id	sid	tid	token	lemma	pos
ejpam-4787	1	1	european	european	PROPN
ejpam-4787	1	2	journal	journal	PROPN
ejpam-4787	1	3	of	of	ADP
ejpam-4787	1	4	pure	pure	ADJ
ejpam-4787	1	5	and	and	CCONJ
ejpam-4787	1	6	applied	apply	VERB
ejpam-4787	1	7	mathematics	mathematic	NOUN
ejpam-4787	1	8	vol	vol	NOUN
ejpam-4787	1	9	.	.	PUNCT
ejpam-4787	2	1	16	16	NUM
ejpam-4787	2	2	,	,	PUNCT
ejpam-4787	2	3	no	no	INTJ
ejpam-4787	2	4	.	.	NOUN
ejpam-4787	2	5	3	3	NUM
ejpam-4787	2	6	,	,	PUNCT
ejpam-4787	2	7	2023	2023	NUM
ejpam-4787	2	8	,	,	PUNCT
ejpam-4787	2	9	1480	1480	NUM
ejpam-4787	2	10	-	-	SYM
ejpam-4787	2	11	1490	1490	NUM
ejpam-4787	2	12	issn	issn	PROPN
ejpam-4787	2	13	1307	1307	NUM
ejpam-4787	2	14	-	-	SYM
ejpam-4787	2	15	5543	5543	NUM
ejpam-4787	2	16	–	–	PUNCT
ejpam-4787	2	17	ejpam.com	ejpam.com	X
ejpam-4787	2	18	published	publish	VERB
ejpam-4787	2	19	by	by	ADP
ejpam-4787	2	20	new	new	PROPN
ejpam-4787	2	21	york	york	PROPN
ejpam-4787	2	22	business	business	PROPN
ejpam-4787	2	23	global	global	ADJ
ejpam-4787	2	24	algebras	algebra	NOUN
ejpam-4787	2	25	satisfying	satisfy	VERB
ejpam-4787	2	26	a	a	DET
ejpam-4787	2	27	polynomial	polynomial	ADJ
ejpam-4787	2	28	identity	identity	NOUN
ejpam-4787	2	29	of	of	ADP
ejpam-4787	2	30	degree	degree	NOUN
ejpam-4787	2	31	six	six	NUM
ejpam-4787	2	32	that	that	PRON
ejpam-4787	2	33	are	be	AUX
ejpam-4787	2	34	principal	principal	ADJ
ejpam-4787	2	35	train	train	NOUN
ejpam-4787	2	36	daouda	daouda	NOUN
ejpam-4787	2	37	kabre1	kabre1	PROPN
ejpam-4787	2	38	,	,	PUNCT
ejpam-4787	2	39	andré	andré	ADJ
ejpam-4787	2	40	conseibo1,∗	conseibo1,∗	NOUN
ejpam-4787	2	41	1	1	NUM
ejpam-4787	2	42	départment	départment	PROPN
ejpam-4787	2	43	de	de	PROPN
ejpam-4787	2	44	mathématiques	mathématiques	PROPN
ejpam-4787	2	45	,	,	PUNCT
ejpam-4787	2	46	université	université	ADJ
ejpam-4787	2	47	norbert	norbert	PROPN
ejpam-4787	2	48	zongo	zongo	PROPN
ejpam-4787	2	49	,	,	PUNCT
ejpam-4787	2	50	koudougou	koudougou	PROPN
ejpam-4787	2	51	,	,	PUNCT
ejpam-4787	2	52	burkina	burkina	PROPN
ejpam-4787	2	53	faso	faso	PROPN
ejpam-4787	2	54	abstract	abstract	NOUN
ejpam-4787	2	55	.	.	PUNCT
ejpam-4787	3	1	in	in	ADP
ejpam-4787	3	2	this	this	DET
ejpam-4787	3	3	paper	paper	NOUN
ejpam-4787	3	4	we	we	PRON
ejpam-4787	3	5	study	study	VERB
ejpam-4787	3	6	the	the	DET
ejpam-4787	3	7	class	class	NOUN
ejpam-4787	3	8	of	of	ADP
ejpam-4787	3	9	algebras	algebra	NOUN
ejpam-4787	3	10	satisfying	satisfy	VERB
ejpam-4787	3	11	a	a	DET
ejpam-4787	3	12	polynomial	polynomial	ADJ
ejpam-4787	3	13	identity	identity	NOUN
ejpam-4787	3	14	of	of	ADP
ejpam-4787	3	15	degree	degree	NOUN
ejpam-4787	3	16	six	six	NUM
ejpam-4787	3	17	that	that	PRON
ejpam-4787	3	18	are	be	AUX
ejpam-4787	3	19	principal	principal	ADJ
ejpam-4787	3	20	train	train	NOUN
ejpam-4787	3	21	algebras	algebra	NOUN
ejpam-4787	3	22	of	of	ADP
ejpam-4787	3	23	rank	rank	NOUN
ejpam-4787	3	24	3	3	NUM
ejpam-4787	3	25	or	or	CCONJ
ejpam-4787	3	26	4	4	NUM
ejpam-4787	3	27	,	,	PUNCT
ejpam-4787	3	28	for	for	ADP
ejpam-4787	3	29	which	which	PRON
ejpam-4787	3	30	we	we	PRON
ejpam-4787	3	31	give	give	VERB
ejpam-4787	3	32	the	the	DET
ejpam-4787	3	33	explicit	explicit	ADJ
ejpam-4787	3	34	form	form	NOUN
ejpam-4787	3	35	of	of	ADP
ejpam-4787	3	36	the	the	DET
ejpam-4787	3	37	train	train	NOUN
ejpam-4787	3	38	equation	equation	NOUN
ejpam-4787	3	39	.	.	PUNCT
ejpam-4787	4	1	if	if	SCONJ
ejpam-4787	4	2	the	the	DET
ejpam-4787	4	3	rank	rank	NOUN
ejpam-4787	4	4	of	of	ADP
ejpam-4787	4	5	a	a	PRON
ejpam-4787	4	6	is	be	AUX
ejpam-4787	4	7	n	n	PRON
ejpam-4787	4	8	≥	≥	NOUN
ejpam-4787	4	9	5	5	NUM
ejpam-4787	4	10	in	in	ADP
ejpam-4787	4	11	general	general	ADJ
ejpam-4787	4	12	,	,	PUNCT
ejpam-4787	4	13	we	we	PRON
ejpam-4787	4	14	provide	provide	VERB
ejpam-4787	4	15	the	the	DET
ejpam-4787	4	16	form	form	NOUN
ejpam-4787	4	17	of	of	ADP
ejpam-4787	4	18	the	the	DET
ejpam-4787	4	19	train	train	NOUN
ejpam-4787	4	20	equation	equation	NOUN
ejpam-4787	4	21	in	in	ADP
ejpam-4787	4	22	some	some	DET
ejpam-4787	4	23	cases	case	NOUN
ejpam-4787	4	24	.	.	PUNCT
ejpam-4787	5	1	2020	2020	NUM
ejpam-4787	5	2	mathematics	mathematic	NOUN
ejpam-4787	5	3	subject	subject	NOUN
ejpam-4787	5	4	classifications	classification	NOUN
ejpam-4787	5	5	:	:	PUNCT
ejpam-4787	5	6	17d92	17d92	NUM
ejpam-4787	5	7	,	,	PUNCT
ejpam-4787	5	8	17a05	17a05	NUM
ejpam-4787	5	9	key	key	ADJ
ejpam-4787	5	10	words	word	NOUN
ejpam-4787	5	11	and	and	CCONJ
ejpam-4787	5	12	phrases	phrase	NOUN
ejpam-4787	5	13	:	:	PUNCT
ejpam-4787	5	14	peirce	peirce	NOUN
ejpam-4787	5	15	decomposition	decomposition	NOUN
ejpam-4787	5	16	,	,	PUNCT
ejpam-4787	5	17	principal	principal	ADJ
ejpam-4787	5	18	train	train	NOUN
ejpam-4787	5	19	algebra	algebra	NOUN
ejpam-4787	5	20	,	,	PUNCT
ejpam-4787	5	21	polynomial	polynomial	ADJ
ejpam-4787	5	22	identity	identity	NOUN
ejpam-4787	5	23	,	,	PUNCT
ejpam-4787	5	24	idempotent	idempotent	ADJ
ejpam-4787	5	25	1	1	NUM
ejpam-4787	5	26	.	.	PUNCT
ejpam-4787	5	27	introduction	introduction	NOUN
ejpam-4787	5	28	in	in	ADP
ejpam-4787	5	29	1923	1923	NUM
ejpam-4787	5	30	,	,	PUNCT
ejpam-4787	5	31	serge	serge	PROPN
ejpam-4787	5	32	bernstein	bernstein	PROPN
ejpam-4787	5	33	gave	give	VERB
ejpam-4787	5	34	a	a	DET
ejpam-4787	5	35	mathematical	mathematical	ADJ
ejpam-4787	5	36	proof	proof	NOUN
ejpam-4787	5	37	of	of	ADP
ejpam-4787	5	38	the	the	DET
ejpam-4787	5	39	principle	principle	NOUN
ejpam-4787	5	40	of	of	ADP
ejpam-4787	5	41	stationarity	stationarity	NOUN
ejpam-4787	5	42	of	of	ADP
ejpam-4787	5	43	hardy	hardy	ADJ
ejpam-4787	5	44	-	-	PUNCT
ejpam-4787	5	45	weinberg	weinberg	NOUN
ejpam-4787	5	46	(	(	PUNCT
ejpam-4787	5	47	[	[	X
ejpam-4787	5	48	3	3	NUM
ejpam-4787	5	49	]	]	PUNCT
ejpam-4787	5	50	)	)	PUNCT
ejpam-4787	5	51	.	.	PUNCT
ejpam-4787	6	1	from	from	ADP
ejpam-4787	6	2	1939	1939	NUM
ejpam-4787	6	3	onwards	onward	NOUN
ejpam-4787	6	4	,	,	PUNCT
ejpam-4787	6	5	etherington	etherington	NOUN
ejpam-4787	6	6	introduced	introduce	VERB
ejpam-4787	6	7	the	the	DET
ejpam-4787	6	8	notion	notion	NOUN
ejpam-4787	6	9	of	of	ADP
ejpam-4787	6	10	weighted	weight	VERB
ejpam-4787	6	11	algebra	algebra	NOUN
ejpam-4787	6	12	and	and	CCONJ
ejpam-4787	6	13	principal	principal	ADJ
ejpam-4787	6	14	train	train	NOUN
ejpam-4787	6	15	algebra	algebra	NOUN
ejpam-4787	6	16	for	for	ADP
ejpam-4787	6	17	an	an	DET
ejpam-4787	6	18	algebraic	algebraic	ADJ
ejpam-4787	6	19	model	model	NOUN
ejpam-4787	6	20	of	of	ADP
ejpam-4787	6	21	genetics	genetic	NOUN
ejpam-4787	6	22	.	.	PUNCT
ejpam-4787	7	1	however	however	ADV
ejpam-4787	7	2	,	,	PUNCT
ejpam-4787	7	3	it	it	PRON
ejpam-4787	7	4	was	be	AUX
ejpam-4787	7	5	not	not	PART
ejpam-4787	7	6	until	until	ADP
ejpam-4787	7	7	1975	1975	NUM
ejpam-4787	7	8	(	(	PUNCT
ejpam-4787	7	9	[	[	X
ejpam-4787	7	10	5])that	5])that	NUM
ejpam-4787	7	11	philip	philip	PROPN
ejpam-4787	7	12	holgate	holgate	PROPN
ejpam-4787	7	13	defined	define	VERB
ejpam-4787	7	14	algebraically	algebraically	ADV
ejpam-4787	7	15	the	the	DET
ejpam-4787	7	16	so	so	ADV
ejpam-4787	7	17	-	-	PUNCT
ejpam-4787	7	18	called	call	VERB
ejpam-4787	7	19	bernstein	bernstein	PROPN
ejpam-4787	7	20	(	(	PUNCT
ejpam-4787	7	21	[	[	X
ejpam-4787	7	22	6	6	NUM
ejpam-4787	7	23	]	]	PUNCT
ejpam-4787	7	24	)	)	PUNCT
ejpam-4787	7	25	.	.	PUNCT
ejpam-4787	8	1	following	follow	VERB
ejpam-4787	8	2	him	he	PRON
ejpam-4787	8	3	,	,	PUNCT
ejpam-4787	8	4	several	several	ADJ
ejpam-4787	8	5	authors	author	NOUN
ejpam-4787	8	6	studied	study	VERB
ejpam-4787	8	7	various	various	ADJ
ejpam-4787	8	8	classes	class	NOUN
ejpam-4787	8	9	of	of	ADP
ejpam-4787	8	10	algebras	algebras	PROPN
ejpam-4787	8	11	satisfying	satisfy	VERB
ejpam-4787	8	12	polynomial	polynomial	ADJ
ejpam-4787	8	13	identities	identity	NOUN
ejpam-4787	8	14	,	,	PUNCT
ejpam-4787	8	15	in	in	ADP
ejpam-4787	8	16	order	order	NOUN
ejpam-4787	8	17	to	to	PART
ejpam-4787	8	18	model	model	VERB
ejpam-4787	8	19	the	the	DET
ejpam-4787	8	20	process	process	NOUN
ejpam-4787	8	21	of	of	ADP
ejpam-4787	8	22	genetic	genetic	ADJ
ejpam-4787	8	23	transmission	transmission	NOUN
ejpam-4787	8	24	.	.	PUNCT
ejpam-4787	9	1	(	(	PUNCT
ejpam-4787	9	2	see	see	VERB
ejpam-4787	9	3	,	,	PUNCT
ejpam-4787	9	4	for	for	ADP
ejpam-4787	9	5	instances	instance	NOUN
ejpam-4787	9	6	,	,	PUNCT
ejpam-4787	9	7	[	[	X
ejpam-4787	9	8	9],[1	9],[1	NUM
ejpam-4787	9	9	]	]	PUNCT
ejpam-4787	9	10	,	,	PUNCT
ejpam-4787	9	11	[	[	X
ejpam-4787	9	12	2	2	NUM
ejpam-4787	9	13	]	]	NUM
ejpam-4787	9	14	)	)	PUNCT
ejpam-4787	9	15	.	.	PUNCT
ejpam-4787	10	1	the	the	DET
ejpam-4787	10	2	aim	aim	NOUN
ejpam-4787	10	3	of	of	ADP
ejpam-4787	10	4	this	this	DET
ejpam-4787	10	5	paper	paper	NOUN
ejpam-4787	10	6	is	be	AUX
ejpam-4787	10	7	to	to	PART
ejpam-4787	10	8	study	study	VERB
ejpam-4787	10	9	the	the	DET
ejpam-4787	10	10	algebras	algebra	NOUN
ejpam-4787	10	11	verifying	verify	VERB
ejpam-4787	10	12	the	the	DET
ejpam-4787	10	13	polynomial	polynomial	ADJ
ejpam-4787	10	14	identity	identity	NOUN
ejpam-4787	10	15	2x2x4	2x2x4	NOUN
ejpam-4787	10	16	=	=	NOUN
ejpam-4787	10	17	ω(x)2x4	ω(x)2x4	NOUN
ejpam-4787	10	18	+	+	CCONJ
ejpam-4787	10	19	ω(x)4x2	ω(x)4x2	NOUN
ejpam-4787	10	20	that	that	PRON
ejpam-4787	10	21	are	be	AUX
ejpam-4787	10	22	principal	principal	ADJ
ejpam-4787	10	23	train	train	NOUN
ejpam-4787	10	24	algebras	algebra	NOUN
ejpam-4787	10	25	.	.	PUNCT
ejpam-4787	11	1	in	in	ADP
ejpam-4787	11	2	(	(	PUNCT
ejpam-4787	11	3	[	[	X
ejpam-4787	11	4	8	8	NUM
ejpam-4787	11	5	]	]	PUNCT
ejpam-4787	11	6	,	,	PUNCT
ejpam-4787	11	7	the	the	DET
ejpam-4787	11	8	authors	author	NOUN
ejpam-4787	11	9	prove	prove	VERB
ejpam-4787	11	10	that	that	SCONJ
ejpam-4787	11	11	such	such	DET
ejpam-4787	11	12	an	an	DET
ejpam-4787	11	13	algebra	algebra	NOUN
ejpam-4787	11	14	,	,	PUNCT
ejpam-4787	11	15	assuming	assume	VERB
ejpam-4787	11	16	the	the	DET
ejpam-4787	11	17	existence	existence	NOUN
ejpam-4787	11	18	of	of	ADP
ejpam-4787	11	19	nonzero	nonzero	PROPN
ejpam-4787	11	20	idempotent	idempotent	NOUN
ejpam-4787	11	21	,	,	PUNCT
ejpam-4787	11	22	admits	admit	VERB
ejpam-4787	11	23	a	a	DET
ejpam-4787	11	24	peirce	peirce	NOUN
ejpam-4787	11	25	decomposition	decomposition	NOUN
ejpam-4787	11	26	.	.	PUNCT
ejpam-4787	12	1	the	the	DET
ejpam-4787	12	2	use	use	NOUN
ejpam-4787	12	3	of	of	ADP
ejpam-4787	12	4	the	the	DET
ejpam-4787	12	5	peirce	peirce	NOUN
ejpam-4787	12	6	decomposition	decomposition	NOUN
ejpam-4787	12	7	will	will	AUX
ejpam-4787	12	8	allow	allow	VERB
ejpam-4787	12	9	us	we	PRON
ejpam-4787	12	10	to	to	PART
ejpam-4787	12	11	finally	finally	ADV
ejpam-4787	12	12	establish	establish	VERB
ejpam-4787	12	13	links	link	NOUN
ejpam-4787	12	14	between	between	ADP
ejpam-4787	12	15	this	this	DET
ejpam-4787	12	16	class	class	NOUN
ejpam-4787	12	17	of	of	ADP
ejpam-4787	12	18	algebras	algebra	NOUN
ejpam-4787	12	19	and	and	CCONJ
ejpam-4787	12	20	principal	principal	ADJ
ejpam-4787	12	21	train	train	NOUN
ejpam-4787	12	22	algebras	algebra	NOUN
ejpam-4787	12	23	.	.	PUNCT
ejpam-4787	13	1	2	2	X
ejpam-4787	13	2	.	.	X
ejpam-4787	13	3	preliminaries	preliminary	NOUN
ejpam-4787	13	4	let	let	VERB
ejpam-4787	13	5	k	k	PRON
ejpam-4787	13	6	be	be	AUX
ejpam-4787	13	7	a	a	DET
ejpam-4787	13	8	commutative	commutative	ADJ
ejpam-4787	13	9	field	field	NOUN
ejpam-4787	13	10	and	and	CCONJ
ejpam-4787	13	11	a	a	DET
ejpam-4787	13	12	a	a	DET
ejpam-4787	13	13	commutative	commutative	ADJ
ejpam-4787	13	14	k	k	NOUN
ejpam-4787	13	15	-	-	NOUN
ejpam-4787	13	16	algebra	algebra	PROPN
ejpam-4787	13	17	,	,	PUNCT
ejpam-4787	13	18	not	not	PART
ejpam-4787	13	19	necessarily	necessarily	ADV
ejpam-4787	13	20	associative	associative	ADJ
ejpam-4787	13	21	.	.	PUNCT
ejpam-4787	14	1	for	for	ADP
ejpam-4787	14	2	any	any	DET
ejpam-4787	14	3	element	element	NOUN
ejpam-4787	14	4	x	x	PUNCT
ejpam-4787	14	5	of	of	ADP
ejpam-4787	14	6	a	a	PRON
ejpam-4787	14	7	we	we	PRON
ejpam-4787	14	8	define	define	VERB
ejpam-4787	14	9	the	the	DET
ejpam-4787	14	10	principal	principal	ADJ
ejpam-4787	14	11	powers	power	NOUN
ejpam-4787	14	12	of	of	ADP
ejpam-4787	14	13	x	x	PUNCT
ejpam-4787	14	14	by	by	ADP
ejpam-4787	14	15	x1	x1	PROPN
ejpam-4787	14	16	=	=	SYM
ejpam-4787	14	17	x	x	PROPN
ejpam-4787	14	18	and	and	CCONJ
ejpam-4787	14	19	xk+1	xk+1	NUM
ejpam-4787	14	20	=	=	SYM
ejpam-4787	14	21	xxk	xxk	PROPN
ejpam-4787	14	22	for	for	ADP
ejpam-4787	14	23	any	any	DET
ejpam-4787	14	24	integer	integer	NOUN
ejpam-4787	14	25	k	k	PROPN
ejpam-4787	14	26	≥	≥	NUM
ejpam-4787	14	27	1	1	NUM
ejpam-4787	14	28	.	.	PUNCT
ejpam-4787	15	1	an	an	DET
ejpam-4787	15	2	idempotent	idempotent	NOUN
ejpam-4787	15	3	is	be	AUX
ejpam-4787	15	4	any	any	DET
ejpam-4787	15	5	element	element	NOUN
ejpam-4787	15	6	e	e	NOUN
ejpam-4787	15	7	of	of	ADP
ejpam-4787	15	8	a	a	DET
ejpam-4787	15	9	such	such	ADJ
ejpam-4787	15	10	that	that	DET
ejpam-4787	15	11	e2	e2	PROPN
ejpam-4787	15	12	=	=	PUNCT
ejpam-4787	15	13	e.	e.	PROPN
ejpam-4787	15	14	in	in	ADP
ejpam-4787	15	15	this	this	DET
ejpam-4787	15	16	paper	paper	NOUN
ejpam-4787	15	17	the	the	DET
ejpam-4787	15	18	idempotents	idempotent	NOUN
ejpam-4787	15	19	considered	consider	VERB
ejpam-4787	15	20	are	be	AUX
ejpam-4787	15	21	all	all	PRON
ejpam-4787	15	22	non	non	ADJ
ejpam-4787	15	23	-	-	ADJ
ejpam-4787	15	24	zero	zero	NUM
ejpam-4787	15	25	.	.	PUNCT
ejpam-4787	16	1	∗corresponding	∗corresponde	VERB
ejpam-4787	16	2	author	author	NOUN
ejpam-4787	16	3	.	.	PUNCT
ejpam-4787	17	1	doi	doi	NOUN
ejpam-4787	17	2	:	:	PUNCT
ejpam-4787	17	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4770	https://doi.org/10.29020/nybg.ejpam.v16i3.4770	NOUN
ejpam-4787	17	4	email	email	NOUN
ejpam-4787	17	5	addresses	address	NOUN
ejpam-4787	17	6	:	:	PUNCT
ejpam-4787	17	7	daoudakabre@yahoo.fr	daoudakabre@yahoo.fr	PROPN
ejpam-4787	17	8	(	(	PUNCT
ejpam-4787	17	9	d.	d.	PROPN
ejpam-4787	17	10	kabre	kabre	PROPN
ejpam-4787	17	11	)	)	PUNCT
ejpam-4787	17	12	,	,	PUNCT
ejpam-4787	17	13	andreconsebo@yahoo.fr	andreconsebo@yahoo.fr	PROPN
ejpam-4787	17	14	(	(	PUNCT
ejpam-4787	17	15	a.	a.	NOUN
ejpam-4787	17	16	conseibo	conseibo	PROPN
ejpam-4787	17	17	)	)	PUNCT
ejpam-4787	17	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4787	17	19	1480	1480	NUM
ejpam-4787	18	1	©	©	PROPN
ejpam-4787	18	2	2023	2023	NUM
ejpam-4787	18	3	ejpam	ejpam	NOUN
ejpam-4787	18	4	all	all	DET
ejpam-4787	18	5	rights	right	NOUN
ejpam-4787	18	6	reserved	reserve	VERB
ejpam-4787	18	7	.	.	PUNCT
ejpam-4787	19	1	d.	d.	PROPN
ejpam-4787	19	2	kabre	kabre	PROPN
ejpam-4787	19	3	,	,	PUNCT
ejpam-4787	19	4	a.	a.	NOUN
ejpam-4787	19	5	conseibo	conseibo	PROPN
ejpam-4787	19	6	/	/	SYM
ejpam-4787	19	7	eur	eur	PROPN
ejpam-4787	19	8	.	.	PUNCT
ejpam-4787	20	1	j.	j.	PROPN
ejpam-4787	20	2	pure	pure	PROPN
ejpam-4787	20	3	appl	appl	PROPN
ejpam-4787	20	4	.	.	PROPN
ejpam-4787	20	5	math	math	PROPN
ejpam-4787	20	6	,	,	PUNCT
ejpam-4787	20	7	16	16	NUM
ejpam-4787	20	8	(	(	PUNCT
ejpam-4787	20	9	3	3	NUM
ejpam-4787	20	10	)	)	PUNCT
ejpam-4787	20	11	(	(	PUNCT
ejpam-4787	20	12	2023	2023	NUM
ejpam-4787	20	13	)	)	PUNCT
ejpam-4787	20	14	,	,	PUNCT
ejpam-4787	20	15	1480	1480	NUM
ejpam-4787	20	16	-	-	SYM
ejpam-4787	20	17	1490	1490	NUM
ejpam-4787	20	18	1481	1481	NUM
ejpam-4787	20	19	definition	definition	NOUN
ejpam-4787	20	20	1	1	NUM
ejpam-4787	20	21	.	.	PUNCT
ejpam-4787	21	1	we	we	PRON
ejpam-4787	21	2	will	will	AUX
ejpam-4787	21	3	say	say	VERB
ejpam-4787	21	4	that	that	SCONJ
ejpam-4787	21	5	the	the	DET
ejpam-4787	21	6	algebra	algebra	NOUN
ejpam-4787	21	7	a	a	PRON
ejpam-4787	21	8	is	be	AUX
ejpam-4787	21	9	a	a	DET
ejpam-4787	21	10	baric	baric	ADJ
ejpam-4787	21	11	if	if	SCONJ
ejpam-4787	21	12	there	there	PRON
ejpam-4787	21	13	exists	exist	VERB
ejpam-4787	21	14	a	a	DET
ejpam-4787	21	15	non	non	ADJ
ejpam-4787	21	16	-	-	ADJ
ejpam-4787	21	17	zero	zero	NUM
ejpam-4787	21	18	morphism	morphism	NOUN
ejpam-4787	21	19	of	of	ADP
ejpam-4787	21	20	algebras	algebras	PROPN
ejpam-4787	21	21	ω	ω	PROPN
ejpam-4787	21	22	:	:	PUNCT
ejpam-4787	21	23	a	a	PROPN
ejpam-4787	21	24	→	→	SYM
ejpam-4787	21	25	k.	k.	NOUN
ejpam-4787	21	26	the	the	DET
ejpam-4787	21	27	morphism	morphism	PROPN
ejpam-4787	21	28	ω	ω	PROPN
ejpam-4787	21	29	is	be	AUX
ejpam-4787	21	30	then	then	ADV
ejpam-4787	21	31	called	call	VERB
ejpam-4787	21	32	the	the	DET
ejpam-4787	21	33	weight	weight	NOUN
ejpam-4787	21	34	function	function	NOUN
ejpam-4787	21	35	of	of	ADP
ejpam-4787	21	36	the	the	DET
ejpam-4787	21	37	algebra	algebra	NOUN
ejpam-4787	21	38	a.	a.	NOUN
ejpam-4787	21	39	the	the	DET
ejpam-4787	21	40	weight	weight	NOUN
ejpam-4787	21	41	of	of	ADP
ejpam-4787	21	42	an	an	DET
ejpam-4787	21	43	element	element	NOUN
ejpam-4787	21	44	x	x	X
ejpam-4787	21	45	of	of	ADP
ejpam-4787	21	46	a	a	PRON
ejpam-4787	21	47	is	be	AUX
ejpam-4787	21	48	the	the	DET
ejpam-4787	21	49	scalar	scalar	ADJ
ejpam-4787	21	50	ω(x	ω(x	NOUN
ejpam-4787	21	51	)	)	PUNCT
ejpam-4787	21	52	.	.	PUNCT
ejpam-4787	22	1	definition	definition	NOUN
ejpam-4787	22	2	2	2	NUM
ejpam-4787	22	3	.	.	PUNCT
ejpam-4787	23	1	a	a	DET
ejpam-4787	23	2	baric	baric	ADJ
ejpam-4787	23	3	k	k	NOUN
ejpam-4787	23	4	-	-	NOUN
ejpam-4787	23	5	algebra	algebra	NOUN
ejpam-4787	23	6	(	(	PUNCT
ejpam-4787	23	7	a	a	DET
ejpam-4787	23	8	,	,	PUNCT
ejpam-4787	23	9	ω	ω	NOUN
ejpam-4787	23	10	)	)	PUNCT
ejpam-4787	23	11	is	be	AUX
ejpam-4787	23	12	a	a	DET
ejpam-4787	23	13	principal	principal	ADJ
ejpam-4787	23	14	train	train	NOUN
ejpam-4787	23	15	algebra	algebra	NOUN
ejpam-4787	23	16	of	of	ADP
ejpam-4787	23	17	rank	rank	PROPN
ejpam-4787	23	18	n	n	PROPN
ejpam-4787	23	19	≥	≥	NUM
ejpam-4787	23	20	2	2	NUM
ejpam-4787	23	21	if	if	SCONJ
ejpam-4787	23	22	there	there	PRON
ejpam-4787	23	23	are	be	VERB
ejpam-4787	23	24	scalars	scalars	PROPN
ejpam-4787	23	25	γ1	γ1	PROPN
ejpam-4787	23	26	,	,	PUNCT
ejpam-4787	23	27	.	.	PUNCT
ejpam-4787	23	28	.	.	PUNCT
ejpam-4787	24	1	.	.	PUNCT
ejpam-4787	25	1	,	,	PUNCT
ejpam-4787	25	2	γn−1	γn−1	PROPN
ejpam-4787	25	3	∈	∈	PROPN
ejpam-4787	26	1	k	k	PROPN
ejpam-4787	26	2	such	such	ADJ
ejpam-4787	26	3	that	that	PRON
ejpam-4787	26	4	xn	xn	PROPN
ejpam-4787	27	1	+	+	NUM
ejpam-4787	27	2	γ1ω(x)x	γ1ω(x)x	ADJ
ejpam-4787	27	3	n−1	n−1	PROPN
ejpam-4787	27	4	+	+	NUM
ejpam-4787	27	5	·	·	PUNCT
ejpam-4787	27	6	·	·	PUNCT
ejpam-4787	27	7	·	·	PUNCT
ejpam-4787	27	8	+	+	NUM
ejpam-4787	27	9	γn−1ω(x	γn−1ω(x	NOUN
ejpam-4787	27	10	)	)	PUNCT
ejpam-4787	27	11	n−1x	n−1x	ADP
ejpam-4787	27	12	=	=	SYM
ejpam-4787	27	13	0	0	PROPN
ejpam-4787	27	14	,	,	PUNCT
ejpam-4787	27	15	where	where	SCONJ
ejpam-4787	27	16	the	the	DET
ejpam-4787	27	17	integer	integer	NOUN
ejpam-4787	27	18	n	n	PRON
ejpam-4787	27	19	≥	≥	NUM
ejpam-4787	27	20	2	2	NUM
ejpam-4787	27	21	is	be	AUX
ejpam-4787	27	22	the	the	DET
ejpam-4787	27	23	smallest	small	ADJ
ejpam-4787	27	24	having	have	VERB
ejpam-4787	27	25	this	this	DET
ejpam-4787	27	26	property	property	NOUN
ejpam-4787	27	27	.	.	PUNCT
ejpam-4787	28	1	definition	definition	NOUN
ejpam-4787	28	2	3	3	NUM
ejpam-4787	28	3	.	.	PUNCT
ejpam-4787	29	1	a	a	DET
ejpam-4787	29	2	baric	baric	ADJ
ejpam-4787	29	3	k	k	NOUN
ejpam-4787	29	4	-	-	NOUN
ejpam-4787	29	5	algebra	algebra	NOUN
ejpam-4787	29	6	(	(	PUNCT
ejpam-4787	29	7	a	a	DET
ejpam-4787	29	8	,	,	PUNCT
ejpam-4787	29	9	ω	ω	NOUN
ejpam-4787	29	10	)	)	PUNCT
ejpam-4787	29	11	is	be	AUX
ejpam-4787	29	12	a	a	DET
ejpam-4787	29	13	bernstein	bernstein	PROPN
ejpam-4787	29	14	algebra	algebra	PROPN
ejpam-4787	29	15	if	if	SCONJ
ejpam-4787	29	16	(	(	PUNCT
ejpam-4787	29	17	x2)2	x2)2	PRON
ejpam-4787	29	18	=	=	PUNCT
ejpam-4787	29	19	ω(x)2x2	ω(x)2x2	NOUN
ejpam-4787	29	20	for	for	ADP
ejpam-4787	29	21	any	any	DET
ejpam-4787	29	22	x	x	NOUN
ejpam-4787	29	23	in	in	ADP
ejpam-4787	29	24	a.	a.	NOUN
ejpam-4787	29	25	in	in	ADP
ejpam-4787	29	26	the	the	DET
ejpam-4787	29	27	rest	rest	NOUN
ejpam-4787	29	28	of	of	ADP
ejpam-4787	29	29	the	the	DET
ejpam-4787	29	30	document	document	NOUN
ejpam-4787	29	31	,	,	PUNCT
ejpam-4787	29	32	k	k	PROPN
ejpam-4787	29	33	denotes	denote	VERB
ejpam-4787	29	34	an	an	DET
ejpam-4787	29	35	algebraically	algebraically	ADV
ejpam-4787	29	36	closed	close	VERB
ejpam-4787	29	37	infinite	infinite	ADJ
ejpam-4787	29	38	commutative	commutative	ADJ
ejpam-4787	29	39	field	field	NOUN
ejpam-4787	29	40	with	with	ADP
ejpam-4787	29	41	characteristic	characteristic	ADJ
ejpam-4787	29	42	different	different	ADV
ejpam-4787	29	43	from	from	ADP
ejpam-4787	29	44	2	2	NUM
ejpam-4787	29	45	.	.	PUNCT
ejpam-4787	30	1	in	in	ADP
ejpam-4787	30	2	[	[	X
ejpam-4787	30	3	11	11	NUM
ejpam-4787	30	4	]	]	PUNCT
ejpam-4787	30	5	,	,	PUNCT
ejpam-4787	30	6	it	it	PRON
ejpam-4787	30	7	is	be	AUX
ejpam-4787	30	8	shown	show	VERB
ejpam-4787	30	9	that	that	SCONJ
ejpam-4787	30	10	if	if	SCONJ
ejpam-4787	30	11	a	a	DET
ejpam-4787	30	12	denotes	denote	NOUN
ejpam-4787	30	13	a	a	DET
ejpam-4787	30	14	bernstein	bernstein	PROPN
ejpam-4787	30	15	algebra	algebra	PROPN
ejpam-4787	30	16	,	,	PUNCT
ejpam-4787	30	17	then	then	ADV
ejpam-4787	30	18	for	for	ADP
ejpam-4787	30	19	any	any	DET
ejpam-4787	30	20	x	x	NOUN
ejpam-4787	30	21	in	in	ADP
ejpam-4787	30	22	a	a	DET
ejpam-4787	30	23	,	,	PUNCT
ejpam-4787	30	24	2xixj	2xixj	PROPN
ejpam-4787	30	25	=	=	SYM
ejpam-4787	30	26	ω(x)ixj	ω(x)ixj	PROPN
ejpam-4787	30	27	+	+	CCONJ
ejpam-4787	30	28	ω(x)jxi	ω(x)jxi	PROPN
ejpam-4787	30	29	,	,	PUNCT
ejpam-4787	30	30	∀i	∀i	NOUN
ejpam-4787	30	31	,	,	PUNCT
ejpam-4787	30	32	j	j	PROPN
ejpam-4787	30	33	≥	≥	NUM
ejpam-4787	30	34	2	2	NUM
ejpam-4787	30	35	;	;	PUNCT
ejpam-4787	30	36	in	in	ADP
ejpam-4787	30	37	particular	particular	ADJ
ejpam-4787	30	38	,	,	PUNCT
ejpam-4787	30	39	for	for	ADP
ejpam-4787	30	40	i	i	PROPN
ejpam-4787	30	41	=	=	SYM
ejpam-4787	30	42	2	2	NUM
ejpam-4787	30	43	and	and	CCONJ
ejpam-4787	30	44	j	j	NOUN
ejpam-4787	30	45	=	=	SYM
ejpam-4787	30	46	4	4	NUM
ejpam-4787	30	47	,	,	PUNCT
ejpam-4787	30	48	2x2x4	2x2x4	NOUN
ejpam-4787	30	49	=	=	SYM
ejpam-4787	30	50	ω(x)2x4	ω(x)2x4	NOUN
ejpam-4787	30	51	+	+	CCONJ
ejpam-4787	30	52	ω(x)4x2,∀x	ω(x)4x2,∀x	VERB
ejpam-4787	30	53	∈	∈	NOUN
ejpam-4787	30	54	a.	a.	NOUN
ejpam-4787	30	55	in	in	ADP
ejpam-4787	30	56	this	this	DET
ejpam-4787	30	57	paper	paper	NOUN
ejpam-4787	30	58	,	,	PUNCT
ejpam-4787	30	59	our	our	PRON
ejpam-4787	30	60	attention	attention	NOUN
ejpam-4787	30	61	will	will	AUX
ejpam-4787	30	62	be	be	AUX
ejpam-4787	30	63	focused	focus	VERB
ejpam-4787	30	64	on	on	ADP
ejpam-4787	30	65	the	the	DET
ejpam-4787	30	66	structure	structure	NOUN
ejpam-4787	30	67	of	of	ADP
ejpam-4787	30	68	algebras	algebra	NOUN
ejpam-4787	30	69	satisfying	satisfy	VERB
ejpam-4787	30	70	the	the	DET
ejpam-4787	30	71	latter	latter	ADJ
ejpam-4787	30	72	polynomial	polynomial	ADJ
ejpam-4787	30	73	identity	identity	NOUN
ejpam-4787	30	74	and	and	CCONJ
ejpam-4787	30	75	that	that	PRON
ejpam-4787	30	76	are	be	AUX
ejpam-4787	30	77	principal	principal	ADJ
ejpam-4787	30	78	train	train	NOUN
ejpam-4787	30	79	.	.	PUNCT
ejpam-4787	31	1	let	let	VERB
ejpam-4787	31	2	us	we	PRON
ejpam-4787	31	3	consider	consider	VERB
ejpam-4787	31	4	the	the	DET
ejpam-4787	31	5	identity	identity	NOUN
ejpam-4787	31	6	2x2x4	2x2x4	NOUN
ejpam-4787	31	7	=	=	NOUN
ejpam-4787	31	8	ω(x)2x4	ω(x)2x4	NOUN
ejpam-4787	32	1	+	+	X
ejpam-4787	32	2	ω(x)4x2	ω(x)4x2	PROPN
ejpam-4787	32	3	(	(	PUNCT
ejpam-4787	32	4	1	1	NUM
ejpam-4787	32	5	)	)	PUNCT
ejpam-4787	32	6	in	in	ADP
ejpam-4787	32	7	the	the	DET
ejpam-4787	32	8	rest	rest	NOUN
ejpam-4787	32	9	of	of	ADP
ejpam-4787	32	10	the	the	DET
ejpam-4787	32	11	paper	paper	NOUN
ejpam-4787	32	12	,	,	PUNCT
ejpam-4787	32	13	k	k	PROPN
ejpam-4787	32	14	=	=	PUNCT
ejpam-4787	32	15	c	c	X
ejpam-4787	32	16	,	,	PUNCT
ejpam-4787	32	17	i.e	i.e	PRON
ejpam-4787	32	18	the	the	DET
ejpam-4787	32	19	field	field	NOUN
ejpam-4787	32	20	of	of	ADP
ejpam-4787	32	21	complex	complex	ADJ
ejpam-4787	32	22	numbers	number	NOUN
ejpam-4787	32	23	.	.	PUNCT
ejpam-4787	33	1	in	in	ADP
ejpam-4787	33	2	[	[	X
ejpam-4787	33	3	8	8	NUM
ejpam-4787	33	4	]	]	PUNCT
ejpam-4787	33	5	,	,	PUNCT
ejpam-4787	33	6	the	the	DET
ejpam-4787	33	7	authors	author	NOUN
ejpam-4787	33	8	obtained	obtain	VERB
ejpam-4787	33	9	the	the	DET
ejpam-4787	33	10	following	follow	VERB
ejpam-4787	33	11	two	two	NUM
ejpam-4787	33	12	theorems	theorem	NOUN
ejpam-4787	33	13	.	.	PUNCT
ejpam-4787	33	14	.	.	PUNCT
ejpam-4787	34	1	theorem	theorem	NOUN
ejpam-4787	34	2	1	1	NUM
ejpam-4787	34	3	.	.	PUNCT
ejpam-4787	35	1	[	[	X
ejpam-4787	35	2	8	8	NUM
ejpam-4787	35	3	]	]	X
ejpam-4787	35	4	let	let	VERB
ejpam-4787	35	5	(	(	PUNCT
ejpam-4787	35	6	a	a	DET
ejpam-4787	35	7	,	,	PUNCT
ejpam-4787	35	8	ω	ω	NOUN
ejpam-4787	35	9	)	)	PUNCT
ejpam-4787	35	10	be	be	VERB
ejpam-4787	35	11	a	a	DET
ejpam-4787	35	12	k	k	NOUN
ejpam-4787	35	13	-	-	ADJ
ejpam-4787	35	14	algebra	algebra	ADJ
ejpam-4787	35	15	verifying	verifying	NOUN
ejpam-4787	35	16	(	(	PUNCT
ejpam-4787	35	17	1	1	NUM
ejpam-4787	35	18	)	)	PUNCT
ejpam-4787	35	19	and	and	CCONJ
ejpam-4787	35	20	e	e	PRON
ejpam-4787	35	21	be	be	AUX
ejpam-4787	35	22	a	a	DET
ejpam-4787	35	23	non	non	ADJ
ejpam-4787	35	24	-	-	ADJ
ejpam-4787	35	25	zero	zero	ADJ
ejpam-4787	35	26	idempotent	idempotent	NOUN
ejpam-4787	35	27	of	of	ADP
ejpam-4787	35	28	a.	a.	NOUN
ejpam-4787	35	29	then	then	ADV
ejpam-4787	35	30	a	a	PRON
ejpam-4787	35	31	admits	admit	VERB
ejpam-4787	35	32	a	a	DET
ejpam-4787	35	33	peirce	peirce	NOUN
ejpam-4787	35	34	decomposition	decomposition	NOUN
ejpam-4787	35	35	relative	relative	ADJ
ejpam-4787	35	36	to	to	ADP
ejpam-4787	35	37	e	e	NOUN
ejpam-4787	35	38	:	:	PUNCT
ejpam-4787	35	39	a	a	DET
ejpam-4787	35	40	=	=	X
ejpam-4787	35	41	ke⊕a0	ke⊕a0	PROPN
ejpam-4787	35	42	⊕a	⊕a	NOUN
ejpam-4787	35	43	1	1	NUM
ejpam-4787	35	44	2	2	NUM
ejpam-4787	35	45	⊕aλ	⊕aλ	NOUN
ejpam-4787	35	46	⊕aλ̄	⊕aλ̄	PROPN
ejpam-4787	35	47	where	where	SCONJ
ejpam-4787	35	48	aα	aα	NOUN
ejpam-4787	35	49	=	=	PRON
ejpam-4787	35	50	{	{	PUNCT
ejpam-4787	35	51	x	x	SYM
ejpam-4787	35	52	∈	∈	PROPN
ejpam-4787	35	53	kerω	kerω	NOUN
ejpam-4787	35	54	,	,	PUNCT
ejpam-4787	35	55	ex	ex	X
ejpam-4787	35	56	=	=	NOUN
ejpam-4787	35	57	αx	αx	NOUN
ejpam-4787	35	58	}	}	PUNCT
ejpam-4787	35	59	,	,	PUNCT
ejpam-4787	35	60	with	with	ADP
ejpam-4787	35	61	α	α	PROPN
ejpam-4787	35	62	∈	∈	PROPN
ejpam-4787	35	63	{	{	PUNCT
ejpam-4787	35	64	0	0	NUM
ejpam-4787	35	65	;	;	PUNCT
ejpam-4787	35	66	12	12	NUM
ejpam-4787	35	67	;	;	PUNCT
ejpam-4787	36	1	λ	λ	X
ejpam-4787	36	2	=	=	PRON
ejpam-4787	36	3	−1−i	−1−i	ADJ
ejpam-4787	36	4	√	√	NUM
ejpam-4787	36	5	23	23	NUM
ejpam-4787	36	6	4	4	NUM
ejpam-4787	36	7	;	;	PUNCT
ejpam-4787	36	8	λ̄	λ̄	ADP
ejpam-4787	37	1	=	=	PUNCT
ejpam-4787	37	2	−1+i	−1+i	NOUN
ejpam-4787	37	3	√	√	NOUN
ejpam-4787	37	4	23	23	NUM
ejpam-4787	37	5	4	4	NUM
ejpam-4787	37	6	}	}	PUNCT
ejpam-4787	37	7	.	.	PUNCT
ejpam-4787	38	1	theorem	theorem	NOUN
ejpam-4787	38	2	2	2	NUM
ejpam-4787	38	3	.	.	PUNCT
ejpam-4787	39	1	[	[	X
ejpam-4787	39	2	8	8	NUM
ejpam-4787	39	3	]	]	PUNCT
ejpam-4787	39	4	let	let	VERB
ejpam-4787	39	5	a	a	DET
ejpam-4787	39	6	=	=	SYM
ejpam-4787	39	7	ke	ke	PROPN
ejpam-4787	39	8	⊕	⊕	PROPN
ejpam-4787	39	9	a0	a0	PROPN
ejpam-4787	39	10	⊕	⊕	PROPN
ejpam-4787	39	11	a	a	DET
ejpam-4787	39	12	1	1	NUM
ejpam-4787	39	13	2	2	NUM
ejpam-4787	39	14	⊕	⊕	PROPN
ejpam-4787	39	15	aλ	aλ	ADP
ejpam-4787	39	16	⊕	⊕	PROPN
ejpam-4787	39	17	aλ̄	aλ̄	NOUN
ejpam-4787	39	18	be	be	AUX
ejpam-4787	39	19	the	the	DET
ejpam-4787	39	20	peirce	peirce	NOUN
ejpam-4787	39	21	decomposition	decomposition	NOUN
ejpam-4787	39	22	of	of	ADP
ejpam-4787	39	23	an	an	DET
ejpam-4787	39	24	algebra	algebra	NOUN
ejpam-4787	39	25	verifying	verifying	NOUN
ejpam-4787	39	26	(	(	PUNCT
ejpam-4787	39	27	1	1	NUM
ejpam-4787	39	28	)	)	PUNCT
ejpam-4787	39	29	,	,	PUNCT
ejpam-4787	39	30	then	then	ADV
ejpam-4787	39	31	:	:	PUNCT
ejpam-4787	39	32	i	i	X
ejpam-4787	39	33	)	)	PUNCT
ejpam-4787	39	34	a0a0	a0a0	X
ejpam-4787	40	1	⊂	⊂	PROPN
ejpam-4787	40	2	a	a	DET
ejpam-4787	40	3	1	1	NUM
ejpam-4787	40	4	2	2	NUM
ejpam-4787	40	5	;	;	PUNCT
ejpam-4787	40	6	ii	ii	X
ejpam-4787	40	7	)	)	PUNCT
ejpam-4787	40	8	a	a	DET
ejpam-4787	40	9	1	1	NUM
ejpam-4787	40	10	2	2	NUM
ejpam-4787	40	11	a	a	DET
ejpam-4787	40	12	1	1	NUM
ejpam-4787	40	13	2	2	NUM
ejpam-4787	40	14	⊂	⊂	PROPN
ejpam-4787	40	15	a0	a0	PROPN
ejpam-4787	40	16	⊕aλ	⊕aλ	PROPN
ejpam-4787	40	17	⊕aλ̄	⊕aλ̄	PROPN
ejpam-4787	40	18	;	;	PUNCT
ejpam-4787	40	19	iii	iii	X
ejpam-4787	40	20	)	)	PUNCT
ejpam-4787	40	21	aλaλ̄	aλaλ̄	NOUN
ejpam-4787	40	22	=	=	SYM
ejpam-4787	40	23	0	0	NUM
ejpam-4787	40	24	;	;	PUNCT
ejpam-4787	40	25	iv	iv	X
ejpam-4787	40	26	)	)	PUNCT
ejpam-4787	40	27	aλaλ	aλaλ	NOUN
ejpam-4787	40	28	=	=	SYM
ejpam-4787	40	29	0	0	NUM
ejpam-4787	40	30	;	;	PUNCT
ejpam-4787	40	31	v̇	v̇	NOUN
ejpam-4787	40	32	)	)	PUNCT
ejpam-4787	41	1	aλ̄aλ̄	aλ̄aλ̄	PROPN
ejpam-4787	42	1	=	=	SYM
ejpam-4787	42	2	0	0	NUM
ejpam-4787	42	3	:	:	PUNCT
ejpam-4787	42	4	vi	vi	X
ejpam-4787	42	5	)	)	PUNCT
ejpam-4787	42	6	a0a	a0a	NOUN
ejpam-4787	42	7	1	1	NUM
ejpam-4787	42	8	2	2	NUM
ejpam-4787	42	9	⊂	⊂	NOUN
ejpam-4787	42	10	a	a	DET
ejpam-4787	42	11	1	1	NUM
ejpam-4787	42	12	2	2	NUM
ejpam-4787	42	13	⊕aλ	⊕aλ	NOUN
ejpam-4787	42	14	⊕aλ̄	⊕aλ̄	PROPN
ejpam-4787	42	15	;	;	PUNCT
ejpam-4787	42	16	vii	vii	PROPN
ejpam-4787	42	17	)	)	PUNCT
ejpam-4787	42	18	aλa	aλa	NOUN
ejpam-4787	42	19	1	1	NUM
ejpam-4787	42	20	2	2	NUM
ejpam-4787	42	21	⊂	⊂	NOUN
ejpam-4787	42	22	a	a	DET
ejpam-4787	42	23	1	1	NUM
ejpam-4787	42	24	2	2	NUM
ejpam-4787	42	25	⊕a0	⊕a0	PROPN
ejpam-4787	42	26	⊕aλ̄	⊕aλ̄	PROPN
ejpam-4787	42	27	;	;	PUNCT
ejpam-4787	42	28	viii	viii	PROPN
ejpam-4787	42	29	)	)	PUNCT
ejpam-4787	42	30	aλ̄a	aλ̄a	NOUN
ejpam-4787	43	1	1	1	NUM
ejpam-4787	43	2	2	2	NUM
ejpam-4787	43	3	⊂	⊂	PRON
ejpam-4787	43	4	a	a	DET
ejpam-4787	43	5	1	1	NUM
ejpam-4787	43	6	2	2	NUM
ejpam-4787	43	7	⊕a0	⊕a0	NUM
ejpam-4787	43	8	⊕aλ	⊕aλ	NOUN
ejpam-4787	43	9	;	;	PUNCT
ejpam-4787	43	10	ix	ix	X
ejpam-4787	43	11	)	)	PUNCT
ejpam-4787	43	12	a0aλ	a0aλ	PUNCT
ejpam-4787	44	1	⊂	⊂	PROPN
ejpam-4787	44	2	a	a	DET
ejpam-4787	44	3	1	1	NUM
ejpam-4787	44	4	2	2	NUM
ejpam-4787	44	5	;	;	PUNCT
ejpam-4787	44	6	d.	d.	PROPN
ejpam-4787	44	7	kabre	kabre	PROPN
ejpam-4787	44	8	,	,	PUNCT
ejpam-4787	44	9	a.	a.	NOUN
ejpam-4787	44	10	conseibo	conseibo	PROPN
ejpam-4787	44	11	/	/	SYM
ejpam-4787	44	12	eur	eur	PROPN
ejpam-4787	44	13	.	.	PUNCT
ejpam-4787	45	1	j.	j.	PROPN
ejpam-4787	45	2	pure	pure	PROPN
ejpam-4787	45	3	appl	appl	PROPN
ejpam-4787	45	4	.	.	PROPN
ejpam-4787	45	5	math	math	PROPN
ejpam-4787	45	6	,	,	PUNCT
ejpam-4787	45	7	16	16	NUM
ejpam-4787	45	8	(	(	PUNCT
ejpam-4787	45	9	3	3	NUM
ejpam-4787	45	10	)	)	PUNCT
ejpam-4787	45	11	(	(	PUNCT
ejpam-4787	45	12	2023	2023	NUM
ejpam-4787	45	13	)	)	PUNCT
ejpam-4787	45	14	,	,	PUNCT
ejpam-4787	45	15	1480	1480	NUM
ejpam-4787	45	16	-	-	SYM
ejpam-4787	45	17	1490	1490	NUM
ejpam-4787	45	18	1482	1482	NUM
ejpam-4787	45	19	x	x	NOUN
ejpam-4787	45	20	)	)	PUNCT
ejpam-4787	45	21	a0aλ̄	a0aλ̄	NOUN
ejpam-4787	46	1	⊂	⊂	PROPN
ejpam-4787	46	2	a	a	DET
ejpam-4787	46	3	1	1	NUM
ejpam-4787	46	4	2	2	NUM
ejpam-4787	46	5	.	.	PUNCT
ejpam-4787	47	1	let	let	AUX
ejpam-4787	47	2	(	(	PUNCT
ejpam-4787	47	3	a	a	DET
ejpam-4787	47	4	,	,	PUNCT
ejpam-4787	47	5	ω	ω	NOUN
ejpam-4787	47	6	)	)	PUNCT
ejpam-4787	47	7	be	be	AUX
ejpam-4787	47	8	a	a	DET
ejpam-4787	47	9	baric	baric	ADJ
ejpam-4787	47	10	commutative	commutative	ADJ
ejpam-4787	47	11	k	k	NOUN
ejpam-4787	47	12	-	-	NOUN
ejpam-4787	47	13	algebra	algebra	NOUN
ejpam-4787	47	14	not	not	PART
ejpam-4787	47	15	necessarily	necessarily	ADV
ejpam-4787	47	16	associative	associative	ADJ
ejpam-4787	47	17	verifying	verify	VERB
ejpam-4787	47	18	the	the	DET
ejpam-4787	47	19	identity	identity	NOUN
ejpam-4787	47	20	(	(	PUNCT
ejpam-4787	47	21	1	1	NUM
ejpam-4787	47	22	)	)	PUNCT
ejpam-4787	47	23	.	.	PUNCT
ejpam-4787	48	1	the	the	DET
ejpam-4787	48	2	partial	partial	ADJ
ejpam-4787	48	3	linearisation	linearisation	NOUN
ejpam-4787	48	4	of	of	ADP
ejpam-4787	48	5	this	this	DET
ejpam-4787	48	6	identity	identity	NOUN
ejpam-4787	48	7	gives	give	VERB
ejpam-4787	48	8	the	the	DET
ejpam-4787	48	9	following	follow	VERB
ejpam-4787	48	10	result	result	NOUN
ejpam-4787	48	11	:	:	PUNCT
ejpam-4787	48	12	proposition	proposition	NOUN
ejpam-4787	48	13	1	1	NUM
ejpam-4787	48	14	.	.	PUNCT
ejpam-4787	49	1	let	let	AUX
ejpam-4787	49	2	(	(	PUNCT
ejpam-4787	49	3	a	a	DET
ejpam-4787	49	4	,	,	PUNCT
ejpam-4787	49	5	ω	ω	NOUN
ejpam-4787	49	6	)	)	PUNCT
ejpam-4787	49	7	be	be	VERB
ejpam-4787	49	8	a	a	DET
ejpam-4787	49	9	k	k	NOUN
ejpam-4787	49	10	-	-	ADJ
ejpam-4787	49	11	algebra	algebra	ADJ
ejpam-4787	49	12	verifying	verifying	NOUN
ejpam-4787	49	13	(	(	PUNCT
ejpam-4787	49	14	1	1	NUM
ejpam-4787	49	15	)	)	PUNCT
ejpam-4787	49	16	.	.	PUNCT
ejpam-4787	50	1	for	for	SCONJ
ejpam-4787	50	2	all	all	DET
ejpam-4787	50	3	x	x	PROPN
ejpam-4787	50	4	,	,	PUNCT
ejpam-4787	50	5	y	y	PROPN
ejpam-4787	50	6	,	,	PUNCT
ejpam-4787	50	7	z	z	PROPN
ejpam-4787	50	8	,	,	PUNCT
ejpam-4787	50	9	t	t	PROPN
ejpam-4787	50	10	in	in	ADP
ejpam-4787	50	11	a	a	PRON
ejpam-4787	50	12	we	we	PRON
ejpam-4787	50	13	have	have	VERB
ejpam-4787	50	14	:	:	PUNCT
ejpam-4787	50	15	4x2[z(t(xy	4x2[z(t(xy	NUM
ejpam-4787	50	16	)	)	PUNCT
ejpam-4787	50	17	)	)	PUNCT
ejpam-4787	51	1	+	+	CCONJ
ejpam-4787	51	2	z(x(ty	z(x(ty	NUM
ejpam-4787	51	3	)	)	PUNCT
ejpam-4787	51	4	)	)	PUNCT
ejpam-4787	52	1	+	+	CCONJ
ejpam-4787	52	2	t(z(xy	t(z(xy	NOUN
ejpam-4787	52	3	)	)	PUNCT
ejpam-4787	52	4	)	)	PUNCT
ejpam-4787	53	1	+	+	CCONJ
ejpam-4787	53	2	x(z(ty	x(z(ty	NOUN
ejpam-4787	53	3	)	)	PUNCT
ejpam-4787	53	4	)	)	PUNCT
ejpam-4787	54	1	+	+	CCONJ
ejpam-4787	54	2	t(x(yz	t(x(yz	X
ejpam-4787	54	3	)	)	PUNCT
ejpam-4787	54	4	)	)	PUNCT
ejpam-4787	55	1	+	+	CCONJ
ejpam-4787	55	2	x(t(yz	x(t(yz	X
ejpam-4787	55	3	)	)	PUNCT
ejpam-4787	55	4	)	)	PUNCT
ejpam-4787	56	1	+	+	CCONJ
ejpam-4787	57	1	z(y(tx	z(y(tx	NUM
ejpam-4787	57	2	)	)	PUNCT
ejpam-4787	57	3	)	)	PUNCT
ejpam-4787	58	1	+	+	CCONJ
ejpam-4787	58	2	t(y(xz	t(y(xz	X
ejpam-4787	58	3	)	)	PUNCT
ejpam-4787	58	4	)	)	PUNCT
ejpam-4787	59	1	+	+	CCONJ
ejpam-4787	59	2	x(y(tz))+y(z(tx))+y(t(xz))+y(x(tz))]+4xt[2z(x(xy))+2x(z(xy))+2x(x(yz))+2x(y(xz))+	x(y(tz))+y(z(tx))+y(t(xz))+y(x(tz))]+4xt[2z(x(xy))+2x(z(xy))+2x(x(yz))+2x(y(xz))+	X
ejpam-4787	59	3	2y(x(xz	2y(x(xz	NUM
ejpam-4787	59	4	)	)	PUNCT
ejpam-4787	59	5	)	)	PUNCT
ejpam-4787	60	1	+	+	CCONJ
ejpam-4787	60	2	z(x2y	z(x2y	X
ejpam-4787	60	3	)	)	PUNCT
ejpam-4787	60	4	+	+	NUM
ejpam-4787	60	5	y(x2z	y(x2z	NOUN
ejpam-4787	60	6	)	)	PUNCT
ejpam-4787	60	7	]	]	PUNCT
ejpam-4787	61	1	+	+	CCONJ
ejpam-4787	61	2	4ty[zx3	4ty[zx3	NUM
ejpam-4787	61	3	+	+	CCONJ
ejpam-4787	61	4	x(zx2	x(zx2	PROPN
ejpam-4787	61	5	)	)	PUNCT
ejpam-4787	61	6	+	+	NUM
ejpam-4787	61	7	2x(x(xz	2x(x(xz	NUM
ejpam-4787	61	8	)	)	PUNCT
ejpam-4787	61	9	)	)	PUNCT
ejpam-4787	61	10	]	]	PUNCT
ejpam-4787	62	1	+	+	PUNCT
ejpam-4787	62	2	4xy[z(tx2	4xy[z(tx2	NUM
ejpam-4787	62	3	)	)	PUNCT
ejpam-4787	63	1	+	+	NUM
ejpam-4787	63	2	2z(x(xt	2z(x(xt	NOUN
ejpam-4787	63	3	)	)	PUNCT
ejpam-4787	63	4	)	)	PUNCT
ejpam-4787	64	1	+	+	X
ejpam-4787	64	2	t(zx2	t(zx2	X
ejpam-4787	64	3	)	)	PUNCT
ejpam-4787	64	4	+	+	NUM
ejpam-4787	64	5	2x(z(xt	2x(z(xt	NUM
ejpam-4787	64	6	)	)	PUNCT
ejpam-4787	64	7	)	)	PUNCT
ejpam-4787	65	1	+	+	CCONJ
ejpam-4787	65	2	2t(x(xz	2t(x(xz	NUM
ejpam-4787	65	3	)	)	PUNCT
ejpam-4787	65	4	)	)	PUNCT
ejpam-4787	66	1	+	+	CCONJ
ejpam-4787	66	2	2x(t(xz	2x(t(xz	NUM
ejpam-4787	66	3	)	)	PUNCT
ejpam-4787	66	4	)	)	PUNCT
ejpam-4787	67	1	+	+	CCONJ
ejpam-4787	67	2	2x(x(tz	2x(x(tz	NUM
ejpam-4787	67	3	)	)	PUNCT
ejpam-4787	67	4	)	)	PUNCT
ejpam-4787	67	5	]	]	PUNCT
ejpam-4787	68	1	+	+	CCONJ
ejpam-4787	68	2	4tz[2x(x(xy	4tz[2x(x(xy	NUM
ejpam-4787	68	3	)	)	PUNCT
ejpam-4787	68	4	)	)	PUNCT
ejpam-4787	69	1	+	+	CCONJ
ejpam-4787	69	2	x(yx2	x(yx2	X
ejpam-4787	69	3	)	)	PUNCT
ejpam-4787	70	1	+	+	X
ejpam-4787	70	2	yx3	yx3	NOUN
ejpam-4787	70	3	]	]	X
ejpam-4787	70	4	+	+	CCONJ
ejpam-4787	70	5	4yz[tx3+x(tx2)+2x(x(xt))]+4xz[2t(x(xy))+2x(t(xy))+2x(x(ty))+t(yx2)+2x(y(xt))+	4yz[tx3+x(tx2)+2x(x(xt))]+4xz[2t(x(xy))+2x(t(xy))+2x(x(ty))+t(yx2)+2x(y(xt))+	NUM
ejpam-4787	70	6	y(tx2	y(tx2	NOUN
ejpam-4787	70	7	)	)	PUNCT
ejpam-4787	70	8	+	+	NUM
ejpam-4787	70	9	2y(x(xt	2y(x(xt	NOUN
ejpam-4787	70	10	)	)	PUNCT
ejpam-4787	70	11	)	)	PUNCT
ejpam-4787	70	12	]	]	PUNCT
ejpam-4787	71	1	=	=	SYM
ejpam-4787	71	2	2ω(tz)[2x(x(xy	2ω(tz)[2x(x(xy	NUM
ejpam-4787	71	3	)	)	PUNCT
ejpam-4787	72	1	+	+	CCONJ
ejpam-4787	73	1	x(x2y	x(x2y	X
ejpam-4787	73	2	)	)	PUNCT
ejpam-4787	73	3	+	+	CCONJ
ejpam-4787	73	4	x3y	x3y	PROPN
ejpam-4787	73	5	]	]	X
ejpam-4787	73	6	+	+	NUM
ejpam-4787	73	7	2ω(xz)[2t(x(xy	2ω(xz)[2t(x(xy	NUM
ejpam-4787	73	8	)	)	PUNCT
ejpam-4787	73	9	+	+	NUM
ejpam-4787	73	10	2x(t(xy	2x(t(xy	NUM
ejpam-4787	73	11	)	)	PUNCT
ejpam-4787	73	12	+	+	NUM
ejpam-4787	73	13	2x(x(ty)+t(x2y)+2x(y(xt)+y(tx2)+2y(x(tx)]+2ω(xt)[2z(x(xy)+2x(z(xy)+2x(x(zy)+	2x(x(ty)+t(x2y)+2x(y(xt)+y(tx2)+2y(x(tx)]+2ω(xt)[2z(x(xy)+2x(z(xy)+2x(x(zy)+	NUM
ejpam-4787	73	14	z(x2y)+2x(y(xz)+y(zx2)+2y(x(zx)]+2ω(x2)[z(t(xy))+z(x(ty))+	z(x2y)+2x(y(xz)+y(zx2)+2y(x(zx)]+2ω(x2)[z(t(xy))+z(x(ty))+	NOUN
ejpam-4787	73	15	t(z(xy))+x(z(ty))+	t(z(xy))+x(z(ty))+	NOUN
ejpam-4787	73	16	t(x(yz	t(x(yz	NOUN
ejpam-4787	73	17	)	)	PUNCT
ejpam-4787	73	18	)	)	PUNCT
ejpam-4787	74	1	+	+	CCONJ
ejpam-4787	74	2	x(t(yz	x(t(yz	X
ejpam-4787	74	3	)	)	PUNCT
ejpam-4787	74	4	)	)	PUNCT
ejpam-4787	75	1	+	+	CCONJ
ejpam-4787	75	2	z(y(xt	z(y(xt	NOUN
ejpam-4787	75	3	)	)	PUNCT
ejpam-4787	75	4	)	)	PUNCT
ejpam-4787	76	1	+	+	CCONJ
ejpam-4787	76	2	t(y(xz	t(y(xz	X
ejpam-4787	76	3	)	)	PUNCT
ejpam-4787	76	4	)	)	PUNCT
ejpam-4787	77	1	+	+	CCONJ
ejpam-4787	77	2	x(y(tz	x(y(tz	NOUN
ejpam-4787	77	3	)	)	PUNCT
ejpam-4787	77	4	)	)	PUNCT
ejpam-4787	78	1	+	+	CCONJ
ejpam-4787	78	2	y(z(xt	y(z(xt	NOUN
ejpam-4787	78	3	)	)	PUNCT
ejpam-4787	78	4	)	)	PUNCT
ejpam-4787	79	1	+	+	CCONJ
ejpam-4787	79	2	y(t(xz	y(t(xz	NOUN
ejpam-4787	79	3	)	)	PUNCT
ejpam-4787	79	4	)	)	PUNCT
ejpam-4787	80	1	+	+	CCONJ
ejpam-4787	80	2	y(x(tz	y(x(tz	NOUN
ejpam-4787	80	3	)	)	PUNCT
ejpam-4787	80	4	)	)	PUNCT
ejpam-4787	80	5	]	]	PUNCT
ejpam-4787	81	1	+	+	CCONJ
ejpam-4787	81	2	24[ω(xyzt)x2+ω(yzx2)xt+ω(ytx2)xz+ω(ztx2)xy]+8[ω(x3y)zt+ω(x3z)yt+ω(x3t)zy]+	24[ω(xyzt)x2+ω(yzx2)xt+ω(ytx2)xz+ω(ztx2)xy]+8[ω(x3y)zt+ω(x3z)yt+ω(x3t)zy]+	NUM
ejpam-4787	81	3	2ω(yz)[tx3	2ω(yz)[tx3	NOUN
ejpam-4787	81	4	+	+	CCONJ
ejpam-4787	81	5	x(tx2	x(tx2	X
ejpam-4787	81	6	)	)	PUNCT
ejpam-4787	81	7	+	+	NUM
ejpam-4787	81	8	2x(x(xt	2x(x(xt	NUM
ejpam-4787	81	9	)	)	PUNCT
ejpam-4787	81	10	)	)	PUNCT
ejpam-4787	81	11	]	]	PUNCT
ejpam-4787	82	1	+	+	CCONJ
ejpam-4787	82	2	2ω(ty)[zx3	2ω(ty)[zx3	NUM
ejpam-4787	82	3	+	+	CCONJ
ejpam-4787	82	4	x(zx2	x(zx2	PROPN
ejpam-4787	82	5	)	)	PUNCT
ejpam-4787	82	6	+	+	NUM
ejpam-4787	82	7	2x(x(xz	2x(x(xz	NUM
ejpam-4787	82	8	)	)	PUNCT
ejpam-4787	82	9	)	)	PUNCT
ejpam-4787	82	10	]	]	PUNCT
ejpam-4787	83	1	+	+	CCONJ
ejpam-4787	83	2	2ω(xy)[z(tx2	2ω(xy)[z(tx2	NUM
ejpam-4787	83	3	)	)	PUNCT
ejpam-4787	84	1	+	+	X
ejpam-4787	84	2	t(zx2	t(zx2	X
ejpam-4787	84	3	)	)	PUNCT
ejpam-4787	84	4	+	+	NUM
ejpam-4787	84	5	2z(x(xt	2z(x(xt	NOUN
ejpam-4787	84	6	)	)	PUNCT
ejpam-4787	84	7	)	)	PUNCT
ejpam-4787	85	1	+	+	CCONJ
ejpam-4787	85	2	2x(z(xt	2x(z(xt	NUM
ejpam-4787	85	3	)	)	PUNCT
ejpam-4787	85	4	)	)	PUNCT
ejpam-4787	86	1	+	+	CCONJ
ejpam-4787	86	2	2t(x(xz	2t(x(xz	NUM
ejpam-4787	86	3	)	)	PUNCT
ejpam-4787	86	4	)	)	PUNCT
ejpam-4787	87	1	+	+	CCONJ
ejpam-4787	87	2	2x(t(xz	2x(t(xz	NUM
ejpam-4787	87	3	)	)	PUNCT
ejpam-4787	87	4	)	)	PUNCT
ejpam-4787	88	1	+	+	CCONJ
ejpam-4787	88	2	2x(x(zt	2x(x(zt	NUM
ejpam-4787	88	3	)	)	PUNCT
ejpam-4787	88	4	)	)	PUNCT
ejpam-4787	88	5	]	]	PUNCT
ejpam-4787	89	1	the	the	DET
ejpam-4787	89	2	previous	previous	ADJ
ejpam-4787	89	3	proposition	proposition	NOUN
ejpam-4787	89	4	allows	allow	VERB
ejpam-4787	89	5	us	we	PRON
ejpam-4787	89	6	to	to	PART
ejpam-4787	89	7	establish	establish	VERB
ejpam-4787	89	8	the	the	DET
ejpam-4787	89	9	following	follow	VERB
ejpam-4787	89	10	lemma	lemma	PROPN
ejpam-4787	89	11	.	.	PUNCT
ejpam-4787	90	1	lemma	lemma	PROPN
ejpam-4787	90	2	1	1	NUM
ejpam-4787	90	3	.	.	PUNCT
ejpam-4787	91	1	for	for	ADP
ejpam-4787	91	2	all	all	DET
ejpam-4787	91	3	x0	x0	PROPN
ejpam-4787	91	4	,	,	PUNCT
ejpam-4787	91	5	y0	y0	PROPN
ejpam-4787	91	6	,	,	PUNCT
ejpam-4787	91	7	z0	z0	PROPN
ejpam-4787	91	8	∈	∈	PROPN
ejpam-4787	91	9	a0	a0	NOUN
ejpam-4787	91	10	;	;	PUNCT
ejpam-4787	91	11	x	x	SYM
ejpam-4787	91	12	1	1	NUM
ejpam-4787	91	13	2	2	NUM
ejpam-4787	91	14	,	,	PUNCT
ejpam-4787	91	15	y	y	PROPN
ejpam-4787	91	16	1	1	NUM
ejpam-4787	91	17	2	2	NUM
ejpam-4787	91	18	,	,	PUNCT
ejpam-4787	91	19	z	z	NOUN
ejpam-4787	91	20	1	1	NUM
ejpam-4787	91	21	2	2	NUM
ejpam-4787	91	22	∈	∈	NOUN
ejpam-4787	91	23	a	a	DET
ejpam-4787	91	24	1	1	NUM
ejpam-4787	91	25	2	2	NUM
ejpam-4787	91	26	;	;	PUNCT
ejpam-4787	91	27	xλ	xλ	PROPN
ejpam-4787	91	28	,	,	PUNCT
ejpam-4787	91	29	yλ	yλ	PROPN
ejpam-4787	91	30	,	,	PUNCT
ejpam-4787	91	31	zλ	zλ	X
ejpam-4787	91	32	∈	∈	ADJ
ejpam-4787	91	33	aλ	aλ	PROPN
ejpam-4787	91	34	;	;	PUNCT
ejpam-4787	91	35	xλ̄	xλ̄	ADJ
ejpam-4787	91	36	,	,	PUNCT
ejpam-4787	91	37	yλ̄	yλ̄	PROPN
ejpam-4787	91	38	,	,	PUNCT
ejpam-4787	91	39	zλ̄	zλ̄	PROPN
ejpam-4787	91	40	∈	∈	PROPN
ejpam-4787	91	41	aλ̄	aλ̄	NOUN
ejpam-4787	91	42	the	the	DET
ejpam-4787	91	43	following	follow	VERB
ejpam-4787	91	44	identities	identity	NOUN
ejpam-4787	91	45	are	be	AUX
ejpam-4787	91	46	verified	verify	VERB
ejpam-4787	91	47	:	:	PUNCT
ejpam-4787	92	1	1	1	X
ejpam-4787	92	2	)	)	PUNCT
ejpam-4787	93	1	[	[	X
ejpam-4787	93	2	z0(x0y0	z0(x0y0	X
ejpam-4787	93	3	)	)	PUNCT
ejpam-4787	94	1	+	+	CCONJ
ejpam-4787	94	2	x0(y0z0	x0(y0z0	PROPN
ejpam-4787	94	3	)	)	PUNCT
ejpam-4787	95	1	+	+	NUM
ejpam-4787	95	2	y0(x0z0)]λ	y0(x0z0)]λ	NOUN
ejpam-4787	95	3	=	=	PUNCT
ejpam-4787	96	1	[	[	X
ejpam-4787	96	2	z0(x0y0	z0(x0y0	X
ejpam-4787	96	3	)	)	PUNCT
ejpam-4787	97	1	+	+	CCONJ
ejpam-4787	97	2	x0(y0z0	x0(y0z0	PROPN
ejpam-4787	97	3	)	)	PUNCT
ejpam-4787	98	1	+	+	NUM
ejpam-4787	98	2	y0(x0z0)]λ̄	y0(x0z0)]λ̄	NOUN
ejpam-4787	98	3	=	=	SYM
ejpam-4787	98	4	0	0	NUM
ejpam-4787	98	5	;	;	PUNCT
ejpam-4787	98	6	2	2	X
ejpam-4787	98	7	)	)	PUNCT
ejpam-4787	99	1	[	[	X
ejpam-4787	99	2	4(x	4(x	NUM
ejpam-4787	99	3	1	1	NUM
ejpam-4787	99	4	2	2	NUM
ejpam-4787	99	5	(	(	PUNCT
ejpam-4787	99	6	y	y	NOUN
ejpam-4787	99	7	1	1	NUM
ejpam-4787	99	8	2	2	NUM
ejpam-4787	99	9	z	z	NOUN
ejpam-4787	99	10	1	1	NUM
ejpam-4787	99	11	2	2	NUM
ejpam-4787	99	12	)	)	PUNCT
ejpam-4787	99	13	0+y	0+y	NUM
ejpam-4787	99	14	1	1	NUM
ejpam-4787	99	15	2	2	NUM
ejpam-4787	99	16	(	(	PUNCT
ejpam-4787	99	17	x	x	NOUN
ejpam-4787	99	18	1	1	NUM
ejpam-4787	99	19	2	2	NUM
ejpam-4787	99	20	z	z	NOUN
ejpam-4787	99	21	1	1	NUM
ejpam-4787	99	22	2	2	NUM
ejpam-4787	99	23	)	)	PUNCT
ejpam-4787	99	24	0+z	0+z	NUM
ejpam-4787	99	25	1	1	NUM
ejpam-4787	99	26	2	2	NUM
ejpam-4787	99	27	(	(	PUNCT
ejpam-4787	99	28	y	y	NOUN
ejpam-4787	99	29	1	1	NUM
ejpam-4787	99	30	2	2	NUM
ejpam-4787	99	31	x	x	SYM
ejpam-4787	99	32	1	1	NUM
ejpam-4787	99	33	2	2	NUM
ejpam-4787	99	34	)	)	PUNCT
ejpam-4787	99	35	0)+(λ+1)(x	0)+(λ+1)(x	NOUN
ejpam-4787	99	36	1	1	NUM
ejpam-4787	99	37	2	2	NUM
ejpam-4787	99	38	(	(	PUNCT
ejpam-4787	99	39	y	y	NOUN
ejpam-4787	99	40	1	1	NUM
ejpam-4787	99	41	2	2	NUM
ejpam-4787	99	42	z	z	NOUN
ejpam-4787	99	43	1	1	NUM
ejpam-4787	99	44	2	2	NUM
ejpam-4787	99	45	)	)	PUNCT
ejpam-4787	99	46	λ+y	λ+y	NOUN
ejpam-4787	99	47	1	1	NUM
ejpam-4787	99	48	2	2	NUM
ejpam-4787	99	49	(	(	PUNCT
ejpam-4787	99	50	x	x	NOUN
ejpam-4787	99	51	1	1	NUM
ejpam-4787	99	52	2	2	NUM
ejpam-4787	99	53	z	z	NOUN
ejpam-4787	99	54	1	1	NUM
ejpam-4787	99	55	2	2	NUM
ejpam-4787	99	56	)	)	PUNCT
ejpam-4787	99	57	λ+z	λ+z	PROPN
ejpam-4787	99	58	1	1	NUM
ejpam-4787	99	59	2	2	NUM
ejpam-4787	99	60	(	(	PUNCT
ejpam-4787	99	61	y	y	NOUN
ejpam-4787	99	62	1	1	NUM
ejpam-4787	99	63	2	2	NUM
ejpam-4787	99	64	x	x	SYM
ejpam-4787	99	65	1	1	NUM
ejpam-4787	99	66	2	2	NUM
ejpam-4787	99	67	)	)	PUNCT
ejpam-4787	99	68	λ)+	λ)+	PROPN
ejpam-4787	99	69	(	(	PUNCT
ejpam-4787	99	70	λ̄+	λ̄+	NUM
ejpam-4787	99	71	1)(x	1)(x	NUM
ejpam-4787	99	72	1	1	NUM
ejpam-4787	99	73	2	2	NUM
ejpam-4787	99	74	(	(	PUNCT
ejpam-4787	99	75	y	y	NOUN
ejpam-4787	99	76	1	1	NUM
ejpam-4787	99	77	2	2	NUM
ejpam-4787	99	78	z	z	NOUN
ejpam-4787	99	79	1	1	NUM
ejpam-4787	99	80	2	2	NUM
ejpam-4787	99	81	)	)	PUNCT
ejpam-4787	99	82	λ̄	λ̄	VERB
ejpam-4787	100	1	+	+	CCONJ
ejpam-4787	100	2	y	y	PROPN
ejpam-4787	100	3	1	1	NUM
ejpam-4787	100	4	2	2	NUM
ejpam-4787	100	5	(	(	PUNCT
ejpam-4787	100	6	x	x	NOUN
ejpam-4787	100	7	1	1	NUM
ejpam-4787	100	8	2	2	NUM
ejpam-4787	100	9	z	z	NOUN
ejpam-4787	100	10	1	1	NUM
ejpam-4787	100	11	2	2	NUM
ejpam-4787	100	12	)	)	PUNCT
ejpam-4787	100	13	λ̄	λ̄	VERB
ejpam-4787	101	1	+	+	CCONJ
ejpam-4787	101	2	z	z	NOUN
ejpam-4787	101	3	1	1	NUM
ejpam-4787	101	4	2	2	NUM
ejpam-4787	101	5	(	(	PUNCT
ejpam-4787	101	6	y	y	NOUN
ejpam-4787	101	7	1	1	NUM
ejpam-4787	101	8	2	2	NUM
ejpam-4787	101	9	x	x	SYM
ejpam-4787	101	10	1	1	NUM
ejpam-4787	101	11	2	2	NUM
ejpam-4787	101	12	)	)	PUNCT
ejpam-4787	101	13	λ̄	λ̄	PUNCT
ejpam-4787	101	14	)	)	PUNCT
ejpam-4787	101	15	]	]	PUNCT
ejpam-4787	101	16	1	1	NUM
ejpam-4787	101	17	2	2	NUM
ejpam-4787	101	18	=	=	SYM
ejpam-4787	101	19	0	0	NUM
ejpam-4787	101	20	;	;	PUNCT
ejpam-4787	101	21	3	3	X
ejpam-4787	101	22	)	)	PUNCT
ejpam-4787	101	23	(	(	PUNCT
ejpam-4787	101	24	x	x	SYM
ejpam-4787	101	25	1	1	NUM
ejpam-4787	101	26	2	2	NUM
ejpam-4787	101	27	(	(	PUNCT
ejpam-4787	101	28	y0z0))0	y0z0))0	X
ejpam-4787	101	29	=	=	SYM
ejpam-4787	101	30	0	0	NUM
ejpam-4787	101	31	;	;	PUNCT
ejpam-4787	101	32	4	4	NUM
ejpam-4787	101	33	)	)	PUNCT
ejpam-4787	101	34	(	(	PUNCT
ejpam-4787	101	35	λ+	λ+	NUM
ejpam-4787	101	36	1)(x	1)(x	NUM
ejpam-4787	101	37	1	1	NUM
ejpam-4787	101	38	2	2	NUM
ejpam-4787	101	39	(	(	PUNCT
ejpam-4787	101	40	y0z0))λ	y0z0))λ	PROPN
ejpam-4787	101	41	=	=	NOUN
ejpam-4787	101	42	−4(y0(x	−4(y0(x	NOUN
ejpam-4787	101	43	1	1	NUM
ejpam-4787	101	44	2	2	NUM
ejpam-4787	101	45	z0	z0	NOUN
ejpam-4787	101	46	)	)	PUNCT
ejpam-4787	101	47	1	1	NUM
ejpam-4787	101	48	2	2	NUM
ejpam-4787	101	49	+	+	CCONJ
ejpam-4787	101	50	z0(y0x	z0(y0x	NUM
ejpam-4787	101	51	1	1	NUM
ejpam-4787	101	52	2	2	NUM
ejpam-4787	101	53	)	)	PUNCT
ejpam-4787	101	54	1	1	NUM
ejpam-4787	101	55	2	2	NUM
ejpam-4787	101	56	)	)	PUNCT
ejpam-4787	101	57	λ	λ	NOUN
ejpam-4787	101	58	;	;	PUNCT
ejpam-4787	101	59	5	5	NUM
ejpam-4787	101	60	)	)	PUNCT
ejpam-4787	101	61	(	(	PUNCT
ejpam-4787	101	62	λ̄+	λ̄+	NUM
ejpam-4787	101	63	1)(x	1)(x	NUM
ejpam-4787	101	64	1	1	NUM
ejpam-4787	101	65	2	2	NUM
ejpam-4787	101	66	(	(	PUNCT
ejpam-4787	101	67	y0z0))λ̄	y0z0))λ̄	PROPN
ejpam-4787	101	68	=	=	NOUN
ejpam-4787	101	69	−4(y0(x	−4(y0(x	NOUN
ejpam-4787	101	70	1	1	NUM
ejpam-4787	101	71	2	2	NUM
ejpam-4787	101	72	z0	z0	NOUN
ejpam-4787	101	73	)	)	PUNCT
ejpam-4787	101	74	1	1	NUM
ejpam-4787	101	75	2	2	NUM
ejpam-4787	101	76	+	+	CCONJ
ejpam-4787	101	77	z0(y0x	z0(y0x	NUM
ejpam-4787	101	78	1	1	NUM
ejpam-4787	101	79	2	2	NUM
ejpam-4787	101	80	)	)	PUNCT
ejpam-4787	101	81	1	1	NUM
ejpam-4787	101	82	2	2	NUM
ejpam-4787	101	83	)	)	PUNCT
ejpam-4787	101	84	λ̄	λ̄	NOUN
ejpam-4787	101	85	;	;	PUNCT
ejpam-4787	101	86	6	6	X
ejpam-4787	101	87	)	)	PUNCT
ejpam-4787	102	1	[	[	X
ejpam-4787	102	2	xλ̄(y0z0)]0	xλ̄(y0z0)]0	X
ejpam-4787	102	3	=	=	SYM
ejpam-4787	103	1	[	[	X
ejpam-4787	103	2	xλ(y0z0)]0	xλ(y0z0)]0	PROPN
ejpam-4787	103	3	=	=	SYM
ejpam-4787	103	4	0	0	NUM
ejpam-4787	103	5	;	;	PUNCT
ejpam-4787	103	6	7	7	X
ejpam-4787	103	7	)	)	PUNCT
ejpam-4787	103	8	[	[	X
ejpam-4787	103	9	yλ(x0zλ	yλ(x0zλ	NOUN
ejpam-4787	103	10	)	)	PUNCT
ejpam-4787	103	11	1	1	NUM
ejpam-4787	103	12	2	2	NUM
ejpam-4787	103	13	]	]	SYM
ejpam-4787	103	14	0	0	PUNCT
ejpam-4787	104	1	=	=	PUNCT
ejpam-4787	105	1	[	[	X
ejpam-4787	105	2	yλ̄(x0zλ̄	yλ̄(x0zλ̄	PROPN
ejpam-4787	105	3	)	)	PUNCT
ejpam-4787	105	4	1	1	NUM
ejpam-4787	105	5	2	2	NUM
ejpam-4787	105	6	]	]	SYM
ejpam-4787	105	7	0	0	NUM
ejpam-4787	106	1	=	=	SYM
ejpam-4787	106	2	0	0	NUM
ejpam-4787	106	3	;	;	PUNCT
ejpam-4787	106	4	8)	8)	NUM
ejpam-4787	106	5	[	[	X
ejpam-4787	106	6	xλ(y0z0	xλ(y0z0	PROPN
ejpam-4787	106	7	)	)	PUNCT
ejpam-4787	106	8	]	]	PUNCT
ejpam-4787	107	1	1	1	NUM
ejpam-4787	107	2	2	2	NUM
ejpam-4787	107	3	=	=	SYM
ejpam-4787	107	4	[	[	X
ejpam-4787	107	5	xλ̄(y0z0	xλ̄(y0z0	PROPN
ejpam-4787	107	6	)	)	PUNCT
ejpam-4787	107	7	]	]	PUNCT
ejpam-4787	107	8	1	1	NUM
ejpam-4787	107	9	2	2	NUM
ejpam-4787	107	10	=	=	SYM
ejpam-4787	107	11	0	0	NUM
ejpam-4787	107	12	;	;	PUNCT
ejpam-4787	107	13	9	9	NUM
ejpam-4787	107	14	)	)	PUNCT
ejpam-4787	107	15	[	[	X
ejpam-4787	107	16	yλ(x0zλ	yλ(x0zλ	NOUN
ejpam-4787	107	17	)	)	PUNCT
ejpam-4787	107	18	1	1	NUM
ejpam-4787	107	19	2	2	NUM
ejpam-4787	107	20	]	]	SYM
ejpam-4787	107	21	1	1	NUM
ejpam-4787	107	22	2	2	NUM
ejpam-4787	107	23	=	=	SYM
ejpam-4787	108	1	[	[	X
ejpam-4787	108	2	yλ̄(x0zλ̄	yλ̄(x0zλ̄	PROPN
ejpam-4787	108	3	)	)	PUNCT
ejpam-4787	108	4	1	1	NUM
ejpam-4787	108	5	2	2	NUM
ejpam-4787	108	6	]	]	SYM
ejpam-4787	108	7	1	1	NUM
ejpam-4787	108	8	2	2	NUM
ejpam-4787	108	9	=	=	SYM
ejpam-4787	108	10	0	0	NUM
ejpam-4787	108	11	;	;	PUNCT
ejpam-4787	108	12	10	10	NUM
ejpam-4787	108	13	)	)	PUNCT
ejpam-4787	109	1	[	[	X
ejpam-4787	109	2	xλ(y0z0	xλ(y0z0	PROPN
ejpam-4787	109	3	)	)	PUNCT
ejpam-4787	109	4	1	1	NUM
ejpam-4787	109	5	2	2	NUM
ejpam-4787	109	6	]	]	PUNCT
ejpam-4787	109	7	λ̄	λ̄	X
ejpam-4787	109	8	=	=	PUNCT
ejpam-4787	110	1	[	[	X
ejpam-4787	110	2	xλ̄(y0z0	xλ̄(y0z0	X
ejpam-4787	110	3	)	)	PUNCT
ejpam-4787	110	4	1	1	NUM
ejpam-4787	110	5	2	2	NUM
ejpam-4787	110	6	]	]	PUNCT
ejpam-4787	110	7	λ	λ	X
ejpam-4787	110	8	=	=	SYM
ejpam-4787	110	9	0	0	NUM
ejpam-4787	110	10	;	;	PUNCT
ejpam-4787	110	11	11	11	NUM
ejpam-4787	110	12	)	)	PUNCT
ejpam-4787	111	1	[	[	X
ejpam-4787	111	2	yλ(x0zλ	yλ(x0zλ	NOUN
ejpam-4787	111	3	)	)	PUNCT
ejpam-4787	111	4	1	1	NUM
ejpam-4787	111	5	2	2	NUM
ejpam-4787	111	6	]	]	PUNCT
ejpam-4787	111	7	λ̄	λ̄	X
ejpam-4787	111	8	=	=	PUNCT
ejpam-4787	112	1	[	[	X
ejpam-4787	112	2	yλ̄(x0zλ̄	yλ̄(x0zλ̄	PROPN
ejpam-4787	112	3	)	)	PUNCT
ejpam-4787	112	4	1	1	NUM
ejpam-4787	112	5	2	2	NUM
ejpam-4787	112	6	]	]	PUNCT
ejpam-4787	112	7	λ̄	λ̄	X
ejpam-4787	112	8	=	=	SYM
ejpam-4787	112	9	0	0	NUM
ejpam-4787	112	10	;	;	PUNCT
ejpam-4787	112	11	d.	d.	PROPN
ejpam-4787	112	12	kabre	kabre	PROPN
ejpam-4787	112	13	,	,	PUNCT
ejpam-4787	112	14	a.	a.	NOUN
ejpam-4787	112	15	conseibo	conseibo	PROPN
ejpam-4787	112	16	/	/	SYM
ejpam-4787	112	17	eur	eur	PROPN
ejpam-4787	112	18	.	.	PUNCT
ejpam-4787	113	1	j.	j.	PROPN
ejpam-4787	113	2	pure	pure	PROPN
ejpam-4787	113	3	appl	appl	PROPN
ejpam-4787	113	4	.	.	PROPN
ejpam-4787	113	5	math	math	PROPN
ejpam-4787	113	6	,	,	PUNCT
ejpam-4787	113	7	16	16	NUM
ejpam-4787	113	8	(	(	PUNCT
ejpam-4787	113	9	3	3	NUM
ejpam-4787	113	10	)	)	PUNCT
ejpam-4787	113	11	(	(	PUNCT
ejpam-4787	113	12	2023	2023	NUM
ejpam-4787	113	13	)	)	PUNCT
ejpam-4787	113	14	,	,	PUNCT
ejpam-4787	113	15	1480	1480	NUM
ejpam-4787	113	16	-	-	SYM
ejpam-4787	113	17	1490	1490	NUM
ejpam-4787	113	18	1483	1483	NUM
ejpam-4787	113	19	12	12	NUM
ejpam-4787	113	20	)	)	PUNCT
ejpam-4787	114	1	[	[	X
ejpam-4787	114	2	y0(xλ̄z0	y0(xλ̄z0	X
ejpam-4787	114	3	)	)	PUNCT
ejpam-4787	114	4	1	1	NUM
ejpam-4787	114	5	2	2	NUM
ejpam-4787	114	6	+	+	NUM
ejpam-4787	114	7	z0(xλ̄y0	z0(xλ̄y0	NOUN
ejpam-4787	114	8	)	)	PUNCT
ejpam-4787	114	9	1	1	NUM
ejpam-4787	114	10	2	2	NUM
ejpam-4787	114	11	]	]	PUNCT
ejpam-4787	114	12	λ̄	λ̄	X
ejpam-4787	114	13	=	=	SYM
ejpam-4787	114	14	0	0	NUM
ejpam-4787	114	15	;	;	PUNCT
ejpam-4787	114	16	13	13	NUM
ejpam-4787	114	17	)	)	PUNCT
ejpam-4787	115	1	[	[	X
ejpam-4787	115	2	y0(xλz0	y0(xλz0	NUM
ejpam-4787	115	3	)	)	PUNCT
ejpam-4787	115	4	1	1	NUM
ejpam-4787	115	5	2	2	NUM
ejpam-4787	115	6	+	+	SYM
ejpam-4787	115	7	z0(xλy0	z0(xλy0	NOUN
ejpam-4787	115	8	)	)	PUNCT
ejpam-4787	115	9	1	1	NUM
ejpam-4787	115	10	2	2	NUM
ejpam-4787	115	11	]	]	PUNCT
ejpam-4787	115	12	λ	λ	X
ejpam-4787	115	13	=	=	SYM
ejpam-4787	115	14	0	0	NUM
ejpam-4787	115	15	;	;	PUNCT
ejpam-4787	115	16	14	14	NUM
ejpam-4787	115	17	)	)	PUNCT
ejpam-4787	115	18	(	(	PUNCT
ejpam-4787	115	19	−2λ−	−2λ−	VERB
ejpam-4787	115	20	1)((y	1)((y	PROPN
ejpam-4787	115	21	1	1	NUM
ejpam-4787	115	22	2	2	NUM
ejpam-4787	115	23	(	(	PUNCT
ejpam-4787	115	24	x0z	x0z	SYM
ejpam-4787	115	25	1	1	NUM
ejpam-4787	115	26	2	2	NUM
ejpam-4787	115	27	)	)	PUNCT
ejpam-4787	115	28	λ)0+(z	λ)0+(z	SYM
ejpam-4787	115	29	1	1	NUM
ejpam-4787	115	30	2	2	NUM
ejpam-4787	115	31	(	(	PUNCT
ejpam-4787	115	32	x0y	x0y	NOUN
ejpam-4787	115	33	1	1	NUM
ejpam-4787	115	34	2	2	NUM
ejpam-4787	115	35	)	)	PUNCT
ejpam-4787	115	36	λ)0)+	λ)0)+	PROPN
ejpam-4787	115	37	(	(	PUNCT
ejpam-4787	115	38	−2λ̄−	−2λ̄−	NOUN
ejpam-4787	115	39	1)((y	1)((y	NOUN
ejpam-4787	115	40	1	1	NUM
ejpam-4787	115	41	2	2	NUM
ejpam-4787	115	42	(	(	PUNCT
ejpam-4787	115	43	x0z	x0z	SYM
ejpam-4787	115	44	1	1	NUM
ejpam-4787	115	45	2	2	NUM
ejpam-4787	115	46	)	)	PUNCT
ejpam-4787	115	47	λ̄)0+(z	λ̄)0+(z	CCONJ
ejpam-4787	115	48	1	1	NUM
ejpam-4787	115	49	2	2	NUM
ejpam-4787	115	50	(	(	PUNCT
ejpam-4787	115	51	x0y	x0y	NOUN
ejpam-4787	115	52	1	1	NUM
ejpam-4787	115	53	2	2	NUM
ejpam-4787	115	54	)	)	PUNCT
ejpam-4787	115	55	λ̄)0)+	λ̄)0)+	NOUN
ejpam-4787	115	56	6(y	6(y	NUM
ejpam-4787	115	57	1	1	NUM
ejpam-4787	115	58	2	2	NUM
ejpam-4787	115	59	(	(	PUNCT
ejpam-4787	115	60	x0z	x0z	SYM
ejpam-4787	115	61	1	1	NUM
ejpam-4787	115	62	2	2	NUM
ejpam-4787	115	63	)	)	PUNCT
ejpam-4787	115	64	1	1	NUM
ejpam-4787	115	65	2	2	NUM
ejpam-4787	115	66	)	)	PUNCT
ejpam-4787	115	67	0	0	PUNCT
ejpam-4787	116	1	+	+	CCONJ
ejpam-4787	116	2	(	(	PUNCT
ejpam-4787	116	3	z	z	NOUN
ejpam-4787	116	4	1	1	NUM
ejpam-4787	116	5	2	2	NUM
ejpam-4787	116	6	(	(	PUNCT
ejpam-4787	116	7	x0y	x0y	NOUN
ejpam-4787	116	8	1	1	NUM
ejpam-4787	116	9	2	2	NUM
ejpam-4787	116	10	)	)	PUNCT
ejpam-4787	116	11	1	1	NUM
ejpam-4787	116	12	2	2	NUM
ejpam-4787	116	13	)	)	PUNCT
ejpam-4787	116	14	0	0	NUM
ejpam-4787	117	1	=	=	SYM
ejpam-4787	117	2	0	0	NUM
ejpam-4787	117	3	;	;	PUNCT
ejpam-4787	117	4	15	15	NUM
ejpam-4787	117	5	)	)	PUNCT
ejpam-4787	117	6	(	(	PUNCT
ejpam-4787	117	7	xλ(y	xλ(y	SYM
ejpam-4787	117	8	1	1	NUM
ejpam-4787	117	9	2	2	NUM
ejpam-4787	117	10	z	z	NOUN
ejpam-4787	117	11	1	1	NUM
ejpam-4787	117	12	2	2	NUM
ejpam-4787	117	13	)	)	PUNCT
ejpam-4787	117	14	0	0	NUM
ejpam-4787	117	15	)	)	PUNCT
ejpam-4787	117	16	1	1	NUM
ejpam-4787	117	17	2	2	NUM
ejpam-4787	117	18	=	=	SYM
ejpam-4787	117	19	(	(	PUNCT
ejpam-4787	117	20	xλ̄(y	xλ̄(y	NOUN
ejpam-4787	117	21	1	1	NUM
ejpam-4787	117	22	2	2	NUM
ejpam-4787	117	23	z	z	NOUN
ejpam-4787	117	24	1	1	NUM
ejpam-4787	117	25	2	2	NUM
ejpam-4787	117	26	)	)	PUNCT
ejpam-4787	117	27	0	0	NUM
ejpam-4787	117	28	)	)	PUNCT
ejpam-4787	117	29	1	1	NUM
ejpam-4787	117	30	2	2	NUM
ejpam-4787	117	31	;	;	PUNCT
ejpam-4787	117	32	16	16	NUM
ejpam-4787	117	33	)	)	PUNCT
ejpam-4787	117	34	(	(	PUNCT
ejpam-4787	117	35	−6λ−13)((y	−6λ−13)((y	NOUN
ejpam-4787	117	36	1	1	NUM
ejpam-4787	117	37	2	2	NUM
ejpam-4787	117	38	(	(	PUNCT
ejpam-4787	117	39	xλz	xλz	PROPN
ejpam-4787	117	40	1	1	NUM
ejpam-4787	117	41	2	2	NUM
ejpam-4787	117	42	)	)	PUNCT
ejpam-4787	117	43	0)λ+(z	0)λ+(z	NOUN
ejpam-4787	117	44	1	1	NUM
ejpam-4787	117	45	2	2	NUM
ejpam-4787	117	46	(	(	PUNCT
ejpam-4787	117	47	xλy	xλy	PROPN
ejpam-4787	117	48	1	1	NUM
ejpam-4787	117	49	2	2	NUM
ejpam-4787	117	50	)	)	PUNCT
ejpam-4787	117	51	0)λ)+(−6λ−2λ̄−7)((y	0)λ)+(−6λ−2λ̄−7)((y	NOUN
ejpam-4787	117	52	1	1	NUM
ejpam-4787	117	53	2	2	NUM
ejpam-4787	117	54	(	(	PUNCT
ejpam-4787	117	55	xλz	xλz	PROPN
ejpam-4787	117	56	1	1	NUM
ejpam-4787	117	57	2	2	NUM
ejpam-4787	117	58	)	)	PUNCT
ejpam-4787	117	59	λ̄)λ+(z	λ̄)λ+(z	NOUN
ejpam-4787	117	60	1	1	NUM
ejpam-4787	117	61	2	2	NUM
ejpam-4787	117	62	(	(	PUNCT
ejpam-4787	117	63	xλy	xλy	PROPN
ejpam-4787	117	64	1	1	NUM
ejpam-4787	117	65	2	2	NUM
ejpam-4787	117	66	)	)	PUNCT
ejpam-4787	117	67	λ̄)λ)+	λ̄)λ)+	NOUN
ejpam-4787	117	68	(	(	PUNCT
ejpam-4787	117	69	−2λ−	−2λ−	NOUN
ejpam-4787	117	70	12)((y	12)((y	NUM
ejpam-4787	117	71	1	1	NUM
ejpam-4787	117	72	2	2	NUM
ejpam-4787	117	73	(	(	PUNCT
ejpam-4787	117	74	xλz	xλz	PROPN
ejpam-4787	117	75	1	1	NUM
ejpam-4787	117	76	2	2	NUM
ejpam-4787	117	77	)	)	PUNCT
ejpam-4787	117	78	1	1	NUM
ejpam-4787	117	79	2	2	NUM
ejpam-4787	117	80	)	)	PUNCT
ejpam-4787	118	1	λ	λ	NOUN
ejpam-4787	118	2	+	+	CCONJ
ejpam-4787	118	3	(	(	PUNCT
ejpam-4787	118	4	z	z	NOUN
ejpam-4787	118	5	1	1	NUM
ejpam-4787	118	6	2	2	NUM
ejpam-4787	118	7	(	(	PUNCT
ejpam-4787	118	8	xλy	xλy	PROPN
ejpam-4787	118	9	1	1	NUM
ejpam-4787	118	10	2	2	NUM
ejpam-4787	118	11	)	)	PUNCT
ejpam-4787	118	12	1	1	NUM
ejpam-4787	118	13	2	2	NUM
ejpam-4787	118	14	)	)	PUNCT
ejpam-4787	118	15	λ	λ	NOUN
ejpam-4787	118	16	)	)	PUNCT
ejpam-4787	118	17	=	=	SYM
ejpam-4787	118	18	0	0	NUM
ejpam-4787	118	19	;	;	PUNCT
ejpam-4787	118	20	17	17	NUM
ejpam-4787	118	21	)	)	PUNCT
ejpam-4787	118	22	(	(	PUNCT
ejpam-4787	118	23	−6λ̄−13)((y	−6λ̄−13)((y	NOUN
ejpam-4787	118	24	1	1	NUM
ejpam-4787	118	25	2	2	NUM
ejpam-4787	118	26	(	(	PUNCT
ejpam-4787	118	27	xλ̄z	xλ̄z	NOUN
ejpam-4787	118	28	1	1	NUM
ejpam-4787	118	29	2	2	NUM
ejpam-4787	118	30	)	)	PUNCT
ejpam-4787	118	31	0)λ̄+(z	0)λ̄+(z	NOUN
ejpam-4787	118	32	1	1	NUM
ejpam-4787	118	33	2	2	NUM
ejpam-4787	118	34	(	(	PUNCT
ejpam-4787	118	35	xλ̄y	xλ̄y	NOUN
ejpam-4787	118	36	1	1	NUM
ejpam-4787	118	37	2	2	NUM
ejpam-4787	118	38	)	)	PUNCT
ejpam-4787	118	39	0)λ̄)+(−6λ̄−2λ−7)((y	0)λ̄)+(−6λ̄−2λ−7)((y	NUM
ejpam-4787	118	40	1	1	NUM
ejpam-4787	118	41	2	2	NUM
ejpam-4787	118	42	(	(	PUNCT
ejpam-4787	118	43	xλ̄z	xλ̄z	PROPN
ejpam-4787	118	44	1	1	NUM
ejpam-4787	118	45	2	2	NUM
ejpam-4787	118	46	)	)	PUNCT
ejpam-4787	118	47	λ)λ̄+(z	λ)λ̄+(z	NOUN
ejpam-4787	118	48	1	1	NUM
ejpam-4787	118	49	2	2	NUM
ejpam-4787	118	50	(	(	PUNCT
ejpam-4787	118	51	xλ̄y	xλ̄y	NOUN
ejpam-4787	118	52	1	1	NUM
ejpam-4787	118	53	2	2	NUM
ejpam-4787	118	54	)	)	PUNCT
ejpam-4787	118	55	λ)λ̄)+	λ)λ̄)+	VERB
ejpam-4787	119	1	(	(	PUNCT
ejpam-4787	119	2	−2λ̄−	−2λ̄−	NOUN
ejpam-4787	119	3	12)((y	12)((y	NUM
ejpam-4787	119	4	1	1	NUM
ejpam-4787	119	5	2	2	NUM
ejpam-4787	119	6	(	(	PUNCT
ejpam-4787	119	7	xλ̄z	xλ̄z	PROPN
ejpam-4787	119	8	1	1	NUM
ejpam-4787	119	9	2	2	NUM
ejpam-4787	119	10	)	)	PUNCT
ejpam-4787	119	11	1	1	NUM
ejpam-4787	119	12	2	2	NUM
ejpam-4787	119	13	)	)	PUNCT
ejpam-4787	119	14	λ̄	λ̄	VERB
ejpam-4787	120	1	+	+	CCONJ
ejpam-4787	120	2	(	(	PUNCT
ejpam-4787	120	3	z	z	NOUN
ejpam-4787	120	4	1	1	NUM
ejpam-4787	120	5	2	2	NUM
ejpam-4787	120	6	(	(	PUNCT
ejpam-4787	120	7	xλ̄y	xλ̄y	NOUN
ejpam-4787	120	8	1	1	NUM
ejpam-4787	120	9	2	2	NUM
ejpam-4787	120	10	)	)	PUNCT
ejpam-4787	120	11	1	1	NUM
ejpam-4787	120	12	2	2	NUM
ejpam-4787	120	13	)	)	PUNCT
ejpam-4787	120	14	λ̄	λ̄	PUNCT
ejpam-4787	120	15	)	)	PUNCT
ejpam-4787	121	1	=	=	SYM
ejpam-4787	121	2	0	0	NUM
ejpam-4787	121	3	;	;	PUNCT
ejpam-4787	121	4	18	18	NUM
ejpam-4787	121	5	)	)	PUNCT
ejpam-4787	121	6	(	(	PUNCT
ejpam-4787	121	7	yλ(x	yλ(x	NOUN
ejpam-4787	121	8	1	1	NUM
ejpam-4787	121	9	2	2	NUM
ejpam-4787	121	10	zλ	zλ	NOUN
ejpam-4787	121	11	)	)	PUNCT
ejpam-4787	121	12	1	1	NUM
ejpam-4787	121	13	2	2	NUM
ejpam-4787	121	14	)	)	PUNCT
ejpam-4787	121	15	0+(zλ(x	0+(zλ(x	NOUN
ejpam-4787	121	16	1	1	NUM
ejpam-4787	121	17	2	2	NUM
ejpam-4787	121	18	yλ	yλ	NOUN
ejpam-4787	121	19	)	)	PUNCT
ejpam-4787	121	20	1	1	NUM
ejpam-4787	121	21	2	2	NUM
ejpam-4787	121	22	)	)	PUNCT
ejpam-4787	121	23	0	0	NUM
ejpam-4787	122	1	=	=	SYM
ejpam-4787	122	2	(	(	PUNCT
ejpam-4787	122	3	yλ̄(x	yλ̄(x	PROPN
ejpam-4787	122	4	1	1	NUM
ejpam-4787	122	5	2	2	NUM
ejpam-4787	122	6	zλ̄	zλ̄	NUM
ejpam-4787	122	7	)	)	PUNCT
ejpam-4787	122	8	1	1	NUM
ejpam-4787	122	9	2	2	NUM
ejpam-4787	122	10	)	)	PUNCT
ejpam-4787	122	11	0+(zλ̄(x	0+(zλ̄(x	NUM
ejpam-4787	122	12	1	1	NUM
ejpam-4787	122	13	2	2	NUM
ejpam-4787	122	14	yλ̄	yλ̄	NOUN
ejpam-4787	122	15	)	)	PUNCT
ejpam-4787	122	16	1	1	NUM
ejpam-4787	122	17	2	2	NUM
ejpam-4787	122	18	)	)	PUNCT
ejpam-4787	122	19	0	0	NUM
ejpam-4787	123	1	=	=	SYM
ejpam-4787	123	2	(	(	PUNCT
ejpam-4787	123	3	yλ(x	yλ(x	NOUN
ejpam-4787	123	4	1	1	NUM
ejpam-4787	123	5	2	2	NUM
ejpam-4787	123	6	zλ	zλ	NOUN
ejpam-4787	123	7	)	)	PUNCT
ejpam-4787	123	8	1	1	NUM
ejpam-4787	123	9	2	2	NUM
ejpam-4787	123	10	)	)	PUNCT
ejpam-4787	123	11	λ̄+(zλ(x	λ̄+(zλ(x	NOUN
ejpam-4787	123	12	1	1	NUM
ejpam-4787	123	13	2	2	NUM
ejpam-4787	123	14	yλ	yλ	NOUN
ejpam-4787	123	15	)	)	PUNCT
ejpam-4787	123	16	1	1	NUM
ejpam-4787	123	17	2	2	NUM
ejpam-4787	123	18	)	)	PUNCT
ejpam-4787	123	19	λ̄	λ̄	NOUN
ejpam-4787	124	1	=	=	PUNCT
ejpam-4787	124	2	(	(	PUNCT
ejpam-4787	124	3	yλ̄(x	yλ̄(x	PROPN
ejpam-4787	124	4	1	1	NUM
ejpam-4787	124	5	2	2	NUM
ejpam-4787	124	6	zλ̄	zλ̄	NUM
ejpam-4787	124	7	)	)	PUNCT
ejpam-4787	124	8	1	1	NUM
ejpam-4787	124	9	2	2	NUM
ejpam-4787	124	10	)	)	PUNCT
ejpam-4787	124	11	λ	λ	NOUN
ejpam-4787	124	12	+	+	CCONJ
ejpam-4787	124	13	(	(	PUNCT
ejpam-4787	124	14	zλ̄(x	zλ̄(x	NUM
ejpam-4787	124	15	1	1	NUM
ejpam-4787	124	16	2	2	NUM
ejpam-4787	124	17	yλ̄	yλ̄	NOUN
ejpam-4787	124	18	)	)	PUNCT
ejpam-4787	124	19	1	1	NUM
ejpam-4787	124	20	2	2	NUM
ejpam-4787	124	21	)	)	PUNCT
ejpam-4787	124	22	λ	λ	NOUN
ejpam-4787	124	23	=	=	SYM
ejpam-4787	124	24	0	0	NUM
ejpam-4787	124	25	;	;	PUNCT
ejpam-4787	124	26	19	19	NUM
ejpam-4787	124	27	)	)	PUNCT
ejpam-4787	124	28	(	(	PUNCT
ejpam-4787	124	29	−14λ−	−14λ−	PROPN
ejpam-4787	124	30	6)((yλ(x	6)((yλ(x	NOUN
ejpam-4787	124	31	1	1	NUM
ejpam-4787	124	32	2	2	NUM
ejpam-4787	124	33	zλ	zλ	NOUN
ejpam-4787	124	34	)	)	PUNCT
ejpam-4787	124	35	1	1	NUM
ejpam-4787	124	36	2	2	NUM
ejpam-4787	124	37	)	)	PUNCT
ejpam-4787	124	38	1	1	NUM
ejpam-4787	124	39	2	2	NUM
ejpam-4787	124	40	+	+	CCONJ
ejpam-4787	124	41	(	(	PUNCT
ejpam-4787	124	42	zλ(x	zλ(x	NUM
ejpam-4787	124	43	1	1	NUM
ejpam-4787	124	44	2	2	NUM
ejpam-4787	124	45	yλ	yλ	NOUN
ejpam-4787	124	46	)	)	PUNCT
ejpam-4787	124	47	1	1	NUM
ejpam-4787	124	48	2	2	NUM
ejpam-4787	124	49	)	)	PUNCT
ejpam-4787	124	50	1	1	NUM
ejpam-4787	124	51	2	2	NUM
ejpam-4787	124	52	)	)	PUNCT
ejpam-4787	124	53	−	−	PROPN
ejpam-4787	125	1	16λ((yλ(x	16λ((yλ(x	NUM
ejpam-4787	125	2	1	1	NUM
ejpam-4787	125	3	2	2	NUM
ejpam-4787	125	4	zλ)0	zλ)0	PROPN
ejpam-4787	125	5	)	)	PUNCT
ejpam-4787	125	6	1	1	NUM
ejpam-4787	125	7	2	2	NUM
ejpam-4787	125	8	+	+	CCONJ
ejpam-4787	125	9	(	(	PUNCT
ejpam-4787	125	10	zλ(x	zλ(x	NUM
ejpam-4787	125	11	1	1	NUM
ejpam-4787	125	12	2	2	NUM
ejpam-4787	125	13	yλ)0	yλ)0	PROPN
ejpam-4787	125	14	)	)	PUNCT
ejpam-4787	125	15	1	1	NUM
ejpam-4787	125	16	2	2	NUM
ejpam-4787	125	17	=	=	SYM
ejpam-4787	125	18	0	0	NUM
ejpam-4787	125	19	;	;	PUNCT
ejpam-4787	125	20	20	20	NUM
ejpam-4787	125	21	)	)	PUNCT
ejpam-4787	125	22	(	(	PUNCT
ejpam-4787	125	23	−14λ̄−	−14λ̄−	PUNCT
ejpam-4787	125	24	6)((yλ̄(x	6)((yλ̄(x	NOUN
ejpam-4787	125	25	1	1	NUM
ejpam-4787	125	26	2	2	NUM
ejpam-4787	125	27	zλ̄	zλ̄	NUM
ejpam-4787	125	28	)	)	PUNCT
ejpam-4787	125	29	1	1	NUM
ejpam-4787	125	30	2	2	NUM
ejpam-4787	125	31	)	)	PUNCT
ejpam-4787	125	32	1	1	NUM
ejpam-4787	125	33	2	2	NUM
ejpam-4787	125	34	+	+	CCONJ
ejpam-4787	125	35	(	(	PUNCT
ejpam-4787	125	36	zλ̄(x	zλ̄(x	NUM
ejpam-4787	125	37	1	1	NUM
ejpam-4787	125	38	2	2	NUM
ejpam-4787	125	39	yλ̄	yλ̄	NOUN
ejpam-4787	125	40	)	)	PUNCT
ejpam-4787	125	41	1	1	NUM
ejpam-4787	125	42	2	2	NUM
ejpam-4787	125	43	)	)	PUNCT
ejpam-4787	125	44	1	1	NUM
ejpam-4787	125	45	2	2	NUM
ejpam-4787	125	46	)	)	PUNCT
ejpam-4787	125	47	−	−	NOUN
ejpam-4787	125	48	16λ̄((yλ̄(x	16λ̄((yλ̄(x	NUM
ejpam-4787	125	49	1	1	NUM
ejpam-4787	125	50	2	2	NUM
ejpam-4787	125	51	zλ̄)0	zλ̄)0	NUM
ejpam-4787	125	52	)	)	PUNCT
ejpam-4787	125	53	1	1	NUM
ejpam-4787	125	54	2	2	NUM
ejpam-4787	125	55	+	+	CCONJ
ejpam-4787	125	56	(	(	PUNCT
ejpam-4787	125	57	zλ̄(x	zλ̄(x	NUM
ejpam-4787	125	58	1	1	NUM
ejpam-4787	125	59	2	2	NUM
ejpam-4787	125	60	yλ̄)0	yλ̄)0	PROPN
ejpam-4787	125	61	)	)	PUNCT
ejpam-4787	125	62	1	1	NUM
ejpam-4787	125	63	2	2	NUM
ejpam-4787	125	64	)	)	PUNCT
ejpam-4787	125	65	=	=	SYM
ejpam-4787	125	66	0	0	NUM
ejpam-4787	125	67	;	;	PUNCT
ejpam-4787	125	68	21	21	NUM
ejpam-4787	125	69	)	)	PUNCT
ejpam-4787	125	70	(	(	PUNCT
ejpam-4787	125	71	xλ(y0z	xλ(y0z	PROPN
ejpam-4787	125	72	1	1	NUM
ejpam-4787	125	73	2	2	NUM
ejpam-4787	125	74	)	)	PUNCT
ejpam-4787	125	75	1	1	NUM
ejpam-4787	125	76	2	2	NUM
ejpam-4787	125	77	)	)	PUNCT
ejpam-4787	125	78	0	0	PUNCT
ejpam-4787	126	1	+	+	CCONJ
ejpam-4787	126	2	(	(	PUNCT
ejpam-4787	126	3	z	z	NOUN
ejpam-4787	126	4	1	1	NUM
ejpam-4787	126	5	2	2	NUM
ejpam-4787	126	6	(	(	PUNCT
ejpam-4787	126	7	xλy0	xλy0	PROPN
ejpam-4787	126	8	)	)	PUNCT
ejpam-4787	126	9	1	1	NUM
ejpam-4787	126	10	2	2	NUM
ejpam-4787	126	11	)	)	PUNCT
ejpam-4787	126	12	0	0	NUM
ejpam-4787	127	1	=	=	SYM
ejpam-4787	127	2	(	(	PUNCT
ejpam-4787	127	3	xλ̄(y0z	xλ̄(y0z	NOUN
ejpam-4787	127	4	1	1	NUM
ejpam-4787	127	5	2	2	NUM
ejpam-4787	127	6	)	)	PUNCT
ejpam-4787	127	7	1	1	NUM
ejpam-4787	127	8	2	2	NUM
ejpam-4787	127	9	)	)	PUNCT
ejpam-4787	127	10	0	0	PUNCT
ejpam-4787	128	1	+	+	CCONJ
ejpam-4787	128	2	(	(	PUNCT
ejpam-4787	128	3	z	z	NOUN
ejpam-4787	128	4	1	1	NUM
ejpam-4787	128	5	2	2	NUM
ejpam-4787	128	6	(	(	PUNCT
ejpam-4787	128	7	xλ̄y0	xλ̄y0	PROPN
ejpam-4787	128	8	)	)	PUNCT
ejpam-4787	128	9	1	1	NUM
ejpam-4787	128	10	2	2	NUM
ejpam-4787	128	11	)	)	PUNCT
ejpam-4787	128	12	0	0	NUM
ejpam-4787	129	1	=	=	SYM
ejpam-4787	129	2	0	0	NUM
ejpam-4787	129	3	;	;	PUNCT
ejpam-4787	129	4	22	22	NUM
ejpam-4787	129	5	)	)	PUNCT
ejpam-4787	130	1	(	(	PUNCT
ejpam-4787	130	2	z	z	NOUN
ejpam-4787	130	3	1	1	NUM
ejpam-4787	130	4	2	2	NUM
ejpam-4787	130	5	(	(	PUNCT
ejpam-4787	130	6	xλy0	xλy0	PROPN
ejpam-4787	130	7	)	)	PUNCT
ejpam-4787	130	8	1	1	NUM
ejpam-4787	130	9	2	2	NUM
ejpam-4787	130	10	)	)	PUNCT
ejpam-4787	130	11	λ	λ	NOUN
ejpam-4787	130	12	+	+	CCONJ
ejpam-4787	130	13	(	(	PUNCT
ejpam-4787	130	14	y0(xλz	y0(xλz	PROPN
ejpam-4787	130	15	1	1	NUM
ejpam-4787	130	16	2	2	NUM
ejpam-4787	130	17	)	)	PUNCT
ejpam-4787	130	18	1	1	NUM
ejpam-4787	130	19	2	2	NUM
ejpam-4787	130	20	)	)	PUNCT
ejpam-4787	130	21	λ	λ	NOUN
ejpam-4787	130	22	=	=	PRON
ejpam-4787	130	23	(	(	PUNCT
ejpam-4787	130	24	z	z	NOUN
ejpam-4787	130	25	1	1	NUM
ejpam-4787	130	26	2	2	NUM
ejpam-4787	130	27	(	(	PUNCT
ejpam-4787	130	28	xλ̄y0	xλ̄y0	PROPN
ejpam-4787	130	29	)	)	PUNCT
ejpam-4787	130	30	1	1	NUM
ejpam-4787	130	31	2	2	NUM
ejpam-4787	130	32	)	)	PUNCT
ejpam-4787	130	33	λ̄	λ̄	VERB
ejpam-4787	131	1	+	+	CCONJ
ejpam-4787	131	2	(	(	PUNCT
ejpam-4787	131	3	y0(xλ̄z	y0(xλ̄z	PROPN
ejpam-4787	131	4	1	1	NUM
ejpam-4787	131	5	2	2	NUM
ejpam-4787	131	6	)	)	PUNCT
ejpam-4787	131	7	1	1	NUM
ejpam-4787	131	8	2	2	NUM
ejpam-4787	131	9	)	)	PUNCT
ejpam-4787	131	10	λ̄	λ̄	NOUN
ejpam-4787	132	1	=	=	PUNCT
ejpam-4787	132	2	0	0	NUM
ejpam-4787	132	3	;	;	PUNCT
ejpam-4787	132	4	23	23	NUM
ejpam-4787	132	5	)	)	PUNCT
ejpam-4787	132	6	(	(	PUNCT
ejpam-4787	132	7	z	z	NOUN
ejpam-4787	132	8	1	1	NUM
ejpam-4787	132	9	2	2	NUM
ejpam-4787	132	10	(	(	PUNCT
ejpam-4787	132	11	xλy0	xλy0	PROPN
ejpam-4787	132	12	)	)	PUNCT
ejpam-4787	132	13	1	1	NUM
ejpam-4787	132	14	2	2	NUM
ejpam-4787	132	15	)	)	PUNCT
ejpam-4787	132	16	λ̄	λ̄	VERB
ejpam-4787	133	1	+	+	CCONJ
ejpam-4787	133	2	(	(	PUNCT
ejpam-4787	133	3	y0(xλz	y0(xλz	PROPN
ejpam-4787	133	4	1	1	NUM
ejpam-4787	133	5	2	2	NUM
ejpam-4787	133	6	)	)	PUNCT
ejpam-4787	133	7	1	1	NUM
ejpam-4787	133	8	2	2	NUM
ejpam-4787	133	9	)	)	PUNCT
ejpam-4787	133	10	λ̄	λ̄	VERB
ejpam-4787	134	1	+	+	CCONJ
ejpam-4787	134	2	(	(	PUNCT
ejpam-4787	134	3	xλ(z	xλ(z	ADP
ejpam-4787	134	4	1	1	NUM
ejpam-4787	134	5	2	2	NUM
ejpam-4787	134	6	y0	y0	NOUN
ejpam-4787	134	7	)	)	PUNCT
ejpam-4787	134	8	1	1	NUM
ejpam-4787	134	9	2	2	NUM
ejpam-4787	134	10	)	)	PUNCT
ejpam-4787	134	11	λ̄	λ̄	NOUN
ejpam-4787	135	1	=	=	PUNCT
ejpam-4787	135	2	0	0	NUM
ejpam-4787	135	3	;	;	PUNCT
ejpam-4787	135	4	24	24	NUM
ejpam-4787	135	5	)	)	PUNCT
ejpam-4787	135	6	(	(	PUNCT
ejpam-4787	135	7	z	z	NOUN
ejpam-4787	135	8	1	1	NUM
ejpam-4787	135	9	2	2	NUM
ejpam-4787	135	10	(	(	PUNCT
ejpam-4787	135	11	xλ̄y0	xλ̄y0	PROPN
ejpam-4787	135	12	)	)	PUNCT
ejpam-4787	135	13	1	1	NUM
ejpam-4787	135	14	2	2	NUM
ejpam-4787	135	15	)	)	PUNCT
ejpam-4787	135	16	λ	λ	NOUN
ejpam-4787	135	17	+	+	CCONJ
ejpam-4787	135	18	(	(	PUNCT
ejpam-4787	135	19	y0(xλ̄z	y0(xλ̄z	PROPN
ejpam-4787	135	20	1	1	NUM
ejpam-4787	135	21	2	2	NUM
ejpam-4787	135	22	)	)	PUNCT
ejpam-4787	135	23	1	1	NUM
ejpam-4787	135	24	2	2	NUM
ejpam-4787	135	25	)	)	PUNCT
ejpam-4787	135	26	λ	λ	NOUN
ejpam-4787	135	27	+	+	CCONJ
ejpam-4787	135	28	(	(	PUNCT
ejpam-4787	135	29	xλ̄(z	xλ̄(z	PROPN
ejpam-4787	135	30	1	1	NUM
ejpam-4787	135	31	2	2	NUM
ejpam-4787	135	32	y0	y0	NOUN
ejpam-4787	135	33	)	)	PUNCT
ejpam-4787	135	34	1	1	NUM
ejpam-4787	135	35	2	2	NUM
ejpam-4787	135	36	)	)	PUNCT
ejpam-4787	135	37	λ	λ	NOUN
ejpam-4787	135	38	=	=	SYM
ejpam-4787	135	39	0	0	NUM
ejpam-4787	135	40	;	;	PUNCT
ejpam-4787	135	41	25	25	NUM
ejpam-4787	135	42	)	)	PUNCT
ejpam-4787	135	43	(	(	PUNCT
ejpam-4787	135	44	−18λ−	−18λ−	PROPN
ejpam-4787	135	45	2λ̄+	2λ̄+	NOUN
ejpam-4787	135	46	5)(zλ(xλ̄y0	5)(zλ(xλ̄y0	NUM
ejpam-4787	135	47	)	)	PUNCT
ejpam-4787	135	48	1	1	NUM
ejpam-4787	135	49	2	2	NUM
ejpam-4787	135	50	)	)	PUNCT
ejpam-4787	135	51	0	0	NUM
ejpam-4787	136	1	+	+	CCONJ
ejpam-4787	136	2	(	(	PUNCT
ejpam-4787	136	3	−18λ̄−	−18λ̄−	PROPN
ejpam-4787	136	4	2λ+	2λ+	NUM
ejpam-4787	136	5	5)(xλ̄(zλy0	5)(xλ̄(zλy0	NUM
ejpam-4787	136	6	)	)	PUNCT
ejpam-4787	136	7	1	1	NUM
ejpam-4787	136	8	2	2	NUM
ejpam-4787	136	9	)	)	PUNCT
ejpam-4787	136	10	0	0	NUM
ejpam-4787	136	11	=	=	SYM
ejpam-4787	136	12	0	0	NUM
ejpam-4787	136	13	;	;	PUNCT
ejpam-4787	136	14	26	26	NUM
ejpam-4787	136	15	)	)	PUNCT
ejpam-4787	136	16	(	(	PUNCT
ejpam-4787	136	17	−3λ+	−3λ+	PROPN
ejpam-4787	136	18	1)(zλ(xλ̄y0	1)(zλ(xλ̄y0	NUM
ejpam-4787	136	19	)	)	SYM
ejpam-4787	136	20	1	1	NUM
ejpam-4787	136	21	2	2	NUM
ejpam-4787	136	22	)	)	PUNCT
ejpam-4787	136	23	1	1	NUM
ejpam-4787	136	24	2	2	NUM
ejpam-4787	136	25	+	+	CCONJ
ejpam-4787	136	26	(	(	PUNCT
ejpam-4787	136	27	−3λ̄+	−3λ̄+	NOUN
ejpam-4787	136	28	1)(xλ̄(zλy0	1)(xλ̄(zλy0	NUM
ejpam-4787	136	29	)	)	PUNCT
ejpam-4787	136	30	1	1	NUM
ejpam-4787	136	31	2	2	NUM
ejpam-4787	136	32	)	)	PUNCT
ejpam-4787	136	33	1	1	NUM
ejpam-4787	136	34	2	2	NUM
ejpam-4787	136	35	=	=	SYM
ejpam-4787	136	36	0	0	NUM
ejpam-4787	136	37	;	;	PUNCT
ejpam-4787	136	38	27	27	NUM
ejpam-4787	136	39	)	)	PUNCT
ejpam-4787	136	40	(	(	PUNCT
ejpam-4787	136	41	zλ(xλ̄y0	zλ(xλ̄y0	NUM
ejpam-4787	136	42	)	)	PUNCT
ejpam-4787	136	43	1	1	NUM
ejpam-4787	136	44	2	2	NUM
ejpam-4787	136	45	)	)	PUNCT
ejpam-4787	136	46	λ̄	λ̄	NOUN
ejpam-4787	136	47	=	=	PUNCT
ejpam-4787	136	48	(	(	PUNCT
ejpam-4787	136	49	xλ̄(zλy0	xλ̄(zλy0	PROPN
ejpam-4787	136	50	)	)	PUNCT
ejpam-4787	136	51	1	1	NUM
ejpam-4787	136	52	2	2	NUM
ejpam-4787	136	53	)	)	PUNCT
ejpam-4787	136	54	λ	λ	NOUN
ejpam-4787	136	55	=	=	SYM
ejpam-4787	136	56	0	0	NUM
ejpam-4787	136	57	;	;	PUNCT
ejpam-4787	136	58	28	28	NUM
ejpam-4787	136	59	)	)	PUNCT
ejpam-4787	136	60	(	(	PUNCT
ejpam-4787	136	61	−12λ−	−12λ−	NOUN
ejpam-4787	136	62	2λ̄+	2λ̄+	NUM
ejpam-4787	136	63	4)(zλ(xλ̄y	4)(zλ(xλ̄y	NOUN
ejpam-4787	136	64	1	1	NUM
ejpam-4787	136	65	2	2	NUM
ejpam-4787	136	66	)	)	PUNCT
ejpam-4787	136	67	1	1	NUM
ejpam-4787	136	68	2	2	NUM
ejpam-4787	136	69	)	)	PUNCT
ejpam-4787	136	70	0	0	NUM
ejpam-4787	137	1	+	+	CCONJ
ejpam-4787	137	2	(	(	PUNCT
ejpam-4787	137	3	−12λ̄−	−12λ̄−	PROPN
ejpam-4787	137	4	2λ+	2λ+	NUM
ejpam-4787	137	5	4)(xλ̄(zλy	4)(xλ̄(zλy	NUM
ejpam-4787	137	6	1	1	NUM
ejpam-4787	137	7	2	2	NUM
ejpam-4787	137	8	)	)	PUNCT
ejpam-4787	137	9	1	1	NUM
ejpam-4787	137	10	2	2	NUM
ejpam-4787	137	11	)	)	PUNCT
ejpam-4787	137	12	0	0	NUM
ejpam-4787	138	1	=	=	SYM
ejpam-4787	138	2	0	0	NUM
ejpam-4787	138	3	;	;	PUNCT
ejpam-4787	138	4	29	29	NUM
ejpam-4787	138	5	)	)	PUNCT
ejpam-4787	138	6	(	(	PUNCT
ejpam-4787	138	7	−12λ+6)(zλ(xλ̄y	−12λ+6)(zλ(xλ̄y	NOUN
ejpam-4787	138	8	1	1	NUM
ejpam-4787	138	9	2	2	NUM
ejpam-4787	138	10	)	)	PUNCT
ejpam-4787	138	11	1	1	NUM
ejpam-4787	138	12	2	2	NUM
ejpam-4787	138	13	)	)	PUNCT
ejpam-4787	138	14	1	1	NUM
ejpam-4787	138	15	2	2	NUM
ejpam-4787	138	16	+	+	NOUN
ejpam-4787	138	17	(	(	PUNCT
ejpam-4787	138	18	−12λ̄+6)(xλ̄(zλy	−12λ̄+6)(xλ̄(zλy	X
ejpam-4787	138	19	1	1	NUM
ejpam-4787	138	20	2	2	NUM
ejpam-4787	138	21	)	)	PUNCT
ejpam-4787	138	22	1	1	NUM
ejpam-4787	138	23	2	2	NUM
ejpam-4787	138	24	)	)	PUNCT
ejpam-4787	138	25	1	1	NUM
ejpam-4787	138	26	2	2	NUM
ejpam-4787	138	27	−16λ(zλ(xλ̄y	−16λ(zλ(xλ̄y	NOUN
ejpam-4787	138	28	1	1	NUM
ejpam-4787	138	29	2	2	NUM
ejpam-4787	138	30	)	)	PUNCT
ejpam-4787	138	31	0	0	NUM
ejpam-4787	138	32	)	)	PUNCT
ejpam-4787	138	33	1	1	NUM
ejpam-4787	138	34	2	2	NUM
ejpam-4787	138	35	−16λ̄(xλ̄(zλy	−16λ̄(xλ̄(zλy	NUM
ejpam-4787	138	36	1	1	NUM
ejpam-4787	138	37	2	2	NUM
ejpam-4787	138	38	)	)	PUNCT
ejpam-4787	138	39	0	0	NUM
ejpam-4787	138	40	)	)	PUNCT
ejpam-4787	138	41	1	1	NUM
ejpam-4787	138	42	2	2	NUM
ejpam-4787	138	43	=	=	SYM
ejpam-4787	138	44	0	0	NUM
ejpam-4787	138	45	;	;	PUNCT
ejpam-4787	138	46	30	30	NUM
ejpam-4787	138	47	)	)	PUNCT
ejpam-4787	138	48	(	(	PUNCT
ejpam-4787	138	49	zλ(xλ̄y	zλ(xλ̄y	NOUN
ejpam-4787	138	50	1	1	NUM
ejpam-4787	138	51	2	2	NUM
ejpam-4787	138	52	)	)	PUNCT
ejpam-4787	138	53	1	1	NUM
ejpam-4787	138	54	2	2	NUM
ejpam-4787	138	55	)	)	PUNCT
ejpam-4787	138	56	λ̄	λ̄	NOUN
ejpam-4787	139	1	=	=	PUNCT
ejpam-4787	139	2	(	(	PUNCT
ejpam-4787	139	3	xλ̄(zλy	xλ̄(zλy	PROPN
ejpam-4787	139	4	1	1	NUM
ejpam-4787	139	5	2	2	NUM
ejpam-4787	139	6	)	)	PUNCT
ejpam-4787	139	7	1	1	NUM
ejpam-4787	139	8	2	2	NUM
ejpam-4787	139	9	)	)	PUNCT
ejpam-4787	139	10	λ	λ	NOUN
ejpam-4787	139	11	=	=	NOUN
ejpam-4787	139	12	0	0	PROPN
ejpam-4787	139	13	.	.	PUNCT
ejpam-4787	139	14	d.	d.	PROPN
ejpam-4787	139	15	kabre	kabre	PROPN
ejpam-4787	139	16	,	,	PUNCT
ejpam-4787	139	17	a.	a.	NOUN
ejpam-4787	139	18	conseibo	conseibo	PROPN
ejpam-4787	139	19	/	/	SYM
ejpam-4787	139	20	eur	eur	PROPN
ejpam-4787	139	21	.	.	PUNCT
ejpam-4787	140	1	j.	j.	PROPN
ejpam-4787	140	2	pure	pure	PROPN
ejpam-4787	140	3	appl	appl	PROPN
ejpam-4787	140	4	.	.	PROPN
ejpam-4787	140	5	math	math	PROPN
ejpam-4787	140	6	,	,	PUNCT
ejpam-4787	140	7	16	16	NUM
ejpam-4787	140	8	(	(	PUNCT
ejpam-4787	140	9	3	3	NUM
ejpam-4787	140	10	)	)	PUNCT
ejpam-4787	140	11	(	(	PUNCT
ejpam-4787	140	12	2023	2023	NUM
ejpam-4787	140	13	)	)	PUNCT
ejpam-4787	140	14	,	,	PUNCT
ejpam-4787	140	15	1480	1480	NUM
ejpam-4787	140	16	-	-	SYM
ejpam-4787	140	17	1490	1490	NUM
ejpam-4787	140	18	1484	1484	NUM
ejpam-4787	140	19	proof	proof	NOUN
ejpam-4787	140	20	.	.	PUNCT
ejpam-4787	141	1	consider	consider	VERB
ejpam-4787	141	2	the	the	DET
ejpam-4787	141	3	identity	identity	NOUN
ejpam-4787	141	4	of	of	ADP
ejpam-4787	141	5	proposition	proposition	NOUN
ejpam-4787	141	6	1	1	NUM
ejpam-4787	141	7	.	.	PUNCT
ejpam-4787	141	8	setting	set	VERB
ejpam-4787	141	9	x	x	PUNCT
ejpam-4787	141	10	=	=	SYM
ejpam-4787	141	11	e	e	NOUN
ejpam-4787	141	12	,	,	PUNCT
ejpam-4787	141	13	y	y	PROPN
ejpam-4787	141	14	∈	∈	PROPN
ejpam-4787	141	15	aα	aα	NOUN
ejpam-4787	141	16	,	,	PUNCT
ejpam-4787	141	17	z	z	PROPN
ejpam-4787	141	18	∈	∈	PROPN
ejpam-4787	141	19	aβ	aβ	PROPN
ejpam-4787	141	20	,	,	PUNCT
ejpam-4787	141	21	t	t	PROPN
ejpam-4787	141	22	∈	∈	PROPN
ejpam-4787	141	23	aγ	aγ	INTJ
ejpam-4787	141	24	,	,	PUNCT
ejpam-4787	141	25	we	we	PRON
ejpam-4787	141	26	have	have	VERB
ejpam-4787	141	27	respectively	respectively	ADV
ejpam-4787	141	28	ey	ey	ADJ
ejpam-4787	141	29	=	=	SYM
ejpam-4787	141	30	αy	αy	PROPN
ejpam-4787	141	31	,	,	PUNCT
ejpam-4787	141	32	ez	ez	PROPN
ejpam-4787	141	33	=	=	SYM
ejpam-4787	141	34	βz	βz	PROPN
ejpam-4787	141	35	,	,	PUNCT
ejpam-4787	141	36	et	et	NOUN
ejpam-4787	141	37	=	=	SYM
ejpam-4787	141	38	γt	γt	NOUN
ejpam-4787	141	39	and	and	CCONJ
ejpam-4787	141	40	:	:	PUNCT
ejpam-4787	141	41	4αe(z(ty	4αe(z(ty	NUM
ejpam-4787	141	42	)	)	PUNCT
ejpam-4787	142	1	+	+	CCONJ
ejpam-4787	143	1	4e(z(e(ty	4e(z(e(ty	NUM
ejpam-4787	143	2	)	)	PUNCT
ejpam-4787	143	3	)	)	PUNCT
ejpam-4787	143	4	)	)	PUNCT
ejpam-4787	144	1	+	+	CCONJ
ejpam-4787	144	2	4αe(t(zy	4αe(t(zy	X
ejpam-4787	144	3	)	)	PUNCT
ejpam-4787	144	4	)	)	PUNCT
ejpam-4787	145	1	+	+	CCONJ
ejpam-4787	145	2	4e(e(z(ty	4e(e(z(ty	NUM
ejpam-4787	145	3	)	)	PUNCT
ejpam-4787	145	4	)	)	PUNCT
ejpam-4787	145	5	)	)	PUNCT
ejpam-4787	146	1	+	+	CCONJ
ejpam-4787	146	2	4e(t(e(yz	4e(t(e(yz	NUM
ejpam-4787	146	3	)	)	PUNCT
ejpam-4787	146	4	)	)	PUNCT
ejpam-4787	146	5	)	)	PUNCT
ejpam-4787	147	1	+	+	CCONJ
ejpam-4787	147	2	4e(e(t(yz)))+	4e(e(t(yz)))+	NUM
ejpam-4787	147	3	4γe(z(yt	4γe(z(yt	NUM
ejpam-4787	147	4	)	)	PUNCT
ejpam-4787	147	5	)	)	PUNCT
ejpam-4787	148	1	+	+	CCONJ
ejpam-4787	148	2	4βe(t(yz	4βe(t(yz	NUM
ejpam-4787	148	3	)	)	PUNCT
ejpam-4787	148	4	)	)	PUNCT
ejpam-4787	149	1	+	+	NUM
ejpam-4787	149	2	4e(e(y(tz	4e(e(y(tz	NOUN
ejpam-4787	149	3	)	)	PUNCT
ejpam-4787	149	4	)	)	PUNCT
ejpam-4787	149	5	)	)	PUNCT
ejpam-4787	150	1	+	+	CCONJ
ejpam-4787	150	2	4γe(y(zt	4γe(y(zt	NUM
ejpam-4787	150	3	)	)	PUNCT
ejpam-4787	150	4	)	)	PUNCT
ejpam-4787	151	1	+	+	NUM
ejpam-4787	151	2	4βey(tz	4βey(tz	NUM
ejpam-4787	151	3	)	)	PUNCT
ejpam-4787	151	4	)	)	PUNCT
ejpam-4787	152	1	+	+	CCONJ
ejpam-4787	152	2	4e(y(e(tz))+	4e(y(e(tz))+	NUM
ejpam-4787	152	3	8γα2t(zy	8γα2t(zy	NUM
ejpam-4787	152	4	)	)	PUNCT
ejpam-4787	153	1	+	+	CCONJ
ejpam-4787	153	2	8γαt(e(zy	8γαt(e(zy	ADJ
ejpam-4787	153	3	)	)	PUNCT
ejpam-4787	153	4	)	)	PUNCT
ejpam-4787	154	1	+	+	CCONJ
ejpam-4787	154	2	8γt(e(e(yz	8γt(e(e(yz	NUM
ejpam-4787	154	3	)	)	PUNCT
ejpam-4787	154	4	)	)	PUNCT
ejpam-4787	154	5	)	)	PUNCT
ejpam-4787	155	1	+	+	CCONJ
ejpam-4787	155	2	8γβt(e(yz	8γβt(e(yz	NUM
ejpam-4787	155	3	)	)	PUNCT
ejpam-4787	155	4	)	)	PUNCT
ejpam-4787	156	1	+	+	CCONJ
ejpam-4787	156	2	8γβ2t(yz	8γβ2t(yz	NUM
ejpam-4787	156	3	)	)	PUNCT
ejpam-4787	157	1	+	+	CCONJ
ejpam-4787	157	2	4γαt(zy)+	4γαt(zy)+	NOUN
ejpam-4787	157	3	4γβt(yz	4γβt(yz	NUM
ejpam-4787	157	4	)	)	PUNCT
ejpam-4787	158	1	+	+	CCONJ
ejpam-4787	158	2	4βz(ty	4βz(ty	NOUN
ejpam-4787	158	3	)	)	PUNCT
ejpam-4787	159	1	+	+	NUM
ejpam-4787	159	2	4β2z(ty	4β2z(ty	X
ejpam-4787	159	3	)	)	PUNCT
ejpam-4787	160	1	+	+	NUM
ejpam-4787	160	2	8β3z(ty	8β3z(ty	NUM
ejpam-4787	160	3	)	)	PUNCT
ejpam-4787	160	4	+	+	CCONJ
ejpam-4787	160	5	4αγy(zt	4αγy(zt	NUM
ejpam-4787	160	6	)	)	PUNCT
ejpam-4787	161	1	+	+	NUM
ejpam-4787	161	2	8αγ2y(zt	8αγ2y(zt	NUM
ejpam-4787	161	3	)	)	PUNCT
ejpam-4787	162	1	+	+	CCONJ
ejpam-4787	162	2	4αβy(tz)+	4αβy(tz)+	NUM
ejpam-4787	162	3	8αγy(e(zt	8αγy(e(zt	NOUN
ejpam-4787	162	4	)	)	PUNCT
ejpam-4787	162	5	)	)	PUNCT
ejpam-4787	163	1	+	+	CCONJ
ejpam-4787	163	2	8αβ2y(tz	8αβ2y(tz	X
ejpam-4787	163	3	)	)	PUNCT
ejpam-4787	164	1	+	+	CCONJ
ejpam-4787	164	2	8αβy(e(tz	8αβy(e(tz	NUM
ejpam-4787	164	3	)	)	PUNCT
ejpam-4787	164	4	)	)	PUNCT
ejpam-4787	165	1	+	+	CCONJ
ejpam-4787	165	2	8αe(e(tz	8αe(e(tz	NUM
ejpam-4787	165	3	)	)	PUNCT
ejpam-4787	165	4	)	)	PUNCT
ejpam-4787	166	1	+	+	CCONJ
ejpam-4787	166	2	8β3y(tz	8β3y(tz	X
ejpam-4787	166	3	)	)	PUNCT
ejpam-4787	167	1	+	+	NUM
ejpam-4787	167	2	4β2y(tz	4β2y(tz	NUM
ejpam-4787	167	3	)	)	PUNCT
ejpam-4787	168	1	+	+	CCONJ
ejpam-4787	168	2	4βy(tz)+	4βy(tz)+	NUM
ejpam-4787	168	3	4γt(yz	4γt(yz	NUM
ejpam-4787	168	4	)	)	PUNCT
ejpam-4787	169	1	+	+	CCONJ
ejpam-4787	170	1	4γ2t(yz	4γ2t(yz	X
ejpam-4787	170	2	)	)	PUNCT
ejpam-4787	170	3	+	+	NUM
ejpam-4787	170	4	8γ3t(yz	8γ3t(yz	NUM
ejpam-4787	170	5	)	)	PUNCT
ejpam-4787	170	6	+	+	NUM
ejpam-4787	170	7	8β3z(ty	8β3z(ty	NUM
ejpam-4787	170	8	)	)	PUNCT
ejpam-4787	170	9	+	+	CCONJ
ejpam-4787	170	10	8β2z(e(ty	8β2z(e(ty	NUM
ejpam-4787	170	11	)	)	PUNCT
ejpam-4787	170	12	)	)	PUNCT
ejpam-4787	171	1	+	+	CCONJ
ejpam-4787	171	2	8βz(e(e(ty	8βz(e(e(ty	NUM
ejpam-4787	171	3	)	)	PUNCT
ejpam-4787	171	4	)	)	PUNCT
ejpam-4787	171	5	)	)	PUNCT
ejpam-4787	172	1	+	+	CCONJ
ejpam-4787	172	2	4β2z(ty)+	4β2z(ty)+	NUM
ejpam-4787	172	3	8βγz(e(yt	8βγz(e(yt	NUM
ejpam-4787	172	4	)	)	PUNCT
ejpam-4787	172	5	)	)	PUNCT
ejpam-4787	173	1	+	+	CCONJ
ejpam-4787	173	2	4βγz(yt	4βγz(yt	NUM
ejpam-4787	173	3	)	)	PUNCT
ejpam-4787	173	4	+	+	NUM
ejpam-4787	173	5	8βγ2z(yt	8βγ2z(yt	X
ejpam-4787	173	6	)	)	PUNCT
ejpam-4787	173	7	=	=	SYM
ejpam-4787	173	8	2βz(ty	2βz(ty	NUM
ejpam-4787	173	9	)	)	PUNCT
ejpam-4787	173	10	+	+	NOUN
ejpam-4787	173	11	2z(e(ty	2z(e(ty	NUM
ejpam-4787	173	12	)	)	PUNCT
ejpam-4787	173	13	)	)	PUNCT
ejpam-4787	174	1	+	+	CCONJ
ejpam-4787	174	2	2αt(zy	2αt(zy	NUM
ejpam-4787	174	3	)	)	PUNCT
ejpam-4787	175	1	+	+	CCONJ
ejpam-4787	175	2	2e(z(ty))+	2e(z(ty))+	NUM
ejpam-4787	175	3	2t(e(yz	2t(e(yz	NUM
ejpam-4787	175	4	)	)	PUNCT
ejpam-4787	176	1	+	+	CCONJ
ejpam-4787	176	2	2e(t(yz	2e(t(yz	NUM
ejpam-4787	176	3	)	)	PUNCT
ejpam-4787	176	4	)	)	PUNCT
ejpam-4787	177	1	+	+	CCONJ
ejpam-4787	177	2	2γz(yt	2γz(yt	NUM
ejpam-4787	177	3	)	)	PUNCT
ejpam-4787	178	1	+	+	CCONJ
ejpam-4787	178	2	2βt(yz	2βt(yz	NUM
ejpam-4787	178	3	)	)	PUNCT
ejpam-4787	178	4	+	+	NUM
ejpam-4787	178	5	2e(y(tz	2e(y(tz	NUM
ejpam-4787	178	6	)	)	PUNCT
ejpam-4787	178	7	)	)	PUNCT
ejpam-4787	179	1	+	+	CCONJ
ejpam-4787	179	2	2γy(zt	2γy(zt	NUM
ejpam-4787	179	3	)	)	PUNCT
ejpam-4787	179	4	+	+	NUM
ejpam-4787	179	5	2βy(tz	2βy(tz	NUM
ejpam-4787	179	6	)	)	PUNCT
ejpam-4787	180	1	+	+	NUM
ejpam-4787	180	2	2y(e(tz	2y(e(tz	NUM
ejpam-4787	180	3	)	)	PUNCT
ejpam-4787	180	4	)	)	PUNCT
ejpam-4787	180	5	(	(	PUNCT
ejpam-4787	180	6	2	2	X
ejpam-4787	180	7	)	)	PUNCT
ejpam-4787	180	8	by	by	ADP
ejpam-4787	180	9	setting	set	VERB
ejpam-4787	180	10	α	α	NOUN
ejpam-4787	180	11	=	=	PUNCT
ejpam-4787	180	12	β	β	X
ejpam-4787	180	13	=	=	PUNCT
ejpam-4787	180	14	γ	γ	X
ejpam-4787	180	15	=	=	SYM
ejpam-4787	180	16	0	0	PROPN
ejpam-4787	180	17	,	,	PUNCT
ejpam-4787	180	18	the	the	DET
ejpam-4787	180	19	relation	relation	NOUN
ejpam-4787	180	20	(	(	PUNCT
ejpam-4787	180	21	2	2	X
ejpam-4787	180	22	)	)	PUNCT
ejpam-4787	180	23	becomes	become	VERB
ejpam-4787	180	24	4e(z(e(ty	4e(z(e(ty	NUM
ejpam-4787	180	25	)	)	PUNCT
ejpam-4787	180	26	)	)	PUNCT
ejpam-4787	180	27	)	)	PUNCT
ejpam-4787	181	1	+	+	CCONJ
ejpam-4787	181	2	4e(e(z(ty	4e(e(z(ty	NUM
ejpam-4787	181	3	)	)	PUNCT
ejpam-4787	181	4	)	)	PUNCT
ejpam-4787	181	5	)	)	PUNCT
ejpam-4787	182	1	+	+	CCONJ
ejpam-4787	182	2	4e(t(e(yz	4e(t(e(yz	NUM
ejpam-4787	182	3	)	)	PUNCT
ejpam-4787	182	4	)	)	PUNCT
ejpam-4787	182	5	)	)	PUNCT
ejpam-4787	183	1	+	+	CCONJ
ejpam-4787	183	2	4e(e(t(yz	4e(e(t(yz	NUM
ejpam-4787	183	3	)	)	PUNCT
ejpam-4787	183	4	)	)	PUNCT
ejpam-4787	183	5	)	)	PUNCT
ejpam-4787	184	1	+	+	CCONJ
ejpam-4787	184	2	4e(e(y(tz	4e(e(y(tz	NOUN
ejpam-4787	184	3	)	)	PUNCT
ejpam-4787	184	4	)	)	PUNCT
ejpam-4787	184	5	)	)	PUNCT
ejpam-4787	185	1	+	+	CCONJ
ejpam-4787	186	1	4e(y(e(tz	4e(y(e(tz	NUM
ejpam-4787	186	2	)	)	PUNCT
ejpam-4787	186	3	)	)	PUNCT
ejpam-4787	187	1	=	=	SYM
ejpam-4787	187	2	2z(e(ty	2z(e(ty	NUM
ejpam-4787	187	3	)	)	PUNCT
ejpam-4787	187	4	)	)	PUNCT
ejpam-4787	188	1	+	+	CCONJ
ejpam-4787	189	1	2e(z(ty	2e(z(ty	NUM
ejpam-4787	189	2	)	)	PUNCT
ejpam-4787	189	3	)	)	PUNCT
ejpam-4787	190	1	+	+	CCONJ
ejpam-4787	190	2	2e(t(yz	2e(t(yz	NUM
ejpam-4787	190	3	)	)	PUNCT
ejpam-4787	190	4	)	)	PUNCT
ejpam-4787	191	1	+	+	CCONJ
ejpam-4787	191	2	2e(y(tz	2e(y(tz	NUM
ejpam-4787	191	3	)	)	PUNCT
ejpam-4787	191	4	)	)	PUNCT
ejpam-4787	192	1	+	+	CCONJ
ejpam-4787	192	2	2y(e(tz	2y(e(tz	NUM
ejpam-4787	192	3	)	)	PUNCT
ejpam-4787	192	4	)	)	PUNCT
ejpam-4787	193	1	+	+	CCONJ
ejpam-4787	193	2	2t(e(yz	2t(e(yz	X
ejpam-4787	193	3	)	)	PUNCT
ejpam-4787	193	4	(	(	PUNCT
ejpam-4787	193	5	3	3	X
ejpam-4787	193	6	)	)	PUNCT
ejpam-4787	193	7	since	since	SCONJ
ejpam-4787	193	8	a2	a2	PROPN
ejpam-4787	193	9	0	0	PROPN
ejpam-4787	194	1	⊂	⊂	PROPN
ejpam-4787	194	2	a	a	DET
ejpam-4787	194	3	1	1	NUM
ejpam-4787	194	4	2	2	NUM
ejpam-4787	194	5	according	accord	VERB
ejpam-4787	194	6	to	to	ADP
ejpam-4787	194	7	theorem	theorem	ADJ
ejpam-4787	194	8	2	2	NUM
ejpam-4787	194	9	,	,	PUNCT
ejpam-4787	194	10	therefore	therefore	ADV
ejpam-4787	194	11	the	the	DET
ejpam-4787	194	12	relation	relation	NOUN
ejpam-4787	194	13	(	(	PUNCT
ejpam-4787	194	14	3	3	X
ejpam-4787	194	15	)	)	PUNCT
ejpam-4787	194	16	becomes	become	VERB
ejpam-4787	194	17	4e(e(z(ty	4e(e(z(ty	NUM
ejpam-4787	194	18	)	)	PUNCT
ejpam-4787	194	19	)	)	PUNCT
ejpam-4787	194	20	)	)	PUNCT
ejpam-4787	195	1	+	+	CCONJ
ejpam-4787	195	2	4e(e(t(yz	4e(e(t(yz	NUM
ejpam-4787	195	3	)	)	PUNCT
ejpam-4787	195	4	)	)	PUNCT
ejpam-4787	195	5	)	)	PUNCT
ejpam-4787	196	1	+	+	CCONJ
ejpam-4787	196	2	4e(e(y(tz	4e(e(y(tz	NOUN
ejpam-4787	196	3	)	)	PUNCT
ejpam-4787	196	4	)	)	PUNCT
ejpam-4787	196	5	)	)	PUNCT
ejpam-4787	197	1	=	=	SYM
ejpam-4787	197	2	z(ty	z(ty	NUM
ejpam-4787	197	3	)	)	PUNCT
ejpam-4787	198	1	+	+	CCONJ
ejpam-4787	198	2	y(tz	y(tz	NUM
ejpam-4787	198	3	)	)	PUNCT
ejpam-4787	198	4	+	+	SYM
ejpam-4787	198	5	t(yz	t(yz	NOUN
ejpam-4787	198	6	)	)	PUNCT
ejpam-4787	198	7	(	(	PUNCT
ejpam-4787	198	8	4	4	X
ejpam-4787	198	9	)	)	PUNCT
ejpam-4787	198	10	using	use	VERB
ejpam-4787	198	11	the	the	DET
ejpam-4787	198	12	relations	relation	NOUN
ejpam-4787	198	13	i	i	NOUN
ejpam-4787	198	14	)	)	PUNCT
ejpam-4787	198	15	and	and	CCONJ
ejpam-4787	198	16	vi	vi	X
ejpam-4787	198	17	)	)	PUNCT
ejpam-4787	198	18	of	of	ADP
ejpam-4787	198	19	theorem	theorem	ADJ
ejpam-4787	198	20	2	2	NUM
ejpam-4787	198	21	,	,	PUNCT
ejpam-4787	198	22	relation	relation	NOUN
ejpam-4787	198	23	(	(	PUNCT
ejpam-4787	198	24	4	4	X
ejpam-4787	198	25	)	)	PUNCT
ejpam-4787	198	26	gives	give	VERB
ejpam-4787	198	27	[	[	PRON
ejpam-4787	198	28	z(ty	z(ty	NUM
ejpam-4787	198	29	)	)	PUNCT
ejpam-4787	198	30	]	]	PUNCT
ejpam-4787	199	1	1	1	NUM
ejpam-4787	199	2	2	2	NUM
ejpam-4787	199	3	+	+	SYM
ejpam-4787	199	4	4λ2[z(ty)]λ	4λ2[z(ty)]λ	NUM
ejpam-4787	199	5	+	+	NUM
ejpam-4787	199	6	4λ̄2[z(ty)]λ̄	4λ̄2[z(ty)]λ̄	NUM
ejpam-4787	199	7	+	+	CCONJ
ejpam-4787	199	8	[	[	X
ejpam-4787	199	9	t(yz	t(yz	NUM
ejpam-4787	199	10	)	)	PUNCT
ejpam-4787	199	11	]	]	PUNCT
ejpam-4787	200	1	1	1	NUM
ejpam-4787	200	2	2	2	NUM
ejpam-4787	200	3	+	+	CCONJ
ejpam-4787	200	4	4λ2[t(yz)]λ	4λ2[t(yz)]λ	NUM
ejpam-4787	200	5	+	+	NUM
ejpam-4787	200	6	4λ̄2[t(yz)]λ̄	4λ̄2[t(yz)]λ̄	NUM
ejpam-4787	200	7	+	+	CCONJ
ejpam-4787	201	1	[	[	X
ejpam-4787	201	2	y(tz	y(tz	NOUN
ejpam-4787	201	3	)	)	PUNCT
ejpam-4787	201	4	]	]	PUNCT
ejpam-4787	201	5	1	1	NUM
ejpam-4787	201	6	2	2	NUM
ejpam-4787	201	7	+	+	NUM
ejpam-4787	201	8	4λ2[y(tz)]λ	4λ2[y(tz)]λ	NUM
ejpam-4787	201	9	+	+	CCONJ
ejpam-4787	201	10	4λ̄2[y(tz)]λ̄	4λ̄2[y(tz)]λ̄	NUM
ejpam-4787	201	11	=	=	SYM
ejpam-4787	202	1	[	[	X
ejpam-4787	202	2	z(ty	z(ty	NUM
ejpam-4787	202	3	)	)	PUNCT
ejpam-4787	202	4	]	]	PUNCT
ejpam-4787	202	5	1	1	NUM
ejpam-4787	202	6	2	2	NUM
ejpam-4787	202	7	+	+	CCONJ
ejpam-4787	203	1	[	[	X
ejpam-4787	203	2	z(ty)]λ	z(ty)]λ	X
ejpam-4787	203	3	+	+	PUNCT
ejpam-4787	204	1	[	[	X
ejpam-4787	204	2	z(ty)]λ̄	z(ty)]λ̄	X
ejpam-4787	204	3	+	+	X
ejpam-4787	204	4	[	[	X
ejpam-4787	204	5	t(yz	t(yz	NOUN
ejpam-4787	204	6	)	)	PUNCT
ejpam-4787	204	7	]	]	PUNCT
ejpam-4787	204	8	1	1	NUM
ejpam-4787	204	9	2	2	NUM
ejpam-4787	204	10	+	+	CCONJ
ejpam-4787	205	1	[	[	X
ejpam-4787	205	2	t(yz)]λ	t(yz)]λ	X
ejpam-4787	205	3	+	+	PUNCT
ejpam-4787	206	1	[	[	X
ejpam-4787	206	2	t(yz)]λ̄	t(yz)]λ̄	X
ejpam-4787	206	3	+	+	X
ejpam-4787	206	4	[	[	X
ejpam-4787	206	5	y(tz	y(tz	NOUN
ejpam-4787	206	6	)	)	PUNCT
ejpam-4787	206	7	]	]	PUNCT
ejpam-4787	206	8	1	1	NUM
ejpam-4787	206	9	2	2	NUM
ejpam-4787	206	10	+	+	CCONJ
ejpam-4787	207	1	[	[	X
ejpam-4787	207	2	y(tz)]λ	y(tz)]λ	X
ejpam-4787	207	3	+	+	NUM
ejpam-4787	208	1	[	[	X
ejpam-4787	208	2	y(tz)]λ̄	y(tz)]λ̄	NOUN
ejpam-4787	208	3	which	which	PRON
ejpam-4787	208	4	implies	imply	VERB
ejpam-4787	208	5	that	that	SCONJ
ejpam-4787	208	6	{	{	PUNCT
ejpam-4787	208	7	(	(	PUNCT
ejpam-4787	208	8	4λ2	4λ2	NUM
ejpam-4787	208	9	−	−	NOUN
ejpam-4787	208	10	1)([z(ty)]λ	1)([z(ty)]λ	NUM
ejpam-4787	208	11	+	+	CCONJ
ejpam-4787	209	1	[	[	X
ejpam-4787	209	2	t(yz)]λ	t(yz)]λ	X
ejpam-4787	209	3	+	+	X
ejpam-4787	210	1	[	[	X
ejpam-4787	210	2	y(tz)]λ	y(tz)]λ	X
ejpam-4787	210	3	)	)	PUNCT
ejpam-4787	210	4	=	=	SYM
ejpam-4787	210	5	0	0	PUNCT
ejpam-4787	210	6	(	(	PUNCT
ejpam-4787	210	7	4λ̄2	4λ̄2	NUM
ejpam-4787	210	8	−	−	NUM
ejpam-4787	210	9	1)([z(ty)]λ̄	1)([z(ty)]λ̄	NUM
ejpam-4787	211	1	+	+	CCONJ
ejpam-4787	212	1	[	[	X
ejpam-4787	212	2	t(yz)]λ̄	t(yz)]λ̄	X
ejpam-4787	212	3	+	+	X
ejpam-4787	212	4	[	[	X
ejpam-4787	212	5	y(tz)]λ̄	y(tz)]λ̄	NOUN
ejpam-4787	212	6	)	)	PUNCT
ejpam-4787	212	7	=	=	SYM
ejpam-4787	212	8	0	0	PUNCT
ejpam-4787	212	9	as	as	ADP
ejpam-4787	212	10	4λ2	4λ2	NUM
ejpam-4787	212	11	−	−	NOUN
ejpam-4787	212	12	1	1	NUM
ejpam-4787	212	13	̸=	̸=	PROPN
ejpam-4787	212	14	0	0	NUM
ejpam-4787	212	15	and	and	CCONJ
ejpam-4787	212	16	4λ̄2	4λ̄2	NUM
ejpam-4787	212	17	−	−	NOUN
ejpam-4787	212	18	1	1	NUM
ejpam-4787	212	19	̸=	̸=	PROPN
ejpam-4787	212	20	0	0	NUM
ejpam-4787	212	21	,	,	PUNCT
ejpam-4787	212	22	then	then	ADV
ejpam-4787	212	23	[	[	X
ejpam-4787	212	24	z(ty)]λ	z(ty)]λ	X
ejpam-4787	212	25	+	+	PUNCT
ejpam-4787	213	1	[	[	X
ejpam-4787	213	2	t(yz)]λ	t(yz)]λ	X
ejpam-4787	213	3	+	+	NUM
ejpam-4787	214	1	[	[	X
ejpam-4787	214	2	y(tz)]λ	y(tz)]λ	X
ejpam-4787	214	3	=	=	PUNCT
ejpam-4787	215	1	[	[	X
ejpam-4787	215	2	z(ty)]λ̄	z(ty)]λ̄	X
ejpam-4787	215	3	+	+	X
ejpam-4787	216	1	[	[	X
ejpam-4787	216	2	t(yz)]λ̄	t(yz)]λ̄	X
ejpam-4787	216	3	+	+	X
ejpam-4787	216	4	[	[	X
ejpam-4787	216	5	y(tz)]λ̄	y(tz)]λ̄	NOUN
ejpam-4787	216	6	=	=	SYM
ejpam-4787	216	7	0	0	NUM
ejpam-4787	216	8	;	;	PUNCT
ejpam-4787	216	9	posing	pose	VERB
ejpam-4787	216	10	t	t	NOUN
ejpam-4787	216	11	=	=	PUNCT
ejpam-4787	216	12	x0	x0	PROPN
ejpam-4787	216	13	;	;	PUNCT
ejpam-4787	216	14	y	y	PROPN
ejpam-4787	216	15	=	=	SYM
ejpam-4787	216	16	y0	y0	PROPN
ejpam-4787	216	17	;	;	PUNCT
ejpam-4787	216	18	z	z	NOUN
ejpam-4787	216	19	=	=	SYM
ejpam-4787	216	20	z0	z0	PROPN
ejpam-4787	216	21	,	,	PUNCT
ejpam-4787	216	22	we	we	PRON
ejpam-4787	216	23	have	have	VERB
ejpam-4787	216	24	(	(	PUNCT
ejpam-4787	216	25	1	1	NUM
ejpam-4787	216	26	)	)	PUNCT
ejpam-4787	216	27	.	.	PUNCT
ejpam-4787	217	1	by	by	ADP
ejpam-4787	217	2	proceeding	proceed	VERB
ejpam-4787	217	3	in	in	ADP
ejpam-4787	217	4	a	a	DET
ejpam-4787	217	5	similar	similar	ADJ
ejpam-4787	217	6	way	way	NOUN
ejpam-4787	217	7	,	,	PUNCT
ejpam-4787	217	8	we	we	PRON
ejpam-4787	217	9	find	find	VERB
ejpam-4787	217	10	the	the	DET
ejpam-4787	217	11	other	other	ADJ
ejpam-4787	217	12	identities	identity	NOUN
ejpam-4787	217	13	.	.	PUNCT
ejpam-4787	218	1	the	the	DET
ejpam-4787	218	2	following	follow	VERB
ejpam-4787	218	3	two	two	NUM
ejpam-4787	218	4	results	result	NOUN
ejpam-4787	218	5	are	be	AUX
ejpam-4787	218	6	immediate	immediate	ADJ
ejpam-4787	218	7	consequences	consequence	NOUN
ejpam-4787	218	8	of	of	ADP
ejpam-4787	218	9	lemma	lemma	PROPN
ejpam-4787	218	10	1	1	NUM
ejpam-4787	218	11	and	and	CCONJ
ejpam-4787	218	12	theorem2	theorem2	PROPN
ejpam-4787	218	13	.	.	PUNCT
ejpam-4787	219	1	corollary	corollary	ADJ
ejpam-4787	219	2	1	1	NUM
ejpam-4787	219	3	.	.	PUNCT
ejpam-4787	220	1	if	if	SCONJ
ejpam-4787	220	2	a0	a0	PROPN
ejpam-4787	220	3	=	=	SYM
ejpam-4787	220	4	0	0	PROPN
ejpam-4787	220	5	,	,	PUNCT
ejpam-4787	220	6	then	then	ADV
ejpam-4787	220	7	a2	a2	PROPN
ejpam-4787	220	8	1	1	NUM
ejpam-4787	220	9	2	2	NUM
ejpam-4787	220	10	⊂	⊂	X
ejpam-4787	220	11	aλ	aλ	PROPN
ejpam-4787	220	12	⊕	⊕	PROPN
ejpam-4787	220	13	aλ̄	aλ̄	PROPN
ejpam-4787	220	14	,	,	PUNCT
ejpam-4787	220	15	a	a	DET
ejpam-4787	220	16	1	1	NUM
ejpam-4787	220	17	2	2	NUM
ejpam-4787	220	18	aλ	aλ	ADP
ejpam-4787	220	19	⊂	⊂	PRON
ejpam-4787	220	20	a	a	DET
ejpam-4787	220	21	1	1	NUM
ejpam-4787	220	22	2	2	NUM
ejpam-4787	220	23	⊕	⊕	PROPN
ejpam-4787	220	24	aλ̄	aλ̄	NOUN
ejpam-4787	220	25	,	,	PUNCT
ejpam-4787	220	26	a	a	DET
ejpam-4787	220	27	1	1	NUM
ejpam-4787	220	28	2	2	NUM
ejpam-4787	220	29	aλ̄	aλ̄	NOUN
ejpam-4787	220	30	⊂	⊂	NOUN
ejpam-4787	220	31	a	a	DET
ejpam-4787	220	32	1	1	NUM
ejpam-4787	220	33	2	2	NUM
ejpam-4787	220	34	⊕	⊕	PROPN
ejpam-4787	220	35	aλ	aλ	PROPN
ejpam-4787	220	36	,	,	PUNCT
ejpam-4787	220	37	a2	a2	PROPN
ejpam-4787	220	38	λ	λ	NOUN
ejpam-4787	220	39	=	=	SYM
ejpam-4787	220	40	a2	a2	PROPN
ejpam-4787	220	41	λ̄	λ̄	X
ejpam-4787	221	1	=	=	PUNCT
ejpam-4787	221	2	aλaλ̄	aλaλ̄	PROPN
ejpam-4787	221	3	=	=	NOUN
ejpam-4787	221	4	0	0	PROPN
ejpam-4787	221	5	and	and	CCONJ
ejpam-4787	221	6	for	for	ADP
ejpam-4787	221	7	all	all	DET
ejpam-4787	221	8	x	x	SYM
ejpam-4787	221	9	1	1	NUM
ejpam-4787	221	10	2	2	NUM
ejpam-4787	221	11	∈	∈	NOUN
ejpam-4787	221	12	a	a	DET
ejpam-4787	221	13	1	1	NUM
ejpam-4787	221	14	2	2	NUM
ejpam-4787	221	15	;	;	PUNCT
ejpam-4787	221	16	xλ	xλ	PROPN
ejpam-4787	221	17	∈	∈	PROPN
ejpam-4787	221	18	aλ	aλ	VERB
ejpam-4787	221	19	;	;	PUNCT
ejpam-4787	221	20	xλ̄	xλ̄	PROPN
ejpam-4787	221	21	∈	∈	PROPN
ejpam-4787	221	22	aλ̄	aλ̄	NOUN
ejpam-4787	221	23	the	the	DET
ejpam-4787	221	24	following	follow	VERB
ejpam-4787	221	25	identities	identity	NOUN
ejpam-4787	221	26	are	be	AUX
ejpam-4787	221	27	verified	verify	VERB
ejpam-4787	221	28	:	:	PUNCT
ejpam-4787	221	29	i	i	X
ejpam-4787	221	30	)	)	PUNCT
ejpam-4787	222	1	[	[	X
ejpam-4787	222	2	(	(	PUNCT
ejpam-4787	222	3	λ+	λ+	PUNCT
ejpam-4787	222	4	1)x	1)x	NUM
ejpam-4787	222	5	1	1	NUM
ejpam-4787	222	6	2	2	NUM
ejpam-4787	222	7	(	(	PUNCT
ejpam-4787	222	8	x21	x21	NUM
ejpam-4787	222	9	2	2	NUM
ejpam-4787	222	10	)	)	PUNCT
ejpam-4787	222	11	λ	λ	NOUN
ejpam-4787	222	12	+	+	CCONJ
ejpam-4787	222	13	(	(	PUNCT
ejpam-4787	222	14	λ̄+	λ̄+	NUM
ejpam-4787	222	15	1)x	1)x	NUM
ejpam-4787	222	16	1	1	NUM
ejpam-4787	222	17	2	2	NUM
ejpam-4787	222	18	(	(	PUNCT
ejpam-4787	222	19	x21	x21	PROPN
ejpam-4787	222	20	2	2	NUM
ejpam-4787	222	21	)	)	PUNCT
ejpam-4787	222	22	λ̄]1/2	λ̄]1/2	NOUN
ejpam-4787	222	23	=	=	SYM
ejpam-4787	222	24	0	0	NUM
ejpam-4787	222	25	;	;	PUNCT
ejpam-4787	222	26	ii	ii	X
ejpam-4787	222	27	)	)	PUNCT
ejpam-4787	222	28	(	(	PUNCT
ejpam-4787	222	29	2λ+	2λ+	NUM
ejpam-4787	222	30	3)(x	3)(x	NUM
ejpam-4787	222	31	1	1	NUM
ejpam-4787	222	32	2	2	NUM
ejpam-4787	222	33	(	(	PUNCT
ejpam-4787	222	34	x	x	NOUN
ejpam-4787	222	35	1	1	NUM
ejpam-4787	222	36	2	2	NUM
ejpam-4787	222	37	xλ)λ̄)λ	xλ)λ̄)λ	PROPN
ejpam-4787	222	38	+	+	CCONJ
ejpam-4787	222	39	(	(	PUNCT
ejpam-4787	222	40	λ+	λ+	NUM
ejpam-4787	222	41	6)(x	6)(x	NUM
ejpam-4787	222	42	1	1	NUM
ejpam-4787	222	43	2	2	NUM
ejpam-4787	222	44	(	(	PUNCT
ejpam-4787	222	45	x	x	NOUN
ejpam-4787	222	46	1	1	NUM
ejpam-4787	222	47	2	2	NUM
ejpam-4787	222	48	xλ	xλ	NOUN
ejpam-4787	222	49	)	)	PUNCT
ejpam-4787	222	50	1	1	NUM
ejpam-4787	222	51	2	2	NUM
ejpam-4787	222	52	)	)	PUNCT
ejpam-4787	222	53	λ	λ	NOUN
ejpam-4787	222	54	=	=	SYM
ejpam-4787	222	55	0	0	NUM
ejpam-4787	222	56	;	;	PUNCT
ejpam-4787	222	57	d.	d.	PROPN
ejpam-4787	222	58	kabre	kabre	PROPN
ejpam-4787	222	59	,	,	PUNCT
ejpam-4787	222	60	a.	a.	NOUN
ejpam-4787	222	61	conseibo	conseibo	PROPN
ejpam-4787	222	62	/	/	SYM
ejpam-4787	222	63	eur	eur	PROPN
ejpam-4787	222	64	.	.	PUNCT
ejpam-4787	223	1	j.	j.	PROPN
ejpam-4787	223	2	pure	pure	PROPN
ejpam-4787	223	3	appl	appl	PROPN
ejpam-4787	223	4	.	.	PROPN
ejpam-4787	223	5	math	math	PROPN
ejpam-4787	223	6	,	,	PUNCT
ejpam-4787	223	7	16	16	NUM
ejpam-4787	223	8	(	(	PUNCT
ejpam-4787	223	9	3	3	NUM
ejpam-4787	223	10	)	)	PUNCT
ejpam-4787	223	11	(	(	PUNCT
ejpam-4787	223	12	2023	2023	NUM
ejpam-4787	223	13	)	)	PUNCT
ejpam-4787	223	14	,	,	PUNCT
ejpam-4787	223	15	1480	1480	NUM
ejpam-4787	223	16	-	-	SYM
ejpam-4787	223	17	1490	1490	NUM
ejpam-4787	223	18	1485	1485	NUM
ejpam-4787	223	19	iii	iii	NOUN
ejpam-4787	223	20	)	)	PUNCT
ejpam-4787	223	21	(	(	PUNCT
ejpam-4787	223	22	2λ̄+	2λ̄+	PROPN
ejpam-4787	223	23	3)(x	3)(x	NUM
ejpam-4787	223	24	1	1	NUM
ejpam-4787	223	25	2	2	NUM
ejpam-4787	223	26	(	(	PUNCT
ejpam-4787	223	27	x	x	NOUN
ejpam-4787	223	28	1	1	NUM
ejpam-4787	223	29	2	2	NUM
ejpam-4787	223	30	xλ̄)λ)λ̄	xλ̄)λ)λ̄	PUNCT
ejpam-4787	223	31	+	+	CCONJ
ejpam-4787	223	32	(	(	PUNCT
ejpam-4787	223	33	λ̄+	λ̄+	NUM
ejpam-4787	223	34	6)(x	6)(x	NUM
ejpam-4787	223	35	1	1	NUM
ejpam-4787	223	36	2	2	NUM
ejpam-4787	223	37	(	(	PUNCT
ejpam-4787	223	38	x	x	NOUN
ejpam-4787	223	39	1	1	NUM
ejpam-4787	223	40	2	2	NUM
ejpam-4787	223	41	xλ̄	xλ̄	NUM
ejpam-4787	223	42	)	)	PUNCT
ejpam-4787	223	43	1	1	NUM
ejpam-4787	223	44	2	2	NUM
ejpam-4787	223	45	)	)	PUNCT
ejpam-4787	223	46	λ̄	λ̄	NOUN
ejpam-4787	224	1	=	=	PUNCT
ejpam-4787	224	2	0	0	NUM
ejpam-4787	224	3	;	;	PUNCT
ejpam-4787	224	4	iv	iv	X
ejpam-4787	224	5	)	)	PUNCT
ejpam-4787	224	6	xλ(xλx	xλ(xλx	NOUN
ejpam-4787	224	7	1	1	NUM
ejpam-4787	224	8	2	2	NUM
ejpam-4787	224	9	)	)	PUNCT
ejpam-4787	224	10	=	=	SYM
ejpam-4787	224	11	0	0	NUM
ejpam-4787	224	12	;	;	PUNCT
ejpam-4787	224	13	v	v	NOUN
ejpam-4787	224	14	)	)	PUNCT
ejpam-4787	224	15	xλ̄(xλ̄x	xλ̄(xλ̄x	VERB
ejpam-4787	224	16	1	1	NUM
ejpam-4787	224	17	2	2	NUM
ejpam-4787	224	18	)	)	PUNCT
ejpam-4787	224	19	=	=	SYM
ejpam-4787	224	20	0	0	NUM
ejpam-4787	224	21	;	;	PUNCT
ejpam-4787	224	22	vi	vi	X
ejpam-4787	224	23	)	)	PUNCT
ejpam-4787	224	24	(	(	PUNCT
ejpam-4787	224	25	xλ(xλ̄x	xλ(xλ̄x	NOUN
ejpam-4787	224	26	1	1	NUM
ejpam-4787	224	27	2	2	NUM
ejpam-4787	224	28	)	)	PUNCT
ejpam-4787	224	29	)	)	PUNCT
ejpam-4787	224	30	λ̄	λ̄	VERB
ejpam-4787	225	1	=	=	PUNCT
ejpam-4787	225	2	0	0	NUM
ejpam-4787	225	3	;	;	PUNCT
ejpam-4787	225	4	vii	vii	PROPN
ejpam-4787	225	5	)	)	PUNCT
ejpam-4787	225	6	(	(	PUNCT
ejpam-4787	225	7	xλ̄(xλx	xλ̄(xλx	PROPN
ejpam-4787	225	8	1	1	NUM
ejpam-4787	225	9	2	2	NUM
ejpam-4787	225	10	)	)	PUNCT
ejpam-4787	225	11	)	)	PUNCT
ejpam-4787	226	1	λ	λ	NOUN
ejpam-4787	226	2	=	=	SYM
ejpam-4787	226	3	0	0	NUM
ejpam-4787	226	4	;	;	PUNCT
ejpam-4787	226	5	viii	viii	ADJ
ejpam-4787	226	6	)	)	PUNCT
ejpam-4787	226	7	(	(	PUNCT
ejpam-4787	227	1	2λ−	2λ−	NUM
ejpam-4787	227	2	1)xλ(xλ̄x	1)xλ(xλ̄x	NUM
ejpam-4787	227	3	1	1	NUM
ejpam-4787	227	4	2	2	NUM
ejpam-4787	227	5	)	)	PUNCT
ejpam-4787	228	1	+	+	CCONJ
ejpam-4787	228	2	(	(	PUNCT
ejpam-4787	228	3	2λ̄−	2λ̄−	NUM
ejpam-4787	228	4	1)xλ̄(xλx	1)xλ̄(xλx	NUM
ejpam-4787	228	5	1	1	NUM
ejpam-4787	228	6	2	2	NUM
ejpam-4787	228	7	)	)	PUNCT
ejpam-4787	228	8	=	=	SYM
ejpam-4787	229	1	0	0	X
ejpam-4787	229	2	.	.	PUNCT
ejpam-4787	229	3	corollary	corollary	ADJ
ejpam-4787	229	4	2	2	NUM
ejpam-4787	229	5	.	.	PUNCT
ejpam-4787	230	1	if	if	SCONJ
ejpam-4787	230	2	aᾱ	aᾱ	PROPN
ejpam-4787	230	3	=	=	NOUN
ejpam-4787	230	4	0	0	NUM
ejpam-4787	230	5	with	with	ADP
ejpam-4787	230	6	α	α	PROPN
ejpam-4787	230	7	∈	∈	PROPN
ejpam-4787	230	8	{	{	PUNCT
ejpam-4787	230	9	λ	λ	NOUN
ejpam-4787	230	10	,	,	PUNCT
ejpam-4787	230	11	λ̄	λ̄	ADP
ejpam-4787	230	12	}	}	PUNCT
ejpam-4787	230	13	,	,	PUNCT
ejpam-4787	230	14	then	then	ADV
ejpam-4787	230	15	the	the	DET
ejpam-4787	230	16	following	follow	VERB
ejpam-4787	230	17	identities	identity	NOUN
ejpam-4787	230	18	are	be	AUX
ejpam-4787	230	19	verified	verify	VERB
ejpam-4787	230	20	:	:	PUNCT
ejpam-4787	230	21	i	i	X
ejpam-4787	230	22	)	)	PUNCT
ejpam-4787	231	1	2ex30	2ex30	PROPN
ejpam-4787	231	2	=	=	SYM
ejpam-4787	231	3	x30	x30	PROPN
ejpam-4787	231	4	;	;	PUNCT
ejpam-4787	231	5	ii	ii	X
ejpam-4787	231	6	)	)	PUNCT
ejpam-4787	232	1	[	[	X
ejpam-4787	232	2	12(x	12(x	NUM
ejpam-4787	232	3	1	1	NUM
ejpam-4787	232	4	2	2	NUM
ejpam-4787	232	5	(	(	PUNCT
ejpam-4787	232	6	x21	x21	NUM
ejpam-4787	232	7	2	2	NUM
ejpam-4787	232	8	)	)	PUNCT
ejpam-4787	232	9	0	0	NUM
ejpam-4787	232	10	)	)	PUNCT
ejpam-4787	233	1	+	+	CCONJ
ejpam-4787	234	1	3(α+	3(α+	NUM
ejpam-4787	234	2	1)(x	1)(x	NUM
ejpam-4787	234	3	1	1	NUM
ejpam-4787	234	4	2	2	NUM
ejpam-4787	234	5	(	(	PUNCT
ejpam-4787	234	6	x21	x21	PROPN
ejpam-4787	234	7	2	2	NUM
ejpam-4787	234	8	)	)	PUNCT
ejpam-4787	234	9	α	α	NOUN
ejpam-4787	234	10	)	)	PUNCT
ejpam-4787	234	11	]	]	PUNCT
ejpam-4787	234	12	1	1	NUM
ejpam-4787	234	13	2	2	NUM
ejpam-4787	234	14	=	=	SYM
ejpam-4787	234	15	0	0	NUM
ejpam-4787	234	16	;	;	PUNCT
ejpam-4787	234	17	iii	iii	X
ejpam-4787	234	18	)	)	PUNCT
ejpam-4787	235	1	[	[	X
ejpam-4787	235	2	(	(	PUNCT
ejpam-4787	235	3	α+	α+	PROPN
ejpam-4787	235	4	1)(x	1)(x	NUM
ejpam-4787	235	5	1	1	NUM
ejpam-4787	235	6	2	2	NUM
ejpam-4787	235	7	(	(	PUNCT
ejpam-4787	235	8	x20	x20	NOUN
ejpam-4787	235	9	)	)	PUNCT
ejpam-4787	235	10	1	1	NUM
ejpam-4787	235	11	2	2	NUM
ejpam-4787	235	12	)	)	PUNCT
ejpam-4787	236	1	+	+	CCONJ
ejpam-4787	236	2	8(x0(x0x	8(x0(x0x	NUM
ejpam-4787	236	3	1	1	NUM
ejpam-4787	236	4	2	2	NUM
ejpam-4787	236	5	)	)	PUNCT
ejpam-4787	236	6	1	1	NUM
ejpam-4787	236	7	2	2	NUM
ejpam-4787	236	8	)	)	PUNCT
ejpam-4787	236	9	]	]	PUNCT
ejpam-4787	236	10	α	α	X
ejpam-4787	236	11	=	=	SYM
ejpam-4787	236	12	0	0	NUM
ejpam-4787	236	13	;	;	PUNCT
ejpam-4787	236	14	iv	iv	X
ejpam-4787	236	15	)	)	PUNCT
ejpam-4787	237	1	[	[	X
ejpam-4787	237	2	(	(	PUNCT
ejpam-4787	237	3	−4α−	−4α−	PROPN
ejpam-4787	237	4	2)(x	2)(x	NUM
ejpam-4787	237	5	1	1	NUM
ejpam-4787	237	6	2	2	NUM
ejpam-4787	237	7	(	(	PUNCT
ejpam-4787	237	8	x0x	x0x	PROPN
ejpam-4787	237	9	1	1	NUM
ejpam-4787	237	10	2	2	NUM
ejpam-4787	237	11	)	)	PUNCT
ejpam-4787	237	12	α	α	NOUN
ejpam-4787	237	13	)	)	PUNCT
ejpam-4787	238	1	+	+	CCONJ
ejpam-4787	238	2	12(x	12(x	NUM
ejpam-4787	238	3	1	1	NUM
ejpam-4787	238	4	2	2	NUM
ejpam-4787	238	5	(	(	PUNCT
ejpam-4787	238	6	x0x	x0x	PROPN
ejpam-4787	238	7	1	1	NUM
ejpam-4787	238	8	2	2	NUM
ejpam-4787	238	9	)	)	PUNCT
ejpam-4787	238	10	1	1	NUM
ejpam-4787	238	11	2	2	NUM
ejpam-4787	238	12	)	)	PUNCT
ejpam-4787	238	13	]	]	PUNCT
ejpam-4787	238	14	0	0	X
ejpam-4787	238	15	=	=	SYM
ejpam-4787	238	16	0	0	NUM
ejpam-4787	238	17	;	;	PUNCT
ejpam-4787	238	18	v	v	NOUN
ejpam-4787	238	19	)	)	PUNCT
ejpam-4787	239	1	[	[	X
ejpam-4787	239	2	(	(	PUNCT
ejpam-4787	239	3	6α+	6α+	NUM
ejpam-4787	239	4	13)(x	13)(x	NUM
ejpam-4787	239	5	1	1	NUM
ejpam-4787	239	6	2	2	NUM
ejpam-4787	239	7	(	(	PUNCT
ejpam-4787	239	8	xαx	xαx	NOUN
ejpam-4787	239	9	1	1	NUM
ejpam-4787	239	10	2	2	NUM
ejpam-4787	239	11	)	)	PUNCT
ejpam-4787	239	12	0	0	NUM
ejpam-4787	239	13	)	)	PUNCT
ejpam-4787	240	1	+	+	CCONJ
ejpam-4787	240	2	(	(	PUNCT
ejpam-4787	240	3	2α+	2α+	NUM
ejpam-4787	240	4	12)(x	12)(x	NOUN
ejpam-4787	240	5	1	1	NUM
ejpam-4787	240	6	2	2	NUM
ejpam-4787	240	7	(	(	PUNCT
ejpam-4787	240	8	xαx	xαx	NOUN
ejpam-4787	240	9	1	1	NUM
ejpam-4787	240	10	2	2	NUM
ejpam-4787	240	11	)	)	PUNCT
ejpam-4787	240	12	1	1	NUM
ejpam-4787	240	13	2	2	NUM
ejpam-4787	240	14	)	)	PUNCT
ejpam-4787	240	15	]	]	PUNCT
ejpam-4787	240	16	α	α	X
ejpam-4787	240	17	=	=	SYM
ejpam-4787	240	18	0	0	NUM
ejpam-4787	240	19	;	;	PUNCT
ejpam-4787	240	20	v	v	NUM
ejpam-4787	240	21	i	i	NOUN
ejpam-4787	240	22	)	)	PUNCT
ejpam-4787	241	1	[	[	X
ejpam-4787	241	2	(	(	PUNCT
ejpam-4787	241	3	7α+	7α+	NUM
ejpam-4787	241	4	3)(xα(xαx	3)(xα(xαx	NOUN
ejpam-4787	241	5	1	1	NUM
ejpam-4787	241	6	2	2	NUM
ejpam-4787	241	7	)	)	PUNCT
ejpam-4787	241	8	1	1	NUM
ejpam-4787	241	9	2	2	NUM
ejpam-4787	241	10	)	)	PUNCT
ejpam-4787	242	1	+	+	CCONJ
ejpam-4787	242	2	8α(xα(xαx	8α(xα(xαx	NUM
ejpam-4787	242	3	1	1	NUM
ejpam-4787	242	4	2	2	NUM
ejpam-4787	242	5	)	)	PUNCT
ejpam-4787	242	6	0	0	NUM
ejpam-4787	242	7	)	)	PUNCT
ejpam-4787	242	8	]	]	PUNCT
ejpam-4787	243	1	1	1	NUM
ejpam-4787	243	2	2	2	NUM
ejpam-4787	243	3	=	=	SYM
ejpam-4787	243	4	0	0	NUM
ejpam-4787	243	5	;	;	PUNCT
ejpam-4787	243	6	v	v	NUM
ejpam-4787	243	7	ii	ii	NOUN
ejpam-4787	243	8	)	)	PUNCT
ejpam-4787	244	1	[	[	X
ejpam-4787	244	2	x	x	SYM
ejpam-4787	244	3	1	1	NUM
ejpam-4787	244	4	2	2	NUM
ejpam-4787	244	5	(	(	PUNCT
ejpam-4787	244	6	x20	x20	NOUN
ejpam-4787	244	7	)	)	PUNCT
ejpam-4787	244	8	1	1	NUM
ejpam-4787	244	9	2	2	NUM
ejpam-4787	244	10	]	]	SYM
ejpam-4787	244	11	0	0	PUNCT
ejpam-4787	245	1	=	=	PUNCT
ejpam-4787	246	1	[	[	X
ejpam-4787	246	2	xα(x	xα(x	NUM
ejpam-4787	246	3	2	2	NUM
ejpam-4787	246	4	0	0	NUM
ejpam-4787	246	5	)	)	PUNCT
ejpam-4787	246	6	1	1	NUM
ejpam-4787	246	7	2	2	NUM
ejpam-4787	246	8	]	]	SYM
ejpam-4787	246	9	0	0	PUNCT
ejpam-4787	247	1	=	=	SYM
ejpam-4787	248	1	[	[	X
ejpam-4787	248	2	xα(x0xα	xα(x0xα	X
ejpam-4787	248	3	)	)	PUNCT
ejpam-4787	248	4	1	1	NUM
ejpam-4787	248	5	2	2	NUM
ejpam-4787	248	6	]	]	SYM
ejpam-4787	248	7	0	0	PUNCT
ejpam-4787	249	1	=	=	PUNCT
ejpam-4787	250	1	[	[	X
ejpam-4787	250	2	xα(x	xα(x	NUM
ejpam-4787	250	3	1	1	NUM
ejpam-4787	250	4	2	2	NUM
ejpam-4787	250	5	xα	xα	CCONJ
ejpam-4787	250	6	)	)	PUNCT
ejpam-4787	250	7	1	1	NUM
ejpam-4787	250	8	2	2	NUM
ejpam-4787	250	9	]	]	SYM
ejpam-4787	250	10	0	0	PUNCT
ejpam-4787	251	1	=	=	PUNCT
ejpam-4787	251	2	[	[	X
ejpam-4787	251	3	xα(x	xα(x	NUM
ejpam-4787	251	4	1	1	NUM
ejpam-4787	251	5	2	2	NUM
ejpam-4787	251	6	x0	x0	NUM
ejpam-4787	251	7	)	)	PUNCT
ejpam-4787	251	8	1	1	NUM
ejpam-4787	251	9	2	2	NUM
ejpam-4787	251	10	]	]	SYM
ejpam-4787	251	11	0	0	NUM
ejpam-4787	251	12	=	=	SYM
ejpam-4787	251	13	0	0	NUM
ejpam-4787	251	14	;	;	PUNCT
ejpam-4787	251	15	v	v	NUM
ejpam-4787	251	16	iii	iii	NOUN
ejpam-4787	251	17	)	)	PUNCT
ejpam-4787	252	1	[	[	X
ejpam-4787	252	2	xα(x	xα(x	NUM
ejpam-4787	252	3	2	2	NUM
ejpam-4787	252	4	0	0	NUM
ejpam-4787	252	5	)	)	PUNCT
ejpam-4787	252	6	1	1	NUM
ejpam-4787	252	7	2	2	NUM
ejpam-4787	252	8	]	]	SYM
ejpam-4787	252	9	1	1	NUM
ejpam-4787	252	10	2	2	NUM
ejpam-4787	252	11	=	=	SYM
ejpam-4787	252	12	[	[	X
ejpam-4787	252	13	xα(x0xα	xα(x0xα	X
ejpam-4787	252	14	)	)	PUNCT
ejpam-4787	252	15	1	1	NUM
ejpam-4787	252	16	2	2	NUM
ejpam-4787	252	17	]	]	SYM
ejpam-4787	252	18	1	1	NUM
ejpam-4787	252	19	2	2	NUM
ejpam-4787	252	20	=	=	SYM
ejpam-4787	253	1	[	[	X
ejpam-4787	253	2	xα(x	xα(x	NUM
ejpam-4787	253	3	2	2	NUM
ejpam-4787	253	4	1	1	NUM
ejpam-4787	253	5	2	2	NUM
ejpam-4787	253	6	)	)	PUNCT
ejpam-4787	253	7	0	0	NUM
ejpam-4787	253	8	]	]	SYM
ejpam-4787	253	9	1	1	NUM
ejpam-4787	253	10	2	2	NUM
ejpam-4787	253	11	=	=	SYM
ejpam-4787	253	12	0	0	NUM
ejpam-4787	253	13	;	;	PUNCT
ejpam-4787	253	14	ix	ix	X
ejpam-4787	253	15	)	)	PUNCT
ejpam-4787	254	1	[	[	X
ejpam-4787	254	2	x0(x0xα	x0(x0xα	X
ejpam-4787	254	3	)	)	PUNCT
ejpam-4787	254	4	1	1	NUM
ejpam-4787	254	5	2	2	NUM
ejpam-4787	254	6	]	]	PUNCT
ejpam-4787	254	7	α	α	X
ejpam-4787	254	8	=	=	X
ejpam-4787	255	1	[	[	X
ejpam-4787	255	2	x	x	SYM
ejpam-4787	255	3	1	1	NUM
ejpam-4787	255	4	2	2	NUM
ejpam-4787	255	5	(	(	PUNCT
ejpam-4787	255	6	x0xα	x0xα	PROPN
ejpam-4787	255	7	)	)	PUNCT
ejpam-4787	255	8	1	1	NUM
ejpam-4787	255	9	2	2	NUM
ejpam-4787	255	10	]	]	PUNCT
ejpam-4787	255	11	α	α	X
ejpam-4787	255	12	=	=	SYM
ejpam-4787	255	13	0	0	PROPN
ejpam-4787	255	14	.	.	PUNCT
ejpam-4787	256	1	in	in	ADP
ejpam-4787	256	2	[	[	X
ejpam-4787	256	3	4	4	NUM
ejpam-4787	256	4	]	]	PUNCT
ejpam-4787	256	5	,	,	PUNCT
ejpam-4787	256	6	the	the	DET
ejpam-4787	256	7	author	author	NOUN
ejpam-4787	256	8	give	give	VERB
ejpam-4787	256	9	peirce	peirce	NOUN
ejpam-4787	256	10	decomposition	decomposition	NOUN
ejpam-4787	256	11	of	of	ADP
ejpam-4787	256	12	a	a	DET
ejpam-4787	256	13	principal	principal	ADJ
ejpam-4787	256	14	train	train	NOUN
ejpam-4787	256	15	algebra	algebra	NOUN
ejpam-4787	256	16	theorem	theorem	VERB
ejpam-4787	256	17	3	3	NUM
ejpam-4787	256	18	.	.	PUNCT
ejpam-4787	256	19	(	(	PUNCT
ejpam-4787	256	20	see	see	VERB
ejpam-4787	256	21	theorem	theorem	NOUN
ejpam-4787	256	22	1	1	NUM
ejpam-4787	256	23	,	,	PUNCT
ejpam-4787	256	24	[	[	X
ejpam-4787	256	25	4	4	NUM
ejpam-4787	256	26	]	]	PUNCT
ejpam-4787	256	27	)	)	PUNCT
ejpam-4787	256	28	let	let	VERB
ejpam-4787	256	29	(	(	PUNCT
ejpam-4787	256	30	a	a	DET
ejpam-4787	256	31	,	,	PUNCT
ejpam-4787	256	32	ω	ω	NOUN
ejpam-4787	256	33	)	)	PUNCT
ejpam-4787	256	34	be	be	VERB
ejpam-4787	256	35	a	a	DET
ejpam-4787	256	36	principal	principal	ADJ
ejpam-4787	256	37	train	train	NOUN
ejpam-4787	256	38	algebra	algebra	NOUN
ejpam-4787	256	39	with	with	ADP
ejpam-4787	256	40	an	an	DET
ejpam-4787	256	41	idempotent	idempotent	ADJ
ejpam-4787	256	42	e	e	NOUN
ejpam-4787	256	43	and	and	CCONJ
ejpam-4787	256	44	with	with	ADP
ejpam-4787	256	45	principal	principal	ADJ
ejpam-4787	256	46	train	train	NOUN
ejpam-4787	256	47	polynomial	polynomial	ADJ
ejpam-4787	256	48	p	p	X
ejpam-4787	256	49	(	(	PUNCT
ejpam-4787	256	50	x	x	NOUN
ejpam-4787	256	51	)	)	PUNCT
ejpam-4787	256	52	=	=	SYM
ejpam-4787	256	53	(	(	PUNCT
ejpam-4787	256	54	x	x	SYM
ejpam-4787	256	55	−	−	PROPN
ejpam-4787	256	56	1)(x	1)(x	NUM
ejpam-4787	256	57	−λ1	−λ1	NOUN
ejpam-4787	256	58	)	)	PUNCT
ejpam-4787	256	59	·	·	PUNCT
ejpam-4787	256	60	·	·	PUNCT
ejpam-4787	256	61	·	·	PUNCT
ejpam-4787	257	1	(	(	PUNCT
ejpam-4787	257	2	x	x	X
ejpam-4787	257	3	−λr−1	−λr−1	X
ejpam-4787	257	4	)	)	PUNCT
ejpam-4787	257	5	(	(	PUNCT
ejpam-4787	257	6	the	the	DET
ejpam-4787	257	7	λi	λi	NOUN
ejpam-4787	257	8	are	be	AUX
ejpam-4787	257	9	two	two	NUM
ejpam-4787	257	10	by	by	ADP
ejpam-4787	257	11	two	two	NUM
ejpam-4787	257	12	distinct	distinct	ADJ
ejpam-4787	257	13	)	)	PUNCT
ejpam-4787	257	14	.	.	PUNCT
ejpam-4787	258	1	then	then	ADV
ejpam-4787	258	2	a	a	DET
ejpam-4787	258	3	splits	split	NOUN
ejpam-4787	258	4	into	into	ADP
ejpam-4787	258	5	the	the	DET
ejpam-4787	258	6	direct	direct	ADJ
ejpam-4787	258	7	sum	sum	NOUN
ejpam-4787	258	8	a	a	DET
ejpam-4787	258	9	=	=	X
ejpam-4787	258	10	ke	ke	PROPN
ejpam-4787	258	11	⊕	⊕	PROPN
ejpam-4787	258	12	v1	v1	PROPN
ejpam-4787	258	13	⊕	⊕	PROPN
ejpam-4787	258	14	v2	v2	PROPN
ejpam-4787	258	15	⊕	⊕	PROPN
ejpam-4787	258	16	·	·	PUNCT
ejpam-4787	258	17	·	·	PUNCT
ejpam-4787	258	18	·	·	PUNCT
ejpam-4787	259	1	⊕	⊕	PROPN
ejpam-4787	259	2	vs	vs	ADP
ejpam-4787	259	3	where	where	SCONJ
ejpam-4787	259	4	vi	vi	NOUN
ejpam-4787	259	5	=	=	SYM
ejpam-4787	259	6	n	n	NOUN
ejpam-4787	259	7	∩	∩	NOUN
ejpam-4787	259	8	(	(	PUNCT
ejpam-4787	259	9	le	le	X
ejpam-4787	259	10	−	−	PROPN
ejpam-4787	259	11	γiid	γiid	NOUN
ejpam-4787	259	12	)	)	PUNCT
ejpam-4787	259	13	,	,	PUNCT
ejpam-4787	259	14	le	le	X
ejpam-4787	259	15	:	:	PUNCT
ejpam-4787	259	16	a	a	DET
ejpam-4787	259	17	→	→	SYM
ejpam-4787	259	18	a	a	NOUN
ejpam-4787	259	19	,	,	PUNCT
ejpam-4787	259	20	x	x	PROPN
ejpam-4787	259	21	7→	7→	NUM
ejpam-4787	259	22	ex	ex	NOUN
ejpam-4787	259	23	,	,	PUNCT
ejpam-4787	259	24	i	i	PROPN
ejpam-4787	259	25	d	d	PROPN
ejpam-4787	259	26	:	:	PUNCT
ejpam-4787	259	27	a	a	DET
ejpam-4787	259	28	→	→	SYM
ejpam-4787	259	29	a	a	NOUN
ejpam-4787	259	30	,	,	PUNCT
ejpam-4787	259	31	x	x	PROPN
ejpam-4787	259	32	7→	7→	NUM
ejpam-4787	259	33	x.	x.	NOUN
ejpam-4787	259	34	in	in	ADP
ejpam-4787	259	35	[	[	X
ejpam-4787	259	36	7	7	X
ejpam-4787	259	37	]	]	PUNCT
ejpam-4787	259	38	the	the	DET
ejpam-4787	259	39	authors	author	NOUN
ejpam-4787	259	40	gave	give	VERB
ejpam-4787	259	41	a	a	DET
ejpam-4787	259	42	characterization	characterization	NOUN
ejpam-4787	259	43	of	of	ADP
ejpam-4787	259	44	principal	principal	ADJ
ejpam-4787	259	45	train	train	NOUN
ejpam-4787	259	46	algebras	algebra	NOUN
ejpam-4787	259	47	of	of	ADP
ejpam-4787	259	48	rank	rank	NOUN
ejpam-4787	259	49	4	4	NUM
ejpam-4787	259	50	.	.	PUNCT
ejpam-4787	259	51	theorem	theorem	VERB
ejpam-4787	259	52	4	4	NUM
ejpam-4787	259	53	.	.	PUNCT
ejpam-4787	259	54	(	(	PUNCT
ejpam-4787	259	55	theorem	theorem	NOUN
ejpam-4787	259	56	5	5	NUM
ejpam-4787	259	57	,	,	PUNCT
ejpam-4787	259	58	[	[	X
ejpam-4787	259	59	7	7	NUM
ejpam-4787	259	60	]	]	PUNCT
ejpam-4787	259	61	)	)	PUNCT
ejpam-4787	259	62	let	let	VERB
ejpam-4787	259	63	(	(	PUNCT
ejpam-4787	259	64	a	a	DET
ejpam-4787	259	65	,	,	PUNCT
ejpam-4787	259	66	ω	ω	NOUN
ejpam-4787	259	67	)	)	PUNCT
ejpam-4787	259	68	be	be	AUX
ejpam-4787	259	69	a	a	DET
ejpam-4787	259	70	baric	baric	ADJ
ejpam-4787	259	71	algebra	algebra	NOUN
ejpam-4787	259	72	.	.	PUNCT
ejpam-4787	260	1	the	the	DET
ejpam-4787	260	2	algebra	algebra	NOUN
ejpam-4787	260	3	a	a	PRON
ejpam-4787	260	4	is	be	AUX
ejpam-4787	260	5	a	a	DET
ejpam-4787	260	6	principal	principal	ADJ
ejpam-4787	260	7	train	train	NOUN
ejpam-4787	260	8	algebra	algebra	NOUN
ejpam-4787	260	9	of	of	ADP
ejpam-4787	260	10	rank	rank	NOUN
ejpam-4787	260	11	4	4	NUM
ejpam-4787	260	12	,	,	PUNCT
ejpam-4787	260	13	with	with	ADP
ejpam-4787	260	14	principal	principal	ADJ
ejpam-4787	260	15	train	train	NOUN
ejpam-4787	260	16	polynomial	polynomial	ADJ
ejpam-4787	260	17	x(x	x(x	PROPN
ejpam-4787	261	1	−	−	PROPN
ejpam-4787	261	2	1)(x	1)(x	NUM
ejpam-4787	262	1	−	−	PROPN
ejpam-4787	262	2	λ1)(x	λ1)(x	NUM
ejpam-4787	262	3	−	−	NOUN
ejpam-4787	262	4	λ2	λ2	PROPN
ejpam-4787	262	5	)	)	PUNCT
ejpam-4787	262	6	where	where	SCONJ
ejpam-4787	262	7	λ1	λ1	ADJ
ejpam-4787	262	8	and	and	CCONJ
ejpam-4787	262	9	λ2	λ2	NOUN
ejpam-4787	262	10	different	different	ADJ
ejpam-4787	262	11	and	and	CCONJ
ejpam-4787	262	12	different	different	ADJ
ejpam-4787	262	13	from	from	ADP
ejpam-4787	262	14	1	1	NUM
ejpam-4787	262	15	2	2	NUM
ejpam-4787	262	16	,	,	PUNCT
ejpam-4787	262	17	if	if	SCONJ
ejpam-4787	262	18	and	and	CCONJ
ejpam-4787	262	19	only	only	ADV
ejpam-4787	262	20	if	if	SCONJ
ejpam-4787	262	21	:	:	PUNCT
ejpam-4787	262	22	1	1	X
ejpam-4787	262	23	)	)	PUNCT
ejpam-4787	262	24	a	a	DET
ejpam-4787	262	25	possesses	possess	VERB
ejpam-4787	262	26	an	an	DET
ejpam-4787	262	27	idempotent	idempotent	ADJ
ejpam-4787	262	28	e	e	NOUN
ejpam-4787	262	29	and	and	CCONJ
ejpam-4787	262	30	,	,	PUNCT
ejpam-4787	262	31	with	with	ADP
ejpam-4787	262	32	respect	respect	NOUN
ejpam-4787	262	33	to	to	ADP
ejpam-4787	262	34	e	e	NOUN
ejpam-4787	262	35	,	,	PUNCT
ejpam-4787	262	36	it	it	PRON
ejpam-4787	262	37	has	have	VERB
ejpam-4787	262	38	the	the	DET
ejpam-4787	262	39	peirce	peirce	NOUN
ejpam-4787	262	40	decomposition	decomposition	NOUN
ejpam-4787	262	41	a	a	DET
ejpam-4787	262	42	=	=	SYM
ejpam-4787	262	43	ke⊕	ke⊕	PROPN
ejpam-4787	262	44	u1/2	u1/2	PROPN
ejpam-4787	262	45	⊕	⊕	PROPN
ejpam-4787	262	46	uλ1	uλ1	VERB
ejpam-4787	262	47	⊕	⊕	PROPN
ejpam-4787	262	48	uλ2	uλ2	VERB
ejpam-4787	262	49	where	where	SCONJ
ejpam-4787	262	50	ui	ui	NOUN
ejpam-4787	262	51	=	=	PUNCT
ejpam-4787	262	52	{	{	PUNCT
ejpam-4787	262	53	x	x	SYM
ejpam-4787	262	54	∈	∈	PROPN
ejpam-4787	262	55	kerω	kerω	NOUN
ejpam-4787	262	56	,	,	PUNCT
ejpam-4787	262	57	ex	ex	X
ejpam-4787	262	58	=	=	NOUN
ejpam-4787	262	59	ix	ix	PROPN
ejpam-4787	262	60	}	}	PUNCT
ejpam-4787	262	61	(	(	PUNCT
ejpam-4787	262	62	i	i	PRON
ejpam-4787	262	63	∈	∈	PROPN
ejpam-4787	262	64	{	{	PUNCT
ejpam-4787	262	65	1/2	1/2	NUM
ejpam-4787	262	66	,	,	PUNCT
ejpam-4787	262	67	λ1	λ1	ADJ
ejpam-4787	262	68	,	,	PUNCT
ejpam-4787	262	69	λ2	λ2	NOUN
ejpam-4787	262	70	}	}	PUNCT
ejpam-4787	262	71	)	)	PUNCT
ejpam-4787	262	72	d.	d.	PROPN
ejpam-4787	262	73	kabre	kabre	PROPN
ejpam-4787	262	74	,	,	PUNCT
ejpam-4787	262	75	a.	a.	NOUN
ejpam-4787	262	76	conseibo	conseibo	PROPN
ejpam-4787	262	77	/	/	SYM
ejpam-4787	262	78	eur	eur	PROPN
ejpam-4787	262	79	.	.	PUNCT
ejpam-4787	263	1	j.	j.	PROPN
ejpam-4787	263	2	pure	pure	PROPN
ejpam-4787	263	3	appl	appl	PROPN
ejpam-4787	263	4	.	.	PROPN
ejpam-4787	263	5	math	math	PROPN
ejpam-4787	263	6	,	,	PUNCT
ejpam-4787	263	7	16	16	NUM
ejpam-4787	263	8	(	(	PUNCT
ejpam-4787	263	9	3	3	NUM
ejpam-4787	263	10	)	)	PUNCT
ejpam-4787	263	11	(	(	PUNCT
ejpam-4787	263	12	2023	2023	NUM
ejpam-4787	263	13	)	)	PUNCT
ejpam-4787	263	14	,	,	PUNCT
ejpam-4787	263	15	1480	1480	NUM
ejpam-4787	263	16	-	-	SYM
ejpam-4787	263	17	1490	1490	NUM
ejpam-4787	263	18	1486	1486	NUM
ejpam-4787	263	19	2	2	NUM
ejpam-4787	263	20	)	)	PUNCT
ejpam-4787	263	21	u2	u2	PROPN
ejpam-4787	263	22	1/2	1/2	NUM
ejpam-4787	263	23	⊂	⊂	PROPN
ejpam-4787	263	24	uλ1⊕uλ2	uλ1⊕uλ2	PROPN
ejpam-4787	263	25	,	,	PUNCT
ejpam-4787	263	26	u1/2uλ1	u1/2uλ1	PROPN
ejpam-4787	263	27	⊂	⊂	PROPN
ejpam-4787	263	28	u1/2⊕uλ2	u1/2⊕uλ2	PROPN
ejpam-4787	263	29	,	,	PUNCT
ejpam-4787	264	1	u1/2uλ2	u1/2uλ2	PROPN
ejpam-4787	264	2	⊂	⊂	PROPN
ejpam-4787	264	3	u1/2⊕uλ1	u1/2⊕uλ1	PROPN
ejpam-4787	264	4	,	,	PUNCT
ejpam-4787	264	5	u	u	NOUN
ejpam-4787	264	6	2	2	NUM
ejpam-4787	264	7	λ1	λ1	PROPN
ejpam-4787	264	8	⊂	⊂	PROPN
ejpam-4787	264	9	uλ2	uλ2	PROPN
ejpam-4787	264	10	,	,	PUNCT
ejpam-4787	264	11	u	u	NOUN
ejpam-4787	264	12	2	2	NUM
ejpam-4787	264	13	λ2	λ2	NOUN
ejpam-4787	264	14	⊂	⊂	X
ejpam-4787	264	15	uλ1	uλ1	NOUN
ejpam-4787	264	16	,	,	PUNCT
ejpam-4787	264	17	uλ1uλ2	uλ1uλ2	PROPN
ejpam-4787	264	18	=	=	SYM
ejpam-4787	264	19	0,(uλ1	0,(uλ1	PROPN
ejpam-4787	264	20	⊕	⊕	PROPN
ejpam-4787	264	21	uλ2	uλ2	PROPN
ejpam-4787	264	22	)	)	PUNCT
ejpam-4787	264	23	3	3	NUM
ejpam-4787	264	24	=	=	SYM
ejpam-4787	264	25	0	0	NUM
ejpam-4787	264	26	.	.	NOUN
ejpam-4787	264	27	3	3	NUM
ejpam-4787	264	28	)	)	PUNCT
ejpam-4787	264	29	for	for	ADP
ejpam-4787	264	30	all	all	DET
ejpam-4787	264	31	x	x	SYM
ejpam-4787	264	32	∈	∈	PROPN
ejpam-4787	264	33	kerω	kerω	NOUN
ejpam-4787	264	34	,	,	PUNCT
ejpam-4787	264	35	u	u	PROPN
ejpam-4787	264	36	∈	∈	PROPN
ejpam-4787	264	37	u1/2	u1/2	NOUN
ejpam-4787	264	38	,	,	PUNCT
ejpam-4787	264	39	v	v	NOUN
ejpam-4787	264	40	∈	∈	PROPN
ejpam-4787	264	41	uλ1	uλ1	NOUN
ejpam-4787	264	42	and	and	CCONJ
ejpam-4787	264	43	w	w	PROPN
ejpam-4787	264	44	∈	∈	PROPN
ejpam-4787	264	45	uλ2	uλ2	PROPN
ejpam-4787	264	46	,	,	PUNCT
ejpam-4787	264	47	the	the	DET
ejpam-4787	264	48	following	follow	VERB
ejpam-4787	264	49	relations	relation	NOUN
ejpam-4787	264	50	are	be	AUX
ejpam-4787	264	51	verified	verify	VERB
ejpam-4787	264	52	:	:	PUNCT
ejpam-4787	264	53	(	(	PUNCT
ejpam-4787	264	54	i	i	NOUN
ejpam-4787	264	55	)	)	PUNCT
ejpam-4787	264	56	(	(	PUNCT
ejpam-4787	264	57	12	12	NUM
ejpam-4787	264	58	−	−	NOUN
ejpam-4787	264	59	λ2)(u(u	λ2)(u(u	NOUN
ejpam-4787	264	60	2)λ1)1/2	2)λ1)1/2	NUM
ejpam-4787	265	1	+	+	CCONJ
ejpam-4787	265	2	(	(	PUNCT
ejpam-4787	265	3	12	12	NUM
ejpam-4787	265	4	−	−	NOUN
ejpam-4787	265	5	λ1)(u(u	λ1)(u(u	NOUN
ejpam-4787	265	6	2)λ2)1/2	2)λ2)1/2	NUM
ejpam-4787	265	7	;	;	PUNCT
ejpam-4787	265	8	(	(	PUNCT
ejpam-4787	265	9	ii	ii	NOUN
ejpam-4787	265	10	)	)	PUNCT
ejpam-4787	265	11	(	(	PUNCT
ejpam-4787	265	12	λ1	λ1	PROPN
ejpam-4787	265	13	−	−	PROPN
ejpam-4787	265	14	λ2)(u(uv)1/2)λ1	λ2)(u(uv)1/2)λ1	NOUN
ejpam-4787	266	1	+	+	CCONJ
ejpam-4787	266	2	(	(	PUNCT
ejpam-4787	266	3	λ1	λ1	ADJ
ejpam-4787	266	4	−	−	PROPN
ejpam-4787	266	5	1	1	NUM
ejpam-4787	266	6	2)(u(uv)λ2)λ1	2)(u(uv)λ2)λ1	NUM
ejpam-4787	266	7	;	;	PUNCT
ejpam-4787	266	8	(	(	PUNCT
ejpam-4787	266	9	iii	iii	X
ejpam-4787	266	10	)	)	PUNCT
ejpam-4787	266	11	(	(	PUNCT
ejpam-4787	266	12	λ2	λ2	NOUN
ejpam-4787	266	13	−	−	NOUN
ejpam-4787	266	14	λ1)(u(uw)1/2)λ2	λ1)(u(uw)1/2)λ2	NOUN
ejpam-4787	266	15	+	+	CCONJ
ejpam-4787	266	16	(	(	PUNCT
ejpam-4787	266	17	λ2	λ2	NOUN
ejpam-4787	266	18	−	−	PROPN
ejpam-4787	266	19	1	1	NUM
ejpam-4787	266	20	2)(u(uw)λ1)λ2	2)(u(uw)λ1)λ2	NUM
ejpam-4787	266	21	;	;	PUNCT
ejpam-4787	266	22	(	(	PUNCT
ejpam-4787	266	23	iv	iv	X
ejpam-4787	266	24	)	)	PUNCT
ejpam-4787	266	25	(	(	PUNCT
ejpam-4787	266	26	1−	1−	NUM
ejpam-4787	266	27	2λ2)(v(uv))1/2	2λ2)(v(uv))1/2	NUM
ejpam-4787	267	1	+	+	CCONJ
ejpam-4787	267	2	(	(	PUNCT
ejpam-4787	267	3	λ1	λ1	ADJ
ejpam-4787	267	4	−	−	PROPN
ejpam-4787	267	5	1	1	NUM
ejpam-4787	267	6	2)uv	2)uv	PROPN
ejpam-4787	267	7	2	2	NUM
ejpam-4787	267	8	;	;	PUNCT
ejpam-4787	267	9	(	(	PUNCT
ejpam-4787	267	10	v	v	NOUN
ejpam-4787	267	11	)	)	PUNCT
ejpam-4787	267	12	(	(	PUNCT
ejpam-4787	267	13	1−	1−	NUM
ejpam-4787	267	14	2λ1)(w(uw))1/2	2λ1)(w(uw))1/2	NUM
ejpam-4787	267	15	+	+	CCONJ
ejpam-4787	267	16	(	(	PUNCT
ejpam-4787	267	17	λ2	λ2	NOUN
ejpam-4787	267	18	−	−	PROPN
ejpam-4787	267	19	1	1	NUM
ejpam-4787	267	20	2)uw	2)uw	PROPN
ejpam-4787	267	21	2	2	NUM
ejpam-4787	267	22	;	;	PUNCT
ejpam-4787	267	23	(	(	PUNCT
ejpam-4787	267	24	vi	vi	NOUN
ejpam-4787	267	25	)	)	PUNCT
ejpam-4787	267	26	(	(	PUNCT
ejpam-4787	267	27	12	12	NUM
ejpam-4787	267	28	−	−	NOUN
ejpam-4787	267	29	λ1)(v(uw)1/2)1/2	λ1)(v(uw)1/2)1/2	INTJ
ejpam-4787	268	1	+	+	CCONJ
ejpam-4787	268	2	(	(	PUNCT
ejpam-4787	268	3	12	12	NUM
ejpam-4787	268	4	−	−	PROPN
ejpam-4787	268	5	λ2)(w(uv)1/2)1/2	λ2)(w(uv)1/2)1/2	PROPN
ejpam-4787	268	6	;	;	PUNCT
ejpam-4787	268	7	(	(	PUNCT
ejpam-4787	268	8	vii	vii	PROPN
ejpam-4787	268	9	)	)	PUNCT
ejpam-4787	268	10	(	(	PUNCT
ejpam-4787	268	11	λ1	λ1	PROPN
ejpam-4787	268	12	−	−	PROPN
ejpam-4787	268	13	λ2)(w(uv)1/2)λ1	λ2)(w(uv)1/2)λ1	VERB
ejpam-4787	269	1	+	+	CCONJ
ejpam-4787	269	2	(	(	PUNCT
ejpam-4787	269	3	λ1	λ1	ADJ
ejpam-4787	269	4	−	−	PROPN
ejpam-4787	269	5	1	1	NUM
ejpam-4787	269	6	2)w(uv)λ2	2)w(uv)λ2	NUM
ejpam-4787	269	7	;	;	PUNCT
ejpam-4787	269	8	(	(	PUNCT
ejpam-4787	269	9	viii	viii	NOUN
ejpam-4787	269	10	)	)	PUNCT
ejpam-4787	269	11	(	(	PUNCT
ejpam-4787	269	12	λ2	λ2	NOUN
ejpam-4787	269	13	−	−	NOUN
ejpam-4787	269	14	λ1)(w(uv)1/2)λ2	λ1)(w(uv)1/2)λ2	X
ejpam-4787	269	15	+	+	CCONJ
ejpam-4787	269	16	(	(	PUNCT
ejpam-4787	269	17	λ2	λ2	NOUN
ejpam-4787	269	18	−	−	PROPN
ejpam-4787	269	19	1	1	NUM
ejpam-4787	269	20	2)w(uv)λ1	2)w(uv)λ1	NUM
ejpam-4787	269	21	;	;	PUNCT
ejpam-4787	269	22	where	where	SCONJ
ejpam-4787	269	23	(	(	PUNCT
ejpam-4787	269	24	x)i	x)i	X
ejpam-4787	269	25	denotes	denote	VERB
ejpam-4787	269	26	the	the	DET
ejpam-4787	269	27	projection	projection	NOUN
ejpam-4787	269	28	of	of	ADP
ejpam-4787	269	29	x	x	PROPN
ejpam-4787	269	30	∈	∈	PROPN
ejpam-4787	269	31	kerω	kerω	NOUN
ejpam-4787	269	32	onto	onto	ADP
ejpam-4787	269	33	the	the	DET
ejpam-4787	269	34	subspace	subspace	NOUN
ejpam-4787	269	35	ui	ui	PROPN
ejpam-4787	269	36	,	,	PUNCT
ejpam-4787	269	37	i	i	PRON
ejpam-4787	269	38	∈	∈	PROPN
ejpam-4787	269	39	{	{	PUNCT
ejpam-4787	269	40	1	1	NUM
ejpam-4787	269	41	2	2	NUM
ejpam-4787	269	42	,	,	PUNCT
ejpam-4787	269	43	λ1	λ1	ADJ
ejpam-4787	269	44	,	,	PUNCT
ejpam-4787	269	45	λ2	λ2	PROPN
ejpam-4787	269	46	}	}	PUNCT
ejpam-4787	269	47	;	;	PUNCT
ejpam-4787	269	48	(	(	PUNCT
ejpam-4787	269	49	ix	ix	X
ejpam-4787	269	50	)	)	PUNCT
ejpam-4787	269	51	x4	x4	PROPN
ejpam-4787	269	52	=	=	SYM
ejpam-4787	270	1	0	0	NUM
ejpam-4787	270	2	.	.	NOUN
ejpam-4787	270	3	3	3	X
ejpam-4787	270	4	.	.	X
ejpam-4787	270	5	relation	relation	NOUN
ejpam-4787	270	6	with	with	ADP
ejpam-4787	270	7	principal	principal	ADJ
ejpam-4787	270	8	train	train	NOUN
ejpam-4787	270	9	algebras	algebras	NOUN
ejpam-4787	270	10	proposition	proposition	NOUN
ejpam-4787	270	11	2	2	X
ejpam-4787	270	12	.	.	PUNCT
ejpam-4787	271	1	let	let	VERB
ejpam-4787	271	2	a	a	DET
ejpam-4787	271	3	=	=	SYM
ejpam-4787	271	4	ke	ke	PROPN
ejpam-4787	271	5	⊕	⊕	PROPN
ejpam-4787	271	6	a0	a0	PROPN
ejpam-4787	271	7	⊕	⊕	PROPN
ejpam-4787	271	8	a	a	DET
ejpam-4787	271	9	1	1	NUM
ejpam-4787	271	10	2	2	NUM
ejpam-4787	271	11	⊕	⊕	PROPN
ejpam-4787	271	12	aλ	aλ	ADP
ejpam-4787	271	13	⊕	⊕	PROPN
ejpam-4787	271	14	aλ̄	aλ̄	NOUN
ejpam-4787	271	15	an	an	DET
ejpam-4787	271	16	algebra	algebra	NOUN
ejpam-4787	271	17	satisfying	satisfy	VERB
ejpam-4787	271	18	the	the	DET
ejpam-4787	271	19	identity	identity	NOUN
ejpam-4787	271	20	2x2x4	2x2x4	NOUN
ejpam-4787	271	21	=	=	SYM
ejpam-4787	271	22	ω(x)2x4	ω(x)2x4	NOUN
ejpam-4787	271	23	+	+	CCONJ
ejpam-4787	271	24	ω(x)4x2	ω(x)4x2	ADJ
ejpam-4787	271	25	.	.	PUNCT
ejpam-4787	272	1	if	if	SCONJ
ejpam-4787	272	2	a	a	DET
ejpam-4787	272	3	1	1	NUM
ejpam-4787	272	4	2	2	NUM
ejpam-4787	272	5	=	=	SYM
ejpam-4787	272	6	0	0	NUM
ejpam-4787	272	7	then	then	ADV
ejpam-4787	272	8	a	a	PRON
ejpam-4787	272	9	is	be	AUX
ejpam-4787	272	10	a	a	DET
ejpam-4787	272	11	principal	principal	ADJ
ejpam-4787	272	12	train	train	NOUN
ejpam-4787	272	13	algebra	algebra	NOUN
ejpam-4787	272	14	satisfying	satisfy	VERB
ejpam-4787	272	15	the	the	DET
ejpam-4787	272	16	equation	equation	NOUN
ejpam-4787	272	17	x5	x5	NOUN
ejpam-4787	272	18	−	−	PROPN
ejpam-4787	272	19	1	1	NUM
ejpam-4787	272	20	2ω(x)x	2ω(x)x	NUM
ejpam-4787	272	21	4	4	NUM
ejpam-4787	272	22	+	+	CCONJ
ejpam-4787	272	23	ω(x)2x3	ω(x)2x3	NOUN
ejpam-4787	272	24	−	−	PROPN
ejpam-4787	272	25	3	3	NUM
ejpam-4787	272	26	2ω(x	2ω(x	NUM
ejpam-4787	272	27	)	)	PUNCT
ejpam-4787	272	28	3x2	3x2	NUM
ejpam-4787	272	29	=	=	SYM
ejpam-4787	272	30	0	0	X
ejpam-4787	272	31	.	.	PUNCT
ejpam-4787	273	1	proof	proof	NOUN
ejpam-4787	273	2	.	.	PUNCT
ejpam-4787	274	1	a	a	DET
ejpam-4787	274	2	1	1	NUM
ejpam-4787	274	3	2	2	NUM
ejpam-4787	274	4	being	be	AUX
ejpam-4787	274	5	zero	zero	NUM
ejpam-4787	274	6	,	,	PUNCT
ejpam-4787	274	7	we	we	PRON
ejpam-4787	274	8	have	have	VERB
ejpam-4787	274	9	a2	a2	PROPN
ejpam-4787	274	10	0	0	PUNCT
ejpam-4787	274	11	=	=	SYM
ejpam-4787	274	12	a2	a2	PROPN
ejpam-4787	274	13	λ	λ	NOUN
ejpam-4787	274	14	=	=	SYM
ejpam-4787	274	15	a2	a2	PROPN
ejpam-4787	274	16	λ̄	λ̄	X
ejpam-4787	275	1	=	=	PUNCT
ejpam-4787	275	2	aλa0	aλa0	NOUN
ejpam-4787	275	3	=	=	SYM
ejpam-4787	275	4	aλ̄a0	aλ̄a0	NOUN
ejpam-4787	275	5	=	=	PUNCT
ejpam-4787	275	6	aλ̄aλ	aλ̄aλ	ADJ
ejpam-4787	275	7	=	=	NOUN
ejpam-4787	275	8	0	0	X
ejpam-4787	275	9	.	.	PUNCT
ejpam-4787	276	1	for	for	ADP
ejpam-4787	276	2	x	x	SYM
ejpam-4787	276	3	=	=	SYM
ejpam-4787	276	4	e	e	PROPN
ejpam-4787	276	5	+	+	NUM
ejpam-4787	276	6	x0	x0	PROPN
ejpam-4787	276	7	+	+	CCONJ
ejpam-4787	276	8	xλ	xλ	PROPN
ejpam-4787	277	1	+	+	CCONJ
ejpam-4787	277	2	xλ̄	xλ̄	ADJ
ejpam-4787	277	3	,	,	PUNCT
ejpam-4787	277	4	we	we	PRON
ejpam-4787	277	5	have	have	VERB
ejpam-4787	277	6	x2	x2	NOUN
ejpam-4787	277	7	=	=	PUNCT
ejpam-4787	277	8	e	e	PROPN
ejpam-4787	278	1	+	+	CCONJ
ejpam-4787	278	2	2λxλ	2λxλ	PROPN
ejpam-4787	278	3	+	+	CCONJ
ejpam-4787	278	4	2λ̄xλ̄	2λ̄xλ̄	NUM
ejpam-4787	278	5	,	,	PUNCT
ejpam-4787	278	6	x	x	X
ejpam-4787	278	7	3	3	NUM
ejpam-4787	278	8	=	=	SYM
ejpam-4787	278	9	e	e	NOUN
ejpam-4787	278	10	−	−	NUM
ejpam-4787	278	11	3xλ	3xλ	ADJ
ejpam-4787	278	12	−	−	NOUN
ejpam-4787	278	13	3xλ̄	3xλ̄	NUM
ejpam-4787	278	14	,	,	PUNCT
ejpam-4787	278	15	x	x	X
ejpam-4787	278	16	4	4	NUM
ejpam-4787	278	17	=	=	NOUN
ejpam-4787	278	18	e−	e−	X
ejpam-4787	278	19	2λxλ	2λxλ	NUM
ejpam-4787	278	20	−	−	ADP
ejpam-4787	278	21	2λ̄xλ̄	2λ̄xλ̄	NUM
ejpam-4787	278	22	,	,	PUNCT
ejpam-4787	278	23	x	x	SYM
ejpam-4787	278	24	5	5	NUM
ejpam-4787	278	25	=	=	NUM
ejpam-4787	278	26	e+	e+	X
ejpam-4787	278	27	(	(	PUNCT
ejpam-4787	278	28	2λ+	2λ+	NUM
ejpam-4787	278	29	3)xλ	3)xλ	NUM
ejpam-4787	278	30	+	+	CCONJ
ejpam-4787	278	31	(	(	PUNCT
ejpam-4787	278	32	2λ̄+	2λ̄+	PROPN
ejpam-4787	278	33	3)xλ̄.	3)xλ̄.	PROPN
ejpam-4787	279	1	so	so	ADV
ejpam-4787	279	2	,	,	PUNCT
ejpam-4787	279	3	x	x	PROPN
ejpam-4787	279	4	5	5	NUM
ejpam-4787	279	5	−	−	NUM
ejpam-4787	279	6	1	1	NUM
ejpam-4787	279	7	2x	2x	NUM
ejpam-4787	279	8	4	4	NUM
ejpam-4787	279	9	+	+	CCONJ
ejpam-4787	279	10	x3	x3	ADJ
ejpam-4787	279	11	−	−	PROPN
ejpam-4787	279	12	3	3	NUM
ejpam-4787	279	13	2x	2x	NUM
ejpam-4787	279	14	2	2	NUM
ejpam-4787	279	15	=	=	SYM
ejpam-4787	279	16	0	0	PUNCT
ejpam-4787	280	1	and	and	CCONJ
ejpam-4787	280	2	we	we	PRON
ejpam-4787	280	3	obtain	obtain	VERB
ejpam-4787	280	4	x5	x5	NOUN
ejpam-4787	280	5	−	−	NOUN
ejpam-4787	280	6	1	1	NUM
ejpam-4787	280	7	2ω(x)x	2ω(x)x	NUM
ejpam-4787	280	8	4	4	NUM
ejpam-4787	280	9	+	+	CCONJ
ejpam-4787	280	10	ω(x)2x3	ω(x)2x3	NOUN
ejpam-4787	280	11	−	−	PROPN
ejpam-4787	280	12	3	3	NUM
ejpam-4787	280	13	2ω(x	2ω(x	NUM
ejpam-4787	280	14	)	)	PUNCT
ejpam-4787	280	15	3x2	3x2	NUM
ejpam-4787	281	1	=	=	SYM
ejpam-4787	281	2	0	0	NUM
ejpam-4787	281	3	because	because	SCONJ
ejpam-4787	281	4	the	the	DET
ejpam-4787	281	5	set	set	NOUN
ejpam-4787	281	6	of	of	ADP
ejpam-4787	281	7	elements	element	NOUN
ejpam-4787	281	8	of	of	ADP
ejpam-4787	281	9	weight	weight	NOUN
ejpam-4787	281	10	1	1	NUM
ejpam-4787	281	11	is	be	AUX
ejpam-4787	281	12	dense	dense	ADJ
ejpam-4787	281	13	in	in	ADP
ejpam-4787	281	14	a	a	DET
ejpam-4787	281	15	according	accord	VERB
ejpam-4787	281	16	to	to	ADP
ejpam-4787	281	17	zariski	zariski	VERB
ejpam-4787	281	18	’s	’s	PART
ejpam-4787	281	19	topology	topology	NOUN
ejpam-4787	281	20	.	.	PUNCT
ejpam-4787	282	1	proposition	proposition	NOUN
ejpam-4787	282	2	3	3	X
ejpam-4787	282	3	.	.	PUNCT
ejpam-4787	283	1	let	let	VERB
ejpam-4787	283	2	a	a	DET
ejpam-4787	283	3	=	=	PUNCT
ejpam-4787	283	4	ke⊕a0⊕a	ke⊕a0⊕a	ADP
ejpam-4787	283	5	1	1	NUM
ejpam-4787	283	6	2	2	NUM
ejpam-4787	283	7	⊕aλ⊕aλ̄	⊕aλ⊕aλ̄	NOUN
ejpam-4787	283	8	be	be	VERB
ejpam-4787	283	9	a	a	DET
ejpam-4787	283	10	peirce	peirce	NOUN
ejpam-4787	283	11	decomposition	decomposition	NOUN
ejpam-4787	283	12	of	of	ADP
ejpam-4787	283	13	an	an	DET
ejpam-4787	283	14	algebra	algebra	NOUN
ejpam-4787	283	15	satisfying	satisfy	VERB
ejpam-4787	283	16	the	the	DET
ejpam-4787	283	17	identity	identity	NOUN
ejpam-4787	283	18	2x2x4	2x2x4	NOUN
ejpam-4787	283	19	=	=	SYM
ejpam-4787	283	20	ω(x)2x4	ω(x)2x4	NOUN
ejpam-4787	284	1	+	+	CCONJ
ejpam-4787	285	1	ω(x)4x2	ω(x)4x2	ADJ
ejpam-4787	285	2	.	.	PUNCT
ejpam-4787	286	1	if	if	SCONJ
ejpam-4787	286	2	a0	a0	PROPN
ejpam-4787	286	3	=	=	SYM
ejpam-4787	286	4	aᾱ	aᾱ	PROPN
ejpam-4787	286	5	=	=	SYM
ejpam-4787	286	6	0	0	NUM
ejpam-4787	286	7	with	with	ADP
ejpam-4787	286	8	α	α	PROPN
ejpam-4787	286	9	∈	∈	PROPN
ejpam-4787	286	10	{	{	PUNCT
ejpam-4787	286	11	λ̄	λ̄	NOUN
ejpam-4787	286	12	,	,	PUNCT
ejpam-4787	286	13	¯̄λ	¯̄λ	NOUN
ejpam-4787	286	14	}	}	PUNCT
ejpam-4787	286	15	,	,	PUNCT
ejpam-4787	286	16	then	then	ADV
ejpam-4787	286	17	a	a	DET
ejpam-4787	286	18	checks	check	NOUN
ejpam-4787	286	19	the	the	DET
ejpam-4787	286	20	train	train	NOUN
ejpam-4787	286	21	equation	equation	NOUN
ejpam-4787	286	22	x3	x3	ADJ
ejpam-4787	286	23	−	−	PROPN
ejpam-4787	286	24	(	(	PUNCT
ejpam-4787	286	25	1	1	NUM
ejpam-4787	286	26	+	+	NUM
ejpam-4787	286	27	α)ω(x)x2	α)ω(x)x2	NOUN
ejpam-4787	286	28	+	+	CCONJ
ejpam-4787	286	29	αω(x)2x	αω(x)2x	X
ejpam-4787	286	30	=	=	SYM
ejpam-4787	286	31	0	0	X
ejpam-4787	286	32	.	.	PUNCT
ejpam-4787	287	1	proof	proof	NOUN
ejpam-4787	287	2	.	.	PUNCT
ejpam-4787	288	1	let	let	VERB
ejpam-4787	288	2	a	a	DET
ejpam-4787	288	3	=	=	SYM
ejpam-4787	288	4	ke	ke	PROPN
ejpam-4787	288	5	⊕	⊕	PROPN
ejpam-4787	288	6	a0	a0	PROPN
ejpam-4787	288	7	⊕	⊕	PROPN
ejpam-4787	288	8	a	a	DET
ejpam-4787	288	9	1	1	NUM
ejpam-4787	288	10	2	2	NUM
ejpam-4787	288	11	⊕	⊕	PROPN
ejpam-4787	288	12	aλ	aλ	ADP
ejpam-4787	288	13	⊕	⊕	PROPN
ejpam-4787	288	14	aλ̄	aλ̄	NOUN
ejpam-4787	288	15	be	be	AUX
ejpam-4787	288	16	an	an	DET
ejpam-4787	288	17	algebra	algebra	NOUN
ejpam-4787	288	18	satisfying	satisfy	VERB
ejpam-4787	288	19	the	the	DET
ejpam-4787	288	20	identity	identity	NOUN
ejpam-4787	288	21	2x2x4	2x2x4	NOUN
ejpam-4787	288	22	=	=	SYM
ejpam-4787	288	23	ω(x)2x4	ω(x)2x4	NOUN
ejpam-4787	288	24	+	+	CCONJ
ejpam-4787	288	25	ω(x)4x2	ω(x)4x2	ADJ
ejpam-4787	288	26	.	.	PUNCT
ejpam-4787	288	27	suppose	suppose	VERB
ejpam-4787	288	28	a0	a0	PROPN
ejpam-4787	288	29	=	=	SYM
ejpam-4787	288	30	aλ̄	aλ̄	PROPN
ejpam-4787	288	31	=	=	NOUN
ejpam-4787	288	32	0	0	X
ejpam-4787	288	33	.	.	PUNCT
ejpam-4787	289	1	let	let	VERB
ejpam-4787	289	2	x	x	PUNCT
ejpam-4787	289	3	=	=	PUNCT
ejpam-4787	289	4	e	e	X
ejpam-4787	289	5	+	+	NOUN
ejpam-4787	289	6	x	x	SYM
ejpam-4787	289	7	1	1	NUM
ejpam-4787	289	8	2	2	NUM
ejpam-4787	289	9	+	+	NUM
ejpam-4787	289	10	xλ	xλ	PROPN
ejpam-4787	289	11	be	be	AUX
ejpam-4787	289	12	an	an	DET
ejpam-4787	289	13	element	element	NOUN
ejpam-4787	289	14	of	of	ADP
ejpam-4787	289	15	weight	weight	NOUN
ejpam-4787	289	16	1	1	NUM
ejpam-4787	289	17	of	of	ADP
ejpam-4787	289	18	a.	a.	NOUN
ejpam-4787	289	19	by	by	ADP
ejpam-4787	289	20	exploiting	exploit	VERB
ejpam-4787	289	21	the	the	DET
ejpam-4787	289	22	relations	relation	NOUN
ejpam-4787	289	23	of	of	ADP
ejpam-4787	289	24	the	the	DET
ejpam-4787	289	25	corrolary	corrolary	ADJ
ejpam-4787	289	26	2	2	NUM
ejpam-4787	289	27	,	,	PUNCT
ejpam-4787	289	28	we	we	PRON
ejpam-4787	289	29	have	have	VERB
ejpam-4787	289	30	:	:	PUNCT
ejpam-4787	289	31	x2	x2	PROPN
ejpam-4787	289	32	=	=	PUNCT
ejpam-4787	289	33	e+x	e+x	PROPN
ejpam-4787	289	34	1	1	NUM
ejpam-4787	289	35	2	2	NUM
ejpam-4787	289	36	+2λxλ+x21	+2λxλ+x21	NUM
ejpam-4787	289	37	2	2	NUM
ejpam-4787	289	38	+2x	+2x	NUM
ejpam-4787	289	39	1	1	NUM
ejpam-4787	289	40	2	2	NUM
ejpam-4787	289	41	xλ	xλ	NOUN
ejpam-4787	289	42	,	,	PUNCT
ejpam-4787	289	43	x	x	PROPN
ejpam-4787	289	44	2−x	2−x	NUM
ejpam-4787	290	1	=	=	SYM
ejpam-4787	290	2	(	(	PUNCT
ejpam-4787	290	3	2λ−1)xλ+x21	2λ−1)xλ+x21	NUM
ejpam-4787	290	4	2	2	NUM
ejpam-4787	290	5	+2x	+2x	NUM
ejpam-4787	290	6	1	1	NUM
ejpam-4787	290	7	2	2	NUM
ejpam-4787	290	8	xλ	xλ	NOUN
ejpam-4787	290	9	,	,	PUNCT
ejpam-4787	290	10	x(x2	x(x2	NOUN
ejpam-4787	291	1	−	−	NOUN
ejpam-4787	291	2	x	x	NOUN
ejpam-4787	291	3	)	)	PUNCT
ejpam-4787	292	1	=	=	SYM
ejpam-4787	292	2	λx21	λx21	PROPN
ejpam-4787	292	3	2	2	NUM
ejpam-4787	292	4	+	+	CCONJ
ejpam-4787	292	5	(	(	PUNCT
ejpam-4787	292	6	2λ2	2λ2	NUM
ejpam-4787	292	7	−	−	PROPN
ejpam-4787	292	8	λ)xλ	λ)xλ	NOUN
ejpam-4787	292	9	+	+	NUM
ejpam-4787	292	10	2λxλx	2λxλx	NUM
ejpam-4787	292	11	1	1	NUM
ejpam-4787	292	12	2	2	NUM
ejpam-4787	292	13	=	=	NOUN
ejpam-4787	292	14	λ(x2	λ(x2	NOUN
ejpam-4787	292	15	−	−	PROPN
ejpam-4787	292	16	x	x	NOUN
ejpam-4787	292	17	)	)	PUNCT
ejpam-4787	292	18	,	,	PUNCT
ejpam-4787	292	19	so	so	ADV
ejpam-4787	292	20	x(x2	x(x2	PROPN
ejpam-4787	293	1	−	−	PROPN
ejpam-4787	293	2	x	x	SYM
ejpam-4787	293	3	)	)	PUNCT
ejpam-4787	293	4	=	=	NOUN
ejpam-4787	293	5	λ(x2	λ(x2	NOUN
ejpam-4787	293	6	−	−	PROPN
ejpam-4787	293	7	x	x	NOUN
ejpam-4787	293	8	)	)	PUNCT
ejpam-4787	293	9	and	and	CCONJ
ejpam-4787	293	10	d.	d.	PROPN
ejpam-4787	293	11	kabre	kabre	PROPN
ejpam-4787	293	12	,	,	PUNCT
ejpam-4787	293	13	a.	a.	NOUN
ejpam-4787	293	14	conseibo	conseibo	PROPN
ejpam-4787	293	15	/	/	SYM
ejpam-4787	293	16	eur	eur	PROPN
ejpam-4787	293	17	.	.	PUNCT
ejpam-4787	294	1	j.	j.	PROPN
ejpam-4787	294	2	pure	pure	PROPN
ejpam-4787	294	3	appl	appl	PROPN
ejpam-4787	294	4	.	.	PROPN
ejpam-4787	294	5	math	math	PROPN
ejpam-4787	294	6	,	,	PUNCT
ejpam-4787	294	7	16	16	NUM
ejpam-4787	294	8	(	(	PUNCT
ejpam-4787	294	9	3	3	NUM
ejpam-4787	294	10	)	)	PUNCT
ejpam-4787	294	11	(	(	PUNCT
ejpam-4787	294	12	2023	2023	NUM
ejpam-4787	294	13	)	)	PUNCT
ejpam-4787	294	14	,	,	PUNCT
ejpam-4787	294	15	1480	1480	NUM
ejpam-4787	294	16	-	-	SYM
ejpam-4787	294	17	1490	1490	NUM
ejpam-4787	294	18	1487	1487	NUM
ejpam-4787	294	19	x3−	x3−	PROPN
ejpam-4787	294	20	(	(	PUNCT
ejpam-4787	294	21	1+λ)x2+λx	1+λ)x2+λx	NUM
ejpam-4787	294	22	=	=	NOUN
ejpam-4787	294	23	0	0	NUM
ejpam-4787	294	24	.	.	PUNCT
ejpam-4787	295	1	since	since	SCONJ
ejpam-4787	295	2	the	the	DET
ejpam-4787	295	3	set	set	NOUN
ejpam-4787	295	4	of	of	ADP
ejpam-4787	295	5	elements	element	NOUN
ejpam-4787	295	6	of	of	ADP
ejpam-4787	295	7	weight	weight	NOUN
ejpam-4787	295	8	1	1	NUM
ejpam-4787	295	9	is	be	AUX
ejpam-4787	295	10	dense	dense	ADJ
ejpam-4787	295	11	in	in	ADP
ejpam-4787	295	12	a	a	PRON
ejpam-4787	295	13	by	by	ADP
ejpam-4787	295	14	the	the	DET
ejpam-4787	295	15	zariski	zariski	NOUN
ejpam-4787	295	16	’s	’s	PART
ejpam-4787	295	17	topology	topology	NOUN
ejpam-4787	295	18	,	,	PUNCT
ejpam-4787	295	19	then	then	ADV
ejpam-4787	295	20	for	for	ADP
ejpam-4787	295	21	any	any	DET
ejpam-4787	295	22	x	x	NOUN
ejpam-4787	295	23	in	in	ADP
ejpam-4787	295	24	a	a	PRON
ejpam-4787	295	25	,	,	PUNCT
ejpam-4787	295	26	we	we	PRON
ejpam-4787	295	27	have	have	VERB
ejpam-4787	295	28	x3	x3	VERB
ejpam-4787	295	29	−	−	PROPN
ejpam-4787	295	30	(	(	PUNCT
ejpam-4787	295	31	1	1	NUM
ejpam-4787	296	1	+	+	NUM
ejpam-4787	296	2	λ)ω(x)x2	λ)ω(x)x2	NOUN
ejpam-4787	297	1	+	+	CCONJ
ejpam-4787	297	2	λω(x)2x	λω(x)2x	PROPN
ejpam-4787	297	3	=	=	SYM
ejpam-4787	297	4	0	0	X
ejpam-4787	297	5	.	.	PUNCT
ejpam-4787	298	1	the	the	DET
ejpam-4787	298	2	proof	proof	NOUN
ejpam-4787	298	3	is	be	AUX
ejpam-4787	298	4	similar	similar	ADJ
ejpam-4787	298	5	when	when	SCONJ
ejpam-4787	298	6	we	we	PRON
ejpam-4787	298	7	assume	assume	VERB
ejpam-4787	298	8	a0	a0	NOUN
ejpam-4787	298	9	=	=	SYM
ejpam-4787	298	10	aλ	aλ	PROPN
ejpam-4787	298	11	=	=	SYM
ejpam-4787	298	12	0	0	PROPN
ejpam-4787	298	13	.	.	PUNCT
ejpam-4787	299	1	theorem	theorem	NOUN
ejpam-4787	299	2	5	5	NUM
ejpam-4787	299	3	.	.	PUNCT
ejpam-4787	300	1	let	let	VERB
ejpam-4787	300	2	a	a	DET
ejpam-4787	300	3	be	be	AUX
ejpam-4787	300	4	an	an	DET
ejpam-4787	300	5	algebra	algebra	NOUN
ejpam-4787	300	6	satisfying	satisfy	VERB
ejpam-4787	300	7	the	the	DET
ejpam-4787	300	8	identity	identity	NOUN
ejpam-4787	300	9	2x2x4	2x2x4	NOUN
ejpam-4787	300	10	=	=	NOUN
ejpam-4787	300	11	ω(x)2x4	ω(x)2x4	NOUN
ejpam-4787	301	1	+	+	CCONJ
ejpam-4787	301	2	ω(x)4x2	ω(x)4x2	ADJ
ejpam-4787	301	3	;	;	PUNCT
ejpam-4787	301	4	then	then	ADV
ejpam-4787	301	5	a	a	PRON
ejpam-4787	301	6	is	be	AUX
ejpam-4787	301	7	a	a	DET
ejpam-4787	301	8	principal	principal	ADJ
ejpam-4787	301	9	train	train	NOUN
ejpam-4787	301	10	algebra	algebra	NOUN
ejpam-4787	301	11	of	of	ADP
ejpam-4787	301	12	rank	rank	NOUN
ejpam-4787	301	13	3	3	NUM
ejpam-4787	301	14	if	if	SCONJ
ejpam-4787	301	15	and	and	CCONJ
ejpam-4787	301	16	only	only	ADV
ejpam-4787	301	17	its	its	PRON
ejpam-4787	301	18	train	train	NOUN
ejpam-4787	301	19	equation	equation	NOUN
ejpam-4787	301	20	is	be	AUX
ejpam-4787	301	21	of	of	ADP
ejpam-4787	301	22	the	the	DET
ejpam-4787	301	23	form	form	NOUN
ejpam-4787	302	1	x3	x3	ADJ
ejpam-4787	302	2	−	−	PROPN
ejpam-4787	302	3	(	(	PUNCT
ejpam-4787	302	4	1	1	NUM
ejpam-4787	302	5	+	+	CCONJ
ejpam-4787	302	6	γ)ω(x)x2	γ)ω(x)x2	ADJ
ejpam-4787	302	7	+	+	CCONJ
ejpam-4787	302	8	γω(x)2x	γω(x)2x	NOUN
ejpam-4787	302	9	=	=	SYM
ejpam-4787	302	10	0	0	NUM
ejpam-4787	302	11	,	,	PUNCT
ejpam-4787	302	12	where	where	SCONJ
ejpam-4787	302	13	γ	γ	X
ejpam-4787	302	14	∈	∈	PROPN
ejpam-4787	302	15	{	{	PUNCT
ejpam-4787	302	16	0	0	NUM
ejpam-4787	302	17	,	,	PUNCT
ejpam-4787	302	18	λ	λ	NOUN
ejpam-4787	302	19	,	,	PUNCT
ejpam-4787	302	20	λ̄	λ̄	ADJ
ejpam-4787	302	21	}	}	PUNCT
ejpam-4787	302	22	proof	proof	NOUN
ejpam-4787	302	23	.	.	PUNCT
ejpam-4787	303	1	let	let	VERB
ejpam-4787	303	2	a	a	DET
ejpam-4787	303	3	be	be	AUX
ejpam-4787	303	4	an	an	DET
ejpam-4787	303	5	algebra	algebra	NOUN
ejpam-4787	303	6	satisfying	satisfy	VERB
ejpam-4787	303	7	the	the	DET
ejpam-4787	303	8	identity	identity	NOUN
ejpam-4787	303	9	2x2x4	2x2x4	NOUN
ejpam-4787	303	10	=	=	SYM
ejpam-4787	303	11	ω(x)2x4	ω(x)2x4	NOUN
ejpam-4787	303	12	+	+	CCONJ
ejpam-4787	303	13	ω(x)4x2	ω(x)4x2	ADJ
ejpam-4787	303	14	.	.	PUNCT
ejpam-4787	303	15	suppose	suppose	VERB
ejpam-4787	303	16	a	a	PRON
ejpam-4787	303	17	is	be	AUX
ejpam-4787	303	18	a	a	DET
ejpam-4787	303	19	principal	principal	ADJ
ejpam-4787	303	20	train	train	NOUN
ejpam-4787	303	21	algebra	algebra	NOUN
ejpam-4787	303	22	of	of	ADP
ejpam-4787	303	23	rank	rank	NOUN
ejpam-4787	303	24	3	3	NUM
ejpam-4787	303	25	,	,	PUNCT
ejpam-4787	303	26	its	its	PRON
ejpam-4787	303	27	equation	equation	NOUN
ejpam-4787	303	28	is	be	AUX
ejpam-4787	303	29	x3	x3	ADJ
ejpam-4787	303	30	−	−	PROPN
ejpam-4787	303	31	(	(	PUNCT
ejpam-4787	303	32	1	1	NUM
ejpam-4787	303	33	+	+	NUM
ejpam-4787	303	34	α)ω(x)x2	α)ω(x)x2	NOUN
ejpam-4787	303	35	+	+	CCONJ
ejpam-4787	303	36	αω(x)2x	αω(x)2x	X
ejpam-4787	303	37	=	=	SYM
ejpam-4787	303	38	0	0	NUM
ejpam-4787	303	39	with	with	SCONJ
ejpam-4787	303	40	α	α	PROPN
ejpam-4787	303	41	∈	∈	PROPN
ejpam-4787	303	42	k	k	X
ejpam-4787	303	43	(	(	PUNCT
ejpam-4787	303	44	5	5	NUM
ejpam-4787	303	45	)	)	PUNCT
ejpam-4787	303	46	and	and	CCONJ
ejpam-4787	303	47	a	a	DET
ejpam-4787	303	48	partial	partial	ADJ
ejpam-4787	303	49	linearisation	linearisation	NOUN
ejpam-4787	303	50	of	of	ADP
ejpam-4787	303	51	(	(	PUNCT
ejpam-4787	303	52	5	5	NUM
ejpam-4787	303	53	)	)	PUNCT
ejpam-4787	303	54	gives	give	VERB
ejpam-4787	303	55	us	we	PRON
ejpam-4787	303	56	x2y	x2y	X
ejpam-4787	304	1	+	+	CCONJ
ejpam-4787	304	2	2x(xy)−	2x(xy)−	NUM
ejpam-4787	304	3	(	(	PUNCT
ejpam-4787	304	4	1	1	NUM
ejpam-4787	304	5	+	+	NUM
ejpam-4787	304	6	α)[ω(y)x2	α)[ω(y)x2	NOUN
ejpam-4787	304	7	+	+	CCONJ
ejpam-4787	304	8	2ω(x)xy	2ω(x)xy	NUM
ejpam-4787	304	9	]	]	X
ejpam-4787	305	1	+	+	CCONJ
ejpam-4787	305	2	α[2ω(xy)x+	α[2ω(xy)x+	NOUN
ejpam-4787	305	3	ω(x)2y	ω(x)2y	NOUN
ejpam-4787	305	4	]	]	X
ejpam-4787	306	1	=	=	SYM
ejpam-4787	306	2	0	0	NUM
ejpam-4787	306	3	(	(	PUNCT
ejpam-4787	306	4	6	6	NUM
ejpam-4787	306	5	)	)	PUNCT
ejpam-4787	306	6	setting	set	VERB
ejpam-4787	306	7	y	y	NOUN
ejpam-4787	306	8	=	=	SYM
ejpam-4787	306	9	x4	x4	PROPN
ejpam-4787	306	10	in	in	ADP
ejpam-4787	306	11	(	(	PUNCT
ejpam-4787	306	12	6	6	NUM
ejpam-4787	306	13	)	)	PUNCT
ejpam-4787	306	14	,	,	PUNCT
ejpam-4787	306	15	we	we	PRON
ejpam-4787	306	16	have	have	VERB
ejpam-4787	306	17	x2x4	x2x4	NOUN
ejpam-4787	307	1	+	+	CCONJ
ejpam-4787	308	1	2x6	2x6	NUM
ejpam-4787	308	2	−	−	NOUN
ejpam-4787	308	3	(	(	PUNCT
ejpam-4787	308	4	1	1	NUM
ejpam-4787	308	5	+	+	CCONJ
ejpam-4787	308	6	α)ω(x)4x2	α)ω(x)4x2	PROPN
ejpam-4787	308	7	−	−	NUM
ejpam-4787	308	8	2(1	2(1	NUM
ejpam-4787	309	1	+	+	CCONJ
ejpam-4787	309	2	α)ω(x)x5	α)ω(x)x5	NOUN
ejpam-4787	309	3	+	+	CCONJ
ejpam-4787	309	4	2αω(x)5x+	2αω(x)5x+	NUM
ejpam-4787	309	5	αω(x)2x4	αω(x)2x4	NOUN
ejpam-4787	309	6	=	=	SYM
ejpam-4787	309	7	0	0	PUNCT
ejpam-4787	309	8	(	(	PUNCT
ejpam-4787	309	9	7	7	NUM
ejpam-4787	309	10	)	)	PUNCT
ejpam-4787	309	11	or	or	CCONJ
ejpam-4787	309	12	2x6	2x6	NUM
ejpam-4787	309	13	=	=	SYM
ejpam-4787	309	14	2(1	2(1	NUM
ejpam-4787	309	15	+	+	CCONJ
ejpam-4787	309	16	α)ω(x)x5	α)ω(x)x5	PROPN
ejpam-4787	309	17	−	−	PROPN
ejpam-4787	309	18	2αω(x)2x4	2αω(x)2x4	NUM
ejpam-4787	309	19	,	,	PUNCT
ejpam-4787	309	20	we	we	PRON
ejpam-4787	309	21	also	also	ADV
ejpam-4787	309	22	know	know	VERB
ejpam-4787	309	23	that	that	PRON
ejpam-4787	309	24	x2x4	x2x4	VERB
ejpam-4787	310	1	=	=	SYM
ejpam-4787	310	2	1	1	NUM
ejpam-4787	310	3	2ω(x	2ω(x	NUM
ejpam-4787	310	4	)	)	PUNCT
ejpam-4787	310	5	2x4	2x4	NUM
ejpam-4787	311	1	+	+	CCONJ
ejpam-4787	311	2	1	1	NUM
ejpam-4787	311	3	2ω(x	2ω(x	NUM
ejpam-4787	311	4	)	)	PUNCT
ejpam-4787	311	5	4x2	4x2	NUM
ejpam-4787	311	6	;	;	PUNCT
ejpam-4787	311	7	substituting	substitute	VERB
ejpam-4787	311	8	2x6	2x6	NUM
ejpam-4787	311	9	and	and	CCONJ
ejpam-4787	311	10	x2x4	x2x4	PART
ejpam-4787	311	11	by	by	ADP
ejpam-4787	311	12	their	their	PRON
ejpam-4787	311	13	expressions	expression	NOUN
ejpam-4787	311	14	in	in	ADP
ejpam-4787	311	15	(	(	PUNCT
ejpam-4787	311	16	7	7	NUM
ejpam-4787	311	17	)	)	PUNCT
ejpam-4787	311	18	,	,	PUNCT
ejpam-4787	311	19	we	we	PRON
ejpam-4787	311	20	get	get	VERB
ejpam-4787	311	21	(	(	PUNCT
ejpam-4787	311	22	1	1	NUM
ejpam-4787	311	23	2	2	NUM
ejpam-4787	311	24	−	−	NOUN
ejpam-4787	311	25	α)ω(x)2x4	α)ω(x)2x4	PRON
ejpam-4787	311	26	−	−	PROPN
ejpam-4787	311	27	(	(	PUNCT
ejpam-4787	311	28	1	1	NUM
ejpam-4787	311	29	2	2	NUM
ejpam-4787	311	30	+	+	CCONJ
ejpam-4787	311	31	α)ω(x)4x2	α)ω(x)4x2	PROPN
ejpam-4787	312	1	+	+	CCONJ
ejpam-4787	312	2	2αω(x)5x	2αω(x)5x	NUM
ejpam-4787	312	3	=	=	SYM
ejpam-4787	312	4	0	0	NUM
ejpam-4787	313	1	(	(	PUNCT
ejpam-4787	313	2	8)	8)	NUM
ejpam-4787	313	3	we	we	PRON
ejpam-4787	313	4	can	can	AUX
ejpam-4787	313	5	notice	notice	VERB
ejpam-4787	313	6	that	that	SCONJ
ejpam-4787	313	7	x3	x3	PROPN
ejpam-4787	313	8	=	=	SYM
ejpam-4787	313	9	(	(	PUNCT
ejpam-4787	313	10	1+α)ω(x)x2−αω(x)2x	1+α)ω(x)x2−αω(x)2x	NUM
ejpam-4787	313	11	;	;	PUNCT
ejpam-4787	313	12	which	which	PRON
ejpam-4787	313	13	implies	imply	VERB
ejpam-4787	313	14	that	that	SCONJ
ejpam-4787	313	15	x4	x4	PROPN
ejpam-4787	313	16	=	=	PRON
ejpam-4787	313	17	(	(	PUNCT
ejpam-4787	313	18	1+α)ω(x)x3−	1+α)ω(x)x3−	NOUN
ejpam-4787	313	19	αω(x)2x2	αω(x)2x2	NUM
ejpam-4787	313	20	=	=	SYM
ejpam-4787	313	21	(	(	PUNCT
ejpam-4787	313	22	1	1	NUM
ejpam-4787	313	23	+	+	NUM
ejpam-4787	313	24	α+	α+	PUNCT
ejpam-4787	313	25	α2)ω(x)2x2	α2)ω(x)2x2	NOUN
ejpam-4787	313	26	+	+	CCONJ
ejpam-4787	313	27	(	(	PUNCT
ejpam-4787	313	28	−α2	−α2	PROPN
ejpam-4787	313	29	−	−	PROPN
ejpam-4787	313	30	α)ω(x)3x	α)ω(x)3x	PROPN
ejpam-4787	313	31	.	.	PUNCT
ejpam-4787	314	1	substituting	substitute	VERB
ejpam-4787	314	2	x4	x4	PROPN
ejpam-4787	314	3	by	by	ADP
ejpam-4787	314	4	its	its	PRON
ejpam-4787	314	5	expression	expression	NOUN
ejpam-4787	314	6	in	in	ADP
ejpam-4787	314	7	(	(	PUNCT
ejpam-4787	314	8	8)	8)	NUM
ejpam-4787	314	9	,	,	PUNCT
ejpam-4787	314	10	we	we	PRON
ejpam-4787	314	11	get	get	VERB
ejpam-4787	314	12	−1	−1	ADV
ejpam-4787	314	13	2α(2α	2α(2α	NUM
ejpam-4787	314	14	2+α+3)ω(x)4(x2−ω(x)x	2+α+3)ω(x)4(x2−ω(x)x	NUM
ejpam-4787	314	15	)	)	PUNCT
ejpam-4787	315	1	=	=	SYM
ejpam-4787	315	2	0	0	X
ejpam-4787	315	3	.	.	PUNCT
ejpam-4787	316	1	the	the	DET
ejpam-4787	316	2	algebra	algebra	NOUN
ejpam-4787	316	3	a	a	DET
ejpam-4787	316	4	being	being	NOUN
ejpam-4787	316	5	of	of	ADP
ejpam-4787	316	6	rank	rank	NOUN
ejpam-4787	316	7	3	3	NUM
ejpam-4787	316	8	,	,	PUNCT
ejpam-4787	316	9	then	then	ADV
ejpam-4787	316	10	x2−ω(x)x	x2−ω(x)x	PROPN
ejpam-4787	316	11	̸=	̸=	PROPN
ejpam-4787	316	12	0	0	NUM
ejpam-4787	316	13	which	which	PRON
ejpam-4787	316	14	implies	imply	VERB
ejpam-4787	316	15	that	that	SCONJ
ejpam-4787	316	16	−1	−1	NOUN
ejpam-4787	316	17	2α(2α	2α(2α	NUM
ejpam-4787	316	18	2	2	NUM
ejpam-4787	316	19	+	+	CCONJ
ejpam-4787	316	20	α+	α+	PUNCT
ejpam-4787	316	21	3	3	NUM
ejpam-4787	316	22	)	)	PUNCT
ejpam-4787	316	23	=	=	SYM
ejpam-4787	316	24	0	0	PUNCT
ejpam-4787	317	1	hence	hence	ADV
ejpam-4787	317	2	α	α	NOUN
ejpam-4787	317	3	=	=	SYM
ejpam-4787	317	4	0	0	PROPN
ejpam-4787	317	5	,	,	PUNCT
ejpam-4787	317	6	α	α	NOUN
ejpam-4787	318	1	=	=	SYM
ejpam-4787	318	2	λ	λ	PROPN
ejpam-4787	318	3	or	or	CCONJ
ejpam-4787	318	4	α	α	NOUN
ejpam-4787	318	5	=	=	SYM
ejpam-4787	318	6	λ̄.	λ̄.	PUNCT
ejpam-4787	318	7	conversely	conversely	ADV
ejpam-4787	318	8	,	,	PUNCT
ejpam-4787	318	9	suppose	suppose	VERB
ejpam-4787	318	10	that	that	SCONJ
ejpam-4787	318	11	a	a	PRON
ejpam-4787	318	12	is	be	AUX
ejpam-4787	318	13	a	a	DET
ejpam-4787	318	14	principal	principal	ADJ
ejpam-4787	318	15	train	train	NOUN
ejpam-4787	318	16	algebra	algebra	NOUN
ejpam-4787	318	17	of	of	ADP
ejpam-4787	318	18	train	train	NOUN
ejpam-4787	318	19	equation	equation	NOUN
ejpam-4787	318	20	x3	x3	ADJ
ejpam-4787	318	21	−	−	PROPN
ejpam-4787	318	22	(	(	PUNCT
ejpam-4787	318	23	1	1	NUM
ejpam-4787	318	24	+	+	NUM
ejpam-4787	318	25	α)ω(x)x2	α)ω(x)x2	NOUN
ejpam-4787	318	26	+	+	CCONJ
ejpam-4787	318	27	αω(x)2x	αω(x)2x	X
ejpam-4787	318	28	=	=	SYM
ejpam-4787	318	29	0	0	NUM
ejpam-4787	318	30	with	with	ADP
ejpam-4787	318	31	α	α	PROPN
ejpam-4787	318	32	∈	∈	PROPN
ejpam-4787	318	33	{	{	PUNCT
ejpam-4787	318	34	0	0	NUM
ejpam-4787	318	35	,	,	PUNCT
ejpam-4787	318	36	λ	λ	X
ejpam-4787	318	37	,	,	PUNCT
ejpam-4787	318	38	λ̄	λ̄	ADP
ejpam-4787	318	39	}	}	PUNCT
ejpam-4787	318	40	(	(	PUNCT
ejpam-4787	318	41	9	9	X
ejpam-4787	318	42	)	)	PUNCT
ejpam-4787	318	43	if	if	SCONJ
ejpam-4787	318	44	α	α	NOUN
ejpam-4787	318	45	=	=	SYM
ejpam-4787	318	46	0	0	PROPN
ejpam-4787	318	47	,	,	PUNCT
ejpam-4787	318	48	a	a	PRON
ejpam-4787	318	49	is	be	AUX
ejpam-4787	318	50	a	a	DET
ejpam-4787	318	51	bernstein	bernstein	PROPN
ejpam-4787	318	52	jordan	jordan	PROPN
ejpam-4787	318	53	algebra	algebra	PROPN
ejpam-4787	318	54	(	(	PUNCT
ejpam-4787	318	55	see	see	VERB
ejpam-4787	318	56	[	[	X
ejpam-4787	318	57	10	10	NUM
ejpam-4787	318	58	]	]	PUNCT
ejpam-4787	318	59	)	)	PUNCT
ejpam-4787	318	60	and	and	CCONJ
ejpam-4787	318	61	therfore	therfore	VERB
ejpam-4787	318	62	satisfies	satisfy	VERB
ejpam-4787	318	63	the	the	DET
ejpam-4787	318	64	identity	identity	NOUN
ejpam-4787	318	65	2x2x4	2x2x4	NOUN
ejpam-4787	318	66	=	=	NOUN
ejpam-4787	318	67	ω(x)2x4	ω(x)2x4	NOUN
ejpam-4787	319	1	+	+	X
ejpam-4787	319	2	ω(x)4x2	ω(x)4x2	NOUN
ejpam-4787	319	3	(	(	PUNCT
ejpam-4787	319	4	see	see	VERB
ejpam-4787	319	5	[	[	X
ejpam-4787	319	6	11	11	NUM
ejpam-4787	319	7	]	]	NUM
ejpam-4787	319	8	)	)	PUNCT
ejpam-4787	319	9	.	.	PUNCT
ejpam-4787	320	1	for	for	ADP
ejpam-4787	320	2	α	α	NOUN
ejpam-4787	320	3	=	=	SYM
ejpam-4787	320	4	λ	λ	PROPN
ejpam-4787	320	5	,	,	PUNCT
ejpam-4787	320	6	the	the	DET
ejpam-4787	320	7	partial	partial	ADJ
ejpam-4787	320	8	linearisation	linearisation	NOUN
ejpam-4787	320	9	of	of	ADP
ejpam-4787	320	10	(	(	PUNCT
ejpam-4787	320	11	9	9	NUM
ejpam-4787	320	12	)	)	PUNCT
ejpam-4787	320	13	gives	give	VERB
ejpam-4787	320	14	us	we	PRON
ejpam-4787	320	15	x2y	x2y	X
ejpam-4787	321	1	+	+	CCONJ
ejpam-4787	322	1	2x(xy)−	2x(xy)−	NUM
ejpam-4787	322	2	(	(	PUNCT
ejpam-4787	322	3	1	1	NUM
ejpam-4787	322	4	+	+	NUM
ejpam-4787	322	5	λ)[ω(y)x2	λ)[ω(y)x2	X
ejpam-4787	322	6	+	+	CCONJ
ejpam-4787	322	7	2ω(x)xy	2ω(x)xy	NUM
ejpam-4787	322	8	]	]	X
ejpam-4787	322	9	+	+	NUM
ejpam-4787	322	10	λ[2ω(xy)x+	λ[2ω(xy)x+	NOUN
ejpam-4787	322	11	ω(x)2y	ω(x)2y	NOUN
ejpam-4787	322	12	]	]	PUNCT
ejpam-4787	322	13	=	=	SYM
ejpam-4787	322	14	0	0	NUM
ejpam-4787	322	15	(	(	PUNCT
ejpam-4787	322	16	10	10	NUM
ejpam-4787	322	17	)	)	PUNCT
ejpam-4787	322	18	by	by	ADP
ejpam-4787	322	19	setting	set	VERB
ejpam-4787	322	20	y	y	PROPN
ejpam-4787	322	21	=	=	SYM
ejpam-4787	322	22	x4	x4	PROPN
ejpam-4787	322	23	,	,	PUNCT
ejpam-4787	322	24	we	we	PRON
ejpam-4787	322	25	have	have	VERB
ejpam-4787	322	26	x2x4	x2x4	NOUN
ejpam-4787	322	27	=	=	NOUN
ejpam-4787	322	28	−2x6+(1+λ)[ω(x)4x2	−2x6+(1+λ)[ω(x)4x2	X
ejpam-4787	322	29	+	+	NOUN
ejpam-4787	322	30	2ω(x)x5]−λ[2ω(x)5x+ω(x)2x4	2ω(x)x5]−λ[2ω(x)5x+ω(x)2x4	NOUN
ejpam-4787	322	31	]	]	X
ejpam-4787	322	32	,	,	PUNCT
ejpam-4787	322	33	so	so	ADV
ejpam-4787	322	34	x2x4	x2x4	X
ejpam-4787	322	35	=	=	SYM
ejpam-4787	323	1	[	[	X
ejpam-4787	323	2	−2x6	−2x6	NUM
ejpam-4787	323	3	+	+	NUM
ejpam-4787	323	4	2(1+λ)ω(x)x5−2λω(x)2x4]+λω(x)2x4+(1+λ)ω(x)4x2−2λω(x)5x	2(1+λ)ω(x)x5−2λω(x)2x4]+λω(x)2x4+(1+λ)ω(x)4x2−2λω(x)5x	NUM
ejpam-4787	323	5	=	=	SYM
ejpam-4787	323	6	(	(	PUNCT
ejpam-4787	323	7	1	1	NUM
ejpam-4787	323	8	+	+	CCONJ
ejpam-4787	323	9	λ)ω(x)4x2	λ)ω(x)4x2	PROPN
ejpam-4787	323	10	−	−	NUM
ejpam-4787	323	11	2λω(x)5x+	2λω(x)5x+	NUM
ejpam-4787	323	12	λω(x)2x4	λω(x)2x4	NOUN
ejpam-4787	323	13	,	,	PUNCT
ejpam-4787	323	14	hence	hence	ADV
ejpam-4787	323	15	x2x4−	x2x4−	PROPN
ejpam-4787	323	16	1	1	NUM
ejpam-4787	323	17	2ω(x	2ω(x	NUM
ejpam-4787	323	18	)	)	PUNCT
ejpam-4787	324	1	4x2−	4x2−	NUM
ejpam-4787	324	2	1	1	NUM
ejpam-4787	324	3	2ω(x	2ω(x	NUM
ejpam-4787	324	4	)	)	PUNCT
ejpam-4787	324	5	2x4	2x4	NUM
ejpam-4787	325	1	=	=	SYM
ejpam-4787	325	2	(	(	PUNCT
ejpam-4787	325	3	λ2	λ2	NOUN
ejpam-4787	325	4	+	+	NOUN
ejpam-4787	325	5	λ	λ	NOUN
ejpam-4787	325	6	2−	2−	NUM
ejpam-4787	325	7	1	1	NUM
ejpam-4787	325	8	2)ω(x	2)ω(x	NUM
ejpam-4787	325	9	)	)	PUNCT
ejpam-4787	326	1	3x3+(−λ2	3x3+(−λ2	NUM
ejpam-4787	326	2	+	+	SYM
ejpam-4787	326	3	3λ	3λ	NUM
ejpam-4787	326	4	2	2	NUM
ejpam-4787	326	5	+	+	CCONJ
ejpam-4787	326	6	1	1	NUM
ejpam-4787	326	7	2)ω(x	2)ω(x	NUM
ejpam-4787	326	8	)	)	PUNCT
ejpam-4787	326	9	4x2−2λω(x)5x	4x2−2λω(x)5x	NUM
ejpam-4787	326	10	,	,	PUNCT
ejpam-4787	326	11	so	so	ADV
ejpam-4787	326	12	x2x4	x2x4	X
ejpam-4787	327	1	−	−	PROPN
ejpam-4787	327	2	1	1	NUM
ejpam-4787	327	3	2ω(x	2ω(x	NUM
ejpam-4787	327	4	)	)	PUNCT
ejpam-4787	327	5	4x2	4x2	NUM
ejpam-4787	328	1	−	−	NOUN
ejpam-4787	328	2	1	1	NUM
ejpam-4787	328	3	2ω(x	2ω(x	NUM
ejpam-4787	328	4	)	)	PUNCT
ejpam-4787	328	5	2x4	2x4	NUM
ejpam-4787	329	1	=	=	SYM
ejpam-4787	329	2	−2ω(x)3x3	−2ω(x)3x3	ADJ
ejpam-4787	329	3	+	+	CCONJ
ejpam-4787	329	4	(	(	PUNCT
ejpam-4787	329	5	2λ	2λ	NOUN
ejpam-4787	329	6	+	+	CCONJ
ejpam-4787	329	7	2)ω(x)4x2	2)ω(x)4x2	NUM
ejpam-4787	329	8	−	−	NUM
ejpam-4787	329	9	2λω(x)5x	2λω(x)5x	NUM
ejpam-4787	329	10	.	.	PUNCT
ejpam-4787	330	1	therefore	therefore	ADV
ejpam-4787	330	2	x2x4−	x2x4−	PROPN
ejpam-4787	330	3	1	1	NUM
ejpam-4787	330	4	2ω(x	2ω(x	NUM
ejpam-4787	330	5	)	)	PUNCT
ejpam-4787	330	6	4x2−	4x2−	NUM
ejpam-4787	330	7	1	1	NUM
ejpam-4787	330	8	2ω(x	2ω(x	NUM
ejpam-4787	330	9	)	)	PUNCT
ejpam-4787	330	10	2x4	2x4	NUM
ejpam-4787	331	1	=	=	SYM
ejpam-4787	331	2	−2ω(x)3(x3−	−2ω(x)3(x3−	X
ejpam-4787	331	3	(	(	PUNCT
ejpam-4787	331	4	λ+1)ω(x)x2+λω(x)2x	λ+1)ω(x)x2+λω(x)2x	PROPN
ejpam-4787	331	5	)	)	PUNCT
ejpam-4787	331	6	=	=	SYM
ejpam-4787	331	7	0	0	NUM
ejpam-4787	331	8	and	and	CCONJ
ejpam-4787	331	9	a	a	DET
ejpam-4787	331	10	satisfies	satisfie	NOUN
ejpam-4787	331	11	the	the	DET
ejpam-4787	331	12	identity	identity	NOUN
ejpam-4787	331	13	2x2x4	2x2x4	NOUN
ejpam-4787	331	14	=	=	SYM
ejpam-4787	331	15	ω(x)2x4	ω(x)2x4	NOUN
ejpam-4787	331	16	+	+	CCONJ
ejpam-4787	331	17	ω(x)4x2	ω(x)4x2	ADJ
ejpam-4787	331	18	.	.	PUNCT
ejpam-4787	332	1	the	the	DET
ejpam-4787	332	2	proof	proof	NOUN
ejpam-4787	332	3	is	be	AUX
ejpam-4787	332	4	similar	similar	ADJ
ejpam-4787	332	5	for	for	ADP
ejpam-4787	332	6	α	α	NOUN
ejpam-4787	332	7	=	=	SYM
ejpam-4787	332	8	λ̄.	λ̄.	PROPN
ejpam-4787	332	9	d.	d.	PROPN
ejpam-4787	332	10	kabre	kabre	PROPN
ejpam-4787	332	11	,	,	PUNCT
ejpam-4787	332	12	a.	a.	NOUN
ejpam-4787	332	13	conseibo	conseibo	PROPN
ejpam-4787	332	14	/	/	SYM
ejpam-4787	332	15	eur	eur	PROPN
ejpam-4787	332	16	.	.	PUNCT
ejpam-4787	333	1	j.	j.	PROPN
ejpam-4787	333	2	pure	pure	PROPN
ejpam-4787	333	3	appl	appl	PROPN
ejpam-4787	333	4	.	.	PROPN
ejpam-4787	333	5	math	math	PROPN
ejpam-4787	333	6	,	,	PUNCT
ejpam-4787	333	7	16	16	NUM
ejpam-4787	333	8	(	(	PUNCT
ejpam-4787	333	9	3	3	NUM
ejpam-4787	333	10	)	)	PUNCT
ejpam-4787	333	11	(	(	PUNCT
ejpam-4787	333	12	2023	2023	NUM
ejpam-4787	333	13	)	)	PUNCT
ejpam-4787	333	14	,	,	PUNCT
ejpam-4787	333	15	1480	1480	NUM
ejpam-4787	333	16	-	-	SYM
ejpam-4787	333	17	1490	1490	NUM
ejpam-4787	333	18	1488	1488	NUM
ejpam-4787	333	19	theorem	theorem	NOUN
ejpam-4787	333	20	6	6	NUM
ejpam-4787	333	21	.	.	PUNCT
ejpam-4787	334	1	let	let	VERB
ejpam-4787	334	2	a	a	DET
ejpam-4787	334	3	=	=	SYM
ejpam-4787	334	4	ke	ke	PROPN
ejpam-4787	334	5	⊕	⊕	PROPN
ejpam-4787	334	6	a0	a0	PROPN
ejpam-4787	334	7	⊕	⊕	PROPN
ejpam-4787	334	8	a	a	DET
ejpam-4787	334	9	1	1	NUM
ejpam-4787	334	10	2	2	NUM
ejpam-4787	334	11	⊕	⊕	PROPN
ejpam-4787	334	12	aλ	aλ	ADP
ejpam-4787	334	13	⊕	⊕	PROPN
ejpam-4787	334	14	aλ̄	aλ̄	NOUN
ejpam-4787	334	15	be	be	AUX
ejpam-4787	334	16	an	an	DET
ejpam-4787	334	17	algebra	algebra	NOUN
ejpam-4787	334	18	satisfying	satisfy	VERB
ejpam-4787	334	19	the	the	DET
ejpam-4787	334	20	identity	identity	NOUN
ejpam-4787	334	21	2x2x4	2x2x4	NOUN
ejpam-4787	334	22	=	=	NOUN
ejpam-4787	334	23	ω(x)2x4	ω(x)2x4	NOUN
ejpam-4787	335	1	+	+	CCONJ
ejpam-4787	335	2	ω(x)4x2	ω(x)4x2	ADJ
ejpam-4787	335	3	;	;	PUNCT
ejpam-4787	335	4	if	if	SCONJ
ejpam-4787	335	5	a	a	PRON
ejpam-4787	335	6	is	be	AUX
ejpam-4787	335	7	a	a	DET
ejpam-4787	335	8	principal	principal	ADJ
ejpam-4787	335	9	train	train	NOUN
ejpam-4787	335	10	algebra	algebra	NOUN
ejpam-4787	335	11	of	of	ADP
ejpam-4787	335	12	rank	rank	NOUN
ejpam-4787	335	13	4	4	NUM
ejpam-4787	335	14	,	,	PUNCT
ejpam-4787	335	15	its	its	PRON
ejpam-4787	335	16	train	train	NOUN
ejpam-4787	335	17	equation	equation	NOUN
ejpam-4787	335	18	is	be	AUX
ejpam-4787	335	19	one	one	NUM
ejpam-4787	335	20	of	of	ADP
ejpam-4787	335	21	the	the	DET
ejpam-4787	335	22	following	follow	VERB
ejpam-4787	335	23	forms	form	NOUN
ejpam-4787	335	24	:	:	PUNCT
ejpam-4787	335	25	i	i	X
ejpam-4787	335	26	)	)	PUNCT
ejpam-4787	336	1	x4	x4	PROPN
ejpam-4787	336	2	−	−	PROPN
ejpam-4787	337	1	(	(	PUNCT
ejpam-4787	337	2	1	1	NUM
ejpam-4787	337	3	+	+	NUM
ejpam-4787	337	4	γ)ω(x)x3	γ)ω(x)x3	PROPN
ejpam-4787	337	5	+	+	CCONJ
ejpam-4787	337	6	γω(x)2x2	γω(x)2x2	X
ejpam-4787	337	7	=	=	SYM
ejpam-4787	337	8	0	0	NUM
ejpam-4787	337	9	,	,	PUNCT
ejpam-4787	337	10	γ	γ	PROPN
ejpam-4787	337	11	∈	∈	PROPN
ejpam-4787	337	12	{	{	PUNCT
ejpam-4787	337	13	0	0	NUM
ejpam-4787	337	14	,	,	PUNCT
ejpam-4787	337	15	λ	λ	X
ejpam-4787	337	16	,	,	PUNCT
ejpam-4787	337	17	λ̄	λ̄	ADP
ejpam-4787	337	18	}	}	PUNCT
ejpam-4787	337	19	;	;	PUNCT
ejpam-4787	337	20	ii	ii	X
ejpam-4787	337	21	)	)	PUNCT
ejpam-4787	337	22	x4	x4	PROPN
ejpam-4787	338	1	−	−	NOUN
ejpam-4787	338	2	1	1	NUM
ejpam-4787	338	3	2ω(x)x	2ω(x)x	NUM
ejpam-4787	338	4	3	3	NUM
ejpam-4787	338	5	+	+	CCONJ
ejpam-4787	338	6	ω(x)2x2	ω(x)2x2	NOUN
ejpam-4787	338	7	−	−	PROPN
ejpam-4787	338	8	3	3	NUM
ejpam-4787	338	9	2ω(x	2ω(x	NUM
ejpam-4787	338	10	)	)	PUNCT
ejpam-4787	338	11	3x	3x	NOUN
ejpam-4787	339	1	=	=	SYM
ejpam-4787	339	2	0	0	NUM
ejpam-4787	339	3	;	;	PUNCT
ejpam-4787	339	4	iii	iii	X
ejpam-4787	339	5	)	)	PUNCT
ejpam-4787	339	6	x4	x4	PROPN
ejpam-4787	339	7	−	−	PROPN
ejpam-4787	340	1	(	(	PUNCT
ejpam-4787	340	2	32	32	NUM
ejpam-4787	340	3	+	+	NUM
ejpam-4787	340	4	γ)ω(x)x3	γ)ω(x)x3	PROPN
ejpam-4787	340	5	+	+	CCONJ
ejpam-4787	340	6	(	(	PUNCT
ejpam-4787	340	7	12	12	NUM
ejpam-4787	340	8	+	+	NUM
ejpam-4787	340	9	3	3	NUM
ejpam-4787	340	10	2γ)ω(x	2γ)ω(x	NUM
ejpam-4787	340	11	)	)	PUNCT
ejpam-4787	340	12	2x2	2x2	NUM
ejpam-4787	340	13	−	−	NOUN
ejpam-4787	340	14	1	1	NUM
ejpam-4787	340	15	2γω(x	2γω(x	NUM
ejpam-4787	340	16	)	)	PUNCT
ejpam-4787	340	17	3x	3x	NOUN
ejpam-4787	340	18	=	=	SYM
ejpam-4787	340	19	0	0	NUM
ejpam-4787	340	20	;	;	PUNCT
ejpam-4787	340	21	γ	γ	PROPN
ejpam-4787	340	22	∈	∈	PROPN
ejpam-4787	340	23	{	{	PUNCT
ejpam-4787	340	24	1	1	NUM
ejpam-4787	340	25	2	2	NUM
ejpam-4787	340	26	,	,	PUNCT
ejpam-4787	340	27	λ	λ	X
ejpam-4787	340	28	,	,	PUNCT
ejpam-4787	340	29	λ̄	λ̄	ADP
ejpam-4787	340	30	}	}	PUNCT
ejpam-4787	340	31	;	;	PUNCT
ejpam-4787	340	32	iv	iv	X
ejpam-4787	340	33	)	)	PUNCT
ejpam-4787	340	34	x4	x4	PROPN
ejpam-4787	340	35	−	−	PROPN
ejpam-4787	340	36	(	(	PUNCT
ejpam-4787	340	37	1	1	NUM
ejpam-4787	340	38	+	+	NUM
ejpam-4787	340	39	2γ)ω(x)x3	2γ)ω(x)x3	NUM
ejpam-4787	340	40	+	+	CCONJ
ejpam-4787	340	41	γ(γ	γ(γ	PROPN
ejpam-4787	340	42	+	+	CCONJ
ejpam-4787	340	43	2)ω(x)2x2	2)ω(x)2x2	NUM
ejpam-4787	340	44	−	−	NOUN
ejpam-4787	340	45	γ2ω(x)3x	γ2ω(x)3x	NUM
ejpam-4787	340	46	=	=	NOUN
ejpam-4787	340	47	0	0	NUM
ejpam-4787	340	48	;	;	PUNCT
ejpam-4787	340	49	γ	γ	PROPN
ejpam-4787	340	50	∈	∈	PROPN
ejpam-4787	340	51	{	{	PUNCT
ejpam-4787	340	52	λ	λ	NOUN
ejpam-4787	340	53	,	,	PUNCT
ejpam-4787	340	54	λ̄	λ̄	ADP
ejpam-4787	340	55	}	}	PUNCT
ejpam-4787	340	56	.	.	PUNCT
ejpam-4787	341	1	proof	proof	NOUN
ejpam-4787	341	2	.	.	PUNCT
ejpam-4787	342	1	let	let	VERB
ejpam-4787	342	2	a	a	DET
ejpam-4787	342	3	=	=	SYM
ejpam-4787	342	4	ke	ke	PROPN
ejpam-4787	342	5	⊕	⊕	PROPN
ejpam-4787	342	6	a0	a0	PROPN
ejpam-4787	342	7	⊕	⊕	PROPN
ejpam-4787	342	8	a	a	DET
ejpam-4787	342	9	1	1	NUM
ejpam-4787	342	10	2	2	NUM
ejpam-4787	342	11	⊕	⊕	PROPN
ejpam-4787	342	12	aλ	aλ	ADP
ejpam-4787	342	13	⊕	⊕	PROPN
ejpam-4787	342	14	aλ̄	aλ̄	NOUN
ejpam-4787	342	15	be	be	AUX
ejpam-4787	342	16	an	an	DET
ejpam-4787	342	17	algebra	algebra	NOUN
ejpam-4787	342	18	satisfying	satisfy	VERB
ejpam-4787	342	19	the	the	DET
ejpam-4787	342	20	identity	identity	NOUN
ejpam-4787	342	21	2x2x4	2x2x4	NOUN
ejpam-4787	342	22	=	=	SYM
ejpam-4787	342	23	ω(x)2x4	ω(x)2x4	NOUN
ejpam-4787	342	24	+	+	CCONJ
ejpam-4787	342	25	ω(x)4x2	ω(x)4x2	ADJ
ejpam-4787	342	26	.	.	PUNCT
ejpam-4787	343	1	assuming	assume	VERB
ejpam-4787	343	2	that	that	SCONJ
ejpam-4787	343	3	a	a	PRON
ejpam-4787	343	4	is	be	AUX
ejpam-4787	343	5	a	a	DET
ejpam-4787	343	6	principal	principal	ADJ
ejpam-4787	343	7	train	train	NOUN
ejpam-4787	343	8	algebra	algebra	NOUN
ejpam-4787	343	9	of	of	ADP
ejpam-4787	343	10	rank	rank	NOUN
ejpam-4787	343	11	4	4	NUM
ejpam-4787	343	12	,	,	PUNCT
ejpam-4787	343	13	its	its	PRON
ejpam-4787	343	14	train	train	NOUN
ejpam-4787	343	15	equation	equation	NOUN
ejpam-4787	343	16	is	be	AUX
ejpam-4787	343	17	of	of	ADP
ejpam-4787	343	18	the	the	DET
ejpam-4787	343	19	form	form	NOUN
ejpam-4787	343	20	x4	x4	ADP
ejpam-4787	343	21	−	−	PROPN
ejpam-4787	344	1	(	(	PUNCT
ejpam-4787	344	2	1	1	NUM
ejpam-4787	344	3	+	+	NUM
ejpam-4787	344	4	α	α	NOUN
ejpam-4787	344	5	+	+	X
ejpam-4787	345	1	β)ω(x)x3	β)ω(x)x3	ADJ
ejpam-4787	345	2	+	+	PUNCT
ejpam-4787	345	3	αω(x)2x2	αω(x)2x2	NUM
ejpam-4787	346	1	+	+	CCONJ
ejpam-4787	346	2	βω(x)3x	βω(x)3x	PUNCT
ejpam-4787	346	3	=	=	SYM
ejpam-4787	346	4	0	0	NUM
ejpam-4787	346	5	with	with	ADP
ejpam-4787	346	6	α	α	PROPN
ejpam-4787	346	7	,	,	PUNCT
ejpam-4787	346	8	β	β	X
ejpam-4787	346	9	∈	∈	X
ejpam-4787	346	10	k	k	X
ejpam-4787	347	1	so	so	ADV
ejpam-4787	347	2	its	its	PRON
ejpam-4787	347	3	minimal	minimal	ADJ
ejpam-4787	347	4	train	train	NOUN
ejpam-4787	347	5	polynomial	polynomial	NOUN
ejpam-4787	347	6	is	be	AUX
ejpam-4787	347	7	p	p	NOUN
ejpam-4787	347	8	(	(	PUNCT
ejpam-4787	347	9	x	x	NOUN
ejpam-4787	347	10	)	)	PUNCT
ejpam-4787	347	11	=	=	SYM
ejpam-4787	347	12	x(x	x(x	PROPN
ejpam-4787	348	1	−	−	PROPN
ejpam-4787	348	2	1)(x	1)(x	NUM
ejpam-4787	348	3	−	−	PROPN
ejpam-4787	348	4	α1)(x	α1)(x	PROPN
ejpam-4787	348	5	−	−	PROPN
ejpam-4787	348	6	α2	α2	ADV
ejpam-4787	348	7	)	)	PUNCT
ejpam-4787	348	8	=	=	PUNCT
ejpam-4787	349	1	x4−(1+α1+α2)x	x4−(1+α1+α2)x	NUM
ejpam-4787	349	2	3+(α1+α2+α1α2)x	3+(α1+α2+α1α2)x	NOUN
ejpam-4787	349	3	2−α1α2x	2−α1α2x	NUM
ejpam-4787	349	4	;	;	PUNCT
ejpam-4787	349	5	we	we	PRON
ejpam-4787	349	6	then	then	ADV
ejpam-4787	349	7	notice	notice	VERB
ejpam-4787	349	8	that	that	SCONJ
ejpam-4787	349	9	α	α	PROPN
ejpam-4787	349	10	=	=	SYM
ejpam-4787	349	11	α1+α2+α1α2	α1+α2+α1α2	PROPN
ejpam-4787	349	12	and	and	CCONJ
ejpam-4787	349	13	β	β	X
ejpam-4787	349	14	=	=	PUNCT
ejpam-4787	350	1	−α1α2	−α1α2	PROPN
ejpam-4787	350	2	therefore	therefore	ADV
ejpam-4787	351	1	x4	x4	PROPN
ejpam-4787	351	2	−	−	PROPN
ejpam-4787	352	1	(	(	PUNCT
ejpam-4787	352	2	1	1	NUM
ejpam-4787	352	3	+	+	NUM
ejpam-4787	352	4	α1	α1	PROPN
ejpam-4787	352	5	+	+	CCONJ
ejpam-4787	352	6	α2)ω(x)x	α2)ω(x)x	NUM
ejpam-4787	352	7	3	3	NUM
ejpam-4787	352	8	+	+	CCONJ
ejpam-4787	352	9	(	(	PUNCT
ejpam-4787	352	10	α1	α1	PROPN
ejpam-4787	352	11	+	+	CCONJ
ejpam-4787	352	12	α2	α2	ADJ
ejpam-4787	352	13	+	+	CCONJ
ejpam-4787	352	14	α1α2)ω(x	α1α2)ω(x	PROPN
ejpam-4787	352	15	)	)	PUNCT
ejpam-4787	352	16	2x2	2x2	NUM
ejpam-4787	352	17	−	−	PROPN
ejpam-4787	352	18	α1α2ω(x	α1α2ω(x	X
ejpam-4787	352	19	)	)	PUNCT
ejpam-4787	352	20	3x	3x	PROPN
ejpam-4787	353	1	=	=	SYM
ejpam-4787	353	2	0	0	PUNCT
ejpam-4787	353	3	(	(	PUNCT
ejpam-4787	353	4	11	11	NUM
ejpam-4787	353	5	)	)	PUNCT
ejpam-4787	353	6	now	now	ADV
ejpam-4787	353	7	let	let	VERB
ejpam-4787	353	8	us	we	PRON
ejpam-4787	353	9	look	look	VERB
ejpam-4787	353	10	at	at	ADP
ejpam-4787	353	11	the	the	DET
ejpam-4787	353	12	different	different	ADJ
ejpam-4787	353	13	cases	case	NOUN
ejpam-4787	353	14	related	relate	VERB
ejpam-4787	353	15	to	to	ADP
ejpam-4787	353	16	the	the	DET
ejpam-4787	353	17	train	train	NOUN
ejpam-4787	353	18	roots	root	NOUN
ejpam-4787	353	19	α1	α1	PROPN
ejpam-4787	353	20	and	and	CCONJ
ejpam-4787	353	21	α2	α2	ADJ
ejpam-4787	353	22	:	:	PUNCT
ejpam-4787	353	23	1st	1st	ADJ
ejpam-4787	353	24	case	case	NOUN
ejpam-4787	353	25	:	:	PUNCT
ejpam-4787	353	26	α1	α1	PROPN
ejpam-4787	353	27	̸=	̸=	PROPN
ejpam-4787	353	28	α2	α2	NOUN
ejpam-4787	353	29	,	,	PUNCT
ejpam-4787	353	30	α1	α1	PROPN
ejpam-4787	353	31	̸=	̸=	PROPN
ejpam-4787	353	32	1	1	NUM
ejpam-4787	353	33	2	2	NUM
ejpam-4787	353	34	and	and	CCONJ
ejpam-4787	353	35	α2	α2	ADJ
ejpam-4787	353	36	̸=	̸=	PROPN
ejpam-4787	353	37	1	1	NUM
ejpam-4787	353	38	2	2	NUM
ejpam-4787	353	39	by	by	ADP
ejpam-4787	353	40	exploiting	exploit	VERB
ejpam-4787	353	41	the	the	DET
ejpam-4787	353	42	theorem	theorem	NOUN
ejpam-4787	353	43	5	5	NUM
ejpam-4787	353	44	of	of	ADP
ejpam-4787	353	45	[	[	X
ejpam-4787	353	46	7	7	NUM
ejpam-4787	353	47	]	]	PUNCT
ejpam-4787	353	48	and	and	CCONJ
ejpam-4787	353	49	the	the	DET
ejpam-4787	353	50	theorem	theorem	NOUN
ejpam-4787	353	51	1	1	NUM
ejpam-4787	353	52	,	,	PUNCT
ejpam-4787	353	53	we	we	PRON
ejpam-4787	353	54	observe	observe	VERB
ejpam-4787	353	55	that	that	SCONJ
ejpam-4787	353	56	a	a	DET
ejpam-4787	353	57	admits	admit	VERB
ejpam-4787	353	58	relatively	relatively	ADV
ejpam-4787	353	59	to	to	ADP
ejpam-4787	353	60	an	an	DET
ejpam-4787	353	61	idempotent	idempotent	ADJ
ejpam-4787	353	62	e	e	NOUN
ejpam-4787	353	63	,	,	PUNCT
ejpam-4787	353	64	the	the	DET
ejpam-4787	353	65	following	follow	VERB
ejpam-4787	353	66	peirce	peirce	NOUN
ejpam-4787	353	67	decomposition	decomposition	NOUN
ejpam-4787	353	68	:	:	PUNCT
ejpam-4787	353	69	a	a	DET
ejpam-4787	353	70	=	=	PUNCT
ejpam-4787	353	71	ke	ke	PROPN
ejpam-4787	353	72	⊕	⊕	PROPN
ejpam-4787	353	73	a	a	DET
ejpam-4787	353	74	1	1	NUM
ejpam-4787	353	75	2	2	NUM
ejpam-4787	353	76	⊕	⊕	NOUN
ejpam-4787	353	77	aα1	aα1	NOUN
ejpam-4787	353	78	⊕	⊕	PROPN
ejpam-4787	353	79	aα2	aα2	PROPN
ejpam-4787	354	1	=	=	SYM
ejpam-4787	354	2	ke⊕a0	ke⊕a0	PROPN
ejpam-4787	354	3	⊕a	⊕a	NOUN
ejpam-4787	354	4	1	1	NUM
ejpam-4787	354	5	2	2	NUM
ejpam-4787	354	6	⊕aλ	⊕aλ	NOUN
ejpam-4787	354	7	⊕aλ̄	⊕aλ̄	PROPN
ejpam-4787	354	8	then	then	ADV
ejpam-4787	354	9	we	we	PRON
ejpam-4787	354	10	have	have	AUX
ejpam-4787	354	11	by	by	ADP
ejpam-4787	354	12	identification	identification	NOUN
ejpam-4787	354	13	α1	α1	NOUN
ejpam-4787	354	14	,	,	PUNCT
ejpam-4787	354	15	α2	α2	PROPN
ejpam-4787	354	16	∈	∈	PROPN
ejpam-4787	354	17	{	{	PUNCT
ejpam-4787	354	18	0	0	NUM
ejpam-4787	354	19	,	,	PUNCT
ejpam-4787	354	20	λ	λ	X
ejpam-4787	354	21	,	,	PUNCT
ejpam-4787	354	22	λ̄	λ̄	ADP
ejpam-4787	354	23	}	}	PUNCT
ejpam-4787	354	24	.	.	PUNCT
ejpam-4787	355	1	indeed	indeed	ADV
ejpam-4787	355	2	:	:	PUNCT
ejpam-4787	355	3	for	for	ADP
ejpam-4787	355	4	α1	α1	PROPN
ejpam-4787	355	5	=	=	SYM
ejpam-4787	355	6	0	0	NUM
ejpam-4787	355	7	and	and	CCONJ
ejpam-4787	355	8	α2	α2	PROPN
ejpam-4787	355	9	=	=	SYM
ejpam-4787	355	10	λ	λ	PROPN
ejpam-4787	355	11	,	,	PUNCT
ejpam-4787	355	12	(	(	PUNCT
ejpam-4787	355	13	11	11	NUM
ejpam-4787	355	14	)	)	PUNCT
ejpam-4787	355	15	becomes	become	VERB
ejpam-4787	355	16	x4	x4	ADV
ejpam-4787	355	17	−	−	PROPN
ejpam-4787	355	18	(	(	PUNCT
ejpam-4787	355	19	1	1	NUM
ejpam-4787	355	20	+	+	CCONJ
ejpam-4787	355	21	λ)ω(x)x3	λ)ω(x)x3	PROPN
ejpam-4787	355	22	+	+	CCONJ
ejpam-4787	355	23	λω(x)2x2	λω(x)2x2	X
ejpam-4787	356	1	=	=	NOUN
ejpam-4787	356	2	0	0	PROPN
ejpam-4787	356	3	,	,	PUNCT
ejpam-4787	356	4	for	for	ADP
ejpam-4787	356	5	α1	α1	PROPN
ejpam-4787	356	6	=	=	SYM
ejpam-4787	356	7	0	0	NUM
ejpam-4787	356	8	and	and	CCONJ
ejpam-4787	356	9	α2	α2	PROPN
ejpam-4787	356	10	=	=	SYM
ejpam-4787	357	1	λ̄	λ̄	NOUN
ejpam-4787	357	2	,	,	PUNCT
ejpam-4787	357	3	the	the	DET
ejpam-4787	357	4	equation	equation	NOUN
ejpam-4787	357	5	(	(	PUNCT
ejpam-4787	357	6	11	11	NUM
ejpam-4787	357	7	)	)	PUNCT
ejpam-4787	357	8	becomes	become	VERB
ejpam-4787	357	9	x4	x4	ADV
ejpam-4787	357	10	−	−	PROPN
ejpam-4787	357	11	(	(	PUNCT
ejpam-4787	357	12	1	1	NUM
ejpam-4787	357	13	+	+	CCONJ
ejpam-4787	357	14	λ̄)ω(x)x3	λ̄)ω(x)x3	NOUN
ejpam-4787	357	15	+	+	CCONJ
ejpam-4787	357	16	λ̄ω(x)2x2	λ̄ω(x)2x2	X
ejpam-4787	357	17	=	=	SYM
ejpam-4787	357	18	0	0	NUM
ejpam-4787	357	19	,	,	PUNCT
ejpam-4787	357	20	and	and	CCONJ
ejpam-4787	357	21	if	if	SCONJ
ejpam-4787	357	22	α1	α1	PROPN
ejpam-4787	357	23	=	=	SYM
ejpam-4787	357	24	λ	λ	X
ejpam-4787	357	25	and	and	CCONJ
ejpam-4787	357	26	α2	α2	PROPN
ejpam-4787	357	27	=	=	SYM
ejpam-4787	357	28	λ̄	λ̄	NOUN
ejpam-4787	357	29	,	,	PUNCT
ejpam-4787	357	30	(	(	PUNCT
ejpam-4787	357	31	11	11	NUM
ejpam-4787	357	32	)	)	PUNCT
ejpam-4787	357	33	becomes	become	VERB
ejpam-4787	357	34	x4	x4	ADV
ejpam-4787	357	35	−	−	PROPN
ejpam-4787	357	36	1	1	NUM
ejpam-4787	357	37	2ω(x)x	2ω(x)x	NUM
ejpam-4787	357	38	3	3	NUM
ejpam-4787	357	39	+	+	CCONJ
ejpam-4787	357	40	ω(x)2x2	ω(x)2x2	NOUN
ejpam-4787	357	41	−	−	PROPN
ejpam-4787	357	42	3	3	NUM
ejpam-4787	357	43	2ω(x	2ω(x	NUM
ejpam-4787	357	44	)	)	PUNCT
ejpam-4787	358	1	3x	3x	NOUN
ejpam-4787	359	1	=	=	SYM
ejpam-4787	359	2	0	0	NUM
ejpam-4787	359	3	2nd	2nd	ADJ
ejpam-4787	359	4	case	case	NOUN
ejpam-4787	359	5	:	:	PUNCT
ejpam-4787	359	6	α1	α1	PROPN
ejpam-4787	359	7	̸=	̸=	PROPN
ejpam-4787	359	8	α2	α2	NOUN
ejpam-4787	359	9	and	and	CCONJ
ejpam-4787	359	10	α1	α1	PROPN
ejpam-4787	359	11	=	=	SYM
ejpam-4787	359	12	1	1	NUM
ejpam-4787	359	13	2	2	NUM
ejpam-4787	359	14	considering	consider	VERB
ejpam-4787	359	15	the	the	DET
ejpam-4787	359	16	theorem	theorem	NOUN
ejpam-4787	359	17	1	1	NUM
ejpam-4787	359	18	of	of	ADP
ejpam-4787	359	19	[	[	X
ejpam-4787	359	20	4	4	NUM
ejpam-4787	359	21	]	]	PUNCT
ejpam-4787	359	22	and	and	CCONJ
ejpam-4787	359	23	the	the	DET
ejpam-4787	359	24	theorem	theorem	NOUN
ejpam-4787	359	25	(	(	PUNCT
ejpam-4787	359	26	1	1	NUM
ejpam-4787	359	27	)	)	PUNCT
ejpam-4787	359	28	,	,	PUNCT
ejpam-4787	359	29	it	it	PRON
ejpam-4787	359	30	follows	follow	VERB
ejpam-4787	359	31	that	that	SCONJ
ejpam-4787	359	32	a	a	DET
ejpam-4787	359	33	admits	admit	VERB
ejpam-4787	359	34	the	the	DET
ejpam-4787	359	35	following	follow	VERB
ejpam-4787	359	36	peirce	peirce	NOUN
ejpam-4787	359	37	decomposition	decomposition	NOUN
ejpam-4787	359	38	:	:	PUNCT
ejpam-4787	359	39	a	a	DET
ejpam-4787	359	40	=	=	PUNCT
ejpam-4787	359	41	ke⊕a	ke⊕a	NOUN
ejpam-4787	359	42	1	1	NUM
ejpam-4787	359	43	2	2	NUM
ejpam-4787	359	44	⊕aα2	⊕aα2	NOUN
ejpam-4787	359	45	with	with	ADP
ejpam-4787	359	46	α2	α2	PROPN
ejpam-4787	359	47	∈	∈	PROPN
ejpam-4787	359	48	{	{	PUNCT
ejpam-4787	359	49	0	0	NUM
ejpam-4787	359	50	,	,	PUNCT
ejpam-4787	359	51	λ	λ	X
ejpam-4787	359	52	,	,	PUNCT
ejpam-4787	359	53	λ̄	λ̄	ADP
ejpam-4787	359	54	}	}	PUNCT
ejpam-4787	359	55	.	.	PUNCT
ejpam-4787	360	1	the	the	DET
ejpam-4787	360	2	train	train	NOUN
ejpam-4787	360	3	equation	equation	NOUN
ejpam-4787	360	4	is	be	AUX
ejpam-4787	360	5	therefore	therefore	ADV
ejpam-4787	360	6	one	one	NUM
ejpam-4787	360	7	of	of	ADP
ejpam-4787	360	8	the	the	DET
ejpam-4787	360	9	following	follow	VERB
ejpam-4787	360	10	forms	form	NOUN
ejpam-4787	360	11	:	:	PUNCT
ejpam-4787	360	12	for	for	ADP
ejpam-4787	360	13	α1	α1	PROPN
ejpam-4787	360	14	=	=	SYM
ejpam-4787	360	15	1	1	NUM
ejpam-4787	360	16	2	2	NUM
ejpam-4787	360	17	and	and	CCONJ
ejpam-4787	360	18	α2	α2	NOUN
ejpam-4787	360	19	=	=	SYM
ejpam-4787	360	20	0	0	NUM
ejpam-4787	360	21	,	,	PUNCT
ejpam-4787	360	22	(	(	PUNCT
ejpam-4787	360	23	11	11	NUM
ejpam-4787	360	24	)	)	PUNCT
ejpam-4787	360	25	becomes	become	VERB
ejpam-4787	360	26	x4	x4	ADV
ejpam-4787	360	27	−	−	PROPN
ejpam-4787	360	28	3	3	NUM
ejpam-4787	360	29	2ω(x)x	2ω(x)x	NUM
ejpam-4787	360	30	3	3	NUM
ejpam-4787	360	31	+	+	CCONJ
ejpam-4787	360	32	1	1	NUM
ejpam-4787	360	33	2ω(x	2ω(x	NUM
ejpam-4787	360	34	)	)	PUNCT
ejpam-4787	360	35	2x2	2x2	NUM
ejpam-4787	361	1	=	=	SYM
ejpam-4787	361	2	0	0	NUM
ejpam-4787	361	3	;	;	PUNCT
ejpam-4787	361	4	for	for	ADP
ejpam-4787	361	5	α1	α1	PROPN
ejpam-4787	361	6	=	=	SYM
ejpam-4787	361	7	1	1	NUM
ejpam-4787	361	8	2	2	NUM
ejpam-4787	361	9	and	and	CCONJ
ejpam-4787	361	10	α2	α2	PROPN
ejpam-4787	361	11	=	=	SYM
ejpam-4787	361	12	λ	λ	PROPN
ejpam-4787	361	13	,	,	PUNCT
ejpam-4787	361	14	the	the	DET
ejpam-4787	361	15	equation	equation	NOUN
ejpam-4787	361	16	(	(	PUNCT
ejpam-4787	361	17	11	11	NUM
ejpam-4787	361	18	)	)	PUNCT
ejpam-4787	361	19	becomes	become	VERB
ejpam-4787	361	20	x4	x4	ADV
ejpam-4787	361	21	−	−	PROPN
ejpam-4787	361	22	(	(	PUNCT
ejpam-4787	361	23	32	32	NUM
ejpam-4787	361	24	+	+	CCONJ
ejpam-4787	361	25	λ)ω(x)x3	λ)ω(x)x3	PROPN
ejpam-4787	361	26	+	+	CCONJ
ejpam-4787	361	27	(	(	PUNCT
ejpam-4787	361	28	12	12	NUM
ejpam-4787	361	29	+	+	NUM
ejpam-4787	361	30	3	3	NUM
ejpam-4787	361	31	2λ)ω(x	2λ)ω(x	NUM
ejpam-4787	361	32	)	)	PUNCT
ejpam-4787	361	33	2x2	2x2	NUM
ejpam-4787	361	34	−	−	NOUN
ejpam-4787	361	35	1	1	NUM
ejpam-4787	361	36	2λω(x	2λω(x	NUM
ejpam-4787	361	37	)	)	PUNCT
ejpam-4787	361	38	3x	3x	PROPN
ejpam-4787	361	39	=	=	SYM
ejpam-4787	361	40	0	0	NUM
ejpam-4787	361	41	;	;	PUNCT
ejpam-4787	361	42	for	for	ADP
ejpam-4787	361	43	α1	α1	PROPN
ejpam-4787	361	44	=	=	SYM
ejpam-4787	361	45	1	1	NUM
ejpam-4787	361	46	2	2	NUM
ejpam-4787	361	47	and	and	CCONJ
ejpam-4787	361	48	α2	α2	NOUN
ejpam-4787	361	49	=	=	SYM
ejpam-4787	361	50	λ̄	λ̄	NOUN
ejpam-4787	361	51	,	,	PUNCT
ejpam-4787	361	52	(	(	PUNCT
ejpam-4787	361	53	11	11	NUM
ejpam-4787	361	54	)	)	PUNCT
ejpam-4787	361	55	becomes	become	VERB
ejpam-4787	361	56	x4	x4	ADV
ejpam-4787	361	57	−	−	PROPN
ejpam-4787	361	58	(	(	PUNCT
ejpam-4787	361	59	32	32	NUM
ejpam-4787	361	60	+	+	CCONJ
ejpam-4787	361	61	λ̄)ω(x)x3	λ̄)ω(x)x3	PROPN
ejpam-4787	361	62	+	+	CCONJ
ejpam-4787	361	63	(	(	PUNCT
ejpam-4787	361	64	12	12	NUM
ejpam-4787	361	65	+	+	NUM
ejpam-4787	361	66	3	3	NUM
ejpam-4787	361	67	2	2	NUM
ejpam-4787	361	68	λ̄)ω(x	λ̄)ω(x	X
ejpam-4787	361	69	)	)	PUNCT
ejpam-4787	361	70	2x2	2x2	NUM
ejpam-4787	361	71	−	−	NOUN
ejpam-4787	361	72	1	1	NUM
ejpam-4787	361	73	2	2	NUM
ejpam-4787	361	74	λ̄ω(x	λ̄ω(x	NOUN
ejpam-4787	361	75	)	)	PUNCT
ejpam-4787	361	76	3x	3x	NOUN
ejpam-4787	361	77	=	=	SYM
ejpam-4787	361	78	0	0	X
ejpam-4787	361	79	.	.	PUNCT
ejpam-4787	362	1	3rd	3rd	ADJ
ejpam-4787	362	2	case	case	NOUN
ejpam-4787	362	3	:	:	PUNCT
ejpam-4787	362	4	α1	α1	PROPN
ejpam-4787	362	5	=	=	SYM
ejpam-4787	362	6	α2	α2	PROPN
ejpam-4787	362	7	,	,	PUNCT
ejpam-4787	362	8	α1	α1	PROPN
ejpam-4787	362	9	̸=	̸=	PROPN
ejpam-4787	362	10	1	1	NUM
ejpam-4787	362	11	2	2	NUM
ejpam-4787	362	12	and	and	CCONJ
ejpam-4787	362	13	α2	α2	ADJ
ejpam-4787	362	14	̸=	̸=	PROPN
ejpam-4787	362	15	1	1	NUM
ejpam-4787	362	16	2	2	NUM
ejpam-4787	362	17	according	accord	VERB
ejpam-4787	362	18	to	to	ADP
ejpam-4787	362	19	the	the	DET
ejpam-4787	362	20	theorem	theorem	NOUN
ejpam-4787	362	21	1	1	NUM
ejpam-4787	362	22	of	of	ADP
ejpam-4787	362	23	[	[	X
ejpam-4787	362	24	4	4	NUM
ejpam-4787	362	25	]	]	PUNCT
ejpam-4787	362	26	and	and	CCONJ
ejpam-4787	362	27	as	as	ADP
ejpam-4787	362	28	a	a	DET
ejpam-4787	362	29	admits	admit	NOUN
ejpam-4787	362	30	nonzero	nonzero	PROPN
ejpam-4787	362	31	idempotents	idempotent	NOUN
ejpam-4787	362	32	,	,	PUNCT
ejpam-4787	362	33	the	the	DET
ejpam-4787	362	34	peirce	peirce	NOUN
ejpam-4787	362	35	decomposition	decomposition	NOUN
ejpam-4787	362	36	of	of	ADP
ejpam-4787	362	37	a	a	PRON
ejpam-4787	362	38	with	with	ADP
ejpam-4787	362	39	respect	respect	NOUN
ejpam-4787	362	40	to	to	ADP
ejpam-4787	362	41	an	an	DET
ejpam-4787	362	42	idempotent	idempotent	NOUN
ejpam-4787	362	43	e	e	NOUN
ejpam-4787	362	44	is	be	AUX
ejpam-4787	362	45	references	reference	NOUN
ejpam-4787	362	46	1489	1489	NUM
ejpam-4787	362	47	a	a	DET
ejpam-4787	362	48	=	=	SYM
ejpam-4787	362	49	ke	ke	PROPN
ejpam-4787	362	50	⊕	⊕	PROPN
ejpam-4787	362	51	a	a	DET
ejpam-4787	362	52	1	1	NUM
ejpam-4787	362	53	2	2	NUM
ejpam-4787	362	54	⊕	⊕	PROPN
ejpam-4787	362	55	b	b	PROPN
ejpam-4787	362	56	with	with	ADP
ejpam-4787	362	57	b	b	NOUN
ejpam-4787	362	58	=	=	SYM
ejpam-4787	362	59	n	n	NOUN
ejpam-4787	362	60	∩	∩	NOUN
ejpam-4787	362	61	ker(ℓe	ker(ℓe	NOUN
ejpam-4787	362	62	−	−	PROPN
ejpam-4787	362	63	α1i	α1i	NOUN
ejpam-4787	362	64	)	)	PUNCT
ejpam-4787	362	65	2	2	NUM
ejpam-4787	362	66	.	.	PUNCT
ejpam-4787	363	1	if	if	SCONJ
ejpam-4787	363	2	b	b	NOUN
ejpam-4787	363	3	=	=	SYM
ejpam-4787	363	4	0	0	NUM
ejpam-4787	363	5	,	,	PUNCT
ejpam-4787	363	6	we	we	PRON
ejpam-4787	363	7	have	have	VERB
ejpam-4787	363	8	x	x	X
ejpam-4787	363	9	=	=	PUNCT
ejpam-4787	363	10	e	e	X
ejpam-4787	363	11	+	+	NOUN
ejpam-4787	363	12	x	x	SYM
ejpam-4787	363	13	1	1	NUM
ejpam-4787	363	14	2	2	NUM
ejpam-4787	363	15	and	and	CCONJ
ejpam-4787	363	16	x2	x2	NOUN
ejpam-4787	364	1	=	=	PUNCT
ejpam-4787	364	2	e+	e+	PUNCT
ejpam-4787	364	3	x	x	PROPN
ejpam-4787	364	4	1	1	NUM
ejpam-4787	364	5	2	2	NUM
ejpam-4787	364	6	so	so	ADV
ejpam-4787	364	7	x2	x2	NOUN
ejpam-4787	365	1	=	=	PUNCT
ejpam-4787	365	2	ω(x)x	ω(x)x	NOUN
ejpam-4787	365	3	which	which	PRON
ejpam-4787	365	4	is	be	AUX
ejpam-4787	365	5	an	an	DET
ejpam-4787	365	6	elementary	elementary	ADJ
ejpam-4787	365	7	bernstein	bernstein	PROPN
ejpam-4787	365	8	algebra	algebra	PROPN
ejpam-4787	365	9	and	and	CCONJ
ejpam-4787	365	10	this	this	PRON
ejpam-4787	365	11	contradicts	contradict	VERB
ejpam-4787	365	12	the	the	DET
ejpam-4787	365	13	fact	fact	NOUN
ejpam-4787	365	14	that	that	SCONJ
ejpam-4787	365	15	a	a	PRON
ejpam-4787	365	16	is	be	AUX
ejpam-4787	365	17	a	a	DET
ejpam-4787	365	18	train	train	NOUN
ejpam-4787	365	19	algebra	algebra	NOUN
ejpam-4787	365	20	of	of	ADP
ejpam-4787	365	21	rank	rank	NOUN
ejpam-4787	365	22	4	4	NUM
ejpam-4787	365	23	.	.	PUNCT
ejpam-4787	366	1	otherwise	otherwise	ADV
ejpam-4787	366	2	,	,	PUNCT
ejpam-4787	366	3	there	there	PRON
ejpam-4787	366	4	are	be	VERB
ejpam-4787	366	5	three	three	NUM
ejpam-4787	366	6	possibilities	possibility	NOUN
ejpam-4787	366	7	.	.	PUNCT
ejpam-4787	367	1	indeed	indeed	ADV
ejpam-4787	367	2	:	:	PUNCT
ejpam-4787	367	3	i	i	PROPN
ejpam-4787	367	4	)	)	PUNCT
ejpam-4787	367	5	α1	α1	PROPN
ejpam-4787	367	6	=	=	SYM
ejpam-4787	367	7	α2	α2	NOUN
ejpam-4787	367	8	=	=	SYM
ejpam-4787	367	9	0	0	NUM
ejpam-4787	367	10	implies	imply	VERB
ejpam-4787	367	11	that	that	SCONJ
ejpam-4787	367	12	the	the	DET
ejpam-4787	367	13	train	train	NOUN
ejpam-4787	367	14	equation	equation	NOUN
ejpam-4787	367	15	of	of	ADP
ejpam-4787	367	16	a	a	PRON
ejpam-4787	367	17	is	be	AUX
ejpam-4787	367	18	x4	x4	ADV
ejpam-4787	367	19	−	−	PROPN
ejpam-4787	367	20	ω(x)x3	ω(x)x3	NOUN
ejpam-4787	367	21	=	=	SYM
ejpam-4787	367	22	0	0	NUM
ejpam-4787	367	23	;	;	PUNCT
ejpam-4787	367	24	ii	ii	X
ejpam-4787	367	25	)	)	PUNCT
ejpam-4787	367	26	α1	α1	PROPN
ejpam-4787	367	27	=	=	SYM
ejpam-4787	367	28	α2	α2	NOUN
ejpam-4787	367	29	=	=	SYM
ejpam-4787	367	30	λ	λ	PROPN
ejpam-4787	367	31	implies	imply	VERB
ejpam-4787	367	32	that	that	SCONJ
ejpam-4787	367	33	the	the	DET
ejpam-4787	367	34	train	train	NOUN
ejpam-4787	367	35	equation	equation	NOUN
ejpam-4787	367	36	of	of	ADP
ejpam-4787	367	37	a	a	PRON
ejpam-4787	367	38	is	be	AUX
ejpam-4787	367	39	x4	x4	PROPN
ejpam-4787	367	40	−	−	PROPN
ejpam-4787	367	41	(	(	PUNCT
ejpam-4787	367	42	1	1	NUM
ejpam-4787	367	43	+	+	NUM
ejpam-4787	367	44	2λ)ω(x)x3	2λ)ω(x)x3	NUM
ejpam-4787	367	45	+	+	CCONJ
ejpam-4787	367	46	λ(λ+	λ(λ+	NOUN
ejpam-4787	367	47	2)ω(x)2x2	2)ω(x)2x2	NUM
ejpam-4787	367	48	−	−	NOUN
ejpam-4787	367	49	λ2ω(x)3x	λ2ω(x)3x	NOUN
ejpam-4787	367	50	=	=	SYM
ejpam-4787	367	51	0	0	NUM
ejpam-4787	367	52	;	;	PUNCT
ejpam-4787	367	53	iii	iii	X
ejpam-4787	367	54	)	)	PUNCT
ejpam-4787	367	55	α1	α1	PROPN
ejpam-4787	367	56	=	=	SYM
ejpam-4787	367	57	α2	α2	NOUN
ejpam-4787	367	58	=	=	SYM
ejpam-4787	367	59	λ̄	λ̄	PROPN
ejpam-4787	367	60	implies	imply	VERB
ejpam-4787	367	61	that	that	SCONJ
ejpam-4787	367	62	the	the	DET
ejpam-4787	367	63	train	train	NOUN
ejpam-4787	367	64	equation	equation	NOUN
ejpam-4787	367	65	of	of	ADP
ejpam-4787	367	66	a	a	PRON
ejpam-4787	367	67	is	be	AUX
ejpam-4787	367	68	x4	x4	PROPN
ejpam-4787	367	69	−	−	PROPN
ejpam-4787	367	70	(	(	PUNCT
ejpam-4787	367	71	1	1	NUM
ejpam-4787	368	1	+	+	CCONJ
ejpam-4787	368	2	2λ̄)ω(x)x3	2λ̄)ω(x)x3	NUM
ejpam-4787	368	3	+	+	SYM
ejpam-4787	368	4	λ̄(λ̄+	λ̄(λ̄+	NOUN
ejpam-4787	368	5	2)ω(x)2x2	2)ω(x)2x2	NUM
ejpam-4787	368	6	−	−	NOUN
ejpam-4787	368	7	λ̄2ω(x)3x	λ̄2ω(x)3x	NOUN
ejpam-4787	368	8	=	=	NOUN
ejpam-4787	368	9	0	0	PROPN
ejpam-4787	368	10	.	.	PUNCT
ejpam-4787	368	11	definition	definition	NOUN
ejpam-4787	368	12	4	4	NUM
ejpam-4787	368	13	.	.	PUNCT
ejpam-4787	369	1	for	for	ADP
ejpam-4787	369	2	any	any	DET
ejpam-4787	369	3	fixed	fixed	ADJ
ejpam-4787	369	4	α	α	NOUN
ejpam-4787	369	5	in	in	ADP
ejpam-4787	369	6	k	k	PROPN
ejpam-4787	369	7	,	,	PUNCT
ejpam-4787	369	8	we	we	PRON
ejpam-4787	369	9	consider	consider	VERB
ejpam-4787	369	10	the	the	DET
ejpam-4787	369	11	map	map	NOUN
ejpam-4787	369	12	φα	φα	X
ejpam-4787	369	13	:	:	PUNCT
ejpam-4787	369	14	k[x	k[x	PROPN
ejpam-4787	369	15	]	]	X
ejpam-4787	369	16	→	→	SYM
ejpam-4787	369	17	k[x	k[x	PROPN
ejpam-4787	369	18	]	]	X
ejpam-4787	369	19	,	,	PUNCT
ejpam-4787	369	20	p	p	PROPN
ejpam-4787	369	21	7→	7→	PROPN
ejpam-4787	369	22	(	(	PUNCT
ejpam-4787	369	23	x	x	NOUN
ejpam-4787	369	24	−	−	NOUN
ejpam-4787	369	25	α)p	α)p	VERB
ejpam-4787	369	26	we	we	PRON
ejpam-4787	369	27	easily	easily	ADV
ejpam-4787	369	28	establish	establish	VERB
ejpam-4787	369	29	the	the	DET
ejpam-4787	369	30	following	follow	VERB
ejpam-4787	369	31	lemma	lemma	PROPN
ejpam-4787	369	32	.	.	PUNCT
ejpam-4787	370	1	lemma	lemma	PROPN
ejpam-4787	370	2	2	2	NUM
ejpam-4787	370	3	.	.	PUNCT
ejpam-4787	371	1	for	for	ADP
ejpam-4787	371	2	α	α	PRON
ejpam-4787	371	3	∈	∈	PROPN
ejpam-4787	371	4	c	c	X
ejpam-4787	371	5	,	,	PUNCT
ejpam-4787	371	6	we	we	PRON
ejpam-4787	371	7	have	have	AUX
ejpam-4787	371	8	φα	φα	ADP
ejpam-4787	371	9	◦	◦	VERB
ejpam-4787	371	10	φᾱ	φᾱ	NOUN
ejpam-4787	371	11	=	=	SYM
ejpam-4787	371	12	φᾱ	φᾱ	PROPN
ejpam-4787	372	1	◦	◦	PROPN
ejpam-4787	372	2	φα	φα	ADP
ejpam-4787	372	3	theorem	theorem	VERB
ejpam-4787	372	4	7	7	NUM
ejpam-4787	372	5	.	.	PUNCT
ejpam-4787	373	1	let	let	VERB
ejpam-4787	373	2	a	a	DET
ejpam-4787	373	3	=	=	SYM
ejpam-4787	373	4	ke	ke	PROPN
ejpam-4787	373	5	⊕	⊕	PROPN
ejpam-4787	373	6	a0	a0	PROPN
ejpam-4787	373	7	⊕	⊕	PROPN
ejpam-4787	373	8	a	a	DET
ejpam-4787	373	9	1	1	NUM
ejpam-4787	373	10	2	2	NUM
ejpam-4787	373	11	⊕	⊕	PROPN
ejpam-4787	373	12	aλ	aλ	ADP
ejpam-4787	373	13	⊕	⊕	PROPN
ejpam-4787	373	14	aλ̄	aλ̄	NOUN
ejpam-4787	373	15	be	be	AUX
ejpam-4787	373	16	an	an	DET
ejpam-4787	373	17	algebra	algebra	NOUN
ejpam-4787	373	18	satisfying	satisfy	VERB
ejpam-4787	373	19	the	the	DET
ejpam-4787	373	20	identity	identity	NOUN
ejpam-4787	373	21	2x2x4	2x2x4	NOUN
ejpam-4787	373	22	=	=	NOUN
ejpam-4787	373	23	ω(x)2x4	ω(x)2x4	NOUN
ejpam-4787	374	1	+	+	CCONJ
ejpam-4787	374	2	ω(x)4x2	ω(x)4x2	NOUN
ejpam-4787	374	3	such	such	ADJ
ejpam-4787	374	4	that	that	DET
ejpam-4787	374	5	a0	a0	NOUN
ejpam-4787	374	6	=	=	SYM
ejpam-4787	374	7	0	0	X
ejpam-4787	374	8	.	.	PUNCT
ejpam-4787	375	1	let	let	VERB
ejpam-4787	375	2	setting	set	VERB
ejpam-4787	375	3	µ	µ	X
ejpam-4787	375	4	=	=	SYM
ejpam-4787	375	5	x2	x2	NOUN
ejpam-4787	375	6	−x	−x	NOUN
ejpam-4787	375	7	.	.	PUNCT
ejpam-4787	376	1	if	if	SCONJ
ejpam-4787	376	2	a	a	PRON
ejpam-4787	376	3	is	be	AUX
ejpam-4787	376	4	principal	principal	ADJ
ejpam-4787	376	5	train	train	NOUN
ejpam-4787	376	6	algebra	algebra	NOUN
ejpam-4787	376	7	of	of	ADP
ejpam-4787	376	8	rank	rank	PROPN
ejpam-4787	376	9	n	n	PROPN
ejpam-4787	376	10	≥	≥	NUM
ejpam-4787	376	11	5	5	NUM
ejpam-4787	376	12	,	,	PUNCT
ejpam-4787	376	13	its	its	PRON
ejpam-4787	376	14	train	train	NOUN
ejpam-4787	376	15	equation	equation	NOUN
ejpam-4787	376	16	is	be	AUX
ejpam-4787	376	17	of	of	ADP
ejpam-4787	376	18	the	the	DET
ejpam-4787	376	19	following	follow	VERB
ejpam-4787	376	20	form	form	NOUN
ejpam-4787	376	21	:	:	PUNCT
ejpam-4787	376	22	ω(x)n((φt	ω(x)n((φt	NOUN
ejpam-4787	377	1	λ̄	λ̄	X
ejpam-4787	377	2	◦	◦	NOUN
ejpam-4787	377	3	φs	φs	ADP
ejpam-4787	377	4	λ	λ	X
ejpam-4787	377	5	◦	◦	NOUN
ejpam-4787	377	6	φr	φr	ADP
ejpam-4787	377	7	1/2)(µ	1/2)(µ	NUM
ejpam-4787	377	8	)	)	PUNCT
ejpam-4787	377	9	(	(	PUNCT
ejpam-4787	377	10	x	x	X
ejpam-4787	377	11	ω(x	ω(x	NOUN
ejpam-4787	377	12	)	)	PUNCT
ejpam-4787	377	13	)	)	PUNCT
ejpam-4787	378	1	=	=	SYM
ejpam-4787	378	2	0	0	NUM
ejpam-4787	378	3	,	,	PUNCT
ejpam-4787	378	4	r	r	NOUN
ejpam-4787	378	5	≥	≥	NOUN
ejpam-4787	378	6	0	0	NUM
ejpam-4787	378	7	,	,	PUNCT
ejpam-4787	378	8	s	s	VERB
ejpam-4787	378	9	≥	≥	NOUN
ejpam-4787	378	10	0	0	NUM
ejpam-4787	378	11	,	,	PUNCT
ejpam-4787	378	12	t	t	PROPN
ejpam-4787	378	13	≥	≥	NUM
ejpam-4787	378	14	0	0	NUM
ejpam-4787	378	15	are	be	AUX
ejpam-4787	378	16	integers	integer	NOUN
ejpam-4787	378	17	and	and	CCONJ
ejpam-4787	378	18	r	r	NOUN
ejpam-4787	378	19	+	+	CCONJ
ejpam-4787	378	20	t+	t+	NOUN
ejpam-4787	378	21	s	s	PART
ejpam-4787	378	22	=	=	PUNCT
ejpam-4787	378	23	n−	n−	NOUN
ejpam-4787	378	24	2	2	NUM
ejpam-4787	378	25	.	.	PUNCT
ejpam-4787	379	1	proof	proof	NOUN
ejpam-4787	379	2	.	.	PUNCT
ejpam-4787	380	1	let	let	VERB
ejpam-4787	380	2	x	x	PUNCT
ejpam-4787	380	3	=	=	PUNCT
ejpam-4787	380	4	e	e	X
ejpam-4787	380	5	+	+	NOUN
ejpam-4787	380	6	x	x	SYM
ejpam-4787	380	7	1	1	NUM
ejpam-4787	380	8	2	2	NUM
ejpam-4787	380	9	+	+	CCONJ
ejpam-4787	380	10	xλ	xλ	PROPN
ejpam-4787	381	1	+	+	CCONJ
ejpam-4787	381	2	xλ̄	xλ̄	X
ejpam-4787	381	3	an	an	DET
ejpam-4787	381	4	element	element	NOUN
ejpam-4787	381	5	of	of	ADP
ejpam-4787	381	6	weight	weight	NOUN
ejpam-4787	381	7	1	1	NUM
ejpam-4787	381	8	in	in	ADP
ejpam-4787	381	9	a.	a.	NOUN
ejpam-4787	381	10	we	we	PRON
ejpam-4787	381	11	have	have	VERB
ejpam-4787	381	12	x2	x2	INTJ
ejpam-4787	381	13	−	−	NOUN
ejpam-4787	381	14	x	x	SYM
ejpam-4787	382	1	=	=	SYM
ejpam-4787	382	2	x21	x21	PROPN
ejpam-4787	382	3	2	2	NUM
ejpam-4787	383	1	+	+	CCONJ
ejpam-4787	383	2	(	(	PUNCT
ejpam-4787	383	3	2λ	2λ	NUM
ejpam-4787	383	4	−	−	PROPN
ejpam-4787	383	5	1)xλ	1)xλ	PROPN
ejpam-4787	383	6	+	+	CCONJ
ejpam-4787	383	7	(	(	PUNCT
ejpam-4787	383	8	2λ̄	2λ̄	NUM
ejpam-4787	383	9	−	−	NOUN
ejpam-4787	384	1	1)xλ̄	1)xλ̄	NUM
ejpam-4787	384	2	+	+	CCONJ
ejpam-4787	384	3	2x	2x	NUM
ejpam-4787	384	4	1	1	NUM
ejpam-4787	384	5	2	2	NUM
ejpam-4787	384	6	xλ	xλ	NOUN
ejpam-4787	384	7	+	+	CCONJ
ejpam-4787	384	8	2x	2x	NUM
ejpam-4787	384	9	1	1	NUM
ejpam-4787	384	10	2	2	NUM
ejpam-4787	384	11	xλ̄.	xλ̄.	X
ejpam-4787	384	12	by	by	ADP
ejpam-4787	384	13	setting	set	VERB
ejpam-4787	384	14	x2	x2	PROPN
ejpam-4787	384	15	−	−	NOUN
ejpam-4787	384	16	x	x	X
ejpam-4787	385	1	=	=	PUNCT
ejpam-4787	385	2	a	a	DET
ejpam-4787	385	3	1	1	NUM
ejpam-4787	385	4	2	2	NUM
ejpam-4787	385	5	+	+	CCONJ
ejpam-4787	385	6	aλ	aλ	PROPN
ejpam-4787	385	7	+	+	NOUN
ejpam-4787	385	8	aλ̄	aλ̄	NOUN
ejpam-4787	385	9	with	with	ADP
ejpam-4787	385	10	aα	aα	PROPN
ejpam-4787	385	11	∈	∈	PROPN
ejpam-4787	385	12	aα	aα	NOUN
ejpam-4787	385	13	,	,	PUNCT
ejpam-4787	385	14	α	α	PROPN
ejpam-4787	385	15	∈	∈	PROPN
ejpam-4787	385	16	{	{	PUNCT
ejpam-4787	385	17	λ	λ	NOUN
ejpam-4787	385	18	,	,	PUNCT
ejpam-4787	385	19	λ̄	λ̄	ADP
ejpam-4787	385	20	}	}	PUNCT
ejpam-4787	385	21	,	,	PUNCT
ejpam-4787	385	22	we	we	PRON
ejpam-4787	385	23	show	show	VERB
ejpam-4787	385	24	using	use	VERB
ejpam-4787	385	25	corollary	corollary	ADJ
ejpam-4787	385	26	1	1	NUM
ejpam-4787	385	27	that	that	SCONJ
ejpam-4787	385	28	there	there	PRON
ejpam-4787	385	29	exists	exist	VERB
ejpam-4787	385	30	an	an	DET
ejpam-4787	385	31	integer	integer	NOUN
ejpam-4787	385	32	r	r	NOUN
ejpam-4787	385	33	≥	≥	NOUN
ejpam-4787	385	34	0	0	NUM
ejpam-4787	385	35	such	such	ADJ
ejpam-4787	385	36	that	that	PRON
ejpam-4787	385	37	φr	φr	ADP
ejpam-4787	385	38	1/2(µ)(x	1/2(µ)(x	PROPN
ejpam-4787	385	39	)	)	PUNCT
ejpam-4787	385	40	=	=	SYM
ejpam-4787	385	41	ar	ar	PROPN
ejpam-4787	385	42	,	,	PUNCT
ejpam-4787	385	43	λ	λ	PROPN
ejpam-4787	385	44	+	+	PROPN
ejpam-4787	385	45	ar	ar	PROPN
ejpam-4787	385	46	,	,	PUNCT
ejpam-4787	385	47	λ̄	λ̄	ADP
ejpam-4787	385	48	,	,	PUNCT
ejpam-4787	385	49	ar	ar	PROPN
ejpam-4787	385	50	,	,	PUNCT
ejpam-4787	385	51	λ	λ	PROPN
ejpam-4787	385	52	∈	∈	PROPN
ejpam-4787	385	53	aλ	aλ	PROPN
ejpam-4787	385	54	,	,	PUNCT
ejpam-4787	385	55	and	and	CCONJ
ejpam-4787	385	56	ar	ar	NOUN
ejpam-4787	385	57	,	,	PUNCT
ejpam-4787	385	58	λ̄	λ̄	ADP
ejpam-4787	385	59	∈	∈	PROPN
ejpam-4787	385	60	aλ̄.	aλ̄.	NOUN
ejpam-4787	385	61	similarly	similarly	ADV
ejpam-4787	385	62	,	,	PUNCT
ejpam-4787	385	63	there	there	PRON
ejpam-4787	385	64	exists	exist	VERB
ejpam-4787	385	65	an	an	DET
ejpam-4787	385	66	integer	integer	NOUN
ejpam-4787	385	67	s	s	PART
ejpam-4787	385	68	≥	≥	NOUN
ejpam-4787	385	69	0	0	NUM
ejpam-4787	386	1	such	such	ADJ
ejpam-4787	386	2	that	that	SCONJ
ejpam-4787	386	3	(	(	PUNCT
ejpam-4787	386	4	φλ	φλ	ADP
ejpam-4787	386	5	◦	◦	NOUN
ejpam-4787	386	6	φr	φr	ADP
ejpam-4787	386	7	1/2)(µ)(x	1/2)(µ)(x	NUM
ejpam-4787	386	8	)	)	PUNCT
ejpam-4787	386	9	=	=	SYM
ejpam-4787	386	10	bλ̄	bλ̄	NOUN
ejpam-4787	386	11	with	with	ADP
ejpam-4787	386	12	bλ̄	bλ̄	PROPN
ejpam-4787	386	13	∈	∈	PROPN
ejpam-4787	386	14	aλ̄.	aλ̄.	NOUN
ejpam-4787	386	15	finally	finally	ADV
ejpam-4787	386	16	,	,	PUNCT
ejpam-4787	386	17	for	for	ADP
ejpam-4787	386	18	some	some	DET
ejpam-4787	386	19	integer	integer	NOUN
ejpam-4787	386	20	t	t	PROPN
ejpam-4787	386	21	≥	≥	NUM
ejpam-4787	386	22	0	0	NUM
ejpam-4787	386	23	,	,	PUNCT
ejpam-4787	386	24	we	we	PRON
ejpam-4787	386	25	have	have	AUX
ejpam-4787	386	26	(	(	PUNCT
ejpam-4787	386	27	φλ̄	φλ̄	VERB
ejpam-4787	386	28	◦	◦	NOUN
ejpam-4787	386	29	φλ	φλ	NOUN
ejpam-4787	386	30	◦	◦	NOUN
ejpam-4787	386	31	φr	φr	ADP
ejpam-4787	386	32	1/2)(µ)(x	1/2)(µ)(x	NUM
ejpam-4787	386	33	)	)	PUNCT
ejpam-4787	386	34	=	=	SYM
ejpam-4787	387	1	0	0	X
ejpam-4787	387	2	.	.	PUNCT
ejpam-4787	388	1	the	the	DET
ejpam-4787	388	2	set	set	NOUN
ejpam-4787	388	3	of	of	ADP
ejpam-4787	388	4	element	element	NOUN
ejpam-4787	388	5	of	of	ADP
ejpam-4787	388	6	weight	weight	NOUN
ejpam-4787	388	7	1	1	NUM
ejpam-4787	388	8	being	be	AUX
ejpam-4787	388	9	dense	dense	ADJ
ejpam-4787	388	10	in	in	ADP
ejpam-4787	388	11	a	a	DET
ejpam-4787	388	12	according	accord	VERB
ejpam-4787	388	13	to	to	ADP
ejpam-4787	388	14	zariski	zariski	ADJ
ejpam-4787	388	15	topology	topology	NOUN
ejpam-4787	388	16	,	,	PUNCT
ejpam-4787	388	17	for	for	ADP
ejpam-4787	388	18	any	any	DET
ejpam-4787	388	19	x	x	NOUN
ejpam-4787	388	20	in	in	ADP
ejpam-4787	388	21	a	a	PRON
ejpam-4787	388	22	,	,	PUNCT
ejpam-4787	388	23	we	we	PRON
ejpam-4787	388	24	have	have	VERB
ejpam-4787	388	25	ω(x)n((φt	ω(x)n((φt	NOUN
ejpam-4787	388	26	λ̄	λ̄	ADJ
ejpam-4787	388	27	◦	◦	NOUN
ejpam-4787	388	28	φs	φs	ADP
ejpam-4787	388	29	λ	λ	X
ejpam-4787	388	30	◦	◦	NOUN
ejpam-4787	388	31	φr	φr	ADP
ejpam-4787	388	32	1/2)(µ	1/2)(µ	NUM
ejpam-4787	388	33	)	)	PUNCT
ejpam-4787	388	34	(	(	PUNCT
ejpam-4787	388	35	x	x	X
ejpam-4787	388	36	ω(x	ω(x	NOUN
ejpam-4787	388	37	)	)	PUNCT
ejpam-4787	388	38	)	)	PUNCT
ejpam-4787	389	1	=	=	PUNCT
ejpam-4787	389	2	0	0	X
ejpam-4787	389	3	.	.	PUNCT
ejpam-4787	389	4	references	reference	NOUN
ejpam-4787	389	5	[	[	X
ejpam-4787	389	6	1	1	X
ejpam-4787	389	7	]	]	PUNCT
ejpam-4787	389	8	j.	j.	PROPN
ejpam-4787	389	9	bayara	bayara	PROPN
ejpam-4787	389	10	,	,	PUNCT
ejpam-4787	389	11	a.	a.	NOUN
ejpam-4787	389	12	conseibo	conseibo	PROPN
ejpam-4787	389	13	,	,	PUNCT
ejpam-4787	389	14	m.	m.	NOUN
ejpam-4787	389	15	ouattara	ouattara	NOUN
ejpam-4787	389	16	,	,	PUNCT
ejpam-4787	389	17	and	and	CCONJ
ejpam-4787	389	18	a.	a.	NOUN
ejpam-4787	389	19	micali	micali	PROPN
ejpam-4787	389	20	.	.	PUNCT
ejpam-4787	390	1	train	train	NOUN
ejpam-4787	390	2	algebras	algebra	NOUN
ejpam-4787	390	3	of	of	ADP
ejpam-4787	390	4	degree	degree	NOUN
ejpam-4787	390	5	2	2	NUM
ejpam-4787	390	6	and	and	CCONJ
ejpam-4787	390	7	exponent	exponent	NOUN
ejpam-4787	390	8	3	3	NUM
ejpam-4787	390	9	.	.	PUNCT
ejpam-4787	390	10	discret	discret	ADJ
ejpam-4787	390	11	and	and	CCONJ
ejpam-4787	390	12	continous	continous	ADJ
ejpam-4787	390	13	dynamical	dynamical	ADJ
ejpam-4787	390	14	systems	system	NOUN
ejpam-4787	390	15	series	series	NOUN
ejpam-4787	390	16	,	,	PUNCT
ejpam-4787	390	17	4	4	NUM
ejpam-4787	390	18	,	,	PUNCT
ejpam-4787	390	19	no	no	DET
ejpam-4787	390	20	6:1971–1986	6:1971–1986	NUM
ejpam-4787	390	21	,	,	PUNCT
ejpam-4787	390	22	2011	2011	NUM
ejpam-4787	390	23	.	.	PUNCT
ejpam-4787	391	1	[	[	X
ejpam-4787	391	2	2	2	X
ejpam-4787	391	3	]	]	PUNCT
ejpam-4787	391	4	j.	j.	PROPN
ejpam-4787	391	5	bayara	bayara	PROPN
ejpam-4787	391	6	,	,	PUNCT
ejpam-4787	391	7	a.	a.	NOUN
ejpam-4787	391	8	conseibo	conseibo	PROPN
ejpam-4787	391	9	,	,	PUNCT
ejpam-4787	391	10	m.	m.	NOUN
ejpam-4787	391	11	ouattara	ouattara	NOUN
ejpam-4787	391	12	,	,	PUNCT
ejpam-4787	391	13	and	and	CCONJ
ejpam-4787	391	14	f.	f.	PROPN
ejpam-4787	391	15	zitan	zitan	PROPN
ejpam-4787	391	16	.	.	PUNCT
ejpam-4787	392	1	power	power	NOUN
ejpam-4787	392	2	-	-	PUNCT
ejpam-4787	392	3	associative	associative	NOUN
ejpam-4787	392	4	algebras	algebra	NOUN
ejpam-4787	392	5	that	that	PRON
ejpam-4787	392	6	are	be	AUX
ejpam-4787	392	7	train	train	NOUN
ejpam-4787	392	8	algebras	algebra	NOUN
ejpam-4787	392	9	.	.	PUNCT
ejpam-4787	393	1	j.	j.	PROPN
ejpam-4787	393	2	algebra	algebra	PROPN
ejpam-4787	393	3	,	,	PUNCT
ejpam-4787	393	4	324:1159–1176	324:1159–1176	NOUN
ejpam-4787	393	5	,	,	PUNCT
ejpam-4787	393	6	2010	2010	NUM
ejpam-4787	393	7	.	.	PUNCT
ejpam-4787	394	1	[	[	X
ejpam-4787	394	2	3	3	X
ejpam-4787	394	3	]	]	X
ejpam-4787	394	4	s.	s.	PROPN
ejpam-4787	394	5	bernstein	bernstein	PROPN
ejpam-4787	394	6	.	.	PUNCT
ejpam-4787	395	1	solution	solution	NOUN
ejpam-4787	395	2	of	of	ADP
ejpam-4787	395	3	a	a	DET
ejpam-4787	395	4	mathematical	mathematical	ADJ
ejpam-4787	395	5	problem	problem	NOUN
ejpam-4787	395	6	connected	connect	VERB
ejpam-4787	395	7	with	with	ADP
ejpam-4787	395	8	the	the	DET
ejpam-4787	395	9	theory	theory	NOUN
ejpam-4787	395	10	of	of	ADP
ejpam-4787	395	11	heredity	heredity	NOUN
ejpam-4787	395	12	.	.	PUNCT
ejpam-4787	396	1	ann	ann	PROPN
ejpam-4787	396	2	.	.	PUNCT
ejpam-4787	396	3	math	math	PROPN
ejpam-4787	396	4	.	.	PUNCT
ejpam-4787	397	1	stat	stat	PROPN
ejpam-4787	397	2	,	,	PUNCT
ejpam-4787	397	3	13:1159–1176	13:1159–1176	NUM
ejpam-4787	397	4	,	,	PUNCT
ejpam-4787	397	5	1942	1942	NUM
ejpam-4787	397	6	.	.	PUNCT
ejpam-4787	398	1	references	reference	NOUN
ejpam-4787	398	2	1490	1490	NUM
ejpam-4787	398	3	[	[	X
ejpam-4787	398	4	4	4	NUM
ejpam-4787	398	5	]	]	X
ejpam-4787	398	6	j.g.f	j.g.f	NOUN
ejpam-4787	398	7	.	.	PUNCT
ejpam-4787	399	1	carlos	carlos	PROPN
ejpam-4787	399	2	.	.	PUNCT
ejpam-4787	400	1	principal	principal	NOUN
ejpam-4787	400	2	and	and	CCONJ
ejpam-4787	400	3	plenary	plenary	ADJ
ejpam-4787	400	4	train	train	NOUN
ejpam-4787	400	5	algebras	algebra	NOUN
ejpam-4787	400	6	.	.	PUNCT
ejpam-4787	401	1	comm	comm	NOUN
ejpam-4787	401	2	.	.	PUNCT
ejpam-4787	402	1	algebra	algebra	PROPN
ejpam-4787	402	2	.	.	PUNCT
ejpam-4787	402	3	,	,	PUNCT
ejpam-4787	402	4	28	28	NUM
ejpam-4787	402	5	,	,	PUNCT
ejpam-4787	402	6	no	no	DET
ejpam-4787	402	7	2:653	2:653	NUM
ejpam-4787	402	8	–	–	PUNCT
ejpam-4787	402	9	667	667	NUM
ejpam-4787	402	10	,	,	PUNCT
ejpam-4787	402	11	2000	2000	NUM
ejpam-4787	402	12	.	.	PUNCT
ejpam-4787	403	1	[	[	X
ejpam-4787	403	2	5	5	X
ejpam-4787	403	3	]	]	X
ejpam-4787	403	4	i.m.h	i.m.h	ADJ
ejpam-4787	403	5	.	.	PUNCT
ejpam-4787	403	6	etherington	etherington	PROPN
ejpam-4787	403	7	.	.	PUNCT
ejpam-4787	404	1	genetics	genetic	NOUN
ejpam-4787	404	2	algebras	algebras	PROPN
ejpam-4787	404	3	.	.	PUNCT
ejpam-4787	405	1	proc	proc	PROPN
ejpam-4787	405	2	.	.	PUNCT
ejpam-4787	406	1	roy	roy	PROPN
ejpam-4787	406	2	.	.	PROPN
ejpam-4787	406	3	soc	soc	PROPN
ejpam-4787	406	4	.	.	PUNCT
ejpam-4787	407	1	edinb	edinb	PROPN
ejpam-4787	407	2	.	.	PUNCT
ejpam-4787	407	3	,	,	PUNCT
ejpam-4787	408	1	59:242–258	59:242–258	NUM
ejpam-4787	408	2	,	,	PUNCT
ejpam-4787	408	3	1939	1939	NUM
ejpam-4787	408	4	.	.	PUNCT
ejpam-4787	409	1	[	[	X
ejpam-4787	409	2	6	6	NUM
ejpam-4787	409	3	]	]	PUNCT
ejpam-4787	409	4	p	p	X
ejpam-4787	409	5	holgate	holgate	PROPN
ejpam-4787	409	6	.	.	PUNCT
ejpam-4787	410	1	genetic	genetic	ADJ
ejpam-4787	410	2	algebras	algebras	PROPN
ejpam-4787	410	3	satisfying	satisfying	PROPN
ejpam-4787	410	4	bernstein	bernstein	PROPN
ejpam-4787	410	5	’s	’s	PART
ejpam-4787	410	6	stationarity	stationarity	PROPN
ejpam-4787	410	7	principle	principle	PROPN
ejpam-4787	410	8	.	.	PUNCT
ejpam-4787	410	9	journal	journal	PROPN
ejpam-4787	410	10	of	of	ADP
ejpam-4787	410	11	london	london	PROPN
ejpam-4787	410	12	mathematical	mathematical	ADJ
ejpam-4787	410	13	society	society	PROPN
ejpam-4787	410	14	,	,	PUNCT
ejpam-4787	410	15	ii	ii	PROPN
ejpam-4787	410	16	.	.	PROPN
ejpam-4787	410	17	ser	ser	PROPN
ejpam-4787	410	18	,	,	PUNCT
ejpam-4787	410	19	9	9	NUM
ejpam-4787	410	20	,	,	PUNCT
ejpam-4787	410	21	no	no	DET
ejpam-4787	410	22	1:51–68	1:51–68	NOUN
ejpam-4787	410	23	,	,	PUNCT
ejpam-4787	410	24	1975	1975	NUM
ejpam-4787	410	25	.	.	PUNCT
ejpam-4787	411	1	[	[	X
ejpam-4787	411	2	7	7	NUM
ejpam-4787	411	3	]	]	SYM
ejpam-4787	411	4	e.s.m	e.s.m	NOUN
ejpam-4787	411	5	.	.	PROPN
ejpam-4787	411	6	rodriguez	rodriguez	PROPN
ejpam-4787	411	7	j.s	j.s	PROPN
ejpam-4787	411	8	.	.	PUNCT
ejpam-4787	411	9	lopez	lopez	PROPN
ejpam-4787	411	10	.	.	PUNCT
ejpam-4787	412	1	on	on	ADP
ejpam-4787	412	2	train	train	NOUN
ejpam-4787	412	3	algebras	algebra	NOUN
ejpam-4787	412	4	of	of	ADP
ejpam-4787	412	5	rank	rank	NOUN
ejpam-4787	412	6	4	4	NUM
ejpam-4787	412	7	.	.	PUNCT
ejpam-4787	412	8	comm	comm	NOUN
ejpam-4787	412	9	.	.	PUNCT
ejpam-4787	413	1	algebra	algebra	NOUN
ejpam-4787	413	2	,	,	PUNCT
ejpam-4787	413	3	24	24	NUM
ejpam-4787	413	4	,	,	PUNCT
ejpam-4787	413	5	no	no	DET
ejpam-4787	413	6	14:4439–4445	14:4439–4445	NOUN
ejpam-4787	413	7	,	,	PUNCT
ejpam-4787	413	8	1996	1996	NUM
ejpam-4787	413	9	.	.	PUNCT
ejpam-4787	414	1	[	[	X
ejpam-4787	414	2	8	8	NUM
ejpam-4787	414	3	]	]	X
ejpam-4787	414	4	d.	d.	PROPN
ejpam-4787	414	5	kabré	kabré	PROPN
ejpam-4787	414	6	and	and	CCONJ
ejpam-4787	414	7	a.	a.	PROPN
ejpam-4787	414	8	conseibo	conseibo	PROPN
ejpam-4787	414	9	.	.	PUNCT
ejpam-4787	415	1	structure	structure	NOUN
ejpam-4787	415	2	of	of	ADP
ejpam-4787	415	3	baric	baric	ADJ
ejpam-4787	415	4	algebras	algebra	NOUN
ejpam-4787	415	5	satisfying	satisfy	VERB
ejpam-4787	415	6	ethal	ethal	NOUN
ejpam-4787	415	7	identity	identity	NOUN
ejpam-4787	415	8	of	of	ADP
ejpam-4787	415	9	degree	degree	NOUN
ejpam-4787	415	10	six	six	NUM
ejpam-4787	415	11	.	.	PUNCT
ejpam-4787	415	12	jp	jp	PROPN
ejpam-4787	415	13	journal	journal	PROPN
ejpam-4787	415	14	of	of	ADP
ejpam-4787	415	15	algebra	algebra	PROPN
ejpam-4787	415	16	,	,	PUNCT
ejpam-4787	415	17	number	number	NOUN
ejpam-4787	415	18	theory	theory	NOUN
ejpam-4787	415	19	and	and	CCONJ
ejpam-4787	415	20	applications	application	NOUN
ejpam-4787	415	21	.	.	PUNCT
ejpam-4787	415	22	,	,	PUNCT
ejpam-4787	415	23	61	61	NUM
ejpam-4787	415	24	,	,	PUNCT
ejpam-4787	415	25	no	no	DET
ejpam-4787	415	26	1:37–52	1:37–52	NOUN
ejpam-4787	415	27	,	,	PUNCT
ejpam-4787	415	28	2023	2023	NUM
ejpam-4787	415	29	.	.	PUNCT
ejpam-4787	416	1	[	[	X
ejpam-4787	416	2	9	9	NUM
ejpam-4787	416	3	]	]	PUNCT
ejpam-4787	416	4	a.	a.	NOUN
ejpam-4787	416	5	labra	labra	PROPN
ejpam-4787	416	6	m.	m.	NOUN
ejpam-4787	416	7	t.	t.	NOUN
ejpam-4787	416	8	alcalde	alcalde	NOUN
ejpam-4787	416	9	,	,	PUNCT
ejpam-4787	416	10	c.	c.	PROPN
ejpam-4787	416	11	burgueño	burgueño	PROPN
ejpam-4787	416	12	and	and	CCONJ
ejpam-4787	416	13	a.	a.	NOUN
ejpam-4787	416	14	micali	micali	PROPN
ejpam-4787	416	15	.	.	PUNCT
ejpam-4787	417	1	sur	sur	PROPN
ejpam-4787	417	2	les	les	PROPN
ejpam-4787	417	3	algèbres	algèbre	NOUN
ejpam-4787	417	4	de	de	X
ejpam-4787	417	5	bernstein	bernstein	PROPN
ejpam-4787	417	6	.	.	PUNCT
ejpam-4787	418	1	(	(	PUNCT
ejpam-4787	418	2	on	on	ADP
ejpam-4787	418	3	bernstein	bernstein	PROPN
ejpam-4787	418	4	algebras	algebras	PROPN
ejpam-4787	418	5	.	.	PUNCT
ejpam-4787	419	1	proc	proc	PROPN
ejpam-4787	419	2	.	.	PUNCT
ejpam-4787	420	1	lond	lond	PROPN
ejpam-4787	420	2	.	.	PUNCT
ejpam-4787	421	1	math	math	NOUN
ejpam-4787	421	2	.	.	PUNCT
ejpam-4787	422	1	soc	soc	PROPN
ejpam-4787	422	2	.	.	PROPN
ejpam-4787	422	3	,	,	PUNCT
ejpam-4787	422	4	58(1):51–68	58(1):51–68	NUM
ejpam-4787	422	5	,	,	PUNCT
ejpam-4787	422	6	1989	1989	NUM
ejpam-4787	422	7	.	.	PUNCT
ejpam-4787	423	1	[	[	X
ejpam-4787	423	2	10	10	NUM
ejpam-4787	423	3	]	]	X
ejpam-4787	423	4	s.	s.	PROPN
ejpam-4787	423	5	walcher	walcher	PROPN
ejpam-4787	423	6	.	.	PUNCT
ejpam-4787	424	1	bernstein	bernstein	PROPN
ejpam-4787	424	2	algebras	algebras	PROPN
ejpam-4787	424	3	which	which	PRON
ejpam-4787	424	4	are	be	AUX
ejpam-4787	424	5	jordan	jordan	PROPN
ejpam-4787	424	6	algebras	algebras	PROPN
ejpam-4787	424	7	.	.	PUNCT
ejpam-4787	425	1	arch.math	arch.math	PROPN
ejpam-4787	425	2	.	.	PROPN
ejpam-4787	425	3	,	,	PUNCT
ejpam-4787	425	4	50	50	NUM
ejpam-4787	425	5	,	,	PUNCT
ejpam-4787	425	6	no	no	DET
ejpam-4787	425	7	3:218	3:218	NOUN
ejpam-4787	425	8	–	–	PUNCT
ejpam-4787	425	9	222	222	NUM
ejpam-4787	425	10	,	,	PUNCT
ejpam-4787	425	11	1988	1988	NUM
ejpam-4787	425	12	.	.	PUNCT
ejpam-4787	426	1	[	[	X
ejpam-4787	426	2	11	11	NUM
ejpam-4787	426	3	]	]	PUNCT
ejpam-4787	426	4	a.	a.	NOUN
ejpam-4787	426	5	wörz	wörz	PROPN
ejpam-4787	426	6	-	-	PUNCT
ejpam-4787	426	7	busekros	busekro	NOUN
ejpam-4787	426	8	.	.	PUNCT
ejpam-4787	426	9	algebras	algebras	PROPN
ejpam-4787	426	10	in	in	ADP
ejpam-4787	426	11	genetics	genetic	NOUN
ejpam-4787	426	12	.	.	PUNCT
ejpam-4787	427	1	lecture	lecture	NOUN
ejpam-4787	427	2	notes	note	NOUN
ejpam-4787	427	3	in	in	ADP
ejpam-4787	427	4	biomathematics,36	biomathematics,36	NOUN
ejpam-4787	427	5	,	,	PUNCT
ejpam-4787	427	6	springer	springer	NOUN
ejpam-4787	427	7	-	-	PUNCT
ejpam-4787	427	8	verlag	verlag	PROPN
ejpam-4787	427	9	,	,	PUNCT
ejpam-4787	427	10	berlin	berlin	PROPN
ejpam-4787	427	11	-	-	PUNCT
ejpam-4787	427	12	new	new	PROPN
ejpam-4787	427	13	york	york	PROPN
ejpam-4787	427	14	,	,	PUNCT
ejpam-4787	427	15	1980	1980	NUM
ejpam-4787	427	16	.	.	PUNCT