id	sid	tid	token	lemma	pos
ejpam-6974	1	1	european	european	PROPN
ejpam-6974	1	2	journal	journal	PROPN
ejpam-6974	1	3	of	of	ADP
ejpam-6974	1	4	pure	pure	ADJ
ejpam-6974	1	5	and	and	CCONJ
ejpam-6974	1	6	applied	applied	ADJ
ejpam-6974	1	7	mathematics	mathematic	NOUN
ejpam-6974	1	8	2025	2025	NUM
ejpam-6974	1	9	,	,	PUNCT
ejpam-6974	1	10	vol	vol	NOUN
ejpam-6974	1	11	.	.	PROPN
ejpam-6974	1	12	18	18	NUM
ejpam-6974	1	13	,	,	PUNCT
ejpam-6974	1	14	issue	issue	NOUN
ejpam-6974	1	15	4	4	NUM
ejpam-6974	1	16	,	,	PUNCT
ejpam-6974	1	17	article	article	NOUN
ejpam-6974	1	18	number	number	NOUN
ejpam-6974	1	19	6974	6974	NUM
ejpam-6974	1	20	issn	issn	VERB
ejpam-6974	1	21	1307	1307	NUM
ejpam-6974	1	22	-	-	SYM
ejpam-6974	1	23	5543	5543	NUM
ejpam-6974	1	24	–	–	PUNCT
ejpam-6974	1	25	ejpam.com	ejpam.com	X
ejpam-6974	1	26	published	publish	VERB
ejpam-6974	1	27	by	by	ADP
ejpam-6974	1	28	new	new	PROPN
ejpam-6974	1	29	york	york	PROPN
ejpam-6974	1	30	business	business	PROPN
ejpam-6974	1	31	global	global	PROPN
ejpam-6974	1	32	group	group	NOUN
ejpam-6974	1	33	-	-	PUNCT
ejpam-6974	1	34	derived	derive	VERB
ejpam-6974	1	35	and	and	CCONJ
ejpam-6974	1	36	non	non	ADJ
ejpam-6974	1	37	-	-	NOUN
ejpam-6974	1	38	group	group	NOUN
ejpam-6974	1	39	-	-	PUNCT
ejpam-6974	1	40	derived	derive	VERB
ejpam-6974	1	41	dual	dual	ADJ
ejpam-6974	1	42	bg	bg	NOUN
ejpam-6974	1	43	-	-	PUNCT
ejpam-6974	1	44	algebra	algebra	PROPN
ejpam-6974	1	45	clive	clive	PROPN
ejpam-6974	1	46	martin	martin	PROPN
ejpam-6974	1	47	g.	g.	PROPN
ejpam-6974	1	48	chan1,∗	chan1,∗	PROPN
ejpam-6974	1	49	,	,	PUNCT
ejpam-6974	1	50	katrina	katrina	PROPN
ejpam-6974	1	51	b.	b.	PROPN
ejpam-6974	1	52	fuentes1	fuentes1	PROPN
ejpam-6974	1	53	1	1	NUM
ejpam-6974	1	54	department	department	NOUN
ejpam-6974	1	55	of	of	ADP
ejpam-6974	1	56	computer	computer	NOUN
ejpam-6974	1	57	,	,	PUNCT
ejpam-6974	1	58	information	information	NOUN
ejpam-6974	1	59	sciences	science	NOUN
ejpam-6974	1	60	and	and	CCONJ
ejpam-6974	1	61	mathematics	mathematic	NOUN
ejpam-6974	1	62	,	,	PUNCT
ejpam-6974	1	63	school	school	NOUN
ejpam-6974	1	64	of	of	ADP
ejpam-6974	1	65	arts	art	NOUN
ejpam-6974	1	66	and	and	CCONJ
ejpam-6974	1	67	sciences	science	NOUN
ejpam-6974	1	68	,	,	PUNCT
ejpam-6974	1	69	university	university	NOUN
ejpam-6974	1	70	of	of	ADP
ejpam-6974	1	71	san	san	PROPN
ejpam-6974	1	72	carlos	carlos	PROPN
ejpam-6974	1	73	,	,	PUNCT
ejpam-6974	1	74	cebu	cebu	NOUN
ejpam-6974	1	75	city	city	PROPN
ejpam-6974	1	76	,	,	PUNCT
ejpam-6974	1	77	cebu	cebu	NOUN
ejpam-6974	1	78	,	,	PUNCT
ejpam-6974	1	79	philippines	philippine	NOUN
ejpam-6974	1	80	abstract	abstract	ADJ
ejpam-6974	1	81	.	.	PUNCT
ejpam-6974	2	1	this	this	DET
ejpam-6974	2	2	study	study	NOUN
ejpam-6974	2	3	introduces	introduce	VERB
ejpam-6974	2	4	the	the	DET
ejpam-6974	2	5	notion	notion	NOUN
ejpam-6974	2	6	of	of	ADP
ejpam-6974	2	7	the	the	DET
ejpam-6974	2	8	dual	dual	ADJ
ejpam-6974	2	9	bg	bg	NOUN
ejpam-6974	2	10	-	-	NOUN
ejpam-6974	2	11	algebra	algebra	PROPN
ejpam-6974	2	12	.	.	PUNCT
ejpam-6974	3	1	the	the	DET
ejpam-6974	3	2	axioms	axiom	NOUN
ejpam-6974	3	3	are	be	AUX
ejpam-6974	3	4	presented	present	VERB
ejpam-6974	3	5	and	and	CCONJ
ejpam-6974	3	6	are	be	AUX
ejpam-6974	3	7	shown	show	VERB
ejpam-6974	3	8	to	to	PART
ejpam-6974	3	9	be	be	AUX
ejpam-6974	3	10	independent	independent	ADJ
ejpam-6974	3	11	.	.	PUNCT
ejpam-6974	4	1	fundamental	fundamental	ADJ
ejpam-6974	4	2	properties	property	NOUN
ejpam-6974	4	3	of	of	ADP
ejpam-6974	4	4	the	the	DET
ejpam-6974	4	5	dual	dual	ADJ
ejpam-6974	4	6	bg	bg	NOUN
ejpam-6974	4	7	-	-	PUNCT
ejpam-6974	4	8	algebra	algebra	PROPN
ejpam-6974	4	9	are	be	AUX
ejpam-6974	4	10	also	also	ADV
ejpam-6974	4	11	provided	provide	VERB
ejpam-6974	4	12	.	.	PUNCT
ejpam-6974	5	1	the	the	DET
ejpam-6974	5	2	concept	concept	NOUN
ejpam-6974	5	3	of	of	ADP
ejpam-6974	5	4	a	a	DET
ejpam-6974	5	5	group	group	NOUN
ejpam-6974	5	6	-	-	PUNCT
ejpam-6974	5	7	derived	derive	VERB
ejpam-6974	5	8	dual	dual	ADJ
ejpam-6974	5	9	bg	bg	NOUN
ejpam-6974	5	10	-	-	NOUN
ejpam-6974	5	11	algebra	algebra	PROPN
ejpam-6974	5	12	and	and	CCONJ
ejpam-6974	5	13	its	its	PRON
ejpam-6974	5	14	characterization	characterization	NOUN
ejpam-6974	5	15	were	be	AUX
ejpam-6974	5	16	established	establish	VERB
ejpam-6974	5	17	.	.	PUNCT
ejpam-6974	6	1	moreover	moreover	ADV
ejpam-6974	6	2	,	,	PUNCT
ejpam-6974	6	3	a	a	DET
ejpam-6974	6	4	non	non	ADJ
ejpam-6974	6	5	-	-	ADJ
ejpam-6974	6	6	group	group	NOUN
ejpam-6974	6	7	-	-	PUNCT
ejpam-6974	6	8	derived	derive	VERB
ejpam-6974	6	9	dual	dual	ADJ
ejpam-6974	6	10	bg	bg	NOUN
ejpam-6974	6	11	-	-	PUNCT
ejpam-6974	6	12	algebra	algebra	PROPN
ejpam-6974	6	13	can	can	AUX
ejpam-6974	6	14	be	be	AUX
ejpam-6974	6	15	constructed	construct	VERB
ejpam-6974	6	16	from	from	ADP
ejpam-6974	6	17	a	a	DET
ejpam-6974	6	18	set	set	NOUN
ejpam-6974	6	19	containing	contain	VERB
ejpam-6974	6	20	at	at	ADV
ejpam-6974	6	21	least	least	ADV
ejpam-6974	6	22	3	3	NUM
ejpam-6974	6	23	elements	element	NOUN
ejpam-6974	6	24	.	.	PUNCT
ejpam-6974	7	1	lastly	lastly	ADV
ejpam-6974	7	2	,	,	PUNCT
ejpam-6974	7	3	this	this	DET
ejpam-6974	7	4	paper	paper	NOUN
ejpam-6974	7	5	also	also	ADV
ejpam-6974	7	6	presented	present	VERB
ejpam-6974	7	7	a	a	DET
ejpam-6974	7	8	python	python	NOUN
ejpam-6974	7	9	script	script	NOUN
ejpam-6974	7	10	used	use	VERB
ejpam-6974	7	11	to	to	PART
ejpam-6974	7	12	verify	verify	VERB
ejpam-6974	7	13	whether	whether	SCONJ
ejpam-6974	7	14	a	a	DET
ejpam-6974	7	15	given	give	VERB
ejpam-6974	7	16	cayley	cayley	ADJ
ejpam-6974	7	17	table	table	NOUN
ejpam-6974	7	18	is	be	AUX
ejpam-6974	7	19	a	a	DET
ejpam-6974	7	20	dual	dual	ADJ
ejpam-6974	7	21	bg	bg	NOUN
ejpam-6974	7	22	-	-	NOUN
ejpam-6974	7	23	algebra	algebra	PROPN
ejpam-6974	7	24	.	.	PUNCT
ejpam-6974	8	1	this	this	PRON
ejpam-6974	8	2	was	be	AUX
ejpam-6974	8	3	utilized	utilize	VERB
ejpam-6974	8	4	throughout	throughout	ADP
ejpam-6974	8	5	the	the	DET
ejpam-6974	8	6	process	process	NOUN
ejpam-6974	8	7	of	of	ADP
ejpam-6974	8	8	this	this	DET
ejpam-6974	8	9	study	study	NOUN
ejpam-6974	8	10	.	.	PUNCT
ejpam-6974	9	1	2020	2020	NUM
ejpam-6974	9	2	mathematics	mathematic	NOUN
ejpam-6974	9	3	subject	subject	NOUN
ejpam-6974	9	4	classifications	classification	NOUN
ejpam-6974	9	5	:	:	PUNCT
ejpam-6974	9	6	06f35	06f35	NUM
ejpam-6974	9	7	,	,	PUNCT
ejpam-6974	9	8	47l45	47l45	NUM
ejpam-6974	9	9	,	,	PUNCT
ejpam-6974	9	10	08c05	08c05	NOUN
ejpam-6974	9	11	,	,	PUNCT
ejpam-6974	9	12	20a05	20a05	NUM
ejpam-6974	9	13	,	,	PUNCT
ejpam-6974	9	14	20f14	20f14	NUM
ejpam-6974	9	15	key	key	ADJ
ejpam-6974	9	16	words	word	NOUN
ejpam-6974	9	17	and	and	CCONJ
ejpam-6974	9	18	phrases	phrase	NOUN
ejpam-6974	9	19	:	:	PUNCT
ejpam-6974	9	20	bg	bg	NOUN
ejpam-6974	9	21	-	-	PUNCT
ejpam-6974	9	22	algebra	algebra	PROPN
ejpam-6974	9	23	,	,	PUNCT
ejpam-6974	9	24	dual	dual	ADJ
ejpam-6974	9	25	bg	bg	NOUN
ejpam-6974	9	26	-	-	PUNCT
ejpam-6974	9	27	algebra	algebra	PROPN
ejpam-6974	9	28	,	,	PUNCT
ejpam-6974	9	29	dual	dual	ADJ
ejpam-6974	9	30	algebra	algebra	NOUN
ejpam-6974	9	31	,	,	PUNCT
ejpam-6974	9	32	group	group	NOUN
ejpam-6974	9	33	-	-	PUNCT
ejpam-6974	9	34	derived	derive	VERB
ejpam-6974	9	35	algebra	algebra	NOUN
ejpam-6974	9	36	1	1	NUM
ejpam-6974	9	37	.	.	PUNCT
ejpam-6974	9	38	introduction	introduction	NOUN
ejpam-6974	9	39	since	since	SCONJ
ejpam-6974	9	40	the	the	DET
ejpam-6974	9	41	1960s	1960	NOUN
ejpam-6974	9	42	,	,	PUNCT
ejpam-6974	9	43	numerous	numerous	ADJ
ejpam-6974	9	44	classes	class	NOUN
ejpam-6974	9	45	of	of	ADP
ejpam-6974	9	46	algebras	algebra	NOUN
ejpam-6974	9	47	have	have	AUX
ejpam-6974	9	48	been	be	AUX
ejpam-6974	9	49	introduced	introduce	VERB
ejpam-6974	9	50	,	,	PUNCT
ejpam-6974	9	51	beginning	begin	VERB
ejpam-6974	9	52	with	with	ADP
ejpam-6974	9	53	bck	bck	PROPN
ejpam-6974	9	54	/	/	SYM
ejpam-6974	9	55	bci	bci	NOUN
ejpam-6974	9	56	-	-	PUNCT
ejpam-6974	9	57	algebras	algebras	X
ejpam-6974	10	1	[	[	X
ejpam-6974	10	2	1	1	NUM
ejpam-6974	10	3	]	]	PUNCT
ejpam-6974	10	4	,	,	PUNCT
ejpam-6974	10	5	later	later	ADV
ejpam-6974	10	6	extended	extend	VERB
ejpam-6974	10	7	to	to	ADP
ejpam-6974	10	8	bch	bch	NOUN
ejpam-6974	10	9	-	-	PUNCT
ejpam-6974	10	10	algebras	algebras	PROPN
ejpam-6974	11	1	[	[	X
ejpam-6974	11	2	2	2	NUM
ejpam-6974	11	3	,	,	PUNCT
ejpam-6974	11	4	3	3	NUM
ejpam-6974	11	5	]	]	PUNCT
ejpam-6974	11	6	,	,	PUNCT
ejpam-6974	11	7	and	and	CCONJ
ejpam-6974	11	8	further	far	ADV
ejpam-6974	11	9	generalized	generalize	VERB
ejpam-6974	11	10	to	to	ADP
ejpam-6974	11	11	bh	bh	NOUN
ejpam-6974	11	12	-	-	PUNCT
ejpam-6974	11	13	algebras	algebras	X
ejpam-6974	11	14	[	[	X
ejpam-6974	11	15	4	4	NUM
ejpam-6974	11	16	]	]	PUNCT
ejpam-6974	11	17	.	.	PUNCT
ejpam-6974	12	1	neggers	negger	NOUN
ejpam-6974	12	2	and	and	CCONJ
ejpam-6974	12	3	kim	kim	PROPN
ejpam-6974	12	4	subsequently	subsequently	ADV
ejpam-6974	12	5	developed	develop	VERB
ejpam-6974	12	6	d	d	NOUN
ejpam-6974	12	7	-	-	PUNCT
ejpam-6974	12	8	algebras	algebras	X
ejpam-6974	13	1	[	[	X
ejpam-6974	13	2	5	5	NUM
ejpam-6974	13	3	]	]	PUNCT
ejpam-6974	13	4	and	and	CCONJ
ejpam-6974	13	5	b	b	X
ejpam-6974	13	6	-	-	PUNCT
ejpam-6974	13	7	algebras	algebras	X
ejpam-6974	14	1	[	[	X
ejpam-6974	14	2	6	6	NUM
ejpam-6974	14	3	]	]	PUNCT
ejpam-6974	14	4	,	,	PUNCT
ejpam-6974	14	5	while	while	SCONJ
ejpam-6974	14	6	kim	kim	PROPN
ejpam-6974	14	7	and	and	CCONJ
ejpam-6974	14	8	kim	kim	PROPN
ejpam-6974	14	9	introduced	introduce	VERB
ejpam-6974	14	10	bg	bg	PROPN
ejpam-6974	14	11	-	-	PUNCT
ejpam-6974	14	12	algebras	algebras	PROPN
ejpam-6974	14	13	as	as	ADP
ejpam-6974	14	14	a	a	DET
ejpam-6974	14	15	generalization	generalization	NOUN
ejpam-6974	14	16	of	of	ADP
ejpam-6974	14	17	b	b	NOUN
ejpam-6974	14	18	-	-	PUNCT
ejpam-6974	14	19	algebras	algebras	X
ejpam-6974	15	1	[	[	X
ejpam-6974	15	2	7	7	NUM
ejpam-6974	15	3	]	]	PUNCT
ejpam-6974	15	4	.	.	PUNCT
ejpam-6974	16	1	in	in	ADP
ejpam-6974	16	2	parallel	parallel	NOUN
ejpam-6974	16	3	,	,	PUNCT
ejpam-6974	16	4	dual	dual	ADJ
ejpam-6974	16	5	algebras	algebra	NOUN
ejpam-6974	16	6	were	be	AUX
ejpam-6974	16	7	also	also	ADV
ejpam-6974	16	8	studied	study	VERB
ejpam-6974	16	9	.	.	PUNCT
ejpam-6974	17	1	kim	kim	PROPN
ejpam-6974	17	2	and	and	CCONJ
ejpam-6974	17	3	yon	yon	PROPN
ejpam-6974	17	4	investigated	investigate	VERB
ejpam-6974	17	5	dual	dual	ADJ
ejpam-6974	17	6	bckalgebras	bckalgebra	NOUN
ejpam-6974	17	7	and	and	CCONJ
ejpam-6974	17	8	their	their	PRON
ejpam-6974	17	9	relation	relation	NOUN
ejpam-6974	17	10	to	to	ADP
ejpam-6974	17	11	mv	mv	PROPN
ejpam-6974	17	12	-algebras	-algebras	PROPN
ejpam-6974	17	13	[	[	X
ejpam-6974	17	14	8	8	NUM
ejpam-6974	17	15	]	]	PUNCT
ejpam-6974	17	16	,	,	PUNCT
ejpam-6974	17	17	kim	kim	PROPN
ejpam-6974	17	18	and	and	CCONJ
ejpam-6974	17	19	kim	kim	PROPN
ejpam-6974	17	20	proposed	propose	VERB
ejpam-6974	17	21	be	be	AUX
ejpam-6974	17	22	-	-	PUNCT
ejpam-6974	17	23	algebras	algebras	X
ejpam-6974	18	1	[	[	X
ejpam-6974	18	2	9	9	NUM
ejpam-6974	18	3	]	]	PUNCT
ejpam-6974	18	4	,	,	PUNCT
ejpam-6974	18	5	walendziak	walendziak	PROPN
ejpam-6974	18	6	showed	show	VERB
ejpam-6974	18	7	commutative	commutative	ADJ
ejpam-6974	18	8	be	be	AUX
ejpam-6974	18	9	-	-	PUNCT
ejpam-6974	18	10	algebras	algebras	ADJ
ejpam-6974	18	11	coincide	coincide	NOUN
ejpam-6974	18	12	with	with	ADP
ejpam-6974	18	13	dual	dual	ADJ
ejpam-6974	18	14	bck	bck	NOUN
ejpam-6974	18	15	-	-	PUNCT
ejpam-6974	18	16	algebras	algebras	NOUN
ejpam-6974	19	1	[	[	X
ejpam-6974	19	2	10	10	NUM
ejpam-6974	19	3	]	]	PUNCT
ejpam-6974	19	4	,	,	PUNCT
ejpam-6974	19	5	meng	meng	PROPN
ejpam-6974	19	6	defined	define	VERB
ejpam-6974	19	7	dual	dual	ADJ
ejpam-6974	19	8	bci	bci	NOUN
ejpam-6974	19	9	-	-	PUNCT
ejpam-6974	19	10	algebras	algebra	NOUN
ejpam-6974	19	11	and	and	CCONJ
ejpam-6974	19	12	ci	ci	NOUN
ejpam-6974	19	13	-	-	PUNCT
ejpam-6974	19	14	algebras	algebras	X
ejpam-6974	20	1	[	[	X
ejpam-6974	20	2	11	11	NUM
ejpam-6974	20	3	]	]	PUNCT
ejpam-6974	20	4	,	,	PUNCT
ejpam-6974	20	5	with	with	SCONJ
ejpam-6974	20	6	saeid	saeid	PROPN
ejpam-6974	20	7	proved	prove	VERB
ejpam-6974	20	8	the	the	DET
ejpam-6974	20	9	equivalence	equivalence	NOUN
ejpam-6974	20	10	of	of	ADP
ejpam-6974	20	11	ci	ci	NOUN
ejpam-6974	20	12	-	-	PUNCT
ejpam-6974	20	13	algebras	algebras	ADJ
ejpam-6974	20	14	and	and	CCONJ
ejpam-6974	20	15	dual	dual	ADJ
ejpam-6974	20	16	q	q	NOUN
ejpam-6974	20	17	-	-	PUNCT
ejpam-6974	20	18	algebras	algebras	X
ejpam-6974	21	1	[	[	X
ejpam-6974	21	2	12	12	NUM
ejpam-6974	21	3	]	]	PUNCT
ejpam-6974	21	4	,	,	PUNCT
ejpam-6974	21	5	and	and	CCONJ
ejpam-6974	21	6	belleza	belleza	NOUN
ejpam-6974	21	7	and	and	CCONJ
ejpam-6974	21	8	vilela	vilela	NOUN
ejpam-6974	21	9	introduced	introduce	VERB
ejpam-6974	21	10	the	the	DET
ejpam-6974	21	11	dual	dual	ADJ
ejpam-6974	21	12	b	b	NOUN
ejpam-6974	21	13	-	-	PUNCT
ejpam-6974	21	14	algebra	algebra	NOUN
ejpam-6974	21	15	and	and	CCONJ
ejpam-6974	21	16	established	establish	VERB
ejpam-6974	21	17	its	its	PRON
ejpam-6974	21	18	relationship	relationship	NOUN
ejpam-6974	21	19	to	to	PART
ejpam-6974	21	20	bck	bck	VERB
ejpam-6974	21	21	-	-	PUNCT
ejpam-6974	21	22	algebra	algebra	NOUN
ejpam-6974	21	23	,	,	PUNCT
ejpam-6974	21	24	ci	ci	NOUN
ejpam-6974	21	25	-	-	NOUN
ejpam-6974	21	26	algebra	algebra	NOUN
ejpam-6974	21	27	,	,	PUNCT
ejpam-6974	21	28	and	and	CCONJ
ejpam-6974	21	29	the	the	DET
ejpam-6974	21	30	dual	dual	ADJ
ejpam-6974	21	31	bci	bci	NOUN
ejpam-6974	21	32	-	-	NOUN
ejpam-6974	21	33	algebra	algebra	NOUN
ejpam-6974	21	34	[	[	X
ejpam-6974	21	35	13	13	NUM
ejpam-6974	21	36	]	]	PUNCT
ejpam-6974	21	37	.	.	PUNCT
ejpam-6974	22	1	while	while	SCONJ
ejpam-6974	22	2	many	many	ADJ
ejpam-6974	22	3	algebras	algebra	NOUN
ejpam-6974	22	4	and	and	CCONJ
ejpam-6974	22	5	dual	dual	ADJ
ejpam-6974	22	6	algebras	algebra	NOUN
ejpam-6974	22	7	have	have	AUX
ejpam-6974	22	8	been	be	AUX
ejpam-6974	22	9	established	establish	VERB
ejpam-6974	22	10	and	and	CCONJ
ejpam-6974	22	11	interconnected	interconnected	ADJ
ejpam-6974	22	12	,	,	PUNCT
ejpam-6974	22	13	no	no	DET
ejpam-6974	22	14	work	work	NOUN
ejpam-6974	22	15	has	have	AUX
ejpam-6974	22	16	addressed	address	VERB
ejpam-6974	22	17	the	the	DET
ejpam-6974	22	18	dual	dual	ADJ
ejpam-6974	22	19	bg	bg	NOUN
ejpam-6974	22	20	-	-	NOUN
ejpam-6974	22	21	algebra	algebra	PROPN
ejpam-6974	22	22	.	.	PUNCT
ejpam-6974	23	1	this	this	DET
ejpam-6974	23	2	study	study	NOUN
ejpam-6974	23	3	introduces	introduce	VERB
ejpam-6974	23	4	its	its	PRON
ejpam-6974	23	5	definition	definition	NOUN
ejpam-6974	23	6	,	,	PUNCT
ejpam-6974	23	7	examines	examine	VERB
ejpam-6974	23	8	its	its	PRON
ejpam-6974	23	9	properties	property	NOUN
ejpam-6974	23	10	,	,	PUNCT
ejpam-6974	23	11	and	and	CCONJ
ejpam-6974	23	12	establishes	establish	VERB
ejpam-6974	23	13	key	key	ADJ
ejpam-6974	23	14	characterizations	characterization	NOUN
ejpam-6974	23	15	,	,	PUNCT
ejpam-6974	23	16	with	with	ADP
ejpam-6974	23	17	particular	particular	ADJ
ejpam-6974	23	18	emphasis	emphasis	NOUN
ejpam-6974	23	19	on	on	ADP
ejpam-6974	23	20	groupderived	groupderive	VERB
ejpam-6974	23	21	and	and	CCONJ
ejpam-6974	23	22	non	non	ADJ
ejpam-6974	23	23	-	-	NOUN
ejpam-6974	23	24	group	group	NOUN
ejpam-6974	23	25	-	-	PUNCT
ejpam-6974	23	26	derived	derive	VERB
ejpam-6974	23	27	dual	dual	ADJ
ejpam-6974	23	28	bg	bg	NOUN
ejpam-6974	23	29	-	-	PUNCT
ejpam-6974	23	30	algebras	algebras	X
ejpam-6974	23	31	.	.	PUNCT
ejpam-6974	24	1	∗corresponding	∗corresponde	VERB
ejpam-6974	24	2	author	author	NOUN
ejpam-6974	24	3	.	.	PUNCT
ejpam-6974	25	1	doi	doi	NOUN
ejpam-6974	25	2	:	:	PUNCT
ejpam-6974	25	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6974	https://doi.org/10.29020/nybg.ejpam.v18i4.6974	PROPN
ejpam-6974	25	4	email	email	NOUN
ejpam-6974	25	5	addresses	address	NOUN
ejpam-6974	25	6	:	:	PUNCT
ejpam-6974	26	1	clivemartinchan@gmail.com	clivemartinchan@gmail.com	X
ejpam-6974	26	2	(	(	PUNCT
ejpam-6974	26	3	c.m	c.m	PROPN
ejpam-6974	26	4	.	.	PROPN
ejpam-6974	26	5	chan	chan	PROPN
ejpam-6974	26	6	)	)	PUNCT
ejpam-6974	26	7	,	,	PUNCT
ejpam-6974	26	8	kebelleza@usc.edu.ph	kebelleza@usc.edu.ph	PROPN
ejpam-6974	26	9	(	(	PUNCT
ejpam-6974	26	10	k.	k.	PROPN
ejpam-6974	26	11	fuentes	fuentes	PROPN
ejpam-6974	26	12	)	)	PUNCT
ejpam-6974	26	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6974	27	1	1	1	NUM
ejpam-6974	27	2	copyright	copyright	NOUN
ejpam-6974	27	3	:	:	PUNCT
ejpam-6974	27	4	©	©	PROPN
ejpam-6974	27	5	2025	2025	NUM
ejpam-6974	27	6	the	the	DET
ejpam-6974	27	7	author(s	author(s	NOUN
ejpam-6974	27	8	)	)	PUNCT
ejpam-6974	27	9	.	.	PUNCT
ejpam-6974	28	1	(	(	PUNCT
ejpam-6974	28	2	cc	cc	NOUN
ejpam-6974	28	3	by	by	ADP
ejpam-6974	28	4	-	-	PUNCT
ejpam-6974	28	5	nc	nc	PROPN
ejpam-6974	28	6	4.0	4.0	NUM
ejpam-6974	28	7	)	)	PUNCT
ejpam-6974	28	8	c.m	c.m	PROPN
ejpam-6974	28	9	.	.	PROPN
ejpam-6974	28	10	chan	chan	PROPN
ejpam-6974	28	11	,	,	PUNCT
ejpam-6974	28	12	k.	k.	PROPN
ejpam-6974	28	13	fuentes	fuentes	PROPN
ejpam-6974	28	14	/	/	SYM
ejpam-6974	28	15	eur	eur	PROPN
ejpam-6974	28	16	.	.	PUNCT
ejpam-6974	29	1	j.	j.	PROPN
ejpam-6974	29	2	pure	pure	PROPN
ejpam-6974	29	3	appl	appl	PROPN
ejpam-6974	29	4	.	.	PROPN
ejpam-6974	29	5	math	math	PROPN
ejpam-6974	29	6	,	,	PUNCT
ejpam-6974	29	7	18	18	NUM
ejpam-6974	29	8	(	(	PUNCT
ejpam-6974	29	9	4	4	NUM
ejpam-6974	29	10	)	)	PUNCT
ejpam-6974	29	11	(	(	PUNCT
ejpam-6974	29	12	2025	2025	NUM
ejpam-6974	29	13	)	)	PUNCT
ejpam-6974	29	14	,	,	PUNCT
ejpam-6974	29	15	6974	6974	NUM
ejpam-6974	29	16	2	2	NUM
ejpam-6974	29	17	of	of	ADP
ejpam-6974	29	18	16	16	NUM
ejpam-6974	29	19	2	2	NUM
ejpam-6974	29	20	.	.	PUNCT
ejpam-6974	29	21	preliminaries	preliminary	NOUN
ejpam-6974	29	22	definition	definition	NOUN
ejpam-6974	29	23	1	1	NUM
ejpam-6974	29	24	.	.	PUNCT
ejpam-6974	30	1	[	[	X
ejpam-6974	30	2	14	14	NUM
ejpam-6974	30	3	]	]	X
ejpam-6974	30	4	a	a	DET
ejpam-6974	30	5	binary	binary	ADJ
ejpam-6974	30	6	operation	operation	NOUN
ejpam-6974	30	7	on	on	ADP
ejpam-6974	30	8	a	a	DET
ejpam-6974	30	9	nonempty	nonempty	ADV
ejpam-6974	30	10	set	set	VERB
ejpam-6974	30	11	b	b	NOUN
ejpam-6974	30	12	(	(	PUNCT
ejpam-6974	30	13	or	or	CCONJ
ejpam-6974	30	14	simply	simply	ADV
ejpam-6974	30	15	an	an	DET
ejpam-6974	30	16	operation	operation	NOUN
ejpam-6974	30	17	on	on	ADP
ejpam-6974	30	18	b	b	NOUN
ejpam-6974	30	19	)	)	PUNCT
ejpam-6974	30	20	is	be	AUX
ejpam-6974	30	21	a	a	DET
ejpam-6974	30	22	function	function	NOUN
ejpam-6974	30	23	f	f	NOUN
ejpam-6974	30	24	:	:	PUNCT
ejpam-6974	30	25	b	b	X
ejpam-6974	30	26	×	×	PROPN
ejpam-6974	30	27	b	b	PROPN
ejpam-6974	30	28	→	→	PROPN
ejpam-6974	30	29	b.	b.	PROPN
ejpam-6974	30	30	commonly	commonly	ADV
ejpam-6974	30	31	,	,	PUNCT
ejpam-6974	30	32	the	the	DET
ejpam-6974	30	33	symbol	symbol	NOUN
ejpam-6974	30	34	∗	∗	NOUN
ejpam-6974	30	35	is	be	AUX
ejpam-6974	30	36	used	use	VERB
ejpam-6974	30	37	instead	instead	ADV
ejpam-6974	30	38	of	of	ADP
ejpam-6974	30	39	f	f	PROPN
ejpam-6974	30	40	to	to	PART
ejpam-6974	30	41	denote	denote	VERB
ejpam-6974	30	42	the	the	DET
ejpam-6974	30	43	operation	operation	NOUN
ejpam-6974	30	44	and	and	CCONJ
ejpam-6974	30	45	write	write	VERB
ejpam-6974	30	46	a	a	DET
ejpam-6974	30	47	∗	∗	NOUN
ejpam-6974	30	48	b	b	NOUN
ejpam-6974	30	49	instead	instead	ADV
ejpam-6974	30	50	of	of	ADP
ejpam-6974	30	51	f(a	f(a	PROPN
ejpam-6974	30	52	,	,	PUNCT
ejpam-6974	30	53	b	b	NOUN
ejpam-6974	30	54	)	)	PUNCT
ejpam-6974	30	55	.	.	PUNCT
ejpam-6974	31	1	definition	definition	NOUN
ejpam-6974	31	2	2	2	NUM
ejpam-6974	31	3	.	.	PUNCT
ejpam-6974	32	1	[	[	X
ejpam-6974	32	2	14	14	NUM
ejpam-6974	32	3	]	]	PUNCT
ejpam-6974	32	4	a	a	DET
ejpam-6974	32	5	group	group	NOUN
ejpam-6974	32	6	is	be	AUX
ejpam-6974	32	7	a	a	DET
ejpam-6974	32	8	nonempty	nonempty	ADJ
ejpam-6974	32	9	set	set	VERB
ejpam-6974	32	10	g	g	NOUN
ejpam-6974	32	11	equipped	equip	VERB
ejpam-6974	32	12	with	with	ADP
ejpam-6974	32	13	a	a	DET
ejpam-6974	32	14	binary	binary	ADJ
ejpam-6974	32	15	operation	operation	NOUN
ejpam-6974	32	16	“	"	PUNCT
ejpam-6974	32	17	∗	∗	NOUN
ejpam-6974	32	18	”	"	PUNCT
ejpam-6974	32	19	that	that	PRON
ejpam-6974	32	20	satisfies	satisfy	VERB
ejpam-6974	32	21	the	the	DET
ejpam-6974	32	22	following	follow	VERB
ejpam-6974	32	23	axioms	axiom	NOUN
ejpam-6974	32	24	:	:	PUNCT
ejpam-6974	32	25	(	(	PUNCT
ejpam-6974	32	26	i	i	NOUN
ejpam-6974	32	27	)	)	PUNCT
ejpam-6974	32	28	associativity	associativity	NOUN
ejpam-6974	32	29	:	:	PUNCT
ejpam-6974	32	30	a	a	DET
ejpam-6974	32	31	∗	∗	NOUN
ejpam-6974	32	32	(	(	PUNCT
ejpam-6974	32	33	b	b	NOUN
ejpam-6974	32	34	∗	∗	NOUN
ejpam-6974	32	35	c	c	NOUN
ejpam-6974	32	36	)	)	PUNCT
ejpam-6974	32	37	=	=	NOUN
ejpam-6974	32	38	(	(	PUNCT
ejpam-6974	32	39	a	a	DET
ejpam-6974	32	40	∗	∗	NOUN
ejpam-6974	32	41	b	b	NOUN
ejpam-6974	32	42	)	)	PUNCT
ejpam-6974	32	43	∗	∗	NOUN
ejpam-6974	32	44	c	c	NOUN
ejpam-6974	32	45	for	for	ADP
ejpam-6974	32	46	all	all	DET
ejpam-6974	32	47	a	a	DET
ejpam-6974	32	48	,	,	PUNCT
ejpam-6974	32	49	b	b	NOUN
ejpam-6974	32	50	,	,	PUNCT
ejpam-6974	32	51	c	c	PROPN
ejpam-6974	32	52	∈	∈	PROPN
ejpam-6974	32	53	g	g	PROPN
ejpam-6974	32	54	;	;	PUNCT
ejpam-6974	32	55	(	(	PUNCT
ejpam-6974	32	56	ii	ii	NOUN
ejpam-6974	32	57	)	)	PUNCT
ejpam-6974	32	58	identity	identity	NOUN
ejpam-6974	32	59	element	element	NOUN
ejpam-6974	32	60	:	:	PUNCT
ejpam-6974	32	61	there	there	PRON
ejpam-6974	32	62	is	be	VERB
ejpam-6974	32	63	an	an	DET
ejpam-6974	32	64	element	element	NOUN
ejpam-6974	32	65	e	e	NOUN
ejpam-6974	32	66	∈	∈	PROPN
ejpam-6974	32	67	g	g	PROPN
ejpam-6974	32	68	such	such	DET
ejpam-6974	32	69	that	that	SCONJ
ejpam-6974	32	70	a	a	DET
ejpam-6974	32	71	∗	∗	NOUN
ejpam-6974	32	72	e	e	NOUN
ejpam-6974	32	73	=	=	NOUN
ejpam-6974	32	74	a	a	DET
ejpam-6974	32	75	=	=	SYM
ejpam-6974	32	76	e	e	NOUN
ejpam-6974	32	77	∗	∗	NOUN
ejpam-6974	32	78	a	a	PRON
ejpam-6974	32	79	for	for	ADP
ejpam-6974	32	80	every	every	DET
ejpam-6974	32	81	a	a	DET
ejpam-6974	32	82	∈	∈	PROPN
ejpam-6974	32	83	g	g	NOUN
ejpam-6974	32	84	;	;	PUNCT
ejpam-6974	32	85	and	and	CCONJ
ejpam-6974	32	86	(	(	PUNCT
ejpam-6974	32	87	iii	iii	X
ejpam-6974	32	88	)	)	PUNCT
ejpam-6974	32	89	inverse	inverse	NOUN
ejpam-6974	32	90	element	element	NOUN
ejpam-6974	32	91	:	:	PUNCT
ejpam-6974	32	92	for	for	ADP
ejpam-6974	32	93	each	each	PRON
ejpam-6974	32	94	a	a	DET
ejpam-6974	32	95	∈	∈	PROPN
ejpam-6974	32	96	g	g	NOUN
ejpam-6974	32	97	,	,	PUNCT
ejpam-6974	32	98	there	there	PRON
ejpam-6974	32	99	is	be	VERB
ejpam-6974	32	100	an	an	DET
ejpam-6974	32	101	element	element	NOUN
ejpam-6974	32	102	d	d	PROPN
ejpam-6974	32	103	∈	∈	PROPN
ejpam-6974	32	104	g	g	PROPN
ejpam-6974	32	105	such	such	DET
ejpam-6974	32	106	that	that	SCONJ
ejpam-6974	32	107	a	a	DET
ejpam-6974	32	108	∗	∗	NOUN
ejpam-6974	32	109	d	d	NOUN
ejpam-6974	32	110	=	=	SYM
ejpam-6974	32	111	e	e	PROPN
ejpam-6974	32	112	and	and	CCONJ
ejpam-6974	32	113	d	d	PROPN
ejpam-6974	32	114	∗	∗	NOUN
ejpam-6974	32	115	a	a	DET
ejpam-6974	32	116	=	=	PUNCT
ejpam-6974	32	117	e.	e.	PROPN
ejpam-6974	32	118	the	the	DET
ejpam-6974	32	119	number	number	NOUN
ejpam-6974	32	120	of	of	ADP
ejpam-6974	32	121	elements	element	NOUN
ejpam-6974	32	122	in	in	ADP
ejpam-6974	32	123	g	g	PROPN
ejpam-6974	32	124	is	be	AUX
ejpam-6974	32	125	called	call	VERB
ejpam-6974	32	126	the	the	DET
ejpam-6974	32	127	order	order	NOUN
ejpam-6974	32	128	of	of	ADP
ejpam-6974	32	129	g	g	NOUN
ejpam-6974	32	130	and	and	CCONJ
ejpam-6974	32	131	is	be	AUX
ejpam-6974	32	132	denoted	denote	VERB
ejpam-6974	32	133	by	by	ADP
ejpam-6974	32	134	|g|	|g|	PROPN
ejpam-6974	32	135	.	.	PUNCT
ejpam-6974	33	1	theorem	theorem	NOUN
ejpam-6974	33	2	1	1	NUM
ejpam-6974	33	3	.	.	PUNCT
ejpam-6974	34	1	[	[	X
ejpam-6974	34	2	14	14	NUM
ejpam-6974	34	3	]	]	PUNCT
ejpam-6974	34	4	let	let	VERB
ejpam-6974	34	5	g	g	PRON
ejpam-6974	34	6	be	be	AUX
ejpam-6974	34	7	a	a	DET
ejpam-6974	34	8	group	group	NOUN
ejpam-6974	34	9	and	and	CCONJ
ejpam-6974	34	10	let	let	VERB
ejpam-6974	34	11	a	a	DET
ejpam-6974	34	12	,	,	PUNCT
ejpam-6974	34	13	b	b	NOUN
ejpam-6974	34	14	,	,	PUNCT
ejpam-6974	34	15	c	c	PROPN
ejpam-6974	34	16	∈	∈	PROPN
ejpam-6974	34	17	g.	g.	NOUN
ejpam-6974	35	1	then	then	ADV
ejpam-6974	35	2	(	(	PUNCT
ejpam-6974	35	3	i	i	NOUN
ejpam-6974	35	4	)	)	PUNCT
ejpam-6974	35	5	g	g	PROPN
ejpam-6974	35	6	has	have	VERB
ejpam-6974	35	7	a	a	DET
ejpam-6974	35	8	unique	unique	ADJ
ejpam-6974	35	9	identity	identity	NOUN
ejpam-6974	35	10	element	element	NOUN
ejpam-6974	35	11	e	e	NOUN
ejpam-6974	35	12	;	;	PUNCT
ejpam-6974	35	13	(	(	PUNCT
ejpam-6974	35	14	ii	ii	NOUN
ejpam-6974	35	15	)	)	PUNCT
ejpam-6974	35	16	each	each	PRON
ejpam-6974	35	17	element	element	VERB
ejpam-6974	35	18	a	a	DET
ejpam-6974	35	19	∈	∈	PROPN
ejpam-6974	35	20	g	g	NOUN
ejpam-6974	35	21	has	have	VERB
ejpam-6974	35	22	a	a	DET
ejpam-6974	35	23	unique	unique	ADJ
ejpam-6974	35	24	inverse	inverse	NOUN
ejpam-6974	35	25	denoted	denote	VERB
ejpam-6974	35	26	by	by	ADP
ejpam-6974	35	27	a−1	a−1	PROPN
ejpam-6974	35	28	;	;	PUNCT
ejpam-6974	35	29	(	(	PUNCT
ejpam-6974	35	30	iii	iii	X
ejpam-6974	35	31	)	)	PUNCT
ejpam-6974	35	32	cancellation	cancellation	NOUN
ejpam-6974	35	33	law	law	NOUN
ejpam-6974	35	34	:	:	PUNCT
ejpam-6974	35	35	for	for	ADP
ejpam-6974	35	36	all	all	DET
ejpam-6974	35	37	a	a	DET
ejpam-6974	35	38	,	,	PUNCT
ejpam-6974	35	39	b	b	NOUN
ejpam-6974	35	40	,	,	PUNCT
ejpam-6974	35	41	c	c	PROPN
ejpam-6974	35	42	∈	∈	PROPN
ejpam-6974	35	43	g	g	PROPN
ejpam-6974	35	44	,	,	PUNCT
ejpam-6974	35	45	if	if	SCONJ
ejpam-6974	35	46	either	either	CCONJ
ejpam-6974	35	47	a	a	DET
ejpam-6974	35	48	∗	∗	NOUN
ejpam-6974	35	49	b	b	X
ejpam-6974	35	50	=	=	PUNCT
ejpam-6974	35	51	a	a	DET
ejpam-6974	35	52	∗	∗	NOUN
ejpam-6974	35	53	c	c	NOUN
ejpam-6974	35	54	or	or	CCONJ
ejpam-6974	35	55	b	b	NOUN
ejpam-6974	35	56	∗	∗	NOUN
ejpam-6974	35	57	a	a	PRON
ejpam-6974	35	58	=	=	SYM
ejpam-6974	35	59	c	c	NOUN
ejpam-6974	35	60	∗	∗	NOUN
ejpam-6974	35	61	a	a	PROPN
ejpam-6974	35	62	,	,	PUNCT
ejpam-6974	35	63	then	then	ADV
ejpam-6974	35	64	b	b	X
ejpam-6974	35	65	=	=	SYM
ejpam-6974	35	66	c	c	X
ejpam-6974	35	67	;	;	PUNCT
ejpam-6974	35	68	(	(	PUNCT
ejpam-6974	35	69	iv	iv	X
ejpam-6974	35	70	)	)	PUNCT
ejpam-6974	35	71	(	(	PUNCT
ejpam-6974	35	72	a	a	DET
ejpam-6974	35	73	∗	∗	NOUN
ejpam-6974	35	74	b)−1	b)−1	NOUN
ejpam-6974	35	75	=	=	SYM
ejpam-6974	35	76	b−1	b−1	PROPN
ejpam-6974	35	77	∗	∗	NOUN
ejpam-6974	35	78	a−1	a−1	PROPN
ejpam-6974	35	79	;	;	PUNCT
ejpam-6974	35	80	and	and	CCONJ
ejpam-6974	35	81	(	(	PUNCT
ejpam-6974	35	82	v	v	NOUN
ejpam-6974	35	83	)	)	PUNCT
ejpam-6974	35	84	(	(	PUNCT
ejpam-6974	35	85	a−1	a−1	PROPN
ejpam-6974	35	86	)	)	PUNCT
ejpam-6974	35	87	−1	−1	NOUN
ejpam-6974	36	1	=	=	PUNCT
ejpam-6974	36	2	a	a	DET
ejpam-6974	36	3	for	for	ADP
ejpam-6974	36	4	all	all	DET
ejpam-6974	36	5	a	a	DET
ejpam-6974	36	6	∈	∈	PROPN
ejpam-6974	36	7	g.	g.	NOUN
ejpam-6974	36	8	definition	definition	NOUN
ejpam-6974	36	9	3	3	NUM
ejpam-6974	36	10	.	.	PUNCT
ejpam-6974	37	1	[	[	X
ejpam-6974	37	2	13	13	NUM
ejpam-6974	37	3	]	]	PUNCT
ejpam-6974	37	4	a	a	DET
ejpam-6974	37	5	dual	dual	ADJ
ejpam-6974	37	6	b	b	NOUN
ejpam-6974	37	7	-	-	PUNCT
ejpam-6974	37	8	algebra	algebra	NOUN
ejpam-6974	37	9	x	x	PUNCT
ejpam-6974	37	10	is	be	AUX
ejpam-6974	37	11	a	a	DET
ejpam-6974	37	12	triple	triple	ADJ
ejpam-6974	37	13	(	(	PUNCT
ejpam-6974	37	14	x	x	NOUN
ejpam-6974	37	15	,	,	PUNCT
ejpam-6974	37	16	◦	◦	NOUN
ejpam-6974	37	17	,	,	PUNCT
ejpam-6974	37	18	1	1	NUM
ejpam-6974	37	19	)	)	PUNCT
ejpam-6974	37	20	where	where	SCONJ
ejpam-6974	37	21	x	x	PRON
ejpam-6974	37	22	is	be	AUX
ejpam-6974	37	23	a	a	DET
ejpam-6974	37	24	nonempty	nonempty	ADV
ejpam-6974	37	25	set	set	VERB
ejpam-6974	37	26	with	with	ADP
ejpam-6974	37	27	a	a	DET
ejpam-6974	37	28	binary	binary	ADJ
ejpam-6974	37	29	operation	operation	NOUN
ejpam-6974	37	30	◦	◦	NOUN
ejpam-6974	37	31	and	and	CCONJ
ejpam-6974	37	32	a	a	DET
ejpam-6974	37	33	constant	constant	ADJ
ejpam-6974	37	34	1	1	NUM
ejpam-6974	37	35	satisying	satisye	VERB
ejpam-6974	37	36	the	the	DET
ejpam-6974	37	37	following	following	ADJ
ejpam-6974	37	38	axioms	axiom	NOUN
ejpam-6974	37	39	for	for	ADP
ejpam-6974	37	40	all	all	DET
ejpam-6974	37	41	x	x	NOUN
ejpam-6974	37	42	,	,	PUNCT
ejpam-6974	37	43	y	y	PROPN
ejpam-6974	37	44	,	,	PUNCT
ejpam-6974	37	45	z	z	PROPN
ejpam-6974	37	46	∈	∈	PROPN
ejpam-6974	38	1	x	x	X
ejpam-6974	38	2	:	:	PUNCT
ejpam-6974	38	3	(	(	PUNCT
ejpam-6974	38	4	db1	db1	NOUN
ejpam-6974	38	5	)	)	PUNCT
ejpam-6974	38	6	x	x	SYM
ejpam-6974	39	1	◦	◦	NOUN
ejpam-6974	39	2	x	x	SYM
ejpam-6974	40	1	=	=	SYM
ejpam-6974	40	2	1	1	NUM
ejpam-6974	40	3	(	(	PUNCT
ejpam-6974	40	4	db2	db2	PROPN
ejpam-6974	40	5	)	)	PUNCT
ejpam-6974	40	6	1	1	NUM
ejpam-6974	40	7	◦	◦	NOUN
ejpam-6974	40	8	x	x	SYM
ejpam-6974	40	9	=	=	SYM
ejpam-6974	40	10	x	x	X
ejpam-6974	40	11	(	(	PUNCT
ejpam-6974	40	12	db3	db3	PROPN
ejpam-6974	40	13	)	)	PUNCT
ejpam-6974	40	14	x	x	SYM
ejpam-6974	40	15	◦	◦	NOUN
ejpam-6974	40	16	(	(	PUNCT
ejpam-6974	40	17	y	y	PROPN
ejpam-6974	40	18	◦	◦	PROPN
ejpam-6974	40	19	z	z	PROPN
ejpam-6974	40	20	)	)	PUNCT
ejpam-6974	40	21	=	=	SYM
ejpam-6974	40	22	(	(	PUNCT
ejpam-6974	40	23	(	(	PUNCT
ejpam-6974	40	24	y	y	NOUN
ejpam-6974	40	25	◦	◦	NOUN
ejpam-6974	40	26	1	1	NUM
ejpam-6974	40	27	)	)	PUNCT
ejpam-6974	40	28	◦	◦	NOUN
ejpam-6974	40	29	x	x	SYM
ejpam-6974	40	30	)	)	PUNCT
ejpam-6974	40	31	◦	◦	NOUN
ejpam-6974	40	32	z	z	NOUN
ejpam-6974	40	33	example	example	NOUN
ejpam-6974	40	34	1	1	NUM
ejpam-6974	40	35	.	.	PUNCT
ejpam-6974	41	1	[	[	X
ejpam-6974	41	2	13	13	NUM
ejpam-6974	41	3	]	]	PUNCT
ejpam-6974	41	4	let	let	VERB
ejpam-6974	41	5	x	x	PUNCT
ejpam-6974	41	6	=	=	PRON
ejpam-6974	41	7	{	{	PUNCT
ejpam-6974	41	8	e	e	NOUN
ejpam-6974	41	9	,	,	PUNCT
ejpam-6974	41	10	a	a	DET
ejpam-6974	41	11	,	,	PUNCT
ejpam-6974	41	12	b	b	NOUN
ejpam-6974	41	13	,	,	PUNCT
ejpam-6974	41	14	c	c	AUX
ejpam-6974	41	15	}	}	PUNCT
ejpam-6974	41	16	be	be	AUX
ejpam-6974	41	17	a	a	DET
ejpam-6974	41	18	set	set	NOUN
ejpam-6974	41	19	with	with	ADP
ejpam-6974	41	20	the	the	DET
ejpam-6974	41	21	following	follow	VERB
ejpam-6974	41	22	cayley	cayley	ADJ
ejpam-6974	41	23	table	table	NOUN
ejpam-6974	41	24	:	:	PUNCT
ejpam-6974	41	25	table	table	NOUN
ejpam-6974	41	26	1	1	NUM
ejpam-6974	41	27	:	:	PUNCT
ejpam-6974	41	28	cayley	cayley	ADJ
ejpam-6974	41	29	table	table	NOUN
ejpam-6974	41	30	of	of	ADP
ejpam-6974	41	31	the	the	DET
ejpam-6974	41	32	dual	dual	ADJ
ejpam-6974	41	33	b	b	NOUN
ejpam-6974	41	34	-	-	PUNCT
ejpam-6974	41	35	algebra	algebra	NOUN
ejpam-6974	41	36	(	(	PUNCT
ejpam-6974	41	37	x	x	X
ejpam-6974	41	38	,	,	PUNCT
ejpam-6974	41	39	◦	◦	NOUN
ejpam-6974	41	40	,	,	PUNCT
ejpam-6974	41	41	e	e	NOUN
ejpam-6974	41	42	)	)	PUNCT
ejpam-6974	41	43	◦	◦	NOUN
ejpam-6974	41	44	e	e	X
ejpam-6974	41	45	a	a	DET
ejpam-6974	41	46	b	b	NOUN
ejpam-6974	41	47	c	c	NOUN
ejpam-6974	41	48	e	e	X
ejpam-6974	41	49	e	e	X
ejpam-6974	41	50	a	a	PRON
ejpam-6974	41	51	b	b	X
ejpam-6974	41	52	c	c	NOUN
ejpam-6974	41	53	a	a	PRON
ejpam-6974	41	54	a	a	DET
ejpam-6974	41	55	e	e	NOUN
ejpam-6974	41	56	c	c	NOUN
ejpam-6974	41	57	b	b	PROPN
ejpam-6974	41	58	b	b	PROPN
ejpam-6974	41	59	b	b	PROPN
ejpam-6974	41	60	c	c	NOUN
ejpam-6974	41	61	e	e	X
ejpam-6974	41	62	a	a	X
ejpam-6974	41	63	c	c	NOUN
ejpam-6974	41	64	c	c	PROPN
ejpam-6974	41	65	b	b	PROPN
ejpam-6974	41	66	a	a	DET
ejpam-6974	41	67	e	e	NOUN
ejpam-6974	41	68	then	then	ADV
ejpam-6974	41	69	(	(	PUNCT
ejpam-6974	41	70	x	x	NOUN
ejpam-6974	41	71	,	,	PUNCT
ejpam-6974	41	72	◦	◦	NOUN
ejpam-6974	41	73	,	,	PUNCT
ejpam-6974	41	74	e	e	NOUN
ejpam-6974	41	75	)	)	PUNCT
ejpam-6974	41	76	is	be	AUX
ejpam-6974	41	77	a	a	DET
ejpam-6974	41	78	dual	dual	ADJ
ejpam-6974	41	79	b	b	NOUN
ejpam-6974	41	80	-	-	PUNCT
ejpam-6974	41	81	algebra	algebra	NOUN
ejpam-6974	41	82	.	.	PUNCT
ejpam-6974	42	1	c.m	c.m	PROPN
ejpam-6974	42	2	.	.	PROPN
ejpam-6974	42	3	chan	chan	PROPN
ejpam-6974	42	4	,	,	PUNCT
ejpam-6974	42	5	k.	k.	PROPN
ejpam-6974	42	6	fuentes	fuentes	PROPN
ejpam-6974	42	7	/	/	SYM
ejpam-6974	42	8	eur	eur	PROPN
ejpam-6974	42	9	.	.	PUNCT
ejpam-6974	43	1	j.	j.	PROPN
ejpam-6974	43	2	pure	pure	PROPN
ejpam-6974	43	3	appl	appl	PROPN
ejpam-6974	43	4	.	.	PROPN
ejpam-6974	43	5	math	math	PROPN
ejpam-6974	43	6	,	,	PUNCT
ejpam-6974	43	7	18	18	NUM
ejpam-6974	43	8	(	(	PUNCT
ejpam-6974	43	9	4	4	NUM
ejpam-6974	43	10	)	)	PUNCT
ejpam-6974	43	11	(	(	PUNCT
ejpam-6974	43	12	2025	2025	NUM
ejpam-6974	43	13	)	)	PUNCT
ejpam-6974	43	14	,	,	PUNCT
ejpam-6974	43	15	6974	6974	NUM
ejpam-6974	43	16	3	3	NUM
ejpam-6974	43	17	of	of	ADP
ejpam-6974	43	18	16	16	NUM
ejpam-6974	43	19	lemma	lemma	PROPN
ejpam-6974	43	20	1	1	NUM
ejpam-6974	43	21	.	.	PUNCT
ejpam-6974	44	1	[	[	X
ejpam-6974	44	2	13	13	NUM
ejpam-6974	44	3	]	]	PUNCT
ejpam-6974	44	4	let	let	VERB
ejpam-6974	44	5	x	x	PRON
ejpam-6974	44	6	be	be	AUX
ejpam-6974	44	7	a	a	DET
ejpam-6974	44	8	dual	dual	ADJ
ejpam-6974	44	9	b	b	NOUN
ejpam-6974	44	10	-	-	PUNCT
ejpam-6974	44	11	algebra	algebra	NOUN
ejpam-6974	44	12	.	.	PUNCT
ejpam-6974	45	1	for	for	ADP
ejpam-6974	45	2	any	any	DET
ejpam-6974	45	3	x	x	NOUN
ejpam-6974	45	4	,	,	PUNCT
ejpam-6974	45	5	y	y	PROPN
ejpam-6974	45	6	∈	∈	PROPN
ejpam-6974	45	7	x	x	X
ejpam-6974	45	8	,	,	PUNCT
ejpam-6974	45	9	(	(	PUNCT
ejpam-6974	45	10	y	y	PROPN
ejpam-6974	45	11	◦	◦	NOUN
ejpam-6974	45	12	1	1	NUM
ejpam-6974	45	13	)	)	PUNCT
ejpam-6974	45	14	◦	◦	NOUN
ejpam-6974	45	15	(	(	PUNCT
ejpam-6974	45	16	y	y	PROPN
ejpam-6974	45	17	◦	◦	NOUN
ejpam-6974	45	18	x	x	X
ejpam-6974	45	19	)	)	PUNCT
ejpam-6974	45	20	=	=	PUNCT
ejpam-6974	45	21	x.	x.	NOUN
ejpam-6974	45	22	definition	definition	NOUN
ejpam-6974	45	23	4	4	NUM
ejpam-6974	45	24	.	.	PUNCT
ejpam-6974	46	1	[	[	X
ejpam-6974	46	2	7	7	X
ejpam-6974	46	3	]	]	X
ejpam-6974	46	4	a	a	DET
ejpam-6974	46	5	bg	bg	NOUN
ejpam-6974	46	6	-	-	PUNCT
ejpam-6974	46	7	algebra	algebra	PROPN
ejpam-6974	46	8	is	be	AUX
ejpam-6974	46	9	a	a	DET
ejpam-6974	46	10	nonempty	nonempty	ADV
ejpam-6974	46	11	set	set	VERB
ejpam-6974	46	12	x	x	PUNCT
ejpam-6974	46	13	with	with	ADP
ejpam-6974	46	14	a	a	DET
ejpam-6974	46	15	constant	constant	ADJ
ejpam-6974	46	16	0	0	NUM
ejpam-6974	46	17	and	and	CCONJ
ejpam-6974	46	18	a	a	DET
ejpam-6974	46	19	binary	binary	ADJ
ejpam-6974	46	20	operation	operation	NOUN
ejpam-6974	46	21	∗	∗	NOUN
ejpam-6974	46	22	satisfying	satisfy	VERB
ejpam-6974	46	23	the	the	DET
ejpam-6974	46	24	following	follow	VERB
ejpam-6974	46	25	axioms	axiom	NOUN
ejpam-6974	46	26	for	for	ADP
ejpam-6974	46	27	all	all	DET
ejpam-6974	46	28	x	x	NOUN
ejpam-6974	46	29	,	,	PUNCT
ejpam-6974	46	30	y	y	PROPN
ejpam-6974	46	31	∈	∈	PROPN
ejpam-6974	46	32	x	x	X
ejpam-6974	46	33	:	:	PUNCT
ejpam-6974	46	34	(	(	PUNCT
ejpam-6974	46	35	bg1	bg1	PROPN
ejpam-6974	46	36	)	)	PUNCT
ejpam-6974	46	37	x	x	SYM
ejpam-6974	46	38	∗	∗	NOUN
ejpam-6974	46	39	x	x	X
ejpam-6974	47	1	=	=	SYM
ejpam-6974	47	2	0	0	NUM
ejpam-6974	47	3	(	(	PUNCT
ejpam-6974	47	4	bg2	bg2	NOUN
ejpam-6974	47	5	)	)	PUNCT
ejpam-6974	47	6	x	x	SYM
ejpam-6974	47	7	∗	∗	NOUN
ejpam-6974	47	8	0	0	NUM
ejpam-6974	48	1	=	=	SYM
ejpam-6974	48	2	x	x	X
ejpam-6974	48	3	(	(	PUNCT
ejpam-6974	48	4	bg3	bg3	PROPN
ejpam-6974	48	5	)	)	PUNCT
ejpam-6974	48	6	(	(	PUNCT
ejpam-6974	48	7	x	x	SYM
ejpam-6974	48	8	∗	∗	PROPN
ejpam-6974	48	9	y	y	NOUN
ejpam-6974	48	10	)	)	PUNCT
ejpam-6974	48	11	∗	∗	NOUN
ejpam-6974	48	12	(	(	PUNCT
ejpam-6974	48	13	0	0	NUM
ejpam-6974	48	14	∗	∗	NUM
ejpam-6974	48	15	y	y	NOUN
ejpam-6974	48	16	)	)	PUNCT
ejpam-6974	48	17	=	=	PUNCT
ejpam-6974	49	1	x	x	PUNCT
ejpam-6974	49	2	example	example	NOUN
ejpam-6974	49	3	2	2	NUM
ejpam-6974	49	4	.	.	PUNCT
ejpam-6974	50	1	[	[	X
ejpam-6974	50	2	7	7	X
ejpam-6974	50	3	]	]	X
ejpam-6974	50	4	let	let	NOUN
ejpam-6974	50	5	x	x	PUNCT
ejpam-6974	50	6	=	=	PUNCT
ejpam-6974	50	7	{	{	PUNCT
ejpam-6974	50	8	0	0	NUM
ejpam-6974	50	9	,	,	PUNCT
ejpam-6974	50	10	1	1	NUM
ejpam-6974	50	11	,	,	PUNCT
ejpam-6974	50	12	2	2	NUM
ejpam-6974	50	13	}	}	PUNCT
ejpam-6974	50	14	be	be	AUX
ejpam-6974	50	15	a	a	DET
ejpam-6974	50	16	set	set	NOUN
ejpam-6974	50	17	with	with	ADP
ejpam-6974	50	18	the	the	DET
ejpam-6974	50	19	following	follow	VERB
ejpam-6974	50	20	cayley	cayley	ADJ
ejpam-6974	50	21	table	table	NOUN
ejpam-6974	50	22	:	:	PUNCT
ejpam-6974	50	23	table	table	NOUN
ejpam-6974	50	24	2	2	NUM
ejpam-6974	50	25	:	:	PUNCT
ejpam-6974	50	26	cayley	cayley	ADJ
ejpam-6974	50	27	table	table	NOUN
ejpam-6974	50	28	of	of	ADP
ejpam-6974	50	29	the	the	DET
ejpam-6974	50	30	bg	bg	PROPN
ejpam-6974	50	31	-	-	PUNCT
ejpam-6974	50	32	algebra	algebra	PROPN
ejpam-6974	50	33	(	(	PUNCT
ejpam-6974	50	34	x	x	X
ejpam-6974	50	35	,	,	PUNCT
ejpam-6974	50	36	∗	∗	NOUN
ejpam-6974	50	37	,	,	PUNCT
ejpam-6974	50	38	0	0	NUM
ejpam-6974	50	39	)	)	PUNCT
ejpam-6974	50	40	∗	∗	NOUN
ejpam-6974	50	41	0	0	NUM
ejpam-6974	51	1	1	1	NUM
ejpam-6974	51	2	2	2	NUM
ejpam-6974	51	3	0	0	NUM
ejpam-6974	51	4	0	0	NUM
ejpam-6974	51	5	1	1	NUM
ejpam-6974	51	6	2	2	NUM
ejpam-6974	51	7	1	1	NUM
ejpam-6974	51	8	1	1	NUM
ejpam-6974	51	9	0	0	NUM
ejpam-6974	51	10	1	1	NUM
ejpam-6974	51	11	2	2	NUM
ejpam-6974	51	12	2	2	NUM
ejpam-6974	51	13	2	2	NUM
ejpam-6974	51	14	0	0	NUM
ejpam-6974	51	15	then	then	ADV
ejpam-6974	51	16	(	(	PUNCT
ejpam-6974	51	17	x	x	X
ejpam-6974	51	18	,	,	PUNCT
ejpam-6974	51	19	∗	∗	NOUN
ejpam-6974	51	20	,	,	PUNCT
ejpam-6974	51	21	0	0	NUM
ejpam-6974	51	22	)	)	PUNCT
ejpam-6974	51	23	is	be	AUX
ejpam-6974	51	24	a	a	DET
ejpam-6974	51	25	bg	bg	NOUN
ejpam-6974	51	26	-	-	PUNCT
ejpam-6974	51	27	algebra	algebra	NOUN
ejpam-6974	51	28	.	.	PUNCT
ejpam-6974	52	1	3	3	X
ejpam-6974	52	2	.	.	X
ejpam-6974	52	3	dual	dual	ADJ
ejpam-6974	52	4	bg	bg	NOUN
ejpam-6974	52	5	-	-	NOUN
ejpam-6974	52	6	algebra	algebra	NOUN
ejpam-6974	52	7	in	in	ADP
ejpam-6974	52	8	this	this	DET
ejpam-6974	52	9	section	section	NOUN
ejpam-6974	52	10	,	,	PUNCT
ejpam-6974	52	11	all	all	PRON
ejpam-6974	52	12	finite	finite	VERB
ejpam-6974	52	13	dual	dual	ADJ
ejpam-6974	52	14	bg	bg	NOUN
ejpam-6974	52	15	-	-	PUNCT
ejpam-6974	52	16	algebra	algebra	NOUN
ejpam-6974	52	17	examples	example	NOUN
ejpam-6974	52	18	were	be	AUX
ejpam-6974	52	19	verified	verify	VERB
ejpam-6974	52	20	using	use	VERB
ejpam-6974	52	21	a	a	DET
ejpam-6974	52	22	python	python	NOUN
ejpam-6974	52	23	script	script	NOUN
ejpam-6974	52	24	developed	develop	VERB
ejpam-6974	52	25	by	by	ADP
ejpam-6974	52	26	the	the	DET
ejpam-6974	52	27	author	author	NOUN
ejpam-6974	52	28	found	find	VERB
ejpam-6974	52	29	in	in	ADP
ejpam-6974	52	30	the	the	DET
ejpam-6974	52	31	appendix	appendix	ADJ
ejpam-6974	52	32	section	section	NOUN
ejpam-6974	52	33	.	.	PUNCT
ejpam-6974	53	1	definition	definition	NOUN
ejpam-6974	53	2	5	5	NUM
ejpam-6974	53	3	.	.	PUNCT
ejpam-6974	54	1	a	a	DET
ejpam-6974	54	2	dual	dual	ADJ
ejpam-6974	54	3	bg	bg	NOUN
ejpam-6974	54	4	-	-	NOUN
ejpam-6974	54	5	algebra	algebra	PROPN
ejpam-6974	54	6	x	x	PUNCT
ejpam-6974	54	7	is	be	AUX
ejpam-6974	54	8	a	a	DET
ejpam-6974	54	9	triple	triple	ADJ
ejpam-6974	54	10	(	(	PUNCT
ejpam-6974	54	11	x	x	NOUN
ejpam-6974	54	12	,	,	PUNCT
ejpam-6974	54	13	◦	◦	NOUN
ejpam-6974	54	14	,	,	PUNCT
ejpam-6974	54	15	1	1	NUM
ejpam-6974	54	16	)	)	PUNCT
ejpam-6974	54	17	where	where	SCONJ
ejpam-6974	54	18	x	x	PRON
ejpam-6974	54	19	is	be	AUX
ejpam-6974	54	20	a	a	DET
ejpam-6974	54	21	nonempty	nonempty	ADV
ejpam-6974	54	22	set	set	VERB
ejpam-6974	54	23	with	with	ADP
ejpam-6974	54	24	a	a	DET
ejpam-6974	54	25	binary	binary	ADJ
ejpam-6974	54	26	operation	operation	NOUN
ejpam-6974	54	27	◦	◦	NOUN
ejpam-6974	54	28	and	and	CCONJ
ejpam-6974	54	29	a	a	DET
ejpam-6974	54	30	constant	constant	ADJ
ejpam-6974	54	31	1	1	NUM
ejpam-6974	54	32	satisying	satisye	VERB
ejpam-6974	54	33	the	the	DET
ejpam-6974	54	34	following	following	ADJ
ejpam-6974	54	35	axioms	axiom	NOUN
ejpam-6974	54	36	for	for	ADP
ejpam-6974	54	37	all	all	DET
ejpam-6974	54	38	x	x	NOUN
ejpam-6974	54	39	,	,	PUNCT
ejpam-6974	54	40	y	y	PROPN
ejpam-6974	54	41	∈	∈	PROPN
ejpam-6974	55	1	x	x	X
ejpam-6974	55	2	:	:	PUNCT
ejpam-6974	55	3	(	(	PUNCT
ejpam-6974	55	4	dbg1	dbg1	ADJ
ejpam-6974	55	5	)	)	PUNCT
ejpam-6974	55	6	x	x	PUNCT
ejpam-6974	55	7	◦	◦	NOUN
ejpam-6974	55	8	x	x	SYM
ejpam-6974	55	9	=	=	SYM
ejpam-6974	55	10	1	1	NUM
ejpam-6974	55	11	(	(	PUNCT
ejpam-6974	55	12	dbg2	dbg2	PROPN
ejpam-6974	55	13	)	)	PUNCT
ejpam-6974	55	14	1	1	NUM
ejpam-6974	55	15	◦	◦	NOUN
ejpam-6974	55	16	x	x	SYM
ejpam-6974	55	17	=	=	SYM
ejpam-6974	55	18	x	x	X
ejpam-6974	55	19	(	(	PUNCT
ejpam-6974	55	20	dbg3	dbg3	PROPN
ejpam-6974	55	21	)	)	PUNCT
ejpam-6974	55	22	(	(	PUNCT
ejpam-6974	55	23	y	y	NOUN
ejpam-6974	55	24	◦	◦	NOUN
ejpam-6974	55	25	1	1	NUM
ejpam-6974	55	26	)	)	PUNCT
ejpam-6974	55	27	◦	◦	NOUN
ejpam-6974	55	28	(	(	PUNCT
ejpam-6974	55	29	y	y	PROPN
ejpam-6974	55	30	◦	◦	NOUN
ejpam-6974	55	31	x	x	X
ejpam-6974	55	32	)	)	PUNCT
ejpam-6974	56	1	=	=	PUNCT
ejpam-6974	56	2	x	x	PUNCT
ejpam-6974	56	3	example	example	NOUN
ejpam-6974	56	4	3	3	X
ejpam-6974	56	5	.	.	PUNCT
ejpam-6974	57	1	let	let	VERB
ejpam-6974	57	2	x	x	PUNCT
ejpam-6974	57	3	=	=	PRON
ejpam-6974	57	4	{	{	PUNCT
ejpam-6974	57	5	1	1	NUM
ejpam-6974	57	6	,	,	PUNCT
ejpam-6974	57	7	a	a	DET
ejpam-6974	57	8	,	,	PUNCT
ejpam-6974	57	9	b	b	NOUN
ejpam-6974	57	10	,	,	PUNCT
ejpam-6974	57	11	c	c	NOUN
ejpam-6974	57	12	,	,	PUNCT
ejpam-6974	57	13	d	d	NOUN
ejpam-6974	57	14	,	,	PUNCT
ejpam-6974	57	15	e	e	AUX
ejpam-6974	57	16	}	}	PUNCT
ejpam-6974	57	17	be	be	AUX
ejpam-6974	57	18	a	a	DET
ejpam-6974	57	19	set	set	NOUN
ejpam-6974	57	20	with	with	ADP
ejpam-6974	57	21	the	the	DET
ejpam-6974	57	22	following	follow	VERB
ejpam-6974	57	23	cayley	cayley	ADJ
ejpam-6974	57	24	table	table	NOUN
ejpam-6974	57	25	:	:	PUNCT
ejpam-6974	57	26	table	table	NOUN
ejpam-6974	57	27	3	3	NUM
ejpam-6974	57	28	:	:	PUNCT
ejpam-6974	57	29	cayley	cayley	ADJ
ejpam-6974	57	30	table	table	NOUN
ejpam-6974	57	31	of	of	ADP
ejpam-6974	57	32	the	the	DET
ejpam-6974	57	33	dual	dual	ADJ
ejpam-6974	57	34	bg	bg	NOUN
ejpam-6974	57	35	-	-	NOUN
ejpam-6974	57	36	algebra	algebra	PROPN
ejpam-6974	57	37	(	(	PUNCT
ejpam-6974	57	38	x	x	NOUN
ejpam-6974	57	39	,	,	PUNCT
ejpam-6974	57	40	◦	◦	NOUN
ejpam-6974	57	41	,	,	PUNCT
ejpam-6974	57	42	1	1	X
ejpam-6974	57	43	)	)	PUNCT
ejpam-6974	57	44	◦	◦	NOUN
ejpam-6974	57	45	1	1	NUM
ejpam-6974	57	46	a	a	DET
ejpam-6974	57	47	b	b	NOUN
ejpam-6974	57	48	c	c	NOUN
ejpam-6974	57	49	d	d	X
ejpam-6974	57	50	e	e	PROPN
ejpam-6974	57	51	1	1	NUM
ejpam-6974	57	52	1	1	NUM
ejpam-6974	57	53	a	a	DET
ejpam-6974	57	54	b	b	NOUN
ejpam-6974	57	55	c	c	NOUN
ejpam-6974	57	56	d	d	PROPN
ejpam-6974	57	57	e	e	PROPN
ejpam-6974	57	58	a	a	PRON
ejpam-6974	57	59	b	b	PROPN
ejpam-6974	57	60	1	1	NUM
ejpam-6974	57	61	a	a	PRON
ejpam-6974	57	62	d	d	X
ejpam-6974	57	63	e	e	NOUN
ejpam-6974	57	64	c	c	NOUN
ejpam-6974	57	65	b	b	PROPN
ejpam-6974	57	66	a	a	DET
ejpam-6974	57	67	b	b	NOUN
ejpam-6974	57	68	1	1	NUM
ejpam-6974	57	69	e	e	NOUN
ejpam-6974	57	70	c	c	NOUN
ejpam-6974	57	71	d	d	NOUN
ejpam-6974	57	72	c	c	NOUN
ejpam-6974	57	73	c	c	NOUN
ejpam-6974	57	74	d	d	X
ejpam-6974	57	75	e	e	PROPN
ejpam-6974	57	76	1	1	NUM
ejpam-6974	57	77	a	a	DET
ejpam-6974	57	78	b	b	NOUN
ejpam-6974	57	79	d	d	X
ejpam-6974	57	80	d	d	PROPN
ejpam-6974	57	81	e	e	PROPN
ejpam-6974	57	82	c	c	NOUN
ejpam-6974	57	83	b	b	PROPN
ejpam-6974	57	84	1	1	NUM
ejpam-6974	57	85	a	a	DET
ejpam-6974	57	86	e	e	NOUN
ejpam-6974	57	87	e	e	NOUN
ejpam-6974	57	88	c	c	NOUN
ejpam-6974	57	89	d	d	X
ejpam-6974	57	90	a	a	PRON
ejpam-6974	57	91	b	b	NOUN
ejpam-6974	57	92	1	1	NUM
ejpam-6974	57	93	then	then	ADV
ejpam-6974	57	94	(	(	PUNCT
ejpam-6974	57	95	x	x	NOUN
ejpam-6974	57	96	,	,	PUNCT
ejpam-6974	57	97	◦	◦	NOUN
ejpam-6974	57	98	,	,	PUNCT
ejpam-6974	57	99	1	1	NUM
ejpam-6974	57	100	)	)	PUNCT
ejpam-6974	57	101	is	be	AUX
ejpam-6974	57	102	a	a	DET
ejpam-6974	57	103	dual	dual	ADJ
ejpam-6974	57	104	bg	bg	NOUN
ejpam-6974	57	105	-	-	NOUN
ejpam-6974	57	106	algebra	algebra	PROPN
ejpam-6974	57	107	.	.	PUNCT
ejpam-6974	57	108	example	example	NOUN
ejpam-6974	58	1	4	4	NUM
ejpam-6974	58	2	.	.	PUNCT
ejpam-6974	58	3	let	let	VERB
ejpam-6974	58	4	x	x	SYM
ejpam-6974	58	5	=	=	SYM
ejpam-6974	58	6	r\{0	r\{0	PROPN
ejpam-6974	58	7	}	}	PUNCT
ejpam-6974	58	8	.	.	PUNCT
ejpam-6974	59	1	define	define	VERB
ejpam-6974	59	2	the	the	DET
ejpam-6974	59	3	binary	binary	ADJ
ejpam-6974	59	4	operation	operation	NOUN
ejpam-6974	59	5	◦	◦	NOUN
ejpam-6974	59	6	as	as	ADP
ejpam-6974	59	7	x	x	X
ejpam-6974	59	8	◦	◦	NOUN
ejpam-6974	59	9	y	y	NOUN
ejpam-6974	59	10	=	=	SYM
ejpam-6974	59	11	y	y	PROPN
ejpam-6974	59	12	x	x	PUNCT
ejpam-6974	59	13	for	for	ADP
ejpam-6974	59	14	all	all	DET
ejpam-6974	59	15	x	x	NOUN
ejpam-6974	59	16	,	,	PUNCT
ejpam-6974	59	17	y	y	PROPN
ejpam-6974	59	18	∈	∈	PROPN
ejpam-6974	59	19	x.	x.	NOUN
ejpam-6974	59	20	note	note	VERB
ejpam-6974	59	21	that	that	SCONJ
ejpam-6974	59	22	x	x	PRON
ejpam-6974	59	23	satisfies	satisfie	NOUN
ejpam-6974	59	24	(	(	PUNCT
ejpam-6974	59	25	dbg1	dbg1	PROPN
ejpam-6974	59	26	):	):	PUNCT
ejpam-6974	59	27	x	x	PUNCT
ejpam-6974	59	28	◦	◦	NOUN
ejpam-6974	59	29	x	x	X
ejpam-6974	59	30	=	=	PUNCT
ejpam-6974	59	31	x	x	SYM
ejpam-6974	59	32	x	x	SYM
ejpam-6974	59	33	=	=	SYM
ejpam-6974	59	34	1	1	NUM
ejpam-6974	59	35	,	,	PUNCT
ejpam-6974	59	36	(	(	PUNCT
ejpam-6974	59	37	dbg2	dbg2	NOUN
ejpam-6974	59	38	):	):	PUNCT
ejpam-6974	59	39	1	1	NUM
ejpam-6974	59	40	◦	◦	NOUN
ejpam-6974	59	41	x	x	SYM
ejpam-6974	59	42	=	=	SYM
ejpam-6974	59	43	x	x	SYM
ejpam-6974	59	44	1	1	NUM
ejpam-6974	59	45	=	=	SYM
ejpam-6974	59	46	x	x	NOUN
ejpam-6974	59	47	,	,	PUNCT
ejpam-6974	59	48	and	and	CCONJ
ejpam-6974	59	49	(	(	PUNCT
ejpam-6974	59	50	dbg3	dbg3	PROPN
ejpam-6974	59	51	):	):	PUNCT
ejpam-6974	59	52	(	(	PUNCT
ejpam-6974	59	53	y	y	PROPN
ejpam-6974	59	54	◦	◦	NOUN
ejpam-6974	59	55	1	1	NUM
ejpam-6974	59	56	)	)	PUNCT
ejpam-6974	59	57	◦	◦	NOUN
ejpam-6974	59	58	(	(	PUNCT
ejpam-6974	59	59	y	y	PROPN
ejpam-6974	59	60	◦	◦	NOUN
ejpam-6974	59	61	x	x	X
ejpam-6974	59	62	)	)	PUNCT
ejpam-6974	60	1	=	=	SYM
ejpam-6974	60	2	y	y	PROPN
ejpam-6974	60	3	◦	◦	NOUN
ejpam-6974	60	4	x	x	SYM
ejpam-6974	60	5	y	y	X
ejpam-6974	60	6	◦	◦	NOUN
ejpam-6974	60	7	1	1	NUM
ejpam-6974	60	8	=	=	SYM
ejpam-6974	60	9	x	x	SYM
ejpam-6974	60	10	y	y	PROPN
ejpam-6974	60	11	1	1	NUM
ejpam-6974	60	12	y	y	NOUN
ejpam-6974	60	13	=	=	PUNCT
ejpam-6974	60	14	x	x	SYM
ejpam-6974	60	15	1	1	X
ejpam-6974	60	16	=	=	SYM
ejpam-6974	60	17	x.	x.	NOUN
ejpam-6974	60	18	therefore	therefore	ADV
ejpam-6974	60	19	,	,	PUNCT
ejpam-6974	60	20	(	(	PUNCT
ejpam-6974	60	21	x	x	NOUN
ejpam-6974	60	22	,	,	PUNCT
ejpam-6974	60	23	◦	◦	NOUN
ejpam-6974	60	24	,	,	PUNCT
ejpam-6974	60	25	1	1	NUM
ejpam-6974	60	26	)	)	PUNCT
ejpam-6974	60	27	is	be	AUX
ejpam-6974	60	28	a	a	DET
ejpam-6974	60	29	dual	dual	ADJ
ejpam-6974	60	30	bg	bg	NOUN
ejpam-6974	60	31	-	-	NOUN
ejpam-6974	60	32	algebra	algebra	PROPN
ejpam-6974	60	33	.	.	PUNCT
ejpam-6974	61	1	c.m	c.m	PROPN
ejpam-6974	61	2	.	.	PROPN
ejpam-6974	61	3	chan	chan	PROPN
ejpam-6974	61	4	,	,	PUNCT
ejpam-6974	61	5	k.	k.	PROPN
ejpam-6974	61	6	fuentes	fuentes	PROPN
ejpam-6974	61	7	/	/	SYM
ejpam-6974	61	8	eur	eur	PROPN
ejpam-6974	61	9	.	.	PUNCT
ejpam-6974	62	1	j.	j.	PROPN
ejpam-6974	62	2	pure	pure	PROPN
ejpam-6974	62	3	appl	appl	PROPN
ejpam-6974	62	4	.	.	PROPN
ejpam-6974	62	5	math	math	PROPN
ejpam-6974	62	6	,	,	PUNCT
ejpam-6974	62	7	18	18	NUM
ejpam-6974	62	8	(	(	PUNCT
ejpam-6974	62	9	4	4	NUM
ejpam-6974	62	10	)	)	PUNCT
ejpam-6974	62	11	(	(	PUNCT
ejpam-6974	62	12	2025	2025	NUM
ejpam-6974	62	13	)	)	PUNCT
ejpam-6974	62	14	,	,	PUNCT
ejpam-6974	62	15	6974	6974	NUM
ejpam-6974	62	16	4	4	NUM
ejpam-6974	62	17	of	of	ADP
ejpam-6974	62	18	16	16	NUM
ejpam-6974	62	19	example	example	NOUN
ejpam-6974	62	20	5	5	NUM
ejpam-6974	62	21	shows	show	VERB
ejpam-6974	62	22	that	that	SCONJ
ejpam-6974	62	23	the	the	DET
ejpam-6974	62	24	axioms	axiom	NOUN
ejpam-6974	62	25	are	be	AUX
ejpam-6974	62	26	independent	independent	ADJ
ejpam-6974	62	27	.	.	PUNCT
ejpam-6974	62	28	example	example	NOUN
ejpam-6974	63	1	5	5	NUM
ejpam-6974	63	2	.	.	PUNCT
ejpam-6974	63	3	let	let	VERB
ejpam-6974	63	4	x1	x1	PROPN
ejpam-6974	63	5	=	=	SYM
ejpam-6974	63	6	(	(	PUNCT
ejpam-6974	63	7	x	x	X
ejpam-6974	63	8	,	,	PUNCT
ejpam-6974	63	9	◦	◦	NOUN
ejpam-6974	63	10	1	1	NUM
ejpam-6974	63	11	,	,	PUNCT
ejpam-6974	63	12	1	1	NUM
ejpam-6974	63	13	)	)	PUNCT
ejpam-6974	63	14	,	,	PUNCT
ejpam-6974	64	1	x2	x2	NOUN
ejpam-6974	64	2	=	=	PRON
ejpam-6974	64	3	(	(	PUNCT
ejpam-6974	64	4	x	x	NOUN
ejpam-6974	64	5	,	,	PUNCT
ejpam-6974	64	6	◦	◦	NOUN
ejpam-6974	64	7	2	2	NUM
ejpam-6974	64	8	,	,	PUNCT
ejpam-6974	64	9	1	1	NUM
ejpam-6974	64	10	)	)	PUNCT
ejpam-6974	64	11	,	,	PUNCT
ejpam-6974	64	12	and	and	CCONJ
ejpam-6974	64	13	x3	x3	ADV
ejpam-6974	64	14	=	=	SYM
ejpam-6974	64	15	(	(	PUNCT
ejpam-6974	64	16	y	y	NOUN
ejpam-6974	64	17	,	,	PUNCT
ejpam-6974	64	18	◦	◦	NOUN
ejpam-6974	64	19	3	3	NUM
ejpam-6974	64	20	,	,	PUNCT
ejpam-6974	64	21	1	1	NUM
ejpam-6974	64	22	)	)	PUNCT
ejpam-6974	64	23	where	where	SCONJ
ejpam-6974	64	24	x	x	X
ejpam-6974	64	25	=	=	PRON
ejpam-6974	64	26	{	{	PUNCT
ejpam-6974	64	27	1	1	NUM
ejpam-6974	64	28	,	,	PUNCT
ejpam-6974	64	29	a	a	DET
ejpam-6974	64	30	,	,	PUNCT
ejpam-6974	64	31	b	b	NOUN
ejpam-6974	64	32	}	}	PUNCT
ejpam-6974	64	33	and	and	CCONJ
ejpam-6974	64	34	y	y	PROPN
ejpam-6974	64	35	=	=	PUNCT
ejpam-6974	64	36	{	{	PUNCT
ejpam-6974	64	37	1	1	NUM
ejpam-6974	64	38	,	,	PUNCT
ejpam-6974	64	39	a	a	DET
ejpam-6974	64	40	,	,	PUNCT
ejpam-6974	64	41	b	b	NOUN
ejpam-6974	64	42	,	,	PUNCT
ejpam-6974	64	43	c	c	NOUN
ejpam-6974	64	44	}	}	PUNCT
ejpam-6974	64	45	.	.	PUNCT
ejpam-6974	65	1	the	the	DET
ejpam-6974	65	2	cayley	cayley	ADJ
ejpam-6974	65	3	tables	table	NOUN
ejpam-6974	65	4	of	of	ADP
ejpam-6974	65	5	the	the	DET
ejpam-6974	65	6	binary	binary	ADJ
ejpam-6974	65	7	operations	operation	NOUN
ejpam-6974	65	8	◦	◦	NOUN
ejpam-6974	65	9	1	1	NUM
ejpam-6974	65	10	,	,	PUNCT
ejpam-6974	65	11	◦	◦	NOUN
ejpam-6974	65	12	2	2	NUM
ejpam-6974	65	13	,	,	PUNCT
ejpam-6974	65	14	and	and	CCONJ
ejpam-6974	65	15	◦	◦	NOUN
ejpam-6974	65	16	3	3	NUM
ejpam-6974	65	17	are	be	AUX
ejpam-6974	65	18	shown	show	VERB
ejpam-6974	65	19	in	in	ADP
ejpam-6974	65	20	table	table	NOUN
ejpam-6974	65	21	4	4	NUM
ejpam-6974	65	22	.	.	PUNCT
ejpam-6974	65	23	table	table	NOUN
ejpam-6974	65	24	4	4	NUM
ejpam-6974	65	25	:	:	PUNCT
ejpam-6974	65	26	cayley	cayley	ADJ
ejpam-6974	65	27	tables	table	NOUN
ejpam-6974	65	28	of	of	ADP
ejpam-6974	65	29	x1	x1	PROPN
ejpam-6974	65	30	,	,	PUNCT
ejpam-6974	65	31	x2	x2	PROPN
ejpam-6974	65	32	,	,	PUNCT
ejpam-6974	65	33	and	and	CCONJ
ejpam-6974	65	34	x3	x3	VERB
ejpam-6974	65	35	◦	◦	NOUN
ejpam-6974	65	36	1	1	NUM
ejpam-6974	65	37	1	1	NUM
ejpam-6974	65	38	a	a	DET
ejpam-6974	65	39	b	b	NUM
ejpam-6974	65	40	1	1	NUM
ejpam-6974	65	41	1	1	NUM
ejpam-6974	65	42	a	a	DET
ejpam-6974	65	43	b	b	NOUN
ejpam-6974	65	44	a	a	DET
ejpam-6974	65	45	a	a	DET
ejpam-6974	65	46	1	1	NUM
ejpam-6974	65	47	b	b	SYM
ejpam-6974	65	48	b	b	PROPN
ejpam-6974	65	49	1	1	NUM
ejpam-6974	65	50	a	a	DET
ejpam-6974	65	51	b	b	NOUN
ejpam-6974	65	52	◦	◦	NOUN
ejpam-6974	65	53	2	2	NUM
ejpam-6974	65	54	1	1	NUM
ejpam-6974	65	55	a	a	DET
ejpam-6974	65	56	b	b	NUM
ejpam-6974	65	57	1	1	NUM
ejpam-6974	65	58	1	1	NUM
ejpam-6974	65	59	b	b	PROPN
ejpam-6974	65	60	a	a	DET
ejpam-6974	65	61	a	a	DET
ejpam-6974	65	62	b	b	NOUN
ejpam-6974	65	63	1	1	NUM
ejpam-6974	65	64	a	a	DET
ejpam-6974	65	65	b	b	NOUN
ejpam-6974	65	66	a	a	DET
ejpam-6974	65	67	b	b	NOUN
ejpam-6974	65	68	1	1	NUM
ejpam-6974	65	69	◦	◦	NOUN
ejpam-6974	65	70	3	3	NUM
ejpam-6974	65	71	1	1	NUM
ejpam-6974	65	72	a	a	DET
ejpam-6974	65	73	b	b	NOUN
ejpam-6974	65	74	c	c	NOUN
ejpam-6974	65	75	1	1	NUM
ejpam-6974	65	76	1	1	NUM
ejpam-6974	65	77	a	a	DET
ejpam-6974	65	78	b	b	NOUN
ejpam-6974	65	79	c	c	NOUN
ejpam-6974	65	80	a	a	DET
ejpam-6974	65	81	b	b	PROPN
ejpam-6974	65	82	1	1	NUM
ejpam-6974	65	83	a	a	DET
ejpam-6974	65	84	c	c	NOUN
ejpam-6974	65	85	b	b	PROPN
ejpam-6974	65	86	c	c	PROPN
ejpam-6974	65	87	a	a	PRON
ejpam-6974	65	88	1	1	NUM
ejpam-6974	65	89	b	b	NOUN
ejpam-6974	65	90	c	c	NOUN
ejpam-6974	65	91	a	a	DET
ejpam-6974	65	92	b	b	NOUN
ejpam-6974	65	93	c	c	ADP
ejpam-6974	65	94	1	1	NUM
ejpam-6974	65	95	the	the	DET
ejpam-6974	65	96	axioms	axiom	NOUN
ejpam-6974	65	97	(	(	PUNCT
ejpam-6974	65	98	dbg2	dbg2	NOUN
ejpam-6974	65	99	)	)	PUNCT
ejpam-6974	65	100	and	and	CCONJ
ejpam-6974	65	101	(	(	PUNCT
ejpam-6974	65	102	dbg3	dbg3	PROPN
ejpam-6974	65	103	)	)	PUNCT
ejpam-6974	65	104	hold	hold	VERB
ejpam-6974	65	105	for	for	ADP
ejpam-6974	65	106	x1	x1	PROPN
ejpam-6974	65	107	.	.	PUNCT
ejpam-6974	66	1	however	however	ADV
ejpam-6974	66	2	,	,	PUNCT
ejpam-6974	66	3	(	(	PUNCT
ejpam-6974	66	4	dbg1	dbg1	ADJ
ejpam-6974	66	5	)	)	PUNCT
ejpam-6974	66	6	does	do	AUX
ejpam-6974	66	7	not	not	PART
ejpam-6974	66	8	hold	hold	VERB
ejpam-6974	66	9	since	since	SCONJ
ejpam-6974	66	10	b	b	PROPN
ejpam-6974	66	11	◦	◦	NOUN
ejpam-6974	66	12	1	1	NUM
ejpam-6974	66	13	b	b	X
ejpam-6974	66	14	=	=	SYM
ejpam-6974	66	15	b	b	PROPN
ejpam-6974	66	16	̸=	̸=	PROPN
ejpam-6974	66	17	1	1	NUM
ejpam-6974	66	18	.	.	PUNCT
ejpam-6974	67	1	for	for	ADP
ejpam-6974	67	2	x2	x2	PROPN
ejpam-6974	67	3	,	,	PUNCT
ejpam-6974	67	4	(	(	PUNCT
ejpam-6974	67	5	dbg1	dbg1	ADJ
ejpam-6974	67	6	)	)	PUNCT
ejpam-6974	67	7	and	and	CCONJ
ejpam-6974	67	8	(	(	PUNCT
ejpam-6974	67	9	dbg3	dbg3	PROPN
ejpam-6974	67	10	)	)	PUNCT
ejpam-6974	67	11	are	be	AUX
ejpam-6974	67	12	satisfied	satisfied	ADJ
ejpam-6974	67	13	but	but	CCONJ
ejpam-6974	67	14	not	not	PART
ejpam-6974	67	15	(	(	PUNCT
ejpam-6974	67	16	dbg2	dbg2	PROPN
ejpam-6974	67	17	)	)	PUNCT
ejpam-6974	67	18	since	since	SCONJ
ejpam-6974	67	19	1	1	NUM
ejpam-6974	67	20	◦	◦	NOUN
ejpam-6974	67	21	2	2	NUM
ejpam-6974	67	22	a	a	DET
ejpam-6974	67	23	=	=	SYM
ejpam-6974	67	24	b	b	NOUN
ejpam-6974	67	25	̸=	̸=	PROPN
ejpam-6974	67	26	a.	a.	NOUN
ejpam-6974	67	27	(	(	PUNCT
ejpam-6974	67	28	dbg1	dbg1	PROPN
ejpam-6974	67	29	)	)	PUNCT
ejpam-6974	67	30	and	and	CCONJ
ejpam-6974	67	31	(	(	PUNCT
ejpam-6974	67	32	dbg2	dbg2	PROPN
ejpam-6974	67	33	)	)	PUNCT
ejpam-6974	67	34	are	be	AUX
ejpam-6974	67	35	satisfied	satisfied	ADJ
ejpam-6974	67	36	in	in	ADP
ejpam-6974	67	37	x3	x3	ADJ
ejpam-6974	67	38	but	but	CCONJ
ejpam-6974	67	39	fails	fail	VERB
ejpam-6974	67	40	on	on	ADP
ejpam-6974	67	41	(	(	PUNCT
ejpam-6974	67	42	dbg3	dbg3	PROPN
ejpam-6974	67	43	)	)	PUNCT
ejpam-6974	67	44	since	since	SCONJ
ejpam-6974	67	45	(	(	PUNCT
ejpam-6974	67	46	b	b	X
ejpam-6974	67	47	◦	◦	NOUN
ejpam-6974	67	48	3	3	NUM
ejpam-6974	67	49	1	1	NUM
ejpam-6974	67	50	)	)	PUNCT
ejpam-6974	67	51	◦	◦	NOUN
ejpam-6974	67	52	3	3	NUM
ejpam-6974	67	53	(	(	PUNCT
ejpam-6974	67	54	b	b	NOUN
ejpam-6974	67	55	◦	◦	NOUN
ejpam-6974	67	56	3	3	NUM
ejpam-6974	67	57	a	a	NOUN
ejpam-6974	67	58	)	)	PUNCT
ejpam-6974	68	1	=	=	SYM
ejpam-6974	68	2	c	c	NOUN
ejpam-6974	68	3	◦	◦	NOUN
ejpam-6974	68	4	3	3	NUM
ejpam-6974	68	5	a	a	DET
ejpam-6974	68	6	=	=	SYM
ejpam-6974	68	7	b	b	NOUN
ejpam-6974	68	8	̸=	̸=	PROPN
ejpam-6974	68	9	a.	a.	NOUN
ejpam-6974	68	10	example	example	NOUN
ejpam-6974	68	11	6	6	NUM
ejpam-6974	68	12	.	.	PUNCT
ejpam-6974	69	1	consider	consider	VERB
ejpam-6974	69	2	the	the	DET
ejpam-6974	69	3	dual	dual	ADJ
ejpam-6974	69	4	bg	bg	NOUN
ejpam-6974	69	5	-	-	NOUN
ejpam-6974	69	6	algebra	algebra	PROPN
ejpam-6974	69	7	(	(	PUNCT
ejpam-6974	69	8	x	x	NOUN
ejpam-6974	69	9	,	,	PUNCT
ejpam-6974	69	10	◦	◦	NOUN
ejpam-6974	69	11	,	,	PUNCT
ejpam-6974	69	12	1	1	NUM
ejpam-6974	69	13	)	)	PUNCT
ejpam-6974	69	14	in	in	ADP
ejpam-6974	69	15	example	example	NOUN
ejpam-6974	69	16	3	3	NUM
ejpam-6974	69	17	where	where	SCONJ
ejpam-6974	69	18	x	x	X
ejpam-6974	69	19	=	=	PRON
ejpam-6974	69	20	{	{	PUNCT
ejpam-6974	69	21	1	1	NUM
ejpam-6974	69	22	,	,	PUNCT
ejpam-6974	69	23	a	a	DET
ejpam-6974	69	24	,	,	PUNCT
ejpam-6974	69	25	b	b	NOUN
ejpam-6974	69	26	,	,	PUNCT
ejpam-6974	69	27	c	c	NOUN
ejpam-6974	69	28	,	,	PUNCT
ejpam-6974	69	29	d	d	NOUN
ejpam-6974	69	30	,	,	PUNCT
ejpam-6974	69	31	e	e	NOUN
ejpam-6974	69	32	}	}	PUNCT
ejpam-6974	69	33	.	.	PUNCT
ejpam-6974	70	1	define	define	VERB
ejpam-6974	70	2	the	the	DET
ejpam-6974	70	3	binary	binary	ADJ
ejpam-6974	70	4	operation	operation	NOUN
ejpam-6974	70	5	“	"	PUNCT
ejpam-6974	70	6	∗	∗	NOUN
ejpam-6974	70	7	”	"	PUNCT
ejpam-6974	70	8	as	as	ADP
ejpam-6974	70	9	x	x	X
ejpam-6974	70	10	∗	∗	NOUN
ejpam-6974	70	11	y	y	NOUN
ejpam-6974	70	12	=	=	SYM
ejpam-6974	70	13	y	y	PROPN
ejpam-6974	70	14	◦	◦	NOUN
ejpam-6974	70	15	x	x	PUNCT
ejpam-6974	70	16	for	for	ADP
ejpam-6974	70	17	all	all	DET
ejpam-6974	70	18	x	x	NOUN
ejpam-6974	70	19	,	,	PUNCT
ejpam-6974	70	20	y	y	PROPN
ejpam-6974	70	21	∈	∈	PROPN
ejpam-6974	70	22	x.	x.	NOUN
ejpam-6974	71	1	the	the	DET
ejpam-6974	71	2	cayley	cayley	ADJ
ejpam-6974	71	3	table	table	NOUN
ejpam-6974	71	4	of	of	ADP
ejpam-6974	71	5	(	(	PUNCT
ejpam-6974	71	6	x	x	NOUN
ejpam-6974	71	7	,	,	PUNCT
ejpam-6974	71	8	∗	∗	NOUN
ejpam-6974	71	9	,	,	PUNCT
ejpam-6974	71	10	1	1	NUM
ejpam-6974	71	11	)	)	PUNCT
ejpam-6974	71	12	is	be	AUX
ejpam-6974	71	13	shown	show	VERB
ejpam-6974	71	14	below	below	ADP
ejpam-6974	71	15	.	.	PUNCT
ejpam-6974	72	1	table	table	NOUN
ejpam-6974	72	2	5	5	NUM
ejpam-6974	72	3	:	:	PUNCT
ejpam-6974	72	4	cayley	cayley	ADJ
ejpam-6974	72	5	table	table	NOUN
ejpam-6974	72	6	of	of	ADP
ejpam-6974	72	7	the	the	DET
ejpam-6974	72	8	bg	bg	PROPN
ejpam-6974	72	9	-	-	PUNCT
ejpam-6974	72	10	algebra	algebra	PROPN
ejpam-6974	72	11	(	(	PUNCT
ejpam-6974	72	12	x	x	X
ejpam-6974	72	13	,	,	PUNCT
ejpam-6974	72	14	∗	∗	NOUN
ejpam-6974	72	15	,	,	PUNCT
ejpam-6974	72	16	1	1	NUM
ejpam-6974	72	17	)	)	PUNCT
ejpam-6974	72	18	∗	∗	NOUN
ejpam-6974	72	19	1	1	NUM
ejpam-6974	72	20	a	a	DET
ejpam-6974	72	21	b	b	NOUN
ejpam-6974	72	22	c	c	NOUN
ejpam-6974	72	23	d	d	X
ejpam-6974	72	24	e	e	PROPN
ejpam-6974	72	25	1	1	NUM
ejpam-6974	72	26	1	1	NUM
ejpam-6974	72	27	b	b	PROPN
ejpam-6974	72	28	a	a	DET
ejpam-6974	72	29	c	c	NOUN
ejpam-6974	72	30	d	d	X
ejpam-6974	72	31	e	e	PROPN
ejpam-6974	72	32	a	a	DET
ejpam-6974	72	33	a	a	DET
ejpam-6974	72	34	1	1	NUM
ejpam-6974	72	35	b	b	NOUN
ejpam-6974	72	36	d	d	PROPN
ejpam-6974	72	37	e	e	PROPN
ejpam-6974	72	38	c	c	PROPN
ejpam-6974	72	39	b	b	PROPN
ejpam-6974	72	40	b	b	PROPN
ejpam-6974	72	41	a	a	DET
ejpam-6974	72	42	1	1	NUM
ejpam-6974	72	43	e	e	NOUN
ejpam-6974	72	44	c	c	NOUN
ejpam-6974	72	45	d	d	NOUN
ejpam-6974	72	46	c	c	NOUN
ejpam-6974	72	47	c	c	NOUN
ejpam-6974	72	48	d	d	X
ejpam-6974	72	49	e	e	PROPN
ejpam-6974	72	50	1	1	NUM
ejpam-6974	72	51	b	b	PROPN
ejpam-6974	72	52	a	a	PROPN
ejpam-6974	72	53	d	d	X
ejpam-6974	72	54	d	d	X
ejpam-6974	72	55	e	e	X
ejpam-6974	72	56	c	c	PROPN
ejpam-6974	72	57	a	a	DET
ejpam-6974	72	58	1	1	NUM
ejpam-6974	72	59	b	b	NOUN
ejpam-6974	72	60	e	e	X
ejpam-6974	72	61	e	e	X
ejpam-6974	72	62	c	c	PROPN
ejpam-6974	72	63	d	d	X
ejpam-6974	72	64	b	b	PROPN
ejpam-6974	72	65	a	a	DET
ejpam-6974	72	66	1	1	NUM
ejpam-6974	72	67	note	note	NOUN
ejpam-6974	72	68	that	that	SCONJ
ejpam-6974	72	69	(	(	PUNCT
ejpam-6974	72	70	x	x	X
ejpam-6974	72	71	,	,	PUNCT
ejpam-6974	72	72	∗	∗	NOUN
ejpam-6974	72	73	,	,	PUNCT
ejpam-6974	72	74	1	1	NUM
ejpam-6974	72	75	)	)	PUNCT
ejpam-6974	72	76	satisfies	satisfie	NOUN
ejpam-6974	72	77	(	(	PUNCT
ejpam-6974	72	78	bg1	bg1	PROPN
ejpam-6974	72	79	):	):	PUNCT
ejpam-6974	72	80	x∗x	x∗x	PUNCT
ejpam-6974	72	81	=	=	SYM
ejpam-6974	72	82	x	x	SYM
ejpam-6974	72	83	◦	◦	NOUN
ejpam-6974	72	84	x	x	SYM
ejpam-6974	72	85	=	=	SYM
ejpam-6974	72	86	1	1	NUM
ejpam-6974	72	87	by	by	ADP
ejpam-6974	72	88	(	(	PUNCT
ejpam-6974	72	89	dbg1	dbg1	ADJ
ejpam-6974	72	90	)	)	PUNCT
ejpam-6974	72	91	,	,	PUNCT
ejpam-6974	72	92	(	(	PUNCT
ejpam-6974	72	93	bg2	bg2	NOUN
ejpam-6974	72	94	):	):	PUNCT
ejpam-6974	72	95	x∗1	x∗1	PROPN
ejpam-6974	72	96	=	=	SYM
ejpam-6974	73	1	1	1	NUM
ejpam-6974	73	2	◦	◦	NOUN
ejpam-6974	73	3	x	x	SYM
ejpam-6974	73	4	=	=	NOUN
ejpam-6974	73	5	x	x	SYM
ejpam-6974	73	6	by	by	ADP
ejpam-6974	73	7	(	(	PUNCT
ejpam-6974	73	8	dbg2	dbg2	PROPN
ejpam-6974	73	9	)	)	PUNCT
ejpam-6974	73	10	,	,	PUNCT
ejpam-6974	73	11	and	and	CCONJ
ejpam-6974	73	12	(	(	PUNCT
ejpam-6974	73	13	bg3	bg3	PROPN
ejpam-6974	73	14	):	):	PUNCT
ejpam-6974	73	15	(	(	PUNCT
ejpam-6974	73	16	x∗y)∗	x∗y)∗	PROPN
ejpam-6974	73	17	(	(	PUNCT
ejpam-6974	73	18	1∗y	1∗y	NUM
ejpam-6974	73	19	)	)	PUNCT
ejpam-6974	73	20	=	=	PUNCT
ejpam-6974	73	21	(	(	PUNCT
ejpam-6974	73	22	1∗y	1∗y	NUM
ejpam-6974	73	23	)	)	PUNCT
ejpam-6974	73	24	◦	◦	NOUN
ejpam-6974	73	25	(	(	PUNCT
ejpam-6974	73	26	x∗y	x∗y	X
ejpam-6974	73	27	)	)	PUNCT
ejpam-6974	73	28	=	=	SYM
ejpam-6974	73	29	(	(	PUNCT
ejpam-6974	73	30	y	y	PROPN
ejpam-6974	73	31	◦	◦	NOUN
ejpam-6974	73	32	1	1	NUM
ejpam-6974	73	33	)	)	PUNCT
ejpam-6974	73	34	◦	◦	NOUN
ejpam-6974	73	35	(	(	PUNCT
ejpam-6974	73	36	y	y	PROPN
ejpam-6974	73	37	◦	◦	NOUN
ejpam-6974	73	38	x	x	NOUN
ejpam-6974	73	39	)	)	PUNCT
ejpam-6974	73	40	=	=	PUNCT
ejpam-6974	73	41	x	x	PUNCT
ejpam-6974	73	42	by	by	ADP
ejpam-6974	73	43	(	(	PUNCT
ejpam-6974	73	44	dbg3	dbg3	PROPN
ejpam-6974	73	45	)	)	PUNCT
ejpam-6974	73	46	.	.	PUNCT
ejpam-6974	74	1	thus	thus	ADV
ejpam-6974	74	2	,	,	PUNCT
ejpam-6974	74	3	(	(	PUNCT
ejpam-6974	74	4	x	x	X
ejpam-6974	74	5	,	,	PUNCT
ejpam-6974	74	6	∗	∗	NOUN
ejpam-6974	74	7	,	,	PUNCT
ejpam-6974	74	8	1	1	NUM
ejpam-6974	74	9	)	)	PUNCT
ejpam-6974	74	10	is	be	AUX
ejpam-6974	74	11	a	a	DET
ejpam-6974	74	12	bg	bg	NOUN
ejpam-6974	74	13	-	-	NOUN
ejpam-6974	74	14	algebra	algebra	NOUN
ejpam-6974	74	15	where	where	SCONJ
ejpam-6974	74	16	1	1	NUM
ejpam-6974	74	17	acts	act	VERB
ejpam-6974	74	18	as	as	ADP
ejpam-6974	74	19	the	the	DET
ejpam-6974	74	20	constant	constant	ADJ
ejpam-6974	74	21	element	element	NOUN
ejpam-6974	74	22	.	.	PUNCT
ejpam-6974	74	23	example	example	NOUN
ejpam-6974	75	1	7	7	NUM
ejpam-6974	75	2	.	.	X
ejpam-6974	75	3	consider	consider	VERB
ejpam-6974	75	4	the	the	DET
ejpam-6974	75	5	bg	bg	NOUN
ejpam-6974	75	6	-	-	NOUN
ejpam-6974	75	7	algebra	algebra	PROPN
ejpam-6974	75	8	(	(	PUNCT
ejpam-6974	75	9	x	x	X
ejpam-6974	75	10	,	,	PUNCT
ejpam-6974	75	11	∗	∗	NOUN
ejpam-6974	75	12	,	,	PUNCT
ejpam-6974	75	13	1	1	NUM
ejpam-6974	75	14	)	)	PUNCT
ejpam-6974	75	15	in	in	ADP
ejpam-6974	75	16	example	example	NOUN
ejpam-6974	75	17	6	6	NUM
ejpam-6974	75	18	where	where	SCONJ
ejpam-6974	75	19	x	x	X
ejpam-6974	75	20	=	=	PRON
ejpam-6974	75	21	{	{	PUNCT
ejpam-6974	75	22	1	1	NUM
ejpam-6974	75	23	,	,	PUNCT
ejpam-6974	75	24	a	a	DET
ejpam-6974	75	25	,	,	PUNCT
ejpam-6974	75	26	b	b	NOUN
ejpam-6974	75	27	,	,	PUNCT
ejpam-6974	75	28	c	c	NOUN
ejpam-6974	75	29	,	,	PUNCT
ejpam-6974	75	30	d	d	NOUN
ejpam-6974	75	31	,	,	PUNCT
ejpam-6974	75	32	e	e	NOUN
ejpam-6974	75	33	}	}	PUNCT
ejpam-6974	75	34	.	.	PUNCT
ejpam-6974	76	1	let	let	VERB
ejpam-6974	76	2	“	"	PUNCT
ejpam-6974	76	3	◦	◦	VERB
ejpam-6974	76	4	”	"	PUNCT
ejpam-6974	76	5	be	be	AUX
ejpam-6974	76	6	a	a	DET
ejpam-6974	76	7	binary	binary	ADJ
ejpam-6974	76	8	operation	operation	NOUN
ejpam-6974	76	9	where	where	SCONJ
ejpam-6974	76	10	x	x	X
ejpam-6974	76	11	◦	◦	NOUN
ejpam-6974	76	12	y	y	NOUN
ejpam-6974	76	13	=	=	SYM
ejpam-6974	76	14	y	y	PROPN
ejpam-6974	76	15	∗	∗	NOUN
ejpam-6974	76	16	x	x	PUNCT
ejpam-6974	77	1	for	for	ADP
ejpam-6974	77	2	all	all	DET
ejpam-6974	77	3	x	x	NOUN
ejpam-6974	77	4	,	,	PUNCT
ejpam-6974	77	5	y	y	PROPN
ejpam-6974	77	6	∈	∈	PROPN
ejpam-6974	77	7	x.	x.	NOUN
ejpam-6974	77	8	then	then	ADV
ejpam-6974	77	9	the	the	DET
ejpam-6974	77	10	cayley	cayley	ADJ
ejpam-6974	77	11	table	table	NOUN
ejpam-6974	77	12	of	of	ADP
ejpam-6974	77	13	(	(	PUNCT
ejpam-6974	77	14	x	x	NOUN
ejpam-6974	77	15	,	,	PUNCT
ejpam-6974	77	16	◦	◦	NOUN
ejpam-6974	77	17	,	,	PUNCT
ejpam-6974	77	18	1	1	NUM
ejpam-6974	77	19	)	)	PUNCT
ejpam-6974	77	20	is	be	AUX
ejpam-6974	77	21	the	the	DET
ejpam-6974	77	22	same	same	ADJ
ejpam-6974	77	23	as	as	ADP
ejpam-6974	77	24	the	the	DET
ejpam-6974	77	25	cayley	cayley	ADJ
ejpam-6974	77	26	table	table	NOUN
ejpam-6974	77	27	in	in	ADP
ejpam-6974	77	28	3	3	NUM
ejpam-6974	77	29	and	and	CCONJ
ejpam-6974	77	30	so	so	ADV
ejpam-6974	77	31	(	(	PUNCT
ejpam-6974	77	32	x	x	NOUN
ejpam-6974	77	33	,	,	PUNCT
ejpam-6974	77	34	◦	◦	NOUN
ejpam-6974	77	35	,	,	PUNCT
ejpam-6974	77	36	1	1	NUM
ejpam-6974	77	37	)	)	PUNCT
ejpam-6974	77	38	is	be	AUX
ejpam-6974	77	39	a	a	DET
ejpam-6974	77	40	dual	dual	ADJ
ejpam-6974	77	41	bg	bg	NOUN
ejpam-6974	77	42	-	-	NOUN
ejpam-6974	77	43	algebra	algebra	NOUN
ejpam-6974	77	44	.	.	PUNCT
ejpam-6974	78	1	every	every	DET
ejpam-6974	78	2	dual	dual	ADJ
ejpam-6974	78	3	bg	bg	NOUN
ejpam-6974	78	4	-	-	PUNCT
ejpam-6974	78	5	algebra	algebra	PROPN
ejpam-6974	78	6	corresponds	correspond	VERB
ejpam-6974	78	7	to	to	ADP
ejpam-6974	78	8	a	a	DET
ejpam-6974	78	9	bg	bg	NOUN
ejpam-6974	78	10	-	-	NOUN
ejpam-6974	78	11	algebra	algebra	NOUN
ejpam-6974	78	12	by	by	ADP
ejpam-6974	78	13	commuting	commute	VERB
ejpam-6974	78	14	the	the	DET
ejpam-6974	78	15	operation	operation	NOUN
ejpam-6974	78	16	.	.	PUNCT
ejpam-6974	79	1	this	this	PRON
ejpam-6974	79	2	is	be	AUX
ejpam-6974	79	3	formalized	formalize	VERB
ejpam-6974	79	4	in	in	ADP
ejpam-6974	79	5	the	the	DET
ejpam-6974	79	6	next	next	ADJ
ejpam-6974	79	7	proposition	proposition	NOUN
ejpam-6974	79	8	.	.	PUNCT
ejpam-6974	80	1	proposition	proposition	NOUN
ejpam-6974	80	2	1	1	NUM
ejpam-6974	80	3	.	.	PUNCT
ejpam-6974	81	1	let	let	AUX
ejpam-6974	81	2	(	(	PUNCT
ejpam-6974	81	3	x	x	NOUN
ejpam-6974	81	4	,	,	PUNCT
ejpam-6974	81	5	◦	◦	NOUN
ejpam-6974	81	6	,	,	PUNCT
ejpam-6974	81	7	1	1	NUM
ejpam-6974	81	8	)	)	PUNCT
ejpam-6974	81	9	be	be	AUX
ejpam-6974	81	10	a	a	DET
ejpam-6974	81	11	dual	dual	ADJ
ejpam-6974	81	12	bg	bg	NOUN
ejpam-6974	81	13	-	-	NOUN
ejpam-6974	81	14	algebra	algebra	PROPN
ejpam-6974	81	15	.	.	PUNCT
ejpam-6974	82	1	then	then	ADV
ejpam-6974	82	2	(	(	PUNCT
ejpam-6974	82	3	x	x	X
ejpam-6974	82	4	,	,	PUNCT
ejpam-6974	82	5	∗	∗	NOUN
ejpam-6974	82	6	,	,	PUNCT
ejpam-6974	82	7	1	1	NUM
ejpam-6974	82	8	)	)	PUNCT
ejpam-6974	82	9	is	be	AUX
ejpam-6974	82	10	a	a	DET
ejpam-6974	82	11	bg	bg	NOUN
ejpam-6974	82	12	-	-	NOUN
ejpam-6974	82	13	algebra	algebra	NOUN
ejpam-6974	82	14	where	where	SCONJ
ejpam-6974	82	15	x	x	PUNCT
ejpam-6974	82	16	∗	∗	VERB
ejpam-6974	82	17	y	y	NOUN
ejpam-6974	82	18	=	=	SYM
ejpam-6974	82	19	y	y	PROPN
ejpam-6974	82	20	◦	◦	NOUN
ejpam-6974	82	21	x	x	PUNCT
ejpam-6974	82	22	for	for	ADP
ejpam-6974	82	23	all	all	DET
ejpam-6974	82	24	x	x	NOUN
ejpam-6974	82	25	,	,	PUNCT
ejpam-6974	82	26	y	y	PROPN
ejpam-6974	82	27	∈	∈	PROPN
ejpam-6974	82	28	x	x	X
ejpam-6974	82	29	and	and	CCONJ
ejpam-6974	82	30	1	1	NUM
ejpam-6974	82	31	corresponds	correspond	NOUN
ejpam-6974	82	32	to	to	ADP
ejpam-6974	82	33	the	the	DET
ejpam-6974	82	34	constant	constant	ADJ
ejpam-6974	82	35	element	element	NOUN
ejpam-6974	82	36	.	.	PUNCT
ejpam-6974	83	1	c.m	c.m	PROPN
ejpam-6974	83	2	.	.	PROPN
ejpam-6974	83	3	chan	chan	PROPN
ejpam-6974	83	4	,	,	PUNCT
ejpam-6974	83	5	k.	k.	PROPN
ejpam-6974	83	6	fuentes	fuentes	PROPN
ejpam-6974	83	7	/	/	SYM
ejpam-6974	83	8	eur	eur	PROPN
ejpam-6974	83	9	.	.	PUNCT
ejpam-6974	84	1	j.	j.	PROPN
ejpam-6974	84	2	pure	pure	PROPN
ejpam-6974	84	3	appl	appl	PROPN
ejpam-6974	84	4	.	.	PROPN
ejpam-6974	84	5	math	math	PROPN
ejpam-6974	84	6	,	,	PUNCT
ejpam-6974	84	7	18	18	NUM
ejpam-6974	84	8	(	(	PUNCT
ejpam-6974	84	9	4	4	NUM
ejpam-6974	84	10	)	)	PUNCT
ejpam-6974	84	11	(	(	PUNCT
ejpam-6974	84	12	2025	2025	NUM
ejpam-6974	84	13	)	)	PUNCT
ejpam-6974	84	14	,	,	PUNCT
ejpam-6974	84	15	6974	6974	NUM
ejpam-6974	84	16	5	5	NUM
ejpam-6974	84	17	of	of	ADP
ejpam-6974	84	18	16	16	NUM
ejpam-6974	84	19	proof	proof	NOUN
ejpam-6974	84	20	.	.	PUNCT
ejpam-6974	85	1	suppose	suppose	VERB
ejpam-6974	85	2	(	(	PUNCT
ejpam-6974	85	3	x	x	X
ejpam-6974	85	4	,	,	PUNCT
ejpam-6974	85	5	◦	◦	NOUN
ejpam-6974	85	6	,	,	PUNCT
ejpam-6974	85	7	1	1	NUM
ejpam-6974	85	8	)	)	PUNCT
ejpam-6974	85	9	is	be	AUX
ejpam-6974	85	10	a	a	DET
ejpam-6974	85	11	dual	dual	ADJ
ejpam-6974	85	12	bg	bg	NOUN
ejpam-6974	85	13	-	-	NOUN
ejpam-6974	85	14	algebra	algebra	PROPN
ejpam-6974	85	15	and	and	CCONJ
ejpam-6974	85	16	define	define	VERB
ejpam-6974	85	17	“	"	PUNCT
ejpam-6974	85	18	∗	∗	NOUN
ejpam-6974	85	19	”	"	PUNCT
ejpam-6974	85	20	as	as	SCONJ
ejpam-6974	85	21	follows	follow	VERB
ejpam-6974	85	22	:	:	PUNCT
ejpam-6974	85	23	x	x	X
ejpam-6974	85	24	∗	∗	NOUN
ejpam-6974	85	25	y	y	NOUN
ejpam-6974	85	26	=	=	SYM
ejpam-6974	85	27	y	y	PROPN
ejpam-6974	85	28	◦	◦	NOUN
ejpam-6974	85	29	x	x	PUNCT
ejpam-6974	85	30	for	for	ADP
ejpam-6974	85	31	all	all	DET
ejpam-6974	85	32	x	x	NOUN
ejpam-6974	85	33	,	,	PUNCT
ejpam-6974	85	34	y	y	PROPN
ejpam-6974	85	35	in	in	ADP
ejpam-6974	85	36	x.	x.	PROPN
ejpam-6974	85	37	then	then	ADV
ejpam-6974	85	38	(	(	PUNCT
ejpam-6974	85	39	x	x	NOUN
ejpam-6974	85	40	,	,	PUNCT
ejpam-6974	85	41	◦	◦	NOUN
ejpam-6974	85	42	,	,	PUNCT
ejpam-6974	85	43	1	1	X
ejpam-6974	85	44	)	)	PUNCT
ejpam-6974	85	45	satisfies	satisfie	NOUN
ejpam-6974	85	46	(	(	PUNCT
ejpam-6974	85	47	bg1	bg1	PROPN
ejpam-6974	85	48	):	):	PUNCT
ejpam-6974	85	49	x	x	X
ejpam-6974	85	50	∗	∗	NOUN
ejpam-6974	85	51	x	x	X
ejpam-6974	85	52	=	=	PUNCT
ejpam-6974	85	53	x	x	PUNCT
ejpam-6974	85	54	◦	◦	NOUN
ejpam-6974	85	55	x	x	SYM
ejpam-6974	85	56	=	=	SYM
ejpam-6974	85	57	1	1	NUM
ejpam-6974	85	58	by	by	ADP
ejpam-6974	85	59	(	(	PUNCT
ejpam-6974	85	60	dbg1	dbg1	ADJ
ejpam-6974	85	61	)	)	PUNCT
ejpam-6974	85	62	,	,	PUNCT
ejpam-6974	85	63	(	(	PUNCT
ejpam-6974	85	64	bg2	bg2	NOUN
ejpam-6974	85	65	):	):	PUNCT
ejpam-6974	85	66	x∗1	x∗1	PROPN
ejpam-6974	85	67	=	=	SYM
ejpam-6974	86	1	1	1	NUM
ejpam-6974	86	2	◦	◦	NOUN
ejpam-6974	86	3	x	x	SYM
ejpam-6974	86	4	=	=	NOUN
ejpam-6974	86	5	x	x	SYM
ejpam-6974	86	6	by	by	ADP
ejpam-6974	86	7	(	(	PUNCT
ejpam-6974	86	8	dbg2	dbg2	PROPN
ejpam-6974	86	9	)	)	PUNCT
ejpam-6974	86	10	,	,	PUNCT
ejpam-6974	86	11	and	and	CCONJ
ejpam-6974	86	12	(	(	PUNCT
ejpam-6974	86	13	bg3	bg3	PROPN
ejpam-6974	86	14	):	):	PUNCT
ejpam-6974	86	15	(	(	PUNCT
ejpam-6974	86	16	x∗y)∗(1∗y	x∗y)∗(1∗y	NUM
ejpam-6974	86	17	)	)	PUNCT
ejpam-6974	86	18	=	=	SYM
ejpam-6974	86	19	(	(	PUNCT
ejpam-6974	86	20	1∗y)	1∗y)	NUM
ejpam-6974	86	21	◦	◦	NOUN
ejpam-6974	86	22	(x∗y	(x∗y	PUNCT
ejpam-6974	86	23	)	)	PUNCT
ejpam-6974	86	24	=	=	SYM
ejpam-6974	86	25	(	(	PUNCT
ejpam-6974	86	26	y	y	NOUN
ejpam-6974	86	27	◦	◦	NOUN
ejpam-6974	86	28	1)	1)	NUM
ejpam-6974	86	29	◦	◦	NOUN
ejpam-6974	86	30	(y	(y	NOUN
ejpam-6974	86	31	◦	◦	NOUN
ejpam-6974	86	32	x	x	NOUN
ejpam-6974	86	33	)	)	PUNCT
ejpam-6974	86	34	=	=	PUNCT
ejpam-6974	86	35	x	x	PUNCT
ejpam-6974	86	36	by	by	ADP
ejpam-6974	86	37	(	(	PUNCT
ejpam-6974	86	38	dbg3	dbg3	PROPN
ejpam-6974	86	39	)	)	PUNCT
ejpam-6974	86	40	.	.	PUNCT
ejpam-6974	87	1	thus	thus	ADV
ejpam-6974	87	2	,	,	PUNCT
ejpam-6974	87	3	(	(	PUNCT
ejpam-6974	87	4	x	x	X
ejpam-6974	87	5	,	,	PUNCT
ejpam-6974	87	6	∗	∗	NOUN
ejpam-6974	87	7	,	,	PUNCT
ejpam-6974	87	8	1	1	NUM
ejpam-6974	87	9	)	)	PUNCT
ejpam-6974	87	10	is	be	AUX
ejpam-6974	87	11	a	a	DET
ejpam-6974	87	12	bg	bg	NOUN
ejpam-6974	87	13	-	-	PUNCT
ejpam-6974	87	14	algebra	algebra	PROPN
ejpam-6974	87	15	.	.	PUNCT
ejpam-6974	88	1	example	example	NOUN
ejpam-6974	88	2	8	8	NUM
ejpam-6974	88	3	.	.	PUNCT
ejpam-6974	89	1	the	the	DET
ejpam-6974	89	2	dual	dual	ADJ
ejpam-6974	89	3	bg	bg	NOUN
ejpam-6974	89	4	-	-	PUNCT
ejpam-6974	89	5	algebra	algebra	PROPN
ejpam-6974	89	6	(	(	PUNCT
ejpam-6974	89	7	r\{0	r\{0	NOUN
ejpam-6974	89	8	}	}	PUNCT
ejpam-6974	89	9	,	,	PUNCT
ejpam-6974	89	10	◦	◦	NOUN
ejpam-6974	89	11	,	,	PUNCT
ejpam-6974	89	12	1	1	NUM
ejpam-6974	89	13	)	)	PUNCT
ejpam-6974	89	14	where	where	SCONJ
ejpam-6974	89	15	x	x	PART
ejpam-6974	89	16	◦	◦	NOUN
ejpam-6974	89	17	y	y	NOUN
ejpam-6974	89	18	=	=	SYM
ejpam-6974	89	19	y	y	PROPN
ejpam-6974	89	20	x	x	PUNCT
ejpam-6974	89	21	for	for	ADP
ejpam-6974	89	22	all	all	DET
ejpam-6974	89	23	x	x	NOUN
ejpam-6974	89	24	,	,	PUNCT
ejpam-6974	89	25	y	y	PROPN
ejpam-6974	89	26	in	in	ADP
ejpam-6974	89	27	r\{0	r\{0	PROPN
ejpam-6974	89	28	}	}	PUNCT
ejpam-6974	89	29	from	from	ADP
ejpam-6974	89	30	example	example	NOUN
ejpam-6974	89	31	4	4	NUM
ejpam-6974	89	32	is	be	AUX
ejpam-6974	89	33	not	not	PART
ejpam-6974	89	34	a	a	DET
ejpam-6974	89	35	bg	bg	NOUN
ejpam-6974	89	36	-	-	NOUN
ejpam-6974	89	37	algebra	algebra	NOUN
ejpam-6974	89	38	since	since	SCONJ
ejpam-6974	89	39	x	x	PART
ejpam-6974	89	40	◦	◦	NOUN
ejpam-6974	89	41	1	1	NUM
ejpam-6974	89	42	=	=	SYM
ejpam-6974	89	43	1	1	NUM
ejpam-6974	89	44	x	x	SYM
ejpam-6974	89	45	̸=	̸=	PROPN
ejpam-6974	89	46	x	x	NUM
ejpam-6974	89	47	,	,	PUNCT
ejpam-6974	89	48	failing	fail	VERB
ejpam-6974	89	49	to	to	PART
ejpam-6974	89	50	satisfy	satisfy	VERB
ejpam-6974	89	51	(	(	PUNCT
ejpam-6974	89	52	bg2	bg2	NOUN
ejpam-6974	89	53	)	)	PUNCT
ejpam-6974	89	54	.	.	PUNCT
ejpam-6974	90	1	by	by	ADP
ejpam-6974	90	2	example	example	NOUN
ejpam-6974	90	3	8	8	NUM
ejpam-6974	90	4	,	,	PUNCT
ejpam-6974	90	5	there	there	PRON
ejpam-6974	90	6	exists	exist	VERB
ejpam-6974	90	7	a	a	DET
ejpam-6974	90	8	dual	dual	ADJ
ejpam-6974	90	9	bg	bg	NOUN
ejpam-6974	90	10	-	-	NOUN
ejpam-6974	90	11	algebra	algebra	NOUN
ejpam-6974	90	12	that	that	PRON
ejpam-6974	90	13	is	be	AUX
ejpam-6974	90	14	not	not	PART
ejpam-6974	90	15	a	a	DET
ejpam-6974	90	16	bg	bg	NOUN
ejpam-6974	90	17	-	-	PUNCT
ejpam-6974	90	18	algebra	algebra	PROPN
ejpam-6974	90	19	,	,	PUNCT
ejpam-6974	90	20	which	which	PRON
ejpam-6974	90	21	leads	lead	VERB
ejpam-6974	90	22	to	to	ADP
ejpam-6974	90	23	the	the	DET
ejpam-6974	90	24	next	next	ADJ
ejpam-6974	90	25	remark	remark	NOUN
ejpam-6974	90	26	.	.	PUNCT
ejpam-6974	91	1	remark	remark	PROPN
ejpam-6974	91	2	1	1	NUM
ejpam-6974	91	3	.	.	PUNCT
ejpam-6974	92	1	not	not	PART
ejpam-6974	92	2	every	every	DET
ejpam-6974	92	3	dual	dual	ADJ
ejpam-6974	92	4	bg	bg	NOUN
ejpam-6974	92	5	-	-	PUNCT
ejpam-6974	92	6	algebra	algebra	PROPN
ejpam-6974	92	7	is	be	AUX
ejpam-6974	92	8	a	a	DET
ejpam-6974	92	9	bg	bg	NOUN
ejpam-6974	92	10	-	-	PUNCT
ejpam-6974	92	11	algebra	algebra	PROPN
ejpam-6974	92	12	.	.	PUNCT
ejpam-6974	92	13	example	example	NOUN
ejpam-6974	93	1	9	9	NUM
ejpam-6974	93	2	.	.	PUNCT
ejpam-6974	94	1	let	let	VERB
ejpam-6974	94	2	x	x	PUNCT
ejpam-6974	94	3	=	=	PRON
ejpam-6974	94	4	{	{	PUNCT
ejpam-6974	94	5	1	1	NUM
ejpam-6974	94	6	,	,	PUNCT
ejpam-6974	94	7	a	a	DET
ejpam-6974	94	8	,	,	PUNCT
ejpam-6974	94	9	b	b	NOUN
ejpam-6974	94	10	,	,	PUNCT
ejpam-6974	94	11	c	c	NOUN
ejpam-6974	94	12	}	}	PUNCT
ejpam-6974	94	13	.	.	PUNCT
ejpam-6974	95	1	consider	consider	VERB
ejpam-6974	95	2	the	the	DET
ejpam-6974	95	3	following	follow	VERB
ejpam-6974	95	4	cayley	cayley	ADJ
ejpam-6974	95	5	table	table	NOUN
ejpam-6974	95	6	for	for	ADP
ejpam-6974	95	7	the	the	DET
ejpam-6974	95	8	binary	binary	ADJ
ejpam-6974	95	9	operation	operation	NOUN
ejpam-6974	95	10	“	"	PUNCT
ejpam-6974	95	11	◦	◦	NOUN
ejpam-6974	95	12	”	"	PUNCT
ejpam-6974	95	13	.	.	PUNCT
ejpam-6974	96	1	then	then	ADV
ejpam-6974	96	2	(	(	PUNCT
ejpam-6974	96	3	x	x	X
ejpam-6974	96	4	,	,	PUNCT
ejpam-6974	96	5	◦	◦	NOUN
ejpam-6974	96	6	,	,	PUNCT
ejpam-6974	96	7	1	1	NUM
ejpam-6974	96	8	)	)	PUNCT
ejpam-6974	96	9	is	be	AUX
ejpam-6974	96	10	a	a	DET
ejpam-6974	96	11	dual	dual	ADJ
ejpam-6974	96	12	bg	bg	NOUN
ejpam-6974	96	13	-	-	NOUN
ejpam-6974	96	14	algebra	algebra	PROPN
ejpam-6974	96	15	.	.	PUNCT
ejpam-6974	97	1	note	note	VERB
ejpam-6974	97	2	that	that	SCONJ
ejpam-6974	97	3	for	for	ADP
ejpam-6974	97	4	any	any	DET
ejpam-6974	97	5	x	x	NOUN
ejpam-6974	97	6	,	,	PUNCT
ejpam-6974	97	7	y	y	PROPN
ejpam-6974	97	8	∈	∈	PROPN
ejpam-6974	97	9	x	x	X
ejpam-6974	97	10	,	,	PUNCT
ejpam-6974	97	11	x	x	PROPN
ejpam-6974	97	12	◦	◦	NOUN
ejpam-6974	97	13	y	y	NOUN
ejpam-6974	97	14	=	=	SYM
ejpam-6974	97	15	y	y	PROPN
ejpam-6974	97	16	◦	◦	NOUN
ejpam-6974	97	17	x.	x.	NOUN
ejpam-6974	97	18	table	table	NOUN
ejpam-6974	97	19	6	6	NUM
ejpam-6974	97	20	:	:	PUNCT
ejpam-6974	97	21	cayley	cayley	ADJ
ejpam-6974	97	22	table	table	NOUN
ejpam-6974	97	23	of	of	ADP
ejpam-6974	97	24	the	the	DET
ejpam-6974	97	25	dual	dual	ADJ
ejpam-6974	97	26	bg	bg	NOUN
ejpam-6974	97	27	-	-	NOUN
ejpam-6974	97	28	algebra	algebra	PROPN
ejpam-6974	97	29	(	(	PUNCT
ejpam-6974	97	30	x	x	NOUN
ejpam-6974	97	31	,	,	PUNCT
ejpam-6974	97	32	◦	◦	NOUN
ejpam-6974	97	33	,	,	PUNCT
ejpam-6974	97	34	1	1	X
ejpam-6974	97	35	)	)	PUNCT
ejpam-6974	97	36	◦	◦	NOUN
ejpam-6974	97	37	1	1	NUM
ejpam-6974	97	38	a	a	DET
ejpam-6974	97	39	b	b	NOUN
ejpam-6974	97	40	c	c	NOUN
ejpam-6974	97	41	1	1	NUM
ejpam-6974	97	42	1	1	NUM
ejpam-6974	97	43	a	a	DET
ejpam-6974	97	44	b	b	NOUN
ejpam-6974	97	45	c	c	ADP
ejpam-6974	97	46	a	a	DET
ejpam-6974	97	47	a	a	DET
ejpam-6974	97	48	1	1	NUM
ejpam-6974	97	49	c	c	NOUN
ejpam-6974	97	50	b	b	PROPN
ejpam-6974	97	51	b	b	PROPN
ejpam-6974	97	52	b	b	PROPN
ejpam-6974	97	53	c	c	PROPN
ejpam-6974	97	54	1	1	NUM
ejpam-6974	97	55	a	a	DET
ejpam-6974	97	56	c	c	NOUN
ejpam-6974	97	57	c	c	NOUN
ejpam-6974	97	58	b	b	PROPN
ejpam-6974	97	59	a	a	DET
ejpam-6974	97	60	1	1	NUM
ejpam-6974	97	61	now	now	ADV
ejpam-6974	97	62	,	,	PUNCT
ejpam-6974	97	63	let	let	VERB
ejpam-6974	97	64	x	x	PRON
ejpam-6974	97	65	∗	∗	VERB
ejpam-6974	97	66	y	y	NOUN
ejpam-6974	97	67	=	=	SYM
ejpam-6974	97	68	y	y	PROPN
ejpam-6974	97	69	◦	◦	NOUN
ejpam-6974	97	70	x	x	PUNCT
ejpam-6974	97	71	for	for	ADP
ejpam-6974	97	72	a	a	DET
ejpam-6974	97	73	binary	binary	ADJ
ejpam-6974	97	74	operation	operation	NOUN
ejpam-6974	97	75	“	"	PUNCT
ejpam-6974	97	76	∗	∗	NOUN
ejpam-6974	97	77	”	"	PUNCT
ejpam-6974	97	78	where	where	SCONJ
ejpam-6974	97	79	x	x	X
ejpam-6974	97	80	,	,	PUNCT
ejpam-6974	97	81	y	y	PROPN
ejpam-6974	97	82	in	in	ADP
ejpam-6974	97	83	x.	x.	PROPN
ejpam-6974	97	84	then	then	ADV
ejpam-6974	97	85	(	(	PUNCT
ejpam-6974	97	86	x	x	X
ejpam-6974	97	87	,	,	PUNCT
ejpam-6974	97	88	∗	∗	NOUN
ejpam-6974	97	89	,	,	PUNCT
ejpam-6974	97	90	1	1	NUM
ejpam-6974	97	91	)	)	PUNCT
ejpam-6974	97	92	is	be	AUX
ejpam-6974	97	93	a	a	DET
ejpam-6974	97	94	bg	bg	NOUN
ejpam-6974	97	95	-	-	PUNCT
ejpam-6974	97	96	algebra	algebra	NOUN
ejpam-6974	97	97	by	by	ADP
ejpam-6974	97	98	proposition	proposition	NOUN
ejpam-6974	97	99	1	1	NUM
ejpam-6974	97	100	.	.	PUNCT
ejpam-6974	98	1	because	because	SCONJ
ejpam-6974	98	2	(	(	PUNCT
ejpam-6974	98	3	x	x	X
ejpam-6974	98	4	,	,	PUNCT
ejpam-6974	98	5	◦	◦	NOUN
ejpam-6974	98	6	,	,	PUNCT
ejpam-6974	98	7	1	1	NUM
ejpam-6974	98	8	)	)	PUNCT
ejpam-6974	98	9	satisfies	satisfie	NOUN
ejpam-6974	98	10	x	x	VERB
ejpam-6974	98	11	◦	◦	VERB
ejpam-6974	98	12	y	y	NOUN
ejpam-6974	98	13	=	=	SYM
ejpam-6974	98	14	y	y	PROPN
ejpam-6974	98	15	◦	◦	NOUN
ejpam-6974	98	16	x	x	PUNCT
ejpam-6974	98	17	for	for	ADP
ejpam-6974	98	18	all	all	DET
ejpam-6974	98	19	x	x	NOUN
ejpam-6974	98	20	,	,	PUNCT
ejpam-6974	98	21	y	y	PROPN
ejpam-6974	98	22	∈	∈	PROPN
ejpam-6974	98	23	x	x	AUX
ejpam-6974	98	24	,	,	PUNCT
ejpam-6974	98	25	it	it	PRON
ejpam-6974	98	26	follows	follow	VERB
ejpam-6974	98	27	that	that	SCONJ
ejpam-6974	98	28	it	it	PRON
ejpam-6974	98	29	is	be	AUX
ejpam-6974	98	30	also	also	ADV
ejpam-6974	98	31	a	a	DET
ejpam-6974	98	32	bg	bg	NOUN
ejpam-6974	98	33	-	-	PUNCT
ejpam-6974	98	34	algebra	algebra	NOUN
ejpam-6974	98	35	.	.	PUNCT
ejpam-6974	99	1	thus	thus	ADV
ejpam-6974	99	2	,	,	PUNCT
ejpam-6974	99	3	there	there	PRON
ejpam-6974	99	4	exists	exist	VERB
ejpam-6974	99	5	a	a	DET
ejpam-6974	99	6	dual	dual	ADJ
ejpam-6974	99	7	bg	bg	NOUN
ejpam-6974	99	8	-	-	NOUN
ejpam-6974	99	9	algebra	algebra	NOUN
ejpam-6974	99	10	that	that	PRON
ejpam-6974	99	11	is	be	AUX
ejpam-6974	99	12	a	a	DET
ejpam-6974	99	13	bg	bg	NOUN
ejpam-6974	99	14	-	-	NOUN
ejpam-6974	99	15	algebra	algebra	NOUN
ejpam-6974	99	16	at	at	ADP
ejpam-6974	99	17	the	the	DET
ejpam-6974	99	18	same	same	ADJ
ejpam-6974	99	19	time	time	NOUN
ejpam-6974	99	20	.	.	PUNCT
ejpam-6974	100	1	this	this	PRON
ejpam-6974	100	2	is	be	AUX
ejpam-6974	100	3	formalized	formalize	VERB
ejpam-6974	100	4	in	in	ADP
ejpam-6974	100	5	the	the	DET
ejpam-6974	100	6	next	next	ADJ
ejpam-6974	100	7	theorem	theorem	PROPN
ejpam-6974	100	8	.	.	PUNCT
ejpam-6974	100	9	theorem	theorem	NOUN
ejpam-6974	100	10	2	2	NUM
ejpam-6974	100	11	.	.	PUNCT
ejpam-6974	101	1	let	let	AUX
ejpam-6974	101	2	(	(	PUNCT
ejpam-6974	101	3	x	x	NOUN
ejpam-6974	101	4	,	,	PUNCT
ejpam-6974	101	5	◦	◦	NOUN
ejpam-6974	101	6	,	,	PUNCT
ejpam-6974	101	7	1	1	NUM
ejpam-6974	101	8	)	)	PUNCT
ejpam-6974	101	9	be	be	AUX
ejpam-6974	101	10	a	a	DET
ejpam-6974	101	11	dual	dual	ADJ
ejpam-6974	101	12	bg	bg	NOUN
ejpam-6974	101	13	-	-	NOUN
ejpam-6974	101	14	algebra	algebra	NOUN
ejpam-6974	101	15	satisfying	satisfying	NOUN
ejpam-6974	101	16	x	x	VERB
ejpam-6974	101	17	◦	◦	NOUN
ejpam-6974	101	18	y	y	NOUN
ejpam-6974	101	19	=	=	SYM
ejpam-6974	101	20	y	y	PROPN
ejpam-6974	101	21	◦	◦	NOUN
ejpam-6974	101	22	x	x	PUNCT
ejpam-6974	101	23	for	for	ADP
ejpam-6974	101	24	all	all	DET
ejpam-6974	101	25	x	x	NOUN
ejpam-6974	101	26	,	,	PUNCT
ejpam-6974	101	27	y	y	PROPN
ejpam-6974	101	28	in	in	ADP
ejpam-6974	101	29	x.	x.	PROPN
ejpam-6974	101	30	then	then	ADV
ejpam-6974	101	31	(	(	PUNCT
ejpam-6974	101	32	x	x	NOUN
ejpam-6974	101	33	,	,	PUNCT
ejpam-6974	101	34	◦	◦	NOUN
ejpam-6974	101	35	,	,	PUNCT
ejpam-6974	101	36	1	1	NUM
ejpam-6974	101	37	)	)	PUNCT
ejpam-6974	101	38	is	be	AUX
ejpam-6974	101	39	also	also	ADV
ejpam-6974	101	40	a	a	DET
ejpam-6974	101	41	bg	bg	NOUN
ejpam-6974	101	42	-	-	PUNCT
ejpam-6974	101	43	algebra	algebra	NOUN
ejpam-6974	101	44	.	.	PUNCT
ejpam-6974	102	1	proof	proof	NOUN
ejpam-6974	102	2	.	.	PUNCT
ejpam-6974	103	1	suppose	suppose	VERB
ejpam-6974	103	2	(	(	PUNCT
ejpam-6974	103	3	x	x	X
ejpam-6974	103	4	,	,	PUNCT
ejpam-6974	103	5	◦	◦	NOUN
ejpam-6974	103	6	,	,	PUNCT
ejpam-6974	103	7	1	1	NUM
ejpam-6974	103	8	)	)	PUNCT
ejpam-6974	103	9	is	be	AUX
ejpam-6974	103	10	a	a	DET
ejpam-6974	103	11	dual	dual	ADJ
ejpam-6974	103	12	bg	bg	NOUN
ejpam-6974	103	13	-	-	NOUN
ejpam-6974	103	14	algebra	algebra	NOUN
ejpam-6974	103	15	where	where	SCONJ
ejpam-6974	103	16	x	x	X
ejpam-6974	103	17	◦	◦	NOUN
ejpam-6974	103	18	y	y	NOUN
ejpam-6974	103	19	=	=	PUNCT
ejpam-6974	103	20	y	y	PROPN
ejpam-6974	103	21	◦	◦	NOUN
ejpam-6974	103	22	x	x	PUNCT
ejpam-6974	103	23	for	for	ADP
ejpam-6974	103	24	all	all	DET
ejpam-6974	103	25	x	x	NOUN
ejpam-6974	103	26	,	,	PUNCT
ejpam-6974	103	27	y	y	PROPN
ejpam-6974	103	28	in	in	ADP
ejpam-6974	103	29	x.	x.	PROPN
ejpam-6974	103	30	then	then	ADV
ejpam-6974	103	31	(	(	PUNCT
ejpam-6974	103	32	x	x	NOUN
ejpam-6974	103	33	,	,	PUNCT
ejpam-6974	103	34	◦	◦	NOUN
ejpam-6974	103	35	,	,	PUNCT
ejpam-6974	103	36	1	1	X
ejpam-6974	103	37	)	)	PUNCT
ejpam-6974	103	38	satisfies	satisfie	NOUN
ejpam-6974	103	39	(	(	PUNCT
ejpam-6974	103	40	bg1	bg1	PROPN
ejpam-6974	103	41	):	):	PUNCT
ejpam-6974	103	42	x	x	PUNCT
ejpam-6974	103	43	◦	◦	NOUN
ejpam-6974	103	44	x	x	SYM
ejpam-6974	103	45	=	=	SYM
ejpam-6974	103	46	1	1	NUM
ejpam-6974	103	47	by	by	ADP
ejpam-6974	103	48	(	(	PUNCT
ejpam-6974	103	49	dbg1	dbg1	ADJ
ejpam-6974	103	50	)	)	PUNCT
ejpam-6974	103	51	,	,	PUNCT
ejpam-6974	103	52	(	(	PUNCT
ejpam-6974	103	53	bg2	bg2	NOUN
ejpam-6974	103	54	):	):	PUNCT
ejpam-6974	103	55	x	x	PUNCT
ejpam-6974	103	56	◦	◦	NOUN
ejpam-6974	103	57	1	1	NUM
ejpam-6974	103	58	=	=	SYM
ejpam-6974	103	59	1	1	NUM
ejpam-6974	103	60	◦	◦	NOUN
ejpam-6974	103	61	x	x	SYM
ejpam-6974	103	62	=	=	NOUN
ejpam-6974	103	63	x	x	SYM
ejpam-6974	103	64	by	by	ADP
ejpam-6974	103	65	(	(	PUNCT
ejpam-6974	103	66	dbg2	dbg2	PROPN
ejpam-6974	103	67	)	)	PUNCT
ejpam-6974	103	68	,	,	PUNCT
ejpam-6974	103	69	and	and	CCONJ
ejpam-6974	103	70	(	(	PUNCT
ejpam-6974	103	71	bg3	bg3	PROPN
ejpam-6974	103	72	):	):	PUNCT
ejpam-6974	103	73	(	(	PUNCT
ejpam-6974	103	74	x	x	SYM
ejpam-6974	103	75	◦	◦	VERB
ejpam-6974	103	76	y	y	NOUN
ejpam-6974	103	77	)	)	PUNCT
ejpam-6974	103	78	◦	◦	NOUN
ejpam-6974	103	79	(	(	PUNCT
ejpam-6974	103	80	1	1	NUM
ejpam-6974	103	81	◦	◦	NOUN
ejpam-6974	103	82	y	y	NOUN
ejpam-6974	103	83	)	)	PUNCT
ejpam-6974	103	84	=	=	PUNCT
ejpam-6974	104	1	(	(	PUNCT
ejpam-6974	104	2	1	1	NUM
ejpam-6974	104	3	◦	◦	NOUN
ejpam-6974	104	4	y	y	NOUN
ejpam-6974	104	5	)	)	PUNCT
ejpam-6974	104	6	◦	◦	NOUN
ejpam-6974	104	7	(	(	PUNCT
ejpam-6974	104	8	x	x	PART
ejpam-6974	104	9	◦	◦	VERB
ejpam-6974	104	10	y	y	NOUN
ejpam-6974	104	11	)	)	PUNCT
ejpam-6974	104	12	=	=	SYM
ejpam-6974	105	1	(	(	PUNCT
ejpam-6974	105	2	y	y	PROPN
ejpam-6974	105	3	◦	◦	NOUN
ejpam-6974	105	4	1	1	NUM
ejpam-6974	105	5	)	)	PUNCT
ejpam-6974	105	6	◦	◦	NOUN
ejpam-6974	105	7	(	(	PUNCT
ejpam-6974	105	8	y	y	PROPN
ejpam-6974	105	9	◦	◦	NOUN
ejpam-6974	105	10	x	x	X
ejpam-6974	105	11	)	)	PUNCT
ejpam-6974	105	12	=	=	PUNCT
ejpam-6974	105	13	x	x	PUNCT
ejpam-6974	105	14	by	by	ADP
ejpam-6974	105	15	(	(	PUNCT
ejpam-6974	105	16	dbg3	dbg3	PROPN
ejpam-6974	105	17	)	)	PUNCT
ejpam-6974	105	18	.	.	PUNCT
ejpam-6974	106	1	thus	thus	ADV
ejpam-6974	106	2	,	,	PUNCT
ejpam-6974	106	3	(	(	PUNCT
ejpam-6974	106	4	x	x	X
ejpam-6974	106	5	,	,	PUNCT
ejpam-6974	106	6	◦	◦	NOUN
ejpam-6974	106	7	,	,	PUNCT
ejpam-6974	106	8	1	1	NUM
ejpam-6974	106	9	)	)	PUNCT
ejpam-6974	106	10	is	be	AUX
ejpam-6974	106	11	also	also	ADV
ejpam-6974	106	12	a	a	DET
ejpam-6974	106	13	bg	bg	NOUN
ejpam-6974	106	14	-	-	PUNCT
ejpam-6974	106	15	algebra	algebra	PROPN
ejpam-6974	106	16	.	.	PUNCT
ejpam-6974	106	17	example	example	NOUN
ejpam-6974	106	18	10	10	NUM
ejpam-6974	106	19	.	.	PUNCT
ejpam-6974	107	1	consider	consider	VERB
ejpam-6974	107	2	the	the	DET
ejpam-6974	107	3	bg	bg	NOUN
ejpam-6974	107	4	-	-	NOUN
ejpam-6974	107	5	algebra	algebra	PROPN
ejpam-6974	107	6	(	(	PUNCT
ejpam-6974	107	7	x	x	X
ejpam-6974	107	8	,	,	PUNCT
ejpam-6974	107	9	∗	∗	NOUN
ejpam-6974	107	10	,	,	PUNCT
ejpam-6974	107	11	0	0	NUM
ejpam-6974	107	12	)	)	PUNCT
ejpam-6974	107	13	in	in	ADP
ejpam-6974	107	14	example	example	NOUN
ejpam-6974	108	1	2	2	X
ejpam-6974	108	2	.	.	PUNCT
ejpam-6974	109	1	this	this	PRON
ejpam-6974	109	2	is	be	AUX
ejpam-6974	109	3	not	not	PART
ejpam-6974	109	4	a	a	DET
ejpam-6974	109	5	dual	dual	ADJ
ejpam-6974	109	6	bgalgebra	bgalgebra	NOUN
ejpam-6974	109	7	because	because	SCONJ
ejpam-6974	109	8	(	(	PUNCT
ejpam-6974	109	9	2	2	NUM
ejpam-6974	109	10	∗	∗	NOUN
ejpam-6974	109	11	0	0	NUM
ejpam-6974	109	12	)	)	PUNCT
ejpam-6974	109	13	∗	∗	NOUN
ejpam-6974	109	14	(	(	PUNCT
ejpam-6974	109	15	2	2	NUM
ejpam-6974	109	16	∗	∗	NOUN
ejpam-6974	109	17	1	1	NUM
ejpam-6974	109	18	)	)	PUNCT
ejpam-6974	109	19	=	=	SYM
ejpam-6974	109	20	2	2	NUM
ejpam-6974	109	21	∗	∗	NOUN
ejpam-6974	109	22	2	2	NUM
ejpam-6974	109	23	=	=	SYM
ejpam-6974	109	24	0	0	NUM
ejpam-6974	110	1	̸=	̸=	PROPN
ejpam-6974	110	2	1	1	NUM
ejpam-6974	110	3	,	,	PUNCT
ejpam-6974	110	4	failing	fail	VERB
ejpam-6974	110	5	to	to	PART
ejpam-6974	110	6	satisfy	satisfy	VERB
ejpam-6974	110	7	(	(	PUNCT
ejpam-6974	110	8	dbg3	dbg3	PROPN
ejpam-6974	110	9	)	)	PUNCT
ejpam-6974	110	10	.	.	PUNCT
ejpam-6974	111	1	by	by	ADP
ejpam-6974	111	2	example	example	NOUN
ejpam-6974	111	3	10	10	NUM
ejpam-6974	111	4	,	,	PUNCT
ejpam-6974	111	5	there	there	PRON
ejpam-6974	111	6	exists	exist	VERB
ejpam-6974	111	7	a	a	DET
ejpam-6974	111	8	bg	bg	NOUN
ejpam-6974	111	9	-	-	PUNCT
ejpam-6974	111	10	algebra	algebra	NOUN
ejpam-6974	111	11	that	that	PRON
ejpam-6974	111	12	is	be	AUX
ejpam-6974	111	13	not	not	PART
ejpam-6974	111	14	a	a	DET
ejpam-6974	111	15	dual	dual	ADJ
ejpam-6974	111	16	bg	bg	NOUN
ejpam-6974	111	17	-	-	NOUN
ejpam-6974	111	18	algebra	algebra	PROPN
ejpam-6974	111	19	,	,	PUNCT
ejpam-6974	111	20	which	which	PRON
ejpam-6974	111	21	leads	lead	VERB
ejpam-6974	111	22	to	to	ADP
ejpam-6974	111	23	the	the	DET
ejpam-6974	111	24	next	next	ADJ
ejpam-6974	111	25	remark	remark	NOUN
ejpam-6974	111	26	.	.	PUNCT
ejpam-6974	112	1	remark	remark	PROPN
ejpam-6974	112	2	2	2	NUM
ejpam-6974	112	3	.	.	PUNCT
ejpam-6974	112	4	not	not	PART
ejpam-6974	112	5	every	every	DET
ejpam-6974	112	6	bg	bg	NOUN
ejpam-6974	112	7	-	-	PUNCT
ejpam-6974	112	8	algebra	algebra	PROPN
ejpam-6974	112	9	is	be	AUX
ejpam-6974	112	10	a	a	DET
ejpam-6974	112	11	dual	dual	ADJ
ejpam-6974	112	12	bg	bg	NOUN
ejpam-6974	112	13	-	-	NOUN
ejpam-6974	112	14	algebra	algebra	PROPN
ejpam-6974	112	15	.	.	PUNCT
ejpam-6974	113	1	lemma	lemma	PROPN
ejpam-6974	113	2	2	2	NUM
ejpam-6974	113	3	shows	show	VERB
ejpam-6974	113	4	some	some	DET
ejpam-6974	113	5	properties	property	NOUN
ejpam-6974	113	6	of	of	ADP
ejpam-6974	113	7	the	the	DET
ejpam-6974	113	8	dual	dual	ADJ
ejpam-6974	113	9	bg	bg	NOUN
ejpam-6974	113	10	-	-	NOUN
ejpam-6974	113	11	algebra	algebra	PROPN
ejpam-6974	113	12	.	.	PUNCT
ejpam-6974	114	1	lemma	lemma	PROPN
ejpam-6974	114	2	2	2	X
ejpam-6974	114	3	.	.	PUNCT
ejpam-6974	115	1	let	let	AUX
ejpam-6974	115	2	(	(	PUNCT
ejpam-6974	115	3	x	x	NOUN
ejpam-6974	115	4	,	,	PUNCT
ejpam-6974	115	5	◦	◦	NOUN
ejpam-6974	115	6	,	,	PUNCT
ejpam-6974	115	7	1	1	NUM
ejpam-6974	115	8	)	)	PUNCT
ejpam-6974	115	9	be	be	AUX
ejpam-6974	115	10	a	a	DET
ejpam-6974	115	11	dual	dual	ADJ
ejpam-6974	115	12	bg	bg	NOUN
ejpam-6974	115	13	-	-	NOUN
ejpam-6974	115	14	algebra	algebra	PROPN
ejpam-6974	115	15	.	.	PUNCT
ejpam-6974	116	1	then	then	ADV
ejpam-6974	116	2	for	for	ADP
ejpam-6974	116	3	any	any	DET
ejpam-6974	116	4	x	x	NOUN
ejpam-6974	116	5	,	,	PUNCT
ejpam-6974	116	6	y	y	PROPN
ejpam-6974	116	7	,	,	PUNCT
ejpam-6974	116	8	z	z	NOUN
ejpam-6974	116	9	in	in	ADP
ejpam-6974	116	10	x	x	PROPN
ejpam-6974	116	11	,	,	PUNCT
ejpam-6974	116	12	c.m	c.m	PROPN
ejpam-6974	116	13	.	.	PROPN
ejpam-6974	116	14	chan	chan	PROPN
ejpam-6974	116	15	,	,	PUNCT
ejpam-6974	116	16	k.	k.	PROPN
ejpam-6974	116	17	fuentes	fuentes	PROPN
ejpam-6974	116	18	/	/	SYM
ejpam-6974	116	19	eur	eur	PROPN
ejpam-6974	116	20	.	.	PUNCT
ejpam-6974	117	1	j.	j.	PROPN
ejpam-6974	117	2	pure	pure	PROPN
ejpam-6974	117	3	appl	appl	PROPN
ejpam-6974	117	4	.	.	PROPN
ejpam-6974	117	5	math	math	PROPN
ejpam-6974	117	6	,	,	PUNCT
ejpam-6974	117	7	18	18	NUM
ejpam-6974	117	8	(	(	PUNCT
ejpam-6974	117	9	4	4	NUM
ejpam-6974	117	10	)	)	PUNCT
ejpam-6974	117	11	(	(	PUNCT
ejpam-6974	117	12	2025	2025	NUM
ejpam-6974	117	13	)	)	PUNCT
ejpam-6974	117	14	,	,	PUNCT
ejpam-6974	117	15	6974	6974	NUM
ejpam-6974	117	16	6	6	NUM
ejpam-6974	117	17	of	of	ADP
ejpam-6974	117	18	16	16	NUM
ejpam-6974	117	19	(	(	PUNCT
ejpam-6974	117	20	i	i	NOUN
ejpam-6974	117	21	)	)	PUNCT
ejpam-6974	117	22	x	x	X
ejpam-6974	118	1	=	=	PRON
ejpam-6974	118	2	(	(	PUNCT
ejpam-6974	118	3	x	x	SYM
ejpam-6974	118	4	◦	◦	NOUN
ejpam-6974	118	5	1	1	NUM
ejpam-6974	118	6	)	)	PUNCT
ejpam-6974	118	7	◦	◦	NOUN
ejpam-6974	118	8	1	1	NUM
ejpam-6974	118	9	;	;	PUNCT
ejpam-6974	118	10	(	(	PUNCT
ejpam-6974	118	11	ii	ii	NOUN
ejpam-6974	118	12	)	)	PUNCT
ejpam-6974	118	13	x	x	X
ejpam-6974	119	1	=	=	PUNCT
ejpam-6974	119	2	y	y	PROPN
ejpam-6974	119	3	◦	◦	NOUN
ejpam-6974	120	1	[	[	X
ejpam-6974	120	2	(	(	PUNCT
ejpam-6974	120	3	y	y	NOUN
ejpam-6974	120	4	◦	◦	NOUN
ejpam-6974	120	5	1	1	NUM
ejpam-6974	120	6	)	)	PUNCT
ejpam-6974	120	7	◦	◦	NOUN
ejpam-6974	120	8	x	x	SYM
ejpam-6974	120	9	]	]	X
ejpam-6974	120	10	;	;	PUNCT
ejpam-6974	120	11	(	(	PUNCT
ejpam-6974	120	12	iii	iii	NOUN
ejpam-6974	120	13	)	)	PUNCT
ejpam-6974	120	14	x	x	PUNCT
ejpam-6974	120	15	◦	◦	NOUN
ejpam-6974	120	16	y	y	NOUN
ejpam-6974	120	17	=	=	PUNCT
ejpam-6974	120	18	x	x	PUNCT
ejpam-6974	120	19	◦	◦	NOUN
ejpam-6974	120	20	z	z	NOUN
ejpam-6974	120	21	implies	imply	VERB
ejpam-6974	120	22	y	y	PROPN
ejpam-6974	120	23	=	=	SYM
ejpam-6974	120	24	z	z	PROPN
ejpam-6974	120	25	;	;	PUNCT
ejpam-6974	120	26	(	(	PUNCT
ejpam-6974	120	27	iv	iv	X
ejpam-6974	120	28	)	)	PUNCT
ejpam-6974	120	29	if	if	SCONJ
ejpam-6974	120	30	x	x	SYM
ejpam-6974	120	31	◦	◦	VERB
ejpam-6974	120	32	y	y	NOUN
ejpam-6974	120	33	=	=	SYM
ejpam-6974	120	34	1	1	NUM
ejpam-6974	120	35	,	,	PUNCT
ejpam-6974	120	36	then	then	ADV
ejpam-6974	120	37	x	x	X
ejpam-6974	120	38	=	=	SYM
ejpam-6974	120	39	y	y	PROPN
ejpam-6974	120	40	;	;	PUNCT
ejpam-6974	120	41	(	(	PUNCT
ejpam-6974	120	42	v	v	NOUN
ejpam-6974	120	43	)	)	PUNCT
ejpam-6974	120	44	if	if	SCONJ
ejpam-6974	120	45	x	x	PART
ejpam-6974	120	46	◦	◦	NOUN
ejpam-6974	120	47	1	1	NUM
ejpam-6974	120	48	=	=	SYM
ejpam-6974	120	49	y	y	PROPN
ejpam-6974	120	50	◦	◦	NOUN
ejpam-6974	120	51	1	1	NUM
ejpam-6974	120	52	,	,	PUNCT
ejpam-6974	120	53	then	then	ADV
ejpam-6974	120	54	x	x	X
ejpam-6974	120	55	=	=	SYM
ejpam-6974	120	56	y	y	PROPN
ejpam-6974	120	57	;	;	PUNCT
ejpam-6974	120	58	and	and	CCONJ
ejpam-6974	120	59	(	(	PUNCT
ejpam-6974	120	60	vi	vi	X
ejpam-6974	120	61	)	)	PUNCT
ejpam-6974	120	62	if	if	SCONJ
ejpam-6974	120	63	x	x	AUX
ejpam-6974	120	64	◦	◦	VERB
ejpam-6974	120	65	y	y	NOUN
ejpam-6974	120	66	=	=	SYM
ejpam-6974	120	67	1	1	NUM
ejpam-6974	120	68	,	,	PUNCT
ejpam-6974	120	69	then	then	ADV
ejpam-6974	120	70	(	(	PUNCT
ejpam-6974	120	71	x	x	X
ejpam-6974	120	72	◦	◦	NOUN
ejpam-6974	120	73	z	z	NOUN
ejpam-6974	120	74	)	)	PUNCT
ejpam-6974	120	75	◦	◦	NOUN
ejpam-6974	120	76	(	(	PUNCT
ejpam-6974	120	77	y	y	PROPN
ejpam-6974	120	78	◦	◦	PROPN
ejpam-6974	120	79	z	z	PROPN
ejpam-6974	120	80	)	)	PUNCT
ejpam-6974	120	81	=	=	SYM
ejpam-6974	120	82	1	1	X
ejpam-6974	120	83	.	.	PUNCT
ejpam-6974	121	1	proof	proof	NOUN
ejpam-6974	121	2	.	.	PUNCT
ejpam-6974	122	1	let	let	VERB
ejpam-6974	122	2	(	(	PUNCT
ejpam-6974	122	3	x	x	NOUN
ejpam-6974	122	4	,	,	PUNCT
ejpam-6974	122	5	◦	◦	NOUN
ejpam-6974	122	6	,	,	PUNCT
ejpam-6974	122	7	1	1	NUM
ejpam-6974	122	8	)	)	PUNCT
ejpam-6974	122	9	be	be	AUX
ejpam-6974	122	10	a	a	DET
ejpam-6974	122	11	dual	dual	ADJ
ejpam-6974	122	12	bg	bg	NOUN
ejpam-6974	122	13	-	-	NOUN
ejpam-6974	122	14	algebra	algebra	PROPN
ejpam-6974	122	15	and	and	CCONJ
ejpam-6974	122	16	x	x	NOUN
ejpam-6974	122	17	,	,	PUNCT
ejpam-6974	122	18	y	y	PROPN
ejpam-6974	122	19	,	,	PUNCT
ejpam-6974	122	20	z	z	VERB
ejpam-6974	122	21	in	in	ADP
ejpam-6974	122	22	x.	x.	NOUN
ejpam-6974	122	23	by	by	ADP
ejpam-6974	122	24	replacing	replace	VERB
ejpam-6974	122	25	y	y	PRON
ejpam-6974	122	26	with	with	ADP
ejpam-6974	122	27	x	x	PRON
ejpam-6974	122	28	in	in	ADP
ejpam-6974	122	29	(	(	PUNCT
ejpam-6974	122	30	dbg3	dbg3	PROPN
ejpam-6974	122	31	)	)	PUNCT
ejpam-6974	122	32	and	and	CCONJ
ejpam-6974	122	33	applying	apply	VERB
ejpam-6974	122	34	(	(	PUNCT
ejpam-6974	122	35	dbg1	dbg1	ADJ
ejpam-6974	122	36	)	)	PUNCT
ejpam-6974	122	37	,	,	PUNCT
ejpam-6974	122	38	(	(	PUNCT
ejpam-6974	122	39	i	i	NOUN
ejpam-6974	122	40	)	)	PUNCT
ejpam-6974	122	41	is	be	AUX
ejpam-6974	122	42	proved	prove	VERB
ejpam-6974	122	43	as	as	SCONJ
ejpam-6974	122	44	shown	show	VERB
ejpam-6974	122	45	:	:	PUNCT
ejpam-6974	122	46	x	x	SYM
ejpam-6974	122	47	=	=	SYM
ejpam-6974	122	48	(	(	PUNCT
ejpam-6974	122	49	y	y	PROPN
ejpam-6974	122	50	◦	◦	NOUN
ejpam-6974	122	51	1	1	NUM
ejpam-6974	122	52	)	)	PUNCT
ejpam-6974	122	53	◦	◦	NOUN
ejpam-6974	122	54	(	(	PUNCT
ejpam-6974	122	55	y	y	PROPN
ejpam-6974	122	56	◦	◦	NOUN
ejpam-6974	122	57	x	x	X
ejpam-6974	122	58	)	)	PUNCT
ejpam-6974	123	1	=	=	SYM
ejpam-6974	123	2	(	(	PUNCT
ejpam-6974	123	3	x	x	SYM
ejpam-6974	123	4	◦	◦	NOUN
ejpam-6974	123	5	1	1	NUM
ejpam-6974	123	6	)	)	PUNCT
ejpam-6974	123	7	◦	◦	NOUN
ejpam-6974	123	8	(	(	PUNCT
ejpam-6974	123	9	x	x	PART
ejpam-6974	123	10	◦	◦	NOUN
ejpam-6974	123	11	x	x	NOUN
ejpam-6974	123	12	)	)	PUNCT
ejpam-6974	123	13	=	=	SYM
ejpam-6974	124	1	(	(	PUNCT
ejpam-6974	124	2	x	x	SYM
ejpam-6974	124	3	◦	◦	NOUN
ejpam-6974	124	4	1	1	NUM
ejpam-6974	124	5	)	)	PUNCT
ejpam-6974	124	6	◦	◦	NOUN
ejpam-6974	124	7	1	1	NUM
ejpam-6974	124	8	.	.	X
ejpam-6974	125	1	for	for	ADP
ejpam-6974	125	2	(	(	PUNCT
ejpam-6974	125	3	ii	ii	NOUN
ejpam-6974	125	4	)	)	PUNCT
ejpam-6974	125	5	,	,	PUNCT
ejpam-6974	125	6	replace	replace	VERB
ejpam-6974	125	7	y	y	PROPN
ejpam-6974	125	8	with	with	ADP
ejpam-6974	125	9	y	y	PROPN
ejpam-6974	125	10	◦	◦	NOUN
ejpam-6974	125	11	1	1	NUM
ejpam-6974	125	12	in	in	ADP
ejpam-6974	125	13	(	(	PUNCT
ejpam-6974	125	14	dbg3	dbg3	PROPN
ejpam-6974	125	15	)	)	PUNCT
ejpam-6974	125	16	and	and	CCONJ
ejpam-6974	125	17	apply	apply	VERB
ejpam-6974	125	18	(	(	PUNCT
ejpam-6974	125	19	i	i	NOUN
ejpam-6974	125	20	)	)	PUNCT
ejpam-6974	125	21	,	,	PUNCT
ejpam-6974	125	22	that	that	ADV
ejpam-6974	125	23	is	is	ADV
ejpam-6974	125	24	,	,	PUNCT
ejpam-6974	125	25	x	x	PUNCT
ejpam-6974	125	26	=	=	PUNCT
ejpam-6974	126	1	[	[	X
ejpam-6974	126	2	(	(	PUNCT
ejpam-6974	126	3	y	y	NOUN
ejpam-6974	126	4	◦	◦	NOUN
ejpam-6974	126	5	1	1	NUM
ejpam-6974	126	6	)	)	PUNCT
ejpam-6974	126	7	◦	◦	NOUN
ejpam-6974	126	8	1	1	NUM
ejpam-6974	126	9	]	]	X
ejpam-6974	126	10	◦	◦	NOUN
ejpam-6974	127	1	[	[	X
ejpam-6974	127	2	(	(	PUNCT
ejpam-6974	127	3	y	y	NOUN
ejpam-6974	127	4	◦	◦	NOUN
ejpam-6974	127	5	1	1	NUM
ejpam-6974	127	6	)	)	PUNCT
ejpam-6974	127	7	◦	◦	NOUN
ejpam-6974	127	8	x	x	X
ejpam-6974	127	9	]	]	X
ejpam-6974	127	10	=	=	PUNCT
ejpam-6974	127	11	y	y	PROPN
ejpam-6974	127	12	◦	◦	NOUN
ejpam-6974	128	1	[	[	X
ejpam-6974	128	2	(	(	PUNCT
ejpam-6974	128	3	y	y	NOUN
ejpam-6974	128	4	◦	◦	NOUN
ejpam-6974	128	5	1	1	NUM
ejpam-6974	128	6	)	)	PUNCT
ejpam-6974	128	7	◦	◦	NOUN
ejpam-6974	128	8	x	x	SYM
ejpam-6974	128	9	]	]	X
ejpam-6974	128	10	.	.	PUNCT
ejpam-6974	129	1	to	to	PART
ejpam-6974	129	2	show	show	VERB
ejpam-6974	129	3	(	(	PUNCT
ejpam-6974	129	4	iii	iii	NOUN
ejpam-6974	129	5	)	)	PUNCT
ejpam-6974	129	6	,	,	PUNCT
ejpam-6974	129	7	replace	replace	VERB
ejpam-6974	129	8	y	y	PROPN
ejpam-6974	129	9	with	with	ADP
ejpam-6974	129	10	x	x	PRON
ejpam-6974	129	11	in	in	ADP
ejpam-6974	129	12	(	(	PUNCT
ejpam-6974	129	13	ii	ii	NOUN
ejpam-6974	129	14	)	)	PUNCT
ejpam-6974	129	15	and	and	CCONJ
ejpam-6974	129	16	so	so	ADV
ejpam-6974	129	17	x	x	SYM
ejpam-6974	130	1	=	=	PUNCT
ejpam-6974	130	2	x	x	PUNCT
ejpam-6974	130	3	◦	◦	NOUN
ejpam-6974	130	4	[	[	X
ejpam-6974	130	5	(	(	PUNCT
ejpam-6974	130	6	x	x	SYM
ejpam-6974	130	7	◦	◦	NOUN
ejpam-6974	130	8	1	1	NUM
ejpam-6974	130	9	)	)	PUNCT
ejpam-6974	130	10	◦	◦	NOUN
ejpam-6974	130	11	x	x	SYM
ejpam-6974	130	12	]	]	X
ejpam-6974	130	13	.	.	PUNCT
ejpam-6974	131	1	using	use	VERB
ejpam-6974	131	2	(	(	PUNCT
ejpam-6974	131	3	i	i	NOUN
ejpam-6974	131	4	)	)	PUNCT
ejpam-6974	131	5	,	,	PUNCT
ejpam-6974	131	6	(	(	PUNCT
ejpam-6974	131	7	iv	iv	X
ejpam-6974	131	8	)	)	PUNCT
ejpam-6974	131	9	immediately	immediately	ADV
ejpam-6974	131	10	follows	follow	VERB
ejpam-6974	131	11	.	.	PUNCT
ejpam-6974	132	1	by	by	ADP
ejpam-6974	132	2	hypothesis	hypothesis	NOUN
ejpam-6974	132	3	and	and	CCONJ
ejpam-6974	132	4	(	(	PUNCT
ejpam-6974	132	5	dbg3	dbg3	PROPN
ejpam-6974	132	6	)	)	PUNCT
ejpam-6974	132	7	,	,	PUNCT
ejpam-6974	132	8	y	y	PROPN
ejpam-6974	132	9	=	=	SYM
ejpam-6974	132	10	(	(	PUNCT
ejpam-6974	132	11	x	x	PART
ejpam-6974	132	12	◦	◦	NOUN
ejpam-6974	132	13	1)	1)	NUM
ejpam-6974	132	14	◦	◦	ADJ
ejpam-6974	132	15	(x	(x	NOUN
ejpam-6974	132	16	◦	◦	NOUN
ejpam-6974	132	17	y	y	NOUN
ejpam-6974	132	18	)	)	PUNCT
ejpam-6974	132	19	=	=	PUNCT
ejpam-6974	132	20	(	(	PUNCT
ejpam-6974	132	21	x	x	PART
ejpam-6974	132	22	◦	◦	NOUN
ejpam-6974	132	23	1)	1)	NUM
ejpam-6974	132	24	◦	◦	ADJ
ejpam-6974	132	25	(x	(x	NOUN
ejpam-6974	132	26	◦	◦	NOUN
ejpam-6974	132	27	z	z	NOUN
ejpam-6974	132	28	)	)	PUNCT
ejpam-6974	132	29	=	=	SYM
ejpam-6974	133	1	z	z	NOUN
ejpam-6974	133	2	,	,	PUNCT
ejpam-6974	133	3	proving	prove	VERB
ejpam-6974	133	4	(	(	PUNCT
ejpam-6974	133	5	v	v	NOUN
ejpam-6974	133	6	)	)	PUNCT
ejpam-6974	133	7	.	.	PUNCT
ejpam-6974	134	1	for	for	ADP
ejpam-6974	134	2	(	(	PUNCT
ejpam-6974	134	3	vi	vi	NOUN
ejpam-6974	134	4	)	)	PUNCT
ejpam-6974	134	5	,	,	PUNCT
ejpam-6974	134	6	if	if	SCONJ
ejpam-6974	134	7	x	x	PROPN
ejpam-6974	134	8	◦	◦	NOUN
ejpam-6974	134	9	y	y	NOUN
ejpam-6974	134	10	=	=	SYM
ejpam-6974	134	11	1	1	NUM
ejpam-6974	134	12	,	,	PUNCT
ejpam-6974	134	13	then	then	ADV
ejpam-6974	134	14	x	x	X
ejpam-6974	134	15	◦	◦	NOUN
ejpam-6974	134	16	y	y	NOUN
ejpam-6974	134	17	=	=	SYM
ejpam-6974	134	18	x	x	SYM
ejpam-6974	134	19	◦	◦	NOUN
ejpam-6974	134	20	x	x	SYM
ejpam-6974	134	21	by	by	ADP
ejpam-6974	134	22	(	(	PUNCT
ejpam-6974	134	23	dbg1	dbg1	ADJ
ejpam-6974	134	24	)	)	PUNCT
ejpam-6974	134	25	.	.	PUNCT
ejpam-6974	135	1	this	this	PRON
ejpam-6974	135	2	implies	imply	VERB
ejpam-6974	135	3	x	x	PUNCT
ejpam-6974	135	4	=	=	SYM
ejpam-6974	135	5	y	y	PROPN
ejpam-6974	135	6	using	use	VERB
ejpam-6974	135	7	(	(	PUNCT
ejpam-6974	135	8	v	v	NOUN
ejpam-6974	135	9	)	)	PUNCT
ejpam-6974	135	10	.	.	PUNCT
ejpam-6974	136	1	by	by	ADP
ejpam-6974	136	2	(	(	PUNCT
ejpam-6974	136	3	dbg3	dbg3	PROPN
ejpam-6974	136	4	)	)	PUNCT
ejpam-6974	136	5	,	,	PUNCT
ejpam-6974	136	6	y	y	PROPN
ejpam-6974	136	7	=	=	PRON
ejpam-6974	136	8	(	(	PUNCT
ejpam-6974	136	9	y	y	PROPN
ejpam-6974	136	10	◦	◦	NOUN
ejpam-6974	136	11	1	1	NUM
ejpam-6974	136	12	)	)	PUNCT
ejpam-6974	136	13	◦	◦	NOUN
ejpam-6974	136	14	(	(	PUNCT
ejpam-6974	136	15	y	y	PROPN
ejpam-6974	136	16	◦	◦	NOUN
ejpam-6974	136	17	y	y	PROPN
ejpam-6974	136	18	)	)	PUNCT
ejpam-6974	136	19	.	.	PUNCT
ejpam-6974	137	1	this	this	PRON
ejpam-6974	137	2	implies	imply	VERB
ejpam-6974	137	3	y	y	PROPN
ejpam-6974	137	4	=	=	PUNCT
ejpam-6974	137	5	(	(	PUNCT
ejpam-6974	137	6	x	x	SYM
ejpam-6974	137	7	◦	◦	NOUN
ejpam-6974	137	8	1	1	NUM
ejpam-6974	137	9	)	)	PUNCT
ejpam-6974	137	10	◦	◦	NOUN
ejpam-6974	137	11	1	1	NUM
ejpam-6974	137	12	after	after	ADP
ejpam-6974	137	13	applying	apply	VERB
ejpam-6974	137	14	the	the	DET
ejpam-6974	137	15	hypothesis	hypothesis	NOUN
ejpam-6974	137	16	and	and	CCONJ
ejpam-6974	137	17	(	(	PUNCT
ejpam-6974	137	18	dbg1	dbg1	PROPN
ejpam-6974	137	19	)	)	PUNCT
ejpam-6974	137	20	.	.	PUNCT
ejpam-6974	138	1	using	use	VERB
ejpam-6974	138	2	(	(	PUNCT
ejpam-6974	138	3	i	i	NOUN
ejpam-6974	138	4	)	)	PUNCT
ejpam-6974	138	5	,	,	PUNCT
ejpam-6974	138	6	x	x	X
ejpam-6974	138	7	=	=	SYM
ejpam-6974	138	8	y	y	PROPN
ejpam-6974	138	9	as	as	SCONJ
ejpam-6974	138	10	needed	need	VERB
ejpam-6974	138	11	in	in	ADP
ejpam-6974	138	12	(	(	PUNCT
ejpam-6974	138	13	vii	vii	PROPN
ejpam-6974	138	14	)	)	PUNCT
ejpam-6974	138	15	.	.	PUNCT
ejpam-6974	139	1	finally	finally	ADV
ejpam-6974	139	2	,	,	PUNCT
ejpam-6974	139	3	if	if	SCONJ
ejpam-6974	139	4	x	x	PART
ejpam-6974	139	5	◦	◦	VERB
ejpam-6974	139	6	y	y	NOUN
ejpam-6974	139	7	=	=	SYM
ejpam-6974	139	8	1	1	NUM
ejpam-6974	139	9	,	,	PUNCT
ejpam-6974	139	10	then	then	ADV
ejpam-6974	139	11	x	x	X
ejpam-6974	139	12	=	=	SYM
ejpam-6974	139	13	y	y	PROPN
ejpam-6974	139	14	by	by	ADP
ejpam-6974	139	15	(	(	PUNCT
ejpam-6974	139	16	vi	vi	NOUN
ejpam-6974	139	17	)	)	PUNCT
ejpam-6974	139	18	.	.	PUNCT
ejpam-6974	140	1	so	so	ADV
ejpam-6974	140	2	,	,	PUNCT
ejpam-6974	140	3	(	(	PUNCT
ejpam-6974	140	4	x	x	PUNCT
ejpam-6974	140	5	◦	◦	NOUN
ejpam-6974	140	6	z	z	NOUN
ejpam-6974	140	7	)	)	PUNCT
ejpam-6974	140	8	◦	◦	NOUN
ejpam-6974	140	9	(	(	PUNCT
ejpam-6974	140	10	y	y	PROPN
ejpam-6974	140	11	◦	◦	PROPN
ejpam-6974	140	12	z	z	PROPN
ejpam-6974	140	13	)	)	PUNCT
ejpam-6974	140	14	=	=	SYM
ejpam-6974	141	1	(	(	PUNCT
ejpam-6974	141	2	x	x	PART
ejpam-6974	141	3	◦	◦	NOUN
ejpam-6974	141	4	z	z	NOUN
ejpam-6974	141	5	)	)	PUNCT
ejpam-6974	141	6	◦	◦	NOUN
ejpam-6974	141	7	(	(	PUNCT
ejpam-6974	141	8	x	x	PART
ejpam-6974	141	9	◦	◦	NOUN
ejpam-6974	141	10	z	z	NOUN
ejpam-6974	141	11	)	)	PUNCT
ejpam-6974	141	12	=	=	SYM
ejpam-6974	141	13	1	1	NUM
ejpam-6974	141	14	by	by	ADP
ejpam-6974	141	15	(	(	PUNCT
ejpam-6974	141	16	dbg1	dbg1	PROPN
ejpam-6974	141	17	)	)	PUNCT
ejpam-6974	141	18	,	,	PUNCT
ejpam-6974	141	19	which	which	PRON
ejpam-6974	141	20	proves	prove	VERB
ejpam-6974	141	21	(	(	PUNCT
ejpam-6974	141	22	viii	viii	NOUN
ejpam-6974	141	23	)	)	PUNCT
ejpam-6974	141	24	.	.	PUNCT
ejpam-6974	142	1	for	for	ADP
ejpam-6974	142	2	any	any	DET
ejpam-6974	142	3	dual	dual	ADJ
ejpam-6974	142	4	bg	bg	NOUN
ejpam-6974	142	5	-	-	NOUN
ejpam-6974	142	6	algebra	algebra	PROPN
ejpam-6974	142	7	,	,	PUNCT
ejpam-6974	142	8	replacing	replace	VERB
ejpam-6974	142	9	y	y	PRON
ejpam-6974	142	10	with	with	ADP
ejpam-6974	142	11	x	x	PUNCT
ejpam-6974	142	12	on	on	ADP
ejpam-6974	142	13	the	the	DET
ejpam-6974	142	14	right	right	ADJ
ejpam-6974	142	15	-	-	PUNCT
ejpam-6974	142	16	hand	hand	NOUN
ejpam-6974	142	17	side	side	NOUN
ejpam-6974	142	18	in	in	ADP
ejpam-6974	142	19	lemma	lemma	PROPN
ejpam-6974	142	20	2(ii	2(ii	NUM
ejpam-6974	142	21	)	)	PUNCT
ejpam-6974	142	22	yields	yield	NOUN
ejpam-6974	142	23	x	x	PUNCT
ejpam-6974	143	1	=	=	PUNCT
ejpam-6974	143	2	x	x	AUX
ejpam-6974	143	3	◦	◦	NOUN
ejpam-6974	143	4	[	[	X
ejpam-6974	143	5	(	(	PUNCT
ejpam-6974	143	6	x	x	SYM
ejpam-6974	143	7	◦	◦	NOUN
ejpam-6974	143	8	1	1	NUM
ejpam-6974	143	9	)	)	PUNCT
ejpam-6974	143	10	◦	◦	NOUN
ejpam-6974	143	11	x	x	SYM
ejpam-6974	143	12	]	]	X
ejpam-6974	143	13	.	.	PUNCT
ejpam-6974	144	1	also	also	ADV
ejpam-6974	144	2	,	,	PUNCT
ejpam-6974	144	3	using	use	VERB
ejpam-6974	144	4	lemma	lemma	PROPN
ejpam-6974	144	5	2(i	2(i	NUM
ejpam-6974	144	6	)	)	PUNCT
ejpam-6974	144	7	,	,	PUNCT
ejpam-6974	144	8	x	x	PUNCT
ejpam-6974	144	9	◦	◦	NOUN
ejpam-6974	144	10	y	y	NOUN
ejpam-6974	144	11	=	=	PUNCT
ejpam-6974	145	1	[	[	X
ejpam-6974	145	2	(	(	PUNCT
ejpam-6974	145	3	x	x	SYM
ejpam-6974	145	4	◦	◦	NOUN
ejpam-6974	145	5	1	1	NUM
ejpam-6974	145	6	)	)	PUNCT
ejpam-6974	145	7	◦	◦	NOUN
ejpam-6974	145	8	1	1	NUM
ejpam-6974	145	9	]	]	X
ejpam-6974	145	10	◦	◦	NOUN
ejpam-6974	145	11	y	y	PRON
ejpam-6974	145	12	follows	follow	VERB
ejpam-6974	145	13	.	.	PUNCT
ejpam-6974	146	1	this	this	PRON
ejpam-6974	146	2	is	be	AUX
ejpam-6974	146	3	formalized	formalize	VERB
ejpam-6974	146	4	in	in	ADP
ejpam-6974	146	5	the	the	DET
ejpam-6974	146	6	next	next	ADJ
ejpam-6974	146	7	remark	remark	NOUN
ejpam-6974	146	8	.	.	PUNCT
ejpam-6974	147	1	remark	remark	PROPN
ejpam-6974	147	2	3	3	NUM
ejpam-6974	147	3	.	.	PUNCT
ejpam-6974	148	1	let	let	AUX
ejpam-6974	148	2	(	(	PUNCT
ejpam-6974	148	3	x	x	NOUN
ejpam-6974	148	4	,	,	PUNCT
ejpam-6974	148	5	◦	◦	NOUN
ejpam-6974	148	6	,	,	PUNCT
ejpam-6974	148	7	1	1	NUM
ejpam-6974	148	8	)	)	PUNCT
ejpam-6974	148	9	be	be	AUX
ejpam-6974	148	10	a	a	DET
ejpam-6974	148	11	dual	dual	ADJ
ejpam-6974	148	12	bg	bg	NOUN
ejpam-6974	148	13	-	-	NOUN
ejpam-6974	148	14	algebra	algebra	PROPN
ejpam-6974	148	15	.	.	PUNCT
ejpam-6974	149	1	then	then	ADV
ejpam-6974	149	2	for	for	ADP
ejpam-6974	149	3	any	any	DET
ejpam-6974	149	4	x	x	NOUN
ejpam-6974	149	5	,	,	PUNCT
ejpam-6974	149	6	y	y	PROPN
ejpam-6974	149	7	,	,	PUNCT
ejpam-6974	149	8	z	z	NOUN
ejpam-6974	149	9	in	in	ADP
ejpam-6974	149	10	x	x	PRON
ejpam-6974	149	11	,	,	PUNCT
ejpam-6974	149	12	(	(	PUNCT
ejpam-6974	149	13	i	i	NOUN
ejpam-6974	149	14	)	)	PUNCT
ejpam-6974	149	15	x	x	X
ejpam-6974	150	1	=	=	PUNCT
ejpam-6974	150	2	x	x	AUX
ejpam-6974	150	3	◦	◦	NOUN
ejpam-6974	150	4	[	[	X
ejpam-6974	150	5	(	(	PUNCT
ejpam-6974	150	6	x	x	SYM
ejpam-6974	150	7	◦	◦	NOUN
ejpam-6974	150	8	1	1	NUM
ejpam-6974	150	9	)	)	PUNCT
ejpam-6974	150	10	◦	◦	NOUN
ejpam-6974	150	11	x	x	X
ejpam-6974	150	12	]	]	X
ejpam-6974	150	13	;	;	PUNCT
ejpam-6974	150	14	(	(	PUNCT
ejpam-6974	150	15	ii	ii	NOUN
ejpam-6974	150	16	)	)	PUNCT
ejpam-6974	150	17	x	x	PUNCT
ejpam-6974	150	18	◦	◦	NOUN
ejpam-6974	150	19	y	y	NOUN
ejpam-6974	150	20	=	=	PUNCT
ejpam-6974	151	1	[	[	X
ejpam-6974	151	2	(	(	PUNCT
ejpam-6974	151	3	x	x	SYM
ejpam-6974	151	4	◦	◦	NOUN
ejpam-6974	151	5	1	1	NUM
ejpam-6974	151	6	)	)	PUNCT
ejpam-6974	151	7	◦	◦	NOUN
ejpam-6974	151	8	1	1	NUM
ejpam-6974	151	9	]	]	X
ejpam-6974	151	10	◦	◦	NOUN
ejpam-6974	151	11	y.	y.	NOUN
ejpam-6974	151	12	the	the	DET
ejpam-6974	151	13	next	next	ADJ
ejpam-6974	151	14	theorem	theorem	NOUN
ejpam-6974	151	15	characterizes	characterize	VERB
ejpam-6974	151	16	the	the	DET
ejpam-6974	151	17	dual	dual	ADJ
ejpam-6974	151	18	bg	bg	NOUN
ejpam-6974	151	19	-	-	NOUN
ejpam-6974	151	20	algebra	algebra	NOUN
ejpam-6974	151	21	given	give	VERB
ejpam-6974	151	22	any	any	DET
ejpam-6974	151	23	algebra	algebra	NOUN
ejpam-6974	151	24	with	with	ADP
ejpam-6974	151	25	a	a	DET
ejpam-6974	151	26	binary	binary	ADJ
ejpam-6974	151	27	operation	operation	NOUN
ejpam-6974	151	28	and	and	CCONJ
ejpam-6974	151	29	a	a	DET
ejpam-6974	151	30	constant	constant	ADJ
ejpam-6974	151	31	element	element	NOUN
ejpam-6974	151	32	,	,	PUNCT
ejpam-6974	151	33	which	which	PRON
ejpam-6974	151	34	will	will	AUX
ejpam-6974	151	35	be	be	AUX
ejpam-6974	151	36	referred	refer	VERB
ejpam-6974	151	37	to	to	ADP
ejpam-6974	151	38	as	as	ADP
ejpam-6974	151	39	an	an	DET
ejpam-6974	151	40	algebra	algebra	NOUN
ejpam-6974	151	41	of	of	ADP
ejpam-6974	151	42	type	type	NOUN
ejpam-6974	151	43	(	(	PUNCT
ejpam-6974	151	44	2	2	NUM
ejpam-6974	151	45	,	,	PUNCT
ejpam-6974	151	46	0	0	NUM
ejpam-6974	151	47	)	)	PUNCT
ejpam-6974	151	48	.	.	PUNCT
ejpam-6974	152	1	theorem	theorem	NOUN
ejpam-6974	152	2	3	3	X
ejpam-6974	152	3	.	.	PUNCT
ejpam-6974	153	1	let	let	AUX
ejpam-6974	153	2	(	(	PUNCT
ejpam-6974	153	3	x	x	NOUN
ejpam-6974	153	4	,	,	PUNCT
ejpam-6974	153	5	◦	◦	NOUN
ejpam-6974	153	6	,	,	PUNCT
ejpam-6974	153	7	1	1	NUM
ejpam-6974	153	8	)	)	PUNCT
ejpam-6974	153	9	be	be	AUX
ejpam-6974	153	10	an	an	DET
ejpam-6974	153	11	algebra	algebra	NOUN
ejpam-6974	153	12	of	of	ADP
ejpam-6974	153	13	type	type	NOUN
ejpam-6974	153	14	(	(	PUNCT
ejpam-6974	153	15	2	2	NUM
ejpam-6974	153	16	,	,	PUNCT
ejpam-6974	153	17	0	0	NUM
ejpam-6974	153	18	)	)	PUNCT
ejpam-6974	153	19	.	.	PUNCT
ejpam-6974	154	1	then	then	ADV
ejpam-6974	154	2	(	(	PUNCT
ejpam-6974	154	3	x	x	X
ejpam-6974	154	4	,	,	PUNCT
ejpam-6974	154	5	◦	◦	NOUN
ejpam-6974	154	6	,	,	PUNCT
ejpam-6974	154	7	1	1	NUM
ejpam-6974	154	8	)	)	PUNCT
ejpam-6974	154	9	is	be	AUX
ejpam-6974	154	10	a	a	DET
ejpam-6974	154	11	dual	dual	ADJ
ejpam-6974	154	12	bg	bg	NOUN
ejpam-6974	154	13	-	-	NOUN
ejpam-6974	154	14	algebra	algebra	NOUN
ejpam-6974	154	15	if	if	SCONJ
ejpam-6974	154	16	and	and	CCONJ
ejpam-6974	154	17	only	only	ADV
ejpam-6974	154	18	if	if	SCONJ
ejpam-6974	154	19	for	for	ADP
ejpam-6974	154	20	any	any	DET
ejpam-6974	154	21	x	x	NOUN
ejpam-6974	154	22	,	,	PUNCT
ejpam-6974	154	23	y	y	PROPN
ejpam-6974	154	24	∈	∈	PROPN
ejpam-6974	154	25	x	x	X
ejpam-6974	154	26	,	,	PUNCT
ejpam-6974	154	27	(	(	PUNCT
ejpam-6974	154	28	i	i	NOUN
ejpam-6974	154	29	)	)	PUNCT
ejpam-6974	154	30	1	1	NUM
ejpam-6974	154	31	◦	◦	NOUN
ejpam-6974	154	32	x	x	SYM
ejpam-6974	154	33	=	=	SYM
ejpam-6974	154	34	x	x	X
ejpam-6974	154	35	;	;	PUNCT
ejpam-6974	154	36	(	(	PUNCT
ejpam-6974	154	37	ii	ii	NOUN
ejpam-6974	154	38	)	)	PUNCT
ejpam-6974	154	39	(	(	PUNCT
ejpam-6974	154	40	y	y	NOUN
ejpam-6974	154	41	◦	◦	NOUN
ejpam-6974	154	42	1	1	NUM
ejpam-6974	154	43	)	)	PUNCT
ejpam-6974	154	44	◦	◦	NOUN
ejpam-6974	154	45	(	(	PUNCT
ejpam-6974	154	46	y	y	PROPN
ejpam-6974	154	47	◦	◦	NOUN
ejpam-6974	154	48	x	x	X
ejpam-6974	154	49	)	)	PUNCT
ejpam-6974	154	50	=	=	SYM
ejpam-6974	155	1	x	x	X
ejpam-6974	155	2	;	;	PUNCT
ejpam-6974	155	3	(	(	PUNCT
ejpam-6974	155	4	iii	iii	NOUN
ejpam-6974	155	5	)	)	PUNCT
ejpam-6974	155	6	x	x	PUNCT
ejpam-6974	155	7	◦	◦	NOUN
ejpam-6974	155	8	y	y	NOUN
ejpam-6974	155	9	=	=	NOUN
ejpam-6974	155	10	1	1	NUM
ejpam-6974	155	11	if	if	SCONJ
ejpam-6974	155	12	and	and	CCONJ
ejpam-6974	155	13	only	only	ADV
ejpam-6974	155	14	if	if	SCONJ
ejpam-6974	155	15	x	x	X
ejpam-6974	155	16	=	=	SYM
ejpam-6974	155	17	y.	y.	NOUN
ejpam-6974	155	18	proof	proof	NOUN
ejpam-6974	155	19	.	.	PUNCT
ejpam-6974	156	1	let	let	VERB
ejpam-6974	156	2	(	(	PUNCT
ejpam-6974	156	3	x	x	NOUN
ejpam-6974	156	4	,	,	PUNCT
ejpam-6974	156	5	◦	◦	NOUN
ejpam-6974	156	6	,	,	PUNCT
ejpam-6974	156	7	1	1	NUM
ejpam-6974	156	8	)	)	PUNCT
ejpam-6974	156	9	be	be	AUX
ejpam-6974	156	10	a	a	DET
ejpam-6974	156	11	dual	dual	ADJ
ejpam-6974	156	12	bg	bg	NOUN
ejpam-6974	156	13	-	-	NOUN
ejpam-6974	156	14	algebra	algebra	PROPN
ejpam-6974	156	15	.	.	PUNCT
ejpam-6974	157	1	then	then	ADV
ejpam-6974	157	2	(	(	PUNCT
ejpam-6974	157	3	i	i	NOUN
ejpam-6974	157	4	)	)	PUNCT
ejpam-6974	157	5	and	and	CCONJ
ejpam-6974	157	6	(	(	PUNCT
ejpam-6974	157	7	ii	ii	NOUN
ejpam-6974	157	8	)	)	PUNCT
ejpam-6974	157	9	immediately	immediately	ADV
ejpam-6974	157	10	follow	follow	VERB
ejpam-6974	157	11	from	from	ADP
ejpam-6974	157	12	(	(	PUNCT
ejpam-6974	157	13	dbg2	dbg2	PROPN
ejpam-6974	157	14	)	)	PUNCT
ejpam-6974	157	15	and	and	CCONJ
ejpam-6974	157	16	(	(	PUNCT
ejpam-6974	157	17	dbg3	dbg3	PROPN
ejpam-6974	157	18	)	)	PUNCT
ejpam-6974	157	19	.	.	PUNCT
ejpam-6974	158	1	if	if	SCONJ
ejpam-6974	158	2	x	x	PRON
ejpam-6974	158	3	◦	◦	VERB
ejpam-6974	158	4	y	y	NOUN
ejpam-6974	158	5	=	=	SYM
ejpam-6974	158	6	1	1	NUM
ejpam-6974	158	7	,	,	PUNCT
ejpam-6974	158	8	then	then	ADV
ejpam-6974	158	9	x	x	X
ejpam-6974	158	10	=	=	SYM
ejpam-6974	158	11	y	y	PROPN
ejpam-6974	158	12	by	by	ADP
ejpam-6974	158	13	lemma	lemma	PROPN
ejpam-6974	158	14	2(iv	2(iv	NUM
ejpam-6974	158	15	)	)	PUNCT
ejpam-6974	158	16	.	.	PUNCT
ejpam-6974	159	1	if	if	SCONJ
ejpam-6974	159	2	x	x	X
ejpam-6974	159	3	=	=	SYM
ejpam-6974	159	4	y	y	PROPN
ejpam-6974	159	5	,	,	PUNCT
ejpam-6974	159	6	then	then	ADV
ejpam-6974	159	7	x	x	X
ejpam-6974	159	8	◦	◦	NOUN
ejpam-6974	159	9	y	y	NOUN
ejpam-6974	159	10	=	=	SYM
ejpam-6974	159	11	y	y	PROPN
ejpam-6974	159	12	◦	◦	NOUN
ejpam-6974	159	13	y	y	NOUN
ejpam-6974	159	14	=	=	SYM
ejpam-6974	159	15	1	1	NUM
ejpam-6974	159	16	by	by	ADP
ejpam-6974	159	17	(	(	PUNCT
ejpam-6974	159	18	dbg1	dbg1	ADJ
ejpam-6974	159	19	)	)	PUNCT
ejpam-6974	159	20	.	.	PUNCT
ejpam-6974	160	1	this	this	PRON
ejpam-6974	160	2	proves	prove	VERB
ejpam-6974	160	3	(	(	PUNCT
ejpam-6974	160	4	iii	iii	NOUN
ejpam-6974	160	5	)	)	PUNCT
ejpam-6974	160	6	.	.	PUNCT
ejpam-6974	161	1	so	so	ADV
ejpam-6974	161	2	,	,	PUNCT
ejpam-6974	161	3	x	x	PRON
ejpam-6974	161	4	satisfies	satisfie	NOUN
ejpam-6974	161	5	(	(	PUNCT
ejpam-6974	161	6	i	i	NOUN
ejpam-6974	161	7	)	)	PUNCT
ejpam-6974	161	8	,	,	PUNCT
ejpam-6974	161	9	(	(	PUNCT
ejpam-6974	161	10	ii	ii	NOUN
ejpam-6974	161	11	)	)	PUNCT
ejpam-6974	161	12	,	,	PUNCT
ejpam-6974	161	13	and	and	CCONJ
ejpam-6974	161	14	(	(	PUNCT
ejpam-6974	161	15	iii	iii	NOUN
ejpam-6974	161	16	)	)	PUNCT
ejpam-6974	161	17	.	.	PUNCT
ejpam-6974	162	1	conversely	conversely	ADV
ejpam-6974	162	2	,	,	PUNCT
ejpam-6974	162	3	(	(	PUNCT
ejpam-6974	162	4	dbg1	dbg1	NOUN
ejpam-6974	162	5	)	)	PUNCT
ejpam-6974	162	6	is	be	AUX
ejpam-6974	162	7	implied	imply	VERB
ejpam-6974	162	8	from	from	ADP
ejpam-6974	162	9	(	(	PUNCT
ejpam-6974	162	10	iii	iii	NOUN
ejpam-6974	162	11	)	)	PUNCT
ejpam-6974	162	12	,	,	PUNCT
ejpam-6974	162	13	(	(	PUNCT
ejpam-6974	162	14	dbg2	dbg2	NOUN
ejpam-6974	162	15	)	)	PUNCT
ejpam-6974	162	16	is	be	AUX
ejpam-6974	162	17	equivalent	equivalent	ADJ
ejpam-6974	162	18	to	to	ADP
ejpam-6974	162	19	(	(	PUNCT
ejpam-6974	162	20	i	i	NOUN
ejpam-6974	162	21	)	)	PUNCT
ejpam-6974	162	22	,	,	PUNCT
ejpam-6974	162	23	and	and	CCONJ
ejpam-6974	162	24	(	(	PUNCT
ejpam-6974	162	25	dbg3	dbg3	PROPN
ejpam-6974	162	26	)	)	PUNCT
ejpam-6974	162	27	is	be	AUX
ejpam-6974	162	28	equivalent	equivalent	ADJ
ejpam-6974	162	29	to	to	ADP
ejpam-6974	162	30	(	(	PUNCT
ejpam-6974	162	31	ii	ii	NOUN
ejpam-6974	162	32	)	)	PUNCT
ejpam-6974	162	33	.	.	PUNCT
ejpam-6974	163	1	hence	hence	ADV
ejpam-6974	163	2	,	,	PUNCT
ejpam-6974	163	3	(	(	PUNCT
ejpam-6974	163	4	x	x	NOUN
ejpam-6974	163	5	,	,	PUNCT
ejpam-6974	163	6	◦	◦	NOUN
ejpam-6974	163	7	,	,	PUNCT
ejpam-6974	163	8	1	1	NUM
ejpam-6974	163	9	)	)	PUNCT
ejpam-6974	163	10	is	be	AUX
ejpam-6974	163	11	a	a	DET
ejpam-6974	163	12	dual	dual	ADJ
ejpam-6974	163	13	bg	bg	NOUN
ejpam-6974	163	14	-	-	NOUN
ejpam-6974	163	15	algebra	algebra	NOUN
ejpam-6974	163	16	.	.	PUNCT
ejpam-6974	164	1	every	every	DET
ejpam-6974	164	2	group	group	NOUN
ejpam-6974	164	3	can	can	AUX
ejpam-6974	164	4	generate	generate	VERB
ejpam-6974	164	5	a	a	DET
ejpam-6974	164	6	dual	dual	ADJ
ejpam-6974	164	7	bg	bg	NOUN
ejpam-6974	164	8	-	-	NOUN
ejpam-6974	164	9	algebra	algebra	PROPN
ejpam-6974	164	10	given	give	VERB
ejpam-6974	164	11	a	a	DET
ejpam-6974	164	12	condition	condition	NOUN
ejpam-6974	164	13	.	.	PUNCT
ejpam-6974	165	1	this	this	PRON
ejpam-6974	165	2	is	be	AUX
ejpam-6974	165	3	formalized	formalize	VERB
ejpam-6974	165	4	in	in	ADP
ejpam-6974	165	5	the	the	DET
ejpam-6974	165	6	next	next	ADJ
ejpam-6974	165	7	proposition	proposition	NOUN
ejpam-6974	165	8	.	.	PUNCT
ejpam-6974	166	1	proposition	proposition	NOUN
ejpam-6974	166	2	2	2	NUM
ejpam-6974	166	3	.	.	PUNCT
ejpam-6974	167	1	let	let	VERB
ejpam-6974	167	2	(	(	PUNCT
ejpam-6974	167	3	x	x	X
ejpam-6974	167	4	,	,	PUNCT
ejpam-6974	167	5	∗	∗	NOUN
ejpam-6974	167	6	,	,	PUNCT
ejpam-6974	167	7	1	1	NUM
ejpam-6974	167	8	)	)	PUNCT
ejpam-6974	167	9	be	be	AUX
ejpam-6974	167	10	a	a	DET
ejpam-6974	167	11	group	group	NOUN
ejpam-6974	167	12	where	where	SCONJ
ejpam-6974	167	13	1	1	NUM
ejpam-6974	167	14	is	be	AUX
ejpam-6974	167	15	the	the	DET
ejpam-6974	167	16	identity	identity	NOUN
ejpam-6974	167	17	element	element	NOUN
ejpam-6974	167	18	.	.	PUNCT
ejpam-6974	168	1	then	then	ADV
ejpam-6974	168	2	(	(	PUNCT
ejpam-6974	168	3	x	x	X
ejpam-6974	168	4	,	,	PUNCT
ejpam-6974	168	5	◦	◦	NOUN
ejpam-6974	168	6	,	,	PUNCT
ejpam-6974	168	7	1	1	NUM
ejpam-6974	168	8	)	)	PUNCT
ejpam-6974	168	9	is	be	AUX
ejpam-6974	168	10	a	a	DET
ejpam-6974	168	11	dual	dual	ADJ
ejpam-6974	168	12	bg	bg	NOUN
ejpam-6974	168	13	-	-	NOUN
ejpam-6974	168	14	algebra	algebra	PROPN
ejpam-6974	168	15	assuming	assume	VERB
ejpam-6974	168	16	x	x	VERB
ejpam-6974	168	17	◦	◦	VERB
ejpam-6974	168	18	y	y	PROPN
ejpam-6974	168	19	=	=	SYM
ejpam-6974	168	20	x−1	x−1	PROPN
ejpam-6974	168	21	∗	∗	NOUN
ejpam-6974	168	22	y	y	PROPN
ejpam-6974	168	23	for	for	ADP
ejpam-6974	168	24	any	any	DET
ejpam-6974	168	25	x	x	NOUN
ejpam-6974	168	26	,	,	PUNCT
ejpam-6974	168	27	y	y	PROPN
ejpam-6974	168	28	∈	∈	PROPN
ejpam-6974	168	29	x.	x.	NOUN
ejpam-6974	169	1	the	the	DET
ejpam-6974	169	2	dual	dual	PROPN
ejpam-6974	169	3	bg	bg	NOUN
ejpam-6974	169	4	-	-	NOUN
ejpam-6974	169	5	algebra	algebra	PROPN
ejpam-6974	169	6	(	(	PUNCT
ejpam-6974	169	7	x	x	NOUN
ejpam-6974	169	8	,	,	PUNCT
ejpam-6974	169	9	◦	◦	NOUN
ejpam-6974	169	10	,	,	PUNCT
ejpam-6974	169	11	1	1	NUM
ejpam-6974	169	12	)	)	PUNCT
ejpam-6974	169	13	is	be	AUX
ejpam-6974	169	14	said	say	VERB
ejpam-6974	169	15	to	to	PART
ejpam-6974	169	16	be	be	AUX
ejpam-6974	169	17	group	group	NOUN
ejpam-6974	169	18	-	-	PUNCT
ejpam-6974	169	19	derived	derive	VERB
ejpam-6974	169	20	.	.	PUNCT
ejpam-6974	170	1	proof	proof	NOUN
ejpam-6974	170	2	.	.	PUNCT
ejpam-6974	171	1	let	let	VERB
ejpam-6974	171	2	(	(	PUNCT
ejpam-6974	171	3	x	x	X
ejpam-6974	171	4	,	,	PUNCT
ejpam-6974	171	5	∗	∗	NOUN
ejpam-6974	171	6	,	,	PUNCT
ejpam-6974	171	7	1	1	NUM
ejpam-6974	171	8	)	)	PUNCT
ejpam-6974	171	9	be	be	AUX
ejpam-6974	171	10	a	a	DET
ejpam-6974	171	11	group	group	NOUN
ejpam-6974	172	1	where	where	SCONJ
ejpam-6974	172	2	x	x	X
ejpam-6974	172	3	,	,	PUNCT
ejpam-6974	172	4	y	y	PROPN
ejpam-6974	172	5	in	in	ADP
ejpam-6974	172	6	x.	x.	PROPN
ejpam-6974	172	7	then	then	ADV
ejpam-6974	172	8	(	(	PUNCT
ejpam-6974	172	9	x	x	NOUN
ejpam-6974	172	10	,	,	PUNCT
ejpam-6974	172	11	◦	◦	NOUN
ejpam-6974	172	12	,	,	PUNCT
ejpam-6974	172	13	1	1	X
ejpam-6974	172	14	)	)	PUNCT
ejpam-6974	172	15	satisfies	satisfie	NOUN
ejpam-6974	172	16	(	(	PUNCT
ejpam-6974	172	17	dbg1	dbg1	PROPN
ejpam-6974	172	18	):	):	PUNCT
ejpam-6974	172	19	x	x	PUNCT
ejpam-6974	172	20	◦	◦	NOUN
ejpam-6974	172	21	x	x	X
ejpam-6974	172	22	=	=	SYM
ejpam-6974	172	23	x−1	x−1	PROPN
ejpam-6974	172	24	∗	∗	NOUN
ejpam-6974	172	25	x	x	PUNCT
ejpam-6974	172	26	=	=	SYM
ejpam-6974	172	27	1	1	NUM
ejpam-6974	172	28	,	,	PUNCT
ejpam-6974	172	29	(	(	PUNCT
ejpam-6974	172	30	dbg2	dbg2	NOUN
ejpam-6974	172	31	):	):	PUNCT
ejpam-6974	172	32	1	1	NUM
ejpam-6974	172	33	◦	◦	NOUN
ejpam-6974	172	34	x	x	SYM
ejpam-6974	172	35	=	=	SYM
ejpam-6974	172	36	1−1	1−1	NUM
ejpam-6974	172	37	∗	∗	NOUN
ejpam-6974	172	38	x	x	X
ejpam-6974	172	39	=	=	SYM
ejpam-6974	172	40	1	1	NUM
ejpam-6974	172	41	∗	∗	NOUN
ejpam-6974	172	42	x	x	X
ejpam-6974	172	43	=	=	SYM
ejpam-6974	172	44	x	x	NOUN
ejpam-6974	172	45	,	,	PUNCT
ejpam-6974	172	46	and	and	CCONJ
ejpam-6974	172	47	(	(	PUNCT
ejpam-6974	172	48	dbg3	dbg3	PROPN
ejpam-6974	172	49	):	):	PUNCT
ejpam-6974	172	50	(	(	PUNCT
ejpam-6974	172	51	y	y	PROPN
ejpam-6974	172	52	◦	◦	NOUN
ejpam-6974	172	53	1	1	NUM
ejpam-6974	172	54	)	)	PUNCT
ejpam-6974	172	55	◦	◦	NOUN
ejpam-6974	172	56	(	(	PUNCT
ejpam-6974	172	57	y	y	PROPN
ejpam-6974	172	58	◦	◦	NOUN
ejpam-6974	172	59	x	x	X
ejpam-6974	172	60	)	)	PUNCT
ejpam-6974	172	61	=	=	SYM
ejpam-6974	172	62	c.m	c.m	PROPN
ejpam-6974	172	63	.	.	PROPN
ejpam-6974	172	64	chan	chan	PROPN
ejpam-6974	172	65	,	,	PUNCT
ejpam-6974	172	66	k.	k.	PROPN
ejpam-6974	172	67	fuentes	fuentes	PROPN
ejpam-6974	172	68	/	/	SYM
ejpam-6974	172	69	eur	eur	PROPN
ejpam-6974	172	70	.	.	PUNCT
ejpam-6974	173	1	j.	j.	PROPN
ejpam-6974	173	2	pure	pure	PROPN
ejpam-6974	173	3	appl	appl	PROPN
ejpam-6974	173	4	.	.	PROPN
ejpam-6974	173	5	math	math	PROPN
ejpam-6974	173	6	,	,	PUNCT
ejpam-6974	173	7	18	18	NUM
ejpam-6974	173	8	(	(	PUNCT
ejpam-6974	173	9	4	4	NUM
ejpam-6974	173	10	)	)	PUNCT
ejpam-6974	173	11	(	(	PUNCT
ejpam-6974	173	12	2025	2025	NUM
ejpam-6974	173	13	)	)	PUNCT
ejpam-6974	173	14	,	,	PUNCT
ejpam-6974	173	15	6974	6974	NUM
ejpam-6974	173	16	7	7	NUM
ejpam-6974	173	17	of	of	ADP
ejpam-6974	173	18	16	16	NUM
ejpam-6974	173	19	(	(	PUNCT
ejpam-6974	173	20	y	y	PROPN
ejpam-6974	173	21	◦	◦	PROPN
ejpam-6974	173	22	1)−1	1)−1	NUM
ejpam-6974	173	23	∗	∗	NOUN
ejpam-6974	173	24	(	(	PUNCT
ejpam-6974	173	25	y	y	PROPN
ejpam-6974	173	26	◦	◦	NOUN
ejpam-6974	173	27	x	x	X
ejpam-6974	173	28	)	)	PUNCT
ejpam-6974	173	29	=	=	SYM
ejpam-6974	174	1	(	(	PUNCT
ejpam-6974	174	2	y−1	y−1	PROPN
ejpam-6974	174	3	∗	∗	NOUN
ejpam-6974	174	4	1	1	NUM
ejpam-6974	174	5	)	)	PUNCT
ejpam-6974	174	6	−1	−1	NOUN
ejpam-6974	174	7	∗	∗	NOUN
ejpam-6974	174	8	(	(	PUNCT
ejpam-6974	174	9	y−1	y−1	PROPN
ejpam-6974	174	10	∗	∗	NOUN
ejpam-6974	174	11	x	x	NOUN
ejpam-6974	174	12	)	)	PUNCT
ejpam-6974	174	13	=	=	SYM
ejpam-6974	174	14	y	y	PROPN
ejpam-6974	174	15	∗	∗	NOUN
ejpam-6974	174	16	(	(	PUNCT
ejpam-6974	174	17	y−1	y−1	NOUN
ejpam-6974	174	18	∗	∗	NOUN
ejpam-6974	174	19	x	x	PUNCT
ejpam-6974	174	20	)	)	PUNCT
ejpam-6974	174	21	=	=	SYM
ejpam-6974	174	22	(	(	PUNCT
ejpam-6974	174	23	y	y	NOUN
ejpam-6974	174	24	∗	∗	X
ejpam-6974	174	25	y−1	y−1	PROPN
ejpam-6974	174	26	)	)	PUNCT
ejpam-6974	174	27	∗	∗	NOUN
ejpam-6974	174	28	x	x	X
ejpam-6974	174	29	=	=	SYM
ejpam-6974	174	30	1	1	NUM
ejpam-6974	174	31	∗	∗	NOUN
ejpam-6974	174	32	x	x	X
ejpam-6974	174	33	=	=	PUNCT
ejpam-6974	174	34	x.	x.	NOUN
ejpam-6974	174	35	thus	thus	ADV
ejpam-6974	174	36	,	,	PUNCT
ejpam-6974	174	37	(	(	PUNCT
ejpam-6974	174	38	x	x	X
ejpam-6974	174	39	,	,	PUNCT
ejpam-6974	174	40	◦	◦	NOUN
ejpam-6974	174	41	,	,	PUNCT
ejpam-6974	174	42	1	1	NUM
ejpam-6974	174	43	)	)	PUNCT
ejpam-6974	174	44	is	be	AUX
ejpam-6974	174	45	a	a	DET
ejpam-6974	174	46	dual	dual	ADJ
ejpam-6974	174	47	bg	bg	NOUN
ejpam-6974	174	48	-	-	NOUN
ejpam-6974	174	49	algebra	algebra	PROPN
ejpam-6974	174	50	.	.	PUNCT
ejpam-6974	175	1	example	example	NOUN
ejpam-6974	175	2	11	11	NUM
ejpam-6974	175	3	shows	show	VERB
ejpam-6974	175	4	a	a	DET
ejpam-6974	175	5	dual	dual	ADJ
ejpam-6974	175	6	bg	bg	NOUN
ejpam-6974	175	7	-	-	NOUN
ejpam-6974	175	8	algebra	algebra	NOUN
ejpam-6974	175	9	that	that	PRON
ejpam-6974	175	10	is	be	AUX
ejpam-6974	175	11	non	non	ADJ
ejpam-6974	175	12	-	-	ADJ
ejpam-6974	175	13	group	group	NOUN
ejpam-6974	175	14	-	-	PUNCT
ejpam-6974	175	15	derived	derive	VERB
ejpam-6974	175	16	.	.	PUNCT
ejpam-6974	175	17	example	example	NOUN
ejpam-6974	176	1	11	11	NUM
ejpam-6974	176	2	.	.	PUNCT
ejpam-6974	177	1	let	let	VERB
ejpam-6974	177	2	(	(	PUNCT
ejpam-6974	177	3	x	x	NOUN
ejpam-6974	177	4	,	,	PUNCT
ejpam-6974	177	5	◦	◦	NOUN
ejpam-6974	177	6	,	,	PUNCT
ejpam-6974	177	7	1	1	NUM
ejpam-6974	177	8	)	)	PUNCT
ejpam-6974	177	9	with	with	ADP
ejpam-6974	177	10	the	the	DET
ejpam-6974	177	11	following	follow	VERB
ejpam-6974	177	12	cayley	cayley	ADJ
ejpam-6974	177	13	table	table	NOUN
ejpam-6974	177	14	:	:	PUNCT
ejpam-6974	177	15	table	table	NOUN
ejpam-6974	177	16	7	7	NUM
ejpam-6974	177	17	:	:	PUNCT
ejpam-6974	177	18	cayley	cayley	ADJ
ejpam-6974	177	19	table	table	NOUN
ejpam-6974	177	20	of	of	ADP
ejpam-6974	177	21	the	the	DET
ejpam-6974	177	22	non	non	ADJ
ejpam-6974	177	23	-	-	NOUN
ejpam-6974	177	24	group	group	NOUN
ejpam-6974	177	25	-	-	PUNCT
ejpam-6974	177	26	derived	derive	VERB
ejpam-6974	177	27	dual	dual	ADJ
ejpam-6974	177	28	bg	bg	NOUN
ejpam-6974	177	29	-	-	NOUN
ejpam-6974	177	30	algebra	algebra	PROPN
ejpam-6974	177	31	(	(	PUNCT
ejpam-6974	177	32	x	x	NOUN
ejpam-6974	177	33	,	,	PUNCT
ejpam-6974	177	34	◦	◦	NOUN
ejpam-6974	177	35	,	,	PUNCT
ejpam-6974	177	36	1	1	X
ejpam-6974	177	37	)	)	PUNCT
ejpam-6974	177	38	◦	◦	NOUN
ejpam-6974	177	39	1	1	NUM
ejpam-6974	177	40	a	a	DET
ejpam-6974	177	41	b	b	NUM
ejpam-6974	177	42	1	1	NUM
ejpam-6974	177	43	1	1	NUM
ejpam-6974	177	44	a	a	DET
ejpam-6974	177	45	b	b	NOUN
ejpam-6974	177	46	a	a	DET
ejpam-6974	177	47	a	a	DET
ejpam-6974	177	48	1	1	NUM
ejpam-6974	177	49	b	b	PROPN
ejpam-6974	177	50	b	b	PROPN
ejpam-6974	177	51	b	b	PROPN
ejpam-6974	177	52	a	a	DET
ejpam-6974	177	53	1	1	NUM
ejpam-6974	177	54	then	then	ADV
ejpam-6974	177	55	(	(	PUNCT
ejpam-6974	177	56	x	x	NOUN
ejpam-6974	177	57	,	,	PUNCT
ejpam-6974	177	58	◦	◦	NOUN
ejpam-6974	177	59	,	,	PUNCT
ejpam-6974	177	60	1	1	NUM
ejpam-6974	177	61	)	)	PUNCT
ejpam-6974	177	62	is	be	AUX
ejpam-6974	177	63	a	a	DET
ejpam-6974	177	64	dual	dual	ADJ
ejpam-6974	177	65	bg	bg	NOUN
ejpam-6974	177	66	-	-	NOUN
ejpam-6974	177	67	algebra	algebra	NOUN
ejpam-6974	177	68	.	.	PUNCT
ejpam-6974	178	1	to	to	PART
ejpam-6974	178	2	show	show	VERB
ejpam-6974	178	3	that	that	SCONJ
ejpam-6974	178	4	it	it	PRON
ejpam-6974	178	5	is	be	AUX
ejpam-6974	178	6	non	non	ADJ
ejpam-6974	178	7	-	-	ADJ
ejpam-6974	178	8	group	group	NOUN
ejpam-6974	178	9	-	-	PUNCT
ejpam-6974	178	10	derived	derive	VERB
ejpam-6974	178	11	,	,	PUNCT
ejpam-6974	178	12	assume	assume	VERB
ejpam-6974	178	13	first	first	ADV
ejpam-6974	178	14	that	that	SCONJ
ejpam-6974	178	15	(	(	PUNCT
ejpam-6974	178	16	x	x	NOUN
ejpam-6974	178	17	,	,	PUNCT
ejpam-6974	178	18	◦	◦	NOUN
ejpam-6974	178	19	,	,	PUNCT
ejpam-6974	178	20	1	1	NUM
ejpam-6974	178	21	)	)	PUNCT
ejpam-6974	178	22	is	be	AUX
ejpam-6974	178	23	group	group	NOUN
ejpam-6974	178	24	-	-	PUNCT
ejpam-6974	178	25	derived	derive	VERB
ejpam-6974	178	26	.	.	PUNCT
ejpam-6974	179	1	so	so	ADV
ejpam-6974	179	2	,	,	PUNCT
ejpam-6974	179	3	x	x	PUNCT
ejpam-6974	179	4	◦	◦	NOUN
ejpam-6974	179	5	y	y	NOUN
ejpam-6974	179	6	=	=	SYM
ejpam-6974	179	7	x−1	x−1	PROPN
ejpam-6974	179	8	∗	∗	NOUN
ejpam-6974	179	9	y	y	PROPN
ejpam-6974	179	10	for	for	ADP
ejpam-6974	179	11	any	any	DET
ejpam-6974	179	12	x	x	NOUN
ejpam-6974	179	13	,	,	PUNCT
ejpam-6974	179	14	y	y	PROPN
ejpam-6974	179	15	from	from	ADP
ejpam-6974	179	16	a	a	DET
ejpam-6974	179	17	group	group	NOUN
ejpam-6974	179	18	(	(	PUNCT
ejpam-6974	179	19	x	x	X
ejpam-6974	179	20	,	,	PUNCT
ejpam-6974	179	21	∗	∗	NOUN
ejpam-6974	179	22	,	,	PUNCT
ejpam-6974	179	23	1	1	NUM
ejpam-6974	179	24	)	)	PUNCT
ejpam-6974	179	25	where	where	SCONJ
ejpam-6974	179	26	1	1	NUM
ejpam-6974	179	27	is	be	AUX
ejpam-6974	179	28	the	the	DET
ejpam-6974	179	29	identity	identity	NOUN
ejpam-6974	179	30	element	element	NOUN
ejpam-6974	179	31	.	.	PUNCT
ejpam-6974	180	1	since	since	SCONJ
ejpam-6974	180	2	x	x	PRON
ejpam-6974	180	3	has	have	VERB
ejpam-6974	180	4	only	only	ADV
ejpam-6974	180	5	3	3	NUM
ejpam-6974	180	6	elements	element	NOUN
ejpam-6974	180	7	,	,	PUNCT
ejpam-6974	180	8	the	the	DET
ejpam-6974	180	9	inverse	inverse	NOUN
ejpam-6974	180	10	of	of	ADP
ejpam-6974	180	11	a	a	DET
ejpam-6974	180	12	has	have	AUX
ejpam-6974	180	13	to	to	PART
ejpam-6974	180	14	be	be	AUX
ejpam-6974	180	15	b	b	NOUN
ejpam-6974	180	16	,	,	PUNCT
ejpam-6974	180	17	that	that	ADV
ejpam-6974	180	18	is	is	ADV
ejpam-6974	180	19	,	,	PUNCT
ejpam-6974	180	20	a−1	a−1	PROPN
ejpam-6974	180	21	=	=	PROPN
ejpam-6974	180	22	b.	b.	PROPN
ejpam-6974	180	23	hence	hence	ADV
ejpam-6974	180	24	,	,	PUNCT
ejpam-6974	180	25	b	b	X
ejpam-6974	180	26	=	=	PUNCT
ejpam-6974	180	27	a	a	DET
ejpam-6974	180	28	◦	◦	NOUN
ejpam-6974	180	29	b	b	NOUN
ejpam-6974	180	30	=	=	SYM
ejpam-6974	180	31	a−1	a−1	PROPN
ejpam-6974	180	32	∗	∗	NOUN
ejpam-6974	180	33	b	b	X
ejpam-6974	180	34	=	=	SYM
ejpam-6974	180	35	b	b	PROPN
ejpam-6974	180	36	∗	∗	X
ejpam-6974	180	37	b	b	NOUN
ejpam-6974	180	38	=	=	SYM
ejpam-6974	180	39	a	a	NOUN
ejpam-6974	180	40	,	,	PUNCT
ejpam-6974	180	41	which	which	PRON
ejpam-6974	180	42	is	be	AUX
ejpam-6974	180	43	a	a	DET
ejpam-6974	180	44	contradiction	contradiction	NOUN
ejpam-6974	180	45	.	.	PUNCT
ejpam-6974	181	1	by	by	ADP
ejpam-6974	181	2	example	example	NOUN
ejpam-6974	181	3	11	11	NUM
ejpam-6974	181	4	,	,	PUNCT
ejpam-6974	181	5	there	there	PRON
ejpam-6974	181	6	exists	exist	VERB
ejpam-6974	181	7	a	a	DET
ejpam-6974	181	8	dual	dual	ADJ
ejpam-6974	181	9	bg	bg	NOUN
ejpam-6974	181	10	-	-	NOUN
ejpam-6974	181	11	algebra	algebra	NOUN
ejpam-6974	181	12	that	that	PRON
ejpam-6974	181	13	is	be	AUX
ejpam-6974	181	14	non	non	ADJ
ejpam-6974	181	15	-	-	ADJ
ejpam-6974	181	16	group	group	NOUN
ejpam-6974	181	17	-	-	PUNCT
ejpam-6974	181	18	derived	derive	VERB
ejpam-6974	181	19	,	,	PUNCT
ejpam-6974	181	20	which	which	PRON
ejpam-6974	181	21	leads	lead	VERB
ejpam-6974	181	22	to	to	ADP
ejpam-6974	181	23	the	the	DET
ejpam-6974	181	24	next	next	ADJ
ejpam-6974	181	25	remark	remark	NOUN
ejpam-6974	181	26	.	.	PUNCT
ejpam-6974	182	1	remark	remark	VERB
ejpam-6974	182	2	4	4	NUM
ejpam-6974	182	3	.	.	PUNCT
ejpam-6974	182	4	not	not	PART
ejpam-6974	182	5	all	all	DET
ejpam-6974	182	6	dual	dual	ADJ
ejpam-6974	182	7	bg	bg	NOUN
ejpam-6974	182	8	-	-	PUNCT
ejpam-6974	182	9	algebras	algebra	NOUN
ejpam-6974	182	10	are	be	AUX
ejpam-6974	182	11	group	group	NOUN
ejpam-6974	182	12	-	-	PUNCT
ejpam-6974	182	13	derived	derive	VERB
ejpam-6974	182	14	.	.	PUNCT
ejpam-6974	183	1	the	the	DET
ejpam-6974	183	2	next	next	ADJ
ejpam-6974	183	3	theorem	theorem	NOUN
ejpam-6974	183	4	shows	show	VERB
ejpam-6974	183	5	that	that	SCONJ
ejpam-6974	183	6	a	a	DET
ejpam-6974	183	7	dual	dual	ADJ
ejpam-6974	183	8	bg	bg	NOUN
ejpam-6974	183	9	-	-	PUNCT
ejpam-6974	183	10	algebra	algebra	PROPN
ejpam-6974	183	11	is	be	AUX
ejpam-6974	183	12	group	group	NOUN
ejpam-6974	183	13	-	-	PUNCT
ejpam-6974	183	14	derived	derive	VERB
ejpam-6974	183	15	when	when	SCONJ
ejpam-6974	183	16	it	it	PRON
ejpam-6974	183	17	satisfies	satisfy	VERB
ejpam-6974	183	18	a	a	DET
ejpam-6974	183	19	certain	certain	ADJ
ejpam-6974	183	20	identity	identity	NOUN
ejpam-6974	183	21	.	.	PUNCT
ejpam-6974	184	1	to	to	PART
ejpam-6974	184	2	establish	establish	VERB
ejpam-6974	184	3	this	this	PRON
ejpam-6974	184	4	,	,	PUNCT
ejpam-6974	184	5	define	define	VERB
ejpam-6974	184	6	a	a	DET
ejpam-6974	184	7	binary	binary	ADJ
ejpam-6974	184	8	operation	operation	NOUN
ejpam-6974	184	9	,	,	PUNCT
ejpam-6974	184	10	show	show	VERB
ejpam-6974	184	11	that	that	SCONJ
ejpam-6974	184	12	it	it	PRON
ejpam-6974	184	13	is	be	AUX
ejpam-6974	184	14	a	a	DET
ejpam-6974	184	15	group	group	NOUN
ejpam-6974	184	16	,	,	PUNCT
ejpam-6974	184	17	and	and	CCONJ
ejpam-6974	184	18	then	then	ADV
ejpam-6974	184	19	use	use	VERB
ejpam-6974	184	20	proposition	proposition	NOUN
ejpam-6974	184	21	2	2	NUM
ejpam-6974	184	22	.	.	PUNCT
ejpam-6974	184	23	theorem	theorem	NOUN
ejpam-6974	184	24	4	4	NUM
ejpam-6974	184	25	.	.	PUNCT
ejpam-6974	185	1	let	let	AUX
ejpam-6974	185	2	(	(	PUNCT
ejpam-6974	185	3	x	x	NOUN
ejpam-6974	185	4	,	,	PUNCT
ejpam-6974	185	5	◦	◦	NOUN
ejpam-6974	185	6	,	,	PUNCT
ejpam-6974	185	7	1	1	NUM
ejpam-6974	185	8	)	)	PUNCT
ejpam-6974	185	9	be	be	AUX
ejpam-6974	185	10	a	a	DET
ejpam-6974	185	11	dual	dual	ADJ
ejpam-6974	185	12	bg	bg	NOUN
ejpam-6974	185	13	-	-	NOUN
ejpam-6974	185	14	algebra	algebra	PROPN
ejpam-6974	185	15	with	with	ADP
ejpam-6974	185	16	the	the	DET
ejpam-6974	185	17	identity	identity	NOUN
ejpam-6974	185	18	x	x	PART
ejpam-6974	185	19	◦	◦	NOUN
ejpam-6974	185	20	(	(	PUNCT
ejpam-6974	185	21	y	y	PROPN
ejpam-6974	185	22	◦	◦	PROPN
ejpam-6974	185	23	z	z	PROPN
ejpam-6974	185	24	)	)	PUNCT
ejpam-6974	185	25	=	=	SYM
ejpam-6974	185	26	(	(	PUNCT
ejpam-6974	185	27	(	(	PUNCT
ejpam-6974	185	28	x	x	SYM
ejpam-6974	185	29	◦	◦	NOUN
ejpam-6974	185	30	(	(	PUNCT
ejpam-6974	185	31	y	y	NOUN
ejpam-6974	185	32	◦	◦	NOUN
ejpam-6974	185	33	1	1	NUM
ejpam-6974	185	34	)	)	PUNCT
ejpam-6974	185	35	)	)	PUNCT
ejpam-6974	186	1	◦	◦	NOUN
ejpam-6974	186	2	1	1	NUM
ejpam-6974	186	3	)	)	PUNCT
ejpam-6974	186	4	◦	◦	NOUN
ejpam-6974	186	5	z	z	NOUN
ejpam-6974	186	6	for	for	ADP
ejpam-6974	186	7	all	all	DET
ejpam-6974	186	8	x	x	NOUN
ejpam-6974	186	9	,	,	PUNCT
ejpam-6974	186	10	y	y	PROPN
ejpam-6974	186	11	,	,	PUNCT
ejpam-6974	186	12	z	z	PROPN
ejpam-6974	186	13	∈	∈	PROPN
ejpam-6974	186	14	x.	x.	NOUN
ejpam-6974	186	15	then	then	ADV
ejpam-6974	186	16	(	(	PUNCT
ejpam-6974	186	17	x	x	X
ejpam-6974	186	18	,	,	PUNCT
ejpam-6974	186	19	◦	◦	NOUN
ejpam-6974	186	20	,	,	PUNCT
ejpam-6974	186	21	1	1	NUM
ejpam-6974	186	22	)	)	PUNCT
ejpam-6974	186	23	is	be	AUX
ejpam-6974	186	24	group	group	NOUN
ejpam-6974	186	25	-	-	PUNCT
ejpam-6974	186	26	derived	derive	VERB
ejpam-6974	186	27	.	.	PUNCT
ejpam-6974	187	1	proof	proof	NOUN
ejpam-6974	187	2	.	.	PUNCT
ejpam-6974	188	1	define	define	VERB
ejpam-6974	188	2	a	a	DET
ejpam-6974	188	3	binary	binary	ADJ
ejpam-6974	188	4	operation	operation	NOUN
ejpam-6974	188	5	“	"	PUNCT
ejpam-6974	188	6	∗	∗	NOUN
ejpam-6974	188	7	”	"	PUNCT
ejpam-6974	188	8	on	on	ADP
ejpam-6974	188	9	x	x	PUNCT
ejpam-6974	188	10	as	as	ADP
ejpam-6974	188	11	x	x	PROPN
ejpam-6974	188	12	∗	∗	NOUN
ejpam-6974	188	13	y	y	NOUN
ejpam-6974	188	14	=	=	SYM
ejpam-6974	188	15	(	(	PUNCT
ejpam-6974	188	16	x	x	SYM
ejpam-6974	188	17	◦	◦	NOUN
ejpam-6974	188	18	1	1	NUM
ejpam-6974	188	19	)	)	PUNCT
ejpam-6974	188	20	◦	◦	NOUN
ejpam-6974	188	21	y.	y.	NOUN
ejpam-6974	188	22	note	note	VERB
ejpam-6974	188	23	that	that	SCONJ
ejpam-6974	188	24	x	x	PROPN
ejpam-6974	188	25	∗	∗	NOUN
ejpam-6974	188	26	1	1	NUM
ejpam-6974	188	27	=	=	SYM
ejpam-6974	188	28	(	(	PUNCT
ejpam-6974	188	29	x	x	SYM
ejpam-6974	188	30	◦	◦	NOUN
ejpam-6974	188	31	1	1	NUM
ejpam-6974	188	32	)	)	PUNCT
ejpam-6974	188	33	◦	◦	NOUN
ejpam-6974	188	34	1	1	NUM
ejpam-6974	188	35	=	=	NOUN
ejpam-6974	188	36	x	x	PUNCT
ejpam-6974	188	37	by	by	ADP
ejpam-6974	188	38	lemma	lemma	PROPN
ejpam-6974	188	39	2(i	2(i	NUM
ejpam-6974	188	40	)	)	PUNCT
ejpam-6974	188	41	and	and	CCONJ
ejpam-6974	188	42	1	1	NUM
ejpam-6974	188	43	∗	∗	NOUN
ejpam-6974	188	44	x	x	X
ejpam-6974	188	45	=	=	SYM
ejpam-6974	188	46	(	(	PUNCT
ejpam-6974	188	47	1	1	NUM
ejpam-6974	188	48	◦	◦	NOUN
ejpam-6974	188	49	1	1	NUM
ejpam-6974	188	50	)	)	PUNCT
ejpam-6974	188	51	◦	◦	NOUN
ejpam-6974	188	52	x	x	SYM
ejpam-6974	188	53	=	=	SYM
ejpam-6974	188	54	1	1	NUM
ejpam-6974	188	55	◦	◦	NOUN
ejpam-6974	188	56	x	x	SYM
ejpam-6974	188	57	=	=	PUNCT
ejpam-6974	188	58	x	x	SYM
ejpam-6974	188	59	by	by	ADP
ejpam-6974	188	60	(	(	PUNCT
ejpam-6974	188	61	dbg1	dbg1	ADJ
ejpam-6974	188	62	)	)	PUNCT
ejpam-6974	188	63	and	and	CCONJ
ejpam-6974	188	64	(	(	PUNCT
ejpam-6974	188	65	dbg2	dbg2	PROPN
ejpam-6974	188	66	)	)	PUNCT
ejpam-6974	188	67	.	.	PUNCT
ejpam-6974	189	1	so	so	ADV
ejpam-6974	189	2	1	1	NUM
ejpam-6974	189	3	is	be	AUX
ejpam-6974	189	4	the	the	DET
ejpam-6974	189	5	identity	identity	NOUN
ejpam-6974	189	6	element	element	NOUN
ejpam-6974	189	7	with	with	ADP
ejpam-6974	189	8	respect	respect	NOUN
ejpam-6974	189	9	to	to	ADP
ejpam-6974	189	10	the	the	DET
ejpam-6974	189	11	binary	binary	PROPN
ejpam-6974	189	12	operation	operation	NOUN
ejpam-6974	189	13	“	"	PUNCT
ejpam-6974	189	14	∗	∗	NOUN
ejpam-6974	189	15	”	"	PUNCT
ejpam-6974	189	16	.	.	PUNCT
ejpam-6974	190	1	also	also	ADV
ejpam-6974	190	2	x	x	VERB
ejpam-6974	190	3	∗	∗	NOUN
ejpam-6974	190	4	(	(	PUNCT
ejpam-6974	190	5	x	x	SYM
ejpam-6974	190	6	◦	◦	NOUN
ejpam-6974	190	7	1	1	NUM
ejpam-6974	190	8	)	)	PUNCT
ejpam-6974	190	9	=	=	SYM
ejpam-6974	190	10	(	(	PUNCT
ejpam-6974	190	11	x	x	SYM
ejpam-6974	190	12	◦	◦	NOUN
ejpam-6974	190	13	1	1	NUM
ejpam-6974	190	14	)	)	PUNCT
ejpam-6974	190	15	◦	◦	NOUN
ejpam-6974	190	16	(	(	PUNCT
ejpam-6974	190	17	x	x	SYM
ejpam-6974	190	18	◦	◦	NOUN
ejpam-6974	190	19	1	1	NUM
ejpam-6974	190	20	)	)	PUNCT
ejpam-6974	190	21	=	=	SYM
ejpam-6974	190	22	1	1	NUM
ejpam-6974	190	23	by	by	ADP
ejpam-6974	190	24	(	(	PUNCT
ejpam-6974	190	25	dbg1	dbg1	ADJ
ejpam-6974	190	26	)	)	PUNCT
ejpam-6974	190	27	and	and	CCONJ
ejpam-6974	190	28	(	(	PUNCT
ejpam-6974	190	29	x	x	X
ejpam-6974	190	30	◦	◦	NOUN
ejpam-6974	190	31	1	1	NUM
ejpam-6974	190	32	)	)	PUNCT
ejpam-6974	190	33	∗x	∗x	NOUN
ejpam-6974	190	34	=	=	SYM
ejpam-6974	190	35	(	(	PUNCT
ejpam-6974	190	36	(	(	PUNCT
ejpam-6974	190	37	x	x	SYM
ejpam-6974	190	38	◦	◦	NOUN
ejpam-6974	190	39	1	1	NUM
ejpam-6974	190	40	)	)	PUNCT
ejpam-6974	190	41	◦	◦	NOUN
ejpam-6974	190	42	1	1	NUM
ejpam-6974	190	43	)	)	PUNCT
ejpam-6974	190	44	◦	◦	NOUN
ejpam-6974	190	45	x	x	SYM
ejpam-6974	190	46	=	=	SYM
ejpam-6974	190	47	x	x	SYM
ejpam-6974	190	48	◦	◦	NOUN
ejpam-6974	190	49	x	x	SYM
ejpam-6974	190	50	=	=	SYM
ejpam-6974	190	51	1	1	NUM
ejpam-6974	190	52	by	by	ADP
ejpam-6974	190	53	lemma	lemma	PROPN
ejpam-6974	190	54	2(i	2(i	NUM
ejpam-6974	190	55	)	)	PUNCT
ejpam-6974	190	56	and	and	CCONJ
ejpam-6974	190	57	(	(	PUNCT
ejpam-6974	190	58	dbg1	dbg1	PROPN
ejpam-6974	190	59	)	)	PUNCT
ejpam-6974	190	60	.	.	PUNCT
ejpam-6974	191	1	thus	thus	ADV
ejpam-6974	191	2	,	,	PUNCT
ejpam-6974	191	3	x	x	X
ejpam-6974	191	4	◦	◦	NOUN
ejpam-6974	191	5	1	1	NUM
ejpam-6974	191	6	is	be	AUX
ejpam-6974	191	7	the	the	DET
ejpam-6974	191	8	inverse	inverse	NOUN
ejpam-6974	191	9	for	for	ADP
ejpam-6974	191	10	x.	x.	NOUN
ejpam-6974	191	11	now	now	ADV
ejpam-6974	191	12	,	,	PUNCT
ejpam-6974	191	13	x∗(y∗z	x∗(y∗z	PROPN
ejpam-6974	191	14	)	)	PUNCT
ejpam-6974	192	1	=	=	PRON
ejpam-6974	192	2	(	(	PUNCT
ejpam-6974	192	3	x	x	PART
ejpam-6974	192	4	◦	◦	NOUN
ejpam-6974	192	5	1)	1)	NUM
ejpam-6974	192	6	◦	◦	NOUN
ejpam-6974	192	7	(y∗z	(y∗z	NOUN
ejpam-6974	192	8	)	)	PUNCT
ejpam-6974	192	9	=	=	SYM
ejpam-6974	192	10	(	(	PUNCT
ejpam-6974	192	11	x	x	X
ejpam-6974	192	12	◦	◦	NOUN
ejpam-6974	192	13	1	1	NUM
ejpam-6974	192	14	)	)	PUNCT
ejpam-6974	192	15	◦	◦	NOUN
ejpam-6974	193	1	[	[	X
ejpam-6974	193	2	(	(	PUNCT
ejpam-6974	193	3	y	y	NOUN
ejpam-6974	193	4	◦	◦	NOUN
ejpam-6974	193	5	1	1	NUM
ejpam-6974	193	6	)	)	PUNCT
ejpam-6974	193	7	◦	◦	NOUN
ejpam-6974	193	8	z	z	X
ejpam-6974	193	9	]	]	X
ejpam-6974	193	10	=	=	PUNCT
ejpam-6974	194	1	[	[	X
ejpam-6974	194	2	[	[	X
ejpam-6974	194	3	(	(	PUNCT
ejpam-6974	194	4	x	x	SYM
ejpam-6974	194	5	◦	◦	NOUN
ejpam-6974	194	6	1	1	NUM
ejpam-6974	194	7	)	)	PUNCT
ejpam-6974	194	8	◦	◦	NOUN
ejpam-6974	195	1	[	[	X
ejpam-6974	195	2	(	(	PUNCT
ejpam-6974	195	3	y	y	NOUN
ejpam-6974	195	4	◦	◦	NOUN
ejpam-6974	195	5	1	1	NUM
ejpam-6974	195	6	)	)	PUNCT
ejpam-6974	195	7	◦	◦	NOUN
ejpam-6974	195	8	1	1	NUM
ejpam-6974	195	9	]	]	PUNCT
ejpam-6974	195	10	]	]	X
ejpam-6974	195	11	◦	◦	NOUN
ejpam-6974	195	12	1]	1]	NUM
ejpam-6974	195	13	◦	◦	NOUN
ejpam-6974	195	14	z	z	NOUN
ejpam-6974	195	15	by	by	ADP
ejpam-6974	195	16	replacing	replace	VERB
ejpam-6974	195	17	x	x	PUNCT
ejpam-6974	195	18	with	with	ADP
ejpam-6974	195	19	x	x	PART
ejpam-6974	195	20	◦	◦	NOUN
ejpam-6974	195	21	1	1	NUM
ejpam-6974	195	22	and	and	CCONJ
ejpam-6974	195	23	y	y	PROPN
ejpam-6974	195	24	with	with	ADP
ejpam-6974	195	25	y	y	PROPN
ejpam-6974	195	26	◦	◦	NOUN
ejpam-6974	195	27	1	1	NUM
ejpam-6974	195	28	in	in	ADP
ejpam-6974	195	29	the	the	DET
ejpam-6974	195	30	given	give	VERB
ejpam-6974	195	31	identity	identity	NOUN
ejpam-6974	195	32	.	.	PUNCT
ejpam-6974	196	1	by	by	ADP
ejpam-6974	196	2	lemma	lemma	PROPN
ejpam-6974	196	3	2(i	2(i	NUM
ejpam-6974	196	4	)	)	PUNCT
ejpam-6974	196	5	,	,	PUNCT
ejpam-6974	196	6	x	x	X
ejpam-6974	196	7	∗	∗	NOUN
ejpam-6974	196	8	(	(	PUNCT
ejpam-6974	196	9	y	y	PROPN
ejpam-6974	196	10	∗	∗	PROPN
ejpam-6974	196	11	z	z	NOUN
ejpam-6974	196	12	)	)	PUNCT
ejpam-6974	196	13	=	=	PUNCT
ejpam-6974	197	1	[	[	X
ejpam-6974	197	2	[	[	X
ejpam-6974	197	3	(	(	PUNCT
ejpam-6974	197	4	x	x	SYM
ejpam-6974	197	5	◦	◦	NOUN
ejpam-6974	197	6	1	1	NUM
ejpam-6974	197	7	)	)	PUNCT
ejpam-6974	197	8	◦	◦	NOUN
ejpam-6974	197	9	y	y	PROPN
ejpam-6974	197	10	]	]	X
ejpam-6974	197	11	◦	◦	NOUN
ejpam-6974	197	12	1	1	NUM
ejpam-6974	197	13	]	]	X
ejpam-6974	197	14	◦	◦	NOUN
ejpam-6974	197	15	z.	z.	PROPN
ejpam-6974	198	1	the	the	DET
ejpam-6974	198	2	continuation	continuation	NOUN
ejpam-6974	198	3	is	be	AUX
ejpam-6974	198	4	as	as	SCONJ
ejpam-6974	198	5	follows	follow	VERB
ejpam-6974	198	6	:	:	PUNCT
ejpam-6974	198	7	x	x	SYM
ejpam-6974	198	8	∗	∗	NOUN
ejpam-6974	198	9	(	(	PUNCT
ejpam-6974	198	10	y	y	PROPN
ejpam-6974	198	11	∗	∗	PROPN
ejpam-6974	198	12	z	z	NOUN
ejpam-6974	198	13	)	)	PUNCT
ejpam-6974	198	14	=	=	PUNCT
ejpam-6974	199	1	[	[	X
ejpam-6974	199	2	(	(	PUNCT
ejpam-6974	199	3	x	x	X
ejpam-6974	199	4	∗	∗	PROPN
ejpam-6974	199	5	y	y	NOUN
ejpam-6974	199	6	)	)	PUNCT
ejpam-6974	199	7	◦	◦	NOUN
ejpam-6974	199	8	1	1	NUM
ejpam-6974	199	9	]	]	X
ejpam-6974	199	10	◦	◦	NOUN
ejpam-6974	199	11	z	z	NOUN
ejpam-6974	199	12	=	=	SYM
ejpam-6974	199	13	(	(	PUNCT
ejpam-6974	199	14	x	x	X
ejpam-6974	199	15	∗	∗	PROPN
ejpam-6974	199	16	y	y	NOUN
ejpam-6974	199	17	)	)	PUNCT
ejpam-6974	199	18	∗	∗	NOUN
ejpam-6974	199	19	z.	z.	PROPN
ejpam-6974	200	1	hence	hence	ADV
ejpam-6974	200	2	,	,	PUNCT
ejpam-6974	200	3	(	(	PUNCT
ejpam-6974	200	4	x	x	X
ejpam-6974	200	5	,	,	PUNCT
ejpam-6974	200	6	∗	∗	NOUN
ejpam-6974	200	7	,	,	PUNCT
ejpam-6974	200	8	1	1	NUM
ejpam-6974	200	9	)	)	PUNCT
ejpam-6974	200	10	is	be	AUX
ejpam-6974	200	11	a	a	DET
ejpam-6974	200	12	group	group	NOUN
ejpam-6974	200	13	by	by	ADP
ejpam-6974	200	14	definition	definition	NOUN
ejpam-6974	200	15	2	2	NUM
ejpam-6974	200	16	.	.	X
ejpam-6974	200	17	observe	observe	VERB
ejpam-6974	200	18	that	that	PRON
ejpam-6974	200	19	x−1	x−1	PROPN
ejpam-6974	200	20	∗	∗	NOUN
ejpam-6974	200	21	y	y	PROPN
ejpam-6974	200	22	=	=	PUNCT
ejpam-6974	200	23	(	(	PUNCT
ejpam-6974	200	24	x−1	x−1	NOUN
ejpam-6974	200	25	◦	◦	NOUN
ejpam-6974	200	26	1	1	NUM
ejpam-6974	200	27	)	)	PUNCT
ejpam-6974	201	1	◦	◦	NOUN
ejpam-6974	201	2	y	y	NOUN
ejpam-6974	202	1	=	=	PUNCT
ejpam-6974	203	1	[	[	X
ejpam-6974	203	2	(	(	PUNCT
ejpam-6974	203	3	x	x	SYM
ejpam-6974	203	4	◦	◦	NOUN
ejpam-6974	203	5	1	1	NUM
ejpam-6974	203	6	)	)	PUNCT
ejpam-6974	203	7	◦	◦	NOUN
ejpam-6974	203	8	1	1	NUM
ejpam-6974	203	9	]	]	X
ejpam-6974	203	10	◦	◦	NOUN
ejpam-6974	203	11	y	y	NOUN
ejpam-6974	203	12	=	=	PUNCT
ejpam-6974	203	13	x	x	PUNCT
ejpam-6974	203	14	◦	◦	NOUN
ejpam-6974	203	15	y.	y.	NOUN
ejpam-6974	203	16	therefore	therefore	ADV
ejpam-6974	203	17	,	,	PUNCT
ejpam-6974	203	18	(	(	PUNCT
ejpam-6974	203	19	x	x	NOUN
ejpam-6974	203	20	,	,	PUNCT
ejpam-6974	203	21	◦	◦	NOUN
ejpam-6974	203	22	,	,	PUNCT
ejpam-6974	203	23	1	1	NUM
ejpam-6974	203	24	)	)	PUNCT
ejpam-6974	203	25	is	be	AUX
ejpam-6974	203	26	a	a	DET
ejpam-6974	203	27	group	group	NOUN
ejpam-6974	203	28	-	-	PUNCT
ejpam-6974	203	29	derived	derive	VERB
ejpam-6974	203	30	dual	dual	ADJ
ejpam-6974	203	31	bg	bg	NOUN
ejpam-6974	203	32	-	-	NOUN
ejpam-6974	203	33	algebra	algebra	NOUN
ejpam-6974	203	34	by	by	ADP
ejpam-6974	203	35	proposition	proposition	NOUN
ejpam-6974	203	36	2	2	NUM
ejpam-6974	203	37	.	.	X
ejpam-6974	204	1	consider	consider	VERB
ejpam-6974	204	2	example	example	NOUN
ejpam-6974	204	3	11	11	NUM
ejpam-6974	204	4	.	.	PUNCT
ejpam-6974	205	1	note	note	VERB
ejpam-6974	205	2	that	that	PRON
ejpam-6974	206	1	b	b	X
ejpam-6974	206	2	◦	◦	NOUN
ejpam-6974	206	3	(	(	PUNCT
ejpam-6974	206	4	a	a	DET
ejpam-6974	206	5	◦	◦	NOUN
ejpam-6974	206	6	b	b	NOUN
ejpam-6974	206	7	)	)	PUNCT
ejpam-6974	206	8	=	=	SYM
ejpam-6974	207	1	b	b	X
ejpam-6974	207	2	◦	◦	NOUN
ejpam-6974	207	3	b	b	NOUN
ejpam-6974	207	4	=	=	SYM
ejpam-6974	207	5	1	1	NUM
ejpam-6974	207	6	while	while	SCONJ
ejpam-6974	207	7	(	(	PUNCT
ejpam-6974	207	8	(	(	PUNCT
ejpam-6974	207	9	b	b	X
ejpam-6974	207	10	◦	◦	NOUN
ejpam-6974	207	11	(	(	PUNCT
ejpam-6974	207	12	a	a	DET
ejpam-6974	207	13	◦	◦	NOUN
ejpam-6974	207	14	1	1	NUM
ejpam-6974	207	15	)	)	PUNCT
ejpam-6974	207	16	)	)	PUNCT
ejpam-6974	208	1	◦	◦	NOUN
ejpam-6974	208	2	1	1	NUM
ejpam-6974	208	3	)	)	PUNCT
ejpam-6974	208	4	◦	◦	NOUN
ejpam-6974	208	5	b	b	PROPN
ejpam-6974	208	6	=	=	PROPN
ejpam-6974	208	7	b.	b.	PROPN
ejpam-6974	209	1	so	so	ADV
ejpam-6974	209	2	,	,	PUNCT
ejpam-6974	209	3	the	the	DET
ejpam-6974	209	4	condition	condition	NOUN
ejpam-6974	209	5	x	x	VERB
ejpam-6974	209	6	◦	◦	NOUN
ejpam-6974	209	7	(	(	PUNCT
ejpam-6974	209	8	y	y	PROPN
ejpam-6974	209	9	◦	◦	PROPN
ejpam-6974	209	10	z	z	PROPN
ejpam-6974	209	11	)	)	PUNCT
ejpam-6974	209	12	=	=	SYM
ejpam-6974	209	13	(	(	PUNCT
ejpam-6974	209	14	(	(	PUNCT
ejpam-6974	209	15	x	x	SYM
ejpam-6974	209	16	◦	◦	NOUN
ejpam-6974	209	17	(	(	PUNCT
ejpam-6974	209	18	y	y	NOUN
ejpam-6974	209	19	◦	◦	NOUN
ejpam-6974	209	20	1	1	NUM
ejpam-6974	209	21	)	)	PUNCT
ejpam-6974	209	22	)	)	PUNCT
ejpam-6974	209	23	◦	◦	NOUN
ejpam-6974	209	24	1	1	NUM
ejpam-6974	209	25	)	)	PUNCT
ejpam-6974	209	26	◦	◦	NOUN
ejpam-6974	209	27	z	z	NOUN
ejpam-6974	209	28	in	in	ADP
ejpam-6974	209	29	theorem	theorem	NOUN
ejpam-6974	209	30	4	4	NUM
ejpam-6974	209	31	is	be	AUX
ejpam-6974	209	32	not	not	PART
ejpam-6974	209	33	necessarily	necessarily	ADV
ejpam-6974	209	34	true	true	ADJ
ejpam-6974	209	35	in	in	ADP
ejpam-6974	209	36	general	general	ADJ
ejpam-6974	209	37	.	.	PUNCT
ejpam-6974	209	38	example	example	NOUN
ejpam-6974	210	1	12	12	NUM
ejpam-6974	210	2	.	.	PUNCT
ejpam-6974	211	1	consider	consider	VERB
ejpam-6974	211	2	the	the	DET
ejpam-6974	211	3	dual	dual	ADJ
ejpam-6974	211	4	bg	bg	NOUN
ejpam-6974	211	5	-	-	NOUN
ejpam-6974	211	6	algebra	algebra	PROPN
ejpam-6974	211	7	(	(	PUNCT
ejpam-6974	211	8	x	x	NOUN
ejpam-6974	211	9	,	,	PUNCT
ejpam-6974	211	10	◦	◦	NOUN
ejpam-6974	211	11	,	,	PUNCT
ejpam-6974	211	12	1	1	NUM
ejpam-6974	211	13	)	)	PUNCT
ejpam-6974	211	14	from	from	ADP
ejpam-6974	211	15	example	example	NOUN
ejpam-6974	211	16	9	9	NUM
ejpam-6974	211	17	.	.	PUNCT
ejpam-6974	212	1	it	it	PRON
ejpam-6974	212	2	satisfies	satisfy	VERB
ejpam-6974	212	3	the	the	DET
ejpam-6974	212	4	identity	identity	NOUN
ejpam-6974	212	5	x	x	PART
ejpam-6974	212	6	◦	◦	NOUN
ejpam-6974	212	7	(	(	PUNCT
ejpam-6974	212	8	y	y	PROPN
ejpam-6974	212	9	◦	◦	PROPN
ejpam-6974	212	10	z	z	PROPN
ejpam-6974	212	11	)	)	PUNCT
ejpam-6974	212	12	=	=	SYM
ejpam-6974	212	13	(	(	PUNCT
ejpam-6974	212	14	(	(	PUNCT
ejpam-6974	212	15	x	x	SYM
ejpam-6974	212	16	◦	◦	NOUN
ejpam-6974	212	17	(	(	PUNCT
ejpam-6974	212	18	y	y	NOUN
ejpam-6974	212	19	◦	◦	NOUN
ejpam-6974	212	20	1	1	NUM
ejpam-6974	212	21	)	)	PUNCT
ejpam-6974	212	22	)	)	PUNCT
ejpam-6974	213	1	◦	◦	NOUN
ejpam-6974	213	2	1	1	NUM
ejpam-6974	213	3	)	)	PUNCT
ejpam-6974	213	4	◦	◦	NOUN
ejpam-6974	213	5	z.	z.	PROPN
ejpam-6974	213	6	hence	hence	ADV
ejpam-6974	213	7	,	,	PUNCT
ejpam-6974	213	8	(	(	PUNCT
ejpam-6974	213	9	x	x	NOUN
ejpam-6974	213	10	,	,	PUNCT
ejpam-6974	213	11	◦	◦	NOUN
ejpam-6974	213	12	,	,	PUNCT
ejpam-6974	213	13	1	1	NUM
ejpam-6974	213	14	)	)	PUNCT
ejpam-6974	213	15	is	be	AUX
ejpam-6974	213	16	a	a	DET
ejpam-6974	213	17	group	group	NOUN
ejpam-6974	213	18	-	-	PUNCT
ejpam-6974	213	19	derived	derive	VERB
ejpam-6974	213	20	dual	dual	ADJ
ejpam-6974	213	21	bgalgebra	bgalgebra	NOUN
ejpam-6974	213	22	by	by	ADP
ejpam-6974	213	23	theorem	theorem	ADJ
ejpam-6974	213	24	4	4	NUM
ejpam-6974	213	25	.	.	PUNCT
ejpam-6974	213	26	c.m	c.m	PROPN
ejpam-6974	213	27	.	.	PROPN
ejpam-6974	213	28	chan	chan	PROPN
ejpam-6974	213	29	,	,	PUNCT
ejpam-6974	213	30	k.	k.	PROPN
ejpam-6974	213	31	fuentes	fuentes	PROPN
ejpam-6974	213	32	/	/	SYM
ejpam-6974	213	33	eur	eur	PROPN
ejpam-6974	213	34	.	.	PUNCT
ejpam-6974	214	1	j.	j.	PROPN
ejpam-6974	214	2	pure	pure	PROPN
ejpam-6974	214	3	appl	appl	PROPN
ejpam-6974	214	4	.	.	PROPN
ejpam-6974	214	5	math	math	PROPN
ejpam-6974	214	6	,	,	PUNCT
ejpam-6974	214	7	18	18	NUM
ejpam-6974	214	8	(	(	PUNCT
ejpam-6974	214	9	4	4	NUM
ejpam-6974	214	10	)	)	PUNCT
ejpam-6974	214	11	(	(	PUNCT
ejpam-6974	214	12	2025	2025	NUM
ejpam-6974	214	13	)	)	PUNCT
ejpam-6974	214	14	,	,	PUNCT
ejpam-6974	214	15	6974	6974	NUM
ejpam-6974	214	16	8	8	NUM
ejpam-6974	214	17	of	of	ADP
ejpam-6974	214	18	16	16	NUM
ejpam-6974	214	19	theorem	theorem	VERB
ejpam-6974	214	20	5	5	NUM
ejpam-6974	214	21	characterizes	characterize	VERB
ejpam-6974	214	22	a	a	DET
ejpam-6974	214	23	group	group	NOUN
ejpam-6974	214	24	-	-	PUNCT
ejpam-6974	214	25	derived	derive	VERB
ejpam-6974	214	26	dual	dual	ADJ
ejpam-6974	214	27	bg	bg	NOUN
ejpam-6974	214	28	-	-	NOUN
ejpam-6974	214	29	algebra	algebra	NOUN
ejpam-6974	214	30	through	through	ADP
ejpam-6974	214	31	the	the	DET
ejpam-6974	214	32	dual	dual	ADJ
ejpam-6974	214	33	b	b	NOUN
ejpam-6974	214	34	-	-	PUNCT
ejpam-6974	214	35	algebra	algebra	NOUN
ejpam-6974	214	36	.	.	PUNCT
ejpam-6974	215	1	theorem	theorem	NOUN
ejpam-6974	215	2	5	5	NUM
ejpam-6974	215	3	.	.	PUNCT
ejpam-6974	216	1	let	let	AUX
ejpam-6974	216	2	(	(	PUNCT
ejpam-6974	216	3	x	x	NOUN
ejpam-6974	216	4	,	,	PUNCT
ejpam-6974	216	5	◦	◦	NOUN
ejpam-6974	216	6	,	,	PUNCT
ejpam-6974	216	7	1	1	NUM
ejpam-6974	216	8	)	)	PUNCT
ejpam-6974	216	9	be	be	AUX
ejpam-6974	216	10	an	an	DET
ejpam-6974	216	11	algebra	algebra	NOUN
ejpam-6974	216	12	of	of	ADP
ejpam-6974	216	13	type	type	NOUN
ejpam-6974	216	14	(	(	PUNCT
ejpam-6974	216	15	2	2	NUM
ejpam-6974	216	16	,	,	PUNCT
ejpam-6974	216	17	0	0	NUM
ejpam-6974	216	18	)	)	PUNCT
ejpam-6974	216	19	.	.	PUNCT
ejpam-6974	217	1	then	then	ADV
ejpam-6974	217	2	(	(	PUNCT
ejpam-6974	217	3	x	x	X
ejpam-6974	217	4	,	,	PUNCT
ejpam-6974	217	5	◦	◦	NOUN
ejpam-6974	217	6	,	,	PUNCT
ejpam-6974	217	7	1	1	NUM
ejpam-6974	217	8	)	)	PUNCT
ejpam-6974	217	9	is	be	AUX
ejpam-6974	217	10	a	a	DET
ejpam-6974	217	11	dual	dual	ADJ
ejpam-6974	217	12	b	b	NOUN
ejpam-6974	217	13	-	-	PUNCT
ejpam-6974	217	14	algebra	algebra	NOUN
ejpam-6974	217	15	if	if	SCONJ
ejpam-6974	218	1	and	and	CCONJ
ejpam-6974	218	2	only	only	ADV
ejpam-6974	218	3	if	if	SCONJ
ejpam-6974	218	4	it	it	PRON
ejpam-6974	218	5	is	be	AUX
ejpam-6974	218	6	a	a	DET
ejpam-6974	218	7	group	group	NOUN
ejpam-6974	218	8	-	-	PUNCT
ejpam-6974	218	9	derived	derive	VERB
ejpam-6974	218	10	dual	dual	ADJ
ejpam-6974	218	11	bg	bg	NOUN
ejpam-6974	218	12	-	-	NOUN
ejpam-6974	218	13	algebra	algebra	NOUN
ejpam-6974	218	14	.	.	PUNCT
ejpam-6974	219	1	proof	proof	NOUN
ejpam-6974	219	2	.	.	PUNCT
ejpam-6974	220	1	let	let	VERB
ejpam-6974	220	2	(	(	PUNCT
ejpam-6974	220	3	x	x	NOUN
ejpam-6974	220	4	,	,	PUNCT
ejpam-6974	220	5	◦	◦	NOUN
ejpam-6974	220	6	,	,	PUNCT
ejpam-6974	220	7	1	1	NUM
ejpam-6974	220	8	)	)	PUNCT
ejpam-6974	220	9	be	be	AUX
ejpam-6974	220	10	a	a	DET
ejpam-6974	220	11	dual	dual	ADJ
ejpam-6974	220	12	b	b	NOUN
ejpam-6974	220	13	-	-	PUNCT
ejpam-6974	220	14	algebra	algebra	NOUN
ejpam-6974	220	15	.	.	PUNCT
ejpam-6974	221	1	(	(	PUNCT
ejpam-6974	221	2	dbg1	dbg1	NOUN
ejpam-6974	221	3	)	)	PUNCT
ejpam-6974	221	4	,	,	PUNCT
ejpam-6974	221	5	(	(	PUNCT
ejpam-6974	221	6	dbg2	dbg2	PROPN
ejpam-6974	221	7	)	)	PUNCT
ejpam-6974	221	8	,	,	PUNCT
ejpam-6974	221	9	and	and	CCONJ
ejpam-6974	221	10	(	(	PUNCT
ejpam-6974	221	11	dbg3	dbg3	PROPN
ejpam-6974	221	12	)	)	PUNCT
ejpam-6974	221	13	immediately	immediately	ADV
ejpam-6974	221	14	follow	follow	VERB
ejpam-6974	221	15	from	from	ADP
ejpam-6974	221	16	(	(	PUNCT
ejpam-6974	221	17	db1	db1	NOUN
ejpam-6974	221	18	)	)	PUNCT
ejpam-6974	221	19	,	,	PUNCT
ejpam-6974	221	20	(	(	PUNCT
ejpam-6974	221	21	db2	db2	PROPN
ejpam-6974	221	22	)	)	PUNCT
ejpam-6974	221	23	,	,	PUNCT
ejpam-6974	221	24	and	and	CCONJ
ejpam-6974	221	25	lemma	lemma	PROPN
ejpam-6974	221	26	1	1	NUM
ejpam-6974	221	27	,	,	PUNCT
ejpam-6974	221	28	respectively	respectively	ADV
ejpam-6974	221	29	.	.	PUNCT
ejpam-6974	222	1	thus	thus	ADV
ejpam-6974	222	2	,	,	PUNCT
ejpam-6974	222	3	(	(	PUNCT
ejpam-6974	222	4	x	x	X
ejpam-6974	222	5	,	,	PUNCT
ejpam-6974	222	6	◦	◦	NOUN
ejpam-6974	222	7	,	,	PUNCT
ejpam-6974	222	8	1	1	NUM
ejpam-6974	222	9	)	)	PUNCT
ejpam-6974	222	10	is	be	AUX
ejpam-6974	222	11	a	a	DET
ejpam-6974	222	12	dual	dual	ADJ
ejpam-6974	222	13	bgalgebra	bgalgebra	NOUN
ejpam-6974	222	14	.	.	PUNCT
ejpam-6974	223	1	define	define	VERB
ejpam-6974	223	2	a	a	DET
ejpam-6974	223	3	binary	binary	ADJ
ejpam-6974	223	4	operation	operation	NOUN
ejpam-6974	223	5	“	"	PUNCT
ejpam-6974	223	6	∗	∗	NOUN
ejpam-6974	223	7	”	"	PUNCT
ejpam-6974	223	8	on	on	ADP
ejpam-6974	223	9	x	x	PUNCT
ejpam-6974	223	10	as	as	ADP
ejpam-6974	223	11	x∗y	x∗y	X
ejpam-6974	223	12	=	=	SYM
ejpam-6974	223	13	(	(	PUNCT
ejpam-6974	223	14	x	x	PART
ejpam-6974	223	15	◦	◦	NOUN
ejpam-6974	223	16	1)	1)	NUM
ejpam-6974	223	17	◦	◦	NOUN
ejpam-6974	223	18	y.	y.	NOUN
ejpam-6974	223	19	note	note	VERB
ejpam-6974	223	20	that	that	SCONJ
ejpam-6974	223	21	x∗1	x∗1	VERB
ejpam-6974	223	22	=	=	SYM
ejpam-6974	223	23	(	(	PUNCT
ejpam-6974	223	24	x	x	PART
ejpam-6974	223	25	◦	◦	NOUN
ejpam-6974	223	26	1)	1)	NUM
ejpam-6974	223	27	◦	◦	NOUN
ejpam-6974	223	28	1	1	NUM
ejpam-6974	223	29	=	=	SYM
ejpam-6974	223	30	x	x	PUNCT
ejpam-6974	223	31	by	by	ADP
ejpam-6974	223	32	lemma	lemma	PROPN
ejpam-6974	223	33	2(i	2(i	NUM
ejpam-6974	223	34	)	)	PUNCT
ejpam-6974	223	35	and	and	CCONJ
ejpam-6974	223	36	1	1	NUM
ejpam-6974	223	37	∗	∗	NOUN
ejpam-6974	223	38	x	x	X
ejpam-6974	223	39	=	=	SYM
ejpam-6974	223	40	(	(	PUNCT
ejpam-6974	223	41	1	1	NUM
ejpam-6974	223	42	◦	◦	NOUN
ejpam-6974	223	43	1	1	NUM
ejpam-6974	223	44	)	)	PUNCT
ejpam-6974	223	45	◦	◦	NOUN
ejpam-6974	223	46	x	x	SYM
ejpam-6974	223	47	=	=	SYM
ejpam-6974	223	48	1	1	NUM
ejpam-6974	223	49	◦	◦	NOUN
ejpam-6974	223	50	x	x	SYM
ejpam-6974	223	51	=	=	PUNCT
ejpam-6974	223	52	x	x	SYM
ejpam-6974	223	53	by	by	ADP
ejpam-6974	223	54	(	(	PUNCT
ejpam-6974	223	55	dbg1	dbg1	ADJ
ejpam-6974	223	56	)	)	PUNCT
ejpam-6974	223	57	and	and	CCONJ
ejpam-6974	223	58	(	(	PUNCT
ejpam-6974	223	59	dbg2	dbg2	PROPN
ejpam-6974	223	60	)	)	PUNCT
ejpam-6974	223	61	.	.	PUNCT
ejpam-6974	224	1	so	so	ADV
ejpam-6974	224	2	1	1	NUM
ejpam-6974	224	3	is	be	AUX
ejpam-6974	224	4	the	the	DET
ejpam-6974	224	5	identity	identity	NOUN
ejpam-6974	224	6	element	element	NOUN
ejpam-6974	224	7	with	with	ADP
ejpam-6974	224	8	respect	respect	NOUN
ejpam-6974	224	9	to	to	ADP
ejpam-6974	224	10	the	the	DET
ejpam-6974	224	11	binary	binary	PROPN
ejpam-6974	224	12	operation	operation	NOUN
ejpam-6974	224	13	“	"	PUNCT
ejpam-6974	224	14	∗	∗	NOUN
ejpam-6974	224	15	”	"	PUNCT
ejpam-6974	224	16	.	.	PUNCT
ejpam-6974	225	1	also	also	ADV
ejpam-6974	225	2	x	x	VERB
ejpam-6974	225	3	∗	∗	NOUN
ejpam-6974	225	4	(	(	PUNCT
ejpam-6974	225	5	x	x	SYM
ejpam-6974	225	6	◦	◦	NOUN
ejpam-6974	225	7	1	1	NUM
ejpam-6974	225	8	)	)	PUNCT
ejpam-6974	225	9	=	=	SYM
ejpam-6974	225	10	(	(	PUNCT
ejpam-6974	225	11	x	x	SYM
ejpam-6974	225	12	◦	◦	NOUN
ejpam-6974	225	13	1	1	NUM
ejpam-6974	225	14	)	)	PUNCT
ejpam-6974	225	15	◦	◦	NOUN
ejpam-6974	225	16	(	(	PUNCT
ejpam-6974	225	17	x	x	SYM
ejpam-6974	225	18	◦	◦	NOUN
ejpam-6974	225	19	1	1	NUM
ejpam-6974	225	20	)	)	PUNCT
ejpam-6974	225	21	=	=	SYM
ejpam-6974	225	22	1	1	NUM
ejpam-6974	225	23	by	by	ADP
ejpam-6974	225	24	(	(	PUNCT
ejpam-6974	225	25	dbg1	dbg1	ADJ
ejpam-6974	225	26	)	)	PUNCT
ejpam-6974	225	27	and	and	CCONJ
ejpam-6974	225	28	(	(	PUNCT
ejpam-6974	225	29	x	x	X
ejpam-6974	225	30	◦	◦	NOUN
ejpam-6974	225	31	1	1	NUM
ejpam-6974	225	32	)	)	PUNCT
ejpam-6974	225	33	∗	∗	NOUN
ejpam-6974	225	34	x	x	X
ejpam-6974	225	35	=	=	SYM
ejpam-6974	225	36	(	(	PUNCT
ejpam-6974	225	37	(	(	PUNCT
ejpam-6974	225	38	x	x	SYM
ejpam-6974	225	39	◦	◦	NOUN
ejpam-6974	225	40	1	1	NUM
ejpam-6974	225	41	)	)	PUNCT
ejpam-6974	225	42	◦	◦	NOUN
ejpam-6974	225	43	1	1	NUM
ejpam-6974	225	44	)	)	PUNCT
ejpam-6974	225	45	◦	◦	NOUN
ejpam-6974	225	46	x	x	X
ejpam-6974	226	1	=	=	PUNCT
ejpam-6974	226	2	x	x	PUNCT
ejpam-6974	226	3	◦	◦	NOUN
ejpam-6974	226	4	x	x	SYM
ejpam-6974	226	5	=	=	SYM
ejpam-6974	226	6	1	1	NUM
ejpam-6974	226	7	by	by	ADP
ejpam-6974	226	8	lemma	lemma	PROPN
ejpam-6974	226	9	2(i	2(i	NUM
ejpam-6974	226	10	)	)	PUNCT
ejpam-6974	226	11	and	and	CCONJ
ejpam-6974	226	12	(	(	PUNCT
ejpam-6974	226	13	dbg1	dbg1	PROPN
ejpam-6974	226	14	)	)	PUNCT
ejpam-6974	226	15	.	.	PUNCT
ejpam-6974	227	1	thus	thus	ADV
ejpam-6974	227	2	,	,	PUNCT
ejpam-6974	227	3	x	x	PUNCT
ejpam-6974	227	4	◦	◦	NOUN
ejpam-6974	227	5	1	1	NUM
ejpam-6974	227	6	is	be	AUX
ejpam-6974	227	7	the	the	DET
ejpam-6974	227	8	inverse	inverse	NOUN
ejpam-6974	227	9	for	for	ADP
ejpam-6974	227	10	x.	x.	NOUN
ejpam-6974	227	11	now	now	ADV
ejpam-6974	227	12	,	,	PUNCT
ejpam-6974	227	13	x	x	X
ejpam-6974	227	14	∗	∗	NOUN
ejpam-6974	227	15	(	(	PUNCT
ejpam-6974	227	16	y	y	PROPN
ejpam-6974	227	17	∗	∗	PROPN
ejpam-6974	227	18	z	z	NOUN
ejpam-6974	227	19	)	)	PUNCT
ejpam-6974	227	20	=	=	SYM
ejpam-6974	228	1	(	(	PUNCT
ejpam-6974	228	2	x	x	SYM
ejpam-6974	228	3	◦	◦	NOUN
ejpam-6974	228	4	1	1	NUM
ejpam-6974	228	5	)	)	PUNCT
ejpam-6974	228	6	◦	◦	NOUN
ejpam-6974	228	7	(	(	PUNCT
ejpam-6974	228	8	y	y	PROPN
ejpam-6974	228	9	∗	∗	PROPN
ejpam-6974	228	10	z	z	NOUN
ejpam-6974	228	11	)	)	PUNCT
ejpam-6974	228	12	=	=	SYM
ejpam-6974	229	1	(	(	PUNCT
ejpam-6974	229	2	x	x	SYM
ejpam-6974	229	3	◦	◦	NOUN
ejpam-6974	229	4	1	1	NUM
ejpam-6974	229	5	)	)	PUNCT
ejpam-6974	229	6	◦	◦	NOUN
ejpam-6974	230	1	[	[	X
ejpam-6974	230	2	(	(	PUNCT
ejpam-6974	230	3	y	y	NOUN
ejpam-6974	230	4	◦	◦	NOUN
ejpam-6974	230	5	1	1	NUM
ejpam-6974	230	6	)	)	PUNCT
ejpam-6974	230	7	◦	◦	NOUN
ejpam-6974	231	1	z	z	X
ejpam-6974	231	2	]	]	X
ejpam-6974	231	3	=	=	PUNCT
ejpam-6974	232	1	[	[	X
ejpam-6974	232	2	[	[	X
ejpam-6974	232	3	(	(	PUNCT
ejpam-6974	232	4	y	y	PROPN
ejpam-6974	232	5	◦	◦	NOUN
ejpam-6974	232	6	1	1	NUM
ejpam-6974	232	7	)	)	PUNCT
ejpam-6974	232	8	◦	◦	NOUN
ejpam-6974	232	9	1	1	NUM
ejpam-6974	232	10	]	]	X
ejpam-6974	232	11	◦	◦	NOUN
ejpam-6974	232	12	(	(	PUNCT
ejpam-6974	232	13	x	x	SYM
ejpam-6974	232	14	◦	◦	NOUN
ejpam-6974	232	15	1	1	NUM
ejpam-6974	232	16	)	)	PUNCT
ejpam-6974	232	17	]	]	PUNCT
ejpam-6974	233	1	◦	◦	NOUN
ejpam-6974	233	2	z	z	VERB
ejpam-6974	233	3	by	by	ADP
ejpam-6974	233	4	replacing	replace	VERB
ejpam-6974	233	5	x	x	PUNCT
ejpam-6974	233	6	with	with	ADP
ejpam-6974	233	7	x	x	PART
ejpam-6974	233	8	◦	◦	NOUN
ejpam-6974	233	9	1	1	NUM
ejpam-6974	233	10	and	and	CCONJ
ejpam-6974	233	11	y	y	PROPN
ejpam-6974	233	12	with	with	ADP
ejpam-6974	233	13	y	y	PROPN
ejpam-6974	233	14	◦	◦	NOUN
ejpam-6974	233	15	1	1	NUM
ejpam-6974	233	16	in	in	ADP
ejpam-6974	233	17	(	(	PUNCT
ejpam-6974	233	18	db3	db3	PROPN
ejpam-6974	233	19	)	)	PUNCT
ejpam-6974	233	20	.	.	PUNCT
ejpam-6974	234	1	by	by	ADP
ejpam-6974	234	2	lemma	lemma	PROPN
ejpam-6974	234	3	2(i	2(i	NUM
ejpam-6974	234	4	)	)	PUNCT
ejpam-6974	234	5	,	,	PUNCT
ejpam-6974	234	6	x	x	X
ejpam-6974	234	7	∗	∗	NOUN
ejpam-6974	234	8	(	(	PUNCT
ejpam-6974	234	9	y	y	PROPN
ejpam-6974	234	10	∗	∗	PROPN
ejpam-6974	234	11	z	z	NOUN
ejpam-6974	234	12	)	)	PUNCT
ejpam-6974	234	13	=	=	PUNCT
ejpam-6974	235	1	[	[	X
ejpam-6974	235	2	y	y	PROPN
ejpam-6974	235	3	◦	◦	NOUN
ejpam-6974	235	4	(	(	PUNCT
ejpam-6974	235	5	x	x	X
ejpam-6974	235	6	◦	◦	NOUN
ejpam-6974	235	7	1	1	NUM
ejpam-6974	235	8	)	)	PUNCT
ejpam-6974	235	9	]	]	PUNCT
ejpam-6974	236	1	◦	◦	NOUN
ejpam-6974	236	2	z.	z.	NOUN
ejpam-6974	236	3	using	use	VERB
ejpam-6974	236	4	(	(	PUNCT
ejpam-6974	236	5	db3	db3	PROPN
ejpam-6974	236	6	)	)	PUNCT
ejpam-6974	236	7	,	,	PUNCT
ejpam-6974	236	8	y	y	PROPN
ejpam-6974	236	9	◦	◦	NOUN
ejpam-6974	236	10	(	(	PUNCT
ejpam-6974	236	11	x	x	X
ejpam-6974	236	12	◦	◦	NOUN
ejpam-6974	236	13	1	1	NUM
ejpam-6974	236	14	)	)	PUNCT
ejpam-6974	237	1	=	=	NOUN
ejpam-6974	238	1	[	[	X
ejpam-6974	238	2	(	(	PUNCT
ejpam-6974	238	3	x	x	SYM
ejpam-6974	238	4	◦	◦	NOUN
ejpam-6974	238	5	1	1	NUM
ejpam-6974	238	6	)	)	PUNCT
ejpam-6974	238	7	◦	◦	NOUN
ejpam-6974	238	8	y	y	PROPN
ejpam-6974	238	9	]	]	X
ejpam-6974	238	10	◦	◦	NOUN
ejpam-6974	238	11	1	1	NUM
ejpam-6974	238	12	and	and	CCONJ
ejpam-6974	238	13	so	so	ADV
ejpam-6974	238	14	x	x	SYM
ejpam-6974	238	15	∗	∗	NOUN
ejpam-6974	238	16	(	(	PUNCT
ejpam-6974	238	17	y	y	PROPN
ejpam-6974	238	18	∗	∗	PROPN
ejpam-6974	238	19	z	z	NOUN
ejpam-6974	238	20	)	)	PUNCT
ejpam-6974	238	21	=	=	PUNCT
ejpam-6974	239	1	[	[	X
ejpam-6974	239	2	[	[	X
ejpam-6974	239	3	(	(	PUNCT
ejpam-6974	239	4	x	x	SYM
ejpam-6974	239	5	◦	◦	NOUN
ejpam-6974	239	6	1	1	NUM
ejpam-6974	239	7	)	)	PUNCT
ejpam-6974	239	8	◦	◦	NOUN
ejpam-6974	239	9	y	y	PROPN
ejpam-6974	239	10	]	]	X
ejpam-6974	239	11	◦	◦	NOUN
ejpam-6974	239	12	1	1	NUM
ejpam-6974	239	13	]	]	X
ejpam-6974	239	14	◦	◦	NOUN
ejpam-6974	239	15	z.	z.	PROPN
ejpam-6974	240	1	the	the	DET
ejpam-6974	240	2	continuation	continuation	NOUN
ejpam-6974	240	3	is	be	AUX
ejpam-6974	240	4	as	as	SCONJ
ejpam-6974	240	5	follows	follow	VERB
ejpam-6974	240	6	:	:	PUNCT
ejpam-6974	240	7	x	x	SYM
ejpam-6974	240	8	∗	∗	NOUN
ejpam-6974	240	9	(	(	PUNCT
ejpam-6974	240	10	y	y	PROPN
ejpam-6974	240	11	∗	∗	PROPN
ejpam-6974	240	12	z	z	NOUN
ejpam-6974	240	13	)	)	PUNCT
ejpam-6974	240	14	=	=	PUNCT
ejpam-6974	241	1	[	[	X
ejpam-6974	241	2	(	(	PUNCT
ejpam-6974	241	3	x	x	X
ejpam-6974	241	4	∗	∗	PROPN
ejpam-6974	241	5	y	y	NOUN
ejpam-6974	241	6	)	)	PUNCT
ejpam-6974	241	7	◦	◦	NOUN
ejpam-6974	241	8	1	1	NUM
ejpam-6974	241	9	]	]	X
ejpam-6974	241	10	◦	◦	NOUN
ejpam-6974	241	11	z	z	NOUN
ejpam-6974	241	12	=	=	SYM
ejpam-6974	241	13	(	(	PUNCT
ejpam-6974	241	14	x	x	X
ejpam-6974	241	15	∗	∗	PROPN
ejpam-6974	241	16	y	y	NOUN
ejpam-6974	241	17	)	)	PUNCT
ejpam-6974	241	18	∗	∗	NOUN
ejpam-6974	241	19	z.	z.	PROPN
ejpam-6974	242	1	thus	thus	ADV
ejpam-6974	242	2	,	,	PUNCT
ejpam-6974	242	3	(	(	PUNCT
ejpam-6974	242	4	x	x	X
ejpam-6974	242	5	,	,	PUNCT
ejpam-6974	242	6	∗	∗	NOUN
ejpam-6974	242	7	,	,	PUNCT
ejpam-6974	242	8	1	1	NUM
ejpam-6974	242	9	)	)	PUNCT
ejpam-6974	242	10	is	be	AUX
ejpam-6974	242	11	a	a	DET
ejpam-6974	242	12	group	group	NOUN
ejpam-6974	242	13	by	by	ADP
ejpam-6974	242	14	definition	definition	NOUN
ejpam-6974	242	15	2	2	NUM
ejpam-6974	242	16	.	.	PUNCT
ejpam-6974	242	17	note	note	VERB
ejpam-6974	242	18	that	that	SCONJ
ejpam-6974	242	19	x−1	x−1	PROPN
ejpam-6974	242	20	∗	∗	NOUN
ejpam-6974	242	21	y	y	PROPN
ejpam-6974	242	22	=	=	PUNCT
ejpam-6974	243	1	(	(	PUNCT
ejpam-6974	243	2	x−1	x−1	NOUN
ejpam-6974	243	3	◦	◦	NOUN
ejpam-6974	243	4	1	1	NUM
ejpam-6974	243	5	)	)	PUNCT
ejpam-6974	243	6	◦	◦	NOUN
ejpam-6974	243	7	y	y	NOUN
ejpam-6974	243	8	=	=	PUNCT
ejpam-6974	244	1	[	[	X
ejpam-6974	244	2	(	(	PUNCT
ejpam-6974	244	3	x	x	SYM
ejpam-6974	244	4	◦	◦	NOUN
ejpam-6974	244	5	1	1	NUM
ejpam-6974	244	6	)	)	PUNCT
ejpam-6974	244	7	◦	◦	NOUN
ejpam-6974	244	8	1	1	NUM
ejpam-6974	244	9	]	]	X
ejpam-6974	244	10	◦	◦	NOUN
ejpam-6974	244	11	y	y	NOUN
ejpam-6974	244	12	=	=	PUNCT
ejpam-6974	244	13	x	x	PUNCT
ejpam-6974	244	14	◦	◦	NOUN
ejpam-6974	244	15	y.	y.	NOUN
ejpam-6974	244	16	therefore	therefore	ADV
ejpam-6974	244	17	,	,	PUNCT
ejpam-6974	244	18	(	(	PUNCT
ejpam-6974	244	19	x	x	NOUN
ejpam-6974	244	20	,	,	PUNCT
ejpam-6974	244	21	◦	◦	NOUN
ejpam-6974	244	22	,	,	PUNCT
ejpam-6974	244	23	1	1	NUM
ejpam-6974	244	24	)	)	PUNCT
ejpam-6974	244	25	is	be	AUX
ejpam-6974	244	26	a	a	DET
ejpam-6974	244	27	group	group	NOUN
ejpam-6974	244	28	-	-	PUNCT
ejpam-6974	244	29	derived	derive	VERB
ejpam-6974	244	30	dual	dual	ADJ
ejpam-6974	244	31	bg	bg	NOUN
ejpam-6974	244	32	-	-	NOUN
ejpam-6974	244	33	algebra	algebra	NOUN
ejpam-6974	244	34	by	by	ADP
ejpam-6974	244	35	proposition	proposition	NOUN
ejpam-6974	244	36	2	2	NUM
ejpam-6974	244	37	.	.	PUNCT
ejpam-6974	245	1	conversely	conversely	ADV
ejpam-6974	245	2	,	,	PUNCT
ejpam-6974	245	3	let	let	VERB
ejpam-6974	245	4	x	x	PUNCT
ejpam-6974	245	5	=	=	PUNCT
ejpam-6974	245	6	(	(	PUNCT
ejpam-6974	245	7	x	x	NOUN
ejpam-6974	245	8	,	,	PUNCT
ejpam-6974	245	9	◦	◦	NOUN
ejpam-6974	245	10	,	,	PUNCT
ejpam-6974	245	11	1	1	NUM
ejpam-6974	245	12	)	)	PUNCT
ejpam-6974	245	13	be	be	AUX
ejpam-6974	245	14	a	a	DET
ejpam-6974	245	15	group	group	NOUN
ejpam-6974	245	16	-	-	PUNCT
ejpam-6974	245	17	derived	derive	VERB
ejpam-6974	245	18	dual	dual	ADJ
ejpam-6974	245	19	bg	bg	NOUN
ejpam-6974	245	20	-	-	NOUN
ejpam-6974	245	21	algebra	algebra	PROPN
ejpam-6974	245	22	.	.	PUNCT
ejpam-6974	246	1	then	then	ADV
ejpam-6974	246	2	(	(	PUNCT
ejpam-6974	246	3	db1	db1	NOUN
ejpam-6974	246	4	)	)	PUNCT
ejpam-6974	246	5	and	and	CCONJ
ejpam-6974	246	6	(	(	PUNCT
ejpam-6974	246	7	db2	db2	PROPN
ejpam-6974	246	8	)	)	PUNCT
ejpam-6974	246	9	follow	follow	VERB
ejpam-6974	246	10	from	from	ADP
ejpam-6974	246	11	(	(	PUNCT
ejpam-6974	246	12	dbg1	dbg1	ADJ
ejpam-6974	246	13	)	)	PUNCT
ejpam-6974	246	14	and	and	CCONJ
ejpam-6974	246	15	(	(	PUNCT
ejpam-6974	246	16	dbg2	dbg2	PROPN
ejpam-6974	246	17	)	)	PUNCT
ejpam-6974	246	18	,	,	PUNCT
ejpam-6974	246	19	respectively	respectively	ADV
ejpam-6974	246	20	.	.	PUNCT
ejpam-6974	247	1	now	now	ADV
ejpam-6974	247	2	,	,	PUNCT
ejpam-6974	247	3	since	since	SCONJ
ejpam-6974	247	4	x	x	PROPN
ejpam-6974	247	5	is	be	AUX
ejpam-6974	247	6	group	group	NOUN
ejpam-6974	247	7	-	-	PUNCT
ejpam-6974	247	8	derived	derive	VERB
ejpam-6974	247	9	,	,	PUNCT
ejpam-6974	247	10	then	then	ADV
ejpam-6974	247	11	it	it	PRON
ejpam-6974	247	12	was	be	AUX
ejpam-6974	247	13	generated	generate	VERB
ejpam-6974	247	14	from	from	ADP
ejpam-6974	247	15	a	a	DET
ejpam-6974	247	16	group	group	NOUN
ejpam-6974	247	17	(	(	PUNCT
ejpam-6974	247	18	x	x	X
ejpam-6974	247	19	,	,	PUNCT
ejpam-6974	247	20	∗	∗	NOUN
ejpam-6974	247	21	,	,	PUNCT
ejpam-6974	247	22	1	1	NUM
ejpam-6974	247	23	)	)	PUNCT
ejpam-6974	247	24	where	where	SCONJ
ejpam-6974	247	25	x−1	x−1	PROPN
ejpam-6974	247	26	∗	∗	VERB
ejpam-6974	247	27	y	y	PROPN
ejpam-6974	248	1	=	=	PUNCT
ejpam-6974	248	2	x	x	PUNCT
ejpam-6974	248	3	◦	◦	NOUN
ejpam-6974	248	4	y	y	PRON
ejpam-6974	248	5	where	where	SCONJ
ejpam-6974	248	6	x	x	X
ejpam-6974	248	7	,	,	PUNCT
ejpam-6974	248	8	y	y	PROPN
ejpam-6974	248	9	∈	∈	PROPN
ejpam-6974	248	10	x.	x.	NOUN
ejpam-6974	248	11	now	now	ADV
ejpam-6974	248	12	,	,	PUNCT
ejpam-6974	248	13	x	x	PUNCT
ejpam-6974	248	14	◦	◦	NOUN
ejpam-6974	248	15	(	(	PUNCT
ejpam-6974	248	16	y	y	PROPN
ejpam-6974	248	17	◦	◦	PROPN
ejpam-6974	248	18	z	z	PROPN
ejpam-6974	248	19	)	)	PUNCT
ejpam-6974	249	1	=	=	SYM
ejpam-6974	249	2	x−1	x−1	PROPN
ejpam-6974	249	3	∗	∗	NOUN
ejpam-6974	249	4	(	(	PUNCT
ejpam-6974	249	5	y	y	PROPN
ejpam-6974	249	6	◦	◦	PROPN
ejpam-6974	249	7	z	z	PROPN
ejpam-6974	249	8	)	)	PUNCT
ejpam-6974	249	9	=	=	SYM
ejpam-6974	249	10	x−1	x−1	PROPN
ejpam-6974	249	11	∗	∗	NOUN
ejpam-6974	249	12	(	(	PUNCT
ejpam-6974	249	13	y−1	y−1	NOUN
ejpam-6974	249	14	∗	∗	NOUN
ejpam-6974	249	15	z	z	NOUN
ejpam-6974	249	16	)	)	PUNCT
ejpam-6974	249	17	=	=	PUNCT
ejpam-6974	250	1	(	(	PUNCT
ejpam-6974	250	2	x−1	x−1	PROPN
ejpam-6974	250	3	∗	∗	NOUN
ejpam-6974	250	4	y−1	y−1	PROPN
ejpam-6974	250	5	)	)	PUNCT
ejpam-6974	250	6	∗	∗	PROPN
ejpam-6974	250	7	z.	z.	PROPN
ejpam-6974	250	8	associative	associative	PROPN
ejpam-6974	250	9	property	property	NOUN
ejpam-6974	250	10	can	can	AUX
ejpam-6974	250	11	be	be	AUX
ejpam-6974	250	12	applied	apply	VERB
ejpam-6974	250	13	since	since	SCONJ
ejpam-6974	250	14	(	(	PUNCT
ejpam-6974	250	15	x	x	X
ejpam-6974	250	16	,	,	PUNCT
ejpam-6974	250	17	∗	∗	NOUN
ejpam-6974	250	18	,	,	PUNCT
ejpam-6974	250	19	1	1	NUM
ejpam-6974	250	20	)	)	PUNCT
ejpam-6974	250	21	is	be	AUX
ejpam-6974	250	22	a	a	DET
ejpam-6974	250	23	group	group	NOUN
ejpam-6974	250	24	.	.	PUNCT
ejpam-6974	251	1	using	use	VERB
ejpam-6974	251	2	theorem	theorem	NOUN
ejpam-6974	251	3	1	1	NUM
ejpam-6974	251	4	,	,	PUNCT
ejpam-6974	251	5	the	the	DET
ejpam-6974	251	6	continuation	continuation	NOUN
ejpam-6974	251	7	is	be	AUX
ejpam-6974	251	8	as	as	SCONJ
ejpam-6974	251	9	follows	follow	VERB
ejpam-6974	251	10	:	:	PUNCT
ejpam-6974	251	11	x	x	X
ejpam-6974	251	12	◦	◦	NOUN
ejpam-6974	251	13	(y	(y	NOUN
ejpam-6974	251	14	◦	◦	NOUN
ejpam-6974	251	15	z	z	NOUN
ejpam-6974	251	16	)	)	PUNCT
ejpam-6974	251	17	=	=	SYM
ejpam-6974	252	1	(	(	PUNCT
ejpam-6974	252	2	y	y	NOUN
ejpam-6974	252	3	∗	∗	X
ejpam-6974	252	4	x)−1∗z	x)−1∗z	PUNCT
ejpam-6974	253	1	=	=	PUNCT
ejpam-6974	254	1	[	[	X
ejpam-6974	254	2	(	(	PUNCT
ejpam-6974	254	3	y−1	y−1	NOUN
ejpam-6974	254	4	)	)	PUNCT
ejpam-6974	254	5	−1	−1	NOUN
ejpam-6974	254	6	∗	∗	NOUN
ejpam-6974	254	7	x	x	PUNCT
ejpam-6974	254	8	]	]	X
ejpam-6974	254	9	−1	−1	NOUN
ejpam-6974	254	10	∗z	∗z	PROPN
ejpam-6974	254	11	=	=	SYM
ejpam-6974	255	1	[	[	X
ejpam-6974	255	2	(	(	PUNCT
ejpam-6974	255	3	y−1	y−1	NOUN
ejpam-6974	255	4	∗	∗	NOUN
ejpam-6974	255	5	1	1	NUM
ejpam-6974	255	6	)	)	PUNCT
ejpam-6974	255	7	−1	−1	NOUN
ejpam-6974	255	8	∗	∗	NOUN
ejpam-6974	255	9	x	x	PUNCT
ejpam-6974	255	10	]	]	X
ejpam-6974	255	11	−1	−1	NOUN
ejpam-6974	255	12	∗z	∗z	PROPN
ejpam-6974	255	13	=	=	SYM
ejpam-6974	256	1	[	[	PUNCT
ejpam-6974	256	2	(	(	PUNCT
ejpam-6974	256	3	y	y	PROPN
ejpam-6974	256	4	◦	◦	NOUN
ejpam-6974	256	5	1)−1	1)−1	NUM
ejpam-6974	256	6	∗	∗	NOUN
ejpam-6974	256	7	x	x	X
ejpam-6974	256	8	]	]	X
ejpam-6974	256	9	−1	−1	NOUN
ejpam-6974	256	10	∗	∗	NOUN
ejpam-6974	256	11	z	z	NOUN
ejpam-6974	257	1	=	=	PUNCT
ejpam-6974	258	1	[	[	X
ejpam-6974	258	2	(	(	PUNCT
ejpam-6974	258	3	y	y	NOUN
ejpam-6974	258	4	◦	◦	NOUN
ejpam-6974	258	5	1	1	NUM
ejpam-6974	258	6	)	)	PUNCT
ejpam-6974	258	7	◦	◦	NOUN
ejpam-6974	258	8	x]−1	x]−1	NOUN
ejpam-6974	258	9	∗	∗	NOUN
ejpam-6974	258	10	z	z	NOUN
ejpam-6974	258	11	=	=	SYM
ejpam-6974	258	12	(	(	PUNCT
ejpam-6974	258	13	(	(	PUNCT
ejpam-6974	258	14	y	y	NOUN
ejpam-6974	258	15	◦	◦	NOUN
ejpam-6974	258	16	1	1	NUM
ejpam-6974	258	17	)	)	PUNCT
ejpam-6974	258	18	◦	◦	NOUN
ejpam-6974	258	19	x	x	SYM
ejpam-6974	258	20	)	)	PUNCT
ejpam-6974	258	21	◦	◦	NOUN
ejpam-6974	258	22	z.	z.	PROPN
ejpam-6974	258	23	hence	hence	ADV
ejpam-6974	258	24	,	,	PUNCT
ejpam-6974	258	25	(	(	PUNCT
ejpam-6974	258	26	db3	db3	PROPN
ejpam-6974	258	27	)	)	PUNCT
ejpam-6974	258	28	is	be	AUX
ejpam-6974	258	29	satisfied	satisfied	ADJ
ejpam-6974	258	30	and	and	CCONJ
ejpam-6974	258	31	so	so	ADV
ejpam-6974	258	32	(	(	PUNCT
ejpam-6974	258	33	x	x	NOUN
ejpam-6974	258	34	,	,	PUNCT
ejpam-6974	258	35	◦	◦	NOUN
ejpam-6974	258	36	,	,	PUNCT
ejpam-6974	258	37	1	1	NUM
ejpam-6974	258	38	)	)	PUNCT
ejpam-6974	258	39	is	be	AUX
ejpam-6974	258	40	a	a	DET
ejpam-6974	258	41	dual	dual	ADJ
ejpam-6974	258	42	b	b	NOUN
ejpam-6974	258	43	-	-	PUNCT
ejpam-6974	258	44	algebra	algebra	NOUN
ejpam-6974	258	45	.	.	PUNCT
ejpam-6974	259	1	this	this	PRON
ejpam-6974	259	2	proves	prove	VERB
ejpam-6974	259	3	the	the	DET
ejpam-6974	259	4	theorem	theorem	PROPN
ejpam-6974	259	5	.	.	PROPN
ejpam-6974	259	6	example	example	NOUN
ejpam-6974	259	7	13	13	NUM
ejpam-6974	259	8	.	.	PUNCT
ejpam-6974	260	1	consider	consider	VERB
ejpam-6974	260	2	the	the	DET
ejpam-6974	260	3	dual	dual	ADJ
ejpam-6974	260	4	bg	bg	NOUN
ejpam-6974	260	5	-	-	NOUN
ejpam-6974	260	6	algebra	algebra	PROPN
ejpam-6974	260	7	(	(	PUNCT
ejpam-6974	260	8	x	x	NOUN
ejpam-6974	260	9	,	,	PUNCT
ejpam-6974	260	10	◦	◦	NOUN
ejpam-6974	260	11	,	,	PUNCT
ejpam-6974	260	12	1	1	NUM
ejpam-6974	260	13	)	)	PUNCT
ejpam-6974	260	14	from	from	ADP
ejpam-6974	260	15	example	example	NOUN
ejpam-6974	260	16	9	9	NUM
ejpam-6974	260	17	.	.	PUNCT
ejpam-6974	261	1	it	it	PRON
ejpam-6974	261	2	was	be	AUX
ejpam-6974	261	3	shown	show	VERB
ejpam-6974	261	4	that	that	SCONJ
ejpam-6974	261	5	it	it	PRON
ejpam-6974	261	6	is	be	AUX
ejpam-6974	261	7	a	a	DET
ejpam-6974	261	8	group	group	NOUN
ejpam-6974	261	9	-	-	PUNCT
ejpam-6974	261	10	derived	derive	VERB
ejpam-6974	261	11	dual	dual	ADJ
ejpam-6974	261	12	bg	bg	NOUN
ejpam-6974	261	13	-	-	NOUN
ejpam-6974	261	14	algebra	algebra	PROPN
ejpam-6974	261	15	in	in	ADP
ejpam-6974	261	16	example	example	NOUN
ejpam-6974	261	17	12	12	NUM
ejpam-6974	261	18	.	.	PUNCT
ejpam-6974	262	1	thus	thus	ADV
ejpam-6974	262	2	,	,	PUNCT
ejpam-6974	262	3	(	(	PUNCT
ejpam-6974	262	4	x	x	X
ejpam-6974	262	5	,	,	PUNCT
ejpam-6974	262	6	◦	◦	NOUN
ejpam-6974	262	7	,	,	PUNCT
ejpam-6974	262	8	1	1	NUM
ejpam-6974	262	9	)	)	PUNCT
ejpam-6974	262	10	is	be	AUX
ejpam-6974	262	11	also	also	ADV
ejpam-6974	262	12	a	a	DET
ejpam-6974	262	13	dual	dual	ADJ
ejpam-6974	262	14	b	b	NOUN
ejpam-6974	262	15	-	-	PUNCT
ejpam-6974	262	16	algebra	algebra	NOUN
ejpam-6974	262	17	by	by	ADP
ejpam-6974	262	18	theorem	theorem	NOUN
ejpam-6974	262	19	5	5	NUM
ejpam-6974	262	20	.	.	PUNCT
ejpam-6974	262	21	indeed	indeed	ADV
ejpam-6974	262	22	,	,	PUNCT
ejpam-6974	262	23	treating	treat	VERB
ejpam-6974	262	24	1	1	NUM
ejpam-6974	262	25	as	as	ADP
ejpam-6974	262	26	e	e	PROPN
ejpam-6974	262	27	,	,	PUNCT
ejpam-6974	262	28	(	(	PUNCT
ejpam-6974	262	29	x	x	NOUN
ejpam-6974	262	30	,	,	PUNCT
ejpam-6974	262	31	◦	◦	NOUN
ejpam-6974	262	32	,	,	PUNCT
ejpam-6974	262	33	1	1	NUM
ejpam-6974	262	34	)	)	PUNCT
ejpam-6974	262	35	is	be	AUX
ejpam-6974	262	36	a	a	DET
ejpam-6974	262	37	dual	dual	ADJ
ejpam-6974	262	38	b	b	NOUN
ejpam-6974	262	39	-	-	PUNCT
ejpam-6974	262	40	algebra	algebra	NOUN
ejpam-6974	262	41	by	by	ADP
ejpam-6974	262	42	example	example	NOUN
ejpam-6974	262	43	1	1	NUM
ejpam-6974	262	44	.	.	PUNCT
ejpam-6974	263	1	it	it	PRON
ejpam-6974	263	2	is	be	AUX
ejpam-6974	263	3	evident	evident	ADJ
ejpam-6974	263	4	from	from	ADP
ejpam-6974	263	5	the	the	DET
ejpam-6974	263	6	proof	proof	NOUN
ejpam-6974	263	7	of	of	ADP
ejpam-6974	263	8	theorem	theorem	NOUN
ejpam-6974	263	9	5	5	NUM
ejpam-6974	263	10	that	that	SCONJ
ejpam-6974	263	11	every	every	DET
ejpam-6974	263	12	dual	dual	ADJ
ejpam-6974	263	13	b	b	X
ejpam-6974	263	14	-	-	PUNCT
ejpam-6974	263	15	algebra	algebra	NOUN
ejpam-6974	263	16	is	be	AUX
ejpam-6974	263	17	a	a	DET
ejpam-6974	263	18	dual	dual	ADJ
ejpam-6974	263	19	bgalgebra	bgalgebra	NOUN
ejpam-6974	263	20	.	.	PUNCT
ejpam-6974	264	1	consequently	consequently	ADV
ejpam-6974	264	2	,	,	PUNCT
ejpam-6974	264	3	non	non	ADJ
ejpam-6974	264	4	-	-	ADJ
ejpam-6974	264	5	group	group	NOUN
ejpam-6974	264	6	-	-	PUNCT
ejpam-6974	264	7	derived	derive	VERB
ejpam-6974	264	8	dual	dual	ADJ
ejpam-6974	264	9	bg	bg	NOUN
ejpam-6974	264	10	-	-	PUNCT
ejpam-6974	264	11	algebras	algebras	PROPN
ejpam-6974	264	12	are	be	AUX
ejpam-6974	264	13	not	not	PART
ejpam-6974	264	14	dual	dual	ADJ
ejpam-6974	264	15	b	b	NOUN
ejpam-6974	264	16	-	-	PUNCT
ejpam-6974	264	17	algebras	algebras	X
ejpam-6974	264	18	.	.	PUNCT
ejpam-6974	265	1	theorem	theorem	NOUN
ejpam-6974	265	2	6	6	NUM
ejpam-6974	265	3	can	can	AUX
ejpam-6974	265	4	be	be	AUX
ejpam-6974	265	5	used	use	VERB
ejpam-6974	265	6	to	to	PART
ejpam-6974	265	7	construct	construct	VERB
ejpam-6974	265	8	infinitely	infinitely	ADV
ejpam-6974	265	9	many	many	ADJ
ejpam-6974	265	10	dual	dual	ADJ
ejpam-6974	265	11	bg	bg	NOUN
ejpam-6974	265	12	-	-	PUNCT
ejpam-6974	265	13	algebras	algebras	PROPN
ejpam-6974	265	14	.	.	PUNCT
ejpam-6974	266	1	these	these	DET
ejpam-6974	266	2	dual	dual	ADJ
ejpam-6974	266	3	bg	bg	NOUN
ejpam-6974	266	4	-	-	PUNCT
ejpam-6974	266	5	algebras	algebra	NOUN
ejpam-6974	266	6	are	be	AUX
ejpam-6974	266	7	also	also	ADV
ejpam-6974	266	8	shown	show	VERB
ejpam-6974	266	9	to	to	PART
ejpam-6974	266	10	be	be	AUX
ejpam-6974	266	11	non	non	ADJ
ejpam-6974	266	12	-	-	ADJ
ejpam-6974	266	13	group	group	NOUN
ejpam-6974	266	14	-	-	PUNCT
ejpam-6974	266	15	derived	derive	VERB
ejpam-6974	266	16	.	.	PUNCT
ejpam-6974	267	1	theorem	theorem	VERB
ejpam-6974	267	2	6	6	NUM
ejpam-6974	267	3	.	.	PUNCT
ejpam-6974	267	4	define	define	VERB
ejpam-6974	267	5	a	a	DET
ejpam-6974	267	6	binary	binary	ADJ
ejpam-6974	267	7	operation	operation	NOUN
ejpam-6974	267	8	“	"	PUNCT
ejpam-6974	267	9	◦	◦	NOUN
ejpam-6974	267	10	”	"	PUNCT
ejpam-6974	267	11	on	on	ADP
ejpam-6974	267	12	a	a	DET
ejpam-6974	267	13	set	set	NOUN
ejpam-6974	267	14	x	x	SYM
ejpam-6974	267	15	where	where	SCONJ
ejpam-6974	267	16	1	1	NUM
ejpam-6974	267	17	∈	∈	NOUN
ejpam-6974	267	18	x	x	PUNCT
ejpam-6974	267	19	by	by	ADP
ejpam-6974	267	20	x	x	SYM
ejpam-6974	267	21	◦	◦	NOUN
ejpam-6974	268	1	y	y	NOUN
ejpam-6974	269	1	=	=	SYM
ejpam-6974	270	1			NOUN
ejpam-6974	270	2	x	x	PUNCT
ejpam-6974	270	3	if	if	SCONJ
ejpam-6974	270	4	y	y	PROPN
ejpam-6974	270	5	=	=	NOUN
ejpam-6974	270	6	1	1	NUM
ejpam-6974	270	7	1	1	NUM
ejpam-6974	270	8	if	if	SCONJ
ejpam-6974	270	9	x	x	NOUN
ejpam-6974	270	10	=	=	VERB
ejpam-6974	270	11	y	y	NOUN
ejpam-6974	270	12	y	y	NOUN
ejpam-6974	270	13	otherwise	otherwise	ADV
ejpam-6974	270	14	,	,	PUNCT
ejpam-6974	270	15	for	for	ADP
ejpam-6974	270	16	any	any	DET
ejpam-6974	270	17	x	x	NOUN
ejpam-6974	270	18	,	,	PUNCT
ejpam-6974	270	19	y	y	PROPN
ejpam-6974	270	20	∈	∈	PROPN
ejpam-6974	271	1	x	x	X
ejpam-6974	271	2	,	,	PUNCT
ejpam-6974	271	3	then	then	ADV
ejpam-6974	271	4	(	(	PUNCT
ejpam-6974	271	5	x	x	NOUN
ejpam-6974	271	6	,	,	PUNCT
ejpam-6974	271	7	◦	◦	NOUN
ejpam-6974	271	8	,	,	PUNCT
ejpam-6974	271	9	1	1	NUM
ejpam-6974	271	10	)	)	PUNCT
ejpam-6974	271	11	is	be	AUX
ejpam-6974	271	12	a	a	DET
ejpam-6974	271	13	dual	dual	ADJ
ejpam-6974	271	14	bg	bg	NOUN
ejpam-6974	271	15	-	-	NOUN
ejpam-6974	271	16	algebra	algebra	PROPN
ejpam-6974	271	17	.	.	PUNCT
ejpam-6974	272	1	moreover	moreover	ADV
ejpam-6974	272	2	,	,	PUNCT
ejpam-6974	272	3	if	if	SCONJ
ejpam-6974	272	4	x	x	PRON
ejpam-6974	272	5	has	have	AUX
ejpam-6974	272	6	at	at	ADV
ejpam-6974	272	7	least	least	ADJ
ejpam-6974	272	8	3	3	NUM
ejpam-6974	272	9	elements	element	NOUN
ejpam-6974	272	10	,	,	PUNCT
ejpam-6974	272	11	then	then	ADV
ejpam-6974	272	12	(	(	PUNCT
ejpam-6974	272	13	x	x	NOUN
ejpam-6974	272	14	,	,	PUNCT
ejpam-6974	272	15	◦	◦	NOUN
ejpam-6974	272	16	,	,	PUNCT
ejpam-6974	272	17	1	1	NUM
ejpam-6974	272	18	)	)	PUNCT
ejpam-6974	272	19	is	be	AUX
ejpam-6974	272	20	non	non	ADJ
ejpam-6974	272	21	-	-	ADJ
ejpam-6974	272	22	group	group	NOUN
ejpam-6974	272	23	-	-	PUNCT
ejpam-6974	272	24	derived	derive	VERB
ejpam-6974	272	25	.	.	PUNCT
ejpam-6974	273	1	c.m	c.m	PROPN
ejpam-6974	273	2	.	.	PROPN
ejpam-6974	273	3	chan	chan	PROPN
ejpam-6974	273	4	,	,	PUNCT
ejpam-6974	273	5	k.	k.	PROPN
ejpam-6974	273	6	fuentes	fuentes	PROPN
ejpam-6974	273	7	/	/	SYM
ejpam-6974	273	8	eur	eur	PROPN
ejpam-6974	273	9	.	.	PUNCT
ejpam-6974	274	1	j.	j.	PROPN
ejpam-6974	274	2	pure	pure	PROPN
ejpam-6974	274	3	appl	appl	PROPN
ejpam-6974	274	4	.	.	PROPN
ejpam-6974	274	5	math	math	PROPN
ejpam-6974	274	6	,	,	PUNCT
ejpam-6974	274	7	18	18	NUM
ejpam-6974	274	8	(	(	PUNCT
ejpam-6974	274	9	4	4	NUM
ejpam-6974	274	10	)	)	PUNCT
ejpam-6974	274	11	(	(	PUNCT
ejpam-6974	274	12	2025	2025	NUM
ejpam-6974	274	13	)	)	PUNCT
ejpam-6974	274	14	,	,	PUNCT
ejpam-6974	274	15	6974	6974	NUM
ejpam-6974	274	16	9	9	NUM
ejpam-6974	274	17	of	of	ADP
ejpam-6974	274	18	16	16	NUM
ejpam-6974	274	19	proof	proof	NOUN
ejpam-6974	274	20	.	.	PUNCT
ejpam-6974	275	1	let	let	VERB
ejpam-6974	275	2	x	x	PRON
ejpam-6974	275	3	,	,	PUNCT
ejpam-6974	275	4	y	y	PROPN
ejpam-6974	275	5	∈	∈	PROPN
ejpam-6974	275	6	x.	x.	NOUN
ejpam-6974	275	7	note	note	VERB
ejpam-6974	275	8	that	that	SCONJ
ejpam-6974	275	9	(	(	PUNCT
ejpam-6974	275	10	x	x	NOUN
ejpam-6974	275	11	,	,	PUNCT
ejpam-6974	275	12	◦	◦	NOUN
ejpam-6974	275	13	,	,	PUNCT
ejpam-6974	275	14	1	1	X
ejpam-6974	275	15	)	)	PUNCT
ejpam-6974	275	16	satisfies	satisfie	NOUN
ejpam-6974	275	17	(	(	PUNCT
ejpam-6974	275	18	dbg1	dbg1	PROPN
ejpam-6974	275	19	):	):	PUNCT
ejpam-6974	275	20	x	x	PUNCT
ejpam-6974	275	21	◦	◦	NOUN
ejpam-6974	275	22	x	x	SYM
ejpam-6974	275	23	=	=	SYM
ejpam-6974	275	24	1	1	NUM
ejpam-6974	275	25	and	and	CCONJ
ejpam-6974	275	26	(	(	PUNCT
ejpam-6974	275	27	dbg2	dbg2	PROPN
ejpam-6974	275	28	):	):	PUNCT
ejpam-6974	275	29	1	1	NUM
ejpam-6974	275	30	◦	◦	NOUN
ejpam-6974	275	31	x	x	X
ejpam-6974	276	1	=	=	PUNCT
ejpam-6974	276	2	x.	x.	NOUN
ejpam-6974	277	1	now	now	ADV
ejpam-6974	277	2	,	,	PUNCT
ejpam-6974	277	3	if	if	SCONJ
ejpam-6974	277	4	y	y	PROPN
ejpam-6974	277	5	=	=	SYM
ejpam-6974	277	6	1	1	NUM
ejpam-6974	277	7	,	,	PUNCT
ejpam-6974	277	8	then	then	ADV
ejpam-6974	277	9	(	(	PUNCT
ejpam-6974	277	10	y	y	NOUN
ejpam-6974	277	11	◦	◦	NOUN
ejpam-6974	277	12	1	1	NUM
ejpam-6974	277	13	)	)	PUNCT
ejpam-6974	277	14	◦	◦	NOUN
ejpam-6974	277	15	(	(	PUNCT
ejpam-6974	277	16	y	y	PROPN
ejpam-6974	277	17	◦	◦	NOUN
ejpam-6974	277	18	x	x	X
ejpam-6974	277	19	)	)	PUNCT
ejpam-6974	277	20	=	=	SYM
ejpam-6974	278	1	(	(	PUNCT
ejpam-6974	278	2	1	1	NUM
ejpam-6974	278	3	◦	◦	NOUN
ejpam-6974	278	4	1	1	NUM
ejpam-6974	278	5	)	)	PUNCT
ejpam-6974	278	6	◦	◦	NOUN
ejpam-6974	278	7	(	(	PUNCT
ejpam-6974	278	8	1	1	NUM
ejpam-6974	278	9	◦	◦	NOUN
ejpam-6974	278	10	x	x	NOUN
ejpam-6974	278	11	)	)	PUNCT
ejpam-6974	278	12	=	=	SYM
ejpam-6974	278	13	1	1	NUM
ejpam-6974	278	14	◦	◦	NOUN
ejpam-6974	278	15	x	x	X
ejpam-6974	279	1	=	=	PUNCT
ejpam-6974	279	2	x.	x.	NOUN
ejpam-6974	279	3	assume	assume	VERB
ejpam-6974	279	4	y	y	PROPN
ejpam-6974	279	5	̸=	̸=	PROPN
ejpam-6974	279	6	1	1	NUM
ejpam-6974	279	7	.	.	PUNCT
ejpam-6974	280	1	if	if	SCONJ
ejpam-6974	280	2	x	x	X
ejpam-6974	280	3	=	=	SYM
ejpam-6974	280	4	y	y	PROPN
ejpam-6974	280	5	,	,	PUNCT
ejpam-6974	280	6	then	then	ADV
ejpam-6974	280	7	(	(	PUNCT
ejpam-6974	280	8	y	y	NOUN
ejpam-6974	280	9	◦	◦	NOUN
ejpam-6974	280	10	1	1	NUM
ejpam-6974	280	11	)	)	PUNCT
ejpam-6974	280	12	◦	◦	NOUN
ejpam-6974	280	13	(	(	PUNCT
ejpam-6974	280	14	y	y	PROPN
ejpam-6974	280	15	◦	◦	NOUN
ejpam-6974	280	16	x	x	X
ejpam-6974	280	17	)	)	PUNCT
ejpam-6974	280	18	=	=	SYM
ejpam-6974	281	1	(	(	PUNCT
ejpam-6974	281	2	x	x	SYM
ejpam-6974	281	3	◦	◦	NOUN
ejpam-6974	281	4	1	1	NUM
ejpam-6974	281	5	)	)	PUNCT
ejpam-6974	281	6	◦	◦	NOUN
ejpam-6974	281	7	(	(	PUNCT
ejpam-6974	281	8	x	x	PART
ejpam-6974	281	9	◦	◦	NOUN
ejpam-6974	281	10	x	x	NOUN
ejpam-6974	281	11	)	)	PUNCT
ejpam-6974	282	1	=	=	SYM
ejpam-6974	282	2	x	x	PUNCT
ejpam-6974	282	3	◦	◦	NOUN
ejpam-6974	282	4	1	1	NUM
ejpam-6974	282	5	=	=	SYM
ejpam-6974	282	6	x.	x.	NOUN
ejpam-6974	282	7	if	if	SCONJ
ejpam-6974	282	8	x	x	PROPN
ejpam-6974	282	9	̸=	̸=	PROPN
ejpam-6974	282	10	y	y	PROPN
ejpam-6974	282	11	,	,	PUNCT
ejpam-6974	282	12	then	then	ADV
ejpam-6974	282	13	(	(	PUNCT
ejpam-6974	282	14	y	y	NOUN
ejpam-6974	282	15	◦	◦	NOUN
ejpam-6974	282	16	1	1	NUM
ejpam-6974	282	17	)	)	PUNCT
ejpam-6974	282	18	◦	◦	NOUN
ejpam-6974	282	19	(	(	PUNCT
ejpam-6974	282	20	y	y	PROPN
ejpam-6974	282	21	◦	◦	NOUN
ejpam-6974	282	22	x	x	X
ejpam-6974	282	23	)	)	PUNCT
ejpam-6974	283	1	=	=	SYM
ejpam-6974	283	2	y	y	PROPN
ejpam-6974	283	3	◦	◦	NOUN
ejpam-6974	283	4	x	x	X
ejpam-6974	283	5	=	=	PUNCT
ejpam-6974	283	6	x.	x.	NOUN
ejpam-6974	283	7	hence	hence	ADV
ejpam-6974	283	8	,	,	PUNCT
ejpam-6974	283	9	(	(	PUNCT
ejpam-6974	283	10	x	x	NOUN
ejpam-6974	283	11	,	,	PUNCT
ejpam-6974	283	12	◦	◦	NOUN
ejpam-6974	283	13	,	,	PUNCT
ejpam-6974	283	14	1	1	X
ejpam-6974	283	15	)	)	PUNCT
ejpam-6974	283	16	satisfies	satisfie	NOUN
ejpam-6974	283	17	(	(	PUNCT
ejpam-6974	283	18	dbg3	dbg3	PROPN
ejpam-6974	283	19	)	)	PUNCT
ejpam-6974	283	20	.	.	PUNCT
ejpam-6974	284	1	therefore	therefore	ADV
ejpam-6974	284	2	,	,	PUNCT
ejpam-6974	284	3	(	(	PUNCT
ejpam-6974	284	4	x	x	X
ejpam-6974	284	5	,	,	PUNCT
ejpam-6974	284	6	◦	◦	NOUN
ejpam-6974	284	7	,	,	PUNCT
ejpam-6974	284	8	1	1	NUM
ejpam-6974	284	9	)	)	PUNCT
ejpam-6974	284	10	is	be	AUX
ejpam-6974	284	11	a	a	DET
ejpam-6974	284	12	dual	dual	ADJ
ejpam-6974	284	13	bg	bg	NOUN
ejpam-6974	284	14	-	-	NOUN
ejpam-6974	284	15	algebra	algebra	PROPN
ejpam-6974	284	16	.	.	PUNCT
ejpam-6974	285	1	now	now	ADV
ejpam-6974	285	2	,	,	PUNCT
ejpam-6974	285	3	assume	assume	VERB
ejpam-6974	285	4	x	x	PUNCT
ejpam-6974	285	5	has	have	VERB
ejpam-6974	285	6	at	at	ADV
ejpam-6974	285	7	least	least	ADJ
ejpam-6974	285	8	3	3	NUM
ejpam-6974	285	9	elements	element	NOUN
ejpam-6974	285	10	.	.	PUNCT
ejpam-6974	286	1	let	let	VERB
ejpam-6974	286	2	x	x	PRON
ejpam-6974	286	3	,	,	PUNCT
ejpam-6974	286	4	y	y	PROPN
ejpam-6974	286	5	,	,	PUNCT
ejpam-6974	286	6	z	z	NOUN
ejpam-6974	286	7	∈	∈	PROPN
ejpam-6974	286	8	x	x	AUX
ejpam-6974	286	9	be	be	AUX
ejpam-6974	286	10	unique	unique	ADJ
ejpam-6974	286	11	elements	element	NOUN
ejpam-6974	286	12	and	and	CCONJ
ejpam-6974	286	13	z	z	NOUN
ejpam-6974	286	14	̸=	̸=	PROPN
ejpam-6974	286	15	1	1	NUM
ejpam-6974	286	16	.	.	PUNCT
ejpam-6974	287	1	then	then	ADV
ejpam-6974	287	2	x	x	PART
ejpam-6974	287	3	◦	◦	NOUN
ejpam-6974	287	4	z	z	NOUN
ejpam-6974	287	5	=	=	SYM
ejpam-6974	287	6	y	y	PROPN
ejpam-6974	287	7	◦	◦	NOUN
ejpam-6974	287	8	z	z	PROPN
ejpam-6974	287	9	=	=	SYM
ejpam-6974	287	10	z.	z.	PROPN
ejpam-6974	287	11	assume	assume	VERB
ejpam-6974	287	12	(	(	PUNCT
ejpam-6974	287	13	x	x	X
ejpam-6974	287	14	,	,	PUNCT
ejpam-6974	287	15	◦	◦	NOUN
ejpam-6974	287	16	,	,	PUNCT
ejpam-6974	287	17	1	1	NUM
ejpam-6974	287	18	)	)	PUNCT
ejpam-6974	287	19	is	be	AUX
ejpam-6974	287	20	a	a	DET
ejpam-6974	287	21	group	group	NOUN
ejpam-6974	287	22	-	-	PUNCT
ejpam-6974	287	23	derived	derive	VERB
ejpam-6974	287	24	dual	dual	ADJ
ejpam-6974	287	25	bg	bg	NOUN
ejpam-6974	287	26	-	-	PUNCT
ejpam-6974	287	27	algebra	algebra	PROPN
ejpam-6974	287	28	obtained	obtain	VERB
ejpam-6974	287	29	from	from	ADP
ejpam-6974	287	30	the	the	DET
ejpam-6974	287	31	group	group	NOUN
ejpam-6974	287	32	(	(	PUNCT
ejpam-6974	287	33	x	x	X
ejpam-6974	287	34	,	,	PUNCT
ejpam-6974	287	35	∗	∗	NOUN
ejpam-6974	287	36	)	)	PUNCT
ejpam-6974	287	37	,	,	PUNCT
ejpam-6974	287	38	then	then	ADV
ejpam-6974	287	39	z	z	NOUN
ejpam-6974	287	40	=	=	PUNCT
ejpam-6974	287	41	x	x	SYM
ejpam-6974	287	42	◦	◦	NOUN
ejpam-6974	287	43	z	z	NOUN
ejpam-6974	287	44	=	=	SYM
ejpam-6974	287	45	x−1	x−1	PROPN
ejpam-6974	287	46	∗z	∗z	PROPN
ejpam-6974	287	47	and	and	CCONJ
ejpam-6974	287	48	z	z	NOUN
ejpam-6974	287	49	=	=	SYM
ejpam-6974	287	50	y	y	PROPN
ejpam-6974	287	51	◦	◦	NOUN
ejpam-6974	287	52	z	z	PROPN
ejpam-6974	287	53	=	=	SYM
ejpam-6974	287	54	y−1	y−1	PROPN
ejpam-6974	287	55	∗z	∗z	PROPN
ejpam-6974	287	56	.	.	PUNCT
ejpam-6974	288	1	this	this	PRON
ejpam-6974	288	2	implies	imply	VERB
ejpam-6974	288	3	x	x	PUNCT
ejpam-6974	288	4	=	=	SYM
ejpam-6974	288	5	y	y	PROPN
ejpam-6974	288	6	,	,	PUNCT
ejpam-6974	288	7	which	which	PRON
ejpam-6974	288	8	is	be	AUX
ejpam-6974	288	9	a	a	DET
ejpam-6974	288	10	contradiction	contradiction	NOUN
ejpam-6974	288	11	since	since	SCONJ
ejpam-6974	288	12	they	they	PRON
ejpam-6974	288	13	are	be	AUX
ejpam-6974	288	14	unique	unique	ADJ
ejpam-6974	288	15	by	by	ADP
ejpam-6974	288	16	hypothesis	hypothesis	NOUN
ejpam-6974	288	17	.	.	PUNCT
ejpam-6974	289	1	so	so	ADV
ejpam-6974	289	2	,	,	PUNCT
ejpam-6974	289	3	the	the	DET
ejpam-6974	289	4	dual	dual	ADJ
ejpam-6974	289	5	bg	bg	NOUN
ejpam-6974	289	6	-	-	NOUN
ejpam-6974	289	7	algebra	algebra	PROPN
ejpam-6974	289	8	(	(	PUNCT
ejpam-6974	289	9	x	x	NOUN
ejpam-6974	289	10	,	,	PUNCT
ejpam-6974	289	11	◦	◦	NOUN
ejpam-6974	289	12	,	,	PUNCT
ejpam-6974	289	13	1	1	NUM
ejpam-6974	289	14	)	)	PUNCT
ejpam-6974	289	15	has	have	VERB
ejpam-6974	289	16	to	to	PART
ejpam-6974	289	17	be	be	AUX
ejpam-6974	289	18	non	non	ADJ
ejpam-6974	289	19	-	-	ADJ
ejpam-6974	289	20	group	group	NOUN
ejpam-6974	289	21	-	-	PUNCT
ejpam-6974	289	22	derived	derive	VERB
ejpam-6974	289	23	.	.	PUNCT
ejpam-6974	290	1	the	the	DET
ejpam-6974	290	2	condition	condition	NOUN
ejpam-6974	290	3	for	for	ADP
ejpam-6974	290	4	x	x	PUNCT
ejpam-6974	290	5	in	in	ADP
ejpam-6974	290	6	theorem	theorem	NOUN
ejpam-6974	290	7	6	6	NUM
ejpam-6974	290	8	to	to	PART
ejpam-6974	290	9	have	have	VERB
ejpam-6974	290	10	at	at	ADV
ejpam-6974	290	11	least	least	ADJ
ejpam-6974	290	12	3	3	NUM
ejpam-6974	290	13	elements	element	NOUN
ejpam-6974	290	14	is	be	AUX
ejpam-6974	290	15	necessary	necessary	ADJ
ejpam-6974	290	16	.	.	PUNCT
ejpam-6974	291	1	to	to	PART
ejpam-6974	291	2	see	see	VERB
ejpam-6974	291	3	this	this	PRON
ejpam-6974	291	4	,	,	PUNCT
ejpam-6974	291	5	if	if	SCONJ
ejpam-6974	291	6	x	x	PRON
ejpam-6974	291	7	has	have	VERB
ejpam-6974	291	8	only	only	ADV
ejpam-6974	291	9	one	one	NUM
ejpam-6974	291	10	element	element	NOUN
ejpam-6974	291	11	,	,	PUNCT
ejpam-6974	291	12	then	then	ADV
ejpam-6974	291	13	it	it	PRON
ejpam-6974	291	14	has	have	VERB
ejpam-6974	291	15	to	to	PART
ejpam-6974	291	16	be	be	AUX
ejpam-6974	291	17	1	1	NUM
ejpam-6974	291	18	and	and	CCONJ
ejpam-6974	291	19	so	so	ADV
ejpam-6974	291	20	x	x	SYM
ejpam-6974	291	21	=	=	NOUN
ejpam-6974	291	22	{	{	PUNCT
ejpam-6974	291	23	1	1	NUM
ejpam-6974	291	24	}	}	PUNCT
ejpam-6974	291	25	.	.	PUNCT
ejpam-6974	292	1	if	if	SCONJ
ejpam-6974	292	2	x	x	PRON
ejpam-6974	292	3	has	have	VERB
ejpam-6974	292	4	two	two	NUM
ejpam-6974	292	5	elements	element	NOUN
ejpam-6974	292	6	,	,	PUNCT
ejpam-6974	292	7	say	say	VERB
ejpam-6974	292	8	x	x	X
ejpam-6974	292	9	=	=	SYM
ejpam-6974	292	10	{	{	PUNCT
ejpam-6974	292	11	1	1	NUM
ejpam-6974	292	12	,	,	PUNCT
ejpam-6974	292	13	a	a	PRON
ejpam-6974	292	14	}	}	PUNCT
ejpam-6974	292	15	,	,	PUNCT
ejpam-6974	292	16	then	then	ADV
ejpam-6974	292	17	1	1	NUM
ejpam-6974	292	18	◦	◦	NOUN
ejpam-6974	292	19	1	1	NUM
ejpam-6974	292	20	=	=	SYM
ejpam-6974	292	21	1	1	NUM
ejpam-6974	292	22	,	,	PUNCT
ejpam-6974	292	23	1	1	NUM
ejpam-6974	292	24	◦	◦	NOUN
ejpam-6974	292	25	a	a	DET
ejpam-6974	292	26	=	=	NOUN
ejpam-6974	292	27	a	a	NOUN
ejpam-6974	292	28	,	,	PUNCT
ejpam-6974	292	29	a	a	DET
ejpam-6974	292	30	◦	◦	NOUN
ejpam-6974	292	31	1	1	NUM
ejpam-6974	292	32	=	=	SYM
ejpam-6974	292	33	a	a	NOUN
ejpam-6974	292	34	,	,	PUNCT
ejpam-6974	292	35	and	and	CCONJ
ejpam-6974	292	36	a	a	DET
ejpam-6974	292	37	◦	◦	NOUN
ejpam-6974	292	38	a	a	DET
ejpam-6974	292	39	=	=	ADJ
ejpam-6974	292	40	1	1	X
ejpam-6974	292	41	.	.	PUNCT
ejpam-6974	293	1	in	in	ADP
ejpam-6974	293	2	any	any	DET
ejpam-6974	293	3	case	case	NOUN
ejpam-6974	293	4	,	,	PUNCT
ejpam-6974	293	5	(	(	PUNCT
ejpam-6974	293	6	x	x	NOUN
ejpam-6974	293	7	,	,	PUNCT
ejpam-6974	293	8	◦	◦	NOUN
ejpam-6974	293	9	,	,	PUNCT
ejpam-6974	293	10	1	1	NUM
ejpam-6974	293	11	)	)	PUNCT
ejpam-6974	293	12	satisfies	satisfie	NOUN
ejpam-6974	293	13	x	x	PART
ejpam-6974	293	14	◦	◦	NOUN
ejpam-6974	293	15	(	(	PUNCT
ejpam-6974	293	16	y	y	PROPN
ejpam-6974	293	17	◦	◦	PROPN
ejpam-6974	293	18	z	z	PROPN
ejpam-6974	293	19	)	)	PUNCT
ejpam-6974	293	20	=	=	SYM
ejpam-6974	294	1	(	(	PUNCT
ejpam-6974	294	2	(	(	PUNCT
ejpam-6974	294	3	x	x	SYM
ejpam-6974	294	4	◦	◦	NOUN
ejpam-6974	294	5	(	(	PUNCT
ejpam-6974	294	6	y	y	NOUN
ejpam-6974	294	7	◦	◦	NOUN
ejpam-6974	294	8	1	1	NUM
ejpam-6974	294	9	)	)	PUNCT
ejpam-6974	294	10	)	)	PUNCT
ejpam-6974	295	1	◦	◦	NOUN
ejpam-6974	295	2	1	1	NUM
ejpam-6974	295	3	)	)	PUNCT
ejpam-6974	295	4	◦	◦	NOUN
ejpam-6974	295	5	z.	z.	PROPN
ejpam-6974	295	6	therefore	therefore	ADV
ejpam-6974	295	7	,	,	PUNCT
ejpam-6974	295	8	(	(	PUNCT
ejpam-6974	295	9	x	x	X
ejpam-6974	295	10	,	,	PUNCT
ejpam-6974	295	11	◦	◦	NOUN
ejpam-6974	295	12	,	,	PUNCT
ejpam-6974	295	13	1	1	NUM
ejpam-6974	295	14	)	)	PUNCT
ejpam-6974	295	15	is	be	AUX
ejpam-6974	295	16	a	a	DET
ejpam-6974	295	17	group	group	NOUN
ejpam-6974	295	18	-	-	PUNCT
ejpam-6974	295	19	derived	derive	VERB
ejpam-6974	295	20	dual	dual	ADJ
ejpam-6974	295	21	bg	bg	NOUN
ejpam-6974	295	22	-	-	NOUN
ejpam-6974	295	23	algebra	algebra	NOUN
ejpam-6974	295	24	by	by	ADP
ejpam-6974	295	25	theorem	theorem	NOUN
ejpam-6974	295	26	4	4	NUM
ejpam-6974	295	27	when	when	SCONJ
ejpam-6974	295	28	x	x	PRON
ejpam-6974	295	29	has	have	VERB
ejpam-6974	295	30	only	only	ADV
ejpam-6974	295	31	1	1	NUM
ejpam-6974	295	32	or	or	CCONJ
ejpam-6974	295	33	2	2	NUM
ejpam-6974	295	34	elements	element	NOUN
ejpam-6974	295	35	.	.	PUNCT
ejpam-6974	296	1	example	example	NOUN
ejpam-6974	296	2	14	14	NUM
ejpam-6974	296	3	.	.	PUNCT
ejpam-6974	297	1	let	let	VERB
ejpam-6974	297	2	x1	x1	PROPN
ejpam-6974	297	3	=	=	SYM
ejpam-6974	297	4	(	(	PUNCT
ejpam-6974	297	5	x	x	X
ejpam-6974	297	6	,	,	PUNCT
ejpam-6974	297	7	◦	◦	NOUN
ejpam-6974	297	8	1	1	NUM
ejpam-6974	297	9	,	,	PUNCT
ejpam-6974	297	10	1	1	NUM
ejpam-6974	297	11	)	)	PUNCT
ejpam-6974	297	12	,	,	PUNCT
ejpam-6974	297	13	y1	y1	NOUN
ejpam-6974	297	14	=	=	SYM
ejpam-6974	297	15	(	(	PUNCT
ejpam-6974	297	16	y	y	NOUN
ejpam-6974	297	17	,	,	PUNCT
ejpam-6974	297	18	◦	◦	NOUN
ejpam-6974	297	19	2	2	NUM
ejpam-6974	297	20	,	,	PUNCT
ejpam-6974	297	21	1	1	NUM
ejpam-6974	297	22	)	)	PUNCT
ejpam-6974	297	23	,	,	PUNCT
ejpam-6974	297	24	and	and	CCONJ
ejpam-6974	297	25	z1	z1	PROPN
ejpam-6974	297	26	=	=	SYM
ejpam-6974	297	27	(	(	PUNCT
ejpam-6974	297	28	z	z	NOUN
ejpam-6974	297	29	,	,	PUNCT
ejpam-6974	297	30	◦	◦	NOUN
ejpam-6974	297	31	3	3	NUM
ejpam-6974	297	32	,	,	PUNCT
ejpam-6974	297	33	1	1	NUM
ejpam-6974	297	34	)	)	PUNCT
ejpam-6974	297	35	where	where	SCONJ
ejpam-6974	297	36	x	x	X
ejpam-6974	297	37	=	=	PRON
ejpam-6974	297	38	{	{	PUNCT
ejpam-6974	297	39	1	1	NUM
ejpam-6974	297	40	,	,	PUNCT
ejpam-6974	297	41	a	a	DET
ejpam-6974	297	42	,	,	PUNCT
ejpam-6974	297	43	b	b	NOUN
ejpam-6974	297	44	,	,	PUNCT
ejpam-6974	297	45	c	c	NOUN
ejpam-6974	297	46	}	}	PUNCT
ejpam-6974	297	47	,	,	PUNCT
ejpam-6974	297	48	y	y	PROPN
ejpam-6974	297	49	=	=	PUNCT
ejpam-6974	297	50	{	{	PUNCT
ejpam-6974	297	51	1	1	NUM
ejpam-6974	297	52	,	,	PUNCT
ejpam-6974	297	53	a	a	DET
ejpam-6974	297	54	,	,	PUNCT
ejpam-6974	297	55	b	b	NOUN
ejpam-6974	297	56	,	,	PUNCT
ejpam-6974	297	57	c	c	NOUN
ejpam-6974	297	58	,	,	PUNCT
ejpam-6974	297	59	d	d	NOUN
ejpam-6974	297	60	}	}	PUNCT
ejpam-6974	297	61	,	,	PUNCT
ejpam-6974	297	62	and	and	CCONJ
ejpam-6974	297	63	z	z	NOUN
ejpam-6974	297	64	=	=	SYM
ejpam-6974	297	65	{	{	PUNCT
ejpam-6974	297	66	1	1	NUM
ejpam-6974	297	67	,	,	PUNCT
ejpam-6974	297	68	a	a	DET
ejpam-6974	297	69	,	,	PUNCT
ejpam-6974	297	70	b	b	NOUN
ejpam-6974	297	71	,	,	PUNCT
ejpam-6974	297	72	c	c	NOUN
ejpam-6974	297	73	,	,	PUNCT
ejpam-6974	297	74	d	d	NOUN
ejpam-6974	297	75	,	,	PUNCT
ejpam-6974	297	76	e	e	NOUN
ejpam-6974	297	77	}	}	PUNCT
ejpam-6974	297	78	.	.	PUNCT
ejpam-6974	298	1	the	the	DET
ejpam-6974	298	2	cayley	cayley	ADJ
ejpam-6974	298	3	tables	table	NOUN
ejpam-6974	298	4	of	of	ADP
ejpam-6974	298	5	the	the	DET
ejpam-6974	298	6	binary	binary	ADJ
ejpam-6974	298	7	operations	operation	NOUN
ejpam-6974	298	8	◦	◦	NOUN
ejpam-6974	298	9	1	1	NUM
ejpam-6974	298	10	,	,	PUNCT
ejpam-6974	298	11	◦	◦	NOUN
ejpam-6974	298	12	2	2	NUM
ejpam-6974	298	13	,	,	PUNCT
ejpam-6974	298	14	and	and	CCONJ
ejpam-6974	298	15	◦	◦	NOUN
ejpam-6974	298	16	3	3	NUM
ejpam-6974	298	17	are	be	AUX
ejpam-6974	298	18	shown	show	VERB
ejpam-6974	298	19	in	in	ADP
ejpam-6974	298	20	table	table	NOUN
ejpam-6974	298	21	8	8	NUM
ejpam-6974	298	22	.	.	PUNCT
ejpam-6974	298	23	table	table	NOUN
ejpam-6974	298	24	8	8	NUM
ejpam-6974	298	25	:	:	PUNCT
ejpam-6974	298	26	cayley	cayley	ADJ
ejpam-6974	298	27	tables	table	NOUN
ejpam-6974	298	28	of	of	ADP
ejpam-6974	298	29	x1	x1	PROPN
ejpam-6974	298	30	,	,	PUNCT
ejpam-6974	298	31	y1	y1	NOUN
ejpam-6974	298	32	,	,	PUNCT
ejpam-6974	298	33	and	and	CCONJ
ejpam-6974	298	34	z1	z1	PROPN
ejpam-6974	298	35	◦	◦	NOUN
ejpam-6974	298	36	1	1	NUM
ejpam-6974	298	37	1	1	NUM
ejpam-6974	298	38	a	a	DET
ejpam-6974	298	39	b	b	NOUN
ejpam-6974	298	40	c	c	NOUN
ejpam-6974	298	41	1	1	NUM
ejpam-6974	298	42	1	1	NUM
ejpam-6974	298	43	a	a	DET
ejpam-6974	298	44	b	b	NOUN
ejpam-6974	298	45	c	c	ADP
ejpam-6974	298	46	a	a	DET
ejpam-6974	298	47	a	a	DET
ejpam-6974	298	48	1	1	NUM
ejpam-6974	298	49	b	b	PROPN
ejpam-6974	298	50	c	c	PROPN
ejpam-6974	298	51	b	b	PROPN
ejpam-6974	298	52	b	b	PROPN
ejpam-6974	298	53	a	a	DET
ejpam-6974	298	54	1	1	NUM
ejpam-6974	298	55	c	c	NOUN
ejpam-6974	298	56	c	c	NOUN
ejpam-6974	298	57	c	c	NOUN
ejpam-6974	298	58	a	a	PRON
ejpam-6974	298	59	b	b	PROPN
ejpam-6974	298	60	1	1	NUM
ejpam-6974	298	61	◦	◦	NOUN
ejpam-6974	298	62	2	2	NUM
ejpam-6974	298	63	1	1	NUM
ejpam-6974	298	64	a	a	DET
ejpam-6974	298	65	b	b	NOUN
ejpam-6974	298	66	c	c	NOUN
ejpam-6974	298	67	d	d	SYM
ejpam-6974	298	68	1	1	NUM
ejpam-6974	298	69	1	1	NUM
ejpam-6974	298	70	a	a	DET
ejpam-6974	298	71	b	b	NOUN
ejpam-6974	298	72	c	c	NOUN
ejpam-6974	299	1	d	d	NOUN
ejpam-6974	299	2	a	a	PRON
ejpam-6974	299	3	a	a	DET
ejpam-6974	299	4	1	1	NUM
ejpam-6974	299	5	b	b	NOUN
ejpam-6974	299	6	c	c	NOUN
ejpam-6974	299	7	d	d	PROPN
ejpam-6974	299	8	b	b	PROPN
ejpam-6974	299	9	b	b	PROPN
ejpam-6974	299	10	a	a	DET
ejpam-6974	299	11	1	1	NUM
ejpam-6974	299	12	c	c	NOUN
ejpam-6974	299	13	d	d	NOUN
ejpam-6974	299	14	c	c	NOUN
ejpam-6974	299	15	c	c	PROPN
ejpam-6974	299	16	a	a	DET
ejpam-6974	299	17	b	b	NOUN
ejpam-6974	299	18	1	1	NUM
ejpam-6974	299	19	d	d	NOUN
ejpam-6974	299	20	d	d	PROPN
ejpam-6974	299	21	d	d	PROPN
ejpam-6974	299	22	a	a	PRON
ejpam-6974	299	23	b	b	PROPN
ejpam-6974	299	24	c	c	NOUN
ejpam-6974	299	25	1	1	NUM
ejpam-6974	299	26	◦	◦	NOUN
ejpam-6974	299	27	3	3	NUM
ejpam-6974	299	28	1	1	NUM
ejpam-6974	299	29	a	a	DET
ejpam-6974	299	30	b	b	NOUN
ejpam-6974	299	31	c	c	NOUN
ejpam-6974	299	32	d	d	X
ejpam-6974	299	33	e	e	PROPN
ejpam-6974	299	34	1	1	NUM
ejpam-6974	299	35	1	1	NUM
ejpam-6974	299	36	a	a	DET
ejpam-6974	299	37	b	b	NOUN
ejpam-6974	299	38	c	c	NOUN
ejpam-6974	299	39	d	d	PROPN
ejpam-6974	299	40	e	e	PROPN
ejpam-6974	299	41	a	a	DET
ejpam-6974	299	42	a	a	DET
ejpam-6974	299	43	1	1	NUM
ejpam-6974	299	44	b	b	NOUN
ejpam-6974	299	45	c	c	NOUN
ejpam-6974	299	46	d	d	PROPN
ejpam-6974	299	47	e	e	PROPN
ejpam-6974	299	48	b	b	PROPN
ejpam-6974	299	49	b	b	PROPN
ejpam-6974	299	50	a	a	DET
ejpam-6974	299	51	1	1	NUM
ejpam-6974	299	52	c	c	NOUN
ejpam-6974	299	53	d	d	NOUN
ejpam-6974	299	54	e	e	X
ejpam-6974	299	55	c	c	NOUN
ejpam-6974	299	56	c	c	PROPN
ejpam-6974	299	57	a	a	DET
ejpam-6974	299	58	b	b	PROPN
ejpam-6974	299	59	1	1	NUM
ejpam-6974	299	60	d	d	NOUN
ejpam-6974	299	61	e	e	PROPN
ejpam-6974	299	62	d	d	PROPN
ejpam-6974	299	63	d	d	PROPN
ejpam-6974	299	64	a	a	DET
ejpam-6974	299	65	b	b	NOUN
ejpam-6974	299	66	c	c	NOUN
ejpam-6974	299	67	1	1	NUM
ejpam-6974	299	68	e	e	NOUN
ejpam-6974	299	69	e	e	X
ejpam-6974	299	70	e	e	X
ejpam-6974	299	71	a	a	PRON
ejpam-6974	299	72	b	b	NOUN
ejpam-6974	299	73	c	c	NOUN
ejpam-6974	299	74	d	d	NOUN
ejpam-6974	299	75	1	1	NUM
ejpam-6974	299	76	then	then	ADV
ejpam-6974	299	77	x1	x1	NUM
ejpam-6974	299	78	,	,	PUNCT
ejpam-6974	299	79	y1	y1	NOUN
ejpam-6974	299	80	,	,	PUNCT
ejpam-6974	299	81	and	and	CCONJ
ejpam-6974	299	82	z1	z1	NOUN
ejpam-6974	299	83	are	be	AUX
ejpam-6974	299	84	all	all	PRON
ejpam-6974	299	85	non	non	ADJ
ejpam-6974	299	86	-	-	ADJ
ejpam-6974	299	87	group	group	NOUN
ejpam-6974	299	88	-	-	PUNCT
ejpam-6974	299	89	derived	derive	VERB
ejpam-6974	299	90	dual	dual	ADJ
ejpam-6974	299	91	bg	bg	NOUN
ejpam-6974	299	92	-	-	PUNCT
ejpam-6974	299	93	algebras	algebras	PROPN
ejpam-6974	299	94	by	by	ADP
ejpam-6974	299	95	theorem	theorem	NOUN
ejpam-6974	299	96	6	6	NUM
ejpam-6974	299	97	.	.	PUNCT
ejpam-6974	299	98	example	example	NOUN
ejpam-6974	299	99	14	14	NUM
ejpam-6974	299	100	shows	show	VERB
ejpam-6974	299	101	some	some	PRON
ejpam-6974	299	102	of	of	ADP
ejpam-6974	299	103	the	the	DET
ejpam-6974	299	104	dual	dual	ADJ
ejpam-6974	299	105	bg	bg	NOUN
ejpam-6974	299	106	-	-	PUNCT
ejpam-6974	299	107	algebras	algebras	PROPN
ejpam-6974	299	108	that	that	PRON
ejpam-6974	299	109	can	can	AUX
ejpam-6974	299	110	be	be	AUX
ejpam-6974	299	111	generated	generate	VERB
ejpam-6974	299	112	using	use	VERB
ejpam-6974	299	113	theorem	theorem	NOUN
ejpam-6974	299	114	6	6	NUM
ejpam-6974	299	115	.	.	NOUN
ejpam-6974	299	116	4	4	NUM
ejpam-6974	299	117	.	.	X
ejpam-6974	299	118	conclusion	conclusion	NOUN
ejpam-6974	299	119	it	it	PRON
ejpam-6974	299	120	was	be	AUX
ejpam-6974	299	121	shown	show	VERB
ejpam-6974	299	122	that	that	SCONJ
ejpam-6974	299	123	the	the	DET
ejpam-6974	299	124	axioms	axiom	NOUN
ejpam-6974	299	125	of	of	ADP
ejpam-6974	299	126	the	the	DET
ejpam-6974	299	127	dual	dual	ADJ
ejpam-6974	299	128	bg	bg	NOUN
ejpam-6974	299	129	-	-	PUNCT
ejpam-6974	299	130	algebra	algebra	PROPN
ejpam-6974	299	131	are	be	AUX
ejpam-6974	299	132	independent	independent	ADJ
ejpam-6974	299	133	.	.	PUNCT
ejpam-6974	300	1	not	not	PART
ejpam-6974	300	2	every	every	DET
ejpam-6974	300	3	dual	dual	ADJ
ejpam-6974	300	4	bg	bg	NOUN
ejpam-6974	300	5	-	-	PUNCT
ejpam-6974	300	6	algebra	algebra	PROPN
ejpam-6974	300	7	is	be	AUX
ejpam-6974	300	8	a	a	DET
ejpam-6974	300	9	bg	bg	NOUN
ejpam-6974	300	10	-	-	PUNCT
ejpam-6974	300	11	algebra	algebra	PROPN
ejpam-6974	300	12	and	and	CCONJ
ejpam-6974	300	13	not	not	PART
ejpam-6974	300	14	every	every	DET
ejpam-6974	300	15	bg	bg	NOUN
ejpam-6974	300	16	-	-	PUNCT
ejpam-6974	300	17	algebra	algebra	PROPN
ejpam-6974	300	18	is	be	AUX
ejpam-6974	300	19	dual	dual	ADJ
ejpam-6974	300	20	bg	bg	NOUN
ejpam-6974	300	21	-	-	NOUN
ejpam-6974	300	22	algebra	algebra	PROPN
ejpam-6974	300	23	.	.	PUNCT
ejpam-6974	301	1	but	but	CCONJ
ejpam-6974	301	2	it	it	PRON
ejpam-6974	301	3	is	be	AUX
ejpam-6974	301	4	possible	possible	ADJ
ejpam-6974	301	5	that	that	SCONJ
ejpam-6974	301	6	a	a	DET
ejpam-6974	301	7	dual	dual	ADJ
ejpam-6974	301	8	bg	bg	NOUN
ejpam-6974	301	9	-	-	PUNCT
ejpam-6974	301	10	algebra	algebra	PROPN
ejpam-6974	301	11	is	be	AUX
ejpam-6974	301	12	also	also	ADV
ejpam-6974	301	13	a	a	DET
ejpam-6974	301	14	bg	bg	NOUN
ejpam-6974	301	15	-	-	PUNCT
ejpam-6974	301	16	algebra	algebra	PROPN
ejpam-6974	301	17	.	.	PUNCT
ejpam-6974	302	1	a	a	DET
ejpam-6974	302	2	characterization	characterization	NOUN
ejpam-6974	302	3	for	for	ADP
ejpam-6974	302	4	the	the	DET
ejpam-6974	302	5	dual	dual	ADJ
ejpam-6974	302	6	bg	bg	NOUN
ejpam-6974	302	7	-	-	PUNCT
ejpam-6974	302	8	algebra	algebra	PROPN
ejpam-6974	302	9	was	be	AUX
ejpam-6974	302	10	established	establish	VERB
ejpam-6974	302	11	.	.	PUNCT
ejpam-6974	303	1	the	the	DET
ejpam-6974	303	2	notion	notion	NOUN
ejpam-6974	303	3	of	of	ADP
ejpam-6974	303	4	a	a	DET
ejpam-6974	303	5	group	group	NOUN
ejpam-6974	303	6	-	-	PUNCT
ejpam-6974	303	7	derived	derive	VERB
ejpam-6974	303	8	and	and	CCONJ
ejpam-6974	303	9	non	non	ADJ
ejpam-6974	303	10	-	-	NOUN
ejpam-6974	303	11	group	group	NOUN
ejpam-6974	303	12	-	-	PUNCT
ejpam-6974	303	13	derived	derive	VERB
ejpam-6974	303	14	dual	dual	ADJ
ejpam-6974	303	15	bg	bg	NOUN
ejpam-6974	303	16	-	-	PUNCT
ejpam-6974	303	17	algebras	algebras	PROPN
ejpam-6974	303	18	were	be	AUX
ejpam-6974	303	19	also	also	ADV
ejpam-6974	303	20	introduced	introduce	VERB
ejpam-6974	303	21	.	.	PUNCT
ejpam-6974	304	1	it	it	PRON
ejpam-6974	304	2	was	be	AUX
ejpam-6974	304	3	shown	show	VERB
ejpam-6974	304	4	that	that	SCONJ
ejpam-6974	304	5	a	a	DET
ejpam-6974	304	6	group	group	NOUN
ejpam-6974	304	7	-	-	PUNCT
ejpam-6974	304	8	derived	derive	VERB
ejpam-6974	304	9	dual	dual	ADJ
ejpam-6974	304	10	bgalgebra	bgalgebra	NOUN
ejpam-6974	304	11	is	be	AUX
ejpam-6974	304	12	characterized	characterize	VERB
ejpam-6974	304	13	by	by	ADP
ejpam-6974	304	14	a	a	DET
ejpam-6974	304	15	dual	dual	ADJ
ejpam-6974	304	16	b	b	NOUN
ejpam-6974	304	17	-	-	PUNCT
ejpam-6974	304	18	algebra	algebra	NOUN
ejpam-6974	304	19	and	and	CCONJ
ejpam-6974	304	20	infinitely	infinitely	ADV
ejpam-6974	304	21	many	many	ADJ
ejpam-6974	304	22	non	non	ADJ
ejpam-6974	304	23	-	-	ADJ
ejpam-6974	304	24	group	group	NOUN
ejpam-6974	304	25	-	-	PUNCT
ejpam-6974	304	26	derived	derive	VERB
ejpam-6974	304	27	dual	dual	ADJ
ejpam-6974	304	28	bg	bg	NOUN
ejpam-6974	304	29	-	-	PUNCT
ejpam-6974	304	30	algebras	algebras	PROPN
ejpam-6974	304	31	can	can	AUX
ejpam-6974	304	32	be	be	AUX
ejpam-6974	304	33	constructed	construct	VERB
ejpam-6974	304	34	.	.	PUNCT
ejpam-6974	305	1	c.m	c.m	PROPN
ejpam-6974	305	2	.	.	PROPN
ejpam-6974	305	3	chan	chan	PROPN
ejpam-6974	305	4	,	,	PUNCT
ejpam-6974	305	5	k.	k.	PROPN
ejpam-6974	305	6	fuentes	fuentes	PROPN
ejpam-6974	305	7	/	/	SYM
ejpam-6974	305	8	eur	eur	PROPN
ejpam-6974	305	9	.	.	PUNCT
ejpam-6974	306	1	j.	j.	PROPN
ejpam-6974	306	2	pure	pure	PROPN
ejpam-6974	306	3	appl	appl	PROPN
ejpam-6974	306	4	.	.	PROPN
ejpam-6974	306	5	math	math	PROPN
ejpam-6974	306	6	,	,	PUNCT
ejpam-6974	306	7	18	18	NUM
ejpam-6974	306	8	(	(	PUNCT
ejpam-6974	306	9	4	4	NUM
ejpam-6974	306	10	)	)	PUNCT
ejpam-6974	306	11	(	(	PUNCT
ejpam-6974	306	12	2025	2025	NUM
ejpam-6974	306	13	)	)	PUNCT
ejpam-6974	306	14	,	,	PUNCT
ejpam-6974	306	15	6974	6974	NUM
ejpam-6974	306	16	10	10	NUM
ejpam-6974	306	17	of	of	ADP
ejpam-6974	306	18	16	16	NUM
ejpam-6974	306	19	5	5	NUM
ejpam-6974	306	20	.	.	PUNCT
ejpam-6974	306	21	recommendations	recommendation	NOUN
ejpam-6974	306	22	in	in	ADP
ejpam-6974	306	23	one	one	NUM
ejpam-6974	306	24	of	of	ADP
ejpam-6974	306	25	the	the	DET
ejpam-6974	306	26	theorems	theorem	NOUN
ejpam-6974	306	27	,	,	PUNCT
ejpam-6974	306	28	it	it	PRON
ejpam-6974	306	29	was	be	AUX
ejpam-6974	306	30	shown	show	VERB
ejpam-6974	306	31	that	that	SCONJ
ejpam-6974	306	32	every	every	DET
ejpam-6974	306	33	dual	dual	ADJ
ejpam-6974	306	34	b	b	X
ejpam-6974	306	35	-	-	PUNCT
ejpam-6974	306	36	algebra	algebra	NOUN
ejpam-6974	306	37	is	be	AUX
ejpam-6974	306	38	a	a	DET
ejpam-6974	306	39	dual	dual	ADJ
ejpam-6974	306	40	bg	bg	NOUN
ejpam-6974	306	41	-	-	NOUN
ejpam-6974	306	42	algebra	algebra	PROPN
ejpam-6974	306	43	.	.	PUNCT
ejpam-6974	307	1	the	the	DET
ejpam-6974	307	2	authors	author	NOUN
ejpam-6974	307	3	recommend	recommend	VERB
ejpam-6974	307	4	exploring	explore	VERB
ejpam-6974	307	5	the	the	DET
ejpam-6974	307	6	relationship	relationship	NOUN
ejpam-6974	307	7	of	of	ADP
ejpam-6974	307	8	the	the	DET
ejpam-6974	307	9	dual	dual	ADJ
ejpam-6974	307	10	bg	bg	NOUN
ejpam-6974	307	11	-	-	NOUN
ejpam-6974	307	12	algebra	algebra	PROPN
ejpam-6974	307	13	to	to	ADP
ejpam-6974	307	14	other	other	ADJ
ejpam-6974	307	15	algebras	algebra	NOUN
ejpam-6974	307	16	and	and	CCONJ
ejpam-6974	307	17	dual	dual	ADJ
ejpam-6974	307	18	algebras	algebra	NOUN
ejpam-6974	307	19	,	,	PUNCT
ejpam-6974	307	20	and	and	CCONJ
ejpam-6974	307	21	not	not	PART
ejpam-6974	307	22	just	just	ADV
ejpam-6974	307	23	the	the	DET
ejpam-6974	307	24	dual	dual	ADJ
ejpam-6974	307	25	b	b	NOUN
ejpam-6974	307	26	-	-	PUNCT
ejpam-6974	307	27	algebra	algebra	NOUN
ejpam-6974	307	28	.	.	PUNCT
ejpam-6974	308	1	other	other	ADJ
ejpam-6974	308	2	structural	structural	ADJ
ejpam-6974	308	3	properties	property	NOUN
ejpam-6974	308	4	may	may	AUX
ejpam-6974	308	5	also	also	ADV
ejpam-6974	308	6	be	be	AUX
ejpam-6974	308	7	considered	consider	VERB
ejpam-6974	308	8	such	such	ADJ
ejpam-6974	308	9	as	as	ADP
ejpam-6974	308	10	ideals	ideal	NOUN
ejpam-6974	308	11	,	,	PUNCT
ejpam-6974	308	12	filters	filter	NOUN
ejpam-6974	308	13	,	,	PUNCT
ejpam-6974	308	14	homomorphisms	homomorphism	NOUN
ejpam-6974	308	15	,	,	PUNCT
ejpam-6974	308	16	among	among	ADP
ejpam-6974	308	17	others	other	NOUN
ejpam-6974	308	18	.	.	PUNCT
ejpam-6974	309	1	references	reference	NOUN
ejpam-6974	309	2	[	[	X
ejpam-6974	309	3	1	1	NUM
ejpam-6974	309	4	]	]	X
ejpam-6974	309	5	y	y	PROPN
ejpam-6974	309	6	imai	imai	PROPN
ejpam-6974	309	7	and	and	CCONJ
ejpam-6974	309	8	k	k	PROPN
ejpam-6974	309	9	iséki	iséki	PROPN
ejpam-6974	309	10	.	.	PROPN
ejpam-6974	310	1	on	on	ADP
ejpam-6974	310	2	axiom	axiom	NOUN
ejpam-6974	310	3	systems	system	NOUN
ejpam-6974	310	4	of	of	ADP
ejpam-6974	310	5	propositional	propositional	ADJ
ejpam-6974	310	6	calculi	calculi	PROPN
ejpam-6974	310	7	.	.	PUNCT
ejpam-6974	311	1	proceedings	proceeding	NOUN
ejpam-6974	311	2	of	of	ADP
ejpam-6974	311	3	the	the	DET
ejpam-6974	311	4	japan	japan	PROPN
ejpam-6974	311	5	academy	academy	PROPN
ejpam-6974	311	6	,	,	PUNCT
ejpam-6974	311	7	42(1):19–22	42(1):19–22	NUM
ejpam-6974	311	8	,	,	PUNCT
ejpam-6974	311	9	1966	1966	NUM
ejpam-6974	311	10	.	.	PUNCT
ejpam-6974	312	1	[	[	X
ejpam-6974	312	2	2	2	X
ejpam-6974	312	3	]	]	X
ejpam-6974	312	4	q	q	X
ejpam-6974	312	5	p	p	X
ejpam-6974	312	6	hu	hu	PROPN
ejpam-6974	312	7	and	and	CCONJ
ejpam-6974	312	8	x	x	SYM
ejpam-6974	312	9	li	li	PROPN
ejpam-6974	312	10	.	.	PROPN
ejpam-6974	312	11	on	on	ADP
ejpam-6974	312	12	bch	bch	PROPN
ejpam-6974	312	13	-	-	PUNCT
ejpam-6974	312	14	algebras	algebras	PROPN
ejpam-6974	312	15	.	.	PUNCT
ejpam-6974	313	1	mathematics	mathematic	NOUN
ejpam-6974	313	2	seminar	seminar	NOUN
ejpam-6974	313	3	notes	note	NOUN
ejpam-6974	313	4	(	(	PUNCT
ejpam-6974	313	5	kobe	kobe	PROPN
ejpam-6974	313	6	university	university	PROPN
ejpam-6974	313	7	)	)	PUNCT
ejpam-6974	313	8	,	,	PUNCT
ejpam-6974	313	9	11(2):313–320	11(2):313–320	PROPN
ejpam-6974	313	10	,	,	PUNCT
ejpam-6974	313	11	1983	1983	NUM
ejpam-6974	313	12	.	.	PUNCT
ejpam-6974	314	1	[	[	X
ejpam-6974	314	2	3	3	X
ejpam-6974	314	3	]	]	X
ejpam-6974	314	4	q	q	X
ejpam-6974	314	5	p	p	X
ejpam-6974	314	6	hu	hu	PROPN
ejpam-6974	314	7	and	and	CCONJ
ejpam-6974	314	8	x	x	SYM
ejpam-6974	314	9	li	li	PROPN
ejpam-6974	314	10	.	.	PROPN
ejpam-6974	314	11	on	on	ADP
ejpam-6974	314	12	proper	proper	ADJ
ejpam-6974	314	13	bch	bch	NOUN
ejpam-6974	314	14	-	-	PUNCT
ejpam-6974	314	15	algebras	algebras	PROPN
ejpam-6974	314	16	.	.	PUNCT
ejpam-6974	315	1	mathematica	mathematica	PROPN
ejpam-6974	315	2	japonica	japonica	PROPN
ejpam-6974	315	3	,	,	PUNCT
ejpam-6974	315	4	30(4):659–661	30(4):659–661	PROPN
ejpam-6974	315	5	,	,	PUNCT
ejpam-6974	315	6	1985	1985	NUM
ejpam-6974	315	7	.	.	PUNCT
ejpam-6974	316	1	[	[	X
ejpam-6974	316	2	4	4	NUM
ejpam-6974	316	3	]	]	X
ejpam-6974	316	4	y	y	PROPN
ejpam-6974	316	5	b	b	PROPN
ejpam-6974	316	6	jun	jun	PROPN
ejpam-6974	316	7	,	,	PUNCT
ejpam-6974	316	8	e	e	PROPN
ejpam-6974	316	9	h	h	PROPN
ejpam-6974	316	10	roh	roh	PROPN
ejpam-6974	316	11	,	,	PUNCT
ejpam-6974	316	12	and	and	CCONJ
ejpam-6974	316	13	h	h	NOUN
ejpam-6974	316	14	s	s	VERB
ejpam-6974	316	15	kim	kim	PROPN
ejpam-6974	316	16	.	.	PUNCT
ejpam-6974	317	1	on	on	ADP
ejpam-6974	317	2	bh	bh	NOUN
ejpam-6974	317	3	-	-	PUNCT
ejpam-6974	317	4	algebras	algebras	PROPN
ejpam-6974	317	5	.	.	PUNCT
ejpam-6974	318	1	scientiae	scientiae	PROPN
ejpam-6974	318	2	mathematicae	mathematicae	PROPN
ejpam-6974	318	3	,	,	PUNCT
ejpam-6974	318	4	1(3):347–354	1(3):347–354	NUM
ejpam-6974	318	5	,	,	PUNCT
ejpam-6974	318	6	1998	1998	NUM
ejpam-6974	318	7	.	.	PUNCT
ejpam-6974	319	1	[	[	X
ejpam-6974	319	2	5	5	NUM
ejpam-6974	319	3	]	]	PUNCT
ejpam-6974	319	4	j	j	PROPN
ejpam-6974	319	5	neggers	negger	NOUN
ejpam-6974	319	6	and	and	CCONJ
ejpam-6974	319	7	h	h	NOUN
ejpam-6974	319	8	s	s	PROPN
ejpam-6974	319	9	kim	kim	PROPN
ejpam-6974	319	10	.	.	PUNCT
ejpam-6974	320	1	on	on	ADP
ejpam-6974	320	2	d	d	PROPN
ejpam-6974	320	3	-	-	PUNCT
ejpam-6974	320	4	algebras	algebras	PROPN
ejpam-6974	320	5	.	.	PUNCT
ejpam-6974	321	1	mathematica	mathematica	PROPN
ejpam-6974	321	2	slovaca	slovaca	PROPN
ejpam-6974	321	3	,	,	PUNCT
ejpam-6974	321	4	49(1):19–26	49(1):19–26	NUM
ejpam-6974	321	5	,	,	PUNCT
ejpam-6974	321	6	1999	1999	NUM
ejpam-6974	321	7	.	.	PUNCT
ejpam-6974	322	1	[	[	X
ejpam-6974	322	2	6	6	NUM
ejpam-6974	322	3	]	]	PUNCT
ejpam-6974	322	4	j	j	PROPN
ejpam-6974	322	5	neggers	negger	NOUN
ejpam-6974	322	6	and	and	CCONJ
ejpam-6974	322	7	h	h	NOUN
ejpam-6974	322	8	s	s	PROPN
ejpam-6974	322	9	kim	kim	PROPN
ejpam-6974	322	10	.	.	PUNCT
ejpam-6974	323	1	on	on	ADP
ejpam-6974	323	2	b	b	NOUN
ejpam-6974	323	3	-	-	PUNCT
ejpam-6974	323	4	algebras	algebra	NOUN
ejpam-6974	323	5	.	.	PUNCT
ejpam-6974	324	1	matematički	matematički	PROPN
ejpam-6974	324	2	vesnik	vesnik	PROPN
ejpam-6974	324	3	,	,	PUNCT
ejpam-6974	324	4	54(1	54(1	PROPN
ejpam-6974	324	5	-	-	SYM
ejpam-6974	324	6	2):21–29	2):21–29	NUM
ejpam-6974	324	7	,	,	PUNCT
ejpam-6974	324	8	2002	2002	NUM
ejpam-6974	324	9	.	.	PUNCT
ejpam-6974	325	1	[	[	X
ejpam-6974	325	2	7	7	NUM
ejpam-6974	325	3	]	]	X
ejpam-6974	325	4	c	c	PROPN
ejpam-6974	325	5	b	b	PROPN
ejpam-6974	325	6	kim	kim	PROPN
ejpam-6974	325	7	and	and	CCONJ
ejpam-6974	325	8	h	h	PROPN
ejpam-6974	325	9	s	s	PROPN
ejpam-6974	325	10	kim	kim	PROPN
ejpam-6974	325	11	.	.	PUNCT
ejpam-6974	326	1	on	on	ADP
ejpam-6974	326	2	bg	bg	PROPN
ejpam-6974	326	3	-	-	PUNCT
ejpam-6974	326	4	algebras	algebras	PROPN
ejpam-6974	326	5	.	.	PROPN
ejpam-6974	326	6	demonstratio	demonstratio	PROPN
ejpam-6974	326	7	mathematica	mathematica	PROPN
ejpam-6974	326	8	,	,	PUNCT
ejpam-6974	326	9	41(3):497–506	41(3):497–506	PROPN
ejpam-6974	326	10	,	,	PUNCT
ejpam-6974	326	11	2008	2008	NUM
ejpam-6974	326	12	.	.	PUNCT
ejpam-6974	327	1	[	[	X
ejpam-6974	327	2	8	8	NUM
ejpam-6974	327	3	]	]	X
ejpam-6974	327	4	k	k	PROPN
ejpam-6974	327	5	h	h	PROPN
ejpam-6974	327	6	kim	kim	PROPN
ejpam-6974	327	7	and	and	CCONJ
ejpam-6974	327	8	y	y	PROPN
ejpam-6974	327	9	h	h	PROPN
ejpam-6974	327	10	yon	yon	PROPN
ejpam-6974	327	11	.	.	PUNCT
ejpam-6974	328	1	dual	dual	ADJ
ejpam-6974	328	2	bck	bck	NOUN
ejpam-6974	328	3	-	-	PUNCT
ejpam-6974	328	4	algebra	algebra	PROPN
ejpam-6974	328	5	and	and	CCONJ
ejpam-6974	328	6	mv	mv	PROPN
ejpam-6974	328	7	-algebra	-algebra	PROPN
ejpam-6974	328	8	.	.	PUNCT
ejpam-6974	329	1	scientiae	scientiae	PROPN
ejpam-6974	329	2	mathematicae	mathematicae	PROPN
ejpam-6974	329	3	japonicae	japonicae	PROPN
ejpam-6974	329	4	,	,	PUNCT
ejpam-6974	329	5	66(2):393–399	66(2):393–399	NOUN
ejpam-6974	329	6	,	,	PUNCT
ejpam-6974	329	7	2007	2007	NUM
ejpam-6974	329	8	.	.	PUNCT
ejpam-6974	330	1	[	[	X
ejpam-6974	330	2	9	9	NUM
ejpam-6974	330	3	]	]	X
ejpam-6974	330	4	h	h	NOUN
ejpam-6974	330	5	s	s	PROPN
ejpam-6974	330	6	kim	kim	PROPN
ejpam-6974	330	7	and	and	CCONJ
ejpam-6974	330	8	y	y	PROPN
ejpam-6974	330	9	h	h	PROPN
ejpam-6974	330	10	kim	kim	PROPN
ejpam-6974	330	11	.	.	PUNCT
ejpam-6974	331	1	on	on	ADP
ejpam-6974	331	2	be	be	AUX
ejpam-6974	331	3	-	-	PUNCT
ejpam-6974	331	4	algebras	algebra	NOUN
ejpam-6974	331	5	.	.	PUNCT
ejpam-6974	332	1	scientiae	scientiae	PROPN
ejpam-6974	332	2	mathematicae	mathematicae	PROPN
ejpam-6974	332	3	japonicae	japonicae	PROPN
ejpam-6974	332	4	,	,	PUNCT
ejpam-6974	332	5	66(1):113–116	66(1):113–116	PROPN
ejpam-6974	332	6	,	,	PUNCT
ejpam-6974	332	7	2007	2007	NUM
ejpam-6974	332	8	.	.	PUNCT
ejpam-6974	333	1	[	[	X
ejpam-6974	333	2	10	10	NUM
ejpam-6974	333	3	]	]	X
ejpam-6974	333	4	a	a	DET
ejpam-6974	333	5	walendziak	walendziak	NOUN
ejpam-6974	333	6	.	.	PUNCT
ejpam-6974	334	1	on	on	ADP
ejpam-6974	334	2	commutative	commutative	ADJ
ejpam-6974	334	3	be	be	AUX
ejpam-6974	334	4	-	-	PUNCT
ejpam-6974	334	5	algebras	algebra	NOUN
ejpam-6974	334	6	.	.	PUNCT
ejpam-6974	335	1	scientiae	scientiae	PROPN
ejpam-6974	335	2	mathematicae	mathematicae	PROPN
ejpam-6974	335	3	japonicae	japonicae	PROPN
ejpam-6974	335	4	,	,	PUNCT
ejpam-6974	335	5	69(2):281–284	69(2):281–284	NOUN
ejpam-6974	335	6	,	,	PUNCT
ejpam-6974	335	7	2009	2009	NUM
ejpam-6974	335	8	.	.	PUNCT
ejpam-6974	336	1	[	[	X
ejpam-6974	336	2	11	11	NUM
ejpam-6974	336	3	]	]	SYM
ejpam-6974	336	4	b	b	NOUN
ejpam-6974	336	5	l	l	X
ejpam-6974	336	6	meng	meng	PROPN
ejpam-6974	336	7	.	.	PUNCT
ejpam-6974	337	1	ci	ci	NOUN
ejpam-6974	337	2	-	-	PUNCT
ejpam-6974	337	3	algebras	algebras	PROPN
ejpam-6974	337	4	.	.	PUNCT
ejpam-6974	338	1	scientiae	scientiae	PROPN
ejpam-6974	338	2	mathematicae	mathematicae	PROPN
ejpam-6974	338	3	japonicae	japonicae	PROPN
ejpam-6974	338	4	,	,	PUNCT
ejpam-6974	338	5	71(1):11–17	71(1):11–17	NUM
ejpam-6974	338	6	,	,	PUNCT
ejpam-6974	338	7	2010	2010	NUM
ejpam-6974	338	8	.	.	PUNCT
ejpam-6974	339	1	[	[	X
ejpam-6974	339	2	12	12	NUM
ejpam-6974	339	3	]	]	PUNCT
ejpam-6974	339	4	a	a	DET
ejpam-6974	339	5	b	b	X
ejpam-6974	339	6	saeid	saeid	PROPN
ejpam-6974	339	7	.	.	PUNCT
ejpam-6974	340	1	ci	ci	NOUN
ejpam-6974	340	2	-	-	PUNCT
ejpam-6974	340	3	algebra	algebra	NOUN
ejpam-6974	340	4	is	be	AUX
ejpam-6974	340	5	equivalent	equivalent	ADJ
ejpam-6974	340	6	to	to	ADP
ejpam-6974	340	7	dual	dual	ADJ
ejpam-6974	340	8	q	q	NOUN
ejpam-6974	340	9	-	-	NOUN
ejpam-6974	340	10	algebra	algebra	NOUN
ejpam-6974	340	11	.	.	PUNCT
ejpam-6974	341	1	journal	journal	NOUN
ejpam-6974	341	2	of	of	ADP
ejpam-6974	341	3	the	the	DET
ejpam-6974	341	4	egyptian	egyptian	PROPN
ejpam-6974	341	5	mathematical	mathematical	PROPN
ejpam-6974	341	6	society	society	NOUN
ejpam-6974	341	7	,	,	PUNCT
ejpam-6974	341	8	21(1):1–2	21(1):1–2	NOUN
ejpam-6974	341	9	,	,	PUNCT
ejpam-6974	341	10	2013	2013	NUM
ejpam-6974	341	11	.	.	PUNCT
ejpam-6974	342	1	[	[	X
ejpam-6974	342	2	13	13	NUM
ejpam-6974	342	3	]	]	X
ejpam-6974	342	4	k	k	PROPN
ejpam-6974	342	5	belleza	belleza	PROPN
ejpam-6974	342	6	and	and	CCONJ
ejpam-6974	342	7	j	j	PROPN
ejpam-6974	342	8	vilela	vilela	NOUN
ejpam-6974	342	9	.	.	PUNCT
ejpam-6974	343	1	the	the	DET
ejpam-6974	343	2	dual	dual	ADJ
ejpam-6974	343	3	b	b	NOUN
ejpam-6974	343	4	-	-	PUNCT
ejpam-6974	343	5	algebra	algebra	NOUN
ejpam-6974	343	6	.	.	PUNCT
ejpam-6974	344	1	european	european	ADJ
ejpam-6974	344	2	journal	journal	PROPN
ejpam-6974	344	3	of	of	ADP
ejpam-6974	344	4	pure	pure	ADJ
ejpam-6974	344	5	and	and	CCONJ
ejpam-6974	344	6	applied	applied	ADJ
ejpam-6974	344	7	mathematics	mathematic	NOUN
ejpam-6974	344	8	,	,	PUNCT
ejpam-6974	344	9	12(4):1497–1507	12(4):1497–1507	NUM
ejpam-6974	344	10	,	,	PUNCT
ejpam-6974	344	11	2019	2019	NUM
ejpam-6974	344	12	.	.	PUNCT
ejpam-6974	345	1	[	[	X
ejpam-6974	345	2	14	14	NUM
ejpam-6974	345	3	]	]	X
ejpam-6974	345	4	t	t	PROPN
ejpam-6974	345	5	hungerford	hungerford	PROPN
ejpam-6974	345	6	.	.	PUNCT
ejpam-6974	346	1	abstract	abstract	ADJ
ejpam-6974	346	2	algebra	algebra	PROPN
ejpam-6974	346	3	:	:	PUNCT
ejpam-6974	346	4	an	an	DET
ejpam-6974	346	5	introduction	introduction	NOUN
ejpam-6974	346	6	.	.	PUNCT
ejpam-6974	347	1	cengage	cengage	PROPN
ejpam-6974	347	2	learning	learning	PROPN
ejpam-6974	347	3	,	,	PUNCT
ejpam-6974	347	4	3rd	3rd	ADJ
ejpam-6974	347	5	edition	edition	NOUN
ejpam-6974	347	6	,	,	PUNCT
ejpam-6974	347	7	2012	2012	NUM
ejpam-6974	347	8	.	.	PUNCT
ejpam-6974	348	1	c.m	c.m	PROPN
ejpam-6974	348	2	.	.	PROPN
ejpam-6974	348	3	chan	chan	PROPN
ejpam-6974	348	4	,	,	PUNCT
ejpam-6974	348	5	k.	k.	PROPN
ejpam-6974	348	6	fuentes	fuentes	PROPN
ejpam-6974	348	7	/	/	SYM
ejpam-6974	348	8	eur	eur	PROPN
ejpam-6974	348	9	.	.	PUNCT
ejpam-6974	349	1	j.	j.	PROPN
ejpam-6974	349	2	pure	pure	PROPN
ejpam-6974	349	3	appl	appl	PROPN
ejpam-6974	349	4	.	.	PROPN
ejpam-6974	349	5	math	math	PROPN
ejpam-6974	349	6	,	,	PUNCT
ejpam-6974	349	7	18	18	NUM
ejpam-6974	349	8	(	(	PUNCT
ejpam-6974	349	9	4	4	NUM
ejpam-6974	349	10	)	)	PUNCT
ejpam-6974	349	11	(	(	PUNCT
ejpam-6974	349	12	2025	2025	NUM
ejpam-6974	349	13	)	)	PUNCT
ejpam-6974	349	14	,	,	PUNCT
ejpam-6974	349	15	6974	6974	NUM
ejpam-6974	349	16	11	11	NUM
ejpam-6974	349	17	of	of	ADP
ejpam-6974	349	18	16	16	NUM
ejpam-6974	349	19	appendix	appendix	VERB
ejpam-6974	349	20	the	the	DET
ejpam-6974	349	21	following	follow	VERB
ejpam-6974	349	22	python	python	NOUN
ejpam-6974	349	23	script	script	NOUN
ejpam-6974	349	24	developed	develop	VERB
ejpam-6974	349	25	by	by	ADP
ejpam-6974	349	26	the	the	DET
ejpam-6974	349	27	author	author	NOUN
ejpam-6974	349	28	was	be	AUX
ejpam-6974	349	29	used	use	VERB
ejpam-6974	349	30	to	to	PART
ejpam-6974	349	31	verify	verify	VERB
ejpam-6974	349	32	if	if	SCONJ
ejpam-6974	349	33	a	a	DET
ejpam-6974	349	34	given	give	VERB
ejpam-6974	349	35	cayley	cayley	ADJ
ejpam-6974	349	36	table	table	NOUN
ejpam-6974	349	37	is	be	AUX
ejpam-6974	349	38	a	a	DET
ejpam-6974	349	39	dual	dual	ADJ
ejpam-6974	349	40	bg	bg	NOUN
ejpam-6974	349	41	-	-	NOUN
ejpam-6974	349	42	algebra	algebra	PROPN
ejpam-6974	349	43	.	.	PUNCT
ejpam-6974	350	1	the	the	DET
ejpam-6974	350	2	verification	verification	NOUN
ejpam-6974	350	3	result	result	NOUN
ejpam-6974	350	4	of	of	ADP
ejpam-6974	350	5	example	example	NOUN
ejpam-6974	350	6	3	3	NUM
ejpam-6974	350	7	using	use	VERB
ejpam-6974	350	8	the	the	DET
ejpam-6974	350	9	script	script	NOUN
ejpam-6974	350	10	is	be	AUX
ejpam-6974	350	11	shown	show	VERB
ejpam-6974	350	12	.	.	PUNCT
ejpam-6974	351	1	def	def	ADJ
ejpam-6974	351	2	dbg1(x	dbg1(x	NOUN
ejpam-6974	351	3	,	,	PUNCT
ejpam-6974	351	4	tbl	tbl	NOUN
ejpam-6974	351	5	):	):	PUNCT
ejpam-6974	351	6	#	#	NOUN
ejpam-6974	351	7	x	x	NOUN
ejpam-6974	351	8	o	o	NOUN
ejpam-6974	351	9	x	x	X
ejpam-6974	352	1	=	=	SYM
ejpam-6974	352	2	1	1	NUM
ejpam-6974	352	3	for	for	ADP
ejpam-6974	352	4	all	all	DET
ejpam-6974	352	5	x	x	SYM
ejpam-6974	352	6	in	in	ADP
ejpam-6974	352	7	x	x	PROPN
ejpam-6974	352	8	shp	shp	NOUN
ejpam-6974	352	9	=	=	SYM
ejpam-6974	352	10	len(tbl	len(tbl	NOUN
ejpam-6974	352	11	)	)	PUNCT
ejpam-6974	352	12	flag	flag	NOUN
ejpam-6974	352	13	=	=	PUNCT
ejpam-6974	352	14	true	true	ADJ
ejpam-6974	352	15	print(f"x	print(f"x	PROPN
ejpam-6974	352	16	=	=	SYM
ejpam-6974	352	17	{	{	PUNCT
ejpam-6974	352	18	x	x	NOUN
ejpam-6974	352	19	}	}	PUNCT
ejpam-6974	352	20	"	"	PUNCT
ejpam-6974	352	21	)	)	PUNCT
ejpam-6974	352	22	print("\ncayley	print("\ncayley	NOUN
ejpam-6974	352	23	table	table	NOUN
ejpam-6974	352	24	"	"	PUNCT
ejpam-6974	352	25	)	)	PUNCT
ejpam-6974	352	26	print(np.array(tbl	print(np.array(tbl	NOUN
ejpam-6974	352	27	)	)	PUNCT
ejpam-6974	352	28	)	)	PUNCT
ejpam-6974	352	29	print	print	NOUN
ejpam-6974	352	30	(	(	PUNCT
ejpam-6974	352	31	"	"	PUNCT
ejpam-6974	352	32	"	"	PUNCT
ejpam-6974	352	33	)	)	PUNCT
ejpam-6974	352	34	constant	constant	ADJ
ejpam-6974	352	35	=	=	PUNCT
ejpam-6974	352	36	x[0	x[0	PROPN
ejpam-6974	352	37	]	]	X
ejpam-6974	352	38	ctr	ctr	PROPN
ejpam-6974	352	39	=	=	PROPN
ejpam-6974	352	40	0	0	PROPN
ejpam-6974	352	41	for	for	ADP
ejpam-6974	352	42	i	i	PRON
ejpam-6974	352	43	in	in	ADP
ejpam-6974	352	44	range(shp	range(shp	NOUN
ejpam-6974	352	45	):	):	PUNCT
ejpam-6974	352	46	ctr	ctr	PROPN
ejpam-6974	353	1	+	+	PROPN
ejpam-6974	353	2	=	=	SYM
ejpam-6974	353	3	1	1	NUM
ejpam-6974	353	4	left	leave	VERB
ejpam-6974	353	5	=	=	PUNCT
ejpam-6974	353	6	tbl[i][i	tbl[i][i	X
ejpam-6974	353	7	]	]	X
ejpam-6974	354	1	right	right	ADJ
ejpam-6974	354	2	=	=	NOUN
ejpam-6974	354	3	constant	constant	ADJ
ejpam-6974	354	4	if	if	SCONJ
ejpam-6974	354	5	(	(	PUNCT
ejpam-6974	354	6	left	leave	VERB
ejpam-6974	354	7	!	!	PUNCT
ejpam-6974	355	1	=	=	NOUN
ejpam-6974	356	1	right	right	ADJ
ejpam-6974	356	2	):	):	PUNCT
ejpam-6974	356	3	print(f"{ctr}.\tx	print(f"{ctr}.\tx	NOUN
ejpam-6974	356	4	=	=	SYM
ejpam-6974	356	5	{	{	PUNCT
ejpam-6974	356	6	x[i]}:\t{x[i	x[i]}:\t{x[i	PROPN
ejpam-6974	356	7	]	]	X
ejpam-6974	356	8	}	}	PUNCT
ejpam-6974	356	9	o	o	NOUN
ejpam-6974	356	10	{	{	PUNCT
ejpam-6974	356	11	x[i	x[i	NOUN
ejpam-6974	356	12	]	]	PUNCT
ejpam-6974	356	13	}	}	PUNCT
ejpam-6974	356	14	!	!	PUNCT
ejpam-6974	357	1	=	=	PRON
ejpam-6974	357	2	{	{	PUNCT
ejpam-6974	357	3	constant}\t-	constant}\t-	X
ejpam-6974	357	4	>	>	X
ejpam-6974	357	5	\t	\t	PROPN
ejpam-6974	357	6	{	{	PUNCT
ejpam-6974	357	7	left	leave	VERB
ejpam-6974	357	8	}	}	PUNCT
ejpam-6974	357	9	!	!	PUNCT
ejpam-6974	358	1	=	=	PRON
ejpam-6974	358	2	{	{	PUNCT
ejpam-6974	358	3	right	right	ADJ
ejpam-6974	358	4	}	}	PUNCT
ejpam-6974	358	5	"	"	PUNCT
ejpam-6974	358	6	)	)	PUNCT
ejpam-6974	358	7	flag	flag	NOUN
ejpam-6974	358	8	=	=	SYM
ejpam-6974	358	9	false	false	ADJ
ejpam-6974	358	10	break	break	NOUN
ejpam-6974	358	11	print(f"{ctr}.\tx	print(f"{ctr}.\tx	NOUN
ejpam-6974	358	12	=	=	SYM
ejpam-6974	358	13	{	{	PUNCT
ejpam-6974	358	14	x[i]}:\t{x[i	x[i]}:\t{x[i	PROPN
ejpam-6974	358	15	]	]	X
ejpam-6974	358	16	}	}	PUNCT
ejpam-6974	358	17	o	o	NOUN
ejpam-6974	358	18	{	{	PUNCT
ejpam-6974	358	19	x[i	x[i	NOUN
ejpam-6974	358	20	]	]	X
ejpam-6974	358	21	}	}	PUNCT
ejpam-6974	358	22	=	=	SYM
ejpam-6974	358	23	{	{	PUNCT
ejpam-6974	358	24	constant}\t-	constant}\t-	X
ejpam-6974	358	25	>	>	X
ejpam-6974	358	26	\t	\t	PROPN
ejpam-6974	358	27	{	{	PUNCT
ejpam-6974	358	28	left	leave	VERB
ejpam-6974	358	29	}	}	PUNCT
ejpam-6974	358	30	=	=	SYM
ejpam-6974	358	31	{	{	PUNCT
ejpam-6974	358	32	right	right	ADJ
ejpam-6974	358	33	}	}	PUNCT
ejpam-6974	358	34	"	"	PUNCT
ejpam-6974	358	35	)	)	PUNCT
ejpam-6974	358	36	if	if	SCONJ
ejpam-6974	358	37	(	(	PUNCT
ejpam-6974	358	38	flag	flag	NOUN
ejpam-6974	358	39	=	=	NOUN
ejpam-6974	358	40	=	=	SYM
ejpam-6974	358	41	true	true	ADJ
ejpam-6974	358	42	):	):	PUNCT
ejpam-6974	358	43	print(f"\nx	print(f"\nx	PROPN
ejpam-6974	358	44	o	o	NOUN
ejpam-6974	358	45	x	x	PUNCT
ejpam-6974	359	1	=	=	NOUN
ejpam-6974	359	2	{	{	PUNCT
ejpam-6974	359	3	constant	constant	ADJ
ejpam-6974	359	4	}	}	PUNCT
ejpam-6974	359	5	for	for	ADP
ejpam-6974	359	6	all	all	DET
ejpam-6974	359	7	x	x	NOUN
ejpam-6974	359	8	in	in	ADP
ejpam-6974	359	9	x	x	NOUN
ejpam-6974	359	10	"	"	PUNCT
ejpam-6974	359	11	)	)	PUNCT
ejpam-6974	359	12	else	else	ADV
ejpam-6974	359	13	:	:	PUNCT
ejpam-6974	359	14	print("\nx	print("\nx	PROPN
ejpam-6974	359	15	does	do	AUX
ejpam-6974	359	16	not	not	PART
ejpam-6974	359	17	satisfy	satisfy	VERB
ejpam-6974	359	18	axiom	axiom	NOUN
ejpam-6974	359	19	dbg1	dbg1	PROPN
ejpam-6974	359	20	.	.	PUNCT
ejpam-6974	359	21	"	"	PUNCT
ejpam-6974	359	22	)	)	PUNCT
ejpam-6974	359	23	return	return	VERB
ejpam-6974	359	24	flag	flag	NOUN
ejpam-6974	359	25	def	def	ADJ
ejpam-6974	359	26	dbg2(x	dbg2(x	NOUN
ejpam-6974	359	27	,	,	PUNCT
ejpam-6974	359	28	tbl	tbl	NOUN
ejpam-6974	359	29	):	):	PUNCT
ejpam-6974	359	30	#	#	NOUN
ejpam-6974	359	31	1	1	NUM
ejpam-6974	359	32	o	o	NOUN
ejpam-6974	359	33	x	x	PUNCT
ejpam-6974	360	1	=	=	PUNCT
ejpam-6974	360	2	x	x	PUNCT
ejpam-6974	360	3	for	for	ADP
ejpam-6974	360	4	all	all	DET
ejpam-6974	360	5	x	x	NOUN
ejpam-6974	360	6	in	in	ADP
ejpam-6974	360	7	x	x	PROPN
ejpam-6974	360	8	c.m	c.m	PROPN
ejpam-6974	360	9	.	.	PROPN
ejpam-6974	360	10	chan	chan	PROPN
ejpam-6974	360	11	,	,	PUNCT
ejpam-6974	360	12	k.	k.	PROPN
ejpam-6974	360	13	fuentes	fuentes	PROPN
ejpam-6974	360	14	/	/	SYM
ejpam-6974	360	15	eur	eur	PROPN
ejpam-6974	360	16	.	.	PUNCT
ejpam-6974	361	1	j.	j.	PROPN
ejpam-6974	361	2	pure	pure	PROPN
ejpam-6974	361	3	appl	appl	PROPN
ejpam-6974	361	4	.	.	PROPN
ejpam-6974	361	5	math	math	PROPN
ejpam-6974	361	6	,	,	PUNCT
ejpam-6974	361	7	18	18	NUM
ejpam-6974	361	8	(	(	PUNCT
ejpam-6974	361	9	4	4	NUM
ejpam-6974	361	10	)	)	PUNCT
ejpam-6974	361	11	(	(	PUNCT
ejpam-6974	361	12	2025	2025	NUM
ejpam-6974	361	13	)	)	PUNCT
ejpam-6974	361	14	,	,	PUNCT
ejpam-6974	361	15	6974	6974	NUM
ejpam-6974	361	16	12	12	NUM
ejpam-6974	361	17	of	of	ADP
ejpam-6974	361	18	16	16	NUM
ejpam-6974	361	19	shp	shp	NOUN
ejpam-6974	361	20	=	=	SYM
ejpam-6974	361	21	len(tbl	len(tbl	NOUN
ejpam-6974	361	22	)	)	PUNCT
ejpam-6974	361	23	flag	flag	NOUN
ejpam-6974	361	24	=	=	PUNCT
ejpam-6974	361	25	true	true	ADJ
ejpam-6974	361	26	print(f"x	print(f"x	PROPN
ejpam-6974	361	27	=	=	SYM
ejpam-6974	361	28	{	{	PUNCT
ejpam-6974	361	29	x	x	NOUN
ejpam-6974	361	30	}	}	PUNCT
ejpam-6974	361	31	"	"	PUNCT
ejpam-6974	361	32	)	)	PUNCT
ejpam-6974	361	33	print("\ncayley	print("\ncayley	NOUN
ejpam-6974	361	34	table	table	NOUN
ejpam-6974	361	35	"	"	PUNCT
ejpam-6974	361	36	)	)	PUNCT
ejpam-6974	361	37	print(np.array(tbl	print(np.array(tbl	NOUN
ejpam-6974	361	38	)	)	PUNCT
ejpam-6974	361	39	)	)	PUNCT
ejpam-6974	361	40	print	print	NOUN
ejpam-6974	361	41	(	(	PUNCT
ejpam-6974	361	42	"	"	PUNCT
ejpam-6974	361	43	"	"	PUNCT
ejpam-6974	361	44	)	)	PUNCT
ejpam-6974	361	45	constant	constant	ADJ
ejpam-6974	361	46	=	=	PUNCT
ejpam-6974	362	1	x[0	x[0	PROPN
ejpam-6974	362	2	]	]	X
ejpam-6974	362	3	ctr	ctr	PROPN
ejpam-6974	362	4	=	=	PROPN
ejpam-6974	362	5	0	0	PROPN
ejpam-6974	363	1	for	for	ADP
ejpam-6974	363	2	i	i	PRON
ejpam-6974	363	3	in	in	ADP
ejpam-6974	363	4	range(shp	range(shp	NOUN
ejpam-6974	363	5	):	):	PUNCT
ejpam-6974	363	6	ctr	ctr	PROPN
ejpam-6974	363	7	+	+	PROPN
ejpam-6974	363	8	=	=	SYM
ejpam-6974	363	9	1	1	NUM
ejpam-6974	363	10	left	leave	VERB
ejpam-6974	363	11	=	=	PUNCT
ejpam-6974	363	12	tbl[0][i	tbl[0][i	NOUN
ejpam-6974	363	13	]	]	X
ejpam-6974	364	1	right	right	ADJ
ejpam-6974	364	2	=	=	SYM
ejpam-6974	364	3	x[i	x[i	NOUN
ejpam-6974	364	4	]	]	X
ejpam-6974	364	5	if	if	SCONJ
ejpam-6974	364	6	(	(	PUNCT
ejpam-6974	364	7	left	leave	VERB
ejpam-6974	364	8	!	!	PUNCT
ejpam-6974	364	9	=	=	NOUN
ejpam-6974	365	1	right	right	ADJ
ejpam-6974	365	2	):	):	PUNCT
ejpam-6974	365	3	print(f"{ctr}.\tx	print(f"{ctr}.\tx	NOUN
ejpam-6974	365	4	=	=	SYM
ejpam-6974	365	5	{	{	PUNCT
ejpam-6974	365	6	x[i]}:\t{constant	x[i]}:\t{constant	ADJ
ejpam-6974	365	7	}	}	PUNCT
ejpam-6974	365	8	o	o	NOUN
ejpam-6974	365	9	{	{	PUNCT
ejpam-6974	365	10	x[i	x[i	NOUN
ejpam-6974	365	11	]	]	PUNCT
ejpam-6974	365	12	}	}	PUNCT
ejpam-6974	365	13	!	!	PUNCT
ejpam-6974	366	1	=	=	PRON
ejpam-6974	366	2	{	{	PUNCT
ejpam-6974	366	3	x[i]}\t-	x[i]}\t-	PROPN
ejpam-6974	366	4	>	>	X
ejpam-6974	366	5	\t	\t	X
ejpam-6974	366	6	{	{	PUNCT
ejpam-6974	366	7	left	leave	VERB
ejpam-6974	366	8	}	}	PUNCT
ejpam-6974	366	9	!	!	PUNCT
ejpam-6974	367	1	=	=	PRON
ejpam-6974	367	2	{	{	PUNCT
ejpam-6974	367	3	right	right	ADJ
ejpam-6974	367	4	}	}	PUNCT
ejpam-6974	367	5	"	"	PUNCT
ejpam-6974	367	6	)	)	PUNCT
ejpam-6974	367	7	flag	flag	NOUN
ejpam-6974	367	8	=	=	SYM
ejpam-6974	367	9	false	false	ADJ
ejpam-6974	367	10	break	break	NOUN
ejpam-6974	367	11	print(f"{ctr}.\tx	print(f"{ctr}.\tx	NOUN
ejpam-6974	367	12	=	=	SYM
ejpam-6974	367	13	{	{	PUNCT
ejpam-6974	367	14	x[i]}:\t{constant	x[i]}:\t{constant	ADJ
ejpam-6974	367	15	}	}	PUNCT
ejpam-6974	367	16	o	o	NOUN
ejpam-6974	367	17	{	{	PUNCT
ejpam-6974	367	18	x[i	x[i	NOUN
ejpam-6974	367	19	]	]	X
ejpam-6974	367	20	}	}	PUNCT
ejpam-6974	367	21	=	=	SYM
ejpam-6974	367	22	{	{	PUNCT
ejpam-6974	367	23	x[i]}\t-	x[i]}\t-	PROPN
ejpam-6974	367	24	>	>	X
ejpam-6974	367	25	\t	\t	X
ejpam-6974	367	26	{	{	PUNCT
ejpam-6974	367	27	left	leave	VERB
ejpam-6974	367	28	}	}	PUNCT
ejpam-6974	367	29	=	=	SYM
ejpam-6974	367	30	{	{	PUNCT
ejpam-6974	367	31	right	right	ADJ
ejpam-6974	367	32	}	}	PUNCT
ejpam-6974	367	33	"	"	PUNCT
ejpam-6974	367	34	)	)	PUNCT
ejpam-6974	367	35	if	if	SCONJ
ejpam-6974	367	36	(	(	PUNCT
ejpam-6974	367	37	flag	flag	NOUN
ejpam-6974	367	38	=	=	NOUN
ejpam-6974	367	39	=	=	SYM
ejpam-6974	367	40	true	true	ADJ
ejpam-6974	367	41	):	):	PUNCT
ejpam-6974	367	42	print(f"\n{constant	print(f"\n{constant	NOUN
ejpam-6974	367	43	}	}	PUNCT
ejpam-6974	367	44	o	o	NOUN
ejpam-6974	367	45	x	x	PUNCT
ejpam-6974	368	1	=	=	PUNCT
ejpam-6974	368	2	x	x	PROPN
ejpam-6974	368	3	for	for	ADP
ejpam-6974	368	4	all	all	DET
ejpam-6974	368	5	x	x	NOUN
ejpam-6974	368	6	in	in	ADP
ejpam-6974	368	7	x	x	NOUN
ejpam-6974	368	8	"	"	PUNCT
ejpam-6974	368	9	)	)	PUNCT
ejpam-6974	368	10	else	else	ADV
ejpam-6974	368	11	:	:	PUNCT
ejpam-6974	368	12	print("\nx	print("\nx	PROPN
ejpam-6974	368	13	does	do	AUX
ejpam-6974	368	14	not	not	PART
ejpam-6974	368	15	satisfy	satisfy	VERB
ejpam-6974	368	16	axiom	axiom	NOUN
ejpam-6974	368	17	dbg2	dbg2	PROPN
ejpam-6974	368	18	.	.	PUNCT
ejpam-6974	368	19	"	"	PUNCT
ejpam-6974	368	20	)	)	PUNCT
ejpam-6974	368	21	return	return	VERB
ejpam-6974	368	22	flag	flag	NOUN
ejpam-6974	368	23	def	def	PROPN
ejpam-6974	368	24	dbg3(x	dbg3(x	PROPN
ejpam-6974	368	25	,	,	PUNCT
ejpam-6974	368	26	tbl	tbl	NOUN
ejpam-6974	368	27	):	):	PUNCT
ejpam-6974	368	28	#	#	NOUN
ejpam-6974	368	29	(	(	PUNCT
ejpam-6974	368	30	y	y	NOUN
ejpam-6974	368	31	o	o	PROPN
ejpam-6974	368	32	1	1	X
ejpam-6974	368	33	)	)	PUNCT
ejpam-6974	368	34	o	o	NOUN
ejpam-6974	368	35	(	(	PUNCT
ejpam-6974	368	36	y	y	NOUN
ejpam-6974	368	37	o	o	NOUN
ejpam-6974	368	38	x	x	X
ejpam-6974	368	39	)	)	PUNCT
ejpam-6974	368	40	=	=	PUNCT
ejpam-6974	369	1	x	x	PROPN
ejpam-6974	369	2	for	for	ADP
ejpam-6974	369	3	all	all	DET
ejpam-6974	369	4	x	x	NOUN
ejpam-6974	369	5	,	,	PUNCT
ejpam-6974	369	6	y	y	PROPN
ejpam-6974	369	7	in	in	ADP
ejpam-6974	369	8	x	x	PROPN
ejpam-6974	369	9	shp	shp	NOUN
ejpam-6974	369	10	=	=	SYM
ejpam-6974	369	11	len(tbl	len(tbl	NOUN
ejpam-6974	369	12	)	)	PUNCT
ejpam-6974	369	13	flag	flag	NOUN
ejpam-6974	369	14	=	=	PUNCT
ejpam-6974	369	15	true	true	ADJ
ejpam-6974	369	16	print(f"x	print(f"x	PROPN
ejpam-6974	369	17	=	=	SYM
ejpam-6974	369	18	{	{	PUNCT
ejpam-6974	369	19	x	x	NOUN
ejpam-6974	369	20	}	}	PUNCT
ejpam-6974	369	21	"	"	PUNCT
ejpam-6974	369	22	)	)	PUNCT
ejpam-6974	369	23	print("\ncayley	print("\ncayley	NOUN
ejpam-6974	369	24	table	table	NOUN
ejpam-6974	369	25	"	"	PUNCT
ejpam-6974	369	26	)	)	PUNCT
ejpam-6974	369	27	print(np.array(tbl	print(np.array(tbl	NOUN
ejpam-6974	369	28	)	)	PUNCT
ejpam-6974	369	29	)	)	PUNCT
ejpam-6974	369	30	print	print	NOUN
ejpam-6974	369	31	(	(	PUNCT
ejpam-6974	369	32	"	"	PUNCT
ejpam-6974	369	33	"	"	PUNCT
ejpam-6974	369	34	)	)	PUNCT
ejpam-6974	369	35	c.m	c.m	PROPN
ejpam-6974	369	36	.	.	PROPN
ejpam-6974	369	37	chan	chan	PROPN
ejpam-6974	369	38	,	,	PUNCT
ejpam-6974	369	39	k.	k.	PROPN
ejpam-6974	369	40	fuentes	fuentes	PROPN
ejpam-6974	369	41	/	/	SYM
ejpam-6974	369	42	eur	eur	PROPN
ejpam-6974	369	43	.	.	PUNCT
ejpam-6974	370	1	j.	j.	PROPN
ejpam-6974	370	2	pure	pure	PROPN
ejpam-6974	370	3	appl	appl	PROPN
ejpam-6974	370	4	.	.	PROPN
ejpam-6974	370	5	math	math	PROPN
ejpam-6974	370	6	,	,	PUNCT
ejpam-6974	370	7	18	18	NUM
ejpam-6974	370	8	(	(	PUNCT
ejpam-6974	370	9	4	4	NUM
ejpam-6974	370	10	)	)	PUNCT
ejpam-6974	370	11	(	(	PUNCT
ejpam-6974	370	12	2025	2025	NUM
ejpam-6974	370	13	)	)	PUNCT
ejpam-6974	370	14	,	,	PUNCT
ejpam-6974	370	15	6974	6974	NUM
ejpam-6974	370	16	13	13	NUM
ejpam-6974	370	17	of	of	ADP
ejpam-6974	370	18	16	16	NUM
ejpam-6974	370	19	constant	constant	ADJ
ejpam-6974	370	20	=	=	PUNCT
ejpam-6974	370	21	x[0	x[0	PROPN
ejpam-6974	370	22	]	]	X
ejpam-6974	370	23	ctr	ctr	PROPN
ejpam-6974	371	1	=	=	PROPN
ejpam-6974	371	2	0	0	PROPN
ejpam-6974	372	1	for	for	SCONJ
ejpam-6974	372	2	i	i	PRON
ejpam-6974	372	3	in	in	ADP
ejpam-6974	372	4	range(shp	range(shp	NOUN
ejpam-6974	372	5	):	):	PUNCT
ejpam-6974	372	6	for	for	ADP
ejpam-6974	372	7	j	j	PROPN
ejpam-6974	372	8	in	in	ADP
ejpam-6974	372	9	range(shp	range(shp	NOUN
ejpam-6974	372	10	):	):	PUNCT
ejpam-6974	372	11	ctr	ctr	PROPN
ejpam-6974	372	12	+	+	PROPN
ejpam-6974	372	13	=	=	SYM
ejpam-6974	372	14	1	1	NUM
ejpam-6974	372	15	y_0	y_0	NOUN
ejpam-6974	372	16	=	=	NOUN
ejpam-6974	372	17	tbl[j][0	tbl[j][0	NUM
ejpam-6974	372	18	]	]	PUNCT
ejpam-6974	372	19	y_x	y_x	SYM
ejpam-6974	372	20	=	=	SYM
ejpam-6974	372	21	tbl[j][i	tbl[j][i	X
ejpam-6974	372	22	]	]	PUNCT
ejpam-6974	372	23	left	leave	VERB
ejpam-6974	372	24	=	=	SYM
ejpam-6974	372	25	tbl[x.index(y_0)][x.index(y_x	tbl[x.index(y_0)][x.index(y_x	PROPN
ejpam-6974	372	26	)	)	PUNCT
ejpam-6974	372	27	]	]	PUNCT
ejpam-6974	373	1	right	right	ADJ
ejpam-6974	373	2	=	=	SYM
ejpam-6974	373	3	x[i	x[i	NOUN
ejpam-6974	373	4	]	]	X
ejpam-6974	373	5	if	if	SCONJ
ejpam-6974	373	6	(	(	PUNCT
ejpam-6974	373	7	left	leave	VERB
ejpam-6974	373	8	!	!	PUNCT
ejpam-6974	373	9	=	=	NOUN
ejpam-6974	374	1	right	right	ADJ
ejpam-6974	374	2	):	):	PUNCT
ejpam-6974	374	3	print(f"{ctr}.\tx	print(f"{ctr}.\tx	NOUN
ejpam-6974	374	4	=	=	SYM
ejpam-6974	374	5	{	{	PUNCT
ejpam-6974	374	6	x[i	x[i	NOUN
ejpam-6974	374	7	]	]	PUNCT
ejpam-6974	374	8	}	}	PUNCT
ejpam-6974	374	9	,	,	PUNCT
ejpam-6974	374	10	y	y	PROPN
ejpam-6974	374	11	=	=	PRON
ejpam-6974	374	12	{	{	PUNCT
ejpam-6974	374	13	x[j	x[j	PROPN
ejpam-6974	374	14	]	]	PUNCT
ejpam-6974	374	15	}	}	PUNCT
ejpam-6974	374	16	:	:	PUNCT
ejpam-6974	374	17	\t({x[j	\t({x[j	PROPN
ejpam-6974	374	18	]	]	PUNCT
ejpam-6974	374	19	}	}	PUNCT
ejpam-6974	374	20	o	o	X
ejpam-6974	374	21	{	{	PUNCT
ejpam-6974	374	22	constant	constant	ADJ
ejpam-6974	374	23	}	}	PUNCT
ejpam-6974	374	24	)	)	PUNCT
ejpam-6974	374	25	o	o	NOUN
ejpam-6974	374	26	(	(	PUNCT
ejpam-6974	374	27	{	{	PUNCT
ejpam-6974	374	28	x[j	x[j	PROPN
ejpam-6974	374	29	]	]	X
ejpam-6974	374	30	}	}	PUNCT
ejpam-6974	374	31	o	o	NOUN
ejpam-6974	374	32	{	{	PUNCT
ejpam-6974	374	33	x[i	x[i	NOUN
ejpam-6974	374	34	]	]	PUNCT
ejpam-6974	374	35	}	}	PUNCT
ejpam-6974	374	36	)	)	PUNCT
ejpam-6974	374	37	!	!	PUNCT
ejpam-6974	374	38	=	=	PRON
ejpam-6974	374	39	{	{	PUNCT
ejpam-6974	374	40	x[i]}\t-	x[i]}\t-	PROPN
ejpam-6974	374	41	>	>	X
ejpam-6974	374	42	\t{y_0	\t{y_0	PROPN
ejpam-6974	374	43	}	}	PUNCT
ejpam-6974	374	44	o	o	NOUN
ejpam-6974	374	45	{	{	PUNCT
ejpam-6974	374	46	y_x	y_x	X
ejpam-6974	374	47	}	}	PUNCT
ejpam-6974	374	48	!	!	PUNCT
ejpam-6974	374	49	=	=	PRON
ejpam-6974	374	50	{	{	PUNCT
ejpam-6974	374	51	x[i]}\t->\t	x[i]}\t->\t	X
ejpam-6974	374	52	{	{	PUNCT
ejpam-6974	374	53	left	leave	VERB
ejpam-6974	374	54	}	}	PUNCT
ejpam-6974	374	55	!	!	PUNCT
ejpam-6974	374	56	=	=	PRON
ejpam-6974	375	1	{	{	PUNCT
ejpam-6974	375	2	right	right	ADJ
ejpam-6974	375	3	}	}	PUNCT
ejpam-6974	375	4	"	"	PUNCT
ejpam-6974	375	5	)	)	PUNCT
ejpam-6974	375	6	flag	flag	NOUN
ejpam-6974	375	7	=	=	SYM
ejpam-6974	375	8	false	false	ADJ
ejpam-6974	375	9	break	break	NOUN
ejpam-6974	375	10	if	if	SCONJ
ejpam-6974	375	11	(	(	PUNCT
ejpam-6974	375	12	left	leave	VERB
ejpam-6974	375	13	=	=	NOUN
ejpam-6974	375	14	=	=	SYM
ejpam-6974	375	15	right	right	ADJ
ejpam-6974	375	16	):	):	PUNCT
ejpam-6974	375	17	print(f"{ctr}.\tx	print(f"{ctr}.\tx	NOUN
ejpam-6974	375	18	=	=	SYM
ejpam-6974	375	19	{	{	PUNCT
ejpam-6974	375	20	x[i	x[i	NOUN
ejpam-6974	375	21	]	]	PUNCT
ejpam-6974	375	22	}	}	PUNCT
ejpam-6974	375	23	,	,	PUNCT
ejpam-6974	375	24	y	y	PROPN
ejpam-6974	375	25	=	=	PRON
ejpam-6974	375	26	{	{	PUNCT
ejpam-6974	375	27	x[j	x[j	PROPN
ejpam-6974	375	28	]	]	PUNCT
ejpam-6974	375	29	}	}	PUNCT
ejpam-6974	375	30	:	:	PUNCT
ejpam-6974	376	1	\t({x[j	\t({x[j	PROPN
ejpam-6974	376	2	]	]	PUNCT
ejpam-6974	376	3	}	}	PUNCT
ejpam-6974	376	4	o	o	X
ejpam-6974	376	5	{	{	PUNCT
ejpam-6974	376	6	constant	constant	ADJ
ejpam-6974	376	7	}	}	PUNCT
ejpam-6974	376	8	)	)	PUNCT
ejpam-6974	376	9	o	o	NOUN
ejpam-6974	376	10	(	(	PUNCT
ejpam-6974	376	11	{	{	PUNCT
ejpam-6974	376	12	x[j	x[j	PROPN
ejpam-6974	376	13	]	]	X
ejpam-6974	376	14	}	}	PUNCT
ejpam-6974	376	15	o	o	NOUN
ejpam-6974	376	16	{	{	PUNCT
ejpam-6974	376	17	x[i	x[i	NOUN
ejpam-6974	376	18	]	]	PUNCT
ejpam-6974	376	19	}	}	PUNCT
ejpam-6974	376	20	)	)	PUNCT
ejpam-6974	376	21	=	=	PRON
ejpam-6974	376	22	{	{	PUNCT
ejpam-6974	376	23	x[i]}\t-	x[i]}\t-	PROPN
ejpam-6974	376	24	>	>	X
ejpam-6974	376	25	\t{y_0	\t{y_0	PROPN
ejpam-6974	376	26	}	}	PUNCT
ejpam-6974	376	27	o	o	NOUN
ejpam-6974	376	28	{	{	PUNCT
ejpam-6974	376	29	y_x	y_x	SYM
ejpam-6974	376	30	}	}	PUNCT
ejpam-6974	376	31	=	=	SYM
ejpam-6974	376	32	{	{	PUNCT
ejpam-6974	376	33	x[i]}\t->\t	x[i]}\t->\t	PROPN
ejpam-6974	376	34	{	{	PUNCT
ejpam-6974	376	35	left	leave	VERB
ejpam-6974	376	36	}	}	PUNCT
ejpam-6974	376	37	=	=	SYM
ejpam-6974	376	38	{	{	PUNCT
ejpam-6974	376	39	right	right	ADJ
ejpam-6974	376	40	}	}	PUNCT
ejpam-6974	376	41	"	"	PUNCT
ejpam-6974	376	42	)	)	PUNCT
ejpam-6974	376	43	if	if	SCONJ
ejpam-6974	376	44	(	(	PUNCT
ejpam-6974	376	45	flag	flag	NOUN
ejpam-6974	376	46	=	=	NOUN
ejpam-6974	376	47	=	=	SYM
ejpam-6974	376	48	false	false	ADJ
ejpam-6974	376	49	):	):	PUNCT
ejpam-6974	376	50	break	break	NOUN
ejpam-6974	376	51	if	if	SCONJ
ejpam-6974	376	52	(	(	PUNCT
ejpam-6974	376	53	flag	flag	NOUN
ejpam-6974	376	54	=	=	NOUN
ejpam-6974	376	55	=	=	NOUN
ejpam-6974	376	56	true	true	ADJ
ejpam-6974	376	57	):	):	PUNCT
ejpam-6974	377	1	print(f"\n(y	print(f"\n(y	PROPN
ejpam-6974	377	2	o	o	X
ejpam-6974	377	3	{	{	PUNCT
ejpam-6974	377	4	constant	constant	ADJ
ejpam-6974	377	5	}	}	PUNCT
ejpam-6974	377	6	)	)	PUNCT
ejpam-6974	378	1	o	o	NOUN
ejpam-6974	378	2	(	(	PUNCT
ejpam-6974	378	3	y	y	NOUN
ejpam-6974	378	4	o	o	NOUN
ejpam-6974	378	5	x	x	X
ejpam-6974	378	6	)	)	PUNCT
ejpam-6974	378	7	=	=	PUNCT
ejpam-6974	379	1	x	x	PROPN
ejpam-6974	379	2	for	for	ADP
ejpam-6974	379	3	all	all	DET
ejpam-6974	379	4	x	x	NOUN
ejpam-6974	379	5	,	,	PUNCT
ejpam-6974	379	6	y	y	PROPN
ejpam-6974	379	7	in	in	ADP
ejpam-6974	379	8	x	x	NOUN
ejpam-6974	379	9	"	"	PUNCT
ejpam-6974	379	10	)	)	PUNCT
ejpam-6974	379	11	else	else	ADV
ejpam-6974	379	12	:	:	PUNCT
ejpam-6974	379	13	print("\nx	print("\nx	PROPN
ejpam-6974	379	14	does	do	AUX
ejpam-6974	379	15	not	not	PART
ejpam-6974	379	16	satisfy	satisfy	VERB
ejpam-6974	379	17	axiom	axiom	NOUN
ejpam-6974	379	18	dbg3	dbg3	PROPN
ejpam-6974	379	19	.	.	PUNCT
ejpam-6974	379	20	"	"	PUNCT
ejpam-6974	379	21	)	)	PUNCT
ejpam-6974	379	22	return	return	VERB
ejpam-6974	379	23	flag	flag	NOUN
ejpam-6974	379	24	def	def	PROPN
ejpam-6974	379	25	dbg(x	dbg(x	PROPN
ejpam-6974	379	26	,	,	PUNCT
ejpam-6974	379	27	tbl	tbl	NOUN
ejpam-6974	379	28	):	):	PUNCT
ejpam-6974	379	29	dbg_flag	dbg_flag	NOUN
ejpam-6974	379	30	=	=	SYM
ejpam-6974	379	31	false	false	ADJ
ejpam-6974	379	32	constant	constant	ADJ
ejpam-6974	379	33	=	=	PUNCT
ejpam-6974	379	34	x[0	x[0	PROPN
ejpam-6974	379	35	]	]	PUNCT
ejpam-6974	379	36	print(f"checking	print(f"checke	VERB
ejpam-6974	379	37	dbg1	dbg1	NOUN
ejpam-6974	379	38	:	:	PUNCT
ejpam-6974	379	39	x	x	PUNCT
ejpam-6974	379	40	o	o	NOUN
ejpam-6974	379	41	x	x	X
ejpam-6974	379	42	=	=	NOUN
ejpam-6974	379	43	{	{	PUNCT
ejpam-6974	379	44	constant	constant	ADJ
ejpam-6974	379	45	}	}	PUNCT
ejpam-6974	379	46	for	for	ADP
ejpam-6974	379	47	all	all	DET
ejpam-6974	379	48	x	x	NOUN
ejpam-6974	379	49	in	in	ADP
ejpam-6974	379	50	x	x	X
ejpam-6974	379	51	...	...	PUNCT
ejpam-6974	379	52	"	"	PUNCT
ejpam-6974	379	53	)	)	PUNCT
ejpam-6974	379	54	dbg1_flag	dbg1_flag	PROPN
ejpam-6974	379	55	=	=	SYM
ejpam-6974	379	56	dbg1(x	dbg1(x	NOUN
ejpam-6974	379	57	,	,	PUNCT
ejpam-6974	379	58	tbl	tbl	NOUN
ejpam-6974	379	59	)	)	PUNCT
ejpam-6974	379	60	c.m	c.m	PROPN
ejpam-6974	379	61	.	.	PROPN
ejpam-6974	379	62	chan	chan	PROPN
ejpam-6974	379	63	,	,	PUNCT
ejpam-6974	379	64	k.	k.	PROPN
ejpam-6974	379	65	fuentes	fuentes	PROPN
ejpam-6974	379	66	/	/	SYM
ejpam-6974	379	67	eur	eur	PROPN
ejpam-6974	379	68	.	.	PUNCT
ejpam-6974	380	1	j.	j.	PROPN
ejpam-6974	380	2	pure	pure	PROPN
ejpam-6974	380	3	appl	appl	PROPN
ejpam-6974	380	4	.	.	PROPN
ejpam-6974	380	5	math	math	PROPN
ejpam-6974	380	6	,	,	PUNCT
ejpam-6974	380	7	18	18	NUM
ejpam-6974	380	8	(	(	PUNCT
ejpam-6974	380	9	4	4	NUM
ejpam-6974	380	10	)	)	PUNCT
ejpam-6974	380	11	(	(	PUNCT
ejpam-6974	380	12	2025	2025	NUM
ejpam-6974	380	13	)	)	PUNCT
ejpam-6974	380	14	,	,	PUNCT
ejpam-6974	380	15	6974	6974	NUM
ejpam-6974	380	16	14	14	NUM
ejpam-6974	380	17	of	of	ADP
ejpam-6974	380	18	16	16	NUM
ejpam-6974	380	19	print("-----------------------------------------------------------\n	print("-----------------------------------------------------------\n	VERB
ejpam-6974	380	20	"	"	PUNCT
ejpam-6974	380	21	)	)	PUNCT
ejpam-6974	380	22	print(f"checking	print(f"checke	VERB
ejpam-6974	380	23	dbg2	dbg2	NOUN
ejpam-6974	380	24	:	:	PUNCT
ejpam-6974	380	25	{	{	PUNCT
ejpam-6974	380	26	constant	constant	ADJ
ejpam-6974	380	27	}	}	PUNCT
ejpam-6974	380	28	o	o	NOUN
ejpam-6974	380	29	x	x	PUNCT
ejpam-6974	380	30	=	=	PUNCT
ejpam-6974	380	31	x	x	PROPN
ejpam-6974	380	32	for	for	ADP
ejpam-6974	380	33	all	all	DET
ejpam-6974	380	34	x	x	NOUN
ejpam-6974	380	35	in	in	ADP
ejpam-6974	380	36	x	x	X
ejpam-6974	380	37	...	...	PUNCT
ejpam-6974	380	38	"	"	PUNCT
ejpam-6974	380	39	)	)	PUNCT
ejpam-6974	380	40	dbg2_flag	dbg2_flag	PROPN
ejpam-6974	380	41	=	=	SYM
ejpam-6974	380	42	dbg2(x	dbg2(x	NOUN
ejpam-6974	380	43	,	,	PUNCT
ejpam-6974	380	44	tbl	tbl	NOUN
ejpam-6974	380	45	)	)	PUNCT
ejpam-6974	380	46	print("-----------------------------------------------------------\n	print("-----------------------------------------------------------\n	VERB
ejpam-6974	380	47	"	"	PUNCT
ejpam-6974	380	48	)	)	PUNCT
ejpam-6974	380	49	print("checking	print("checke	VERB
ejpam-6974	380	50	dbg3	dbg3	NOUN
ejpam-6974	380	51	:	:	PUNCT
ejpam-6974	380	52	\n	\n	X
ejpam-6974	380	53	"	"	PUNCT
ejpam-6974	380	54	)	)	PUNCT
ejpam-6974	380	55	print(f"(y	print(f"(y	NOUN
ejpam-6974	381	1	o	o	X
ejpam-6974	381	2	{	{	PUNCT
ejpam-6974	381	3	constant	constant	ADJ
ejpam-6974	381	4	}	}	PUNCT
ejpam-6974	381	5	)	)	PUNCT
ejpam-6974	382	1	o	o	NOUN
ejpam-6974	382	2	(	(	PUNCT
ejpam-6974	382	3	y	y	NOUN
ejpam-6974	382	4	o	o	NOUN
ejpam-6974	382	5	x	x	X
ejpam-6974	382	6	)	)	PUNCT
ejpam-6974	382	7	=	=	PUNCT
ejpam-6974	383	1	x	x	PROPN
ejpam-6974	383	2	for	for	ADP
ejpam-6974	383	3	all	all	DET
ejpam-6974	383	4	x	x	NOUN
ejpam-6974	383	5	,	,	PUNCT
ejpam-6974	383	6	y	y	PROPN
ejpam-6974	383	7	in	in	ADP
ejpam-6974	383	8	x	x	X
ejpam-6974	383	9	...	...	PUNCT
ejpam-6974	383	10	"	"	PUNCT
ejpam-6974	383	11	)	)	PUNCT
ejpam-6974	383	12	dbg3_flag	dbg3_flag	NOUN
ejpam-6974	383	13	=	=	SYM
ejpam-6974	383	14	dbg3(x	dbg3(x	NOUN
ejpam-6974	383	15	,	,	PUNCT
ejpam-6974	383	16	tbl	tbl	NOUN
ejpam-6974	383	17	)	)	PUNCT
ejpam-6974	383	18	print("-----------------------------------------------------------\n	print("-----------------------------------------------------------\n	VERB
ejpam-6974	383	19	"	"	PUNCT
ejpam-6974	383	20	)	)	PUNCT
ejpam-6974	383	21	if	if	SCONJ
ejpam-6974	383	22	(	(	PUNCT
ejpam-6974	383	23	dbg1_flag	dbg1_flag	NOUN
ejpam-6974	383	24	,	,	PUNCT
ejpam-6974	383	25	dbg2_flag	dbg2_flag	PROPN
ejpam-6974	383	26	,	,	PUNCT
ejpam-6974	383	27	dbg3_flag	dbg3_flag	NOUN
ejpam-6974	383	28	)	)	PUNCT
ejpam-6974	383	29	=	=	SYM
ejpam-6974	383	30	=	=	SYM
ejpam-6974	383	31	(	(	PUNCT
ejpam-6974	383	32	true	true	ADJ
ejpam-6974	383	33	,	,	PUNCT
ejpam-6974	383	34	true	true	ADJ
ejpam-6974	383	35	,	,	PUNCT
ejpam-6974	383	36	true	true	ADJ
ejpam-6974	383	37	):	):	PUNCT
ejpam-6974	383	38	dbg_flag	dbg_flag	NOUN
ejpam-6974	383	39	=	=	PUNCT
ejpam-6974	383	40	true	true	ADJ
ejpam-6974	383	41	if	if	SCONJ
ejpam-6974	383	42	(	(	PUNCT
ejpam-6974	383	43	dbg_flag	dbg_flag	NOUN
ejpam-6974	383	44	=	=	X
ejpam-6974	383	45	=	=	NOUN
ejpam-6974	383	46	true	true	ADJ
ejpam-6974	383	47	):	):	PUNCT
ejpam-6974	383	48	print("x	print("x	PROPN
ejpam-6974	383	49	satisfies	satisfy	VERB
ejpam-6974	383	50	dbg1	dbg1	PROPN
ejpam-6974	383	51	,	,	PUNCT
ejpam-6974	383	52	dbg2	dbg2	PROPN
ejpam-6974	383	53	,	,	PUNCT
ejpam-6974	383	54	and	and	CCONJ
ejpam-6974	383	55	dbg3	dbg3	PROPN
ejpam-6974	383	56	.	.	PUNCT
ejpam-6974	383	57	"	"	PUNCT
ejpam-6974	383	58	)	)	PUNCT
ejpam-6974	384	1	print("\ntherefore	print("\ntherefore	X
ejpam-6974	384	2	,	,	PUNCT
ejpam-6974	384	3	x	x	X
ejpam-6974	384	4	is	be	AUX
ejpam-6974	384	5	a	a	DET
ejpam-6974	384	6	dual	dual	ADJ
ejpam-6974	384	7	bg	bg	NOUN
ejpam-6974	384	8	-	-	NOUN
ejpam-6974	384	9	algebra	algebra	NOUN
ejpam-6974	384	10	.	.	PUNCT
ejpam-6974	384	11	"	"	PUNCT
ejpam-6974	384	12	)	)	PUNCT
ejpam-6974	384	13	else	else	ADV
ejpam-6974	384	14	:	:	PUNCT
ejpam-6974	384	15	print("\nx	print("\nx	PROPN
ejpam-6974	384	16	is	be	AUX
ejpam-6974	384	17	not	not	PART
ejpam-6974	384	18	a	a	DET
ejpam-6974	384	19	dual	dual	ADJ
ejpam-6974	384	20	bg	bg	NOUN
ejpam-6974	384	21	-	-	NOUN
ejpam-6974	384	22	algebra	algebra	NOUN
ejpam-6974	384	23	.	.	PUNCT
ejpam-6974	384	24	"	"	PUNCT
ejpam-6974	384	25	)	)	PUNCT
ejpam-6974	384	26	return	return	VERB
ejpam-6974	384	27	dbg_flag	dbg_flag	NOUN
ejpam-6974	384	28	c.m	c.m	PROPN
ejpam-6974	384	29	.	.	PROPN
ejpam-6974	384	30	chan	chan	PROPN
ejpam-6974	384	31	,	,	PUNCT
ejpam-6974	384	32	k.	k.	PROPN
ejpam-6974	384	33	fuentes	fuentes	PROPN
ejpam-6974	384	34	/	/	SYM
ejpam-6974	384	35	eur	eur	PROPN
ejpam-6974	384	36	.	.	PUNCT
ejpam-6974	385	1	j.	j.	PROPN
ejpam-6974	385	2	pure	pure	PROPN
ejpam-6974	385	3	appl	appl	PROPN
ejpam-6974	385	4	.	.	PROPN
ejpam-6974	385	5	math	math	PROPN
ejpam-6974	385	6	,	,	PUNCT
ejpam-6974	385	7	18	18	NUM
ejpam-6974	385	8	(	(	PUNCT
ejpam-6974	385	9	4	4	NUM
ejpam-6974	385	10	)	)	PUNCT
ejpam-6974	385	11	(	(	PUNCT
ejpam-6974	385	12	2025	2025	NUM
ejpam-6974	385	13	)	)	PUNCT
ejpam-6974	385	14	,	,	PUNCT
ejpam-6974	385	15	6974	6974	NUM
ejpam-6974	385	16	15	15	NUM
ejpam-6974	385	17	of	of	ADP
ejpam-6974	385	18	16	16	NUM
ejpam-6974	385	19	dbg1	dbg1	ADJ
ejpam-6974	385	20	verification	verification	NOUN
ejpam-6974	385	21	dbg2	dbg2	PROPN
ejpam-6974	385	22	verification	verification	PROPN
ejpam-6974	385	23	c.m	c.m	PROPN
ejpam-6974	385	24	.	.	PROPN
ejpam-6974	385	25	chan	chan	PROPN
ejpam-6974	385	26	,	,	PUNCT
ejpam-6974	385	27	k.	k.	PROPN
ejpam-6974	385	28	fuentes	fuentes	PROPN
ejpam-6974	385	29	/	/	SYM
ejpam-6974	385	30	eur	eur	PROPN
ejpam-6974	385	31	.	.	PUNCT
ejpam-6974	386	1	j.	j.	PROPN
ejpam-6974	386	2	pure	pure	PROPN
ejpam-6974	386	3	appl	appl	PROPN
ejpam-6974	386	4	.	.	PROPN
ejpam-6974	386	5	math	math	PROPN
ejpam-6974	386	6	,	,	PUNCT
ejpam-6974	386	7	18	18	NUM
ejpam-6974	386	8	(	(	PUNCT
ejpam-6974	386	9	4	4	NUM
ejpam-6974	386	10	)	)	PUNCT
ejpam-6974	386	11	(	(	PUNCT
ejpam-6974	386	12	2025	2025	NUM
ejpam-6974	386	13	)	)	PUNCT
ejpam-6974	386	14	,	,	PUNCT
ejpam-6974	386	15	6974	6974	NUM
ejpam-6974	386	16	16	16	NUM
ejpam-6974	386	17	of	of	ADP
ejpam-6974	386	18	16	16	NUM
ejpam-6974	386	19	dbg3	dbg3	NOUN
ejpam-6974	386	20	verification	verification	NOUN
ejpam-6974	386	21	example	example	NOUN
ejpam-6974	386	22	3	3	NUM
ejpam-6974	386	23	is	be	AUX
ejpam-6974	386	24	a	a	DET
ejpam-6974	386	25	dual	dual	ADJ
ejpam-6974	386	26	bg	bg	NOUN
ejpam-6974	386	27	-	-	NOUN
ejpam-6974	386	28	algebra	algebra	PROPN