id	sid	tid	token	lemma	pos
ejpam-1853	1	1	european	european	PROPN
ejpam-1853	1	2	journal	journal	PROPN
ejpam-1853	1	3	of	of	ADP
ejpam-1853	1	4	pure	pure	ADJ
ejpam-1853	1	5	and	and	CCONJ
ejpam-1853	1	6	applied	apply	VERB
ejpam-1853	1	7	mathematics	mathematic	NOUN
ejpam-1853	1	8	vol	vol	NOUN
ejpam-1853	1	9	.	.	PROPN
ejpam-1853	2	1	6	6	NUM
ejpam-1853	2	2	,	,	PUNCT
ejpam-1853	2	3	no	no	INTJ
ejpam-1853	2	4	.	.	NOUN
ejpam-1853	2	5	4	4	NUM
ejpam-1853	2	6	,	,	PUNCT
ejpam-1853	2	7	2013	2013	NUM
ejpam-1853	2	8	,	,	PUNCT
ejpam-1853	2	9	469	469	NUM
ejpam-1853	2	10	-	-	SYM
ejpam-1853	2	11	484	484	NUM
ejpam-1853	2	12	issn	issn	PROPN
ejpam-1853	2	13	1307	1307	NUM
ejpam-1853	2	14	-	-	SYM
ejpam-1853	2	15	5543	5543	NUM
ejpam-1853	2	16	–	–	PUNCT
ejpam-1853	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1853	2	18	vector	vector	NOUN
ejpam-1853	2	19	space	space	NOUN
ejpam-1853	2	20	–	–	PUNCT
ejpam-1853	2	21	groupoids	groupoids	PROPN
ejpam-1853	2	22	mihai	mihai	PROPN
ejpam-1853	2	23	ivan	ivan	PROPN
ejpam-1853	2	24	department	department	PROPN
ejpam-1853	2	25	of	of	ADP
ejpam-1853	2	26	educational	educational	ADJ
ejpam-1853	2	27	sciences	sciences	PROPN
ejpam-1853	2	28	,	,	PUNCT
ejpam-1853	2	29	west	west	PROPN
ejpam-1853	2	30	university	university	PROPN
ejpam-1853	2	31	of	of	ADP
ejpam-1853	2	32	timi̧	timi̧	PROPN
ejpam-1853	2	33	soara	soara	PROPN
ejpam-1853	2	34	,	,	PUNCT
ejpam-1853	2	35	timi̧	timi̧	PROPN
ejpam-1853	2	36	soara	soara	PROPN
ejpam-1853	2	37	,	,	PUNCT
ejpam-1853	2	38	romania	romania	PROPN
ejpam-1853	2	39	abstract	abstract	NOUN
ejpam-1853	2	40	.	.	PUNCT
ejpam-1853	3	1	we	we	PRON
ejpam-1853	3	2	define	define	VERB
ejpam-1853	3	3	the	the	DET
ejpam-1853	3	4	notion	notion	NOUN
ejpam-1853	3	5	of	of	ADP
ejpam-1853	3	6	vector	vector	NOUN
ejpam-1853	3	7	space	space	NOUN
ejpam-1853	3	8	-	-	PUNCT
ejpam-1853	3	9	groupoid	groupoid	PROPN
ejpam-1853	3	10	.	.	PUNCT
ejpam-1853	4	1	the	the	DET
ejpam-1853	4	2	main	main	ADJ
ejpam-1853	4	3	purpose	purpose	NOUN
ejpam-1853	4	4	of	of	ADP
ejpam-1853	4	5	this	this	DET
ejpam-1853	4	6	paper	paper	NOUN
ejpam-1853	4	7	is	be	AUX
ejpam-1853	4	8	to	to	PART
ejpam-1853	4	9	give	give	VERB
ejpam-1853	4	10	the	the	DET
ejpam-1853	4	11	basic	basic	ADJ
ejpam-1853	4	12	properties	property	NOUN
ejpam-1853	4	13	of	of	ADP
ejpam-1853	4	14	vector	vector	NOUN
ejpam-1853	4	15	space	space	NOUN
ejpam-1853	4	16	-	-	PUNCT
ejpam-1853	4	17	groupoids	groupoid	NOUN
ejpam-1853	4	18	.	.	PUNCT
ejpam-1853	5	1	2010	2010	NUM
ejpam-1853	5	2	mathematics	mathematic	NOUN
ejpam-1853	5	3	subject	subject	NOUN
ejpam-1853	5	4	classifications	classification	NOUN
ejpam-1853	5	5	:	:	PUNCT
ejpam-1853	5	6	20l13	20l13	NUM
ejpam-1853	5	7	,	,	PUNCT
ejpam-1853	5	8	20l99	20l99	NUM
ejpam-1853	5	9	key	key	ADJ
ejpam-1853	5	10	words	word	NOUN
ejpam-1853	5	11	and	and	CCONJ
ejpam-1853	5	12	phrases	phrase	NOUN
ejpam-1853	5	13	:	:	PUNCT
ejpam-1853	5	14	groupoid	groupoid	PROPN
ejpam-1853	5	15	,	,	PUNCT
ejpam-1853	5	16	group	group	NOUN
ejpam-1853	5	17	-	-	PUNCT
ejpam-1853	5	18	groupoid	groupoid	PROPN
ejpam-1853	5	19	,	,	PUNCT
ejpam-1853	5	20	vector	vector	NOUN
ejpam-1853	5	21	space	space	NOUN
ejpam-1853	5	22	-	-	PUNCT
ejpam-1853	5	23	groupoid	groupoid	PROPN
ejpam-1853	5	24	1	1	PROPN
ejpam-1853	5	25	.	.	PUNCT
ejpam-1853	6	1	introduction	introduction	NOUN
ejpam-1853	6	2	in	in	ADP
ejpam-1853	6	3	the	the	DET
ejpam-1853	6	4	category	category	NOUN
ejpam-1853	6	5	theoretical	theoretical	ADJ
ejpam-1853	6	6	approach	approach	NOUN
ejpam-1853	6	7	,	,	PUNCT
ejpam-1853	6	8	a	a	DET
ejpam-1853	6	9	groupoid	groupoid	NOUN
ejpam-1853	6	10	is	be	AUX
ejpam-1853	6	11	a	a	DET
ejpam-1853	6	12	small	small	ADJ
ejpam-1853	6	13	category	category	NOUN
ejpam-1853	6	14	in	in	ADP
ejpam-1853	6	15	which	which	PRON
ejpam-1853	6	16	every	every	DET
ejpam-1853	6	17	morphism	morphism	NOUN
ejpam-1853	6	18	is	be	AUX
ejpam-1853	6	19	an	an	DET
ejpam-1853	6	20	isomorphism	isomorphism	NOUN
ejpam-1853	6	21	[	[	X
ejpam-1853	6	22	6	6	NUM
ejpam-1853	6	23	]	]	PUNCT
ejpam-1853	6	24	.	.	PUNCT
ejpam-1853	7	1	the	the	DET
ejpam-1853	7	2	concept	concept	NOUN
ejpam-1853	7	3	of	of	ADP
ejpam-1853	7	4	groupoid	groupoid	PROPN
ejpam-1853	7	5	was	be	AUX
ejpam-1853	7	6	first	first	ADV
ejpam-1853	7	7	introduced	introduce	VERB
ejpam-1853	7	8	by	by	ADP
ejpam-1853	7	9	h.	h.	PROPN
ejpam-1853	7	10	brandt	brandt	PROPN
ejpam-1853	8	1	[	[	X
ejpam-1853	8	2	1	1	X
ejpam-1853	8	3	]	]	PUNCT
ejpam-1853	8	4	and	and	CCONJ
ejpam-1853	8	5	it	it	PRON
ejpam-1853	8	6	is	be	AUX
ejpam-1853	8	7	developed	develop	VERB
ejpam-1853	8	8	by	by	ADP
ejpam-1853	8	9	p.	p.	PROPN
ejpam-1853	8	10	j.	j.	PROPN
ejpam-1853	8	11	higgins	higgins	PROPN
ejpam-1853	8	12	in	in	ADP
ejpam-1853	8	13	[	[	X
ejpam-1853	8	14	6	6	NUM
ejpam-1853	8	15	]	]	PUNCT
ejpam-1853	8	16	.	.	PUNCT
ejpam-1853	9	1	the	the	DET
ejpam-1853	9	2	topological	topological	ADJ
ejpam-1853	9	3	and	and	CCONJ
ejpam-1853	9	4	differentiable	differentiable	ADJ
ejpam-1853	9	5	versions	version	NOUN
ejpam-1853	9	6	of	of	ADP
ejpam-1853	9	7	the	the	DET
ejpam-1853	9	8	groupoids	groupoid	NOUN
ejpam-1853	9	9	were	be	AUX
ejpam-1853	9	10	defined	define	VERB
ejpam-1853	9	11	by	by	ADP
ejpam-1853	9	12	c.	c.	PROPN
ejpam-1853	9	13	ehresmann	ehresmann	PROPN
ejpam-1853	10	1	[	[	X
ejpam-1853	10	2	5	5	NUM
ejpam-1853	10	3	]	]	PUNCT
ejpam-1853	10	4	.	.	PUNCT
ejpam-1853	11	1	the	the	DET
ejpam-1853	11	2	notion	notion	NOUN
ejpam-1853	11	3	of	of	ADP
ejpam-1853	11	4	group	group	NOUN
ejpam-1853	11	5	-	-	PUNCT
ejpam-1853	11	6	groupoid	groupoid	PROPN
ejpam-1853	11	7	was	be	AUX
ejpam-1853	11	8	defined	define	VERB
ejpam-1853	11	9	by	by	ADP
ejpam-1853	11	10	r.	r.	PROPN
ejpam-1853	11	11	brown	brown	PROPN
ejpam-1853	11	12	and	and	CCONJ
ejpam-1853	11	13	spencer	spencer	PROPN
ejpam-1853	11	14	in	in	ADP
ejpam-1853	11	15	the	the	DET
ejpam-1853	11	16	paper	paper	NOUN
ejpam-1853	12	1	[	[	X
ejpam-1853	12	2	4	4	NUM
ejpam-1853	12	3	]	]	PUNCT
ejpam-1853	12	4	.	.	PUNCT
ejpam-1853	13	1	in	in	ADP
ejpam-1853	13	2	this	this	DET
ejpam-1853	13	3	paper	paper	NOUN
ejpam-1853	13	4	,	,	PUNCT
ejpam-1853	13	5	the	the	DET
ejpam-1853	13	6	group	group	NOUN
ejpam-1853	13	7	-	-	PUNCT
ejpam-1853	13	8	groupoid	groupoid	PROPN
ejpam-1853	13	9	is	be	AUX
ejpam-1853	13	10	extended	extend	VERB
ejpam-1853	13	11	to	to	ADP
ejpam-1853	13	12	notion	notion	NOUN
ejpam-1853	13	13	of	of	ADP
ejpam-1853	13	14	vector	vector	NOUN
ejpam-1853	13	15	space	space	NOUN
ejpam-1853	13	16	-	-	PUNCT
ejpam-1853	13	17	groupoid	groupoid	PROPN
ejpam-1853	13	18	.	.	PUNCT
ejpam-1853	14	1	another	another	DET
ejpam-1853	14	2	algebraic	algebraic	ADJ
ejpam-1853	14	3	concept	concept	NOUN
ejpam-1853	14	4	considered	consider	VERB
ejpam-1853	14	5	in	in	ADP
ejpam-1853	14	6	this	this	DET
ejpam-1853	14	7	paper	paper	NOUN
ejpam-1853	14	8	is	be	AUX
ejpam-1853	14	9	the	the	DET
ejpam-1853	14	10	vector	vector	NOUN
ejpam-1853	14	11	groupoid	groupoid	PROPN
ejpam-1853	14	12	.	.	PUNCT
ejpam-1853	15	1	this	this	DET
ejpam-1853	15	2	new	new	ADJ
ejpam-1853	15	3	mathematical	mathematical	ADJ
ejpam-1853	15	4	structure	structure	NOUN
ejpam-1853	15	5	was	be	AUX
ejpam-1853	15	6	defined	define	VERB
ejpam-1853	15	7	by	by	ADP
ejpam-1853	15	8	v.	v.	ADP
ejpam-1853	15	9	popuţa	popuţa	PROPN
ejpam-1853	15	10	and	and	CCONJ
ejpam-1853	15	11	gh	gh	PROPN
ejpam-1853	15	12	.	.	PUNCT
ejpam-1853	16	1	ivan	ivan	PROPN
ejpam-1853	17	1	[	[	X
ejpam-1853	17	2	13	13	NUM
ejpam-1853	17	3	,	,	PUNCT
ejpam-1853	17	4	14	14	NUM
ejpam-1853	17	5	]	]	PUNCT
ejpam-1853	17	6	.	.	PUNCT
ejpam-1853	18	1	the	the	DET
ejpam-1853	18	2	groupoids	groupoid	NOUN
ejpam-1853	18	3	,	,	PUNCT
ejpam-1853	18	4	groupgroupoids	groupgroupoid	NOUN
ejpam-1853	18	5	and	and	CCONJ
ejpam-1853	18	6	their	their	PRON
ejpam-1853	18	7	generalizations	generalization	NOUN
ejpam-1853	18	8	(	(	PUNCT
ejpam-1853	18	9	topological	topological	ADJ
ejpam-1853	18	10	groupoids	groupoid	NOUN
ejpam-1853	18	11	,	,	PUNCT
ejpam-1853	18	12	lie	lie	NOUN
ejpam-1853	18	13	groupoids	groupoid	NOUN
ejpam-1853	18	14	etc	etc	X
ejpam-1853	18	15	.	.	X
ejpam-1853	18	16	)	)	PUNCT
ejpam-1853	18	17	are	be	AUX
ejpam-1853	18	18	mathematical	mathematical	ADJ
ejpam-1853	18	19	structures	structure	NOUN
ejpam-1853	18	20	that	that	PRON
ejpam-1853	18	21	have	have	AUX
ejpam-1853	18	22	proved	prove	VERB
ejpam-1853	18	23	to	to	PART
ejpam-1853	18	24	be	be	AUX
ejpam-1853	18	25	useful	useful	ADJ
ejpam-1853	18	26	in	in	ADP
ejpam-1853	18	27	many	many	ADJ
ejpam-1853	18	28	areas	area	NOUN
ejpam-1853	18	29	of	of	ADP
ejpam-1853	18	30	science	science	NOUN
ejpam-1853	18	31	(	(	PUNCT
ejpam-1853	18	32	see	see	VERB
ejpam-1853	18	33	for	for	ADP
ejpam-1853	18	34	instance	instance	NOUN
ejpam-1853	18	35	[	[	X
ejpam-1853	18	36	2	2	NUM
ejpam-1853	18	37	,	,	PUNCT
ejpam-1853	18	38	7	7	NUM
ejpam-1853	18	39	,	,	PUNCT
ejpam-1853	18	40	9–12	9–12	NOUN
ejpam-1853	18	41	,	,	PUNCT
ejpam-1853	18	42	15	15	NUM
ejpam-1853	18	43	]	]	PUNCT
ejpam-1853	18	44	.	.	PUNCT
ejpam-1853	19	1	the	the	DET
ejpam-1853	19	2	paper	paper	NOUN
ejpam-1853	19	3	is	be	AUX
ejpam-1853	19	4	organized	organize	VERB
ejpam-1853	19	5	as	as	SCONJ
ejpam-1853	19	6	follows	follow	VERB
ejpam-1853	19	7	.	.	PUNCT
ejpam-1853	20	1	in	in	ADP
ejpam-1853	20	2	section	section	NOUN
ejpam-1853	20	3	2	2	NUM
ejpam-1853	20	4	we	we	PRON
ejpam-1853	20	5	present	present	VERB
ejpam-1853	20	6	some	some	DET
ejpam-1853	20	7	concepts	concept	NOUN
ejpam-1853	20	8	and	and	CCONJ
ejpam-1853	20	9	main	main	ADJ
ejpam-1853	20	10	results	result	NOUN
ejpam-1853	20	11	related	relate	VERB
ejpam-1853	20	12	to	to	ADP
ejpam-1853	20	13	groupoids	groupoid	NOUN
ejpam-1853	20	14	and	and	CCONJ
ejpam-1853	20	15	group	group	NOUN
ejpam-1853	20	16	-	-	PUNCT
ejpam-1853	20	17	groupoids	groupoid	NOUN
ejpam-1853	20	18	[	[	X
ejpam-1853	20	19	4	4	NUM
ejpam-1853	20	20	]	]	PUNCT
ejpam-1853	20	21	.	.	PUNCT
ejpam-1853	21	1	in	in	ADP
ejpam-1853	21	2	section	section	NOUN
ejpam-1853	21	3	3	3	NUM
ejpam-1853	21	4	we	we	PRON
ejpam-1853	21	5	introduce	introduce	VERB
ejpam-1853	21	6	the	the	DET
ejpam-1853	21	7	concept	concept	NOUN
ejpam-1853	21	8	of	of	ADP
ejpam-1853	21	9	vector	vector	NOUN
ejpam-1853	21	10	space	space	NOUN
ejpam-1853	21	11	-	-	PUNCT
ejpam-1853	21	12	groupoid	groupoid	PROPN
ejpam-1853	21	13	.	.	PUNCT
ejpam-1853	22	1	this	this	PRON
ejpam-1853	22	2	is	be	AUX
ejpam-1853	22	3	viewed	view	VERB
ejpam-1853	22	4	as	as	ADP
ejpam-1853	22	5	a	a	DET
ejpam-1853	22	6	groupoid	groupoid	NOUN
ejpam-1853	22	7	object	object	NOUN
ejpam-1853	22	8	in	in	ADP
ejpam-1853	22	9	the	the	DET
ejpam-1853	22	10	category	category	NOUN
ejpam-1853	22	11	of	of	ADP
ejpam-1853	22	12	vector	vector	NOUN
ejpam-1853	22	13	spaces	space	NOUN
ejpam-1853	22	14	.	.	PUNCT
ejpam-1853	23	1	the	the	DET
ejpam-1853	23	2	useful	useful	ADJ
ejpam-1853	23	3	properties	property	NOUN
ejpam-1853	23	4	of	of	ADP
ejpam-1853	23	5	vector	vector	NOUN
ejpam-1853	23	6	space	space	NOUN
ejpam-1853	23	7	-	-	PUNCT
ejpam-1853	23	8	groupoids	groupoid	NOUN
ejpam-1853	23	9	are	be	AUX
ejpam-1853	23	10	established	establish	VERB
ejpam-1853	23	11	.	.	PUNCT
ejpam-1853	24	1	finally	finally	ADV
ejpam-1853	24	2	,	,	PUNCT
ejpam-1853	24	3	we	we	PRON
ejpam-1853	24	4	prove	prove	VERB
ejpam-1853	24	5	that	that	SCONJ
ejpam-1853	24	6	each	each	DET
ejpam-1853	24	7	vector	vector	NOUN
ejpam-1853	24	8	space	space	NOUN
ejpam-1853	24	9	-	-	PUNCT
ejpam-1853	24	10	groupoid	groupoid	PROPN
ejpam-1853	24	11	is	be	AUX
ejpam-1853	24	12	a	a	DET
ejpam-1853	24	13	vector	vector	NOUN
ejpam-1853	24	14	groupoid	groupoid	NOUN
ejpam-1853	24	15	.	.	PUNCT
ejpam-1853	25	1	email	email	NOUN
ejpam-1853	25	2	address	address	NOUN
ejpam-1853	25	3	:	:	PUNCT
ejpam-1853	25	4	ivan@math.uvt.ro	ivan@math.uvt.ro	ADJ
ejpam-1853	25	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1853	25	6	469	469	NUM
ejpam-1853	26	1	c	c	X
ejpam-1853	26	2	©	©	PROPN
ejpam-1853	26	3	2013	2013	NUM
ejpam-1853	26	4	ejpam	ejpam	NOUN
ejpam-1853	26	5	all	all	DET
ejpam-1853	26	6	rights	right	NOUN
ejpam-1853	26	7	reserved	reserve	VERB
ejpam-1853	26	8	.	.	PUNCT
ejpam-1853	27	1	m.	m.	NOUN
ejpam-1853	27	2	ivan	ivan	PROPN
ejpam-1853	27	3	/	/	PUNCT
ejpam-1853	27	4	eur	eur	PROPN
ejpam-1853	27	5	.	.	PUNCT
ejpam-1853	28	1	j.	j.	PROPN
ejpam-1853	28	2	pure	pure	PROPN
ejpam-1853	28	3	appl	appl	PROPN
ejpam-1853	28	4	.	.	PROPN
ejpam-1853	28	5	math	math	PROPN
ejpam-1853	28	6	,	,	PUNCT
ejpam-1853	28	7	6	6	NUM
ejpam-1853	28	8	(	(	PUNCT
ejpam-1853	28	9	2013	2013	NUM
ejpam-1853	28	10	)	)	PUNCT
ejpam-1853	28	11	,	,	PUNCT
ejpam-1853	28	12	469	469	NUM
ejpam-1853	28	13	-	-	SYM
ejpam-1853	28	14	484	484	NUM
ejpam-1853	28	15	470	470	NUM
ejpam-1853	28	16	2	2	NUM
ejpam-1853	28	17	.	.	PUNCT
ejpam-1853	28	18	preliminaries	preliminary	NOUN
ejpam-1853	28	19	about	about	ADP
ejpam-1853	28	20	group	group	NOUN
ejpam-1853	28	21	-	-	PUNCT
ejpam-1853	28	22	groupoids	groupoid	NOUN
ejpam-1853	28	23	we	we	PRON
ejpam-1853	28	24	begin	begin	VERB
ejpam-1853	28	25	with	with	ADP
ejpam-1853	28	26	the	the	DET
ejpam-1853	28	27	presentation	presentation	NOUN
ejpam-1853	28	28	of	of	ADP
ejpam-1853	28	29	some	some	DET
ejpam-1853	28	30	necessary	necessary	ADJ
ejpam-1853	28	31	backgrounds	background	NOUN
ejpam-1853	28	32	on	on	ADP
ejpam-1853	28	33	groupoids	groupoid	NOUN
ejpam-1853	28	34	(	(	PUNCT
ejpam-1853	28	35	for	for	ADP
ejpam-1853	28	36	further	further	ADJ
ejpam-1853	28	37	details	detail	NOUN
ejpam-1853	28	38	see	see	VERB
ejpam-1853	28	39	e.g.	e.g.	ADV
ejpam-1853	28	40	[	[	X
ejpam-1853	28	41	8	8	NUM
ejpam-1853	28	42	,	,	PUNCT
ejpam-1853	28	43	9	9	NUM
ejpam-1853	28	44	]	]	PUNCT
ejpam-1853	28	45	)	)	PUNCT
ejpam-1853	28	46	.	.	PUNCT
ejpam-1853	29	1	definition	definition	NOUN
ejpam-1853	29	2	1	1	NUM
ejpam-1853	29	3	(	(	PUNCT
ejpam-1853	29	4	[	[	X
ejpam-1853	29	5	9	9	NUM
ejpam-1853	29	6	]	]	NUM
ejpam-1853	29	7	)	)	PUNCT
ejpam-1853	29	8	.	.	PUNCT
ejpam-1853	30	1	a	a	DET
ejpam-1853	30	2	groupoid	groupoid	PROPN
ejpam-1853	30	3	g	g	PROPN
ejpam-1853	30	4	over	over	ADP
ejpam-1853	30	5	g0	g0	PROPN
ejpam-1853	30	6	is	be	AUX
ejpam-1853	30	7	a	a	DET
ejpam-1853	30	8	pair	pair	NOUN
ejpam-1853	30	9	(	(	PUNCT
ejpam-1853	30	10	g	g	NOUN
ejpam-1853	30	11	,	,	PUNCT
ejpam-1853	30	12	g0	g0	NOUN
ejpam-1853	30	13	)	)	PUNCT
ejpam-1853	30	14	of	of	ADP
ejpam-1853	30	15	sets	set	NOUN
ejpam-1853	30	16	endowed	endow	VERB
ejpam-1853	30	17	with	with	ADP
ejpam-1853	30	18	two	two	NUM
ejpam-1853	30	19	surjective	surjective	ADJ
ejpam-1853	30	20	maps	map	NOUN
ejpam-1853	30	21	α	α	NOUN
ejpam-1853	30	22	,	,	PUNCT
ejpam-1853	30	23	β	β	X
ejpam-1853	30	24	:	:	PUNCT
ejpam-1853	30	25	g→	g→	PROPN
ejpam-1853	30	26	g0	g0	NOUN
ejpam-1853	30	27	(	(	PUNCT
ejpam-1853	30	28	source	source	NOUN
ejpam-1853	30	29	and	and	CCONJ
ejpam-1853	30	30	target	target	NOUN
ejpam-1853	30	31	)	)	PUNCT
ejpam-1853	30	32	,	,	PUNCT
ejpam-1853	30	33	a	a	DET
ejpam-1853	30	34	partially	partially	ADV
ejpam-1853	30	35	binary	binary	ADJ
ejpam-1853	30	36	operation	operation	NOUN
ejpam-1853	30	37	(	(	PUNCT
ejpam-1853	30	38	multiplication	multiplication	NOUN
ejpam-1853	30	39	)	)	PUNCT
ejpam-1853	30	40	m	m	VERB
ejpam-1853	30	41	:	:	PUNCT
ejpam-1853	30	42	g(2	g(2	ADJ
ejpam-1853	30	43	)	)	PUNCT
ejpam-1853	30	44	:	:	PUNCT
ejpam-1853	31	1	=	=	SYM
ejpam-1853	31	2	{	{	PUNCT
ejpam-1853	31	3	(	(	PUNCT
ejpam-1853	31	4	x	x	INTJ
ejpam-1853	31	5	,	,	PUNCT
ejpam-1853	31	6	y	y	PROPN
ejpam-1853	31	7	)	)	PUNCT
ejpam-1853	31	8	∈	∈	PROPN
ejpam-1853	31	9	g	g	ADP
ejpam-1853	31	10	×	×	PROPN
ejpam-1853	31	11	g|β(x	g|β(x	NOUN
ejpam-1853	31	12	)	)	PUNCT
ejpam-1853	31	13	=	=	SYM
ejpam-1853	31	14	α(y	α(y	NOUN
ejpam-1853	31	15	)	)	PUNCT
ejpam-1853	31	16	}	}	PUNCT
ejpam-1853	31	17	→	→	SYM
ejpam-1853	31	18	g	g	PROPN
ejpam-1853	31	19	,	,	PUNCT
ejpam-1853	31	20	(	(	PUNCT
ejpam-1853	31	21	x	x	X
ejpam-1853	31	22	,	,	PUNCT
ejpam-1853	31	23	y	y	PROPN
ejpam-1853	31	24	)	)	PUNCT
ejpam-1853	31	25	→	→	SYM
ejpam-1853	31	26	m(x	m(x	PROPN
ejpam-1853	31	27	,	,	PUNCT
ejpam-1853	31	28	y	y	PROPN
ejpam-1853	31	29	)	)	PUNCT
ejpam-1853	31	30	:	:	PUNCT
ejpam-1853	31	31	=	=	PUNCT
ejpam-1853	31	32	x	x	SYM
ejpam-1853	31	33	·	·	PUNCT
ejpam-1853	31	34	y	y	X
ejpam-1853	31	35	,	,	PUNCT
ejpam-1853	31	36	(	(	PUNCT
ejpam-1853	31	37	g(2	g(2	NOUN
ejpam-1853	31	38	)	)	PUNCT
ejpam-1853	31	39	is	be	AUX
ejpam-1853	31	40	the	the	DET
ejpam-1853	31	41	set	set	NOUN
ejpam-1853	31	42	of	of	ADP
ejpam-1853	31	43	composable	composable	ADJ
ejpam-1853	31	44	pairs	pair	NOUN
ejpam-1853	31	45	)	)	PUNCT
ejpam-1853	31	46	,	,	PUNCT
ejpam-1853	32	1	an	an	DET
ejpam-1853	32	2	injective	injective	ADJ
ejpam-1853	32	3	map	map	NOUN
ejpam-1853	32	4	ε	ε	PROPN
ejpam-1853	32	5	:	:	PUNCT
ejpam-1853	32	6	g0	g0	PROPN
ejpam-1853	32	7	→	→	SYM
ejpam-1853	32	8	g	g	PROPN
ejpam-1853	32	9	(	(	PUNCT
ejpam-1853	32	10	inclusion	inclusion	NOUN
ejpam-1853	32	11	map	map	NOUN
ejpam-1853	32	12	)	)	PUNCT
ejpam-1853	32	13	and	and	CCONJ
ejpam-1853	32	14	a	a	DET
ejpam-1853	32	15	map	map	NOUN
ejpam-1853	32	16	i	i	PRON
ejpam-1853	32	17	:	:	PUNCT
ejpam-1853	32	18	g	g	PROPN
ejpam-1853	32	19	→	→	SYM
ejpam-1853	32	20	g	g	PROPN
ejpam-1853	32	21	,	,	PUNCT
ejpam-1853	32	22	x	x	INTJ
ejpam-1853	32	23	→	→	SYM
ejpam-1853	32	24	i(x	i(x	PROPN
ejpam-1853	32	25	)	)	PUNCT
ejpam-1853	32	26	:	:	PUNCT
ejpam-1853	33	1	=	=	PUNCT
ejpam-1853	33	2	x−1	x−1	PROPN
ejpam-1853	33	3	(	(	PUNCT
ejpam-1853	33	4	inversion	inversion	NOUN
ejpam-1853	33	5	)	)	PUNCT
ejpam-1853	33	6	.	.	PUNCT
ejpam-1853	34	1	these	these	DET
ejpam-1853	34	2	maps	map	NOUN
ejpam-1853	34	3	must	must	AUX
ejpam-1853	34	4	verify	verify	VERB
ejpam-1853	34	5	the	the	DET
ejpam-1853	34	6	following	follow	VERB
ejpam-1853	34	7	conditions	condition	NOUN
ejpam-1853	34	8	:	:	PUNCT
ejpam-1853	34	9	(	(	PUNCT
ejpam-1853	34	10	g1	g1	PROPN
ejpam-1853	34	11	)	)	PUNCT
ejpam-1853	34	12	(	(	PUNCT
ejpam-1853	34	13	associativity	associativity	NOUN
ejpam-1853	34	14	):	):	PUNCT
ejpam-1853	34	15	if	if	SCONJ
ejpam-1853	34	16	(	(	PUNCT
ejpam-1853	34	17	x	x	X
ejpam-1853	34	18	,	,	PUNCT
ejpam-1853	34	19	y	y	PROPN
ejpam-1853	34	20	)	)	PUNCT
ejpam-1853	34	21	∈	∈	PROPN
ejpam-1853	34	22	g(2	g(2	PROPN
ejpam-1853	34	23	)	)	PUNCT
ejpam-1853	34	24	and	and	CCONJ
ejpam-1853	34	25	(	(	PUNCT
ejpam-1853	34	26	y	y	PROPN
ejpam-1853	34	27	,	,	PUNCT
ejpam-1853	34	28	z	z	NOUN
ejpam-1853	34	29	)	)	PUNCT
ejpam-1853	34	30	∈	∈	PROPN
ejpam-1853	34	31	g(2	g(2	PROPN
ejpam-1853	34	32	)	)	PUNCT
ejpam-1853	34	33	,	,	PUNCT
ejpam-1853	34	34	then	then	ADV
ejpam-1853	34	35	so	so	ADV
ejpam-1853	34	36	(	(	PUNCT
ejpam-1853	34	37	x	x	X
ejpam-1853	34	38	·	·	PUNCT
ejpam-1853	34	39	y	y	X
ejpam-1853	34	40	,	,	PUNCT
ejpam-1853	34	41	z	z	NOUN
ejpam-1853	34	42	)	)	PUNCT
ejpam-1853	34	43	∈	∈	PROPN
ejpam-1853	34	44	g(2	g(2	PROPN
ejpam-1853	34	45	)	)	PUNCT
ejpam-1853	34	46	and	and	CCONJ
ejpam-1853	34	47	(	(	PUNCT
ejpam-1853	34	48	x	x	X
ejpam-1853	34	49	,	,	PUNCT
ejpam-1853	34	50	y	y	PROPN
ejpam-1853	34	51	·	·	PUNCT
ejpam-1853	34	52	z	z	X
ejpam-1853	34	53	)	)	PUNCT
ejpam-1853	34	54	∈	∈	PROPN
ejpam-1853	34	55	g(2	g(2	PROPN
ejpam-1853	34	56	)	)	PUNCT
ejpam-1853	34	57	,	,	PUNCT
ejpam-1853	34	58	and	and	CCONJ
ejpam-1853	34	59	the	the	DET
ejpam-1853	34	60	relation	relation	NOUN
ejpam-1853	34	61	,	,	PUNCT
ejpam-1853	34	62	(	(	PUNCT
ejpam-1853	34	63	x	x	X
ejpam-1853	34	64	·	·	PUNCT
ejpam-1853	34	65	y	y	X
ejpam-1853	34	66	)	)	PUNCT
ejpam-1853	34	67	·	·	PUNCT
ejpam-1853	34	68	z	z	X
ejpam-1853	35	1	=	=	PUNCT
ejpam-1853	35	2	x	x	SYM
ejpam-1853	35	3	·	·	PUNCT
ejpam-1853	35	4	(	(	PUNCT
ejpam-1853	35	5	y	y	PROPN
ejpam-1853	35	6	·	·	PUNCT
ejpam-1853	35	7	z	z	X
ejpam-1853	35	8	)	)	PUNCT
ejpam-1853	35	9	is	be	AUX
ejpam-1853	35	10	satisfied	satisfied	ADJ
ejpam-1853	35	11	;	;	PUNCT
ejpam-1853	35	12	(	(	PUNCT
ejpam-1853	35	13	g2	g2	PROPN
ejpam-1853	35	14	)	)	PUNCT
ejpam-1853	35	15	(	(	PUNCT
ejpam-1853	35	16	units	unit	NOUN
ejpam-1853	35	17	):	):	PUNCT
ejpam-1853	35	18	α	α	NOUN
ejpam-1853	35	19	◦	◦	NOUN
ejpam-1853	35	20	ε	ε	PROPN
ejpam-1853	35	21	=	=	SYM
ejpam-1853	35	22	β	β	PUNCT
ejpam-1853	35	23	◦	◦	NOUN
ejpam-1853	35	24	ε	ε	PROPN
ejpam-1853	35	25	=	=	SYM
ejpam-1853	35	26	idg0	idg0	PROPN
ejpam-1853	35	27	and	and	CCONJ
ejpam-1853	35	28	ε(α(x	ε(α(x	NOUN
ejpam-1853	35	29	)	)	PUNCT
ejpam-1853	35	30	)	)	PUNCT
ejpam-1853	35	31	·	·	PUNCT
ejpam-1853	36	1	x	x	PUNCT
ejpam-1853	36	2	=	=	PUNCT
ejpam-1853	36	3	x	x	SYM
ejpam-1853	36	4	=	=	PUNCT
ejpam-1853	36	5	x	x	SYM
ejpam-1853	36	6	·	·	PUNCT
ejpam-1853	36	7	ε(β(x	ε(β(x	NOUN
ejpam-1853	36	8	)	)	PUNCT
ejpam-1853	36	9	)	)	PUNCT
ejpam-1853	36	10	,	,	PUNCT
ejpam-1853	36	11	(	(	PUNCT
ejpam-1853	36	12	∀)x	∀)x	PROPN
ejpam-1853	36	13	∈	∈	PROPN
ejpam-1853	36	14	g	g	NOUN
ejpam-1853	36	15	;	;	PUNCT
ejpam-1853	36	16	(	(	PUNCT
ejpam-1853	36	17	g3	g3	NOUN
ejpam-1853	36	18	)	)	PUNCT
ejpam-1853	36	19	(	(	PUNCT
ejpam-1853	36	20	inverses	inverse	NOUN
ejpam-1853	36	21	):	):	PUNCT
ejpam-1853	36	22	for	for	ADP
ejpam-1853	36	23	each	each	DET
ejpam-1853	36	24	x	x	SYM
ejpam-1853	36	25	∈	∈	PROPN
ejpam-1853	36	26	g	g	NOUN
ejpam-1853	36	27	we	we	PRON
ejpam-1853	36	28	have	have	VERB
ejpam-1853	36	29	α(x−1	α(x−1	NUM
ejpam-1853	36	30	)	)	PUNCT
ejpam-1853	36	31	=	=	SYM
ejpam-1853	37	1	β(x	β(x	NOUN
ejpam-1853	37	2	)	)	PUNCT
ejpam-1853	37	3	,	,	PUNCT
ejpam-1853	37	4	β(x−1	β(x−1	NOUN
ejpam-1853	37	5	)	)	PUNCT
ejpam-1853	37	6	=	=	SYM
ejpam-1853	37	7	α(x	α(x	NOUN
ejpam-1853	37	8	)	)	PUNCT
ejpam-1853	37	9	,	,	PUNCT
ejpam-1853	38	1	x−1	x−1	PROPN
ejpam-1853	38	2	·	·	PUNCT
ejpam-1853	38	3	x	x	X
ejpam-1853	39	1	=	=	PUNCT
ejpam-1853	39	2	ε(β(x	ε(β(x	NOUN
ejpam-1853	39	3	)	)	PUNCT
ejpam-1853	39	4	)	)	PUNCT
ejpam-1853	40	1	and	and	CCONJ
ejpam-1853	40	2	x	x	PUNCT
ejpam-1853	40	3	·	·	PUNCT
ejpam-1853	40	4	x−1	x−1	NUM
ejpam-1853	40	5	=	=	SYM
ejpam-1853	40	6	ε(α(x	ε(α(x	NOUN
ejpam-1853	40	7	)	)	PUNCT
ejpam-1853	40	8	)	)	PUNCT
ejpam-1853	40	9	.	.	PUNCT
ejpam-1853	41	1	we	we	PRON
ejpam-1853	41	2	sometimes	sometimes	ADV
ejpam-1853	41	3	use	use	VERB
ejpam-1853	41	4	the	the	DET
ejpam-1853	41	5	notation	notation	NOUN
ejpam-1853	41	6	x	x	PUNCT
ejpam-1853	41	7	y	y	NOUN
ejpam-1853	41	8	instead	instead	ADV
ejpam-1853	41	9	of	of	ADP
ejpam-1853	41	10	the	the	DET
ejpam-1853	41	11	product	product	NOUN
ejpam-1853	41	12	x	x	PUNCT
ejpam-1853	41	13	·	·	PUNCT
ejpam-1853	41	14	y	y	X
ejpam-1853	41	15	.	.	PUNCT
ejpam-1853	42	1	whenever	whenever	SCONJ
ejpam-1853	42	2	we	we	PRON
ejpam-1853	42	3	write	write	VERB
ejpam-1853	42	4	a	a	DET
ejpam-1853	42	5	product	product	NOUN
ejpam-1853	42	6	in	in	ADP
ejpam-1853	42	7	a	a	DET
ejpam-1853	42	8	given	give	VERB
ejpam-1853	42	9	groupoid	groupoid	NOUN
ejpam-1853	42	10	,	,	PUNCT
ejpam-1853	42	11	we	we	PRON
ejpam-1853	42	12	are	be	AUX
ejpam-1853	42	13	assuming	assume	VERB
ejpam-1853	42	14	that	that	SCONJ
ejpam-1853	42	15	it	it	PRON
ejpam-1853	42	16	is	be	AUX
ejpam-1853	42	17	defined	define	VERB
ejpam-1853	42	18	.	.	PUNCT
ejpam-1853	43	1	the	the	DET
ejpam-1853	43	2	element	element	ADJ
ejpam-1853	43	3	ε(α(x	ε(α(x	NOUN
ejpam-1853	43	4	)	)	PUNCT
ejpam-1853	43	5	)	)	PUNCT
ejpam-1853	43	6	(	(	PUNCT
ejpam-1853	43	7	resp	resp	NOUN
ejpam-1853	43	8	.	.	PUNCT
ejpam-1853	43	9	,	,	PUNCT
ejpam-1853	43	10	ε(β(x	ε(β(x	NOUN
ejpam-1853	43	11	)	)	PUNCT
ejpam-1853	43	12	)	)	PUNCT
ejpam-1853	43	13	)	)	PUNCT
ejpam-1853	43	14	is	be	AUX
ejpam-1853	43	15	called	call	VERB
ejpam-1853	43	16	the	the	DET
ejpam-1853	43	17	left	left	ADJ
ejpam-1853	43	18	unit	unit	NOUN
ejpam-1853	43	19	(	(	PUNCT
ejpam-1853	43	20	resp	resp	PROPN
ejpam-1853	43	21	.	.	PUNCT
ejpam-1853	44	1	,	,	PUNCT
ejpam-1853	44	2	right	right	ADJ
ejpam-1853	44	3	unit	unit	NOUN
ejpam-1853	44	4	)	)	PUNCT
ejpam-1853	44	5	of	of	ADP
ejpam-1853	44	6	x	x	PRON
ejpam-1853	44	7	;	;	PUNCT
ejpam-1853	44	8	ε(g0	ε(g0	PROPN
ejpam-1853	44	9	)	)	PUNCT
ejpam-1853	44	10	is	be	AUX
ejpam-1853	44	11	called	call	VERB
ejpam-1853	44	12	the	the	DET
ejpam-1853	44	13	unit	unit	NOUN
ejpam-1853	44	14	set	set	NOUN
ejpam-1853	44	15	;	;	PUNCT
ejpam-1853	44	16	x−1	x−1	PROPN
ejpam-1853	44	17	is	be	AUX
ejpam-1853	44	18	called	call	VERB
ejpam-1853	44	19	the	the	DET
ejpam-1853	44	20	inverse	inverse	NOUN
ejpam-1853	44	21	of	of	ADP
ejpam-1853	44	22	x	x	X
ejpam-1853	44	23	.	.	PUNCT
ejpam-1853	45	1	for	for	ADP
ejpam-1853	45	2	a	a	DET
ejpam-1853	45	3	groupoid	groupoid	NOUN
ejpam-1853	45	4	we	we	PRON
ejpam-1853	45	5	use	use	VERB
ejpam-1853	45	6	the	the	DET
ejpam-1853	45	7	notation	notation	NOUN
ejpam-1853	45	8	(	(	PUNCT
ejpam-1853	45	9	g	g	PROPN
ejpam-1853	45	10	,	,	PUNCT
ejpam-1853	45	11	α	α	X
ejpam-1853	45	12	,	,	PUNCT
ejpam-1853	45	13	β	β	X
ejpam-1853	45	14	,	,	PUNCT
ejpam-1853	45	15	m	m	PROPN
ejpam-1853	45	16	,	,	PUNCT
ejpam-1853	45	17	ε	ε	PROPN
ejpam-1853	45	18	,	,	PUNCT
ejpam-1853	45	19	i	i	PROPN
ejpam-1853	45	20	,	,	PUNCT
ejpam-1853	45	21	g0	g0	PROPN
ejpam-1853	45	22	)	)	PUNCT
ejpam-1853	45	23	or	or	CCONJ
ejpam-1853	45	24	(	(	PUNCT
ejpam-1853	45	25	g	g	PROPN
ejpam-1853	45	26	,	,	PUNCT
ejpam-1853	45	27	g0	g0	NOUN
ejpam-1853	45	28	)	)	PUNCT
ejpam-1853	45	29	or	or	CCONJ
ejpam-1853	45	30	g.	g.	X
ejpam-1853	45	31	the	the	DET
ejpam-1853	45	32	functions	function	NOUN
ejpam-1853	45	33	α	α	NOUN
ejpam-1853	45	34	,	,	PUNCT
ejpam-1853	45	35	β	β	PROPN
ejpam-1853	45	36	,	,	PUNCT
ejpam-1853	45	37	m	m	PROPN
ejpam-1853	45	38	,	,	PUNCT
ejpam-1853	45	39	ε	ε	PROPN
ejpam-1853	45	40	,	,	PUNCT
ejpam-1853	45	41	i	i	PRON
ejpam-1853	45	42	are	be	AUX
ejpam-1853	45	43	called	call	VERB
ejpam-1853	45	44	structure	structure	NOUN
ejpam-1853	45	45	functions	function	NOUN
ejpam-1853	45	46	.	.	PUNCT
ejpam-1853	46	1	for	for	ADP
ejpam-1853	46	2	each	each	DET
ejpam-1853	46	3	u	u	PROPN
ejpam-1853	46	4	∈	∈	PROPN
ejpam-1853	46	5	g0	g0	NOUN
ejpam-1853	46	6	,	,	PUNCT
ejpam-1853	46	7	the	the	DET
ejpam-1853	46	8	set	set	NOUN
ejpam-1853	46	9	α−1(u	α−1(u	PROPN
ejpam-1853	46	10	)	)	PUNCT
ejpam-1853	46	11	(	(	PUNCT
ejpam-1853	46	12	resp	resp	NOUN
ejpam-1853	46	13	.	.	PUNCT
ejpam-1853	46	14	,	,	PUNCT
ejpam-1853	46	15	β−1(u	β−1(u	PROPN
ejpam-1853	46	16	)	)	PUNCT
ejpam-1853	46	17	)	)	PUNCT
ejpam-1853	46	18	is	be	AUX
ejpam-1853	46	19	called	call	VERB
ejpam-1853	46	20	α−fibre	α−fibre	PROPN
ejpam-1853	46	21	(	(	PUNCT
ejpam-1853	46	22	resp	resp	NOUN
ejpam-1853	46	23	.	.	PUNCT
ejpam-1853	46	24	,	,	PUNCT
ejpam-1853	46	25	β−fibre	β−fibre	PUNCT
ejpam-1853	46	26	)	)	PUNCT
ejpam-1853	46	27	of	of	ADP
ejpam-1853	46	28	g	g	PROPN
ejpam-1853	46	29	at	at	ADP
ejpam-1853	46	30	u	u	PROPN
ejpam-1853	46	31	∈	∈	PROPN
ejpam-1853	46	32	g0	g0	PROPN
ejpam-1853	46	33	.	.	PUNCT
ejpam-1853	47	1	for	for	ADP
ejpam-1853	47	2	any	any	DET
ejpam-1853	47	3	u	u	PROPN
ejpam-1853	47	4	∈	∈	PROPN
ejpam-1853	47	5	g0	g0	NOUN
ejpam-1853	47	6	,	,	PUNCT
ejpam-1853	47	7	the	the	DET
ejpam-1853	47	8	set	set	NOUN
ejpam-1853	47	9	g(u	g(u	PROPN
ejpam-1853	47	10	)	)	PUNCT
ejpam-1853	47	11	:	:	PUNCT
ejpam-1853	47	12	=	=	SYM
ejpam-1853	47	13	α−1(u)∩β−1(u	α−1(u)∩β−1(u	NOUN
ejpam-1853	47	14	)	)	PUNCT
ejpam-1853	47	15	is	be	AUX
ejpam-1853	47	16	a	a	DET
ejpam-1853	47	17	group	group	NOUN
ejpam-1853	47	18	under	under	ADP
ejpam-1853	47	19	the	the	DET
ejpam-1853	47	20	restriction	restriction	NOUN
ejpam-1853	47	21	of	of	ADP
ejpam-1853	47	22	the	the	DET
ejpam-1853	47	23	multiplication	multiplication	NOUN
ejpam-1853	47	24	,	,	PUNCT
ejpam-1853	47	25	called	call	VERB
ejpam-1853	47	26	the	the	DET
ejpam-1853	47	27	isotropy	isotropy	ADJ
ejpam-1853	47	28	group	group	NOUN
ejpam-1853	47	29	at	at	ADP
ejpam-1853	47	30	u	u	NOUN
ejpam-1853	47	31	of	of	ADP
ejpam-1853	47	32	the	the	DET
ejpam-1853	47	33	groupoid	groupoid	PROPN
ejpam-1853	47	34	(	(	PUNCT
ejpam-1853	47	35	g	g	PROPN
ejpam-1853	47	36	,	,	PUNCT
ejpam-1853	47	37	g0	g0	NOUN
ejpam-1853	47	38	)	)	PUNCT
ejpam-1853	47	39	.	.	PUNCT
ejpam-1853	48	1	the	the	DET
ejpam-1853	48	2	map	map	NOUN
ejpam-1853	48	3	(	(	PUNCT
ejpam-1853	48	4	α	α	X
ejpam-1853	48	5	,	,	PUNCT
ejpam-1853	48	6	β	β	NOUN
ejpam-1853	48	7	)	)	PUNCT
ejpam-1853	48	8	:	:	PUNCT
ejpam-1853	48	9	g	g	PROPN
ejpam-1853	48	10	→	→	SYM
ejpam-1853	48	11	g0	g0	ADJ
ejpam-1853	48	12	×	×	PROPN
ejpam-1853	48	13	g0	g0	NOUN
ejpam-1853	48	14	defined	define	VERB
ejpam-1853	48	15	by	by	ADP
ejpam-1853	48	16	(	(	PUNCT
ejpam-1853	48	17	α	α	X
ejpam-1853	48	18	,	,	PUNCT
ejpam-1853	48	19	β)(x	β)(x	NOUN
ejpam-1853	48	20	)	)	PUNCT
ejpam-1853	48	21	:	:	PUNCT
ejpam-1853	48	22	=	=	SYM
ejpam-1853	48	23	(	(	PUNCT
ejpam-1853	48	24	α(x),β(x	α(x),β(x	NOUN
ejpam-1853	48	25	)	)	PUNCT
ejpam-1853	48	26	)	)	PUNCT
ejpam-1853	48	27	,	,	PUNCT
ejpam-1853	48	28	(	(	PUNCT
ejpam-1853	48	29	∀)x	∀)x	PROPN
ejpam-1853	48	30	∈	∈	PROPN
ejpam-1853	48	31	g	g	NOUN
ejpam-1853	48	32	is	be	AUX
ejpam-1853	48	33	called	call	VERB
ejpam-1853	48	34	the	the	DET
ejpam-1853	48	35	anchor	anchor	NOUN
ejpam-1853	48	36	map	map	NOUN
ejpam-1853	48	37	of	of	ADP
ejpam-1853	48	38	g.	g.	PROPN
ejpam-1853	48	39	a	a	DET
ejpam-1853	48	40	groupoid	groupoid	PROPN
ejpam-1853	48	41	is	be	AUX
ejpam-1853	48	42	transitive	transitive	ADJ
ejpam-1853	48	43	,	,	PUNCT
ejpam-1853	48	44	if	if	SCONJ
ejpam-1853	48	45	its	its	PRON
ejpam-1853	48	46	anchor	anchor	NOUN
ejpam-1853	48	47	map	map	NOUN
ejpam-1853	48	48	is	be	AUX
ejpam-1853	48	49	surjective	surjective	ADJ
ejpam-1853	48	50	.	.	PUNCT
ejpam-1853	49	1	in	in	ADP
ejpam-1853	49	2	particular	particular	ADJ
ejpam-1853	49	3	,	,	PUNCT
ejpam-1853	49	4	if	if	SCONJ
ejpam-1853	49	5	(	(	PUNCT
ejpam-1853	49	6	g	g	NOUN
ejpam-1853	49	7	,	,	PUNCT
ejpam-1853	49	8	α	α	X
ejpam-1853	49	9	,	,	PUNCT
ejpam-1853	49	10	β	β	X
ejpam-1853	49	11	,	,	PUNCT
ejpam-1853	49	12	m	m	PROPN
ejpam-1853	49	13	,	,	PUNCT
ejpam-1853	49	14	ε	ε	PROPN
ejpam-1853	49	15	,	,	PUNCT
ejpam-1853	49	16	i	i	PROPN
ejpam-1853	49	17	,	,	PUNCT
ejpam-1853	49	18	g0	g0	PROPN
ejpam-1853	49	19	)	)	PUNCT
ejpam-1853	49	20	is	be	AUX
ejpam-1853	49	21	a	a	DET
ejpam-1853	49	22	groupoid	groupoid	NOUN
ejpam-1853	49	23	such	such	ADJ
ejpam-1853	49	24	that	that	DET
ejpam-1853	49	25	g0	g0	NOUN
ejpam-1853	49	26	⊆	⊆	NUM
ejpam-1853	49	27	g	g	NOUN
ejpam-1853	49	28	and	and	CCONJ
ejpam-1853	49	29	ε	ε	PROPN
ejpam-1853	49	30	:	:	PUNCT
ejpam-1853	49	31	g0	g0	PROPN
ejpam-1853	49	32	→	→	SYM
ejpam-1853	49	33	g	g	PROPN
ejpam-1853	49	34	is	be	AUX
ejpam-1853	49	35	the	the	DET
ejpam-1853	49	36	inclusion	inclusion	NOUN
ejpam-1853	49	37	map	map	NOUN
ejpam-1853	49	38	,	,	PUNCT
ejpam-1853	49	39	then	then	ADV
ejpam-1853	49	40	(	(	PUNCT
ejpam-1853	49	41	g	g	NOUN
ejpam-1853	49	42	,	,	PUNCT
ejpam-1853	49	43	α	α	X
ejpam-1853	49	44	,	,	PUNCT
ejpam-1853	49	45	β	β	X
ejpam-1853	49	46	,	,	PUNCT
ejpam-1853	49	47	m	m	PROPN
ejpam-1853	49	48	,	,	PUNCT
ejpam-1853	49	49	i	i	PRON
ejpam-1853	49	50	,	,	PUNCT
ejpam-1853	49	51	g0	g0	PROPN
ejpam-1853	49	52	)	)	PUNCT
ejpam-1853	49	53	is	be	AUX
ejpam-1853	49	54	a	a	DET
ejpam-1853	49	55	brandt	brandt	PROPN
ejpam-1853	49	56	groupoid	groupoid	PROPN
ejpam-1853	49	57	,	,	PUNCT
ejpam-1853	49	58	called	call	VERB
ejpam-1853	49	59	g0−groupoid	g0−groupoid	NOUN
ejpam-1853	49	60	.	.	PUNCT
ejpam-1853	50	1	some	some	DET
ejpam-1853	50	2	elementary	elementary	ADJ
ejpam-1853	50	3	properties	property	NOUN
ejpam-1853	50	4	of	of	ADP
ejpam-1853	50	5	groupoids	groupoid	NOUN
ejpam-1853	50	6	are	be	AUX
ejpam-1853	50	7	contained	contain	VERB
ejpam-1853	50	8	in	in	ADP
ejpam-1853	50	9	the	the	DET
ejpam-1853	50	10	following	follow	VERB
ejpam-1853	50	11	proposition	proposition	NOUN
ejpam-1853	50	12	.	.	PUNCT
ejpam-1853	51	1	theorem	theorem	NOUN
ejpam-1853	51	2	1	1	NUM
ejpam-1853	51	3	.	.	PUNCT
ejpam-1853	52	1	[	[	X
ejpam-1853	52	2	8	8	NUM
ejpam-1853	52	3	]	]	PUNCT
ejpam-1853	52	4	in	in	ADP
ejpam-1853	52	5	a	a	DET
ejpam-1853	52	6	groupoid	groupoid	NOUN
ejpam-1853	52	7	(	(	PUNCT
ejpam-1853	52	8	g	g	PROPN
ejpam-1853	52	9	,	,	PUNCT
ejpam-1853	52	10	g0	g0	NOUN
ejpam-1853	52	11	)	)	PUNCT
ejpam-1853	52	12	the	the	DET
ejpam-1853	52	13	following	follow	VERB
ejpam-1853	52	14	assertions	assertion	NOUN
ejpam-1853	52	15	hold	hold	VERB
ejpam-1853	52	16	:	:	PUNCT
ejpam-1853	52	17	(	(	PUNCT
ejpam-1853	52	18	i	i	NOUN
ejpam-1853	52	19	)	)	PUNCT
ejpam-1853	52	20	α(x	α(x	PROPN
ejpam-1853	52	21	y	y	NOUN
ejpam-1853	52	22	)	)	PUNCT
ejpam-1853	52	23	=	=	SYM
ejpam-1853	52	24	α(x	α(x	NOUN
ejpam-1853	52	25	)	)	PUNCT
ejpam-1853	52	26	and	and	CCONJ
ejpam-1853	52	27	β(x	β(x	NOUN
ejpam-1853	52	28	y	y	NOUN
ejpam-1853	52	29	)	)	PUNCT
ejpam-1853	52	30	=	=	PUNCT
ejpam-1853	53	1	β(y	β(y	PROPN
ejpam-1853	53	2	)	)	PUNCT
ejpam-1853	53	3	for	for	ADP
ejpam-1853	53	4	any	any	DET
ejpam-1853	53	5	(	(	PUNCT
ejpam-1853	53	6	x	x	NOUN
ejpam-1853	53	7	,	,	PUNCT
ejpam-1853	53	8	y	y	PROPN
ejpam-1853	53	9	)	)	PUNCT
ejpam-1853	53	10	∈	∈	PROPN
ejpam-1853	53	11	g(2	g(2	PROPN
ejpam-1853	53	12	)	)	PUNCT
ejpam-1853	53	13	;	;	PUNCT
ejpam-1853	54	1	(	(	PUNCT
ejpam-1853	54	2	ii	ii	NOUN
ejpam-1853	54	3	)	)	PUNCT
ejpam-1853	54	4	α	α	NOUN
ejpam-1853	54	5	◦	◦	NOUN
ejpam-1853	55	1	i	i	PRON
ejpam-1853	55	2	=	=	SYM
ejpam-1853	55	3	β	β	X
ejpam-1853	55	4	,	,	PUNCT
ejpam-1853	55	5	β	β	X
ejpam-1853	55	6	◦	◦	NOUN
ejpam-1853	56	1	i	i	NOUN
ejpam-1853	56	2	=	=	SYM
ejpam-1853	56	3	α	α	PROPN
ejpam-1853	57	1	and	and	CCONJ
ejpam-1853	57	2	i	i	PRON
ejpam-1853	57	3	◦	◦	VERB
ejpam-1853	57	4	i	i	PRON
ejpam-1853	57	5	=	=	PROPN
ejpam-1853	57	6	idg	idg	PROPN
ejpam-1853	57	7	;	;	PUNCT
ejpam-1853	57	8	(	(	PUNCT
ejpam-1853	57	9	iii	iii	X
ejpam-1853	57	10	)	)	PUNCT
ejpam-1853	57	11	i	i	PRON
ejpam-1853	57	12	◦	◦	VERB
ejpam-1853	57	13	ε	ε	PROPN
ejpam-1853	57	14	=	=	SYM
ejpam-1853	57	15	ε	ε	PROPN
ejpam-1853	57	16	and	and	CCONJ
ejpam-1853	57	17	ε(u	ε(u	PROPN
ejpam-1853	57	18	)	)	PUNCT
ejpam-1853	57	19	·	·	PUNCT
ejpam-1853	58	1	ε(u	ε(u	X
ejpam-1853	58	2	)	)	PUNCT
ejpam-1853	58	3	=	=	SYM
ejpam-1853	58	4	ε(u	ε(u	PROPN
ejpam-1853	58	5	)	)	PUNCT
ejpam-1853	58	6	for	for	ADP
ejpam-1853	58	7	each	each	DET
ejpam-1853	58	8	u	u	PROPN
ejpam-1853	58	9	∈	∈	PROPN
ejpam-1853	58	10	g0	g0	NOUN
ejpam-1853	58	11	;	;	PUNCT
ejpam-1853	58	12	(	(	PUNCT
ejpam-1853	58	13	iv	iv	X
ejpam-1853	58	14	)	)	PUNCT
ejpam-1853	58	15	i(x	i(x	PROPN
ejpam-1853	58	16	·	·	PUNCT
ejpam-1853	58	17	y	y	X
ejpam-1853	58	18	)	)	PUNCT
ejpam-1853	58	19	=	=	SYM
ejpam-1853	58	20	i(y	i(y	NOUN
ejpam-1853	58	21	)	)	PUNCT
ejpam-1853	58	22	·	·	PUNCT
ejpam-1853	58	23	i(x	i(x	NOUN
ejpam-1853	58	24	)	)	PUNCT
ejpam-1853	58	25	,	,	PUNCT
ejpam-1853	58	26	for	for	ADP
ejpam-1853	58	27	all	all	DET
ejpam-1853	58	28	(	(	PUNCT
ejpam-1853	58	29	x	x	INTJ
ejpam-1853	58	30	,	,	PUNCT
ejpam-1853	58	31	y	y	PROPN
ejpam-1853	58	32	)	)	PUNCT
ejpam-1853	58	33	∈	∈	PROPN
ejpam-1853	58	34	g(2	g(2	PROPN
ejpam-1853	58	35	)	)	PUNCT
ejpam-1853	58	36	;	;	PUNCT
ejpam-1853	58	37	(	(	PUNCT
ejpam-1853	58	38	v	v	NOUN
ejpam-1853	58	39	)	)	PUNCT
ejpam-1853	58	40	ϕ	ϕ	NOUN
ejpam-1853	58	41	:	:	PUNCT
ejpam-1853	58	42	g(α(x))→	g(α(x))→	NOUN
ejpam-1853	58	43	g(β(x	g(β(x	NOUN
ejpam-1853	58	44	)	)	PUNCT
ejpam-1853	58	45	)	)	PUNCT
ejpam-1853	58	46	,	,	PUNCT
ejpam-1853	58	47	ϕ(z	ϕ(z	PROPN
ejpam-1853	58	48	)	)	PUNCT
ejpam-1853	58	49	:	:	PUNCT
ejpam-1853	58	50	=	=	NOUN
ejpam-1853	58	51	x−1zx	x−1zx	PROPN
ejpam-1853	58	52	is	be	AUX
ejpam-1853	58	53	an	an	DET
ejpam-1853	58	54	isomorphism	isomorphism	NOUN
ejpam-1853	58	55	of	of	ADP
ejpam-1853	58	56	groups	group	NOUN
ejpam-1853	58	57	.	.	PUNCT
ejpam-1853	59	1	(	(	PUNCT
ejpam-1853	59	2	vi	vi	X
ejpam-1853	59	3	)	)	PUNCT
ejpam-1853	59	4	if	if	SCONJ
ejpam-1853	59	5	(	(	PUNCT
ejpam-1853	59	6	g	g	NOUN
ejpam-1853	59	7	,	,	PUNCT
ejpam-1853	59	8	g0	g0	NOUN
ejpam-1853	59	9	)	)	PUNCT
ejpam-1853	59	10	is	be	AUX
ejpam-1853	59	11	transitive	transitive	ADJ
ejpam-1853	59	12	,	,	PUNCT
ejpam-1853	59	13	then	then	ADV
ejpam-1853	59	14	all	all	PRON
ejpam-1853	59	15	isotropy	isotropy	ADJ
ejpam-1853	59	16	groups	group	NOUN
ejpam-1853	59	17	are	be	AUX
ejpam-1853	59	18	isomorphic	isomorphic	ADJ
ejpam-1853	59	19	.	.	PUNCT
ejpam-1853	60	1	m.	m.	PROPN
ejpam-1853	60	2	ivan	ivan	PROPN
ejpam-1853	60	3	/	/	PUNCT
ejpam-1853	60	4	eur	eur	PROPN
ejpam-1853	60	5	.	.	PUNCT
ejpam-1853	61	1	j.	j.	PROPN
ejpam-1853	61	2	pure	pure	PROPN
ejpam-1853	61	3	appl	appl	PROPN
ejpam-1853	61	4	.	.	PROPN
ejpam-1853	61	5	math	math	PROPN
ejpam-1853	61	6	,	,	PUNCT
ejpam-1853	61	7	6	6	NUM
ejpam-1853	61	8	(	(	PUNCT
ejpam-1853	61	9	2013	2013	NUM
ejpam-1853	61	10	)	)	PUNCT
ejpam-1853	61	11	,	,	PUNCT
ejpam-1853	61	12	469	469	NUM
ejpam-1853	61	13	-	-	SYM
ejpam-1853	61	14	484	484	NUM
ejpam-1853	61	15	471	471	NUM
ejpam-1853	61	16	example	example	NOUN
ejpam-1853	61	17	1	1	NUM
ejpam-1853	61	18	.	.	PUNCT
ejpam-1853	62	1	(	(	PUNCT
ejpam-1853	62	2	i	i	NOUN
ejpam-1853	62	3	)	)	PUNCT
ejpam-1853	62	4	a	a	DET
ejpam-1853	62	5	nonempty	nonempty	ADV
ejpam-1853	62	6	set	set	VERB
ejpam-1853	62	7	g0	g0	NOUN
ejpam-1853	62	8	may	may	AUX
ejpam-1853	62	9	be	be	AUX
ejpam-1853	62	10	considered	consider	VERB
ejpam-1853	62	11	to	to	PART
ejpam-1853	62	12	be	be	AUX
ejpam-1853	62	13	a	a	DET
ejpam-1853	62	14	groupoid	groupoid	NOUN
ejpam-1853	62	15	over	over	ADP
ejpam-1853	62	16	g0	g0	PROPN
ejpam-1853	62	17	,	,	PUNCT
ejpam-1853	62	18	called	call	VERB
ejpam-1853	62	19	the	the	DET
ejpam-1853	62	20	null	null	ADJ
ejpam-1853	62	21	groupoid	groupoid	PROPN
ejpam-1853	62	22	associated	associate	VERB
ejpam-1853	62	23	to	to	ADP
ejpam-1853	62	24	g0	g0	PROPN
ejpam-1853	62	25	.	.	PUNCT
ejpam-1853	63	1	for	for	ADP
ejpam-1853	63	2	this	this	PRON
ejpam-1853	63	3	,	,	PUNCT
ejpam-1853	63	4	we	we	PRON
ejpam-1853	63	5	take	take	VERB
ejpam-1853	63	6	α=	α=	NOUN
ejpam-1853	63	7	β	β	X
ejpam-1853	63	8	=	=	PUNCT
ejpam-1853	63	9	ε	ε	PROPN
ejpam-1853	63	10	=	=	SYM
ejpam-1853	63	11	i	i	PROPN
ejpam-1853	63	12	=	=	SYM
ejpam-1853	63	13	idg0	idg0	PROPN
ejpam-1853	63	14	and	and	CCONJ
ejpam-1853	63	15	u	u	NOUN
ejpam-1853	63	16	·	·	PUNCT
ejpam-1853	63	17	u=	u=	NOUN
ejpam-1853	63	18	u	u	NOUN
ejpam-1853	63	19	for	for	ADP
ejpam-1853	63	20	all	all	DET
ejpam-1853	63	21	u	u	PROPN
ejpam-1853	63	22	∈	∈	PROPN
ejpam-1853	63	23	g0	g0	PROPN
ejpam-1853	63	24	.	.	PUNCT
ejpam-1853	64	1	(	(	PUNCT
ejpam-1853	64	2	ii	ii	NOUN
ejpam-1853	64	3	)	)	PUNCT
ejpam-1853	64	4	a	a	DET
ejpam-1853	64	5	group	group	NOUN
ejpam-1853	64	6	g	g	NOUN
ejpam-1853	64	7	having	have	VERB
ejpam-1853	64	8	e	e	NOUN
ejpam-1853	64	9	as	as	ADP
ejpam-1853	64	10	unity	unity	NOUN
ejpam-1853	64	11	has	have	VERB
ejpam-1853	64	12	a	a	DET
ejpam-1853	64	13	structure	structure	NOUN
ejpam-1853	64	14	of	of	ADP
ejpam-1853	64	15	{	{	PUNCT
ejpam-1853	64	16	e}−groupoid	e}−groupoid	X
ejpam-1853	64	17	with	with	ADP
ejpam-1853	64	18	respect	respect	NOUN
ejpam-1853	64	19	to	to	ADP
ejpam-1853	64	20	maps	map	NOUN
ejpam-1853	64	21	:	:	PUNCT
ejpam-1853	64	22	α(x	α(x	NUM
ejpam-1853	64	23	)	)	PUNCT
ejpam-1853	64	24	=	=	SYM
ejpam-1853	64	25	β(x	β(x	NOUN
ejpam-1853	64	26	)	)	PUNCT
ejpam-1853	64	27	:	:	PUNCT
ejpam-1853	65	1	=	=	SYM
ejpam-1853	65	2	e	e	X
ejpam-1853	65	3	,	,	PUNCT
ejpam-1853	65	4	g(2	g(2	PROPN
ejpam-1853	65	5	)	)	PUNCT
ejpam-1853	65	6	=	=	PUNCT
ejpam-1853	66	1	g	g	ADP
ejpam-1853	66	2	×	×	PROPN
ejpam-1853	66	3	g	g	NOUN
ejpam-1853	66	4	,	,	PUNCT
ejpam-1853	66	5	m(x	m(x	PROPN
ejpam-1853	66	6	,	,	PUNCT
ejpam-1853	66	7	y	y	PROPN
ejpam-1853	66	8	)	)	PUNCT
ejpam-1853	66	9	:	:	PUNCT
ejpam-1853	67	1	=	=	PUNCT
ejpam-1853	67	2	x	x	SYM
ejpam-1853	67	3	y	y	PROPN
ejpam-1853	67	4	,	,	PUNCT
ejpam-1853	67	5	ε(e	ε(e	PROPN
ejpam-1853	67	6	)	)	PUNCT
ejpam-1853	67	7	:	:	PUNCT
ejpam-1853	67	8	=	=	SYM
ejpam-1853	67	9	e	e	NOUN
ejpam-1853	67	10	and	and	CCONJ
ejpam-1853	67	11	i(x	i(x	PROPN
ejpam-1853	67	12	)	)	PUNCT
ejpam-1853	67	13	:	:	PUNCT
ejpam-1853	68	1	=	=	PUNCT
ejpam-1853	68	2	x−1	x−1	NOUN
ejpam-1853	68	3	.	.	PUNCT
ejpam-1853	69	1	conversely	conversely	ADV
ejpam-1853	69	2	,	,	PUNCT
ejpam-1853	69	3	a	a	DET
ejpam-1853	69	4	groupoid	groupoid	NOUN
ejpam-1853	69	5	with	with	ADP
ejpam-1853	69	6	one	one	NUM
ejpam-1853	69	7	unit	unit	NOUN
ejpam-1853	69	8	(	(	PUNCT
ejpam-1853	69	9	i.e.	i.e.	X
ejpam-1853	69	10	,	,	PUNCT
ejpam-1853	69	11	g0	g0	NOUN
ejpam-1853	69	12	=	=	SYM
ejpam-1853	69	13	{	{	PUNCT
ejpam-1853	69	14	e	e	NOUN
ejpam-1853	69	15	}	}	PUNCT
ejpam-1853	69	16	)	)	PUNCT
ejpam-1853	69	17	is	be	AUX
ejpam-1853	69	18	a	a	DET
ejpam-1853	69	19	group	group	NOUN
ejpam-1853	69	20	.	.	PUNCT
ejpam-1853	70	1	(	(	PUNCT
ejpam-1853	70	2	iii	iii	NOUN
ejpam-1853	70	3	)	)	PUNCT
ejpam-1853	70	4	for	for	ADP
ejpam-1853	70	5	the	the	DET
ejpam-1853	70	6	groupoids	groupoid	NOUN
ejpam-1853	70	7	(	(	PUNCT
ejpam-1853	70	8	g	g	PROPN
ejpam-1853	70	9	j	j	PROPN
ejpam-1853	70	10	,	,	PUNCT
ejpam-1853	70	11	α	α	PROPN
ejpam-1853	70	12	j	j	PROPN
ejpam-1853	70	13	,	,	PUNCT
ejpam-1853	70	14	β	β	PROPN
ejpam-1853	70	15	j	j	PROPN
ejpam-1853	70	16	,	,	PUNCT
ejpam-1853	70	17	m	m	VERB
ejpam-1853	70	18	j	j	PROPN
ejpam-1853	70	19	,	,	PUNCT
ejpam-1853	70	20	ε	ε	PROPN
ejpam-1853	70	21	j	j	PROPN
ejpam-1853	70	22	,	,	PUNCT
ejpam-1853	70	23	i	i	PRON
ejpam-1853	70	24	j	j	PROPN
ejpam-1853	70	25	,	,	PUNCT
ejpam-1853	70	26	g	g	PROPN
ejpam-1853	70	27	j,0	j,0	PROPN
ejpam-1853	70	28	)	)	PUNCT
ejpam-1853	70	29	,	,	PUNCT
ejpam-1853	70	30	j	j	PROPN
ejpam-1853	70	31	=	=	SYM
ejpam-1853	70	32	1,2	1,2	NUM
ejpam-1853	70	33	,	,	PUNCT
ejpam-1853	70	34	one	one	PRON
ejpam-1853	70	35	may	may	AUX
ejpam-1853	70	36	construct	construct	VERB
ejpam-1853	70	37	the	the	DET
ejpam-1853	70	38	groupoid	groupoid	PROPN
ejpam-1853	70	39	g1×g2	g1×g2	PROPN
ejpam-1853	70	40	whose	whose	DET
ejpam-1853	70	41	its	its	PRON
ejpam-1853	70	42	structure	structure	NOUN
ejpam-1853	70	43	functions	function	NOUN
ejpam-1853	70	44	are	be	AUX
ejpam-1853	70	45	given	give	VERB
ejpam-1853	70	46	by	by	ADP
ejpam-1853	70	47	:	:	PUNCT
ejpam-1853	70	48	α	α	NOUN
ejpam-1853	70	49	:	:	PUNCT
ejpam-1853	70	50	=	=	SYM
ejpam-1853	70	51	α1×α2	α1×α2	PROPN
ejpam-1853	70	52	,	,	PUNCT
ejpam-1853	70	53	β	β	X
ejpam-1853	70	54	:	:	PUNCT
ejpam-1853	70	55	=	=	SYM
ejpam-1853	70	56	β1×β2	β1×β2	ADV
ejpam-1853	70	57	,	,	PUNCT
ejpam-1853	70	58	ε	ε	PROPN
ejpam-1853	70	59	:	:	PUNCT
ejpam-1853	70	60	=	=	SYM
ejpam-1853	70	61	ε1×ε2	ε1×ε2	PROPN
ejpam-1853	70	62	,	,	PUNCT
ejpam-1853	70	63	i	i	PRON
ejpam-1853	70	64	:	:	PUNCT
ejpam-1853	70	65	=	=	PROPN
ejpam-1853	70	66	i1	i1	PROPN
ejpam-1853	70	67	×	×	PROPN
ejpam-1853	70	68	i2	i2	PROPN
ejpam-1853	70	69	and	and	CCONJ
ejpam-1853	70	70	m((g1	m((g1	NOUN
ejpam-1853	70	71	,	,	PUNCT
ejpam-1853	70	72	g2	g2	PROPN
ejpam-1853	70	73	)	)	PUNCT
ejpam-1853	70	74	,	,	PUNCT
ejpam-1853	70	75	(	(	PUNCT
ejpam-1853	70	76	g	g	PROPN
ejpam-1853	70	77	′1	′1	PROPN
ejpam-1853	70	78	,	,	PUNCT
ejpam-1853	70	79	g	g	NOUN
ejpam-1853	70	80	′2	′2	NOUN
ejpam-1853	70	81	)	)	PUNCT
ejpam-1853	70	82	)	)	PUNCT
ejpam-1853	71	1	=	=	PRON
ejpam-1853	71	2	(	(	PUNCT
ejpam-1853	71	3	m1(g1	m1(g1	PROPN
ejpam-1853	71	4	,	,	PUNCT
ejpam-1853	71	5	g	g	PROPN
ejpam-1853	71	6	′1	′1	NOUN
ejpam-1853	71	7	)	)	PUNCT
ejpam-1853	71	8	,	,	PUNCT
ejpam-1853	71	9	m2(g2	m2(g2	NOUN
ejpam-1853	71	10	,	,	PUNCT
ejpam-1853	71	11	g	g	NOUN
ejpam-1853	71	12	′2	′2	NOUN
ejpam-1853	71	13	)	)	PUNCT
ejpam-1853	71	14	)	)	PUNCT
ejpam-1853	71	15	for	for	ADP
ejpam-1853	71	16	all	all	DET
ejpam-1853	71	17	(	(	PUNCT
ejpam-1853	71	18	g	g	NOUN
ejpam-1853	71	19	,	,	PUNCT
ejpam-1853	71	20	g	g	PROPN
ejpam-1853	71	21	′1	′1	AUX
ejpam-1853	71	22	)	)	PUNCT
ejpam-1853	71	23	∈	∈	PROPN
ejpam-1853	71	24	g(2	g(2	PROPN
ejpam-1853	71	25	)	)	PUNCT
ejpam-1853	71	26	,	,	PUNCT
ejpam-1853	71	27	(	(	PUNCT
ejpam-1853	71	28	g2	g2	PROPN
ejpam-1853	71	29	,	,	PUNCT
ejpam-1853	71	30	g	g	NOUN
ejpam-1853	71	31	′2	′2	NOUN
ejpam-1853	71	32	)	)	PUNCT
ejpam-1853	71	33	∈	∈	PROPN
ejpam-1853	71	34	g(2	g(2	PROPN
ejpam-1853	71	35	)	)	PUNCT
ejpam-1853	71	36	.	.	PUNCT
ejpam-1853	72	1	then	then	ADV
ejpam-1853	72	2	(	(	PUNCT
ejpam-1853	72	3	g1	g1	VERB
ejpam-1853	72	4	×	×	PROPN
ejpam-1853	72	5	g2,α	g2,α	PROPN
ejpam-1853	72	6	,	,	PUNCT
ejpam-1853	72	7	m	m	PROPN
ejpam-1853	72	8	,	,	PUNCT
ejpam-1853	72	9	ε	ε	PROPN
ejpam-1853	72	10	,	,	PUNCT
ejpam-1853	72	11	i	i	PRON
ejpam-1853	72	12	,	,	PUNCT
ejpam-1853	72	13	g1,0	g1,0	PROPN
ejpam-1853	72	14	×	×	PROPN
ejpam-1853	72	15	g2,0	g2,0	PROPN
ejpam-1853	72	16	)	)	PUNCT
ejpam-1853	72	17	is	be	AUX
ejpam-1853	72	18	a	a	DET
ejpam-1853	72	19	groupoid	groupoid	NOUN
ejpam-1853	72	20	,	,	PUNCT
ejpam-1853	72	21	called	call	VERB
ejpam-1853	72	22	the	the	DET
ejpam-1853	72	23	direct	direct	ADJ
ejpam-1853	72	24	product	product	NOUN
ejpam-1853	72	25	of	of	ADP
ejpam-1853	72	26	(	(	PUNCT
ejpam-1853	72	27	g1	g1	X
ejpam-1853	72	28	,	,	PUNCT
ejpam-1853	72	29	g1,0	g1,0	PROPN
ejpam-1853	72	30	)	)	PUNCT
ejpam-1853	72	31	and	and	CCONJ
ejpam-1853	72	32	(	(	PUNCT
ejpam-1853	72	33	g2	g2	PROPN
ejpam-1853	72	34	,	,	PUNCT
ejpam-1853	72	35	g2,0	g2,0	PROPN
ejpam-1853	72	36	)	)	PUNCT
ejpam-1853	72	37	.	.	PUNCT
ejpam-1853	73	1	definition	definition	NOUN
ejpam-1853	73	2	2	2	NUM
ejpam-1853	73	3	(	(	PUNCT
ejpam-1853	73	4	[	[	X
ejpam-1853	73	5	8	8	NUM
ejpam-1853	73	6	]	]	PUNCT
ejpam-1853	73	7	)	)	PUNCT
ejpam-1853	73	8	.	.	PUNCT
ejpam-1853	74	1	let	let	AUX
ejpam-1853	74	2	(	(	PUNCT
ejpam-1853	74	3	g	g	NOUN
ejpam-1853	74	4	,	,	PUNCT
ejpam-1853	74	5	α	α	X
ejpam-1853	74	6	,	,	PUNCT
ejpam-1853	74	7	β	β	X
ejpam-1853	74	8	,	,	PUNCT
ejpam-1853	74	9	m	m	PROPN
ejpam-1853	74	10	,	,	PUNCT
ejpam-1853	74	11	ε	ε	PROPN
ejpam-1853	74	12	,	,	PUNCT
ejpam-1853	74	13	i	i	PROPN
ejpam-1853	74	14	,	,	PUNCT
ejpam-1853	74	15	g0	g0	PROPN
ejpam-1853	74	16	)	)	PUNCT
ejpam-1853	74	17	be	be	AUX
ejpam-1853	74	18	a	a	DET
ejpam-1853	74	19	groupoid	groupoid	NOUN
ejpam-1853	74	20	.	.	PUNCT
ejpam-1853	75	1	(	(	PUNCT
ejpam-1853	75	2	i	i	NOUN
ejpam-1853	75	3	)	)	PUNCT
ejpam-1853	75	4	a	a	DET
ejpam-1853	75	5	pair	pair	NOUN
ejpam-1853	75	6	(	(	PUNCT
ejpam-1853	75	7	h	h	NOUN
ejpam-1853	75	8	,	,	PUNCT
ejpam-1853	75	9	h0	h0	PROPN
ejpam-1853	75	10	)	)	PUNCT
ejpam-1853	75	11	of	of	ADP
ejpam-1853	75	12	nonempty	nonempty	ADJ
ejpam-1853	75	13	subsets	subset	NOUN
ejpam-1853	75	14	where	where	SCONJ
ejpam-1853	75	15	h	h	NOUN
ejpam-1853	75	16	⊆	⊆	NUM
ejpam-1853	75	17	g	g	NOUN
ejpam-1853	75	18	and	and	CCONJ
ejpam-1853	75	19	h0	h0	PROPN
ejpam-1853	75	20	⊆	⊆	NUM
ejpam-1853	75	21	g0	g0	NOUN
ejpam-1853	75	22	,	,	PUNCT
ejpam-1853	75	23	is	be	AUX
ejpam-1853	75	24	called	call	VERB
ejpam-1853	75	25	subgroupoid	subgroupoid	NOUN
ejpam-1853	75	26	of	of	ADP
ejpam-1853	75	27	g	g	NOUN
ejpam-1853	75	28	,	,	PUNCT
ejpam-1853	75	29	if	if	SCONJ
ejpam-1853	75	30	:	:	PUNCT
ejpam-1853	75	31	(	(	PUNCT
ejpam-1853	75	32	1	1	X
ejpam-1853	75	33	)	)	PUNCT
ejpam-1853	75	34	α(h	α(h	NOUN
ejpam-1853	75	35	)	)	PUNCT
ejpam-1853	75	36	=	=	SYM
ejpam-1853	75	37	h0	h0	NOUN
ejpam-1853	75	38	and	and	CCONJ
ejpam-1853	75	39	β(h	β(h	ADJ
ejpam-1853	75	40	)	)	PUNCT
ejpam-1853	75	41	=	=	SYM
ejpam-1853	75	42	h0	h0	PROPN
ejpam-1853	75	43	;	;	PUNCT
ejpam-1853	75	44	(	(	PUNCT
ejpam-1853	75	45	2	2	X
ejpam-1853	75	46	)	)	PUNCT
ejpam-1853	75	47	h	h	NOUN
ejpam-1853	75	48	is	be	AUX
ejpam-1853	75	49	closed	close	VERB
ejpam-1853	75	50	under	under	ADP
ejpam-1853	75	51	partially	partially	ADV
ejpam-1853	75	52	multiplication	multiplication	NOUN
ejpam-1853	75	53	and	and	CCONJ
ejpam-1853	75	54	inversion	inversion	NOUN
ejpam-1853	75	55	,	,	PUNCT
ejpam-1853	75	56	that	that	PRON
ejpam-1853	75	57	is	be	AUX
ejpam-1853	75	58	:	:	PUNCT
ejpam-1853	75	59	(	(	PUNCT
ejpam-1853	75	60	a	a	X
ejpam-1853	75	61	)	)	PUNCT
ejpam-1853	75	62	(	(	PUNCT
ejpam-1853	75	63	∀	∀	NUM
ejpam-1853	75	64	)	)	PUNCT
ejpam-1853	75	65	x	x	X
ejpam-1853	75	66	,	,	PUNCT
ejpam-1853	75	67	y	y	PROPN
ejpam-1853	75	68	∈	∈	PROPN
ejpam-1853	75	69	h	h	NOUN
ejpam-1853	75	70	such	such	ADJ
ejpam-1853	75	71	that	that	SCONJ
ejpam-1853	75	72	(	(	PUNCT
ejpam-1853	75	73	x	x	X
ejpam-1853	75	74	,	,	PUNCT
ejpam-1853	75	75	y	y	PROPN
ejpam-1853	75	76	)	)	PUNCT
ejpam-1853	75	77	∈	∈	PROPN
ejpam-1853	75	78	g(2	g(2	PROPN
ejpam-1853	75	79	)	)	PUNCT
ejpam-1853	75	80	we	we	PRON
ejpam-1853	75	81	have	have	VERB
ejpam-1853	75	82	x	x	X
ejpam-1853	75	83	·	·	PUNCT
ejpam-1853	75	84	y	y	PROPN
ejpam-1853	75	85	∈	∈	PROPN
ejpam-1853	75	86	h	h	NOUN
ejpam-1853	75	87	;	;	PUNCT
ejpam-1853	76	1	(	(	PUNCT
ejpam-1853	76	2	b	b	X
ejpam-1853	76	3	)	)	PUNCT
ejpam-1853	76	4	x−1	x−1	NOUN
ejpam-1853	76	5	∈	∈	PROPN
ejpam-1853	76	6	h	h	NOUN
ejpam-1853	76	7	,	,	PUNCT
ejpam-1853	76	8	for	for	ADP
ejpam-1853	76	9	all	all	DET
ejpam-1853	76	10	x	x	SYM
ejpam-1853	76	11	∈	∈	PROPN
ejpam-1853	76	12	h.	h.	PROPN
ejpam-1853	76	13	(	(	PUNCT
ejpam-1853	76	14	ii	ii	PROPN
ejpam-1853	76	15	)	)	PUNCT
ejpam-1853	76	16	a	a	DET
ejpam-1853	76	17	subgroupoid	subgroupoid	NOUN
ejpam-1853	76	18	(	(	PUNCT
ejpam-1853	76	19	h	h	NOUN
ejpam-1853	76	20	,	,	PUNCT
ejpam-1853	76	21	h0	h0	PROPN
ejpam-1853	76	22	)	)	PUNCT
ejpam-1853	76	23	of	of	ADP
ejpam-1853	76	24	(	(	PUNCT
ejpam-1853	76	25	g	g	PROPN
ejpam-1853	76	26	,	,	PUNCT
ejpam-1853	76	27	g0	g0	PROPN
ejpam-1853	76	28	)	)	PUNCT
ejpam-1853	76	29	is	be	AUX
ejpam-1853	76	30	said	say	VERB
ejpam-1853	76	31	to	to	PART
ejpam-1853	76	32	be	be	AUX
ejpam-1853	76	33	wide	wide	ADJ
ejpam-1853	76	34	,	,	PUNCT
ejpam-1853	76	35	if	if	SCONJ
ejpam-1853	76	36	h0	h0	PROPN
ejpam-1853	76	37	=	=	PROPN
ejpam-1853	76	38	g0	g0	PROPN
ejpam-1853	76	39	.	.	PUNCT
ejpam-1853	77	1	(	(	PUNCT
ejpam-1853	77	2	iii	iii	X
ejpam-1853	77	3	)	)	PUNCT
ejpam-1853	77	4	a	a	DET
ejpam-1853	77	5	wide	wide	ADJ
ejpam-1853	77	6	subgroupoid	subgroupoid	NOUN
ejpam-1853	77	7	(	(	PUNCT
ejpam-1853	77	8	n	n	CCONJ
ejpam-1853	77	9	,	,	PUNCT
ejpam-1853	77	10	n0	n0	NUM
ejpam-1853	77	11	)	)	PUNCT
ejpam-1853	77	12	of	of	ADP
ejpam-1853	77	13	(	(	PUNCT
ejpam-1853	77	14	g	g	PROPN
ejpam-1853	77	15	,	,	PUNCT
ejpam-1853	77	16	g0	g0	PROPN
ejpam-1853	77	17	)	)	PUNCT
ejpam-1853	77	18	is	be	AUX
ejpam-1853	77	19	called	call	VERB
ejpam-1853	77	20	normal	normal	ADJ
ejpam-1853	77	21	,	,	PUNCT
ejpam-1853	77	22	if	if	SCONJ
ejpam-1853	77	23	for	for	ADP
ejpam-1853	77	24	all	all	DET
ejpam-1853	77	25	x	x	SYM
ejpam-1853	77	26	∈	∈	PROPN
ejpam-1853	77	27	g	g	NOUN
ejpam-1853	77	28	and	and	CCONJ
ejpam-1853	77	29	a	a	DET
ejpam-1853	77	30	∈	∈	NOUN
ejpam-1853	77	31	n	n	CCONJ
ejpam-1853	77	32	we	we	PRON
ejpam-1853	77	33	have	have	VERB
ejpam-1853	77	34	x	x	X
ejpam-1853	77	35	·	·	PUNCT
ejpam-1853	77	36	a	a	DET
ejpam-1853	77	37	·	·	PUNCT
ejpam-1853	77	38	x−1	x−1	PROPN
ejpam-1853	77	39	∈	∈	PROPN
ejpam-1853	77	40	n.	n.	PROPN
ejpam-1853	77	41	definition	definition	NOUN
ejpam-1853	77	42	3	3	NUM
ejpam-1853	77	43	(	(	PUNCT
ejpam-1853	77	44	[	[	X
ejpam-1853	77	45	9	9	NUM
ejpam-1853	77	46	]	]	PUNCT
ejpam-1853	77	47	)	)	PUNCT
ejpam-1853	77	48	.	.	PUNCT
ejpam-1853	78	1	let	let	VERB
ejpam-1853	78	2	(	(	PUNCT
ejpam-1853	78	3	g	g	NOUN
ejpam-1853	78	4	,	,	PUNCT
ejpam-1853	78	5	α	α	NOUN
ejpam-1853	78	6	,	,	PUNCT
ejpam-1853	78	7	β	β	X
ejpam-1853	78	8	,	,	PUNCT
ejpam-1853	78	9	g0	g0	PROPN
ejpam-1853	78	10	)	)	PUNCT
ejpam-1853	78	11	and	and	CCONJ
ejpam-1853	78	12	(	(	PUNCT
ejpam-1853	78	13	g′,α′,β	g′,α′,β	INTJ
ejpam-1853	78	14	′	′	NUM
ejpam-1853	78	15	,	,	PUNCT
ejpam-1853	78	16	g′0	g′0	ADJ
ejpam-1853	78	17	)	)	PUNCT
ejpam-1853	78	18	be	be	VERB
ejpam-1853	78	19	two	two	NUM
ejpam-1853	78	20	groupoids	groupoid	NOUN
ejpam-1853	78	21	.	.	PUNCT
ejpam-1853	79	1	(	(	PUNCT
ejpam-1853	79	2	i	i	NOUN
ejpam-1853	79	3	)	)	PUNCT
ejpam-1853	79	4	a	a	DET
ejpam-1853	79	5	morphism	morphism	NOUN
ejpam-1853	79	6	of	of	ADP
ejpam-1853	79	7	groupoids	groupoid	NOUN
ejpam-1853	79	8	or	or	CCONJ
ejpam-1853	79	9	groupoid	groupoid	PROPN
ejpam-1853	79	10	morphism	morphism	NOUN
ejpam-1853	79	11	from	from	ADP
ejpam-1853	79	12	g	g	NOUN
ejpam-1853	79	13	into	into	ADP
ejpam-1853	79	14	g′	g′	NOUN
ejpam-1853	79	15	is	be	AUX
ejpam-1853	79	16	a	a	DET
ejpam-1853	79	17	pair	pair	NOUN
ejpam-1853	79	18	(	(	PUNCT
ejpam-1853	79	19	f	f	NOUN
ejpam-1853	79	20	,	,	PUNCT
ejpam-1853	79	21	f0	f0	PROPN
ejpam-1853	79	22	)	)	PUNCT
ejpam-1853	79	23	of	of	ADP
ejpam-1853	79	24	maps	map	NOUN
ejpam-1853	79	25	f	f	PROPN
ejpam-1853	79	26	:	:	PUNCT
ejpam-1853	79	27	g→	g→	PROPN
ejpam-1853	79	28	g′	g′	NOUN
ejpam-1853	79	29	and	and	CCONJ
ejpam-1853	79	30	f0	f0	PROPN
ejpam-1853	79	31	:	:	PUNCT
ejpam-1853	79	32	g0→	g0→	X
ejpam-1853	79	33	g′0	g′0	VERB
ejpam-1853	79	34	such	such	ADJ
ejpam-1853	79	35	that	that	SCONJ
ejpam-1853	79	36	the	the	DET
ejpam-1853	79	37	following	follow	VERB
ejpam-1853	79	38	conditions	condition	NOUN
ejpam-1853	79	39	hold	hold	VERB
ejpam-1853	79	40	:	:	PUNCT
ejpam-1853	79	41	(	(	PUNCT
ejpam-1853	79	42	i1	i1	NOUN
ejpam-1853	79	43	)	)	PUNCT
ejpam-1853	79	44	α′	α′	NUM
ejpam-1853	80	1	◦	◦	NOUN
ejpam-1853	80	2	f	f	NOUN
ejpam-1853	80	3	=	=	SYM
ejpam-1853	80	4	f0	f0	PROPN
ejpam-1853	80	5	◦	◦	NOUN
ejpam-1853	80	6	α	α	NOUN
ejpam-1853	80	7	,	,	PUNCT
ejpam-1853	80	8	β	β	X
ejpam-1853	80	9	′	′	NUM
ejpam-1853	81	1	◦	◦	NOUN
ejpam-1853	81	2	f	f	X
ejpam-1853	82	1	=	=	SYM
ejpam-1853	82	2	f0	f0	PROPN
ejpam-1853	82	3	◦	◦	NOUN
ejpam-1853	82	4	β	β	NOUN
ejpam-1853	82	5	;	;	PUNCT
ejpam-1853	82	6	(	(	PUNCT
ejpam-1853	82	7	i2	i2	PROPN
ejpam-1853	82	8	)	)	PUNCT
ejpam-1853	82	9	f	f	PROPN
ejpam-1853	82	10	(	(	PUNCT
ejpam-1853	82	11	m(x	m(x	PROPN
ejpam-1853	82	12	,	,	PUNCT
ejpam-1853	82	13	y	y	PROPN
ejpam-1853	82	14	)	)	PUNCT
ejpam-1853	82	15	)	)	PUNCT
ejpam-1853	83	1	=	=	SYM
ejpam-1853	83	2	m′	m′	NOUN
ejpam-1853	83	3	(	(	PUNCT
ejpam-1853	83	4	f	f	PROPN
ejpam-1853	83	5	(	(	PUNCT
ejpam-1853	83	6	x	x	NOUN
ejpam-1853	83	7	)	)	PUNCT
ejpam-1853	83	8	,	,	PUNCT
ejpam-1853	83	9	f	f	PROPN
ejpam-1853	83	10	(	(	PUNCT
ejpam-1853	83	11	y	y	NOUN
ejpam-1853	83	12	)	)	PUNCT
ejpam-1853	83	13	)	)	PUNCT
ejpam-1853	83	14	for	for	ADP
ejpam-1853	83	15	all	all	DET
ejpam-1853	83	16	(	(	PUNCT
ejpam-1853	83	17	x	x	INTJ
ejpam-1853	83	18	,	,	PUNCT
ejpam-1853	83	19	y	y	PROPN
ejpam-1853	83	20	)	)	PUNCT
ejpam-1853	83	21	∈	∈	PROPN
ejpam-1853	83	22	g(2	g(2	PROPN
ejpam-1853	83	23	)	)	PUNCT
ejpam-1853	83	24	.	.	PUNCT
ejpam-1853	84	1	(	(	PUNCT
ejpam-1853	84	2	ii	ii	NOUN
ejpam-1853	84	3	)	)	PUNCT
ejpam-1853	84	4	if	if	SCONJ
ejpam-1853	84	5	g0	g0	NOUN
ejpam-1853	84	6	=	=	SYM
ejpam-1853	84	7	g′0	g′0	NOUN
ejpam-1853	84	8	and	and	CCONJ
ejpam-1853	84	9	f0	f0	PROPN
ejpam-1853	84	10	=	=	SYM
ejpam-1853	84	11	idg0	idg0	PROPN
ejpam-1853	84	12	,	,	PUNCT
ejpam-1853	84	13	we	we	PRON
ejpam-1853	84	14	say	say	VERB
ejpam-1853	84	15	that	that	SCONJ
ejpam-1853	84	16	f	f	PROPN
ejpam-1853	84	17	is	be	AUX
ejpam-1853	84	18	a	a	DET
ejpam-1853	84	19	g0−morphism	g0−morphism	NOUN
ejpam-1853	84	20	of	of	ADP
ejpam-1853	84	21	groupoids	groupoid	NOUN
ejpam-1853	84	22	.	.	PUNCT
ejpam-1853	85	1	(	(	PUNCT
ejpam-1853	85	2	iii	iii	X
ejpam-1853	85	3	)	)	PUNCT
ejpam-1853	85	4	a	a	DET
ejpam-1853	85	5	groupoid	groupoid	PROPN
ejpam-1853	85	6	morphism	morphism	NOUN
ejpam-1853	85	7	(	(	PUNCT
ejpam-1853	85	8	f	f	PROPN
ejpam-1853	85	9	,	,	PUNCT
ejpam-1853	85	10	f0	f0	PROPN
ejpam-1853	85	11	)	)	PUNCT
ejpam-1853	85	12	:	:	PUNCT
ejpam-1853	85	13	(	(	PUNCT
ejpam-1853	85	14	g	g	NOUN
ejpam-1853	85	15	,	,	PUNCT
ejpam-1853	85	16	g0)→	g0)→	X
ejpam-1853	85	17	(	(	PUNCT
ejpam-1853	85	18	g′	g′	NOUN
ejpam-1853	85	19	,	,	PUNCT
ejpam-1853	85	20	g′0	g′0	ADJ
ejpam-1853	85	21	)	)	PUNCT
ejpam-1853	85	22	such	such	ADJ
ejpam-1853	85	23	that	that	SCONJ
ejpam-1853	85	24	f	f	PROPN
ejpam-1853	85	25	and	and	CCONJ
ejpam-1853	85	26	f0	f0	PROPN
ejpam-1853	85	27	are	be	AUX
ejpam-1853	85	28	bijective	bijective	ADJ
ejpam-1853	85	29	maps	map	NOUN
ejpam-1853	85	30	,	,	PUNCT
ejpam-1853	85	31	is	be	AUX
ejpam-1853	85	32	called	call	VERB
ejpam-1853	85	33	isomorphism	isomorphism	NOUN
ejpam-1853	85	34	of	of	ADP
ejpam-1853	85	35	groupoids	groupoid	NOUN
ejpam-1853	85	36	.	.	PUNCT
ejpam-1853	86	1	if	if	SCONJ
ejpam-1853	86	2	(	(	PUNCT
ejpam-1853	86	3	f	f	X
ejpam-1853	86	4	,	,	PUNCT
ejpam-1853	86	5	f0	f0	PROPN
ejpam-1853	86	6	)	)	PUNCT
ejpam-1853	86	7	:	:	PUNCT
ejpam-1853	86	8	(	(	PUNCT
ejpam-1853	86	9	g	g	NOUN
ejpam-1853	86	10	,	,	PUNCT
ejpam-1853	86	11	g0)→	g0)→	X
ejpam-1853	86	12	(	(	PUNCT
ejpam-1853	86	13	g′	g′	NOUN
ejpam-1853	86	14	,	,	PUNCT
ejpam-1853	86	15	g′0	g′0	ADJ
ejpam-1853	86	16	)	)	PUNCT
ejpam-1853	86	17	is	be	AUX
ejpam-1853	86	18	a	a	DET
ejpam-1853	86	19	groupoid	groupoid	PROPN
ejpam-1853	86	20	morphism	morphism	NOUN
ejpam-1853	86	21	,	,	PUNCT
ejpam-1853	86	22	then	then	ADV
ejpam-1853	86	23	[	[	X
ejpam-1853	86	24	8	8	NUM
ejpam-1853	86	25	]	]	PUNCT
ejpam-1853	86	26	:	:	PUNCT
ejpam-1853	86	27	f	f	X
ejpam-1853	86	28	◦	◦	NOUN
ejpam-1853	86	29	ε	ε	X
ejpam-1853	86	30	=	=	SYM
ejpam-1853	86	31	ε′	ε′	NOUN
ejpam-1853	86	32	◦	◦	NOUN
ejpam-1853	86	33	f0	f0	PROPN
ejpam-1853	86	34	and	and	CCONJ
ejpam-1853	86	35	f	f	PROPN
ejpam-1853	86	36	◦	◦	NOUN
ejpam-1853	86	37	i	i	NOUN
ejpam-1853	86	38	=	=	NOUN
ejpam-1853	86	39	i′	i′	NOUN
ejpam-1853	86	40	◦	◦	NOUN
ejpam-1853	86	41	f	f	X
ejpam-1853	86	42	.	.	PUNCT
ejpam-1853	87	1	(	(	PUNCT
ejpam-1853	87	2	1	1	X
ejpam-1853	87	3	)	)	PUNCT
ejpam-1853	87	4	m.	m.	NOUN
ejpam-1853	87	5	ivan	ivan	PROPN
ejpam-1853	87	6	/	/	PUNCT
ejpam-1853	87	7	eur	eur	PROPN
ejpam-1853	87	8	.	.	PUNCT
ejpam-1853	88	1	j.	j.	PROPN
ejpam-1853	88	2	pure	pure	PROPN
ejpam-1853	88	3	appl	appl	PROPN
ejpam-1853	88	4	.	.	PROPN
ejpam-1853	88	5	math	math	PROPN
ejpam-1853	88	6	,	,	PUNCT
ejpam-1853	88	7	6	6	NUM
ejpam-1853	88	8	(	(	PUNCT
ejpam-1853	88	9	2013	2013	NUM
ejpam-1853	88	10	)	)	PUNCT
ejpam-1853	88	11	,	,	PUNCT
ejpam-1853	88	12	469	469	NUM
ejpam-1853	88	13	-	-	SYM
ejpam-1853	88	14	484	484	NUM
ejpam-1853	88	15	472	472	NUM
ejpam-1853	88	16	in	in	ADP
ejpam-1853	88	17	the	the	DET
ejpam-1853	88	18	sequel	sequel	NOUN
ejpam-1853	88	19	we	we	PRON
ejpam-1853	88	20	describe	describe	VERB
ejpam-1853	88	21	the	the	DET
ejpam-1853	88	22	notion	notion	NOUN
ejpam-1853	88	23	of	of	ADP
ejpam-1853	88	24	group	group	NOUN
ejpam-1853	88	25	-	-	PUNCT
ejpam-1853	88	26	groupoid	groupoid	PROPN
ejpam-1853	88	27	as	as	ADP
ejpam-1853	88	28	algebraic	algebraic	ADJ
ejpam-1853	88	29	structure	structure	NOUN
ejpam-1853	88	30	(	(	PUNCT
ejpam-1853	88	31	for	for	ADP
ejpam-1853	88	32	definition	definition	NOUN
ejpam-1853	88	33	see	see	VERB
ejpam-1853	88	34	[	[	X
ejpam-1853	88	35	4	4	NUM
ejpam-1853	88	36	]	]	NUM
ejpam-1853	88	37	)	)	PUNCT
ejpam-1853	88	38	.	.	PUNCT
ejpam-1853	89	1	a	a	DET
ejpam-1853	89	2	group	group	NOUN
ejpam-1853	89	3	structure	structure	NOUN
ejpam-1853	89	4	on	on	ADP
ejpam-1853	89	5	a	a	DET
ejpam-1853	89	6	nonempty	nonempty	ADJ
ejpam-1853	89	7	set	set	NOUN
ejpam-1853	89	8	is	be	AUX
ejpam-1853	89	9	regarded	regard	VERB
ejpam-1853	89	10	as	as	ADP
ejpam-1853	89	11	an	an	DET
ejpam-1853	89	12	universal	universal	ADJ
ejpam-1853	89	13	algebra	algebra	NOUN
ejpam-1853	89	14	determined	determine	VERB
ejpam-1853	89	15	by	by	ADP
ejpam-1853	89	16	a	a	DET
ejpam-1853	89	17	binary	binary	ADJ
ejpam-1853	89	18	operation	operation	NOUN
ejpam-1853	89	19	,	,	PUNCT
ejpam-1853	89	20	an	an	DET
ejpam-1853	89	21	nullary	nullary	ADJ
ejpam-1853	89	22	operation	operation	NOUN
ejpam-1853	89	23	and	and	CCONJ
ejpam-1853	89	24	an	an	DET
ejpam-1853	89	25	unary	unary	ADJ
ejpam-1853	89	26	operation	operation	NOUN
ejpam-1853	89	27	.	.	PUNCT
ejpam-1853	90	1	let	let	AUX
ejpam-1853	90	2	(	(	PUNCT
ejpam-1853	90	3	g	g	NOUN
ejpam-1853	90	4	,	,	PUNCT
ejpam-1853	90	5	α	α	X
ejpam-1853	90	6	,	,	PUNCT
ejpam-1853	90	7	β	β	X
ejpam-1853	90	8	,	,	PUNCT
ejpam-1853	90	9	m	m	PROPN
ejpam-1853	90	10	,	,	PUNCT
ejpam-1853	90	11	ε	ε	PROPN
ejpam-1853	90	12	,	,	PUNCT
ejpam-1853	90	13	i	i	PROPN
ejpam-1853	90	14	,	,	PUNCT
ejpam-1853	90	15	g0	g0	PROPN
ejpam-1853	90	16	)	)	PUNCT
ejpam-1853	90	17	be	be	AUX
ejpam-1853	90	18	a	a	DET
ejpam-1853	90	19	groupoid	groupoid	NOUN
ejpam-1853	90	20	.	.	PUNCT
ejpam-1853	91	1	we	we	PRON
ejpam-1853	91	2	suppose	suppose	VERB
ejpam-1853	91	3	that	that	SCONJ
ejpam-1853	91	4	on	on	ADP
ejpam-1853	91	5	g	g	PROPN
ejpam-1853	91	6	is	be	AUX
ejpam-1853	91	7	defined	define	VERB
ejpam-1853	91	8	a	a	DET
ejpam-1853	91	9	group	group	NOUN
ejpam-1853	91	10	structure	structure	NOUN
ejpam-1853	91	11	ω	ω	NOUN
ejpam-1853	91	12	:	:	PUNCT
ejpam-1853	91	13	g	g	PROPN
ejpam-1853	91	14	×	×	PROPN
ejpam-1853	91	15	g→	g→	PROPN
ejpam-1853	91	16	g	g	NOUN
ejpam-1853	91	17	,	,	PUNCT
ejpam-1853	91	18	(	(	PUNCT
ejpam-1853	91	19	x	x	X
ejpam-1853	91	20	,	,	PUNCT
ejpam-1853	91	21	y	y	PROPN
ejpam-1853	91	22	)	)	PUNCT
ejpam-1853	91	23	7→ω(x	7→ω(x	NUM
ejpam-1853	91	24	,	,	PUNCT
ejpam-1853	91	25	y	y	PROPN
ejpam-1853	91	26	)	)	PUNCT
ejpam-1853	91	27	:	:	PUNCT
ejpam-1853	92	1	=	=	SYM
ejpam-1853	92	2	x	x	SYM
ejpam-1853	92	3	⊕	⊕	PROPN
ejpam-1853	92	4	y	y	PROPN
ejpam-1853	92	5	.	.	PUNCT
ejpam-1853	93	1	the	the	DET
ejpam-1853	93	2	unit	unit	NOUN
ejpam-1853	93	3	element	element	NOUN
ejpam-1853	93	4	of	of	ADP
ejpam-1853	93	5	the	the	DET
ejpam-1853	93	6	group	group	NOUN
ejpam-1853	93	7	g	g	PROPN
ejpam-1853	93	8	is	be	AUX
ejpam-1853	93	9	denoted	denote	VERB
ejpam-1853	93	10	by	by	ADP
ejpam-1853	93	11	e	e	NOUN
ejpam-1853	93	12	,	,	PUNCT
ejpam-1853	93	13	that	that	PRON
ejpam-1853	93	14	is	is	ADV
ejpam-1853	93	15	ν	ν	NOUN
ejpam-1853	93	16	:	:	PUNCT
ejpam-1853	93	17	{	{	PUNCT
ejpam-1853	93	18	λ	λ	X
ejpam-1853	93	19	}	}	PUNCT
ejpam-1853	93	20	→	→	SYM
ejpam-1853	93	21	g	g	PROPN
ejpam-1853	93	22	,	,	PUNCT
ejpam-1853	93	23	λ	λ	PROPN
ejpam-1853	93	24	7→	7→	NUM
ejpam-1853	93	25	ν(λ	ν(λ	NOUN
ejpam-1853	93	26	)	)	PUNCT
ejpam-1853	93	27	:	:	PUNCT
ejpam-1853	93	28	=	=	SYM
ejpam-1853	93	29	e	e	X
ejpam-1853	93	30	(	(	PUNCT
ejpam-1853	93	31	here	here	ADV
ejpam-1853	93	32	{	{	PUNCT
ejpam-1853	93	33	λ	λ	X
ejpam-1853	93	34	}	}	PUNCT
ejpam-1853	93	35	is	be	AUX
ejpam-1853	93	36	a	a	DET
ejpam-1853	93	37	singleton	singleton	NOUN
ejpam-1853	93	38	)	)	PUNCT
ejpam-1853	93	39	.	.	PUNCT
ejpam-1853	94	1	the	the	DET
ejpam-1853	94	2	inverse	inverse	NOUN
ejpam-1853	94	3	of	of	ADP
ejpam-1853	94	4	x	x	SYM
ejpam-1853	94	5	∈	∈	PROPN
ejpam-1853	94	6	g	g	NOUN
ejpam-1853	94	7	is	be	AUX
ejpam-1853	94	8	denoted	denote	VERB
ejpam-1853	94	9	by	by	ADP
ejpam-1853	94	10	x̄	x̄	NOUN
ejpam-1853	94	11	,	,	PUNCT
ejpam-1853	94	12	that	that	ADV
ejpam-1853	94	13	is	is	ADV
ejpam-1853	94	14	σ	σ	NOUN
ejpam-1853	94	15	:	:	PUNCT
ejpam-1853	94	16	g	g	PROPN
ejpam-1853	94	17	→	→	SYM
ejpam-1853	94	18	g	g	PROPN
ejpam-1853	94	19	,	,	PUNCT
ejpam-1853	94	20	x	x	PROPN
ejpam-1853	94	21	7→	7→	NUM
ejpam-1853	94	22	σ(x	σ(x	NUM
ejpam-1853	94	23	)	)	PUNCT
ejpam-1853	94	24	:	:	PUNCT
ejpam-1853	94	25	=	=	SYM
ejpam-1853	94	26	x̄	x̄	NOUN
ejpam-1853	94	27	.	.	PUNCT
ejpam-1853	95	1	also	also	ADV
ejpam-1853	95	2	,	,	PUNCT
ejpam-1853	95	3	we	we	PRON
ejpam-1853	95	4	suppose	suppose	VERB
ejpam-1853	95	5	that	that	SCONJ
ejpam-1853	95	6	on	on	ADP
ejpam-1853	95	7	g0	g0	PROPN
ejpam-1853	95	8	is	be	AUX
ejpam-1853	95	9	defined	define	VERB
ejpam-1853	95	10	a	a	DET
ejpam-1853	95	11	group	group	NOUN
ejpam-1853	95	12	structure	structure	NOUN
ejpam-1853	95	13	ω0	ω0	ADV
ejpam-1853	95	14	:	:	PUNCT
ejpam-1853	95	15	g0×	g0×	PROPN
ejpam-1853	95	16	g0→	g0→	PROPN
ejpam-1853	95	17	g0	g0	PROPN
ejpam-1853	95	18	,	,	PUNCT
ejpam-1853	95	19	(	(	PUNCT
ejpam-1853	95	20	u	u	NOUN
ejpam-1853	95	21	,	,	PUNCT
ejpam-1853	95	22	v	v	NOUN
ejpam-1853	95	23	)	)	PUNCT
ejpam-1853	95	24	7→ω0(u	7→ω0(u	NUM
ejpam-1853	95	25	,	,	PUNCT
ejpam-1853	95	26	v	v	NOUN
ejpam-1853	95	27	)	)	PUNCT
ejpam-1853	95	28	:	:	PUNCT
ejpam-1853	95	29	=	=	SYM
ejpam-1853	95	30	u⊕	u⊕	NOUN
ejpam-1853	95	31	v.	v.	CCONJ
ejpam-1853	95	32	the	the	DET
ejpam-1853	95	33	neutral	neutral	ADJ
ejpam-1853	95	34	element	element	NOUN
ejpam-1853	95	35	of	of	ADP
ejpam-1853	95	36	the	the	DET
ejpam-1853	95	37	group	group	NOUN
ejpam-1853	95	38	g0	g0	PROPN
ejpam-1853	95	39	is	be	AUX
ejpam-1853	95	40	denoted	denote	VERB
ejpam-1853	95	41	by	by	ADP
ejpam-1853	95	42	e0	e0	PROPN
ejpam-1853	95	43	,	,	PUNCT
ejpam-1853	95	44	that	that	PRON
ejpam-1853	95	45	is	be	AUX
ejpam-1853	95	46	ν0	ν0	PROPN
ejpam-1853	95	47	:	:	PUNCT
ejpam-1853	95	48	{	{	PUNCT
ejpam-1853	95	49	λ	λ	X
ejpam-1853	95	50	}	}	PUNCT
ejpam-1853	95	51	→	→	SYM
ejpam-1853	95	52	g0	g0	PROPN
ejpam-1853	95	53	,	,	PUNCT
ejpam-1853	95	54	λ	λ	PROPN
ejpam-1853	95	55	7→	7→	NUM
ejpam-1853	95	56	ν0(λ	ν0(λ	NOUN
ejpam-1853	95	57	)	)	PUNCT
ejpam-1853	95	58	:	:	PUNCT
ejpam-1853	95	59	=	=	SYM
ejpam-1853	95	60	e0	e0	PROPN
ejpam-1853	95	61	.	.	PUNCT
ejpam-1853	96	1	the	the	DET
ejpam-1853	96	2	inverse	inverse	NOUN
ejpam-1853	96	3	of	of	ADP
ejpam-1853	96	4	u	u	PROPN
ejpam-1853	96	5	∈	∈	PROPN
ejpam-1853	96	6	g0	g0	NOUN
ejpam-1853	96	7	is	be	AUX
ejpam-1853	96	8	denoted	denote	VERB
ejpam-1853	96	9	by	by	ADP
ejpam-1853	96	10	ū	ū	NOUN
ejpam-1853	96	11	,	,	PUNCT
ejpam-1853	96	12	that	that	PRON
ejpam-1853	96	13	is	be	AUX
ejpam-1853	96	14	σ0	σ0	NOUN
ejpam-1853	96	15	:	:	PUNCT
ejpam-1853	96	16	g0→	g0→	PROPN
ejpam-1853	97	1	g0	g0	PROPN
ejpam-1853	97	2	,	,	PUNCT
ejpam-1853	97	3	u	u	PROPN
ejpam-1853	97	4	7→	7→	NUM
ejpam-1853	97	5	σ0(u	σ0(u	NUM
ejpam-1853	97	6	)	)	PUNCT
ejpam-1853	97	7	:	:	PUNCT
ejpam-1853	97	8	=	=	SYM
ejpam-1853	97	9	ū.	ū.	PUNCT
ejpam-1853	97	10	definition	definition	NOUN
ejpam-1853	97	11	4	4	NUM
ejpam-1853	97	12	(	(	PUNCT
ejpam-1853	97	13	[	[	X
ejpam-1853	97	14	4	4	NUM
ejpam-1853	97	15	]	]	NUM
ejpam-1853	97	16	)	)	PUNCT
ejpam-1853	97	17	.	.	PUNCT
ejpam-1853	98	1	a	a	DET
ejpam-1853	98	2	group	group	NOUN
ejpam-1853	98	3	-	-	PUNCT
ejpam-1853	98	4	groupoid	groupoid	PROPN
ejpam-1853	98	5	or	or	CCONJ
ejpam-1853	98	6	g−groupoid	g−groupoid	PROPN
ejpam-1853	98	7	,	,	PUNCT
ejpam-1853	98	8	is	be	AUX
ejpam-1853	98	9	a	a	DET
ejpam-1853	98	10	groupoid	groupoid	NOUN
ejpam-1853	98	11	(	(	PUNCT
ejpam-1853	98	12	g	g	PROPN
ejpam-1853	98	13	,	,	PUNCT
ejpam-1853	98	14	g0	g0	NOUN
ejpam-1853	98	15	)	)	PUNCT
ejpam-1853	98	16	such	such	ADJ
ejpam-1853	98	17	that	that	SCONJ
ejpam-1853	98	18	the	the	DET
ejpam-1853	98	19	following	follow	VERB
ejpam-1853	98	20	conditions	condition	NOUN
ejpam-1853	98	21	hold	hold	VERB
ejpam-1853	98	22	:	:	PUNCT
ejpam-1853	98	23	(	(	PUNCT
ejpam-1853	98	24	i	i	NOUN
ejpam-1853	98	25	)	)	PUNCT
ejpam-1853	98	26	(	(	PUNCT
ejpam-1853	98	27	g	g	PROPN
ejpam-1853	98	28	,	,	PUNCT
ejpam-1853	98	29	ω	ω	PROPN
ejpam-1853	98	30	,	,	PUNCT
ejpam-1853	98	31	ν	ν	NOUN
ejpam-1853	98	32	,	,	PUNCT
ejpam-1853	98	33	σ	σ	PROPN
ejpam-1853	98	34	)	)	PUNCT
ejpam-1853	98	35	and	and	CCONJ
ejpam-1853	98	36	(	(	PUNCT
ejpam-1853	98	37	g0,ω0,ν0,σ0	g0,ω0,ν0,σ0	PROPN
ejpam-1853	98	38	)	)	PUNCT
ejpam-1853	98	39	are	be	AUX
ejpam-1853	98	40	groups	group	NOUN
ejpam-1853	98	41	.	.	PUNCT
ejpam-1853	99	1	(	(	PUNCT
ejpam-1853	99	2	ii	ii	X
ejpam-1853	99	3	)	)	PUNCT
ejpam-1853	99	4	the	the	DET
ejpam-1853	99	5	maps	map	NOUN
ejpam-1853	99	6	(	(	PUNCT
ejpam-1853	99	7	ω	ω	NOUN
ejpam-1853	99	8	,	,	PUNCT
ejpam-1853	99	9	ω0	ω0	PROPN
ejpam-1853	99	10	)	)	PUNCT
ejpam-1853	99	11	:	:	PUNCT
ejpam-1853	99	12	(	(	PUNCT
ejpam-1853	99	13	g×	g×	X
ejpam-1853	99	14	g	g	NOUN
ejpam-1853	99	15	,	,	PUNCT
ejpam-1853	99	16	g0×	g0×	NOUN
ejpam-1853	99	17	g0)→	g0)→	X
ejpam-1853	99	18	(	(	PUNCT
ejpam-1853	99	19	g	g	PROPN
ejpam-1853	99	20	,	,	PUNCT
ejpam-1853	99	21	g0	g0	NOUN
ejpam-1853	99	22	)	)	PUNCT
ejpam-1853	99	23	,	,	PUNCT
ejpam-1853	99	24	ν	ν	X
ejpam-1853	99	25	:	:	PUNCT
ejpam-1853	99	26	{	{	PUNCT
ejpam-1853	99	27	λ	λ	X
ejpam-1853	99	28	}	}	PUNCT
ejpam-1853	99	29	→	→	SYM
ejpam-1853	99	30	g	g	PROPN
ejpam-1853	99	31	and	and	CCONJ
ejpam-1853	99	32	(	(	PUNCT
ejpam-1853	99	33	σ	σ	PROPN
ejpam-1853	99	34	,	,	PUNCT
ejpam-1853	99	35	σ0	σ0	PROPN
ejpam-1853	99	36	)	)	PUNCT
ejpam-1853	99	37	:	:	PUNCT
ejpam-1853	99	38	(	(	PUNCT
ejpam-1853	99	39	g	g	NOUN
ejpam-1853	99	40	,	,	PUNCT
ejpam-1853	99	41	g0)→	g0)→	X
ejpam-1853	99	42	(	(	PUNCT
ejpam-1853	99	43	g	g	PROPN
ejpam-1853	99	44	,	,	PUNCT
ejpam-1853	99	45	g0	g0	NOUN
ejpam-1853	99	46	)	)	PUNCT
ejpam-1853	99	47	are	be	AUX
ejpam-1853	99	48	groupoid	groupoid	PROPN
ejpam-1853	99	49	morphisms	morphism	NOUN
ejpam-1853	99	50	.	.	PUNCT
ejpam-1853	100	1	we	we	PRON
ejpam-1853	100	2	shall	shall	AUX
ejpam-1853	100	3	denote	denote	VERB
ejpam-1853	100	4	a	a	DET
ejpam-1853	100	5	group	group	NOUN
ejpam-1853	100	6	-	-	PUNCT
ejpam-1853	100	7	groupoid	groupoid	NOUN
ejpam-1853	100	8	by	by	ADP
ejpam-1853	100	9	(	(	PUNCT
ejpam-1853	100	10	g	g	PROPN
ejpam-1853	100	11	,	,	PUNCT
ejpam-1853	100	12	α	α	X
ejpam-1853	100	13	,	,	PUNCT
ejpam-1853	100	14	β	β	X
ejpam-1853	100	15	,	,	PUNCT
ejpam-1853	100	16	m	m	PROPN
ejpam-1853	100	17	,	,	PUNCT
ejpam-1853	100	18	i	i	PRON
ejpam-1853	100	19	,	,	PUNCT
ejpam-1853	100	20	ε,⊕	ε,⊕	PROPN
ejpam-1853	100	21	,	,	PUNCT
ejpam-1853	100	22	g0	g0	NOUN
ejpam-1853	100	23	)	)	PUNCT
ejpam-1853	100	24	or	or	CCONJ
ejpam-1853	100	25	(	(	PUNCT
ejpam-1853	100	26	g	g	PROPN
ejpam-1853	100	27	,	,	PUNCT
ejpam-1853	100	28	α	α	X
ejpam-1853	100	29	,	,	PUNCT
ejpam-1853	100	30	β	β	X
ejpam-1853	100	31	,	,	PUNCT
ejpam-1853	100	32	m,⊕	m,⊕	NOUN
ejpam-1853	100	33	,	,	PUNCT
ejpam-1853	100	34	g0	g0	PROPN
ejpam-1853	100	35	)	)	PUNCT
ejpam-1853	100	36	.	.	PUNCT
ejpam-1853	101	1	theorem	theorem	NOUN
ejpam-1853	101	2	2	2	NUM
ejpam-1853	101	3	.	.	PUNCT
ejpam-1853	102	1	if	if	SCONJ
ejpam-1853	102	2	g	g	PROPN
ejpam-1853	102	3	,	,	PUNCT
ejpam-1853	102	4	α	α	X
ejpam-1853	102	5	,	,	PUNCT
ejpam-1853	102	6	β	β	X
ejpam-1853	102	7	,	,	PUNCT
ejpam-1853	102	8	m	m	PROPN
ejpam-1853	102	9	,	,	PUNCT
ejpam-1853	102	10	ε	ε	PROPN
ejpam-1853	102	11	,	,	PUNCT
ejpam-1853	102	12	i,⊕	i,⊕	NOUN
ejpam-1853	102	13	,	,	PUNCT
ejpam-1853	102	14	g0	g0	NOUN
ejpam-1853	102	15	)	)	PUNCT
ejpam-1853	102	16	is	be	AUX
ejpam-1853	102	17	a	a	DET
ejpam-1853	102	18	group	group	NOUN
ejpam-1853	102	19	-	-	PUNCT
ejpam-1853	102	20	groupoid	groupoid	PROPN
ejpam-1853	102	21	,	,	PUNCT
ejpam-1853	102	22	then	then	ADV
ejpam-1853	102	23	:	:	PUNCT
ejpam-1853	102	24	(	(	PUNCT
ejpam-1853	102	25	i	i	NOUN
ejpam-1853	102	26	)	)	PUNCT
ejpam-1853	102	27	the	the	DET
ejpam-1853	102	28	multiplication	multiplication	NOUN
ejpam-1853	102	29	m	m	PROPN
ejpam-1853	102	30	and	and	CCONJ
ejpam-1853	102	31	the	the	DET
ejpam-1853	102	32	binary	binary	PROPN
ejpam-1853	102	33	operation	operation	PROPN
ejpam-1853	102	34	ω	ω	NOUN
ejpam-1853	102	35	are	be	AUX
ejpam-1853	102	36	compatible	compatible	ADJ
ejpam-1853	102	37	,	,	PUNCT
ejpam-1853	102	38	that	that	PRON
ejpam-1853	102	39	is	be	AUX
ejpam-1853	102	40	:	:	PUNCT
ejpam-1853	102	41	(	(	PUNCT
ejpam-1853	102	42	x	x	X
ejpam-1853	102	43	·	·	PUNCT
ejpam-1853	102	44	y)⊕	y)⊕	NOUN
ejpam-1853	102	45	(	(	PUNCT
ejpam-1853	102	46	z	z	NOUN
ejpam-1853	102	47	·	·	PUNCT
ejpam-1853	102	48	t	t	X
ejpam-1853	102	49	)	)	PUNCT
ejpam-1853	102	50	=	=	SYM
ejpam-1853	102	51	(	(	PUNCT
ejpam-1853	102	52	x	x	PROPN
ejpam-1853	102	53	⊕	⊕	PROPN
ejpam-1853	102	54	z	z	PROPN
ejpam-1853	102	55	)	)	PUNCT
ejpam-1853	102	56	·	·	PUNCT
ejpam-1853	103	1	(	(	PUNCT
ejpam-1853	103	2	y	y	PROPN
ejpam-1853	103	3	⊕	⊕	PROPN
ejpam-1853	103	4	t	t	PROPN
ejpam-1853	103	5	)	)	PUNCT
ejpam-1853	103	6	,	,	PUNCT
ejpam-1853	103	7	(	(	PUNCT
ejpam-1853	103	8	∀)(x	∀)(x	PROPN
ejpam-1853	103	9	,	,	PUNCT
ejpam-1853	103	10	y	y	PROPN
ejpam-1853	103	11	)	)	PUNCT
ejpam-1853	103	12	,	,	PUNCT
ejpam-1853	103	13	(	(	PUNCT
ejpam-1853	103	14	z	z	X
ejpam-1853	103	15	,	,	PUNCT
ejpam-1853	103	16	t	t	PROPN
ejpam-1853	103	17	)	)	PUNCT
ejpam-1853	103	18	∈	∈	PROPN
ejpam-1853	103	19	g(2	g(2	PROPN
ejpam-1853	103	20	)	)	PUNCT
ejpam-1853	103	21	;	;	PUNCT
ejpam-1853	103	22	(	(	PUNCT
ejpam-1853	103	23	2	2	X
ejpam-1853	103	24	)	)	PUNCT
ejpam-1853	103	25	(	(	PUNCT
ejpam-1853	103	26	ii	ii	NOUN
ejpam-1853	103	27	)	)	PUNCT
ejpam-1853	103	28	the	the	DET
ejpam-1853	103	29	structure	structure	NOUN
ejpam-1853	103	30	functions	function	NOUN
ejpam-1853	103	31	α	α	NOUN
ejpam-1853	103	32	,	,	PUNCT
ejpam-1853	103	33	β	β	X
ejpam-1853	103	34	:	:	PUNCT
ejpam-1853	103	35	(	(	PUNCT
ejpam-1853	103	36	g,⊕)→	g,⊕)→	NOUN
ejpam-1853	103	37	(	(	PUNCT
ejpam-1853	103	38	g0,⊕	g0,⊕	NOUN
ejpam-1853	103	39	)	)	PUNCT
ejpam-1853	103	40	,	,	PUNCT
ejpam-1853	103	41	ε	ε	PROPN
ejpam-1853	103	42	:	:	PUNCT
ejpam-1853	103	43	(	(	PUNCT
ejpam-1853	103	44	g0,⊕)→	g0,⊕)→	NOUN
ejpam-1853	103	45	(	(	PUNCT
ejpam-1853	103	46	g,⊕	g,⊕	NOUN
ejpam-1853	103	47	)	)	PUNCT
ejpam-1853	103	48	and	and	CCONJ
ejpam-1853	103	49	i	i	PRON
ejpam-1853	103	50	:	:	PUNCT
ejpam-1853	103	51	(	(	PUNCT
ejpam-1853	103	52	g,⊕)→	g,⊕)→	NOUN
ejpam-1853	103	53	(	(	PUNCT
ejpam-1853	103	54	g,⊕	g,⊕	NOUN
ejpam-1853	103	55	)	)	PUNCT
ejpam-1853	103	56	are	be	AUX
ejpam-1853	103	57	morphisms	morphism	NOUN
ejpam-1853	103	58	of	of	ADP
ejpam-1853	103	59	groups	group	NOUN
ejpam-1853	103	60	;	;	PUNCT
ejpam-1853	103	61	(	(	PUNCT
ejpam-1853	103	62	iii	iii	X
ejpam-1853	103	63	)	)	PUNCT
ejpam-1853	103	64	the	the	DET
ejpam-1853	103	65	multiplication	multiplication	NOUN
ejpam-1853	103	66	m	m	PROPN
ejpam-1853	103	67	and	and	CCONJ
ejpam-1853	103	68	the	the	DET
ejpam-1853	103	69	unary	unary	ADJ
ejpam-1853	103	70	operation	operation	NOUN
ejpam-1853	103	71	σ	σ	NOUN
ejpam-1853	103	72	are	be	AUX
ejpam-1853	103	73	compatible	compatible	ADJ
ejpam-1853	103	74	,	,	PUNCT
ejpam-1853	103	75	that	that	PRON
ejpam-1853	103	76	is	be	AUX
ejpam-1853	103	77	:	:	PUNCT
ejpam-1853	104	1	σ(x	σ(x	PROPN
ejpam-1853	104	2	·	·	PUNCT
ejpam-1853	104	3	y	y	X
ejpam-1853	104	4	)	)	PUNCT
ejpam-1853	104	5	=	=	SYM
ejpam-1853	104	6	σ(x	σ(x	PROPN
ejpam-1853	104	7	)	)	PUNCT
ejpam-1853	104	8	·	·	PUNCT
ejpam-1853	104	9	σ(y	σ(y	NOUN
ejpam-1853	104	10	)	)	PUNCT
ejpam-1853	104	11	,	,	PUNCT
ejpam-1853	104	12	(	(	PUNCT
ejpam-1853	104	13	∀)(x	∀)(x	PROPN
ejpam-1853	104	14	,	,	PUNCT
ejpam-1853	104	15	y	y	PROPN
ejpam-1853	104	16	)	)	PUNCT
ejpam-1853	104	17	∈	∈	PROPN
ejpam-1853	104	18	g(2	g(2	PROPN
ejpam-1853	104	19	)	)	PUNCT
ejpam-1853	104	20	.	.	PUNCT
ejpam-1853	105	1	(	(	PUNCT
ejpam-1853	105	2	3	3	X
ejpam-1853	105	3	)	)	PUNCT
ejpam-1853	105	4	proof	proof	NOUN
ejpam-1853	105	5	.	.	PUNCT
ejpam-1853	106	1	by	by	ADP
ejpam-1853	106	2	definition	definition	NOUN
ejpam-1853	106	3	3	3	NUM
ejpam-1853	106	4	,	,	PUNCT
ejpam-1853	106	5	since	since	SCONJ
ejpam-1853	106	6	(	(	PUNCT
ejpam-1853	106	7	ω	ω	NOUN
ejpam-1853	106	8	,	,	PUNCT
ejpam-1853	106	9	ω0	ω0	NOUN
ejpam-1853	106	10	)	)	PUNCT
ejpam-1853	106	11	is	be	AUX
ejpam-1853	106	12	a	a	DET
ejpam-1853	106	13	groupoid	groupoid	PROPN
ejpam-1853	106	14	morphism	morphism	NOUN
ejpam-1853	106	15	it	it	PRON
ejpam-1853	106	16	follows	follow	VERB
ejpam-1853	106	17	that	that	SCONJ
ejpam-1853	106	18	:	:	PUNCT
ejpam-1853	106	19	(	(	PUNCT
ejpam-1853	106	20	a	a	X
ejpam-1853	106	21	)	)	PUNCT
ejpam-1853	107	1	α	α	PROPN
ejpam-1853	107	2	◦	◦	NOUN
ejpam-1853	107	3	ω	ω	NOUN
ejpam-1853	107	4	=	=	NOUN
ejpam-1853	107	5	ω0	ω0	ADV
ejpam-1853	107	6	◦	◦	NOUN
ejpam-1853	107	7	(	(	PUNCT
ejpam-1853	107	8	α×α	α×α	NUM
ejpam-1853	107	9	)	)	PUNCT
ejpam-1853	107	10	and	and	CCONJ
ejpam-1853	107	11	β	β	PROPN
ejpam-1853	107	12	◦	◦	NOUN
ejpam-1853	107	13	ω	ω	NOUN
ejpam-1853	107	14	=	=	NOUN
ejpam-1853	107	15	ω0	ω0	ADV
ejpam-1853	107	16	◦	◦	NOUN
ejpam-1853	107	17	(	(	PUNCT
ejpam-1853	107	18	β	β	X
ejpam-1853	107	19	×	×	NOUN
ejpam-1853	107	20	β	β	NOUN
ejpam-1853	107	21	)	)	PUNCT
ejpam-1853	107	22	;	;	PUNCT
ejpam-1853	107	23	(	(	PUNCT
ejpam-1853	107	24	b	b	X
ejpam-1853	107	25	)	)	PUNCT
ejpam-1853	107	26	ω(mg×g((x	ω(mg×g((x	ADJ
ejpam-1853	107	27	,	,	PUNCT
ejpam-1853	107	28	y	y	PROPN
ejpam-1853	107	29	)	)	PUNCT
ejpam-1853	107	30	,	,	PUNCT
ejpam-1853	107	31	(	(	PUNCT
ejpam-1853	107	32	z	z	X
ejpam-1853	107	33	,	,	PUNCT
ejpam-1853	107	34	t	t	PROPN
ejpam-1853	107	35	)	)	PUNCT
ejpam-1853	107	36	)	)	PUNCT
ejpam-1853	107	37	)	)	PUNCT
ejpam-1853	108	1	=	=	PRON
ejpam-1853	108	2	mg(ω(x	mg(ω(x	X
ejpam-1853	108	3	,	,	PUNCT
ejpam-1853	108	4	z),ω(y	z),ω(y	NUM
ejpam-1853	108	5	,	,	PUNCT
ejpam-1853	108	6	t	t	PROPN
ejpam-1853	108	7	)	)	PUNCT
ejpam-1853	108	8	)	)	PUNCT
ejpam-1853	108	9	,	,	PUNCT
ejpam-1853	108	10	(	(	PUNCT
ejpam-1853	108	11	∀)(x	∀)(x	PROPN
ejpam-1853	108	12	,	,	PUNCT
ejpam-1853	108	13	y	y	PROPN
ejpam-1853	108	14	)	)	PUNCT
ejpam-1853	108	15	,	,	PUNCT
ejpam-1853	108	16	(	(	PUNCT
ejpam-1853	108	17	z	z	X
ejpam-1853	108	18	,	,	PUNCT
ejpam-1853	108	19	t	t	PROPN
ejpam-1853	108	20	)	)	PUNCT
ejpam-1853	108	21	∈	∈	PROPN
ejpam-1853	108	22	g(2	g(2	PROPN
ejpam-1853	108	23	)	)	PUNCT
ejpam-1853	108	24	.	.	PUNCT
ejpam-1853	109	1	(	(	PUNCT
ejpam-1853	109	2	i	i	NOUN
ejpam-1853	109	3	)	)	PUNCT
ejpam-1853	109	4	we	we	PRON
ejpam-1853	109	5	have	have	VERB
ejpam-1853	109	6	ω(mg×g((x	ω(mg×g((x	PUNCT
ejpam-1853	109	7	,	,	PUNCT
ejpam-1853	109	8	y	y	PROPN
ejpam-1853	109	9	)	)	PUNCT
ejpam-1853	109	10	,	,	PUNCT
ejpam-1853	109	11	(	(	PUNCT
ejpam-1853	109	12	z	z	X
ejpam-1853	109	13	,	,	PUNCT
ejpam-1853	109	14	t	t	PROPN
ejpam-1853	109	15	)	)	PUNCT
ejpam-1853	109	16	)	)	PUNCT
ejpam-1853	109	17	)	)	PUNCT
ejpam-1853	110	1	=	=	PUNCT
ejpam-1853	110	2	ω(mg(x	ω(mg(x	NUM
ejpam-1853	110	3	,	,	PUNCT
ejpam-1853	110	4	y	y	PROPN
ejpam-1853	110	5	)	)	PUNCT
ejpam-1853	110	6	,	,	PUNCT
ejpam-1853	110	7	mg(z	mg(z	PROPN
ejpam-1853	110	8	,	,	PUNCT
ejpam-1853	110	9	t	t	PROPN
ejpam-1853	110	10	)	)	PUNCT
ejpam-1853	110	11	)	)	PUNCT
ejpam-1853	111	1	=	=	SYM
ejpam-1853	111	2	ω(x	ω(x	X
ejpam-1853	111	3	·	·	PUNCT
ejpam-1853	111	4	y	y	PROPN
ejpam-1853	111	5	,	,	PUNCT
ejpam-1853	111	6	z	z	PROPN
ejpam-1853	111	7	·	·	PUNCT
ejpam-1853	111	8	t	t	X
ejpam-1853	111	9	)	)	PUNCT
ejpam-1853	111	10	=	=	SYM
ejpam-1853	111	11	(	(	PUNCT
ejpam-1853	111	12	x	x	X
ejpam-1853	111	13	·	·	PUNCT
ejpam-1853	111	14	y)⊕	y)⊕	NOUN
ejpam-1853	111	15	(	(	PUNCT
ejpam-1853	111	16	z	z	NOUN
ejpam-1853	111	17	·	·	PUNCT
ejpam-1853	111	18	t	t	X
ejpam-1853	111	19	)	)	PUNCT
ejpam-1853	111	20	and	and	CCONJ
ejpam-1853	111	21	mg(ω(x	mg(ω(x	NOUN
ejpam-1853	111	22	,	,	PUNCT
ejpam-1853	111	23	z),ω(y	z),ω(y	NUM
ejpam-1853	111	24	,	,	PUNCT
ejpam-1853	111	25	t	t	PROPN
ejpam-1853	111	26	)	)	PUNCT
ejpam-1853	111	27	)	)	PUNCT
ejpam-1853	112	1	=	=	SYM
ejpam-1853	112	2	mg(x	mg(x	NUM
ejpam-1853	113	1	⊕	⊕	PROPN
ejpam-1853	113	2	z	z	PROPN
ejpam-1853	113	3	,	,	PUNCT
ejpam-1853	113	4	y	y	PROPN
ejpam-1853	113	5	⊕	⊕	PROPN
ejpam-1853	113	6	t	t	PROPN
ejpam-1853	113	7	)	)	PUNCT
ejpam-1853	113	8	=	=	SYM
ejpam-1853	113	9	(	(	PUNCT
ejpam-1853	113	10	x	x	PROPN
ejpam-1853	113	11	⊕	⊕	PROPN
ejpam-1853	113	12	z	z	PROPN
ejpam-1853	113	13	)	)	PUNCT
ejpam-1853	113	14	·	·	PUNCT
ejpam-1853	113	15	(	(	PUNCT
ejpam-1853	113	16	y	y	PROPN
ejpam-1853	113	17	⊕	⊕	PROPN
ejpam-1853	113	18	t	t	PROPN
ejpam-1853	113	19	)	)	PUNCT
ejpam-1853	113	20	.	.	PUNCT
ejpam-1853	114	1	using	use	VERB
ejpam-1853	114	2	(	(	PUNCT
ejpam-1853	114	3	b	b	NOUN
ejpam-1853	114	4	)	)	PUNCT
ejpam-1853	114	5	one	one	NOUN
ejpam-1853	114	6	obtains	obtain	VERB
ejpam-1853	114	7	(	(	PUNCT
ejpam-1853	114	8	x	x	SYM
ejpam-1853	114	9	·	·	PUNCT
ejpam-1853	114	10	y)⊕	y)⊕	NOUN
ejpam-1853	114	11	(	(	PUNCT
ejpam-1853	114	12	z	z	NOUN
ejpam-1853	114	13	·	·	PUNCT
ejpam-1853	114	14	t	t	X
ejpam-1853	114	15	)	)	PUNCT
ejpam-1853	114	16	=	=	SYM
ejpam-1853	114	17	(	(	PUNCT
ejpam-1853	114	18	x	x	PROPN
ejpam-1853	114	19	⊕	⊕	PROPN
ejpam-1853	114	20	z	z	PROPN
ejpam-1853	114	21	)	)	PUNCT
ejpam-1853	114	22	·	·	PUNCT
ejpam-1853	115	1	(	(	PUNCT
ejpam-1853	115	2	y	y	PROPN
ejpam-1853	115	3	⊕	⊕	PROPN
ejpam-1853	115	4	t	t	PROPN
ejpam-1853	115	5	)	)	PUNCT
ejpam-1853	115	6	,	,	PUNCT
ejpam-1853	115	7	and	and	CCONJ
ejpam-1853	115	8	(	(	PUNCT
ejpam-1853	115	9	2	2	X
ejpam-1853	115	10	)	)	PUNCT
ejpam-1853	115	11	holds	hold	NOUN
ejpam-1853	115	12	.	.	PUNCT
ejpam-1853	116	1	m.	m.	NOUN
ejpam-1853	116	2	ivan	ivan	PROPN
ejpam-1853	116	3	/	/	PUNCT
ejpam-1853	116	4	eur	eur	PROPN
ejpam-1853	116	5	.	.	PUNCT
ejpam-1853	117	1	j.	j.	PROPN
ejpam-1853	117	2	pure	pure	PROPN
ejpam-1853	117	3	appl	appl	PROPN
ejpam-1853	117	4	.	.	PROPN
ejpam-1853	117	5	math	math	PROPN
ejpam-1853	117	6	,	,	PUNCT
ejpam-1853	117	7	6	6	NUM
ejpam-1853	117	8	(	(	PUNCT
ejpam-1853	117	9	2013	2013	NUM
ejpam-1853	117	10	)	)	PUNCT
ejpam-1853	117	11	,	,	PUNCT
ejpam-1853	117	12	469	469	NUM
ejpam-1853	117	13	-	-	SYM
ejpam-1853	117	14	484	484	NUM
ejpam-1853	117	15	473	473	NUM
ejpam-1853	117	16	(	(	PUNCT
ejpam-1853	117	17	ii	ii	NOUN
ejpam-1853	117	18	)	)	PUNCT
ejpam-1853	117	19	for	for	ADP
ejpam-1853	117	20	each	each	DET
ejpam-1853	117	21	(	(	PUNCT
ejpam-1853	117	22	x	x	PROPN
ejpam-1853	117	23	,	,	PUNCT
ejpam-1853	117	24	y	y	PROPN
ejpam-1853	117	25	)	)	PUNCT
ejpam-1853	117	26	∈	∈	PROPN
ejpam-1853	117	27	g×	g×	PUNCT
ejpam-1853	117	28	g	g	NOUN
ejpam-1853	117	29	,	,	PUNCT
ejpam-1853	117	30	we	we	PRON
ejpam-1853	117	31	have	have	VERB
ejpam-1853	117	32	α(ω(x	α(ω(x	NOUN
ejpam-1853	117	33	,	,	PUNCT
ejpam-1853	117	34	y	y	NOUN
ejpam-1853	117	35	)	)	PUNCT
ejpam-1853	117	36	)	)	PUNCT
ejpam-1853	118	1	=	=	SYM
ejpam-1853	118	2	α(x	α(x	PROPN
ejpam-1853	118	3	⊕	⊕	PROPN
ejpam-1853	118	4	y	y	PROPN
ejpam-1853	118	5	)	)	PUNCT
ejpam-1853	118	6	and	and	CCONJ
ejpam-1853	118	7	ω0((α×α)(x	ω0((α×α)(x	PROPN
ejpam-1853	118	8	,	,	PUNCT
ejpam-1853	118	9	y	y	PROPN
ejpam-1853	118	10	)	)	PUNCT
ejpam-1853	118	11	)	)	PUNCT
ejpam-1853	119	1	=	=	SYM
ejpam-1853	119	2	ω0(α(x),α(y	ω0(α(x),α(y	NOUN
ejpam-1853	119	3	)	)	PUNCT
ejpam-1853	119	4	)	)	PUNCT
ejpam-1853	119	5	=	=	SYM
ejpam-1853	119	6	α(x)⊕α(y	α(x)⊕α(y	PROPN
ejpam-1853	119	7	)	)	PUNCT
ejpam-1853	119	8	.	.	PUNCT
ejpam-1853	120	1	according	accord	VERB
ejpam-1853	120	2	to	to	ADP
ejpam-1853	120	3	the	the	DET
ejpam-1853	120	4	first	first	ADJ
ejpam-1853	120	5	equality	equality	NOUN
ejpam-1853	120	6	(	(	PUNCT
ejpam-1853	120	7	a	a	X
ejpam-1853	120	8	)	)	PUNCT
ejpam-1853	120	9	,	,	PUNCT
ejpam-1853	120	10	it	it	PRON
ejpam-1853	120	11	follows	follow	VERB
ejpam-1853	120	12	α(x	α(x	PROPN
ejpam-1853	120	13	⊕	⊕	PROPN
ejpam-1853	120	14	y	y	NOUN
ejpam-1853	120	15	)	)	PUNCT
ejpam-1853	120	16	=	=	SYM
ejpam-1853	121	1	α(x)⊕	α(x)⊕	NUM
ejpam-1853	121	2	α(y	α(y	NOUN
ejpam-1853	121	3	)	)	PUNCT
ejpam-1853	121	4	,	,	PUNCT
ejpam-1853	121	5	and	and	CCONJ
ejpam-1853	121	6	α	α	PRON
ejpam-1853	121	7	is	be	AUX
ejpam-1853	121	8	a	a	DET
ejpam-1853	121	9	group	group	NOUN
ejpam-1853	121	10	morphism	morphism	NOUN
ejpam-1853	121	11	.	.	PUNCT
ejpam-1853	122	1	similarly	similarly	ADV
ejpam-1853	122	2	,	,	PUNCT
ejpam-1853	122	3	we	we	PRON
ejpam-1853	122	4	prove	prove	VERB
ejpam-1853	122	5	that	that	SCONJ
ejpam-1853	122	6	β	β	NOUN
ejpam-1853	122	7	is	be	AUX
ejpam-1853	122	8	a	a	DET
ejpam-1853	122	9	group	group	NOUN
ejpam-1853	122	10	morphism	morphism	NOUN
ejpam-1853	122	11	.	.	PUNCT
ejpam-1853	123	1	since	since	SCONJ
ejpam-1853	123	2	(	(	PUNCT
ejpam-1853	123	3	ω	ω	NOUN
ejpam-1853	123	4	,	,	PUNCT
ejpam-1853	123	5	ω0	ω0	NOUN
ejpam-1853	123	6	)	)	PUNCT
ejpam-1853	123	7	is	be	AUX
ejpam-1853	123	8	a	a	DET
ejpam-1853	123	9	groupoid	groupoid	PROPN
ejpam-1853	123	10	morphism	morphism	NOUN
ejpam-1853	123	11	,	,	PUNCT
ejpam-1853	123	12	from	from	ADP
ejpam-1853	123	13	(	(	PUNCT
ejpam-1853	123	14	1	1	X
ejpam-1853	123	15	)	)	PUNCT
ejpam-1853	123	16	it	it	PRON
ejpam-1853	123	17	follows	follow	VERB
ejpam-1853	123	18	.	.	PUNCT
ejpam-1853	124	1	(	(	PUNCT
ejpam-1853	124	2	c	c	X
ejpam-1853	124	3	)	)	PUNCT
ejpam-1853	124	4	ω	ω	NOUN
ejpam-1853	124	5	◦	◦	NOUN
ejpam-1853	124	6	(	(	PUNCT
ejpam-1853	124	7	ε×	ε×	NOUN
ejpam-1853	124	8	ε	ε	PROPN
ejpam-1853	124	9	)	)	PUNCT
ejpam-1853	124	10	=	=	PUNCT
ejpam-1853	124	11	ε	ε	PROPN
ejpam-1853	124	12	◦	◦	NOUN
ejpam-1853	124	13	ω0	ω0	PROPN
ejpam-1853	124	14	and	and	CCONJ
ejpam-1853	124	15	i	i	PRON
ejpam-1853	124	16	◦	◦	NOUN
ejpam-1853	124	17	ω	ω	VERB
ejpam-1853	124	18	=	=	PROPN
ejpam-1853	124	19	ω	ω	PROPN
ejpam-1853	124	20	◦	◦	NOUN
ejpam-1853	124	21	(	(	PUNCT
ejpam-1853	124	22	i×	i×	PROPN
ejpam-1853	124	23	i	i	PROPN
ejpam-1853	124	24	)	)	PUNCT
ejpam-1853	124	25	.	.	PUNCT
ejpam-1853	125	1	for	for	ADP
ejpam-1853	125	2	all	all	DET
ejpam-1853	125	3	u	u	NOUN
ejpam-1853	125	4	,	,	PUNCT
ejpam-1853	125	5	v	v	PROPN
ejpam-1853	125	6	∈	∈	PROPN
ejpam-1853	125	7	g0	g0	NOUN
ejpam-1853	125	8	,	,	PUNCT
ejpam-1853	125	9	we	we	PRON
ejpam-1853	125	10	have	have	VERB
ejpam-1853	125	11	ω((ε×	ω((ε×	ADV
ejpam-1853	125	12	ε)(u	ε)(u	ADJ
ejpam-1853	125	13	,	,	PUNCT
ejpam-1853	125	14	v	v	NOUN
ejpam-1853	125	15	)	)	PUNCT
ejpam-1853	125	16	)	)	PUNCT
ejpam-1853	126	1	=	=	SYM
ejpam-1853	126	2	ω(ε(u),ε(v	ω(ε(u),ε(v	NOUN
ejpam-1853	126	3	)	)	PUNCT
ejpam-1853	126	4	)	)	PUNCT
ejpam-1853	127	1	=	=	SYM
ejpam-1853	127	2	ε(u)⊕	ε(u)⊕	NOUN
ejpam-1853	127	3	ε(v	ε(v	NOUN
ejpam-1853	127	4	)	)	PUNCT
ejpam-1853	127	5	and	and	CCONJ
ejpam-1853	127	6	ε(ω0(u	ε(ω0(u	PROPN
ejpam-1853	127	7	,	,	PUNCT
ejpam-1853	127	8	v	v	NOUN
ejpam-1853	127	9	)	)	PUNCT
ejpam-1853	127	10	)	)	PUNCT
ejpam-1853	128	1	=	=	PUNCT
ejpam-1853	128	2	ε(u	ε(u	PROPN
ejpam-1853	128	3	⊕	⊕	PROPN
ejpam-1853	128	4	v	v	NOUN
ejpam-1853	128	5	)	)	PUNCT
ejpam-1853	128	6	.	.	PUNCT
ejpam-1853	129	1	from	from	ADP
ejpam-1853	129	2	the	the	DET
ejpam-1853	129	3	first	first	ADJ
ejpam-1853	129	4	equality	equality	NOUN
ejpam-1853	129	5	(	(	PUNCT
ejpam-1853	129	6	c	c	NOUN
ejpam-1853	129	7	)	)	PUNCT
ejpam-1853	129	8	,	,	PUNCT
ejpam-1853	129	9	it	it	PRON
ejpam-1853	129	10	follows	follow	VERB
ejpam-1853	129	11	ε(u	ε(u	PROPN
ejpam-1853	129	12	⊕	⊕	PROPN
ejpam-1853	129	13	v	v	NOUN
ejpam-1853	129	14	)	)	PUNCT
ejpam-1853	129	15	=	=	SYM
ejpam-1853	129	16	ε(u	ε(u	NOUN
ejpam-1853	129	17	)	)	PUNCT
ejpam-1853	129	18	⊕	⊕	PROPN
ejpam-1853	129	19	ε(v	ε(v	PROPN
ejpam-1853	129	20	)	)	PUNCT
ejpam-1853	129	21	.	.	PUNCT
ejpam-1853	130	1	hence	hence	ADV
ejpam-1853	130	2	,	,	PUNCT
ejpam-1853	130	3	ε	ε	PROPN
ejpam-1853	130	4	is	be	AUX
ejpam-1853	130	5	a	a	DET
ejpam-1853	130	6	group	group	NOUN
ejpam-1853	130	7	morphism	morphism	NOUN
ejpam-1853	130	8	.	.	PUNCT
ejpam-1853	131	1	for	for	ADP
ejpam-1853	131	2	all	all	DET
ejpam-1853	131	3	x	x	SYM
ejpam-1853	131	4	,	,	PUNCT
ejpam-1853	131	5	y	y	PROPN
ejpam-1853	131	6	∈	∈	PROPN
ejpam-1853	131	7	g	g	PROPN
ejpam-1853	131	8	,	,	PUNCT
ejpam-1853	131	9	we	we	PRON
ejpam-1853	131	10	have	have	VERB
ejpam-1853	131	11	i(ω(x	i(ω(x	PROPN
ejpam-1853	131	12	,	,	PUNCT
ejpam-1853	131	13	y	y	NOUN
ejpam-1853	131	14	)	)	PUNCT
ejpam-1853	131	15	)	)	PUNCT
ejpam-1853	132	1	=	=	SYM
ejpam-1853	133	1	i(x	i(x	PROPN
ejpam-1853	133	2	⊕	⊕	PROPN
ejpam-1853	133	3	y	y	NOUN
ejpam-1853	133	4	)	)	PUNCT
ejpam-1853	133	5	and	and	CCONJ
ejpam-1853	133	6	ω(i(x	ω(i(x	NOUN
ejpam-1853	133	7	)	)	PUNCT
ejpam-1853	133	8	,	,	PUNCT
ejpam-1853	133	9	i(y	i(y	NOUN
ejpam-1853	133	10	)	)	PUNCT
ejpam-1853	133	11	)	)	PUNCT
ejpam-1853	134	1	=	=	PRON
ejpam-1853	134	2	i(x)⊕	i(x)⊕	VERB
ejpam-1853	134	3	i(y	i(y	NOUN
ejpam-1853	134	4	)	)	PUNCT
ejpam-1853	134	5	.	.	PUNCT
ejpam-1853	135	1	using	use	VERB
ejpam-1853	135	2	the	the	DET
ejpam-1853	135	3	second	second	ADJ
ejpam-1853	135	4	equality	equality	NOUN
ejpam-1853	135	5	(	(	PUNCT
ejpam-1853	135	6	c	c	NOUN
ejpam-1853	135	7	)	)	PUNCT
ejpam-1853	135	8	,	,	PUNCT
ejpam-1853	135	9	it	it	PRON
ejpam-1853	135	10	follows	follow	VERB
ejpam-1853	135	11	i(x	i(x	PROPN
ejpam-1853	135	12	⊕	⊕	PROPN
ejpam-1853	135	13	y	y	NOUN
ejpam-1853	135	14	)	)	PUNCT
ejpam-1853	136	1	=	=	PRON
ejpam-1853	136	2	i(x)⊕	i(x)⊕	VERB
ejpam-1853	136	3	i(y	i(y	NOUN
ejpam-1853	136	4	)	)	PUNCT
ejpam-1853	136	5	,	,	PUNCT
ejpam-1853	136	6	and	and	CCONJ
ejpam-1853	136	7	i	i	PRON
ejpam-1853	136	8	is	be	AUX
ejpam-1853	136	9	a	a	DET
ejpam-1853	136	10	group	group	NOUN
ejpam-1853	136	11	morphism	morphism	NOUN
ejpam-1853	136	12	.	.	PUNCT
ejpam-1853	137	1	(	(	PUNCT
ejpam-1853	137	2	iii	iii	NOUN
ejpam-1853	137	3	)	)	PUNCT
ejpam-1853	137	4	since	since	SCONJ
ejpam-1853	137	5	(	(	PUNCT
ejpam-1853	137	6	σ	σ	PROPN
ejpam-1853	137	7	,	,	PUNCT
ejpam-1853	137	8	σ0	σ0	PROPN
ejpam-1853	137	9	)	)	PUNCT
ejpam-1853	137	10	is	be	AUX
ejpam-1853	137	11	a	a	DET
ejpam-1853	137	12	groupoid	groupoid	PROPN
ejpam-1853	137	13	morphism	morphism	NOUN
ejpam-1853	137	14	,	,	PUNCT
ejpam-1853	137	15	for	for	ADP
ejpam-1853	137	16	all	all	DET
ejpam-1853	137	17	(	(	PUNCT
ejpam-1853	137	18	x	x	INTJ
ejpam-1853	137	19	,	,	PUNCT
ejpam-1853	137	20	y	y	PROPN
ejpam-1853	137	21	)	)	PUNCT
ejpam-1853	137	22	∈	∈	PROPN
ejpam-1853	137	23	g(2	g(2	PROPN
ejpam-1853	137	24	)	)	PUNCT
ejpam-1853	137	25	we	we	PRON
ejpam-1853	137	26	have	have	VERB
ejpam-1853	137	27	σ(m(x	σ(m(x	PROPN
ejpam-1853	137	28	,	,	PUNCT
ejpam-1853	137	29	y	y	NOUN
ejpam-1853	137	30	)	)	PUNCT
ejpam-1853	137	31	)	)	PUNCT
ejpam-1853	138	1	=	=	SYM
ejpam-1853	138	2	m(σ(x),σ(y	m(σ(x),σ(y	PROPN
ejpam-1853	138	3	)	)	PUNCT
ejpam-1853	138	4	)	)	PUNCT
ejpam-1853	138	5	;	;	PUNCT
ejpam-1853	139	1	i.e.	i.e.	X
ejpam-1853	139	2	,	,	PUNCT
ejpam-1853	139	3	σ(x	σ(x	PROPN
ejpam-1853	139	4	·	·	PUNCT
ejpam-1853	139	5	y	y	X
ejpam-1853	139	6	)	)	PUNCT
ejpam-1853	139	7	=	=	SYM
ejpam-1853	139	8	σ(x	σ(x	PROPN
ejpam-1853	139	9	)	)	PUNCT
ejpam-1853	139	10	·	·	PUNCT
ejpam-1853	139	11	σ(y	σ(y	NOUN
ejpam-1853	139	12	)	)	PUNCT
ejpam-1853	139	13	.	.	PUNCT
ejpam-1853	140	1	hence	hence	ADV
ejpam-1853	140	2	(	(	PUNCT
ejpam-1853	140	3	3	3	X
ejpam-1853	140	4	)	)	PUNCT
ejpam-1853	140	5	holds	hold	VERB
ejpam-1853	140	6	.	.	PUNCT
ejpam-1853	141	1	the	the	DET
ejpam-1853	141	2	relation	relation	NOUN
ejpam-1853	141	3	(	(	PUNCT
ejpam-1853	141	4	2	2	NUM
ejpam-1853	141	5	)	)	PUNCT
ejpam-1853	141	6	(	(	PUNCT
ejpam-1853	141	7	resp	resp	NOUN
ejpam-1853	141	8	.	.	PUNCT
ejpam-1853	141	9	,	,	PUNCT
ejpam-1853	141	10	(	(	PUNCT
ejpam-1853	141	11	3	3	NUM
ejpam-1853	141	12	)	)	PUNCT
ejpam-1853	141	13	)	)	PUNCT
ejpam-1853	141	14	is	be	AUX
ejpam-1853	141	15	called	call	VERB
ejpam-1853	141	16	the	the	DET
ejpam-1853	141	17	interchange	interchange	NOUN
ejpam-1853	141	18	law	law	NOUN
ejpam-1853	141	19	between	between	ADP
ejpam-1853	141	20	groupoid	groupoid	PROPN
ejpam-1853	141	21	multiplication	multiplication	PROPN
ejpam-1853	141	22	m	m	PROPN
ejpam-1853	141	23	and	and	CCONJ
ejpam-1853	141	24	group	group	PROPN
ejpam-1853	141	25	operation	operation	PROPN
ejpam-1853	141	26	ω	ω	PROPN
ejpam-1853	141	27	(	(	PUNCT
ejpam-1853	141	28	resp	resp	PROPN
ejpam-1853	141	29	.	.	PUNCT
ejpam-1853	141	30	,	,	PUNCT
ejpam-1853	141	31	σ	σ	PROPN
ejpam-1853	141	32	)	)	PUNCT
ejpam-1853	141	33	.	.	PUNCT
ejpam-1853	142	1	we	we	PRON
ejpam-1853	142	2	say	say	VERB
ejpam-1853	142	3	that	that	SCONJ
ejpam-1853	142	4	the	the	DET
ejpam-1853	142	5	group	group	NOUN
ejpam-1853	142	6	-	-	PUNCT
ejpam-1853	142	7	groupoid	groupoid	PROPN
ejpam-1853	142	8	(	(	PUNCT
ejpam-1853	142	9	g	g	PROPN
ejpam-1853	142	10	,	,	PUNCT
ejpam-1853	142	11	α	α	X
ejpam-1853	142	12	,	,	PUNCT
ejpam-1853	142	13	β	β	X
ejpam-1853	142	14	,	,	PUNCT
ejpam-1853	142	15	m	m	PROPN
ejpam-1853	142	16	,	,	PUNCT
ejpam-1853	142	17	i	i	PRON
ejpam-1853	142	18	,	,	PUNCT
ejpam-1853	142	19	ε,⊕	ε,⊕	PROPN
ejpam-1853	142	20	,	,	PUNCT
ejpam-1853	142	21	g0	g0	PROPN
ejpam-1853	142	22	)	)	PUNCT
ejpam-1853	142	23	is	be	AUX
ejpam-1853	142	24	a	a	DET
ejpam-1853	142	25	commutative	commutative	ADJ
ejpam-1853	142	26	group	group	NOUN
ejpam-1853	142	27	-	-	PUNCT
ejpam-1853	142	28	groupoid	groupoid	PROPN
ejpam-1853	142	29	,	,	PUNCT
ejpam-1853	142	30	if	if	SCONJ
ejpam-1853	142	31	the	the	DET
ejpam-1853	142	32	groups	group	NOUN
ejpam-1853	142	33	g	g	PROPN
ejpam-1853	142	34	and	and	CCONJ
ejpam-1853	142	35	g0	g0	PROPN
ejpam-1853	142	36	are	be	AUX
ejpam-1853	142	37	commutative	commutative	ADJ
ejpam-1853	142	38	.	.	PUNCT
ejpam-1853	143	1	remark	remark	PROPN
ejpam-1853	143	2	1	1	NUM
ejpam-1853	143	3	.	.	PUNCT
ejpam-1853	144	1	(	(	PUNCT
ejpam-1853	144	2	i	i	NOUN
ejpam-1853	144	3	)	)	PUNCT
ejpam-1853	144	4	let	let	VERB
ejpam-1853	144	5	(	(	PUNCT
ejpam-1853	144	6	g	g	NOUN
ejpam-1853	144	7	,	,	PUNCT
ejpam-1853	144	8	g0	g0	PROPN
ejpam-1853	144	9	)	)	PUNCT
ejpam-1853	144	10	be	be	AUX
ejpam-1853	144	11	a	a	DET
ejpam-1853	144	12	g−groupoid	g−groupoid	NOUN
ejpam-1853	144	13	.	.	PUNCT
ejpam-1853	145	1	for	for	ADP
ejpam-1853	145	2	all	all	DET
ejpam-1853	145	3	x	x	SYM
ejpam-1853	145	4	,	,	PUNCT
ejpam-1853	145	5	y	y	PROPN
ejpam-1853	145	6	∈	∈	PROPN
ejpam-1853	145	7	g	g	PROPN
ejpam-1853	145	8	,	,	PUNCT
ejpam-1853	145	9	we	we	PRON
ejpam-1853	145	10	have	have	VERB
ejpam-1853	145	11	σ(x	σ(x	PROPN
ejpam-1853	145	12	⊕	⊕	PROPN
ejpam-1853	145	13	y	y	PROPN
ejpam-1853	145	14	)	)	PUNCT
ejpam-1853	145	15	=	=	SYM
ejpam-1853	145	16	σ(y)⊕σ(x	σ(y)⊕σ(x	PROPN
ejpam-1853	145	17	)	)	PUNCT
ejpam-1853	145	18	and	and	CCONJ
ejpam-1853	145	19	σ(σ(x	σ(σ(x	PROPN
ejpam-1853	145	20	)	)	PUNCT
ejpam-1853	145	21	)	)	PUNCT
ejpam-1853	146	1	=	=	PUNCT
ejpam-1853	146	2	x	x	X
ejpam-1853	146	3	;	;	PUNCT
ejpam-1853	146	4	(	(	PUNCT
ejpam-1853	146	5	ii	ii	NOUN
ejpam-1853	146	6	)	)	PUNCT
ejpam-1853	146	7	if	if	SCONJ
ejpam-1853	146	8	(	(	PUNCT
ejpam-1853	146	9	g	g	NOUN
ejpam-1853	146	10	,	,	PUNCT
ejpam-1853	146	11	g0	g0	PROPN
ejpam-1853	146	12	)	)	PUNCT
ejpam-1853	146	13	is	be	AUX
ejpam-1853	146	14	a	a	DET
ejpam-1853	146	15	commutative	commutative	ADJ
ejpam-1853	146	16	group	group	NOUN
ejpam-1853	146	17	-	-	PUNCT
ejpam-1853	146	18	groupoid	groupoid	PROPN
ejpam-1853	146	19	,	,	PUNCT
ejpam-1853	146	20	then	then	ADV
ejpam-1853	146	21	x	x	PROPN
ejpam-1853	146	22	⊕	⊕	NOUN
ejpam-1853	146	23	y	y	PROPN
ejpam-1853	146	24	=	=	PUNCT
ejpam-1853	146	25	x̄	x̄	PROPN
ejpam-1853	146	26	⊕	⊕	PROPN
ejpam-1853	146	27	ȳ	ȳ	PROPN
ejpam-1853	146	28	,	,	PUNCT
ejpam-1853	146	29	(	(	PUNCT
ejpam-1853	146	30	∀	∀	X
ejpam-1853	146	31	)	)	PUNCT
ejpam-1853	146	32	x	x	X
ejpam-1853	146	33	,	,	PUNCT
ejpam-1853	146	34	y	y	PROPN
ejpam-1853	146	35	∈	∈	PROPN
ejpam-1853	146	36	g.	g.	PROPN
ejpam-1853	146	37	theorem	theorem	VERB
ejpam-1853	146	38	3	3	X
ejpam-1853	146	39	.	.	PUNCT
ejpam-1853	147	1	if	if	SCONJ
ejpam-1853	147	2	(	(	PUNCT
ejpam-1853	147	3	g	g	NOUN
ejpam-1853	147	4	,	,	PUNCT
ejpam-1853	147	5	α	α	X
ejpam-1853	147	6	,	,	PUNCT
ejpam-1853	147	7	β	β	X
ejpam-1853	147	8	,	,	PUNCT
ejpam-1853	147	9	m	m	PROPN
ejpam-1853	147	10	,	,	PUNCT
ejpam-1853	147	11	ε	ε	PROPN
ejpam-1853	147	12	,	,	PUNCT
ejpam-1853	147	13	i,⊕	i,⊕	NOUN
ejpam-1853	147	14	,	,	PUNCT
ejpam-1853	147	15	g0	g0	NOUN
ejpam-1853	147	16	)	)	PUNCT
ejpam-1853	147	17	is	be	AUX
ejpam-1853	147	18	a	a	DET
ejpam-1853	147	19	g−groupoid	g−groupoid	NOUN
ejpam-1853	147	20	,	,	PUNCT
ejpam-1853	147	21	then	then	ADV
ejpam-1853	147	22	:	:	PUNCT
ejpam-1853	147	23	e	e	X
ejpam-1853	147	24	·	·	PUNCT
ejpam-1853	147	25	y	y	X
ejpam-1853	147	26	=	=	SYM
ejpam-1853	147	27	y	y	PROPN
ejpam-1853	147	28	,	,	PUNCT
ejpam-1853	147	29	(	(	PUNCT
ejpam-1853	147	30	∀)y	∀)y	NOUN
ejpam-1853	147	31	∈	∈	NOUN
ejpam-1853	147	32	α−1(e0	α−1(e0	NOUN
ejpam-1853	147	33	)	)	PUNCT
ejpam-1853	147	34	and	and	CCONJ
ejpam-1853	147	35	x	x	SYM
ejpam-1853	147	36	·	·	PUNCT
ejpam-1853	147	37	e	e	X
ejpam-1853	147	38	=	=	PUNCT
ejpam-1853	147	39	x	x	SYM
ejpam-1853	147	40	,	,	PUNCT
ejpam-1853	147	41	(	(	PUNCT
ejpam-1853	147	42	∀)x	∀)x	PROPN
ejpam-1853	147	43	∈	∈	PROPN
ejpam-1853	147	44	β−1(e0	β−1(e0	PROPN
ejpam-1853	147	45	)	)	PUNCT
ejpam-1853	147	46	;	;	PUNCT
ejpam-1853	147	47	(	(	PUNCT
ejpam-1853	147	48	4	4	X
ejpam-1853	147	49	)	)	PUNCT
ejpam-1853	147	50	x	x	X
ejpam-1853	147	51	·	·	PUNCT
ejpam-1853	147	52	(	(	PUNCT
ejpam-1853	147	53	y	y	PROPN
ejpam-1853	147	54	⊕	⊕	PROPN
ejpam-1853	147	55	t	t	PROPN
ejpam-1853	147	56	)	)	PUNCT
ejpam-1853	147	57	=	=	PUNCT
ejpam-1853	148	1	x	x	PUNCT
ejpam-1853	148	2	·	·	PUNCT
ejpam-1853	148	3	y	y	PROPN
ejpam-1853	148	4	⊕	⊕	PROPN
ejpam-1853	148	5	t	t	PROPN
ejpam-1853	148	6	,	,	PUNCT
ejpam-1853	148	7	(	(	PUNCT
ejpam-1853	148	8	∀)(x	∀)(x	PROPN
ejpam-1853	148	9	,	,	PUNCT
ejpam-1853	148	10	y	y	PROPN
ejpam-1853	148	11	)	)	PUNCT
ejpam-1853	148	12	∈	∈	PROPN
ejpam-1853	148	13	g(2	g(2	PROPN
ejpam-1853	148	14	)	)	PUNCT
ejpam-1853	148	15	and	and	CCONJ
ejpam-1853	148	16	t	t	PROPN
ejpam-1853	148	17	∈	∈	PROPN
ejpam-1853	148	18	α−1(e0	α−1(e0	PROPN
ejpam-1853	148	19	)	)	PUNCT
ejpam-1853	148	20	;	;	PUNCT
ejpam-1853	148	21	(	(	PUNCT
ejpam-1853	148	22	5	5	X
ejpam-1853	148	23	)	)	PUNCT
ejpam-1853	148	24	(	(	PUNCT
ejpam-1853	148	25	x	x	PROPN
ejpam-1853	148	26	⊕	⊕	PROPN
ejpam-1853	148	27	z	z	PROPN
ejpam-1853	148	28	)	)	PUNCT
ejpam-1853	148	29	·	·	PUNCT
ejpam-1853	149	1	y	y	X
ejpam-1853	149	2	=	=	PUNCT
ejpam-1853	149	3	x	x	PUNCT
ejpam-1853	149	4	·	·	PUNCT
ejpam-1853	149	5	y	y	PROPN
ejpam-1853	149	6	⊕	⊕	PROPN
ejpam-1853	149	7	z	z	PROPN
ejpam-1853	149	8	,	,	PUNCT
ejpam-1853	149	9	(	(	PUNCT
ejpam-1853	149	10	∀)(x	∀)(x	PROPN
ejpam-1853	149	11	,	,	PUNCT
ejpam-1853	149	12	y	y	PROPN
ejpam-1853	149	13	)	)	PUNCT
ejpam-1853	149	14	∈	∈	PROPN
ejpam-1853	149	15	g(2	g(2	PROPN
ejpam-1853	149	16	)	)	PUNCT
ejpam-1853	149	17	and	and	CCONJ
ejpam-1853	149	18	z	z	NOUN
ejpam-1853	149	19	∈	∈	PROPN
ejpam-1853	149	20	β−1(e0	β−1(e0	PROPN
ejpam-1853	149	21	)	)	PUNCT
ejpam-1853	149	22	.	.	PUNCT
ejpam-1853	150	1	(	(	PUNCT
ejpam-1853	150	2	6	6	X
ejpam-1853	150	3	)	)	PUNCT
ejpam-1853	150	4	m.	m.	NOUN
ejpam-1853	150	5	ivan	ivan	PROPN
ejpam-1853	150	6	/	/	PUNCT
ejpam-1853	150	7	eur	eur	PROPN
ejpam-1853	150	8	.	.	PUNCT
ejpam-1853	151	1	j.	j.	PROPN
ejpam-1853	151	2	pure	pure	PROPN
ejpam-1853	151	3	appl	appl	PROPN
ejpam-1853	151	4	.	.	PROPN
ejpam-1853	151	5	math	math	PROPN
ejpam-1853	151	6	,	,	PUNCT
ejpam-1853	151	7	6	6	NUM
ejpam-1853	151	8	(	(	PUNCT
ejpam-1853	151	9	2013	2013	NUM
ejpam-1853	151	10	)	)	PUNCT
ejpam-1853	151	11	,	,	PUNCT
ejpam-1853	151	12	469	469	NUM
ejpam-1853	151	13	-	-	SYM
ejpam-1853	151	14	484	484	NUM
ejpam-1853	151	15	474	474	NUM
ejpam-1853	151	16	proof	proof	NOUN
ejpam-1853	151	17	.	.	PUNCT
ejpam-1853	152	1	if	if	SCONJ
ejpam-1853	152	2	y	y	PROPN
ejpam-1853	152	3	∈	∈	PROPN
ejpam-1853	152	4	α−1(e0	α−1(e0	PROPN
ejpam-1853	152	5	)	)	PUNCT
ejpam-1853	152	6	,	,	PUNCT
ejpam-1853	152	7	then	then	ADV
ejpam-1853	152	8	α(y	α(y	NOUN
ejpam-1853	152	9	)	)	PUNCT
ejpam-1853	152	10	=	=	SYM
ejpam-1853	152	11	e0	e0	PROPN
ejpam-1853	152	12	.	.	PUNCT
ejpam-1853	153	1	we	we	PRON
ejpam-1853	153	2	have	have	VERB
ejpam-1853	153	3	β(ε(e0	β(ε(e0	NOUN
ejpam-1853	153	4	)	)	PUNCT
ejpam-1853	153	5	)	)	PUNCT
ejpam-1853	154	1	=	=	SYM
ejpam-1853	154	2	e0	e0	PROPN
ejpam-1853	154	3	,	,	PUNCT
ejpam-1853	154	4	since	since	SCONJ
ejpam-1853	154	5	β	β	X
ejpam-1853	154	6	◦	◦	NOUN
ejpam-1853	154	7	ε	ε	PROPN
ejpam-1853	154	8	=	=	SYM
ejpam-1853	154	9	idg0	idg0	PROPN
ejpam-1853	154	10	.	.	PUNCT
ejpam-1853	155	1	so	so	ADV
ejpam-1853	155	2	(	(	PUNCT
ejpam-1853	155	3	ε(e0	ε(e0	NUM
ejpam-1853	155	4	)	)	PUNCT
ejpam-1853	155	5	,	,	PUNCT
ejpam-1853	155	6	y	y	X
ejpam-1853	155	7	)	)	PUNCT
ejpam-1853	155	8	∈	∈	PROPN
ejpam-1853	155	9	g(2	g(2	PROPN
ejpam-1853	155	10	)	)	PUNCT
ejpam-1853	155	11	.	.	PUNCT
ejpam-1853	156	1	using	use	VERB
ejpam-1853	156	2	the	the	DET
ejpam-1853	156	3	condition	condition	NOUN
ejpam-1853	156	4	(	(	PUNCT
ejpam-1853	156	5	g2	g2	PROPN
ejpam-1853	156	6	)	)	PUNCT
ejpam-1853	156	7	from	from	ADP
ejpam-1853	156	8	definition	definition	NOUN
ejpam-1853	156	9	1	1	NUM
ejpam-1853	156	10	,	,	PUNCT
ejpam-1853	156	11	one	one	NOUN
ejpam-1853	156	12	obtains	obtain	VERB
ejpam-1853	156	13	e	e	NOUN
ejpam-1853	156	14	·	·	PUNCT
ejpam-1853	156	15	y	y	PROPN
ejpam-1853	156	16	=	=	SYM
ejpam-1853	156	17	ε(e0	ε(e0	X
ejpam-1853	156	18	)	)	PUNCT
ejpam-1853	156	19	·	·	PUNCT
ejpam-1853	157	1	y	y	X
ejpam-1853	157	2	=	=	SYM
ejpam-1853	157	3	ε(α(y	ε(α(y	PROPN
ejpam-1853	157	4	)	)	PUNCT
ejpam-1853	157	5	)	)	PUNCT
ejpam-1853	157	6	·	·	PUNCT
ejpam-1853	158	1	y	y	X
ejpam-1853	158	2	=	=	SYM
ejpam-1853	158	3	y	y	PROPN
ejpam-1853	158	4	.	.	PUNCT
ejpam-1853	159	1	hence	hence	ADV
ejpam-1853	159	2	the	the	DET
ejpam-1853	159	3	first	first	ADJ
ejpam-1853	159	4	relation	relation	NOUN
ejpam-1853	159	5	of	of	ADP
ejpam-1853	159	6	(	(	PUNCT
ejpam-1853	159	7	4	4	NUM
ejpam-1853	159	8	)	)	PUNCT
ejpam-1853	159	9	holds	hold	NOUN
ejpam-1853	159	10	.	.	PUNCT
ejpam-1853	160	1	similarly	similarly	ADV
ejpam-1853	160	2	,	,	PUNCT
ejpam-1853	160	3	we	we	PRON
ejpam-1853	160	4	prove	prove	VERB
ejpam-1853	160	5	that	that	SCONJ
ejpam-1853	160	6	the	the	DET
ejpam-1853	160	7	second	second	ADJ
ejpam-1853	160	8	relation	relation	NOUN
ejpam-1853	160	9	of	of	ADP
ejpam-1853	160	10	(	(	PUNCT
ejpam-1853	160	11	4	4	X
ejpam-1853	160	12	)	)	PUNCT
ejpam-1853	160	13	hold	hold	NOUN
ejpam-1853	160	14	.	.	PUNCT
ejpam-1853	161	1	for	for	ADP
ejpam-1853	161	2	to	to	PART
ejpam-1853	161	3	prove	prove	VERB
ejpam-1853	161	4	the	the	DET
ejpam-1853	161	5	relation	relation	NOUN
ejpam-1853	161	6	(	(	PUNCT
ejpam-1853	161	7	5	5	X
ejpam-1853	161	8	)	)	PUNCT
ejpam-1853	161	9	we	we	PRON
ejpam-1853	161	10	apply	apply	VERB
ejpam-1853	161	11	the	the	DET
ejpam-1853	161	12	interchange	interchange	NOUN
ejpam-1853	161	13	law	law	NOUN
ejpam-1853	161	14	(	(	PUNCT
ejpam-1853	161	15	2	2	NUM
ejpam-1853	161	16	)	)	PUNCT
ejpam-1853	161	17	and	and	CCONJ
ejpam-1853	161	18	(	(	PUNCT
ejpam-1853	161	19	4	4	NUM
ejpam-1853	161	20	)	)	PUNCT
ejpam-1853	161	21	.	.	PUNCT
ejpam-1853	162	1	indeed	indeed	ADV
ejpam-1853	162	2	,	,	PUNCT
ejpam-1853	162	3	if	if	SCONJ
ejpam-1853	162	4	in	in	ADP
ejpam-1853	162	5	(	(	PUNCT
ejpam-1853	162	6	2	2	X
ejpam-1853	162	7	)	)	PUNCT
ejpam-1853	162	8	we	we	PRON
ejpam-1853	162	9	replace	replace	VERB
ejpam-1853	162	10	z	z	NOUN
ejpam-1853	162	11	with	with	ADP
ejpam-1853	162	12	e	e	NOUN
ejpam-1853	162	13	,	,	PUNCT
ejpam-1853	162	14	one	one	PRON
ejpam-1853	162	15	obtains	obtain	VERB
ejpam-1853	162	16	(	(	PUNCT
ejpam-1853	162	17	x	x	SYM
ejpam-1853	162	18	·	·	PUNCT
ejpam-1853	163	1	y)⊕	y)⊕	NOUN
ejpam-1853	163	2	(	(	PUNCT
ejpam-1853	163	3	e	e	X
ejpam-1853	163	4	·	·	PUNCT
ejpam-1853	163	5	t	t	X
ejpam-1853	163	6	)	)	PUNCT
ejpam-1853	163	7	=	=	SYM
ejpam-1853	163	8	(	(	PUNCT
ejpam-1853	163	9	x	x	PROPN
ejpam-1853	163	10	⊕	⊕	PROPN
ejpam-1853	163	11	e	e	NOUN
ejpam-1853	163	12	)	)	PUNCT
ejpam-1853	163	13	·	·	PUNCT
ejpam-1853	164	1	(	(	PUNCT
ejpam-1853	164	2	y	y	PROPN
ejpam-1853	164	3	⊕	⊕	PROPN
ejpam-1853	164	4	t	t	PROPN
ejpam-1853	164	5	)	)	PUNCT
ejpam-1853	164	6	,	,	PUNCT
ejpam-1853	164	7	(	(	PUNCT
ejpam-1853	164	8	∀)(x	∀)(x	PROPN
ejpam-1853	164	9	,	,	PUNCT
ejpam-1853	164	10	y	y	PROPN
ejpam-1853	164	11	)	)	PUNCT
ejpam-1853	164	12	,	,	PUNCT
ejpam-1853	164	13	(	(	PUNCT
ejpam-1853	164	14	e	e	NOUN
ejpam-1853	164	15	,	,	PUNCT
ejpam-1853	164	16	t	t	PROPN
ejpam-1853	164	17	)	)	PUNCT
ejpam-1853	164	18	∈	∈	PROPN
ejpam-1853	164	19	g(2	g(2	PROPN
ejpam-1853	164	20	)	)	PUNCT
ejpam-1853	164	21	.	.	PUNCT
ejpam-1853	165	1	it	it	PRON
ejpam-1853	165	2	follows	follow	VERB
ejpam-1853	165	3	(	(	PUNCT
ejpam-1853	165	4	x	x	X
ejpam-1853	165	5	·	·	PUNCT
ejpam-1853	165	6	y)⊕	y)⊕	NOUN
ejpam-1853	165	7	t	t	NOUN
ejpam-1853	165	8	=	=	PUNCT
ejpam-1853	165	9	x	x	SYM
ejpam-1853	165	10	·	·	PUNCT
ejpam-1853	165	11	(	(	PUNCT
ejpam-1853	165	12	y	y	PROPN
ejpam-1853	165	13	⊕	⊕	PROPN
ejpam-1853	165	14	t	t	PROPN
ejpam-1853	165	15	)	)	PUNCT
ejpam-1853	165	16	,	,	PUNCT
ejpam-1853	165	17	since	since	SCONJ
ejpam-1853	165	18	x	x	PROPN
ejpam-1853	165	19	⊕	⊕	PROPN
ejpam-1853	165	20	e	e	NOUN
ejpam-1853	165	21	=	=	PUNCT
ejpam-1853	165	22	x	x	SYM
ejpam-1853	165	23	,	,	PUNCT
ejpam-1853	165	24	β(e	β(e	PROPN
ejpam-1853	165	25	)	)	PUNCT
ejpam-1853	165	26	=	=	SYM
ejpam-1853	165	27	e0	e0	PROPN
ejpam-1853	165	28	and	and	CCONJ
ejpam-1853	165	29	t	t	NOUN
ejpam-1853	165	30	∈	∈	PROPN
ejpam-1853	165	31	α−1(e0	α−1(e0	PRON
ejpam-1853	165	32	)	)	PUNCT
ejpam-1853	165	33	.	.	PUNCT
ejpam-1853	166	1	hence	hence	ADV
ejpam-1853	166	2	,	,	PUNCT
ejpam-1853	166	3	the	the	DET
ejpam-1853	166	4	relation	relation	NOUN
ejpam-1853	166	5	(	(	PUNCT
ejpam-1853	166	6	5	5	NUM
ejpam-1853	166	7	)	)	PUNCT
ejpam-1853	166	8	holds	hold	VERB
ejpam-1853	166	9	.	.	PUNCT
ejpam-1853	167	1	similarly	similarly	ADV
ejpam-1853	167	2	,	,	PUNCT
ejpam-1853	167	3	if	if	SCONJ
ejpam-1853	167	4	in	in	ADP
ejpam-1853	167	5	(	(	PUNCT
ejpam-1853	167	6	2	2	X
ejpam-1853	167	7	)	)	PUNCT
ejpam-1853	167	8	we	we	PRON
ejpam-1853	167	9	replace	replace	VERB
ejpam-1853	167	10	t	t	PROPN
ejpam-1853	167	11	with	with	ADP
ejpam-1853	167	12	e	e	NOUN
ejpam-1853	167	13	,	,	PUNCT
ejpam-1853	167	14	one	one	PRON
ejpam-1853	167	15	obtains	obtain	VERB
ejpam-1853	167	16	(	(	PUNCT
ejpam-1853	167	17	x	x	SYM
ejpam-1853	167	18	·	·	PUNCT
ejpam-1853	167	19	y)⊕	y)⊕	NOUN
ejpam-1853	167	20	(	(	PUNCT
ejpam-1853	167	21	z	z	NOUN
ejpam-1853	167	22	·	·	PUNCT
ejpam-1853	168	1	e	e	X
ejpam-1853	168	2	)	)	PUNCT
ejpam-1853	168	3	=	=	SYM
ejpam-1853	168	4	(	(	PUNCT
ejpam-1853	168	5	x	x	PROPN
ejpam-1853	168	6	⊕	⊕	PROPN
ejpam-1853	168	7	y	y	PROPN
ejpam-1853	168	8	)	)	PUNCT
ejpam-1853	168	9	·	·	PUNCT
ejpam-1853	169	1	(	(	PUNCT
ejpam-1853	169	2	y	y	PROPN
ejpam-1853	169	3	⊕	⊕	PROPN
ejpam-1853	169	4	e	e	PROPN
ejpam-1853	169	5	)	)	PUNCT
ejpam-1853	169	6	,	,	PUNCT
ejpam-1853	169	7	(	(	PUNCT
ejpam-1853	169	8	∀)(x	∀)(x	PROPN
ejpam-1853	169	9	,	,	PUNCT
ejpam-1853	169	10	y	y	PROPN
ejpam-1853	169	11	)	)	PUNCT
ejpam-1853	169	12	,	,	PUNCT
ejpam-1853	169	13	(	(	PUNCT
ejpam-1853	169	14	y	y	NOUN
ejpam-1853	169	15	,	,	PUNCT
ejpam-1853	169	16	e	e	NOUN
ejpam-1853	169	17	)	)	PUNCT
ejpam-1853	169	18	∈	∈	PROPN
ejpam-1853	169	19	g(2	g(2	PROPN
ejpam-1853	169	20	)	)	PUNCT
ejpam-1853	169	21	.	.	PUNCT
ejpam-1853	170	1	it	it	PRON
ejpam-1853	170	2	follows	follow	VERB
ejpam-1853	170	3	(	(	PUNCT
ejpam-1853	170	4	x	x	X
ejpam-1853	170	5	·	·	PUNCT
ejpam-1853	170	6	y)⊕	y)⊕	NOUN
ejpam-1853	170	7	z	z	NOUN
ejpam-1853	170	8	=	=	SYM
ejpam-1853	170	9	(	(	PUNCT
ejpam-1853	170	10	x	x	PROPN
ejpam-1853	170	11	⊕	⊕	PROPN
ejpam-1853	170	12	z	z	PROPN
ejpam-1853	170	13	)	)	PUNCT
ejpam-1853	170	14	·	·	PUNCT
ejpam-1853	171	1	y	y	NOUN
ejpam-1853	171	2	,	,	PUNCT
ejpam-1853	171	3	since	since	SCONJ
ejpam-1853	171	4	y	y	PROPN
ejpam-1853	171	5	⊕	⊕	PROPN
ejpam-1853	171	6	e	e	PROPN
ejpam-1853	171	7	=	=	PUNCT
ejpam-1853	171	8	y	y	PROPN
ejpam-1853	171	9	,	,	PUNCT
ejpam-1853	171	10	α(e	α(e	PROPN
ejpam-1853	171	11	)	)	PUNCT
ejpam-1853	171	12	=	=	VERB
ejpam-1853	171	13	e0	e0	PROPN
ejpam-1853	171	14	and	and	CCONJ
ejpam-1853	171	15	z	z	NOUN
ejpam-1853	171	16	∈	∈	PROPN
ejpam-1853	171	17	β−1(e0	β−1(e0	PROPN
ejpam-1853	171	18	)	)	PUNCT
ejpam-1853	171	19	.	.	PUNCT
ejpam-1853	172	1	hence	hence	ADV
ejpam-1853	172	2	,	,	PUNCT
ejpam-1853	172	3	the	the	DET
ejpam-1853	172	4	relation	relation	NOUN
ejpam-1853	172	5	(	(	PUNCT
ejpam-1853	172	6	6	6	NUM
ejpam-1853	172	7	)	)	PUNCT
ejpam-1853	172	8	holds	hold	NOUN
ejpam-1853	172	9	.	.	PUNCT
ejpam-1853	173	1	theorem	theorem	NOUN
ejpam-1853	173	2	4	4	NUM
ejpam-1853	173	3	.	.	PUNCT
ejpam-1853	174	1	[	[	X
ejpam-1853	174	2	3	3	X
ejpam-1853	174	3	]	]	X
ejpam-1853	174	4	if	if	SCONJ
ejpam-1853	174	5	(	(	PUNCT
ejpam-1853	174	6	g	g	NOUN
ejpam-1853	174	7	,	,	PUNCT
ejpam-1853	174	8	α	α	X
ejpam-1853	174	9	,	,	PUNCT
ejpam-1853	174	10	β	β	X
ejpam-1853	174	11	,	,	PUNCT
ejpam-1853	174	12	m	m	PROPN
ejpam-1853	174	13	,	,	PUNCT
ejpam-1853	174	14	ε	ε	PROPN
ejpam-1853	174	15	,	,	PUNCT
ejpam-1853	174	16	i,⊕	i,⊕	NOUN
ejpam-1853	174	17	,	,	PUNCT
ejpam-1853	174	18	g0	g0	NOUN
ejpam-1853	174	19	)	)	PUNCT
ejpam-1853	174	20	is	be	AUX
ejpam-1853	174	21	a	a	DET
ejpam-1853	174	22	g−groupoid	g−groupoid	NOUN
ejpam-1853	174	23	,	,	PUNCT
ejpam-1853	174	24	then	then	ADV
ejpam-1853	174	25	:	:	PUNCT
ejpam-1853	174	26	x	x	X
ejpam-1853	174	27	·	·	PUNCT
ejpam-1853	174	28	y	y	X
ejpam-1853	174	29	=	=	SYM
ejpam-1853	174	30	x	x	PROPN
ejpam-1853	174	31	⊕	⊕	PROPN
ejpam-1853	174	32	ε(β(x))⊕	ε(β(x))⊕	VERB
ejpam-1853	174	33	y	y	PROPN
ejpam-1853	174	34	,	,	PUNCT
ejpam-1853	174	35	(	(	PUNCT
ejpam-1853	174	36	∀)(x	∀)(x	PROPN
ejpam-1853	174	37	,	,	PUNCT
ejpam-1853	174	38	y	y	PROPN
ejpam-1853	174	39	)	)	PUNCT
ejpam-1853	174	40	∈	∈	PROPN
ejpam-1853	174	41	g(2	g(2	PROPN
ejpam-1853	174	42	)	)	PUNCT
ejpam-1853	174	43	;	;	PUNCT
ejpam-1853	174	44	(	(	PUNCT
ejpam-1853	174	45	7	7	X
ejpam-1853	174	46	)	)	PUNCT
ejpam-1853	174	47	x−1	x−1	NOUN
ejpam-1853	175	1	=	=	SYM
ejpam-1853	175	2	ε(α(x))⊕	ε(α(x))⊕	PROPN
ejpam-1853	175	3	x̄	x̄	PROPN
ejpam-1853	175	4	⊕	⊕	PROPN
ejpam-1853	175	5	ε(β(x	ε(β(x	PROPN
ejpam-1853	175	6	)	)	PUNCT
ejpam-1853	175	7	)	)	PUNCT
ejpam-1853	175	8	,	,	PUNCT
ejpam-1853	175	9	(	(	PUNCT
ejpam-1853	175	10	∀)x	∀)x	PROPN
ejpam-1853	175	11	∈	∈	PROPN
ejpam-1853	175	12	g.	g.	NOUN
ejpam-1853	175	13	(	(	PUNCT
ejpam-1853	175	14	8)	8)	NUM
ejpam-1853	175	15	proof	proof	NOUN
ejpam-1853	175	16	.	.	PUNCT
ejpam-1853	176	1	let	let	VERB
ejpam-1853	176	2	(	(	PUNCT
ejpam-1853	176	3	x	x	X
ejpam-1853	176	4	,	,	PUNCT
ejpam-1853	176	5	y	y	PROPN
ejpam-1853	176	6	)	)	PUNCT
ejpam-1853	176	7	∈	∈	PROPN
ejpam-1853	176	8	g(2	g(2	PROPN
ejpam-1853	176	9	)	)	PUNCT
ejpam-1853	176	10	.	.	PUNCT
ejpam-1853	177	1	then	then	ADV
ejpam-1853	177	2	β(x	β(x	NOUN
ejpam-1853	177	3	)	)	PUNCT
ejpam-1853	177	4	=	=	SYM
ejpam-1853	177	5	α(y	α(y	NOUN
ejpam-1853	177	6	)	)	PUNCT
ejpam-1853	177	7	.	.	PUNCT
ejpam-1853	178	1	we	we	PRON
ejpam-1853	178	2	have	have	VERB
ejpam-1853	178	3	x	x	X
ejpam-1853	178	4	·	·	PUNCT
ejpam-1853	178	5	y	y	X
ejpam-1853	178	6	=	=	SYM
ejpam-1853	178	7	(	(	PUNCT
ejpam-1853	178	8	x	x	PROPN
ejpam-1853	178	9	⊕	⊕	PROPN
ejpam-1853	178	10	(	(	PUNCT
ejpam-1853	178	11	ε(β(x))⊕	ε(β(x))⊕	ADV
ejpam-1853	178	12	ε(β(x	ε(β(x	NOUN
ejpam-1853	178	13	)	)	PUNCT
ejpam-1853	178	14	)	)	PUNCT
ejpam-1853	178	15	)	)	PUNCT
ejpam-1853	178	16	)	)	PUNCT
ejpam-1853	178	17	·	·	PUNCT
ejpam-1853	179	1	(	(	PUNCT
ejpam-1853	179	2	e⊕	e⊕	PROPN
ejpam-1853	179	3	y	y	PROPN
ejpam-1853	179	4	)	)	PUNCT
ejpam-1853	179	5	,	,	PUNCT
ejpam-1853	179	6	since	since	SCONJ
ejpam-1853	179	7	ε(β(x))⊕	ε(β(x))⊕	VERB
ejpam-1853	179	8	ε(β(x	ε(β(x	NOUN
ejpam-1853	179	9	)	)	PUNCT
ejpam-1853	179	10	)	)	PUNCT
ejpam-1853	180	1	=	=	PUNCT
ejpam-1853	180	2	e	e	X
ejpam-1853	180	3	,	,	PUNCT
ejpam-1853	180	4	x	x	PROPN
ejpam-1853	180	5	⊕	⊕	NOUN
ejpam-1853	180	6	e	e	NOUN
ejpam-1853	180	7	=	=	PUNCT
ejpam-1853	180	8	x	x	X
ejpam-1853	180	9	and	and	CCONJ
ejpam-1853	180	10	e⊕	e⊕	PROPN
ejpam-1853	180	11	y	y	PROPN
ejpam-1853	180	12	=	=	PROPN
ejpam-1853	180	13	y	y	PROPN
ejpam-1853	180	14	.	.	PUNCT
ejpam-1853	181	1	from	from	ADP
ejpam-1853	181	2	the	the	DET
ejpam-1853	181	3	associativity	associativity	NOUN
ejpam-1853	181	4	of	of	ADP
ejpam-1853	181	5	the	the	DET
ejpam-1853	181	6	law	law	NOUN
ejpam-1853	181	7	⊕	⊕	PROPN
ejpam-1853	181	8	and	and	CCONJ
ejpam-1853	181	9	β(x	β(x	PROPN
ejpam-1853	181	10	)	)	PUNCT
ejpam-1853	181	11	=	=	SYM
ejpam-1853	181	12	α(y	α(y	NOUN
ejpam-1853	181	13	)	)	PUNCT
ejpam-1853	181	14	,	,	PUNCT
ejpam-1853	181	15	one	one	PRON
ejpam-1853	181	16	obtains	obtain	VERB
ejpam-1853	181	17	x	x	X
ejpam-1853	181	18	·	·	PUNCT
ejpam-1853	181	19	y	y	X
ejpam-1853	181	20	=	=	SYM
ejpam-1853	181	21	(	(	PUNCT
ejpam-1853	181	22	(	(	PUNCT
ejpam-1853	181	23	x	x	PROPN
ejpam-1853	181	24	⊕	⊕	NOUN
ejpam-1853	181	25	ε(β(x)))⊕	ε(β(x)))⊕	VERB
ejpam-1853	181	26	ε(α(y	ε(α(y	PROPN
ejpam-1853	181	27	)	)	PUNCT
ejpam-1853	181	28	)	)	PUNCT
ejpam-1853	181	29	)	)	PUNCT
ejpam-1853	181	30	·	·	PUNCT
ejpam-1853	182	1	(	(	PUNCT
ejpam-1853	182	2	e⊕	e⊕	NOUN
ejpam-1853	182	3	y	y	PROPN
ejpam-1853	182	4	)	)	PUNCT
ejpam-1853	182	5	.	.	PUNCT
ejpam-1853	183	1	applying	apply	VERB
ejpam-1853	183	2	the	the	DET
ejpam-1853	183	3	interchange	interchange	NOUN
ejpam-1853	183	4	law	law	NOUN
ejpam-1853	183	5	(	(	PUNCT
ejpam-1853	183	6	2	2	NUM
ejpam-1853	183	7	)	)	PUNCT
ejpam-1853	183	8	,	,	PUNCT
ejpam-1853	183	9	the	the	DET
ejpam-1853	183	10	relations	relation	NOUN
ejpam-1853	183	11	(	(	PUNCT
ejpam-1853	183	12	4	4	NUM
ejpam-1853	183	13	)	)	PUNCT
ejpam-1853	183	14	and	and	CCONJ
ejpam-1853	183	15	(	(	PUNCT
ejpam-1853	183	16	g.2	g.2	PROPN
ejpam-1853	183	17	)	)	PUNCT
ejpam-1853	183	18	,	,	PUNCT
ejpam-1853	183	19	we	we	PRON
ejpam-1853	183	20	have	have	VERB
ejpam-1853	183	21	x	x	X
ejpam-1853	183	22	·	·	PUNCT
ejpam-1853	183	23	y	y	SYM
ejpam-1853	183	24	=	=	SYM
ejpam-1853	183	25	(	(	PUNCT
ejpam-1853	183	26	(	(	PUNCT
ejpam-1853	183	27	x	x	PROPN
ejpam-1853	183	28	⊕	⊕	PROPN
ejpam-1853	183	29	(	(	PUNCT
ejpam-1853	183	30	ε(β(x	ε(β(x	PROPN
ejpam-1853	183	31	)	)	PUNCT
ejpam-1853	183	32	)	)	PUNCT
ejpam-1853	183	33	·	·	PUNCT
ejpam-1853	184	1	e)⊕	e)⊕	PROPN
ejpam-1853	184	2	(	(	PUNCT
ejpam-1853	184	3	ε(α(y	ε(α(y	PROPN
ejpam-1853	184	4	)	)	PUNCT
ejpam-1853	184	5	)	)	PUNCT
ejpam-1853	184	6	·	·	PUNCT
ejpam-1853	184	7	y	y	X
ejpam-1853	184	8	)	)	PUNCT
ejpam-1853	184	9	⇒	⇒	NOUN
ejpam-1853	184	10	x	x	X
ejpam-1853	184	11	·	·	PUNCT
ejpam-1853	184	12	y	y	X
ejpam-1853	184	13	=	=	SYM
ejpam-1853	184	14	x	x	PROPN
ejpam-1853	184	15	⊕	⊕	PROPN
ejpam-1853	184	16	ε(β(x))⊕	ε(β(x))⊕	VERB
ejpam-1853	184	17	y.	y.	PROPN
ejpam-1853	184	18	hence	hence	PROPN
ejpam-1853	184	19	,	,	PUNCT
ejpam-1853	184	20	the	the	DET
ejpam-1853	184	21	relation	relation	NOUN
ejpam-1853	184	22	(	(	PUNCT
ejpam-1853	184	23	7	7	X
ejpam-1853	184	24	)	)	PUNCT
ejpam-1853	184	25	holds	hold	VERB
ejpam-1853	184	26	.	.	PUNCT
ejpam-1853	185	1	applying	apply	VERB
ejpam-1853	185	2	the	the	DET
ejpam-1853	185	3	fact	fact	NOUN
ejpam-1853	185	4	that	that	SCONJ
ejpam-1853	185	5	α	α	PRON
ejpam-1853	185	6	is	be	AUX
ejpam-1853	185	7	a	a	DET
ejpam-1853	185	8	group	group	NOUN
ejpam-1853	185	9	morphism	morphism	NOUN
ejpam-1853	185	10	and	and	CCONJ
ejpam-1853	185	11	the	the	DET
ejpam-1853	185	12	relation	relation	NOUN
ejpam-1853	185	13	α	α	NOUN
ejpam-1853	185	14	◦	◦	NOUN
ejpam-1853	185	15	ε	ε	PROPN
ejpam-1853	185	16	=	=	SYM
ejpam-1853	185	17	idg0	idg0	PROPN
ejpam-1853	185	18	,	,	PUNCT
ejpam-1853	185	19	one	one	NOUN
ejpam-1853	185	20	obtains	obtain	VERB
ejpam-1853	185	21	α(a	α(a	NOUN
ejpam-1853	185	22	)	)	PUNCT
ejpam-1853	185	23	=	=	SYM
ejpam-1853	186	1	α(ε(α(x)))⊕α	α(ε(α(x)))⊕α	ADJ
ejpam-1853	186	2	(	(	PUNCT
ejpam-1853	186	3	x̄)⊕α(ε(β(x	x̄)⊕α(ε(β(x	NOUN
ejpam-1853	186	4	)	)	PUNCT
ejpam-1853	186	5	)	)	PUNCT
ejpam-1853	186	6	)	)	PUNCT
ejpam-1853	187	1	=	=	PUNCT
ejpam-1853	187	2	α(x)⊕α	α(x)⊕α	NUM
ejpam-1853	187	3	(	(	PUNCT
ejpam-1853	187	4	x̄)⊕	x̄)⊕	PROPN
ejpam-1853	187	5	β(x	β(x	PROPN
ejpam-1853	187	6	)	)	PUNCT
ejpam-1853	187	7	=	=	SYM
ejpam-1853	187	8	α(x	α(x	PROPN
ejpam-1853	187	9	⊕	⊕	PROPN
ejpam-1853	187	10	x̄)⊕	x̄)⊕	PROPN
ejpam-1853	187	11	β(x	β(x	PROPN
ejpam-1853	187	12	)	)	PUNCT
ejpam-1853	187	13	=	=	SYM
ejpam-1853	187	14	β(x	β(x	NOUN
ejpam-1853	187	15	)	)	PUNCT
ejpam-1853	187	16	.	.	PUNCT
ejpam-1853	188	1	from	from	ADP
ejpam-1853	188	2	α(a	α(a	NOUN
ejpam-1853	188	3	)	)	PUNCT
ejpam-1853	188	4	=	=	SYM
ejpam-1853	188	5	β(x	β(x	NOUN
ejpam-1853	188	6	)	)	PUNCT
ejpam-1853	188	7	it	it	PRON
ejpam-1853	188	8	follows	follow	VERB
ejpam-1853	188	9	that	that	SCONJ
ejpam-1853	188	10	the	the	DET
ejpam-1853	188	11	product	product	NOUN
ejpam-1853	188	12	x	x	PUNCT
ejpam-1853	188	13	·	·	PUNCT
ejpam-1853	188	14	a	a	PRON
ejpam-1853	188	15	is	be	AUX
ejpam-1853	188	16	defined	define	VERB
ejpam-1853	188	17	.	.	PUNCT
ejpam-1853	189	1	applying	apply	VERB
ejpam-1853	189	2	the	the	DET
ejpam-1853	189	3	interchange	interchange	NOUN
ejpam-1853	189	4	law	law	NOUN
ejpam-1853	189	5	(	(	PUNCT
ejpam-1853	189	6	2	2	NUM
ejpam-1853	189	7	)	)	PUNCT
ejpam-1853	189	8	and	and	CCONJ
ejpam-1853	189	9	(	(	PUNCT
ejpam-1853	189	10	4	4	NUM
ejpam-1853	189	11	)	)	PUNCT
ejpam-1853	189	12	,	,	PUNCT
ejpam-1853	189	13	we	we	PRON
ejpam-1853	189	14	have	have	VERB
ejpam-1853	189	15	x	x	X
ejpam-1853	189	16	·	·	PUNCT
ejpam-1853	189	17	a	a	DET
ejpam-1853	189	18	=(	=(	NOUN
ejpam-1853	189	19	e⊕	e⊕	PROPN
ejpam-1853	189	20	x	x	PROPN
ejpam-1853	189	21	)	)	PUNCT
ejpam-1853	189	22	·	·	PUNCT
ejpam-1853	189	23	(	(	PUNCT
ejpam-1853	189	24	(	(	PUNCT
ejpam-1853	189	25	ε(α(x))⊕	ε(α(x))⊕	NOUN
ejpam-1853	189	26	x̄)⊕	x̄)⊕	PROPN
ejpam-1853	189	27	ε(β(x	ε(β(x	NOUN
ejpam-1853	189	28	)	)	PUNCT
ejpam-1853	189	29	)	)	PUNCT
ejpam-1853	189	30	)	)	PUNCT
ejpam-1853	190	1	=	=	PUNCT
ejpam-1853	190	2	(	(	PUNCT
ejpam-1853	190	3	e	e	NOUN
ejpam-1853	190	4	·	·	PUNCT
ejpam-1853	190	5	(	(	PUNCT
ejpam-1853	190	6	ε(α(x))⊕	ε(α(x))⊕	NOUN
ejpam-1853	190	7	x̄))⊕	x̄))⊕	PROPN
ejpam-1853	190	8	(	(	PUNCT
ejpam-1853	190	9	x	x	X
ejpam-1853	190	10	·	·	PUNCT
ejpam-1853	190	11	ε(β(x	ε(β(x	NOUN
ejpam-1853	190	12	)	)	PUNCT
ejpam-1853	190	13	)	)	PUNCT
ejpam-1853	190	14	)	)	PUNCT
ejpam-1853	191	1	=	=	NOUN
ejpam-1853	191	2	ε(α(x))⊕	ε(α(x))⊕	NOUN
ejpam-1853	191	3	x̄	x̄	PRON
ejpam-1853	191	4	⊕	⊕	PROPN
ejpam-1853	191	5	x	x	PUNCT
ejpam-1853	191	6	=	=	PUNCT
ejpam-1853	191	7	ε(α(x	ε(α(x	NOUN
ejpam-1853	191	8	)	)	PUNCT
ejpam-1853	191	9	)	)	PUNCT
ejpam-1853	191	10	.	.	PUNCT
ejpam-1853	192	1	hence	hence	ADV
ejpam-1853	192	2	,	,	PUNCT
ejpam-1853	192	3	x	x	X
ejpam-1853	192	4	·	·	PUNCT
ejpam-1853	192	5	a	a	DET
ejpam-1853	192	6	=	=	ADJ
ejpam-1853	192	7	ε(α(x	ε(α(x	NOUN
ejpam-1853	192	8	)	)	PUNCT
ejpam-1853	192	9	)	)	PUNCT
ejpam-1853	192	10	.	.	PUNCT
ejpam-1853	193	1	similarly	similarly	ADV
ejpam-1853	193	2	,	,	PUNCT
ejpam-1853	193	3	we	we	PRON
ejpam-1853	193	4	verify	verify	VERB
ejpam-1853	193	5	that	that	SCONJ
ejpam-1853	193	6	a	a	DET
ejpam-1853	193	7	·	·	PUNCT
ejpam-1853	193	8	x	x	SYM
ejpam-1853	193	9	=	=	PUNCT
ejpam-1853	193	10	ε(β(x	ε(β(x	NOUN
ejpam-1853	193	11	)	)	PUNCT
ejpam-1853	193	12	)	)	PUNCT
ejpam-1853	193	13	.	.	PUNCT
ejpam-1853	194	1	then	then	ADV
ejpam-1853	194	2	a	a	DET
ejpam-1853	194	3	=	=	X
ejpam-1853	194	4	x−1	x−1	PROPN
ejpam-1853	194	5	and	and	CCONJ
ejpam-1853	194	6	the	the	DET
ejpam-1853	194	7	relation	relation	NOUN
ejpam-1853	194	8	(	(	PUNCT
ejpam-1853	194	9	8)	8)	NUM
ejpam-1853	194	10	holds	hold	NOUN
ejpam-1853	194	11	.	.	PUNCT
ejpam-1853	195	1	m.	m.	NOUN
ejpam-1853	195	2	ivan	ivan	PROPN
ejpam-1853	195	3	/	/	PUNCT
ejpam-1853	195	4	eur	eur	PROPN
ejpam-1853	195	5	.	.	PUNCT
ejpam-1853	196	1	j.	j.	PROPN
ejpam-1853	196	2	pure	pure	PROPN
ejpam-1853	196	3	appl	appl	PROPN
ejpam-1853	196	4	.	.	PROPN
ejpam-1853	196	5	math	math	PROPN
ejpam-1853	196	6	,	,	PUNCT
ejpam-1853	196	7	6	6	NUM
ejpam-1853	196	8	(	(	PUNCT
ejpam-1853	196	9	2013	2013	NUM
ejpam-1853	196	10	)	)	PUNCT
ejpam-1853	196	11	,	,	PUNCT
ejpam-1853	196	12	469	469	NUM
ejpam-1853	196	13	-	-	SYM
ejpam-1853	196	14	484	484	NUM
ejpam-1853	196	15	475	475	NUM
ejpam-1853	196	16	corollary	corollary	ADJ
ejpam-1853	196	17	1	1	NUM
ejpam-1853	196	18	.	.	PUNCT
ejpam-1853	197	1	if	if	SCONJ
ejpam-1853	197	2	(	(	PUNCT
ejpam-1853	197	3	g	g	NOUN
ejpam-1853	197	4	,	,	PUNCT
ejpam-1853	197	5	α	α	X
ejpam-1853	197	6	,	,	PUNCT
ejpam-1853	197	7	β	β	X
ejpam-1853	197	8	,	,	PUNCT
ejpam-1853	197	9	m	m	PROPN
ejpam-1853	197	10	,	,	PUNCT
ejpam-1853	197	11	ε	ε	PROPN
ejpam-1853	197	12	,	,	PUNCT
ejpam-1853	197	13	i,⊕	i,⊕	NOUN
ejpam-1853	197	14	,	,	PUNCT
ejpam-1853	197	15	g0	g0	NOUN
ejpam-1853	197	16	)	)	PUNCT
ejpam-1853	197	17	is	be	AUX
ejpam-1853	197	18	a	a	DET
ejpam-1853	197	19	g−groupoid	g−groupoid	NOUN
ejpam-1853	197	20	,	,	PUNCT
ejpam-1853	197	21	then	then	ADV
ejpam-1853	197	22	:	:	PUNCT
ejpam-1853	197	23	x	x	X
ejpam-1853	197	24	·	·	PUNCT
ejpam-1853	197	25	y	y	X
ejpam-1853	197	26	=	=	PUNCT
ejpam-1853	197	27	x	x	SYM
ejpam-1853	197	28	⊕	⊕	PROPN
ejpam-1853	197	29	y	y	PROPN
ejpam-1853	197	30	and	and	CCONJ
ejpam-1853	197	31	x−1	x−1	PROPN
ejpam-1853	197	32	=	=	PUNCT
ejpam-1853	197	33	x̄	x̄	PROPN
ejpam-1853	197	34	,	,	PUNCT
ejpam-1853	197	35	(	(	PUNCT
ejpam-1853	197	36	∀)x	∀)x	INTJ
ejpam-1853	197	37	,	,	PUNCT
ejpam-1853	197	38	y	y	PROPN
ejpam-1853	197	39	∈	∈	PROPN
ejpam-1853	197	40	g(e0	g(e0	PROPN
ejpam-1853	197	41	)	)	PUNCT
ejpam-1853	197	42	.	.	PUNCT
ejpam-1853	198	1	(	(	PUNCT
ejpam-1853	198	2	9	9	X
ejpam-1853	198	3	)	)	PUNCT
ejpam-1853	198	4	proof	proof	NOUN
ejpam-1853	198	5	.	.	PUNCT
ejpam-1853	199	1	let	let	VERB
ejpam-1853	199	2	x	x	PRON
ejpam-1853	199	3	,	,	PUNCT
ejpam-1853	199	4	y	y	PROPN
ejpam-1853	199	5	∈	∈	PROPN
ejpam-1853	199	6	g(e0	g(e0	PROPN
ejpam-1853	199	7	)	)	PUNCT
ejpam-1853	199	8	.	.	PUNCT
ejpam-1853	200	1	then	then	ADV
ejpam-1853	200	2	α(x	α(x	NOUN
ejpam-1853	200	3	)	)	PUNCT
ejpam-1853	200	4	=	=	SYM
ejpam-1853	200	5	α(y	α(y	NOUN
ejpam-1853	200	6	)	)	PUNCT
ejpam-1853	200	7	=	=	PUNCT
ejpam-1853	200	8	β(x	β(x	NOUN
ejpam-1853	200	9	)	)	PUNCT
ejpam-1853	200	10	=	=	SYM
ejpam-1853	200	11	β(y	β(y	X
ejpam-1853	200	12	)	)	PUNCT
ejpam-1853	200	13	=	=	SYM
ejpam-1853	200	14	e0	e0	PROPN
ejpam-1853	200	15	and	and	CCONJ
ejpam-1853	200	16	(	(	PUNCT
ejpam-1853	200	17	x	x	X
ejpam-1853	200	18	,	,	PUNCT
ejpam-1853	200	19	y	y	PROPN
ejpam-1853	200	20	)	)	PUNCT
ejpam-1853	200	21	∈	∈	PROPN
ejpam-1853	200	22	g(2	g(2	PROPN
ejpam-1853	200	23	)	)	PUNCT
ejpam-1853	200	24	.	.	PUNCT
ejpam-1853	201	1	applying	apply	VERB
ejpam-1853	201	2	(	(	PUNCT
ejpam-1853	201	3	7	7	NUM
ejpam-1853	201	4	)	)	PUNCT
ejpam-1853	201	5	,	,	PUNCT
ejpam-1853	201	6	we	we	PRON
ejpam-1853	201	7	have	have	VERB
ejpam-1853	201	8	x	x	X
ejpam-1853	201	9	·	·	PUNCT
ejpam-1853	201	10	y	y	SYM
ejpam-1853	201	11	=	=	PUNCT
ejpam-1853	201	12	x	x	SYM
ejpam-1853	201	13	⊕	⊕	PROPN
ejpam-1853	201	14	y	y	PROPN
ejpam-1853	201	15	,	,	PUNCT
ejpam-1853	201	16	since	since	SCONJ
ejpam-1853	201	17	ε(β(x	ε(β(x	NOUN
ejpam-1853	201	18	)	)	PUNCT
ejpam-1853	201	19	)	)	PUNCT
ejpam-1853	202	1	=	=	SYM
ejpam-1853	202	2	ε(e0	ε(e0	X
ejpam-1853	202	3	)	)	PUNCT
ejpam-1853	202	4	=	=	SYM
ejpam-1853	203	1	e.	e.	PROPN
ejpam-1853	203	2	hence	hence	ADV
ejpam-1853	203	3	,	,	PUNCT
ejpam-1853	203	4	the	the	DET
ejpam-1853	203	5	first	first	ADJ
ejpam-1853	203	6	equality	equality	NOUN
ejpam-1853	203	7	from	from	ADP
ejpam-1853	203	8	(	(	PUNCT
ejpam-1853	203	9	9	9	NUM
ejpam-1853	203	10	)	)	PUNCT
ejpam-1853	203	11	holds	hold	NOUN
ejpam-1853	203	12	.	.	PUNCT
ejpam-1853	204	1	also	also	ADV
ejpam-1853	204	2	,	,	PUNCT
ejpam-1853	204	3	we	we	PRON
ejpam-1853	204	4	have	have	VERB
ejpam-1853	204	5	ε(α(x	ε(α(x	NOUN
ejpam-1853	204	6	)	)	PUNCT
ejpam-1853	204	7	)	)	PUNCT
ejpam-1853	205	1	=	=	PUNCT
ejpam-1853	205	2	ε(β(x	ε(β(x	NOUN
ejpam-1853	205	3	)	)	PUNCT
ejpam-1853	205	4	)	)	PUNCT
ejpam-1853	205	5	=	=	SYM
ejpam-1853	205	6	ε(e0	ε(e0	X
ejpam-1853	205	7	)	)	PUNCT
ejpam-1853	205	8	=	=	SYM
ejpam-1853	206	1	e.	e.	PROPN
ejpam-1853	206	2	applying	apply	VERB
ejpam-1853	206	3	now	now	ADV
ejpam-1853	206	4	(	(	PUNCT
ejpam-1853	206	5	8)	8)	NUM
ejpam-1853	206	6	,	,	PUNCT
ejpam-1853	206	7	we	we	PRON
ejpam-1853	206	8	have	have	VERB
ejpam-1853	206	9	x−1	x−1	X
ejpam-1853	206	10	=	=	SYM
ejpam-1853	206	11	x̄	x̄	PROPN
ejpam-1853	206	12	.	.	PUNCT
ejpam-1853	207	1	hence	hence	ADV
ejpam-1853	207	2	,	,	PUNCT
ejpam-1853	207	3	the	the	DET
ejpam-1853	207	4	second	second	ADJ
ejpam-1853	207	5	equality	equality	NOUN
ejpam-1853	207	6	from	from	ADP
ejpam-1853	207	7	(	(	PUNCT
ejpam-1853	207	8	9	9	NUM
ejpam-1853	207	9	)	)	PUNCT
ejpam-1853	207	10	holds	hold	NOUN
ejpam-1853	207	11	.	.	PUNCT
ejpam-1853	208	1	3	3	X
ejpam-1853	208	2	.	.	X
ejpam-1853	208	3	category	category	NOUN
ejpam-1853	208	4	of	of	ADP
ejpam-1853	208	5	vector	vector	NOUN
ejpam-1853	208	6	space	space	NOUN
ejpam-1853	208	7	-	-	PUNCT
ejpam-1853	208	8	groupoids	groupoid	NOUN
ejpam-1853	208	9	let	let	VERB
ejpam-1853	208	10	(	(	PUNCT
ejpam-1853	208	11	v	v	NOUN
ejpam-1853	208	12	,	,	PUNCT
ejpam-1853	208	13	α	α	NOUN
ejpam-1853	208	14	,	,	PUNCT
ejpam-1853	208	15	β	β	X
ejpam-1853	208	16	,	,	PUNCT
ejpam-1853	208	17	m	m	PROPN
ejpam-1853	208	18	,	,	PUNCT
ejpam-1853	208	19	ε	ε	PROPN
ejpam-1853	208	20	,	,	PUNCT
ejpam-1853	208	21	i	i	PROPN
ejpam-1853	208	22	,	,	PUNCT
ejpam-1853	208	23	v0	v0	PROPN
ejpam-1853	208	24	)	)	PUNCT
ejpam-1853	208	25	be	be	AUX
ejpam-1853	208	26	a	a	DET
ejpam-1853	208	27	groupoid	groupoid	NOUN
ejpam-1853	208	28	.	.	PUNCT
ejpam-1853	209	1	we	we	PRON
ejpam-1853	209	2	suppose	suppose	VERB
ejpam-1853	209	3	that	that	SCONJ
ejpam-1853	209	4	v	v	NOUN
ejpam-1853	209	5	(	(	PUNCT
ejpam-1853	209	6	resp	resp	NOUN
ejpam-1853	209	7	.	.	PROPN
ejpam-1853	209	8	,	,	PUNCT
ejpam-1853	209	9	v0	v0	PROPN
ejpam-1853	209	10	)	)	PUNCT
ejpam-1853	209	11	is	be	AUX
ejpam-1853	209	12	a	a	DET
ejpam-1853	209	13	vector	vector	NOUN
ejpam-1853	209	14	space	space	NOUN
ejpam-1853	209	15	over	over	ADP
ejpam-1853	209	16	a	a	DET
ejpam-1853	209	17	field	field	NOUN
ejpam-1853	209	18	k	k	X
ejpam-1853	209	19	.	.	PUNCT
ejpam-1853	210	1	for	for	ADP
ejpam-1853	210	2	the	the	DET
ejpam-1853	210	3	binary	binary	ADJ
ejpam-1853	210	4	operation	operation	NOUN
ejpam-1853	210	5	and	and	CCONJ
ejpam-1853	210	6	unary	unary	ADJ
ejpam-1853	210	7	operation	operation	NOUN
ejpam-1853	210	8	in	in	ADP
ejpam-1853	210	9	the	the	DET
ejpam-1853	210	10	group	group	NOUN
ejpam-1853	210	11	v	v	NOUN
ejpam-1853	210	12	(	(	PUNCT
ejpam-1853	210	13	resp	resp	NOUN
ejpam-1853	210	14	.	.	PROPN
ejpam-1853	210	15	,	,	PUNCT
ejpam-1853	210	16	v0	v0	PROPN
ejpam-1853	210	17	)	)	PUNCT
ejpam-1853	210	18	we	we	PRON
ejpam-1853	210	19	will	will	AUX
ejpam-1853	210	20	use	use	VERB
ejpam-1853	210	21	the	the	DET
ejpam-1853	210	22	notations	notation	NOUN
ejpam-1853	210	23	ω	ω	NOUN
ejpam-1853	210	24	:	:	PUNCT
ejpam-1853	210	25	=	=	SYM
ejpam-1853	210	26	+	+	CCONJ
ejpam-1853	210	27	(	(	PUNCT
ejpam-1853	210	28	resp	resp	NOUN
ejpam-1853	210	29	.	.	PUNCT
ejpam-1853	210	30	,	,	PUNCT
ejpam-1853	210	31	ω0	ω0	ADV
ejpam-1853	210	32	:	:	PUNCT
ejpam-1853	210	33	=	=	PUNCT
ejpam-1853	211	1	+	+	ADJ
ejpam-1853	211	2	)	)	PUNCT
ejpam-1853	211	3	and	and	CCONJ
ejpam-1853	211	4	σ(x	σ(x	NOUN
ejpam-1853	211	5	)	)	PUNCT
ejpam-1853	211	6	:	:	PUNCT
ejpam-1853	211	7	=	=	NOUN
ejpam-1853	211	8	−x	−x	NOUN
ejpam-1853	211	9	,	,	PUNCT
ejpam-1853	211	10	x	x	PUNCT
ejpam-1853	211	11	∈	∈	NOUN
ejpam-1853	211	12	v	v	NOUN
ejpam-1853	211	13	(	(	PUNCT
ejpam-1853	211	14	resp	resp	NOUN
ejpam-1853	211	15	.	.	PUNCT
ejpam-1853	211	16	,	,	PUNCT
ejpam-1853	211	17	σ0(u	σ0(u	X
ejpam-1853	211	18	)	)	PUNCT
ejpam-1853	211	19	:	:	PUNCT
ejpam-1853	211	20	=	=	SYM
ejpam-1853	211	21	−u	−u	PROPN
ejpam-1853	211	22	,	,	PUNCT
ejpam-1853	211	23	u	u	PROPN
ejpam-1853	211	24	∈	∈	PROPN
ejpam-1853	211	25	v0	v0	NOUN
ejpam-1853	211	26	)	)	PUNCT
ejpam-1853	211	27	.	.	PUNCT
ejpam-1853	212	1	the	the	DET
ejpam-1853	212	2	null	null	ADJ
ejpam-1853	212	3	vector	vector	NOUN
ejpam-1853	212	4	of	of	ADP
ejpam-1853	212	5	v	v	NOUN
ejpam-1853	212	6	(	(	PUNCT
ejpam-1853	212	7	resp	resp	NOUN
ejpam-1853	212	8	.	.	PROPN
ejpam-1853	212	9	,	,	PUNCT
ejpam-1853	212	10	v0	v0	PROPN
ejpam-1853	212	11	)	)	PUNCT
ejpam-1853	212	12	is	be	AUX
ejpam-1853	212	13	e	e	NOUN
ejpam-1853	212	14	(	(	PUNCT
ejpam-1853	212	15	resp	resp	NOUN
ejpam-1853	212	16	.	.	PUNCT
ejpam-1853	212	17	,	,	PUNCT
ejpam-1853	212	18	e0	e0	PROPN
ejpam-1853	212	19	)	)	PUNCT
ejpam-1853	212	20	.	.	PUNCT
ejpam-1853	213	1	the	the	DET
ejpam-1853	213	2	scalar	scalar	ADJ
ejpam-1853	213	3	multiplication	multiplication	NOUN
ejpam-1853	213	4	ϕ	ϕ	NOUN
ejpam-1853	213	5	:	:	PUNCT
ejpam-1853	213	6	k×v	k×v	PROPN
ejpam-1853	213	7	→	→	SYM
ejpam-1853	213	8	v	v	PROPN
ejpam-1853	213	9	(	(	PUNCT
ejpam-1853	213	10	resp	resp	NOUN
ejpam-1853	213	11	.	.	PUNCT
ejpam-1853	213	12	,	,	PUNCT
ejpam-1853	213	13	ϕ0	ϕ0	NOUN
ejpam-1853	213	14	:	:	PUNCT
ejpam-1853	213	15	k	k	PROPN
ejpam-1853	213	16	×	×	PROPN
ejpam-1853	213	17	v0→	v0→	PRON
ejpam-1853	213	18	v0	v0	NOUN
ejpam-1853	213	19	)	)	PUNCT
ejpam-1853	213	20	is	be	AUX
ejpam-1853	213	21	given	give	VERB
ejpam-1853	213	22	by	by	ADP
ejpam-1853	213	23	(	(	PUNCT
ejpam-1853	213	24	k	k	X
ejpam-1853	213	25	,	,	PUNCT
ejpam-1853	213	26	x	x	NOUN
ejpam-1853	213	27	)	)	PUNCT
ejpam-1853	213	28	7→	7→	NUM
ejpam-1853	213	29	ϕ(k	ϕ(k	NOUN
ejpam-1853	213	30	,	,	PUNCT
ejpam-1853	213	31	x	x	NOUN
ejpam-1853	213	32	)	)	PUNCT
ejpam-1853	213	33	:	:	PUNCT
ejpam-1853	213	34	=	=	NUM
ejpam-1853	213	35	kx	kx	PROPN
ejpam-1853	213	36	(	(	PUNCT
ejpam-1853	213	37	resp	resp	PROPN
ejpam-1853	213	38	.	.	PUNCT
ejpam-1853	213	39	,	,	PUNCT
ejpam-1853	213	40	(	(	PUNCT
ejpam-1853	213	41	k	k	X
ejpam-1853	213	42	,	,	PUNCT
ejpam-1853	213	43	u	u	NOUN
ejpam-1853	213	44	)	)	PUNCT
ejpam-1853	213	45	7→	7→	NUM
ejpam-1853	213	46	ϕ0(k	ϕ0(k	NUM
ejpam-1853	213	47	,	,	PUNCT
ejpam-1853	213	48	u	u	NOUN
ejpam-1853	213	49	)	)	PUNCT
ejpam-1853	213	50	:	:	PUNCT
ejpam-1853	213	51	=	=	SYM
ejpam-1853	213	52	ku	ku	PROPN
ejpam-1853	213	53	)	)	PUNCT
ejpam-1853	213	54	.	.	PUNCT
ejpam-1853	214	1	consider	consider	VERB
ejpam-1853	214	2	the	the	DET
ejpam-1853	214	3	direct	direct	ADJ
ejpam-1853	214	4	product	product	NOUN
ejpam-1853	214	5	(	(	PUNCT
ejpam-1853	214	6	k×v	k×v	PROPN
ejpam-1853	214	7	,	,	PUNCT
ejpam-1853	214	8	id×α	id×α	NOUN
ejpam-1853	214	9	,	,	PUNCT
ejpam-1853	214	10	id×β	id×β	ADJ
ejpam-1853	214	11	,	,	PUNCT
ejpam-1853	214	12	id×m	id×m	NOUN
ejpam-1853	214	13	,	,	PUNCT
ejpam-1853	214	14	id×ε	id×ε	PROPN
ejpam-1853	214	15	,	,	PUNCT
ejpam-1853	214	16	id×	id×	ADJ
ejpam-1853	214	17	i	i	PROPN
ejpam-1853	214	18	,	,	PUNCT
ejpam-1853	214	19	k×v0	k×v0	PROPN
ejpam-1853	214	20	)	)	PUNCT
ejpam-1853	214	21	of	of	ADP
ejpam-1853	214	22	the	the	DET
ejpam-1853	214	23	null	null	ADJ
ejpam-1853	214	24	groupoid	groupoid	PROPN
ejpam-1853	214	25	associated	associate	VERB
ejpam-1853	214	26	to	to	ADP
ejpam-1853	214	27	k	k	PROPN
ejpam-1853	214	28	and	and	CCONJ
ejpam-1853	214	29	groupoid	groupoid	PROPN
ejpam-1853	214	30	(	(	PUNCT
ejpam-1853	214	31	v	v	NOUN
ejpam-1853	214	32	,	,	PUNCT
ejpam-1853	214	33	v0	v0	NOUN
ejpam-1853	214	34	)	)	PUNCT
ejpam-1853	214	35	.	.	PUNCT
ejpam-1853	215	1	its	its	PRON
ejpam-1853	215	2	set	set	NOUN
ejpam-1853	215	3	of	of	ADP
ejpam-1853	215	4	composable	composable	ADJ
ejpam-1853	215	5	elements	element	NOUN
ejpam-1853	215	6	is	be	AUX
ejpam-1853	215	7	(	(	PUNCT
ejpam-1853	215	8	k	k	PROPN
ejpam-1853	215	9	×	×	PROPN
ejpam-1853	215	10	v	v	NOUN
ejpam-1853	215	11	)	)	PUNCT
ejpam-1853	215	12	(	(	PUNCT
ejpam-1853	215	13	2	2	X
ejpam-1853	215	14	)	)	PUNCT
ejpam-1853	215	15	=	=	PRON
ejpam-1853	215	16	{	{	PUNCT
ejpam-1853	215	17	(	(	PUNCT
ejpam-1853	215	18	(	(	PUNCT
ejpam-1853	215	19	k1	k1	NOUN
ejpam-1853	215	20	,	,	PUNCT
ejpam-1853	215	21	x	x	NOUN
ejpam-1853	215	22	)	)	PUNCT
ejpam-1853	215	23	,	,	PUNCT
ejpam-1853	215	24	(	(	PUNCT
ejpam-1853	215	25	k2	k2	X
ejpam-1853	215	26	,	,	PUNCT
ejpam-1853	215	27	y	y	NOUN
ejpam-1853	215	28	)	)	PUNCT
ejpam-1853	215	29	)	)	PUNCT
ejpam-1853	216	1	∈	∈	PROPN
ejpam-1853	216	2	(	(	PUNCT
ejpam-1853	216	3	k	k	NOUN
ejpam-1853	216	4	×	×	PROPN
ejpam-1853	216	5	v	v	NOUN
ejpam-1853	216	6	)	)	PUNCT
ejpam-1853	216	7	2	2	NUM
ejpam-1853	216	8	|	|	NOUN
ejpam-1853	216	9	k1	k1	NOUN
ejpam-1853	216	10	=	=	SYM
ejpam-1853	216	11	k2	k2	NOUN
ejpam-1853	216	12	,	,	PUNCT
ejpam-1853	216	13	β(x	β(x	PROPN
ejpam-1853	216	14	)	)	PUNCT
ejpam-1853	216	15	=	=	SYM
ejpam-1853	216	16	α(y	α(y	NOUN
ejpam-1853	216	17	)	)	PUNCT
ejpam-1853	216	18	}	}	PUNCT
ejpam-1853	216	19	.	.	PUNCT
ejpam-1853	217	1	the	the	DET
ejpam-1853	217	2	multiplication	multiplication	NOUN
ejpam-1853	217	3	in	in	ADP
ejpam-1853	217	4	k	k	PROPN
ejpam-1853	217	5	×	×	PROPN
ejpam-1853	217	6	v	v	NOUN
ejpam-1853	217	7	is	be	AUX
ejpam-1853	217	8	given	give	VERB
ejpam-1853	217	9	by	by	ADP
ejpam-1853	217	10	(	(	PUNCT
ejpam-1853	217	11	k	k	X
ejpam-1853	217	12	,	,	PUNCT
ejpam-1853	217	13	x	x	NOUN
ejpam-1853	217	14	)	)	PUNCT
ejpam-1853	217	15	·	·	PUNCT
ejpam-1853	218	1	(	(	PUNCT
ejpam-1853	218	2	k	k	X
ejpam-1853	218	3	,	,	PUNCT
ejpam-1853	218	4	y	y	PROPN
ejpam-1853	218	5	)	)	PUNCT
ejpam-1853	218	6	:	:	PUNCT
ejpam-1853	219	1	=	=	SYM
ejpam-1853	219	2	(	(	PUNCT
ejpam-1853	219	3	k	k	X
ejpam-1853	219	4	,	,	PUNCT
ejpam-1853	219	5	x	x	X
ejpam-1853	219	6	·	·	PUNCT
ejpam-1853	219	7	y	y	X
ejpam-1853	219	8	)	)	PUNCT
ejpam-1853	219	9	,	,	PUNCT
ejpam-1853	219	10	(	(	PUNCT
ejpam-1853	219	11	∀)(x	∀)(x	PROPN
ejpam-1853	219	12	,	,	PUNCT
ejpam-1853	219	13	y	y	PROPN
ejpam-1853	219	14	)	)	PUNCT
ejpam-1853	219	15	∈	∈	PROPN
ejpam-1853	219	16	v(2	v(2	PROPN
ejpam-1853	219	17	)	)	PUNCT
ejpam-1853	219	18	,	,	PUNCT
ejpam-1853	219	19	k	k	PROPN
ejpam-1853	219	20	∈	∈	PROPN
ejpam-1853	219	21	k	k	X
ejpam-1853	219	22	.	.	PUNCT
ejpam-1853	220	1	definition	definition	NOUN
ejpam-1853	220	2	5	5	NUM
ejpam-1853	220	3	.	.	PUNCT
ejpam-1853	221	1	a	a	DET
ejpam-1853	221	2	vector	vector	NOUN
ejpam-1853	221	3	space	space	NOUN
ejpam-1853	221	4	-	-	PUNCT
ejpam-1853	221	5	groupoid	groupoid	PROPN
ejpam-1853	221	6	or	or	CCONJ
ejpam-1853	221	7	vs−groupoid	vs−groupoid	PROPN
ejpam-1853	221	8	,	,	PUNCT
ejpam-1853	221	9	is	be	AUX
ejpam-1853	221	10	a	a	DET
ejpam-1853	221	11	groupoid	groupoid	NOUN
ejpam-1853	221	12	(	(	PUNCT
ejpam-1853	221	13	v	v	NOUN
ejpam-1853	221	14	,	,	PUNCT
ejpam-1853	221	15	v0	v0	NOUN
ejpam-1853	221	16	)	)	PUNCT
ejpam-1853	221	17	such	such	ADJ
ejpam-1853	221	18	that	that	SCONJ
ejpam-1853	221	19	the	the	DET
ejpam-1853	221	20	following	follow	VERB
ejpam-1853	221	21	conditions	condition	NOUN
ejpam-1853	221	22	hold	hold	VERB
ejpam-1853	221	23	:	:	PUNCT
ejpam-1853	221	24	(	(	PUNCT
ejpam-1853	221	25	5.1	5.1	NUM
ejpam-1853	221	26	)	)	PUNCT
ejpam-1853	221	27	(	(	PUNCT
ejpam-1853	221	28	v,+,ϕ	v,+,ϕ	PROPN
ejpam-1853	221	29	)	)	PUNCT
ejpam-1853	221	30	and	and	CCONJ
ejpam-1853	221	31	(	(	PUNCT
ejpam-1853	221	32	v0,+,ϕ0	v0,+,ϕ0	NOUN
ejpam-1853	221	33	)	)	PUNCT
ejpam-1853	221	34	are	be	AUX
ejpam-1853	221	35	vector	vector	NOUN
ejpam-1853	221	36	spaces	space	NOUN
ejpam-1853	221	37	;	;	PUNCT
ejpam-1853	221	38	(	(	PUNCT
ejpam-1853	221	39	5.2	5.2	NUM
ejpam-1853	221	40	)	)	PUNCT
ejpam-1853	221	41	(	(	PUNCT
ejpam-1853	221	42	v	v	NOUN
ejpam-1853	221	43	,	,	PUNCT
ejpam-1853	221	44	α	α	NOUN
ejpam-1853	221	45	,	,	PUNCT
ejpam-1853	221	46	β	β	X
ejpam-1853	221	47	,	,	PUNCT
ejpam-1853	221	48	m	m	PROPN
ejpam-1853	221	49	,	,	PUNCT
ejpam-1853	221	50	ε	ε	PROPN
ejpam-1853	221	51	,	,	PUNCT
ejpam-1853	221	52	i,+	i,+	PRON
ejpam-1853	221	53	,	,	PUNCT
ejpam-1853	221	54	v0	v0	NOUN
ejpam-1853	221	55	)	)	PUNCT
ejpam-1853	221	56	is	be	AUX
ejpam-1853	221	57	a	a	DET
ejpam-1853	221	58	commutative	commutative	ADJ
ejpam-1853	221	59	group	group	NOUN
ejpam-1853	221	60	-	-	PUNCT
ejpam-1853	221	61	groupoid	groupoid	PROPN
ejpam-1853	221	62	;	;	PUNCT
ejpam-1853	221	63	(	(	PUNCT
ejpam-1853	221	64	5.3	5.3	NUM
ejpam-1853	221	65	)	)	PUNCT
ejpam-1853	221	66	the	the	DET
ejpam-1853	221	67	pair	pair	NOUN
ejpam-1853	221	68	(	(	PUNCT
ejpam-1853	221	69	ϕ,ϕ0	ϕ,ϕ0	PROPN
ejpam-1853	221	70	)	)	PUNCT
ejpam-1853	221	71	:	:	PUNCT
ejpam-1853	221	72	(	(	PUNCT
ejpam-1853	221	73	k	k	X
ejpam-1853	221	74	×	×	PROPN
ejpam-1853	221	75	v	v	NOUN
ejpam-1853	221	76	,	,	PUNCT
ejpam-1853	221	77	k	k	PROPN
ejpam-1853	221	78	×	×	PROPN
ejpam-1853	221	79	v0)→	v0)→	INTJ
ejpam-1853	221	80	(	(	PUNCT
ejpam-1853	221	81	v	v	NOUN
ejpam-1853	221	82	,	,	PUNCT
ejpam-1853	221	83	v0	v0	NOUN
ejpam-1853	221	84	)	)	PUNCT
ejpam-1853	221	85	is	be	AUX
ejpam-1853	221	86	a	a	DET
ejpam-1853	221	87	groupoid	groupoid	PROPN
ejpam-1853	221	88	morphism	morphism	NOUN
ejpam-1853	221	89	.	.	PUNCT
ejpam-1853	222	1	we	we	PRON
ejpam-1853	222	2	shall	shall	AUX
ejpam-1853	222	3	denote	denote	VERB
ejpam-1853	222	4	a	a	DET
ejpam-1853	222	5	vector	vector	NOUN
ejpam-1853	222	6	space	space	NOUN
ejpam-1853	222	7	-	-	PUNCT
ejpam-1853	222	8	groupoid	groupoid	NOUN
ejpam-1853	222	9	by	by	ADP
ejpam-1853	222	10	(	(	PUNCT
ejpam-1853	222	11	v	v	NOUN
ejpam-1853	222	12	,	,	PUNCT
ejpam-1853	222	13	α	α	NOUN
ejpam-1853	222	14	,	,	PUNCT
ejpam-1853	222	15	β	β	X
ejpam-1853	222	16	,	,	PUNCT
ejpam-1853	222	17	m	m	PROPN
ejpam-1853	222	18	,	,	PUNCT
ejpam-1853	222	19	i	i	PRON
ejpam-1853	222	20	,	,	PUNCT
ejpam-1853	222	21	ε,+,ϕ	ε,+,ϕ	PROPN
ejpam-1853	222	22	,	,	PUNCT
ejpam-1853	222	23	v0	v0	PROPN
ejpam-1853	222	24	)	)	PUNCT
ejpam-1853	222	25	or	or	CCONJ
ejpam-1853	222	26	(	(	PUNCT
ejpam-1853	222	27	v	v	NOUN
ejpam-1853	222	28	,	,	PUNCT
ejpam-1853	222	29	v0	v0	NOUN
ejpam-1853	222	30	)	)	PUNCT
ejpam-1853	222	31	.	.	PUNCT
ejpam-1853	223	1	theorem	theorem	NOUN
ejpam-1853	223	2	5	5	NUM
ejpam-1853	223	3	.	.	PUNCT
ejpam-1853	224	1	if	if	SCONJ
ejpam-1853	224	2	(	(	PUNCT
ejpam-1853	224	3	v	v	NOUN
ejpam-1853	224	4	,	,	PUNCT
ejpam-1853	224	5	α	α	NOUN
ejpam-1853	224	6	,	,	PUNCT
ejpam-1853	224	7	β	β	X
ejpam-1853	224	8	,	,	PUNCT
ejpam-1853	224	9	m	m	PROPN
ejpam-1853	224	10	,	,	PUNCT
ejpam-1853	224	11	i	i	PRON
ejpam-1853	224	12	,	,	PUNCT
ejpam-1853	224	13	ε,+,ϕ	ε,+,ϕ	PROPN
ejpam-1853	224	14	,	,	PUNCT
ejpam-1853	224	15	v0	v0	PROPN
ejpam-1853	224	16	)	)	PUNCT
ejpam-1853	224	17	is	be	AUX
ejpam-1853	224	18	a	a	DET
ejpam-1853	224	19	vector	vector	NOUN
ejpam-1853	224	20	space	space	NOUN
ejpam-1853	224	21	-	-	PUNCT
ejpam-1853	224	22	groupoid	groupoid	NOUN
ejpam-1853	224	23	,	,	PUNCT
ejpam-1853	224	24	then	then	ADV
ejpam-1853	224	25	:	:	PUNCT
ejpam-1853	224	26	(	(	PUNCT
ejpam-1853	224	27	i	i	NOUN
ejpam-1853	224	28	)	)	PUNCT
ejpam-1853	224	29	the	the	DET
ejpam-1853	224	30	multiplication	multiplication	NOUN
ejpam-1853	224	31	m	m	PROPN
ejpam-1853	224	32	and	and	CCONJ
ejpam-1853	224	33	the	the	DET
ejpam-1853	224	34	additive	additive	ADJ
ejpam-1853	224	35	operation	operation	NOUN
ejpam-1853	224	36	ω	ω	NOUN
ejpam-1853	224	37	are	be	AUX
ejpam-1853	224	38	compatible	compatible	ADJ
ejpam-1853	224	39	,	,	PUNCT
ejpam-1853	224	40	that	that	PRON
ejpam-1853	224	41	is	be	AUX
ejpam-1853	224	42	:	:	PUNCT
ejpam-1853	224	43	(	(	PUNCT
ejpam-1853	224	44	x	x	X
ejpam-1853	224	45	·	·	PUNCT
ejpam-1853	224	46	y	y	X
ejpam-1853	224	47	)	)	PUNCT
ejpam-1853	225	1	+	+	CCONJ
ejpam-1853	225	2	(	(	PUNCT
ejpam-1853	225	3	z	z	NOUN
ejpam-1853	225	4	·	·	PUNCT
ejpam-1853	225	5	t	t	X
ejpam-1853	225	6	)	)	PUNCT
ejpam-1853	225	7	=	=	PUNCT
ejpam-1853	225	8	(	(	PUNCT
ejpam-1853	225	9	x	x	X
ejpam-1853	225	10	+	+	NUM
ejpam-1853	225	11	z	z	NOUN
ejpam-1853	225	12	)	)	PUNCT
ejpam-1853	225	13	·	·	PUNCT
ejpam-1853	226	1	(	(	PUNCT
ejpam-1853	226	2	y	y	PROPN
ejpam-1853	226	3	+	+	PROPN
ejpam-1853	226	4	t	t	PROPN
ejpam-1853	226	5	)	)	PUNCT
ejpam-1853	226	6	,	,	PUNCT
ejpam-1853	226	7	(	(	PUNCT
ejpam-1853	226	8	∀)(x	∀)(x	PROPN
ejpam-1853	226	9	,	,	PUNCT
ejpam-1853	226	10	y	y	PROPN
ejpam-1853	226	11	)	)	PUNCT
ejpam-1853	226	12	,	,	PUNCT
ejpam-1853	226	13	(	(	PUNCT
ejpam-1853	226	14	z	z	X
ejpam-1853	226	15	,	,	PUNCT
ejpam-1853	226	16	t	t	PROPN
ejpam-1853	226	17	)	)	PUNCT
ejpam-1853	226	18	∈	∈	PROPN
ejpam-1853	226	19	v(2	v(2	PROPN
ejpam-1853	226	20	)	)	PUNCT
ejpam-1853	226	21	;	;	PUNCT
ejpam-1853	226	22	(	(	PUNCT
ejpam-1853	226	23	10	10	NUM
ejpam-1853	226	24	)	)	PUNCT
ejpam-1853	226	25	(	(	PUNCT
ejpam-1853	226	26	ii	ii	NOUN
ejpam-1853	226	27	)	)	PUNCT
ejpam-1853	226	28	the	the	DET
ejpam-1853	226	29	structure	structure	NOUN
ejpam-1853	226	30	functions	function	NOUN
ejpam-1853	226	31	α	α	NOUN
ejpam-1853	226	32	,	,	PUNCT
ejpam-1853	226	33	β	β	X
ejpam-1853	226	34	:	:	PUNCT
ejpam-1853	226	35	(	(	PUNCT
ejpam-1853	226	36	v,+)→	v,+)→	PROPN
ejpam-1853	226	37	(	(	PUNCT
ejpam-1853	226	38	v0,+	v0,+	PROPN
ejpam-1853	226	39	)	)	PUNCT
ejpam-1853	226	40	,	,	PUNCT
ejpam-1853	226	41	ε	ε	PROPN
ejpam-1853	226	42	:	:	PUNCT
ejpam-1853	226	43	(	(	PUNCT
ejpam-1853	226	44	v0,+)→	v0,+)→	PROPN
ejpam-1853	226	45	(	(	PUNCT
ejpam-1853	226	46	v,+	v,+	NUM
ejpam-1853	226	47	)	)	PUNCT
ejpam-1853	226	48	and	and	CCONJ
ejpam-1853	226	49	i	i	PRON
ejpam-1853	226	50	:	:	PUNCT
ejpam-1853	226	51	(	(	PUNCT
ejpam-1853	226	52	v,+)→	v,+)→	PROPN
ejpam-1853	226	53	(	(	PUNCT
ejpam-1853	226	54	v,+	v,+	NUM
ejpam-1853	226	55	)	)	PUNCT
ejpam-1853	226	56	are	be	AUX
ejpam-1853	226	57	linear	linear	ADJ
ejpam-1853	226	58	maps	map	NOUN
ejpam-1853	226	59	;	;	PUNCT
ejpam-1853	226	60	m.	m.	NOUN
ejpam-1853	226	61	ivan	ivan	PROPN
ejpam-1853	226	62	/	/	PUNCT
ejpam-1853	226	63	eur	eur	PROPN
ejpam-1853	226	64	.	.	PUNCT
ejpam-1853	227	1	j.	j.	PROPN
ejpam-1853	227	2	pure	pure	PROPN
ejpam-1853	227	3	appl	appl	PROPN
ejpam-1853	227	4	.	.	PROPN
ejpam-1853	227	5	math	math	PROPN
ejpam-1853	227	6	,	,	PUNCT
ejpam-1853	227	7	6	6	NUM
ejpam-1853	227	8	(	(	PUNCT
ejpam-1853	227	9	2013	2013	NUM
ejpam-1853	227	10	)	)	PUNCT
ejpam-1853	227	11	,	,	PUNCT
ejpam-1853	227	12	469	469	NUM
ejpam-1853	227	13	-	-	SYM
ejpam-1853	227	14	484	484	NUM
ejpam-1853	227	15	476	476	NUM
ejpam-1853	227	16	(	(	PUNCT
ejpam-1853	227	17	iii	iii	NOUN
ejpam-1853	227	18	)	)	PUNCT
ejpam-1853	227	19	the	the	DET
ejpam-1853	227	20	multiplication	multiplication	NOUN
ejpam-1853	227	21	m	m	PROPN
ejpam-1853	227	22	and	and	CCONJ
ejpam-1853	227	23	the	the	DET
ejpam-1853	227	24	scalar	scalar	ADJ
ejpam-1853	227	25	multiplication	multiplication	NOUN
ejpam-1853	227	26	ϕ	ϕ	NOUN
ejpam-1853	227	27	are	be	AUX
ejpam-1853	227	28	compatible	compatible	ADJ
ejpam-1853	227	29	,	,	PUNCT
ejpam-1853	227	30	that	that	PRON
ejpam-1853	227	31	is	be	AUX
ejpam-1853	227	32	:	:	PUNCT
ejpam-1853	227	33	k(x	k(x	X
ejpam-1853	227	34	·	·	PUNCT
ejpam-1853	227	35	y	y	X
ejpam-1853	227	36	)	)	PUNCT
ejpam-1853	227	37	=	=	SYM
ejpam-1853	227	38	(	(	PUNCT
ejpam-1853	227	39	kx	kx	PROPN
ejpam-1853	227	40	)	)	PUNCT
ejpam-1853	227	41	·	·	PUNCT
ejpam-1853	228	1	(	(	PUNCT
ejpam-1853	228	2	k	k	NOUN
ejpam-1853	228	3	y	y	PROPN
ejpam-1853	228	4	)	)	PUNCT
ejpam-1853	228	5	,	,	PUNCT
ejpam-1853	228	6	(	(	PUNCT
ejpam-1853	228	7	∀)(x	∀)(x	PROPN
ejpam-1853	228	8	,	,	PUNCT
ejpam-1853	228	9	y	y	PROPN
ejpam-1853	228	10	)	)	PUNCT
ejpam-1853	228	11	∈	∈	PROPN
ejpam-1853	228	12	v(2	v(2	PROPN
ejpam-1853	228	13	)	)	PUNCT
ejpam-1853	228	14	and	and	CCONJ
ejpam-1853	228	15	k	k	PROPN
ejpam-1853	228	16	∈	∈	PROPN
ejpam-1853	229	1	k	k	NOUN
ejpam-1853	229	2	;	;	PUNCT
ejpam-1853	229	3	(	(	PUNCT
ejpam-1853	229	4	11	11	NUM
ejpam-1853	229	5	)	)	PUNCT
ejpam-1853	229	6	(	(	PUNCT
ejpam-1853	229	7	iv	iv	X
ejpam-1853	229	8	)	)	PUNCT
ejpam-1853	229	9	the	the	DET
ejpam-1853	229	10	multiplication	multiplication	NOUN
ejpam-1853	229	11	m	m	PROPN
ejpam-1853	229	12	and	and	CCONJ
ejpam-1853	229	13	the	the	DET
ejpam-1853	229	14	unary	unary	ADJ
ejpam-1853	229	15	operation	operation	NOUN
ejpam-1853	229	16	σ	σ	NOUN
ejpam-1853	229	17	are	be	AUX
ejpam-1853	229	18	compatible	compatible	ADJ
ejpam-1853	229	19	,	,	PUNCT
ejpam-1853	229	20	that	that	PRON
ejpam-1853	229	21	is	be	AUX
ejpam-1853	229	22	:	:	PUNCT
ejpam-1853	229	23	−(x	−(x	NOUN
ejpam-1853	229	24	·	·	PUNCT
ejpam-1853	229	25	y	y	X
ejpam-1853	229	26	)	)	PUNCT
ejpam-1853	230	1	=	=	SYM
ejpam-1853	230	2	(	(	PUNCT
ejpam-1853	230	3	−x	−x	NOUN
ejpam-1853	230	4	)	)	PUNCT
ejpam-1853	230	5	·	·	PUNCT
ejpam-1853	230	6	(	(	PUNCT
ejpam-1853	230	7	−y	−y	NOUN
ejpam-1853	230	8	)	)	PUNCT
ejpam-1853	230	9	,	,	PUNCT
ejpam-1853	230	10	(	(	PUNCT
ejpam-1853	230	11	∀)(x	∀)(x	PROPN
ejpam-1853	230	12	,	,	PUNCT
ejpam-1853	230	13	y	y	PROPN
ejpam-1853	230	14	)	)	PUNCT
ejpam-1853	230	15	∈	∈	PROPN
ejpam-1853	230	16	v(2	v(2	PROPN
ejpam-1853	230	17	)	)	PUNCT
ejpam-1853	230	18	.	.	PUNCT
ejpam-1853	231	1	(	(	PUNCT
ejpam-1853	231	2	12	12	NUM
ejpam-1853	231	3	)	)	PUNCT
ejpam-1853	231	4	proof	proof	NOUN
ejpam-1853	231	5	.	.	PUNCT
ejpam-1853	232	1	(	(	PUNCT
ejpam-1853	232	2	i	i	NOUN
ejpam-1853	232	3	)	)	PUNCT
ejpam-1853	232	4	and	and	CCONJ
ejpam-1853	232	5	(	(	PUNCT
ejpam-1853	232	6	iv	iv	X
ejpam-1853	232	7	)	)	PUNCT
ejpam-1853	232	8	.	.	PUNCT
ejpam-1853	233	1	since	since	SCONJ
ejpam-1853	233	2	(	(	PUNCT
ejpam-1853	233	3	v	v	NOUN
ejpam-1853	233	4	,	,	PUNCT
ejpam-1853	233	5	α	α	NOUN
ejpam-1853	233	6	,	,	PUNCT
ejpam-1853	233	7	β	β	X
ejpam-1853	233	8	,	,	PUNCT
ejpam-1853	233	9	m	m	PROPN
ejpam-1853	233	10	,	,	PUNCT
ejpam-1853	233	11	ε	ε	PROPN
ejpam-1853	233	12	,	,	PUNCT
ejpam-1853	233	13	i,+	i,+	PRON
ejpam-1853	233	14	,	,	PUNCT
ejpam-1853	233	15	v0	v0	NOUN
ejpam-1853	233	16	)	)	PUNCT
ejpam-1853	233	17	is	be	AUX
ejpam-1853	233	18	a	a	DET
ejpam-1853	233	19	group	group	NOUN
ejpam-1853	233	20	-	-	PUNCT
ejpam-1853	233	21	groupoid	groupoid	PROPN
ejpam-1853	233	22	,	,	PUNCT
ejpam-1853	233	23	it	it	PRON
ejpam-1853	233	24	follows	follow	VERB
ejpam-1853	233	25	that	that	SCONJ
ejpam-1853	233	26	the	the	DET
ejpam-1853	233	27	relation	relation	NOUN
ejpam-1853	233	28	(	(	PUNCT
ejpam-1853	233	29	10	10	NUM
ejpam-1853	233	30	)	)	PUNCT
ejpam-1853	233	31	holds	hold	NOUN
ejpam-1853	233	32	and	and	CCONJ
ejpam-1853	233	33	the	the	DET
ejpam-1853	233	34	structure	structure	NOUN
ejpam-1853	233	35	functions	function	NOUN
ejpam-1853	233	36	α	α	NOUN
ejpam-1853	233	37	,	,	PUNCT
ejpam-1853	233	38	β	β	PROPN
ejpam-1853	233	39	,	,	PUNCT
ejpam-1853	233	40	ε	ε	PROPN
ejpam-1853	233	41	,	,	PUNCT
ejpam-1853	233	42	i	i	PRON
ejpam-1853	233	43	are	be	AUX
ejpam-1853	233	44	morphisms	morphism	NOUN
ejpam-1853	233	45	from	from	ADP
ejpam-1853	233	46	the	the	DET
ejpam-1853	233	47	corresponding	corresponding	ADJ
ejpam-1853	233	48	additive	additive	ADJ
ejpam-1853	233	49	groups	group	NOUN
ejpam-1853	233	50	.	.	PUNCT
ejpam-1853	234	1	also	also	ADV
ejpam-1853	234	2	,	,	PUNCT
ejpam-1853	234	3	theorem	theorem	VERB
ejpam-1853	234	4	2(iii	2(iii	NOUN
ejpam-1853	234	5	)	)	PUNCT
ejpam-1853	234	6	it	it	PRON
ejpam-1853	234	7	implies	imply	VERB
ejpam-1853	234	8	that	that	SCONJ
ejpam-1853	234	9	the	the	DET
ejpam-1853	234	10	equality	equality	NOUN
ejpam-1853	234	11	(	(	PUNCT
ejpam-1853	234	12	12	12	NUM
ejpam-1853	234	13	)	)	PUNCT
ejpam-1853	234	14	is	be	AUX
ejpam-1853	234	15	verified	verify	VERB
ejpam-1853	234	16	.	.	PUNCT
ejpam-1853	235	1	from	from	ADP
ejpam-1853	235	2	the	the	DET
ejpam-1853	235	3	fact	fact	NOUN
ejpam-1853	235	4	that	that	SCONJ
ejpam-1853	235	5	(	(	PUNCT
ejpam-1853	235	6	ϕ,ϕ0	ϕ,ϕ0	NOUN
ejpam-1853	235	7	)	)	PUNCT
ejpam-1853	235	8	is	be	AUX
ejpam-1853	235	9	a	a	DET
ejpam-1853	235	10	groupoid	groupoid	PROPN
ejpam-1853	235	11	morphism	morphism	NOUN
ejpam-1853	235	12	,	,	PUNCT
ejpam-1853	235	13	we	we	PRON
ejpam-1853	235	14	have	have	VERB
ejpam-1853	235	15	:	:	PUNCT
ejpam-1853	235	16	(	(	PUNCT
ejpam-1853	235	17	a	a	X
ejpam-1853	235	18	)	)	PUNCT
ejpam-1853	235	19	α	α	PRON
ejpam-1853	235	20	◦	◦	NOUN
ejpam-1853	235	21	ϕ	ϕ	NOUN
ejpam-1853	235	22	=	=	SYM
ejpam-1853	235	23	ϕ0	ϕ0	NOUN
ejpam-1853	235	24	◦	◦	NOUN
ejpam-1853	235	25	(	(	PUNCT
ejpam-1853	235	26	i	i	NOUN
ejpam-1853	235	27	d	d	PROPN
ejpam-1853	235	28	×α	×α	PROPN
ejpam-1853	235	29	)	)	PUNCT
ejpam-1853	235	30	and	and	CCONJ
ejpam-1853	235	31	β	β	PROPN
ejpam-1853	235	32	◦	◦	NOUN
ejpam-1853	235	33	ϕ	ϕ	NOUN
ejpam-1853	235	34	=	=	SYM
ejpam-1853	235	35	ϕ0	ϕ0	NOUN
ejpam-1853	235	36	◦	◦	NOUN
ejpam-1853	235	37	(	(	PUNCT
ejpam-1853	235	38	i	i	NOUN
ejpam-1853	235	39	d	d	PROPN
ejpam-1853	235	40	×	×	PROPN
ejpam-1853	235	41	β	β	NOUN
ejpam-1853	235	42	)	)	PUNCT
ejpam-1853	235	43	;	;	PUNCT
ejpam-1853	235	44	(	(	PUNCT
ejpam-1853	235	45	b	b	X
ejpam-1853	235	46	)	)	PUNCT
ejpam-1853	235	47	ϕ((id	ϕ((id	PROPN
ejpam-1853	235	48	×m)((k	×m)((k	NOUN
ejpam-1853	235	49	,	,	PUNCT
ejpam-1853	235	50	x	x	NOUN
ejpam-1853	235	51	)	)	PUNCT
ejpam-1853	235	52	,	,	PUNCT
ejpam-1853	235	53	(	(	PUNCT
ejpam-1853	235	54	k	k	X
ejpam-1853	235	55	,	,	PUNCT
ejpam-1853	235	56	y	y	NOUN
ejpam-1853	235	57	)	)	PUNCT
ejpam-1853	235	58	)	)	PUNCT
ejpam-1853	235	59	)	)	PUNCT
ejpam-1853	236	1	=	=	PUNCT
ejpam-1853	236	2	m(ϕ(k	m(ϕ(k	PROPN
ejpam-1853	236	3	,	,	PUNCT
ejpam-1853	236	4	x),ϕ(k	x),ϕ(k	PROPN
ejpam-1853	236	5	,	,	PUNCT
ejpam-1853	236	6	y	y	NOUN
ejpam-1853	236	7	)	)	PUNCT
ejpam-1853	236	8	)	)	PUNCT
ejpam-1853	236	9	,	,	PUNCT
ejpam-1853	236	10	(	(	PUNCT
ejpam-1853	236	11	∀)(x	∀)(x	PROPN
ejpam-1853	236	12	,	,	PUNCT
ejpam-1853	236	13	y	y	PROPN
ejpam-1853	236	14	)	)	PUNCT
ejpam-1853	236	15	∈	∈	PROPN
ejpam-1853	236	16	v(2	v(2	PROPN
ejpam-1853	236	17	)	)	PUNCT
ejpam-1853	236	18	,	,	PUNCT
ejpam-1853	236	19	k	k	PROPN
ejpam-1853	236	20	∈	∈	PROPN
ejpam-1853	236	21	k	k	X
ejpam-1853	236	22	.	.	PUNCT
ejpam-1853	237	1	(	(	PUNCT
ejpam-1853	237	2	ii	ii	NOUN
ejpam-1853	237	3	)	)	PUNCT
ejpam-1853	237	4	and	and	CCONJ
ejpam-1853	237	5	(	(	PUNCT
ejpam-1853	237	6	iii	iii	NOUN
ejpam-1853	237	7	)	)	PUNCT
ejpam-1853	237	8	.	.	PUNCT
ejpam-1853	238	1	for	for	ADP
ejpam-1853	238	2	each	each	PRON
ejpam-1853	238	3	(	(	PUNCT
ejpam-1853	238	4	k	k	X
ejpam-1853	238	5	,	,	PUNCT
ejpam-1853	238	6	x	x	X
ejpam-1853	238	7	)	)	PUNCT
ejpam-1853	238	8	∈	∈	PROPN
ejpam-1853	239	1	k	k	X
ejpam-1853	239	2	×	×	PROPN
ejpam-1853	239	3	v	v	INTJ
ejpam-1853	239	4	,	,	PUNCT
ejpam-1853	239	5	we	we	PRON
ejpam-1853	239	6	have	have	VERB
ejpam-1853	239	7	α(ϕ(k	α(ϕ(k	PROPN
ejpam-1853	239	8	,	,	PUNCT
ejpam-1853	239	9	x	x	NOUN
ejpam-1853	239	10	)	)	PUNCT
ejpam-1853	239	11	)	)	PUNCT
ejpam-1853	240	1	=	=	SYM
ejpam-1853	240	2	α(kx	α(kx	PROPN
ejpam-1853	240	3	)	)	PUNCT
ejpam-1853	240	4	and	and	CCONJ
ejpam-1853	240	5	ϕ0((id	ϕ0((id	NUM
ejpam-1853	240	6	×α)(k	×α)(k	NOUN
ejpam-1853	240	7	,	,	PUNCT
ejpam-1853	240	8	x	x	NOUN
ejpam-1853	240	9	)	)	PUNCT
ejpam-1853	240	10	)	)	PUNCT
ejpam-1853	241	1	=	=	SYM
ejpam-1853	241	2	ϕ0(k	ϕ0(k	PROPN
ejpam-1853	241	3	,	,	PUNCT
ejpam-1853	241	4	α(x	α(x	NOUN
ejpam-1853	241	5	)	)	PUNCT
ejpam-1853	241	6	)	)	PUNCT
ejpam-1853	242	1	=	=	SYM
ejpam-1853	242	2	kα(x	kα(x	PROPN
ejpam-1853	242	3	)	)	PUNCT
ejpam-1853	242	4	.	.	PUNCT
ejpam-1853	243	1	according	accord	VERB
ejpam-1853	243	2	to	to	ADP
ejpam-1853	243	3	the	the	DET
ejpam-1853	243	4	first	first	ADJ
ejpam-1853	243	5	equality	equality	NOUN
ejpam-1853	243	6	(	(	PUNCT
ejpam-1853	243	7	a	a	X
ejpam-1853	243	8	)	)	PUNCT
ejpam-1853	243	9	,	,	PUNCT
ejpam-1853	243	10	it	it	PRON
ejpam-1853	243	11	follows	follow	VERB
ejpam-1853	243	12	α(kx	α(kx	PROPN
ejpam-1853	243	13	)	)	PUNCT
ejpam-1853	243	14	=	=	SYM
ejpam-1853	243	15	kα(x	kα(x	NOUN
ejpam-1853	243	16	)	)	PUNCT
ejpam-1853	243	17	,	,	PUNCT
ejpam-1853	243	18	and	and	CCONJ
ejpam-1853	243	19	α	α	PRON
ejpam-1853	243	20	is	be	AUX
ejpam-1853	243	21	a	a	DET
ejpam-1853	243	22	linear	linear	ADJ
ejpam-1853	243	23	map	map	NOUN
ejpam-1853	243	24	.	.	PUNCT
ejpam-1853	244	1	similarly	similarly	ADV
ejpam-1853	244	2	,	,	PUNCT
ejpam-1853	244	3	we	we	PRON
ejpam-1853	244	4	prove	prove	VERB
ejpam-1853	244	5	that	that	SCONJ
ejpam-1853	244	6	β	β	NOUN
ejpam-1853	244	7	is	be	AUX
ejpam-1853	244	8	a	a	DET
ejpam-1853	244	9	linear	linear	ADJ
ejpam-1853	244	10	map	map	NOUN
ejpam-1853	244	11	.	.	PUNCT
ejpam-1853	245	1	we	we	PRON
ejpam-1853	245	2	have	have	VERB
ejpam-1853	245	3	ϕ((id	ϕ((id	PROPN
ejpam-1853	245	4	×m)((k	×m)((k	NOUN
ejpam-1853	245	5	,	,	PUNCT
ejpam-1853	245	6	x	x	NOUN
ejpam-1853	245	7	)	)	PUNCT
ejpam-1853	245	8	,	,	PUNCT
ejpam-1853	245	9	(	(	PUNCT
ejpam-1853	245	10	k	k	X
ejpam-1853	245	11	,	,	PUNCT
ejpam-1853	245	12	y	y	NOUN
ejpam-1853	245	13	)	)	PUNCT
ejpam-1853	245	14	)	)	PUNCT
ejpam-1853	245	15	)	)	PUNCT
ejpam-1853	246	1	=	=	SYM
ejpam-1853	246	2	ϕ(k	ϕ(k	PROPN
ejpam-1853	246	3	,	,	PUNCT
ejpam-1853	246	4	m(x	m(x	PROPN
ejpam-1853	246	5	,	,	PUNCT
ejpam-1853	246	6	y	y	NOUN
ejpam-1853	246	7	)	)	PUNCT
ejpam-1853	246	8	)	)	PUNCT
ejpam-1853	247	1	=	=	SYM
ejpam-1853	247	2	km(x	km(x	X
ejpam-1853	247	3	,	,	PUNCT
ejpam-1853	247	4	y	y	PROPN
ejpam-1853	247	5	)	)	PUNCT
ejpam-1853	247	6	=	=	SYM
ejpam-1853	248	1	k(x	k(x	PROPN
ejpam-1853	248	2	·	·	PUNCT
ejpam-1853	248	3	y	y	X
ejpam-1853	248	4	)	)	PUNCT
ejpam-1853	248	5	and	and	CCONJ
ejpam-1853	248	6	m(ϕ(k	m(ϕ(k	PROPN
ejpam-1853	248	7	,	,	PUNCT
ejpam-1853	248	8	x),ϕ(k	x),ϕ(k	PROPN
ejpam-1853	248	9	,	,	PUNCT
ejpam-1853	248	10	y	y	NOUN
ejpam-1853	248	11	)	)	PUNCT
ejpam-1853	248	12	)	)	PUNCT
ejpam-1853	249	1	=	=	SYM
ejpam-1853	249	2	m(kx	m(kx	PROPN
ejpam-1853	249	3	,	,	PUNCT
ejpam-1853	249	4	k	k	PROPN
ejpam-1853	249	5	y	y	PROPN
ejpam-1853	249	6	)	)	PUNCT
ejpam-1853	249	7	=	=	PRON
ejpam-1853	249	8	(	(	PUNCT
ejpam-1853	249	9	kx	kx	PROPN
ejpam-1853	249	10	)	)	PUNCT
ejpam-1853	249	11	·	·	PUNCT
ejpam-1853	250	1	(	(	PUNCT
ejpam-1853	250	2	k	k	NOUN
ejpam-1853	250	3	y	y	PROPN
ejpam-1853	250	4	)	)	PUNCT
ejpam-1853	250	5	.	.	PUNCT
ejpam-1853	251	1	using	use	VERB
ejpam-1853	251	2	(	(	PUNCT
ejpam-1853	251	3	b	b	NOUN
ejpam-1853	251	4	)	)	PUNCT
ejpam-1853	251	5	one	one	NOUN
ejpam-1853	251	6	obtains	obtain	VERB
ejpam-1853	251	7	k(x	k(x	PROPN
ejpam-1853	251	8	·	·	PUNCT
ejpam-1853	251	9	y	y	X
ejpam-1853	251	10	)	)	PUNCT
ejpam-1853	251	11	=	=	SYM
ejpam-1853	251	12	(	(	PUNCT
ejpam-1853	251	13	kx	kx	PROPN
ejpam-1853	251	14	)	)	PUNCT
ejpam-1853	251	15	·	·	PUNCT
ejpam-1853	252	1	(	(	PUNCT
ejpam-1853	252	2	k	k	NOUN
ejpam-1853	252	3	y	y	PROPN
ejpam-1853	252	4	)	)	PUNCT
ejpam-1853	252	5	,	,	PUNCT
ejpam-1853	252	6	and	and	CCONJ
ejpam-1853	252	7	(	(	PUNCT
ejpam-1853	252	8	11	11	NUM
ejpam-1853	252	9	)	)	PUNCT
ejpam-1853	252	10	holds	hold	VERB
ejpam-1853	252	11	.	.	PUNCT
ejpam-1853	253	1	since	since	SCONJ
ejpam-1853	253	2	(	(	PUNCT
ejpam-1853	253	3	ϕ,ϕ0	ϕ,ϕ0	PROPN
ejpam-1853	253	4	)	)	PUNCT
ejpam-1853	253	5	is	be	AUX
ejpam-1853	253	6	a	a	DET
ejpam-1853	253	7	groupoid	groupoid	PROPN
ejpam-1853	253	8	morphism	morphism	NOUN
ejpam-1853	253	9	,	,	PUNCT
ejpam-1853	253	10	from	from	ADP
ejpam-1853	253	11	(	(	PUNCT
ejpam-1853	253	12	1	1	X
ejpam-1853	253	13	)	)	PUNCT
ejpam-1853	253	14	it	it	PRON
ejpam-1853	253	15	follows	follow	VERB
ejpam-1853	253	16	(	(	PUNCT
ejpam-1853	253	17	c	c	NOUN
ejpam-1853	253	18	)	)	PUNCT
ejpam-1853	253	19	ϕ	ϕ	NOUN
ejpam-1853	253	20	◦	◦	NOUN
ejpam-1853	253	21	(	(	PUNCT
ejpam-1853	253	22	i	i	NOUN
ejpam-1853	253	23	d	d	PROPN
ejpam-1853	253	24	×	×	PROPN
ejpam-1853	253	25	ε	ε	PROPN
ejpam-1853	253	26	)	)	PUNCT
ejpam-1853	253	27	=	=	SYM
ejpam-1853	253	28	ε	ε	PROPN
ejpam-1853	253	29	◦	◦	NOUN
ejpam-1853	253	30	ϕ0	ϕ0	PROPN
ejpam-1853	254	1	and	and	CCONJ
ejpam-1853	254	2	i	i	PRON
ejpam-1853	254	3	◦	◦	VERB
ejpam-1853	254	4	ϕ	ϕ	NOUN
ejpam-1853	254	5	=	=	X
ejpam-1853	254	6	ϕ	ϕ	PROPN
ejpam-1853	254	7	◦	◦	NOUN
ejpam-1853	254	8	(	(	PUNCT
ejpam-1853	254	9	i	i	NOUN
ejpam-1853	254	10	d	d	PROPN
ejpam-1853	254	11	×	×	PROPN
ejpam-1853	254	12	i	i	PROPN
ejpam-1853	254	13	)	)	PUNCT
ejpam-1853	254	14	.	.	PUNCT
ejpam-1853	255	1	for	for	ADP
ejpam-1853	255	2	all	all	DET
ejpam-1853	255	3	u	u	PROPN
ejpam-1853	255	4	∈	∈	PROPN
ejpam-1853	255	5	v0	v0	NOUN
ejpam-1853	255	6	and	and	CCONJ
ejpam-1853	255	7	k	k	PROPN
ejpam-1853	255	8	∈	∈	PROPN
ejpam-1853	256	1	k	k	NOUN
ejpam-1853	256	2	,	,	PUNCT
ejpam-1853	256	3	we	we	PRON
ejpam-1853	256	4	have	have	VERB
ejpam-1853	256	5	ϕ((id	ϕ((id	NUM
ejpam-1853	256	6	×	×	PROPN
ejpam-1853	256	7	ε)(k	ε)(k	PROPN
ejpam-1853	256	8	,	,	PUNCT
ejpam-1853	256	9	u	u	NOUN
ejpam-1853	256	10	)	)	PUNCT
ejpam-1853	256	11	)	)	PUNCT
ejpam-1853	257	1	=	=	SYM
ejpam-1853	257	2	ϕ(k	ϕ(k	NOUN
ejpam-1853	257	3	,	,	PUNCT
ejpam-1853	257	4	ε(u	ε(u	PROPN
ejpam-1853	257	5	)	)	PUNCT
ejpam-1853	257	6	)	)	PUNCT
ejpam-1853	258	1	=	=	SYM
ejpam-1853	258	2	kε(u	kε(u	NOUN
ejpam-1853	258	3	)	)	PUNCT
ejpam-1853	258	4	and	and	CCONJ
ejpam-1853	258	5	ε(ϕ0(k	ε(ϕ0(k	PROPN
ejpam-1853	258	6	,	,	PUNCT
ejpam-1853	258	7	u	u	NOUN
ejpam-1853	258	8	)	)	PUNCT
ejpam-1853	258	9	)	)	PUNCT
ejpam-1853	259	1	=	=	PUNCT
ejpam-1853	259	2	ε(ku	ε(ku	PROPN
ejpam-1853	259	3	)	)	PUNCT
ejpam-1853	259	4	.	.	PUNCT
ejpam-1853	260	1	from	from	ADP
ejpam-1853	260	2	the	the	DET
ejpam-1853	260	3	first	first	ADJ
ejpam-1853	260	4	equality	equality	NOUN
ejpam-1853	260	5	(	(	PUNCT
ejpam-1853	260	6	c	c	NOUN
ejpam-1853	260	7	)	)	PUNCT
ejpam-1853	260	8	,	,	PUNCT
ejpam-1853	260	9	it	it	PRON
ejpam-1853	260	10	follows	follow	VERB
ejpam-1853	260	11	ε(ku	ε(ku	PROPN
ejpam-1853	260	12	)	)	PUNCT
ejpam-1853	260	13	=	=	SYM
ejpam-1853	260	14	kε(u	kε(u	NOUN
ejpam-1853	260	15	)	)	PUNCT
ejpam-1853	260	16	.	.	PUNCT
ejpam-1853	261	1	hence	hence	ADV
ejpam-1853	261	2	,	,	PUNCT
ejpam-1853	261	3	ε	ε	PROPN
ejpam-1853	261	4	is	be	AUX
ejpam-1853	261	5	a	a	DET
ejpam-1853	261	6	linear	linear	ADJ
ejpam-1853	261	7	map	map	NOUN
ejpam-1853	261	8	.	.	PUNCT
ejpam-1853	262	1	for	for	ADP
ejpam-1853	262	2	all	all	DET
ejpam-1853	262	3	x	x	SYM
ejpam-1853	262	4	∈	∈	PROPN
ejpam-1853	262	5	v	v	NOUN
ejpam-1853	262	6	and	and	CCONJ
ejpam-1853	262	7	k	k	PROPN
ejpam-1853	262	8	∈	∈	PROPN
ejpam-1853	262	9	k	k	NOUN
ejpam-1853	262	10	,	,	PUNCT
ejpam-1853	262	11	we	we	PRON
ejpam-1853	262	12	have	have	VERB
ejpam-1853	262	13	i(ϕ(k	i(ϕ(k	PROPN
ejpam-1853	262	14	,	,	PUNCT
ejpam-1853	262	15	x	x	NOUN
ejpam-1853	262	16	)	)	PUNCT
ejpam-1853	262	17	)	)	PUNCT
ejpam-1853	263	1	=	=	SYM
ejpam-1853	263	2	i(kx	i(kx	X
ejpam-1853	263	3	)	)	PUNCT
ejpam-1853	263	4	and	and	CCONJ
ejpam-1853	263	5	ϕ(k	ϕ(k	PROPN
ejpam-1853	263	6	,	,	PUNCT
ejpam-1853	263	7	i(x	i(x	NOUN
ejpam-1853	263	8	)	)	PUNCT
ejpam-1853	263	9	)	)	PUNCT
ejpam-1853	263	10	=	=	SYM
ejpam-1853	264	1	ki(x	ki(x	NUM
ejpam-1853	264	2	)	)	PUNCT
ejpam-1853	264	3	.	.	PUNCT
ejpam-1853	265	1	using	use	VERB
ejpam-1853	265	2	the	the	DET
ejpam-1853	265	3	second	second	ADJ
ejpam-1853	265	4	equality	equality	NOUN
ejpam-1853	265	5	(	(	PUNCT
ejpam-1853	265	6	c	c	NOUN
ejpam-1853	265	7	)	)	PUNCT
ejpam-1853	265	8	,	,	PUNCT
ejpam-1853	265	9	it	it	PRON
ejpam-1853	265	10	follows	follow	VERB
ejpam-1853	265	11	i(kx	i(kx	PRON
ejpam-1853	265	12	)	)	PUNCT
ejpam-1853	265	13	=	=	SYM
ejpam-1853	266	1	ki(x	ki(x	NUM
ejpam-1853	266	2	)	)	PUNCT
ejpam-1853	267	1	,	,	PUNCT
ejpam-1853	267	2	and	and	CCONJ
ejpam-1853	267	3	i	i	PRON
ejpam-1853	267	4	is	be	AUX
ejpam-1853	267	5	a	a	DET
ejpam-1853	267	6	linear	linear	ADJ
ejpam-1853	267	7	map	map	NOUN
ejpam-1853	267	8	.	.	PUNCT
ejpam-1853	268	1	the	the	DET
ejpam-1853	268	2	relation	relation	NOUN
ejpam-1853	268	3	(	(	PUNCT
ejpam-1853	268	4	10	10	NUM
ejpam-1853	268	5	)	)	PUNCT
ejpam-1853	268	6	(	(	PUNCT
ejpam-1853	268	7	resp	resp	NOUN
ejpam-1853	268	8	.	.	PUNCT
ejpam-1853	268	9	,	,	PUNCT
ejpam-1853	268	10	(	(	PUNCT
ejpam-1853	268	11	11	11	NUM
ejpam-1853	268	12	)	)	PUNCT
ejpam-1853	268	13	)	)	PUNCT
ejpam-1853	268	14	is	be	AUX
ejpam-1853	268	15	called	call	VERB
ejpam-1853	268	16	the	the	DET
ejpam-1853	268	17	interchange	interchange	NOUN
ejpam-1853	268	18	law	law	NOUN
ejpam-1853	268	19	between	between	ADP
ejpam-1853	268	20	groupoid	groupoid	PROPN
ejpam-1853	268	21	multiplication	multiplication	PROPN
ejpam-1853	268	22	m	m	PROPN
ejpam-1853	268	23	and	and	CCONJ
ejpam-1853	268	24	scalar	scalar	ADJ
ejpam-1853	268	25	multiplication	multiplication	NOUN
ejpam-1853	268	26	ω	ω	PROPN
ejpam-1853	268	27	(	(	PUNCT
ejpam-1853	268	28	resp	resp	PROPN
ejpam-1853	268	29	.	.	PUNCT
ejpam-1853	268	30	,	,	PUNCT
ejpam-1853	268	31	ϕ	ϕ	NOUN
ejpam-1853	268	32	)	)	PUNCT
ejpam-1853	268	33	.	.	PUNCT
ejpam-1853	269	1	the	the	DET
ejpam-1853	269	2	relation	relation	NOUN
ejpam-1853	269	3	(	(	PUNCT
ejpam-1853	269	4	12	12	NUM
ejpam-1853	269	5	)	)	PUNCT
ejpam-1853	269	6	is	be	AUX
ejpam-1853	269	7	called	call	VERB
ejpam-1853	269	8	the	the	DET
ejpam-1853	269	9	interchange	interchange	NOUN
ejpam-1853	269	10	law	law	NOUN
ejpam-1853	269	11	between	between	ADP
ejpam-1853	269	12	groupoid	groupoid	PROPN
ejpam-1853	269	13	multiplication	multiplication	PROPN
ejpam-1853	269	14	m	m	PROPN
ejpam-1853	269	15	and	and	CCONJ
ejpam-1853	269	16	group	group	NOUN
ejpam-1853	269	17	operation	operation	PROPN
ejpam-1853	269	18	σ	σ	PROPN
ejpam-1853	269	19	.	.	PROPN
ejpam-1853	269	20	from	from	ADP
ejpam-1853	269	21	the	the	DET
ejpam-1853	269	22	theorems	theorem	NOUN
ejpam-1853	269	23	5	5	NUM
ejpam-1853	269	24	,	,	PUNCT
ejpam-1853	269	25	1,3	1,3	NUM
ejpam-1853	269	26	,	,	PUNCT
ejpam-1853	269	27	4	4	NUM
ejpam-1853	269	28	follows	follow	VERB
ejpam-1853	269	29	the	the	DET
ejpam-1853	269	30	following	follow	VERB
ejpam-1853	269	31	corollary	corollary	NOUN
ejpam-1853	269	32	.	.	PUNCT
ejpam-1853	270	1	corollary	corollary	ADJ
ejpam-1853	270	2	2	2	NUM
ejpam-1853	270	3	.	.	PUNCT
ejpam-1853	271	1	let	let	AUX
ejpam-1853	271	2	(	(	PUNCT
ejpam-1853	271	3	v	v	NOUN
ejpam-1853	271	4	,	,	PUNCT
ejpam-1853	271	5	α	α	NOUN
ejpam-1853	271	6	,	,	PUNCT
ejpam-1853	271	7	β	β	X
ejpam-1853	271	8	,	,	PUNCT
ejpam-1853	271	9	m	m	PROPN
ejpam-1853	271	10	,	,	PUNCT
ejpam-1853	271	11	i	i	PRON
ejpam-1853	271	12	,	,	PUNCT
ejpam-1853	271	13	ε,+,ϕ	ε,+,ϕ	PROPN
ejpam-1853	271	14	,	,	PUNCT
ejpam-1853	271	15	v0	v0	PROPN
ejpam-1853	271	16	)	)	PUNCT
ejpam-1853	271	17	be	be	AUX
ejpam-1853	271	18	a	a	DET
ejpam-1853	271	19	vs−groupoid	vs−groupoid	NOUN
ejpam-1853	271	20	.	.	PUNCT
ejpam-1853	272	1	then	then	ADV
ejpam-1853	272	2	:	:	PUNCT
ejpam-1853	272	3	(	(	PUNCT
ejpam-1853	272	4	i	i	NOUN
ejpam-1853	272	5	)	)	PUNCT
ejpam-1853	272	6	the	the	DET
ejpam-1853	272	7	source	source	NOUN
ejpam-1853	272	8	and	and	CCONJ
ejpam-1853	272	9	target	target	VERB
ejpam-1853	272	10	α	α	NOUN
ejpam-1853	272	11	,	,	PUNCT
ejpam-1853	272	12	β	β	X
ejpam-1853	272	13	:	:	PUNCT
ejpam-1853	272	14	v	v	X
ejpam-1853	272	15	→	→	SYM
ejpam-1853	272	16	v0	v0	NOUN
ejpam-1853	272	17	are	be	AUX
ejpam-1853	272	18	surjective	surjective	ADJ
ejpam-1853	272	19	linear	linear	ADJ
ejpam-1853	272	20	maps	map	NOUN
ejpam-1853	272	21	,	,	PUNCT
ejpam-1853	272	22	and	and	CCONJ
ejpam-1853	272	23	α(e	α(e	NUM
ejpam-1853	272	24	)	)	PUNCT
ejpam-1853	273	1	=	=	PUNCT
ejpam-1853	273	2	β(e	β(e	X
ejpam-1853	273	3	)	)	PUNCT
ejpam-1853	273	4	=	=	SYM
ejpam-1853	273	5	e0	e0	PROPN
ejpam-1853	273	6	,	,	PUNCT
ejpam-1853	273	7	α(−x	α(−x	NUM
ejpam-1853	273	8	)	)	PUNCT
ejpam-1853	273	9	=	=	SYM
ejpam-1853	273	10	−α(x	−α(x	NOUN
ejpam-1853	273	11	)	)	PUNCT
ejpam-1853	273	12	and	and	CCONJ
ejpam-1853	273	13	β(−x	β(−x	NUM
ejpam-1853	273	14	)	)	PUNCT
ejpam-1853	274	1	=	=	SYM
ejpam-1853	274	2	−β(x	−β(x	NOUN
ejpam-1853	274	3	)	)	PUNCT
ejpam-1853	274	4	,	,	PUNCT
ejpam-1853	274	5	(	(	PUNCT
ejpam-1853	274	6	∀	∀	X
ejpam-1853	274	7	)	)	PUNCT
ejpam-1853	274	8	x	x	SYM
ejpam-1853	274	9	∈	∈	NOUN
ejpam-1853	274	10	v	v	NOUN
ejpam-1853	274	11	;	;	PUNCT
ejpam-1853	274	12	(	(	PUNCT
ejpam-1853	274	13	ii	ii	X
ejpam-1853	274	14	)	)	PUNCT
ejpam-1853	274	15	the	the	DET
ejpam-1853	274	16	inclusion	inclusion	NOUN
ejpam-1853	274	17	map	map	NOUN
ejpam-1853	274	18	ε	ε	PROPN
ejpam-1853	274	19	:	:	PUNCT
ejpam-1853	274	20	v0→	v0→	NUM
ejpam-1853	274	21	v	v	NOUN
ejpam-1853	274	22	is	be	AUX
ejpam-1853	274	23	an	an	DET
ejpam-1853	274	24	injective	injective	ADJ
ejpam-1853	274	25	linear	linear	NOUN
ejpam-1853	274	26	map	map	NOUN
ejpam-1853	274	27	,	,	PUNCT
ejpam-1853	274	28	and	and	CCONJ
ejpam-1853	274	29	ε(e0	ε(e0	NOUN
ejpam-1853	274	30	)	)	PUNCT
ejpam-1853	274	31	=	=	SYM
ejpam-1853	274	32	e	e	NOUN
ejpam-1853	274	33	,	,	PUNCT
ejpam-1853	274	34	ε(−u	ε(−u	NOUN
ejpam-1853	274	35	)	)	PUNCT
ejpam-1853	274	36	=	=	SYM
ejpam-1853	274	37	−ε(u	−ε(u	NOUN
ejpam-1853	274	38	)	)	PUNCT
ejpam-1853	274	39	,	,	PUNCT
ejpam-1853	274	40	(	(	PUNCT
ejpam-1853	274	41	∀	∀	X
ejpam-1853	274	42	)	)	PUNCT
ejpam-1853	274	43	u	u	PROPN
ejpam-1853	274	44	∈	∈	PROPN
ejpam-1853	274	45	v0	v0	NOUN
ejpam-1853	274	46	;	;	PUNCT
ejpam-1853	274	47	m.	m.	PROPN
ejpam-1853	274	48	ivan	ivan	PROPN
ejpam-1853	274	49	/	/	SYM
ejpam-1853	274	50	eur	eur	PROPN
ejpam-1853	274	51	.	.	PUNCT
ejpam-1853	275	1	j.	j.	PROPN
ejpam-1853	275	2	pure	pure	PROPN
ejpam-1853	275	3	appl	appl	PROPN
ejpam-1853	275	4	.	.	PROPN
ejpam-1853	275	5	math	math	PROPN
ejpam-1853	275	6	,	,	PUNCT
ejpam-1853	275	7	6	6	NUM
ejpam-1853	275	8	(	(	PUNCT
ejpam-1853	275	9	2013	2013	NUM
ejpam-1853	275	10	)	)	PUNCT
ejpam-1853	275	11	,	,	PUNCT
ejpam-1853	275	12	469	469	NUM
ejpam-1853	275	13	-	-	SYM
ejpam-1853	275	14	484	484	NUM
ejpam-1853	275	15	477	477	NUM
ejpam-1853	275	16	(	(	PUNCT
ejpam-1853	275	17	iii	iii	NOUN
ejpam-1853	275	18	)	)	PUNCT
ejpam-1853	275	19	the	the	DET
ejpam-1853	275	20	inversion	inversion	NOUN
ejpam-1853	275	21	i	i	PRON
ejpam-1853	275	22	:	:	PUNCT
ejpam-1853	275	23	v	v	X
ejpam-1853	275	24	→	→	SYM
ejpam-1853	275	25	v	v	PROPN
ejpam-1853	275	26	is	be	AUX
ejpam-1853	275	27	a	a	DET
ejpam-1853	275	28	linear	linear	ADJ
ejpam-1853	275	29	automorphism	automorphism	NOUN
ejpam-1853	275	30	,	,	PUNCT
ejpam-1853	275	31	and	and	CCONJ
ejpam-1853	275	32	i(e	i(e	NOUN
ejpam-1853	275	33	)	)	PUNCT
ejpam-1853	276	1	=	=	SYM
ejpam-1853	276	2	e	e	NOUN
ejpam-1853	276	3	,	,	PUNCT
ejpam-1853	276	4	i(−x	i(−x	NOUN
ejpam-1853	276	5	)	)	PUNCT
ejpam-1853	276	6	=	=	SYM
ejpam-1853	276	7	−i(x	−i(x	ADJ
ejpam-1853	276	8	)	)	PUNCT
ejpam-1853	276	9	,	,	PUNCT
ejpam-1853	276	10	(	(	PUNCT
ejpam-1853	276	11	∀	∀	X
ejpam-1853	276	12	)	)	PUNCT
ejpam-1853	276	13	x	x	SYM
ejpam-1853	276	14	∈	∈	NOUN
ejpam-1853	276	15	v	v	NOUN
ejpam-1853	276	16	;	;	PUNCT
ejpam-1853	276	17	(	(	PUNCT
ejpam-1853	276	18	iv	iv	X
ejpam-1853	276	19	)	)	PUNCT
ejpam-1853	276	20	the	the	DET
ejpam-1853	276	21	following	follow	VERB
ejpam-1853	276	22	assertions	assertion	NOUN
ejpam-1853	276	23	hold	hold	VERB
ejpam-1853	276	24	:	:	PUNCT
ejpam-1853	276	25	e	e	X
ejpam-1853	276	26	·	·	PUNCT
ejpam-1853	276	27	y	y	X
ejpam-1853	276	28	=	=	SYM
ejpam-1853	276	29	y	y	PROPN
ejpam-1853	276	30	,	,	PUNCT
ejpam-1853	276	31	(	(	PUNCT
ejpam-1853	276	32	∀)y	∀)y	NOUN
ejpam-1853	276	33	∈	∈	NOUN
ejpam-1853	276	34	α−1(e0	α−1(e0	NOUN
ejpam-1853	276	35	)	)	PUNCT
ejpam-1853	276	36	and	and	CCONJ
ejpam-1853	276	37	x	x	SYM
ejpam-1853	276	38	·	·	PUNCT
ejpam-1853	276	39	e	e	X
ejpam-1853	276	40	=	=	PUNCT
ejpam-1853	276	41	x	x	SYM
ejpam-1853	276	42	,	,	PUNCT
ejpam-1853	276	43	(	(	PUNCT
ejpam-1853	276	44	∀)x	∀)x	PROPN
ejpam-1853	276	45	∈	∈	PROPN
ejpam-1853	276	46	β−1(e0	β−1(e0	PROPN
ejpam-1853	276	47	)	)	PUNCT
ejpam-1853	276	48	;	;	PUNCT
ejpam-1853	276	49	(	(	PUNCT
ejpam-1853	276	50	13	13	NUM
ejpam-1853	276	51	)	)	PUNCT
ejpam-1853	276	52	x	x	X
ejpam-1853	276	53	·	·	PUNCT
ejpam-1853	277	1	(	(	PUNCT
ejpam-1853	277	2	y	y	PROPN
ejpam-1853	277	3	+	+	PROPN
ejpam-1853	277	4	t	t	PROPN
ejpam-1853	277	5	)	)	PUNCT
ejpam-1853	277	6	=	=	PUNCT
ejpam-1853	278	1	x	x	PUNCT
ejpam-1853	278	2	·	·	PUNCT
ejpam-1853	278	3	y	y	PROPN
ejpam-1853	278	4	+	+	PROPN
ejpam-1853	278	5	t	t	PROPN
ejpam-1853	278	6	,	,	PUNCT
ejpam-1853	278	7	(	(	PUNCT
ejpam-1853	278	8	∀)(x	∀)(x	PROPN
ejpam-1853	278	9	,	,	PUNCT
ejpam-1853	278	10	y	y	PROPN
ejpam-1853	278	11	)	)	PUNCT
ejpam-1853	278	12	∈	∈	PROPN
ejpam-1853	278	13	v(2	v(2	PROPN
ejpam-1853	278	14	)	)	PUNCT
ejpam-1853	278	15	and	and	CCONJ
ejpam-1853	278	16	t	t	PROPN
ejpam-1853	278	17	∈	∈	PROPN
ejpam-1853	278	18	α−1(e0	α−1(e0	PROPN
ejpam-1853	278	19	)	)	PUNCT
ejpam-1853	278	20	;	;	PUNCT
ejpam-1853	278	21	(	(	PUNCT
ejpam-1853	278	22	14	14	NUM
ejpam-1853	278	23	)	)	PUNCT
ejpam-1853	278	24	(	(	PUNCT
ejpam-1853	278	25	x	x	X
ejpam-1853	279	1	+	+	NUM
ejpam-1853	279	2	z	z	NOUN
ejpam-1853	279	3	)	)	PUNCT
ejpam-1853	279	4	·	·	PUNCT
ejpam-1853	280	1	y	y	X
ejpam-1853	280	2	=	=	PUNCT
ejpam-1853	280	3	x	x	PUNCT
ejpam-1853	280	4	·	·	PUNCT
ejpam-1853	280	5	y	y	PROPN
ejpam-1853	280	6	+	+	CCONJ
ejpam-1853	280	7	z	z	PROPN
ejpam-1853	280	8	,	,	PUNCT
ejpam-1853	280	9	(	(	PUNCT
ejpam-1853	280	10	∀)(x	∀)(x	PROPN
ejpam-1853	280	11	,	,	PUNCT
ejpam-1853	280	12	y	y	PROPN
ejpam-1853	280	13	)	)	PUNCT
ejpam-1853	280	14	∈	∈	PROPN
ejpam-1853	280	15	v(2	v(2	PROPN
ejpam-1853	280	16	)	)	PUNCT
ejpam-1853	280	17	and	and	CCONJ
ejpam-1853	280	18	z	z	NOUN
ejpam-1853	280	19	∈	∈	PROPN
ejpam-1853	280	20	β−1(e0	β−1(e0	PROPN
ejpam-1853	280	21	)	)	PUNCT
ejpam-1853	280	22	;	;	PUNCT
ejpam-1853	280	23	(	(	PUNCT
ejpam-1853	280	24	15	15	X
ejpam-1853	280	25	)	)	PUNCT
ejpam-1853	280	26	x	x	X
ejpam-1853	280	27	·	·	PUNCT
ejpam-1853	280	28	y	y	X
ejpam-1853	280	29	=	=	PUNCT
ejpam-1853	280	30	x	x	PROPN
ejpam-1853	281	1	+	+	NUM
ejpam-1853	281	2	y	y	PROPN
ejpam-1853	281	3	−	−	NOUN
ejpam-1853	281	4	ε(β(x	ε(β(x	NOUN
ejpam-1853	281	5	)	)	PUNCT
ejpam-1853	281	6	)	)	PUNCT
ejpam-1853	281	7	,	,	PUNCT
ejpam-1853	281	8	(	(	PUNCT
ejpam-1853	281	9	∀)(x	∀)(x	PROPN
ejpam-1853	281	10	,	,	PUNCT
ejpam-1853	281	11	y	y	PROPN
ejpam-1853	281	12	)	)	PUNCT
ejpam-1853	281	13	∈	∈	PROPN
ejpam-1853	281	14	v(2	v(2	PROPN
ejpam-1853	281	15	)	)	PUNCT
ejpam-1853	281	16	;	;	PUNCT
ejpam-1853	281	17	(	(	PUNCT
ejpam-1853	281	18	16	16	NUM
ejpam-1853	281	19	)	)	PUNCT
ejpam-1853	281	20	x−1	x−1	NOUN
ejpam-1853	282	1	=	=	NOUN
ejpam-1853	282	2	ε(α(x	ε(α(x	NOUN
ejpam-1853	282	3	)	)	PUNCT
ejpam-1853	282	4	)	)	PUNCT
ejpam-1853	283	1	+	+	CCONJ
ejpam-1853	284	1	ε(β(x))−	ε(β(x))−	ADP
ejpam-1853	284	2	x	x	X
ejpam-1853	284	3	,	,	PUNCT
ejpam-1853	284	4	(	(	PUNCT
ejpam-1853	284	5	∀)x	∀)x	PROPN
ejpam-1853	284	6	∈	∈	PROPN
ejpam-1853	284	7	v.	v.	CCONJ
ejpam-1853	284	8	(	(	PUNCT
ejpam-1853	284	9	17	17	NUM
ejpam-1853	284	10	)	)	PUNCT
ejpam-1853	284	11	corollary	corollary	NOUN
ejpam-1853	284	12	3	3	NUM
ejpam-1853	284	13	.	.	PUNCT
ejpam-1853	285	1	if	if	SCONJ
ejpam-1853	285	2	(	(	PUNCT
ejpam-1853	285	3	v	v	NOUN
ejpam-1853	285	4	,	,	PUNCT
ejpam-1853	285	5	α	α	NOUN
ejpam-1853	285	6	,	,	PUNCT
ejpam-1853	285	7	β	β	X
ejpam-1853	285	8	,	,	PUNCT
ejpam-1853	285	9	m	m	PROPN
ejpam-1853	285	10	,	,	PUNCT
ejpam-1853	285	11	i	i	PRON
ejpam-1853	285	12	,	,	PUNCT
ejpam-1853	285	13	ε,+,ϕ	ε,+,ϕ	PROPN
ejpam-1853	285	14	,	,	PUNCT
ejpam-1853	285	15	v0	v0	PROPN
ejpam-1853	285	16	)	)	PUNCT
ejpam-1853	285	17	is	be	AUX
ejpam-1853	285	18	a	a	DET
ejpam-1853	285	19	vs−groupoid	vs−groupoid	NOUN
ejpam-1853	285	20	,	,	PUNCT
ejpam-1853	285	21	then	then	ADV
ejpam-1853	285	22	:	:	PUNCT
ejpam-1853	285	23	x	x	X
ejpam-1853	285	24	·	·	PUNCT
ejpam-1853	285	25	y	y	X
ejpam-1853	285	26	=	=	PUNCT
ejpam-1853	286	1	x	x	PROPN
ejpam-1853	286	2	+	+	CCONJ
ejpam-1853	286	3	y	y	PROPN
ejpam-1853	286	4	and	and	CCONJ
ejpam-1853	286	5	x−1	x−1	PUNCT
ejpam-1853	287	1	=	=	NOUN
ejpam-1853	287	2	−x	−x	PROPN
ejpam-1853	287	3	,	,	PUNCT
ejpam-1853	287	4	(	(	PUNCT
ejpam-1853	287	5	∀)x	∀)x	INTJ
ejpam-1853	287	6	,	,	PUNCT
ejpam-1853	287	7	y	y	PROPN
ejpam-1853	287	8	∈	∈	PROPN
ejpam-1853	287	9	v	v	PROPN
ejpam-1853	287	10	(	(	PUNCT
ejpam-1853	287	11	e0	e0	PROPN
ejpam-1853	287	12	)	)	PUNCT
ejpam-1853	287	13	.	.	PUNCT
ejpam-1853	288	1	(	(	PUNCT
ejpam-1853	288	2	18	18	NUM
ejpam-1853	288	3	)	)	PUNCT
ejpam-1853	288	4	proof	proof	NOUN
ejpam-1853	288	5	.	.	PUNCT
ejpam-1853	289	1	it	it	PRON
ejpam-1853	289	2	follows	follow	VERB
ejpam-1853	289	3	immediately	immediately	ADV
ejpam-1853	289	4	from	from	ADP
ejpam-1853	289	5	(	(	PUNCT
ejpam-1853	289	6	16	16	NUM
ejpam-1853	289	7	)	)	PUNCT
ejpam-1853	289	8	and	and	CCONJ
ejpam-1853	289	9	(	(	PUNCT
ejpam-1853	289	10	17	17	NUM
ejpam-1853	289	11	)	)	PUNCT
ejpam-1853	289	12	.	.	PUNCT
ejpam-1853	290	1	theorem	theorem	VERB
ejpam-1853	290	2	6	6	NUM
ejpam-1853	290	3	.	.	PUNCT
ejpam-1853	291	1	let	let	AUX
ejpam-1853	291	2	(	(	PUNCT
ejpam-1853	291	3	v	v	NOUN
ejpam-1853	291	4	,	,	PUNCT
ejpam-1853	291	5	α	α	NOUN
ejpam-1853	291	6	,	,	PUNCT
ejpam-1853	291	7	β	β	X
ejpam-1853	291	8	,	,	PUNCT
ejpam-1853	291	9	m	m	PROPN
ejpam-1853	291	10	,	,	PUNCT
ejpam-1853	291	11	ε	ε	PROPN
ejpam-1853	291	12	,	,	PUNCT
ejpam-1853	291	13	i	i	PROPN
ejpam-1853	291	14	,	,	PUNCT
ejpam-1853	291	15	v0	v0	PROPN
ejpam-1853	291	16	)	)	PUNCT
ejpam-1853	291	17	be	be	AUX
ejpam-1853	291	18	a	a	DET
ejpam-1853	291	19	groupoid	groupoid	NOUN
ejpam-1853	291	20	.	.	PUNCT
ejpam-1853	292	1	if	if	SCONJ
ejpam-1853	292	2	the	the	DET
ejpam-1853	292	3	following	follow	VERB
ejpam-1853	292	4	conditions	condition	NOUN
ejpam-1853	292	5	are	be	AUX
ejpam-1853	292	6	satisfied	satisfied	ADJ
ejpam-1853	292	7	:	:	PUNCT
ejpam-1853	292	8	(	(	PUNCT
ejpam-1853	292	9	i	i	NOUN
ejpam-1853	292	10	)	)	PUNCT
ejpam-1853	292	11	(	(	PUNCT
ejpam-1853	292	12	v,+,ϕ	v,+,ϕ	PROPN
ejpam-1853	292	13	)	)	PUNCT
ejpam-1853	292	14	and	and	CCONJ
ejpam-1853	292	15	(	(	PUNCT
ejpam-1853	292	16	v0,+,ϕ0	v0,+,ϕ0	NOUN
ejpam-1853	292	17	)	)	PUNCT
ejpam-1853	292	18	are	be	AUX
ejpam-1853	292	19	vector	vector	NOUN
ejpam-1853	292	20	spaces	space	NOUN
ejpam-1853	292	21	;	;	PUNCT
ejpam-1853	292	22	(	(	PUNCT
ejpam-1853	292	23	ii	ii	X
ejpam-1853	292	24	)	)	PUNCT
ejpam-1853	292	25	α	α	PROPN
ejpam-1853	292	26	,	,	PUNCT
ejpam-1853	292	27	β	β	X
ejpam-1853	292	28	:	:	PUNCT
ejpam-1853	292	29	v	v	X
ejpam-1853	292	30	→	→	SYM
ejpam-1853	292	31	v0	v0	NOUN
ejpam-1853	292	32	,	,	PUNCT
ejpam-1853	292	33	ε	ε	PROPN
ejpam-1853	292	34	:	:	PUNCT
ejpam-1853	292	35	v0→	v0→	VERB
ejpam-1853	292	36	v	v	NOUN
ejpam-1853	293	1	and	and	CCONJ
ejpam-1853	293	2	i	i	PRON
ejpam-1853	293	3	:	:	PUNCT
ejpam-1853	293	4	v	v	X
ejpam-1853	293	5	→	→	SYM
ejpam-1853	293	6	v	v	NUM
ejpam-1853	293	7	are	be	AUX
ejpam-1853	293	8	linear	linear	ADJ
ejpam-1853	293	9	maps	map	NOUN
ejpam-1853	293	10	;	;	PUNCT
ejpam-1853	293	11	(	(	PUNCT
ejpam-1853	293	12	iii	iii	X
ejpam-1853	293	13	)	)	PUNCT
ejpam-1853	293	14	the	the	DET
ejpam-1853	293	15	interchange	interchange	NOUN
ejpam-1853	293	16	law	law	NOUN
ejpam-1853	293	17	(	(	PUNCT
ejpam-1853	293	18	10	10	NUM
ejpam-1853	293	19	)	)	PUNCT
ejpam-1853	293	20	between	between	ADP
ejpam-1853	293	21	the	the	DET
ejpam-1853	293	22	operations	operation	NOUN
ejpam-1853	293	23	m	m	VERB
ejpam-1853	293	24	and	and	CCONJ
ejpam-1853	293	25	ω	ω	NUM
ejpam-1853	293	26	holds	hold	NOUN
ejpam-1853	293	27	,	,	PUNCT
ejpam-1853	293	28	then	then	ADV
ejpam-1853	293	29	(	(	PUNCT
ejpam-1853	293	30	v	v	NOUN
ejpam-1853	293	31	,	,	PUNCT
ejpam-1853	293	32	α	α	NOUN
ejpam-1853	293	33	,	,	PUNCT
ejpam-1853	293	34	β	β	X
ejpam-1853	293	35	,	,	PUNCT
ejpam-1853	293	36	m	m	PROPN
ejpam-1853	293	37	,	,	PUNCT
ejpam-1853	293	38	ε	ε	PROPN
ejpam-1853	293	39	,	,	PUNCT
ejpam-1853	293	40	i,+,ϕ	i,+,ϕ	NOUN
ejpam-1853	293	41	,	,	PUNCT
ejpam-1853	293	42	v0	v0	PROPN
ejpam-1853	293	43	)	)	PUNCT
ejpam-1853	293	44	is	be	AUX
ejpam-1853	293	45	a	a	DET
ejpam-1853	293	46	vector	vector	NOUN
ejpam-1853	293	47	space	space	NOUN
ejpam-1853	293	48	-	-	PUNCT
ejpam-1853	293	49	groupoid	groupoid	NOUN
ejpam-1853	293	50	.	.	PUNCT
ejpam-1853	294	1	proof	proof	NOUN
ejpam-1853	294	2	.	.	PUNCT
ejpam-1853	295	1	by	by	ADP
ejpam-1853	295	2	hypothesis	hypothesis	NOUN
ejpam-1853	295	3	,	,	PUNCT
ejpam-1853	295	4	the	the	DET
ejpam-1853	295	5	condition	condition	NOUN
ejpam-1853	295	6	(	(	PUNCT
ejpam-1853	295	7	5.1	5.1	NUM
ejpam-1853	295	8	)	)	PUNCT
ejpam-1853	295	9	from	from	ADP
ejpam-1853	295	10	definition	definition	NOUN
ejpam-1853	295	11	5	5	NUM
ejpam-1853	295	12	is	be	AUX
ejpam-1853	295	13	verified	verify	VERB
ejpam-1853	295	14	.	.	PUNCT
ejpam-1853	296	1	we	we	PRON
ejpam-1853	296	2	prove	prove	VERB
ejpam-1853	296	3	now	now	ADV
ejpam-1853	296	4	the	the	DET
ejpam-1853	296	5	condition	condition	NOUN
ejpam-1853	296	6	(	(	PUNCT
ejpam-1853	296	7	5.2	5.2	NUM
ejpam-1853	296	8	)	)	PUNCT
ejpam-1853	296	9	from	from	ADP
ejpam-1853	296	10	definition	definition	NOUN
ejpam-1853	296	11	5	5	NUM
ejpam-1853	296	12	is	be	AUX
ejpam-1853	296	13	satisfied	satisfied	ADJ
ejpam-1853	296	14	.	.	PUNCT
ejpam-1853	297	1	the	the	DET
ejpam-1853	297	2	condition	condition	NOUN
ejpam-1853	297	3	(	(	PUNCT
ejpam-1853	297	4	i	i	NOUN
ejpam-1853	297	5	)	)	PUNCT
ejpam-1853	297	6	from	from	ADP
ejpam-1853	297	7	definition	definition	NOUN
ejpam-1853	297	8	4	4	NUM
ejpam-1853	297	9	holds	hold	VERB
ejpam-1853	297	10	,	,	PUNCT
ejpam-1853	297	11	since	since	SCONJ
ejpam-1853	297	12	(	(	PUNCT
ejpam-1853	297	13	v	v	PROPN
ejpam-1853	297	14	,	,	PUNCT
ejpam-1853	297	15	ω	ω	PROPN
ejpam-1853	297	16	,	,	PUNCT
ejpam-1853	297	17	ν	ν	NOUN
ejpam-1853	297	18	,	,	PUNCT
ejpam-1853	297	19	σ	σ	PROPN
ejpam-1853	297	20	)	)	PUNCT
ejpam-1853	297	21	and	and	CCONJ
ejpam-1853	297	22	(	(	PUNCT
ejpam-1853	297	23	v0,ω0,ν0,σ0	v0,ω0,ν0,σ0	NUM
ejpam-1853	297	24	)	)	PUNCT
ejpam-1853	297	25	are	be	AUX
ejpam-1853	297	26	commutative	commutative	ADJ
ejpam-1853	297	27	groups	group	NOUN
ejpam-1853	297	28	.	.	PUNCT
ejpam-1853	298	1	(	(	PUNCT
ejpam-1853	298	2	a	a	X
ejpam-1853	298	3	)	)	PUNCT
ejpam-1853	298	4	we	we	PRON
ejpam-1853	298	5	prove	prove	VERB
ejpam-1853	298	6	that	that	SCONJ
ejpam-1853	298	7	(	(	PUNCT
ejpam-1853	298	8	ω	ω	NOUN
ejpam-1853	298	9	,	,	PUNCT
ejpam-1853	298	10	ω0	ω0	PROPN
ejpam-1853	298	11	)	)	PUNCT
ejpam-1853	298	12	:	:	PUNCT
ejpam-1853	298	13	(	(	PUNCT
ejpam-1853	298	14	v	v	X
ejpam-1853	298	15	×	×	PROPN
ejpam-1853	298	16	v	v	NOUN
ejpam-1853	298	17	,	,	PUNCT
ejpam-1853	298	18	v0	v0	PROPN
ejpam-1853	298	19	×	×	PROPN
ejpam-1853	298	20	v0	v0	NOUN
ejpam-1853	298	21	)	)	PUNCT
ejpam-1853	298	22	→	→	SYM
ejpam-1853	298	23	(	(	PUNCT
ejpam-1853	298	24	v	v	NOUN
ejpam-1853	298	25	,	,	PUNCT
ejpam-1853	298	26	v0	v0	NOUN
ejpam-1853	298	27	)	)	PUNCT
ejpam-1853	298	28	is	be	AUX
ejpam-1853	298	29	a	a	DET
ejpam-1853	298	30	morphism	morphism	NOUN
ejpam-1853	298	31	of	of	ADP
ejpam-1853	298	32	groupoids	groupoid	NOUN
ejpam-1853	298	33	.	.	PUNCT
ejpam-1853	299	1	since	since	SCONJ
ejpam-1853	299	2	α	α	PROPN
ejpam-1853	299	3	is	be	AUX
ejpam-1853	299	4	a	a	DET
ejpam-1853	299	5	morphism	morphism	NOUN
ejpam-1853	299	6	of	of	ADP
ejpam-1853	299	7	groups	group	NOUN
ejpam-1853	299	8	,	,	PUNCT
ejpam-1853	299	9	it	it	PRON
ejpam-1853	299	10	follows	follow	VERB
ejpam-1853	299	11	α(x	α(x	PROPN
ejpam-1853	299	12	+	+	CCONJ
ejpam-1853	299	13	y	y	NOUN
ejpam-1853	299	14	)	)	PUNCT
ejpam-1853	299	15	=	=	SYM
ejpam-1853	299	16	α(x	α(x	NOUN
ejpam-1853	299	17	)	)	PUNCT
ejpam-1853	300	1	+	+	CCONJ
ejpam-1853	300	2	α(y	α(y	NOUN
ejpam-1853	300	3	)	)	PUNCT
ejpam-1853	300	4	,	,	PUNCT
ejpam-1853	300	5	for	for	ADP
ejpam-1853	300	6	all	all	DET
ejpam-1853	300	7	x	x	SYM
ejpam-1853	300	8	,	,	PUNCT
ejpam-1853	300	9	y	y	PROPN
ejpam-1853	300	10	∈	∈	PROPN
ejpam-1853	300	11	v	v	NOUN
ejpam-1853	300	12	.	.	PUNCT
ejpam-1853	301	1	then	then	ADV
ejpam-1853	301	2	α(ω(x	α(ω(x	PROPN
ejpam-1853	301	3	,	,	PUNCT
ejpam-1853	301	4	y	y	NOUN
ejpam-1853	301	5	)	)	PUNCT
ejpam-1853	301	6	)	)	PUNCT
ejpam-1853	302	1	=	=	SYM
ejpam-1853	302	2	ω0(α(x),α(y	ω0(α(x),α(y	NOUN
ejpam-1853	302	3	)	)	PUNCT
ejpam-1853	302	4	)	)	PUNCT
ejpam-1853	302	5	,	,	PUNCT
ejpam-1853	302	6	and	and	CCONJ
ejpam-1853	302	7	it	it	PRON
ejpam-1853	302	8	follows	follow	VERB
ejpam-1853	302	9	α(ω(x	α(ω(x	PROPN
ejpam-1853	302	10	,	,	PUNCT
ejpam-1853	302	11	y	y	NOUN
ejpam-1853	302	12	)	)	PUNCT
ejpam-1853	302	13	)	)	PUNCT
ejpam-1853	303	1	=	=	PRON
ejpam-1853	303	2	ω0((α×α)(x	ω0((α×α)(x	PROPN
ejpam-1853	303	3	,	,	PUNCT
ejpam-1853	303	4	y	y	PROPN
ejpam-1853	303	5	)	)	PUNCT
ejpam-1853	303	6	)	)	PUNCT
ejpam-1853	303	7	;	;	PUNCT
ejpam-1853	303	8	i.e.	i.e.	X
ejpam-1853	303	9	,	,	PUNCT
ejpam-1853	303	10	α	α	PROPN
ejpam-1853	303	11	◦	◦	NOUN
ejpam-1853	303	12	ω	ω	NOUN
ejpam-1853	303	13	=	=	SYM
ejpam-1853	303	14	ω0	ω0	ADP
ejpam-1853	303	15	◦	◦	NOUN
ejpam-1853	303	16	(	(	PUNCT
ejpam-1853	303	17	α	α	NOUN
ejpam-1853	303	18	×	×	PROPN
ejpam-1853	303	19	α	α	NOUN
ejpam-1853	303	20	)	)	PUNCT
ejpam-1853	303	21	.	.	PUNCT
ejpam-1853	304	1	similarly	similarly	ADV
ejpam-1853	304	2	,	,	PUNCT
ejpam-1853	304	3	we	we	PRON
ejpam-1853	304	4	prove	prove	VERB
ejpam-1853	304	5	that	that	SCONJ
ejpam-1853	304	6	β	β	X
ejpam-1853	304	7	◦	◦	NOUN
ejpam-1853	304	8	ω	ω	NOUN
ejpam-1853	304	9	=	=	SYM
ejpam-1853	304	10	ω0	ω0	ADP
ejpam-1853	304	11	◦	◦	NOUN
ejpam-1853	304	12	(	(	PUNCT
ejpam-1853	304	13	β	β	X
ejpam-1853	304	14	×	×	NOUN
ejpam-1853	304	15	β	β	NOUN
ejpam-1853	304	16	)	)	PUNCT
ejpam-1853	304	17	.	.	PUNCT
ejpam-1853	305	1	hence	hence	ADV
ejpam-1853	305	2	the	the	DET
ejpam-1853	305	3	condition	condition	NOUN
ejpam-1853	305	4	(	(	PUNCT
ejpam-1853	305	5	i1	i1	PROPN
ejpam-1853	305	6	)	)	PUNCT
ejpam-1853	305	7	from	from	ADP
ejpam-1853	305	8	definition	definition	NOUN
ejpam-1853	305	9	3(i	3(i	NUM
ejpam-1853	305	10	)	)	PUNCT
ejpam-1853	305	11	is	be	AUX
ejpam-1853	305	12	satisfied	satisfied	ADJ
ejpam-1853	305	13	.	.	PUNCT
ejpam-1853	306	1	we	we	PRON
ejpam-1853	306	2	suppose	suppose	VERB
ejpam-1853	306	3	that	that	SCONJ
ejpam-1853	306	4	the	the	DET
ejpam-1853	306	5	interchange	interchange	NOUN
ejpam-1853	306	6	law	law	NOUN
ejpam-1853	306	7	(	(	PUNCT
ejpam-1853	306	8	10	10	NUM
ejpam-1853	306	9	)	)	PUNCT
ejpam-1853	306	10	holds	hold	VERB
ejpam-1853	306	11	.	.	PUNCT
ejpam-1853	307	1	then	then	ADV
ejpam-1853	307	2	,	,	PUNCT
ejpam-1853	307	3	for	for	ADP
ejpam-1853	307	4	all	all	DET
ejpam-1853	307	5	(	(	PUNCT
ejpam-1853	307	6	x	x	INTJ
ejpam-1853	307	7	,	,	PUNCT
ejpam-1853	307	8	y	y	PROPN
ejpam-1853	307	9	)	)	PUNCT
ejpam-1853	307	10	and	and	CCONJ
ejpam-1853	307	11	(	(	PUNCT
ejpam-1853	307	12	z	z	PROPN
ejpam-1853	307	13	,	,	PUNCT
ejpam-1853	307	14	t	t	PROPN
ejpam-1853	307	15	)	)	PUNCT
ejpam-1853	307	16	in	in	ADP
ejpam-1853	307	17	g(2	g(2	PROPN
ejpam-1853	307	18	)	)	PUNCT
ejpam-1853	307	19	we	we	PRON
ejpam-1853	307	20	have	have	VERB
ejpam-1853	307	21	(	(	PUNCT
ejpam-1853	307	22	x	x	X
ejpam-1853	307	23	·	·	PUNCT
ejpam-1853	307	24	y	y	X
ejpam-1853	307	25	)	)	PUNCT
ejpam-1853	308	1	+	+	CCONJ
ejpam-1853	308	2	(	(	PUNCT
ejpam-1853	308	3	z	z	NOUN
ejpam-1853	308	4	·	·	PUNCT
ejpam-1853	308	5	t	t	X
ejpam-1853	308	6	)	)	PUNCT
ejpam-1853	308	7	=	=	PUNCT
ejpam-1853	308	8	(	(	PUNCT
ejpam-1853	308	9	x	x	X
ejpam-1853	308	10	+	+	NUM
ejpam-1853	308	11	z	z	NOUN
ejpam-1853	308	12	)	)	PUNCT
ejpam-1853	308	13	·	·	PUNCT
ejpam-1853	309	1	(	(	PUNCT
ejpam-1853	309	2	y	y	PROPN
ejpam-1853	309	3	+	+	PROPN
ejpam-1853	309	4	t	t	PROPN
ejpam-1853	309	5	)	)	PUNCT
ejpam-1853	309	6	.	.	PUNCT
ejpam-1853	310	1	from	from	ADP
ejpam-1853	310	2	the	the	DET
ejpam-1853	310	3	last	last	ADJ
ejpam-1853	310	4	equality	equality	NOUN
ejpam-1853	310	5	it	it	PRON
ejpam-1853	310	6	follows	follow	VERB
ejpam-1853	310	7	m(x	m(x	PROPN
ejpam-1853	310	8	,	,	PUNCT
ejpam-1853	310	9	y)⊕m(z	y)⊕m(z	NUM
ejpam-1853	310	10	,	,	PUNCT
ejpam-1853	310	11	t	t	PROPN
ejpam-1853	310	12	)	)	PUNCT
ejpam-1853	310	13	=	=	NOUN
ejpam-1853	310	14	ω(x	ω(x	X
ejpam-1853	310	15	,	,	PUNCT
ejpam-1853	310	16	z	z	NOUN
ejpam-1853	310	17	)	)	PUNCT
ejpam-1853	310	18	·	·	PUNCT
ejpam-1853	310	19	ω(y	ω(y	PROPN
ejpam-1853	310	20	,	,	PUNCT
ejpam-1853	310	21	t	t	PROPN
ejpam-1853	310	22	)	)	PUNCT
ejpam-1853	310	23	⇒	⇒	NOUN
ejpam-1853	310	24	ω(m(x	ω(m(x	PUNCT
ejpam-1853	310	25	,	,	PUNCT
ejpam-1853	310	26	y	y	PROPN
ejpam-1853	310	27	)	)	PUNCT
ejpam-1853	310	28	,	,	PUNCT
ejpam-1853	310	29	m(z	m(z	PROPN
ejpam-1853	310	30	,	,	PUNCT
ejpam-1853	310	31	t	t	PROPN
ejpam-1853	310	32	)	)	PUNCT
ejpam-1853	310	33	)	)	PUNCT
ejpam-1853	311	1	=	=	SYM
ejpam-1853	311	2	m(ω(x	m(ω(x	PROPN
ejpam-1853	311	3	,	,	PUNCT
ejpam-1853	311	4	z	z	NOUN
ejpam-1853	311	5	)	)	PUNCT
ejpam-1853	311	6	,	,	PUNCT
ejpam-1853	311	7	(	(	PUNCT
ejpam-1853	311	8	ω(y	ω(y	PROPN
ejpam-1853	311	9	,	,	PUNCT
ejpam-1853	311	10	t	t	PROPN
ejpam-1853	311	11	)	)	PUNCT
ejpam-1853	311	12	)	)	PUNCT
ejpam-1853	311	13	.	.	PUNCT
ejpam-1853	312	1	then	then	ADV
ejpam-1853	312	2	ω(mg×g((x	ω(mg×g((x	ADJ
ejpam-1853	312	3	,	,	PUNCT
ejpam-1853	312	4	y	y	PROPN
ejpam-1853	312	5	)	)	PUNCT
ejpam-1853	312	6	,	,	PUNCT
ejpam-1853	312	7	(	(	PUNCT
ejpam-1853	312	8	z	z	X
ejpam-1853	312	9	,	,	PUNCT
ejpam-1853	312	10	t	t	PROPN
ejpam-1853	312	11	)	)	PUNCT
ejpam-1853	312	12	)	)	PUNCT
ejpam-1853	312	13	)	)	PUNCT
ejpam-1853	313	1	=	=	SYM
ejpam-1853	313	2	m(ω(x	m(ω(x	PROPN
ejpam-1853	313	3	,	,	PUNCT
ejpam-1853	313	4	z	z	NOUN
ejpam-1853	313	5	)	)	PUNCT
ejpam-1853	313	6	,	,	PUNCT
ejpam-1853	313	7	(	(	PUNCT
ejpam-1853	313	8	ω(y	ω(y	PROPN
ejpam-1853	313	9	,	,	PUNCT
ejpam-1853	313	10	t	t	PROPN
ejpam-1853	313	11	)	)	PUNCT
ejpam-1853	313	12	)	)	PUNCT
ejpam-1853	313	13	,	,	PUNCT
ejpam-1853	313	14	and	and	CCONJ
ejpam-1853	313	15	the	the	DET
ejpam-1853	313	16	condition	condition	NOUN
ejpam-1853	313	17	(	(	PUNCT
ejpam-1853	313	18	i2	i2	PROPN
ejpam-1853	313	19	)	)	PUNCT
ejpam-1853	313	20	from	from	ADP
ejpam-1853	313	21	definition	definition	NOUN
ejpam-1853	313	22	3(i	3(i	NUM
ejpam-1853	313	23	)	)	PUNCT
ejpam-1853	313	24	holds	hold	VERB
ejpam-1853	313	25	.	.	PUNCT
ejpam-1853	314	1	hence	hence	ADV
ejpam-1853	314	2	,	,	PUNCT
ejpam-1853	314	3	(	(	PUNCT
ejpam-1853	314	4	ω	ω	NOUN
ejpam-1853	314	5	,	,	PUNCT
ejpam-1853	314	6	ω0	ω0	NOUN
ejpam-1853	314	7	)	)	PUNCT
ejpam-1853	314	8	is	be	AUX
ejpam-1853	314	9	a	a	DET
ejpam-1853	314	10	groupoid	groupoid	PROPN
ejpam-1853	314	11	morphism	morphism	NOUN
ejpam-1853	314	12	.	.	PUNCT
ejpam-1853	315	1	m.	m.	PROPN
ejpam-1853	315	2	ivan	ivan	PROPN
ejpam-1853	315	3	/	/	PUNCT
ejpam-1853	315	4	eur	eur	PROPN
ejpam-1853	315	5	.	.	PUNCT
ejpam-1853	316	1	j.	j.	PROPN
ejpam-1853	316	2	pure	pure	PROPN
ejpam-1853	316	3	appl	appl	PROPN
ejpam-1853	316	4	.	.	PROPN
ejpam-1853	316	5	math	math	PROPN
ejpam-1853	316	6	,	,	PUNCT
ejpam-1853	316	7	6	6	NUM
ejpam-1853	316	8	(	(	PUNCT
ejpam-1853	316	9	2013	2013	NUM
ejpam-1853	316	10	)	)	PUNCT
ejpam-1853	316	11	,	,	PUNCT
ejpam-1853	316	12	469	469	NUM
ejpam-1853	316	13	-	-	SYM
ejpam-1853	316	14	484	484	NUM
ejpam-1853	316	15	478	478	NUM
ejpam-1853	316	16	(	(	PUNCT
ejpam-1853	316	17	b	b	X
ejpam-1853	316	18	)	)	PUNCT
ejpam-1853	316	19	we	we	PRON
ejpam-1853	316	20	prove	prove	VERB
ejpam-1853	316	21	that	that	SCONJ
ejpam-1853	316	22	(	(	PUNCT
ejpam-1853	316	23	ν	ν	NOUN
ejpam-1853	316	24	,	,	PUNCT
ejpam-1853	316	25	ν0	ν0	PROPN
ejpam-1853	316	26	)	)	PUNCT
ejpam-1853	316	27	is	be	AUX
ejpam-1853	316	28	a	a	DET
ejpam-1853	316	29	morphism	morphism	NOUN
ejpam-1853	316	30	of	of	ADP
ejpam-1853	316	31	groupoids	groupoid	NOUN
ejpam-1853	316	32	(	(	PUNCT
ejpam-1853	316	33	here	here	ADV
ejpam-1853	316	34	{	{	PUNCT
ejpam-1853	316	35	λ	λ	X
ejpam-1853	316	36	}	}	PUNCT
ejpam-1853	316	37	is	be	AUX
ejpam-1853	316	38	regarded	regard	VERB
ejpam-1853	316	39	as	as	ADP
ejpam-1853	316	40	null	null	ADJ
ejpam-1853	316	41	groupoid	groupoid	PROPN
ejpam-1853	316	42	with	with	ADP
ejpam-1853	316	43	the	the	DET
ejpam-1853	316	44	structure	structure	NOUN
ejpam-1853	316	45	functions	function	NOUN
ejpam-1853	316	46	α′0	α′0	NOUN
ejpam-1853	316	47	,	,	PUNCT
ejpam-1853	316	48	β	β	X
ejpam-1853	316	49	′0	′0	NOUN
ejpam-1853	316	50	,	,	PUNCT
ejpam-1853	316	51	ε′0	ε′0	NOUN
ejpam-1853	316	52	,	,	PUNCT
ejpam-1853	316	53	i′0	i′0	ADJ
ejpam-1853	316	54	and	and	CCONJ
ejpam-1853	316	55	multiplication	multiplication	NOUN
ejpam-1853	316	56	m′0	m′0	NOUN
ejpam-1853	316	57	)	)	PUNCT
ejpam-1853	316	58	.	.	PUNCT
ejpam-1853	317	1	since	since	SCONJ
ejpam-1853	317	2	α	α	PROPN
ejpam-1853	317	3	and	and	CCONJ
ejpam-1853	317	4	ε	ε	PROPN
ejpam-1853	317	5	are	be	AUX
ejpam-1853	317	6	group	group	NOUN
ejpam-1853	317	7	morphisms	morphism	NOUN
ejpam-1853	317	8	,	,	PUNCT
ejpam-1853	317	9	we	we	PRON
ejpam-1853	317	10	have	have	VERB
ejpam-1853	317	11	α(e	α(e	NOUN
ejpam-1853	317	12	)	)	PUNCT
ejpam-1853	318	1	=	=	SYM
ejpam-1853	318	2	e0	e0	PROPN
ejpam-1853	318	3	and	and	CCONJ
ejpam-1853	318	4	ε(e0	ε(e0	NOUN
ejpam-1853	318	5	)	)	PUNCT
ejpam-1853	318	6	=	=	SYM
ejpam-1853	318	7	e.	e.	PROPN
ejpam-1853	318	8	from	from	ADP
ejpam-1853	318	9	α(ν(λ	α(ν(λ	NOUN
ejpam-1853	318	10	)	)	PUNCT
ejpam-1853	318	11	)	)	PUNCT
ejpam-1853	319	1	=	=	SYM
ejpam-1853	319	2	α(e	α(e	PROPN
ejpam-1853	319	3	)	)	PUNCT
ejpam-1853	319	4	=	=	SYM
ejpam-1853	319	5	e0	e0	PROPN
ejpam-1853	319	6	and	and	CCONJ
ejpam-1853	319	7	ν0(λ	ν0(λ	PROPN
ejpam-1853	319	8	)	)	PUNCT
ejpam-1853	319	9	=	=	SYM
ejpam-1853	319	10	e0	e0	PROPN
ejpam-1853	319	11	,	,	PUNCT
ejpam-1853	319	12	it	it	PRON
ejpam-1853	319	13	follows	follow	VERB
ejpam-1853	319	14	α	α	NOUN
ejpam-1853	319	15	◦	◦	NOUN
ejpam-1853	319	16	ν	ν	NOUN
ejpam-1853	319	17	=	=	SYM
ejpam-1853	319	18	ν0	ν0	PROPN
ejpam-1853	319	19	◦	◦	VERB
ejpam-1853	319	20	i	i	PRON
ejpam-1853	319	21	d.	d.	PROPN
ejpam-1853	319	22	similarly	similarly	ADV
ejpam-1853	319	23	,	,	PUNCT
ejpam-1853	319	24	we	we	PRON
ejpam-1853	319	25	have	have	VERB
ejpam-1853	319	26	β	β	NOUN
ejpam-1853	319	27	◦	◦	NOUN
ejpam-1853	319	28	ν	ν	NOUN
ejpam-1853	319	29	=	=	SYM
ejpam-1853	319	30	ν0	ν0	PROPN
ejpam-1853	319	31	◦	◦	VERB
ejpam-1853	319	32	i	i	PRON
ejpam-1853	319	33	d.	d.	PROPN
ejpam-1853	319	34	also	also	ADV
ejpam-1853	319	35	,	,	PUNCT
ejpam-1853	319	36	we	we	PRON
ejpam-1853	319	37	have	have	VERB
ejpam-1853	319	38	ν(m′0(λ	ν(m′0(λ	NOUN
ejpam-1853	319	39	,	,	PUNCT
ejpam-1853	319	40	λ	λ	NOUN
ejpam-1853	319	41	)	)	PUNCT
ejpam-1853	319	42	)	)	PUNCT
ejpam-1853	320	1	=	=	SYM
ejpam-1853	320	2	ν(λ	ν(λ	NOUN
ejpam-1853	320	3	)	)	PUNCT
ejpam-1853	320	4	=	=	SYM
ejpam-1853	320	5	e	e	NOUN
ejpam-1853	320	6	and	and	CCONJ
ejpam-1853	320	7	m(ν(λ),ν(λ	m(ν(λ),ν(λ	NOUN
ejpam-1853	320	8	)	)	PUNCT
ejpam-1853	320	9	)	)	PUNCT
ejpam-1853	321	1	=	=	PUNCT
ejpam-1853	321	2	e	e	X
ejpam-1853	321	3	·	·	PUNCT
ejpam-1853	321	4	e	e	X
ejpam-1853	321	5	=	=	PUNCT
ejpam-1853	321	6	ε(α(e	ε(α(e	PROPN
ejpam-1853	321	7	)	)	PUNCT
ejpam-1853	321	8	)	)	PUNCT
ejpam-1853	321	9	·	·	PUNCT
ejpam-1853	322	1	e	e	X
ejpam-1853	322	2	=	=	PUNCT
ejpam-1853	322	3	e.	e.	PROPN
ejpam-1853	322	4	then	then	ADV
ejpam-1853	322	5	,	,	PUNCT
ejpam-1853	322	6	ν(m′0(λ	ν(m′0(λ	NOUN
ejpam-1853	322	7	,	,	PUNCT
ejpam-1853	322	8	λ	λ	NOUN
ejpam-1853	322	9	)	)	PUNCT
ejpam-1853	322	10	)	)	PUNCT
ejpam-1853	323	1	=	=	SYM
ejpam-1853	323	2	m(ν(λ),ν(λ	m(ν(λ),ν(λ	NOUN
ejpam-1853	323	3	)	)	PUNCT
ejpam-1853	323	4	)	)	PUNCT
ejpam-1853	323	5	.	.	PUNCT
ejpam-1853	324	1	hence	hence	ADV
ejpam-1853	324	2	,	,	PUNCT
ejpam-1853	324	3	(	(	PUNCT
ejpam-1853	324	4	ν	ν	X
ejpam-1853	324	5	,	,	PUNCT
ejpam-1853	324	6	ν0	ν0	PROPN
ejpam-1853	324	7	)	)	PUNCT
ejpam-1853	324	8	is	be	AUX
ejpam-1853	324	9	a	a	DET
ejpam-1853	324	10	groupoid	groupoid	PROPN
ejpam-1853	324	11	morphism	morphism	NOUN
ejpam-1853	324	12	.	.	PUNCT
ejpam-1853	325	1	(	(	PUNCT
ejpam-1853	325	2	c	c	X
ejpam-1853	325	3	)	)	PUNCT
ejpam-1853	325	4	we	we	PRON
ejpam-1853	325	5	prove	prove	VERB
ejpam-1853	325	6	that	that	SCONJ
ejpam-1853	325	7	(	(	PUNCT
ejpam-1853	325	8	σ	σ	PROPN
ejpam-1853	325	9	,	,	PUNCT
ejpam-1853	325	10	σ0	σ0	PROPN
ejpam-1853	325	11	)	)	PUNCT
ejpam-1853	325	12	is	be	AUX
ejpam-1853	325	13	a	a	DET
ejpam-1853	325	14	groupoid	groupoid	PROPN
ejpam-1853	325	15	morphism	morphism	NOUN
ejpam-1853	325	16	.	.	PUNCT
ejpam-1853	326	1	applying	apply	VERB
ejpam-1853	326	2	the	the	DET
ejpam-1853	326	3	fact	fact	NOUN
ejpam-1853	326	4	that	that	SCONJ
ejpam-1853	326	5	α	α	PROPN
ejpam-1853	326	6	is	be	AUX
ejpam-1853	326	7	group	group	NOUN
ejpam-1853	326	8	morphism	morphism	NOUN
ejpam-1853	326	9	,	,	PUNCT
ejpam-1853	326	10	we	we	PRON
ejpam-1853	326	11	have	have	VERB
ejpam-1853	326	12	α(σ(x	α(σ(x	PROPN
ejpam-1853	326	13	)	)	PUNCT
ejpam-1853	326	14	)	)	PUNCT
ejpam-1853	327	1	=	=	SYM
ejpam-1853	327	2	α(−x	α(−x	X
ejpam-1853	327	3	)	)	PUNCT
ejpam-1853	328	1	=	=	NOUN
ejpam-1853	328	2	−α(x	−α(x	NOUN
ejpam-1853	328	3	)	)	PUNCT
ejpam-1853	328	4	and	and	CCONJ
ejpam-1853	328	5	σ0(α(x	σ0(α(x	NUM
ejpam-1853	328	6	)	)	PUNCT
ejpam-1853	328	7	)	)	PUNCT
ejpam-1853	329	1	=	=	NOUN
ejpam-1853	329	2	−α(x	−α(x	NOUN
ejpam-1853	329	3	)	)	PUNCT
ejpam-1853	329	4	.	.	PUNCT
ejpam-1853	330	1	then	then	ADV
ejpam-1853	330	2	α	α	X
ejpam-1853	330	3	◦	◦	NOUN
ejpam-1853	330	4	σ	σ	NOUN
ejpam-1853	330	5	=	=	SYM
ejpam-1853	330	6	σ0	σ0	PROPN
ejpam-1853	330	7	◦	◦	NOUN
ejpam-1853	330	8	α	α	NOUN
ejpam-1853	330	9	.	.	PUNCT
ejpam-1853	331	1	similarly	similarly	ADV
ejpam-1853	331	2	,	,	PUNCT
ejpam-1853	331	3	we	we	PRON
ejpam-1853	331	4	have	have	VERB
ejpam-1853	331	5	β	β	NOUN
ejpam-1853	331	6	◦	◦	NOUN
ejpam-1853	331	7	σ	σ	NOUN
ejpam-1853	331	8	=	=	SYM
ejpam-1853	331	9	σ0	σ0	PROPN
ejpam-1853	331	10	◦	◦	NOUN
ejpam-1853	331	11	β	β	X
ejpam-1853	331	12	.	.	PUNCT
ejpam-1853	332	1	we	we	PRON
ejpam-1853	332	2	shall	shall	AUX
ejpam-1853	332	3	prove	prove	VERB
ejpam-1853	332	4	that	that	SCONJ
ejpam-1853	332	5	:	:	PUNCT
ejpam-1853	332	6	(	(	PUNCT
ejpam-1853	332	7	c1	c1	NOUN
ejpam-1853	332	8	)	)	PUNCT
ejpam-1853	332	9	−x	−x	NOUN
ejpam-1853	332	10	·	·	PUNCT
ejpam-1853	332	11	y	y	X
ejpam-1853	332	12	=	=	SYM
ejpam-1853	332	13	(	(	PUNCT
ejpam-1853	332	14	−x	−x	NOUN
ejpam-1853	332	15	)	)	PUNCT
ejpam-1853	332	16	·	·	PUNCT
ejpam-1853	332	17	(	(	PUNCT
ejpam-1853	332	18	−y	−y	NOUN
ejpam-1853	332	19	)	)	PUNCT
ejpam-1853	332	20	,	,	PUNCT
ejpam-1853	332	21	(	(	PUNCT
ejpam-1853	332	22	∀	∀	X
ejpam-1853	332	23	)	)	PUNCT
ejpam-1853	332	24	(	(	PUNCT
ejpam-1853	332	25	x	x	X
ejpam-1853	332	26	,	,	PUNCT
ejpam-1853	332	27	y	y	PROPN
ejpam-1853	332	28	)	)	PUNCT
ejpam-1853	332	29	∈	∈	PROPN
ejpam-1853	332	30	v(2	v(2	PROPN
ejpam-1853	332	31	)	)	PUNCT
ejpam-1853	332	32	.	.	PUNCT
ejpam-1853	333	1	from	from	ADP
ejpam-1853	333	2	(	(	PUNCT
ejpam-1853	333	3	x	x	INTJ
ejpam-1853	333	4	,	,	PUNCT
ejpam-1853	333	5	y	y	PROPN
ejpam-1853	333	6	)	)	PUNCT
ejpam-1853	333	7	∈	∈	PROPN
ejpam-1853	333	8	v(2	v(2	PROPN
ejpam-1853	333	9	)	)	PUNCT
ejpam-1853	333	10	we	we	PRON
ejpam-1853	333	11	have	have	VERB
ejpam-1853	333	12	β(x	β(x	NOUN
ejpam-1853	333	13	)	)	PUNCT
ejpam-1853	333	14	=	=	SYM
ejpam-1853	333	15	α(y	α(y	NOUN
ejpam-1853	333	16	)	)	PUNCT
ejpam-1853	333	17	.	.	PUNCT
ejpam-1853	334	1	then	then	ADV
ejpam-1853	334	2	β(−x	β(−x	PUNCT
ejpam-1853	334	3	)	)	PUNCT
ejpam-1853	334	4	=	=	SYM
ejpam-1853	334	5	α(−y	α(−y	NOUN
ejpam-1853	334	6	)	)	PUNCT
ejpam-1853	334	7	.	.	PUNCT
ejpam-1853	335	1	therefore	therefore	ADV
ejpam-1853	335	2	(	(	PUNCT
ejpam-1853	335	3	−x	−x	INTJ
ejpam-1853	335	4	,	,	PUNCT
ejpam-1853	335	5	−y	−y	NOUN
ejpam-1853	335	6	)	)	PUNCT
ejpam-1853	335	7	∈	∈	PROPN
ejpam-1853	335	8	v(2	v(2	PROPN
ejpam-1853	335	9	)	)	PUNCT
ejpam-1853	335	10	.	.	PUNCT
ejpam-1853	336	1	using	use	VERB
ejpam-1853	336	2	now	now	ADV
ejpam-1853	336	3	(	(	PUNCT
ejpam-1853	336	4	10	10	NUM
ejpam-1853	336	5	)	)	PUNCT
ejpam-1853	336	6	one	one	NOUN
ejpam-1853	336	7	obtains	obtain	VERB
ejpam-1853	336	8	(	(	PUNCT
ejpam-1853	336	9	c2	c2	PROPN
ejpam-1853	336	10	)	)	PUNCT
ejpam-1853	336	11	(	(	PUNCT
ejpam-1853	336	12	x	x	X
ejpam-1853	336	13	·	·	PUNCT
ejpam-1853	336	14	y	y	X
ejpam-1853	336	15	)	)	PUNCT
ejpam-1853	337	1	+	+	CCONJ
ejpam-1853	337	2	(	(	PUNCT
ejpam-1853	337	3	(	(	PUNCT
ejpam-1853	337	4	−x	−x	NOUN
ejpam-1853	337	5	)	)	PUNCT
ejpam-1853	337	6	·	·	PUNCT
ejpam-1853	337	7	(	(	PUNCT
ejpam-1853	337	8	−y	−y	NOUN
ejpam-1853	337	9	)	)	PUNCT
ejpam-1853	337	10	)	)	PUNCT
ejpam-1853	338	1	=	=	PUNCT
ejpam-1853	338	2	(	(	PUNCT
ejpam-1853	338	3	x	x	SYM
ejpam-1853	338	4	+	+	CCONJ
ejpam-1853	338	5	(	(	PUNCT
ejpam-1853	338	6	−x	−x	NOUN
ejpam-1853	338	7	)	)	PUNCT
ejpam-1853	338	8	)	)	PUNCT
ejpam-1853	338	9	·	·	PUNCT
ejpam-1853	339	1	(	(	PUNCT
ejpam-1853	339	2	y	y	NOUN
ejpam-1853	339	3	+	+	CCONJ
ejpam-1853	339	4	(	(	PUNCT
ejpam-1853	339	5	−y	−y	NOUN
ejpam-1853	339	6	)	)	PUNCT
ejpam-1853	339	7	)	)	PUNCT
ejpam-1853	339	8	and	and	CCONJ
ejpam-1853	339	9	(	(	PUNCT
ejpam-1853	339	10	c3	c3	PROPN
ejpam-1853	339	11	)	)	PUNCT
ejpam-1853	339	12	(	(	PUNCT
ejpam-1853	339	13	(	(	PUNCT
ejpam-1853	339	14	−x	−x	NOUN
ejpam-1853	339	15	)	)	PUNCT
ejpam-1853	339	16	·	·	PUNCT
ejpam-1853	339	17	(	(	PUNCT
ejpam-1853	339	18	−y	−y	NOUN
ejpam-1853	339	19	)	)	PUNCT
ejpam-1853	339	20	)	)	PUNCT
ejpam-1853	340	1	+	+	CCONJ
ejpam-1853	340	2	(	(	PUNCT
ejpam-1853	340	3	x	x	X
ejpam-1853	340	4	·	·	PUNCT
ejpam-1853	340	5	y	y	X
ejpam-1853	340	6	)	)	PUNCT
ejpam-1853	340	7	=	=	SYM
ejpam-1853	341	1	(	(	PUNCT
ejpam-1853	341	2	(	(	PUNCT
ejpam-1853	341	3	−x	−x	NOUN
ejpam-1853	341	4	)	)	PUNCT
ejpam-1853	341	5	+	+	NUM
ejpam-1853	341	6	x	x	X
ejpam-1853	341	7	)	)	PUNCT
ejpam-1853	341	8	·	·	PUNCT
ejpam-1853	341	9	(	(	PUNCT
ejpam-1853	341	10	(	(	PUNCT
ejpam-1853	341	11	−y	−y	NOUN
ejpam-1853	341	12	)	)	PUNCT
ejpam-1853	341	13	+	+	NOUN
ejpam-1853	341	14	y	y	NOUN
ejpam-1853	341	15	)	)	PUNCT
ejpam-1853	341	16	.	.	PUNCT
ejpam-1853	342	1	since	since	SCONJ
ejpam-1853	342	2	a+	a+	PRON
ejpam-1853	342	3	(	(	PUNCT
ejpam-1853	342	4	−a	−a	NOUN
ejpam-1853	342	5	)	)	PUNCT
ejpam-1853	342	6	=	=	PUNCT
ejpam-1853	342	7	(	(	PUNCT
ejpam-1853	342	8	−a	−a	ADV
ejpam-1853	342	9	)	)	PUNCT
ejpam-1853	343	1	+	+	CCONJ
ejpam-1853	343	2	a	a	DET
ejpam-1853	343	3	=	=	SYM
ejpam-1853	343	4	e	e	NOUN
ejpam-1853	343	5	,	,	PUNCT
ejpam-1853	343	6	and	and	CCONJ
ejpam-1853	343	7	e	e	X
ejpam-1853	343	8	·	·	PUNCT
ejpam-1853	343	9	e	e	X
ejpam-1853	343	10	=	=	SYM
ejpam-1853	343	11	e	e	PROPN
ejpam-1853	343	12	,	,	PUNCT
ejpam-1853	343	13	from	from	ADP
ejpam-1853	343	14	(	(	PUNCT
ejpam-1853	343	15	c2	c2	PROPN
ejpam-1853	343	16	)	)	PUNCT
ejpam-1853	343	17	and	and	CCONJ
ejpam-1853	343	18	(	(	PUNCT
ejpam-1853	343	19	c3	c3	PROPN
ejpam-1853	343	20	)	)	PUNCT
ejpam-1853	343	21	,	,	PUNCT
ejpam-1853	343	22	we	we	PRON
ejpam-1853	343	23	have	have	VERB
ejpam-1853	343	24	(	(	PUNCT
ejpam-1853	343	25	c4	c4	NOUN
ejpam-1853	343	26	)	)	PUNCT
ejpam-1853	343	27	(	(	PUNCT
ejpam-1853	343	28	x	x	X
ejpam-1853	343	29	·	·	PUNCT
ejpam-1853	343	30	y	y	X
ejpam-1853	343	31	)	)	PUNCT
ejpam-1853	344	1	+	+	CCONJ
ejpam-1853	344	2	(	(	PUNCT
ejpam-1853	344	3	(	(	PUNCT
ejpam-1853	344	4	−x	−x	NOUN
ejpam-1853	344	5	)	)	PUNCT
ejpam-1853	344	6	·	·	PUNCT
ejpam-1853	344	7	(	(	PUNCT
ejpam-1853	344	8	−y	−y	NOUN
ejpam-1853	344	9	)	)	PUNCT
ejpam-1853	344	10	)	)	PUNCT
ejpam-1853	345	1	=	=	SYM
ejpam-1853	345	2	e	e	NOUN
ejpam-1853	345	3	and	and	CCONJ
ejpam-1853	345	4	(	(	PUNCT
ejpam-1853	345	5	(	(	PUNCT
ejpam-1853	345	6	−x	−x	NOUN
ejpam-1853	345	7	)	)	PUNCT
ejpam-1853	345	8	·	·	PUNCT
ejpam-1853	345	9	(	(	PUNCT
ejpam-1853	345	10	−y	−y	NOUN
ejpam-1853	345	11	)	)	PUNCT
ejpam-1853	345	12	)	)	PUNCT
ejpam-1853	346	1	+	+	CCONJ
ejpam-1853	347	1	(	(	PUNCT
ejpam-1853	347	2	x	x	X
ejpam-1853	347	3	·	·	PUNCT
ejpam-1853	347	4	y	y	X
ejpam-1853	347	5	)	)	PUNCT
ejpam-1853	347	6	=	=	SYM
ejpam-1853	348	1	e.	e.	PROPN
ejpam-1853	348	2	from	from	ADP
ejpam-1853	348	3	(	(	PUNCT
ejpam-1853	348	4	c4	c4	NOUN
ejpam-1853	348	5	)	)	PUNCT
ejpam-1853	348	6	one	one	NOUN
ejpam-1853	348	7	obtains	obtain	VERB
ejpam-1853	348	8	that	that	SCONJ
ejpam-1853	348	9	the	the	DET
ejpam-1853	348	10	equality	equality	NOUN
ejpam-1853	348	11	(	(	PUNCT
ejpam-1853	348	12	c1	c1	NOUN
ejpam-1853	348	13	)	)	PUNCT
ejpam-1853	348	14	holds	hold	VERB
ejpam-1853	348	15	.	.	PUNCT
ejpam-1853	349	1	the	the	DET
ejpam-1853	349	2	relation	relation	NOUN
ejpam-1853	349	3	(	(	PUNCT
ejpam-1853	349	4	c1	c1	PROPN
ejpam-1853	349	5	)	)	PUNCT
ejpam-1853	349	6	is	be	AUX
ejpam-1853	349	7	equivalently	equivalently	ADV
ejpam-1853	349	8	with	with	ADP
ejpam-1853	350	1	σ(x	σ(x	PROPN
ejpam-1853	350	2	·	·	PUNCT
ejpam-1853	350	3	y	y	X
ejpam-1853	350	4	)	)	PUNCT
ejpam-1853	350	5	=	=	SYM
ejpam-1853	350	6	si	si	X
ejpam-1853	350	7	gma(x	gma(x	PROPN
ejpam-1853	350	8	)	)	PUNCT
ejpam-1853	350	9	·	·	PUNCT
ejpam-1853	350	10	σ(y	σ(y	NOUN
ejpam-1853	350	11	)	)	PUNCT
ejpam-1853	350	12	.	.	PUNCT
ejpam-1853	351	1	then	then	ADV
ejpam-1853	351	2	σ(m(x	σ(m(x	PROPN
ejpam-1853	351	3	,	,	PUNCT
ejpam-1853	351	4	y	y	NOUN
ejpam-1853	351	5	)	)	PUNCT
ejpam-1853	351	6	)	)	PUNCT
ejpam-1853	352	1	=	=	SYM
ejpam-1853	352	2	m(σ(x),σ(y	m(σ(x),σ(y	PROPN
ejpam-1853	352	3	)	)	PUNCT
ejpam-1853	352	4	)	)	PUNCT
ejpam-1853	352	5	.	.	PUNCT
ejpam-1853	353	1	hence	hence	ADV
ejpam-1853	353	2	,	,	PUNCT
ejpam-1853	353	3	(	(	PUNCT
ejpam-1853	353	4	σ	σ	PROPN
ejpam-1853	353	5	,	,	PUNCT
ejpam-1853	353	6	σ0	σ0	PROPN
ejpam-1853	353	7	)	)	PUNCT
ejpam-1853	353	8	is	be	AUX
ejpam-1853	353	9	a	a	DET
ejpam-1853	353	10	groupoid	groupoid	PROPN
ejpam-1853	353	11	morphism	morphism	NOUN
ejpam-1853	353	12	.	.	PUNCT
ejpam-1853	354	1	therefore	therefore	ADV
ejpam-1853	354	2	,	,	PUNCT
ejpam-1853	354	3	(	(	PUNCT
ejpam-1853	354	4	v	v	NOUN
ejpam-1853	354	5	,	,	PUNCT
ejpam-1853	354	6	α	α	NOUN
ejpam-1853	354	7	,	,	PUNCT
ejpam-1853	354	8	β	β	X
ejpam-1853	354	9	,	,	PUNCT
ejpam-1853	354	10	m	m	PROPN
ejpam-1853	354	11	,	,	PUNCT
ejpam-1853	354	12	ε	ε	PROPN
ejpam-1853	354	13	,	,	PUNCT
ejpam-1853	354	14	i,+	i,+	PRON
ejpam-1853	354	15	,	,	PUNCT
ejpam-1853	354	16	v0	v0	NOUN
ejpam-1853	354	17	)	)	PUNCT
ejpam-1853	354	18	is	be	AUX
ejpam-1853	354	19	a	a	DET
ejpam-1853	354	20	commutative	commutative	ADJ
ejpam-1853	354	21	group	group	NOUN
ejpam-1853	354	22	-	-	PUNCT
ejpam-1853	354	23	groupoid	groupoid	PROPN
ejpam-1853	354	24	and	and	CCONJ
ejpam-1853	354	25	the	the	DET
ejpam-1853	354	26	condition	condition	NOUN
ejpam-1853	354	27	(	(	PUNCT
ejpam-1853	354	28	5.2	5.2	NUM
ejpam-1853	354	29	)	)	PUNCT
ejpam-1853	354	30	from	from	ADP
ejpam-1853	354	31	definition	definition	NOUN
ejpam-1853	354	32	5	5	NUM
ejpam-1853	354	33	holds	hold	NOUN
ejpam-1853	354	34	.	.	PUNCT
ejpam-1853	355	1	we	we	PRON
ejpam-1853	355	2	shall	shall	AUX
ejpam-1853	355	3	prove	prove	VERB
ejpam-1853	355	4	that	that	SCONJ
ejpam-1853	355	5	(	(	PUNCT
ejpam-1853	355	6	ϕ,ϕ0	ϕ,ϕ0	NOUN
ejpam-1853	355	7	)	)	PUNCT
ejpam-1853	355	8	:	:	PUNCT
ejpam-1853	355	9	(	(	PUNCT
ejpam-1853	355	10	k	k	X
ejpam-1853	355	11	×	×	PROPN
ejpam-1853	355	12	v	v	NOUN
ejpam-1853	355	13	,	,	PUNCT
ejpam-1853	355	14	k	k	PROPN
ejpam-1853	355	15	×	×	PROPN
ejpam-1853	355	16	v0)→	v0)→	INTJ
ejpam-1853	355	17	(	(	PUNCT
ejpam-1853	355	18	v	v	NOUN
ejpam-1853	355	19	,	,	PUNCT
ejpam-1853	355	20	v0	v0	NOUN
ejpam-1853	355	21	)	)	PUNCT
ejpam-1853	355	22	is	be	AUX
ejpam-1853	355	23	a	a	DET
ejpam-1853	355	24	groupoid	groupoid	PROPN
ejpam-1853	355	25	morphism	morphism	NOUN
ejpam-1853	355	26	.	.	PUNCT
ejpam-1853	356	1	applying	apply	VERB
ejpam-1853	356	2	the	the	DET
ejpam-1853	356	3	fact	fact	NOUN
ejpam-1853	356	4	that	that	SCONJ
ejpam-1853	356	5	α	α	PRON
ejpam-1853	356	6	is	be	AUX
ejpam-1853	356	7	a	a	DET
ejpam-1853	356	8	linear	linear	ADJ
ejpam-1853	356	9	map	map	NOUN
ejpam-1853	356	10	,	,	PUNCT
ejpam-1853	356	11	for	for	ADP
ejpam-1853	356	12	all	all	DET
ejpam-1853	356	13	x	x	SYM
ejpam-1853	356	14	∈	∈	PROPN
ejpam-1853	356	15	v	v	NOUN
ejpam-1853	356	16	and	and	CCONJ
ejpam-1853	356	17	k	k	PROPN
ejpam-1853	356	18	∈	∈	PROPN
ejpam-1853	357	1	k	k	X
ejpam-1853	357	2	we	we	PRON
ejpam-1853	357	3	have	have	VERB
ejpam-1853	357	4	α(ϕ(k	α(ϕ(k	PROPN
ejpam-1853	357	5	,	,	PUNCT
ejpam-1853	357	6	x	x	NOUN
ejpam-1853	357	7	)	)	PUNCT
ejpam-1853	357	8	)	)	PUNCT
ejpam-1853	358	1	=	=	SYM
ejpam-1853	358	2	α(kx	α(kx	PROPN
ejpam-1853	358	3	)	)	PUNCT
ejpam-1853	358	4	=	=	SYM
ejpam-1853	358	5	kα(x	kα(x	X
ejpam-1853	358	6	)	)	PUNCT
ejpam-1853	358	7	and	and	CCONJ
ejpam-1853	358	8	ϕ0((id	ϕ0((id	NUM
ejpam-1853	358	9	×α)(k	×α)(k	NOUN
ejpam-1853	358	10	,	,	PUNCT
ejpam-1853	358	11	x	x	NOUN
ejpam-1853	358	12	)	)	PUNCT
ejpam-1853	358	13	)	)	PUNCT
ejpam-1853	359	1	=	=	SYM
ejpam-1853	359	2	ϕ0(k	ϕ0(k	PROPN
ejpam-1853	359	3	,	,	PUNCT
ejpam-1853	359	4	α(x	α(x	NOUN
ejpam-1853	359	5	)	)	PUNCT
ejpam-1853	359	6	)	)	PUNCT
ejpam-1853	360	1	=	=	SYM
ejpam-1853	360	2	kα(x	kα(x	PROPN
ejpam-1853	360	3	)	)	PUNCT
ejpam-1853	360	4	.	.	PUNCT
ejpam-1853	361	1	then	then	ADV
ejpam-1853	361	2	α	α	X
ejpam-1853	361	3	◦	◦	NOUN
ejpam-1853	361	4	ϕ	ϕ	NOUN
ejpam-1853	361	5	=	=	SYM
ejpam-1853	361	6	ϕ0	ϕ0	NOUN
ejpam-1853	361	7	◦	◦	NOUN
ejpam-1853	361	8	(	(	PUNCT
ejpam-1853	361	9	i	i	NOUN
ejpam-1853	361	10	d	d	PROPN
ejpam-1853	361	11	×α	×α	PROPN
ejpam-1853	361	12	)	)	PUNCT
ejpam-1853	361	13	.	.	PUNCT
ejpam-1853	362	1	similarly	similarly	ADV
ejpam-1853	362	2	,	,	PUNCT
ejpam-1853	362	3	we	we	PRON
ejpam-1853	362	4	have	have	VERB
ejpam-1853	362	5	β	β	X
ejpam-1853	362	6	◦	◦	NOUN
ejpam-1853	362	7	ϕ	ϕ	NOUN
ejpam-1853	362	8	=	=	SYM
ejpam-1853	362	9	ϕ0	ϕ0	NOUN
ejpam-1853	362	10	◦	◦	NOUN
ejpam-1853	362	11	(	(	PUNCT
ejpam-1853	362	12	i	i	NOUN
ejpam-1853	362	13	d	d	PROPN
ejpam-1853	362	14	×	×	PROPN
ejpam-1853	362	15	β	β	NOUN
ejpam-1853	362	16	)	)	PUNCT
ejpam-1853	362	17	.	.	PUNCT
ejpam-1853	363	1	we	we	PRON
ejpam-1853	363	2	consider	consider	VERB
ejpam-1853	363	3	x	x	PRON
ejpam-1853	363	4	,	,	PUNCT
ejpam-1853	363	5	y	y	PROPN
ejpam-1853	363	6	∈	∈	PROPN
ejpam-1853	363	7	v	v	ADP
ejpam-1853	363	8	such	such	ADJ
ejpam-1853	363	9	that	that	SCONJ
ejpam-1853	363	10	(	(	PUNCT
ejpam-1853	363	11	x	x	X
ejpam-1853	363	12	,	,	PUNCT
ejpam-1853	363	13	y	y	PROPN
ejpam-1853	363	14	)	)	PUNCT
ejpam-1853	363	15	∈	∈	PROPN
ejpam-1853	363	16	v(2	v(2	PROPN
ejpam-1853	363	17	)	)	PUNCT
ejpam-1853	363	18	.	.	PUNCT
ejpam-1853	364	1	we	we	PRON
ejpam-1853	364	2	have	have	VERB
ejpam-1853	364	3	also	also	ADV
ejpam-1853	364	4	(	(	PUNCT
ejpam-1853	364	5	kx	kx	PROPN
ejpam-1853	364	6	,	,	PUNCT
ejpam-1853	364	7	k	k	PROPN
ejpam-1853	364	8	y	y	X
ejpam-1853	364	9	)	)	PUNCT
ejpam-1853	364	10	∈	∈	PROPN
ejpam-1853	364	11	v2	v2	PROPN
ejpam-1853	364	12	.	.	PUNCT
ejpam-1853	365	1	indeed	indeed	ADV
ejpam-1853	365	2	,	,	PUNCT
ejpam-1853	365	3	using	use	VERB
ejpam-1853	365	4	the	the	DET
ejpam-1853	365	5	linearity	linearity	NOUN
ejpam-1853	365	6	of	of	ADP
ejpam-1853	365	7	α	α	PROPN
ejpam-1853	365	8	and	and	CCONJ
ejpam-1853	365	9	β	β	X
ejpam-1853	365	10	,	,	PUNCT
ejpam-1853	365	11	from	from	ADP
ejpam-1853	365	12	β(x	β(x	NOUN
ejpam-1853	365	13	)	)	PUNCT
ejpam-1853	365	14	=	=	SYM
ejpam-1853	365	15	α(y	α(y	NOUN
ejpam-1853	365	16	)	)	PUNCT
ejpam-1853	365	17	follows	follow	VERB
ejpam-1853	365	18	β(kx	β(kx	NOUN
ejpam-1853	365	19	)	)	PUNCT
ejpam-1853	365	20	=	=	PUNCT
ejpam-1853	366	1	α(k	α(k	PROPN
ejpam-1853	366	2	y	y	NOUN
ejpam-1853	366	3	)	)	PUNCT
ejpam-1853	366	4	.	.	PUNCT
ejpam-1853	367	1	applying	apply	VERB
ejpam-1853	367	2	now	now	ADV
ejpam-1853	367	3	the	the	DET
ejpam-1853	367	4	relation	relation	NOUN
ejpam-1853	367	5	(	(	PUNCT
ejpam-1853	367	6	16	16	NUM
ejpam-1853	367	7	)	)	PUNCT
ejpam-1853	367	8	,	,	PUNCT
ejpam-1853	367	9	linearity	linearity	NOUN
ejpam-1853	367	10	of	of	ADP
ejpam-1853	367	11	ε	ε	PROPN
ejpam-1853	367	12	and	and	CCONJ
ejpam-1853	367	13	β	β	PROPN
ejpam-1853	367	14	and	and	CCONJ
ejpam-1853	367	15	the	the	DET
ejpam-1853	367	16	fact	fact	NOUN
ejpam-1853	367	17	that	that	SCONJ
ejpam-1853	367	18	v	v	NOUN
ejpam-1853	367	19	is	be	AUX
ejpam-1853	367	20	a	a	DET
ejpam-1853	367	21	vector	vector	NOUN
ejpam-1853	367	22	space	space	NOUN
ejpam-1853	367	23	,	,	PUNCT
ejpam-1853	367	24	we	we	PRON
ejpam-1853	367	25	have	have	VERB
ejpam-1853	367	26	k(x	k(x	PROPN
ejpam-1853	367	27	·	·	PUNCT
ejpam-1853	367	28	y	y	X
ejpam-1853	367	29	)	)	PUNCT
ejpam-1853	367	30	=	=	SYM
ejpam-1853	368	1	k(x	k(x	PROPN
ejpam-1853	368	2	+	+	CCONJ
ejpam-1853	368	3	y	y	PROPN
ejpam-1853	368	4	−	−	NOUN
ejpam-1853	368	5	ε(β(x	ε(β(x	NOUN
ejpam-1853	368	6	)	)	PUNCT
ejpam-1853	368	7	)	)	PUNCT
ejpam-1853	368	8	)	)	PUNCT
ejpam-1853	369	1	=	=	PUNCT
ejpam-1853	369	2	kx	kx	PROPN
ejpam-1853	370	1	+	+	CCONJ
ejpam-1853	370	2	k	k	PROPN
ejpam-1853	370	3	y	y	PROPN
ejpam-1853	370	4	−	−	PROPN
ejpam-1853	370	5	kε(β(x	kε(β(x	NOUN
ejpam-1853	370	6	)	)	PUNCT
ejpam-1853	370	7	)	)	PUNCT
ejpam-1853	371	1	and	and	CCONJ
ejpam-1853	371	2	(	(	PUNCT
ejpam-1853	371	3	kx	kx	PROPN
ejpam-1853	371	4	)	)	PUNCT
ejpam-1853	371	5	·	·	PUNCT
ejpam-1853	372	1	(	(	PUNCT
ejpam-1853	372	2	k	k	NOUN
ejpam-1853	372	3	y	y	PROPN
ejpam-1853	372	4	)	)	PUNCT
ejpam-1853	373	1	=	=	SYM
ejpam-1853	373	2	kx	kx	PROPN
ejpam-1853	374	1	+	+	CCONJ
ejpam-1853	374	2	k	k	PROPN
ejpam-1853	374	3	y	y	PROPN
ejpam-1853	374	4	−	−	PROPN
ejpam-1853	374	5	ε(β(kx	ε(β(kx	PROPN
ejpam-1853	374	6	)	)	PUNCT
ejpam-1853	374	7	)	)	PUNCT
ejpam-1853	374	8	)	)	PUNCT
ejpam-1853	375	1	=	=	PUNCT
ejpam-1853	375	2	kx	kx	PROPN
ejpam-1853	376	1	+	+	CCONJ
ejpam-1853	376	2	k	k	PROPN
ejpam-1853	376	3	y	y	PROPN
ejpam-1853	376	4	−	−	PROPN
ejpam-1853	376	5	kε(β(x	kε(β(x	NOUN
ejpam-1853	376	6	)	)	PUNCT
ejpam-1853	376	7	)	)	PUNCT
ejpam-1853	376	8	.	.	PUNCT
ejpam-1853	377	1	then	then	ADV
ejpam-1853	377	2	k(x	k(x	PROPN
ejpam-1853	377	3	·	·	PUNCT
ejpam-1853	377	4	y	y	X
ejpam-1853	377	5	)	)	PUNCT
ejpam-1853	377	6	=	=	SYM
ejpam-1853	377	7	(	(	PUNCT
ejpam-1853	377	8	kx	kx	PROPN
ejpam-1853	377	9	)	)	PUNCT
ejpam-1853	377	10	·	·	PUNCT
ejpam-1853	377	11	(	(	PUNCT
ejpam-1853	377	12	k	k	NOUN
ejpam-1853	377	13	y	y	PROPN
ejpam-1853	377	14	)	)	PUNCT
ejpam-1853	377	15	,	,	PUNCT
ejpam-1853	377	16	for	for	ADP
ejpam-1853	377	17	all	all	DET
ejpam-1853	377	18	(	(	PUNCT
ejpam-1853	377	19	x	x	INTJ
ejpam-1853	377	20	,	,	PUNCT
ejpam-1853	377	21	y	y	PROPN
ejpam-1853	377	22	)	)	PUNCT
ejpam-1853	377	23	∈	∈	PROPN
ejpam-1853	377	24	v(2	v(2	PROPN
ejpam-1853	377	25	)	)	PUNCT
ejpam-1853	377	26	and	and	CCONJ
ejpam-1853	377	27	k	k	PROPN
ejpam-1853	377	28	∈	∈	PROPN
ejpam-1853	377	29	k	k	NOUN
ejpam-1853	377	30	;	;	PUNCT
ejpam-1853	377	31	i.e.	i.e.	X
ejpam-1853	377	32	the	the	DET
ejpam-1853	377	33	interchange	interchange	NOUN
ejpam-1853	377	34	law	law	NOUN
ejpam-1853	377	35	(	(	PUNCT
ejpam-1853	377	36	11	11	NUM
ejpam-1853	377	37	)	)	PUNCT
ejpam-1853	377	38	holds	hold	VERB
ejpam-1853	377	39	.	.	PUNCT
ejpam-1853	378	1	from	from	ADP
ejpam-1853	378	2	(	(	PUNCT
ejpam-1853	378	3	11	11	NUM
ejpam-1853	378	4	)	)	PUNCT
ejpam-1853	378	5	it	it	PRON
ejpam-1853	378	6	follows	follow	VERB
ejpam-1853	378	7	ϕ(k	ϕ(k	PROPN
ejpam-1853	378	8	,	,	PUNCT
ejpam-1853	378	9	m(x	m(x	PROPN
ejpam-1853	378	10	,	,	PUNCT
ejpam-1853	378	11	y	y	PROPN
ejpam-1853	378	12	)	)	PUNCT
ejpam-1853	378	13	)	)	PUNCT
ejpam-1853	379	1	=	=	SYM
ejpam-1853	379	2	ϕ(k	ϕ(k	X
ejpam-1853	379	3	,	,	PUNCT
ejpam-1853	379	4	x	x	NOUN
ejpam-1853	379	5	)	)	PUNCT
ejpam-1853	379	6	·	·	PUNCT
ejpam-1853	379	7	ϕ(k	ϕ(k	PROPN
ejpam-1853	379	8	,	,	PUNCT
ejpam-1853	379	9	y	y	NOUN
ejpam-1853	379	10	)	)	PUNCT
ejpam-1853	379	11	⇒	⇒	VERB
ejpam-1853	379	12	ϕ((id	ϕ((id	PROPN
ejpam-1853	379	13	×m)((k	×m)((k	NOUN
ejpam-1853	379	14	,	,	PUNCT
ejpam-1853	379	15	x	x	NOUN
ejpam-1853	379	16	)	)	PUNCT
ejpam-1853	379	17	,	,	PUNCT
ejpam-1853	379	18	(	(	PUNCT
ejpam-1853	379	19	k	k	X
ejpam-1853	379	20	,	,	PUNCT
ejpam-1853	379	21	y	y	NOUN
ejpam-1853	379	22	)	)	PUNCT
ejpam-1853	379	23	)	)	PUNCT
ejpam-1853	379	24	)	)	PUNCT
ejpam-1853	380	1	=	=	PUNCT
ejpam-1853	380	2	m(ϕ(k	m(ϕ(k	PROPN
ejpam-1853	380	3	,	,	PUNCT
ejpam-1853	380	4	x),ϕ(k	x),ϕ(k	PROPN
ejpam-1853	380	5	,	,	PUNCT
ejpam-1853	380	6	y	y	NOUN
ejpam-1853	380	7	)	)	PUNCT
ejpam-1853	380	8	)	)	PUNCT
ejpam-1853	380	9	.	.	PUNCT
ejpam-1853	381	1	therefore	therefore	ADV
ejpam-1853	381	2	,	,	PUNCT
ejpam-1853	381	3	(	(	PUNCT
ejpam-1853	381	4	ϕ,ϕ0	ϕ,ϕ0	NOUN
ejpam-1853	381	5	)	)	PUNCT
ejpam-1853	381	6	is	be	AUX
ejpam-1853	381	7	a	a	DET
ejpam-1853	381	8	groupoid	groupoid	PROPN
ejpam-1853	381	9	morphism	morphism	NOUN
ejpam-1853	381	10	.	.	PUNCT
ejpam-1853	382	1	hence	hence	ADV
ejpam-1853	382	2	,	,	PUNCT
ejpam-1853	382	3	(	(	PUNCT
ejpam-1853	382	4	v	v	NOUN
ejpam-1853	382	5	,	,	PUNCT
ejpam-1853	382	6	α	α	NOUN
ejpam-1853	382	7	,	,	PUNCT
ejpam-1853	382	8	β	β	X
ejpam-1853	382	9	,	,	PUNCT
ejpam-1853	382	10	m	m	PROPN
ejpam-1853	382	11	,	,	PUNCT
ejpam-1853	382	12	ε	ε	PROPN
ejpam-1853	382	13	,	,	PUNCT
ejpam-1853	382	14	i,+,ϕ	i,+,ϕ	NOUN
ejpam-1853	382	15	,	,	PUNCT
ejpam-1853	382	16	v0	v0	PROPN
ejpam-1853	382	17	)	)	PUNCT
ejpam-1853	382	18	is	be	AUX
ejpam-1853	382	19	vector	vector	NOUN
ejpam-1853	382	20	space	space	NOUN
ejpam-1853	382	21	-	-	PUNCT
ejpam-1853	382	22	groupoid	groupoid	PROPN
ejpam-1853	382	23	.	.	PUNCT
ejpam-1853	383	1	m.	m.	PROPN
ejpam-1853	383	2	ivan	ivan	PROPN
ejpam-1853	383	3	/	/	PUNCT
ejpam-1853	383	4	eur	eur	PROPN
ejpam-1853	383	5	.	.	PUNCT
ejpam-1853	384	1	j.	j.	PROPN
ejpam-1853	384	2	pure	pure	PROPN
ejpam-1853	384	3	appl	appl	PROPN
ejpam-1853	384	4	.	.	PROPN
ejpam-1853	384	5	math	math	PROPN
ejpam-1853	384	6	,	,	PUNCT
ejpam-1853	384	7	6	6	NUM
ejpam-1853	384	8	(	(	PUNCT
ejpam-1853	384	9	2013	2013	NUM
ejpam-1853	384	10	)	)	PUNCT
ejpam-1853	384	11	,	,	PUNCT
ejpam-1853	384	12	469	469	NUM
ejpam-1853	384	13	-	-	SYM
ejpam-1853	384	14	484	484	NUM
ejpam-1853	384	15	479	479	NUM
ejpam-1853	384	16	according	accord	VERB
ejpam-1853	384	17	to	to	ADP
ejpam-1853	384	18	theorems	theorem	NOUN
ejpam-1853	384	19	5	5	NUM
ejpam-1853	384	20	and	and	CCONJ
ejpam-1853	384	21	6	6	NUM
ejpam-1853	384	22	,	,	PUNCT
ejpam-1853	384	23	we	we	PRON
ejpam-1853	384	24	can	can	AUX
ejpam-1853	384	25	give	give	VERB
ejpam-1853	384	26	another	another	DET
ejpam-1853	384	27	definition	definition	NOUN
ejpam-1853	384	28	for	for	ADP
ejpam-1853	384	29	the	the	DET
ejpam-1853	384	30	notion	notion	NOUN
ejpam-1853	384	31	of	of	ADP
ejpam-1853	384	32	vector	vector	NOUN
ejpam-1853	384	33	space	space	NOUN
ejpam-1853	384	34	-	-	PUNCT
ejpam-1853	384	35	groupoid	groupoid	NOUN
ejpam-1853	384	36	(	(	PUNCT
ejpam-1853	384	37	this	this	PRON
ejpam-1853	384	38	is	be	AUX
ejpam-1853	384	39	equivalent	equivalent	ADJ
ejpam-1853	384	40	with	with	ADP
ejpam-1853	384	41	definition	definition	NOUN
ejpam-1853	384	42	5	5	NUM
ejpam-1853	384	43	)	)	PUNCT
ejpam-1853	384	44	.	.	PUNCT
ejpam-1853	385	1	definition	definition	NOUN
ejpam-1853	385	2	6	6	NUM
ejpam-1853	385	3	.	.	PUNCT
ejpam-1853	386	1	a	a	DET
ejpam-1853	386	2	vector	vector	NOUN
ejpam-1853	386	3	space	space	NOUN
ejpam-1853	386	4	-	-	PUNCT
ejpam-1853	386	5	groupoid	groupoid	PROPN
ejpam-1853	386	6	is	be	AUX
ejpam-1853	386	7	a	a	DET
ejpam-1853	386	8	groupoid	groupoid	NOUN
ejpam-1853	386	9	(	(	PUNCT
ejpam-1853	386	10	v	v	NOUN
ejpam-1853	386	11	,	,	PUNCT
ejpam-1853	386	12	α	α	NOUN
ejpam-1853	386	13	,	,	PUNCT
ejpam-1853	386	14	β	β	X
ejpam-1853	386	15	,	,	PUNCT
ejpam-1853	386	16	m	m	PROPN
ejpam-1853	386	17	,	,	PUNCT
ejpam-1853	386	18	ε	ε	PROPN
ejpam-1853	386	19	,	,	PUNCT
ejpam-1853	386	20	i	i	PROPN
ejpam-1853	386	21	,	,	PUNCT
ejpam-1853	386	22	v0	v0	PROPN
ejpam-1853	386	23	)	)	PUNCT
ejpam-1853	386	24	such	such	ADJ
ejpam-1853	386	25	that	that	SCONJ
ejpam-1853	386	26	the	the	DET
ejpam-1853	386	27	following	follow	VERB
ejpam-1853	386	28	conditions	condition	NOUN
ejpam-1853	386	29	are	be	AUX
ejpam-1853	386	30	satisfied	satisfied	ADJ
ejpam-1853	386	31	:	:	PUNCT
ejpam-1853	386	32	(	(	PUNCT
ejpam-1853	386	33	i	i	NOUN
ejpam-1853	386	34	)	)	PUNCT
ejpam-1853	386	35	(	(	PUNCT
ejpam-1853	386	36	v,+,ϕ	v,+,ϕ	PROPN
ejpam-1853	386	37	)	)	PUNCT
ejpam-1853	386	38	and	and	CCONJ
ejpam-1853	386	39	(	(	PUNCT
ejpam-1853	386	40	v0,+,ϕ0	v0,+,ϕ0	NOUN
ejpam-1853	386	41	)	)	PUNCT
ejpam-1853	386	42	are	be	AUX
ejpam-1853	386	43	vector	vector	NOUN
ejpam-1853	386	44	spaces	space	NOUN
ejpam-1853	386	45	;	;	PUNCT
ejpam-1853	386	46	(	(	PUNCT
ejpam-1853	386	47	ii	ii	X
ejpam-1853	386	48	)	)	PUNCT
ejpam-1853	386	49	α	α	PROPN
ejpam-1853	386	50	,	,	PUNCT
ejpam-1853	386	51	β	β	X
ejpam-1853	386	52	:	:	PUNCT
ejpam-1853	386	53	v	v	X
ejpam-1853	386	54	→	→	SYM
ejpam-1853	386	55	v0	v0	NOUN
ejpam-1853	386	56	,	,	PUNCT
ejpam-1853	386	57	ε	ε	PROPN
ejpam-1853	386	58	:	:	PUNCT
ejpam-1853	386	59	v0→	v0→	VERB
ejpam-1853	386	60	v	v	NOUN
ejpam-1853	387	1	and	and	CCONJ
ejpam-1853	387	2	i	i	PRON
ejpam-1853	387	3	:	:	PUNCT
ejpam-1853	387	4	v	v	X
ejpam-1853	387	5	→	→	SYM
ejpam-1853	387	6	v	v	NUM
ejpam-1853	387	7	are	be	AUX
ejpam-1853	387	8	linear	linear	ADJ
ejpam-1853	387	9	maps	map	NOUN
ejpam-1853	387	10	;	;	PUNCT
ejpam-1853	387	11	(	(	PUNCT
ejpam-1853	387	12	iii	iii	X
ejpam-1853	387	13	)	)	PUNCT
ejpam-1853	387	14	the	the	DET
ejpam-1853	387	15	interchange	interchange	NOUN
ejpam-1853	387	16	law	law	NOUN
ejpam-1853	387	17	(	(	PUNCT
ejpam-1853	387	18	10	10	NUM
ejpam-1853	387	19	)	)	PUNCT
ejpam-1853	387	20	between	between	ADP
ejpam-1853	387	21	the	the	DET
ejpam-1853	387	22	operations	operation	NOUN
ejpam-1853	387	23	m	m	VERB
ejpam-1853	387	24	and	and	CCONJ
ejpam-1853	387	25	ω	ω	NUM
ejpam-1853	387	26	holds	hold	VERB
ejpam-1853	387	27	.	.	PUNCT
ejpam-1853	388	1	if	if	SCONJ
ejpam-1853	388	2	in	in	ADP
ejpam-1853	388	3	definition	definition	NOUN
ejpam-1853	388	4	6	6	NUM
ejpam-1853	388	5	,	,	PUNCT
ejpam-1853	388	6	we	we	PRON
ejpam-1853	388	7	consider	consider	VERB
ejpam-1853	388	8	v0	v0	NOUN
ejpam-1853	388	9	⊆	⊆	NUM
ejpam-1853	388	10	v	v	NOUN
ejpam-1853	388	11	and	and	CCONJ
ejpam-1853	388	12	ε	ε	PROPN
ejpam-1853	388	13	:	:	PUNCT
ejpam-1853	388	14	v0	v0	PROPN
ejpam-1853	388	15	→	→	SYM
ejpam-1853	388	16	v	v	PROPN
ejpam-1853	388	17	is	be	AUX
ejpam-1853	388	18	the	the	DET
ejpam-1853	388	19	inclusion	inclusion	NOUN
ejpam-1853	388	20	map	map	NOUN
ejpam-1853	388	21	,	,	PUNCT
ejpam-1853	388	22	then	then	ADV
ejpam-1853	388	23	(	(	PUNCT
ejpam-1853	388	24	v	v	NOUN
ejpam-1853	388	25	,	,	PUNCT
ejpam-1853	388	26	α	α	NOUN
ejpam-1853	388	27	,	,	PUNCT
ejpam-1853	388	28	β	β	X
ejpam-1853	388	29	,	,	PUNCT
ejpam-1853	388	30	m	m	PROPN
ejpam-1853	388	31	,	,	PUNCT
ejpam-1853	388	32	i,+,ϕ	i,+,ϕ	NOUN
ejpam-1853	388	33	,	,	PUNCT
ejpam-1853	388	34	v0	v0	PROPN
ejpam-1853	388	35	)	)	PUNCT
ejpam-1853	388	36	is	be	AUX
ejpam-1853	388	37	a	a	DET
ejpam-1853	388	38	vector	vector	NOUN
ejpam-1853	388	39	space	space	NOUN
ejpam-1853	388	40	-	-	PUNCT
ejpam-1853	388	41	groupoid	groupoid	PROPN
ejpam-1853	388	42	.	.	PUNCT
ejpam-1853	389	1	in	in	ADP
ejpam-1853	389	2	this	this	DET
ejpam-1853	389	3	case	case	NOUN
ejpam-1853	389	4	,	,	PUNCT
ejpam-1853	389	5	we	we	PRON
ejpam-1853	389	6	will	will	AUX
ejpam-1853	389	7	say	say	VERB
ejpam-1853	389	8	that	that	SCONJ
ejpam-1853	389	9	(	(	PUNCT
ejpam-1853	389	10	v	v	NOUN
ejpam-1853	389	11	,	,	PUNCT
ejpam-1853	389	12	v0	v0	NOUN
ejpam-1853	389	13	)	)	PUNCT
ejpam-1853	389	14	is	be	AUX
ejpam-1853	389	15	a	a	DET
ejpam-1853	389	16	vector	vector	NOUN
ejpam-1853	389	17	space−v0−groupoid	space−v0−groupoid	NOUN
ejpam-1853	389	18	.	.	PUNCT
ejpam-1853	390	1	example	example	NOUN
ejpam-1853	391	1	2	2	NUM
ejpam-1853	391	2	.	.	PUNCT
ejpam-1853	391	3	(	(	PUNCT
ejpam-1853	391	4	i	i	NOUN
ejpam-1853	391	5	)	)	PUNCT
ejpam-1853	391	6	let	let	AUX
ejpam-1853	391	7	(	(	PUNCT
ejpam-1853	391	8	v,+,ϕ	v,+,ϕ	X
ejpam-1853	391	9	)	)	PUNCT
ejpam-1853	391	10	be	be	VERB
ejpam-1853	391	11	a	a	DET
ejpam-1853	391	12	vector	vector	NOUN
ejpam-1853	391	13	space	space	NOUN
ejpam-1853	391	14	.	.	PUNCT
ejpam-1853	392	1	then	then	ADV
ejpam-1853	392	2	v	v	X
ejpam-1853	392	3	has	have	VERB
ejpam-1853	392	4	a	a	DET
ejpam-1853	392	5	structure	structure	NOUN
ejpam-1853	392	6	of	of	ADP
ejpam-1853	392	7	null	null	ADJ
ejpam-1853	392	8	groupoid	groupoid	PROPN
ejpam-1853	392	9	over	over	ADP
ejpam-1853	392	10	v	v	NOUN
ejpam-1853	392	11	(	(	PUNCT
ejpam-1853	392	12	see	see	VERB
ejpam-1853	392	13	example	example	NOUN
ejpam-1853	392	14	1(i	1(i	NUM
ejpam-1853	392	15	)	)	PUNCT
ejpam-1853	392	16	)	)	PUNCT
ejpam-1853	392	17	.	.	PUNCT
ejpam-1853	393	1	we	we	PRON
ejpam-1853	393	2	have	have	VERB
ejpam-1853	393	3	that	that	DET
ejpam-1853	393	4	v0	v0	NOUN
ejpam-1853	393	5	=	=	SYM
ejpam-1853	393	6	v	v	PROPN
ejpam-1853	393	7	and	and	CCONJ
ejpam-1853	393	8	α	α	NOUN
ejpam-1853	393	9	,	,	PUNCT
ejpam-1853	393	10	β	β	PROPN
ejpam-1853	393	11	,	,	PUNCT
ejpam-1853	393	12	ε	ε	PROPN
ejpam-1853	393	13	,	,	PUNCT
ejpam-1853	393	14	i	i	PRON
ejpam-1853	393	15	are	be	AUX
ejpam-1853	393	16	linear	linear	ADJ
ejpam-1853	393	17	maps	map	NOUN
ejpam-1853	393	18	.	.	PUNCT
ejpam-1853	394	1	it	it	PRON
ejpam-1853	394	2	is	be	AUX
ejpam-1853	394	3	easy	easy	ADJ
ejpam-1853	394	4	to	to	PART
ejpam-1853	394	5	verify	verify	VERB
ejpam-1853	394	6	that	that	SCONJ
ejpam-1853	394	7	the	the	DET
ejpam-1853	394	8	interchange	interchange	NOUN
ejpam-1853	394	9	law	law	NOUN
ejpam-1853	394	10	(	(	PUNCT
ejpam-1853	394	11	10	10	NUM
ejpam-1853	394	12	)	)	PUNCT
ejpam-1853	394	13	holds	hold	VERB
ejpam-1853	394	14	.	.	PUNCT
ejpam-1853	395	1	then	then	ADV
ejpam-1853	395	2	v	v	NOUN
ejpam-1853	395	3	is	be	AUX
ejpam-1853	395	4	a	a	DET
ejpam-1853	395	5	vector	vector	NOUN
ejpam-1853	395	6	space	space	NOUN
ejpam-1853	395	7	-	-	PUNCT
ejpam-1853	395	8	groupoid	groupoid	PROPN
ejpam-1853	395	9	,	,	PUNCT
ejpam-1853	395	10	called	call	VERB
ejpam-1853	395	11	the	the	DET
ejpam-1853	395	12	null	null	ADJ
ejpam-1853	395	13	vector	vector	NOUN
ejpam-1853	395	14	space	space	NOUN
ejpam-1853	395	15	-	-	PUNCT
ejpam-1853	395	16	groupoid	groupoid	PROPN
ejpam-1853	395	17	associated	associate	VERB
ejpam-1853	395	18	to	to	ADP
ejpam-1853	395	19	v	v	NOUN
ejpam-1853	395	20	.	.	PUNCT
ejpam-1853	396	1	(	(	PUNCT
ejpam-1853	396	2	ii	ii	NOUN
ejpam-1853	396	3	)	)	PUNCT
ejpam-1853	396	4	let	let	VERB
ejpam-1853	396	5	(	(	PUNCT
ejpam-1853	396	6	v,+,ϕ	v,+,ϕ	X
ejpam-1853	396	7	)	)	PUNCT
ejpam-1853	396	8	be	be	VERB
ejpam-1853	396	9	a	a	DET
ejpam-1853	396	10	vector	vector	NOUN
ejpam-1853	396	11	space	space	NOUN
ejpam-1853	396	12	having	have	VERB
ejpam-1853	396	13	{	{	PUNCT
ejpam-1853	396	14	e	e	NOUN
ejpam-1853	396	15	}	}	PUNCT
ejpam-1853	396	16	as	as	ADP
ejpam-1853	396	17	null	null	ADJ
ejpam-1853	396	18	vector	vector	NOUN
ejpam-1853	396	19	.	.	PUNCT
ejpam-1853	397	1	the	the	DET
ejpam-1853	397	2	set	set	NOUN
ejpam-1853	397	3	v	v	NOUN
ejpam-1853	397	4	is	be	AUX
ejpam-1853	397	5	a	a	DET
ejpam-1853	397	6	{	{	PUNCT
ejpam-1853	397	7	e}−groupoid	e}−groupoid	X
ejpam-1853	397	8	(	(	PUNCT
ejpam-1853	397	9	see	see	VERB
ejpam-1853	397	10	example	example	NOUN
ejpam-1853	397	11	1(ii	1(ii	NUM
ejpam-1853	397	12	)	)	PUNCT
ejpam-1853	397	13	)	)	PUNCT
ejpam-1853	397	14	.	.	PUNCT
ejpam-1853	398	1	in	in	ADP
ejpam-1853	398	2	this	this	DET
ejpam-1853	398	3	case	case	NOUN
ejpam-1853	398	4	,	,	PUNCT
ejpam-1853	398	5	m	m	VERB
ejpam-1853	398	6	=	=	PUNCT
ejpam-1853	398	7	+	+	ADJ
ejpam-1853	398	8	.	.	PUNCT
ejpam-1853	398	9	we	we	PRON
ejpam-1853	398	10	have	have	VERB
ejpam-1853	398	11	that	that	DET
ejpam-1853	398	12	v0	v0	NOUN
ejpam-1853	398	13	:	:	PUNCT
ejpam-1853	398	14	=	=	SYM
ejpam-1853	398	15	{	{	PUNCT
ejpam-1853	398	16	e	e	NOUN
ejpam-1853	398	17	}	}	PUNCT
ejpam-1853	398	18	is	be	AUX
ejpam-1853	398	19	a	a	DET
ejpam-1853	398	20	vector	vector	NOUN
ejpam-1853	398	21	subspace	subspace	NOUN
ejpam-1853	398	22	in	in	ADP
ejpam-1853	398	23	v	v	NOUN
ejpam-1853	398	24	and	and	CCONJ
ejpam-1853	398	25	α	α	NOUN
ejpam-1853	398	26	,	,	PUNCT
ejpam-1853	398	27	β	β	X
ejpam-1853	398	28	,	,	PUNCT
ejpam-1853	398	29	ε	ε	PROPN
ejpam-1853	398	30	and	and	CCONJ
ejpam-1853	398	31	i	i	PRON
ejpam-1853	398	32	are	be	AUX
ejpam-1853	398	33	linear	linear	ADJ
ejpam-1853	398	34	maps	map	NOUN
ejpam-1853	398	35	.	.	PUNCT
ejpam-1853	399	1	the	the	DET
ejpam-1853	399	2	relation	relation	NOUN
ejpam-1853	399	3	(	(	PUNCT
ejpam-1853	399	4	10	10	NUM
ejpam-1853	399	5	)	)	PUNCT
ejpam-1853	399	6	holds	hold	NOUN
ejpam-1853	399	7	.	.	PUNCT
ejpam-1853	400	1	indeed	indeed	ADV
ejpam-1853	400	2	,	,	PUNCT
ejpam-1853	400	3	for	for	ADP
ejpam-1853	400	4	x	x	SYM
ejpam-1853	400	5	,	,	PUNCT
ejpam-1853	400	6	y	y	PROPN
ejpam-1853	400	7	,	,	PUNCT
ejpam-1853	400	8	z	z	PROPN
ejpam-1853	400	9	,	,	PUNCT
ejpam-1853	400	10	t	t	PROPN
ejpam-1853	400	11	∈	∈	PROPN
ejpam-1853	400	12	v	v	ADP
ejpam-1853	400	13	we	we	PRON
ejpam-1853	400	14	have	have	VERB
ejpam-1853	400	15	(	(	PUNCT
ejpam-1853	400	16	x	x	X
ejpam-1853	400	17	+	+	NUM
ejpam-1853	400	18	y	y	NOUN
ejpam-1853	400	19	)	)	PUNCT
ejpam-1853	401	1	+	+	CCONJ
ejpam-1853	401	2	(	(	PUNCT
ejpam-1853	401	3	z+	z+	NUM
ejpam-1853	401	4	t	t	NOUN
ejpam-1853	401	5	)	)	PUNCT
ejpam-1853	401	6	=	=	PUNCT
ejpam-1853	402	1	(	(	PUNCT
ejpam-1853	402	2	x	x	X
ejpam-1853	402	3	+	+	NUM
ejpam-1853	402	4	z	z	NOUN
ejpam-1853	402	5	)	)	PUNCT
ejpam-1853	403	1	+	+	CCONJ
ejpam-1853	403	2	(	(	PUNCT
ejpam-1853	403	3	y	y	PROPN
ejpam-1853	403	4	+	+	PROPN
ejpam-1853	403	5	t	t	PROPN
ejpam-1853	403	6	)	)	PUNCT
ejpam-1853	403	7	,	,	PUNCT
ejpam-1853	403	8	since	since	SCONJ
ejpam-1853	403	9	the	the	DET
ejpam-1853	403	10	addition	addition	NOUN
ejpam-1853	403	11	operation	operation	NOUN
ejpam-1853	403	12	is	be	AUX
ejpam-1853	403	13	associative	associative	ADJ
ejpam-1853	403	14	and	and	CCONJ
ejpam-1853	403	15	commutative	commutative	ADJ
ejpam-1853	403	16	.	.	PUNCT
ejpam-1853	404	1	hence	hence	ADV
ejpam-1853	404	2	(	(	PUNCT
ejpam-1853	404	3	v	v	NOUN
ejpam-1853	404	4	,	,	PUNCT
ejpam-1853	404	5	α	α	NOUN
ejpam-1853	404	6	,	,	PUNCT
ejpam-1853	404	7	β	β	X
ejpam-1853	404	8	,	,	PUNCT
ejpam-1853	404	9	m	m	PROPN
ejpam-1853	404	10	,	,	PUNCT
ejpam-1853	404	11	ε	ε	PROPN
ejpam-1853	404	12	,	,	PUNCT
ejpam-1853	404	13	i,+,ϕ	i,+,ϕ	NOUN
ejpam-1853	404	14	,	,	PUNCT
ejpam-1853	404	15	{	{	PUNCT
ejpam-1853	404	16	e	e	NOUN
ejpam-1853	404	17	}	}	PUNCT
ejpam-1853	404	18	)	)	PUNCT
ejpam-1853	404	19	is	be	AUX
ejpam-1853	404	20	a	a	DET
ejpam-1853	404	21	vector	vector	NOUN
ejpam-1853	404	22	space	space	NOUN
ejpam-1853	404	23	-	-	PUNCT
ejpam-1853	404	24	groupoid	groupoid	NOUN
ejpam-1853	404	25	called	call	VERB
ejpam-1853	404	26	the	the	DET
ejpam-1853	404	27	vector	vector	NOUN
ejpam-1853	404	28	space	space	NOUN
ejpam-1853	404	29	-	-	PUNCT
ejpam-1853	404	30	groupoid	groupoid	NOUN
ejpam-1853	404	31	with	with	ADP
ejpam-1853	404	32	a	a	DET
ejpam-1853	404	33	single	single	ADJ
ejpam-1853	404	34	unit	unit	NOUN
ejpam-1853	404	35	associated	associate	VERB
ejpam-1853	404	36	to	to	ADP
ejpam-1853	404	37	v	v	NOUN
ejpam-1853	404	38	.	.	PUNCT
ejpam-1853	405	1	therefore	therefore	ADV
ejpam-1853	405	2	,	,	PUNCT
ejpam-1853	405	3	each	each	DET
ejpam-1853	405	4	vector	vector	NOUN
ejpam-1853	405	5	space	space	NOUN
ejpam-1853	405	6	v	v	NOUN
ejpam-1853	405	7	has	have	VERB
ejpam-1853	405	8	a	a	DET
ejpam-1853	405	9	structure	structure	NOUN
ejpam-1853	405	10	of	of	ADP
ejpam-1853	405	11	vector	vector	NOUN
ejpam-1853	405	12	space−{e}−groupoid	space−{e}−groupoid	PROPN
ejpam-1853	405	13	.	.	PUNCT
ejpam-1853	406	1	definition	definition	NOUN
ejpam-1853	406	2	7	7	NUM
ejpam-1853	406	3	.	.	PUNCT
ejpam-1853	407	1	let	let	VERB
ejpam-1853	407	2	(	(	PUNCT
ejpam-1853	407	3	v	v	NOUN
ejpam-1853	407	4	,	,	PUNCT
ejpam-1853	407	5	α	α	NOUN
ejpam-1853	407	6	,	,	PUNCT
ejpam-1853	407	7	β	β	X
ejpam-1853	407	8	,	,	PUNCT
ejpam-1853	407	9	m	m	PROPN
ejpam-1853	407	10	,	,	PUNCT
ejpam-1853	407	11	ε	ε	PROPN
ejpam-1853	407	12	,	,	PUNCT
ejpam-1853	407	13	i,+,ϕ	i,+,ϕ	NOUN
ejpam-1853	407	14	,	,	PUNCT
ejpam-1853	407	15	{	{	PUNCT
ejpam-1853	407	16	e	e	NOUN
ejpam-1853	407	17	}	}	PUNCT
ejpam-1853	407	18	)	)	PUNCT
ejpam-1853	407	19	be	be	AUX
ejpam-1853	407	20	a	a	DET
ejpam-1853	407	21	vector	vector	NOUN
ejpam-1853	407	22	space	space	NOUN
ejpam-1853	407	23	-	-	PUNCT
ejpam-1853	407	24	groupoid	groupoid	PROPN
ejpam-1853	407	25	.	.	PUNCT
ejpam-1853	408	1	(	(	PUNCT
ejpam-1853	408	2	i	i	NOUN
ejpam-1853	408	3	)	)	PUNCT
ejpam-1853	408	4	by	by	ADP
ejpam-1853	408	5	a	a	DET
ejpam-1853	408	6	vector	vector	NOUN
ejpam-1853	408	7	space	space	NOUN
ejpam-1853	408	8	-	-	PUNCT
ejpam-1853	408	9	subgroupoid	subgroupoid	NOUN
ejpam-1853	408	10	(	(	PUNCT
ejpam-1853	408	11	resp	resp	NOUN
ejpam-1853	408	12	.	.	PUNCT
ejpam-1853	408	13	,	,	PUNCT
ejpam-1853	408	14	vector	vector	NOUN
ejpam-1853	408	15	space	space	NOUN
ejpam-1853	408	16	-	-	PUNCT
ejpam-1853	408	17	wide	wide	ADJ
ejpam-1853	408	18	subgroupoid	subgroupoid	NOUN
ejpam-1853	408	19	or	or	CCONJ
ejpam-1853	408	20	vector	vector	NOUN
ejpam-1853	408	21	space	space	NOUN
ejpam-1853	408	22	−v0−subgroupoid	−v0−subgroupoid	PROPN
ejpam-1853	408	23	)	)	PUNCT
ejpam-1853	408	24	of	of	ADP
ejpam-1853	408	25	(	(	PUNCT
ejpam-1853	408	26	v	v	NOUN
ejpam-1853	408	27	,	,	PUNCT
ejpam-1853	408	28	v0	v0	NOUN
ejpam-1853	408	29	)	)	PUNCT
ejpam-1853	408	30	,	,	PUNCT
ejpam-1853	408	31	we	we	PRON
ejpam-1853	408	32	mean	mean	VERB
ejpam-1853	408	33	a	a	DET
ejpam-1853	408	34	subgroupoid	subgroupoid	NOUN
ejpam-1853	408	35	(	(	PUNCT
ejpam-1853	408	36	resp	resp	NOUN
ejpam-1853	408	37	.	.	PUNCT
ejpam-1853	408	38	,	,	PUNCT
ejpam-1853	408	39	wide	wide	ADJ
ejpam-1853	408	40	subgroupoid	subgroupoid	NOUN
ejpam-1853	408	41	)	)	PUNCT
ejpam-1853	408	42	(	(	PUNCT
ejpam-1853	408	43	w	w	PROPN
ejpam-1853	408	44	,	,	PUNCT
ejpam-1853	408	45	w0	w0	PROPN
ejpam-1853	408	46	)	)	PUNCT
ejpam-1853	408	47	of	of	ADP
ejpam-1853	408	48	the	the	DET
ejpam-1853	408	49	groupoid	groupoid	PROPN
ejpam-1853	408	50	(	(	PUNCT
ejpam-1853	408	51	v	v	NOUN
ejpam-1853	408	52	,	,	PUNCT
ejpam-1853	408	53	v0	v0	NOUN
ejpam-1853	408	54	)	)	PUNCT
ejpam-1853	408	55	with	with	ADP
ejpam-1853	408	56	the	the	DET
ejpam-1853	408	57	property	property	NOUN
ejpam-1853	408	58	that	that	PRON
ejpam-1853	408	59	w	w	NOUN
ejpam-1853	408	60	and	and	CCONJ
ejpam-1853	408	61	w0	w0	PROPN
ejpam-1853	408	62	are	be	AUX
ejpam-1853	408	63	vector	vector	NOUN
ejpam-1853	408	64	subspaces	subspace	NOUN
ejpam-1853	408	65	in	in	ADP
ejpam-1853	408	66	v	v	NOUN
ejpam-1853	408	67	and	and	CCONJ
ejpam-1853	408	68	v0	v0	NOUN
ejpam-1853	408	69	,	,	PUNCT
ejpam-1853	408	70	respectively	respectively	ADV
ejpam-1853	408	71	.	.	PUNCT
ejpam-1853	409	1	(	(	PUNCT
ejpam-1853	409	2	ii	ii	NOUN
ejpam-1853	409	3	)	)	PUNCT
ejpam-1853	409	4	a	a	DET
ejpam-1853	409	5	vector	vector	NOUN
ejpam-1853	409	6	space	space	NOUN
ejpam-1853	409	7	-	-	PUNCT
ejpam-1853	409	8	subgroupoid	subgroupoid	NOUN
ejpam-1853	409	9	(	(	PUNCT
ejpam-1853	409	10	n	n	NOUN
ejpam-1853	409	11	,	,	PUNCT
ejpam-1853	409	12	v0	v0	NOUN
ejpam-1853	409	13	)	)	PUNCT
ejpam-1853	409	14	of	of	ADP
ejpam-1853	409	15	(	(	PUNCT
ejpam-1853	409	16	v	v	NOUN
ejpam-1853	409	17	,	,	PUNCT
ejpam-1853	409	18	v0	v0	NOUN
ejpam-1853	409	19	)	)	PUNCT
ejpam-1853	409	20	is	be	AUX
ejpam-1853	409	21	called	call	VERB
ejpam-1853	409	22	vector	vector	NOUN
ejpam-1853	409	23	space	space	NOUN
ejpam-1853	409	24	-	-	PUNCT
ejpam-1853	409	25	normal	normal	ADJ
ejpam-1853	409	26	subgroupoid	subgroupoid	NOUN
ejpam-1853	409	27	,	,	PUNCT
ejpam-1853	409	28	if	if	SCONJ
ejpam-1853	409	29	(	(	PUNCT
ejpam-1853	409	30	n	n	X
ejpam-1853	409	31	,	,	PUNCT
ejpam-1853	409	32	v0	v0	NOUN
ejpam-1853	409	33	)	)	PUNCT
ejpam-1853	409	34	is	be	AUX
ejpam-1853	409	35	a	a	DET
ejpam-1853	409	36	normal	normal	ADJ
ejpam-1853	409	37	subgroupoid	subgroupoid	NOUN
ejpam-1853	409	38	of	of	ADP
ejpam-1853	409	39	the	the	DET
ejpam-1853	409	40	groupoid	groupoid	PROPN
ejpam-1853	409	41	(	(	PUNCT
ejpam-1853	409	42	v	v	NOUN
ejpam-1853	409	43	,	,	PUNCT
ejpam-1853	409	44	v0	v0	NOUN
ejpam-1853	409	45	)	)	PUNCT
ejpam-1853	409	46	.	.	PUNCT
ejpam-1853	410	1	according	accord	VERB
ejpam-1853	410	2	to	to	ADP
ejpam-1853	410	3	the	the	DET
ejpam-1853	410	4	definition	definition	NOUN
ejpam-1853	410	5	6	6	NUM
ejpam-1853	410	6	,	,	PUNCT
ejpam-1853	410	7	if	if	SCONJ
ejpam-1853	410	8	(	(	PUNCT
ejpam-1853	410	9	w	w	NOUN
ejpam-1853	410	10	,	,	PUNCT
ejpam-1853	410	11	w0	w0	PROPN
ejpam-1853	410	12	)	)	PUNCT
ejpam-1853	410	13	is	be	AUX
ejpam-1853	410	14	a	a	DET
ejpam-1853	410	15	vector	vector	NOUN
ejpam-1853	410	16	space	space	NOUN
ejpam-1853	410	17	-	-	PUNCT
ejpam-1853	410	18	subgroupoid	subgroupoid	NOUN
ejpam-1853	410	19	of	of	ADP
ejpam-1853	410	20	(	(	PUNCT
ejpam-1853	410	21	v	v	NOUN
ejpam-1853	410	22	,	,	PUNCT
ejpam-1853	410	23	v0	v0	NOUN
ejpam-1853	410	24	)	)	PUNCT
ejpam-1853	410	25	,	,	PUNCT
ejpam-1853	410	26	then	then	ADV
ejpam-1853	410	27	the	the	DET
ejpam-1853	410	28	pair	pair	NOUN
ejpam-1853	410	29	(	(	PUNCT
ejpam-1853	410	30	w	w	NOUN
ejpam-1853	410	31	,	,	PUNCT
ejpam-1853	410	32	w0	w0	PROPN
ejpam-1853	410	33	)	)	PUNCT
ejpam-1853	410	34	endowed	endow	VERB
ejpam-1853	410	35	with	with	ADP
ejpam-1853	410	36	the	the	DET
ejpam-1853	410	37	restrictions	restriction	NOUN
ejpam-1853	410	38	of	of	ADP
ejpam-1853	410	39	the	the	DET
ejpam-1853	410	40	functions	function	NOUN
ejpam-1853	410	41	α	α	NOUN
ejpam-1853	410	42	,	,	PUNCT
ejpam-1853	410	43	β	β	PROPN
ejpam-1853	410	44	,	,	PUNCT
ejpam-1853	410	45	i	i	PRON
ejpam-1853	410	46	and	and	CCONJ
ejpam-1853	410	47	+	+	X
ejpam-1853	410	48	to	to	ADP
ejpam-1853	410	49	w	w	NOUN
ejpam-1853	410	50	,	,	PUNCT
ejpam-1853	410	51	the	the	DET
ejpam-1853	410	52	restriction	restriction	NOUN
ejpam-1853	410	53	of	of	ADP
ejpam-1853	410	54	ε	ε	PROPN
ejpam-1853	410	55	to	to	PART
ejpam-1853	410	56	w0	w0	PROPN
ejpam-1853	410	57	and	and	CCONJ
ejpam-1853	410	58	the	the	DET
ejpam-1853	410	59	restriction	restriction	NOUN
ejpam-1853	410	60	of	of	ADP
ejpam-1853	410	61	m	m	PRON
ejpam-1853	410	62	to	to	ADP
ejpam-1853	410	63	w(2	w(2	NOUN
ejpam-1853	410	64	)	)	PUNCT
ejpam-1853	410	65	,	,	PUNCT
ejpam-1853	410	66	is	be	AUX
ejpam-1853	410	67	a	a	DET
ejpam-1853	410	68	vector	vector	NOUN
ejpam-1853	410	69	space	space	NOUN
ejpam-1853	410	70	-	-	PUNCT
ejpam-1853	410	71	groupoid	groupoid	PROPN
ejpam-1853	410	72	,	,	PUNCT
ejpam-1853	410	73	denoted	denote	VERB
ejpam-1853	410	74	by	by	ADP
ejpam-1853	410	75	(	(	PUNCT
ejpam-1853	410	76	w	w	PROPN
ejpam-1853	410	77	,	,	PUNCT
ejpam-1853	410	78	w0	w0	PROPN
ejpam-1853	410	79	)	)	PUNCT
ejpam-1853	410	80	.	.	PUNCT
ejpam-1853	411	1	theorem	theorem	ADJ
ejpam-1853	411	2	7	7	NUM
ejpam-1853	411	3	.	.	PUNCT
ejpam-1853	412	1	let	let	VERB
ejpam-1853	412	2	(	(	PUNCT
ejpam-1853	412	3	v	v	NOUN
ejpam-1853	412	4	,	,	PUNCT
ejpam-1853	412	5	α	α	NOUN
ejpam-1853	412	6	,	,	PUNCT
ejpam-1853	412	7	β	β	X
ejpam-1853	412	8	,	,	PUNCT
ejpam-1853	412	9	m	m	PROPN
ejpam-1853	412	10	,	,	PUNCT
ejpam-1853	412	11	ε	ε	PROPN
ejpam-1853	412	12	,	,	PUNCT
ejpam-1853	412	13	i,+,ϕ	i,+,ϕ	NOUN
ejpam-1853	412	14	,	,	PUNCT
ejpam-1853	412	15	v0	v0	PROPN
ejpam-1853	412	16	)	)	PUNCT
ejpam-1853	412	17	be	be	VERB
ejpam-1853	412	18	a	a	DET
ejpam-1853	412	19	vector	vector	NOUN
ejpam-1853	412	20	space	space	NOUN
ejpam-1853	412	21	-	-	PUNCT
ejpam-1853	412	22	groupoid	groupoid	PROPN
ejpam-1853	412	23	.	.	PUNCT
ejpam-1853	413	1	then	then	ADV
ejpam-1853	413	2	:	:	PUNCT
ejpam-1853	413	3	m.	m.	PROPN
ejpam-1853	413	4	ivan	ivan	PROPN
ejpam-1853	413	5	/	/	PUNCT
ejpam-1853	413	6	eur	eur	PROPN
ejpam-1853	413	7	.	.	PUNCT
ejpam-1853	414	1	j.	j.	PROPN
ejpam-1853	414	2	pure	pure	PROPN
ejpam-1853	414	3	appl	appl	PROPN
ejpam-1853	414	4	.	.	PROPN
ejpam-1853	414	5	math	math	PROPN
ejpam-1853	414	6	,	,	PUNCT
ejpam-1853	414	7	6	6	NUM
ejpam-1853	414	8	(	(	PUNCT
ejpam-1853	414	9	2013	2013	NUM
ejpam-1853	414	10	)	)	PUNCT
ejpam-1853	414	11	,	,	PUNCT
ejpam-1853	414	12	469	469	NUM
ejpam-1853	414	13	-	-	SYM
ejpam-1853	414	14	484	484	NUM
ejpam-1853	414	15	480	480	NUM
ejpam-1853	414	16	(	(	PUNCT
ejpam-1853	414	17	i	i	NOUN
ejpam-1853	414	18	)	)	PUNCT
ejpam-1853	414	19	the	the	DET
ejpam-1853	414	20	fibres	fibre	NOUN
ejpam-1853	414	21	α−1(e0	α−1(e0	NOUN
ejpam-1853	414	22	)	)	PUNCT
ejpam-1853	414	23	and	and	CCONJ
ejpam-1853	414	24	β−1(e0	β−1(e0	PUNCT
ejpam-1853	414	25	)	)	PUNCT
ejpam-1853	414	26	are	be	AUX
ejpam-1853	414	27	vector	vector	NOUN
ejpam-1853	414	28	subspaces	subspace	NOUN
ejpam-1853	414	29	in	in	ADP
ejpam-1853	414	30	v	v	NOUN
ejpam-1853	414	31	.	.	PUNCT
ejpam-1853	415	1	(	(	PUNCT
ejpam-1853	415	2	ii	ii	NOUN
ejpam-1853	415	3	)	)	PUNCT
ejpam-1853	415	4	the	the	DET
ejpam-1853	415	5	isotropy	isotropy	ADJ
ejpam-1853	415	6	group	group	NOUN
ejpam-1853	415	7	v	v	PROPN
ejpam-1853	415	8	(	(	PUNCT
ejpam-1853	415	9	e0	e0	PROPN
ejpam-1853	415	10	)	)	PUNCT
ejpam-1853	415	11	is	be	AUX
ejpam-1853	415	12	a	a	DET
ejpam-1853	415	13	vector	vector	NOUN
ejpam-1853	415	14	space−{e0}−subgroupoid	space−{e0}−subgroupoid	PROPN
ejpam-1853	415	15	of	of	ADP
ejpam-1853	415	16	v	v	PROPN
ejpam-1853	415	17	.	.	PUNCT
ejpam-1853	416	1	(	(	PUNCT
ejpam-1853	416	2	iii	iii	NOUN
ejpam-1853	416	3	)	)	PUNCT
ejpam-1853	416	4	ε(v0	ε(v0	NOUN
ejpam-1853	416	5	)	)	PUNCT
ejpam-1853	416	6	is	be	AUX
ejpam-1853	416	7	a	a	DET
ejpam-1853	416	8	vector	vector	NOUN
ejpam-1853	416	9	space	space	NOUN
ejpam-1853	416	10	−normal	−normal	NOUN
ejpam-1853	416	11	subgroupoid	subgroupoid	NOUN
ejpam-1853	416	12	of	of	ADP
ejpam-1853	416	13	v	v	PROPN
ejpam-1853	416	14	.	.	PUNCT
ejpam-1853	417	1	(	(	PUNCT
ejpam-1853	417	2	iv	iv	X
ejpam-1853	417	3	)	)	PUNCT
ejpam-1853	417	4	is(v	is(v	PUNCT
ejpam-1853	417	5	)	)	PUNCT
ejpam-1853	418	1	:	:	PUNCT
ejpam-1853	418	2	=	=	SYM
ejpam-1853	418	3	{	{	PUNCT
ejpam-1853	418	4	x	x	SYM
ejpam-1853	418	5	∈	∈	PROPN
ejpam-1853	418	6	v	v	ADP
ejpam-1853	418	7	|	|	NOUN
ejpam-1853	418	8	α(x	α(x	NOUN
ejpam-1853	418	9	)	)	PUNCT
ejpam-1853	418	10	=	=	SYM
ejpam-1853	419	1	β(x	β(x	NOUN
ejpam-1853	419	2	)	)	PUNCT
ejpam-1853	419	3	}	}	PUNCT
ejpam-1853	419	4	is	be	AUX
ejpam-1853	419	5	a	a	DET
ejpam-1853	419	6	vector	vector	NOUN
ejpam-1853	419	7	space	space	NOUN
ejpam-1853	419	8	−normal	−normal	NOUN
ejpam-1853	419	9	subgroupoid	subgroupoid	NOUN
ejpam-1853	419	10	of	of	ADP
ejpam-1853	419	11	v	v	NOUN
ejpam-1853	419	12	.	.	PUNCT
ejpam-1853	420	1	proof	proof	NOUN
ejpam-1853	420	2	.	.	PUNCT
ejpam-1853	421	1	(	(	PUNCT
ejpam-1853	421	2	i	i	NOUN
ejpam-1853	421	3	)	)	PUNCT
ejpam-1853	421	4	for	for	ADP
ejpam-1853	421	5	all	all	PRON
ejpam-1853	421	6	x	x	SYM
ejpam-1853	421	7	,	,	PUNCT
ejpam-1853	421	8	y	y	PROPN
ejpam-1853	421	9	∈	∈	PROPN
ejpam-1853	421	10	α−1(e0	α−1(e0	PROPN
ejpam-1853	421	11	)	)	PUNCT
ejpam-1853	421	12	and	and	CCONJ
ejpam-1853	422	1	k	k	PROPN
ejpam-1853	422	2	∈	∈	PROPN
ejpam-1853	422	3	k	k	NOUN
ejpam-1853	422	4	,	,	PUNCT
ejpam-1853	422	5	we	we	PRON
ejpam-1853	422	6	have	have	VERB
ejpam-1853	422	7	α(x	α(x	PROPN
ejpam-1853	422	8	−	−	PROPN
ejpam-1853	422	9	y	y	NOUN
ejpam-1853	422	10	)	)	PUNCT
ejpam-1853	422	11	=	=	SYM
ejpam-1853	423	1	α(x)−α(y	α(x)−α(y	X
ejpam-1853	423	2	)	)	PUNCT
ejpam-1853	423	3	=	=	SYM
ejpam-1853	423	4	e0	e0	PROPN
ejpam-1853	423	5	and	and	CCONJ
ejpam-1853	423	6	α(kx	α(kx	NUM
ejpam-1853	423	7	)	)	PUNCT
ejpam-1853	423	8	=	=	SYM
ejpam-1853	423	9	kα(x	kα(x	X
ejpam-1853	423	10	)	)	PUNCT
ejpam-1853	424	1	=	=	SYM
ejpam-1853	424	2	ke0	ke0	NOUN
ejpam-1853	424	3	=	=	PUNCT
ejpam-1853	424	4	e0	e0	PROPN
ejpam-1853	424	5	.	.	PUNCT
ejpam-1853	425	1	then	then	ADV
ejpam-1853	425	2	x	x	X
ejpam-1853	425	3	−	−	PROPN
ejpam-1853	425	4	y	y	PROPN
ejpam-1853	425	5	,	,	PUNCT
ejpam-1853	425	6	kx	kx	PROPN
ejpam-1853	425	7	∈	∈	PROPN
ejpam-1853	425	8	α−1(e0	α−1(e0	PROPN
ejpam-1853	425	9	)	)	PUNCT
ejpam-1853	425	10	.	.	PUNCT
ejpam-1853	426	1	hence	hence	ADV
ejpam-1853	426	2	α−1(e0	α−1(e0	NOUN
ejpam-1853	426	3	)	)	PUNCT
ejpam-1853	426	4	is	be	AUX
ejpam-1853	426	5	a	a	DET
ejpam-1853	426	6	vector	vector	NOUN
ejpam-1853	426	7	subspace	subspace	NOUN
ejpam-1853	426	8	.	.	PUNCT
ejpam-1853	427	1	similarly	similarly	ADV
ejpam-1853	427	2	,	,	PUNCT
ejpam-1853	427	3	we	we	PRON
ejpam-1853	427	4	prove	prove	VERB
ejpam-1853	427	5	that	that	SCONJ
ejpam-1853	427	6	β−1(e0	β−1(e0	NOUN
ejpam-1853	427	7	)	)	PUNCT
ejpam-1853	427	8	is	be	AUX
ejpam-1853	427	9	a	a	DET
ejpam-1853	427	10	vector	vector	NOUN
ejpam-1853	427	11	subspace	subspace	NOUN
ejpam-1853	427	12	.	.	PUNCT
ejpam-1853	428	1	(	(	PUNCT
ejpam-1853	428	2	ii	ii	NOUN
ejpam-1853	428	3	)	)	PUNCT
ejpam-1853	428	4	v	v	NOUN
ejpam-1853	428	5	(	(	PUNCT
ejpam-1853	428	6	e0	e0	PROPN
ejpam-1853	428	7	)	)	PUNCT
ejpam-1853	428	8	is	be	AUX
ejpam-1853	428	9	a	a	DET
ejpam-1853	428	10	vector	vector	NOUN
ejpam-1853	428	11	subspace	subspace	NOUN
ejpam-1853	428	12	,	,	PUNCT
ejpam-1853	428	13	since	since	SCONJ
ejpam-1853	428	14	v	v	X
ejpam-1853	428	15	(	(	PUNCT
ejpam-1853	428	16	e0	e0	PROPN
ejpam-1853	428	17	)	)	PUNCT
ejpam-1853	429	1	=	=	SYM
ejpam-1853	429	2	α−1(e0)∩	α−1(e0)∩	PROPN
ejpam-1853	429	3	β−1(e0	β−1(e0	PROPN
ejpam-1853	429	4	)	)	PUNCT
ejpam-1853	429	5	.	.	PUNCT
ejpam-1853	430	1	also	also	ADV
ejpam-1853	430	2	,	,	PUNCT
ejpam-1853	430	3	v	v	X
ejpam-1853	430	4	(	(	PUNCT
ejpam-1853	430	5	e0	e0	PROPN
ejpam-1853	430	6	)	)	PUNCT
ejpam-1853	430	7	is	be	AUX
ejpam-1853	430	8	a	a	DET
ejpam-1853	430	9	{	{	PUNCT
ejpam-1853	430	10	e0}−subgroupoid	e0}−subgroupoid	X
ejpam-1853	430	11	.	.	PUNCT
ejpam-1853	431	1	then	then	ADV
ejpam-1853	431	2	,	,	PUNCT
ejpam-1853	431	3	v	v	INTJ
ejpam-1853	431	4	(	(	PUNCT
ejpam-1853	431	5	e0	e0	PROPN
ejpam-1853	431	6	)	)	PUNCT
ejpam-1853	431	7	is	be	AUX
ejpam-1853	431	8	a	a	DET
ejpam-1853	431	9	vector	vector	NOUN
ejpam-1853	431	10	space−{e0}−subgroupoid	space−{e0}−subgroupoid	PROPN
ejpam-1853	431	11	of	of	ADP
ejpam-1853	431	12	v	v	NOUN
ejpam-1853	431	13	.	.	PUNCT
ejpam-1853	432	1	for	for	ADP
ejpam-1853	432	2	to	to	PART
ejpam-1853	432	3	prove	prove	VERB
ejpam-1853	432	4	the	the	DET
ejpam-1853	432	5	following	follow	VERB
ejpam-1853	432	6	assertions	assertion	NOUN
ejpam-1853	432	7	,	,	PUNCT
ejpam-1853	432	8	we	we	PRON
ejpam-1853	432	9	apply	apply	VERB
ejpam-1853	432	10	the	the	DET
ejpam-1853	432	11	theorem	theorem	NOUN
ejpam-1853	432	12	1	1	NUM
ejpam-1853	432	13	.	.	PUNCT
ejpam-1853	432	14	(	(	PUNCT
ejpam-1853	432	15	iii	iii	NOUN
ejpam-1853	432	16	)	)	PUNCT
ejpam-1853	432	17	for	for	ADP
ejpam-1853	432	18	x	x	SYM
ejpam-1853	432	19	,	,	PUNCT
ejpam-1853	432	20	y	y	PROPN
ejpam-1853	432	21	∈	∈	PROPN
ejpam-1853	432	22	ε(v0	ε(v0	NOUN
ejpam-1853	432	23	)	)	PUNCT
ejpam-1853	432	24	there	there	PRON
ejpam-1853	432	25	exist	exist	VERB
ejpam-1853	432	26	u	u	NOUN
ejpam-1853	432	27	,	,	PUNCT
ejpam-1853	432	28	v	v	PROPN
ejpam-1853	432	29	∈	∈	PROPN
ejpam-1853	432	30	v0	v0	NOUN
ejpam-1853	432	31	such	such	ADJ
ejpam-1853	432	32	that	that	SCONJ
ejpam-1853	432	33	ε(u	ε(u	NOUN
ejpam-1853	432	34	)	)	PUNCT
ejpam-1853	432	35	=	=	SYM
ejpam-1853	432	36	x	x	PROPN
ejpam-1853	432	37	and	and	CCONJ
ejpam-1853	432	38	ε(v	ε(v	NOUN
ejpam-1853	432	39	)	)	PUNCT
ejpam-1853	432	40	=	=	SYM
ejpam-1853	432	41	y	y	PROPN
ejpam-1853	432	42	.	.	PUNCT
ejpam-1853	433	1	it	it	PRON
ejpam-1853	433	2	follows	follow	VERB
ejpam-1853	433	3	β(x	β(x	NOUN
ejpam-1853	433	4	)	)	PUNCT
ejpam-1853	433	5	=	=	SYM
ejpam-1853	433	6	β(ε(u	β(ε(u	PROPN
ejpam-1853	433	7	)	)	PUNCT
ejpam-1853	433	8	)	)	PUNCT
ejpam-1853	434	1	=	=	SYM
ejpam-1853	434	2	u	u	NOUN
ejpam-1853	434	3	and	and	CCONJ
ejpam-1853	434	4	α(y	α(y	NOUN
ejpam-1853	434	5	)	)	PUNCT
ejpam-1853	435	1	=	=	SYM
ejpam-1853	435	2	α(ε(v	α(ε(v	NOUN
ejpam-1853	435	3	)	)	PUNCT
ejpam-1853	435	4	)	)	PUNCT
ejpam-1853	436	1	=	=	PUNCT
ejpam-1853	437	1	v.	v.	CCONJ
ejpam-1853	437	2	we	we	PRON
ejpam-1853	437	3	suppose	suppose	VERB
ejpam-1853	437	4	that	that	SCONJ
ejpam-1853	437	5	the	the	DET
ejpam-1853	437	6	product	product	NOUN
ejpam-1853	437	7	x	x	X
ejpam-1853	437	8	·	·	PUNCT
ejpam-1853	437	9	y	y	NOUN
ejpam-1853	437	10	is	be	AUX
ejpam-1853	437	11	defined	define	VERB
ejpam-1853	437	12	.	.	PUNCT
ejpam-1853	438	1	from	from	ADP
ejpam-1853	438	2	β(x	β(x	NOUN
ejpam-1853	438	3	)	)	PUNCT
ejpam-1853	438	4	=	=	SYM
ejpam-1853	438	5	α(y	α(y	NOUN
ejpam-1853	438	6	)	)	PUNCT
ejpam-1853	438	7	it	it	PRON
ejpam-1853	438	8	follows	follow	VERB
ejpam-1853	438	9	x	x	PUNCT
ejpam-1853	438	10	=	=	SYM
ejpam-1853	438	11	y	y	PROPN
ejpam-1853	438	12	.	.	PUNCT
ejpam-1853	439	1	then	then	ADV
ejpam-1853	439	2	x	x	X
ejpam-1853	439	3	·	·	PUNCT
ejpam-1853	439	4	y	y	X
ejpam-1853	439	5	=	=	SYM
ejpam-1853	439	6	ε(u	ε(u	PROPN
ejpam-1853	439	7	)	)	PUNCT
ejpam-1853	439	8	·	·	PUNCT
ejpam-1853	440	1	ε(u	ε(u	X
ejpam-1853	440	2	)	)	PUNCT
ejpam-1853	440	3	=	=	SYM
ejpam-1853	440	4	ε(u	ε(u	NOUN
ejpam-1853	440	5	)	)	PUNCT
ejpam-1853	440	6	∈	∈	PROPN
ejpam-1853	440	7	ε(v0	ε(v0	NOUN
ejpam-1853	440	8	)	)	PUNCT
ejpam-1853	440	9	.	.	PUNCT
ejpam-1853	441	1	also	also	ADV
ejpam-1853	441	2	,	,	PUNCT
ejpam-1853	441	3	for	for	ADP
ejpam-1853	441	4	x	x	PROPN
ejpam-1853	441	5	∈	∈	PROPN
ejpam-1853	441	6	ε(v0	ε(v0	NOUN
ejpam-1853	441	7	)	)	PUNCT
ejpam-1853	441	8	,	,	PUNCT
ejpam-1853	441	9	we	we	PRON
ejpam-1853	441	10	have	have	VERB
ejpam-1853	441	11	x−1	x−1	PROPN
ejpam-1853	441	12	=	=	SYM
ejpam-1853	441	13	i(x	i(x	PROPN
ejpam-1853	441	14	)	)	PUNCT
ejpam-1853	441	15	=	=	SYM
ejpam-1853	441	16	i(ε(u	i(ε(u	PROPN
ejpam-1853	441	17	)	)	PUNCT
ejpam-1853	441	18	)	)	PUNCT
ejpam-1853	442	1	=	=	PUNCT
ejpam-1853	442	2	ε(u	ε(u	NOUN
ejpam-1853	442	3	)	)	PUNCT
ejpam-1853	442	4	∈	∈	PROPN
ejpam-1853	442	5	ε(v0	ε(v0	NOUN
ejpam-1853	442	6	)	)	PUNCT
ejpam-1853	442	7	.	.	PUNCT
ejpam-1853	443	1	let	let	VERB
ejpam-1853	443	2	now	now	ADV
ejpam-1853	443	3	a	a	DET
ejpam-1853	443	4	∈	∈	NOUN
ejpam-1853	443	5	v	v	NOUN
ejpam-1853	444	1	and	and	CCONJ
ejpam-1853	444	2	x	x	PUNCT
ejpam-1853	444	3	∈	∈	PROPN
ejpam-1853	444	4	ε(v0	ε(v0	NOUN
ejpam-1853	444	5	)	)	PUNCT
ejpam-1853	444	6	such	such	ADJ
ejpam-1853	444	7	that	that	SCONJ
ejpam-1853	444	8	a	a	PRON
ejpam-1853	444	9	·	·	PUNCT
ejpam-1853	444	10	x	x	SYM
ejpam-1853	444	11	·	·	PUNCT
ejpam-1853	444	12	a−1	a−1	NOUN
ejpam-1853	444	13	is	be	AUX
ejpam-1853	444	14	defined	define	VERB
ejpam-1853	444	15	.	.	PUNCT
ejpam-1853	445	1	from	from	ADP
ejpam-1853	445	2	x	x	X
ejpam-1853	445	3	=	=	SYM
ejpam-1853	445	4	ε(u	ε(u	PROPN
ejpam-1853	445	5	)	)	PUNCT
ejpam-1853	445	6	and	and	CCONJ
ejpam-1853	445	7	β(a	β(a	PROPN
ejpam-1853	445	8	)	)	PUNCT
ejpam-1853	445	9	=	=	SYM
ejpam-1853	445	10	α(x	α(x	NOUN
ejpam-1853	445	11	)	)	PUNCT
ejpam-1853	445	12	it	it	PRON
ejpam-1853	445	13	follows	follow	VERB
ejpam-1853	445	14	β(a	β(a	PROPN
ejpam-1853	445	15	)	)	PUNCT
ejpam-1853	445	16	=	=	SYM
ejpam-1853	445	17	α(ε(u	α(ε(u	PROPN
ejpam-1853	445	18	)	)	PUNCT
ejpam-1853	445	19	)	)	PUNCT
ejpam-1853	446	1	=	=	SYM
ejpam-1853	446	2	u	u	NOUN
ejpam-1853	446	3	and	and	CCONJ
ejpam-1853	446	4	x	x	X
ejpam-1853	446	5	=	=	PUNCT
ejpam-1853	446	6	ε(β(a	ε(β(a	PROPN
ejpam-1853	446	7	)	)	PUNCT
ejpam-1853	446	8	)	)	PUNCT
ejpam-1853	446	9	.	.	PUNCT
ejpam-1853	447	1	then	then	ADV
ejpam-1853	447	2	a	a	PRON
ejpam-1853	447	3	·	·	PUNCT
ejpam-1853	447	4	x	x	SYM
ejpam-1853	447	5	·	·	PUNCT
ejpam-1853	447	6	a−1	a−1	PROPN
ejpam-1853	447	7	=	=	SYM
ejpam-1853	447	8	(	(	PUNCT
ejpam-1853	447	9	a	a	DET
ejpam-1853	447	10	·	·	PUNCT
ejpam-1853	447	11	ε(β(a	ε(β(a	PROPN
ejpam-1853	447	12	)	)	PUNCT
ejpam-1853	447	13	)	)	PUNCT
ejpam-1853	447	14	)	)	PUNCT
ejpam-1853	447	15	·	·	PUNCT
ejpam-1853	448	1	a−1	a−1	NOUN
ejpam-1853	448	2	=	=	PUNCT
ejpam-1853	448	3	a	a	DET
ejpam-1853	448	4	·	·	PUNCT
ejpam-1853	448	5	a−1	a−1	PROPN
ejpam-1853	448	6	=	=	PUNCT
ejpam-1853	448	7	ε(α(a	ε(α(a	PROPN
ejpam-1853	448	8	)	)	PUNCT
ejpam-1853	448	9	)	)	PUNCT
ejpam-1853	449	1	∈	∈	PROPN
ejpam-1853	449	2	ε(v0	ε(v0	NOUN
ejpam-1853	449	3	)	)	PUNCT
ejpam-1853	449	4	.	.	PUNCT
ejpam-1853	450	1	hence	hence	ADV
ejpam-1853	450	2	,	,	PUNCT
ejpam-1853	450	3	ε(v0	ε(v0	NOUN
ejpam-1853	450	4	)	)	PUNCT
ejpam-1853	450	5	is	be	AUX
ejpam-1853	450	6	a	a	DET
ejpam-1853	450	7	normal	normal	ADJ
ejpam-1853	450	8	subgroupoid	subgroupoid	NOUN
ejpam-1853	450	9	.	.	PUNCT
ejpam-1853	451	1	also	also	ADV
ejpam-1853	451	2	,	,	PUNCT
ejpam-1853	451	3	ε(v0	ε(v0	NOUN
ejpam-1853	451	4	)	)	PUNCT
ejpam-1853	451	5	is	be	AUX
ejpam-1853	451	6	a	a	DET
ejpam-1853	451	7	vector	vector	NOUN
ejpam-1853	451	8	subspace	subspace	NOUN
ejpam-1853	451	9	in	in	ADP
ejpam-1853	451	10	v	v	NUM
ejpam-1853	451	11	,	,	PUNCT
ejpam-1853	451	12	since	since	SCONJ
ejpam-1853	451	13	ε	ε	PROPN
ejpam-1853	451	14	:	:	PUNCT
ejpam-1853	451	15	v0→	v0→	NUM
ejpam-1853	451	16	v	v	NOUN
ejpam-1853	451	17	is	be	AUX
ejpam-1853	451	18	a	a	DET
ejpam-1853	451	19	linear	linear	ADJ
ejpam-1853	451	20	map	map	NOUN
ejpam-1853	451	21	.	.	PUNCT
ejpam-1853	452	1	therefore	therefore	ADV
ejpam-1853	452	2	,	,	PUNCT
ejpam-1853	452	3	ε(v0	ε(v0	NOUN
ejpam-1853	452	4	)	)	PUNCT
ejpam-1853	452	5	is	be	AUX
ejpam-1853	452	6	a	a	DET
ejpam-1853	452	7	vector	vector	NOUN
ejpam-1853	452	8	space	space	NOUN
ejpam-1853	452	9	-	-	PUNCT
ejpam-1853	452	10	normal	normal	ADJ
ejpam-1853	452	11	subgroupoid	subgroupoid	NOUN
ejpam-1853	452	12	.	.	PUNCT
ejpam-1853	453	1	(	(	PUNCT
ejpam-1853	453	2	iv	iv	X
ejpam-1853	453	3	)	)	PUNCT
ejpam-1853	453	4	clearly	clearly	ADV
ejpam-1853	453	5	,	,	PUNCT
ejpam-1853	453	6	α(is(v	α(is(v	PROPN
ejpam-1853	453	7	)	)	PUNCT
ejpam-1853	453	8	)	)	PUNCT
ejpam-1853	454	1	=	=	PUNCT
ejpam-1853	454	2	β(is(v	β(is(v	NOUN
ejpam-1853	454	3	)	)	PUNCT
ejpam-1853	454	4	)	)	PUNCT
ejpam-1853	455	1	=	=	SYM
ejpam-1853	455	2	v0	v0	PROPN
ejpam-1853	455	3	.	.	PUNCT
ejpam-1853	456	1	let	let	VERB
ejpam-1853	456	2	x	x	PRON
ejpam-1853	456	3	,	,	PUNCT
ejpam-1853	456	4	y	y	PROPN
ejpam-1853	456	5	∈	∈	PROPN
ejpam-1853	456	6	is(v	is(v	X
ejpam-1853	456	7	)	)	PUNCT
ejpam-1853	456	8	with	with	ADP
ejpam-1853	456	9	(	(	PUNCT
ejpam-1853	456	10	x	x	INTJ
ejpam-1853	456	11	,	,	PUNCT
ejpam-1853	456	12	y	y	PROPN
ejpam-1853	456	13	)	)	PUNCT
ejpam-1853	456	14	∈	∈	PROPN
ejpam-1853	456	15	v(2	v(2	PROPN
ejpam-1853	456	16	)	)	PUNCT
ejpam-1853	456	17	.	.	PUNCT
ejpam-1853	457	1	then	then	ADV
ejpam-1853	457	2	α(x	α(x	NOUN
ejpam-1853	457	3	)	)	PUNCT
ejpam-1853	457	4	=	=	SYM
ejpam-1853	458	1	β(x	β(x	NOUN
ejpam-1853	458	2	)	)	PUNCT
ejpam-1853	458	3	=	=	SYM
ejpam-1853	458	4	α(y	α(y	NOUN
ejpam-1853	458	5	)	)	PUNCT
ejpam-1853	458	6	=	=	PUNCT
ejpam-1853	458	7	β(y	β(y	NOUN
ejpam-1853	458	8	)	)	PUNCT
ejpam-1853	458	9	.	.	PUNCT
ejpam-1853	459	1	we	we	PRON
ejpam-1853	459	2	have	have	VERB
ejpam-1853	459	3	α(x	α(x	PROPN
ejpam-1853	459	4	y	y	NOUN
ejpam-1853	459	5	)	)	PUNCT
ejpam-1853	459	6	=	=	NOUN
ejpam-1853	459	7	β(x	β(x	NOUN
ejpam-1853	459	8	y	y	NOUN
ejpam-1853	459	9	)	)	PUNCT
ejpam-1853	459	10	and	and	CCONJ
ejpam-1853	459	11	α(x−1	α(x−1	NUM
ejpam-1853	459	12	)	)	PUNCT
ejpam-1853	459	13	=	=	SYM
ejpam-1853	459	14	β(x−1	β(x−1	NOUN
ejpam-1853	459	15	)	)	PUNCT
ejpam-1853	459	16	.	.	PUNCT
ejpam-1853	460	1	it	it	PRON
ejpam-1853	460	2	follows	follow	VERB
ejpam-1853	460	3	that	that	SCONJ
ejpam-1853	460	4	x	x	PUNCT
ejpam-1853	460	5	y	y	PROPN
ejpam-1853	460	6	,	,	PUNCT
ejpam-1853	460	7	x−1	x−1	PROPN
ejpam-1853	460	8	∈	∈	PROPN
ejpam-1853	460	9	is(v	is(v	PRON
ejpam-1853	460	10	)	)	PUNCT
ejpam-1853	460	11	.	.	PUNCT
ejpam-1853	461	1	let	let	VERB
ejpam-1853	461	2	now	now	ADV
ejpam-1853	461	3	a	a	DET
ejpam-1853	461	4	∈	∈	NOUN
ejpam-1853	461	5	v	v	NOUN
ejpam-1853	461	6	and	and	CCONJ
ejpam-1853	461	7	x	x	NOUN
ejpam-1853	461	8	∈	∈	PROPN
ejpam-1853	461	9	is(v	is(v	PRON
ejpam-1853	461	10	)	)	PUNCT
ejpam-1853	461	11	such	such	ADJ
ejpam-1853	461	12	that	that	SCONJ
ejpam-1853	461	13	a	a	PRON
ejpam-1853	461	14	·	·	PUNCT
ejpam-1853	461	15	x	x	SYM
ejpam-1853	461	16	·	·	PUNCT
ejpam-1853	461	17	a−1	a−1	NOUN
ejpam-1853	461	18	is	be	AUX
ejpam-1853	461	19	defined	define	VERB
ejpam-1853	461	20	.	.	PUNCT
ejpam-1853	462	1	from	from	ADP
ejpam-1853	462	2	α(a	α(a	NOUN
ejpam-1853	462	3	·	·	PUNCT
ejpam-1853	462	4	x	x	SYM
ejpam-1853	462	5	·	·	PUNCT
ejpam-1853	462	6	a−1	a−1	NOUN
ejpam-1853	462	7	)	)	PUNCT
ejpam-1853	462	8	=	=	SYM
ejpam-1853	462	9	α(a	α(a	NOUN
ejpam-1853	462	10	)	)	PUNCT
ejpam-1853	462	11	and	and	CCONJ
ejpam-1853	462	12	β(a	β(a	NOUN
ejpam-1853	462	13	·	·	PUNCT
ejpam-1853	462	14	x	x	X
ejpam-1853	462	15	·	·	PUNCT
ejpam-1853	462	16	a−1	a−1	NOUN
ejpam-1853	462	17	)	)	PUNCT
ejpam-1853	462	18	=	=	PUNCT
ejpam-1853	462	19	β(a−1	β(a−1	X
ejpam-1853	462	20	)	)	PUNCT
ejpam-1853	462	21	=	=	SYM
ejpam-1853	462	22	α(a	α(a	NOUN
ejpam-1853	462	23	)	)	PUNCT
ejpam-1853	462	24	it	it	PRON
ejpam-1853	462	25	follows	follow	VERB
ejpam-1853	462	26	α(a	α(a	NOUN
ejpam-1853	462	27	·	·	PUNCT
ejpam-1853	462	28	x	x	SYM
ejpam-1853	462	29	·	·	PUNCT
ejpam-1853	462	30	a−1	a−1	PROPN
ejpam-1853	462	31	)	)	PUNCT
ejpam-1853	463	1	=	=	NOUN
ejpam-1853	464	1	β(a	β(a	NOUN
ejpam-1853	464	2	·	·	PUNCT
ejpam-1853	464	3	x	x	X
ejpam-1853	464	4	·	·	PUNCT
ejpam-1853	464	5	a−1	a−1	PROPN
ejpam-1853	464	6	)	)	PUNCT
ejpam-1853	464	7	.	.	PUNCT
ejpam-1853	465	1	then	then	ADV
ejpam-1853	465	2	a	a	DET
ejpam-1853	465	3	·	·	PUNCT
ejpam-1853	465	4	x	x	X
ejpam-1853	465	5	·	·	PUNCT
ejpam-1853	465	6	a−1	a−1	PROPN
ejpam-1853	465	7	∈	∈	PROPN
ejpam-1853	465	8	is(v	is(v	X
ejpam-1853	465	9	)	)	PUNCT
ejpam-1853	465	10	and	and	CCONJ
ejpam-1853	465	11	is(v	is(v	NOUN
ejpam-1853	465	12	)	)	PUNCT
ejpam-1853	465	13	is	be	AUX
ejpam-1853	465	14	a	a	DET
ejpam-1853	465	15	normal	normal	ADJ
ejpam-1853	465	16	subgroupoid	subgroupoid	NOUN
ejpam-1853	465	17	.	.	PUNCT
ejpam-1853	466	1	using	use	VERB
ejpam-1853	466	2	the	the	DET
ejpam-1853	466	3	linearity	linearity	NOUN
ejpam-1853	466	4	of	of	ADP
ejpam-1853	466	5	α	α	PROPN
ejpam-1853	466	6	and	and	CCONJ
ejpam-1853	466	7	β	β	PROPN
ejpam-1853	466	8	,	,	PUNCT
ejpam-1853	466	9	we	we	PRON
ejpam-1853	466	10	have	have	VERB
ejpam-1853	466	11	α(x	α(x	PROPN
ejpam-1853	466	12	−	−	PROPN
ejpam-1853	466	13	y	y	NOUN
ejpam-1853	466	14	)	)	PUNCT
ejpam-1853	466	15	=	=	NOUN
ejpam-1853	467	1	β(x	β(x	NOUN
ejpam-1853	467	2	−	−	PROPN
ejpam-1853	467	3	y	y	NOUN
ejpam-1853	467	4	)	)	PUNCT
ejpam-1853	467	5	and	and	CCONJ
ejpam-1853	467	6	α(kx	α(kx	NUM
ejpam-1853	467	7	)	)	PUNCT
ejpam-1853	467	8	=	=	SYM
ejpam-1853	467	9	β(kx	β(kx	X
ejpam-1853	467	10	)	)	PUNCT
ejpam-1853	467	11	for	for	ADP
ejpam-1853	467	12	all	all	DET
ejpam-1853	467	13	x	x	SYM
ejpam-1853	467	14	,	,	PUNCT
ejpam-1853	467	15	y	y	PROPN
ejpam-1853	467	16	∈	∈	PROPN
ejpam-1853	467	17	is(v	is(v	PRON
ejpam-1853	467	18	)	)	PUNCT
ejpam-1853	467	19	and	and	CCONJ
ejpam-1853	467	20	k	k	PROPN
ejpam-1853	467	21	∈	∈	PROPN
ejpam-1853	468	1	k	k	X
ejpam-1853	468	2	.	.	PUNCT
ejpam-1853	469	1	therefore	therefore	ADV
ejpam-1853	469	2	,	,	PUNCT
ejpam-1853	469	3	is(v	is(v	X
ejpam-1853	469	4	)	)	PUNCT
ejpam-1853	469	5	is	be	AUX
ejpam-1853	469	6	a	a	DET
ejpam-1853	469	7	vector	vector	NOUN
ejpam-1853	469	8	subspace	subspace	NOUN
ejpam-1853	469	9	.	.	PUNCT
ejpam-1853	470	1	hence	hence	ADV
ejpam-1853	470	2	,	,	PUNCT
ejpam-1853	470	3	is(v	is(v	PUNCT
ejpam-1853	470	4	)	)	PUNCT
ejpam-1853	470	5	is	be	AUX
ejpam-1853	470	6	a	a	DET
ejpam-1853	470	7	vector	vector	NOUN
ejpam-1853	470	8	space−	space−	ADJ
ejpam-1853	470	9	normal	normal	ADJ
ejpam-1853	470	10	subgroupoid	subgroupoid	NOUN
ejpam-1853	470	11	.	.	PUNCT
ejpam-1853	471	1	the	the	DET
ejpam-1853	471	2	group	group	NOUN
ejpam-1853	471	3	-	-	PUNCT
ejpam-1853	471	4	subgroupoid	subgroupoid	NOUN
ejpam-1853	471	5	is(v	is(v	PUNCT
ejpam-1853	471	6	)	)	PUNCT
ejpam-1853	471	7	is	be	AUX
ejpam-1853	471	8	the	the	DET
ejpam-1853	471	9	union	union	NOUN
ejpam-1853	471	10	of	of	ADP
ejpam-1853	471	11	all	all	PRON
ejpam-1853	471	12	isotropy	isotropy	VERB
ejpam-1853	471	13	groups	group	NOUN
ejpam-1853	471	14	of	of	ADP
ejpam-1853	471	15	v	v	NUM
ejpam-1853	471	16	and	and	CCONJ
ejpam-1853	471	17	it	it	PRON
ejpam-1853	471	18	is	be	AUX
ejpam-1853	471	19	called	call	VERB
ejpam-1853	471	20	the	the	DET
ejpam-1853	471	21	isotropy	isotropy	ADJ
ejpam-1853	471	22	bundle	bundle	NOUN
ejpam-1853	471	23	of	of	ADP
ejpam-1853	471	24	the	the	DET
ejpam-1853	471	25	vector	vector	NOUN
ejpam-1853	471	26	space	space	NOUN
ejpam-1853	471	27	-	-	PUNCT
ejpam-1853	471	28	groupoid	groupoid	NOUN
ejpam-1853	471	29	(	(	PUNCT
ejpam-1853	471	30	v	v	NOUN
ejpam-1853	471	31	,	,	PUNCT
ejpam-1853	471	32	v0	v0	NOUN
ejpam-1853	471	33	)	)	PUNCT
ejpam-1853	471	34	.	.	PUNCT
ejpam-1853	472	1	example	example	NOUN
ejpam-1853	473	1	3	3	X
ejpam-1853	473	2	.	.	PUNCT
ejpam-1853	473	3	let	let	VERB
ejpam-1853	473	4	a	a	DET
ejpam-1853	473	5	∈	∈	PROPN
ejpam-1853	473	6	r	r	NOUN
ejpam-1853	473	7	,	,	PUNCT
ejpam-1853	473	8	a	a	PRON
ejpam-1853	473	9	6=	6=	NUM
ejpam-1853	473	10	1	1	NUM
ejpam-1853	473	11	.	.	PUNCT
ejpam-1853	473	12	consider	consider	VERB
ejpam-1853	473	13	the	the	DET
ejpam-1853	473	14	vector	vector	NOUN
ejpam-1853	473	15	spaces	space	NOUN
ejpam-1853	473	16	groups	group	NOUN
ejpam-1853	473	17	v	v	ADP
ejpam-1853	473	18	:	:	PUNCT
ejpam-1853	473	19	=	=	SYM
ejpam-1853	473	20	r3	r3	PROPN
ejpam-1853	473	21	and	and	CCONJ
ejpam-1853	473	22	v0	v0	NOUN
ejpam-1853	473	23	:	:	PUNCT
ejpam-1853	473	24	=	=	SYM
ejpam-1853	473	25	r.	r.	PROPN
ejpam-1853	473	26	for	for	ADP
ejpam-1853	473	27	(	(	PUNCT
ejpam-1853	473	28	v	v	NOUN
ejpam-1853	473	29	,	,	PUNCT
ejpam-1853	473	30	v0	v0	NOUN
ejpam-1853	473	31	)	)	PUNCT
ejpam-1853	473	32	,	,	PUNCT
ejpam-1853	473	33	we	we	PRON
ejpam-1853	473	34	define	define	VERB
ejpam-1853	473	35	the	the	DET
ejpam-1853	473	36	structure	structure	NOUN
ejpam-1853	473	37	functions	function	NOUN
ejpam-1853	473	38	α	α	NOUN
ejpam-1853	473	39	,	,	PUNCT
ejpam-1853	473	40	β	β	X
ejpam-1853	473	41	:	:	PUNCT
ejpam-1853	473	42	r3→	r3→	SYM
ejpam-1853	473	43	r	r	NOUN
ejpam-1853	473	44	,	,	PUNCT
ejpam-1853	473	45	ε	ε	PROPN
ejpam-1853	473	46	:	:	PUNCT
ejpam-1853	473	47	r→	r→	PROPN
ejpam-1853	473	48	r3	r3	PROPN
ejpam-1853	473	49	and	and	CCONJ
ejpam-1853	473	50	m.	m.	PROPN
ejpam-1853	473	51	ivan	ivan	PROPN
ejpam-1853	473	52	/	/	PUNCT
ejpam-1853	473	53	eur	eur	PROPN
ejpam-1853	473	54	.	.	PUNCT
ejpam-1853	474	1	j.	j.	PROPN
ejpam-1853	474	2	pure	pure	PROPN
ejpam-1853	474	3	appl	appl	PROPN
ejpam-1853	474	4	.	.	PROPN
ejpam-1853	474	5	math	math	PROPN
ejpam-1853	474	6	,	,	PUNCT
ejpam-1853	474	7	6	6	NUM
ejpam-1853	474	8	(	(	PUNCT
ejpam-1853	474	9	2013	2013	NUM
ejpam-1853	474	10	)	)	PUNCT
ejpam-1853	474	11	,	,	PUNCT
ejpam-1853	474	12	469	469	NUM
ejpam-1853	474	13	-	-	SYM
ejpam-1853	474	14	484	484	NUM
ejpam-1853	475	1	481	481	NUM
ejpam-1853	475	2	i	i	INTJ
ejpam-1853	475	3	:	:	PUNCT
ejpam-1853	475	4	r3	r3	PROPN
ejpam-1853	475	5	→	→	SYM
ejpam-1853	475	6	r3	r3	PROPN
ejpam-1853	475	7	as	as	SCONJ
ejpam-1853	475	8	follows	follow	VERB
ejpam-1853	475	9	:	:	PUNCT
ejpam-1853	475	10	α(x1	α(x1	ADJ
ejpam-1853	475	11	,	,	PUNCT
ejpam-1853	475	12	x2	x2	PROPN
ejpam-1853	475	13	,	,	PUNCT
ejpam-1853	475	14	x3	x3	ADJ
ejpam-1853	475	15	)	)	PUNCT
ejpam-1853	475	16	:	:	PUNCT
ejpam-1853	476	1	=	=	PUNCT
ejpam-1853	476	2	ax1	ax1	PROPN
ejpam-1853	476	3	+	+	CCONJ
ejpam-1853	476	4	x2	x2	ADJ
ejpam-1853	476	5	,	,	PUNCT
ejpam-1853	476	6	β(x1	β(x1	ADJ
ejpam-1853	476	7	,	,	PUNCT
ejpam-1853	476	8	x2	x2	PROPN
ejpam-1853	476	9	,	,	PUNCT
ejpam-1853	476	10	x3	x3	ADJ
ejpam-1853	476	11	)	)	PUNCT
ejpam-1853	476	12	:	:	PUNCT
ejpam-1853	477	1	=	=	SYM
ejpam-1853	477	2	x1	x1	PROPN
ejpam-1853	478	1	+	+	CCONJ
ejpam-1853	478	2	x2	x2	ADJ
ejpam-1853	478	3	,	,	PUNCT
ejpam-1853	478	4	ε(x2	ε(x2	NOUN
ejpam-1853	478	5	)	)	PUNCT
ejpam-1853	478	6	:	:	PUNCT
ejpam-1853	479	1	=	=	SYM
ejpam-1853	479	2	(	(	PUNCT
ejpam-1853	479	3	0	0	NUM
ejpam-1853	479	4	,	,	PUNCT
ejpam-1853	479	5	x2	x2	PROPN
ejpam-1853	479	6	,	,	PUNCT
ejpam-1853	479	7	0	0	NUM
ejpam-1853	479	8	)	)	PUNCT
ejpam-1853	479	9	and	and	CCONJ
ejpam-1853	479	10	i(x1	i(x1	ADJ
ejpam-1853	479	11	,	,	PUNCT
ejpam-1853	479	12	x2	x2	PROPN
ejpam-1853	479	13	,	,	PUNCT
ejpam-1853	479	14	x3	x3	ADJ
ejpam-1853	479	15	)	)	PUNCT
ejpam-1853	479	16	:	:	PUNCT
ejpam-1853	480	1	=	=	SYM
ejpam-1853	480	2	(	(	PUNCT
ejpam-1853	480	3	−x1	−x1	PROPN
ejpam-1853	480	4	,	,	PUNCT
ejpam-1853	480	5	(	(	PUNCT
ejpam-1853	480	6	a+	a+	X
ejpam-1853	480	7	1)x1	1)x1	NUM
ejpam-1853	480	8	+	+	NOUN
ejpam-1853	480	9	x2,−x3	x2,−x3	NUM
ejpam-1853	480	10	)	)	PUNCT
ejpam-1853	480	11	,	,	PUNCT
ejpam-1853	480	12	for	for	ADP
ejpam-1853	480	13	all	all	DET
ejpam-1853	480	14	x1	x1	PROPN
ejpam-1853	480	15	,	,	PUNCT
ejpam-1853	480	16	x2	x2	PROPN
ejpam-1853	480	17	,	,	PUNCT
ejpam-1853	480	18	x3	x3	PROPN
ejpam-1853	480	19	∈	∈	PROPN
ejpam-1853	480	20	r.	r.	PROPN
ejpam-1853	480	21	let	let	VERB
ejpam-1853	480	22	v(2	v(2	PROPN
ejpam-1853	480	23	)	)	PUNCT
ejpam-1853	480	24	:	:	PUNCT
ejpam-1853	480	25	=	=	SYM
ejpam-1853	480	26	{	{	PUNCT
ejpam-1853	480	27	(	(	PUNCT
ejpam-1853	480	28	(	(	PUNCT
ejpam-1853	480	29	x1	x1	PROPN
ejpam-1853	480	30	,	,	PUNCT
ejpam-1853	480	31	x2	x2	PROPN
ejpam-1853	480	32	,	,	PUNCT
ejpam-1853	480	33	x3	x3	ADJ
ejpam-1853	480	34	)	)	PUNCT
ejpam-1853	480	35	,	,	PUNCT
ejpam-1853	480	36	(	(	PUNCT
ejpam-1853	480	37	y1	y1	INTJ
ejpam-1853	480	38	,	,	PUNCT
ejpam-1853	480	39	y2	y2	PROPN
ejpam-1853	480	40	,	,	PUNCT
ejpam-1853	480	41	y3	y3	NOUN
ejpam-1853	480	42	)	)	PUNCT
ejpam-1853	480	43	)	)	PUNCT
ejpam-1853	481	1	∈	∈	PROPN
ejpam-1853	481	2	r3×r3	r3×r3	NOUN
ejpam-1853	481	3	|	|	ADV
ejpam-1853	482	1	y2	y2	NOUN
ejpam-1853	482	2	=	=	SYM
ejpam-1853	483	1	x1	x1	PROPN
ejpam-1853	484	1	+	+	PROPN
ejpam-1853	484	2	x2−	x2−	PROPN
ejpam-1853	484	3	a	a	DET
ejpam-1853	484	4	y1	y1	NOUN
ejpam-1853	484	5	}	}	PUNCT
ejpam-1853	484	6	be	be	AUX
ejpam-1853	484	7	the	the	DET
ejpam-1853	484	8	set	set	NOUN
ejpam-1853	484	9	of	of	ADP
ejpam-1853	484	10	composable	composable	ADJ
ejpam-1853	484	11	pairs	pair	NOUN
ejpam-1853	484	12	.	.	PUNCT
ejpam-1853	485	1	the	the	DET
ejpam-1853	485	2	multiplication	multiplication	NOUN
ejpam-1853	485	3	m	m	VERB
ejpam-1853	485	4	:	:	PUNCT
ejpam-1853	485	5	v(2)→	v(2)→	NUM
ejpam-1853	485	6	v	v	NOUN
ejpam-1853	485	7	is	be	AUX
ejpam-1853	485	8	given	give	VERB
ejpam-1853	485	9	by	by	ADP
ejpam-1853	485	10	:	:	PUNCT
ejpam-1853	485	11	(	(	PUNCT
ejpam-1853	485	12	x1	x1	PROPN
ejpam-1853	485	13	,	,	PUNCT
ejpam-1853	485	14	x2	x2	PROPN
ejpam-1853	485	15	,	,	PUNCT
ejpam-1853	485	16	x3	x3	ADJ
ejpam-1853	485	17	)	)	PUNCT
ejpam-1853	485	18	·	·	PUNCT
ejpam-1853	485	19	(	(	PUNCT
ejpam-1853	485	20	y1	y1	INTJ
ejpam-1853	485	21	,	,	PUNCT
ejpam-1853	485	22	y2	y2	PROPN
ejpam-1853	485	23	,	,	PUNCT
ejpam-1853	485	24	y3	y3	PROPN
ejpam-1853	485	25	)	)	PUNCT
ejpam-1853	485	26	:	:	PUNCT
ejpam-1853	485	27	=	=	SYM
ejpam-1853	485	28	(	(	PUNCT
ejpam-1853	485	29	x1	x1	PROPN
ejpam-1853	485	30	+	+	X
ejpam-1853	485	31	y1	y1	NOUN
ejpam-1853	485	32	,	,	PUNCT
ejpam-1853	485	33	x2−	x2−	PROPN
ejpam-1853	485	34	a	a	DET
ejpam-1853	485	35	y1	y1	PROPN
ejpam-1853	485	36	,	,	PUNCT
ejpam-1853	485	37	x3	x3	ADJ
ejpam-1853	485	38	+	+	CCONJ
ejpam-1853	485	39	y3	y3	NOUN
ejpam-1853	485	40	)	)	PUNCT
ejpam-1853	485	41	,	,	PUNCT
ejpam-1853	485	42	if	if	SCONJ
ejpam-1853	485	43	y2	y2	PROPN
ejpam-1853	485	44	=	=	SYM
ejpam-1853	486	1	x1	x1	PROPN
ejpam-1853	487	1	+	+	PROPN
ejpam-1853	487	2	x2−	x2−	PROPN
ejpam-1853	487	3	a	a	DET
ejpam-1853	487	4	y1	y1	NOUN
ejpam-1853	487	5	.	.	PUNCT
ejpam-1853	488	1	it	it	PRON
ejpam-1853	488	2	is	be	AUX
ejpam-1853	488	3	easy	easy	ADJ
ejpam-1853	488	4	to	to	PART
ejpam-1853	488	5	check	check	VERB
ejpam-1853	488	6	that	that	SCONJ
ejpam-1853	488	7	the	the	DET
ejpam-1853	488	8	above	above	ADJ
ejpam-1853	488	9	structure	structure	NOUN
ejpam-1853	488	10	functions	function	NOUN
ejpam-1853	488	11	determine	determine	VERB
ejpam-1853	488	12	on	on	ADP
ejpam-1853	488	13	v	v	ADP
ejpam-1853	488	14	a	a	DET
ejpam-1853	488	15	structure	structure	NOUN
ejpam-1853	488	16	of	of	ADP
ejpam-1853	488	17	a	a	DET
ejpam-1853	488	18	groupoid	groupoid	PROPN
ejpam-1853	488	19	over	over	ADP
ejpam-1853	488	20	v0	v0	PROPN
ejpam-1853	488	21	.	.	PUNCT
ejpam-1853	489	1	also	also	ADV
ejpam-1853	489	2	,	,	PUNCT
ejpam-1853	489	3	the	the	DET
ejpam-1853	489	4	maps	map	NOUN
ejpam-1853	489	5	α	α	PRON
ejpam-1853	489	6	,	,	PUNCT
ejpam-1853	489	7	β	β	PROPN
ejpam-1853	489	8	,	,	PUNCT
ejpam-1853	489	9	ε	ε	PROPN
ejpam-1853	489	10	and	and	CCONJ
ejpam-1853	489	11	i	i	PRON
ejpam-1853	489	12	are	be	AUX
ejpam-1853	489	13	linear	linear	ADJ
ejpam-1853	489	14	maps	map	NOUN
ejpam-1853	489	15	.	.	PUNCT
ejpam-1853	490	1	therefore	therefore	ADV
ejpam-1853	490	2	,	,	PUNCT
ejpam-1853	490	3	the	the	DET
ejpam-1853	490	4	conditions	condition	NOUN
ejpam-1853	490	5	(	(	PUNCT
ejpam-1853	490	6	i	i	NOUN
ejpam-1853	490	7	)	)	PUNCT
ejpam-1853	490	8	and	and	CCONJ
ejpam-1853	490	9	(	(	PUNCT
ejpam-1853	490	10	ii	ii	NOUN
ejpam-1853	490	11	)	)	PUNCT
ejpam-1853	490	12	from	from	ADP
ejpam-1853	490	13	the	the	DET
ejpam-1853	490	14	definition	definition	NOUN
ejpam-1853	490	15	6	6	NUM
ejpam-1853	490	16	hold	hold	NOUN
ejpam-1853	490	17	.	.	PUNCT
ejpam-1853	491	1	let	let	VERB
ejpam-1853	491	2	x	x	SYM
ejpam-1853	491	3	,	,	PUNCT
ejpam-1853	491	4	y	y	PROPN
ejpam-1853	491	5	,	,	PUNCT
ejpam-1853	491	6	z	z	PROPN
ejpam-1853	491	7	,	,	PUNCT
ejpam-1853	491	8	t	t	PROPN
ejpam-1853	491	9	∈	∈	PROPN
ejpam-1853	491	10	r3	r3	PROPN
ejpam-1853	491	11	such	such	ADJ
ejpam-1853	491	12	that	that	SCONJ
ejpam-1853	491	13	x	x	X
ejpam-1853	491	14	·	·	PUNCT
ejpam-1853	491	15	y	y	PROPN
ejpam-1853	491	16	and	and	CCONJ
ejpam-1853	491	17	z	z	PROPN
ejpam-1853	491	18	·	·	PUNCT
ejpam-1853	491	19	t	t	NOUN
ejpam-1853	491	20	are	be	AUX
ejpam-1853	491	21	defined	define	VERB
ejpam-1853	491	22	.	.	PUNCT
ejpam-1853	492	1	then	then	ADV
ejpam-1853	492	2	x	x	X
ejpam-1853	492	3	=	=	PRON
ejpam-1853	492	4	(	(	PUNCT
ejpam-1853	492	5	x1	x1	PROPN
ejpam-1853	492	6	,	,	PUNCT
ejpam-1853	492	7	x2	x2	PROPN
ejpam-1853	492	8	,	,	PUNCT
ejpam-1853	492	9	x3	x3	ADJ
ejpam-1853	492	10	)	)	PUNCT
ejpam-1853	492	11	,	,	PUNCT
ejpam-1853	492	12	y	y	PROPN
ejpam-1853	492	13	=	=	SYM
ejpam-1853	492	14	(	(	PUNCT
ejpam-1853	492	15	y1	y1	PROPN
ejpam-1853	492	16	,	,	PUNCT
ejpam-1853	492	17	y2	y2	PROPN
ejpam-1853	492	18	,	,	PUNCT
ejpam-1853	492	19	y3	y3	PROPN
ejpam-1853	492	20	)	)	PUNCT
ejpam-1853	492	21	,	,	PUNCT
ejpam-1853	492	22	z	z	NOUN
ejpam-1853	492	23	=	=	SYM
ejpam-1853	492	24	(	(	PUNCT
ejpam-1853	492	25	z1	z1	PROPN
ejpam-1853	492	26	,	,	PUNCT
ejpam-1853	492	27	z2	z2	PROPN
ejpam-1853	492	28	,	,	PUNCT
ejpam-1853	492	29	z3	z3	PROPN
ejpam-1853	492	30	)	)	PUNCT
ejpam-1853	492	31	,	,	PUNCT
ejpam-1853	492	32	t	t	PROPN
ejpam-1853	492	33	=	=	SYM
ejpam-1853	492	34	(	(	PUNCT
ejpam-1853	492	35	t1	t1	NOUN
ejpam-1853	492	36	,	,	PUNCT
ejpam-1853	492	37	t2	t2	NOUN
ejpam-1853	492	38	,	,	PUNCT
ejpam-1853	492	39	t3	t3	PROPN
ejpam-1853	492	40	)	)	PUNCT
ejpam-1853	493	1	such	such	ADJ
ejpam-1853	493	2	that	that	DET
ejpam-1853	493	3	y2	y2	NOUN
ejpam-1853	493	4	=	=	PUNCT
ejpam-1853	494	1	x1	x1	PROPN
ejpam-1853	495	1	+	+	CCONJ
ejpam-1853	496	1	x1	x1	NUM
ejpam-1853	496	2	−	−	PROPN
ejpam-1853	496	3	a	a	DET
ejpam-1853	496	4	y1	y1	NOUN
ejpam-1853	496	5	and	and	CCONJ
ejpam-1853	496	6	t2	t2	NOUN
ejpam-1853	496	7	=	=	SYM
ejpam-1853	496	8	z1	z1	PROPN
ejpam-1853	496	9	+	+	CCONJ
ejpam-1853	496	10	z2	z2	PROPN
ejpam-1853	496	11	−	−	PROPN
ejpam-1853	496	12	at1	at1	PROPN
ejpam-1853	496	13	.	.	PUNCT
ejpam-1853	497	1	we	we	PRON
ejpam-1853	497	2	have	have	VERB
ejpam-1853	497	3	x	x	X
ejpam-1853	497	4	·	·	PUNCT
ejpam-1853	497	5	y	y	SYM
ejpam-1853	497	6	=	=	SYM
ejpam-1853	497	7	(	(	PUNCT
ejpam-1853	497	8	x1	x1	PROPN
ejpam-1853	497	9	+	+	X
ejpam-1853	497	10	y1	y1	NOUN
ejpam-1853	497	11	,	,	PUNCT
ejpam-1853	497	12	x2−	x2−	PROPN
ejpam-1853	497	13	a	a	DET
ejpam-1853	497	14	y1	y1	PROPN
ejpam-1853	497	15	,	,	PUNCT
ejpam-1853	497	16	x3	x3	ADJ
ejpam-1853	497	17	+	+	CCONJ
ejpam-1853	497	18	y3	y3	NOUN
ejpam-1853	497	19	)	)	PUNCT
ejpam-1853	497	20	,	,	PUNCT
ejpam-1853	497	21	z	z	NOUN
ejpam-1853	497	22	·	·	PUNCT
ejpam-1853	497	23	t	t	NOUN
ejpam-1853	497	24	=	=	SYM
ejpam-1853	497	25	(	(	PUNCT
ejpam-1853	497	26	z1	z1	PROPN
ejpam-1853	497	27	+	+	X
ejpam-1853	497	28	t1	t1	NOUN
ejpam-1853	497	29	,	,	PUNCT
ejpam-1853	497	30	z2−	z2−	PROPN
ejpam-1853	497	31	at1	at1	PROPN
ejpam-1853	497	32	,	,	PUNCT
ejpam-1853	497	33	z3	z3	PROPN
ejpam-1853	497	34	+	+	CCONJ
ejpam-1853	497	35	t3	t3	PROPN
ejpam-1853	497	36	)	)	PUNCT
ejpam-1853	497	37	.	.	PUNCT
ejpam-1853	498	1	then	then	ADV
ejpam-1853	498	2	(	(	PUNCT
ejpam-1853	498	3	x	x	X
ejpam-1853	498	4	·	·	PUNCT
ejpam-1853	498	5	y	y	X
ejpam-1853	498	6	)	)	PUNCT
ejpam-1853	498	7	+	+	CCONJ
ejpam-1853	498	8	(	(	PUNCT
ejpam-1853	498	9	z	z	NOUN
ejpam-1853	498	10	·	·	PUNCT
ejpam-1853	498	11	t	t	X
ejpam-1853	498	12	)	)	PUNCT
ejpam-1853	498	13	=	=	PUNCT
ejpam-1853	498	14	(	(	PUNCT
ejpam-1853	498	15	x1	x1	PROPN
ejpam-1853	498	16	+	+	NUM
ejpam-1853	498	17	y1	y1	ADJ
ejpam-1853	498	18	+	+	X
ejpam-1853	498	19	z1	z1	ADJ
ejpam-1853	498	20	+	+	X
ejpam-1853	498	21	t1	t1	NOUN
ejpam-1853	498	22	,	,	PUNCT
ejpam-1853	498	23	x2−	x2−	PROPN
ejpam-1853	498	24	a	a	DET
ejpam-1853	498	25	y1	y1	NOUN
ejpam-1853	498	26	+	+	X
ejpam-1853	498	27	z2−	z2−	PROPN
ejpam-1853	498	28	at1	at1	PROPN
ejpam-1853	498	29	,	,	PUNCT
ejpam-1853	498	30	x3	x3	ADJ
ejpam-1853	498	31	+	+	CCONJ
ejpam-1853	498	32	y3	y3	NOUN
ejpam-1853	498	33	+	+	CCONJ
ejpam-1853	498	34	z3	z3	PROPN
ejpam-1853	498	35	+	+	CCONJ
ejpam-1853	498	36	t3	t3	NOUN
ejpam-1853	498	37	)	)	PUNCT
ejpam-1853	498	38	and	and	CCONJ
ejpam-1853	498	39	(	(	PUNCT
ejpam-1853	498	40	x	x	X
ejpam-1853	498	41	+	+	NUM
ejpam-1853	498	42	z	z	NOUN
ejpam-1853	498	43	)	)	PUNCT
ejpam-1853	498	44	·	·	PUNCT
ejpam-1853	499	1	(	(	PUNCT
ejpam-1853	499	2	y	y	PROPN
ejpam-1853	499	3	+	+	PROPN
ejpam-1853	499	4	t	t	PROPN
ejpam-1853	499	5	)	)	PUNCT
ejpam-1853	499	6	=	=	PUNCT
ejpam-1853	499	7	(	(	PUNCT
ejpam-1853	499	8	x1	x1	PROPN
ejpam-1853	499	9	+	+	PROPN
ejpam-1853	499	10	z1	z1	ADJ
ejpam-1853	499	11	+	+	NUM
ejpam-1853	499	12	y1	y1	NOUN
ejpam-1853	499	13	+	+	X
ejpam-1853	499	14	t1	t1	NOUN
ejpam-1853	499	15	,	,	PUNCT
ejpam-1853	499	16	x2	x2	PROPN
ejpam-1853	499	17	+	+	X
ejpam-1853	499	18	z2−	z2−	NOUN
ejpam-1853	499	19	a(y1	a(y1	ADJ
ejpam-1853	499	20	+	+	CCONJ
ejpam-1853	499	21	t1	t1	NOUN
ejpam-1853	499	22	)	)	PUNCT
ejpam-1853	499	23	,	,	PUNCT
ejpam-1853	499	24	x3	x3	ADJ
ejpam-1853	499	25	+	+	SYM
ejpam-1853	499	26	z3	z3	ADJ
ejpam-1853	499	27	+	+	SYM
ejpam-1853	499	28	y3	y3	NOUN
ejpam-1853	499	29	+	+	CCONJ
ejpam-1853	499	30	t3	t3	NOUN
ejpam-1853	499	31	)	)	PUNCT
ejpam-1853	499	32	.	.	PUNCT
ejpam-1853	500	1	hence	hence	ADV
ejpam-1853	500	2	,	,	PUNCT
ejpam-1853	500	3	(	(	PUNCT
ejpam-1853	500	4	x	x	X
ejpam-1853	500	5	·	·	PUNCT
ejpam-1853	500	6	y	y	X
ejpam-1853	500	7	)	)	PUNCT
ejpam-1853	500	8	+	+	CCONJ
ejpam-1853	500	9	(	(	PUNCT
ejpam-1853	500	10	z	z	NOUN
ejpam-1853	500	11	·	·	PUNCT
ejpam-1853	500	12	t	t	X
ejpam-1853	500	13	)	)	PUNCT
ejpam-1853	500	14	=	=	SYM
ejpam-1853	501	1	(	(	PUNCT
ejpam-1853	501	2	x	x	X
ejpam-1853	501	3	+	+	NUM
ejpam-1853	501	4	y	y	NOUN
ejpam-1853	501	5	)	)	PUNCT
ejpam-1853	501	6	·	·	PUNCT
ejpam-1853	502	1	(	(	PUNCT
ejpam-1853	502	2	z	z	X
ejpam-1853	502	3	+	+	NUM
ejpam-1853	502	4	t	t	PROPN
ejpam-1853	502	5	)	)	PUNCT
ejpam-1853	502	6	and	and	CCONJ
ejpam-1853	502	7	the	the	DET
ejpam-1853	502	8	interchange	interchange	NOUN
ejpam-1853	502	9	law	law	NOUN
ejpam-1853	502	10	(	(	PUNCT
ejpam-1853	502	11	10	10	NUM
ejpam-1853	502	12	)	)	PUNCT
ejpam-1853	502	13	holds	hold	VERB
ejpam-1853	502	14	.	.	PUNCT
ejpam-1853	503	1	therefore	therefore	ADV
ejpam-1853	503	2	,	,	PUNCT
ejpam-1853	503	3	(	(	PUNCT
ejpam-1853	503	4	r3,α	r3,α	PROPN
ejpam-1853	503	5	,	,	PUNCT
ejpam-1853	503	6	β	β	X
ejpam-1853	503	7	,	,	PUNCT
ejpam-1853	503	8	m	m	PROPN
ejpam-1853	503	9	,	,	PUNCT
ejpam-1853	503	10	ε	ε	PROPN
ejpam-1853	503	11	,	,	PUNCT
ejpam-1853	503	12	i,+,ϕ,r	i,+,ϕ,r	PROPN
ejpam-1853	503	13	)	)	PUNCT
ejpam-1853	503	14	is	be	AUX
ejpam-1853	503	15	a	a	DET
ejpam-1853	503	16	vector	vector	NOUN
ejpam-1853	503	17	space	space	NOUN
ejpam-1853	503	18	-	-	PUNCT
ejpam-1853	503	19	groupoid	groupoid	PROPN
ejpam-1853	503	20	.	.	PUNCT
ejpam-1853	504	1	we	we	PRON
ejpam-1853	504	2	have	have	AUX
ejpam-1853	504	3	ε(v0	ε(v0	VERB
ejpam-1853	504	4	)	)	PUNCT
ejpam-1853	505	1	=	=	PRON
ejpam-1853	505	2	{	{	PUNCT
ejpam-1853	505	3	(	(	PUNCT
ejpam-1853	505	4	0	0	NUM
ejpam-1853	505	5	,	,	PUNCT
ejpam-1853	505	6	u	u	NOUN
ejpam-1853	505	7	,	,	PUNCT
ejpam-1853	505	8	0)|u	0)|u	NUM
ejpam-1853	505	9	∈	∈	NOUN
ejpam-1853	505	10	r	r	NOUN
ejpam-1853	505	11	}	}	PUNCT
ejpam-1853	505	12	and	and	CCONJ
ejpam-1853	505	13	is(v	is(v	X
ejpam-1853	505	14	)	)	PUNCT
ejpam-1853	506	1	=	=	PRON
ejpam-1853	506	2	{	{	PUNCT
ejpam-1853	506	3	(	(	PUNCT
ejpam-1853	506	4	0	0	NUM
ejpam-1853	506	5	,	,	PUNCT
ejpam-1853	506	6	u	u	NOUN
ejpam-1853	506	7	,	,	PUNCT
ejpam-1853	506	8	v)|u	v)|u	NOUN
ejpam-1853	506	9	,	,	PUNCT
ejpam-1853	506	10	v	v	NOUN
ejpam-1853	506	11	∈	∈	NOUN
ejpam-1853	506	12	r	r	NOUN
ejpam-1853	506	13	}	}	PUNCT
ejpam-1853	506	14	are	be	AUX
ejpam-1853	506	15	vector	vector	NOUN
ejpam-1853	506	16	space	space	NOUN
ejpam-1853	506	17	-	-	PUNCT
ejpam-1853	506	18	normal	normal	ADJ
ejpam-1853	506	19	subgroupoid	subgroupoid	NOUN
ejpam-1853	506	20	.	.	PUNCT
ejpam-1853	507	1	the	the	DET
ejpam-1853	507	2	isotropy	isotropy	ADJ
ejpam-1853	507	3	group	group	NOUN
ejpam-1853	507	4	at	at	ADP
ejpam-1853	507	5	e0	e0	PROPN
ejpam-1853	507	6	=	=	X
ejpam-1853	507	7	0	0	PUNCT
ejpam-1853	507	8	is	be	AUX
ejpam-1853	507	9	v	v	NOUN
ejpam-1853	507	10	(	(	PUNCT
ejpam-1853	507	11	0	0	NUM
ejpam-1853	507	12	)	)	PUNCT
ejpam-1853	507	13	=	=	PRON
ejpam-1853	507	14	{	{	PUNCT
ejpam-1853	507	15	(	(	PUNCT
ejpam-1853	507	16	0,0	0,0	NOUN
ejpam-1853	507	17	,	,	PUNCT
ejpam-1853	507	18	v)|v	v)|v	NOUN
ejpam-1853	507	19	∈	∈	NOUN
ejpam-1853	507	20	r	r	NOUN
ejpam-1853	507	21	}	}	PUNCT
ejpam-1853	507	22	.	.	PUNCT
ejpam-1853	508	1	let	let	VERB
ejpam-1853	508	2	us	we	PRON
ejpam-1853	508	3	we	we	PRON
ejpam-1853	508	4	consider	consider	VERB
ejpam-1853	508	5	the	the	DET
ejpam-1853	508	6	euclidean	euclidean	ADJ
ejpam-1853	508	7	space	space	NOUN
ejpam-1853	508	8	r3	r3	PROPN
ejpam-1853	508	9	with	with	ADP
ejpam-1853	508	10	the	the	DET
ejpam-1853	508	11	cartesian	cartesian	ADJ
ejpam-1853	508	12	coordinate	coordinate	NOUN
ejpam-1853	508	13	system	system	NOUN
ejpam-1853	508	14	ox1	ox1	PROPN
ejpam-1853	508	15	x2	x2	NOUN
ejpam-1853	508	16	x3	x3	PROPN
ejpam-1853	508	17	.	.	PUNCT
ejpam-1853	509	1	the	the	DET
ejpam-1853	509	2	α−fibres	α−fibres	NUM
ejpam-1853	509	3	α−1(u	α−1(u	NOUN
ejpam-1853	509	4	)	)	PUNCT
ejpam-1853	509	5	for	for	SCONJ
ejpam-1853	509	6	u	u	NOUN
ejpam-1853	509	7	∈	∈	PROPN
ejpam-1853	509	8	r	r	NOUN
ejpam-1853	509	9	are	be	AUX
ejpam-1853	509	10	represented	represent	VERB
ejpam-1853	509	11	by	by	ADP
ejpam-1853	509	12	parallel	parallel	ADJ
ejpam-1853	509	13	planes	plane	NOUN
ejpam-1853	509	14	of	of	ADP
ejpam-1853	509	15	equation	equation	NOUN
ejpam-1853	509	16	x1	x1	PROPN
ejpam-1853	510	1	+	+	PROPN
ejpam-1853	510	2	2x2−u=	2x2−u=	NOUN
ejpam-1853	510	3	0	0	NUM
ejpam-1853	510	4	.	.	PUNCT
ejpam-1853	511	1	also	also	ADV
ejpam-1853	511	2	,	,	PUNCT
ejpam-1853	511	3	the	the	DET
ejpam-1853	511	4	β−fibres	β−fibre	NOUN
ejpam-1853	511	5	β−1(v	β−1(v	SYM
ejpam-1853	511	6	)	)	PUNCT
ejpam-1853	511	7	for	for	ADP
ejpam-1853	511	8	v	v	NOUN
ejpam-1853	511	9	∈	∈	NOUN
ejpam-1853	511	10	r	r	NOUN
ejpam-1853	511	11	are	be	AUX
ejpam-1853	511	12	represented	represent	VERB
ejpam-1853	511	13	by	by	ADP
ejpam-1853	511	14	parallel	parallel	ADJ
ejpam-1853	511	15	planes	plane	NOUN
ejpam-1853	511	16	of	of	ADP
ejpam-1853	511	17	equation	equation	NOUN
ejpam-1853	511	18	x1	x1	PROPN
ejpam-1853	512	1	+	+	PROPN
ejpam-1853	512	2	x2−	x2−	PROPN
ejpam-1853	512	3	v	v	NOUN
ejpam-1853	512	4	=	=	SYM
ejpam-1853	512	5	0	0	X
ejpam-1853	512	6	.	.	PUNCT
ejpam-1853	513	1	let	let	AUX
ejpam-1853	513	2	be	be	AUX
ejpam-1853	513	3	the	the	DET
ejpam-1853	513	4	points	point	NOUN
ejpam-1853	513	5	a1	a1	NOUN
ejpam-1853	513	6	,	,	PUNCT
ejpam-1853	513	7	a2	a2	PROPN
ejpam-1853	513	8	,	,	PUNCT
ejpam-1853	513	9	a3	a3	NOUN
ejpam-1853	513	10	,	,	PUNCT
ejpam-1853	513	11	a4	a4	NOUN
ejpam-1853	513	12	associated	associate	VERB
ejpam-1853	513	13	to	to	ADP
ejpam-1853	513	14	elements	element	NOUN
ejpam-1853	513	15	ε(β(x	ε(β(x	NOUN
ejpam-1853	513	16	)	)	PUNCT
ejpam-1853	513	17	)	)	PUNCT
ejpam-1853	513	18	,	,	PUNCT
ejpam-1853	513	19	x	x	X
ejpam-1853	513	20	,	,	PUNCT
ejpam-1853	513	21	x	x	X
ejpam-1853	513	22	·	·	PUNCT
ejpam-1853	513	23	y	y	X
ejpam-1853	513	24	,	,	PUNCT
ejpam-1853	513	25	y	y	PROPN
ejpam-1853	513	26	∈	∈	PROPN
ejpam-1853	513	27	v	v	NOUN
ejpam-1853	513	28	,	,	PUNCT
ejpam-1853	513	29	for	for	ADP
ejpam-1853	513	30	β(x	β(x	NOUN
ejpam-1853	513	31	)	)	PUNCT
ejpam-1853	513	32	=	=	SYM
ejpam-1853	513	33	α(y	α(y	NOUN
ejpam-1853	513	34	)	)	PUNCT
ejpam-1853	513	35	.	.	PUNCT
ejpam-1853	514	1	we	we	PRON
ejpam-1853	514	2	have	have	VERB
ejpam-1853	514	3	a1(0	a1(0	PROPN
ejpam-1853	514	4	,	,	PUNCT
ejpam-1853	514	5	b1	b1	NOUN
ejpam-1853	514	6	+	+	CCONJ
ejpam-1853	514	7	b2	b2	NOUN
ejpam-1853	514	8	,	,	PUNCT
ejpam-1853	514	9	0	0	NUM
ejpam-1853	514	10	)	)	PUNCT
ejpam-1853	514	11	,	,	PUNCT
ejpam-1853	514	12	a2(b1	a2(b1	NOUN
ejpam-1853	514	13	,	,	PUNCT
ejpam-1853	514	14	b2	b2	NOUN
ejpam-1853	514	15	,	,	PUNCT
ejpam-1853	514	16	b3	b3	PROPN
ejpam-1853	514	17	)	)	PUNCT
ejpam-1853	514	18	,	,	PUNCT
ejpam-1853	514	19	a3(b1	a3(b1	ADP
ejpam-1853	514	20	+	+	X
ejpam-1853	514	21	c1	c1	NOUN
ejpam-1853	514	22	,	,	PUNCT
ejpam-1853	514	23	b2	b2	NOUN
ejpam-1853	514	24	−	−	PROPN
ejpam-1853	514	25	ac1	ac1	PROPN
ejpam-1853	514	26	,	,	PUNCT
ejpam-1853	514	27	b3	b3	PROPN
ejpam-1853	514	28	+	+	CCONJ
ejpam-1853	514	29	c3	c3	PROPN
ejpam-1853	514	30	)	)	PUNCT
ejpam-1853	514	31	and	and	CCONJ
ejpam-1853	514	32	a4(c1	a4(c1	PROPN
ejpam-1853	514	33	,	,	PUNCT
ejpam-1853	514	34	b1	b1	NOUN
ejpam-1853	514	35	+	+	CCONJ
ejpam-1853	514	36	b2−	b2−	PROPN
ejpam-1853	514	37	ac1	ac1	PROPN
ejpam-1853	514	38	,	,	PUNCT
ejpam-1853	514	39	c3	c3	PROPN
ejpam-1853	514	40	)	)	PUNCT
ejpam-1853	514	41	.	.	PUNCT
ejpam-1853	515	1	then	then	ADV
ejpam-1853	515	2	:	:	PUNCT
ejpam-1853	515	3	the	the	DET
ejpam-1853	515	4	simple	simple	ADJ
ejpam-1853	515	5	quadrilateral	quadrilateral	ADJ
ejpam-1853	515	6	a1a2a3a4	a1a2a3a4	PROPN
ejpam-1853	515	7	is	be	AUX
ejpam-1853	515	8	a	a	DET
ejpam-1853	515	9	parallelogram	parallelogram	NOUN
ejpam-1853	515	10	.	.	PUNCT
ejpam-1853	516	1	indeed	indeed	ADV
ejpam-1853	516	2	,	,	PUNCT
ejpam-1853	516	3	the	the	DET
ejpam-1853	516	4	straight	straight	ADJ
ejpam-1853	516	5	line	line	NOUN
ejpam-1853	516	6	through	through	ADP
ejpam-1853	516	7	a1	a1	NOUN
ejpam-1853	516	8	and	and	CCONJ
ejpam-1853	516	9	a4	a4	NOUN
ejpam-1853	516	10	has	have	VERB
ejpam-1853	516	11	the	the	DET
ejpam-1853	516	12	equation	equation	NOUN
ejpam-1853	516	13	:	:	PUNCT
ejpam-1853	516	14	x1	x1	PROPN
ejpam-1853	516	15	c1	c1	PROPN
ejpam-1853	516	16	=	=	PUNCT
ejpam-1853	516	17	x2−(b1+b2	x2−(b1+b2	PROPN
ejpam-1853	516	18	)	)	PUNCT
ejpam-1853	517	1	−ac1	−ac1	NOUN
ejpam-1853	517	2	=	=	SYM
ejpam-1853	517	3	x3	x3	PROPN
ejpam-1853	517	4	c3	c3	PROPN
ejpam-1853	517	5	and	and	CCONJ
ejpam-1853	517	6	the	the	DET
ejpam-1853	517	7	distance	distance	NOUN
ejpam-1853	517	8	from	from	ADP
ejpam-1853	517	9	a1	a1	NOUN
ejpam-1853	517	10	and	and	CCONJ
ejpam-1853	517	11	a4	a4	NOUN
ejpam-1853	517	12	is	be	AUX
ejpam-1853	517	13	d(a1	d(a1	NOUN
ejpam-1853	517	14	,	,	PUNCT
ejpam-1853	517	15	a4	a4	NUM
ejpam-1853	517	16	)	)	PUNCT
ejpam-1853	517	17	=	=	SYM
ejpam-1853	518	1	p	p	X
ejpam-1853	518	2	(	(	PUNCT
ejpam-1853	518	3	1	1	NUM
ejpam-1853	518	4	+	+	NUM
ejpam-1853	518	5	a2)c2	a2)c2	X
ejpam-1853	518	6	1	1	NUM
ejpam-1853	518	7	+	+	NUM
ejpam-1853	518	8	c2	c2	PROPN
ejpam-1853	518	9	3	3	NUM
ejpam-1853	518	10	.	.	PUNCT
ejpam-1853	519	1	also	also	ADV
ejpam-1853	519	2	,	,	PUNCT
ejpam-1853	519	3	the	the	DET
ejpam-1853	519	4	straight	straight	ADJ
ejpam-1853	519	5	line	line	NOUN
ejpam-1853	519	6	through	through	ADP
ejpam-1853	519	7	a2	a2	PROPN
ejpam-1853	519	8	and	and	CCONJ
ejpam-1853	519	9	a3	a3	NOUN
ejpam-1853	519	10	has	have	VERB
ejpam-1853	519	11	the	the	DET
ejpam-1853	519	12	equation	equation	NOUN
ejpam-1853	519	13	:	:	PUNCT
ejpam-1853	519	14	x1−b1	x1−b1	PROPN
ejpam-1853	519	15	c1	c1	NOUN
ejpam-1853	519	16	=	=	PUNCT
ejpam-1853	520	1	x2−b2	x2−b2	PROPN
ejpam-1853	520	2	−ac1	−ac1	X
ejpam-1853	520	3	=	=	SYM
ejpam-1853	520	4	x3−b3	x3−b3	PROPN
ejpam-1853	520	5	c3	c3	NOUN
ejpam-1853	520	6	and	and	CCONJ
ejpam-1853	520	7	the	the	DET
ejpam-1853	520	8	distance	distance	NOUN
ejpam-1853	520	9	from	from	ADP
ejpam-1853	520	10	a2	a2	PROPN
ejpam-1853	520	11	and	and	CCONJ
ejpam-1853	520	12	a3	a3	NOUN
ejpam-1853	520	13	is	be	AUX
ejpam-1853	520	14	d(a2	d(a2	NOUN
ejpam-1853	520	15	,	,	PUNCT
ejpam-1853	520	16	a3	a3	NOUN
ejpam-1853	520	17	)	)	PUNCT
ejpam-1853	521	1	=	=	SYM
ejpam-1853	522	1	p	p	X
ejpam-1853	522	2	(	(	PUNCT
ejpam-1853	522	3	1	1	NUM
ejpam-1853	522	4	+	+	NUM
ejpam-1853	522	5	a2)c2	a2)c2	X
ejpam-1853	522	6	1	1	NUM
ejpam-1853	522	7	+	+	NUM
ejpam-1853	522	8	c2	c2	PROPN
ejpam-1853	522	9	3	3	NUM
ejpam-1853	522	10	.	.	PUNCT
ejpam-1853	523	1	let	let	AUX
ejpam-1853	523	2	be	be	AUX
ejpam-1853	523	3	the	the	DET
ejpam-1853	523	4	points	point	NOUN
ejpam-1853	523	5	b1	b1	NOUN
ejpam-1853	523	6	,	,	PUNCT
ejpam-1853	523	7	b2	b2	NOUN
ejpam-1853	523	8	,	,	PUNCT
ejpam-1853	523	9	b3	b3	NOUN
ejpam-1853	523	10	,	,	PUNCT
ejpam-1853	523	11	b4	b4	NOUN
ejpam-1853	523	12	associated	associate	VERB
ejpam-1853	523	13	to	to	ADP
ejpam-1853	523	14	ε(α(x	ε(α(x	NOUN
ejpam-1853	523	15	)	)	PUNCT
ejpam-1853	523	16	)	)	PUNCT
ejpam-1853	523	17	,	,	PUNCT
ejpam-1853	523	18	x	x	X
ejpam-1853	523	19	,	,	PUNCT
ejpam-1853	523	20	ε(β(x	ε(β(x	NOUN
ejpam-1853	523	21	)	)	PUNCT
ejpam-1853	523	22	)	)	PUNCT
ejpam-1853	523	23	,	,	PUNCT
ejpam-1853	523	24	x−1	x−1	PROPN
ejpam-1853	523	25	∈	∈	PROPN
ejpam-1853	523	26	v	v	NOUN
ejpam-1853	523	27	.	.	PUNCT
ejpam-1853	524	1	we	we	PRON
ejpam-1853	524	2	have	have	VERB
ejpam-1853	524	3	b1(0	b1(0	NOUN
ejpam-1853	524	4	,	,	PUNCT
ejpam-1853	524	5	ab1	ab1	X
ejpam-1853	524	6	+	+	X
ejpam-1853	524	7	b2	b2	NOUN
ejpam-1853	524	8	,	,	PUNCT
ejpam-1853	524	9	0	0	NUM
ejpam-1853	524	10	)	)	PUNCT
ejpam-1853	524	11	,	,	PUNCT
ejpam-1853	524	12	b2(b1	b2(b1	VERB
ejpam-1853	524	13	,	,	PUNCT
ejpam-1853	524	14	b2	b2	NOUN
ejpam-1853	524	15	,	,	PUNCT
ejpam-1853	524	16	b3	b3	PROPN
ejpam-1853	524	17	)	)	PUNCT
ejpam-1853	524	18	,	,	PUNCT
ejpam-1853	524	19	b3(0	b3(0	PROPN
ejpam-1853	524	20	,	,	PUNCT
ejpam-1853	524	21	b1	b1	NOUN
ejpam-1853	524	22	+	+	X
ejpam-1853	524	23	b2	b2	NOUN
ejpam-1853	524	24	,	,	PUNCT
ejpam-1853	524	25	0	0	NUM
ejpam-1853	524	26	)	)	PUNCT
ejpam-1853	524	27	and	and	CCONJ
ejpam-1853	524	28	b4(−b1	b4(−b1	NOUN
ejpam-1853	524	29	,	,	PUNCT
ejpam-1853	524	30	(	(	PUNCT
ejpam-1853	524	31	a+1)b1	a+1)b1	VERB
ejpam-1853	524	32	+	+	SYM
ejpam-1853	524	33	b2,−b3	b2,−b3	NOUN
ejpam-1853	524	34	)	)	PUNCT
ejpam-1853	524	35	.	.	PUNCT
ejpam-1853	525	1	then	then	ADV
ejpam-1853	525	2	:	:	PUNCT
ejpam-1853	525	3	the	the	DET
ejpam-1853	525	4	simple	simple	ADJ
ejpam-1853	525	5	quadrilateral	quadrilateral	ADJ
ejpam-1853	525	6	b1b2b3b4	b1b2b3b4	PROPN
ejpam-1853	525	7	is	be	AUX
ejpam-1853	525	8	a	a	DET
ejpam-1853	525	9	parallelogram	parallelogram	NOUN
ejpam-1853	525	10	.	.	PUNCT
ejpam-1853	526	1	indeed	indeed	ADV
ejpam-1853	526	2	,	,	PUNCT
ejpam-1853	526	3	the	the	DET
ejpam-1853	526	4	straight	straight	ADJ
ejpam-1853	526	5	line	line	NOUN
ejpam-1853	526	6	through	through	ADP
ejpam-1853	526	7	b1	b1	NOUN
ejpam-1853	526	8	and	and	CCONJ
ejpam-1853	526	9	b2	b2	NOUN
ejpam-1853	526	10	has	have	VERB
ejpam-1853	526	11	the	the	DET
ejpam-1853	526	12	equation	equation	NOUN
ejpam-1853	526	13	:	:	PUNCT
ejpam-1853	526	14	x1	x1	PROPN
ejpam-1853	526	15	b1	b1	NOUN
ejpam-1853	526	16	=	=	SYM
ejpam-1853	526	17	x2−(ab1+b2	x2−(ab1+b2	NOUN
ejpam-1853	526	18	)	)	PUNCT
ejpam-1853	526	19	−ab1	−ab1	PUNCT
ejpam-1853	527	1	=	=	PUNCT
ejpam-1853	527	2	x3	x3	PROPN
ejpam-1853	527	3	b3	b3	PROPN
ejpam-1853	527	4	and	and	CCONJ
ejpam-1853	527	5	d(b1	d(b1	NOUN
ejpam-1853	527	6	,	,	PUNCT
ejpam-1853	527	7	b2	b2	NOUN
ejpam-1853	527	8	)	)	PUNCT
ejpam-1853	527	9	=	=	SYM
ejpam-1853	527	10	p	p	X
ejpam-1853	527	11	(	(	PUNCT
ejpam-1853	527	12	1	1	NUM
ejpam-1853	527	13	+	+	CCONJ
ejpam-1853	527	14	a2)b2	a2)b2	NOUN
ejpam-1853	527	15	1	1	NUM
ejpam-1853	527	16	+	+	NUM
ejpam-1853	527	17	b2	b2	NOUN
ejpam-1853	527	18	3	3	NUM
ejpam-1853	527	19	.	.	PUNCT
ejpam-1853	528	1	also	also	ADV
ejpam-1853	528	2	,	,	PUNCT
ejpam-1853	528	3	the	the	DET
ejpam-1853	528	4	straight	straight	ADJ
ejpam-1853	528	5	line	line	NOUN
ejpam-1853	528	6	through	through	ADP
ejpam-1853	528	7	b3	b3	PROPN
ejpam-1853	528	8	and	and	CCONJ
ejpam-1853	528	9	b4	b4	NOUN
ejpam-1853	528	10	has	have	VERB
ejpam-1853	528	11	the	the	DET
ejpam-1853	528	12	equation	equation	NOUN
ejpam-1853	528	13	:	:	PUNCT
ejpam-1853	528	14	x1	x1	PROPN
ejpam-1853	528	15	−b1	−b1	PROPN
ejpam-1853	528	16	=	=	PUNCT
ejpam-1853	528	17	x2−(b1+b2	x2−(b1+b2	NUM
ejpam-1853	528	18	)	)	PUNCT
ejpam-1853	528	19	ab1	ab1	VERB
ejpam-1853	529	1	=	=	SYM
ejpam-1853	529	2	x3	x3	ADJ
ejpam-1853	529	3	−b3	−b3	PROPN
ejpam-1853	529	4	and	and	CCONJ
ejpam-1853	529	5	d(b3	d(b3	NOUN
ejpam-1853	529	6	,	,	PUNCT
ejpam-1853	529	7	b4	b4	NOUN
ejpam-1853	529	8	)	)	PUNCT
ejpam-1853	529	9	=	=	SYM
ejpam-1853	529	10	d(b1	d(b1	NOUN
ejpam-1853	529	11	,	,	PUNCT
ejpam-1853	529	12	b2	b2	NOUN
ejpam-1853	529	13	)	)	PUNCT
ejpam-1853	529	14	.	.	PUNCT
ejpam-1853	530	1	definition	definition	NOUN
ejpam-1853	530	2	8	8	NUM
ejpam-1853	530	3	.	.	PUNCT
ejpam-1853	531	1	let	let	VERB
ejpam-1853	531	2	(	(	PUNCT
ejpam-1853	531	3	vj	vj	INTJ
ejpam-1853	531	4	,	,	PUNCT
ejpam-1853	531	5	α	α	PROPN
ejpam-1853	531	6	j	j	PROPN
ejpam-1853	531	7	,	,	PUNCT
ejpam-1853	531	8	β	β	PROPN
ejpam-1853	531	9	j	j	PROPN
ejpam-1853	531	10	,	,	PUNCT
ejpam-1853	531	11	m	m	VERB
ejpam-1853	531	12	j	j	PROPN
ejpam-1853	531	13	,	,	PUNCT
ejpam-1853	531	14	ε	ε	PROPN
ejpam-1853	531	15	j	j	PROPN
ejpam-1853	531	16	,	,	PUNCT
ejpam-1853	531	17	i	i	PRON
ejpam-1853	531	18	j	j	PROPN
ejpam-1853	531	19	,	,	PUNCT
ejpam-1853	532	1	+	+	CCONJ
ejpam-1853	532	2	j	j	PROPN
ejpam-1853	532	3	,	,	PUNCT
ejpam-1853	532	4	ϕ	ϕ	PROPN
ejpam-1853	532	5	j	j	PROPN
ejpam-1853	532	6	,	,	PUNCT
ejpam-1853	532	7	vj,0	vj,0	PROPN
ejpam-1853	532	8	)	)	PUNCT
ejpam-1853	532	9	,	,	PUNCT
ejpam-1853	532	10	j	j	PROPN
ejpam-1853	532	11	=	=	SYM
ejpam-1853	532	12	1	1	NUM
ejpam-1853	532	13	,	,	PUNCT
ejpam-1853	532	14	2	2	NUM
ejpam-1853	532	15	be	be	VERB
ejpam-1853	532	16	two	two	NUM
ejpam-1853	532	17	vector	vector	NOUN
ejpam-1853	532	18	space	space	NOUN
ejpam-1853	532	19	-	-	PUNCT
ejpam-1853	532	20	groupoids	groupoid	NOUN
ejpam-1853	532	21	.	.	PUNCT
ejpam-1853	533	1	a	a	DET
ejpam-1853	533	2	groupoid	groupoid	PROPN
ejpam-1853	533	3	morphism	morphism	NOUN
ejpam-1853	533	4	(	(	PUNCT
ejpam-1853	533	5	f	f	PROPN
ejpam-1853	533	6	,	,	PUNCT
ejpam-1853	533	7	f0	f0	PROPN
ejpam-1853	533	8	)	)	PUNCT
ejpam-1853	533	9	:	:	PUNCT
ejpam-1853	533	10	(	(	PUNCT
ejpam-1853	533	11	v1	v1	NOUN
ejpam-1853	533	12	,	,	PUNCT
ejpam-1853	533	13	v1,0)→	v1,0)→	PUNCT
ejpam-1853	533	14	(	(	PUNCT
ejpam-1853	533	15	v2	v2	NOUN
ejpam-1853	533	16	,	,	PUNCT
ejpam-1853	533	17	v2,0	v2,0	PROPN
ejpam-1853	533	18	)	)	PUNCT
ejpam-1853	533	19	with	with	ADP
ejpam-1853	533	20	property	property	NOUN
ejpam-1853	533	21	that	that	PRON
ejpam-1853	533	22	f	f	X
ejpam-1853	533	23	:	:	PUNCT
ejpam-1853	533	24	v1→	v1→	X
ejpam-1853	533	25	v2	v2	VERB
ejpam-1853	533	26	and	and	CCONJ
ejpam-1853	533	27	m.	m.	NOUN
ejpam-1853	533	28	ivan	ivan	PROPN
ejpam-1853	533	29	/	/	PUNCT
ejpam-1853	533	30	eur	eur	PROPN
ejpam-1853	533	31	.	.	PUNCT
ejpam-1853	534	1	j.	j.	PROPN
ejpam-1853	534	2	pure	pure	PROPN
ejpam-1853	534	3	appl	appl	PROPN
ejpam-1853	534	4	.	.	PROPN
ejpam-1853	534	5	math	math	PROPN
ejpam-1853	534	6	,	,	PUNCT
ejpam-1853	534	7	6	6	NUM
ejpam-1853	534	8	(	(	PUNCT
ejpam-1853	534	9	2013	2013	NUM
ejpam-1853	534	10	)	)	PUNCT
ejpam-1853	534	11	,	,	PUNCT
ejpam-1853	534	12	469	469	NUM
ejpam-1853	534	13	-	-	SYM
ejpam-1853	534	14	484	484	NUM
ejpam-1853	534	15	482	482	NUM
ejpam-1853	534	16	f0	f0	NOUN
ejpam-1853	534	17	:	:	PUNCT
ejpam-1853	534	18	v1,0	v1,0	PROPN
ejpam-1853	534	19	→	→	SYM
ejpam-1853	534	20	v2,0	v2,0	NOUN
ejpam-1853	534	21	are	be	AUX
ejpam-1853	534	22	linear	linear	ADJ
ejpam-1853	534	23	maps	map	NOUN
ejpam-1853	534	24	,	,	PUNCT
ejpam-1853	534	25	is	be	AUX
ejpam-1853	534	26	called	call	VERB
ejpam-1853	534	27	vector	vector	NOUN
ejpam-1853	534	28	space	space	NOUN
ejpam-1853	534	29	-	-	PUNCT
ejpam-1853	534	30	groupoid	groupoid	NOUN
ejpam-1853	534	31	morphism	morphism	NOUN
ejpam-1853	534	32	or	or	CCONJ
ejpam-1853	534	33	morphism	morphism	NOUN
ejpam-1853	534	34	of	of	ADP
ejpam-1853	534	35	vector	vector	NOUN
ejpam-1853	534	36	space	space	NOUN
ejpam-1853	534	37	-	-	PUNCT
ejpam-1853	534	38	groupoids	groupoid	NOUN
ejpam-1853	534	39	.	.	PUNCT
ejpam-1853	535	1	if	if	SCONJ
ejpam-1853	535	2	v2,0	v2,0	PROPN
ejpam-1853	535	3	=	=	SYM
ejpam-1853	535	4	v1,0	v1,0	PROPN
ejpam-1853	535	5	and	and	CCONJ
ejpam-1853	535	6	f0	f0	PROPN
ejpam-1853	535	7	=	=	SYM
ejpam-1853	535	8	idv1,0	idv1,0	PROPN
ejpam-1853	535	9	,	,	PUNCT
ejpam-1853	535	10	then	then	ADV
ejpam-1853	535	11	we	we	PRON
ejpam-1853	535	12	say	say	VERB
ejpam-1853	535	13	that	that	SCONJ
ejpam-1853	535	14	(	(	PUNCT
ejpam-1853	535	15	f	f	X
ejpam-1853	535	16	,	,	PUNCT
ejpam-1853	535	17	idv1,0	idv1,0	PROPN
ejpam-1853	535	18	)	)	PUNCT
ejpam-1853	535	19	:	:	PUNCT
ejpam-1853	535	20	(	(	PUNCT
ejpam-1853	535	21	v1	v1	NOUN
ejpam-1853	535	22	,	,	PUNCT
ejpam-1853	535	23	v1,0	v1,0	PROPN
ejpam-1853	535	24	)	)	PUNCT
ejpam-1853	535	25	→	→	SYM
ejpam-1853	535	26	(	(	PUNCT
ejpam-1853	535	27	v2	v2	PROPN
ejpam-1853	535	28	,	,	PUNCT
ejpam-1853	535	29	v1,0	v1,0	PROPN
ejpam-1853	535	30	)	)	PUNCT
ejpam-1853	535	31	is	be	AUX
ejpam-1853	535	32	a	a	DET
ejpam-1853	535	33	v1,0−morphism	v1,0−morphism	NOUN
ejpam-1853	535	34	of	of	ADP
ejpam-1853	535	35	vector	vector	NOUN
ejpam-1853	535	36	space	space	NOUN
ejpam-1853	535	37	-	-	PUNCT
ejpam-1853	535	38	groupoids	groupoid	NOUN
ejpam-1853	535	39	.	.	PUNCT
ejpam-1853	536	1	it	it	PRON
ejpam-1853	536	2	is	be	AUX
ejpam-1853	536	3	denoted	denote	VERB
ejpam-1853	536	4	by	by	ADP
ejpam-1853	536	5	f	f	PROPN
ejpam-1853	536	6	:	:	PUNCT
ejpam-1853	536	7	v1→	v1→	X
ejpam-1853	536	8	v2	v2	PROPN
ejpam-1853	536	9	.	.	PUNCT
ejpam-1853	537	1	the	the	DET
ejpam-1853	537	2	category	category	NOUN
ejpam-1853	537	3	of	of	ADP
ejpam-1853	537	4	vector	vector	NOUN
ejpam-1853	537	5	space	space	NOUN
ejpam-1853	537	6	-	-	PUNCT
ejpam-1853	537	7	groupoids	groupoid	NOUN
ejpam-1853	537	8	,	,	PUNCT
ejpam-1853	537	9	denoted	denote	VERB
ejpam-1853	537	10	by	by	ADP
ejpam-1853	537	11	vsgpd	vsgpd	NOUN
ejpam-1853	537	12	,	,	PUNCT
ejpam-1853	537	13	has	have	VERB
ejpam-1853	537	14	its	its	PRON
ejpam-1853	537	15	objects	object	NOUN
ejpam-1853	537	16	all	all	DET
ejpam-1853	537	17	vector	vector	NOUN
ejpam-1853	537	18	space	space	NOUN
ejpam-1853	537	19	-	-	PUNCT
ejpam-1853	537	20	groupoids	groupoid	NOUN
ejpam-1853	537	21	(	(	PUNCT
ejpam-1853	537	22	v	v	NOUN
ejpam-1853	537	23	,	,	PUNCT
ejpam-1853	537	24	v0	v0	NOUN
ejpam-1853	537	25	)	)	PUNCT
ejpam-1853	537	26	and	and	CCONJ
ejpam-1853	537	27	as	as	ADP
ejpam-1853	537	28	morphisms	morphism	NOUN
ejpam-1853	537	29	from	from	ADP
ejpam-1853	537	30	(	(	PUNCT
ejpam-1853	537	31	v	v	NOUN
ejpam-1853	537	32	,	,	PUNCT
ejpam-1853	537	33	v0	v0	NOUN
ejpam-1853	537	34	)	)	PUNCT
ejpam-1853	537	35	to	to	ADP
ejpam-1853	537	36	(	(	PUNCT
ejpam-1853	537	37	v	v	NUM
ejpam-1853	537	38	′	′	NUM
ejpam-1853	537	39	,	,	PUNCT
ejpam-1853	537	40	v	v	NOUN
ejpam-1853	537	41	′0	′0	NOUN
ejpam-1853	537	42	)	)	PUNCT
ejpam-1853	537	43	the	the	DET
ejpam-1853	537	44	set	set	NOUN
ejpam-1853	537	45	of	of	ADP
ejpam-1853	537	46	all	all	DET
ejpam-1853	537	47	morphisms	morphism	NOUN
ejpam-1853	537	48	of	of	ADP
ejpam-1853	537	49	vector	vector	NOUN
ejpam-1853	537	50	space	space	NOUN
ejpam-1853	537	51	-	-	PUNCT
ejpam-1853	537	52	groupoids	groupoid	NOUN
ejpam-1853	537	53	.	.	PUNCT
ejpam-1853	538	1	finally	finally	ADV
ejpam-1853	538	2	we	we	PRON
ejpam-1853	538	3	will	will	AUX
ejpam-1853	538	4	present	present	VERB
ejpam-1853	538	5	the	the	DET
ejpam-1853	538	6	concept	concept	NOUN
ejpam-1853	538	7	of	of	ADP
ejpam-1853	538	8	vector	vector	NOUN
ejpam-1853	538	9	groupoid	groupoid	PROPN
ejpam-1853	538	10	defined	define	VERB
ejpam-1853	538	11	by	by	ADP
ejpam-1853	538	12	v.	v.	ADP
ejpam-1853	538	13	popuţa	popuţa	PROPN
ejpam-1853	538	14	and	and	CCONJ
ejpam-1853	538	15	gh	gh	PROPN
ejpam-1853	538	16	.	.	PUNCT
ejpam-1853	539	1	ivan	ivan	PROPN
ejpam-1853	540	1	[	[	X
ejpam-1853	540	2	13	13	NUM
ejpam-1853	540	3	,	,	PUNCT
ejpam-1853	540	4	14	14	NUM
ejpam-1853	540	5	]	]	PUNCT
ejpam-1853	540	6	.	.	PUNCT
ejpam-1853	541	1	definition	definition	NOUN
ejpam-1853	541	2	9	9	NUM
ejpam-1853	541	3	(	(	PUNCT
ejpam-1853	541	4	[	[	X
ejpam-1853	541	5	13	13	NUM
ejpam-1853	541	6	]	]	NUM
ejpam-1853	541	7	)	)	PUNCT
ejpam-1853	541	8	.	.	PUNCT
ejpam-1853	542	1	by	by	ADP
ejpam-1853	542	2	vector	vector	NOUN
ejpam-1853	542	3	groupoid	groupoid	PROPN
ejpam-1853	542	4	,	,	PUNCT
ejpam-1853	542	5	we	we	PRON
ejpam-1853	542	6	mean	mean	VERB
ejpam-1853	542	7	a	a	DET
ejpam-1853	542	8	groupoid	groupoid	NOUN
ejpam-1853	542	9	(	(	PUNCT
ejpam-1853	542	10	v	v	NOUN
ejpam-1853	542	11	,	,	PUNCT
ejpam-1853	542	12	α	α	NOUN
ejpam-1853	542	13	,	,	PUNCT
ejpam-1853	542	14	β	β	X
ejpam-1853	542	15	,	,	PUNCT
ejpam-1853	542	16	m	m	PROPN
ejpam-1853	542	17	,	,	PUNCT
ejpam-1853	542	18	ε	ε	PROPN
ejpam-1853	542	19	,	,	PUNCT
ejpam-1853	542	20	i	i	PROPN
ejpam-1853	542	21	,	,	PUNCT
ejpam-1853	542	22	v0	v0	PROPN
ejpam-1853	542	23	)	)	PUNCT
ejpam-1853	542	24	which	which	PRON
ejpam-1853	542	25	verifies	verify	VERB
ejpam-1853	542	26	the	the	DET
ejpam-1853	542	27	following	following	ADJ
ejpam-1853	542	28	conditions	condition	NOUN
ejpam-1853	542	29	:	:	PUNCT
ejpam-1853	542	30	(	(	PUNCT
ejpam-1853	542	31	9.1	9.1	X
ejpam-1853	542	32	)	)	PUNCT
ejpam-1853	542	33	v	v	NOUN
ejpam-1853	542	34	and	and	CCONJ
ejpam-1853	542	35	v0	v0	NOUN
ejpam-1853	542	36	are	be	AUX
ejpam-1853	542	37	vector	vector	NOUN
ejpam-1853	542	38	spaces	space	NOUN
ejpam-1853	542	39	;	;	PUNCT
ejpam-1853	542	40	(	(	PUNCT
ejpam-1853	542	41	9.2	9.2	X
ejpam-1853	542	42	)	)	PUNCT
ejpam-1853	542	43	α	α	NOUN
ejpam-1853	542	44	,	,	PUNCT
ejpam-1853	542	45	β	β	X
ejpam-1853	542	46	:	:	PUNCT
ejpam-1853	542	47	v	v	X
ejpam-1853	542	48	→	→	SYM
ejpam-1853	542	49	v0	v0	NOUN
ejpam-1853	542	50	are	be	AUX
ejpam-1853	542	51	linear	linear	ADJ
ejpam-1853	542	52	maps	map	NOUN
ejpam-1853	542	53	;	;	PUNCT
ejpam-1853	542	54	(	(	PUNCT
ejpam-1853	542	55	9.3	9.3	NUM
ejpam-1853	542	56	)	)	PUNCT
ejpam-1853	542	57	the	the	DET
ejpam-1853	542	58	inclusion	inclusion	NOUN
ejpam-1853	542	59	ε	ε	PROPN
ejpam-1853	542	60	:	:	PUNCT
ejpam-1853	542	61	v0	v0	PROPN
ejpam-1853	542	62	→	→	SYM
ejpam-1853	542	63	v	v	PROPN
ejpam-1853	542	64	and	and	CCONJ
ejpam-1853	542	65	the	the	DET
ejpam-1853	542	66	inversion	inversion	NOUN
ejpam-1853	543	1	i	i	PRON
ejpam-1853	543	2	:	:	PUNCT
ejpam-1853	543	3	v	v	X
ejpam-1853	543	4	→	→	SYM
ejpam-1853	543	5	v	v	NUM
ejpam-1853	543	6	are	be	AUX
ejpam-1853	543	7	linear	linear	PROPN
ejpam-1853	543	8	maps	map	NOUN
ejpam-1853	543	9	and	and	CCONJ
ejpam-1853	543	10	the	the	DET
ejpam-1853	543	11	following	follow	VERB
ejpam-1853	543	12	condition	condition	NOUN
ejpam-1853	543	13	is	be	AUX
ejpam-1853	543	14	verified	verify	VERB
ejpam-1853	543	15	:	:	PUNCT
ejpam-1853	543	16	(	(	PUNCT
ejpam-1853	543	17	9.3.1	9.3.1	NUM
ejpam-1853	543	18	)	)	PUNCT
ejpam-1853	543	19	x	x	PUNCT
ejpam-1853	544	1	+	+	PUNCT
ejpam-1853	544	2	i(x	i(x	NOUN
ejpam-1853	544	3	)	)	PUNCT
ejpam-1853	544	4	=	=	SYM
ejpam-1853	544	5	ε(α(x	ε(α(x	NOUN
ejpam-1853	544	6	)	)	PUNCT
ejpam-1853	544	7	)	)	PUNCT
ejpam-1853	545	1	+	+	CCONJ
ejpam-1853	545	2	ε(β(x	ε(β(x	NOUN
ejpam-1853	545	3	)	)	PUNCT
ejpam-1853	545	4	)	)	PUNCT
ejpam-1853	545	5	for	for	ADP
ejpam-1853	545	6	all	all	PRON
ejpam-1853	545	7	x	x	SYM
ejpam-1853	545	8	∈	∈	PROPN
ejpam-1853	545	9	v	v	NOUN
ejpam-1853	545	10	;	;	PUNCT
ejpam-1853	545	11	(	(	PUNCT
ejpam-1853	545	12	9.4	9.4	NUM
ejpam-1853	545	13	)	)	PUNCT
ejpam-1853	545	14	the	the	DET
ejpam-1853	545	15	multiplication	multiplication	NOUN
ejpam-1853	545	16	m	m	VERB
ejpam-1853	545	17	:	:	PUNCT
ejpam-1853	545	18	v(2)→	v(2)→	NUM
ejpam-1853	545	19	v	v	NOUN
ejpam-1853	545	20	satisfy	satisfy	VERB
ejpam-1853	545	21	the	the	DET
ejpam-1853	545	22	following	follow	VERB
ejpam-1853	545	23	relations	relation	NOUN
ejpam-1853	545	24	:	:	PUNCT
ejpam-1853	545	25	(	(	PUNCT
ejpam-1853	545	26	9.4.1	9.4.1	NUM
ejpam-1853	545	27	)	)	PUNCT
ejpam-1853	545	28	x	x	X
ejpam-1853	545	29	·	·	PUNCT
ejpam-1853	546	1	(	(	PUNCT
ejpam-1853	546	2	y	y	NOUN
ejpam-1853	546	3	+	+	CCONJ
ejpam-1853	546	4	z−	z−	ADJ
ejpam-1853	546	5	ε(β(x	ε(β(x	NOUN
ejpam-1853	546	6	)	)	PUNCT
ejpam-1853	546	7	)	)	PUNCT
ejpam-1853	546	8	)	)	PUNCT
ejpam-1853	547	1	=	=	PUNCT
ejpam-1853	547	2	x	x	PUNCT
ejpam-1853	547	3	·	·	PUNCT
ejpam-1853	547	4	y	y	X
ejpam-1853	547	5	+	+	NOUN
ejpam-1853	547	6	x	x	X
ejpam-1853	547	7	·	·	PUNCT
ejpam-1853	547	8	z−	z−	X
ejpam-1853	547	9	x	x	SYM
ejpam-1853	547	10	,	,	PUNCT
ejpam-1853	547	11	(	(	PUNCT
ejpam-1853	547	12	∀	∀	X
ejpam-1853	547	13	)	)	PUNCT
ejpam-1853	547	14	x	x	SYM
ejpam-1853	547	15	,	,	PUNCT
ejpam-1853	547	16	y	y	PROPN
ejpam-1853	547	17	,	,	PUNCT
ejpam-1853	547	18	z	z	PROPN
ejpam-1853	547	19	∈	∈	PROPN
ejpam-1853	547	20	v	v	ADP
ejpam-1853	547	21	such	such	ADJ
ejpam-1853	547	22	that	that	SCONJ
ejpam-1853	547	23	α(y	α(y	NOUN
ejpam-1853	547	24	)	)	PUNCT
ejpam-1853	547	25	=	=	PUNCT
ejpam-1853	547	26	β(x	β(x	NOUN
ejpam-1853	547	27	)	)	PUNCT
ejpam-1853	547	28	=	=	SYM
ejpam-1853	547	29	α(z	α(z	NOUN
ejpam-1853	547	30	)	)	PUNCT
ejpam-1853	547	31	;	;	PUNCT
ejpam-1853	547	32	(	(	PUNCT
ejpam-1853	547	33	9.4.2	9.4.2	NUM
ejpam-1853	547	34	)	)	PUNCT
ejpam-1853	547	35	x	x	X
ejpam-1853	547	36	·	·	PUNCT
ejpam-1853	548	1	(	(	PUNCT
ejpam-1853	548	2	k	k	NOUN
ejpam-1853	548	3	y	y	PROPN
ejpam-1853	548	4	+	+	CCONJ
ejpam-1853	548	5	(	(	PUNCT
ejpam-1853	548	6	1−	1−	NUM
ejpam-1853	548	7	k)ε(β(x	k)ε(β(x	NOUN
ejpam-1853	548	8	)	)	PUNCT
ejpam-1853	548	9	)	)	PUNCT
ejpam-1853	548	10	)	)	PUNCT
ejpam-1853	549	1	=	=	SYM
ejpam-1853	549	2	k(x	k(x	X
ejpam-1853	549	3	·	·	PUNCT
ejpam-1853	549	4	y	y	X
ejpam-1853	549	5	)	)	PUNCT
ejpam-1853	549	6	+	+	CCONJ
ejpam-1853	549	7	(	(	PUNCT
ejpam-1853	549	8	1−	1−	NUM
ejpam-1853	549	9	k)x	k)x	X
ejpam-1853	549	10	,	,	PUNCT
ejpam-1853	549	11	(	(	PUNCT
ejpam-1853	549	12	∀	∀	X
ejpam-1853	549	13	)	)	PUNCT
ejpam-1853	549	14	(	(	PUNCT
ejpam-1853	549	15	x	x	X
ejpam-1853	549	16	,	,	PUNCT
ejpam-1853	549	17	y	y	PROPN
ejpam-1853	549	18	)	)	PUNCT
ejpam-1853	549	19	∈	∈	PROPN
ejpam-1853	549	20	v(2	v(2	PROPN
ejpam-1853	549	21	)	)	PUNCT
ejpam-1853	549	22	;	;	PUNCT
ejpam-1853	549	23	(	(	PUNCT
ejpam-1853	549	24	9.4.3	9.4.3	X
ejpam-1853	549	25	)	)	PUNCT
ejpam-1853	549	26	(	(	PUNCT
ejpam-1853	549	27	y	y	PROPN
ejpam-1853	549	28	+	+	CCONJ
ejpam-1853	549	29	z−	z−	PROPN
ejpam-1853	549	30	ε(α(x	ε(α(x	NOUN
ejpam-1853	549	31	)	)	PUNCT
ejpam-1853	549	32	)	)	PUNCT
ejpam-1853	549	33	)	)	PUNCT
ejpam-1853	549	34	·	·	PUNCT
ejpam-1853	549	35	x	x	X
ejpam-1853	549	36	=	=	PUNCT
ejpam-1853	549	37	y	y	PROPN
ejpam-1853	549	38	·	·	PUNCT
ejpam-1853	549	39	x	x	PUNCT
ejpam-1853	550	1	+	+	PUNCT
ejpam-1853	550	2	z	z	NOUN
ejpam-1853	550	3	·	·	PUNCT
ejpam-1853	550	4	x	x	SYM
ejpam-1853	551	1	−	−	NOUN
ejpam-1853	551	2	x	x	SYM
ejpam-1853	551	3	,	,	PUNCT
ejpam-1853	551	4	(	(	PUNCT
ejpam-1853	551	5	∀	∀	X
ejpam-1853	551	6	)	)	PUNCT
ejpam-1853	551	7	x	x	SYM
ejpam-1853	551	8	,	,	PUNCT
ejpam-1853	551	9	y	y	PROPN
ejpam-1853	551	10	,	,	PUNCT
ejpam-1853	551	11	z	z	PROPN
ejpam-1853	551	12	∈	∈	PROPN
ejpam-1853	551	13	v	v	ADP
ejpam-1853	551	14	such	such	ADJ
ejpam-1853	551	15	that	that	DET
ejpam-1853	551	16	α(x	α(x	NOUN
ejpam-1853	551	17	)	)	PUNCT
ejpam-1853	551	18	=	=	SYM
ejpam-1853	551	19	β(y	β(y	PROPN
ejpam-1853	551	20	)	)	PUNCT
ejpam-1853	551	21	=	=	SYM
ejpam-1853	551	22	β(z	β(z	PROPN
ejpam-1853	551	23	)	)	PUNCT
ejpam-1853	551	24	;	;	PUNCT
ejpam-1853	551	25	(	(	PUNCT
ejpam-1853	551	26	9.4.4	9.4.4	X
ejpam-1853	551	27	)	)	PUNCT
ejpam-1853	551	28	(	(	PUNCT
ejpam-1853	551	29	k	k	NOUN
ejpam-1853	551	30	y	y	PROPN
ejpam-1853	551	31	+	+	CCONJ
ejpam-1853	551	32	(	(	PUNCT
ejpam-1853	551	33	1−	1−	NUM
ejpam-1853	551	34	k)ε(α(x	k)ε(α(x	NOUN
ejpam-1853	551	35	)	)	PUNCT
ejpam-1853	551	36	)	)	PUNCT
ejpam-1853	551	37	)	)	PUNCT
ejpam-1853	551	38	·	·	PUNCT
ejpam-1853	551	39	x	x	PUNCT
ejpam-1853	552	1	=	=	PUNCT
ejpam-1853	552	2	k(y	k(y	PROPN
ejpam-1853	552	3	·	·	PUNCT
ejpam-1853	552	4	x	x	X
ejpam-1853	552	5	)	)	PUNCT
ejpam-1853	552	6	+	+	CCONJ
ejpam-1853	552	7	(	(	PUNCT
ejpam-1853	552	8	1−	1−	NUM
ejpam-1853	552	9	k)x	k)x	X
ejpam-1853	552	10	,	,	PUNCT
ejpam-1853	552	11	(	(	PUNCT
ejpam-1853	552	12	∀	∀	X
ejpam-1853	552	13	)	)	PUNCT
ejpam-1853	552	14	(	(	PUNCT
ejpam-1853	552	15	y	y	NOUN
ejpam-1853	552	16	,	,	PUNCT
ejpam-1853	552	17	x	x	NOUN
ejpam-1853	552	18	)	)	PUNCT
ejpam-1853	552	19	∈	∈	PROPN
ejpam-1853	552	20	v(2	v(2	PROPN
ejpam-1853	552	21	)	)	PUNCT
ejpam-1853	552	22	.	.	PUNCT
ejpam-1853	553	1	theorem	theorem	VERB
ejpam-1853	553	2	8	8	NUM
ejpam-1853	553	3	.	.	PUNCT
ejpam-1853	554	1	each	each	DET
ejpam-1853	554	2	vector	vector	NOUN
ejpam-1853	554	3	space	space	NOUN
ejpam-1853	554	4	-	-	PUNCT
ejpam-1853	554	5	groupoid	groupoid	PROPN
ejpam-1853	554	6	is	be	AUX
ejpam-1853	554	7	a	a	DET
ejpam-1853	554	8	vector	vector	NOUN
ejpam-1853	554	9	groupoid	groupoid	NOUN
ejpam-1853	554	10	in	in	ADP
ejpam-1853	554	11	the	the	DET
ejpam-1853	554	12	sense	sense	NOUN
ejpam-1853	554	13	of	of	ADP
ejpam-1853	554	14	definition	definition	NOUN
ejpam-1853	554	15	9	9	NUM
ejpam-1853	554	16	.	.	PUNCT
ejpam-1853	555	1	proof	proof	NOUN
ejpam-1853	555	2	.	.	PUNCT
ejpam-1853	556	1	we	we	PRON
ejpam-1853	556	2	suppose	suppose	VERB
ejpam-1853	556	3	that	that	SCONJ
ejpam-1853	556	4	(	(	PUNCT
ejpam-1853	556	5	v	v	NOUN
ejpam-1853	556	6	,	,	PUNCT
ejpam-1853	556	7	α	α	NOUN
ejpam-1853	556	8	,	,	PUNCT
ejpam-1853	556	9	β	β	X
ejpam-1853	556	10	,	,	PUNCT
ejpam-1853	556	11	m	m	PROPN
ejpam-1853	556	12	,	,	PUNCT
ejpam-1853	556	13	ε	ε	PROPN
ejpam-1853	556	14	,	,	PUNCT
ejpam-1853	556	15	i,+,ϕ	i,+,ϕ	NOUN
ejpam-1853	556	16	,	,	PUNCT
ejpam-1853	556	17	v0	v0	PROPN
ejpam-1853	556	18	)	)	PUNCT
ejpam-1853	556	19	is	be	AUX
ejpam-1853	556	20	a	a	DET
ejpam-1853	556	21	vector	vector	NOUN
ejpam-1853	556	22	space	space	NOUN
ejpam-1853	556	23	-	-	PUNCT
ejpam-1853	556	24	groupoid	groupoid	PROPN
ejpam-1853	556	25	.	.	PUNCT
ejpam-1853	557	1	from	from	ADP
ejpam-1853	557	2	definition	definition	NOUN
ejpam-1853	557	3	6	6	NUM
ejpam-1853	557	4	and	and	CCONJ
ejpam-1853	557	5	(	(	PUNCT
ejpam-1853	557	6	17	17	NUM
ejpam-1853	557	7	)	)	PUNCT
ejpam-1853	557	8	it	it	PRON
ejpam-1853	557	9	follows	follow	VERB
ejpam-1853	557	10	that	that	SCONJ
ejpam-1853	557	11	the	the	DET
ejpam-1853	557	12	conditions	condition	NOUN
ejpam-1853	557	13	(	(	PUNCT
ejpam-1853	557	14	9.1)−	9.1)−	NUM
ejpam-1853	557	15	(	(	PUNCT
ejpam-1853	557	16	9.3	9.3	NUM
ejpam-1853	557	17	)	)	PUNCT
ejpam-1853	557	18	are	be	AUX
ejpam-1853	557	19	satisfied	satisfied	ADJ
ejpam-1853	557	20	.	.	PUNCT
ejpam-1853	558	1	let	let	VERB
ejpam-1853	558	2	x	x	SYM
ejpam-1853	558	3	,	,	PUNCT
ejpam-1853	558	4	y	y	PROPN
ejpam-1853	558	5	,	,	PUNCT
ejpam-1853	558	6	z	z	PROPN
ejpam-1853	558	7	∈	∈	PROPN
ejpam-1853	558	8	v	v	ADP
ejpam-1853	558	9	such	such	ADJ
ejpam-1853	558	10	that	that	SCONJ
ejpam-1853	558	11	α(y	α(y	NOUN
ejpam-1853	558	12	)	)	PUNCT
ejpam-1853	558	13	=	=	PUNCT
ejpam-1853	559	1	β(x	β(x	NOUN
ejpam-1853	559	2	)	)	PUNCT
ejpam-1853	559	3	=	=	SYM
ejpam-1853	559	4	α(z	α(z	NOUN
ejpam-1853	559	5	)	)	PUNCT
ejpam-1853	559	6	.	.	PUNCT
ejpam-1853	560	1	denote	denote	VERB
ejpam-1853	560	2	t	t	NOUN
ejpam-1853	560	3	:	:	PUNCT
ejpam-1853	561	1	=	=	SYM
ejpam-1853	561	2	y	y	PROPN
ejpam-1853	562	1	+	+	NOUN
ejpam-1853	562	2	z	z	NOUN
ejpam-1853	563	1	−	−	NOUN
ejpam-1853	563	2	ε(β(x	ε(β(x	NOUN
ejpam-1853	563	3	)	)	PUNCT
ejpam-1853	563	4	)	)	PUNCT
ejpam-1853	563	5	.	.	PUNCT
ejpam-1853	564	1	using	use	VERB
ejpam-1853	564	2	the	the	DET
ejpam-1853	564	3	linearity	linearity	NOUN
ejpam-1853	564	4	of	of	ADP
ejpam-1853	564	5	α	α	PRON
ejpam-1853	564	6	,	,	PUNCT
ejpam-1853	564	7	we	we	PRON
ejpam-1853	564	8	have	have	VERB
ejpam-1853	564	9	α(t	α(t	NOUN
ejpam-1853	564	10	)	)	PUNCT
ejpam-1853	565	1	=	=	SYM
ejpam-1853	565	2	α(y	α(y	NOUN
ejpam-1853	565	3	)	)	PUNCT
ejpam-1853	565	4	+	+	NOUN
ejpam-1853	565	5	α(z)−α(ε(β(x	α(z)−α(ε(β(x	NOUN
ejpam-1853	565	6	)	)	PUNCT
ejpam-1853	565	7	)	)	PUNCT
ejpam-1853	565	8	)	)	PUNCT
ejpam-1853	566	1	=	=	PUNCT
ejpam-1853	566	2	β(x	β(x	NOUN
ejpam-1853	566	3	)	)	PUNCT
ejpam-1853	566	4	and	and	CCONJ
ejpam-1853	566	5	(	(	PUNCT
ejpam-1853	566	6	x	x	X
ejpam-1853	566	7	,	,	PUNCT
ejpam-1853	566	8	t	t	PROPN
ejpam-1853	566	9	)	)	PUNCT
ejpam-1853	566	10	∈	∈	PROPN
ejpam-1853	566	11	v(2	v(2	PROPN
ejpam-1853	566	12	)	)	PUNCT
ejpam-1853	566	13	.	.	PUNCT
ejpam-1853	567	1	applying	apply	VERB
ejpam-1853	567	2	(	(	PUNCT
ejpam-1853	567	3	16	16	NUM
ejpam-1853	567	4	)	)	PUNCT
ejpam-1853	567	5	,	,	PUNCT
ejpam-1853	567	6	we	we	PRON
ejpam-1853	567	7	have	have	VERB
ejpam-1853	567	8	x	x	X
ejpam-1853	567	9	·	·	PUNCT
ejpam-1853	567	10	t	t	X
ejpam-1853	567	11	=	=	PUNCT
ejpam-1853	568	1	x	x	PROPN
ejpam-1853	568	2	+	+	NUM
ejpam-1853	568	3	t	t	PROPN
ejpam-1853	568	4	−	−	NOUN
ejpam-1853	568	5	ε(β(x	ε(β(x	NOUN
ejpam-1853	568	6	)	)	PUNCT
ejpam-1853	568	7	)	)	PUNCT
ejpam-1853	569	1	=	=	PUNCT
ejpam-1853	569	2	x	x	PUNCT
ejpam-1853	570	1	+	+	NUM
ejpam-1853	570	2	y	y	PROPN
ejpam-1853	570	3	+	+	CCONJ
ejpam-1853	570	4	z−	z−	PROPN
ejpam-1853	570	5	2ε(β(x	2ε(β(x	NOUN
ejpam-1853	570	6	)	)	PUNCT
ejpam-1853	570	7	)	)	PUNCT
ejpam-1853	571	1	and	and	CCONJ
ejpam-1853	571	2	x	x	X
ejpam-1853	571	3	·	·	PUNCT
ejpam-1853	571	4	y	y	PROPN
ejpam-1853	571	5	+	+	NOUN
ejpam-1853	571	6	x	x	X
ejpam-1853	571	7	·	·	PUNCT
ejpam-1853	571	8	z−	z−	X
ejpam-1853	571	9	x	x	X
ejpam-1853	572	1	=	=	PUNCT
ejpam-1853	572	2	(	(	PUNCT
ejpam-1853	572	3	x	x	X
ejpam-1853	572	4	+	+	NUM
ejpam-1853	572	5	y	y	PROPN
ejpam-1853	572	6	−	−	NOUN
ejpam-1853	572	7	ε(β(x	ε(β(x	NOUN
ejpam-1853	572	8	)	)	PUNCT
ejpam-1853	572	9	)	)	PUNCT
ejpam-1853	572	10	)	)	PUNCT
ejpam-1853	573	1	+	+	CCONJ
ejpam-1853	573	2	(	(	PUNCT
ejpam-1853	573	3	x	x	SYM
ejpam-1853	573	4	+	+	SYM
ejpam-1853	573	5	z−	z−	ADJ
ejpam-1853	573	6	ε(β(x)))−	ε(β(x)))−	NUM
ejpam-1853	574	1	x	x	X
ejpam-1853	575	1	=	=	PUNCT
ejpam-1853	576	1	x	x	PUNCT
ejpam-1853	577	1	+	+	NUM
ejpam-1853	577	2	y	y	PROPN
ejpam-1853	577	3	+	+	CCONJ
ejpam-1853	577	4	z−	z−	PROPN
ejpam-1853	577	5	2ε(β(x	2ε(β(x	NOUN
ejpam-1853	577	6	)	)	PUNCT
ejpam-1853	577	7	)	)	PUNCT
ejpam-1853	577	8	.	.	PUNCT
ejpam-1853	578	1	then	then	ADV
ejpam-1853	578	2	,	,	PUNCT
ejpam-1853	578	3	x	x	X
ejpam-1853	578	4	·	·	PUNCT
ejpam-1853	578	5	t	t	X
ejpam-1853	578	6	=	=	PUNCT
ejpam-1853	578	7	x	x	PUNCT
ejpam-1853	578	8	·	·	PUNCT
ejpam-1853	578	9	y	y	PROPN
ejpam-1853	578	10	+	+	NOUN
ejpam-1853	578	11	x	x	X
ejpam-1853	578	12	·	·	PUNCT
ejpam-1853	578	13	z−	z−	X
ejpam-1853	578	14	x	x	X
ejpam-1853	578	15	.	.	PUNCT
ejpam-1853	579	1	hence	hence	ADV
ejpam-1853	579	2	,	,	PUNCT
ejpam-1853	579	3	the	the	DET
ejpam-1853	579	4	relation	relation	NOUN
ejpam-1853	579	5	(	(	PUNCT
ejpam-1853	579	6	9.4.1	9.4.1	NUM
ejpam-1853	579	7	)	)	PUNCT
ejpam-1853	579	8	holds	hold	VERB
ejpam-1853	579	9	.	.	PUNCT
ejpam-1853	580	1	let	let	VERB
ejpam-1853	580	2	y	y	PRON
ejpam-1853	580	3	,	,	PUNCT
ejpam-1853	580	4	x	x	NOUN
ejpam-1853	580	5	)	)	PUNCT
ejpam-1853	580	6	∈	∈	PROPN
ejpam-1853	580	7	v(2	v(2	PROPN
ejpam-1853	580	8	)	)	PUNCT
ejpam-1853	580	9	.	.	PUNCT
ejpam-1853	581	1	denote	denote	VERB
ejpam-1853	581	2	v	v	ADP
ejpam-1853	581	3	:	:	PUNCT
ejpam-1853	582	1	=	=	SYM
ejpam-1853	582	2	k	k	PROPN
ejpam-1853	582	3	y	y	PROPN
ejpam-1853	583	1	+	+	PUNCT
ejpam-1853	583	2	(	(	PUNCT
ejpam-1853	583	3	1	1	NUM
ejpam-1853	583	4	−	−	PROPN
ejpam-1853	583	5	k)ε(α(x	k)ε(α(x	NOUN
ejpam-1853	583	6	)	)	PUNCT
ejpam-1853	583	7	)	)	PUNCT
ejpam-1853	583	8	.	.	PUNCT
ejpam-1853	584	1	using	use	VERB
ejpam-1853	584	2	the	the	DET
ejpam-1853	584	3	linearity	linearity	NOUN
ejpam-1853	584	4	of	of	ADP
ejpam-1853	584	5	β	β	PROPN
ejpam-1853	584	6	,	,	PUNCT
ejpam-1853	584	7	we	we	PRON
ejpam-1853	584	8	have	have	VERB
ejpam-1853	584	9	β(v	β(v	NOUN
ejpam-1853	584	10	)	)	PUNCT
ejpam-1853	584	11	=	=	SYM
ejpam-1853	584	12	kβ(y	kβ(y	X
ejpam-1853	584	13	)	)	PUNCT
ejpam-1853	585	1	+	+	CCONJ
ejpam-1853	585	2	(	(	PUNCT
ejpam-1853	585	3	1−	1−	NUM
ejpam-1853	585	4	k)β(ε(α(x	k)β(ε(α(x	NOUN
ejpam-1853	585	5	)	)	PUNCT
ejpam-1853	585	6	)	)	PUNCT
ejpam-1853	585	7	)	)	PUNCT
ejpam-1853	586	1	=	=	SYM
ejpam-1853	586	2	α(x	α(x	NOUN
ejpam-1853	586	3	)	)	PUNCT
ejpam-1853	586	4	,	,	PUNCT
ejpam-1853	586	5	since	since	SCONJ
ejpam-1853	586	6	β(y	β(y	NOUN
ejpam-1853	586	7	)	)	PUNCT
ejpam-1853	586	8	=	=	SYM
ejpam-1853	586	9	α(x	α(x	NOUN
ejpam-1853	586	10	)	)	PUNCT
ejpam-1853	586	11	.	.	PUNCT
ejpam-1853	587	1	then	then	ADV
ejpam-1853	587	2	(	(	PUNCT
ejpam-1853	587	3	v	v	NOUN
ejpam-1853	587	4	,	,	PUNCT
ejpam-1853	587	5	x	x	NOUN
ejpam-1853	587	6	)	)	PUNCT
ejpam-1853	587	7	∈	∈	PROPN
ejpam-1853	587	8	v(2	v(2	PROPN
ejpam-1853	587	9	)	)	PUNCT
ejpam-1853	587	10	.	.	PUNCT
ejpam-1853	588	1	references	reference	NOUN
ejpam-1853	588	2	483	483	NUM
ejpam-1853	588	3	applying	apply	VERB
ejpam-1853	588	4	(	(	PUNCT
ejpam-1853	588	5	16	16	NUM
ejpam-1853	588	6	)	)	PUNCT
ejpam-1853	588	7	,	,	PUNCT
ejpam-1853	588	8	we	we	PRON
ejpam-1853	588	9	have	have	VERB
ejpam-1853	588	10	v	v	PRON
ejpam-1853	588	11	·	·	PUNCT
ejpam-1853	588	12	x	x	SYM
ejpam-1853	589	1	=	=	PUNCT
ejpam-1853	589	2	v	v	PROPN
ejpam-1853	589	3	+	+	NOUN
ejpam-1853	589	4	x	x	SYM
ejpam-1853	589	5	−	−	NOUN
ejpam-1853	589	6	ε(β(v	ε(β(v	ADV
ejpam-1853	589	7	)	)	PUNCT
ejpam-1853	589	8	)	)	PUNCT
ejpam-1853	590	1	=	=	PUNCT
ejpam-1853	590	2	x	x	PUNCT
ejpam-1853	591	1	+	+	CCONJ
ejpam-1853	591	2	k	k	PROPN
ejpam-1853	591	3	y	y	PROPN
ejpam-1853	591	4	−	−	PROPN
ejpam-1853	591	5	kε(α(x	kε(α(x	PROPN
ejpam-1853	591	6	)	)	PUNCT
ejpam-1853	591	7	)	)	PUNCT
ejpam-1853	591	8	and	and	CCONJ
ejpam-1853	591	9	k(y	k(y	PROPN
ejpam-1853	591	10	·	·	PUNCT
ejpam-1853	591	11	x	x	X
ejpam-1853	591	12	)	)	PUNCT
ejpam-1853	592	1	+	+	CCONJ
ejpam-1853	592	2	(	(	PUNCT
ejpam-1853	592	3	1−	1−	NUM
ejpam-1853	592	4	k)x	k)x	X
ejpam-1853	592	5	=	=	PUNCT
ejpam-1853	593	1	k(y	k(y	PROPN
ejpam-1853	593	2	+	+	CCONJ
ejpam-1853	593	3	x	x	SYM
ejpam-1853	593	4	−	−	NOUN
ejpam-1853	593	5	ε(β(y	ε(β(y	NOUN
ejpam-1853	593	6	)	)	PUNCT
ejpam-1853	593	7	)	)	PUNCT
ejpam-1853	593	8	)	)	PUNCT
ejpam-1853	594	1	+	+	CCONJ
ejpam-1853	594	2	(	(	PUNCT
ejpam-1853	594	3	1−	1−	NUM
ejpam-1853	594	4	k)x	k)x	X
ejpam-1853	594	5	=	=	PUNCT
ejpam-1853	594	6	x	x	PUNCT
ejpam-1853	595	1	+	+	CCONJ
ejpam-1853	595	2	k	k	PROPN
ejpam-1853	595	3	y	y	PROPN
ejpam-1853	595	4	−	−	PROPN
ejpam-1853	595	5	kε(α(x	kε(α(x	PROPN
ejpam-1853	595	6	)	)	PUNCT
ejpam-1853	595	7	)	)	PUNCT
ejpam-1853	595	8	.	.	PUNCT
ejpam-1853	596	1	then	then	ADV
ejpam-1853	596	2	,	,	PUNCT
ejpam-1853	596	3	v	v	INTJ
ejpam-1853	596	4	·	·	PUNCT
ejpam-1853	596	5	x	x	X
ejpam-1853	597	1	=	=	PUNCT
ejpam-1853	597	2	k(y	k(y	PROPN
ejpam-1853	597	3	·	·	PUNCT
ejpam-1853	597	4	x	x	X
ejpam-1853	597	5	)	)	PUNCT
ejpam-1853	598	1	+	+	CCONJ
ejpam-1853	598	2	(	(	PUNCT
ejpam-1853	598	3	1−	1−	NUM
ejpam-1853	598	4	k)x	k)x	X
ejpam-1853	598	5	.	.	PUNCT
ejpam-1853	599	1	hence	hence	ADV
ejpam-1853	599	2	,	,	PUNCT
ejpam-1853	599	3	(	(	PUNCT
ejpam-1853	599	4	9.4.4	9.4.4	X
ejpam-1853	599	5	)	)	PUNCT
ejpam-1853	599	6	holds	hold	NOUN
ejpam-1853	599	7	.	.	PUNCT
ejpam-1853	600	1	similarly	similarly	ADV
ejpam-1853	600	2	,	,	PUNCT
ejpam-1853	600	3	we	we	PRON
ejpam-1853	600	4	prove	prove	VERB
ejpam-1853	600	5	that	that	SCONJ
ejpam-1853	600	6	(	(	PUNCT
ejpam-1853	600	7	9.4.2	9.4.2	NUM
ejpam-1853	600	8	)	)	PUNCT
ejpam-1853	600	9	and	and	CCONJ
ejpam-1853	600	10	(	(	PUNCT
ejpam-1853	600	11	9.4.3	9.4.3	X
ejpam-1853	600	12	)	)	PUNCT
ejpam-1853	600	13	are	be	AUX
ejpam-1853	600	14	verified	verify	VERB
ejpam-1853	600	15	.	.	PUNCT
ejpam-1853	601	1	therefore	therefore	ADV
ejpam-1853	601	2	,	,	PUNCT
ejpam-1853	601	3	(	(	PUNCT
ejpam-1853	601	4	v	v	NOUN
ejpam-1853	601	5	,	,	PUNCT
ejpam-1853	601	6	v0	v0	NOUN
ejpam-1853	601	7	)	)	PUNCT
ejpam-1853	601	8	is	be	AUX
ejpam-1853	601	9	a	a	DET
ejpam-1853	601	10	vector	vector	NOUN
ejpam-1853	601	11	groupoid	groupoid	NOUN
ejpam-1853	601	12	.	.	PUNCT
ejpam-1853	602	1	references	reference	NOUN
ejpam-1853	602	2	[	[	X
ejpam-1853	602	3	1	1	NUM
ejpam-1853	602	4	]	]	PUNCT
ejpam-1853	602	5	h.	h.	PROPN
ejpam-1853	602	6	brandt	brandt	PROPN
ejpam-1853	602	7	.	.	PUNCT
ejpam-1853	603	1	über	über	PROPN
ejpam-1853	603	2	eine	eine	PROPN
ejpam-1853	603	3	verallgemeinerung	verallgemeinerung	PROPN
ejpam-1853	603	4	des	des	PROPN
ejpam-1853	603	5	gruppenbegriffes	gruppenbegriffes	PROPN
ejpam-1853	603	6	.	.	PUNCT
ejpam-1853	604	1	mathematische	mathematische	PROPN
ejpam-1853	604	2	annalen	annalen	PROPN
ejpam-1853	604	3	,	,	PUNCT
ejpam-1853	604	4	96(1	96(1	NUM
ejpam-1853	604	5	):	):	PUNCT
ejpam-1853	604	6	360	360	NUM
ejpam-1853	604	7	-	-	SYM
ejpam-1853	604	8	366	366	NUM
ejpam-1853	604	9	,	,	PUNCT
ejpam-1853	604	10	1926	1926	NUM
ejpam-1853	604	11	.	.	PUNCT
ejpam-1853	605	1	[	[	X
ejpam-1853	605	2	2	2	NUM
ejpam-1853	605	3	]	]	PUNCT
ejpam-1853	605	4	r.	r.	PROPN
ejpam-1853	605	5	brown	brown	PROPN
ejpam-1853	605	6	.	.	PUNCT
ejpam-1853	606	1	topology	topology	NOUN
ejpam-1853	606	2	and	and	CCONJ
ejpam-1853	606	3	groupoids	groupoid	NOUN
ejpam-1853	606	4	.	.	PUNCT
ejpam-1853	607	1	booksurge	booksurge	PROPN
ejpam-1853	607	2	llc	llc	PROPN
ejpam-1853	607	3	,	,	PUNCT
ejpam-1853	607	4	u.k	u.k	PROPN
ejpam-1853	607	5	.	.	PROPN
ejpam-1853	607	6	,	,	PUNCT
ejpam-1853	607	7	2006	2006	NUM
ejpam-1853	607	8	.	.	PUNCT
ejpam-1853	608	1	[	[	X
ejpam-1853	608	2	3	3	X
ejpam-1853	608	3	]	]	X
ejpam-1853	608	4	r.	r.	PROPN
ejpam-1853	608	5	brown	brown	PROPN
ejpam-1853	608	6	and	and	CCONJ
ejpam-1853	608	7	o.	o.	NOUN
ejpam-1853	608	8	mucuk	mucuk	NOUN
ejpam-1853	608	9	.	.	PUNCT
ejpam-1853	609	1	covering	cover	VERB
ejpam-1853	609	2	groups	group	NOUN
ejpam-1853	609	3	of	of	ADP
ejpam-1853	609	4	non	non	ADJ
ejpam-1853	609	5	-	-	ADJ
ejpam-1853	609	6	connected	connected	ADJ
ejpam-1853	609	7	topological	topological	ADJ
ejpam-1853	609	8	groups	group	NOUN
ejpam-1853	609	9	revisited	revisit	VERB
ejpam-1853	609	10	.	.	PUNCT
ejpam-1853	610	1	mathematical	mathematical	ADJ
ejpam-1853	610	2	proceedings	proceeding	NOUN
ejpam-1853	610	3	of	of	ADP
ejpam-1853	610	4	the	the	DET
ejpam-1853	610	5	cambridge	cambridge	PROPN
ejpam-1853	610	6	philosophical	philosophical	ADJ
ejpam-1853	610	7	society	society	NOUN
ejpam-1853	610	8	,	,	PUNCT
ejpam-1853	610	9	115	115	NUM
ejpam-1853	610	10	:	:	PUNCT
ejpam-1853	610	11	97	97	NUM
ejpam-1853	610	12	-	-	SYM
ejpam-1853	610	13	110	110	NUM
ejpam-1853	610	14	,	,	PUNCT
ejpam-1853	610	15	1994	1994	NUM
ejpam-1853	610	16	.	.	PUNCT
ejpam-1853	611	1	[	[	X
ejpam-1853	611	2	4	4	NUM
ejpam-1853	611	3	]	]	X
ejpam-1853	611	4	r.	r.	PROPN
ejpam-1853	611	5	brown	brown	PROPN
ejpam-1853	611	6	and	and	CCONJ
ejpam-1853	611	7	c.b	c.b	PROPN
ejpam-1853	611	8	.	.	PROPN
ejpam-1853	611	9	spencer	spencer	PROPN
ejpam-1853	611	10	.	.	PUNCT
ejpam-1853	612	1	g−groupoids	g−groupoid	NOUN
ejpam-1853	612	2	,	,	PUNCT
ejpam-1853	612	3	crossed	cross	VERB
ejpam-1853	612	4	modules	module	NOUN
ejpam-1853	612	5	and	and	CCONJ
ejpam-1853	612	6	the	the	DET
ejpam-1853	612	7	fundamental	fundamental	ADJ
ejpam-1853	612	8	groupoid	groupoid	NOUN
ejpam-1853	612	9	of	of	ADP
ejpam-1853	612	10	a	a	DET
ejpam-1853	612	11	topological	topological	ADJ
ejpam-1853	612	12	group	group	NOUN
ejpam-1853	612	13	.	.	PUNCT
ejpam-1853	613	1	proceedings	proceeding	NOUN
ejpam-1853	613	2	of	of	ADP
ejpam-1853	613	3	the	the	DET
ejpam-1853	613	4	koninklijke	koninklijke	PROPN
ejpam-1853	613	5	nederlandse	nederlandse	PROPN
ejpam-1853	613	6	akademie	akademie	PROPN
ejpam-1853	613	7	van	van	PROPN
ejpam-1853	613	8	wetenschappen	wetenschappen	NOUN
ejpam-1853	613	9	,	,	PUNCT
ejpam-1853	613	10	serie	serie	VERB
ejpam-1853	613	11	a	a	DET
ejpam-1853	613	12	:	:	PUNCT
ejpam-1853	613	13	mathematical	mathematical	ADJ
ejpam-1853	613	14	sciences	science	NOUN
ejpam-1853	613	15	,	,	PUNCT
ejpam-1853	613	16	79	79	NUM
ejpam-1853	613	17	:	:	PUNCT
ejpam-1853	613	18	296	296	NUM
ejpam-1853	613	19	-	-	SYM
ejpam-1853	613	20	302	302	NUM
ejpam-1853	613	21	,	,	PUNCT
ejpam-1853	613	22	1976	1976	NUM
ejpam-1853	613	23	.	.	PUNCT
ejpam-1853	614	1	[	[	X
ejpam-1853	614	2	5	5	X
ejpam-1853	614	3	]	]	PUNCT
ejpam-1853	614	4	c.	c.	PROPN
ejpam-1853	614	5	ehresmann	ehresmann	PROPN
ejpam-1853	614	6	.	.	PUNCT
ejpam-1853	615	1	oèuvres	oèuvre	NOUN
ejpam-1853	615	2	complètes	complète	NOUN
ejpam-1853	615	3	.	.	PUNCT
ejpam-1853	616	1	dunod	dunod	PROPN
ejpam-1853	616	2	,	,	PUNCT
ejpam-1853	616	3	paris	paris	PROPN
ejpam-1853	616	4	,	,	PUNCT
ejpam-1853	616	5	1950	1950	NUM
ejpam-1853	616	6	.	.	PUNCT
ejpam-1853	617	1	[	[	X
ejpam-1853	617	2	6	6	NUM
ejpam-1853	617	3	]	]	PUNCT
ejpam-1853	617	4	p.	p.	NOUN
ejpam-1853	617	5	j.	j.	PROPN
ejpam-1853	617	6	higgins	higgins	PROPN
ejpam-1853	617	7	.	.	PUNCT
ejpam-1853	618	1	notes	note	NOUN
ejpam-1853	618	2	on	on	ADP
ejpam-1853	618	3	categories	category	NOUN
ejpam-1853	618	4	and	and	CCONJ
ejpam-1853	618	5	groupoids	groupoid	NOUN
ejpam-1853	618	6	.	.	PUNCT
ejpam-1853	619	1	von	von	PROPN
ejpam-1853	619	2	nostrand	nostrand	PROPN
ejpam-1853	619	3	reinhold	reinhold	PROPN
ejpam-1853	619	4	mathematical	mathematical	PROPN
ejpam-1853	619	5	studies	study	NOUN
ejpam-1853	619	6	32	32	NUM
ejpam-1853	619	7	,	,	PUNCT
ejpam-1853	619	8	london,1971	london,1971	ADJ
ejpam-1853	619	9	.	.	PUNCT
ejpam-1853	619	10	reprints	reprint	NOUN
ejpam-1853	619	11	in	in	ADP
ejpam-1853	619	12	theory	theory	NOUN
ejpam-1853	619	13	and	and	CCONJ
ejpam-1853	619	14	applications	application	NOUN
ejpam-1853	619	15	of	of	ADP
ejpam-1853	619	16	categories	category	NOUN
ejpam-1853	619	17	,	,	PUNCT
ejpam-1853	619	18	no	no	INTJ
ejpam-1853	619	19	.	.	NOUN
ejpam-1853	619	20	7	7	NUM
ejpam-1853	619	21	:	:	SYM
ejpam-1853	619	22	1195	1195	NUM
ejpam-1853	619	23	,	,	PUNCT
ejpam-1853	619	24	2005	2005	NUM
ejpam-1853	619	25	.	.	PUNCT
ejpam-1853	620	1	[	[	X
ejpam-1853	620	2	7	7	X
ejpam-1853	620	3	]	]	X
ejpam-1853	620	4	i.	i.	PROPN
ejpam-1853	620	5	i̇cen	i̇cen	PROPN
ejpam-1853	620	6	,	,	PUNCT
ejpam-1853	620	7	a.	a.	PROPN
ejpam-1853	620	8	f.	f.	PROPN
ejpam-1853	620	9	özcan	özcan	PROPN
ejpam-1853	620	10	,	,	PUNCT
ejpam-1853	620	11	and	and	CCONJ
ejpam-1853	620	12	m.	m.	PROPN
ejpam-1853	620	13	h.	h.	PROPN
ejpam-1853	620	14	gürsoy	gürsoy	PROPN
ejpam-1853	620	15	.	.	PUNCT
ejpam-1853	621	1	topological	topological	ADJ
ejpam-1853	621	2	group	group	NOUN
ejpam-1853	621	3	-	-	PUNCT
ejpam-1853	621	4	groupoids	groupoid	NOUN
ejpam-1853	621	5	and	and	CCONJ
ejpam-1853	621	6	their	their	PRON
ejpam-1853	621	7	coverings	covering	NOUN
ejpam-1853	621	8	.	.	PUNCT
ejpam-1853	622	1	indian	indian	ADJ
ejpam-1853	622	2	journal	journal	PROPN
ejpam-1853	622	3	of	of	ADP
ejpam-1853	622	4	pure	pure	ADJ
ejpam-1853	622	5	and	and	CCONJ
ejpam-1853	622	6	applied	applied	ADJ
ejpam-1853	622	7	mathematics	mathematic	NOUN
ejpam-1853	622	8	,	,	PUNCT
ejpam-1853	622	9	36(9	36(9	NUM
ejpam-1853	622	10	):	):	PUNCT
ejpam-1853	622	11	493	493	NUM
ejpam-1853	622	12	-	-	SYM
ejpam-1853	622	13	502	502	NUM
ejpam-1853	622	14	,	,	PUNCT
ejpam-1853	622	15	2005	2005	NUM
ejpam-1853	622	16	.	.	PUNCT
ejpam-1853	623	1	[	[	X
ejpam-1853	623	2	8	8	NUM
ejpam-1853	623	3	]	]	X
ejpam-1853	623	4	gh	gh	PROPN
ejpam-1853	623	5	.	.	PROPN
ejpam-1853	623	6	ivan	ivan	PROPN
ejpam-1853	623	7	.	.	PUNCT
ejpam-1853	624	1	strong	strong	ADJ
ejpam-1853	624	2	morphisms	morphism	NOUN
ejpam-1853	624	3	of	of	ADP
ejpam-1853	624	4	groupoids	groupoid	NOUN
ejpam-1853	624	5	.	.	PUNCT
ejpam-1853	625	1	balkan	balkan	PROPN
ejpam-1853	625	2	journal	journal	PROPN
ejpam-1853	625	3	of	of	ADP
ejpam-1853	625	4	geometry	geometry	NOUN
ejpam-1853	625	5	and	and	CCONJ
ejpam-1853	625	6	its	its	PRON
ejpam-1853	625	7	applications	application	NOUN
ejpam-1853	625	8	(	(	PUNCT
ejpam-1853	625	9	bjga	bjga	X
ejpam-1853	625	10	)	)	PUNCT
ejpam-1853	625	11	,	,	PUNCT
ejpam-1853	625	12	4(1	4(1	NOUN
ejpam-1853	625	13	):	):	PUNCT
ejpam-1853	625	14	91	91	NUM
ejpam-1853	625	15	-	-	SYM
ejpam-1853	625	16	102	102	NUM
ejpam-1853	625	17	,	,	PUNCT
ejpam-1853	625	18	1999	1999	NUM
ejpam-1853	625	19	.	.	PUNCT
ejpam-1853	626	1	[	[	X
ejpam-1853	626	2	9	9	NUM
ejpam-1853	626	3	]	]	PUNCT
ejpam-1853	626	4	k.	k.	PROPN
ejpam-1853	626	5	mackenzie	mackenzie	PROPN
ejpam-1853	626	6	.	.	PUNCT
ejpam-1853	627	1	lie	lie	PROPN
ejpam-1853	627	2	groupoids	groupoid	NOUN
ejpam-1853	627	3	and	and	CCONJ
ejpam-1853	627	4	lie	lie	VERB
ejpam-1853	627	5	algebroids	algebroid	NOUN
ejpam-1853	627	6	in	in	ADP
ejpam-1853	627	7	differential	differential	ADJ
ejpam-1853	627	8	geometry	geometry	NOUN
ejpam-1853	627	9	.	.	PUNCT
ejpam-1853	628	1	london	london	PROPN
ejpam-1853	628	2	mathematical	mathematical	ADJ
ejpam-1853	628	3	society	society	NOUN
ejpam-1853	628	4	,	,	PUNCT
ejpam-1853	628	5	lecture	lecture	NOUN
ejpam-1853	628	6	notes	note	NOUN
ejpam-1853	628	7	series	series	NOUN
ejpam-1853	628	8	,	,	PUNCT
ejpam-1853	628	9	213	213	NUM
ejpam-1853	628	10	,	,	PUNCT
ejpam-1853	628	11	cambridge	cambridge	PROPN
ejpam-1853	628	12	university	university	PROPN
ejpam-1853	628	13	press	press	NOUN
ejpam-1853	628	14	,	,	PUNCT
ejpam-1853	628	15	2005	2005	NUM
ejpam-1853	628	16	.	.	PUNCT
ejpam-1853	629	1	[	[	X
ejpam-1853	629	2	10	10	NUM
ejpam-1853	629	3	]	]	X
ejpam-1853	629	4	o.	o.	NOUN
ejpam-1853	629	5	mucuk	mucuk	NOUN
ejpam-1853	629	6	.	.	PUNCT
ejpam-1853	630	1	covering	covering	NOUN
ejpam-1853	630	2	and	and	CCONJ
ejpam-1853	630	3	ring	ring	NOUN
ejpam-1853	630	4	-	-	PUNCT
ejpam-1853	630	5	groupoids	groupoid	NOUN
ejpam-1853	630	6	.	.	PUNCT
ejpam-1853	631	1	georgian	georgian	PROPN
ejpam-1853	631	2	mathematical	mathematical	PROPN
ejpam-1853	631	3	journal	journal	PROPN
ejpam-1853	631	4	,	,	PUNCT
ejpam-1853	631	5	5(5	5(5	NUM
ejpam-1853	631	6	):	):	PUNCT
ejpam-1853	631	7	475	475	NUM
ejpam-1853	631	8	-	-	SYM
ejpam-1853	631	9	482	482	NUM
ejpam-1853	631	10	,	,	PUNCT
ejpam-1853	631	11	1998	1998	NUM
ejpam-1853	631	12	.	.	PUNCT
ejpam-1853	632	1	[	[	X
ejpam-1853	632	2	11	11	NUM
ejpam-1853	632	3	]	]	X
ejpam-1853	632	4	a.f	a.f	PROPN
ejpam-1853	632	5	.	.	PROPN
ejpam-1853	632	6	özcan	özcan	PROPN
ejpam-1853	632	7	,	,	PUNCT
ejpam-1853	632	8	i.	i.	PROPN
ejpam-1853	632	9	i̇cen	i̇cen	PROPN
ejpam-1853	632	10	,	,	PUNCT
ejpam-1853	632	11	and	and	CCONJ
ejpam-1853	632	12	m.	m.	PROPN
ejpam-1853	632	13	h.	h.	PROPN
ejpam-1853	632	14	gürsoy	gürsoy	PROPN
ejpam-1853	632	15	.	.	PUNCT
ejpam-1853	633	1	topological	topological	ADJ
ejpam-1853	633	2	ring	ring	NOUN
ejpam-1853	633	3	-	-	PUNCT
ejpam-1853	633	4	groupoids	groupoid	NOUN
ejpam-1853	633	5	and	and	CCONJ
ejpam-1853	633	6	liftings	lifting	NOUN
ejpam-1853	633	7	.	.	PUNCT
ejpam-1853	634	1	iranian	iranian	ADJ
ejpam-1853	634	2	journal	journal	PROPN
ejpam-1853	634	3	of	of	ADP
ejpam-1853	634	4	science	science	NOUN
ejpam-1853	634	5	and	and	CCONJ
ejpam-1853	634	6	technology	technology	NOUN
ejpam-1853	634	7	transactions	transaction	NOUN
ejpam-1853	634	8	.	.	PUNCT
ejpam-1853	635	1	a	a	DET
ejpam-1853	635	2	:	:	PUNCT
ejpam-1853	635	3	science	science	NOUN
ejpam-1853	635	4	,	,	PUNCT
ejpam-1853	635	5	30(3	30(3	NUM
ejpam-1853	635	6	):	):	PUNCT
ejpam-1853	635	7	305	305	NUM
ejpam-1853	635	8	-	-	SYM
ejpam-1853	635	9	362	362	NUM
ejpam-1853	635	10	,	,	PUNCT
ejpam-1853	635	11	2007	2007	NUM
ejpam-1853	635	12	.	.	PUNCT
ejpam-1853	636	1	[	[	X
ejpam-1853	636	2	12	12	NUM
ejpam-1853	636	3	]	]	X
ejpam-1853	636	4	v.	v.	ADP
ejpam-1853	636	5	popuţa	popuţa	NOUN
ejpam-1853	636	6	.	.	PUNCT
ejpam-1853	637	1	some	some	DET
ejpam-1853	637	2	classes	class	NOUN
ejpam-1853	637	3	of	of	ADP
ejpam-1853	637	4	brandt	brandt	PROPN
ejpam-1853	637	5	groupoids	groupoids	PROPN
ejpam-1853	637	6	.	.	PUNCT
ejpam-1853	638	1	scientific	scientific	ADJ
ejpam-1853	638	2	bulletin	bulletin	NOUN
ejpam-1853	638	3	of	of	ADP
ejpam-1853	638	4	"	"	PUNCT
ejpam-1853	638	5	politehnica	politehnica	PROPN
ejpam-1853	638	6	"	"	PUNCT
ejpam-1853	638	7	university	university	NOUN
ejpam-1853	638	8	of	of	ADP
ejpam-1853	638	9	timi̧soara	timi̧soara	PROPN
ejpam-1853	638	10	,	,	PUNCT
ejpam-1853	638	11	52(66	52(66	NUM
ejpam-1853	638	12	)	)	PUNCT
ejpam-1853	638	13	,	,	PUNCT
ejpam-1853	638	14	no	no	INTJ
ejpam-1853	638	15	.	.	PUNCT
ejpam-1853	639	1	1:50	1:50	NUM
ejpam-1853	639	2	-	-	SYM
ejpam-1853	639	3	54	54	NUM
ejpam-1853	639	4	,	,	PUNCT
ejpam-1853	639	5	2007	2007	NUM
ejpam-1853	639	6	.	.	PUNCT
ejpam-1853	640	1	[	[	X
ejpam-1853	640	2	13	13	NUM
ejpam-1853	640	3	]	]	X
ejpam-1853	640	4	v.	v.	ADP
ejpam-1853	640	5	popuţa	popuţa	PROPN
ejpam-1853	640	6	and	and	CCONJ
ejpam-1853	640	7	gh	gh	PROPN
ejpam-1853	640	8	.	.	PROPN
ejpam-1853	640	9	ivan	ivan	PROPN
ejpam-1853	640	10	.	.	PUNCT
ejpam-1853	641	1	a	a	DET
ejpam-1853	641	2	groupoid	groupoid	PROPN
ejpam-1853	641	3	structure	structure	NOUN
ejpam-1853	641	4	on	on	ADP
ejpam-1853	641	5	a	a	DET
ejpam-1853	641	6	vector	vector	NOUN
ejpam-1853	641	7	space	space	NOUN
ejpam-1853	641	8	.	.	PUNCT
ejpam-1853	642	1	bul	bul	PROPN
ejpam-1853	642	2	.	.	PUNCT
ejpam-1853	643	1	ştiinţ.	ştiinţ.	PROPN
ejpam-1853	643	2	univ	univ	PROPN
ejpam-1853	643	3	.	.	PUNCT
ejpam-1853	644	1	politeh	politeh	NOUN
ejpam-1853	644	2	.	.	PUNCT
ejpam-1853	645	1	timi̧soara	timi̧soara	PROPN
ejpam-1853	645	2	,	,	PUNCT
ejpam-1853	645	3	ser	ser	NOUN
ejpam-1853	645	4	.	.	PROPN
ejpam-1853	646	1	mat	mat	PROPN
ejpam-1853	646	2	.	.	PUNCT
ejpam-1853	647	1	fiz	fiz	PROPN
ejpam-1853	647	2	.	.	PROPN
ejpam-1853	647	3	,	,	PUNCT
ejpam-1853	647	4	56(70	56(70	NUM
ejpam-1853	647	5	)	)	PUNCT
ejpam-1853	647	6	,	,	PUNCT
ejpam-1853	647	7	no.1	no.1	NUM
ejpam-1853	647	8	:	:	PUNCT
ejpam-1853	647	9	55	55	NUM
ejpam-1853	647	10	-	-	SYM
ejpam-1853	647	11	64	64	NUM
ejpam-1853	647	12	,	,	PUNCT
ejpam-1853	647	13	2011	2011	NUM
ejpam-1853	647	14	.	.	PUNCT
ejpam-1853	648	1	references	reference	NOUN
ejpam-1853	648	2	484	484	NUM
ejpam-1853	649	1	[	[	X
ejpam-1853	649	2	14	14	NUM
ejpam-1853	649	3	]	]	X
ejpam-1853	649	4	v.	v.	ADP
ejpam-1853	649	5	popuţa	popuţa	PROPN
ejpam-1853	649	6	and	and	CCONJ
ejpam-1853	649	7	gh	gh	PROPN
ejpam-1853	649	8	.	.	PUNCT
ejpam-1853	649	9	ivan	ivan	PROPN
ejpam-1853	649	10	.	.	PUNCT
ejpam-1853	650	1	vector	vector	NOUN
ejpam-1853	650	2	groupoids	groupoid	NOUN
ejpam-1853	650	3	.	.	PUNCT
ejpam-1853	651	1	theoretical	theoretical	ADJ
ejpam-1853	651	2	mathematics	mathematics	PROPN
ejpam-1853	651	3	&	&	CCONJ
ejpam-1853	651	4	applications	application	NOUN
ejpam-1853	651	5	,	,	PUNCT
ejpam-1853	651	6	2(2):112	2(2):112	NUM
ejpam-1853	651	7	,	,	PUNCT
ejpam-1853	651	8	2012	2012	NUM
ejpam-1853	651	9	.	.	PUNCT
ejpam-1853	652	1	[	[	X
ejpam-1853	652	2	15	15	NUM
ejpam-1853	652	3	]	]	X
ejpam-1853	652	4	a.	a.	NOUN
ejpam-1853	652	5	ramsey	ramsey	PROPN
ejpam-1853	652	6	and	and	CCONJ
ejpam-1853	652	7	j.	j.	PROPN
ejpam-1853	652	8	renault	renault	PROPN
ejpam-1853	652	9	.	.	PUNCT
ejpam-1853	653	1	groupoids	groupoid	NOUN
ejpam-1853	653	2	in	in	ADP
ejpam-1853	653	3	analysis	analysis	NOUN
ejpam-1853	653	4	,	,	PUNCT
ejpam-1853	653	5	geometry	geometry	NOUN
ejpam-1853	653	6	and	and	CCONJ
ejpam-1853	653	7	physics	physics	NOUN
ejpam-1853	653	8	.	.	PUNCT
ejpam-1853	654	1	contemporary	contemporary	ADJ
ejpam-1853	654	2	mathematics	mathematics	PROPN
ejpam-1853	654	3	,	,	PUNCT
ejpam-1853	654	4	282	282	NUM
ejpam-1853	654	5	,	,	PUNCT
ejpam-1853	654	6	ams	am	NOUN
ejpam-1853	654	7	providence	providence	NOUN
ejpam-1853	654	8	,	,	PUNCT
ejpam-1853	654	9	ri	ri	PROPN
ejpam-1853	654	10	,	,	PUNCT
ejpam-1853	654	11	2001	2001	NUM
ejpam-1853	654	12	.	.	PUNCT