-6031	99	6	−	−	PROPN
ejpam-6031	99	7	i	i	PROPN
ejpam-6031	99	8	d	d	PROPN
ejpam-6031	99	9	)	)	PUNCT
ejpam-6031	99	10	.	.	PUNCT
ejpam-6031	100	1	(	(	PUNCT
ejpam-6031	100	2	vi	vi	NOUN
ejpam-6031	100	3	)	)	PUNCT
ejpam-6031	100	4	fix	fix	NOUN
ejpam-6031	100	5	(	(	PUNCT
ejpam-6031	100	6	(	(	PUNCT
ejpam-6031	100	7	2β	2β	NOUN
ejpam-6031	100	8	pu	pu	NOUN
ejpam-6031	100	9	−	−	PROPN
ejpam-6031	101	1	i	i	PROPN
ejpam-6031	101	2	d	d	PROPN
ejpam-6031	101	3	)	)	PUNCT
ejpam-6031	101	4	◦	◦	NOUN
ejpam-6031	101	5	(	(	PUNCT
ejpam-6031	101	6	−	−	PROPN
ejpam-6031	101	7	i	i	PROPN
ejpam-6031	101	8	d	d	PROPN
ejpam-6031	101	9	)	)	PUNCT
ejpam-6031	101	10	)	)	PUNCT
ejpam-6031	102	1	=	=	PRON
ejpam-6031	102	2	fix	fix	NOUN
ejpam-6031	102	3	(	(	PUNCT
ejpam-6031	102	4	−	−	PROPN
ejpam-6031	102	5	(	(	PUNCT
ejpam-6031	102	6	2β	2β	NUM
ejpam-6031	102	7	pu	pu	NOUN
ejpam-6031	102	8	−	−	PROPN
ejpam-6031	102	9	i	i	PROPN
ejpam-6031	102	10	d	d	PROPN
ejpam-6031	102	11	)	)	PUNCT
ejpam-6031	102	12	)	)	PUNCT
ejpam-6031	103	1	=	=	PRON
ejpam-6031	103	2	fix	fix	NOUN
ejpam-6031	103	3	(	(	PUNCT
ejpam-6031	103	4	βru	βru	NOUN
ejpam-6031	103	5	+	+	PROPN
ejpam-6031	103	6	(	(	PUNCT
ejpam-6031	103	7	1−	1−	NUM
ejpam-6031	103	8	β)(−	β)(−	ADJ
ejpam-6031	103	9	i	i	PROPN
ejpam-6031	103	10	d	d	PROPN
ejpam-6031	103	11	)	)	PUNCT
ejpam-6031	103	12	)	)	PUNCT
ejpam-6031	104	1	=	=	SYM
ejpam-6031	104	2	u⊥.	u⊥.	NOUN
ejpam-6031	104	3	proof	proof	NOUN
ejpam-6031	104	4	.	.	PUNCT
ejpam-6031	105	1	(	(	PUNCT
ejpam-6031	105	2	i	i	NOUN
ejpam-6031	105	3	):	):	PUNCT
ejpam-6031	105	4	see	see	VERB
ejpam-6031	105	5	[	[	X
ejpam-6031	105	6	9	9	NUM
ejpam-6031	105	7	,	,	PUNCT
ejpam-6031	105	8	lemma	lemma	PROPN
ejpam-6031	105	9	6.2	6.2	NUM
ejpam-6031	105	10	(	(	PUNCT
ejpam-6031	105	11	i	i	NOUN
ejpam-6031	105	12	)	)	PUNCT
ejpam-6031	105	13	]	]	PUNCT
ejpam-6031	105	14	.	.	PUNCT
ejpam-6031	106	1	(	(	PUNCT
ejpam-6031	106	2	ii	ii	NOUN
ejpam-6031	106	3	):	):	PUNCT
ejpam-6031	106	4	using	use	VERB
ejpam-6031	106	5	(	(	PUNCT
ejpam-6031	106	6	7	7	X
ejpam-6031	106	7	)	)	PUNCT
ejpam-6031	106	8	gives	give	VERB
ejpam-6031	106	9	(	(	PUNCT
ejpam-6031	106	10	2β	2β	NUM
ejpam-6031	106	11	pu	pu	PROPN
ejpam-6031	106	12	−	−	PROPN
ejpam-6031	107	1	i	i	PROPN
ejpam-6031	107	2	d	d	PROPN
ejpam-6031	107	3	)	)	PUNCT
ejpam-6031	108	1	=	=	PUNCT
ejpam-6031	109	1	2β	2β	NUM
ejpam-6031	109	2	pu	pu	NOUN
ejpam-6031	109	3	−	−	NOUN
ejpam-6031	110	1	id+β	id+β	PROPN
ejpam-6031	110	2	id−β	id−β	NOUN
ejpam-6031	111	1	i	i	PROPN
ejpam-6031	111	2	d	d	PROPN
ejpam-6031	111	3	=	=	PUNCT
ejpam-6031	111	4	(	(	PUNCT
ejpam-6031	111	5	2β	2β	NOUN
ejpam-6031	111	6	pu	pu	PROPN
ejpam-6031	111	7	−β	−β	PROPN
ejpam-6031	112	1	i	i	PROPN
ejpam-6031	112	2	d	d	PROPN
ejpam-6031	112	3	)	)	PUNCT
ejpam-6031	113	1	+	+	CCONJ
ejpam-6031	113	2	(	(	PUNCT
ejpam-6031	113	3	1	1	NUM
ejpam-6031	113	4	−	−	NOUN
ejpam-6031	113	5	β)(−	β)(−	ADV
ejpam-6031	113	6	i	i	PROPN
ejpam-6031	113	7	d	d	PROPN
ejpam-6031	113	8	)	)	PUNCT
ejpam-6031	113	9	=	=	SYM
ejpam-6031	113	10	βru	βru	PROPN
ejpam-6031	113	11	+	+	CCONJ
ejpam-6031	113	12	(	(	PUNCT
ejpam-6031	113	13	1	1	NUM
ejpam-6031	113	14	−	−	NOUN
ejpam-6031	113	15	β)(−	β)(−	ADV
ejpam-6031	113	16	i	i	PROPN
ejpam-6031	113	17	d	d	PROPN
ejpam-6031	113	18	)	)	PUNCT
ejpam-6031	113	19	.	.	PUNCT
ejpam-6031	114	1	(	(	PUNCT
ejpam-6031	114	2	iii	iii	X
ejpam-6031	114	3	):	):	PUNCT
ejpam-6031	114	4	applying	apply	VERB
ejpam-6031	114	5	(	(	PUNCT
ejpam-6031	114	6	7	7	NUM
ejpam-6031	114	7	)	)	PUNCT
ejpam-6031	114	8	yields	yield	NOUN
ejpam-6031	114	9	(	(	PUNCT
ejpam-6031	114	10	2β	2β	NUM
ejpam-6031	114	11	pu⊥	pu⊥	NOUN
ejpam-6031	114	12	−	−	PROPN
ejpam-6031	114	13	i	i	NOUN
ejpam-6031	114	14	d	d	PROPN
ejpam-6031	114	15	)	)	PUNCT
ejpam-6031	115	1	=	=	SYM
ejpam-6031	116	1	2β	2β	NOUN
ejpam-6031	116	2	pu⊥	pu⊥	NOUN
ejpam-6031	116	3	−	−	NOUN
ejpam-6031	117	1	id+β	id+β	PROPN
ejpam-6031	117	2	id−β	id−β	PROPN
ejpam-6031	118	1	i	i	PROPN
ejpam-6031	118	2	d	d	PROPN
ejpam-6031	118	3	=	=	PUNCT
ejpam-6031	118	4	(	(	PUNCT
ejpam-6031	118	5	2β	2β	NUM
ejpam-6031	118	6	pu⊥	pu⊥	NOUN
ejpam-6031	118	7	−β	−β	NOUN
ejpam-6031	118	8	i	i	PROPN
ejpam-6031	118	9	d	d	PROPN
ejpam-6031	118	10	)	)	PUNCT
ejpam-6031	119	1	+	+	CCONJ
ejpam-6031	119	2	(	(	PUNCT
ejpam-6031	119	3	1	1	NUM
ejpam-6031	119	4	−	−	NOUN
ejpam-6031	119	5	β)(−	β)(−	ADV
ejpam-6031	119	6	i	i	PROPN
ejpam-6031	119	7	d	d	PROPN
ejpam-6031	119	8	)	)	PUNCT
ejpam-6031	119	9	=	=	SYM
ejpam-6031	120	1	βru⊥	βru⊥	PROPN
ejpam-6031	120	2	+	+	CCONJ
ejpam-6031	120	3	(	(	PUNCT
ejpam-6031	120	4	1	1	NUM
ejpam-6031	120	5	−	−	NUM
ejpam-6031	120	6	β)(−	β)(−	ADV
ejpam-6031	120	7	i	i	PROPN
ejpam-6031	120	8	d	d	PROPN
ejpam-6031	120	9	)	)	PUNCT
ejpam-6031	120	10	.	.	PUNCT
ejpam-6031	121	1	(	(	PUNCT
ejpam-6031	121	2	iv	iv	X
ejpam-6031	121	3	):	):	PUNCT
ejpam-6031	121	4	using	use	VERB
ejpam-6031	121	5	(	(	PUNCT
ejpam-6031	121	6	7	7	NUM
ejpam-6031	121	7	)	)	PUNCT
ejpam-6031	121	8	,	,	PUNCT
ejpam-6031	121	9	(	(	PUNCT
ejpam-6031	121	10	8)	8)	NUM
ejpam-6031	121	11	,	,	PUNCT
ejpam-6031	121	12	and	and	CCONJ
ejpam-6031	121	13	(	(	PUNCT
ejpam-6031	121	14	ii	ii	NOUN
ejpam-6031	121	15	)	)	PUNCT
ejpam-6031	121	16	,	,	PUNCT
ejpam-6031	121	17	we	we	PRON
ejpam-6031	121	18	obtain	obtain	VERB
ejpam-6031	121	19	−	−	PROPN
ejpam-6031	121	20	(	(	PUNCT
ejpam-6031	121	21	2β	2β	NUM
ejpam-6031	121	22	pu	pu	NOUN
ejpam-6031	121	23	−	−	PROPN
ejpam-6031	122	1	i	i	PROPN
ejpam-6031	122	2	d	d	PROPN
ejpam-6031	122	3	)	)	PUNCT
ejpam-6031	123	1	=	=	SYM
ejpam-6031	123	2	−	−	PROPN
ejpam-6031	123	3	(	(	PUNCT
ejpam-6031	123	4	βru	βru	NOUN
ejpam-6031	123	5	+	+	CCONJ
ejpam-6031	123	6	(	(	PUNCT
ejpam-6031	123	7	1	1	NUM
ejpam-6031	123	8	−	−	NUM
ejpam-6031	123	9	β)(−	β)(−	ADV
ejpam-6031	123	10	i	i	PROPN
ejpam-6031	123	11	d	d	PROPN
ejpam-6031	123	12	)	)	PUNCT
ejpam-6031	123	13	)	)	PUNCT
ejpam-6031	124	1	=	=	NOUN
ejpam-6031	124	2	−βru	−βru	NOUN
ejpam-6031	124	3	+	+	CCONJ
ejpam-6031	124	4	(	(	PUNCT
ejpam-6031	124	5	1	1	NUM
ejpam-6031	124	6	−	−	NOUN
ejpam-6031	124	7	β	β	X
ejpam-6031	124	8	)	)	PUNCT
ejpam-6031	124	9	i	i	PROPN
ejpam-6031	125	1	d	d	NOUN
ejpam-6031	125	2	=	=	SYM
ejpam-6031	125	3	−β	−β	PROPN
ejpam-6031	125	4	(	(	PUNCT
ejpam-6031	125	5	2	2	NUM
ejpam-6031	125	6	pu	pu	NOUN
ejpam-6031	125	7	−	−	PROPN
ejpam-6031	125	8	i	i	PROPN
ejpam-6031	125	9	d	d	PROPN
ejpam-6031	125	10	)	)	PUNCT
ejpam-6031	126	1	+	+	CCONJ
ejpam-6031	126	2	(	(	PUNCT
ejpam-6031	126	3	1	1	NUM
ejpam-6031	126	4	−	−	NOUN
ejpam-6031	126	5	β	β	X
ejpam-6031	126	6	)	)	PUNCT
ejpam-6031	127	1	i	i	PROPN
ejpam-6031	127	2	d	d	NOUN
ejpam-6031	127	3	=	=	SYM
ejpam-6031	127	4	−β	−β	PROPN
ejpam-6031	127	5	(	(	PUNCT
ejpam-6031	127	6	pu	pu	PROPN
ejpam-6031	127	7	−	−	PROPN
ejpam-6031	127	8	(	(	PUNCT
ejpam-6031	127	9	id−pu	id−pu	PROPN
ejpam-6031	127	10	)	)	PUNCT
ejpam-6031	127	11	)	)	PUNCT
ejpam-6031	128	1	+	+	CCONJ
ejpam-6031	128	2	(	(	PUNCT
ejpam-6031	128	3	1	1	NUM
ejpam-6031	128	4	−	−	NOUN
ejpam-6031	128	5	β	β	X
ejpam-6031	128	6	)	)	PUNCT
ejpam-6031	128	7	i	i	PROPN
ejpam-6031	128	8	d	d	NOUN
ejpam-6031	128	9	=	=	SYM
ejpam-6031	128	10	−β	−β	PROPN
ejpam-6031	128	11	(	(	PUNCT
ejpam-6031	128	12	pu	pu	PROPN
ejpam-6031	128	13	−pu⊥	−pu⊥	PROPN
ejpam-6031	128	14	)	)	PUNCT
ejpam-6031	129	1	+	+	CCONJ
ejpam-6031	129	2	(	(	PUNCT
ejpam-6031	129	3	1	1	NUM
ejpam-6031	129	4	−	−	NOUN
ejpam-6031	129	5	β	β	X
ejpam-6031	129	6	)	)	PUNCT
ejpam-6031	129	7	i	i	PROPN
ejpam-6031	129	8	d	d	NOUN
ejpam-6031	129	9	=	=	SYM
ejpam-6031	129	10	−β	−β	PROPN
ejpam-6031	129	11	(	(	PUNCT
ejpam-6031	129	12	pu	pu	PROPN
ejpam-6031	129	13	−pu⊥	−pu⊥	PROPN
ejpam-6031	129	14	+	+	PROPN
ejpam-6031	129	15	pu⊥	pu⊥	PROPN
ejpam-6031	129	16	−pu⊥	−pu⊥	PROPN
ejpam-6031	129	17	)	)	PUNCT
ejpam-6031	130	1	+	+	CCONJ
ejpam-6031	130	2	(	(	PUNCT
ejpam-6031	130	3	1	1	NUM
ejpam-6031	130	4	−	−	NOUN
ejpam-6031	130	5	β	β	X
ejpam-6031	130	6	)	)	PUNCT
ejpam-6031	130	7	i	i	PROPN
ejpam-6031	130	8	d	d	PROPN
ejpam-6031	130	9	s.th	s.th	PROPN
ejpam-6031	130	10	.	.	PUNCT
ejpam-6031	130	11	alwadani	alwadani	PROPN
ejpam-6031	130	12	/	/	SYM
ejpam-6031	130	13	eur	eur	PROPN
ejpam-6031	130	14	.	.	PUNCT
ejpam-6031	131	1	j.	j.	PROPN
ejpam-6031	131	2	pure	pure	PROPN
ejpam-6031	131	3	appl	appl	PROPN
ejpam-6031	131	4	.	.	PROPN
ejpam-6031	131	5	math	math	PROPN
ejpam-6031	131	6	,	,	PUNCT
ejpam-6031	131	7	18	18	NUM
ejpam-6031	131	8	(	(	PUNCT
ejpam-6031	131	9	2	2	NUM
ejpam-6031	131	10	)	)	PUNCT
ejpam-6031	131	11	(	(	PUNCT
ejpam-6031	131	12	2025	2025	NUM
ejpam-6031	131	13	)	)	PUNCT
ejpam-6031	131	14	,	,	PUNCT
ejpam-6031	131	15	6031	6031	NUM
ejpam-6031	131	16	5	5	NUM
ejpam-6031	131	17	of	of	ADP
ejpam-6031	131	18	13	13	NUM
ejpam-6031	131	19	=	=	NOUN
ejpam-6031	131	20	−β	−β	NOUN
ejpam-6031	131	21	(	(	PUNCT
ejpam-6031	131	22	pu	pu	PROPN
ejpam-6031	131	23	+	+	PROPN
ejpam-6031	131	24	pu⊥	pu⊥	PROPN
ejpam-6031	131	25	−2	−2	NOUN
ejpam-6031	131	26	pu⊥	pu⊥	PROPN
ejpam-6031	131	27	)	)	PUNCT
ejpam-6031	132	1	+	+	CCONJ
ejpam-6031	132	2	(	(	PUNCT
ejpam-6031	132	3	1	1	NUM
ejpam-6031	132	4	−	−	NOUN
ejpam-6031	132	5	β	β	X
ejpam-6031	132	6	)	)	PUNCT
ejpam-6031	133	1	i	i	PROPN
ejpam-6031	133	2	d	d	NOUN
ejpam-6031	133	3	=	=	SYM
ejpam-6031	133	4	−β	−β	PROPN
ejpam-6031	133	5	(	(	PUNCT
ejpam-6031	133	6	id−2	id−2	NOUN
ejpam-6031	133	7	pu⊥	pu⊥	PROPN
ejpam-6031	133	8	)	)	PUNCT
ejpam-6031	134	1	+	+	CCONJ
ejpam-6031	134	2	(	(	PUNCT
ejpam-6031	134	3	1	1	NUM
ejpam-6031	134	4	−	−	NOUN
ejpam-6031	134	5	β	β	X
ejpam-6031	134	6	)	)	PUNCT
ejpam-6031	134	7	i	i	PROPN
ejpam-6031	134	8	d	d	NOUN
ejpam-6031	134	9	=	=	SYM
ejpam-6031	134	10	βru⊥	βru⊥	PROPN
ejpam-6031	134	11	+	+	CCONJ
ejpam-6031	134	12	(	(	PUNCT
ejpam-6031	134	13	1	1	NUM
ejpam-6031	134	14	−	−	NOUN
ejpam-6031	134	15	β	β	X
ejpam-6031	134	16	)	)	PUNCT
ejpam-6031	134	17	i	i	PROPN
ejpam-6031	134	18	d	d	PROPN
ejpam-6031	134	19	,	,	PUNCT
ejpam-6031	134	20	as	as	SCONJ
ejpam-6031	134	21	required	require	VERB
ejpam-6031	134	22	.	.	PUNCT
ejpam-6031	135	1	(	(	PUNCT
ejpam-6031	135	2	v	v	NOUN
ejpam-6031	135	3	):	):	PUNCT
ejpam-6031	135	4	let	let	VERB
ejpam-6031	135	5	x	x	X
ejpam-6031	135	6	∈	∈	PROPN
ejpam-6031	135	7	h.	h.	PROPN
ejpam-6031	135	8	by	by	ADP
ejpam-6031	135	9	using	use	VERB
ejpam-6031	135	10	(	(	PUNCT
ejpam-6031	135	11	ii	ii	NOUN
ejpam-6031	135	12	)	)	PUNCT
ejpam-6031	135	13	and	and	CCONJ
ejpam-6031	135	14	(	(	PUNCT
ejpam-6031	135	15	iv	iv	X
ejpam-6031	135	16	)	)	PUNCT
ejpam-6031	135	17	,	,	PUNCT
ejpam-6031	135	18	we	we	PRON
ejpam-6031	135	19	have	have	VERB
ejpam-6031	135	20	(	(	PUNCT
ejpam-6031	135	21	2β	2β	NUM
ejpam-6031	136	1	pu	pu	PROPN
ejpam-6031	136	2	−	−	PROPN
ejpam-6031	137	1	i	i	PROPN
ejpam-6031	137	2	d	d	PROPN
ejpam-6031	137	3	)	)	PUNCT
ejpam-6031	137	4	◦	◦	NOUN
ejpam-6031	137	5	(	(	PUNCT
ejpam-6031	137	6	−	−	PROPN
ejpam-6031	137	7	id)(x	id)(x	NOUN
ejpam-6031	137	8	)	)	PUNCT
ejpam-6031	138	1	=	=	PRON
ejpam-6031	138	2	(	(	PUNCT
ejpam-6031	138	3	2β	2β	NUM
ejpam-6031	139	1	pu	pu	NOUN
ejpam-6031	139	2	−	−	PROPN
ejpam-6031	140	1	i	i	PROPN
ejpam-6031	140	2	d	d	PROPN
ejpam-6031	140	3	)	)	PUNCT
ejpam-6031	140	4	(	(	PUNCT
ejpam-6031	140	5	−x	−x	NOUN
ejpam-6031	140	6	)	)	PUNCT
ejpam-6031	140	7	=	=	SYM
ejpam-6031	141	1	2β	2β	NOUN
ejpam-6031	141	2	pu(−x)−	pu(−x)−	NOUN
ejpam-6031	141	3	(	(	PUNCT
ejpam-6031	141	4	−x	−x	NOUN
ejpam-6031	141	5	)	)	PUNCT
ejpam-6031	141	6	=	=	SYM
ejpam-6031	142	1	−2β	−2β	NOUN
ejpam-6031	142	2	pu(x	pu(x	NOUN
ejpam-6031	142	3	)	)	PUNCT
ejpam-6031	143	1	+	+	CCONJ
ejpam-6031	143	2	x	x	X
ejpam-6031	143	3	=	=	SYM
ejpam-6031	143	4	−	−	PROPN
ejpam-6031	143	5	(	(	PUNCT
ejpam-6031	143	6	2β	2β	NUM
ejpam-6031	143	7	pu	pu	NOUN
ejpam-6031	143	8	x	x	NOUN
ejpam-6031	143	9	−	−	PROPN
ejpam-6031	143	10	x	x	SYM
ejpam-6031	143	11	)	)	PUNCT
ejpam-6031	144	1	=	=	SYM
ejpam-6031	144	2	βru⊥x	βru⊥x	PROPN
ejpam-6031	145	1	+	+	CCONJ
ejpam-6031	145	2	(	(	PUNCT
ejpam-6031	145	3	1	1	NUM
ejpam-6031	145	4	−	−	NOUN
ejpam-6031	145	5	β)x	β)x	NOUN
ejpam-6031	145	6	(	(	PUNCT
ejpam-6031	145	7	vi	vi	NUM
ejpam-6031	145	8	):	):	PUNCT
ejpam-6031	145	9	it	it	PRON
ejpam-6031	145	10	follows	follow	VERB
ejpam-6031	145	11	from	from	ADP
ejpam-6031	145	12	(	(	PUNCT
ejpam-6031	145	13	ii	ii	NOUN
ejpam-6031	145	14	)	)	PUNCT
ejpam-6031	145	15	,	,	PUNCT
ejpam-6031	145	16	(	(	PUNCT
ejpam-6031	145	17	iv	iv	X
ejpam-6031	145	18	)	)	PUNCT
ejpam-6031	145	19	,	,	PUNCT
ejpam-6031	145	20	and	and	CCONJ
ejpam-6031	145	21	(	(	PUNCT
ejpam-6031	145	22	v	v	NOUN
ejpam-6031	145	23	)	)	PUNCT
ejpam-6031	145	24	that	that	PRON
ejpam-6031	145	25	fix	fix	NOUN
ejpam-6031	145	26	(	(	PUNCT
ejpam-6031	145	27	(	(	PUNCT
ejpam-6031	145	28	2β	2β	NOUN
ejpam-6031	145	29	pu	pu	NOUN
ejpam-6031	145	30	−	−	PROPN
ejpam-6031	146	1	i	i	PROPN
ejpam-6031	146	2	d	d	PROPN
ejpam-6031	146	3	)	)	PUNCT
ejpam-6031	146	4	◦	◦	NOUN
ejpam-6031	146	5	(	(	PUNCT
ejpam-6031	146	6	−	−	PROPN
ejpam-6031	146	7	i	i	PROPN
ejpam-6031	146	8	d	d	PROPN
ejpam-6031	146	9	)	)	PUNCT
ejpam-6031	146	10	)	)	PUNCT
ejpam-6031	147	1	=	=	PRON
ejpam-6031	147	2	fix	fix	NOUN
ejpam-6031	147	3	(	(	PUNCT
ejpam-6031	147	4	−	−	PROPN
ejpam-6031	147	5	(	(	PUNCT
ejpam-6031	147	6	2β	2β	NUM
ejpam-6031	147	7	pu	pu	NOUN
ejpam-6031	147	8	−	−	PROPN
ejpam-6031	147	9	i	i	PROPN
ejpam-6031	147	10	d	d	PROPN
ejpam-6031	147	11	)	)	PUNCT
ejpam-6031	147	12	)	)	PUNCT
ejpam-6031	148	1	=	=	PRON
ejpam-6031	148	2	fix	fix	NOUN
ejpam-6031	148	3	(	(	PUNCT
ejpam-6031	148	4	βru	βru	NOUN
ejpam-6031	148	5	+	+	CCONJ
ejpam-6031	148	6	(	(	PUNCT
ejpam-6031	148	7	1	1	NUM
ejpam-6031	148	8	−	−	NUM
ejpam-6031	148	9	β)(−	β)(−	ADV
ejpam-6031	148	10	i	i	PROPN
ejpam-6031	148	11	d	d	PROPN
ejpam-6031	148	12	)	)	PUNCT
ejpam-6031	148	13	)	)	PUNCT
ejpam-6031	148	14	.	.	PUNCT
ejpam-6031	149	1	let	let	VERB
ejpam-6031	149	2	x	x	SYM
ejpam-6031	149	3	∈	∈	PROPN
ejpam-6031	149	4	h.	h.	NOUN
ejpam-6031	149	5	then	then	ADV
ejpam-6031	149	6	x	x	X
ejpam-6031	149	7	=	=	SYM
ejpam-6031	149	8	βru⊥(x	βru⊥(x	PROPN
ejpam-6031	149	9	)	)	PUNCT
ejpam-6031	150	1	+	+	CCONJ
ejpam-6031	150	2	(	(	PUNCT
ejpam-6031	150	3	1	1	NUM
ejpam-6031	150	4	−	−	NOUN
ejpam-6031	150	5	β)x	β)x	NOUN
ejpam-6031	150	6	=	=	SYM
ejpam-6031	150	7	βru⊥(x	βru⊥(x	NOUN
ejpam-6031	150	8	)	)	PUNCT
ejpam-6031	151	1	+	+	CCONJ
ejpam-6031	151	2	x	x	X
ejpam-6031	151	3	−	−	NOUN
ejpam-6031	152	1	βx	βx	NOUN
ejpam-6031	152	2	,	,	PUNCT
ejpam-6031	152	3	therefore	therefore	ADV
ejpam-6031	152	4	,	,	PUNCT
ejpam-6031	152	5	x	x	NOUN
ejpam-6031	152	6	−	−	NOUN
ejpam-6031	152	7	x	x	X
ejpam-6031	152	8	=	=	PUNCT
ejpam-6031	152	9	βru⊥(x)−	βru⊥(x)−	NOUN
ejpam-6031	152	10	βx	βx	ADP
ejpam-6031	152	11	0	0	NUM
ejpam-6031	153	1	=	=	SYM
ejpam-6031	153	2	β	β	X
ejpam-6031	153	3	(	(	PUNCT
ejpam-6031	153	4	2	2	NUM
ejpam-6031	153	5	pu⊥	pu⊥	PROPN
ejpam-6031	153	6	x	x	NOUN
ejpam-6031	153	7	−	−	PROPN
ejpam-6031	153	8	x	x	SYM
ejpam-6031	153	9	)	)	PUNCT
ejpam-6031	153	10	−	−	PROPN
ejpam-6031	153	11	βx	βx	NOUN
ejpam-6031	153	12	0	0	NUM
ejpam-6031	154	1	=	=	SYM
ejpam-6031	155	1	2β	2β	NOUN
ejpam-6031	155	2	pu⊥	pu⊥	NOUN
ejpam-6031	155	3	x	x	PUNCT
ejpam-6031	155	4	−	−	PROPN
ejpam-6031	155	5	2βx	2βx	ADV
ejpam-6031	155	6	,	,	PUNCT
ejpam-6031	155	7	and	and	CCONJ
ejpam-6031	155	8	2βx	2βx	ADJ
ejpam-6031	155	9	=	=	PUNCT
ejpam-6031	156	1	2β	2β	NOUN
ejpam-6031	156	2	pu⊥	pu⊥	NUM
ejpam-6031	156	3	x.	x.	NOUN
ejpam-6031	156	4	hence	hence	ADV
ejpam-6031	156	5	,	,	PUNCT
ejpam-6031	156	6	x	x	PUNCT
ejpam-6031	156	7	=	=	SYM
ejpam-6031	156	8	pu⊥	pu⊥	NUM
ejpam-6031	156	9	x	x	PUNCT
ejpam-6031	156	10	⇔	⇔	NUM
ejpam-6031	156	11	fix	fix	NOUN
ejpam-6031	156	12	(	(	PUNCT
ejpam-6031	156	13	(	(	PUNCT
ejpam-6031	156	14	2β	2β	NOUN
ejpam-6031	156	15	pu	pu	NOUN
ejpam-6031	156	16	−	−	PROPN
ejpam-6031	157	1	i	i	PROPN
ejpam-6031	157	2	d	d	PROPN
ejpam-6031	157	3	)	)	PUNCT
ejpam-6031	157	4	◦	◦	NOUN
ejpam-6031	157	5	(	(	PUNCT
ejpam-6031	157	6	−	−	PROPN
ejpam-6031	157	7	i	i	PROPN
ejpam-6031	157	8	d	d	PROPN
ejpam-6031	157	9	)	)	PUNCT
ejpam-6031	157	10	)	)	PUNCT
ejpam-6031	158	1	=	=	PUNCT
ejpam-6031	158	2	u⊥.	u⊥.	PROPN
ejpam-6031	159	1	■	■	PUNCT
ejpam-6031	159	2	lemma	lemma	PROPN
ejpam-6031	159	3	2	2	X
ejpam-6031	159	4	.	.	PUNCT
ejpam-6031	159	5	let	let	VERB
ejpam-6031	159	6	u	u	PRON
ejpam-6031	159	7	be	be	AUX
ejpam-6031	159	8	a	a	DET
ejpam-6031	159	9	closed	closed	ADJ
ejpam-6031	159	10	linear	linear	ADJ
ejpam-6031	159	11	subspace	subspace	NOUN
ejpam-6031	159	12	of	of	ADP
ejpam-6031	159	13	h	h	NOUN
ejpam-6031	159	14	,	,	PUNCT
ejpam-6031	159	15	and	and	CCONJ
ejpam-6031	159	16	let	let	VERB
ejpam-6031	159	17	γ	γ	NOUN
ejpam-6031	159	18	,	,	PUNCT
ejpam-6031	159	19	β	β	X
ejpam-6031	159	20	∈]0	∈]0	X
ejpam-6031	159	21	,	,	PUNCT
ejpam-6031	159	22	1	1	NUM
ejpam-6031	159	23	]	]	PUNCT
ejpam-6031	159	24	.	.	PUNCT
ejpam-6031	160	1	then	then	ADV
ejpam-6031	160	2	the	the	DET
ejpam-6031	160	3	following	follow	VERB
ejpam-6031	160	4	holds	hold	VERB
ejpam-6031	160	5	:	:	PUNCT
ejpam-6031	160	6	(	(	PUNCT
ejpam-6031	160	7	2β	2β	NUM
ejpam-6031	160	8	pu⊥	pu⊥	NOUN
ejpam-6031	160	9	−	−	PROPN
ejpam-6031	161	1	i	i	PROPN
ejpam-6031	161	2	d	d	PROPN
ejpam-6031	161	3	)	)	PUNCT
ejpam-6031	161	4	(	(	PUNCT
ejpam-6031	161	5	2γ	2γ	X
ejpam-6031	161	6	pu	pu	PROPN
ejpam-6031	161	7	−	−	PROPN
ejpam-6031	161	8	i	i	PROPN
ejpam-6031	161	9	d	d	PROPN
ejpam-6031	161	10	)	)	PUNCT
ejpam-6031	162	1	=	=	PUNCT
ejpam-6031	162	2			PRON
ejpam-6031	162	3	−	−	PROPN
ejpam-6031	163	1	i	i	PROPN
ejpam-6031	163	2	d	d	PROPN
ejpam-6031	163	3	,	,	PUNCT
ejpam-6031	163	4	for	for	ADP
ejpam-6031	163	5	β	β	X
ejpam-6031	163	6	=	=	SYM
ejpam-6031	163	7	γ	γ	X
ejpam-6031	163	8	=	=	SYM
ejpam-6031	163	9	1	1	NUM
ejpam-6031	163	10	0	0	NUM
ejpam-6031	163	11	,	,	PUNCT
ejpam-6031	163	12	for	for	ADP
ejpam-6031	163	13	β	β	X
ejpam-6031	163	14	=	=	SYM
ejpam-6031	163	15	γ	γ	X
ejpam-6031	163	16	=	=	SYM
ejpam-6031	163	17	1/2	1/2	NUM
ejpam-6031	163	18	id−2	id−2	NOUN
ejpam-6031	163	19	(	(	PUNCT
ejpam-6031	163	20	β	β	X
ejpam-6031	163	21	pu⊥	pu⊥	VERB
ejpam-6031	163	22	+	+	PROPN
ejpam-6031	163	23	γ	γ	X
ejpam-6031	163	24	pu	pu	PROPN
ejpam-6031	163	25	)	)	PUNCT
ejpam-6031	163	26	,	,	PUNCT
ejpam-6031	163	27	for	for	ADP
ejpam-6031	163	28	β	β	X
ejpam-6031	163	29	,	,	PUNCT
ejpam-6031	163	30	γ	γ	PROPN
ejpam-6031	163	31	̸=	̸=	PROPN
ejpam-6031	163	32	1	1	NUM
ejpam-6031	163	33	=	=	SYM
ejpam-6031	163	34	(	(	PUNCT
ejpam-6031	163	35	2γ	2γ	X
ejpam-6031	163	36	pu	pu	PROPN
ejpam-6031	163	37	−	−	PROPN
ejpam-6031	163	38	i	i	PROPN
ejpam-6031	163	39	d	d	PROPN
ejpam-6031	163	40	)	)	PUNCT
ejpam-6031	163	41	(	(	PUNCT
ejpam-6031	163	42	2β	2β	NUM
ejpam-6031	164	1	pu⊥	pu⊥	NOUN
ejpam-6031	164	2	−	−	PROPN
ejpam-6031	164	3	i	i	PROPN
ejpam-6031	164	4	d	d	PROPN
ejpam-6031	164	5	)	)	PUNCT
ejpam-6031	164	6	.	.	PUNCT
ejpam-6031	165	1	s.th	s.th	PROPN
ejpam-6031	165	2	.	.	PUNCT
ejpam-6031	165	3	alwadani	alwadani	PROPN
ejpam-6031	165	4	/	/	SYM
ejpam-6031	165	5	eur	eur	PROPN
ejpam-6031	165	6	.	.	PUNCT
ejpam-6031	166	1	j.	j.	PROPN
ejpam-6031	166	2	pure	pure	PROPN
ejpam-6031	166	3	appl	appl	PROPN
ejpam-6031	166	4	.	.	PROPN
ejpam-6031	166	5	math	math	PROPN
ejpam-6031	166	6	,	,	PUNCT
ejpam-6031	166	7	18	18	NUM
ejpam-6031	166	8	(	(	PUNCT
ejpam-6031	166	9	2	2	NUM
ejpam-6031	166	10	)	)	PUNCT
ejpam-6031	166	11	(	(	PUNCT
ejpam-6031	166	12	2025	2025	NUM
ejpam-6031	166	13	)	)	PUNCT
ejpam-6031	166	14	,	,	PUNCT
ejpam-6031	166	15	6031	6031	NUM
ejpam-6031	166	16	6	6	NUM
ejpam-6031	166	17	of	of	ADP
ejpam-6031	166	18	13	13	NUM
ejpam-6031	166	19	proof	proof	NOUN
ejpam-6031	166	20	.	.	PUNCT
ejpam-6031	167	1	using	use	VERB
ejpam-6031	167	2	lemma	lemma	PROPN
ejpam-6031	167	3	1	1	NUM
ejpam-6031	167	4	,	,	PUNCT
ejpam-6031	167	5	(	(	PUNCT
ejpam-6031	167	6	i	i	NOUN
ejpam-6031	167	7	)	)	PUNCT
ejpam-6031	167	8	,	,	PUNCT
ejpam-6031	167	9	(	(	PUNCT
ejpam-6031	167	10	ii	ii	NOUN
ejpam-6031	167	11	)	)	PUNCT
ejpam-6031	167	12	,	,	PUNCT
ejpam-6031	167	13	and	and	CCONJ
ejpam-6031	167	14	(	(	PUNCT
ejpam-6031	167	15	iii	iii	NOUN
ejpam-6031	167	16	)	)	PUNCT
ejpam-6031	167	17	yields	yield	NOUN
ejpam-6031	167	18	(	(	PUNCT
ejpam-6031	167	19	2β	2β	NUM
ejpam-6031	167	20	pu⊥	pu⊥	NOUN
ejpam-6031	167	21	−	−	PROPN
ejpam-6031	167	22	i	i	PROPN
ejpam-6031	167	23	d	d	PROPN
ejpam-6031	167	24	)	)	PUNCT
ejpam-6031	167	25	(	(	PUNCT
ejpam-6031	167	26	2γ	2γ	X
ejpam-6031	167	27	pu	pu	PROPN
ejpam-6031	167	28	−	−	PROPN
ejpam-6031	167	29	i	i	PROPN
ejpam-6031	167	30	d	d	PROPN
ejpam-6031	167	31	)	)	PUNCT
ejpam-6031	168	1	=	=	PRON
ejpam-6031	168	2	(	(	PUNCT
ejpam-6031	168	3	βru⊥	βru⊥	PROPN
ejpam-6031	168	4	+	+	CCONJ
ejpam-6031	168	5	(	(	PUNCT
ejpam-6031	168	6	1	1	NUM
ejpam-6031	168	7	−	−	NUM
ejpam-6031	168	8	β)(−	β)(−	ADV
ejpam-6031	168	9	i	i	PROPN
ejpam-6031	168	10	d	d	PROPN
ejpam-6031	168	11	)	)	PUNCT
ejpam-6031	168	12	)	)	PUNCT
ejpam-6031	168	13	(	(	PUNCT
ejpam-6031	168	14	γru	γru	X
ejpam-6031	168	15	+	+	CCONJ
ejpam-6031	168	16	(	(	PUNCT
ejpam-6031	168	17	1	1	NUM
ejpam-6031	168	18	−	−	NOUN
ejpam-6031	168	19	γ)(−	γ)(−	PROPN
ejpam-6031	168	20	i	i	PROPN
ejpam-6031	168	21	d	d	PROPN
ejpam-6031	168	22	)	)	PUNCT
ejpam-6031	168	23	)	)	PUNCT
ejpam-6031	169	1	=	=	PUNCT
ejpam-6031	169	2	−βγ	−βγ	NOUN
ejpam-6031	169	3	id+β(1	id+β(1	NOUN
ejpam-6031	169	4	−	−	PROPN
ejpam-6031	169	5	γ)ru	γ)ru	PROPN
ejpam-6031	169	6	−	−	PROPN
ejpam-6031	169	7	(	(	PUNCT
ejpam-6031	169	8	1	1	NUM
ejpam-6031	169	9	−	−	NOUN
ejpam-6031	169	10	β)γru	β)γru	NOUN
ejpam-6031	169	11	+	+	CCONJ
ejpam-6031	169	12	(	(	PUNCT
ejpam-6031	169	13	1	1	NUM
ejpam-6031	169	14	−	−	NOUN
ejpam-6031	169	15	β)(1	β)(1	PUNCT
ejpam-6031	170	1	−	−	PROPN
ejpam-6031	170	2	γ	γ	X
ejpam-6031	170	3	)	)	PUNCT
ejpam-6031	170	4	i	i	PROPN
ejpam-6031	170	5	d	d	NOUN
ejpam-6031	170	6	=	=	PUNCT
ejpam-6031	170	7	βru	βru	NOUN
ejpam-6031	170	8	−	−	PROPN
ejpam-6031	170	9	γru	γru	ADV
ejpam-6031	170	10	−	−	PROPN
ejpam-6031	170	11	(	(	PUNCT
ejpam-6031	170	12	β	β	X
ejpam-6031	170	13	+	+	CCONJ
ejpam-6031	170	14	γ	γ	X
ejpam-6031	170	15	)	)	PUNCT
ejpam-6031	170	16	id+	id+	PROPN
ejpam-6031	171	1	i	i	PROPN
ejpam-6031	171	2	d	d	PROPN
ejpam-6031	171	3	=	=	SYM
ejpam-6031	171	4	id−2	id−2	PROPN
ejpam-6031	171	5	(	(	PUNCT
ejpam-6031	171	6	β	β	X
ejpam-6031	171	7	pu⊥	pu⊥	VERB
ejpam-6031	171	8	+	+	PROPN
ejpam-6031	171	9	γ	γ	X
ejpam-6031	171	10	pu	pu	PROPN
ejpam-6031	171	11	)	)	PUNCT
ejpam-6031	171	12	.	.	PUNCT
ejpam-6031	172	1	there	there	PRON
ejpam-6031	172	2	are	be	VERB
ejpam-6031	172	3	3	3	NUM
ejpam-6031	172	4	cases	case	NOUN
ejpam-6031	172	5	:	:	PUNCT
ejpam-6031	172	6	case	case	NOUN
ejpam-6031	172	7	1	1	NUM
ejpam-6031	172	8	:	:	PUNCT
ejpam-6031	172	9	if	if	SCONJ
ejpam-6031	172	10	β	β	X
ejpam-6031	172	11	=	=	SYM
ejpam-6031	172	12	γ	γ	X
ejpam-6031	172	13	=	=	SYM
ejpam-6031	172	14	1	1	NUM
ejpam-6031	172	15	,	,	PUNCT
ejpam-6031	172	16	then	then	ADV
ejpam-6031	172	17	(	(	PUNCT
ejpam-6031	172	18	2β	2β	NUM
ejpam-6031	172	19	pu⊥	pu⊥	NOUN
ejpam-6031	172	20	−	−	PROPN
ejpam-6031	172	21	i	i	PROPN
ejpam-6031	172	22	d	d	PROPN
ejpam-6031	172	23	)	)	PUNCT
ejpam-6031	172	24	(	(	PUNCT
ejpam-6031	172	25	2γ	2γ	X
ejpam-6031	172	26	pu	pu	PROPN
ejpam-6031	172	27	−	−	PROPN
ejpam-6031	172	28	i	i	PROPN
ejpam-6031	172	29	d	d	PROPN
ejpam-6031	172	30	)	)	PUNCT
ejpam-6031	173	1	=	=	PUNCT
ejpam-6031	173	2	id−2	id−2	NOUN
ejpam-6031	173	3	(	(	PUNCT
ejpam-6031	173	4	pu⊥	pu⊥	PROPN
ejpam-6031	173	5	+	+	PROPN
ejpam-6031	173	6	pu	pu	PROPN
ejpam-6031	173	7	)	)	PUNCT
ejpam-6031	173	8	=	=	PUNCT
ejpam-6031	174	1	id−2	id−2	PROPN
ejpam-6031	175	1	i	i	PROPN
ejpam-6031	175	2	d	d	PROPN
ejpam-6031	175	3	=	=	PUNCT
ejpam-6031	175	4	−	−	PROPN
ejpam-6031	175	5	i	i	PROPN
ejpam-6031	175	6	d	d	PROPN
ejpam-6031	175	7	,	,	PUNCT
ejpam-6031	175	8	by	by	ADP
ejpam-6031	175	9	(	(	PUNCT
ejpam-6031	175	10	8)	8)	NUM
ejpam-6031	175	11	.	.	PUNCT
ejpam-6031	175	12	case	case	NOUN
ejpam-6031	175	13	2	2	NUM
ejpam-6031	175	14	:	:	PUNCT
ejpam-6031	175	15	if	if	SCONJ
ejpam-6031	175	16	β	β	X
ejpam-6031	175	17	=	=	SYM
ejpam-6031	175	18	γ	γ	X
ejpam-6031	175	19	=	=	SYM
ejpam-6031	175	20	1/2	1/2	NUM
ejpam-6031	175	21	,	,	PUNCT
ejpam-6031	175	22	then	then	ADV
ejpam-6031	175	23	(	(	PUNCT
ejpam-6031	175	24	pu⊥	pu⊥	PROPN
ejpam-6031	175	25	−	−	PROPN
ejpam-6031	175	26	i	i	PROPN
ejpam-6031	175	27	d	d	PROPN
ejpam-6031	175	28	)	)	PUNCT
ejpam-6031	175	29	(	(	PUNCT
ejpam-6031	175	30	pu	pu	PROPN
ejpam-6031	175	31	−	−	PROPN
ejpam-6031	176	1	i	i	PROPN
ejpam-6031	176	2	d	d	PROPN
ejpam-6031	176	3	)	)	PUNCT
ejpam-6031	177	1	=	=	PUNCT
ejpam-6031	177	2	id−	id−	NOUN
ejpam-6031	177	3	(	(	PUNCT
ejpam-6031	177	4	pu⊥	pu⊥	PROPN
ejpam-6031	177	5	+	+	PROPN
ejpam-6031	177	6	pu	pu	PROPN
ejpam-6031	177	7	)	)	PUNCT
ejpam-6031	177	8	=	=	PUNCT
ejpam-6031	178	1	id−	id−	PUNCT
ejpam-6031	178	2	i	i	NOUN
ejpam-6031	178	3	d	d	PROPN
ejpam-6031	178	4	=	=	SYM
ejpam-6031	178	5	0	0	NUM
ejpam-6031	178	6	,	,	PUNCT
ejpam-6031	178	7	case	case	NOUN
ejpam-6031	178	8	3	3	NUM
ejpam-6031	178	9	:	:	PUNCT
ejpam-6031	178	10	if	if	SCONJ
ejpam-6031	178	11	β	β	X
ejpam-6031	178	12	,	,	PUNCT
ejpam-6031	178	13	γ	γ	PROPN
ejpam-6031	178	14	̸=	̸=	PROPN
ejpam-6031	178	15	1	1	NUM
ejpam-6031	178	16	and	and	CCONJ
ejpam-6031	178	17	β	β	NOUN
ejpam-6031	178	18	,	,	PUNCT
ejpam-6031	178	19	γ	γ	PROPN
ejpam-6031	178	20	̸=	̸=	PROPN
ejpam-6031	178	21	1/2,then	1/2,then	NUM
ejpam-6031	178	22	(	(	PUNCT
ejpam-6031	178	23	2β	2β	NUM
ejpam-6031	178	24	pu⊥	pu⊥	NOUN
ejpam-6031	178	25	−	−	PROPN
ejpam-6031	179	1	i	i	PROPN
ejpam-6031	179	2	d	d	PROPN
ejpam-6031	179	3	)	)	PUNCT
ejpam-6031	179	4	(	(	PUNCT
ejpam-6031	179	5	2γ	2γ	X
ejpam-6031	179	6	pu	pu	PROPN
ejpam-6031	179	7	−	−	PROPN
ejpam-6031	179	8	i	i	PROPN
ejpam-6031	179	9	d	d	PROPN
ejpam-6031	179	10	)	)	PUNCT
ejpam-6031	180	1	=	=	SYM
ejpam-6031	180	2	id−2	id−2	NOUN
ejpam-6031	180	3	(	(	PUNCT
ejpam-6031	180	4	β	β	X
ejpam-6031	180	5	pu⊥	pu⊥	VERB
ejpam-6031	180	6	+	+	PROPN
ejpam-6031	180	7	γ	γ	X
ejpam-6031	180	8	pu	pu	PROPN
ejpam-6031	180	9	)	)	PUNCT
ejpam-6031	180	10	.	.	PUNCT
ejpam-6031	181	1	applying	apply	VERB
ejpam-6031	181	2	lemma	lemma	PROPN
ejpam-6031	181	3	1	1	NUM
ejpam-6031	181	4	,	,	PUNCT
ejpam-6031	181	5	(	(	PUNCT
ejpam-6031	181	6	i	i	NOUN
ejpam-6031	181	7	)	)	PUNCT
ejpam-6031	181	8	,	,	PUNCT
ejpam-6031	181	9	(	(	PUNCT
ejpam-6031	181	10	ii	ii	NOUN
ejpam-6031	181	11	)	)	PUNCT
ejpam-6031	181	12	,	,	PUNCT
ejpam-6031	181	13	and	and	CCONJ
ejpam-6031	181	14	(	(	PUNCT
ejpam-6031	181	15	iii	iii	NOUN
ejpam-6031	181	16	)	)	PUNCT
ejpam-6031	181	17	,	,	PUNCT
ejpam-6031	181	18	the	the	DET
ejpam-6031	181	19	same	same	ADJ
ejpam-6031	181	20	strategy	strategy	NOUN
ejpam-6031	181	21	can	can	AUX
ejpam-6031	181	22	be	be	AUX
ejpam-6031	181	23	appied	appie	VERB
ejpam-6031	181	24	to	to	PART
ejpam-6031	181	25	show	show	VERB
ejpam-6031	181	26	that	that	SCONJ
ejpam-6031	181	27	(	(	PUNCT
ejpam-6031	181	28	2γ	2γ	X
ejpam-6031	181	29	pu	pu	PROPN
ejpam-6031	181	30	−	−	PROPN
ejpam-6031	181	31	i	i	PROPN
ejpam-6031	181	32	d	d	PROPN
ejpam-6031	181	33	)	)	PUNCT
ejpam-6031	181	34	(	(	PUNCT
ejpam-6031	181	35	2β	2β	NUM
ejpam-6031	181	36	pu⊥	pu⊥	NOUN
ejpam-6031	181	37	−	−	PROPN
ejpam-6031	182	1	i	i	NOUN
ejpam-6031	182	2	d	d	PROPN
ejpam-6031	182	3	)	)	PUNCT
ejpam-6031	183	1	=	=	PUNCT
ejpam-6031	183	2			PRON
ejpam-6031	183	3	−	−	PROPN
ejpam-6031	184	1	i	i	PROPN
ejpam-6031	184	2	d	d	PROPN
ejpam-6031	184	3	,	,	PUNCT
ejpam-6031	184	4	for	for	ADP
ejpam-6031	184	5	γ	γ	X
ejpam-6031	184	6	=	=	SYM
ejpam-6031	184	7	β	β	X
ejpam-6031	184	8	=	=	SYM
ejpam-6031	184	9	1	1	NUM
ejpam-6031	184	10	0	0	NUM
ejpam-6031	184	11	,	,	PUNCT
ejpam-6031	184	12	for	for	ADP
ejpam-6031	184	13	γ	γ	X
ejpam-6031	184	14	=	=	SYM
ejpam-6031	184	15	β	β	X
ejpam-6031	184	16	=	=	SYM
ejpam-6031	184	17	1/2	1/2	NUM
ejpam-6031	184	18	id−2	id−2	NOUN
ejpam-6031	184	19	(	(	PUNCT
ejpam-6031	184	20	γ	γ	X
ejpam-6031	184	21	pu	pu	PROPN
ejpam-6031	184	22	+	+	PROPN
ejpam-6031	184	23	β	β	X
ejpam-6031	184	24	pu⊥	pu⊥	PROPN
ejpam-6031	184	25	)	)	PUNCT
ejpam-6031	184	26	,	,	PUNCT
ejpam-6031	184	27	for	for	ADP
ejpam-6031	184	28	γ	γ	PROPN
ejpam-6031	184	29	,	,	PUNCT
ejpam-6031	184	30	β	β	X
ejpam-6031	184	31	̸=	̸=	PROPN
ejpam-6031	184	32	1	1	NUM
ejpam-6031	184	33	therefore	therefore	ADV
ejpam-6031	184	34	,	,	PUNCT
ejpam-6031	184	35	(	(	PUNCT
ejpam-6031	184	36	2β	2β	NOUN
ejpam-6031	185	1	pu⊥	pu⊥	NOUN
ejpam-6031	185	2	−	−	PROPN
ejpam-6031	186	1	i	i	PROPN
ejpam-6031	186	2	d	d	PROPN
ejpam-6031	186	3	)	)	PUNCT
ejpam-6031	186	4	(	(	PUNCT
ejpam-6031	186	5	2γ	2γ	X
ejpam-6031	186	6	pu	pu	PROPN
ejpam-6031	186	7	−	−	PROPN
ejpam-6031	186	8	i	i	PROPN
ejpam-6031	186	9	d	d	PROPN
ejpam-6031	186	10	)	)	PUNCT
ejpam-6031	187	1	=	=	PUNCT
ejpam-6031	187	2	(	(	PUNCT
ejpam-6031	187	3	2γ	2γ	X
ejpam-6031	187	4	pu	pu	PROPN
ejpam-6031	187	5	−	−	PROPN
ejpam-6031	187	6	i	i	PROPN
ejpam-6031	187	7	d	d	PROPN
ejpam-6031	187	8	)	)	PUNCT
ejpam-6031	187	9	(	(	PUNCT
ejpam-6031	187	10	2β	2β	NUM
ejpam-6031	187	11	pu⊥	pu⊥	NOUN
ejpam-6031	187	12	−	−	PROPN
ejpam-6031	187	13	i	i	PROPN
ejpam-6031	187	14	d	d	PROPN
ejpam-6031	187	15	)	)	PUNCT
ejpam-6031	187	16	.	.	PUNCT
ejpam-6031	188	1	■	■	PUNCT
ejpam-6031	188	2	example	example	NOUN
ejpam-6031	188	3	4	4	X
ejpam-6031	188	4	.	.	PUNCT
ejpam-6031	189	1	let	let	VERB
ejpam-6031	189	2	x	x	NOUN
ejpam-6031	189	3	=	=	PUNCT
ejpam-6031	189	4	r2	r2	PROPN
ejpam-6031	189	5	and	and	CCONJ
ejpam-6031	189	6	suppose	suppose	VERB
ejpam-6031	189	7	that	that	SCONJ
ejpam-6031	189	8	u	u	PRON
ejpam-6031	189	9	=	=	NOUN
ejpam-6031	189	10	r×	r×	NOUN
ejpam-6031	189	11	{	{	PUNCT
ejpam-6031	189	12	0	0	NUM
ejpam-6031	189	13	}	}	PUNCT
ejpam-6031	189	14	and	and	CCONJ
ejpam-6031	189	15	x	x	SYM
ejpam-6031	189	16	=	=	SYM
ejpam-6031	189	17	(	(	PUNCT
ejpam-6031	189	18	2	2	NUM
ejpam-6031	189	19	,	,	PUNCT
ejpam-6031	189	20	2	2	NUM
ejpam-6031	189	21	)	)	PUNCT
ejpam-6031	189	22	.	.	PUNCT
ejpam-6031	190	1	then	then	ADV
ejpam-6031	190	2	u⊥	u⊥	PROPN
ejpam-6031	190	3	=	=	PUNCT
ejpam-6031	190	4	{	{	PUNCT
ejpam-6031	190	5	0	0	NUM
ejpam-6031	190	6	}	}	PUNCT
ejpam-6031	190	7	×r	×r	NOUN
ejpam-6031	190	8	,	,	PUNCT
ejpam-6031	190	9	and	and	CCONJ
ejpam-6031	190	10	by	by	ADP
ejpam-6031	190	11	lemma	lemma	PROPN
ejpam-6031	190	12	2	2	NUM
ejpam-6031	190	13	,	,	PUNCT
ejpam-6031	190	14	we	we	PRON
ejpam-6031	190	15	obtain	obtain	VERB
ejpam-6031	190	16	the	the	DET
ejpam-6031	190	17	following	following	NOUN
ejpam-6031	190	18	:	:	PUNCT
ejpam-6031	190	19	case	case	NOUN
ejpam-6031	190	20	1	1	X
ejpam-6031	190	21	.	.	PUNCT
ejpam-6031	191	1	if	if	SCONJ
ejpam-6031	191	2	β	β	PRON
ejpam-6031	191	3	=	=	SYM
ejpam-6031	191	4	γ	γ	X
ejpam-6031	191	5	=	=	SYM
ejpam-6031	191	6	1	1	NUM
ejpam-6031	191	7	,	,	PUNCT
ejpam-6031	191	8	then	then	ADV
ejpam-6031	191	9	(	(	PUNCT
ejpam-6031	191	10	2	2	NUM
ejpam-6031	191	11	p{0}×r	p{0}×r	NOUN
ejpam-6031	192	1	−	−	PROPN
ejpam-6031	192	2	i	i	PROPN
ejpam-6031	192	3	d	d	PROPN
ejpam-6031	192	4	)	)	PUNCT
ejpam-6031	192	5	(	(	PUNCT
ejpam-6031	192	6	2	2	NUM
ejpam-6031	192	7	pr×{0}(2	pr×{0}(2	NOUN
ejpam-6031	192	8	,	,	PUNCT
ejpam-6031	192	9	2)−	2)−	NUM
ejpam-6031	192	10	(	(	PUNCT
ejpam-6031	192	11	2	2	NUM
ejpam-6031	192	12	,	,	PUNCT
ejpam-6031	192	13	2	2	NUM
ejpam-6031	192	14	)	)	PUNCT
ejpam-6031	192	15	)	)	PUNCT
ejpam-6031	193	1	=	=	PUNCT
ejpam-6031	193	2	(	(	PUNCT
ejpam-6031	193	3	2	2	NUM
ejpam-6031	193	4	pr×{0	pr×{0	VERB
ejpam-6031	193	5	}	}	PUNCT
ejpam-6031	193	6	−	−	PROPN
ejpam-6031	193	7	i	i	PROPN
ejpam-6031	193	8	d	d	PROPN
ejpam-6031	193	9	)	)	PUNCT
ejpam-6031	193	10	(	(	PUNCT
ejpam-6031	193	11	2	2	NUM
ejpam-6031	193	12	p{0}×r(2	p{0}×r(2	NOUN
ejpam-6031	193	13	,	,	PUNCT
ejpam-6031	193	14	2)−	2)−	NUM
ejpam-6031	193	15	(	(	PUNCT
ejpam-6031	193	16	2	2	NUM
ejpam-6031	193	17	,	,	PUNCT
ejpam-6031	193	18	2	2	NUM
ejpam-6031	193	19	)	)	PUNCT
ejpam-6031	193	20	)	)	PUNCT
ejpam-6031	193	21	=	=	PUNCT
ejpam-6031	193	22	(	(	PUNCT
ejpam-6031	193	23	−2,−2	−2,−2	VERB
ejpam-6031	193	24	)	)	PUNCT
ejpam-6031	193	25	.	.	PUNCT
ejpam-6031	194	1	s.th	s.th	PROPN
ejpam-6031	194	2	.	.	PUNCT
ejpam-6031	194	3	alwadani	alwadani	PROPN
ejpam-6031	194	4	/	/	SYM
ejpam-6031	194	5	eur	eur	PROPN
ejpam-6031	194	6	.	.	PUNCT
ejpam-6031	195	1	j.	j.	PROPN
ejpam-6031	195	2	pure	pure	PROPN
ejpam-6031	195	3	appl	appl	PROPN
ejpam-6031	195	4	.	.	PROPN
ejpam-6031	195	5	math	math	PROPN
ejpam-6031	195	6	,	,	PUNCT
ejpam-6031	195	7	18	18	NUM
ejpam-6031	195	8	(	(	PUNCT
ejpam-6031	195	9	2	2	NUM
ejpam-6031	195	10	)	)	PUNCT
ejpam-6031	195	11	(	(	PUNCT
ejpam-6031	195	12	2025	2025	NUM
ejpam-6031	195	13	)	)	PUNCT
ejpam-6031	195	14	,	,	PUNCT
ejpam-6031	195	15	6031	6031	NUM
ejpam-6031	195	16	7	7	NUM
ejpam-6031	195	17	of	of	ADP
ejpam-6031	195	18	13	13	NUM
ejpam-6031	195	19	case	case	NOUN
ejpam-6031	195	20	2	2	NUM
ejpam-6031	195	21	.	.	PUNCT
ejpam-6031	196	1	if	if	SCONJ
ejpam-6031	196	2	β	β	PRON
ejpam-6031	196	3	=	=	SYM
ejpam-6031	196	4	γ	γ	X
ejpam-6031	196	5	=	=	SYM
ejpam-6031	196	6	1/2	1/2	NUM
ejpam-6031	196	7	,	,	PUNCT
ejpam-6031	196	8	then	then	ADV
ejpam-6031	196	9	(	(	PUNCT
ejpam-6031	196	10	p{0}×r	p{0}×r	PROPN
ejpam-6031	196	11	−	−	PROPN
ejpam-6031	196	12	i	i	PROPN
ejpam-6031	196	13	d	d	PROPN
ejpam-6031	196	14	)	)	PUNCT
ejpam-6031	196	15	(	(	PUNCT
ejpam-6031	196	16	pr×{0}(2	pr×{0}(2	NOUN
ejpam-6031	196	17	,	,	PUNCT
ejpam-6031	196	18	2)−	2)−	NUM
ejpam-6031	196	19	(	(	PUNCT
ejpam-6031	196	20	2	2	NUM
ejpam-6031	196	21	,	,	PUNCT
ejpam-6031	196	22	2	2	NUM
ejpam-6031	196	23	)	)	PUNCT
ejpam-6031	196	24	)	)	PUNCT
ejpam-6031	197	1	=	=	PUNCT
ejpam-6031	197	2	(	(	PUNCT
ejpam-6031	197	3	pr×{0	pr×{0	X
ejpam-6031	197	4	}	}	PUNCT
ejpam-6031	197	5	−	−	PROPN
ejpam-6031	197	6	i	i	PROPN
ejpam-6031	197	7	d	d	PROPN
ejpam-6031	197	8	)	)	PUNCT
ejpam-6031	197	9	(	(	PUNCT
ejpam-6031	197	10	p{0}×r(2	p{0}×r(2	NOUN
ejpam-6031	197	11	,	,	PUNCT
ejpam-6031	197	12	2)−	2)−	NUM
ejpam-6031	197	13	(	(	PUNCT
ejpam-6031	197	14	2	2	NUM
ejpam-6031	197	15	,	,	PUNCT
ejpam-6031	197	16	2	2	NUM
ejpam-6031	197	17	)	)	PUNCT
ejpam-6031	197	18	)	)	PUNCT
ejpam-6031	197	19	=	=	PUNCT
ejpam-6031	198	1	(	(	PUNCT
ejpam-6031	198	2	0	0	NUM
ejpam-6031	198	3	,	,	PUNCT
ejpam-6031	198	4	0	0	NUM
ejpam-6031	198	5	)	)	PUNCT
ejpam-6031	198	6	.	.	PUNCT
ejpam-6031	199	1	case	case	NOUN
ejpam-6031	200	1	3	3	X
ejpam-6031	200	2	.	.	PUNCT
ejpam-6031	201	1	if	if	SCONJ
ejpam-6031	201	2	β	β	X
ejpam-6031	201	3	,	,	PUNCT
ejpam-6031	201	4	γ	γ	PROPN
ejpam-6031	201	5	̸=	̸=	PROPN
ejpam-6031	201	6	1/2	1/2	NUM
ejpam-6031	201	7	and	and	CCONJ
ejpam-6031	201	8	β	β	NOUN
ejpam-6031	201	9	,	,	PUNCT
ejpam-6031	201	10	γ	γ	PROPN
ejpam-6031	201	11	̸=	̸=	PROPN
ejpam-6031	201	12	1	1	NUM
ejpam-6031	201	13	,	,	PUNCT
ejpam-6031	201	14	then	then	ADV
ejpam-6031	201	15	(	(	PUNCT
ejpam-6031	201	16	2β	2β	NOUN
ejpam-6031	201	17	p{0}×r	p{0}×r	PROPN
ejpam-6031	202	1	−	−	PROPN
ejpam-6031	202	2	i	i	PROPN
ejpam-6031	202	3	d	d	PROPN
ejpam-6031	202	4	)	)	PUNCT
ejpam-6031	202	5	(	(	PUNCT
ejpam-6031	202	6	2γ	2γ	NUM
ejpam-6031	202	7	pr×{0}(2	pr×{0}(2	NOUN
ejpam-6031	202	8	,	,	PUNCT
ejpam-6031	202	9	2)−	2)−	NUM
ejpam-6031	202	10	(	(	PUNCT
ejpam-6031	202	11	2	2	NUM
ejpam-6031	202	12	,	,	PUNCT
ejpam-6031	202	13	2	2	NUM
ejpam-6031	202	14	)	)	PUNCT
ejpam-6031	202	15	)	)	PUNCT
ejpam-6031	203	1	=	=	PUNCT
ejpam-6031	203	2	(	(	PUNCT
ejpam-6031	203	3	2γ	2γ	X
ejpam-6031	203	4	pr×{0	pr×{0	X
ejpam-6031	203	5	}	}	PUNCT
ejpam-6031	203	6	−	−	PROPN
ejpam-6031	203	7	i	i	PROPN
ejpam-6031	203	8	d	d	PROPN
ejpam-6031	203	9	)	)	PUNCT
ejpam-6031	203	10	(	(	PUNCT
ejpam-6031	203	11	2β	2β	NUM
ejpam-6031	203	12	p{0}×r(2	p{0}×r(2	NOUN
ejpam-6031	203	13	,	,	PUNCT
ejpam-6031	203	14	2)−	2)−	NUM
ejpam-6031	203	15	(	(	PUNCT
ejpam-6031	203	16	2	2	NUM
ejpam-6031	203	17	,	,	PUNCT
ejpam-6031	203	18	2	2	NUM
ejpam-6031	203	19	)	)	PUNCT
ejpam-6031	203	20	)	)	PUNCT
ejpam-6031	203	21	=	=	PUNCT
ejpam-6031	204	1	(	(	PUNCT
ejpam-6031	204	2	2	2	NUM
ejpam-6031	204	3	,	,	PUNCT
ejpam-6031	204	4	2)−	2)−	NUM
ejpam-6031	204	5	2	2	NUM
ejpam-6031	204	6	(	(	PUNCT
ejpam-6031	204	7	β(0	β(0	PROPN
ejpam-6031	204	8	,	,	PUNCT
ejpam-6031	204	9	2	2	NUM
ejpam-6031	204	10	)	)	PUNCT
ejpam-6031	204	11	+	+	CCONJ
ejpam-6031	204	12	γ(2	γ(2	PROPN
ejpam-6031	204	13	,	,	PUNCT
ejpam-6031	204	14	0	0	NUM
ejpam-6031	204	15	)	)	PUNCT
ejpam-6031	204	16	)	)	PUNCT
ejpam-6031	204	17	note	note	VERB
ejpam-6031	204	18	that	that	SCONJ
ejpam-6031	204	19	when	when	SCONJ
ejpam-6031	204	20	β	β	X
ejpam-6031	204	21	,	,	PUNCT
ejpam-6031	204	22	γ	γ	X
ejpam-6031	204	23	→	→	SYM
ejpam-6031	204	24	0	0	NUM
ejpam-6031	204	25	,	,	PUNCT
ejpam-6031	204	26	then	then	ADV
ejpam-6031	204	27	(	(	PUNCT
ejpam-6031	204	28	2β	2β	NOUN
ejpam-6031	204	29	p{0}×r	p{0}×r	PROPN
ejpam-6031	204	30	−	−	PROPN
ejpam-6031	205	1	i	i	PROPN
ejpam-6031	205	2	d	d	PROPN
ejpam-6031	205	3	)	)	PUNCT
ejpam-6031	205	4	(	(	PUNCT
ejpam-6031	205	5	2γ	2γ	NUM
ejpam-6031	205	6	pr×{0}(2	pr×{0}(2	NOUN
ejpam-6031	205	7	,	,	PUNCT
ejpam-6031	205	8	2)−	2)−	NUM
ejpam-6031	205	9	(	(	PUNCT
ejpam-6031	205	10	2	2	NUM
ejpam-6031	205	11	,	,	PUNCT
ejpam-6031	205	12	2	2	NUM
ejpam-6031	205	13	)	)	PUNCT
ejpam-6031	205	14	)	)	PUNCT
ejpam-6031	205	15	→	→	PUNCT
ejpam-6031	205	16	(	(	PUNCT
ejpam-6031	205	17	2	2	NUM
ejpam-6031	205	18	,	,	PUNCT
ejpam-6031	205	19	2	2	NUM
ejpam-6031	205	20	)	)	PUNCT
ejpam-6031	205	21	.	.	PUNCT
ejpam-6031	206	1	additionally	additionally	ADV
ejpam-6031	206	2	,	,	PUNCT
ejpam-6031	206	3	when	when	SCONJ
ejpam-6031	206	4	β	β	X
ejpam-6031	206	5	,	,	PUNCT
ejpam-6031	206	6	γ	γ	X
ejpam-6031	206	7	→	→	SYM
ejpam-6031	206	8	1	1	NUM
ejpam-6031	206	9	,	,	PUNCT
ejpam-6031	206	10	then	then	ADV
ejpam-6031	206	11	(	(	PUNCT
ejpam-6031	206	12	2β	2β	NOUN
ejpam-6031	206	13	p{0}×r	p{0}×r	PROPN
ejpam-6031	207	1	−	−	PROPN
ejpam-6031	207	2	i	i	PROPN
ejpam-6031	207	3	d	d	PROPN
ejpam-6031	207	4	)	)	PUNCT
ejpam-6031	207	5	(	(	PUNCT
ejpam-6031	207	6	2γ	2γ	NUM
ejpam-6031	207	7	pr×{0}(2	pr×{0}(2	NOUN
ejpam-6031	207	8	,	,	PUNCT
ejpam-6031	207	9	2)−	2)−	NUM
ejpam-6031	207	10	(	(	PUNCT
ejpam-6031	207	11	2	2	NUM
ejpam-6031	207	12	,	,	PUNCT
ejpam-6031	207	13	2	2	NUM
ejpam-6031	207	14	)	)	PUNCT
ejpam-6031	207	15	)	)	PUNCT
ejpam-6031	207	16	→	→	PUNCT
ejpam-6031	207	17	(	(	PUNCT
ejpam-6031	207	18	−2,−2	−2,−2	VERB
ejpam-6031	207	19	)	)	PUNCT
ejpam-6031	207	20	,	,	PUNCT
ejpam-6031	207	21	which	which	PRON
ejpam-6031	207	22	satisfies	satisfy	VERB
ejpam-6031	207	23	the	the	DET
ejpam-6031	207	24	first	first	ADJ
ejpam-6031	207	25	case	case	NOUN
ejpam-6031	207	26	.	.	PUNCT
ejpam-6031	208	1	from	from	ADP
ejpam-6031	208	2	now	now	ADV
ejpam-6031	208	3	and	and	CCONJ
ejpam-6031	208	4	on	on	ADV
ejpam-6031	208	5	,	,	PUNCT
ejpam-6031	208	6	deffine	deffine	VERB
ejpam-6031	208	7	the	the	DET
ejpam-6031	208	8	modified	modify	VERB
ejpam-6031	208	9	reflector	reflector	NOUN
ejpam-6031	208	10	operators	operator	NOUN
ejpam-6031	208	11	;	;	PUNCT
ejpam-6031	208	12	ru	ru	PROPN
ejpam-6031	208	13	,	,	PUNCT
ejpam-6031	208	14	γ	γ	X
ejpam-6031	208	15	:	:	PUNCT
ejpam-6031	208	16	=	=	SYM
ejpam-6031	208	17	2γ	2γ	NUM
ejpam-6031	208	18	pu	pu	PROPN
ejpam-6031	208	19	−	−	PROPN
ejpam-6031	208	20	i	i	PROPN
ejpam-6031	208	21	d	d	PROPN
ejpam-6031	208	22	,	,	PUNCT
ejpam-6031	208	23	(	(	PUNCT
ejpam-6031	208	24	9	9	X
ejpam-6031	208	25	)	)	PUNCT
ejpam-6031	208	26	ru⊥,β	ru⊥,β	NOUN
ejpam-6031	208	27	:	:	PUNCT
ejpam-6031	209	1	=	=	SYM
ejpam-6031	209	2	2β	2β	NOUN
ejpam-6031	209	3	pu⊥	pu⊥	NOUN
ejpam-6031	209	4	−	−	PROPN
ejpam-6031	210	1	i	i	PROPN
ejpam-6031	210	2	d	d	PROPN
ejpam-6031	210	3	,	,	PUNCT
ejpam-6031	210	4	(	(	PUNCT
ejpam-6031	210	5	10	10	NUM
ejpam-6031	210	6	)	)	PUNCT
ejpam-6031	210	7	rv	rv	PROPN
ejpam-6031	210	8	,	,	PUNCT
ejpam-6031	210	9	α	α	NOUN
ejpam-6031	210	10	:	:	PUNCT
ejpam-6031	210	11	=	=	SYM
ejpam-6031	210	12	2α	2α	PUNCT
ejpam-6031	211	1	pv	pv	INTJ
ejpam-6031	211	2	−	−	PROPN
ejpam-6031	212	1	i	i	PROPN
ejpam-6031	212	2	d	d	PROPN
ejpam-6031	212	3	.	.	PUNCT
ejpam-6031	213	1	(	(	PUNCT
ejpam-6031	213	2	11	11	NUM
ejpam-6031	213	3	)	)	PUNCT
ejpam-6031	213	4	theorem	theorem	NOUN
ejpam-6031	213	5	1	1	NUM
ejpam-6031	213	6	.	.	PUNCT
ejpam-6031	214	1	let	let	VERB
ejpam-6031	214	2	u	u	PRON
ejpam-6031	214	3	and	and	CCONJ
ejpam-6031	214	4	v	v	NOUN
ejpam-6031	214	5	be	be	AUX
ejpam-6031	214	6	claosed	claose	VERB
ejpam-6031	214	7	linear	linear	ADJ
ejpam-6031	214	8	subspaces	subspace	NOUN
ejpam-6031	214	9	of	of	ADP
ejpam-6031	214	10	h.	h.	NOUN
ejpam-6031	214	11	suppose	suppose	VERB
ejpam-6031	214	12	that	that	SCONJ
ejpam-6031	214	13	β	β	NOUN
ejpam-6031	214	14	,	,	PUNCT
ejpam-6031	214	15	γ	γ	X
ejpam-6031	214	16	,	,	PUNCT
ejpam-6031	214	17	α	α	PRON
ejpam-6031	214	18	∈]0	∈]0	ADJ
ejpam-6031	214	19	,	,	PUNCT
ejpam-6031	214	20	1	1	NUM
ejpam-6031	214	21	]	]	PUNCT
ejpam-6031	214	22	and	and	CCONJ
ejpam-6031	214	23	recall	recall	VERB
ejpam-6031	214	24	from	from	ADP
ejpam-6031	214	25	(	(	PUNCT
ejpam-6031	214	26	9	9	NUM
ejpam-6031	214	27	)	)	PUNCT
ejpam-6031	214	28	,	,	PUNCT
ejpam-6031	214	29	(	(	PUNCT
ejpam-6031	214	30	10	10	NUM
ejpam-6031	214	31	)	)	PUNCT
ejpam-6031	214	32	,	,	PUNCT
ejpam-6031	214	33	and	and	CCONJ
ejpam-6031	214	34	(	(	PUNCT
ejpam-6031	214	35	11	11	NUM
ejpam-6031	214	36	)	)	PUNCT
ejpam-6031	214	37	the	the	DET
ejpam-6031	214	38	modified	modify	VERB
ejpam-6031	214	39	reflector	reflector	NOUN
ejpam-6031	214	40	operators	operator	NOUN
ejpam-6031	214	41	.	.	PUNCT
ejpam-6031	215	1	if	if	SCONJ
ejpam-6031	215	2	β	β	X
ejpam-6031	215	3	,	,	PUNCT
ejpam-6031	215	4	γ	γ	NOUN
ejpam-6031	215	5	=	=	SYM
ejpam-6031	215	6	1	1	NUM
ejpam-6031	215	7	,	,	PUNCT
ejpam-6031	215	8	then	then	ADV
ejpam-6031	215	9	the	the	DET
ejpam-6031	215	10	following	following	NOUN
ejpam-6031	215	11	are	be	AUX
ejpam-6031	215	12	holds	hold	NOUN
ejpam-6031	215	13	true	true	ADJ
ejpam-6031	215	14	:	:	PUNCT
ejpam-6031	215	15	(	(	PUNCT
ejpam-6031	215	16	i	i	NOUN
ejpam-6031	215	17	)	)	PUNCT
ejpam-6031	215	18	rv	rv	PROPN
ejpam-6031	215	19	,	,	PUNCT
ejpam-6031	215	20	αru⊥,βru	αru⊥,βru	PROPN
ejpam-6031	215	21	,	,	PUNCT
ejpam-6031	215	22	γ	γ	PROPN
ejpam-6031	215	23	=	=	SYM
ejpam-6031	215	24	αrv⊥	αrv⊥	PROPN
ejpam-6031	216	1	+	+	CCONJ
ejpam-6031	216	2	(	(	PUNCT
ejpam-6031	216	3	1	1	NUM
ejpam-6031	216	4	−	−	PROPN
ejpam-6031	216	5	α	α	X
ejpam-6031	216	6	)	)	PUNCT
ejpam-6031	216	7	i	i	PROPN
ejpam-6031	216	8	d	d	PROPN
ejpam-6031	216	9	(	(	PUNCT
ejpam-6031	216	10	ii	ii	PROPN
ejpam-6031	216	11	)	)	PUNCT
ejpam-6031	216	12	rv	rv	PROPN
ejpam-6031	216	13	,	,	PUNCT
ejpam-6031	216	14	αru	αru	NOUN
ejpam-6031	216	15	,	,	PUNCT
ejpam-6031	216	16	γru⊥,β	γru⊥,β	NOUN
ejpam-6031	216	17	=	=	SYM
ejpam-6031	216	18	αrv⊥	αrv⊥	PROPN
ejpam-6031	217	1	+	+	CCONJ
ejpam-6031	217	2	(	(	PUNCT
ejpam-6031	217	3	1	1	NUM
ejpam-6031	217	4	−	−	PROPN
ejpam-6031	217	5	α	α	X
ejpam-6031	217	6	)	)	PUNCT
ejpam-6031	217	7	i	i	PROPN
ejpam-6031	217	8	d	d	PROPN
ejpam-6031	217	9	(	(	PUNCT
ejpam-6031	217	10	iii	iii	NOUN
ejpam-6031	217	11	)	)	PUNCT
ejpam-6031	217	12	ru⊥,βru	ru⊥,βru	NOUN
ejpam-6031	217	13	,	,	PUNCT
ejpam-6031	217	14	γrv	γrv	PROPN
ejpam-6031	217	15	,	,	PUNCT
ejpam-6031	217	16	α	α	NOUN
ejpam-6031	217	17	=	=	PUNCT
ejpam-6031	217	18	αrv⊥	αrv⊥	PROPN
ejpam-6031	218	1	+	+	CCONJ
ejpam-6031	218	2	(	(	PUNCT
ejpam-6031	218	3	1	1	NUM
ejpam-6031	218	4	−	−	PROPN
ejpam-6031	218	5	α	α	X
ejpam-6031	218	6	)	)	PUNCT
ejpam-6031	218	7	i	i	PROPN
ejpam-6031	218	8	d	d	PROPN
ejpam-6031	218	9	(	(	PUNCT
ejpam-6031	218	10	iv	iv	X
ejpam-6031	218	11	)	)	PUNCT
ejpam-6031	218	12	ru	ru	PROPN
ejpam-6031	218	13	,	,	PUNCT
ejpam-6031	218	14	γru⊥,βrv	γru⊥,βrv	PROPN
ejpam-6031	218	15	,	,	PUNCT
ejpam-6031	218	16	α	α	PROPN
ejpam-6031	218	17	=	=	PUNCT
ejpam-6031	218	18	αrv⊥	αrv⊥	PROPN
ejpam-6031	218	19	+	+	CCONJ
ejpam-6031	218	20	(	(	PUNCT
ejpam-6031	218	21	1	1	NUM
ejpam-6031	218	22	−	−	PROPN
ejpam-6031	218	23	α	α	X
ejpam-6031	218	24	)	)	PUNCT
ejpam-6031	218	25	i	i	PROPN
ejpam-6031	218	26	d	d	PROPN
ejpam-6031	218	27	(	(	PUNCT
ejpam-6031	218	28	v	v	NOUN
ejpam-6031	218	29	)	)	PUNCT
ejpam-6031	218	30	fix	fix	NOUN
ejpam-6031	218	31	(	(	PUNCT
ejpam-6031	218	32	rv	rv	NOUN
ejpam-6031	218	33	,	,	PUNCT
ejpam-6031	218	34	αru⊥,βru	αru⊥,βru	PROPN
ejpam-6031	218	35	,	,	PUNCT
ejpam-6031	218	36	γ	γ	X
ejpam-6031	218	37	)	)	PUNCT
ejpam-6031	218	38	=	=	SYM
ejpam-6031	218	39	v⊥	v⊥	NOUN
ejpam-6031	218	40	(	(	PUNCT
ejpam-6031	218	41	vi	vi	NOUN
ejpam-6031	218	42	)	)	PUNCT
ejpam-6031	218	43	fix	fix	NOUN
ejpam-6031	218	44	(	(	PUNCT
ejpam-6031	218	45	rv	rv	NOUN
ejpam-6031	218	46	,	,	PUNCT
ejpam-6031	218	47	αru	αru	NOUN
ejpam-6031	218	48	,	,	PUNCT
ejpam-6031	218	49	γru⊥,β	γru⊥,β	NOUN
ejpam-6031	218	50	)	)	PUNCT
ejpam-6031	219	1	=	=	SYM
ejpam-6031	219	2	v⊥	v⊥	NOUN
ejpam-6031	219	3	(	(	PUNCT
ejpam-6031	219	4	vii	vii	PROPN
ejpam-6031	219	5	)	)	PUNCT
ejpam-6031	219	6	fix	fix	NOUN
ejpam-6031	219	7	(	(	PUNCT
ejpam-6031	219	8	ru⊥,βru	ru⊥,βru	NOUN
ejpam-6031	219	9	,	,	PUNCT
ejpam-6031	219	10	γrv	γrv	PROPN
ejpam-6031	219	11	,	,	PUNCT
ejpam-6031	219	12	α	α	NOUN
ejpam-6031	219	13	)	)	PUNCT
ejpam-6031	220	1	=	=	SYM
ejpam-6031	220	2	v⊥	v⊥	NOUN
ejpam-6031	220	3	(	(	PUNCT
ejpam-6031	220	4	viii	viii	NOUN
ejpam-6031	220	5	)	)	PUNCT
ejpam-6031	220	6	fix	fix	NOUN
ejpam-6031	220	7	(	(	PUNCT
ejpam-6031	220	8	ru	ru	PROPN
ejpam-6031	220	9	,	,	PUNCT
ejpam-6031	220	10	γru⊥,βrv	γru⊥,βrv	PROPN
ejpam-6031	220	11	,	,	PUNCT
ejpam-6031	220	12	α	α	NOUN
ejpam-6031	220	13	)	)	PUNCT
ejpam-6031	221	1	=	=	NOUN
ejpam-6031	221	2	v⊥	v⊥	VERB
ejpam-6031	221	3	additionally	additionally	ADV
ejpam-6031	221	4	,	,	PUNCT
ejpam-6031	221	5	if	if	SCONJ
ejpam-6031	221	6	β	β	X
ejpam-6031	221	7	,	,	PUNCT
ejpam-6031	221	8	γ	γ	PROPN
ejpam-6031	221	9	̸=	̸=	PROPN
ejpam-6031	221	10	1	1	NUM
ejpam-6031	221	11	and	and	CCONJ
ejpam-6031	221	12	α	α	NOUN
ejpam-6031	221	13	=	=	SYM
ejpam-6031	221	14	1	1	NUM
ejpam-6031	221	15	,	,	PUNCT
ejpam-6031	221	16	then	then	ADV
ejpam-6031	221	17	the	the	DET
ejpam-6031	221	18	following	follow	VERB
ejpam-6031	221	19	hold	hold	VERB
ejpam-6031	221	20	true	true	ADJ
ejpam-6031	221	21	:	:	PUNCT
ejpam-6031	221	22	s.th	s.th	PROPN
ejpam-6031	221	23	.	.	PUNCT
ejpam-6031	221	24	alwadani	alwadani	PROPN
ejpam-6031	221	25	/	/	SYM
ejpam-6031	221	26	eur	eur	PROPN
ejpam-6031	221	27	.	.	PUNCT
ejpam-6031	222	1	j.	j.	PROPN
ejpam-6031	222	2	pure	pure	PROPN
ejpam-6031	222	3	appl	appl	PROPN
ejpam-6031	222	4	.	.	PROPN
ejpam-6031	222	5	math	math	PROPN
ejpam-6031	222	6	,	,	PUNCT
ejpam-6031	222	7	18	18	NUM
ejpam-6031	222	8	(	(	PUNCT
ejpam-6031	222	9	2	2	NUM
ejpam-6031	222	10	)	)	PUNCT
ejpam-6031	222	11	(	(	PUNCT
ejpam-6031	222	12	2025	2025	NUM
ejpam-6031	222	13	)	)	PUNCT
ejpam-6031	222	14	,	,	PUNCT
ejpam-6031	222	15	6031	6031	NUM
ejpam-6031	222	16	8	8	NUM
ejpam-6031	222	17	of	of	ADP
ejpam-6031	222	18	13	13	NUM
ejpam-6031	222	19	(	(	PUNCT
ejpam-6031	222	20	ix	ix	PROPN
ejpam-6031	222	21	)	)	PUNCT
ejpam-6031	222	22	rv	rv	PROPN
ejpam-6031	222	23	,	,	PUNCT
ejpam-6031	222	24	αru⊥,βru	αru⊥,βru	PROPN
ejpam-6031	222	25	,	,	PUNCT
ejpam-6031	222	26	γ	γ	NOUN
ejpam-6031	222	27	=	=	SYM
ejpam-6031	222	28	2	2	NUM
ejpam-6031	222	29	pv	pv	NOUN
ejpam-6031	222	30	+2γ	+2γ	NUM
ejpam-6031	222	31	pu	pu	NOUN
ejpam-6031	222	32	+2β	+2β	NUM
ejpam-6031	222	33	pu⊥	pu⊥	PROPN
ejpam-6031	222	34	−4γ	−4γ	ADV
ejpam-6031	222	35	pv	pv	INTJ
ejpam-6031	222	36	pu	pu	PROPN
ejpam-6031	222	37	−4β	−4β	PROPN
ejpam-6031	222	38	pv	pv	INTJ
ejpam-6031	223	1	pu⊥	pu⊥	PROPN
ejpam-6031	223	2	−	−	PROPN
ejpam-6031	224	1	i	i	PRON
ejpam-6031	224	2	d.	d.	PROPN
ejpam-6031	224	3	(	(	PUNCT
ejpam-6031	224	4	x	x	X
ejpam-6031	224	5	)	)	PUNCT
ejpam-6031	224	6	rv	rv	PROPN
ejpam-6031	224	7	,	,	PUNCT
ejpam-6031	224	8	αru	αru	NOUN
ejpam-6031	224	9	,	,	PUNCT
ejpam-6031	224	10	γru⊥,β	γru⊥,β	NOUN
ejpam-6031	224	11	=	=	SYM
ejpam-6031	224	12	rv	rv	PROPN
ejpam-6031	224	13	,	,	PUNCT
ejpam-6031	224	14	αru⊥,βru	αru⊥,βru	PROPN
ejpam-6031	224	15	,	,	PUNCT
ejpam-6031	224	16	γ	γ	X
ejpam-6031	224	17	(	(	PUNCT
ejpam-6031	224	18	xi	xi	NOUN
ejpam-6031	224	19	)	)	PUNCT
ejpam-6031	224	20	ru⊥,βru	ru⊥,βru	NOUN
ejpam-6031	224	21	,	,	PUNCT
ejpam-6031	224	22	γrv	γrv	PROPN
ejpam-6031	224	23	,	,	PUNCT
ejpam-6031	224	24	α	α	NOUN
ejpam-6031	224	25	=	=	SYM
ejpam-6031	224	26	2	2	NUM
ejpam-6031	224	27	pv	pv	NOUN
ejpam-6031	224	28	+2γ	+2γ	NUM
ejpam-6031	224	29	pu	pu	NOUN
ejpam-6031	224	30	+2β	+2β	NUM
ejpam-6031	224	31	pu⊥	pu⊥	PROPN
ejpam-6031	224	32	−4γ	−4γ	PROPN
ejpam-6031	224	33	pu	pu	PROPN
ejpam-6031	224	34	pv	pv	PROPN
ejpam-6031	224	35	−4β	−4β	PROPN
ejpam-6031	224	36	pu⊥	pu⊥	PROPN
ejpam-6031	224	37	pv	pv	ADP
ejpam-6031	224	38	−	−	PUNCT
ejpam-6031	225	1	i	i	INTJ
ejpam-6031	225	2	d	d	PROPN
ejpam-6031	225	3	(	(	PUNCT
ejpam-6031	225	4	xii	xii	PROPN
ejpam-6031	225	5	)	)	PUNCT
ejpam-6031	225	6	ru	ru	PROPN
ejpam-6031	225	7	,	,	PUNCT
ejpam-6031	225	8	γru⊥,βrv	γru⊥,βrv	PROPN
ejpam-6031	225	9	,	,	PUNCT
ejpam-6031	225	10	α	α	NOUN
ejpam-6031	225	11	=	=	PUNCT
ejpam-6031	225	12	ru⊥,βru	ru⊥,βru	NOUN
ejpam-6031	225	13	,	,	PUNCT
ejpam-6031	225	14	γrv	γrv	PROPN
ejpam-6031	225	15	,	,	PUNCT
ejpam-6031	225	16	α	α	NOUN
ejpam-6031	225	17	.	.	PUNCT
ejpam-6031	226	1	moreover	moreover	ADV
ejpam-6031	226	2	,	,	PUNCT
ejpam-6031	226	3	if	if	SCONJ
ejpam-6031	226	4	β	β	X
ejpam-6031	226	5	,	,	PUNCT
ejpam-6031	226	6	γ	γ	X
ejpam-6031	226	7	,	,	PUNCT
ejpam-6031	226	8	α	α	PROPN
ejpam-6031	226	9	̸=	̸=	PROPN
ejpam-6031	226	10	1	1	NUM
ejpam-6031	226	11	,	,	PUNCT
ejpam-6031	226	12	then	then	ADV
ejpam-6031	226	13	the	the	DET
ejpam-6031	226	14	following	follow	VERB
ejpam-6031	226	15	hold	hold	VERB
ejpam-6031	226	16	true	true	ADJ
ejpam-6031	226	17	:	:	PUNCT
ejpam-6031	226	18	(	(	PUNCT
ejpam-6031	226	19	xiii	xiii	X
ejpam-6031	226	20	)	)	PUNCT
ejpam-6031	226	21	rv	rv	PROPN
ejpam-6031	226	22	,	,	PUNCT
ejpam-6031	226	23	αru⊥,βru	αru⊥,βru	PROPN
ejpam-6031	226	24	,	,	PUNCT
ejpam-6031	226	25	γ	γ	NOUN
ejpam-6031	226	26	=	=	SYM
ejpam-6031	226	27	2α	2α	NOUN
ejpam-6031	226	28	pv	pv	NOUN
ejpam-6031	227	1	+2γ	+2γ	NUM
ejpam-6031	227	2	pu	pu	NOUN
ejpam-6031	227	3	+2β	+2β	NUM
ejpam-6031	227	4	pu⊥	pu⊥	PROPN
ejpam-6031	227	5	−4αγ	−4αγ	NOUN
ejpam-6031	228	1	pv	pv	INTJ
ejpam-6031	228	2	pu	pu	PROPN
ejpam-6031	228	3	−4αβ	−4αβ	CCONJ
ejpam-6031	228	4	pv	pv	PROPN
ejpam-6031	229	1	pu⊥	pu⊥	NOUN
ejpam-6031	229	2	−	−	PROPN
ejpam-6031	230	1	i	i	PRON
ejpam-6031	230	2	d.	d.	PROPN
ejpam-6031	230	3	(	(	PUNCT
ejpam-6031	230	4	xiv	xiv	PROPN
ejpam-6031	230	5	)	)	PUNCT
ejpam-6031	230	6	rv	rv	PROPN
ejpam-6031	230	7	,	,	PUNCT
ejpam-6031	230	8	αru	αru	NOUN
ejpam-6031	230	9	,	,	PUNCT
ejpam-6031	230	10	γru⊥,β	γru⊥,β	NOUN
ejpam-6031	230	11	=	=	SYM
ejpam-6031	230	12	rv	rv	PROPN
ejpam-6031	230	13	,	,	PUNCT
ejpam-6031	230	14	αru⊥,βru	αru⊥,βru	PROPN
ejpam-6031	230	15	,	,	PUNCT
ejpam-6031	230	16	γ	γ	X
ejpam-6031	230	17	(	(	PUNCT
ejpam-6031	230	18	xv	xv	PROPN
ejpam-6031	230	19	)	)	PUNCT
ejpam-6031	230	20	ru⊥,βru	ru⊥,βru	NOUN
ejpam-6031	230	21	,	,	PUNCT
ejpam-6031	230	22	γrv	γrv	PROPN
ejpam-6031	230	23	,	,	PUNCT
ejpam-6031	230	24	α	α	NOUN
ejpam-6031	230	25	=	=	X
ejpam-6031	230	26	2α	2α	NOUN
ejpam-6031	230	27	pv	pv	NOUN
ejpam-6031	231	1	+2γ	+2γ	NUM
ejpam-6031	231	2	pu	pu	NOUN
ejpam-6031	231	3	+2β	+2β	NUM
ejpam-6031	232	1	pu⊥	pu⊥	NOUN
ejpam-6031	232	2	−4γα	−4γα	NOUN
ejpam-6031	232	3	pu	pu	PROPN
ejpam-6031	232	4	pv	pv	PROPN
ejpam-6031	233	1	−4βα	−4βα	PROPN
ejpam-6031	233	2	pu⊥	pu⊥	PROPN
ejpam-6031	233	3	pv	pv	ADP
ejpam-6031	233	4	−	−	PROPN
ejpam-6031	234	1	i	i	PROPN
ejpam-6031	234	2	d	d	PROPN
ejpam-6031	234	3	(	(	PUNCT
ejpam-6031	234	4	xvi	xvi	PROPN
ejpam-6031	234	5	)	)	PUNCT
ejpam-6031	234	6	ru	ru	PROPN
ejpam-6031	234	7	,	,	PUNCT
ejpam-6031	234	8	γru⊥,βrv	γru⊥,βrv	PROPN
ejpam-6031	234	9	,	,	PUNCT
ejpam-6031	234	10	α	α	NOUN
ejpam-6031	234	11	=	=	PUNCT
ejpam-6031	234	12	ru⊥,βru	ru⊥,βru	NOUN
ejpam-6031	234	13	,	,	PUNCT
ejpam-6031	234	14	γrv	γrv	PROPN
ejpam-6031	234	15	,	,	PUNCT
ejpam-6031	234	16	α	α	NOUN
ejpam-6031	234	17	.	.	PUNCT
ejpam-6031	235	1	proof	proof	NOUN
ejpam-6031	235	2	.	.	PUNCT
ejpam-6031	236	1	(	(	PUNCT
ejpam-6031	236	2	i	i	NOUN
ejpam-6031	236	3	):	):	PUNCT
ejpam-6031	236	4	using	use	VERB
ejpam-6031	236	5	lemma	lemma	PROPN
ejpam-6031	236	6	1	1	NUM
ejpam-6031	236	7	,	,	PUNCT
ejpam-6031	236	8	(	(	PUNCT
ejpam-6031	236	9	i	i	NOUN
ejpam-6031	236	10	)	)	PUNCT
ejpam-6031	236	11	,	,	PUNCT
ejpam-6031	236	12	(	(	PUNCT
ejpam-6031	236	13	iv	iv	X
ejpam-6031	236	14	)	)	PUNCT
ejpam-6031	236	15	,	,	PUNCT
ejpam-6031	236	16	and	and	CCONJ
ejpam-6031	236	17	(	(	PUNCT
ejpam-6031	236	18	v	v	NOUN
ejpam-6031	236	19	)	)	PUNCT
ejpam-6031	236	20	gives	give	VERB
ejpam-6031	236	21	rv	rv	PRON
ejpam-6031	236	22	,	,	PUNCT
ejpam-6031	236	23	αru⊥,1ru,1	αru⊥,1ru,1	PROPN
ejpam-6031	236	24	=	=	SYM
ejpam-6031	236	25	rv	rv	PROPN
ejpam-6031	236	26	,	,	PUNCT
ejpam-6031	236	27	α	α	PROPN
ejpam-6031	236	28	(	(	PUNCT
ejpam-6031	236	29	−	−	PROPN
ejpam-6031	236	30	i	i	NOUN
ejpam-6031	236	31	d	d	PROPN
ejpam-6031	236	32	)	)	PUNCT
ejpam-6031	237	1	=	=	SYM
ejpam-6031	237	2	−rv	−rv	NOUN
ejpam-6031	237	3	,	,	PUNCT
ejpam-6031	237	4	α	α	NOUN
ejpam-6031	237	5	=	=	SYM
ejpam-6031	237	6	αrv⊥	αrv⊥	PROPN
ejpam-6031	237	7	+	+	CCONJ
ejpam-6031	237	8	(	(	PUNCT
ejpam-6031	237	9	1	1	NUM
ejpam-6031	237	10	−	−	PROPN
ejpam-6031	237	11	α	α	X
ejpam-6031	237	12	)	)	PUNCT
ejpam-6031	237	13	i	i	PROPN
ejpam-6031	237	14	d	d	PROPN
ejpam-6031	237	15	(	(	PUNCT
ejpam-6031	237	16	ii	ii	NOUN
ejpam-6031	237	17	)	)	PUNCT
ejpam-6031	237	18	,	,	PUNCT
ejpam-6031	237	19	(	(	PUNCT
ejpam-6031	237	20	iii	iii	NOUN
ejpam-6031	237	21	)	)	PUNCT
ejpam-6031	237	22	,	,	PUNCT
ejpam-6031	237	23	(	(	PUNCT
ejpam-6031	237	24	iv	iv	X
ejpam-6031	237	25	):	):	PUNCT
ejpam-6031	237	26	the	the	DET
ejpam-6031	237	27	proof	proof	NOUN
ejpam-6031	237	28	follows	follow	VERB
ejpam-6031	237	29	a	a	DET
ejpam-6031	237	30	similar	similar	ADJ
ejpam-6031	237	31	approach	approach	NOUN
ejpam-6031	237	32	as	as	ADP
ejpam-6031	237	33	in	in	ADP
ejpam-6031	237	34	(	(	PUNCT
ejpam-6031	237	35	i	i	NOUN
ejpam-6031	237	36	)	)	PUNCT
ejpam-6031	237	37	.	.	PUNCT
ejpam-6031	238	1	(	(	PUNCT
ejpam-6031	238	2	v	v	NOUN
ejpam-6031	238	3	):	):	PUNCT
ejpam-6031	238	4	it	it	PRON
ejpam-6031	238	5	follows	follow	VERB
ejpam-6031	238	6	from	from	ADP
ejpam-6031	238	7	(	(	PUNCT
ejpam-6031	238	8	i	i	NOUN
ejpam-6031	238	9	)	)	PUNCT
ejpam-6031	238	10	that	that	SCONJ
ejpam-6031	238	11	rv	rv	PROPN
ejpam-6031	238	12	,	,	PUNCT
ejpam-6031	238	13	αru⊥,βru	αru⊥,βru	PROPN
ejpam-6031	238	14	,	,	PUNCT
ejpam-6031	238	15	γ	γ	PROPN
ejpam-6031	238	16	=	=	SYM
ejpam-6031	238	17	αrv⊥	αrv⊥	PROPN
ejpam-6031	239	1	+	+	CCONJ
ejpam-6031	239	2	(	(	PUNCT
ejpam-6031	239	3	1−	1−	NUM
ejpam-6031	239	4	α	α	NOUN
ejpam-6031	239	5	)	)	PUNCT
ejpam-6031	239	6	i	i	PROPN
ejpam-6031	239	7	d	d	PROPN
ejpam-6031	239	8	,	,	PUNCT
ejpam-6031	239	9	and	and	CCONJ
ejpam-6031	239	10	using	use	VERB
ejpam-6031	239	11	(	(	PUNCT
ejpam-6031	239	12	6	6	NUM
ejpam-6031	239	13	)	)	PUNCT
ejpam-6031	239	14	and	and	CCONJ
ejpam-6031	239	15	(	(	PUNCT
ejpam-6031	239	16	i	i	NOUN
ejpam-6031	239	17	)	)	PUNCT
ejpam-6031	239	18	gives	give	VERB
ejpam-6031	239	19	fix	fix	NOUN
ejpam-6031	239	20	(	(	PUNCT
ejpam-6031	239	21	rv	rv	NOUN
ejpam-6031	239	22	,	,	PUNCT
ejpam-6031	239	23	αru⊥,βru	αru⊥,βru	PROPN
ejpam-6031	239	24	,	,	PUNCT
ejpam-6031	239	25	γ	γ	X
ejpam-6031	239	26	)	)	PUNCT
ejpam-6031	240	1	=	=	SYM
ejpam-6031	240	2	fix	fix	NOUN
ejpam-6031	240	3	(	(	PUNCT
ejpam-6031	240	4	αrv⊥	αrv⊥	PROPN
ejpam-6031	240	5	+	+	CCONJ
ejpam-6031	240	6	(	(	PUNCT
ejpam-6031	240	7	1	1	NUM
ejpam-6031	240	8	−	−	PROPN
ejpam-6031	240	9	α	α	X
ejpam-6031	240	10	)	)	PUNCT
ejpam-6031	240	11	i	i	PROPN
ejpam-6031	240	12	d	d	PROPN
ejpam-6031	240	13	)	)	PUNCT
ejpam-6031	240	14	.	.	PUNCT
ejpam-6031	241	1	next	next	ADV
ejpam-6031	241	2	,	,	PUNCT
ejpam-6031	241	3	applying	apply	VERB
ejpam-6031	241	4	lemma	lemma	PROPN
ejpam-6031	241	5	1	1	NUM
ejpam-6031	241	6	(	(	PUNCT
ejpam-6031	241	7	vi	vi	NOUN
ejpam-6031	241	8	)	)	PUNCT
ejpam-6031	241	9	yields	yield	NOUN
ejpam-6031	241	10	,	,	PUNCT
ejpam-6031	241	11	x	x	SYM
ejpam-6031	241	12	∈	∈	PRON
ejpam-6031	241	13	fix	fix	NOUN
ejpam-6031	241	14	(	(	PUNCT
ejpam-6031	241	15	rv	rv	NOUN
ejpam-6031	241	16	,	,	PUNCT
ejpam-6031	241	17	αru⊥,βru	αru⊥,βru	PROPN
ejpam-6031	241	18	,	,	PUNCT
ejpam-6031	241	19	γ	γ	NOUN
ejpam-6031	241	20	)	)	PUNCT
ejpam-6031	241	21	⇔	⇔	PROPN
ejpam-6031	241	22	x	x	SYM
ejpam-6031	241	23	∈	∈	PROPN
ejpam-6031	241	24	v⊥.	v⊥.	NOUN
ejpam-6031	241	25	(	(	PUNCT
ejpam-6031	241	26	vi	vi	NOUN
ejpam-6031	241	27	):	):	PUNCT
ejpam-6031	241	28	the	the	DET
ejpam-6031	241	29	proof	proof	NOUN
ejpam-6031	241	30	follows	follow	VERB
ejpam-6031	241	31	a	a	DET
ejpam-6031	241	32	similar	similar	ADJ
ejpam-6031	241	33	approach	approach	NOUN
ejpam-6031	241	34	as	as	ADP
ejpam-6031	241	35	in	in	ADP
ejpam-6031	241	36	statement	statement	NOUN
ejpam-6031	241	37	(	(	PUNCT
ejpam-6031	241	38	v	v	NOUN
ejpam-6031	241	39	)	)	PUNCT
ejpam-6031	241	40	,	,	PUNCT
ejpam-6031	241	41	combining	combine	VERB
ejpam-6031	241	42	(	(	PUNCT
ejpam-6031	241	43	6	6	NUM
ejpam-6031	241	44	)	)	PUNCT
ejpam-6031	241	45	,	,	PUNCT
ejpam-6031	241	46	(	(	PUNCT
ejpam-6031	241	47	ii	ii	NOUN
ejpam-6031	241	48	)	)	PUNCT
ejpam-6031	241	49	,	,	PUNCT
ejpam-6031	241	50	and	and	CCONJ
ejpam-6031	241	51	lemma	lemma	PROPN
ejpam-6031	241	52	1	1	NUM
ejpam-6031	241	53	with	with	ADP
ejpam-6031	241	54	(	(	PUNCT
ejpam-6031	241	55	vi	vi	NOUN
ejpam-6031	241	56	)	)	PUNCT
ejpam-6031	241	57	.	.	PUNCT
ejpam-6031	242	1	(	(	PUNCT
ejpam-6031	242	2	vii	vii	PROPN
ejpam-6031	242	3	):	):	PUNCT
ejpam-6031	242	4	the	the	DET
ejpam-6031	242	5	proof	proof	NOUN
ejpam-6031	242	6	adopts	adopt	VERB
ejpam-6031	242	7	a	a	DET
ejpam-6031	242	8	similar	similar	ADJ
ejpam-6031	242	9	method	method	NOUN
ejpam-6031	242	10	to	to	ADP
ejpam-6031	242	11	that	that	PRON
ejpam-6031	242	12	used	use	VERB
ejpam-6031	242	13	in	in	ADP
ejpam-6031	242	14	statement	statement	NOUN
ejpam-6031	242	15	(	(	PUNCT
ejpam-6031	242	16	v	v	NOUN
ejpam-6031	242	17	)	)	PUNCT
ejpam-6031	242	18	,	,	PUNCT
ejpam-6031	242	19	combining	combine	VERB
ejpam-6031	242	20	(	(	PUNCT
ejpam-6031	242	21	6	6	NUM
ejpam-6031	242	22	)	)	PUNCT
ejpam-6031	242	23	,	,	PUNCT
ejpam-6031	242	24	(	(	PUNCT
ejpam-6031	242	25	iii	iii	X
ejpam-6031	242	26	)	)	PUNCT
ejpam-6031	242	27	and	and	CCONJ
ejpam-6031	242	28	lemma	lemma	PROPN
ejpam-6031	242	29	1	1	NUM
ejpam-6031	242	30	(	(	PUNCT
ejpam-6031	242	31	vi	vi	NOUN
ejpam-6031	242	32	)	)	PUNCT
ejpam-6031	242	33	.	.	PUNCT
ejpam-6031	243	1	(	(	PUNCT
ejpam-6031	243	2	viii	viii	ADJ
ejpam-6031	243	3	):	):	PUNCT
ejpam-6031	243	4	the	the	DET
ejpam-6031	243	5	proof	proof	NOUN
ejpam-6031	243	6	follows	follow	VERB
ejpam-6031	243	7	a	a	DET
ejpam-6031	243	8	similar	similar	ADJ
ejpam-6031	243	9	approach	approach	NOUN
ejpam-6031	243	10	as	as	ADP
ejpam-6031	243	11	in	in	ADP
ejpam-6031	243	12	statement	statement	NOUN
ejpam-6031	243	13	(	(	PUNCT
ejpam-6031	243	14	v	v	NOUN
ejpam-6031	243	15	)	)	PUNCT
ejpam-6031	243	16	,	,	PUNCT
ejpam-6031	243	17	combining	combine	VERB
ejpam-6031	243	18	(	(	PUNCT
ejpam-6031	243	19	6	6	NUM
ejpam-6031	243	20	)	)	PUNCT
ejpam-6031	243	21	,	,	PUNCT
ejpam-6031	243	22	(	(	PUNCT
ejpam-6031	243	23	iv	iv	X
ejpam-6031	243	24	)	)	PUNCT
ejpam-6031	243	25	and	and	CCONJ
ejpam-6031	243	26	lemma	lemma	PROPN
ejpam-6031	243	27	1	1	NUM
ejpam-6031	243	28	with	with	ADP
ejpam-6031	243	29	(	(	PUNCT
ejpam-6031	243	30	vi	vi	NOUN
ejpam-6031	243	31	)	)	PUNCT
ejpam-6031	243	32	.	.	PUNCT
ejpam-6031	244	1	(	(	PUNCT
ejpam-6031	244	2	ix	ix	ADV
ejpam-6031	244	3	):	):	PUNCT
ejpam-6031	244	4	using	use	VERB
ejpam-6031	244	5	lemma	lemma	PROPN
ejpam-6031	244	6	2	2	PROPN
ejpam-6031	244	7	and	and	CCONJ
ejpam-6031	244	8	(	(	PUNCT
ejpam-6031	244	9	3	3	X
ejpam-6031	244	10	)	)	PUNCT
ejpam-6031	244	11	gives	give	VERB
ejpam-6031	244	12	rv	rv	PROPN
ejpam-6031	244	13	,	,	PUNCT
ejpam-6031	244	14	αru⊥,βru	αru⊥,βru	PROPN
ejpam-6031	244	15	,	,	PUNCT
ejpam-6031	244	16	γ	γ	NOUN
ejpam-6031	244	17	=	=	SYM
ejpam-6031	244	18	rv,1ru⊥,βru	rv,1ru⊥,βru	PROPN
ejpam-6031	244	19	,	,	PUNCT
ejpam-6031	244	20	γ	γ	NOUN
ejpam-6031	244	21	=	=	SYM
ejpam-6031	244	22	rv,1	rv,1	NOUN
ejpam-6031	244	23	−	−	PROPN
ejpam-6031	245	1	rv,12γ	rv,12γ	NOUN
ejpam-6031	245	2	pu	pu	PROPN
ejpam-6031	245	3	+	+	PROPN
ejpam-6031	245	4	rv,12β	rv,12β	PROPN
ejpam-6031	245	5	pu⊥	pu⊥	NOUN
ejpam-6031	245	6	=	=	PUNCT
ejpam-6031	245	7	(	(	PUNCT
ejpam-6031	245	8	2	2	NUM
ejpam-6031	245	9	pv	pv	NOUN
ejpam-6031	245	10	−	−	PROPN
ejpam-6031	245	11	i	i	PROPN
ejpam-6031	245	12	d	d	PROPN
ejpam-6031	245	13	)	)	PUNCT
ejpam-6031	245	14	−	−	PROPN
ejpam-6031	246	1	(	(	PUNCT
ejpam-6031	246	2	2	2	NUM
ejpam-6031	246	3	pv	pv	NOUN
ejpam-6031	246	4	−	−	PROPN
ejpam-6031	247	1	i	i	PROPN
ejpam-6031	247	2	d	d	PROPN
ejpam-6031	247	3	)	)	PUNCT
ejpam-6031	248	1	2γ	2γ	VERB
ejpam-6031	248	2	pu	pu	PROPN
ejpam-6031	249	1	+	+	CCONJ
ejpam-6031	249	2	(	(	PUNCT
ejpam-6031	249	3	2	2	NUM
ejpam-6031	249	4	pv	pv	NOUN
ejpam-6031	249	5	−	−	PROPN
ejpam-6031	249	6	i	i	PROPN
ejpam-6031	249	7	d	d	PROPN
ejpam-6031	249	8	)	)	PUNCT
ejpam-6031	250	1	2β	2β	NOUN
ejpam-6031	250	2	pu⊥	pu⊥	NOUN
ejpam-6031	250	3	=	=	NOUN
ejpam-6031	250	4	2	2	NUM
ejpam-6031	250	5	pv	pv	NOUN
ejpam-6031	250	6	+2γ	+2γ	NUM
ejpam-6031	250	7	pu	pu	NOUN
ejpam-6031	250	8	+2β	+2β	NUM
ejpam-6031	250	9	pu⊥	pu⊥	PROPN
ejpam-6031	250	10	−4γ	−4γ	ADV
ejpam-6031	250	11	pv	pv	INTJ
ejpam-6031	250	12	pu	pu	PROPN
ejpam-6031	250	13	−4β	−4β	PROPN
ejpam-6031	250	14	pv	pv	INTJ
ejpam-6031	250	15	pu⊥	pu⊥	NOUN
ejpam-6031	250	16	−	−	PROPN
ejpam-6031	250	17	i	i	PROPN
ejpam-6031	250	18	d	d	PROPN
ejpam-6031	250	19	.	.	PUNCT
ejpam-6031	251	1	(	(	PUNCT
ejpam-6031	251	2	x	x	X
ejpam-6031	251	3	):	):	PUNCT
ejpam-6031	251	4	following	follow	VERB
ejpam-6031	251	5	the	the	DET
ejpam-6031	251	6	same	same	ADJ
ejpam-6031	251	7	approach	approach	NOUN
ejpam-6031	251	8	as	as	ADP
ejpam-6031	251	9	in	in	ADP
ejpam-6031	251	10	statement	statement	NOUN
ejpam-6031	251	11	(	(	PUNCT
ejpam-6031	251	12	ix	ix	ADV
ejpam-6031	251	13	)	)	PUNCT
ejpam-6031	251	14	gives	give	VERB
ejpam-6031	251	15	rv	rv	PROPN
ejpam-6031	251	16	,	,	PUNCT
ejpam-6031	251	17	αru	αru	NOUN
ejpam-6031	251	18	,	,	PUNCT
ejpam-6031	251	19	γru⊥,β	γru⊥,β	NOUN
ejpam-6031	251	20	=	=	NOUN
ejpam-6031	251	21	rv,1ru	rv,1ru	VERB
ejpam-6031	251	22	,	,	PUNCT
ejpam-6031	251	23	γru⊥	γru⊥	PROPN
ejpam-6031	251	24	=	=	PUNCT
ejpam-6031	252	1	2	2	NUM
ejpam-6031	252	2	pv	pv	NOUN
ejpam-6031	252	3	+2γ	+2γ	NUM
ejpam-6031	252	4	pu	pu	NOUN
ejpam-6031	252	5	+2β	+2β	NUM
ejpam-6031	252	6	pu⊥	pu⊥	PROPN
ejpam-6031	252	7	−4γ	−4γ	ADV
ejpam-6031	252	8	pv	pv	INTJ
ejpam-6031	252	9	pu	pu	PROPN
ejpam-6031	252	10	−4β	−4β	PROPN
ejpam-6031	252	11	pv	pv	INTJ
ejpam-6031	252	12	pu⊥	pu⊥	NOUN
ejpam-6031	252	13	−	−	PROPN
ejpam-6031	253	1	i	i	PROPN
ejpam-6031	253	2	d	d	PROPN
ejpam-6031	253	3	.	.	PUNCT
ejpam-6031	254	1	combining	combine	VERB
ejpam-6031	254	2	this	this	DET
ejpam-6031	254	3	result	result	NOUN
ejpam-6031	254	4	with	with	ADP
ejpam-6031	254	5	(	(	PUNCT
ejpam-6031	254	6	x	x	X
ejpam-6031	254	7	)	)	PUNCT
ejpam-6031	254	8	illustrates	illustrate	VERB
ejpam-6031	254	9	that	that	SCONJ
ejpam-6031	254	10	when	when	SCONJ
ejpam-6031	254	11	α	α	PROPN
ejpam-6031	254	12	=	=	SYM
ejpam-6031	254	13	1	1	NUM
ejpam-6031	254	14	rv	rv	PROPN
ejpam-6031	254	15	,	,	PUNCT
ejpam-6031	254	16	αru	αru	NOUN
ejpam-6031	254	17	,	,	PUNCT
ejpam-6031	254	18	γru⊥,β	γru⊥,β	PROPN
ejpam-6031	254	19	=	=	SYM
ejpam-6031	254	20	rv	rv	PROPN
ejpam-6031	254	21	,	,	PUNCT
ejpam-6031	254	22	αru	αru	NOUN
ejpam-6031	254	23	,	,	PUNCT
ejpam-6031	254	24	γru⊥,β	γru⊥,β	NOUN
ejpam-6031	254	25	.	.	PUNCT
ejpam-6031	255	1	(	(	PUNCT
ejpam-6031	255	2	xi	xi	ADP
ejpam-6031	255	3	):	):	PUNCT
ejpam-6031	255	4	using	use	VERB
ejpam-6031	255	5	lemma	lemma	PROPN
ejpam-6031	255	6	2	2	PROPN
ejpam-6031	255	7	and	and	CCONJ
ejpam-6031	255	8	(	(	PUNCT
ejpam-6031	255	9	3	3	X
ejpam-6031	255	10	)	)	PUNCT
ejpam-6031	255	11	yields	yield	NOUN
ejpam-6031	255	12	ru⊥,βru	ru⊥,βru	NOUN
ejpam-6031	255	13	,	,	PUNCT
ejpam-6031	255	14	γrv	γrv	PROPN
ejpam-6031	255	15	,	,	PUNCT
ejpam-6031	255	16	α	α	NOUN
ejpam-6031	255	17	=	=	PUNCT
ejpam-6031	255	18	ru⊥,βru	ru⊥,βru	NOUN
ejpam-6031	255	19	,	,	PUNCT
ejpam-6031	255	20	γrv,1	γrv,1	NOUN
ejpam-6031	256	1	=	=	PUNCT
ejpam-6031	256	2	rv,1	rv,1	NOUN
ejpam-6031	256	3	−	−	PROPN
ejpam-6031	256	4	(	(	PUNCT
ejpam-6031	256	5	2γ	2γ	NUM
ejpam-6031	256	6	pu)rv,1	pu)rv,1	NOUN
ejpam-6031	256	7	+	+	CCONJ
ejpam-6031	256	8	(	(	PUNCT
ejpam-6031	256	9	2β	2β	NUM
ejpam-6031	256	10	pu⊥)rv,1	pu⊥)rv,1	NOUN
ejpam-6031	256	11	s.th	s.th	PROPN
ejpam-6031	256	12	.	.	PUNCT
ejpam-6031	256	13	alwadani	alwadani	PROPN
ejpam-6031	256	14	/	/	SYM
ejpam-6031	256	15	eur	eur	PROPN
ejpam-6031	256	16	.	.	PUNCT
ejpam-6031	257	1	j.	j.	PROPN
ejpam-6031	257	2	pure	pure	PROPN
ejpam-6031	257	3	appl	appl	PROPN
ejpam-6031	257	4	.	.	PROPN
ejpam-6031	257	5	math	math	PROPN
ejpam-6031	257	6	,	,	PUNCT
ejpam-6031	257	7	18	18	NUM
ejpam-6031	257	8	(	(	PUNCT
ejpam-6031	257	9	2	2	NUM
ejpam-6031	257	10	)	)	PUNCT
ejpam-6031	257	11	(	(	PUNCT
ejpam-6031	257	12	2025	2025	NUM
ejpam-6031	257	13	)	)	PUNCT
ejpam-6031	257	14	,	,	PUNCT
ejpam-6031	257	15	6031	6031	NUM
ejpam-6031	257	16	9	9	NUM
ejpam-6031	257	17	of	of	ADP
ejpam-6031	257	18	13	13	NUM
ejpam-6031	257	19	=	=	SYM
ejpam-6031	257	20	(	(	PUNCT
ejpam-6031	257	21	2	2	NUM
ejpam-6031	257	22	pv	pv	NOUN
ejpam-6031	257	23	−	−	PROPN
ejpam-6031	257	24	i	i	PROPN
ejpam-6031	257	25	d	d	PROPN
ejpam-6031	257	26	)	)	PUNCT
ejpam-6031	258	1	−	−	PROPN
ejpam-6031	258	2	2γ	2γ	NOUN
ejpam-6031	258	3	pu	pu	PROPN
ejpam-6031	258	4	(	(	PUNCT
ejpam-6031	258	5	2	2	NUM
ejpam-6031	258	6	pv	pv	NOUN
ejpam-6031	258	7	−	−	PROPN
ejpam-6031	259	1	i	i	NOUN
ejpam-6031	259	2	d	d	PROPN
ejpam-6031	259	3	)	)	PUNCT
ejpam-6031	260	1	+	+	CCONJ
ejpam-6031	260	2	2β	2β	NUM
ejpam-6031	260	3	pu⊥	pu⊥	NOUN
ejpam-6031	260	4	(	(	PUNCT
ejpam-6031	260	5	2	2	NUM
ejpam-6031	260	6	pv	pv	NOUN
ejpam-6031	260	7	−	−	PROPN
ejpam-6031	261	1	i	i	NOUN
ejpam-6031	261	2	d	d	PROPN
ejpam-6031	261	3	)	)	PUNCT
ejpam-6031	262	1	=	=	SYM
ejpam-6031	262	2	2	2	NUM
ejpam-6031	262	3	pv	pv	NOUN
ejpam-6031	262	4	+2γ	+2γ	NUM
ejpam-6031	262	5	pu	pu	NOUN
ejpam-6031	262	6	+2β	+2β	NUM
ejpam-6031	262	7	pu⊥	pu⊥	PROPN
ejpam-6031	262	8	−4γ	−4γ	PROPN
ejpam-6031	262	9	pu	pu	PROPN
ejpam-6031	262	10	pv	pv	PROPN
ejpam-6031	262	11	−4β	−4β	PROPN
ejpam-6031	263	1	pu⊥	pu⊥	PROPN
ejpam-6031	263	2	pv	pv	ADP
ejpam-6031	263	3	−	−	PUNCT
ejpam-6031	264	1	i	i	PROPN
ejpam-6031	264	2	d	d	PROPN
ejpam-6031	264	3	.	.	PUNCT
ejpam-6031	265	1	(	(	PUNCT
ejpam-6031	265	2	xii	xii	NOUN
ejpam-6031	265	3	):	):	PUNCT
ejpam-6031	265	4	applying	apply	VERB
ejpam-6031	265	5	the	the	DET
ejpam-6031	265	6	same	same	ADJ
ejpam-6031	265	7	method	method	NOUN
ejpam-6031	265	8	as	as	ADP
ejpam-6031	265	9	in	in	ADP
ejpam-6031	265	10	statement	statement	NOUN
ejpam-6031	265	11	(	(	PUNCT
ejpam-6031	265	12	xi	xi	PROPN
ejpam-6031	265	13	)	)	PUNCT
ejpam-6031	265	14	gives	give	VERB
ejpam-6031	265	15	ru	ru	PROPN
ejpam-6031	265	16	,	,	PUNCT
ejpam-6031	265	17	γru⊥,βrv	γru⊥,βrv	PROPN
ejpam-6031	265	18	,	,	PUNCT
ejpam-6031	265	19	α	α	PROPN
ejpam-6031	265	20	=	=	SYM
ejpam-6031	265	21	ru	ru	PROPN
ejpam-6031	265	22	,	,	PUNCT
ejpam-6031	265	23	γru⊥rv,1	γru⊥rv,1	ADP
ejpam-6031	266	1	=	=	SYM
ejpam-6031	266	2	2	2	NUM
ejpam-6031	266	3	pv	pv	NOUN
ejpam-6031	266	4	+2γ	+2γ	NUM
ejpam-6031	266	5	pu	pu	NOUN
ejpam-6031	266	6	+2β	+2β	NUM
ejpam-6031	266	7	pu⊥	pu⊥	PROPN
ejpam-6031	266	8	−4γ	−4γ	PROPN
ejpam-6031	266	9	pu	pu	PROPN
ejpam-6031	266	10	pv	pv	PROPN
ejpam-6031	266	11	−4β	−4β	PROPN
ejpam-6031	267	1	pu⊥	pu⊥	PROPN
ejpam-6031	267	2	pv	pv	ADP
ejpam-6031	267	3	−	−	PUNCT
ejpam-6031	268	1	i	i	PROPN
ejpam-6031	268	2	d	d	PROPN
ejpam-6031	268	3	.	.	PUNCT
ejpam-6031	269	1	combining	combine	VERB
ejpam-6031	269	2	this	this	DET
ejpam-6031	269	3	result	result	NOUN
ejpam-6031	269	4	with	with	ADP
ejpam-6031	269	5	(	(	PUNCT
ejpam-6031	269	6	xi	xi	PROPN
ejpam-6031	269	7	)	)	PUNCT
ejpam-6031	269	8	illustrates	illustrate	VERB
ejpam-6031	269	9	that	that	SCONJ
ejpam-6031	269	10	when	when	SCONJ
ejpam-6031	269	11	α	α	PROPN
ejpam-6031	269	12	=	=	SYM
ejpam-6031	269	13	1	1	NUM
ejpam-6031	269	14	ru	ru	NOUN
ejpam-6031	269	15	,	,	PUNCT
ejpam-6031	269	16	γru⊥,βrv	γru⊥,βrv	PROPN
ejpam-6031	269	17	,	,	PUNCT
ejpam-6031	269	18	α	α	PROPN
ejpam-6031	269	19	=	=	SYM
ejpam-6031	269	20	ru	ru	PROPN
ejpam-6031	269	21	,	,	PUNCT
ejpam-6031	269	22	γru⊥,βrv	γru⊥,βrv	PROPN
ejpam-6031	269	23	,	,	PUNCT
ejpam-6031	269	24	α	α	X
ejpam-6031	269	25	.	.	PUNCT
ejpam-6031	270	1	(	(	PUNCT
ejpam-6031	270	2	xiii	xiii	PROPN
ejpam-6031	270	3	):	):	PUNCT
ejpam-6031	270	4	using	use	VERB
ejpam-6031	270	5	lemma	lemma	PROPN
ejpam-6031	270	6	2	2	PROPN
ejpam-6031	270	7	and	and	CCONJ
ejpam-6031	270	8	(	(	PUNCT
ejpam-6031	270	9	11	11	NUM
ejpam-6031	270	10	)	)	PUNCT
ejpam-6031	270	11	gives	give	VERB
ejpam-6031	270	12	rv	rv	PROPN
ejpam-6031	270	13	,	,	PUNCT
ejpam-6031	270	14	αru⊥,βru	αru⊥,βru	PROPN
ejpam-6031	270	15	,	,	PUNCT
ejpam-6031	270	16	γ	γ	PROPN
ejpam-6031	270	17	=	=	SYM
ejpam-6031	270	18	rv	rv	PROPN
ejpam-6031	270	19	,	,	PUNCT
ejpam-6031	270	20	α	α	PROPN
ejpam-6031	270	21	−	−	PROPN
ejpam-6031	270	22	rv	rv	PROPN
ejpam-6031	270	23	,	,	PUNCT
ejpam-6031	270	24	α2γ	α2γ	PROPN
ejpam-6031	270	25	pu	pu	PROPN
ejpam-6031	270	26	+	+	PROPN
ejpam-6031	270	27	rv	rv	PROPN
ejpam-6031	270	28	,	,	PUNCT
ejpam-6031	270	29	α2β	α2β	PROPN
ejpam-6031	270	30	pu⊥	pu⊥	PROPN
ejpam-6031	270	31	=	=	PUNCT
ejpam-6031	270	32	(	(	PUNCT
ejpam-6031	270	33	2α	2α	NOUN
ejpam-6031	270	34	pv	pv	INTJ
ejpam-6031	270	35	−	−	PROPN
ejpam-6031	271	1	i	i	PROPN
ejpam-6031	271	2	d	d	PROPN
ejpam-6031	271	3	)	)	PUNCT
ejpam-6031	272	1	−	−	PROPN
ejpam-6031	272	2	(	(	PUNCT
ejpam-6031	272	3	2α	2α	NOUN
ejpam-6031	272	4	pv	pv	INTJ
ejpam-6031	272	5	−	−	PROPN
ejpam-6031	273	1	i	i	PROPN
ejpam-6031	273	2	d	d	PROPN
ejpam-6031	273	3	)	)	PUNCT
ejpam-6031	274	1	2γ	2γ	VERB
ejpam-6031	274	2	pu	pu	PROPN
ejpam-6031	275	1	+	+	CCONJ
ejpam-6031	275	2	(	(	PUNCT
ejpam-6031	275	3	2α	2α	NOUN
ejpam-6031	275	4	pv	pv	INTJ
ejpam-6031	275	5	−	−	PROPN
ejpam-6031	276	1	i	i	NOUN
ejpam-6031	276	2	d	d	PROPN
ejpam-6031	276	3	)	)	PUNCT
ejpam-6031	277	1	2β	2β	NOUN
ejpam-6031	277	2	pu⊥	pu⊥	NOUN
ejpam-6031	277	3	=	=	PUNCT
ejpam-6031	277	4	2α	2α	X
ejpam-6031	277	5	pv	pv	NOUN
ejpam-6031	277	6	+2γ	+2γ	NUM
ejpam-6031	277	7	pu	pu	NOUN
ejpam-6031	277	8	+2β	+2β	NUM
ejpam-6031	277	9	pu⊥	pu⊥	PROPN
ejpam-6031	277	10	−4αγ	−4αγ	NOUN
ejpam-6031	277	11	pv	pv	INTJ
ejpam-6031	278	1	pu	pu	PROPN
ejpam-6031	278	2	−4αβ	−4αβ	CCONJ
ejpam-6031	278	3	pv	pv	INTJ
ejpam-6031	279	1	pu⊥	pu⊥	NOUN
ejpam-6031	279	2	−	−	PROPN
ejpam-6031	280	1	i	i	PROPN
ejpam-6031	280	2	d	d	PROPN
ejpam-6031	280	3	.	.	PUNCT
ejpam-6031	281	1	(	(	PUNCT
ejpam-6031	281	2	xiv	xiv	PROPN
ejpam-6031	281	3	):	):	PUNCT
ejpam-6031	281	4	following	follow	VERB
ejpam-6031	281	5	the	the	DET
ejpam-6031	281	6	same	same	ADJ
ejpam-6031	281	7	approach	approach	NOUN
ejpam-6031	281	8	as	as	ADP
ejpam-6031	281	9	in	in	ADP
ejpam-6031	281	10	statement	statement	NOUN
ejpam-6031	281	11	(	(	PUNCT
ejpam-6031	281	12	xiii	xiii	PROPN
ejpam-6031	281	13	)	)	PUNCT
ejpam-6031	281	14	gives	give	VERB
ejpam-6031	281	15	rv	rv	PROPN
ejpam-6031	281	16	,	,	PUNCT
ejpam-6031	281	17	αru	αru	NOUN
ejpam-6031	281	18	,	,	PUNCT
ejpam-6031	281	19	γru⊥,β	γru⊥,β	NOUN
ejpam-6031	281	20	=	=	NOUN
ejpam-6031	281	21	2α	2α	NOUN
ejpam-6031	282	1	pv	pv	NOUN
ejpam-6031	282	2	+2γ	+2γ	NUM
ejpam-6031	282	3	pu	pu	NOUN
ejpam-6031	282	4	+2β	+2β	NUM
ejpam-6031	283	1	pu⊥	pu⊥	PROPN
ejpam-6031	283	2	−4αγ	−4αγ	NOUN
ejpam-6031	284	1	pv	pv	INTJ
ejpam-6031	284	2	pu	pu	PROPN
ejpam-6031	284	3	−4αβ	−4αβ	CCONJ
ejpam-6031	284	4	pv	pv	INTJ
ejpam-6031	285	1	pu⊥	pu⊥	NOUN
ejpam-6031	285	2	−	−	PROPN
ejpam-6031	286	1	i	i	PROPN
ejpam-6031	286	2	d	d	PROPN
ejpam-6031	286	3	.	.	PUNCT
ejpam-6031	287	1	combining	combine	VERB
ejpam-6031	287	2	this	this	DET
ejpam-6031	287	3	result	result	NOUN
ejpam-6031	287	4	with	with	ADP
ejpam-6031	287	5	(	(	PUNCT
ejpam-6031	287	6	xiii	xiii	PROPN
ejpam-6031	287	7	)	)	PUNCT
ejpam-6031	287	8	illustrates	illustrate	VERB
ejpam-6031	287	9	that	that	SCONJ
ejpam-6031	287	10	when	when	SCONJ
ejpam-6031	287	11	α	α	PROPN
ejpam-6031	287	12	̸=	̸=	PROPN
ejpam-6031	287	13	1	1	NUM
ejpam-6031	287	14	rv	rv	PROPN
ejpam-6031	287	15	,	,	PUNCT
ejpam-6031	287	16	αru	αru	NOUN
ejpam-6031	287	17	,	,	PUNCT
ejpam-6031	287	18	γru⊥,β	γru⊥,β	PROPN
ejpam-6031	287	19	=	=	SYM
ejpam-6031	287	20	rv	rv	PROPN
ejpam-6031	287	21	,	,	PUNCT
ejpam-6031	287	22	αru	αru	NOUN
ejpam-6031	287	23	,	,	PUNCT
ejpam-6031	287	24	γru⊥,β	γru⊥,β	NOUN
ejpam-6031	287	25	.	.	PUNCT
ejpam-6031	288	1	(	(	PUNCT
ejpam-6031	288	2	xv	xv	ADV
ejpam-6031	288	3	):	):	PUNCT
ejpam-6031	288	4	using	use	VERB
ejpam-6031	288	5	lemma	lemma	PROPN
ejpam-6031	288	6	2	2	PROPN
ejpam-6031	288	7	and	and	CCONJ
ejpam-6031	288	8	(	(	PUNCT
ejpam-6031	288	9	11	11	NUM
ejpam-6031	288	10	)	)	PUNCT
ejpam-6031	288	11	yields	yield	NOUN
ejpam-6031	288	12	ru⊥,βru	ru⊥,βru	NOUN
ejpam-6031	288	13	,	,	PUNCT
ejpam-6031	288	14	γrv	γrv	PROPN
ejpam-6031	288	15	,	,	PUNCT
ejpam-6031	288	16	α	α	NOUN
ejpam-6031	288	17	=	=	SYM
ejpam-6031	288	18	rv	rv	PROPN
ejpam-6031	288	19	,	,	PUNCT
ejpam-6031	288	20	α	α	PROPN
ejpam-6031	288	21	−	−	PROPN
ejpam-6031	288	22	(	(	PUNCT
ejpam-6031	288	23	2γ	2γ	X
ejpam-6031	288	24	pu)rv	pu)rv	NOUN
ejpam-6031	288	25	,	,	PUNCT
ejpam-6031	288	26	α	α	NOUN
ejpam-6031	288	27	+	+	X
ejpam-6031	288	28	(	(	PUNCT
ejpam-6031	288	29	2β	2β	NUM
ejpam-6031	288	30	pu⊥)rv	pu⊥)rv	NOUN
ejpam-6031	288	31	,	,	PUNCT
ejpam-6031	288	32	α	α	X
ejpam-6031	288	33	=	=	PUNCT
ejpam-6031	288	34	(	(	PUNCT
ejpam-6031	288	35	2α	2α	NOUN
ejpam-6031	288	36	pv	pv	INTJ
ejpam-6031	288	37	−	−	PROPN
ejpam-6031	289	1	i	i	PROPN
ejpam-6031	289	2	d	d	PROPN
ejpam-6031	289	3	)	)	PUNCT
ejpam-6031	290	1	−	−	PROPN
ejpam-6031	290	2	2γ	2γ	X
ejpam-6031	290	3	pu	pu	PROPN
ejpam-6031	290	4	(	(	PUNCT
ejpam-6031	290	5	2α	2α	NOUN
ejpam-6031	290	6	pv	pv	INTJ
ejpam-6031	290	7	−	−	PROPN
ejpam-6031	291	1	i	i	NOUN
ejpam-6031	291	2	d	d	PROPN
ejpam-6031	291	3	)	)	PUNCT
ejpam-6031	292	1	+	+	CCONJ
ejpam-6031	292	2	2β	2β	NUM
ejpam-6031	292	3	pu⊥	pu⊥	NOUN
ejpam-6031	292	4	(	(	PUNCT
ejpam-6031	292	5	2α	2α	NOUN
ejpam-6031	292	6	pv	pv	INTJ
ejpam-6031	292	7	−	−	PROPN
ejpam-6031	293	1	i	i	NOUN
ejpam-6031	293	2	d	d	PROPN
ejpam-6031	293	3	)	)	PUNCT
ejpam-6031	294	1	=	=	SYM
ejpam-6031	294	2	2α	2α	NOUN
ejpam-6031	294	3	pv	pv	NOUN
ejpam-6031	295	1	+2γ	+2γ	NUM
ejpam-6031	295	2	pu	pu	NOUN
ejpam-6031	295	3	+2β	+2β	NUM
ejpam-6031	296	1	pu⊥	pu⊥	NOUN
ejpam-6031	296	2	−4γα	−4γα	NOUN
ejpam-6031	296	3	pu	pu	PROPN
ejpam-6031	296	4	pv	pv	PROPN
ejpam-6031	297	1	−4βα	−4βα	PROPN
ejpam-6031	297	2	pu⊥	pu⊥	PROPN
ejpam-6031	297	3	pv	pv	ADP
ejpam-6031	297	4	−	−	PROPN
ejpam-6031	298	1	i	i	PROPN
ejpam-6031	298	2	d	d	PROPN
ejpam-6031	298	3	.	.	PUNCT
ejpam-6031	299	1	(	(	PUNCT
ejpam-6031	299	2	xvi	xvi	NOUN
ejpam-6031	299	3	):	):	PUNCT
ejpam-6031	299	4	applying	apply	VERB
ejpam-6031	299	5	the	the	DET
ejpam-6031	299	6	same	same	ADJ
ejpam-6031	299	7	method	method	NOUN
ejpam-6031	299	8	as	as	ADP
ejpam-6031	299	9	in	in	ADP
ejpam-6031	299	10	statement	statement	NOUN
ejpam-6031	299	11	(	(	PUNCT
ejpam-6031	299	12	xv	xv	PROPN
ejpam-6031	299	13	)	)	PUNCT
ejpam-6031	299	14	gives	give	VERB
ejpam-6031	299	15	ru	ru	PROPN
ejpam-6031	299	16	,	,	PUNCT
ejpam-6031	299	17	γru⊥,βrv	γru⊥,βrv	PROPN
ejpam-6031	299	18	,	,	PUNCT
ejpam-6031	299	19	α	α	NOUN
ejpam-6031	299	20	=	=	X
ejpam-6031	299	21	2α	2α	NOUN
ejpam-6031	300	1	pv	pv	NOUN
ejpam-6031	300	2	+2γ	+2γ	NUM
ejpam-6031	300	3	pu	pu	NOUN
ejpam-6031	300	4	+2β	+2β	NUM
ejpam-6031	301	1	pu⊥	pu⊥	NOUN
ejpam-6031	301	2	−4γα	−4γα	NOUN
ejpam-6031	301	3	pu	pu	PROPN
ejpam-6031	301	4	pv	pv	PROPN
ejpam-6031	302	1	−4βα	−4βα	PROPN
ejpam-6031	302	2	pu⊥	pu⊥	PROPN
ejpam-6031	302	3	pv	pv	ADP
ejpam-6031	302	4	−	−	PROPN
ejpam-6031	303	1	i	i	PROPN
ejpam-6031	303	2	d	d	PROPN
ejpam-6031	303	3	.	.	PUNCT
ejpam-6031	304	1	combining	combine	VERB
ejpam-6031	304	2	this	this	DET
ejpam-6031	304	3	result	result	NOUN
ejpam-6031	304	4	with	with	ADP
ejpam-6031	304	5	(	(	PUNCT
ejpam-6031	304	6	xv	xv	PROPN
ejpam-6031	304	7	)	)	PUNCT
ejpam-6031	304	8	illustrates	illustrate	VERB
ejpam-6031	304	9	that	that	SCONJ
ejpam-6031	304	10	when	when	SCONJ
ejpam-6031	304	11	α	α	PROPN
ejpam-6031	304	12	̸=	̸=	PROPN
ejpam-6031	304	13	1	1	NUM
ejpam-6031	304	14	ru	ru	NOUN
ejpam-6031	304	15	,	,	PUNCT
ejpam-6031	304	16	γru⊥,βrv	γru⊥,βrv	PROPN
ejpam-6031	304	17	,	,	PUNCT
ejpam-6031	304	18	α	α	PROPN
ejpam-6031	304	19	=	=	SYM
ejpam-6031	304	20	ru	ru	PROPN
ejpam-6031	304	21	,	,	PUNCT
ejpam-6031	304	22	γru⊥,βrv	γru⊥,βrv	PROPN
ejpam-6031	304	23	,	,	PUNCT
ejpam-6031	304	24	α	α	X
ejpam-6031	304	25	.	.	PUNCT
ejpam-6031	305	1	■	■	PUNCT
ejpam-6031	305	2	remark	remark	NOUN
ejpam-6031	305	3	1	1	NUM
ejpam-6031	305	4	.	.	PUNCT
ejpam-6031	306	1	regarding	regard	VERB
ejpam-6031	306	2	theorem	theorem	NOUN
ejpam-6031	306	3	1	1	NUM
ejpam-6031	306	4	,	,	PUNCT
ejpam-6031	306	5	if	if	SCONJ
ejpam-6031	306	6	β	β	X
ejpam-6031	306	7	=	=	SYM
ejpam-6031	306	8	γ	γ	X
ejpam-6031	306	9	=	=	SYM
ejpam-6031	306	10	α	α	NOUN
ejpam-6031	306	11	=	=	SYM
ejpam-6031	306	12	1	1	NUM
ejpam-6031	306	13	,	,	PUNCT
ejpam-6031	306	14	then	then	ADV
ejpam-6031	306	15	the	the	DET
ejpam-6031	306	16	following	follow	VERB
ejpam-6031	306	17	holds	hold	VERB
ejpam-6031	306	18	:	:	PUNCT
ejpam-6031	306	19	(	(	PUNCT
ejpam-6031	306	20	i	i	NOUN
ejpam-6031	306	21	)	)	PUNCT
ejpam-6031	306	22	rv	rv	PROPN
ejpam-6031	306	23	,	,	PUNCT
ejpam-6031	306	24	αru⊥,βru	αru⊥,βru	PROPN
ejpam-6031	306	25	,	,	PUNCT
ejpam-6031	306	26	γ	γ	PROPN
ejpam-6031	306	27	=	=	SYM
ejpam-6031	306	28	rv⊥	rv⊥	PROPN
ejpam-6031	306	29	(	(	PUNCT
ejpam-6031	306	30	ii	ii	NOUN
ejpam-6031	306	31	)	)	PUNCT
ejpam-6031	306	32	rv	rv	PROPN
ejpam-6031	306	33	,	,	PUNCT
ejpam-6031	306	34	αru	αru	NOUN
ejpam-6031	306	35	,	,	PUNCT
ejpam-6031	306	36	γru⊥,β	γru⊥,β	NOUN
ejpam-6031	306	37	=	=	PUNCT
ejpam-6031	306	38	rv⊥	rv⊥	PROPN
ejpam-6031	306	39	(	(	PUNCT
ejpam-6031	306	40	iii	iii	NOUN
ejpam-6031	306	41	)	)	PUNCT
ejpam-6031	306	42	ru⊥,βru	ru⊥,βru	NOUN
ejpam-6031	306	43	,	,	PUNCT
ejpam-6031	306	44	γrv	γrv	PROPN
ejpam-6031	306	45	,	,	PUNCT
ejpam-6031	306	46	α	α	NOUN
ejpam-6031	306	47	=	=	PUNCT
ejpam-6031	306	48	rv⊥	rv⊥	PROPN
ejpam-6031	306	49	s.th	s.th	PROPN
ejpam-6031	306	50	.	.	PUNCT
ejpam-6031	307	1	alwadani	alwadani	PROPN
ejpam-6031	307	2	/	/	SYM
ejpam-6031	307	3	eur	eur	PROPN
ejpam-6031	307	4	.	.	PUNCT
ejpam-6031	308	1	j.	j.	PROPN
ejpam-6031	308	2	pure	pure	PROPN
ejpam-6031	308	3	appl	appl	PROPN
ejpam-6031	308	4	.	.	PROPN
ejpam-6031	308	5	math	math	PROPN
ejpam-6031	308	6	,	,	PUNCT
ejpam-6031	308	7	18	18	NUM
ejpam-6031	308	8	(	(	PUNCT
ejpam-6031	308	9	2	2	NUM
ejpam-6031	308	10	)	)	PUNCT
ejpam-6031	308	11	(	(	PUNCT
ejpam-6031	308	12	2025	2025	NUM
ejpam-6031	308	13	)	)	PUNCT
ejpam-6031	308	14	,	,	PUNCT
ejpam-6031	308	15	6031	6031	NUM
ejpam-6031	308	16	10	10	NUM
ejpam-6031	308	17	of	of	ADP
ejpam-6031	308	18	13	13	NUM
ejpam-6031	308	19	(	(	PUNCT
ejpam-6031	308	20	iv	iv	X
ejpam-6031	308	21	)	)	PUNCT
ejpam-6031	308	22	ru	ru	PROPN
ejpam-6031	308	23	,	,	PUNCT
ejpam-6031	308	24	γru⊥,βrv	γru⊥,βrv	PROPN
ejpam-6031	308	25	,	,	PUNCT
ejpam-6031	308	26	α	α	PROPN
ejpam-6031	308	27	=	=	PUNCT
ejpam-6031	308	28	rv⊥	rv⊥	PROPN
ejpam-6031	308	29	(	(	PUNCT
ejpam-6031	308	30	v	v	NOUN
ejpam-6031	308	31	)	)	PUNCT
ejpam-6031	308	32	fix	fix	NOUN
ejpam-6031	308	33	(	(	PUNCT
ejpam-6031	308	34	rv	rv	NOUN
ejpam-6031	308	35	,	,	PUNCT
ejpam-6031	308	36	αru⊥,βru	αru⊥,βru	PROPN
ejpam-6031	308	37	,	,	PUNCT
ejpam-6031	308	38	γ	γ	X
ejpam-6031	308	39	)	)	PUNCT
ejpam-6031	308	40	=	=	SYM
ejpam-6031	308	41	v⊥	v⊥	NOUN
ejpam-6031	308	42	(	(	PUNCT
ejpam-6031	308	43	vi	vi	NOUN
ejpam-6031	308	44	)	)	PUNCT
ejpam-6031	308	45	fix	fix	NOUN
ejpam-6031	308	46	(	(	PUNCT
ejpam-6031	308	47	rv	rv	NOUN
ejpam-6031	308	48	,	,	PUNCT
ejpam-6031	308	49	αru	αru	NOUN
ejpam-6031	308	50	,	,	PUNCT
ejpam-6031	308	51	γru⊥,β	γru⊥,β	NOUN
ejpam-6031	308	52	)	)	PUNCT
ejpam-6031	309	1	=	=	SYM
ejpam-6031	309	2	v⊥	v⊥	NOUN
ejpam-6031	309	3	(	(	PUNCT
ejpam-6031	309	4	vii	vii	PROPN
ejpam-6031	309	5	)	)	PUNCT
ejpam-6031	309	6	fix	fix	NOUN
ejpam-6031	309	7	(	(	PUNCT
ejpam-6031	309	8	ru⊥,βru	ru⊥,βru	NOUN
ejpam-6031	309	9	,	,	PUNCT
ejpam-6031	309	10	γrv	γrv	PROPN
ejpam-6031	309	11	,	,	PUNCT
ejpam-6031	309	12	α	α	NOUN
ejpam-6031	309	13	)	)	PUNCT
ejpam-6031	310	1	=	=	SYM
ejpam-6031	310	2	v⊥	v⊥	NOUN
ejpam-6031	310	3	(	(	PUNCT
ejpam-6031	310	4	viii	viii	NOUN
ejpam-6031	310	5	)	)	PUNCT
ejpam-6031	310	6	fix	fix	NOUN
ejpam-6031	310	7	(	(	PUNCT
ejpam-6031	310	8	ru	ru	PROPN
ejpam-6031	310	9	,	,	PUNCT
ejpam-6031	310	10	γru⊥,βrv	γru⊥,βrv	PROPN
ejpam-6031	310	11	,	,	PUNCT
ejpam-6031	310	12	α	α	NOUN
ejpam-6031	310	13	)	)	PUNCT
ejpam-6031	311	1	=	=	SYM
ejpam-6031	311	2	v⊥	v⊥	NOUN
ejpam-6031	311	3	proof	proof	NOUN
ejpam-6031	311	4	.	.	PUNCT
ejpam-6031	312	1	(	(	PUNCT
ejpam-6031	312	2	i	i	NOUN
ejpam-6031	312	3	)	)	PUNCT
ejpam-6031	312	4	,	,	PUNCT
ejpam-6031	312	5	(	(	PUNCT
ejpam-6031	312	6	ii	ii	NOUN
ejpam-6031	312	7	)	)	PUNCT
ejpam-6031	312	8	,	,	PUNCT
ejpam-6031	312	9	(	(	PUNCT
ejpam-6031	312	10	iii	iii	NOUN
ejpam-6031	312	11	)	)	PUNCT
ejpam-6031	312	12	,	,	PUNCT
ejpam-6031	312	13	(	(	PUNCT
ejpam-6031	312	14	iv	iv	X
ejpam-6031	312	15	)	)	PUNCT
ejpam-6031	312	16	,	,	PUNCT
ejpam-6031	312	17	(	(	PUNCT
ejpam-6031	312	18	v	v	NOUN
ejpam-6031	312	19	)	)	PUNCT
ejpam-6031	312	20	,	,	PUNCT
ejpam-6031	312	21	(	(	PUNCT
ejpam-6031	312	22	vi	vi	NOUN
ejpam-6031	312	23	)	)	PUNCT
ejpam-6031	312	24	,	,	PUNCT
ejpam-6031	312	25	(	(	PUNCT
ejpam-6031	312	26	vii	vii	PROPN
ejpam-6031	312	27	)	)	PUNCT
ejpam-6031	312	28	,	,	PUNCT
ejpam-6031	312	29	and	and	CCONJ
ejpam-6031	312	30	(	(	PUNCT
ejpam-6031	312	31	viii	viii	ADJ
ejpam-6031	312	32	):	):	PUNCT
ejpam-6031	312	33	see	see	VERB
ejpam-6031	313	1	[	[	X
ejpam-6031	313	2	9	9	NUM
ejpam-6031	313	3	,	,	PUNCT
ejpam-6031	313	4	proposition	proposition	NOUN
ejpam-6031	313	5	6.3	6.3	NUM
ejpam-6031	313	6	(	(	PUNCT
ejpam-6031	313	7	i	i	NOUN
ejpam-6031	313	8	)	)	PUNCT
ejpam-6031	313	9	,	,	PUNCT
ejpam-6031	313	10	(	(	PUNCT
ejpam-6031	313	11	ii	ii	NOUN
ejpam-6031	313	12	)	)	PUNCT
ejpam-6031	313	13	,	,	PUNCT
ejpam-6031	313	14	(	(	PUNCT
ejpam-6031	313	15	iii	iii	NOUN
ejpam-6031	313	16	)	)	PUNCT
ejpam-6031	313	17	,	,	PUNCT
ejpam-6031	313	18	(	(	PUNCT
ejpam-6031	313	19	iv	iv	X
ejpam-6031	313	20	)	)	PUNCT
ejpam-6031	313	21	,	,	PUNCT
ejpam-6031	313	22	(	(	PUNCT
ejpam-6031	313	23	v	v	NOUN
ejpam-6031	313	24	)	)	PUNCT
ejpam-6031	313	25	,	,	PUNCT
ejpam-6031	313	26	(	(	PUNCT
ejpam-6031	313	27	vi	vi	NOUN
ejpam-6031	313	28	)	)	PUNCT
ejpam-6031	313	29	,	,	PUNCT
ejpam-6031	313	30	(	(	PUNCT
ejpam-6031	313	31	vii	vii	PROPN
ejpam-6031	313	32	)	)	PUNCT
ejpam-6031	313	33	,	,	PUNCT
ejpam-6031	313	34	and	and	CCONJ
ejpam-6031	313	35	(	(	PUNCT
ejpam-6031	313	36	viii	viii	NOUN
ejpam-6031	313	37	)	)	PUNCT
ejpam-6031	313	38	]	]	PUNCT
ejpam-6031	313	39	for	for	ADP
ejpam-6031	313	40	the	the	DET
ejpam-6031	313	41	proof	proof	NOUN
ejpam-6031	313	42	.	.	PUNCT
ejpam-6031	314	1	■	■	PUNCT
ejpam-6031	314	2	theorem	theorem	ADJ
ejpam-6031	314	3	2	2	NUM
ejpam-6031	314	4	.	.	PUNCT
ejpam-6031	314	5	let	let	VERB
ejpam-6031	314	6	u	u	PRON
ejpam-6031	314	7	and	and	CCONJ
ejpam-6031	314	8	v	v	NOUN
ejpam-6031	314	9	be	be	AUX
ejpam-6031	314	10	claosed	claose	VERB
ejpam-6031	314	11	linear	linear	ADJ
ejpam-6031	314	12	subspaces	subspace	NOUN
ejpam-6031	314	13	of	of	ADP
ejpam-6031	314	14	h.	h.	NOUN
ejpam-6031	314	15	suppose	suppose	VERB
ejpam-6031	314	16	that	that	SCONJ
ejpam-6031	314	17	β	β	NOUN
ejpam-6031	314	18	,	,	PUNCT
ejpam-6031	314	19	γ	γ	X
ejpam-6031	314	20	,	,	PUNCT
ejpam-6031	314	21	α	α	PRON
ejpam-6031	314	22	∈]0	∈]0	ADJ
ejpam-6031	314	23	,	,	PUNCT
ejpam-6031	314	24	1	1	NUM
ejpam-6031	314	25	]	]	PUNCT
ejpam-6031	314	26	and	and	CCONJ
ejpam-6031	314	27	recall	recall	VERB
ejpam-6031	314	28	from	from	ADP
ejpam-6031	314	29	(	(	PUNCT
ejpam-6031	314	30	9	9	NUM
ejpam-6031	314	31	)	)	PUNCT
ejpam-6031	314	32	,	,	PUNCT
ejpam-6031	314	33	(	(	PUNCT
ejpam-6031	314	34	10	10	NUM
ejpam-6031	314	35	)	)	PUNCT
ejpam-6031	314	36	,	,	PUNCT
ejpam-6031	314	37	and	and	CCONJ
ejpam-6031	314	38	(	(	PUNCT
ejpam-6031	314	39	11	11	NUM
ejpam-6031	314	40	)	)	PUNCT
ejpam-6031	314	41	the	the	DET
ejpam-6031	314	42	modified	modify	VERB
ejpam-6031	314	43	reflector	reflector	NOUN
ejpam-6031	314	44	operators	operator	NOUN
ejpam-6031	314	45	.	.	PUNCT
ejpam-6031	315	1	if	if	SCONJ
ejpam-6031	315	2	β	β	X
ejpam-6031	315	3	=	=	SYM
ejpam-6031	315	4	γ	γ	X
ejpam-6031	315	5	=	=	SYM
ejpam-6031	315	6	α	α	NOUN
ejpam-6031	315	7	=	=	SYM
ejpam-6031	315	8	1	1	NUM
ejpam-6031	315	9	,	,	PUNCT
ejpam-6031	315	10	then	then	ADV
ejpam-6031	315	11	the	the	DET
ejpam-6031	315	12	following	follow	VERB
ejpam-6031	315	13	holds	hold	VERB
ejpam-6031	315	14	:	:	PUNCT
ejpam-6031	315	15	(	(	PUNCT
ejpam-6031	315	16	i	i	NOUN
ejpam-6031	315	17	)	)	PUNCT
ejpam-6031	315	18	ru	ru	PROPN
ejpam-6031	315	19	,	,	PUNCT
ejpam-6031	315	20	γrv	γrv	PROPN
ejpam-6031	315	21	,	,	PUNCT
ejpam-6031	315	22	αru⊥,β	αru⊥,β	NOUN
ejpam-6031	315	23	=	=	SYM
ejpam-6031	315	24	id+2	id+2	PROPN
ejpam-6031	316	1	pv	pv	INTJ
ejpam-6031	317	1	+8	+8	INTJ
ejpam-6031	317	2	pu	pu	PROPN
ejpam-6031	318	1	pv	pv	INTJ
ejpam-6031	318	2	pu⊥	pu⊥	PROPN
ejpam-6031	318	3	−4	−4	INTJ
ejpam-6031	319	1	pu	pu	PROPN
ejpam-6031	319	2	pv	pv	INTJ
ejpam-6031	320	1	−4	−4	INTJ
ejpam-6031	321	1	pv	pv	INTJ
ejpam-6031	321	2	pu⊥	pu⊥	PROPN
ejpam-6031	321	3	(	(	PUNCT
ejpam-6031	321	4	ii	ii	NOUN
ejpam-6031	321	5	)	)	PUNCT
ejpam-6031	321	6	ru⊥,βrv	ru⊥,βrv	PROPN
ejpam-6031	321	7	,	,	PUNCT
ejpam-6031	321	8	αru	αru	NOUN
ejpam-6031	321	9	,	,	PUNCT
ejpam-6031	321	10	γ	γ	NOUN
ejpam-6031	321	11	=	=	SYM
ejpam-6031	321	12	id+2	id+2	PROPN
ejpam-6031	322	1	pv	pv	INTJ
ejpam-6031	323	1	+8	+8	INTJ
ejpam-6031	323	2	pu⊥	pu⊥	PROPN
ejpam-6031	324	1	pv	pv	INTJ
ejpam-6031	324	2	pu	pu	PROPN
ejpam-6031	324	3	−4	−4	INTJ
ejpam-6031	325	1	pu⊥	pu⊥	NOUN
ejpam-6031	325	2	pv	pv	INTJ
ejpam-6031	325	3	−4	−4	INTJ
ejpam-6031	325	4	pv	pv	INTJ
ejpam-6031	325	5	pu	pu	PROPN
ejpam-6031	325	6	(	(	PUNCT
ejpam-6031	325	7	iii	iii	NOUN
ejpam-6031	325	8	)	)	PUNCT
ejpam-6031	325	9	fix	fix	NOUN
ejpam-6031	325	10	(	(	PUNCT
ejpam-6031	325	11	ru	ru	NOUN
ejpam-6031	325	12	,	,	PUNCT
ejpam-6031	325	13	γrv	γrv	ADJ
ejpam-6031	325	14	,	,	PUNCT
ejpam-6031	325	15	αru⊥,β	αru⊥,β	NOUN
ejpam-6031	325	16	)	)	PUNCT
ejpam-6031	326	1	=	=	SYM
ejpam-6031	326	2	ru	ru	PROPN
ejpam-6031	326	3	(	(	PUNCT
ejpam-6031	326	4	v⊥	v⊥	PROPN
ejpam-6031	326	5	)	)	PUNCT
ejpam-6031	326	6	(	(	PUNCT
ejpam-6031	326	7	iv	iv	X
ejpam-6031	326	8	)	)	PUNCT
ejpam-6031	326	9	fix	fix	NOUN
ejpam-6031	326	10	(	(	PUNCT
ejpam-6031	326	11	ru⊥,βrv	ru⊥,βrv	NOUN
ejpam-6031	326	12	,	,	PUNCT
ejpam-6031	326	13	αru	αru	NOUN
ejpam-6031	326	14	,	,	PUNCT
ejpam-6031	326	15	γ	γ	NOUN
ejpam-6031	326	16	)	)	PUNCT
ejpam-6031	326	17	=	=	SYM
ejpam-6031	327	1	ru	ru	PROPN
ejpam-6031	327	2	(	(	PUNCT
ejpam-6031	327	3	v⊥	v⊥	PROPN
ejpam-6031	327	4	)	)	PUNCT
ejpam-6031	327	5	.	.	PUNCT
ejpam-6031	328	1	additionally	additionally	ADV
ejpam-6031	328	2	,	,	PUNCT
ejpam-6031	328	3	if	if	SCONJ
ejpam-6031	328	4	β	β	X
ejpam-6031	328	5	,	,	PUNCT
ejpam-6031	328	6	γ	γ	NOUN
ejpam-6031	328	7	=	=	SYM
ejpam-6031	328	8	1	1	NUM
ejpam-6031	328	9	,	,	PUNCT
ejpam-6031	328	10	then	then	ADV
ejpam-6031	328	11	the	the	DET
ejpam-6031	328	12	following	follow	VERB
ejpam-6031	328	13	holds	hold	VERB
ejpam-6031	328	14	:	:	PUNCT
ejpam-6031	328	15	(	(	PUNCT
ejpam-6031	328	16	v	v	NOUN
ejpam-6031	328	17	)	)	PUNCT
ejpam-6031	328	18	ru	ru	PROPN
ejpam-6031	328	19	,	,	PUNCT
ejpam-6031	328	20	γrv	γrv	PROPN
ejpam-6031	328	21	,	,	PUNCT
ejpam-6031	328	22	αru⊥,β	αru⊥,β	NOUN
ejpam-6031	328	23	=	=	PUNCT
ejpam-6031	328	24	id+2α	id+2α	NOUN
ejpam-6031	328	25	pv	pv	INTJ
ejpam-6031	329	1	+8α	+8α	PROPN
ejpam-6031	330	1	pu	pu	NOUN
ejpam-6031	331	1	pv	pv	INTJ
ejpam-6031	332	1	pu⊥	pu⊥	PROPN
ejpam-6031	332	2	−4α	−4α	PROPN
ejpam-6031	332	3	pu	pu	PROPN
ejpam-6031	332	4	pv	pv	X
ejpam-6031	332	5	−4α	−4α	PROPN
ejpam-6031	332	6	pv	pv	INTJ
ejpam-6031	332	7	pu⊥	pu⊥	PROPN
ejpam-6031	332	8	(	(	PUNCT
ejpam-6031	332	9	vi	vi	NOUN
ejpam-6031	332	10	)	)	PUNCT
ejpam-6031	332	11	ru⊥,βrv	ru⊥,βrv	NOUN
ejpam-6031	332	12	,	,	PUNCT
ejpam-6031	332	13	αru	αru	NOUN
ejpam-6031	332	14	,	,	PUNCT
ejpam-6031	332	15	γ	γ	NOUN
ejpam-6031	332	16	=	=	SYM
ejpam-6031	332	17	id+2α	id+2α	PROPN
ejpam-6031	332	18	pv	pv	INTJ
ejpam-6031	332	19	+8α	+8α	PROPN
ejpam-6031	333	1	pu⊥	pu⊥	VERB
ejpam-6031	333	2	pv	pv	INTJ
ejpam-6031	333	3	pu	pu	PROPN
ejpam-6031	333	4	−4α	−4α	PROPN
ejpam-6031	333	5	pu⊥	pu⊥	PROPN
ejpam-6031	333	6	pv	pv	NOUN
ejpam-6031	333	7	−4α	−4α	PROPN
ejpam-6031	334	1	pv	pv	INTJ
ejpam-6031	334	2	pu	pu	PROPN
ejpam-6031	334	3	(	(	PUNCT
ejpam-6031	334	4	vii	vii	PROPN
ejpam-6031	334	5	)	)	PUNCT
ejpam-6031	334	6	fix	fix	NOUN
ejpam-6031	334	7	(	(	PUNCT
ejpam-6031	334	8	ru	ru	NOUN
ejpam-6031	334	9	,	,	PUNCT
ejpam-6031	334	10	γrv	γrv	ADJ
ejpam-6031	334	11	,	,	PUNCT
ejpam-6031	334	12	αru⊥,β	αru⊥,β	NOUN
ejpam-6031	334	13	)	)	PUNCT
ejpam-6031	335	1	=	=	PUNCT
ejpam-6031	335	2	ru,1	ru,1	NOUN
ejpam-6031	335	3	(	(	PUNCT
ejpam-6031	335	4	v⊥	v⊥	NUM
ejpam-6031	335	5	)	)	PUNCT
ejpam-6031	335	6	(	(	PUNCT
ejpam-6031	335	7	viii	viii	NOUN
ejpam-6031	335	8	)	)	PUNCT
ejpam-6031	335	9	fix	fix	NOUN
ejpam-6031	335	10	(	(	PUNCT
ejpam-6031	335	11	ru⊥,βrv	ru⊥,βrv	NOUN
ejpam-6031	335	12	,	,	PUNCT
ejpam-6031	335	13	αru	αru	NOUN
ejpam-6031	335	14	,	,	PUNCT
ejpam-6031	335	15	γ	γ	NOUN
ejpam-6031	335	16	)	)	PUNCT
ejpam-6031	335	17	=	=	SYM
ejpam-6031	335	18	ru,1	ru,1	NOUN
ejpam-6031	335	19	(	(	PUNCT
ejpam-6031	335	20	v⊥	v⊥	NOUN
ejpam-6031	335	21	)	)	PUNCT
ejpam-6031	335	22	moreover	moreover	ADV
ejpam-6031	335	23	,	,	PUNCT
ejpam-6031	335	24	if	if	SCONJ
ejpam-6031	335	25	β	β	X
ejpam-6031	335	26	,	,	PUNCT
ejpam-6031	335	27	γ	γ	PROPN
ejpam-6031	335	28	̸=	̸=	PROPN
ejpam-6031	335	29	1	1	NUM
ejpam-6031	335	30	and	and	CCONJ
ejpam-6031	335	31	α	α	NOUN
ejpam-6031	335	32	=	=	SYM
ejpam-6031	335	33	1	1	NUM
ejpam-6031	335	34	,	,	PUNCT
ejpam-6031	335	35	then	then	ADV
ejpam-6031	335	36	the	the	DET
ejpam-6031	335	37	following	follow	VERB
ejpam-6031	335	38	holds	hold	VERB
ejpam-6031	335	39	:	:	PUNCT
ejpam-6031	335	40	(	(	PUNCT
ejpam-6031	335	41	ix	ix	INTJ
ejpam-6031	335	42	)	)	PUNCT
ejpam-6031	335	43	we	we	PRON
ejpam-6031	335	44	obtain	obtain	VERB
ejpam-6031	335	45	ru	ru	NOUN
ejpam-6031	335	46	,	,	PUNCT
ejpam-6031	335	47	γrv	γrv	PROPN
ejpam-6031	335	48	,	,	PUNCT
ejpam-6031	335	49	αru⊥,β	αru⊥,β	NOUN
ejpam-6031	336	1	=	=	SYM
ejpam-6031	336	2	8γβ	8γβ	ADJ
ejpam-6031	336	3	pu	pu	PROPN
ejpam-6031	337	1	pv	pv	INTJ
ejpam-6031	338	1	pu⊥	pu⊥	PROPN
ejpam-6031	338	2	−4γ	−4γ	PROPN
ejpam-6031	338	3	pu	pu	PROPN
ejpam-6031	338	4	pv	pv	PROPN
ejpam-6031	338	5	−4β	−4β	PROPN
ejpam-6031	338	6	pv	pv	INTJ
ejpam-6031	338	7	pu⊥	pu⊥	NOUN
ejpam-6031	338	8	+2	+2	PROPN
ejpam-6031	338	9	(	(	PUNCT
ejpam-6031	338	10	γ	γ	X
ejpam-6031	338	11	pu	pu	PROPN
ejpam-6031	338	12	+	+	PROPN
ejpam-6031	338	13	β	β	X
ejpam-6031	338	14	pu⊥	pu⊥	NOUN
ejpam-6031	338	15	+	+	PROPN
ejpam-6031	338	16	pv	pv	NOUN
ejpam-6031	338	17	)	)	PUNCT
ejpam-6031	339	1	−	−	PROPN
ejpam-6031	340	1	i	i	PRON
ejpam-6031	340	2	d	d	PROPN
ejpam-6031	340	3	(	(	PUNCT
ejpam-6031	340	4	x	x	X
ejpam-6031	340	5	)	)	PUNCT
ejpam-6031	340	6	also	also	ADV
ejpam-6031	340	7	,	,	PUNCT
ejpam-6031	340	8	ru⊥,βrv	ru⊥,βrv	PROPN
ejpam-6031	340	9	,	,	PUNCT
ejpam-6031	340	10	αru	αru	NOUN
ejpam-6031	340	11	,	,	PUNCT
ejpam-6031	340	12	γ	γ	NOUN
ejpam-6031	340	13	=	=	SYM
ejpam-6031	340	14	8βγ	8βγ	NOUN
ejpam-6031	341	1	pu⊥	pu⊥	NOUN
ejpam-6031	341	2	pv	pv	INTJ
ejpam-6031	341	3	pu	pu	PROPN
ejpam-6031	341	4	−4β	−4β	PROPN
ejpam-6031	342	1	pu⊥	pu⊥	PROPN
ejpam-6031	342	2	pv	pv	NOUN
ejpam-6031	342	3	−4γ	−4γ	ADV
ejpam-6031	342	4	pv	pv	NOUN
ejpam-6031	342	5	pu	pu	PROPN
ejpam-6031	342	6	+2	+2	PROPN
ejpam-6031	342	7	(	(	PUNCT
ejpam-6031	342	8	β	β	X
ejpam-6031	342	9	pu⊥	pu⊥	VERB
ejpam-6031	342	10	+	+	CCONJ
ejpam-6031	342	11	γ	γ	X
ejpam-6031	342	12	pu	pu	PROPN
ejpam-6031	342	13	+	+	PROPN
ejpam-6031	342	14	pv	pv	NOUN
ejpam-6031	342	15	)	)	PUNCT
ejpam-6031	342	16	−	−	PROPN
ejpam-6031	343	1	i	i	NOUN
ejpam-6031	343	2	d	d	PROPN
ejpam-6031	343	3	proof	proof	NOUN
ejpam-6031	343	4	.	.	PUNCT
ejpam-6031	344	1	(	(	PUNCT
ejpam-6031	344	2	i	i	NOUN
ejpam-6031	344	3	):	):	PUNCT
ejpam-6031	344	4	from	from	ADP
ejpam-6031	344	5	(	(	PUNCT
ejpam-6031	344	6	3	3	NUM
ejpam-6031	344	7	)	)	PUNCT
ejpam-6031	344	8	,	,	PUNCT
ejpam-6031	344	9	we	we	PRON
ejpam-6031	344	10	have	have	VERB
ejpam-6031	344	11	ru	ru	NOUN
ejpam-6031	344	12	,	,	PUNCT
ejpam-6031	344	13	γrv	γrv	PROPN
ejpam-6031	344	14	,	,	PUNCT
ejpam-6031	344	15	αru⊥,β	αru⊥,β	NOUN
ejpam-6031	344	16	=	=	SYM
ejpam-6031	344	17	ru,1rv,1ru⊥,1	ru,1rv,1ru⊥,1	NOUN
ejpam-6031	344	18	=	=	SYM
ejpam-6031	344	19	(	(	PUNCT
ejpam-6031	344	20	2	2	NUM
ejpam-6031	344	21	pu	pu	NOUN
ejpam-6031	344	22	−	−	PROPN
ejpam-6031	345	1	i	i	PROPN
ejpam-6031	345	2	d	d	PROPN
ejpam-6031	345	3	)	)	PUNCT
ejpam-6031	345	4	(	(	PUNCT
ejpam-6031	345	5	4	4	NUM
ejpam-6031	345	6	pv	pv	NOUN
ejpam-6031	345	7	pu⊥	pu⊥	PROPN
ejpam-6031	345	8	−2	−2	NOUN
ejpam-6031	346	1	pv	pv	INTJ
ejpam-6031	346	2	−2	−2	NOUN
ejpam-6031	346	3	pu⊥	pu⊥	NOUN
ejpam-6031	347	1	+	+	CCONJ
ejpam-6031	347	2	i	i	PROPN
ejpam-6031	347	3	d	d	PROPN
ejpam-6031	347	4	)	)	PUNCT
ejpam-6031	348	1	=	=	SYM
ejpam-6031	348	2	8	8	NUM
ejpam-6031	348	3	pu	pu	NOUN
ejpam-6031	348	4	pv	pv	INTJ
ejpam-6031	349	1	pu⊥	pu⊥	NOUN
ejpam-6031	349	2	−4	−4	INTJ
ejpam-6031	350	1	pu	pu	PROPN
ejpam-6031	350	2	pv	pv	INTJ
ejpam-6031	350	3	+2	+2	PROPN
ejpam-6031	351	1	pu	pu	INTJ
ejpam-6031	351	2	−4	−4	INTJ
ejpam-6031	352	1	pv	pv	INTJ
ejpam-6031	352	2	pu⊥	pu⊥	NOUN
ejpam-6031	352	3	+2	+2	ADV
ejpam-6031	353	1	pv	pv	INTJ
ejpam-6031	353	2	+2	+2	ADV
ejpam-6031	354	1	pu⊥	pu⊥	PROPN
ejpam-6031	354	2	−	−	PROPN
ejpam-6031	355	1	i	i	NOUN
ejpam-6031	355	2	d	d	PROPN
ejpam-6031	355	3	=	=	SYM
ejpam-6031	355	4	8	8	NUM
ejpam-6031	355	5	pu	pu	NOUN
ejpam-6031	355	6	pv	pv	INTJ
ejpam-6031	355	7	pu⊥	pu⊥	NOUN
ejpam-6031	355	8	−4	−4	INTJ
ejpam-6031	356	1	pu	pu	PROPN
ejpam-6031	356	2	pv	pv	INTJ
ejpam-6031	356	3	+2	+2	PROPN
ejpam-6031	356	4	(	(	PUNCT
ejpam-6031	356	5	pu	pu	PROPN
ejpam-6031	356	6	+	+	PROPN
ejpam-6031	356	7	pu⊥	pu⊥	PROPN
ejpam-6031	356	8	)	)	PUNCT
ejpam-6031	356	9	−	−	PROPN
ejpam-6031	357	1	id−4	id−4	NOUN
ejpam-6031	357	2	pv	pv	INTJ
ejpam-6031	357	3	pu⊥	pu⊥	NOUN
ejpam-6031	357	4	+2	+2	PRON
ejpam-6031	357	5	pv	pv	NOUN
ejpam-6031	358	1	=	=	SYM
ejpam-6031	358	2	8	8	NUM
ejpam-6031	358	3	pu	pu	NOUN
ejpam-6031	358	4	pv	pv	INTJ
ejpam-6031	358	5	pu⊥	pu⊥	NOUN
ejpam-6031	358	6	−4	−4	INTJ
ejpam-6031	359	1	pu	pu	PROPN
ejpam-6031	359	2	pv	pv	PROPN
ejpam-6031	360	1	+	+	CCONJ
ejpam-6031	360	2	id−4	id−4	NOUN
ejpam-6031	360	3	pv	pv	INTJ
ejpam-6031	361	1	pu⊥	pu⊥	NOUN
ejpam-6031	361	2	+2	+2	NOUN
ejpam-6031	361	3	pv	pv	INTJ
ejpam-6031	362	1	=	=	SYM
ejpam-6031	362	2	id+2	id+2	PROPN
ejpam-6031	363	1	pv	pv	INTJ
ejpam-6031	364	1	+8	+8	INTJ
ejpam-6031	364	2	pu	pu	PROPN
ejpam-6031	365	1	pv	pv	INTJ
ejpam-6031	365	2	pu⊥	pu⊥	PROPN
ejpam-6031	365	3	−4	−4	INTJ
ejpam-6031	366	1	pu	pu	PROPN
ejpam-6031	366	2	pv	pv	INTJ
ejpam-6031	367	1	−4	−4	INTJ
ejpam-6031	368	1	pv	pv	INTJ
ejpam-6031	368	2	pu⊥	pu⊥	PROPN
ejpam-6031	368	3	(	(	PUNCT
ejpam-6031	368	4	ii	ii	PROPN
ejpam-6031	368	5	):	):	PUNCT
ejpam-6031	368	6	the	the	DET
ejpam-6031	368	7	proof	proof	NOUN
ejpam-6031	368	8	follows	follow	VERB
ejpam-6031	368	9	a	a	DET
ejpam-6031	368	10	similar	similar	ADJ
ejpam-6031	368	11	approach	approach	NOUN
ejpam-6031	368	12	as	as	ADP
ejpam-6031	368	13	in	in	ADP
ejpam-6031	368	14	(	(	PUNCT
ejpam-6031	368	15	i	i	NOUN
ejpam-6031	368	16	)	)	PUNCT
ejpam-6031	368	17	.	.	PUNCT
ejpam-6031	369	1	(	(	PUNCT
ejpam-6031	369	2	iii	iii	NOUN
ejpam-6031	369	3	)	)	PUNCT
ejpam-6031	369	4	,	,	PUNCT
ejpam-6031	369	5	(	(	PUNCT
ejpam-6031	369	6	iv	iv	X
ejpam-6031	369	7	):	):	PUNCT
ejpam-6031	369	8	see	see	VERB
ejpam-6031	369	9	[	[	X
ejpam-6031	369	10	9	9	NUM
ejpam-6031	369	11	,	,	PUNCT
ejpam-6031	369	12	proposition	proposition	NOUN
ejpam-6031	369	13	6.5	6.5	NUM
ejpam-6031	369	14	(	(	PUNCT
ejpam-6031	369	15	i	i	NOUN
ejpam-6031	369	16	)	)	PUNCT
ejpam-6031	369	17	and	and	CCONJ
ejpam-6031	369	18	(	(	PUNCT
ejpam-6031	369	19	ii	ii	NOUN
ejpam-6031	369	20	)	)	PUNCT
ejpam-6031	369	21	]	]	PUNCT
ejpam-6031	369	22	.	.	PUNCT
ejpam-6031	370	1	(	(	PUNCT
ejpam-6031	370	2	v	v	NOUN
ejpam-6031	370	3	):	):	PUNCT
ejpam-6031	370	4	using	use	VERB
ejpam-6031	370	5	(	(	PUNCT
ejpam-6031	370	6	3	3	NUM
ejpam-6031	370	7	)	)	PUNCT
ejpam-6031	370	8	yields	yield	NOUN
ejpam-6031	370	9	ru	ru	PROPN
ejpam-6031	370	10	,	,	PUNCT
ejpam-6031	370	11	γrv	γrv	PROPN
ejpam-6031	370	12	,	,	PUNCT
ejpam-6031	370	13	αru⊥,β	αru⊥,β	NOUN
ejpam-6031	370	14	=	=	PUNCT
ejpam-6031	370	15	ru,1rv	ru,1rv	NOUN
ejpam-6031	370	16	,	,	PUNCT
ejpam-6031	370	17	αru⊥,1	αru⊥,1	NUM
ejpam-6031	370	18	s.th	s.th	PROPN
ejpam-6031	370	19	.	.	PUNCT
ejpam-6031	370	20	alwadani	alwadani	PROPN
ejpam-6031	370	21	/	/	SYM
ejpam-6031	370	22	eur	eur	PROPN
ejpam-6031	370	23	.	.	PUNCT
ejpam-6031	371	1	j.	j.	PROPN
ejpam-6031	371	2	pure	pure	PROPN
ejpam-6031	371	3	appl	appl	PROPN
ejpam-6031	371	4	.	.	PROPN
ejpam-6031	371	5	math	math	PROPN
ejpam-6031	371	6	,	,	PUNCT
ejpam-6031	371	7	18	18	NUM
ejpam-6031	371	8	(	(	PUNCT
ejpam-6031	371	9	2	2	NUM
ejpam-6031	371	10	)	)	PUNCT
ejpam-6031	371	11	(	(	PUNCT
ejpam-6031	371	12	2025	2025	NUM
ejpam-6031	371	13	)	)	PUNCT
ejpam-6031	371	14	,	,	PUNCT
ejpam-6031	371	15	6031	6031	NUM
ejpam-6031	371	16	11	11	NUM
ejpam-6031	371	17	of	of	ADP
ejpam-6031	371	18	13	13	NUM
ejpam-6031	371	19	=	=	SYM
ejpam-6031	371	20	(	(	PUNCT
ejpam-6031	371	21	2	2	NUM
ejpam-6031	371	22	pu	pu	NOUN
ejpam-6031	371	23	−	−	PROPN
ejpam-6031	372	1	i	i	PROPN
ejpam-6031	372	2	d	d	PROPN
ejpam-6031	372	3	)	)	PUNCT
ejpam-6031	372	4	(	(	PUNCT
ejpam-6031	372	5	4α	4α	NOUN
ejpam-6031	372	6	pv	pv	INTJ
ejpam-6031	373	1	pu⊥	pu⊥	NOUN
ejpam-6031	374	1	−2α	−2α	PROPN
ejpam-6031	374	2	pv	pv	INTJ
ejpam-6031	374	3	−2	−2	NOUN
ejpam-6031	375	1	pu⊥	pu⊥	NOUN
ejpam-6031	375	2	+	+	CCONJ
ejpam-6031	375	3	i	i	PROPN
ejpam-6031	375	4	d	d	PROPN
ejpam-6031	375	5	)	)	PUNCT
ejpam-6031	376	1	=	=	SYM
ejpam-6031	377	1	8α	8α	NUM
ejpam-6031	377	2	pu	pu	NOUN
ejpam-6031	377	3	pv	pv	INTJ
ejpam-6031	378	1	pu⊥	pu⊥	PROPN
ejpam-6031	378	2	−4α	−4α	PROPN
ejpam-6031	378	3	pu	pu	PROPN
ejpam-6031	379	1	pv	pv	INTJ
ejpam-6031	379	2	+2	+2	PROPN
ejpam-6031	379	3	pu	pu	PROPN
ejpam-6031	379	4	−4α	−4α	PROPN
ejpam-6031	379	5	pv	pv	INTJ
ejpam-6031	380	1	pu⊥	pu⊥	NOUN
ejpam-6031	380	2	+2α	+2α	PRON
ejpam-6031	381	1	pv	pv	INTJ
ejpam-6031	381	2	+2	+2	ADV
ejpam-6031	382	1	pu⊥	pu⊥	INTJ
ejpam-6031	382	2	−	−	PROPN
ejpam-6031	383	1	i	i	NOUN
ejpam-6031	383	2	d	d	PROPN
ejpam-6031	383	3	=	=	SYM
ejpam-6031	383	4	8α	8α	NUM
ejpam-6031	383	5	pu	pu	NOUN
ejpam-6031	383	6	pv	pv	INTJ
ejpam-6031	384	1	pu⊥	pu⊥	PROPN
ejpam-6031	384	2	−4α	−4α	PROPN
ejpam-6031	384	3	pu	pu	PROPN
ejpam-6031	385	1	pv	pv	INTJ
ejpam-6031	385	2	+2	+2	PROPN
ejpam-6031	385	3	(	(	PUNCT
ejpam-6031	385	4	pu	pu	PROPN
ejpam-6031	385	5	+	+	PROPN
ejpam-6031	385	6	pu⊥	pu⊥	PROPN
ejpam-6031	385	7	)	)	PUNCT
ejpam-6031	385	8	−	−	PROPN
ejpam-6031	386	1	id−4α	id−4α	NOUN
ejpam-6031	386	2	pv	pv	INTJ
ejpam-6031	387	1	pu⊥	pu⊥	NOUN
ejpam-6031	387	2	+2α	+2α	PRON
ejpam-6031	387	3	pv	pv	NOUN
ejpam-6031	388	1	=	=	SYM
ejpam-6031	388	2	8α	8α	NUM
ejpam-6031	388	3	pu	pu	NOUN
ejpam-6031	388	4	pv	pv	INTJ
ejpam-6031	389	1	pu⊥	pu⊥	PROPN
ejpam-6031	389	2	−4α	−4α	PROPN
ejpam-6031	389	3	pu	pu	NOUN
ejpam-6031	390	1	pv	pv	NOUN
ejpam-6031	391	1	+	+	CCONJ
ejpam-6031	391	2	id−4α	id−4α	NUM
ejpam-6031	392	1	pv	pv	INTJ
ejpam-6031	392	2	pu⊥	pu⊥	NOUN
ejpam-6031	392	3	+2α	+2α	PRON
ejpam-6031	392	4	pv	pv	NOUN
ejpam-6031	393	1	=	=	PUNCT
ejpam-6031	393	2	id+2α	id+2α	NOUN
ejpam-6031	393	3	pv	pv	INTJ
ejpam-6031	394	1	+8α	+8α	PROPN
ejpam-6031	394	2	pu	pu	NOUN
ejpam-6031	394	3	pv	pv	INTJ
ejpam-6031	395	1	pu⊥	pu⊥	PROPN
ejpam-6031	395	2	−4α	−4α	PROPN
ejpam-6031	395	3	pu	pu	PROPN
ejpam-6031	395	4	pv	pv	X
ejpam-6031	395	5	−4α	−4α	PROPN
ejpam-6031	395	6	pv	pv	INTJ
ejpam-6031	395	7	pu⊥	pu⊥	PROPN
ejpam-6031	395	8	(	(	PUNCT
ejpam-6031	395	9	vi	vi	ADJ
ejpam-6031	395	10	):	):	PUNCT
ejpam-6031	395	11	the	the	DET
ejpam-6031	395	12	proof	proof	NOUN
ejpam-6031	395	13	adopts	adopt	VERB
ejpam-6031	395	14	a	a	DET
ejpam-6031	395	15	similar	similar	ADJ
ejpam-6031	395	16	method	method	NOUN
ejpam-6031	395	17	to	to	ADP
ejpam-6031	395	18	that	that	PRON
ejpam-6031	395	19	used	use	VERB
ejpam-6031	395	20	in	in	ADP
ejpam-6031	395	21	statement	statement	NOUN
ejpam-6031	395	22	(	(	PUNCT
ejpam-6031	395	23	v	v	NOUN
ejpam-6031	395	24	)	)	PUNCT
ejpam-6031	395	25	.	.	PUNCT
ejpam-6031	396	1	(	(	PUNCT
ejpam-6031	396	2	vii	vii	PROPN
ejpam-6031	396	3	):	):	PUNCT
ejpam-6031	396	4	using	use	VERB
ejpam-6031	396	5	[	[	X
ejpam-6031	396	6	9	9	NUM
ejpam-6031	396	7	,	,	PUNCT
ejpam-6031	396	8	lemma	lemma	PROPN
ejpam-6031	396	9	6.4	6.4	NUM
ejpam-6031	396	10	]	]	PUNCT
ejpam-6031	396	11	and	and	CCONJ
ejpam-6031	396	12	lemma	lemma	PROPN
ejpam-6031	396	13	1	1	NUM
ejpam-6031	396	14	(	(	PUNCT
ejpam-6031	396	15	vi	vi	NOUN
ejpam-6031	396	16	)	)	PUNCT
ejpam-6031	396	17	gives	give	VERB
ejpam-6031	396	18	fix	fix	NOUN
ejpam-6031	396	19	(	(	PUNCT
ejpam-6031	396	20	ru	ru	NOUN
ejpam-6031	396	21	,	,	PUNCT
ejpam-6031	396	22	γrv	γrv	ADJ
ejpam-6031	396	23	,	,	PUNCT
ejpam-6031	396	24	αru⊥,β	αru⊥,β	NOUN
ejpam-6031	396	25	)	)	PUNCT
ejpam-6031	397	1	=	=	SYM
ejpam-6031	397	2	fix	fix	NOUN
ejpam-6031	397	3	(	(	PUNCT
ejpam-6031	397	4	ru,1rv	ru,1rv	NOUN
ejpam-6031	397	5	,	,	PUNCT
ejpam-6031	397	6	αru⊥,1	αru⊥,1	NUM
ejpam-6031	397	7	)	)	PUNCT
ejpam-6031	397	8	=	=	SYM
ejpam-6031	397	9	ru,1	ru,1	NOUN
ejpam-6031	397	10	(	(	PUNCT
ejpam-6031	397	11	fix	fix	NOUN
ejpam-6031	397	12	rv	rv	PROPN
ejpam-6031	397	13	,	,	PUNCT
ejpam-6031	397	14	αru⊥,1ru,1	αru⊥,1ru,1	PROPN
ejpam-6031	397	15	)	)	PUNCT
ejpam-6031	397	16	=	=	VERB
ejpam-6031	397	17	ru,1	ru,1	NOUN
ejpam-6031	397	18	(	(	PUNCT
ejpam-6031	397	19	fix	fix	NOUN
ejpam-6031	397	20	(	(	PUNCT
ejpam-6031	397	21	rv	rv	PROPN
ejpam-6031	397	22	,	,	PUNCT
ejpam-6031	397	23	α(−	α(−	PRON
ejpam-6031	397	24	i	i	NOUN
ejpam-6031	397	25	d	d	PROPN
ejpam-6031	397	26	)	)	PUNCT
ejpam-6031	397	27	)	)	PUNCT
ejpam-6031	397	28	)	)	PUNCT
ejpam-6031	398	1	=	=	PRON
ejpam-6031	398	2	ru,1	ru,1	NOUN
ejpam-6031	398	3	(	(	PUNCT
ejpam-6031	398	4	fix	fix	VERB
ejpam-6031	398	5	rv⊥,α	rv⊥,α	ADJ
ejpam-6031	398	6	)	)	PUNCT
ejpam-6031	399	1	=	=	SYM
ejpam-6031	400	1	ru,1	ru,1	NOUN
ejpam-6031	400	2	(	(	PUNCT
ejpam-6031	400	3	v⊥	v⊥	NOUN
ejpam-6031	400	4	)	)	PUNCT
ejpam-6031	400	5	,	,	PUNCT
ejpam-6031	400	6	as	as	SCONJ
ejpam-6031	400	7	required	require	VERB
ejpam-6031	400	8	.	.	PUNCT
ejpam-6031	401	1	(	(	PUNCT
ejpam-6031	401	2	viii	viii	ADJ
ejpam-6031	401	3	):	):	PUNCT
ejpam-6031	401	4	the	the	DET
ejpam-6031	401	5	proof	proof	NOUN
ejpam-6031	401	6	follows	follow	VERB
ejpam-6031	401	7	a	a	DET
ejpam-6031	401	8	similar	similar	ADJ
ejpam-6031	401	9	approach	approach	NOUN
ejpam-6031	401	10	as	as	ADP
ejpam-6031	401	11	in	in	ADP
ejpam-6031	401	12	(	(	PUNCT
ejpam-6031	401	13	vii	vii	PROPN
ejpam-6031	401	14	)	)	PUNCT
ejpam-6031	401	15	.	.	PUNCT
ejpam-6031	402	1	(	(	PUNCT
ejpam-6031	402	2	ix	ix	ADV
ejpam-6031	402	3	):	):	PUNCT
ejpam-6031	402	4	using	use	VERB
ejpam-6031	402	5	(	(	PUNCT
ejpam-6031	402	6	9	9	NUM
ejpam-6031	402	7	)	)	PUNCT
ejpam-6031	402	8	,	,	PUNCT
ejpam-6031	402	9	(	(	PUNCT
ejpam-6031	402	10	10	10	NUM
ejpam-6031	402	11	)	)	PUNCT
ejpam-6031	402	12	,	,	PUNCT
ejpam-6031	402	13	and	and	CCONJ
ejpam-6031	402	14	(	(	PUNCT
ejpam-6031	402	15	11	11	NUM
ejpam-6031	402	16	)	)	PUNCT
ejpam-6031	402	17	gives	give	VERB
ejpam-6031	402	18	ru	ru	PROPN
ejpam-6031	402	19	,	,	PUNCT
ejpam-6031	402	20	γrv	γrv	PROPN
ejpam-6031	402	21	,	,	PUNCT
ejpam-6031	402	22	αru⊥,β	αru⊥,β	NOUN
ejpam-6031	402	23	=	=	SYM
ejpam-6031	402	24	ru	ru	PROPN
ejpam-6031	402	25	,	,	PUNCT
ejpam-6031	402	26	γrv,1ru⊥,β	γrv,1ru⊥,β	PROPN
ejpam-6031	402	27	=	=	SYM
ejpam-6031	402	28	ru	ru	PROPN
ejpam-6031	402	29	,	,	PUNCT
ejpam-6031	402	30	γ	γ	X
ejpam-6031	402	31	(	(	PUNCT
ejpam-6031	402	32	4β	4β	NUM
ejpam-6031	402	33	pv	pv	NOUN
ejpam-6031	402	34	pu⊥	pu⊥	NUM
ejpam-6031	403	1	−2	−2	NOUN
ejpam-6031	403	2	pv	pv	INTJ
ejpam-6031	404	1	−2β	−2β	PUNCT
ejpam-6031	404	2	pu⊥	pu⊥	PROPN
ejpam-6031	404	3	+	+	CCONJ
ejpam-6031	404	4	i	i	PROPN
ejpam-6031	404	5	d	d	PROPN
ejpam-6031	404	6	)	)	PUNCT
ejpam-6031	405	1	=	=	PUNCT
ejpam-6031	405	2	(	(	PUNCT
ejpam-6031	405	3	2γ	2γ	X
ejpam-6031	405	4	pu	pu	PROPN
ejpam-6031	405	5	−	−	PROPN
ejpam-6031	405	6	i	i	PROPN
ejpam-6031	405	7	d	d	PROPN
ejpam-6031	405	8	)	)	PUNCT
ejpam-6031	405	9	(	(	PUNCT
ejpam-6031	405	10	4β	4β	NUM
ejpam-6031	405	11	pv	pv	NOUN
ejpam-6031	405	12	pu⊥	pu⊥	NUM
ejpam-6031	405	13	−2	−2	NOUN
ejpam-6031	405	14	pv	pv	INTJ
ejpam-6031	406	1	−2β	−2β	PUNCT
ejpam-6031	406	2	pu⊥	pu⊥	PROPN
ejpam-6031	406	3	+	+	CCONJ
ejpam-6031	406	4	i	i	PROPN
ejpam-6031	406	5	d	d	NOUN
ejpam-6031	406	6	)	)	PUNCT
ejpam-6031	407	1	=	=	SYM
ejpam-6031	408	1	8γβ	8γβ	ADJ
ejpam-6031	408	2	pu	pu	PROPN
ejpam-6031	408	3	pv	pv	INTJ
ejpam-6031	409	1	pu⊥	pu⊥	PROPN
ejpam-6031	409	2	−4γ	−4γ	PROPN
ejpam-6031	409	3	pu	pu	PROPN
ejpam-6031	409	4	pv	pv	PROPN
ejpam-6031	409	5	−4β	−4β	PROPN
ejpam-6031	409	6	pv	pv	INTJ
ejpam-6031	409	7	pu⊥	pu⊥	NOUN
ejpam-6031	409	8	+2	+2	PROPN
ejpam-6031	409	9	(	(	PUNCT
ejpam-6031	409	10	γ	γ	X
ejpam-6031	409	11	pu	pu	PROPN
ejpam-6031	409	12	+	+	PROPN
ejpam-6031	409	13	β	β	X
ejpam-6031	409	14	pu⊥	pu⊥	NOUN
ejpam-6031	409	15	+	+	PROPN
ejpam-6031	409	16	pv	pv	NOUN
ejpam-6031	409	17	)	)	PUNCT
ejpam-6031	410	1	−	−	PROPN
ejpam-6031	411	1	i	i	PROPN
ejpam-6031	411	2	d	d	PROPN
ejpam-6031	411	3	,	,	PUNCT
ejpam-6031	411	4	as	as	SCONJ
ejpam-6031	411	5	required	require	VERB
ejpam-6031	411	6	.	.	PUNCT
ejpam-6031	412	1	(	(	PUNCT
ejpam-6031	412	2	x	x	X
ejpam-6031	412	3	):	):	PUNCT
ejpam-6031	412	4	the	the	DET
ejpam-6031	412	5	proof	proof	NOUN
ejpam-6031	412	6	follows	follow	VERB
ejpam-6031	412	7	a	a	DET
ejpam-6031	412	8	similar	similar	ADJ
ejpam-6031	412	9	approach	approach	NOUN
ejpam-6031	412	10	as	as	ADP
ejpam-6031	412	11	in	in	ADP
ejpam-6031	412	12	(	(	PUNCT
ejpam-6031	412	13	ix	ix	ADJ
ejpam-6031	412	14	)	)	PUNCT
ejpam-6031	412	15	.	.	PUNCT
ejpam-6031	413	1	■	■	PUNCT
ejpam-6031	413	2	theorem	theorem	ADJ
ejpam-6031	413	3	3	3	X
ejpam-6031	413	4	.	.	PUNCT
ejpam-6031	414	1	let	let	VERB
ejpam-6031	414	2	x	x	PRON
ejpam-6031	414	3	,	,	PUNCT
ejpam-6031	414	4	y	y	PROPN
ejpam-6031	414	5	,	,	PUNCT
ejpam-6031	414	6	and	and	CCONJ
ejpam-6031	414	7	z	z	NOUN
ejpam-6031	414	8	be	be	AUX
ejpam-6031	414	9	closed	close	VERB
ejpam-6031	414	10	subspaces	subspace	NOUN
ejpam-6031	414	11	of	of	ADP
ejpam-6031	414	12	h.	h.	NOUN
ejpam-6031	414	13	suppose	suppose	VERB
ejpam-6031	414	14	that	that	SCONJ
ejpam-6031	414	15	β	β	NOUN
ejpam-6031	414	16	,	,	PUNCT
ejpam-6031	414	17	γ	γ	X
ejpam-6031	414	18	,	,	PUNCT
ejpam-6031	414	19	α	α	PRON
ejpam-6031	414	20	∈]0	∈]0	ADJ
ejpam-6031	414	21	,	,	PUNCT
ejpam-6031	414	22	1	1	NUM
ejpam-6031	414	23	]	]	PUNCT
ejpam-6031	414	24	and	and	CCONJ
ejpam-6031	414	25	recall	recall	VERB
ejpam-6031	414	26	from	from	ADP
ejpam-6031	414	27	(	(	PUNCT
ejpam-6031	414	28	9	9	NUM
ejpam-6031	414	29	)	)	PUNCT
ejpam-6031	414	30	the	the	DET
ejpam-6031	414	31	modified	modify	VERB
ejpam-6031	414	32	reflector	reflector	NOUN
ejpam-6031	414	33	operator	operator	NOUN
ejpam-6031	414	34	.	.	PUNCT
ejpam-6031	415	1	then	then	ADV
ejpam-6031	415	2	fix(rx	fix(rx	NOUN
ejpam-6031	415	3	,	,	PUNCT
ejpam-6031	415	4	αry	αry	NOUN
ejpam-6031	415	5	,	,	PUNCT
ejpam-6031	415	6	βrz	βrz	NOUN
ejpam-6031	415	7	,	,	PUNCT
ejpam-6031	415	8	γ	γ	NOUN
ejpam-6031	415	9	)	)	PUNCT
ejpam-6031	415	10	=	=	SYM
ejpam-6031	415	11	fix	fix	NOUN
ejpam-6031	415	12	(	(	PUNCT
ejpam-6031	415	13	α	α	X
ejpam-6031	415	14	px	px	PROPN
ejpam-6031	416	1	+	+	PROPN
ejpam-6031	416	2	β	β	X
ejpam-6031	416	3	py	py	NOUN
ejpam-6031	416	4	+	+	PROPN
ejpam-6031	416	5	γ	γ	X
ejpam-6031	416	6	pz	pz	ADJ
ejpam-6031	416	7	+4αβγ	+4αβγ	PROPN
ejpam-6031	416	8	px	px	PROPN
ejpam-6031	416	9	py	py	PROPN
ejpam-6031	416	10	pz	pz	PROPN
ejpam-6031	416	11	−2αβ	−2αβ	PROPN
ejpam-6031	416	12	px	px	PROPN
ejpam-6031	416	13	py	py	PROPN
ejpam-6031	416	14	−	−	PROPN
ejpam-6031	416	15	2αγ	2αγ	PROPN
ejpam-6031	417	1	px	px	PROPN
ejpam-6031	417	2	pz	pz	PROPN
ejpam-6031	417	3	−2βγ	−2βγ	PROPN
ejpam-6031	417	4	py	py	PROPN
ejpam-6031	417	5	pz	pz	PROPN
ejpam-6031	417	6	)	)	PUNCT
ejpam-6031	417	7	and	and	CCONJ
ejpam-6031	417	8	fix(rx	fix(rx	NOUN
ejpam-6031	417	9	,	,	PUNCT
ejpam-6031	417	10	αry	αry	NOUN
ejpam-6031	417	11	,	,	PUNCT
ejpam-6031	417	12	βrz	βrz	NOUN
ejpam-6031	417	13	,	,	PUNCT
ejpam-6031	417	14	γ	γ	NOUN
ejpam-6031	417	15	)	)	PUNCT
ejpam-6031	417	16	⊆	⊆	NUM
ejpam-6031	417	17	x	x	SYM
ejpam-6031	418	1	+	+	PUNCT
ejpam-6031	418	2	y	y	PROPN
ejpam-6031	418	3	+	+	NUM
ejpam-6031	418	4	z	z	NOUN
ejpam-6031	418	5	(	(	PUNCT
ejpam-6031	418	6	12	12	NUM
ejpam-6031	418	7	)	)	PUNCT
ejpam-6031	418	8	proof	proof	NOUN
ejpam-6031	418	9	.	.	PUNCT
ejpam-6031	419	1	using	use	VERB
ejpam-6031	419	2	(	(	PUNCT
ejpam-6031	419	3	9	9	NUM
ejpam-6031	419	4	)	)	PUNCT
ejpam-6031	419	5	implies	imply	VERB
ejpam-6031	419	6	that	that	SCONJ
ejpam-6031	419	7	ry	ry	NOUN
ejpam-6031	419	8	,	,	PUNCT
ejpam-6031	419	9	βrz	βrz	PROPN
ejpam-6031	419	10	,	,	PUNCT
ejpam-6031	419	11	γ	γ	X
ejpam-6031	419	12	=	=	X
ejpam-6031	419	13	(	(	PUNCT
ejpam-6031	419	14	2β	2β	NUM
ejpam-6031	420	1	py	py	INTJ
ejpam-6031	420	2	−	−	PROPN
ejpam-6031	420	3	i	i	PROPN
ejpam-6031	420	4	d	d	PROPN
ejpam-6031	420	5	)	)	PUNCT
ejpam-6031	420	6	(	(	PUNCT
ejpam-6031	420	7	2γ	2γ	X
ejpam-6031	420	8	pz	pz	NOUN
ejpam-6031	420	9	−	−	PROPN
ejpam-6031	420	10	i	i	PROPN
ejpam-6031	420	11	d	d	PROPN
ejpam-6031	420	12	)	)	PUNCT
ejpam-6031	421	1	=	=	PUNCT
ejpam-6031	421	2	4βγ	4βγ	ADJ
ejpam-6031	421	3	py	py	INTJ
ejpam-6031	421	4	pz	pz	INTJ
ejpam-6031	421	5	−2β	−2β	PROPN
ejpam-6031	421	6	py	py	PROPN
ejpam-6031	421	7	−2γ	−2γ	PROPN
ejpam-6031	421	8	pz	pz	NOUN
ejpam-6031	422	1	+	+	CCONJ
ejpam-6031	422	2	i	i	PROPN
ejpam-6031	422	3	d	d	PROPN
ejpam-6031	422	4	.	.	PUNCT
ejpam-6031	423	1	next	next	ADV
ejpam-6031	423	2	,	,	PUNCT
ejpam-6031	423	3	rx	rx	VERB
ejpam-6031	423	4	,	,	PUNCT
ejpam-6031	423	5	α	α	PROPN
ejpam-6031	423	6	(	(	PUNCT
ejpam-6031	423	7	4βγ	4βγ	ADJ
ejpam-6031	423	8	py	py	INTJ
ejpam-6031	423	9	pz	pz	PROPN
ejpam-6031	424	1	−2β	−2β	PROPN
ejpam-6031	424	2	py	py	PROPN
ejpam-6031	424	3	−2γ	−2γ	PROPN
ejpam-6031	424	4	pz	pz	NOUN
ejpam-6031	424	5	+	+	CCONJ
ejpam-6031	424	6	i	i	PROPN
ejpam-6031	424	7	d	d	NOUN
ejpam-6031	424	8	)	)	PUNCT
ejpam-6031	425	1	=	=	PUNCT
ejpam-6031	425	2	(	(	PUNCT
ejpam-6031	425	3	2α	2α	NOUN
ejpam-6031	425	4	px	px	PROPN
ejpam-6031	425	5	−	−	PROPN
ejpam-6031	426	1	i	i	PROPN
ejpam-6031	426	2	d	d	PROPN
ejpam-6031	426	3	)	)	PUNCT
ejpam-6031	426	4	(	(	PUNCT
ejpam-6031	426	5	4βγ	4βγ	ADJ
ejpam-6031	426	6	py	py	INTJ
ejpam-6031	426	7	pz	pz	PROPN
ejpam-6031	427	1	−2β	−2β	PROPN
ejpam-6031	427	2	py	py	PROPN
ejpam-6031	427	3	−2γ	−2γ	PROPN
ejpam-6031	427	4	pz	pz	NOUN
ejpam-6031	427	5	+	+	CCONJ
ejpam-6031	427	6	i	i	PROPN
ejpam-6031	427	7	d	d	PROPN
ejpam-6031	427	8	)	)	PUNCT
ejpam-6031	427	9	s.th	s.th	PROPN
ejpam-6031	427	10	.	.	PUNCT
ejpam-6031	427	11	alwadani	alwadani	PROPN
ejpam-6031	427	12	/	/	SYM
ejpam-6031	427	13	eur	eur	PROPN
ejpam-6031	427	14	.	.	PUNCT
ejpam-6031	428	1	j.	j.	PROPN
ejpam-6031	428	2	pure	pure	PROPN
ejpam-6031	428	3	appl	appl	PROPN
ejpam-6031	428	4	.	.	PROPN
ejpam-6031	428	5	math	math	PROPN
ejpam-6031	428	6	,	,	PUNCT
ejpam-6031	428	7	18	18	NUM
ejpam-6031	428	8	(	(	PUNCT
ejpam-6031	428	9	2	2	NUM
ejpam-6031	428	10	)	)	PUNCT
ejpam-6031	428	11	(	(	PUNCT
ejpam-6031	428	12	2025	2025	NUM
ejpam-6031	428	13	)	)	PUNCT
ejpam-6031	428	14	,	,	PUNCT
ejpam-6031	428	15	6031	6031	NUM
ejpam-6031	428	16	12	12	NUM
ejpam-6031	428	17	of	of	ADP
ejpam-6031	428	18	13	13	NUM
ejpam-6031	428	19	=	=	SYM
ejpam-6031	428	20	2α	2α	NOUN
ejpam-6031	429	1	px	px	X
ejpam-6031	429	2	+2β	+2β	NUM
ejpam-6031	429	3	py	py	PROPN
ejpam-6031	429	4	+2γ	+2γ	PROPN
ejpam-6031	429	5	pz	pz	NOUN
ejpam-6031	429	6	+8αβγ	+8αβγ	PROPN
ejpam-6031	429	7	px	px	PROPN
ejpam-6031	429	8	py	py	PROPN
ejpam-6031	429	9	pz	pz	PROPN
ejpam-6031	429	10	−4αβ	−4αβ	PRON
ejpam-6031	429	11	px	px	X
ejpam-6031	429	12	py	py	PROPN
ejpam-6031	429	13	−	−	PROPN
ejpam-6031	429	14	4αγ	4αγ	PROPN
ejpam-6031	429	15	px	px	PROPN
ejpam-6031	429	16	pz	pz	PROPN
ejpam-6031	429	17	−4βγ	−4βγ	PROPN
ejpam-6031	429	18	py	py	INTJ
ejpam-6031	429	19	pz	pz	NOUN
ejpam-6031	429	20	−	−	PROPN
ejpam-6031	429	21	i	i	PROPN
ejpam-6031	429	22	d	d	PROPN
ejpam-6031	429	23	.	.	PUNCT
ejpam-6031	430	1	therefore	therefore	ADV
ejpam-6031	430	2	,	,	PUNCT
ejpam-6031	430	3	rx	rx	VERB
ejpam-6031	430	4	,	,	PUNCT
ejpam-6031	430	5	αry	αry	NOUN
ejpam-6031	430	6	,	,	PUNCT
ejpam-6031	430	7	βrz	βrz	NOUN
ejpam-6031	430	8	,	,	PUNCT
ejpam-6031	430	9	γ	γ	X
ejpam-6031	430	10	=	=	SYM
ejpam-6031	430	11	2α	2α	NOUN
ejpam-6031	431	1	px	px	X
ejpam-6031	431	2	+2β	+2β	NUM
ejpam-6031	431	3	py	py	PROPN
ejpam-6031	431	4	+2γ	+2γ	PROPN
ejpam-6031	431	5	pz	pz	NOUN
ejpam-6031	431	6	+8αβγ	+8αβγ	PROPN
ejpam-6031	431	7	px	px	PROPN
ejpam-6031	431	8	py	py	PROPN
ejpam-6031	431	9	pz	pz	PROPN
ejpam-6031	431	10	−4αβ	−4αβ	PRON
ejpam-6031	431	11	px	px	PROPN
ejpam-6031	431	12	py	py	PROPN
ejpam-6031	431	13	−4αγ	−4αγ	PROPN
ejpam-6031	431	14	px	px	PROPN
ejpam-6031	431	15	pz	pz	PROPN
ejpam-6031	431	16	−	−	PROPN
ejpam-6031	431	17	4βγ	4βγ	NOUN
ejpam-6031	432	1	py	py	INTJ
ejpam-6031	432	2	pz	pz	NOUN
ejpam-6031	432	3	−	−	PROPN
ejpam-6031	433	1	i	i	PROPN
ejpam-6031	433	2	d	d	PROPN
ejpam-6031	433	3	.	.	PUNCT
ejpam-6031	434	1	let	let	VERB
ejpam-6031	434	2	x	x	PUNCT
ejpam-6031	434	3	∈	∈	PROPN
ejpam-6031	434	4	fix	fix	NOUN
ejpam-6031	434	5	(	(	PUNCT
ejpam-6031	434	6	rx	rx	ADJ
ejpam-6031	434	7	,	,	PUNCT
ejpam-6031	434	8	αry	αry	NOUN
ejpam-6031	434	9	,	,	PUNCT
ejpam-6031	434	10	βrz	βrz	NOUN
ejpam-6031	434	11	,	,	PUNCT
ejpam-6031	434	12	γ	γ	NOUN
ejpam-6031	434	13	)	)	PUNCT
ejpam-6031	434	14	.	.	PUNCT
ejpam-6031	435	1	then	then	ADV
ejpam-6031	435	2	we	we	PRON
ejpam-6031	435	3	obtain	obtain	VERB
ejpam-6031	435	4	x	x	ADP
ejpam-6031	435	5	=	=	SYM
ejpam-6031	435	6	rx	rx	ADJ
ejpam-6031	435	7	,	,	PUNCT
ejpam-6031	435	8	αry	αry	NOUN
ejpam-6031	435	9	,	,	PUNCT
ejpam-6031	435	10	βrz	βrz	NOUN
ejpam-6031	435	11	,	,	PUNCT
ejpam-6031	435	12	γ(x	γ(x	NOUN
ejpam-6031	435	13	)	)	PUNCT
ejpam-6031	435	14	⇔	⇔	X
ejpam-6031	435	15	2x	2x	NUM
ejpam-6031	435	16	=	=	NOUN
ejpam-6031	435	17	2α	2α	NOUN
ejpam-6031	435	18	px(x	px(x	ADV
ejpam-6031	435	19	)	)	PUNCT
ejpam-6031	436	1	+	+	CCONJ
ejpam-6031	436	2	2β	2β	NOUN
ejpam-6031	436	3	py(x	py(x	NOUN
ejpam-6031	436	4	)	)	PUNCT
ejpam-6031	436	5	+	+	CCONJ
ejpam-6031	436	6	2γ	2γ	NOUN
ejpam-6031	436	7	pz(x	pz(x	ADJ
ejpam-6031	436	8	)	)	PUNCT
ejpam-6031	436	9	+	+	CCONJ
ejpam-6031	436	10	8αβγ	8αβγ	PROPN
ejpam-6031	436	11	px	px	NOUN
ejpam-6031	436	12	py	py	INTJ
ejpam-6031	436	13	pz(x)−	pz(x)−	PROPN
ejpam-6031	436	14	4αβ	4αβ	PROPN
ejpam-6031	436	15	px	px	PROPN
ejpam-6031	436	16	py(x	py(x	NOUN
ejpam-6031	436	17	)	)	PUNCT
ejpam-6031	436	18	−	−	PROPN
ejpam-6031	436	19	4αγ	4αγ	NOUN
ejpam-6031	437	1	px	px	VERB
ejpam-6031	437	2	pz(x)−	pz(x)−	PROPN
ejpam-6031	437	3	4βγ	4βγ	PROPN
ejpam-6031	437	4	py	py	ADP
ejpam-6031	437	5	pz(x	pz(x	NOUN
ejpam-6031	437	6	)	)	PUNCT
ejpam-6031	437	7	⇔	⇔	NOUN
ejpam-6031	437	8	x	x	X
ejpam-6031	437	9	=	=	SYM
ejpam-6031	437	10	α	α	NOUN
ejpam-6031	437	11	px(x	px(x	PUNCT
ejpam-6031	437	12	)	)	PUNCT
ejpam-6031	438	1	+	+	CCONJ
ejpam-6031	438	2	β	β	X
ejpam-6031	438	3	py(x	py(x	NOUN
ejpam-6031	438	4	)	)	PUNCT
ejpam-6031	438	5	+	+	CCONJ
ejpam-6031	438	6	γ	γ	NOUN
ejpam-6031	438	7	pz(x	pz(x	ADJ
ejpam-6031	438	8	)	)	PUNCT
ejpam-6031	438	9	+	+	CCONJ
ejpam-6031	439	1	4αβγ	4αβγ	PROPN
ejpam-6031	439	2	px	px	INTJ
ejpam-6031	439	3	py	py	INTJ
ejpam-6031	439	4	pz(x)−	pz(x)−	PROPN
ejpam-6031	439	5	2αβ	2αβ	PROPN
ejpam-6031	439	6	px	px	PROPN
ejpam-6031	439	7	py(x	py(x	NOUN
ejpam-6031	439	8	)	)	PUNCT
ejpam-6031	439	9	−	−	NUM
ejpam-6031	439	10	2αγ	2αγ	NOUN
ejpam-6031	439	11	px	px	VERB
ejpam-6031	439	12	pz(x)−	pz(x)−	PROPN
ejpam-6031	439	13	2βγ	2βγ	NOUN
ejpam-6031	439	14	py	py	PROPN
ejpam-6031	439	15	pz(x	pz(x	NOUN
ejpam-6031	439	16	)	)	PUNCT
ejpam-6031	439	17	as	as	ADP
ejpam-6031	439	18	a	a	DET
ejpam-6031	439	19	result	result	NOUN
ejpam-6031	439	20	,	,	PUNCT
ejpam-6031	439	21	fix(rx	fix(rx	ADJ
ejpam-6031	439	22	,	,	PUNCT
ejpam-6031	439	23	αry	αry	NOUN
ejpam-6031	439	24	,	,	PUNCT
ejpam-6031	439	25	βrz	βrz	NOUN
ejpam-6031	439	26	,	,	PUNCT
ejpam-6031	439	27	γ	γ	NOUN
ejpam-6031	439	28	)	)	PUNCT
ejpam-6031	439	29	=	=	SYM
ejpam-6031	439	30	fix	fix	NOUN
ejpam-6031	439	31	(	(	PUNCT
ejpam-6031	439	32	α	α	X
ejpam-6031	439	33	px	px	PROPN
ejpam-6031	440	1	+	+	PROPN
ejpam-6031	440	2	β	β	X
ejpam-6031	440	3	py	py	NOUN
ejpam-6031	440	4	+	+	PROPN
ejpam-6031	440	5	γ	γ	X
ejpam-6031	440	6	pz	pz	ADJ
ejpam-6031	440	7	+4αβγ	+4αβγ	PROPN
ejpam-6031	440	8	px	px	PROPN
ejpam-6031	440	9	py	py	PROPN
ejpam-6031	440	10	pz	pz	PROPN
ejpam-6031	440	11	−2αβ	−2αβ	PROPN
ejpam-6031	440	12	px	px	PROPN
ejpam-6031	440	13	py	py	PROPN
ejpam-6031	440	14	−	−	PROPN
ejpam-6031	440	15	2αγ	2αγ	PROPN
ejpam-6031	441	1	px	px	PROPN
ejpam-6031	441	2	pz	pz	PROPN
ejpam-6031	441	3	−2βγ	−2βγ	PROPN
ejpam-6031	441	4	py	py	PROPN
ejpam-6031	441	5	pz	pz	PROPN
ejpam-6031	441	6	)	)	PUNCT
ejpam-6031	441	7	consequently	consequently	ADV
ejpam-6031	441	8	,	,	PUNCT
ejpam-6031	441	9	fix(rx	fix(rx	ADJ
ejpam-6031	441	10	,	,	PUNCT
ejpam-6031	441	11	αry	αry	NOUN
ejpam-6031	441	12	,	,	PUNCT
ejpam-6031	441	13	βrz	βrz	NOUN
ejpam-6031	441	14	,	,	PUNCT
ejpam-6031	441	15	γ	γ	NOUN
ejpam-6031	441	16	)	)	PUNCT
ejpam-6031	441	17	⊆	⊆	NUM
ejpam-6031	441	18	x	x	SYM
ejpam-6031	442	1	+	+	NUM
ejpam-6031	442	2	y	y	PROPN
ejpam-6031	443	1	+	+	PROPN
ejpam-6031	443	2	z.	z.	PROPN
ejpam-6031	443	3	■	■	PUNCT
ejpam-6031	443	4	references	reference	NOUN
ejpam-6031	443	5	[	[	X
ejpam-6031	443	6	1	1	NUM
ejpam-6031	443	7	]	]	PUNCT
ejpam-6031	443	8	oluwatayomi	oluwatayomi	NOUN
ejpam-6031	443	9	rereloluwa	rereloluwa	PROPN
ejpam-6031	443	10	adegboye	adegboye	PROPN
ejpam-6031	443	11	,	,	PUNCT
ejpam-6031	443	12	afi	afi	PROPN
ejpam-6031	443	13	kekeli	kekeli	PROPN
ejpam-6031	443	14	feda	feda	PROPN
ejpam-6031	443	15	,	,	PUNCT
ejpam-6031	443	16	opeoluwa	opeoluwa	ADJ
ejpam-6031	443	17	seun	seun	NOUN
ejpam-6031	443	18	ojekemi	ojekemi	PROPN
ejpam-6031	443	19	,	,	PUNCT
ejpam-6031	443	20	ephraim	ephraim	PROPN
ejpam-6031	443	21	bonah	bonah	PROPN
ejpam-6031	443	22	agyekum	agyekum	PROPN
ejpam-6031	443	23	,	,	PUNCT
ejpam-6031	443	24	abdelazim	abdelazim	VERB
ejpam-6031	443	25	g	g	PROPN
ejpam-6031	443	26	hussien	hussien	PROPN
ejpam-6031	443	27	,	,	PUNCT
ejpam-6031	443	28	and	and	CCONJ
ejpam-6031	443	29	salah	salah	PROPN
ejpam-6031	443	30	kamel	kamel	PROPN
ejpam-6031	443	31	.	.	PUNCT
ejpam-6031	444	1	chaotic	chaotic	ADJ
ejpam-6031	444	2	opposition	opposition	NOUN
ejpam-6031	444	3	learning	learn	VERB
ejpam-6031	444	4	with	with	ADP
ejpam-6031	444	5	mirror	mirror	NOUN
ejpam-6031	444	6	reflection	reflection	NOUN
ejpam-6031	444	7	and	and	CCONJ
ejpam-6031	444	8	worst	bad	ADJ
ejpam-6031	444	9	individual	individual	ADJ
ejpam-6031	444	10	disturbance	disturbance	NOUN
ejpam-6031	444	11	grey	grey	ADJ
ejpam-6031	444	12	wolf	wolf	PROPN
ejpam-6031	444	13	optimizer	optimizer	NOUN
ejpam-6031	444	14	for	for	ADP
ejpam-6031	444	15	continuous	continuous	ADJ
ejpam-6031	444	16	global	global	ADJ
ejpam-6031	444	17	numerical	numerical	PROPN
ejpam-6031	444	18	optimization	optimization	NOUN
ejpam-6031	444	19	.	.	PUNCT
ejpam-6031	445	1	scientific	scientific	ADJ
ejpam-6031	445	2	reports	report	NOUN
ejpam-6031	445	3	,	,	PUNCT
ejpam-6031	445	4	14(1):4660	14(1):4660	NUM
ejpam-6031	445	5	,	,	PUNCT
ejpam-6031	445	6	2024	2024	NUM
ejpam-6031	445	7	.	.	PUNCT
ejpam-6031	446	1	[	[	X
ejpam-6031	446	2	2	2	NUM
ejpam-6031	446	3	]	]	PUNCT
ejpam-6031	446	4	heinz	heinz	ADJ
ejpam-6031	446	5	h	h	PROPN
ejpam-6031	446	6	bauschke	bauschke	PROPN
ejpam-6031	446	7	,	,	PUNCT
ejpam-6031	446	8	patrick	patrick	PROPN
ejpam-6031	446	9	l	l	PROPN
ejpam-6031	446	10	combettes	combettes	PROPN
ejpam-6031	446	11	,	,	PUNCT
ejpam-6031	446	12	heinz	heinz	ADJ
ejpam-6031	446	13	h	h	NOUN
ejpam-6031	446	14	bauschke	bauschke	NOUN
ejpam-6031	446	15	,	,	PUNCT
ejpam-6031	446	16	and	and	CCONJ
ejpam-6031	446	17	patrick	patrick	PROPN
ejpam-6031	446	18	l	l	PROPN
ejpam-6031	446	19	combettes	combettes	PROPN
ejpam-6031	446	20	.	.	PUNCT
ejpam-6031	446	21	correction	correction	NOUN
ejpam-6031	446	22	to	to	PART
ejpam-6031	446	23	:	:	PUNCT
ejpam-6031	446	24	convex	convex	VERB
ejpam-6031	446	25	analysis	analysis	NOUN
ejpam-6031	446	26	and	and	CCONJ
ejpam-6031	446	27	monotone	monotone	ADJ
ejpam-6031	446	28	operator	operator	NOUN
ejpam-6031	446	29	theory	theory	NOUN
ejpam-6031	446	30	in	in	ADP
ejpam-6031	446	31	hilbert	hilbert	PROPN
ejpam-6031	446	32	spaces	space	NOUN
ejpam-6031	446	33	.	.	PUNCT
ejpam-6031	447	1	springer	springer	NOUN
ejpam-6031	447	2	,	,	PUNCT
ejpam-6031	447	3	2017	2017	NUM
ejpam-6031	447	4	.	.	PUNCT
ejpam-6031	448	1	[	[	X
ejpam-6031	448	2	3	3	X
ejpam-6031	448	3	]	]	X
ejpam-6031	448	4	andrzej	andrzej	PROPN
ejpam-6031	448	5	cegielski	cegielski	PROPN
ejpam-6031	448	6	.	.	PUNCT
ejpam-6031	449	1	iterative	iterative	NOUN
ejpam-6031	449	2	methods	method	NOUN
ejpam-6031	449	3	for	for	ADP
ejpam-6031	449	4	fixed	fix	VERB
ejpam-6031	449	5	point	point	NOUN
ejpam-6031	449	6	problems	problem	NOUN
ejpam-6031	449	7	in	in	ADP
ejpam-6031	449	8	hilbert	hilbert	PROPN
ejpam-6031	449	9	spaces	space	NOUN
ejpam-6031	449	10	,	,	PUNCT
ejpam-6031	449	11	volume	volume	NOUN
ejpam-6031	449	12	2057	2057	NUM
ejpam-6031	449	13	.	.	PUNCT
ejpam-6031	450	1	springer	springer	NOUN
ejpam-6031	450	2	,	,	PUNCT
ejpam-6031	450	3	2012	2012	NUM
ejpam-6031	450	4	.	.	PUNCT
ejpam-6031	451	1	[	[	X
ejpam-6031	451	2	4	4	X
ejpam-6031	451	3	]	]	X
ejpam-6031	451	4	john	john	PROPN
ejpam-6031	451	5	b	b	PROPN
ejpam-6031	451	6	conway	conway	PROPN
ejpam-6031	451	7	.	.	PUNCT
ejpam-6031	452	1	a	a	DET
ejpam-6031	452	2	course	course	NOUN
ejpam-6031	452	3	in	in	ADP
ejpam-6031	452	4	functional	functional	ADJ
ejpam-6031	452	5	analysis	analysis	NOUN
ejpam-6031	452	6	,	,	PUNCT
ejpam-6031	452	7	volume	volume	NOUN
ejpam-6031	452	8	96	96	NUM
ejpam-6031	452	9	.	.	PUNCT
ejpam-6031	452	10	springer	springer	NOUN
ejpam-6031	452	11	,	,	PUNCT
ejpam-6031	452	12	2019	2019	NUM
ejpam-6031	452	13	.	.	PUNCT
ejpam-6031	453	1	[	[	X
ejpam-6031	453	2	5	5	X
ejpam-6031	453	3	]	]	X
ejpam-6031	453	4	jonathan	jonathan	PROPN
ejpam-6031	453	5	eckstein	eckstein	PROPN
ejpam-6031	453	6	and	and	CCONJ
ejpam-6031	453	7	dimitri	dimitri	PROPN
ejpam-6031	453	8	p	p	PROPN
ejpam-6031	453	9	bertsekas	bertsekas	PROPN
ejpam-6031	453	10	.	.	PUNCT
ejpam-6031	454	1	on	on	ADP
ejpam-6031	454	2	the	the	DET
ejpam-6031	454	3	douglas	douglas	PROPN
ejpam-6031	454	4	—	—	PUNCT
ejpam-6031	454	5	rachford	rachford	ADJ
ejpam-6031	454	6	splitting	splitting	NOUN
ejpam-6031	454	7	method	method	NOUN
ejpam-6031	454	8	and	and	CCONJ
ejpam-6031	454	9	the	the	DET
ejpam-6031	454	10	proximal	proximal	ADJ
ejpam-6031	454	11	point	point	NOUN
ejpam-6031	454	12	algorithm	algorithm	NOUN
ejpam-6031	454	13	for	for	ADP
ejpam-6031	454	14	maximal	maximal	ADJ
ejpam-6031	454	15	monotone	monotone	ADJ
ejpam-6031	454	16	operators	operator	NOUN
ejpam-6031	454	17	.	.	PUNCT
ejpam-6031	455	1	mathematical	mathematical	ADJ
ejpam-6031	455	2	programming	programming	NOUN
ejpam-6031	455	3	,	,	PUNCT
ejpam-6031	455	4	55:293–318	55:293–318	NUM
ejpam-6031	455	5	,	,	PUNCT
ejpam-6031	455	6	1992	1992	NUM
ejpam-6031	455	7	.	.	PUNCT
ejpam-6031	456	1	s.th	s.th	PROPN
ejpam-6031	456	2	.	.	PUNCT
ejpam-6031	456	3	alwadani	alwadani	PROPN
ejpam-6031	456	4	/	/	SYM
ejpam-6031	456	5	eur	eur	PROPN
ejpam-6031	456	6	.	.	PUNCT
ejpam-6031	457	1	j.	j.	PROPN
ejpam-6031	457	2	pure	pure	PROPN
ejpam-6031	457	3	appl	appl	PROPN
ejpam-6031	457	4	.	.	PROPN
ejpam-6031	457	5	math	math	PROPN
ejpam-6031	457	6	,	,	PUNCT
ejpam-6031	457	7	18	18	NUM
ejpam-6031	457	8	(	(	PUNCT
ejpam-6031	457	9	2	2	NUM
ejpam-6031	457	10	)	)	PUNCT
ejpam-6031	457	11	(	(	PUNCT
ejpam-6031	457	12	2025	2025	NUM
ejpam-6031	457	13	)	)	PUNCT
ejpam-6031	457	14	,	,	PUNCT
ejpam-6031	457	15	6031	6031	NUM
ejpam-6031	457	16	13	13	NUM
ejpam-6031	457	17	of	of	ADP
ejpam-6031	457	18	13	13	NUM
ejpam-6031	457	19	[	[	SYM
ejpam-6031	457	20	6	6	NUM
ejpam-6031	457	21	]	]	X
ejpam-6031	457	22	robert	robert	PROPN
ejpam-6031	457	23	e	e	PROPN
ejpam-6031	457	24	megginson	megginson	PROPN
ejpam-6031	457	25	.	.	PUNCT
ejpam-6031	458	1	a	a	DET
ejpam-6031	458	2	course	course	NOUN
ejpam-6031	458	3	in	in	ADP
ejpam-6031	458	4	functional	functional	ADJ
ejpam-6031	458	5	analysis	analysis	NOUN
ejpam-6031	458	6	.	.	PUNCT
ejpam-6031	459	1	[	[	X
ejpam-6031	459	2	7	7	X
ejpam-6031	459	3	]	]	X
ejpam-6031	459	4	mustafa	mustafa	PROPN
ejpam-6031	459	5	nurmuhammed	nurmuhammed	PROPN
ejpam-6031	459	6	,	,	PUNCT
ejpam-6031	459	7	ozan	ozan	PROPN
ejpam-6031	459	8	akdağ	akdağ	PROPN
ejpam-6031	459	9	,	,	PUNCT
ejpam-6031	459	10	and	and	CCONJ
ejpam-6031	459	11	teoman	teoman	NOUN
ejpam-6031	459	12	karadağ.	karadağ.	PROPN
ejpam-6031	459	13	modified	modify	VERB
ejpam-6031	459	14	archimedes	archimedes	PROPN
ejpam-6031	459	15	optimization	optimization	NOUN
ejpam-6031	459	16	algorithm	algorithm	NOUN
ejpam-6031	459	17	for	for	ADP
ejpam-6031	459	18	global	global	ADJ
ejpam-6031	459	19	optimization	optimization	NOUN
ejpam-6031	459	20	problems	problem	NOUN
ejpam-6031	459	21	:	:	PUNCT
ejpam-6031	459	22	a	a	DET
ejpam-6031	459	23	comparative	comparative	ADJ
ejpam-6031	459	24	study	study	NOUN
ejpam-6031	459	25	.	.	PUNCT
ejpam-6031	460	1	neural	neural	ADJ
ejpam-6031	460	2	computing	computing	NOUN
ejpam-6031	460	3	and	and	CCONJ
ejpam-6031	460	4	applications	application	NOUN
ejpam-6031	460	5	,	,	PUNCT
ejpam-6031	460	6	36(14):8007–8038	36(14):8007–8038	PROPN
ejpam-6031	460	7	,	,	PUNCT
ejpam-6031	460	8	2024	2024	NUM
ejpam-6031	460	9	.	.	PUNCT
ejpam-6031	461	1	[	[	X
ejpam-6031	461	2	8	8	X
ejpam-6031	461	3	]	]	X
ejpam-6031	461	4	chao	chao	PROPN
ejpam-6031	461	5	qian	qian	PROPN
ejpam-6031	461	6	,	,	PUNCT
ejpam-6031	461	7	ido	ido	PROPN
ejpam-6031	461	8	kaminer	kaminer	NOUN
ejpam-6031	461	9	,	,	PUNCT
ejpam-6031	461	10	and	and	CCONJ
ejpam-6031	461	11	hongsheng	hongsheng	PROPN
ejpam-6031	461	12	chen	chen	PROPN
ejpam-6031	461	13	.	.	PUNCT
ejpam-6031	462	1	a	a	DET
ejpam-6031	462	2	guidance	guidance	NOUN
ejpam-6031	462	3	to	to	ADP
ejpam-6031	462	4	intelligent	intelligent	ADJ
ejpam-6031	462	5	metamaterials	metamaterial	NOUN
ejpam-6031	462	6	and	and	CCONJ
ejpam-6031	462	7	metamaterials	metamaterial	NOUN
ejpam-6031	462	8	intelligence	intelligence	NOUN
ejpam-6031	462	9	.	.	PUNCT
ejpam-6031	463	1	nature	nature	NOUN
ejpam-6031	463	2	communications	communication	NOUN
ejpam-6031	463	3	,	,	PUNCT
ejpam-6031	463	4	16(1):1154	16(1):1154	NUM
ejpam-6031	463	5	,	,	PUNCT
ejpam-6031	463	6	2025	2025	NUM
ejpam-6031	463	7	.	.	PUNCT
ejpam-6031	464	1	[	[	X
ejpam-6031	464	2	9	9	NUM
ejpam-6031	464	3	]	]	PUNCT
ejpam-6031	464	4	salihah	salihah	ADJ
ejpam-6031	464	5	thabet	thabet	ADJ
ejpam-6031	464	6	alwadani	alwadani	ADJ
ejpam-6031	464	7	.	.	PUNCT
ejpam-6031	465	1	on	on	ADP
ejpam-6031	465	2	the	the	DET
ejpam-6031	465	3	behaviour	behaviour	NOUN
ejpam-6031	465	4	of	of	ADP
ejpam-6031	465	5	algorithms	algorithm	NOUN
ejpam-6031	465	6	featuring	feature	VERB
ejpam-6031	465	7	compositions	composition	NOUN
ejpam-6031	465	8	of	of	ADP
ejpam-6031	465	9	projectors	projector	NOUN
ejpam-6031	465	10	and	and	CCONJ
ejpam-6031	465	11	proximal	proximal	ADJ
ejpam-6031	465	12	mappings	mapping	NOUN
ejpam-6031	465	13	with	with	ADP
ejpam-6031	465	14	no	no	DET
ejpam-6031	465	15	solutions	solution	NOUN
ejpam-6031	465	16	.	.	PUNCT
ejpam-6031	466	1	phd	phd	NOUN
ejpam-6031	466	2	thesis	thesis	PROPN
ejpam-6031	466	3	,	,	PUNCT
ejpam-6031	466	4	university	university	PROPN
ejpam-6031	466	5	of	of	ADP
ejpam-6031	466	6	british	british	PROPN
ejpam-6031	466	7	columbia	columbia	PROPN
ejpam-6031	466	8	,	,	PUNCT
ejpam-6031	466	9	2021	2021	NUM
ejpam-6031	466	10	.	.	PUNCT
ejpam-6031	467	1	[	[	X
ejpam-6031	467	2	10	10	NUM
ejpam-6031	467	3	]	]	X
ejpam-6031	467	4	salihah	salihah	ADJ
ejpam-6031	467	5	alwadani	alwadani	ADJ
ejpam-6031	467	6	,	,	PUNCT
ejpam-6031	467	7	heinz	heinz	PROPN
ejpam-6031	467	8	h	h	NOUN
ejpam-6031	467	9	bauschke	bauschke	NOUN
ejpam-6031	467	10	,	,	PUNCT
ejpam-6031	467	11	and	and	CCONJ
ejpam-6031	467	12	xianfu	xianfu	PROPN
ejpam-6031	467	13	wang	wang	PROPN
ejpam-6031	467	14	.	.	PUNCT
ejpam-6031	468	1	fixed	fix	VERB
ejpam-6031	468	2	points	point	NOUN
ejpam-6031	468	3	of	of	ADP
ejpam-6031	468	4	compositions	composition	NOUN
ejpam-6031	468	5	of	of	ADP
ejpam-6031	468	6	nonexpansive	nonexpansive	ADJ
ejpam-6031	468	7	mappings	mapping	NOUN
ejpam-6031	468	8	:	:	PUNCT
ejpam-6031	468	9	finitely	finitely	ADV
ejpam-6031	468	10	many	many	ADJ
ejpam-6031	468	11	linear	linear	ADJ
ejpam-6031	468	12	reflectors	reflector	NOUN
ejpam-6031	468	13	.	.	PUNCT
ejpam-6031	469	1	arxiv	arxiv	PROPN
ejpam-6031	469	2	preprint	preprint	PROPN
ejpam-6031	469	3	arxiv:2004.12582	arxiv:2004.12582	PROPN
ejpam-6031	469	4	,	,	PUNCT
ejpam-6031	469	5	2020	2020	NUM
ejpam-6031	469	6	.	.	PUNCT
ejpam-6031	470	1	[	[	X
ejpam-6031	470	2	11	11	NUM
ejpam-6031	470	3	]	]	X
ejpam-6031	470	4	heinz	heinz	PROPN
ejpam-6031	470	5	h	h	PROPN
ejpam-6031	470	6	bauschke	bauschke	PROPN
ejpam-6031	470	7	.	.	PUNCT
ejpam-6031	471	1	the	the	DET
ejpam-6031	471	2	approximation	approximation	NOUN
ejpam-6031	471	3	of	of	ADP
ejpam-6031	471	4	fixed	fix	VERB
ejpam-6031	471	5	points	point	NOUN
ejpam-6031	471	6	of	of	ADP
ejpam-6031	471	7	compositions	composition	NOUN
ejpam-6031	471	8	of	of	ADP
ejpam-6031	471	9	nonexpansive	nonexpansive	ADJ
ejpam-6031	471	10	mappings	mapping	NOUN
ejpam-6031	471	11	in	in	ADP
ejpam-6031	471	12	hilbert	hilbert	NOUN
ejpam-6031	471	13	space	space	NOUN
ejpam-6031	471	14	.	.	PUNCT
ejpam-6031	472	1	journal	journal	PROPN
ejpam-6031	472	2	of	of	ADP
ejpam-6031	472	3	mathematical	mathematical	ADJ
ejpam-6031	472	4	analysis	analysis	NOUN
ejpam-6031	472	5	and	and	CCONJ
ejpam-6031	472	6	applications	application	NOUN
ejpam-6031	472	7	,	,	PUNCT
ejpam-6031	472	8	202(1):150–159	202(1):150–159	NUM
ejpam-6031	472	9	,	,	PUNCT
ejpam-6031	472	10	1996	1996	NUM
ejpam-6031	472	11	.	.	PUNCT
ejpam-6031	473	1	[	[	X
ejpam-6031	473	2	12	12	NUM
ejpam-6031	473	3	]	]	X
ejpam-6031	473	4	heinz	heinz	PROPN
ejpam-6031	473	5	h	h	PROPN
ejpam-6031	473	6	bauschke	bauschke	NOUN
ejpam-6031	473	7	and	and	CCONJ
ejpam-6031	473	8	walaa	walaa	PROPN
ejpam-6031	473	9	m	m	PROPN
ejpam-6031	473	10	moursi	moursi	ADJ
ejpam-6031	473	11	.	.	PUNCT
ejpam-6031	474	1	the	the	DET
ejpam-6031	474	2	magnitude	magnitude	NOUN
ejpam-6031	474	3	of	of	ADP
ejpam-6031	474	4	the	the	DET
ejpam-6031	474	5	minimal	minimal	ADJ
ejpam-6031	474	6	displacement	displacement	ADJ
ejpam-6031	474	7	vector	vector	NOUN
ejpam-6031	474	8	for	for	ADP
ejpam-6031	474	9	compositions	composition	NOUN
ejpam-6031	474	10	and	and	CCONJ
ejpam-6031	474	11	convex	convex	NOUN
ejpam-6031	474	12	combinations	combination	NOUN
ejpam-6031	474	13	of	of	ADP
ejpam-6031	474	14	firmly	firmly	ADV
ejpam-6031	474	15	nonexpansive	nonexpansive	ADJ
ejpam-6031	474	16	mappings	mapping	NOUN
ejpam-6031	474	17	.	.	PUNCT
ejpam-6031	475	1	optimization	optimization	NOUN
ejpam-6031	475	2	letters	letter	NOUN
ejpam-6031	475	3	,	,	PUNCT
ejpam-6031	475	4	12:1465–1474	12:1465–1474	NUM
ejpam-6031	475	5	,	,	PUNCT
ejpam-6031	475	6	2018	2018	NUM
ejpam-6031	475	7	.	.	PUNCT
ejpam-6031	476	1	[	[	X
ejpam-6031	476	2	13	13	NUM
ejpam-6031	476	3	]	]	PUNCT
ejpam-6031	476	4	heinz	heinz	PROPN
ejpam-6031	476	5	h	h	PROPN
ejpam-6031	476	6	bauschke	bauschke	PROPN
ejpam-6031	476	7	,	,	PUNCT
ejpam-6031	476	8	victoria	victoria	PROPN
ejpam-6031	476	9	martı́n	martı́n	PROPN
ejpam-6031	476	10	-	-	PROPN
ejpam-6031	476	11	márquez	márquez	PROPN
ejpam-6031	476	12	,	,	PUNCT
ejpam-6031	476	13	sarah	sarah	PROPN
ejpam-6031	476	14	m	m	PROPN
ejpam-6031	476	15	moffat	moffat	PROPN
ejpam-6031	476	16	,	,	PUNCT
ejpam-6031	476	17	and	and	CCONJ
ejpam-6031	476	18	xianfu	xianfu	PROPN
ejpam-6031	476	19	wang	wang	PROPN
ejpam-6031	476	20	.	.	PUNCT
ejpam-6031	476	21	compositions	composition	NOUN
ejpam-6031	476	22	and	and	CCONJ
ejpam-6031	476	23	convex	convex	NOUN
ejpam-6031	476	24	combinations	combination	NOUN
ejpam-6031	476	25	of	of	ADP
ejpam-6031	476	26	asymptotically	asymptotically	ADV
ejpam-6031	476	27	regular	regular	ADJ
ejpam-6031	476	28	firmly	firmly	ADV
ejpam-6031	476	29	nonexpansive	nonexpansive	ADJ
ejpam-6031	476	30	mappings	mapping	NOUN
ejpam-6031	476	31	are	be	AUX
ejpam-6031	476	32	also	also	ADV
ejpam-6031	476	33	asymptotically	asymptotically	ADV
ejpam-6031	476	34	regular	regular	ADJ
ejpam-6031	476	35	.	.	PUNCT
ejpam-6031	477	1	fixed	fix	VERB
ejpam-6031	477	2	point	point	NOUN
ejpam-6031	477	3	theory	theory	NOUN
ejpam-6031	477	4	and	and	CCONJ
ejpam-6031	477	5	applications	application	NOUN
ejpam-6031	477	6	,	,	PUNCT
ejpam-6031	477	7	2012:1–11	2012:1–11	NUM
ejpam-6031	477	8	,	,	PUNCT
ejpam-6031	477	9	2012	2012	NUM
ejpam-6031	477	10	.	.	PUNCT
ejpam-6031	478	1	[	[	X
ejpam-6031	478	2	14	14	NUM
ejpam-6031	478	3	]	]	X
ejpam-6031	478	4	salihah	salihah	ADJ
ejpam-6031	478	5	alwadani	alwadani	ADJ
ejpam-6031	478	6	,	,	PUNCT
ejpam-6031	478	7	heinz	heinz	PROPN
ejpam-6031	478	8	h	h	PROPN
ejpam-6031	478	9	bauschke	bauschke	PROPN
ejpam-6031	478	10	,	,	PUNCT
ejpam-6031	478	11	julian	julian	PROPN
ejpam-6031	478	12	p	p	PROPN
ejpam-6031	478	13	revalski	revalski	PROPN
ejpam-6031	478	14	,	,	PUNCT
ejpam-6031	478	15	and	and	CCONJ
ejpam-6031	478	16	xianfu	xianfu	PROPN
ejpam-6031	478	17	wang	wang	PROPN
ejpam-6031	478	18	.	.	PUNCT
ejpam-6031	479	1	resolvents	resolvent	NOUN
ejpam-6031	479	2	and	and	CCONJ
ejpam-6031	479	3	yosida	yosida	PROPN
ejpam-6031	479	4	approximations	approximation	NOUN
ejpam-6031	479	5	of	of	ADP
ejpam-6031	479	6	displacement	displacement	ADJ
ejpam-6031	479	7	mappings	mapping	NOUN
ejpam-6031	479	8	of	of	ADP
ejpam-6031	479	9	isometries	isometry	NOUN
ejpam-6031	479	10	.	.	PUNCT
ejpam-6031	480	1	setvalued	setvalued	ADJ
ejpam-6031	480	2	and	and	CCONJ
ejpam-6031	480	3	variational	variational	ADJ
ejpam-6031	480	4	analysis	analysis	NOUN
ejpam-6031	480	5	,	,	PUNCT
ejpam-6031	480	6	29:721–733	29:721–733	NUM
ejpam-6031	480	7	,	,	PUNCT
ejpam-6031	480	8	2021	2021	NUM
ejpam-6031	480	9	.	.	PUNCT
ejpam-6031	481	1	[	[	X
ejpam-6031	481	2	15	15	NUM
ejpam-6031	481	3	]	]	X
ejpam-6031	481	4	r	r	NOUN
ejpam-6031	481	5	tyrrell	tyrrell	NOUN
ejpam-6031	481	6	rockafellar	rockafellar	ADJ
ejpam-6031	481	7	and	and	CCONJ
ejpam-6031	481	8	roger	roger	PROPN
ejpam-6031	481	9	j	j	PROPN
ejpam-6031	481	10	-	-	PUNCT
ejpam-6031	481	11	b	b	NOUN
ejpam-6031	481	12	wets	wet	VERB
ejpam-6031	481	13	.	.	PUNCT
ejpam-6031	482	1	springer	springer	NOUN
ejpam-6031	482	2	-	-	PUNCT
ejpam-6031	482	3	verlag	verlag	PROPN
ejpam-6031	482	4	,	,	PUNCT
ejpam-6031	482	5	corrected	correct	VERB
ejpam-6031	482	6	3rd	3rd	ADJ
ejpam-6031	482	7	printing	printing	NOUN
ejpam-6031	482	8	,	,	PUNCT
ejpam-6031	482	9	2009	2009	NUM
ejpam-6031	482	10	.	.	PUNCT
ejpam-6031	483	1	[	[	X
ejpam-6031	483	2	16	16	NUM
ejpam-6031	483	3	]	]	X
ejpam-6031	483	4	heinz	heinz	PROPN
ejpam-6031	483	5	h	h	PROPN
ejpam-6031	483	6	bauschke	bauschke	NOUN
ejpam-6031	483	7	and	and	CCONJ
ejpam-6031	483	8	walaa	walaa	PROPN
ejpam-6031	483	9	m	m	PROPN
ejpam-6031	483	10	moursi	moursi	ADJ
ejpam-6031	483	11	.	.	PUNCT
ejpam-6031	484	1	on	on	ADP
ejpam-6031	484	2	the	the	DET
ejpam-6031	484	3	order	order	NOUN
ejpam-6031	484	4	of	of	ADP
ejpam-6031	484	5	the	the	DET
ejpam-6031	484	6	operators	operator	NOUN
ejpam-6031	484	7	in	in	ADP
ejpam-6031	484	8	the	the	DET
ejpam-6031	484	9	douglas	douglas	PROPN
ejpam-6031	484	10	–	–	PUNCT
ejpam-6031	484	11	rachford	rachford	ADJ
ejpam-6031	484	12	algorithm	algorithm	NOUN
ejpam-6031	484	13	.	.	PUNCT
ejpam-6031	485	1	optimization	optimization	NOUN
ejpam-6031	485	2	letters	letter	NOUN
ejpam-6031	485	3	,	,	PUNCT
ejpam-6031	485	4	10:447–455	10:447–455	NUM
ejpam-6031	485	5	,	,	PUNCT
ejpam-6031	485	6	2016	2016	NUM
ejpam-6031	485	7	.	.	PUNCT
ejpam-6031	486	1	[	[	X
ejpam-6031	486	2	17	17	NUM
ejpam-6031	486	3	]	]	PUNCT
ejpam-6031	486	4	salihah	salihah	ADJ
ejpam-6031	486	5	alwadani	alwadani	ADJ
ejpam-6031	486	6	,	,	PUNCT
ejpam-6031	486	7	heinz	heinz	PROPN
ejpam-6031	486	8	h	h	PROPN
ejpam-6031	486	9	bauschke	bauschke	PROPN
ejpam-6031	486	10	,	,	PUNCT
ejpam-6031	486	11	walaa	walaa	PROPN
ejpam-6031	486	12	m	m	VERB
ejpam-6031	486	13	moursi	moursi	ADJ
ejpam-6031	486	14	,	,	PUNCT
ejpam-6031	486	15	and	and	CCONJ
ejpam-6031	486	16	xianfu	xianfu	PROPN
ejpam-6031	486	17	wang	wang	PROPN
ejpam-6031	486	18	.	.	PUNCT
ejpam-6031	487	1	on	on	ADP
ejpam-6031	487	2	the	the	DET
ejpam-6031	487	3	asymptotic	asymptotic	ADJ
ejpam-6031	487	4	behaviour	behaviour	NOUN
ejpam-6031	487	5	of	of	ADP
ejpam-6031	487	6	the	the	DET
ejpam-6031	487	7	aragón	aragón	PROPN
ejpam-6031	487	8	artacho	artacho	ADJ
ejpam-6031	487	9	–	–	PUNCT
ejpam-6031	487	10	campoy	campoy	ADJ
ejpam-6031	487	11	algorithm	algorithm	NOUN
ejpam-6031	487	12	.	.	PUNCT
ejpam-6031	488	1	operations	operation	NOUN
ejpam-6031	488	2	research	research	NOUN
ejpam-6031	488	3	letters	letter	NOUN
ejpam-6031	488	4	,	,	PUNCT
ejpam-6031	488	5	46(6):585–587	46(6):585–587	PROPN
ejpam-6031	488	6	,	,	PUNCT
ejpam-6031	488	7	2018	2018	NUM
ejpam-6031	488	8	.	.	PUNCT