id	sid	tid	token	lemma	pos
ejpam-3526	1	1	european	european	PROPN
ejpam-3526	1	2	journal	journal	PROPN
ejpam-3526	1	3	of	of	ADP
ejpam-3526	1	4	pure	pure	ADJ
ejpam-3526	1	5	and	and	CCONJ
ejpam-3526	1	6	applied	apply	VERB
ejpam-3526	1	7	mathematics	mathematic	NOUN
ejpam-3526	1	8	vol	vol	NOUN
ejpam-3526	1	9	.	.	PROPN
ejpam-3526	2	1	12	12	NUM
ejpam-3526	2	2	,	,	PUNCT
ejpam-3526	2	3	no	no	INTJ
ejpam-3526	2	4	.	.	NOUN
ejpam-3526	2	5	4	4	NUM
ejpam-3526	2	6	,	,	PUNCT
ejpam-3526	2	7	2019	2019	NUM
ejpam-3526	2	8	,	,	PUNCT
ejpam-3526	2	9	1497	1497	NUM
ejpam-3526	2	10	-	-	SYM
ejpam-3526	2	11	1507	1507	NUM
ejpam-3526	2	12	issn	issn	PROPN
ejpam-3526	2	13	1307	1307	NUM
ejpam-3526	2	14	-	-	SYM
ejpam-3526	2	15	5543	5543	NUM
ejpam-3526	2	16	–	–	PUNCT
ejpam-3526	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3526	2	18	published	publish	VERB
ejpam-3526	2	19	by	by	ADP
ejpam-3526	3	1	new	new	PROPN
ejpam-3526	3	2	york	york	PROPN
ejpam-3526	3	3	business	business	PROPN
ejpam-3526	3	4	global	global	PROPN
ejpam-3526	3	5	the	the	DET
ejpam-3526	3	6	dual	dual	ADJ
ejpam-3526	3	7	b	b	NOUN
ejpam-3526	3	8	-	-	PUNCT
ejpam-3526	3	9	algebra	algebra	PROPN
ejpam-3526	3	10	katrina	katrina	PROPN
ejpam-3526	3	11	e.	e.	PROPN
ejpam-3526	3	12	belleza1,∗	belleza1,∗	PROPN
ejpam-3526	3	13	,	,	PUNCT
ejpam-3526	3	14	jocelyn	jocelyn	PROPN
ejpam-3526	3	15	p.	p.	PROPN
ejpam-3526	3	16	vilela2	vilela2	PROPN
ejpam-3526	3	17	1	1	NUM
ejpam-3526	3	18	department	department	NOUN
ejpam-3526	3	19	of	of	ADP
ejpam-3526	3	20	mathematics	mathematic	NOUN
ejpam-3526	3	21	,	,	PUNCT
ejpam-3526	3	22	school	school	NOUN
ejpam-3526	3	23	of	of	ADP
ejpam-3526	3	24	arts	art	NOUN
ejpam-3526	3	25	and	and	CCONJ
ejpam-3526	3	26	sciences	science	NOUN
ejpam-3526	3	27	,	,	PUNCT
ejpam-3526	3	28	university	university	NOUN
ejpam-3526	3	29	of	of	ADP
ejpam-3526	3	30	san	san	PROPN
ejpam-3526	3	31	carlos	carlos	PROPN
ejpam-3526	3	32	,	,	PUNCT
ejpam-3526	3	33	6000	6000	NUM
ejpam-3526	3	34	cebu	cebu	NOUN
ejpam-3526	3	35	city	city	NOUN
ejpam-3526	3	36	,	,	PUNCT
ejpam-3526	3	37	philippines	philippines	PROPN
ejpam-3526	3	38	2	2	NUM
ejpam-3526	3	39	department	department	NOUN
ejpam-3526	3	40	of	of	ADP
ejpam-3526	3	41	mathematics	mathematic	NOUN
ejpam-3526	3	42	and	and	CCONJ
ejpam-3526	3	43	statistics	statistic	NOUN
ejpam-3526	3	44	,	,	PUNCT
ejpam-3526	3	45	college	college	NOUN
ejpam-3526	3	46	of	of	ADP
ejpam-3526	3	47	science	science	NOUN
ejpam-3526	3	48	and	and	CCONJ
ejpam-3526	3	49	mathematics	mathematic	NOUN
ejpam-3526	3	50	,	,	PUNCT
ejpam-3526	3	51	center	center	NOUN
ejpam-3526	3	52	of	of	ADP
ejpam-3526	3	53	graph	graph	NOUN
ejpam-3526	3	54	theory	theory	NOUN
ejpam-3526	3	55	,	,	PUNCT
ejpam-3526	3	56	algebra	algebra	NOUN
ejpam-3526	3	57	and	and	CCONJ
ejpam-3526	3	58	analysis	analysis	NOUN
ejpam-3526	3	59	,	,	PUNCT
ejpam-3526	3	60	premier	premier	PROPN
ejpam-3526	3	61	research	research	PROPN
ejpam-3526	3	62	institute	institute	PROPN
ejpam-3526	3	63	of	of	ADP
ejpam-3526	3	64	science	science	NOUN
ejpam-3526	3	65	and	and	CCONJ
ejpam-3526	3	66	mathematics	mathematic	NOUN
ejpam-3526	3	67	,	,	PUNCT
ejpam-3526	3	68	mindanao	mindanao	PROPN
ejpam-3526	3	69	state	state	PROPN
ejpam-3526	3	70	university	university	PROPN
ejpam-3526	3	71	-	-	PUNCT
ejpam-3526	3	72	iligan	iligan	PROPN
ejpam-3526	3	73	institute	institute	PROPN
ejpam-3526	3	74	of	of	ADP
ejpam-3526	3	75	technology	technology	PROPN
ejpam-3526	3	76	,	,	PUNCT
ejpam-3526	3	77	9200	9200	NUM
ejpam-3526	3	78	iligan	iligan	ADJ
ejpam-3526	3	79	city	city	NOUN
ejpam-3526	3	80	,	,	PUNCT
ejpam-3526	3	81	philippines	philippine	NOUN
ejpam-3526	3	82	abstract	abstract	ADJ
ejpam-3526	3	83	.	.	PUNCT
ejpam-3526	4	1	this	this	DET
ejpam-3526	4	2	paper	paper	NOUN
ejpam-3526	4	3	introduces	introduce	NOUN
ejpam-3526	4	4	and	and	CCONJ
ejpam-3526	4	5	characterizes	characterize	VERB
ejpam-3526	4	6	the	the	DET
ejpam-3526	4	7	notion	notion	NOUN
ejpam-3526	4	8	of	of	ADP
ejpam-3526	4	9	a	a	DET
ejpam-3526	4	10	dual	dual	ADJ
ejpam-3526	4	11	b	b	NOUN
ejpam-3526	4	12	-	-	PUNCT
ejpam-3526	4	13	algebra	algebra	NOUN
ejpam-3526	4	14	.	.	PUNCT
ejpam-3526	5	1	moreover	moreover	ADV
ejpam-3526	5	2	,	,	PUNCT
ejpam-3526	5	3	this	this	DET
ejpam-3526	5	4	study	study	NOUN
ejpam-3526	5	5	investigates	investigate	VERB
ejpam-3526	5	6	the	the	DET
ejpam-3526	5	7	relationship	relationship	NOUN
ejpam-3526	5	8	between	between	ADP
ejpam-3526	5	9	a	a	DET
ejpam-3526	5	10	dual	dual	ADJ
ejpam-3526	5	11	b	b	NOUN
ejpam-3526	5	12	-	-	PUNCT
ejpam-3526	5	13	algebra	algebra	NOUN
ejpam-3526	5	14	and	and	CCONJ
ejpam-3526	5	15	a	a	DET
ejpam-3526	5	16	bck	bck	NOUN
ejpam-3526	5	17	-	-	PUNCT
ejpam-3526	5	18	algebra	algebra	NOUN
ejpam-3526	5	19	.	.	PUNCT
ejpam-3526	6	1	commutativity	commutativity	NOUN
ejpam-3526	6	2	of	of	ADP
ejpam-3526	6	3	a	a	DET
ejpam-3526	6	4	dual	dual	ADJ
ejpam-3526	6	5	b	b	NOUN
ejpam-3526	6	6	-	-	PUNCT
ejpam-3526	6	7	algebra	algebra	NOUN
ejpam-3526	6	8	is	be	AUX
ejpam-3526	6	9	also	also	ADV
ejpam-3526	6	10	discussed	discuss	VERB
ejpam-3526	6	11	and	and	CCONJ
ejpam-3526	6	12	its	its	PRON
ejpam-3526	6	13	relation	relation	NOUN
ejpam-3526	6	14	to	to	ADP
ejpam-3526	6	15	some	some	DET
ejpam-3526	6	16	algebras	algebra	NOUN
ejpam-3526	6	17	such	such	ADJ
ejpam-3526	6	18	as	as	ADP
ejpam-3526	6	19	ci	ci	NOUN
ejpam-3526	6	20	-	-	NOUN
ejpam-3526	6	21	algebra	algebra	NOUN
ejpam-3526	6	22	and	and	CCONJ
ejpam-3526	6	23	dual	dual	ADJ
ejpam-3526	6	24	bci	bci	NOUN
ejpam-3526	6	25	-	-	NOUN
ejpam-3526	6	26	algebra	algebra	NOUN
ejpam-3526	6	27	is	be	AUX
ejpam-3526	6	28	examined	examine	VERB
ejpam-3526	6	29	.	.	PUNCT
ejpam-3526	7	1	2010	2010	NUM
ejpam-3526	7	2	mathematics	mathematic	NOUN
ejpam-3526	7	3	subject	subject	NOUN
ejpam-3526	7	4	classifications	classification	NOUN
ejpam-3526	7	5	:	:	PUNCT
ejpam-3526	7	6	06f35	06f35	NUM
ejpam-3526	7	7	,	,	PUNCT
ejpam-3526	7	8	47l45	47l45	NUM
ejpam-3526	7	9	,	,	PUNCT
ejpam-3526	7	10	08c05	08c05	NOUN
ejpam-3526	7	11	key	key	ADJ
ejpam-3526	7	12	words	word	NOUN
ejpam-3526	7	13	and	and	CCONJ
ejpam-3526	7	14	phrases	phrase	NOUN
ejpam-3526	7	15	:	:	PUNCT
ejpam-3526	7	16	b	b	X
ejpam-3526	7	17	-	-	PUNCT
ejpam-3526	7	18	algebra	algebra	NOUN
ejpam-3526	7	19	,	,	PUNCT
ejpam-3526	7	20	dual	dual	ADJ
ejpam-3526	7	21	b	b	NOUN
ejpam-3526	7	22	-	-	PUNCT
ejpam-3526	7	23	algebra	algebra	NOUN
ejpam-3526	7	24	,	,	PUNCT
ejpam-3526	7	25	dual	dual	ADJ
ejpam-3526	7	26	algebra	algebra	NOUN
ejpam-3526	7	27	1	1	NUM
ejpam-3526	7	28	.	.	PUNCT
ejpam-3526	7	29	introduction	introduction	NOUN
ejpam-3526	7	30	in	in	ADP
ejpam-3526	7	31	2002	2002	NUM
ejpam-3526	7	32	,	,	PUNCT
ejpam-3526	7	33	j.neggers	j.negger	NOUN
ejpam-3526	7	34	and	and	CCONJ
ejpam-3526	7	35	h.s	h.s	PROPN
ejpam-3526	7	36	.	.	PROPN
ejpam-3526	7	37	kim	kim	PROPN
ejpam-3526	8	1	[	[	X
ejpam-3526	8	2	9	9	NUM
ejpam-3526	8	3	]	]	PUNCT
ejpam-3526	8	4	introduced	introduce	VERB
ejpam-3526	8	5	and	and	CCONJ
ejpam-3526	8	6	investigated	investigate	VERB
ejpam-3526	8	7	b	b	NOUN
ejpam-3526	8	8	-	-	PUNCT
ejpam-3526	8	9	algebras	algebra	NOUN
ejpam-3526	8	10	which	which	PRON
ejpam-3526	8	11	is	be	AUX
ejpam-3526	8	12	related	relate	VERB
ejpam-3526	8	13	to	to	ADP
ejpam-3526	8	14	several	several	ADJ
ejpam-3526	8	15	classes	class	NOUN
ejpam-3526	8	16	of	of	ADP
ejpam-3526	8	17	algebras	algebra	NOUN
ejpam-3526	8	18	such	such	ADJ
ejpam-3526	8	19	as	as	ADP
ejpam-3526	8	20	bch	bch	PROPN
ejpam-3526	8	21	/	/	SYM
ejpam-3526	8	22	bci	bci	PROPN
ejpam-3526	8	23	/	/	SYM
ejpam-3526	8	24	bck	bck	NOUN
ejpam-3526	8	25	-	-	PUNCT
ejpam-3526	8	26	algebras	algebras	PROPN
ejpam-3526	8	27	and	and	CCONJ
ejpam-3526	8	28	established	establish	VERB
ejpam-3526	8	29	that	that	PRON
ejpam-3526	8	30	b	b	X
ejpam-3526	8	31	-	-	PUNCT
ejpam-3526	8	32	algebras	algebra	NOUN
ejpam-3526	8	33	are	be	AUX
ejpam-3526	8	34	related	relate	VERB
ejpam-3526	8	35	to	to	ADP
ejpam-3526	8	36	groups	group	NOUN
ejpam-3526	8	37	.	.	PUNCT
ejpam-3526	9	1	in	in	ADP
ejpam-3526	9	2	the	the	DET
ejpam-3526	9	3	same	same	ADJ
ejpam-3526	9	4	year	year	NOUN
ejpam-3526	9	5	,	,	PUNCT
ejpam-3526	9	6	m.kondo	m.kondo	PROPN
ejpam-3526	9	7	and	and	CCONJ
ejpam-3526	9	8	y.b	y.b	PROPN
ejpam-3526	9	9	.	.	PROPN
ejpam-3526	9	10	jun	jun	PROPN
ejpam-3526	9	11	[	[	X
ejpam-3526	9	12	4	4	X
ejpam-3526	9	13	]	]	PUNCT
ejpam-3526	9	14	showed	show	VERB
ejpam-3526	9	15	that	that	SCONJ
ejpam-3526	9	16	every	every	DET
ejpam-3526	9	17	b	b	X
ejpam-3526	9	18	-	-	PUNCT
ejpam-3526	9	19	algebra	algebra	NOUN
ejpam-3526	9	20	is	be	AUX
ejpam-3526	9	21	group	group	NOUN
ejpam-3526	9	22	-	-	PUNCT
ejpam-3526	9	23	derived	derive	VERB
ejpam-3526	9	24	.	.	PUNCT
ejpam-3526	10	1	in	in	ADP
ejpam-3526	10	2	2010	2010	NUM
ejpam-3526	10	3	,	,	PUNCT
ejpam-3526	10	4	n.o	n.o	PROPN
ejpam-3526	10	5	.	.	PROPN
ejpam-3526	10	6	al	al	PROPN
ejpam-3526	10	7	-	-	PUNCT
ejpam-3526	10	8	shehrie	shehrie	NOUN
ejpam-3526	11	1	[	[	X
ejpam-3526	11	2	1	1	NUM
ejpam-3526	11	3	]	]	PUNCT
ejpam-3526	11	4	introduced	introduce	VERB
ejpam-3526	11	5	the	the	DET
ejpam-3526	11	6	left	left	ADJ
ejpam-3526	11	7	-	-	PUNCT
ejpam-3526	11	8	right	right	NOUN
ejpam-3526	11	9	(	(	PUNCT
ejpam-3526	11	10	resp	resp	NOUN
ejpam-3526	11	11	.	.	PUNCT
ejpam-3526	12	1	right	right	ADJ
ejpam-3526	12	2	-	-	PUNCT
ejpam-3526	12	3	left	left	ADJ
ejpam-3526	12	4	)	)	PUNCT
ejpam-3526	12	5	derivation	derivation	NOUN
ejpam-3526	12	6	on	on	ADP
ejpam-3526	12	7	a	a	DET
ejpam-3526	12	8	b	b	NOUN
ejpam-3526	12	9	-	-	PUNCT
ejpam-3526	12	10	algebra	algebra	NOUN
ejpam-3526	12	11	and	and	CCONJ
ejpam-3526	12	12	some	some	DET
ejpam-3526	12	13	related	related	ADJ
ejpam-3526	12	14	properties	property	NOUN
ejpam-3526	12	15	were	be	AUX
ejpam-3526	12	16	investigated	investigate	VERB
ejpam-3526	12	17	.	.	PUNCT
ejpam-3526	13	1	in	in	ADP
ejpam-3526	13	2	1996	1996	NUM
ejpam-3526	13	3	,	,	PUNCT
ejpam-3526	13	4	y.imai	y.imai	PROPN
ejpam-3526	13	5	and	and	CCONJ
ejpam-3526	13	6	k.iseki	k.iseki	X
ejpam-3526	13	7	[	[	X
ejpam-3526	13	8	2	2	X
ejpam-3526	13	9	]	]	PUNCT
ejpam-3526	13	10	introduced	introduce	VERB
ejpam-3526	13	11	two	two	NUM
ejpam-3526	13	12	classes	class	NOUN
ejpam-3526	13	13	of	of	ADP
ejpam-3526	13	14	algebras	algebra	NOUN
ejpam-3526	13	15	:	:	PUNCT
ejpam-3526	13	16	bckalgebras	bckalgebras	PROPN
ejpam-3526	13	17	and	and	CCONJ
ejpam-3526	13	18	bci	bci	NOUN
ejpam-3526	13	19	-	-	PUNCT
ejpam-3526	13	20	algebras	algebras	X
ejpam-3526	13	21	.	.	PUNCT
ejpam-3526	14	1	it	it	PRON
ejpam-3526	14	2	is	be	AUX
ejpam-3526	14	3	known	know	VERB
ejpam-3526	14	4	that	that	SCONJ
ejpam-3526	14	5	a	a	DET
ejpam-3526	14	6	bci	bci	NOUN
ejpam-3526	14	7	-	-	NOUN
ejpam-3526	14	8	algebra	algebra	NOUN
ejpam-3526	14	9	is	be	AUX
ejpam-3526	14	10	a	a	DET
ejpam-3526	14	11	generalization	generalization	NOUN
ejpam-3526	14	12	of	of	ADP
ejpam-3526	14	13	a	a	DET
ejpam-3526	14	14	bckalgebra	bckalgebra	NOUN
ejpam-3526	14	15	.	.	PUNCT
ejpam-3526	15	1	in	in	ADP
ejpam-3526	15	2	2007	2007	NUM
ejpam-3526	15	3	,	,	PUNCT
ejpam-3526	15	4	dual	dual	ADJ
ejpam-3526	15	5	bck	bck	NOUN
ejpam-3526	15	6	-	-	PUNCT
ejpam-3526	15	7	algebra	algebra	NOUN
ejpam-3526	15	8	was	be	AUX
ejpam-3526	15	9	introduced	introduce	VERB
ejpam-3526	15	10	by	by	ADP
ejpam-3526	15	11	k.h	k.h	PROPN
ejpam-3526	15	12	.	.	PROPN
ejpam-3526	15	13	kim	kim	PROPN
ejpam-3526	15	14	and	and	CCONJ
ejpam-3526	15	15	y.h	y.h	PROPN
ejpam-3526	15	16	.	.	PROPN
ejpam-3526	15	17	yon	yon	NOUN
ejpam-3526	16	1	[	[	X
ejpam-3526	16	2	3	3	X
ejpam-3526	16	3	]	]	PUNCT
ejpam-3526	16	4	and	and	CCONJ
ejpam-3526	16	5	some	some	DET
ejpam-3526	16	6	properties	property	NOUN
ejpam-3526	16	7	were	be	AUX
ejpam-3526	16	8	also	also	ADV
ejpam-3526	16	9	studied	study	VERB
ejpam-3526	16	10	.	.	PUNCT
ejpam-3526	17	1	moreover	moreover	ADV
ejpam-3526	17	2	,	,	PUNCT
ejpam-3526	17	3	k.h	k.h	PROPN
ejpam-3526	17	4	.	.	PROPN
ejpam-3526	17	5	kim	kim	PROPN
ejpam-3526	17	6	and	and	CCONJ
ejpam-3526	17	7	y.h	y.h	PROPN
ejpam-3526	17	8	.	.	PROPN
ejpam-3526	17	9	yon	yon	NOUN
ejpam-3526	18	1	[	[	X
ejpam-3526	18	2	3	3	NUM
ejpam-3526	18	3	]	]	PUNCT
ejpam-3526	18	4	investigated	investigate	VERB
ejpam-3526	18	5	the	the	DET
ejpam-3526	18	6	relationship	relationship	NOUN
ejpam-3526	18	7	between	between	ADP
ejpam-3526	18	8	a	a	DET
ejpam-3526	18	9	dual	dual	ADJ
ejpam-3526	18	10	bck	bck	NOUN
ejpam-3526	18	11	-	-	PUNCT
ejpam-3526	18	12	algebra	algebra	NOUN
ejpam-3526	18	13	and	and	CCONJ
ejpam-3526	18	14	an	an	DET
ejpam-3526	18	15	mv	mv	PROPN
ejpam-3526	18	16	-algebra	-algebra	PROPN
ejpam-3526	18	17	.	.	PUNCT
ejpam-3526	19	1	on	on	ADP
ejpam-3526	19	2	the	the	DET
ejpam-3526	19	3	other	other	ADJ
ejpam-3526	19	4	hand	hand	NOUN
ejpam-3526	19	5	,	,	PUNCT
ejpam-3526	19	6	a.	a.	NOUN
ejpam-3526	19	7	walendziak	walendziak	PROPN
ejpam-3526	20	1	[	[	X
ejpam-3526	20	2	12	12	NUM
ejpam-3526	20	3	]	]	PUNCT
ejpam-3526	20	4	defined	define	VERB
ejpam-3526	20	5	commutative	commutative	ADJ
ejpam-3526	20	6	be	be	AUX
ejpam-3526	20	7	-	-	PUNCT
ejpam-3526	20	8	algebras	algebras	ADJ
ejpam-3526	20	9	in	in	ADP
ejpam-3526	20	10	2008	2008	NUM
ejpam-3526	20	11	and	and	CCONJ
ejpam-3526	20	12	proved	prove	VERB
ejpam-3526	20	13	that	that	SCONJ
ejpam-3526	20	14	these	these	PRON
ejpam-3526	20	15	are	be	AUX
ejpam-3526	20	16	equivalent	equivalent	ADJ
ejpam-3526	20	17	to	to	ADP
ejpam-3526	20	18	the	the	DET
ejpam-3526	20	19	commutative	commutative	ADJ
ejpam-3526	20	20	dual	dual	ADJ
ejpam-3526	20	21	bck	bck	NOUN
ejpam-3526	20	22	-	-	PUNCT
ejpam-3526	20	23	algebras	algebras	PROPN
ejpam-3526	20	24	.	.	PUNCT
ejpam-3526	21	1	in	in	ADP
ejpam-3526	21	2	2009	2009	NUM
ejpam-3526	21	3	,	,	PUNCT
ejpam-3526	21	4	the	the	DET
ejpam-3526	21	5	notions	notion	NOUN
ejpam-3526	21	6	of	of	ADP
ejpam-3526	21	7	dual	dual	ADJ
ejpam-3526	21	8	bcialgebra	bcialgebra	NOUN
ejpam-3526	21	9	and	and	CCONJ
ejpam-3526	21	10	ci	ci	NOUN
ejpam-3526	21	11	-	-	PUNCT
ejpam-3526	21	12	algebra	algebra	NOUN
ejpam-3526	21	13	were	be	AUX
ejpam-3526	21	14	introduced	introduce	VERB
ejpam-3526	21	15	by	by	ADP
ejpam-3526	21	16	b.l	b.l	PROPN
ejpam-3526	21	17	.	.	PROPN
ejpam-3526	21	18	meng	meng	PROPN
ejpam-3526	22	1	[	[	X
ejpam-3526	22	2	5	5	NUM
ejpam-3526	22	3	]	]	PUNCT
ejpam-3526	22	4	together	together	ADV
ejpam-3526	22	5	with	with	ADP
ejpam-3526	22	6	some	some	PRON
ejpam-3526	22	7	of	of	ADP
ejpam-3526	22	8	their	their	PRON
ejpam-3526	22	9	properties	property	NOUN
ejpam-3526	22	10	.	.	PUNCT
ejpam-3526	23	1	it	it	PRON
ejpam-3526	23	2	is	be	AUX
ejpam-3526	23	3	shown	show	VERB
ejpam-3526	23	4	that	that	SCONJ
ejpam-3526	23	5	ci	ci	NOUN
ejpam-3526	23	6	-	-	PUNCT
ejpam-3526	23	7	algebra	algebra	NOUN
ejpam-3526	23	8	is	be	AUX
ejpam-3526	23	9	a	a	DET
ejpam-3526	23	10	generalization	generalization	NOUN
ejpam-3526	23	11	of	of	ADP
ejpam-3526	23	12	dual	dual	ADJ
ejpam-3526	23	13	bck	bck	PROPN
ejpam-3526	23	14	/	/	SYM
ejpam-3526	23	15	bci	bci	PROPN
ejpam-3526	23	16	/	/	SYM
ejpam-3526	23	17	bchalgebras	bchalgebra	NOUN
ejpam-3526	23	18	.	.	PUNCT
ejpam-3526	24	1	in	in	ADP
ejpam-3526	24	2	2013	2013	NUM
ejpam-3526	24	3	,	,	PUNCT
ejpam-3526	24	4	a.b	a.b	PROPN
ejpam-3526	24	5	.	.	PROPN
ejpam-3526	24	6	saeid	saeid	PROPN
ejpam-3526	24	7	[	[	X
ejpam-3526	24	8	11	11	NUM
ejpam-3526	24	9	]	]	PUNCT
ejpam-3526	24	10	established	establish	VERB
ejpam-3526	24	11	the	the	DET
ejpam-3526	24	12	relationship	relationship	NOUN
ejpam-3526	24	13	between	between	ADP
ejpam-3526	24	14	ci	ci	NOUN
ejpam-3526	24	15	-	-	PUNCT
ejpam-3526	24	16	algebra	algebra	NOUN
ejpam-3526	24	17	and	and	CCONJ
ejpam-3526	24	18	dual	dual	ADJ
ejpam-3526	24	19	q	q	NOUN
ejpam-3526	24	20	-	-	NOUN
ejpam-3526	24	21	algebra	algebra	NOUN
ejpam-3526	24	22	.	.	PUNCT
ejpam-3526	25	1	∗corresponding	∗corresponde	VERB
ejpam-3526	25	2	author	author	NOUN
ejpam-3526	25	3	.	.	PUNCT
ejpam-3526	26	1	doi	doi	NOUN
ejpam-3526	26	2	:	:	PUNCT
ejpam-3526	26	3	https://doi.org/10.29020/nybg.ejpam.v12i4.3526	https://doi.org/10.29020/nybg.ejpam.v12i4.3526	NOUN
ejpam-3526	26	4	email	email	NOUN
ejpam-3526	26	5	addresses	address	NOUN
ejpam-3526	26	6	:	:	PUNCT
ejpam-3526	26	7	kebelleza@usc.edu.ph	kebelleza@usc.edu.ph	PROPN
ejpam-3526	26	8	(	(	PUNCT
ejpam-3526	26	9	k.	k.	PROPN
ejpam-3526	26	10	belleza	belleza	PROPN
ejpam-3526	26	11	)	)	PUNCT
ejpam-3526	26	12	,	,	PUNCT
ejpam-3526	26	13	jocelyn.vilela@g.msuiit.edu.ph	jocelyn.vilela@g.msuiit.edu.ph	PROPN
ejpam-3526	26	14	(	(	PUNCT
ejpam-3526	26	15	j.	j.	PROPN
ejpam-3526	26	16	vilela	vilela	PROPN
ejpam-3526	26	17	)	)	PUNCT
ejpam-3526	26	18	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3526	27	1	1497	1497	NUM
ejpam-3526	27	2	c	c	X
ejpam-3526	27	3	©	©	PROPN
ejpam-3526	27	4	2019	2019	NUM
ejpam-3526	27	5	ejpam	ejpam	NOUN
ejpam-3526	27	6	all	all	DET
ejpam-3526	27	7	rights	right	NOUN
ejpam-3526	27	8	reserved	reserve	VERB
ejpam-3526	27	9	.	.	PUNCT
ejpam-3526	28	1	k.	k.	PROPN
ejpam-3526	28	2	belleza	belleza	PROPN
ejpam-3526	28	3	,	,	PUNCT
ejpam-3526	28	4	j.	j.	PROPN
ejpam-3526	28	5	vilela	vilela	PROPN
ejpam-3526	28	6	/	/	SYM
ejpam-3526	28	7	eur	eur	PROPN
ejpam-3526	28	8	.	.	PUNCT
ejpam-3526	29	1	j.	j.	PROPN
ejpam-3526	29	2	pure	pure	PROPN
ejpam-3526	29	3	appl	appl	PROPN
ejpam-3526	29	4	.	.	PROPN
ejpam-3526	29	5	math	math	PROPN
ejpam-3526	29	6	,	,	PUNCT
ejpam-3526	29	7	12	12	NUM
ejpam-3526	29	8	(	(	PUNCT
ejpam-3526	29	9	4	4	NUM
ejpam-3526	29	10	)	)	PUNCT
ejpam-3526	29	11	(	(	PUNCT
ejpam-3526	29	12	2019	2019	NUM
ejpam-3526	29	13	)	)	PUNCT
ejpam-3526	29	14	,	,	PUNCT
ejpam-3526	29	15	1497	1497	NUM
ejpam-3526	29	16	-	-	SYM
ejpam-3526	29	17	1507	1507	NUM
ejpam-3526	29	18	1498	1498	NUM
ejpam-3526	29	19	this	this	DET
ejpam-3526	29	20	paper	paper	NOUN
ejpam-3526	29	21	aims	aim	VERB
ejpam-3526	29	22	to	to	PART
ejpam-3526	29	23	characterize	characterize	VERB
ejpam-3526	29	24	a	a	DET
ejpam-3526	29	25	dual	dual	ADJ
ejpam-3526	29	26	b	b	NOUN
ejpam-3526	29	27	-	-	PUNCT
ejpam-3526	29	28	algebra	algebra	NOUN
ejpam-3526	29	29	and	and	CCONJ
ejpam-3526	29	30	to	to	PART
ejpam-3526	29	31	investigate	investigate	VERB
ejpam-3526	29	32	the	the	DET
ejpam-3526	29	33	relationship	relationship	NOUN
ejpam-3526	29	34	between	between	ADP
ejpam-3526	29	35	a	a	DET
ejpam-3526	29	36	dual	dual	ADJ
ejpam-3526	29	37	b	b	NOUN
ejpam-3526	29	38	-	-	PUNCT
ejpam-3526	29	39	algebra	algebra	NOUN
ejpam-3526	29	40	and	and	CCONJ
ejpam-3526	29	41	bck	bck	NOUN
ejpam-3526	29	42	-	-	PUNCT
ejpam-3526	29	43	algebra	algebra	NOUN
ejpam-3526	29	44	.	.	PUNCT
ejpam-3526	30	1	moreover	moreover	ADV
ejpam-3526	30	2	,	,	PUNCT
ejpam-3526	30	3	commutativity	commutativity	NOUN
ejpam-3526	30	4	of	of	ADP
ejpam-3526	30	5	a	a	DET
ejpam-3526	30	6	dual	dual	ADJ
ejpam-3526	30	7	balgebra	balgebra	NOUN
ejpam-3526	30	8	will	will	AUX
ejpam-3526	30	9	also	also	ADV
ejpam-3526	30	10	be	be	AUX
ejpam-3526	30	11	considered	consider	VERB
ejpam-3526	30	12	.	.	PUNCT
ejpam-3526	31	1	relationships	relationship	NOUN
ejpam-3526	31	2	between	between	ADP
ejpam-3526	31	3	commutative	commutative	ADJ
ejpam-3526	31	4	dual	dual	ADJ
ejpam-3526	31	5	b	b	NOUN
ejpam-3526	31	6	-	-	PUNCT
ejpam-3526	31	7	algebra	algebra	NOUN
ejpam-3526	31	8	and	and	CCONJ
ejpam-3526	31	9	other	other	ADJ
ejpam-3526	31	10	algebras	algebra	NOUN
ejpam-3526	31	11	such	such	ADJ
ejpam-3526	31	12	as	as	ADP
ejpam-3526	31	13	ci	ci	NOUN
ejpam-3526	31	14	-	-	NOUN
ejpam-3526	31	15	algebra	algebra	NOUN
ejpam-3526	31	16	and	and	CCONJ
ejpam-3526	31	17	dual	dual	ADJ
ejpam-3526	31	18	bci	bci	NOUN
ejpam-3526	31	19	-	-	NOUN
ejpam-3526	31	20	algebra	algebra	NOUN
ejpam-3526	31	21	will	will	AUX
ejpam-3526	31	22	be	be	AUX
ejpam-3526	31	23	investigated	investigate	VERB
ejpam-3526	31	24	in	in	ADP
ejpam-3526	31	25	this	this	DET
ejpam-3526	31	26	paper	paper	NOUN
ejpam-3526	31	27	.	.	PUNCT
ejpam-3526	32	1	2	2	X
ejpam-3526	32	2	.	.	NUM
ejpam-3526	32	3	preliminaries	preliminary	NOUN
ejpam-3526	32	4	an	an	DET
ejpam-3526	32	5	algebra	algebra	NOUN
ejpam-3526	32	6	of	of	ADP
ejpam-3526	32	7	type	type	NOUN
ejpam-3526	32	8	(	(	PUNCT
ejpam-3526	32	9	2,0	2,0	NOUN
ejpam-3526	32	10	)	)	PUNCT
ejpam-3526	32	11	is	be	AUX
ejpam-3526	32	12	an	an	DET
ejpam-3526	32	13	algebra	algebra	NOUN
ejpam-3526	32	14	with	with	ADP
ejpam-3526	32	15	a	a	DET
ejpam-3526	32	16	binary	binary	ADJ
ejpam-3526	32	17	operation	operation	NOUN
ejpam-3526	32	18	and	and	CCONJ
ejpam-3526	32	19	a	a	DET
ejpam-3526	32	20	constant	constant	ADJ
ejpam-3526	32	21	element	element	NOUN
ejpam-3526	32	22	.	.	PUNCT
ejpam-3526	33	1	definition	definition	NOUN
ejpam-3526	33	2	1	1	NUM
ejpam-3526	33	3	.	.	PUNCT
ejpam-3526	34	1	[	[	X
ejpam-3526	34	2	9	9	NUM
ejpam-3526	34	3	]	]	PUNCT
ejpam-3526	34	4	a	a	DET
ejpam-3526	34	5	b	b	X
ejpam-3526	34	6	-	-	PUNCT
ejpam-3526	34	7	algebra	algebra	NOUN
ejpam-3526	34	8	is	be	AUX
ejpam-3526	34	9	a	a	DET
ejpam-3526	34	10	non	non	ADJ
ejpam-3526	34	11	-	-	ADJ
ejpam-3526	34	12	empty	empty	ADJ
ejpam-3526	34	13	set	set	NOUN
ejpam-3526	34	14	x	x	PUNCT
ejpam-3526	34	15	with	with	ADP
ejpam-3526	34	16	a	a	DET
ejpam-3526	34	17	constant	constant	ADJ
ejpam-3526	34	18	0	0	NUM
ejpam-3526	34	19	and	and	CCONJ
ejpam-3526	34	20	a	a	DET
ejpam-3526	34	21	binary	binary	ADJ
ejpam-3526	34	22	operation	operation	NOUN
ejpam-3526	34	23	“	"	PUNCT
ejpam-3526	34	24	∗	∗	NOUN
ejpam-3526	34	25	”	"	PUNCT
ejpam-3526	34	26	satisfying	satisfy	VERB
ejpam-3526	34	27	the	the	DET
ejpam-3526	34	28	following	following	ADJ
ejpam-3526	34	29	axioms	axiom	NOUN
ejpam-3526	34	30	for	for	ADP
ejpam-3526	34	31	all	all	DET
ejpam-3526	34	32	x	x	NOUN
ejpam-3526	34	33	,	,	PUNCT
ejpam-3526	34	34	y	y	PROPN
ejpam-3526	34	35	,	,	PUNCT
ejpam-3526	34	36	z	z	VERB
ejpam-3526	34	37	in	in	ADP
ejpam-3526	34	38	x	x	NOUN
ejpam-3526	34	39	:	:	PUNCT
ejpam-3526	34	40	(	(	PUNCT
ejpam-3526	34	41	b1	b1	NOUN
ejpam-3526	34	42	)	)	PUNCT
ejpam-3526	34	43	x	x	SYM
ejpam-3526	34	44	∗	∗	NOUN
ejpam-3526	34	45	x	x	X
ejpam-3526	35	1	=	=	SYM
ejpam-3526	35	2	0	0	NUM
ejpam-3526	35	3	(	(	PUNCT
ejpam-3526	35	4	b2	b2	NOUN
ejpam-3526	35	5	)	)	PUNCT
ejpam-3526	35	6	x	x	SYM
ejpam-3526	35	7	∗	∗	NOUN
ejpam-3526	35	8	0	0	NUM
ejpam-3526	36	1	=	=	SYM
ejpam-3526	36	2	x	x	X
ejpam-3526	36	3	(	(	PUNCT
ejpam-3526	36	4	b3	b3	PROPN
ejpam-3526	36	5	)	)	PUNCT
ejpam-3526	36	6	(	(	PUNCT
ejpam-3526	36	7	x	x	SYM
ejpam-3526	36	8	∗	∗	PROPN
ejpam-3526	36	9	y	y	NOUN
ejpam-3526	36	10	)	)	PUNCT
ejpam-3526	36	11	∗	∗	NOUN
ejpam-3526	36	12	z	z	NOUN
ejpam-3526	36	13	=	=	PUNCT
ejpam-3526	36	14	x	x	X
ejpam-3526	36	15	∗	∗	NOUN
ejpam-3526	37	1	[	[	X
ejpam-3526	37	2	z	z	X
ejpam-3526	37	3	∗	∗	NOUN
ejpam-3526	37	4	(	(	PUNCT
ejpam-3526	37	5	0	0	NUM
ejpam-3526	37	6	∗	∗	NOUN
ejpam-3526	37	7	y	y	PROPN
ejpam-3526	37	8	)	)	PUNCT
ejpam-3526	37	9	]	]	PUNCT
ejpam-3526	37	10	example	example	NOUN
ejpam-3526	38	1	1	1	NUM
ejpam-3526	38	2	.	.	PUNCT
ejpam-3526	39	1	[	[	X
ejpam-3526	39	2	8	8	NUM
ejpam-3526	39	3	]	]	PUNCT
ejpam-3526	39	4	let	let	VERB
ejpam-3526	39	5	x	x	PRON
ejpam-3526	39	6	:	:	PUNCT
ejpam-3526	39	7	=	=	SYM
ejpam-3526	39	8	{	{	PUNCT
ejpam-3526	39	9	0	0	NUM
ejpam-3526	39	10	,	,	PUNCT
ejpam-3526	39	11	1	1	NUM
ejpam-3526	39	12	,	,	PUNCT
ejpam-3526	39	13	2	2	NUM
ejpam-3526	39	14	,	,	PUNCT
ejpam-3526	39	15	3	3	NUM
ejpam-3526	39	16	,	,	PUNCT
ejpam-3526	39	17	4	4	NUM
ejpam-3526	39	18	,	,	PUNCT
ejpam-3526	39	19	5	5	NUM
ejpam-3526	39	20	}	}	PUNCT
ejpam-3526	39	21	be	be	AUX
ejpam-3526	39	22	a	a	DET
ejpam-3526	39	23	set	set	NOUN
ejpam-3526	39	24	with	with	ADP
ejpam-3526	39	25	the	the	DET
ejpam-3526	39	26	following	follow	VERB
ejpam-3526	39	27	cayley	cayley	ADJ
ejpam-3526	39	28	table	table	NOUN
ejpam-3526	39	29	:	:	PUNCT
ejpam-3526	39	30	∗	∗	NOUN
ejpam-3526	39	31	0	0	NUM
ejpam-3526	39	32	1	1	NUM
ejpam-3526	39	33	2	2	NUM
ejpam-3526	39	34	3	3	NUM
ejpam-3526	39	35	4	4	NUM
ejpam-3526	39	36	5	5	NUM
ejpam-3526	39	37	0	0	NUM
ejpam-3526	39	38	0	0	NUM
ejpam-3526	39	39	2	2	NUM
ejpam-3526	39	40	1	1	NUM
ejpam-3526	39	41	3	3	NUM
ejpam-3526	39	42	4	4	NUM
ejpam-3526	39	43	5	5	NUM
ejpam-3526	39	44	1	1	NUM
ejpam-3526	39	45	1	1	NUM
ejpam-3526	39	46	0	0	NUM
ejpam-3526	39	47	2	2	NUM
ejpam-3526	39	48	4	4	NUM
ejpam-3526	39	49	5	5	NUM
ejpam-3526	39	50	3	3	NUM
ejpam-3526	39	51	2	2	NUM
ejpam-3526	39	52	2	2	NUM
ejpam-3526	39	53	1	1	NUM
ejpam-3526	39	54	0	0	NUM
ejpam-3526	39	55	5	5	NUM
ejpam-3526	39	56	3	3	NUM
ejpam-3526	39	57	4	4	NUM
ejpam-3526	39	58	3	3	NUM
ejpam-3526	39	59	3	3	NUM
ejpam-3526	39	60	4	4	NUM
ejpam-3526	39	61	5	5	NUM
ejpam-3526	39	62	0	0	NUM
ejpam-3526	39	63	2	2	NUM
ejpam-3526	39	64	1	1	NUM
ejpam-3526	39	65	4	4	NUM
ejpam-3526	39	66	4	4	NUM
ejpam-3526	39	67	5	5	NUM
ejpam-3526	39	68	3	3	NUM
ejpam-3526	39	69	1	1	NUM
ejpam-3526	39	70	0	0	NUM
ejpam-3526	39	71	2	2	NUM
ejpam-3526	39	72	5	5	NUM
ejpam-3526	39	73	5	5	NUM
ejpam-3526	39	74	3	3	NUM
ejpam-3526	39	75	4	4	NUM
ejpam-3526	39	76	2	2	NUM
ejpam-3526	39	77	1	1	NUM
ejpam-3526	39	78	0	0	NUM
ejpam-3526	39	79	then	then	ADV
ejpam-3526	39	80	(	(	PUNCT
ejpam-3526	39	81	x	x	NOUN
ejpam-3526	39	82	;	;	PUNCT
ejpam-3526	39	83	∗	∗	NOUN
ejpam-3526	39	84	,	,	PUNCT
ejpam-3526	39	85	0	0	NUM
ejpam-3526	39	86	)	)	PUNCT
ejpam-3526	39	87	is	be	AUX
ejpam-3526	39	88	a	a	DET
ejpam-3526	39	89	b	b	NOUN
ejpam-3526	39	90	-	-	PUNCT
ejpam-3526	39	91	algebra	algebra	NOUN
ejpam-3526	39	92	.	.	PUNCT
ejpam-3526	40	1	definition	definition	NOUN
ejpam-3526	40	2	2	2	NUM
ejpam-3526	40	3	.	.	PUNCT
ejpam-3526	41	1	[	[	X
ejpam-3526	41	2	6	6	NUM
ejpam-3526	41	3	]	]	PUNCT
ejpam-3526	41	4	an	an	DET
ejpam-3526	41	5	algebra	algebra	NOUN
ejpam-3526	41	6	(	(	PUNCT
ejpam-3526	41	7	x	x	X
ejpam-3526	41	8	,	,	PUNCT
ejpam-3526	41	9	∗	∗	NOUN
ejpam-3526	41	10	,	,	PUNCT
ejpam-3526	41	11	0	0	NUM
ejpam-3526	41	12	)	)	PUNCT
ejpam-3526	41	13	of	of	ADP
ejpam-3526	41	14	type	type	NOUN
ejpam-3526	41	15	(	(	PUNCT
ejpam-3526	41	16	2	2	NUM
ejpam-3526	41	17	,	,	PUNCT
ejpam-3526	41	18	0	0	NUM
ejpam-3526	41	19	)	)	PUNCT
ejpam-3526	41	20	is	be	AUX
ejpam-3526	41	21	called	call	VERB
ejpam-3526	41	22	a	a	DET
ejpam-3526	41	23	bck	bck	NOUN
ejpam-3526	41	24	-	-	PUNCT
ejpam-3526	41	25	algebra	algebra	NOUN
ejpam-3526	41	26	if	if	SCONJ
ejpam-3526	41	27	for	for	ADP
ejpam-3526	41	28	all	all	DET
ejpam-3526	41	29	x	x	NOUN
ejpam-3526	41	30	,	,	PUNCT
ejpam-3526	41	31	y	y	PROPN
ejpam-3526	41	32	,	,	PUNCT
ejpam-3526	41	33	z	z	NOUN
ejpam-3526	41	34	in	in	ADP
ejpam-3526	41	35	x	x	PRON
ejpam-3526	41	36	,	,	PUNCT
ejpam-3526	41	37	the	the	DET
ejpam-3526	41	38	following	follow	VERB
ejpam-3526	41	39	hold	hold	NOUN
ejpam-3526	41	40	:	:	PUNCT
ejpam-3526	41	41	(	(	PUNCT
ejpam-3526	41	42	bck1	bck1	PROPN
ejpam-3526	41	43	)	)	PUNCT
ejpam-3526	42	1	[	[	X
ejpam-3526	42	2	(	(	PUNCT
ejpam-3526	42	3	x	x	SYM
ejpam-3526	42	4	∗	∗	PROPN
ejpam-3526	42	5	y	y	NOUN
ejpam-3526	42	6	)	)	PUNCT
ejpam-3526	42	7	∗	∗	NOUN
ejpam-3526	42	8	(	(	PUNCT
ejpam-3526	42	9	x	x	X
ejpam-3526	42	10	∗	∗	PROPN
ejpam-3526	42	11	z	z	NOUN
ejpam-3526	42	12	)	)	PUNCT
ejpam-3526	42	13	]	]	PUNCT
ejpam-3526	43	1	∗	∗	NOUN
ejpam-3526	43	2	(	(	PUNCT
ejpam-3526	43	3	z	z	NOUN
ejpam-3526	43	4	∗	∗	NOUN
ejpam-3526	43	5	y	y	NOUN
ejpam-3526	43	6	)	)	PUNCT
ejpam-3526	43	7	=	=	SYM
ejpam-3526	43	8	0	0	PROPN
ejpam-3526	43	9	(	(	PUNCT
ejpam-3526	43	10	bck4	bck4	PROPN
ejpam-3526	43	11	)	)	PUNCT
ejpam-3526	43	12	x	x	PROPN
ejpam-3526	44	1	∗	∗	NOUN
ejpam-3526	44	2	y	y	NOUN
ejpam-3526	44	3	=	=	SYM
ejpam-3526	44	4	0	0	PROPN
ejpam-3526	45	1	and	and	CCONJ
ejpam-3526	45	2	y	y	PROPN
ejpam-3526	45	3	∗	∗	NOUN
ejpam-3526	45	4	x	x	PUNCT
ejpam-3526	46	1	=	=	SYM
ejpam-3526	46	2	0	0	NUM
ejpam-3526	46	3	imply	imply	VERB
ejpam-3526	46	4	x	x	X
ejpam-3526	46	5	=	=	SYM
ejpam-3526	46	6	y	y	PROPN
ejpam-3526	46	7	(	(	PUNCT
ejpam-3526	46	8	bck2	bck2	PROPN
ejpam-3526	46	9	)	)	PUNCT
ejpam-3526	47	1	[	[	X
ejpam-3526	47	2	x	x	X
ejpam-3526	47	3	∗	∗	NOUN
ejpam-3526	47	4	(	(	PUNCT
ejpam-3526	47	5	x	x	X
ejpam-3526	47	6	∗	∗	PROPN
ejpam-3526	47	7	y	y	PROPN
ejpam-3526	47	8	)	)	PUNCT
ejpam-3526	47	9	]	]	PUNCT
ejpam-3526	48	1	∗	∗	NOUN
ejpam-3526	48	2	y	y	PROPN
ejpam-3526	48	3	=	=	SYM
ejpam-3526	48	4	0	0	PROPN
ejpam-3526	49	1	(	(	PUNCT
ejpam-3526	49	2	bck5	bck5	PROPN
ejpam-3526	49	3	)	)	PUNCT
ejpam-3526	49	4	0	0	NUM
ejpam-3526	50	1	∗	∗	NOUN
ejpam-3526	50	2	x	x	X
ejpam-3526	51	1	=	=	SYM
ejpam-3526	51	2	0	0	NUM
ejpam-3526	51	3	(	(	PUNCT
ejpam-3526	51	4	bck3	bck3	PROPN
ejpam-3526	51	5	)	)	PUNCT
ejpam-3526	51	6	x	x	SYM
ejpam-3526	51	7	∗	∗	NOUN
ejpam-3526	51	8	x	x	X
ejpam-3526	51	9	=	=	SYM
ejpam-3526	51	10	0	0	NUM
ejpam-3526	51	11	lemma	lemma	PROPN
ejpam-3526	51	12	1	1	NUM
ejpam-3526	51	13	.	.	PUNCT
ejpam-3526	52	1	[	[	X
ejpam-3526	52	2	2	2	NUM
ejpam-3526	52	3	]	]	PUNCT
ejpam-3526	52	4	in	in	ADP
ejpam-3526	52	5	any	any	DET
ejpam-3526	52	6	bck	bck	NOUN
ejpam-3526	52	7	-	-	PUNCT
ejpam-3526	52	8	algebra	algebra	NOUN
ejpam-3526	52	9	(	(	PUNCT
ejpam-3526	52	10	x	x	X
ejpam-3526	52	11	,	,	PUNCT
ejpam-3526	52	12	∗	∗	NOUN
ejpam-3526	52	13	,	,	PUNCT
ejpam-3526	52	14	0	0	NUM
ejpam-3526	52	15	)	)	PUNCT
ejpam-3526	52	16	,	,	PUNCT
ejpam-3526	52	17	the	the	DET
ejpam-3526	52	18	following	follow	VERB
ejpam-3526	52	19	hold	hold	NOUN
ejpam-3526	52	20	for	for	ADP
ejpam-3526	52	21	all	all	DET
ejpam-3526	52	22	x	x	NOUN
ejpam-3526	52	23	,	,	PUNCT
ejpam-3526	52	24	y	y	PROPN
ejpam-3526	52	25	,	,	PUNCT
ejpam-3526	52	26	z	z	VERB
ejpam-3526	52	27	in	in	ADP
ejpam-3526	52	28	x	x	NOUN
ejpam-3526	52	29	:	:	PUNCT
ejpam-3526	52	30	(	(	PUNCT
ejpam-3526	52	31	i	i	NOUN
ejpam-3526	52	32	)	)	PUNCT
ejpam-3526	52	33	x	x	SYM
ejpam-3526	52	34	∗	∗	NOUN
ejpam-3526	52	35	0	0	NUM
ejpam-3526	53	1	=	=	SYM
ejpam-3526	53	2	x	x	SYM
ejpam-3526	53	3	(	(	PUNCT
ejpam-3526	53	4	ii	ii	NOUN
ejpam-3526	53	5	)	)	PUNCT
ejpam-3526	53	6	(	(	PUNCT
ejpam-3526	53	7	x	x	SYM
ejpam-3526	53	8	∗	∗	PROPN
ejpam-3526	53	9	y	y	NOUN
ejpam-3526	53	10	)	)	PUNCT
ejpam-3526	53	11	∗	∗	NOUN
ejpam-3526	53	12	z	z	NOUN
ejpam-3526	53	13	=	=	SYM
ejpam-3526	53	14	(	(	PUNCT
ejpam-3526	53	15	x	x	X
ejpam-3526	53	16	∗	∗	PROPN
ejpam-3526	53	17	z	z	NOUN
ejpam-3526	53	18	)	)	PUNCT
ejpam-3526	53	19	∗	∗	VERB
ejpam-3526	53	20	y	y	PROPN
ejpam-3526	53	21	definition	definition	NOUN
ejpam-3526	53	22	3	3	NUM
ejpam-3526	53	23	.	.	PUNCT
ejpam-3526	54	1	[	[	X
ejpam-3526	54	2	7	7	X
ejpam-3526	54	3	]	]	X
ejpam-3526	54	4	a	a	DET
ejpam-3526	54	5	q	q	NOUN
ejpam-3526	54	6	-	-	PUNCT
ejpam-3526	54	7	algebra	algebra	NOUN
ejpam-3526	54	8	is	be	AUX
ejpam-3526	54	9	a	a	DET
ejpam-3526	54	10	nonempty	nonempty	ADV
ejpam-3526	54	11	set	set	VERB
ejpam-3526	54	12	x	x	PUNCT
ejpam-3526	54	13	with	with	ADP
ejpam-3526	54	14	a	a	DET
ejpam-3526	54	15	constant	constant	ADJ
ejpam-3526	54	16	0	0	NUM
ejpam-3526	54	17	and	and	CCONJ
ejpam-3526	54	18	a	a	DET
ejpam-3526	54	19	binary	binary	ADJ
ejpam-3526	54	20	operation	operation	NOUN
ejpam-3526	54	21	∗	∗	NOUN
ejpam-3526	54	22	satisfying	satisfy	VERB
ejpam-3526	54	23	the	the	DET
ejpam-3526	54	24	following	follow	VERB
ejpam-3526	54	25	axioms	axiom	NOUN
ejpam-3526	54	26	:	:	PUNCT
ejpam-3526	54	27	for	for	ADP
ejpam-3526	54	28	all	all	DET
ejpam-3526	54	29	x	x	NOUN
ejpam-3526	54	30	,	,	PUNCT
ejpam-3526	54	31	y	y	PROPN
ejpam-3526	54	32	,	,	PUNCT
ejpam-3526	54	33	z	z	NOUN
ejpam-3526	54	34	in	in	ADP
ejpam-3526	54	35	x	x	SYM
ejpam-3526	54	36	,	,	PUNCT
ejpam-3526	54	37	(	(	PUNCT
ejpam-3526	54	38	q1	q1	PROPN
ejpam-3526	54	39	)	)	PUNCT
ejpam-3526	54	40	x	x	SYM
ejpam-3526	54	41	∗	∗	NOUN
ejpam-3526	54	42	x	x	X
ejpam-3526	54	43	=	=	SYM
ejpam-3526	54	44	0	0	NUM
ejpam-3526	54	45	(	(	PUNCT
ejpam-3526	54	46	q2	q2	NOUN
ejpam-3526	54	47	)	)	PUNCT
ejpam-3526	55	1	x	x	SYM
ejpam-3526	55	2	∗	∗	NOUN
ejpam-3526	55	3	0	0	NUM
ejpam-3526	56	1	=	=	SYM
ejpam-3526	56	2	x	x	X
ejpam-3526	56	3	(	(	PUNCT
ejpam-3526	56	4	q3	q3	PROPN
ejpam-3526	56	5	)	)	PUNCT
ejpam-3526	56	6	(	(	PUNCT
ejpam-3526	56	7	x	x	SYM
ejpam-3526	56	8	∗	∗	PROPN
ejpam-3526	56	9	y	y	NOUN
ejpam-3526	56	10	)	)	PUNCT
ejpam-3526	56	11	∗	∗	NOUN
ejpam-3526	56	12	z	z	NOUN
ejpam-3526	56	13	=	=	SYM
ejpam-3526	56	14	(	(	PUNCT
ejpam-3526	56	15	x	x	X
ejpam-3526	56	16	∗	∗	PROPN
ejpam-3526	56	17	z	z	NOUN
ejpam-3526	56	18	)	)	PUNCT
ejpam-3526	56	19	∗	∗	VERB
ejpam-3526	56	20	y	y	PROPN
ejpam-3526	56	21	definition	definition	NOUN
ejpam-3526	56	22	4	4	NUM
ejpam-3526	56	23	.	.	PUNCT
ejpam-3526	57	1	[	[	X
ejpam-3526	57	2	11	11	NUM
ejpam-3526	57	3	]	]	X
ejpam-3526	57	4	let	let	VERB
ejpam-3526	57	5	(	(	PUNCT
ejpam-3526	57	6	x	x	NOUN
ejpam-3526	57	7	,	,	PUNCT
ejpam-3526	57	8	∗	∗	NOUN
ejpam-3526	57	9	,	,	PUNCT
ejpam-3526	57	10	0	0	NUM
ejpam-3526	57	11	)	)	PUNCT
ejpam-3526	57	12	be	be	AUX
ejpam-3526	57	13	a	a	DET
ejpam-3526	57	14	q	q	NOUN
ejpam-3526	57	15	-	-	PUNCT
ejpam-3526	57	16	algebra	algebra	NOUN
ejpam-3526	57	17	and	and	CCONJ
ejpam-3526	57	18	a	a	DET
ejpam-3526	57	19	binary	binary	ADJ
ejpam-3526	57	20	operation	operation	NOUN
ejpam-3526	57	21	◦	◦	NOUN
ejpam-3526	57	22	on	on	ADP
ejpam-3526	57	23	x	x	PUNCT
ejpam-3526	57	24	is	be	AUX
ejpam-3526	57	25	defined	define	VERB
ejpam-3526	57	26	as	as	ADP
ejpam-3526	57	27	:	:	PUNCT
ejpam-3526	57	28	x	x	X
ejpam-3526	57	29	◦	◦	NOUN
ejpam-3526	57	30	y	y	NOUN
ejpam-3526	57	31	=	=	SYM
ejpam-3526	57	32	y	y	PROPN
ejpam-3526	57	33	∗x	∗x	PROPN
ejpam-3526	57	34	.	.	PUNCT
ejpam-3526	58	1	then	then	ADV
ejpam-3526	58	2	(	(	PUNCT
ejpam-3526	58	3	x	x	X
ejpam-3526	58	4	,	,	PUNCT
ejpam-3526	58	5	◦	◦	NOUN
ejpam-3526	58	6	,	,	PUNCT
ejpam-3526	58	7	1	1	NUM
ejpam-3526	58	8	)	)	PUNCT
ejpam-3526	58	9	is	be	AUX
ejpam-3526	58	10	called	call	VERB
ejpam-3526	58	11	a	a	DET
ejpam-3526	58	12	dual	dual	ADJ
ejpam-3526	58	13	q	q	NOUN
ejpam-3526	58	14	-	-	NOUN
ejpam-3526	58	15	algebra	algebra	NOUN
ejpam-3526	58	16	.	.	PUNCT
ejpam-3526	59	1	in	in	ADP
ejpam-3526	59	2	fact	fact	NOUN
ejpam-3526	59	3	,	,	PUNCT
ejpam-3526	59	4	its	its	PRON
ejpam-3526	59	5	axioms	axiom	NOUN
ejpam-3526	59	6	are	be	AUX
ejpam-3526	59	7	as	as	SCONJ
ejpam-3526	59	8	follows	follow	VERB
ejpam-3526	59	9	for	for	ADP
ejpam-3526	59	10	all	all	DET
ejpam-3526	59	11	x	x	NOUN
ejpam-3526	59	12	,	,	PUNCT
ejpam-3526	59	13	y	y	PROPN
ejpam-3526	59	14	,	,	PUNCT
ejpam-3526	59	15	z	z	VERB
ejpam-3526	59	16	in	in	ADP
ejpam-3526	59	17	x	x	NOUN
ejpam-3526	59	18	:	:	PUNCT
ejpam-3526	59	19	(	(	PUNCT
ejpam-3526	59	20	dq1	dq1	NOUN
ejpam-3526	59	21	)	)	PUNCT
ejpam-3526	59	22	x	x	PUNCT
ejpam-3526	60	1	◦	◦	NOUN
ejpam-3526	60	2	x	x	SYM
ejpam-3526	61	1	=	=	SYM
ejpam-3526	61	2	1	1	NUM
ejpam-3526	61	3	(	(	PUNCT
ejpam-3526	61	4	dq2	dq2	NOUN
ejpam-3526	61	5	)	)	PUNCT
ejpam-3526	61	6	1	1	NUM
ejpam-3526	61	7	◦	◦	NOUN
ejpam-3526	61	8	x	x	SYM
ejpam-3526	61	9	=	=	SYM
ejpam-3526	61	10	x	x	X
ejpam-3526	61	11	(	(	PUNCT
ejpam-3526	61	12	dq3	dq3	NOUN
ejpam-3526	61	13	)	)	PUNCT
ejpam-3526	61	14	x	x	SYM
ejpam-3526	61	15	◦	◦	NOUN
ejpam-3526	61	16	(	(	PUNCT
ejpam-3526	61	17	y	y	PROPN
ejpam-3526	61	18	◦	◦	PROPN
ejpam-3526	61	19	z	z	PROPN
ejpam-3526	61	20	)	)	PUNCT
ejpam-3526	61	21	=	=	SYM
ejpam-3526	61	22	y	y	PROPN
ejpam-3526	61	23	◦	◦	NOUN
ejpam-3526	61	24	(	(	PUNCT
ejpam-3526	61	25	x	x	PART
ejpam-3526	61	26	◦	◦	NOUN
ejpam-3526	61	27	z	z	PROPN
ejpam-3526	61	28	)	)	PUNCT
ejpam-3526	61	29	k.	k.	PROPN
ejpam-3526	61	30	belleza	belleza	PROPN
ejpam-3526	61	31	,	,	PUNCT
ejpam-3526	61	32	j.	j.	PROPN
ejpam-3526	61	33	vilela	vilela	PROPN
ejpam-3526	61	34	/	/	SYM
ejpam-3526	61	35	eur	eur	PROPN
ejpam-3526	61	36	.	.	PUNCT
ejpam-3526	62	1	j.	j.	PROPN
ejpam-3526	62	2	pure	pure	PROPN
ejpam-3526	62	3	appl	appl	PROPN
ejpam-3526	62	4	.	.	PROPN
ejpam-3526	62	5	math	math	PROPN
ejpam-3526	62	6	,	,	PUNCT
ejpam-3526	62	7	12	12	NUM
ejpam-3526	62	8	(	(	PUNCT
ejpam-3526	62	9	4	4	NUM
ejpam-3526	62	10	)	)	PUNCT
ejpam-3526	62	11	(	(	PUNCT
ejpam-3526	62	12	2019	2019	NUM
ejpam-3526	62	13	)	)	PUNCT
ejpam-3526	62	14	,	,	PUNCT
ejpam-3526	62	15	1497	1497	NUM
ejpam-3526	62	16	-	-	SYM
ejpam-3526	62	17	1507	1507	NUM
ejpam-3526	62	18	1499	1499	NUM
ejpam-3526	62	19	definition	definition	NOUN
ejpam-3526	62	20	5	5	NUM
ejpam-3526	62	21	.	.	PUNCT
ejpam-3526	63	1	[	[	X
ejpam-3526	63	2	5	5	NUM
ejpam-3526	63	3	]	]	PUNCT
ejpam-3526	63	4	a	a	DET
ejpam-3526	63	5	ci	ci	NOUN
ejpam-3526	63	6	-	-	PUNCT
ejpam-3526	63	7	algebra	algebra	NOUN
ejpam-3526	63	8	is	be	AUX
ejpam-3526	63	9	an	an	DET
ejpam-3526	63	10	algebra	algebra	NOUN
ejpam-3526	63	11	(	(	PUNCT
ejpam-3526	63	12	x	x	X
ejpam-3526	63	13	,	,	PUNCT
ejpam-3526	63	14	∗	∗	NOUN
ejpam-3526	63	15	,	,	PUNCT
ejpam-3526	63	16	1	1	NUM
ejpam-3526	63	17	)	)	PUNCT
ejpam-3526	63	18	of	of	ADP
ejpam-3526	63	19	type	type	NOUN
ejpam-3526	63	20	(	(	PUNCT
ejpam-3526	63	21	2	2	NUM
ejpam-3526	63	22	,	,	PUNCT
ejpam-3526	63	23	0	0	NUM
ejpam-3526	63	24	)	)	PUNCT
ejpam-3526	63	25	satisfying	satisfy	VERB
ejpam-3526	63	26	the	the	DET
ejpam-3526	63	27	following	follow	VERB
ejpam-3526	63	28	axioms	axiom	NOUN
ejpam-3526	63	29	:	:	PUNCT
ejpam-3526	63	30	for	for	ADP
ejpam-3526	63	31	all	all	DET
ejpam-3526	63	32	x	x	NOUN
ejpam-3526	63	33	,	,	PUNCT
ejpam-3526	63	34	y	y	PROPN
ejpam-3526	63	35	,	,	PUNCT
ejpam-3526	63	36	z	z	NOUN
ejpam-3526	63	37	in	in	ADP
ejpam-3526	63	38	x	x	PRON
ejpam-3526	63	39	,	,	PUNCT
ejpam-3526	63	40	(	(	PUNCT
ejpam-3526	63	41	ci1	ci1	X
ejpam-3526	63	42	)	)	PUNCT
ejpam-3526	63	43	x	x	X
ejpam-3526	63	44	∗	∗	NOUN
ejpam-3526	63	45	x	x	X
ejpam-3526	64	1	=	=	SYM
ejpam-3526	64	2	1	1	NUM
ejpam-3526	64	3	(	(	PUNCT
ejpam-3526	64	4	ci2	ci2	NOUN
ejpam-3526	64	5	)	)	PUNCT
ejpam-3526	64	6	1	1	NUM
ejpam-3526	64	7	∗	∗	NOUN
ejpam-3526	64	8	x	x	X
ejpam-3526	64	9	=	=	SYM
ejpam-3526	64	10	x	x	X
ejpam-3526	64	11	(	(	PUNCT
ejpam-3526	64	12	ci3	ci3	NOUN
ejpam-3526	64	13	)	)	PUNCT
ejpam-3526	64	14	x	x	SYM
ejpam-3526	64	15	∗	∗	NOUN
ejpam-3526	64	16	(	(	PUNCT
ejpam-3526	64	17	y	y	PROPN
ejpam-3526	64	18	∗	∗	PROPN
ejpam-3526	64	19	z	z	NOUN
ejpam-3526	64	20	)	)	PUNCT
ejpam-3526	65	1	=	=	SYM
ejpam-3526	65	2	y	y	PROPN
ejpam-3526	65	3	∗	∗	NOUN
ejpam-3526	65	4	(	(	PUNCT
ejpam-3526	65	5	x	x	X
ejpam-3526	65	6	∗	∗	PROPN
ejpam-3526	65	7	z	z	NOUN
ejpam-3526	65	8	)	)	PUNCT
ejpam-3526	65	9	theorem	theorem	NOUN
ejpam-3526	65	10	1	1	NUM
ejpam-3526	65	11	.	.	PUNCT
ejpam-3526	66	1	[	[	X
ejpam-3526	66	2	11	11	NUM
ejpam-3526	66	3	]	]	PUNCT
ejpam-3526	66	4	any	any	DET
ejpam-3526	66	5	ci	ci	NOUN
ejpam-3526	66	6	-	-	PUNCT
ejpam-3526	66	7	algebra	algebra	NOUN
ejpam-3526	66	8	is	be	AUX
ejpam-3526	66	9	equivalent	equivalent	ADJ
ejpam-3526	66	10	to	to	ADP
ejpam-3526	66	11	a	a	DET
ejpam-3526	66	12	dual	dual	ADJ
ejpam-3526	66	13	q	q	NOUN
ejpam-3526	66	14	-	-	NOUN
ejpam-3526	66	15	algebra	algebra	NOUN
ejpam-3526	66	16	.	.	PUNCT
ejpam-3526	67	1	definition	definition	NOUN
ejpam-3526	67	2	6	6	NUM
ejpam-3526	67	3	.	.	PUNCT
ejpam-3526	68	1	[	[	X
ejpam-3526	68	2	5	5	NUM
ejpam-3526	68	3	]	]	PUNCT
ejpam-3526	68	4	a	a	DET
ejpam-3526	68	5	dual	dual	ADJ
ejpam-3526	68	6	bci	bci	NOUN
ejpam-3526	68	7	-	-	NOUN
ejpam-3526	68	8	algebra	algebra	NOUN
ejpam-3526	68	9	is	be	AUX
ejpam-3526	68	10	an	an	DET
ejpam-3526	68	11	algebra	algebra	NOUN
ejpam-3526	68	12	(	(	PUNCT
ejpam-3526	68	13	x	x	X
ejpam-3526	68	14	,	,	PUNCT
ejpam-3526	68	15	∗	∗	NOUN
ejpam-3526	68	16	,	,	PUNCT
ejpam-3526	68	17	1	1	NUM
ejpam-3526	68	18	)	)	PUNCT
ejpam-3526	68	19	of	of	ADP
ejpam-3526	68	20	type	type	NOUN
ejpam-3526	68	21	(	(	PUNCT
ejpam-3526	68	22	2,0	2,0	NUM
ejpam-3526	68	23	)	)	PUNCT
ejpam-3526	68	24	satisfying	satisfy	VERB
ejpam-3526	68	25	the	the	DET
ejpam-3526	68	26	following	follow	VERB
ejpam-3526	68	27	axioms	axiom	NOUN
ejpam-3526	68	28	:	:	PUNCT
ejpam-3526	68	29	for	for	ADP
ejpam-3526	68	30	all	all	DET
ejpam-3526	68	31	x	x	NOUN
ejpam-3526	68	32	,	,	PUNCT
ejpam-3526	68	33	y	y	PROPN
ejpam-3526	68	34	,	,	PUNCT
ejpam-3526	68	35	z	z	NOUN
ejpam-3526	68	36	in	in	ADP
ejpam-3526	68	37	x	x	X
ejpam-3526	68	38	,	,	PUNCT
ejpam-3526	68	39	(	(	PUNCT
ejpam-3526	68	40	dbci1	dbci1	NOUN
ejpam-3526	68	41	)	)	PUNCT
ejpam-3526	68	42	x	x	SYM
ejpam-3526	68	43	∗	∗	NOUN
ejpam-3526	68	44	x	x	X
ejpam-3526	68	45	=	=	SYM
ejpam-3526	68	46	1	1	NUM
ejpam-3526	68	47	(	(	PUNCT
ejpam-3526	68	48	dbci3	dbci3	PROPN
ejpam-3526	68	49	)	)	PUNCT
ejpam-3526	68	50	(	(	PUNCT
ejpam-3526	68	51	x	x	SYM
ejpam-3526	68	52	∗	∗	PROPN
ejpam-3526	68	53	y	y	NOUN
ejpam-3526	68	54	)	)	PUNCT
ejpam-3526	68	55	∗	∗	NOUN
ejpam-3526	69	1	[	[	X
ejpam-3526	69	2	(	(	PUNCT
ejpam-3526	69	3	y	y	PROPN
ejpam-3526	69	4	∗	∗	PROPN
ejpam-3526	69	5	z	z	PROPN
ejpam-3526	69	6	)	)	PUNCT
ejpam-3526	69	7	∗	∗	NOUN
ejpam-3526	69	8	(	(	PUNCT
ejpam-3526	69	9	x	x	X
ejpam-3526	69	10	∗	∗	NOUN
ejpam-3526	69	11	z	z	NOUN
ejpam-3526	69	12	)	)	PUNCT
ejpam-3526	69	13	]	]	PUNCT
ejpam-3526	70	1	=	=	SYM
ejpam-3526	70	2	1	1	NUM
ejpam-3526	70	3	(	(	PUNCT
ejpam-3526	70	4	dbci2	dbci2	NOUN
ejpam-3526	70	5	)	)	PUNCT
ejpam-3526	70	6	x	x	X
ejpam-3526	70	7	∗	∗	NOUN
ejpam-3526	70	8	y	y	NOUN
ejpam-3526	70	9	=	=	SYM
ejpam-3526	70	10	y	y	PROPN
ejpam-3526	70	11	∗	∗	NOUN
ejpam-3526	70	12	x	x	PUNCT
ejpam-3526	70	13	=	=	SYM
ejpam-3526	70	14	1	1	NUM
ejpam-3526	70	15	implies	imply	VERB
ejpam-3526	70	16	x	x	PUNCT
ejpam-3526	70	17	=	=	SYM
ejpam-3526	70	18	y	y	PROPN
ejpam-3526	70	19	(	(	PUNCT
ejpam-3526	70	20	dbci4	dbci4	PROPN
ejpam-3526	70	21	)	)	PUNCT
ejpam-3526	70	22	x	x	SYM
ejpam-3526	71	1	∗	∗	NOUN
ejpam-3526	71	2	[	[	X
ejpam-3526	71	3	(	(	PUNCT
ejpam-3526	71	4	x	x	X
ejpam-3526	71	5	∗	∗	PROPN
ejpam-3526	71	6	y	y	NOUN
ejpam-3526	71	7	)	)	PUNCT
ejpam-3526	71	8	∗	∗	NOUN
ejpam-3526	71	9	y	y	PROPN
ejpam-3526	71	10	]	]	X
ejpam-3526	71	11	=	=	SYM
ejpam-3526	71	12	1	1	NUM
ejpam-3526	71	13	proposition	proposition	NOUN
ejpam-3526	71	14	1	1	NUM
ejpam-3526	71	15	.	.	PUNCT
ejpam-3526	72	1	[	[	X
ejpam-3526	72	2	5	5	NUM
ejpam-3526	72	3	]	]	X
ejpam-3526	72	4	let	let	VERB
ejpam-3526	72	5	(	(	PUNCT
ejpam-3526	72	6	x	x	NOUN
ejpam-3526	72	7	,	,	PUNCT
ejpam-3526	72	8	∗	∗	NOUN
ejpam-3526	72	9	,	,	PUNCT
ejpam-3526	72	10	1	1	NUM
ejpam-3526	72	11	)	)	PUNCT
ejpam-3526	72	12	be	be	AUX
ejpam-3526	72	13	a	a	DET
ejpam-3526	72	14	dual	dual	ADJ
ejpam-3526	72	15	bci	bci	NOUN
ejpam-3526	72	16	-	-	NOUN
ejpam-3526	72	17	algebra	algebra	NOUN
ejpam-3526	72	18	.	.	PUNCT
ejpam-3526	73	1	then	then	ADV
ejpam-3526	73	2	for	for	ADP
ejpam-3526	73	3	all	all	DET
ejpam-3526	73	4	x	x	NOUN
ejpam-3526	73	5	,	,	PUNCT
ejpam-3526	73	6	y	y	PROPN
ejpam-3526	73	7	,	,	PUNCT
ejpam-3526	73	8	z	z	NOUN
ejpam-3526	73	9	in	in	ADP
ejpam-3526	73	10	x	x	PRON
ejpam-3526	73	11	,	,	PUNCT
ejpam-3526	73	12	the	the	DET
ejpam-3526	73	13	following	follow	VERB
ejpam-3526	73	14	hold	hold	NOUN
ejpam-3526	73	15	:	:	PUNCT
ejpam-3526	73	16	(	(	PUNCT
ejpam-3526	73	17	i	i	NOUN
ejpam-3526	73	18	)	)	PUNCT
ejpam-3526	73	19	x	x	PROPN
ejpam-3526	73	20	∗	∗	NOUN
ejpam-3526	73	21	y	y	NOUN
ejpam-3526	73	22	=	=	SYM
ejpam-3526	73	23	1	1	NUM
ejpam-3526	73	24	implies	imply	VERB
ejpam-3526	73	25	(	(	PUNCT
ejpam-3526	73	26	y	y	PROPN
ejpam-3526	73	27	∗	∗	PROPN
ejpam-3526	73	28	z	z	PROPN
ejpam-3526	73	29	)	)	PUNCT
ejpam-3526	73	30	∗	∗	NOUN
ejpam-3526	73	31	(	(	PUNCT
ejpam-3526	73	32	x	x	X
ejpam-3526	73	33	∗	∗	PROPN
ejpam-3526	73	34	z	z	NOUN
ejpam-3526	73	35	)	)	PUNCT
ejpam-3526	73	36	=	=	SYM
ejpam-3526	73	37	1	1	NUM
ejpam-3526	73	38	(	(	PUNCT
ejpam-3526	73	39	iii	iii	NOUN
ejpam-3526	73	40	)	)	PUNCT
ejpam-3526	73	41	y	y	PROPN
ejpam-3526	73	42	∗	∗	NOUN
ejpam-3526	73	43	(	(	PUNCT
ejpam-3526	73	44	z	z	NOUN
ejpam-3526	73	45	∗	∗	NOUN
ejpam-3526	73	46	x	x	NOUN
ejpam-3526	73	47	)	)	PUNCT
ejpam-3526	74	1	=	=	SYM
ejpam-3526	74	2	z	z	NOUN
ejpam-3526	74	3	∗	∗	NOUN
ejpam-3526	74	4	(	(	PUNCT
ejpam-3526	74	5	y	y	PROPN
ejpam-3526	74	6	∗	∗	NOUN
ejpam-3526	74	7	x	x	NOUN
ejpam-3526	74	8	)	)	PUNCT
ejpam-3526	74	9	(	(	PUNCT
ejpam-3526	74	10	ii	ii	NOUN
ejpam-3526	74	11	)	)	PUNCT
ejpam-3526	74	12	x	x	PROPN
ejpam-3526	75	1	∗	∗	NOUN
ejpam-3526	75	2	y	y	NOUN
ejpam-3526	75	3	=	=	SYM
ejpam-3526	75	4	1	1	NUM
ejpam-3526	75	5	and	and	CCONJ
ejpam-3526	75	6	y	y	PROPN
ejpam-3526	75	7	∗	∗	NOUN
ejpam-3526	75	8	z	z	NOUN
ejpam-3526	76	1	=	=	SYM
ejpam-3526	76	2	1	1	NUM
ejpam-3526	76	3	imply	imply	VERB
ejpam-3526	76	4	x	x	X
ejpam-3526	76	5	∗	∗	NOUN
ejpam-3526	76	6	z	z	NOUN
ejpam-3526	76	7	=	=	SYM
ejpam-3526	76	8	1	1	NUM
ejpam-3526	76	9	(	(	PUNCT
ejpam-3526	76	10	iv	iv	X
ejpam-3526	76	11	)	)	PUNCT
ejpam-3526	76	12	1	1	NUM
ejpam-3526	76	13	∗	∗	NOUN
ejpam-3526	76	14	x	x	X
ejpam-3526	77	1	=	=	PUNCT
ejpam-3526	77	2	x	x	SYM
ejpam-3526	77	3	3	3	X
ejpam-3526	77	4	.	.	PUNCT
ejpam-3526	77	5	dual	dual	ADJ
ejpam-3526	77	6	b	b	NOUN
ejpam-3526	77	7	-	-	PUNCT
ejpam-3526	77	8	algebra	algebra	NOUN
ejpam-3526	77	9	definition	definition	NOUN
ejpam-3526	77	10	7	7	NUM
ejpam-3526	77	11	.	.	PUNCT
ejpam-3526	78	1	a	a	DET
ejpam-3526	78	2	dual	dual	ADJ
ejpam-3526	78	3	b	b	NOUN
ejpam-3526	78	4	-	-	PUNCT
ejpam-3526	78	5	algebra	algebra	NOUN
ejpam-3526	78	6	xd	xd	INTJ
ejpam-3526	78	7	is	be	AUX
ejpam-3526	78	8	a	a	DET
ejpam-3526	78	9	triple	triple	ADJ
ejpam-3526	78	10	(	(	PUNCT
ejpam-3526	78	11	x	x	NOUN
ejpam-3526	78	12	,	,	PUNCT
ejpam-3526	78	13	◦	◦	NOUN
ejpam-3526	78	14	,	,	PUNCT
ejpam-3526	78	15	1	1	NUM
ejpam-3526	78	16	)	)	PUNCT
ejpam-3526	78	17	where	where	SCONJ
ejpam-3526	78	18	x	x	PRON
ejpam-3526	78	19	is	be	AUX
ejpam-3526	78	20	a	a	DET
ejpam-3526	78	21	non	non	ADJ
ejpam-3526	78	22	-	-	ADJ
ejpam-3526	78	23	empty	empty	ADJ
ejpam-3526	78	24	set	set	NOUN
ejpam-3526	78	25	with	with	ADP
ejpam-3526	78	26	a	a	DET
ejpam-3526	78	27	binary	binary	ADJ
ejpam-3526	78	28	operation	operation	NOUN
ejpam-3526	78	29	“	"	PUNCT
ejpam-3526	78	30	◦	◦	NOUN
ejpam-3526	78	31	”	"	PUNCT
ejpam-3526	78	32	and	and	CCONJ
ejpam-3526	78	33	a	a	DET
ejpam-3526	78	34	constant	constant	ADJ
ejpam-3526	78	35	1	1	NUM
ejpam-3526	78	36	satisfying	satisfy	VERB
ejpam-3526	78	37	the	the	DET
ejpam-3526	78	38	following	follow	VERB
ejpam-3526	78	39	axioms	axiom	NOUN
ejpam-3526	78	40	for	for	ADP
ejpam-3526	78	41	all	all	DET
ejpam-3526	78	42	x	x	NOUN
ejpam-3526	78	43	,	,	PUNCT
ejpam-3526	78	44	y	y	PROPN
ejpam-3526	78	45	,	,	PUNCT
ejpam-3526	78	46	z	z	VERB
ejpam-3526	78	47	in	in	ADP
ejpam-3526	78	48	xd	xd	ADP
ejpam-3526	78	49	:	:	PUNCT
ejpam-3526	78	50	(	(	PUNCT
ejpam-3526	78	51	db1	db1	NOUN
ejpam-3526	78	52	)	)	PUNCT
ejpam-3526	78	53	x	x	SYM
ejpam-3526	79	1	◦	◦	NOUN
ejpam-3526	79	2	x	x	SYM
ejpam-3526	80	1	=	=	SYM
ejpam-3526	80	2	1	1	NUM
ejpam-3526	80	3	(	(	PUNCT
ejpam-3526	80	4	db2	db2	PROPN
ejpam-3526	80	5	)	)	PUNCT
ejpam-3526	80	6	1	1	NUM
ejpam-3526	80	7	◦	◦	NOUN
ejpam-3526	80	8	x	x	SYM
ejpam-3526	80	9	=	=	SYM
ejpam-3526	80	10	x	x	X
ejpam-3526	80	11	(	(	PUNCT
ejpam-3526	80	12	db3	db3	PROPN
ejpam-3526	80	13	)	)	PUNCT
ejpam-3526	80	14	x	x	SYM
ejpam-3526	80	15	◦	◦	NOUN
ejpam-3526	80	16	(	(	PUNCT
ejpam-3526	80	17	y	y	PROPN
ejpam-3526	80	18	◦	◦	PROPN
ejpam-3526	80	19	z	z	PROPN
ejpam-3526	80	20	)	)	PUNCT
ejpam-3526	80	21	=	=	SYM
ejpam-3526	80	22	(	(	PUNCT
ejpam-3526	80	23	(	(	PUNCT
ejpam-3526	80	24	y	y	NOUN
ejpam-3526	80	25	◦	◦	NOUN
ejpam-3526	80	26	1	1	NUM
ejpam-3526	80	27	)	)	PUNCT
ejpam-3526	80	28	◦	◦	NOUN
ejpam-3526	80	29	x	x	SYM
ejpam-3526	80	30	)	)	PUNCT
ejpam-3526	80	31	◦	◦	NOUN
ejpam-3526	80	32	z	z	NOUN
ejpam-3526	80	33	remark	remark	NOUN
ejpam-3526	80	34	1	1	NUM
ejpam-3526	80	35	.	.	PUNCT
ejpam-3526	81	1	if	if	SCONJ
ejpam-3526	81	2	(	(	PUNCT
ejpam-3526	81	3	x	x	X
ejpam-3526	81	4	,	,	PUNCT
ejpam-3526	81	5	∗	∗	NOUN
ejpam-3526	81	6	,	,	PUNCT
ejpam-3526	81	7	0	0	NUM
ejpam-3526	81	8	)	)	PUNCT
ejpam-3526	81	9	is	be	AUX
ejpam-3526	81	10	a	a	DET
ejpam-3526	81	11	b	b	NOUN
ejpam-3526	81	12	-	-	PUNCT
ejpam-3526	81	13	algebra	algebra	NOUN
ejpam-3526	81	14	,	,	PUNCT
ejpam-3526	81	15	define	define	VERB
ejpam-3526	81	16	“	"	PUNCT
ejpam-3526	81	17	◦	◦	NOUN
ejpam-3526	81	18	”	"	PUNCT
ejpam-3526	81	19	as	as	SCONJ
ejpam-3526	81	20	follows	follow	VERB
ejpam-3526	81	21	:	:	PUNCT
ejpam-3526	81	22	x	x	PUNCT
ejpam-3526	82	1	◦	◦	VERB
ejpam-3526	82	2	y	y	NOUN
ejpam-3526	82	3	=	=	SYM
ejpam-3526	82	4	y	y	PROPN
ejpam-3526	82	5	∗	∗	NOUN
ejpam-3526	82	6	x	x	PUNCT
ejpam-3526	82	7	for	for	ADP
ejpam-3526	82	8	all	all	DET
ejpam-3526	82	9	x	x	NOUN
ejpam-3526	82	10	,	,	PUNCT
ejpam-3526	82	11	y	y	PROPN
ejpam-3526	82	12	in	in	ADP
ejpam-3526	82	13	x.	x.	PROPN
ejpam-3526	82	14	then	then	ADV
ejpam-3526	82	15	(	(	PUNCT
ejpam-3526	82	16	x	x	NOUN
ejpam-3526	82	17	,	,	PUNCT
ejpam-3526	82	18	◦	◦	NOUN
ejpam-3526	82	19	,	,	PUNCT
ejpam-3526	82	20	0	0	NUM
ejpam-3526	82	21	)	)	PUNCT
ejpam-3526	82	22	is	be	AUX
ejpam-3526	82	23	a	a	DET
ejpam-3526	82	24	dual	dual	ADJ
ejpam-3526	82	25	b	b	NOUN
ejpam-3526	82	26	-	-	PUNCT
ejpam-3526	82	27	algebra	algebra	NOUN
ejpam-3526	82	28	,	,	PUNCT
ejpam-3526	82	29	called	call	VERB
ejpam-3526	82	30	the	the	DET
ejpam-3526	82	31	derived	derive	VERB
ejpam-3526	82	32	dual	dual	ADJ
ejpam-3526	82	33	b	b	NOUN
ejpam-3526	82	34	-	-	PUNCT
ejpam-3526	82	35	algebra	algebra	NOUN
ejpam-3526	82	36	.	.	PUNCT
ejpam-3526	83	1	example	example	NOUN
ejpam-3526	83	2	2	2	NUM
ejpam-3526	83	3	.	.	X
ejpam-3526	83	4	consider	consider	VERB
ejpam-3526	83	5	the	the	DET
ejpam-3526	83	6	b	b	NOUN
ejpam-3526	83	7	-	-	PUNCT
ejpam-3526	83	8	algebra	algebra	NOUN
ejpam-3526	83	9	x	x	X
ejpam-3526	83	10	=	=	SYM
ejpam-3526	83	11	{	{	PUNCT
ejpam-3526	83	12	0	0	NUM
ejpam-3526	83	13	,	,	PUNCT
ejpam-3526	83	14	1	1	NUM
ejpam-3526	83	15	,	,	PUNCT
ejpam-3526	83	16	2	2	NUM
ejpam-3526	83	17	,	,	PUNCT
ejpam-3526	83	18	3	3	NUM
ejpam-3526	83	19	,	,	PUNCT
ejpam-3526	83	20	4	4	NUM
ejpam-3526	83	21	,	,	PUNCT
ejpam-3526	83	22	5	5	NUM
ejpam-3526	83	23	}	}	PUNCT
ejpam-3526	83	24	in	in	ADP
ejpam-3526	83	25	example	example	NOUN
ejpam-3526	83	26	1	1	X
ejpam-3526	83	27	.	.	PUNCT
ejpam-3526	84	1	the	the	DET
ejpam-3526	84	2	dual	dual	ADJ
ejpam-3526	84	3	balgebra	balgebra	NOUN
ejpam-3526	84	4	of	of	ADP
ejpam-3526	84	5	x	x	VERB
ejpam-3526	84	6	is	be	AUX
ejpam-3526	84	7	xd	xd	ADP
ejpam-3526	84	8	=	=	SYM
ejpam-3526	84	9	(	(	PUNCT
ejpam-3526	84	10	x	x	X
ejpam-3526	84	11	,	,	PUNCT
ejpam-3526	84	12	◦	◦	NOUN
ejpam-3526	84	13	,	,	PUNCT
ejpam-3526	84	14	0	0	NUM
ejpam-3526	84	15	)	)	PUNCT
ejpam-3526	84	16	with	with	ADP
ejpam-3526	84	17	the	the	DET
ejpam-3526	84	18	following	follow	VERB
ejpam-3526	84	19	table	table	NOUN
ejpam-3526	84	20	:	:	PUNCT
ejpam-3526	84	21	◦	◦	NOUN
ejpam-3526	84	22	0	0	NUM
ejpam-3526	84	23	1	1	NUM
ejpam-3526	84	24	2	2	NUM
ejpam-3526	84	25	3	3	NUM
ejpam-3526	84	26	4	4	NUM
ejpam-3526	84	27	5	5	NUM
ejpam-3526	84	28	0	0	NUM
ejpam-3526	84	29	0	0	NUM
ejpam-3526	84	30	1	1	NUM
ejpam-3526	84	31	2	2	NUM
ejpam-3526	84	32	3	3	NUM
ejpam-3526	84	33	4	4	NUM
ejpam-3526	84	34	5	5	NUM
ejpam-3526	84	35	1	1	NUM
ejpam-3526	84	36	2	2	NUM
ejpam-3526	84	37	0	0	NUM
ejpam-3526	84	38	1	1	NUM
ejpam-3526	84	39	4	4	NUM
ejpam-3526	84	40	5	5	NUM
ejpam-3526	84	41	3	3	NUM
ejpam-3526	84	42	2	2	NUM
ejpam-3526	84	43	1	1	NUM
ejpam-3526	84	44	2	2	NUM
ejpam-3526	84	45	0	0	NUM
ejpam-3526	84	46	5	5	NUM
ejpam-3526	84	47	3	3	NUM
ejpam-3526	84	48	4	4	NUM
ejpam-3526	84	49	3	3	NUM
ejpam-3526	84	50	3	3	NUM
ejpam-3526	84	51	4	4	NUM
ejpam-3526	84	52	5	5	NUM
ejpam-3526	84	53	0	0	NUM
ejpam-3526	84	54	1	1	NUM
ejpam-3526	84	55	2	2	NUM
ejpam-3526	84	56	4	4	NUM
ejpam-3526	84	57	4	4	NUM
ejpam-3526	84	58	5	5	NUM
ejpam-3526	84	59	3	3	NUM
ejpam-3526	84	60	2	2	NUM
ejpam-3526	84	61	0	0	NUM
ejpam-3526	84	62	1	1	NUM
ejpam-3526	84	63	5	5	NUM
ejpam-3526	84	64	5	5	NUM
ejpam-3526	84	65	3	3	NUM
ejpam-3526	84	66	4	4	NUM
ejpam-3526	84	67	1	1	NUM
ejpam-3526	84	68	2	2	NUM
ejpam-3526	84	69	0	0	NUM
ejpam-3526	84	70	define	define	VERB
ejpam-3526	84	71	“	"	PUNCT
ejpam-3526	84	72	·	·	PUNCT
ejpam-3526	84	73	”	"	PUNCT
ejpam-3526	84	74	as	as	SCONJ
ejpam-3526	84	75	follows	follow	VERB
ejpam-3526	84	76	:	:	PUNCT
ejpam-3526	84	77	x	x	X
ejpam-3526	84	78	·	·	PUNCT
ejpam-3526	84	79	y	y	X
ejpam-3526	84	80	=	=	SYM
ejpam-3526	84	81	y	y	PROPN
ejpam-3526	84	82	◦	◦	NOUN
ejpam-3526	84	83	x.	x.	NOUN
ejpam-3526	84	84	then	then	ADV
ejpam-3526	84	85	xdd	xdd	PROPN
ejpam-3526	84	86	=	=	SYM
ejpam-3526	84	87	(	(	PUNCT
ejpam-3526	84	88	x	x	X
ejpam-3526	84	89	,	,	PUNCT
ejpam-3526	84	90	·	·	PUNCT
ejpam-3526	84	91	,	,	PUNCT
ejpam-3526	84	92	0	0	NUM
ejpam-3526	84	93	)	)	PUNCT
ejpam-3526	84	94	is	be	AUX
ejpam-3526	84	95	the	the	DET
ejpam-3526	84	96	b	b	NOUN
ejpam-3526	84	97	-	-	PUNCT
ejpam-3526	84	98	algebra	algebra	NOUN
ejpam-3526	84	99	x	x	PUNCT
ejpam-3526	84	100	with	with	ADP
ejpam-3526	84	101	cayley	cayley	ADJ
ejpam-3526	84	102	table	table	NOUN
ejpam-3526	84	103	in	in	ADP
ejpam-3526	84	104	example	example	NOUN
ejpam-3526	84	105	1	1	NUM
ejpam-3526	84	106	.	.	X
ejpam-3526	84	107	proposition	proposition	NOUN
ejpam-3526	84	108	2	2	NUM
ejpam-3526	84	109	.	.	PUNCT
ejpam-3526	85	1	let	let	VERB
ejpam-3526	85	2	xd	xd	INTJ
ejpam-3526	85	3	=	=	SYM
ejpam-3526	85	4	(	(	PUNCT
ejpam-3526	85	5	x	x	X
ejpam-3526	85	6	,	,	PUNCT
ejpam-3526	85	7	◦	◦	NOUN
ejpam-3526	85	8	,	,	PUNCT
ejpam-3526	85	9	0	0	NUM
ejpam-3526	85	10	)	)	PUNCT
ejpam-3526	85	11	be	be	AUX
ejpam-3526	85	12	a	a	DET
ejpam-3526	85	13	dual	dual	ADJ
ejpam-3526	85	14	b	b	NOUN
ejpam-3526	85	15	-	-	PUNCT
ejpam-3526	85	16	algebra	algebra	NOUN
ejpam-3526	85	17	.	.	PUNCT
ejpam-3526	86	1	then	then	ADV
ejpam-3526	86	2	xdd	xdd	PROPN
ejpam-3526	86	3	=	=	SYM
ejpam-3526	86	4	(	(	PUNCT
ejpam-3526	86	5	x	x	X
ejpam-3526	86	6	,	,	PUNCT
ejpam-3526	86	7	·	·	PUNCT
ejpam-3526	86	8	,	,	PUNCT
ejpam-3526	86	9	0	0	NUM
ejpam-3526	86	10	)	)	PUNCT
ejpam-3526	86	11	is	be	AUX
ejpam-3526	86	12	a	a	DET
ejpam-3526	86	13	b	b	NOUN
ejpam-3526	86	14	-	-	PUNCT
ejpam-3526	86	15	algebra	algebra	NOUN
ejpam-3526	86	16	where	where	SCONJ
ejpam-3526	86	17	x	x	X
ejpam-3526	86	18	·	·	PUNCT
ejpam-3526	86	19	y	y	X
ejpam-3526	86	20	=	=	PUNCT
ejpam-3526	86	21	y	y	PROPN
ejpam-3526	86	22	◦	◦	NOUN
ejpam-3526	86	23	x	x	PUNCT
ejpam-3526	86	24	for	for	ADP
ejpam-3526	86	25	all	all	DET
ejpam-3526	86	26	x	x	NOUN
ejpam-3526	86	27	,	,	PUNCT
ejpam-3526	86	28	y	y	PROPN
ejpam-3526	86	29	in	in	ADP
ejpam-3526	86	30	xd	xd	ADP
ejpam-3526	86	31	.	.	PUNCT
ejpam-3526	87	1	proof	proof	NOUN
ejpam-3526	87	2	:	:	PUNCT
ejpam-3526	87	3	suppose	suppose	VERB
ejpam-3526	87	4	xd	xd	INTJ
ejpam-3526	87	5	is	be	AUX
ejpam-3526	87	6	a	a	DET
ejpam-3526	87	7	dual	dual	ADJ
ejpam-3526	87	8	b	b	NOUN
ejpam-3526	87	9	-	-	PUNCT
ejpam-3526	87	10	algebra	algebra	NOUN
ejpam-3526	87	11	and	and	CCONJ
ejpam-3526	87	12	define	define	VERB
ejpam-3526	87	13	“	"	PUNCT
ejpam-3526	87	14	·	·	PUNCT
ejpam-3526	87	15	”	"	PUNCT
ejpam-3526	87	16	as	as	SCONJ
ejpam-3526	87	17	follows	follow	VERB
ejpam-3526	87	18	:	:	PUNCT
ejpam-3526	87	19	x	x	X
ejpam-3526	87	20	·	·	PUNCT
ejpam-3526	87	21	y	y	X
ejpam-3526	87	22	=	=	PUNCT
ejpam-3526	87	23	y	y	PROPN
ejpam-3526	87	24	◦	◦	NOUN
ejpam-3526	87	25	x	x	PUNCT
ejpam-3526	87	26	for	for	ADP
ejpam-3526	87	27	all	all	DET
ejpam-3526	87	28	x	x	NOUN
ejpam-3526	87	29	,	,	PUNCT
ejpam-3526	87	30	y	y	PROPN
ejpam-3526	87	31	in	in	ADP
ejpam-3526	87	32	xd	xd	ADP
ejpam-3526	87	33	.	.	PUNCT
ejpam-3526	88	1	then	then	ADV
ejpam-3526	88	2	the	the	DET
ejpam-3526	88	3	axioms	axiom	NOUN
ejpam-3526	88	4	of	of	ADP
ejpam-3526	88	5	xdd	xdd	PROPN
ejpam-3526	88	6	=	=	SYM
ejpam-3526	88	7	(	(	PUNCT
ejpam-3526	88	8	x	x	X
ejpam-3526	88	9	,	,	PUNCT
ejpam-3526	88	10	·	·	PUNCT
ejpam-3526	88	11	,	,	PUNCT
ejpam-3526	88	12	0	0	NUM
ejpam-3526	88	13	)	)	PUNCT
ejpam-3526	88	14	coincide	coincide	NOUN
ejpam-3526	88	15	with	with	ADP
ejpam-3526	88	16	that	that	PRON
ejpam-3526	88	17	of	of	ADP
ejpam-3526	88	18	a	a	DET
ejpam-3526	88	19	b	b	NOUN
ejpam-3526	88	20	-	-	PUNCT
ejpam-3526	88	21	algebra	algebra	NOUN
ejpam-3526	88	22	.	.	PUNCT
ejpam-3526	89	1	hence	hence	ADV
ejpam-3526	89	2	,	,	PUNCT
ejpam-3526	89	3	xdd	xdd	PROPN
ejpam-3526	89	4	is	be	AUX
ejpam-3526	89	5	a	a	DET
ejpam-3526	89	6	b	b	NOUN
ejpam-3526	89	7	-	-	PUNCT
ejpam-3526	89	8	algebra	algebra	NOUN
ejpam-3526	89	9	.	.	PUNCT
ejpam-3526	90	1	k.	k.	PROPN
ejpam-3526	90	2	belleza	belleza	PROPN
ejpam-3526	90	3	,	,	PUNCT
ejpam-3526	90	4	j.	j.	PROPN
ejpam-3526	90	5	vilela	vilela	PROPN
ejpam-3526	90	6	/	/	SYM
ejpam-3526	90	7	eur	eur	PROPN
ejpam-3526	90	8	.	.	PUNCT
ejpam-3526	91	1	j.	j.	PROPN
ejpam-3526	91	2	pure	pure	PROPN
ejpam-3526	91	3	appl	appl	PROPN
ejpam-3526	91	4	.	.	PROPN
ejpam-3526	91	5	math	math	PROPN
ejpam-3526	91	6	,	,	PUNCT
ejpam-3526	91	7	12	12	NUM
ejpam-3526	91	8	(	(	PUNCT
ejpam-3526	91	9	4	4	NUM
ejpam-3526	91	10	)	)	PUNCT
ejpam-3526	91	11	(	(	PUNCT
ejpam-3526	91	12	2019	2019	NUM
ejpam-3526	91	13	)	)	PUNCT
ejpam-3526	91	14	,	,	PUNCT
ejpam-3526	91	15	1497	1497	NUM
ejpam-3526	91	16	-	-	SYM
ejpam-3526	91	17	1507	1507	NUM
ejpam-3526	91	18	1500	1500	NUM
ejpam-3526	91	19	example	example	NOUN
ejpam-3526	91	20	3	3	X
ejpam-3526	91	21	.	.	PUNCT
ejpam-3526	92	1	let	let	VERB
ejpam-3526	92	2	x	x	PUNCT
ejpam-3526	92	3	=	=	SYM
ejpam-3526	92	4	r	r	NOUN
ejpam-3526	92	5	and	and	CCONJ
ejpam-3526	92	6	◦	◦	NOUN
ejpam-3526	92	7	be	be	AUX
ejpam-3526	92	8	defined	define	VERB
ejpam-3526	92	9	as	as	ADP
ejpam-3526	92	10	x	x	X
ejpam-3526	92	11	◦	◦	NOUN
ejpam-3526	92	12	y	y	NOUN
ejpam-3526	92	13	=	=	SYM
ejpam-3526	92	14	y	y	PROPN
ejpam-3526	92	15	x	x	PUNCT
ejpam-3526	92	16	for	for	ADP
ejpam-3526	92	17	all	all	DET
ejpam-3526	92	18	x	x	NOUN
ejpam-3526	92	19	,	,	PUNCT
ejpam-3526	92	20	y	y	PROPN
ejpam-3526	92	21	in	in	ADP
ejpam-3526	92	22	x	x	PUNCT
ejpam-3526	92	23	with	with	ADP
ejpam-3526	92	24	x	x	SYM
ejpam-3526	92	25	6=	6=	ADP
ejpam-3526	92	26	0	0	NUM
ejpam-3526	92	27	.	.	PUNCT
ejpam-3526	92	28	note	note	VERB
ejpam-3526	92	29	that	that	SCONJ
ejpam-3526	92	30	x	x	PRON
ejpam-3526	92	31	satisfies	satisfie	NOUN
ejpam-3526	92	32	(	(	PUNCT
ejpam-3526	92	33	db1	db1	NOUN
ejpam-3526	92	34	):	):	PUNCT
ejpam-3526	92	35	x	x	PUNCT
ejpam-3526	92	36	◦	◦	NOUN
ejpam-3526	92	37	x	x	X
ejpam-3526	93	1	=	=	PUNCT
ejpam-3526	93	2	x	x	SYM
ejpam-3526	93	3	x	x	SYM
ejpam-3526	93	4	=	=	SYM
ejpam-3526	93	5	1	1	NUM
ejpam-3526	93	6	,	,	PUNCT
ejpam-3526	93	7	(	(	PUNCT
ejpam-3526	93	8	db2	db2	PROPN
ejpam-3526	93	9	):	):	PUNCT
ejpam-3526	93	10	1	1	NUM
ejpam-3526	93	11	◦	◦	NOUN
ejpam-3526	93	12	x	x	SYM
ejpam-3526	93	13	=	=	SYM
ejpam-3526	93	14	x	x	SYM
ejpam-3526	93	15	1	1	NUM
ejpam-3526	93	16	=	=	SYM
ejpam-3526	93	17	x	x	NOUN
ejpam-3526	93	18	,	,	PUNCT
ejpam-3526	93	19	and	and	CCONJ
ejpam-3526	93	20	(	(	PUNCT
ejpam-3526	93	21	db3	db3	PROPN
ejpam-3526	93	22	):	):	PUNCT
ejpam-3526	93	23	x	x	SYM
ejpam-3526	94	1	◦	◦	NOUN
ejpam-3526	94	2	(	(	PUNCT
ejpam-3526	94	3	y	y	PROPN
ejpam-3526	94	4	◦	◦	PROPN
ejpam-3526	94	5	z	z	PROPN
ejpam-3526	94	6	)	)	PUNCT
ejpam-3526	95	1	=	=	SYM
ejpam-3526	95	2	y	y	PROPN
ejpam-3526	95	3	◦	◦	NOUN
ejpam-3526	95	4	z	z	NOUN
ejpam-3526	95	5	x	x	PUNCT
ejpam-3526	96	1	=	=	PUNCT
ejpam-3526	96	2	z	z	NOUN
ejpam-3526	96	3	xy	xy	NOUN
ejpam-3526	97	1	=	=	PUNCT
ejpam-3526	97	2	z	z	NOUN
ejpam-3526	97	3	x	x	SYM
ejpam-3526	97	4	y	y	PROPN
ejpam-3526	97	5	◦	◦	NOUN
ejpam-3526	97	6	1	1	NUM
ejpam-3526	97	7	=	=	SYM
ejpam-3526	97	8	z	z	NOUN
ejpam-3526	97	9	(	(	PUNCT
ejpam-3526	97	10	y	y	NOUN
ejpam-3526	97	11	◦	◦	NOUN
ejpam-3526	97	12	1	1	NUM
ejpam-3526	97	13	)	)	PUNCT
ejpam-3526	97	14	◦	◦	NOUN
ejpam-3526	97	15	x	x	SYM
ejpam-3526	98	1	=	=	SYM
ejpam-3526	98	2	(	(	PUNCT
ejpam-3526	98	3	(	(	PUNCT
ejpam-3526	98	4	y	y	NOUN
ejpam-3526	98	5	◦	◦	NOUN
ejpam-3526	98	6	1	1	NUM
ejpam-3526	98	7	)	)	PUNCT
ejpam-3526	98	8	◦	◦	NOUN
ejpam-3526	98	9	x	x	SYM
ejpam-3526	98	10	)	)	PUNCT
ejpam-3526	98	11	◦	◦	NOUN
ejpam-3526	98	12	z.	z.	PROPN
ejpam-3526	98	13	hence	hence	ADV
ejpam-3526	98	14	,	,	PUNCT
ejpam-3526	98	15	(	(	PUNCT
ejpam-3526	98	16	r	r	NOUN
ejpam-3526	98	17	,	,	PUNCT
ejpam-3526	98	18	◦	◦	NOUN
ejpam-3526	98	19	,	,	PUNCT
ejpam-3526	98	20	1	1	NUM
ejpam-3526	98	21	)	)	PUNCT
ejpam-3526	98	22	is	be	AUX
ejpam-3526	98	23	a	a	DET
ejpam-3526	98	24	dual	dual	ADJ
ejpam-3526	98	25	b	b	NOUN
ejpam-3526	98	26	-	-	PUNCT
ejpam-3526	98	27	algebra	algebra	NOUN
ejpam-3526	98	28	.	.	PUNCT
ejpam-3526	99	1	observe	observe	VERB
ejpam-3526	99	2	that	that	SCONJ
ejpam-3526	99	3	(	(	PUNCT
ejpam-3526	99	4	r	r	NOUN
ejpam-3526	99	5	,	,	PUNCT
ejpam-3526	99	6	◦	◦	NOUN
ejpam-3526	99	7	,	,	PUNCT
ejpam-3526	99	8	1	1	NUM
ejpam-3526	99	9	)	)	PUNCT
ejpam-3526	99	10	is	be	AUX
ejpam-3526	99	11	not	not	PART
ejpam-3526	99	12	a	a	DET
ejpam-3526	99	13	b	b	NOUN
ejpam-3526	99	14	-	-	PUNCT
ejpam-3526	99	15	algebra	algebra	NOUN
ejpam-3526	99	16	since	since	SCONJ
ejpam-3526	99	17	4	4	NUM
ejpam-3526	99	18	◦	◦	NOUN
ejpam-3526	99	19	1	1	NUM
ejpam-3526	100	1	=	=	SYM
ejpam-3526	100	2	1	1	NUM
ejpam-3526	100	3	4	4	NUM
ejpam-3526	100	4	6=	6=	SYM
ejpam-3526	100	5	4	4	NUM
ejpam-3526	100	6	.	.	PUNCT
ejpam-3526	101	1	this	this	PRON
ejpam-3526	101	2	leads	lead	VERB
ejpam-3526	101	3	to	to	ADP
ejpam-3526	101	4	the	the	DET
ejpam-3526	101	5	next	next	ADJ
ejpam-3526	101	6	remark	remark	NOUN
ejpam-3526	101	7	.	.	PUNCT
ejpam-3526	102	1	remark	remark	PROPN
ejpam-3526	102	2	2	2	NUM
ejpam-3526	102	3	.	.	PUNCT
ejpam-3526	102	4	not	not	PART
ejpam-3526	102	5	every	every	DET
ejpam-3526	102	6	dual	dual	ADJ
ejpam-3526	102	7	b	b	X
ejpam-3526	102	8	-	-	PUNCT
ejpam-3526	102	9	algebra	algebra	NOUN
ejpam-3526	102	10	is	be	AUX
ejpam-3526	102	11	a	a	DET
ejpam-3526	102	12	b	b	NOUN
ejpam-3526	102	13	-	-	PUNCT
ejpam-3526	102	14	algebra	algebra	NOUN
ejpam-3526	102	15	.	.	PUNCT
ejpam-3526	103	1	example	example	NOUN
ejpam-3526	104	1	4	4	NUM
ejpam-3526	104	2	.	.	PUNCT
ejpam-3526	104	3	let	let	VERB
ejpam-3526	104	4	x	x	PUNCT
ejpam-3526	104	5	=	=	PUNCT
ejpam-3526	104	6	{	{	PUNCT
ejpam-3526	104	7	e	e	NOUN
ejpam-3526	104	8	,	,	PUNCT
ejpam-3526	104	9	a	a	DET
ejpam-3526	104	10	,	,	PUNCT
ejpam-3526	104	11	b	b	NOUN
ejpam-3526	104	12	,	,	PUNCT
ejpam-3526	104	13	c	c	AUX
ejpam-3526	104	14	}	}	PUNCT
ejpam-3526	104	15	be	be	AUX
ejpam-3526	104	16	the	the	DET
ejpam-3526	104	17	klein-4	klein-4	PROPN
ejpam-3526	104	18	b	b	X
ejpam-3526	104	19	-	-	PUNCT
ejpam-3526	104	20	algebra	algebra	NOUN
ejpam-3526	104	21	with	with	ADP
ejpam-3526	104	22	the	the	DET
ejpam-3526	104	23	following	follow	VERB
ejpam-3526	104	24	table	table	NOUN
ejpam-3526	104	25	:	:	PUNCT
ejpam-3526	104	26	◦	◦	NOUN
ejpam-3526	104	27	e	e	X
ejpam-3526	104	28	a	a	DET
ejpam-3526	104	29	b	b	NOUN
ejpam-3526	104	30	c	c	NOUN
ejpam-3526	104	31	e	e	X
ejpam-3526	104	32	e	e	X
ejpam-3526	104	33	a	a	PRON
ejpam-3526	104	34	b	b	X
ejpam-3526	104	35	c	c	NOUN
ejpam-3526	104	36	a	a	PRON
ejpam-3526	104	37	a	a	DET
ejpam-3526	104	38	e	e	NOUN
ejpam-3526	104	39	c	c	NOUN
ejpam-3526	104	40	b	b	PROPN
ejpam-3526	104	41	b	b	PROPN
ejpam-3526	104	42	b	b	PROPN
ejpam-3526	104	43	c	c	NOUN
ejpam-3526	104	44	e	e	X
ejpam-3526	104	45	a	a	X
ejpam-3526	104	46	c	c	NOUN
ejpam-3526	104	47	c	c	PROPN
ejpam-3526	104	48	b	b	PROPN
ejpam-3526	104	49	a	a	DET
ejpam-3526	104	50	e	e	NOUN
ejpam-3526	104	51	then	then	ADV
ejpam-3526	104	52	the	the	DET
ejpam-3526	104	53	dual	dual	ADJ
ejpam-3526	104	54	xd	xd	INTJ
ejpam-3526	104	55	of	of	ADP
ejpam-3526	104	56	x	x	PUNCT
ejpam-3526	104	57	is	be	AUX
ejpam-3526	104	58	itself	itself	PRON
ejpam-3526	104	59	.	.	PUNCT
ejpam-3526	105	1	hence	hence	ADV
ejpam-3526	105	2	,	,	PUNCT
ejpam-3526	105	3	the	the	DET
ejpam-3526	105	4	klein-4	klein-4	PROPN
ejpam-3526	105	5	b	b	X
ejpam-3526	105	6	-	-	PUNCT
ejpam-3526	105	7	algebra	algebra	NOUN
ejpam-3526	105	8	is	be	AUX
ejpam-3526	105	9	a	a	DET
ejpam-3526	105	10	dual	dual	ADJ
ejpam-3526	105	11	b	b	NOUN
ejpam-3526	105	12	-	-	PUNCT
ejpam-3526	105	13	algebra	algebra	NOUN
ejpam-3526	105	14	.	.	PUNCT
ejpam-3526	106	1	observe	observe	VERB
ejpam-3526	106	2	that	that	SCONJ
ejpam-3526	106	3	the	the	PRON
ejpam-3526	106	4	klein-4	klein-4	PROPN
ejpam-3526	106	5	b	b	X
ejpam-3526	106	6	-	-	PUNCT
ejpam-3526	106	7	algebra	algebra	NOUN
ejpam-3526	106	8	has	have	VERB
ejpam-3526	106	9	a	a	DET
ejpam-3526	106	10	symmetric	symmetric	ADJ
ejpam-3526	106	11	cayley	cayley	ADJ
ejpam-3526	106	12	table	table	NOUN
ejpam-3526	106	13	and	and	CCONJ
ejpam-3526	106	14	is	be	AUX
ejpam-3526	106	15	a	a	DET
ejpam-3526	106	16	dual	dual	ADJ
ejpam-3526	106	17	b	b	NOUN
ejpam-3526	106	18	-	-	PUNCT
ejpam-3526	106	19	algebra	algebra	NOUN
ejpam-3526	106	20	itself	itself	PRON
ejpam-3526	106	21	.	.	PUNCT
ejpam-3526	107	1	hence	hence	ADV
ejpam-3526	107	2	,	,	PUNCT
ejpam-3526	107	3	there	there	PRON
ejpam-3526	107	4	exists	exist	VERB
ejpam-3526	107	5	a	a	DET
ejpam-3526	107	6	b	b	NOUN
ejpam-3526	107	7	-	-	PUNCT
ejpam-3526	107	8	algebra	algebra	NOUN
ejpam-3526	107	9	that	that	PRON
ejpam-3526	107	10	is	be	AUX
ejpam-3526	107	11	also	also	ADV
ejpam-3526	107	12	a	a	DET
ejpam-3526	107	13	dual	dual	ADJ
ejpam-3526	107	14	b	b	NOUN
ejpam-3526	107	15	-	-	PUNCT
ejpam-3526	107	16	algebra	algebra	NOUN
ejpam-3526	107	17	.	.	PUNCT
ejpam-3526	108	1	this	this	PRON
ejpam-3526	108	2	is	be	AUX
ejpam-3526	108	3	generalized	generalize	VERB
ejpam-3526	108	4	in	in	ADP
ejpam-3526	108	5	the	the	DET
ejpam-3526	108	6	next	next	ADJ
ejpam-3526	108	7	theorem	theorem	NOUN
ejpam-3526	108	8	.	.	PUNCT
ejpam-3526	109	1	let	let	VERB
ejpam-3526	109	2	(	(	PUNCT
ejpam-3526	109	3	x	x	X
ejpam-3526	109	4	,	,	PUNCT
ejpam-3526	109	5	∗	∗	NOUN
ejpam-3526	109	6	,	,	PUNCT
ejpam-3526	109	7	0	0	NUM
ejpam-3526	109	8	)	)	PUNCT
ejpam-3526	109	9	be	be	VERB
ejpam-3526	109	10	any	any	DET
ejpam-3526	109	11	algebra	algebra	NOUN
ejpam-3526	109	12	of	of	ADP
ejpam-3526	109	13	type	type	NOUN
ejpam-3526	109	14	(	(	PUNCT
ejpam-3526	109	15	2	2	NUM
ejpam-3526	109	16	,	,	PUNCT
ejpam-3526	109	17	0	0	NUM
ejpam-3526	109	18	)	)	PUNCT
ejpam-3526	109	19	satisfying	satisfy	VERB
ejpam-3526	109	20	x∗y	x∗y	X
ejpam-3526	110	1	=	=	SYM
ejpam-3526	110	2	y	y	PROPN
ejpam-3526	110	3	∗x	∗x	PROPN
ejpam-3526	110	4	for	for	ADP
ejpam-3526	110	5	all	all	DET
ejpam-3526	110	6	x	x	NOUN
ejpam-3526	110	7	,	,	PUNCT
ejpam-3526	110	8	y	y	PROPN
ejpam-3526	110	9	in	in	ADP
ejpam-3526	110	10	x.	x.	NOUN
ejpam-3526	110	11	then	then	ADV
ejpam-3526	110	12	we	we	PRON
ejpam-3526	110	13	say	say	VERB
ejpam-3526	110	14	that	that	SCONJ
ejpam-3526	110	15	(	(	PUNCT
ejpam-3526	110	16	x	x	X
ejpam-3526	110	17	,	,	PUNCT
ejpam-3526	110	18	∗	∗	NOUN
ejpam-3526	110	19	,	,	PUNCT
ejpam-3526	110	20	0	0	NUM
ejpam-3526	110	21	)	)	PUNCT
ejpam-3526	110	22	satisfies	satisfy	VERB
ejpam-3526	110	23	a	a	DET
ejpam-3526	110	24	symmetric	symmetric	ADJ
ejpam-3526	110	25	condition	condition	NOUN
ejpam-3526	110	26	.	.	PUNCT
ejpam-3526	111	1	theorem	theorem	NOUN
ejpam-3526	111	2	2	2	NUM
ejpam-3526	111	3	.	.	PUNCT
ejpam-3526	112	1	let	let	VERB
ejpam-3526	112	2	x	x	PRON
ejpam-3526	112	3	be	be	AUX
ejpam-3526	112	4	a	a	DET
ejpam-3526	112	5	b	b	NOUN
ejpam-3526	112	6	-	-	PUNCT
ejpam-3526	112	7	algebra	algebra	NOUN
ejpam-3526	112	8	satisfying	satisfy	VERB
ejpam-3526	112	9	a	a	DET
ejpam-3526	112	10	symmetric	symmetric	ADJ
ejpam-3526	112	11	condition	condition	NOUN
ejpam-3526	112	12	.	.	PUNCT
ejpam-3526	113	1	then	then	ADV
ejpam-3526	113	2	x	x	PRON
ejpam-3526	113	3	itself	itself	PRON
ejpam-3526	113	4	is	be	AUX
ejpam-3526	113	5	a	a	DET
ejpam-3526	113	6	dual	dual	ADJ
ejpam-3526	113	7	b	b	NOUN
ejpam-3526	113	8	-	-	PUNCT
ejpam-3526	113	9	algebra	algebra	NOUN
ejpam-3526	113	10	,	,	PUNCT
ejpam-3526	113	11	that	that	ADV
ejpam-3526	113	12	is	is	ADV
ejpam-3526	113	13	,	,	PUNCT
ejpam-3526	113	14	x	x	PUNCT
ejpam-3526	113	15	=	=	SYM
ejpam-3526	113	16	xd	xd	NOUN
ejpam-3526	113	17	.	.	PUNCT
ejpam-3526	113	18	proof	proof	NOUN
ejpam-3526	113	19	:	:	PUNCT
ejpam-3526	113	20	suppose	suppose	VERB
ejpam-3526	113	21	x	x	PRON
ejpam-3526	113	22	is	be	AUX
ejpam-3526	113	23	a	a	DET
ejpam-3526	113	24	b	b	NOUN
ejpam-3526	113	25	-	-	PUNCT
ejpam-3526	113	26	algebra	algebra	NOUN
ejpam-3526	113	27	satisfying	satisfy	VERB
ejpam-3526	113	28	a	a	DET
ejpam-3526	113	29	symmetric	symmetric	ADJ
ejpam-3526	113	30	condition	condition	NOUN
ejpam-3526	113	31	.	.	PUNCT
ejpam-3526	114	1	then	then	ADV
ejpam-3526	114	2	the	the	DET
ejpam-3526	114	3	dual	dual	ADJ
ejpam-3526	114	4	b	b	NOUN
ejpam-3526	114	5	-	-	PUNCT
ejpam-3526	114	6	algebra	algebra	ADJ
ejpam-3526	114	7	axioms	axiom	NOUN
ejpam-3526	114	8	hold	hold	VERB
ejpam-3526	114	9	,	,	PUNCT
ejpam-3526	114	10	namely	namely	ADV
ejpam-3526	114	11	(	(	PUNCT
ejpam-3526	114	12	db1	db1	NOUN
ejpam-3526	114	13	):	):	PUNCT
ejpam-3526	114	14	x	x	X
ejpam-3526	114	15	∗	∗	NOUN
ejpam-3526	114	16	x	x	X
ejpam-3526	115	1	=	=	SYM
ejpam-3526	115	2	0	0	NUM
ejpam-3526	115	3	by	by	ADP
ejpam-3526	115	4	(	(	PUNCT
ejpam-3526	115	5	b1	b1	NOUN
ejpam-3526	115	6	)	)	PUNCT
ejpam-3526	115	7	,	,	PUNCT
ejpam-3526	115	8	(	(	PUNCT
ejpam-3526	115	9	db2	db2	PROPN
ejpam-3526	115	10	):	):	PUNCT
ejpam-3526	115	11	0	0	NUM
ejpam-3526	115	12	∗	∗	NOUN
ejpam-3526	115	13	x	x	X
ejpam-3526	115	14	=	=	PUNCT
ejpam-3526	115	15	x	x	SYM
ejpam-3526	115	16	∗	∗	NOUN
ejpam-3526	115	17	0	0	NUM
ejpam-3526	116	1	=	=	NOUN
ejpam-3526	116	2	x	x	SYM
ejpam-3526	116	3	by	by	ADP
ejpam-3526	116	4	(	(	PUNCT
ejpam-3526	116	5	b2	b2	NOUN
ejpam-3526	116	6	)	)	PUNCT
ejpam-3526	116	7	,	,	PUNCT
ejpam-3526	116	8	and	and	CCONJ
ejpam-3526	116	9	(	(	PUNCT
ejpam-3526	116	10	db3	db3	PROPN
ejpam-3526	116	11	):	):	PUNCT
ejpam-3526	116	12	x	x	SYM
ejpam-3526	116	13	∗	∗	NOUN
ejpam-3526	116	14	(	(	PUNCT
ejpam-3526	116	15	y	y	PROPN
ejpam-3526	116	16	∗	∗	PROPN
ejpam-3526	116	17	z	z	NOUN
ejpam-3526	116	18	)	)	PUNCT
ejpam-3526	116	19	=	=	PUNCT
ejpam-3526	116	20	(	(	PUNCT
ejpam-3526	116	21	z	z	NOUN
ejpam-3526	116	22	∗	∗	PROPN
ejpam-3526	116	23	y	y	NOUN
ejpam-3526	116	24	)	)	PUNCT
ejpam-3526	116	25	∗x	∗x	NOUN
ejpam-3526	116	26	=	=	SYM
ejpam-3526	116	27	z	z	NOUN
ejpam-3526	116	28	∗	∗	NOUN
ejpam-3526	117	1	[	[	X
ejpam-3526	117	2	x	x	X
ejpam-3526	117	3	∗	∗	NOUN
ejpam-3526	117	4	(	(	PUNCT
ejpam-3526	117	5	0	0	NUM
ejpam-3526	117	6	∗	∗	NOUN
ejpam-3526	117	7	y	y	PROPN
ejpam-3526	117	8	)	)	PUNCT
ejpam-3526	117	9	]	]	PUNCT
ejpam-3526	118	1	=	=	PUNCT
ejpam-3526	119	1	[	[	X
ejpam-3526	119	2	(	(	PUNCT
ejpam-3526	119	3	y	y	PROPN
ejpam-3526	119	4	∗	∗	NOUN
ejpam-3526	119	5	0	0	NUM
ejpam-3526	119	6	)	)	PUNCT
ejpam-3526	119	7	∗x	∗x	NOUN
ejpam-3526	119	8	]	]	X
ejpam-3526	119	9	∗	∗	NOUN
ejpam-3526	119	10	z	z	NOUN
ejpam-3526	119	11	by	by	ADP
ejpam-3526	119	12	(	(	PUNCT
ejpam-3526	119	13	b3	b3	PROPN
ejpam-3526	119	14	)	)	PUNCT
ejpam-3526	119	15	.	.	PUNCT
ejpam-3526	120	1	hence	hence	ADV
ejpam-3526	120	2	,	,	PUNCT
ejpam-3526	120	3	x	x	X
ejpam-3526	120	4	is	be	AUX
ejpam-3526	120	5	a	a	DET
ejpam-3526	120	6	dual	dual	ADJ
ejpam-3526	120	7	b	b	NOUN
ejpam-3526	120	8	-	-	PUNCT
ejpam-3526	120	9	algebra	algebra	NOUN
ejpam-3526	120	10	.	.	PUNCT
ejpam-3526	121	1	example	example	NOUN
ejpam-3526	121	2	5	5	NUM
ejpam-3526	121	3	.	.	PUNCT
ejpam-3526	122	1	let	let	VERB
ejpam-3526	122	2	x	x	PUNCT
ejpam-3526	122	3	=	=	PUNCT
ejpam-3526	122	4	{	{	PUNCT
ejpam-3526	122	5	0	0	NUM
ejpam-3526	122	6	,	,	PUNCT
ejpam-3526	122	7	1	1	NUM
ejpam-3526	122	8	,	,	PUNCT
ejpam-3526	122	9	2	2	NUM
ejpam-3526	122	10	}	}	PUNCT
ejpam-3526	122	11	be	be	AUX
ejpam-3526	122	12	a	a	DET
ejpam-3526	122	13	set	set	NOUN
ejpam-3526	122	14	with	with	ADP
ejpam-3526	122	15	the	the	DET
ejpam-3526	122	16	following	follow	VERB
ejpam-3526	122	17	table	table	NOUN
ejpam-3526	122	18	:	:	PUNCT
ejpam-3526	122	19	∗	∗	NOUN
ejpam-3526	122	20	0	0	NUM
ejpam-3526	123	1	1	1	NUM
ejpam-3526	123	2	2	2	NUM
ejpam-3526	123	3	0	0	NUM
ejpam-3526	123	4	0	0	NUM
ejpam-3526	123	5	2	2	NUM
ejpam-3526	123	6	1	1	NUM
ejpam-3526	123	7	1	1	NUM
ejpam-3526	123	8	1	1	NUM
ejpam-3526	123	9	0	0	NUM
ejpam-3526	123	10	2	2	NUM
ejpam-3526	123	11	2	2	NUM
ejpam-3526	123	12	2	2	NUM
ejpam-3526	123	13	1	1	NUM
ejpam-3526	123	14	0	0	NUM
ejpam-3526	123	15	then	then	ADV
ejpam-3526	123	16	(	(	PUNCT
ejpam-3526	123	17	x	x	X
ejpam-3526	123	18	,	,	PUNCT
ejpam-3526	123	19	∗	∗	NOUN
ejpam-3526	123	20	,	,	PUNCT
ejpam-3526	123	21	0	0	NUM
ejpam-3526	123	22	)	)	PUNCT
ejpam-3526	123	23	is	be	AUX
ejpam-3526	123	24	a	a	DET
ejpam-3526	123	25	b	b	NOUN
ejpam-3526	123	26	-	-	PUNCT
ejpam-3526	123	27	algebra	algebra	NOUN
ejpam-3526	123	28	[	[	X
ejpam-3526	123	29	9	9	NUM
ejpam-3526	123	30	]	]	PUNCT
ejpam-3526	123	31	.	.	PUNCT
ejpam-3526	124	1	observe	observe	VERB
ejpam-3526	124	2	that	that	SCONJ
ejpam-3526	124	3	in	in	ADP
ejpam-3526	124	4	this	this	DET
ejpam-3526	124	5	example	example	NOUN
ejpam-3526	124	6	,	,	PUNCT
ejpam-3526	124	7	1	1	NUM
ejpam-3526	124	8	∗	∗	NOUN
ejpam-3526	124	9	(	(	PUNCT
ejpam-3526	124	10	2	2	NUM
ejpam-3526	124	11	∗	∗	NOUN
ejpam-3526	124	12	0	0	NUM
ejpam-3526	124	13	)	)	PUNCT
ejpam-3526	124	14	=	=	SYM
ejpam-3526	124	15	1	1	NUM
ejpam-3526	124	16	∗	∗	NOUN
ejpam-3526	124	17	2	2	NUM
ejpam-3526	124	18	=	=	SYM
ejpam-3526	124	19	2	2	NUM
ejpam-3526	124	20	6=	6=	SYM
ejpam-3526	124	21	1	1	NUM
ejpam-3526	124	22	=	=	SYM
ejpam-3526	124	23	1	1	NUM
ejpam-3526	124	24	∗	∗	NOUN
ejpam-3526	124	25	0	0	NUM
ejpam-3526	124	26	=	=	SYM
ejpam-3526	124	27	(	(	PUNCT
ejpam-3526	124	28	2	2	NUM
ejpam-3526	124	29	∗	∗	NOUN
ejpam-3526	124	30	1	1	NUM
ejpam-3526	124	31	)	)	PUNCT
ejpam-3526	124	32	∗	∗	NOUN
ejpam-3526	124	33	0	0	NUM
ejpam-3526	125	1	=	=	SYM
ejpam-3526	126	1	[	[	X
ejpam-3526	126	2	(	(	PUNCT
ejpam-3526	126	3	2	2	NUM
ejpam-3526	126	4	∗	∗	NOUN
ejpam-3526	126	5	0	0	NUM
ejpam-3526	126	6	)	)	PUNCT
ejpam-3526	126	7	∗	∗	NOUN
ejpam-3526	126	8	1	1	NUM
ejpam-3526	126	9	]	]	PUNCT
ejpam-3526	126	10	∗	∗	NOUN
ejpam-3526	126	11	0	0	NUM
ejpam-3526	126	12	.	.	PUNCT
ejpam-3526	127	1	this	this	PRON
ejpam-3526	127	2	implies	imply	VERB
ejpam-3526	127	3	that	that	SCONJ
ejpam-3526	127	4	x	x	PRON
ejpam-3526	127	5	is	be	AUX
ejpam-3526	127	6	not	not	PART
ejpam-3526	127	7	a	a	DET
ejpam-3526	127	8	dual	dual	ADJ
ejpam-3526	127	9	b	b	NOUN
ejpam-3526	127	10	-	-	PUNCT
ejpam-3526	127	11	algebra	algebra	NOUN
ejpam-3526	127	12	.	.	PUNCT
ejpam-3526	128	1	remark	remark	NOUN
ejpam-3526	128	2	3	3	NUM
ejpam-3526	128	3	.	.	PUNCT
ejpam-3526	129	1	not	not	PART
ejpam-3526	129	2	every	every	DET
ejpam-3526	129	3	b	b	X
ejpam-3526	129	4	-	-	PUNCT
ejpam-3526	129	5	algebra	algebra	NOUN
ejpam-3526	129	6	is	be	AUX
ejpam-3526	129	7	a	a	DET
ejpam-3526	129	8	dual	dual	ADJ
ejpam-3526	129	9	b	b	NOUN
ejpam-3526	129	10	-	-	PUNCT
ejpam-3526	129	11	algebra	algebra	NOUN
ejpam-3526	129	12	.	.	PUNCT
ejpam-3526	130	1	k.	k.	PROPN
ejpam-3526	130	2	belleza	belleza	PROPN
ejpam-3526	130	3	,	,	PUNCT
ejpam-3526	130	4	j.	j.	PROPN
ejpam-3526	130	5	vilela	vilela	PROPN
ejpam-3526	130	6	/	/	SYM
ejpam-3526	130	7	eur	eur	PROPN
ejpam-3526	130	8	.	.	PUNCT
ejpam-3526	131	1	j.	j.	PROPN
ejpam-3526	131	2	pure	pure	PROPN
ejpam-3526	131	3	appl	appl	PROPN
ejpam-3526	131	4	.	.	PROPN
ejpam-3526	131	5	math	math	PROPN
ejpam-3526	131	6	,	,	PUNCT
ejpam-3526	131	7	12	12	NUM
ejpam-3526	131	8	(	(	PUNCT
ejpam-3526	131	9	4	4	NUM
ejpam-3526	131	10	)	)	PUNCT
ejpam-3526	131	11	(	(	PUNCT
ejpam-3526	131	12	2019	2019	NUM
ejpam-3526	131	13	)	)	PUNCT
ejpam-3526	131	14	,	,	PUNCT
ejpam-3526	131	15	1497	1497	NUM
ejpam-3526	131	16	-	-	SYM
ejpam-3526	131	17	1507	1507	NUM
ejpam-3526	131	18	1501	1501	NUM
ejpam-3526	131	19	lemma	lemma	PROPN
ejpam-3526	131	20	2	2	NUM
ejpam-3526	131	21	.	.	PUNCT
ejpam-3526	132	1	let	let	VERB
ejpam-3526	132	2	xd	xd	INTJ
ejpam-3526	132	3	be	be	AUX
ejpam-3526	132	4	a	a	DET
ejpam-3526	132	5	dual	dual	ADJ
ejpam-3526	132	6	b	b	NOUN
ejpam-3526	132	7	-	-	PUNCT
ejpam-3526	132	8	algebra	algebra	NOUN
ejpam-3526	132	9	.	.	PUNCT
ejpam-3526	133	1	then	then	ADV
ejpam-3526	133	2	for	for	ADP
ejpam-3526	133	3	any	any	DET
ejpam-3526	133	4	x	x	NOUN
ejpam-3526	133	5	,	,	PUNCT
ejpam-3526	133	6	y	y	PROPN
ejpam-3526	133	7	,	,	PUNCT
ejpam-3526	133	8	z	z	VERB
ejpam-3526	133	9	in	in	ADP
ejpam-3526	133	10	xd	xd	ADP
ejpam-3526	133	11	,	,	PUNCT
ejpam-3526	133	12	we	we	PRON
ejpam-3526	133	13	have	have	VERB
ejpam-3526	133	14	(	(	PUNCT
ejpam-3526	133	15	i	i	NOUN
ejpam-3526	133	16	)	)	PUNCT
ejpam-3526	133	17	x	x	VERB
ejpam-3526	134	1	◦	◦	NOUN
ejpam-3526	134	2	y	y	NOUN
ejpam-3526	134	3	=	=	PUNCT
ejpam-3526	135	1	[	[	X
ejpam-3526	135	2	(	(	PUNCT
ejpam-3526	135	3	x	x	SYM
ejpam-3526	135	4	◦	◦	NOUN
ejpam-3526	135	5	1	1	NUM
ejpam-3526	135	6	)	)	PUNCT
ejpam-3526	135	7	◦	◦	NOUN
ejpam-3526	135	8	1	1	NUM
ejpam-3526	135	9	]	]	X
ejpam-3526	135	10	◦	◦	NOUN
ejpam-3526	135	11	y	y	PROPN
ejpam-3526	135	12	(	(	PUNCT
ejpam-3526	135	13	vi	vi	PROPN
ejpam-3526	135	14	)	)	PUNCT
ejpam-3526	135	15	x	x	SYM
ejpam-3526	135	16	◦	◦	NOUN
ejpam-3526	135	17	1	1	NUM
ejpam-3526	135	18	=	=	SYM
ejpam-3526	135	19	y	y	PROPN
ejpam-3526	135	20	◦	◦	NOUN
ejpam-3526	135	21	1	1	NUM
ejpam-3526	135	22	implies	imply	VERB
ejpam-3526	135	23	x	x	PUNCT
ejpam-3526	135	24	=	=	SYM
ejpam-3526	135	25	y	y	PROPN
ejpam-3526	135	26	(	(	PUNCT
ejpam-3526	135	27	ii	ii	PROPN
ejpam-3526	135	28	)	)	PUNCT
ejpam-3526	135	29	(	(	PUNCT
ejpam-3526	135	30	x	x	X
ejpam-3526	135	31	◦	◦	NOUN
ejpam-3526	135	32	1	1	NUM
ejpam-3526	135	33	)	)	PUNCT
ejpam-3526	135	34	◦	◦	NOUN
ejpam-3526	135	35	(	(	PUNCT
ejpam-3526	135	36	x	x	PART
ejpam-3526	135	37	◦	◦	VERB
ejpam-3526	135	38	y	y	NOUN
ejpam-3526	135	39	)	)	PUNCT
ejpam-3526	136	1	=	=	SYM
ejpam-3526	136	2	y	y	PROPN
ejpam-3526	136	3	(	(	PUNCT
ejpam-3526	136	4	vii	vii	PROPN
ejpam-3526	136	5	)	)	PUNCT
ejpam-3526	136	6	x	x	X
ejpam-3526	136	7	=	=	PRON
ejpam-3526	136	8	(	(	PUNCT
ejpam-3526	136	9	x	x	SYM
ejpam-3526	136	10	◦	◦	NOUN
ejpam-3526	136	11	1	1	NUM
ejpam-3526	136	12	)	)	PUNCT
ejpam-3526	136	13	◦	◦	NOUN
ejpam-3526	136	14	1	1	NUM
ejpam-3526	136	15	(	(	PUNCT
ejpam-3526	136	16	iii	iii	NOUN
ejpam-3526	136	17	)	)	PUNCT
ejpam-3526	136	18	(	(	PUNCT
ejpam-3526	136	19	y	y	PROPN
ejpam-3526	136	20	◦	◦	PROPN
ejpam-3526	136	21	z	z	PROPN
ejpam-3526	136	22	)	)	PUNCT
ejpam-3526	136	23	◦	◦	NOUN
ejpam-3526	136	24	x	x	SYM
ejpam-3526	136	25	=	=	PUNCT
ejpam-3526	136	26	z	z	X
ejpam-3526	136	27	◦	◦	NOUN
ejpam-3526	137	1	[	[	X
ejpam-3526	137	2	(	(	PUNCT
ejpam-3526	137	3	y	y	NOUN
ejpam-3526	137	4	◦	◦	NOUN
ejpam-3526	137	5	1	1	NUM
ejpam-3526	137	6	)	)	PUNCT
ejpam-3526	137	7	◦	◦	NOUN
ejpam-3526	137	8	x	x	X
ejpam-3526	137	9	]	]	X
ejpam-3526	137	10	(	(	PUNCT
ejpam-3526	137	11	viii	viii	NOUN
ejpam-3526	137	12	)	)	PUNCT
ejpam-3526	137	13	(	(	PUNCT
ejpam-3526	137	14	y	y	PROPN
ejpam-3526	137	15	◦	◦	NOUN
ejpam-3526	137	16	x	x	NOUN
ejpam-3526	137	17	)	)	PUNCT
ejpam-3526	137	18	◦	◦	NOUN
ejpam-3526	137	19	(	(	PUNCT
ejpam-3526	137	20	y	y	NOUN
ejpam-3526	137	21	◦	◦	NOUN
ejpam-3526	137	22	1	1	NUM
ejpam-3526	137	23	)	)	PUNCT
ejpam-3526	137	24	=	=	SYM
ejpam-3526	137	25	x	x	PUNCT
ejpam-3526	137	26	◦	◦	NOUN
ejpam-3526	137	27	1	1	NUM
ejpam-3526	137	28	(	(	PUNCT
ejpam-3526	137	29	iv	iv	X
ejpam-3526	137	30	)	)	PUNCT
ejpam-3526	137	31	z	z	NOUN
ejpam-3526	137	32	◦	◦	NOUN
ejpam-3526	137	33	x	x	X
ejpam-3526	137	34	=	=	SYM
ejpam-3526	137	35	z	z	X
ejpam-3526	137	36	◦	◦	NOUN
ejpam-3526	137	37	y	y	PROPN
ejpam-3526	137	38	implies	imply	VERB
ejpam-3526	137	39	x	x	PUNCT
ejpam-3526	137	40	=	=	SYM
ejpam-3526	137	41	y	y	PROPN
ejpam-3526	137	42	(	(	PUNCT
ejpam-3526	137	43	ix	ix	PROPN
ejpam-3526	137	44	)	)	PUNCT
ejpam-3526	137	45	x	x	PUNCT
ejpam-3526	138	1	◦	◦	NOUN
ejpam-3526	138	2	[	[	X
ejpam-3526	138	3	(	(	PUNCT
ejpam-3526	138	4	x	x	SYM
ejpam-3526	138	5	◦	◦	NOUN
ejpam-3526	138	6	1	1	NUM
ejpam-3526	138	7	)	)	PUNCT
ejpam-3526	138	8	◦	◦	NOUN
ejpam-3526	138	9	x	x	X
ejpam-3526	138	10	]	]	X
ejpam-3526	138	11	=	=	PUNCT
ejpam-3526	138	12	x	x	SYM
ejpam-3526	138	13	(	(	PUNCT
ejpam-3526	138	14	v	v	NOUN
ejpam-3526	138	15	)	)	PUNCT
ejpam-3526	138	16	x	x	VERB
ejpam-3526	138	17	◦	◦	NOUN
ejpam-3526	138	18	y	y	NOUN
ejpam-3526	138	19	=	=	SYM
ejpam-3526	138	20	1	1	NUM
ejpam-3526	138	21	implies	imply	VERB
ejpam-3526	138	22	x	x	PUNCT
ejpam-3526	138	23	=	=	SYM
ejpam-3526	138	24	y	y	PROPN
ejpam-3526	138	25	(	(	PUNCT
ejpam-3526	138	26	x	x	X
ejpam-3526	138	27	)	)	PUNCT
ejpam-3526	138	28	x	x	VERB
ejpam-3526	138	29	◦	◦	NOUN
ejpam-3526	138	30	y	y	NOUN
ejpam-3526	138	31	=	=	SYM
ejpam-3526	138	32	1	1	NUM
ejpam-3526	138	33	implies	imply	VERB
ejpam-3526	138	34	(	(	PUNCT
ejpam-3526	138	35	x	x	SYM
ejpam-3526	138	36	◦	◦	NOUN
ejpam-3526	138	37	z	z	NOUN
ejpam-3526	138	38	)	)	PUNCT
ejpam-3526	138	39	◦	◦	NOUN
ejpam-3526	138	40	(	(	PUNCT
ejpam-3526	138	41	y	y	PROPN
ejpam-3526	138	42	◦	◦	PROPN
ejpam-3526	138	43	z	z	PROPN
ejpam-3526	138	44	)	)	PUNCT
ejpam-3526	138	45	=	=	SYM
ejpam-3526	138	46	1	1	X
ejpam-3526	138	47	.	.	X
ejpam-3526	139	1	proof	proof	NOUN
ejpam-3526	139	2	:	:	PUNCT
ejpam-3526	139	3	let	let	VERB
ejpam-3526	139	4	xd	xd	INTJ
ejpam-3526	139	5	be	be	AUX
ejpam-3526	139	6	a	a	DET
ejpam-3526	139	7	dual	dual	ADJ
ejpam-3526	139	8	b	b	NOUN
ejpam-3526	139	9	-	-	PUNCT
ejpam-3526	139	10	algebra	algebra	NOUN
ejpam-3526	139	11	and	and	CCONJ
ejpam-3526	139	12	x	x	NOUN
ejpam-3526	139	13	,	,	PUNCT
ejpam-3526	139	14	y	y	PROPN
ejpam-3526	139	15	,	,	PUNCT
ejpam-3526	139	16	z	z	PROPN
ejpam-3526	139	17	∈	∈	PROPN
ejpam-3526	140	1	xd	xd	INTJ
ejpam-3526	140	2	.	.	PUNCT
ejpam-3526	141	1	(	(	PUNCT
ejpam-3526	141	2	i	i	NOUN
ejpam-3526	141	3	)	)	PUNCT
ejpam-3526	141	4	by	by	ADP
ejpam-3526	141	5	(	(	PUNCT
ejpam-3526	141	6	db2	db2	PROPN
ejpam-3526	141	7	)	)	PUNCT
ejpam-3526	141	8	and	and	CCONJ
ejpam-3526	141	9	(	(	PUNCT
ejpam-3526	141	10	db3	db3	PROPN
ejpam-3526	141	11	)	)	PUNCT
ejpam-3526	141	12	,	,	PUNCT
ejpam-3526	141	13	x	x	PUNCT
ejpam-3526	141	14	◦	◦	VERB
ejpam-3526	141	15	y	y	NOUN
ejpam-3526	141	16	=	=	SYM
ejpam-3526	141	17	1	1	NUM
ejpam-3526	141	18	◦	◦	NOUN
ejpam-3526	141	19	(	(	PUNCT
ejpam-3526	141	20	x	x	PART
ejpam-3526	141	21	◦	◦	VERB
ejpam-3526	141	22	y	y	NOUN
ejpam-3526	141	23	)	)	PUNCT
ejpam-3526	142	1	=	=	PUNCT
ejpam-3526	143	1	[	[	X
ejpam-3526	143	2	(	(	PUNCT
ejpam-3526	143	3	x	x	SYM
ejpam-3526	143	4	◦	◦	NOUN
ejpam-3526	143	5	1	1	NUM
ejpam-3526	143	6	)	)	PUNCT
ejpam-3526	143	7	◦	◦	NOUN
ejpam-3526	143	8	1	1	NUM
ejpam-3526	143	9	]	]	X
ejpam-3526	143	10	◦	◦	NOUN
ejpam-3526	143	11	y.	y.	PROPN
ejpam-3526	143	12	(	(	PUNCT
ejpam-3526	143	13	ii	ii	PROPN
ejpam-3526	143	14	)	)	PUNCT
ejpam-3526	143	15	by	by	ADP
ejpam-3526	143	16	(	(	PUNCT
ejpam-3526	143	17	db3	db3	PROPN
ejpam-3526	143	18	)	)	PUNCT
ejpam-3526	143	19	,	,	PUNCT
ejpam-3526	143	20	(	(	PUNCT
ejpam-3526	143	21	db1	db1	NOUN
ejpam-3526	143	22	)	)	PUNCT
ejpam-3526	143	23	,	,	PUNCT
ejpam-3526	143	24	and	and	CCONJ
ejpam-3526	143	25	(	(	PUNCT
ejpam-3526	143	26	db2	db2	PROPN
ejpam-3526	143	27	)	)	PUNCT
ejpam-3526	143	28	,	,	PUNCT
ejpam-3526	143	29	(	(	PUNCT
ejpam-3526	143	30	x	x	X
ejpam-3526	143	31	◦	◦	NOUN
ejpam-3526	143	32	1	1	NUM
ejpam-3526	143	33	)	)	PUNCT
ejpam-3526	143	34	◦	◦	NOUN
ejpam-3526	143	35	(	(	PUNCT
ejpam-3526	143	36	x	x	PART
ejpam-3526	143	37	◦	◦	VERB
ejpam-3526	143	38	y	y	NOUN
ejpam-3526	143	39	)	)	PUNCT
ejpam-3526	143	40	=	=	PUNCT
ejpam-3526	144	1	[	[	X
ejpam-3526	144	2	(	(	PUNCT
ejpam-3526	144	3	x	x	SYM
ejpam-3526	144	4	◦	◦	NOUN
ejpam-3526	144	5	1	1	NUM
ejpam-3526	144	6	)	)	PUNCT
ejpam-3526	144	7	◦	◦	NOUN
ejpam-3526	144	8	(	(	PUNCT
ejpam-3526	144	9	x	x	X
ejpam-3526	144	10	◦	◦	NOUN
ejpam-3526	144	11	1	1	NUM
ejpam-3526	144	12	)	)	PUNCT
ejpam-3526	144	13	]	]	PUNCT
ejpam-3526	145	1	◦	◦	NOUN
ejpam-3526	145	2	y	y	NOUN
ejpam-3526	145	3	=	=	SYM
ejpam-3526	145	4	1	1	NUM
ejpam-3526	145	5	◦	◦	NOUN
ejpam-3526	145	6	y	y	PROPN
ejpam-3526	145	7	=	=	PUNCT
ejpam-3526	145	8	y.	y.	PROPN
ejpam-3526	145	9	(	(	PUNCT
ejpam-3526	145	10	iii	iii	NOUN
ejpam-3526	145	11	)	)	PUNCT
ejpam-3526	145	12	by	by	ADP
ejpam-3526	145	13	(	(	PUNCT
ejpam-3526	145	14	i	i	NOUN
ejpam-3526	145	15	)	)	PUNCT
ejpam-3526	145	16	and	and	CCONJ
ejpam-3526	145	17	(	(	PUNCT
ejpam-3526	145	18	db3	db3	PROPN
ejpam-3526	145	19	)	)	PUNCT
ejpam-3526	145	20	,	,	PUNCT
ejpam-3526	145	21	(	(	PUNCT
ejpam-3526	145	22	y	y	PROPN
ejpam-3526	145	23	◦	◦	PROPN
ejpam-3526	145	24	z	z	PROPN
ejpam-3526	145	25	)	)	PUNCT
ejpam-3526	145	26	◦	◦	NOUN
ejpam-3526	145	27	x	x	SYM
ejpam-3526	146	1	=	=	PUNCT
ejpam-3526	146	2	[	[	PUNCT
ejpam-3526	146	3	(	(	PUNCT
ejpam-3526	146	4	(	(	PUNCT
ejpam-3526	146	5	y	y	NOUN
ejpam-3526	146	6	◦	◦	NOUN
ejpam-3526	146	7	1	1	NUM
ejpam-3526	146	8	)	)	PUNCT
ejpam-3526	146	9	◦	◦	NOUN
ejpam-3526	146	10	1	1	NUM
ejpam-3526	146	11	)	)	PUNCT
ejpam-3526	146	12	◦	◦	NOUN
ejpam-3526	146	13	z	z	NOUN
ejpam-3526	146	14	]	]	PUNCT
ejpam-3526	147	1	◦	◦	NOUN
ejpam-3526	147	2	x	x	SYM
ejpam-3526	147	3	=	=	PUNCT
ejpam-3526	148	1	z	z	AUX
ejpam-3526	148	2	◦	◦	NOUN
ejpam-3526	148	3	[	[	X
ejpam-3526	148	4	(	(	PUNCT
ejpam-3526	148	5	y	y	NOUN
ejpam-3526	148	6	◦	◦	NOUN
ejpam-3526	148	7	1	1	NUM
ejpam-3526	148	8	)	)	PUNCT
ejpam-3526	148	9	◦	◦	NOUN
ejpam-3526	148	10	x	x	SYM
ejpam-3526	148	11	]	]	X
ejpam-3526	148	12	.	.	PUNCT
ejpam-3526	149	1	(	(	PUNCT
ejpam-3526	149	2	iv	iv	X
ejpam-3526	149	3	)	)	PUNCT
ejpam-3526	149	4	suppose	suppose	VERB
ejpam-3526	149	5	z	z	NOUN
ejpam-3526	149	6	◦	◦	NOUN
ejpam-3526	149	7	x	x	X
ejpam-3526	150	1	=	=	SYM
ejpam-3526	150	2	z	z	AUX
ejpam-3526	150	3	◦	◦	NOUN
ejpam-3526	150	4	y.	y.	NOUN
ejpam-3526	150	5	then	then	ADV
ejpam-3526	151	1	(	(	PUNCT
ejpam-3526	151	2	z	z	NOUN
ejpam-3526	151	3	◦	◦	NOUN
ejpam-3526	151	4	1	1	NUM
ejpam-3526	151	5	)	)	PUNCT
ejpam-3526	151	6	◦	◦	NOUN
ejpam-3526	151	7	(	(	PUNCT
ejpam-3526	151	8	z	z	NOUN
ejpam-3526	151	9	◦	◦	NOUN
ejpam-3526	151	10	x	x	X
ejpam-3526	151	11	)	)	PUNCT
ejpam-3526	151	12	=	=	SYM
ejpam-3526	152	1	(	(	PUNCT
ejpam-3526	152	2	z	z	NOUN
ejpam-3526	152	3	◦	◦	NOUN
ejpam-3526	152	4	1	1	NUM
ejpam-3526	152	5	)	)	PUNCT
ejpam-3526	152	6	◦	◦	NOUN
ejpam-3526	152	7	(	(	PUNCT
ejpam-3526	152	8	z	z	AUX
ejpam-3526	152	9	◦	◦	NOUN
ejpam-3526	152	10	y	y	NOUN
ejpam-3526	152	11	)	)	PUNCT
ejpam-3526	152	12	implies	imply	VERB
ejpam-3526	152	13	x	x	PUNCT
ejpam-3526	152	14	=	=	SYM
ejpam-3526	152	15	y	y	PROPN
ejpam-3526	152	16	by	by	ADP
ejpam-3526	152	17	(	(	PUNCT
ejpam-3526	152	18	ii	ii	NOUN
ejpam-3526	152	19	)	)	PUNCT
ejpam-3526	152	20	.	.	PUNCT
ejpam-3526	153	1	(	(	PUNCT
ejpam-3526	153	2	v	v	NOUN
ejpam-3526	153	3	)	)	PUNCT
ejpam-3526	153	4	suppose	suppose	VERB
ejpam-3526	153	5	x	x	PUNCT
ejpam-3526	153	6	◦	◦	VERB
ejpam-3526	153	7	y	y	NOUN
ejpam-3526	153	8	=	=	ADJ
ejpam-3526	153	9	1	1	X
ejpam-3526	153	10	.	.	PUNCT
ejpam-3526	153	11	by	by	ADP
ejpam-3526	153	12	(	(	PUNCT
ejpam-3526	153	13	db1	db1	NOUN
ejpam-3526	153	14	)	)	PUNCT
ejpam-3526	153	15	and	and	CCONJ
ejpam-3526	153	16	(	(	PUNCT
ejpam-3526	153	17	iv	iv	X
ejpam-3526	153	18	)	)	PUNCT
ejpam-3526	153	19	,	,	PUNCT
ejpam-3526	153	20	we	we	PRON
ejpam-3526	153	21	get	get	VERB
ejpam-3526	153	22	x	x	VERB
ejpam-3526	153	23	◦	◦	NOUN
ejpam-3526	153	24	y	y	NOUN
ejpam-3526	153	25	=	=	PUNCT
ejpam-3526	153	26	x	x	PUNCT
ejpam-3526	153	27	◦	◦	NOUN
ejpam-3526	153	28	x	x	SYM
ejpam-3526	153	29	implying	imply	VERB
ejpam-3526	153	30	x	x	X
ejpam-3526	153	31	=	=	SYM
ejpam-3526	153	32	y.	y.	NOUN
ejpam-3526	153	33	(	(	PUNCT
ejpam-3526	153	34	vi	vi	NOUN
ejpam-3526	153	35	)	)	PUNCT
ejpam-3526	153	36	suppose	suppose	VERB
ejpam-3526	153	37	x	x	X
ejpam-3526	153	38	◦	◦	NOUN
ejpam-3526	153	39	1	1	NUM
ejpam-3526	153	40	=	=	SYM
ejpam-3526	153	41	y◦1.by	y◦1.by	PROPN
ejpam-3526	153	42	(	(	PUNCT
ejpam-3526	153	43	db1	db1	NOUN
ejpam-3526	153	44	)	)	PUNCT
ejpam-3526	153	45	,	,	PUNCT
ejpam-3526	153	46	(	(	PUNCT
ejpam-3526	153	47	db2),(db3	db2),(db3	NOUN
ejpam-3526	153	48	)	)	PUNCT
ejpam-3526	153	49	,	,	PUNCT
ejpam-3526	153	50	and	and	CCONJ
ejpam-3526	153	51	(	(	PUNCT
ejpam-3526	153	52	i	i	NOUN
ejpam-3526	153	53	)	)	PUNCT
ejpam-3526	153	54	we	we	PRON
ejpam-3526	153	55	have	have	VERB
ejpam-3526	153	56	1	1	NUM
ejpam-3526	153	57	=	=	SYM
ejpam-3526	153	58	x	x	SYM
ejpam-3526	153	59	◦	◦	NOUN
ejpam-3526	153	60	x	x	SYM
ejpam-3526	153	61	=	=	SYM
ejpam-3526	153	62	1	1	NUM
ejpam-3526	153	63	◦	◦	NOUN
ejpam-3526	153	64	(x	(x	PROPN
ejpam-3526	153	65	◦	◦	NOUN
ejpam-3526	153	66	x	x	NOUN
ejpam-3526	153	67	)	)	PUNCT
ejpam-3526	153	68	=	=	PUNCT
ejpam-3526	154	1	[	[	X
ejpam-3526	154	2	(	(	PUNCT
ejpam-3526	154	3	x	x	SYM
ejpam-3526	154	4	◦	◦	NOUN
ejpam-3526	154	5	1	1	NUM
ejpam-3526	154	6	)	)	PUNCT
ejpam-3526	154	7	◦	◦	NOUN
ejpam-3526	154	8	1	1	NUM
ejpam-3526	154	9	]	]	X
ejpam-3526	154	10	◦	◦	NOUN
ejpam-3526	154	11	x	x	X
ejpam-3526	154	12	=	=	PUNCT
ejpam-3526	155	1	[	[	X
ejpam-3526	155	2	(	(	PUNCT
ejpam-3526	155	3	y	y	NOUN
ejpam-3526	155	4	◦	◦	NOUN
ejpam-3526	155	5	1	1	NUM
ejpam-3526	155	6	)	)	PUNCT
ejpam-3526	155	7	◦	◦	NOUN
ejpam-3526	155	8	1	1	NUM
ejpam-3526	155	9	]	]	X
ejpam-3526	155	10	◦	◦	NOUN
ejpam-3526	155	11	x	x	X
ejpam-3526	155	12	=	=	PUNCT
ejpam-3526	155	13	y	y	PROPN
ejpam-3526	155	14	◦	◦	NOUN
ejpam-3526	155	15	x.	x.	NOUN
ejpam-3526	155	16	hence	hence	ADV
ejpam-3526	155	17	,	,	PUNCT
ejpam-3526	155	18	y	y	PROPN
ejpam-3526	155	19	=	=	PUNCT
ejpam-3526	155	20	x	x	PUNCT
ejpam-3526	155	21	by	by	ADP
ejpam-3526	155	22	(	(	PUNCT
ejpam-3526	155	23	v	v	NOUN
ejpam-3526	155	24	)	)	PUNCT
ejpam-3526	155	25	.	.	PUNCT
ejpam-3526	156	1	(	(	PUNCT
ejpam-3526	156	2	vii	vii	PROPN
ejpam-3526	156	3	)	)	PUNCT
ejpam-3526	156	4	by	by	ADP
ejpam-3526	156	5	(	(	PUNCT
ejpam-3526	156	6	db2	db2	PROPN
ejpam-3526	156	7	)	)	PUNCT
ejpam-3526	156	8	,	,	PUNCT
ejpam-3526	156	9	(	(	PUNCT
ejpam-3526	156	10	db3	db3	PROPN
ejpam-3526	156	11	)	)	PUNCT
ejpam-3526	156	12	,	,	PUNCT
ejpam-3526	156	13	and	and	CCONJ
ejpam-3526	156	14	(	(	PUNCT
ejpam-3526	156	15	vi	vi	NOUN
ejpam-3526	156	16	)	)	PUNCT
ejpam-3526	156	17	,	,	PUNCT
ejpam-3526	156	18	x	x	SYM
ejpam-3526	156	19	◦	◦	NOUN
ejpam-3526	156	20	1	1	NUM
ejpam-3526	156	21	=	=	SYM
ejpam-3526	156	22	1	1	NUM
ejpam-3526	156	23	◦	◦	NOUN
ejpam-3526	156	24	(x	(x	NOUN
ejpam-3526	156	25	◦	◦	NOUN
ejpam-3526	156	26	1	1	NUM
ejpam-3526	156	27	)	)	PUNCT
ejpam-3526	156	28	=	=	PUNCT
ejpam-3526	157	1	[	[	X
ejpam-3526	157	2	(	(	PUNCT
ejpam-3526	157	3	x	x	NOUN
ejpam-3526	157	4	◦	◦	NOUN
ejpam-3526	157	5	1)	1)	NUM
ejpam-3526	157	6	◦	◦	NOUN
ejpam-3526	157	7	1]	1]	NUM
ejpam-3526	157	8	◦	◦	NOUN
ejpam-3526	157	9	1	1	NUM
ejpam-3526	157	10	implies	imply	VERB
ejpam-3526	157	11	that	that	SCONJ
ejpam-3526	157	12	x	x	SYM
ejpam-3526	157	13	=	=	SYM
ejpam-3526	157	14	(	(	PUNCT
ejpam-3526	157	15	x	x	PART
ejpam-3526	157	16	◦	◦	NOUN
ejpam-3526	157	17	1)	1)	NUM
ejpam-3526	157	18	◦	◦	NOUN
ejpam-3526	157	19	1	1	NUM
ejpam-3526	157	20	.	.	PUNCT
ejpam-3526	158	1	(	(	PUNCT
ejpam-3526	158	2	viii	viii	NOUN
ejpam-3526	158	3	)	)	PUNCT
ejpam-3526	158	4	by	by	ADP
ejpam-3526	158	5	(	(	PUNCT
ejpam-3526	158	6	iii	iii	NOUN
ejpam-3526	158	7	)	)	PUNCT
ejpam-3526	158	8	and	and	CCONJ
ejpam-3526	158	9	(	(	PUNCT
ejpam-3526	158	10	db1	db1	NOUN
ejpam-3526	158	11	)	)	PUNCT
ejpam-3526	158	12	,	,	PUNCT
ejpam-3526	158	13	(	(	PUNCT
ejpam-3526	158	14	y	y	PROPN
ejpam-3526	158	15	◦	◦	NOUN
ejpam-3526	158	16	x	x	NOUN
ejpam-3526	158	17	)	)	PUNCT
ejpam-3526	158	18	◦	◦	NOUN
ejpam-3526	158	19	(	(	PUNCT
ejpam-3526	158	20	y	y	NOUN
ejpam-3526	158	21	◦	◦	NOUN
ejpam-3526	158	22	1	1	NUM
ejpam-3526	158	23	)	)	PUNCT
ejpam-3526	158	24	=	=	SYM
ejpam-3526	159	1	x	x	PUNCT
ejpam-3526	159	2	◦	◦	NOUN
ejpam-3526	159	3	[	[	X
ejpam-3526	159	4	(	(	PUNCT
ejpam-3526	159	5	y	y	NOUN
ejpam-3526	159	6	◦	◦	NOUN
ejpam-3526	159	7	1	1	NUM
ejpam-3526	159	8	)	)	PUNCT
ejpam-3526	159	9	◦	◦	NOUN
ejpam-3526	159	10	(	(	PUNCT
ejpam-3526	159	11	y	y	NOUN
ejpam-3526	159	12	◦	◦	NOUN
ejpam-3526	159	13	1	1	NUM
ejpam-3526	159	14	)	)	PUNCT
ejpam-3526	159	15	]	]	PUNCT
ejpam-3526	160	1	=	=	PUNCT
ejpam-3526	160	2	x	x	PUNCT
ejpam-3526	160	3	◦	◦	NOUN
ejpam-3526	160	4	1	1	NUM
ejpam-3526	160	5	.	.	PUNCT
ejpam-3526	160	6	(	(	PUNCT
ejpam-3526	160	7	ix	ix	ADV
ejpam-3526	160	8	)	)	PUNCT
ejpam-3526	160	9	take	take	VERB
ejpam-3526	160	10	y	y	NOUN
ejpam-3526	160	11	=	=	PUNCT
ejpam-3526	160	12	z	z	NOUN
ejpam-3526	160	13	=	=	PUNCT
ejpam-3526	160	14	x	x	X
ejpam-3526	160	15	in	in	ADP
ejpam-3526	160	16	(	(	PUNCT
ejpam-3526	160	17	iii	iii	NOUN
ejpam-3526	160	18	)	)	PUNCT
ejpam-3526	160	19	.	.	PUNCT
ejpam-3526	161	1	then	then	ADV
ejpam-3526	161	2	apply	apply	VERB
ejpam-3526	161	3	(	(	PUNCT
ejpam-3526	161	4	db1	db1	NOUN
ejpam-3526	161	5	)	)	PUNCT
ejpam-3526	161	6	and	and	CCONJ
ejpam-3526	161	7	(	(	PUNCT
ejpam-3526	161	8	db2	db2	PROPN
ejpam-3526	161	9	)	)	PUNCT
ejpam-3526	161	10	.	.	PUNCT
ejpam-3526	162	1	(	(	PUNCT
ejpam-3526	162	2	x	x	X
ejpam-3526	162	3	)	)	PUNCT
ejpam-3526	162	4	by	by	ADP
ejpam-3526	162	5	(	(	PUNCT
ejpam-3526	162	6	v	v	NOUN
ejpam-3526	162	7	)	)	PUNCT
ejpam-3526	162	8	,	,	PUNCT
ejpam-3526	162	9	x	x	X
ejpam-3526	162	10	◦	◦	NOUN
ejpam-3526	162	11	y	y	NOUN
ejpam-3526	162	12	=	=	SYM
ejpam-3526	162	13	1	1	NUM
ejpam-3526	162	14	implies	imply	VERB
ejpam-3526	162	15	x	x	PUNCT
ejpam-3526	162	16	=	=	PUNCT
ejpam-3526	162	17	y.	y.	NOUN
ejpam-3526	162	18	hence	hence	ADV
ejpam-3526	162	19	by	by	ADP
ejpam-3526	162	20	(	(	PUNCT
ejpam-3526	162	21	db1	db1	NOUN
ejpam-3526	162	22	)	)	PUNCT
ejpam-3526	162	23	,	,	PUNCT
ejpam-3526	162	24	(	(	PUNCT
ejpam-3526	162	25	x	x	X
ejpam-3526	162	26	◦	◦	NOUN
ejpam-3526	162	27	z)	z)	NUM
ejpam-3526	162	28	◦	◦	NOUN
ejpam-3526	162	29	(y	(y	NOUN
ejpam-3526	162	30	◦	◦	NOUN
ejpam-3526	162	31	z	z	NOUN
ejpam-3526	162	32	)	)	PUNCT
ejpam-3526	162	33	=	=	SYM
ejpam-3526	162	34	(	(	PUNCT
ejpam-3526	162	35	x	x	X
ejpam-3526	162	36	◦	◦	NOUN
ejpam-3526	162	37	z)	z)	NUM
ejpam-3526	162	38	◦	◦	ADJ
ejpam-3526	162	39	(x	(x	NOUN
ejpam-3526	162	40	◦	◦	NOUN
ejpam-3526	162	41	z	z	NOUN
ejpam-3526	162	42	)	)	PUNCT
ejpam-3526	162	43	=	=	SYM
ejpam-3526	163	1	1	1	X
ejpam-3526	163	2	.	.	PUNCT
ejpam-3526	164	1	the	the	DET
ejpam-3526	164	2	following	follow	VERB
ejpam-3526	164	3	theorem	theorem	NOUN
ejpam-3526	164	4	is	be	AUX
ejpam-3526	164	5	a	a	DET
ejpam-3526	164	6	characterization	characterization	NOUN
ejpam-3526	164	7	of	of	ADP
ejpam-3526	164	8	a	a	DET
ejpam-3526	164	9	dual	dual	ADJ
ejpam-3526	164	10	b	b	NOUN
ejpam-3526	164	11	-	-	PUNCT
ejpam-3526	164	12	algebra	algebra	NOUN
ejpam-3526	164	13	given	give	VERB
ejpam-3526	164	14	any	any	DET
ejpam-3526	164	15	algebra	algebra	NOUN
ejpam-3526	164	16	with	with	ADP
ejpam-3526	164	17	a	a	DET
ejpam-3526	164	18	binary	binary	ADJ
ejpam-3526	164	19	operation	operation	NOUN
ejpam-3526	164	20	and	and	CCONJ
ejpam-3526	164	21	a	a	DET
ejpam-3526	164	22	constant	constant	ADJ
ejpam-3526	164	23	element	element	NOUN
ejpam-3526	164	24	.	.	PUNCT
ejpam-3526	165	1	theorem	theorem	NOUN
ejpam-3526	165	2	3	3	X
ejpam-3526	165	3	.	.	PUNCT
ejpam-3526	166	1	let	let	VERB
ejpam-3526	166	2	x	x	PUNCT
ejpam-3526	166	3	=	=	PUNCT
ejpam-3526	166	4	(	(	PUNCT
ejpam-3526	166	5	x	x	NOUN
ejpam-3526	166	6	,	,	PUNCT
ejpam-3526	166	7	◦	◦	NOUN
ejpam-3526	166	8	,	,	PUNCT
ejpam-3526	166	9	1	1	NUM
ejpam-3526	166	10	)	)	PUNCT
ejpam-3526	166	11	be	be	AUX
ejpam-3526	166	12	any	any	DET
ejpam-3526	166	13	algebra	algebra	NOUN
ejpam-3526	166	14	of	of	ADP
ejpam-3526	166	15	type	type	NOUN
ejpam-3526	166	16	(	(	PUNCT
ejpam-3526	166	17	2	2	NUM
ejpam-3526	166	18	,	,	PUNCT
ejpam-3526	166	19	0	0	NUM
ejpam-3526	166	20	)	)	PUNCT
ejpam-3526	166	21	.	.	PUNCT
ejpam-3526	167	1	then	then	ADV
ejpam-3526	167	2	x	x	PRON
ejpam-3526	167	3	is	be	AUX
ejpam-3526	167	4	a	a	DET
ejpam-3526	167	5	dual	dual	ADJ
ejpam-3526	167	6	b	b	NOUN
ejpam-3526	167	7	-	-	PUNCT
ejpam-3526	167	8	algebra	algebra	NOUN
ejpam-3526	167	9	if	if	SCONJ
ejpam-3526	167	10	and	and	CCONJ
ejpam-3526	167	11	only	only	ADV
ejpam-3526	167	12	if	if	SCONJ
ejpam-3526	167	13	for	for	ADP
ejpam-3526	167	14	any	any	DET
ejpam-3526	167	15	x	x	NOUN
ejpam-3526	167	16	,	,	PUNCT
ejpam-3526	167	17	y	y	PROPN
ejpam-3526	167	18	,	,	PUNCT
ejpam-3526	167	19	z	z	NOUN
ejpam-3526	167	20	in	in	ADP
ejpam-3526	167	21	x	x	PRON
ejpam-3526	167	22	,	,	PUNCT
ejpam-3526	167	23	(	(	PUNCT
ejpam-3526	167	24	i	i	NOUN
ejpam-3526	167	25	)	)	PUNCT
ejpam-3526	167	26	x	x	PUNCT
ejpam-3526	168	1	◦	◦	NOUN
ejpam-3526	168	2	x	x	SYM
ejpam-3526	168	3	=	=	NOUN
ejpam-3526	168	4	1	1	NUM
ejpam-3526	168	5	;	;	PUNCT
ejpam-3526	168	6	(	(	PUNCT
ejpam-3526	168	7	ii	ii	NOUN
ejpam-3526	168	8	)	)	PUNCT
ejpam-3526	168	9	x	x	X
ejpam-3526	169	1	=	=	PRON
ejpam-3526	169	2	(	(	PUNCT
ejpam-3526	169	3	x	x	SYM
ejpam-3526	169	4	◦	◦	NOUN
ejpam-3526	169	5	1	1	NUM
ejpam-3526	169	6	)	)	PUNCT
ejpam-3526	169	7	◦	◦	NOUN
ejpam-3526	169	8	1	1	NUM
ejpam-3526	169	9	;	;	PUNCT
ejpam-3526	169	10	(	(	PUNCT
ejpam-3526	169	11	iii	iii	X
ejpam-3526	169	12	)	)	PUNCT
ejpam-3526	169	13	(	(	PUNCT
ejpam-3526	169	14	x	x	X
ejpam-3526	169	15	◦	◦	VERB
ejpam-3526	169	16	y	y	NOUN
ejpam-3526	169	17	)	)	PUNCT
ejpam-3526	169	18	◦	◦	NOUN
ejpam-3526	169	19	(	(	PUNCT
ejpam-3526	169	20	x	x	PART
ejpam-3526	169	21	◦	◦	NOUN
ejpam-3526	169	22	z	z	NOUN
ejpam-3526	169	23	)	)	PUNCT
ejpam-3526	170	1	=	=	SYM
ejpam-3526	170	2	y	y	PROPN
ejpam-3526	170	3	◦	◦	NOUN
ejpam-3526	170	4	z.	z.	PROPN
ejpam-3526	170	5	proof	proof	NOUN
ejpam-3526	170	6	:	:	PUNCT
ejpam-3526	170	7	suppose	suppose	VERB
ejpam-3526	170	8	x	x	X
ejpam-3526	170	9	=	=	SYM
ejpam-3526	170	10	(	(	PUNCT
ejpam-3526	170	11	x	x	NOUN
ejpam-3526	170	12	,	,	PUNCT
ejpam-3526	170	13	◦	◦	NOUN
ejpam-3526	170	14	,	,	PUNCT
ejpam-3526	170	15	1	1	NUM
ejpam-3526	170	16	)	)	PUNCT
ejpam-3526	170	17	is	be	AUX
ejpam-3526	170	18	a	a	DET
ejpam-3526	170	19	dual	dual	ADJ
ejpam-3526	170	20	b	b	NOUN
ejpam-3526	170	21	-	-	PUNCT
ejpam-3526	170	22	algebra	algebra	NOUN
ejpam-3526	170	23	.	.	PUNCT
ejpam-3526	171	1	then	then	ADV
ejpam-3526	171	2	x	x	X
ejpam-3526	171	3	satisfies	satisfie	NOUN
ejpam-3526	171	4	(	(	PUNCT
ejpam-3526	171	5	db1	db1	NOUN
ejpam-3526	171	6	)	)	PUNCT
ejpam-3526	171	7	and	and	CCONJ
ejpam-3526	171	8	lemma	lemma	PROPN
ejpam-3526	171	9	2(vii	2(vii	PROPN
ejpam-3526	171	10	)	)	PUNCT
ejpam-3526	171	11	.	.	PUNCT
ejpam-3526	172	1	by	by	ADP
ejpam-3526	172	2	(	(	PUNCT
ejpam-3526	172	3	db3	db3	PROPN
ejpam-3526	172	4	)	)	PUNCT
ejpam-3526	172	5	,	,	PUNCT
ejpam-3526	172	6	(	(	PUNCT
ejpam-3526	172	7	db1	db1	NOUN
ejpam-3526	172	8	)	)	PUNCT
ejpam-3526	172	9	,	,	PUNCT
ejpam-3526	172	10	and	and	CCONJ
ejpam-3526	172	11	(	(	PUNCT
ejpam-3526	172	12	db2	db2	PROPN
ejpam-3526	172	13	)	)	PUNCT
ejpam-3526	172	14	,	,	PUNCT
ejpam-3526	172	15	(	(	PUNCT
ejpam-3526	172	16	x	x	X
ejpam-3526	172	17	◦	◦	NOUN
ejpam-3526	172	18	y)	y)	NOUN
ejpam-3526	172	19	◦	◦	ADJ
ejpam-3526	172	20	(x	(x	NOUN
ejpam-3526	172	21	◦	◦	NOUN
ejpam-3526	172	22	z	z	NOUN
ejpam-3526	172	23	)	)	PUNCT
ejpam-3526	172	24	=	=	PUNCT
ejpam-3526	173	1	[	[	X
ejpam-3526	173	2	(	(	PUNCT
ejpam-3526	173	3	x	x	PART
ejpam-3526	173	4	◦	◦	NOUN
ejpam-3526	173	5	1)	1)	NUM
ejpam-3526	173	6	◦	◦	ADJ
ejpam-3526	173	7	(x	(x	NOUN
ejpam-3526	173	8	◦	◦	NOUN
ejpam-3526	173	9	y)]	y)]	NOUN
ejpam-3526	173	10	◦	◦	NOUN
ejpam-3526	173	11	z	z	NOUN
ejpam-3526	173	12	=	=	SYM
ejpam-3526	174	1	[	[	X
ejpam-3526	174	2	(	(	PUNCT
ejpam-3526	174	3	(	(	PUNCT
ejpam-3526	174	4	x	x	NOUN
ejpam-3526	174	5	◦	◦	NOUN
ejpam-3526	174	6	1)	1)	NUM
ejpam-3526	174	7	◦	◦	NOUN
ejpam-3526	174	8	(x	(x	NOUN
ejpam-3526	174	9	◦	◦	NOUN
ejpam-3526	174	10	1	1	NUM
ejpam-3526	174	11	)	)	PUNCT
ejpam-3526	174	12	)	)	PUNCT
ejpam-3526	175	1	◦	◦	VERB
ejpam-3526	175	2	y	y	SYM
ejpam-3526	175	3	]	]	PUNCT
ejpam-3526	175	4	◦	◦	NOUN
ejpam-3526	175	5	z	z	NOUN
ejpam-3526	175	6	=	=	SYM
ejpam-3526	175	7	(	(	PUNCT
ejpam-3526	175	8	1	1	NUM
ejpam-3526	175	9	◦	◦	NOUN
ejpam-3526	175	10	y)	y)	NOUN
ejpam-3526	175	11	◦	◦	NOUN
ejpam-3526	175	12	z	z	NOUN
ejpam-3526	175	13	=	=	SYM
ejpam-3526	175	14	y	y	PROPN
ejpam-3526	175	15	◦	◦	NOUN
ejpam-3526	175	16	z.	z.	PROPN
ejpam-3526	175	17	it	it	PRON
ejpam-3526	175	18	follows	follow	VERB
ejpam-3526	175	19	that	that	SCONJ
ejpam-3526	175	20	x	x	PRON
ejpam-3526	175	21	satisfies	satisfie	NOUN
ejpam-3526	175	22	(	(	PUNCT
ejpam-3526	175	23	i	i	NOUN
ejpam-3526	175	24	)	)	PUNCT
ejpam-3526	175	25	,	,	PUNCT
ejpam-3526	175	26	(	(	PUNCT
ejpam-3526	175	27	ii	ii	NOUN
ejpam-3526	175	28	)	)	PUNCT
ejpam-3526	175	29	,	,	PUNCT
ejpam-3526	175	30	and	and	CCONJ
ejpam-3526	175	31	(	(	PUNCT
ejpam-3526	175	32	iii	iii	NOUN
ejpam-3526	175	33	)	)	PUNCT
ejpam-3526	175	34	.	.	PUNCT
ejpam-3526	176	1	conversely	conversely	ADV
ejpam-3526	176	2	by	by	ADP
ejpam-3526	176	3	(	(	PUNCT
ejpam-3526	176	4	iii	iii	NOUN
ejpam-3526	176	5	)	)	PUNCT
ejpam-3526	176	6	,	,	PUNCT
ejpam-3526	176	7	(	(	PUNCT
ejpam-3526	176	8	i	i	NOUN
ejpam-3526	176	9	)	)	PUNCT
ejpam-3526	176	10	,	,	PUNCT
ejpam-3526	176	11	and	and	CCONJ
ejpam-3526	176	12	(	(	PUNCT
ejpam-3526	176	13	ii	ii	NOUN
ejpam-3526	176	14	)	)	PUNCT
ejpam-3526	176	15	,	,	PUNCT
ejpam-3526	176	16	1	1	NUM
ejpam-3526	176	17	◦	◦	NOUN
ejpam-3526	176	18	x	x	SYM
ejpam-3526	176	19	=	=	SYM
ejpam-3526	176	20	(	(	PUNCT
ejpam-3526	176	21	x	x	PART
ejpam-3526	176	22	◦	◦	NOUN
ejpam-3526	176	23	1)	1)	NUM
ejpam-3526	176	24	◦	◦	ADJ
ejpam-3526	176	25	(x	(x	NOUN
ejpam-3526	176	26	◦	◦	NOUN
ejpam-3526	176	27	x	x	NOUN
ejpam-3526	176	28	)	)	PUNCT
ejpam-3526	176	29	=	=	SYM
ejpam-3526	176	30	(	(	PUNCT
ejpam-3526	176	31	x	x	PART
ejpam-3526	176	32	◦	◦	NOUN
ejpam-3526	176	33	1)	1)	NUM
ejpam-3526	176	34	◦	◦	NOUN
ejpam-3526	176	35	1	1	NUM
ejpam-3526	176	36	=	=	SYM
ejpam-3526	176	37	x.	x.	NOUN
ejpam-3526	176	38	hence	hence	ADV
ejpam-3526	176	39	,	,	PUNCT
ejpam-3526	176	40	x	x	PRON
ejpam-3526	176	41	satisfies	satisfie	NOUN
ejpam-3526	176	42	(	(	PUNCT
ejpam-3526	176	43	db2	db2	PROPN
ejpam-3526	176	44	)	)	PUNCT
ejpam-3526	176	45	.	.	PUNCT
ejpam-3526	177	1	for	for	SCONJ
ejpam-3526	177	2	x	x	SYM
ejpam-3526	177	3	to	to	PART
ejpam-3526	177	4	satisfy	satisfy	VERB
ejpam-3526	177	5	(	(	PUNCT
ejpam-3526	177	6	db3	db3	PROPN
ejpam-3526	177	7	)	)	PUNCT
ejpam-3526	177	8	,	,	PUNCT
ejpam-3526	177	9	we	we	PRON
ejpam-3526	177	10	have	have	VERB
ejpam-3526	177	11	x	x	NOUN
ejpam-3526	177	12	◦	◦	NOUN
ejpam-3526	177	13	(y	(y	NOUN
ejpam-3526	177	14	◦	◦	NOUN
ejpam-3526	177	15	z	z	NOUN
ejpam-3526	177	16	)	)	PUNCT
ejpam-3526	177	17	=	=	PUNCT
ejpam-3526	178	1	[	[	X
ejpam-3526	178	2	(	(	PUNCT
ejpam-3526	178	3	y	y	PROPN
ejpam-3526	178	4	◦	◦	NOUN
ejpam-3526	178	5	1)	1)	NUM
ejpam-3526	178	6	◦	◦	NOUN
ejpam-3526	178	7	x	x	NOUN
ejpam-3526	178	8	]	]	X
ejpam-3526	178	9	◦	◦	NOUN
ejpam-3526	178	10	[	[	X
ejpam-3526	178	11	(	(	PUNCT
ejpam-3526	178	12	y	y	NOUN
ejpam-3526	178	13	◦	◦	NOUN
ejpam-3526	178	14	1)	1)	NUM
ejpam-3526	178	15	◦	◦	NOUN
ejpam-3526	178	16	(y	(y	NOUN
ejpam-3526	178	17	◦	◦	NOUN
ejpam-3526	178	18	z	z	NOUN
ejpam-3526	178	19	)	)	PUNCT
ejpam-3526	178	20	]	]	PUNCT
ejpam-3526	179	1	=	=	PUNCT
ejpam-3526	180	1	[	[	X
ejpam-3526	180	2	(	(	PUNCT
ejpam-3526	180	3	y	y	PROPN
ejpam-3526	180	4	◦	◦	NOUN
ejpam-3526	180	5	1)	1)	NUM
ejpam-3526	180	6	◦	◦	NOUN
ejpam-3526	180	7	x]	x]	NOUN
ejpam-3526	180	8	◦	◦	NOUN
ejpam-3526	180	9	(1	(1	NOUN
ejpam-3526	180	10	◦	◦	NOUN
ejpam-3526	180	11	z	z	NOUN
ejpam-3526	180	12	)	)	PUNCT
ejpam-3526	181	1	=	=	PUNCT
ejpam-3526	182	1	[	[	X
ejpam-3526	182	2	(	(	PUNCT
ejpam-3526	182	3	y	y	PROPN
ejpam-3526	182	4	◦	◦	NOUN
ejpam-3526	182	5	1)	1)	NUM
ejpam-3526	182	6	◦	◦	NOUN
ejpam-3526	182	7	x]	x]	NOUN
ejpam-3526	182	8	◦	◦	NOUN
ejpam-3526	182	9	z	z	NOUN
ejpam-3526	182	10	by	by	ADP
ejpam-3526	182	11	(	(	PUNCT
ejpam-3526	182	12	iii	iii	NOUN
ejpam-3526	182	13	)	)	PUNCT
ejpam-3526	182	14	and	and	CCONJ
ejpam-3526	182	15	(	(	PUNCT
ejpam-3526	182	16	db2	db2	PROPN
ejpam-3526	182	17	)	)	PUNCT
ejpam-3526	182	18	.	.	PUNCT
ejpam-3526	183	1	therefore	therefore	ADV
ejpam-3526	183	2	,	,	PUNCT
ejpam-3526	183	3	x	x	X
ejpam-3526	183	4	is	be	AUX
ejpam-3526	183	5	a	a	DET
ejpam-3526	183	6	dual	dual	ADJ
ejpam-3526	183	7	b	b	NOUN
ejpam-3526	183	8	-	-	PUNCT
ejpam-3526	183	9	algebra	algebra	NOUN
ejpam-3526	183	10	.	.	PUNCT
ejpam-3526	184	1	comparing	compare	VERB
ejpam-3526	184	2	the	the	DET
ejpam-3526	184	3	axioms	axiom	NOUN
ejpam-3526	184	4	of	of	ADP
ejpam-3526	184	5	a	a	DET
ejpam-3526	184	6	dual	dual	ADJ
ejpam-3526	184	7	b	b	NOUN
ejpam-3526	184	8	-	-	PUNCT
ejpam-3526	184	9	algebra	algebra	NOUN
ejpam-3526	184	10	and	and	CCONJ
ejpam-3526	184	11	a	a	DET
ejpam-3526	184	12	bck	bck	NOUN
ejpam-3526	184	13	-	-	PUNCT
ejpam-3526	184	14	algebra	algebra	NOUN
ejpam-3526	184	15	,	,	PUNCT
ejpam-3526	184	16	we	we	PRON
ejpam-3526	184	17	have	have	VERB
ejpam-3526	184	18	the	the	DET
ejpam-3526	184	19	following	follow	VERB
ejpam-3526	184	20	remark	remark	NOUN
ejpam-3526	184	21	.	.	PUNCT
ejpam-3526	185	1	remark	remark	PROPN
ejpam-3526	185	2	4	4	NUM
ejpam-3526	185	3	.	.	PUNCT
ejpam-3526	186	1	(	(	PUNCT
ejpam-3526	186	2	db1	db1	NOUN
ejpam-3526	186	3	)	)	PUNCT
ejpam-3526	186	4	is	be	AUX
ejpam-3526	186	5	equivalent	equivalent	ADJ
ejpam-3526	186	6	to	to	ADP
ejpam-3526	186	7	(	(	PUNCT
ejpam-3526	186	8	bck3	bck3	PROPN
ejpam-3526	186	9	)	)	PUNCT
ejpam-3526	186	10	and	and	CCONJ
ejpam-3526	186	11	lemma	lemma	PROPN
ejpam-3526	186	12	2(v	2(v	NUM
ejpam-3526	186	13	)	)	PUNCT
ejpam-3526	186	14	is	be	AUX
ejpam-3526	186	15	equivalent	equivalent	ADJ
ejpam-3526	186	16	to	to	ADP
ejpam-3526	186	17	(	(	PUNCT
ejpam-3526	186	18	bck4	bck4	PROPN
ejpam-3526	186	19	)	)	PUNCT
ejpam-3526	186	20	where	where	SCONJ
ejpam-3526	186	21	the	the	DET
ejpam-3526	186	22	constant	constant	ADJ
ejpam-3526	186	23	1	1	NUM
ejpam-3526	186	24	corresponds	correspond	NOUN
ejpam-3526	186	25	to	to	ADP
ejpam-3526	186	26	the	the	DET
ejpam-3526	186	27	constant	constant	ADJ
ejpam-3526	186	28	0	0	NUM
ejpam-3526	186	29	in	in	ADP
ejpam-3526	186	30	a	a	DET
ejpam-3526	186	31	dual	dual	ADJ
ejpam-3526	186	32	b	b	NOUN
ejpam-3526	186	33	-	-	PUNCT
ejpam-3526	186	34	algebra	algebra	NOUN
ejpam-3526	186	35	and	and	CCONJ
ejpam-3526	186	36	bck	bck	NOUN
ejpam-3526	186	37	-	-	PUNCT
ejpam-3526	186	38	algebra	algebra	NOUN
ejpam-3526	186	39	,	,	PUNCT
ejpam-3526	186	40	respectively	respectively	ADV
ejpam-3526	186	41	.	.	PUNCT
ejpam-3526	186	42	example	example	NOUN
ejpam-3526	187	1	6	6	NUM
ejpam-3526	187	2	.	.	PUNCT
ejpam-3526	187	3	consider	consider	VERB
ejpam-3526	187	4	the	the	DET
ejpam-3526	187	5	dual	dual	ADJ
ejpam-3526	187	6	b	b	NOUN
ejpam-3526	187	7	-	-	PUNCT
ejpam-3526	187	8	algebra	algebra	NOUN
ejpam-3526	187	9	x	x	X
ejpam-3526	187	10	=	=	SYM
ejpam-3526	187	11	{	{	PUNCT
ejpam-3526	187	12	0	0	NUM
ejpam-3526	187	13	,	,	PUNCT
ejpam-3526	187	14	1	1	NUM
ejpam-3526	187	15	,	,	PUNCT
ejpam-3526	187	16	2	2	NUM
ejpam-3526	187	17	,	,	PUNCT
ejpam-3526	187	18	3	3	NUM
ejpam-3526	187	19	,	,	PUNCT
ejpam-3526	187	20	4	4	NUM
ejpam-3526	187	21	,	,	PUNCT
ejpam-3526	187	22	5	5	NUM
ejpam-3526	187	23	}	}	PUNCT
ejpam-3526	187	24	in	in	ADP
ejpam-3526	187	25	example	example	NOUN
ejpam-3526	187	26	2	2	NUM
ejpam-3526	187	27	.	.	X
ejpam-3526	187	28	note	note	VERB
ejpam-3526	187	29	that	that	SCONJ
ejpam-3526	187	30	(	(	PUNCT
ejpam-3526	187	31	x	x	NOUN
ejpam-3526	187	32	,	,	PUNCT
ejpam-3526	187	33	◦	◦	NOUN
ejpam-3526	187	34	,	,	PUNCT
ejpam-3526	187	35	0	0	NUM
ejpam-3526	187	36	)	)	PUNCT
ejpam-3526	187	37	is	be	AUX
ejpam-3526	187	38	not	not	PART
ejpam-3526	187	39	a	a	DET
ejpam-3526	187	40	bck	bck	NOUN
ejpam-3526	187	41	-	-	PUNCT
ejpam-3526	187	42	algebra	algebra	NOUN
ejpam-3526	187	43	since	since	SCONJ
ejpam-3526	187	44	(	(	PUNCT
ejpam-3526	187	45	bck2	bck2	PROPN
ejpam-3526	187	46	)	)	PUNCT
ejpam-3526	187	47	is	be	AUX
ejpam-3526	187	48	not	not	PART
ejpam-3526	187	49	satisfied	satisfied	ADJ
ejpam-3526	187	50	,	,	PUNCT
ejpam-3526	187	51	that	that	ADV
ejpam-3526	187	52	is	is	ADV
ejpam-3526	187	53	,	,	PUNCT
ejpam-3526	187	54	[	[	X
ejpam-3526	187	55	1	1	NUM
ejpam-3526	187	56	◦	◦	NOUN
ejpam-3526	187	57	(	(	PUNCT
ejpam-3526	187	58	1	1	NUM
ejpam-3526	187	59	◦	◦	NOUN
ejpam-3526	187	60	5	5	NUM
ejpam-3526	187	61	)	)	PUNCT
ejpam-3526	187	62	]	]	PUNCT
ejpam-3526	188	1	◦	◦	NOUN
ejpam-3526	188	2	5	5	NUM
ejpam-3526	188	3	=	=	SYM
ejpam-3526	188	4	(	(	PUNCT
ejpam-3526	188	5	1	1	NUM
ejpam-3526	188	6	◦	◦	NOUN
ejpam-3526	188	7	3	3	NUM
ejpam-3526	188	8	)	)	PUNCT
ejpam-3526	188	9	◦	◦	NOUN
ejpam-3526	188	10	5	5	NUM
ejpam-3526	188	11	=	=	SYM
ejpam-3526	188	12	4	4	NUM
ejpam-3526	188	13	◦	◦	NOUN
ejpam-3526	188	14	5	5	NUM
ejpam-3526	188	15	=	=	SYM
ejpam-3526	188	16	1	1	NUM
ejpam-3526	188	17	6=	6=	NUM
ejpam-3526	188	18	0	0	NUM
ejpam-3526	188	19	.	.	PUNCT
ejpam-3526	189	1	also	also	ADV
ejpam-3526	189	2	,	,	PUNCT
ejpam-3526	189	3	2	2	NUM
ejpam-3526	189	4	◦	◦	NOUN
ejpam-3526	189	5	1	1	NUM
ejpam-3526	189	6	=	=	SYM
ejpam-3526	189	7	2	2	NUM
ejpam-3526	189	8	6=	6=	SYM
ejpam-3526	189	9	1	1	NUM
ejpam-3526	189	10	=	=	SYM
ejpam-3526	189	11	1	1	NUM
ejpam-3526	189	12	◦	◦	NOUN
ejpam-3526	189	13	2	2	NUM
ejpam-3526	189	14	.	.	PUNCT
ejpam-3526	189	15	k.	k.	PROPN
ejpam-3526	189	16	belleza	belleza	PROPN
ejpam-3526	189	17	,	,	PUNCT
ejpam-3526	189	18	j.	j.	PROPN
ejpam-3526	189	19	vilela	vilela	PROPN
ejpam-3526	189	20	/	/	SYM
ejpam-3526	189	21	eur	eur	PROPN
ejpam-3526	189	22	.	.	PUNCT
ejpam-3526	190	1	j.	j.	PROPN
ejpam-3526	190	2	pure	pure	PROPN
ejpam-3526	190	3	appl	appl	PROPN
ejpam-3526	190	4	.	.	PROPN
ejpam-3526	190	5	math	math	PROPN
ejpam-3526	190	6	,	,	PUNCT
ejpam-3526	190	7	12	12	NUM
ejpam-3526	190	8	(	(	PUNCT
ejpam-3526	190	9	4	4	NUM
ejpam-3526	190	10	)	)	PUNCT
ejpam-3526	190	11	(	(	PUNCT
ejpam-3526	190	12	2019	2019	NUM
ejpam-3526	190	13	)	)	PUNCT
ejpam-3526	190	14	,	,	PUNCT
ejpam-3526	190	15	1497	1497	NUM
ejpam-3526	190	16	-	-	SYM
ejpam-3526	190	17	1507	1507	NUM
ejpam-3526	190	18	1502	1502	NUM
ejpam-3526	190	19	example	example	NOUN
ejpam-3526	190	20	7	7	NUM
ejpam-3526	190	21	.	.	X
ejpam-3526	190	22	consider	consider	VERB
ejpam-3526	190	23	the	the	DET
ejpam-3526	190	24	klein-4	klein-4	PROPN
ejpam-3526	190	25	dual	dual	ADJ
ejpam-3526	190	26	b	b	NOUN
ejpam-3526	190	27	-	-	PUNCT
ejpam-3526	190	28	algebra	algebra	NOUN
ejpam-3526	190	29	xd	xd	INTJ
ejpam-3526	190	30	in	in	ADP
ejpam-3526	190	31	example	example	NOUN
ejpam-3526	190	32	4	4	NUM
ejpam-3526	190	33	.	.	X
ejpam-3526	191	1	observe	observe	VERB
ejpam-3526	191	2	that	that	SCONJ
ejpam-3526	191	3	this	this	DET
ejpam-3526	191	4	example	example	NOUN
ejpam-3526	191	5	satisfies	satisfy	VERB
ejpam-3526	191	6	the	the	DET
ejpam-3526	191	7	symmetric	symmetric	ADJ
ejpam-3526	191	8	condition	condition	NOUN
ejpam-3526	191	9	but	but	CCONJ
ejpam-3526	191	10	is	be	AUX
ejpam-3526	191	11	not	not	PART
ejpam-3526	191	12	a	a	DET
ejpam-3526	191	13	bck	bck	NOUN
ejpam-3526	191	14	-	-	PUNCT
ejpam-3526	191	15	algebra	algebra	NOUN
ejpam-3526	191	16	since	since	SCONJ
ejpam-3526	191	17	e	e	NOUN
ejpam-3526	191	18	◦	◦	NOUN
ejpam-3526	191	19	x	x	SYM
ejpam-3526	191	20	6=	6=	ADP
ejpam-3526	191	21	e	e	NOUN
ejpam-3526	191	22	for	for	ADP
ejpam-3526	191	23	all	all	DET
ejpam-3526	191	24	x	x	SYM
ejpam-3526	191	25	∈	∈	PROPN
ejpam-3526	191	26	x.	x.	NOUN
ejpam-3526	191	27	lemma	lemma	PROPN
ejpam-3526	192	1	3	3	X
ejpam-3526	192	2	.	.	PUNCT
ejpam-3526	193	1	let	let	VERB
ejpam-3526	193	2	xd	xd	INTJ
ejpam-3526	193	3	=	=	SYM
ejpam-3526	193	4	(	(	PUNCT
ejpam-3526	193	5	x	x	X
ejpam-3526	193	6	,	,	PUNCT
ejpam-3526	193	7	◦	◦	NOUN
ejpam-3526	193	8	,	,	PUNCT
ejpam-3526	193	9	1	1	NUM
ejpam-3526	193	10	)	)	PUNCT
ejpam-3526	193	11	be	be	AUX
ejpam-3526	193	12	a	a	DET
ejpam-3526	193	13	dual	dual	ADJ
ejpam-3526	193	14	b	b	NOUN
ejpam-3526	193	15	-	-	PUNCT
ejpam-3526	193	16	algebra	algebra	NOUN
ejpam-3526	193	17	satisfying	satisfy	VERB
ejpam-3526	193	18	a	a	DET
ejpam-3526	193	19	symmetric	symmetric	ADJ
ejpam-3526	193	20	condition	condition	NOUN
ejpam-3526	193	21	.	.	PUNCT
ejpam-3526	194	1	then	then	ADV
ejpam-3526	194	2	for	for	ADP
ejpam-3526	194	3	all	all	DET
ejpam-3526	194	4	x	x	NOUN
ejpam-3526	194	5	,	,	PUNCT
ejpam-3526	194	6	y	y	PROPN
ejpam-3526	194	7	,	,	PUNCT
ejpam-3526	194	8	z	z	NOUN
ejpam-3526	194	9	in	in	ADP
ejpam-3526	194	10	x	x	PRON
ejpam-3526	194	11	,	,	PUNCT
ejpam-3526	194	12	(	(	PUNCT
ejpam-3526	194	13	x	x	SYM
ejpam-3526	194	14	◦	◦	VERB
ejpam-3526	194	15	y	y	NOUN
ejpam-3526	194	16	)	)	PUNCT
ejpam-3526	194	17	◦	◦	NOUN
ejpam-3526	194	18	(	(	PUNCT
ejpam-3526	194	19	z	z	AUX
ejpam-3526	194	20	◦	◦	NOUN
ejpam-3526	194	21	y	y	NOUN
ejpam-3526	194	22	)	)	PUNCT
ejpam-3526	195	1	=	=	PUNCT
ejpam-3526	195	2	x	x	PUNCT
ejpam-3526	195	3	◦	◦	NOUN
ejpam-3526	195	4	z.	z.	NOUN
ejpam-3526	195	5	proof	proof	NOUN
ejpam-3526	195	6	:	:	PUNCT
ejpam-3526	195	7	by	by	ADP
ejpam-3526	195	8	(	(	PUNCT
ejpam-3526	195	9	db3	db3	PROPN
ejpam-3526	195	10	)	)	PUNCT
ejpam-3526	195	11	,	,	PUNCT
ejpam-3526	195	12	hypothesis	hypothesis	NOUN
ejpam-3526	195	13	,	,	PUNCT
ejpam-3526	195	14	lemma	lemma	PROPN
ejpam-3526	195	15	2(iii	2(iii	NUM
ejpam-3526	195	16	)	)	PUNCT
ejpam-3526	195	17	and	and	CCONJ
ejpam-3526	195	18	(	(	PUNCT
ejpam-3526	195	19	i	i	NOUN
ejpam-3526	195	20	)	)	PUNCT
ejpam-3526	195	21	,	,	PUNCT
ejpam-3526	195	22	(	(	PUNCT
ejpam-3526	195	23	db1	db1	NOUN
ejpam-3526	195	24	)	)	PUNCT
ejpam-3526	195	25	,	,	PUNCT
ejpam-3526	195	26	and	and	CCONJ
ejpam-3526	195	27	(	(	PUNCT
ejpam-3526	195	28	db2	db2	PROPN
ejpam-3526	195	29	)	)	PUNCT
ejpam-3526	195	30	,	,	PUNCT
ejpam-3526	195	31	we	we	PRON
ejpam-3526	195	32	have	have	AUX
ejpam-3526	195	33	(	(	PUNCT
ejpam-3526	195	34	x	x	SYM
ejpam-3526	195	35	◦	◦	VERB
ejpam-3526	195	36	y	y	NOUN
ejpam-3526	195	37	)	)	PUNCT
ejpam-3526	195	38	◦	◦	NOUN
ejpam-3526	195	39	(	(	PUNCT
ejpam-3526	195	40	z	z	AUX
ejpam-3526	195	41	◦	◦	NOUN
ejpam-3526	195	42	y	y	NOUN
ejpam-3526	195	43	)	)	PUNCT
ejpam-3526	196	1	=	=	PUNCT
ejpam-3526	197	1	[	[	X
ejpam-3526	197	2	(	(	PUNCT
ejpam-3526	197	3	z	z	NOUN
ejpam-3526	197	4	◦	◦	NOUN
ejpam-3526	197	5	1	1	NUM
ejpam-3526	197	6	)	)	PUNCT
ejpam-3526	197	7	◦	◦	NOUN
ejpam-3526	197	8	(	(	PUNCT
ejpam-3526	197	9	x	x	PART
ejpam-3526	197	10	◦	◦	VERB
ejpam-3526	197	11	y	y	PROPN
ejpam-3526	197	12	)	)	PUNCT
ejpam-3526	197	13	]	]	PUNCT
ejpam-3526	198	1	◦	◦	NOUN
ejpam-3526	198	2	y	y	NOUN
ejpam-3526	198	3	=	=	PUNCT
ejpam-3526	199	1	[	[	X
ejpam-3526	199	2	z	z	X
ejpam-3526	199	3	◦	◦	NOUN
ejpam-3526	199	4	(	(	PUNCT
ejpam-3526	199	5	x	x	PART
ejpam-3526	199	6	◦	◦	VERB
ejpam-3526	199	7	y	y	PROPN
ejpam-3526	199	8	)	)	PUNCT
ejpam-3526	199	9	]	]	PUNCT
ejpam-3526	200	1	◦	◦	NOUN
ejpam-3526	200	2	y	y	NOUN
ejpam-3526	200	3	=	=	PUNCT
ejpam-3526	201	1	[	[	X
ejpam-3526	201	2	(	(	PUNCT
ejpam-3526	201	3	x	x	SYM
ejpam-3526	201	4	◦	◦	VERB
ejpam-3526	201	5	y	y	NOUN
ejpam-3526	201	6	)	)	PUNCT
ejpam-3526	201	7	◦	◦	NOUN
ejpam-3526	201	8	z	z	X
ejpam-3526	201	9	]	]	X
ejpam-3526	201	10	◦	◦	NOUN
ejpam-3526	201	11	y	y	NOUN
ejpam-3526	201	12	=	=	PUNCT
ejpam-3526	202	1	(	(	PUNCT
ejpam-3526	202	2	[	[	X
ejpam-3526	202	3	(	(	PUNCT
ejpam-3526	202	4	x	x	SYM
ejpam-3526	202	5	◦	◦	NOUN
ejpam-3526	202	6	y	y	NOUN
ejpam-3526	202	7	)	)	PUNCT
ejpam-3526	202	8	◦	◦	NOUN
ejpam-3526	202	9	1	1	NUM
ejpam-3526	202	10	]	]	X
ejpam-3526	202	11	◦	◦	NOUN
ejpam-3526	202	12	z	z	NOUN
ejpam-3526	202	13	)	)	PUNCT
ejpam-3526	203	1	◦	◦	NOUN
ejpam-3526	203	2	y	y	NOUN
ejpam-3526	203	3	=	=	SYM
ejpam-3526	203	4	z	z	X
ejpam-3526	204	1	◦	◦	NOUN
ejpam-3526	205	1	[	[	X
ejpam-3526	205	2	(	(	PUNCT
ejpam-3526	205	3	x	x	SYM
ejpam-3526	205	4	◦	◦	NOUN
ejpam-3526	205	5	y)	y)	NOUN
ejpam-3526	205	6	◦	◦	NOUN
ejpam-3526	205	7	y	y	NOUN
ejpam-3526	205	8	]	]	X
ejpam-3526	205	9	=	=	SYM
ejpam-3526	205	10	z	z	X
ejpam-3526	205	11	◦	◦	NOUN
ejpam-3526	205	12	(	(	PUNCT
ejpam-3526	205	13	y	y	X
ejpam-3526	205	14	◦	◦	VERB
ejpam-3526	206	1	[	[	X
ejpam-3526	206	2	(	(	PUNCT
ejpam-3526	206	3	x	x	PART
ejpam-3526	206	4	◦	◦	NOUN
ejpam-3526	206	5	1)	1)	NUM
ejpam-3526	206	6	◦	◦	NOUN
ejpam-3526	206	7	y	y	NOUN
ejpam-3526	206	8	]	]	PUNCT
ejpam-3526	206	9	)	)	PUNCT
ejpam-3526	207	1	=	=	PUNCT
ejpam-3526	207	2	z	z	AUX
ejpam-3526	207	3	◦	◦	NOUN
ejpam-3526	207	4	[	[	X
ejpam-3526	207	5	y	y	PROPN
ejpam-3526	207	6	◦	◦	NOUN
ejpam-3526	207	7	(	(	PUNCT
ejpam-3526	207	8	x	x	NOUN
ejpam-3526	207	9	◦	◦	NOUN
ejpam-3526	207	10	y	y	NOUN
ejpam-3526	207	11	)	)	PUNCT
ejpam-3526	207	12	]	]	PUNCT
ejpam-3526	208	1	=	=	PUNCT
ejpam-3526	208	2	z	z	AUX
ejpam-3526	208	3	◦	◦	NOUN
ejpam-3526	208	4	[	[	X
ejpam-3526	208	5	y	y	PROPN
ejpam-3526	208	6	◦	◦	PROPN
ejpam-3526	208	7	(	(	PUNCT
ejpam-3526	208	8	y	y	PROPN
ejpam-3526	208	9	◦	◦	NOUN
ejpam-3526	208	10	x	x	NOUN
ejpam-3526	208	11	)	)	PUNCT
ejpam-3526	208	12	]	]	PUNCT
ejpam-3526	209	1	=	=	PUNCT
ejpam-3526	209	2	z	z	X
ejpam-3526	209	3	◦	◦	NOUN
ejpam-3526	209	4	(	(	PUNCT
ejpam-3526	209	5	y	y	X
ejpam-3526	209	6	◦	◦	VERB
ejpam-3526	210	1	[	[	X
ejpam-3526	210	2	(	(	PUNCT
ejpam-3526	210	3	y	y	PROPN
ejpam-3526	210	4	◦	◦	NOUN
ejpam-3526	210	5	1)	1)	NUM
ejpam-3526	210	6	◦	◦	NOUN
ejpam-3526	210	7	x	x	NOUN
ejpam-3526	210	8	]	]	X
ejpam-3526	210	9	)	)	PUNCT
ejpam-3526	211	1	=	=	PUNCT
ejpam-3526	211	2	z	z	X
ejpam-3526	212	1	◦	◦	NOUN
ejpam-3526	213	1	[	[	X
ejpam-3526	213	2	(	(	PUNCT
ejpam-3526	213	3	[	[	X
ejpam-3526	213	4	(	(	PUNCT
ejpam-3526	213	5	y	y	NOUN
ejpam-3526	213	6	◦	◦	NOUN
ejpam-3526	213	7	1	1	NUM
ejpam-3526	213	8	)	)	PUNCT
ejpam-3526	213	9	◦	◦	NOUN
ejpam-3526	213	10	1	1	NUM
ejpam-3526	213	11	]	]	X
ejpam-3526	213	12	◦	◦	NOUN
ejpam-3526	213	13	y	y	PROPN
ejpam-3526	213	14	)	)	PUNCT
ejpam-3526	213	15	◦	◦	NOUN
ejpam-3526	213	16	x	x	X
ejpam-3526	213	17	]	]	X
ejpam-3526	213	18	=	=	PUNCT
ejpam-3526	213	19	z	z	AUX
ejpam-3526	213	20	◦	◦	NOUN
ejpam-3526	214	1	[	[	X
ejpam-3526	214	2	(	(	PUNCT
ejpam-3526	214	3	y	y	PROPN
ejpam-3526	214	4	◦	◦	NOUN
ejpam-3526	214	5	y	y	PROPN
ejpam-3526	214	6	)	)	PUNCT
ejpam-3526	214	7	◦	◦	NOUN
ejpam-3526	214	8	x	x	X
ejpam-3526	214	9	]	]	X
ejpam-3526	214	10	=	=	SYM
ejpam-3526	214	11	z	z	X
ejpam-3526	214	12	◦	◦	NOUN
ejpam-3526	214	13	(	(	PUNCT
ejpam-3526	214	14	1	1	NUM
ejpam-3526	214	15	◦	◦	NOUN
ejpam-3526	214	16	x	x	NOUN
ejpam-3526	214	17	)	)	PUNCT
ejpam-3526	215	1	=	=	SYM
ejpam-3526	215	2	z	z	NOUN
ejpam-3526	215	3	◦	◦	NOUN
ejpam-3526	215	4	x	x	X
ejpam-3526	215	5	=	=	SYM
ejpam-3526	215	6	x	x	PUNCT
ejpam-3526	215	7	◦	◦	NOUN
ejpam-3526	215	8	z.	z.	NOUN
ejpam-3526	215	9	proposition	proposition	NOUN
ejpam-3526	215	10	3	3	X
ejpam-3526	215	11	.	.	PUNCT
ejpam-3526	216	1	let	let	VERB
ejpam-3526	216	2	xd	xd	INTJ
ejpam-3526	216	3	=	=	SYM
ejpam-3526	216	4	(	(	PUNCT
ejpam-3526	216	5	x	x	X
ejpam-3526	216	6	,	,	PUNCT
ejpam-3526	216	7	◦	◦	NOUN
ejpam-3526	216	8	,	,	PUNCT
ejpam-3526	216	9	1	1	NUM
ejpam-3526	216	10	)	)	PUNCT
ejpam-3526	216	11	be	be	AUX
ejpam-3526	216	12	a	a	DET
ejpam-3526	216	13	dual	dual	ADJ
ejpam-3526	216	14	b	b	NOUN
ejpam-3526	216	15	-	-	PUNCT
ejpam-3526	216	16	algebra	algebra	NOUN
ejpam-3526	216	17	satisfying	satisfy	VERB
ejpam-3526	216	18	a	a	DET
ejpam-3526	216	19	symmetric	symmetric	ADJ
ejpam-3526	216	20	condition	condition	NOUN
ejpam-3526	216	21	.	.	PUNCT
ejpam-3526	217	1	then	then	ADV
ejpam-3526	217	2	xd	xd	INTJ
ejpam-3526	217	3	satisfies	satisfie	NOUN
ejpam-3526	217	4	(	(	PUNCT
ejpam-3526	217	5	bck1	bck1	PROPN
ejpam-3526	217	6	)	)	PUNCT
ejpam-3526	217	7	,	,	PUNCT
ejpam-3526	217	8	(	(	PUNCT
ejpam-3526	217	9	bck2	bck2	PROPN
ejpam-3526	217	10	)	)	PUNCT
ejpam-3526	217	11	,	,	PUNCT
ejpam-3526	217	12	(	(	PUNCT
ejpam-3526	217	13	bck3	bck3	PROPN
ejpam-3526	217	14	)	)	PUNCT
ejpam-3526	217	15	,	,	PUNCT
ejpam-3526	217	16	and	and	CCONJ
ejpam-3526	217	17	(	(	PUNCT
ejpam-3526	217	18	bck4	bck4	PROPN
ejpam-3526	217	19	)	)	PUNCT
ejpam-3526	217	20	of	of	ADP
ejpam-3526	217	21	a	a	DET
ejpam-3526	217	22	bck	bck	NOUN
ejpam-3526	217	23	-	-	PUNCT
ejpam-3526	217	24	algebra	algebra	NOUN
ejpam-3526	217	25	.	.	PUNCT
ejpam-3526	218	1	proof	proof	NOUN
ejpam-3526	218	2	:	:	PUNCT
ejpam-3526	218	3	suppose	suppose	VERB
ejpam-3526	218	4	xd	xd	INTJ
ejpam-3526	218	5	is	be	AUX
ejpam-3526	218	6	a	a	DET
ejpam-3526	218	7	dual	dual	ADJ
ejpam-3526	218	8	b	b	NOUN
ejpam-3526	218	9	-	-	PUNCT
ejpam-3526	218	10	algebra	algebra	NOUN
ejpam-3526	218	11	satisfying	satisfy	VERB
ejpam-3526	218	12	a	a	DET
ejpam-3526	218	13	symmetric	symmetric	ADJ
ejpam-3526	218	14	condition	condition	NOUN
ejpam-3526	218	15	.	.	PUNCT
ejpam-3526	219	1	then	then	ADV
ejpam-3526	219	2	by	by	ADP
ejpam-3526	219	3	(	(	PUNCT
ejpam-3526	219	4	db2	db2	PROPN
ejpam-3526	219	5	)	)	PUNCT
ejpam-3526	219	6	and	and	CCONJ
ejpam-3526	219	7	the	the	DET
ejpam-3526	219	8	hypothesis	hypothesis	NOUN
ejpam-3526	219	9	,	,	PUNCT
ejpam-3526	219	10	x	x	PUNCT
ejpam-3526	219	11	=	=	SYM
ejpam-3526	219	12	1	1	NUM
ejpam-3526	219	13	◦	◦	NOUN
ejpam-3526	219	14	x	x	SYM
ejpam-3526	219	15	=	=	SYM
ejpam-3526	219	16	x	x	PUNCT
ejpam-3526	219	17	◦	◦	NOUN
ejpam-3526	219	18	1	1	NUM
ejpam-3526	219	19	for	for	ADP
ejpam-3526	219	20	all	all	DET
ejpam-3526	219	21	x	x	NOUN
ejpam-3526	219	22	in	in	ADP
ejpam-3526	219	23	xd	xd	ADP
ejpam-3526	219	24	.	.	PUNCT
ejpam-3526	220	1	by	by	ADP
ejpam-3526	220	2	remark	remark	NOUN
ejpam-3526	220	3	4	4	NUM
ejpam-3526	220	4	,	,	PUNCT
ejpam-3526	220	5	it	it	PRON
ejpam-3526	220	6	remains	remain	VERB
ejpam-3526	220	7	to	to	PART
ejpam-3526	220	8	show	show	VERB
ejpam-3526	220	9	that	that	SCONJ
ejpam-3526	220	10	xd	xd	INTJ
ejpam-3526	220	11	satisfies	satisfie	NOUN
ejpam-3526	220	12	(	(	PUNCT
ejpam-3526	220	13	bck1	bck1	PROPN
ejpam-3526	220	14	)	)	PUNCT
ejpam-3526	220	15	and	and	CCONJ
ejpam-3526	220	16	(	(	PUNCT
ejpam-3526	220	17	bck2	bck2	PROPN
ejpam-3526	220	18	)	)	PUNCT
ejpam-3526	220	19	.	.	PUNCT
ejpam-3526	221	1	let	let	VERB
ejpam-3526	221	2	x	x	PRON
ejpam-3526	221	3	,	,	PUNCT
ejpam-3526	221	4	y	y	PROPN
ejpam-3526	221	5	,	,	PUNCT
ejpam-3526	221	6	z	z	PROPN
ejpam-3526	221	7	∈	∈	PROPN
ejpam-3526	221	8	xd	xd	INTJ
ejpam-3526	221	9	.	.	PUNCT
ejpam-3526	222	1	by	by	ADP
ejpam-3526	222	2	(	(	PUNCT
ejpam-3526	222	3	db3	db3	PROPN
ejpam-3526	222	4	)	)	PUNCT
ejpam-3526	222	5	,	,	PUNCT
ejpam-3526	222	6	hypothesis	hypothesis	NOUN
ejpam-3526	222	7	,	,	PUNCT
ejpam-3526	222	8	(	(	PUNCT
ejpam-3526	222	9	db1	db1	NOUN
ejpam-3526	222	10	)	)	PUNCT
ejpam-3526	222	11	and	and	CCONJ
ejpam-3526	222	12	(	(	PUNCT
ejpam-3526	222	13	db2	db2	PROPN
ejpam-3526	222	14	)	)	PUNCT
ejpam-3526	222	15	,	,	PUNCT
ejpam-3526	223	1	[	[	X
ejpam-3526	223	2	x	x	SYM
ejpam-3526	223	3	◦	◦	ADJ
ejpam-3526	223	4	(x	(x	NOUN
ejpam-3526	223	5	◦	◦	NOUN
ejpam-3526	223	6	y)]	y)]	NOUN
ejpam-3526	223	7	◦	◦	NOUN
ejpam-3526	223	8	y	y	NOUN
ejpam-3526	223	9	=	=	SYM
ejpam-3526	223	10	(	(	PUNCT
ejpam-3526	223	11	[	[	X
ejpam-3526	223	12	(	(	PUNCT
ejpam-3526	223	13	x	x	PART
ejpam-3526	223	14	◦	◦	NOUN
ejpam-3526	223	15	1)	1)	NUM
ejpam-3526	223	16	◦	◦	NOUN
ejpam-3526	223	17	x]	x]	PROPN
ejpam-3526	223	18	◦	◦	NOUN
ejpam-3526	223	19	y	y	PROPN
ejpam-3526	223	20	)	)	PUNCT
ejpam-3526	223	21	◦	◦	NOUN
ejpam-3526	223	22	y	y	NOUN
ejpam-3526	223	23	=	=	SYM
ejpam-3526	224	1	[	[	X
ejpam-3526	224	2	(	(	PUNCT
ejpam-3526	224	3	x	x	NOUN
ejpam-3526	224	4	◦	◦	NOUN
ejpam-3526	224	5	x)	x)	NUM
ejpam-3526	224	6	◦	◦	NOUN
ejpam-3526	224	7	y]	y]	NOUN
ejpam-3526	224	8	◦	◦	NOUN
ejpam-3526	224	9	y	y	NOUN
ejpam-3526	224	10	=	=	SYM
ejpam-3526	224	11	(	(	PUNCT
ejpam-3526	224	12	1	1	NUM
ejpam-3526	224	13	◦	◦	NOUN
ejpam-3526	224	14	y)	y)	NOUN
ejpam-3526	224	15	◦	◦	NOUN
ejpam-3526	224	16	y	y	NOUN
ejpam-3526	224	17	=	=	SYM
ejpam-3526	224	18	y	y	PROPN
ejpam-3526	224	19	◦	◦	NOUN
ejpam-3526	224	20	y	y	NOUN
ejpam-3526	224	21	=	=	SYM
ejpam-3526	224	22	1	1	NUM
ejpam-3526	224	23	.	.	PUNCT
ejpam-3526	224	24	thus	thus	ADV
ejpam-3526	224	25	,	,	PUNCT
ejpam-3526	224	26	xd	xd	INTJ
ejpam-3526	224	27	satisfies	satisfie	NOUN
ejpam-3526	224	28	(	(	PUNCT
ejpam-3526	224	29	bck2	bck2	PROPN
ejpam-3526	224	30	)	)	PUNCT
ejpam-3526	224	31	.	.	PUNCT
ejpam-3526	225	1	by	by	ADP
ejpam-3526	225	2	lemma	lemma	PROPN
ejpam-3526	225	3	2	2	NUM
ejpam-3526	225	4	(	(	PUNCT
ejpam-3526	225	5	iii	iii	NOUN
ejpam-3526	225	6	)	)	PUNCT
ejpam-3526	225	7	and	and	CCONJ
ejpam-3526	225	8	hypothesis	hypothesis	NOUN
ejpam-3526	225	9	,	,	PUNCT
ejpam-3526	225	10	[	[	X
ejpam-3526	225	11	(	(	PUNCT
ejpam-3526	225	12	x	x	SYM
ejpam-3526	225	13	◦	◦	VERB
ejpam-3526	225	14	y	y	NOUN
ejpam-3526	225	15	)	)	PUNCT
ejpam-3526	225	16	◦	◦	NOUN
ejpam-3526	225	17	(	(	PUNCT
ejpam-3526	225	18	x	x	PART
ejpam-3526	225	19	◦	◦	NOUN
ejpam-3526	225	20	z	z	NOUN
ejpam-3526	225	21	)	)	PUNCT
ejpam-3526	225	22	]	]	PUNCT
ejpam-3526	226	1	◦	◦	NOUN
ejpam-3526	226	2	(	(	PUNCT
ejpam-3526	226	3	z	z	AUX
ejpam-3526	226	4	◦	◦	NOUN
ejpam-3526	226	5	y	y	NOUN
ejpam-3526	226	6	)	)	PUNCT
ejpam-3526	226	7	=	=	PRON
ejpam-3526	227	1	(	(	PUNCT
ejpam-3526	227	2	x	x	PART
ejpam-3526	227	3	◦	◦	NOUN
ejpam-3526	227	4	z	z	NOUN
ejpam-3526	227	5	)	)	PUNCT
ejpam-3526	227	6	◦	◦	NOUN
ejpam-3526	227	7	(	(	PUNCT
ejpam-3526	227	8	[	[	X
ejpam-3526	227	9	(	(	PUNCT
ejpam-3526	227	10	x	x	SYM
ejpam-3526	227	11	◦	◦	NOUN
ejpam-3526	227	12	y	y	NOUN
ejpam-3526	227	13	)	)	PUNCT
ejpam-3526	227	14	◦	◦	NOUN
ejpam-3526	227	15	1	1	NUM
ejpam-3526	227	16	]	]	X
ejpam-3526	227	17	◦	◦	NOUN
ejpam-3526	227	18	(	(	PUNCT
ejpam-3526	227	19	z	z	NOUN
ejpam-3526	227	20	◦	◦	NOUN
ejpam-3526	227	21	y	y	NOUN
ejpam-3526	227	22	)	)	PUNCT
ejpam-3526	227	23	)	)	PUNCT
ejpam-3526	228	1	=	=	PUNCT
ejpam-3526	228	2	(	(	PUNCT
ejpam-3526	228	3	x	x	PART
ejpam-3526	228	4	◦	◦	NOUN
ejpam-3526	228	5	z	z	NOUN
ejpam-3526	228	6	)	)	PUNCT
ejpam-3526	228	7	◦	◦	NOUN
ejpam-3526	229	1	[	[	X
ejpam-3526	229	2	(	(	PUNCT
ejpam-3526	229	3	x	x	SYM
ejpam-3526	229	4	◦	◦	VERB
ejpam-3526	229	5	y	y	NOUN
ejpam-3526	229	6	)	)	PUNCT
ejpam-3526	229	7	◦	◦	NOUN
ejpam-3526	229	8	(	(	PUNCT
ejpam-3526	229	9	z	z	AUX
ejpam-3526	229	10	◦	◦	NOUN
ejpam-3526	229	11	y	y	PROPN
ejpam-3526	229	12	)	)	PUNCT
ejpam-3526	229	13	]	]	PUNCT
ejpam-3526	229	14	.	.	PUNCT
ejpam-3526	230	1	by	by	ADP
ejpam-3526	230	2	the	the	DET
ejpam-3526	230	3	hypothesis	hypothesis	NOUN
ejpam-3526	230	4	,	,	PUNCT
ejpam-3526	230	5	lemma	lemma	PROPN
ejpam-3526	230	6	3	3	NUM
ejpam-3526	230	7	and	and	CCONJ
ejpam-3526	230	8	(	(	PUNCT
ejpam-3526	230	9	db1	db1	NOUN
ejpam-3526	230	10	)	)	PUNCT
ejpam-3526	230	11	,	,	PUNCT
ejpam-3526	230	12	[	[	X
ejpam-3526	230	13	(	(	PUNCT
ejpam-3526	230	14	x	x	SYM
ejpam-3526	230	15	◦	◦	VERB
ejpam-3526	230	16	y	y	NOUN
ejpam-3526	230	17	)	)	PUNCT
ejpam-3526	230	18	◦	◦	NOUN
ejpam-3526	230	19	(	(	PUNCT
ejpam-3526	230	20	x	x	PART
ejpam-3526	230	21	◦	◦	NOUN
ejpam-3526	230	22	z	z	NOUN
ejpam-3526	230	23	)	)	PUNCT
ejpam-3526	230	24	]	]	PUNCT
ejpam-3526	231	1	◦	◦	NOUN
ejpam-3526	231	2	(	(	PUNCT
ejpam-3526	231	3	z	z	AUX
ejpam-3526	231	4	◦	◦	NOUN
ejpam-3526	231	5	y	y	NOUN
ejpam-3526	231	6	)	)	PUNCT
ejpam-3526	231	7	=	=	PUNCT
ejpam-3526	232	1	[	[	X
ejpam-3526	232	2	(	(	PUNCT
ejpam-3526	232	3	y	y	PROPN
ejpam-3526	232	4	◦	◦	NOUN
ejpam-3526	232	5	x	x	NOUN
ejpam-3526	232	6	)	)	PUNCT
ejpam-3526	232	7	◦	◦	NOUN
ejpam-3526	232	8	(	(	PUNCT
ejpam-3526	232	9	z	z	NOUN
ejpam-3526	232	10	◦	◦	NOUN
ejpam-3526	232	11	x	x	X
ejpam-3526	232	12	)	)	PUNCT
ejpam-3526	232	13	]	]	PUNCT
ejpam-3526	233	1	◦	◦	NOUN
ejpam-3526	233	2	(	(	PUNCT
ejpam-3526	233	3	y	y	PROPN
ejpam-3526	233	4	◦	◦	PROPN
ejpam-3526	233	5	z	z	PROPN
ejpam-3526	233	6	)	)	PUNCT
ejpam-3526	233	7	=	=	SYM
ejpam-3526	233	8	(	(	PUNCT
ejpam-3526	233	9	y	y	PROPN
ejpam-3526	233	10	◦	◦	PROPN
ejpam-3526	233	11	z	z	PROPN
ejpam-3526	233	12	)	)	PUNCT
ejpam-3526	233	13	◦	◦	NOUN
ejpam-3526	233	14	(	(	PUNCT
ejpam-3526	233	15	y	y	PROPN
ejpam-3526	233	16	◦	◦	PROPN
ejpam-3526	233	17	z	z	PROPN
ejpam-3526	233	18	)	)	PUNCT
ejpam-3526	233	19	=	=	SYM
ejpam-3526	233	20	1	1	X
ejpam-3526	233	21	.	.	PUNCT
ejpam-3526	234	1	so	so	ADV
ejpam-3526	234	2	,	,	PUNCT
ejpam-3526	234	3	xd	xd	INTJ
ejpam-3526	234	4	satisfies	satisfie	NOUN
ejpam-3526	234	5	(	(	PUNCT
ejpam-3526	234	6	bck1	bck1	PROPN
ejpam-3526	234	7	)	)	PUNCT
ejpam-3526	234	8	.	.	PUNCT
ejpam-3526	235	1	example	example	NOUN
ejpam-3526	236	1	8	8	NUM
ejpam-3526	236	2	.	.	PUNCT
ejpam-3526	237	1	let	let	VERB
ejpam-3526	237	2	x	x	PUNCT
ejpam-3526	237	3	=	=	PUNCT
ejpam-3526	237	4	{	{	PUNCT
ejpam-3526	237	5	0	0	NUM
ejpam-3526	237	6	,	,	PUNCT
ejpam-3526	237	7	a	a	DET
ejpam-3526	237	8	,	,	PUNCT
ejpam-3526	237	9	b	b	NOUN
ejpam-3526	237	10	,	,	PUNCT
ejpam-3526	237	11	c	c	NOUN
ejpam-3526	237	12	,	,	PUNCT
ejpam-3526	237	13	d	d	AUX
ejpam-3526	237	14	}	}	PUNCT
ejpam-3526	237	15	be	be	AUX
ejpam-3526	237	16	a	a	DET
ejpam-3526	237	17	bck	bck	NOUN
ejpam-3526	237	18	-	-	PUNCT
ejpam-3526	237	19	algebra	algebra	NOUN
ejpam-3526	237	20	[	[	X
ejpam-3526	237	21	10	10	NUM
ejpam-3526	237	22	]	]	PUNCT
ejpam-3526	237	23	with	with	ADP
ejpam-3526	237	24	the	the	DET
ejpam-3526	237	25	following	follow	VERB
ejpam-3526	237	26	cayley	cayley	ADJ
ejpam-3526	237	27	table	table	NOUN
ejpam-3526	237	28	:	:	PUNCT
ejpam-3526	237	29	∗	∗	NOUN
ejpam-3526	237	30	0	0	PUNCT
ejpam-3526	238	1	a	a	DET
ejpam-3526	238	2	b	b	NOUN
ejpam-3526	238	3	c	c	NOUN
ejpam-3526	238	4	d	d	NOUN
ejpam-3526	238	5	0	0	NUM
ejpam-3526	238	6	0	0	NUM
ejpam-3526	238	7	0	0	NUM
ejpam-3526	238	8	0	0	NUM
ejpam-3526	238	9	0	0	NUM
ejpam-3526	238	10	0	0	NUM
ejpam-3526	238	11	a	a	DET
ejpam-3526	238	12	a	a	DET
ejpam-3526	238	13	0	0	NUM
ejpam-3526	238	14	a	a	PRON
ejpam-3526	238	15	0	0	NUM
ejpam-3526	238	16	0	0	NUM
ejpam-3526	239	1	b	b	PROPN
ejpam-3526	239	2	b	b	PROPN
ejpam-3526	239	3	b	b	PROPN
ejpam-3526	239	4	0	0	NUM
ejpam-3526	239	5	b	b	NOUN
ejpam-3526	239	6	0	0	NUM
ejpam-3526	239	7	c	c	NOUN
ejpam-3526	239	8	c	c	NOUN
ejpam-3526	239	9	c	c	NOUN
ejpam-3526	239	10	c	c	NOUN
ejpam-3526	239	11	0	0	PUNCT
ejpam-3526	240	1	c	c	NOUN
ejpam-3526	240	2	d	d	PROPN
ejpam-3526	240	3	d	d	PROPN
ejpam-3526	240	4	d	d	PROPN
ejpam-3526	240	5	d	d	X
ejpam-3526	240	6	d	d	SYM
ejpam-3526	240	7	0	0	NUM
ejpam-3526	240	8	note	note	VERB
ejpam-3526	240	9	that	that	SCONJ
ejpam-3526	240	10	b	b	NOUN
ejpam-3526	240	11	∗	∗	VERB
ejpam-3526	240	12	a	a	DET
ejpam-3526	240	13	=	=	SYM
ejpam-3526	240	14	b	b	PROPN
ejpam-3526	240	15	6=	6=	ADP
ejpam-3526	240	16	a	a	DET
ejpam-3526	240	17	=	=	X
ejpam-3526	240	18	a	a	DET
ejpam-3526	240	19	∗	∗	X
ejpam-3526	240	20	b.	b.	NOUN
ejpam-3526	241	1	in	in	ADP
ejpam-3526	241	2	fact	fact	NOUN
ejpam-3526	241	3	,	,	PUNCT
ejpam-3526	241	4	0	0	NUM
ejpam-3526	241	5	∗	∗	NOUN
ejpam-3526	241	6	b	b	NOUN
ejpam-3526	241	7	=	=	SYM
ejpam-3526	241	8	0	0	PROPN
ejpam-3526	241	9	6=	6=	NUM
ejpam-3526	241	10	b.	b.	PROPN
ejpam-3526	242	1	so	so	ADV
ejpam-3526	242	2	,	,	PUNCT
ejpam-3526	242	3	x	x	PRON
ejpam-3526	242	4	does	do	AUX
ejpam-3526	242	5	not	not	PART
ejpam-3526	242	6	satisfy	satisfy	VERB
ejpam-3526	242	7	(	(	PUNCT
ejpam-3526	242	8	db2	db2	PROPN
ejpam-3526	242	9	)	)	PUNCT
ejpam-3526	242	10	and	and	CCONJ
ejpam-3526	242	11	hence	hence	ADV
ejpam-3526	242	12	,	,	PUNCT
ejpam-3526	242	13	is	be	AUX
ejpam-3526	242	14	not	not	PART
ejpam-3526	242	15	a	a	DET
ejpam-3526	242	16	dual	dual	ADJ
ejpam-3526	242	17	b	b	NOUN
ejpam-3526	242	18	-	-	PUNCT
ejpam-3526	242	19	algebra	algebra	NOUN
ejpam-3526	242	20	.	.	PUNCT
ejpam-3526	243	1	the	the	DET
ejpam-3526	243	2	following	follow	VERB
ejpam-3526	243	3	theorem	theorem	NOUN
ejpam-3526	243	4	shows	show	VERB
ejpam-3526	243	5	that	that	SCONJ
ejpam-3526	243	6	if	if	SCONJ
ejpam-3526	243	7	the	the	DET
ejpam-3526	243	8	symmetric	symmetric	ADJ
ejpam-3526	243	9	condition	condition	NOUN
ejpam-3526	243	10	holds	hold	VERB
ejpam-3526	243	11	in	in	ADP
ejpam-3526	243	12	a	a	DET
ejpam-3526	243	13	bck	bck	NOUN
ejpam-3526	243	14	-	-	PUNCT
ejpam-3526	243	15	algebra	algebra	NOUN
ejpam-3526	243	16	x	x	NOUN
ejpam-3526	243	17	,	,	PUNCT
ejpam-3526	243	18	then	then	ADV
ejpam-3526	243	19	x	x	PUNCT
ejpam-3526	243	20	is	be	AUX
ejpam-3526	243	21	a	a	DET
ejpam-3526	243	22	dual	dual	ADJ
ejpam-3526	243	23	b	b	NOUN
ejpam-3526	243	24	-	-	PUNCT
ejpam-3526	243	25	algebra	algebra	NOUN
ejpam-3526	243	26	.	.	PUNCT
ejpam-3526	244	1	theorem	theorem	NOUN
ejpam-3526	244	2	4	4	NUM
ejpam-3526	244	3	.	.	PUNCT
ejpam-3526	245	1	if	if	SCONJ
ejpam-3526	245	2	(	(	PUNCT
ejpam-3526	245	3	x	x	NOUN
ejpam-3526	245	4	,	,	PUNCT
ejpam-3526	245	5	◦	◦	NOUN
ejpam-3526	245	6	,	,	PUNCT
ejpam-3526	245	7	1	1	NUM
ejpam-3526	245	8	)	)	PUNCT
ejpam-3526	245	9	is	be	AUX
ejpam-3526	245	10	a	a	DET
ejpam-3526	245	11	bck	bck	NOUN
ejpam-3526	245	12	-	-	PUNCT
ejpam-3526	245	13	algebra	algebra	NOUN
ejpam-3526	245	14	satisfying	satisfy	VERB
ejpam-3526	245	15	a	a	DET
ejpam-3526	245	16	symmetric	symmetric	ADJ
ejpam-3526	245	17	condition	condition	NOUN
ejpam-3526	245	18	,	,	PUNCT
ejpam-3526	245	19	then	then	ADV
ejpam-3526	245	20	x	x	PUNCT
ejpam-3526	245	21	is	be	AUX
ejpam-3526	245	22	a	a	DET
ejpam-3526	245	23	dual	dual	ADJ
ejpam-3526	245	24	b	b	NOUN
ejpam-3526	245	25	-	-	PUNCT
ejpam-3526	245	26	algebra	algebra	NOUN
ejpam-3526	245	27	.	.	PUNCT
ejpam-3526	246	1	proof	proof	NOUN
ejpam-3526	246	2	:	:	PUNCT
ejpam-3526	246	3	suppose	suppose	VERB
ejpam-3526	246	4	x	x	PRON
ejpam-3526	246	5	is	be	AUX
ejpam-3526	246	6	a	a	DET
ejpam-3526	246	7	bck	bck	NOUN
ejpam-3526	246	8	-	-	PUNCT
ejpam-3526	246	9	algebra	algebra	NOUN
ejpam-3526	246	10	satisfying	satisfying	NOUN
ejpam-3526	246	11	x	x	VERB
ejpam-3526	246	12	◦	◦	NOUN
ejpam-3526	246	13	y	y	NOUN
ejpam-3526	246	14	=	=	SYM
ejpam-3526	246	15	y	y	PROPN
ejpam-3526	246	16	◦	◦	NOUN
ejpam-3526	246	17	x	x	PUNCT
ejpam-3526	246	18	for	for	ADP
ejpam-3526	246	19	all	all	DET
ejpam-3526	246	20	x	x	NOUN
ejpam-3526	246	21	,	,	PUNCT
ejpam-3526	246	22	y	y	PROPN
ejpam-3526	246	23	in	in	ADP
ejpam-3526	246	24	x.	x.	NOUN
ejpam-3526	246	25	by	by	ADP
ejpam-3526	246	26	remark	remark	NOUN
ejpam-3526	246	27	4	4	NUM
ejpam-3526	246	28	,	,	PUNCT
ejpam-3526	246	29	it	it	PRON
ejpam-3526	246	30	remains	remain	VERB
ejpam-3526	246	31	to	to	PART
ejpam-3526	246	32	show	show	VERB
ejpam-3526	246	33	that	that	SCONJ
ejpam-3526	246	34	x	x	PRON
ejpam-3526	246	35	satisfies	satisfie	NOUN
ejpam-3526	246	36	(	(	PUNCT
ejpam-3526	246	37	db3	db3	PROPN
ejpam-3526	246	38	)	)	PUNCT
ejpam-3526	246	39	and	and	CCONJ
ejpam-3526	246	40	(	(	PUNCT
ejpam-3526	246	41	db2	db2	PROPN
ejpam-3526	246	42	)	)	PUNCT
ejpam-3526	246	43	.	.	PUNCT
ejpam-3526	247	1	by	by	ADP
ejpam-3526	247	2	lemma	lemma	PROPN
ejpam-3526	247	3	1(i	1(i	NUM
ejpam-3526	247	4	)	)	PUNCT
ejpam-3526	247	5	and	and	CCONJ
ejpam-3526	247	6	(	(	PUNCT
ejpam-3526	247	7	ii	ii	NOUN
ejpam-3526	247	8	)	)	PUNCT
ejpam-3526	247	9	of	of	ADP
ejpam-3526	247	10	a	a	DET
ejpam-3526	247	11	bck	bck	NOUN
ejpam-3526	247	12	-	-	PUNCT
ejpam-3526	247	13	algebra	algebra	NOUN
ejpam-3526	247	14	,	,	PUNCT
ejpam-3526	247	15	[	[	X
ejpam-3526	247	16	(	(	PUNCT
ejpam-3526	247	17	y	y	PROPN
ejpam-3526	247	18	◦	◦	NOUN
ejpam-3526	247	19	1)	1)	NUM
ejpam-3526	247	20	◦	◦	NOUN
ejpam-3526	247	21	x	x	NOUN
ejpam-3526	247	22	]	]	X
ejpam-3526	247	23	◦	◦	NOUN
ejpam-3526	247	24	z	z	NOUN
ejpam-3526	247	25	=	=	SYM
ejpam-3526	247	26	(	(	PUNCT
ejpam-3526	247	27	y	y	PROPN
ejpam-3526	247	28	◦	◦	NOUN
ejpam-3526	247	29	x)	x)	PROPN
ejpam-3526	247	30	◦	◦	NOUN
ejpam-3526	247	31	z	z	NOUN
ejpam-3526	247	32	=	=	SYM
ejpam-3526	247	33	(	(	PUNCT
ejpam-3526	247	34	y	y	PROPN
ejpam-3526	247	35	◦	◦	PROPN
ejpam-3526	247	36	z)	z)	NUM
ejpam-3526	247	37	◦	◦	NOUN
ejpam-3526	247	38	x.	x.	NOUN
ejpam-3526	247	39	since	since	SCONJ
ejpam-3526	247	40	x	x	PROPN
ejpam-3526	247	41	◦	◦	NOUN
ejpam-3526	247	42	y	y	NOUN
ejpam-3526	247	43	=	=	SYM
ejpam-3526	247	44	y	y	PROPN
ejpam-3526	247	45	◦	◦	NOUN
ejpam-3526	247	46	x	x	VERB
ejpam-3526	247	47	for	for	ADP
ejpam-3526	247	48	all	all	DET
ejpam-3526	247	49	x	x	NOUN
ejpam-3526	247	50	,	,	PUNCT
ejpam-3526	247	51	y	y	PROPN
ejpam-3526	247	52	in	in	ADP
ejpam-3526	247	53	x	x	PRON
ejpam-3526	247	54	,	,	PUNCT
ejpam-3526	247	55	(	(	PUNCT
ejpam-3526	247	56	y	y	PROPN
ejpam-3526	247	57	◦	◦	PROPN
ejpam-3526	247	58	z	z	PROPN
ejpam-3526	247	59	)	)	PUNCT
ejpam-3526	247	60	◦	◦	NOUN
ejpam-3526	247	61	x	x	SYM
ejpam-3526	247	62	=	=	SYM
ejpam-3526	247	63	x	x	SYM
ejpam-3526	247	64	◦	◦	NOUN
ejpam-3526	247	65	(	(	PUNCT
ejpam-3526	247	66	y	y	PROPN
ejpam-3526	247	67	◦	◦	PROPN
ejpam-3526	247	68	z	z	PROPN
ejpam-3526	247	69	)	)	PUNCT
ejpam-3526	247	70	.	.	PUNCT
ejpam-3526	248	1	hence	hence	ADV
ejpam-3526	248	2	,	,	PUNCT
ejpam-3526	248	3	x	x	PRON
ejpam-3526	248	4	satisfies	satisfie	NOUN
ejpam-3526	248	5	(	(	PUNCT
ejpam-3526	248	6	db3	db3	PROPN
ejpam-3526	248	7	)	)	PUNCT
ejpam-3526	248	8	.	.	PUNCT
ejpam-3526	249	1	by	by	ADP
ejpam-3526	249	2	lemma	lemma	PROPN
ejpam-3526	249	3	1(i	1(i	NUM
ejpam-3526	249	4	)	)	PUNCT
ejpam-3526	249	5	and	and	CCONJ
ejpam-3526	249	6	the	the	DET
ejpam-3526	249	7	hypothesis	hypothesis	NOUN
ejpam-3526	249	8	,	,	PUNCT
ejpam-3526	249	9	x	x	PUNCT
ejpam-3526	249	10	=	=	PUNCT
ejpam-3526	249	11	x	x	PUNCT
ejpam-3526	249	12	◦	◦	NOUN
ejpam-3526	249	13	1	1	NUM
ejpam-3526	249	14	=	=	SYM
ejpam-3526	249	15	1	1	NUM
ejpam-3526	249	16	◦	◦	NOUN
ejpam-3526	249	17	x.	x.	NOUN
ejpam-3526	249	18	this	this	PRON
ejpam-3526	249	19	implies	imply	VERB
ejpam-3526	249	20	that	that	SCONJ
ejpam-3526	249	21	x	x	SYM
ejpam-3526	249	22	satisfies	satisfie	NOUN
ejpam-3526	249	23	(	(	PUNCT
ejpam-3526	249	24	db2	db2	PROPN
ejpam-3526	249	25	)	)	PUNCT
ejpam-3526	249	26	.	.	PUNCT
ejpam-3526	250	1	k.	k.	PROPN
ejpam-3526	250	2	belleza	belleza	PROPN
ejpam-3526	250	3	,	,	PUNCT
ejpam-3526	250	4	j.	j.	PROPN
ejpam-3526	250	5	vilela	vilela	PROPN
ejpam-3526	250	6	/	/	SYM
ejpam-3526	250	7	eur	eur	PROPN
ejpam-3526	250	8	.	.	PUNCT
ejpam-3526	251	1	j.	j.	PROPN
ejpam-3526	251	2	pure	pure	PROPN
ejpam-3526	251	3	appl	appl	PROPN
ejpam-3526	251	4	.	.	PROPN
ejpam-3526	251	5	math	math	PROPN
ejpam-3526	251	6	,	,	PUNCT
ejpam-3526	251	7	12	12	NUM
ejpam-3526	251	8	(	(	PUNCT
ejpam-3526	251	9	4	4	NUM
ejpam-3526	251	10	)	)	PUNCT
ejpam-3526	251	11	(	(	PUNCT
ejpam-3526	251	12	2019	2019	NUM
ejpam-3526	251	13	)	)	PUNCT
ejpam-3526	251	14	,	,	PUNCT
ejpam-3526	251	15	1497	1497	NUM
ejpam-3526	251	16	-	-	SYM
ejpam-3526	251	17	1507	1507	NUM
ejpam-3526	251	18	1503	1503	NUM
ejpam-3526	251	19	4	4	NUM
ejpam-3526	251	20	.	.	PUNCT
ejpam-3526	252	1	commutativity	commutativity	NOUN
ejpam-3526	252	2	in	in	ADP
ejpam-3526	252	3	a	a	DET
ejpam-3526	252	4	dual	dual	ADJ
ejpam-3526	252	5	b	b	NOUN
ejpam-3526	252	6	-	-	PUNCT
ejpam-3526	252	7	algebra	algebra	ADJ
ejpam-3526	252	8	definition	definition	NOUN
ejpam-3526	252	9	8	8	NUM
ejpam-3526	252	10	.	.	PUNCT
ejpam-3526	253	1	let	let	VERB
ejpam-3526	253	2	xd	xd	INTJ
ejpam-3526	253	3	be	be	AUX
ejpam-3526	253	4	a	a	DET
ejpam-3526	253	5	dual	dual	ADJ
ejpam-3526	253	6	b	b	NOUN
ejpam-3526	253	7	-	-	PUNCT
ejpam-3526	253	8	algebra	algebra	NOUN
ejpam-3526	253	9	.	.	PUNCT
ejpam-3526	254	1	define	define	VERB
ejpam-3526	254	2	a	a	DET
ejpam-3526	254	3	binary	binary	ADJ
ejpam-3526	254	4	operation	operation	NOUN
ejpam-3526	254	5	“	"	PUNCT
ejpam-3526	254	6	+	+	CCONJ
ejpam-3526	254	7	”	"	PUNCT
ejpam-3526	254	8	on	on	ADP
ejpam-3526	254	9	x	x	PUNCT
ejpam-3526	254	10	as	as	SCONJ
ejpam-3526	254	11	follows	follow	VERB
ejpam-3526	254	12	:	:	PUNCT
ejpam-3526	254	13	x	x	X
ejpam-3526	255	1	+	+	CCONJ
ejpam-3526	255	2	y	y	NOUN
ejpam-3526	255	3	=	=	SYM
ejpam-3526	255	4	(	(	PUNCT
ejpam-3526	255	5	x	x	SYM
ejpam-3526	255	6	◦	◦	NOUN
ejpam-3526	255	7	1	1	NUM
ejpam-3526	255	8	)	)	PUNCT
ejpam-3526	255	9	◦	◦	NOUN
ejpam-3526	255	10	y	y	NOUN
ejpam-3526	255	11	for	for	ADP
ejpam-3526	255	12	all	all	DET
ejpam-3526	255	13	x	x	NOUN
ejpam-3526	255	14	,	,	PUNCT
ejpam-3526	255	15	y	y	PROPN
ejpam-3526	255	16	in	in	ADP
ejpam-3526	255	17	xd	xd	ADP
ejpam-3526	255	18	.	.	PUNCT
ejpam-3526	256	1	a	a	DET
ejpam-3526	256	2	dual	dual	ADJ
ejpam-3526	256	3	b	b	NOUN
ejpam-3526	256	4	-	-	PUNCT
ejpam-3526	256	5	algebra	algebra	NOUN
ejpam-3526	256	6	is	be	AUX
ejpam-3526	256	7	said	say	VERB
ejpam-3526	256	8	to	to	PART
ejpam-3526	256	9	be	be	AUX
ejpam-3526	256	10	commutative	commutative	ADJ
ejpam-3526	256	11	if	if	SCONJ
ejpam-3526	256	12	x	x	PROPN
ejpam-3526	257	1	+	+	NUM
ejpam-3526	257	2	y	y	PROPN
ejpam-3526	257	3	=	=	SYM
ejpam-3526	257	4	y	y	PROPN
ejpam-3526	257	5	+	+	CCONJ
ejpam-3526	257	6	x	x	X
ejpam-3526	257	7	,	,	PUNCT
ejpam-3526	257	8	that	that	ADV
ejpam-3526	257	9	is	is	ADV
ejpam-3526	257	10	,	,	PUNCT
ejpam-3526	257	11	(	(	PUNCT
ejpam-3526	257	12	x	x	X
ejpam-3526	257	13	◦	◦	NOUN
ejpam-3526	257	14	1	1	NUM
ejpam-3526	257	15	)	)	PUNCT
ejpam-3526	257	16	◦	◦	NOUN
ejpam-3526	257	17	y	y	NOUN
ejpam-3526	257	18	=	=	SYM
ejpam-3526	257	19	(	(	PUNCT
ejpam-3526	257	20	y	y	PROPN
ejpam-3526	257	21	◦	◦	NOUN
ejpam-3526	257	22	1	1	NUM
ejpam-3526	257	23	)	)	PUNCT
ejpam-3526	257	24	◦	◦	NOUN
ejpam-3526	257	25	x	x	SYM
ejpam-3526	257	26	for	for	ADP
ejpam-3526	257	27	all	all	DET
ejpam-3526	257	28	x	x	NOUN
ejpam-3526	257	29	,	,	PUNCT
ejpam-3526	257	30	y	y	PROPN
ejpam-3526	257	31	in	in	ADP
ejpam-3526	257	32	xd	xd	ADP
ejpam-3526	257	33	.	.	PROPN
ejpam-3526	257	34	example	example	NOUN
ejpam-3526	257	35	9	9	NUM
ejpam-3526	257	36	.	.	PUNCT
ejpam-3526	258	1	the	the	DET
ejpam-3526	258	2	dual	dual	ADJ
ejpam-3526	258	3	b	b	NOUN
ejpam-3526	258	4	-	-	PUNCT
ejpam-3526	258	5	algebra	algebra	NOUN
ejpam-3526	258	6	x	x	PUNCT
ejpam-3526	258	7	=	=	PUNCT
ejpam-3526	258	8	r	r	NOUN
ejpam-3526	258	9	in	in	ADP
ejpam-3526	258	10	example	example	NOUN
ejpam-3526	258	11	3	3	NUM
ejpam-3526	258	12	is	be	AUX
ejpam-3526	258	13	commutative	commutative	ADJ
ejpam-3526	258	14	since	since	SCONJ
ejpam-3526	258	15	for	for	ADP
ejpam-3526	258	16	all	all	DET
ejpam-3526	258	17	x	x	NOUN
ejpam-3526	258	18	,	,	PUNCT
ejpam-3526	258	19	y	y	PROPN
ejpam-3526	258	20	in	in	ADP
ejpam-3526	258	21	r	r	PROPN
ejpam-3526	258	22	,	,	PUNCT
ejpam-3526	258	23	(	(	PUNCT
ejpam-3526	258	24	x	x	X
ejpam-3526	258	25	◦	◦	NOUN
ejpam-3526	258	26	1	1	NUM
ejpam-3526	258	27	)	)	PUNCT
ejpam-3526	258	28	◦	◦	NOUN
ejpam-3526	259	1	y	y	NOUN
ejpam-3526	259	2	=	=	SYM
ejpam-3526	259	3	y	y	PROPN
ejpam-3526	259	4	x	x	PUNCT
ejpam-3526	259	5	◦	◦	NOUN
ejpam-3526	259	6	1	1	NUM
ejpam-3526	259	7	=	=	SYM
ejpam-3526	259	8	y	y	PROPN
ejpam-3526	259	9	1	1	NUM
ejpam-3526	259	10	x	x	X
ejpam-3526	259	11	=	=	PUNCT
ejpam-3526	260	1	xy	xy	NOUN
ejpam-3526	260	2	=	=	PUNCT
ejpam-3526	260	3	x	x	SYM
ejpam-3526	260	4	1	1	NUM
ejpam-3526	260	5	y	y	NOUN
ejpam-3526	260	6	=	=	PUNCT
ejpam-3526	260	7	x	x	SYM
ejpam-3526	260	8	y	y	PROPN
ejpam-3526	260	9	◦	◦	NOUN
ejpam-3526	260	10	1	1	NUM
ejpam-3526	260	11	=	=	SYM
ejpam-3526	260	12	(	(	PUNCT
ejpam-3526	260	13	y	y	NOUN
ejpam-3526	260	14	◦	◦	NOUN
ejpam-3526	260	15	1	1	NUM
ejpam-3526	260	16	)	)	PUNCT
ejpam-3526	260	17	◦	◦	NOUN
ejpam-3526	260	18	x.	x.	NOUN
ejpam-3526	260	19	however	however	ADV
ejpam-3526	260	20	,	,	PUNCT
ejpam-3526	260	21	the	the	DET
ejpam-3526	260	22	dual	dual	ADJ
ejpam-3526	260	23	b	b	NOUN
ejpam-3526	260	24	-	-	PUNCT
ejpam-3526	260	25	algebra	algebra	NOUN
ejpam-3526	260	26	in	in	ADP
ejpam-3526	260	27	example	example	NOUN
ejpam-3526	260	28	2	2	NUM
ejpam-3526	260	29	is	be	AUX
ejpam-3526	260	30	not	not	PART
ejpam-3526	260	31	commutative	commutative	ADJ
ejpam-3526	260	32	since	since	SCONJ
ejpam-3526	260	33	(	(	PUNCT
ejpam-3526	260	34	1	1	NUM
ejpam-3526	260	35	◦	◦	NOUN
ejpam-3526	260	36	0	0	NUM
ejpam-3526	260	37	)	)	PUNCT
ejpam-3526	260	38	◦	◦	NOUN
ejpam-3526	260	39	4	4	NUM
ejpam-3526	260	40	=	=	SYM
ejpam-3526	260	41	2	2	NUM
ejpam-3526	260	42	◦	◦	NOUN
ejpam-3526	260	43	4	4	NUM
ejpam-3526	260	44	=	=	SYM
ejpam-3526	260	45	3	3	NUM
ejpam-3526	260	46	6=	6=	SYM
ejpam-3526	260	47	5	5	NUM
ejpam-3526	260	48	=	=	SYM
ejpam-3526	260	49	4	4	NUM
ejpam-3526	260	50	◦	◦	NOUN
ejpam-3526	260	51	1	1	NUM
ejpam-3526	260	52	=	=	SYM
ejpam-3526	260	53	(	(	PUNCT
ejpam-3526	260	54	4	4	NUM
ejpam-3526	260	55	◦	◦	NOUN
ejpam-3526	260	56	0	0	NUM
ejpam-3526	260	57	)	)	PUNCT
ejpam-3526	260	58	◦	◦	NOUN
ejpam-3526	260	59	1	1	NUM
ejpam-3526	260	60	.	.	X
ejpam-3526	261	1	observe	observe	VERB
ejpam-3526	261	2	that	that	SCONJ
ejpam-3526	261	3	(	(	PUNCT
ejpam-3526	261	4	1	1	NUM
ejpam-3526	261	5	◦	◦	NOUN
ejpam-3526	261	6	0	0	NUM
ejpam-3526	261	7	)	)	PUNCT
ejpam-3526	261	8	◦	◦	NOUN
ejpam-3526	261	9	(	(	PUNCT
ejpam-3526	261	10	3	3	NUM
ejpam-3526	261	11	◦	◦	NOUN
ejpam-3526	261	12	0	0	NUM
ejpam-3526	261	13	)	)	PUNCT
ejpam-3526	261	14	=	=	SYM
ejpam-3526	261	15	2	2	NUM
ejpam-3526	261	16	◦	◦	NOUN
ejpam-3526	261	17	3	3	NUM
ejpam-3526	261	18	=	=	SYM
ejpam-3526	261	19	5	5	NUM
ejpam-3526	261	20	6=	6=	SYM
ejpam-3526	261	21	4	4	NUM
ejpam-3526	261	22	=	=	SYM
ejpam-3526	261	23	3	3	NUM
ejpam-3526	261	24	◦	◦	NOUN
ejpam-3526	261	25	1	1	NUM
ejpam-3526	261	26	and	and	CCONJ
ejpam-3526	261	27	(	(	PUNCT
ejpam-3526	261	28	2	2	NUM
ejpam-3526	261	29	◦	◦	NOUN
ejpam-3526	261	30	5	5	NUM
ejpam-3526	261	31	)	)	PUNCT
ejpam-3526	261	32	◦	◦	NOUN
ejpam-3526	261	33	5	5	NUM
ejpam-3526	261	34	=	=	SYM
ejpam-3526	261	35	4	4	NUM
ejpam-3526	261	36	◦	◦	NOUN
ejpam-3526	261	37	5	5	NUM
ejpam-3526	261	38	=	=	SYM
ejpam-3526	261	39	1	1	NUM
ejpam-3526	261	40	6=	6=	NUM
ejpam-3526	261	41	2	2	NUM
ejpam-3526	261	42	.	.	PUNCT
ejpam-3526	262	1	however	however	ADV
ejpam-3526	262	2	,	,	PUNCT
ejpam-3526	262	3	for	for	ADP
ejpam-3526	262	4	a	a	DET
ejpam-3526	262	5	commutative	commutative	ADJ
ejpam-3526	262	6	dual	dual	ADJ
ejpam-3526	262	7	b	b	NOUN
ejpam-3526	262	8	-	-	PUNCT
ejpam-3526	262	9	algebra	algebra	NOUN
ejpam-3526	262	10	,	,	PUNCT
ejpam-3526	262	11	the	the	DET
ejpam-3526	262	12	following	follow	VERB
ejpam-3526	262	13	proposition	proposition	NOUN
ejpam-3526	262	14	holds	hold	VERB
ejpam-3526	262	15	.	.	PUNCT
ejpam-3526	263	1	proposition	proposition	NOUN
ejpam-3526	263	2	4	4	NUM
ejpam-3526	263	3	.	.	PUNCT
ejpam-3526	263	4	suppose	suppose	VERB
ejpam-3526	263	5	xd	xd	INTJ
ejpam-3526	263	6	is	be	VERB
ejpam-3526	263	7	a	a	DET
ejpam-3526	263	8	commutative	commutative	ADJ
ejpam-3526	263	9	b	b	NOUN
ejpam-3526	263	10	-	-	PUNCT
ejpam-3526	263	11	algebra	algebra	NOUN
ejpam-3526	263	12	.	.	PUNCT
ejpam-3526	264	1	then	then	ADV
ejpam-3526	264	2	the	the	DET
ejpam-3526	264	3	following	follow	VERB
ejpam-3526	264	4	hold	hold	NOUN
ejpam-3526	264	5	for	for	ADP
ejpam-3526	264	6	all	all	DET
ejpam-3526	264	7	x	x	NOUN
ejpam-3526	264	8	,	,	PUNCT
ejpam-3526	264	9	y	y	PROPN
ejpam-3526	264	10	in	in	ADP
ejpam-3526	264	11	xd	xd	ADP
ejpam-3526	264	12	:	:	PUNCT
ejpam-3526	264	13	(	(	PUNCT
ejpam-3526	264	14	i	i	NOUN
ejpam-3526	264	15	)	)	PUNCT
ejpam-3526	264	16	(	(	PUNCT
ejpam-3526	264	17	x	x	X
ejpam-3526	264	18	◦	◦	NOUN
ejpam-3526	264	19	1	1	NUM
ejpam-3526	264	20	)	)	PUNCT
ejpam-3526	264	21	◦	◦	NOUN
ejpam-3526	264	22	(	(	PUNCT
ejpam-3526	264	23	y	y	NOUN
ejpam-3526	264	24	◦	◦	NOUN
ejpam-3526	264	25	1	1	NUM
ejpam-3526	264	26	)	)	PUNCT
ejpam-3526	265	1	=	=	SYM
ejpam-3526	265	2	y	y	PROPN
ejpam-3526	265	3	◦	◦	NOUN
ejpam-3526	265	4	x	x	SYM
ejpam-3526	265	5	(	(	PUNCT
ejpam-3526	265	6	ii	ii	NOUN
ejpam-3526	265	7	)	)	PUNCT
ejpam-3526	265	8	(	(	PUNCT
ejpam-3526	265	9	y	y	PROPN
ejpam-3526	265	10	◦	◦	NOUN
ejpam-3526	265	11	x	x	NOUN
ejpam-3526	265	12	)	)	PUNCT
ejpam-3526	265	13	◦	◦	NOUN
ejpam-3526	265	14	x	x	X
ejpam-3526	265	15	=	=	PUNCT
ejpam-3526	265	16	y.	y.	NOUN
ejpam-3526	265	17	proof	proof	NOUN
ejpam-3526	265	18	:	:	PUNCT
ejpam-3526	265	19	let	let	VERB
ejpam-3526	265	20	xd	xd	INTJ
ejpam-3526	265	21	be	be	AUX
ejpam-3526	265	22	a	a	DET
ejpam-3526	265	23	commutative	commutative	ADJ
ejpam-3526	265	24	b	b	NOUN
ejpam-3526	265	25	-	-	PUNCT
ejpam-3526	265	26	algebra	algebra	NOUN
ejpam-3526	265	27	.	.	PUNCT
ejpam-3526	266	1	(	(	PUNCT
ejpam-3526	266	2	i)by	i)by	ADJ
ejpam-3526	266	3	definition	definition	NOUN
ejpam-3526	266	4	8	8	NUM
ejpam-3526	266	5	and	and	CCONJ
ejpam-3526	266	6	lemma	lemma	PROPN
ejpam-3526	266	7	2(i	2(i	NUM
ejpam-3526	266	8	)	)	PUNCT
ejpam-3526	266	9	,	,	PUNCT
ejpam-3526	266	10	(	(	PUNCT
ejpam-3526	266	11	x	x	X
ejpam-3526	266	12	◦	◦	NOUN
ejpam-3526	266	13	1	1	NUM
ejpam-3526	266	14	)	)	PUNCT
ejpam-3526	266	15	◦	◦	NOUN
ejpam-3526	266	16	(	(	PUNCT
ejpam-3526	266	17	y	y	NOUN
ejpam-3526	266	18	◦	◦	NOUN
ejpam-3526	266	19	1	1	NUM
ejpam-3526	266	20	)	)	PUNCT
ejpam-3526	267	1	=	=	NOUN
ejpam-3526	268	1	[	[	X
ejpam-3526	268	2	(	(	PUNCT
ejpam-3526	268	3	y	y	NOUN
ejpam-3526	268	4	◦	◦	NOUN
ejpam-3526	268	5	1	1	NUM
ejpam-3526	268	6	)	)	PUNCT
ejpam-3526	268	7	◦	◦	NOUN
ejpam-3526	268	8	1	1	NUM
ejpam-3526	268	9	]	]	X
ejpam-3526	268	10	◦	◦	NOUN
ejpam-3526	268	11	x	x	X
ejpam-3526	268	12	=	=	PUNCT
ejpam-3526	268	13	y	y	PROPN
ejpam-3526	268	14	◦	◦	NOUN
ejpam-3526	268	15	x.	x.	NOUN
ejpam-3526	268	16	(	(	PUNCT
ejpam-3526	268	17	ii)applying	ii)applye	VERB
ejpam-3526	268	18	lemma	lemma	PROPN
ejpam-3526	268	19	2(iii	2(iii	NUM
ejpam-3526	268	20	)	)	PUNCT
ejpam-3526	268	21	,	,	PUNCT
ejpam-3526	268	22	definition	definition	NOUN
ejpam-3526	268	23	8	8	NUM
ejpam-3526	268	24	,	,	PUNCT
ejpam-3526	268	25	(	(	PUNCT
ejpam-3526	268	26	db3	db3	PROPN
ejpam-3526	268	27	)	)	PUNCT
ejpam-3526	268	28	,	,	PUNCT
ejpam-3526	268	29	lemma	lemma	PROPN
ejpam-3526	268	30	2(i	2(i	NUM
ejpam-3526	268	31	)	)	PUNCT
ejpam-3526	268	32	,	,	PUNCT
ejpam-3526	268	33	(	(	PUNCT
ejpam-3526	268	34	db1	db1	NOUN
ejpam-3526	268	35	)	)	PUNCT
ejpam-3526	268	36	,	,	PUNCT
ejpam-3526	268	37	and	and	CCONJ
ejpam-3526	268	38	(	(	PUNCT
ejpam-3526	268	39	db2	db2	PROPN
ejpam-3526	268	40	)	)	PUNCT
ejpam-3526	268	41	,	,	PUNCT
ejpam-3526	268	42	(	(	PUNCT
ejpam-3526	268	43	y	y	PROPN
ejpam-3526	268	44	◦	◦	NOUN
ejpam-3526	268	45	x	x	NOUN
ejpam-3526	268	46	)	)	PUNCT
ejpam-3526	268	47	◦	◦	NOUN
ejpam-3526	268	48	x	x	SYM
ejpam-3526	269	1	=	=	PUNCT
ejpam-3526	269	2	x	x	PUNCT
ejpam-3526	269	3	◦	◦	NOUN
ejpam-3526	269	4	[	[	X
ejpam-3526	269	5	(	(	PUNCT
ejpam-3526	269	6	y	y	NOUN
ejpam-3526	269	7	◦	◦	NOUN
ejpam-3526	269	8	1	1	NUM
ejpam-3526	269	9	)	)	PUNCT
ejpam-3526	269	10	◦	◦	NOUN
ejpam-3526	269	11	x	x	X
ejpam-3526	269	12	]	]	X
ejpam-3526	269	13	=	=	PUNCT
ejpam-3526	269	14	x	x	PUNCT
ejpam-3526	269	15	◦	◦	NOUN
ejpam-3526	269	16	[	[	X
ejpam-3526	269	17	(	(	PUNCT
ejpam-3526	269	18	x	x	SYM
ejpam-3526	269	19	◦	◦	NOUN
ejpam-3526	269	20	1	1	NUM
ejpam-3526	269	21	)	)	PUNCT
ejpam-3526	269	22	◦	◦	NOUN
ejpam-3526	269	23	y	y	NOUN
ejpam-3526	269	24	]	]	X
ejpam-3526	269	25	=(	=(	NOUN
ejpam-3526	270	1	[	[	X
ejpam-3526	270	2	(	(	PUNCT
ejpam-3526	270	3	x	x	SYM
ejpam-3526	270	4	◦	◦	NOUN
ejpam-3526	270	5	1	1	NUM
ejpam-3526	270	6	)	)	PUNCT
ejpam-3526	270	7	◦	◦	NOUN
ejpam-3526	270	8	1	1	NUM
ejpam-3526	270	9	]	]	X
ejpam-3526	270	10	◦	◦	NOUN
ejpam-3526	270	11	x	x	PUNCT
ejpam-3526	270	12	)	)	PUNCT
ejpam-3526	271	1	◦	◦	NOUN
ejpam-3526	271	2	y	y	NOUN
ejpam-3526	271	3	=	=	SYM
ejpam-3526	271	4	(	(	PUNCT
ejpam-3526	271	5	x	x	PART
ejpam-3526	271	6	◦	◦	NOUN
ejpam-3526	271	7	x	x	NOUN
ejpam-3526	271	8	)	)	PUNCT
ejpam-3526	271	9	◦	◦	NOUN
ejpam-3526	271	10	y	y	NOUN
ejpam-3526	271	11	=	=	SYM
ejpam-3526	271	12	1	1	NUM
ejpam-3526	271	13	◦	◦	NOUN
ejpam-3526	271	14	y	y	NOUN
ejpam-3526	271	15	=	=	PUNCT
ejpam-3526	271	16	y.	y.	PROPN
ejpam-3526	271	17	lemma	lemma	PROPN
ejpam-3526	272	1	4	4	X
ejpam-3526	272	2	.	.	PUNCT
ejpam-3526	273	1	if	if	SCONJ
ejpam-3526	273	2	xd	xd	PRON
ejpam-3526	273	3	is	be	VERB
ejpam-3526	273	4	a	a	DET
ejpam-3526	273	5	commutative	commutative	ADJ
ejpam-3526	273	6	dual	dual	ADJ
ejpam-3526	273	7	b	b	NOUN
ejpam-3526	273	8	-	-	PUNCT
ejpam-3526	273	9	algebra	algebra	NOUN
ejpam-3526	273	10	,	,	PUNCT
ejpam-3526	273	11	then	then	ADV
ejpam-3526	273	12	the	the	DET
ejpam-3526	273	13	right	right	ADJ
ejpam-3526	273	14	cancellation	cancellation	NOUN
ejpam-3526	273	15	law	law	NOUN
ejpam-3526	273	16	holds	hold	VERB
ejpam-3526	273	17	,	,	PUNCT
ejpam-3526	273	18	that	that	ADV
ejpam-3526	273	19	is	is	ADV
ejpam-3526	273	20	,	,	PUNCT
ejpam-3526	273	21	x	x	PUNCT
ejpam-3526	273	22	◦	◦	NOUN
ejpam-3526	273	23	z	z	NOUN
ejpam-3526	273	24	=	=	SYM
ejpam-3526	273	25	y	y	PROPN
ejpam-3526	273	26	◦	◦	NOUN
ejpam-3526	273	27	z	z	NOUN
ejpam-3526	273	28	implies	imply	VERB
ejpam-3526	273	29	x	x	PUNCT
ejpam-3526	273	30	=	=	SYM
ejpam-3526	273	31	y	y	PROPN
ejpam-3526	273	32	for	for	ADP
ejpam-3526	273	33	all	all	DET
ejpam-3526	273	34	x	x	PROPN
ejpam-3526	273	35	,	,	PUNCT
ejpam-3526	273	36	y	y	PROPN
ejpam-3526	273	37	,	,	PUNCT
ejpam-3526	273	38	z	z	NOUN
ejpam-3526	273	39	in	in	ADP
ejpam-3526	273	40	xd	xd	ADP
ejpam-3526	273	41	.	.	PUNCT
ejpam-3526	274	1	proof	proof	NOUN
ejpam-3526	274	2	:	:	PUNCT
ejpam-3526	274	3	suppose	suppose	VERB
ejpam-3526	274	4	xd	xd	INTJ
ejpam-3526	274	5	is	be	VERB
ejpam-3526	274	6	commutative	commutative	ADJ
ejpam-3526	274	7	and	and	CCONJ
ejpam-3526	274	8	x	x	PART
ejpam-3526	274	9	◦	◦	NOUN
ejpam-3526	274	10	z	z	NOUN
ejpam-3526	274	11	=	=	SYM
ejpam-3526	274	12	y	y	PROPN
ejpam-3526	274	13	◦	◦	NOUN
ejpam-3526	274	14	z	z	NOUN
ejpam-3526	274	15	for	for	ADP
ejpam-3526	274	16	any	any	DET
ejpam-3526	274	17	x	x	NOUN
ejpam-3526	274	18	,	,	PUNCT
ejpam-3526	274	19	y	y	PROPN
ejpam-3526	274	20	,	,	PUNCT
ejpam-3526	274	21	z	z	VERB
ejpam-3526	274	22	in	in	ADP
ejpam-3526	274	23	xd	xd	ADP
ejpam-3526	274	24	.	.	PUNCT
ejpam-3526	275	1	then	then	ADV
ejpam-3526	275	2	by	by	ADP
ejpam-3526	275	3	proposition	proposition	NOUN
ejpam-3526	275	4	4(ii	4(ii	NUM
ejpam-3526	275	5	)	)	PUNCT
ejpam-3526	275	6	,	,	PUNCT
ejpam-3526	275	7	we	we	PRON
ejpam-3526	275	8	can	can	AUX
ejpam-3526	275	9	write	write	VERB
ejpam-3526	275	10	x	x	X
ejpam-3526	275	11	=	=	SYM
ejpam-3526	275	12	(	(	PUNCT
ejpam-3526	275	13	x	x	PART
ejpam-3526	275	14	◦	◦	NOUN
ejpam-3526	275	15	z	z	NOUN
ejpam-3526	275	16	)	)	PUNCT
ejpam-3526	275	17	◦	◦	NOUN
ejpam-3526	275	18	z	z	NOUN
ejpam-3526	276	1	=	=	SYM
ejpam-3526	276	2	(	(	PUNCT
ejpam-3526	276	3	y	y	PROPN
ejpam-3526	276	4	◦	◦	PROPN
ejpam-3526	276	5	z	z	PROPN
ejpam-3526	276	6	)	)	PUNCT
ejpam-3526	276	7	◦	◦	NOUN
ejpam-3526	276	8	z	z	NOUN
ejpam-3526	276	9	=	=	PUNCT
ejpam-3526	276	10	y.	y.	NOUN
ejpam-3526	276	11	proposition	proposition	NOUN
ejpam-3526	276	12	5	5	NUM
ejpam-3526	276	13	.	.	PUNCT
ejpam-3526	277	1	if	if	SCONJ
ejpam-3526	277	2	xd	xd	PRON
ejpam-3526	277	3	is	be	VERB
ejpam-3526	277	4	a	a	DET
ejpam-3526	277	5	commutative	commutative	ADJ
ejpam-3526	277	6	dual	dual	ADJ
ejpam-3526	277	7	b	b	NOUN
ejpam-3526	277	8	-	-	PUNCT
ejpam-3526	277	9	algebra	algebra	NOUN
ejpam-3526	277	10	,	,	PUNCT
ejpam-3526	277	11	then	then	ADV
ejpam-3526	277	12	the	the	DET
ejpam-3526	277	13	following	follow	VERB
ejpam-3526	277	14	hold	hold	NOUN
ejpam-3526	277	15	for	for	ADP
ejpam-3526	277	16	all	all	DET
ejpam-3526	277	17	x	x	NOUN
ejpam-3526	277	18	,	,	PUNCT
ejpam-3526	277	19	y	y	PROPN
ejpam-3526	277	20	,	,	PUNCT
ejpam-3526	277	21	z	z	VERB
ejpam-3526	277	22	in	in	ADP
ejpam-3526	277	23	xd	xd	ADP
ejpam-3526	277	24	:	:	PUNCT
ejpam-3526	277	25	(	(	PUNCT
ejpam-3526	277	26	i	i	NOUN
ejpam-3526	277	27	)	)	PUNCT
ejpam-3526	277	28	x	x	VERB
ejpam-3526	278	1	◦	◦	NOUN
ejpam-3526	278	2	(	(	PUNCT
ejpam-3526	278	3	y	y	PROPN
ejpam-3526	278	4	◦	◦	PROPN
ejpam-3526	278	5	z	z	PROPN
ejpam-3526	278	6	)	)	PUNCT
ejpam-3526	278	7	=	=	SYM
ejpam-3526	278	8	y	y	PROPN
ejpam-3526	278	9	◦	◦	NOUN
ejpam-3526	278	10	(	(	PUNCT
ejpam-3526	278	11	x	x	PART
ejpam-3526	278	12	◦	◦	NOUN
ejpam-3526	278	13	z	z	NOUN
ejpam-3526	278	14	)	)	PUNCT
ejpam-3526	278	15	(	(	PUNCT
ejpam-3526	278	16	iii	iii	NOUN
ejpam-3526	278	17	)	)	PUNCT
ejpam-3526	278	18	x	x	SYM
ejpam-3526	278	19	◦	◦	NOUN
ejpam-3526	278	20	(	(	PUNCT
ejpam-3526	278	21	y	y	PROPN
ejpam-3526	278	22	◦	◦	NOUN
ejpam-3526	278	23	x	x	X
ejpam-3526	278	24	)	)	PUNCT
ejpam-3526	278	25	=	=	SYM
ejpam-3526	278	26	(	(	PUNCT
ejpam-3526	278	27	x	x	SYM
ejpam-3526	278	28	◦	◦	VERB
ejpam-3526	278	29	y	y	NOUN
ejpam-3526	278	30	)	)	PUNCT
ejpam-3526	278	31	◦	◦	NOUN
ejpam-3526	278	32	(	(	PUNCT
ejpam-3526	278	33	x	x	X
ejpam-3526	278	34	◦	◦	NOUN
ejpam-3526	278	35	1	1	NUM
ejpam-3526	278	36	)	)	PUNCT
ejpam-3526	278	37	(	(	PUNCT
ejpam-3526	278	38	ii	ii	NOUN
ejpam-3526	278	39	)	)	PUNCT
ejpam-3526	278	40	(	(	PUNCT
ejpam-3526	278	41	x	x	X
ejpam-3526	278	42	◦	◦	VERB
ejpam-3526	278	43	y	y	NOUN
ejpam-3526	278	44	)	)	PUNCT
ejpam-3526	278	45	◦	◦	NOUN
ejpam-3526	278	46	z	z	NOUN
ejpam-3526	279	1	=	=	SYM
ejpam-3526	280	1	(	(	PUNCT
ejpam-3526	280	2	z	z	NOUN
ejpam-3526	280	3	◦	◦	NOUN
ejpam-3526	280	4	y	y	NOUN
ejpam-3526	280	5	)	)	PUNCT
ejpam-3526	280	6	◦	◦	NOUN
ejpam-3526	280	7	x	x	SYM
ejpam-3526	280	8	(	(	PUNCT
ejpam-3526	280	9	iv	iv	X
ejpam-3526	280	10	)	)	PUNCT
ejpam-3526	280	11	y	y	PROPN
ejpam-3526	280	12	◦	◦	NOUN
ejpam-3526	281	1	[	[	X
ejpam-3526	281	2	(	(	PUNCT
ejpam-3526	281	3	y	y	PROPN
ejpam-3526	281	4	◦	◦	NOUN
ejpam-3526	281	5	x	x	NOUN
ejpam-3526	281	6	)	)	PUNCT
ejpam-3526	281	7	◦	◦	NOUN
ejpam-3526	281	8	x	x	X
ejpam-3526	281	9	]	]	X
ejpam-3526	281	10	=	=	SYM
ejpam-3526	281	11	1	1	X
ejpam-3526	281	12	.	.	X
ejpam-3526	282	1	proof	proof	NOUN
ejpam-3526	282	2	:	:	PUNCT
ejpam-3526	282	3	suppose	suppose	VERB
ejpam-3526	282	4	xd	xd	INTJ
ejpam-3526	282	5	is	be	AUX
ejpam-3526	282	6	commutative	commutative	ADJ
ejpam-3526	282	7	and	and	CCONJ
ejpam-3526	282	8	x	x	NOUN
ejpam-3526	282	9	,	,	PUNCT
ejpam-3526	282	10	y	y	PROPN
ejpam-3526	282	11	,	,	PUNCT
ejpam-3526	282	12	z	z	PROPN
ejpam-3526	282	13	∈	∈	PROPN
ejpam-3526	283	1	xd	xd	INTJ
ejpam-3526	283	2	.	.	PUNCT
ejpam-3526	284	1	(	(	PUNCT
ejpam-3526	284	2	i	i	NOUN
ejpam-3526	284	3	)	)	PUNCT
ejpam-3526	284	4	by	by	ADP
ejpam-3526	284	5	(	(	PUNCT
ejpam-3526	284	6	db3	db3	PROPN
ejpam-3526	284	7	)	)	PUNCT
ejpam-3526	284	8	and	and	CCONJ
ejpam-3526	284	9	definition	definition	NOUN
ejpam-3526	284	10	8	8	NUM
ejpam-3526	284	11	,	,	PUNCT
ejpam-3526	284	12	x	x	X
ejpam-3526	284	13	◦	◦	NOUN
ejpam-3526	284	14	(	(	PUNCT
ejpam-3526	284	15	y	y	PROPN
ejpam-3526	284	16	◦	◦	PROPN
ejpam-3526	284	17	z	z	PROPN
ejpam-3526	284	18	)	)	PUNCT
ejpam-3526	284	19	=	=	PUNCT
ejpam-3526	285	1	[	[	X
ejpam-3526	285	2	(	(	PUNCT
ejpam-3526	285	3	y	y	NOUN
ejpam-3526	285	4	◦	◦	NOUN
ejpam-3526	285	5	1	1	NUM
ejpam-3526	285	6	)	)	PUNCT
ejpam-3526	285	7	◦	◦	NOUN
ejpam-3526	285	8	x	x	SYM
ejpam-3526	285	9	]	]	X
ejpam-3526	285	10	◦	◦	NOUN
ejpam-3526	285	11	z	z	NOUN
ejpam-3526	285	12	=	=	PUNCT
ejpam-3526	286	1	[	[	X
ejpam-3526	286	2	(	(	PUNCT
ejpam-3526	286	3	x	x	SYM
ejpam-3526	286	4	◦	◦	NOUN
ejpam-3526	286	5	1	1	NUM
ejpam-3526	286	6	)	)	PUNCT
ejpam-3526	286	7	◦	◦	NOUN
ejpam-3526	286	8	y	y	SYM
ejpam-3526	286	9	]	]	X
ejpam-3526	286	10	◦	◦	NOUN
ejpam-3526	286	11	z	z	NOUN
ejpam-3526	286	12	=	=	SYM
ejpam-3526	286	13	y	y	PROPN
ejpam-3526	286	14	◦	◦	NOUN
ejpam-3526	286	15	(	(	PUNCT
ejpam-3526	286	16	x	x	PART
ejpam-3526	286	17	◦	◦	NOUN
ejpam-3526	286	18	z	z	NOUN
ejpam-3526	286	19	)	)	PUNCT
ejpam-3526	286	20	.	.	PUNCT
ejpam-3526	287	1	(	(	PUNCT
ejpam-3526	287	2	ii	ii	NOUN
ejpam-3526	287	3	)	)	PUNCT
ejpam-3526	287	4	applying	apply	VERB
ejpam-3526	287	5	lemma	lemma	PROPN
ejpam-3526	287	6	2(iii	2(iii	NUM
ejpam-3526	287	7	)	)	PUNCT
ejpam-3526	287	8	and	and	CCONJ
ejpam-3526	287	9	since	since	SCONJ
ejpam-3526	287	10	xd	xd	INTJ
ejpam-3526	287	11	is	be	VERB
ejpam-3526	287	12	commutative	commutative	ADJ
ejpam-3526	287	13	,	,	PUNCT
ejpam-3526	287	14	(	(	PUNCT
ejpam-3526	287	15	x	x	SYM
ejpam-3526	287	16	◦	◦	VERB
ejpam-3526	287	17	y	y	NOUN
ejpam-3526	287	18	)	)	PUNCT
ejpam-3526	287	19	◦	◦	NOUN
ejpam-3526	287	20	z	z	NOUN
ejpam-3526	288	1	=	=	SYM
ejpam-3526	288	2	y	y	PROPN
ejpam-3526	288	3	◦	◦	NOUN
ejpam-3526	289	1	[	[	X
ejpam-3526	289	2	(	(	PUNCT
ejpam-3526	289	3	x	x	SYM
ejpam-3526	289	4	◦	◦	NOUN
ejpam-3526	289	5	1	1	NUM
ejpam-3526	289	6	)	)	PUNCT
ejpam-3526	289	7	◦	◦	NOUN
ejpam-3526	289	8	z	z	X
ejpam-3526	289	9	]	]	X
ejpam-3526	289	10	=	=	PUNCT
ejpam-3526	289	11	y	y	PROPN
ejpam-3526	289	12	◦	◦	NOUN
ejpam-3526	290	1	[	[	X
ejpam-3526	290	2	(	(	PUNCT
ejpam-3526	290	3	z	z	NOUN
ejpam-3526	290	4	◦	◦	NOUN
ejpam-3526	290	5	1	1	NUM
ejpam-3526	290	6	)	)	PUNCT
ejpam-3526	290	7	◦	◦	NOUN
ejpam-3526	290	8	x	x	X
ejpam-3526	290	9	]	]	X
ejpam-3526	290	10	=	=	SYM
ejpam-3526	290	11	(	(	PUNCT
ejpam-3526	290	12	z	z	NOUN
ejpam-3526	290	13	◦	◦	NOUN
ejpam-3526	290	14	y	y	NOUN
ejpam-3526	290	15	)	)	PUNCT
ejpam-3526	290	16	◦	◦	NOUN
ejpam-3526	290	17	x.	x.	NOUN
ejpam-3526	290	18	(	(	PUNCT
ejpam-3526	290	19	iii	iii	X
ejpam-3526	290	20	)	)	PUNCT
ejpam-3526	290	21	write	write	NOUN
ejpam-3526	290	22	x	x	SYM
ejpam-3526	290	23	◦	◦	NOUN
ejpam-3526	290	24	(	(	PUNCT
ejpam-3526	290	25	y	y	PROPN
ejpam-3526	290	26	◦	◦	NOUN
ejpam-3526	290	27	x	x	X
ejpam-3526	290	28	)	)	PUNCT
ejpam-3526	291	1	=	=	SYM
ejpam-3526	291	2	y	y	PROPN
ejpam-3526	291	3	◦	◦	NOUN
ejpam-3526	291	4	(	(	PUNCT
ejpam-3526	291	5	x	x	PART
ejpam-3526	291	6	◦	◦	NOUN
ejpam-3526	291	7	x	x	X
ejpam-3526	291	8	)	)	PUNCT
ejpam-3526	291	9	by	by	ADP
ejpam-3526	291	10	(	(	PUNCT
ejpam-3526	291	11	i	i	NOUN
ejpam-3526	291	12	)	)	PUNCT
ejpam-3526	291	13	.	.	PUNCT
ejpam-3526	292	1	then	then	ADV
ejpam-3526	292	2	y	y	PROPN
ejpam-3526	292	3	◦	◦	NOUN
ejpam-3526	292	4	(	(	PUNCT
ejpam-3526	292	5	x	x	PART
ejpam-3526	292	6	◦	◦	NOUN
ejpam-3526	292	7	x	x	NOUN
ejpam-3526	292	8	)	)	PUNCT
ejpam-3526	293	1	=	=	SYM
ejpam-3526	293	2	y	y	PROPN
ejpam-3526	293	3	◦	◦	NOUN
ejpam-3526	293	4	1	1	NUM
ejpam-3526	293	5	=	=	SYM
ejpam-3526	293	6	(	(	PUNCT
ejpam-3526	293	7	x	x	SYM
ejpam-3526	293	8	◦	◦	VERB
ejpam-3526	293	9	y	y	NOUN
ejpam-3526	293	10	)	)	PUNCT
ejpam-3526	293	11	◦	◦	NOUN
ejpam-3526	293	12	(	(	PUNCT
ejpam-3526	293	13	x	x	X
ejpam-3526	293	14	◦	◦	NOUN
ejpam-3526	293	15	1	1	NUM
ejpam-3526	293	16	)	)	PUNCT
ejpam-3526	293	17	by	by	ADP
ejpam-3526	293	18	(	(	PUNCT
ejpam-3526	293	19	db1	db1	NOUN
ejpam-3526	293	20	)	)	PUNCT
ejpam-3526	293	21	and	and	CCONJ
ejpam-3526	293	22	lemma	lemma	PROPN
ejpam-3526	293	23	2(viii	2(viii	NUM
ejpam-3526	293	24	)	)	PUNCT
ejpam-3526	293	25	.	.	PUNCT
ejpam-3526	294	1	(	(	PUNCT
ejpam-3526	294	2	iv	iv	X
ejpam-3526	294	3	)	)	PUNCT
ejpam-3526	294	4	follows	follow	VERB
ejpam-3526	294	5	directly	directly	ADV
ejpam-3526	294	6	from	from	ADP
ejpam-3526	294	7	proposition	proposition	NOUN
ejpam-3526	294	8	4(ii	4(ii	NUM
ejpam-3526	294	9	)	)	PUNCT
ejpam-3526	295	1	and	and	CCONJ
ejpam-3526	295	2	(	(	PUNCT
ejpam-3526	295	3	db1	db1	NOUN
ejpam-3526	295	4	)	)	PUNCT
ejpam-3526	295	5	.	.	PUNCT
ejpam-3526	296	1	corollary	corollary	ADJ
ejpam-3526	296	2	1	1	NUM
ejpam-3526	296	3	.	.	PUNCT
ejpam-3526	297	1	if	if	SCONJ
ejpam-3526	297	2	xd	xd	INTJ
ejpam-3526	297	3	is	be	VERB
ejpam-3526	297	4	a	a	DET
ejpam-3526	297	5	dual	dual	ADJ
ejpam-3526	297	6	b	b	NOUN
ejpam-3526	297	7	-	-	PUNCT
ejpam-3526	297	8	algebra	algebra	NOUN
ejpam-3526	297	9	satisfying	satisfy	VERB
ejpam-3526	297	10	a	a	DET
ejpam-3526	297	11	symmetric	symmetric	ADJ
ejpam-3526	297	12	condition	condition	NOUN
ejpam-3526	297	13	,	,	PUNCT
ejpam-3526	297	14	then	then	ADV
ejpam-3526	297	15	xd	xd	INTJ
ejpam-3526	297	16	is	be	VERB
ejpam-3526	297	17	commutative	commutative	ADJ
ejpam-3526	297	18	.	.	PUNCT
ejpam-3526	298	1	proof	proof	NOUN
ejpam-3526	298	2	:	:	PUNCT
ejpam-3526	298	3	let	let	VERB
ejpam-3526	298	4	xd	xd	INTJ
ejpam-3526	298	5	be	be	AUX
ejpam-3526	298	6	a	a	DET
ejpam-3526	298	7	dual	dual	ADJ
ejpam-3526	298	8	b	b	NOUN
ejpam-3526	298	9	-	-	PUNCT
ejpam-3526	298	10	algebra	algebra	NOUN
ejpam-3526	298	11	satisfying	satisfy	VERB
ejpam-3526	298	12	a	a	DET
ejpam-3526	298	13	symmetric	symmetric	ADJ
ejpam-3526	298	14	condition	condition	NOUN
ejpam-3526	298	15	.	.	PUNCT
ejpam-3526	299	1	then	then	ADV
ejpam-3526	299	2	(	(	PUNCT
ejpam-3526	299	3	x	x	X
ejpam-3526	299	4	◦	◦	NOUN
ejpam-3526	299	5	1)	1)	NUM
ejpam-3526	299	6	◦	◦	NOUN
ejpam-3526	299	7	y	y	NOUN
ejpam-3526	299	8	=	=	SYM
ejpam-3526	299	9	(	(	PUNCT
ejpam-3526	299	10	1	1	NUM
ejpam-3526	299	11	◦	◦	NOUN
ejpam-3526	299	12	x)	x)	PROPN
ejpam-3526	299	13	◦	◦	NOUN
ejpam-3526	299	14	y	y	NOUN
ejpam-3526	299	15	=	=	SYM
ejpam-3526	299	16	x	x	PROPN
ejpam-3526	299	17	◦	◦	VERB
ejpam-3526	299	18	y	y	NOUN
ejpam-3526	299	19	=	=	SYM
ejpam-3526	299	20	y	y	PROPN
ejpam-3526	299	21	◦	◦	NOUN
ejpam-3526	299	22	x	x	SYM
ejpam-3526	299	23	=	=	SYM
ejpam-3526	299	24	(	(	PUNCT
ejpam-3526	299	25	1	1	NUM
ejpam-3526	299	26	◦	◦	NOUN
ejpam-3526	299	27	y)	y)	NOUN
ejpam-3526	299	28	◦	◦	NOUN
ejpam-3526	299	29	x	x	SYM
ejpam-3526	299	30	=	=	SYM
ejpam-3526	299	31	(	(	PUNCT
ejpam-3526	299	32	y	y	NOUN
ejpam-3526	299	33	◦	◦	NOUN
ejpam-3526	299	34	1)	1)	NUM
ejpam-3526	299	35	◦	◦	NOUN
ejpam-3526	299	36	x.	x.	NOUN
ejpam-3526	299	37	this	this	PRON
ejpam-3526	299	38	implies	imply	VERB
ejpam-3526	299	39	that	that	SCONJ
ejpam-3526	299	40	xd	xd	INTJ
ejpam-3526	299	41	is	be	VERB
ejpam-3526	299	42	commutative	commutative	ADJ
ejpam-3526	299	43	.	.	PUNCT
ejpam-3526	300	1	the	the	DET
ejpam-3526	300	2	following	follow	VERB
ejpam-3526	300	3	corollary	corollary	NOUN
ejpam-3526	300	4	follows	follow	VERB
ejpam-3526	300	5	from	from	ADP
ejpam-3526	300	6	theorem	theorem	ADJ
ejpam-3526	300	7	4	4	NUM
ejpam-3526	300	8	and	and	CCONJ
ejpam-3526	300	9	corollary	corollary	ADJ
ejpam-3526	300	10	1	1	NUM
ejpam-3526	300	11	.	.	PUNCT
ejpam-3526	301	1	k.	k.	PROPN
ejpam-3526	301	2	belleza	belleza	PROPN
ejpam-3526	301	3	,	,	PUNCT
ejpam-3526	301	4	j.	j.	PROPN
ejpam-3526	301	5	vilela	vilela	PROPN
ejpam-3526	301	6	/	/	SYM
ejpam-3526	301	7	eur	eur	PROPN
ejpam-3526	301	8	.	.	PUNCT
ejpam-3526	302	1	j.	j.	PROPN
ejpam-3526	302	2	pure	pure	PROPN
ejpam-3526	302	3	appl	appl	PROPN
ejpam-3526	302	4	.	.	PROPN
ejpam-3526	302	5	math	math	PROPN
ejpam-3526	302	6	,	,	PUNCT
ejpam-3526	302	7	12	12	NUM
ejpam-3526	302	8	(	(	PUNCT
ejpam-3526	302	9	4	4	NUM
ejpam-3526	302	10	)	)	PUNCT
ejpam-3526	302	11	(	(	PUNCT
ejpam-3526	302	12	2019	2019	NUM
ejpam-3526	302	13	)	)	PUNCT
ejpam-3526	302	14	,	,	PUNCT
ejpam-3526	302	15	1497	1497	NUM
ejpam-3526	302	16	-	-	SYM
ejpam-3526	302	17	1507	1507	NUM
ejpam-3526	302	18	1504	1504	NUM
ejpam-3526	302	19	corollary	corollary	NOUN
ejpam-3526	302	20	2	2	NUM
ejpam-3526	302	21	.	.	PUNCT
ejpam-3526	302	22	suppose	suppose	VERB
ejpam-3526	302	23	x	x	PRON
ejpam-3526	302	24	is	be	AUX
ejpam-3526	302	25	a	a	DET
ejpam-3526	302	26	bck	bck	NOUN
ejpam-3526	302	27	-	-	PUNCT
ejpam-3526	302	28	algebra	algebra	NOUN
ejpam-3526	302	29	satisfying	satisfy	VERB
ejpam-3526	302	30	a	a	DET
ejpam-3526	302	31	symmetric	symmetric	ADJ
ejpam-3526	302	32	condition	condition	NOUN
ejpam-3526	302	33	.	.	PUNCT
ejpam-3526	303	1	then	then	ADV
ejpam-3526	303	2	x	x	PRON
ejpam-3526	303	3	is	be	AUX
ejpam-3526	303	4	a	a	DET
ejpam-3526	303	5	commutative	commutative	ADJ
ejpam-3526	303	6	dual	dual	ADJ
ejpam-3526	303	7	b	b	NOUN
ejpam-3526	303	8	-	-	PUNCT
ejpam-3526	303	9	algebra	algebra	NOUN
ejpam-3526	303	10	.	.	PUNCT
ejpam-3526	304	1	the	the	DET
ejpam-3526	304	2	following	follow	VERB
ejpam-3526	304	3	results	result	NOUN
ejpam-3526	304	4	present	present	VERB
ejpam-3526	304	5	the	the	DET
ejpam-3526	304	6	relationship	relationship	NOUN
ejpam-3526	304	7	between	between	ADP
ejpam-3526	304	8	a	a	DET
ejpam-3526	304	9	commutative	commutative	ADJ
ejpam-3526	304	10	dual	dual	ADJ
ejpam-3526	304	11	b	b	NOUN
ejpam-3526	304	12	-	-	PUNCT
ejpam-3526	304	13	algebra	algebra	NOUN
ejpam-3526	304	14	and	and	CCONJ
ejpam-3526	304	15	some	some	DET
ejpam-3526	304	16	algebras	algebra	NOUN
ejpam-3526	304	17	,	,	PUNCT
ejpam-3526	304	18	namely	namely	ADV
ejpam-3526	304	19	,	,	PUNCT
ejpam-3526	304	20	ci	ci	NOUN
ejpam-3526	304	21	-	-	NOUN
ejpam-3526	304	22	algebra	algebra	PROPN
ejpam-3526	304	23	and	and	CCONJ
ejpam-3526	304	24	dual	dual	ADJ
ejpam-3526	304	25	bci	bci	NOUN
ejpam-3526	304	26	-	-	NOUN
ejpam-3526	304	27	algebra	algebra	NOUN
ejpam-3526	304	28	.	.	PUNCT
ejpam-3526	305	1	comparing	compare	VERB
ejpam-3526	305	2	the	the	DET
ejpam-3526	305	3	axioms	axiom	NOUN
ejpam-3526	305	4	and	and	CCONJ
ejpam-3526	305	5	properties	property	NOUN
ejpam-3526	305	6	of	of	ADP
ejpam-3526	305	7	commutative	commutative	ADJ
ejpam-3526	305	8	dual	dual	ADJ
ejpam-3526	305	9	b	b	NOUN
ejpam-3526	305	10	-	-	PUNCT
ejpam-3526	305	11	algebra	algebra	NOUN
ejpam-3526	305	12	,	,	PUNCT
ejpam-3526	305	13	ci	ci	NOUN
ejpam-3526	305	14	-	-	NOUN
ejpam-3526	305	15	algebra	algebra	PROPN
ejpam-3526	305	16	and	and	CCONJ
ejpam-3526	305	17	dual	dual	ADJ
ejpam-3526	305	18	bci	bci	NOUN
ejpam-3526	305	19	-	-	NOUN
ejpam-3526	305	20	algebra	algebra	NOUN
ejpam-3526	305	21	,	,	PUNCT
ejpam-3526	305	22	we	we	PRON
ejpam-3526	305	23	have	have	VERB
ejpam-3526	305	24	the	the	DET
ejpam-3526	305	25	following	follow	VERB
ejpam-3526	305	26	remarks	remark	NOUN
ejpam-3526	305	27	.	.	PUNCT
ejpam-3526	306	1	remark	remark	NOUN
ejpam-3526	306	2	5	5	NUM
ejpam-3526	306	3	.	.	PUNCT
ejpam-3526	307	1	(	(	PUNCT
ejpam-3526	307	2	i	i	NOUN
ejpam-3526	307	3	)	)	PUNCT
ejpam-3526	307	4	the	the	DET
ejpam-3526	307	5	class	class	NOUN
ejpam-3526	307	6	of	of	ADP
ejpam-3526	307	7	commutative	commutative	ADJ
ejpam-3526	307	8	dual	dual	ADJ
ejpam-3526	307	9	b	b	NOUN
ejpam-3526	307	10	-	-	PUNCT
ejpam-3526	307	11	algebras	algebras	PROPN
ejpam-3526	307	12	is	be	AUX
ejpam-3526	307	13	a	a	DET
ejpam-3526	307	14	subclass	subclass	NOUN
ejpam-3526	307	15	of	of	ADP
ejpam-3526	307	16	ci	ci	NOUN
ejpam-3526	307	17	-	-	PUNCT
ejpam-3526	307	18	algebras	algebras	NOUN
ejpam-3526	307	19	since	since	SCONJ
ejpam-3526	307	20	(	(	PUNCT
ejpam-3526	307	21	db1	db1	NOUN
ejpam-3526	307	22	)	)	PUNCT
ejpam-3526	307	23	is	be	AUX
ejpam-3526	307	24	equivalent	equivalent	ADJ
ejpam-3526	307	25	to	to	ADP
ejpam-3526	307	26	(	(	PUNCT
ejpam-3526	307	27	ci1	ci1	PROPN
ejpam-3526	307	28	)	)	PUNCT
ejpam-3526	307	29	,	,	PUNCT
ejpam-3526	307	30	(	(	PUNCT
ejpam-3526	307	31	db2	db2	NOUN
ejpam-3526	307	32	)	)	PUNCT
ejpam-3526	307	33	is	be	AUX
ejpam-3526	307	34	equivalent	equivalent	ADJ
ejpam-3526	307	35	to	to	ADP
ejpam-3526	307	36	(	(	PUNCT
ejpam-3526	307	37	ci2	ci2	NOUN
ejpam-3526	307	38	)	)	PUNCT
ejpam-3526	307	39	,	,	PUNCT
ejpam-3526	307	40	and	and	CCONJ
ejpam-3526	307	41	proposition	proposition	NOUN
ejpam-3526	307	42	5(i	5(i	NOUN
ejpam-3526	307	43	)	)	PUNCT
ejpam-3526	307	44	is	be	AUX
ejpam-3526	307	45	equivalent	equivalent	ADJ
ejpam-3526	307	46	to	to	ADP
ejpam-3526	307	47	(	(	PUNCT
ejpam-3526	307	48	ci3	ci3	NOUN
ejpam-3526	307	49	)	)	PUNCT
ejpam-3526	307	50	.	.	PUNCT
ejpam-3526	308	1	(	(	PUNCT
ejpam-3526	308	2	ii	ii	NOUN
ejpam-3526	308	3	)	)	PUNCT
ejpam-3526	308	4	(	(	PUNCT
ejpam-3526	308	5	db1	db1	NOUN
ejpam-3526	308	6	)	)	PUNCT
ejpam-3526	308	7	is	be	AUX
ejpam-3526	308	8	equivalent	equivalent	ADJ
ejpam-3526	308	9	to	to	ADP
ejpam-3526	308	10	(	(	PUNCT
ejpam-3526	308	11	dbci1	dbci1	NOUN
ejpam-3526	308	12	)	)	PUNCT
ejpam-3526	308	13	,	,	PUNCT
ejpam-3526	308	14	lemma	lemma	PROPN
ejpam-3526	308	15	2(v	2(v	NUM
ejpam-3526	308	16	)	)	PUNCT
ejpam-3526	308	17	is	be	AUX
ejpam-3526	308	18	equivalent	equivalent	ADJ
ejpam-3526	308	19	to	to	ADP
ejpam-3526	308	20	(	(	PUNCT
ejpam-3526	308	21	dbci2	dbci2	PROPN
ejpam-3526	308	22	)	)	PUNCT
ejpam-3526	308	23	,	,	PUNCT
ejpam-3526	308	24	proposition	proposition	NOUN
ejpam-3526	308	25	5(iv	5(iv	NUM
ejpam-3526	308	26	)	)	PUNCT
ejpam-3526	308	27	is	be	AUX
ejpam-3526	308	28	equivalent	equivalent	ADJ
ejpam-3526	308	29	to	to	ADP
ejpam-3526	308	30	(	(	PUNCT
ejpam-3526	308	31	dbci4	dbci4	PROPN
ejpam-3526	308	32	)	)	PUNCT
ejpam-3526	308	33	,	,	PUNCT
ejpam-3526	308	34	(	(	PUNCT
ejpam-3526	308	35	db2	db2	NOUN
ejpam-3526	308	36	)	)	PUNCT
ejpam-3526	308	37	is	be	AUX
ejpam-3526	308	38	equivalent	equivalent	ADJ
ejpam-3526	308	39	to	to	PART
ejpam-3526	308	40	proposition	proposition	VERB
ejpam-3526	308	41	1(iv	1(iv	NUM
ejpam-3526	308	42	)	)	PUNCT
ejpam-3526	308	43	example	example	NOUN
ejpam-3526	309	1	10	10	NUM
ejpam-3526	309	2	.	.	PUNCT
ejpam-3526	310	1	consider	consider	VERB
ejpam-3526	310	2	the	the	DET
ejpam-3526	310	3	non	non	ADJ
ejpam-3526	310	4	-	-	ADJ
ejpam-3526	310	5	commutative	commutative	ADJ
ejpam-3526	310	6	dual	dual	ADJ
ejpam-3526	310	7	b	b	NOUN
ejpam-3526	310	8	-	-	PUNCT
ejpam-3526	310	9	algebra	algebra	NOUN
ejpam-3526	310	10	x	x	X
ejpam-3526	310	11	=	=	SYM
ejpam-3526	310	12	{	{	PUNCT
ejpam-3526	310	13	0	0	NUM
ejpam-3526	310	14	,	,	PUNCT
ejpam-3526	310	15	1	1	NUM
ejpam-3526	310	16	,	,	PUNCT
ejpam-3526	310	17	2	2	NUM
ejpam-3526	310	18	,	,	PUNCT
ejpam-3526	310	19	3	3	NUM
ejpam-3526	310	20	,	,	PUNCT
ejpam-3526	310	21	4	4	NUM
ejpam-3526	310	22	,	,	PUNCT
ejpam-3526	310	23	5	5	NUM
ejpam-3526	310	24	}	}	PUNCT
ejpam-3526	310	25	in	in	ADP
ejpam-3526	310	26	example	example	NOUN
ejpam-3526	311	1	2	2	X
ejpam-3526	311	2	.	.	PUNCT
ejpam-3526	311	3	now	now	ADV
ejpam-3526	311	4	2	2	NUM
ejpam-3526	311	5	◦	◦	NOUN
ejpam-3526	311	6	(	(	PUNCT
ejpam-3526	311	7	4	4	NUM
ejpam-3526	311	8	◦	◦	NOUN
ejpam-3526	311	9	5	5	NUM
ejpam-3526	311	10	)	)	PUNCT
ejpam-3526	311	11	=	=	SYM
ejpam-3526	311	12	2	2	NUM
ejpam-3526	311	13	◦	◦	NOUN
ejpam-3526	311	14	1	1	NUM
ejpam-3526	311	15	=	=	SYM
ejpam-3526	311	16	2	2	NUM
ejpam-3526	311	17	6=	6=	SYM
ejpam-3526	311	18	0	0	NUM
ejpam-3526	311	19	=	=	SYM
ejpam-3526	311	20	4	4	NUM
ejpam-3526	311	21	◦	◦	NOUN
ejpam-3526	311	22	4	4	NUM
ejpam-3526	311	23	=	=	SYM
ejpam-3526	311	24	4	4	NUM
ejpam-3526	311	25	◦	◦	NOUN
ejpam-3526	311	26	(	(	PUNCT
ejpam-3526	311	27	2	2	NUM
ejpam-3526	311	28	◦	◦	NOUN
ejpam-3526	311	29	5	5	NUM
ejpam-3526	311	30	)	)	PUNCT
ejpam-3526	311	31	.	.	PUNCT
ejpam-3526	312	1	hence	hence	ADV
ejpam-3526	312	2	,	,	PUNCT
ejpam-3526	312	3	x	x	PRON
ejpam-3526	312	4	does	do	AUX
ejpam-3526	312	5	not	not	PART
ejpam-3526	312	6	satisfy	satisfy	VERB
ejpam-3526	312	7	(	(	PUNCT
ejpam-3526	312	8	ci3	ci3	NOUN
ejpam-3526	312	9	)	)	PUNCT
ejpam-3526	312	10	.	.	PUNCT
ejpam-3526	313	1	the	the	DET
ejpam-3526	313	2	following	follow	VERB
ejpam-3526	313	3	corollaries	corollary	NOUN
ejpam-3526	313	4	follow	follow	VERB
ejpam-3526	313	5	from	from	ADP
ejpam-3526	313	6	remark	remark	NOUN
ejpam-3526	313	7	5	5	NUM
ejpam-3526	313	8	and	and	CCONJ
ejpam-3526	313	9	theorem	theorem	VERB
ejpam-3526	313	10	1	1	NUM
ejpam-3526	313	11	.	.	PUNCT
ejpam-3526	313	12	corollary	corollary	ADJ
ejpam-3526	313	13	3	3	X
ejpam-3526	313	14	.	.	PUNCT
ejpam-3526	314	1	if	if	SCONJ
ejpam-3526	314	2	xd	xd	PRON
ejpam-3526	314	3	is	be	VERB
ejpam-3526	314	4	a	a	DET
ejpam-3526	314	5	commutative	commutative	ADJ
ejpam-3526	314	6	dual	dual	ADJ
ejpam-3526	314	7	b	b	NOUN
ejpam-3526	314	8	-	-	PUNCT
ejpam-3526	314	9	algebra	algebra	NOUN
ejpam-3526	314	10	,	,	PUNCT
ejpam-3526	314	11	then	then	ADV
ejpam-3526	314	12	xd	xd	INTJ
ejpam-3526	314	13	is	be	VERB
ejpam-3526	314	14	a	a	DET
ejpam-3526	314	15	ci	ci	NOUN
ejpam-3526	314	16	-	-	PUNCT
ejpam-3526	314	17	algebra	algebra	NOUN
ejpam-3526	314	18	.	.	PUNCT
ejpam-3526	315	1	corollary	corollary	ADJ
ejpam-3526	315	2	4	4	NUM
ejpam-3526	315	3	.	.	PUNCT
ejpam-3526	316	1	every	every	DET
ejpam-3526	316	2	commutative	commutative	ADJ
ejpam-3526	316	3	dual	dual	ADJ
ejpam-3526	316	4	b	b	NOUN
ejpam-3526	316	5	-	-	PUNCT
ejpam-3526	316	6	algebra	algebra	NOUN
ejpam-3526	316	7	is	be	AUX
ejpam-3526	316	8	a	a	DET
ejpam-3526	316	9	dual	dual	ADJ
ejpam-3526	316	10	q	q	NOUN
ejpam-3526	316	11	-	-	NOUN
ejpam-3526	316	12	algebra	algebra	NOUN
ejpam-3526	316	13	.	.	PUNCT
ejpam-3526	317	1	the	the	DET
ejpam-3526	317	2	converse	converse	NOUN
ejpam-3526	317	3	of	of	ADP
ejpam-3526	317	4	corollary	corollary	ADJ
ejpam-3526	317	5	3	3	NUM
ejpam-3526	317	6	is	be	AUX
ejpam-3526	317	7	not	not	PART
ejpam-3526	317	8	always	always	ADV
ejpam-3526	317	9	true	true	ADJ
ejpam-3526	317	10	as	as	SCONJ
ejpam-3526	317	11	shown	show	VERB
ejpam-3526	317	12	in	in	ADP
ejpam-3526	317	13	the	the	DET
ejpam-3526	317	14	following	follow	VERB
ejpam-3526	317	15	example	example	NOUN
ejpam-3526	317	16	.	.	PUNCT
ejpam-3526	318	1	example	example	NOUN
ejpam-3526	319	1	11	11	NUM
ejpam-3526	319	2	.	.	PUNCT
ejpam-3526	320	1	let	let	VERB
ejpam-3526	320	2	x	x	PUNCT
ejpam-3526	320	3	=	=	PRON
ejpam-3526	320	4	{	{	PUNCT
ejpam-3526	320	5	1	1	NUM
ejpam-3526	320	6	,	,	PUNCT
ejpam-3526	320	7	a	a	DET
ejpam-3526	320	8	,	,	PUNCT
ejpam-3526	320	9	b	b	NOUN
ejpam-3526	320	10	,	,	PUNCT
ejpam-3526	320	11	c	c	NOUN
ejpam-3526	320	12	,	,	PUNCT
ejpam-3526	320	13	d	d	AUX
ejpam-3526	320	14	}	}	PUNCT
ejpam-3526	320	15	be	be	AUX
ejpam-3526	320	16	a	a	DET
ejpam-3526	320	17	set	set	NOUN
ejpam-3526	320	18	with	with	ADP
ejpam-3526	320	19	the	the	DET
ejpam-3526	320	20	following	follow	VERB
ejpam-3526	320	21	cayley	cayley	ADJ
ejpam-3526	320	22	table	table	NOUN
ejpam-3526	320	23	:	:	PUNCT
ejpam-3526	320	24	∗	∗	NOUN
ejpam-3526	320	25	1	1	NUM
ejpam-3526	320	26	a	a	DET
ejpam-3526	320	27	b	b	NOUN
ejpam-3526	320	28	c	c	NOUN
ejpam-3526	320	29	d	d	SYM
ejpam-3526	320	30	1	1	NUM
ejpam-3526	320	31	1	1	NUM
ejpam-3526	320	32	a	a	DET
ejpam-3526	320	33	b	b	NOUN
ejpam-3526	320	34	c	c	NOUN
ejpam-3526	320	35	d	d	NOUN
ejpam-3526	320	36	a	a	DET
ejpam-3526	320	37	1	1	NUM
ejpam-3526	320	38	1	1	NUM
ejpam-3526	320	39	b	b	PROPN
ejpam-3526	320	40	b	b	PROPN
ejpam-3526	320	41	d	d	PROPN
ejpam-3526	320	42	b	b	PROPN
ejpam-3526	320	43	1	1	NUM
ejpam-3526	320	44	a	a	DET
ejpam-3526	320	45	1	1	NUM
ejpam-3526	320	46	a	a	DET
ejpam-3526	320	47	d	d	X
ejpam-3526	320	48	c	c	NOUN
ejpam-3526	320	49	1	1	NUM
ejpam-3526	320	50	1	1	NUM
ejpam-3526	320	51	1	1	NUM
ejpam-3526	320	52	1	1	NUM
ejpam-3526	320	53	d	d	NOUN
ejpam-3526	320	54	d	d	PROPN
ejpam-3526	320	55	d	d	PROPN
ejpam-3526	320	56	d	d	PROPN
ejpam-3526	320	57	d	d	PROPN
ejpam-3526	320	58	d	d	PROPN
ejpam-3526	320	59	1	1	NUM
ejpam-3526	320	60	then	then	ADV
ejpam-3526	320	61	(	(	PUNCT
ejpam-3526	320	62	x	x	X
ejpam-3526	320	63	,	,	PUNCT
ejpam-3526	320	64	∗	∗	NOUN
ejpam-3526	320	65	,	,	PUNCT
ejpam-3526	320	66	1	1	NUM
ejpam-3526	320	67	)	)	PUNCT
ejpam-3526	320	68	is	be	AUX
ejpam-3526	320	69	a	a	DET
ejpam-3526	320	70	ci	ci	NOUN
ejpam-3526	320	71	-	-	NOUN
ejpam-3526	320	72	algebra	algebra	NOUN
ejpam-3526	321	1	[	[	X
ejpam-3526	321	2	5	5	NUM
ejpam-3526	321	3	]	]	PUNCT
ejpam-3526	322	1	but	but	CCONJ
ejpam-3526	322	2	is	be	AUX
ejpam-3526	322	3	not	not	PART
ejpam-3526	322	4	a	a	DET
ejpam-3526	322	5	dual	dual	ADJ
ejpam-3526	322	6	b	b	NOUN
ejpam-3526	322	7	-	-	PUNCT
ejpam-3526	322	8	algebra	algebra	NOUN
ejpam-3526	322	9	since	since	SCONJ
ejpam-3526	322	10	it	it	PRON
ejpam-3526	322	11	does	do	AUX
ejpam-3526	322	12	not	not	PART
ejpam-3526	322	13	satisfy	satisfy	VERB
ejpam-3526	322	14	(	(	PUNCT
ejpam-3526	322	15	db3	db3	PROPN
ejpam-3526	322	16	)	)	PUNCT
ejpam-3526	322	17	.	.	PUNCT
ejpam-3526	323	1	indeed	indeed	ADV
ejpam-3526	323	2	,	,	PUNCT
ejpam-3526	323	3	a	a	DET
ejpam-3526	323	4	◦	◦	NOUN
ejpam-3526	323	5	(	(	PUNCT
ejpam-3526	323	6	b	b	X
ejpam-3526	323	7	◦	◦	NOUN
ejpam-3526	323	8	c	c	NOUN
ejpam-3526	323	9	)	)	PUNCT
ejpam-3526	323	10	=	=	SYM
ejpam-3526	324	1	a	a	DET
ejpam-3526	324	2	◦	◦	NOUN
ejpam-3526	324	3	a	a	DET
ejpam-3526	324	4	=	=	SYM
ejpam-3526	324	5	1	1	NUM
ejpam-3526	324	6	6=	6=	SYM
ejpam-3526	324	7	b	b	X
ejpam-3526	324	8	=	=	SYM
ejpam-3526	324	9	a	a	DET
ejpam-3526	324	10	◦	◦	NOUN
ejpam-3526	324	11	c	c	NOUN
ejpam-3526	324	12	=	=	SYM
ejpam-3526	324	13	(	(	PUNCT
ejpam-3526	324	14	1	1	NUM
ejpam-3526	324	15	◦	◦	NOUN
ejpam-3526	324	16	a	a	X
ejpam-3526	324	17	)	)	PUNCT
ejpam-3526	324	18	◦	◦	NOUN
ejpam-3526	324	19	c	c	NOUN
ejpam-3526	325	1	=	=	PUNCT
ejpam-3526	326	1	[	[	X
ejpam-3526	326	2	(	(	PUNCT
ejpam-3526	326	3	b	b	X
ejpam-3526	326	4	◦	◦	NOUN
ejpam-3526	326	5	1	1	NUM
ejpam-3526	326	6	)	)	PUNCT
ejpam-3526	326	7	◦	◦	NOUN
ejpam-3526	326	8	a	a	DET
ejpam-3526	326	9	]	]	X
ejpam-3526	326	10	◦	◦	NOUN
ejpam-3526	326	11	c.	c.	NOUN
ejpam-3526	326	12	theorem	theorem	VERB
ejpam-3526	326	13	5	5	NUM
ejpam-3526	326	14	.	.	PUNCT
ejpam-3526	327	1	if	if	SCONJ
ejpam-3526	327	2	x	x	PRON
ejpam-3526	327	3	is	be	AUX
ejpam-3526	327	4	a	a	DET
ejpam-3526	327	5	ci	ci	NOUN
ejpam-3526	327	6	-	-	NOUN
ejpam-3526	327	7	algebra	algebra	NOUN
ejpam-3526	327	8	satisfying	satisfy	VERB
ejpam-3526	327	9	a	a	DET
ejpam-3526	327	10	symmetric	symmetric	ADJ
ejpam-3526	327	11	condition	condition	NOUN
ejpam-3526	327	12	,	,	PUNCT
ejpam-3526	327	13	then	then	ADV
ejpam-3526	327	14	x	x	PUNCT
ejpam-3526	327	15	is	be	AUX
ejpam-3526	327	16	a	a	DET
ejpam-3526	327	17	commutative	commutative	ADJ
ejpam-3526	327	18	dual	dual	ADJ
ejpam-3526	327	19	b	b	NOUN
ejpam-3526	327	20	-	-	PUNCT
ejpam-3526	327	21	algebra	algebra	NOUN
ejpam-3526	327	22	.	.	PUNCT
ejpam-3526	328	1	proof	proof	NOUN
ejpam-3526	328	2	:	:	PUNCT
ejpam-3526	328	3	suppose	suppose	VERB
ejpam-3526	328	4	x	x	PRON
ejpam-3526	328	5	is	be	AUX
ejpam-3526	328	6	a	a	DET
ejpam-3526	328	7	ci	ci	NOUN
ejpam-3526	328	8	-	-	NOUN
ejpam-3526	328	9	algebra	algebra	NOUN
ejpam-3526	328	10	satisfying	satisfy	VERB
ejpam-3526	328	11	a	a	DET
ejpam-3526	328	12	symmetric	symmetric	ADJ
ejpam-3526	328	13	condition	condition	NOUN
ejpam-3526	328	14	.	.	PUNCT
ejpam-3526	329	1	by	by	ADP
ejpam-3526	329	2	remark	remark	NOUN
ejpam-3526	329	3	5	5	NUM
ejpam-3526	329	4	,	,	PUNCT
ejpam-3526	329	5	it	it	PRON
ejpam-3526	329	6	remains	remain	VERB
ejpam-3526	329	7	to	to	PART
ejpam-3526	329	8	show	show	VERB
ejpam-3526	329	9	that	that	SCONJ
ejpam-3526	329	10	x	x	PRON
ejpam-3526	329	11	satisfies	satisfie	NOUN
ejpam-3526	329	12	(	(	PUNCT
ejpam-3526	329	13	db3	db3	PROPN
ejpam-3526	329	14	)	)	PUNCT
ejpam-3526	329	15	and	and	CCONJ
ejpam-3526	329	16	that	that	SCONJ
ejpam-3526	329	17	x	x	PRON
ejpam-3526	329	18	is	be	AUX
ejpam-3526	329	19	commutative	commutative	ADJ
ejpam-3526	329	20	.	.	PUNCT
ejpam-3526	330	1	applying	apply	VERB
ejpam-3526	330	2	(	(	PUNCT
ejpam-3526	330	3	ci3	ci3	ADJ
ejpam-3526	330	4	)	)	PUNCT
ejpam-3526	330	5	and	and	CCONJ
ejpam-3526	330	6	the	the	DET
ejpam-3526	330	7	hypothesis	hypothesis	NOUN
ejpam-3526	330	8	,	,	PUNCT
ejpam-3526	330	9	x	x	SYM
ejpam-3526	331	1	◦	◦	NOUN
ejpam-3526	331	2	(	(	PUNCT
ejpam-3526	331	3	y	y	PROPN
ejpam-3526	331	4	◦	◦	PROPN
ejpam-3526	331	5	z	z	PROPN
ejpam-3526	331	6	)	)	PUNCT
ejpam-3526	331	7	=	=	SYM
ejpam-3526	331	8	y	y	PROPN
ejpam-3526	331	9	◦	◦	NOUN
ejpam-3526	331	10	(	(	PUNCT
ejpam-3526	331	11	x	x	PART
ejpam-3526	331	12	◦	◦	NOUN
ejpam-3526	331	13	z	z	NOUN
ejpam-3526	331	14	)	)	PUNCT
ejpam-3526	331	15	=	=	SYM
ejpam-3526	332	1	(	(	PUNCT
ejpam-3526	332	2	y	y	PROPN
ejpam-3526	332	3	◦	◦	NOUN
ejpam-3526	332	4	1	1	NUM
ejpam-3526	332	5	)	)	PUNCT
ejpam-3526	332	6	◦	◦	NOUN
ejpam-3526	332	7	(	(	PUNCT
ejpam-3526	332	8	z	z	NOUN
ejpam-3526	332	9	◦	◦	NOUN
ejpam-3526	332	10	x	x	X
ejpam-3526	332	11	)	)	PUNCT
ejpam-3526	332	12	=	=	SYM
ejpam-3526	332	13	z	z	X
ejpam-3526	332	14	◦	◦	NOUN
ejpam-3526	333	1	[	[	X
ejpam-3526	333	2	(	(	PUNCT
ejpam-3526	333	3	y	y	NOUN
ejpam-3526	333	4	◦	◦	NOUN
ejpam-3526	333	5	1	1	NUM
ejpam-3526	333	6	)	)	PUNCT
ejpam-3526	333	7	◦	◦	NOUN
ejpam-3526	333	8	x	x	X
ejpam-3526	333	9	]	]	X
ejpam-3526	333	10	=	=	SYM
ejpam-3526	334	1	[	[	X
ejpam-3526	334	2	(	(	PUNCT
ejpam-3526	334	3	y	y	NOUN
ejpam-3526	334	4	◦	◦	NOUN
ejpam-3526	334	5	1	1	NUM
ejpam-3526	334	6	)	)	PUNCT
ejpam-3526	334	7	◦	◦	NOUN
ejpam-3526	334	8	x	x	SYM
ejpam-3526	334	9	]	]	X
ejpam-3526	334	10	◦	◦	NOUN
ejpam-3526	334	11	z.	z.	PROPN
ejpam-3526	334	12	hence	hence	ADV
ejpam-3526	334	13	,	,	PUNCT
ejpam-3526	334	14	x	x	PRON
ejpam-3526	334	15	satisfies	satisfie	NOUN
ejpam-3526	334	16	(	(	PUNCT
ejpam-3526	334	17	db3	db3	PROPN
ejpam-3526	334	18	)	)	PUNCT
ejpam-3526	334	19	.	.	PUNCT
ejpam-3526	335	1	by	by	ADP
ejpam-3526	335	2	corollary	corollary	ADJ
ejpam-3526	335	3	1	1	NUM
ejpam-3526	335	4	,	,	PUNCT
ejpam-3526	335	5	it	it	PRON
ejpam-3526	335	6	follows	follow	VERB
ejpam-3526	335	7	that	that	SCONJ
ejpam-3526	335	8	x	x	PRON
ejpam-3526	335	9	is	be	AUX
ejpam-3526	335	10	commutative	commutative	ADJ
ejpam-3526	335	11	.	.	PUNCT
ejpam-3526	336	1	k.	k.	PROPN
ejpam-3526	336	2	belleza	belleza	PROPN
ejpam-3526	336	3	,	,	PUNCT
ejpam-3526	336	4	j.	j.	PROPN
ejpam-3526	336	5	vilela	vilela	PROPN
ejpam-3526	336	6	/	/	SYM
ejpam-3526	336	7	eur	eur	PROPN
ejpam-3526	336	8	.	.	PUNCT
ejpam-3526	337	1	j.	j.	PROPN
ejpam-3526	337	2	pure	pure	PROPN
ejpam-3526	337	3	appl	appl	PROPN
ejpam-3526	337	4	.	.	PROPN
ejpam-3526	337	5	math	math	PROPN
ejpam-3526	337	6	,	,	PUNCT
ejpam-3526	337	7	12	12	NUM
ejpam-3526	337	8	(	(	PUNCT
ejpam-3526	337	9	4	4	NUM
ejpam-3526	337	10	)	)	PUNCT
ejpam-3526	337	11	(	(	PUNCT
ejpam-3526	337	12	2019	2019	NUM
ejpam-3526	337	13	)	)	PUNCT
ejpam-3526	337	14	,	,	PUNCT
ejpam-3526	337	15	1497	1497	NUM
ejpam-3526	337	16	-	-	SYM
ejpam-3526	337	17	1507	1507	NUM
ejpam-3526	337	18	1505	1505	NUM
ejpam-3526	337	19	example	example	NOUN
ejpam-3526	337	20	12	12	NUM
ejpam-3526	337	21	.	.	PUNCT
ejpam-3526	338	1	consider	consider	VERB
ejpam-3526	338	2	the	the	DET
ejpam-3526	338	3	non	non	ADJ
ejpam-3526	338	4	-	-	ADJ
ejpam-3526	338	5	commutative	commutative	ADJ
ejpam-3526	338	6	dual	dual	ADJ
ejpam-3526	338	7	b	b	NOUN
ejpam-3526	338	8	-	-	PUNCT
ejpam-3526	338	9	algebra	algebra	NOUN
ejpam-3526	338	10	x	x	X
ejpam-3526	338	11	=	=	SYM
ejpam-3526	338	12	{	{	PUNCT
ejpam-3526	338	13	0	0	NUM
ejpam-3526	338	14	,	,	PUNCT
ejpam-3526	338	15	1	1	NUM
ejpam-3526	338	16	,	,	PUNCT
ejpam-3526	338	17	2	2	NUM
ejpam-3526	338	18	,	,	PUNCT
ejpam-3526	338	19	3	3	NUM
ejpam-3526	338	20	,	,	PUNCT
ejpam-3526	338	21	4	4	NUM
ejpam-3526	338	22	,	,	PUNCT
ejpam-3526	338	23	5	5	NUM
ejpam-3526	338	24	}	}	PUNCT
ejpam-3526	338	25	in	in	ADP
ejpam-3526	338	26	example	example	NOUN
ejpam-3526	338	27	2	2	NUM
ejpam-3526	338	28	.	.	X
ejpam-3526	338	29	observe	observe	VERB
ejpam-3526	338	30	that	that	SCONJ
ejpam-3526	338	31	(	(	PUNCT
ejpam-3526	338	32	1	1	NUM
ejpam-3526	338	33	◦	◦	NOUN
ejpam-3526	338	34	2	2	NUM
ejpam-3526	338	35	)	)	PUNCT
ejpam-3526	339	1	◦	◦	NOUN
ejpam-3526	340	1	[	[	X
ejpam-3526	340	2	(	(	PUNCT
ejpam-3526	340	3	2	2	NUM
ejpam-3526	340	4	◦	◦	NOUN
ejpam-3526	340	5	4	4	NUM
ejpam-3526	340	6	)	)	PUNCT
ejpam-3526	340	7	◦	◦	NOUN
ejpam-3526	340	8	(	(	PUNCT
ejpam-3526	340	9	1	1	NUM
ejpam-3526	340	10	◦	◦	NOUN
ejpam-3526	340	11	4	4	NUM
ejpam-3526	340	12	)	)	PUNCT
ejpam-3526	340	13	]	]	PUNCT
ejpam-3526	341	1	=	=	SYM
ejpam-3526	341	2	1	1	NUM
ejpam-3526	341	3	◦	◦	NOUN
ejpam-3526	341	4	(	(	PUNCT
ejpam-3526	341	5	3	3	NUM
ejpam-3526	341	6	◦	◦	NOUN
ejpam-3526	341	7	5	5	NUM
ejpam-3526	341	8	)	)	PUNCT
ejpam-3526	341	9	=	=	SYM
ejpam-3526	341	10	1	1	NUM
ejpam-3526	341	11	◦	◦	NOUN
ejpam-3526	341	12	2	2	NUM
ejpam-3526	341	13	=	=	SYM
ejpam-3526	341	14	1	1	NUM
ejpam-3526	341	15	6=	6=	NUM
ejpam-3526	341	16	0	0	NUM
ejpam-3526	341	17	.	.	PUNCT
ejpam-3526	342	1	hence	hence	ADV
ejpam-3526	342	2	,	,	PUNCT
ejpam-3526	342	3	xd	xd	INTJ
ejpam-3526	342	4	does	do	AUX
ejpam-3526	342	5	not	not	PART
ejpam-3526	342	6	satisfy	satisfy	VERB
ejpam-3526	342	7	(	(	PUNCT
ejpam-3526	342	8	dbci3	dbci3	PROPN
ejpam-3526	342	9	)	)	PUNCT
ejpam-3526	342	10	and	and	CCONJ
ejpam-3526	342	11	so	so	ADV
ejpam-3526	342	12	xd	xd	INTJ
ejpam-3526	342	13	is	be	AUX
ejpam-3526	342	14	not	not	PART
ejpam-3526	342	15	a	a	DET
ejpam-3526	342	16	dual	dual	ADJ
ejpam-3526	342	17	bci	bci	NOUN
ejpam-3526	342	18	-	-	NOUN
ejpam-3526	342	19	algebra	algebra	NOUN
ejpam-3526	342	20	.	.	PUNCT
ejpam-3526	343	1	however	however	ADV
ejpam-3526	343	2	,	,	PUNCT
ejpam-3526	343	3	if	if	SCONJ
ejpam-3526	343	4	commutativity	commutativity	NOUN
ejpam-3526	343	5	holds	hold	VERB
ejpam-3526	343	6	for	for	ADP
ejpam-3526	343	7	a	a	DET
ejpam-3526	343	8	dual	dual	ADJ
ejpam-3526	343	9	b	b	NOUN
ejpam-3526	343	10	-	-	PUNCT
ejpam-3526	343	11	algebra	algebra	NOUN
ejpam-3526	343	12	,	,	PUNCT
ejpam-3526	343	13	then	then	ADV
ejpam-3526	343	14	it	it	PRON
ejpam-3526	343	15	is	be	AUX
ejpam-3526	343	16	also	also	ADV
ejpam-3526	343	17	a	a	DET
ejpam-3526	343	18	dual	dual	ADJ
ejpam-3526	343	19	bcialgebra	bcialgebra	NOUN
ejpam-3526	343	20	as	as	SCONJ
ejpam-3526	343	21	shown	show	VERB
ejpam-3526	343	22	in	in	ADP
ejpam-3526	343	23	the	the	DET
ejpam-3526	343	24	next	next	ADJ
ejpam-3526	343	25	theorem	theorem	PROPN
ejpam-3526	343	26	.	.	PUNCT
ejpam-3526	343	27	theorem	theorem	VERB
ejpam-3526	343	28	6	6	NUM
ejpam-3526	343	29	.	.	PUNCT
ejpam-3526	344	1	every	every	DET
ejpam-3526	344	2	commutative	commutative	ADJ
ejpam-3526	344	3	dual	dual	ADJ
ejpam-3526	344	4	b	b	NOUN
ejpam-3526	344	5	-	-	PUNCT
ejpam-3526	344	6	algebra	algebra	NOUN
ejpam-3526	344	7	is	be	AUX
ejpam-3526	344	8	a	a	DET
ejpam-3526	344	9	dual	dual	ADJ
ejpam-3526	344	10	bci	bci	NOUN
ejpam-3526	344	11	-	-	NOUN
ejpam-3526	344	12	algebra	algebra	NOUN
ejpam-3526	344	13	.	.	PUNCT
ejpam-3526	345	1	proof	proof	NOUN
ejpam-3526	345	2	:	:	PUNCT
ejpam-3526	345	3	let	let	VERB
ejpam-3526	345	4	xd	xd	INTJ
ejpam-3526	345	5	be	be	AUX
ejpam-3526	345	6	a	a	DET
ejpam-3526	345	7	commutative	commutative	ADJ
ejpam-3526	345	8	dual	dual	ADJ
ejpam-3526	345	9	b	b	NOUN
ejpam-3526	345	10	-	-	PUNCT
ejpam-3526	345	11	algebra	algebra	NOUN
ejpam-3526	345	12	.	.	PUNCT
ejpam-3526	346	1	by	by	ADP
ejpam-3526	346	2	remark	remark	NOUN
ejpam-3526	346	3	5	5	NUM
ejpam-3526	346	4	,	,	PUNCT
ejpam-3526	346	5	it	it	PRON
ejpam-3526	346	6	remains	remain	VERB
ejpam-3526	346	7	to	to	PART
ejpam-3526	346	8	show	show	VERB
ejpam-3526	346	9	that	that	SCONJ
ejpam-3526	346	10	xd	xd	INTJ
ejpam-3526	346	11	satisfies	satisfie	NOUN
ejpam-3526	346	12	(	(	PUNCT
ejpam-3526	346	13	dbci3	dbci3	NOUN
ejpam-3526	346	14	)	)	PUNCT
ejpam-3526	346	15	.	.	PUNCT
ejpam-3526	347	1	by	by	ADP
ejpam-3526	347	2	proposition	proposition	NOUN
ejpam-3526	347	3	5(ii	5(ii	NUM
ejpam-3526	347	4	)	)	PUNCT
ejpam-3526	347	5	,	,	PUNCT
ejpam-3526	347	6	proposition	proposition	NOUN
ejpam-3526	347	7	4(ii	4(ii	NUM
ejpam-3526	347	8	)	)	PUNCT
ejpam-3526	347	9	,	,	PUNCT
ejpam-3526	347	10	and	and	CCONJ
ejpam-3526	347	11	(	(	PUNCT
ejpam-3526	347	12	db1	db1	NOUN
ejpam-3526	347	13	)	)	PUNCT
ejpam-3526	347	14	,	,	PUNCT
ejpam-3526	347	15	(	(	PUNCT
ejpam-3526	347	16	x	x	X
ejpam-3526	347	17	◦	◦	VERB
ejpam-3526	347	18	y	y	NOUN
ejpam-3526	347	19	)	)	PUNCT
ejpam-3526	347	20	◦	◦	NOUN
ejpam-3526	348	1	[	[	X
ejpam-3526	348	2	(	(	PUNCT
ejpam-3526	348	3	y	y	PROPN
ejpam-3526	348	4	◦	◦	PROPN
ejpam-3526	348	5	z	z	PROPN
ejpam-3526	348	6	)	)	PUNCT
ejpam-3526	348	7	◦	◦	NOUN
ejpam-3526	348	8	(	(	PUNCT
ejpam-3526	348	9	x	x	PART
ejpam-3526	348	10	◦	◦	NOUN
ejpam-3526	348	11	z	z	NOUN
ejpam-3526	348	12	)	)	PUNCT
ejpam-3526	348	13	]	]	PUNCT
ejpam-3526	349	1	=	=	PUNCT
ejpam-3526	349	2	(	(	PUNCT
ejpam-3526	349	3	x	x	SYM
ejpam-3526	349	4	◦	◦	VERB
ejpam-3526	349	5	y	y	NOUN
ejpam-3526	349	6	)	)	PUNCT
ejpam-3526	349	7	◦	◦	NOUN
ejpam-3526	349	8	(	(	PUNCT
ejpam-3526	349	9	[	[	X
ejpam-3526	349	10	(	(	PUNCT
ejpam-3526	349	11	x	x	SYM
ejpam-3526	349	12	◦	◦	NOUN
ejpam-3526	349	13	z	z	NOUN
ejpam-3526	349	14	)	)	PUNCT
ejpam-3526	349	15	◦	◦	NOUN
ejpam-3526	349	16	z	z	X
ejpam-3526	349	17	]	]	X
ejpam-3526	349	18	◦	◦	NOUN
ejpam-3526	349	19	y	y	PROPN
ejpam-3526	349	20	)	)	PUNCT
ejpam-3526	350	1	=	=	PUNCT
ejpam-3526	350	2	(	(	PUNCT
ejpam-3526	350	3	x	x	SYM
ejpam-3526	350	4	◦	◦	VERB
ejpam-3526	350	5	y	y	NOUN
ejpam-3526	350	6	)	)	PUNCT
ejpam-3526	350	7	◦	◦	NOUN
ejpam-3526	350	8	(	(	PUNCT
ejpam-3526	350	9	x	x	PART
ejpam-3526	350	10	◦	◦	VERB
ejpam-3526	350	11	y	y	NOUN
ejpam-3526	350	12	)	)	PUNCT
ejpam-3526	351	1	=	=	SYM
ejpam-3526	351	2	1	1	X
ejpam-3526	351	3	.	.	PUNCT
ejpam-3526	352	1	hence	hence	ADV
ejpam-3526	352	2	,	,	PUNCT
ejpam-3526	352	3	x	x	PRON
ejpam-3526	352	4	satisfies	satisfie	NOUN
ejpam-3526	352	5	(	(	PUNCT
ejpam-3526	352	6	dbci3	dbci3	NOUN
ejpam-3526	352	7	)	)	PUNCT
ejpam-3526	352	8	.	.	PUNCT
ejpam-3526	353	1	therefore	therefore	ADV
ejpam-3526	353	2	,	,	PUNCT
ejpam-3526	353	3	x	x	X
ejpam-3526	353	4	is	be	AUX
ejpam-3526	353	5	a	a	DET
ejpam-3526	353	6	dual	dual	ADJ
ejpam-3526	353	7	bci	bci	NOUN
ejpam-3526	353	8	-	-	NOUN
ejpam-3526	353	9	algebra	algebra	NOUN
ejpam-3526	353	10	.	.	PUNCT
ejpam-3526	354	1	note	note	VERB
ejpam-3526	354	2	that	that	SCONJ
ejpam-3526	354	3	the	the	DET
ejpam-3526	354	4	converse	converse	NOUN
ejpam-3526	354	5	of	of	ADP
ejpam-3526	354	6	theorem	theorem	NOUN
ejpam-3526	354	7	6	6	NUM
ejpam-3526	354	8	is	be	AUX
ejpam-3526	354	9	not	not	PART
ejpam-3526	354	10	always	always	ADV
ejpam-3526	354	11	true	true	ADJ
ejpam-3526	354	12	as	as	SCONJ
ejpam-3526	354	13	shown	show	VERB
ejpam-3526	354	14	in	in	ADP
ejpam-3526	354	15	the	the	DET
ejpam-3526	354	16	following	follow	VERB
ejpam-3526	354	17	example	example	NOUN
ejpam-3526	354	18	.	.	PUNCT
ejpam-3526	355	1	example	example	NOUN
ejpam-3526	355	2	13	13	NUM
ejpam-3526	355	3	.	.	PUNCT
ejpam-3526	356	1	let	let	VERB
ejpam-3526	356	2	x	x	PUNCT
ejpam-3526	356	3	=	=	PUNCT
ejpam-3526	356	4	{	{	PUNCT
ejpam-3526	356	5	0	0	NUM
ejpam-3526	356	6	,	,	PUNCT
ejpam-3526	356	7	1	1	NUM
ejpam-3526	356	8	,	,	PUNCT
ejpam-3526	356	9	a	a	DET
ejpam-3526	356	10	,	,	PUNCT
ejpam-3526	356	11	b	b	NOUN
ejpam-3526	356	12	,	,	PUNCT
ejpam-3526	356	13	c	c	NOUN
ejpam-3526	356	14	}	}	PUNCT
ejpam-3526	356	15	with	with	ADP
ejpam-3526	356	16	binary	binary	ADJ
ejpam-3526	356	17	operation	operation	NOUN
ejpam-3526	356	18	“	"	PUNCT
ejpam-3526	356	19	∗	∗	NOUN
ejpam-3526	356	20	”	"	PUNCT
ejpam-3526	356	21	on	on	ADP
ejpam-3526	356	22	x	x	PUNCT
ejpam-3526	356	23	defined	define	VERB
ejpam-3526	356	24	by	by	ADP
ejpam-3526	356	25	the	the	DET
ejpam-3526	356	26	following	follow	VERB
ejpam-3526	356	27	table	table	NOUN
ejpam-3526	356	28	on	on	ADP
ejpam-3526	356	29	the	the	DET
ejpam-3526	356	30	left	left	NOUN
ejpam-3526	356	31	:	:	PUNCT
ejpam-3526	356	32	∗	∗	NOUN
ejpam-3526	356	33	0	0	NUM
ejpam-3526	356	34	1	1	NUM
ejpam-3526	356	35	a	a	DET
ejpam-3526	356	36	b	b	NOUN
ejpam-3526	356	37	c	c	NOUN
ejpam-3526	356	38	0	0	NUM
ejpam-3526	356	39	0	0	NUM
ejpam-3526	356	40	0	0	NUM
ejpam-3526	356	41	a	a	DET
ejpam-3526	356	42	a	a	DET
ejpam-3526	356	43	a	a	DET
ejpam-3526	356	44	1	1	NUM
ejpam-3526	356	45	1	1	NUM
ejpam-3526	356	46	0	0	NUM
ejpam-3526	356	47	a	a	DET
ejpam-3526	356	48	a	a	DET
ejpam-3526	356	49	a	a	DET
ejpam-3526	356	50	a	a	PRON
ejpam-3526	356	51	a	a	PRON
ejpam-3526	356	52	a	a	PRON
ejpam-3526	356	53	0	0	NUM
ejpam-3526	356	54	0	0	NUM
ejpam-3526	356	55	0	0	NUM
ejpam-3526	357	1	b	b	X
ejpam-3526	357	2	b	b	PROPN
ejpam-3526	357	3	a	a	DET
ejpam-3526	357	4	1	1	NUM
ejpam-3526	357	5	0	0	NUM
ejpam-3526	357	6	1	1	NUM
ejpam-3526	357	7	c	c	NOUN
ejpam-3526	357	8	c	c	NOUN
ejpam-3526	357	9	a	a	DET
ejpam-3526	357	10	1	1	NUM
ejpam-3526	357	11	1	1	NUM
ejpam-3526	357	12	0	0	NUM
ejpam-3526	357	13	◦	◦	NOUN
ejpam-3526	357	14	0	0	NUM
ejpam-3526	357	15	1	1	NUM
ejpam-3526	357	16	a	a	DET
ejpam-3526	357	17	b	b	NOUN
ejpam-3526	357	18	c	c	NOUN
ejpam-3526	357	19	0	0	NUM
ejpam-3526	357	20	0	0	NUM
ejpam-3526	357	21	1	1	NUM
ejpam-3526	357	22	a	a	DET
ejpam-3526	357	23	b	b	NOUN
ejpam-3526	357	24	c	c	NOUN
ejpam-3526	357	25	1	1	NUM
ejpam-3526	357	26	0	0	NUM
ejpam-3526	357	27	0	0	NUM
ejpam-3526	357	28	a	a	DET
ejpam-3526	357	29	a	a	DET
ejpam-3526	357	30	a	a	DET
ejpam-3526	357	31	a	a	DET
ejpam-3526	357	32	a	a	DET
ejpam-3526	357	33	a	a	DET
ejpam-3526	357	34	0	0	NUM
ejpam-3526	357	35	1	1	NUM
ejpam-3526	357	36	1	1	NUM
ejpam-3526	357	37	b	b	PROPN
ejpam-3526	357	38	a	a	DET
ejpam-3526	357	39	a	a	DET
ejpam-3526	357	40	0	0	NUM
ejpam-3526	357	41	0	0	NUM
ejpam-3526	357	42	1	1	NUM
ejpam-3526	357	43	c	c	NOUN
ejpam-3526	357	44	a	a	DET
ejpam-3526	357	45	a	a	DET
ejpam-3526	357	46	0	0	NUM
ejpam-3526	357	47	1	1	NUM
ejpam-3526	357	48	0	0	NUM
ejpam-3526	357	49	then	then	ADV
ejpam-3526	357	50	x	x	SYM
ejpam-3526	357	51	=	=	SYM
ejpam-3526	357	52	(	(	PUNCT
ejpam-3526	357	53	x	x	X
ejpam-3526	357	54	,	,	PUNCT
ejpam-3526	357	55	∗	∗	NOUN
ejpam-3526	357	56	,	,	PUNCT
ejpam-3526	357	57	0	0	NUM
ejpam-3526	357	58	)	)	PUNCT
ejpam-3526	357	59	is	be	AUX
ejpam-3526	357	60	a	a	DET
ejpam-3526	357	61	bci	bci	NOUN
ejpam-3526	357	62	-	-	NOUN
ejpam-3526	357	63	algebra	algebra	NOUN
ejpam-3526	357	64	[	[	X
ejpam-3526	357	65	13	13	NUM
ejpam-3526	357	66	]	]	PUNCT
ejpam-3526	357	67	.	.	PUNCT
ejpam-3526	358	1	note	note	VERB
ejpam-3526	358	2	that	that	SCONJ
ejpam-3526	358	3	(	(	PUNCT
ejpam-3526	358	4	x	x	NOUN
ejpam-3526	358	5	,	,	PUNCT
ejpam-3526	358	6	◦	◦	NOUN
ejpam-3526	358	7	,	,	PUNCT
ejpam-3526	358	8	0	0	NUM
ejpam-3526	358	9	)	)	PUNCT
ejpam-3526	358	10	is	be	AUX
ejpam-3526	358	11	a	a	DET
ejpam-3526	358	12	dual	dual	ADJ
ejpam-3526	358	13	bci	bci	NOUN
ejpam-3526	358	14	-	-	NOUN
ejpam-3526	358	15	algebra	algebra	NOUN
ejpam-3526	358	16	.	.	PUNCT
ejpam-3526	359	1	now	now	ADV
ejpam-3526	359	2	,	,	PUNCT
ejpam-3526	359	3	1	1	NUM
ejpam-3526	359	4	◦	◦	NOUN
ejpam-3526	359	5	(	(	PUNCT
ejpam-3526	359	6	b	b	X
ejpam-3526	359	7	◦	◦	NOUN
ejpam-3526	359	8	c	c	NOUN
ejpam-3526	359	9	)	)	PUNCT
ejpam-3526	359	10	=	=	SYM
ejpam-3526	359	11	1	1	NUM
ejpam-3526	359	12	◦	◦	NOUN
ejpam-3526	359	13	1	1	NUM
ejpam-3526	359	14	=	=	SYM
ejpam-3526	359	15	0	0	NUM
ejpam-3526	359	16	6=	6=	SYM
ejpam-3526	359	17	1	1	NUM
ejpam-3526	359	18	=	=	SYM
ejpam-3526	359	19	a	a	DET
ejpam-3526	359	20	◦	◦	NOUN
ejpam-3526	359	21	c	c	NOUN
ejpam-3526	360	1	=	=	SYM
ejpam-3526	360	2	(	(	PUNCT
ejpam-3526	360	3	a	a	DET
ejpam-3526	360	4	◦	◦	NOUN
ejpam-3526	360	5	1	1	NUM
ejpam-3526	360	6	)	)	PUNCT
ejpam-3526	360	7	◦	◦	NOUN
ejpam-3526	360	8	c	c	NOUN
ejpam-3526	361	1	=	=	PUNCT
ejpam-3526	362	1	[	[	X
ejpam-3526	362	2	(	(	PUNCT
ejpam-3526	362	3	b	b	X
ejpam-3526	362	4	◦	◦	NOUN
ejpam-3526	362	5	0	0	NUM
ejpam-3526	362	6	)	)	PUNCT
ejpam-3526	362	7	◦	◦	NOUN
ejpam-3526	362	8	1	1	NUM
ejpam-3526	362	9	]	]	X
ejpam-3526	362	10	◦	◦	NOUN
ejpam-3526	362	11	c.	c.	NOUN
ejpam-3526	362	12	thus	thus	ADV
ejpam-3526	362	13	,	,	PUNCT
ejpam-3526	362	14	x	x	PRON
ejpam-3526	362	15	does	do	AUX
ejpam-3526	362	16	not	not	PART
ejpam-3526	362	17	satisfy	satisfy	VERB
ejpam-3526	362	18	(	(	PUNCT
ejpam-3526	362	19	db3	db3	PROPN
ejpam-3526	362	20	)	)	PUNCT
ejpam-3526	362	21	.	.	PUNCT
ejpam-3526	363	1	hence	hence	ADV
ejpam-3526	363	2	,	,	PUNCT
ejpam-3526	363	3	x	x	PRON
ejpam-3526	363	4	is	be	AUX
ejpam-3526	363	5	not	not	PART
ejpam-3526	363	6	a	a	DET
ejpam-3526	363	7	dual	dual	ADJ
ejpam-3526	363	8	b	b	NOUN
ejpam-3526	363	9	-	-	PUNCT
ejpam-3526	363	10	algebra	algebra	NOUN
ejpam-3526	363	11	.	.	PUNCT
ejpam-3526	364	1	however	however	ADV
ejpam-3526	364	2	if	if	SCONJ
ejpam-3526	364	3	a	a	DET
ejpam-3526	364	4	dual	dual	ADJ
ejpam-3526	364	5	bci	bci	NOUN
ejpam-3526	364	6	-	-	NOUN
ejpam-3526	364	7	algebra	algebra	NOUN
ejpam-3526	364	8	x	x	PRON
ejpam-3526	364	9	satisfies	satisfy	VERB
ejpam-3526	364	10	the	the	DET
ejpam-3526	364	11	symmetric	symmetric	ADJ
ejpam-3526	364	12	condition	condition	NOUN
ejpam-3526	364	13	,	,	PUNCT
ejpam-3526	364	14	then	then	ADV
ejpam-3526	364	15	x	x	PUNCT
ejpam-3526	364	16	is	be	AUX
ejpam-3526	364	17	also	also	ADV
ejpam-3526	364	18	a	a	DET
ejpam-3526	364	19	dual	dual	ADJ
ejpam-3526	364	20	b	b	NOUN
ejpam-3526	364	21	-	-	PUNCT
ejpam-3526	364	22	algebra	algebra	NOUN
ejpam-3526	364	23	as	as	SCONJ
ejpam-3526	364	24	shown	show	VERB
ejpam-3526	364	25	in	in	ADP
ejpam-3526	364	26	the	the	DET
ejpam-3526	364	27	next	next	ADJ
ejpam-3526	364	28	theorem	theorem	PROPN
ejpam-3526	364	29	.	.	PUNCT
ejpam-3526	365	1	theorem	theorem	VERB
ejpam-3526	365	2	7	7	NUM
ejpam-3526	365	3	.	.	PUNCT
ejpam-3526	366	1	if	if	SCONJ
ejpam-3526	366	2	x	x	PRON
ejpam-3526	366	3	is	be	AUX
ejpam-3526	366	4	a	a	DET
ejpam-3526	366	5	dual	dual	ADJ
ejpam-3526	366	6	bci	bci	NOUN
ejpam-3526	366	7	-	-	NOUN
ejpam-3526	366	8	algebra	algebra	NOUN
ejpam-3526	366	9	satisfying	satisfy	VERB
ejpam-3526	366	10	a	a	DET
ejpam-3526	366	11	symmetric	symmetric	ADJ
ejpam-3526	366	12	condition	condition	NOUN
ejpam-3526	366	13	,	,	PUNCT
ejpam-3526	366	14	then	then	ADV
ejpam-3526	366	15	x	x	PUNCT
ejpam-3526	366	16	is	be	AUX
ejpam-3526	366	17	a	a	DET
ejpam-3526	366	18	commutative	commutative	ADJ
ejpam-3526	366	19	dual	dual	ADJ
ejpam-3526	366	20	b	b	NOUN
ejpam-3526	366	21	-	-	PUNCT
ejpam-3526	366	22	algebra	algebra	NOUN
ejpam-3526	366	23	.	.	PUNCT
ejpam-3526	367	1	proof	proof	NOUN
ejpam-3526	367	2	:	:	PUNCT
ejpam-3526	367	3	suppose	suppose	VERB
ejpam-3526	367	4	x	x	PRON
ejpam-3526	367	5	is	be	AUX
ejpam-3526	367	6	a	a	DET
ejpam-3526	367	7	dual	dual	ADJ
ejpam-3526	367	8	bci	bci	NOUN
ejpam-3526	367	9	-	-	NOUN
ejpam-3526	367	10	algebra	algebra	NOUN
ejpam-3526	367	11	satisfying	satisfy	VERB
ejpam-3526	367	12	a	a	DET
ejpam-3526	367	13	symmetric	symmetric	ADJ
ejpam-3526	367	14	condition	condition	NOUN
ejpam-3526	367	15	.	.	PUNCT
ejpam-3526	368	1	then	then	ADV
ejpam-3526	368	2	proposition	proposition	NOUN
ejpam-3526	368	3	1(iv	1(iv	NUM
ejpam-3526	368	4	)	)	PUNCT
ejpam-3526	368	5	becomes	become	VERB
ejpam-3526	368	6	x	x	NOUN
ejpam-3526	368	7	=	=	SYM
ejpam-3526	368	8	1	1	NUM
ejpam-3526	368	9	◦	◦	NOUN
ejpam-3526	368	10	x	x	SYM
ejpam-3526	368	11	=	=	SYM
ejpam-3526	368	12	x	x	PUNCT
ejpam-3526	368	13	◦	◦	NOUN
ejpam-3526	368	14	1	1	NUM
ejpam-3526	368	15	.	.	PUNCT
ejpam-3526	369	1	by	by	ADP
ejpam-3526	369	2	remark	remark	NOUN
ejpam-3526	369	3	5	5	NUM
ejpam-3526	369	4	,	,	PUNCT
ejpam-3526	369	5	it	it	PRON
ejpam-3526	369	6	remains	remain	VERB
ejpam-3526	369	7	to	to	PART
ejpam-3526	369	8	show	show	VERB
ejpam-3526	369	9	that	that	SCONJ
ejpam-3526	369	10	x	x	PRON
ejpam-3526	369	11	satisfies	satisfie	NOUN
ejpam-3526	369	12	(	(	PUNCT
ejpam-3526	369	13	db3	db3	PROPN
ejpam-3526	369	14	)	)	PUNCT
ejpam-3526	369	15	and	and	CCONJ
ejpam-3526	369	16	is	be	AUX
ejpam-3526	369	17	commutative	commutative	ADJ
ejpam-3526	369	18	.	.	PUNCT
ejpam-3526	370	1	applying	apply	VERB
ejpam-3526	370	2	the	the	DET
ejpam-3526	370	3	hypothesis	hypothesis	NOUN
ejpam-3526	370	4	,	,	PUNCT
ejpam-3526	370	5	propositon	propositon	NOUN
ejpam-3526	370	6	1(iii	1(iii	NUM
ejpam-3526	370	7	)	)	PUNCT
ejpam-3526	370	8	and	and	CCONJ
ejpam-3526	370	9	(	(	PUNCT
ejpam-3526	370	10	iv	iv	X
ejpam-3526	370	11	)	)	PUNCT
ejpam-3526	370	12	,	,	PUNCT
ejpam-3526	370	13	x	x	PUNCT
ejpam-3526	370	14	◦	◦	NOUN
ejpam-3526	370	15	(	(	PUNCT
ejpam-3526	370	16	y	y	PROPN
ejpam-3526	370	17	◦	◦	PROPN
ejpam-3526	370	18	z	z	PROPN
ejpam-3526	370	19	)	)	PUNCT
ejpam-3526	370	20	=	=	SYM
ejpam-3526	370	21	x	x	PUNCT
ejpam-3526	370	22	◦	◦	NOUN
ejpam-3526	370	23	(	(	PUNCT
ejpam-3526	370	24	z	z	AUX
ejpam-3526	370	25	◦	◦	NOUN
ejpam-3526	370	26	y	y	NOUN
ejpam-3526	370	27	)	)	PUNCT
ejpam-3526	370	28	=	=	SYM
ejpam-3526	370	29	z	z	X
ejpam-3526	370	30	◦	◦	NOUN
ejpam-3526	370	31	(	(	PUNCT
ejpam-3526	370	32	x	x	PART
ejpam-3526	370	33	◦	◦	VERB
ejpam-3526	370	34	y	y	NOUN
ejpam-3526	370	35	)	)	PUNCT
ejpam-3526	370	36	=	=	SYM
ejpam-3526	370	37	z	z	X
ejpam-3526	370	38	◦	◦	NOUN
ejpam-3526	370	39	[	[	X
ejpam-3526	370	40	x	x	PART
ejpam-3526	370	41	◦	◦	NOUN
ejpam-3526	370	42	(	(	PUNCT
ejpam-3526	370	43	1	1	NUM
ejpam-3526	370	44	◦	◦	NOUN
ejpam-3526	370	45	y	y	NOUN
ejpam-3526	370	46	)	)	PUNCT
ejpam-3526	370	47	]	]	PUNCT
ejpam-3526	371	1	=	=	PUNCT
ejpam-3526	372	1	[	[	X
ejpam-3526	372	2	x	x	X
ejpam-3526	372	3	◦	◦	NOUN
ejpam-3526	372	4	(	(	PUNCT
ejpam-3526	372	5	1	1	NUM
ejpam-3526	372	6	◦	◦	NOUN
ejpam-3526	372	7	y	y	NOUN
ejpam-3526	372	8	)	)	PUNCT
ejpam-3526	372	9	]	]	PUNCT
ejpam-3526	373	1	◦	◦	NOUN
ejpam-3526	373	2	z	z	NOUN
ejpam-3526	374	1	=	=	PUNCT
ejpam-3526	375	1	[	[	X
ejpam-3526	375	2	(	(	PUNCT
ejpam-3526	375	3	1	1	NUM
ejpam-3526	375	4	◦	◦	NOUN
ejpam-3526	375	5	y	y	NOUN
ejpam-3526	375	6	)	)	PUNCT
ejpam-3526	375	7	◦	◦	NOUN
ejpam-3526	375	8	x	x	SYM
ejpam-3526	375	9	]	]	X
ejpam-3526	375	10	◦	◦	NOUN
ejpam-3526	375	11	z	z	NOUN
ejpam-3526	375	12	=	=	SYM
ejpam-3526	376	1	[	[	X
ejpam-3526	376	2	(	(	PUNCT
ejpam-3526	376	3	y	y	NOUN
ejpam-3526	376	4	◦	◦	NOUN
ejpam-3526	376	5	1	1	NUM
ejpam-3526	376	6	)	)	PUNCT
ejpam-3526	376	7	◦	◦	NOUN
ejpam-3526	376	8	x	x	SYM
ejpam-3526	376	9	]	]	X
ejpam-3526	376	10	◦	◦	NOUN
ejpam-3526	376	11	z.	z.	PROPN
ejpam-3526	376	12	hence	hence	ADV
ejpam-3526	376	13	,	,	PUNCT
ejpam-3526	376	14	x	x	PRON
ejpam-3526	376	15	satisfies	satisfie	NOUN
ejpam-3526	376	16	(	(	PUNCT
ejpam-3526	376	17	db3	db3	PROPN
ejpam-3526	376	18	)	)	PUNCT
ejpam-3526	376	19	.	.	PUNCT
ejpam-3526	377	1	also	also	ADV
ejpam-3526	377	2	by	by	ADP
ejpam-3526	377	3	the	the	DET
ejpam-3526	377	4	hypothesis	hypothesis	NOUN
ejpam-3526	377	5	and	and	CCONJ
ejpam-3526	377	6	proposition	proposition	NOUN
ejpam-3526	377	7	1(iii	1(iii	NUM
ejpam-3526	377	8	)	)	PUNCT
ejpam-3526	377	9	,	,	PUNCT
ejpam-3526	377	10	(	(	PUNCT
ejpam-3526	377	11	x	x	X
ejpam-3526	377	12	◦	◦	NOUN
ejpam-3526	377	13	1	1	NUM
ejpam-3526	377	14	)	)	PUNCT
ejpam-3526	377	15	◦	◦	NOUN
ejpam-3526	377	16	y	y	NOUN
ejpam-3526	377	17	=	=	SYM
ejpam-3526	377	18	y	y	PROPN
ejpam-3526	377	19	◦	◦	NOUN
ejpam-3526	377	20	(	(	PUNCT
ejpam-3526	377	21	x	x	X
ejpam-3526	377	22	◦	◦	NOUN
ejpam-3526	377	23	1	1	NUM
ejpam-3526	377	24	)	)	PUNCT
ejpam-3526	377	25	=	=	SYM
ejpam-3526	378	1	x	x	PUNCT
ejpam-3526	378	2	◦	◦	NOUN
ejpam-3526	378	3	(	(	PUNCT
ejpam-3526	378	4	y	y	NOUN
ejpam-3526	378	5	◦	◦	NOUN
ejpam-3526	378	6	1	1	NUM
ejpam-3526	378	7	)	)	PUNCT
ejpam-3526	378	8	=	=	SYM
ejpam-3526	379	1	(	(	PUNCT
ejpam-3526	379	2	y	y	NOUN
ejpam-3526	379	3	◦	◦	NOUN
ejpam-3526	379	4	1	1	NUM
ejpam-3526	379	5	)	)	PUNCT
ejpam-3526	379	6	◦	◦	NOUN
ejpam-3526	379	7	x.	x.	NOUN
ejpam-3526	379	8	therefore	therefore	ADV
ejpam-3526	379	9	,	,	PUNCT
ejpam-3526	379	10	x	x	PUNCT
ejpam-3526	379	11	is	be	AUX
ejpam-3526	379	12	commutative	commutative	ADJ
ejpam-3526	379	13	.	.	PUNCT
ejpam-3526	380	1	references	reference	NOUN
ejpam-3526	380	2	1506	1506	NUM
ejpam-3526	380	3	5	5	NUM
ejpam-3526	380	4	.	.	PUNCT
ejpam-3526	380	5	conclusion	conclusion	NOUN
ejpam-3526	380	6	in	in	ADP
ejpam-3526	380	7	this	this	DET
ejpam-3526	380	8	paper	paper	NOUN
ejpam-3526	380	9	,	,	PUNCT
ejpam-3526	380	10	the	the	DET
ejpam-3526	380	11	notion	notion	NOUN
ejpam-3526	380	12	of	of	ADP
ejpam-3526	380	13	a	a	PRON
ejpam-3526	380	14	dual	dual	ADJ
ejpam-3526	380	15	b	b	NOUN
ejpam-3526	380	16	-	-	PUNCT
ejpam-3526	380	17	algebra	algebra	NOUN
ejpam-3526	380	18	is	be	AUX
ejpam-3526	380	19	presented	present	VERB
ejpam-3526	380	20	together	together	ADV
ejpam-3526	380	21	with	with	ADP
ejpam-3526	380	22	some	some	PRON
ejpam-3526	380	23	of	of	ADP
ejpam-3526	380	24	its	its	PRON
ejpam-3526	380	25	properties	property	NOUN
ejpam-3526	380	26	and	and	CCONJ
ejpam-3526	380	27	characterizations	characterization	NOUN
ejpam-3526	380	28	.	.	PUNCT
ejpam-3526	381	1	not	not	PART
ejpam-3526	381	2	every	every	DET
ejpam-3526	381	3	b	b	X
ejpam-3526	381	4	-	-	PUNCT
ejpam-3526	381	5	algebra	algebra	NOUN
ejpam-3526	381	6	is	be	AUX
ejpam-3526	381	7	a	a	DET
ejpam-3526	381	8	dual	dual	ADJ
ejpam-3526	381	9	b	b	NOUN
ejpam-3526	381	10	-	-	PUNCT
ejpam-3526	381	11	algebra	algebra	NOUN
ejpam-3526	381	12	and	and	CCONJ
ejpam-3526	381	13	not	not	PART
ejpam-3526	381	14	every	every	DET
ejpam-3526	381	15	dual	dual	ADJ
ejpam-3526	381	16	b	b	X
ejpam-3526	381	17	-	-	PUNCT
ejpam-3526	381	18	algebra	algebra	NOUN
ejpam-3526	381	19	is	be	AUX
ejpam-3526	381	20	a	a	DET
ejpam-3526	381	21	b	b	NOUN
ejpam-3526	381	22	-	-	PUNCT
ejpam-3526	381	23	algebra	algebra	NOUN
ejpam-3526	381	24	.	.	PUNCT
ejpam-3526	382	1	however	however	ADV
ejpam-3526	382	2	,	,	PUNCT
ejpam-3526	382	3	there	there	PRON
ejpam-3526	382	4	exists	exist	VERB
ejpam-3526	382	5	an	an	DET
ejpam-3526	382	6	algebra	algebra	NOUN
ejpam-3526	382	7	that	that	PRON
ejpam-3526	382	8	is	be	AUX
ejpam-3526	382	9	both	both	CCONJ
ejpam-3526	382	10	a	a	DET
ejpam-3526	382	11	b	b	NOUN
ejpam-3526	382	12	-	-	PUNCT
ejpam-3526	382	13	algebra	algebra	NOUN
ejpam-3526	382	14	and	and	CCONJ
ejpam-3526	382	15	a	a	DET
ejpam-3526	382	16	dual	dual	ADJ
ejpam-3526	382	17	b	b	NOUN
ejpam-3526	382	18	-	-	PUNCT
ejpam-3526	382	19	algebra	algebra	NOUN
ejpam-3526	382	20	.	.	PUNCT
ejpam-3526	383	1	the	the	DET
ejpam-3526	383	2	different	different	ADJ
ejpam-3526	383	3	relationships	relationship	NOUN
ejpam-3526	383	4	of	of	ADP
ejpam-3526	383	5	the	the	DET
ejpam-3526	383	6	dual	dual	ADJ
ejpam-3526	383	7	b	b	NOUN
ejpam-3526	383	8	-	-	PUNCT
ejpam-3526	383	9	algebra	algebra	NOUN
ejpam-3526	383	10	to	to	PART
ejpam-3526	383	11	bck	bck	VERB
ejpam-3526	383	12	-	-	PUNCT
ejpam-3526	383	13	algebra	algebra	NOUN
ejpam-3526	383	14	,	,	PUNCT
ejpam-3526	383	15	ci	ci	NOUN
ejpam-3526	383	16	-	-	NOUN
ejpam-3526	383	17	algebra	algebra	NOUN
ejpam-3526	383	18	,	,	PUNCT
ejpam-3526	383	19	and	and	CCONJ
ejpam-3526	383	20	dual	dual	ADJ
ejpam-3526	383	21	bci	bci	NOUN
ejpam-3526	383	22	-	-	NOUN
ejpam-3526	383	23	algebra	algebra	NOUN
ejpam-3526	383	24	is	be	AUX
ejpam-3526	383	25	given	give	VERB
ejpam-3526	383	26	.	.	PUNCT
ejpam-3526	384	1	the	the	DET
ejpam-3526	384	2	concept	concept	NOUN
ejpam-3526	384	3	of	of	ADP
ejpam-3526	384	4	commutativity	commutativity	NOUN
ejpam-3526	384	5	in	in	ADP
ejpam-3526	384	6	a	a	DET
ejpam-3526	384	7	dual	dual	ADJ
ejpam-3526	384	8	b	b	NOUN
ejpam-3526	384	9	-	-	PUNCT
ejpam-3526	384	10	algebra	algebra	NOUN
ejpam-3526	384	11	was	be	AUX
ejpam-3526	384	12	introduced	introduce	VERB
ejpam-3526	384	13	and	and	CCONJ
ejpam-3526	384	14	some	some	DET
ejpam-3526	384	15	properties	property	NOUN
ejpam-3526	384	16	were	be	AUX
ejpam-3526	384	17	provided	provide	VERB
ejpam-3526	384	18	.	.	PUNCT
ejpam-3526	385	1	acknowledgements	acknowledgement	NOUN
ejpam-3526	385	2	this	this	DET
ejpam-3526	385	3	research	research	NOUN
ejpam-3526	385	4	is	be	AUX
ejpam-3526	385	5	funded	fund	VERB
ejpam-3526	385	6	by	by	ADP
ejpam-3526	385	7	the	the	DET
ejpam-3526	385	8	commission	commission	NOUN
ejpam-3526	385	9	on	on	ADP
ejpam-3526	385	10	higher	high	ADJ
ejpam-3526	385	11	education	education	NOUN
ejpam-3526	385	12	(	(	PUNCT
ejpam-3526	385	13	ched	che	VERB
ejpam-3526	385	14	)	)	PUNCT
ejpam-3526	385	15	and	and	CCONJ
ejpam-3526	385	16	mindanao	mindanao	PROPN
ejpam-3526	385	17	state	state	PROPN
ejpam-3526	385	18	university	university	PROPN
ejpam-3526	385	19	-	-	PUNCT
ejpam-3526	385	20	iligan	iligan	PROPN
ejpam-3526	385	21	institute	institute	PROPN
ejpam-3526	385	22	of	of	ADP
ejpam-3526	385	23	technology	technology	PROPN
ejpam-3526	385	24	,	,	PUNCT
ejpam-3526	385	25	philippines	philippine	NOUN
ejpam-3526	385	26	.	.	PUNCT
ejpam-3526	386	1	references	reference	NOUN
ejpam-3526	386	2	[	[	X
ejpam-3526	386	3	1	1	NUM
ejpam-3526	386	4	]	]	X
ejpam-3526	386	5	n.	n.	PROPN
ejpam-3526	386	6	al	al	PROPN
ejpam-3526	386	7	-	-	PUNCT
ejpam-3526	386	8	shehrie	shehrie	NOUN
ejpam-3526	386	9	.	.	PUNCT
ejpam-3526	387	1	derivations	derivation	NOUN
ejpam-3526	387	2	of	of	ADP
ejpam-3526	387	3	b	b	NOUN
ejpam-3526	387	4	-	-	PUNCT
ejpam-3526	387	5	algebras	algebras	PROPN
ejpam-3526	387	6	.	.	PUNCT
ejpam-3526	388	1	jkau	jkau	NOUN
ejpam-3526	388	2	:	:	PUNCT
ejpam-3526	389	1	sci	sci	PROPN
ejpam-3526	389	2	.	.	PROPN
ejpam-3526	389	3	,	,	PUNCT
ejpam-3526	389	4	22(1):71–83	22(1):71–83	NUM
ejpam-3526	389	5	,	,	PUNCT
ejpam-3526	389	6	2010	2010	NUM
ejpam-3526	389	7	.	.	PUNCT
ejpam-3526	390	1	[	[	X
ejpam-3526	390	2	2	2	NUM
ejpam-3526	390	3	]	]	X
ejpam-3526	390	4	y.	y.	PROPN
ejpam-3526	390	5	imai	imai	PROPN
ejpam-3526	390	6	and	and	CCONJ
ejpam-3526	390	7	k.	k.	PROPN
ejpam-3526	390	8	iseki	iseki	PROPN
ejpam-3526	390	9	.	.	PUNCT
ejpam-3526	391	1	on	on	ADP
ejpam-3526	391	2	axiom	axiom	NOUN
ejpam-3526	391	3	systems	system	NOUN
ejpam-3526	391	4	of	of	ADP
ejpam-3526	391	5	propositional	propositional	ADJ
ejpam-3526	391	6	calculi	calculi	PROPN
ejpam-3526	391	7	.	.	PUNCT
ejpam-3526	392	1	proceedings	proceeding	NOUN
ejpam-3526	392	2	of	of	ADP
ejpam-3526	392	3	japan	japan	PROPN
ejpam-3526	392	4	academy	academy	PROPN
ejpam-3526	392	5	,	,	PUNCT
ejpam-3526	392	6	42(1):19–22	42(1):19–22	NUM
ejpam-3526	392	7	,	,	PUNCT
ejpam-3526	392	8	1966	1966	NUM
ejpam-3526	392	9	.	.	PUNCT
ejpam-3526	393	1	[	[	X
ejpam-3526	393	2	3	3	X
ejpam-3526	393	3	]	]	PUNCT
ejpam-3526	393	4	k.	k.	PROPN
ejpam-3526	393	5	kim	kim	PROPN
ejpam-3526	393	6	and	and	CCONJ
ejpam-3526	393	7	y.	y.	PROPN
ejpam-3526	393	8	yon	yon	PROPN
ejpam-3526	393	9	.	.	PUNCT
ejpam-3526	394	1	dual	dual	ADJ
ejpam-3526	394	2	bck	bck	NOUN
ejpam-3526	394	3	-	-	PUNCT
ejpam-3526	394	4	algebra	algebra	PROPN
ejpam-3526	394	5	and	and	CCONJ
ejpam-3526	394	6	mv	mv	NOUN
ejpam-3526	394	7	-	-	NOUN
ejpam-3526	394	8	algebra	algebra	NOUN
ejpam-3526	394	9	.	.	PUNCT
ejpam-3526	395	1	scientiae	scientiae	PROPN
ejpam-3526	395	2	mathematicae	mathematicae	PROPN
ejpam-3526	395	3	japonicae	japonicae	PROPN
ejpam-3526	395	4	,	,	PUNCT
ejpam-3526	395	5	42(1):393–399	42(1):393–399	PROPN
ejpam-3526	395	6	,	,	PUNCT
ejpam-3526	395	7	2007	2007	NUM
ejpam-3526	395	8	.	.	PUNCT
ejpam-3526	396	1	[	[	X
ejpam-3526	396	2	4	4	X
ejpam-3526	396	3	]	]	PUNCT
ejpam-3526	396	4	m.	m.	NOUN
ejpam-3526	396	5	kondo	kondo	PROPN
ejpam-3526	396	6	and	and	CCONJ
ejpam-3526	396	7	y.b	y.b	PROPN
ejpam-3526	396	8	.	.	PROPN
ejpam-3526	396	9	jun	jun	PROPN
ejpam-3526	396	10	.	.	PUNCT
ejpam-3526	397	1	the	the	DET
ejpam-3526	397	2	class	class	NOUN
ejpam-3526	397	3	of	of	ADP
ejpam-3526	397	4	b	b	NOUN
ejpam-3526	397	5	-	-	PUNCT
ejpam-3526	397	6	algebras	algebras	PROPN
ejpam-3526	397	7	coincides	coincide	VERB
ejpam-3526	397	8	with	with	ADP
ejpam-3526	397	9	the	the	DET
ejpam-3526	397	10	class	class	NOUN
ejpam-3526	397	11	of	of	ADP
ejpam-3526	397	12	groups	group	NOUN
ejpam-3526	397	13	.	.	PUNCT
ejpam-3526	398	1	scientiae	scientiae	PROPN
ejpam-3526	398	2	mathematicae	mathematicae	PROPN
ejpam-3526	398	3	japonicae	japonicae	PROPN
ejpam-3526	398	4	,	,	PUNCT
ejpam-3526	398	5	7:175–177	7:175–177	NUM
ejpam-3526	398	6	,	,	PUNCT
ejpam-3526	398	7	2002	2002	NUM
ejpam-3526	398	8	.	.	PUNCT
ejpam-3526	399	1	[	[	X
ejpam-3526	399	2	5	5	NUM
ejpam-3526	399	3	]	]	X
ejpam-3526	399	4	b.l	b.l	PROPN
ejpam-3526	399	5	.	.	PROPN
ejpam-3526	399	6	meng	meng	PROPN
ejpam-3526	399	7	.	.	PUNCT
ejpam-3526	400	1	ci	ci	NOUN
ejpam-3526	400	2	-	-	PUNCT
ejpam-3526	400	3	algebra	algebra	NOUN
ejpam-3526	400	4	.	.	PUNCT
ejpam-3526	401	1	scientiae	scientiae	PROPN
ejpam-3526	401	2	mathematicae	mathematicae	PROPN
ejpam-3526	401	3	japonicae	japonicae	PROPN
ejpam-3526	401	4	,	,	PUNCT
ejpam-3526	401	5	2009:695–701	2009:695–701	NOUN
ejpam-3526	401	6	,	,	PUNCT
ejpam-3526	401	7	2009	2009	NUM
ejpam-3526	401	8	.	.	PUNCT
ejpam-3526	402	1	[	[	X
ejpam-3526	402	2	6	6	NUM
ejpam-3526	402	3	]	]	PUNCT
ejpam-3526	402	4	j.	j.	PROPN
ejpam-3526	402	5	meng	meng	PROPN
ejpam-3526	402	6	and	and	CCONJ
ejpam-3526	402	7	y.	y.	PROPN
ejpam-3526	402	8	jun	jun	PROPN
ejpam-3526	402	9	.	.	PUNCT
ejpam-3526	403	1	bck	bck	PROPN
ejpam-3526	403	2	-	-	PUNCT
ejpam-3526	403	3	algebra	algebra	NOUN
ejpam-3526	403	4	.	.	PUNCT
ejpam-3526	404	1	kyung	kyung	PROPN
ejpam-3526	404	2	moonsa	moonsa	PROPN
ejpam-3526	404	3	,	,	PUNCT
ejpam-3526	404	4	seoul	seoul	PROPN
ejpam-3526	404	5	,	,	PUNCT
ejpam-3526	404	6	1994	1994	NUM
ejpam-3526	404	7	.	.	PUNCT
ejpam-3526	405	1	[	[	X
ejpam-3526	405	2	7	7	X
ejpam-3526	405	3	]	]	X
ejpam-3526	405	4	j.	j.	PROPN
ejpam-3526	405	5	neggers	neggers	PROPN
ejpam-3526	405	6	and	and	CCONJ
ejpam-3526	405	7	s.s	s.s	PROPN
ejpam-3526	405	8	.	.	PROPN
ejpam-3526	405	9	ahn	ahn	PROPN
ejpam-3526	405	10	.	.	PROPN
ejpam-3526	406	1	on	on	ADP
ejpam-3526	406	2	q	q	NOUN
ejpam-3526	406	3	-	-	PUNCT
ejpam-3526	406	4	algebras	algebra	NOUN
ejpam-3526	406	5	.	.	PUNCT
ejpam-3526	407	1	international	international	ADJ
ejpam-3526	407	2	journal	journal	PROPN
ejpam-3526	407	3	of	of	ADP
ejpam-3526	407	4	mathematics	mathematics	PROPN
ejpam-3526	407	5	and	and	CCONJ
ejpam-3526	407	6	mathematical	mathematical	ADJ
ejpam-3526	407	7	sciences	science	NOUN
ejpam-3526	407	8	,	,	PUNCT
ejpam-3526	407	9	27:749–757	27:749–757	NOUN
ejpam-3526	407	10	,	,	PUNCT
ejpam-3526	407	11	2001	2001	NUM
ejpam-3526	407	12	.	.	PUNCT
ejpam-3526	408	1	[	[	X
ejpam-3526	408	2	8	8	X
ejpam-3526	408	3	]	]	X
ejpam-3526	408	4	j.	j.	PROPN
ejpam-3526	408	5	neggers	neggers	PROPN
ejpam-3526	408	6	and	and	CCONJ
ejpam-3526	408	7	h.	h.	PROPN
ejpam-3526	408	8	kim	kim	PROPN
ejpam-3526	408	9	.	.	PUNCT
ejpam-3526	409	1	a	a	DET
ejpam-3526	409	2	fundamental	fundamental	ADJ
ejpam-3526	409	3	theorem	theorem	NOUN
ejpam-3526	409	4	of	of	ADP
ejpam-3526	409	5	b	b	NOUN
ejpam-3526	409	6	-	-	PUNCT
ejpam-3526	409	7	homomorphism	homomorphism	NOUN
ejpam-3526	409	8	for	for	ADP
ejpam-3526	409	9	b	b	NOUN
ejpam-3526	409	10	-	-	PUNCT
ejpam-3526	409	11	algebras	algebras	PROPN
ejpam-3526	409	12	.	.	PUNCT
ejpam-3526	410	1	inter.math.j	inter.math.j	PROPN
ejpam-3526	410	2	.	.	PROPN
ejpam-3526	410	3	,	,	PUNCT
ejpam-3526	410	4	2:207–214	2:207–214	NUM
ejpam-3526	410	5	,	,	PUNCT
ejpam-3526	410	6	2002	2002	NUM
ejpam-3526	410	7	.	.	PUNCT
ejpam-3526	411	1	[	[	X
ejpam-3526	411	2	9	9	NUM
ejpam-3526	411	3	]	]	X
ejpam-3526	411	4	j.	j.	PROPN
ejpam-3526	411	5	neggers	neggers	PROPN
ejpam-3526	411	6	and	and	CCONJ
ejpam-3526	411	7	h.	h.	PROPN
ejpam-3526	411	8	kim	kim	PROPN
ejpam-3526	411	9	.	.	PUNCT
ejpam-3526	412	1	on	on	ADP
ejpam-3526	412	2	b	b	NOUN
ejpam-3526	412	3	-	-	PUNCT
ejpam-3526	412	4	algebras	algebras	PROPN
ejpam-3526	412	5	.	.	PUNCT
ejpam-3526	412	6	mat	mat	PROPN
ejpam-3526	412	7	.	.	PROPN
ejpam-3526	412	8	vesnik	vesnik	PROPN
ejpam-3526	412	9	,	,	PUNCT
ejpam-3526	412	10	54:21–29	54:21–29	NUM
ejpam-3526	412	11	,	,	PUNCT
ejpam-3526	412	12	2002	2002	NUM
ejpam-3526	412	13	.	.	PUNCT
ejpam-3526	413	1	[	[	X
ejpam-3526	413	2	10	10	NUM
ejpam-3526	413	3	]	]	X
ejpam-3526	413	4	e.	e.	PROPN
ejpam-3526	413	5	roh	roh	PROPN
ejpam-3526	413	6	and	and	CCONJ
ejpam-3526	413	7	y.	y.	PROPN
ejpam-3526	413	8	jun	jun	PROPN
ejpam-3526	413	9	.	.	PUNCT
ejpam-3526	414	1	positive	positive	ADJ
ejpam-3526	414	2	implicative	implicative	ADJ
ejpam-3526	414	3	ideals	ideal	NOUN
ejpam-3526	414	4	of	of	ADP
ejpam-3526	414	5	bck	bck	NOUN
ejpam-3526	414	6	-	-	PUNCT
ejpam-3526	414	7	algebras	algebras	PROPN
ejpam-3526	414	8	based	base	VERB
ejpam-3526	414	9	on	on	ADP
ejpam-3526	414	10	intersectional	intersectional	ADJ
ejpam-3526	414	11	soft	soft	ADJ
ejpam-3526	414	12	sets	set	NOUN
ejpam-3526	414	13	.	.	PUNCT
ejpam-3526	415	1	journal	journal	NOUN
ejpam-3526	415	2	of	of	ADP
ejpam-3526	415	3	applied	apply	VERB
ejpam-3526	415	4	mathematics	mathematic	NOUN
ejpam-3526	415	5	,	,	PUNCT
ejpam-3526	415	6	2013	2013	NUM
ejpam-3526	415	7	.	.	PUNCT
ejpam-3526	416	1	[	[	X
ejpam-3526	416	2	11	11	NUM
ejpam-3526	416	3	]	]	PUNCT
ejpam-3526	416	4	a.	a.	PROPN
ejpam-3526	416	5	saeid	saeid	PROPN
ejpam-3526	416	6	.	.	PUNCT
ejpam-3526	417	1	ci	ci	NOUN
ejpam-3526	417	2	-	-	PUNCT
ejpam-3526	417	3	algebra	algebra	NOUN
ejpam-3526	417	4	is	be	AUX
ejpam-3526	417	5	equivalent	equivalent	ADJ
ejpam-3526	417	6	to	to	ADP
ejpam-3526	417	7	dual	dual	ADJ
ejpam-3526	417	8	q	q	NOUN
ejpam-3526	417	9	-	-	NOUN
ejpam-3526	417	10	algebra	algebra	NOUN
ejpam-3526	417	11	.	.	PUNCT
ejpam-3526	418	1	journal	journal	NOUN
ejpam-3526	418	2	of	of	ADP
ejpam-3526	418	3	the	the	DET
ejpam-3526	418	4	egyptian	egyptian	PROPN
ejpam-3526	418	5	mathematical	mathematical	PROPN
ejpam-3526	418	6	society	society	NOUN
ejpam-3526	418	7	,	,	PUNCT
ejpam-3526	418	8	21:1–2	21:1–2	NUM
ejpam-3526	418	9	,	,	PUNCT
ejpam-3526	418	10	2013	2013	NUM
ejpam-3526	418	11	.	.	PUNCT
ejpam-3526	419	1	[	[	X
ejpam-3526	419	2	12	12	NUM
ejpam-3526	419	3	]	]	PUNCT
ejpam-3526	419	4	a.	a.	NOUN
ejpam-3526	419	5	walendziak	walendziak	PROPN
ejpam-3526	419	6	.	.	PUNCT
ejpam-3526	420	1	on	on	ADP
ejpam-3526	420	2	commutative	commutative	ADJ
ejpam-3526	420	3	be	be	AUX
ejpam-3526	420	4	-	-	PUNCT
ejpam-3526	420	5	algebras	algebra	NOUN
ejpam-3526	420	6	.	.	PUNCT
ejpam-3526	421	1	scientiae	scientiae	PROPN
ejpam-3526	421	2	mathematicae	mathematicae	PROPN
ejpam-3526	421	3	japonicae	japonicae	PROPN
ejpam-3526	421	4	,	,	PUNCT
ejpam-3526	421	5	2008:585–588	2008:585–588	NUM
ejpam-3526	421	6	,	,	PUNCT
ejpam-3526	421	7	2008	2008	NUM
ejpam-3526	421	8	.	.	PUNCT
ejpam-3526	422	1	references	reference	NOUN
ejpam-3526	422	2	1507	1507	NUM
ejpam-3526	422	3	[	[	X
ejpam-3526	422	4	13	13	NUM
ejpam-3526	422	5	]	]	X
ejpam-3526	422	6	o.	o.	NOUN
ejpam-3526	422	7	zahiri	zahiri	PROPN
ejpam-3526	422	8	and	and	CCONJ
ejpam-3526	422	9	r.	r.	PROPN
ejpam-3526	422	10	burzooei	burzooei	PROPN
ejpam-3526	422	11	.	.	PUNCT
ejpam-3526	423	1	graph	graph	NOUN
ejpam-3526	423	2	of	of	ADP
ejpam-3526	423	3	bci	bci	NOUN
ejpam-3526	423	4	-	-	PUNCT
ejpam-3526	423	5	algebras	algebra	NOUN
ejpam-3526	423	6	.	.	PUNCT
ejpam-3526	424	1	international	international	ADJ
ejpam-3526	424	2	journal	journal	PROPN
ejpam-3526	424	3	of	of	ADP
ejpam-3526	424	4	mathematics	mathematics	PROPN
ejpam-3526	424	5	and	and	CCONJ
ejpam-3526	424	6	mathematical	mathematical	ADJ
ejpam-3526	424	7	sciences	science	NOUN
ejpam-3526	424	8	,	,	PUNCT
ejpam-3526	424	9	2012	2012	NUM
ejpam-3526	424	10	.	.	PUNCT